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⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠰⣿⣿⣷⠖⠋⣩⡍⠀⠀⠀⣿⡟⠀⠀⢀⣿⣿⣏⠁⠶⠊⠉⠛⠳⣤⣈⣛⣿⣿⠉⣿⣿⣿⢿⡿⢾⣭⣿⣿⣦⡄⠀⣿⠀⠀⠀⣸⣿⣿⡾⠀⠐⣰⡟⠐⣶⣾⣿⡮⣿⣤⣀⠴⠋⠙⠛⢾⡉⠉⢹⣶⣿⣧⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⢹⣿⡁⠠⠞⠁⠀⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠙⠛⣿⡇⠀⠙⢹⣧⢈⠙⣷⡿⣿⣿⠿⠁⠀⣿⠀⠀⠀⣿⣿⣿⠁⣴⡞⠋⠐⢻⣿⣿⣟⠁⠀⣴⣿⡷⠀⠀⢰⣼⣷⠀⢰⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⢀⣿⣿⣧⠁⠀⠀⠈⠦⠀⠀⠀⢠⣶⠀⠀⠀⢸⡇⠀⠀⠈⣿⣿⣏⠀⠀⢀⡿⠀⠀⣸⣿⣿⣿⡞⠋⠀⠀⣠⣼⣿⣿⡟⠿⠾⣟⣿⣧⠐⢻⣿⣿⣿⡶⣦⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠈⠿⢿⠀⠾⠿⣿⣷⣿⠀⢸⣇⣰⣶⣰⡀⠀⠀⠏⠸⠿⠿⣿⣇⠀⠇⠀⢸⣿⣿⠇⠀⢸⡇⠀⢰⣿⣿⣿⢇⠁⠀⣾⡿⠉⠁⣿⣿⣷⣶⡿⢿⣿⣿⣾⡿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠴⠟⠿⠂⠀⢰⣦⣤⣤⠀⠀⠀⢰⠀⠀⠀⣿⠀⠣⠀⣸⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⠀⠠⣿⣷⣤⣀⣴⣯⣁⠀⠀⣿⠀⢠⣿⣿⣿⠃⠈⢀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣇⠸⢿⣟⣿⣯⠙⡿⢿⣿⣿⡇⠀⡉⠉⢹⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⣸⣿⣿⠀⠀⠀⢀⣠⡀⠀⠀⣿⠀⢄⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣗⢸⣿⡟⠀⢰⡇⠀⠀⣿⣿⠃⠀⠀⣿⠀⣻⢠⡀⠀⢸⣷⣶⣾⣿⠀⠘⡛⣿⢽⣈⣿⣿⠛⣿⠀⠀⣧⠀⢸⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⢸⣿⠇⠀⢠⣶⣾⣿⠁⠀⠀⣿⠀⢀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⣀⣾⡇⠀⠀⣧⠀⠀⢻⣿⡀⠀⠀⣿⠀⣿⢘⡇⠀⢸⣿⡿⣿⣿⣦⡈⠋⣿⠀⣿⣿⣯⠀⢸⠀⠀⣿⣄⠸⠃⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠦⣀⡐⠻⠶⣄⠰⠟⠀⠶⠿⠏⠀⠀⢸⣿⣿⡏⠀⠀⢀⣿⠀⢈⠀⠚⠛⠛⠛⠛⠃⠀⠀⠂⠀⢠⣤⣤⣿⣿⣿⣷⢼⡿⠃⠀⠀⠈⠀⢤⡀⢻⡇⠀⠀⣿⠀⣿⠀⠀⠀⢸⣿⡿⣹⣿⣿⡇⠀⢿⡄⡿⣿⣿⡆⠆⠀⠀⢻⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣤⣴⣶⢶⣿⣿⣿⣿⣶⣶⣼⣿⣶⣤⣤⣄⣀⣀⠀⠙⠛⠋⠀⠀⠀⠀⠿⣤⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⢸⢿⣏⣹⣿⣯⣼⣷⣤⣤⠶⠖⠀⣾⣯⠈⣟⠁⠀⣿⠄⣿⠀⠀⠀⢸⣿⣿⣽⡿⣿⡇⠀⢸⣏⠀⣿⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣾⣿⣦⣶⠿⢾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣤⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣀⣠⣿⡆⣻⠀⠀⠀⢸⣿⣿⣿⡇⢸⡇⠀⠈⣿⢿⣿⣿⣿⡄⠀⠀⢻⣿⡗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠉⣽⣿⣿⡇⠈⢻⣿⡉⠀⠉⠉⠛⠛⣿⡿⢿⣯⣽⣿⣿⣷⣾⣯⣭⣭⣉⢉⣉⠉⡉⠉⠁⠀⣀⡀⣀⣀⣤⣴⣶⠶⠾⠛⠻⢿⣷⢤⣌⣷⣿⣿⣿⠛⣹⡆⣻⡀⠀⠀⢸⣿⣿⣿⡇⠈⡇⠀⠃⠟⠈⣿⣿⣏⠐⠀⠀⠸⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣸⣿⣿⣿⣿⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠉⠉⠉⠉⠛⠛⠿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠚⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⣿⠀⡤⠀⠀⠀⠀⠠⠘⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠿⠿⠿⠇⠀⠀⠀⡀⠸⣿⣀⣟⣳⣦⣤⣶⣾⣿⡀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣽⣶⣿⣶⣿⣿⠉⠙⠛⠻⢿⣿⡀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣁⣤⣤⠀⠀⠀⠈⠁⠀⠈⠋⠀⠀ ⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡄⠀⠀⢿⣷⣿⣶⣶⣶⣶⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠈⠉⣙⣛⠛⣋⡉⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣭⣽⣾⣟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀