Ai Nude Art Emojis & Text

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⣿⠐⢀⡈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠁⢰⣿⢻⣿⣰⣿⣿⡟⢋⣷⣿⣿⣿⣿⣿⣽⣿⣿⠧⠀⣿⣿⢹⡄⠀⠀⠀⣷⡞⣿⣿⠄⠀⠀⢹⣿⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡉⠍⠍⣿⣿⣿⠟⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⡀⠂⣠⣮⣿⣧⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢼⣿⡮⠀⠀⠀⠀⢻⡿⣴⡏⠀⠀⠀⠀⣿⡆⠀⠈⠙⠳⢤⣄⡀⠀⠀⢀⣶⠟⠁⠀⠃⠅⢠⣿⣿⠛⢷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⡼⣣⡾⢛⣿⢣⣿⣿⣿⣿⠏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠉⡿⢹⡋⠁⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣴⣿⠇⣾⣿⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⠇⠄⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣤⣾⣿⣳⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠰⣿⣿⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢿⡀⠀⠀⠀⠀⠀⠘⢿⣿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⠟⣰⣧⣿⠀⣀⣠⡶⠟⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⣿⢣⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠛⣷⡿⠟⢿⣿⣿⣄⡀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⠤⠤⠼⢿⢟⠿⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠻⣟⠟⠛⠆⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⠇⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⡀⠩⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣻⣿⣿⣄⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣭⣈⡛⠿⣛⣫⡴⠾⣋⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢹⣇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⢿⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⢠⣿⣿⡆⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢷⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣹⡟⠱⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣱⡿⣿⣿⣿⡇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣧⠀⠀⡹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣃⠀⠀⠀⠀⠀⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⢾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢋⣼⣿⣿⣿⣿⣄⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠸⡇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠀⠈⠁⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⣿⣷⡌⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⢟⣼⣿⣿⠹⣆⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣿⡀⠀⠀⠀⠈⠹⠿⣶⣄⣀⣀⣀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⡿⠃⠀⠹⣦⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢲⡈⢻⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⢋⣿⠁⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⡿⣥⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⢀⡾⣻⠗⠈⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠤⠤⠤⠤⠴⠶⠞⠛⠉⠉⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡟⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡞⠃⠀⢦⢈⠀⠀⠄⠀⠀⢀⠀⠀⠘⣷⡟⠀⢀⡀⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣵⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠟⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣾⣿⣯⣄⠆⠀⢠⠄⠀⠀⠔⠀⠀⠀⣹⣇⠀⣾⣃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣸⣛⠁⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣾⡍⡄⠀⠉⡈⠂⠀⠀⣿⣿⡄⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⣿⣻⡤⠶⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠆⢠⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡌⠂⠄⠀⠀⠠⠠⠉⠨⠻⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⣿⠻⢧⣝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡆⠠⠀⠀⠰⡄⠀⠀⠈⠛⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⣍⡐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡠⣄⡄⢓⡀⣀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⢴⣯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠡⠧⠤⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣶⣤⣀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠀⢠⣥⣼⣿⣿⣿

⠀⠀⠀⣠⠔⠒⣂⣠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⡀⠀⠀⠀ ⠀⢀⣾⠏⠀⣰⡏⠉⠉⠙⠓⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⢇⠀⠀⠀ ⣰⣽⣿⣆⣜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣄⡀⠸⠀⠀⠀ ⢻⣼⡍⠃⠛⠤⢤⣀⣈⣶⣶⣶⣦⣤⣤⣤⣄⣀⠀⠀⠉⠗⠂⠄⠀ ⠀⢃⠈⢓⣄⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠢⠍⠙⣷⢦⡀⠀⢼⣦ ⠀⠘⡀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⣤⣾⠎ ⠀⢠⡇⠀⠀⠀⠀⠀⠐⠒⠀⠒⠚⠛⠓⠒⠂⠠⠤⠀⠀⠉⢛⡿⠁ ⠀⣸⠧⠀⠀⠤⠀⠀⠠⠤⠤⣀⣀⣀⣀⡠⠤⠀⠀⠀⠒⡶⠉⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀ ⠀⢸⠃⠀⠀⠠⠤⠤⢈⣉⡁⠀⠀⠉⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⠀⠘⣶⡯⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢹⡄⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠈⠉⠉⠑⠒⠂⠐⠴⠂⠀⠀⠙⢶⠇⠀⠀⠀⠀ ⠀⠸⣶⣶⣤⣀⡐⠒⢛⣓⣬⣭⣭⣥⣀⡀⠀⠀⠀⣴⠀⠀⠀⠀⠀ ⠀⠀⢻⣆⠉⠛⠛⠋⢉⡔⠁⠀⢆⠉⠉⠛⠲⠶⢖⠃⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡿⠶⠒⠒⠁⠀⡄⠀⢎⠳⣤⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠏⠀⠀⡜⠀⠀⠀⡇⠀⠀⢆⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠀⠰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠐⠃⠀⠀⠈⠄⠀⠀⠀⠈⢦⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡴⠛⡆⠀⠀ ⠀⠀⠀⡁⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⠖⠋⠀⠀⡇⠀⠀ ⠀⠀⠀⡏⠉⠓⠲⠿⠷⠤⣤⣤⣤⣴⣶⠟⠉⠀⠀⠀⠀⢰⡇⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀

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⣿⣟⣿⣻⣟⣿⢻⣟⣿⣻⣽⣻⢯⣟⡿⣽⢯⡿⣝⣯⢿⣹⢯⣟⡿⡽⢯⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡻⡜⡼⣿⣿⡗⣷⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣞⣷⣻⢾⣭⢿⣞⣷⣻⢶⣯⣟⡾⣽⣳⢯⣷⣻⡼⢯⣯⡟⣾⡝⣿⣹⡽⣞⡿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⠿⢿⠿⠛⠉⠉⠉⠉⠉⠛⠻⠿⣿⡿⢿⢿⡿⢿⠿⣳⢙⠼⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣾ ⡿⣞⡷⣯⣟⣾⣻⣞⡷⣯⣟⣮⡽⣽⡞⣽⣫⢶⣯⢽⣻⢶⣛⣧⡟⣧⢷⣛⣮⢽⡳⣽⣚⣷⢫⣟⣷⣬⣙⠋⣡⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⡙⢎⡓⣦⠟⠚⠉⣀⠤⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡽⢯⣷⢻⣞⡷⢯⢿⣵⣻⣼⢻⣵⡻⡷⢯⣻⢮⣟⣳⢯⣛⣶⢟⣉⣉⠉⠉⠉⠉⠉⠓⠾⣟⣾⡭⢖⡾⠛⡱⠋⠉⠭⣁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡳⠊⠁⠀⣠⣞⣵⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣷⡻⣟⣾⢻⡾⣽⢯⣟⢮⡷⣞⣟⠾⣽⣛⣯⡽⢯⡾⣭⣻⢭⣿⠸⣿⡿⠛⠲⢄⡀⠀⣠⣾⢟⠕⣸⠋⠀⡼⢰⠀⠀⢰⠀⠉⠐⠤⡉⠢⣄⠀⠀⠈⠂⢄⠈⠢⡁⠀⠀⢀⡼⠁⠀⠀⢀⣠⣄⠀⢸⣬⡿⣟⣿⣿⣿⣻ ⣷⣻⡽⣞⣯⢷⡯⣟⡾⣫⢷⣛⣾⢻⣳⡟⣼⢯⡟⣞⢧⡟⣞⡿⣏⠙⠛⠟⠆⠀⢻⣾⠟⡵⠋⣸⠃⠀⣸⢱⢠⠀⠀⢿⠀⠀⠀⠀⠈⠂⢌⠫⡂⢄⠀⠀⠁⡄⠐⢄⠀⠉⠉⢢⣀⠀⡇⠻⣉⣻⣿⣿⣿⣹⣿⢽⢽⣿ ⣷⢯⣽⣻⢼⢯⢾⣽⣹⢯⣻⣽⣚⣯⢗⣻⣝⣮⡽⣫⢟⡼⣏⡾⣽⡆⠘⣺⢛⣳⣾⡇⡾⢁⠞⡏⡀⠀⡏⠈⡎⠀⠀⢸⡄⠂⠀⠀⠀⠀⠀⠐⠈⢆⠑⠄⠀⠈⢂⠀⢳⡀⠀⠀⠀⡳⢿⣿⣦⣸⣿⣼⣿⣭⣿⣿⣿⣿ ⣯⣟⡶⣯⢯⣛⣯⣞⣽⣳⢯⣶⣛⣮⢟⣳⢞⡶⣽⡹⣞⡽⣺⣝⣾⢻⣮⠳⢯⣿⡻⢱⠁⡼⢸⢹⠃⠀⡇⠀⢧⢆⠀⠈⣟⡄⠀⠀⠀⠀⠀⢠⡀⠁⠣⡀⠑⢀⠀⠃⠀⢱⡄⠀⠀⢱⣼⢹⠻⠿⠿⠃⢻⣿⣾⣾⣾⣿ ⣷⣫⢷⢯⣏⡿⢶⣻⢮⡷⣛⣶⢻⡜⣯⡽⢾⣹⢶⣫⢷⣹⢳⡾⣩⢏⣿⣆⡟⣼⠁⣾⠃⠁⣯⢸⡆⠀⠃⢀⢸⣎⠀⠀⠈⠞⢄⠀⠀⠀⠀⠀⠑⡀⠀⢣⠀⠈⢂⠀⢡⠀⢳⡀⠀⠈⠟⠁⠀⠡⡀⠀⠘⡍⢎⠥⣫⠝ ⣷⢫⣯⠿⣼⣻⢯⣛⡷⣻⣝⡮⣟⡽⣳⢽⣛⣮⢷⡹⣎⠷⡿⣰⡏⡷⢧⣿⠁⡇⢸⡟⠰⢰⡏⠸⡇⠀⠀⠸⡈⡏⢆⠀⠀⠸⡆⠣⡀⠀⠀⠀⠀⠘⡄⠈⢆⠀⠀⢣⠀⠀⠀⡗⡀⠀⠂⢠⠀⠀⠑⡀⠀⡗⣌⡓⢦⢛ ⣯⢟⣼⣻⣳⡽⣫⣽⢳⣏⡾⣵⢫⡾⣝⡮⣗⢮⣳⡝⣾⣹⣷⢿⡇⣿⣧⣿⠸⣏⡿⡅⢸⢸⢷⡀⢿⠀⠀⠀⠃⢧⠀⠑⢄⠀⣿⡳⡀⠀⠀⠀⠀⠀⠘⣆⠘⡀⠀⠀⢆⠰⠀⠸⡘⡄⠀⠸⠀⠀⠀⠠⠀⣗⠤⣋⢮⠱ ⣯⣟⣞⣳⢧⣟⣳⡭⣷⢺⡵⣫⢷⣹⢎⡷⣭⣛⠶⣽⢲⣿⣿⣻⡜⣿⣷⡇⡸⡇⣿⠀⡌⣮⠘⣇⠘⣇⠈⣆⠀⠘⡆⠀⠀⠡⢹⠱⡹⣧⡀⠀⠀⠀⠘⡸⡄⢇⠀⠀⠈⠆⠃⢀⠡⡘⡄⠀⠀⠀⠀⠀⡇⢸⡖⡭⢲⡍ ⣷⣛⣮⢯⢷⡺⣵⡻⣜⣧⢻⡵⣫⢞⡽⣺⢵⡫⣟⢮⠷⣿⢧⢿⣼⢻⣽⡇⣽⡇⣿⠀⡃⡇⢠⣿⣣⠸⡄⠸⡄⠀⢱⠘⡄⠀⡚⡄⠱⡜⣯⡷⢄⡠⠀⠀⢹⢸⠰⠀⢠⠀⠀⠈⡄⠑⡁⠀⡆⠀⠀⠀⢻⠀⣧⠹⣥⢚ ⣷⢻⣜⢯⣞⣳⢧⡟⣵⣚⣧⢻⡵⣛⢾⡹⣎⡷⣹⣎⡟⣿⣏⣾⣼⣛⣿⣷⣹⣿⠥⡇⡅⢇⢸⠈⢿⡄⣷⠀⠹⡄⠀⠀⢳⠀⡇⢳⠀⠘⣌⡼⠻⢝⠲⣤⡀⣿⠀⡆⠈⠀⢠⠀⠸⡦⣈⠢⠀⠀⠀⠆⠘⡀⠸⡳⡼⢭ ⣯⢳⡞⡽⣎⢷⣫⢞⣳⣝⢮⡳⣽⡹⣎⢷⡻⣜⠷⣮⡝⣶⢻⣼⣿⢧⣿⣿⣾⣿⡇⢿⡤⢙⣻⠠⢈⣿⣌⢧⠀⠙⣄⠀⠈⣧⢻⣤⠦⠚⠁⣡⣤⣶⣿⣿⢿⣿⣷⠇⠀⠆⠀⠀⢀⠱⠈⠁⠒⡄⠀⠰⠀⢱⠀⢻⡱⣏ ⡽⣣⢟⣵⢫⣞⡵⣫⡗⡾⣭⢳⢧⡻⣝⢮⡳⣝⡻⢶⡹⣎⠷⣎⣿⡧⣿⣿⢫⡗⣿⢌⣷⠐⢾⣐⣀⣀⣙⣿⣷⡄⠘⢦⡀⠘⣾⠙⢆⢰⣾⣿⣿⣿⣿⣿⡞⣼⢻⠀⢸⠀⠀⠈⢸⣆⠱⡄⠀⠇⠀⠀⡇⠀⢧⡈⢷⣹ ⣻⢵⣫⢞⡽⢮⣝⣳⢽⡳⣭⣛⢮⢷⡹⢮⣳⢭⣛⢧⡻⣜⡻⣼⣹⣇⡿⣡⣿⣿⢹⡖⣼⣷⣾⣿⣿⣿⣶⣿⡿⣿⠳⣄⠻⣄⠘⣧⠀⠈⠙⢄⣙⠧⣜⣫⠞⠋⡜⢀⡾⢘⠈⠀⠸⡏⠣⣹⠀⢸⠘⡀⠰⠀⠸⣻⣌⢳ ⡽⣎⢷⣫⢞⡯⣞⡵⣫⢗⣧⣛⢮⡳⣝⢧⣛⢮⡝⣮⢳⣭⢳⡧⢟⣫⣾⡏⢸⣿⢸⢷⣷⡘⡟⣷⣄⠉⢿⣿⠿⣻⡇⠀⠙⠪⠷⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠃⡆⢆⢣⠀⢧⠀⢸⡘⠸⡄⢁⠀⡇⠀⢷⢭⢳ ⡽⣎⢷⡹⣎⢷⡹⣞⡵⣏⠶⣭⡳⣝⢮⡻⣜⢧⡻⣵⢫⣞⢳⡞⣯⢻⡧⡇⢢⣿⣹⡼⣷⡹⢶⣊⢿⠓⠒⠊⠉⠁⠀⠀⠀⢀⡀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣸⢾⠏⣴⠏⣞⡀⠄⢸⡀⠘⡏⡀⣷⠈⠆⢱⠀⣸⣎⠳ ⠹⣎⡷⣹⢎⡷⣹⢎⡷⣭⣛⢶⡹⣎⢷⡹⣎⢷⡹⣎⠷⣎⢷⡹⣞⣽⢱⡇⢒⣿⣿⡇⣿⣷⡌⢻⣯⣷⣌⠀⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⢎⣼⠏⠀⣹⣆⠈⠀⢳⠀⡗⠀⠸⣇⠈⠈⣧⠸⣇⢏ ⠀⠹⡾⣵⢫⡽⣣⡟⣼⣓⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⣛⣮⢷⣹⢎⡟⡦⡁⢼⣿⡟⣠⡟⣿⢿⣆⠹⣧⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡵⠊⡾⠀⡃⣷⣿⣦⠡⡀⠱⣇⠀⠀⢻⡆⠡⠸⡷⢏⡜ ⠀⠀⢻⣾⣹⣾⣵⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠄⣿⡿⣱⣿⢸⣿⡄⢻⣿⣮⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣫⢿⠏⢰⠃⠴⠁⣿⡷⡏⢱⣌⠑⣬⣖⠀⠘⡞⢄⠀⠹⣖⣸ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣏⣸⣯⣾⣿⣇⣿⣿⡇⠀⣿⢹⡙⢾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⣿⠀⡸⡄⠸⠀⣿⡷⣿⠘⡇⠈⣖⠯⡇⢠⠘⡌⢆⠈⢿⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⡇⣼⠿⢛⡿⠯⢍⣹⣿⠀⣿⢸⣿⣸⣿⣿⣿⣿⣶⡦⢄⡀⠀⠀⣀⠴⢋⠆⠃⡼⣧⠀⡇⡇⠈⠀⣿⡿⣽⡄⠁⠀⣿⢒⠼⡠⡇⢱⣈⠳⡀⠻ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⠟⠁⠴⠊⠀⣀⠀⣿⡟⢠⣷⢹⣾⣿⣿⣿⡿⠛⡛⣧⠀⠈⠉⣉⠡⢂⠅⠠⣰⡇⡇⠂⠇⡁⠀⠀⣿⣿⣿⣧⠀⠀⣿⣭⠚⣧⣻⠀⢧⢂⠹⣆ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡿⠁⠀⠀⠀⠀⡸⠀⣠⡿⡕⣸⠏⣾⣿⣿⣿⠋⢠⡑⢬⣟⠀⠀⠀⠀⢂⠁⠂⣴⠃⡇⢻⢂⢸⡇⠀⠀⢿⡿⣿⣿⣤⣤⣿⣎⣏⢿⣿⡄⠘⣦⠀⢹ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⢿⣽⠏⠀⠀⠀⢀⣠⡶⣟⣻⠋⠘⡰⢃⣾⣿⣿⠟⠁⢤⣁⢂⠂⣿⣷⠀⠀⡈⢀⣠⡞⠁⠈⢻⢸⠈⡇⢧⠀⢠⠸⣵⣿⣿⡿⠋⠉⠉⠉⠉⠉⠁⠢⢽⣆⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⢇⠉⠳⠘⠀⠙⠂⣼⣽⣿⠃⢀⣀⣤⣶⣿⣟⣿⠟⠁⣠⠜⢀⣾⢿⣿⣿⣤⡀⠀⠈⠙⠻⠏⠁⠀⠀⠠⡞⠉⠀⠀⠀⣸⣿⡀⣿⣎⠀⢸⡄⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇ ⠀⠀⠀⠀⠀⠀⢸⣓⠋⠉⠀⠀⠀⠁⠀⠀⠀⢀⡞⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⢁⣤⠞⢃⣠⣿⣫⣾⣷⣿⣾⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣉⣥⣤⡴⢾⡿⣿⡇⠐⠹⣆⠀⣿⢤⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣾⣿⣫⣷⣿⣗⣒⣀⣤⣴⣶⣯⣷⣾⣻⢟⡛⠿⠿⣿⣿⣿⣿⣿⣷⣾⣾⣵⣯⣝⣻⢶⡾⢯⣭⣙⡛⡿⣧⣷⡘⣄⠙⡄⠸⣄⣹⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠴⠛⠛⠉⠉⠉⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣯⣾⣶⣶⣤⣐⡌⣉⠛⠾⢷⣭⣯⣭⢯⣝⣛⣛⠳⠯⠯⠽⢿⣱⣤⣣⡀⢧⠘⣦⡈⠻⣇⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡠⢒⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢝⠛⠻⠿⢿⣿⣿⣿⣿⣶⣾⣽⣿⣯⣾⣱⣞⡽⣛⠿⣿⣶⣿⡻⣭⣷⣎⡄⢸⣿⣷⣯⣄⡀⠘⢖⣤⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡮⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⢀⡽⠋⠉⡙⢛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣧⣯⣽⣯⣿⢿⣷⠘⣿⣿⣿⡆⠀⠁⠸⡞⢀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠉⠉⠛⠛⠻⢽⣟⡿⣿⡿⢸⣿⣿⣿⣿⡄⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠀⣼⣿⣏⡳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣇⣼⣿⣿⣿⣿⣷⠀⠀⡏⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢨⣟⡿⣟⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⣠⣤⢄⣠⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠆⣰⢋⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠿⡜⢬⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡘⣞⣿⣼⡼⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠟⡠⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⡅⢈⠍⠓⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢏⣎⠱⡐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠂⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡮⣌⠳⣌⠡⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣭⢳⡘⢦⡁⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⢂⠔⠠⠐⠠⡀⠄⡀⢀⠀⡀⠀⠀⢀⠀⡀⠠⢀⠂⠌⢂⡔⣱⣿⡄⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⢷⣛⢦⣹⡘⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢍⢢⡑⢌⠡⠒⡌⡐⢢⠐⠤⠡⠌⡀⢂⡐⣀⡦⠞⠚⠓⠚⠛⠓⠻⣄⠑⡈⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⢾⣹⢮⡵⣙⢮⡑⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣎⠲⡌⢎⠒⣍⠰⡡⢆⡉⢆⠱⡈⠔⣡⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣌⣐⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⡽⣏⡷⣯⡽⣏⡶⣳⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢘⣷⣍⡮⠱⣌⢣⠱⡌⠒⡌⣂⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣻⣽⣞⣧⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⡙⢎⡙⢛⠲⠖⠷⢖⠻⠟⢋⠄⣠⠀⡄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣐⡀⠂⠄⡀⢀⠀⢀⠀⡄⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣳⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣔⠉⠆⡌⢢⠑⡌⠒⡌⢢⣉⣦⡼⢤⠧⠼⠤⢧⡤⠧⠼⠤⠤⠤⠴⠖⠚⠒⠓⠒⠻⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠲⡶⢤⣬⣦⣼⣶⣿⡿⣻⢿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣟⠟⠛⠶⠾⠴⠳⠚⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠢⡑⢴⡬⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡚⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠋⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠁⠪⣉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡄⠈⠪⡓⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⣬⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡿⠶⠒⠖⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢢⣄⠘⢾⣶⣤⠈⠉⡟⠇⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

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⠁⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠁⡀⠐⠈⠀⠐⠈⠀⠐⠀⠐⠀⡀⠂⠀⠐⠀⠠⠐⠀⠀⠄⠀⠠⠀⠀⠄⠀⠀⠄⠀⠀⢸⡿⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀ ⠀⠁⠈⢀⠀⠄⠈⠀⠁⠈⠀⠁⠈⠀⠄⠀⢀⠈⠀⠠⠀⠀⠀⠂⠀⠀⣄⣠⣤⣤⠴⠶⢶⡶⠶⠬⠿⢤⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠄⠈⢀⠀⠠⠀⠂⠁⢀⠈⠀⠄⠁⢀⠠⠀⠀⡀⠐⠀⢀⠈⢀⣤⠶⠛⠉⠁⣠⠀⠀⡠⠀⣤⢋⠁⠐⠠⡀⢈⠙⠒⢤⣀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀ ⠐⠀⡀⠠⠀⠠⠐⠀⠀⡀⠂⠀⠠⠀⠀⠠⠀⠀⡀⠄⣠⣴⡿⠋⠀⢀⣴⠞⠁⢀⠜⣠⠞⢡⠃⠀⢠⠀⠑⡄⠑⢄⠀⠈⠓⢤⡀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⡁⠀⠄⠀⠐⠀⡀⠄⠁⠀⡀⠄⠁⠀⠐⠀⡀⠁⣠⣾⡿⠟⠀⠀⣰⡿⠃⠀⠠⢁⡴⠁⢀⡇⢠⠃⢸⠀⠀⢸⡄⠀⢣⠈⠠⡀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⡀⠂⢀⠈⠀⠄⠀⠀⠄⠂⠀⢀⠠⠈⠀⡀⢀⡼⣿⠏⡁⣠⠃⣼⠟⡀⠀⠀⣿⡾⡅⠀⣼⠀⡼⠀⠈⡇⠀⢸⢣⠀⠀⠃⢠⠑⢤⡈⠳⡀⠀⠀⠁⣀⣠⣤⠤⠄⠒⠒ ⠄⠀⡀⠀⠂⢀⠈⠀⡀⠄⠂⠀⢀⠠⠀⢠⡿⣽⢫⠖⢰⠃⣸⣏⡞⠀⢀⣾⣿⠇⠀⡄⡇⢸⡇⠀⠀⢳⠀⢸⡼⡄⠀⠀⠀⡇⠀⠱⡀⢳⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀ ⠄⠐⠀⠀⠂⠀⠠⠀⢀⠀⠀⠂⠀⠀⣴⡿⣻⠃⡞⢀⠃⢀⣏⡞⠀⠀⣾⣿⣿⣀⢰⠃⣇⠀⢧⠀⡃⠈⣇⢸⣷⡇⠀⠀⠀⢸⠀⠀⢱⣀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠁⢀⠈⠀⠠⠀⠀⠂⠀⢁⣾⣿⣱⠏⢸⠇⠀⡤⢾⣿⠓⠛⢻⣿⠋⣟⠀⣸⠃⣷⠀⠘⢦⡇⠀⠸⣟⣿⡆⠀⠀⠀⠘⡆⠀⠀⣿⣳⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠄⠂⠀⠐⠀⠀⠁⡀⢨⣾⣿⢃⡿⢀⣹⡤⢁⠀⣿⣟⠀⠀⣿⡿⠀⣯⠀⣿⣷⠸⣇⢤⡈⢷⡀⠀⢸⢿⣷⠦⣀⠀⢈⡇⠀⠀⠸⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠈⠀⠀⠐⠀⠈⠀⠄⢠⣿⢣⡏⣼⣏⠀⢿⣷⠀⢢⣿⣯⡀⢸⢿⣇⠀⢹⡆⣿⣿⣤⡻⣦⣿⣦⣽⣶⣾⣈⣻⣤⠈⠙⢺⡇⠰⠀⠀⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠂⠁⠀⢀⣿⠇⣾⡐⣿⣿⠈⢾⣿⡆⣹⣇⣹⣷⣾⣬⣿⡀⠈⣿⣯⢻⣿⣧⠉⢻⡟⣷⡄⢹⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⢹⠈⡟⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠠⠈⢸⡿⢸⣷⡚⣿⣿⡡⢘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄⠈⠎⠢⢽⣿⣷⣄⡇⠈⣿⣿⣄⣀⣿⠀⢠⣿⠃⠀⡀⠀⣽⠀⣷⣿⡄⢠⠀⡄⡀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡧⣿⣿⡔⣿⣿⣇⠄⣿⡇⠈⢧⠈⢿⣿⣾⡶⠋⠁⠀⠀⠀⠀⠙⠙⠻⣷⣾⡿⣿⣿⣿⣿⣤⣿⡿⠠⠀⡄⢠⣿⠀⣿⣽⡇⠢⠑⠈⡜⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣿⢧⣿⣿⣿⣖⡸⣷⠀⠀⠑⠤⠭⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⡍⠸⣿⣿⣧⠀⢨⣇⣾⣿⠀⣟⢸⡇⠀⠀⠀⡜⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⣿⣿⡿⣿⣿⣿⣿⢿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢤⠀⠀⠀⠀⠤⣛⣛⣋⠀⠈⢁⣿⠇⡀⣾⣽⢿⡁⢠⡟⣼⡇⠀⢀⠒⡌⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠳⣄⡀⠀⠀⠀⠀⠀⠀⢧⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⡰⣰⣿⡟⣾⢠⣾⣧⣿⠀⢀⠌⡓⣌⢣ ⠀⠀⠀⠀⣀⣤⡴⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣟⣵⣿⡟⢧⣿⣿⣿⡿⠃⠀⡌⢎⡱⢌⡖ ⠀⢀⣴⠟⠉⣠⣴⣾⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⠿⢿⣷⡀⠀⠀⠀⠀⠠⣤⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠤⢞⣻⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⣀⠣⡜⢢⡙⢮⡜ ⢠⡟⠁⣠⢞⠿⣩⣾⡽⠋⣠⡷⠻⠀⠀⠙⣿⢻⡀⠀⠉⠛⣤⠀⠀⠀⠀⠈⠑⠒⠠⠤⠞⠛⠀⠀⠀⠀⠀⠀⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠰⣀⠳⡌⢧⡹⢣⢞ ⢸⢀⡞⡵⠋⣴⡿⢋⠀⣰⠟⠠⢁⠂⠄⠀⢹⡆⢹⡀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣤⣇⣌⠳⣜⣣⠽⣍⢾ ⢀⡟⡞⢀⣾⠟⡵⠃⣰⠏⠀⠀⣼⠀⡙⣂⡏⢹⣀⡧⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠋⠁⠀⣼⣯⢿⡟⣻⠇⢨⡉⢤⡀⠙⢶⣍⠻⣟⠶⣭⢞⣭⠏ ⢸⢹⠁⡼⢥⡾⠁⣰⠏⠀⠀⣰⡟⠀⣇⣼⠁⣸⣸⠇⠈⠀⠤⠀⣿⣿⣿⡿⣷⣤⣴⣶⣿⣿⣿⠿⡇⠀⠀⢠⣿⣣⡟⠡⡿⢠⠀⢿⠀⠘⢳⡈⢿⣳⣌⠳⣬⣻⡎⠀ ⠸⣿⣰⠏⣾⠃⢀⡿⠀⠀⢠⡿⠁⢨⡼⠃⢠⣯⠏⠀⠀⠀⠀⠀⣿⣋⢿⣽⣳⢯⣞⣼⡿⠋⠈⠘⡇⠀⠀⣾⢳⣿⠁⣸⡇⢸⠀⢸⢀⠀⠸⣷⡄⢻⡽⡆⢿⠟⢟⠂ ⠀⠙⣿⣼⡏⣄⣸⡇⠀⠀⡞⠁⠄⣾⠃⢀⣿⠋⠀⠀⠀⠀⠀⠀⣿⠐⣈⠹⠷⣫⣾⠏⠀⠀⠀⠀⡇⠀⣸⣿⣿⣿⠀⡼⡇⢸⠀⠘⡌⣆⠀⠘⣧⡌⢿⡇⣸⠀⠈⢳ ⠀⣼⣯⣿⣸⡇⣿⠀⠀⣸⠇⠀⣼⠁⣀⣾⠃⠀⠀⠀⠀⠀⠀⢀⡯⠰⡏⠁⠀⠜⠁⠀⠀⠀⠀⠀⣇⢠⣏⢿⣿⣿⡀⣇⣧⣾⡀⠀⠀⣿⢠⡀⢹⣷⠘⡷⠃⠀⠀⠀ ⣸⠿⣿⡟⣼⡇⣿⠀⠀⣿⣰⢽⡇⠀⢿⡇⠀⠀⠀⠀⢀⣠⢴⣿⠄⠁⢧⠀⠀⠀⠀⠀⣰⠀⠀⠀⢘⡿⢧⣾⣿⣿⣷⣿⠈⣿⣇⠀⠀⣻⢸⡇⠰⣿⣇⢳⠀⠀⠀⠀ ⡏⠀⣿⡿⣼⡇⣿⡡⠀⣿⣿⣿⠀⢀⠘⣄⣀⣠⠤⠒⠍⠂⠘⢿⡀⠂⠸⡄⠀⠀⠀⣰⡏⠀⠀⠀⣼⠃⠀⠈⠙⠻⢿⣿⣇⣿⣿⣆⡀⢹⢾⣇⠰⡏⢹⠘⡇⠀⠀⠀ ⠀⠀⠘⣿⢲⣷⣿⣽⣇⡿⠟⠋⠉⠉⠀⠀⠒⠶⢬⣝⣒⣦⣄⣸⣇⠀⢀⣃⠀⠀⢠⠋⢁⣀⣀⣠⡿⠤⠞⠒⠒⠃⠀⠀⠀⠈⠄⠁⠉⠉⠛⠻⢌⡇⢸⡀⡇⠀⠀⡰ ⠀⠀⠀⠹⣧⣻⣾⠟⠉⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠉⠉⢻⡏⠉⠉⠑⠀⠘⠋⠁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣱⠇⠀⠈⠀ ⠀⠀⠀⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⠀⠀⠀ ⡀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡆⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⢧⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⢳⣀⢸⢁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠙⢿⢂⡐⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣤⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢸⡇⡐⠀⠀⠀⠀⠀⠀⡀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣭⣯⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀ ⠀⠀⠀⠘⡷⣈⠐⠀⠀⠀⢀⠐⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⣷⡱⢊⠐⡀⠂⠌⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⣀⣀⣀⣸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⡀⠢⠀ ⠀⠀⢠⡴⢻⣕⠣⠄⡡⢁⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣹⠟⢄⠁ ⠀⢰⣿⠟⢩⣯⠓⡌⠐⣠⡟⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⣦⡀⠀⠀⢹⡀⠀⠀⠀⠀⣿⡇⠈⣧ ⠀⣿⡃⠀⣼⣹⡗⡌⠡⢼⠃⠀⠀⠀⡼⣿⣿⡗⢠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣾⡇⡷⠀⠀⠀⣧⠀⠀⠀⠀⡿⠁⢠⡟ ⠀⠹⠷⠦⢹⣟⡷⣌⠡⣿⠀⠀⠀⠀⠙⠬⠽⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠿⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⡷⢤⡿⠞ ⠀⠀⠀⠀⠀⠛⣿⠰⢦⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡍⡆⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⢿⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣯⠄⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢯⣟⡶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⡼⡎⡑⢌⠻⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠛⠁⠀⠀⢸⠀⠈⠙⠻⢽⣷⢦⣄⣀⡀⢀⠀⢀⠀⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢰⢻⡔⣈⠒⣿⢩⢛⣟⠾⣳⣛⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠛⠛⠉⠁⣼⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡪⡕⣣⠤⣉⣿⠀⢊⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠳⢆⡱⠠⢿⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡁⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⡻⢜⡰⡉⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠐⠀⠀⠀⡀⠌⢸⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⢩⠖⣡⠇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠩⠄⢂⠁⡰⠈⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⢽⢠⢋⠴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣆⡘⠤⢂⡱⢈⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡜⢢⠉⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠠⢉⠻⢶⠡⢆⢃⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⠤⡉⠆⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣇⠑⣈⠒⠤⢋⠴⣩⡇⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢂⠱⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢻⣄⠂⢍⣸⣡⣾⠟⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡦⢑⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠈⢿⡞⣎⡷⠋⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡱⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢥⠃⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢰⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡼⠁⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢀⡿⣜ ⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⡀⢡⠂⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⡟⣼ ⠀⠀⠀⠀⠀⠀⣼⡷⢋⡐⢈⠄⢂⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣸⣽⡳ ⠀⠀⠀⠀⠀⣼⠟⡡⢂⠔⢂⠈⠄⠂⠌⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⣿⡞⣽ ⠀⠀⠀⠀⣰⢏⠦⡑⢌⡐⠢⡈⠤⠁⠌⡐⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣯⢿⡼ ⠀⠀⠀⢀⡿⣈⠖⡈⠆⡌⠱⡐⢢⢁⠂⡐⠀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⣟ ⠀⠀⠀⣸⡓⠴⡈⠴⠡⢌⠱⡈⠆⡌⡐⠠⠁⠂⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡾ ⠀⠀⢀⡟⡬⢱⠘⡄⢃⠎⡰⢁⠎⡐⠀⠑⣆⠁⢂⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣳ ⠀⠀⢸⢏⡔⡃⢎⠰⡁⠎⡐⠂⠄⠠⠀⠀⠈⢶⡀⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡵ ⠀⠀⣾⢡⠚⣌⠢⡑⠄⡃⠄⠁⡘⠀⠀⠀⠀⠀⠹⣄⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⢠⢈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻ ⠀⠀⣟⡌⢳⠠⣃⠌⠒⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠙⣦⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣀⡾⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷ ⠀⠀⡯⡜⣡⠒⡡⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡴⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿ ⠀⠈⡷⣑⠢⡱⠡⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡁⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿ ⠀⠀⡷⢡⢓⡰⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⠀⠀⠀⠀⢀⣾⠣⡘⠠⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷ ⠀⠀⢽⡡⢆⡱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣹⣯⣀⣀⣤⣿⠡⠆⡁⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⣾⢰⢃⠦⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠋⠹⠟⢻⡿⣡⠃⠜⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡽ ⠀⠀⢽⡎⡜⢢⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⣾⡱⡂⠥⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽ ⠀⠀⢸⡧⡙⢆⠣⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠔⢸⢧⡓⣁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻ ⠀⠀⠸⣗⠭⣊⠕⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⢎⡱⠠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣟ ⠀⠀⠀⣿⡜⢢⢍⠰⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⣯⢛⠴⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣳⢾ ⠀⠀⠀⢹⣎⠇⣎⠒⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣏⢎⡒⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣽⣻ ⠀⠀⠀⠈⣯⢚⠤⡃⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⣏⠖⡨⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⢾⣽ ⠀⠀⠀⠀⢻⣍⠖⣩⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣟⡯⠜⡰⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣟⣾ ⠀⠀⠀⠀⠘⣯⢚⠤⡃⠤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⡧⢋⠤⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⠸⣿⣽ ⠀⠀⠀⠀⢀⢻⡍⡖⢱⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢻⣿⡧⢩⢀⠃⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠀⢿⣿ ⠀⠀⢈⣄⣠⠸⣏⡼⠡⡌⡑⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⣇⠃⠆⡘⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣲⠤⠘⣿ ⠀⠐⠀⠀⠀⡀⢿⡜⡱⢂⡑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢺⣿⡧⢉⠰⢀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢀⡀⠄⢹

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⠿⣿⣿⣟⣿⣿⡿⠿⠛⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⣸⠒⣆⠂⠒⢱⠒⠒⠣⢊⠈⠈⠻⡷⡒⢢⡤⣤⣶⣶⣆⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⡯⢵⠤⢼⠤⠴⠭⢽⠭⠿⠷⠬⠽⡮⠖⠐⢢⡒⢶⠉⠩⢍⠛⠋⠙⡉⠒⠓⠖⡒⠤⢬⣸⣽⣴⣵⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⣾⣿⣷⡺⡐⠚⡖⠂⡂⠂⡗⠂⠒⢐⠐⠉⢍⠋⡉⠉⠉⠉⠍⠉⠛⡍⠉⠒⠳⡒⠲⠤⠦⣴⣻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣿⣿⡷⣧⣿⣿⣷⢷⠐⠸⡄⢗⠀⠚⢆⠁⠙⢞⠒⠒⢓⠒⡖⠒⠲⡒⠚⠖⠚⢯⠷⢖⣬⣦⡀⠀⣮⣿⣿⣿⣿⣿⣯⣿⣷⣄⠀⠀ ⠀⠀⠀⣴⡿⣵⣿⣿⡏⠟⡿⡿⣿⣯⢣⡤⠵⡴⡤⠤⠤⣧⠤⠤⢧⠤⠤⠵⣌⣆⣀⣈⣢⣀⣒⣄⡱⣄⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⠀ ⠀⠀⣯⣿⣾⣿⣿⣿⣟⣷⣿⡿⡽⣿⣧⣳⣤⣼⣾⣶⣦⣦⣭⣭⣭⣽⣭⣭⡿⣿⣖⣒⣤⣌⣦⣀⣣⣈⢯⠙⣯⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣷⡇⠀ ⠀⢸⣷⣿⢷⣿⡿⢿⠗⠯⢽⡟⡇⡾⣯⠿⠿⠧⠖⠟⠇⠟⠝⠖⠖⠟⠛⠒⠛⠒⠒⠒⠚⠛⠛⠛⠛⠛⠿⣷⣿⣿⣿⣿⣿⣷⣿⣿⡯⣿⣿⣿⡇⠀ ⠀⢦⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣯⣷⣿⣷⣿⣷⣿⠀⠀ ⠀⠈⠷⣟⣿⡿⣿⣿⣿⣯⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣏⣍⣛⣋⣛⢿⣷⡿⠃⠀⠀ ⠀⠀⠀⠙⣿⡿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣻⣿⣿⣿⡿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠉⠉⠉⠻⠯⠯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⣠⡤⢤⡄⠀⠀⢠⣿⡿⠿⠿⠕⠋⠀⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠳⡄⠀⣿⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⢸⡟⠏⣹⢿⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠙⢆⡉⠛⠻⠵⠃⠀⠀⠀⠀⢀⡤⠀⠀⠈⠓⣄⠀⠀⠀⠀⠉⠉⡩⠗⠉⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⡇⠀⠀⠀ ⠀⠀⠀⠀⣟⣿⣗⣄⡀⠀⠀⠀⠀⠙⡎⠉⠑⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠉⠉⠀⠀⠀⡧⣤⣤⣤⣖⣲⣽⣟⠟⠁⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⡇⠉⠻⣻⣿⣿⣿⣿⡿⣯⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⣇⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⣸⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣕⢠⣟⣆⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢋⣵⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣧⢸⠳⣸⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣯⠋⠀⠀⠀⠀⠀⠀⣀⡤⢖⠉⣀⡟⠁⢸⣾⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⢻⣄⢘⠑⢄⡇⢨⠢⢄⡀⠀⠀⠀⠀⡏⣿⡯⠀⠀⢀⣠⣔⡏⢁⡆⠔⢚⠉⠀⣇⡔⢹⡨⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⢸⠀⢹⠢⣄⡋⢙⠉⠓⠛⢛⠦⠤⣄⣃⣿⡧⣎⣎⣀⡇⡀⡇⣀⣃⠄⢼⠒⠋⡇⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⠉⢺⠒⠒⡏⢹⠓⡗⠒⢺⠒⠒⡗⢺⣿⡧⡇⢳⠠⡧⠤⡧⠄⡧⠤⢼⠒⠒⡏⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢂⣤⣴⠖⠉⠉⠲⣶⣤⠀⠀⢀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡤⢇⣾⣏⣿⠀⢠⠀⠄⣿⣿⣿⡄⠘⠃⠀⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢡⣀⠉⠀⠚⣿⣿⣿⣴⣿⢸⣿⣿⣿⡿⠀⠖⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⣨⠃⣿⣿⣿⣿⣾⣹⣿⣿⠃⣄⣴⡞⠑⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⣬⣤⣴⣶⣾⣿⣿⣯⣽⣿⣿⣷⣧⡎⠈⣿⠐⠐⠇⢴⠖ ⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠈⢙⠉⡹⠋⠉⠀⠀⠉⠙⠻⣦⡃⠒⣲⢀⠿⠄ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣾⠀⠀⠀ ⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀ ⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀ ⠀⠀⠈⣷⣦⣀⣀⣀⠀⣀⣠⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⡽⢿⣿⣿⡟⠹⣿⣷⣦⣤⣤⣤⣤⣶⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣽⣿⣿⢿⡟⣿⡟⠡⣄⣽⣉⣻⣿⣟⣟⢟⡿⡭⣤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡿⠛⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠁⣄⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⠁⠀⠀⠙⠻⢿⣧⠀⢠⠋⠀⢱⡄⠒⠉⢲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠼⣿⠀⠀⠘⠀⠀⠀⣿⢃⠇⠀⢠⠂⠀⢀⠀⠀⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡅⠀⡆⠀⠈⢹⡅⢸⠀⡰⠃⠀⠀⣾⡆⠀⠘⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡰⡇⠀⠀⠘⣷⣮⠔⠁⠀⠀⡼⡇⢹⢦⠀⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠘⢄⠀⠀⠀⠉⠀⠀⠀⣰⠁⢈⡀⠣⣷⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⣸⣧⡀⠀⠀⠀⠀⣰⠃⠀⠘⣷⢤⣼⣀⠀⠱⡀⠀⠀ ⡀⡄⠀⢀⠃⠈⠙⠛⠃⠙⠶⢤⣤⠴⠃⠀⠀⠀⠘⠀⠙⢿⠙⢦⣸⣶⡄ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠀⠀⢀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣧⡀⣿⣷⡆⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⡿⠟⠻⢻⢹⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⢘⣧⢣⡀⠀⠀⣸⣴⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⣼⢿⣆⣋⠕⢉⡜⡈⠧⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠹⠩⡿⠉⡏⡆⠚⠇⣆⠂⡄⢀⠇⠀⠀⠀⣠⠖⠈⠑⢆ ⠀⠀⠀⠀⠀⠀⠈⡄⢡⡁⣳⡿⠁⠀⠈⠛⠀⠛⠎⡆⢀⡠⠊⠀⠀⠀⠀⠸ ⢀⠤⠤⢀⡀⠀⠀⢡⠀⢣⡁⠀⢀⠀⠀⠀⠠⠴⠗⡩⠊⠀⢀⠎⠀⠀⠀⠇ ⡇⠀⠀⠀⡀⠉⠐⠠⢄⡀⢱⡀⠁⠀⠀⠁⠀⡠⠋⠀⠀⢠⠂⠀⠀⠀⢠⠀ ⠡⡀⠀⠀⠈⠂⢄⠀⠀⠈⠙⠠⡀⢀⣤⢀⡔⠁⠀⠀⠀⡆⠀⠀⠀⠀⠎⠀ ⠀⠈⢄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⣉⣳⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠊⠀⠀ ⠀⠀⠀⠁⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠘⠔⠀⠀⠀⠀⢠⠩⠦⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⡀⠠⠈⠢⢀⠀⠀⠀⡸⠄⣀⣀⣠⡇⠀⢀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⡗⠖⠊⠀⠀⠀⠀⢦⠘⡶⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣍⡆⣸⠀⠀⠀⠀⠀⠈⠳⣸⠫⠑⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠅⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠶⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣄⠀⠀⠀⣀⣤⣶⣀⣀⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⣶⠿⠛⠋⠉⠉⠉⠉⠉⠛⠾⡟⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠀⣠⣤⣤⢤⣮⠿⣧⣤⣀⡐⠳⢤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡿⠀⢠⡟⠉⠻⣄⠀⣻⡀⢠⣯⠈⣹⣷⣄⠿⣿⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠃⠀⣾⠳⣄⣀⣿⣷⣿⣿⠟⢿⣿⣿⣿⣿⣷⣬⣉⣛⣛⣛⣷⡶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⡟⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⠀⣦⣿⣀⣼⡿⣿⢽⣾⣧⣴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⠟⠁⠀⠀⠀⠀⢀⣴⡾⠉⢀⡿⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠈⣿⣇⣀⣽⠏⠨⣬⣬⠽⠙⠘⠋⠁⠈⠁⢸⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⣀⣴⣿⡿⠀⠀⢸⠁⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⡿⡅⢙⣿⣴⣲⣶⠀⠊⢁⠀⠀⠀⡎⢀⡀⣸⣿⣿⣷⣿⣿⣿⣷⣿⣿⡿⢿⢵⡟⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢷⣿⣿⣿⣇⡹⠃⠀⠀⠈⠀⠀⠀⠙⠾⣿⢿⣿⠿⠛⠛⠻⢷⡿⢡⠟⣰⠃⡾⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣏⢿⣯⣷⠒⠀⠀⠀⠀⠰⡟⠉⡇⢠⡿⠋⠀⠀⠀⠀⠀⣼⠀⡏⢠⡇⠀⢻⡀⠀⠀⠀⣿⡀⠀⠀⢦ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠙⢿⣼⣿⡿⣷⣄⣠⠆⢀⣀⡈⢂⣀⡞⠀⠀⠀⠀⠀⠀⠀⢹⡆⢷⡀⢧⡀⠀⠳⣄⠀⠀⠈⠻⣄⡀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⣿⣧⣴⣿⣿⣿⢟⣻⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⣀⣸⣧⣈⣷⣌⠛⢦⣀⡙⠀⠀⠀⠀⠈⠙⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⢿⣿⣛⡿⠟⠛⠉⠉⠛⠫⣟⠋⠀⡐⢚⡛⠓⠛⠛⠋⠉⠉⢻⣿⡿⢷⣀⠈⣿⣷⣶⣦⣤⡤⠖⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠉⢀⡾⠃⠀⠀⠀⠀⣠⣾⣥⣶⠟⠙⣋⠁⠀⠀⠀⠀⠁⠀⢐⣿⣷⣤⡼⠓⠾⠟⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⡜⠁⠀⠀⠀⣀⡾⢋⣭⡞⠁⠒⠚⠛⢉⣉⣀⣀⠀⠄⠀⢀⣺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⢿⠀⠀⠀⠀⣴⡿⢋⣻⠅⣠⣴⠦⠚⠋⠉⠉⠉⠉⠉⠉⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠿⣄⠀⠀⣸⣗⡴⠟⣡⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣤⣞⡛⠒⠶⢿⣷⣴⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡛⠿⣍⠛⠯⣄⡉⢍⡐⠨⣍⠙⡲⣿⣿⣾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠉⠲⡈⠳⣄⠀⠙⢲⠀⢀⠀⣽⣿⣾⣿⡿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⠀⠀⠙⠀⠙⢦⠀⠀⣧⢺⡇⡿⣿⡿⠃⠀⠀⠀⠀⡇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡄⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢰⡃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⢠⠀⠀⠐⢠⣿⡿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢠⣟⡀⣠⡴⠿⠿⠾⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡷⠿⠟⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⡝⠓⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⡇⠘⡆⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⠀⠹⡦⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢧⣼⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⢧⣧⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣠⡫⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢤⡀⠀⠀⠀⠀⠀⠀⣶⣿⡗⠾⠀⢀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀

⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡀ ⢸⣿⡁⠀⢠⣦⠀⠀⣤⣤⠀⠀⣴⡄⠀⢈⣿⡇ ⠈⢿⣷⣀⠈⠁⠀⣀⣿⣿⣀⠀⠈⠁⣀⣾⡿⠁ ⠀⠀⣿⣿⣿⣿⣿⠿⠋⠙⠿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⡀⠀⠀ ⠀⠀⣼⣿⠁⠀⠀⠀⠻⠟⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⣼⣿⠃⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠘⣿⣧⠀ ⢠⣿⡇⠀⠀⠀⠻⣿⣦⣴⣿⠟⠀⠀⠀⢸⣿⡄ ⢸⣿⠁⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠈⣿⡇ ⠸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠇ ⠀⢻⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⡟⠀ ⠀⠈⢿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⡿⠁⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⢹⣿⣘⡿⣿⣿⣿⣿⣿⣿⣿⢧⠙⣿⣿⣿⣿⣿⣿⣏⡇⢂⠈⠀⠀⠀⠀⢀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣀⢤⡾⠋⣼⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠹⣄⠸⣆⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⠉⠻⡆⢻⣿⣿⣿⣻⣧⢿⣝⡄⠡⡀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠉⢀⣼⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⡥⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢗⠒⠍⠀⠀⢀⣰⣿⣷⣿⠿⠛⠛⠛⠛⠻⠄⡀⢸⣼⣿⣿⣿⣽⣟⣾⣻⡼⢶⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣽⡿⣿⣿⣿⣿ ⢲⠲⢾⣤⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⣿⣿⣷⣟⣿⣷⢮⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⠛⣰⡇⢻⣿⣿⣿ ⢦⠑⣸⢱⠀⠈⢆⠀⠀⠀⠀⠀⠀⠎⡎⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⡟⢸⣿⣿⣟⣿⣿⡹⢿⣿⣿⣷⣻⠇⣻⣦⣄⣀⣀⣤⣴⡶⢛⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠕⠈⢠⠏⣧⠊⣿⣿⣿ ⠀⠀⢀⡾⠉⠄⠈⠆⠀⠀⠀⠀⠀⠣⠐⡀⠀⠀⡔⠻⡿⠃⠀⠀⠀⠀⠀⢉⠒⠀⢀⠲⠊⠹⢿⣾⣿⢿⣯⡝⡹⢛⠷⣞⢻⣛⡇⠡⢠⠙⡾⡱⠯⠞⡡⠜⡡⢾⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⢂⣄⡼⠋⡰⠹⣆⢹⣿⣿ ⠀⠀⠎⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠨⣆⠀⠆⠴⠓⢉⣉⠿⠷⠶⣲⠾⣖⣉⠀⠀⠀⠀⣸⣿⢯⡿⠙⢿⣔⡉⠖⡈⠖⣼⠃⡔⠀⠐⠠⠑⠈⠄⠁⢌⣱⣿⣿⣯⣿⣿⣿⣿⢿⠀⠠⠐⠠⣀⣤⠚⠀⠀⠘⣼⣿⣿ ⠀⠈⠀⠀⠀⠀⡰⠀⡃⠀⠀⠀⠀⠀⠀⢀⠨⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠻⠶⢶⣾⣿⠽⠞⠁⠄⠂⠉⠻⣦⣍⠒⡨⢁⠇⠀⠁⠀⠀⠀⠠⢨⢶⠋⣿⣿⣿⣿⣿⣿⣏⣼⣷⣶⢾⠳⠋⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠠⠊⠀⠀⠇⠀⠀⠀⡀⠔⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡈⠠⠁⠌⡀⠀⠙⣧⠐⠡⠈⠀⠀⠀⠀⠀⣰⠋⢺⣠⣿⣿⣿⣿⣿⡿⢛⡋⢿⣧⡊⠄⠀⠀⠀⠀⢀⣀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⢸⠀⡠⡐⠌⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠠⠁⠄⠛⠀⠀⠀⠀⠀⠀⢀⣜⣁⣀⠸⣿⣳⢟⣿⣟⣹⡷⢦⣉⣖⡼⣟⣶⣤⠶⠶⠿⣛⢻⣿⣿⣿ ⡀⠀⠀⠀⢀⢰⢖⡽⢮⠌⠀⠀⠠⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⢁⠈⡐⠠⠐⠀⢈⠀⡰⠟⠃⠉⠉⠙⠻⣧⡻⢿⡷⠬⢿⡆⠡⠈⠙⠒⠦⢴⡈⠬⠑⡌⣾⢟⠣⡟ ⠠⠑⣈⠐⠀⠺⣯⢂⡿⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⠠⢊⠔⣁⢂⡁⠂⠀⠀⠀⠀⠀⣀⡀⠀⢇⠙⠻⡇⡇⠀⠳⡄⠁⠌⡐⡁⢆⡘⢳⡴⢫⠁⣎⣞⢱ ⠀⠀⠀⢈⠀⣸⡟⠫⡔⠣⠜⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡠⠑⡌⢒⠠⠂⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠢⠀⢻⣱⠀⠀⠈⠓⠦⠐⢨⠐⢌⠢⢹⣶⣿⣯⣶⣿ ⠀⠀⠈⠀⡐⢸⢡⠃⡌⡑⠃⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⡘⣄⠋⡔⢁⠂⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣷⣥⠴⠴⠀⠀⡐⠠⠈⠄⠂⠡⢸⡟⢥⠲⣌ ⠀⠀⠠⠐⠀⣹⡀⠂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⣑⠲⠤⡉⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⢦⠤⢴⠆⠁⠀⠀⠁⠈⣗⣮⣷⢾ ⠀⠀⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠰⣠⠓⣌⢣⢃⡑⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠳⣼⠂⠀⠀⠀⠀⠀⢹⣟⡾⢋ ⠀⠀⠀⠀⠀⠌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠌⡐⠰⣠⠓⡴⣩⢒⠣⢎⡘⠤⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⡇⠀⠀⠀⠀⠀⢸⣯⠑⡂ ⠀⠀⠀⠀⠀⠘⡸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠄⢂⠡⠘⣠⢑⡣⢖⣹⠲⣥⢋⠞⡰⣈⠒⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢻⡀⠀⠀⠀⠀⢸⡗⠘⡄ ⠀⠀⠀⠀⠀⠠⡑⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⢁⠌⡐⠄⣢⡵⢦⠛⡼⣙⠶⣙⢦⣋⠮⡑⠤⣉⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠄⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣇⡘⠄ ⠀⠀⠀⠀⠀⠠⡑⣿⡝⣳⢦⣀⠀⠀⠀⠀⠀⠀⠠⠁⢂⠠⢀⠂⢌⡐⣂⡶⡼⠾⡛⢅⢃⢚⠷⣩⠏⡝⢦⣣⡗⣉⠒⠄⡌⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠀⠀⠀⡀⠀⡀⢼⡄⠀⠀⠀⠀⡧⢍⡳ ⠀⠀⠀⠀⠀⠰⢡⡟⠠⠁⠛⠭⣟⣶⣤⣤⣀⣄⣡⣄⣦⣴⣦⠿⠞⡫⢙⠰⡁⢆⠱⡈⢆⢺⡹⣃⠞⡨⢍⣷⢺⢵⢈⠒⠠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠤⢁⠠⢸⡇⠀⠀⠀⠀⢹⡎⡵ ⠀⠂⠀⠀⠠⢁⡿⠁⠀⠐⠀⠠⠀⠆⡜⣿⣟⡻⢏⡛⡋⢥⠂⡅⢣⠰⠁⠆⡑⠨⠄⡱⢈⡶⠃⠔⡨⢑⠞⠈⢯⢞⣆⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⢌⢢⣵⢾⣲⡡⠆⣸⠇⠀⠀⠀⠀⢸⡽⣱ ⠀⡁⢀⠂⠁⠌⠀⠀⠀⠀⡐⠠⡁⢞⣼⣟⠮⣕⢫⠐⢥⠢⡑⠌⠢⠄⠉⠀⠀⠀⠀⠰⡙⠁⠈⠐⡠⠃⠀⠀⠈⢯⢾⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠱⣊⢽⣯⣿⣿⠧⣁⣿⠀⠀⠀⠀⠀⢸⣓⢧ ⠀⡁⠈⠀⠄⠀⡀⢀⠀⠄⣁⢢⣱⣾⣿⡟⢶⡙⢌⠲⠌⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠀⠀⡰⠃⠀⠀⠀⠀⠘⣎⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⡩⢜⠻⢿⢋⠆⣹⡟⠀⠀⠀⠀⠀⠈⡿⣜ ⠀⠄⠡⠀⠌⢀⢀⠂⣌⠲⣴⣿⣿⢿⣽⢙⠦⡑⡈⢂⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⣆⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⣈⠱⣸⠊⢴⣿⠃⠀⠀⠀⠀⠀⠈⡇⢞ ⠀⡘⢄⠡⢊⡔⣌⣾⣴⣿⠿⠿⣽⣯⣿⡘⢢⠁⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡝⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠢⢁⣬⡿⡹⠀⠀⠀⠀⠀⠀⢠⣇⠠ ⠠⡑⣪⡵⠷⡞⠉⠁⠀⠀⠀⢸⣿⡷⡿⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⡕⡻⣦⣄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢠⢃⣾⢋⡔⠃⠀⠀⠀⠀⠀⠀⡿⡛⡐ ⠀⠁⠘⣄⠣⡇⠀⠀⠀⠀⠀⢸⣿⡿⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡱⣉⠟⡷⣤⣂⠔⠡⢄⠠⠀⠄⡐⡈⣄⣶⣷⣿⣏⠒⡌⠀⠀⠀⠀⠀⠀⢸⢃⠔⠁ ⠀⠀⠀⢳⠀⣇⠀⠀⠀⠀⠀⣿⣿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣍⡚⠴⣡⠋⡟⣳⡞⣶⣿⣶⡟⢉⠡⠄⣈⠻⣮⠱⡀⠀⠀⠀⠀⠀⠀⠚⠀⡀⠂ ⠀⠀⠀⠀⡆⠈⠀⠀⠀⢀⠎⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⡑⢆⡹⢐⠏⡼⢉⡙⢻⣷⠠⠁⡌⢀⠒⣿⡡⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠚ ⠀⠀⠀⠀⠰⠀⠀⠀⢠⠊⢀⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠆⡰⣋⡾⢁⠂⠜⢠⠻⣧⡑⠠⠌⠂⠽⡇⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡐⢀⢸⡃⢆⢈⠘⢄⡘⢧⢏⡱⢌⠘⡈⣷⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢰⢻⣿⣇⠌⡄⠊⡄⡘⢌⢮⠱⢌⢂⠡⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢎⠆⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⢻⢻⣿⣾⣤⣃⡔⡈⢆⢪⡑⢎⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠂⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡏⢧⠻⡿⣿⣿⣿⣿⣾⣦⠝⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠃⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⡄⢣⠜⢎⠻⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡀⠀⣠⠜⣹⢟⠛⠯⢶⡦⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣀⠝⣽⡧⢤⣿⡻⢝⣻⡦⠳⡄⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣖⠉⢦⡀⢀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠉⢸⢸⠈⣏⣍⢾⣽⣹⡁⣇⠙⡆⠀⠀⠀⠀⠀⣾⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠀⠀⠀⢹⢦⠰⢰⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢹⣄⢳⡿⢿⠶⣃⡿⢳⣽⣴⠧⠀⢀⣀⣤⣾⣰⡇⠀⠀⠀⡀⠠⠠⢀⡄⠀⠀⢀⢔⡿⠁⠀⠀⠀⠀⠀⣷⡏⠾⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢯⡙⢯⣭⣯⡭⣤⣞⣟⠁⠉⠉⢉⡴⠟⣾⣿⣇⡄⢠⡿⣰⣤⣾⣴⢀⡆⠀⠀⡟⠀⠀⠀⠀⠀⣠⠆⣿⣿⣶⢻⢆⠀⠀⠀⠘⣀⡀⣄⣦⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠨⠷⠤⠭⠽⠟⠉⠉⠀⠀⠀⣢⣤⣶⣿⢿⠟⢇⣼⣧⣿⣸⣯⣿⣸⡟⣴⣾⠀⠀⠀⠀⡠⣊⣸⠀⠁⢻⣿⣿⣧⡀⠀⢀⣐⣿⢿⣿⣿⣿⣧⣄⣤⠆⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⢀⣾⣿⣿⣿⡿⡯⢠⢸⣽⣿⣿⣿⣿⣿⡟⣿⣽⡿⠀⠀⠀⠀⣱⣿⡫⠀⠀⠀⠻⢿⡟⡍⢰⣾⣜⣻⣦⣽⣿⣿⣿⣿⠃⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⣷⣿⢸⠋⣿⣿⣏⣿⠟⣿⣿⣿⣇⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⣼⡧⠗⠊⢉⢻⣟⠓⠈⢹⣾⣿⣏⠀⠀⠀⠀ ⣷⣶⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣞⣽⣿⣗⣼⣿⣿⣟⡿⣿⣷⣻⡝⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡓⡶⠀⠪⢨⣿⡇⠀⠈⣿⣿⣿⡀⠀⠀⠀ ⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡯⢾⡿⣿⣿⣿⢟⣽⣿⣶⡿⣿⣦⣵⡄⠙⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⢴⣗⣀⣠⣾⡟⠁⠀⣠⣿⣿⣿⣇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⡿⠙⢀⣀⡴⠋⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣗⢄⣀⠀⠀⠀⠀⠖⠈⣹⣟⣿⣏⣏⣨⣿⠙⠻⣶⣾⣿⣿⣟⣻⣿⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⢆⣴⠟⠉⠀⢴⣷⣿⡿⢚⣿⣯⠟⠛⠛⠃⢻⣿⠾⠿⢷⣦⠽⠓⣚⣙⠒⢴⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣽⣿⣿⢿⠻⣿⣷⠀⠀ ⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣷⡷⠛⠁⣠⣞⣵⣛⣽⣿⡿⠟⠍⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠐⠊⢸⢋⣟⣳⡆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⡏⣷⡀ ⣿⣿⣿⣿⡄⠀⠀⣀⣼⣿⣿⡽⢡⣴⣶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣷⢾⢥⡤⣤⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⣷ ⣦⡈⠻⣿⣿⣶⡾⡟⡽⢻⣻⣷⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⡿⣃⡀⣈⡉⠛⠿⣿⣿⣿⣿⣿⣧⠀⢠⣴⣾⣿ ⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠋⠀⣿⢯⡿⡿⠀⢀⡞⠁⠉⢻⣿⣿⣤⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡹⣿⡇⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡨⣤⣄⠀⠰⠿⠿⠋⠀⢠⣿⣧⠀⠀⠀⠙⣿⡿⢿⣿⣿⣿ ⠋⠉⠙⠛⠛⣿⣿⣿⣿⣿⠸⣇⢻⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠈⢠⠟⣿⣷⣦⣄⡀⠀⠀⠈⠺⣿⣇⠀⠀⠀⠉⠁⠀⢻⡿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⢻⣿⣷⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⣽⣉⠉⠻⠿⠾⠇⠀⠀⠀⠈⠁⠈ ⠀⠀⠀⠀⢣⣙⣛⣿⠟⢻⡗⡄⣾⣿⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢠⠜⠹⢆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣶⣾⣻⣥⣀⠀ ⠀⠀⠀⠀⢸⣿⠋⣠⣶⣛⣽⣼⣿⠏⣇⠀⠀⢷⡀⠀⠀⠀⠀⠀⠊⠢⢤⣸⢴⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⠿⠿⠿⠿ ⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢀⣤⠽⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢹⣷⣆⡰⠀⠀⠻⢯⡁⠢⢻⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣟⣸⢖⣽⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠐⣲⡄⣰⣾⣿⡿⠁⠀⠀⠀⠀⠁⠀⠀⡿⠂⠀⠀⠀⠀⠈⠂⠀⠀⣼⣿⣿⣿⣿⣿⣇⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣾⣿⣿⡿⠁⠀⠀⢀⣀⣀⡀⢀⣀⣇⣤⣶⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠘⢿⣿⣿⣿⣥⣶⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⡩⣻⠟⠋⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠄⢻⡃⠀⢠⡮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢟⢿⡿⣟⠀⠀⣇⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⢇⠀⢷⣿⠰⢠⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⢶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠲⡀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⣿⣿⣿⣿⠁⣾⠺⡆⠈⣿⠀⠀⢧⣇⠀⠀⠀⢀⡠⠊⠉⠇⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱⡀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⢀⡼⠋⠙⣿ ⣿⣿⣿⣿⣄⢸⣷⠁⠀⠁⠀⠀⠘⣿⣓⣲⠶⠋⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⠳⡢⠄⠀⠀⠀⣿⡆⢀⣤⠞⠁⠀⠀⢠⢿ ⣿⡏⠻⡿⠽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢷⡤⢀⣀⣀⠼⡿⣯⠁⠀⠀⣀⣠⠋⠈ ⣿⣧⢢⠀⢠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠈⠂⠈⠀⠐⠚⠁⠘⣧⣾⣋⣿⠃⠀⠐ ⣿⣿⡎⠀⡎⡼⠌⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡏⠿⠿⠋⠀ ⣿⣿⡇⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡀⠱⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣠⣤⣤⣞ ⣿⡿⣷⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⡴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⣼⡿⢆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠔⠋⠁⠀ ⣿⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⠀⠀⠀⠀⠐⠲⢤⠀⠠⡀⠀⢸⣦⣔⢠⠞ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠡⡀⠉⠁⠈⢿⠁⢈⠉ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣽⣾⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢸⢀⢿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⠾⢽⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣰⠟⢁⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣴⠺⣧⣤⡹⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢃⣠⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣟⣼⠗⠀⠘⣷⠉⠙⢿⣄⣴⣶⣶⣄⡂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⠟⠸⠀⠀⢸⡏⠀⠄⢘⣿⣿⣿⣿⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⢷⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣶⣿

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠀⠀⠉⠉⠑⠲⢶⣫⣵⣲⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸ ⣇⡤⠔⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⣠⠤⠒⠚⠉⠀⢀⣀⢼ ⡏⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⡀⠀⠀⠀⠀⠀⠙⢦⣀⠤⠴⠒⠉⢁⣀⣸ ⡿⢗⣲⣦⣤⡀⠀⠈⠻⣧⡀⠀⠀⠀⠀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⢣⡤⠤⠒⠋⣩⣤⣾ ⣇⢴⣿⢹⠻⣿⣿⣦⡀⠈⢷⣄⣦⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡇⡀⡆⢳⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣾⠁⢸ ⣇⡆⣇⡸⠖⠋⠉⠉⠉⠉⠘⠛⠯⢭⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸⢡⡧⡇⠘⠄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢿⠀⢸ ⣿⢠⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡴⢡⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣼⠀⢸ ⡿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢁⠴⠋⠀⣾⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿⠀⢸ ⡇⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡜⠁⠀⠀⠘⠛⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣾⣤⣼ ⣗⣾⠀⠀⠀⠀⡅⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸ ⡇⠸⠀⠀⠀⢸⡇⢀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣜⣀⣀⢀⡴⢒⡤⠖⠊⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸ ⡇⡀⠀⢸⡄⢸⢷⣌⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠰⢋⡴⢯⠀⠀⠀⠸⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸ ⡇⡇⠀⠀⠀⠸⢸⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⣾⣁⡤⠒⠊⠁⢀⡀⠑⠦⡀⠀⢣⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸ ⡇⠇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡼⡏⠀⠈⠲⣄⠀⠀⠙⢆⠀⠈⠑⢬⡦⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸ ⡇⠘⠀⠀⠀⠐⡞⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣼⢷⣤⣤⣤⣬⣷⣤⡄⠀⠃⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⢿⠀⢠⣿⡿⢟⣯⣤⣿⣿⣇⣛⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⡧⢳⢻⣿⣿⣿⣿⡿⠛⡘⠀⠘⣩⣶⣿⢿⡛⠻⣿⠙⢿⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣶⣿⣿⣏⡁⠀⢱⡀⠀⠀⠀⠯⠚⠓⠚⠉⠐⠛⠓⠉⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⢻⣟⣿⠯⠙⢄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⣿⣿ ⣟⠉⣿⠔⠊⠑⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡹⠃⣾⡏⣿⣿⣿ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⡿⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⣀⡀⢀⡄⠀⠀⠉⠀⠀⢸⠟⣿⣿ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣪⣴⣶⣾⣿⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸⣴⣿⣿ ⣣⣧⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⣿⠛⣲⡟⠊⠁⠀⠀⡠⢲⠆⠀⢠⣿⣿⣿⣿ ⣄⠩⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⢳⠁⢣⠀⠀⠀⡜⠀⢸⠀⣠⡿⠛⣻⣿⣿ ⣿⣿⣦⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⢣⡈⡆⠀⢣⠀⠀⡇⠀⢠⣼⡟⠁⣰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠱⡼⡄⠀⢣⡀⡇⠀⢸⡏⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠶⣶⣤⣤⣄⣈⣷⡀⠀⠹⡇⠀⢸⠁⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⠀⠉⠉⠛⠛⠛⠳⡄⠀⡇⠀⢸⠀⢠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠑⠢⠤⣀⡀⢀⣸⡥⡇⠀⠀⡇⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⡴⠒⢤⡀⠀⢀⡜⡛⢶⣹⠀⠀⠀⢱⡏⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⡀⠀⠑⣤⣎⠘⠜⡸⡍⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠱⡤⢂⠿⢿⣿⡾⢣⠃⠀⠀⠀⠀⡇⠀⢹⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⢀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠣⡀⠀⠒⣶⣿⣿⣿⡏⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⢸⣶⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢀⡞⠁⠀⠀⠙⣆⠀⣀⡴⠾⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠉⠛⠿⢿⣿⣧⡀⠀⠀⡾⠀⠀⠀⠀⠀⣸⡾⠋⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣽⣿⣿⠀⣸⠇⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⠉⣿⣿⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⣿⡟⠁⢠⡟⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢿⠀⠀⠀⣼⠀⠀⠀⠀⠐⠒⣿⡏⠀⠀⣼⠃⠀⠀⣰⡟⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣽⣧⠀⠀⣿⠀⠀⣼⠏⠀⠀⠀⠀⠀⢠⣿⢿⡿⡄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⢿⣿⡄⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⣾⡏⠀⢻⡹⣦⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡟⣿⡄⠀⠀⠀⠀⠀⠘⣿⣷⣾⣧⡞⠁⠀⠀⠀⠀⠀⠀⣸⠛⢧⠀⠀⢷⡘⢷⡄⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣾⠀⠘⣷⡀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠈⢳⡄⠈⢳⡌⢻⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⣾⡅⠀⠀⠙⢿⣿⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠸⣿⣧⣀⣀⡀⠀⣿⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏⠀⠀⣀⣀⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠘⢿⣏⠻⢿⣾⣿⣦⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⠁⠀⠛⠛⠿⠿⠿⠿⠃⠻⣿⣶⣄⡀⠀⠀⢀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⢿⣿⡟⠻⣷⣦⡀⠀⣿⣦⣄⡀⠀ ⢀⣠⡤⠴⠒⠒⠒⠒⢋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢻⣿⡀⠀⠙⢿⣦⣽⣿⣿⡿⠆ ⠀⠀⠉⠉⠉⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡿⣿⢿⡿⣿⣻⢿⣻⣟⣿⣻⣽⣻⢯⣟⣯⠿⡽⢯⡿⣝⣯⢻⡽⣭⢯⡽⣭⢻⣭⢻⣭⢻⣭⢻⣭⢻⡝⣯⢻⡝⣯⢻⡽⣭⢋⡷⣉⠒⡔⡰⣌⡳⣭⢳⡹⡜⣂⠆⠀⡀⠠⡄ ⣿⣿⣿⣽⣾⣿⣽⣾⣿⣾⣷⣿⣻⣽⣿⣻⣽⡿⣽⣷⣻⢯⣟⣾⣳⣟⡾⣭⣟⡾⣵⣻⣽⣻⣜⣯⣞⣧⢻⡜⣮⢳⣭⢳⣎⠷⣎⢷⢪⢗⣮⢳⣝⣮⣻⡼⣭⣳⡝⣦⢏⠴⡡⣍⠶⣱⢣⣝⠲⡍⠖⠩⠔⢠⢡⠰⡱⢌ ⣿⡿⣾⣟⣷⡿⣽⣷⣻⣾⣳⢯⣟⡷⣯⣟⣷⣻⣟⡾⣽⣻⣞⡷⣻⢞⣽⠷⠞⣋⣉⣩⣽⣯⣷⠟⢛⠫⢭⡉⢉⠉⠒⠯⣜⡻⣜⣣⠟⣮⡚⢷⣚⡖⡧⣝⠶⣣⠞⣔⡊⢖⡱⣌⠳⣍⠳⡈⠁⠀⠀⠀⠀⢂⢎⡱⡑⢎ ⣿⣟⣷⢿⣯⣟⡿⣞⡷⣯⣟⡿⣾⣽⣳⡟⣾⣳⢯⣟⣳⠿⣼⠽⠛⣩⡴⢞⡛⠭⣑⡯⢛⠡⢂⡍⠦⢹⡧⣝⣦⣻⣒⠤⡀⠉⠓⢮⣛⠶⣹⢧⢳⡞⣵⢫⢞⣥⡛⣤⢋⢦⠳⣌⠳⣌⡑⢂⠀⠀⠀⠀⠀⡜⣢⢱⡉⢆ ⣿⣞⣯⢿⡾⣽⣻⣽⣻⢗⣯⣟⢾⡶⢯⣟⣳⢯⣟⣼⡯⢛⣡⡶⢛⠡⠘⢠⣸⠟⣉⠆⠁⠀⠁⠀⢠⡿⠡⣿⡄⢣⢻⣇⠘⣕⢤⠈⠙⢾⡱⢎⡷⣚⣥⠻⡜⢦⣙⢦⣋⢎⡳⢌⠳⡰⢌⠣⡄⠀⢀⠠⡼⣸⢥⠳⣜⠡ ⣟⡾⣽⢯⣟⣷⣻⣞⣭⣟⡾⣞⣯⣽⢻⡾⣝⣷⣞⠇⣠⢾⠗⣘⠀⠀⣠⠞⣡⠔⠃⠀⠀⠀⠀⢀⠞⠀⢸⣏⡇⠘⡆⠻⣶⣘⣦⠙⠄⠀⠙⢯⡲⣙⠦⣏⡝⢮⠜⣦⡙⢮⣑⡋⢶⢱⡩⣓⢬⡓⢎⡳⣱⢣⢞⡱⢎⡐ ⡿⣽⢯⣟⣾⣳⢯⣞⡷⣯⡽⣞⣧⣟⣻⣼⡿⠱⣃⡞⠃⡡⠖⣁⣴⠟⢁⡜⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⣼⣻⠁⡀⡇⠀⠈⢳⡽⣷⣄⠑⡈⠀⢻⣬⢛⠴⣊⠇⢯⡰⣙⠦⣣⡙⢦⢣⠳⣌⠶⣙⢮⡱⢣⢏⢎⡱⠂⠀ ⡿⣽⣛⣞⡳⣯⢟⡾⡽⣞⣽⣳⠾⣭⢷⣟⢠⡷⢋⡤⠋⣠⡾⠛⡵⡺⠉⠀⢀⠀⡀⠀⠀⢁⠎⠀⠀⢰⣿⢃⢠⢳⡇⠀⠀⠀⠹⡘⢿⣦⡈⢆⠀⠹⡣⡝⢢⡙⠦⡱⡘⢎⡵⣘⢣⡝⢲⡡⠞⡌⡖⣩⠓⠎⠐⠀⠀⠀ ⡟⠄⠁⠀⠱⣭⡻⣝⢷⣛⢶⣫⢟⣵⡿⣨⡟⣡⢏⣠⡾⠋⢠⡞⡽⠁⠀⡠⠁⠀⠀⠀⢠⡟⠀⠀⢰⣿⣧⢎⢎⢸⠃⠀⠀⠀⢀⣿⠾⠿⡷⡀⢠⠀⢹⣽⢦⡙⢦⠱⣙⠮⢴⣉⠶⣘⠧⡜⡱⡘⠴⣁⠊⠀⠀⠀⠀⠀ ⢦⣀⣀⢠⠖⣧⢻⡝⣮⡝⣮⢳⢫⣾⣱⢟⡸⣥⡾⢋⡄⣠⠏⡰⠀⠀⡰⠁⠀⡠⢀⣴⡟⠀⠌⣠⡟⠁⡼⡀⠈⡜⠀⠀⠀⠀⠀⢸⣄⣀⣹⣌⠄⢇⠘⡿⢮⣳⡌⢳⡡⢞⡡⢎⡱⢃⡞⡰⢥⡙⠆⠄⠀⠀⠀⠀⠀⠀ ⢧⡳⢎⡷⢻⡜⣣⢟⡲⡝⣎⡳⣻⡗⣋⢮⣽⢯⡴⠋⣴⢋⡖⡀⢀⣼⠁⢀⢈⣠⣾⠯⠀⣠⣼⣿⣶⣿⣿⣿⣤⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠸⡄⢹⢧⢳⢻⡡⠞⡬⣑⢎⡱⢍⠲⡑⠦⡑⢈⠀⠀⠀⠀⠀⠀⠀ ⢧⣙⡳⣜⡣⢽⡱⢎⣳⡙⢶⡩⣿⢱⣺⡿⣹⢏⠴⣹⢇⡞⣰⢣⣾⢏⡜⢢⣮⡿⢉⣄⣲⣿⣿⣿⠿⣿⣿⡿⣿⠂⠀⠀⠀⠀⣿⣏⣿⡿⣿⣿⣿⡀⢱⠘⡜⠎⣧⢻⡘⠴⡡⢎⠰⢉⠒⡉⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀ ⠞⡴⢳⡜⣱⢣⠝⣎⠶⡙⢦⣹⣧⣿⣿⢛⢧⢫⢼⢫⣾⣱⣯⣿⠟⣼⣬⣿⠋⡐⢤⣾⡿⣿⣿⠉⠲⣛⣯⠕⡸⠀⠀⠀⠀⠀⠘⢘⢓⣃⡿⢷⡞⣷⡌⠄⢣⡘⢼⢸⢌⢣⠱⡈⠆⠠⢀⠀⠡⠐⠠⠈⠀⠀⠀⠀⠀⠀ ⡹⣜⢣⢞⡱⢊⡳⢌⡚⢥⠓⣼⣷⡟⣥⢋⣎⣷⢎⣽⡿⣭⣿⣵⣿⣫⠞⡁⢦⣽⣾⡉⢑⠢⡉⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⠘⣯⢿⣻⡀⢸⡎⢸⢸⢂⡌⢣⠱⡈⡐⠠⠌⢂⠉⡀⠀⠀⠀⠀⠀⠀⠀ ⡱⣊⠜⠢⠁⠃⠘⠠⠙⠢⢙⣴⡿⣘⢦⣻⡾⣽⣾⣿⣷⠿⣿⡵⠟⡁⢮⣴⣿⣻⡿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡿⠂⠀⠀⣹⣯⣇⢧⢨⡇⡝⣸⠠⢎⠡⢆⡑⢌⠡⢊⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣁⠎⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⢯⣿⢯⡿⡽⣬⣷⣾⠿⡋⣴⢥⣿⡿⣋⢾⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣻⠸⡇⣿⡷⢃⡜⢨⠑⡢⠘⡄⢣⠁⢎⡐⡁⠐⠀⠀⠀⠀⠀⠀ ⠢⠅⢎⠀⠀⡀⠀⠀⢀⠀⢄⢺⣏⢷⣟⡺⡴⣿⣿⣟⢣⢧⣟⣵⣿⠏⣴⡏⣿⠀⢻⣿⣹⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⣻⠇⠀⣸⣿⡧⢹⢸⠃⡟⢡⠂⡜⢠⠃⡔⠣⠘⠤⡉⢢⠐⡌⡐⠀⠀⠀⠀⠀⠀ ⢭⣓⠮⣜⣠⠐⡠⠒⠤⣉⠂⢾⣯⢿⡸⡗⣽⣿⡿⣌⣳⣾⣿⡟⣏⢾⡿⣱⣯⣆⠈⣿⣏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠰⢡⡿⢀⡏⣞⢸⢁⠆⡱⢈⠆⡱⠈⢆⠩⠄⡑⠤⢁⠐⠠⠁⠀⠀⠀⠀⠀ ⠀⠈⢁⠒⢾⣿⣿⣿⣶⣤⣍⣂⢿⡷⣯⣹⣿⣿⢳⣼⣟⡾⣿⡼⣼⣿⢣⣿⣷⢩⢷⣼⣿⣼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡟⠁⡼⣸⠇⡏⠰⡈⢄⠃⡔⠠⠉⡄⢊⠤⢁⠂⠄⠈⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠠⠘⣺⣿⣿⣿⣿⣿⣿⣿⣾⣯⣷⡽⣧⣿⡿⣏⣾⡝⡧⣿⡿⣵⣿⢿⣿⢢⠈⠙⢿⣿⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣼⡰⢃⡼⢀⡑⢈⠄⠊⠄⡁⠒⣀⠢⠐⠠⢈⠀⠂⢀⠐⡈⠐⠠⢀⠀ ⢿⡶⣦⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣹⣿⢸⡱⣯⣿⣟⢣⣿⣿⡇⠄⠀⠘⣿⣟⣿⣟⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡜⢀⣴⠟⣠⠋⣀⠂⡐⠈⠄⠃⠄⡁⠂⠄⢂⠁⡂⠄⠂⠐⠀⢂⠄⡁⠂⠄⠀ ⢆⡙⠶⢩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣻⡷⣾⡿⢹⣿⣇⠂⠀⠀⢹⣿⣹⣿⡇⠀⠈⠉⠙⣿⡿⣾⢞⠿⢋⣡⣴⠿⠉⠈⠄⠂⠄⠂⠄⠡⢈⠐⡈⠄⡁⠊⠄⠡⠀⠀⠀⠀⠀⠀⠂⢄⠁⠂⠀ ⠀⢈⠙⠲⠾⣽⣿⣿⣿⣿⣿⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣿⣿⣧⠖⠀⠀⢿⡿⣿⣿⣀⠀⠀⢰⣿⢟⠵⣋⠔⡯⠞⠁⠄⣈⠐⡈⠐⡈⠐⠈⡀⠂⠐⠀⡐⠀⠡⢈⠀⡁⠀⠀⠀⠀⠀⠌⠠⢈⠐⠀ ⠀⠀⡀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⣼⣿⣼⣿⣿⡷⣆⢾⡇⣨⡞⢁⠚⣦⠴⢦⢤⠀⠂⠄⠁⢀⠁⠐⠀⠈⠀⠐⠀⠀⡁⠀⠠⠐⠀⠠⠀⠀⠂⠌⠐⠠⠈⠀ ⠀⠀⠀⠄⠁⠀⠂⠀⠀⠀⢩⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⠿⣻⣝⢾⣹⣿⣿⣿⣾⣿⣿⣷⣤⣬⠟⠛⢓⢦⡈⠀⢀⠀⠂⠀⠁⠀⠐⠀⠀⠀⠁⠀⢈⠀⠀⡁⠐⠀⠌⠀⡐⠀ ⠀⠈⠀⡀⠄⢂⡠⠤⠤⠶⣧⠊⠀⣀⣠⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⡿⣟⣿⣷⢷⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣼⢿⣧⣀⠀⣀⣠⣐⣈⠀⠠⠀⠂⠁⠀⠈⠀⠀⢀⠀⠄⠂⠀⠂⢀⠀ ⠀⠀⠁⠀⣴⡯⣳⠖⠉⣸⣇⣀⣮⣵⡿⣟⢫⡝⢭⠛⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢯⣿⡞⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣬⣿⢿⣿⣿⢿⣝⣦⣄⠀⠀⠐⠀⠀⠈⠀⠀⠀⢀⠐⠀⠀⠀ ⠀⠔⣚⠉⣟⡰⠁⠀⣠⣽⢛⣿⢟⡧⣛⡬⠃⠜⡀⢣⠘⣆⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⣿⣾⣿⣿⣻⣿⣗⣦⠀⠀⠁⠀⢀⠈⠀⠀⠀⠐⠀ ⢠⠊⢀⢠⣿⣥⣶⣿⣿⣵⡿⣹⢞⡼⠡⠄⢃⠒⣬⣶⣿⣿⣿⠿⡛⢯⡹⢏⣛⠻⢟⣿⣿⣿⣿⣯⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣼⣿⣿⣟⣵⣿⣿⣟⣼⣿⣿⢣⣿⣧⡀⠀⠄⠀⠀⢀⠀⠁⠀⠀ ⠃⣴⢯⡾⠋⠉⠉⢀⣾⡟⣼⡛⢎⡰⢁⣎⣶⣿⣿⠿⠛⡉⠄⠣⡙⢦⡙⡎⢴⣉⣶⡼⡾⢿⢿⣟⣾⣽⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣾⣿⣿⣫⣿⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠐⠀ ⣿⠷⠛⢿⠷⠶⠞⣿⡻⣼⠋⡘⣠⣵⣿⣿⠟⡛⢁⠂⠡⠐⡈⣴⢜⣶⣽⠿⣟⢿⣹⢚⡵⣋⣞⣻⣷⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣷⣿⣿⣿⢿⣿⣿⣧⠀⠀⠐⠀⠁⠀⠀ ⠇⠀⣰⡟⠀⢀⡾⢧⠽⣁⣶⣿⣿⠿⠋⠆⠑⡀⠁⠈⣤⡵⠻⡙⠋⡁⠎⡙⣌⣶⢥⣻⢾⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣶⣮⣝⡛⠶⣤⣀⠀⠀⠂⠀ ⣶⠟⠋⠀⢠⡟⣱⣋⣶⣿⣿⢫⠱⢈⠡⠈⡀⠄⣬⠟⠃⠌⡁⢀⣂⣥⢾⣿⣹⣾⣾⣿⣿⣿⣿⡿⢍⡿⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣿⣽⣓⡶⣄ ⠁⠀⠀⠀⣾⡸⣧⣿⣿⣛⢦⠣⠌⡀⠆⣡⡴⠛⠁⠠⠁⣂⣴⣿⣏⣾⣿⣿⣿⣿⡿⣿⢿⣿⡿⡜⣿⠁⠂⢿⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⣿⢗⠈⠛⢿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣿⣽⢿⡝⡶⣭⢒⡱⢂⡱⠌⠡⢀⠁⢂⣴⣿⣫⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢳⣸⡷⠀⠀⠘⣿⣧⣉⠂⢈⣁⠀⡈⢆⣿⡸⠈⠀⠀⠀⠉⠻⢿⣻⣿⣮⠻⡄⢻⣿⣟⢿⣛⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⡿⣹⢮⡝⡳⢜⡢⢕⠣⡐⢌⠡⢂⣜⣾⣿⣽⣿⣿⣿⣿⡿⢟⣿⣿⣿⣷⣿⣾⡿⡇⢻⠃⠀⠀⠀⣿⠻⠿⠷⠶⠬⠯⠿⣿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣳⣌⢦⣿⣿⡲⣭⠞⣿⣿⣿⣿⣿⣽⡌⠙⠻ ⠀⠀⠀⣾⢳⡝⡞⡜⣱⢍⡚⣌⠢⡱⢌⢣⣻⣟⣾⣿⣿⣿⢿⣽⣶⣿⣛⣿⣿⣿⣿⣳⢯⣷⡩⢸⡆⠀⠀⢠⡿⣧⣅⣂⡄⢡⣔⣠⣶⢴⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣳⣽⣟⣿⣲⢛⣦⢻⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⢰⢣⡟⣼⢱⣹⠗⣎⠱⣂⢧⡱⢮⣹⣿⣿⣿⣿⣿⣯⣿⡟⢣⢦⠹⢾⣿⣿⣿⣽⣳⢚⣷⣼⠁⠀⠀⣼⠱⡈⠍⠛⠿⠿⠿⣿⣷⢚⣆⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣯⣶⣿⣞⣿⣿⣿⣿⣣⠀ ⠀⢀⣏⡳⣝⢎⡿⣍⠞⡤⢳⡘⢦⣽⢯⣿⣿⣿⣿⣿⣿⣿⣿⣯⢇⢮⣙⠦⣟⣿⣿⣿⣮⡝⡼⣏⠀⠀⣰⠷⣥⣘⠀⠃⠄⡐⠂⡔⣸⢸⠀⠉⠢⠄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣟⢿⣛⣿⣿⣿⣿⣧⠇ ⠀⡲⣬⢳⣽⣞⠳⣜⡚⠴⢣⣙⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢶⣩⡞⣽⢾⣿⣿⣿⣞⡱⡽⡆⢠⣿⣮⣐⣉⠛⠛⠺⠶⠷⠾⣶⢺⠀⠠⡾⡦⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣻⣧⣛⢯⣿⣿⣿⣿⡆ ⡘⡵⣭⣳⢏⡮⢳⢬⡙⣭⣳⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡹⣎⢿⣽⣿⣿⣿⣿⣳⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⢻⠀⠀⠣⣿⠟⡄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢏⣟⣳⢿⣿⣿⡽ ⣸⢳⣯⣛⢮⠵⣋⠶⣙⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡹⣎⣷⣟⣻⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⠀⠀⠀⠀⢐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣟⡾⣭⣛⢺⡽⣿⣿ ⡞⣯⡳⡝⣎⠳⣍⢞⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠆⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣳⣝⢮⢇⡿⣽⣿ ⡽⣣⢏⡕⣊⢗⢮⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠠⠀⠀⠁⢌⣿⣿⣿⣿⣿⣿⣾⣿⣽⣯⣿⣽⣿⣧⠟⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣿⣿⣷⣚⣯⣞⠼⣳⣿ ⡳⢇⡞⣌⡳⢮⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⠈⠀⣠⡾⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⠿⠿⠾⢞⡻⣙⠦ ⡝⣎⠼⣎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣏⢿⣄⡾⢿⣽⢇⣿⣿⣷⣯⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣜⠀⠀⠀⢀⣴⠟⠀⢷⣤⠀⡀⢀⡀⣤⡴⠋⠙⠳⣯⡿⣿⣿⢖⡱⣊⠴⣩⡾ ⡾⣼⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⡆⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⣿⣿⣷⣧⣿⢿⠀⢠⣶⠿⠃⠆⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠛⠻⠿⢷⣧⣿⠾⠟⠀ ⡼⣱⣾⣿⣽⣿⣿⢿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⢿⣫⢿⣾⣖⣻⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⢞⠫⠁⠀⠁⠀⠀⠀⣿⣿⣿⡿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡵⣟⣿⣿⣿⣿⢯⣿⣻⣾⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⢺⠥⣏⢿⣿⣶⣿⢿⣗⣻⣷⣿⢉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⣿⣿⣟⣿⡿⣯⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢯⣿⣌⡳⢭⢿⣿⣚⢿⡹⣿⡋⠄⠌⠐⠠⢀⠆⢭⡙⢏⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡽⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣻⢾⣽⣻⣟⣿⣿⣿⣿⢯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣣⣏⣿⢿⣞⡿⣴⡉⠆⡈⠄⢡⠈⠞⣤⢋⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣟⣿⣮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡷⣯⣟⣾⣳⣿⣿⣿⢿⣽⣟⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⡉⠏⠻⠜⡸⢛⠿⣿⣴⣀⢎⠰⣈⠞⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣳⢯⣿⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣽⡳⣽⣺⣽⣷⣿⢿⣻⢷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠄⠉⠘⠌⢛⠿⠾⡷⠿⠾⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢯⡟⣾⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⢧⡟⣶⢯⣟⣯⡿⣯⢯⢷⣯⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢯⣝⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢞⣧⢻⣼⣻⡽⣏⠿⣜⣻⢾⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣯⢞⡾⣿⢻⠀⠀⠀⠀⣀⠀⠀⠀⢀⡰⣞⣯ ⣿⢺⡬⣓⢮⡳⣝⢮⡻⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣻⠾⣭⢞⣿⣏⡇⠀⠀⣿⣽⣶⡠⣄⢾⣽⣟⠃ ⣏⠷⡸⢥⢳⣙⢮⡳⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣿⣿⣿⣿⣿⣻⣽⣻⡜⣯⣿⣇⡇⠀⠈⣷⣿⣿⣷⣯⣿⡽⢊⠀ ⣏⢞⡱⣋⡞⣬⢳⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠀⢘⣿⣿⣿⣿⣻⣽⣳⢧⣛⠶⣿⣿⢢⠀⡰⢯⣿⣿⢿⣽⣳⢿⣥⠂ ⣏⠮⣕⣣⡝⢮⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡏⠀⢘⣿⣿⣿⣿⢯⡿⣽⡳⣭⢻⣽⣯⢹⣾⣽⣿⣿⣯⡟⣶⣹⣿⣾⣟ ⣎⠿⡴⣓⣾⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⠀⠀⢘⣿⣿⣿⣿⢯⣟⡷⡽⣎⣟⣾⣷⢚⣿⣿⣿⣿⣿⣽⣾⣷⣿⣻⣾ ⣎⢯⣵⣻⣞⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠇⠀⠀⢈⣿⣿⣿⣟⡿⣞⡽⣳⡝⣮⢿⣿⣎⣿⣿⣿⣿⣿⣿⢿⣾⠳⡝⢺ ⣮⢷⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⢰⣿⣿⣿⡿⣽⢞⣳⢧⡻⣼⣻⣿⠴⣿⣿⣿⣿⣿⣿⣟⢧⢃⠈⢄ ⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⣸⣿⣿⣿⣟⣧⢟⡧⢯⣳⢷⣻⣿⣞⣿⣿⣿⣿⣿⣿⡾⣏⣦⣳⢮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠄⡁⠂⠄⣿⣿⣿⣿⢿⡜⣯⢞⣯⠿⣽⣻⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢈⠔⡂⢅⠊⣼⣿⣿⣿⣿⣻⢼⣣⣟⣾⣻⡽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢄⠊⠴⡈⠴⣈⢒⣿⣿⣿⣿⡿⣝⢮⡳⢾⣱⣯⣟⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⡐⠌⡜⢢⢉⠲⢄⢮⣿⣿⣿⣿⢿⡹⢮⡽⢯⣷⣻⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢆⠱⡘⢄⢣⠘⣂⠎⣼⣿⣿⣿⣟⡯⣝⣳⡟⣿⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠢⡑⠌⡌⢢⢉⠤⢩⣿⣿⣿⣿⢯⣳⠽⡾⣽⣳⣯⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠰⠁⢆⠱⠈⡄⠂⠄⢻⣿⣿⣿⣯⡗⣯⢿⣽⣳⣿⣽⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⢂⠍⡠⢂⠁⠀⠐⠈⡸⣿⣿⣿⢮⡽⣞⡿⣾⣽⣻⣿⣃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠤⠁⠎⡐⠄⠀⠀⠀⠀⠀⡑⢼⣿⣯⢟⡽⣯⣟⣷⣿⣿⡙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⢊⠔⡩⠐⠀⠀⠀⠀⠀⠀⠀⠐⡸⣿⣞⣯⣟⡷⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣄⢣⠰⡁⠎⠄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⢻⣞⡷⣯⣟⣷⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⡊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢤⣳⡾⢇⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⣿⣽⣳⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠌⡐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⣉⣾⢏⣱⢎⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣳⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢂⠥⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡷⡞⡃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡌⠄⢃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡜⡡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣇⡘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⠠⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⡏⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡅⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡁⠀⢘⣇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡨⢄⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠜⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡀⠀⢈⡧⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⢾⡛⡽⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⡡⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠄⡀⠨⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⡭⣭⠱⣜⣦⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⣷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⠀⢰⣯⣧⣤⣄⣄⣠⣠⣤⣤⣶⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣯⣞⡼⣩⢿⡟⠲⠶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡐⠤⠁⣾⣿⣿⣿⣾⣷⣯⣷⣶⣷⣾⡿⢿⣿⣻⢿⣽⣧⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⣿⣷⣷⣾⣧⡑⠌⡐⠠⠀⢀⠉⠙⣻⠟⡛⢳⠲⣖⠶⠾⢾⢳⠷⡾⢶⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣶⣿⣿⡾⢿⠿⢿⡻⢟⡽⣺⢼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣮⣝⣻⣟⡿⣿⣷⣶⣧⣤⣄⣂⣤⣨⢑⣣⠳⣜⣏⡻⣬⢳⣫⡝⣧⢽⣿⣿⣿⢻⣟⢛⡹⠩⠍⠩⢁⠒⠤⢑⠊⡜⢢⡙⢮⡱⢧⣻⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⣟⡿⣿⢿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⢾⡹⣏⠲⡄⠣⠌⣁⠊⢌⠢⡁⠞⣠⠣⡜⢣⡝⢮⣹⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⢻⣜⢯⣿⡐⠦⠡⢉⠉⠉⠉⠋⠛⠛⢛⠛⡟⡻⢟⡿⢿⠿⣟⡿⣻⢽⣿⣿⣯⢟⣿⠳⣌⠱⡈⠤⡘⢄⠣⡘⢔⡡⢒⡍⣲⡙⢮⣹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣞⣟⡮⣗⣿⣍⠲⡁⢆⠐⡀⠀⢀⠂⠡⡈⢆⠱⡑⠮⣜⣣⢟⡼⣳⡝⣾⣿⣿⣯⣛⣿⠳⡌⢆⡑⢢⠑⡌⡒⡡⢎⠰⢣⠜⡴⣩⢓⢾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣼⡝⡷⢾⣧⢣⡑⠌⡐⠀⠌⢀⠈⠤⡑⢌⠒⣍⠺⢴⣩⢞⡵⣣⡟⣾⣿⣿⣳⡝⣾⡝⡜⡄⠎⣄⢃⡒⣡⠱⣈⢇⠣⢞⣡⢳⣋⡞⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⡻⣽⣛⢶⣣⠜⢢⠑⣈⠐⡀⠎⠰⣈⢌⠚⡤⢛⠦⣝⢮⡝⣧⣛⣿⣿⣿⢷⡻⡼⡟⡴⣈⠧⣐⠊⡔⢢⠱⡌⢎⡹⢎⡖⢯⡼⡜⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣟⣧⢟⣳⢮⡙⢆⠱⡀⠆⠐⡈⠑⡠⢊⠱⣌⡙⢮⣙⢮⡽⣲⢏⣿⣿⡿⣯⢷⡹⣿⠴⣡⠒⠥⠚⡌⠥⡓⡜⡬⣓⢭⣚⢧⡳⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⣼⣿⠂⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⣰⣺⣿⠟⠛⢢⡀⠀⢣⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⠃⠀⠀⣽⣿⠃⠀⡞⢁⣿⢶⠋⠚⣿⣠⡀ ⠀⠀⠀⠀⢆⠀⢰⠀⠀⠀⢰⣿⣀⡀⣐⣿⡏⠀⣸⣷⣿⣿⢬⠀⠀⣸⠋⠀ ⠀⠀⠀⠑⠌⢧⢨⣇⡄⠀⣎⣈⡌⠛⢻⢿⣀⢀⡿⣿⣿⡏⣼⠀⢸⠁⠀⠀ ⠀⠀⠀⠱⡄⢢⡷⡆⠷⣾⣼⣯⣿⣧⣼⣏⠻⢾⣷⠀⢻⣷⢸⠀⠈⣆⠀⠀ ⠀⠀⠀⠀⠘⡏⢀⠔⠉⠉⢉⣻⡧⢌⣿⣎⠾⠜⠻⢴⣿⣿⣸⠀⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠘⡎⠀⠀⠀⠿⣽⠓⢄⠈⠀⠀⠀⠀⠀⠉⠻⣛⠒⢤⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⡟⡆⠀⠀⠸⠘⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⣹⡇⠀ ⠀⠀⠀⠀⠀⢀⠀⡟⠆⠀⡐⠃⡄⠁⡆⠀⠀⠀⠀⠐⣶⠒⠒⠒⠋⠋⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠘⡀⠀⠃⠀⡇⠀⠁⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⣡⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠸⡀⠀⠀⠀⠈⣦⡖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⢇⠀⠀⠀⠀⠇⠀⠀⢀⠔⠹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠀⢀⡾⠃⠙⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠙⠲⣤⣠⣄⣀⠀⠀ ⠐⠉⠀⠀⠀⠀⡿⠀⠀⠀⠱⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠑⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠆⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡷⢄⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡆ ⠀⠀⠰⠀⠀⠑⢑⣄⠀⠀⠀⠀⠀⣨⣿⣇⢀⡀⠀⠀⢀⡀⠄⠂⠋⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⣈⡩⠤⠤⠤⠴⠿⠟⠛⠷⠶⢶⣒⠶⠤⣀⡀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣯⡿⣝⣯⠿⣽⢯⣟⡿⣻⣟⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣶⣾⣷⣬⡁⠈⢀⣀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣽⢯⣟⢾⣵⣻⡽⣾⡽⣽⣳⢯⣟⣿⣿⣯⣿⢾⣿⣿⣟⡾⣯⢿⣿⣿⣿⣷⣤⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠁⠊⠀⠁⠀⠀⠀⠀⠀⠂⠘⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⣿⢯⣿⢾⣟⡾⣳⣟⣳⣟⡷⣯⣟⣾⣿⣿⣿⢾⣿⣟⡾⣿⣿⣽⣿⣿⣏⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡳⣞⣿⣿⡯⣿⢾⣽⣳⢯⡷⣯⣟⣷⣻⣽⣿⣿⣿⣿⡽⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣗⣻⣿⣟⡾⣽⢿⣛⣾⡽⣯⢟⣷⣻⢾⣽⣿⣿⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠿⣻⠿⠛⢹⣿⢿⠟⠛⠉⠐⣌⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣝⣾⣿⡟⣼⣻⣏⣿⣹⢺⣟⣵⣫⣶⡿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢀⣠⣴⡾⢋⣽⣿⣯⣿⠋⡔⠉⣼⣿⠇⠀⠀⠀⠣⢌⣻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⣿⣟⢾⣿⡵⣯⢾⣱⣯⣿⣷⢯⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣴⣿⣿⣿⣿⠃⢌⠀⢰⣿⡏⠀⠀⠀⠀⠱⢨⠼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣿⣯⢿⣿⣟⣯⣿⣯⣿⣿⣿⣯⣿⣟⣿⣿⣳⣿⣿⣿⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⢣⠘⣀⡞⢸⣿⠁⠀⠀⠀⠀⢀⠃⢾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣽⣿⣿⣯⢿⣿⣻⣾⢿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣿⢋⢆⠃⣾⠀⣸⡟⠀⠀⠀⠀⠀⠀⠎⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣽⣿⣿⣿⣯⣿⣿⣏⣿⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⢣⢍⣢⣭⡇⢀⣿⢃⠀⠀⠀⠀⠀⢈⢒⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⢰⣿⢾⣿⣯⣷⣿⣿⣿⣞⣿⣿⣿⣿⣦⣛⢿⣿⣿⣿⣿⣿⣿⣽⠏⠉⠗⣚⣩⣾⠟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣷⣿⡏⢠⠃⢸⡟⠰⠀⠀⠀⠀⠀⢌⣺⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠀⣾⡏⣿⣿⡷⣿⣿⣿⣿⣧⣧⣼⣿⣿⣿⣿⣶⡹⢿⣿⣿⣿⣿⡸⢄⠉⠉⡙⣉⠡⣚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣇⡞⠀⣼⠁⠁⠀⠀⠀⠀⠈⡴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⢸⡟⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢾⣫⣼⠗⠀⠙⢟⡻⣿⣷⡂⠀⠀⠐⠀⠂⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃⣿⣿⠟⠀⢠⡇⠀⠀⠀⠀⠀⠀⣘⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢀⣿⠁⠀⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣬⠉⡒⠋⠁⠀⠀⠀⣤⠙⠌⠻⢆⡀⠀⠀⢀⣰⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋⠀⠀⣸⠁⠀⠀⠀⠀⠀⠐⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢀⣾⠏⠀⢰⡿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢡⣁⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠤⠚⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠇⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⣹⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣾⠟⠀⢀⣾⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢎⣀⣀⠄⠀⠀⣤⣠⣤⡀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⠀⠀⢠⠏⠀⠀⠀⠀⠀⠠⣜⡾⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣟⡞⠀⠀⣼⣿⣞⡿⣾⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡼⢏⣵⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠋⠀⢀⣴⠏⠀⡄⠀⠀⠀⣀⢳⡞⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣟⣷⣇⢀⣼⠏⢸⢾⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡲⢤⣄⣀⣠⠖⣏⣱⣾⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠓⢶⣾⠟⠁⠀⡜⠀⠀⠀⡰⣬⠟⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⡳⠋⢸⢾⡾⡟⠀⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣃⢎⠲⣁⠏⣴⣿⡿⢻⢽⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠈⣆⠀⠀⠀⣠⠞⠀⠀⢀⡰⣳⠋⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀ ⣰⣻⠞⠀⢀⣼⣿⣿⠀⢰⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡜⣻⣆⠣⠜⡒⢼⡿⣈⠗⣚⣏⠿⣼⣿⡿⣿⣿⣿⢿⣙⢮⡿⠃⠀⠈⠒⠶⠾⠋⠀⠀⢀⢦⡟⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⡗⠁⠀⣠⡾⢃⣽⡾⣧⡾⣽⣯⣿⣿⣿⣿⣿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣯⣇⠎⡴⢡⢎⠳⡜⢺⣄⢛⣦⢙⡴⢪⠜⣆⣛⣷⣿⣿⣟⢣⠎⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀ ⠀⢀⣾⢋⣴⠟⠁⠻⣽⡿⣿⣾⣿⣿⡟⠉⠉⢿⣄⠀⡸⠛⢉⠛⣿⣿⣿⣷⣮⣛⠍⠲⢌⠣⡜⡄⠛⡷⢏⠲⡌⣧⣻⠞⣋⢶⣿⣿⣏⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⣴⣿⣵⠟⠁⠀⢀⣼⣿⣿⢷⣿⣿⡟⠀⠀⠀⠀⠙⣏⠀⠁⢢⡀⠸⣿⣿⣿⣿⠿⣿⣷⡾⠶⢶⣌⢓⡰⢊⣕⡾⢛⠤⡙⡔⢺⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⣣⣼⡏⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀ ⠟⢏⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠂⣿⣿⣿⣿⣿⣷⣤⡙⣷⣬⡘⠳⠐⢃⠌⡰⢉⠆⡱⢈⣽⣿⡎⢿⡆⠰⣇⠀⡀⢄⠢⣍⣶⣿⣿⡅⢺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀ ⠀⠀⠉⠒⢀⡾⠛⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢠⣿⣿⣿⣇⢻⣿⣿⢿⣾⣿⣷⠀⠁⠂⠌⢀⠁⠂⠁⢰⣿⣿⣷⡈⢻⡄⢹⡖⣈⠦⡿⣾⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀ ⡰⢪⡕⡴⠃⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⣼⣿⠟⣹⠇⠀⢿⣿⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣻⣿⣿⣦⣽⣾⣧⣝⣾⣷⢻⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀ ⢡⣣⠞⠀⣰⣿⣿⢋⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠟⠊⠁⠀⣠⣿⣏⣾⣿⣾⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀ ⠚⠁⠀⢀⣿⣷⠏⣼⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢀⣠⣶⢿⡟⠀⠀⢀⠄⢊⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠒⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣟⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⣀⣤⣾⣿⠟⣉⢾⠇⠀⠐⣁⢶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡆⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣟⣾⣿⣿⣿⣿⣿⣿⣿⠇⢀⣤⠾⠛⠋⠁⠀⠈⡔⣾⠖⢀⠜⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢄⡀⠻⣿⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⣟⡷⣯⣿⢿⣿⣿⡿⣿⣿⣿⡴⠋⠀⠀⠀⠀⠀⠀⠐⣸⡿⠀⠘⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢿⣷⡀⠀⠻⡷⣄⠀⠀⠀⠀⠀⠀ ⡸⠋⠉⠙⢣⣿⣿⣿⣇⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣦⡘⣧⡀⠀⠉⢌⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡛⠁⢣⠀⠀⠀⠡⡘⢆⠀⠀⠀ ⣦⣀⣀⣤⢾⣿⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡚⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⢸⠀⠀⠀⠀⠐⣌⡆⠀⠀ ⢿⡟⠏⠻⢿⣷⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡝⡔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⡇⠀⠀⠀⠀⢸⡷⠀⠀ ⡏⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡹⢬⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⢀⣾⣿⠀⠀ ⢇⡀⠂⠀⠀⠀⠈⠙⠿⣯⠀⠀⠀⠀⠀⠀⢀⠑⡂⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣽⡝⢦⡃⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣷⣄⠀⢀⣾⣿⡇⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠠⢃⡕⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢼⡟⡼⣩⠿⣦⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣌⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⠁⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⢳⡄⠀⢠⠡⢣⠜⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⣹⢾⡙⠶⡡⢞⡩⢷⣯⡰⠡⢄⠠⣀⠀⡄⢠⢂⡜⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⢻⡄⢣⠜⣡⢞⣿⣿⣷⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢤⡷⢏⢧⡙⣣⠕⡪⠜⡡⢞⡹⠿⣮⣵⣦⣹⣬⣷⣾⣾⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢦⡙⢦⡙⢦⣻⢡⣿⣿⣿⣦⣐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣈⣦⢽⢫⠜⡩⢆⡱⢢⠙⠄⠃⠁⠊⠔⢫⠔⢦⠣⣝⢲⣿⠿⣿⡅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⣿⣿⣿⣇⢤⠀⠀⠀⠀⠀⠀⠀⢈⠒⡜⢦⣹⣳⣿⣿⣿⣿⣿⡿⢠⣷⠶⢤⣤⣀⣀⣀⣄⣠⣤⣬⠶⢓⢋⠆⢣⠊⠌⠑⡀⠂⠁⠈⠀⠀⠀⠀⠈⠐⣊⠦⡙⢦⣿⣿⣨⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣿⣿⣿⣿⣿⣶⢄⡀⠀⠀⠀⠀⠠⢩⢜⣣⢷⢃⣿⣿⣿⣿⣿⣇⣿⣿⣧⠀⠀⠈⠉⠉⠈⠁⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢎⣹⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⣿⣦⣿⣥⣤⣀⣀⠂⡇⣞⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣨⡿⢻⣿⣿⠏⠀⣸⣿⣿⣿⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⣿⣿ ⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣾⣾⣿⣯⣿⣿⣿⣏⣼⡿⠛⠙⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣿⣿⣿⡿⣏⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⡿⢸⣿⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣿⡿⠟⠛⢫⡹⠖⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⡿⢻⡇⠉⣹⣿⣿⣿⡟⣿⣿⡿⢀⣼⣡⣿⣿⣿⣿⣿⣿⣯ ⡿⢿⠟⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣁⡤⠒⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡀⠘⢛⣿⣿⣿⣿⡟⢀⣿⣿⣅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⢰⣿⣿⣿⣿⣿⠛⢣⠐⢌⣖⠡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠙⢿⡿⠿⣻⣿⣿⣿⠟⣠⣿⡿⣻⣿⣿⢟⣋⣱⣿⣿⣿⣿⣿⣿ ⣿⢿⢿⣿⣭⡿⠃⠄⠀⡠⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣹⣾⣿⣿⣿⣿⣾⠿⠋⠀⠹⡸⣏⡉⠉⣿⣿⣿⣿⣿⣿⠋ ⡟⠁⢸⡾⠋⠀⢡⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢽⠂⢀⣼⣿⠟⠉⠉⠋⠉⠀⠀⠀⣆⣠⠇⠀⠀⣼⣿⣿⣿⣿⣿⣧⡀ ⣇⠀⠋⠀⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢻⡇⢸⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠏⠉⠉ ⣿⡀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡑⣇⠘⣿⠈⢆⡀⠀⠀⠀⣀⠀⠀⣀⠤⣊⡽⢟⠿⠛⠉⠁⠐⠠⠀⠀

⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀ ⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀ ⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀ ⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀ ⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀ ⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀ ⣾⡿⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠸⣿⡄ ⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇ ⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀ ⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀ ⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢢⣀⡀⠀⠀⢠⣾⣙⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡶⣶⣤⢿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⡿⣰⡾⢭⡝⣿⣾⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣿⣟⡓⠋⠀⠹⣿⡿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣇⣀⠠⠞⠛⠛⠛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠁⠀⢀⠀⠀⠀⣀⠀⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⢢⣸⡵⣁⠽⠐⠒⠚⠓⠳⡤⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⢀⡨⠋⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⡀⠀⠀⠀⠀⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡅ ⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢹⡀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠍⠉⠒⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⠀⢀⣀⢀⣌⡀⠀⠀⠀⣀⠠⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠸⣽⡏⠁⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠒⠠⠀⢠⠛⡔⡤⠐⠀⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡘⠁⠀⠈⠣⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠐⠄⠀⠘⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣄⠜⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢡⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⢽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠜⣣⣼⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠠⢾⠀⠀⠀⠀⠀⠀⠀⠴⡭⢤⡞⢻⠿⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠔⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣼⡆⡄⢀⠃⠀⢸⠀⡀⡇⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⣼⠡⠇⢻⠀⢠⠸⡄⡇⢹⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⢀⢢⡇⢦⠀⣸⡀⢰⠀⣷⣷⠈⣇⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣆⣼⡿⠤⣼⣠⣏⣇⣼⣶⣹⣾⠧⠼⢦⣀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠙⠹⢿⠋⠁⠀⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢄⠀⠀⠀ ⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢢⠀⠀ ⠀⢠⠃⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⢡⠀ ⠀⣼⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⣦⢹⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡄ ⠀⣿⠀⠀⢷⠀⠀⠀⠀⠀⢀⡀⢀⡏⠀⣿⠀⡏⠑⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠃ ⠀⢹⡆⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⣷⠀⣗⢠⡿⠛⠁⠀⠀⠀⠀⢈⡇⠀⠀⢀⠀ ⠀⠀⢿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡎⠀ ⠀⠀⠘⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⡞⠀⠀ ⠀⠀⠀⠹⡇⠀⠸⣆⡀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⠃⠀⣼⠃⠀⠀ ⠀⠀⠀⠀⢿⣦⠀⠹⣆⠀⠀⠀⣀⣤⣿⣿⣷⣄⠀⠀⣀⣴⣿⡧⣀⣼⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⠏⣿⣿⣿⡟⠻⣿⣻⣿⡇⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⣿⣿⣿⡇⠀⢹⣿⣿⣠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣇⣀⢸⣿⣿⣯⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⠇⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣯⢸⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⡏⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⣿⠿⠃⠐⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠁⠀⢸⡏⠁⠀⠹⣿⠀⠀⠀⠘⡇⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠻⠀⠀⠀⠀⢷⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⡱⢈⢆⠳⢌⡚⢬⡑⣌⣢⠟⠉⠁⠀⢢⡀⠀⠀⠀⠀⣀⡴⢺⣍⣿⣿⠏⠀⠀⠀⠈⣿⣯⢿⣻⢿⡏⣜⢺⢿⠀⣿⡄⠀⣸⠀⠀⠀⠉⠓⢮⡐⠄⠰⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡔⡉⠦⣉⠆⡩⢆⠒⡤⠀⠀⠀⡀⠀⠀⠈⠛⠭⣭⣙⣤⡣⠗⢾⣾⡋⠀⠀⠀⠀⠀⢸⣿⣏⣾⡿⡘⢦⡉⠆⡐⣼⡇⢀⠆⡀⠀⠀⣐⣁⣀⣑⡬⠦⠼⠮⠦⣈⣿⣿⣿⣿⣿⣿⣿⡿⣟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢦⠉⢆⢅⢪⠑⣌⠿⣅⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⣀⠈⡱⠤⠤⠤⠄⢈⣿⣾⣿⣵⣽⣯⣴⣵⣶⣿⣷⡿⠞⢋⠉⡉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⡌⠢⢌⠢⢍⡰⢣⡿⣠⠋⠀⠀⡀⠔⠀⢀⡠⠤⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⢿⣛⡩⠱⢋⠡⠘⡀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿ ⠀⠱⡁⠎⠰⠈⡔⢱⡞⠁⠀⡠⠊⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠉⠑⣆⠡⠂⠄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠐⣷⠈⢱⠀⡌⢹⠀⣤⡟⣶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢸⡄⠁⠂⢡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡔⣦⣿⣿⣿⣿ ⠀⢀⢻⣧⡂⠱⢈⡟⣴⡿⠋⠁⠠⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠸⡆⠱⠈⠄⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣿⣿⣿⣿⣿⣿ ⠀⠘⡆⢻⡝⣧⣼⡿⠋⠄⡈⠄⠡⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⡃⢍⡐⢀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⣽⣿⣿⣿ ⠀⢠⢎⣰⣹⣷⠋⠄⡁⢂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⡘⠤⣈⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⡟⢡⠘⠠⠐⢀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡍⡖⢤⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿ ⣿⣿⣿⡟⢨⠆⣈⠁⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⢦⡙⠤⢁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⣿⣿⡟⢌⠲⡐⠠⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⣑⠃⢆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⣿⣿⠜⣨⠱⣀⠃⠄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣯⢘⠢⡁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⢍⢆⡓⠄⣊⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⢏⡒⠡⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⡘⢦⡘⠡⢄⢈⠐⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠤⢿⡢⡙⢄⠃⢄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⡘⢦⢡⠃⢌⠠⢈⠐⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⢆⠀⠏⢷⡈⠌⠤⠈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⡘⢆⠣⢎⠠⠂⠄⢂⠠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢸⡴⡇⢸⠈⡗⡌⠄⢃⡈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⣿⡑⢎⡒⡌⢢⠐⠠⢈⠀⢂⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⢸⣇⠇⠈⣦⡇⠥⠐⡈⠡⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿ ⣿⣿⡜⢥⠚⡤⢃⠜⠠⠀⡈⠄⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⢸⣼⣺⠀⣿⠄⠁⠂⠄⡁⢂⠐⠠⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣿⣿⣿⣿ ⣿⣿⣎⢣⠝⡤⢃⠜⡠⠀⠄⠂⡁⠄⠁⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⢀⡏⣿⡏⠇⢸⠀⠀⠀⠀⠀⠂⠌⡐⢀⠂⠄⢁⠠⠀⠀⠀⠀⠀⠀⢀⢎⣾⣿⣿⣿⣿ ⣿⣿⣧⢫⡜⡰⣉⠒⠤⠁⠂⠁⡄⢈⠐⡀⠁⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣠⡟⠀⣿⣻⢊⣿⠀⠀⠀⠈⢀⠈⡐⢀⠂⡌⠐⠠⢀⠐⠀⡀⠀⠀⣠⠋⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⢚⡱⢌⡱⢊⠡⡈⠔⡀⠂⠄⠠⢁⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢻⠙⢷⡀⣟⡗⣹⢭⣳⡄⠀⠄⡀⠠⠐⢂⠡⡐⣉⠰⢀⠂⡁⢀⢂⡼⠁⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡯⣜⠲⡌⢆⡱⢈⠔⡠⠑⣈⠐⠠⠐⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⡆⢸⣗⡏⣴⢏⡖⢦⡙⣆⠰⢠⠡⡘⢤⠣⡔⢄⠣⠌⡐⢠⡖⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣬⢓⡜⢢⠆⢣⠘⡄⠡⠄⠌⠠⠁⠄⡐⠀⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠞⠁⠀⠀⢸⣷⣿⣿⣿⢏⡞⠼⣑⠮⡰⢍⡆⣣⠙⢦⠱⡘⠌⢆⢱⠼⠃⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡜⣬⢃⠎⣅⠣⢌⠱⡈⠌⢡⠈⡐⢀⠂⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣿⡟⢮⡜⣣⢇⣚⠱⢎⠴⢣⡙⢆⠣⣉⠘⡄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⢆⡏⡼⢠⢋⡜⢢⠑⡌⢄⠂⠅⢂⠐⢈⠐⠈⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⡯⣜⣳⢚⣥⢚⡬⣙⢎⡱⣃⠞⡈⢆⣤⣿⣿⣿⣿⡿⢫⣾⡿⢯⣽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣚⡴⣃⠎⡔⢣⡑⢢⠌⢒⡈⠤⠈⠄⡈⠐⡀⠂⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⡿⣝⢮⣓⢯⢲⡍⢶⣩⠚⣴⣡⣾⣾⣿⣿⣿⡿⠟⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡍⡞⣌⢣⠌⡥⠚⠤⡐⢂⡉⠰⠈⡔⠠⢁⠂⠌⡀⠂⠄⠀⠀⠀⢀⠄⠀⠀⠈⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣜⠧⣜⡠⡛⢤⠣⢄⡘⢃⠤⡀⢇⠠⡘⠠⢀⠃⢠⠀⠄⠀⠘⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣶⣷⣽⣆⣙⢦⡘⡌⢦⡑⣌⠒⡥⢓⡌⣎⣡⣮⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⡿⠟⠩⠄⢢⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣯⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⡩⠁⡔⠈⠆⢡⡟⠀⢀⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣖⢏⡞⡱⢏⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡫⠑⡌⢢⠁⡃⢄⠃⠤⢉⠂⢹⠀⣠⣿⣿⣿⢿⣿⠿⠾⣿⣿⢳⣿⣿⢟⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡮⢜⡱⢣⠜⡑⢆⠢⡅⢫⠍⣋⢛⡛⣛⢛⡛⢛⠩⢋⠉⠉⠉⠉⠉⠉⠉⠙⠊⠓⢺⡿⢋⠔⡃⠔⡡⠒⠠⠡⠌⡠⢊⠰⠈⠀⠁⡰⣿⣿⣿⡿⡿⣿⣿⡯⣝⣞⣬⣿⣿⡸⣿⣷⡸⣯⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⣋⠴⣃⢎⠱⢊⡱⢈⠖⡘⢄⠣⡐⢂⠆⡘⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢃⠅⠊⢄⠣⠠⢁⠃⡁⠆⡁⠆⢁⠂⢀⣴⣿⡿⣩⡵⣿⣏⣭⣾⢳⣾⢻⣷⣾⣻⣷⣿⣿⣿⣯⣵

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⠀⠀⠄⠀⠀⠄⠈⠀⠀⢀⠈⠀⠀⠀⢀⠀⢁⣾⡟⡾⠁⣾⠃⡈⢼⣻⠀⠂⠀⣿⣿⠀⠀⢠⣿⣿⠀⠀⣿⠀⣿⣿⡇⠸⣷⠘⣧⡄⠙⢦⡀⢐⡏⠻⣟⠉⠓⠦⣄⠀⡇⠀⠀⠀⠈⣧⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠠⠀⠁⠀⠀⣼⡟⢸⠇⢸⡿⡄⠐⣸⢹⡄⠡⢰⡿⣿⡄⠂⢸⠹⣿⠀⠀⢻⡆⡿⣿⣷⢤⡘⣷⣜⣿⣷⡶⢽⣶⣧⡤⢹⡗⠄⠀⠈⢹⡇⠀⠁⠀⠀⢿⠀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠐⣸⣿⢁⡿⠈⣿⡗⣯⠀⢼⣿⣧⠐⢸⣇⣸⣿⣾⣿⣤⣿⣆⠀⠈⣿⣽⡘⢿⣽⣧⠀⠙⢿⠛⣷⣄⠠⡇⠀⢸⡷⠀⠀⠀⣼⡏⠀⠈⠀⠀⢸⡀⢿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣿⠃⣼⣹⠖⣿⢹⣿⠀⠸⣿⣿⣿⣿⡿⡿⢿⣟⢿⣿⣿⣿⣇⠀⠘⢎⠳⣈⣿⣿⣷⡀⢸⡀⠈⢿⣦⣇⠀⠀⣿⠀⠀⢠⣿⠇⠀⠨⠀⠀⢸⡅⢸⣈⣷⠀⢀⠀⡀⢀⠠⢀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⢠⣟⣿⣀⢻⣿⣿⡀⢁⢻⣿⠈⠻⣇⠀⢿⣿⣿⣹⣏⣿⠙⠃⠀⠀⠀⠈⠙⢿⢿⣟⡮⣧⣴⣿⣿⣿⣿⣾⣿⡄⢀⣾⣿⠀⠀⢸⠀⠀⣾⠁⢸⡇⣿⡇⢂⢂⡡⠆⠲⣄⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⢸⣿⣿⡆⣻⣾⣿⣧⢂⠸⣿⡀⠀⠈⢄⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣽⣯⡽⣿⡿⢿⢻⣿⡟⣿⡇⡀⠀⢸⠀⣰⢿⠂⢸⡇⢿⡇⠈⠀⠀⠀⠥⡘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⣿⣿⣿⣱⡿⣿⣿⣿⣎⣆⢻⣧⠀⠀⠀⠉⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣷⠆⠘⣽⢟⡿⡽⠀⠀⣾⣸⢿⣼⠀⢸⡇⢸⡇⠀⠀⠀⠀⢢⠑⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣎⡇⣿⣿⣿⣾⣹⣎⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⢄⠀⠀⠀⠀⠀⠢⣍⣛⣛⡁⠀⠈⠁⣸⣿⠃⢀⣸⢯⣿⢸⠍⠀⣾⠇⣼⡇⠀⠀⢠⠘⠤⡉⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⣿⣿⣿⣿⣿⣇⢻⣿⣿⣾⣿⣏⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⡐⢠⡿⣼⠇⣻⢀⣤⣿⢠⣿⠀⠀⠐⢢⡉⠖⣡⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡦⠭⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢧⡜⣤⣿⣷⢿⢀⡟⣼⣿⣏⣾⠃⠀⢠⠉⢦⡘⡘⠴⣈ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⢉⣩⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡣⣟⣼⣯⣿⣏⣠⣿⣿⣿⣿⠟⠁⠀⡐⢂⡍⠲⣌⢱⠣⡜ ⠀⠀⠀⠀⢀⡶⠋⠁⢀⣤⢞⡿⢟⡿⣻⡽⢛⠉⢉⡛⠻⢿⣿⣿⣿⠏⠙⠿⣷⣆⠀⠀⠀⠀⠀⠀⠾⣟⠋⠓⠒⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠘⢉⣡⣾⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠤⡑⢬⡐⢣⡜⢪⡱⢜ ⠀⠀⠀⢠⡟⠁⢀⡴⣫⠞⢉⣴⣫⡾⠉⢀⣼⠏⢋⠀⠀⠀⠘⣿⠻⡄⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠉⢉⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⡜⢠⡑⠦⡘⡵⢊⢧⡙⣬ ⠀⠀⠀⢸⠀⣴⢋⡴⠃⣰⢏⡼⠋⠄⢠⡞⠁⠌⠀⠄⢠⠀⠀⣿⡆⠹⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣿⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣀⣐⡄⢣⠘⢦⡹⡜⣭⢒⡹⡼ ⠀⠀⠀⠈⡾⢁⠎⠀⣼⡿⢋⡴⠃⢠⡟⠀⠀⠀⣰⠀⢸⠠⠀⡇⢳⠀⢻⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⣸⡟⣻⡿⠛⣿⠋⢈⠛⢏⠀⠈⠳⣬⡙⠯⣓⠿⣆⣳⠱⢦⣋⠶⠃ ⠀⠀⠀⢸⢃⡟⠀⣼⠳⢡⡞⠁⢠⡟⠀⠀⠀⢠⡿⠀⠼⡐⣶⠃⢸⠧⣼⠃⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⡀⠀⠀⣀⣀⣤⣴⣶⣿⣿⠃⠀⠀⠀⢰⣿⢟⣡⡟⢠⡿⠀⡊⢱⠈⠙⢦⣄⠈⢿⣳⣌⠳⣬⡛⢿⣢⣽⠁⠀ ⠀⠀⠀⢸⢸⡇⢰⠏⣰⡿⠀⢀⣿⠁⠀⠀⢠⣿⠇⠀⢃⣼⡏⠀⣾⢡⡏⠀⠀⠀⠘⠀⠨⣷⣻⣿⡳⣟⡿⣻⢟⡻⣽⢿⣿⣿⠛⢹⠀⠀⠀⠀⣿⢋⣼⡟⠀⢸⠇⠀⠀⢰⡆⠀⠀⢻⣧⠈⢷⡹⣦⡈⢿⣦⡙⢇⠀⠀ ⠀⠀⠀⠸⣿⡆⡟⢠⣿⠁⠀⣸⡇⠀⠀⠀⣾⠝⠀⠘⣰⠏⠀⢰⣧⡞⠀⠀⠀⠀⠀⠀⠀⣿⠡⢻⣿⡼⣳⢏⣯⢳⣭⠟⠁⠀⠈⢺⠀⠀⠀⣼⡏⣼⣿⢀⠀⣻⠀⢸⠀⠘⡇⢀⠀⠈⢾⡧⡈⢷⣹⣧⠸⡿⠉⢻⡳⡄ ⠀⠀⠀⠀⠙⣿⡇⣾⡇⡀⠀⣿⠀⠀⠀⣸⠃⠀⠜⣸⡏⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣯⠱⠀⠘⣻⣵⣫⣾⡿⠃⠀⠀⠀⠀⢸⠀⠀⢰⣿⡡⣿⣿⠀⢂⣿⠀⢸⠀⠀⠇⢸⡄⠀⠈⢿⣱⠈⢿⣿⢀⡇⠀⠀⠱⡄ ⠀⠀⠀⠀⣠⣿⢰⣿⢰⡇⢸⡏⠀⠀⢰⡇⠀⠀⢰⠋⡇⢠⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢢⡕⠃⠀⠀⣡⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⢻⣿⣿⣿⠀⣸⢸⠀⣿⠀⠀⠈⢸⡇⢠⡀⠘⣿⣇⠸⡯⡼⠃⠀⠀⠀⢻ ⠀⠀⠀⢰⡿⣿⣼⡇⣿⡇⣸⡇⠀⠀⣾⠃⣀⢸⡏⠀⢧⢿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠐⡀⢇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⣇⠚⣿⣯⣿⣇⢾⡘⢿⣿⡇⠀⠀⠀⣿⠘⡇⠀⢹⣿⡤⢿⠁⠀⠀⠀⠀⠈ ⠀⠀⠀⣿⠁⣿⣿⡱⢏⡇⣽⡇⠀⠀⣿⢰⡇⣿⠁⠀⢸⡾⠀⠀⠀⠀⠀⢀⡤⠖⢛⣿⡖⠐⠀⠸⡄⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣸⡏⠛⠾⣽⣿⣿⣿⣿⡇⠈⣿⣿⡀⠀⠀⢻⡄⣷⠀⢘⡿⣿⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⠀⢹⣿⣱⢋⡇⢿⣇⠠⠀⣿⡿⣾⡟⠀⢀⠀⣹⣀⣠⡤⠶⠋⢡⠤⠂⠀⢸⣧⠀⠀⠀⣧⠀⠀⠀⠀⢀⡏⠃⠀⠀⠀⢀⣿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣤⣿⣽⣷⣀⡀⢸⠅⣿⠀⢸⡀⢸⡀⣷⠀⠀⠀⠀⢀ ⠀⠀⣿⠀⠀⠀⢻⣧⢋⣧⢹⣿⣸⣆⣿⣥⡟⠋⠉⠉⠉⠀⠐⢲⣤⣦⣅⣑⣲⣤⣀⠀⣿⡆⠀⠀⠙⠂⠀⠀⠀⡞⠀⠀⠀⠀⠀⣼⣏⣤⣭⡕⠒⠒⠊⠀⠁⠀⠀⠀⢠⠀⠈⠉⠙⠛⢻⣥⣸⡇⢸⡇⢹⠀⠀⠀⢀⡞ ⠀⢀⡇⠀⠀⠀⠘⣯⣟⣹⡼⣿⣽⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠿⠿⣿⠧⠿⠟⠻⢄⠀⠀⣠⠤⠛⠛⠀⢀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⢨⡇⣼⠀⠀⠠⠋⠀ ⠀⢸⡇⠀⠀⠀⠀⠹⣶⣣⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡏⠀⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⢈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⢀⡞⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡗⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⣄⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⣿⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⣶⣶⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⢆⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣭⣭⣭⣭⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢎⡰⠀⠄⠀⠀⠀⠀⠀⡐⢈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⢒⠡⠀⠄⠀⠀⠄⠡⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡌⢣⠈⠄⠡⠈⠄⣁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣦⣤⣤⣤⣤⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠈⢆⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠣⡜⣡⠊⠔⣹⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠌⠠⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡝⠴⡡⢎⠰⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⢀⠂⠡⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢚⠥⡓⣌⠢⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢈⠡⢀⠀⠀⠄⠂⠌⠐⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢎⠲⡱⢨⡑⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣆⠐⡡⠐⣀⠂⡁⠎⣘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢣⡑⢣⡘⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠻⣧⣀⠱⢀⠆⣑⠢⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠚⡄⠃⡜⠰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⢄⡀⠛⠳⢌⠒⠤⡃⣽⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠐⡡⢂⡑⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠁⢂⠰⢁⠲⠨⠜⡰⢱⣿⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠘⠄⡡⢐⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢻⡌⠐⣀⠣⢌⡑⣊⣴⡿⠃⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣆⠈⠔⣡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢿⣆⢀⣢⡴⢺⡿⠋⠀⠀⠀⠀⠀⠀⢠⢟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣹⠀⢦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⢿⣌⣳⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠴⣩⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⡰⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣲

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢱⣹⣿⣿⣿⣿⣿⠟⢻⡛⢿⣹⣇⢻⣦⢂⠣⣱⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢷⢰⢸⣿⣿⠛⣿⠉⠀⠀⠀⠙⡄⢻⠙⣼⣿⣿⡄⠁⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣿⠀⣸⣿⡇⠀⣿⠀⠈⠓⠲⣶⡿⢾⣷⣿⣿⣿⣿⣦⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢰⣿⣷⣻⣿⡞⣦⠐⡄⠀⠀⠀⠀⠀⠀⠻⣿⣯⠙⢦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⣷⣿⠿⢏⡁⠀⠂⢉⡤⣠⡀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠈⠳⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡾⠁⠀⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⣠⡾⢫⣿⠀⠀⠀⠀⠀⣉⣛⣻⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣥⣿⠁⠁⠀⢸⠿⣆⠀⠀⠀⠀⢿⡿⠿⢿⡿⠀⠀⠉⣁⡴⠟⣿⣤⠴⠖⠋⠉⠉⠉⢯⣥⣤⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢖⠀⠀⠉⣁⡠⠞⠉⠉⠉⠉⠙⠻⢿⣆⣀⣀⠀⠈⣣⣤⡴⣃⡀⢂⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⢴⠒⣩⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠺⣉⠁⠀⠀⡈⠉⠐⣂⠤⠴⠦⢝⣉⡉⠹⠟⠀⠠⠄⠈⠉⠩⢭⣙⠒⠤⠤⣀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣡⠴⠊⠁⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠀⠀⢀⣡⣤⣤⣽⠀⠀⠀⠀⠈⠁⢲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠹⠦⢶⣽⣶⠂⠀⣠⣾⠧⠖⠊⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢢⡀⠀⠀⠀⢀⣤⠼⢥⣿⣇⠀⡿⠿⠛⠉⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⠈⠙⢻⢯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⣿⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡌⢆⠀⠀⠀⠀⠀⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⡸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⣿⡼⣿⠀⣷⠀⠀⠀⠀⣰⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢆⠀⠀⠀⠐⣿⡇⢿⢹⣟⠀⠀⠀⠰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⢢⡀⠀⠀⠹⣳⣸⠟⡜⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⢔⡮⠒⠒⠒⠂⢌⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⢿⠆⣤⣀⠀⠀⠈⠪⡢⡈⠳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⢠⣤⣸⠿⠓⠛⠦⢔⢄⡈⢟⢞⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⢫⡅⢠⠀⠉⢩⣭⡿⢿⣾⣼⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⡄⠀⢣⣌⣤⠀⠀⠈⠀⠈⢹⣿⠇⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠙⡈⠐⢕⡅⠀⠀⣀⣔⠆⡜⠇⠀⠀⠔⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠠⣙⡖⠀⠭⢄⡞⠁⠀⣴⠊⠀⠀⣧⠀⠃⠀⠀⠀⢀⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⡐⠈⠀⠈⠤⣤⣤⠠⠀⠈⠁⠀⠀⠀⠘⢧⢸⠀⠀⠠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡤⢈⡎⡄⢀⠁⠀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⠀⠈⢻⠀⠀⠀⠀⠘⡄⠘⠫⠧⠶⠻⠠⡈⡎⠀⠀⡄⠡⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⢀⠀⠀⠣⣀⠓⠀⡴⠁⠀⠀⠀⠀⠐⠒⢲⠀⠀⠀⠘⢄⠈⠂⡀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠉⠪⢄⠀⠀⠀⠀⡔⠁⠀⡘⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱⡆⠀⠚⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⡀⠀⠘⡄⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⡀⠄⠒⠉⠁⠀⠀⠀⠀⠈⠳⣄⠀⠈⢦⡀⠀⠀⠀⢣⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⡄⠀⢀⠀⣀⠀⠤⠉⢳⡄⠈⢌⢢⢀⢠⡤⣡⠔⠺⡧⠬⢶⠀ ⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⣄⡀⠀⢻⢄⠀⠑⢿⣾⣿⣾⣷⣾⣧⣄⣀⣧ ⠀⠀⠢⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣵⠯⠜⢀⣠⣤⣝⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠤⠤⢠⠒⡒⠉⠉⡇⠀⡄⠀⠀⢰⡄⠀⠀⡱⣃⠠⡀⠀⠱⡀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠃⠀⢠⣷⠀⡇⡀⠀⠘⣿⠀⠀⠸⣿⠀⡷⠀⠘⣧⠀⢃⠀⠀⢠⠀ ⠀⠀⠀⡾⡀⠀⠀⢸⠈⢆⢹⡇⠀⠀⣣⡷⠖⠂⢟⣄⠋⠷⢲⠟⡆⠈⡆⠀⠀⠤ ⠀⠀⢀⠻⣧⡇⠀⢸⠒⠸⣾⡹⠔⠒⠛⢠⡰⣞⣨⣯⣤⣀⠈⡎⠑⠀⢰⠀⠀⠀ ⠀⠀⣟⠋⠉⠳⠂⠙⡆⠀⢳⡉⠉⠉⠉⣯⡾⠟⡹⠀⠀⠉⡷⠇⡀⠀⠀⣇⠀⠀ ⠔⢲⣾⣅⣴⠾⡿⣿⣿⠆⠐⠁⠀⠀⠀⠋⠈⣉⣤⡤⠤⢔⢅⢀⡇⠸⠀⢹⡄⠀ ⠀⣸⡟⢿⡇⠀⣈⣒⣂⢀⠴⡀⠀⠀⠀⣠⡿⢫⠎⢔⠔⣽⣫⠞⢳⡆⠀⢸⢱⡀ ⠀⠃⣧⠈⢃⣏⣝⢔⡧⠒⠀⠀⠀⠀⠈⠁⠀⠀⠐⢁⠝⠉⠧⠀⡰⢠⠀⠈⠀⣷ ⠀⢸⣾⣧⢐⢫⠊⠟⠀⠀⠀⢀⣀⠠⠄⣀⠀⠀⡠⠁⠀⠀⣀⡴⠑⡿⠀⠀⠀⠼ ⢇⠘⣿⡏⠲⠅⠈⠀⠠⣄⣔⣥⣶⣾⣿⣶⣿⣿⠃⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀ ⢸⠢⡘⢿⡄⠀⣸⠀⠀⠈⣿⡟⠛⣿⠟⠉⢹⠏⠀⠀⠀⠀⠀⢀⣼⣿⡇⢠⠀⢀ ⡽⠀⣸⣷⣾⣶⡒⠁⠀⠀⢘⠁⠀⡏⠀⠀⣾⠀⠀⠀⠀⢀⣠⣿⣿⣏⡳⣸⢄⠈ ⠑⠚⠿⣿⣯⣿⢈⣷⣄⡀⠰⠀⠠⠇⠀⡠⠓⠃⠀⣀⣴⣿⣿⣽⣿⣿⢧⣿⣜⠦ ⠀⠀⠀⠈⠙⠷⡾⣿⣿⣿⣶⣇⠀⢠⠎⠀⢀⡤⣚⣻⠿⠟⠛⠉⠉⠁⣾⡗⠙⢆ ⠀⠀⠀⠀⠀⠀⠈⠢⡈⠉⠉⠉⠹⠉⡶⠾⠓⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠁⠀

⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢃⢸⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣼⣿⠿⠧ ⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠏⠀⢀ ⠹⣿⣿⣿⡏⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⣸⠃⢀⡔⠁ ⠀⠘⢿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠀⢀⣿⡶⡡⢀⠀ ⢠⠐⡀⢻⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢼⣿⠡⠁⡎⠀ ⡀⠇⢱⡀⣿⣿⣿⣦⣤⣀⡤⠞⠀⠀⠀⠀⠙⢦⣀⣀⠀⣀⡤⠋⣾⣿⣅⢼⠁⠨ ⡇⠘⢠⢇⢹⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⢸⣿⣿⣷⡘⠀⠀ ⢃⢀⠌⠀⠼⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠛⠚⠀

⠀⠀⠀⠀⠀⠁⠒⠤⣀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢷⣦⣤⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢂⣀⣀⡀⠀⠀⠀⢸⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠤⠒⠊⠁⠀⢀⣀⠴⠬⣭⣖⡼⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠈⠉⠀⠀⠉⠉⠙⠛⣿⣷⣬⣼⣿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠛⠿⣧⣬⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠐⠒⠂⠤⢀⡉⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⢿⣤⡀⠀⠀⠀⠀⠀⢀⣔⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⠒⢄⣀⣠⣵⣟⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⣋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢌⡱ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢢⢽ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⢣⣿ ⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠖⣿ ⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡹⣿ ⣿⣿⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢤⣳⣿ ⣿⣿⣞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠡⠀⠀⠀⢀⠂⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⢄⡱⢎⣿⣿ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⢂⠑⡄⠣⠘⡀⠂⠌⠠⡁⢂⠐⠠⠀⢄⠀⠀⠀⠀⠀⠀⡀⠄⠠⠌⠠⠈⠄⠁⠄⠂⢀⡀⢎⣖⡽⢺⣿⣿ ⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢺⡄⡃⢆⠢⠑⠠⠐⢂⠡⠌⡐⠄⠂⠌⡐⢀⠂⠄⠂⠤⣁⠐⠂⠄⠂⠄⡐⠠⠀⡄⣌⠱⣺⡝⡱⢎⣿⣿ ⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⡑⢆⡽⣵⠈⡄⠃⠌⡐⠀⢂⠒⢀⢊⠌⡐⠠⢂⠌⠌⡑⠂⠄⠉⠐⠈⢀⠂⢄⠡⢃⠴⠈⠓⠁⠌⡱⢫⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠊⡴⣉⠶⣜⣻⣷⠈⢇⠐⡀⡍⢂⠀⢆⠈⡐⠠⢁⠂⠌⠐⠀⠁⠀⠀⢀⠈⠄⡈⠄⠂⠁⠀⠀⠀⢔⡞⣡⢛⣿⣿ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣀⠣⣒⠱⣎⣷⡭⣿⣛⣌⠱⣐⡔⣧⠐⡀⠃⡀⢁⠂⡈⠠⠐⡈⠄⢂⢌⠠⢈⠐⠀⣀⠂⢄⢂⡱⢚⢭⡑⢬⡟⣾⣿ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡰⢠⠓⣌⡳⣽⣺⢷⣹⣷⣾⣧⣿⡟⡥⢒⢤⣑⣌⣆⣦⠵⠄⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠹⣎⣇⡐⠢⢹⣿⣿ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢃⡔⢃⠞⣴⢻⡼⣯⣟⣧⢿⣿⣿⣿⣿⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠁⢀⣿⣿⣿ ⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⡈⢆⡜⣌⠻⣜⣯⣟⣷⡿⣞⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⢸⣿⣿⣿ ⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⢢⠐⣡⠒⣌⠖⣯⡽⣞⣯⣿⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿ ⠈⠄⠂⠠⠀⠄⠀⠂⢈⠐⡀⢆⠡⣊⠴⣉⢦⣛⡶⣿⣻⣿⣽⣯⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⠃⠜⠠⢀⠘⠀⢃⠘⡀⠄⡠⠘⣄⠣⣄⢣⡜⣧⢿⣻⣿⣟⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⡘⠤⢁⠂⢌⠐⢂⠰⢠⠑⢢⢍⡰⢣⢜⡲⣽⣞⣿⣿⣟⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿ ⠰⡈⢆⠨⠄⣊⢄⠣⢜⡨⢃⠦⣑⣣⢞⡽⣾⣽⣿⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿ ⠱⢌⠢⡑⢬⡐⢪⠜⣢⠱⣩⠖⣥⢳⣯⣟⣷⡿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿ ⡍⢆⡓⡜⡰⢌⡣⢎⡥⢳⢥⢻⣜⣻⢾⣽⣿⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣢⣀⣤⡶⠧⠬⠷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⢋⣠⡤⢤⠶⣤⣀⠫⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠒⠺⠀⡯⣀⣷⣼⣶⢷⣼⣿⣯⣛⢷⣦⣤⣤⠀⠀⠀⠀⢀⣠⡶⡏ ⠀⠀⠀⠀⠀⠑⡇⣴⠣⣿⠻⠿⠧⠿⠿⠿⢿⣿⣿⣿⣷⠋⠀⠀⢀⡴⠋⡸⢱⠀ ⠀⠀⠀⠀⠀⠀⢧⢿⣙⣧⣶⡍⠃⡀⠀⡆⣈⣿⣿⣿⣿⣶⣶⢾⣽⠁⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⡎⠀⠀⢠⠤⡌⡿⠛⠉⠉⢹⢣⢣⠃⡇⠀⠀⣇⠀⢀ ⠀⠀⠀⠀⠈⢃⠀⠙⣿⣿⢷⣤⣠⣤⣡⣼⠁⠀⠀⠀⠸⡜⡌⢆⠘⠆⠀⠈⠢⣈ ⠀⠀⠀⠀⠀⠈⡄⠀⣿⣿⡿⠟⠛⠛⢿⠋⣐⡒⠖⠒⠛⠛⣿⠦⣉⣲⣦⣤⠤⠼ ⠀⠀⠀⠀⠀⠀⢱⠀⠀⡜⠁⠀⢀⡴⣳⠏⠬⠦⠀⠀⠀⠀⢻⡷⠋⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⣼⠀⠀⣰⢟⠾⣡⠖⠂⠉⠉⠉⠉⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢠⣞⠭⢷⣴⡷⡫⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⠫⡓⣍⠒⢔⠀⢂⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠈⠈⢢⠀⣷⣧⣿⠋⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⡄⠀⢸⡿⣻⡿⠁⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣼⡧⠔⠋⠉⠉⠃⠀⠀⠀⠀⠀⣶⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠳⣣⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠭⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢀⣾⠤⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡫⠡⠀⡨⠭⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⡡⠒⡠⠥⠆⡐⢌⢢⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⢃⠞⣠⠊⠐⠀⡀⡸⡄⠲⣄⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⢁⠎⣠⣿⣰⡷⣾⠱⣴⣹⡄⠈⡆⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⣼⢠⣿⣿⣿⠿⢃⠀⠈⣿⠟⢹⣿⣾⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡧⣿⣿⠁⠉⠁⠀⠉⠿⢒⠏⣙⣾⣿⡧⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠙⣿⣿⣦⡀⠀⠀⠀⠀⢁⡴⣿⣿⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣌⡦⢤⡴⢊⠗⢁⣻⣿⣤⣀⠀⠀⠀⠀⠀ ⠀⢀⠐⣈⣾⣿⣿⣿⣿⣿⣿⣬⣹⣄⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀ ⢰⣾⣶⣿⣿⣿⣿⣿⣿⣯⣭⣍⢛⠛⣛⠻⣿⣿⣿⣏⠹⢟⠻⣿⠀⠀ ⣸⣿⣿⣿⣿⣿⡫⠿⢟⡿⠿⣿⣿⣾⣿⣿⣥⣾⣿⣯⣠⠊⣸⣿⡇⠀ ⠹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠑⠶⠤⠄⠈⠉⠩⢝⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⡄⠐⡀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠈⠛⠛⠛⠑⠒⠒⠉⠀⠀⠱⣄⡀⠀⣀⠴⢙⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡆⠀⠹⣿⣿⣿⠟⠀ ⠀⠀⠀⠀⢀⣴⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⢀⣾⢱⠡⠂⠁⠂⠠⠤⠤⠤⠤⠐⡚⢳⠑⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⡌⠀⢀⠀⠉⠑⠐⠂⠰⠂⠉⠰⠀⡆⠸⡷⡀⠀⠀⠀⠀ ⠀⠀⢸⢣⢃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣴⠀⡆⠸⡀⢱⡰⡀⠀⠀⠀ ⠀⢀⡏⣸⠸⠀⣈⠀⡄⠀⠄⠀⠀⢰⠀⠘⡄⢰⠀⢡⠀⢧⢱⠀⠀⠀ ⠀⢸⣤⡟⡄⠀⣿⠀⡄⠀⠀⠀⠀⠈⠀⠀⡇⠀⡇⠈⣆⣸⡟⠃⠀⠀ ⠀⠀⠀⢿⣗⣦⣇⠀⠀⠀⡀⠀⠀⠀⡇⠀⢷⠀⣽⣶⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠸⣯⠙⠿⣵⣷⣦⣇⢀⣆⠄⣷⣄⣾⠿⠋⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⢈⣻⣿⣙⣻⣉⡉⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢠⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⡇⢠⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⠘⣿⣶⣶⣶⣖⡀ ⠀⠀⠀⠀⢀⡤⣲⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢰⣿⣿⡿⠋⠉⠙ ⠀⠀⠀⣴⣯⣏⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣼⢿⢻⠀⠀⠀⢀ ⣦⣤⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣿⡊⠀⠀⠀⣠⠞ ⠈⠿⣿⣿⣿⣿⣿⣿⠀⣰⣳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣷⡏⢇⠀⠀⠀⠀⣿⡇⠁⠀⣠⠟⠁⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣿⡟⠀⠀⠀⢰⣿⣷⣶⠊⡅⠀⠀⠀ ⡀⠀⢀⠈⢻⣿⣿⣿⣆⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⠃⡼⠁⣰⠆⠀ ⠹⣄⠀⢧⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⠃⡰⠁⢀⡏⠀⢀ ⠀⢻⡄⠘⣆⠀⢻⣿⣿⣿⣯⣦⣀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠈⢿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣸⣿⣿⢠⠃⢀⣾⠁⠀⢈ ⡇⠀⢿⠀⢹⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣴⣶⣤⣤⣤⡶⠛⠁⢀⣿⣿⣿⣞⡆⢻⣿⠀⠀⠏ ⣷⠀⢨⠃⢠⣧⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢠⠀⣸⣿⣿⣿⣧⣿⠚⠻⠀⢸⠀ ⡏⠀⡸⠀⡾⠈⢧⣈⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣂⣀⡇⠀ ⢱⡀⢁⡰⠁⠀⠀⢛⡛⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡿⠉⠉⢉⠁⠀

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⡘⠦⡑⡌⢆⠣⡜⠤⠣⢜⡠⠣⠜⠤⡓⢬⢣⡝⢮⡽⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢀⢲⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠹⣟⢿⣿⣇⠀⠀⠀⠀⢀ ⢌⡱⠘⡌⣌⠣⢌⢣⢉⠆⣡⠣⡙⢢⡙⢆⡣⢞⡱⣞⡵⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠀⠀⢨ ⠢⢌⠓⠬⠤⡙⢂⠎⡔⢊⠤⢃⠥⣃⠜⡢⢝⢮⡱⢏⣞⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⡜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣿⡇⠀⠀⠀⠀⢆ ⡑⢊⠍⠲⣁⠎⡅⢎⠰⡉⢆⠩⡒⢌⡜⡱⢎⠶⣙⢯⡞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣗⢀⢂⠀⠀⠀⠀⢡⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⢿⣇⠀⠀⠀⡈⠤ ⢨⠑⣊⠱⣐⠪⠔⣊⠱⡈⢆⠱⡘⢤⠚⡴⢩⠞⣭⢺⡝⣷⣿⣿⣿⣿⣿⣿⣿⣿⠡⡈⠄⠀⠀⠀⠀⠀⣍⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣽⣿⡄⢠⢁⠐⡈ ⢠⠓⡄⢣⠢⡑⠣⠌⢆⠱⡈⢆⡑⢢⡙⠴⣋⠞⣜⢧⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡄⠡⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⢺⢯⣿⣿⣖⡠⠀⠠ ⢂⠱⡈⢆⠱⢌⠣⡉⢆⠡⡘⠠⠌⡅⢎⡱⢎⡝⣎⡳⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠈⠂⠀⠀⠀⠀⠀⢣⢛⣾⣿⣿⡇⠀⠀ ⠈⢆⠱⡈⢎⠰⢃⠜⡠⠃⡌⠱⡈⢆⠣⡜⡜⣜⠲⣝⢯⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣆⠀⠲⣤⠀⠀⠀⡀⠀⢊⣿⣿⣿⣿⡒⠄⠀⠀⠀⠀⠀⢌⡳⣞⣿⣿⣷⡀⠀ ⠘⡄⢃⠜⡠⢉⠆⡘⢄⠣⢌⠱⣈⢌⡓⢜⡰⢎⡝⢮⣻⣿⣿⣯⣽⡳⢿⡽⣿⣿⣿⣿⣧⠀⠈⢠⠀⠀⠈⠄⡐⠸⣿⣿⣿⣷⡈⠠⠀⠀⠀⠀⠀⢱⢻⣼⣿⣿⣧⠀ ⠐⡈⢆⡘⢄⠣⡘⠌⢢⠑⡌⠒⣌⠢⠜⢢⡑⢮⡜⢧⣿⣿⣿⣳⡾⣙⢧⢻⣽⣿⣿⣿⣿⣧⡀⠠⠄⠀⠀⠐⠔⡩⢞⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⡙⣧⣿⣿⡟⠀ ⠠⢁⠆⡈⢆⡑⢌⡘⠄⠣⢌⠱⡠⢍⢪⠱⡌⣇⢞⣧⣿⣿⣿⡛⠆⢡⢊⡷⣻⣿⣿⣿⣿⣿⣆⠀⠈⠤⠀⠀⠐⠗⠬⣻⣿⣿⣿⣇⠠⡀⠀⠀⠀⠀⢱⢋⣿⣿⠃⠀ ⠐⠠⢂⠡⢂⠌⢂⠔⡉⢒⠈⢆⠱⠌⣆⠳⡸⢬⡻⣼⣿⣿⡷⢉⠐⠀⡌⢷⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠃⠀⠀⠀⠐⠳⣿⣿⡯⢿⣆⠀⠀⠀⠀⠀⢡⢪⣿⠏⠀⠀ ⠈⡐⠄⠢⢁⠌⠠⢂⠐⡈⠜⡠⢍⠚⡤⢓⣭⢳⡽⣿⣿⣿⡑⠂⠀⡀⠘⣧⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢣⣿⣏⡻⣿⣆⠀⠀⠀⠀⢠⣿⢟⡀⠀⠀ ⠐⠠⢈⠐⢂⠈⡐⠠⢁⠒⡈⠔⡌⢣⠜⣣⢎⣿⣽⣿⣿⢣⡑⠈⠀⡄⠱⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢿⡇⣱⡟⣿⣆⠀⠀⠀⣿⡟⠸⠂⠀⠀ ⠀⠂⠄⢈⠀⢂⠠⢁⠂⠤⠑⡌⡰⢃⢾⣴⣿⣿⣿⣿⣯⠳⡉⠔⡰⢉⢶⣹⣿⣿⣿⣿⣿⣿⡿⣟⢣⡟⣕⠀⠀⠀⠀⣠⠈⣽⢃⠖⣿⣿⣿⣶⡴⢹⣿⠀⠀⠀⠀⠀ ⠀⠀⠄⠂⠀⠄⡐⠠⡈⠔⡡⢢⢑⣎⣷⣿⢿⣻⣿⡿⠧⠓⠄⡑⢤⡛⣮⣿⣿⣿⣿⣿⣿⣿⠳⡌⢧⡟⡾⣆⡀⢸⠝⠁⢸⡏⢸⠸⣽⣿⣿⣿⡇⣾⠉⠀⠀⠀⠀⠀ ⠀⠀⠠⢀⠁⢂⠤⠑⡈⢆⠡⡖⣭⣾⡿⣏⠾⣽⣿⣏⢰⠋⠑⡄⣣⢽⣿⣿⣿⣿⢯⡝⣿⡏⠱⡘⢄⠻⣵⣻⣆⠸⠀⠐⣎⠔⡘⢥⣛⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⡈⠄⠂⠤⢁⠂⢆⣽⣿⡿⡱⢯⣾⣿⣟⡿⠎⠀⡰⣡⢟⣾⣿⣿⣿⠉⢿⣷⣿⣽⠆⡀⠉⢆⡙⢧⣿⣆⢳⡼⠛⠠⡘⢆⡻⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠄⡁⠂⠄⡘⣸⣿⣯⠳⣍⢣⣿⠍⡾⠇⠀⡰⣱⣯⣿⣿⣯⣿⣿⡆⠹⣿⣿⣿⡿⣷⢯⣮⣝⣮⣳⣿⣷⠏⢁⠞⡠⢍⡞⣷⣻⣿⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢈⠀⡐⠈⡐⠀⢿⣿⣳⡟⣼⢱⣿⣾⣋⣴⡶⣷⣿⣿⣿⣷⣿⡟⣾⣧⠲⡈⠉⠙⠿⣯⣿⣾⣯⣿⣿⣿⠋⠀⠀⡰⢁⠎⡼⣳⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⢀⠂⡐⠀⠤⢙⣿⣿⣳⡿⠃⢨⣿⣿⣿⣾⣿⡿⣿⣹⣿⡿⠛⡸⡽⣿⣇⢌⠒⢄⣀⡙⠻⣿⣿⣿⣿⠏⠀⠀⠤⢳⠊⡼⣵⣿⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠄⠂⡐⠠⢁⠂⣥⢾⣿⣿⠻⠀⠀⢻⣯⢻⡽⣭⣷⣿⡿⠋⢠⢜⡳⣝⣻⣿⣦⡝⢢⣌⢲⡀⢹⣿⣿⠏⠀⠀⠀⠐⢃⣾⣿⣿⠏⡐⠡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⠀⠂⠄⢡⠂⣜⠶⣿⣿⡿⠀⠀⠀⠩⣿⢧⣿⣿⣿⠏⢠⡜⣣⣾⢻⣼⣻⣿⣟⣯⢱⢊⠖⡇⠸⣿⠏⠀⠀⠀⠀⣈⠰⣾⡿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠡⠈⠤⣸⣌⠘⣼⣿⡇⠀⠀⠀⠆⣿⣿⣿⣿⠇⢐⡳⣾⡽⣣⣟⣏⣿⣿⣞⡷⠎⣍⡾⠁⣸⠟⢀⠔⠀⠀⠰⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⠐⢀⢣⡖⢠⠐⠤⣹⣿⠁⠀⠀⠀⠀⠛⣿⣿⣏⠀⣬⢳⡝⣞⡵⣞⣿⣿⣿⢾⣳⢩⡼⠁⣴⠟⠀⠆⠀⠀⠐⢣⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠂⠄⢂⠓⡠⠍⣒⣹⣿⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⡣⣟⡼⣣⢿⣽⣾⣿⣿⡿⢁⡚⠀⢼⣵⠆⠀⠀⠀⠀⠀⡍⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠈⡐⠠⢡⠘⣤⡳⣿⡿⠀⠀⠀⠀⠀⢀⠸⣹⣧⣄⠀⡽⢷⡹⢾⣹⣿⣿⣿⠆⣷⢡⢠⣟⠃⡀⠀⠀⠀⠀⠠⡔⠋⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡀⠡⠀⡅⢢⡑⣞⣵⣿⡇⠀⠀⠀⠀⠀⠈⠃⠠⣿⣧⣄⠋⢿⡽⣯⢷⣿⣿⣿⣛⠬⡙⣿⠁⡐⠀⠀⠀⠀⠀⠰⣈⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠁⠂⢄⠡⢌⣳⡟⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠆⣯⣟⡿⣄⢚⡷⣯⢾⣿⣿⣿⣟⡦⠓⡏⠰⠃⠀⠀⠀⠀⢐⡢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⢂⠁⢆⡼⢋⡜⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠒⢷⢧⣏⢿⡽⣧⢻⡿⣿⣿⣿⣿⣏⡷⣾⡱⠁⠀⠀⠀⠀⢀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢈⠰⣈⠣⣐⠣⡼⡛⠀⠀⠀⠀⡀⠀⠈⠁⠀⠈⢀⠊⣽⡎⢿⡽⣿⣿⣿⣿⣿⡿⠉⣼⠏⠀⠀⠀⠀⠀⠠⢂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢈⠰⠀⢅⠂⡝⠂⠁⠀⠀⠀⢀⡃⠁⠀⠀⠀⠀⢸⠹⡞⣷⢈⠛⣷⣿⣿⣿⡿⢁⣾⠟⡀⠎⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⢀⠁⡂⠌⠠⢈⠐⡀⢁⠠⠀⠅⠠⢄⠀⠀⠀⠈⢦⠳⣹⣏⡄⠜⣿⣿⣿⠁⣼⣏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⢂⠐⠈⡐⢀⢂⠐⡀⢂⠡⡘⠄⡩⠄⠀⠀⠀⢎⡀⢽⣽⣟⠀⠸⣿⣟⢸⡟⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠠⢀⠂⡐⠄⢂⢂⡐⢁⠂⡔⢡⠂⠀⠀⠀⠀⠈⠱⠘⣥⠿⣷⡀⠈⣿⣸⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⠐⠀⢂⠐⠌⠄⢂⠐⡠⢁⠒⠤⠘⠀⠀⠀⠀⠀⠀⠇⠘⣧⢻⣿⠄⣿⢧⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠌⡐⠈⠄⢂⠐⠠⢊⠄⡁⠀⠀⠀⠀⠀⠀⢩⣀⠿⣡⣏⡐⣿⡶⢋⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠁⡀⠂⠌⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣯⢾⣜⣶⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣞⣹⢹⡬⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣦⣵⢦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢼⣽⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠂⡐⡈⠄⡈⠠⠰⢀⠀⠠⡌⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠔⡠⢡⠐⠂⠄⣁⠒⣨⡇⢐⡏⣰⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⡡⢢⡁⠎⠐⠠⠀⡁⠻⡇⢈⠛⣦⠅⡘⡎⠡⠆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠣⣅⠘⡌⠀⠁⠀⣠⣙⣿⣄⢫⡇⣹⡔⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢃⠌⡓⣯⠂⠈⠓⠢⠽⢻⣿⣿⣾⣿⡍⢼⡈⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⢴⢇⡣⠆⠁⠀⠐⢨⣾⢻⣿⡭⣿⠞⣤⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠠⠍⡁⣤⠛⣉⠒⡜⡛⣷⢯⡟⢦⡩⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠤⠉⠤⢋⢎⡱⠮⡑⣎⢾⣹⢣⢳⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡉⠂⢅⠊⡔⢡⠓⡌⢖⡣⢏⠶⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠊⠔⠨⣀⠒⢨⠘⡸⢩⡒⢅⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⡀⠌⠠⠌⠰⡣⠜⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠱⠑⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠹⢌⡱⢌⠭⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠳⣌⠲⣌⠢⣅⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⠀⠀ ⡱⢠⢃⡄⠓⡌⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢌⠱⡈⠄ ⡡⢃⠎⠌⠳⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎⠲⣡⠊ ⢡⢃⠚⡌⠱⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢎⡕⢢⢍ ⢅⠪⡐⠤⢡⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣎⠼⣡⢎ ⢢⠑⡌⢠⠁⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣃⠿⣇⡳⢎ ⡂⢍⡐⠡⢈⠒⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠆⡃⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡕⡺⢽⡷⣭ ⡘⠤⠘⡐⢂⠰⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣇⡇⠎⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡳⢜⡱⢣⢟⣶ ⠔⡡⢃⠔⡠⢂⠁⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡿⢿⡒⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠱⣌⠧⣙⠧⣾⠽ ⡘⠔⡨⢐⡀⢂⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡜⣰⡧⠽⣦⠈⡀⢀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢥⠛⣤⣛⢼⠫⡑⢌ ⢌⡘⢠⢁⠘⠠⠌⡐⢀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣿⠏⠉⢁⠳⣤⠈⢢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣸⡬⠟⢩⠐⡌⢢⠑⣊ ⢂⠍⡒⢌⡘⡐⢂⡐⠠⢀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⠀⠀⠀⠁⡆⠝⠲⣽⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠚⡁⠆⡑⢢⠡⡘⢄⠣⠔ ⢌⠲⡁⠦⡐⢄⠂⡄⢁⠂⠈⠨⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡼⠀⢀⠀⠀⠃⢀⠃⠈⣯⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⡐⠌⡡⠘⠤⡑⢢⠑⣌⠢⢍⡊ ⠶⠥⠜⣤⣁⣊⠐⡈⠂⠌⡁⠆⠠⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡾⠀⠈⠀⠀⠀⠀⠀⠀⢼⡀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⠌⢢⠡⡐⢌⡐⢩⠐⡌⢢⠑⡄⠳⣈⠖ ⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠬⠤⢅⣂⣈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠌⡐⠠⢈⠀⠂⠄⠠⠀⠄⡀⢂⡐⢨⡴⡟⡉⢆⠡⢊⠔⢂⠡⢂⠜⡠⢃⠜⡠⢣⠜⡱⢌⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⣳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀⠎⠤⢑⠠⡘⠰⡈⠔⡩⣐⣡⡶⢛⠍⡒⠤⡑⢌⠢⡁⠎⡄⠣⢌⠢⡑⡌⣒⢡⢃⢎⡱⢊⡬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡌⢭⠓⡖⢦⠤⣤⢤⣤⣤⣤⣤⣷⣷⠀⠄⡐⢀⠀⠀⠀⢼⢿⡾⣴⢧⡶⣥⣷⡼⢗⡛⢩⡑⢌⡒⡸⢀⠇⡘⡄⠣⣌⠱⣨⠱⢌⡒⢥⢒⡡⢎⡜⢢⡕⢫⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣙⡜⣌⠳⡌⠶⣘⢬⠹⣹⢻⣾⡍⡒⠌⣤⡆⠀⠀⠀⠻⣗⠎⢧⡙⣶⡛⡜⢢⠜⡡⢎⢢⠑⠦⣉⠖⡱⢌⡱⢂⠳⣄⠳⡌⡜⢢⢣⢜⢢⠞⣡⠞⣥⢛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⡚⣬⢣⡝⡱⢎⣎⣳⢏⡼⣹⣷⣉⡾⠋⠀⠀⠀⢀⠰⣹⡏⢦⣹⢇⡳⢌⠣⢎⡱⢌⠦⡙⢦⡑⢎⡱⢊⡴⣉⠶⣈⢳⡘⣜⢣⡍⣎⠳⣎⠵⣫⢼⣩ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⢣⢞⣱⢋⣶⢏⡎⡱⢂⢻⣍⣓⠃⠄⡐⠠⢀⢒⡸⣿⢼⣏⠞⣜⢪⡙⢦⡑⢎⡲⣉⠦⡙⢦⣑⢣⠖⣡⢞⡡⢧⡹⡜⢦⡹⢬⡳⢎⡽⡲⢧⡳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡭⣞⣬⢻⡼⣏⡼⢡⠎⡬⡑⢦⡘⠤⡑⣂⠆⡎⡴⢻⣟⣬⣛⢬⢣⡝⢦⡙⢮⡑⢮⡱⣙⠦⣍⠞⡼⡱⢎⡵⣣⢳⢭⡳⣭⢳⣭⢻⡼⣹⢧⣛ ⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣜⢮⡳⣿⣣⡝⣦⡙⢶⣙⢦⣙⠶⡱⡜⡼⣸⢵⣻⡝⡶⣭⢞⣣⠞⣥⡛⢶⡹⣒⢧⡝⣺⣌⢟⣜⡳⢫⠶⣭⣛⢮⡵⣣⢟⡲⣏⢾⡵⣫⣞ ⡘⠤⡐⡈⡐⠠⡀⠄⠠⢀⠀⡀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢚⣯⡗⣯⡽⣷⣻⢶⣹⡳⣎⡿⣼⢫⣷⣹⢳⣝⣮⡿⣝⣳⡽⣎⢷⣛⢶⡹⢧⣛⡵⢮⡽⣱⢞⡾⡼⣹⢯⡝⣶⡹⣎⢷⡝⣾⣹⡽⣞⣽⣳⡽ ⠥⣓⠰⣁⠦⡑⡄⢣⡘⢄⠒⣐⠢⡐⠤⡁⢎⡐⠄⡡⠌⠤⠡⢌⠰⡀⢮⣳⣽⣳⡽⢯⡷⣯⣷⣻⣽⣳⢯⣟⡶⣯⣛⣾⣾⡿⣝⣧⣟⣞⣧⡻⢮⣽⢳⣝⡞⣧⣻⢵⣫⠾⣵⢏⣾⣹⢶⡻⣽⣺⠽⣧⢷⣛⡾⣧⢿⡽ ⡳⣌⠳⡜⣢⠵⣌⠣⡜⣌⠳⢌⠲⡑⢦⡉⢦⡘⢦⡑⢎⡜⡡⢎⠦⣙⣮⢷⣳⣟⡾⣯⣟⣷⣻⡽⣯⣟⣿⡿⣟⣿⣻⢯⣟⡿⣽⢾⡽⣞⣳⣟⢿⣼⣛⣮⣟⣳⡽⣾⣹⢯⣷⢻⣮⠷⣏⡿⣵⢯⡿⣽⢯⣻⡽⣯⢿⣽

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⠏⠀⠀⢠⡾⠋⡰⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⡟⠀⠀⣰⣿⠁⠀⡃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢋⡟⢿⣿⡟⠂⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣯⣿⣿⢿⠛⠉⠻⢯⠙⠓⠢⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠋⠀⠀⠀⣠⣿⣿⣿⠀⢀⡅⠀⠀⠀⠀⠀ ⣿⣿⡟⠁⣎⠀⠀⠀⠈⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⠤⡴⠚⠉⠉⠙⢿⣆⣹⡇⠀⠀⠀⠀⠀ ⣿⡟⠀⢠⠻⡆⣇⠀⠀⢸⠀⠀⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢟⣿⡿⢁⣤⣞⣉⣿⠃⠀⠀⠀⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀ ⣿⠀⢰⡟⠀⢡⢹⡄⢀⣾⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢩⢿⣯⡿⠛⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣦⡜⠙⠟⣿⡴⣡⡾⡿⣄⠐⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣾⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡉⠀⠀⠐⣿⡴⢿⡗⢣⠈⠢⣙⠒⢀⣙⣛⡿⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢸⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⡤⠀⠈⠁⡇⢨⢱⣤⡤⠤⠒⠉⠁⠈⠻⡍⠛⠂⣿⠋⠉⠔⡏⠀⠀⠀⠀⠘⣼⠒⠛⠓⠒⠦⢤⣀⠔⠊⡿⣿⢀⡀⠀⠀⠀⠀⠀⠀ ⣶⣿⣷⣶⣶⣿⡇⢸⠏⠀⠀⠀⢤⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠰⠋⠉⠉⠉⠓⠲⢼⣿⣷⣾⠀⠛⠎⠉⠀⢠⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣸⡀⠀⠀⠀⠀⢠⣿⣷⣦⣀⣡⡀⠀⠀⠀⠀⣸⡦⢀⠀⠀⡗⠒⠒⠒⠤⢄⣀⠀⠈⢻⣿⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢠⣿⣿⣯⠟⠈⠑⢄⡉⠀⠺⠉⠉⢣⠀⠀⡸⠉⠉⠙⠒⠢⢮⣉⠿⣶⣞⠉⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⣳⢸⣿⣿⠃⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⢳⣾⡷⠒⠒⢤⣤⣄⡊⠙⣹⣿⣇⠀⠀⠀⠀⠀⣠⣾⡷⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⠏⡏⠀⠀⠀⠛⠓⠀⠉⠓⠢⡄⠀⠀⠀⠀⠈⠣⣤⡠⠤⣿⠗⠋⠉⣹⣾⠋⠉⡜⢻⠏⠀⣸⠿⡷⠒⢻⣿⣥⠀⠀⣀⣾ ⣿⣿⣿⣿⣿⣿⣄⣷⡀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⡟⠀⠀⠸⡀⠀⡴⢹⠇⠀⢸⠀⡎⠀⠀⡇⢸⠁⠀⣏⢸⡇⠀⢸⣿⠁ ⡩⠀⠀⠀⠀⠐⠀⠀⠀⠈⠙⢧⡈⠉⠉⠉⠛⠓⠀⠒⠒⠒⠒⠉⠉⠀⠀⢀⡱⠼⣥⣼⣄⣀⢸⣄⣣⣀⡀⣇⣸⣀⡀⣿⣸⣇⣀⣸⣀⣀ ⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠛⣤⣤⣈⣈⣉⠉⠁⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⣇⢹⣿⣿⣿⣿⣿⣿⣿⡷⢿⣟⠻⣿⢻⢹⡈⣿⣆⢧⠙⣆⢳⡀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⠀⢠⢸⣿⣿⣿⠿⣿⠿⠛⠁⠀⠀⠙⣆⠈⢧⢧⣇⣿⣿⣆⣇⠘⡌⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡄⡞⢸⣿⣿⠃⠀⣿⠀⠀⢠⠄⠀⣀⣈⣇⣈⣆⠸⣼⣿⣿⣿⣆⠀⢻⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢰⢿⡇⠁⣼⣿⢻⠀⢀⣿⠀⠀⠈⠉⠉⢉⣿⠷⠿⣿⣭⣿⣿⣿⢿⣿⣧⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⠃⣼⣿⣧⣼⣿⣭⡼⢢⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⡏⠹⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡽⣧⣿⡟⣼⣿⣿⡿⠋⠉⢀⡅⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠈⢳⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⠏⠀⣿⣿⣿⠈⠠⠞⠉⠀⠀⣰⣺⣭⣬⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣧⠀⠀⠀⠙⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢡⣾⢃⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⠟⢡⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀⣉⣛⣿⣿⣿⢿⡿⠋⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣿⠇⠈⠀⠀⢰⡿⢿⡄⠀⠀⠀⠀⠀⢹⣿⣿⢿⣟⣿⡟⠀⠀⠉⠁⢀⣴⡿⢛⣿⣠⡤⠶⠚⠋⠉⠉⠀⠀⢬⣤⢤⣤⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣄⣉⠉⠀⠘⠛⠛⠉⢁⡽⠛⠛⠛⠛⠻⠾⢧⣾⣿⡄⠀⠀⠀⠀⠀⠻⡄⠀⢀⣽⢁⣀⣀⠀⠋⠉⠀⣠⠿⠋⠁⠀⠀⠀⠀⠄⢒⣀⡴⠶⣻⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⣒⣦⠖⠚⠉⠀⠠⣄⣀⡀⠀⠀⠀⠈⠙⢿⣶⣶⠦⢤⣤⠴⠛⠛⠋⠵⠶⠦⠤⢖⣀⡴⠋⠁⠀⠀⠐⠀⠀⠀⠀⠀⠈⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⢀⣀⢤⠀⢀⣨⠥⠖⠚⠉⠓⠺⠤⣤⣀⡐⠊⠉⠀⠐⠂⠀⠀⠀⣐⠒⣢⡌⠉⠙⠒⠢⠤⣄⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣍⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⣾⠁⠀⠀⣉⣡⠤⣤⣦⣧⠀⠀⠀⠀⠀⠀⠈⠙⢲⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⣤⢖⣂⣤⠤⠀⠉⣡⣶⣟⣉⡬⠏⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢤⡀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠟⢳⣿⡄⠀⣚⣫⣭⣭⡦⠖⠂⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠹⣆⠀⠀⠀⠀⠀⠴⣿⣉⣉⣾⢻⣳⠀⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⡇⠀⠀⠀⠀⠀⠀⠉⢉⡿⢸⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠀⠀⠀⠀⠀⠀⢠⢿⣵⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠦⢄⣀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡌⢷⡀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠇⣾⠀⠀⠀⠀⠀⠀⠀⣸⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⠀⡿⡄⠀⠀⠀⠀⠀⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢠⡇⣧⢹⡿⢰⣇⡇⠀⠀⠀⠀⡰⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⣦⢻⠀⡇⣼⢻⡀⠀⠀⠀⠘⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠹⡎⣧⣿⠏⣾⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣾⠿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠙⢆⠀⠀⠀ ⠀⡰⠟⢥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠡⡀⠀ ⡰⢁⠔⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠂⠀⠀⠀⠀⣡⠀⠀⠀⠐⡀ ⠁⠂⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐ ⠀⠀⠀⢀⠔⠁⠀⠀⠉⠀⢡⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⣄⠀⠀⠀⠀⠀⠰⠿⡿⠻⠛⠛⠻⡴⢶⠀⠀⡰⣿ ⠀⠀⠀⠀⠀⣀⣤⠶⢟⠛⠋⠉⠋⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⢘⠄⣸⣟⣏ ⠀⠀⠀⢐⣶⠟⠁⠠⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣿⣜⣼ ⢀⣀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⣷⣿⣻⣿ ⡈⠳⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣠⡀⠀⠀⠈⢂⠀⠀⡇⠀⠀⠀ ⠈⢢⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄⠀⠀⠀⢳⢤⠁⠀⠀⠀ ⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⠿⢿⣧⠀⠀⠀⢠⠃⢀⠄⠀⠀ ⡀⠀⠺⠇⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡆⠈⢻⠀⠀⠠⠃⣠⠎⠀⠀⠀ ⠈⠑⠂⠠⣤⠽⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠐⠀⢸⠀⡰⢁⡾⠁⠀⠀⠀⢀ ⣤⠀⠀⠀⠈⠀⠈⠢⡁⠢⢄⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⠰⠑⠁⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⢀⡀⠀⠀⠀⠑⠄⠈⠻⣶⡀⣤⣤⡀⣀⣆⢠⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢂⠀⢉⣐⣦⡖⠲⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢋⢤⠖⠈⠉⠑⡈⠑⢄⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⣰⠅⠄⠀⠀⠘⠀⠸⠀⡈⡄⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⢀⡍⣸⠀⠀⣀⡆⠠⠀⡀⢠⣸⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⢸⣷⣽⡄⣠⣟⡇⡄⠁⡇⢸⣿⣾⠇⠀⠀⠀⠀ ⠀⠀⢀⡤⠐⠁⢀⣿⣧⢇⠻⠃⠛⠿⣽⣽⣴⠀⣸⣟⢏⠃⠀⠀⠀⠀ ⠀⣠⣿⡀⣤⠊⢀⡵⣿⣏⠁⠀⠀⠀⢨⠅⣁⡴⠻⣸⡾⠀⠀⠀⠀⠀ ⢠⠃⢿⣿⣿⡴⢉⢀⣿⣿⣷⣄⡀⠤⠐⠁⠑⣔⠒⠁⠀⠀⠀⠀⠀⠀ ⢸⢀⠔⢉⣿⣌⣻⡿⣿⣿⡏⠀⢡⣤⠀⠀⠀⣸⣷⣤⡀⠀⠀⠀⠀⠀ ⠘⠓⠒⠛⠉⠉⢁⠴⠿⣿⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⠀⠀⢿⣦⡴⠶⠛⠛⢿⣿⣿⠶⣲⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣆⠀⠀⢸⠏⠀⠀⠀⠀⠈⣿⠇⠚⢁⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠳⢾⣿⣇⠀⠀⠀⠀⣰⣧⠖⢁⣎⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣾⣿⡿⠋⢀⣴⣿⡟⢌⠳⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣵⣿⡟⠀⠀⣠⡟⡵⢹⢸⠀⢸⣽⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⣿⠟⠉⢀⣿⣾⣤⣾⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣍⣁⣤⣔⣫⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⠉⠉⣹⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⢻⣿⣿⣿⣿⣿⡧⢀⣾⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀ ⠀⢠⢪⠀⠀⡠⣂⠄⠒⣄⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⡏⡄⢀⣼⠊⢀⣤⠄⡿⣆⠀⣦⣸⠀⠀⠀⠀ ⠀⠃⢡⣿⢭⡁⠀⠰⢖⣿⡞⡀⡟⡼⡄⠀⠀⠀ ⠀⠸⡈⢏⠹⠧⡀⠀⠘⠛⠀⢰⠿⡀⢣⠀⠀⠀ ⠀⠀⠡⠈⡆⡀⠣⠤⠀⠀⡀⢸⢰⢃⠈⣇⠀⠀ ⠀⠀⠀⢑⢧⡟⡆⢤⠔⠈⠀⣼⡸⡈⡀⡜⡆⠀ ⠀⠀⠀⠎⣌⠠⠗⠘⠀⠀⠀⡇⠑⠄⣷⡧⠃⠀ ⠀⡐⠈⠉⠁⠀⠒⠂⠀⠀⠒⢳⡒⠀⠈⠁⠢⡀ ⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⠀⣹ ⠀⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠃ ⡈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⠀⠀⡌⠀ ⡏⠃⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠒⢀⠀⢸⠀⠀ ⠈⠢⣀⣀⡀⠔⠀⠐⢄⠀⠀⠀⣀⠌⠀⡆⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠠⡀⠀⠉⠁⡈⠀⢰⠀⠀⠀ ⠀⠀⢸⡆⠀⠠⠀⠀⠈⠠⠀⠀⠃⠀⡆⠀⠀⠀ ⠀⠀⠀⣇⠀⢠⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀ ⠀⠀⢀⠃⠀⢸⡄⠀⠀⠀⠀⠀⠑⡃⠀⠀⠀⠀ ⠀⠀⡌⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠠⠋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⡢⠒⠀⢀⠇⠒⠒⢄⡀⠀⠠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣌⠄⠠⠈⠑⠚⠚⠣⠀⠀⣯⢳⣦⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢻⠀⡇⠀⠀⠀⠀⣠⣶⣇⢿⣾⡇⢣⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣟⠸⡆⢻⣶⣤⣄⠈⠯⠿⡟⠀⠙⢩⡿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡀⢡⠀⢋⠁⠀⠀⠀⠠⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢇⡌⠢⣈⣶⠅⢤⠀⠀⡠⢁⢧⠀⣳⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⡁⢀⢨⠾⣉⢁⣠⢾⢞⠁⢀⠹⠁⢀⠬⡦⠤⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠉⠐⠇⠐⠈⣲⠁⠀⠀⡯⠭⠤⠄⠀⠝⠣⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠢⠤⠶⠙⢖⡤⠀⣀⡀⠀⢑⡄ ⠀⠀⠀⢠⢤⠾⠁⠘⡚⣶⣦⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⡌⢀⠒⠄⣀⠀⠀⡋ ⠀⠀⢀⠁⠐⣂⣀⡐⠖⠁⠀⢀⠀⠀⠀⢈⠁⢲⣁⣀⡀⠀⠀⠀⢡⠀⠀⠁⠀⠙ ⠀⠀⢸⡠⠒⠉⠀⠀⠀⠀⠀⠀⢂⢀⠜⠁⠀⠈⠒⢠⠄⠀⣀⠀⠈⢣⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠉⠒⠀⡀⠀⠀⠁⠀⠀⠀ ⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠑⠄⠀⢸⠁⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⡸⠀⠀⠀⠀⠀ ⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠐⠒⠐⡎⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⣀⣀⠤⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢠⣿⣿⡿⠟⠛⠝⠿⢿⣥⢊⡆⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⢸⣿⢀⡁⠐⠠⡾⢮⣾⣿⣧⢰⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⠞⢛⠹⠐⠀⠀⠀⠀⢻⡇⠳⣻⣿⣿⣿⣿⣿⣿ ⠈⠻⣿⣿⣿⣿⣿⡟⡷⡁⢹⡇⠁⠀⢸⣿⣷⡄⢀⡰⢻⡇⠀⢀⣈⣛⡻⠿⠟⠁ ⠀⠀⠈⠻⠛⠛⢛⡺⠓⠒⠾⢷⣀⠀⠘⢏⡙⠃⠀⠒⡩⠓⠉⠀⠄⡤⡙⠊⠀⠀ ⠀⠀⠀⠀⠑⠨⣀⠠⢅⠠⠐⠒⠭⣭⣙⣀⠈⠉⠉⠅⠒⠀⠄⡀⢀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠐⠆⣴⣥⢀⡸⠯⠅⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠲⠷⢿⡐⠋⠉⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⠆⠀⠀⠀⣿⣿⠠⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⢘⠋⡟⣦⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠈⡶⣷⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠙⢿⣛⠭⢗⣒⠲⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠈⠑⢄⡀⠉⠲⢄⠈⠻⡲⢄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠙⢦⡀⠀⠑⢄⠈⠓⢍⠲⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠁⠀⠀⠀⠱⡄⠀⣁⠀⠑⢄⠀⠀⠀⠀⠀ ⡶⠋⠀⠀⣀⠔⡿⢡⠆⠀⢀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢣⡀⠀⠀⠀⠈⢦⠹⣿⡄⠀⠀⠀⠀⠀⠀⠘⣄⠈⠑⢴⠀⠳⡄⠀⠀⠀ ⠀⠰⠶⠈⣠⠞⡰⠁⠀⠀⡎⠀⢸⡄⠀⠀⢤⡀⢀⡀⠀⠸⠀⠀⠑⢄⠀⠀⠀⣀⣑⡘⢿⡄⠀⠀⠀⠀⠀⠀⠘⣦⣀⠈⠃⠀⡿⢆⠀⠀ ⠀⠀⠀⢀⠎⡜⠁⠀⠀⢸⠁⠀⡏⢧⠀⠀⠀⠙⢿⡷⢦⡶⠤⠤⠒⠚⠻⣿⠯⣁⠀⠉⠻⣷⠂⠀⠀⠀⠀⠀⠀⢻⣿⠗⠦⡀⠑⢌⢧⠀ ⠀⠀⠀⠎⡼⠀⠀⡰⠀⡌⠀⢰⢃⡿⡄⠀⠀⠀⠀⡇⢠⠗⠀⢤⠤⠤⢤⠼⢧⡤⠷⠦⣄⠙⣇⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠙⠀⠀⠈⢣ ⠀⠀⠀⠀⠁⠀⢠⠇⠀⡇⠀⢸⣸⠠⢼⡄⢠⡀⠀⢱⡘⠀⠀⢀⣤⣶⣿⠶⡿⣻⠟⠛⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⣰⢷⣰⣾⠃⠀⠀⠙⣜⡗⢄⠀⢧⠀⠀⠘⣻⠛⠒⠒⠚⣁⢠⣠⣴⢿⣋⡇⠀⡄⠀⡀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⣿⡴⢿⣾⣠⠞⠂⠀⠈⢻⡀⠙⠺⢦⡀⡀⠀⣠⣤⣶⠭⢚⣹⢿⡧⠴⠛⡇⠀⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⡟⠀⢈⢿⣧⣤⣶⣦⡀⢸⡃⣠⡾⡞⠉⠁⣹⣻⣽⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⠃⣴⣿⣿⡯⠵⠋⢀⣠⡾⠋⠩⠊⠀⠐⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⢸⣶⠚⠃⠀⠀⢀ ⠀⠀⠀⠀⠀⢸⣿⣘⡄⢿⡇⢀⣤⣴⣞⣹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⡄ ⠀⠀⠀⢀⢧⠈⣿⡷⣇⡛⠿⢟⡩⠞⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠿⣷⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠁ ⠀⠀⠀⠘⢈⣆⢹⢷⠸⣥⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡜⠀⢿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡔⠀ ⠀⠀⠀⠘⠈⢾⣼⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⣉⣉⣹⣷⣦⣄⠀⠀⠀⠀⠀⢠⡿⠁⠀⣾⠀⠀⠀⠀⠀⠀⣼⡧⠃⣼⠀⠀ ⠀⠀⠀⠀⡀⠘⡟⢷⠸⡄⠀⠀⠀⠀⠀⠀⠀⣾⣤⢶⣾⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠚⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⣏⣠⣾⣿⡶⠀ ⠀⠀⠀⠀⡇⠀⢱⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠀⠞⢣⠀⠀⠀⠀⣀⣼⡇⠀⡀⠀⢸⠀⢰⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⢳⠀⠸⡄⠀⢘⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⢰⡏⠀⠀⢇⢈⣆⠀⠀⠀⠀⢸⡇⢰⠀⠀⡎⠀⣸⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢇⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢧⠀⠀⠹⣿⠛⠷⣦⣀⣀⣾⠃⡆⠀⢰⠁⢠⣿⡿⡹⠋⠁⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠸⡄⡆⢣⠘⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⣀⠑⠦⡀⢳⠀⠀⠀⣹⣿⡟⢰⠁⠀⡏⢀⣾⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⢱⠸⠸⣧⠹⡝⠢⡀⠀⠀⠀⠀⠙⠯⢄⡠⠭⠔⠚⠳⠦⣄⡴⠂⣠⣾⣿⣿⢃⡆⠀⣼⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠘⡤⡀⠀⠱⣇⢣⠣⡙⣄⠈⠑⠴⣀⠀⠀⠀⠀⠀⢠⣤⠖⠀⠀⠀⣠⣾⣿⣿⣿⡏⡘⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢦⠀⢱⢱⡀⠀⠻⡌⢧⠘⢎⢦⡀⠀⡈⠉⠲⢤⣀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠟⡽⠐⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⣀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢄⠋⢀⣤⡟⢿⣪⣭⠟⣿⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠄⢆⣞⣿⡿⣿⣷⣿⣦⣻⣯⣻⡦⣀⠤⠊⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢄⡈⡈⣿⡿⠃⠘⣿⣿⠃⣽⣿⣿⣿⡅⠀⢀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢌⡷⣿⣿⠇⠂⠁⣾⢿⣴⣿⣿⣽⣿⢿⢂⡽⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢁⠋⠻⣶⠀⠀⢠⣿⣿⢿⣿⣿⣿⣴⠟⣥⡯⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠈⡄⠂⠀⠉⠉⠘⠉⠋⠘⠛⠉⠙⠁⠀⡸⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢛⠛⠻⣣⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢰⡧⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢀⡑⢢⣧⠀⠃⠀⠀⠃⠀⢀⠂⠠⡀⠀⡎⡼⠁⠠⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢙⡏⢰⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⢡⡇⠐⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠘⡇⠀⠀⠀⠚⠀⠀⠀⢀⢎⠻⠂⠰⣄⡀⠀⠀⠀⠀ ⠀⢢⣄⡯⠀⠀⠀⣀⠔⢣⠔⠀⠀⠀⠀⠀⠀⠀⢀⡏⢊⠎⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠒⠬⠥⢤⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡯⢐⠄⠀⠉⠂⠄⠀⠀⠀ ⠀⣖⠭⠀⠀⡠⣲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣤⣁⠢⡀⠀⠀⠀⠀⠀ ⠀⠈⢣⠧⠊⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠉⠳⡈⠢⡀⠀⠀⠀ ⠀⡔⢡⠎⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠐⡄⠐⡀⢀⣤ ⠜⠀⢋⢾⠙⢦⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡔⡄⡟⠣⣄⠈⢲⣾⣿⣿ ⠀⠀⣾⠚⠛⢷⡢⠀⠀⠀⠄⢠⣎⡉⡀⠀⠀⠀⠀⠈⠀⡰⣹⡀⢹⠧⠀⠻⣿⣿ ⠀⠐⠀⠀⠀⠐⢯⣕⠀⠤⣤⣞⠉⢳⡥⣀⠀⠀⢀⡠⣾⠟⠁⠀⠹⡇⠀⠀⠙⣿ ⠀⠀⠀⠀⠀⠀⠠⠥⠷⡶⠿⠉⠉⠙⠓⠤⠈⠯⠵⠺⠄⠀⠀⠀⠀⢸⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠟⠛⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠙⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠐⠂⢀⣼⡿⠻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢑⠒⢒⡻⠿⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⢻⡄⠐⠏⠁⣀⠀⢢⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠀⠱⠁⠀⠹⢽⠗⠈⡆⠀⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣯⠂⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠀⢀⠃⢨⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⢀⡤⠊⠀⠀⠀⠈⠉⠐⠢⡜⠀⣼⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⡜⣿⠃⠀⠀⢀⠀⠀⠀⠀⠘⠀⠇⢀⣿⣿⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⢡⡿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⣰⡀⠀⠀⠀ ⠀⠀⠀⠀⠐⠚⠃⠯⠠⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⢿⣷⣏⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠝⢿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡄⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣤⣤⡶⢾⣿⣿⡆⢰⠋⠀⠈⠉⡏⡁⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶ ⣉⣭⣭⣽⣽⣿⣿⣿⣿⡏⣽⢃⡜⠀⠀⠀⠀⠀⠡⢹⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿ ⠿⠿⠟⠛⠉⠀⢸⣿⠇⢹⡇⡸⠇⠀⠀⠀⠀⠄⠠⠄⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡿⢿⣿⣟⣫⣽⣿⣿⣏⣿⣯⣭⣭⣭⣼⣬⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠲⠖⠒⠤⠤⣔⠒⠒⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⠉⠁⠀⢀⠔⢀⡠⠀⢠⠀⠘⣧⠀⢢⠀⢣⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⡴⠃⠀⡿⠀⠀⢸⡆⠀⠘⡄⠀⡆⠘⣯⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⢀⠔⣠⠞⠀⢀⡼⠁⠀⢠⡿⣷⠀⠀⡇⠀⢹⠀⣿⣧⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡰⠁⡼⠁⠀⣠⠟⠁⠋⣩⡽⠟⣿⠀⣼⡇⠀⣼⡇⡸⢸⣇⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢁⡞⠀⠠⣶⢣⣤⣶⣞⣿⡇⢠⡏⣼⣿⢁⣼⡿⣾⡇⢸⡟⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⣾⠁⠀⢰⡏⣿⣿⣷⣿⡟⠃⡼⣷⣽⢣⣾⣿⣿⢻⠇⣸⡇⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢸⣿⠀⠀⣼⣷⠇⢸⣿⣿⠃⠀⠹⢻⣿⣿⣯⣷⣿⡸⢠⠏⠀⢿⣵⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣾⢿⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⢸⣷⠋⢀⡗⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣱⣿⢠⣷⣼⣿⢸⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢰⣿⠇⢀⣼⢰⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣿⣧⣾⣿⣿⣿⡆⠓⢤⡀⠀⠀⠘⠛⠀⠀⠀⢠⣿⡟⣠⢾⡿⣻⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢧⣄⠀⠀⢿⡿⣧⣿⣿⡟⣆⠀⠙⠢⣄⣀⣠⣤⣴⣶⣿⣿⣾⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢉⢉⣱⣒⡶⠊⠀⠀⠀⢠⣈⠉⠢⣄⢠⣤⠀⠀⠉⠙⢦⡄⢀⡤⠿⠿⠿⠿⠛⠓⠻⢾⣿⣧⣀⠴⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⠾⢛⣛⣩⣽⠏⠀⠀⠀⠀⣀⣀⠤⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠰⣄⢤⠿⠇⠀⠒⠒⠂⠞⢆⠀⠀⠀⠀⠀ ⢉⡤⣖⡋⢉⢡⡿⠀⠀⠀⠀⡴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢴⣉⠉⠛⠒⠲⠈⢧⠀⠀⠀⠀ ⣫⠞⡟⡵⣽⣿⡇⠰⠒⠒⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠈⢦⣄⣀⠀ ⠁⣸⢀⣼⣟⡾⠁⠀⠀⢰⠁⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣄⠀⠀⠀⠘⣿⣶⣭ ⣦⣿⣸⣿⣿⠃⠀⢠⠀⢸⠀⠘⣆⠙⣦⣄⣀⣀⣀⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⢓⢤⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡹⠷⠀⠀⣿⡈⣿ ⠀⠀⠈⠉⠙⠒⠤⠤⢄⣸⡤⠐⠛⠒⠳⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⣖⢋⠁⢻⣿⡟⠁⠀⠀⢰⣟⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⣤⠀⠀⡿⣿⠀⠈⢿⠃⠀⠀⠀⢸⣿⡀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡃⠈⢦⡠⠃⠀⠀⠀⠀⣸⡇⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢼⡁⠀⠀⠀⠀⢀⣿⢣⡿⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣲⣄⠀⢀⡞⣁⣾⠼⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡽⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⢁⢀⡌⠉⡥⡆⠈⠝⠄⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⢧⢹⡀⢧⢹⣀⣦⣿⡀⠀⠀ ⠀⠘⣿⣿⠹⣿⣿⠧⣆⣿⣿⡿⠟⠿⢳⣿⣇⣿⣧⣾⣿⣷⢾⣿⣟⣿⣹⡇⠀⠀ ⠀⠀⣿⡟⢀⡺⠡⠤⢀⢹⡏⠀⠀⢀⠜⡿⡏⠈⢻⣿⡟⢷⢀⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠹⢱⠁⠀⠀⠀⠀⠙⢧⣀⣴⠋⠀⠆⠀⠀⠀⠀⠁⠈⠁⢻⣿⣿⠿⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠢⣘⡆⠀⠀⣀⠠⠂⠀⠀⢿⠟⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠐⠤⡀⠀⠀⠀⠁⠢⢀⣡⣶⣿⠟⣀⣀⣀⡀⠊⠘⠣⣀⠰⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣤⡀ ⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⣄⣠⣤⠔⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠰⠀⢀⣧⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⠀⣽⡄⠀⠀⠀⠀⠀⠈⠐⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⣿⠟⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⣏⡸⠁⠀⠐⠀⠀⠀⠀⠀⠀⣰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡏⠀⠀⠀⠀⠀⠀⠀⠳⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⠂⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠲⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡀⠀⢡⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⡸⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡞⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠗⠂⠈⠉⠁⠉⠁⠀⠀⠂⠀⠑⡄⠀⠀⠀⠀

⠀⠀⠀⠀⣀⢀⣠⣤⠴⠶⠚⠛⠉⣹⡇⠀⢸⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠈⢦⢰⠀⠀⠀⠀⠀⠈⢳⡀⠈⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⡏⠀⢰⠃⠀⠀⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⢸⣸⡆⠀⠀⠀⠰⣌⣧⡆⠀⢷⡀⠀⠀⣄⢳⠀⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⢀⣿⣇⠀⠸⡇⣆⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢹⣾⡇⠀⢸⢣⠀⠀⠘⣿⣇⠀⠈⢧⠀⠀⠘⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡀⠀⠀⠀⢸⠈⢻⡄⠀⢷⣿⠀⠀⠀⠀⢹⡏⣇⠀⣀⣀⠀⣿⣧⠀⢸⠾⣇⣠⣄⣸⣿⡄⠀⠘⡆⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⣾⢿⠀⠇⠀⠀⠀⢸⠀⠀⢳⡀⢸⣿⡆⠀⠀⠀⣬⣿⡿⠟⠋⠉⠙⠻⣽⣀⡏⠀⠙⠃⢹⡙⡿⣷⠀⠀⢹⠀⠀⠀⠀⠰⠒ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⠀⠀⠀⢸⣦⣤⡀⣷⣸⡟⢧⣀⡴⠶⠿⠻⡄⣀⣤⣴⡾⠖⠚⠿⡀⠀⠀⠀⠈⣧⠁⠹⠆⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣀⣼⣿⣼⡆⠀⢀⡘⡇⠀⠀⠹⡟⢷⡜⢉⣠⣠⣠⣀⣤⡿⣛⣥⣶⣾⡿⠛⠿⠿⣶⣦⡤⢹⠀⢀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⡛⠁⠀⠙⢿⠋⠉⠉⠻⠀⠀⠀⢿⣄⠈⠁⠀⠀⠀⢉⢟⣴⡿⠿⠟⢁⠇⠀⠀⠀⠀⠹⣿⠻⡇⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⣀⣀⣘⣿⡇⠀⢀⣠⣤⣶⣶⣶⣾⣦⡀⠀⠈⡿⠀⠀⠀⠀⠀⠀⣿⠟⠳⠦⡤⠊⠀⠀⠀⠀⠀⣸⠇⠀⡇⣼⠀⢰⠀⠀⢹⣇⠀⠀⠀ ⠛⠁⠈⣿⣷⣧⣴⣿⠿⠛⣿⠿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⣶⠿⠿⠿⡷⢛⠕⠷⡄⣧⣿⠀⢸⠀⠀⠸⣿⡄⠀⠀ ⠀⠀⢠⣿⢿⣿⣿⠁⠀⠀⠈⠳⠤⠶⠃⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣱⠒⡠⢆⡴⣣⣯⢞⣴⡟⢿⡄⡏⠀⠀⠀⡏⢷⡀⠀ ⠀⠀⡌⣿⠀⠙⣿⡦⢀⣤⡴⣶⠖⣲⠆⢀⠞⠁⠱⠀⠀⠀⠀⠀⠠⣾⠟⠛⡡⠞⠁⢀⡴⢋⢎⣽⡿⣫⠋⠀⠘⢷⠃⡄⠀⠀⡇⠈⣿⡀ ⠀⠀⣇⢹⣦⠀⠼⢃⡾⢋⣶⢃⡼⣹⡳⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠⠋⠀⡰⠋⠀⢘⣇⡇⠀⢠⠟⠀⡇⠀⠀⠀⠀⢹⡵ ⠀⠀⢻⣌⢿⡆⠀⡝⣼⠟⣩⢏⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⣠⠏⣠⣾⡇⠀⠀⠀⠀⠘⣷ ⡀⠀⢸⣿⣿⣷⠆⢠⠏⡴⠃⡡⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠤⣄⣀⠀⠀⢀⣰⠏⠀⠀⠀⠀⢀⣠⡾⠗⠋⢰⠏⡇⠀⠀⠘⠀⠰⢻ ⣇⠀⠘⣿⣿⣟⠻⣄⡞⠀⠐⠁⠀⠀⠀⠀⠀⣠⠞⣩⣤⣶⣶⣾⣷⣶⣬⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠹⣿⣿⡄⠀⠉⠉⠀⡀⠀⠀⠈⢻⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣧⠀⠀⠀⠀⠀⠀ ⠀⣿⢦⣀⠘⢿⣷⡀⠀⠀⡀⢦⠀⠀⠀⠀⠹⣿⣿⠏⠙⢻⣿⡿⠛⠉⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⡆⠀⠀⡀ ⢼⣿⠀⠈⢳⣤⣉⣻⣤⣀⣉⣩⠆⠀⠀⠀⠀⠹⡿⠀⠀⠈⡿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠓⠂⠀⣠⣾⣿⣿⡿⢿⡄⠀⣧⠀⠀⠹ ⣾⠃⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢠⠴⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣧⣀⠧⣰⣻⢄⠀⠀ ⠛⠶⢾⣿⣽⣭⣽⣭⢹⣷⠀⢹⣦⣀⠀⠀⠀⠀⡄⠀⠀⣸⡀⠀⠀⠁⣰⣧⣽⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⣻⣿⣿⣿⣿⢠⣿⣧⡸⣷⣄ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⠏⠀⣾⣿⣿⣷⣦⣀⠀⢇⠀⠀⠈⠁⠀⣠⠔⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣼⣿⠏⣷⡈⠉ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠀⠀⡾⠁⠀⠀⠀⣀⡴⠞⠛⣛⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⢰⣿⡿⠂⠈⠻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠉⠛⠻⠿⠿⠿⠿⠿⣇⠠⠸⣇⣀⣤⣴⣾⡭⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠈⣳⠀⣿⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡯⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣼⣿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠉⠛⢦ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⣄⡀⣀⣀⣀⣈⣀⣀⣤⣄⠀⠀⣀⣾⣾⣷⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠿⠛⠋⠉⠉⠉⠙⠻⢿⣿⣷⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠁⠉⠛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⠀⢰⣷⡄⠈⠉⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠋⠀⠻⣿⣷⡄⠀⠀⠀⠀⠻⣿⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠙⢿⣿⣷⣦⣤⠀⠀⠀⠀⠀⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡽⠀⠀⠀⠀⢀⣿⠘⣯⢿⣦⠀⠀⠀⠀⠀⠀⢯⠻⣿⣿⣿⠀⠀⠀⠀⠀⠈⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⢿⣇⠙⢿⣿⡀⠀⠀⠀⠀⠀⢸⣗⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠻⣆⢀⣿⣧⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣧⣿⣿⡆⠀⠀⠘⣹⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣁⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣶⡾⠟⠛⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀ ⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣸⣏⣣⠀⠀⠀⠀⢀⠀⢨⣿⠟⠻⡉⠉⠀⠀⠀⢸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣤⣾⣿⣿⣿⣿⣿⡷⢤⣤⡴⢾⢋⠇⠀⡆⣇⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠡⠽⠟⠉⢻⣿⣿⣧⠀⠀⢀⣼⡾⠀⠀⠁⠋⠀⠀⠀⠀⠸⣿⣿⠈⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠈⠻⣿⣿⠄⠀⠈⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⠀⣠⣲⢿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣅⡾⠿⣿⣀⠀⠹⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡾⠃⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠛⠻⡗⢛⡟⠒⠒⠈⢿⣶⣤

Hot Porn fuck ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠁⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⠛⠿⣿⣓⠶⣤⣀⠀⠀⠀⠀⠀⢰⡟⠀⣰⣿⡿⣼⡄⠐⠀⣴⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢫⣧⠀⠀⠀⠀⠀⠀⠀⣼⣏⠙⠳⠿⣷⣦⣤⣹⣿⣶⣌⣙⣷⠆⠀⢀⣿⢁⣦⠿⢱⢷⣿⠁⠀⣠⡿⡟⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⡞⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⢩⡦⠀⠀⠀⠀⠀⣸⣟⠿⠀⠀⠀⠀⢹⣿⣗⡿⠛⡟⣹⡇⠀⠀⣼⣇⡾⢾⡄⣏⣿⠇⠀⢠⣿⣷⣇⣤⠀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣼⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⢃⡸⣶⢷⣆⡀⠀⣾⣿⣼⢁⣴⡇⡿⠀⠀⢰⣿⣼⣷⣟⣻⣿⣯⣀⠀⣼⣿⣿⡿⢿⣷⣷⣤⡀⠀⠀⠙⣿⣿⣿⣿⣿⢿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⣺⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡄⢱⣏⠛⠺⢽⣷⣿⢧⡿⣸⣿⣽⠃⢀⣠⠟⠉⠀⠀⠀⠀⠀⠉⠙⢛⣿⣿⡼⠁⠀⠛⠿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣾⣿⢻⡄⠀⢠⡀⠈⣷⠄⢻⡄⠀⠀⣾⡿⣾⣿⣿⣿⡿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣟⣿⣧⣤⠼⣧⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⣀⣠⣾⡿⠃⠈⢿⡄⠀⠁⠀⠸⡏⠈⢷⣄⣸⣿⣷⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡮⣤⣸⣿⣿⢿⣦⣽⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠀⠐⢾⣷⡀⠀⡄⠀⢯⡓⢘⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠀⠈⠻⢿⣿⡷⠯⠄⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠻⣷⡀⡃⠀⠈⣷⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠴⠛⠐⢦⣹⣜⠻⣅⣤⣹⣿⣷⣤⣶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠒⠦ ⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠸⣧⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠛⠋⠁⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠚⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠘⢻⡦⣼⡄⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣌⣻⣷⠙⣗⠦⣄⡀⢀⣠⠾⠓⠂⠄⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠳⠿⠿⠶⠾⣦⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⠀ ⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠒⠾⠻⠯⢧⣀⣀⢀⣠⡶⠉⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠛⠻⣷⡶⣶⣿⠟⠋⠉⠉⠉⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀⣴⠇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠂⠠⢄⣀⡀⠀⣴⣯⣿⡟⢁⡤⠀⠀⠀⠀⠀⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣀⡴⠋⣹⡿⠉⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⢤⣤⣍⠉⠓⠲⢭⣴⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠚⠚⠋⠁⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠙⢻⡿⠻⣿⣿⡞⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠶⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⡰⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⢀⡤⠔⠚⢯⣄⠴⠶⠿⡿⠃⠀⠀⠀⠀⠀⠀⣤⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣸⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣶⣶⣉⣀⣀⣀⣀⣈⣹⣶⣿⣥⣤⣄⣀⣀⣀⣴⣏⣙⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢉⠉⠀⠁⠀⠀⠀⠀⢉⣉⣃⣈⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⠿⠛⠛⠓⠶⣭⡀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⡈⠙⠻⣿⣿⣿ ⣿⣿⡿⠋⡠⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠰⢹⠄⡘⢿⢻ ⢫⢟⠀⠁⠀⠀⣠⠤⠐⠠⢄⠀⣸⠀⠀⠀⢀⣷⣀⠔⡨⠭⠥⡢⠉⡏⠉⠈⠺⡇ ⣼⠁⠀⠀⠀⡼⠁⡴⢉⣦⡴⢞⠉⠓⠀⠀⠈⠀⢮⣛⠲⠦⣄⣸⢀⠤⠀⠀⢠⡇ ⠸⣆⠀⠀⣀⣧⠶⠛⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⢻⣀ ⣰⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠛⠋⠉⠁⠉⠚⠃⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠉⠀⠀⠀⠀⠀⠀⠉⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠤⠤⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠠⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠒⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠈⠃⠀⢀⢃⠀⠀⠀⠀⠀⠀⢀⣔⠁⣰⢹⠡⡘⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀ ⠀⢀⠄⠁⡜⠀⠀⠀⠀⠀⡔⠁⠀⡜⠙⠉⡖⡌⢿⣂⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀ ⠉⠀⠀⢀⠗⠒⢄⠀⠀⠜⠀⡠⠊⢀⣅⣀⡑⢇⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢶⠊⠣⠀⢀⢘⠇⠀⣜⠈⢀⠀⠘⡴⢥⡾⠈⡗⠀⢇⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠹⠀⠀⢠⡊⠀⠀⠨⣆⠈⢆⢘⣾⣟⣃⠀⠑⠄⠸⡀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⡠⠤⠊⠀⠈⠂⢀⠀⠘⢄⡀⠉⡛⠳⡖⠐⠠⢀⢀⡧⡒⠒⠇⡀⠀⠀⠀⠀ ⡠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠘⢠⣙⠀⠒⠂⠁⡅⠀⠈⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠈⠈⢂⠀⠀⠀⠈⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡀⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢾⡭⠈⠀⠀⠀⠀⠈⡶⠫⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠉⠉⢁⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀ ⠀⠀⢸⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣞⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⣶⣿⣇⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⠿⢟⠛⠛⠿⠿⢯⣝⣛⠻⢿⣛⡛⠋⠉⠁⠙⣯⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢿⣿⣿⣿⢳⣶⣦⣤⣀⡀⠉⢍⡙⠛⠿⠷⣶⣤⠀⠈⠹⣧⠀⠀⣄⠀⣀⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡁⠀⠀⠀⠻⢽⣲⣼⣿⣷⣄⠈⠻⣅⡀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⢀⣾⢿⣿⡏⠉⠉⣿⡿⠿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠙⢷⡮⠙⢿⣷⣤⣨⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢾⣿⣵⠀⠀⠙⣧⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣦⠠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⡏⢻⣿⣶⡀⠀⢿⣷⣄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣄⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡁⠀⣿⣿⣿⣷⡀⠙⢿⣷⣦⣘⡟⢿⣿⣶⣤⣤⣄⣀⣼⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠞⠉⠀⠈⣇⠀⣿⢻⣿⡿⣿⡀⠀⠁⠻⣿⣷⣤⣉⣛⣿⣿⣿⠿⢛⣃⡉⠹⣿⡟⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠒⠉⠁⠀⠀⠀⠀⠀⣸⡆⢻⣼⣿⡇⠙⣷⣤⡀⠀⠈⠙⠿⢿⣯⡍⣙⡓⠐⠻⠿⠿⣿⣿⡀⠀⠀⠀⢀⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⠃⠀⠹⣿⢱⡄⠀⠙⠿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢀⣤⡤⠴⣷⡀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⣿⠀⠀⠀⣿⠀⠙⢦⣀⠀⠀⠰⠄⠀⠀⠀⠒⠦⣄⣀⢁⡏⠀⠒⠂⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⢀⡟⠀⠀⣴⢃⡇⠀⠀⠿⠑⠦⣄⡀⠀⠀⠀⠓⠒⢶⠾⢻⡷⢾⣶⣶⣦⣾⣧⡀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⡿⠉⠀⠀⠀⠀ ⠀⠀⣠⡶⠋⠀⠀⠀⠀⢀⡞⠀⠀⢰⡧⠞⣅⠀⠀⠀⠀⠀⠀⠀⣼⠃⠰⠶⠤⠤⡤⡿⠄⠀⠨⡍⢹⣿⣿⣿⠷⠿⠟⠛⠛⠉⠉⠀⣴⢟⠁⠀⠀⠀⠀⠀ ⠀⠘⠉⠀⠀⠀⠀⠀⢠⡎⠀⠀⢀⡾⠁⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣠⠤⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣼⠀⠀⠀⠀⢀⡆ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⡀⡼⠁⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢀⣼⠃⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⢸⢰⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⣀⠀⠋⠁⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀