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⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡄⡇⠀⡷⣁⢠⡇⠄⡅⡴⠀⠀⠀⠸⡎⠀⠀⠀⠀⠀⠀⠇⡿⣰⢀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠦⠘⡀⣀⢤⠳⠙⠒⠙⠄⠀⣀⡤⣖⣻⢽⣿⠙⠘⢀⠀⠀⡇⢸⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣸⠀⡇⡃⠀⡇⠃⣰⠀⠀⠁⠃⢁⢰⠀⠀⠀⠀⠀⠋⡕⢀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢘⠀⠀⠀⠀⡀⣦⣿⢿⠻⠈⠀⠀⠀⣄⣦⠷⣟⠿⠑⠈⠀⢹⢸⠀⠀⠀⣷⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⡇⡇⠀⡃⢠⠀⠀⠞⢠⡄⡆⠉⠀⠀⠀⠀⣞⢠⡤⠞⢀⠀⠀⠀⠁⠀⠷⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠈⠀⠀⠃⣧⣿⣿⣷⠻⠈⠀⠀⠀⠀⡀⣤⢶⣻⠿⣿⠉⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⡄⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⡇⡇⠁⣰⠀⠁⡴⢀⠀⠀⢸⣆⢹⠀⠀⠓⢠⠁⡰⠀⠉⠹⠏⠀⡸⠀⡘⠀⠸⠀⡌⠀⢸⠉⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⣌⠇⠀⢸⠀⣏⠀⠀⡞⣄⣿⣿⡼⣿⣧⢿⠛⠈⠀⠀⠀⠀⠀⣄⣶⣿⠿⠙⠈⡇⡏⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⢰⡇⡇⡌⠀⠋⣠⠀⠀⠃⠇⢀⠁⣆⠹⡄⡇⠁⡱⠔⣀⠉⠲⣧⢦⢸⠀⢸⠁⢠⠀⢸⠇⢀⢻⠇⠀⡜⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⠑⣉⢯⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄⠃⢠⠀⢰⠁⠶⢀⠁⣿⣿⢹⣿⡀⣅⣦⣾⢿⠚⠈⠀⠀⠉⠈⠀⣄⣦⣷⣶⣿⢿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡄⠠⡇⡁⢸⠏⢠⠀⠀⠀⡜⡟⠀⠀⠀⣧⠈⡇⡎⢠⠋⡠⡁⠺⡇⠀⢸⠀⢰⡇⠀⠇⠀⡘⡇⢹⡜⠃⢠⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⢠⢸⡆⠀⡇⠀⡍⢻⠟⡟⡟⣿⢻⣼⠀⠀⢦⠛⠈⣢⣧⢷⠻⠿⣟⠻⠉⠀⠀⠀⡀⣄⣦⣿⢝⠐⠀⠈⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⡿⣿⣸⠀⠀⠀⠃⢀⣸⠀⠀⠀⡀⢿⡄⢠⠇⢀⠞⣎⢸⡇⠀⢹⠀⠀⡅⠀⡎⠁⢰⡜⡝⢰⡏⠀⡜⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢀⠸⠀⢸⡁⣾⣇⢧⠺⡙⢈⡀⣄⠘⠀⠀⣦⢆⠉⠙⠀⡀⣄⣶⣿⣿⠿⠙⠉⠉⠀⠀⡀⡠⣤⠲⠙⢎⠸⠀⠀⠉⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⡇⢻⣼⡀⠀⠀⠀⡀⡇⠀⠀⠀⡀⠀⡇⣽⠀⠸⡎⢃⢠⢀⡆⠀⣷⢤⠈⠀⠀⢸⡇⠇⢃⣾⠁⢰⠁⢰⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⢰⠇⢀⡎⢰⠸⡎⠇⣄⢿⠈⠀⢦⠺⠈⠀⠃⢛⣄⢳⠈⠀⠀⠀⣀⣦⣷⣟⣿⠙⠀⠀⠀⠀⠀⡀⣇⣿⢿⠻⡙⢌ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡟⣿⣄⠓⠿⠠⠀⠀⡜⠀⠀⠀⠀⠀⡀⡼⡘⠇⢰⡏⠐⠀⠀⠀⡀⠀⠑⢆⠀⢠⡱⡘⡑⢰⡎⠀⡇⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡌⡆⠀⣰⠁⣫⠖⢀⢠⣸⠇⣠⢿⠀⠈⣄⡘⠣⡀⡀⠸⢀⣆⠙⠀⠀⠀⠀⡀⣿⣧⣿⣝⠻⠙⠀⠀⠀⠀⢀⠀⣄⢦⣳ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⣯⣸⠀⡇⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⢇⡟⡄⣿⠃⠰⠦⡠⢠⠁⣗⢼⡿⡇⣾⣞⣱⠉⢨⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⢚⠛⠺⠀⣿⣽⠀⡀⢁⠜⢠⠀⣏⢸⠇⠀⢇⠀⢱⠀⡆⠀⡀⣷⠛⠈⠀⠀⠀⠀⡇⠀⣄⣦⡿⣽⠺⠙⠀⠈⠀⠀⠀⠀ ⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡟⣿⢠⠀⡇⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⠼⣼⣿⠀⠀⠀⠁⣾⣴⣭⣭⣬⣷⣻⠿⡜⠸⠀⠀⠁⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠿⠶⣵⣭⣭⣦⣽⠹⠀⢄⡶⢠⠀⣼⣿⠀⠁⠀⢸⡇⠿⠸⠳⠁⠀⣿⣆⠹⠀⠀⠀⡟⠸⠀⠀⠀⣀⣦⣷⢝⣿⠻⠙⠀⠀ ⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣯⠀⠀⡿⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⢿⣇⣿⠸⠀⠄⡾⠃⡿⣴⣛⣿⡇⣿⡟⣿⢸⠀⠀⡗⢻⡬⠷⠬⢤⣓⠮⠣⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⢡⡿⣡⣛⣌⣿⣿⣿⠀⠀⠀⠀⠀⢸⣸⠁⡀⠀⠁⡇⡄⢿⠀⡆⢻⡇⠘⣇⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⣀⣤⣄⣶⣿⠻ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⣇⡿⠘⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⣦⡿⠻⠛⢿⡜⣷⡹⣷⣽⡿⣿⣟⣿⢰⠀⠀⡄⢻⢇⡇⠈⠀⠀⡀⣢⠈⣡⠢⠈⠀⠀⠀⠀⠀⠀⠀⣆⣿⡎⣿⡌⣷⢻⣇⢿⣎⠀⠀⠀⠁⠉⢸⢸⡊⠀⠀⡀⡆⠀⣄⢽⠀⡛⡿⢸⡄⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⡇⣿⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⡀⣷⡯⣿⣫⠻⣝⣿⣿⣿⣿⣿⣿⠀⠀⠉⠘⣿⠈⣸⢸⠀⠀⠀⠀⢆⡈⠣⡄⠱⠀⠀⠀⠀⠃⠙⠆⣞⢿⣝⣶⣿⢻⣿⣹⢹⠋⠽⡻⣿⣿⢇⢁⠜⠁⠚⢴⣨⠀⠀⣇⠘⣇⣷⢹⠉⠈⠀⠃⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⡆⣿⠀⡇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠀⣀⢱⣀⣀⢦⡿⣻⣯⣿⢿⣿⢿⡿⣿⣾⢛⣿⢸⢡⢸⠀⠀⠀⠀⠀⢇⠀⢡⠀⢣⠀⠀⠀⠀⣵⢯⣟⡻⣭⣾⣿⣿⣿⣟⣿⣶⣴⣤⣂⡖⡏⠊⡤⢀⠀⡀⠀⠀⠀⡀⢹⡏⠀⢻⡀⣄⠳⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⣿⠀⡇⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢺⠀⠀⣆⢹⠀⠐⠉⠉⣈⣀⣀⣀⣀⠀⣄⠩⢈⣇⠀⡒⢠⠀⠀⠀⢀⠈⠀⢱⡀⠘⠀⢣⠀⠀⠀⡀⣄⠲⣙⣋⣈⣀⣀⣀⠀⠉⠉⠂⠓⠿⣾⣠⠋⠀⠀⠊⡰⠀⠀⠀⠀⣶⣠⠀⣿⠘⠀⠀⣧⠈⢸⠀⠀⠀⠁⠉⠉⠛⠛⠛⠙⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠂⠷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⢀⠁⠕⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⠖⢒⠊⠔⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠋⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠛⠀⠀⠀⠀⠀⡀⢳⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣴⢀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡰⢀⠀⠁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡤⣽⣾⢀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡠⠀⠀⠁⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠘⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠀⡀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠴⣀⠁⠛⡴⣠⠸⠊⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠥⠚⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠄⠠⣁⠉⠛⠿⡴⣠⢁⠚⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠁⠖⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⢀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠤⠒⠒⠁⠉⠉⠀⠀⠀⠀⠁⠉⠶⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⣠⣀⣀⠁⠛⠿⡿⣶⣤⣉⠊⠔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⢀⠀⠊⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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