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

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