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⠀⢸⠁⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠐⢤⡈⠑⠢⢄⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠈⠳⢦⣄⡈⠑⠢⣤⠔⠁⣀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡲⢤⣀⠀⠈⠈⠳⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠉⠲⠤⠄⠈⠑⢄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⢆⠀⠀⣀⡴⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢳⣀⣨⡻⠯⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠁⠀⠀⠄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠘⣄⠸⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠾⠃⠘⠣⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠛⠒⠒⠲⢤⣀⢣⠀⠀⠀⠀⠀⠀⠈⠛⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⠀⠀⠀⠀⠂⠈⢹⠀⠀⡀⠈⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⠀⠀⠀⣰⡟⠀⣴⡏⢀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠘⡆⠀⡀⣠⠞⢉⡇⣸⣼⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡆⠀⡀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⢳⠀⣴⡃⠀⡼⠀⣿⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡄⢱⡀⠀⡾⠀⡴⠒⠈⠒⣆⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣸⡄⠈⠉⠛⠃⢸⣼⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⢣⠀⡇⠀⠀⠀⠀⠀⣽⠀⠀⠀⠘⠦⣀⡀⠀⠀⣠⠇⢀⡤⠞⢁⣤⠞⢛⣷⣶⣾⠋⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⡇⢤⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠉⠙⣻⡵⠚⢁⡤⠾⣿⣇⣴⣿⡏⠙⣿⣦⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⢧⣈⡳⠶⠚⠁⠀⠀⠀⠀⠀⢀⣠⠴⠋⣁⡤⠚⠉⠀⠀⣻⣿⡛⣿⣿⣿⣿⣿⠿⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⡀⠉⠉⠙⠓⠒⠒⠲⠖⠚⢉⣠⠴⠚⠁⠀⢀⣠⣴⡿⠛⣿⣇⠙⢿⣿⣿⣿⣧⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣍⣉⠉⠈⠙⠓⠒⠒⠒⠛⢁⣀⣠⣤⣶⣾⠿⠛⠁⠀⠀⡼⠛⠛⠛⠛⠛⢿⡿⠁⣰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⣿⠙⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢰⠃⡐⠀⠀⠑⠢⣄⠁⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠁⠀⠀⡼⠀⢨⠇⣸⣽⣿⣶⣶⣶⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡌⠀⠀⢠⠃⠀⡞⢰⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣷⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠇⢠⠁⠀⠀⡟⠀⡼⢠⣾⣏⡽⠻⣿⣟⣫⣿⣿⣷⠋ ⠀⠀⠀⠀⠀⠀⠠⡁⠀⡀⠀⠀⠻⣿⣟⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⢻⠀⠈⠀⠀⣸⠁⣰⠁⣸⣿⣏⠀⢠⢿⣿⠏⠁⢻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠁⠀⠀⢀⠈⢻⣿⣦⣀⣀⣴⣶⣄⠀⠀⠀⠀⢀⣤⣤⣼⡆⠀⠀⢀⣇⡴⠃⣼⣿⡟⣻⠀⠎⢹⣷⠿⣷⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣹⣄⡀⠠⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣇⠀⢀⡼⢋⣴⣿⣿⣿⣿⣧⣄⣼⣿⣿⣾⣏⣼⣷⠀ ⠀⠀⠀⠀⠀⠀⡜⣡⣶⣾⣷⣤⣴⣿⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠞⠋⢹⣿⣿⠉⠉⠉⠉⠉⠙⣿⣿⡏⠉⠉⠉⢉⣿⣿⠋⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⣿⡏⠈⢿⣿⠀ ⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⢸⢸⡿⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⢸⣼⡆⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⣤⣿⠇⠀⠸⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⠇⠀⢻⣿⡆
⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡴⠞⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠙⠳⣦⡀⠀⠀ ⢀⣼⠋⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠻⣆⠀ ⣼⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⡇ ⡟⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣿ ⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡿ ⠘⣷⡀⠀⠘⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⣠⡾⠁ ⠀⠈⠻⣦⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣼⠋⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀ ⠀⠀⠀⢸⡇⢠⣶⣿⣿⣦⡀⠀⠀⠀ ⡠⣦⣿⣷⣦⡀⢸⡇⠀⠀⠀ ⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣶⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⢸⡇⠀⠀⠀ ⠀⠀⠀⢰⣇⢻⣿⣿⣿⣿⡟⠀⠀⠀ ⢿⣿⣿⣿⣟⡟⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⣻⣆⠙⠛⠛⠋⠀⠀⠀⠀ ⠈⠙ ⠛⠛⢁⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⡿⣶⣦⣤⣤⣀⣀⣀⣀⣤⣤⡶⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⡆⣱⣾⠟⠉⣽⢋⡟⣯⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⠟⠁⣠⡾⠁⠜⢸⡉⠁⡽⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣠⡾⠋⢀⠆⠀⣼⢷⡀⠸⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠉⣀⡴⠋⠀⣰⢿⠀⠻⣄⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣡⡾⠋⠀⣠⣷⣿⡈⢧⡀⠘⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠏⠄⢠⣾⣿⣿⣿⣿⣌⠳⣄⢹⡷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⡷⠏⣿⣿⡏⠈⣿⣿⣿⣾⣿⠛⠻⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⢹⣿⡇ ⠀⣿⡟⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀ ⠉⠀⠀⠀⠀
⣿⣿⣛⣛⣛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢹⡿⣭ ⣿⣿⡟⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠉⣉⠉⠁⣀⣠⠴⠚⢉⣽⠇⠌⡍⠀ ⣿⡟⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⢀⣀⠀⢠⣐⡭⠴⠒⠋⠁⠀⣀⣠⡾⠁⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣼⠋⠉⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⣸⡄⠀⠙⠻⠛⠋⠁⠀⠀⠀⣠⣴⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢩⣝⠀⣀⡤⠾⢙⢦⢴⣶⣿⣿⠟⣵⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣔⢻⡙⡇⢴⣔⣒⢤⠀⣿⣟⣫⣴⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣦⡁⠢⣭⣽⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣾⣶⣌⣁⢂⢐⣿⣿⢟⣿⣿⣿⣿⣿⣿⣷⣎⢽⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⡀⠈⢏⣾⣻⣿⣿⣏⢻⣿⣿⣿⣿⣞⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢃⣿⣏⠠⡀⢻⣿⣽⣿⣿⣧⢻⣿⡿⣿⣿⣾⡽⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⣿⡏⢆⠈⠌⣿⣿⣿⣾⣾⣎⢿⡇⣿⣦⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎⣼⡟⣼⣿⣆⠁⠹⣿⣿⣿⠟⣿⡘⣷⣼⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢡⣿⡅⣿⣿⣿⡆⠀⠉⣿⣿⡆⣿⣷⠼⣿⣿⣗⣽⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣾⣿⢰⣿⣿⣿⡷⠀⢈⣿⣿⢇⣿⣿⣷⣮⣝⣛⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⢸⣿⣿⣿⢻⠂⠈⢻⣲⡀⠙⢿⣿⣻⣿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣛⣿⣿⣿⣿⣧⣿⣿⠟⠔⡹⣄⣀⡜⠓⣼⣷⠈⣿⣟⣿⣬⡻⣿⣿⣧⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣻⠏⣶⣍⡏⠋⣠⣠⣾⣶⣼⣭⣿⣷⣿⠀⣩⣿⣿⣿⣿⣞⠿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣟⡟⣼⣿⣿⢸⠟⢁⣴⣼⣿⣻⣟⣿⣿⣿⣿⣿⣷⣆⠙⠟⣿⣿⣿⣿⢺⣿⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢿⢸⣿⣿⡧⢠⠂⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣷⣄⠘⣿⣿⣿⡸⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢸⣿⣿⠁⢿⡇⡿⣿⣿⣿⣿⣿⣶⣶⡿⠛⢯⣿⣿⣿⣗⢀⢹⣿⣿⡇⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢸⡿⠏⣴⣿⡇⣿⣿⣿⣯⢰⣲⣦⣄⣤⣴⡆⢻⣿⣿⣿⠨⣦⠘⢻⠇⣿⢿⣿⣧⡀⠀ ⠀⠀⠀⠀⣾⣿⠘⢁⣼⣿⣿⡇⣿⣿⣿⡇⣾⡿⣿⣿⣿⣿⣿⡈⣿⣿⣿⠀⣿⣿⣦⢀⡉⠻⢿⣟⡻⣆ ⠀⠀⠀⠀⣿⡏⢨⣾⣿⣿⣿⡇⣿⣿⣿⡇⣷⣿⣷⣿⣿⣿⣿⡆⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣬⣤⡈⢈ ⠀⠀⠀⠀⠏⣰⣿⣿⣿⣿⣿⡇⣿⣿⣟⡇⣿⣷⣿⣿⣿⣿⣿⣧⢹⣿⣿⡆⢿⣿⣿⡙⣿⣿⣷⣭⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⡟⣼⣿⣿⣷⢸⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⡇⢸⣿⣿⣷⢺⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠹⣿⡟⢸⣿⣿⣿⣿⡜⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⡇⡦⣿⣿⣿⡜⣿⣿⣿⣿⣿ ⣆⣅⠀⠀⠀⠈⠓⠻⠿⠿⣷⡟⡇⣻⡿⢇⢸⣿⣿⣿⣿⣿⣿⢿⣷⣸⣿⡇⣇⣿⡿⠿⠾⠛⢛⣛⣫⠟ ⠿⠹⠨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢻⣺⡄⢚⠉⠉⠀⠀⠀⠀⠀⠀⠿⣇⢻⡄⣦⠀⠀⢠⢨⣨⣿⢾ ⢶⣴⣴⣽⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣟⢻⢈⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣷⣹⢸⣆⢲⣿⠿⡿⠿⠾
⠄⠂⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣮⣿⣾⡤⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⣿⣿⡿⠋⠀⠀⠀⢀⣠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⢋⣡⣾⡿⠋⠀⠀⠀⢀⣴⣿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⣰⣿⡟⠋⠀⠀⠀⣀⣴⣿⠟⠁⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠁⠀⣠⣾⡿⠋⠀⠀⠀⢠⣶⣿⠟⠁⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⢀⣼⣿⠟⠀⠀⠀⢀⣶⣿⠟⠁⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢀⣾⣿⠁⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⠟⠁⠀⠀⣠⣿⡿⠁⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⢠⣿⡟⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡁⠀⠀⠀⢀⣿⡟⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⣼⣿⣧⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⣾⣧⡀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢀⣴⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⣰⣿⣿⣿⣿⠃⢀⣰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢿⣿⡃⠘⣿⣿⣿⢟⢃⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣷⣶⣯⣶⣼⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠟⠻⠿⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⣛⢟⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⢟⣯⣱⣷⣿⠿⠛⠉⠀⠀⢻⣿⣿⡄⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⢿⣹⣶⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣻⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⡐⠣⡄⠀⠀⠀⠑⡄⠙⠆⠀⠀⠀⠀⠀⠀ ⡇⠘⢄⡄⠂⠉⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀ ⢃⡐⠁⠀⠀⠀⠀⠀⠀⡼⠆⠀⠀⢀⣴⠂ ⠀⢁⠀⠀⣠⡀⠀⠀⠀⠀⢸⢀⣴⣿⠏⠀ ⠀⠈⣿⡄⢹⣿⡄⠀⢀⡀⢠⣿⣿⠏⠀⠀ ⠀⠀⠈⢇⠀⢉⣥⣾⣿⣷⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣯⠱⡀⠀⠀ ⠀⠀⠀⠀⠙⠋⢻⣿⣿⣿⣿⣿⡄⡇⠀⠀ ⠀⠀⠀⠀⠀⠘⣼⣿⣿⣿⣿⣿⣷⡇⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⡿⣿⡇⡇⠀⠀ ⠀⠀⠀⠀⠠⠟⠋⠀⠈⠂⠌⠺⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠀⠀⠀⠀⠀⣈⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⣤⣴⣤⣤⣄⠀⢠⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠈⢻⣿⡝⠁⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣠⣿⣿⣧⣀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠟⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡾⠿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀ ⠀⣰⡟⠉⣼⣿⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀ ⢠⣿⠀⠀⣿⣿⣾⠿⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠑⡀ ⠈⣿⠀⡼⢿⡏⠀⠀⠀⠹⣿⡆⠉⠻⣿⣿⣿⣿⣿⡻⢿⣿⠷⠞⠁ ⠀⢸⠇⠀⠈⡇⠀⠀⠀⠀⠘⢿⡄⠀⠸⡏⠀⠀⠉⡇⠀⠹⢦⡄⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡴⠞⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡉⠙⠳⣦⡀⠀⠀ ⢀⣼⠋⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠻⣆⠀ ⣼⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⡇ ⡟⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣿ ⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡿ ⠘⣷⡀⠀⠘⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⣠⡾⠁ ⠀⠈⠻⣦⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣼⠋⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀ ⠀⠀⠀⢸⡇⢠⣶⣿⣿⣦⡀⠀⠀⠀ ⡠⣦⣿⣷⣦⡀⢸⡇⠀⠀⠀ ⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣶⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⢸⡇⠀⠀⠀ ⠀⠀⠀⢰⣇⢻⣿⣿⣿⣿⡟⠀⠀⠀ ⢿⣿⣿⣿⣟⡟⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⣻⣆⠙⠛⠛⠋⠀⠀⠀⠀ ⠈⠙ ⠛⠛⢁⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⡿⣶⣦⣤⣤⣀⣀⣀⣀⣤⣤⡶⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⡆⣱⣾⠟⠉⣽⢋⡟⣯⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⠟⠁⣠⡾⠁⠜⢸⡉⠁⡽⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣠⡾⠋⢀⠆⠀⣼⢷⡀⠸⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠉⣀⡴⠋⠀⣰⢿⠀⠻⣄⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣡⡾⠋⠀⣠⣷⣿⡈⢧⡀⠘⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠏⠄⢠⣾⣿⣿⣿⣿⣌⠳⣄⢹⡷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⡷⠏⣿⣿⡏⠈⣿⣿⣿⣾⣿⠛⠻⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⢹⣿⡇ ⠀⣿⡟⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠏⣋⣡⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢶⣤⣀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣿⣥⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⢀⣶⣾⣷⡄⢠⣀⣰⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡇⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣤⣾⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣀⣤⣾⣿⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⣽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⢀⣮⣿⠯⠋⣵⣷⣶⣶⣦⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣳⡭⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣖⠿⠟⠁⠀⢰⣿⣿⣿⣿⣿⣿⣧⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⣯⣿⡹⣞⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⡾⣿⣯⣟⣷⡝⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⠁⠀⠀⠀⠀⢀⣤⣶⣿⡏⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⡿⣿⣻⡽⣯⣟⣿⣿⣿⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡟⠀⠀⢀⣴⣾⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡗⠀⣸⣿⣿⣿⣿⣿⡿⣽⣳⣯⢿⣳⣯⣿⣿⡿⣟⢮⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⡆⠀⠀⠀⠀⠀⠀⠐⢾⡁⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⣏⠀⢀⡠⠔⠒⠉⠉⠉⢹⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣈⠶⠛⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡆⠀⠀⠀⠀⠀⣠⣴⠇ ⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⠀⠀⠀⣠⣾⣿⡟⠀ ⠀⠀⢸⣀⠀⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⣾⣿⣿⡟⠀⠀ ⠀⠀⠈⣿⣷⡀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠘⣿⣷⠀⠈⢿⣿⡇⠀⢀⣠⣴⡖⢀⣼⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡁⠀⠈⠉⣠⣶⣿⣿⣿⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢨⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡯⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠋⠉⠘⡝⢿⣿⣿⠘⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠙⠦⣀⠘⢮⣿⣿⠀⠣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⠞⠛⠛⢿⣿⣿⣿⣿⢋⣴⠟⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠈⣿⠙⣿⡏⣾⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣯⠀⠀⠀⠀⢀⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⣠⣾⣿⣿⣿⣿⣿⣧⣀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡉⠀⢀⣠⣤⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣾⣿⣽⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⡿⠛⠁⢀⣿⣿⣿⣿⡿⠋⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀ ⢰⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⡏⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣾⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣤⣾⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠻⠆⠀ ⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⢿⣿⣿⣿⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⢠⣄ ⢻⣿⣧⠀⠀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋ ⠘⢿⣿⠀⢰⡿⠋⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⠀⠀⠈⠙⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡄⠉⠻⣿⣿⣿⠛⠉⠉⠀⠀⠀ ⠀⠈⣿⣧⠈⠁⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠈⠙⢻⣿⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀ ⠀⢰⡿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠈⠛⠿⠶⠖⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠻⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠋⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠸⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⢰⠤⠒⠂⠉⠉⠉⠉⠐⠒⢤⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⡄⠀⢠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢙⠦⠄⠀⠀⣴⣿⣷⠀⠀⠀⣾⣿⣧⠀⠸⡒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⠀⠀⠸⣿⣿⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢄⠐⠛⠃⠛⠟⠃⠀⠀⠀⠙⠋⠁⠉⡳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠒⠠⣤⣤⣤⣀⣀⣀⣠⣤⣤⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠤⢄⣞⣽⢿⣿⡽⣯⣿⡼⣿⣟⢿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀ ⠉⣠⡐⡩⣳⠿⠀⣹⣿⣫⡾⣻⣳⣿⣿⣻⡿⣯⣻⡗⠤⠤⠤⠤⠤⠀⠀⠀⠀ ⠈⠭⠉⠉⠉⣀⠀⠀⠉⣉⠉⠁⠛⠁⠁⠙⠃⠙⣉⣁⣀⣀⡀⠀⠀⠒⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠇⠀⠰⣶⡄ ⢸⣿⣄⣤⣤⣽⣷ ⠀⣹⣿⣿⣿⣿⣧ ⠀⡝⣿⣇⢻⣿⣿ ⠀⠙⣿⣿⣿⣿⡅ ⠚⣾⣿⣿⣿⣿⣇ ⠀⠘⢿⣿⣿⣿⡿ ⠀⠀⠸⠏⠛⢹⠃
⠀⠀⢀⣾⣰⠀⠀⠀⠀⢠⣄⣠⣄⠀⠀ ⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀ ⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄ ⠀⢸⣿⣿⣷⣀⣤⣶⣶⣶⣶⣾⣿⣿⡇ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⣾⠿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⡀⢻⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿ ⠀⠀⠹⣧⣸⣿⣿⣿⣦⣼⣿⣿⣿⣿⠃ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀ ⢀⣀⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠸⠹⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⢻⣿⠇⠘⠿⠇⢹⣿⡏⠀ ⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢴⠊⠁⡆⠀⢸⠀⠀⡆⢣⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢸⠀⠀⢻⠀⢨⢣⠀⡇⠈⢳⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠨⠀⠀⠸⠀⠸⠀⠳⠇⠀⠸⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠉⠉⠒⢄⠀⠀⠀ ⠀⡰⠊⠁⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢅⠀⠀⠀⢣⠀⠀ ⢰⠃⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀ ⢸⡀⠀⠀⢧⡀⠀⠀⠀⢘⠡⠔⠒⠒⠒⠢⠤⠊⠀⠀⠀⢠⠃⠀ ⠀⠳⣀⠀⠀⠈⠉⠀⠈⢁⣠⣀⠀⠀⣠⣶⣦⡀⡀⣀⠔⢁⡠⠂ ⠀⠀⢈⡑⠢⠤⠄⡄⣰⣿⣿⣿⡆⠀⣿⣿⣿⣷⢷⠀⠀⠀⠤⠄ ⠀⠀⣀⠠⠍⠀⠀⡇⢹⣿⣿⣿⡇⠞⠹⣿⣿⡟⢸⣴⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣶⣼⣄⠙⠛⠋⠀⠀⠀⠀⠀⣠⠟⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣍⠑⠦⢤⣀⣀⣀⠤⠞⠁⠐⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣁⠀⢰⡃⠀⠀⠀⢀⠀⠤⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⡾⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣹⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠛⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⣇⣠⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠒⠲⢤⣀⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠘⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠁⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢠⣦⣦⡄⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠹⣿⣿⡿⠋⠴⢴⡶⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢠⣾⣡⣿⡿⣿⣿⣷⣿⠻⣼⣿⣿⡜⣿⣿⣯⡻⢿⡓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀ ⠐⠒⠂⠀⣀⡤⠞⢳⣴⣶⡆⠀⠰⣿⣿⣿⡟⢁⣽⣿⣿⢇⣿⣿⣿⣿⣿⣾⣿⣯⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣯⣥⡐⣦⣦⣿⠛⠁⠀⠰⢿⣿⣿⣾⣿⣏⣾⢷⣾⣷⢹⣿⢏⣾⣷⡎⣿⣷⣬⣿⡄⠉⠉⠉⠉⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⢀⣈⣉⣉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⠛⠋⠀⠀⠈⠛⠛⠁⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠆ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠊⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣶⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⢿⣿⣷⣴⣿⣿⠻⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣴⣿⣿⣿⡟⠉⢻⣿⣿⣿⣦⣿⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⣿⣿⡿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣾⠟⠛⣿⣿⣿⣟⠉⠹⣿⣿⠛⠛⣿⠛⣻⣿⡿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢿⣽⣾⡇⠀⠀⠀⠸⡿⢿⠛⠛⠆⠀⠉⠉⠉⠛⠓⠚⠿⢿⣦⣤⣿⣿⣿⣏⢀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠇⠺⠛⠟⣷⠀⠀⠀⠀⢻⡖⠠⠖⠀⠒⠀⠐⠀⠒⠀⠄⠀⠀⠀⠙⠚⠉⢹⡛⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢟⠫⠍⠀⠠⠀⠚⠋⢳⡀⠀⠀⠀⠙⠶⠒⠒⠚⠚⠂⠀⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⡾⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣗⡢⠆⠈⠀⠀⠀⠀⣸⣄⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠈⠙⠻⠿⣿⣿⣿⣿ ⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠈⠀⠀⠀⠀⠁⠈⠙⠛⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡚⠁⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⣯⣿⣦⡉⠛⠛⠛⠁⠀⠀⠀⠀⠈⠛⠛⠛⣉⣴⡓⠤⡀⠀⠀⠀⣀⣤⣴⠞⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣄⡀⢀⣀⣠⠤⣒⡽⢞⣵⣾⣷⡿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣦⡼⡗⢒⡯⢗⣉⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠘⢶⣯⣭⣴⣶⢟⣯⣾⣿⡿⠿⠶⣛⣿⣿⣿⠁⠈⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣡⣴⡾⣏⡓⢶⣦⣤⣄⡉⠳⣄⢀⡀⢀ ⠀⣼⠹⣄⣠⠤⢛⣫⡶⢛⣋⡥⠴⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣽⡿⠛⠋⢁⣾⣤⣾⣿⣿⣿⣿⣦⣈⠓⢭⡛⠻⠭⣿⣭⡷⠗⣫ ⣄⢿⣶⣶⣶⢶⣫⠵⣪⣭⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠉⠁⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢤⡙⣿⣿⣶⣶⣶⣾⣿ ⣿⣭⣭⣭⣶⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢀⣶⣁⣤⣶⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣯⡻⣿⣿ ⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣾⣿⣿⡟⠿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠁⠀⣠⣴⣾⣿⣿⣿⣿⣧⣤⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣤⣼⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣽⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡅⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⣞⡛⠀⠈⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠘⠷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠼⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⠘⣧⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⣗⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⢈⡧⠞⠓⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠆ ⠈⢷⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢻⡀⠀⠀⠀⠀⠀⢠⣶⣿⡟⠀ ⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀ ⠀⠀⠀⣷⡀⠀⠀⠀⠀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣼⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠹⣿⣷⡀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⡄⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠙⣿⣿⡇⠀⠀⣠⣴⣾⣿⠃⣠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠈⠉⣀⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡏⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠋⠉⠻⡙⢿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠉⠙⢦⣄⠀⠀⠱⣄⢻⣿⣿⠁⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠋⠀⠀⠀⠀⠀⠈⠳⠤⣀⠈⠳⣿⣿⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠐⠈⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠐⠠⡀⠀⠀ ⠀⠠⠊⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂⠄⠀⠀⠈⠢⡀ ⢀⠃⠀⠀⡠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀⠀⠀⢡ ⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸ ⠈⢇⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡌ ⠀⠈⠣⣀⠀⠁⠢⠄⠠⠤⠀⠀⠀⠀⠠⠤⠄⣀⡠⠒⠁⠀⡠⠊⠀ ⠀⠀⠀⠀⠉⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⢰⣿⣿⣧⠀⠀⣿⣿⣷⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣄⣸⣿⣿⠏⠀⠀⢿⣿⡿⣠⡘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡀⠀⠀⠀⠀⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⣿⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡏⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠶⠀⢀⠀⠀⠀⣆⠀⠀⠀⣄⠀⢷⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠞⡏⠀⠀⠀⢸⠀⠀⠀⣿⡄⠀⠀⣿⠀⠘⣧⠀⢠⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⡟⢿⡀⠀⢿⠀⠀⠙⢷⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇⠀⠀⣷⠈⢷⡀⢸⠄⠀⠀⠀⣧⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠷⠀⠀⠿⠀⠀⠻⠿⠀⠀⠀⠰⣿⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⢠⡶⠋⠁⠀⢸⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⣯⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⣀⣀⣀⣀⣈⣙⣀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⢿⡀⠀⠀⠀⠀⠻⢦⣀⡀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠈⢳⣄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠁⠀⣀⡀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⠀⣀⡴⠋⠀⣀⠤⠀ ⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⢰⣿⣿⣿⣿⣿⣌⢦⠐⠋⠁⠀⠀⠚⠁⠀⠀ ⠀⠀⢠⣀⡀⠉⠓⠒⠶⠒⢰⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⢼⡇⠀⠀⠀⠀⠘⠒⠦⠄ ⠀⠀⠀⠀⠈⢉⡓⠀⠀⠀⢸⡄⠘⣿⣿⣿⣿⣿⣿⣿⢀⣾⠿⣿⣿⣿⣿⣿⣿⠀⣧⣠⣶⣶⠀⠀⠀⠀⠀ ⠀⢠⠤⠔⠚⠉⠀⠀⠀⠀⠈⣧⠀⠻⣿⣿⣿⣿⣿⠇⠀⠁⠀⠘⠿⣿⣿⠿⠁⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣦⣼⣧⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣀⠀⠙⠓⠶⣤⣤⣄⣀⣤⣤⠶⠞⠋⠀⠀⠈⠉⠛⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠗⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⡤⠿⣄⡀⠀⠀⠀⠀⠀⢰⡖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀ ⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠖⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠤⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⢀⡞⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠹⡄ ⣼⠁⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⢳ ⣿⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸ ⢹⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣼ ⠈⢿⡀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣰⠃ ⠀⠈⠳⣄⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡴⠃⠀ ⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠉⠓⠲⠒⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠒⠒⠤⠴⠚⠁⠀⠀⠀⣀⠴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⠀⢀⣾⣿⣿⣷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⢸⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⡟⣀⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠛⠋⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢹⣿⣿⡟⢻⣿⣿⠏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣁⣤⣤⣴⣶⣶⣤⣤⣄⣀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠹⣿⣿⡟⣰⠋⠀⠀⠈⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⠀⠀⠀⢀⣿⣿⣇⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣠⣾⣿⣿⣿⣿⣤⣀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣀⣤⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⠟⠉⣸⣿⣿⣿⠟⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀ ⢰⣿⡿⠁⠀⠀⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⣾⣿⠁⠀⠀⠀⣿⣿⣷⣿⣿⠿⠛⠉⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⠈⠙⠀ ⢻⣿⡀⠀⢠⣾⣿⣿⡟⠉⠀⠀⠀⠀⠹⣿⣿⣇⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡾ ⠘⢿⡇⢠⡿⠋⢹⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠉⠻⣿⣿⡿⠿⠿⣿⣿⣷⡉⠙⢿⣿⣟⠛⠉⠁⠀ ⠀⢘⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⢹⣿⠀⠀⠀⠀⠈⠹⣷⠀⠀⠙⢿⣆⣀⣀⠀ ⠀⠈⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠘⠿⣦⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣨⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⢁⣼⣿⣿⡉⣿⣿⣶⣿⣿⣿⣿⣦⠀⠀⠹⣿⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡿⢿⣿⣷⠛⣿⡿⢻⣟⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⢹⡾⡇⠀⠈⣏⣋⠁⠈⠉⢉⢉⠉⠓⢾⠿⠿⣼⡟⠀⠀⣼⣿⣿⣿⣿ ⣿⠟⠛⠁⠀⢐⠛⡄⠀⠈⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠟⠀⠀⣰⣿⣿⣿⣿⣿ ⠏⠋⠀⠀⠀⠘⠒⣜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠙⠛⢿ ⠀⠀⠀⠀⠀⠀⠉⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠⣾⣿⣦⡀⠀⠀⣰⣾⣿⡆⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣆⢿⣿⣿⠇⠀⠀⢿⣿⡿⢣⠁⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⣄⠀⣀⡠⣰⢞⣿⣼⣿⣷⣤⣄⣀⣀⣀⣀⣤⣾⣿⣵⡦⣴⢞⣋⠀⠀⠀⠀ ⢀⣴⠙⢲⡾⣻⠿⢟⣛⣿⣿⣿⣄⣿⡟⢻⣿⡿⢟⢟⣩⣴⣿⡨⡲⣶⣤⣵⣤⡠ ⣼⣦⣭⣖⣟⣮⣵⣶⣿⣿⣿⣿⣿⠿⠗⠊⣁⣤⣾⣿⣿⣿⣿⣿⡦⣽⣶⣾⣷⣾ ⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣰⣷⡾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⣿⣿⣿⣿⣿⡿⠟⣿⡏⣠⣴⣿⣿⣿⣦⣿⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⡄⠀⠀⠀⢰⡄⠀⠀⠀⠀⡄⠀⠸⡇⠀⠀⠀⢸⡇⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⠛⠉⠀⠀⠀⣇⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⠀⠀⢿⡄⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠁⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⣧⠀⠀⠀⣿⡇⠀⢘⣿⡄⢀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⡀⠀⠀⠸⡇⢻⣇⠀⠀⢻⡇⠀⠀⠈⠻⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⣇⠀⢻⣦⠀⢸⡇⠀⠀⠀⠀⣿⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣸⣧⠀⠀⠀⣿⠀⠀⠹⣷⣼⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠙⠉⠀⠀⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠒⠛⠛⠛⠓⠲⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⠿⠋⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡽⠶⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀ ⠀⠀⣴⡟⠁⠀⠀⠀⠀⠾⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀ ⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⢸⣟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠛⠳⡀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣠⡴⠶⠒⠛⠉⠉⠉⠛⠓⠶⢦⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀ ⠀⢹⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣀⡀⠀⠀⠀⢀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀ ⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⣀⠴⠂ ⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄⢷⡄⡤⠶⠛⠉⠀⠀⢠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀ ⠀⠀⠀⠐⠶⠤⣀⣀⡀⠉⠉⠉⠉⠉⢰⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃ ⠀⠀⠀⠀⠀⠀⠀⠉⢉⡛⠀⠀⠀⠀⢸⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣜⡿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⢀⣴⣾⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡤⠴⠞⠋⠀⠀⠀⠀⠀⠈⣷⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠋⠀⠀⠻⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⢹⣇⠀⠈⠻⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠙⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣄⠀⠈⠙⠻⢶⣦⣄⣀⣀⠀⠀⠀⣀⣀⣠⣶⠾⠋⠁⠀⠀⠚⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣤⡄⠀⠀⠀⠉⢙⡿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡁⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⡤⠼⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⠦⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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