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⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⡐⠠⣰⠟⠀⢠⣿⣧⣿⠀⢠⠀⣸⠟⣾⣤⣛⠎⣞⣿⣶⣿⣿⡿⣯⣷⣿⡾⣿⣻⣽⡿⣟⣿⢿⣻⣿⢿⣽⣿⣻⣷⡿⣽⣯⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣿⣻⣟⣿⡿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣳⣿⢏⠠⣰⠾⠁⠀⠀⢸⣟⠛⡿⡆⢸⢀⣿⠿⡋⢧⣸⣾⣿⣿⣿⢿⣽⡿⣿⣽⣾⢿⣟⣿⣽⡿⣟⣿⣿⣻⣽⣿⣻⣾⣟⣷⣿⢿⣽⣷⡿⣯⣿⣯⣿⣟⣿⣿⣿⣿⣿⡿⣿⣽⣾⣟⣯⣿⣟⣷⣿⣽⢿⣻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡴⠿⠛⠋⡽⠒⠛⠁⠀⠀⠀⠀⣼⠁⠂⣧⢧⠘⣿⠇⠜⢠⣳⣿⣿⡿⣽⣿⣻⣯⣿⢿⣽⣾⣿⣻⣯⣷⣿⢿⣻⣾⣟⣿⣾⣟⣷⣿⣻⣾⣿⣻⣾⢿⣟⣷⣿⣳⣿⣟⣾⣷⢿⣾⣟⣿⣽⣾⣟⣯⣷⣿⣻⣾⣟⣿⢿⣳⣿⣻⣿⣿⣶⣄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢴⣿⣶⣶⣿⡎⠆⣿⣷⣶⣾⣿⣿⣷⢿⣿⣳⣿⢯⣿⣟⣯⣷⣿⣻⣽⣷⡿⣿⣻⣷⣿⣻⣾⢿⣽⣾⣟⣷⣿⣻⣽⣿⣻⣿⢾⣟⣷⣿⣻⣾⣿⣻⣾⢿⣽⣾⣟⣯⣿⣾⣟⣷⣿⣻⡿⣿⣽⣟⣷⣿⣽⣿⣷⣄⠀⠳⣄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⡷⣿⣟⣯⣿⣻⣿⣻⣾⢿⣽⣾⣟⣿⡾⣟⣿⣯⣷⣿⣻⣽⡿⣯⣷⣿⣻⣾⣟⣿⣾⢿⣽⣿⣻⣿⢾⣟⣷⣿⣻⣽⣿⣻⣾⣟⣯⣷⡿⣯⣿⣾⣟⣿⢿⣽⣾⢿⣾⣯⣷⡿⣿⣷⡄⠈⢦⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣯⣷⣿⣷⠃⢻⣿⣿⣿⣽⡿⣯⣿⣽⣿⣳⣿⣻⣿⢯⣷⡿⣯⣿⢿⣯⣷⣿⣳⣿⣯⣿⢿⣽⣾⣟⣷⣿⣻⣾⣿⣻⣾⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣽⡿⣟⣷⡿⣯⣿⢿⣯⣿⢿⣳⣿⣽⣿⣻⡿⣿⣦⡀⠳⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣾⣿⣿⣿⣧⢈⣿⣿⣷⣿⣻⣿⣽⣾⢿⣽⡿⣽⣿⣻⣯⣿⢿⣽⡿⣯⣷⣿⣻⣷⡿⣽⣿⢯⣷⣿⣻⣾⣟⣷⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⡿⣽⣿⣻⣾⡿⣿⣽⣾⢿⣽⡿⣟⣿⣷⡀⠹⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⣽⡿⣿⣿⡷⣿⣿⣎⣿⣿⣾⢷⣿⣻⣾⣟⣿⣯⣿⣟⣷⡿⣯⣿⢿⣯⣿⢿⣽⣾⣟⣷⣿⢿⣽⡿⣯⣷⣿⣻⣾⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣷⡿⣯⣿⢿⣽⣿⣻⣯⣿⢿⣯⣿⣷⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⣠⡴⠞⣻⡟⠸⣿⣿⣿⣟⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣽⣷⣿⣻⣾⣯⣿⢯⣿⣿⣽⡿⣯⣿⢿⣯⣷⡿⣿⣾⢿⣻⣿⢿⣽⣷⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣽⣿⣻⣿⣻⣾⢿⣽⣿⣻⣯⣿⣻⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠶⣛⠱⣈⣱⠏⠀⠀⣿⣿⣿⢯⣿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢾⣿⣽⣷⡿⣯⣿⢿⣾⢿⣽⡿⣯⣿⢿⣽⣿⣻⣽⡿⣿⣽⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡁⢆⡘⢄⠢⡉⢍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣽⣷⣿⣻⣿⣻⣾⢿⣽⣷⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡑⠄⢃⣰⡏⠀⠀⠀⣽⣿⣿⣿⣻⣾⣟⣿⣽⣿⣿⣿⡟⣿⣿⣾⢿⣽⣿⣻⣾⣯⣿⢿⣽⡿⣯⣿⣟⣿⡿⣽⣿⣻⣾⣟⣯⣿⣿⣽⣾⣟⣷⣿⣿⣿⣿⣿⣿⡿⠋⠤⡉⠔⠂⢀⠂⠐⡈⢀⠉⠞⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣽⣷⣿⣻⡿⣿⣾⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡇⠈⢀⡿⠀⠀⠀⢠⢟⣿⣿⣷⣿⣳⣿⣻⣾⣿⣿⣿⠒⣽⣿⣿⣿⣿⣾⣟⣷⡿⣯⣿⣟⣿⡿⣽⣾⣟⣿⡿⣽⡿⣷⣿⣻⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⠤⣉⠂⢁⠐⡈⠄⢈⠐⡀⠂⠄⢂⠈⢀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⢸⡇⠀⠀⠀⣼⠸⣿⣿⣿⢾⣟⣷⣿⣿⢿⣿⠧⣉⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢄⡁⠂⠀⡀⠀⢂⠠⠀⠂⠄⠐⡀⠂⠄⡈⠄⠠⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡖⡟⡏⠀⠀⢠⡇⢰⣿⣿⣿⣻⣿⣿⢿⣽⣿⡿⢢⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢥⣠⡷⠛⠁⠐⡀⠀⠂⠀⠀⠂⠠⠀⡁⠐⢈⠀⡐⠈⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣇⡗⠀⠀⣾⢀⣿⣿⣿⣷⢿⣳⣿⣯⣿⣿⡇⢣⣿⣿⠰⣉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣍⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⢀⠀⠄⠀⠂⢀⠂⠐⢀⠂⠈⠄⡁⠂⠄⠀⠀⠀⠈⢙⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⠓⣿⣿⣿⣿⣯⣿⣟⡷⣿⣿⣿⡇⣿⣿⣿⡵⡈⣞⣦⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠭⣔⣼⠟⠋⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⠀⠀⠄⠈⢀⠀⡈⠀⠂⡀⠄⠀⠁⠀⢈⠐⠄⠨⠐⡈⠄⠠⠀⡀⠀⠻⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢉⢈⡿⣿⣿⣿⣽⣾⣿⣿⣿⣯⣿⣷⣿⣿⣿⠿⢛⠉⠄⠀⢀⠂⠁⠢⡐⢌⠩⡉⢍⠩⡉⢍⠩⡑⢂⠔⡌⢱⣼⠟⠁⠀⠠⠀⡐⠈⠠⠀⠐⠀⠀⠐⠀⠀⠂⠐⠀⠀⠂⠀⠐⠀⠀⠠⠐⠀⠁⠠⠀⠌⡐⠡⠐⡈⠄⠡⠐⢈⠰⣿⣦⠘⡉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣠⣞⡗⠻⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⢟⠑⠨⠀⠌⠀⢈⠀⠄⡁⠂⠌⡀⠣⠜⡠⢃⠜⡠⢃⠜⡠⢊⢰⡿⠃⠠⠐⢈⠀⢂⠠⠀⡁⢀⠡⠀⠁⠈⠀⡀⠀⠠⠈⠀⠄⠁⠠⠈⠀⢁⠠⠈⠀⠁⠌⡀⠠⠁⠆⡐⡈⠄⡁⠂⠄⠻⣟⣷⠙⠾⠃⢻⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠏⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣦⣥⠷⠾⠴⠆⠠⡈⠔⡠⢁⠂⠐⡀⠠⠑⠀⢊⠐⠈⠀⠄⣂⡿⠁⠂⡁⠂⠄⠂⢀⠂⠠⠐⢀⠠⠐⠀⠐⠀⠀⡀⠁⠀⠂⠀⠂⠐⠀⠂⢀⠀⠐⠀⠂⠐⠀⢂⠁⡐⠀⠆⠂⠄⠡⢈⣶⣿⣹⣷⠾⢦⣼⣇⠈⢧⠀⠀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⣸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡰⠋⡅⢂⢂⠀⠀⠀⠰⣷⣌⠰⢄⢊⠐⠠⢀⠂⢈⠠⠀⡁⠂⠄⣿⠃⠈⠄⡀⠡⠈⠄⠂⠠⠁⠀⠄⠠⠈⠀⠈⡀⠁⠀⡈⠀⡁⠄⠡⠀⠈⠄⠀⡈⠠⠁⠄⠈⠀⠄⠂⠄⡈⠄⠡⠘⠠⢀⠘⠛⠚⢻⣧⠀⢠⡾⡆⠈⠛⢦⡹⣄⠀⠀⠀⠀ ⠐⣶⡤⠤⠤⢴⣾⣿⠃⢠⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣫⠟⠛⠛⠛⠿⠻⢾⠟⣻⣦⣥⣈⡻⣷⣄⠊⡜⣀⠂⡐⠀⡐⠀⠄⢀⠘⣼⠀⡈⠄⠐⡠⠁⢂⠈⠄⠐⢣⠀⡀⠁⡐⠀⠐⡀⢁⠀⡀⠐⡀⠐⢀⠂⡀⠂⢀⠀⠄⡀⢂⠀⠌⡐⢀⠀⡈⠄⡁⠂⠄⢂⠀⠄⠐⣿⣇⠀⢷⣿⣆⠀⠀⢳⠈⠳⡄⠀⠀ ⠀⠀⠉⠉⠉⠉⣰⠃⢀⣾⡷⠀⠀⣿⣿⣿⣿⡿⠋⠉⠁⠲⠶⣶⣶⣤⣤⣿⣴⠃⠀⠈⠙⠛⠿⣿⣢⠐⡤⢁⠄⠂⠠⠁⠂⡀⠂⠹⢿⠇⡐⠠⠐⣀⠂⢈⠐⠠⠀⢡⠀⠄⠠⢀⠀⠄⠀⠄⠠⠀⠄⠡⠀⠠⠀⠌⠀⠠⠀⠄⠠⠀⠂⠄⠠⠐⠀⠐⠠⠐⠈⡀⠄⠠⠀⠡⣿⡆⠀⣾⢹⡀⠀⠈⡇⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⢀⣾⣿⣧⠀⢰⠃⢹⡿⠋⠀⠀⠠⠘⣤⣧⣽⣇⠀⠀⠉⠙⠛⠿⣷⣲⢤⡄⠈⣷⣎⡗⠨⢌⠁⠂⠄⡁⠠⠀⠄⡀⠠⠀⡁⠄⠀⠄⠢⠤⠤⣐⡀⢀⠀⠁⠀⡈⠄⡈⠐⠠⠀⠂⠐⠈⢀⠂⠐⢈⠀⡁⢀⠂⢈⠐⡀⢂⠀⡁⠈⠄⡈⠐⠠⠐⡀⢁⠀⢻⣧⠀⢹⠝⠛⢦⣀⢿⠀⠘⡇⠀ ⠀⠀⠀⠀⢰⠇⠀⡾⣽⢻⢹⡆⠀⣼⠟⠁⠀⠀⢠⠡⢉⠄⠂⢸⢛⠓⠶⣤⣄⣀⡀⠀⠈⠉⠓⠶⣼⣿⣏⠡⠌⠢⠁⠄⠠⠐⠈⠀⠄⠁⠀⠀⠐⠠⠀⠀⠀⠀⠀⢀⠉⠉⠘⠒⠤⣀⡀⠈⢀⠁⢂⠡⠐⠀⠄⠈⠄⠀⠄⠂⢀⠂⠄⠠⢀⠐⠀⡁⠄⡀⠁⢂⠐⠀⡀⠂⠤⣹⡆⠀⢠⢤⡄⠀⠈⢳⠀⠙⠆ ⠀⠀⠀⠀⠸⣆⠀⠼⣿⠀⠀⣹⡾⠁⠀⠀⠀⢐⡀⠒⡀⠀⠀⣾⠎⠀⠀⠀⠀⠉⠙⠓⠶⢦⣤⣀⡀⢹⣷⠈⡌⡑⠌⠠⠁⠌⢀⠀⡀⠈⠀⡀⠂⠀⠈⠀⠁⠈⠀⠀⠈⠐⠠⢀⠀⡀⠈⠓⠠⣄⠀⡀⠁⠂⠄⡁⠄⠈⡀⠌⠀⠄⠂⡐⢀⠀⢂⠀⢸⡇⠀⢂⠈⠄⠐⠈⡀⢻⣧⠀⣸⢾⡅⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠙⢳⣾⡿⣆⣼⠏⠀⠀⠀⠀⡐⠠⠈⠄⠐⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡘⢠⠑⡈⠅⠌⡐⢀⠀⡀⠐⠀⠀⠀⠂⠀⠀⠂⠐⠀⠂⠀⠂⠀⠀⡐⠀⠂⠄⡀⠀⠁⠒⠤⡐⠀⠐⠈⠄⢀⠐⠈⡐⠀⠐⠀⠠⠀⠀⣿⠃⠌⠀⠂⠌⠠⢁⠐⣨⣿⢀⠟⠉⠙⠿⠂⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡝⠀⣸⠋⠀⠀⠀⠀⡐⡈⠄⡡⠈⠀⣠⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢢⠑⡌⢌⠰⣀⠂⠄⡐⠠⠀⢁⠀⠌⡀⠀⡁⠠⠀⠀⠁⠀⡈⢀⠀⠁⠄⢂⠀⠁⠄⠂⢀⠈⠃⡄⠀⠈⠄⢀⠂⠄⡁⠄⠈⠄⢂⣽⣯⠐⡀⠡⠈⠄⡁⢂⠂⢸⣿⠀⣴⣤⣶⡀⠀⣰⠇⠀⠀ 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⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠛⠦⠀⠀⠈⠻⣿⡷⣯⣯⣶⣹⣎⢷⣫⡝⢯⡻⣝⢯⡻⢿⡶⣧⣤⣃⡘⠤⠈⢆⠰⠐⡂⢌⡑⢂⣡⣘⣄⣦⣵⣶⢿⣻⣭⡿⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣯⣝⣻⢻⠷⣾⢿⣧⣿⣬⡷⣹⢧⡟⣾⣭⣛⡿⣟⢿⡻⣟⢿⡻⣟⡻⣟⡻⣝⣫⣝⣮⣷⡿⠛⢃⠰⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢫⢛⠷⣿⣼⣣⣛⢶⡹⢶⡹⢶⡹⢶⡹⣎⡟⣿⣶⣿⣼⣧⣿⣼⣷⣭⡷⣷⠟⠋⠉⠁⠘⢾⠏⠑⠮⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠱⠳⣤⣄⡈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⢉⣀⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠡⢃⡀⠉⠙⠛⠶⣦⠤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠞⠋⠉⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣇⠱⢀⠆⠈⠀⠀⠀⠉⠙⠛⣿⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠃⡔⢂⠀⠂⠁⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⢏⠔⡠⢂⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡌⢆⠡⢂⠰⠀⠄⡀⠌⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠂⠐⠀⠐⠀⢂⠀⣱⣿⠰⡘⡌⢆⠡⢂⡑⢀⠂⡐⠀⠄⠂⡀⠂⠄⠠⠐⡀⠂⠄⠂⠄⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣷⣄⠀⠈⠀⡀⢁⠀⠄⠀⠡⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠄⢈⠠⠀⢄⠈⠄⠡⢈⠤⢁⠂⣤⣿⣃⠧⡱⡘⣌⢡⠃⡌⢢⠡⠌⡌⠌⠤⢁⡉⠤⠡⡁⢌⠰⡈⢰⣸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠟⢠⡏⢸⠙⢷⣄⡄⠀⢀⠠⠂⢀⠂⡐⢀⠐⡀⠂⠐⠀⡀⠂⠐⠀⠒⠀⢂⠈⡐⢂⢂⠉⡄⢊⡘⠰⣈⠐⢢⣱⡿⢻⡜⣲⢡⠓⣌⠦⡙⢤⢃⡜⢢⢘⡘⣐⠣⣘⠐⢣⡘⡄⢣⣬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠈⢻⡇⢸⡐⢊⡏⢛⢾⣤⣂⣰⠀⢂⠐⡀⠢⠐⡈⠤⢁⠠⠈⠄⢂⠡⠌⠠⢡⠐⠢⢄⠣⢌⠢⢌⡱⣠⢫⣝⡞⠁⢸⣷⢡⢏⠞⣤⢣⡙⢆⠣⡜⣂⠧⡘⢤⠓⡬⣙⢢⣱⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣼⣱⢢⣙⡬⠓⢤⡘⠧⣂⡜⠣⢆⡙⢣⣤⠞⢏⢡⣷⢸⠁⡞⣝⢫⣠⡱⢌⠢⢌⠣⢄⠢⠐⢡⠠⠌⠡⢂⠄⠈⠠⢁⠤⡈⠐⠢⡀⠐⢂⠀⣰⣂⣤⢾⢛⡏⢊⡐⢸⡇⢻⠈⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣬⢣⡄⡘⢣⠐⣘⠣⣐⡘⢘⢢⡜⢃⢤⡙⠦⣌⠓⢡⣲⡜⢻⡿⣱⢢⠐⣈⠰⡘⢊⡄⠉⢂⢂⡐⠈⢂⠀⠒⠀⠐⠂⡀⠀⠐⠂⡀⠐⢀⡐⠂⢀⠂⠠⢀⠀⡄⣄⢷⠙⢸⡏⢠⠟⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣸⢰⡈⠰⢌⡁⠡⠤⡉⢁⠤⠌⡌⠌⠡⢢⡌⠃⢡⣌⡘⡱⠧⣃⣿⣤⠂⢁⠤⢈⠡⠄⠈⢄⠀⠠⢈⠄⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠡⠀⠄⠀⢁⡀⠀⠈⠀⣄⣷⢿⡼⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢁⠄⠂⠄⠂⡀⠐⠠⠄⠂⡀⠂⠄⠀⡐⠂⢀⡑⢂⠡⢆⡌⡘⠰⣿⣱⠀⢂⠀⠐⠀⠐⠂⠀⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠌⡀⠄⠀⠰⢂⠡⢆⡌⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⢂⡠⠔⢏⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠀⠀⠀⠀⠀⠁⠂⠀⢂⡔⠃⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣶⣿⠛⠙⠉⠀⠀⠀⠈⠆⢀⠱⣇⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠉⠋⠞⠶⠤⠤⣤⣤⣤⣤⣤⣤⠤⣦⠶⠛⠙⠉⡀⢃⠡⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣦⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⣀⢉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⡈⣄⣤⠳⠱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣧⠮⠑⠏⢾⠘⠁⠉⠋⠟⣷⡷⣭⣷⣼⣿⣧⣼⣿⣶⣿⡟⣎⡹⢶⡹⢶⡹⢶⡹⢶⣛⣣⣼⣿⠷⢛⢫⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⠰⢃⠛⡿⣷⣮⣝⣫⣝⡻⣟⡻⣟⡻⢿⣟⡻⢿⣟⡿⣛⣭⣾⡟⢧⣹⡷⣬⣿⣧⢿⣾⠷⢻⣻⣝⣯⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠛⡿⣭⣻⢿⣶⣵⣦⣄⣘⣡⢂⡑⢌⡂⠐⠰⢆⠈⠤⡘⣃⣤⣧⡶⢿⡻⢯⣝⡻⢯⡝⣫⢷⣎⣹⣶⣯⣯⡷⣿⠻⠈⠀⠀⠦⠛⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣦⣔⢃⠠⢎⡁⠢⢆⡈⠑⢠⠰⡘⢌⡐⠤⢊⡄⠎⡀⠜⡉⠤⠌⠠⣍⣂⣡⣆⣁⣴⣃⣤⣼⣥⣴⣮⣥⣶⣿⣿⣽⠿⠛⠉⠀⣄⡦⢯⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠻⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⣨⡑⠤⡐⠡⡔⠊⢁⠤⢂⡐⠊⣁⠔⠃⠄⡘⢅⠂⢠⠜⢃⠄⠐⢨⡑⢆⠁⠰⢊⡡⠆⡈⠱⢆⡉⡐⠣⢄⡘⠆⢈⡰⣜⣥⣶⣿⢿⠻⠀⡀⡳⣮⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢿⠺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣑⠎⡁⠢⣁⠤⠌⠡⢂⡁⢂⠡⢌⠃⡠⠙⠤⠎⡐⠘⢡⠌⠲⡐⢉⡌⠃⡄⠉⡰⠌⢃⠠⢌⠡⢄⠊⡡⠐⢣⠄⢃⡄⠎⡁⠰⢎⡁⣦⣿⣿⠛⠐⣆⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠨⠐⢈⡀⠐⠄⠀⠐⠡⡀⠌⠀⠠⠐⠠⠄⠱⢈⠔⠂⠠⠐⢂⡠⠔⡈⠱⢄⠡⠢⢄⠒⡄⠐⢢⡄⠒⢀⡰⠆⡁⢐⡨⠔⢊⡄⠘⢢⡑⡆⣿⣿⠻⠠⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⡟⣡⡟⣧⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢂⠄⠀⠐⢁⡀⠂⢀⡀⠐⠠⠂⢀⡐⠂⢁⡀⠈⢂⠀⠠⢂⡀⢁⢀⡁⠂⠑⡠⠌⠡⣂⠄⡈⠐⢠⡌⠂⣉⠡⣂⠌⡐⠒⢁⠰⢌⡑⢆⡈⠱⣌⣷⣿⢹⠀⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⡀⠊⢁⡄⠀⠀⠀⠀⠀⠀⠀⠃⣼⣰⠋⡖⢠ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠏⣿⢱⢈⠠⢂⠄⠀⡈⠁⠠⢀⠠⠐⠠⠐⠠⠀⠐⠂⠀⠠⢀⠄⠀⠌⠀⡁⠀⠠⠀⠡⠀⠠⠐⠡⠄⠂⢀⠌⠀⠈⠰⠌⠄⡐⠡⡠⠔⡉⠡⢆⡈⠰⡘⡆⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠁⠋⠛⠾⠴⣤⣠⣀⣀⣄⣥⣽⢞⡠⢀⠀⠀ ⠀⠀⠀⠀⠀⣯⣛⢻⠧⠰⠀⠏⣼⡑⠢⡌⠐⢈⡀⠌⠀⡎⠁⢀⡀⠈⢂⡁⠀⢂⠀⢈⠂⢀⡈⠂⢀⠐⡈⠂⡀⠐⡀⠂⠀⢀⠠⠂⠁⢀⠐⠌⠂⠁⠄⠂⢁⡠⠐⣈⠔⠊⠠⢒⡌⠆⡈⢑⡤⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠾⣤⣐⠢⢁⠀⠀⠀⠀⠀⠁⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡈⣦⣼⣼⠀⠇⣽⣴⠈⠠⠔⠂⠁⢀⠂⠅⣿⠛⠈⢀⠐⠠⠐⠂⢀⠄⠈⠐⢀⠄⠀⠠⠌⠀⠌⠀⠠⢀⠄⠁⠀⠈⢀⠈⠀⠠⠐⠄⠀⠠⠌⠀⡈⠄⠃⢠⠌⡠⠜⡉⢂⢌⡑⠢⣇⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣀⠐⢈⡱⠄⠈⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣷⡏⠻⠇⠀⡏⣸⠌⠀⡰⠂⢁⠂⡀⠁⣿⣿⣿⠄⠀⠂⢀⡀⠐⠂⢀⠁⠢⡈⠀⠠⢀⠈⢀⠌⠂⢀⡀⠂⠀⠀⠀⠀⠀⢀⠐⠠⡀⠐⢀⠂⠄⠂⢁⠂⠄⠂⢂⠄⠐⢨⡔⠊⢡⡆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣰⠀⢁⠆⡁⠄⠠⠀⠀⠀⠀⠃⣼⠀⠁⠛⠛⠚⠀⠀⠀ ⠀⠀⠇⣰⠀⡀⣶⣤⣴⠀⣿⢸⠂⢂⡁⠄⠈⠡⡀⠐⣯⣽⢂⠄⠈⠄⡁⠄⠂⢀⠄⠈⠀⡄⠃⠈⢀⠂⠄⠁⠀⢂⠄⠁⠀⢀⡈⠀⠁⠀⠀⠠⡁⠀⡀⠌⠀⢁⠀⠠⡐⠄⠂⣀⠰⢌⡌⠑⢢⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣯⣠⠀⠈⡡⠄⡈⡐⠀⠀⠀⠀⠋⣸⠀⡝⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠂⠿⠙⠉⠟⢀⣿⣨⠐⢁⠠⠌⠂⠀⠌⠃⣿⠀⠀⠠⠀⠐⠀⡐⠈⠐⢀⠄⠈⠐⠀⡐⠤⠒⠁⠀⡀⠄⠂⠀⡐⠀⠀⠂⠀⠂⠀⠐⠂⠀⠀⠂⠀⠀⠀⠐⡀⠀⢀⡐⠌⠅⡈⠑⢠⡘⣿⢻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠐⠄⠈⠠⡐⠀⠀⠀⠀⠏⣼⣆⡿⣾⢳⠙⠀⠀⠀⠀⠀ ⠀⠀⡇⠈⠀⠀⡅⢾⣸⠀⣧⢻⡀⠈⠐⠄⠈⢂⠀⡇⢸⠀⢂⠀⢀⡐⠂⠄⠀⠌⡀⠈⠄⡁⠄⠂⠁⡀⠀⣄⠠⠓⠈⡀⠀⢀⠠⠐⠈⠀⠀⠈⠁⠀⠈⠀⠂⡀⠀⠈⡀⠀⢀⠌⠁⠠⠌⡑⡌⠈⣷⢹⡀⣀⣤⢦⠶⠓⠙⠉⠀⠀⠀⠀⠎⣾⠀⠀⡀⠒⡀⢐⠀⠀⠀⠁⡾⣹⠀⠀⣿⠼⠀⣆⠸⠀⠀⠀⠀ ⠆⠙⠀⢳⠈⠀⡄⢤⢠⠀⡆⣹⠤⠂⡀⠀⠐⢂⠁⡀⠄⡁⠀⠐⢀⠠⠄⠂⢀⠂⠄⠀⠄⠈⠄⠀⠐⠡⢂⠁⢀⠈⡀⣀⠤⠒⠘⠉⠉⢀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠁⠄⠀⠈⠐⠠⠄⠁⠢⠌⠡⣏⣿⣼⠶⠓⠉⠈⠀⡀⣀⣄⣤⠶⠓⢛⢸⠂⠄⢉⠡⢠⠀⠀⠁⠟⣼⠀⡆⢹⢻⣽⡾⠀⠇⢰⠀⠀⠀⠀ ⠀⡇⠘⠀⢿⣀⢦⠛⠝⢹⠀⣧⢻⠀⢁⡀⠐⠠⠐⡈⠄⠈⡁⠀⢂⡀⠐⢈⠂⢀⡁⠀⢈⠐⠂⢀⠈⠐⠂⠀⠠⠐⡈⠄⡈⠀⠁⠀⢀⡀⣐⠤⠤⠢⠄⠀⠄⡁⠀⠠⡀⠄⠀⠠⡁⠄⠂⠁⢌⠨⡗⣎⣷⠈⡄⢤⣲⣷⠿⠛⠙⠉⠀⠀⣇⣽⣧⣤⠘⠠⠀⠀⠋⡿⢹⠃⢰⠀⣧⣿⣾⢀⠁⣼⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⡇⠈⠀⡀⢹⣾⠀⡆⣿⠡⠀⠠⠄⡀⠈⠐⠠⠐⠀⠐⠠⠄⠂⠀⠠⠄⠀⠠⠀⠌⠀⠠⠀⠡⠄⠀⠠⠄⠀⠄⠀⢀⠠⠄⠀⢡⠀⠠⠐⢈⠂⣀⠐⠠⡐⠇⢿⠹⠂⡀⠂⠁⠠⠂⠄⢁⡤⠐⣢⣿⠿⠛⠙⠈⠀⠃⣴⣿⣤⣤⣶⣶⠶⠲⠁⠉⠋⡿⣿⣿⣿⣿⠀⠀⡷⣾⢀⠃⣰⠉⠉⠉⠉⠀⠀ ⠀⠀⡄⠳⠈⢳⠀⠀⣆⣿⢷⠀⣇⣿⠐⠄⠀⢂⠄⠂⡁⠄⡈⠀⢀⡐⠌⠀⢂⡀⠄⠀⢀⠂⡀⠂⢀⠐⡀⠐⡀⠀⢁⡀⠐⠀⡐⠁⡀⠀⢣⠐⠄⠈⢂⠁⡠⠐⠄⡈⠀⣼⠘⢀⠄⠀⡐⠀⡐⠂⣀⡜⠊⣄⣷⡻⣈⣥⣦⣻⠟⢾⠻⠿⠛⠛⠛⠟⣫⣿⣿⣿⣿⣿⣿⢸⠀⠀⣿⢠⠃⣿⣾⢴⠤⠤⡤⣶⠐ ⠀⠀⠀⠀⣄⡹⢦⠛⠈⡆⡾⢠⠀⣧⢻⠚⠛⠘⢀⠠⠘⠡⠄⡈⠄⠂⠄⠀⠈⠄⠁⠠⡈⠀⠄⠈⠀⠡⠄⡁⠀⡈⠀⠁⡀⠈⠀⠈⠠⠄⠀⠁⠠⠂⠄⠈⠡⡀⠄⠈⠃⣿⠄⠂⡁⠀⠠⢈⠂⢀⠠⠐⢊⢄⠰⣌⣷⠰⠀⠀⠀⢂⢂⡅⠋⡰⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⣸⠏⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⢧⠈⣇⣼⢦⠾⣷⣹⣿⣶⢈⠡⠄⠂⠆⠀⡐⠁⢂⠀⠐⠂⠀⠐⠀⢀⠂⠀⠐⠂⠀⠂⠀⠁⡀⠀⠀⠐⠀⠐⠠⢀⠐⠠⠂⢀⠂⠄⠂⡁⠂⠁⡿⣂⠄⠀⠈⠐⢊⠀⠑⠠⡀⠐⠂⢁⡠⠔⡈⠠⠆⠴⠾⠷⣥⣦⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣾⠏⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⠃⠾⠙⣷⣟⠻⠄⠂⡁⠄⡈⡐⠆⠁⠠⡀⠌⠁⠀⠈⠠⢁⠀⠈⠠⠁⠄⠀⠈⠠⠀⡀⠀⠈⠁⠀⠡⢀⡁⠀⠠⢂⠀⢈⠐⠠⠃⡿⢰⢊⡠⠜⢃⡠⠜⢃⡠⠜⠣⡀⠌⠂⡁⠄⠀⢈⠀⠌⠀⠨⠑⢟⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⠻⡗⣞⣠⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⡉⠘⣦⣿⠰⢈⠐⠡⠄⡈⠐⠡⡐⠌⠀⠠⠁⠀⠐⠠⠀⠀⠐⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠐⠀⠠⠈⡐⠀⠠⠀⠁⠟⣼⢱⡌⠔⢂⡑⠩⢍⡉⠩⢍⡉⠩⢌⡐⠢⠁⠂⢀⠀⠄⠉⢛⠿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣾⣽⣿⣿⣿⡿⢈⢉⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠻⠀⡀⠀⠠⠄⡈⠐⠨⠄⠐⢈⠀⠁⠀⠄⡀⠂⠀⡈⠀⢀⠈⠄⠀⠀⠈⠀⡀⠀⠀⢀⠀⠀⠀⠀⠋⠟⣼⣔⠭⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠟⠿⣿⣦⣞⡈⡵⣿⣿⣿⡇⣿⣿⣿⡷⣟⣿⣯⣿⣿⣿⣿⠓⢸⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢙⠈⠀⠀⠀⠄⠂⡁⠄⠈⠂⢀⠐⠂⢀⠂⠀⠄⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣴⣍⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣉⠰⣿⣿⢣⡇⣿⣿⣯⣿⣳⢿⣷⣿⣿⣿⢀⣾⠀⠀⡗⣇⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⢻⠚⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⡐⠀⢈⠐⡁⠀⠠⠂⠀⠀⠂⠀⡀⠐⠁⠛⡷⣠⢥⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣹⢢⡿⣿⣽⢿⣿⣿⣻⣿⣿⣿⢰⡇⢠⠀⠀⡏⡟⡖⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠠⠄⡈⠄⠂⡀⠐⠄⠂⠀⠠⢂⠀⡀⠀⠂⡁⢄⠋⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣉⠧⣿⢿⣿⣿⣷⣟⢾⣿⣿⣿⠸⣼⠀⠀⠀⡇⢸⠀⣷⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⠻⠙⠉⠉⠀⠀⢀⠈⢂⠄⠂⡀⠐⢈⠄⡈⠐⢁⠂⣉⠤⠋⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣻⣿⣷⡿⣽⡿⣿⣟⣾⣽⡿⣿⣟⣿⣯⡿⣷⣟⣾⣿⣿⣿⣿⣽⠒⣿⣿⣿⣾⣻⣿⣳⣿⣷⣿⣿⢟⢠⠀⠀⠀⡿⢀⠈⡇⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣿⣾⣿⡿⣻⣿⣷⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠶⠞⠉⢀⡈⠐⠂⢀⠂⠔⡉⠤⠋⡿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣽⣿⣿⣯⣟⣾⣻⣿⣽⡿⣿⣟⣿⣯⡿⣽⢿⣿⣯⣾⣻⣿⣽⢿⣾⣿⣿⡟⣿⣿⣿⣽⣿⣟⣾⣻⣿⣿⣿⣽⠀⠀⠀⡏⣰⢃⠄⡑⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡇⣿⣷⣽⢿⣾⣻⣿⣻⣿⣷⣽⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⢍⡉⠢⢄⡘⢆⡁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣽⣿⡿⣽⣻⣿⣽⢿⣿⣯⡿⣽⢿⣾⢿⣿⣯⡿⣷⣽⣿⢾⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣞⣿⢯⣿⣿⣿⠀⠀⠏⣱⣈⠱⣛⠶⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⡇⣻⣿⣯⣻⣿⣽⢿⣾⣻⣿⣻⣿⣽⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡿⣷⣽⢿⣿⣻⢿⣾⣿⡿⣷⣯⢿⣿⣯⡿⣽⣿⣿⢯⣿⣯⣾⣻⣿⣷⣽⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣟⣿⣿⣿⠸⡟⣻⠞⡴⣠⠀⠁⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⣷⣿⣯⢿⣿⣯⣻⣿⣽⢿⣿⣯⡿⣷⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⣻⣿⣷⣯⡿⣽⢿⣿⣷⣟⣾⣽⢿⣿⣯⢿⣿⣯⡿⣷⣟⣿⣯⣿⣟⣾⣻⣿⢷⣾⣿⣿⣎⣿⣿⡷⣿⣿⡿⣽⡿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⡀⣷⣿⣟⡿⣽⢿⣾⣽⣿⡿⣾⣻⣿⣽⡿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣷⣟⣾⣻⣿⣷⢯⣿⣽⡿⣷⣻⣿⣷⣯⡿⣽⢿⣿⣯⣻⣿⣽⡿⣽⢿⣾⣽⣿⣻⣿⣷⣿⣿⢈⣧⣿⣿⣿⣾⣿⡿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⡀⠳⡀⣦⣿⡿⣻⣿⣽⣿⣳⢿⣿⣯⢿⣿⣯⡿⣷⣟⡿⣽⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣾⣻⣿⣾⣻⣿⣷⣟⣾⣽⢿⣿⣯⣿⣳⣿⣷⣯⢿⣿⣯⡿⣷⢯⣿⣻⣿⣳⣿⣽⣿⣯⡿⣽⣿⣿⣿⢻⠃⣷⣿⣷⣯⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⢦⠈⡄⣷⣿⡿⣷⣯⣾⢿⣾⣽⢿⣿⣟⣾⣿⣯⡿⣷⣯⣟⣾⣻⣿⣽⣻⣿⣷⣟⢾⣿⣻⣿⣽⢿⣾⣿⣟⣾⣻⣿⣷⣯⡿⣽⣻⣿⣷⣯⣿⣟⡾⣿⣟⣾⣽⢿⣾⣻⣿⣻⣿⣯⣟⣿⡷⣿⣿⣿⣿⢸⡀⣷⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀ 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