⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄

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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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▒▒▒░░░░░░░░░░▄▐░░░░ ▒░░░░░░▄▄▄░░▄██▄░░░ ░░░░░░▐▀█▀▌░░░░▀█▄░ ░░░░░░▐█▄█▌░░░░░░▀█▄ ░░░░░░░▀▄▀░░░▄▄▄▄▄▀▀ ░░░░░▄▄▄██▀▀▀▀░░░░░ ░░░░█▀▄▄▄█░▀▀░░░░░░ ░░░░▌░▄▄▄▐▌▀▀▀░░░░░ ░▄░▐░░░▄▄░█░▀▀░░░░░ ░▀█▌░░░▄░▀█▀░▀░░░░░ ░░░░░░░░▄▄▐▌▄▄░░░░░ ░░░░░░░░▀███▀█░▄░░░ ░░░░░░░▐▌▀▄▀▄▀▐▄░░░ ░░░░░░░▐▀░░░░░░▐▌░░ ░░░░░░░█░░░░░░░░█░░ ░░░░░░▐▌░░░░░░░░░█░

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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.

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Gioi thieu SIEU TOC Marketing | Agency chuyen nganh Dich vu - San xuat - Nha Phan phoi Sieu Toc Marketing sở hữu hệ sinh thái đa dạng gồm Siêu Tốc Academy, Siêu Tốc Branding, Siêu Tốc Media, Quảng Cáo Siêu Tốc và Web Siêu Tốc. Với đội ngũ chuyên gia thực chiến, công ty cam kết đồng hành xuyên suốt, tư vấn chiến lược rõ ràng và mang đến hiệu quả bền vững. https://www.sutori.com/en/user/gioi-thieu-sieu-toc-marketing

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢶⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠒⠪⢝⠻⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢉⡀⠀⠈⠐⠄⢿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⡄⠤⢀⠈⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣟⣕⡤⡠⠘⠀⠀⠀⢱⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣞⣄⠮⠔⠈⡢⠄⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⢽⡻⣿⣿⣿⣽⣵⣾⡽⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣿⡟⠈⠉⠚⢽⣻⢷⡝⣿⡿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⢩⣯⣭⣾⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣿⡿⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣿⣿⣯⡶⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣟⣿⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⡯⣿⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠈⠀⠻⣿⣿⣿⣿⣿⣟⣛⣿⣿⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠐⠤⢀⡀⠀⢀⣙⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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Hello, guys! I hope we can be friends. ^^ I don't play this game very often, though.

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In idol and pokemon hell. Usually play every other day.

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hi weebs that are stuck in idol hell and pkgo heaven

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