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⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠿⡀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⣠⠾⠁⣀⣄⡈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠁⠀⠀⠈⠙⠛⠂⠈⣿⣿⣿⣿⣿⠿⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀⠀⢻⣿⣿⠭⢤⣴⣦⣤⣹⠀⠀⠀⢀⢴⣶⣆ ⠀⠀⢀⣾⣿⣿⣿⣷⣮⣽⣾⣿⣥⣴⣿⣿⡿⢂⠔⢚⡿⢿⣿⣦⣴⣾⠁⠸⣼⡿ ⠀⢀⡞⠁⠙⠻⠿⠟⠉⠀⠛⢹⣿⣿⣿⣿⣿⣌⢤⣼⣿⣾⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⣾⣷⣶⠇⠀⠀⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠉⠈⠉⠀⠀⢦⡈⢻⣿⣿⣿⣶⣶⣶⣶⣤⣽⡹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡻⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉
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i didnt even use a real email omegalul
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣀⣀⣀⣀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠀⠈⠉⠻⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⢀⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣉⠉⣉⢉⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢿⣿⠋⠉⣹⠻⢿⣿⣿⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⢀⣀⣠⡾⠛⠋⠀⢀⡞⠀⠀⠀⠛⠀⠀⢹⡟⠻⣿⣿⣧⣄⡀⠀⣶⣤⣤⠀ ⢠⣿⣷⣿⣿⠟⣛⣇⠀⠀⠀⣈⡷⣄⡀⠀⠀⠀⣠⣾⡟⠉⠉⠉⠉⢉⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⣿⠛⠁⠈⠙⢷⣦⠀⠀⠀⠀⠀⠈⢉⠋⢁⣼⣏⣡⣤⣤⢐⣺⣿⣿⣿⣿⠟⠁ ⠀⠙⠿⣿⣷⢤⣀⡀⢸⢿⠀⠀⠀⠀⠒⣄⠈⢡⣾⣉⡤⠚⣩⢴⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠙⢿⣷⣈⡙⠻⢿⣧⠀⠀⠀⠀⠸⡀⠈⠻⣯⡴⠋⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣿⢶⣤⣿⠈⠁⠀⠀⠀⠳⡄⠀⠙⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣿⡀⠀⠀⠀⠀⠀⠿⣤⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⢀⣤⣾⣿⣿⡿⠛⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣸⣿⡿⢻⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠀⠈⠻⣷⣿⣿⡇⠈⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⢀⣤⣶⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⡰⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀
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is that… a GIRL?!!!? Uhhhhhhhhhhhh girls? uhhhhhhhhhhhhh like, here? *starts sweating* uuuuuuuuuuuhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh *starts drooling* uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh *wide eyed* UUUUUUUUUUUUUUUUUUHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH *starts farting* UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH *starts shitting with bloodshot eyes* UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH *poopie leaking out of my shorts* UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH *starts convulsing which makes the shit run down my shaved legs even faster* UUU-UUU-UUU-UUU-UUU-UUU-UUU-UUU-UUU-UUU-UUU-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH-HHH *gets a boner* UUUHHH-UHHH-UHHHHH-UUUUHHHH-UHHHH-UUUUHHHHHHH-UUUUHHHHHHHHH-UHHHHH-UUUUUUHHHHHHHHH *passes out*
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⠄⢸⣿⡟⠛⠛⠃⢸⣿⡇⠄⠄⣿⡇⠄⣼⣿⠟⠻⣿⣆⠄⣿⣿⢠⣾⣿⠋⠄⠄ ⠄⢸⣿⣷⣶⣶⠄⢸⣿⡇⠄⠄⣿⡇⠄⣿⡏⠄⠄⠄⠄⠄⣿⣿⣿⣿⣇⠄⠄⠄ ⠄⢸⣿⡇⠄⠄⠄⠘⣿⣧⣀⣰⣿⡇⠄⢿⣿⣀⣠⣿⡶⠄⣿⣿⠃⢹⣿⣆⠄⠄ ⠄⠘⠛⠃⠄⠄⠄⠄⠘⠛⠛⠛⠋⠄⠄⠈⠛⠛⠛⠛⠁⠄⠛⠛⠄⠄⠛⠛⠃⠄ ⠄⠄⠄⠄⢠⣤⡄⠄⠄⣤⣤⠄⢀⣠⣤⣄⡀⠄⢠⣤⡄⠄⠄⣤⣤⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⢻⣿⣄⣼⣿⠃⣰⣿⠟⠛⢿⣿⡄⢸⣿⡇⠄⠄⣿⣿⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠻⣿⡿⠁⠄⣿⣿⠄⠄⢸⣿⡇⢸⣿⡇⠄⠄⣿⣿⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣿⡇⠄⠄⠹⣿⣦⣤⣼⣿⠃⠄⣿⣷⣤⣴⣿⡏⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠛⠃⠄⠄⠄⠈⠛⠛⠋⠁⠄⠄⠈⠙⠛⠛⠉⠄⠄⠄⠄⠄⠄
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▒▒▒░░░░░░░░░░▄▐░░░░ ▒░░░░░░▄▄▄░░▄██▄░░░ ░░░░░░▐▀█▀▌░░░░▀█▄░ ░░░░░░▐█▄█▌░░░░░░▀█▄ ░░░░░░░▀▄▀░░░▄▄▄▄▄▀▀ ░░░░░▄▄▄██▀▀▀▀░░░░░ ░░░░█▀▄▄▄█░▀▀░░░░░░ ░░░░▌░▄▄▄▐▌▀▀▀░░░░░ ░▄░▐░░░▄▄░█░▀▀░░░░░ ░▀█▌░░░▄░▀█▀░▀░░░░░ ░░░░░░░░▄▄▐▌▄▄░░░░░ ░░░░░░░░▀███▀█░▄░░░ ░░░░░░░▐▌▀▄▀▄▀▐▄░░░ ░░░░░░░▐▀░░░░░░▐▌░░ ░░░░░░░█░░░░░░░░█░░ ░░░░░░▐▌░░░░░░░░░█░
AmberlynnWEED
Being a hentai actress must be so weird. Imagine this: you’re in a soundproof room pleasurably screaming into an 800,000¥ microphone about how much you love old man dick at 10:47 AM on a Tuesday in October while your 45-year-old boss oversees you through a glass window from the other room. You eventually look up after 2 hours of practicing your unnaturally high-pitched moans and see him give you a big thumbs up as you pretend to have an orgasm.
AmberlynnWEED
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀