Get fit Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠉⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠄⠀⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⡔⠁⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡔⠃⠂⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⢀⣀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠋⠁⠐⠱⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⡇⠀⢁⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⢈⠄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠐⠀⠀⠉⠀⠈⠀⠀⠀⠳⠀⠀⠀⢀⠔⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠔⠁⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠘⠑⢄⠀⢀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠑⠠⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠤
⠀⠀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠂⠄⡀⠀⡠⠂⠀⠀⠀⠈⠐⠠⠄⡀⠀⢀⠃⠀⠀⠀⠃
⠀⠈⡌⠀⠈⡜⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠆
⠀⠠⠀⢀⠼⠁⠖⠂⠀⠀⠤⠤⠀⢀⣀⠀⠀⢀⠔
⡄⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠰
⠧⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠜⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠈⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⠀⠂⠀⠄⠐⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣤⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⢸⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠡⠌⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⡏⠀⠀⠸⡿⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⡆⠀⠀⠠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⢀⠀⠙⠀⠀⠀⠀⠀⠤⠁⠀⠖⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢹⡗⠀⢬⣀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠂⠀⡀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣄⣠⠇⠘⡄⢀⡏⠀⠀⠐⠀⠠⠉⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⠀⠀⢻⡅⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⢀⡠⠀⠀⠀⢠⠤⢢⠄⠀⠀⠀⠀⠀⠁⠀⠈⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠀⠾⠀⠀⠀⠀⢀⠈⠀⠀⠠⠐⠉⡐⣇⠀⠀⠀⠁⡐⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠉⠐⠃⠀⠀⠢⡀⠠⠂⡜⠉⠁⠀⠢⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠙⠒⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠂⠀⡀⠁⠀⠀⠀⠈⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠢⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠰

⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠑⠎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢄⡀
⠀⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠰⠚⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛
⡠⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⢀⡀
⠈⠀⣄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⣤⣤⣬⣵⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠔⠲⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⣦⠒⠁⠐⠆⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣴⠓⠂⠀⠀⢀⣀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠍⠀⠀⠀⣀⢀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠈⠀⠈⠋⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠉⠀⠀⠀⠀⠀⢀⠆⠈⠍⠒⠚⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠤⠀⠀⡧⠀⠊⠀⠀⠈⠢⠤⠁⠘⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠄⠈⢄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠖⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠆⠀⠀⠀⠀⢀⠄⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠊⠀⠰⠀⠀⢀⠔⠁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡀⠀⠦⠀⣀⠀⠀⠀⠀⢀⠊⠈⢆⠀⠀⠣⠂⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠈⠉⠀⠰⠊⠀⠀⠈⢆⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣼⠆⠠⠤⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡙⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠑⡖⠤⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⡔⠁⠑⢄⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌
⠀⠀⠀⠀⠀⡜⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠨
⠀⠀⠀⠀⠜⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣤⠁
⠀⢀⡠⡎⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⠡⡀
⡠⡊⠁⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠥⣂⠄⡀⠈⠢⡀
⠑⠘⡢⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠲⠞
⠀⠀⠈⠳⢤⡘⠄
⣶⣶⣶⢶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⢺⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠉⠀⣤⣴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⡿⠉⠙⠃⡴⠿⠿⢾⡿⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⣀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄⡀⣰⣾⣿⣿⣿⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠹⡿⠿⡿⠟⠿⠿⣿⡿⠁⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⡦⠀⠀⠀⠀⡀⠀⢰⣿⣿⣿⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣀⣨⣿⣿⣿⣧⣀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡴⠑⣶⡇⢸⡇⣸⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⢸⡇⢸⣶⠀⢦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⣧⣀⣿⣧⣼⠇⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⡘⣧⣼⢿⡀⣾⡇⠈⡇
⠀⠀⠀⠀⢀⣤⣤⣤⢠⣴⢿⣷⣾⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣼⣿⣿⣴⣾⡿⣦⡄⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠸⠿⢻⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢹⣿⣿⣿⣿⣿⣿⣿⡟⠿⠇⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⠀⣀⠀⠀⠈⠁⠀⠠⣖⣉⠉⠙⡆⠀⡄⡀⠀⠀⠀⠀⠀⠀⠈⡡⠄⡄⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣧⣤⡠⣠⢰⡄⠀⠀⠒⢒⡼⢃⣖⣜⣵⣆⡴⢠⡆⣖⠀⣞⠀⠀⡵⣡⣠⣰⠫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢁⠞⠈⠀⠁⠀⠀⠁⠀⠀⠀⠘⠁⠀⠁⠉⠀⠁⠁⠈⠀⠁⠀⠈⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⡀⣀⠀⢀⡀⠀⡀⠀⣀⣀⣀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠹⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠉⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠀⠀⢻⣦⠀⠀⢰⣿⣷⡄⠀⢀⣾⠃⠀⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠸⣿⣿⠃⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⣿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠁⠀⠘⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣅⠀⠀⣿⣿⣿⣿⣿⠃⠀⣨⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⣿⣿⣿⣿⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⣿⣿⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣛⣛⣿⣿⣿⣿⣦
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠘⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⣶⣶⣶⣶⣦⣤⣀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀⢀⣠⣶⣦⣀
⣸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⣿⣿⣿⣿⣿⣯⡀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠘⣿⣿⣿⣿⣿⣿⣶⣄⡈⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠈⠙⠛⠻⢿⣿⡿⠿⠛⠃⠀⠲⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠙⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣤⣴⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣑⣲⣾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣒⣒⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣚⣋⣍⡓⢄⠀⠀⠀⡰⢣⣾⣿⣿⣿⣿⣷⡜⢆⠀⠀⠀⡠⢚⣭⣙⣓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣴⣿⣿⣿⣿⡿⢨⠇⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠸⡅⢿⣿⣿⣿⣿⣦⡙⢦
⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⣿⣿⢆⣉⡭⠥⠖⠉⠀⠀⠀⢇⢹⣿⣿⣿⣿⣿⣿⡏⡸⠀⠀⠀⠉⠲⠭⢭⣉⡐⣿⣿⣦⡑⣄
⠀⠀⠀⠀⠀⢀⡜⣡⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⣿⣿⣿⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣌⢣⡀
⠀⠀⠀⠀⢀⡞⣰⣿⣿⣿⣿⡇⠾⠤⣄⡤⢖⣚⣛⣓⡒⠚⣥⣬⡛⠿⠿⢛⣥⣮⠓⢒⣚⣛⣓⡲⢤⣠⠤⠧⢸⣿⣿⣿⣿⣆⢳⡀
⠀⠀⠀⠀⢸⢠⣿⣿⣿⣿⠟⣰⣿⣷⣶⣤⣿⣿⣿⣿⣿⣷⣦⣙⠻⢿⡿⠟⣋⣴⣾⣿⣿⣿⣿⣿⣤⣶⣾⣿⣆⠻⣿⣿⣿⣿⡄⡇
⠀⠀⠀⠀⢸⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠘⠦⣉⣛⠻⢿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠤⠤⠒⢦⠐⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢂⡴⠒⠦⠤⠤⠴⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣦⣭⣭⣭⣭⣴⣿⣿⣦⣭⣭⣭⣭⣴⡏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣿⣿⣿⠟⣫⣴⣾⣷⣦⣝⠻⣿⣿⣿⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⣿⢋⣾⣿⣿⣿⣿⣿⣿⣷⡙⣿⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠇

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡄⠀⠀⠀⠀⠀⢀⣴⡶⢶⣄⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠫⠀⠌⠛⠀⠀⠀⠀⠀⣞⠡⠀⠄⢻⡆⠀⠀⠀⢰⡟⠩⠉⠙⢻⠀⠀⠀⠀⠀⠀⠟⡛⠉⠿
⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣴⡄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠋⠀⠀⠀⠀⠀⢛⣦⣠⣴⡋⠀⠀⠀⠀⠀⠀⢠⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣹⡏⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠞⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠠⣤⠀⠀⠀⠀⠀⠀⠈⢋⡥⠀⠀⠀⠀⠀⠀⠀⢠⡄⠿⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⢷⡄⠀⠀⠀⠀⠀⣴⣿⠷⣶⡀⠀⠀⠀⠀⠀⣾⣿⡿⣿⡄⠀⠀⠀⠀⢠⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⠁⠀⠀⠀⠀⠀⡍⠀⠐⢈⡅⠀⠀⠀⠀⠀⠉⠀⠐⠈⠁⠀⠀⠀⠀⣟⠡⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣴⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⣶⣴⣦⠀⠀⠀⠀⠀⠙⠂⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠙⠿⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠈⠁⠀⠀⠀⠀⠀⠠⠖⠰⠆⠀⠀⠀⠀⠀⠀⠈⠃⠶⠀⠀⠀⠀⠀⠲⠖⠁⠀⠀⠀⠺⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⣿⣿⡇⢤⠄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀⠀⠀⠀⠘⠃⠀⠀⠀⡤⠤⣀⣶⣶⡦⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⣿⣿⡇⠼⠄⠀⠀⠀⠸⢢⠆⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠩⢹⡇⠀⣿⠿⠿⠟⠛⠋⠀⠣⣰⣾⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⡷⠤⠴⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡇⠀⢠⣶⣾⢸⡀⠀⠀⢠⡎⠉⠉⠉⠉⠉⠀⠀⠀⢀⠄⢠⢰⡆⣿⡇
⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⡇⠀⢬⣿⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠛⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣀⣀⣀⣀⣘⣃⣿⡇
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠒⠒⠀⠀⠀⠀⣶⣦⣤⠤⣤⣤⢤⣤⣤⣤⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡓⣿⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠚⠛⠛⠛⠀⠀⠀⠀⣿⣿⣶⡇⠀⠀⢀⣀⣠⣤⠀⠀⠛⠉⠀⠁⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⡶⠆
⠀⠀⠀⠀⠀⢀⣀⠀⣠⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⣠⡟⠛⠻⢯⣀⠀⠀⠀⢸⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣀⡊⠓⠲⢻⠀⠀⠀⢸⣷⣿⣾⣿⣿
⠀⠀⠀⠀⢈⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠀⠀⠀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠛⠛⠒⠀⢸⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⢫⠀⠀⠀⠀⠀⢶⣦⣤⣴⡾⠉⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⠻⠟⠿⠟⢃⡀⠀⠀⠀⠛⠘⠳⠁⠠⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠤⠴⠦⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣀⡈⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡛⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢟⠀⢘⠧⠤⠀⠀⠀⠀⠀⠀⠀⢀⠄⠖⡇⢹⠀⢈⠑⠒⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠠⢰⠈⠀⠀⠀⠀⠀⠀⠄⠀⢲⡧⠬⠈⠁⠀⢰⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⡈⡀⠐⢉⠧⠰⠀⠀⠀⠈⠧⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢠⠁⠀⡠⢃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⣀⡀⠠⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡰⡀⢠⠀⡀⣘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⠿⣁⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢠⠀⠀⠀⣰⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠜⠒⠒⠴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡀⠀⠀⠀⢠⠟⣽⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠐⠀⠀⢧⠂⠀⣿⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠓⠀⠀⠀⠐⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡁⠀⠐⠉⠓⠉⠈⡈⠉⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⢀⠀⢸⡥⠤⠥⡴⣀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠁⠃⠀⠀⠀⠀⠀⠸⣇⠀⠆⠀⠀⠆⡉⠉⠉⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢸⠀⠀⠈⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠘⢩⠁⠀⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠀⠀⢈⣷⠋⠁⠀⠀⠀⠑⠄⠀⠀⠀⡍⢶⡇
⠀⠀⠀⠀⠀⠔⠋⢡⠀⠀⡼⢹⠑⠠⠆⡱⠀⣠⣛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣆⢀⡜⠛⢀⡀⠀⠀⠀⠀⠈⠢⠀⠀⡁⠘⠙⣄
⠀⠀⢀⠔⠁⠀⠁⠁⠀⠀⠈⠈⠀⠈⠐⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠁⠀⠉
⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⡀⠄⠐⠀⣰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠃⠀⠀⠀⠠⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠢⠄⡀⠀⠂⠀⠀⠀⢀⠠⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⢀⠀⠀⠋⡏⠀⠀⠘⡍⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣂⠁⠀⠈⡈⠀⢥⠀⠀⠀⢠⠀⠀⢴⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡔⠁⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠈⠀⠀⠀⡀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣂⡴⠣⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⢀⠀⠈⠉⠀⠀⠀⠠⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⢀⠄⠀⠀⠈⣄⡠⠄⠊⠀⠀⠁⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠢⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣀

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠤⢊⠀⠂⠒⠒⠬⡑⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⢀⠔⡨⠄⠒⠈⠉⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠐⡀⠇⠀⠀⡀⠖⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⢊⠔⡩⠂⠡⠀⠀⣠⠖⠄⠀⢹⠀⡄⠀⠀⠠⡀⠀⠀⠈⠀⠀⠱⡀⢢⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡐⠁⠠⠊⠀⠀⠀⠀⠀⠣⠀⠀⠴⠉⠐⠇⠀⠀⠐⡄⠀⢁⠂⠀⠀⠀⠀⠀⠁⠡⡀⢆⢀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡈⠀⠁⠀⠀⠀⠐⠀⠘⢇⠐⠈⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⠀⠙⠂⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠇⠘⠀⠀⡛⢉⡖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢰⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡹⡷⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⡁⠀⠰⢠⠆⠀⠀⠀⠀⠕⠀⠁⠀⠀⠄⠠⠀⡀⢢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡀
⠀⠀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠉⣀⠠⠾⡦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠞⠄⠉⠀⢀⠀⠀⠂⠀⠀⠀⠀⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠐⡀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⡈⠠⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠑⠂⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠂⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠂⠂⠀⠂⠀⠄⠐⠀⣤⠀⡆⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⢀⡀⡄⠀⢰⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠊⠀⠀⠀⠉⠣⡀⠀⠡⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠶⠛⠋⠛⠋⠀⢏⠉⢣⡢⡀
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⠈
⠀⠀⠠⠈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⢜⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡢⢀⠀⣀⡀⠀⠀⠉⠢⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⣴⠛⡏⠉⠷⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⣤⢴⠆⠈⠁⠒⡭⠄⠀⠀⠚⠉⠀⠀⡀⠀⢀⡡⠀⠦⠌⢛⠡⠂⠀⠘⣄⢀⠾⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡗⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠊
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢄⠀⡀⠄⡧⠀⠀⠀⠠⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⢀⠔⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠑⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡜⠃⠀⠀⣀⠄⠈⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠂⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠚⠀⡠⠁⠀⠰⠇⠐⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⢠⠃⡇⢀⠄⢲⢀⡀⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⡇⠈⠛⠀⠉⠁⠀⠈⠉⠱⠇⠀⢳⣴⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢳⡉⠛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢁⣀⡀⢀⣀⠤⠒⠉⠁⠀⠈⡱⠂⠀⠀⠀⠐⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢅⠀⠀⠀⡠⠒⢧⠀⢠⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⢱⠀⠀⣧⠀⢸⠇⡀⠿⣀⠤⠦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⡣⢃⠤⠀⠳⠔⠃⣰⡇⠀⠉⠰⢢⠇⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡀⠀⠀⠀⢀⣤⣾⠿⢿⠀⠀⠈⣙⣤⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠹⣿⣿⣿⡟⠀⣠⠏⢀⡴⢺⠥⢶⠒⠪⡕⠒⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡢⠤⡈⠓⢤⣙⠣⠤⠗⠋⠁⣀⠞⠀⠘⣄⡸⠀⡞⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⢼⢁⠀⡇⠀⠀⠈⠉⠉⡻⠛⠉⠀⣠⠔⠋⠁⠀⠀⠈⠫⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢔⡚⠥⠢⡀⠢⠤⠤⣯⠟⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢉⣋⣀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡉⠑⠚⠉⠀⠀⠀⠉⢙⡎⠀⠀⠀⢠⡴⠶⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⣽⢳⠀⣀⣤⡀⠀⡀⠀⠈⠓⢦⡀⢀⠽⡒⢤⠀⠈⡷⢕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⠀⠙⠋⠁⠀⠉⠉⢣⡀⢀⡠⢞⣠⢊⡱⠞⠛⠮⣎⠤⠞
⠀⠀⠀⠀⠀⢠⠶⠭⠟⣛⡭⣓⡼⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠦⠔⠋
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠈⠑⠿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣒⣒⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⢈⡷⣄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡀⠀⠀⠀⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⡤⠒⠁⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣠⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠛⠢⡺⣯⡆⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⠀⢠⠉⠈⣀⠙⣷⡀⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠐⢹⠀⣿⠀⢸⣿⡑⢾⡇⠀⠀⠀⣿⠃⠀⠐⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⡟⠉⠛⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢿⣀⣠⠄⠐⢸⣧⣄⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠨⠀⠀⢸⡟⠉⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡿⠛⠛⠒⠚⠀⠀⠘⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠰⠁⠀⠀⢠⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡶⣛⠶⠥⠾⠶⢦⡴⡟⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣥⣼⣿⣿⡿⣿⣿⣷
⠀⢸⢹⢳⡒⣿⣥⣄⡴⠛⣁⠀⠀⠄⠤⠊⠀⡇⠀⡇⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⣸⣿⡇
⠀⢸⣏⠀⠀⢸⡟⣡⠂⢩⠃⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⣿⡟⠁⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠘⠋⠀⠀⢸⢸⡇⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠰⠀⠀⠀⠀⠀⠛⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠿⢯⣑⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⡧⠓⢒⡲⠀⠀⠀⠀⠀⠀⣽⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⡀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢤⣼⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡃
⠀⠀⠀⠀⠀⠀⠘⣽⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⡵⠃
⠀⠀⠀⠀⠀⠀⢀⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⡉⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠱⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⢠⡟⠿⠂⠀⠀⠀⠀⠀⠀⢸⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⢧⠘⣆⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢇⡀
⠀⠀⠀⠀⠀⠠⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢹⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⡀⠈⣿⣷
⠀⠀⠀⠀⠀⢀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡀⠀⠀⠀⠀⠀⠀⢰⡋⠀⣰⡋⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠑⢾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠘⠻⡄
⠀⠀⠀⠀⠀⠀⣀⣼⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣿⠉⠁⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣿⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠋⢛⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠛⠂⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄

⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣆
⠀⠀⠀⠀⠙⢣⣁⣸⣇⣹⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠾⢿⡿⠷⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠉⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠏⡇
⠀⠀⠀⠀⠀⠀⠀⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⢷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡗
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣮⡉
⣿⣿⣿⣿⣿⣿⡿⠁⣠⠆⠀⠀⠀⠘⠋⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⣿⣿⣷⣴⣾⠟
⣿⣿⣿⣿⣿⣿⣧⣴⣿⠀⠀⠀⢿⣦⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠟⠁⣿⣿⣿⣃⠙⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣛⠻⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⣿⡿
⣿⣿⣿⣿⣿⣿⡏⠀⣠⣶⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠈⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⡄⠀⠀⠀⡀⠀⠄⠀⠀⢠⠀⠀⡠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢠⠀⠠
⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠁⠀⠈⠀⠀⠆⠀⠃⠀⢸⠀⠠⠀⢀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄⢀⡴⣇⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣴⣾⡀⣆⣠⣦⠖⠀⢸⠀⢠⡄⢒⢫⣴⣷⣿⣅⠀⠀⠀⠀⠀⡀⢦⢎⠃
⠀⠀⢀⣼⢉⣼⣿⠟⠞⢁⣼⣾⡾⢰⠇⠀⠙⢾⠯⡽⣿⡷⢀⢴⢐⣆⡘⣿⣿⡟⡳⠇⠀⠀⠀⠀⡀⡄⠠⠤⠬⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠉⣁⠀⣸⡿⠇⣀⣒⠀⢲⡈⣩⣆⣄⣾⣴⢎⠲⢑⣠⣃⠈⠠⣤⣒⠊⠀⠆⠀⠐⠇
⠀⠀⠀⠀⠀⠀⡂⠀⡀⢡⡄⡠⠨⣱⣏⣯⠁⠀⠀⠀⣀⣶⣿⠦⢅⠀⠄⠋⢩⢤⡯⢤⠀⢉⣀⠆⠤⢤⢲⠆⠂⢀⣴⠂
⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠙⢿⡅⢌⠀⠀⠳⠀⠀⢉⠁⡆⠈⠁⠀⠘⠉⣉⠁⠀⠀⠈⠉⠁⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠘⠑⡞⠒⠓⠻⠘⠛⠐⡶⠀⡟⠉⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⢖⢀⣀⡂⣟⠂⡐⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⢻⣿⠧⡀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣄⠀⠀⣤⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⡀⠀⠻⣄⣠⣾⣿⣶⣤⡀⠀⢶⣿⣿⡷⣄⠀⣰⣾⣿⣿⡇⠀⠀⢀⣾⣿⡷⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠞⠹⣿⣿⠀⢹⠇⠀⠀⠀⠐⠒⠶⢿⣿⣿⠈⣿⠀⠀⠙⠉⣿⣿⣇⡤⢗⣀⣼⣿⣿⡴⠋⣸⠁⢸⣿⡿⠃⠀⢀⣨⣿⣿⣀⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠞⠁⠀⠀⣀⣤⣿⣿⡏⠀⠈⠁⣸⣿⣿⡆⠀⠉⢀⣾⣿⣷⠀⠀⠈⢠⣿⣿⡅⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣆⣀⣀⣀⣠⣤⠀⣸⡿⢻⣿⠀⠀⠀⠿⣿⣏⠙⣿⡟⠀⠀⢀⣿⠟⣿⡗⠀⠀⣼⡟⢹⣿⠀⠀⢠⣿⠟⣿⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⠈⠛⠛⠉⠉⠈⠹⢷⣿⠁⠈⠿⠿⠶⢤⣆⠈⠙⣷⣿⣧⡀⠀⢸⡏⠀⠘⠟⠛⢻⣿⡆⠈⠛⠻⠷⣿⣏⠀⠻⠷⠶⠤⣤⠀⠀⢸
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠛⠀⠀⠟⠁⠙⢷⡀⢸⡇⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠙⠀⠀⢸
⠀⠀⠐⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣼⡇⠀⠀⠀⠶⠿⠇⠀⠀⠀⠤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢀⢹⣿⣿⣼⣿⣿⣿⣿⣿⣮⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡟⠀⠀⠀⠸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣀⠀⠀⠀⣧⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⣽⣿⡿⠤⠤⠤⠄⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡦⣶⣿⠺⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣿⣿⣿⣿⣿⡟⢟⣿⠟⠉⠃⠘⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⣿⣿⣿⣿⣿⣿⠿⣿⡀⠀⠄⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⡟⠁⠀⡀⣿⣿⣿⣿⣿⡇⠀⣿⠁⠄⣼⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⢠⣿⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠠⣿⠀⢷⣻⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠋⠀⠀⣺⣿⣿⡿⢿⣿⣿⠇⠀⠉⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⢸⣿⡿⠀⠀⠀⠀⠀⠁⡸⣿⣿⣿⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢼⣿⠃⠀⠀⠀⠀⠀⠀⠐⠹⣿⣿⡘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣄⡀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡀⠀⠀⠙⢦⣿⡠⠂⣤⠄⠐⠈⣱⡀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣠⠴⠞⠉⠑⢤⡀⠀⠀⢻⠃⠀⠠⠀⠀⠀⠄⠘⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠄⢸⡇⠀⠀⠀⠀⡀⠉⢦⢰⡋⠀⠀⠀⠀⠐⠀⢀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠄⢸⡆⡀⠠⠀⠀⠀⠀⢸⠀⠹⡄⠸⣬⣤⣀⣭⡴⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠆⠀⠷⡶⠶⠤⣤⠏⣠⠎⠀⠀⠙⢤⡈⠒⠀⠂⢁⠜⠁⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠋⠁⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢶⡤⠼⢦⣁⠈⠁⣾⢧⣤⢄⡰⢤⡖⢿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⡁⡠⠒⣦⣀⣤⠞⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⠶⡇⠀⠀⣇⣀⣀⠀⠉⣀⣤⠴⠇⢀⡀⠟⠋⠉⠉⠙⢦⠀⠀⠀⢉⠟⠉⡠⠴⠶⠱⣄
⢠⠎⠉⡉⢲⠀⠀⠀⠀⠀⠀⡜⢀⡎⠀⠑⠒⠚⠉⠉⠏⣹⠟⠁⠀⣀⡀⠀⢀⠠⠄⠒⠀⠀⠀⢳⡀⠀⢸⠀⠞⠀⠀⠀⢀⠙
⢸⡀⠀⠰⢛⠀⠀⠀⠀⠀⢸⢁⡟⡸⠀⢀⣉⡀⠀⢠⣞⣁⠀⣀⠊⠀⠘⢣⠀⠐⠂⣀⠉⢠⢀⠤⢷⠀⠈⡟⠀⠀⠁⠀⠈⠀⡀
⠀⠉⢣⡀⢇⠀⢀⡠⢤⣤⡇⠐⣇⠁⠆⠈⠀⠂⠀⡟⠡⠉⠉⠁⠀⠀⠀⠘⡇⠈⠀⠀⠀⠀⣏⠀⠀⢣⠀⠙⢃⠰⡶⠶⡾⣰⠃
⠀⠀⠈⡇⠈⣷⡏⢀⢨⡼⠀⢠⣿⠀⠀⠦⣠⠀⢸⡀⠀⠀⢀⡠⡔⠒⠙⡊⠀⡁⠀⠀⠀⠀⢸⢣⡀⠀⠆⠀⠀⠁⠈⠁⡞⠁
⠀⠀⠀⣸⠞⠉⢇⠠⣘⣀⣠⠿⣟⠀⠀⠀⠀⠀⠬⠙⡟⠉⠁⠀⣃⠠⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⢳⡀⠸⠄⡤⢿⠀⢀⡷⢠⡀
⠀⠀⠰⣧⣤⢀⡀⠉⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢙⡇⠀⠞⢁⠈⠹⠏⠁⢠⣇⠀⢀⡔⢪⠙⢦
⠀⠀⠰⢉⠈⠋⠓⢻⢴⣀⠀⢠⠿⣄⣀⠀⠀⣀⣀⡠⠇⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠃⠀⠀⡇⠈⠠⠤⢉⠈⡈⡉⠓⠉⠀⣈⢑⠸
⠀⠀⣾⢀⠀⠀⠈⠀⠈⢹⡔⠋⠓⡏⠉⠉⠉⠉⢁⠀⠈⢆⡼⠓⠲⢤⣀⣀⠀⠀⠀⠀⣀⣠⢼⢷⠀⠀⢠⠇⢀⠠⠄⠀⠨⠁⢱⠔⠒⠋⠁
⠀⠀⠸⡹⢓⡲⠞⢀⠞⠉⠀⠀⠀⢧⠀⠀⣀⠔⠁⠀⢀⡞⠁⠀⠀⠀⠀⠉⠉⠉⢉⡉⠁⠀⠘⡌⠣⠔⡏⠀⠈⠉⠁⠉⠀⠀⠺⠁
⠀⠀⠀⠈⠂⠀⠈⠻⡄⠢⠰⣤⠄⠘⢇⠘⠃⠀⢄⠀⡜⠁⠀⠓⠢⣄⡀⢀⣤⠴⠊⠀⠀⠀⠀⢳⡀⠀⢡⠀⢀⣀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠴⠚⠁⢀⠌⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⠟⠸⡄⠀⠀⠀⠀⠀⠈⢷⠀⠘⠋⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⣀⣤⠶⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣧⠀⠀⢃⠀⢀⣀⣤⢤⠖⠚⠀⢸⠀⠀⠀⠀⡆⠀⠀⢀⡈⠦⡀
⠀⠀⠀⠀⠀⠀⡽⠒⠒⠙⢇⠀⠀⢷⠀⠀⠀⠀⣴⠳⣄⡀⣀⡤⠊⠅⡟⠀⠀⠈⡏⠉⠁⠀⢸⡇⠀⠀⢸⠤⠄⢀⡐⠙⢦⡔⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣈⣄⡤⠚⢣⡀⠀⠈⠈⢆⡌⠀⠀⢀⢜⡜⠀⠀⠀⠀⢸⡄⠀⢀⠈⡷⠖⠒⡞⠀⠀⢠⠁⠀⠀⠈⡖⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⡄⢻⡀⠀⢱⡄⠀⠀⠘⣇⠀⠐⣡⠞⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢻⢤⡀⠀⠀⠀⠈⠀⠀⣀⡜⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠉⠉⠁⠈⡦⠤⠒⢻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⢀⡿⠤⠄⠂⠀⠀⢸⠀⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⠀⣷⡀⠀⠀⢀⠞⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⡋⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠋⣸⠇⠀⢀⡏⠀⠀⢔⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠴⠴⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠇
⠀⠀⠀⠀⠀⠀⠸⣅⡀⠄⠊⠀⠀⠀⠈⠻⠝⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠩⠤⠚
⣿⣿⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣿⣶⣿⣿⣿⢿⠿⣿⡿⢿⣿⡾⠷⣾⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠉⠡⠌⡁⠀⣐⠂⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢁⣀⣀⠀⠀⠀⡀⢄⠀⠈⠊⠀⠐⠂⠐⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⡱⠊⠓⠠⠀⠤⠂⠁⠀⢎⠀⡠⠔⠀⢀⠀⡀⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡀⡀⡨⠂⠢⠄⠀⠁⠀⠀⠁⠑⠄⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠘⢅⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠐⠠⢄⣁⠀⢬⡄
⠀⠀⠀⠀⠀⠀⣤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⠉⠁⠐⠐⠃⠂⠤⢀⢁⡀⢀⠀⠀⠀⠀⠀⠀⢁⠄⠘⠒⡀⠀⢢⡀⠠⠤⡀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠐⠂⢁⣀⡀⠸⡀⠀⠀⠐⠀⠀⠠⠂⠀⠀⠡⠌⠀⠁⠐⠃⠀⠠
⠀⠀⠀⠀⠀⢠⠈⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠲⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠁⡅
⠀⠀⠀⠀⠀⠀⡀⠠⡈⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡄⠀⠀⠀⠀⠀⡀⠤⡾⠃⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⢄⠐⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⣐⠣⡀⢀⣀⠐⠒⠊⡘⠁⠀⠸⠄⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠔⠁⠔⠍⠀⠈⠉⢀⠡⠞⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢈⠙⠋⠒⠒⠲⠖⠀⣀⣀⣀⣀⡒⠈⠅⠀⠒⠈⡠⠴⠁⠀⠦⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠤⠤⠤⠤⠤⠀⠐⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠤⠶⠶⠖⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠶⠖⠒⠒⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⣰⠋⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢦⣄⣀⡀⢀⣀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⣴⣯⡀⠀⠈⠉⢙⣯⣭⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣍⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠉⠀⠀⠀⠀⠀⠈⠻⡟⠶⣄⡀⢸⡇⠈⢳⡄⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣉⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⢻⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠈⣹⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠳⣄⠀⢀⣤⠞⠋⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠛⠉⠈⠙⣷⠖⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣼⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠹⢦⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠙⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠸⢧⡀⠀⠀⣠⠟⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⢹⠀⣼⠁⠀⠀⠀⠈⠙⠓⠶⢤⣀⡀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣴⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⢠⣾⣏⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⢀⡴⠋⣸⢿⠀⣠⠟⢳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢻⡅
⠀⣠⠟⠀⢠⡇⠸⣿⠁⢠⡏⠀⠀⠈⠙⠛⠓⠶⠶⠦⠤⣤⣹⣦⣄⡀⠀⠀⠀⠀⠈⣷⣀⣠⡴⠶⠛⠉⠀⠀⠀⠀⢳
⡞⠁⠀⠀⣼⠷⠶⠛⠋⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠓⢦⣄⡀⣰⠇⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⢸⡆
⢻⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠛⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⡇
⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣤⣄⡀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⠶⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⠦⢤⠤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⢀⣴⣃⡼⠧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⢿⣭⣀⣀⠀⠀⠉⠓⣦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣶⣶⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣯⣷⣦⣶⣶⣦⣄⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠻⠿⠿⠿⠿⠟⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠠⠊⠉⠐⠀⠐⠀⠐⠄⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢦⠁⠀⠀⣤⡄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠐⠒⠊⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠀⠀⠀⠀⠀⢰⠂⡀⠀⠀⠐⠦⠤⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣦⣌⡐⠠⠀⣀⡀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠻⠛⢿⠃⠈⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠈⠐⢶⣿⠁⠄⠀⠀⠄⠈⠦⣀⠀⠀⠀⠈⠐⠘⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠑⢄⡸⠀⠀⢼⠓⠦⢄⣀⡀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⡐⠛⠒⠤⣀⠀⠜⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠂⠤⠄⠉⣉⣉⣉⠉⠉⠂⠀⠀⠀⠀⠀⡀⠄⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠌⠀⠀⠀⠉⢢⠀⠈⡀
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠐⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢢⡀⠀⠀⣠⠃⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⣀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠀⡘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⠀⠈⠉⠉⠓⠈⠀⡠
⠀⠀⠀⠀⠀⠉⠣⣀⡀⢄⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠤⠂⠁⠀⠀⠀⠀⠈⣉⣁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡠⠉⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣠⠀⠀⡹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⠅⠈⠁⠀⠃⢰⠁⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⠂⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐⡈⠻⠍⠛⠛⠉⠉⠉⠉⠁⠀⣠⡾⠿⠤⠤⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⠄⠈⠀⢀⠠⠄⠒⣂⠌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⢀⢔⠑⠁⠀⣠⠊⠀⠀⠀⠀⡇⢀⠌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠔⠕⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠊⠁⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⢀⣴⠍⠡⢄⠀⠀⠀⠠⠆⠐⠀⣀⠀⠤⢧⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠠⠤⠄⣀⣀⡀⢀⣧⡶⠁⠀⠀⠀⠀⠀⡰⠁
⢠⠔⠁⠀⠀⢀⡀⠙⠁⡐⡠⡖⠁⠀⢀⠐⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⢉⠃⠀⠀⠀⠀⠀⡔
⠻⠦⠤⠴⠚⠉⠀⠀⠀⠑⠀⢇⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠛⠀⠤⠤⠤⠀⠚⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡰⠒⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⢐⠲⢌⡉⠉⠉⠉⠋⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠐⠀⠄⡐⠁⠀⠀⠀⠀⠱⠀⡀⢤⠦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠤⠀⠐⠊⠁⠀⠀⣀⠠⡐⠊⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣀⠠⢄⠒⠌⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣀⣀⠐⠢⠌⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀
⠀⠀⠀⠀⠀⢀⡠⢔⠂⠀⠄⠀⠀⠀⠂⠀⠀⠉⠢⠑⡀⠀⠀⠀⣠⡤⠀⠀⠀⠤⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⢁⠪⢀⠀⠠⡀⠉⠑⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡩⣫⣵⣤⣀⣠⣄⡀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠐⠁⠐⠁⠀⠀⠀⠸⠀⠀⠔⠃⢆⠀⠀⢂⠀⢃⠀⠀⢈⢨⠀⠁⠊⢡⢄⣐⠟⠋⠀⠀⠀⡤⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠘⠀⠙⢄⠂⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠘⢃⠀⡀⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠠⠤⠀⠀⠀⡠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠆⠀⠀⠀⠘⣿⣇⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢠⢀⡄⠀⡀⠁⠢⢐⠀⠀⠀⠀⠀⠀⠒⠒⠰⠦⠤⠤⣄⡀⠀⠀⠓⠀⠀⠀⠄
⠀⢠⢣⠀⠀⠀⠀⠀⠈⢁⠤⢾⡧⣄⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠉⠀⠀⠀⠀⠀⠀⠀⡐⠐⠏⠃⠀⢹⠁⢰⠋⢢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⣤⠀⠀⣄⡀⠀⢸⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⢰⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢣⡀⠀⡄⠀⠀⠀⠀⠀⠀⢰⣂⣀⠀⢰⠀⢠⡀⡘⠀⠀⠀⠀⢀⠀⠤⠄⠄⠀⠀⠀⠈⠀⠀⠀⠀⢈
⠀⠀⢀⠔⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⡉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠮⠁⠀⡐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠸⡀
⠀⠀⢀⠀⠀⠂⢄⢐⣋⠀⠘⠢⡀⠀⠀⢠⡤⠂⠀⠐⡄⠘⠒⡄⠀⠀⢸⠉⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢸⡄⠀⠀⠂⠋⣨⢇⣂⡀⠀⠢⡀⢤⠀⠀⣴⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⢠⠑⠂⠀⠤⠴⠇⠀⠀⠈⠐⠄⠈⢀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⢸⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠑⢄⠒⠐⠚⡇⠀⠀⣀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠂⠢⠄⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠈⠓⠤⠀⢀⠺⡤⡤⠟⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡓⠀⠀⢀⠀⠒⠉⠉⠉⠛⠃⢦⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⡀⠀⠀⠘⠛⠁⠀⣠⡦⠀⠀⠀⠀⢀⠉⠀⠀⠙⣇
⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⢠⣿⣾⡀⢀⠀⠀⠀⠀⠠⢀⠄⣿
⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠊⠁⠀⠈⣷⠊⢡⡄⠁⠀⠀⠀⠀⠄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠲⠟⠀⠠⠈⠃⠀⠀⠀⠀⠀⠙⢉⣄⣐⠂⠀⠀⠀⠈⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣶⣶⣶⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠋⠙⣿⡇⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠆⠀⣿⠇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠢⣄⡀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠇⣀⠀⠀⠉⠛⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠥⠒⠒⠒⠢⡉⢦⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠈⠁⠂⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣠⡤⠰⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣀⠰⠃⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⡀⠤⠔⠊⠉⠀⣠⠔⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠸⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠉⠐⠢⠤⣀⠀⢀⣰⠄⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⠰⠆⠀⣀⠀⠀⠈⠀⠈⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠛⠿⢿⣿⣿⣿⣿⡿⠀⠉⠁⠀⠉⠒⢄⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠙⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⢀⠎⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢡

⣀⡤⡴⠊⠣⡀⣀⡀⠤⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡄
⢻⡄⠘⣶⡞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢡
⠀⢻⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⡄
⠀⠀⠻⣆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢡⡀
⠀⠀⠀⠹⣦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠪⣳⣤⣴⠖⠉⢁⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⢉⣠⣴⠾⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣾⣋⣉⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⠈⠄
⠀⠀⠀⢔⠐⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡱⠀⠀⢠⣿⣿⠿⠛⠉⣇⠸⡀
⠀⠀⠀⣀⣽⣿⠦⡁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠸⠱⠀⠀⠘⣿⣇⠀⠀⠀⡇⠀⠈⡄
⠀⠀⢠⣿⣿⡁⠀⠈⠢⡬⠒⢄⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠈⢻⣷⡖⠈⢳⠐⢄⡁
⠀⠀⠀⠙⢿⣥⣀⣀⠠⠧⡄⠀⠵⢄⠀⠀⠀⠀⠡⠘⠁⠀⠀⠀⡜⠁⠈⠁⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠔⠁⠀⠀⠀⠈⠢⡀⠀⠀⠙⠢⠄⠐⠘⡀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠔⠁⠐⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠐⡀⢀⠤⠒⠐⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⠀⠀⠘⡳⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠃⠂⠈⠉⠢⡀⠀⠀⢀⡠⠄⠂⠁⠀⢡⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠎⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡘⠀⠀⠀⢀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡌⠀⠀⡠⠊⠉⢄⠀⠀⠃⠀⢀⠁⠀⡠⠂⠁⠈⠢⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠢⠄⠀⠀⡘⠀⢀⠎⠀⠀⠀⠀⠡⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠈⠢⡀⠆
⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⡰⢀⠔⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⠦


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣁⡀⣤⡄⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⣇⣀⠁⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣠⡄⣠⣄⢲⡶⣿⣄⣒⠂⠀⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣵⣿⠟⠁⠸⣿⠈⣤⣿⣿⣧⡤⢾⡇⠀⢹⠓⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢽⣿⣿⣯⠤⠄⢀⣿⠃⢽⠉⠛⢻⣀⣞⢓⡂⣾⣿⡋⠁⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⣿⢋⣴⡿⠋⢙⠿⣶⣾⣏⢹⠁⠀⠉⠒⠒⠛⠛⠛⠀⣿⢻⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⠃⠸⠟⠷⠛⠉⢠⣽⣿⣿⣫⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣧⣾⣶⣾
⠀⠀⠀⠀⠀⠀⠀⣈⣵⡟⠊⡠⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣦⣤⡀⠠⣄⣀⣤⣴⠟⣿⣿⠀⠉⠈⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡯⠉⠙⠋⠉⠀⠀⠈⠉⠸⠇⠀⢜⣿⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⣻⠿⠃⠸⡀
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⡇⠐⠀⠚⠁⢀⣀⣤⠃
⠀⠀⠀⠀⠀⠻⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠈⣻⣿⣿⣶⣶⣾⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠉⡉⠉⠉⠉⠁⠀⠀⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⢿⣦⡀⠀⣀⣀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⡇⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⣿⣿⣶⡖⠒⠪⣿⣿⢿⣿⣥⡄⠒⠂⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠁⠀⣸⢀⣧⣾⣿⣿⣧⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⣹⠞⢿⡿⠏⣿⣿⣄⡸⣇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣶⠋⠀⠀⠑⠚⢧⣹⣿⣿⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⣿⣿⣽⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⢹⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⣿⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⣿⡏⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠷⠾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠂
⢀⢀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣯⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⡟⠿⢻
⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⢸⡇⠀⢸⡀
⠀⠀⠀⠀⢸⡇⣶⠿⠯⠭⠭⠽⠿⣆
⠀⠀⠀⠀⢸⡇⢻⣤⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⣠⣿⣿⠟⠻⠛⠛⠻⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡴⠒⢺⢛⣡⢄⠀⠈⠀⠀⠀⠈⠁⠀⣠⠈⡛⣗⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠉⠙⠻⣿⣿⠟⠿⢿⣿⣿⡄
⢧⡀⢻⠀⠉⠉⠀⠀⠢⠄⠠⠔⠁⠀⠈⠉⠁⣽⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇⠀⠰⠀⠀⠀⠰⠆⠀⠘⠷⢀⣀⣿⠿⣿⠃
⠀⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡁⠀⠐⠤⠔⠀⠀⠘⠑⠀⠀⠁⠀⠀⢸⠆
⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣾⣄
⠀⠀⠀⠀⠐⡿⢻⠛⡖⠒⠒⣲⠛⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⡖⠒⠒⠒⢛⡏⠛⣿⣿⡿⠟⠛
⠀⠀⠀⠀⢰⠃⡞⠀⠘⠒⠒⠁⠀⢻⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠈⢳⡙⣟⠿⢿⠋⠙⠦⡀⢸⡿⠿⠄
⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⢘⡇⢸⠀⠀⠀⠀⠀⠸⡆⢧
⠀⠀⠀⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⡼⢁⠞⠀⠀⠀⠀⠀⠀⣇⠘⡄
⠀⠀⣠⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢶⠿⡖⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠳⡀
⠀⠀⠙⠒⢺⡗⡶⢶⡦⠤⠴⢶⡶⢶⡞⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠀⣷⡶⣶⠤⠤⠴⢶⡶⢶⠛⠒⠚⠁
⠀⠀⠀⠀⢸⡇⢧⠀⠈⡗⢺⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⢹⡒⢺⡅⠀⢸
⠀⠀⠀⠀⢸⡇⢸⡄⠀⡇⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢻⠀⢸⡇⠀⡇⠀⢸
⠀⠀⠀⠀⢸⡇⢈⣇⠀⣇⣸⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⡆⠀⡇⠀⣧⠀⣸
⠀⠀⠀⣴⠚⠉⠉⣽⣀⡿⢹⣀⣺⠉⠉⠛⣢⠀⠀⠀⠀⠐⠒⠀⠒⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⡗⠛⣇⣀⡏⠉⣿⣀⡸⠓⠒⠢⣄
⠀⠀⠀⡏⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡗⠒⠒⠲⠶⠶⠶⠒⠒⠒⠚⠉⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠀⠠⡀⠙⠿⠋⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⣀⢂⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⠑⠀⠁⡌⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠄⠀⣀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⣀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡸⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢁⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡈⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠠⠆⣀⣀⡀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢰⣿⡿⠁⠀⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡙⠻⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⠃⠀⠀⢻⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⡉⠻⣿⣿⣿⣿⣿⡀
⠀⠀⣾⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⣿⣿⣆⠘⣿⣿⣿⣿⡇
⠀⠀⣿⡇⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⡄⢹⣿⣿⣿⣷
⡆⠀⣿⡇⠀⢠⠓⣼⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣿⣷⠀⣿⣿⣿⣿⡆
⡇⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⢸⣿⣿⣿⣷
⠇⣰⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣷⣄
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢻⣿⣿⣿⣿⣿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠸⣿⡿⠟⠉⠀⢀⠁⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⡿⠟⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⣿⣿⡏⠀⠙⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣳⣿⣿⣿⣿⣿⣿⣷⣄⢀⣤⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠸⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠙⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⢶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⢄⠒⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠁⡄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡆⢠⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠘⢠⢸⠸⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢑⠂⢙⢂⡀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢸⡄⠠⠀⠀⢘⣎⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢈⡀⠀⣉⠇⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢒⣦⡤⠼⡅⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⣤⠶⢺⠮⠥⠤⠤⠤⢤
⠀⣀⣀⣀⠀⠀⠀⠀⡈⢐⠁⢠⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠃⠰⢦⠤⠤⣤⠀⢰
⣗⡏⣀⠈⣀⠀⢀⡜⠡⡈⠀⠀⠁⠈⠀⢳⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⠀⠀⢀⠞⡲⡀⠀⠀⠈⣆⣀⣇⣀⣸
⢹⣻⡇⣸⠁⠉⠉⠀⢀⣷⠀⠀⠀⠀⢀⡸⠤⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⢉⡏⠑⠋⠀⣱⣴⠀⠀⠀⠘⣷⠀⢈⠁
⠀⠉⠉⠉⠢⢄⣀⣠⢾⡇⣆⠀⠀⢠⢧⣀⠀⡸⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠚⠓⠦⢄⠰⠁⢸⡇⠀⠀⠀⠛⢿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⢦⠀⠀⠙⠛⠛⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡀⠤⠐⠊⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠓⠒⠒⠒⠒⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡼⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡠⠔⠋⠑⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⠓⠒⠒⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡠⠖⠻⣄⠀⠀⠀⠀⠀⠈⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡾⠋⠀⠑⠦⣀⠀⠀⠀⠀⢀⡀⢠⡟⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡜⠁⠀⠀⠈⠓⠤⣄⣀⣀⣀⠀⠀⢠⡟⡿⠙⢲
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠓⠶⠚⠉⠉⠙⢾⣧⢸⡴⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣷⢠⢣
⠀⠀⠀⠀⣀⡴⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⢠⣤⣀⡀⠀⠀⣟⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠏
⡀⢤⣤⣼⣥⣄⣀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠊⠀⠀⠀⠘⠾⣌⠛⠥⠼⣬⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠏
⠈⠒⠽⣦⣉⣈⢙⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡢⢄⣠⠇

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢀⠀⡠⠤⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠈⠀⡀⠀⡇⠀⠀⠀⢀⠠⠠⠀⠀⠀⠀⠀⠀⡤⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⢸⠀⢢⢄
⠀⡄⠁⠀⡇⠀⡇⠐⠂⠰⡃⠀⢀⡘⢂⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠘⠒⠀⠀⠀⠰⠁⣀⠀⠀⠡⠄⢸⠀⢸⠸
⠀⠀⠁⠀⡇⠀⡇⢸⠀⠀⠹⡁⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠎⠀⠧⠤⠡⠆⠈⠀⠸⠀⣩
⠀⠀⠘⠀⠃⠀⡇⢸⠀⠀⠀⡁⠀⡜⠀⠀⠀⠀⠀⣀⠀⠀⠢⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⡆⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠐⢤⠀⠐⠀⠄⠈⠁⠀⡄⠄⠀⠀⠁⠀⠀⠀⠁⠀⢠⣠⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠱⡀⠀⠁⠀⠀⠀⢆⠀⠀⠐⠀⠀⡰⠀⠀⠤⠀⠀⠠⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠐⠂⠀⢠⠤⡕⠢⠀⠠⡊⠀⡤⡀⡀⠄⠂⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀⢀⠎⠀⡇⠀⠀⠀⠂⠈⡅⢩⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠰⢄⡀⠀⡀⠎⢠⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⡆⠀⠀⠈⡀⠠⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣶⣶⣷⣆⠀⠀⠃⠀⣃⣉⢡⠀⢃⢀⣠⣼⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⢻⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠋⠁⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠖⢪⠉⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⠇⠀⡠⠀⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠑⢄⣹⡿⠿⠟⠛⠛⠛⠛⠿⠿⠿⣿⡿⠦⠊⠀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⠤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡯⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢶⡀
⠀⠀⠀⠀⠀⢀⠊⠁⠈⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⠈⠈⠉⠒⠄
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣷⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⣄⠸⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣾⣿⣷⣌⠙⠻⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⣉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣤⣤⣴⡄⠀⠀⠀⣰⣿⣿⣿⠋⠀⢀⣤⣶⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⣼⣿⣿⡟⠁⠀⠀⠘⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠤⢄⡀⠀⠀⠀⢀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠘⡄⡠⠚⠁⠀⠀⠀⠀⠈⠲⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠔⠙⡄⠀⠀⠀⠀⢸⠁⠈⠒⠄⣀⣀⣀⣤⠀⠀⡘
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠀⠀⢣⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠀⢇⣀⠄⠒⢤⠇⠀⠀⠀⠀⠀⠀⠀⠆⢉⠀⠀⠀⠀⠀⠱⢄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠱⡩⠁
⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀⠼⡜⡀⠀⠀⠀⠀⠀⣠⠷⣤⠥⢄⡀⠀⠀⠀⢀⠔⠛⠁
⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠂⣀⡎⠀⠀⠀⠀⡀⠀⠘⢷⡄⠀⠀⢀⢔⠕⠀⠃⠀⠀⢱⣀⢀⡔⠉⣆
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣤⢤⡼⠀⠀⠀⠀⠑⢄⣀⣀⡈⠥⠟⠋⠁⠀⠀⠀⠀⠀⠈⣅⠜⠀⠀⢠⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⡇⢦⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⡔⠂⠀⠈⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⢸⠀⢀⣧⠀⠀⠀⣟⠒⣌⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⣠⠅⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⢀⠤
⠀⠀⠀⠀⡌⠀⠘⢸⠀⠀⠀⠁⠈⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠊⠁⠘⠀⠀⠀⠀⠀⡠⡀⠀⠸⡀⠀⠀⠀⠀⡠⠔⠁⢀⠤⠊⠁
⠀⠀⠀⢀⠃⠀⠇⠸⠀⠀⠀⢰⠀⡇⢠⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⡆⠀⠀⠀⣰⠁⠃⠀⠀⠱⡀⣀⠴⠈⢀⠤⠊⠁
⠀⠀⠀⠸⠀⢀⠀⠀⡄⠀⠀⢸⢀⠀⣸⠀⠘⠸⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠀⠀⢀⡧⠤⠤⡠⣛⠀⠘⢄⣀⠴⠋⣀⠔⠊
⠀⠀⠀⠸⠀⡈⠀⠀⡇⠀⠀⠸⢻⠈⢹⠀⠀⡆⢇⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⡈⡆⢐⠙⣖⢂⠀⢳⠁⣀⡤⠚⡡⠔⢿
⠀⠀⠀⡂⢠⠁⠀⠀⠇⠀⠀⠀⣦⠇⠸⠀⠀⠰⠘⠄⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠃⠱⡀⠑⠳⣒⣂⡼⠚⣩⡔⠉⠀⠀⠀⠃
⠀⠀⢀⠃⡜⠀⠀⠀⠀⠀⠀⠀⡏⠀⡆⠀⠀⠀⠇⠈⢆⠀⠀⠈⠉⠒⠠⢄⡀⠀⢀⠀⠈⠉⠋⢩⡩⠔⠉⠀⠘⢆⠀⠀⠀⡆
⠀⠀⡘⢠⠁⠀⠀⠀⠘⠀⠀⠀⠇⢀⠁⠀⠀⠀⠘⠄⠈⠢⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠙⠒⠊
⠀⠀⠃⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠂

⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠑⠀⠀⠶⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠢⡙⢆⡀⠉⣉⡀⡀⠩⠀⠰⠂⠙⠀⡰⣰⠀⠠
⠔⠠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢄⡀⠀⠀⡆⠀⠀⠀⠀⠠⢈⠉⠀⠀⢨⡁⠀⠀⡙⠢⡀⠀⠀⠀⢀⡔⠔⣠⢮⡼⠁
⠐⠂⣄⠀⠀⠊⠂⡀⠀⡧⠐⢁⡠⡄⡀⠀⠀⠸⣀⣀⠀⠀⠄⠀⠡⠀⡄⢀⠁⠂⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠖⠋⠑
⠀⢀⠈⠀⠃⠈⢀⢐⠀⠀⠠⠍⠀⡀⢀⠐⠀⠀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠰⠆⠀⢀⠠⠔⠀⠁⠀⠤⠠⠏⠀⡁⠀⠀⠌⠀⠆⠠
⠀⠀⠀⠐⠈⠀⠁⠨⠀⠀⠀⠀⠀⠶⠅⠠⡨⠀⠀⠀⠀⠀⠠⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠁⠀⠁
⠒⠂⠀⡀⢈⡁⠀⠀⡠⠂⠢⡀⠀⢀⣔⣽⠣⠁⡠⠒⠀⣈⡀⠄⠀⠀⠈⠀⠊⠁⠀⠐⠀⠀⢀⠀⠀⠤⠀⠔⠁⡇⠀⠀⠀⣀⡘
⠀⠀⡀⣉⢠⢀⠀⠐⠀⠀⠀⠃⢠⡵⠋⠄⠁⠀⠁⠆⠣⠀⠈⠁⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⡋⠀⠀⠀⠉
⠈⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠱⣞⡖⠀⡀⡀⠐⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⡀⠄⢀⠄⠀⠄⠄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣒⠒⠂⠀⠀⠀⠀⠀⠌⡀⡟⡁⠀⠀⢈⠆⠀⡀⢁⠁⡀⠀⠀⠀⠐⠊⠀⡀⠀⡀⠀⠐⠂⠜
⠀⠌⠂⡀⠀⠡⠀⠈⠁⠀⠀⠀⠀⠀⠀⠴⠃⡇⠹⠀⠀⠀⠀⠀⠀⢁⠀⡤⢨⠀⠀⠠⣀⠀⠀⣷⡄⠀⠈⠀⠁⠀⠀⠀⠀⠀⣤
⠄⠘⢀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡔⢇⠀⣃⣤⠁⠈⠠⣀⠄⠀⠀⠀⠶⠂⠀⠀⢀⠠⠄⡀⠀⠄⠀⠀⠀⠀⠈⠛⠀⠒⠒⠊⢀⠤
⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠌⠀⠀⠰⠀⣠⠀⠀⠀⠀⠸⠐⠂⠀⠀⠰⠅⡀⡂⢀⢔⠀⠰⠴⠃⡄⠠⠀⠀⠀⠀⠀⢀⠂
⠠⠀⠠⠄⠒⠂⢄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠌⠋⠀⠘⠁⠄⠐⠘⠂⠁⠂⠀⠀⠀⠐⠒⠅⣀⠄⠢⡀⠀⠄⢀⠈⢖⡰⠀⣀⣄
⠀⠅⠰⡂⠢⠄⠀⠅⠀⠀⠰⠀⢀⠔⠁⠀⠀⠤⠤⡞⠁⡀⠀⠀⠀⠀⠀⢃⠁⡄⠀⠠⠊⠀⠀⠀⡗⠀⢀⡌⠀⠉⠀⡀⢀⠀⠂
⠈⠀⠀⠏⠡⠂⠀⠂⠀⣄⡀⠤⠁⠠⢊⡡⡁⠐⠄⠀⠠⣧⠀⠀⠀⠀⢁⡀⢠⠀⠀⠅⠀⠀⢈⠈⠀⠀⢉⠀⠀⠀⠀⡀⠀⠐
⠀⠉⠈⠐⣀⠀⠀⠈⠀⠐⢀⠀⠀⠁⠠⠀⠈⡠⠂⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠑⠊⢀⡎⢀⡀⠃⠀⠐⠀⠒⠀⠀⠀⢀
⠄⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠂⠀⠀⠀⠧⠔⠂⠀⠀⠀⠑⡀⠀⠂⠈⠈⠠⠀⡁⠀⡁⡀⠀⠀⡙⢈⠁⠀⠀⣠⣁
⢉⠂⡄⢊⠐⠁⠀⠀⠀⠀⠀⣀⠊⢀⡀⠀⢠⡠⡠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⡄⢁⠒⠀⠂⠈⢻⣿⠀⠀⠀⠀⠈⠐⠀⠀⠀⠒
⢀⠄⡉⠠⢎⠶⠀⠀⠀⢀⠆⠀⠐⠀⠐⠔⠐⠒⠀⢂⢀⡀⠀⠀⠒⠀⠀⣀⠀⠁⠄⠁⠀⠠⢤⠀⠇⠀⢀⠤
⢈⠀⠆⠀⠆⢺⣡⠧⠔⣸⠀⢀⠀⡀⠆⠀⠀⠀⠀⠸⠀⠉⠀⠀⠒⠉⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠈⠤⠈⢁⢆⡸
⠀⠀⠂⠂⠀⠡⠗⠆⠀⣆⠔⢠⣠⢀⠈⠂⠤⠠⠐⠁⢄⠒⢬⡀⠀⠀⣂⠀⠀⢀⢂⠀⡀⠀⠐⠒⠒⡄⠈⢀⡉⠈⠋⠀⠀⠀⢀
⠂⠄⢀⠆⠀⠀⢀⠀⠀⢀⡴⣲⢏⠂⣠⢠⡄⠐⠀⢤⡠⢀⠀⢈⠓⢊⠰⠁⠂⠡⠈⠈⠀⠀⠀⠀⢸⠀⠀⢉
⠘⠄⠋⠠⠐⠂⠀⠂⠀⠠⠟⠁⠂⠀⠀⠣⡕⣠⠊⠒⢝⡷⡒⠀⠀⠀⡀⠲⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠐⠂⠀⠤⠀⠀⡠
⠀⠀⠁⠀⠀⠀⢀⠐⡀⠀⠂⠄⠀⠀⠀⢐⢻⣅⠅⠀⠀⠙⠙⠂⠀⠀⠁⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛⠊⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢰⠹⡀⠀⣀⢤⡄⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠣⡄⠀⠳⠞⠀⠀⠳⠞⣄⡇⠙⢦⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠓⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠤⠬⠆⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⢲⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠴⢤⢀⠤⠔⠚⠁⠀⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣄⠀⠀⠀⡴⠛⠺⡄⠀⢸⢀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⡇⠀⢰⣧⠀⢀⡇⢠⡼⠯⣀⠤⠶⡄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡟⡸⢁⣄⠈⠧⠤⠊⢀⣼⠀⠀⠃⢴⠆⡽⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠁⠀⠀⠀⢀⣤⣾⣿⡆⠀⠀⠒⠚⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠑⠲⣤⣤⣴⣾⣿⠟⠁⣰⠇⠀⢀⣴⢞⣉⣁⣒⣲⢄⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⣤⡀⠹⣿⠟⠛⣏⣠⠴⠋⠀⡼⠋⢸⡉⠉⡧⠀⡼⠁⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢭⠝⠛⣆⠀⠙⠲⢬⣍⣉⣉⣀⣠⠤⠞⠁⠀⣀⠧⠔⠃⠘⣅⡰⠆⢠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢏⡰⠁⢏⠀⠀⠀⠀⢀⢀⡼⠋⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠳⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠬⠭⠔⠳⣄⠑⠲⠤⠼⣯⠋⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣹⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢖⠒⠒⠒⠒⠉⠉⠉⠉⠉⠑⢲⡇⠀⠀⠀⠀⣠⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⣲⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠻⢤⣀⠀⠀⢸⡩⢄⠈⠉⠙⣯⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠙⠺⡦⠔⠋⠙⠦⠤⣖⠀⠀⠀⢀⡼⠀⡸⢭⣱⡤⣇⠆⡰⠁⣹⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⢴⡙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⠴⣏⠱⢚⡤⠊⠉⠀⠈⠛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢾⠉⠐⠒⠪⠭⣖⡮⣝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠉⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠉⠉⠉⠁⠒⢤⡤⠒⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣠⣤⣶⠶⠶⠶⠶⣶⣤⡈⢿⡆⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⡁⠤⠤⢀⡀⠀⠀⠈⢻⣌⠻⠦⡀⠀⠀⠑⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⣁⡀⠀⠀⠤⣄⠀⠈⢆⠂⠀⡆⠆⠈⠉⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⣦⠀⠀⠶⠀⠀⠀⠘⢤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⡤⠄⠊⠅⠀⠀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡀⠉⠀⠀⣀⠔⠋⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣩⠀⠀⠀⣒⠖⠂⠁⠀⠸⠉⠉⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠀⠀⠊⢠⠀⠀⠀⠀⡧⠀⠀⠠⢄⠀⠈⠢⡀
⡔⠀⠚⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠁⠂⠀⡞⠀⠀⠀⠀⠀⠑⢄⠀⠑⡀
⠁⠀⢠⣿⠉⠐⠀⠠⢀⡀⠀⠀⢀⠄⠈⠑⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⡀
⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⠈⠉⠀⠀⡠⠔⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠐⠂⠁⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⡰⠉⠆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠒⢄⠀⠀⣀⠤⠊⠀⠀⠈⢆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢏⠁⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠎⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣿⠃⠀⣱⠆⠀⠀⠀⠀⠀⠀⢂⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠁⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢏⡴⡚⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢖⠻⠊
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⡶⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⢀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀⠀⠀⠀⠶⣀⣐⣪⠴⡈⡆⠀⠀⡠⠔⠊⠉⠉⠉⠀⠒⠒⠒⡺
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢤⣄⡀⠀⠀⡇⡇⣠⠊⢀⡠⠄⣒⣂⣤⡀⠤⠄⠊
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢌⢢⠀⡇⡷⠁⣤⠏⢂⡩⠤⠤⣀⠬⠷⠦⣀
⠀⠀⠀⠀⠀⡧⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠀⠀⠀⠀⠀⠈⢆⢳⣷⢁⣺⠵⠾⡅⠀⡠⠊⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⢐⢀⡠⠔⡖⢻⠿⠿⣼⠿⣫⠔⠚⡇⡅⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠉⢆⠀⠀⠀⠀⡇⢰⠋⠀⠀⠣⣈⠒⠤⣳⣊⣹⣆⠀⠳⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢠⠃⠀⠘⡄⠀⠀⠀⣷⡇⠀⠀⠈⠐⠤⡉⠒⠒⠒⠒⠉⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⡇⠀⠀⠀⠰⡀⠀⠀⣇⡥⠔⢄⠢⢄⠀⠀⠉⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠸⠀⠀⠀⠀⠀⣧⠀⢀⠏⣤⡞⠊⡀⠀⠀⡡⠊⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⢡⠀⠀⠀⠀⠀⠀⢣⣌⠮⠴⢥⣀⡀⠈⡞⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡎⢠⠁
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢑⢢⣤⡤⢊⢣⣼⡟⠊⠉⣀⣉⡡⠽⡃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡸⠀⡎
⠀⠀⠀⠀⠀⡧⠼⠤⠤⠤⠍⠲⢲⡶⡶⢋⡟⢫⡙⠃⢌⡀⠀⠀⠹⡄⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡰⠁⡜
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠋⡠⠊⡇⠈⡍⠳⢄⡙⢆⠀⠀⡇⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⠜⢁⠜
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠚⢰⠉⠀⠀⢡⠀⡇⠀⠀⠉⠚⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠐⠐⢧⡀⠀⠈⠶⠀⠀⠀⠀⠀⢀⡔⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠉⠳⠦⣆⠀⠀⠶⠒⣉⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⡿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣔⣡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡰⡩⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⠢⡀⠀⡁⠰⡐⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠎⠑⢌⢢⡇⢸⢃⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣁⡀⠀⣀⠱⡱⠸⡞⡐⠪⡓⠄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠬⡙⣷⢡⡁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠬⣠⠤⠄⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⠳⣄⠀⣀⣠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠙⡯⠗⣚⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⢀⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⣀⣤⣀⡠⠐⠂⢄⠔⠚⠚⠟⠋⠤⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⣶⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢑⡖⠋⠀⠀⠀⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⡿⠋⠹⣓⠦⢖⣤⡭⣭⠶⣄⢄⣀⠼⡸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⡩⢮⡺⠟⢸⡏⠑⠲⡮⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⢀⠤⢊⠴⠋⠈⠀⡀⣇⠀⠀⠱⡴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠤⠍⠔⠊⠁⠀⠀⠸⠴⠡⠜⠀⠀⠀⠈⠢⠂

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣟⣻⣿⣻⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⣠⣿⠀⢹⣇⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢺⣏⠉⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⢉⣿⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠶⠶⠶⣤⣤⡟⠀⠀⢀⣿⠃⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⢿⣤⣤⠶⠶⠶⠛⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠇⠀⠀⣾⠋⠀⠀⠀⠈⢻⡄⠀⠀⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢿⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⢷⣄⣀⣠⣴⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠧⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠟⠳⢶⣤⠀⢠⡴⠾⠛⠷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⢿⣤⣤⣤⠿⠈⠙⠳⣦⣤⠶⠛⠉⠸⣧⣤⣤⣼⠇⠈⠛⠶⣤⣴⠞⠋⠁⠿⣤⣤⣤⠿⠀⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⢀
⣿⡟⡋⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⠂⠀⠈⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⢀⡠⠤⢄⠀⠀⠀⠀⡇⠠⠄⠀⠈⠁⢀⡠⠈⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣳⣤⣞⠀⠀⠀⢳⠀⠀⠀⠘⢦⣀⠀⠄⠀⠀⢀⡼⠁⠀⠀⠀⢀⡴⠋⣉⣀⣠⣤⣤⣤⣭⣭⣉⡓⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠈⢳⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠁⠀⠀⠀⠀⢀⡾⠞⠛⠉⠁⠈⠀⠀⠀⣀⠤⢬⣉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡇⠀⠀⠀⢨⣧⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⢤⣤⣤⣄⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴
⠀⠀⠀⣰⡿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡫⠉⠐⠒⠈⠐⠒⠂⠈⢍⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠜⣅⢀⠀⡀⢀⢀⠀⡀⣀⢂⡡⣰⠌⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣭⣥⣿⣿⣿⡿
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢁⣤⡔⢕⢁⣬⡀⠗⣩⣍⠦⢗⣴⡁⡘⠄⢿⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⣷⣾⣿⣿⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣟⡵⠋⠀⢙⣒⠋⠈⠓⠞⠁⠉⠛⣋⡈⠙⢶⣔⢸⠀⠀⠀⠀⠀⢀⣴⣿⣖⣋⣩⣯⣿⣷⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠻⠟⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⢠⠚⡇⠀⠀⠀⣾⣷⠀⠀⠀⣤⠀⠀⠀⣾⡆⠀⠀⠀⣼⠓⡀
⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⠶⣬⣦⢷⠀⠀⣤⠈⠁⣠⣤⡤⠤⢤⣤⣄⠀⠠⡤⠀⢀⣯⣞⡵⢦⠀⠀⠀⠀⠀⣠⣤⣤⣴⣧⠤⣤⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣴⠉⠸⠥⢈⡏⢧⡀⠀⠀⠀⠳⣄⡀⠀⣀⣠⠏⠀⠀⠀⣠⠎⣟⠀⡽⠊⢱⡄⠀⠀⢸⠁⠀⠙⠛⠋⠁⠀⢻
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠦⣤⣠⠾⢦⡀⠉⠲⢤⣄⣀⣀⠉⠉⢉⣀⣀⣤⠴⠚⠁⢀⠼⢦⣀⣤⠞⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⠒⠛⠉⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠓⠒⠉⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠉⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡴⠚⡉⢱⠀⠀⢀⠜⠁⣸⠁⠀⠀⠀⠀⠀⠀⢧⣤⣤⣀⣀⣀⣀⣠⣤⣤⡿⠀⠀⠀⠀⠀⢀⣠⡤⠴⢶⣶⡯⣍⠉⠓⠦⣌⠉⠓⢦⡀
⠀⠀⠀⠀⠀⡜⠘⡆⠱⠀⣡⠖⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⣮⡇⠀⠀⠈⡧⠀⠀⣹
⠀⠀⠀⠀⠰⡇⠀⣀⡤⠚⠡⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣠⡾⣄⣀⣄⣠⠇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢰⢯⠀⠀⢠⡖⠁⢀⡟⠁
⠀⠀⠀⠀⠠⡏⠉⠁⢄⠙⠆⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⣒⣺⠀⣿⣒⣲⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⣿⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⢀⣸⠆⣏⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣸⡿⢤⡼⠧⠤⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠙⠶⠚⠉⠉⠉⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠑⠢⢤⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⡀⠀⠈⠑⢦⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡠⢄⡀⠀⠀⡠⠋⢤⢃⡞⠉⠑⠀⠀⠉⠀⣀⡀⠀⠀⠱⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⡀⡆⠉⢶⡴⢱⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡆⠀⠀⣈⢷⠤⠄⠀⠀⠘⡄⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⣀⡜⠁⠈⣇⠀⠀⠀⠀⢳⡀⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠳⣀⠀⠀⠀⠙⠦⢄⣤⠤⠃⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠎⠈⠋⠈⢇⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣹⠉⠉⣏⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠘⢀⠈⡄⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⠚⠛⠉⠉⠉⠉⠙⢆⠱⡄⠀⠀⠀⠈⠍⠉⠉⠙⠢⢄⡀⠀⠀⠈⢇⠀⠻⡓⣣⣀⠷⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⢢⠀⡀⡰⠀⠀⠀⠀⢠⠀⠉⠢⡀⠀⠀⠑⠂⢈⠇
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠖⠒⣇⣤⠤⠒⢲⡂⠀⠀⠀⠀⠈⠢⡉⡔⠁⠀⠀⠀⠀⠘⣧⠴⠲⣞⠀⢀⠎⠀⡎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠏⠀⠈⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠳⠃⠀⣸
⠀⠀⠀⠀⠀⠀⢀⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡀⠀⢀⡇
⠀⠀⠀⡤⠂⠀⠈⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠑⠋
⠀⠀⠸⡆⠀⠀⠀⢀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠉⠉⠉⠉⠀⢀⠭⠷⠄
⠀⠀⠀⠙⢣⣠⡀⡎⣰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡰⠃⠀⡄⠀⢰
⠀⠀⠀⠀⢀⡤⣥⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠃⠀⡎
⠀⠀⠀⡴⡡⠊⠤⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⠤⢤⣤⣄⣀⣀⣀⣤⡤⠤⠖⠚⠉⠀⠈⠙⠲⠤⣀⣀⠀⠀⡼⠉⡟⠀⠀⠀⠘
⠀⢀⠎⡜⠀⠈⠒⢁⠼⠤⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⢰⠃⠀⠀⢠⠃
⢀⠎⡜⠀⠀⡀⠀⣞⡀⡐⠀⠉⠒⠤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠆⢀⡤⠶⠒⠐⠒⠢⣀
⡈⡼⢇⠀⠀⠀⣰⠃⠈⠳⢄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠉⡹⠚⠁⠀⡘⠀⠀⠐⠂⠘
⣗⠃⠈⠦⣄⡴⠃⠀⠀⠀⠀⠑⢄⠀⠀⠸⡄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢞⠥⡀⠔⠈⠀⠀⠀⠀⠀⣠
⠹⣄⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⣘⢄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢕⡴⠊⠀⠀⠀⠀⢀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⢀⡀⠤⠒⠊⠉
⣷⣿⣷⢾⣶⠾⣷⣶⣾⢷⣿⡾⣷⣾⣾⣾⣿⣿⣾⣷⣿⣿⣿⣿⣾⣶⣷⣷⣿⣾⣶⣷⣷⣶⣶⣶⣷⣿⣶⣶⣷⣾⣾⣿⣿⣿⣶⣶⣾⣷⣾⣷⣿⣶⣾
⣿⣿⣦⣶⣧⣾⣤⣶⣿⣾⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣸⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠉⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⣿⣿⣶⣴⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣷⣦⡀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢿⣿⣿⣿
⠀⠀⣾⣿⣿⡿⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠋⠀⠀⣾⣿⣿⣿
⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤
⣿⣯⣬⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣿⣶⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⣨⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇⡀⢠⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⡀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠁⢠⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢉⠂⠠⢬⠀⠀⢠⡾⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⠀⠀⠀⠘⠣⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢠⢀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠄⢠⠀⠂⢳⣄⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠐⣿⣷⣤⣿⣏⣤⣤⣌⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⢿⣿⣿⣿⣿⣿⣿⠈⠀⠈⠳⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⠀⠈⠉⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠴⠢⣄⡀⠈⠀⠀⠀⢀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠿⣿⣿⣿⣷⣶⣀⠢⠄⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠂⠸⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣶⣶⣾⣿⡾⠿⢒⣰⣶⡖⠐⠛⠀⠀⠰⠶⠒⠶⢒⡤⠀⠀⢀⣀⠀⠀⠀⣀⣀⣀⣀⡀
⠿⠍⠡⠥⠶⠞⠛⠛⠟⠈⣰⣾⢋⣬⣼⣿⠿⠋⢁⣀⡀⢀⣉⣁⡀⣴⠶⠟⢫⣿⣿⣿⣿⣥⣂⠀⠀⠠⠄
⣶⣤⡀⠀⠀⠀⠀⠀⠀⠙⣯⣵⣶⠿⢛⣁⣤⣾⣿⣿⣏⠛⠿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣽⣿⣷⣶⣶⣾⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠄⠀⠄⠄⠀⠈⠳⠀⠀⠀⢀⡄⢠⡀⠢⠀⠀⡎⠀⠀⣀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠷⠀⠂⠀⠀⢀⠀⢠⠤⠄⠐⠀⠀⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢯⡥⠀⢀⠆⠀⠑⠀⠠⡀⠈⢢⡁⣶
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⣎⠁⠀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠁⠀⠀⠀⠀⡀⠠⣤⡀⢳⣿
⠀⠀⠀⠀⠀⣀⣈⣀⠒⠒⠁⠀⠀⢀⡄⠠⢀⠀⠀⠲⣚⠀⠇⠀⠀⠘⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡄
⠀⠀⠀⠐⠁⣤⣀⠈⢣⠀⠀⡉⠀⠛⠹⠄⠀⢁⠀⠀⠉⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠉
⠀⠀⠀⠀⠠⣿⣧⠆⢀⠀⠀⠃⣀⠀⠀⠀⠀⠌⠀⠐⠙⢄⠀⠀⠀⠀⠀⠣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠈⠀⠀⠀⠔⠃⠀⠀⠀⠙⠀⠀⡠⠊⠀⠀⣠⣸⠆⠖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠠⠀⠀⠀⠐⠀⠀⢱⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠚
⠀⠀⠀⠀⠀⠀⠈⠀⠒⢤⣄⡀⠀⠀⠐⠀⠀⠀⠈⠢⣤⣤⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⡄⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢤⣀⡇
⠀⠀⠀⠀⠀⠐⠲⣤⡄⠐⠶⠦⠤⣤⣀⡍⠈⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣘⣦⠀⠀⠀⠀⡆⠀⠀⢰⠀⢙⠁⠀⠀⠄⠘⠀⠀⡦⠀⠂⠀⠈⠃⠀⠠⣀⣠⡶⠀⠀⠄⠁⠀⠀⠁⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣍⡳⡄⠀⠀⡇⠀⠀⠈⠀⢘⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⢀⡀⡀⢸⠀⠀⠀⠀⠈⠀⢠⢀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⡀⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠀⠀⠀⠁⠈⠈⠀⠀⠘⠀⠀⠂⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠉⠀⠈⠁⠀⠉⢢⠀⠀⠀⠀⠀⡄⡰⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⣇⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣂⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⡀⠀⢸⠀⠀⠆⠀⠀⠈⠺⠏⠁⠄⠀⠀⣠⠤
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁
⠀⠀⠀⠀⡰⠁⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢐⡀⠀⢰⠂⠀⢀⡀⠀⡄⠀⣀⠀⢀⠌⠀⠀⠀⠀⠐⠀⣠⠊⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠠⠀⠈⠁⠀⠀⣵⠊⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠈⠃⠀⡰⠁⠀⠈⢀⠀⠀⠀⠀⠀⠠⠀⠂⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠒⠹⢆⠀⢀⡤⢀⠀⠀⡠
⠀⠀⠀⠀⠻⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠤⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠂⠉⠀⠈⡆⠸⢇⡀⠤⠊⠀⢰⣄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠄⠀⠈⠐⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⣀⣀⣠⣴⠄⠀⠀⠀⠀⠀⢴⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣁⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⢄⠀⣠⢤⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢐⣿
⠀⠀⠀⠘⣧⡺⠛⢿⣘⠃⠀⠀⠀⣰⣿⣀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣿⡅⣸⠀⠀⠀⠀⠀⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠃⠀⠀⠈⠉⠉⠉⢼⡇⠙⠀⠀⠀⠀⠀⠸⠁⠣

⠀⠀⠀⢠⡄⣀⠀⣀⢠⡄⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠀⢤⡀
⠀⠀⠀⠘⠁⢸⣿⡇⠈⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⡯⠖⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣯⣸⡇⠀⠀⠀⠀⠀⣠⠏⢳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⠛⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠐⠒⠒⠚⠓⠒⠃⠀⠀⠀⠀⠇⠀⠀⠀⠸

⠀⠀⠀⠀⡀⢤⣶⡤⢄⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣤⣄⠀⠀⠀⠀⠀⣶⡆⡀
⠀⠀⠀⠀⡇⢀⠠⣂⢸⠀⠀⠀⠀⠠⣶⣿⣦⡎⠀⠀⠀⠀⠸⣿⠿⡟⢿⣿⣿⠀⠀⠀⠀⣶⡿⢴⡇
⠀⠀⠀⠀⡇⣄⣶⣿⢸⠀⠀⠀⠀⠈⠈⠛⢿⣿⣄⠀⠀⠀⠀⠙⢿⣼⣿⡿⠃⠀⠀⠀⠸⣿⣥⡴⢦⡀
⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠙

⠀⠀⠀⢀⡤⡤⡤⡤⣤⡀⠀⠀⠀⠀⢰⣤⣴⡂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤
⠀⠀⠀⡃⠀⠀⡀⢀⣀⡃⠀⠀⠀⠠⣿⣿⣿⡧⠄⠀⠀⠀⠠⣤⣊⣀⣀⣘⣓⠀⠀⠀⠀⠈⠇⠀⠸⠁
⠀⠀⠀⢅⡀⠀⠀⢪⣒⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡍⠉⠉⠉⡉⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠛⢻⣿⣷⣿⢿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⡿⣛⣵⣴⣦⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠿⠟⣷⣿⣿⣿⣿⣦⣀⡀⠀⠀⢽⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠅⠒⠄⣶⣍⡻⢿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⣿⣿⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢼⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣧⠀⠀⠐⡟⢡⡿⣻⣿⣿⣿⣿⣿⠶⣄⣀⡲⢿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠆⠀⢘⢆⡾⣱⣿⣿⣿⠻⣿⢿⠑⠈⠹⣙⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣏⡿⠃⡭⡸⣿⣿⡿⠋⠙⣿⡝⠧⡄⣰⡀⣻⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡞⣹⡇⢠⡶⠐⠻⣿⣿⣧⣶⢹⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣹⣿⣿⣿⠟⠁⢹⣿⠜⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡟⠉⠀⠘⣸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠯⠀⠀⠀⠀⠿⠼⠻⠿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉