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⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⢀⣠⣤⣀⣠⣤⣠⣤⣀⣠⣤⣀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠀⠀⠙⢿⠟⠁⠀⠙⢿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣴⣶⣿⣿⣷⣶⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠟⠋⠉⠛⢇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⣤⣴⣷⣤⡄⠀⣤⣴⣷⣤⡄⠀⠀ ⠀⠀⠀⢨⣿⣿⣯⠀⠀⢨⣿⣿⣯⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠁⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠐⣿⣿⡗⢺⣿⣿⠂⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣤⠁⣤⣦⡌⢠⣴⣤⠀⠀⠀ ⠀⠀⠀⠹⢿⠿⡉⠿⡿⢏⠹⢿⠿⠁⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⡧⢼⣿⣿⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣄⣴⣄⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⡟⢙⣍⠻⣫⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣻⣯⡙⣟⣽⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠋⠺⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣶⣾⠂⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣯⠀⠀⠀⠐⢲⣿⣷⠒⠀ ⠀⠀⠈⣿⣿⣿⣿⣦⣀⡀⡀⠘⠉⠙⠀⠀ ⠀⠀⠀⠘⠿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⣧⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢙⣿⣿⣟⠁⠀⢀⠀⠀⠀ ⠀⠠⢤⣾⣦⠤⠘⠋⠉⠛⠠⢤⣾⣦⠤⠀ ⠀⠀⠸⠛⠻⠀⠀⠀⠀⠀⠀⠸⠛⠻⠀⠀
⠀⠀⠀⣸⣿⠿⠛⠻⠿⠛⠻⢿⣿⡀⠀⠀ ⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀ ⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢷⣄⢀⣴⠿⠋⠀⠀⠀⠀
⠀⠀⠀⣼⡄⠀⠀⠀⡄⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣤⣼⣿⣤⣤⠄⠀⡄⠀⠀ ⠀⠀⠀⢀⠀⠀⢨⣿⣿⣯⠀⠀⠘⠛⠀⠀ ⠀⠀⠀⠾⠆⠀⠈⠁⠀⢉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣤⣠⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠁⠀⠙⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣈⡛⠻⠛⠋⠀⡀⠙⠛⠟⠛⣁⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⡆⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢛⣯⣴⣤⣌⠉⠋⣩⣤⣦⣬⡛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣤⣠⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⢠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣷⡤⠄⠀⠀⠠⢤⣾⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠀⠀⠀⠸⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣄⣀⠀⠀⢀⣀⣼⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⠀⠀⠀⠀⢸⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣴⣦⣤⣠⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣤⣠⣤⣶⣤⣄⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠙⠻⣿⣿⡿⠛⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠀⠙⠻⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣿⣿⣧⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣼⣿⣄⣀⣀⣀⠀⠀⡿⠛⠁⠀⠙⠻⡇⠀⢀⣀⣀⣀⣼⣿⣄⣀⣀⣀⠀ ⠀⠀⠉⠻⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠋⠁⠀ ⠀⠀⠀⠀⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⡇⠀⠀⠀ ⠀⠀⠀⠘⠉⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⣸⣿⣿⣿⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⠙⠉⣠⣤⣦⣥⡀⢿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⣾⣿⣿⣿⣿⣿⡆⠈⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⡏⢈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣠⣈⠻⠿⡿⡿⠋⣾⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢉⣿⣿⣿⣇⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⢹⣿⣿⣿⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣦⣄⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠉⠀⠀⠈⠙⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⣼⣿⣿⣿⣿⣿⡄⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠈⠻⠿⡿⠿⠋⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠃⣠⣴⣶⣷⣶⣤⡘⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡄⠻⢿⣿⣿⣿⠿⢣⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠀⣠⣤⣧⣤⡀⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⢿⣿⣿⣿⣿⣿⠇⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠛⠙⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣟⠀⠀⠀⠀⢘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣀⢀⣀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣦⣄⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⢀⣠⣤⣤⣀⢀⣠⣤⣤⣀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⢸⣿⣿⡏⠁⠈⠉⠀⠉⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⢿⣿⣇⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠻⣿⣷⣄⢀⣴⣿⡿⠃⠀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠈⠙⠿⡿⠟⠉⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠁⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣰⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠟⠋⠀⠀⠀⠀⠙⠻⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠻⠇⠀⠀⠀⠀⠀⠀⠸⠟⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⣤⣼⣿⣤⣤⠄⠀⠐⠶⣶⣶⣿⣿⣷⣶⡶⠖⠀⠀⢤⣤⣼⣿⣤⣤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⢠⠿⠋⠉⠻⢧⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣷⣀⣀⡀⠀⠀⠀⣀⣀⣰⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣟⠉⠀⠀⠀⠀⠈⢙⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢶⣮⢿⣳⣯⣿⣻⣽⣾⢷⣟⣷⣟⣷⡿⣾⢿⣽⣟⣿⣗⣮⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣯⣿⣻⣟⣿⣽⣿⣻⣽⣾⢿⣽⣾⢿⣻⣽⣯⣷⡿⣟⣿⣽⣯⣷⡿⣯⣷⡿⣯⣿⢮⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣻⣿⡽⠾⠫⠋⠫⠋⠫⠻⢿⣽⣿⣻⣾⢿⣿⣽⣾⣯⣿⢿⣯⠷⢛⠙⠝⠋⠛⠟⢿⢿⣟⣯⣿⢮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⢎⠑⠑⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣿⣟⣷⢿⣾⣷⡏⠍⠚⣮⡀⠀⠀⠀⠀⠀⠀⠑⢝⢿⣿⣿⣽⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣻⢳⢴⣼⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣻⣽⠊⢳⣤⣮⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⡿⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⢿⣾⠃⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⡅⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣟⣿⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣻⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣻⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢟⠯⡫⡠⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡠⢙⠝⡏⡟⡷⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠅⢕⠰⠨⡊⠔⢌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣯⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡢⡑⢌⠢⡑⢌⠢⡊⢄⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢊⢢⢑⢑⢌⢊⠢⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⢹⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠆⡊⡢⡑⢌⠢⡑⢌⢂⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠊⠔⠐⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢜⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠐⠐⠌⠢⠑⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣯⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⠻⡮⣦⣠⡠⢀⠠⠀⠀⠀⠀⡀⣄⢮⣾⢿⣾⢿⣧⣅⠄⠀⠀⡀⠀⡀⡀⡀⣄⣔⣼⢞⢽⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣫⠀⠈⠈⠙⠙⢟⠽⢾⣾⣾⣮⣾⣾⣿⣿⣿⣿⣿⣷⣿⣿⣾⣮⣶⣷⢺⠻⠝⠓⠉⠀⠀⢜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢶⣮⢿⣳⣯⣿⣻⣽⣾⢷⣟⣷⣟⣷⡿⣾⢿⣽⣟⣿⣗⣮⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣯⡿⣿⣻⢿⣿⣿⣻⣽⣾⢿⣽⣾⢿⣻⣽⣯⣷⡿⣟⣿⣽⣯⣷⡿⣯⣷⢿⣯⡿⣮⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡽⡟⠯⢧⣧⡠⡀⠀⠁⠙⠻⡿⣿⣿⣻⣾⢿⣿⣽⣾⣯⡿⣟⣯⣷⡿⣾⣟⣯⣿⣻⣷⢿⣟⣷⡿⣮⣤⡠⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡻⡈⠀⠀⠑⣿⣿⣮⠄⠀⠀⠀⠈⢚⣿⣿⣿⣻⡷⣿⢾⡷⣿⢿⣻⣽⣟⣯⣿⣽⣯⣿⢾⡿⣯⣷⡿⣟⣷⣯⢎⢖⣯⣿⣵⡀⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⡗⠈⣿⣦⣦⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣿⣻⣟⣿⣟⣿⣽⣯⡿⣷⢿⣾⣻⣟⣿⣯⣷⣿⢿⣻⣾⢿⡿⣿⣻⡽⠑⠁⠁⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⣿⠐⠀⠘⢿⢿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣽⣯⡿⣷⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⢿⣽⡿⣯⡊⠈⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣷⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⣿⣿⢾⡷⣿⣿⣿⢿⡿⣟⣿⣻⣽⣿⣽⣯⡿⣟⣿⣿⣿⣿⣯⣿⣻⡊⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⢿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣻⣟⣯⣷⡿⣟⣿⣻⣯⣿⣽⣾⢷⣟⣿⣻⣟⡾⡷⡿⡾⣯⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣽⣯⡿⣯⣷⣿⢿⣯⡿⣷⣟⣷⢿⣻⡯⡯⡓⢍⠪⡊⡪⢊⠪⡃⣂⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣗⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⣿⣟⣷⡿⣟⣷⢿⣻⣷⢿⣯⣿⣽⢿⣯⢣⠪⡨⠪⡘⢌⢌⢪⢘⢌⠢⡢⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢯⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣵⡿⣿⣽⢷⣿⣟⣿⣟⣯⣿⣻⡷⣿⢾⣟⣯⣷⣕⡜⡌⡪⠢⡱⠨⡢⠡⠃⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⢔⣀⠄⠀⠀⠀⠀⡀⠠⡠⣵⣻⣷⢿⡿⣾⢿⡷⣟⣷⡿⣯⣿⣽⣟⣿⣻⣿⣽⢷⣿⢽⠫⠊⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠻⡾⣮⣾⣶⣾⣟⣿⣯⣿⣾⢿⣻⣟⣿⣻⣟⣯⣿⢿⣾⣷⣿⣯⣿⣾⢿⢟⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠑⠙⠋⠛⠙⠟⢟⠿⠟⠿⡻⠟⠿⡻⠟⠟⠙⠝⠙⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣔⡶⣶⣮⢿⣻⣟⣿⣟⣿⣟⣿⣳⣶⢶⣦⣤⣄⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣤⣤⣠⣀⣄⣖⣮⣿⣽⣿⣽⣾⢿⣻⣾⢿⣻⣽⣷⢿⡷⣟⣯⣿⣽⢿⡷⣟⣷⡿⣟⣷⣶⣤⣠⣀⣤⢴⣰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣨⣿⣽⠿⠻⠟⢟⢿⣿⣿⣿⣿⣿⣽⣿⣻⣽⣾⢿⣻⡿⣯⣷⣿⣿⣿⣻⣿⣿⠿⢟⢟⢿⣿⣽⣮⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣖⣿⣟⠏⠂⠁⠀⠀⠀⠁⠑⠙⢿⣽⣹⣻⣿⣯⣿⣽⢿⣻⣿⣟⠏⠂⠃⠑⠁⠀⠁⠉⠫⡳⣧⣹⢻⣿⣾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣻⣿⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣦⡙⢿⣿⣾⢿⣿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣧⡙⢿⣿⣿⣕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⢁⢿⣿⣿⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣷⢁⢿⣿⣾⣗⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣟⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⡆⣹⣿⣷⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⣿⣿⡆⣹⣿⣿⢾⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⠀⠀⠀⢀⣷⣅⠀⠀⠀⠀⠀⠀⠠⣸⣾⣿⣿⢇⢸⣿⣯⠂⠀⠀⢀⣷⣅⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⣿⢇⢸⣿⣿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣷⡅⡀⠀⠀⢺⣿⣷⣥⣠⣠⣐⣬⣾⣿⣿⣿⡿⡁⣾⣿⣷⡅⠀⠀⠀⢺⣿⣯⣦⣠⣠⣐⣬⣾⣿⣿⣿⣟⠅⣾⣿⣯⡯⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⣯⣆⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣑⣼⣿⡿⣯⣿⡤⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡡⣺⣿⣟⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢻⣟⣷⡤⡀⠀⠙⠽⢿⣿⣿⣿⣿⡟⣛⣾⣾⣿⣟⣿⣻⣽⣿⣷⣄⢀⠀⠙⠽⢿⣿⣿⣿⣿⢟⢻⣼⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢛⢿⢷⡦⣦⡠⣠⣑⣭⣮⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⡷⣾⢶⣦⣥⣕⣩⣸⣼⣼⡿⣿⢝⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⡹⡸⡪⡎⣖⡿⣟⣿⣯⣿⣻⡾⣷⢿⡾⣷⢿⢝⢝⢜⢮⢣⢫⣟⣿⢿⡿⡿⡯⢗⠫⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢜⢔⢱⡹⡘⠘⠙⠟⢗⢿⢾⡻⣟⣿⣻⣟⣿⢽⡱⡱⡝⡮⡱⢝⠯⠫⠋⠍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢧⠣⢢⡣⡣⠊⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠨⢨⢣⢣⢱⢹⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣲⣶⣮⣿⣻⣟⣿⣟⣿⣟⣿⢷⣶⣶⣦⣦⣤⣴⣤⣤⣦⣤⣤⣠⣀⡀⡀⠀⠀⠀⢀⢠⡠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠽⠓⠛⠙⠕⣩⣭⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⣽⡷⣿⢷⣿⢿⣿⢿⣟⣿⣽⣟⣿⣻⣟⣧⣫⡉⡙⠝⠫⠳⠇⠀⠀⡎⣞⢼⢕⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡢⣗⣿⣻⣾⢿⢿⢿⢿⢿⣻⣿⣻⣟⣿⣻⣾⣟⣿⣻⣽⣿⣻⣿⣽⡿⡾⣿⢽⣯⣿⣯⣿⣽⣶⢦⡀⠀⠀⠀⠀⢸⡸⡕⣇⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣮⣿⣟⠟⠝⠈⠀⠀⠐⠀⠉⠙⠝⢿⣿⣽⡿⣾⣯⣿⣽⢿⣾⢿⠺⠙⠈⠈⠀⠀⠀⠀⠙⠝⢿⣿⣻⣟⣦⡀⡀⢨⢪⢎⡗⡵⡅⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⢿⡷⡛⠀⠀⠀⠀⠀⠰⡰⣤⣦⣀⡀⠀⠙⢿⣿⡿⣾⢷⡿⣟⠏⠁⠀⠀⠀⠀⠀⢐⠴⣔⣴⣀⡀⠙⢿⣿⣯⣷⡦⡁⠁⠁⠁⠁⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⢻⣿⣿⣻⡿⠑⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠻⣿⣿⣦⢀⢻⣿⣷⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣗⡁⠀⢿⣿⣟⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣗⠄⢿⣿⣻⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣻⡷⠁⠀⠀⠠⡣⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⡆⠀⢹⣿⣟⠀⠀⠀⠀⠠⡣⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⡣⢸⣿⣿⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⠀⠀⠀⠐⣻⣵⡀⡀⠀⡀⣐⣼⣿⣿⣿⣿⠕⠀⢹⣿⡿⡀⠀⠀⠀⠐⢿⣕⡄⠀⠀⡀⢄⣵⣿⣿⣿⣿⠃⢼⣿⣿⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣇⠀⠀⠀⠘⢿⣿⣾⣶⣾⣿⣿⣿⣿⣿⢓⠀⣐⣿⣿⣿⡥⡀⡀⠀⠀⠊⢿⣿⣷⣷⣾⣿⣿⣿⣿⣿⠏⢨⣻⣿⡯⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣻⣆⢀⠀⠀⠈⠻⡻⣿⣿⣿⣿⣿⣿⡯⡶⠺⡚⠝⠙⠙⠋⠛⠞⠮⡶⣤⣑⠻⢿⢿⣿⣿⣿⡿⢟⠃⡨⣾⣿⠯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣷⣄⢀⠀⠀⠀⠈⠁⣹⡿⡟⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠉⠈⠁⠃⠈⣀⣶⣿⢟⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠟⣶⢦⣠⣠⣐⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣿⣇⣄⣔⣼⣾⠿⡙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠽⢻⢿⢿⣿⣵⣀⢄⢀⠀⠀⠀⠀⠀⢀⢀⠠⣀⣦⣾⣿⡿⡿⠝⠏⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠋⠛⠗⢟⠞⠞⠞⠮⠶⠻⠫⠋⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡾⣎⢍⢍⢒⠲⡐⠤⢄⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⢄⢐⠄⡢⠡⡑⣜⣷⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⢯⣗⡔⡐⢅⢊⠌⡂⠆⡊⣔⣽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣵⡡⡂⠕⡈⡂⡢⠡⡂⢕⢜⣯⣿⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣷⡪⡐⡐⠅⡊⢌⢮⣾⣻⣞⡀⡀⢠⣀⢄⣄⣦⣔⣤⣢⣔⣤⣢⣔⣤⡠⣀⢄⢀⢀⢸⣟⣾⡷⣧⡑⢌⠢⠨⡂⢪⣸⣟⣯⣷⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢷⣿⣪⢐⠅⣪⣺⣯⣿⣽⣷⢿⡾⣿⢾⣿⣽⣾⣯⣿⣽⢿⣽⢿⣽⣯⡿⣟⣿⢷⣯⣿⣽⣷⡿⣟⣿⣲⡡⡑⢌⣲⡷⣟⣯⣿⠕⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣽⢞⠧⣳⠯⠗⠏⠫⣻⣟⡏⠻⢟⢿⣷⣿⡾⣷⢿⡾⣿⣻⡿⡽⠺⡿⡟⢟⠫⢋⢿⣟⡗⠻⢻⢿⣿⣽⣮⣲⣯⡿⣟⣯⣿⢅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡃⠁⠀⠀⠀⠀⢔⣽⣿⣿⣿⣦⠀⠈⠈⠻⣿⣿⣟⣿⣻⣽⢇⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣦⠀⠀⠑⠻⣻⣷⣿⣻⣟⣯⣿⠅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣾⠍⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⢿⣿⣯⣿⣻⠇⠀⠀⠀⠀⢐⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠨⣻⣿⣯⡋⢋⠚⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣟⠄⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢵⣿⣿⣾⣟⠄⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⣸⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣽⣿⣵⡀⠀⠀⠀⠈⣺⣿⣿⣿⣿⣿⠁⠀⠀⢀⢬⣿⣿⣻⣾⣻⣵⡀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⠂⠀⠀⢀⢔⣿⣿⢷⡿⡕⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⣷⣿⢾⣿⢶⣄⢄⠀⠐⠻⣿⣿⡟⡃⡁⣠⣢⣿⣿⢿⣽⢿⡾⣟⣿⢿⣖⣤⡀⡀⠈⠻⣿⣿⡟⡃⢠⢠⣢⣿⣿⢿⣻⣟⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⢀⠀⠀⠈⢻⡺⡻⡹⢫⢛⠯⢿⢺⣶⢿⣿⣶⣷⡿⣿⣟⣯⣿⣻⣿⣿⣿⣿⣟⣿⣻⣽⡿⣿⢾⣞⣾⣿⣶⢯⢿⠻⡛⡝⢞⢛⠯⡟⠍⠀⠀⡀⢀⢀⢀⢀⠀⠀ ⠀⠀⢉⠈⠌⡈⠌⢊⡪⡢⡑⡌⢆⠪⡢⡑⡌⢆⠣⡪⣻⣷⣿⡾⣟⣯⣿⣽⣯⣿⢾⣟⣿⣷⢿⣽⣯⣿⣻⣟⣿⣻⣽⣷⠫⡊⢆⠣⡑⡌⡪⢂⢣⢑⠕⢜⡢⡁⠅⡁⠡⢁⠁⠀ ⠀⠀⢁⢉⢡⢡⣉⠢⠢⠪⠂⠎⠜⢌⠢⢪⠨⡢⡣⣪⡾⣷⣟⣿⣻⣯⡿⣷⣿⣾⣿⣻⣿⣟⣿⣿⣽⣯⣿⣽⣯⡿⣯⣿⣵⡱⡡⢣⢑⠬⡘⢌⠢⡡⠣⠅⢆⢌⢅⣉⡉⡈⡀⠀ ⠀⠀⠁⠁⠀⠀⠀⠈⠀⠀⠀⠈⠈⠀⠁⠁⠈⠘⠙⠯⢟⡯⣿⣽⣯⣷⡿⣿⢾⣯⣿⣻⣿⣽⢿⡾⣷⢿⡾⣷⣟⣿⣻⢾⠳⠛⠙⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠘⠑⠋⠻⠻⠳⠻⠽⠺⠽⠻⠻⠝⠋⠋⠓⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⢿⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⣦⡠⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣦⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣦⣦⣤⣠⣀⢀⠀⠀⠀⠀⠀⡀⣔⣼⠂ ⠀⠀⢿⣿⣿⣦⣤⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣄⣦⣾⣾⣿⢃⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠬⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣞⣿⣻⡷⣿⡾⡟⠟⠙⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⠛⠛⠿⡿⣿⣿⣽⣾⡿⣷⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣻⣽⣯⣿⠏⠊⠀⠀⣦⣢⣴⣄⡈⠙⣿⣿⣯⣿⣽⢿⣽⢿⣽⢏⠊⠀⠀⣴⣤⣦⣄⡈⠪⣿⣷⣿⣻⣯⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣽⣾⠇⠁⠀⠀⠀⠈⢻⣿⣿⣿⣗⡌⣿⣿⣾⣻⣿⣽⣿⡋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⡨⣻⣿⣽⡾⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⡿⡈⣤⡀⡀⠀⡠⣽⣿⣿⣿⣿⣿⣼⣿⣿⣽⣾⢷⡿⡀⣔⡄⠀⠀⡠⣵⣿⣿⣿⣿⣿⣾⣿⣿⢏⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣿⠠⡿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣟⣿⣿⠠⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⡻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⢕⠨⡊⢜⢘⠍⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣳⣿⣯⠺⣿⣿⣿⣿⣿⣿⡿⡫⡙⢔⢑⡑⢔⢐⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⡑⢅⠕⢌⠆⢕⢑⠸⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⢿⣯⣎⣟⣿⣿⣿⣿⡜⡰⡘⢔⠡⡊⡢⡑⢌⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠂⠑⠅⢑⠁⠊⠚⢿⢿⣿⣿⡿⣿⣻⣾⢷⣿⣻⣟⣿⡾⣿⢯⣿⢷⣷⣿⣿⡿⠟⠒⠈⠢⠑⠌⠂⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣊⢗⢟⢟⣿⢾⡿⣽⡯⣟⣷⢿⣻⣟⣯⠿⡝⣚⠌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⡄⣆⡦⣄⠄⡀⠀⠈⣈⣗⣿⡽⡯⡟⠽⡓⠫⡫⠫⠻⠽⢽⢽⡯⣿⢌⠁⠀⠀⡀⡄⡦⣔⣄⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣢⡷⣿⢯⡿⣯⢿⣖⣄⢮⡾⣞⢗⠩⢂⠊⢌⢐⠡⠂⠅⠅⠅⠅⠕⠹⢽⣻⣗⣄⣲⣳⣟⡿⣯⢿⣽⣖⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⣲⣳⡿⣯⣟⣯⡿⣯⡷⣿⢽⢏⠪⢐⠨⠠⡑⡐⡐⠌⠌⠌⠌⢌⠌⠌⢌⢂⢓⢯⡿⣾⣽⢾⣻⣽⢿⣺⣽⢯⠂⠀⠀⠀ ⠀⠀⠀⠀⡷⣿⢽⣷⣻⢷⣻⣯⢿⣽⣻⢐⠡⠂⠅⢅⢂⠢⠨⠨⠨⡈⡊⠔⠨⡈⡂⡂⠢⡹⣽⢷⣻⣻⣽⢯⡿⣯⢿⣽⡃⠀⠀⠀ ⠀⠀⠀⠀⢻⡽⣟⣾⢯⣿⣻⢾⣻⣗⣯⣂⠊⠌⠌⠔⡐⠨⠨⠨⠨⡐⡐⠡⢑⢐⠐⠌⡂⡽⣽⢿⣽⣻⣾⣻⣯⣟⣯⡷⡁⠀⠀⠀ ⠀⠀⠀⣀⢮⡿⣯⣟⣯⡷⣟⣿⢽⢞⡿⣮⣪⠨⠨⢂⠌⠌⢌⠊⠔⡐⡨⢈⢂⠂⢅⢕⣼⣽⡻⢽⢷⣻⣾⣳⣟⣾⢯⡷⣄⠀⠀⠀ ⠀⠀⠀⣾⣻⣽⢷⣻⢷⣟⣿⡊⠁⢀⡩⣟⣾⢯⣎⡦⡨⡨⠂⢅⢑⠐⢄⢅⡢⣕⣵⢷⢷⣳⢁⠀⠉⣷⣻⣞⡿⣞⣿⣻⣽⠕⠀⠀ ⠀⠀⠀⠑⠯⣟⣿⢽⢿⢽⠚⡠⣪⡾⣯⢿⡽⣯⡷⣿⣻⣽⣞⣮⣶⡽⣞⣷⣻⣯⣟⣟⣿⢽⣷⣳⢅⠘⢽⢾⣻⣯⢷⡟⠎⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⠉⠁⠁⠀⣯⡿⣽⣟⣯⡿⣯⢿⡽⣷⣻⡾⡕⠁⣟⣯⣷⢿⢾⣽⣻⢾⣻⡾⣯⢿⠕⠀⠈⠈⠈⠁⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣜⡾⣯⢿⣞⣷⣟⣯⣿⣻⣽⣗⠏⠂⠀⠩⡳⣟⣟⣯⣷⣟⣿⡽⣯⣟⣿⣳⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣽⢾⣻⣽⢿⣽⢾⣽⢾⣗⣿⣞⡷⠃⠀⠀⠀⢯⢿⣽⣻⣞⣷⢯⣿⣽⢾⣷⣻⣗⡯⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠋⠺⠻⠺⠻⠝⢏⠓⠃⠅⠁⠀⠀⠀⠀⠀⠁⠑⠙⠺⠝⠯⠳⡫⠟⠊⠣⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣾⣻⣾⣻⣖⠄⠀⠀⠀⠀⠀⣀⣠⣰⣲⣮⢿⣳⣯⣿⣻⣽⣾⢷⣟⣷⣟⣷⡿⣾⢿⣽⣟⣿⣗⣮⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⣟⣾⢿⣶ ⠀⠀⠀⠀⠀⠀⠻⣞⣿⣾⣻⡽⠁⠀⢀⢄⣦⣷⢷⡿⣾⢿⣽⣿⣻⣽⣾⢿⣽⣾⢿⣻⣽⣯⣷⡿⣟⣿⣽⣯⣷⡿⣯⣷⢿⣯⡿⣮⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡷⣿⣻⣯⢷ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⢯⠃⠀⡡⣜⣮⣿⢿⡾⣿⣻⣟⣿⢷⣿⣽⢿⣾⢿⣻⣾⢿⣿⣽⣾⣯⡿⣟⣯⣷⣿⡾⣟⣯⣿⣻⣷⢿⣟⣷⡿⣮⣄⠀⠀⠀⠀⠀⠀⠀⠈⢫⣟⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢼⣾⣻⣯⣿⡻⠫⠛⢟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⡷⣿⢾⡷⣿⡟⠏⠫⢻⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣻⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⡿⣯⣿⢾⣷⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣯⠂⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣻⡿⣾⢿⣿⣧⣢⣠⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣿⣧⣢⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣯⣷⡿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⢿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢷⡿⡕⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣰⣤⣪⡾⣷⣻⣟⡿⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⢿⣻⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⢿⣻⣟⡿⠅⠀⠀⠀⡠⣢⣦⣢⡀ ⠀⠀⠀⠀⠀⠿⣽⣾⢿⢽⠱⡑⢔⢑⠕⢌⠫⡫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⢿⣾⣻⣟⣯⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠫⡃⡣⡑⡱⡐⢕⢍⠄⠄⠀⠀⢟⣿⢾⣯⢟ ⠀⠀⠀⠀⠀⠈⠸⢯⠫⡊⡪⡨⢢⢑⢅⠣⡱⡘⢔⢝⣿⣿⣿⣿⣿⣿⡿⣯⣿⣽⣿⣽⣯⣿⣽⡷⣟⣿⣽⣾⣿⣿⣿⣿⣿⡱⠡⡣⡑⡌⡪⡐⡅⢕⢔⢑⠕⡠⠀⠀⠹⡻⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡑⢌⢌⠆⡕⢌⡊⡆⣎⣮⡿⣯⣿⣿⣿⣿⣟⣿⣻⣾⢷⡿⣾⢷⡿⣾⣟⣿⣯⣷⡿⣾⣟⣿⣿⣿⡾⣕⣔⡑⡌⢆⢪⠨⡢⢊⠂⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠺⢽⣯⣷⡿⣟⣷⣟⣯⣷⣿⣽⢿⡾⣿⣻⣟⣿⣻⣯⣿⣳⣿⢾⣟⣯⣿⣻⣯⣷⣿⣟⣷⠻⠈⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢟⢿⢿⣿⣯⣿⣯⣷⣿⣾⢿⣻⣿⣽⣯⣿⣽⣷⢿⣽⣾⣿⣻⣽⣯⣿⣾⡿⣾⢟⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠊⠉⠫⠛⠙⠽⠻⠿⠻⡻⠻⠻⡻⠻⠟⠿⠻⠙⠋⠛⠙⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⣫⣛⢝⡻⡟⠍⡩⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠋⠛⣚⣷⡿⡯⠋⡰⡨⣀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢶⣮⢿⣳⣯⣿⣻⣽⣾⢷⣟⣷⣟⣷⡿⣾⢿⣽⣟⣿⣗⣮⣦⣄⣀⠀⠀⠀⠀⣐⡼⡾⡷⡯⣔⡤⣢⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣯⣿⣻⣟⣿⣽⣿⣻⣽⣾⢿⣽⣾⢿⣻⣽⣯⣷⡿⣟⣿⣽⣯⣷⡿⣯⣷⢿⣯⡿⣮⡴⣼⣞⠏⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣻⣿⣽⣾⣯⣿⣽⣾⣯⣿⣽⣾⢿⣻⣾⢿⣿⣽⣾⣯⡿⣟⣯⣷⡿⣾⣟⣯⣿⣻⣷⢿⣟⣿⡿⣾⣲⡷⡵⡷⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⢾⡿⣾⢷⡿⣾⡷⣿⡾⣷⢿⣾⣻⣟⣿⣽⣟⣷⡿⣾⢷⡿⣿⣻⣽⣟⣯⣿⣽⣯⣿⡾⣿⣻⣽⣟⣿⣽⢷⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣻⡷⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣾⡿⣷⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⢿⣾⣿⣿⣿⣿⡿⣿⣟⣿⣟⣿⢿⡿⣿⢿⣿⣿⣿⣿⣻⣯⣿⣿⣿⣿⡿⣟⣿⣻⣟⣿⣽⣟⣿⢿⣿⣿⣿⣿⣷⣿⣟⣯⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣻⣿⢿⣯⣷⢿⣻⣯⣿⣳⡿⣯⡿⣟⣿⣻⣽⣯⣿⢿⣻⣽⡿⣿⣯⣷⣿⢿⣻⣽⣯⣷⣿⣽⣟⣯⣷⣿⣽⢿⡿⣯⣿⣽⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣻⣽⣿⣽⣾⢿⣻⡷⣿⣽⢿⣻⣟⣿⣯⣿⣽⣾⣟⣿⣻⣽⣟⣿⢾⡷⣿⣻⣿⣽⡾⣟⣾⡷⣟⣯⣷⡿⣾⢿⣻⣯⣷⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢻⠱⡛⡺⢹⢻⢻⣟⣿⢾⣿⣻⣽⡷⣿⢾⣻⣾⢯⣿⣽⣯⣿⣽⢿⣻⣿⣽⣾⢷⣿⣟⣯⣿⣟⣯⢷⠻⡫⢻⠹⡹⢞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⢌⢢⢡⠱⡨⡨⠢⡡⡑⢕⢟⣿⣽⣯⣿⣻⣟⣿⣻⣽⣿⣻⡾⣷⢿⣾⢿⣻⡷⣿⢾⡿⣷⣟⣯⡷⡏⡪⠢⡑⡌⡢⠱⡨⡂⡣⢡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⠢⡑⢔⢑⢔⢘⢌⠢⡊⡆⣯⡿⣷⢿⡾⣯⣿⣽⢿⣽⡾⣟⣿⣻⣿⣽⢿⣻⣟⣿⣻⣟⣯⣿⣽⢿⡌⡆⡣⢊⠔⠜⢌⠢⡊⡌⡢⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠕⠐⠅⠢⢣⢗⣿⣽⣟⣿⣻⣟⣯⣷⡿⣿⣽⢿⣻⣯⣿⢾⣻⣟⣿⣽⣯⣿⣽⣯⣷⡿⣟⣿⣳⢼⠰⠑⢉⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠙⠻⣟⣯⣿⣯⣷⣿⣿⣾⣿⣟⣷⣿⣿⣻⣽⣿⣾⣷⣿⣾⡿⡾⡟⠟⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠋⠋⠟⠽⠻⠻⠫⠟⠟⠟⠝⠑⠋⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧⠀⡀⣀⣀⢄⣤⣤⣤⣤⣤⣤⣤⣤⣄⡠⣀⡀⡀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⡀⠀⠀⠀⠀⠀⠀⣀⡠⣲⣿⣿⣿⣽⣯⡿⣿⣽⡾⣿⢾⣯⣿⣽⣾⣯⣿⣻⣽⣾⣿⣿⣧⣄⢄⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠨⡃⠁⠉⠀⠀⣄⣦⣷⣷⣿⣿⣿⣿⣿⣿⣷⢿⣻⡷⣿⣟⣿⣽⣾⢿⡾⣷⣟⣯⣿⣿⣿⣿⣿⣿⣟⣿⢮⣤⡀⠀⠈⠈⠨⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣄⣮⣾⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣾⣟⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⣄⠄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⣿⣿⣿⣿⣿⣿⣿⣿⠫⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠫⠑⠉⠙⢿⣿⣿⣿⣿⣿⣿⢿⣯⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣞⣿⣻⣾⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣽⢿⣻⣟⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣽⣿⣽⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⡽⣿⢾⣟⣯⣿⣿⣿⣯⣆⢀⢀⢠⣮⣿⣿⣿⣻⣾⣻⣟⣿⣽⢿⡾⣿⣿⣿⣷⣅⢀⢀⢠⣪⣿⣿⣿⣻⣿⣽⣾⢷⣿⢯⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣾⣻⣟⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣯⣿⢾⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣾⢷⣿⣻⣽⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢗⢏⢏⢏⢏⢟⢿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣾⣟⣿⡾⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⢝⢏⢗⢻⢹⢻⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⡪⡘⡌⢆⠣⡊⢆⠕⢜⠌⡏⣿⣽⣾⢿⡷⣟⣿⢿⣿⣿⣽⣯⣷⡿⣟⣿⣻⣿⢿⣻⣿⣽⣾⢷⣿⡽⡏⡇⢕⡑⢕⢔⠱⡨⡊⡢⡱⡐⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢌⠆⡎⡪⡘⡌⢆⢍⢆⢣⢪⣺⣾⣻⣟⣿⣟⣿⣻⣷⡿⣾⢷⡿⡿⡿⣟⣿⣽⣿⣟⣷⡿⣾⢿⡷⣟⣮⠸⡰⡘⢔⢅⢕⢌⠪⡢⡑⠌⠄⠀⠀⠀⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⢐⠑⢜⢬⣢⣧⡷⣟⣯⣿⣽⡿⠯⠋⠋⠈⠁⠁⠀⠀⠀⠀⠈⠀⠀⠁⠑⠉⠙⠻⡻⣿⣿⣻⣽⣟⣦⣧⣣⢢⠑⠌⠊⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡳⡿⣿⣻⣿⡿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣽⣯⢿⠺⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢟⢿⢷⣤⢄⢄⢀⢀⠀⡀⠀⡀⠄⠀⠀⢀⢀⢀⢀⢄⣔⣼⢿⡻⠓⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠓⠫⠳⠖⢗⠶⢲⠳⠳⠖⠏⠓⠋⠋⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Anime dot art uses braille Unicode characters to build detailed pixel-style anime and manga scenes. These multi-line pieces go far beyond simple kaomoji faces, creating recognisable characters and iconic scenes.
💡 Platform tip: Anime dot art is extremely popular in Japanese fan communities and Discord anime servers. Braille-based pieces preserve intricate details that emoji pixel art can't achieve.