⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠁⣄⣿⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⢷⡄⠀⠙⢿⣯⡻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣉⣐⡒⠲⣿⣿⡍⠛⠷⣦⣄⠘⣷⡀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠠⠀⠌ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢸⣿⡿⠀⠀⠟⠀⠀⠀⠀⠀⠀⣤⡠⢿⣇⠀⠀⠀⠀⠀⠀⢻⣟⣧⡈⢿⡀⠀⠀⠙⢿⣿⣿⡹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠙⢿⣧⠀⠀⠈⠻⣷⣽⣇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⣸⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⣿⡄⠀⠀⠀⠀⠀⠈⢿⡌⢻⣌⢷⡄⠀⠀⠀⠈⠻⢿⣦⣈⠿⣦⣄⡀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠈⣿⣿⡀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⢸⣷⡀⠀⠀⠀⠀⠀⠘⣷⡀⠙⣾⣷⡀⠀⠀⠀⠀⠀⠉⠛⢿⡆⠉⡟⠛⠉⢐⣤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠤⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢰⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄ ⠀⠀⠀⡀⠀⠀⣿⡟⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠐⣿⣧⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠈⢹⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⢘⣷⡀⠀⣿⣧⡀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠙⡷⠀⠀⠀⣀⣤⠼⠋⠻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⣿⡟⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⣿⡟⡅⠀⠀⠀⢿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣧⢿⡄⠀⢀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠸⣿⡄⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⠀⣻⡟⡇⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠹⡎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢀⠸⠟⠁⠀⠀⠀⠀⢰⣾⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣇⠀⠀⢀⣠⣿⣩⣄⣠⣴⣤⣴⠶⠂⠀⢿⣆⠀⠀⠀⠀⠀⠀⢿⣷⠀⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣇⣿⡇⠁⠀⠀⠀⠈⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢀⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠛⣿⡆⠸⣷⠈⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡈⢷⠀⠻⣆⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⣠⣶⣿⣿⣿⣿⣵⣿⣿⡿⡿⠿⠿⠻⠛⠟⠻⠿⢶⡤⠀⢿⣧⠀⠀⠀⠀⠀⠀⣻⣧⢀⡇⠀⠀⠙⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣷⢀⡇⠀⠀⠀⣸⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⣯⢷⡘⣇⠀⠙⢷⡀⠀⢠⡾⠋⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⣠⣾⣿⣿⣿⣷⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⢿⣿⣸⣧⠀⠀⠀⠀⠁⠄⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⠸⡇⠀⠀⠀⠉⣿⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⡎⢻⣽⣦⡀⠈⠻⣦⡿⠁⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠙⠢⠌⣽⣦⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢢⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⡆⣷⠀⠀⠀⠀⢿⡆⠈⢷⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢿⡄⠉⠻⣷⡀⠀⠉⠀⣀⣤⠞⠋⠀⣀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⣦⣤⣉⡉⠀⠀⠤⣄⡀⠀⠀⠀⠹⣧⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠸⣿⣷⢿⡄⠀⠀⠀⠘⣷⠀⠈⠂⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠙⣷⡀⣤⣶⠟⠁⠀⠀⠛⠉⠋⠙⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣀⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠤⣄⣈⠙⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠹⣧⠀⠀⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⡌⢷⡀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢿⣧⠘⣇⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣛⡀⡀⣀⣀⣀⣠⣴⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠹⠿⣿⣿⣶⣄⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣶⣄⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠸⣧⠀⢀⣠⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣷⣄⠀⠝⢿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢹⣷⠿⠁⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⢿⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠸⣷⠀⠀⣄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢻⡇⠀⠘⢧⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣿⡀⠀⠘⣷⡀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⠶⠶⢾⣿⠟⠛⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⣷⡀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⢀⣼⠏⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⢻⣿⡄⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣟⣿⡈⣿⣷⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡘⣷⠺⣿⣿⣷⣄⡙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣾⡗⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢹⡇⠸⣿⡏⠉⠻⣿⣿⣶⣤⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣸⣷⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢸⣧⠀⢹⣧⠀⠀⠀⠙⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣶⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢿⡄⠀⣿⠀⠈⣿⡆⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⡿⢻⣟⣟⣼⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⢻⣿⣹⣯⠛⠿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⣧⠀⢻⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡞⢡⣾⣧⣤⣴⣿⣝⣿⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠙⣿⣿⣤⡆⠈⡙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣈⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢿⣿⣿⣿⣾⣏⣹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⠹⢿⣄⣀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠌⣿⡀⠀⠀⠀⠀⠀⠀⢼⣷⡶⠀⠀⠈⣹⣇⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣯⣾⡿⠋⠙⠿⣿⣿⣷⣾⣿⣿⣿⣧⣾⠁⠀⠀⡀⢀⡀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣈⣻⣯⣄⡀⡀⠀⠀⠀⠀⠙⠻⢶⣦⣄⣄⣼⣧⡄⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⢈⣿⣘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⢀⡀⢀⣀⠀⡀⠉⢹⡛⠋⠁⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡅⠀⠀⣾⣿⣿⣿⣿⣿⠿⠿⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿