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║║║║╩╣╚╣═╣║║║║║╩╣
╚══╩═╩═╩═╩═╩╩╩╩═╝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣆⠳⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⡄⢱⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢇⠀⡄
⠀⠀⠀⡠⠔⠒⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⠀⡇
⠀⡴⠋⢀⣤⡔⠒⠤⣈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⡇
⣜⣠⠚⠉⠑⠊⢶⢄⠈⠳⡄⢳⡄⠀⠀⠀⠀⠀⡞⠀⠀⡇⣰⠃
⠉⠁⠀⠀⠀⠀⠀⠙⢦⡀⠘⡆⢷⡀⠀⠀⠀⠀⠃⠀⡼⢠⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠸⡌⣧⡤⠀⠀⠸⠀⣰⢁⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣺⣧⣼⣿⣿⢦⡀⡇⢀⢣⠟⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠢⢤⡴⠟⣺⣿⡿⠛⠿⣿⡿⢄⣎⣯⡼⠙⡄⠀
⠀⠀⠀⠀⠀⢀⡴⠋⣠⡮⠾⡏⠻⣷⣄⠈⢻⡀⠙⣇⠀⠀⣇⡄
⠀⠀⠀⠀⠀⡞⢀⣴⣏⠀⠘⢧⠤⠬⢿⣆⠀⢇⠀⢈⠳⡀⠟⡇
⠀⠀⠀⠀⢸⣰⣿⢻⣼⡆⢀⢠⡶⣶⣌⣿⡄⢸⠀⠀⢳⠿⢦⡷
⠀⠀⠀⠀⢸⣿⠃⣼⠿⠃⢀⠿⠉⠙⡋⠙⡇⡜⠀⠀⣯⣄⠋⠀
⠀⠀⠀⠀⠘⢸⠀⡇⠫⠗⠀⠁⠀⠀⠈⢸⢰⡇⠀⠀⣾⡟⠀⠀
⠀⠀⠀⠀⠀⠈⡇⢡⠘⠍⠉⠈⠀⠀⣠⣷⣷⠁⠀⢠⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡆⢡⣀⣀⣀⣀⣬⠵⢋⡏⠀⢠⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡰⡈⣭⣻⠋⢀⡴⢿⣣⣴⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⣿⣹⡖⠉⡔⠟⠙⠺⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⣺⠟⣿⡟⠳⣼⠁⠀⠀⠀⠙⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠰⠀⣰⣿⠁⠀⢹⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣧⡇⢰⣿⠏⠀⠀⢸⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀
⠀⠀⠀⡀⣠⠖⠉⠀⡸⠋⠀⠀⠀⡇⠀⠀⠀⠀⡜⢸⠀⠀⠀⠀
⠀⠀⣰⣿⡅⠀⢠⣾⢷⣤⡀⠀⢰⠇⠀⠀⠀⢰⠁⡼⠀⠀⠀⠀
⠀⠀⣯⢼⣽⣴⣿⡧⢑⡝⢿⣦⡜⠀⠀⠀⠀⡎⣸⠁⠀⠀⠀⠀
⠀⠀⣷⣉⣿⣿⣽⡇⠀⠙⠃⣿⠇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠈⠛⣿⣿⣿⣷⣤⣇⡄⡞⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠉⠙⢿⢿⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠁⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡌⠀⠀⠀⡆⢣⡰⣶⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠃⠀⠀⠐⠃⠈⠳⠁⠛⠇⠀⠀⠀⠀