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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⡴⣦⠹⠉⢳⡌⡟⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢱⠀⠉⠉⡖⠀⠀⡄⠑⠄⢀⠀⠀⠁⠉⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⢄⠒⠁⠈⠀⡀⢄⡢⠱⡇⣷⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣹⣏⣼⣢⠙⠈⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⠿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠉⠉⠈⠀⡇⠀⠀⠷⠙⠀⠀⠀⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⣽⢼⡠⢀⡇⢸⠇⢠⠀⠀⠁⠾⠀⠀⠀⠀⠀⠀⣼⡀⣀⠀⠀⠀⠀⠁⠉⠋⢷⠐⠤⡠⣠⣄⣀⢤⠠⠓⡝⣄⢤⣻⠭⠒⠉⠈⠀⠀⠀⡀⢄⠠⠂⠐⠀⣯⠽⣌⣷⣿⣿⣿⣿⣿⣷⣟⣿⣿⣟⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⡀⣅⣿⡾⢒⠀⡼⠀⠀⠀⢅⠹⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⢿⢈⡆⡞⠀⠀⠀⠀⡝⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠇⢱⠹⠜⣀⠀⠀⣀⢀⠀⠏⣰⠀⠀⠀⠀⠀⠟⠙⠈⠀⡀⢷⠢⣿⠐⢄⠢⠑⠉⠈⠀⠀⠁⠉⠉⠉⠉⡜⣿⠽⣁⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠃⠒⠒⠔⠹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣘⢣⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⡾⢠⠀⠀⠀⠀⠀⠏⣰⠀⠀⡏⠈⠀⠀⠀⠀⠀⠃⡿⣀⢠⠀⠁⠊⠀⠀⠀⡆⣠⠉⠉⠍⠤⠤⣠⢀⠀⡀⠢⠒⠒⢹⡈⢳⠘⠀⠀⠀⡀⣀⣀⣀⢻⠈⠀⠀⠀⣷⣿⣿⣿⣿⣷⣿⣿⣷⣿⢿⣿⣿⣿⣿⣽⡿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣠⢀⠀⠀⡞⠦⠱⠚⡀⠱⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢾⠈⠀⠀⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠀⠊⡤⣀⠀⠀⠀⠀⠁⠝⢃⢠⠀⠀⠃⣠⠀⠋⠒⠀⠁⡸⢄⢀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠆⣈⡀⢿⠑⠀⠀⠀⠀⠀⠃⢠⣱⠐⠀⠀⡄⣷⣿⣿⣿⣿⣾⣻⣿⣽⣿⣾⣿⣿⣿⣷⣯⣿⣿⣯⣻⢿⣿⢿⣿⣿⣿⣿⠻⠈⢢⠈⠀⢾⠤⡴⠤⠤⠸⠀⠀⠀⢱⠀⠀⠀⠀⢋⢻⠀⠀⡆⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡅⠀⠀⠀⠀⠀⠀⠂⡾⡄⡼⠀⠋⠔⣇⠋⡴⢀⠀⠀⠀⡀⣀⠀⠀⠀⣿⢸⠀⠀⠷⠓⠁⠉⠉⣎⠈⡇⠀⢦⠈⠀⠀⠃⢠⠀⡇⡄⠱⠀⠀⡀⣦⣿⣿⣿⣿⣷⢯⣾⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣴⣤⣀⣇⣀⣀⣀⣤⣦⣿⠹⡀⡦⠉⠔⣠⠀⠀⢇⠀⠀⠁⡔⠀⠀⠀⠆⡒⢸⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠂⠀⠀⠀⠀⠀⠀⠄⢀⠀⡀⠤⠙⠀⠃⢠⠀⠃⠔⡤⠀⠀⠉⠚⠒⠒⣿⣻⠉⠀⡞⢤⠲⠉⠉⠐⡍⠹⠉⠈⡆⠘⠀⣸⠀⠀⡗⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⣿⣴⢀⠀⠀⠏⢰⠀⠀⠀⠀⠀⡀⣧⠸⠀⣇⠀⠀⠀⠀⠀⢄⠤⢀⠉⠒⠀⠤⠠⠑⠈⠁⠒⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⡤⠤⠮⢠⠀⠉⠴⣋⠿⣿⠿⡟⣿⢸⠀⣀⢀⠦⠽⣀⠀⠀⠀⠀⠀⡀⣄⢦⠑⢸⠀⠀⡀⡠⠀⠀⠀⠀⡜⠀⣼⣷⣿⣿⣿⣯⡿⣽⡿⣿⣿⣿⣴⢠⠁⠋⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⡄⠈⠀⠶⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠸⡾⢀⠛⡔⢀⠀⠀⠀⡆⣿⣿⣿⠀⠀⠀⠀⠀⡆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⢀⠀⠀⠟⢀⠀⢸⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⢸⠀⠅⣿⠙⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⢇⠚⡵⢀⠀⠀⠀⠀⠀⠇⣿⣿⣿⢐⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⠀⠀⠀⠆⣧⠀⡞⢀⠀⡀⣦⣿⣿⣿⣿⣿⣶⣶⣧⣿⢘⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉⡰⠀⠀⠀⢘⠀⠂⡘⢣⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⣧⠘⠀⠀⠀⠀⠢⠛⡉⢫⠈⢀⠤⠒⠈⠀⠋⣿⣿⣿⣿⠟⣿⣶⣤⣤⠤⠂⡄⠘⠀⢄⠐⠀⠀⠀⠀⠀⠀⣷⠘⠁⠘⠀⠀⡄⡽⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⡟⣿⢸⠀⠀⠀⠀⡇⠈⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠰⠀⠀⢸⠸⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠈⠀⡆⢸⠀⠁⠀⠀⠀⠀⠀⡁⣚⢆⠴⠀⠄⠏⣿⣿⣿⣿⣿⣴⢀⠀⠊⠀⠀⠊⠰⡀⠳⠀⠂⠈⠀⠀⠀⠀⠀⡆⣏⡸⠀⠀⠀⠰⣧⣿⢿⠿⠛⠛⠛⠛⠛⠛⠟⠿⣿⣿⣴⢀⠑⠈⠂⠝⢀⢄⡠⣄⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠓⢶⠀⠀⠋⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⢸⠀⠰⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⢰⠒⠠⢉⠔⡠⣀⠀⠃⠀⠁⢆⠙⠀⠢⠈⠀⠀⠀⠀⠀⢄⠼⠒⠉⠀⡧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣀⢀⠀⠀⠀⣄⢿⡟⠀⠁⠛⠀⡀⠣⠈⠀⠀⠀⠀⠃⢩⠀⡀⣄⠐⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢇⡄⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⠀⠊⡠⠄⠳⠀⠀⠀⡎⠁⠘⢣⠀⣄⠱⡄⠑⠀⠀⠀⠀⠀⡄⠑⠀⢀⡄⣿⣿⣿⣿⣿⣴⣀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⣿⢰⠀⡗⠛⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣀⠳⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⡟⠸⡆⠈⠀⠀⠀⠀⠀⡆⣿⠘⠀⠀⡇⣿⣿⣿⣿⣿⣿⣹⠀⠀⠀⡇⠂⠀⠇⢠⡀⣄⠢⢟⠈⡀⢣⡈⠄⠀⣄⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⠈⠉⡿⣿⣿⣿⣿⠿⠷⠛⠟⡿⣸⠀⠀⠧⡿⣽⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠇⡤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣾⣷⣿⣿⠙⢸⠀⠀⠀⠀⠀⠀⣆⣿⠙⠈⠀⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⣼⠀⠃⢠⠀⠀⠀⠀⠀⣧⠴⣀⡀⢆⠘⠀⠀⠀⠀⠀⠁⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠻⠀⣇⠹⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⠙⡰⠁⠉⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⠀⠀⠀⠀⡀⣀⢦⠙⠀⠀⠀⠀⠀⠀⡀⣦⣿⠿⣿⣿⣿⣿⣿⣿⣦⣿⣿⠹⢸⠀⡼⠋⠘⠀⠀⠃⡔⢀⠀⡤⣠⢤⡦⠢⠉⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣾⣶⣴⣀⢣⡀⢚⠤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠁⡬⣀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠻⠈⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⠘⡄⣿⣿⠘⠀⣿⣩⣷⠀⡴⢀⠀⠐⠀⠀⠀⠀⣀⣇⡸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⣀⣦⣿⠻⠈⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣦⣷⠩⠒⡀⠺⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣸⡀⢄⠷⡿⠿⠻⠛⢉⠀⠀⣄⣷⣿⣿⣿⢻⠀⣗⣿⢹⠀⡆⡿⣿⡸⠈⡇⡿⣨⣘⢠⠀⠀⠘⡄⢸⠀⣧⣿⣿⣿⣾⣴⣠⣀⣀⣤⣶⣿⣿⠈⠀⠀⠀⠀⠀⠀⡀⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⠀⡧⣘⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⣇⣿⣿⣿⣿⢿⠻⠙⠈⣧⣿⣿⣿⢹⡿⣿⣿⠙⠂⣾⣼⢇⢩⡿⣿⣿⢛⠿⠻⠒⢠⠀⢧⣬⠿⣷⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣄⣶⠛⠉⠉⠋⡴⠀⠀⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡝⢀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⣀⣿⣿⣿⣿⣿⠼⡾⣠⣃⣜⠀⠣⣀⣀⠄⣤⣿⣿⣸⢄⠻⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠂⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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