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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⣿⠇⠀⣸⣿⠇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇⠀⠀⠀⢠⡇⢸⠃⠀⠀⠀⢸⠆⠀⠀⠀⠀⣼⠀⠀⣿⢀⣇⠘⣦⠀⠹⣆⠲⣙⢾⣿⡝⣎⢧⠀⠀⢸⡇⠀⡏⠀⣇⢸⡄⣧⣿⠀⠸⣷⢠⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣼⣿⠀⢠⣿⣿⠀⠀⠀⠀⢠⡏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⠀⠀⠀⠀⡾⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⣿⢧⡈⢷⣄⠙⠆⠘⢦⡛⣿⡜⣮⢧⠀⠘⣇⢀⡇⠀⢹⣄⣧⢸⣿⣆⠀⣿⡟⣿⡆⡍⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣿⠏⢰⣿⣽⡇⠀⠀⠀⣰⣿⠀⢠⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⢰⠇⢰⡇⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⢀⡟⣸⣿⠈⠳⣄⠻⢿⣦⡀⢺⣝⠙⣿⡜⣿⣇⠀⣿⠠⡇⣾⠈⢻⢹⠈⢻⣿⡆⣿⣷⣋⢠⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⣿⢀⣿⣿⡿⠀⠀⠀⣰⠃⡇⠀⣾⠀⠀⣼⡇⠀⠀⡄⠀⠀⠀⠀⣼⢸⠁⠀⡄⠀⣿⠀⣼⠀⠀⣸⠀⠀⣿⠄⠀⠀⠀⢰⡇⢀⣾⠃⡿⡏⠀⠀⠈⠳⢤⢻⣿⣄⢹⣦⣹⣿⡾⣿⠀⣹⢀⠀⢸⠀⢸⡘⡇⢸⣇⢻⣼⡏⢸⣾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⡇⡼⢸⣿⡇⠀⠀⡼⢣⣾⠃⢰⠇⠀⡼⣻⠁⠀⣸⠁⠀⠀⠀⠀⣿⣼⠀⢰⡇⢸⠇⢠⡏⠀⢰⡏⠀⠀⣿⠀⠀⡀⠀⢸⡇⡎⣾⢀⣇⣥⣤⡶⢶⢾⠋⠙⠻⣿⣷⣿⣿⣿⣿⣟⢷⣹⣈⠀⢸⠀⠸⡇⣧⠘⣿⠈⣿⣧⣰⡏⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⢰⠇⣿⣿⠀⠀⣸⠁⣾⡇⠀⡾⠀⣰⢃⡏⠀⢀⡟⠀⠀⠀⠀⢠⡟⡇⠀⢸⠀⡟⠀⣼⠃⠀⣾⡇⠀⠀⡟⡇⢠⠇⠀⣸⠻⢳⡿⢸⠛⠉⣩⠀⢰⠀⠑⢤⡀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇⠀⣿⢸⠀⣽⡇⢿⣿⠛⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣼⡇⣾⢸⣧⡇⠀⢰⣇⣼⣿⠁⢰⠇⢠⡿⣿⠁⠀⣼⠀⠀⠀⠀⣰⢨⣧⡇⠀⣸⢸⡧⢠⡏⠀⢰⠇⣿⠀⢀⡏⡇⢸⠀⠀⣿⠀⣾⡇⣾⠀⡴⠃⠀⠞⠀⢀⣤⠝⠂⢀⣴⢎⣹⣻⣿⣿⣿⡇⠀⢸⣿⡆⢻⠘⡇⠋⣷⢸⡟⢈⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⢰⢇⣿⣿⠃⠀⣼⢣⣿⡏⠀⡾⢀⣿⢣⡇⠀⢀⡇⡆⠀⠀⠀⡇⣼⢹⠃⠀⣇⡿⠀⣸⠁⠀⡿⣦⣿⢀⣾⣷⠇⡼⠀⢠⡿⣸⣿⢁⡇⢾⣡⠤⢖⡾⢋⣭⣵⣾⣿⣿⡟⠿⠿⠟⠛⡈⠙⣷⠀⢸⠇⠇⢸⡇⡇⠀⣿⡈⡇⣼⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⣾⡾⢻⡿⠀⣸⢏⣿⠃⠀⢠⡇⣼⡟⣾⠀⠀⢸⠁⡇⠀⠀⢸⣧⣿⠸⠀⠀⢸⣿⢃⣿⠀⢸⠇⡄⣿⡄⢹⣿⠀⡇⠀⢸⣷⣿⡟⢸⢿⡿⣄⣠⣉⣴⣿⣿⡿⢿⣋⠙⢽⡆⠀⠀⢀⣴⠀⣿⠀⢸⡇⠀⢸⡇⣿⡄⢸⣿⣿⠃⢀⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⢣⣿⠃⣾⡇⢰⡟⣼⣽⠀⠀⡼⢠⣿⢠⡇⠀⠀⣼⢰⠃⢸⠀⢸⢻⡇⠈⠀⠀⣿⡇⣾⣿⠀⡿⣸⠃⣿⡇⣸⡇⢠⡇⠀⣿⡿⢿⡇⣾⢸⠀⢈⣼⣿⡿⠻⡇⠀⠸⠏⢀⣠⣧⣤⣶⣿⠗⠀⣿⢰⣼⡇⣠⣌⡇⢹⡃⠘⣿⡇⠀⡼⠁⢰⢉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⡏⣸⡏⠀⣿⠁⣾⢡⣿⡟⠀⢰⡇⣼⠇⣾⠘⢡⣆⡟⢸⠀⣿⠀⣼⣿⠇⠀⠀⠀⣿⢸⣿⡟⢸⣿⡏⠀⢹⣷⣿⠃⢸⠁⢸⣿⢧⣿⢱⡏⢹⣚⣿⡿⠋⠀⠀⢻⣤⣴⣾⣿⣿⠞⠛⢂⡀⠀⠀⣿⢸⣿⡇⢻⣄⡇⢸⡇⠀⢿⡏⣼⠃⠀⡾⢸⣧⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⢃⣿⠁⠀⡏⢸⡇⢾⣻⠃⠀⣼⢰⡟⢰⣿⠁⢸⣿⡇⢸⠀⣿⠀⣏⣿⠀⠀⠀⣸⠇⣿⣿⠁⣿⣿⠆⠀⠸⣿⣿⠀⡾⠀⣿⠟⢻⡿⣾⡟⢛⠉⠟⣠⣤⣶⣾⡭⠟⠛⠋⠀⠀⠀⠀⠀⢧⠀⠀⣿⣿⢿⡇⣸⡇⣷⡼⣇⠀⣿⣷⣿⠀⠀⠃⢸⣿⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢸⡟⠀⠀⡇⡿⠀⣾⣿⠀⢰⡇⣼⠃⣾⡏⠀⣼⢹⠇⡟⢀⣿⢰⣧⣿⣰⠀⣴⡟⢸⣿⡟⢰⡇⠈⢳⣦⡀⣿⣿⠐⠃⣸⣿⣇⣾⣿⣿⢡⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⣿⣿⣸⣧⣿⠃⣿⣰⣿⡏⣿⡇⣿⠀⠀⠀⣾⢿⠇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢰⡧⣼⠃⠀⠀⣿⡇⢰⣿⡏⢠⣿⢰⡏⢠⣿⠁⠀⡇⢸⠀⡇⣸⠟⢸⢹⣿⡿⣰⣿⠃⣿⣿⠃⣿⣿⣿⣿⣾⣿⣿⣏⠀⢰⣿⢃⣼⣿⣿⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⣹⢸⡋⣿⣿⡅⣸⣷⠇⠀⠀⢰⡏⡿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣤⡿⠀⠀⢀⣿⠃⣼⣿⢡⢂⡇⣾⠁⣸⣿⠀⠀⡇⣸⠀⡇⡇⠂⣸⣼⣿⣇⣿⡟⣸⣿⡿⣰⠏⠹⣿⣙⣽⣯⣽⣿⠀⣸⡏⢈⣿⣿⣯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣿⠏⣿⣾⠁⣿⣿⡇⣿⠟⠀⠀⠀⣼⢰⢃⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣸⣿⢠⣿⡟⠋⣸⣼⡏⢀⣿⡇⠀⠀⡇⡏⠀⡇⡇⠀⡿⢹⣿⠙⣿⠃⣿⣿⣷⡿⣤⣶⣿⠿⣿⣫⠩⢻⣦⣿⠇⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⣿⣿⠀⢟⡏⠀⣿⣿⡇⢿⡇⡴⢠⢼⣷⣿⣿⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡇⠀⠀⣿⣿⣾⣿⡇⢀⣿⣿⡇⣼⣿⡇⠀⢰⡇⡇⢸⠃⠁⠀⡇⢸⣿⢠⡿⢰⡿⣿⣿⢷⡿⠝⠛⠉⠁⠀⠐⡄⣿⣿⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣼⣿⡇⠰⣸⠁⢠⣿⣿⣇⣾⢁⠁⣩⣿⣿⣿⣿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⣿⣿⡿⢻⠀⣼⣿⡧⠀⣿⣿⠁⠀⢸⡇⡇⢸⠀⠂⠀⡇⣸⣾⣼⣧⣾⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⢠⢇⣿⡟⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⣸⣟⢀⣸⣿⣿⣿⣿⣩⣿⣿⡿⣿⣿⣤⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣘⡇⠀⠀⣿⣿⡇⡞⠀⢡⣿⡇⢸⣿⣿⠀⠀⢸⡇⡇⢸⠀⡇⠀⡇⣿⣿⣿⢻⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⡞⣸⢹⡇⣿⠏⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇⣼⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠉⢻⣿⠇⠀⣸⡇⣷⡘⣽⣿⠀⠀⢸⡇⡇⡜⢰⡇⠀⣿⡿⢿⣿⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⠞⢱⡏⠀⠠⣜⣀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣼⣥⣿⠟⣼⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡾⣰⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⣾⠉⠀⠀⣿⠀⢸⡇⣿⣿⠀⠀⢸⡇⡇⡇⢸⠧⡀⡏⡇⣸⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⡾⢰⡇⠱⡾⠀⠀⠀⠀⠙⠻⠷⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠰⢁⣼⣷⣿⣿⡿⠟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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