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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢶⣶⣿⠋⢿⣿⠉⠉⠈⠉⠉⠙⠛⢷⣶⡶⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡟⠀⠀⢸⣿⣿⡆⣿⡇⢀⠀⠀⠀⣴⣾⠖⠨⣿⣧⠀⠈⠙⠛⠶⣤⣀⠀⠀ ⠀⠀⠀⣀⡴⠞⠉⠀⢸⣿⠀⠀⠘⢸⣿⣿⣷⣿⣿⢼⣃⠀⢸⣿⠹⠆⢰⣿⣿⠀⠀⠀⠀⠀⠀⠉⢹⡶ ⠀⢠⣾⠋⠀⠀⠀⡴⢾⣇⠀⠀⢀⠸⡿⣹⣿⣿⣿⣼⡹⢠⡟⠁⠁⠀⠸⣿⣿⡄⠀⠀⠀⠀⠚⢆⡾⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⣿⣿⠁⠁⠟⢃⢄⠘⣿⣿⣿⣿⡱⠘⡇⠄⠀⠀⢀⣿⣿⣧⠀⠀⢀⣹⣿⢿⡇⠀ ⠀⠀⠀⢿⡀⠀⢰⣶⣿⣧⡀⠀⠀⣷⡈⠀⢻⣿⣿⣿⡇⠀⠻⣬⡀⢂⣿⣿⣿⣿⣆⠀⠟⣿⣇⣼⠀⠀ ⠀⠀⠀⠈⣇⣀⣼⣿⣴⣿⣧⣤⣈⠛⠀⠀⢌⣿⣿⣿⡇⢀⠀⠀⣻⣼⣿⣿⣿⣿⣿⡷⣼⣿⣿⡏⠀⠀ ⠀⠀⣠⣾⣿⣟⣯⣟⣾⡽⣯⣟⡿⣷⣤⠁⠚⣿⢿⣿⣧⢂⢠⣿⣿⣻⣽⣳⣟⣾⣳⣟⣿⣻⣿⣇⠀⠀ ⠀⣴⣿⢯⣷⣻⢾⡽⣾⡽⣷⢯⡿⣽⣻⣷⡄⡍⢸⣿⡇⣰⣿⣟⡷⣯⢷⣟⣾⣳⣟⣾⣳⣟⡾⣿⣧⠀ ⢰⣿⣟⡿⣾⡽⣯⣟⡷⣿⡽⣯⣟⡷⣯⣟⣷⠀⢸⣿⣃⣿⣟⡾⣽⣻⣟⣾⣳⣟⣾⣳⣟⣾⣻⡽⣿⡇ ⢸⣿⢯⣟⣷⣻⢷⣯⣟⣷⣻⢷⣯⣟⡷⣯⣿⠠⠈⣿⡜⣿⣞⡿⣽⣳⣟⣾⣳⣯⢷⣟⣾⣳⣯⢿⣽⡇ ⠘⣿⡿⣞⣷⣻⣟⡾⣽⣞⣯⢿⡾⣽⣻⢷⡏⡄⣴⣿⠀⢿⣯⢿⣽⣳⢿⣞⡷⣯⢿⣞⡷⣟⣾⢯⣿⠇ ⠀⠹⢿⣟⣾⣳⣯⣟⡷⣯⣟⣯⣟⣷⣻⠿⢠⣶⠿⠃⠰⠈⢿⣟⣾⣽⣻⣞⡿⣽⣻⣞⡿⣽⣾⣿⠏⠀ ⠀⠀⠀⠙⣿⣷⣻⣞⣿⣳⣟⣾⣽⡟⠙⢠⣾⠏⠀⠀⠀⠀⠝⠏⢿⣾⣳⣯⢿⣽⣳⣯⣿⣷⠟⠁⠀⠀ ⠀⠀⠀⠀⣹⡇⠈⠙⢻⣍⠌⣿⠉⠀⢀⣾⡏⠂⣠⣴⠶⡟⠚⠂⢸⣿⡟⠉⠛⢻⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢶⣿⠀⠀⢸⣿⡇⠈⠉⠈⠀⠀⠀⠀⢰⣿⡇⣀⡴⠛⢩⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⣿⠓⠲⣾⣿⣇⣠⣀⣀⣀⣖⣤⣤⢾⣿⡟⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠁⠉⠙⣿⢿⠋⠁⠀⣀⡉⠁⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⢶⣶⣤⣀⣠⣏⢸⣦⣤⣾⣿⡟⣷⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣝⣳⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣧⣿⣿⣿⣹⣾⣽⣯⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠏⣇⣿⣿⣿⣿⣿⣿⣿⣿⢸⡃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⢻⣾⣿⣿⣿⠿⢿⣿⢻⡿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢛⣦⠀⠉⢛⠛⠿⠿⣾⠟⣋⠀⠀⣼⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡟⠛⢆⡴⡟⠀⠀⢰⣿⡇⢸⣿⡄⠋⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⣰⣿⣀⡇⠀⠀⠀⠉⠀⠀⡧⣿⣆⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢹⡿⡇⠀⠀⠀⠀⠀⢠⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⠁⣧⠀⠀⠀⠀⠀⢸⡃⢼⣯⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣜⠃⣿⣠⡿⠀⠀⠀⠀⠁⣿⡀⣸⣿⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣿⣸⡀⣿⠁⠀⠀⠀⠀⡿⣠⣿⠃⣜⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣯⢼⡃⢸⠀⠀⠀⠀⠀⣧⠁⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⡇⢠⠀⠀⠀⠀⠀⡇⡿⢹⣯⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠈⣆⣿⡧⠀⠀⠉⠀⠀⠀⡇⣀⣿⣰⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⠋⡄⣿⢸⡇⣿⢰⠀⠀⡟⡴⢆⠛⡟⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡛⣼⠀⠀⣋⠟⣾⠿⠿⠛⢛⠉⠀⣦⢛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⡿⢻⣿⢿⠿⣿⣿⣿⣾⢻⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠏⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣯⣽⣾⣹⣿⣿⣿⣧⡟⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⣿⣿⣿⣳⣝⣿⣿⣿⣿⣿⣿⣾⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄⣷⡟⣿⣾⣤⣦⢸⣏⣠⣀⣤⣶⢶⣤⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠁⡉⣀⠀⠁⠋⢿⣿⠙⠉⠁⠉⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠁⡟⣿⢾⣤⣤⣖⣀⣀⣀⣠⣇⣿⣾⠲⠓⣿⠈⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⣿⢩⠛⡴⣀⡇⣿⢰⠀⠀⠀⠀⠈⠉⠈⡇⣿⢸⠀⠀⣿⢶⠙⠀⠀⠀⡇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣿⣿⢻⠛⠉⡟⣿⢸⠂⠚⡟⠶⣴⣠⠂⡏⣾⢀⠀⠉⣿⠌⣍⢻⠙⠈⡇⣹⠀⠀⠀⠀ ⠀⠀⠁⠟⣷⣿⣯⣳⣽⢿⣯⣳⣾⢿⠏⠝⠀⠀⠀⠀⠏⣾⢠⠙⡟⣽⣾⣟⣳⣿⣞⣻⣷⣿⠙⠀⠀⠀ ⠀⠏⣿⣾⣽⡿⣞⣻⣽⡿⣞⣻⣽⣾⣟⢿⠈⠰⠃⠿⣶⢠⠿⣻⣷⣟⣯⣟⣯⡷⣟⣯⣳⣾⣟⢿⠹⠀ ⠇⣿⢯⣾⣟⡷⣞⢿⣯⡷⣞⢿⣳⣽⢿⣯⢿⠀⣿⣴⡄⡏⢷⣻⣽⡾⢿⣯⣞⣽⡾⣟⣻⣷⣞⡿⣿⠘ ⡇⣽⢿⣯⣳⣾⣟⢷⣯⣳⣾⣟⣳⣽⡿⣞⣿⡜⣿⠈⠠⣿⣯⡷⣟⣯⢷⣻⣷⣟⣯⢷⣻⣷⣟⢯⣿⢸ ⡇⣿⡽⣻⣾⣟⣳⣾⣟⣳⣾⣟⣻⣽⡾⣟⣿⣃⣿⢸⠀⣷⣟⣯⡷⣟⣯⡽⣿⡷⣟⣯⡽⣾⡿⣟⣿⢰ ⠀⣧⣿⡾⣟⣳⣾⣟⣳⣾⣟⢷⣯⡷⣟⣿⣰⡇⣿⢸⡍⡄⣷⣻⣽⡿⢯⣷⡽⣾⡽⢾⣻⣷⢯⣿⣴⠀ ⠀⠀⣇⣿⣻⣿⣟⣳⣾⣟⣳⣽⣻⣿⣿⢠⢂⣧⣿⢿⣿⠚⠁⣤⣷⡿⣟⣯⡽⣾⣟⣯⣟⣿⣾⣠⠀⠀ ⠀⠀⡏⣿⣿⣼⡷⣿⣿⣿⣿⣿⣼⣻⠀⠀⢀⡇⣿⣿⣿⢌⠀⠀⠛⣈⣤⣧⣿⣴⣿⣼⣀⣇⠈⠀⠀⠀ ⠀⠀⣼⣇⣿⠟⠀⣆⣿⣿⣿⣿⢂⡀⣬⠻⠀⡇⣿⣿⣿⢻⠀⡈⣷⠀⠀⡀⣧⣿⣶⢰⠀⡀⢿⠀⠀⠀ ⠀⡇⢿⣿⣹⢀⠀⠀⣧⣿⣿⢀⠀⠀⠄⡇⠘⡱⣿⣿⣿⣿⠘⢄⢃⠟⠁⠁⣿⣿⠀⠀⠀⠀⣆⢻⠀⠀ ⠀⡾⢆⠚⠀⠀⠀⠀⡄⣿⣿⠸⠀⠁⠁⡟⢠⡹⣼⣿⣿⣿⣹⡿⠸⢀⠀⠀⣇⢾⡴⠀⠀⠀⠋⣾⢠⠀ ⡶⢹⠉⠀⠀⠀⠀⠀⠀⣿⣿⢰⠆⠹⣿⢸⠀⣃⢼⣿⣿⣷⣿⣿⢸⠘⠀⠀⣿⢸⠀⠉⠞⡴⣀⠀⠀⠀ ⠀⠀⣀⣤⠶⠛⠙⠈⠀⣧⣿⠨⠖⣾⣴⠀⠀⠀⢀⡇⣿⡆⣿⣿⢸⠀⠀⡟⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⣤⡶⣶⢷⠛⠙⠉⠉⠈⠉⠉⣿⢿⠋⣿⣶⢶⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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