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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⢠⣄⡉⠛⠿⠿⠿⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⠇⢀⣤⣶⣄⠀⢾⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢾⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⠃⣰⣿⣿⣿⣿⡇⠈⠻⢿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠻⠿⠃⣴⣿⣿⣿⡏⢀⣿⣿⣿⣿⡿⠁⣼⣶⣄⡉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⠈⢿⣿⡿⠛⢁⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠻⢿⣿⣿⠂⣠⣠⣤⣶⣿⣿⣿⡟⢁⣼⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⠀⠉⠁⢰⣿⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⢀⣤⠈⠙⠻⣿⣿⠀⠀⢀⣠⣌⡙⠻⢿⣿⠏⢠⣾⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⢀⡾⠁⣰⡟⠀⣄⠉⠀⢴⣿⣿⣿⣿⣦⠀⠉⠀⠀⠙⠻⣿⣿⣿⡿⠁⠀ ⠀⠀⢠⡞⠀⣼⠟⢀⣼⠏⠀⣴⠄⠈⠛⠿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀ ⠀⣠⡟⠀⣼⠏⢀⣾⠃⢀⣼⠃⢠⡿⠁⣠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⢀⣾⠃⢠⡿⠁⢀⣾⠃⢠⡿⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠚⠃⠐⠛⠀⠀⠚⠃⠀⠛⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⡟⠻⢶⣤⣀⣀⣀⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣸⡿⠛⠉⠻⣿⡁⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⡁⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⣼⠏⠀⠀⠀⠀⢸⣷⣄⡀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣷⣶⣤⣄⣀⣼⠋⠀⠀⠀⢰⡿⠀⠀⠀⠀⢀⣾⠃⠉⠻⢶⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⣷⡀⠀⢀⣤⡾⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦⣄⡀⠀⠀⣽⠟⠟⠛⠉⠀⠀⠀⢠⡾⠃⠘⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠉⣿⣶⣾⡏⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠈⢿⣿⣿ ⣿⣿⣿⣿⡿⠛⣷⣦⣄⠀⠀⣿⣿⡿⠟⠳⢦⣄⡀⠀⣰⡟⠁⠀⠀⠀⠀⠈⢻⣿ ⣿⣿⣿⡿⢁⣾⠏⢠⣿⠻⣶⣿⡋⠀⠀⠀⠀⠙⣿⣶⣿⣿⣦⣄⠀⠀⠀⢀⣾⣿ ⣿⣿⡟⢡⣿⠃⣠⡿⠃⣰⣿⠋⣻⣷⣤⣀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣦⣠⣿⣿⣿ ⣿⠟⢠⣿⠃⣰⡿⠁⣼⡿⠃⣼⡟⢀⣾⠟⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣠⡿⠁⣼⡟⢀⣾⡿⠁⣼⡟⢀⣾⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣥⣼⣯⣤⣿⣿⣥⣼⣿⣤⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿