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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⢉⠩⢍⡙⠛⠋⣉⠉⠍⢉⣉⣉⣉⠩⢉⠉⠛⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠂⡠⠑⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠐⠁⢊⠀⠄⠈⢦⠀⠀⠀ ⠀⣠⡾⠁⠀⠀⠄⣴⡪⠽⣿⡓⢦⠀⠀⡀⠀⣠⢖⣻⣿⣒⣦⠀⡀⢀⣈⢦⡀⠀ ⣰⠑⢰⠋⢩⡙⠒⠦⠖⠋⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠘⠦⠤⠴⠒⡟⠲⡌⠛⣆ ⢹⡰⡸⠈⢻⣈⠓⡦⢤⣀⡀⢾⠩⠤⠀⠀⠤⠌⡳⠐⣒⣠⣤⠖⢋⡟⠒⡏⡄⡟ ⠀⠙⢆⠀⠀⠻⡙⡿⢦⣄⣹⠙⠒⢲⠦⠴⡖⠒⠚⣏⣁⣤⣾⢚⡝⠁⠀⣨⠞⠀ ⠀⠀⠈⢧⠀⠀⠙⢧⡀⠈⡟⠛⠷⡾⣶⣾⣷⠾⠛⢻⠉⢀⡽⠋⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠑⢤⡠⢂⠌⡛⠦⠤⣄⣇⣀⣀⣸⣀⡤⠼⠚⡉⢄⠠⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠮⣔⡁⠦⠀⣤⠤⠤⣤⠄⠰⠌⣂⡬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⣀⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
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this site doesnt even check emails for verification lmao
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?G̭̺̙͔̦̖̭E̞̫͙T͕͇?̩̩̭̗O̝̗̯̖͍͙̬͎U̲͎͕̳͓̱̖̯T̤?̞̮͓̙O͍͉̥̻̣̺̩̗F͔̜̻͙̥̱ͅ?̦͖͚͚̺͚M͙Y̘?͉̝̘̖̮̜H̱̬̲̯E̘̗̥̹͚͕ͅA̠̰̳͇̻̖͇̬D̩͍̩͔̭͓?͖̹G̻̞̺̬͓̫͙͔E̻̫̙̞T̹̙̹?̞͙͔̣̪̩O͙̪̹͙͈̪͖̘U͍͚̱͖T̫̫̝̰̝?̫̤̥̱̖̳̜O͎̼͔͖̥̩F͇̫̳͔̝?̬͉M͎̙̤̦̰̱͙Y̫̭̜͚̦͈̰?͈̖̰͎͉H̳̳̬͔͙̲ͅͅE̻͇̹̬̰̜̖̱A͈̜D̜̣͕̫̯̻̝̭?̰G̠̲͔̻͔̙̯E̯͚̙̘T̙̜͍̳̩̣͕̭?̠̪̪͎̱O̹̰̺͙̘̪̭̞̱U̻̮͔͈̠ͅT̫͍͖̪̞͚?͎̖̥͇O͕̩̯̠̹̜͖F̗͉͚͈̤?̘̠͈̲̦͉̠M̝͈̰̥̹̗̯ͅY̻͕̳͔̠̟̼̙̣?̜̗̩̼͓͖H̪͍̞͓̟̠̼̻E̥̰͕̳̣͉̪̭A͔D̗̮?͔̜̜͙̤̹̩G̗̤͙̩̤̳E̜̗̥̼̲̺T̫͇̞̺̞?̭̩̦̹̹̭O̭̯͉̫͎̻̮U̮͇͇͔̗T̞̭̦̼̗̹?̜̪͖͍O̰͓͎̘̜̙͕F̞̝̖?̩̟͖̭͍̦M̺̖̙̺Y͙̫̤̺̠̰?̞̫̩H̖̤͍̣͔̟ͅE̞̹̞̗̭̳Ḁ̗͚͔͖D͓͇̱͍̖͙ͅ?͈̳G̟̫̣͎̞͖͔͇Ẹ̘̦̭ͅT̩̻͎̹͓̭?̺̦̞͔̫̟O̫U̪̪̩T͉̻̰͎̙̹̣̯?͍̲̰̟O̞̬͚̻̞̹̪̳ͅF͚͓̤͓͕̱͖?̦̟̣̖͇̦͕̞M͍̬͚̠̪̙Y̖̮̟̜̗̻̺?̪H̬̝̬̼̫̺̗̦E͈̱A͈̗̜͚̭̱͇̙ͅD̳̻?̫̣͚̭̪͉͔̲G̠̼̘͖E̥͎̯̥T̲͎̭̱?̟̻̥͈̹͙O̠͍͖̥͍͓U̖͇͇̫T̤̯̳̗͔̣͇̳?̳̮͈̭̠̖̬̠O͈̩̻̟̤F͈̱͕͈?̣͈͍̜̖̺M̰͍̙̺̗͍Y̖̬̜̗̝̦?̟͓͈̦H̝͔̪̣̜̪͔͉E̩͖̞͈̲̦͇̠A̤̰͍̟̝̳̦D͎͖̬̟̠̤̦̙?̦͖̪̗̥͔G͓̲̥E̙̣T̠̱̝͉̦̬̪̟?̞̼͕̥O͍͎̗̺͙U͉̦̞̼̪̳̹̼T̲͚͓̙?̙̯̗̞O̘͇̟̩̯F̝̟?̟̱̬M̖̭̲͇̩̘̗Y͇̯̘̱̳̥̖?ͅH͔͔̰̺̬̙E͇͈̮̠͚̫͉̻A̘̻̰̳̦D͓ͅ?͚͈̜̝͕̺G͉̙̺̞̰E̳͈̯̗̞̮T͙̯̺̺͍̯?̮̩O̰ͅU̖ͅT͍̜?̪̫̘̠O̯̘̹̮̮̞̟̤F̱̲͇͙?͎̺͉̞̝̰M̼͓̰͎͚̯Y̭̬̟̜̮?̪̘̩H̬̹͎͓̞̺͉E̬̬̦A̪͈D̜̖̖̫͈̝?̼̹͖͕̥̺̠͎G͎̜̯̗͇͓̮E̖̤̜͓Ț͇̭͉̳?̙͚̙͖̠̹O̫͚̞U͔͖̭͕͇̭T̫̜̬?͇̥̳O̮͓̟͓͚F̦̟̲̣͇̙̬̦?̜̬̭̱̯̳ͅM̼̝̰̤̻̪Y͙̣̘ͅ?̜̮͇̪H̺̘̱͍͖̠̳̣E̻̦͎̝̠̙̬̖̥A̺̻͈͉̤ͅD̟̺̮̭̗̹?̟̺̠̪̣̲G̬͚̠E̱̥̱͍̝͕͎͓T͇̪̗͙̟?͉͈O͕͉U̫̤̫̞T̼̯͉̹̳͓̫̬?̭͍͙̣̹̪̼̙̜O̹̱̠͈̥̰ͅF̫͕͍̪͓̙̰?̝͎̣͇̹̫̞̩M̳̻̟̫Y̪̲̞̝?̖̯H̺͉̲Ḙ͕͓͎A̹͕̹̩D͓͚̗͓͕̼͕͇͍?̱̝̥̜͉̟G͍̤̦͎͇͍E̠͙̫Ṯ̭͖̳̘͖?̩͚O̞̲̠U̖͚̳ͅT̜̤̯̤?̤͇͔̮̯͎͓͖O̳͉F̯͙̭͕̬ͅ?̬̜̠̪̲̟M̙̼͉̪̲̗͙͓͈Y̯̦̩͈?̪̯̬͙̟̳H͈̯͖͍̪E̲̹A̺D̠͍͖͚̫͍̰?͕͉͎͕̙͕͓ͅG͎̰͇͕̦Ẹ̮̥̹͎̯Ṭ̘̻?̳̠͓͔̻̟O̻̘͓̭̟͙̹̣U̮̭̭͙͙͍̯̘T̻͔̥͙̠̬͇ͅ?̙͙̜ͅO̪̯̺̤̮͈F̙̺̖͉̞?͍̻M̬̟͇Y͈̖̰̭?̘H̤̬̪E͕̟͙̱A͇̪̗̤̼D̪̟?̠͈̙̗G̫̘̪̖̼̦̭͎E̼T͚͕̟̰̼̭̬͕?͕ͅỌ̙U͕̦̳͍͔̭͕̦̝T̥̺͓͍̺̭̥?͚O̰̤̰ͅF̻͉̞͚̱͓͓̥ͅ?̣̩̪̠̬̝M͕Y͈̫̩̼̲̱̪?̲̼͇͕̠͈̼H͉͚̬̥̮ͅẸ͖A̱̘͙͚̱̥͇ͅD͚̪̥̮̲̹̱?̜̠G͙̘͚͙̮̫E͎T͔̝̳̬̗̗͓?͎͕͎̞͖͚̱̣̲O͔̮̪̭̣̼U͙͚̫͕T͚̝̯͔̮̱ͅ?̗̱̥̝̥̻̩̩O̫̞F̩͇̻͚̪̰͙?̱M̘̻͖Y̰̝̠̫̱̥̺̭?̭̜̮͉H̫͖E̜̝̜͎͍̲͙̮͍A̺̼̻̱̝̜͎̙D̯̭̝?̘̹̱G̗̞͔͔͎̼̟̩E͚̗̤̩̹T̗̤͓̭̱̦ͅ?̻̙̖̱ͅO̹͎̙̺̰U̞̣̰͙͇T̖͓͉̗͕͇̰̳?̩̠̮̞̫ͅO͎̟͚̞̙̼͎̖ͅF̰̱?̪͙͉̗̗͖M̫̤̝͔Y̭͙͙͈͇̳̤̤̩?̼̥̥H̻͍͓E̲̦͙̘̰͚A̙̞D͎̪̭͓̮̝͇͍?̰̹̱͖͓͉̲G̩͓͍̠̘̱E̼̩̗̮̲͕T͙̙̤͖͓̝̬̺?̮͙̰̙͈̗O͚̟U̠͍̫̙̲͍̫͓̝T̻?̦͖̫̞͉̟͕̣O͍̣ͅF͚̹̩?̭̮̦̖̰̦̳̭M̭̱̝Y̻̯̗͚̻?̭͔̬̱H͙̠E̩̼͔͓̣̣̯̝A͈̱D̖͉̥̜?̵̧͔̖̩̻̹̥̲͍͇̳̻̺͉͍̯̱̠̫̯̹̰̲̪̦̠̺̘͖̹̳͖̙̄͒́́͌̐̋̆̀̄͑̾̃͐̓͗͂͘͜͠ͅͅ█̸̡͍̹̭̮̩͈̖͙̞͖̠̬̞͎͚͖̫̭̞̠͍͕̩̭̪̖͚̌̑̉̑͛̓̅̏̽̔̈̆͂͊̃̾̔̃͊̎͊͆̿͗̊̽̓́̓̋̇̈́̇̋͋͒͘̚͜͝͠͝█̴̧̡̨͉̝͉͚͖̭̘͎̭̲͖̘̲̹͙̰̩͔̠͈̭̫̙̼̘͑͂̃͑̍̂ͅͅ║̸͉̦̺͓̫̬̞͈͔͖̯͈̼̤̟̿̃̃͌̀̓́͒̽͗̈́͒͆̂́̑͊͜͝͠ͅ░̴̧̧̪̘̱̥̝̬̹̺͉͇̻͓̙̥̫̹͙̄̈́͑̇̀̽́͋͋͌͒͜͜ͅ░̶̧̧̹̣̺̪͔͖̙̳̹̬͔̼͇̘̔̑͊̀̈̈̂̾͛̓̎̚█̶̢̮̜̖̬͎̭̝͔̦̉̆͂̒̌̍̀̌̓̃̆̄͗̓͛̉̓́̾̈̆͋͌̄̏̓̔̕͝͝͠͝͠ͅ█̶̨͖͕͖̬̗̞̫̐̇̅̂͋́͗̀́̿̓̔̕║̷̢̡̣̘̣͎̘͇̦̰̪̖̳̗̑̈́̀̈̔͌̑̆̌̾́̉̑̒̄̏̕͘͠͝█̴̡̢̛̠̱̼̪̝̣̩͖̭͖̰̯̺͇͍̤̻̻̥̜̘͉̠̫͓̜̤͕̻̖͚̫̞̲̃͋̊̈́̈̎̍̒̓̋̄̑́̒̀̕̚̕͝͝͠͝ͅ█̶̛̛͍̲͇͙̭̠͇͉͊͊̂́̽͌͑̐͛̄͌̔͋̀̉̏̿͐͑̈́̋̕͘̕͝͠͝█̷̡̢̧̨̛̙̝̗̣͖͚̲͍̖̫̲̘̺̱̜̩̖̰̹̙̞̉̒͂̍̿̽̅̇́͋̔̐̀̔͐̐͒́̐̋̉̚͝█̶̨̛̩̰̘͍̤̥͇̖̻̠͚͓̈́͆͐̐̉͐͗̐̈́̑͛̾̾̏̆̉̓̀̓̏̇͆̆̚͘̕͝͝͠͝͝█̸̨̢̢̢̢̝̱̩̼̺̳̩͇͉̙̲͇̞̗͇̣̳̱͓̜̗͙̞͖̪̥͕͈͔̀͌̏̈̃̓█̴̨̢̢̧̢̛͕͍̳̼͍̦̳͈̬̗̳̦̳͕̣̪͓̳͇͍͙̣̞̏̀͂̃̋̈́̔̒̎̆̎͂͑̂̃̇̉̋̿̓͋̾͊̚̕̚͝͠͠█̸̡̛̼̙̙̗͚̱̯̤̯̹̹͆̑̓͊͛̄͗̀͒̇͝͠║̵̢̢̤̘͓͕̜̫͍͚̘̞͕̊̌͐̐͐̿̃̄̇̎̎̋͗̿͋̾̓̄̂̎̓̾̄̇̓͐͗̌̑̉̏͛̀̈̅͘̕͠͝╚̶̧̥̗͙̣͉̹̟͓̼͍̟̜̩͖̹͎̦̼͖̘̬̰̻̜̞͈͇̩̼̙̠̠̖͇͚̠̩͍͚̺̭͊͊͗̔̑̀̋͒͆̽̌̌̈̅͆̌̓̉͌̿̑̿̈́̈́̃̄̎̏͗̕̕͝͝͝͝͝͝͠ͅͅ█̷̡̠̘̭̓́̃̈̀́͒͌͆͌̍̉͂͆́́̉̇̐̾̓̀͒̄̐͗̓͘̚͝͝█̸̨̧̡̨̧̢̖̰͈̪͍͓̙̲͚̥̖̙͙̻̪͓̹̹͍̲͙̙͔̟̝̙̻͚̺̮̱̦̹̰̼̇̈́̊͐̓́̏͆͐̽̊͒̐͑̎͋̌͘̚͜͝ͅ█̴̡̧͚̲͙̜̮̳͎̗͖̥̳̺̱̭̼̫̬̦͍͚̳̪̈͌͊͒͐̅̃̈́́̚͜͜█̴̢̛̤̜͈̠̰̹̻̖̺̺̖̆͌͋̈́̒̔̓̈́͛̍͌̔̈́͐̃͌͆̋̆̏̓͘█̸̢̡̺̫͇̣͍͇͕̺̪̲̯͉̥͔̐͒̅͂̐̂̑̅́̈́̿̓̾͑̿̀͗̒͛̋̏̓̏͂̿̏̊͂̃̚̕͜͜͠ͅ╗̴̧̧̙̱̟̮͈͙̼̻͚͕̥̤͇̠̲̗̟͙̫͍̤̟̫͗̍͛̉͛̃̓̇͊̋̀̏̽͒͊̍͜͜ͅͅ░̸̨̡̡̡̨̢̨̛̘͖͍̜͉̠̦̱̙͇̙̩͎̘̳̪̥̪͙̲͔̺͈̯̟̬̳̱̠̙̩̦̺̀́͊̅͂͌̈́̉̌́̓̋̈́͗̓͊̆͋͛͛͒́̓̆̀̓̾̏͗͐͆̽̍̋̈́̐̓̇̕͜͝͝ͅͅ█̸̨̧̟̹̠̰̞̀̋͒͌̂́̏͊̉͂̂̌̾̌̐̽͒͒̆̋̏͝͝ͅͅ█̴̢̨̳̗̝̲͉̤͎̱̖̘̟̖̘̞̹͔͓͎̹̈́̍̉̐̉̌̀̊̄̀́̈́̂͋͑͐̃̂̇̇̓̈̽́̌̑͛̓̅̓͜͝͝║̵̡̻̺̂͌̽̑̂̆͗̐̊̄̓̍̀̊͐͌̀͋̈́̍̔͊͗̏̒̽̐̇̂̓̈͑͐̽̔̀̿̀̚͝͝░̸̡̢̨̨̛̩̱̤̯̱̱̠̥̼̞̖̟̳̠̺̼͎̗͔̗̟̱͚̳͉̯̻̹͉̻͉̣̗̞̥͉̣͇̤̔̃͗͛͒̃͑̓͌̌͋̄̍̎͛̈́̀̐̐̓͛̅̑͋̏̐̐͛̄̇̔̋̊̈́͘̕͜͝░̷͔͓͙͔̣̃̈͑̌̃̓̓͆̈́̓͐̌̈͋̈́̑̿͑̎̊̊͐̄̆̎̈́̓̿̌̂̈́͆̂̕͠͠͠█̴̨̨̡͓͕͍͈͕̗̗̣͈͚͚̥͆̑́͒̃͋͒█̶̢̨̨̡̨̡̡̛̛̝̠̰̹̝͍̲̱̗̩̩̬̞̜͎̗̞̟͈̳̟̫̳̙͙̙̯͍̼͙͙̭̬̥̹̜͛͌́̋͛̆͑̋͐̈̃̀͛̑̾̄͌̋̀̌̉͋̄̽̏̏̓̑̀̎͛́̒͒͊̈́̑̚͝͝͠͝║̶̢̝̻̻̭̲̫̗̖̖͎̰̣̼͕̳̮͍̻̤̻͍̳͙̬͎̪̥̙̀̐̓̇͐̈́͊͋̔̆̈͒̍̄̽̈́̉̎́̉̈́̋̏̋͒̎̿̋͗͘͘͝ͅ█̷̢̛̼͍̜͙͎̫̺̱͍̰͍̺̩̖͙̖͛̔̅̿́͂̿̍̾́̑̀̑͂͑̓́̕̚█̵̝̬̦͚̙̤̦͎͕̝̪͙͖̝͈͓̖͎̩̘̾̒̊̓͑̀̋̈́̐͂̌̈́̓̍͛̃̀͑̾̆̃̎̒͘ͅ█̷̨̢̢̧̧̛̖͉͍̗̳̣̫̟̟̯͉͓̱̫̗̯̝̩̪̻̩̥͚̤̘̃̃͒̈́͂̋̂͗̽͐̄̏̍̆͋̊͋͂͐́̅̽͌̓̏͊̈̈́̔͊́̂͘͘͝͠͝͠█̸̢̧̘̤̜̫͚͍͈̜͉̰̞͖̭̘̓͐̏͗͐̈́̄̌̔̐̀̓̑͌̎͊͊̓̍͒͐͗̋̓͂̈́̑̏͒͆͘͘͠ͅ█̸̢̧̢̢̭͕̤̰̘̬̭̹̣̰͈͍̹͚̺̟͙̪̺͙͙̯͔͐̇̏́͛̏̆̒̈́͒̿̈͐̊̃̓̅̈́́̓̇͋̇́̈͊̈́̕͝ͅͅ█̸̡̩̰͓̳̞͉̞͇͗͌█̶̢̢͈͙̖̮̹̦̹̟̫̭̺̱͙̔̃ͅ║̵̨̖̪̗̦͔̂̀̐̓͆͑͐̆̅̌̐̅͗̽̓̈́̽̒̐̔͛̒̐̈́̿͆̕̚̕͝͝͝͝͝͝█̸̡̡̢̨̡̛̺͔̳̳̳̙͖̖̫̳̳͙̣̻̺͉̘͓̩̟̹͇͖͓̭̹̠̼̲̩̜̯̝̘̼͍̮̘̗͗́̒̈́͆̾̽̑̎̒̀̍͑́̾̉͆̒͆͑͒̈́̀̿͠͠͠͝͝͝█̷̛̛̱̤̭̝̬͇͍̖̦̗̠̭̤̟͈̯̘͇͉̱͙̺̤͔̹̟̺̘͍̪̱̣̇̑̀̈̈̅̈͌̄̅̈́͌̆̔́͊̌͘͝█̵̨̯̦̲̟͚̰̗̻̤͚̰͇͎̭̬̙͉̣͇͕͔̘̙̯̘͉̞̣͇͇̼͕̣̘͙͖͋͒̑̽̂͊̎̆̆̒̐̆̊̔̄̅̒̉̒̿̚̚͝͠█̷̧̡̧̡̡̛̰͈͔̬͖͍̩͖̥͖̲͈͙̜̖̻̠̖̹̭̙̫̤̮̺̭̼͕̤̟̻̥̖̜̺̝͐̆̂̈́̒̇̋̑̽̔̔͗́̓̿̀̋̇̀́͋̉̏̿̔̋̈́̏̕͜͠ͅ█̷̨̡̡͔̬̫͖̮̜̗̯̦̟̥̠̻̦̗̺̰̯̦̥͓͔͓̼͚͍͔͖͍̠̰͖̦̠̯́́̂͊̃̀͗̓̄͊̓́̊̆̏̑̏̔͆͆̕ͅ█̶̧̡̨̫͚̗̫̳͍͔͎̳̭̬̫̺͔̮͎͇̈́̾ͅ█̸̱̯̗̲̺̗̖̤̰̖͈̄͊̽̄̋͋̈̄͗║̶̸̢̨̡̧̨̡̢̨̧̢̢̧̧̛̻̱̤̖̬̪͕͔̤̺̦͙̝̰͇̟̪͓͚̣͔͙̪̭̤̘̘̹̯̪̘̱̬̗̻̥͍͉̻̯̼͚̲̖̞͖̟̖̣̙̺͔͕͙̠̪̞̪̉̿̓̄̏̋̒̀̓̌̎̈̒͆͊͋̍͋̎̇̏̍̃̈́͐͘͜͝ͅ█̶̧̛̱̠̟̠̞͎̭̞͎͍̙̳̝̝̘̗̘̰̲͋̉̓͐̈͋̒͊͊̒̔͐̾̈̌̎̄̉̊̊̂̋̚̕̚̕̕͝͝ͅ█̸̢̢̧̡̛̛̖̖̗͎͍̟͇͎͇͚̟̣̱͔͍̖͔͖̮̳̜̜̭̙̦̮̱̺͍͑̾͑̓̆́̎̾̈́̇̋̅̓̀̌̿͊́́̔̎̋͋̔̃̚̚͜͜͝͝ͅ║̸̨̯̘̞̐̋̊̍͌͑̋́̓̍̏̉̅͊̔͐̆̈́̑̄̓̀̇̽͑̎̓̿̑́̕̕̚̚͝͠░̵̧̡̡̧̢̡̡͚͈̭͔͚̭͕̱̪̺͇̠̘̟̩̟͕̖͙͔͖͎͉̗̣͚̥̫̳̹̣̞̞̻̂͆͗͗̂͛̔̂̿̄͊̏̀́̍̃̔̔̍͘͜͜͠͠͝░̶̛̣̭̝́̈̀̒̂͐́̊͌̎͒̍̀͂̀͑́̌̓̋̔̋̀͑̅̕̕̚̕͠͝͝█̵̧̨̢̧̢͍͇͕̬̞͖̯̙̤̻̫̖̩̞̼̈́̀͋̈́́̅̀̓͐̆͐͜͝█̵̧̙͓̻͍̞͖̱̩̖̥͖̝̈́̋͐̈║̶̢̡̨̢̬̣̮̘̺̞̘̥͓̯͓̺͙͇̯̲̞͖̞̱̣̭̫̠͔̘̠̼̎̀̉̈́́̆̎̐̇̎̀̈́̈́̏̔̾͠͠͝█̶̨̧͙̗̼̪̟̱̣̼̦͇̠̥̞͕̗̩͎̻̣̻̺̩̻̦̟̫͓̝̱̥̱̖́̌̌̄̓͗̄͒̓̈̒̈̏͐̀̆͒̆͐̔͘̕̚͜͜͝█̷̢̡̧̨̧̧̛̛̟̗̞̬̥̖̠̱̩̫̹̫̼͔̞̫͕̝̪̫̣͉̜͖̱̟̹̯̙̣͕̄̃͑̃͌̅̌̇̈͌̿͆́̈̉͒́͊̃͑͂̅̀͋͌́̿͊͛̒̊̾̚̕̕͜ͅ╔̷̧̨͕͍̬̜̻͕̝̪͔̖̗̳̯̺͎̜̤̗̹͖͕̘̼͉̥̪͎̭̰͔̗̖̘͖̣͕̘̈́̉̇̓̅̈́͛͑͊̅͑̆̄̾͐͌̿́͌́͋͋̾̓̑̋͂̒͋̈̈̚̚̚͜͝͝͝═̵̛̯͖́̆̾̾̍̄̍̇́̔̔̾̃͐̎̑̀̂͊̓̍̒̊̈́͛̌̏́͑͒̋͋͘̕̕͝͝═̷̢̛̛̛̛̳͈̩̘͈͉̹͒̊͑̂͊̈͆̌͆͛̿̆̉͂̈́̑̾̒̄̔̂͛͛̀̌̊̈̃̊͛̅̋͛̏͛͊̚͘͝͝█̷̛͚̀͑̓́͊͂͆̒̈́͘̚█̵̧̨̨̲͙͖̞͉͕͈̬͕̹̥̜̩̼̫͕̳͂̈͊̽͋͘ͅ║̴̛͍͈̝͈̬̮͉͉̳̤̰̱̟̠̌͗̐̓̿̊́̃̈́̔̂̿̇̍̄͆͂̇̐͆͑͊͛͒̿̾̿̓̇̈̓͗̏̕͘͘͘͜͠͝͠ͅ░̶̡̨̧̡͚̘̣͎͇͓͔̬̹͇̝̖̖͈̖̦̠͖̳͔͕̯̯̤̘̅̓͘͘͜͜͠͠͠͝╚̷̨̢̧̨̛̛̛͚̖̲̞͈̩̭͙̟͙̥̱̠͚̪̟̞̺̟̖̗̻̥̹͉̀̍͊͑͌̉͛͆̈͛̂̏͑̌̍̈́̌͋͘͘̕͜͝ͅ═̴̧̺̤͉̲̝̭̬̥̭̱͎̬̋͛̋̍̈́̎̐̎͌̆͘͜͝ͅ═̶̨̢̧̢̡̛̥̻̯͓͚̘͉̘͇̻̻̲̩̫̯̼͉͔̜̠͇̟̹̺̭̪̜̟̱͔͚̣̻̹̞͎̱̈́̋́̒̄͠ͅ═̷̢͙̼̙͓̮̞̠̼͓̪̲̀̌͗̾̒̽͆͗̍̋̓̀͆̎͛̍̂͆͋́͆̇̓̓͂̋̓͘͘͠͠͠█̷̙̻̱͇̇͒̐̃̈́̃́͒̈̐̌̆̃̊̑̚͝͠͝█̴̧̧̛͚̠̝̪̻̤̲͈̳̯̮̫̪͇̻̙̘̞͙̞̬͔͕̝͎̹̱͙̜̼͈͚̪̦̉̉͋̍͆͒̈́̋̍̉͛͒͌̌͒̀̆̊̇́́̓͒̈́̈́̒͐̾͆́́̕̚̕͝͝ͅͅ╗̸̧̧̨̧̛͔̯͈͖̯͚͖̪̹͈̥̮̘̙̦̻̗̭̠̲̤̫̜̤̲̺̫̲̼̙͚͕̦͂̊̿̓̈͊͆̿̉̂̉̆̊̐̑̂̄̈͊̈́̈́̚͝͝█̸̨̢̛̩̫̮̹͖̭̺̺͙̩̮̳̞̲̤͗́̅̆̓͐̃̎͑̀̋̈́̉̓̄̋͒͌̀͑̆̓͑̏̓̂͌̈́̾̔̇̚͘͠͠͝ͅ█̷̡̨̢̨̛̖̮̦̯̦͍̰̰̪͕̬̻̰̣̝͎͎͎͔̫̊̔̐̍̆͊̔̑͌͒͂͒̓̾̍͌̊̓͒̓͋͑̋̓̓̂̊̃͛̌̏͌̍͘͜͜͠║̷̮̤͔͓͎͖̱̗̠͇̜̳̖̮̗̬͙̹͔̜̜̬̹̯͛͒͋͑̚ͅ░̵̨̛̮̙̹̪̣͙̪̩͈̰̜̗̠̘̱͕͖̺͚͈̠̤̼̳͕̝̂̽̀͛̒̒́̆̀́́͛̒̿͑̇̒̐͂́̈́̒̆͋̔͛͆́̆͐͛̑̕͘͜͝͝░̶̛̛͙͉̙͇̞͖̳̪̦͖̳̘̘̖͇͉̻̥̖̖̖̬͚̖̃͛̀̈́͐͆̆̄͗̈́̅͌̇̏̈̽̂̆̓́̕̚͜͝͝͝ͅ█̴̨̢̧̛̻̖͙̹̜̝͚̠̘͙̱̗͔͍̱̪̼̩̞̤̪̯͙̖̗̺͉͇̞̬̦̱̱̲̘͊͒̄̏̀̀̑́̍̄̌̂̔͐̓̓̇̆͂͛́͑͊̑͂̃̓̊̅͆̀́̍̕͜͜ͅͅ█̵̢̧̢̛̛̠̥͚͈̜̻̦̬͕͎͓͇̗̲͖̪̣͇̮̳̙̣̫͈̳͔̜̥͇̥̹̙̬̣̪̭̙̾̄̐̅̍́͛̎͐̉͋́̊̈́̿̈́̔͂̈́̂̎͜͜ͅͅ║̴̬̰̖̲̲͈̳́̀́͆̚█̸̡̡̡̨̧̨̪̬͍͎̝̺͖͓͙̓̾̀̐̅́͂͋̃͗̑͆̏̈́͒̋́̀̒͋̔͆̋̃̕̕͘͝͝█̵̞͋̈͒̈́̇̃̉̒͂̈́̾̍̃͋̒̉͐̐̐̇́̀͌̆͊̚̚͘̚͘̚̕͝╔̷̢̢̢̢̛̺͖͖͍͇̳̗̗̼̹̲̰͍͉̙̳̯͇̪͇̝̼̬̗̣͇̮̣̣̺͉̬͉̮̠͕̆͊̎̑̍͌̋̋̃̆͊͂̽̌͐̑̏͛̍̀͘̕͝͝ͅ═̸̢̛̤̺̳̠̮̖͇̉̈́̆̊̍̎̒̈́͋́̑̌̓̎̄̿̊̎̈́̅̌̿́͆̌̈́̐̀͊̑͌̚̚̕̕̚͠͠═̵̡̨̨̛̲͔̤̼̝͇͎̩̌̆͗̾̈͗̈̅͌͊̿̔͒̂̊̐̀̇̿̉͐̈́͒̀̊̓̀̾̈́̍͠͠█̶̡̡̢̧̨̖̟̝̹͖̜̠͈̥̙̠̙̺͍͔̮̲͚͚̝̣͎̘͔̰̾̒̉̈́͒̑̋͌̃̉̃͜ͅ█̸̢̢̧̛̦̗͓͇̺͓̤͎̳͇̖̬̬̮̭̳͍͈̼̟̘̠̊̀͒͐̒̔̒̄̈́͑́̇͂͜ͅ║̸̧̢̧̠̫̟̬̬͈̣͓͖̣͙̣̲̱̤̤̖̖̳̠̰͍͚͉̱̩̭̝͙̥͔̩͎͗͛́̍͒̑̋̈́͒̅̈̆̓͐̈́̃̇̇̀́͋͗̾̐̌̓̒̿̇̈́̔̋̈́̆̈́͊̓͂͑͜͜͜͝ͅͅ█̶̡͇̲̭̦͎̮͔̜̤̘̎̅̅̅́͐͒̄̍̽̑̃́̈́̒͑͗̌̓͘͠͝͝█̶̢̢̱͇̮͓̩̜̪̞̺̗̰̺̪͍͍̠̭͍̘̘̭̥͎̺͙͙̙̭̣͊̇͒̍͗̎̑͗̌͑̽̀̔͛͌͑̓́̈̉́̓̇̔̇͊͑̋̍̏̎́͘̚͜͜͠͝╔̷̨̡̛̛̲͖͚̯̥͓̠͇̗̻̉̐̇̓̾͊͒̎̔́̇͆̋̆̃͠═̴̢̪̱͕̠̘̲̞̘͔̻̟͎̫̹͎̮̟̙͔̱͍̻̣̟͔͈̀̀̀̓̄̊̈̎̐̀̊̈́̍͂̾͘̕̚̚̕͜͝͝͝ͅ═̴̡̡̡̢̨̝̭̰͉̹̻͔̹͙̖̥̗͓͔̼̜͓̬̥̟̠͔͍̳̰̪̝̠̖̑́̈́̏̕͜ͅ█̷̨̯̯͍̹̬̙͍̙̞͈͈̲̥̜̾̇̓̀́͋͆̽̎͛̔̏̐̀͌̂̆̎̀̏̐̕͘͝ͅ█̷̢̨̡̛̖̲̰̣̪̲̼̫̩͓̈́̑̓̾͐̊͑̔͊̽̏̓́̀́͛̔̅͋͋̎̄̓̅̂́̈́͛͂̅̌͒̐̈́̆̊͐͂̎̚̚̚ͅ║̷̵̨̢̡̡̧̨̢̛̬͙͇̞̻̰͓̳̘̱͈̪̥̙̫̤͙͇͈̲͙̤̬̪̼͕͔̞̟̹̖̥̼͈̘͕͉͔͙͕͉̬̯͚̝̫̥͙̱̠̤̙̪̝̫̘̗͙͇̥̜͖̗̯̖͕̖̝͆̍̾̉͋͌͊͌̈́̂́̀̽̅̓̎̑̌̽̑̆̊̎̆͂̒͋͂̂̑̈́̍̒̊̈́͘̚̚͜͜͝͠͠͝ͅ█̴̡̛̛̛̛̮̩͉̺̦͈̾̄̈́͐̑͒͋̆̎̆̂̀̒́̓͌̆̅͗̍̌̀͂͌͛̓͆͑̔́̕̕̚͘͝͝█̷̡̢̢̛̛̝͍͈̝͇̹̯͙̣͖̖̜͎͇̺̣̰͙̗̖͕͙̯͈̼̱̦̼̓͆̍̀́̿̈̓̿͂̒̿͋̄̂͊̇̕̚͜͜ͅ█̸̢̡̢̢̨̢̛̻̝͖̞̣̙̣̯̭͖̲̺̥̦̘̙͎͎̥͎̙̤̟̝̙͚̐̋͑́̇̆̎́̄́̅͆̄̇́͆͂̍̆͂͋͒͑̈̐̍̈́̿̀͆͒͐͂̕̚̚̕͠█̶̧̢̙̤͔̩͕̥̹̯͙̗̱̼̙̝̺͕̤̬͉̗̬͓̣̣͚̜͕̗̗̩̜̞̠̼̗͙͇̳̦̆̈́͆͗̍̈́̌͂̃̾͌́̃̉̆̈́̎̈́̋̐̎̈͘͝͝█̴̛͎̮̮͚̰̼͖͕̗̖͆̾̑̏͗̈́͒͑̌̈́̄̈́͂̈̈́́͋̂́̃̏́͘̚̕͝͝͝ͅ█̵̡̭̠͉͙͖͈̻͇͇̘͙̫̱͓̮̺̼͎̲̦͕̉̀̌̌͛̔̂̄̈́͒̾͊͑͑͐̽̉̄̀̕͝ͅ╔̵̢̛͚̦͍͇̼̗̫̦̤̯̤͕͈͇̦͈͇̪̝͎̉̊͌̽͑̔͗͐̇̑͌̀̏̀̏͗̄̍̂̈́̈́͐́̓͘͜͜͝͝͝͝ͅ╝̷̧̢̨̙͕͎̠̻̞̺̯̗̼͔̯͇̳̙͔͚͈̞̟̼̬̰̜̺͙̙̋̄̀̊́̿̽͐͌͊̓̅̄́̌̾͒̑̚͘̕͘͜͜͠͝ͅͅ█̴̡̧̢̲͓͔͖̺̟̪͖̣̮̘͉̝̩͎͕̗̼̹̝͙̈́ͅ█̵̮̘̉̇̅̑͛̈́͒̂̀̉́̉͛̾̑͐͛̀̇̍̚̚͠͠ͅ║̴̡̡̭̩͉̰͕̘̘̹̼͈̪̬̖̥̭͉̺̭̯̦̜͙̣͇͚̥̰̞̰̑̇́̈́͊͑̌̀̉̄̑͊̐̓̍̀͑̍̾́̆̓̒̇̋́̅͂̽̏͝͠░̴̨̮̖͈͔̮͙̬͇̮͇͔̥͖͕̒̾̓̍͋̚░̶̡̨̡̡̛͖͉̫̦̟̦̼̠͓͙͎̮̠̘͕̜̽̆̀̈̌̊̇́̏̏̆̓̀̓̈́͋̈̏̆̾͋̂͌̉̑́͊̌̚͘͝͝͠͠█̷̛̜̞̪̲̝̲̩̤̬̣͊͆̎̿̒̐̔́̈͆̾͛̑̃̽̎̾█̸̢̛̮̉̾͋̎͐̈́́́͒̀͊̆͌̋̊̽͒̅̀̂͐̈́̋̒̏̓̾̑͛̃͂̀̿̚̕͘̕͝͠͝║̵̢̛̛̦̰̣̙̳͉͓̥͎̟͈̥̘̰̦̯̖̮̻̫̬͙͖̗̠͉̦̼̜̠̮̑́͆̊̋̐́͒̂̏̿͗̇̉͂̄̿̂̑̈͛͜͠͝█̸̢̧̛̯͍̤͍̭̠͓̠̱̠͉̪̲̫̖͈͔͙̱̘̝͓̗̭̠̼̪̤̟͉̙̞͓͕̬̩͕̲̙̂̾̄́̏̎̾͐̈́̍͗͒̑̓͋͑͒͋̌́̋͋̏̐̇͌̍̇̇͂́̏̀͆̅̎͂̒̐͒̚͜͜͝͠ͅ█̶̢̯̤̍͆̀́̽̌̉͗̿́͑̋̆̑͑̀̉̽͋̌͊͑̈́͘̕͝█̴̰̦̭͖̹̞̱̩͇͎̜͉̖̗̙̖̳͍̼̞̩̈́͆̏͆̔̒̏̈́̚͜͝█̸̧̡̡̼̭͔̥̯̱̞̯̟͖͈̻̗̳̞̬͇̣̺̯͍̯͇̯̱̪̩̬̣͚͈̠͎̳̱͖̺̦̯̋̇͗́̉̌̀̈̍̿̌̓̽̿̉͐̽͊̄̈́͒̂̉͆͂́̓̄̇̔̅̋̚͜͜͠͝͝͝█̴̨̡̨̛͚̩͚̼̖͚̭͍͍̼̖̬̣̤̜̣̯̀̓̑̌̏̌͊͛̄͑͂̇̏́̓͗͘͘͝͝█̷̨̧̨̡̨̙̰̝͓͓̬̱̰̗̥̞̣̮̼̞̝̦̱͚̬͈̰͈̦̞̞̠̬̥̣͚̻͎͎̱̹̖̜̎́̍̽̎͂̈́̎̊̑̎̋͛̐̆̅̓̏́̾̈́̓̋╔̵̢̛̛̩͍͖̹͙̥̋̑͋͐̒͂̐͑̅͒̒̐͌̎̀̿͆̈̂̾̆̍̀͐͑̈̕͘̕̕̚͘͠͝╝̶̨̢̧͇͔̼̟͕̹͙̬̪͉̞̼͔̖̼͖̮͉̘͍͈̝͍̮̼̯̱̺̤̱͉̞͖̞͕̜̟̱̤̯̃̈̆̋͋͛̆͘͘̕͜█̵̡̡̧̢͍̟̤̲̮̙̜̺͕̜̰͈͉̬̤̤͇̠͎̺͕̣̀̐̂̀̃͌̏̎͗̍̆̃̒͒̇̒́̈͗̈́̅̉̓̓̃̈́͊̉́͘͝ͅͅ█̵̧̮̣̝̈́̉█̶̨̙̹̯̖̻͇̭̹̥͚͍͍̦̘͇̘͕̮̈́̇̍̂̿̾͌̉́̿̍̓̋̒̂͗̑̓͂͆͆̾̾̈́̈̀͆͑̆̏̓͆͘̕̚̚̚̚͘͜͜͠͝█̸̺͈̬̦͖̜̳͍̝̦̝̿̄̆̂͐́̎̾̅́̓̽̀͗͋̀͑̆̿̌̎̀̉̀̽̈́͗̑͆̈͛͘͜͠█̷̨̨̢̢̠̺̩̯̙̩̥̝̮͚̜̩͕̞̮̬̂̌͊̽̽͂͗̍͑̒͂̐̄̈͊̓̓͆̽̐̔̓̄̀̌̎̚͘͘͘̚̚͝
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How do I get my husband to stop going ‘Goblin Mode’ during sex? TLDR; My husband says ‘Goblin Mode activated’ when we start to have sex, growls and acts like a caveman, and then says ‘Goblin Mode off’ when we stop, and then pretends not to remember afterward. I really love my husband and he’s always been great in bed. But recently he’s been acting really weird. So, a couple of days ago, my son went on a rampage through our house and said he was in ‘Goblin Mode’. We didn’t really know what to do with him, so we sent him to live with my parents so he can go to a special needs school. My husband a really great relationship with our son and loved him more than anything. Naturally, he was upset when he had to leave. He’s an incredibly tough man, but this was the first time I’ve ever seen him cry. I think since then, he’s been a little emotionally unwell. I’ve heard him muttering, ‘Goblin’ repeatedly when he didn’t notice me, staring blankly into his food, and just going alone by himself to do who knows what. I feel awful for him, but we both agreed that this was for the best. Last night, the day after our son went away, we decided to have sex to relieve our stress. However, my husband said ‘Goblin Mode activated’, starting growling, and went wild having sex with me. Admittedly, it was some of the best and most experimental sex I’ve ever had, but I’m worried that something might be going on with my husband. Any advice? Edit: The problem isn’t the ‘Goblin Mode’, it’s that he could be ill
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gaia fucking online is more active than this shitass webbed site
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠍⡅⠆⠪⠄⣀⣀⡠⣀⣀⣠⡤⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣮⠲⣿⠿⠦⣠⣴⣿⠘⣻⣧⣤⡠⠛⠛⢄⠐⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠵⠧⠟⠬⠭⣵⣶⣿⣻⡿⠠⠭⠝⣻⡥⠔⠪⡙⢠⣶⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠟⣗⣠⠀⠀⠙⠛⠛⠉⠀⠀⡐⢫⣉⡍⠂⠀⣋⢿⣿⠏⡇⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣫⣄⠀⠉⠆⠀⠀⠀⠀⠀⠠⠋⠀⢀⣤⡑⡀⠻⣢⠀⣶⠈⣆⠔⠒⠲⠕⡇⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⠗⠀⢀⠌⡀⡀⠀⠀⠀⠠⡀⠀⠘⠿⡣⠁⠀⡇⠓⠙⣁⠃⠀⠀⡠⠃⢡⣞⢳⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣒⠥⠊⡸⠀⠀⠀⠀⠀⠘⠋⠭⠑⠊⠆⡔⠘⢢⢹⣿⡤⠔⣾⣿⢿⡘⠖⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣠⠔⠁⡆⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠸⢌⡍⠚⣾⢌⡇⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⣾⠿⠛⣋⣉⠭⠄⠀⢴⣿⠿⠆⠀⠸⣀⡒⢪⢌⠀⢹⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠊⠭⠔⠚⠭⢀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣘⣂⠾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠰⡿⣿⣿⡏⠉⠉⠉⠉⠉⠩⣿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣮⢄⠁⠀⠀⠀⠀⠀⠀⠀⡌⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠍⡅⠆⠪⠄⣀⣀⡠⣀⣀⣠⡤⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣮⠲⣿⠿⠦⣠⣴⣿⠘⣻⣧⣤⡠⠛⠛⢄⠐⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠵⠧⠟⠬⠭⣵⣶⣿⣻⡿⠠⠭⠝⣻⡥⠔⠪⡙⢠⣶⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠟⣗⣠⠀⠀⠙⠛⠛⠉⠀⠀⡐⢫⣉⡍⠂⠀⣋⢿⣿⠏⡇⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣫⣄⠀⠉⠆⠀⠀⠀⠀⠀⠠⠋⠀⢀⣤⡑⡀⠻⣢⠀⣶⠈⣆⠔⠒⠲⠕⡇⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⠗⠀⢀⠌⡀⡀⠀⠀⠀⠠⡀⠀⠘⠿⡣⠁⠀⡇⠓⠙⣁⠃⠀⠀⡠⠃⢡⣞⢳⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣒⠥⠊⡸⠀⠀⠀⠀⠀⠘⠋⠭⠑⠊⠆⡔⠘⢢⢹⣿⡤⠔⣾⣿⢿⡘⠖⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣠⠔⠁⡆⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠸⢌⡍⠚⣾⢌⡇⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⣾⠿⠛⣋⣉⠭⠄⠀⢴⣿⠿⠆⠀⠸⣀⡒⢪⢌⠀⢹⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠊⠭⠔⠚⠭⢀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣘⣂⠾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠰⡿⣿⣿⡏⠉⠉⠉⠉⠉⠩⣿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣮⢄⠁⠀⠀⠀⠀⠀⠀⠀⡌⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠍⡅⠆⠪⠄⣀⣀⡠⣀⣀⣠⡤⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣮⠲⣿⠿⠦⣠⣴⣿⠘⣻⣧⣤⡠⠛⠛⢄⠐⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠵⠧⠟⠬⠭⣵⣶⣿⣻⡿⠠⠭⠝⣻⡥⠔⠪⡙⢠⣶⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠟⣗⣠⠀⠀⠙⠛⠛⠉⠀⠀⡐⢫⣉⡍⠂⠀⣋⢿⣿⠏⡇⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣫⣄⠀⠉⠆⠀⠀⠀⠀⠀⠠⠋⠀⢀⣤⡑⡀⠻⣢⠀⣶⠈⣆⠔⠒⠲⠕⡇⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⠗⠀⢀⠌⡀⡀⠀⠀⠀⠠⡀⠀⠘⠿⡣⠁⠀⡇⠓⠙⣁⠃⠀⠀⡠⠃⢡⣞⢳⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣒⠥⠊⡸⠀⠀⠀⠀⠀⠘⠋⠭⠑⠊⠆⡔⠘⢢⢹⣿⡤⠔⣾⣿⢿⡘⠖⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣠⠔⠁⡆⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠸⢌⡍⠚⣾⢌⡇⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⣾⠿⠛⣋⣉⠭⠄⠀⢴⣿⠿⠆⠀⠸⣀⡒⢪⢌⠀⢹⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠊⠭⠔⠚⠭⢀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣘⣂⠾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠰⡿⣿⣿⡏⠉⠉⠉⠉⠉⠩⣿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣮⢄⠁⠀⠀⠀⠀⠀⠀⠀⡌⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠍⡅⠆⠪⠄⣀⣀⡠⣀⣀⣠⡤⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣮⠲⣿⠿⠦⣠⣴⣿⠘⣻⣧⣤⡠⠛⠛⢄⠐⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠵⠧⠟⠬⠭⣵⣶⣿⣻⡿⠠⠭⠝⣻⡥⠔⠪⡙⢠⣶⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠟⣗⣠⠀⠀⠙⠛⠛⠉⠀⠀⡐⢫⣉⡍⠂⠀⣋⢿⣿⠏⡇⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣫⣄⠀⠉⠆⠀⠀⠀⠀⠀⠠⠋⠀⢀⣤⡑⡀⠻⣢⠀⣶⠈⣆⠔⠒⠲⠕⡇⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠻⠗⠀⢀⠌⡀⡀⠀⠀⠀⠠⡀⠀⠘⠿⡣⠁⠀⡇⠓⠙⣁⠃⠀⠀⡠⠃⢡⣞⢳⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣒⠥⠊⡸⠀⠀⠀⠀⠀⠘⠋⠭⠑⠊⠆⡔⠘⢢⢹⣿⡤⠔⣾⣿⢿⡘⠖⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣠⠔⠁⡆⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠸⢌⡍⠚⣾⢌⡇⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⣾⠿⠛⣋⣉⠭⠄⠀⢴⣿⠿⠆⠀⠸⣀⡒⢪⢌⠀⢹⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠊⠭⠔⠚⠭⢀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣘⣂⠾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠰⡿⣿⣿⡏⠉⠉⠉⠉⠉⠩⣿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣮⢄⠁⠀⠀⠀⠀⠀⠀⠀⡌⣆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⣽⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
Reikarin
Hi,guess who,it is ShiyaAzuki in School Idol Tomodachi!!
OnlyNi17
I need to finish updating my profile tomorrow. I need to wake up early...