Cat in a box Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠈⠑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⢂⠀⠀⠀⠀⠀⠀⢀⣾⢘⠀⠀⠀⠀⠀⢂⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠁⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠠⠠⠀⠀⠈⢶⢶⠂⠀⠀⠀⠀⠑⠠⡀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡇⠀⠀⠀⠀⠀⣴⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠒⢬⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠎⡁⠀⠀⠀⠀⠀⠸⡁⠀⠠⠀⠀⢀⠀⡍⠁⠀⠀⠀⠀⠀⠀⠙⢦⣨⠀⠀⢀⣖⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢤⣙⢦⣀⡀⠀⠀⠀⠀⠉⠀⠀⢐⡄⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡿⠀⣀⡸⠷⠒⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⡉⠋⠑⠐⠊⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠧⠓⠈⠁⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣠⣀⠀⠀⠀⠀⠀⠄⣀⣠⠴⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⣄
⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⢈⠁⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠰⠀⠂⠊⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠑⠲⠤⣈⣀⡀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⡀⠀⠠⠀⣀⡤⠒⠉⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⢈⢀⢀⠀⠄⠘⠢⠒⠋⠁⣀⡤⠖⠉⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠠⠀⠂⢀⢠⣠⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⠀⠀⢈⠀⣐⣠⠄⠓⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⡄⠀⠀⠀⠀⠀⠀⢀⠎⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠘⢄⠀⠀⠀⠀⢀⠎⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣦⡀⠀⠐⠉⠃⠀⠀⠀⠊⠒⠀⡠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠧⠄⠀⢀⠀⠀⠘⣟⠀⠀⢀⠄⠐⢺⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢉⢹⠤⠄⠀⠈⠒⠤⠚⠈⠢⠔⠊⠀⠒⢺⠯⠉⠉⠉⡩⢻⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠊⠀⢸⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣷⠉⠀⠀⠀⢈⠖⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢸
⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠔⠉⠀⠀⠀⠀⡠⠴⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⡠⠒⣄⡠⠤⣀⣄⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠑⣄⢀⠔⠢⠤⠀⠀⠀⠀⢀⡠⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠺⠒⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠓⠊⠉⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠂⠄⡀⠀⢀⡀⠀⠀⢀⡀⡠⠊⡠⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⡉⡰⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⣅⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠬⡆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠈⣁⠀⠀⠀⠁⠀⠡⡤⠈⠀⠈⠀⠀⠀⠤⠤⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠣⠀⠀⠀⠀⠈⠈⠉⠈⠀⠀⠀⠀⠠⢄⡌⠀⠀⠀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⠀⣀⡀⠀⠀⣀⡀⠀⠄⢖⠁⠀⢁⡠⠊⢀⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡔⠁⣤⣊⠁⣀⣀⢀⢀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠁⠀⣇⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡆⠀⠈⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠼⠤⢌⣀⠀⢀⡱⠤⠤⠄⢔⣀⠀⢀⡡⠤⠧⠴⠤⠧⠤⠤⠤⠤⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠠⠀⠢⢀⠀⠤⠀⠀⠠⠀⢀⠠⢀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⡗⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢐⡀⠀⠈⠉⠁⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⡔⢈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠠⢠⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠈⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢁⣀⡀⣀⢈⠊⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠠⠎⣤⠄⠀⠀⣀⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠆⠀⢀⠠⠄⢠⠞⢀⡈⢑⢁⡄⠈⢶⠀⠤⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠁⠀⠢⡀⠠⠊⠂⠀⡠⠂⠀⠁⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠈⠀⠰⠀⠙⢄⡀⠀⡀⠄⠊⠀⠑⠄⠄⠂⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠊⢠⠁⡆⠂⠠⠀⢄⢀⠐⠁⠈⠁⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠰
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢁⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠈⢂
⠀⠀⠀⡠⠄⣚⠀⠀⢐⠤⢄⠑⣄⠀⠀⢀⠌⠐⠄⣀⣀⠀⠐⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⣓⡠⢄
⠀⢀⠌⠀⠀⠈⢤⠊⠀⠀⠀⡡⢀⡰⠈⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠈
⠀⠂⠀⠀⠀⠀⠀⠐⠒⠀⠁⠀⠀⠀⠀⠈⠐⠂⠀⠀⢀⣸⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠁⠒⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠤⠁⠀⠀⠀⠈⠤⠀⠐⠂⠁
⠀⠀⠀⠐⠂⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⢄⣠⣀⠀⠐⠈
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣠⡶⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⢻⠿⣾⣻⡍⠛⢛⡃⢠⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⣼⡾⠋⠁⠀⢶⠐⣿⠗⢠⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡄⠴⠶⢦⣄⠙⠀⠘⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢳⡟⠀⠀⡀⠐⠊⠀⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⠋⣿⣾⣿⠀⢶⣀⠀⠀⠀⠀⢀⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠠⠿⢶⡿⣇⠀⠠⠀⠉⠓⠲⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠉⠀⠀⠳⡀⠀⠀⠀⠠⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠖⢲⠦⣤⡀⠀⢄⡀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣞⣛⠀⠀⠀⠀⠀⠈⢢⠈⠇⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣯⡷⣤⡀
⠀⠀⠀⠀⠀⠀⢊⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢳⣿⣦⣼⠀⠀⣀⠀⢽⣿⣿⣿⣿⣿⢻⡿⠛⠁⠙⢢⡀
⠀⠀⠀⠀⠀⣠⣾⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡤⢥⣼⣷⣄⣾⣿⣿⣿⣿⠏⠉
⠀⠀⠀⠐⡫⠋⠉⠙⠓⠶⢶⣽⣦⣤⣤⣶⣾⣶⣤⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠿⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⢄⡀
⠀⠀⠀⠀⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠸⣿⣟⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⢰⡂⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⣼⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠁⠐⠒⠦⡀⠀⢀⡀⠤⠤⠀⠀⠀⠤⠤⢄⡀⠀⠀⠀⣠⠔⠒⠀⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢰⠀⠒⢢⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠯⣀⠤⠒⢢⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡌⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣾⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣽⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⡀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⣣⣤⠤⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠆⠀⠸⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠶⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠗⡠⠶⠦⣤⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠉⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⠛⠓⠂⠤⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠊⠉⠀⢠⠀⡠⡀⠀⢀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠦⢄⡀⠀⠀⠀⣠⠔⠉⠈⠉⢰⠒⠒⠒⠒⡎⠉⠈⠑⠢⣀⠀⢰⠀⠈⡘⡀⠘⠐⠊⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠔⠁⠀⠀⡆⠀⠉⠢⢀⠞⠁⠀⢠⠀⠠⠃⠀⠀⠀⠀⠸⡀⠰⡀⠀⠈⠢⣘⡀⠀⡇⠈⠓⠒⠒⠁
⠀⠀⠀⠀⣀⠤⢄⠀⠈⠀⢃⠉⠑⡄⠀⡸⠀⠀⠀⣸⠃⠀⠀⢠⠏⢀⠇⠀⠀⠀⠀⠀⠀⠱⠀⢳⠀⠀⠀⠹⡇⠀⠱⣄
⠀⠀⢴⠛⠢⣄⠀⠱⣔⠀⢸⠀⢀⠁⢠⠁⠀⠀⢀⠛⠤⠄⣀⣼⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⣇⣀⣀⡀⠧⠔⠚⢙
⠀⠀⠈⠢⡀⠀⠑⣄⠘⡄⢸⠀⡜⢠⠃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠉⠀⠁⢹⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡤⠄⠤⠤⢌⣒⣄⡈⠣⡐⡌⡰⢡⠃⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡃⠀⠀⢀⣀⡀⠉⠙⠒⣽⡟⡱⠃⠀⠀⢀⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠰⣀⣀⣀⣀⡀⠤⣤⠞⣟⡰⠁⠀⠀⢀⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡖⠉⢀⣀⠴⠊⢡⢎⡜⠁⠀⠀⢠⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠻⣍⠉⠀⡠⠖⢡⠎⠀⠀⠀⡠⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡰⠁⠑⠉⠀⡰⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡃⠀⠀⣠⠊⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣀⡠⠚⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠊
⠀⠈⠑⠢⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠚⠒⠒⠒⠛⠒⠂⠀⠉⠉⠉
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣮⣙⡓⢶⣶⣦⡶⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⠡⡤⠀⠘⠁⢀⠈⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠺⣿⡆⠀⠀⢰⡶⣦⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡍⠛⠫⢤⡀⢲⡖⢀⡔⠾⢿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⠀⠀⠀⠌⢥⡜⠫⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠁⠠⠄⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣆⡀⠀⠀⠀⠀⠀⣀⣴⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⣄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠋⠙⠁⠀⠀⠀⠀⠀⠚⠛⠛⣿⠁⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠿⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡆⠀⢠⠀⠀⠀⠀⢸⠏⠀⠀⣀⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⣶⣾⡇⠀⠲⢾⡇⠀⣸⠓⠂⢠⣤⣾⠀⠛⠛⠛⠉⢹⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⢸⣿⣿⣿⣿⠔⢂⣴⣧⣴⣿⣷⡶⠖⢻⣿⣿⠒⠶⣦⣴⣾⣿⣿⣿⣿⠟⠋⢹⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠁⠈⠉⠉⠉⠉⠉⠉⠙⠛⠒⠛⠛⠛⣻⣿⣿⣧⠀⠀⢹⣿⣦⠶⠿⠿⠿⣿⡿⠋⠁⠆⠀⣼⡀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠨⠿⣷⣤⡼⠋⠀⠀⠀⢀⣴⡟⠀⡀⠀⠀⠈⢺⠓⠒⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡅⠀⣠⡾⠟⠁⠀⠀⠀⣠⡞⠁⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡼⠋⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠟⠻⠗⠳⠺⠚⠒⠓⠒⠒⠒⠒⠒⠚⠒⠒⠒⠲⠲⠒⠲⠒⠲⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⠀⢀⠀⠀⢀⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⠶⠶⢶⣶⡶⠶⠶⢶⡶⠶⡶⢶

⠀⠀⠀⠀⠀⣴⣾⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⢀⡜⠁⠀⠈⢹⡿⣳⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣷⣶⠏⠀⠀⣀⠀⠿⢣⡿⣻⡿⠉⠉⢩⠇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⡯⠇⠀⠀⠀⢳⠀⠀⠀⠉⡀⠀⢀⡏
⠀⠀⠀⠀⣠⢤⣰⠛⠋⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣏⠁⠀⠀⠀⠀⢤⡀⠐⠋⠉⠁⣸
⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢿⣿⣿⣷⣤⣀⠀⠀⠚⠀⠀⠀⠀⣶⡗⠄
⢿⣀⣀⣀⠤⡶⠚⠓⠒⠒⠾⣁⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠳⡶⠤⢤⡤⠼⠻⠌
⠀⠀⠀⢀⡞⠁⠀⣠⠤⠤⠤⠤⠟⠉⠛⠒⠒⠒⠲⠦⢤⡀⠀⠀⠀⠹⡀⠀⢳
⠀⠀⠀⠸⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠄⠀⠱⡄⠨⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠤⠴⢷⡀⠘⠀⠘⢦⠈⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠯⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠱⣄⡇⠉⠉⡒⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠴⠋⠀⣀⣀⣠⠤⠤⠖⠚⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⢀⣀⣀⡤⠤⠶⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢤⡀⠀⠀⠀⠀⢀⢀⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠲⣄⠀⠀⢨⠎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠦⠏⠀⢸⢳⠀⠀⣀⣀⡤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⢸⠘⠋⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⣸⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⠈⠉⠉⠙⠛⠓⠶⠶⠦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠙⢷⠒⠶⠤⢤⠖⠚⠲⣤⠀⠀⠉⠉⠉⠛⠒⠒⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠛⠛⠓⠶⠶⢤⣤⣄⣀⣠⡾⠋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⣄⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠤⣄⡀⠀⠈⠳⣄⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣤⣀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠙⢧⡀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⡄⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠻⣄⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⢷⡀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣀⣙⣦⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⣠⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⣴⡋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡉⠉⠻⣄⠀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡀⠛⠒⠚⠋⠀⣠⠞⠁⠀⠀⠀⣠⠖⠋⠉⠉⠉⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⡟⢈⣉⡽⢷⡾⠛⠁
⠀⠀⠀⠀⠀⠀⢰⠿⠷⢾⣟⣛⣛⠛⠛⠛⠛⠋⠀⠀⠀⠀⡼⠁⠀⢠⠖⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⠾⠛⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⠙⠛⠲⠦⠤⣤⣀⣀⢀⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⢀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠿⢦⣤⣄⣀⡀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠋⠁⠀⠀⠀⢀⣠⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⢾⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠻⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⢀⠀⣀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⢀⣤⡀⠀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⢻⡆⢸⡇⠈⠉⠉⣿⠁⠉⠉⢹⡟⠀⢀⡟⢻⡄⠀⠀⠀⠀⢠⡿⠁⠈⠃⠀⣼⠏⣿⡀⠈⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣸⡇⢸⡇⠀⠀⣸⡏⠀⠀⢀⡿⠁⠀⢸⡇⢸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠾⠋⠀⢸⡇⠀⢰⡟⠀⠀⠀⣾⠃⠀⠀⣾⣷⣶⣿⡀⠀⠀⠀⢸⣇⠀⢠⡷⢰⡿⠶⠾⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠸⠇⠀⠿⠷⠶⠀⠸⠿⠶⠦⠀⡿⠀⠀⠸⠇⠀⠀⠀⠀⠛⠶⠟⠁⠸⠇⠀⠀⠿⠀⠀⠿


⠀⠈
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣄⠀⠀⠀⠀⠀⠀⢀⢔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠓⠂⠀⠀⠐⠒⠊⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠀⠀⣠⣄⠀⠀⠘⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠤⣀⠀⠻⠟⠀⠀⠛⠛⢀⠠⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠁⠀⡀⢸⡇⢀⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠆⠀⠀⢀⠎⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠰⠦⡀⠀⠉⠉⠀⠀⡠⠾⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⠈⠀⠀⡞⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠁⠒⠒⠂⠉⠀⠀⠈⢢⠀⠀⢠⠎⠈⠂⢄⠀⠀⠀⢃⠀⠀⢃⢀⠃⠀⡜⠀⡠⠔⠊⠁⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⡀⠀⠀⠀⠉⠢⣀⠈⢆⠀⢸⡌⢀⡾⠔⠉⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠖⠀⠓⠄⠀⠀⠀⠀⢀⠆⠁⠈⠑⡘⠃⠀⠈⠑⢀⡀⠀⠀⠀⠑⠢⣆⢘⣡⠟⣁⣤⡴⢊⢁⣀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠒⠓⠳⢤⡀⣀⡔⠒⠒⠒⠒⠚⠤⢄⢀⣀⠍⠉⠉⠉⠁⠈⠀⠑⠤⡀⠀⠀⠈⠙⠿⣍⡉⠀⠀⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠈⠓⢍⡙⠐⠒⠒⠈
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⡔
⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠙⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠻⣦⣀⡀⠀⣀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⠁⠀⢣⠀⠙⠲⠴⠦⠌⠍⢛⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏
⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡉⠳⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢸⡇
⠀⡠⠒⠁⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⢀⠜⠀⠀⣀⠴⠒⠋⠉⠉⠉⠛⠲⢤⡀⣿
⡎⠀⠀⠠⠀⠀⠀⢹⠛⠓⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠁⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⡇⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠁⠀⠀⠀⠀⢣⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠸⡀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠱⣄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠙⠶⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠛⠻⠿⠶⠶⠶⠶⠖⠛⢋⣩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠑⠤⣄⣀⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠤⠤⠤⠤⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢀⠀⠀⢀⠄⠀⠀⠀⠉⡹⠛⠒⠒⠒⠚⠛⠋⠁⠀⠀⢠⣴⡟⠉⠀⠀⡀⠀⠀⣄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠦⢤⣤⣤⣤⠤⠾⢧⣖⠀⠀⠀⣠⠀⠀⠀⠀⢀⡼⠈⠉⠛⠒⠚⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠀⢀⡇
⠀⠀⠀⠀⠀⢠⠂⢀⢳⠢⡀⠀⠀⡔⠉⠑⠄⠀⠀⢀⣀⡀⠀⢈⠅
⠀⠀⠀⠀⠀⡏⠀⢠⡑⡇⠈⢢⡌⠀⠀⡠⠂⠀⠂⠁⠀⢸⠄⠋
⠀⠀⠀⠀⢰⢗⠀⠀⣑⠤⠄⠀⠑⠤⠀⠦⢐⠉⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠈⣀⠖⣉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠊⠁⢀⠄⠂⠀⠀⡆
⡤⡀⠀⠠⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠷⣂⠀⠀⠀⡇
⢃⠉⠀⠀⢴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢨⠊⠁⠀⠀⣸⡃
⠀⠀⠀⠀⢠⠰⣿⡄⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠰⡀⠀⢀⠔⡑
⠀⢢⠀⣒⡦⡙⠛⠃⠀⠀⠀⠀⠔⢋⣽⣿⣿⠂⠀⠀⠀⠈⠂⠄⠄⡀
⠀⠀⢳⡒⠚⠻⡆⠀⡠⠀⠀⠀⠠⠤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⢘⣲⠄
⠀⠀⠀⠑⢄⠀⠐⠒⠦⡄⠀⠼⢅⡒⠬⢍⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠈⠓⢄⡐⠀⠀⠀⠀⠀⠉⠢⡀⠁⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠰⡶⠀⢌⡐⠀⠀⢀⡴⠊⠁⠉⠲⡐⠈⠁
⠀⠀⠀⠀⡘⠀⠀⠀⠈⠁⠀⡞
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⢀
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠔⠁⠋⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⡌⠢⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡈⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⣊⠄⡀⠀⠀⢠⠀⠀⠀⠘⡁⠀⠑⠄⠀⠀⡠⠃⠀⠀⢀⣀⣀⠠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠆⠊⠀⠀⠀⠀⠘⡄⠤⠠⠜⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠈⠻⢷⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢆⣤⠹⢗⢀⡘⠿⡖⠿⢁⡀⢀⡇⢶⡄⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⢹⠋⣀⠘⣼⢟⡔⢱⡶⣸⡿⠀⢹⠀⣄⣀⠈⢻⣧⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⡉⠀⢐⠛⢷⠛⢆⣸⡟⠀⠀⣠⠻⡆⠻⢻⡷⠙⣣⣤⡆⢈⡉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⣼⡾⢾⡟⠈⢛⣷⠀⡟⢋⡔⠐⣿⢫⣧⡦⢈⢻⡇⢘⡟⠐⡿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠈⠙⡁⠙⢷⣾⠺⢃⣴⣿⣾⡟⢫⣤⡀⠀⣸⡇⠀⠻⣷⡷⢻⣿⡍⠀⣬⢩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠷⣄⠙⣆⣴⠝⣷⣄⢰⡄⢻⣧⠀⣉⢡⢠⣿⣧⣶⠟⠋⠀⣶⠏⢡⣌⠛⢉⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡝⢻⣷⣶⣾⣿⣿⣦⣈⣿⣾⠟⢸⣿⡿⠋⠁⢾⡇⡀⣶⠆⣈⡿⠻⠷⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠺⢻⡇⠀⠀⢠⡄⠛⠻⣿⣿⣿⣿⣿⣿⣷⣴⣶⠟⠛⠛⠻⢿⣉⢠⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⢧⠀⠀⠀⠀⠀⠙⣆⠀⠒⠂⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠄⠂⠀⢸⡄⠀⠀⠀⠀⠀⠈⢷⡒⠒⣲⠏
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠛⠶⣄⠀⣠⡤⢤⡀⠈⢦⡀⠀⣠⡼⠋⢹⡆⠀⠀⢀⡀⠀⠻⣴⠃⠀⠀⠀⢰⡟⠛⠛⠳⠦⣄⡀
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⠓⠿⠀⠀⠙⢧⣠⡽⢋⠉⠓⠧⣼⡇⠀⢀⡟⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⣨⡿
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⢸⣇⢀⡞⠠⡀⠀⠙⣦⠀⠀⠀⠀⠈⡿⠙⠓⣦⡾⠋
⠀⠀⢀⣠⡤⠶⠾⠷⡄⠀⠈⠀⠀⠀⢉⣲⣤⢤⣀⣀⣀⣉⠛⠛⠋⠉⠉⠙⠓⠦⣀⣀⣀⣈⣷⣤⣀⡀⠀⢳⣰⡶⠋
⠀⢠⡟⠁⠀⠀⠀⠀⠀⣠⢤⡴⠒⠋⠉⠀⠀⢸⠀⠀⡴⠿⡍⣩⡝⠒⡒⠶⠤⢤⣀⣉⣉⣁⡀⠀⠈⠙⢶⣌⠉
⠀⢸⠀⠀⠀⠀⠀⠀⣰⠃⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⢹⠇⡇⡜⢉⡙⣇⡴⠒⢲⢠⣍⠉⣉⠉⠉⠉⠙⠛⠛⢻⡆
⠀⠈⢧⣀⣀⣀⡴⠞⠁⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⣷⡀⠀⣿⠃⢛⠁⣿⠀⣴⡋⢸⠸⠼⠉⣧⠖⠛⠳⡄⠀⢸⠃
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠁⠉⠛⠙⠒⠚⠳⠾⣄⣀⡹⡇⣸⢳⠀⣟⠐⠿⠂⣹⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⠶⠒⠛⠛⠉⠉⠉⠉⠛⠓⠒⠶⠶⠤⠤⣤⣤⣉⣁⣉⡁⠉⠛⠉⠲⠶⠖⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠒⠶⠶⠦⠤⣤⣤⣄⣀⡀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠒⣲⣶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠲⠶⠶⠶⠖⠋⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡄⣀⣤
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣷⡄
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢛⣽⣿⣿⣿⣿⣯⣯⣿⣽⣿⠹⠘⣿⣆⣿⡏⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠃⠉⠛⠉⠛⠓⠈⠉⠁⠛⠘⠒⠃⠿⠋⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠘⠛⢿⣦⠀⠀⠀⠀⠀⠀⣿⡟⣿⡄⣠⣾⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⠄⠀⠀⠀⠈⣿⣆⠀⣀⣤⣤⣤⣿⣧⣿⣿⠟⣁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⣥⣭⣽⣿⡟⠛⣿⣿⣯⣤⣤
⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⣶⣾⡟⠛⠛⠛⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠁⠀⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⣄⠈⠁⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡇⠀⣤⣶⣤⣈⡉
⠀⠀⠀⠀⠀⢸⣿⣿⠟⢿⠿⠻⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⠁⠀⠙⠻⠛⠻⠿
⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⣀⣼⡇⠀⠀⠘⢿⣿⣿⣟⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⡆⠀⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⢿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠀⠀⡈⠉⢁⣤⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⡇⠀⠀⢸⣿⣿⡀⠙⠋⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠿⠇⠀⣿⠟⠻⢿⣿
⠀⠀⠀⠀⠀⢸⣯⡀⠉⠀⣸⣿⡇⠀⠀⠈⢻⣿⣿⣶⣾⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢉⣀⣤⣤⡀⠀⣀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠸⠿⠿⠷⠾⠿⠿⠇⠀⠀⠰⠿⠿⠿⠿⠿⠧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣦⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⣠⣾⠇⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣿⣿⣼⣿⣶⡿⠟
⠀⢠⡲⣦⡀⢰⣿⣵⡿⢛⣉⡀⢀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣶⢿⡟⣻⣿⣿⡿⢷⣦⡀
⠀⠘⣷⡜⣿⣿⣿⣿⣿⣌⢿⣿⣌⢻⣿⣷⡝⢿⣿⣷⡜⢿⣿⣷⣜⢿⣿⡆⠀⠰⣾⣷⡌⠀⠀⠀⠉⢀⣾⣿⣿⣿⣿⣿⣀⠉⠛⠂
⠀⠀⢘⣿⡘⣿⣿⣧⠹⣿⣎⢻⣿⣧⡙⣿⣿⣦⡻⣿⣿⣎⢻⣿⣿⣦⠻⣿⡇⢷⣝⢿⣿⣆⠀⠀⢀⣾⡿⢿⣿⣿⣉⣿⣿⣧
⠀⠀⢤⡙⣧⢹⠟⣿⣷⡹⣿⣧⠹⣿⣿⣌⢿⣿⣷⣜⢿⣿⣧⡹⣿⣿⣷⣼⣿⡘⣿⣷⣬⡛⠀⠀⢼⣿⣿⣾⣿⣿⣿⣿⣿⣯⣤⡀
⠀⠀⠀⣿⡜⠀⠀⠙⠿⠷⠹⠿⠷⠙⠿⠿⠦⠻⠿⠿⠦⠻⠿⠷⠌⠿⠿⣿⣿⣧⠹⢿⣿⡇⠀⠐⠒⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠃
⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣹⡿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠤⠤⠤⣤⣄⠀⠀⡠⠤⠶⠒⢶⡀
⠀⠀⠀⣴⠛⠛⠓⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢸⠇
⠀⠀⠀⢹⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠶⠒⢀⣀⣤⡤⠤⠼⣧
⠀⠀⠀⠠⢤⡧⠤⠤⣤⣤⣉⣉⡃⠀⠰⣯⠆⠀⣠⣖⣚⣩⣥⣤⣤⣤⣤⣿⡀
⠀⠀⠠⠤⢾⡗⠒⠒⢒⣒⣒⣲⣿⡖⢀⡼⢆⣈⣹⠟⠒⠒⠒⠲⠶⠶⢤⡯⡀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠼⢷⠚⠋⠉⠉⠀⠀⠈⠉⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣶⣶⣶⣄⡠⢄⣀⠠⡴⠾⠋⠉⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⢀⣀⠄⣂⣩⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡻⣿⣿⡾⠁⠀⣴⣦⠀⠀⣀⡀⠰⣿⣷⣦⠀⠀⠉⠻⡏⢱⣿⣿⣿⣿⣷⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢿⣿⣿⣿⠷⠆⠀⠀⠀⠉⠁⠀⠀⠿⠃⠀⠀⠉⠁⠀⠀⣴⣤⡀⠚⣛⣶⣾⣿⣿⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣿⣿⠃⠀⠀⣀⠀⣠⡄⠀⢠⣄⠀⣠⣄⠀⠀⠀⢀⣀⡈⠛⠃⠀⠈⠈⢷⣿⣏⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⣠⡾⠿⢶⣿⣷⠀⠀⠛⠀⠛⠃⠀⣴⣾⠟⠛⠻⣷⣦⡀⠀⠀⠀⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠉⣴⣾⣂⡉⡛⠀⠀⠀⠀⠀⠀⠀⠙⣁⣸⣭⣥⣄⡙⢛⠦⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠞⣿⠹⣿⡿⢿⡆⠀⠀⠀⠀⠀⡞⣼⠛⣿⣿⠄⡛⢛⡛⠻⣶⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢤⠙⠦⠀⠠⢊⠀⠀⠀⠀⠀⢀⢠⣍⠓⠀⠀⠀⣡⣾⣷⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡈⠷⣶⠖⣠⢟⡄⠀⠀⠀⠀⠈⠣⠙⢄⠀⠈⠉⠛⠋⠁⠀⠀⠉⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⡙⠶⠁⣰⣯⡞⠀⠀⠀⠀⠀⢀⠀⡀⠘⣷⡄⢀⣠⣤⣤⠟⣸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠟⢻⣾⣤⣀⣀⣀⣀⣨⣁⣿⣿⠿⠁⠙⠛⠉⣁⡼⠋⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⡀⠀⠀⠈⠫⣤⡈⠁⣠⡶⠋⠁⠀⠀⡀⣰⣾⣿⠋⠀⣸⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡦⢳⠲⠦⠀⠀⠀⠁⣶⡈⠀⠀⠀⠀⠈⠀⡟⠸⠿⠟⠀⠋⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠁⠈⠲⡃⠀⢀⣠⠞⠋⠛⠲⣤⣀⣐⣀⣼⠇⠀⠀⠀⠀⢸⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⡀⠻⠀⠀⣈⠛⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿⢁⣴⡄⢀⡀⠀⠀⠉⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠛⠀⠀⠀⡴⠻⠆⠉⠛⠶⠶⠖⠀⠶⠞⠫⠞⠀⠀⢹⠛⠳⠀⠀⠀⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⢠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠀⠀⠀⠙⠻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡉⠀⠀⠀⠀⠞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡖⠀⠀⠀⠐⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢴⠟⠀⡔⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⣧⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠉⠀⠀⠀⠠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣧⠀⠀⠀⠀⠀⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⠶⠶⠶⠖⠛⠛⠶⣤⣀
⣤⣶⣶⣿⣟⣛⡛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡴⠿⢿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠉⠉⠛⣻⣷⣶⡖⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⢦⣍⠉⠛⠳⣦⣀
⠀⠀⠀⢀⣠⡶⠟⠋⣠⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠳⣦⣀⠀⠙⠳⣦⣀
⠀⠀⠀⠻⣧⡀⠘⢠⠇⠇⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⣡⣾⠆⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡶⠾⠿⣶⣦⣤⣤⣤⣙⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⢻⣤⣥⣤⡴⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⢀⡤⣠⠆⠹⣧⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢰⡙⢷⣄⠀⠀⣠⡾⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⢣⠖⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠸⠌⣇⠀⠙⢷⡾⠋⠀⢸⡇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⣀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⢿⣄⣀⣠⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠋⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⣄⠀⣿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢳⠹⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⠏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡼⢡⠆⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣼⡇

⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠲⠒⢶⣶⣄⠀⠀⠐⠺⠿⠿⠶⠀⠀⠒⠤⣀⡀
⠀⠀⠀⢸⡌⠙⠷⣶⣶⠆⠐⠘⠉⠁⠰⠖⠘⠃⠀⢀⣈⣩⣥⠴⠒⠀⢦⠉⠁⢠⣤⣀⡀⠐⠮⠳⣄
⠀⠀⠀⠀⠻⣄⠀⣨⡝⠛⣠⡖⠀⣀⠀⠶⠀⠀⠀⠺⠟⢫⣷⡤⣀⣦⣿⠃⠀⠙⢿⠿⠟
⠀⠀⠀⠀⠀⠀⠱⣄⢋⡄⠉⠀⠀⠋⢀⡀⠰⠟⠖⠀⠀⢈⡉⠾⢏⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠏⠴⠛⠻⠿⣴⡟⠋⠲⣦⠛⠂⠀⠀⣷⡄⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡢⢾⣿⠺⠆⢸⠁⠘⠃⡰⣶⡤⠀⠀⢸⡇⢿⡇⣾⣷⣦⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣤⣾⡏⠀⠘⡁⠸⠀⢰⣷⣈⡁⠀⠀⢸⣇⡜⠀⠻⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⢰⣯⡙⣳⡀⠀⡇⠀⠀⣸⡿⠟⢹⣇⠀⠘⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⢘⠁⠀⠀⠀⢀⠛⠋⠠⠾⡏⣀⠈⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠟⠀⠀⠀⠀⠘⠆⠀⠀⣠⠺⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠀⣴⡀⠀⣰⡟⠀⢀⣄⠀⠀⠀⢀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣦⠀⠀⠀⠀⠼⢃⠴⡿⠃⠀⢸⣿⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⣴⣀⣀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⢄⣀
⠀⠀⠀⠀⠀⠀⢠⠒⠛⢳⡟⠛⠒⡄⠀⠀⠀⠀⠀⢰⠒⠛⢺⡟⠛⠒⡆⠀⠀⠀⠀⠀⢠⣿⣾⣾⣯⣾⣤
⠀⠀⠀⠀⠀⠀⠈⠛⠁⢹⡏⠉⠋⠁⠀⠀⠀⠀⠀⠈⢹⣭⣽⣯⣭⡏⠁⠀⠀⠀⠀⠀⠈⡏⠁⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣸⣇⣀⡄⠀⠀⠀⠀⠀⠀⠀⣇⣀⣿⣀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣾⣯⣤⠀⠀⠀⠀⠀⠀⠀⣤⣽⣷⣾⣯⣥⠀⠀⠀⠀⠀⠀⢠⣬⣶⣿⣶⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡟⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠛⠛


⠀⠀⠀⠀⠀⠀⢀⡀⠤⡐⢒⠤⢀⠀⠀⠀⠀⠀⠀⠀⡀⣖⢦⡴⣲⢀⠀⠀⠀⠀⠀⠀⢀⠠⣶⣶⡶⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠖⠿⢢⠔⠿⠚⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⡅⠀⠸⠁⠀⠀⠀⠀⠀⠸⢴⡟⣩⠙⡦⠝
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢸⠂⢨⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠀⠁



⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⢨⠉⠙⢍⢉⡲⠤⠒⠒⠒⠒⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⢣⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢎⠉⠉⣉⢱⡄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠚⠉⠀⠀⠀⠀⠒⠀⠀⠀⠈⣦⠊⢀⠞
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠒⠓⠄⠀⠀⠔⠓⢄⠀⠀⠀⢸⠖⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡰⡀⠀⠀⢠⣀⡲⠀⠀⠀⢀⢀⡴⠁⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣸
⠰⡖⠶⠒⣒⠐⠠⣴⡥⠴⠛⠓⠲⠴⠋⠤⠤⢤⡖⠛⠉⢀⣰⣀⣀⣀⣙⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡞⠁
⠀⠙⣄⠀⢀⡵⠊⠁⠀⢀⡠⠔⠀⠀⣀⠀⠀⠀⠉⠳⣎⠉⡀⠄⠀⠂⠉⡽⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠇
⠀⠀⠈⢣⠎⠀⠀⠀⣀⣤⣀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠈⢣⠀⠀⠀⣠⢞⠀⠤⠤⠼⠦⠤⢤⣀⣀⠀⠀⠀⠀⣸⠃⣼
⠀⠀⠀⡼⠀⠀⠀⠐⠁⠀⠈⠇⠀⠀⡴⠋⠉⠳⡄⠀⠀⠀⣇⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡚⠁⣠⠏
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁
⠀⠀⠀⠘⣆⠀⡼⠓⠀⠀⠀⢄⠐⠀⢀⠀⠀⢀⡀⠀⠀⢠⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣸⠈⠢⣧⡀⠀⠀⠀⠀⡓⠋⠁⠀⠀⠀⢹⠀⣠⠋⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⠒⠦⠀⠀⠈⢧
⡔⠉⠁⠸⣀⣄⠨⠛⠦⣤⡤⠚⠹⣄⠀⠀⠀⣠⣮⠚⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢧⡀⠀⠉⠒⠒⠂⠐⠈⢉⣫⢉⠴⠦⢟⣋⣻⡉⢀⡠⠞⠁⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠙⠒⠤⠤⠤⣀⡀⠀⢬⣼⢝⡒⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠓⠤⠤⣤⣀⣤⠤⠤⠤⠔⠒⠉⠓⠢⠤⢄⣀⣀⢔⡒⠐⠒⠂⠤⣳⡄⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⡴⠚⠉⠉⠉⠒⠒⠤⢄⣀⠉⢻⣠⡆⠀⣰⡀⠀⠉⠒⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣈⠉⠁⠈⠙⠲⠤⣄⣀⣸⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢄⣀⣀⣀⣀⡠⠔⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠈⠙⠛⠛⠛⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⣿⣿⣿⠀⠘⠃⠀⢠⡆⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⣷⣶⠶⣶⡿⠗⠀⠀⠀⠀⣤⣶⠶⠄
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⠿⠟⠋⠉⣀⣤⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣔⣣⣿⠀⠀⠀⠀⠀⣸⡟
⣿⣿⣿⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⣠⣤⣤⣤⣴⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⡏⢀⣿⠀⢿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢻⣯⠉⠉⣿⡟⢻⣧⡀
⣿⣿⣿⣿⣿⠏⢀⣼⣿⡄⠘⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣦⣀⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠙⠃⠀⠛⠁⠀⠙⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿
⢀⣀⡀⢘⣿⣷⣦⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣿⣿⣿⠟⠋⠉⠉⠉⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠈⢻⣿⣿⣿⠙⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠀⠈⠿⠿⠿⠿⠿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠠⠄⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣸⣿⡏⠀⣿⣿⡇⠀⠀⠀⢸⣿⠟⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠈⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠿⠋⠀⠀⠘⣿⡇⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡀⠀⣀⣀⣀⣀⠀⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣴⣿⣿⣿⣿⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⣉⡻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠒⠛⠓⠲⠦⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠤⠶⠖⠚⠋⠉⠉⣀⣀⠠⠤⢖⡂⠘⠓⠲⢥⣤⣀⡉⠉⠉⢛⡛⠒⠒⠶⠶⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⣶⠿⣿⡯⠭⠭⠭⠤⠤⢤⣶⣔⠓⠒⠲⢍⡁⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⢄⡀⠉⠝⠛⠒⠲⠦⠤⣄⣀⣀⣠⠀⠤⠤⣬⣽⣦
⠀⠀⠀⠀⡏⠣⡀⠈⠙⠲⠤⣄⡀⠀⠀⠙⠛⠶⢤⣀⠈⠑⠲⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡲⠤⠴⠒⠚⠉⢉⣀⠠⠤⠖⠒⠋⢉⡞⡟
⠀⠀⠀⠀⡗⠀⠱⣤⢤⣀⠀⠀⠉⠙⠒⠤⣀⡀⠀⠈⠉⠓⠦⣀⣀⣉⡱⠦⠔⠒⠚⠉⠉⠀⣀⣀⠤⠖⠚⠉⠁⠀⠀⠀⣀⠀⢀⡞⠀⡇
⠀⠀⠀⠀⢧⠀⠀⣿⠀⠀⠉⢱⠢⢤⣀⠀⠀⠉⠙⠒⠤⣄⣀⡀⠹⡄⠀⢀⣀⡤⠤⠒⠚⠉⠁⠀⠀⠀⠀⠈⠁⠀⣀⣀⣠⣤⠎⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⢻⠀⠀⠀⢸⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠈⠉⢙⣷⢾⡉⠀⠀⠀⣀⣀⣤⠤⠤⠶⠒⠒⠊⠉⠉⡏⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠒⠦⡴⠋⠀⠀⠙⡶⠒⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠈⡇⠈⠸⡄⠀⡄⠀⡆⠐⠀⡄⠀⢸⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠁⠂⠀⢸⠀⠃⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠐⠀⠀⠀⢸⠀⢰⠀⡆⠀⢹⠀⠀⠀⠀⡆⢠⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⢠⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠘⠀⠀⡇⠀⡇⠈⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⠀⠐⠀⡇
⠀⠀⠀⠀⠀⣷⠈⠀⣿⠀⠀⠀⠃⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠠⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⡇⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⠁⠀⢀⠀⠀⠃⠀⠀⠀⢠⠼⡇⠀⢸⠠⠀⠀⣧
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⢧⡀⡞⠁⢸⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⡀⢀⠜⠲⢄⡀⢸⠀⠀⠀⠀⣀⣀⠴⢶⠀⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⣧⠤⠾⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣷⠃⠀⠀⠀⠈⠙⠢⢄⣀⠀⢿⠈⡇⢰⡷⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⢰⠀⠀⢀⣀⣸⠤⠔⠒⠋⢉⠀⠀⠀⠈⠳⡄⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣐⠂⠀⠀⠀⠈⠉⠚⠤⣈⠙⡇⢀⡇⠀⠀⡇⠀⣃⣀⣠⠤⠞⠚⠉⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⣨⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠁⠀⠀⠀⠉⠓⢤⠃⠀⠀⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢢⠀⢰⠀⡼⠀⠀⠀⠀⠐⠊⠁⣀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⢣⠸⡴⠁⠀⢀⣀⡤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣿⡷⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⢿⣾⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠁⠈⠛⠿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣾⣷⣦⣿⡇
⠀⠀⠀⠀⠀⠀⣰⣾⠋⠀⢋⣿⣿⡙⠂⠉⢿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⣿⣿⣿⣿⣶⣤⣾⣿⣷
⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⣶⣾⣿⣿⣶⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⣾⣷⣿⣶
⠀⠙⢿⣿⣿⠟⠀⠛⢸⣿⣿⣿⣿⣿⣿⣿⠘⠃⠹⢿⣿⡿⠏
⠀⠀⠀⢹⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡟
⠀⠀⠀⢸⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣾⡇
⠀⠀⠀⠀⢻⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⡿⠁⢀⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⡟⠁⣀⡀⠈⢻⣧
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⠀⢰⣿⡃⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⣿⣇⠀⠛⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⠿⠟⠋⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣶⡿⠛⠁

⣿⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣽⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⢠⣄⣦⣷⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣧⣿⣿⣿⣿⡿⢣⠀⠀⠐⠀⠲⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢲⠀⡙⠂⠀⠀⠀⠐⠄⠀⠀⠛⢠⣿⣿⡿⢻⢁⢣⣏⠀⠀⠀⠰⠀⠸⠿⡉⠀⡈⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠧⡆⠉⠉⠑⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠉⠉⠠⡦⠘⠃⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⠉
⠈⠓⢀⢰⠠⠈⠂⠉⠈⠀⠀⠀⠰⠐⡇⠘⠂⡐
⠀⠀⠀⠉⠁⠀⠀⡦⣘⠦⠤⠄⠒⠤⠇⠀⢋⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠤⠇⠀⠴⠘⡿⠦⡀⠀⠀⠀⡰⠀⠀⠈⣆⡀⠀⠀⠘⣮⣽⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣴⡀⣈⡶⠄⠐⠳⠦⠄⠀⠉⠉⠁⠀⠈⠀⡉⠜⢿⣿⣶⣄⠀⠀⠀⠀⠴⠟⠛⠿⠟⢃⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠚⠊⠉
⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⢀⣠⣤⣄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⣻⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠻⠿⣿⡿⡻⢿⣝⠋
⠀⠀⠐⠴⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⢻⡿⠿⠿⠟⣛⠀⠀⠀⠀⠀⠀⠐⠋⢀⣨⣠⣀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠋⠂
⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡤⡈⠂⠀⠀⠀⠀⠀⠀⠀⡀⠔⡨⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣔⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⢰⠇⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠒⣑⢤
⠀⠀⠀⠀⠀⠀⢀⡱⢫⣤⠀⠀⠀⠘⠀⢠⡄⠀⢀⠀⢁⡀⠑⠈⠀⢀⡄⣠⡶⠀⠃⠀⡠⠀⠀⠉⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠈⠠⠁⠀⠀⠀⠀⠀⢸⡇⠀⣿⣴⡏⢸⡇⣾⣇⡞⡇⣿⠀⠀⠆⠈⠀⡀⠊⠀⠀⠀⠀⢀⠔⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠁⠀⣿⣁⣠⡟⣿⠀⢸⡇⣿⠙⢸⡇⣿⠒⠀⠀⠠⠊⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢿⠁⠸⡇⠻⣄⠼⠁⡿⠀⠸⡃⠙⢋⠀⣰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡦⠀⢠⠀⢀⢶⢰⢰⠋⢸⢹⠀⡏⠀⠘⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣧⠀⢸⡀⣾⢸⣸⢺⡄⢸⣏⠀⣷⠀⠘⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠈⠉⠀⠈⠟⠋⠸⠘⠎⢁⣈⣀⣤⣤⠄⠐⠀⠀⠀⠀⠀⡌⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠘⣰⡎⡅⠀⠀⠀⣛⠉⠉⣿⡅⠀⠀⠀⡆⠀⠀⠀⡜⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⣁⣃⠀⢠⡞⣿⡄⠀⣿⡇⠐⢂⣤⠀⠀⡠⠊⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣸⡇⠘⠃⢸⠁⢹⣇⠀⢻⡇⢸⡇⢳⣈⡭⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡇⠀⠀⢸⡆⢘⣿⠀⢸⣿⠀⢧⠠⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠸⣿⠀⠀⠘⣟⠉⠻⠇⠀⡩⠴⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠘⡇⡙⠠⠐⠊⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠋⠁⠐⡄⠀⠀⠀⠀⠀⠀⠢⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠳⢦⣤⠤⠶⠶⠶⠶⠤⣤⣀⣤⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⣧⠀⠀⠀⡿⠀⢠⢲⣶⣶⣦⡀⠀⠀⢀⣴⣾⡿⢦⢢⢹
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡴⠃⠀⠰⢶⡧⠤⠰⣿⣿⣷⣼⡻⠀⠀⢪⣿⣿⣷⣿⠎⢸⣇⡀
⠀⠀⠀⣼⠁⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣟⣫⠄⠈⠙⠛⠉⠀⣀⣀⡀⠈⠉⠉⠁⠩⢽⣯⡅
⠀⠀⠀⡇⠀⠀⢠⠇⠀⢀⣠⡤⠤⠶⠖⠒⠒⠒⠒⠛⠉⢛⡿⣦⡀⠀⠀⠀⠀⠠⢌⣍⣡⠄⠀⠀⠀⢛⡾⠦⠄
⠀⠀⠀⢳⠀⠀⠘⣆⡔⠋⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠉⠓⠲⠶⠶⠤⠤⠤⠤⠤⠴⠖⠚⠛⢦
⠀⠀⠀⠈⢣⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢠⠶⢖⣛⡏⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠠⡄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡴⠃⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣧⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣠⠤⠤⣤⣤⣤⠤⠞⠉⠑⣄
⠾⣁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠈⣧⠀⢀⣸⡄⠀⢀⠀⠀⢳⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢣
⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡖⠒⠛⠉⠉⠁⠳⣄⠀⠀⠀⣸⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⡴⠒⠋⠉
⠀⠀⠀⠀⣯⠙⠲⢄⡀⠀⠀⠀⢀⡴⠉⡿⡄⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⢀⣀⣤⠤⠖⠒⠋⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠸⣂⠀⠀⠉⠳⢤⣰⠋⠀⠀⡇⢱⡀⠀⠀⠀⣀⣀⡤⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇
⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠳⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠠⡇⠀⢀⣀⣤⠤⠖⠚⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⢒⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠊⡃⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢀⠀⠇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣿⣉⣭⠛⠾⠖⠒⠂⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠰⣦⠴⠶⠒⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⢠⡇⢀⠀⡶⠖⠂⠂⠒⠒⠒⢂⣈⡉⡍⠽⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⣱⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠘⡤⠤⢤⠀⠤⠠⠠⠄⡀⣀⣀⣀⣐⣗⣀⣥⣧⣼⡀⡇⢠⡤⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡖⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠠⢀⡀⠀⣀⣀⠄⠴⠒⠊⠉⠁⣷⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠤⠂⠒⠒⠋⠩⢻⠀⠀⠀⢸⢃⠎⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠄⠀⠀⠀⠀⠀⣏⡇⢸⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠨⠀⠀⠀⢸⠅⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠆⠀⠀⢸⢀⡮⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠂⢀⠀⠀⠀⠀⣸⠑⠀⠀⢨⣮⣵⡷⢶⠶⠦
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠧⡷⢀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⢼⠀⠴⠂⠚⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⣀⣠⠼⠗⠀⢓⠌⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⢀⣀⣤⡶⠚⠋⠫⠤⠀⠀⠁⠀⠀⠈⠑⠄⡀⠀⠇⠀⠀⣀⣀⣠⣤⣤⠴⠖⠚⠛⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠛⠻⠛⠫⠿⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⢈⡂⠤⠀⠐⠒⠒⠂⠀⠤⠀⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⡌⠀⠀⡀⠄⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠊⠀⡠⠄⠠⢄⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦⠀⠀⠀⠀⢰⣷⠄⠀⠈⠀⠆⠀⡌⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣦⠀⠀⠈⠀⠀⢸⡇⠀⠀⠁⠀⠀⣴⣾⠤⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠒⠀⠄⠄⠘⠠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⡠⠒⠈⠁⠀⠀⠈⠁⠒⢄⠀⠀⠁⠃⠀⠁⠈⠐⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠋⠂⢄⠀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢨⡆⠀⢠
⠀⠀⠀⠀⢀⡀⠀⡔⠐⡒⠣⡀⠀⡰⠀⠀⢀⢶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⢸⡀
⠀⠀⡔⠪⡀⠈⠢⡇⠀⡇⠀⠄⢠⠃⠀⠀⡸⠼⢀⣘⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡂⣀⡇⠠⠔⢺
⠀⠀⠑⢄⠀⠑⠄⠱⠀⠇⠰⢀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠉⠉⠀⠘⠁⠉⠈⠃⠉⠈⠉⠀⠀⠀⠀⠀⢸
⡄⠒⠀⠠⠅⣦⣈⠢⣡⣢⢃⠂⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡏⠐⠀⠀⠠⠤⠬⣵⡿⠩⠃⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠐⠒⡠⠜⡑⡳⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢤⠀⠒⠁⡠⠊⠔⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡘⠑⠐⠊⢠⠊⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠁⠀⢀⠔⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣀⠔⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠊
⣀⣀⣁⣢⣤⣒⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡶⠚⠛⠳⠟⠁⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⢀⡴⠄⠀⠀⠐⠀⠀⠀⠘⠿⣧
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠙⠚⠛⠀⠞⠛⠳⡆⠀⠀⠙⣷
⣀⣀⣠⣤⣤⢤⡾⠁⠀⠖⣦⡀⢀⣠⣤⡀⠀⠀⠀⢀⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢶
⣿⠉⠀⠀⠀⠈⠁⠀⠀⠜⠉⠱⣋⣀⣼⡇⠀⠀⣠⠞⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠹⣦⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠉⠉⢹⠖⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⢀
⠀⠙⠳⣦⡉⠀⠀⠠⠺⡀⠀⠀⠀⠀⠀⡼⠀⣠⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢀⡾
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣄⣠⡤⠞⠳⠞⠋⠄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠢⣄⣀⣰⠟⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣽⠏
⠀⠀⠀⠀⠀⠙⠿⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠁⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⣿⢦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⡟⠛⠛⠛⠉⠁⠀⠀⣀⡴⠋⠈⢿⡄⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣀⡤⠔⠊⠁⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⢻⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠁⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⢻⡄⠀⠀⠀⠘⣟⠓⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣼⡆⠀⣇⣠⢾⡄⢹⡄⠀⠀⢀⠞⣷⠀⠀⠀⠀⢻⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⠀⣿⠀⠀⢷⠀⣧⣤⠔⠋⠀⢻⡄⠀⠀⠀⠘⡗⠒⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠳⡀⣿⠲⣿⠀⢸⠒⠒⢻⡄⢹⠀⠀⣀⣠⣼⣇⠀⠀⠀⠀⣿⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢱⣽⠀⣿⠀⢸⠀⠀⠘⡇⢸⣆⡼⠋⠁⠀⠉⠳⣄⠀⠀⢸⣄⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⠒⣿⠀⢸⠦⠤⠴⡇⢸⣿⠃⠀⠀⠀⠀⠀⢹⡄⠀⢸⡏⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢫⡀⣿⠀⣾⠀⠀⢠⡇⢸⣿⡀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⡟⠀⣿⠀⠀⢸⡇⢸⡛⣇⠀⠀⠀⠀⠀⠀⣿⣀⠞⠙⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢰⡇⢠⡏⠉⠉⣹⠀⣼⠉⢹⡄⠀⠀⠀⠀⢠⠟⣏⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣆⠀⡾⠀⢸⠁⠀⠀⡿⠀⣿⠀⠀⢻⡄⠀⠀⠀⠸⡀⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣀⣬⠿⠃⢀⡏⣀⣤⠼⠷⠶⠷⠴⠤⠤⠿⠀⠀⠀⠙⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⣠⠀⡀⢸⡿⡁⠀⢀⣀⣤⣤⡤⠤⠤⠤⠤⠤⢤⣤⠟
⣤⣄⣤⣤⣠⣤⣤⣤⣤⣤⣠⣤⣤⣤⣍⣍⣉⣩⣽⣷⣶⣏⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠤⢌⣑⠤⠐⠒⠂⠀⠀⠐⠒⠚⠤⡊⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠁⠀⠀⢠⠴⢤⠀⠀⢠⠴⠤⡀⠀⠀⠐⠒⠚⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠐⡔⠀⡀⠀⠀⠀⠀⠒⠒⢰⠂⠄⠀⡰⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠑⡀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠐⠠⣤⡃⠀⠀⢀⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⣀⣀⠀⠀⠀⣀⣀⠀⠠⠰⡈⠀⠈⢁⠠⠊⢀⠌
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⡜⠁⣤⣊⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠁⠸⠘⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⣎⣀⣀⣀⣀⣀⣀⣠⣀⣠⠊⠉⠈⠑⣄⣀⣀⣀⡠⠊⠁⠈⠐⣀⣸⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠚⠒⠒⠋⠁⠀⠀⠀⠈⠈⠒⠚⠉⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠙⡄⠀⠀⠀⠀⠀⢠⠞⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢹⡀⠀⠀⠀⣰⠋⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⠀⠀⠐⠚⠓⠒⠒⠒⠓⠆⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⣠⠞⠛⠛⢶⡄⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⠟⠒⠚⠛⠛⠻⡆⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⣳⣾⣏⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣀⠀⠁⠀⠀⠀⢀⣀⣠⠴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣶⡌⠉⢻⡋⠉⠙⠓⠲⠶⠒⠚⠉⠉⠉⠻⠿⠛⠉⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣮⠟⠿⠯⣥⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣼⡥⠎⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⠉⠉⠉⠯⠽⣫⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⣇⠘⠯⠃⠀⣞⡦⠸⣽⠆⢉⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠦⢴⣶⣒⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠤⠤⣤⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠻⣿⣿⣦⡴⠶⠶⠤⠤⢤⣾⣶⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⠟⣷⣦⣴⣾⠻⣿⣿⣦⡀⠀⢀⣴⡿⠋⡤⢤⠙⢿⣶⡤⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠔⢋⣵⣿⣿⠟⠁⠀⣭⣭⣭⣭⠀⠈⠻⣿⣿⣶⡿⠋⠀⠀⠛⠛⠀⠀⠙⢿⣦⡈⠐
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡿⢠⡿⠉⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡿⠈⠿⣤⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠠⡀⢀⡀⡄⠀⡀⢠⠀⢠⠀⡄⡄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⡁⠈⠀⠀⠀⠈⠀⢁⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




⣿⡿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠙⢶⣄⣀⣀⣀⣀⣀⣀⡴⠟⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠘⣆
⢀⣀⣀⣀⣀⣀⡾⠀⠀⠀⠀⠀⢰⣤⣿⣿⡄⠀⠀⠀⠀⠀⣄⣼⣿⣇⠀⠀⠀⠀⢹⡆⠀⣀⣀⣀⣀⣀
⠛⠛⠛⠿⣿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⠻⠃⠀⠀⠀⠀⠀⣿⣿⡟⠏⠀⠀⠀⠀⠀⠙⢿⡿⠿⠟⠛⠛⠃
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠐⠛⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠟⠐⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⠆
⠀⠀⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣄⡀
⠰⡿⠟⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠛⠿⡷⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⣾⠁⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠙⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡟
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠶⠚⠋⠀⠀⠀⣰⠏
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠚⠋⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⢄⣤⣤⣤⣤⣴⢷⣤⣤⣤⢤⡤⠾⢦⣤⣤⣴⣤⡴⣦⣤⣤⣤⣤⣤⠞
⣿⣿⠟⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠛⠻⠷⣤⣀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⡠⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⡎⠀⣶⣶⡇⠀⠀⠀⣠⠖⠒⢦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⠟⠁⠀⠀⢰⡅⢴⣷⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠀⠀⠀⠀⢀⡼⠋
⠀⠀⢸⡟⠀⠀⠀⢠⡖⠒⠲⠶⠤⣤⣀⡀⠀⠀⠀⠈⠳⣌⣫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⢀⣴⠟⠁⠀⠀⣀⣤⠶⢶⣤
⠀⠀⣾⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠙⢳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠉⣀⣴⠟⠁⠀⠀⠀⣰⠏⠀⠀⠀⠈
⠀⠀⣿⡇⠀⠀⠀⠀⠹⣧⣄⣤⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠁⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⢠⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣿⡀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀
⠀⠀⠀⢻⣧⠐⠚⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢻⣧⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠉⠃⠀⢄⣀⣀⣀⣤⡶⠟⠁⢀⣾⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠣⣄⡀⣠⡟
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠈⠻⢿⣿⣿⣄⣀⣴⣿⣿⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠾⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⠏⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠉⠉⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠙⠛⠿⢷⣶⣦⣤⣤⣤⣬⣭⣀⣤⣤⣤⣶⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⡘⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⣀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⡔⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢦⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⠈⠁⠀⠀⠀⠀⠀⠀⣀⢽⣆⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠤⠖⠒⠚⠉⢀⠽⣧⠀⠀⠀⠀⠀⢹⡟⠒⠒⠚⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠸⣧⠀⠀⠀⠀⠈⣿⠤⠄⠤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡠⠴⠋⠀⠀⠀⢀⣠⠼⣧⠀⠀⠀⠀⢿⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣾⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡾⠛⠛⠉⠙⠛⠁⠀⠈⠉⠛⠛⠚⠛⠛⠋⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠸⡇⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣾⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⡇⠀⠀⣿⡇
⠀⠀⠀⣠⠞⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠁⠀⢰⡿
⠀⣠⠞⠁⠀⠀⢀⣴⠟⠀⠀⠀⠀⣀⣤⡤⠴⠿⠶⠶⠶⠶⠶⢦⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⢠⡿⠁
⣼⠃⠀⠀⣠⡶⠋⠁⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⢻⣦⣇⡾⠁⢀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠉⠙⢷⣤⣿⠀⠀⢸⡇⣠⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡿⠋⠛⠿⠶⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⣤⣼⣇⠀⠀⣀⣼⠏⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣿⣿⣿⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠁⠙⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠉⠒⢤⣀⣀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⣶⣍⢢⠀⢸⠀⣩⣽⣿⣯⣭⢩⣉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⣄⢴⠃⠀⠀⠀⠀⠀⣤⠒⣾⣮⣮⡇⣼⣴⢋⣋⡩⠟⣇⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡘⠀⠀⣈⣳⣦⣄⣀⣀⣾⣯⣝⣿⣿⣋⣉⣹⣿⣿⣯⣀⣠⣯⣌⣭⣀⣽⠃
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠈⠉⠉⠀⠁⠁⠈⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣶⣾⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣿⡿⠁⢠⣶⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠈⢿⡆⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠸⣿⣤⡄⠀⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠋⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⠛⠛⣷⡄⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠉⠉⠁⣀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⣸⠟⢿⣦⣴⡿⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⢤⣤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣦⡄⠲⡛⠁⠈⠁⠀⠀⠀⠀⠙⠻⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠜⡊⠻⠁⢶⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢺⡏⠁⣀⠀⠀⠀⣠⣤⣴⣿⢦⡀⠀⠀⠃⢰⣶⣼⣛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⠀⠰⠟⠀⠀⠀⠀⠈⠳⠍⢸⣧⠀⠀⠀⠈⢣⡾⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⣤⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡤⠡⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣴⡇⠁⠀⠀⠀⠀⠀⠀⠀⢀⡘⣋⠙⢃⡞⢀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⠈⢻⣥⣶⠄⠐⠆⠀⠀⠀⠀⣀⠤⢀⡤⠾⠦⡐⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠂⠀⠘⠿⡃⠰⠦⠀⠀⢴⣶⠤⠂⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡶⠀⠻⠆⠀⠉⠉⠃⠀⠲⢦⣄⡀⠀⢀⡤⠞⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡷⡦⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠿⠏⠉⢠⡀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠺⠓⠀⢀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⢠⣖⠃⣘⢎⢳
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠁⠀⠀⠀⠘⠟⠀⠀⠀⣤⡄⠀⠀⠀⢶⠄⠀⠉⠀⠀⠠⣄⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠲⣌⣎⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⡀⣀⡀⠈⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠉⠛⢷⣄⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⢀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠷⢦⣤⣀⠉⠳⠄⣠⠚⠁⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⡿⠀⠐⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠩⣭⣭⣤⣭⣭⣭⣭⣭⣬⢩⣭⣽⢩⣥⣭⣿⣿⣭⣭⣥⣽⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⣿⣿⣿⢸⣿⣿⢸⣿⢯⣮⣟⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡙⢽⣷⡍⣻⣾⣿⢸⣿⣿⣸⣷⡝⠿⠇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢘⣻⣃⣿⣿⣿⢸⣿⣿⣾⣿⣷⣾⣿⣿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⡋⣿⣿⡿⣿⣿⡇⣿⣿⣿⣿⢯⡽⠿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢼⣿⡿⣠⣿⣇⣿⣿⡇⣿⣿⣿⣄⢿⢿⡗⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⣦⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣴⣿⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠉⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢄⠀⠀⠀⡀⠂⠀⠀⠀⠀⣾⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢢⠴⡾⣿⣿⠟⣿⠶⠊⢀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣰⠃⠀⠃⣿⠃⠘⠁⠀⠀⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⡠⠲⡀⠉⠀⡴⠒⢦⠀⠀⢀⡴⠁⢀⠴⣶⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢹⡏⢏⠇⠀⠈⢏⢹⡋⣿⠀⠘⢳⠆⠃⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠛⠉⡘⡝⠂⠀⠑⠒⠋⠀⣨⠇⠘⡇⠀⠀⢸⠀⠙⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣉⣉⠉⢀⣀⣠⠔⠊⠑⣄⠀⠣⡀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠀⠀⡏⠀⠀⠀⠈⢢⠀⠙⢦⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢣⠀⠀⠑⡄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢆⠀⠀⠰⠁⠀⠀⠀⡰⠀⠀⠀⢆⠀⠀⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠱⢤⡇⠀⠀⠀⢠⠁⠀⠀⠀⠘⡀⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⣥⡀⠀⠀⢸⡄⠀⠀⠀⠀⢡⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⢸⠀⢡⠀⠀⢸⠏⠀⠀⠀⠀⢸⠀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣇⠀⢸⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢠⡤⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣹⡄⠈⣆⣾⠀⢀⠆⠀⠀⠀⠀⢀⡾⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠤⠋⢣⡠⠾⠤⠤⠄⠒⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⢖⠠⣀⢀⣀⣀⢀⡠⢐⠶⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠋⢁⠀⢀⠀⢀⠉⠣⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠜⢅⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣑⡁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠄⠀⠀⠀⠀⢤⠂⠁⢀⠤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⡀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⠀⡴⡀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠱⠀⠀⠀⠀⠀⠰⠁⠘⡜⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⢖⣠⣇⠀⡷⡇⢀⣧⣐⠎⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠄⣀⣈⣉⣀⣈⣉⣀⡀⠤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⢠⡌⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⢠⣼⠛⣵⣤⣶⣿⠙⣿⣷⡆⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢷⣤⣿⣿⣿⣿⣻⡀⢿⣿⣿⣸⣷⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⢾⣿⢽⣋⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡖⠀⢸⣿⣿⠿⠟⣝⣡⡄⠀⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⢂⡁⠀⠀⠀⠀⠀⡀⠀⠀⠤⠤⠞⢣⡒⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡍⢿⡴⢂⡐⠆⠀⠀⠻⠆⠀⠒⠊⡍⠀⢲⣄⡀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣡⡼⠱⣷⢰⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⣉⠳⠖⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⡀⢻⡘⣿⣿⣿⣷⣶⡤⠠⣤⣤⣶⡾⠃⠀⠣⢠⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠘⣧⣤⣿⡇⢿⣿⣿⣿⣿⠐⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠞⡉⢿⡶⠟⠿⡀⣿⣿⣿⡯⢹⣿⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⠿⢡⡞⣱⠏⣠⠀⠈⠇⢀⠈⠉⠠⠉⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⣡⢖⣻⡖⡟⠡⠁⠐⠃⠀⠀⠸⠿⠀⢠⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣩⠾⠃⣾⢃⣾⡞⠁⠀⠀⠀⠀⠀⠀⠆⠰⢸⡄⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢀⣤⡿⢡⣾⠃⣼⡿⠀⠀⠀⠀⠂⠀⠀⠀⠰⣴⣟⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠇⢤⣿⠆⠀⠀⠀⠀⠀⠀⣠⠂⠀⢹⣏⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢸⠋⣰⣿⠏⠀⠀⠀⠈⠀⠐⠂⠁⠀⠀⡄⠙⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⡙⣮⢠⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢨⠂⠀⠀⠀⠀⠸⠎⠇
⠀⠀⠀⠀⠀⢦⣷⡿⠀⡎⣼⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣾⡄⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⡠⠔⢂⣀
⠀⠀⠀⠀⢀⣿⣟⠃⠀⠀⠠⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠙⣧⠀⠀⠀⠀⠀⣤⢌⠙
⠀⠀⠀⢠⣾⣿⡀⠀⠂⠀⠀⠀⠀⠀⠌⢈⠀⠀⠀⠀⠀⠀⠀⠼⠀⢠⢹⡇⠀⠀⠀⠀⠡⣾
⠀⠀⠀⠀⠻⣴⡇⢀⣀⢰⣶⣄⡀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠠⠆⣀⣀⣾⣿⣀⣀⣤⡴⢃⡟
⠀⠀⠀⠀⢠⡁⡅⢺⣿⠀⠍⣹⡟⣶⡶⠶⠶⠖⠲⠶⣿⣶⣿⡟⠻⠉⣿⢿⣿⡟⠁⡆⢸⡄
⠀⠀⠀⠀⠀⠙⢾⣶⡟⠂⠀⣿⢿⣿⡧⠄⠀⡆⠸⠂⠋⢹⢸⣯⡟⠀⢿⣾⣿⣅⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢷⣬⣿⠇⠀⢀⡃⠤⠀⢷⣟⣿⣿⣿⣆⠀⢸⡿⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⠀⠀⢠⡆⠰⠿⣯⣿⣷⣭⣿⣾⡆⢱⠾⠃⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣁⣠⣠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠆⢱⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠠⢠⣤⣤⢀⢄⣤⣤⣄⣠⢄⢠⣤⢠⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡤⠴⠲⠤⣄⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠂⢰⠋⠀⠀⠀⣠⠀⢳⠔⠀⠀⠒⢤
⠀⠀⠀⢀⣀⣀⣀⣿⠀⠛⠀⠀⠀⠀⢀⡂⠀⠀⢀⡠⠃
⠀⡠⠔⠁⠀⠀⠀⠀⠑⠢⡀⠀⠀⣠⠎⢉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠉⠄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠙⠒⠢⢀⠠⠤⠤⠊⠁⠀⠀⠰⠒⠢⣀⠼⠇⠙⠦⠤⢄⠠⠐⠢⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠸⠊⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣤⠄⠀⠀⠀⣤⡄⠀⠀⣸⠀⠀⠀⢠⠃⡀⠀⠘⡄
⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⠀⠠⠀⠠⠉⠀⠀⢡⠏⠀⠀⢀⠇⠀⠀⠀⠀⠹⡀
⠀⡄⠈⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠇
⠈⠄⠀⢀⣠⠅⠀⠀⠂⠐⠀⠀⠀⠀⠀⡌⠉⠙⠛⠛⠉⠁⠘⢤⣀⠀⠀⠘⠃⠂⠀⠀⠄⠂⠰
⠀⠀⠁⠀⠘⠀⠀⠀⡠⠀⠀⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠉⠓⢄⢰⠀⠀⠀⠀⠀⠆
⠀⢀⡀⣄⠀⠀⠀⠀⢁⣀⣀⣀⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠦⠀⠀⢀⠎
⠀⠰⠏⠁⠉⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇⠘⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠼⠚⠁⠀⠉⠉⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡎⠑⠄⠀⡇⠀⠂⣧⠀⠀⢠⠀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⠁⠀⠀⠀⠙⠒⠒⠚⣏⣁⣀⠞⠒⠒⠛⠢⠦⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⣌⣿⠀⠀⣀⣀⣀⡀⠀⠘⠛⠛⠳⣆⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⢀⣠⡿⠀⠈⢻⣿⠉⠛⣷⡀⠀⠀⠀⠈⢷⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⣿⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠿⠋
⠀⠀⠀⠀⠀⠀⢀⣸⣿⠁⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠹⣏⠁⠀⢴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⣀⣀⣀⣤⣤⣤⣤⣶⡶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⢷⣤⡀
⠀⠀⠀⢀⣀⣤⠶⠿⠷⠶⠶⠛⠉⢉⣉⡉⠀⠀⠀⠤⠄⠐⠒⠒⠀⠀⠀⠲⡛⠉⠀⠀⠀⠀⠀⠀⢸⣇
⣠⡶⠿⠛⠛⠒⠒⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⡄⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢿⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⡇
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⡀⠀⠈⠆⠀⠀⠀⠀⠀⢸⣇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠄⠀⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⡄⠀⠀⣿
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠀⠰⡀⠀⠀⠀⠸⡀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠀⠀⠑⡄⠀⠀⠀⠱⡀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⢡⠀⠘
⠀⢸⡇⠀⠀⠀⠀⠀⠐⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⢳
⠀⢸⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢳
⠀⠸⡇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⣿⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀
⠀⠀⣿⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸
⠀⠀⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣸
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⢻⡄⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⢸⡇⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠘⣧⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⠀⠀⠀⣿⣀⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⡶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠢⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠀⠠⢀⠀⠀⠀⠉⡴⠃⠀⡈⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠤⠀⠉⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⠄⠀⠐⢤⠋⠀⠀⠀⢠⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⢁⠀⠀⠈⠣⠂⠉⠉⠐⠀⠈⠂⡀⠀⡀⠀⠀⣀⠀⠀⠠⠊⠀⠀⠁⢀⠈⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠓⠀⢠⠀⢠⠁⡘⠁⣀⡁⠀⠐⠄⠀⠉⠀⠑⡀⠛⠀⠔⠀⠀⡁⢄⠄⠀⠀⠀⠠⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠠⠀⡀⠈⠢⠀⠀⢸⠀⠀⡈⢰⣆⠐⠀⠈⠐⠀⠂⠈⠀⣄⠈⠡⠀⠀⡶⠀⠀⠀⠀⠀⠁⠐⠊
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢁⠈⠁⠈⢠⡐⠀⠀⠄⢀⠀⠈⠑⣠⠄⠀⠀⠀⠀⠀⠜⠁⠐⢄
⠀⡊⠀⠀⠂⠐⠉⡀⠁⠐⠠⢄⡀⠀⢀⡠⠂⠘⠀⠀⠀⠻⢿⡠⠠⡄⠀⠙⠀⡠⠄⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠁
⡌⠀⢀⠀⢄⡠⠀⠀⠀⡸⠀⠀⠂⠉⠘⠡⡈⠀⠈⠂⠄⠠⠎⡁⢀⠜⠀⠀⠀⡀⠀⠀⠀⠀⣔⠃⠀⠈⠀⠚
⠃⡄⠁⠀⠀⡠⠂⠉⠉⠁⠃⠠⠘⠀⠀⠀⠍⠒⠤⠀⠀⠳⠀⢠⠑⠒⠀⠐⠂⠁⠀⡀⠀⠀⠀⠑⠂⢀⠉
⠀⠐⠆⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⠀⠄⠀⠂⠄⡀⠀⠠⠀⠀⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠀⠀⠀⠀⠐⢔⠠⠨⠄⠀⡀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠊⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄⠁⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠆⠀⠀⠀⠀⠀⠀⢠⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⠀⠀⠀⠀⠀⡀⢔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⡄⠀⠀⠀⣀⠁⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡀⠀⠀⢀⢈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠑⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠰⢎⠒⠒⠛⣄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⢀⣂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠄⠀⠢⠌⠃⢤⡐⠂⠀⠀⠈⠲⠀⠤⠤⠄⠀⠒⠀⠀⠀⠀⠶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⠀⠠⠁⢀⠀⠄⢀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣄⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⢂⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠏⠀⠀⠛⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣀⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⣿⣆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⡀⠀⠈⠙⠛⠉⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠛⠋⠁⠀⢀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⣉⣉⣉⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⢠⣌⠃⢠⠀⠀⢀⣠⣴⣶⣦⣄⣠⣤⣴⣤⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣤⣼⣿⣇⢰⣷⣾⣿⣿⣿⣿⣿⣿⡿⠛⠡⢿⣿⣖⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⣼⢿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣼⣿⣇⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⡠⠬⣟⣷⣿⣿⣝⣿⣿⣿⣿⣿⣫⣾⣷⣷⣶⡖⠀⠀⣹⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⣠⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣀⣠⣀⣈⣿⣿⣿⣿⣿⣿⣿⡿⣟⡛⠋⠈⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠁⠉⠛⠀⠀⠀⣁⣸⣿⣿⣯⠛⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠋⠉⠋⡡⢻⣿⣿⣿⣆⣀⣴⣶⣿⣿⣿⣿⣿⠿⢁⣰⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣦⠀⠘⢀⣾⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⠁⣼⣧⡄⠀⠉⠙⠻⠿⠟⢉⣽⣿⣿⣿⣿⣯⣿⣿⢻⡟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠙⣷⠀⠈⠀⢻⣿⣇⠉⠢⠄⠀⢠⣴⣿⣿⣿⣿⣿⣿⠿⠿⣿⣧⣼⣯⢿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣹⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⣿⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⡏⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡀⣰⡀⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣙⣿⣼⣷⡎⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣉⣩⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠁

⣿⠋⠉⠙⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⢹⣭⡏⡉
⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⠛⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⡄⠈⠂
⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⣿⣿⠆⠀⠀⠈⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃
⠀⠀⣤⣄⠀⠀⢻⡄⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢸⣿⡆⠀⢈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⡟
⠀⠀⢸⣿⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠤⠤
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠠
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣠⣤⣀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⢈⡁⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣄⢈⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠃⠀⠃
⠀⠀⠀⢀⢀⡴⠦
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠄⠒⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠿⠒⠢⠄⠠⠀⢠⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⣀⣀⣀⠀⠻⡿⠋⢹⣿⠿⣫⠖⠀⠀⠀⠶⡿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⡤⠀⠤⢶⣆⣀⣀⣈⣉⣷⣶⣄⡀⢸⣧⣾⣿⣶⣶⣤⣄⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢦⡀⠀⠶⣌⡙⢿⣿⠿⢿⣿⣿⠁⣿⣿⣿⣿⣽⣿⠟⠛⠻⠆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⣿⣦⣀⠈⠉⠓⠒⠲⠿⣿⡇⠀⣿⣧⣄⣙⣿⣋⣀⣤⠔⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠉⠛⠻⣿⣶⣄⣶⠁⠀⠀⠙⠀⠀⠛⡉⠈⢿⡉⠉⣀⣤⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢸⣄⠙⠛⢶⣶⣤⣤⣴⣦⣤⣄⣤⣼⣵⡾⢿⠋⡉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣙⣿⣿⣿⣭⣭⣭⣿⣿⣿⠋⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠖⠀⠀⠀⠀⠀⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⢠⠟⠁⣠⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣍⠻⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡽⣠⣿⠇⢸⣿⡏⢻⣿⣿⣷⠈
⠀⠀⠀⠀⠀⢀⣼⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⡿⠀⠈⠃⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⢰⢏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⢀⢠⣼⣿⣿⠷⠄
⠀⠀⠀⠀⣼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣄
⠀⠀⠀⠀⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⢷⡄⣿⣿⡏⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⠇⢠⣞⢲⣄
⠀⠀⠀⠀⢹⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠸⣿⣿⣿⣿⡇⣸⡇⢠⣶⠀⠀⣿⣿⣿⣿⣷⣿⠁⠘⣿⡓
⠀⠀⠀⠀⠀⢷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⢠⣿⣟⣿⣿⣷⣿⡇⢼⣿⣦⣸⣿⣿⣿⣯⣿⣿⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣸⣿⡟⣿⡏⢹⣿⣧⢸⣿⣿⣿⣿⡏⢿⣿⣿⣿⣞⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⢸⣿⢣⣾⣿⣿⣿⡿⡇⣼⣿⣿⣿⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣷⣤⣄⠘⣿⣿⣿⣿⣿⣻⣷⣼⣿⢀⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⠃⣿⣇⡿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡌⣿⠹⣿⣻⣿⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢰⣂⢉⠉⣀⡀⣈⣓⣦⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⠐⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇
⠀⠀⠀⠀⣴⣿⣿⣟⣧⡗⢹⣟⣹⣿⣧⢀⣠⣿⣿⣧⣦⣽⣿⡟⠀⢿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣶⣿⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⣉⣽⣿⣷⣤⣼⣿⣶⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣴⣿⣿⡆
⠀⠀⠀⠀⢸⣟⡛⢻⠁
⠀⠀⠀⠀⢸⡋⣵⣿
⠀⠀⠀⠀⠀⢷⣶⠞⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄
⠀⠀⠀⠀⠀⠈⢧⠚⠋⠙⢦⣤⣤⣀⣀⣀⡀⠀⠀⠀⢀⣼⡁⠀⣼⠏⢉⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠳⣾⡇⠀⣿⢰⣿⡇⣼⣿⡿⢓⣲⠎⠉⠉⣀⠻⠄⣼⢣⡿⣡⡿⠉⢩⠇
⠀⠀⠀⠀⠀⠀⠀⡴⠉⠂⠀⢿⡌⣿⡇⣿⣿⠁⠤⡯⠇⠀⠀⠀⢳⠀⠃⠋⠈⡉⣤⣀⡏
⠀⠀⠀⠀⣠⢤⣰⠃⠀⠀⠀⠈⠃⠹⡧⢻⡇⠀⠛⣯⣥⣤⡄⠀⠀⢤⡀⠐⠋⠉⠀⢹
⢀⣀⠤⠚⠁⠀⢠⡀⢳⣄⡀⡀⠀⠀⠀⠈⠗⠀⠀⠈⠛⢧⣾⠀⠀⠚⢀⠀⣤⠀⣶⡗⠄
⢿⣀⣀⣀⡤⡶⠚⠛⡒⢛⠿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡶⠾⢦⡿⠾⠻⠌
⠀⠀⠀⢀⡞⠁⠀⣠⠿⠦⠿⠶⠟⠉⠛⠒⠒⠒⠲⠦⢤⡀⠀⠀⠶⠿⡀⠛⣷
⠀⠀⠀⠸⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠄⠚⢳⡌⢙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⠤⠴⢷⡀⠀⠉⠙⢮⠉⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠯⣉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠙⢄⠀⠀⠀⠱⣄⡇⠉⠛⠓⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠴⠋⠀⣀⣀⣠⠤⠤⠖⠚⠋⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⢀⣀⣀⡤⠤⠶⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢤⡀⠀⠀⠀⠀⢀⢀⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠲⣄⠀⠀⢈⠎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠒⠚⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠙⠦⠏⠀⢸⢳⠀⠀⣀⣀⡤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⣐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⢸⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⣸⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣶⣶⠶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⣠⣶⣿⣿⡝⠋⣉⢻⣄⠈⠋⠿⠿⢿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣴⣷⣶⠛⠛⠀⣠⣾⣿⣿⣿⣿⣿⢸⢿⡞⡿⠃⠀⠰⢿⣿⣿⠟⠉⣠⣽⢿⢏⣿⣿⣿⣿⢾⠿⡿⠇
⠀⠀⠀⢸⣿⣿⣉⣉⣉⣵⣶⣿⣿⣼⣿⣿⡇⣿⡟⢠⠏⠸⠀⣤⣰⣦⣼⣿⣿⣶⣤⡌⣻⣊⣸⣿⣿⣿⣇
⠀⠀⠀⠹⣿⣿⣿⣿⡿⢻⣿⡟⢨⣿⣿⣿⣿⣿⣧⣬⣶⣶⠶⣿⣿⣿⡿⣿⣿⣿⣿⣿⡻⣿⣿⣷⣿⣿⣿⣷⣦⢀⣀⢀
⠀⠀⠀⠀⠈⠉⠋⠙⠧⠈⠉⠓⠒⠛⠉⠁⠄⠉⠉⠉⠀⠀⠈⠹⠉⠩⠔⠟⠻⠿⠿⠟⠋⠉⠙⠙⠛⠋⠙⠛⠛⠓⠛⠋


⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿