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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣰⡏⠀⠀⢠⢛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠙⠛⠿⣿⣿⣯⣅⡀⠀⣿⣿⣴⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⣀⣠⡏⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣽⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣠⠤⠤⣄⣀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣭⣉⣻⣿⣿⣷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠷⣶⣿⣭⣷⣾⣿⠏⣿⣿⢿⡽⢯⡿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠈⠉⢉⣣⣼⣿⣻⢎⣟⡷⣽⣚⢿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡽⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣀⣴⣿⣿⣿⣏⣷⣫⣾⣵⣧⢿⣾⣼⣿⣷⡿⠋⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⢀⣠⠦⡢⣿⡟⠁⣠⣴⣾⣿⣿⣿⢿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⣀⠜⣦⢻⣷⣶⣤⣂⣖⣲⣬⣷⠟⣉⣤⣿⣿⣿⣿⣿⣟⣯⣿⣟⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⡒⠀⠈⠛⠶⣤⣤⣄⡳⣬⣻⣼⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣷⣿⣻⣽⡿⣯⡿⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣟⣳⠶⣤⣤⣭⣭⣿⣷⣿⣾⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢻⣿⠻⠷⡿⢿⠷⣿⣛⡿⠟⠱⣉⠘⣿⡄⡀⠀⠀⠀⠀⢸⡟⣿⣂⠀⠀⠀⠀⢀⣴⢳⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⣶⣿⣿⣿⣿⣿⣿⢿⣻⣿⣧⠀⠀⠀⠀⠀⢯⡟⠳⠶⣤⡆⠠⠤⠀⠌⡑⢠⢃⠩⣿⠇⠀⠀⠀⠀⠀⠙⣬⢿⣶⣀⣤⡶⠛⣡⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⣷⣿⣿⡿⣿⣿⣷⡀⠀⠀⢠⡾⢋⡑⢣⠐⡡⢃⠀⢤⣄⣀⣀⣀⣀⣿⠠⠀⠀⠀⠀⠀⠀⠈⢻⣿⣏⣁⣰⡚⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣾⣿⣿⣻⣿⣿⣆⢀⡟⢠⠡⠜⡠⣍⠰⢀⣶⠂⠀⠀⠈⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢙⠉⢷⡀⠀⠀⣀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠿⠋⠛⠛⠛⠉⠈⠻⣧⠠⡉⢆⠡⢻⡆⠌⡟⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⠘⣧⠖⣪⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡱⠨⢌⡡⢻⣼⠛⢦⡀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠡⠒⡄⢛⢿⣄⠀⠈⠓⠦⣀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⠁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠒⠒⠒⠦⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣴⣶⡶⠀⠀⠀⠀⠀⠀⠀⢉⠓⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⣶⣿⣽⣻⣿⡇⠀⠀⠀⠀⠀⢀⡜⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠲⣬⣯⣿⣷⡿⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣳⢳⡞⣼⡹⣗⣦⡀⠀⠀⢠⣿⠃⠀⢀⡏⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢯⡷⣭⢳⡝⣶⠝⣮⣿⣿⣶⣾⣟⢿⡟⣻⢻⣄⠀⠀⣼⡇⠀⠀⠀⢀⣀⣠⡤⣤⠴⣶⠶⠂⠀⠀ ⠀⠀⠀⠀⠀⠤⢶⣶⣿⣿⢋⣹⢻⣗⡓⣋⢭⣀⣼⣿⣿⣿⣿⣿⣿⢊⣿⡵⡊⠘⡆⢠⣿⣟⣠⢖⡛⣍⣖⣧⣽⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡫⣖⡹⣷⡹⡞⣼⢲⣿⣿⡻⠿⠻⣿⣿⠆⣹⡗⣜⠭⣷⣾⣿⡟⣼⣞⣽⣻⠾⠋⠁⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡷⣌⠳⣿⣷⡹⣧⣿⠏⠁⠀⠀⢀⣠⣿⡏⣾⣿⡼⣟⣿⣿⣿⣽⣿⢾⣿⣷⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣎⢳⣿⣿⣿⣿⡟⠀⢀⣤⣞⣿⣿⣿⡱⣿⣽⣷⣿⣿⣿⣿⣿⢿⡿⢿⡟⣯⣟⣶⢦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⣾⣿⣿⠿⣿⣧⠀⠈⢿⣿⣿⠛⣿⣵⣟⡭⣿⣿⣿⡽⣞⢫⢏⡝⡫⠝⠡⣏⡝⣛⡻⡹⠿⣷⢦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢅⣹⣼⠇⠀⠘⡿⢟⣰⣿⣿⣿⢳⣿⣿⣿⣿⣾⣵⣎⣼⣱⢫⣝⣲⣜⣵⣭⣿⠽⠞⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⢻⡟⠉⢣⣉⠉⠉⠉⢉⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠣⣄⠀⠀⠀⠀⣠⣾⣿⣿⡟⢿⣿⣿⣮⠛⠿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⠲⠤⣚⣩⣿⣿⣿⣿⡶⣬⠽⠿⠷⣄⠀⠈⠉⠙⠓⠛⠻⠟⠷⠶⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡇⣈⠽⣿⢿⣿⣿⡿⠛⢻⠀⠱⡄⡠⠊⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣰⣿⣿⣿⠏⢈⣛⣭⣥⣤⡿⡄⠀⢹⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠛⠉⠁⣀⡴⠞⠋⠁⠀⡶⠷⣷⣶⣿⡛⢧⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⣇⣀⣀⠈⣿⢷⠈⠳⣀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢄⠀⠀⠀⢿⠀⠀⠀⣀⠤⠋⠈⠉⠉⢻⠃⠘⣿⠭⠖⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⣦⣤⣉⣒⡶⢾⣿⣶⣿⠧⠤⠴⢖⣲⡿⠋⠀⠀⠘⡧⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢨⡿⢛⡿⢿⠻⢿⣿⣿⣿⣿⣿⣿⣋⣀⠀⠀⠀⠀⠸⡵⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⡿⠃⠘⡯⠮⠽⠾⢿⣿⣟⡧⣽⠛⣿⣿⠃⠀⠀⠀⠀⠹⡙⡄⢱⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⢀⣴⣶⣶⣶⣶⣶⣶⡾⠁⣠⣿⣿⣿⣿⢧⣤⣴⣒⡤⠤⢾⣳⠽⢿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡈⠈⣳⣶⣶⣶⣶⣿⣯⣍⢹⡆⠀⠀ ⢸⣿⣿⠟⠛⠛⠛⡿⠀⡐⣟⣉⠟⠉⠙⠻⣶⣦⣤⣠⣤⠉⢣⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣬⣿⣧⣼⣿⣟⣫⣼⡇⠀⠀ ⠘⣿⣿⠀⠀⠀⡰⠁⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢸⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⢻⠀⠀⠀⢹⡉⠁⠈⠀⠉⠉⠉⠀⠀⠀ ⠀⣿⣿⠀⠀⢠⠇⠀⡼⠃⠀⠀⠀⠀⠀⠤⠴⠞⠋⠙⠛⠘⠘⡇⠀⠀⠀⠀⠘⣿⣿⣿⡏⠈⢳⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣄⣀⡼⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣧⠀⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⢳⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣷⣼⡏⣱⡇⠀⠀⠀⠀⠢⣄⢀⠀⠀⢀⣶⣿⣷⡆⠀⣿⠀⠀⠀⢀⣠⢶⣿⣿⣿⣆⠀⠀⢱⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠀⢹⠁⡧⡏⠓⠶⢤⣀⣀⠀⠉⠛⠛⠛⠹⠿⠏⠁⠀⣿⣦⡶⠟⠋⠁⠘⣿⡉⠉⠁⠀⠀⠀⢿⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣇⠚⣼⡇⠀⠀⠀⠉⠻⣿⣿⣶⣶⡶⠶⢶⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⢙⣇⠀⠀⠀⠀⠀⣘⣷⣀⢷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡧⠭⣿⡿⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⠃⠀⠀⢿⡛⠉⠀⠀⠀⠀⠀⠘⡄⠀⢹⡄⠀⠀⠀⠀⢑⠾⠖⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⢹⠙⡇⠀⠀⠀⠀⠀⠀⢸⢾⡟⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣧⠀⠀⠀⠠⣏⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢠⣿⠉⡇⠀⠀⠀⠀⠀⠀⣸⢿⠇⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⠇⣸⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⠀⠀⠈⣧⣿⣦⣽⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⢹⣿⠻⣼⠀⠀⠀⠀⠀⢸⣷⠇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⢹⡟⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡆⣿⡄⢸⡀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⣇⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣻⠇⠀⡇⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀
⣿⣶⢻⣿⡿⠂⣼⣿⣿⣭⣍⣽⣛⣟⣓⡙⠻⣟⢫⢖⣩⠭⢍⡓⠦⣄⠀⠀⠀⠀ ⣾⣿⡿⡏⣱⣿⣿⣿⣿⣿⣷⣽⣻⣧⣬⣿⣛⢯⣻⣫⡾⡴⣾⡎⢳⣌⠻⣤⡀⢀ ⣿⣿⡿⣾⣿⣻⣫⣿⣿⣿⣵⣟⣿⣿⠿⠛⠉⠉⠿⡞⣽⣾⠏⢧⣠⡏⠳⡝⡷⢿ ⣿⡿⢹⣷⣿⡿⣯⡿⣿⢯⣾⣟⡟⠁⠀⠀⠀⠀⢰⣳⡟⣻⢟⣹⣿⡧⢰⡿⣼⡜ ⣿⣣⣷⡷⡿⣿⣽⣿⣿⡟⣽⣛⣿⣦⡀⠀⠀⠀⣿⣿⣯⣯⣾⢹⣿⣽⣼⣹⣯⢧ ⣯⣿⣿⣿⣷⢷⣿⣿⡿⣰⠿⠁⠀⡏⠃⠀⠀⢸⣿⣿⣿⣿⡇⣼⣿⡿⣿⢿⣿⣼ ⢸⣯⣻⣿⡿⣿⣯⣿⣫⣘⠀⠀⠀⢸⠀⠀⠀⢸⢋⣿⣿⡿⡏⣷⣿⣯⣾⣿⡿⣿ ⣿⣧⢿⣻⣏⢹⣿⣿⢯⠙⠛⡶⣄⠀⠆⠀⠀⢸⢿⢸⡟⣿⡸⡿⣿⣯⣿⡟⣟⡟ ⠟⠸⣿⡇⡯⣿⣿⣼⢱⠀⠀⡇⠿⠓⠀⠀⠀⠘⡽⣼⠿⣧⣿⡿⣟⣿⡟⣿⣿⣇ ⣼⡆⢻⣿⣷⣿⣧⣻⣮⠉⡉⣉⠉⠁⠀⠀⠀⠀⢫⣿⣿⣫⣽⣿⣿⣿⢾⡿⡧⢾ ⣿⣿⡼⠸⣿⡏⣿⡏⡭⡀⠝⠋⠀⠀⠀⢠⡂⠀⠀⠻⡙⣿⡟⣿⢷⡇⣾⣷⣷⣧ ⣿⣿⡿⡶⡝⠿⠃⡄⣿⠈⣄⠀⠀⠠⣄⣀⣀⡀⠤⡄⠘⠿⡇⠫⣤⢭⣏⣹⣽⠷ ⣿⣵⣿⡿⡟⣷⡞⣧⡇⠀⠈⠤⡀⠀⡇⠀⠇⠀⠀⡨⠀⠀⡨⠞⠁⠀⠀⠀⠀⠀ ⣿⣿⡅⣿⢿⡯⣿⢼⣷⡂⣀⠀⠈⡏⠛⠢⠤⠴⠥⠒⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡟⠈⠻⣯⣿⣿⣉⠉⠉⠁⡸⠀⣟⢦⡴⣛⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
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