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⠀⣧⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣴⣀⢀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣄⣄⣤⣶⣷⣿⣿⣼⣀⣿⢰⠀⠀⠀⠀⣧⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿ ⠀⡇⠘⠀⠀⠀⠀⡄⣿⣧⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢠⠀⣿⢐⠁⠀⠀⠀⡏⠀⠀⠀⠀⡀⣀⢀⠀⡀⠀⢀⠀⠀ ⠀⡀⢿⠐⠀⠀⠀⠀⡆⠹⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⠀⠀⣿⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢹⣆⣿⡇⢼⠂⠈⠛⠐⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢸⠀⠀⠔⣠⠟⣿⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣾⡇⢠⠁⠟⢠⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⢷⠧⠻⠉⡟⣿⢃⣿⣾⣶⣴⢤⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣤⣠⣀⣄⢶⢹⣇⠙⠇⣸⠀⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡆⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⠀⠀⠟⣰⠀⠀⠀⠀⠀⠀⠀⡀⣦⣼⡿⢰⡞⢀⡡⢿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⢦⡇⢻⠋⣿⣿⣽⢁⠞⠦⠰⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠁⡼⢠⠀⠀⠀⠀⠀⠞⣤⣄⠷⠀⣇⡿⠏⢀⠀⡇⣼⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠸⡀⢸⡇⣿⣿⢰⡗⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠹⠀⣖⡣⢰⠀⣿⣸⠘⠃⡇⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣿⣾⠎⢹⣹⣷⣿⠸⡄⡱⠉⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⢦⠶⣠⠀⠃⣿⢰⢿⢘⣿⢿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⣟⣿⣿⡐⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣾⠄⣟⢳⣺⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⣾⣿⢻⡏⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⡠⢀⠋⡼⣏⣿⢸⠟⣥⡏⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢼⣇⣷⣸⣻⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡤⢯⠿⣻⠟⣿⣿⢻⣿⡤⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢯⠉⡿⣿⣼⣿⣿⢮⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣾⣿⠏⣿⣼⣡⣿⣾⣿⣿⢻⠛⡝⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣆⡟⣿⡛⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣷⢸⡄⣿⣿⢻⡿⣿⣿⣿⣿⣴⢯⢻⣷⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣾⣾⣌⣯⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⢋⡶⣼⣼⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣻⢯⣈⢦⡒⣿⣿⣿⣯⣿⣯⣿⠿⠘⠀⠀⠋⠶⠒⠉⠀⠀⠀⣏⣿⣿⣾⣿⣿⣿⣿⣿⣿⠉⠛⣹⣟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣷⣭⣯⣻⣿⣯⣿⣻⣯⢿⣿⣿⢿⢋⡠⢀⠀⠀⡀⣄⠡⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣯⣿⣿⣿⣸⢀⠆⠀⠀⠀⠀⠀⡇⣿⣧⣿⣿⣿⣿⣿⣹⡇⣏⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣿⣿⣿⣻⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⣇⣿⣿⣿⣷⣿⢿⣿⠀⠀⠀⠀⠀⠷⠈⠀⣇⣯⣿⣿⣿⣿⣿⣿⣵⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣏⣿⣿⣿⢰⠀⠉⠛⠛⣛⢩⠀⡇⣿⣯⣿⣿⣿⣿⣿⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣯⣿⣾⣿⣿⠟⣴⣠⠀⠀⡀⣄⣶⣷⣿⣿⣿⣿⣿⣿⣿⣸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢟⣿⣯⢻⣿⣴⢀⠀⠋⠿⠽⠿⠙⠀⡀⣇⣿⣿⣿⣿⣿⣿⢻⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣗⣻⣿⣿⣿⣿⠐⠀⠀⣀⣆⣴⣢⠠⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⣿⣿⢿⣿⣼⠀⠀⠀⠀⣷⣼⣿⢰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⢀⠤⠢⠒⠉⠈⠀⠀⠀⣯⣿⣿⣿⢻⠀⠉⠉⠉⡉⠁⡀⠛⠿⠿⡟⣧⣷⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠲⡟⣿⣿⣿⣿⡹⣬⣤⣥⣝⠀⠀⣛⣛⣛⣝⣻⡟⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣯⢿⡬⣤⢀⠀⠀⠀⠀⠂⣿⣿⣿⢿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣝⣿⠙⠀⠀⠀⠀⠀⠁⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠦⠷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⠏⠿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣦⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⢶⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀