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⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢯⣿⣹⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠛⠛⠻⣿⣦⡴⢯⡴⢶⡛⣭⠳⣟⠋⠙⢦⣀⠀⣠⣾⠏⠀⠀⠉⢀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⠃⢀⣓⡦⡤⢭⣙⡛⡾⣽⣻⣶⣴⣿⡿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠻⠛⠃⠀⠘⠙⠟⢦⣤⣤⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡽⣿⣳⠇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠈⣷⡜⢣⢞⡡⡝⣤⣋⣿⣿⣶⣿⣿⣾⣏⢿⡀⠀⠀⠀⠀⠀⠈⣟⠻⢿⣿⣿⣿⣯⣿⣿⡇⠀⡗⢠⡏⠀⠙⣇⠳⣬⠱⣓⠬⣿⠉⠀⢹⣿⣞⠛⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠁⠀⠀⠀⠀⠀⣠⣶⡿⣿⢯⣷⣻⢿⡽⣷⡾⣽⡶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡿⣾⣟⡿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠙⣿⣷⣤⣀⣐⡿⣘⣧⣎⣵⣿⣿⣿⣿⣿⡿⣿⣿⣯⠈⠁⠙⠛⠶⣤⠠⡤⠀⠈⢻⣦⣉⠙⠻⠿⣿⣿⣷⠀⣏⠀⠑⠦⠚⡁⠳⡰⢋⣦⠟⠁⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠉⠉⠉⠛⠿⢷⣻⣯⢿⣽⣻⣽⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣻⣽⣾⢿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢡⠞⠁⢻⡵⣻⡷⠀⠀⠀⠀⠀⣹⠧⢤⣄⣤⣀⣈⣭⣭⣶⣶⣿⢛⠛⢧⣹⡀⠀⢀⣠⣤⠵⠞⠋⠁⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣯⣟⣯⣟⡷⣄⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡷⣟⣿⣾⡿⢹⡆⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⣀⠉⠛⠋⠁⣀⣤⣾⣿⣿⡿⠡⣏⡶⣟⡻⣜⡳⣿⡄⠀⠀⣠⠞⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣮⡉⣿⣃⠴⢋⠤⣀⣦⣤⣤⣦⣶⣾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢿⡷⣯⣟⣾⢦⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣽⢿⣳⣿⠡⢛⣧⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠈⠛⠮⣗⣯⢳⢿⣟⣶⠜⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣤⣄⣙⣻⣿⣷⣎⣾⠟⠛⠛⠛⠿⠿⠟⡿⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣿⣽⢾⣯⢷⡀⠀⠀ ⠀⣿⣿⣿⣿⣿⣷⣻⣿⣿⢁⢣⡍⣺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡿⠋⠀⠀⠀⢀⣾⣯⣿⣿⣿⡿⣿⡿⣿⠿⣟⣻⣛⢯⡛⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣯⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡂⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⣠⣴⣖⣒⣦⣤⡀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣿⣻⣞⣿⣱⠀⠀ ⢰⣿⣿⣿⣿⣿⡾⣟⣾⠇⣾⣿⣿⢧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⠀⠀⠀⣠⠟⣻⣿⣿⣿⣶⡝⣧⡝⣶⢻⡜⡧⢞⣣⡝⢮⣘⠻⣿⣿⣿⣶⣄⣀⠀⠀⠀⠙⠮⠽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣼⣻⠀⠀⠀⠀⠀⣰⠿⣿⣽⣾⡿⣽⣳⡿⣵⡄⠀⠀⠀⠀⠀⢸⠀⠘⣿⣽⣞⣯⣧⠀ ⢸⣿⣿⣿⣿⣿⣟⣿⡏⢼⣿⣿⠻⣿⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄⣴⡿⠛⢦⣀⠤⠚⠁⠂⣿⣿⣿⣿⣿⣽⣲⣝⣮⢳⠽⣱⢋⠶⣙⢦⢣⡓⢬⠻⣿⣿⡿⢾⣿⣷⣶⣶⣶⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⡇⣿⠀⠀⠀⠀⢰⢧⠚⡌⢻⣿⣇⠀⠻⣽⡷⣿⠀⠀⠀⠀⠀⢸⡄⠀⠸⣿⢾⣽⡾⡄ ⢸⣿⣿⣿⣿⣿⣯⣿⢀⢻⣿⣏⣐⣻⣿⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⣟⠛⠻⢿⠏⢁⣠⣴⣾⣿⣟⣛⡉⢉⣩⣭⣙⠻⢾⣿⣧⢋⣎⢳⡉⣎⢳⡌⢷⣙⠮⣻⣿⣯⣛⣏⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢹⠼⡆⠀⠀⠀⠘⣦⠓⡌⣅⢢⡟⠀⠀⣿⣟⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⢿⣿⢾⣽⣇ ⢸⣿⣿⣿⣿⣿⣿⠇⡈⣿⣿⠛⠛⢿⣟⣷⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⡟⠋⠀⢰⣿⡿⢋⣵⣳⠞⢁⠘⣰⣯⡿⠉⡙⠻⡝⢿⡿⣌⢣⡕⣊⢦⡙⢎⢿⣛⣋⠛⢿⣿⣜⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⣀⠘⡇⠿⣄⠀⠀⠀⠈⠳⢬⡴⠟⠁⠀⣰⠿⣯⡟⠀⠀⠀⠀⠀⣻⠀⠀⠀⠸⣿⣻⢾⣷ ⠸⣿⣿⣿⣿⣿⣿⠀⣽⣿⠁⠀⠀⠀⠈⠻⣽⣻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⡿⣦⡀⢸⣿⣥⣼⢿⣧⣀⣠⣼⣿⠏⠀⠐⢄⠣⣚⣎⢿⠑⡲⢜⣣⠎⣜⢣⢚⣿⡟⠛⠻⠾⣿⡗⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣽⢨⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⢃⢼⡝⠀⠀⠀⠀⠀⢠⠇⠂⠀⠀⠀⣿⣯⣟⣿ ⠐⣿⣿⣿⣿⢿⣿⣖⡿⡇⠀⠀⠀⠀⠀⠀⠘⢯⣟⡿⣌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠷⣿⣮⣿⣿⣿⣿⣿⣿⣿⣶⡾⣿⣿⣿⣷⣿⣿⣴⣾⣷⢧⠣⡜⢯⡔⣋⠶⡐⢿⣦⡁⠳⢤⡉⢂⢘⣟⠷⣝⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣍⠒⡌⠳⠤⣄⣠⡤⠴⢋⣔⡭⠋⠀⠀⠀⠀⠀⢠⢏⠀⠀⠀⠀⠀⣿⡷⣯⣿ ⠀⢻⣿⣿⣿⡎⢿⣿⣯⣇⠀⠀⣾⡙⢦⠀⠀⠀⢻⣽⣻⣦⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢹⣿⠱⣊⠵⣊⠵⣳⡘⣲⢩⠒⡽⣷⡐⢦⣉⠲⢆⡉⠲⢌⡙⠢⢍⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⢵⣃⣜⣠⠧⠟⠋⠉⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢰⢿⣟⣷⡿ ⠀⠈⣿⣿⣿⣿⣈⠻⣿⣿⠀⠀⢸⣿⣼⣇⠀⠀⠀⢻⣵⣻⣿⣆⠀⡉⠱⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠛⢢⡕⡚⣌⢖⣣⠟⡤⣃⠯⣐⠻⣷⡀⠬⣓⠦⣉⡑⠦⣈⡙⠢⢍⣐⠠⠉⠑⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡞⢸⣿⢾⡗ ⠀⠀⠘⣿⣿⣿⣧⠹⡌⠻⣇⠀⠀⠹⣿⡏⠀⠀⠀⠀⢻⣷⣻⣿⠄⠐⠠⠀⠄⠈⠙⠒⠒⠖⠒⠖⠒⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⠄⠀⠀⠀⠙⠦⣉⠶⣘⠿⣔⡱⢊⡥⣋⢽⣷⡐⢤⣙⠢⢍⡓⠶⣍⡓⠤⢄⣉⠓⠦⢄⣀⠀⠉⠓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⢺⣟⣯⠇ ⠀⠀⠀⠘⢿⣿⣿⡖⣹⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⠀⠈⠄⣱⣾⣶⣦⡒⠒⠖⠲⠠⠀⢀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠎⡡⢟⡼⡒⣍⠲⡅⡎⢿⣧⠐⣈⠙⠲⢬⣑⠠⢬⣑⠒⠬⢍⡒⠢⢤⣉⠓⠒⠤⠤⣀⣉⠓⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⡿⣽⠀ ⠀⠀⠀⠀⠘⣿⣿⣷⡉⢧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡀⠠⢰⣿⣿⣿⣿⡇⠀⣀⠢⠤⠤⠬⠄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢺⡵⣣⢙⠦⣑⠣⢞⣿⡄⢩⠐⡠⢈⡙⠲⠾⣍⠒⠤⢌⡑⠢⠬⢍⣒⠢⠤⢤⣉⡙⠒⠒⠤⠤⠉⠛⠒⠒⠢⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣿⡷⡏⠀ 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