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⣎⣧⠙⣦⣹⣎⡟⠀⠀⠀⠀⠣⡈⢿⣹⡌⠢⡀⠀⠀⠀⠀⠀⠱⣀⠀⣀⣈⠡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣠⢿⣗⡻⣜⡶⣻⡜⢯⠛⠛⠚⢿⣿⣿⡻⣝⢮⡳⣭⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠈⠻⣦⡈⠻⣿⡇⠀⠀⡶⠦⠤⣌⣪⣧⢻⣄⠈⠢⢄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⣰⠋⠠⣏⢷⡹⣞⡵⣫⢻⠀⠀⠀⠸⣷⢯⡿⣮⣗⣳⢣⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠘⠓⠠⢘⣿⠀⠀⣇⠢⡑⠤⢉⣻⠓⢯⣦⡀⠀⠉⠒⠤⢀⣀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡹⣶⠷⠚⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⡄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠰⣹⢎⡷⣹⡜⢧⣛⠀⠀⠀⠀⢻⣿⡼⣏⠿⣷⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⠟⢡⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠠⢁⠡⠈⢽⣇⠀⠹⣆⠡⢊⠤⢹⡀⠀⠈⠙⠦⠀⠀⠀⠀⠀⠉⠐⠒⠳⠆⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⢾⡀⢧⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⡵⣋⢾⡱⣚⢧⠣⠀⠀⠀⠀⠈⢿⣷⣯⡟⣧⣏⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢠⠋⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠐⠄⣂⠡⢀⠺⣧⠀⠘⢧⣌⠢⢡⠙⡒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡠⠊⠀⠈⡱⣾⠀⠀⠀⢠⡞⠀⠀⠀⠀⢳⡞⣹⢖⣣⠝⣬⠓⠀⠀⠀⠀⠀⠀⠹⣿⣟⣶⢫⣗⡯⣞⢧⣛⣾⡹⣞⣳⡽⣻⣦⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠠⢉⠐⡀⠢⠄⠂⠌⠳⣦⡀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣀⠀⠀⢀⡤⠋⠀⠀⢀⡤⠚⡧⠀⠀⠀⢃⠸⠄⠀⠀⡾⠀⠀⠀⠀⠀⣣⢟⡵⣫⢖⡹⢢⢏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡽⣿⠻⣭⣟⡽⢶⣻⣭⢷⣹⢷⣽⠋⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀ ⠠⢁⠆⡐⢀⠀⠠⢈⠐⠠⠀⠙⠓⠶⠤⢤⣤⣤⣤⣴⣶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣠⣴⣿⣷⣡⠇⠀⠀⠀⠸⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣜⢫⢞⡵⢫⡜⢥⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⡇⠀⠉⠛⠿⢶⣽⣾⡽⠞⠁⠀⠄⢀⠈⠙⠲⣄⠀⠀⠀⠀⠈⣇⠀⠀ ⠡⠂⠆⡘⠠⡈⠐⠠⢈⠐⠠⠈⢀⠀⡀⠀⠐⣿⡿⠻⣿⣓⠦⣍⣿⢲⢦⢤⣄⣀⣀⣀⡀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣴⣾⣟⣯⡟⣽⣿⢯⠀⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⠀⠀⣜⢣⢞⡱⢣⠜⢢⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠁⠄⡀⢀⠀⠀⢀⠀⠄⡈⠄⠠⠈⠀⠄⠘⢦⠀⠀⠀⠀⠘⡄⠀ ⢡⠑⢂⠰⠁⠄⠡⠁⠂⠌⠀⠂⠄⠂⠐⠀⠈⠿⠁⠀⣿⣇⣿⠞⣿⣣⣞⡾⣿⠙⣧⠐⡌⠢⢌⡑⢢⠐⡄⠢⢄⡟⡠⢙⣿⣿⣶⡻⢷⡟⣆⢣⠀⠀⠀⠀⢠⠀⣸⠁⠀⠀⠀⠀⠀⠀⣌⠳⢎⠴⡁⢎⢡⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣇⠀⠂⠀⠄⠀⠌⠀⡀⠄⠀⢀⠂⠁⡈⠠⢀⠀⣇⠀⠀⠀⠀⠘⡄ ⢢⠘⡀⢢⠁⠊⠄⠡⢈⠀⠐⠠⢀⠡⠈⠄⠀⠀⠀⠘⢛⣫⣵⣾⡿⣿⣧⣼⠃⡜⠡⢃⠌⡑⢢⠘⡄⠣⢌⡑⣾⠑⡄⢣⠸⣿⣷⣿⠟⠀⠘⠆⢇⠀⠀⠀⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⢮⡙⢎⡒⡉⠆⡌⢎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢿⣿⠀⠄⠁⢀⠂⠀⢂⠀⡐⠈⠀⡐⠀⠄⠁⢀⠀⡞⠀⠀⠀⠀⠀⠸ ⠂⡅⠒⠠⠌⡁⠌⠐⡀⠂⠄⠐⠠⠀⠡⠀⠀⠠⠀⣶⣿⣿⣟⣳⢿⣹⢿⣿⣎⠰⡁⢎⠰⡁⢆⠱⡈⢅⠢⡐⢿⡨⢐⠡⢚⡏⢿⠏⠀⠀⠀⠀⠈⣆⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⢦⡑⠌⡒⢈⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠸⣿⠀⠀⠌⠀⢀⠐⠀⠄⠐⠈⠠⠐⠈⡀⠌⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⢡⠂⡅⢘⠠⠐⡈⠐⢀⠐⢀⠈⡐⠈⢄⠡⠈⢠⡿⠋⠋⢿⣿⣯⢯⣯⣟⡽⣿⣧⡘⠄⡃⠜⡠⢃⠜⡠⢃⠜⡨⢐⠡⣎⣼⡷⠋⢣⢀⠀⠀⠀⢠⡘⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢮⡹⡖⡌⠰⠀⠌⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠂⠈⠀⡀⠌⠀⠌⡀⠡⢀⠁⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⢂⠌⡐⢠⠂⡁⠄⠂⠄⡈⢀⠐⢀⠁⣊⠰⣰⡟⣀⠀⠀⠀⠈⢏⠟⠓⠾⠿⠿⢿⣷⣌⣰⣁⠆⡡⢂⢱⣈⣦⣵⣾⣿⣿⡿⠀⠀⠀⢧⢣⡀⠀⠀⢳⡽⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡻⢜⠈⡑⢈⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⡈⠀⢀⠐⠈⡀⠐⢀⠂⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⣂⠡⢀⠆⠠⠈⠐⠠⠐⠂⠠⢀⠂⠄⣳⠏⠀⠀⠉⠢⡀⠀⠀⠳⡰⡄⠀⠀⠀⠀⢣⣀⣬⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡬⣧⡧⠤⠒⠉⢹⣱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠳⠌⠀⠀⢂⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⠀⡀⠐⠀⡈⠄⠠⢁⠠⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⡄⢀⠄⠃⡘⢀⠃⠄⢃⠠⠀⠄⡘⡿⠀⠀⠀⠀⠀⠘⡄⠀⠀⠣⡸⡄⠀⠀⠀⢀⢇⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠛⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⠄⠀⡀⠠⠀⠠⠀⠄⠀⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⠃⠄⢡⠂⠁⡀⠂⢈⠀⢂⠀⡁⠠⣼⠃⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠱⡜⣆⠀⠀⠈⢾⡄⠀⠀⠉⠛⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⢹⡸⡆⢀⣤⡶⠾⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠄⠀⢂⠀⠄⡁⠐⠈⠀⡁⠀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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