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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣯⣽⣿⣿⣿⣿⣧⡿⣿⣦⡀⠀⠀⠀⢲⠀⠸⣿⣤⣶⡀⠀⠀⠀⠀⠀⣴⣷⣿⡿⠋⠀⣴⣿⣿⣿⣿⣿⠿⣿⣶⣿⣿⣿⣿⠀⢴⡿⣿⣿⣿⢠⣾⣿⣿⠉⠀⠀⠒⣿⣿⢹⣿⣷⠀⠀⠘⢿⣿⣿⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣶⣾⣿⡿⠋⠉⣹⣿⣩⣭⣿⣿⣿⣁⣶⣿⠽⣿⣿⣿⣿⣷⣠⣬⣝⣻⣿⣿⡿⠿⢿⣧⠹⣿⣿⣦⣤⣴⣿⣷⡄⠘⢿⣿⣿⣆⡰⠷⠀⣰⣿⣿⠏⠀⢀⣼⣿⣿⣿⣯⣭⣥⣤⣿⡿⠿⠿⣿⣿⠀⠀⠀⢻⣿⡇⣾⡟⠙⣿⣧⣀⠀⠀⢸⣿⡟⢿⣿⣦⣄⡀⠘⣿⣿⣿⣿⠋⠁⠀⠀⠀⠈⠉⠉⣉⡻⠶⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣭⣝⣛⢻⣿⣿⣿⣿⣧⣤⣈⣛⣿⣿⣿⠛⠛⠿⠻⣿⣿⠀⠈⣻⣿⣿⣿⢹⣿⣿⣿⣿⠋⠀⠀⠈⠻⣦⠈⠻⠟⠉⠛⠛⠛⠛⠀⠀⠙⠿⣿⣇⣀⣴⡿⠟⠃⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⢹⠏⠀⠀⠀⢿⣿⠛⠃⠀⣸⣿⠁⣿⡇⠀⠉⠙⡻⠷⣄⣸⣿⠷⢾⣿⣿⢹⣿⡀⣿⣿⢿⣿⢄⣀⣀⡀⣴⣦⣄⣼⣟⣿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⢻⣿⡆⢀⠻⠿⠃⠙⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⠉⠛⠙⢿⡎⢻⣿⡿⢿⡆⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢀⣀⣤⣤⣾⣿⠀⠀⠀⣿⠇⢠⣿⣧⠀⠀⠀⠁⠀⠀⢹⣿⠀⢸⣿⣿⠀⢹⣿⣿⡟⠘⣻⣿⡟⠙⠻⢿⣿⣿⣏⠹⣿⣿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢀⣦⡘⠀⠀⠀⢀⣄⠀⢶⣶⣾⣿⣿⣿⣿⣿⣄⠘⢿⣿⡀⠀⠀⠀⠈⣷⣶⣤⣤⡀⠘⣷⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢁⣿⡟⠉⢹⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠻⣿⠋⠉⠀⢸⣿⣿⣤⣼⣿⣿⡇⠀⠀⠀⣟⠻⣷⡆⢉⣿⣿⣷⡏⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡶⢸⣿⡼⣿⣿⡟⢇⠀⣠⣿⣤⠀⣠⡙⢿⣿⣮⡉⠉⣿⠀⠘⣿⣿⡄⠀⠀⠀⢺⣿⣿⣏⠀⠀⢹⣿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⡾⠋⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⣿⢿⣿⡇⠀⠀⠀⠀⣿⠀⠒⢢⣿⣿⠁⠉⢻⣿⣿⠇⠀⠀⠀⣿⣷⡀⠀⠘⠿⠷⠜⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣾⣿⡇⠘⣿⡇⠈⢻⣿⣿⣿⡀⠘⣷⡈⣿⣿⣿⣦⣿⠀⠀⣹⣿⣧⣄⣀⡄⠀⠙⣿⣿⣧⣄⠀⢹⣇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⡇⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⢀⣿⡾⢿⣷⠀⠀⠀⠀⣿⣤⣤⣿⣿⡿⠀⢠⣾⣿⣧⠀⠀⠀⠂⣿⣿⣧⠀⢰⣶⡆⠀⢹⣿⣦ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⢻⡟⠻⣷⠀⢸⣿⠀⠸⣧⣿⣿⣧⠀⢹⣿⣿⡟⠿⢿⣿⡀⠀⠛⢻⣿⣿⣿⠁⠀⠀⢸⣿⣿⢹⡆⠘⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⢿⣿⢃⣿⠇⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⣿⣄⠀⢸⣶⣿⣿⠿⣿⣿⣤⣄⣸⣿⠀⢀⡀⢠⣤⠾⠟⠻⣿⡆⠸⣿⠁⠀⠻⣿⣧ ⠀⠀⠀⢠⣾⠟⢻⣿⡟⠁⢰⣿⡿⢻⣶⣿⣇⣰⣿⠀⠀⠙⣿⣿⣿⠀⠀⠈⣿⣿⣿⡿⣿⡇⠀⠀⣿⣿⣿⣿⣷⠀⠀⠈⣿⣿⣷⠀⠀⢹⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⣸⣟⣾⠃⠀⠀⠀⢸⣹⣿⡇⠀⠀⠀⢠⣾⡏⠀⠀⣿⣿⠀⠀⢿⣿⣷⣤⣿⣿⣿⠙⠉⠉⢰⣿⣧⠀⣀⠀⠀⠀⣿⣷⡄⢿⣧⡀⠀⠀⢹ ⠀⠀⣰⡿⠁⣴⣿⣿⠁⢠⣿⢻⣷⣾⢿⣿⣿⡏⠉⠀⠀⠀⢘⣿⣿⣦⠀⠀⢿⡿⠛⣣⣿⣧⣤⣴⠉⣿⣿⣿⣯⠀⣠⣜⠛⢿⣿⣦⠀⠘⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢀⣾⣿⡇⢀⣠⣼⣿⣷⣤⢴⣿⣿⣿⣿⣿⣿⡄⠀⢠⣼⣿⣿⢿⣿⠇⠀⠀⠸⣿⠇⠈⠙⢃⡀⠀⠀ ⠀⢠⡟⠁⢠⣿⣿⡏⠀⢸⣧⡾⠟⠃⠀⠙⢿⣷⠀⠀⠀⠀⠚⣿⣿⣿⣧⠀⠀⠓⠘⢿⣟⣿⣿⡇⠀⠿⢿⣿⣿⡀⠈⢿⣄⠀⢻⣿⡃⠀⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⣼⡿⠟⠁⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⣸⣿⣿⣷⠿⠿⢿⣿⢿⡧⠾⢿⣿⣿⣿⣿⣿⡅⠀⠈⠉⣿⡧⠸⠁⠀⠀⠀⠀⢿⡆⢀⠀⢸⣷⠀⣶ ⣴⡟⣀⣤⣼⡟⠁⠀⠀⣸⡇⢀⣤⠀⠀⠀⢀⣿⣷⣤⣾⠇⢠⣿⣿⣿⠉⠀⠀⠀⠀⠀⣿⡟⠛⠛⠀⠀⠸⠿⣿⡇⠀⠈⢻⡇⠈⣿⣿⣀⠻⣿⢸⣟⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⣀⠀⠿⠟⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⣰⣿⣿⣿⡇⠀⠀⣼⣧⠀⠀⠀⢸⣿⠁⠀⠘⣿⠃⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣾⠃⠀⠿⠀⠀