Numbers game Emojis & Symbols

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠠⠄⠠⠀⠀⠀⠀⠂⢀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⠠⠀⢤⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠂⡄⠠⠠⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠠⡀⠀⠀⠈⠁⠀⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠈⠀⠀⠀⠰⠑⠂⠁⠀⠀⠂⡀⠀⠀⠈⢀⠀⢀⠤
⡇⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⡔⠀⠀⠈⠀⠁⠀⠂
⡇⢈⠀⠀⠀⠀⢀⠀⠀⠐⠢⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠈⠀⠀⠂⠀⠎⠁⠈
⡇⠁⠀⠀⠀⠰⢄⢀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠀⠀⠀⡤⠀⠀⠊
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠆
⡇⠐⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢂⠀⠀⠂⢐⠈⠈⠀⠀⠀⠀⠀⠀⠈⢁⡁⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠐⠀⠘
⡇⠀⠈⠀⠒⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠂⠀⠀⠘⠂⠀⠠⡘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠂⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠄⠀⠀⠀⠠⠐⠂⠀⣤⠄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠈⢠⠈⠀⠀⢈⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠁⠀⠘
⡇⠀⠐⠠⠄⠂⠀⠁⠀⠒⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⡀⠀⠀⢀⠀⠀⠆⠐⢀⠀⠀⠀⡠⠆⣀
⡇⠇⠲⠀⢃⠄⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⢹⡬⠆⠈⠗⢘⡶⣻⡞⠑⠋
⡇⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠤⠰⠄⠀⠀⠀⠀⠀⠀⡂⠀⠂⠀⠀⠀⠀⠈⠀⠀⠤⠀⠈⠃⢛⣀⣤⣤
⡇⠀⠐⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢲⠐⠂⠁⠀⡀⠀⠘⢣⠚⠂⠛⠓⠉⠘⠓⠶⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⡇⠘⠰⠀⠀⡠⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁
⡇⢤⠀⢠⠈⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⢢
⡇⠀⠀⠀⠀⠐⢁⠀⡀⠈⠀⠀⣀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⡐⠈⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⡄⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁
⣇⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⣿⠟⠉⠛⠋⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⣿⢹⡏⠉⢙
⠛⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠀⠛⠛⠃⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣷⠆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢷

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⢠⣾⠟⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠟⠻⠿⠟⠠⠾⢿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⠋⢸⣿⠀⠀⠘⢿⣷⣤⣼⡟⠀⠀⠀⠀⢀⣴⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣦⣤⣄⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢰⣿⣧⣤⣼⣿⣦⡄⢠⣾⠛⠛⠿⣿⣦⠀⠀⠀⠸⣿⣃⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⡆⠀⢘⣿⡇
⠀⠀⠀⠀⠈⠁⠉⠉⢹⣿⠉⠀⢻⣿⣦⣄⣤⣿⠏⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣠⣾⡿⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣴⡂⢀⡂
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠄⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⢸⡁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠁⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⢠⣿⠋⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⠻⣷⡄⠀⣼⠿⢛⣹⣷⠀⢠⣿⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣩⣴⡿⠃⠀⢻⣷⣬⣹⡟⠀⠘⣿⣭⣭⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⡀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣀⣠⣤⡄⠠⣤⣀⠀⠀⣠⣤⡀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢾⣿⣿⡯⠀⠰⢿⡿⠗⠀⢿⣼⡇⠸⣿⣿⣿⣿⣿⣛⢿⣿⠿⠟⢀⣾⡿⠁⠀⠀⠈⢻⣿⡄
⠀⣿⣿⣧⣤⣼⣿⣿⣶⠀⠀⣴⣶⣶⣶⣿⣿⠇⠀⢀⣭⣿⣿⠖⠂⢀⡀⠀⠀⠛⠞⠃⠀⠀⠀⠉⠉⠉⠛⠛⠛⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡷
⠀⠛⠛⠛⠛⠛⠟⠻⠿⠀⠀⠻⠿⠿⠛⠛⠁⠀⠀⠸⣿⣿⣧⡀⢘⣿⡿⠃⠀⣾⠻⠆⠀⠀⣠⠖⠛⠓⢦⡀⠀⠀⠀⠈⢿⣷⣀⠀⠀⢀⣼⡿⠃
⠀⣤⠤⠄⣤⣤⣤⢠⣤⣤⡀⣠⣤⣤⡀⢀⣤⣄⠀⢀⣀⣈⣉⣁⣈⣁⣀⠀⠀⢙⣻⡇⠀⢸⡃⠀⠀⠳⡄⢹⠀⠀⣿⠀⠀⣬⠉⠙⠋⠉⠉
⠀⣧⣀⠀⠀⣸⡿⢻⣧⣿⡇⣿⡇⣿⡇⣿⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣄⡀⠀⠈⠳⢤⣤⠾⠁⣸⠀⠀⣿⠀⠀⣿⠀⠀⢀⢴⣾⡇
⠀⠀⠈⡷⠀⣿⡇⣾⡏⣿⡷⣙⡛⣿⡇⣿⠀⢸⠇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⠇⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠻⠿⠿⣿⠂⠀⠀⠀⣿⡇
⠀⠒⠊⠁⠈⠛⠁⠈⠛⠛⠁⠙⠛⠛⠁⠈⠛⠋⠀⢀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠘⠋⠀⠀⠀⠲⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢰⠀⠀⠀⣠⣴⠶⠶⠶⠶⢶⣦⣄⠀⢟⠛⢛⡃⠀⠀⣾⣿⣿⣿⠀⠠⣤⣴⠟⣷⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⣿⡇
⠀⠀⠰⠢⠀⠀⠸⣿⣏⠀⠀⠀⠀⢀⣿⣿⠀⢼⠓⣬⡅⠀⢀⣿⣿⣿⣿⠀⠀⠀⠙⠛⠋⠀⠀⢸⣏⠙⠲⢤⣀⠀⠀⠀⠀⢈⣿⠄⠀⠀⣿⡇
⠀⠀⠀⢀⠀⠀⠀⠈⢙⣻⣶⢶⣾⣟⡋⠁⠀⣚⢃⡘⡂⠀⢸⣿⣿⣿⡇⠀⠀⣶⣶⣶⣶⠆⠀⠸⢿⡀⠀⠀⠉⠛⠳⠶⠶⠛⠋⠀⠀⠀⣿⡇
⠀⠀⠀⢼⠀⠀⠀⣼⣿⠋⠀⠀⠀⢹⣿⡆⠀⠈⠯⣙⡁⠀⣼⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⢀⣤⢤⡀⣤⣤⢠⡄⣄⢀⡤⠤⣄⠀⠀⠀⣿⡇
⠀⠀⠀⠒⠀⠀⠀⠈⠛⠷⠶⠶⠶⠟⠛⠁⠀⠛⠟⠊⠁⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡟⠀⢈⣿⢾⣁⣾⢃⠹⠧⠅⢾⠀⠀⢸⠆⠀⢀⣿⡇
⠀⠀⢲⣶⠖⠀⠀⢀⣀⡀⠀⣀⣀⠀⣠⣀⢀⣀⡀⠀⠀⢸⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⡇⠀⠀⠛⠘⠉⠛⠋⠘⠛⠃⠈⠓⠒⠋⠀⠀⠉⠉⠉⠁
⠀⠀⠀⣿⠀⠀⢰⠁⠀⠙⡆⠍⢭⡈⢣⡿⢻⡧⣟⠀⠀⣸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠁⠀⣀⢤⣤⡄⠀⠀⢀⣤⣤⣶⢦⣤⣄⡀⠀⠀⢀
⠀⠀⠀⣿⠀⠀⠈⠲⠤⠞⠁⠗⠼⠓⠿⠦⠻⠇⠟⠀⠀⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⠀⠀⣩⣑⣤⠀⠀⠰⣿⣏⠀⠀⠀⠈⣿⣿⠀⠀⠠⠁
⠀⠀⠀⣿⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⠀⠘⢲⣦⠀⠠⣿⢿⣿⡿⠀⠀⢸⣿⣿⣿⡇⠀⠀⢥⠙⣤⠅⠀⠀⢉⣻⣷⣶⣶⣿⣛⠁
⠀⠀⠀⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠉⠓⢦⣀⢸⡇⠀⠀⣠⣤⣄⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⣛⡳⣼⠂⠀⣾⣿⠋⠁⠀⠀⠈⢹⣿⡆⠀⠀⠊
⠀⠀⠀⣿⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⢿⣤⡟⠻⠆⠀⣿⣿⣿⣿⠀⠀⠀⣭⣥⣭⠄⠀⠙⠻⢷⣤⣤⣤⣴⡾⠟⠁
⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠀⠀⢀⣶⡄⠀⢰⣿⣿⣿⡏⠀⠀⠀⠈⠁⣀⣀⠀⢀⣀⣀⠀⢀⣀⣀⠀⢀⣀⠀⢀⣀⣀
⠀⠀⠀⣿⣄⠀⠀⠀⣿⠷⠶⣶⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣼⣽⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠁⠉⡇⣿⣏⣛⠃⣿⡏⣿⡇⣼⡏⠠⡏
⠀⠀⠀⠟⠁⠀⠀⠀⣽⠀⠀⣿⠀⢀⡏⢀⡴⠒⠲⣤⠀⠀⢀⣘⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⡇⣿⡏⣿⡇⣽⡿⣿⣁⣿⠃⠀⠙⠒⡆
⠀⠀⢀⣀⣀⣀⣀⣀⠉⠀⠀⠿⠀⠘⡇⠸⣄⠀⠀⢸⡇⠀⠿⢿⡄⠀⠈⠉⠉⡉⢉⣉⠉⠉⠁⠘⠳⠞⠃⠻⠷⠿⠃⠻⠷⠿⠹⠿⠷⠆⠶⠶⠇
⠀⣴⣿⠋⠁⠀⠈⠙⣿⣆⠀⠀⠀⠀⠙⢦⣄⣠⡤⠞⠀⠀⠺⠾⠇⠀⠀⣾⣿⣧⠈⢹⣿⣿⣦⠀⠀⣠⣤⣴⣶⣶⡆⠀⢠⣶⣶⣶⣦⣶⣶⣤⣦
⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣤⣤⣤⣄⣀⡀⠀⠀⠀⣴⡶⠆⠀⠀⠀⠉⠀⠤⣾⣿⣛⡁⠀⣾⣿⡿⠿⠿⠿⠇⠀⠸⠿⣿⣿⠻⠻⣿⣿⣿
⠀⢻⣿⣄⠀⠀⠀⣠⣿⠟⠀⣤⣼⣿⣧⣭⣽⣿⣿⣿⣿⠀⣿⣻⡇⠀⢰⣶⣶⡦⠀⢸⣿⣿⣿⠀⢻⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⠇⠀⣿⣿⣿
⣀⣀⣈⣙⣛⣛⣛⣋⣁⣀⣀⣉⣙⣛⣋⣉⣉⣉⣉⣉⣉⣀⣈⣉⣁⣀⣀⣉⣙⣃⣐⣛⣛⣉⣁⣀⣀⣉⣙⣛⣛⣛⣛⣛⣛⣛⣋⣁⣀⣀⣉⣉⣁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣿⢿⣷⣾⣿⣿⣶⣾⣿⢿⣶⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣶⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢀⠹⡏⠏⣿⢉⠉⣿⢨⢹⡏⣹⢉⣽⡏⢿⣿⡏⣉⠉⡿⠍⢿⠧⣿⢉⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⢿⡿⣶⢿⣿⢿⣿⣶⠾⣷⣿⡿⣿⠷⢿⡟⣿⣿⢿⡟⢷⣿⡶⣿⣾⣿⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡁⢾⡛⣸⣇⣦⣰⣯⢰⣿⣿⣀⣉⣼⡗⣿⣰⣿⣇⣜⣿⢚⣇⣶⣹⡀⣿⣐⣿⣞⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠧⣾⣿⡿⠿⣿⣿⡿⢿⣿⣿⠿⣿⣿⡿⢿⣿⣿⠿⣿⣿⡿⢿⣿⣿⠿⢿⣿⣿⠿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠉⠉⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠄⢷⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⠀⠤⠀⠀⠀⠄⠠⠄⠈⠲⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠡⢄⠀⠀⢠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠥⠄⠀⠀⣤⠀⠠⠤⠀⠄⠀⠀⠠⠄⠀⠼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡼⠀⠀⠀⢀⢀⡇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⠂⠀⠈⡇⠀⠐⠋⠉⠉⢹⠏⠉⠀⠀⠀⠀⠀⡇⣠⠞⠉⠉⠲⣄⠀⠀⠀⠀⠆⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡿⠁⠀⠀⠀⠀⠘⣦⠄⠀⠀⠃⠀⠀⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⡸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⠀⠀⢀⣀⣀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⡀⠀⠀⡇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⠀⠀⠈⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⡇⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠉⠉⠁⠀⣿⠉⠉⠁⠀⠀⡈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠂⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠐⠐⡄⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠓⠀⢰⡀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⡇⠀⢸
⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣇⠀⠀⡀⠀⠀⣀⠀⢠⠋⠘⣇⠀⠀⠐⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠇⠀⢸⠉⠁⠉⠉⠉⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⣿⠀⠀⠘⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠉⠁⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠒⠒⠒⠒⠲⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠗⠒⠒⠖⠒⠒⠀⢐⡇⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠄⠤⠀⠀⢀⠀⠀⠀⣦⠠⠤⠤⠤⡄⠀⠀⢣⠀⠀⠀⠀⠀⢀⡞⠀⠤⠠⡆⠀⠀⠠⡬⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⣅⠀⠀⠀⢱⣄⠀⠀⣠⠎⠀⠀⠀⠀⠅⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⣈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠉⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠄⠀⠀⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢠⢄⣴⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠧⢤⣤⠀⠀⠀⠀⠀⠀⠀⣠⢠⠶⠂⠀⠲⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠆⠀⢸⡇⠀⠀⣀⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⣀⡀⠀⠀⢀⣀⠴⠊⠀⠿⡏⠀⠐⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠲⠖⠀⠀⠀⠐⢢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠴⠒⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡂⠠⣄⠙⠀⢀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠓
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢐⣣⣶⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢠⣧⡤⠀⠄⣀
⠀⠀⠀⠀⠀⢠⣿⡗⠀⠀⠀⠀⠘⠸⣿⠷⠖⠀⠉⠀⠐⠀⠀⢠⣭⣿⠿⠋⠉⠉⠀⠀⠂⣈⠉⠁⠰⠷
⠀⠀⠀⡄⠀⠀⠏⠀⠀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡅
⠀⣠⣀⣠⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⣶⣾⣿⣿⣷
⠀⠀⠀⠉⠉⠀⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⢠⣴⡄⠈⣇⠀⠀⠀⠀⣲⠖⠒⠁⠀⠀⠀⠀⠀⠰⢄⣼⠁⠀⠀⢀⣰⠀⠀⠰⠔⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠋⢣⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣤⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠃⠘⠒⠊⠀⠈⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠰⠶⡀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡔⠀⠀⠀⠈⠀⠚⠛⢀⠀⠈⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠂⠄⠀⠈⠀⠀⡰⠿⠀⢀⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠃⠀⡠⡊⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠋⠀⠘⠀⠀⠀⠀⠈⠉⠀⠀⢀⣄⣠⡄⠀⠉⠀⠀⠈⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢠⡄⡀⠀⠀⠀⠃⠉⣿⡁⠀⡠⠂⠀⠀⢀⡀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠖⠹⠗⠀⠀⠀⢉⢁⣤⠐⠂⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⠤⠄⠀⠀⠀⠀⣀⠀⡀⠠⠀⠛⠀⠄⠁⠉⠁⠀⠐⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡾⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠈⠈⠋⠐⠀⢀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠁⠸⠇⢀⡀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠄⢄⢹⡇⠀⠁⢀⠄⠀⠔⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠺⢂⠈⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠰⡆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠈⠀⠀⠁⠈⠦⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⡆⠀⠐⠀⢷⠄
⠀⠀⢀⡔⠲⡄⠀⠀⣀⢤⠿⠟⠤⣀⠀⠀⠀⠀⠀⠀⠠⠚⠃⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⡈⠑⠢⡄⠀⠀⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⢀⠀⣠⠻⢂⠄
⠀⠀⡾⠀⠀⡇⠺⡾⠁⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠂⠀⠀⡀⠀⢀⠀⠀⡀⡻⠀⠀⠹⣄⠀⡀⢠⢀⣌⠁⠐⠀⠀⠀⢙⠁⠉⠛⡀
⠀⠰⡃⠀⣸⠁⠀⡇⢂⡴⠀⠀⠀⠀⠀⡁⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⢠⡄⠀⠘⠟⠀⠀⠠⠉⠀⠙⠟⠀⠉⠐
⠀⠈⣇⠄⡇⠀⠀⠙⣤⠆⠤⠐⣉⠆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠨⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠱⡀⣅⠀⠀⣀⠤⠖⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠹⣌⣦⠚⠁⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢧⡀⠀⡄⠀⠠⡄⢐⡄⠀⢡
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠉⣦⢰⣀⣀⡟⠁⠑⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⢀⠐⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠒⠉⡀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠘⢄
⠀⠀⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⡀⠀⠀⠀⠘⢎⠀⢈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠢⡀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠐⠮⣁⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠄⠄⢂⡀
⠀⠀⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠁⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠁⠀⠀⠘⠄⠀⠀⡀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠐⠊⠜⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢠⠊⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠀⠁⠀⠀⠀⠠
⡆⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⡁
⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠗⢲⠀⠀⠀⠄⠂⠀⡀⠀⠀⠀⠈⠑⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠑⠀⠊⠈⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣄⡀⢀⣀⣀⢀⣠⣀⠀⣀⣀⡀⣀⣀⡀⢀⣠⣀⠀⣠⣀⠀⣀⣀⡀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠻⢿⢿⡿⡿⠿⢿⠛⢿⡿⣿⠿⣿⢿⣿⣿⠿⠿⣿⠿⣿⢿⡿⢿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣴⣬⣯⣡⣧⣦⣼⣼⣽⣧⣿⣼⣿⣬⣿⣿⣴⣤⡯⣤⣿⣹⣧⣾⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⣛⡯⢹⠏⡍⣹⠫⣽⣿⡏⠛⣻⡽⡏⣩⣿⢙⣿⡽⣇⡍⡿⢹⡏⣿⡦⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣼⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠉⠁⠀⠉⠉⠀⠉⠉⠀⠈⠉⠀⠈⠉⠁⠀⠉⠁⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠆⠠⠼⠆⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠚⠋⠀⠀⠀⠀⠈⠀⠑⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠈⠀⠀⠴⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠤⠄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠀⠀⠉⠁⠉⠀⠈⠀⠀⠀⠾⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡰⠁⠠⠄⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠰⠄⠀⠂⠀⠀⠄⠀⠊⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠠⠀⠀⢀⠀⢠⠀⠀⣀⠀⠠⠉⢧⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠤⠤⠤⠤⠤⠤⠦⠤⢠⡌⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣇⣀⡀⠀⠀⣧⠄⠤⠤⠄⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⠄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⠀⠀⠀⠀⡇⠀⠐⠀⡞⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠁⠀⡇⠀⠀⠀⠀⡆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⠂⠀⠀⡇⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠒⠒⠃⠀⠀⠀⠀⠃⠈⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠄⠀⠀⠠⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡇⠀⢀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢧⠀⣤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⣰⣟⠀⢈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠠⠄⠠⠤⠤⠴⠤⠤⠀⠀⠰⠠⠤⠤⠀⣧⠔⠂⠀⠙⠁⡀⡘⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⢀⣀⣀⣀⠀⢐⣀⣀⣀⠠⠤⠒⠈⠀⠀⠀⠀⠀⣄⣉⡁⠀⢤⡈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⢠⠄
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠕⠒⠤⣀⣀⣚⠑⠤⣀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠤⠥⣪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠨⡀⠀⠈⠙⠲⣖⠊⡉⠀⠋⠁⠐⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠵⠢⠤⣄⣀⡥⠒⠒⠒⠒⠚⠢⣄⠀⠀⣀⡠⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠑⠂⠤⡀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠄⠀⠄⢀⣠⠤⠔⣫⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣜⡉⠀⠉⠁⠐⠀⣨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢀⠵⠦⠤⢀⣀⡆⠀⠀⠀⠀⢠⠃⠀⠀⠀⣀⠠⢴⡃⠐⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠀⣰⠁⠀⠀⢀⣠⠊⠉⠒⢆⣀⡤⠋⠉⠉⠉⠁⠀⠀⠀⠈⣆⡰⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠛⠒⢒⡢⢯⡀⠀⠀⠀⠀⠹⠦⠤⠤⠤⠤⠤⠖⠒⠊⠉⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⠚⠉⢁⡞⠁⠈⠓⢤⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠔⠁⠀⠀⠀⠀⢰⠉⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢈⡔⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠙⠒⠤⠤⠤⢀⣀⣀⡠⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠐⡇⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠎⠉⠁⠉⠉⠉⠉⠉⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠈⠲⡔⠁⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠾⠤⠄⠀⠀⠠⠤⠤⡠⠃

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

⡅⠀⠀⠀⠀⠈⠡⠉⠀⠁⠉⠡⠀⠁⠁⠉⠀⠁⠀⠍⠁⠈⠀⠀⠈⡁⡠⠀⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠠⠄⠁⠀⠀⠀⠀⠈
⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⡃⠈⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⢀⢀⠄⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀
⡀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠘⠃⡠⠄⠀⠠⢀⡀⢁⠠⠂⡀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠐⠠⠀⠀⠀⢀⠌
⡇⠈⠀⠀⠀⠈⢂⠄⠂⢀⡑⠄⠂⣈⢀⠀⠀⠄⡀⡐⠈⠀⡀⠠⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⠀⠀⠀⡀⠠⡀⠄⠁⠀⠀⠀⠠⠀⠑⢤⠂⠀⠀⠀⠂⠀⠨⠀⠀⠀⠈⠉⠂⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠈⠀⠀⠌⠀⠀⠀⣐⢀⠁⠈⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⡇⠀⠀⠖⠊⠠⠌⠀⠀⠈⠲⡀⠢⠐⠢⡅⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡂⠀⠀⠀⠠⠅⠀⠀⠀⢉⠀⢀⠀⠀⠰⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢄
⡅⠠⢂⠀⠁⠀⠀⠂⢄⠀⠁⠢⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠳⠄⠀⠄
⡆⠈⠠⡐⠀⠤⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⢠
⡆⠀⢀⠀⠔⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠓⠂⠂⠀⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡈
⡃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠
⡁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠐⢀⣀⠀⠀⠀⠀⠁⠃⡀⢀⣈⡆⠈⣾
⠃⢀⡀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠈⠉⠁⠀⠤⡠⠊⣉⠻⢠⠉⠦⠈
⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠈⠀⠖⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢀⠀⠀⠢
⡇⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠙⡠⡀⠀⠐
⡁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⣁⢀⠀⠀⠤
⠇⢀⢀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠰⠀⠀⠀⠀⠀⡐⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡀⠘⠁⠰
⡁⠋⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠐⠀⠐⢀⠀⢀⠂⠀⠀⠀⠀⠁⠀⠁⠀⠀⠠⠀⠠⠖⢀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠀⢀
⠇⠈⠀⠠⢐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⡂⠀⠀⡀⠈⡀⠀⠈⠀⡠⠀⠀⠹
⡆⠀⢀⡀⠀⡀⠀⠀⣀⣂⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⠑⠀⣰⣘⠂⣁⢀⠁⣃⣂⣀⣈⣁⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⣠⠴⠒⠒⠒⠦⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣪⠴⠖⠒⠲⠦⣭⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡠⠔⠒⠒⠦⣌
⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⠀⣶⠀⠀⠀⠙⣄⢀⠀⠀⠀⠀⠀⠀⢠⣳⠞⠁⠀⢠⠶⣦⠀⠀⠹⣎⢂⠀⠀⠀⠀⠀⢀⠊⠔⠁⠀⢠⠶⣦⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡄⡀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠈⢀⣿⠀⠀⠀⠸⡆⠆⠀⠀⠀⠀⡌⠾⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠇⠃⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⢰⠟⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠇⠄⠀⠀⠀⠀⠉⣿⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠡⡹⣄⠀⠀⠀⠿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠰⡻⣄⠀⠀⢸⣤⣤⠀⠀⢀⡞⡐⠀⠀⠀⠀⠀⠘⡀⢄⠀⠀⠸⢦⠿⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠐⠘⡳⢤⣄⣀⣠⡤⠖⠩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣳⣤⣄⣀⣀⣤⢶⡫⠊⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⢤⣄⣀⣀⣤⠔⡋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠴⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡴⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⡤⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⢈⡴⠋⠀⣀⠀⣀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⡀⣴⠋⠁⠀⣤⣤⡄⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢪⡞⠉⠀⢀⣤⣀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⡌⡾⠀⠀⠀⣿⠀⣿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠰⣼⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣈⡟⠀⠀⠀⣿⠀⠉⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠄⣇⠀⠀⠀⠻⠤⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠛⠙⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠟⣇⠀⠀⠀⣿⠛⣷⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠰⡹⣄⠀⠀⠀⠀⣿⠀⠀⠀⣰⠃⠁⠀⠀⠀⠀⠈⠜⣆⠀⠀⠀⣦⣠⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠐⠻⡄⠀⠀⢿⣀⡿⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠐⢝⠳⣄⣀⣀⣉⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⡳⣤⣀⡀⠁⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⠶⣄⣀⣉⣀⣀⡴⠞⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣂⡥⠶⠶⠶⢬⣔⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⡥⠴⠦⢬⣅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣢⡭⠥⠬⣥⣒⠤⡀
⠀⠀⠀⠀⠀⠠⢢⠞⠁⠀⢠⣤⣄⠀⠈⠳⣌⠀⠀⠀⠀⠀⠀⠀⠐⡱⠋⠁⢀⣠⣄⠀⠈⠙⢆⠠⠀⠀⠀⠀⠀⠀⠀⣼⡵⠋⠀⠀⣤⣄⠀⠈⠳⣌⢄
⠀⠀⠀⠀⠀⢡⡏⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠘⣸⠁⠀⠀⢸⡇⢸⠀⠀⠀⠈⣇⢁⠀⠀⠀⠀⠀⡸⡿⠀⠀⠀⢸⡇⢸⠀⠀⠀⠸⡆⠄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⢨⡇⠇⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡗⢿⠀⠀⠀⠀⣽⠠⠀⠀⠀⠀⠀⠟⣇⠀⠀⠀⠘⠷⢾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢣⢳⡀⠀⠀⢰⡇⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⡘⣄⠀⠀⢸⣇⣸⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠐⢻⡄⠀⠀⢰⣄⣸⠀⠀⠀⣼⢣⠁
⠀⠀⠀⠀⠀⠀⠑⢝⣦⣄⣈⡀⣀⣀⡴⢚⠔⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⣄⣀⠉⠁⣀⣠⠔⡃⠂⠀⠀⠀⠀⠀⠀⠀⠑⢟⣦⣄⣀⠈⢁⣀⡤⢞⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⠟⠉⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠍⠩⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠻⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢐⣒⣂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠖⠋⠉⠉⠉⠙⠳⣮⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡾⠁⠀⠀⢸⠋⣷⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠃⠀⠀⠀⢸⠀⣿⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡆⠀⠀⠀⢸⠀⣿⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡹⣄⠀⠀⠘⠶⠛⠀⠀⣠⠟⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⢶⣤⣤⣤⠴⣚⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉

⠁⠐⠓⡆⠀⠀⠀⠀⠘⠋⠀⠀⠀⠠⠠⡄⠀⠀⢠⠖⢋⠒⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡷⠀⠀⠘⠦⠞⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢼⠁⣹⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⡇⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠩⠟⠀⠀⠀⠚⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢖⠢⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⠀⠀⡐⢦⠀⠀⠘⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀
⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠂⠀⠀⠀⠁⠀⠀⢞⢈⡆
⠀⠀⠀⡀⠀⠀⠀⡇⠑⠒⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠚
⠀⠀⠲⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠨⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⡴⠲⢦⣄⠀⠀⠀⢸⡙⢦⣀⣸⠀⠀⠀⠀⠀⠱⠄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠐⠋⠀⠀⠀⣰⡍⣰
⠀⠀⢧⣤⠜⢸⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⢄⠀⠀⠀⠈⠣⠟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁
⢀⣠⠀⠀⠀⠀⠀⠯⡄⠀⠀⠀⡀⠀⠀⢇⣘⠉⠳⠀⠀⢀⠔⣀⠀⠀⠀⠀⠐⣀⠀⠀⣀⡀⠀⠀⡖⠀⡆⡆
⠈⠐⠄⠀⠀⠀⠀⠁⠁⠀⠀⠸⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠊⣉⠇⠀⠀⠳⠉⠁⠀⠀⠒⠉⠀⠀⠙⠚⠁
⠀⠀⢀⡀⠀⠀⠀⢀⠀⠤⠀⠀⢀⢤⡀
⠀⠀⠈⢣⠀⠀⠀⠀⠓⠀⠀⠀⢳⡀⢹⠄⠀⠀⠀⠀⠐⡉⠀⠀⠀⠄⣞⡀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⠀⠋⡡
⢀⡴⡀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⣰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠃⠃⠀⠀⠤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠼⠊⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡽⠀⠀⠀⡔⠒⠂⠀⠀⠀⡀⢤
⠀⠀⠀⠀⠀⠠⠉⠀⠀⢀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⣀⡖⠀⠀⠘⠒⠚⠁⠀⠀⠀⠑⣖⢀⡄⠀⠀⠉⠈
⢠⢤⡀⠀⠀⠀⠀⠀⠀⡟⡠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⢀⣠⠴⠖⠛⠋⠉⠉⠙⠛⢶⣤⡀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣠⣴⣏⠡⠐⠑⣀⣀⣁⣀⠀⠀⠀⠙⢋⢦⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣿⣟⣟⣿⣳⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠙⢿⣧⠀⠀⢸⡇⠄⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠿⢾⡧⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⡇⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⢀⣿⡑⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡽⠁⢀⡼⠑⠂⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣁⠄⠀⣠⡾⡛⢁⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣃⠚⠁⣠⣾⡿⠓⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡡⠒⠁⣠⣾⡿⠚⢠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⠂⠀⣠⣾⡿⠋⣠⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠔⠁⢠⣾⣿⢿⢁⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠌⠀⢰⣿⣿⠻⠛⠛⠛⠛⠛⠒⠛⠛⠛⠛⡛⢻⣿⣿⣷⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⠋⣠⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣯⣾⣿⣿⣿⣿⡷⠿⣿⡿⠿⠝⠛⠻⠟⣿⣽⣿⣷⣄⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⣿⣿⣾⣶⣾⣶⣷⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⢹⡇⠀⢹⡇⠀⠀⠀⠀⠀⢸⡏⠀⠈⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡄⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠚⠛⠒⠚⠛⠓⠀⠀⠀⠀⠒⠛⠓⠒⠛⠓⠒⠛⠛⠂⠀⠀⠀⠐⠚⠛⠂⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠈⣿⠋⠀⠀⠀⠀⠈⢹⣏⠁⠈⢹⡏⠉⢹⣟⠁⠀⠀⠀⠀⠉⣿⡉⠀⠉⣿⠉⠉⣿⡏⠉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡟⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⡇⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⡇⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠄⠀⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⠸⠿⠧⠀⠀⠰⠿⠧⠰⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠐⢲⣖⠂⠐⢲⡖⠒⢲⣶⠒⠒⣶⠒⠒⣶⠒⠀⠀⠀⠀⠐⣶⡖⠒⢲⣖⠂⠐⣶⠒⠂⠀⠀⠀⠀⠒⣶⡂⠀⢲⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣼⡇⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡆⣼⠏⠀⠀⠀⠀⠀⠀⠀⠘⣷⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡏⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠇⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣾⠃⠸⣧⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠄⠀⠀⠼⠿⠤⠤⠿⠤⠤⠿⠤⠀⠀⠀⠀⠠⠿⠧⠤⠼⠧⠄⠠⠿⠦⠄⠀⠀⠀⠀⠤⠿⠄⠀⠼⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⠀⠠⣦⠴⠀⢦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⡆⠀⢰⡤⠆⠰⣶⠤⠴⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣰⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⣾⠁⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢹⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠈⣿⡀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏⠀⢀⣻⣆⣀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡁⠀⣸⣧⣀⣀⣿⣀⣀⣿⣀

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠐⠒⠛⠛⠛⠓⠛⠛⠛⠃
⠀⠀⠀⢀⠆⡆⠀⠀⠀⢀⠤⠶⢦⣅⠀⠀⠀⠀⡤⠀⠦⠾⡤⠀⠀⠀⠀⡠⠹⢡⠀⠀⠀⠀⠀⠄⠴⠤
⠀⠀⣂⣁⠀⠆⠀⠀⠀⠃⠔⠒⠀⢸⠀⠀⠀⠀⠁⠐⠂⣔⠀⠀⠀⠀⡰⠁⠖⢠⠀⠀⠀⠀⠀⠀⠎⢁⠈
⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠎⠀⠀⠀⠀⠈⠒⠆⠀⢡⠀⠀⣀⡀⠈⠀⠈⣰⠀⠀⠀⠀⠁⢢⠀⠱
⠀⠀⠀⢨⣀⡄⠀⠀⠀⠰⣁⣀⡀⠀⡱⠀⠀⠀⣏⣉⣁⡠⠎⠀⠀⠀⠀⠀⢁⢸⠁⠀⠀⠀⢸⣉⣁⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣤⡉⣄⠀⠀⠀⡀⠀⣠⡌⢢⡀⠀⠀⠀⣀⣀⣃⠀⠀⠀⠀⢀⡀⣠⢀⡀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠞⠀⣔⡒⠂⠀⠀⠠⠤⠤⡄⠀⣠⠇⠀⠀⡌⢠⣀⠀⡃⠀⠀⢠⠃⢠⠒⡆⢸⠀⠀⢀⠜⠡⠐⠢⡈⢆
⠀⢘⠀⠠⠀⡀⢳⠀⠀⠀⢀⠎⢀⠞⠁⠀⠀⢀⠜⢀⣀⠐⢅⠀⠀⠈⠦⣈⡉⠁⢀⠀⠀⢸⠀⡇⠀⠀⡇⢸
⠀⠘⡄⠐⠔⠃⡸⠀⠀⠀⡌⠀⡎⠀⠀⠀⠀⢸⡀⠡⠤⠃⣰⠀⠀⠀⡤⠐⠉⣀⠌⠀⠀⠘⢆⠈⠒⠊⢀⡜
⠀⠀⠈⠁⠒⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠐⠒⠊⠁⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠
⣤⣤⣤⣤⣄⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⢀⣴⣄⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣴⣄⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⣠⣤⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢹⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢻⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠉⣿⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡆⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠐⢿⠆⠀⠀⠀⠀⠀⠐⢿⠗⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⢾⡷⠀⠐⢿⠗⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⠺⡿⠂⠀⠀⠀⠰⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⢹⡟⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⢸⡟⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢈⣿⠓⠀⠘⣿⠁⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⠇⠀⠀⠀⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡿⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠀⠀⠀⢠⣿⠄⠀⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⠷⠀⠐⣿⠇⠀⠺⣿⠂⠀⢾⡗⠀⠀⠀⠀⠀⠀⠐⢿⡗⠀⠸⢿⡇⠀⠀⢀⣿⠷⠀⠀⠀⠀⠐⢿⣇⠀⠀⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣸⠁⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡏⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⢀⣿⡀⠀⣠⣷⡀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⢠⣴⡏⠀⠀⠘⣷⣤⠀⠀⠀⠀⠀⣴⡟⠀⠀⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠈⠋⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠛⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢐⣾⡆⠀⢴⣷⠄⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⣾⡷⠀⠠⣾⠄⠀⢴⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢀⡾⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣼⠋⠀⠀⠀⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢳⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣄⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⢻⣄⡀⠀⢀⣇⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠹⣦⡀⠀⠀⣿⡀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠂⠀⠀⠐⠻⠇⠀⠙⠟⠁⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠛⠏⠀⠈⠛⠁⠀⠙⠟⠁

⣶⣶⣶⣶⣶⡾⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾⣶⢿⠾⣷⠶⣶⡶⠶⠶⢿

⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣧⠀⠀⢸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡆⠀⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⣸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠐⠓⠛⠓⠃⠀⠀⠀⠀⠓⠛⠓⠓⠘⠓⠛⠛⠃⠀⠀⠀⠘⠚⠛⠚⠂⠓⠛⠛⠚⠐⠓⠛⠓⠃⠀⠀⠀⠚⠚⠛⠒⠀⠀⠀⠚⠛⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⢿⡍⠁⠉⣽⠏⠉⠀⠀⠀⠀⠉⠹⣿⠉⠈⢩⡿⠉⠁⠉⢹⣿⠉⠁⠀⠀⠈⠉⢻⡏⠁⠈⢹⡏⠉⠀⠉⢹⡏⠉⠈⠉⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣼⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢰⡿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠴⠄⠀⠀⠰⠴⠿⠴⠀⠀⠀⠀⠀⠀⠶⠾⠷⠶⠀⠀⠀⠶⠾⠷⠶⠰⠶⠿⠶⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡟⠃⠘⢻⡟⠙⠃⠛⢻⡟⠛⠀⠛⣿⠛⠃⠘⢻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⠘⠋⢿⣟⠃⠘⣻⡟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣆⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⠏⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠿⢤⠀⠀⠀⣤⠼⠧⢤⠠⡤⠿⠦⡄⢠⠼⠿⢤⠄⠀⠀⠀⠀⠀⠀⢤⠼⠧⣤⠠⡤⠾⢧⡄⢠⠽⠧⢤


⠀⠀⠀⠀⠰⠲⣶⡲⠂⠶⣶⡖⠒⠀⠀⠀⠀⠀⠰⠒⣶⡶⠆⠲⣶⡶⠲⠐⠖⣶⡖⠆⠀⠀⠀⠲⠲⣶⠲⠀⠖⣶⠖⠆⠰⠲⣶⠲⠆⠲⢲⡶⠲
⠀⠀⠀⠀⠀⠀⠘⣷⡀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⣰⡟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠹⣧⠀⣼⠏⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⡃⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⠛⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣀⣾⣃⡀⣈⣿⣄⣀⠀⠀⠀⠀⠀⢀⣀⣼⣏⡀⣀⣿⣆⣀⠀⣀⣿⣇⡀⠀⠀⠀⣀⣠⣿⣁⠀⣈⣷⣄⣀⢀⣀⣿⣀⡀⣀⣸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⡶⡶⠶⣶⣶⠶⠶⢶

⠳⡄⢤⡀⢀⠈⣆⣠⠖⠊⠀⠀⢠⣴⡆⠐⢶⡄⣤⡀⢀⠘⣆⡤⠶⠃⠀⠀⢠⢸⠀⠔⢷⡌⣤⡀⣀⠘⣂⡤⠖⠃⠀⠀⢠⢼⠀⠔⢶⡀⣄⡀⣀⠰⣀⡤⠖⠃
⠀⣃⡈⠉⠉⠤⢥⡄⠀⠀⢀⠄⠊⠀⢰⢀⠀⣇⡈⠉⠁⠤⢥⡄⠀⠀⣀⠀⠈⠀⢠⣀⠀⣇⠈⠉⠁⠤⢥⡀⠀⠰⡀⠀⠉⠀⠀⡀⠈⣇⠈⠉⠁⠤⣥⡀⠀⠐⡀
⠐⠉⢇⠄⢀⣀⡀⢀⠀⠀⡿⠀⠘⢳⡜⠁⠐⠉⠇⠀⢀⣀⠀⢰⢀⠀⡟⠀⠘⢷⠘⠁⠈⠉⢃⠀⢀⣀⠀⢠⠀⢀⠇⠀⠛⢷⠘⠁⠈⠙⢃⠀⣀⣀⠀⣀⠀⢨⠇
⡶⠖⢸⣦⠀⠈⠷⢸⠸⠣⣆⠀⠀⡸⠁⢶⡶⠖⢸⣦⠀⠈⠷⢸⠸⢠⡆⠀⠀⡜⠀⢶⠶⠖⢹⡄⠀⠉⠇⣾⠺⢠⡆⠀⠀⠜⠀⣶⠶⠆⢾⡄⠀⠙⡇⣷⠿⢠⡆
⠃⢠⡤⠛⢒⣦⣤⡈⠠⠴⣿⠛⠁⣀⣃⡈⠁⢠⡬⠛⢒⣤⣤⠈⠠⠶⣿⠛⠁⣀⣃⡘⠀⢠⠜⠛⣒⣤⣤⠈⠠⠶⣟⠋⠀⣀⣃⡘⠀⢠⠜⠛⣒⣤⣄⠉⠠⠶⣟
⠆⠀⣤⡴⠉⠀⠹⢷⠀⠀⢸⡤⢨⡁⠈⠹⠆⠀⣤⡖⠁⠀⠹⣶⠀⠀⢸⡄⢨⠁⠈⢻⠀⠀⣤⡖⠁⠀⠹⣶⠀⠀⢸⡄⢨⠁⠈⢻⠀⠠⣤⠆⠁⠀⢹⣶⠀⠀⣻
⣠⠴⠚⣇⠀⣀⠀⠘⠷⢶⡄⢰⠈⠳⠶⣂⣤⠴⠚⣇⠀⣀⠀⠘⠷⢶⡀⢸⠈⠳⠶⣂⡤⠖⢺⣆⠀⣀⠀⠘⠷⢶⡀⣶⠘⠳⠶⣂⡤⠖⢺⡄⠀⡀⠀⠹⠶⣶
⣀⡀⠀⠙⣻⣥⣰⣄⠀⠈⢳⡜⢧⡐⠿⣭⣀⡀⠀⠙⣫⣥⣸⣄⠀⠈⢱⠘⣦⡐⠿⣭⣀⠀⠀⠙⣫⣅⣸⣀⠀⠘⢳⠸⣦⡰⢿⣥⣀⠀⠈⠛⣫⣄⣾⡀⠀⠈⢲
⠉⢛⠀⠰⣄⠈⢳⠉⠉⢀⠀⢀⣿⡛⠃⠀⠉⣛⠀⢰⣄⠈⣷⢉⠉⣀⠀⢀⣛⡛⠁⠀⠉⣋⠀⢰⣄⠈⡇⠉⠉⡀⠀⣀⣟⡛⠀⠀⠉⣣⠀⢸⡀⠈⡇⠉⠉⡀
⠚⠁⠶⠀⠽⠁⠈⠼⠓⢸⡄⠀⠀⢻⠀⠰⠚⠁⠶⠀⠝⠁⠀⠼⠓⢹⡄⠀⠈⢳⠀⠴⠊⠁⠶⠀⠝⠁⠁⠼⠓⢹⠀⠀⠈⢳⠀⠴⠊⠑⠶⠀⠝⠀⠡⠾⠓⢻
⠖⠋⠀⠀⢠⣴⡇⠐⠻⡆⢴⣀⣀⠀⣇⡤⠒⠃⠀⠀⢠⢼⡄⠐⢻⡄⣶⣀⣀⠈⣇⠤⠒⠃⠀⠀⢠⢸⠀⠘⢳⡄⣦⣀⣀⠘⣆⠤⠚⠃⠀⠀⣠⢼⠀⠚⢳⡀⣦
⠀⠀⣀⠀⠈⠀⢀⣀⠀⣇⡀⠉⠁⠴⢶⡄⠀⠠⣠⠀⠈⠀⢀⣀⠀⣁⡀⠉⠡⠴⢦⡄⠀⠀⣀⠀⠈⠀⢈⡀⠀⣇⡈⠉⠁⠴⢦⡀⠄⠀⡀⠀⠁⠀⢀⡀⢀⣁⠈
⠁⠀⠿⠀⠈⢻⡎⠁⠀⠉⢃⠀⢀⣄⡀⢠⠀⠄⠏⠀⠉⢳⡎⠁⠈⠉⢣⠀⢀⣄⡀⠀⠀⡄⠏⠀⠉⢳⠈⠀⠈⠉⢇⠀⢀⣄⠀⡘⠀⠠⠇⠀⠉⢷⠈⠀⠊⠙⣇
⠸⠃⣆⠀⠀⠘⠁⢻⡶⠒⢸⣆⠀⠈⠗⢸⠸⠠⣆⠀⠀⠘⠀⢿⠶⠊⢸⡆⠀⠈⠇⢿⠸⢰⣆⠀⠀⠞⡀⢿⠶⠂⢸⡆⠀⠈⠇⣧⠻⢰⣆⠀⠀⠎⡀⣷⠶⠂⢿
⠠⠒⢿⠉⠀⣠⣇⣈⠁⠠⠖⠙⣛⣧⣤⠈⠠⠲⢯⠉⠀⣠⣇⡈⠀⠠⠞⠙⣻⣧⣤⠈⠠⠲⣯⠉⢀⣠⣅⡈⠀⠠⠞⠙⣻⣦⣤⠈⠐⠲⣏⠉⢀⣸⣅⡈⠀⠠⠎
⡀⠀⢸⡤⢨⡁⠀⠹⠆⠀⡴⡖⠁⠀⠸⢷⡀⠀⢸⡄⢨⡁⠀⢹⠀⠀⠶⡆⠁⠀⢸⢷⠀⠀⢸⡄⢨⠁⠀⠹⠀⠠⠶⠎⠀⠀⠹⣦⠀⠀⢨⡄⣭⠀⠈⠻⠀⠠⢶
⠳⢶⡆⢸⠈⠛⠖⣂⡤⠖⠛⣇⣀⣀⠀⠘⠳⢶⡄⢰⠈⠛⢖⣂⡤⠖⠳⣇⣀⡠⠀⠘⠷⢶⡀⣷⠈⠳⢖⣀⡤⠒⢻⣇⢀⡀⠀⠘⠷⢶⠀⣇⠈⠳⢒⣠⡴⠚⢹
⣀⡀⠱⡌⢷⣐⠻⢧⣄⡀⠀⠙⠩⢥⣸⣄⣀⡀⠱⠜⢧⣐⠿⢥⣄⡀⠀⠙⠯⣤⣸⣄⣀⠀⢱⠘⣦⡐⠿⣤⣄⡀⠀⠙⠭⣤⣺⣄⣀⠈⢳⠘⣦⡘⠿⣤⣀⡀⠈
⡉⢀⠂⢀⣭⡙⠁⠀⠈⣉⠀⠸⣄⠀⠷⢈⡉⢠⠀⣠⣭⡉⠁⠀⠈⣩⠀⢸⣄⠈⠇⢉⠁⣀⠀⣠⣭⡙⠁⠀⠈⣩⠀⢰⣄⠈⡇⢉⠁⡀⠀⣠⣭⡉⠀⠀⢉⣡
⠛⠸⠆⠀⠀⢹⠀⠴⠊⠁⠲⠀⠜⠁⠀⠜⠛⢹⠄⠀⠀⢹⠀⠴⠋⠁⠳⠀⠜⠁⠀⠜⠛⢹⠄⠀⠀⢿⠀⠔⠋⠀⠷⠀⠝⠀⠠⠞⠋⢻⠀⠀⠈⠇⠀⠖⠋⠐⠷
⠻⡆⢰⣄⣀⠈⣧⠴⠚⠋⠀⠀⢠⢼⠇⠘⠻⡆⢶⣀⣠⠈⣦⠴⠚⠁⠀⠀⢠⢼⠀⠘⠻⡄⢶⣀⡠⠘⣧⠴⠚⠁⠂⠀⢰⢾⠀⠚⢻⡄⣦⣀⡠⢐⡦⠔⠛⠁
⠀⣡⡀⠈⠀⠐⠶⡄⠀⠀⣠⠀⠈⠀⢰⣠⠀⣧⡀⠈⠀⠔⢶⡄⠀⠀⣤⠀⠀⠀⢰⡠⠀⣧⡀⠉⠀⠒⢶⠄⠀⠐⡠⠀⠁⠀⢀⡀⢈⣥⡀⠁⠀⠒⢶⠄⠀⠀⡤
⠈⠀⢃⠄⢀⣤⡀⢰⠀⡀⠟⠀⠈⢻⡎⠀⠀⠀⢃⠄⣀⣤⡀⢰⢀⠀⠇⠀⠈⢻⠈⠀⠈⠈⢣⠀⣠⣤⡀⠰⢀⠠⠇⠀⠈⢻⠈⠀⠊⠈⢣⠀⣠⣄⡀⡤⢀⠰⠇
⡷⠊⢸⣶⠀⠀⠛⢸⡘⠡⣆⡀⠀⠜⡀⢻⡖⠋⢸⣶⠀⠀⠟⢸⠘⠰⣇⠀⠀⠜⡀⢿⠖⠃⢸⣆⠀⠈⠇⢷⠛⠰⣇⠀⠀⠞⡀⢿⠖⠃⢻⡆⠀⠈⠇⣷⠛⢰⣇
⠁⠠⠖⠉⣫⡵⣦⡀⠀⠒⢿⠉⢁⣠⣥⣌⠁⠠⠖⠉⣫⡵⣦⠈⠐⠒⢯⠉⢀⣤⣥⡈⠀⠰⠞⠉⣫⣵⣦⠈⠐⠒⣯⠉⢀⣬⣥⡈⠀⠰⠎⠙⣫⣷⣦⠀⠐⠲⣯
⠇⠀⠶⡞⠀⠀⠘⢿⡀⠀⢸⠤⢨⡀⠀⠙⠆⠀⠶⡆⠀⠀⠘⢿⡀⠀⠸⢄⢨⡀⠀⠹⠀⠀⠶⠎⠀⠀⠸⢾⠀⠀⢸⠄⢨⡀⠀⠹⠀⠠⠶⠆⠀⠀⠹⣷⠀⠀⠹
⠴⠞⠋⣧⣀⡠⠀⠘⠻⢾⡆⢸⠀⠛⢚⣣⠴⠚⠉⣧⣀⡠⠀⠘⠳⢾⡄⢺⠈⠛⢚⣡⠴⠚⠹⣆⣀⡠⢀⠘⠳⢾⡀⣷⠈⠛⢚⣡⠴⠚⢹⣆⣀⡄⢀⠘⠳⢿
⣤⣀⠀⠉⠭⢦⡼⣆⣀⠀⠹⠎⣷⣜⡻⢦⣤⣀⠀⠉⠽⢦⡸⣄⣀⠈⢹⠈⣷⣜⡻⢦⣄⣀⠀⠉⠽⢦⣸⣄⣀⠈⠹⠘⣧⣘⠻⢦⣄⡀⠀⢉⠽⣦⣺⣄⣀⠈⠳
⠀⣩⠄⠸⣦⡀⢻⢈⡁⢠⠂⡠⢭⣍⠁⠀⠀⣩⠀⠸⣄⡀⠷⢈⡁⣀⠀⡠⢭⡉⠁⠀⢈⣩⠀⠸⣄⠀⡇⢈⡁⣄⠀⡨⢭⡉⠁⠀⢈⡩⠀⢺⣄⠈⡇⢈⠁⣐⠁
⠋⢀⠻⠀⠜⠁⠀⠚⠛⠸⠆⠀⠀⠹⠀⠔⠋⠀⠳⠀⠞⠁⠀⠚⡋⠸⠆⠀⠀⢻⠀⠖⠉⠀⠓⠀⠎⠀⠀⠚⡋⢹⠀⠀⠀⢻⠀⠖⠉⡈⠗⠀⠋⢀⠠⠚⠋⢹

⠀⠀⠀⠀⣠⣶⣖⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⢿⣶⣄⠀⠀⠀⠀⢠⡶⠒⠲⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⣶⠴⠶⠶⣴⠂
⠀⠀⠀⠀⠛⣯⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⣿⣿⠀⠀⠀⠀⢈⣀⡀⢀⣿⠇⠀⠀⠀⠀⠀⠀⣰⡏⢸⣿⡇⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠈
⠀⠀⠀⣀⠀⣯⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⡼⠟⠃⢠⡀⠀⠀⠀⠑⠚⠛⢷⢤⠠⠀⠀⠀⠀⣰⠟⣨⢸⣿⡇⢰⡆⠀⠀⠀⠈⠉⠉⠋⢻⡿⣄⠢
⠀⠀⠀⠈⠀⣟⡷⢀⠀⠀⠀⠀⣶⣾⣶⡏⠁⠀⠠⢠⠈⠇⠀⠀⣤⠁⠀⠄⢸⣭⢡⠄⠀⠀⠀⣿⣾⡿⢾⣿⡷⠟⠁⠀⠀⠀⣤⣀⠀⠂⠀⡯⡿⠃
⠀⠀⠀⠀⠰⠿⠷⠄⠀⠀⠀⠀⠱⠟⠿⠿⠿⠿⠿⠿⠀⠀⠀⠘⠛⠳⠤⠴⠛⠃⢿⡀⠀⠀⠀⠛⠛⠳⠾⠿⠷⠞⠀⠀⠀⠈⠛⠷⠦⠤⠾⠛⠁


⠀⠀⠀⣠⡴⠶⢦⣤⠀⠀⠀⠀⠀⢠⡦⠶⢤⣦⣶⠂⠀⠀⠀⠀⢀⡤⠀⠦⣤⡀⠀⠀⠀⠀⠀⣠⡤⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⢶⣄
⠀⠀⣾⡿⣏⣀⣀⠼⠤⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⣄⣾⣧⣤⣀⣿⡇⠀⠀⠀⠀⡼⣿⠀⠀⡂⢻⡷⠀⠀⠀⠀⠤⣼⣿⠀⠄⠈⣿⣧
⠀⢸⣿⣿⣋⡉⠙⣿⣆⠀⠀⠀⠀⡀⣀⢀⣾⢁⡀⠀⠀⠀⠀⢛⣾⣿⠿⣿⣿⣄⠀⠀⠐⠞⢿⣿⡀⠀⢀⣼⣛⡇⠀⠀⠀⢰⣿⡇⢀⣄⣀⣿⣿
⠀⣘⣿⣿⢛⣉⠀⣼⣿⢀⠀⠀⠀⣉⣹⣿⣿⠛⠀⠀⠀⠀⢀⢸⣿⠑⠓⠈⣿⣿⡗⠀⠀⠘⠁⠈⠛⠛⢛⣿⣿⢷⣶⠀⠀⡀⣿⣿⠈⣛⢻⣿⣿⠶⢆
⠀⣿⠛⠻⠦⣡⡴⢟⣁⠀⠀⠀⠀⠈⢸⣯⣿⡘⠁⠀⠀⠀⢰⠚⠻⢦⣎⣥⠾⠟⠛⠁⠀⠀⠀⠿⡦⣤⣾⡿⠷⠊⠀⠀⠀⠀⠈⠻⢦⣭⠼⠋⠀⠃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⣠⡶⠒⢢⡀⠀⠀⠀⠀⢠⡶⠒⣦⠀⠀⠀⠀⢠⡆⠀⠀⢰⠀⠀⠀⠀⡴⠖⠲⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⣷⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⠀⣾⠁⠀⢠⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⢰⠇⠀⠀⣼⠀⠀⠀⠀⢰⣇⡠⠤⢤⣀
⠀⠀⠀⠀⠐⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠸⠋⠉⠹⣆⠀⠀⠉⠉⠛⢻⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢀⣼⠇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠸⣆⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠐⠒⠛⠒⠀⠀⠀⠀⠛⠓⠒⠒⠒⠒⠂⠀⠀⠘⠛⠒⠒⠛⠁⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠁

⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⣰⠖⠢⡀⠀⣀⣤⠀⠀⠀⠀⣠⠖⠒⢲⡀⠀⠀⢠⡶⠒⠒⠦⣄⠀⠀⠀⠀⢀⡴⠒⠒⣄
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠉⣹⠃⠀⠀⠀⢰⡏⠀⠀⣸⠃⠀⠐⠟⠀⠀⠀⠀⠸⣆⠀⠀⢠⡟⠀⠀⠀⢸⡆
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⢷⣀⣴⠏⠀⠀⠘⣗⡀⠀⠀⠀⣀⣟⠀⠀⣿⠃⠀⠀⠀⢸⡇
⠀⠀⣿⠀⢀⣤⠶⠶⢤⣄⠀⠀⠀⠀⠠⠶⣾⠶⠖⠀⠀⠀⣠⠜⠛⢦⡀⠀⠀⠀⠈⠻⠦⠤⠶⠋⣿⠀⠀⡿⠀⠀⠀⠀⢸⡇
⠀⠀⢹⣴⠋⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⣆⠀⢠⡄⠀⠀⠀⠀⢰⡇⠀⠀⣧⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠻⣄⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣠⠏⠀⠸⣇⠀⠀⠀⢀⡾⠀⠀⠀⢹⡄⠀⠀⣸⠏
⠀⠀⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⠐⠒⠛⠒⠀⠀⠀⠀⠈⠙⠒⠒⠊⠁⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠙⠲⠚⠁

⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⢸⣿⣷⣒⣒⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠘⢻⣏⡟⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⠛⢿⣿⣿⡆⠀⠀⠀⠀⠈⠛⠛⠛⣻⣿⣿⣷⣿⠗⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⣫⡁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⢀⣤⣠⡀
⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⡄⠀⠀⠀⠀⠀⢸⣯⣯⣏⣀⣀⣸⣿⣸⡇
⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣤⣄⣤⡀⠀⠀⢘⣯⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣾⣷⣧⣄⣴⣤⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⢸⣿⢸⡇
⠀⠀⠀⠀⠸⠿⠇⡇⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣻⣟⣛⣛⣿⡇⣿⣿⣹⠀⠀⠀⠀⠀⠀⣠⣾⣯⣿⣽⣷⡄
⠀⠀⢸⣟⣟⡛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠛⢁⣿⣾⣺⠀⠀⠀⠀⠀⠀⣿⡿⠻⣻⣿⡯⣷
⠀⠀⢸⣿⣿⢨⣟⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⢀⣵⣾⣷⣿⣿⣿⢇
⠀⠀⢸⡿⣿⠽⠛⠛⢿⣿⣿⣦⠀⠀⠀⠀⣸⣿⣿⡟⠚⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⢀⡿⣿⣿⠟⠋⠻⣵⣿⣷
⠀⠀⢠⣄⣤⡀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢸⣷⣷⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣟⣿⣇⠀⠀⠀⣽⣯⣿
⠀⠀⠘⣿⣿⣿⣶⣴⣾⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⣷⣦⣖⣽⣿⡿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣾⣿⣿⠏
⠀⠀⠀⠈⠙⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠻⢿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⡿⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⠀⠀⠀⢈⣿⣿⠗⠀⠀⠀⠀⣿⣿⣿⠁⠀⠈⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⢆⣾⣿⣿⠃⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣏⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠿⠋

⣿⠿⠿⠿⡿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣻⣿⣿⣻⣿⣿⣿⣟⣻⣿

⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⡞⡠⢄⠈⡆⠀⠀⢀⠞⠁⠀⡇⠀⠀⢀⣀⡐⢂⢱⠀⠀⠀⠾⣤⠒⡀⡤⠀⠀⠀⢠⠎⠀⢸
⠀⠀⠀⢸⠅⡀⢸⠇⡇⠀⠀⠘⠋⡇⠀⡇⠀⠀⠀⠉⢀⡼⡸⠀⠀⠀⠀⠰⢞⡻⡅⠀⠀⢠⢃⡞⢻⣸⡀
⠀⠀⠀⠸⣆⠳⠞⢠⠃⠀⠀⠀⠀⡇⢸⡇⠀⠀⢀⡴⠛⠒⠠⡄⠀⠀⡔⠲⣀⠇⡐⠀⠀⠿⠬⡭⡁⣴⠇
⠀⠀⠀⠀⠈⠒⠒⠃⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠚⠒⠒⠒⠒⠃⠀⠀⠈⠒⠢⠒⠁⠀⠀⠀⠀⠀⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠐⠀⡀⢀⠄⠀⠀⢀⠞⡁⣉⡂⠀⠀⢚⣋⡛⠋⠙⡇⠀⠀⡜⢁⠤⡍⢢⠀⠀⢠⡞⣋⣉⠲⡄
⠀⠀⠀⠀⣇⣰⡆⠄⠀⠀⠀⢾⠸⠄⠥⡄⠀⠀⠀⠀⢨⠃⡄⠀⠀⠀⣻⠌⠒⢃⡜⠀⠀⡟⢸⡃⣽⠀⢱
⠀⠀⠀⠀⣀⡁⢘⡆⡆⠀⠀⠘⠀⠀⠂⢹⠀⠀⠀⢀⠇⡀⠀⠀⠀⠀⡇⠰⡁⡇⢹⠀⠀⠙⣮⠿⢷⠀⡜
⠀⠀⠀⠈⢧⡁⢋⠐⠁⠀⠀⠐⢀⣁⣠⠎⠀⠀⠀⢸⣠⡇⠀⠀⠀⠀⠷⣄⠈⣀⠞⠀⠀⠘⢍⡑⢋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⢴⠀⠀⠀⠀⢰⠀⢰⠆⠀⠀⠀⢰⡆⢰⡆⢰⡆⠀⠀⠀⠀⡆⠀⣆⠀⠀⢰⠀⠀⠀⠀⢰⡄⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⢻⡀⠀⡆⠀⠀⠀⠀⠈⣇⠀⢠⠁
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠘⡇⢠⠁⠀⠀⠀⠀⠀⢹⡀⡘
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠀⢿⡜⠀⠀⠀⠀⠀⠀⠘⣧⠃
⠀⠀⠀⠙⠀⠀⠀⠀⠘⠀⠘⠁⠀⠀⠀⠘⠃⠘⠃⠘⠃⠀⠀⠀⠀⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⣀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢀⡀⢀⡀⢀⡀
⠀⠀⠀⠀⣷⠀⠀⡘⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⢀⠇⠀⡇⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⡸⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢸⡆⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⣷⠀⡸⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠇⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⣧⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠧⠀⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠄⠸⠇⠸⠇


⠀⠀⠀⣶⠀⠰⡀⢀⡖⠀⠀⠀⠀⠐⡆⠀⣶⠀⠀⠀⠀⠀⢂⠀⢰⠆⠀⣶⠀⠀⠀⠀⠲⡀⢀⡖⠀⢲⠂⢰⠂
⠀⠀⠀⣿⠀⠀⢣⡼⠁⠀⠀⠀⠀⠀⠘⣰⠃⠀⠀⠀⠀⠀⠈⢦⡏⠀⠀⣿⠀⠀⠀⠀⠀⢣⣼⠁⠀⢸⠀⢸
⠀⠀⠀⣿⠀⠀⣸⢇⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⣿⠀⠀⠀⠀⠀⣸⢇⠀⠀⢸⠀⢸
⠀⠀⠀⣿⠀⢠⡏⠈⡄⠀⠀⠀⠀⠀⡾⠀⢃⠀⠀⠀⠀⠀⣸⠃⠱⠀⠀⣿⠀⠀⠀⠀⢠⡏⠘⡄⠀⢸⠀⢸
⠀⠀⠀⠉⠀⠈⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡇⠀⠀⠀⠀⠀⢠⡦⢞⣥⣠⣽⣾⢦⠀⠀⠀⠀⠀⠀⢀⣾⠛⣠⠟⣷⠙⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡟
⠀⠀⠀⠀⠀⠀⢀⡘⢂⡼⠃⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⣽⡇⡇⠀⠀⠀⠀⠀⠬⡿⠿⠁⠀⠀⢰⣯⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣼⢃
⠀⠀⠀⠀⠀⠀⠀⢺⣍⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡏⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣥⡾⢛⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡧⢔⡁⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⣷⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⡯⠀⢽⣾
⠀⠀⠀⠀⠀⠀⠀⢈⡷⢋⡆⠀⠀⠀⠀⠀⢀⡀⢧⣈⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣭⡀⠀⠀⠀⠀⠀⢀⢀⡽⢶⣟⠀⢾⣼⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⡇⠀⠀⠀⠀⠀⣈⡙⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡠⣶⠄⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⣠⣿⡿⣛⣆⣹⣯⣽⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣫⣽⡆⠀⠀⠀⠀⠀⡙⣫⣼⡟⣿⣡⣭⣦⡇⠀⠀⠀⠀⠀⠀⠸⠋⣠⣏⣀⠛⠰⠋⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⣻⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙


⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⢤⣤⠀⡦⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣦⣤⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣶⢠⣤⣤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠲⡴⢆⢀⡀
⠀⠀⠀⠀⠀⠀⣠⠚⢹⠀⠹⠷⠔⠃⠀⠀⠀⠀⠀⠀⣠⠞⢹⠈⠹⠧⠴⣁⡄⠀⠀⠀⠀⠀⠈⠀⠞⠻⠁⠸⣅⡀⠀⠀⠀⠀⢀⡌⣯⣭⠆⠿⠉⢩⣧⡀
⠀⠀⠀⠀⠀⠀⢹⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡌⠀⠀⠀⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡥⠀⠀⠀⠀⠀⠘⡧⠙⡃⠀⠀⠀⠟⣉⡃
⠀⠀⠀⠀⠀⠀⠼⣟⠛⣠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣻⠆⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢞⡿⠀⠀⠀⠀⠀⠀⠀⣧⣶⣥⣦⠀⣰⢁⣠⠁
⠀⠀⠀⠀⠀⠀⢠⢞⠛⢿⡮⣻⣽⣦⡀⠀⠀⠀⠀⠸⣠⡜⠻⣿⠌⣛⣼⣧⡀⠀⠀⠀⠀⠀⠀⢀⡜⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢅⡈⢿⡏⠀⠧
⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢰⣶⢾⡇⠀⠀⠀⠀⠀⣟⣥⡷⠀⠀⠀⣭⢿⡟⠀⠀⠀⠀⠀⠀⣸⣉⣥⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣷⠋⠀⠀⠀⣠⠶⡦
⠀⠀⠀⠀⠀⠸⡟⢻⡦⢀⡀⢼⣿⣾⠁⠀⠀⠀⠀⠀⠿⠮⠴⢄⡀⢤⣿⣾⡷⠀⠀⠀⠀⠀⢰⡿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣿⣤⣄⡠⣼⣯⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠾⢥⡎⠉⠋⠁⠋⠀⠀⠀⠀⠀⠀⠀⠘⢥⠊⠐⠋⠡⠊⠀⠀⠀⠀⠀⢠⡟⣠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣵⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡐⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣁⡛⠯⢴⣮⠷⠆⠀⠀⠀⠀⠀⢠⣾⣧⣽⠸⠡⠓⣚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡹⠃⠀⠀⠀⢱⣞⢂⠀⠀⠀⠀⠀⢚⠛⠻⠀⠀⠀⠸⣐⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⢀⡤⢶⠑⢿⣃⠀⠀⠀⠀⠀⢫⣵⠆⠀⠀⠀⢠⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢯⡄⠹⣠⣞⣥⠀⠀⠀⠀⠀⢙⡧⠤⠀⠀⠀⠈⠟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⠅⠀⠀⠀⠀⠀⣾⡶⣞⠀⠀⠀⠰⣠⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡙⢻⢀⡀⢴⣿⡙⡿⠀⠀⠀⠀⠀⠻⣐⡨⣦⠀⠀⠴⠟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣟⣛⣠⠹⠇⠀⠀⠀⠀⠀⠀⠀⠛⢷⣯⣠⣴⠾⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⢀⡀⠀⣀⠀⣀⣀⡀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⣟⡋⠘⢸⢶⡏⢻⡎⣓⡄⠉⣹⠁⠀⣇⣘⠉⣿⡁⠄⣶⠄⢱⣜⡧⠤⣿
⠀⠀⠀⠀⠀⠀⠝⠛⣿⢠⢸⡆⣴⣏⣠⡿⣦⢰⡯⠀⠰⡇⣲⢐⠶⡃⡅⠛⡈⣸⡏⣓⣶⡋
⠀⠀⠀⠀⠀⠀⣾⣇⣿⢠⢌⠨⠉⠉⢹⡧⣬⢰⠛⡆⢀⣅⣹⠹⢼⣧⣭⣟⠻⡟⠁⢉⣠⡿
⠀⠀⠀⠀⠀⠀⠨⢭⣡⠚⡏⡆⠀⠐⠸⣧⣿⢨⠛⡅⢀⣻⠙⢁⠈⠁⣾⢘⠋⠑⡄⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠒⡴⢁⠮⢡⡶⣦⠛⣼⠠⣤⠘⠤⠃⠀⣇⡕⠘⠰⢐⡃⣿⣔⡊⡀⢿⣼⢧
⠀⠀⠀⠀⠀⠀⠈⠉⢸⣹⢸⡷⣿⢰⣶⠈⣳⠰⢯⡁⠀⣮⡇⡘⣴⢸⡇⣿⢸⡅⠗⠊⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠛⠘⠋⠓⠋⠙⠚⠁⠈⠓⠁⠀⠛⠁⠈⠙⠛⠘
⠀⠀⠀⠀⠀⠀⡖⡂⢖⡶⣶⡖⣢⡞⣶⣶⢐⢴⣲⠀⢠⠂⢲⢰⡆⠀⠀⠆⠴⠶⣦⢰⡂⢴
⠀⠀⠀⠀⠀⠀⣇⡃⠿⢹⡆⣴⣃⡴⠇⡈⣐⠒⣿⠀⠀⢱⠎⢀⣷⣖⠲⣷⣾⣛⣋⠂⣉⠘
⠀⠀⠀⠀⠀⠀⡄⣿⣀⢻⡆⢿⠟⣹⢋⢅⢡⡆⣻⠃⠰⣿⡦⣷⡄⣍⡇⣯⣩⡏⠉⠴⢣⢦
⠀⠀⠀⠀⠀⠀⠓⠋⠙⠟⠱⢐⠘⣿⣮⣜⠈⡙⣿⠀⠀⠩⣲⡮⢶⡟⣶⣼⣌⠀⡂⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠺⣿⣼⠞⡇⠚⢸⢁⠙⢿⡇⢙⠡⠀⠠⣠⠿⠸⢠⡞⣷⡛⠳⣷⠀⢣⡶⣧
⠀⠀⠀⠀⠀⠀⢲⡶⠾⠗⢿⣽⠈⠁⡀⢭⡄⢀⢈⠁⠰⢳⡆⡇⣾⣷⢳⡅⣰⣹⢔⠘⠧⣿
⠀⠀⠀⠀⠀⠀⠚⡇⢮⡹⠸⡽⠀⠀⠀⢤⡇⠄⠠⠀⠰⣯⠄⡟⢯⡼⠿⠰⠈⠁⠸⠟⠷⠟

⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠋⣀⣀⣈⣉⡉⠉⠉⠉⣩⣿⣿⠏⠀⠀⠀⠀⠿⠿⠿⠿⠿⢿⣿⣿⡆⠀⢀⣀⣀⣀⣀
⣿⣿⣿⡆⠀⣀⣴⣾⣿⣿⣿⣶⣦⡈⠁⠀⢠⣾⣿⣿⣿⣿⣿⣷⠀⠀⠻⢿⣿⣆⠀⠀⣀⣴⣶⣶⣶⣦⣄⠸⣿⣿⡇⢰⣿⣿⣿⣿⣿
⣿⣿⣿⠃⢰⣿⣿⡟⠉⠛⠻⣿⣿⣷⡀⢀⣿⣿⡏⠁⠀⠈⢻⣿⣇⠀⠀⢠⣿⣿⠀⢰⣿⣿⠟⠉⢻⣿⣿⡀⢿⣿⠇⠈⠛⠻⠟⠛⠛
⣿⣿⠏⠀⢸⣿⣿⡀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⠁⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⠟⠀⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰
⣿⠋⠀⠀⠸⣿⣿⣷⣤⣶⣶⣾⣿⣿⡿⢸⣿⣿⣶⣿⣿⣿⣦⡈⠙⠿⠛⠛⣁⡀⠀⢹⣿⣿⠀⠀⢰⣿⣿⡇⠀⣤⡀⠀⠀⠀⠀⣴⣿
⠃⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⣿⣿⡇⢸⣿⣿⣿⠿⠿⢿⣿⣷⠀⠀⣠⣾⣿⡇⠀⢸⣿⣿⠀⠀⢸⣿⣿⡇⢀⣿⡇⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠸⣿⣿⡇⠀⠀⣠⣿⣿⢠⣾⣿⣿⣿⡇⠀⠘⣿⣿⣦⣤⣾⣿⣿⠃⢸⣿⡇⠀⠀⣼⣿⣿⡿
⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⡇⠀⠀⠈⠛⠛⠿⠿⠛⠁⠀⠸⣿⠇⠀⣸⣿⣿⡿⠁
⠀⠀⢸⣿⣿⡟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣉⣙⣛⣛⠛⠁⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠻⡿⠛⠁
⣄⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⣠⣤⣤
⠿⠀⣿⣿⣿⣇⣀⣤⣄⣀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⢻⣿⣿⡇⠀⠀⠘⣿⣿⠃⠀⠀⢸⣿⣿⡿⠉⠀⠀⣿⣿⣿⡀⠀⠀⠻⠿⠿⠿
⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣠⡀⠀⠀⢸⣿⣿⣷⣄⡀⢀⣿⣿⣿⡇⠀⠀⠀⢀⣠⣤
⣿⡄⠘⠻⠟⠛⠛⠛⠻⢿⣿⣿⣿⣇⢠⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⢠⣾⡿⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣾⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠸⣿⣿⠁⠀⠀⠀⣿⣿⠇⠀⣰⣿⡿⢡⣾⣦⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠻⠟⠁⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⢰⣿⣿⠀⣼⣿⣿⣦⣾⣿⡇⠀⢠⣾⣿⣿⠟⠋⠀⠻⣿⣿⡄⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠸⣿⣿⣆⠀⠀⣸⣿⣿⠀⠙⠛⠛⠛⢻⣿⡇⠀⣿⣿⡿⠁⠀⠀⠀⢀⣿⣿⣿⠀⠀⢀⣾⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣷⠀⢿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠟⠀⢠⣾⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠹⢿⠏⠀⠀⠙⠻⠿⠿⠿⠿⠿⠟⠉⠀⠀⠘⠛⠛⠛⠿
⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⠀⠀⣴⣶⣶⣶⣶⣶⠆⠀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣄⠀⠀⠀⣠⣶⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⠟⠋⠛⢿⣿⣇⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⠄⠀⢰⣿⣿⠋⠉⠉⢿
⠀⠀⢀⣼⣿⣿⣏⡀⠀⠀⢸⣿⣿⡀⠀⢀⣼⣿⣿⠀⢠⣾⣿⣿⣿⣿⡄⠀⣿⣧⣤⣄⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⣾⣿⣯⣤⣤⣤⣀
⡀⠀⠸⣿⡿⠿⣿⣿⡆⠀⠀⠻⣿⣿⣾⣿⣿⡿⠁⠀⠻⠟⠁⠀⣽⣿⡇⠀⠻⠋⠙⣿⣷⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣼⣿⡇⠀⢀⣼⣿⠟⠻⣿⣿⣧⠀⠀⠀⢀⣴⣾⣿⡟⢀⣴⣦⣀⣤⣿⣿⠀⠀⣸⣿⣿⡏⠀⢀⡀⣿⣿⣿⠀⠀⠈⣿
⢣⣤⣤⣄⣠⣼⣿⡿⠃⠀⣾⣿⡏⠀⠀⠈⣿⣿⡇⣠⣾⣿⣿⣟⣉⣀⣈⣻⣿⡿⠿⠛⠁⠀⢰⣿⣿⡿⠀⢀⣿⣿⢻⣿⣿⣦⣤⣾⣿
⠘⢿⣿⣿⣿⡿⠟⠁⠀⠐⣿⣿⣧⣀⣀⣼⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣥⣤⣼⣿⣿⠈⠻⢿⣿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡋⠉⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣴⣿⣿⠀⠀⢿⣿⣿⡿⠋⠀⠀⠈⠁⣀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡄⠘⢿⣿⡿⠀⠀⣀⠉⠁⢀⣤⣄⠀⠀⣾⣿⣿⡄⠙⠛⣛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⠀⠀⠈⢀⡀⠸⠿⠷⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⣿⣿⣿⠀⢸⣿⣿⣿⡆⢀⣤⣤⣄⡈⠁⠀⠀⠈⠛⠛⠁⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢈⣛⠋⠁⢀⣀⠉⠛⠛⠁⢸⣿⣿⠿⣿⣦⠀⠶⣿⣷⠄⢰⣶⡄⠀⢈⡉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⠺⠿⠇⢠⣿⠟⠋⠁⠀⠀⠀⠈⢳⣄⡀⠉⠀⠈⠉⠁⢰⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⣿⣷⣄⠈⠻⢿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠃⠀⠈⠻⠿⠟⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠁⢀⣴⣦⠀⢀⣴⣆⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⠇⢀⣾⣿⣿⠀⢾⣿⡿⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢁⣤⣀⡙⠋⠀⠘⣿⣿⠇⠀⢀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⢿⣿⣿⣿⣷⡄⠀⠈⠉⠀⠀⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠀⠈⢿⣿⣿⡿⠃⠀⣴⣿⣦⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣶⣶⡄⠈⠉⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⣾⣷⡝⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⣄⣰⣶⣦⡈⠀⠀⢠⣾⣧⠀⠙⠛⣁⡀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡷⠀⠀⣿⣿⣿⠀⢠⣾⣿⣿⡇⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠈⠙⠁⠀⣿⣿⣿⡿⠁⠈⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠙⠛⠋⠀⠀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠀⠀⢨⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢀⣤⣶⡆⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣿⡿⠃⠀⠀⠘⣿⣿⣿⡿⠉⠲⢤⣄⣀⣀⣠⠞⠙⠛⠁⠀⠈⠻⠟⠁⠀⠸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠉⠀⣠⣶⣦⡄⠈⠉⠉⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⡆⠀⢀⣤⣤⡀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠹⢿⠟⠁⣠⣴⣶⣶⣦⠀⠙⠿⢿⡿⠏⠀⠀⠻⣿⣿⠇⠀⣿⣿⣿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠀⠀⠀⣀⡀⠀⠹⣿⣿⣿⣿⠇⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠘⠻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣰⣿⣿⣿⣷⣄⠈⠉⠋⠁⢠⣶⣿⣿⣿⣆⠀⣾⣿⣿⣿⡿⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⢀⣈⣻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣦⡄⠀⠀⢸⣿⣶⣶⣤⡄⠀⠀⢸⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⣠⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠴⠦⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣿⣆⠀⠀⠀⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣿⠟⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠶⣶⠶⠀⠀⠀⠰⢶⡶⠆⠲⢶⠶⠀⠀⠀⠰⢶⡶⠆⠶⣶⠶⠀⠶⡶⠆⠀⠀⠐⠶⡶⠆⠰⢲⡶⠆⠶⣶⠶
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣇⣿
⠀⠀⠀⣀⣿⣀⠀⠀⠀⢀⣸⣇⡀⢀⣸⣀⠀⠀⠀⢀⣸⣇⡀⣀⣿⣀⠀⣀⣇⡀⠀⠀⠀⣀⣇⡀⠀⠀⢀⣿⣇
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠈⠹⣏⠁⢉⡿⠉⠀⠀⠀⠈⢹⡏⠁⢉⡟⠉⠈⢹⡟⠁⠀⠀⠈⠙⣿⠁⠉⣿⠉⠁⠉⣿⠉⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⢿⡀⣸⠇⠀⠀⠀⠀⠀⠀⢿⠀⣸⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⡟⠀⠀⠀⠀⠀⠀⠀⠸⣧⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢤⠿⢧⠄⠀⠀⠀⠀⠀⠀⢤⠿⢥⠀⠀⠠⡼⠧⡤⠀⠀⠀⠀⢠⠽⢧⠄⠀⠀⡤⠿⡤⠠⡼⠧⡄

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⡀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣧⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡞⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠀⠀⠐⠚⠓⠂⠒⠚⠓⠂⠒⠛⠒⠀⠀⠀⠀⠀⠐⠚⠓⠂⠒⠛⠓⠐⠚⠓⠒

⠀⠀⠀⠰⠶⣶⠆⠴⣶⠶⠄⠀⠀⠀⠀⠶⣶⠆⠰⣶⠶⠆⠶⣶⠶⠀⠀⠀⠶⣶⡶⠠⢶⡶⠆⠰⢶⡶⠄⠶⣶⠶
⠀⠀⠀⠀⠀⠹⣆⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⣠⡟⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⢀⣾⠁⠘⣧⡀⠀⠀⠀⠀⠀⢀⣼⠃⢈⣷⡀⠀⠀⣿⢀⠀⠀⠀⠀⣰⡏⠈⢻⡄⡀⠀⣸⡇⠀⡀⣿
⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣍⠄⢰⠀⠀⠀⠀⢠⠒⣠⡆⣅⣀⠀⣄⡩⣛⡸
⠀⠀⠀⢀⡤⠶⠴⢾⢎⡎⠀⢀⡀⣠⠺⣁⣀⣀⠉⠛⢯⠀⠀⠀⠀⡎⠀⡴⠮⠭⢠⡟⠀⡤⠀⡇
⠀⠀⡰⠋⢠⠔⠒⠪⡉⢹⡤⠊⠑⢺⠀⠈⠀⣸⠃⠀⡼⠀⠀⠀⠰⢥⣀⠑⠢⣀⠞⢀⡎⡑⠀⡇
⠀⢰⠃⢠⠇⠀⠀⠀⡷⡏⢀⡄⠐⢸⣠⠤⠊⠁⣠⠞⠡⢀⠴⣀⣀⠀⢈⠆⠀⢹⡀⠀⠀⠁⠀⠉⢹
⠀⢸⠀⠘⢆⡀⣀⡴⠁⢹⠃⣧⠀⢸⡀⠀⠀⠛⢳⠔⠳⠚⠿⠻⡀⠉⠁⠀⢀⡜⠉⠉⠉⡇⠀⡏
⠀⠈⠣⣀⠀⠉⠁⠀⣠⠏⠀⢸⠀⠘⡏⠓⠒⠤⣾⠀⠸⣁⠕⠀⡟⠛⠒⡋⠁⣀⠀⠀⠀⠓⠒⠃
⠀⠀⠀⠈⠉⠓⠚⠉⠁⠀⢀⠸⢤⠤⠇⠀⠀⠀⡨⠓⠀⠀⠀⠺⢄⢀⣠⣤⣃⣹⣀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⡖⠤⠤⣡⡖⡍⢃⠀⠀⠀⢸⠀⠠⡏⠉⣱⠀⡼⠉⢀⡠⠬⣥⣏⣄⡿⠦⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠸⣅⣀⣀⡀⠈⠒⠁⡧⢄⡌⡼⣒⡇⠈⠉⠁⡜⠀⠀⠈⠉⠲⢤⠇⠀⡖⠉⢢⢀⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠚⠧⠄⣈⠉⠚⡭⠋⠉⠉⡇⠀⡜⠉⢱⠀⢸⣇⠀⠓⠔⠋⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡴⠁⠀⠀⡔⠊⠁⢠⡊⠀⠀⠀⠀⢧⡀⠙⠒⠊⠀⡸⠉⠲⠤⠴⢶⠀⠀⡞
⠀⠀⠀⠀⠀⢀⡎⠀⢠⠏⠀⠀⠀⠀⠓⠒⡄⠀⠘⡆⠀⠀⠀⠀⠙⠒⠒⠒⠋⠀⠀⠀⡤⠚⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠓⠒⠚⠀⠀⠀⢰⠓⠒⠒⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠒⠉
⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣴⢳⡆⠀⠀⠀⠀⣴⢱⣎⢱⡆⠀⠀⠀⣴⢹⡎⢱⡆⠀⠀⠀⠀⢠⡞⢱⡆⠀⠀⠀⠀⠈⢱⡍⣶⠙
⠀⠀⠀⠀⠀⠘⠴⢇⡁⠀⠀⠀⠀⠸⠏⠀⢀⣿⠀⠀⠀⠐⢃⡰⢧⡟⠀⠀⠀⣀⢿⡼⢇⡄⠀⠀⠀⠀⡸⢧⡤⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⡀⢰⣾⠋⠀⠀⠀⠀⠸⠷⠞⢳⡄⠀⢀⠛⡞⢠⡞⠃⠀⠀⠀⠀⠱⠞⠒⠋⣶
⠀⠀⠀⠀⠀⠀⠀⣱⡇⠀⠀⠀⢀⠶⣸⠟⠁⢀⠀⠀⠀⠄⡀⢀⡰⢇⡇⠀⠀⣿⣸⣏⡸⣇⡂⠀⠀⠀⢀⠀⢀⠾⣠
⠀⠀⠀⠀⠀⠀⣬⢧⣼⡇⠀⠀⢚⣼⣣⣜⣣⣿⠃⠀⠈⠤⣻⣼⡧⠎⠀⠀⠀⠀⠀⠘⣣⡄⠀⠀⠀⠐⠜⣣⣟⠴⠃




⠀⠀⠀⠀⠀⠀⠀⣠⢦⣤⠀⠀⢠⠒⣤⢲⡔⢢⡄⠀⠀⠀⣤⠒⣴⢢⡀⠀⠀⠀⣠⠒⣤⢢⡀⠀⠀⠀⠀⡄⢠⡄⣀
⠀⠀⠀⠀⠀⠀⣶⠹⠊⠉⠀⠀⠈⠉⠉⢉⢱⡾⠁⠀⠀⢰⣉⠋⢉⡎⣱⠀⠀⠀⡉⡞⠉⠊⢱⡄⠀⠀⢘⣱⠏⠙⣏⡆
⠀⠀⠀⠀⠀⡾⣁⣿⣰⢆⠀⠀⠀⠀⠀⣼⠿⠀⠀⠀⠀⢀⠿⣤⢿⡼⠃⠀⠀⠀⠿⣤⢀⡼⢧⡄⠀⠀⣼⠻⠀⠀⠛⣤
⠀⠀⠀⠀⠈⣧⠏⠀⢠⡜⠃⠀⠀⠀⢰⢹⠇⠀⠀⠀⠀⠈⣶⠉⠀⢱⣞⠀⠀⠀⠀⠛⣶⢱⡾⠀⠀⠀⢱⡖⠀⠀⣶⡙
⠀⠀⠀⠀⠀⠉⡿⣀⢾⡹⠁⠀⠀⠀⣀⢿⠀⠀⠀⠀⠀⠘⢀⠶⣰⢇⡜⠀⠀⠀⣀⠾⣸⠟⠁⠀⠀⠀⠀⡸⢇⡼⣥⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠀⢀⡄⢀⡀⠈⠉⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡇⠰⡇⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠎⠀⢀⡄⢠⣄⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡌⠀⠀⢸⣇⢸⣿⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠰⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡃⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⡠⠈⠀⠀⠈⠢⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡜⠀⠠⠆⣠⠆⠀⠐⡀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⣴⢫⡤⠀⠀⢡⠀⠀⠀⠀⠰⠁⢠⡄⢠⡄⢄⠀⢠⡄⢠⡄⠱
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢸⡇⢸⡆⠈⡆⢸⡇⣸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⢀⠂⠁⠀⠑⢄⠀⠀⠇⡄⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠜⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠃⢀⠃⠀⣀⠀⠀⠀⡆⠀⡄⠃⠀⠀⠀⠀⠑⠠⠀⣀⣀⣀⣀⠤⠒⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠠⠂⢠⠀⠈⠻⣧⡅⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢺⡀⡀⠀⠀⠘⠃⠀⠄⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠕⡐⢄⠀⠀⣀⠜⢔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠪⡢⠌⠩⠔⡢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⣀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢀
⠀⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⠀⠠⡖
⠚⠃⠙⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⠀⠁⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⡄⠀⠰⠐⠀⠀⡀⠀⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣀⣠⡀⠈
⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠀⠀⠀⣀⢀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢧⢀⡀
⠀⠀⠀⠰⠿⠀⠸⣀⣀⣄⣀⠽⠛⠉⠁⠀⠀⠀⠂⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⣠⠶⠂⣠
⠀⠀⠀⡄⠀⠀⠐⠇⠈⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠞⠒⠁
⠀⠀⠀⢸⡀
⣤⣤⣤⣬⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⠀⠀⠀⠀⠀⠀⡠⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⡤⣤
⠀⠀⠀⠀⠀⢈⡭⢾⣋⣻⠀⠀⠀⠀⠀⠘⠴⠚⠒⢦⡀⢐⠀⠀⠀⠀⠀⠣⠒⠓⢲⡀⠱⠀⠀⠀⠀⠀⠀⢀⣞⣿⡍⢹⠀⠀⠀⠀⠀⠀⡷⢾⠗⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣒⣺⠀⠀⠀⠀⠀⠀⢤⢤⠺⣁⠜⠀⠀⠀⠀⠀⢠⠯⡼⠁⠥⢼⠀⠀⠀⠀⠀⢠⣟⣟⢒⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⠀⠀⣠⣞⣒⡶⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠑⡄⠀⠀⠀⢰⠯⣿⢤⣴⢯⢽⠦⠀⠀⠀⠀⠈⠁⠉⠙⢳⡀⢘
⠀⠀⠀⠀⠀⠀⠀⢰⠠⡆⠀⠀⠀⠀⠀⢠⢮⢵⠶⢧⠤⢤⠄⠀⠀⠀⢀⠦⣤⡤⡴⠏⢀⠇⠀⠀⠀⠘⠛⠛⠛⠛⡟⢺⠚⠀⠀⠀⠀⢠⢤⣀⣠⡾⠁⡔
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠚⠚⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠓⠃⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠘⠚⠒⠓⠛⠉


⠀⠀⠀⠀⠀⠀⣀⡤⡤⡖⠀⠀⠀⠀⠀⢰⢶⡖⡖⢲⢲⠲⠀⠀⠀⠀⠀⢀⠤⡒⣒⠦⣄⠀⠀⠀⠀⠀⢀⢄⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⢤⡀
⠀⠀⠀⠀⣰⠫⣤⠞⠛⠉⠀⠀⠀⠀⠀⠘⠚⠓⠓⣻⣾⡾⠀⠀⠀⠀⢰⠅⣼⠉⠉⡯⠨⡅⠀⠀⠀⢠⠍⢀⡟⠙⢣⠀⢓⠀⠀⠀⠀⢰⠁⡼⠋⢻⡁⠱
⠀⠀⠀⢠⣇⣷⢟⣏⡉⠐⢄⠀⠀⠀⠀⠀⠀⠀⣰⠯⡴⠁⠀⠀⠀⠀⠀⢣⡨⢷⣞⣭⣞⠀⠀⠀⠀⠸⠀⠸⣆⣀⢼⡭⢸⠀⠀⠀⠀⡇⢀⡇⠀⠀⡧⢩⡇
⠀⠀⠀⢸⡻⢿⠁⠀⢹⣂⢈⠀⠀⠀⠀⠀⠀⣰⠿⣻⠁⠀⠀⠀⠀⠀⠰⠫⣶⠋⠙⣦⠈⢢⠀⠀⠀⠀⠉⠂⠤⠐⡾⠋⡹⠀⠀⠀⠀⡧⢐⡇⠀⢠⡇⢸⠇
⠀⠀⠀⠀⢃⡘⠣⡤⠾⠁⡜⠀⠀⠀⠀⠀⢰⣋⣹⠁⠀⠀⠀⠀⠀⠀⠨⣀⠹⢤⢴⠟⢁⡆⠀⠀⠀⠀⢠⢠⠶⠋⢁⠘⠁⠀⠀⠀⠀⠹⡀⠹⠦⠞⢁⠜
⠀⠀⠀⠀⠀⠈⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠊⠁⠀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠊⠈



⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠂⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⡄⠀⠀⠀⠀⠀⠀⠀⡠⠱⠃⠀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠴⠖⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢀⠔⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡜⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⡀⠀⠀⠀⠀⣰⠀⠀⣇⣇
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠈⠀⠀⠀⠠⠀⡤⠄⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⡀⡸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⠁⠠⣤⠀⠀⠀⠀⠈⠘⠀⠀⢀⢌⠆⠀⠀⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠲⠗⠀⠐⠀⠀⠀⠀⠀⠀⠠⠿⠄⠀⠀⠠⠤⠠⠤⠤⠭⠈⠀⠀⠀⠀⠀⠠⠄⠤⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠄⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠠⢄⣀
⠀⠀⠀⠀⢠⢤⡄⠀⠐⠊⠀⠀⠀⠀⠀⠀⢀⠎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠂⠀⠀⠀⢠⠆⠀⠀⢑⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠩⡠⠀⠀⠀⠀⠀⠠⠮⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠊⠀⠀⠀⠀⠛⠂⠀⢀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢀⣀⡀⠀⠈⠠⠢⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⣀⡀⠀⠈⠻⡢⡀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠃⠅⠀⠀⠀⠀⡘⠐⠀⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠈⠁⠀⢀⢔⠜⠀⠀⠀⠀⠈⠒⠒⠀⠀⢠⢂⠆⠀⠀⠀⣰⡰⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⢀⠂⠃
⠀⠀⠀⠀⠒⠒⠚⠓⠂⠀⠀⠀⠀⠀⠂⠀⠠⠴⠖⠓⠁⠀⠐⠒⠐⠓⠃⠀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠈⠆⠄⠀⠀⠀⠀⠠⠖⠃⠀⠀⠀⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢡⣀⠀⠀⢀⢁⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠄⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⡤⣀⠀⠀⠀⠀⢀⣤⣄⣤⡤⡀⠀⠀⠀⠀⣀⢤⣄⣤⢄⡀
⠀⠀⠀⠀⠀⠀⡰⣿⣿⠿⢻⣿⣷⡷⡀⠀⡔⣵⡿⣫⣝⢿⣮⣢⠀⢀⢾⣾⡟⣩⡙⣿⣿⠆
⠀⠀⠀⠀⠀⠀⡷⣿⣿⣾⢸⣿⣿⡷⡇⠀⣹⣿⣿⡿⢋⣼⣿⣏⠀⢸⢾⣿⣿⣯⣅⢿⣿⢾
⠀⠀⠀⠀⠀⠀⠱⡻⣿⣿⣸⣿⡿⡳⠁⠀⢫⣿⣏⣐⣛⣻⣟⡝⠀⠈⢞⢿⣧⣛⣫⣾⢟⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠓⠋⠀⠀⠀⠀⠉⠚⠋⠙⠓⠉⠀⠀⠀⠀⠙⠚⠉⠙⠚⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⣴⣯⣷⡶⣾⣕⢄⠀⠀⢀⢔⣽⠷⠶⢯⣖⣄⠀⠀⣠⣺⣽⠶⢾⣯⡢⡀⠀⠀⡠⣪⠿⠶⠾⣽⣦⡀
⠀⡜⣾⣿⢟⡄⣿⣿⣷⡇⠀⣯⣿⡿⢘⡛⢿⣿⡟⡄⢠⢳⣿⡇⢞⠳⣿⣿⣽⠀⢸⣼⣿⣿⡟⣰⣿⣷⢣
⠀⢣⢿⣧⣬⡅⣽⣿⣟⠇⠀⢟⣿⣟⢿⡿⣸⣿⢧⠁⠈⡼⣿⣇⢿⡗⣸⣿⡻⠀⠸⣻⣿⣿⢰⣿⣿⡿⡜
⠀⠀⠓⢝⣻⣿⣟⠯⠊⠀⠀⠈⠪⢟⣿⣾⣟⠕⠁⠀⠀⠈⠪⣛⣷⣾⡻⠕⠁⠀⠀⠑⠽⣻⣿⣟⡯⠊


⠀⠀⠀⠀⠀⠀⠀⢀⢤⣖⣲⣦⢄⠀⠀⠀⠀⣠⢤⣖⣲⡤⣀⠀⠀⠀⠀⡠⣴⣒⣶⡤⡀
⠀⠀⠀⠀⠀⠀⡰⣵⣿⢫⣭⢻⣷⡵⡀⠀⣜⣿⡟⣩⣍⢿⣿⣣⠀⢀⢮⣾⡟⣭⡝⣿⣮⢆
⠀⠀⠀⠀⠀⠀⡿⣿⡿⢢⣥⠺⣿⡷⡇⠀⣹⣿⣧⣙⣋⢸⣿⣏⠀⢸⢿⣿⡁⣿⡇⣹⣿⢿
⠀⠀⠀⠀⠀⠀⠐⣽⢿⣬⣫⣼⢿⡽⠀⠀⠣⡻⣷⣽⣥⣾⢟⠞⠀⠈⢪⡿⣧⣝⣥⡿⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠙⠓⠁⠀⠀⠀⠀⠈⠑⠋⠙⠊⠁⠀⠀⠀⠀⠉⠚⠋⠓⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣾⠛⠱⣦⠀⠀⠀⠀⣴⠾⣷⠀⠀⠀⠀⠐⠾⠛⠿⣦⠀⠀⠀⠀⣴⡶⠤⡀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⢠⣾⠛⣿
⠀⠀⢻⣇⠀⢀⣿⠃⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠉⠙⣷⡀⠀⢴⣿⣥⣼⣿⣤
⠀⠀⠈⠻⠷⠿⠋⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠐⠟⠷⠒⠶⠂⠀⠀⠀⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⣿

⠀⠀⠀⢰⡶⠶⠶⠀⠀⠀⠀⢀⣤⣴⡶⠀⠀⠀⢠⣤⣴⣤⣴⡄⠀⠀⢀⣤⣤⣴⣤⡀⠀⠀⠀⣀⣤⢤⡀
⠀⠀⢀⣿⣤⣤⡀⠀⠀⠀⢰⣿⣋⣀⣀⠀⠀⠀⠀⠁⠀⣼⡿⠁⠀⠀⠺⣯⠀⣨⣿⠇⠀⠀⢰⣏⠀⠈⣿⡄
⠀⠀⠈⠉⠉⠻⣿⡆⠀⠀⢾⣿⠏⠉⠻⣷⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣠⡿⠛⠻⣧⡀⠀⠀⠈⠿⠶⢾⣿⡇
⠀⠀⢠⣶⣴⣾⠟⠀⠀⠀⠘⢿⣦⣤⣴⠟⠀⠀⠀⣼⡏⠀⠀⠀⠀⠸⣿⣧⣄⣀⣿⠇⠀⠀⢠⣤⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣼⣿⠁⠈⣿⣷⠀⠀⠀⠀⣿⣿⡇⠀⠀⠠⣿⡷⢈⣿⣷⠀⠀⠀⣿⡷⢸⣿⡷⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡼⠟⠁⠀⠀⠀⠀⠐⠺⣿⣤⠀⠀⠀⢀⠎⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⡄⢀⣿⡿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣤⣮⣤⣤⣾⠀⠀⠠⣾⡗⠀⣿⡿⠀⠀⠀⠛⠒⢺⣿⣿⠺
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⢰⡷⣶⣶⡾⠀⠀⠀⢠⣶⠏⢉⣷⡆⠀⠀⣾⣿⣿⣿⣿⠀⠀⢀⣶⣿⠉⣿⣷⡄⠀⠀⣤⣾⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠸⠇⠤⣤⣄⠀⠀⠀⣿⣿⠄⢾⣯⡀⠀⠀⠉⠀⢀⡴⠁⠀⠀⠈⠻⣿⣤⣿⡛⠁⠀⠀⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⡄⣿⣿⡇⠀⠀⣿⣿⠀⢸⣿⡗⠀⠀⠀⣰⣿⠁⠀⠀⠀⢰⣿⡿⠀⣿⣿⡆⠀⠀⣨⣿⠁⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠿⠤⠟⠋⠀⠀⠀⠙⠻⠦⠜⠛⠁⠀⠀⠀⠻⠿⠀⠀⠀⠀⠈⠻⠿⠤⠿⠛⠁⠀⠀⠙⠿⠤⠟⠋

⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢲⣤
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢸⣿⡆⠀⠀⠀⠀⣿⠉⣿⢠⠎⠀⠀⠀⠀⠀⠀⢿⣷⣼⡋⢤⠀⠀⠀⠀⢀⡔⢁⡄⢠⡈⢳
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡿⠀⠀⠀⠀⠉⠈⣡⢋⡤⣄⠀⠀⠀⠀⢰⣿⠙⠻⣿⣿⡀⠀⠀⠀⢸⠀⣿⠇⣾⡇⢸
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⡴⠃⢿⣇⡿⠀⠀⠀⠀⠈⠛⠓⣂⡈⣿⠇⠀⠀⠀⠈⠣⣈⠁⠉⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠉

⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠾⣷⠀⢀⣴⡄⠀⠐⠒⠒⠒⠀⠀⠉⢡⣾⠟⠀⠀⣀⣠⣅⣀⠀⠀⢶⣾⣴⠆⠀⠀⢻⠟⢻⠛
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠈⠉⠉⠉⠀⠀⠀⣸⡁⠀⠀⠀⠀⠰⠄⠀⠀⠀⠋⠿⠙⠁⠀⠘⢻⠛⡿⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⡀⠀⠀⠀⢠⠈⠀⠂
⠀⠀⠀⠀⠀⠀⢠⣼⣦⣲⣦⠀⠘⠆⠀⣤⠼⢿⣷⣦⣄⡀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⢈⠝⠉⣉⣀⡄⠀⠀⢀⠠⠐⠛⠉⠁⣀⣀⡠⢈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠐⢀
⠀⠀⠀⢀⠁⠀⠄⢾⠆⠀⠘⡷⠞⣡⠀⠁⠀⠀⠊⡭⠽⢷⠷⠞⠂⢀⡄⠀⢤⣴⣶⠿⠷⠀⡀⠀⠀⢰⢣⣀⣠⡛⣿⣷⠀⠀⠣
⠀⠀⠰⣚⣧⡀⠀⠀⠀⠀⠀⢠⣺⣷⣤⡔⢁⠔⠁⠀⠀⠀⠀⠀⠀⣁⠼⡄⠈⠁⣀⣀⣀⠀⠀⠠⡀⠘⠿⠿⠿⠟⠠⠟⠀⠀⡄
⠀⠀⠀⠐⠺⠿⣯⣿⣬⠥⠖⠀⠉⠀⠈⠙⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠓⡻⣴⣿⣾⣿⠿⠇⠀⢀⠣⠀⢀⠄⠂⠀⢀⣀⣴⡺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⠿⣿⠆⠀⠒⠀⢈⡽⢶⣶⠀⠀⠀⠀⠀⠐⢋⡃⠀⠀⢀⣀⢴⣫⢃⡴⠁⠀⠐⠚⠿⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢳⣤⣀⡈⠀⣠⣖⣻⣵⡄⠘⡆⢬⡏⠀⠀⠀⠀⠀⠀⠈⠝⠿⠿⠟⠞⠋⠁⡮⣇⣀⣀⣀⣀⣀⣀⠀⠀⡈
⠀⠀⢠⠄⠀⠀⠀⠃⠑⠛⢻⠀⠀⢀⠋⠉⢡⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⢺⡿⠿⠿⢷⠶⠼⠿⠿⢿⣿⡷
⠀⢼⠁⠀⣴⣒⣷⡄⠀⠨⢍⣦⣀⠀⠁⠀⢀⡤⡀⢢⡏⠀⠀⠀⡀⠠⣷⡀⠈⢿⡿⠁⠀⣀⡀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⡀
⠘⢸⠀⠀⠈⠋⠁⠀⣀⣀⠀⠹⡿⢭⣿⣿⠥⠞⠁⢺⣿⣿⣾⣤⠀⠈⣔⣣⡀⠀⠀⠀⠀⣈⢿⣷⣄⠈⠀⢤⣶⢿⡷⣦⠀⠈
⠈⢋⢧⠀⠀⠸⠀⢘⠟⢿⠇⠀⠑⠀⠀⠀⢀⠠⠀⠂⠀⠁⠀⠀⠂⠀⠭⣄⣻⣿⣲⡀⠄⠉⠉⠉⡇⠀⢈⣈⡉⠀⠠⣝⣖⣦
⠀⠘⢒⢷⣦⣀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠐⠁⠀⣤⢤⣶⣶⣶⣤⠤⢤⡀⠈⢯⠉⠛⠁⠀⠀⠀⠐⡆⠀⠻⠿⠿⠆⠀⡙⡉⠉
⠀⠀⠀⠈⠙⢻⣿⣽⣾⣍⣥⠗⠂⠀⣀⡸⣄⠀⠈⠛⠛⠛⠙⢉⢻⠿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢁⢧⡀⠈⠀⠀⢀⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⢴⡀⠀⠀⠀⠀⠀⠀⠘⠍⣻⣷⣶⣩⣵⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣽⣯⣿⣽⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉

⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⣴⣿⣿⣷⣤⡀⠀⠀⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⠀⠀⢿⣿⢿⣿⣿⡇⠀⠀⠸⣿⣿⠏⣿⣿⡗⠀⠀⠈⠉⣩⣿⣿⣿⠟⠀⠀⠀⢀⣾⣿⠃⣀⣀⠀⠀⠀⣼⣿⣿⣿⣍⡀
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠿⡿⣿⣿⣧⠀⠀⢀⣾⣿⣿⣶⣿⣿⡆⠀⠀⠉⠁⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣴⣿⡿⢃⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠺⠿⠛⠛⢻⣿⣿⠁⠀⠀⢀⠀⠀⠀⣼⣿⡗
⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⢠⣤⣀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠸⣿⣷⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠘⠛⠛⠛⠋⠀⠀⠘⠉⠉⠉⠉⠁⠀⠀⠘⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⢀⣴⣿⣿⣿⠆⠀⠀⠻⣿⢿⣿⣿⣿⣿⡟⠀⠀⢠⣾⣿⠟⢿⣷⡄⠀⠀⠀⢀⣴⣾⣿⣶⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⣾⣿⡟⢉⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠸⣿⣿⣤⣿⣿⣇⡀⠀⠀⣿⣿⡇⠙⣿⣿⣿⠀⠀⣰⣿⣿⠋⠀⢻⣿⣷
⠀⢸⣿⣿⣿⣿⢿⣷⣦⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⢠⣾⣿⡿⠿⣿⣿⣷⠀⠀⠻⣿⣷⣼⣿⣿⣿⠀⠀⣿⣿⣟⠀⠀⢸⣿⣿
⠀⠸⣿⣿⣿⡏⢀⣿⣿⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⠁⠀⣸⣿⡿⠀⠀⢀⣈⠉⢁⣿⣿⠋⠀⠀⢻⣿⣿⣄⣠⣾⣿⡟
⠀⠀⠙⠿⣿⣿⠾⠟⠃⠀⠀⠉⠛⢿⣿⠃⠀⠀⠀⠀⠹⢿⣿⣷⡶⠟⠋⠀⠀⠀⠙⠿⠶⠿⠛⠁⠀⠀⠀⠀⠻⢿⣿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣄
⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⢀⣿⣿⡆
⠀⢠⣶⣾⣿⣷⣶⡄⠀⠀⣶⣶⣶⣶⣿⣶⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⣶⣶⣶⣶⡶⠀⠀⢸⣿⣿⣿⣏⠀⠀⠀⠙⠃⣠⣾⣿⠟
⠀⠀⠉⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠰⣶⠄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢠⠔⢿⣿⠀⠠⠖⣿⡇⠀⠀⠀⣠⠖⠉⠀⠀⠉⠻⣦⠀⠀⠀⢀⣾⠉⠀⠀⠉⢷⣄⠀⠀⠠⠚⠛⠛⠛⠛⠛⡻⠋⠀⠀⠀⠀⠀⠀⣠⠞⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠿⠆⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣿⡇⠀⠀⠈⢿⣶⣤⠴⠂⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⣤⣖⠋⠀⠀⠀⠀⠀⠀⢀⡴⠓⠒⢲⣄⠀⠀⣠⠞⠁⠀⠀⠀⣿⡇⢀
⠀⣠⡤⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⢀⣠⠄⠀⠀⠀⠈⣿⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠛⠛⠛⠛⠛⠛⣿⡟⠻
⠀⢿⣇⠀⠀⢀⡼⠋⠀⠀⠀⠀⣿⣧⠆⠀⠀⣀⠤⠚⠋⠁⠀⠀⣀⠀⠀⢿⣯⠀⠀⠀⠀⢀⣿⠇⠀⣼⡏⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠉⠙⠊⠉⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠚⠛⠛⠛⠛⠛⠻⠿⠿⠀⠀⠀⠙⠳⠦⠤⠶⠛⠁⠀⠀⠈⠛⠲⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⠷⣦⣤⠤⠀⢠⣿⢃⠤⠒⠛⠳⢶⣄⠀⠀⠀⡴⠿⠶⠶⠶⠶⠶⣶⠖⠀⢀⣴⠞⠉⠉⠓⣦⡄⠀⠀⠀⠀⣴⠞⠉⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣾⡗⠁⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢸⣏⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠋⠉⠙⣷⣆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢙⣢⠄⠀⣴⣛⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣷
⠀⢠⡴⠂⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢹⣷⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠘⢧⡀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⣠⠞⠋⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡸⠋⠀⠀⠀⠘⢧⣀⠀⠀⡠⠊⣾⠃
⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠤⠚⠁

⣿⣿⡟⢛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠤⠀⢠⡆⠀⠀⠀⠀⡠⠤⠤⠀⢠⠄⠀⠀⠀⠀⡠⠠⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼
⠀⣀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⣠⠤⠀⠀⠙⡆⠀⠀⢀⠀⢀⡄⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢀⠀⠀⡏
⠅⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠇⠀⠀⠀⠐⠈⢀⠠⠁⠀⠎⠀⠀⡀⠀⠀⣠⠟⠀⢀⡇⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⠀⠀⠀⡀⠀⠀⢨⠀⠀⠘⠀⠀⠀⠂⠘⠛⠛⠛⠀⠘⠀⠀⣸
⠀⢀⠀⠀⠀⠀⢼⢀⡀⠀⠀⠀⢠⣾⠋⠀⠀⣀⢲⠂⠀⠀⠀⢰⣉⢀⠀⠀⢸⠀⠈⠀⠀⠀⠀⡀⠀⣴⡆⠈⠁
⠀⠁⠀⠀⠀⠀⠀⠼⠃⠀⠀⠐⠤⠡⠀⠀⠀⠡⠟⠀⠀⠂⠀⠀⠉⠀⠀⠠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠈⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠁⠀⠀⣀⡀⠪⠂⠀⠀⢀⡀⠈⠀⠀⠁⠠⠰⠀⠀⠀⠀⠁⢀⡄⠀⠹⡄
⠀⠀⠐⠿⠿⠿⠟⠶⠏⠀⠀⠀⠁⠀⠾⠃⠐⠀⠉⠀⠀⠀⠀⠚⠉⠐⠂⠀⠀⠀⡾⠀⠀⠀⠀⠀⠺⠇⠀⢀⠇
⠐⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠀⢀⡄⠀⠛
⠀⠀⢀⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⣷⡀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈
⠀⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠉⠃⠐⠀⢀⠜⠁⠀⠀⢠⠀⠀⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⢀⠆⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠐⠂⠀⠀⢴⡄
⠀⠀⢀⡖⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⡟⠀⠀⢹⡄
⠀⡀⠘⠳⠶⠶⠂⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢘⡇
⠀⢈⢀⠂⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⣄⠀⠀⢈⠇
⠀⠀⠛⠛⠛⠋⠀⠠⠎⠀⠀⠀⠀⠀⠈⠃⠀⣠⠎
⠀⠒⠠⠄⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠠⣾⠟⠛⣿⡆⠀⠀⠀⠀⠀⠾⠟⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠈⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠰⠿⣿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣏⣀⡀⠀⠀⠀⠀⠀⣤⣄⢀⣼⡷⠀⠀⠀⠀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⢀⣿⣟⣛⠛⠁⠀⠀⠀⠀⢀⣾⡏⣉⠻⠃⠀⠀⠀⠀⠀⠻⣿⣶⣿⡿⠃
⠀⠀⠀⢠⣾⠋⣿⣿⠀⠀⠀⠀⠀⠸⠿⠛⠻⣷⡄⠀⠀⠀⠀⢸⣿⡿⠛⣿⡆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠻⠿⠿⣿⣿⠗⠀⠀⠀⠀⢰⣶⣤⣴⣿⠇⠀⠀⠀⠀⠈⢿⣧⣠⣾⡟⠀⠀⠀⠀⠀⠙⠋⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠸⠿⠿⢿⣿⡇⠀⠀⠀⠀⢠⣾⠿⢿⣦⠀⠀⠀⠀⠀⠀⣴⡿⠿⣶⡄⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠘⣿⣷⣾⣟⠀⠀⠀⠀⠀⠘⣿⣇⣠⣿⣷⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⡆⠀⠀⠀⠀⠀⣈⡛⠛⣻⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁

⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⢰⣿⡏⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣇⣀⣀
⠀⠀⠀⢸⣿⡄⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠿⠿⢿⣿⡿⠿⠟
⠀⠀⠀⠘⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⢤⡀
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⢀⡞⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⡼⠀⠀⠀⠀⢀⡼⠁⠀⢠⠀⠀⠀⢀⡤⠒⠊⠁⠠⠀⠀⠀⠀⡀⢠⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢳
⢠⡇⠀⠀⠀⢀⡞⠀⠀⠀⠂⠀⡠⠚⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠕⢦⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠸
⢸⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⠞⠀⠈⠀⢈⠀⣇⣀⠤⢤⠒⠒⠒⠒⠢⠤⣀⠀⠀⠀⠐⠁⠀⠙⡄⠀⠀⠀⠀⠸⡆
⠘⡇⠀⠀⠀⣿⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⠔⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⢳⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣇⠀⠀⠀⢀⡇⠀⠀⠀⠀⡼
⠀⠈⢧⠀⠀⠘⣆⠀⠀⠸⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢈⠂⠀⠀⠀⠘⡄⠀⠀⠀⡏⠀⠀⠀⡼⠁⠀⠀⠀⣸⠃
⠀⠀⠈⢧⡀⠀⠙⣆⠀⠀⢣⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠇⠀⠀⣰⠁⠀⠀⡴⠃⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠙⢦⡀⠈⠣⡀⠀⠳⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⢀⠞⠀⢀⡴⠁⠀⣠⠞⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠲⣄⡈⠢⣄⠙⠦⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠴⠋⣀⠴⠋⢀⡠⠞⠁⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡙⠲⠤⣉⡒⠬⢕⣒⣠⠤⠤⠤⠤⢤⣒⡊⠥⠒⣊⣡⠴⠚⠉⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣌⣉⡓⠒⠒⠾⠿⠯⠿⠖⠒⠒⠋⢉⣁⣀⠤⠴⠚⠉⠁

⠀⠀⠀⠻⠃⠀⠀⢸⣿⠁⠀⠈⠿⡶⠿⠋⠀⢀⣾⠟⠛⣦⡈⢻⣶⡟⠛⢿⣆⠃⠀⠃⠀⢼⡏⠉⢹⡧⢠⣿
⣶⣦⣤⡄⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⢀⣶⡄⠈⢿⣦⣶⡿⠁⠀⠉⣠⣤⣼⠏⠀⠀⣀⠀⠘⠻⠿⠟⠁⠈⣁⣀
⠀⢀⣽⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣾⢻⣷⠀⢀⡀⠀⠀⠹⠀⠀⠈⢉⣡⣤⣄⡀⢻⣇⠀⠺⠋⠛⠀⠘⠉⢙
⠀⡿⠃⠀⣶⡶⠶⢶⣶⠀⠉⠙⡃⣸⣯⣬⣿⡶⠈⢀⣴⢶⣦⡀⢦⠀⢸⡏⠉⠉⠛⠿⠿⠆⠀⠀⠀⢴⡇⠀⠻
⠰⠄⠀⠀⢈⣿⣾⠟⠋⠀⢀⣾⠏⠈⠉⠁⠹⠇⠀⢸⣷⡀⠙⢿⣦⠀⠈⠻⠿⠀⡀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤
⣀⠀⠀⠀⠙⠉⢛⠵⠂⠀⣼⡟⠀⠀⢀⡀⠀⣤⠀⠢⠙⣿⣤⣈⣿⠀⠀⠠⣴⠿⣁⠴⣶⡄⠂⠀⠀⠉⣩⡿⠋
⠄⠀⣴⣶⠿⠇⠐⣾⠇⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⣴⡶⠆⠉⠋⠁⠀⠀⣀⠀⠸⣯⣀⣼⡟⢰⠀⠀⣰⡟⠁
⠀⠀⠛⢷⠀⢀⣀⣀⡀⠀⢀⡄⠛⠛⠉⠉⠁⠀⡀⢹⣷⠾⢶⣄⠀⠀⢀⣿⣷⡀⠉⢹⣿⠃⠸⠄⠀⠿⠁
⣤⣤⣄⠀⢠⣿⠋⠙⠿⠀⠈⠁⠀⠀⠰⠆⣶⣿⣁⠈⡁⠀⣸⣿⠀⠀⠘⠃⠙⣿⣄⠈⠁⣀⡄⠀⠀⣀⣀⣀
⠃⣨⡿⠀⠼⡿⠛⢻⣦⠰⢠⣾⠟⢷⡆⠀⠀⢉⡿⠃⣀⡀⠉⠁⠀⠸⠆⠀⠀⠈⠻⠃⢀⡉⢹⡄⢸⡟⠉⣻⡇
⠀⠉⠁⢠⣤⣤⣀⣈⣭⠀⠠⠿⢶⡾⠃⠀⡀⠀⠀⠘⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠀⠀⢠⡿⠁
⡾⠆⠀⠈⠻⣯⡛⣻⡿⠷⠂⢀⣠⠀⠀⣀⡀⠀⠀⣶⣶⠾⠋⠀⠃⣰⡿⠛⠁⢀⡀⠀⠀⣤⠰⠷⠷⠀⣿⡷⠟
⣴⠦⣤⣀⠀⠈⠿⣿⠁⠀⠀⠘⠋⢠⣿⠛⢻⣧⢰⣦⠀⢰⣷⠀⠇⢹⣷⠀⣼⡟⢻⣷⠀⠏⠀⠀⠀⣂⠀⠀⣤
⣃⣀⣨⣿⣀⣹⣷⣀⣀⣀⣀⣀⣀⣘⣿⣤⣾⣿⣀⣁⣰⣿⣧⣀⣀⣾⣏⣀⣿⣇⣀⣿⣆⣀⣀⣀⣀⣻⣷⣾⣟
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⣠⠐⠒⠲⣶⣄⠀⠀⠀⣠⠐⠒⢶⣦⡄⠀⠀⢠⣶⣶⡀⠀⣀⡄⠀⠀⢠⣶⡶⢶⣶⣤⣤⠆
⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⣿⣄⣤⠀⣹⣿⡇⠀⠀⣿⣤⠄⢈⣿⡿⠀⠀⠈⠀⢹⠇⢻⣿⡇⠀⠀⢸⣿⡇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠙⠛⠋⣰⣿⡿⠁⠀⠀⠈⠁⠀⠾⣟⡁⠀⠀⠀⠀⠌⠀⢸⣿⡇⠀⠀⠸⠛⠓⠒⢶⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⣀⣀⠀⠀⢹⣿⡆⠀⠀⡈⠀⠀⢸⣿⡇⠀⠀⠀⣀⣀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣜⣋⣀⣀⣀⣀⠀⠀⢼⡿⠛⠃⠀⢸⣿⡟⠀⠀⠁⠀⠀⢹⣿⡏⠃⠀⢼⡿⠻⠃⠀⣸⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠈⠣⠄⠀⠤⠿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠈⠣⠄⢀⠴⠿⠋

⠀⠀⠀⠀⠀⣠⡶⠊⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣾⠉⢿⣦⡀⠀⠀⢠⣴⠏⠉⢳⣦⡀⠀⠀⠀⠀⣤⡾⠉⠹⣶⡄
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⠏⠀⠀⠸⣿⣿⠀⣸⣿⠇⠀⢀⣿⣿⠀⠀⠘⣿⣷⠀⠀⠀⣾⣿⠃⠀⠀⢻⣿⡆
⠀⠀⠀⣸⣿⣿⠋⠈⣷⣦⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⢙⣻⠦⣿⣋⠀⠀⠈⣿⣿⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⢰⣿⡟⠀⠀⠀⠀⣴⣿⠃⠀⠈⣿⣧⠀⠀⠈⠻⠦⠠⠾⣿⡿⠀⠀⠸⣿⣿⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠸⣿⣇⠀⠀⣸⣿⠇⠀⠀⣿⣿⡇⠀⠀⠀⠀⢿⣿⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢻⣿⡄⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠙⠻⠦⠤⠟⠋⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠈⠛⠷⠄⠼⠛⠁⠀⠀⠀⠀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠙⠷⠄⠼⠛⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠛⠛⣿⠟⠛⠁⠀⠀⠈⢻⣿⠛⣿⠛⠁⠀⠀⠙⢻⡟⢻⣿⠛⣿⠛⠀⠀⠀⠙⢻⡟⠻⣿⠛⠛⢻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢻⡇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣰⡿
⠀⠀⠀⠀⠀⣀⣠⣿⣄⣀⡀⠀⠀⢀⣸⣿⣀⣿⣀⠀⠀⠀⣀⣼⣇⣸⣿⣀⣿⣀⠀⠀⠀⣀⣼⣇⣀⣀⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠁⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠙⣿⡟⠉⠙⣿⡟⠉⠀⠀⠈⠙⣿⡟⠉⠙⣿⠏⢻⡟⠉⠀⠀⠀⠉⢿⡟⠉⠙⣿⠏⢻⡟⠙⣿⠋
⠀⠀⠀⠀⠀⠀⢸⣧⠀⢠⣿⠀⠀⠀⠀⠀⠀⠸⣧⠀⢸⡟⠀⢸⡇⠀⠀⠀⠀⠀⠸⣷⠀⢰⡿⠀⢸⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣆⣿⠃⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣄⣀⡀⠀⠀⠀⣀⣀⣸⣿⣿⣀⣀⣸⣧⣀⠀⠀⠀⣀⣀⣸⣿⣿⣀⣀⣸⣷⣠⣿⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠉⣿⡏⠉⠉⣿⠋⢹⡟⢹⣿⠉⣿⠋⠁⠀⠀⠈⢻⡟⠉⢿⡏⢹⡿⠋⠁⠀⠀⠈⠙⣿⡋⣻⡟⠉
⠀⠀⠀⠀⠀⠀⢸⣧⠀⣸⡟⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⠁⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⡿⣷⡀
⠀⠀⠀⠀⢀⣀⣀⣸⣿⣯⣀⣀⣼⣧⣸⣿⣠⣿⣄⡀⠀⠀⢀⣼⣧⣠⣾⣧⣸⣷⣄⡀⠀⠀⢀⣠⣿⣅⣽⣧⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣏⢹⣿⠋⢹⣟⠉⠀⠀⠉⠹⣿⠉⣿⠏⠉⣿⠉⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣆⠀⢸⣧⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⣸⣿⣄⣼⣿⣄⠀⠀⣀⣴⣿⣤⣿⣧⣠⣿⣤⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠈⠙⣷⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢠⡴⠾⢿⣤⡀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⣾⣧⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠈⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠄⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⣴⡶⠦⠀⠀⢠⡄⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠐⢶⣦⣤⣤⡤⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⣻⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂⠀⠀⠀⠀⣻⠀⠀⠂⠀⠀⠀⠉⠀⣠⢞⠟⠁⠀⠐⠂⠀⠀⠀⠈⠲⠶⢿⠄⠀⢀⡴⡻
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⡀⠀⠀⢸⢸⠀⠀⠐⠁⠀⠀⠀⡰⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⠉⢦
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⣼⠃⠈⠂⣠⢜⡇⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⢐⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡇⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠑⢤⣤⣤⣠⣤⡦⠈⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡜⡬⠀⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠱⣄⠀⠀⠀⠀⣠⡮⠀⠀⠀⠀⠀⢂⡀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠐⠶⠶⠷⠇⠀⠀⠀⠀⣤⣤⠀⠀⠹⡦⠀⠀⠈⠉⠓⠒⠚⠋⠁
⠀⠀⠀⠀⠤⡴⠂⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⢰⡆⠀⠀⡠⠀⠀⠀⠀⠀⠀⣤⣠⣼⡜⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣿⠄⠀⠀⠈⠲⠾⠾⠇⠀⠀⠠⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣀⡀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠙⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠉⢭⡉⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⢀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⣦⠀⠀⠀⠀⠀⠈⠀⣀⢀⣀⢤⣄⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠈⠈⠋⠉⠁⠀⠀⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠋⠀⠀⠀⠀⠰⢤⣤⠤⠤⠤⡤⣴⣿⠀⠀⠀⠀⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⡀⠈⠢⠀⠀⠀⠀⠀⢿⡉⠉⠙⠀⠀⣷⠀⠀⠀⠀⠀⠀⢰⡿⠛⠂⠀⠀⣹⠀⠀⠀⠀⠀⠑⠦⣤⣤⣐⠷⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠏⠈⠁⠀⢸⡇⠀⠀⢣⡀⠀⠉⠀⠁⢀⠰⠏⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⣔⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣠⡄⠀⢸⡇⠀⠀⠀⠙⠳⠶⠶⠾⠗⠊⠀⠀⠈⠀⠀⠀⠀⢀⡤⢤⣄⠀⠉⣄⠀⠀⠀⢠⠂⠁⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠇⠀⣸⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢯⡎⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡽⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠉⠀⠀⠀⡠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢠⣄⡲⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠖⠋⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⢀⢄⠨⡂⠀⠀⠀⠀⠀⠀⢀⠀⢅⠀⠀⠀⢀⣌⡰⢂⢳⠀⠀⠀⠀⠀⠀⠄⢀⠤⡆⠀⠀⠀⠀⠀⢠⠹⡶⠯⢡
⠀⠀⠀⣠⠞⠚⠛⠪⠕⠳⡄⠀⠀⠀⠀⡠⠝⠬⡿⠀⣠⠊⠁⠉⠉⠛⠛⣆⠀⠀⢰⠒⠒⢜⠧⣻⠗⡶⠀⠀⠀⢀⠞⠉⠉⠒⡇
⠀⠀⣴⠁⢠⠖⠉⠙⢢⡀⠙⡄⢀⡴⠊⠀⠀⡀⣷⠀⠳⢤⠔⠛⢲⠀⠀⣿⠀⠀⠘⠒⠂⡴⠀⢀⡞⠁⠀⠀⢠⠏⠀⡼⡇⠀⡇
⠀⢠⡇⠀⡞⠀⠀⠀⠀⡇⠀⢷⠈⠧⠖⢺⠀⠀⣿⠀⠀⠀⠀⢀⠞⠀⢠⠏⠀⠀⠀⡴⠋⠀⠀⠾⢄⠀⠀⢠⠋⠀⠮⠤⠇⠀⣇⣀
⠀⠸⡇⠀⢻⡀⠀⠀⣰⠃⠀⣾⠀⠀⠀⢸⠀⠀⣿⠀⠀⢀⡴⠋⠀⣰⣋⣀⣀⠀⠀⠙⠒⠲⡄⠀⠀⢧⢰⣃⣀⣀⣀⣀⠀⠀⣀⣸
⠀⠀⢳⡀⠀⠉⠛⠋⠁⠀⣰⠇⠀⠀⠀⢸⠀⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⢹⠀⣰⠤⠤⠶⠃⠀⠀⡼⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠙⠲⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠸⠤⠤⠟⠀⠀⠛⠛⠒⠒⠒⠒⠒⠋⠀⢯⣄⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠘⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⡰⢄⠤⢍⠀⠀⠀⠀⠀⠀⠐⠂⠔⠳⠀⠀⠀⢀⣀⣀⣴⢡⡞⡥⢱⣄⡀⠀⠀⢀⡀⢠⡄⠀⠀⠀⠀⠀⢠⢂⣄⡚⠅
⠀⠀⠀⢰⡋⠪⠓⠼⠞⠉⡇⠀⠀⠀⡠⠖⠟⠻⠖⢹⠀⠀⢸⠀⠀⠀⠁⠈⠒⠩⢸⠇⠀⣀⣧⣼⣤⣼⡀⠀⠀⢠⠞⠉⠒⣛⠵⠛⢦
⠀⠀⠀⢸⠀⠀⡞⠋⠉⠉⠁⠀⢀⡞⠀⢀⣔⣚⠛⠛⠀⠀⠙⠒⠒⢒⠖⠀⠀⣠⠞⠀⡜⠁⢠⠄⢬⠀⢹⡄⠀⡏⠀⢰⠋⠉⢳⠀⣸⡇
⠀⠀⠀⢸⣀⣀⠉⠙⠲⣄⠀⠀⣸⠀⠀⠈⣀⡈⠉⢢⡀⠀⠀⠀⣰⠋⠀⣠⠞⠁⠀⠀⢧⡀⠘⠒⠊⢀⡼⠁⠀⢧⠀⠈⠓⠒⠋⠈⠁⡏
⠀⠀⠀⠀⠁⠉⢹⡄⠀⠘⡆⠀⣧⠀⠀⡎⠀⠙⡆⠀⣧⠀⠀⣸⠁⠀⣰⠋⠀⠀⠀⣠⠞⠁⢀⣀⣀⠉⠓⣄⠀⠈⠓⠶⠤⡤⠀⠀⢠⠇
⠀⠀⠀⡰⠒⠒⠊⠀⠀⢠⠇⠀⠸⡄⠀⠓⠦⠞⠁⢀⠇⠀⢰⠇⠀⢠⡏⠀⠀⠀⠀⡇⠀⠰⣇⠀⣸⠆⠀⢸⠀⢰⠶⠒⠊⠁⠀⣠⠏
⠀⠀⠀⠳⠤⣤⣤⠤⠖⠁⠀⠀⠀⠙⠲⠤⣤⠤⠖⠋⠀⠀⠘⠓⠒⠚⠁⠀⠀⠀⠀⠳⣄⠀⠈⠉⠁⢀⣠⠎⠀⠸⢤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠙⠛⠿⣦⣄
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⣦
⠀⠀⠀⠀⢀⣿⠁⠠⠂⣁⠀⠐⠄⠀⠀⠈⣿⡀⢀⣿⠁⠀⠀⢠⠞⢁⠤⡤⠌⢢⡀⠀⢻⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠐⢀⡈⠁⡄⠀⠀⠀⣸⡇⢸⣿⠀⠀⠀⢄⠀⢃⠀⠘⡃⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠈⣿⡄⠀⠀⠘⢤⠀⠉⠁⢀⠜⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⣿⣦⣄⡀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠘⢿⣄⠀⠀⠀⠈⠁⠈⠁⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⣿⡇⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣤⣠⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠉⠉
⢿⡿⠛⠛⠻⣿⠟⠛⠛⠛⠛⢿⡿⠛⠛⠛⠛⣿⡿⠋⠀⠀⣸⡟
⠘⣿⡄⠀⠀⠿⠀⣀⡀⠀⠀⠸⠇⠀⠀⣠⡾⠏⠀⠀⠀⢠⣿⠁
⠀⠈⢿⣄⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠻⢷⣤⣀⣿⣇⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⠶⢶⣶⠂
⠀⠀⠀⠀⠀⣽⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠈⣿⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⡶⠾⠿⠿⣿⡇
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⠶⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣶⠶⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠶⠾⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢠⡴⠶⣄⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⡿⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠞⠛⠁⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⣾⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢒⠀⠀⠀⠀⠀⠀⠐⠟⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠩⠥⠤⠆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡰⠒⠒⠀⠈⠀⠀⠀⠒⢒⣀⣘⠛⠁⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⡄⠲⡔⢂⢰⡇⡀⡀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢠⣤⠤⠀⠀⠀⠀⠠⠧⠮⠹
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠃⠋⣛⣛⣙⠀⣤⣤⣤⡄⠀⠾⠆⠀⠈⢁⠀⠀⠘⠛⠋⠃⠀⢈
⠀⠀⠀⠀⠉⠀⢠⣤⣤⡦⡄⢀⣀⡂⠚⢂⣛⡀⢀⣀⣀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⣀⣀⣀⣀⡀⠀⠈⡶⣶⣶⡶⡆⠀⣻⣿⡿⣿⡯⣿⣟⣿⣿⠏⣿⡇⢠⣤⠬⠀⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠛⠛⠻⠝⠁⠀⠴⠤⢠⠄⠒⠂⠀⠿⠿⠶⠻⠿⠿⠻⠿⠷⠆⠿⠇⠀⣀⡀⢀⣀⡀⣀⡀
⠀⢈⠁⠀⠀⠲⠖⠀⠀⠤⢼⡇⠀⣖⠘⠁⠀⠀⠀⠰⣔⠀⠀⠀⠠⡤⠍⠀⠉⣁⣛⣽⠛⠋⠃⠸⠀⣖⢀
⠀⢀⠀⠀⠀⠀⢭⠅⠀⢀⣈⡁⢐⣟⠀⠀⣶⣒⠲⠼⠿⠶⠰⠀⠤⡀⠀⠀⠀⢈⣸⣿⠀⠔⠒⠲⠄⠛⠈
⠀⠀⣾⣶⣴⣤⢽⠁⠘⠈⠀⠒⠲⠂⠀⠀⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⣎
⠀⠀⠠⣶⡶⣲⠀⠲⠀⠀⠀⠉⠀⠀⠀⠈⠉⠡⢀⣀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠠
⠀⠀⠀⠚⠓⠁⠈⠁⠀⠀⠀⠐⠒⠂⠀⠀⠈⣠⣤⣄⣦⣀⠠⠤⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⠈⡁⠀⠀⠀⢫⣹⣻⣏⢘⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⡤⠄⠀⠄
⠀⠀⠀⠀⠀⠤⠤⠀⠀⠴⠆⠿⠀⠀⠀⠀⡴⠀⠀⣿⢰⣶⣷⣶⢶⡆⡀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠒⠼⠙⠛⠉⠓⠐⠒⠀⣀⢤⡖⣀⣟⠀⠀⠶⠶⠂⠰⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠋⠻⠄⠀⠀⠀⠈⠂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢀⠈⣠⣾⣤⡄⣀⢀⡀⢇⣶⢀⢀⠀⠀⢀⢉⣤⣾⣤⡀⣀⢀⠀⣅⣶⠠⢀⠀⠀⢀⢉⣤⣾⣤⡀⡀⢀⠠⣅⣶⠠⢀
⠀⠀⠀⠀⢶⣾⣿⠀⢸⠋⢈⠈⠸⣿⣿⡕⠂⠁⠀⢾⡾⠋⠉⠙⢿⠋⢉⠀⠸⣿⡕⠀⠁⠀⢾⣾⠋⠉⠉⢻⠏⢉⠀⢸⣿⡕⠀⠁
⠀⠀⠀⠀⢹⣿⣿⠀⠸⠀⢸⠀⠀⣿⣛⣥⠀⠀⠀⣻⣷⡶⠃⢀⣼⠀⢸⡆⠀⣋⡥⠀⠀⠀⣿⣿⣶⠂⠀⠾⠀⢸⠀⠀⣋⡥
⠀⠀⠀⠀⠀⠛⢟⠀⢠⣀⠘⠀⢀⣹⡟⠂⠀⠀⠀⠈⠋⠀⠀⠘⢻⣀⠘⢀⣠⡟⠀⠀⠀⠀⠈⠋⠁⠁⠀⣠⡀⠘⠀⣠⡟
⠀⠀⠀⠀⠐⠋⣬⠙⡻⠿⠻⠧⠉⠉⠀⠀⠀⠀⠀⠘⢃⣤⠘⡻⠿⠻⠧⠉⠉⠀⠀⠀⠀⠀⠘⢣⣬⠘⡻⠿⠻⠧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢸⣿⣧⣿⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠋⠛⠁⠀⠀⠀⠠⠈⠂⠐
⠀⠀⠀⠀⠀⠰⢀⣠⣀⠀⠀⠁⠀⡄⣀⠀⠀⠀⠀⠀⠰⢀⣠⣀⠀⠀⠁⠀⡄⣀⠀⠀⠀⠀⠀⠖⢀⣤⣀⠀⠀⠁⠀⡀⣄
⠀⠀⠀⠀⣨⣴⣿⡿⠿⢷⡲⠸⠂⠹⣿⡎⠌⠂⠀⣸⣴⠛⠻⠛⢳⡳⠼⠂⢽⣿⡊⠄⠂⠀⣸⣴⠿⠟⠿⣷⡳⠾⠀⢹⣿⡪⠑
⠀⠀⠀⠀⢽⣿⡟⠁⠀⢸⠃⢰⡆⠀⠿⠃⠀⠀⠀⢿⣿⠀⠘⠛⠿⠀⣰⠀⢸⡿⠃⠀⠀⠀⢿⣿⠀⠒⠀⢾⠁⢰⡄⠀⡿⠆
⠀⠀⠀⠀⠘⠿⠁⢘⠁⠈⡀⠸⠇⠀⣾⠍⠀⠀⠀⠙⠿⠓⠛⠀⠀⠀⠿⠀⢘⣾⠉⠀⠀⠀⠙⠯⠀⢾⠀⢨⠀⠸⠇⠀⣾⠉
⠀⠀⠀⠀⠠⠦⡰⠫⢤⣼⢿⡆⠴⠞⠃⠀⠀⠀⠀⠠⠦⡐⠶⢶⣿⢶⡄⠶⠞⠃⠀⠀⠀⠀⠠⠆⡐⠤⢴⣿⢷⡄⠴⠞⠃
⠀⠀⠀⠀⠀⠀⠛⠀⠆⠈⠀⠉⠀⠀⡀⠀⡀⢀⡀⢀⣈⠛⠐⠆⠈⠀⠉⠀⣀⢀⣀⡀⣀⡀⠀⢈⣋⡐⠆⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣸⣿⣸⣇⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣽⡷⣟⣿⣇⣿⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠄⠀⠈⠉⠈⠀⠉⠉⠀⠁⠀⠀⠐⠆⠀⠀⠀⠉⠉⠁⠉⠈⠉⠁⠉⠁⠀⠐⠄
⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠂⠀⡀⢀⠀⠀⠀⠀⠀⢤⠀⣠⠀⠀⠀⠂⠀⡀⣀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢐⣠⣾⣿⣿⣦⣦⠰⠄⢳⣿⢔⡐⠄⠀⢰⣠⡾⠿⢿⣦⣦⡴⠀⢳⣿⢔⡒⠄⠀⣰⣠⣾⣿⣿⣦⠦⠴⠀⢳⣿⢔⠒⠄
⠀⠀⠀⠀⣽⣷⣤⡤⠀⢀⠇⠀⡆⠀⣿⠇⠀⠀⠀⣿⣿⠀⢰⠀⣹⠃⢰⡄⠈⣿⠇⠀⠀⠀⣿⡿⠀⣠⠀⠹⠃⢰⡄⠈⣿⠅
⠀⠀⠀⠀⠸⣿⣿⠃⠀⣾⠁⢸⡇⠀⣴⡚⠀⠀⠀⠺⡿⠀⣴⠀⠙⠀⢸⡇⠀⣴⠒⠀⠀⠀⠺⣿⣄⡈⠀⢠⠀⢸⠇⠀⣴⠓
⠀⠀⠀⠀⢀⣄⠡⢠⣤⣿⣷⡄⢤⡴⠏⠀⠀⠀⠀⢀⡄⠀⢩⣀⣼⣦⡄⢤⡴⠏⠀⠀⠀⠀⢀⡄⠠⢈⣄⣼⣦⡄⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠟⠠⡎⠉⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠠⡎⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠠⡎⠉⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⢤⠀⠀⠀⠀⠀⠀⣀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⠀⣭⣥⣍⣬⢠⡄⠀⠀⠈⠀⠈⠁⠀⢀⡀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠛⠛⠙⠈⠉⠈⣉⡉⠈⠁⠀⠀⠀⠐⠒⠀⠀⡄⠡⠀⠄⠠⠀⠀⠠⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠘⠀⠀⠁⠀⢏⡅⠌⡁⠄⠀⠀⢀⣙⢛⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠿⠾⢸⠄⠐⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠠⣰⡀⣀⡚⠂⠂⠋⠓⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⣀⣀⠀⣤⣤⡤⣤⡀⠠⠶⠂⠀⠀⠒⠒⠀⠀⠁⠙⢠⣥⣠⣤⣠⣤⣠⡀⣀⣈⣡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠁⢘⣢⡄⠃⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠹⠿⠻⠯⠸⠇⠊⠋⠓⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠤⠀⢨⣭⠀⢸⢞⡃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣂⢐⠲⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠆⠂⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠜⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠀⠁⠁⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣙⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⠽⢥⠹⠷⠶⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣶⣶⢶⠄⢦⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠒⠇⠀⠀⠀⠀⠀⠤⠄⠀⠤⠍⢠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣿⣿⣵⢴⡄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⣿⠐⠀⠀⠀⠀⠀⠄⠨⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠾⠯⠛⠀⠀⠀⠀⠐⠓⠶⢷⠖⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣠⣀⣄⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⠙⠛⠛⠃⠛⠀⠀⡤⣄⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡆⣤⢄⢤⠀⠀⠀⠀⠀⠀⠀⠀⣥⣬⡄⠀⠖⠲⢶⠒⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠠⠀⠄⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⡂⡩⠭⠀⠀⠀⠀⠀⠀⣤⣤⠁⠀⠀⠀⠀⠘⠛⠛⠃⣸⡿⣾⣿⣺⡿⢺⡆⠀⠐⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠓⠇⠷⠀⣀⠐⠓⠂⠉⠀⡿⡦⠀⠀⡀⢀⢀⠀⡀⠀⠀⠠⠤⠬⠁⠈⠀⠈⠀⠒⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣤⣤⣤⡅⣠⣤⣤⣤⡀⣿⠿⠀⢀⡌⢄⢠⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠛⠋⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠈⠀⠀⠀⠀⠐⠒⠊⠉⠄⠀⠛⠛⢀⡀⠈⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠰⠾⠔⠒⠀⡰⠟⠿⠾⢸⣀⠀⠼⠻⠯⠙⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠄

⢰⠶⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢄⡀
⠀⠐⠀⠂⠀⢀⠀⠀⠁⠠⠂⠀⠀⠱⢦⡀⠀⡠⠀⠠⢀⠀⢀⠀⠀⠀⠀⠈⠙⠒⠂⠑⠂⠀⡐⠉⠀⠀⠀⢦⡩⠀⠀⠜⠀⠀⠉⠁⠀⢌⣉⠀⠐⢰⠆
⠀⠀⠀⠀⠂⠉⢀⡀⠀⡠⠀⢄⠀⠈⣀⠀⠀⢄⠀⠀⢀⠆⠰⠚⠆⠰⠀⠀⠀⠀⠀⢠⠀⠀⣖⢐⠀⡀⠀⢈⡑⠀⠀⠐⠀⠀⠁⠀⠀⠐⠁⠀⠀⠋
⠀⢡⡜⠀⠀⠀⠀⡩⠀⠄⠀⠀⠆⠀⠇⢢⠄⠀⠉⡩⠋⠀⢀⡀⠀⠘⠋⠐⡚⠀⠰⠖⠀⡄⠈⠀⠀⠨⠄⠀⡀⠀⠀⡀⠐⠈⠀⠘⡄⠀⢀
⠀⡀⠀⠀⡀⣀⠄⠀⠀⠈⠂⠂⠀⠀⠀⠀⣠⠀⠀⠀⠀⢯⢀⠀⢠⣢⠀⠐⠀⠀⡠⡀⠀⠈⡗⠀⡠⠀⠀⢰⠀⢄⠀⠉⠀⠈⠀⠈⠀⠰⠃⠒⢆
⠀⠥⡆⠀⠀⠃⠀⢀⠀⡶⣤⠀⠀⠀⠒⠀⢉⡀⠀⠀⣀⠀⠚⠁⠀⠊⠈⠑⠀⠈⠀⠌⠀⠀⠠⣎⣀⠀⠀⠘⠤⠀⠀⢠⡂⠁⠀⠀⡆⠈⠂⠐⠁⡀
⠀⠀⠀⣀⠀⠀⢎⢀⡇⠀⠉⠂⠀⠤⠇⠀⠀⠀⠈⣠⣜⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⠈⠁⢤⠀⠀⠀⢠⠃⠀⣀⠀⠀⠀⠬⠃⠀⠘⠁⠀⠀⠀⠰⠰⠇
⠀⠀⠠⢠⠂⠀⠀⠘⠁⠲⠄⠀⢀⠀⠀⠿⡦⠄⠀⠀⠀⠄⠀⠀⠐⠗⠀⠀⠀⠰⠈⠃⠀⡸⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠈⠉⡇
⠀⠀⠒⠁⠀⠀⠀⠂⠔⠊⠀⠀⠁⡆⠀⠀⠀⠂⠀⡂⠍⠀⠀⠀⠀⠀⠘⠈⠀⠀⢘⡆⠀⠀⠀⠮⡉⠀⠀⠀⠈⠁⠀⢀⣀⣀⠀⠣⠤⠘⡅⠀⠴⡉
⠀⢀⣤⠀⠰⠂⠉⢀⠤⡀⠀⠀⣀⠋⠁⠄⡄⠀⠸⠐⠂⠀⢠⠖⠊⠁⠀⠉⠁⠀⠀⢀⣎⣠⠀⠂⠊⡀⠀⠀⢉⡸⠀⠀⠓⠁⠀⢀⠠⠔⠁⠀⠤⠂
⠀⠻⠐⠀⠈⠀⡂⠀⠤⠛⠀⠁⠀⠀⠀⠰⠔⠀⢀⠁⠀⠀⠘⠈⢉⠆⠀⢀⠄⠀⠀⠈⠁⠁⠀⠀⠀⠘⠛⠀⠈⠉⡢⠀⡄⢄⠀⢀⣤⠀⠀⠠⢄
⠀⠲⣀⠀⠐⠉⠀⠀⠀⠂⠀⠀⠰⠖⠀⠀⡀⠀⠨⡖⠄⠀⠀⠒⠁⠀⠀⢸⢊⠕⠀⠀⠖⠉⡇⠀⠰⠃⠠⢦⡈⠉⠀⠀⢀⢂⡀⠰⠃⠀⢠⣀⠀⠱⠄
⠀⠀⠋⠠⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⢡⣀⠀⠀⠀⢰⠄⢀⠴⠀⠀⠀⡠⠄⠀⠀⠀⢀⠜⠀⡀⠰⠂⠀⠘⠁⣎⢀⡀⠀⢀⡤⠄⠀⠐⠁⠈
⠀⣤⠀⠾⡁⠀⠈⡆⠀⠧⠤⡆⠀⠐⢢⠄⠀⡀⢤⠐⠚⠀⠈⢷⠀⠀⠀⠀⣠⠤⠀⠀⠉⠉⡁⠀⠀⠐⢉⠀⠀⠑⠒⠁⠀⠀⠈⠀⠀⠀⠀⠀⡊⠉⡂
⠀⢈⡁⠀⢠⠐⠈⠀⢀⡀⢀⡁⠀⢄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠀⢤⠄⠀⠀⡊⠉⡆⠀⠨⡇⠀⠀⢈⠟⢦⠀⠀⠀⡤⠀⠤⠄⠀⠨⡇⠀⠀⣉⠞⠁
⠀⠀⡀⠀⠀⠴⠀⠀⣙⠄⠀⠁⠀⡘⠀⠀⠀⢤⡃⠀⢠⠀⢠⡄⠀⣈⠂⠀⠀⠱⠊⠀⠐⠒⠁⠀⣠⠜⠊⠐⣢⠀⠘⠓⢢⠀⠀⠐⠒⠁⠀⡀⠀⡠
⠀⠒⠓⠠⠒⠀⠢⠀⠀⢖⡀⠀⠰⠀⠂⠠⢆⠀⠠⡄⠈⠈⠁⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⡄⠈⠛⠂⡀⠤⣉⠀⠒⠐⠋⣴⣂⠀⠀⢀⠎⠀⠀⠘⠃
⠀⠠⡀⠘⠢⢤⡞⠀⠀⠈⠁⠀⠀⢲⠀⠀⢉⠀⡀⠈⠆⠀⠀⠄⠀⠀⠴⠈⠁⠘⢓⠂⠀⠘⢣⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⡓⠊⠠⣄⠙⠒⠲⠋
⠀⠐⠣⠀⠀⠈⠀⠀⠠⠊⠀⠀⠀⠺⠀⠀⠘⢤⡼⠀⠀⠀⢈⡢⢠⠤⠀⣸⠄⠀⠀⠀⠀⠒⠁⠀⠀⠈⠁⠐⠏⠀⠀⠀⠁⠀⡆⠀⠛⠀⠀⠀⠀⣀⡀
⠀⠈⠀⠀⠄⠃⠀⢠⣁⡀⢀⡔⠀⠀⠀⠀⠠⠂⠀⠀⢀⠈⠉⠀⠠⠃⢀⣀⠀⠰⠀⡄⠀⠀⢯⡄⠀⠓⠈⠀⣀⠀⠀⠀⡀⠘⠀⠀⢀⡝⠁⠀⠀⠴⠁
⢀⡄⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⣀⠀⠀⢀⡔⢤⠀⠠⣎⠀⠈⠉⠃⠀⠤⠄⠀⣄⠀⠀⠦⠎⠀⠒⠥⠀⠄⠀⠀⠤⠃⠀⠀⠀⣠
⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠃⠀⡠⠒⠀⠀⡀⡀⠀⢀⠜⠀⢀⠀⠀⣠⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡀⢀⠀⣆⠀⠀⠀⠀⠀⠀⠠⢲⠀⠀⡳
⠀⠠⡀⠀⠀⠋⠙⠂⠀⠀⠢⡀⠀⢇⠀⢰⡠⠄⠠⢀⠳⠓⠀⠚⠈⠀⠺⠂⠈⣸⡀⠀⠀⢈⠏⠁⠀⠀⠀⣌⣠⠀⠀⠨⡳⠀⠲⡁⡙⠀⠠⠖⠄⣀
⠀⠀⠛⠀⠠⣦⡀⠀⠀⠠⠔⠁⠀⠀⠁⠈⠄⣀⣀⠠⠃⠀⠀⠀⡠⠄⠰⠀⠀⢀⠀⢰⡀⠀⠀⠀⢠⠲⠀⠀⠈⠀⣀⠄⠀⠀⢀⠛⣄⠀⠀⠀⠸⡸⡆
⠀⡠⠢⠀⠀⢈⠀⠀⠀⠄⠀⠀⠀⢠⣜⠀⠀⠀⠀⠀⠐⢃⠀⠐⠂⢠⠀⠀⠴⢡⡄⠘⢋⣀⠀⠀⠸⠧⠀⠀⠀⠼⠦⠀⠀⠀⠃⠰⠊⠀⠀⠀⢀
⠀⠠⠎⠀⠐⠀⡆⠀⠂⠉⠀⠀⠀⠀⠈⠝⠀⠈⢀⡄⠀⡁⠀⠠⠄⠊⢀⡀⠀⠊⠀⠀⠁⠞⠒⠄⠀⠀⠀⠀⠀⠰⠊⠀⠘⣁⡀⠀⠀⠠⠚⠃⠊
⠠⠄⠀⠢⡀⠀⡤⠀⢠⡀⠀⠇⢾⠀⣀⠀⠀⠃⣍⠃⠀⠃⠠⠲⠀⠀⢠⡅⠀⠪⢽⠀⠀⠠⠤⠂⠀⠐⢉⡇⠀⠠⠆⠀⠀⠔⣡⠀⠀⢀⡆⠀⢀⣙⠁
⠀⠛⠀⠈⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠰⠂⠀⠤⠆⠀⠳⠂⠀⠶⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠚⠀⠀⠀⠰⠀⠀⠀⠁⠀⠨⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⢀⣁⡂⣘⡤⠤⠄⠀⠀⠀⠀⣄⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢦⣤⡐⠀⠀⠀⢀
⠀⠀⢀⢸⣯⣷⣋⡀⠀⠀⠀⠀⠀⠂⢺⡟⠀⣠⣤⡀⠀⠀⠀⣲⡞⠀⣠⣄⠀⠡⠀⠀⠀⠰⢲⡟⠀⠀⣾
⠀⠀⠀⠈⠙⠛⣿⡇⠀⠀⠀⠀⠀⠈⠠⠶⠖⢀⡼⠁⠀⠀⠀⠈⠙⠛⣉⠝⠀⡀⠀⠀⠀⠄⢸⠁⠀⠀⠿
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⡀⠀⠀⠀⠀⢀⡴⠋⢀⣄⠀⡀⠀⠀⠀⠀⣿⣤⡀⠈⠠⠀⠀⢀⣧⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⢤⢠⡄⠀⢠⠎⠀⣰⣋⣿⣄⠀⠀⢠⡂⠐⠀⠀⡻⠀⠀⡯⣄⠂⠀⠉⠉⢹⡁⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠠⣛⣄⣠⡿⠒⠾⢀⠁⣎⣀⣀⣀⣀⠀⠀⠀⠀⠈⢷⣄⠀⠁⠀⣀⣴⠗⠷⠁⠀⠀⠀⡸⡇⠀⠘⢈⡱⠂
⠀⠀⠀⠀⠀⠘⠛⠋⠁⠉⠟⢠⠀⠀⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠉⠛⠛⠛⠉⠠⠐⠀⠀⠀⠀⠀⠻⠿⠟⠃⠈⠖⠀⠂
⠀⠀⠀⠀⠠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣾⠰⣗⡠
⠀⠀⠀⠀⠛⣾⠇⠀⣀⣀⣀⠀⠀⠀⢠⣰⡿⠋⠀⣀⡀⠀⠀⠀⠀⢲⠉⠉⠁⠉⠀⠀⠀⠀⠀⣔⢠⠖⡠⢤⡌⠂
⠀⠀⠀⠀⠀⣿⠀⠀⠍⠉⠁⠀⠀⠀⠠⣺⠁⠀⠈⠈⠉⠀⠀⠀⠀⠸⠿⠿⡿⠂⠀⣠⠀⠈⠠⢮⣿⡄⠂⠠⠃⡀
⠀⠀⠀⠀⠀⣯⣤⣄⡀⠀⠀⠀⠀⠀⠀⢛⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡐⠁⠀⠀⠄⣸⠏⢀⠴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⡆⡂⠐⠀⢻⠀⠈⠉⠙⡇⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢹
⠀⠀⠀⠀⢷⣄⠀⠀⠀⢀⡜⠨⠃⠀⠀⠈⢷⣄⡀⢊⣁⡴⢂⡠⠀⢰⡇⠀⢠⡇⠩⡄⠁⠀⠀⠘⢷⣄⡀⠀⢀⡠⠄⠠
⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⢀⡆⠂⠁⠛⠛⠛⠻⠁⡊⢀⠁⠀⠀⠀⠀⠉⠙⠟⣉⣁⠶⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠃⢀⣀⡀⠀⠀⠀⠀⠀⢠⣴⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⡄⠀⠋⠉⣿⠀⠀⠀⠀⠀⠛⣿⠀⢠⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠒⠋⠀⢀⣐⡀⠀⢠⣿⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠟⠳⠶⣶⠀⢸⠏⣃⠁⢘⣺⠀⠐⢀⠼⠀⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠈⠁⣀⡞⠚⠁⠀⠀⣧⣧⣀⣀⣀⣠⣟⣛⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉⠠⠀⠀⠀⠀⠈⠛⠻⠟⠛⠩⠀⠺

⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣶⣥⣄⠀⣷⠀⠀⠀⠘⠇⣀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢤⡟⢀⠀⠀⠀⡰⠋⡟
⠀⠀⠸⠏⢿⡋⣠⠟⠀⠀⠀⢘⡟⠟⠀⠀⠀⠀⣠⠞⡁⠀⠀⠀⠀⣄⢀⣶⠈⠀⠀⠘⠓⠚⣟⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⣿⣉⠉⠀⠀⠀⠀⠀⣠⣎⣉⠁⠀⠀⠀⠈⠉⣹⠃⠀⠀⠀⣞⠉⣷⠀⠀⠀⠀⣴⠋⠙⣦⡀
⠀⠀⠀⠉⠨⣿⣿⠀⠀⠀⣸⣿⣯⠌⢹⠄⠀⠀⠀⣰⠃⠀⠀⠀⢠⡞⠉⢳⡄⠀⠀⠀⠙⠦⢾⣿⡗
⠀⠀⠀⠲⠴⠛⠉⠀⠀⠀⠈⠙⠓⠔⠋⠀⠀⠀⠐⠋⠀⠀⠀⠀⠘⠳⠤⠞⠁⠀⠀⠀⠐⠦⠔⠃

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

⣽⣿⣏⡿⣤⣴⢸⡹⣦⣼⣾⡁⣖⣦⣈⡝⢮⣁⣞⠯⢟⣖⣛⠃
⣬⡿⢸⡷⠿⡗⠒⠈⠉⠋⡴⢣⢔⣭⣖⣋⣛⡹⠾⡄⠨⣀⠴⠁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠠⢀⠀⠀⢠⢄⠄⠐⠀⡀⠠⠄
⣧⡔⠉⣷⢲⣿⡾⣟⠛⡋⠉⠉⠽⡟⠑⣾⠋⡹⠉⠛⢉⣉⣸⣻⡴⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⢨⣶⣶⢻⣝⣻⣄⣻⠞⣡⣬⠓⠤⠟⣒⣨⠯⣀⣒⠭⣉⢡⡉⣀⢹⠟⢭⡆
⠛⢏⣙⣟⣹⠋⣈⠉⠿⠒⣉⠓⠀⢸⠁⢰⡛⠉⣽⠟⠷⠚⢫⠀⠈⢒⡉⣠⢦⡀
⣳⠞⢙⡽⠋⣩⣽⠀⣴⡛⣎⠓⢤⣿⠚⣦⣹⠛⢧⡔⢒⣋⣭⣴⣊⢭⠗⣓⡮⢿
⠈⣶⠛⣧⣐⣛⣿⡏⠫⠖⣡⡶⠤⣉⠉⢸⠛⠛⠋⢱⡯⠤⣤⣀⣉⠈⠀⡏⠀⠂
⠴⢚⣯⠗⠋⠱⠒⢳⠀⠣⣀⣝⡷⢢⢡⣏⡴⣂⠙⠪⢝⠲⠤⣬⢏⣙⣶⠷⠶⢶⡟
⠖⢛⣟⣉⡇⠶⠲⠭⣤⣒⡛⠓⢲⣧⠙⢺⢣⢮⠙⠺⣛⠲⣄⣴⠛⣡⠟⡀⢀⡟⠀⠀⢀
⢉⣙⡾⠥⣠⡞⠉⣱⠙⠒⠚⠒⠛⢿⠁⠘⠈⠙⠷⣄⣙⢯⡉⢈⡟⠳⣬⠉⠛⠓⢦⡖⣾⣷⣄
⢯⣈⠻⢷⡛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁⠀⠀⠠⣤⣶⣿⣿⣿⣿⣦⡀
⠀⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⡐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠓⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠸⠂⢀⠑⠢⠀⠠⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠀⠆⠀⠆⠀⠀⠀⠀⠈⠹
⠀⠀⠀⠁⠀⠈⠀⠀⠰⠀⢘⡎⠁⠀⠀⢸⠀⠀⠀⠠⠈⠀⡠⠂⠀⠀⠀⠀⠀⠀⡀⡠⠊⠀⠮⠀⠀⠇⠄⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠈⠓⠂⠀⠀⢸⢠⠊⠀⠀⠐⠂⠀⠒⠐⠀⠀⠀⠀⠀⠀⠐⠓⠂⢠⠀⠀⠤⠂⠸⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠡⡀⠀⠀⠀⢀⠔⠀⠀⡇⠀⠀⠘⠘⠀⠀⠀⣄⠀⠆⠰⠀⢀⠄⠉⠀⠔⠀⠀⠀⠀⠴⠠⡴⠀⠠⡐⠀⠑⠀⠈⠀⠀⡠
⠀⠀⠀⠀⠈⠀⠲⠂⠁⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠈⠀⠈⠀⡄⠁⢀⠀⠠⠀⠈⡄⠀⠀⠂⠄⠀⠀⠀⠈⠀⠂⠠⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠣⠂

⠀⠀⠀⡠⠀⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠨⠀⠐⠀⠀⠀⠀⡀⠠⠄⢀⠀⠀⠀⠀⠀⢠⠀⠂⣄⠀⡀
⠀⠀⡘⠀⠀⣐⠁⠀⡀⠀⠠⠀⠐⠀⠀⠅⠐⠐⠀⢈⠀⠐⠀⠐⠀⠀⠇⠔⠁⠀⠀⠀⠀⠀⢄⠀⡀⠀⠈⠀⠒⠁⠀⠁⠀⠑⠄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠠⠀⠀⠀⠄⠀⠀⠂⢀⠀⠁⠀⠀⠀⠀⠑⠄⢀⠀⠈⠂⠀⠀⠀⢀⠀⣅⡀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⢄⠀⠀⠁⠀⠁⠀⡸⠀⠀⠀⡀⠀⠀⠌⠀⢀⠀⠀⠘⠀⠈⠀⢀⠄⠀⠁⠀⠀⠞⠀⠀⠌⠀⠀⡄⠀⠀⠀⠐⠀⢀⠌
⠀⠀⠀⠁⠂⠠⠄⠐⠚⠨⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠀⠀⠁⠀⠀⠀⠀⠊⣀⢀⠌⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠧⢤⡄⠴⠀⣀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⠒⡞⠋⠉⠉⠉⠻⡉⠹⣏⠉⠉⢹⠉⠙⢯⡭⠟⡿⠓⠒⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣠⠋⠀⢹⡀⠀⠀⠀⣠⢇⡤⣌⠉⠉⠁⢀⣀⡀⠀⠀⣇⠀⢀⣠⠴⠊⠀⣈⣓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠓⠒⠉⣀⣤⡀⠀⠙⠒⠒⠋⠁⣏⠀⣈⠆⠀⣰⠋⠀⢹⠀⢀⣈⣉⠉⢠⠤⣄⢸⡁⠈⡇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣆⠀⢰⠁⠀⠙⢦⠀⡴⠦⡄⠀⣀⣉⣁⣀⠀⠸⣄⣀⡞⢠⡏⠀⠈⢧⠈⠳⠞⠀⠙⠞⠁⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠸⡀⠀⠀⢘⡆⠳⠚⠁⢞⠀⠀⠀⠀⢹⠄⠀⢀⡀⠈⢇⠀⠀⣸⠀⢰⠉⠉⣹⠄⣰⠋⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠀⣀⣑⡶⠖⠋⣠⠤⢤⡀⠘⣆⠀⠀⢀⡜⠀⠸⡉⢹⠀⠈⠓⠚⠁⠀⠈⢓⣚⣁⡀⠘⢦⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⢭⣆⣰⣁⣀⣀⣷⣀⣈⣓⣚⣩⣖⣒⣦⡈⠁⢀⡴⠒⠢⡄⠀⢰⠋⠀⠀⠙⡆⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠆⢸⠀⠀⠀⠘⡆⠘⢦⣠⡤⠖⢃⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢺⠀⠀⠀⢀⡇⣀⡤⣄⠀⣴⠉⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠳⡜⢆⣠⠴⠋⡰⠁⠀⣸⠂⠘⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⠀⠀⠀⠀⠘⠒⠚⢁⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣉⣓⠦⠴⠒⢁⣠⠴⠚⠋⠓⢦⠀⡇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡏⠀⠈⠉⠲⡀⣎⠀⠀⠀⠀⠀⢸⠀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠀⢹⡀⠀⠀⠀⡇⠈⠙⠒⠶⠤⠖⠋⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⠙⠲⠶⠚⣡⠖⠓⡄⢰⡋⢱⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢧⡀⠀⠀⢀⡼⠁⢀⠀⠰⣇⠀⢀⡿⠀⠉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠑⢦⠉⠉⠉⠉⡴⠋⠉⠹⡄⠈⠉⣩⢄⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⡸⠀⣠⠤⡀⢣⡀⠀⢀⠇⠀⠀⡇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⣍⠉⠀⠸⣁⢀⡇⠀⠉⠒⢋⣠⠤⢄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡄⠀⠈⣉⣀⠀⢀⡔⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠃⡰⠋⠀⠈⡆⢎⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠦⣤⡤⠞⠁⠘⠥⠤⠴⠞⠁⠘⢦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠒⠒⢲⠀⢀⡤⠖⠚⠉⢳⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣏⣀⣞⣀⡠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣶⢶⣦⡶⣰⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡤⠀⠀⠀⠀⠀⡤⠀⠀⠀⠐⠂⠀⣤⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠒⣒⢓⣀⣀⡀⢸⠀⣽⠇⣄⡀⠡⡤⠀⠉⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠻⣿⢿⡟⢹⡇⢈⣀⠉⠁⡀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣒⠂⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⢸⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡁⠀⣾⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠤⠖⠀⠀⠈⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠆⡉⠀⠀⠀⠀⠸⠻⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⣴⠠⠀⠀⠀⠀⢀⣲⣶⣐⢲⠶⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠨⠉⢨⣭⣭⣬⣥⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠶⠂⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⡀⠀⠙⠫⠿⠉⢛⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠀⠀⠶⡖⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠒⠀⡄⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢐⡒⠂⠀⠀⠶⠦⠂
⠀⠀⠀⠀⠀⠀⠀⢶⠖⣃⠀⠃⡀⠀⠀⠀⠂⡀⢡⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣤⡄⣤⢠⡀⡀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⣤⣤⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⢛⡛⡛⡘⠃⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡲⡔⡄⡶⡏⠨⠅⠩⠈⣤⣆⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠇⠓⠠⠤⠠⠶⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣥⡁⣅⢀⡁⠀⢀⣟⡀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢴⡟⢻⣆⠛⣿⠶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣛⢯⣸⠇⠀⠉⠉⠉⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣃⢸⣇⣸⡇⣴⣋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠛⠏⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠉⠉⠁⢉⣉⣄⣉⡉⠡⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡞⠐⠀⢄⡀⢤⠀⠀⠈⡉⠁⠀⠠⠄⢀⠀⠀⠀⠀⠀⢀⠐⠀⠋⠛⠛⠙⠿⠈⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣽⡟⣿⣿⣽⡟⣿⠀⣀⠘⠀⠀⠀⠀⠀⠀⠁⠠⠀⢈⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣄⣤⡄⣽⡠⡏⠋⠁⢠⣗⣶⣆⣷⣲⡀⠈⠉⠍⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠿⠈⠛⠛⠛⠐⠓⠀⠶⠶⠶⠆⠀⠀⠀⣀⣀⡀⠀⠀⠃⠀⠀⠐⠓⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠙⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⣠⣤⠀⠀⠤

⠀⠉⠉⠉⠛⠒⠾⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢠⠞⠲⡀⠀⠀⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⠀⠹⡬⠆⠈⠀⢶⢤⣀⠀⠀⣿⠀⠀⠀⡴⠒⢢⡀⠀⠀⢠⠤⢿⣈⡆
⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠘⢦⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣧⠈⠙⠋⠁⠀⠀⣴⠓⠄⠈⠁⠀⠀⠈⠦⠼⠃⠀⠀⠴
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢹⡄⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠁⠀⠀⠀⡴⠚⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡾⠀⠀⡖⢻⡤⠜⠀⢠⠖⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⢠⡖⠙⠂⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠐⠙⣶⠀⠀⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠈⠉⠀⠀⠀⢸⣄⣀⣠⠇⢹⠀⠀⠀⠀⠀⠀⠈⠓⡖⠀⡄
⣤⡀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡜⢇⠀⠀⠀⠀⠈⠉⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡴⠒
⠈⢳⠀⠀⠀⠀⠀⡞⠉⢳⡀⠀⠀⣄⡀⠀⠀⠀⠀⠈⠙⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠦⠀⠀⠀⠘⢧⡀
⠒⠋⠀⠀⠀⠀⠀⢧⡀⢸⠇⠀⠀⣷⠈⠙⠓⠒⠀⠀⠀⠀⡀⣀⠀⠀⠀⢶⣉⡆⠀⠀⠀⠀⠀⠀⠛⠶⠆⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣴⠚⢻⠁⠀⠀⠀⢸⣉⡹⠀⠀⣀⡀⠀⠀⠈⠉⠁⠀⠘⡹⠋
⠋⠙⡟⢦⠀⠀⠀⠀⣾⠋⠙⢦⠀⠀⠀⠀⢲⡀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠋⢻⡄⠀⠀⠀⠀⠀⠀⠸⣀⡰
⠶⠶⠃⠸⠀⠀⢠⡶⠺⣦⣤⠼⠃⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠘⠧⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⡴⠒⠊⠁
⠀⠀⣠⠎⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡖⠙⢦⠀⠀⢤⡀⠙⢤⣤⣴⠃⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⠓⠐⠂
⠀⠀⢿⡞⠉⠹⡆⠀⢰⡋⠈⠀⠀⠀⠀⠓⠖⢹⠇⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠼⠀⠀⠀⠈⢳⣾⠉⡇⠀⠀⠀⠀⡴⠒⠒
⠀⠀⠈⠳⠤⠴⠃⠀⠀⠉⢻⣀⡜⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱⠄⠀⣤⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠀⠙⠲⠶
⡀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⢀⠀⠘⠯⡉⠉⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀
⣻⢳⡀⠀⠀⠀⡖⢻⠤⠼⠀⠀⢰⣷⠚⠛⢦⡀⠀⠀⢰⢛⣉⡀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⢄⠀⣾⠉⠉⣣⠀⠀⢰⠉
⠋⠀⠃⢀⣀⡀⠉⠋⠀⠀⠀⠀⠈⢿⣀⣀⡼⠃⠀⠀⠈⡉⠉⢹⠀⠀⠀⢀⣀⡟⠀⠀⠀⠀⠀⠈⠢⢬⡶⠶⠋⠀⠀⠈⠛
⠀⠀⡀⢻⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⣸⠋⣙⠷
⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠠⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠤⠀⠀⠀⠿⠚⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣤⢤⡀⠀⠈⠳⢦⡀⢸⠆
⠀⢀⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢻⣤⠄⠀⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠴⠃⣸⠃⠀⠀⠀⠀⠑⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠒⣂⠤⣌⠃⠀⠀⡜⣷⣴⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⢀⣠⠴⠒⢺⣵⣠⢋⠙⡗⠀⠀⠀⠀⠀⠀⡾⠉⠣⠷⡇⢶⡸⣤⣀⣰⠧⠤⠣⣥⡼⠁
⠀⠀⠀⠀⠀⠀⣀⡤⢮⣲⣼⢫⣍⢳⠁⢀⠁⢤⠒⠢⡐⣏⠀⠀⠀⠀⠈⠙⠿⢾⡁⠀⠀⠀⠀⠀⢰⠇⠀⢠⠦⢬⣍⣀⣀⣿⠋⠀⣀⠠⠀⣷
⠀⠀⠀⠀⣠⠞⠁⠀⣀⣀⣈⠳⠕⢻⡄⠰⣌⡿⢌⣻⠃⠈⠳⠛⠉⠙⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⡾⠀⠀⠾⣀⡀⠀⠈⣽⠃⠀⡰⢻⠀⠀⣿
⠀⠀⢀⡾⠁⠀⣰⠋⠁⠀⠈⢳⡀⢀⣻⠞⠁⠀⠀⢸⡀⠀⠀⠀⢀⡼⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠓⠶⢤⡀⠀⠙⢦⡼⠁⠀⣼⣁⣸⠀⠀⣿⣀⣀
⠀⠀⣸⠃⠀⢰⠃⠀⠀⠀⠀⢸⡗⡏⠀⢀⣀⠐⠜⢸⣇⣀⡤⠖⠉⠀⠀⣠⠞⢁⠦⣀⠴⢆⠀⡀⠀⠀⠀⣷⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⢸⡀⠀⠀⠀⠀⣼⠁⠷⣶⠋⢿⠀⠀⠘⡏⠁⠀⠀⠠⢴⣟⡁⣀⣧⣤⣿⠤⢼⡞⠉⠛⠒⠚⠁⠀⠀⢀⡟⠒⠒⠒⠒⣶⠀⠀⣾⠛⠛
⠀⠀⢻⡄⠀⠈⠳⢤⣤⡤⠞⠁⠀⢠⡏⠀⢸⠀⠀⠀⣧⣀⡀⠀⠀⠀⢀⡝⠁⠀⣩⢤⣉⠁⠙⣦⣀⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢸⡆⠀⠀⣿⠈⠉⠛⠲⠦⣼⡇⠀⠸⣇⣀⡼⠀⠀⡿⠉⠉⠛⢉⠉⠀⢀⠀⠀⠀⠀⠀⠛⠒⠒⠛
⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠶⠛⠁⠀⠀⠀⢸⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⢳⡤⠀⠀⠀⠀⢤⣞⠁⠀⠀⢠⠈⠠⠖⠙⡇⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⢉⣯⡍⠉⠀⠀⠀⠀⢀⡞⠁⠀⢀⣤⢤⣄⠀⠈⠱⣄⡴⠚⠚⠛⢾⡤⠛⡦⡤⠤⣞⡉⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠒⠲⠶⢇⣰⣾⢡⡀⢱⡀⠀⠀⠀⠀⢸⠀⠀⠀⣏⠀⠀⢸⡇⢀⡼⠃⠀⠀⣠⠤⠤⢤⣼⢣⣇⣐⡿⠥⠞⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠘⠢⠔⡋⢹⡃⠀⢀⠇⢸⠦⢬⡂⠈⠛⠛⠉⠀⡞⠀⠀⠀⠘⠓⠲⢦⡀⢰⠏⠀⢉⡴⠒⠲⡄⠀⢪⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⣶⠆⠁⠀⡉⢂⣿⠉⠉⠻⣜⢦⡸⣦⠧⣤⣤⣤⡤⣼⠁⠀⠀⣠⠤⠤⡀⠀⠘⣿⠀⠀⢸⡀⠀⢀⡿⠐⠋⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡤⠞⠋⠛⠲⠦⣤⡤⠀⠩⢡⠞⠁⠀⠀⠀⢾⠀⠀⢰⠁⠀⠀⢸⠀⠀⢸⣆⠀⠀⠙⠛⠋⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢀⡴⠋⠀⠀⠀⢀⡤⠚⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⠤⠴⠋⠀⢀⡟⠘⠷⣤⣤⣤⡤⣶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⣠⠟⠁⠀⠀⠀⠀⢸⣀⣀⡀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⢀⣀⣤⠞⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠶⠟⠀⠀⠀⠀⠀⣰⠛⠲⠶⠶⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣄⣀⠀⠀⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠁

⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⣀⡀⠤⢄⡀⠀⠀⠀⠀⠀⣠⠄⠒⣀⠀⠰⠄⠀⠀⢠⠂⢲⠀⠀⠀⢰⢊⠱⡄⠀⠀⢰⡫⠙⠩⠙⠛⠁⢦
⠀⡠⠶⢡⡬⠦⡌⢀⡆⠀⠀⡜⢁⡱⢤⣸⠀⠱⡄⠀⠀⠸⡥⠋⠀⠈⡗⢁⡄⠀⠀⢰⠊⣸⠀⠀⠀⠘⣃⠄⡇⠀⠀⢸⠔⢁⠋⠉⠉⠈⠁
⡔⢒⣨⠍⠀⠀⡷⠁⡀⠀⠘⣄⢚⠄⠀⠈⢲⠀⣰⠀⠀⠀⠀⢀⡠⠞⡡⠋⠀⠀⠀⢸⠂⡅⠀⠀⠀⢘⡁⢴⠇⠀⠀⠘⡖⠉⡢⠤
⠙⠐⠁⠀⠀⠀⡁⠐⡇⠀⠀⠀⠀⠀⠀⢀⠖⢊⠏⠀⠀⠀⡔⢋⠘⠋⢉⠶⡀⠀⠀⣸⠘⣧⢠⠤⡤⠎⠀⠼⠀⠀⠀⠀⠉⠈⠉⢢⠂⠉⠄
⠀⠀⠀⠀⠀⢸⠁⡠⡇⠀⠀⠀⠀⢀⡴⠃⡰⠋⠀⠀⠀⠀⠑⠉⠁⠈⢃⠀⠲⠀⠀⠣⠴⠠⠄⠴⠐⢳⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠹
⠀⠀⠀⠀⠀⢸⠊⠀⢇⠀⠀⠀⣠⠋⠰⠆⣤⠀⠤⣄⠀⠀⠀⠀⠀⢀⡎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡗⢈⡇⠀⠀⠀⣀⣀⣀⡀⠜⠁⠁⡙
⠀⠀⠀⠀⠀⠘⠣⠤⠃⠀⠀⠀⠑⠒⠒⠀⠒⠐⠒⠛⠀⠐⣍⠒⣈⣁⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠨⠇⠀⠀⢸⠀⠂⠀⠑⣄⡨⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠈⠁
⠀⠀⠀⠀⠀⡀⠀⡀⣀⠀⠀⠀⢀⣠⠀⠤⠤⠤⢤⣀⠀⠀⢀⠴⢂⠉⣏⣉⠋⢢⡀⠀⠀⢀⢤⠀⠀⠉⠀⣱⠀⠀⠀⠀⢀⠴⡂⢑⠒⢄
⠀⠀⠀⡄⠁⢠⠴⢤⠀⢳⠀⠀⠀⠠⠘⠂⠓⣤⠁⡸⠀⠀⡮⠠⢤⠋⠀⠙⡆⠀⡇⠀⢀⠆⢀⡶⠊⣶⡀⢀⡀⠀⠀⠠⠓⠄⢡⣸⠀⠌⠣
⠀⠀⣄⠀⠰⠀⠀⠸⡖⡹⠀⠀⠀⠀⠀⠀⢠⠗⣚⣁⠀⠀⣆⠀⠜⠦⠐⠚⢁⠘⠀⠀⠘⡄⠐⠓⠊⢃⢠⡠⠇⠀⠀⠓⢀⠈⠋⠀⠛⢀⠰
⠀⠠⠀⢈⠃⠀⠀⠀⠈⠀⠀⠀⠀⢔⢈⣁⠭⢜⠁⠄⠀⠀⠈⠲⡂⠀⣀⣴⡋⠀⠀⠀⠀⠘⠦⣴⡀⠸⢚⡀⡄⠀⢸⠀⠀⠛⠀⠀⠘⠁⣀
⠀⢀⠀⠺⠖⠂⠒⠢⡀⠀⠀⠀⠀⠀⠀⠞⢀⠁⠀⠀⠀⠀⠠⠚⠍⡢⡈⠀⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡀⠀⠈⠀⠈⡃⠀⠀⣘⠉
⠀⠠⡀⠀⢰⠓⡦⠀⢸⠀⠀⠀⠀⠀⠞⢀⠃⠀⠀⠀⠀⢀⠃⠢⡔⠉⠉⢹⡇⠔⠃⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠂⠈⠙⠦⠖⠩⡉⢈
⠀⠀⠙⢄⡀⢈⣁⠔⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠘⡄⠈⢱⠤⠔⠢⢀⡰⠃⠀⢀⠤⡤⢤⠤⠎⡁⡸⠁⠀⠈⢆⡀⠁⠀⠐⡀⢈⠏
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠘⠒⠉⠀⠀⠀⠘⠠⠤⠀⠦⠐⠉⠀⠀⠀⠀⠀⠑⠒⠦⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣭⢳⠀⠀⢠⠴⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡉⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⠚⠁⠀⡰⠃⠺⠀⠀⠀⠀⠀⠠⠤⡤⠤⢤⠤⡄
⠀⠀⠀⠀⡤⢤⠤⠞⡡⠚⢒⡚⡢⠀⠀⢌⣔⣁⣎⣠⠉⠜⠁⠀⠀⠀⠀⠀⠀⡜⠃⡙⠁⠀⠀⠀⠀⠲⠤⠮⠤⠴⠥⠐⠁
⠀⠀⠀⠀⠈⠉⠉⠛⣆⢘⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠎⠀⠀⠀⠀⠀⠀⠔⡒⠀⠋⠉⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡰⠃⠀⢀⢴⣠⡀⠀⠀⠚⠒⠓⠒⠋⠈

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣴⣯⣿⣿⣿⣧⣼⣿⡼⣿⣿
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡂⠀⠀⠀⠀⠀⠀⠀⢦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⡔⠓⢹⠀⠀⠀⠀⢀⠔⠉⠛⠳⠲⡄⠀⠀⠀⠀⠀⡃⠉⠒⠘⢫⠃⠀⠀⠀⠀⠀⡜⠒⠑⡆⠀⠀⠀⠀⠀⢰⠁⢚⢸⠊⠁
⠀⠀⢐⢁⣀⠀⢸⠀⠀⠀⠀⠈⠢⠚⠙⡄⠀⡇⠀⠀⠀⠀⠀⢉⠝⠁⢠⡃⠀⠀⠀⠀⢀⠌⢀⠞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠄⡀
⠀⠀⠈⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⢀⠜⠀⡼⠁⠀⠀⠀⠀⠀⠙⠖⢦⠀⠈⠆⠀⠀⢀⠎⠀⠛⠊⠀⠘⢲⠀⠀⠀⠀⠘⠓⠲⡀⠈⢦
⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⡔⠁⠀⠈⠁⠘⡆⠀⠀⠀⢠⠖⠶⠊⠀⢀⠆⠀⠀⠈⠁⠉⠀⢳⠀⠘⠉⠀⠀⠀⠀⠔⠂⠚⠀⢀⡌
⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠚⠃⠀⠀⠀⠘⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠀⠀⠀⢀⣀⣈⢁⡀⠀⠀⠀⢀⣀⣀⢀⣄⡓⣄⠀⠀⠀⠀⠀⡐⢀⠒⠀⠀⠀⠀⠀⠀⠀⡐⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐
⠀⠀⢀⠔⠉⢁⠭⠤⠇⠀⠀⠀⢈⠀⠀⠁⠁⠘⢸⠀⠀⠀⠀⠔⢉⠉⡉⠱⡄⠀⠀⠀⢠⠊⢀⠬⢅⠉⢢⠀⠀⠀⠀⡔⠉⡨⢭⡉⠳⡄
⠀⠀⡎⠀⠐⠓⠒⠦⡀⠀⠀⠀⠈⠉⣩⠋⢀⡴⠊⠀⠀⠀⠐⣆⠈⠒⠃⡠⠃⠀⠀⠀⢸⠀⠰⢤⠼⠀⢹⠀⠀⠀⡜⠀⡎⠀⠀⢸⡀⢱
⠀⠀⡇⠀⡆⠉⢣⠀⢷⠀⠀⠀⠀⡴⠁⢠⠎⠀⠀⠀⠀⠀⡜⠁⡠⠤⢄⠈⢢⠀⠀⠀⠈⠳⠤⣤⠀⠀⡸⠀⠀⠀⡇⠀⢇⠀⠀⣨⠃⢸
⠀⠀⢳⡀⠑⠒⠃⢀⠎⠀⠀⠀⢰⠃⠀⡞⠀⠀⠀⠀⠀⠀⢇⠀⠑⠠⠊⠀⡼⠀⠀⠀⠀⡖⠂⠁⢀⡴⠃⠀⠀⠀⠹⣄⠈⠉⠉⠁⣀⠞
⠀⠀⠀⠉⠓⠒⠊⠁⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋⠀⠀⠀⠀⠀⠓⠂⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣭⣭⣭⣭⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣾⣿⣿⣿⣿⣽⣿⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡤⠀⢀⣤⡀⠀⣠⣤⡀⢠⡄⢠⡄⢀⣤⣤⠀⠀⣀⣤⡀⢠⣤⣤⡄⠀⢀⣤⡀⠀⣀⣤⡀⠀⢀⣠⣄⠀⠀⢸
⠀⠀⠘⣿⡇⠈⣡⡿⠀⠡⢼⡃⠸⠧⢼⡇⠐⠟⢲⡄⢠⣿⣤⡄⠀⢠⣾⡇⢀⣼⣿⣧⠀⢿⣼⣿⠀⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠸⠃⠸⠷⠶⠀⠲⠞⠃⠀⠀⠸⠇⠀⠶⠞⠁⠈⠻⠿⠃⠀⠸⠟⠀⠀⠻⠿⠋⠀⠲⠖⠃⠀⠙⠿⠟⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠙⣿⡿⠋⠈⠛⣿⡟⠋⠀⠀⠀⠀⠛⣿⡟⠋⠈⠻⣿⡟⠃⠈⠻⣿⡟⠁⠀⠀⠀⠙⢿⣿⠋⠀⠉⠻⣿⡋⠀⠈⢻⣿⠋⠁
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣧⠀⢠⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⣆⣾⡏
⠀⠀⠀⠀⣨⣿⣄⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⢀⣿⣇⡀⠀⠀⠀⠀⢀⣿⣇⡀⠀⣠⣿⣇⠀⠀⣠⣿⣇⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⢘⣿⣟
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉


⠀⠀⠀⠀⡀⢀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⢀⣀⡀⣀⠀⢀⢀⡀⢀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⡀⠀⢀⡀⠀⡀⠀⢀⠀⠀⡀⣀⢀
⠀⠀⠀⠈⠙⣿⡏⠁⠀⢉⣿⠟⠉⠀⠀⠀⠀⠀⠉⢻⣿⠉⠀⠉⣿⡟⠉⠁⠉⢻⣿⠋⠀⠀⠀⠀⠀⠉⠻⣿⡉⠀⠈⢹⣿⠋⠁⠈⠻⣿⠏⠁⠈⢻⣿⠏⠁
⠀⠀⠀⠀⠀⠘⣿⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣰⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⢹⣷⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣏⡀⠀⠀⠀⢀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡀⠀⠀⠀⢀⣠⣿⣄⡀⢀⣸⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁


⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠈⠙⣿⡍⠀⠀⢹⣿⠋⠁⠈⠙⣿⡏⠁⠈⠙⣿⡏⠁⠈⠙⣿⠏⠁⠀⠀⠀⠈⠹⣿⠏⠁⠈⠙⣿⣇⠀⣹⡿⠋⠁⠀⠀⠀⠀⠉⢿⣯⠀⣨⣿⠋⠁
⠀⠀⠀⠀⠀⠹⣷⡀⢀⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣧⣼⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣷⡄
⠀⠀⠀⠀⠀⠀⣈⣿⣿⣀⠀⠀⠀⢀⣠⣿⣧⡀⢀⣰⣿⣧⡀⢀⣰⣿⣆⡀⠀⠀⠀⢀⣰⣿⣆⡀⢀⣠⣿⣏⠀⣹⣷⣄⡀⠀⠀⠀⢀⣠⣾⣏⠀⢘⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⠀⣼⡿⠉⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠈⢻⣯⡀⣨⣿⠋⠀⠀⠙⣿⡏⠀⠀⠙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣏⠀⣹⣿⣄⡀⢀⣼⣿⣤⡀⠀⠀⠀⢀⣠⣾⣏⠀⢈⣿⣦⡀⢀⣴⣿⣧⡀⢀⣴⣿⣧⡀