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⠀⠀⠀⠀⠀⣽⣿⣽⣿⣽⣿⣽⣿⡜⣬⢰⠋⢰⠟⠟⣿⢻⣿⠟⣿⠋⠟⡟⣽⠟⣽⣽⣿⠟⣽⠟⣽⠟⣽⣽⣿⠟⣬⠄⢰⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿
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⠀⠀⠀⠀⠀⣽⣿⣽⢰⠄⡜⣬⠟⠠⠠⠠⣽⣽⠟⠄⣽⠟⣿⣬⢰⠄⠟⢻⣽⢻⡟⠄⠠⡟⣽⠟⣽⠟⣿⠠⢰⣽⣽⠟⣿⠟⠠⠟⣿⠄⠠⡜⣿⣽⣿
⠀⠀⠀⠀⠀⣿⠟⠠⠄⠟⣽⣽⢰⠟⢻⣿⡟⣽⠄⣽⣽⣿⠟⠠⣽⡜⣤⣿⠟⣿⠠⠟⣬⢰⣽⣽⠟⣽⡟⣿⠄⣬⣽⣽⠟⣿⣽⠠⠄⢰⠄⠠⣽⣿⣽
⠀⠀⠀⠀⠀⣽⣿⣽⣿⣽⢻⠄⡜⣽⣿⣽⣿⠄⠋⠟⠟⡜⠠⠄⣿⠋⣤⣽⣽⣽⠠⡜⣬⠄⠟⡟⣿⢻⣿⣽⠟⠄⣿⡟⣽⣽⣽⠄⣬⠄⠋⠄⡜⣽⣿
⠀⠀⠀⠀⠀⣿⣽⣿⣽⢰⠄⠟⡜⡜⡜⣿⡟⠠⠟⣽⠟⠠⠋⣿⣽⠟⠄⣿⠟⣽⠄⣿⣽⠟⠄⡜⠠⠋⢰⢻⠟⠠⠠⣿⣽⣽⠄⠟⠄⣽⣽⣿⠟⠠⣽
⠀⠀⠀⠀⠀⣽⣿⣽⢰⠄⠟⠠⠠⠄⣬⣤⠠⢰⣿⣽⣬⣬⣿⣽⣿⠟⠠⣽⣿⠟⠠⣽⣿⣽⢰⡜⣿⠟⣬⠟⣽⠄⠠⢰⣿⠄⣬⠠⠟⣽⣿⡟⢻⠄⣬
⠀⠀⠀⠀⠀⣿⣽⣬⠄⢰⠄⣽⢰⢰⣬⠟⠄⠟⠋⠠⠄⢰⢻⣿⣽⣿⠄⣿⣽⣿⠄⣿⣽⣿⢻⢰⣽⣿⣽⣿⣽⠠⠟⢰⣬⠠⡟⠠⢰⠟⢰⡜⣤⠋⢰
⠀⠀⠀⠀⠀⣽⣿⠄⠠⣬⣿⣽⠠⠋⢻⠠⢰⠟⢰⠠⣿⣬⠠⠄⡟⣽⠟⠄⠟⢰⠠⣽⣿⠟⠟⠄⠠⠠⣽⠟⣬⠄⢻⠋⠠⠠⠟⠠⠋⡜⣬⣤⠟⢰⣬
⠀⠀⠀⠀⠀⣿⠟⣬⣽⣿⣽⣿⠄⡟⠠⠠⢰⠟⠄⣿⣽⣿⠋⠠⠄⣿⣽⠠⠠⠋⠠⣽⠄⠠⣬⣿⠄⠟⢰⣬⠠⠠⢰⡜⠄⣬⠄⠠⠋⠟⠋⣬⡜⣬⢰
⠀⠀⠀⠀⠀⣽⣿⣽⣿⣽⣿⠟⠠⠠⡜⠠⣬⠄⠟⢰⠠⠠⠟⣽⣿⣽⣿⣽⠠⠄⢰⣽⣿⣬⣤⠠⠠⠠⠟⣬⢰⠠⣬⢰⢰⠄⠟⠄⠟⡜⣬⠋⠟⢰⣬
⠀⠀⠀⠀⠀⣿⣽⣿⣽⣿⣽⡟⠄⢰⠟⠠⠠⠠⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⠠⠄⣿⣽⣿⣽⣿⣤⠠⣬⠟⠄⡜⠟⣬⣤⢰⠟⢰⡜⠟⠋⣬⡜⡜⢰
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⠀⠀⠀⠀⠀⣿⣽⣿⣽⣿⣽⣿⢰⡜⢰⠠⠄⠠⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⢻⣿⣽⣿⡜⠠⠠⢰⠠⡜⠄⠋⠄⢰⠟⠠⣬⠟⠋⣬⡜⣬⢰
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⠀⠀⠀⠀⠀⣿⣽⣿⣽⣿⣽⣬⠄⡟⣤⠠⠄⢰⣽⣿⠋⠋⠠⣬⡜⣽⣽⣿⣽⣿⣽⣿⠟⠟⢰⣬⠄⠟⠄⣬⣽⣿⣽⣿⣽⣿⣤⠠⣬⠟⠋⣬⠋⣬⢰
⠀⠀⠀⠀⠀⣽⣿⣽⣿⣽⣿⠄⣬⡜⠟⠠⠠⣤⣿⣽⣿⣽⣿⣽⣿⠟⠠⠄⠠⢰⠠⠄⣤⣬⣿⣽⢰⠠⠠⣽⣿⣽⣿⣽⣿⣽⡜⠄⠟⠋⣬⠋⠟⠋⣤
⠀⠀⠀⠀⠀⣿⣽⣿⣽⣿⠟⠠⡜⠟⡜⡟⠄⡟⣽⣿⣽⣿⣽⣿⣽⡜⠄⠠⠄⡜⠋⠠⢻⠋⣽⣿⠄⠠⠟⣿⣽⣿⣽⣿⣽⣿⢰⢰⡜⠟⠋⣬⠋⠟⠠
⠀⠀⠀⠀⠀⣽⣿⣽⣿⣽⠠⠠⠟⠋⠟⣬⠠⠟⣽⣬⣿⣽⣿⢻⠠⠄⢰⠄⣬⠄⠠⠠⣽⠄⣿⡟⠠⡜⣿⣽⣿⣽⣿⣽⣿⣽⣬⠄⠟⠋⣬⠋⠟⣬⢰
⠀⠀⠀⠀⠀⣿⣽⣿⣽⣿⠄⠟⠋⣬⠋⠟⠄⠟⡜⣬⣬⣿⣽⠠⢰⠠⠄⣿⠋⠠⢰⣬⠠⠠⣽⣽⠋⣿⣽⣿⣽⣿⣽⣿⣽⣿⣤⠠⣬⠟⠋⣬⠋⠟⠠
⠀⠀⠀⠀⠀⣽⣿⣽⣿⢰⠠⣬⣬⠋⠟⣤⠠⣽⠟⣽⠟⣬⠠⢰⣿⠄⡜⠋⢰⣬⣽⠟⠠⠄⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⠟⠄⠟⠋⣬⠋⣬⡜⣬
⠀⠀⠀⠀⠀⣿⣽⣿⣽⠠⢰⠟⠋⣬⡜⣬⠄⣿⠟⠟⠟⠠⠄⣽⢰⠠⠠⠟⣬⠟⣬⠟⠄⣬⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣬⠠⣬⠟⠋⣬⠋⣬⡜
⠀⠀⠀⠀⠀⣽⣿⣽⣽⠄⠟⠋⣬⠋⠟⢰⠠⣽⣬⠄⣿⣽⠠⠄⢰⣤⡜⢰⠟⣬⢻⠠⠠⠟⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣽⠄⠟⠋⣬⠋⣬⠋⠟
⠀⠀⠀⠀⠀⣿⣽⣿⢰⠠⡜⣬⠋⣬⠋⣬⠄⣿⣽⣤⢰⠟⢰⣬⣤⣬⡟⠟⠄⠟⣬⠠⢰⢰⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⠠⠋⣬⠋⣬⣤⣬⡜
⠀⠀⠀⠀⠀⣽⣿⣽⢰⢰⣬⠋⠟⡜⠟⠋⠠⣽⣿⣽⣬⠠⣿⣽⠟⠄⠠⡟⣿⠄⠋⢰⣿⠠⠟⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⣽⣿⠄⣬⣬⠟⣬⠋⢰⡟