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⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢷⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠏⠀⡆⣸⠏⢢⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠖⠉⠀⠀⠀⢄⣀⠀⠀⠀⢠⠀⣰⡩⢴⣶⣶⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢀⣠⠞⣆⠀⠀⠀⠠⣄⠀⠀⠀⠉⠒⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠲⠒⠉⠀⡠⠢⡴⠙⡶⣢⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡔⢺⣾⣶⠂⡌⡇⠀⠈⡄⠀⠓⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡉⠽⠧⠀⠀⠧⣆⠀⠀⢸⡍⠲⣄⠀⠒⠥⠀⠀⠀⠈⠉⠉⠉⠒⠒⠒⠒⠒⠊⠉⠉⠀⠀⠀⠀⠐⠒⣻⠾⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠑⠚⠛⠓⠊⠁⠁⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀ ⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠶⠂⠀⠀⠀⠀⣄⠩⠇⠰⠷⢛⢲⢤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠄⠀⠀⠰⣤⠔⠊⣁⣀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⣩⠥⣴⡀⠈⠃⠀⠀⠀⠈⠈⠋⠰⠆⢈⠟⠍⠐⠒⠒⠒⢴⠇⠀⠀⠀⠀⠀⠓⠤⡀⠀⠀⠘⢆⡁⠒⠓⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⣉⣉⣉⣉⡉⠉⠉⠐⠒⠒⠒⠀⠤⠄⠀⠠⠤⠤⠤⠄⠀⣀⡀⠀⠀⠀⠈⢢⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⣀⠀⠀⠀⢠⠀⠀⠀⣠⣴⣷⣚⣦⠀⠀⢀⣼⠀⠀⠀⠀⠈⠉⠁⠒⠤⠤⢀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠤⠤⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡟⠆⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠔⣊⡙⠒⠀⠤⠄⠀⢀⡉⠐⠠⠄⠀⣀⡀⠀⠠⠤⠄⠐⠒⠒⠀⠠⢄⡈⠢⠄⠀⠀⢣⠀⠀⠀⠀⠉⠑⠒⠤⢤⡀⠀⠀⠀⠈⠙⠊⠰⢋⠀⠀⠀⠈⠳⣄⢸⢼⡟⠋⡏⣽⡤⠔⢣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⡜⡷⡘⠢⣀⠀⠀⠀⠀ ⠀⢨⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠤⠄⠒⠒⠀⠀⠐⠒⠂⠤⢈⠒⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠛⠮⠭⠩⠞⠁⠀⠀⠯⠠⠄⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡃⠀⠀⠀⢠⡜⢀⣾⣡⣁⣀⡃⠀⣆⡀⢠⠀⠀⢐⢿⡍⣺⠹⣱⠀⠀⠀⠈⠁⠂⠤ ⠀⠉⠁⠒⠈⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⡀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡄⢠⠋⠀⣾⣿⣿⣿⣿⣿⣦⡀⠋⠸⣼⠠⡃⠞⢤⢯⠢⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢇⣷⡟⡀⢻⣿⣿⣿⣿⣿⠟⡏⠀⠀⠸⠐⠁⡤⡟⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⠛⠛⠃⢊⡩⠽⠭⠖⣒⠒⠤⢤⡤⠤⠤⠤⠤⠤⠀⠀⣤⣤⣤⣴⣲⠖⣒⣒⣤⣄⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢼⠫⢇⠃⠀⢟⠛⠛⢛⡡⠊⠀⠀⠀⠀⣀⣾⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢊⡠⢤⣤⣤⣀⠀⠑⢄⠀⠀⠑⠀⠀⠀⠀⢠⠚⠁⢀⠤⢒⣀⡉⠉⠐⢄⠀⠈⠉⠋⡍⠐⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣴⡿⡁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⣿⣿⣿⣿⠈⣐⣢⠁⠀⣰⠠⡼⠋⠑⡼⡄⠀⡠⢴⣿⣿⣿⡈⢱⠀⠀⠀⠀⠀⢡⢀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠙⡗⠸⣄⣄⠀⢠⡄⣦⡠⡼⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠢⣀⠀⠀⢀⡠⠔⠀⠀⡰⢡⡟⠀⠀⠀⠘⡙⢄⠩⣐⠛⠛⠋⠁⠀⣀⠄⠀⠀⠀⡾⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⠙⠏⠝⠑⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠤⣀⡀⠀⠀⠈⠉⠀⣀⣀⣠⡼⠄⢃⠁⠀⠀⠀⠀⢱⡀⠑⢄⠉⠀⠈⠉⠀⠀⣀⣠⠤⢺⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡆⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⢠⠖⡄⠀⠀⠀⠀⠀⢸⠀⠀⡇⠻⣿⣿⣿⣿⣿⣿⣿⡇⡌⠈⠁⢰⠀⠈⢦⠎⡆⣿⡏⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⣸⠀⠀⠀⠀⠀⡸⡆⠀⠰⡀⠘⣿⣿⣿⣿⣿⡿⠁⡇⠀⠀⡖⠂⡐⢣⢠⣹⡿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⠀⡀⢢⠀⡇⠀⣀⠃⠁⢰⠀⢡⠀⠈⠻⠿⠟⠋⠁⠀⡆⠀⠀⣇⠸⠃⢆⣼⡃⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⡄⣃⠈⡄⠃⡀⢃⠀⠀⠜⡎⠀⢃⠀⠀⠀⠀⠀⢀⡰⠀⡀⡄⢉⠀⢰⡼⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠧⣏⡄⠰⡀⠰⡈⠀⢰⠀⢣⢀⠀⠑⠒⠒⠠⠈⠁⠀⠀⣣⠁⢺⣠⢿⠙⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠠⣏⠗⢤⠑⠆⣳⠀⢸⠀⢸⢀⠣⠀⡆⠀⢠⡀⡅⠀⠾⠃⡦⣸⢻⢧⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠑⠲⣹⡇⢸⢠⢘⠀⡆⡄⠃⢰⠓⢣⢣⠀⢠⢠⣷⢧⠁⠈⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡗⢤⡄⢸⡄⢣⣇⡐⢩⠂⣬⣾⢇⣼⢿⠉⠀⠀⠀⠀⡌⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⡖⠀⠁⠘⠃⡇⣀⣹⣧⣃⣼⢿⡟⡇⠊⠁⡇⠀⠀⠀⠀⠇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀