⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡖⣖⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠃⡧⠀⠑⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⠥⠤⠥⠤⠆⢇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀
⠀⢠⠋⠉⠑⣇⠀⠀⠀⠀⠀⡾⢄⣀⡀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆
⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠉⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠈⠉⠁⠃⠒⠒⠒⠒⠒⠋⠁⠀

⠀⠀⠀⠀⠀⠀⡴⠋⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠀⠀⠘⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⢧⣀⡠⠤⠞⠙⠢⣄⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠈⠩⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡟⠆⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⠀⡇⢧⠀⠀⠀⠀⠀⢸⡄⢀⡤⠤⡄⠀⠀⠀
⠀⡴⠋⠀⠀⠀⠙⡿⡸⡄⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠙⡄⠀
⡜⠀⠀⠀⠀⠀⠀⣧⡃⢇⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠘⡆

⠀⠀⠀⠀⠀⢀⡀⣀⣀⠤⠄⠂⠔⠒⠒⢒⢒⠒⠒⠦⡦⡀⣀⣀⣀⣶⣗⡴⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠤⢞⠉⠀⠀⠉⠁⠓⠢⣈⠁⠁⠂⠀⠈⠈⠈⠐⠤⢀⠀⠀⢐⠁⠀⠀⢈⣶⠀⠀⠀
⠀⠀⠀⢠⡗⠃⠀⠂⠀⠁⠀⢰⢤⣤⣤⣭⣅⡅⡤⠤⡄⣀⣄⣀⡀⣈⣈⠈⡀⠀⠀⣈⣿⠀⠀⠀
⠀⠀⠀⡿⡁⠁⠀⠀⡂⠐⠀⢹⣽⣯⡋⡇⠁⠉⠉⠉⠁⠋⠋⠉⠉⠉⠉⠩⠥⠟⠍⠁⠀⠀⠀⠀
⠀⠀⠀⢗⡇⡄⠨⠒⠀⠐⠈⣾⡟⠁⣢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠓⠧⣲⣒⣇⣤⣏⣁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡴⢹⠙⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⠀⠘⠀⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡧⢤⣤⣤⠴⢻⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⣀⠤⢄⣰⠀⠀⠀⠀⣸⠂⠉⠲⡄⠀
⠈⣹⠁⠀⠀⠈⣧⠀⠀⠘⠊⠀⠀⠐⢺⠂
⠐⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠋⠀
⠀⠀⠈⠻⠦⠴⡤⠒⠈⠀⠒⠒⠚⠧⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢐⠊⠀⠀⠀
⠊⠈⠐⠨⠔⠈⠉⠂
⠀⠀⢀⢤⢄⠀⠀⠀
⠀⠀⡍⠈⠁⡃⠀⠀
⠀⠀⡇⠀⠀⡇⠀⠀
⠀⠀⡃⠀⠀⡃⠀⠀
⡊⠉⠉⢰⠔⠃⢄⠀
⠉⠢⠤⢇⣀⣀⡌⠀

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(.(....(....(..../.)..)..
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