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