⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁⠁
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏⠀
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟⠀
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟⠀
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋⠀

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⡀⣾⣿⣿⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⡇⠘⠛⠁⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣉⣤⣾⣿⣿⡆⠉⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⡀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠋⠁⠀

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╔═╗╗─╔╔╗─╦╔═╗╔╦╗╔╦╗╔╗╔═╗
║──╠═╣╠╩╗║╚═╗─║─║║║╠╣╚═╗
╚═╝╝─╚╝─╩╩╚═╝─╩─╝╩╚╩╩╚═╝
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.................................⣼⠓⢄⠀⠀♡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢹⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠘⠄
⣤⣤⡤⢤⣀⣀⠀⠀⠀⠀⢀⠃⠀⠈⠒⠢⢤⡀⡁⠀⠀⠀⠀⢀🍒⣤⠤⢄⣀
⡏⠉⠒⠒⠤⡀⠉⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⣠⠞⢛⠛⠋⡈⡀⠌⢣
⠸⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠲⠀⠀⠱⠀⠀⡎⠄⡁⠄⡁⠄⡀⠄⡁⠸⡀
⠀⠱⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠨⠀⢘⠡⡀⠄⡀⠄⡀⠄⡀⠨⡎
⠀⠀⠈⠺⡇⠀⢀⡞⠉⠉⠂⠀⠀⠀⢀⠀⠀⠀⢀⣹⡉⡩⢢⡀⠄⡀⠄⡀⠄⣠⠏⡅
⠀⠀⠀⠀⢇⠀⠈⠃⠀⠀⠀⣀⠜⠓⢻⠀⠀⠀⡰⠗⠉⠀⢀⡍⢦⣄⣤⣴⠟⠋⠀⡸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠑⠤⠜⠀⠀⠊⠀⠀⢀⠞⠉⠀⠀⠈⢣⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⡳⠧⡥⢦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⢀⠞⠀⡞⠀⡎
⠀⠀⢠⠃⢀⠎⠀⢸