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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀⢀⡠⠤⠒⠂⠉⠉⠁⠀⠀⠉⠉⠉⠒⠂⠤⣄⡤⠐⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⠴⠋⢁⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠉⠓⢄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡔⠁⠀⣴⣯⡀⠀⠀⠈⠳⡄⠀⠀⠀⠀⣼⣅⠀⠀⠀⠈⢳⡀⠀⠙⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠼⣿⡿⠗⠀⠀⠀⠀⡇⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⣇⠀⠀⠨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠈⠳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠑⢒⠶⠛⠻⣾⣿⣿⣿⡦⠀⠈⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡄⠀⢣⡀⠀⠀ ⠀⠀⡰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀ ⠀⡰⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢣⠀ ⢠⠃⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⡇ ⡎⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸ ⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸ ⢷⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡀⠀⠀⣀⡼ ⠀⠛⠰⠟⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠃⠙⠛⠒⠛⠁ ⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢱⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠈⠉⢒⡶⠒⠒⠒⠒⠒⠒⢲⠈⠉⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⠀⢲⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣉⣹⠦⠴⠖⠒⠚⠛⠓⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣸⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⠤⢴⢤⠀⠀⠀⠀ ⠀⠀⠠⣿⠁⠉⠁⢀⡟⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠘⢧⡀⠀⣆⡾⠁⠀⠀⠀ ⠀⠀⠀⠹⢧⡀⣠⢜⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⢀⣠⡀⢀⣀ ⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠵⠒⠒⠲⠦⣄⡀⠀⠀⠀⠹⣄⠀⠀⣇⠀⠈⠀⣀ ⣠⡖⠋⠉⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠆⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣆⠀⠈⠓⢤⡔⠁ ⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠸⡆⠀⠀⠨⠀⠀ ⠈⡣⣄⣀⣰⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⣧⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⡜⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠲⠻⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠊⠁⢢⠄⠒⠂⠀⠀⠁⠐⠚⠠⢀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣤⣄⣤⡀⠹⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⡀⠀⠀⠈⢆⣀⡀⠀⢠ ⠀⣸⠤⠐⠂⠀⠀⠀⠒⠰⡄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠘⡖⠈⠀⠀⠀⠀⠉⠚ ⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠀⠀⠀⡇⠠⠤⠄⠤⠤⠄⠀⡏⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡸⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⡃⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠄⠊⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢒⡄⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡇⠀⠀⠀⢀ ⠁⠀⠀⠀⠐⠒⠚⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠤⠧⠤⠤⠾⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⣿⡄⠀⠀⠀⠀⠀
⠟⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠉⠛⢶⣄⠀⠀⢀⣀⣠⣤⡤⠤⠾⡇⠀⠀⠀⠀⡈⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⠽⠚⠋⠉⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠁⠸⠷⣤⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠹⣆⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠒⠄⡀⠙⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡈⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⣀⡤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⡏⠀⠀⠀⠘⠿⡷⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠀⠀⢇⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣰⠚⠁⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣄⡠⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣿⣿⣿⣿⣇⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⣿⣿⣽⣾⠟⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⠟⠿⣷⣀⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⠃⢩⡝⠛⠛⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡾⣯⣹⣏⣄⣤⣤⣷⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣷⠏⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡄⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣽⣯⣭⣹⣿⣟⣹⣟⣽⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣻⣿⣿⣿⣹⣾⣟⣽⣻⣽⢾⣽⣾⡿⣞⣻⣽⣻⣷⢯⣳⣽⣻⢯⡶⢻⣶⣟⢧⠟⠧⠼⠻⡼⣻⢷⣽⣭⠿⠮⡿⣛⣄⣬⢦⣦⣹⣉⢯⣻⢾⣤⣤⣤⣠⣀⣈⣈⣉⣁⣉⣉⣶⣤⣤⣤⣤⣡⣋⣉⣏⣻⢿⣿⡽⣩⡼⢏⣦⣟⣿⣟⡿⣿⣻⣿⡿⣷⣎⡱⣯⡿⣿⣿⣿ ⢸⠃⠒⠒⠒⠒⠖⠒⠓⠈⣾⣻⣾⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡷⣟⣼⣤⣦⢶⣾⢶⣶⡶⢷⣻⣽⡿⢶⣻⣾⣛⣾⢶⣻⢯⣻⣟⢫⣽⡻⣿⣿⣿⠫⢀⡾⣇⣜⣿⠩⠉⠊⠛⠚⠛⠟⠛⠘⠧⠋⣍⣽⣭⣩⣭⣻⣷⢛⠋⠙⠋⠉⠛⠓⡾⣻⢾⠷⠿⠶⡽⡾⢛⣢⠜⣳⣽⡻⣟⣿⣿⢣⢳⢌⡻⢯⣷⣿⣿⣿ ⢸⡧⠀⠼⠶⠶⠾⠸⡇⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣽⠿⠸⠟⠿⠭⡻⢷⣯⡿⣶⢶⣶⣿⠾⠰⡤⢬⠧⣮⣀⢀⠉⣟⣿⣰⣿⠀⢀⡃⢋⠟⣽⡻⢿⣟⣿⣿⣿⣿⢸⢱⣲⣳⣿⣽⡾⣛⢷⣯⡷⣮⣟⣳⣾⣟⣳⣿⣯⠷⠻⡿⣾⣟⣯⣳⣿⣟⢯⣿⣽⣿⣿⣟⣱⠿⣏⠷⣫⣽⡿⣿⣿ ⢹⡄⠀⢸⡅⣭⢨⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣽⠾⣽⡿⣴⣤⣦⠤⠤⠤⠂⠀⡤⣦⣶⣷⣶⣴⣤⣀⣦⢸⠀⣧⠀⠇⢤⣟⠾⠿⠻⠛⠟⣿⣿⣿⢨⢸⢸⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣿⣿⣿⡿⣞⣿⣿⢿⣻⢷⣎⣹⣾⡿⣹⢶⡏⣿⣯⣟⣯⡾⣽⣻⢷⣎⡱⣼⡿ ⢸⣇⠀⢤⡶⣶⢶⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⢿⣿⡿⣟⣻⣽⣿⠛⢉⡒⣠⢓⠩⢋⡠⢀⣍⣿⣽⣿⢾⠀⣰⠀⡸⢄⠃⣿⣿⣿⣿⣿⣿⣿⢸⢸⢸⢀⠰⡃⣿⣭⣿⣾⣤⢀⠀⢸⠃⡤⣠⣠⣴⣷⣿⣟⣷⣾⣿⣻⢿⣛⣽⢿⣽⡞⢏⣷⣯⣿⣿⣿⣷⣺⢽⡀⢸⡞⣟ ⢹⡈⣉⡉⣉⣉⣭⣍⣭⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢠⠀⠀⠃⢀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⢣⢸⠀⡎⢳⡿⣰⢀⠀⠀⡏⠁⠰⠀⠀⠀⠀⠀⣀⣳⣿⣟⣽⣿⣿⣯⣷⣭⣾⡿⣟⣾⣿⣿⣿⣿⣿⣯⠱⢎⡛⢧⣟ ⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡘⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣟⣿⣿⣯⠂⠀⠀⠀⡈⠀⡯⣿⣿⣿⣠⣾⣱⢼⡷⢤⠀⡇⢀⡇⣽⣾⢀⠀⠀⠀⠃⢾⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡿⢿⣻⣽⡻⢟⣯⠷⣻⣷⣟⣳⣾⣟⣷⣿⣻⢿⣽⣻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⣿⣿⣺⢀⠌⠀⠀⠀⢸⠀⣿⣿⣾⣽⡶⣎⡏⢑⣰⢀⠀⡘⠀⡇⣼⢊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢺⡹⢳⣎⠹⣿⡿⣿⣽⡶⣋⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⢄⠚⢀⠀⠇⢀⠁⣿⣾⣇⡑⢮⢏⣾⣟⠄⠀⠀⡀⠀⡇⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣻⣿⣾⣟⣾⣿⣯⣽⢻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣯⣵⣾⣿⣿⣿⣼⣿⣿⠁⡱⠆⠈⠀⡇⡇⡇⣫⠵⣛⡳⢏⣾⠃⢸⢸⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣞⢵⣳⣬⣛⣦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣟⣻⣽⢿⣻⣿⢸⣿⣷⡈⠰⢉⡒⠌⡆⡟⡿⢼⡹⡷⡿⣼⠘⠱⣿⢈⠐⠀⠀⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣻⣿⣟⣷⣻⢿⣾⣽⡻⢷⠻⣿ ⣿⣿⣿⡷⣯⣻⣿⣽⢿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡅⢿⣿⣸⣇⣿⣹⣰⡂⠒⢌⢂⠤⢀⡄⢸⣿⡱⣞⡷⣿⢰⡎⠇⣯⡀⠐⠄⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣽⣿⡼⢿⣧⣞⣻⣿⣿⣿ ⣿⣿⣞⣿⣳⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣯⣳⣽⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⢿⣿⢻⡿⣶⢡⡓⢌⠠⢀⠀⠀⠀⠀⣁⣻⡿⢟⣼⣐⢬⠃⣷⢠⣀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣞⣶⣷⣶⣷⣿⣷⣼⡻⣿⣿⣵⡼⡷⣬⣵⣮⣽⣵⣮⣯ ⣿⡿⣟⣿⣯⣿⣿⣿⣾⣿⣿⡿⢿⣳⣾⣽⣿⣟⣾⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡱⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣾⡏⣷⣿⣵⣏⠂⡇⡇⢀⠀⠀⠀⠀⠀⠁⡟⣿⣾⣩⠰⢒⠀⡭⡜⠀⠀⠀⠈⠀⡜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⢌⡠⠕⣢⡜⠜⢫⡹⣳⣝⢾⣠⡙⢦⡱⢢⢜⡡⠞⢫⣿ ⣾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⢟⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡄⣿⣿⣿⣿⣿⣿⢹⡿⣿⣎⣿⣯⣸⡞⡇⠅⠀⣿⠀⠀⠀⠀⠀⠀⡟⣽⣿⢹⢆⡀⠀⠀⣀⠀⠀⠀⠀⢸⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠰⡀⡋⢡⢸⢇⢦⣝⡬⣚⡘⢵⡊⢥⡊⢖⡙⢬⡹⢿⣿ ⣿⣿⣾⣿⣼⡿⣽⢿⣻⣼⣿⣷⣮⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣇⣾⣿⣯⣿⣿⣿⣿⣿⢏⣡⣼⠃⢡⡴⠀⠃⣧⠀⠀⠀⠀⠀⠀⣼⡁⢶⠙⠀⠀⠀⠀⠀⠁⠀⠀⠄⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠀⠁⠚⡸⠀⡸⢇⡱⢶⢃⡤⠚⡣⢔⡩⢟⠾⣽⣿⣿⣿ ⢯⣹⣾⢟⣮⡝⣧⣷⡿⣳⣜⡺⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡌⣿⣽⣿⣿⣿⣿⣿⣾⣯⡇⠁⡿⣼⠀⠀⡀⡠⠀⠀⠀⠁⠌⠞⢠⡀⣀⣀⣀⣅⠸⠁⠂⢀⠀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢁⠚⠆⣠⠜⠀⠀⠇⣡⡲⠬⣈⡜⡐⢏⡿⣽⢾⣿⣯⢿⣷⣿ ⢮⡝⣯⣟⢮⡙⣳⣼⣛⣦⡜⢏⣱⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⣿⢠⣇⡟⡇⣸⡔⠀⠀⠀⠀⠀⠀⠃⢠⠞⠶⠷⠿⠉⠉⠏⠴⣠⠀⠀⠁⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡼⠀⠁⠄⠀⠀⠐⢣⡤⠞⢃⠇⣡⡟⣷⢯⣳⣿⣯⣟⣻⣷⣿ ⢎⡙⢧⣻⢖⡩⢷⣮⠓⣦⠑⣳⣮⣟⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣖⢯⣿⣿⣿⣰⠀⡇⣽⣹⢸⢎⠀⠀⠀⠀⠁⠟⣪⡥⢊⡤⡤⣀⣀⣀⣀⣀⢤⠦⠱⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣵⢠⢸⠀⠅⡈⠐⠀⠠⢡⡆⠜⢢⡜⡟⣿⣻⣽⣻⢷⣻⢾⣿⣯⣿ ⢏⡃⢦⡹⢲⡱⢾⣛⢡⣺⡇⡶⢟⣣⢼⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡼⣏⣿⣿⣰⠀⠀⡅⣿⠸⣸⠘⢡⠐⠁⠛⡾⣦⡞⣧⣡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣆⠚⢡⢰⠀⠀⠱⢂⠀⢠⠡⡤⡚⢏⣇⣿⣿⣿⡽⡽⣯⡷⣟⣽⣞⣿ ⠧⡑⢮⣍⡱⢦⡍⢳⡬⠓⣧⢥⡲⢯⡗⣏⣿⣿⣝⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⢳⠉⠁⠂⠄⡏⢸⢸⢑⠡⡞⣶⣬⡈⠰⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢧⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡬⢣⢠⢹⣱⠨⠀⡈⠀⠀⠀⠐⡡⠆⠀⢽⡂⣿⣿⣿⣿⡽⣟⣯⡷⣛⣽⣿ ⡱⠲⢎⣙⡰⢇⣌⠳⣅⠱⣎⡑⢭⢻⡿⡟⣿⡿⣿⢿⡈⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣿⣽⣋⢼⢠⣇⣿⠁⠝⣿⢻⡟⠹⠠⡑⢣⠄⡍⠀⢸⡼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡼⢀⢸⡀⢱⡇⡓⢨⠐⠀⢀⠀⠀⠀⢂⠀⡡⠆⢈⣷⣻⣿⣿⣿⡿⣟⣷⡾⣟⣿ ⡹⠦⢎⡒⢅⡂⡕⢊⡡⠟⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠻⠈⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⡑⠈⠀⣀⢀⠀⠀⠀⣷⡁⡿⣭⠿⣧⣷⣽⡋⠘⢠⠐⠋⢧⢤⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢛⡴⣀⢄⠲⠀⠀⠀⠀⠀⠉⠝⣱⢎⡱⠀⠼⡀⠦⡁⠶⣍⠀⠀⢀⠀⠀⠀⠀⠠⠐⠠⡑⢧⣿⣷⣿⣿⣯⡽⣳⣽⣫⣿ ⡞⢣⢌⣘⠣⢀⡰⠟⣿⣿⣿⣿⣷⣾⣽⣿⣿⣿⣿⣷⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡿⣘⢤⣤⢤⠓⠀⠀⠀⠀⣀⣤⢶⣶⢛⣹⣿⣦⣖⣩⣶⠻⣝⣠⡑⢊⡐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⠀⠀⠀⠀⢄⠑⠋⠝⡿⣿⣿⠳⣌⡹⠆⠁⢠⠱⢂⡥⢒⠌⠀⠀⠀⠀⠀⠀⠂⡁⠄⡂⡝⣿⣿⣿⣿⣳⣽⣻⡶⢟⣯ ⡭⢱⠲⣌⠓⢀⡟⣿⣷⣯⣟⡿⣿⣿⣿⣶⣳⣿⣿⣿⣿⡿⣿⣿⢿⣌⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠭⠛⠙⠓⠈⠀⠀⠀⠀⠀⠀⠀⠠⡀⣄⣴⢳⢹⣮⡗⣿⢿⡿⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣮⠈⠀⠀⠀⠀⠀⣧⣿⣟⣿⣿⢺⢥⡖⠈⡐⢘⠣⢀⡹⢧⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⡞⣧⣿⣣⣶⣯⣳⡼⣼⠿⣏ ⣏⡱⣞⠀⠸⡟⣯⣟⣶⣮⣕⢊⢡⢛⠶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⡈⠠⠀⠀⠀⠀⠀⠀⠀⠄⣦⢳⣙⠉⠉⠛⠛⠚⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣞⣿⣻⢄⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⣫⢞⣄⠙⠀⠀⠀⠁⠀⣧⣿⡾⣿⣿⣃⠤⢙⠠⠐⢣⡀⡔⡻⢈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⢳⢫⣹⢦⣙⢷⣎⡵⢏⡧ ⣛⢧⡜⢏⡇⣿⢯⣜⡼⢎⡡⠜⣢⡱⢞⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣍⠲⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠇⣿⢏⡱⢮⠳⠉⠀⠀⠀⠀⠀⠀⠀⡄⡘⣬⢷⠹⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⣿⣛⢀⡀⢄⠑⠈⠀⢄⡑⣿⣿⣿⣟⠻⣡⠱⣈⠐⠃⢀⡆⠞⣉⠲⠀⠀⠀⠀⠀⠀⢁⠀⠂⣉⡼⠞⣘⠤⣚⡹⢷⣫⡼⣟ ⡵⠮⣙⠴⡿⣯⠷⣎⡜⢏⣡⡡⠄⡲⣝⡇⣯⣷⣟⣭⡟⣯⣶⣿⣷⣿⣷⣿⣷⡿⡙⢮⡙⢆⠩⠒⠩⠀⠉⠂⠄⠋⠿⡿⣿⣿⣿⣿⠿⢛⡙⣌⠦⠛⠘⠀⠀⠀⠀⡀⠄⠐⣀⣤⢶⠉⠀⠀⠀⠀⠀⠀⠄⣧⠾⡟⣠⠀⠁⠉⡷⣿⣄⠢⠀⡇⣾⣿⣽⣿⠸⠤⠐⡁⠄⠡⠄⢞⡡⡜⢂⠀⠀⠀⠀⠀⠠⠀⠀⢧⡎⣍⠸⢀⠞⣏⡳⢯⣜⡿ ⡻⢌⡷⡇⣿⢻⣱⢾⣏⣰⠒⡁⠰⣮⡗⠌⣻⣽⡾⣛⢯⣱⣾⡝⣳⣟⣯⡽⣾⡽⣿⢿⣙⢯⣍⠭⡛⢟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⠙⠈⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⡷⣶⣮⣳⢀⣀⣧⣸⠀⠀⠀⠀⣧⣏⡶⣟⢿⠂⡄⠘⡀⢂⡇⠍⢣⡱⢌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣌⠰⠀⠏⢥⣻⢶⣯⣟ ⢻⣭⠲⣏⣿⣏⡳⣿⣾⡁⠘⢣⡀⢞⣯⡑⢾⣻⣿⢎⣹⣶⡞⣝⡻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢜⠫⣆⠳⠛⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠈⠀⠀⣆⣬⣤⣀⠀⠀⡇⢸⠀⠀⠀⠈⡅⣻⣷⣟⣿⠀⡐⠋⣠⠁⠆⡓⠆⡡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⢸⠀⠆⣜⡻⣽⢿⣯ ⣹⢿⡬⡗⣿⢻⣯⣟⢼⠣⡈⠱⢂⢱⣷⡘⣿⢷⣻⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡌⠘⣡⠰⡿⣟⠿⠘⠀⠁⠈⠉⡞⢡⠊⣕⣻⠪⠉⠟⣬⠷⠓⠚⠜⡠⢀⢞⢠⠊⠄⠉⣷⣯⡿⢼⡌⠃⢠⠀⠀⢸⠡⢂⢡⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⣎⢹⠀⡄⡏⢷⣫⡽⣿ ⣞⢫⣽⡇⣿⢷⣯⡷⢸⠢⢌⡁⢢⣘⡳⢬⣟⣾⡿⣟⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡜⢃⡠⡗⣹⣿⣿⣿⣿⣿⣾⢿⠧⣝⣨⠈⡀⣤⣦⣶⣾⡷⣤⠀⣄⡴⠙⡝⠉⡟⣽⣿⢯⣿⢸⠃⣰⠀⠀⠀⢧⡃⠀⡜⡞⠀⠀⠀⠁⡜⠀⠀⠀⠀⠈⢒⣮⠘⠀⣽⡿⢯⣳⣿ ⣟⢺⣽⠆⣿⣻⣶⡿⢿⢆⡅⠐⢡⡘⢮⣏⡇⣟⣿⣿⡿⢿⣯⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣁⡿⣿⣾⣿⣶⣴⢤⣤⢃⣾⣉⡔⠀⠀⠀⠁⡕⢞⡶⠼⠠⠁⠜⣞⢢⣝⢿⣯⡽⢿⣿⠡⣰⠀⠀⠀⠀⡇⡈⠐⠎⢠⠀⠀⠀⡱⠘⠀⠀⠀⠀⠀⠐⢆⣎⠈⣽⡾⣟⣳⣿ ⢿⣮⡙⢳⣧⣻⣷⣾⡟⣜⡘⠁⡾⠌⣓⢦⡜⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢏⣧⡿⣿⣿⣞⣩⠚⠎⠡⠔⣞⢐⡰⠁⠀⠋⠿⣭⡟⡠⢀⠀⠃⡠⡀⣷⢷⡮⢻⣿⣞⡽⣿⡘⠀⠀⠀⠀⠀⢸⠀⠃⢰⠀⠀⠋⠡⡼⠃⠐⠀⠀⠀⡀⠄⠂⢄⣞⣻⣷⣞⣻⣷ ⢿⣮⣛⡱⢸⣧⣻⣷⢟⣯⠘⡼⢣⢄⡘⢳⣌⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣟⣯⣝⣻⢿⣾⣽⢿⠻⢌⣳⣷⣿⣿⣿⣿⣾⣿⣷⣾⣷⣷⡸⢷⣻⣧⣿⣿⣻⣿⣻⡱⠟⢟⡴⣋⠘⠀⡅⠤⣿⣿⣿⣿⣿⢿⣠⡄⣿⠸⠀⣧⣏⣽⢿⣯⣟⣯⠘⢳⠀⠀⠀⠀⠀⠉⣰⠀⠀⠀⢃⡴⠀⡀⠀⠀⠀⠀⠀⡀⠀⡁⠖⣌⣻⣷⣞⣿ ⢿⣯⣞⡼⠁⡌⣷⣻⡽⢾⣿⠌⡁⠰⡅⠣⣌⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣟⣿⣶⣋⣿⣿⢿⣬⣘⢘⢢⠀⢄⡄⠠⠤⣷⠼⣏⣿⣿⣿⢯⣻⡷⢿⣿⢛⠉⢞⢠⠀⡄⠫⠀⣄⡒⣥⣽⣇⠀⠋⣷⢻⠘⠀⣧⣾⡿⢷⣻⣽⢻⡀⠻⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆⡄⣻⣷⣟ ⣿⣛⣾⢁⠬⡞⢊⣧⡿⣞⣟⣯⠘⡃⡀⠳⢆⣯⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⡽⣞⣯⣿⣿⣿⢿⣿⣿⣿⣿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠃⣿⠟⣿⣿⣿⢾⣿⣿⢿⣳⣷⣾⣿⠿⠉⠁⣀⠠⠀⠀⠂⠿⡟⡿⢿⡾⣡⠀⠀⠀⣠⣷⣯⡽⣿⣺⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢊⡄⣽⡿ ⣿⢻⣈⠾⢏⢢⣜⠓⣤⣿⢾⣟⣯⢳⡈⡒⢌⣟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⣾⢟⣯⣿⠻⣿⣿⣿⣿⣿⣿⣿⢿⠛⠙⠀⠀⠀⠀⠀⣿⣷⣣⣿⢿⣿⣿⣿⣯⣺⢵⣿⡼⣯⣷⣿⣾⣇⠷⠙⠿⣿⣾⢟⣿⢿⢰⠀⠀⠀⠟⣽⢿⣯⡷⢺⢐⡄⠳⠈⠀⠀⠀⠀⠀⠂⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢫⡄⡿ ⣿⣿⣿⢓⣽⢣⣝⠣⣼⡉⣶⢿⣻⣵⢿⠛⢤⡒⣿⣿⣿⡾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⠴⠲⠙⠈⣿⣘⡿⣯⣿⣿⣿⣿⠻⢧⡽⡿⣿⣎⣽⣿⢿⡟⢲⡟⣿⣿⣽⣿⣿⣿⠘⠀⠀⠏⢿⣯⡷⣞⣿⢣⢠⡁⠂⣄⠳⠉⠈⠃⠟⡳⣽⡾⣿⠻⠀⠀⠁⠀⠀⠀⡠⠓⠀⠃⠀⢠⠱⢮⣗ ⣿⣿⣽⡾⣛⢧⡟⣡⠛⣿⡖⡉⣦⣿⡻⣵⣿⡟⣿⣿⣿⣽⢿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢧⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡻⠈⠘⠂⢁⠏⢞⣴⡟⣳⣟⣿⣿⣿⣿⢿⣭⡳⣽⣷⢿⡿⡞⣸⣿⣾⡟⣼⣾⣿⢾⣿⣿⣿⠀⠏⣧⢟⣳⣾⣟⣿⢠⡜⠈⠃⡍⢪⡑⠌⠧⣟⣯⡷⣟⣯⡽⣾⣸⡽⢳⠈⠀⡍⠠⠐⠡⠂⢀⠰⡜⣛ ⣿⣿⣿⣳⣟⡾⢃⡽⡿⢻⣰⠞⢣⡀⣷⣿⡻⣶⣽⣿⣿⣿⢿⣭⣞⣻⣿⣿⣿⣿⣿⣿⣿⣽⠷⢫⢾⣿⣿⣿⣦⣿⣿⣾⣴⣀⠀⠀⣀⣆⡜⠱⡇⡿⢦⡇⢷⣯⡿⣶⣞⣽⣶⣷⣼⣾⡷⣯⡛⣯⢹⢶⣡⠏⣖⡯⣴⢤⣣⠻⣌⣲⠿⢹⣶⡟⣳⣟⢯⣿⡄⠞⢉⠷⢦⢋⣱⠞⣏⡷⣟⣯⡽⢿⣹⢽⣲⡞⢏⣦⠻⡉⢧⠀⠂⡁⠀⢐⡸⡗ ⣿⣿⣿⣻⣼⠃⣽⣿⢓⣯⢧⡍⢛⡿⣿⣾⣦⣿⣟⡯⣷⣿⢿⣫⣷⢯⡷⣟⣿⣿⣿⣿⣽⡻⢿⣿⡿⣿⣴⢀⠃⣻⣷⢿⠙⠀⠀⠀⠀⠀⡀⠀⡆⠄⠠⡽⢾⣭⡳⣜⢞⡱⣭⠭⣛⣞⣰⣼⣆⣼⢤⡲⣵⣿⣽⢶⡿⣍⣻⢺⣝⠹⢧⡹⣷⣟⡭⢾⣻⣿⢠⠘⣃⡡⢖⢩⡴⠞⣏⣷⡽⢿⣯⡷⣞⡻⢭⢺⢱⣾⡝⣳⢿⠀⠘⢂⠁⠠⡘⣎ ⣿⣿⣿⣻⠖⣯⡾⣝⠻⢿⣿⣿⣿⣶⣭⠆⢠⡜⣏⢷⣯⡵⣿⣷⣻⣷⣯⡿⣷⣻⣤⣦⣷⣾⣾⣴⣠⠀⠜⠀⠱⣷⠀⡀⣦⢿⠙⠈⠀⠀⠀⠀⠀⠀⡖⡶⢶⣶⠶⡴⣤⣤⣠⣀⠀⠀⠎⢀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠋⡗⣽⡼⣾⡝⣻⢷⣻⢯⣵⡿⢃⡄⠣⡑⢶⡅⡜⢣⣝⣾⡿⢯⣳⣾⣟⢣⣶⡝⣣⡗⣎⣱⡾⢹⡀⠀⠀⠀⠀⣆ ⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣽⣚⢣⡑⢆⢉⡇⢋⣧⣿⣿⡳⣽⣿⣿⣟⣿⣯⣿⢻⠀⠀⣧⢈⠀⠀⠁⠈⠀⠀⣦⠹⠀⠀⡀⣄⣶⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠝⡧⢗⣮⡟⣭⢷⣏⡷⣯⡷⢻⣳⣷⠉⠴⢊⡠⡌⢃⡰⢲⡭⣿⢷⣻⣽⢾⢫⣱⢮⡱⢼⡳⣞⣱⢾⣝⠻⠀⠀⠀⠀⡄ ⣿⣿⣿⣿⣿⣿⣿⣼⣼⢋⢿⣳⠜⢣⡘⠬⠓⠄⡸⢽⣷⣿⣿⡽⡽⣾⣿⣟⢿⣯⣿⢿⠛⡭⣷⠾⢿⣶⡽⠢⠀⠀⣄⠳⠀⠀⠀⠀⠀⣀⣤⢦⠳⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⠻⠛⠒⠛⠛⠒⠟⠯⣳⣾⣞⡌⣳⡽⢎⢳⣡⢾⡟⣯⣟⣷⡽⣾⡿⢋⡠⠀⠀⡑⠄⡰⢎⣇⡽⣾⡿⣟⢯⢳⣻⢧⣞⡟⢣⣽⣫⡷⢎⡹⢲⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣲⣜⡟⣿⣱⢾⣋⠿⠘⣘⠣⢁⡬⡛⣧⣿⣿⣿⡽⣟⣯⣻⡿⣞⣿⣿⣿⣟⡮⠳⡀⣾⣠⢆⠾⠒⠀⠀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠤⠧⠾⣣⣀⣤⣤⢢⠑⠈⠀⡁⣦⡟⢻⣢⠜⢏⠀⡆⡙⣏⡺⣝⠖⣻⢿⣷⣯⣳⣿⣷⢘⠎⡉⢰⡩⠰⠌⢃⣯⡽⣟⢯⣶⡝⢮⡹⢷⣏⡳⢬⡳⢯⣳⢯⢣⣸⠑⠀⠀⠀ ⣿⣿⣿⣿⣽⢲⣽⡟⢯⣺⡱⢿⣿⣿⢌⠣⣀⠸⢆⡍⡰⣿⣿⣿⣿⡽⢯⣿⣻⣽⣿⣯⣿⣿⠿⣽⢠⠦⠽⡤⠲⠀⠀⠀⠀⠋⣟⠻⠙⠉⠀⠀⠀⠀⠀⠀⠉⠒⡠⡜⢀⣧⠙⠀⠀⠀⠀⡀⠢⠛⡽⢿⣟⢿⡿⢻⡽⠚⡽⢓⢦⡝⣦⡟⣯⣽⣿⣯⣻⣿⢾⢏⡠⡜⢃⡰⠝⣻⢷⣯⡷⣟⣯⡖⢯⣜⡻⢧⢻⣥⠳⣬⢿⢣⣾⣁⠤⠀⠀⠀ ⣿⣽⣿⣿⣿⣽⡾⣟⢯⣟⣿⣿⣿⢻⣞⠃⢄⡸⢇⡌⠳⣧⢿⣿⣷⡿⣗⡿⣾⣛⢿⣿⣿⣿⣿⣿⠿⠿⠾⠿⠛⠟⠿⠮⣱⣯⣷⣿⣿⣿⣾⢰⣀⠁⣐⣠⠀⠀⡽⠋⠖⣶⣠⢀⠀⠀⠀⠀⠁⣴⣿⡿⣷⣞⣿⠷⡾⣾⣏⡱⢮⡝⢦⡹⢾⣽⡿⢯⣳⣿⠦⢓⣌⠚⢡⡿⣎⡹⢾⣻⣼⡿⣜⣻⢧⣜⡻⢧⣞⣻⠵⣎⠽⣳⣼⠀⠀⠀⠀⠀ ⣿⣿⠿⣎⣷⣿⣿⣳⣿⣿⣶⣿⣾⣿⠜⢪⡜⠃⢢⡌⠳⣌⣿⡽⣿⣻⣷⣟⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⡟⡿⣿⣿⣻⡝⠡⠜⢋⠔⢀⠀⡇⣠⢀⠀⠀⠁⠀⠀⠉⠈⠉⠟⣿⣿⣿⣿⣽⣻⣿⣟⣮⣛⡭⢖⡩⢶⡎⣝⡳⢮⣻⣷⢼⣩⠱⢮⠃⣻⢷⣭⡾⢟⣱⣿⢫⣶⡝⢻⣧⡜⣻⣽⣿⡹⣜⡻⣽⠂⠁⠢⠀⠀⠜ ⣿⣿⣿⣿⢿⠿⡽⣾⣟⡹⣼⡷⣿⣷⣻⢞⡍⠱⢎⡉⠦⡙⣿⣿⣿⣺⣽⡟⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠴⡠⠀⠀⠀⠀⠀⠀⠀⣄⠷⡿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣯⡵⢾⣹⣉⢾⣫⢵⢮⡱⢮⢎⣓⣧⡆⢃⡴⠏⣽⢾⣹⢿⣧⡵⣻⢯⣱⡾⢏⡳⣝⡮⢷⣯⡷⣞⡽⠧⣸⡱⢚⢡⠰⠀⡽ ⣿⣿⣿⣻⣿⢿⣫⣵⢿⣣⡼⣛⣧⣽⣾⢿⣹⠿⢏⡱⣜⡚⣯⣿⣹⡶⢋⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠂⡟⣖⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⡿⣏⣹⡽⢎⡹⣜⡳⢖⢎⡹⣗⠀⠁⡝⢾⣻⣷⣞⡹⣽⡳⢯⣹⣿⢧⣻⢧⡟⣏⣳⣟⣳⣽⣻⢼⡱⢮⡘⣓⠆⣩⡗ ⢿⣿⣿⣽⣿⣿⣜⡼⡜⢳⣎⡙⣱⣿⣟⣮⣷⡾⢿⣿⡟⢾⣷⣆⡁⠟⣻⣽⢿⣳⣿⣻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠋⠉⠉⠉⠒⠟⣟⢺⡀⣷⣧⣿⣿⣿⣿⣿⢿⣿⣯⣿⣼⣟⣩⣵⢎⣱⣈⢤⡦⡕⢫⡵⢎⡱⡞⠃⡻⣥⣞⣻⣽⢿⣯⡝⣻⢞⣺⡽⣽⡞⣹⢾⡽⣯⡽⣿⡿⣷⡁⢲⢌⡜⠣⢦⣙⡽ ⣿⣿⣯⣿⣾⡿⣽⡞⣍⠳⢦⡜⡛⣳⣽⣾⢻⣛⢝⡩⢭⡋⢚⠿⣶⣿⣿⣟⡾⣿⢯⣼⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡴⣀⣦⣶⠿⢿⣿⢻⠁⡈⣷⡿⣼⣿⣿⣷⣼⣿⣞⣷⣯⠶⣝⡳⢭⣹⡶⠛⠈⠀⢄⡳⢎⢱⢼⢫⠴⣚⡭⢶⣻⢷⢯⡽⠾⣞⢯⣜⡻⣗⡮⢟⣫⢷⣿⣬⡜⡱⢎⡱⢎⡀⢱⣺⢧⡟ ⣿⣟⣿⣽⣿⣽⣿⡽⣞⡻⢧⣘⡳⢮⣹⣾⣟⣽⡾⣻⣷⢿⣯⣟⣯⢷⣯⣿⣿⣹⣳⣽⢾⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠿⡷⣿⢙⣏⣷⠻⡈⣷⣿⡿⣷⡗⢸⣿⢰⣿⣿⣽⡾⢻⣽⡟⣱⢿⣏⢧⣘⠽⣕⡹⠶⢊⡱⢎⣊⡵⣎⣻⢷⣻⣵⢿⢫⣵⡞⢧⣜⠿⣞⣰⠰⣋⡟⢣⠶⣉⠱⢣⣱⡜⢪⡷ ⣿⣿⣿⣿⣽⣿⣯⣻⣵⣻⣷⡜⢫⢷⢎⣭⡶⡟⣧⣞⣯⣷⢿⡹⢶⣫⣖⣯⣿⡿⣿⡽⢿⣷⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⣿⣿⣯⣿⢿⣿⣿⡿⢿⣿⣿⢿⣿⣿⡿⣾⡽⣿⡧⣹⣼⠏⣻⢿⣿⣟⢯⡼⡿⣏⠷⣭⢻⣧⡜⡳⣮⣻⢓⣡⠼⢎⡩⢴⣛⣥⡽⣾⡽⢺⣭⡜⢫⣴⢀⠁⠋⡷⣹⡾⣙⡲⢍⡰⡞⡹⢷⢋⢧ ⣿⣿⣿⣿⣿⣿⣟⣿⣯⡼⣻⣞⢫⡧⢎⣙⣱⢼⢫⢧⣌⡳⣎⣻⣷⢛⣦⢛⣥⣿⢿⣿⣳⡭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡜⣿⣿⡗⣿⣻⣿⣟⣯⣿⣯⣟⣿⢿⣯⣼⢻⡧⣏⣿⢿⣿⣿⣿⣻⣿⢿⣯⢷⣫⡷⣚⡽⣹⡼⢻⢦⣞⡹⢲⡱⢞⣉⡴⠛⣡⠼⣞⡹⢿⢞⣠⠁⠚⠽⣱⡼⡾⡟⢬⡚⢥⡜⡏⣷⣞⡽⢫⣷ ⣿⣿⢿⣿⣿⣷⣿⣿⣻⣷⢯⣱⢾⣓⢬⡸⡼⡞⢋⣱⡜⢣⣜⡯⣷⠿⣮⠗⣊⡵⣟⣯⣿⣿⣿⣽⣿⣿⣿⣿⡽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣾⣿⢻⣿⣿⣟⢯⣻⣽⣻⣽⣞⢻⣽⢻⣿⣿⣥⣦⣤⣷⣿⣿⣟⡾⣟⣣⢼⣻⡷⣚⡽⣞⡹⢷⣊⣿⡵⢊⡱⠎⣩⠞⣣⡕⢮⣟⣰⠁⠟⣱⢮⡝⡣⢧⢏⣶⠃⢡⢰⡟⣳⣾⢟⣧⡹⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⣽⣮⡜⢳⣎⡜⢛⢦⢛⡥⡜⢪⡵⢎⣽⡿⣿⢻⣱⢮⡹⢿⣯⣿⣿⣿⣿⣿⣷⡿⣷⡹⣷⣿⣿⣿⣿⣿⢿⠀⡀⠏⡿⣿⣿⣿⣯⣾⣿⣷⣿⣾⣷⣿⣿⣿⣿⣎⣴⠠⠀⠀⠉⠉⠋⡛⣿⣿⣽⣿⣷⣻⣿⣟⣮⣝⣾⢷⣽⣎⡱⢞⣩⠶⢎⡑⢦⡚⢇⢰⠋⣳⣬⡷⢎⡱⢮⢣⣼⠣⢀⡰⡞⡽⣻⣷⣟⢭⡼⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⢎⣍⠱⢲⢎⠑⢦⡜⡣⠔⠻⣂⠽⣞⡽⣿⣿⣿⠿⣟⡷⣞⣯⣷⣾⣏⣻⣿⣿⣿⣯⢻⣽⣿⣿⣿⣿⣿⢻⡆⣿⣿⣿⣯⣷⣽⣯⣖⢻⣷⣏⣳⣯⣷⣿⣷⣟⢯⣳⣿⣿⣟⣯⣽⣿⣻⣟⣞⣻⣿⣻⢿⣳⢿⣯⣝⢾⡿⢎⣹⠶⢓⢬⠳⣂⠵⢊⢠⠆⢉⢢⣭⠷⣎⡹⢗⢠⠐⢠⡀⠗⢎⣵⡞⣻⢧⣳⣞⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣽⡞⡍⠳⢌⡱⠖⡉⠱⡬⠓⣬⠞⣯⣝⡿⣿⣿⣿⣿⣿⢿⣛⣽⣯⢿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⠹⣷⣿⢿⣻⣿⡟⣻⣿⣛⡽⣻⡿⣛⣻⣿⣿⡿⣻⣿⡿⣿⡿⢿⣿⡻⣽⣛⣯⣟⢿⣿⡿⣿⡿⢿⣻⣿⣟⣯⣛⣭⠳⣏⠣⣬⠚⢀⠔⡎⠕⢮⡙⢯⣝⡻⢠⡄⠀⠁⡜⡳⣌⡳⢥⣚⣭⡿⣟⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠀⣀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢁⡨⢂⠡⠤⢀⠀⠀⠀⢀⡠⠤⢍⠂⢄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡹⠂⢀⣿⡆⠀⠀⠃⠀⠀⣾⡦⠀⠀⢃⠀⠹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠁⠀⠀⠣⢀⣀⣤⣃⣤⣀⠑⢄⣀⠠⠃⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢡⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠡⠀⠀ ⠀⡔⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠡⠀ ⠐⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⢁ ⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸ ⠳⢄⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡞⢤⡰⠎ ⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠀⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡧⠀⠀⠈⠁⡲⠒⠒⠒⠒⠖⠈⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠚⠒⠒⠈⠀⠀⠀⠀⠀⠀⠑⠂⠘⠐⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡨⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠙⡄⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠘⠄⠸⠒⠈⠉⠉⠉⠀⠉⠉⠉⠙⠂⠀⣠⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠋⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠰⠁⠀⠀⠀⠀⠻⠂⠀⢀⣀⣀⣀⠀⠘⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⢠⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠴ ⠀⠀⡆⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠃⠀⠀⠈⢂⠀⠀⠀⢰⣤⣲ ⠀⠸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆⢳ ⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢱⣿ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢸⡦ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡇ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠚⠛⠓⠒⠒⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⢀⡽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣴⡊⠉⠙⢢⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⠢⡀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡁⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢳⡀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣀⣠⣤⣤⣴⣶⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⠀⠀⠘⡄⢳⠀⠀⠀⠀⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⡇⠀⠀⠀ ⣿⡿⠿⠿⠿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⡿⠛⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡇⠀⠀⠀ ⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠁⠀⠀⠀ ⡆⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⠀⠀⠀⠀ ⣇⠀⠀⠀⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠞⠁⠀⢠⠇⠈⣧⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀ ⡘⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠀⠀⠀ ⠇⢹⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢧⠀⡇⠀⠀⠀ ⢠⣿⣀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⡇⠀⠀⠀ ⡏⢿⠉⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡄⠀⠀ ⡇⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠂⠀⠀⠀⠀⠀⠸⡀⢸⡀⠀ ⢧⣄⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀ ⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣠⠎⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠛⠒⠚⠓⠒⠒⠒⠲⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠼⠤⠶⠧⠤⠄⠒⠒⠒⠒⠒⠚⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒ ⣤⣤⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣾⣶⣶ ⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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