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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢂⡭⠯⣯⠝⡝⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠕⢛⢯⣦⠹⢷⡬⠢⡀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣌⣠⣄⡐⠁⢉⡑⠖⠒⡠⣀⢰⣏⡎⠋⢮⣑⡾⡤⠠⡇⡄⣿⠄⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠽⡟⢳⣿⣿⡿⢠⣦⣦⡦⠜⣿⡇⠀⠀⣟⡿⣿⡖⡃⢇⣸⡞⠈⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡮⠀⡻⣿⢀⡨⠓⠋⢡⢨⡿⣧⣂⡘⣿⡿⠋⢳⢸⢿⣧⣿⡅⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡃⢀⢿⡏⢈⠀⠀⠀⣘⢟⢿⣼⣏⢁⣧⡇⠀⢈⣷⢯⣿⣿⢭⣴⣴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡑⠀⢪⣾⡇⡄⠀⠀⠀⡟⣸⡷⢏⣿⣎⡗⠏⠤⠠⢨⢿⣽⣿⣷⠸⡎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⠁⢀⣞⢼⡇⡇⠀⣀⡤⢟⣿⣿⢎⣹⡿⢷⣤⣀⡀⢸⢡⣿⣿⣿⡾⡙⠘⣎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⣬⠠⠸⣷⢵⠾⡉⢋⣰⣿⠝⣰⣿⡿⣞⣟⣿⣂⣿⣿⣯⢿⡟⡆⠓⠀⡇⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡏⠐⠀⣻⡦⠈⢻⠀⠀⢱⣸⣷⣿⡇⡟⣿⣧⣿⣿⢙⣿⣿⡌⣿⣽⡄⣷⠐⣡⣿⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠀⢀⠔⠛⠀⠀⢸⠀⠀⢀⣿⣿⡿⣿⣄⣻⣿⣿⣿⡷⠼⣿⣫⢜⣿⣇⡇⣣⣿⣽⡿⢢⡇⠀⠀⠀⠀⠀⠀⠀ ⠹⠠⣼⠲⣦⡤⠤⣼⡂⠔⢱⠻⠛⡷⣷⣾⣬⠽⣮⣷⡅⠛⠛⣻⣿⣿⣿⣦⢳⡽⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⡆⠀⢷⣿⣫⣿⣽⡿⠁⠀⠀⡤⣟⣵⢻⣿⣾⣼⡟⣯⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢰⠰⡘⢿⠛⡿⣮⣱⢀⡊⣈⣿⣿⣯⠕⡟⣷⣘⡟⢟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡦⠀⠀⢇⠘⢮⣗⣦⣜⢿⣿⣟⣿⣶⣿⣽⢛⠜⣱⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠇⠀⢀⠨⡒⠀⠙⠷⣝⢷⣿⣾⣾⣿⣿⣾⣿⣀⠻⣧⠁⠈⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡏⡇⠀⠀⠀⢰⡠⢉⣠⣀⣀⣀⣠⣼⣧⣾⣇⣼⣯⣿⡻⣏⡀⠉⠋⢷⡣⡆⠈⢢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⡃⠀⠀⠀⡆⣨⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣯⣟⡟⡇⠀⠀⠀⠈⠺⢎⣠⠐⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢀⢣⠃⢀⣦⡀⡀⢸⠀⠀⠀⠂⠀⠀⠀⡈⠀⢱⢠⠀⠀⠀⠀⠀⠀⢟⠂⠀⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⣸⡇⢀⡾⢸⡇⢡⠸⠀⠀⠀⡆⠀⠀⠀⣇⠀⠘⣧⡆⠀⠀⠀⠀⠀⢸⢆⢰⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⢿⠀⣼⠁⢒⠀⠀⡆⡇⠀⠀⡇⠀⠀⠀⢻⠀⠀⠘⡵⡀⠀⠀⠀⠀⠈⡼⢨⡄⡏ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⢻⡟⠀⠋⠀⠝⢀⡀⣧⠃⠄⡀⡇⠀⠀⠀⠸⡄⠀⠀⠱⣶⡀⠀⠀⠀⠀⠹⣧⣧⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣎⠛⣰⣦⣶⠶⣴⠀⣬⣵⠰⢠⣡⠠⡐⢐⢪⡥⣆⣄⣶⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⣟⠘⠾⣽⣿⡏⠁⢀⠀⠀⠉⢈⠀⢸⢻⠉⠀⠀⠓⠏⠁⠀⠀⠹⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣸⣇⠀⠀⠀⠉⠟⡔⠀⠄⠠⠄⠄⠔⠘⢞⡄⠠⠤⣀⠠⡤⠀⠤⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢅⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⢠⡇⠡⣄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⠀⠀⠀⠀⢱⠆⠀⠀⠀⠀⠀⢆⡇⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢷⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⡆⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢨⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢨⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡂⡄⠀⠀⠀⠀⢋⢯⣦⣀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⢨⣦⠤⠤⠤⣤⡟⠀⠀⠀⠘⣾⡴⠮⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢊⡸⡆⠀⠀⠀⠀⠀⠀⠀⣏⡇⠈⠹⣩⣣⡃⠀⢠⢻⡾⣮⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⡟⢃⠀⠀⣏⣱⡇⠀⣎⣼⣩⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⣿⡙⡀⠀⢱⣄⣇⡼⢇⢺⣷⣾⡿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢣⢿⢣⠀⢸⠙⡜⠀⣸⣁⣭⣭⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢟⠚⡇⠈⣍⢷⣯⣋⢙⣿⠽⣕⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⠌⠟⢻⣷⢹⠆⣻⢭⣿⣃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⢧⠈⠈⣈⣮⢻⣟⣏⣊⡚⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡗⠩⡑⢮⠈⢽⣀⠻⣇⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⢀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢴⡻⢿⠃⠀⠈⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⡀⡍⠀⠇⢀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣔⢣⠾⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠄⠙⠛⠋⠊⠉⠉⠙⠻⠊⢑⣿⢳⠀⠀⠀⠐⠋⠈⡙⠉⠰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⣀⡀⠀⠀⠀⢐⣆⣦⣀⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠒⠒⠒⠒⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀