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⠀⠀⠁⢸⠀⠀⠉⠚⢒⠽⡭⣒⢔⠤⣠⢀⠀⠀⠀⠀⠦⡓⣌⠻⣝⣦⢿⣿⣿⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀ ⠀⠈⡇⠟⡮⣖⠤⡠⣀⢀⠀⠀⠀⠀⠀⠦⠓⣙⣍⠦⠓⣟⣭⢿⣻⣶⠴⣤⣧⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠃⣾⠀⣄⠧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⣒⣷⣿⣶⣤⣀⠀⠀⠀⠁⡾⣿⣻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⣿⢰⠀⠀⣿⣠⢀⠂⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢀⠀⠀⠀⠀⠀⠁⠃⣷⣽⣼⣷⢻⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣧⣀⣀⢀⠀⡀⣿⣿⣿⣿⣿ ⣿⢾⠉⠃⣿⠀⠀⠀⠀⣿⣿⠿⠻⠛⠉⠉⠻⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣆⣿⠀⡄⢧⡈⢤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣷⣿⡜⡧⣸⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠁⠂⠽⠿⠿⠻⠙⠈⠀⣀⢤⠢⠒⠑⠉⠈⠀⠀⠒⣷⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠆⣮⢿⣿⢸⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠭⢠⢀⣤⡅⣖⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⡄⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠳⣄⣳⣿⣿⠹⠀⠀⡟⣿⣿⣿⣿⣿⣿⣸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠏⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⡀⢷⠙⣿⣿⣿⠘⠀⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⠘⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⣆⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⣿⣿⣿⣿⣿⣿⢸⢹⠃⡵⣏⠚⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⣇⣷⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⢸⣇⡟⣿⣿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡆⣷⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣼⣸⣣⣿⡀⣿⣧⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢠⠀⠀⠀⠀⠀⠖⡿⠾⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⢰⠘⠀⣾⠀⣿⠀⣸⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⢸⠀⠀⠀⠀⠤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠸⢸⠃⢸⡅⣿⠀⢺⢹⣿⣿ ⢣⠉⠀⠀⠄⠐⠀⠀⠀⠀⣇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢹⢠⡄⠀⠇⢸⡏⢀⢡⣿⣿ ⠀⣿⠹⠀⠀⠄⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠻⠀⠀⡀⣎⡀⠀⡟⣿⣿ ⢸⣿⣿⢿⠀⠀⠂⠀⠀⠀⡄⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⢻⠀⠀⠀⢠⠇⣻⣆⣘ ⣇⢿⣄⣿⢻⠇⠀⡄⠐⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⢹⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢿⠛⠛⠟⣼⢀⠋⢸ ⡀⣧⢻⡇⣿⠸⢱⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⠀⠀⣦⠀⣧⣿⡜⠀⠀⠒⡇⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⡟⣿⣿⣿⣿⣿⣿⣿⣹⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⢤⠳⡌⣿⣿⣿⣿⣿⣸⠀⣷⠈⠀ ⠀⠙⠀⠈⡏⣷⣏⡜⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⣿⣴⣤⣠⣀⣀⣇⣰⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣇⣿⣿⣿⣿⢀⠀⠀⠀⠀ ⠀⡆⠘⢄⡇⡝⣧⣿⡜⠹⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣟⣽⠮⠶⠶⠒⠗⣱⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠴⠧⠻⠈⠀⠀⠀⡄⣿⣿⣿⣰⠀⠀⠀⠀⠀ ⢻⠈⣍⠛⡾⣷⣬⣶⣿⡜⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⣄⣠⣄⢤⠲⠟⡿⣿⢿⡻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣹⢸⠀⠀⠀⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⡀⣄⢤⡲⠓⠉⠂⠀⣌⣦⠹⠀⠒⠒⠴⠥⠯⣠⠀⠀⠀⠀⠀⠀⠀⠆⣿⣿⣻⣙⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡶⣶⣤⠀⠀⠀⠀⡤⣷⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣀⠤⡀⢄⡶⣶⠤⠤⣠⣈⣤⠤⠲⠙⠈⠀⠀⠀⠀⠏⣿⣿⣽⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢰⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠙⠀⡏⣿⣿⣿⣿⣾⣿⠿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣴⢀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠈⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀ ⠀⠀⠀⠀⠀⠀⠁⠙⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣝⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠋⠒⢶⠘⡀⣁⣿⠦⠒⠚⠐⠀⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⠹⠈⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣂⣟⣝⣷⣎⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠟⡿⢽⠬⠀⠀⠄⠉⠿⣿⣿⢿⣿⣿⣿⡿⠾⠬⡤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠀⡇⣿⣴⢘⠛⠒⠒⠓⠛⠛⠛⠙⠙⠉⠉⠉⠉⣍⣿⠿⣙⣇⣿⢻⣿⣿⣿⣿⣿⣿⣾⣤⠀⠀⣀⣦⣷⣿⠿⠉⠇⣿⣿⣿⣿⣿⣿⣿⣿⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣿⣿⠀⡇⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣁⠋⡽⣾⣶⠹⠀⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⣿⣾⠀⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣸⠀⠁⠋⣛⣿⢾⣷⢻⠁⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⣽⢸⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⣇⣧⣿⠄⣤⠀⠰⠀⠀⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⡇⣿⢰⠀⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⠁⡉⣾⢀⡀⢠⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡇⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⡛⣟⣿⣰⡇⣿⡿⣯⣿⠻⠈⠀⠀⠇⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⣿⡿⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣽⠀⡀⣄⠦⡖⣿⣝⣮⣶⣶⢷⠠⠏⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣿⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠈⠀⠀⠀⠀⠀⣄⣤⣤⣤⣁⠏⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢸⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢿⠘⠑⠁⠈⠀⠋⡟⢟⠿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡞⣷⣿⣝⣿⡿⢟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀