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⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠻⣦⡀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⠀⢻⡆⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠹⣧⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢿⡄⠈⣧⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠹⣇⠀ ⢀⡼⠃⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣼⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣀⣿⣀⣀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢻⣿ ⡾⠁⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡟⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣾⣿⠿⡿⠿⠿⠿⣿⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⢿ ⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣤⣤⣤⣻⣇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣸⡏⡁⠀⣿⢀⡟⠀⠀⠀⠀⢠⡿⢻⣿⣿⣀⠀⠀⠀⠀⠀⠀⣾⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈ ⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⢿⡄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⠿⢿⣿⠉⠉⠉⠙⢻⣆⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿⠘⠃⢠⡿⢸⣇⣤⣴⣶⣶⣿⣷⣶⣿⣬⣝⣷⣦⠀⠀⢀⣼⠋⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⠀⠀⠀⠀⣿⢸⣿⣄⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢸⡇⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣸⢧⡄⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡾⠃⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠹⣦⠀ ⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻⣧⠀⠀⠀⣿⠈⣿⠻⣦⣴⡿⠛⠁⣀⣀⣤⣤⣤⣤⣬⣿⣧⣄⣀⠀⠀⠀⢻⣆⠀⠀⠀⠘⣷⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡟⡈⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣸⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠙⣧ ⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠹⣧⡀⠀⢿⡄⢹⣷⡿⢿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠹⣦⠀⠀⠀⣿⡀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⡿⠁⠀⠛⢹⣿⣿⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠘ ⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⢷⣄⠸⣇⠈⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠙⢷⡄⠀⢸⣇⠀⢿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡿⠃⠀⠀⠀⣾⡿⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⣿⣾⣷⣶⣶⣶⣍⠛⠻⣿⣿⣆⠀⠀⠈⢻⣦⠀⢿⡀⣾⠁⠈⢿⣄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢰⣾⠇⠀⠀⠀⠘⠟⠀⠀⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠉⠛⢷⠀⠀⠈⠙⢷⣼⣿⣿⠄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢻⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡉⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⣿⣿⣿⣿⣿⠟⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⣿⣿⣿⣿⡿⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠉⢿⣿⣿⣿⣿⣿⠇⠉⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠖⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠻⢿⣿⣿⠏⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⣀⣀⣀⡀⠀⠀⠀⣠⣿⡇⣀⣀⣀⠀⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠍⠛⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡇⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠇⠀⠀⠀⠀ ⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠉⠛⠶⣦⣤⢶⣾⡿⠶⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢹⣆⢸⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⣿⣷⡾⠟⠉⠀⠀⠀⣀⣿⡿⠟⠋⠙⠛⠉⠉⠀⠙⣿⠀ ⣦⣄⡀⠀⠀⠀⢿⡌⣿⡄⠈⠻⣶⣄⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⢸⣿⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⢉⣿⢟⠀⠀⠈⢿⣾⡇⣦⡀⠀⠙⠻⢦⣄⡀⠀⠀⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠙⠷⣄⠀⠀⠀⠀⣿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄ ⠀⢸⣿⣎⡻⢶⣤⣀⠻⣷⠈⠙⢶⣄⠀⠀⠈⢻⡷⢶⣬⣿⣻⡿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⢷⣄⠀⠀⠀⠈⠁⠀⠀⠀⣿⣴⡟⠁⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⣴⡾⠋⢹⡇ ⠀⢸⡇⠙⠻⣦⣌⡙⠻⢷⣤⣀⠀⠙⠻⣦⡀⢸⠇⠀⠈⠙⠃⠻⣆⠉⠛⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⢻⣏⠁⠀⠀⠀⠀⠠⠙⣷⣄⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣠⣶⠟⠉⠀⠀⣾⠁ ⠀⢸⡄⠀⠀⠀⠙⠻⢶⣤⡈⠙⠻⣦⣄⠈⠻⣾⡀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⣾⠋⠛⠻⠶⢶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠛⠉⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⡆⠀⣿⠀⠀⠀⠀⣠⣾⠟⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⢰⡟⠀ ⠀⢸⣷⡀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠙⢳⣦⠈⢷⣄⠀⠀⠀⣾⠀⠈⣿⣠⣿⠃⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠛⠛⠛⠛⠓⠶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢿⠀⣿⠀⠀⢀⣾⡿⠁⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀ ⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣌⠳⣄⠻⣦⠀⠀⡏⠀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⢰⡇⠀⣰⣿⣏⣴⠿⠛⠀⠀⠀⠀⠀⠀⢀⠀⣠⡿⠃⠀⠀ ⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡙⣧⠀⡇⠀⣸⣿⡁⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢸⣧⠀⢸⠃⣼⣯⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡹⣾⡇⢠⡟⠉⠁⠀⠀⠀⢀⣠⣶⣿⡛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⢻⣆⡀⠀⠀⠀⠀⠀⣠⣴⠟⠛⢿⣦⣀⠀⠀⠀⠀⣿⠀⠟⣸⣿⠟⠁⠀⠀⠀⠀⢀⣀⣤⣤⡶⢿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠈⠹⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠁⣿⠁⠀⠀⠀⣠⣴⣿⠿⠋⠉⢷⡘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⡿⠛⠿⣶⣤⡆⣠⣾⠋⠀⢀⣴⠟⠻⣿⣷⣆⠀⠀⢸⡇⣰⡟⠁⠀⣠⣤⣴⣶⡿⠛⠋⠉⠈⢷⡀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠉⣙⡛⠷⠶⢶⣤⣤⣴⣄⣀⠘⢻⣾⡏⠀⣠⣶⣿⣿⠋⠁⠀⠀⠀⠘⣷⣼⡇⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠻⣦⡉⠳⠆⡀⠀⠀⠉⡉⠛⣻⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⢠⣴⢟⠀⠀⣀⡀⢙⣿⠟⠁⠤⠶⠂⠀⠀⠀⠀⠙⠿⣿⣆⣸⣿⣿⣴⣾⡿⢿⣋⠉⡁⠀⠀⠀⠀⠀⠈⣷⠀⢹⣷⠀⠀⠀⠀
⣿⣿⣿⣻⣟⣿⣿⡿⣿⡿⣫⡶⣿⣿⣿⣿⡿⣿⣻⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⢿⣿⡿⢶⣿⣟⣿⣿⡻⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⣿⣿⡷⣟⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣾⣟⢮⡻⣿⣯⣟⡿⣟⣶⣿⣿ ⣿⣻⣿⣿⡿⣫⣾⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣛⣿⣿⣿⣛⣻⢿⣿⣿⣿⣿⣿⣿⣷⣽⢿⣿⣿⣷⣝⢮⣿⣾⣿⣻⣾⣿⣿ ⣯⢿⣟⢫⣾⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⢿⣻⣭⣷⢿⣻⢯⡿⣽⢯⡿⣽⣻⣟⡿⣾⢯⣟⡿⣿⣿⣿⣿⣽⢿⣿⣿⣷⣝⢿⣯⣿⣿⣿⣿ ⣿⣟⣵⣿⣿⣿⣟⣵⣿⣿⣿⣿⢟⣽⣶⢿⣽⣾⣽⣯⣿⣯⣿⣽⣯⣿⣷⣿⣾⣷⢹⣯⣟⡿⣷⣽⡿⣿⣿⣷⣝⢿⣿⣿⣮⣩⣿⣿⣿⣿ ⣿⣾⣿⣿⣟⣵⣿⣿⣿⡿⣫⣾⢿⣻⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣿⣹⢮⡻⣿⣿⣷⡿⣿⣿⣷⡽⣿⣿⣿ ⣿⣿⣿⣫⣿⣿⣿⣿⠽⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡻⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣮⣿⣿⣿⡝⣿⣿ ⣿⣿⣽⣿⣿⣟⣡⣽⣿⣿⣿⣿⣿⣿⣷⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣳⢽⣿⣿⢿⣿⣿⣿⣿⣼⣿⢿⣿⣷⣽⣿⣿⡜⣿ ⣿⣾⣿⡿⣻⣾⣹⣿⣿⣿⣿⣿⣿⣿⣹⣸⣹⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠏⠛⠿⢿⢫⣿⣿⣿⣿⣹⣿⣷⣝⣿⣿⣮⢿⣿⡎ ⣿⣿⢟⣾⣿⣟⣹⣿⣧⢿⣿⣿⡿⠟⡋⡉⣓⢻⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡗⠻⠿⠗⠆⠼⣿⣿⢯⢻⣿⣿⣿⣮⢿⣿⣷⣻⣿ ⣿⣯⣿⣿⣿⣿⣜⣿⣿⣸⢟⣭⠾⠻⠷⠤⠿⡧⡻⣿⣿⡜⣿⣿⣿⣿⣿⣽⣿⢷⣽⡁⠀⡀⠀⣀⠀⠀⠉⠫⠞⢟⣿⣿⣿⣷⡻⣿⣿⡿ ⣷⣿⣿⣿⣿⡿⢾⣮⡣⠇⠉⠀⣀⠠⠤⠤⣀⠪⣷⣝⣧⡿⣟⢿⣿⣿⣯⣿⡿⣷⣟⣴⠋⡀⠀⠀⠈⠳⣄⠀⠈⠹⣿⣿⣿⣿⣿⣙⣿⣿ ⣿⣿⣿⣿⣿⣿⣭⡁⠀⢀⡤⠊⠀⠀⠀⠀⠘⣿⣾⣿⣯⠲⣿⣷⣝⣿⣾⢯⣿⣿⣿⣿⠙⠛⠃⠀⠀⠀⠈⢷⣄⠀⠙⣿⣿⣿⣿⡿⣎⢿ ⣿⣿⣿⣿⣿⡇⠏⠀⣠⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣴⡀⠀⣰⢤⡀⠘⣿⣧⠀⢈⣹⣿⣿⡇⣿⣯ ⢿⣿⣿⣿⣿⠏⠀⣰⣿⡇⠀⢀⡄⠀⠀⣰⢆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣫⠿⣹⢮⡳⡄⡿⣿⢄⣿⣿⣿⡟⡇⣿⢾ ⣾⣿⣿⣯⣍⡀⠀⣿⣿⣇⢀⡾⣹⡟⡾⣝⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⣧⢿⣻ ⡼⡿⣿⣿⣿⣿⣲⣾⣽⣿⣮⣾⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⢧⢷⣿⣿ ⣇⢷⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣶⣾⣿⣿⣿⢹⣿⣷⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣼⣿⣿ ⣿⡸⡼⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢹⣿⣿⣿⣿⣿⣾⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡹⣏⡿⣵⡿ ⣿⣧⢷⡹⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡿⣻⡼⢘⣮⣛⣭⢶ ⡻⠟⣏⡜⣯⡻⣿⣿⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢫⣿⣾⡾⢟⣣⣶⣿⣿⣿⢻ ⡷⣝⢽⣢⢿⣝⢷⢻⣗⣊⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣫⣽⣎⠿⣷⣿⡷⣵⣿⢿⣿⡿⢟⣵⢸ ⡷⢟⣿⣮⣗⡮⣷⢟⣿⡟⣮⡟⣼⣾⣯⢭⣽⣿⣟⣛⣻⢿⣿⣿⣿⣿⣿⣿⠿⠿⠝⣵⡾⣿⢷⡹⣷⣻⣷⢹⣿⢸⡿⣫⢟⣭⣾⢿⠏⡼ ⣿⣌⠿⣾⣽⣻⢾⣝⢫⢿⣇⣼⣷⡻⢎⢞⣯⢷⣻⢿⡝⡁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣎⢿⣽⣻⡷⢜⠻⣾⣧⢿⡿⣪⣶⣿⢯⠿⢋⣜⡳ ⣿⢡⢿⣬⣑⡟⡻⢾⠳⡹⡾⢛⣨⣴⣯⠏⣟⡯⢟⣫⣴⣟⣷⣦⣤⠀⠀⣠⣴⣿⣿⢿⣷⣭⢃⡾⣫⣶⣌⡻⡐⠜⣋⣭⢖⣿⡾⡎⢶⡹
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