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