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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠷⠶⠤⢤⠀⠀⠀⠒⠀⠒⠒⠒⠦⡀⠀⠈⠒⠒⠛⠀⠈⠁⠒⠲⢦⡀⠘⠒⠒⠒⠀⠒⠒⠲⠶⣄⠀⠤⠴⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⡀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡷⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠒⠒⠦⡄⠀⠀⠀⠘⠉⠉⠉⠙⠓⠒⠶⢤⡀⠀⠀⠀⠀⠀⠒⠒⠒⠲⢤⡀⠀⠀⠠⠶⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⢻⡆⠀⠀⠀⠀⠀⠂⠒⠤⡀⢹⡄⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⡏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡤⠶⠂⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢷⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⢀⣠⠋⠀⠀⠀⠀⠠⠤⢤⣄⣀⣀⣀⣀⣀⡠⠀⠀⠀⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⠈⠁⠀⢀⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣀⣤⡤⣿⣿⣯⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⡤⣤⣀⠀⠀⠀⠀⠀⠈⠹⣏⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠞⠉⠀⠀⣿⣼⡇⠀⠉⠛⣆⠀⠀⢀⣰⠛⠉⠀⢸⣿⣿⠀⠀⠉⠻⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣿⠉⠈⠁⠀⠀⠀⠀⠈⠉⠹⣇⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⣿⠉⠉⠙⣧⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⣼⠋⠉⠁⠀⠀⠉⠀⠀⠉⠙⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⡀⢀⣀⣀⣤⠞⠃⠀⠀⠀⠘⠷⣤⣀⣀⣀⢀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠩⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢉⠛⠓⠦⡀⠀⠀⠉⠉⢳⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⠁⢦⠀⢻⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣶⣶⡶⠶⠾⠿⠿⠶⢶⣶⣤⣄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠢⡀⠀⠀⠤⠤⠤⠤⠤⠤⡤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⠿⣷⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠠⠤⢤⣞⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⠈⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢸⠀⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀ ⠘⣶⣦⣤⣀⠀⠸⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠇⠀⠀⣠⡴⣿⣃⣀⣤⡴⣶⠇ ⠀⠹⣿⡉⠉⠛⠿⣿⣶⣍⠳⢦⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣫⣷⠾⠟⠋⠉⢀⣶⡏⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠉⠙⠻⢦⡉⠳⢦⣀⠀⠀⠀⠀⠀⠉⠙⠳⢦⠀⠀⠀⠐⠒⠒⠒⠓⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠀⣠⡶⣻⣵⠞⠉⠀⠀⠀⠀⠀⣼⡿⠁⠀ ⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠙⠳⢦⣀⠀⠀⠀⠑⢄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠙⡆⠀⠀⠀⠀⠀⠀⣀⡴⢛⣵⠾⠛⠀⠀⠀⠀⠀⠀⠀⠰⣽⠃⠀⠀ ⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡀⠉⠳⣄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢰⠀⠀⠀⢀⠴⠊⢁⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡴⠞⠉⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⢀⡴⠞⠉⠀⠄⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀ 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