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⠀⠀⠀⠀⠀⡎⠒⠤⠤⣀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⣀⡤⠖⠚⢩⠉⠩⠉⠛⠲⢾⣍⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠁⠀⠀⢰⡇⠀⣬⠄⠀⠀⠀⠈⠳⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠠⢰⠏⠀⠀⢀⡠⠤⠤⡒⠋⠉⠙⣷⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠘⠦⢤⣰⣀⣀⣨⠶⠋⠀⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠉⠹⡍⠁⠀⠀⠀⢀⡀⠠⢜⡀⠀⠀⠀⠀⢀⡾⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠽⣅⠀⠀⠀⡇⠀⠀⠀⢈⠆⠀⢀⣴⢟⠳⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⢠⠏⠙⠢⠄⠒⢀⣀⣀⣠⠤⠖⠋⠁⠀⠢⣳⠀⠀⢠⠴⠒⠒⢤⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡇⢠⠇⢀⢤⠀⠘⡆⠀ ⠀⠀⠀⢠⡇⠀⠈⡆⠀⢡⠀⠀⠀⠀⢠⠀⠀⠱⡀⠀⠀⢹⢸⠀⡞⠈⡇⠀⣇⠀ ⠀⠀⠀⢸⠀⠀⢰⠁⠀⠸⠀⠀⠀⠀⠘⡄⠀⠀⢇⠀⠀⢸⢸⠀⢹⠐⡇⠀⠈⢳ ⠀⠀⠀⢸⠀⢀⠃⠀⠀⢠⠀⠀⠀⠀⠀⢇⢀⠀⡸⠂⡄⢸⠋⢀⡏⠀⠙⠲⠖⠋ ⠀⠀⠀⢸⡀⠧⠴⠤⠧⠜⠀⠀⠀⠀⠀⠘⠤⠧⠜⠒⠁⣸⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠓⠶⠤⠤⣤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠙⢳⣦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⢀⣠⣤⠶⠶⠞⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⣠⡴⠞⠛⠉⢉⠁⠀⢀⡌⠉⠙⠛⠿⢷⣿⣅⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⠋⠁⠀⠀⠀⣠⠾⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠛⢿⣦⣀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠸⣿⣶⠀⠀⢶⣷⠈⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠤⢄⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣤⠶⠿⠾⠿⢶⣦⡀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⢢⣿⠁⠀⠀⠀⠀⢀⡴⠟⠋⠙⠛⢧⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠸⣷⣄⣀⠀⢰⠀⠀⠀⠀⢈⣧⣴⠟⠁⠀⠀⠀⠀⠀⠒⣿⡗⠛⠛⠋⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣼⣧⣀⣀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠾⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⡤⠂⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠉⠓⢦⠀⠀⠀⠀⠀⢀⣴⣿⣏⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⢻⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⣀⣴⡿⠻⡄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠞⠁⠀⣸⠏⠛⠶⣄⡀⠰⢤⠜⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠋⠀⠀⠙⢆⠸⣧⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠉⠙⠒⠀⠀⠠⠤⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠱⢿⡆⠀⠀⢠⡾⠋⠀⠀⠀⠀⠙⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠀⠀⣀⣤⡀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢦⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⡄⢸⡇⠀⢰⡟⠙⣧⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⠁⠀⣿⠀⠀⠘⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣧⢸⡇⠀⢸⡆⠀⣿⠀⠀⠀⠘⢿⣆ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢰⠇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⠀⢿⡄⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣧⠤⣄⠀⠀⣿⠟⠁⠀⣾⠃⠀⠈⠻⠷⣶⣶⠾⠋ ⠀⠀⠀⠀⠀⢸⡇⠀⣤⠚⠀⢠⠀⢠⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣆⠀⢰⡀⢀⣼⠂⠀⣿⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠻⣦⡴⢧⣠⡾⠦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠽⠶⠞⠋⠉⠀⠀⢠⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⡤⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡞⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣧⠤⠤⠄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣇⣠⠤⣖⡶⠖⣠⠏⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠟⠉⠛⣍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⠞⠁⠐⠛⠧⠤⣴⡁⣠⠂⠀⠀⡷⠒⠢⢄⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢀⠄⠀⠘⢆⠀⠈⠑⠢⠤⢄⣀⣀⢀⡞⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠛⠓⠲⢤⣷⣴⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡜⠀⠀⠀⠈⢧⠀⠀⠀⢀⣀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⢿⣿⢯⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⡠⠊⠉⠉⢳⡀⠀⠀⠀⠙⡆⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⣼⢹⡇⠀⠀⠀⠀⠀⠙⢯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣴⠃⠀⠀⠀⣀⠽⠒⢦⡴⠀⠀⠀⠀⠘⢧⡉⢳⠀⠀⠀⠀⠀⠿⠞⣡⣤⣄⡀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⡀⠀⠀⡜⠁⢀⡴⠋⣰⠂⠀⠀⠀⠀⣀⣈⡂⠀⠀⠀⠀⠀⠀⢰⣿⣯⣈⡟⣶⡄⠀⠀⠀⠙⠳⢦⣄⣀⣀⠀⠀⠀⠀ ⠀⠀⠙⣿⣄⡀⠁⠰⢿⠏⢰⠁⠀⠀⠀⢠⣾⣿⣿⣙⣷⡀⠀⠀⠀⠀⠸⣇⠙⢿⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⢲⣼⢀⡾⠀⠀⠀⠀⣾⠁⠙⣿⢁⡼⠀⡄⠀⠀⠀⠰⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⣹⡿⠂⠀⠀⠀⠀⠉⠉⠓⠋⠉⠀⠀⡇⣀⣀⣠⣴⣦⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⣈⣷⡄⠀⠀⠀⠀⠀⠀⠀⡼⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⢀⡁⠠⠉⠙⠿⡿⠁⠉⠠⠠⣀⢈⡟⠀⠀⠀⠀⠀⣠⠞⠁⡎⠀⠀⠀ ⠀⠀⠀⠀⢠⣞⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡁⢠⡄⠀⠈⠁⠄⢀⣿⣀⣉⠐⠠⠄⡸⠁⣀⣤⣶⠶⠋⠁⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢯⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣀⡄⠀⢀⡴⠋⠀⠀⠈⠙⢦⡤⠖⢋⣵⠟⠁⠀⢀⡠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⣰⠋⠀⠀⠀⠀⡠⠖⠉⠀⣠⣾⠥⠖⠒⠓⣻⠿⢯⣅⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠲⣶⡶⠦⠤⢄⣀⠁⠀⠀⠀⡠⠊⠀⠀⠀⠈⠉⠀⠀⠀⣤⠾⢥⣤⣀⢠⣽⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠶⣦⠤⠀⠀⠀⠀⣙⡷⠀⠀⠀⠉⠑⡀⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠙⠲⣖⠻⢧⣀⡈⢢⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠂⠀⢠⡾⠥⢤⡄⠀⠀⠐⣾⡇⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡀⠀⠉⠙⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠁⠀⠀⠀⠀⠀⠀⣸⣁⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⡶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠷⡶⠋⠁⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡾⠻⢶⠶⣤⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣤⣤⣤⠤⠤⣤⣤⣤⠄⠀ ⠀⠀⡇⠀⠀⠉⠢⣈⠛⠛⠛⠉⠉⠉⠉⠛⠋⠉⠉⠀⠀⢀⠠⠔⠊⢉⡼⠋⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⢀⡟⠢⢀⡀⠀⠀⣀⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠞⠁⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠈⢫⠋⣿⡖⢦⠀⠀⠀⢀⡴⣿⢙⡏⢉⡏⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠓⢣⠀⠀⡞⠓⠚⠊⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠇⠀⢀⠔⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⣗⡜⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⣉⣉⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⡄ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢷ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸ ⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢸ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠ ⠀⠀⠀⢻⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸ ⠀⠀⠀⠘⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⡏ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢱⡦⣤⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣾⠁ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣀⡆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣧⣀⣾⣤⡤⠞⠁⠀⠀⠀⠀⠙⣦⣄⣰⣧⣬⣿⠟⠀⠀⠀⠀⠀

⠀⢰⠲⢄⡀⠀⠀⠀⠀⠀⡏⠒⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⣀⠙⣦⠀⠀⣀⣰⡣⢸⠢⡈⠢⡀⠀⠀⠀⠀ ⠀⠀⠸⡰⡰⠈⠉⠉⠀⠀⠀⠈⠑⠰⡀⠘⡄⠀⠀⠀ ⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⢀⣾⡀⢳⢤⣀⠤⠀⠀⠀⢠⣀⣀⡀⠔⠀⠀⣸⠀⠀ ⠘⢦⡀⡎⠀⡼⠁⠀⢻⠃⠀⠸⡄⠀⡅⠀⠈⢽⠀⠀ ⠀⠀⠙⠤⣰⠃⠀⠀⠁⡖⠒⢼⡀⠐⣄⠤⠋⠁⠀⠀ ⠀⠀⠀⠀⢀⡝⠒⡆⠀⠘⡄⠀⠻⣫⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠊⣀⡼⠀⠀⠀⠈⠢⢀⡠⠃⠀⠀⡰⠊⢱ ⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡠⠊⣠⠔⠁ ⠀⠀⠀⠀⠀⢸⠀⢤⠤⠤⠤⢤⠄⡯⠓⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡠⠇⠀⠀⠀⠈⢆⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠀⠈⠓⠦⣉⠛⠻⢷⣦⣄⣀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣄⣀⣤⣤⣤⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⣛⣻⠿⢛⣿⡿⠁⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠓⢦⡀⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠉⠉⠀⣠⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠙⢦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠀⠀⠀⠈⠉⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⡷⠒⣶⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣖⢲⣶⠖⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠀⠿⠿⠇⢹⢣⡀⠀⠀⠀⠀⢠⢿⠹⠿⠿⢠⡿⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠿⠾⢷⠀⠀⠀⠀⡿⠞⠓⠒⠒⠋⠀⠀⠀⠈⠻⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⠃⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡆⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣷⠊⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠛⠉⠁⠀⣈⣧⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⡇ ⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣤⣤⣤⣤⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠀⢠⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠉⠉⠉⠉⠉⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠷⣾⡟⠀⠀⢀⣤⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⢠⣤⠀⠀⣶⣦⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣤⣼⡿⠷⠶⠿⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⢷⣦⣤⣿⣿⣿⢾⣿⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⠒⠚⠹⣄⣀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠒⠒⠚⠛⠓⠒⠒⠤⣀⠀⠀ ⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼ ⠀⢀⡜⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⢘⠇⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠙⢲⡀⠀⠀⠀⠀⢠⠎⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⠞⢀⣠⣤⣄⠀⠀⣷⠀⠀⠀⠀⡼⠀⣰⣶⣦⡄⠙⣆⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢠⠏⠀⣾⣿⣯⣽⡆⠀⡏⠀⠀⠀⠀⣇⠀⣿⣿⣾⣷⠀⠘⡆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢯⠀⠀⠹⣿⣿⡿⠃⡸⠁⠀⠀⠀⠀⠸⡄⠙⠿⠿⠃⠀⠀⢻⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠴⠊⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠙⠲⠤⠴⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠉⠉⠁⠒⠉⠉⠹⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠦⣴⠗⠒⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠽⢤⠀⠀⠀⠀⠀⠀⠲⠄⣀⡀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⢶⡋⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠞⠓⠲⠶⢄⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠖⠊⠑⠋⠀⠀⠀⠙⢦⣀⡴⠋⠉⡟⠉⠉⡷⠚⢳⠀⠀⠀⠀⠀⣠⠖⢲⠖⠒⣤⠖⢢⠞⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⠃⠀⣰⠃⠀⣸⠒⠒⠢⠤⢤⡇⠀⡎⠀⣸⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠖⠙⠤⠴⠛⠦⠴⠃⠀⠀⠀⠀⠀⠣⣤⣧⣠⣧⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡖⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣄⣿⠀⢠⣄⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⢠⢤⡀⠈⣳⣄⠀⠀⢀⣀⣤⡿⡝⠧⠘⡌⠱⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⢆⠘⣦⠘⠏⠓⠊⠉⠁⠀⠀⠁⡀⠀⠛⠢⣜⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣸⠞⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⣤⡿⠀⠸⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢸⠀⠀⠀⠀ ⠠⡾⠿⠗⠀⠀⣹⠛⠓⠺⣟⠉⠀⢀⣄⣀⡀⠈⠛⢶⡦⠴⠒⠋⡧⠀⠀⠀⣀⣾⡀⠀⠀⠀ ⠀⠙⠶⣄⠀⢸⡁⠀⠀⣶⠏⠀⠀⠘⢳⠛⠁⠀⠀⠸⣇⠀⠀⢾⡀⠀⠀⠀⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠙⢦⡏⠁⠀⣸⣇⠀⠀⠀⠀⠛⠃⣤⣄⡀⢠⠏⠀⠀⣼⠃⠀⠀⣠⡴⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠶⣽⡏⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⢮⣦⠀⠀⣈⣧⡴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠶⠤⣄⠀⠀⠀⢧⡀⠀⠀⠻⡷⢿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢠⠇⠀⠀⠀⠀⠳⡄⠀⠀⠈⠲⢻⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⣀⡼⠁⠀⠀⠀⠀⣰⠞⠉⢹⡇ ⠀⠀⠀⠀⠀⠀⠘⠶⠖⠋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⣠⠞⠁⠀⣠⠾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣠⠾⠋⣀⡤⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣹⣉⡭⠾⠒⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣹⠋⠉⠁⠀⠀⠉⠹⡍⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠏⠀⠀⠀⠀⠀⠀⠀⢻⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄ ⢽⠀⠈⠉⠉⠒⠦⢤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠉⠀⠀⢸ ⢸⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠉⠉⠉⠉⠉⠑⠒⠦⢤⡖⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⢸⡄⠀⠀⠀⠰⠋⢿⣯⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⣧⠀⠀⠀⠀⠀⠀⢰⡇⣼⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠹⣆⢈⡇⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡞⠀⠀ ⠀⠀⢈⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣰⠋⠀⠀⠀ ⠀⠀⠾⣾⣃⣀⣤⣶⣿⣤⢰⣦⣴⢰⣠⢯⣕⡢⣄⣀⠀⠀⠀⠀⠻⡅⠀⠀⠀⠀ ⠀⠀⢠⢃⡿⡟⠋⠁⠀⣿⣾⣿⣿⣾⡟⠀⠈⠙⠛⠿⣮⣭⡆⠀⢰⡿⠄⠀⠀⠀ ⠀⢀⡏⠸⡇⣧⠀⠀⢠⣿⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⡷⠀⡧⠀⠀⣷⠀⠀⠀⠀ ⠀⢾⡀⠀⠇⠘⠧⠤⠞⠛⠘⠉⠙⠉⢻⡄⠀⠀⠀⣰⠃⣸⠋⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠀⠀⠠⢶⣤⠀⠀⠀⠉⠓⠒⠚⠑⢯⠿⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⣄⣴⣄⣀⣄⡀⠀⠀⠀⠀⠀⢸⣀⡴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣯⣉⣉⣉⣉⣉⣉⣁⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣧⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣴⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠏⠁⠀⠈⢻⣦⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠉⠉⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠃⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠹⣧⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢶⣤⣄⢰⡟⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⣠⣴⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⡀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠗⠀⠈⠻⣦⡀⠈⣿⡀⠀⠀⠀⠀ ⠸⣇⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⢋⣠⣶⡄⠀⠀⠀⠈⠻⣦⣸⣧⠀⠀⠀⠀ ⠀⠋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⣠⣦⠀⢹⡆⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠛⠉⢿⡄⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⠉⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢠⡿⢷⡄⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⢻⡆⠀⠀⠀⠾⠃⠈⢿⡄⠀ ⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠴⠶⠾⠃⠀⠀⠀⠀⠀⠀⠈⢿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⣇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠁⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡉⢡⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠀⠀⠀⠀⠀⠀⢻ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠺⠶⠶⢶⣦⣤⣤⣤⡀⠀⠀⢸ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸ ⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠇⠀⠀⠀⠀⢀⣠⡶⠟⠛⠛⠉⠛⠛⠷⣦⣀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⣿ ⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⣼⠇ ⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣠⡾⠋⠀ ⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡷⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⠀⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⢠⡤⢀⠎⠀⡗⠉⠀⠇⠀⠀⠀⠀⠀⠀ ⡜⠋⠙⡑⠢⣀⠀⠀⠀⠠⠃⠊⠐⢓⣒⣥⣆⡀⡇⡐⠢⢸⠀⠀⠀⠀⠀⠀ ⣧⠃⠀⠘⡄⠀⢈⡉⠰⠁⠀⠀⠀⠀⠀⢀⣀⠈⠙⠶⡶⣰⠀⠀⠀⠀⠀⠀ ⢹⡆⠊⠀⠈⡤⢀⡀⠃⠀⢞⠳⡀⠀⠀⣦⢟⣀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠁⣴⢈⠂⠀⠀⣠⡥⡀⠀⠀⠀⡞⣧⢝⠆⠀⠀⠑⠢⠤⡄⠀⠀ ⠀⠀⠙⠶⡮⡎⡜⠀⠀⣜⠙⡗⡹⠀⠀⠀⢔⠒⠋⠀⠀⠀⠀⠀⡔⠁⠀⠀ ⠀⠀⠀⠀⠑⡿⠁⠀⠀⠀⠈⠁⠀⢠⣶⣶⣿⠀⠘⢦⠀⠀⠀⠈⠀⣶⠀⠀ ⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢠⠣⠤⢀⡉⠻⡋⣃⠠⢍⠇⠀⢀⡠⠊⡘⠀⠀ ⠀⠀⠀⠳⡒⠂⠀⠀⠀⠀⠸⡄⢁⠀⣨⠜⠁⠒⢌⠬⢒⠟⠉⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠈⡰⠆⠀⠀⢀⣀⣈⡀⠐⠁⠀⡠⠂⠁⠰⠓⠈⣩⡛⠓⣢⡀⠀ ⠀⠀⠀⠀⠘⠓⠲⣆⠀⠀⡩⠆⠀⠉⣂⠈⢤⡀⠀⠀⠀⠈⠓⢞⠫⢌⣢⡀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠉⣝⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣀⠼⠃ ⠀⠀⠀⠀⠀⠛⢳⠋⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⠀⠀⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠁⠀⡐⠁⠀⠈⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣤⠶⠋⠉⠙⢳⠄⠀⠐⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠀⠀⢀⠄⠀⠠⠄⠈⠑⢧⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠁⠀⡀⡬⢳⣶⡄⡐⣿⣿⠍⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠸⢧⠼⡑⡁⡽⠾⡛⠀⠀⣸⠖⠒⠢⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⢹⠙⢗⢗⠀⠈⡟⠀⠀⠀⠘⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡌⠀⠀⢹⠀⠀⡇⠀⣴⡄⠀⠀⡧⠤⠀⠀⠤⣄⣀⠀⠀⠀ ⠀⠀⠀⡸⠀⣰⡁⠀⠀⠈⡄⠀⣧⢰⠃⠹⡄⠀⣇⣀⡀⠀⠀⠀⠑⢦⡀⠀ ⠀⠠⠏⠠⠜⠒⠀⠀⠒⠺⠃⠀⠫⠿⠀⠀⠘⠴⠁⠀⠈⠳⠄⠀⠀⠀⠹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣆⠠⠤⣤⠤⠤⠤⠤⠤⠤⠀⠤⣔⠒⢀⡨⠛⢵⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠃⠀⠀⠀⠀⠈⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⣀⣀⣀⣒⣀⣀⡲⠀⠀⣂⣀⣀⣒⣂⣀⣀⡀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢫⣍⡻⢟⣉⠽⠳⣖⣲⠞⠫⣁⡛⢋⣠⠜⠁⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠋⠁⠀⢀⡡⠚⠓⢄⡀⠀⠀⠁⠁⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢄⠏⠀⠐⠀⠀⠸⠂⡄⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡴⠋⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆ ⠀⢀⠤⠐⠒⠉⠉⡇⡠⠤⣇⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⠀⠀⠀⠀⢰⡡⠒⢄⡸ ⡰⠁⠀⣀⣄⣀⡀⢹⣱⡞⡜⡄⠀⠀⠀⠀⡇⠁⠀⠊⢠⠀⠀⠀⢀⠏⠰⡲⣮⣷ ⢇⠀⠀⠀⠀⠈⢹⠉⠚⠒⢣⠼⣀⠀⠀⠀⡐⠉⠉⠉⠹⡀⠀⠀⡀⢯⣳⠊⠀⠀ ⠈⠢⢀⣀⣀⠤⠃⠀⠀⠀⠳⠧⠄⠬⠤⠔⠁⠀⠀⠀⠀⠑⠂⠀⠓⠊⠀⠀⠀⠀

⢠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⡏⣧⣦⣄⣤⣤⣠⣤⢒⣲⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠘⣻⢻⢯⣦⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣹⢿⡿⠀⠀⠀⠀⠀ ⠀⢈⣟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣿⣿⣷⣥⡘⠀⠀⠀⠀⠀ ⢰⡟⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠁⢫⣿⣿⣿⠷⣾⣷⣆⠀⠀⠀⠀ ⠐⣷⢹⣿⣿⣿⣷⣮⣴⣿⣿⠇⠀⠘⢿⣧⣽⣴⣿⣿⣿⠀⠀⠀⠀ ⠀⣏⡻⣿⣿⣿⣿⣿⣿⠟⠃⠤⡀⡠⠌⠿⣿⣿⣟⡟⠘⠀⠀⠀⠀ ⠀⠃⠙⠿⠿⣿⡿⣿⠀⠀⢀⠠⠚⠢⡀⠀⢈⠶⢶⣶⠆⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⠑⠊⠁⠀⠀⠁⠀⠀⠀⠈⢠⣶⠧⠓⠂⠀⠈⠢⡀⠀ ⠀⠀⡠⠂⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣨⡂ ⠀⠀⠀⣚⣠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢈⠀⢕⣔⣴⣯⣢⠁ ⠀⠀⠸⠿⣿⣷⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣾⡟⠁⠀ ⢀⡔⠁⠀⠠⢙⡻⢢⣅⡷⠊⠀⠀⠀⠀⢦⣀⣤⣤⠀⠀⠉⠀⠀⠀ ⠈⠀⠀⠠⡀⡀⠜⠚⠉⡀⠔⠀⠀⢀⡄⠀⠟⠉⠀⠀⠉⠉⠉⠀⠀ ⠈⠁⠀⠈⠁⠀⠀⠀⠀⠑⠆⠴⠠⠄⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⠀⠳⣄⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⡠⡞⠀⠀ ⠀⠀⠀⠑⢕⢄⠀⠀⠁⠢⠤⠒⠒⠒⠒⠒⠒⠒⠒⠠⠔⠊⠀⠀⡠⠪⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡧⠐⡾⠉⠀⠀⠀⡰⡴⢄⢦⠀⠀⠀⠀⠀⠀⢴⠕⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠉⣏⠀⢤⣀⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⣀⣠⠀⢹⠏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⢄⠈⠢⠙⠩⠆⢀⠇⠈⡄⠰⠬⠙⠔⠁⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠈⠒⠤⣀⣀⠔⢪⣤⢤⣈⠢⢄⢀⠠⠐⠁⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠀⢀⡠⠄⠒⣺⡻⠆⣀⠬⠯⣁⠀⠝⣓⠒⠠⠄⡀⠀⠱⡀⠀⠀⠀ ⠀⠀⡠⠃⠀⠐⠁⢀⠔⠉⠈⠢⠬⢀⣉⣈⣁⠵⠔⠁⠈⠢⡀⠈⠑⠀⠈⢆⠀⠀ ⠀⡰⠁⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢢⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⢀⣀⣀⣠⣤⠤⠤⠤⣴⡶⠤⠤⠢⠤⠤⢤⡤⠴⠒⠒⠛⠉⠉⠉⠛⠒⠲⠦⢤⡀ ⠈⠳⡤⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⢴⡒⠉⠉⠁⠀⡩⢙⡥⠞⠋⠉ ⠀⠀⠙⣎⢗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⡠⢊⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⢼⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢡⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠑⠢⡀⠈⠖⠀⠀⠀⠀⢀⡠⠔⠂⠉⠉⠒⣼⣿⣵⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡦⡤⣈⢱⠂⣆⡐⠒⠉⠁⠀⠀⠀⠀⠀⠀⢸⠸⡄⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡇⢣⢷⣾⣹⠀⡇⠁⢸⠙⣿⣉⣩⣿⠏⡹⠉⡝⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⡀⠉⡫⠓⡶⣻⢄⠀⠳⣌⣙⣛⡡⠜⣁⠜⠀⣠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣍⣀⣀⠕⡉⠀⠉⠒⠂⠤⠤⠒⢈⣡⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡓⢒⡒⠒⠒⠚⢛⣉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⡞⠀⢰⠀⡴⠁⣀⡝⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣙⣳⢫⢙⢦⣾⣲⣵⣶⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⡺⣛⠍⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠟⣁⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⣔⡒⠒⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠅⠒⣮⠔⣖⣾⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀ ⠀⣀⡀⠘⠂⠤⠯⠘⢿⣼⢗⣀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡄⠀⠀⠀⠈⠢⡀⠀⠀ ⢠⣿⠉⠯⢲⣤⣀⠀⠀⠀⠀⠉⠉⠁⠐⢂⣽⣟⠟⠁⣨⣧⡀⠀⠀⠀⠀⠰⠀⠀ ⢸⣹⠀⠀⠀⠉⡛⠿⡏⠊⠉⠉⠉⠈⢡⣿⠟⠂⠀⠀⢹⣿⢗⠀⠀⠀⠀⠀⢃⠀ ⠘⣿⣷⡠⣴⣿⣛⡛⣿⣶⣴⠀⣾⣦⣾⣿⣿⣧⣶⣲⣾⡏⠀⠁⠂⢄⠀⠀⠀⠄ ⠀⢘⢟⣽⣿⣄⣈⣛⣣⡿⠋⢶⠿⢷⣄⣛⣃⣴⣿⠿⠻⣦⠀⠀⠀⠀⠈⢂⠀⠜ ⠀⠗⠘⠿⣿⣿⣿⡿⠋⠀⡰⠈⠑⡀⠙⢆⣸⣿⠿⠙⠀⡼⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠈⠢⢀⠀⠀⠽⣧⡀⠀⢧⡄⢀⡇⣀⡼⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⢀⡇⠀⠑⠂⠤⢀⣈⠀⠀⠉⠉⠀⣀⣀⠡⠄⢶⡁⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⢀⡇⢠⠀ ⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢠⡏⠀⠆⠀ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡜⠀⢠⠾⠃⠀⡘⠀⠀ ⠀⠀⠀⠀⠀⠟⠦⣀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⠀⠀⣾⠀⡼⠁⠀⠀⠠⡇⠀⠀ ⠀⠀⠀⠀⠀⢸⠄⠀⠉⠒⢩⠒⢰⠊⠁⠀⠀⠀⢀⣾⠇⠛⠙⡶⠀⠀⠄⡑⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⡝⠀⠀⡀⡀⠀⠀⢀⣾⠎⠀⠀⠀⠋⠐⠈⡐⠁⠀⠀ ⠀⠀⠀⢰⠋⠉⠉⠙⡳⠊⠀⠀⢀⡷⠷⠿⠷⠻⡏⠀⠀⠘⠄⢀⡀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠒⠈⠀⠀⠀⠀⠘⠄⣀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠙⠫⡙⠫⣍⠑⠒⣲⡶⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠶⣖⡒⠂⣉⠍⢛⡭⠋ ⠀⠀⠀⠈⢦⠀⣱⠋⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠉⣿⠁⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⣀⠀⠀⠀⢠⠁⠆⠀⠀⠀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠈⠹⣝⠿⢿⡻⠓⠄⠀⠠⠒⢯⡻⠿⣋⠟⠉⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠺⣃⢠⠤⣚⣻⣛⡦⣄⣑⠓⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⣦⡀⠀⡡⠒⠑⠉⠀⣀⠀⠉⠊⠑⠌⠀⠀⣠⢶⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠐⠢⠤⢀⣀⣈⠀⢉⣀⣀⠠⠤⠒⢹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠶⠚⠑⣺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣷⠊⠑⠲⣄⠀ ⠀⠀⡟⠀⠀⠀⢿⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⢰⠎⠀⠀⠀⣽⠀⠀⠀⢸⠀ ⠀⠀⢹⡄⠀⠀⠘⣆⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⢼⠀⠀⠀⢠⠏⠀⠀⢀⡞⠀ ⢀⣴⣏⣹⠶⢢⠄⠈⠂⢀⡤⣯⣄⠀⠀⣸⠀⠀⢀⢼⢤⡀⠀⠋⠀⢔⠶⣯⡀⠀ ⠊⡞⠺⣆⣀⠁⠀⠀⠀⡏⡜⢠⠃⠀⠀⣿⡀⠀⠈⠆⢱⢸⡄⠀⠀⠈⡆⣸⡽⠀ ⠀⣿⣀⠀⠉⠉⠉⠩⠿⠛⠳⠾⠶⠶⣶⣯⣗⡒⠒⠓⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⢝⣆⠤⢐⣦⣤⡤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⣄⠀⢀⣠⡗⠒⠉⠙⠒⠛⠚⠛⠊⠉⠒⠒⣥⡀⠀⢀⠀ ⠀⣿⡾⠋⠁⠀⠀⣀⣴⣠⡖⠰⣆⢢⣀⠀⠀⠈⠉⣷⣿⠀ ⠀⢹⠏⠀⢠⣤⠤⣿⣿⣿⠀⠃⢿⣿⣿⡥⢤⣤⠀⠈⣿⠀ ⠀⠂⠀⠴⣿⣷⣄⣀⣿⠟⠀⠀⠘⣿⣇⣣⣴⣿⡷⠄⠈⠀ ⠀⠀⡆⠸⣿⣿⣿⠿⠋⠀⠺⡟⠀⠘⠻⣿⣿⣿⠇⠈⡀⠆ ⠰⢐⠁⣠⠋⠉⠹⡃⢀⢔⡈⠉⡀⡀⠀⡫⠉⠉⢢⠀⠣⢀ ⠣⠀⠀⠊⠒⠆⡒⠑⠂⠹⠋⠙⠋⠈⠖⢓⡀⠞⠈⠀⠁⡸ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀

⠀⠀⢰⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣲⠀⠀ ⠀⠀⠘⢿⢆⠀⠈⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⣠⣾⠇⠀⠀ ⠀⠀⠀⠈⢻⡳⣄⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⣠⢞⡵⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢬⠳⣄⠀⠀⠀⠀⠀⠉⠓⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠋⠀⠀⠀⠀⠀⢀⠜⣡⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣎⣧⡀⠀⣄⣹⠛⠂⠀⠀⠀⠀⠀⢀⡀⢠⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢛⣀⣽⠉⠀⠀⠀⠀⠀⠀⢠⡟⢻⠋⠙⡾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢹⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠿⠁⠀⠀⢷⠦⠤⣀⣀⠀⠀⠀⠀⢰⠀⠀⣤⠀⠀⠀⠀⢀⣀⡤⠤⢶⠃⠀⠀⠿⠃⢘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⢧⡀⠙⠉⣙⡶⠀⠀⣸⠀⠀⢻⠀⠀⢰⣏⠉⠛⢀⡴⠋⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⣄⠀⠀⠈⠉⠉⠁⠀⠀⣰⠇⠀⠀⠘⢧⡀⠀⠈⠉⠉⠉⠀⠀⢀⡶⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⣠⠴⠋⢁⣤⢤⠤⣤⣀⠙⠲⣄⡀⠀⣀⠤⠚⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣀⣀⣩⣟⣧⡄⠀⠈⠛⢻⡟⠟⠋⠀⠀⡤⣿⣏⣁⣀⡀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠁⠀⠀⢀⡠⠖⠊⠉⠁⣀⣼⡬⠟⠂⢀⡠⠖⣛⣙⠲⢤⡀⠀⠒⠤⣿⣀⠀⠉⠙⠲⢤⣀⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠀⠀⠀⠖⠉⠀⠀⢀⠴⠊⠁⠀⠳⣄⣰⠋⠀⠈⠁⠀⠉⠀⠙⢦⣀⠜⠁⠀⠉⠲⣄⠀⠀⠈⠳⠄⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠂⠀⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣

⢠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠍⢻⡹⣦⣢⣠⡆⣠⣄⡀⣀⣤⡔⠋⠐⣾⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⡿⠿⡉⣿⣤⣾⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣻⣯⡿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢩⣝⣋⡛⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡿⣻⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠛⣿⠿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⡿⠖⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⢱⣿⣿⣿⣿⣿⣽⡿⠟⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠊⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢘⣿⡘⠿⣿⣿⣿⣿⣿⣷⣄⠛⠟⠀⣹⣿⣿⣿⡿⠀⠀⢀⣿⣿⣿⠋⠹⡯⠀⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⢈⣿⣇⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠙⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠈⡟⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡍⠈⠇⠀⠀⠀⠀⠀⠀ ⠀⡟⢲⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠉⠳⣴⠞⠉⠀⠈⠙⢿⣿⠿⠿⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠉⠻⠾⠿⣿⣿⣯⣭⣽⡟⠀⠀⠀⠀⠀⣠⠖⠛⠲⣄⠀⠀⠀⠀⠸⣿⣯⡽⣛⣲⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⠛⣉⠽⠿⠋⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠳⡀⠀⣄⣙⠦⣤⣍⡑⠋⠀⠀⠠⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢽⡟⠓⠀⠈⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⢀⡬⠂⠀⡰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠢⣄⠙⡧⠀ ⠀⠀⠴⠋⠀⢠⠎⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⣀⠰⣄⠉⢢⣱⣮⠳⣛⠄ ⠀⠀⠀⠀⠔⡃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠢⢌⣳⣌⢳⣴⣿⣌⢣⠈⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣦⣧⡹⣏⢳⣽⣿⠛⠂⠀ ⠀⠀⠀⠘⠛⠿⢿⣿⣿⣷⣶⣦⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣾⣿⡿⠁⠀⠀⠀ ⠀⠀⡴⠃⠀⠀⠀⠀⠻⢿⣿⣷⣒⠃⢰⣥⠞⠋⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⣀⡀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀ ⣰⠏⠀⠀⠀⠀⠈⠉⠲⡴⣌⢨⣿⣿⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠉⢻⣷⣤⣿⡿⠿⠤⢠⣄⣀⣀⣀⡀⠀⠀⠀ ⠃⠀⠀⠀⠀⢠⡀⠀⢀⣠⠜⠛⠉⠀⡀⢀⠔⠁⠀⠀⠀⠀⢀⡀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⠤⠤⠤⠤⠤⠕⠚⠉⠀⠀⠀⠀⠀⠸⣀⢀⠀⠀⡀⠀⠀⢻⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠾⠇⠐⠒⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⡤⠤⠴⠒⠒⢚⣻⡿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⢳⣄⡀⠈⠹⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠀⠀⠀⣴⣯⡄⠀⠸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡃⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⣤⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡼⠀⠀⠀⠸⣅⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡠⡄⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⢯⡉⠉⠻⣿⡿⠉⠉⢉⡿⢧⣤⢠⡴⣦⡽⠿⣉⠉⠘⠿⠿⠋⠀⢀⡼⠋⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠻⣷⣶⡤⠴⠲⠚⢩⠐⠄⠙⣾⣟⠋⠁⠀⠈⡙⠲⠶⢤⣖⠾⠅⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⡴⠚⠉⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢷⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⡀⠀⠀⠀⠀⠀⠈⠦⡍⠤⠀⠀⠀⠀⠀⠀⠀⠬⣁⠼⠃⠀⠀⠀⠀⠀⢀⣠⢾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⠃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢳ ⠀⠀⢀⣠⠤⠖⠒⠉⠉⠁⠀⠀⡇⢀⡤⠤⢬⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡁⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠒⠲⣤⣀⡾ ⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠾⣄⣤⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠘⡇⠱⡀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠀⢠⡿⠃⢠⣤⣤⡼⢹⡧ ⣸⠁⠀⠀⠀⠴⠶⢷⠦⣤⣄⣀⣸⡤⣿⡏⢸⡆⠹⡄⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⢾⣁⠀⠙⢦⣹⠿⠯⠿ ⢧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⡏⠉⠓⠛⠓⠻⣄⣀⣹⡄⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠁⠉⢳⠀⠀⢀⠀⣀⡀⠼⣏⠙⣦⠞⠁⠀⠀⠀ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣞⢡⡞⠓⠒⢠⠖⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠧⣄⠈⠀⠉⣷⣀⣸⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⢤⣀⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠙⠚⠛⠦⠤⠟⠳⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠻⢿⣟⠻⠿⣟⡛⠛⠓⠒⠶⠶⢦⣤⣄⣀⣤⣤⣤⡶⠶⠶⠶⢶⡶⠶⠶⠶⣶⣦⣤⣤⣄⣤⣤⡶⠶⠶⠒⠒⠛⢛⣛⠿⠟⢛⡿⠗ ⠀⠀⠀⠀⠙⠳⣄⠀⠙⠳⣄⢀⣠⡶⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢶⣤⣀⣠⠖⠋⠀⣠⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⣸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢀⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣠⠶⣶⠶⣶⣶⣶⣶⣦⣤⣀⠀⠋⠀⠀⠙⠀⣀⣤⣴⣶⣶⣶⣶⠶⣶⠦⢄⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⡈⠛⠛⢛⡵⠛⠉⠙⠂⠀⠀⠐⠋⠉⠻⣮⡛⠛⠛⣁⡴⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⠫⢽⠯⠍⠀⠀⢀⣠⠿⣹⣏⢷⣦⠀⠀⠐⠩⠽⠭⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⣀⠤⠐⣲⠟⣩⡤⠶⠾⠷⠶⢯⣍⠻⣗⠢⠤⢀⡀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣦⡀⠀⠀⠀⣀⠔⠋⠀⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⠙⠢⣄⠈⠀⠀⢀⣴⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠻⣶⢤⣌⡀⠀⠀⠀⠀⠀⠀⠲⠿⠽⡦⠀⠀⠀⠀⠀⠀⢀⣁⡤⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠉⠛⠒⠶⠤⠤⢤⣄⠀⢀⣀⡤⠤⠤⠖⠒⠛⠉⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠶⠶⠦⢤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡤⠴⠶⠶⣤⣄⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⣷⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⡾⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣾⠇⠀ ⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣼⠏⠀⠀ ⠀⢀⣠⣾⡋⢙⣷⣶⣶⣆⡀⠀⠙⠷⠀⠀⠀⣀⣼⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣻⣧⣀⠀⠀⠀⠼⠋⠀⢀⣤⢶⣶⣾⠋⠀⠀⠀ ⢠⡾⢿⣟⣵⢿⠏⠁⢠⠋⠁⠀⠀⠀⠀⣠⡿⢋⡽⠋⣻⠦⠀⠀⠀⣾⣇⠀⠀⠀⠴⡟⠙⢯⡙⢷⣄⠀⠀⠀⠀⠈⠑⡄⠈⠹⡿⣦⡀⠀ ⠉⢀⡟⠘⢷⣾⡀⠀⡇⠀⠀⠀⠀⠀⠠⣿⠀⡾⠀⣰⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⡆⠀⢷⠀⣿⠄⠀⠀⠀⠀⠀⢸⠀⣀⣧⡾⠃⠀ ⠀⢸⣷⡇⠀⠉⠉⠛⠛⠒⠲⠶⠶⢶⣶⣿⣶⣧⣄⣿⣄⣀⣀⣠⣴⣟⠻⣦⣀⣀⣀⣠⣿⣠⡼⠷⠛⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀ ⠀⠘⡟⣧⣰⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⠛⠛⠻⠿⠶⠤⣤⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⢦⣄⠀⢶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣽⣯⣓⠲⠤⣭⣿⣿⣿⣛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢰⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⢰⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠈⢧⡀⢀⣠⠤⢾⣇⣤⣤⣄⣀⣤⣤⣠⣷⠦⢤⣀⠀⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⡀⠀⠀⢀⣤⣼⢯⠉⠉⠀⠀⠀⠈⠉⠁⠉⠋⠁⠈⠉⠀⠀⠀⠈⠉⠹⢻⣤⡄⠀⠀⠀⣼⠀⠀ ⠀⠀⢸⣿⣤⣾⠿⠋⠃⠀⠀⠀⠀⠀⢀⣠⠀⣀⡄⠐⣄⡀⢠⣀⠀⠀⠀⠀⠀⠀⠋⠻⢿⣦⣾⡟⠀⠀ ⠀⠀⠈⣿⣿⠓⠀⠀⠀⠀⠀⠀⣠⡐⣾⣧⣾⡿⢀⣇⠹⣷⣬⣿⡄⣠⠀⠀⠀⠀⠀⠀⠘⣹⣿⡇⠀⠀ ⠀⠀⠀⣿⣿⠁⠀⠀⣄⣀⣤⣤⣿⣿⣿⣿⣿⡇⠘⠹⠄⣿⣿⣿⣿⣿⣧⣤⣄⣀⡴⠀⠀⢹⣿⡇⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⣠⣿⣿⠉⠀⡏⠙⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡟⠉⡇⠈⢹⣿⣤⡀⠀⠀⠹⡇⠀⠀ ⠀⠀⢰⠁⠀⠠⢾⣿⣿⣿⣷⣄⣃⣠⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣧⣀⣃⣴⣿⣿⣿⣿⠦⠀⠀⢳⠀⠀ ⠀⠀⡏⠀⢰⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣶⣶⣦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⠀⠘⡇⠀ ⠀⢸⠃⠀⡏⠀⠈⢙⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣟⠉⠀⠈⡦⠀⢷⠀ ⠀⢸⠀⣠⠏⠀⢀⡼⠆⠙⠛⢛⡏⠀⠀⠀⣠⠔⠋⠉⠓⢤⡀⠀⠀⠘⡟⠛⠛⠁⠾⣄⠀⠈⢧⠀⢸⠀ ⢀⡏⠀⠘⡄⠐⣳⣀⣀⠀⠀⠉⡶⠀⢀⡜⣡⣜⣠⢦⣰⣦⡙⡄⠀⠰⡎⠁⠀⢀⣀⣸⡓⠀⡜⠀⠘⣆ ⠈⢳⡀⠀⠀⠀⠉⠘⠹⢶⣈⣉⣁⠾⠋⠀⠘⠹⠁⠀⠹⠛⠀⠘⠻⣄⣉⣉⣰⠿⠙⠉⠁⠀⠀⠀⣰⠋ ⠀⠀⠓⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠞⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠶⠾⠿⠛⠛⠛⠛⠛⠿⠷⠶⣶⣤⣤⣀⡀⠀⠀ ⠙⣶⡶⠶⠶⠚⠛⠛⠛⠉⠉⠉⢉⣭⡿⠛⠉⠉⠉⠀⠀⠀⠉⠉⠉⡩⠿⠛⠉⠉⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⣤⣤⣀⣀⠀⠉⣉⣻⣷⡤ ⠀⠈⢿⣦⢄⡀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡖⠋⠉⠁⠀⠀⠀⠀⠀⢀⡤⠞⣡⣴⠿⠛⠉⠀⠀ ⠀⠀⠀⠻⣧⡙⢶⣄⣀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⣀⡶⢋⣴⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡌⢷⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⡴⠋⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣸⣏⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠢⣄⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠙⠳⣦⣾⣽⣭⡽⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⠑⢤⣀⡸⢀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⡟⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⣶⢦⣄⠀⣿⠁⢸⡏⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠏⠸⡄⣿⣦⣈⡟⢻⠀⢸⡇⠛⠒⢲⡟⠛⣿⣿⠛⠉⠉⢻⣿⡿⠛⢻⠛⠛⢺⠇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡄⠀⠹⣌⣻⣿⢷⡏⠀⢀⣧⠀⠀⠀⢷⡀⠙⣿⣷⣶⣾⣿⡿⠁⣠⠏⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠙⣩⠞⠻⣯⠽⠛⣦⡀⠀⠈⢷⣄⡀⠉⠛⠛⢉⣠⠴⠋⢀⣴⠋⠀⠀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⠴⠚⠁⠀⠀⢛⡶⠟⠆⠙⠳⢤⣄⣉⠛⠛⠛⠛⢉⣁⣤⠶⠋⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⣠⠜⠹⣄⠀⠀⠀⠀⠀⠉⠉⠛⠓⠚⠉⠁⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⣿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠋⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣄⠀⡶⠀⠀⢀⠀⠀⠀⣠⡴⠶⠦⣄⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢷⠃⠀⠀⢸⠀⠀⣼⠃⠀⠀⢀⡼⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣿⣠⣶⣿⣄⠀⢀⣸⣄⢰⠃⣀⣠⣽⠿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣴⣁⣼⡏⣼⠀⡜⢳⣾⣿⣭⣿⣶⣾⡯⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠧⣯⣽⠟⡋⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣫⡴⠊⠁⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣡⡟⣡⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠒⠒⠛⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠛⢻⣴⠖⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡥⠒⠚⣻⣤⠄⣶⣒⣿⣆⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡏⠀⠐⠒⣿⠏⢠⣼⣟⢙⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠀⠉⠉⠓⠲⠒⠛⠉⠙⠿⣿⣟⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀ ⣸⣹⡟⠙⣿⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠲⠖⠚⢓⣶⣾⣿⠟⠃⠀⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⣿⣿⡀⠀⠉⠙⠛⢿⣿⣷⣦⣤⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⣠⠀⣠⣾⣿⡿⠛⠁⠀⠀⢰⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⣧⢹⡁⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡟⠐⠀⠀⠀⠀⠈⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀ ⣿⣿⣷⡄⠀⠀⢀⣤⣶⣷⣶⣶⣾⣥⣄⡀⢠⠀⠀⢀⣤⠀⣀⣹⣿⣿⣦⣤⠀⡀⣠⣤⣀⣿⣿⡧⠬⠷⢄⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠸⣯⣿⣷⣄⢲⣾⣿⣯⣭⣉⣉⣹⣿⣿⣷⣼⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣿⣿⣼⣿⣿⡿⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠙⠀ ⠀⠙⣿⣟⣙⣿⣿⣇⠀⠈⠻⠿⠿⢋⣽⣿⠟⢠⣬⣿⣿⣯⡀⠈⠻⠿⠃⠀⣸⣿⣿⣿⡿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣫ ⠀⣴⠉⢴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⡟⠁⠀⠈⣿⣁⠉⠻⢿⣷⠶⠶⠶⣾⣿⣿⣿⡍⡁⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠉⠀ ⠰⡟⠀⠙⠿⣿⣝⣿⣿⣿⣿⣿⠋⠁⠀⠀⡴⠋⠀⠈⢦⠀⠀⠙⣿⣀⣩⡿⠿⢯⠏⠙⠁⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀ ⠀⠳⣦⠀⠀⠈⠉⠉⢩⣿⣿⣏⠀⠀⠀⢰⣇⠀⠀⠀⢨⡆⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⡷⢦⡀⠀⠀⠀⠙⢻⣿⣦⣀⠀⠀⢷⣔⡤⢄⣸⡇⢠⣤⡾⠟⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀ ⠀⠀⣾⠃⠀⠈⠓⠤⣀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠛⠛⠋⠀⠀⠀⠠⠒⠋⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⡇⠀ ⠀⠐⣿⡂⠀⠀⠀⠀⠀⠉⠙⠒⠒⠢⠤⠤⠤⠠⠤⠤⠤⠤⠄⠒⠒⠒⠊⠉⠁⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⡇⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⠀⢠⠃⠀ ⠀⠀⢹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡜⠀⠀ ⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠃⠀⢸⠁⠀⠀ ⠀⠀⠀⠀⠻⠗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠀⠀⠀⠀⣠⠎⠀⠀⢀⣰⣿⠇⠀⠀⢀⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⣼⠏⠀⢀⣞⡿⠛⠁⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡯⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠛⠲⠦⣤⡴⠦⣄⡀⠀⣀⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⣿⡏⣢⣼⢿⣄⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠀⠀⠀⠀⠀⠉⢱⡏⠉⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⠀⢹⡏⠀⠀⠀⡰⠀⣸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠼⠃⠀⠤⠚⠁⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣿⣦⣤⣤⣤⠀⢰⡾⠁⠀⠀⠀⢸⡀⢰⠀⢀⣀⡀⣀⣴⣿⡏⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠉⠉⠋⣳⠎⠀⠀⠀⠀⠀⢸⣿⡾⡿⠿⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠳⢄⣀⡀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⠤⣄⣀⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣀⡀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠇⠈⣾⡜⣿⡌⣇⢰⡇⢠⣷⣄⡄⢀⣤⣄⣏⠀⠀⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣻⣿⣿⣿⣿⠿⣝⢏⠋⣿⡄⣶⣿⣿⣻⣧⣿⣿⣧⣾⣿⣿⣿⣿⣿⣯⣿⢸⣿⡏⢭⢇⣽⢿⣿⣿⣿⣿⡥⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡝⠻⢿⠿⡝⢳⣄⣸⢦⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⡟⣿⣯⠀⣩⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣽⣿⢶⣶⡊⣀⢻⡿⣿⣿⣿⣿⣻⣿⣿⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢾⡵⢋⠰⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠉⠉⣻⡿⢫⣻⣷⣿⣿⢿⣿⡿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⡟⢸⣧⣿⢟⣵⣿⠾⢏⣀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⣣⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣸⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⡭⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⣽⣻⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠽⣋⣿⣿⣿⣿⣿⣿⣿⣶⣿⢿⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣽⡏⠛⢻⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⠗⠛⣺⣿⣿⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⡙⠋⢀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣿⣿⣯⠀⠘⢿⠆⢀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣙⢿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣟⣯⣽⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠛⣿⣿⣾⣷⣶⡶⣶⣿⣷⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡿⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⡈⠙⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠛⠉⠑⠲⣤⣄⠀⣀⣤⣴⠆⠈⠻⣿⣿⣿⣿⣿⣿⣏⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢽⣓⠶⣬⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡉⠁⠁⠀⠀⠀⠀⠀⠘⢳⠞⠃⠀⠀⠀⠀⠈⠻⢯⡛⠛⠛⠛⠋⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠃⠀⠈⠩⣓⣶⠾⢿⣿⣏⣭⣭⣭⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠓⢦⣄⠀⠀⠀⠀⠀⠐⣟⣿⡯⠭⣝⣛⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣼⡿⠛⢋⣽⣿⠟⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠈⢷⡄⠀⢀⠀⠸⢦⣀⢉⡙⠛⡦⠟⠁⠀⠀⢄⡀⠀⠀⠀⠀⠀ ⠀⠃⠀⠂⠀⠀⠀⠀⢀⠉⠠⠤⠞⠉⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢈⢧⠳⣳⣌⠙⠻⠟⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠸⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⢑⣆⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠀⠀⢠⠎⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⠳⣦⠀⠙⠷⣄ ⠀⠀⠀⣠⡾⠁⠀⢀⡴⠋⠀⡴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢢⡀⠙⠲⣌⠲⣌⡳⡾⢿⣄ ⠀⠀⠀⠀⠀⠀⣠⢏⠀⠀⡴⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠉⠲⣄⠙⢦⡀⢘⣧⡙⣷⡀⠑⠌ ⠀⠀⠀⠀⠀⠚⣡⣁⣀⣾⡁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢄⡀⠈⠑⢦⣜⣿⣌⣻⡾⢽⣻⣎⣗⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣧⣤⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣶⣦⣧⡙⢯⡉⢳⣬⣿⡟⠙⠃⠀ ⠀⠀⠀⠀⢸⠽⢿⣿⣿⣿⣾⣿⣡⣴⣤⣄⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡻⣶⣽⣾⣿⡉⠁⠀⠀⠀ ⠀⠀⠀⢀⣤⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣋⣀⡤⠀⢰⠀⣀⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⢀⣠⠚⠀⠀⠀⠀⠀⣀⡀⠉⠛⠿⡿⢿⣥⣀⡀⣻⡞⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⡀⠀⢠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⡜⣦⡄⢸⣮⣿⡿⠋⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣼⣿⣿⡿⠷⠤⣤⣤⣄⣠⣄⣀⣀⣀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢁⣨⠷⠛⠋⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡀⠀⠀⠀⠀⠀⠙⣣⣠⡴⠖⠉⠀⠀⠀⠀⠀⠈⡆⠚⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⠆⠀⣠⡼⠀⠀⠀⣿⡴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠛⠓⠒⠛⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀ ⠀⠀⠀⢸⣤⡀⠉⠙⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠉⠁⡤⡾⠀⠀⠀ ⠀⠀⠀⠀⢻⡿⣄⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠉⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣮⠳⣄⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⣠⡾⢣⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠲⠦⢤⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡝⢷⡀⠀⠀⠀⠀⢠⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠿⣆⠀⠀⣤⣼⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣦⡀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠇⢀⣹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢿⡟⠁⠻⡾⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢷⡦⢿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣧⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⠾⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⢸⣿⡯⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠀⠛⠃⠀⠀⠀⢸⣏⠙⠒⣶⣤⣄⡀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⣴⠖⠛⢉⡟⠃⠀⠀⠐⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠆⠀⠀⠀⠻⣆⡀⠘⠃⠈⣙⣷⠄⠀⠀⣸⠀⠀⠀⢻⠀⠀⠀⣶⣏⠉⠈⠛⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⢦⡀⠀⠀⠈⠙⠓⠒⠚⠉⠀⠀⠀⣠⡟⠀⠀⠀⠸⣧⡀⠀⠀⠉⠙⠒⠒⠛⠁⠀⠀⠀⣤⡔⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⣄⡀⣀⡴⠛⠁⠀⣰⢾⡛⣛⢛⣳⣦⡄⠀⠙⠳⣄⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠛⠶⣤⠀⠀⠈⠉⠻⣿⠹⠛⠉⠀⠀⠠⡴⠾⢻⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⡴⠖⠛⠉⠉⠉⢹⣏⣽⣷⡦⠀⠀⣀⣴⠖⠛⠳⢦⣄⡀⠀⠠⣧⣭⣍⣟⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⣠⠴⠚⠉⢻⡄⠀⠀⣠⠞⠉⠴⠒⠒⠒⠲⠈⠙⢦⡀⠀⠀⣼⠋⠙⠲⣤⡀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠦⠤⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⣨⡷⠤⠞⠁⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

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⠀⠈⠑⢿⣿⡿⠿⢿⣿⣷⠶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣀⣀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⢀⣀⣀⣤⣤⣶⣶⠶⠶⠶⠶⠶⠶⣿⣿⠿⠿⣿⣶⠖ ⠀⠀⠀⠀⠈⠻⢷⣄⠀⠙⠛⢶⣄⠀⠀⠀⠀⣠⣤⣾⠿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⢿⣦⣤⡀⠀⠀⠀⢀⣤⠞⠛⠁⢀⣤⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠙⢳⣄⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣴⠟⠁⠀⠀⣴⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⣠⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⡄⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⣤⠴⣶⡿⢿⣿⣿⣿⣶⣶⣤⣤⣄⡀⠀⠚⠀⠀⠀⠘⠆⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⠿⣷⡶⠤⣄⡀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠉⠀⠀⠹⣧⡀⠻⢿⣿⣿⠿⢃⣽⠟⠛⠳⠄⠀⠀⠀⠀⠴⠞⠟⢿⣌⠻⢿⣿⡿⠿⠃⣠⡿⠃⠀⠀⠉⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣝⠲⢤⣤⡴⠖⠛⠁⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⢹⡛⠶⢤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠟⠉⠀⣀⣀⣠⡾⠟⠲⣼⡴⠚⢿⣆⣀⣀⣀⠈⠙⠿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠚⣋⠿⠃⣨⡷⠶⠿⠿⠿⠷⠶⣦⡀⠻⢯⣙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣆⣲⡀⠀⠀⠀⠀⠉⠀⣀⡴⠛⠁⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠉⠳⢤⡀⠈⠉⠀⠀⠀⠀⣠⢶⣾⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠓⢿⣶⣄⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⢀⣴⣾⠷⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠙⠷⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠓⠾⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠟⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⠉⠙⠛⠲⠶⠦⠤⠤⠤⠄⠀⢀⢀⡤⠤⠤⠶⠶⠚⠛⠉⠉⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⣦⣄⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣤⡶⠶⣶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠸⣿⡤⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀ ⠀⠀⠀⠀⣠⣾⠿⣿⣄⠀⣀⣀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⡀⢀⣼⡿⠃⠀⠀⠀ ⠀⠀⣠⣾⣿⣥⢀⣨⣿⣿⠿⠿⣶⣆⠀⠀⠈⠙⠂⠀⠀⢀⣤⣴⣿⣇⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣠⣿⣷⣤⣄⠀⠀⠀⠘⠋⠀⠀⠀⣶⡾⠿⠿⣿⣏⣀⠀⠀⠀⠀ ⢠⣾⠿⣻⡏⣴⡿⣻⠋⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢐⣴⡿⠋⣽⠟⠉⢙⡷⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡴⢿⠋⠙⢷⡍⠛⣷⣄⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠈⢻⡿⣷⣄⠀⠀ ⠛⠁⢰⡿⠸⣿⣀⣟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⠃⠀⢠⠏⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⢻⡄⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⣇⣸⡿⠀⠀ ⠀⠀⣿⢡⡆⠉⠻⠿⢶⣦⣼⣄⣀⣀⣀⣀⣀⣀⣀⣻⣇⢀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⡏⣿⡆⠀⠀⠀⠀⠀⢘⣇⠀⠘⣷⢀⣿⣃⣀⣀⣀⣀⣀⣀⣀⣼⣤⣶⠾⠿⠋⠁⠀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣩⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣇⣙⠛⠲⠶⠶⣶⡶⠾⠷⠖⠚⠛⠉⠁⠀⠈⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡻⣷⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠛⠛⠛⠿⠿⠿⣦⣤⣤⣤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠹⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣭⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣝⢷⣄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠙⣷⣦⣄⡀⠀⠀⠢⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠳⣾⣿⣮⣉⡛⠳⢶⣶⣽⣿⣿⡯⣍⡉⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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