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⠀⠀⠀⡤⣂⣭⣭⣅⠢⡀⠤⢀⣀⣀⠂⠾⡿⠛⢿⣦⢡
⠀⠀⡌⢰⡿⠉⠉⠙⣡⣶⣿⣿⣿⣿⣿⣷⣦⡀⣸⡿⠸
⠀⠀⢃⠸⣿⡤⢀⣾⣿⡿⠛⣿⣿⣿⣿⠛⢻⣿⣄⢶⠁
⠀⠀⠀⠁⢒⢠⣿⣿⣿⣇⣀⢟⡛⠛⠛⡠⢼⣿⣿⡄⡆
⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⢱⡿⣷⡦⢴⠇⡇⣿⣿⠃⠇
⠀⠀⠀⠀⠀⠣⢙⠻⢿⣿⣧⣝⣲⠾⢗⣫⠼⢛⠅⠉⠀
⠀⠀⠀⠀⠀⡀⠤⣃⡒⣬⣭⣭⣭⡭⠭⢴⣦⠑⠠⣀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠄⣪⣴⣿⣿⡷⢸⣿⡟⣵⣾⣿⣷⣮⢣⢻⣶⣭⠒⣂⣔⢂⠀
⢀⢊⣴⣾⣿⣿⣿⣿⠇⡿⠟⣃⡛⠿⣿⣿⣿⡏⡆⢿⡟⢸⣿⡤⠆⡄
⢨⠨⡀⠀⠉⢿⣿⠟⡌⡴⢙⡀⣏⠙⡌⣿⣿⣿⢸⠈⣤⢸⣿⡇⠀⡇
⠀⠑⠬⠑⣒⠪⢄⠺⡇⣿⠉⠀⠀⠉⡇⡿⠿⣣⢏⣼⣿⣿⣿⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠢⠙⣄⠀⠀⢠⢃⡛⠩⠀⠈⠩⠭⠭⠭⠍⠑⠁

⠄⢠⠎⣠⣿⣿⠏⠄⠄⠄⠄⡈⣴⣿⣿⣶⣦⣤⣤⠄⠄⠄⠄⠄⠄⢠
⣠⢃⣴⣿⣿⠋⠄⠄⠄⠄⡴⠱⠛⠻⢿⣿⣿⣿⣯⠄⠄⠄⠄⠄⠄⢸
⢁⣼⣿⡿⠁⠄⠄⠄⢀⡖⢡⣞⠉⠄⢀⣽⡿⠛⠉⠄⠄⠄⠄⠄⠄⢸
⣾⣿⡟⠄⠄⠄⠂⠄⠐⠄⢸⣿⣷⣶⣿⡟⠄⢀⡀⠄⠄⠄⠄⠄⠄⢸
⣿⠏⠄⠄⡀⠄⠄⠄⠄⠄⣿⣿⣿⣿⣟⠋⠄⣾⣿⣿⣧⠄⠄⠄⠄⢸
⠛⠄⠄⠰⠄⠄⠄⠄⠄⠄⢿⣟⠩⠴⠬⠁⠾⣿⣿⣿⣿⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⢺⣿⣛⡷⢬⣵⠈⡿⠛⠁⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢰⡀⠄⠻⠉⠛⠛⠁⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⢿⣤⣀⣀⣀⣀⣤⡤⠄⠄⠄⠄⠄⢠⠃
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠉⠉⠉⠉⠁⠄⠄⠄⠄⠄⠄⠄⠄

⠄⢠⠎⣠⣿⣿⠏⠄⠄⠄⠄⡈⣴⣿⣿⣶⣦⣤⣤⠄⠄⠄⠄⠄⠄⢠
⣠⢃⣴⣿⣿⠋⠄⠄⠄⠄⡴⠱⠛⠻⢿⣿⣿⣿⣯⠄⠄⠄⠄⠄⠄⢸
⢁⣼⣿⡿⠁⠄⠄⠄⢀⡖⢡⣞⠉⠄⢀⣽⡿⠛⠉⠄⠄⠄⠄⠄⠄⢸
⣾⣿⡟⠄⠄⠄⠂⠄⠐⠄⢸⣿⣷⣶⣿⡟⠄⢀⡀⠄⠄⠄⠄⠄⠄⢸
⣿⠏⠄⠄⡀⠄⠄⠄⠄⠄⣿⣿⣿⣿⣟⠋⠄⣾⣿⣿⣧⠄⠄⠄⠄⢸
⠛⠄⠄⠰⠄⠄⠄⠄⠄⠄⢿⣟⠩⠴⠬⠁⠾⣿⣿⣿⣿⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⢺⣿⣛⡷⢬⣵⠈⡿⠛⠁⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢰⡀⠄⠻⠉⠛⠛⠁⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⢿⣤⣀⣀⣀⣀⣤⡤⠄⠄⠄⠄⠄⢠⠃
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠉⠉⠉⠉⠁⠄⠄⠄⠄⠄⠄⠄⠄

⠄⢠⠎⣠⣿⣿⠏⠄⠄⠄⠄⡈⣴⣿⣿⣶⣦⣤⣤⠄⠄⠄⠄⠄⠄⢠
⣠⢃⣴⣿⣿⠋⠄⠄⠄⠄⡴⠱⠛⠻⢿⣿⣿⣿⣯⠄⠄⠄⠄⠄⠄⢸
⢁⣼⣿⡿⠁⠄⠄⠄⢀⡖⢡⣞⠉⠄⢀⣽⡿⠛⠉⠄⠄⠄⠄⠄⠄⢸
⣾⣿⡟⠄⠄⠄⠂⠄⠐⠄⢸⣿⣷⣶⣿⡟⠄⢀⡀⠄⠄⠄⠄⠄⠄⢸
⣿⠏⠄⠄⡀⠄⠄⠄⠄⠄⣿⣿⣿⣿⣟⠋⠄⣾⣿⣿⣧⠄⠄⠄⠄⢸
⠛⠄⠄⠰⠄⠄⠄⠄⠄⠄⢿⣟⠩⠴⠬⠁⠾⣿⣿⣿⣿⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⢺⣿⣛⡷⢬⣵⠈⡿⠛⠁⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢰⡀⠄⠻⠉⠛⠛⠁⠄⠄⠄⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⢿⣤⣀⣀⣀⣀⣤⡤⠄⠄⠄⠄⠄⢠⠃
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠉⠉⠉⠉⠉⠁⠄⠄⠄⠄⠄⠄⠄⠄