Cumulus cloud Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠂⢠⠀⠀⠀⠀⠀⠈⠀⠠⣀⠠⠐⠂⢐
⠀⠂⠐⢄⢠⡠⢔⡁⣼⡴⠶⠶⠀⠀⣀⡚⠈⠐⡀⠀⠈⠘⠷⠀⠀⠀⠁⠀⠀⠀⠀⢩⡹⠒⠁⠁
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠺⠄⠀⠸⠃⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠁⡀⢔⠊
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠈⠁
⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠰⠀⠌⢂⠀⠀⠉⠙⠀⠀⢀⡠⠜⠑⠦⠀⠔⠀⠀⠀⢀⡀
⠀⠀⠁⠀⠀⠦⠄⠄⣀⠠⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠺⠤⣤⡄⡀⣀⣀⢀⠤⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠐⠦⡀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠲⢂⢐⢐⡩⠂⣠⠞⠀⠀⠰⠂⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢀⠜
⠀⠀⠀⠉⠘⠁⠂⠒⡤⣆⠀⠐⠂⡀⠀⠀⢠⠈⠄⠀⣀⠀⠀⠐⠂⠠⠖⠂⠈⢀⡀⠐⠢⢄⣀⣀⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠈⠐⠂⠉

⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠲⠒⠒⠶⠶⣦⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣶⣐⣠⣤⣄⣤
⠀⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣻⢽
⠀⡟⠿⠿⠿⠿⠷⢶⡤⢼⡿⢤⡴⠖⠲⢤⡜⡖⠠⠀⠀⠀⠀⠀⠀⠀⢾⠿⠿⣿⡍⠋⠉⠙⢟⠛⠓⢚⣫⣿⣽
⠀⡥⠤⡤⠀⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢃⢀⣀⡀⠀⠀⣠⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠉⢫⢽⢿⣛⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢂⡀⠀⠒⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠦⠤⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡆⠁
⠀⠀⡠⠒⢀⣀⠀⡖⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠂
⠀⠘⠀⠀⠀⢈⡢⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⠅⠀⠆⣀⠠⠀⠁⠀⠀⠀⠀⣠⠄
⢀⣀⣀⣀⣐⠢⠀⠀⠄⠠⠀⢀⡀⠀⠈⠈⠁⢀⠀⠤⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠂⠀⢀
⠀⠄⠈⠉⠉⠀⠀⠐⠂⠊⠋⡐⠛⠓⠒⠒⠂⠐⠒⠒⠀⠐⡒⢚⠀⠐⠒⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠠⠤⠽
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠠⠒⠀⠀⠐⠂⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠤⢀⠀⣀⠤⠐⠒⠒⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⣀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠉⠀⠀⠈⡢⠔⠒⠈⠒⠄⠀⠀⠀⠀⠀⠀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡀⠤⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⡀⠤⠠⠄⠠⠄⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡀⠬⠒⠒⠒⠂⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠒⠈⠉⠑⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠂⠓⠂⠤⢀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠠⠤⣠⠊⠁⠈⠁⠢⣀⠀⠀⠀⠀⣀⠔⠈⠁⠈⠑⣄⠤⠄⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢢⠀⠀⡔⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⣡⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠶⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡌
⢀⠔⠉⠀⠀⠈⠱⡀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠠⢀⠀⡀⠤⠄⠀⠤⠼⡀⢀⠧⠤⠀⠠⠤⢀⠀⡀⠄⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⠎⠁⠀⠀⠉⠢
⡌⠀⠀⠀⠀⡀⠤⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠬⠤⢀
⠇⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⠊⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠈⠀⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠁⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡿⠿⠿⠿⢿⣦⣴⣾⠿⠛⠛⠉⠙⠛⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⢀⣀⣤⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⣤⣾⠿⠛⠉⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣶⣦⣄⡀
⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠙⢿⣦
⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠋
⠀⠀⠈⠛⠿⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣤⣤⣶⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠻⠿⣶⣶⣤⣶⣶⠿⠟⠉⠀⠈⠻⢿⣶⣦⣴⣶⡿⠟⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠂⠐⠒⢄⣀⠤⠒⠈⠉⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⠀⣀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⡰⠔⠂⠈⠐⠢⠀⠀⠀⠀⠀⠀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⠠⠤⠠⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢈⡢⠠⠤⠤⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠠⠒⠓⠢⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠠⠤⠆⢄⣀
⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠒⠚⠂⠄⡀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠢⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠈⠙⢢⠀⠀⠀⠀⠈⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⢠⠚⠁⠉⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠜⠒⠂⢄⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠉⢢⠀⠀⠀⠀⠀⠀⢀⠄⠒⠚⠤⡀
⢠⠋⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠒⢤⠔⠂⠉⠀⠈⠉⠓⢤⠔⠋⠉⠀⠈⠁⠒⣤⠔⠒⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠢
⠃⠀⠀⠀⠀⠔⠒⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠘⢄⠀⠀⣀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠤⠄⠒⠈⠑⠂⠤⠄⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⣀⡀⠀⢀⠜
⣶⣶⡶⠿⣿⠿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠋⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⠟⠉⠁⠀⠈⠙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⢀⣤⠾⠛⠛⠻⠾⠏⠀⠀⠀⠀⠀⠀⠀⠹⠷⠛⠛⠻⢶⣄⡀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠉⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠈⢿⡄
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠻⢶⣌⣷
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⡀
⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠈⠛⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⡶⠶⡶⠶⣶⠶⢶⠶⢶⠶⣶⠶⢶⠶⠶⡶⠶⠶⢶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⣠⠤⣴⠚⠛⢦⣀⡀⠀⢀⡴⠒⠉⢦⡀⠀⠀⢀⣀⣠⡶⠛⠛⠓⢦⡀
⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠈⠁⠹⢤⠈⠓⠒⠒⠚⠁⠀⡴⠋⠉⠉⠀⠀⠀⠀⠀⠋⠉⠳⡄
⠀⠀⠀⠀⠻⣄⣀⠀⢀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠓⠒⠋⠛⠁⣀⣤⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠹⣄⠈⠧⣄⣀⣰⣄⠀⠀⢳⡀⠀⠀⠀⠀⣠⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⣠⣤⣈⠙⠓⠚⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⠦⠤⠴⠚⠁
⠀⠀⠀⠀⢀⣠⠏⠀⠀⠘⠁⠀⠈⡧⣀⠀⠀⢠⠖⠋⠉⢙⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠋⠑⢦
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠸⢴⣄⣄⣤⠴⠃⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠘⠓⡄
⠀⠀⠀⠀⠈⠙⠛⢦⣀⣀⠷⢤⠴⠓⠋⢀⣀⠀⠀⠀⠀⠀⢀⡴⠚⠳⠦⣄⠀⠀⠉⠛⠛⠓⠒⠒⠊
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡴⠏⠉⠉⠙⢦⠀⠀⠀⢯⡀⠀⡀⢠⣼⠆⠀⠀⣠⠤⣄⣤⣄
⠀⠀⠀⠀⣴⠋⠉⠉⢣⠀⠀⠀⠘⠦⠤⠤⠤⠤⠴⠃⢀⡀⠀⠈⠉⠉⠉⠀⠀⢰⠋⠁⠀⠈⠀⠈⢳⡄
⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠉⠉⢲⠤⣄⠀⠀⠀⠀⠈⠛⢦⣀⣤⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠒⠒⢤⣀⣀⠀⠸⡇⡀⠀⠀⠀⠈⠀⠉⣦⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⡞⠁⠈⠃⠀⠀⠈⠁⠈⢳⡀⠉⠳⣄⣸⣦⣀⣠⠎⣁⣠⠎⠁⠀⠀⠹⣦⠤⣤⡀
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⠀⠀⠀⠀⠈⠁⠀⠀⣹⡀
⠀⠀⠀⠀⠙⢦⣤⣴⠁⠀⠀⠀⠀⠀⣠⣠⠾⠀⠀⠀⠀⠀⡴⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠶⠲⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠚

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀
⠀⠀⢀⠄⠘⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀⠊⠈⠁⠁⠑⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠉⢂
⠀⢐⠉⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠶⠦⡈⡅⠀⠀⠀⠀⠀⣀⠑⠐⠢
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⡀⠄⠠⡀
⠀⢀⠁⠀⠈⠒⠰⠈⠑⣆⠀⠠⠂⠊⠀⠀⠱⠀⠀⡠⠒⠀⠐⠁⠀⠑⠂⢄⠀⠀⠀⠀⠀⡠⠜⠉⠀⠀⠀⠘⠒⢄
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠀⢈⠀⠀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣲⠀⠀⢎⡀⠀⠀⠀⠀⠀⢀⢀⡀⠅
⠀⠀⠀⢀⣀⠤⠒⠠⠀⠀⠀⠀⠈⠒⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡑⠂⠒⠁
⠀⢀⠴⠀⠀⠀⠀⠀⠓⠠⡀⠀⠀⡐⠁⠀⠑⠒⠂⢄⠀⠀⠄⠐⠁⠀⠈⠒⢄⠀⠀⢀⠄⠠⠊⠀⠀⢡⣀⣠⠤⠤
⠀⠠⡀⠀⠀⠀⠀⠀⠀⡠⠃⠐⠊⠀⠀⠀⠀⠀⠀⢀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠆⢂⠀⠀⠀⠀⠀⠸⡀⠀⠒⠂⡅
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠑⠀⠂⠀⠀⠁⠀⠀⠈⠒⠢⡀⡠⠄⣀⠠⠃⠀⠡⠀⠀⣀⠀⢀⠇⠀⠀⡔⠁
⠀⠀⡔⠈⠲⢄⠎⡠⠘⠓⢄⠀⠀⠀⠀⠀⠔⠈⠁⠢⠄⣤⢀⡀⠀⣀⠀⠀⠀⠀⢀⠀⡀⢈⠁⡀⠈⠁⠈⠑⠊
⠀⠨⣀⣀⠤⠃⠀⠀⠀⠀⠘⠒⢄⠀⡤⠊⠀⠀⠠⠤⠊⠀⠀⠀⠀⠀⢡⠀⢀⣠⣁⡠⠀⠢⡀⠈⠄⢄⡠⠄
⠀⠀⠀⠈⠄⣀⣀⣀⣀⣀⣀⣀⠜⠀⠉⠁⠐⡎⠁⠀⠀⠀⠀⠀⠀⢀⠌⠠⠉⠀⠀⠀⠀⠀⠀⠈⠆⢀⣀⣀⣁⣐⡄
⠀⠀⠀⠀⠀⡠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠉⡉⠁⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀
⠀⠀⡀⠔⠉⠀⠀⣀⡩⠓⠒⢄⠀⠀⠀⠀⠀⠀⠔⠐⠁⢀⠨⢄⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠒⠊⠀⠈⢂
⠀⢰⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⢢⠀⠤⠁⠀⠀⠉⠙⡀⠉⠐⠀⠀⢐⠁⠀⠀⠑⠀⠄⠊⠁⠢⠈⡃
⠀⠀⠑⠀⠪⢄⢀⡀⡀⠀⠀⢀⠀⠤⠂⠀⠤⠴⢎⣉⠀⠀⠀⠀⠀⠀⣘⣒⡚⠄⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡤⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⠀⣀⠠⠤⠄⢀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⠂⠉⠉⠒⢄⠀⣀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠑⢆⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⡜⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⡀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⢀⣀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠑⠤⠠⣀⡀⠀⠀⠀⠀⠀⡀
⠀⡀⠤⡰⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠇⠈⠠⢀⡀⠀⠀⠀⠀⠀⠉⠑⡤⢄⡀⠀⠈⠉
⠸⣄⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠆
⠀⠀⠁⠀⠉⠉⠉⢏⣠⡉⠀⠉⢀⣀⣉⡁⠘⠊⠡⠂⠀⠀⠒⠀⠁⠉⠃⠉⠚⠋⠭⠠⠐⠊⠑⠒⠒⠂⠻⠵⡄⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠫⠤⢤⣀⡠⢄⣀⣀⣀⣠⣀⡠⠀⠤⠈⠀⠀⠀⠤⠀⠀⣀⣀⠠⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄
⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠔⠀⠀⠐⠀⠀⠀⠈⠒⠠⠔⠒⠂⠀⠐⠂⠂⠠⠤⠀⠒⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⣀⡀⠀⠀⣀⢄⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠐⠀⠊⠁⠂⠐⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠑⠒⠊⠒⠒⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⣀⡤⣤⡀
⣿⣿⠛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠐⠢⡠⠐⠀⠉⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠂⢀⣀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠂⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀
⠀⠀⠀⠀⢀⠠⠐⠁⠈⠁⠐⢄⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠈⠀⠀⠑⢀⠠⠀⡀⠀⠀⠀⠀⠀⢀⠗⠀⠈⠀⠀⠀⢄
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠐⠪⠀⠀⠀⠈⠢⡀⠀⠀⡠⠊⠀⠀⠀⡨⠂⠐⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨
⠀⡠⠐⠁⠀⠠⡀⠀⠀⠀⠀⡔⠁⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀⡠⠀⠠⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⡠⠒⠀⠑⠠⡀
⡘⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⠀⠀⠀⠀⠈⠐⠌⠀⠀⠀⠀⢈⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠁⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠄⠄⠐⠈⠑⠀⠀⠠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⢀⠐⠁
⣿⣿⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⢉⣽⣿⡏⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡾⡿⠉⠋⠀⠀⠀⠀⠀⠙⢶⣄⡀⢄⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣠⡶⢛⡽⡻⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣧⣢⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢀⣴⠞⠉⣰⠟⠀⠀⠸⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠀⢣
⠀⠠⠊⠀⢀⣠⣤⣤⣤⣤⠠⠀⢀⣠⣿⣿⣿⠃⠀⢰⡟⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠈⡀
⠀⠅⣰⡟⠉⠀⠀⠀⣀⣠⣤⣭⣿⠿⠟⠛⠁⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠇
⠀⠀⢿⠀⠀⠀⠀⠘⠻⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⢧⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠊
⠀⠀⠀⣸⠾⠖⠛⠛⠁⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢶⡀⠀⠀⠀⠀⣦⡿⢁⣄⣴⣾⣦⣤⣤⠴⠞⠋⠁
⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣦⡀⠀⠠⠀⡤⠞⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⡷⠛⠉⠉⠉
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣙⣮⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡟
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠼⠛⠛⠛⠛⠛⠛⠻⠷⣶⣄⣀⣀⣤⡄⠔⠀⠀⠀⠀⡸
⠀⠸⡀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠿⢶⣤⣴⣄⣤⣤⣾⡀
⠀⠀⢳⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⠏⣇
⠀⠀⡸⠃⠀⠀⠀⠀⠀⢀⣀⠄⢠⡤⣤⣤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠸
⠀⢰⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⢿⣿⣿⣿⣿⢿⠁⠀⣠⡇
⠀⡏⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠖⠲⠖⠚⢚⣽⠟⠉⠀⠀⠀⡰⠟
⠀⡇⢀⠀⠀⠀⠀⠀⠀⢀⣠⢼⠟⠋⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⡴⠋
⠀⣷⡃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⢀⠞
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠒⠊⠁
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣡⣴⡤⠔⠚⠉⠁⠁
⠀⠀⠀⢣⢠⡇⠀⠀⠀⠀⣰⠟⠉⢸⣇⡀⢀⠀⠀⠠
⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⠃⠀⠀⠀⣿⡴⠗⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⡟⠁
⠀⠀⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢰⠁
⠀⢠⣇⡀⢀⣠⡴⠖⠁⡠⠀⠀⠀⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠄⠶⠂⠶⠀⠱⣆⠉⠓⠈⠁⠀⡈⢳⠐⠒⠐⠆⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠃⠀⠀⠀⠀⠈⠀⠽⡅⢰⣄⠨⣥⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⢀⠀⠀⠐⠆⢀⠀⢈⣀⠀⠐⠂⠀⠒⠂⠀⠤⠐⠂⣈⠀⠀⠀⠀⢩⣀⠠⠤⠉⠙⠋⠓⠀⠀⠛⠀⠠⠄
⠀⠀⠀⠀⠰⠦⠀⠈⠁⠈⠋⠁⡀⠀⠀⠀⢀⡂⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⢤⣐⠳⠀⠀⠘⠳⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⢭⡉⠁⠀⠠⠀⠀⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠐⠂⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠤⠀⠠⠄⠀⠒⠶⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠤⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠐⢀⠰⣲⠟⠴⣶⡄⠀⠀⠀⠈⠁⠐⢄⠀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⣄⡀⠄⠂⠀⠀⠈⠙⠀⠐⠉⠀⠀⢀⡀⠈⠛⠐⠋⠀⠀⠀⠠⡂⠀⠀⠀⠀⠠⠎⠀⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⢄⡀⠀⠀⠀⣤⣖⣊⡛⢖⠀⠀⠀⠨⠶⠂⡀⣀⢐⣤⠔⠢⠤⠆⠀⢀⣠⡶⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡐⠐⠞⠀⠀⠀⡤⠀⠀⠀⠻⠋⢁⣠⡖⠚⠛⣋⠉⣨⣤⠄⢰⠉⠉⠫⠕⠃⠀⠀⢀⡀⠀⠀⠀⠀⢛⣦⠀⠀⠈⣀⠄⠄⠤⡀
⠀⠀⠀⡀⠂⠎⠈⠁⠀⠀⠀⣴⢞⡶⠖⢄⠀⠀⡀⠬⠏⠁⢀⣟⡅⠺⢿⣵⢾⠞⠁⠀⠀⠀⠀⠀⠰⢟⣥⡶⣾⣩⡶⠞⠛⠿⠃⢀⣀⣤⠄⠀⢃⣀⡀
⠀⢠⠂⠁⠀⢰⣆⣤⣶⣶⣁⡁⠈⠁⠛⠿⣃⣀⣁⠀⠀⠀⢞⡍⡀⠀⣀⠘⢋⣁⠀⠀⣴⠂⣀⡀⠀⠈⠉⠐⡿⠻⠇⠀⠀⠢⠆⣤⠴⠾⠖⠀⠀⠀⠀⣆
⠀⠸⠀⠤⠄⠀⠀⠀⠀⠈⢁⠀⠉⣀⠤⢌⣀⣉⣉⡀⠀⢀⠠⠄⣀⠠⢄⣀⡈⠤⠤⢄⡀⠠⠁⠢⣀⢀⡀⣀⡁⠀⠠⣀⠤⠀⠀⠤⠔⠀⠒⠂⠉⠂⠈
⠀⠀⠀⠀⠈⠀⠐⠤⠄⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠙⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠀⠀⠉⠉⠋⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠐⠒⠦⡀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠤⠔⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢠⠁
⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠒⢄⠀⠀⠀⠈⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠣
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠉⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢦⡀⠀⠀⠀⠀⠀⣼⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⢦⡀⠀⠀⣼⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠶⠶⠛⠛⠛⠛⠛⠛⠶⠶⣧⣀⠀⠀⣀⣀⣤⣤⣤
⠀⠀⠀⣤⣤⣄⣀⡀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡉⠉⠀⣰⠏
⠀⠀⠀⠙⢷⣌⠉⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣴⣿⠴⠶⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⢀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⣠⡶⠞⠛⠉⠀⢻⡄⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠉⠛⠛⠳⣶⣶⠾⠿⠛⠛⠛⠳⠶⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢶⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠙⠛⠶⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢔⡶⠢⢤⡄⠀⠀⠈⠁⠂⡀⠀⠀⠀⠀⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠄⠀⠂⠀⠀⠈⠃⠐⠁⠀⢀⣤⠀⠉⠐⠁⠀⠀⠠⡀⠀⠀⠀⠠⠂⠀⠀⠉⢁
⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠉⠀⠀⣴⡤⠀⠀⣶⣯⡭⠭⠇⠀⢀⢘⣡⠄⡄⠘⠒⠉⠒⠃⠀⢰⡞⠀⠀⠅
⠀⠀⠀⠀⡠⠀⠁⠈⠀⣀⣼⣁⣄⠀⠈⠀⢺⠇⠀⡴⢂⣴⣟⣧⡢⠀⠀⠁⠀⠀⣠⠆⣠⣠⢤⣤⢿⣥⡄⠀⢊⡉⠉⡆
⠀⠠⠘⠀⢠⣀⣠⣤⡄⡋⠙⠑⢾⠆⠀⠃⠀⠀⡸⡟⡀⠀⡙⠞⠀⠀⢠⡄⢀⠀⠀⠛⠫⣿⢿⠄⠀⣀⣄⣈⣽⣧⠀⠈⠉⢂
⠀⠂⠠⠄⠀⠈⠁⠉⠉⠀⢃⠀⠄⠉⠉⢋⠀⢀⠠⠄⠀⠬⢀⡈⠅⠤⡀⠀⠉⠀⣀⠀⢀⡁⠀⢀⠠⠀⠀⠤⠂⠂⠂⠑⠂⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣤⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠶⣤⣤⣀⣤⠴⠛⠶⢤⣤⣤⠴⠞⠁
⠀⠀⠀⠀⣠⠖⠉⠉⠉⠉⠓⢦⣀⡴⠚⠉⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄
⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠛⠛⠶⠤⢤⣀⣠⣤⣀
⠙⢷⣄⣀⠀⣀⣠⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡶⠦⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣄⣀⡀
⠀⠀⠀⠉⠉⠉⠀⠀⠈⠛⠷⠶⣶⣶⠶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠦⠤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⢦⣤⣤⡴⠞⠛⠓⠶⠶⠶⠚⠁
⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠐⢂⠠⠄⠀⠈⠳⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠂⠀⠀⠀⠀⠄⠀⠉⠀⢙⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡄⢀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠈⣤⠒⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⠠⣀⠀⠀⠙⣆⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠅⠀⢀⡠⠊⠉⠉⠀⠑⢄⣀⡀⠀⠈⠀⠙⠂⠀⠈⠉⠂⣈⠀⢀⣁⠉⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠔⠁⠀⠀⡸⠋⠃⠀⠀⠀⠀⣀⡀⢉⣳⣄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠙⠀⢄⢀⣀⠀⠸⢆
⠀⠀⠀⠀⠀⣀⠠⠄⠞⠁⠀⠐⠈⡃⠀⠠⠼⠆⠀⠀⠀⠀⠉⡀⠀⠀⠈⠻⠦⣀⣠⣷⢇⡠⠶⠔⠖⠦⠤⠴⠶⠦⢾⣓⣤⣈⣀⡤
⠀⠀⠀⠉⠉⠉⠒⠒⠙⠓⠒⠒⠛⠛⠓⠒⠒⠒⠦⢦⣀⣤⠤⣡⠤⠤⠤⠤⠤⠴⠤⠬⠩⣅⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠢⡀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢦⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⢠⠎⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠊⠀⣀⠤⠒⠒⠒⠒⠒⠢⢤⡀⠈⠢⠔⠁
⠀⠀⠀⠀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠈⠉⠒⠬⣉⠉⠙⠒⠢⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡠⠒⠚⠉⢉⡩⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠔⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠓⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡔⠉⠒⠤⣀
⠀⠀⠀⠀⣀⡤⠖⣊⣁⠤⠤⠶⠚⠁⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠙⠲⠦⠤⢄⣉⡒⠦⣄⡀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⠀⠈⠑⠒⠶⠄⠴⠖⠒⠉⠀⢠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣠⠊⠀⠀⠀⠀⢠⠤⢤⠀⠀⠀⠀⠈⢢⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠙⢦⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠜⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣷⣴⣾⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣅⣸⣿⠿⣿⣾⣿⣿⣿⡏⢻⣿⣿⣤⣿⣿⡿⣿⣧⣼⣿⣿⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡘⠻⠿⠿⠀⣿⡟⠟⢿⣿⣧⣼⣿⣿⡿⢿⣿⠀⣿⣿⣿⢿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠹⢯⣳⣿⣿⡿⠀⠟⠉⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠈⠁⠘⡿⠿⣿⠁
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣵⣖⠂⠉⠉⠉⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠿⡿⠿⠛⠋⠉⠀⠀⠀⠠⠴⠛⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⢨⣤⣄
⠀⠀⢠⣶⣦⣾⠋⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⣀⡀⠀⠀⢸⣿⣿⡀
⠀⢀⠄⡹⠟⣡⣤⣦⢿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠿⢿⠟⢿⣿⠋
⣿⡷⠋⠀⠀⠀⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⣀⣀⣹⣶⡿⠁⣀
⠀⠀⠀⣀⣀⣾⠿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡦⠀⠀⢀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠰⠚⠛⠉⠹⠛⣿⠛⠛⠉⠉
⣀⣀⠐⣿⣿⡟⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠀⠘⣗⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣿⣤⣀⣀⣀
⣿⣿⣿⣿⣿⡁⠀⣀⣴⣶⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣼⣿⠀⠰⣾⣿⠀⣠⠖⠂⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿
⠉⠛⠛⣿⣿⡏⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⡿⣿⣿⣿⠃⠀⢘⠳⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠹⣿⣿⡟⠋⠁⠀⠀⢸⣿⣿⠀⠀⢸⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇
⠀⠀⠀⣸⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠁⠀⠀⠀⠀⢠⣿⣿⠀⠀⠸⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠃
⣠⣀⣀⣿⣿⣿⢿⡟⢃⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⢳⠀⠀⠀⠀⣼⣿⣿⣀⠀⢀⣿⣿⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡶⠂
⣿⢿⣿⣿⣄⠀⢠⠉⢦⡠⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣦⣀⣤⣾⣿⣿⣿⣿⠾⠛⠻⠏⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠆
⠀⠀⠛⠉⠛⠃⣾⠀⠀⠛⠿⢦⡀⠀⠀⣿⠟⠁⠙⠛⠻⢿⣿⣿⣿⣿⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠂⠐⠒⠀⠁⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⣰⣄⡀
⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣶⡆
⡀⠀⠔⡰⠋⠀⠀⠀⠀⢠⣴⡦⠾⠟⠋⠀⠀⠀⠀⠀⠲⢶⣶⣦⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣅⣀⡀
⣿⠔⠋⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⠏⠀⠀⠈⠙⠒⠂⠀⣀
⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⣀⣀⣀⣤⣤⣦⣤⣴⡾⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠋⠻⣿⣿⣿⣿⣿⠷⠦⠄⠶⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠛⠉⠉⠁⠉⠉⠙⠟⠁⠀⠀⠀⠀⠄⠐⠻⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠄⢀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠇⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠹
⠀⠀⠀⠀⠀⠀⠘⣄⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⡀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣴⠍⠁⠀⠘⣿⣶⣶⣷⡀⠀⠁⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢺⣧⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠈⠻⣿⣿⣰⣇⣀⡾⠿⣿⠟⠛⠁⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⣸⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢠⣆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⢀⣿⣆
⠀⠀⠀⣿⣿⠉⠉⠁⢻⠹⣷⣀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣴⠄⣀⣠⣄⣀⣽⣿⣾⣇⠀⠀⠀⠀⢠⠟⠋⠀⠀⠀⠀⢘⢣⠋⠀⠲⣾⣶⡆⢠⣄⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠉⠛⢶⣤⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⢶⣶⣦⣤⣄⣀⠀⠀⠀⠀⣤⡶⠛⠉⠁⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⡴⠛⠁⢀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⡀⠈⠛⢦⡀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠟⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠻⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⣀⣠⣤⣶⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣶⣤⣀⡀
⣀⣤⡴⠶⠛⠋⠁⢠⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡄⠈⠙⠛⠶⢦⣤
⠉⠙⠳⠶⣤⣄⣀⠘⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠃⢀⣠⣤⠶⠞⠛
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠈⠳⣤⡀⠈⠙⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠛⠁⢀⣤⠞⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢀⣀⣤⠾⠛⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠛⠷⣤⣄⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢮⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣠⡶⠛⠉⠉⠙⠟⠁⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⣠⡴⠚⠛⠉⠙⠛⠓⠶⣄⣀⣀⠀⢀⡴⠞⠋⠉⠉⠉⠉⠛⠯⡀⠀⠀⠀⠀⠚⠂⠀⠀⢀⠀⣿⣀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⣸⠃⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠹⣄⠀⠀⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠈⠹⣇⠁⠁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠙⠳⠦⣤⠴⠶⠦⢤⣤⡔⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠠⠃⠀⢀⠃⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⢶⣅⣀⣀⣀⣀⣤⣎⣀⣀⣀⣀⣀⣠⣴⣁⣀⣠⣤⢶⣤⣤⠴⠟⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡬⠀⣀⢀⠘⡄⠀⠀⣀⢀⣄
⠀⠀⡠⠊⠀⠗⠉⢠⠀⢤⠎⢁⣀⠀⠀⠈⠄⢄⠀⠀⠀⠀⠀⢀⡀⡀⠄⠀⠀⠈⠉⢙⠕⢁⡞⠀⠀⠀⠀⠠⠄⠈⠁⠐⠁⠀⢆⣀⡈⠢⠚⠈⡀⣁⡥⠤⡀
⠀⠰⡴⠁⣄⡀⢀⣈⣲⣠⠖⠉⣈⣇⣠⣶⣤⣼⠄⠀⠀⠀⠰⠶⠂⠛⣤⠀⠄⠀⠀⠉⠶⢳⡂⠀⠀⠀⠐⠉⠁⠀⠒⠢⠀⠀⠀⢽⠈⣳⠴⠎⠑⠁⠀⠀⠄
⠀⠀⠈⠑⠒⠒⠃⠛⠧⠤⠽⠆⠛⠚⠉⠉⠁⠀⠀⠀⠦⠞⠩⠥⡍⠁⣰⠆⠀⠀⠠⢤⡴⠈⠁⠀⠀⠐⠠⠆⠠⠀⠀⠀⠀⠐⠄⠸⠚⡁⠀⠀⠀⡄⠂⠠⣈⣐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠖⠀⠂⠐⠛⠀⠀⠀⠀⠀⠐⠤⠀⠀⡀⠀⠀⢀⣀⣀⡀⠐⠀⠀⠀⠀⠀⣀⠤⢊⡉
⠀⠀⠀⠄⠐⠀⠰⠔⠀⠀⠀⠀⠀⠂⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠁⠀⠀⠈⠙⠙⠈⠉⠉⠉⠙⠊⠉
⠀⠀⠁⠦⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⠀⠀⠊⠤⡠⣅⠤⢀⠀⠀⠀⠄⠀⣤⠄⠈⠡⠄⠠⠖
⠀⠀⠠⠀⠐⣀⠀⠀⠀⢀⣠⠀⠀⡠⠄⠈⠋⢀⠒⠈⢁⠰⠀⠀⠀⠀⠁⠚⠂⠡⠄⣄⠴⠖⠚⠉⠱⠶⠤⠖⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀
⠀⠀⢄⠑⣂⡀⡀⠐⢄⡀⠤⠄⠀⠀⢘⡅⠰⡙⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣞⣁⣀⠋⣁⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠐⠓⠑⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡄⠐⠀⠂⠁⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠤⠥⠼⠽⠯⠭⠶⠥⠿⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠐⠀⠀⡄⠀⠀⢀⠀⢀⠐⠀⠐⠀⠀⠐⢄⢀
⠀⠀⠀⠀⠀⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠤⠀⠀⢀⡀⠀⠀⠀⠠⠠⠤⠤⠀⢀⡠⠄⠐⠒⠤⠄⠘⠁⠀⠀⠀⠀⠀⢠⠂⠀⠁⠒⠈⠄
⠀⢀⣀⣀⠀⣀⡀⢹⡄⠐⠚⡋⢉⡦⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⢠⡆⠀⣎
⠀⠈⠻⠌⡄⣥⡡⣅⠶⣙⣀⡴⢏⡒⢂⡁⠀⠾⠋⠀⠀⠀⠀⠖⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢀⠁⠂⠤⠄⢀⠀⠀⠀⣠⠒⠁⠠⠀⡰⠏⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠘⠋⠸⠟⠣⠍⠄⠶⢀⣤⢄⡠⠅⣶⠄⠀⠠⠈⠤⠀⢀⠀⠊⣀⠀⠑⢄⠀⠀⡈⢁⡦⠤⢀⣁⣰⠦⠔⠈⠃⡀⢀⠀⠰⠧⣄⡀⠀⠀⠀⢀⣀⡀⡰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠃⠀⠤⠄⠀⠐⢇⡁⠀⠐⢈⠋⡀⣀⣈⢠⣼⠇⠀⠀⠀⠀⠀⠀⠸⢀⣤⡀⣀⣠⠴⠖⠃⠀⠀⠈⠑⠒⠐⠚⠛⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⡀⠀⠀⠀⠀⠀⠀⢙⡏⠛⠉⠉⠉⠉⠉⡉⢙⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠋⠉⠉⠳⣤⠤⣄⠀⠀⠘⠛⢳⡀⠀⠀⠀⠀⣰⠏⠉⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠇⠀⠀⠀⠀⠀⠀⢨⡧⢤⣠⣤⣤⠟⠀⠀⠀⠀⠳⠤⣤⣤⣤⡼⠣⣄⣠⠤⠼⠳⡄
⠀⠀⠀⠀⠀⠀⢠⣠⠖⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠛⢦⣠⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠀⠀⠀⠀⠈⠀⠀⣷⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠙⠒⠋⢧⣀⡼⠳⣀⣀⣀⡴⠺⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⣦⠤⢤⡀⣀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⣀⡏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠳⣄⣠⠿⣄⠀⠀⢀⡴⠻⣄⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⠲⢤⣀⠀⠀⢰⠃⠀⠀⢧⠀⠀⢀⣠⠴⠊⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣈⣙⡶⠧⠤⠤⠤⠬⢶⣞⣉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠑⠒⠦⠤⣀⣀⣧⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣼⣁⣀⡤⠤⠖⠒⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡰⠋⠀⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⢹⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠓⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠉⢓⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣆⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⢀⣼⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣀⣀⡤⠼⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠣⠤⣀⣀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠁⠀⠀⠀⠀⡇⠉⠑⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠊⠉⠘⡆⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⡤⠖⠋⠁⢫⠉⠉⠉⣸⠁⠉⠓⠦⣄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠋⠁⠀⠀⠀⠀⠈⣇⠀⢠⠇⠀⠀⠀⠀⠀⠉⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡎

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠰⣄⠀⠀⣆⠀⠀⠀⠈⢠⠀⢀⠆⠘⠁⠀⠀⠀⠋⠑⠄⢀⡀
⠀⠀⠀⠀⠢⠤⠴⠶⣤⣤⠴⠶⠤⠔⠋⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠑⠒⠒⠒⠒⠒⠂⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠀⠐⠁⠀⠀⠀⠃⠠⢄⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠈⠁⠂⣀⡄
⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠓⠂⠠⠒⠠⠄⠊⠉⠁
⠀⠀⠀⠀⠈⠀⠐⠒⠲⠦⠤⠤⠤⠖⠒⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⠤⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⠉⠉⠉⠀⠀⠀⠀⠛⠢⡀
⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠳⠤⡤⢤⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱
⠀⠀⠀⠈⠁⠐⢄⣀⠀⣀⡠⢀⠴⠂⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠢⢄⣠⠔⠒⠲⠤⣤⠜⠉⠋⠁