⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀⠀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⠠⣀⠑⡄
⢀⡀⠤⡙⠄⢡⡀⠘⡀
⠦⢹⣦⣌⢆⠀⢡⡀⢣
⠈⢢⠉⢻⣿⣷⡄⢳⡌⡆
⢨⣮⣑⢤⡙⢧⡳⣌⣷⡱
⠀⠑⡭⣳⢿⣗⠻⣷⣻⣷⠷
⠀⠀⢙⣿⣿⣟⠓⢽⣿⡟⠈⡇⢀⡀
⠀⠀⠀⢭⠿⣿⣷⣦⣹⣇⢲⣿⢨⠃⡠⠄⠠⢄⡀
⠀⠀⠀⠐⢺⣿⣶⣾⣿⣯⣿⢯⣇⡎⢄⡀⠀⢠⡬⠴⠶⠦⠤⡄
⠀⠀⠀⠀⢲⣉⣽⣶⣿⣿⣯⣿⣷⣟⢦⣣⠗⠁
⠀⠀⠀⠘⠉⣩⠵⣺⣾⣿⣿⣿⣷⣿⣻⠊
⠀⠀⠀⠀⠀⢠⠪⣝⣿⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠠⠃⣔⣿⢹⣉⢉⠁
⠀⠀⠀⢀⣼⣿⣿⣿⠘⡇⣄⠃
⠀⠀⢀⣾⣿⣿⡟⣿⡀⠸⡌⠂
⠀⠀⡎⣼⡟⣿⠇⡿⡇⣥⢱⡀
⠀⠀⠹⠏⠈⡿⠀⢿⠇⠃⠳⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠿⣿⡟⢸⠿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⡉⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⣿
⠀⡀⠐⢋⣬⡓⣠⠟⣉⡵⠆⣴⡿⣡⣵⡦⠑⠜⠃⢸
⡾⠃⢦⡙⢫⠎⣵⢊⣵⣾⣿⣿⣿⣿⣿⠿⣶⡐⣅⢸
⠀⠀⠀⢠⠇⣼⢱⣿⣧⡾⣿⣿⣿⣿⣿⢖⢾⣿⢹⢸
⠀⠀⠀⣸⡇⣿⣟⡑⢒⠛⠊⣿⣿⣟⠴⠀⣼⣜⠅⢸
⠀⠀⠀⠙⠀⣿⣏⠱⠌⢀⣸⣿⡉⣹⣦⣤⣴⣿⡆⢸
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⢥⢰⣿⣿⣿⡿⠁⢸
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⢸
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠙⠉⠁⠀⣀⣤⣤⡄⠰⠈⠲⡀
⠀⠀⠀⠀⢠⣿⣿⡇⢀⣠⣤⣤⣴⣿⣇⠉⠙⠓⢀⠩⠁
⠀⠀⠀⠀⣼⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸
⠀⠀⠀⠐⠿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾
⠀⠀⠀⠀⠈⠀⢀⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⠹⣿⣿⠀⠀⣿

⠀⠀⠀⢠⡶⢦⡀⠀⠀⠀⢀⣴⠖⣦
⠀⠀⠀⡿⢀⠀⢳⡀⠀⢀⡾⢁⢤⠘⡇
⠀⠀⢸⡇⡇⢣⢸⡧⠶⢼⠃⡜⢸⠀⡇⠀
⠀⠀⢸⡀⢃⠞⠀⠀⠀⠀⠀⠉⠁⠀⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⡀
⠀⠀⣾⠁⠀⣤⡀⠀⢀⠀⢰⣿⠀⠀⡲⣿⡖⠂⠀⠀⠀
⢒⣲⣟⠀⠀⠉⠁⠀⠈⠈⠀⠀⠀⠀⣀⡿⢁⣤⠖⢲⡆
⠀⠈⠳⣤⣄⣀⣀⠀⠀⠀⠀⠀⠰⣾⠋⠀⡜⠁⠐⢸⠃
⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠙⡇⠀⡇⠀⠀⡏
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⡇
⠀⠀⠀⡼⠁⢀⠀⠀⠀⠠⢀⠀⠀⠀⠜⣷⠇⠀⠀⡇
⠀⠀⣴⠃⠀⢺⠀⠀⠀⠀⠈⠀⠀⠀⠐⠠⠂⠑⢰⠇
⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⡆⠀⠀⡆⠀⠃⣠⠟⠀⠀
⠀⠀⠈⢦⡀⠀⢰⠀⠀⢠⠀⡇⠀⠀⠁⠀⣿⠁
⠀⠀⠀⠀⠈⠛⠢⢷⣤⡬⠤⢧⣠⡼⠤⠚⠁

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▐████▄░░▐░▌░░▄████▌
▌▀█▀███▄▀█▀▄███▀█▀▐
░░▀░▀█▀▀███▀▀█▀░▀░░
░░░░░░░░▐░▌░░░░░░░░

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠛⣿⠁⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠓⡆⠛⣶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠓⡄⢹⡆⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢹⠈⢹⡇⠀⡿⣤
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠈⣿⣀⣹⠀⠙⠛⠃⠘⠛⢣⣄
⠀⠀⠀⠀⣰⠶⠞⠛⠛⠛⠛⠳⠶⣆⡿⠀⠀⠀⠀⢀⣀⣤⠀⠙⣷
⠀⠀⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠿⠿⢀⠀⣉⣷
⠀⢸⡏⠀⠀⠀⡤⠖⠲⠀⠀⠀⠀⠀⠀⠐⠂⠒⠐⢒⣐⠒⠂⠠⠉⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠉⣠⣧⣤⡟⣟⠑
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⡖⢹⣿⠀⠀⠈⢦
⠸⢧⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠚⠁⢸⣿⠀⠀⠀⠈
⠀⠺⣧⡀⢠⣀⠀⠀⣀⣿⠛⠛⣧⣄⡀⠀⠀⣸⡇⠀⣿⠉
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛