⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣶⣲⣦⣤⡖⠚⠛⠻⢿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠙⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⢀⠀⠀⠀⣠⢠⠀⠀⢀⢀⣤⠀⠀⢀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⠋⠀⠀⠀⡾⣸⢇⡼⣣⢸⡘⣆⢸⢸⣎⢳⠸⢈⢧⡀⠀⠀⠀⠻⣿⡷⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣤⣙⣦⠖⠒⣶⢷⢉⡿⢱⠟⠘⢧⠹⠸⠈⠹⡎⣧⠘⢦⠓⢾⡛⢛⣶⡏⠀⢄⣀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠉⢀⣽⡿⢾⣶⠏⠀⢀⠀⠀⠀⠀⢀⡇⣀⠀⠀⣸⡏⠀⠀⠀⠈⣿⡾⡿⡷⣄⣀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⢹⣧⣾⡟⠀⠀⣼⠀⠀⣰⣦⢿⣵⣿⠀⣰⠟⢷⣰⠸⣆⠀⢸⣏⢿⡇⢠⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⢸⣿⡿⢠⡆⢰⡿⡆⢰⣿⠏⣾⠋⣿⣿⠏⠀⠸⣿⣶⣿⡄⣾⢻⣿⡇⢀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣸⡈⢠⣾⣷⣾⠀⢻⡿⠋⠀⠃⣸⠟⠁⠀⠀⠀⢻⣿⡇⣿⣿⣼⣨⣷⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⣼⡟⠈⡟⠉⡙⠓⠦⢤⣀⠀⠀⠀⢀⣤⡤⠼⠟⠓⢻⡟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡖⠿⠿⣿⣿⡿⡶⢾⣦⣀⣰⡿⢿⢿⣿⣿⡿⣾⣶⣿⡿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠿⣿⠷⣄⡀⠉⠛⠃⣀⡴⠿⠋⠻⣧⣀⠀⠛⠛⣀⡤⢿⣿⡇⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠠⣟⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢠⡿⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣬⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣮⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣉⠁⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⠀⠀⠀⢠⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡆⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣧⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣿⡀⢸⣿⣇⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣧⣤⣀⣀⣀⠀⠀⠀⠀⣧⣤⣈⣉⡉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣷⣶⣾⣿⡏⢸⡟⡇⠀⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⣉⣉⣉⣡⣽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀ ⢰⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣉⣽⣿⡃⣸⡇⢱⣀⢸⣿⣧⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⣿⣶⣶⣶⣶⣾⣿⣿⣿⡿⠿⡇ ⢸⣿⣦⣤⣤⣤⣀⣀⣀⣀⣿⡷⠀⠀⠀⠀⣸⣿⡏⠉⠉⠛⠛⠛⠛⠿⣿⡿⠉⠁⡁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣿⣧⣀⠀⠀⠀⣿⠛⠋⠉⠉⢉⣉⣀⣠⣤⣴⡗ ⢸⡟⠛⠿⠿⠿⠿⢿⣿⣿⣿⣧⣤⣴⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⢰⡃⠀⢀⣀⣀⣠⠤⠤⠔⠒⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⠋ ⠀⣽⡏⠁⠀⠒⠒⢲⣶⠾⠻⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡻⣦⣼⠖⠒⠒⠒⠚⣿⡋⠀ ⢠⣿⠃⠀⠀⠀⠀⠘⣿⡄⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡟⠀⠀⠀⠀⠀⢹⡇⠀ ⣾⠏⠀⠀⠀⢀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠄⡇⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡖⡏⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⣿⠁⠀⠀⠀⣨⠇⠀⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢠⠷⠄⠀⠀⠀⢹⡇ ⠘⢦⡤⡄⠘⠧⠳⣄⣹⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⠀⡼⠣⠀⣰⣰⣦⠟⠀ 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