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║║║║╩╣╚╣═╣║║║║║╩╣
╚══╩═╩═╩═╩═╩╩╩╩═╝ ن٥ﻻ ﻉ√٥ﺎ ٱ



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⡇⠀⢤⡀⠀⠀⠀⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠇⠀⡜⠀⠀⠀⠀⠀⢰⣽⠀⢸⠀⠈⣆⠀⠘⠀⠀⠱⡄⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣿⠀⢰⠃⠀⠀⠀⠀⠀⣸⣿⠀⣿⡆⠀⠸⠀⢀⢃⠀⠀⢹⣶⣤⣼⣷⣷⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣰⡏⡜⡇⠀⣿⠀⠀⠀⠀⠀⠀⣿⢸⠀⡏⢇⠀⠀⠀⢸⢸⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢦⡀⠀
⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⡿⢀⡃⡇⢠⡟⢠⠀⠀⠀⠀⢸⡏⠸⡀⡇⠸⡀⠀⠀⣼⣿⡇⠀⠀⠀⠉⠉⢹⣠⣿⣿⠁⢸⣿⡿⣷⣄⠹⣄
⠀⠀⠀⠀⠀⣤⡇⠀⠀⣼⠁⣿⠀⢧⢈⠛⢸⡄⠀⠀⠀⢸⠇⢴⡇⡇⠀⣧⠀⠀⠸⡘⣿⡀⠀⠀⠀⢀⣿⣿⠟⠃⠀⢸⣿⡇⠈⢻⣦⡽
⠀⠀⠀⠀⣸⢿⡇⠀⠀⡟⠠⣜⠀⠸⡈⢸⡐⢳⠀⠀⠀⢸⠀⠀⢱⣰⠀⠈⢇⠀⠀⡇⠘⢧⠀⠀⢀⣾⣿⠏⢰⠀⠀⢸⣿⡇⠀⠀⠉⠀
⠀⠀⢀⣾⡿⠸⢇⠀⢸⡇⡾⠟⢿⣶⡀⠀⢻⡀⢣⡀⠀⠈⠀⠀⠀⠓⠆⠀⠈⢢⠀⠡⠀⠈⣆⠀⣾⣿⠏⠀⡎⠀⠀⢸⣿⣇⠀⠀⠀⠀
⠀⠀⠈⢿⣿⠰⠸⡄⢸⠀⠀⠀⢻⣿⡷⠀⠀⠑⠠⣳⡀⢢⣠⣤⣶⣶⣶⣶⣤⣤⡧⠀⠀⠀⠸⣤⡿⠛⠀⢸⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡆⠀⣹⣼⡆⠀⢸⣯⣿⠃⠀⠀⠀⠀⠈⠙⢾⡟⠉⠁⠻⣿⠉⠙⢻⣿⣶⣷⠀⠀⡹⠁⠀⢀⠇⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⣼⣿⣿⠃⠀⠘⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣞⡛⣷⠶⣿⡿⠈⠋⠀⡰⠃⠀⢀⠎⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⠟⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠟⢻⠦⠿⠃⠀⢀⡜⢡⠆⣠⠏⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡾⠛⠁⠀⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠒⠋⠀⠀⣠⠊⡰⠃⠰⠁⠀⠀⠀⢠⢟⡞⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠟⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣥⠞⠀⠀⠀⠀⠀⠀⢠⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀
⡔⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢛⡽⠁⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠋⠀⠀⠀⠀⡠⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠖⠉⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠙⢦⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⠔⠋⠀⢠⠶⠛⠉⠀⠀⣠⢞⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠈⠉⠉⠉⣿⠉⢀⡤⠚⠁⣠⠔⠊⠁⠀⠀⢀⣤⡞⣡⡿⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⢀⣀⣠⣿⢔⣫⠤⠒⠉⠀⠀⠀⢀⣠⠔⣻⢋⣴⣿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠋⠁⣀⡠⠤⠒⠊⠉⠉⢉⣤⡿⠟⠋⠁⠀⠀⠀⢀⣠⠔⠋⢀⠞⢡⡟⠁⡟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣴⡶⢯⠒⠊⠉⠀⢀⣀⣀⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⣠⡴⠛⠷⢶⠖⠃⠀⣼⠀⢸⡇⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⠽⠖⠑⠂⠉⠉⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢀⣴⣟⣉⣀⣀⣶⣿⣷⣶⣮⣝⢲⡼⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⢤⣀⣀⣀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠏⠉⠀⠀⠀⠀⢀⣀⡈⠻⣿⣄⡃⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⠶⠶⣶⡭⠉⠁⠀⠀⠀⠀⠀⢀⢀⣠⠞⠋⠁⢀⣀⠤⢴⣶⠾⠛⠛⠚⠛⢿⣦⡙⣿⠻⠀⢸⡏⠀⠀⠀
⠀⠀⠀⠀

⠀⠀⠀⢀⡠⠤⠔⢲⢶⡖⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡚⠁⢀⠀⠀⢄⢻⣿⠀⠀⠀⡙⣷⢤⡀⠀⠀⠀⠀⠀⠀
⠀⡜⢱⣇⠀⣧⢣⡀⠀⡀⢻⡇⠀⡄⢰⣿⣷⡌⣢⡀⠀⠀⠀⠀
⠸⡇⡎⡿⣆⠹⣷⡹⣄⠙⣽⣿⢸⣧⣼⣿⣿⣿⣶⣼⣆⠀⠀⠀
⣷⡇⣷⡇⢹⢳⡽⣿⡽⣷⡜⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⣿⡇⡿⣿⠀⠣⠹⣾⣿⣮⠿⣞⣿⢸⣿⣛⢿⣿⡟⠯⠉⠙⠛⠓
⣿⣇⣷⠙⡇⠀⠁⠀⠉⣽⣷⣾⢿⢸⣿⠀⢸⣿⢿⠀⠀⠀⠀⠀
⡟⢿⣿⣷⣾⣆⠀⠀⠘⠘⠿⠛⢸⣼⣿⢖⣼⣿⠘⡆⠀⠀⠀⠀
⠃⢸⣿⣿⡘⠋⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠇⠀⠀⠀⠀
⠀⢸⡿⣿⣇⠀⠈⠀⠤⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⢸⠀⠀⠀⠀
⠀⠈⡇⣿⣿⣷⣤⣀⠀⣀⠔⠋⣿⣿⣿⣿⣿⡟⣿⡞⡄⠀⠀⠀
⠀⠀⢿⢸⣿⣿⣿⣿⣿⡇⠀⢠⣿⡏⢿⣿⣿⡇⢸⣇⠇⠀⠀⠀
⠀⠀⢸⡏⣿⣿⣿⠟⠋⣀⠠⣾⣿⠡⠀⢉⢟⠷⢼⣿⣿⠀⠀⠀
⠀⠀⠈⣷⡏⡱⠁⠀⠊⠀⠀⣿⣏⣀⡠⢣⠃⠀⠀⢹⣿⡄⠀⠀
⠀⠀⠘⢼⣿⠀⢠⣤⣀⠉⣹⡿⠀⠁⠀⡸⠀⠀⠀⠈⣿⡇⠀⠀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⡟⠉⣻⣿⣿⡏⠰⣷⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠙⣻⣿⣿⣄⣠⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣭⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠞⢡⣽⣿⣿⠿⢻⣿⣿⣿⣏⣿⣿⣿⣧⣤⣤⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣴⡨⠛⠋⠁⠀⣼⣿⣿⣿⡟⣿⣿⣿⣿⣯⢈⣿⣿⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣤⣿⣷⡜⣿⣧⡉⠉⠙⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⣾⣿⡟⠀⠀