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⣿⡇⠀⠀⠀⠀⠰⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡶⠂⠀⠄⠒⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠊⠉⠉⢲⡄⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠊⠉⢹⣷⣦⡀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡖⠀⢀⣴⣶⣾⡟⠀⠀⠀⠀⠀⠀⣀⣴⡶⠚⠉⠉⠐⣆⢀⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⠆⠀⣠⣶⣶⣾⠏⠀⠀⠀⠀⠀⢀⣤⣶⠞⠉⠀⠉⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⠂⠀⠀⠀⠀⣠⣶⣶⣶⠂⠀⠀⠀⠀⠀⣰⣶⣶⣶⠆⢀⠠⠒⠺⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠚⠉⠉⠑⣦⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⢈⠥⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠡⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣿⡿⠉⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⢀⣾⣿⣿⠇⠀⠀⠀⠀⣰⣿⣿⣿⠏⡠⠂⢹⣿⣿⡿⠀⠀⠀⠀⢀⣴⣾⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⢃⠄⠊⣿⣿⣿⡏⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⣴⣿⣿⡿⠃⠄⠁⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣾⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡋⠈⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⢀⣤⣾⡿⠟⠁⠀⠀⠀⢀⣴⣿⣿⣿⠣⠈⠀⠀⠸⣿⣿⣧⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⠔⠁⠀⠀⢿⣿⣿⣇⠀⠀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠄⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠄⠁⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⡇⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣤⣤⠒⠁⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⡄⠊⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⡄⠊⠀⠀⠀⠀⠈⢻⣿⣿⣷⣶⡖⠋⠀⢹⣿⣿⡄⠀⡄⠊⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣤⣤⣴⠒⠉⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⡖⠊⢰⣿⣿⡟⠁⠀⡔⠊⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⣴⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⡔⠂⠀⠀⠘⣿⣿⠀⠀⡔⠊⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⢠⠐⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣶⠊⠀⠘⣿⣿⡇⠀⢠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣰⣿⣿⡿⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⢘⡉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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