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░╔╦═╦╗───╔╗──────╔╗─▄▄─▄▄▀▀▄▀▀▄
░║║║║╠═╦═╣╠╦═╦═╦╦╝║███████───▄▀
░║║║║║╩╣╩╣═╣╩╣║║║╬║▀█████▀▀▄▀
░╚═╩═╩═╩═╩╩╩═╩╩═╩═╝──▀█▀ ♥♥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⡀
⠀⠀⠀⣴⡿⠟⠷⠆⣠⠋⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠏⡆⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡟⢦⡀⠇⠀⠀⣀⠞⠀⠀⠘⡀⢀⡠⠚⣉⠤⠂⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⡇⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠘⢧⠔⣉⠤⠒⠒⠉⠉⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣤⠶⠶⢶⡄⠀⠀⠀⠀⢹⡆
⠀⣀⠤⠒⠒⢺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢸⠀⡿⠀⡀⠀⣀⡟⠀⠀⠀⠀⢸⡇
⠈⠀⠀⣠⠴⠚⢯⡀⠐⠒⠚⠉⠀⢶⠂⠀⣀⠜⠀⢿⡀⠉⠚⠉⠀⠀⠀⠀⣠⠟
⠀⠠⠊⠀⠀⠀⠀⠙⠂⣴⠒⠒⣲⢔⠉⠉⣹⣞⣉⣈⠿⢦⣀⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉

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░██░░██░║╬╚╣╬║╬║║║░░░░║║║╔╗╔╗║╔╔╗╦╗╔╣░░
░██▄▄██░╚══╣╔╣╔╬╗║░░░░║║║╠╝╠╝╠╣╠╝║║║║░░
░██▀▀██░░░░╚╝╚╝╚═╝░░░░╚╩╝╚╝╚╝╝╚╚╝╝╝╚╝░░
▄██░░██▄

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆
𝐻𝒶𝓋𝑒 𝒶 𝓁𝑜𝓋𝑒𝓁𝓎 𝒹𝒶𝓎

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡴⢧⣀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠏⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⣒⣶⠦⣤⣀⠀
⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠲⡌⠙⢦⠈⢧⠀
⠀⠀⠀⣠⢴⡾⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⢃⡠⠋⣠⠋⠀
⠐⠀⠞⣱⠋⢰⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣋⡥⢖⣫⠔⠋⠀⠀⠀
⠈⠠⡀⠹⢤⣈⣙⠚⠶⠤⠤⠤⠴⠶⣒⣒⣚⣩⠭⢵⣒⣻⠭⢖⠏⠁⢀⣀⠀⠀
⠠⠀⠈⠓⠒⠦⠭⠭⠭⣭⠭⠭⠭⠭⠿⠓⠒⠛⠉⠉⠀⠀⣠⠏⠀⠀⠘⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⣰⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠉⢳⡞⠉