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⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓ ⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀ ⠀⠀⠛⠤⣠⡀⠀⠀⠉⠑⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣁⡴⠃ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠈⠙⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⠤⠀⠀⠀⠀⢀⡤⡖⠉⠀⠖⠞⠁⢀⠀ ⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠹⣆⠀⢹⡤⡀⠀⢀⣴⢫⣥⢀⠾⠁⠀⠀⠀⢀⣶⠋⠀⣧⢀⠀⣠⠤⠖⠉⠀ ⠀⠀⠀⠀⠀⠉⠑⠒⠆⠀⠀⠸⡇⠀⠀⠀⠹⡦⠈⠓⡥⣄⠈⠉⠘⠋⢸⢀⠀⠀⠀⠀⣸⠉⠀⢠⡻⠈⠀⢋⣀⡤⠀⠀ ⠀⠀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⢳⠀⠀⠀⠀⠉⢧⣄⠓⢚⣪⡤⠀⠀⠀⢳⡄⠀⠀⣴⠃⠀⢀⣾⠁⠀⠘⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⣀⠈⣧⣄⠀⠀⠀⠀⠑⠶⣀⣀⡀⠀⠀⠀⠀⢯⠶⠉⠀⢀⢀⡾⠈⠘⠚⠒⡤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠒⠊⠉⠁⠀⠈⠱⣄⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡆⣠⣠⠶⢫⣀⠋⠒⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⡀⠀⠉⠓⠒⠤⠤⠤⠴⠀⠀⠀⠀⠀⢸⡄⠈⠸⢤⠈⠉⢦⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⡴⠋⠀⢠⡆⠀⢀⠀⠀⡗⠀⠀⠀⠀⢠⢯⡙⢧⡄⠀⢷⡦⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢀⡴⠋⠀⡰⠏⠀⡞⠎⢰⢄⢀⣰⡟⠈⢲⡄⠹⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠁⢀⠞⠀⠀⢸⡯⡟⠹⡦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⣠⠞⠋⢰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⣿⠀⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡏⠀⢹⠁⠀⢠⠶⠓⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⠀⠀⢧⡀⡀⠀⢀⡼⠂⢀⠀⠀⠀⡴⠛⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⢧⣄⣰⠮⣩⠍⠉⠀⣠⠞⠂⠀⠀⢫⣤⣠⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡎⠛⣷⣝⠶⢏⣩⣍⣁⣠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⢻⣦⡈⠿⣍⣍⡉⠀⠀⠀⠀⣀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⢫⣄⠈⠳⣈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⣀⣠⣀⣉⢻⣷⣾⣯⣰⣶⣿⣿⣿⣷⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣿⣯⡍⣿⣏⠉⠙⣿⣯⠉⠉⣭⣿⣶⣦⣀⢀⣶⣶⣤⣴⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⣼⣿⣿⡿⠛⣿⠿⣿⣿⣿⣿⡟⡈⠙⠿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⣿⣿⣿⣿⣿⢀⣠⣿⣿⣷⣤⣿⣿⣟⣛⣻⡍⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢉⠡⠀⠘⣽⣦⣀⢠⣽⣿⣧⡌⠂⢵⣮⣿⣿⣹⣿⣿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣻⣿⣿⠄⢠⣼⣿⣿⣧⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣿⣿⣧⠊⠀⣤⣿⣿⣿⠿⣿⣿⣿⣿⡀⠌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⠟⠘⠻⠟⠻⠟⠋⠉⠻⠟⠙⠻⠿⠛⠉⠀⠻⠿⠛⠻⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⢂⢲⣿⡿⣯⡴⠶⠞⣯⣹⣿⣿⣞⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣧⡿⣿⣿⠿⠀⠔⠒⠛⣿⣿⢻⣿⣿⣿⣿⣿⣿⡿⢙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣟⣉⣉⣉⣙⣉⣉⣹⣉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢿⣿⣿⣿⣷⠹⢿⣶⣤⣴⣶⠿⢿⣿⣸⣿⣿⣿⣿⣿⣿⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⣿⡟⢉⣻⡛⣿⣛⡟⢿⣇⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⣿⣿⣿⡤⢈⠁⠉⠁⠀⠀⣲⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣟⣿⡿⣙⣲⣽⣫⣿⣿⣿⣿⣿⣿⣧⢀⣀⣠⣶⠟⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣻⣻⣿⢿⣷⣬⣝⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠴⡄⠀⠀⢰⣶⣦⣿⣷⣿⣿⣿⣿⣿⣿⣿⣛⣹⣾⣧⣄⣀⣠⣴⣿⣿⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀⠀⠙⠛⠻⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⣾⣿⠟⠛⠻⠟⡿⠉⠀⠀⠀⠀⢀⣹⣿⣧⣀⠙⠻⠛⠛⠿⣿⣟⠛⢿⣿⣿⣷⠂⠀⠀⠀⣤⣿⣿⡿⢟⣁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⠿⣿⢿⡿⣟⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠲⣶⣿⣿⡿⢿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢰⣧⠙⠿⢿⣿⣷⣤⡀⠀⠴⣦⣄⠀⠛⠿⣿⣟⠀⠀⣴⣾⣿⣿⠟⣩⣾⣿⠿⠛⢉⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣿⣶⣿⣷⣿⣾⣷⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢙⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠂⠀⠀⠈⢷⣮⣽⡖⠀⠀⠙⢲⣤⡀⡘⣻⣶⣎⣿⣿⠏⣠⣶⡿⠋⢀⣠⣶⣿⠿⠛⠁⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠟⠛⡛⠋⢻⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠙⠻⢿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⠶⣄⣀⡈⠙⠻⢷⣤⣀⢸⡿⠟⠃⣻⣿⣿⡟⣡⣾⡟⠋⣀⣶⣿⣻⣭⣤⣴⣤⣤⣦⣼⡿⠟⠻⠋⠉⠉⠥⠄⠠⠀⠀⠐⠚⠛⠛⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀ ⣀⣴⣿⠿⢁⣀⣤⣤⣿⣿⡿⣽⣿⣿⢯⣽⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠙⠛⠿⢷⣤⣄⣀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠦⠼⠿⠿⣷⣄⣀⣿⣿⣿⣤⠾⠿⠿⠿⠟⠛⠛⢉⡉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢉⣴⣿⣥ ⣿⢟⣯⣴⣿⣿⣿⣿⣿⡟⢱⣾⣿⣿⣿⣿⢈⡱⠈⢾⣿⢏⡛⢿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡄⠀⠀⠂⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠞⢋⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄⢩⠉⢹ ⣿⣿⣿⣿⣿⣵⣿⣿⣯⢀⣾⣿⣿⣿⣿⣇⠆⣂⠡⣿⣿⠂⡀⠈⣽⣿⣿⣿⣿⣿⣦⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢐⠊⠁⠚⠃⠰⠿ ⣿⣿⣿⣿⣿⡿⢋⣠⣬⣿⣿⣿⣿⣿⣿⡷⣘⠄⠲⣿⣧⠐⡄⢂⣿⣿⡇⠀⠹⣿⣿⡄⠙⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠚⠓⢦ ⠀⢹⣿⣿⠏⣀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣟⠨⢌⡱⣿⣿⠐⡌⢦⣾⣿⡇⠀⠀⢿⣿⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣁⠶⣿ ⢀⣼⣿⡿⠀⣴⣿⡿⠃⢜⣻⣿⣿⣿⣿⣧⢿⣦⣽⣿⣿⠀⢲⣾⣿⣿⣷⡀⠀⠹⣿⣧⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀ ⣿⣿⠟⠃⠰⣿⡿⠇⠁⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⠀⠸⣿⣷⣀⠐⣻⣿⡄⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠎⠁⠀⠀⠀⠀⠀⠂⠀⠒⠒⠀⠀⠴⠂⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⢠⠈⠀ ⠟⠋⠀⠀⠀⠼⢁⡰⣰⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡗⠋⠙⣿⣿⠀⣹⣿⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⣀⡸ ⠀⠀⠀⠀⢠⣶⡷⣘⣿⣿⡟⢠⣿⠏⠈⣿⡷⣿⣿⣿⡟⣿⣿⣿⠁⠀⠈⣿⠁⠀⢹⣿⣿⣄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠈⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢸⡟⠉⠻⣿⡿⠀⣼⡟⠀⠀⢾⣿⣿⣿⣿⠸⣿⣿⡏⠀⠀⢀⣿⣾⠏⠀⢹⣿⣿⡄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⣠⢀⠀⣀⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⣿⡇⣠⣠⣼⣿⣿⣿⣿⣰⣿⡿⠂⠀⠀⢾⠟⣿⣆⣀⣼⣿⡿⣿⡄⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⡟⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡼⢁⣾⣿⡇⠀⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⡀⠀⠀⠀⠀⢀⣴⢏⠔⣥⣿⢿⣿⠁⣠⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠟⠀⠀⣀⣤⠶⢋⣡⡶⠿⠋⠥⣛⣥⣾⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣟⣿⡟⢿⣄⢙⣿⣷⠟⠋⠉⣀⣒⣛⣛⣋⣉⣀⡴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠿⠋⠀⣸⣿⣾⡟⣀⣴⠾⠛⠛⠛⣛⣿⣿⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣿⣿⡟⡴⠋⣀⣀⡐⠲⠾⠛⠛⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠎⠀⢊⣁⠨⣝⣶⣤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢠⠞⠉⠙⢿⡌⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠨⠲⢦⢰⣼⣷⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⢹⡆⡀⣾⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠡⣿⡘⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⡇⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢩⣿⣿⠁⢨⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⢟⠃⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠛⠉⠉⢉⡅⠂⣿⢠⡿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠃⠀⠀⠀⢰⣿⣤⣾⡏⢸⢁⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉⠀⠸⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢀⣸⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠴⠔⠂⠀⠀⠀⠀⠀⠐⠂⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣗⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⣛⠮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣵⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣞⣟⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢿⣝⡧⣄⠀⠀⠀⠀ ⠀⠀⠀⣰⣻⡼⣾⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣞⣽⣳⢆⠀⠀⠀ ⠀⠀⣸⢷⣫⢷⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣼⣫⢿⣅⠀⠀ ⠀⢸⣯⢯⡽⣞⣯⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⢦⣴⢶⣯⣛⣻⣞⣄⠀⠀⠀⠀⠀⠀⢸⡿⣵⢯⣟⡾⣆⠀ ⢀⡿⣞⣯⣽⣛⡶⣇⠀⠀⠀⠀⠀⠀⠈⢉⣾⢿⣽⣻⣞⣷⡻⠊⠛⠂⠀⠀⠀⠀⠀⣸⢿⣽⣻⣞⣿⣽⠀ ⢸⣿⡽⣞⣷⣯⢿⣽⡀⠀⠀⠀⠀⠀⢠⠿⢯⡿⣞⣷⣻⡼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣞⣷⢿⡾⣽⡇ ⢸⣷⢿⣯⣿⣾⣻⣞⡷⡄⠀⠀⠀⠀⠀⣠⣾⢿⣽⣳⣏⣷⣻⣇⠀⠀⠀⠀⠀⣀⣿⢯⣷⢿⣿⣯⣟⣯⡇ ⢸⣿⣻⢻⣽⡾⣷⢯⡿⣷⣦⡀⠀⠀⣸⡿⣽⣻⡾⣗⣯⢾⡵⣯⢧⠀⠀⢀⣴⣻⣽⢿⣾⣻⣾⡟⣯⣟⡇ ⠘⣿⠇⣾⢯⣿⣽⣻⣽⣷⣻⣟⣶⣴⣿⣻⣽⢷⣟⡿⣞⣯⢿⣽⣻⣤⢾⣻⣾⡽⣯⡿⣞⣷⣯⡇⠸⣿⠃ ⠀⠻⠀⣿⣿⣳⣯⣟⣾⡷⣟⣾⣽⡏⢷⡿⣽⣻⡾⣿⡽⣾⣟⣾⡯⢻⣿⡽⣞⣿⣷⣿⣻⢷⣯⡧⠀⠟⠀ ⠀⠀⠀⢹⣷⣯⣷⡟⣿⣟⣯⢿⣾⠁⠘⣿⣯⣷⢿⣳⡿⣷⢯⡿⠁⢸⣷⢿⣻⢷⡏⢷⣿⣻⣷⡇⠀⠀⠀ ⠀⠀⠀⠘⣿⣾⣿⠁⣿⣻⡾⣿⣽⠀⠀⢹⣷⣯⡿⣯⢿⣽⢿⡇⠀⠘⣯⡿⣯⣿⣻⠈⣿⣟⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡯⠀⢹⣿⣽⣷⣿⡀⠀⠈⣿⣷⣿⣟⣯⡿⡿⠀⠀⢘⣿⣽⣷⣿⡇⠀⣽⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠀⠀⠻⣿⣿⣾⡇⠀⠀⢸⣿⣿⣯⣿⢿⡇⠀⠀⢸⣿⣿⣾⠏⠀⠀⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆⠀⠀⠸⣿⣿⣿⡃⠀⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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