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⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⢠⣼⣆⢄⣴⡦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡂⣀⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⡿⣥⡻⡿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢯⠙⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⡀⠀⠀⠀⢀⣀⣀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠉⠀⢙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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