Mathematical Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⡂⠀⠀⠀⢰⠀⠀⠆⠀⠆⠀⠀⠀⢐⡀⡀⠀⠈⠠⠀⠠⠀⠀⠄⠀⠄⡃⠀⠀⢀⡑⢄⠐⠂⠐⠀⡇
⠀⠠⣀⣆⣆⣠⡠⠀⠀⠠⠀⠂⠀⠀⠐⡀⢀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⢑⡝⠀⠑⢄⠈⠀⡇
⠀⠐⠭⡯⡯⢽⢹⠀⠀⠲⣐⠆⠀⠀⠀⠿⠛⠀⠀⠠⡄⠀⠀⢠⡄⠠⠀⢠⠅⢰⣃⡎⠀⣀⡀⡀⠑⢄⡁
⠀⠐⠀⠁⠉⠉⠈⠂⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢢⡃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⠔⢁⠄⠠⠈⠂⡀⠁
⠀⡾⠭⠭⠬⠭⠷⠀⠠⠊⠀⢽⡖⡽⣆⠀⠀⢀⢳⡞⡀⠀⠀⢀⠂⠈⠄⠀⠀⠀⠘⠀⠃⠀⠀⠘⠀⠃⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⡋⠀⠀⢂⠁⠈⠐⠀⠀⠂⢀⡀⡈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠈⠛⠛⠛⠛⠃⠀⠀⠀⠒⠐⠀⠃⠐⠂
⠀⠣⠀⠀⠀⡀⠔⠀⠀⠀⠀⠒⠒⡂⠀⠰⠂⠂⠰⠀⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⡀⠠⣴⠤⣄
⠀⢠⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠐⡂⠀⠀⡀⠤⠒⠢⠄⡀⠀⠀⠀⡈⣀⢀⢀⡀⡀⠀⡌⠀⠀⣿⣊⣸⡆
⠀⡷⠎⠱⠈⠎⠁⢺⠀⠀⢀⠀⡂⡇⠀⡘⢀⠂⠀⠀⠄⠱⠀⠀⠀⢜⣿⣻⣻⠟⠀⠀⢃⠀⠀⠀⠀⢨
⠀⡧⠄⢰⠀⠆⡢⢼⠀⠀⠈⠀⢁⠁⠈⠁⠀⠉⠉⠉⠁⠀⠩⠀⠀⠁⠛⠘⠘⠃⠠⠀⠀⠐⠀⠀⠐⠁
⠀⢂⠒⠒⠒⠒⠒⠘⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⡒⣂⣄⠀⠠⠤⢄
⠀⠀⠐⢄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⢢⠃⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠀⡍
⠀⠀⠀⡄⠑⢄⠀⠀⡘⡈⠉⠔⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠁⠀⠠⡳⡛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡃
⠀⠀⠀⠄⠠⠀⠑⢄⠀⢸⡺⠀⠀⠀⠀⣐⢂⠀⡀⢀⣒⠂⠄⠀⠨⠁⠉⠁⠀⠰⠀⠀⠀⠀⠜⠀⠈⠿⠋
⠀⠀⠒⠒⣒⣖⡒⠒⠓⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠊⠀⢸⣷⣿⡆⠀⠐⠂⠒⠘⠀⠐⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢈⠐⠂⠁⠀⠀⠁⠀⠐⡀
⠀⠀⠀⠀⠈⠉⡩⠀⠀⠠⡞⡃⠀⠐⠈⠁⡄⠀⢈⠐⠐⠐⠂⠀⠀⠀⢈⠀⠀⠀⡦⣴⠀⠀⣦⣤⣆⣤⡴
⠀⠀⠀⠐⠒⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⡂
⠀⠠⣤⠤⠠⠴⠖⠀⠄⠰⠆⠀⠈⠂⠀⠀⠀⢠⠅⠀⠀⠈⠀⠀⠀⠂
⢀⡁⠀⠈⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⢈⠌⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠈⠄⠀⠀⠀⠀⠘⠂⠀⡀
⠘⠒⠇⠀⠂⠀⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡄⠀⠀⠀⠅⠀⠀⠨⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠊⠁⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⣀⠀⠁⡀⣀⠀⠀⠀⣤
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠲⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀
⠀⠁⠀⠀⡀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⠂⡁⠠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⢷⠄⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠀⠀⢰⠰⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠐⠲⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄⣤⠄
⠀⡄⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣾⣿⢿⣿⣿⣷⣶⣷⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣿⣿⣾⣿⣯⣿⣿⣟⣿⣿⣿⡿⢿⣶⣶⣶⣦⣤
⠢⠑⢀⡀⢀⠀⠀⠠⢤⠃⠀⠈⠁⠀⠀⢀⢀⠀⠀⠀⠀⠐⢿⡿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣿⣼⣿⠿⠿⠟⠁
⢰⡄⠀⠀⠈⠀⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣄⠉⠉⠋⠁⠉⠁⠆
⠀⡄⠀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠑⠦⠄
⠀⠃⠀⠀⠁⠀⠀⠁⠀⠈⠀⠠⠂⠀⠀⢀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⢉⡼⡇
⠀⠀⠀⠀⠀⠀⣿⠑⡤⠶⠶⠒⠚⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⡇
⠀⠀⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠔⢳⠄⠀⠠⠤⠄⠀⢉⣼⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⢸⠇⣿⠀⠀⠀⠀⠀⠐⡏⠀⠀⠚⠟⠁⣀⣴⣋⠀⠀⠚⠉⠀⢠⣠⠞⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠶⠓⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠁
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⣩⣇⠀⠠⠖⠒⠀⠀⡠⠋⠀⠀⠬⠤⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠠⠤⠊⠀⠀⠀⠀⠐⠋⠙⠋⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣸⠀⣾
⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⢠⡇
⠀⠀⠀⠀⢸⣠⠞⠒⠒⠒⠂⠉⠉⠁⠉⠉⠉⠉⠉⣉⣉⣀⣀⣀⣠⣶⣶⣶⣶⣶⣶⠀⣀⣀⣀⣈⡩⠤⢼⡅
⠀⠀⡠⠖⠋⢩⠭⠭⠭⠭⠭⠭⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⣀⣠⡾⠁
⠀⠘⠓⠲⠦⠬⠭⠭⠭⠭⠭⠭⠭⠤⠴⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠰⠆⠴⠀⠤



⠀⠀⠀⣠⡶⣆⠀⠀⠠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⡄⠀⠀⠀⠐
⠀⠀⠀⠻⠧⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠄⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠄⠀⠀⠠⠀⠠
⠀⠀⠀⢻⣍⣿⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡇⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⠀⠀⠣
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢼⣟⣷⠀⠀⠀⠀⠀⢰⣿⣹⡇⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠃⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠶
⢠⣿⣿⡆⢰⣟⣿⡆⢰⡯⣷⠀⣾⡏⣷⠀⣾⣛⣷⠀⣾⣻⡆⢰⣟⣻⡆⢰⡿⣵⡆⣾⣟⣷⠀⣾⣛⣷⠀⣾⢻⡧⢰⣿⣿⡆⠀⠀⠐⠂⠀⠂⠀⠆⠀⠒
⠀⢙⡋⠁⠈⣋⡋⠀⠈⣉⡉⠀⢈⣙⠉⠀⢉⣛⠁⠀⢉⣛⠁⠀⢙⣉⠁⠈⣙⡋⠀⠈⣋⠋⠀⢉⣙⠁⠀⢙⣛⠁⠀⢙⣋⠁⠀⠀⠀⠀⡄⠀⠀⠀⣤
⠰⣿⣿⡇⢸⣿⣿⡆⢸⣿⣿⠄⣾⣿⣿⠀⣾⣟⣷⠀⣿⣽⡗⠰⣿⣻⡇⢸⣿⣿⡆⢾⣿⣿⠀⣿⣿⣷⠠⣿⣿⡇⢰⣿⣹⡇⠀⠀⠠⠄⠠⠄⠀⠤⠀⠠
⣀⣈⣉⣀⣀⣉⣁⣀⣀⣉⣁⣀⣀⣉⣁⣀⣈⣉⣁⣀⣈⣉⣀⣀⣉⣉⣀⣀⣉⣁⣀⣀⣉⣁⣀⣈⣉⣁⣀⣈⣉⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡡⠤⣟⣋⡛⢛⣛⣛⡙⢋⣙⣛⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⢀⡠⠔⠀⠀⠆⠀⡠⢠
⠀⠀⢀⠀⡀⠀⡀⠈⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠘⠀⠀⠁⠀⠟⢒⠀⠈⠉⠉⠀⠀⠀⡆⠀⠀⠃⠄
⠀⠂⠈⠀⠃⠀⢁⣄⡀⢲⡆⠀⣄⠄⠰⠀⠆⡆⡠⢀⣀⢀⢁⠀⡄⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠃⠀⠠⠋⡗⠀⣾
⠀⠀⠠⠎⠑⡄⠸⣦⡿⢸⣇⠀⠰⠀⠋⠐⠐⠀⠃⠎⠡⠞⠸⠸⠣⠀⠂⠀⠀⠰⠇⠠⠀⠀⠀⢁⠀⠀⠀⠀⠀⡀⠀⢸⠁⣰⡇
⠀⣀⠁⠀⠀⢸⡀⠀⢀⠸⡏⢰⣶⣄⠀⠀⢀⠀⠢⠀⠀⠀⠀⡀⡀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠠⠀⠀⠀⣤⠍⡽
⠀⡏⠀⠀⠀⠀⣧⠞⠁⠀⣷⠘⠿⠟⣀⠆⠀⠀⠀⠀⠀⠄⠀⠜⠄⢀⢀⠞⠈⠀⠀⠀⠀⠀⠀⢸⠔⠀⠀⠀⠀⢀⣀⠳⠴⠃
⠀⡇⠀⠀⠀⢠⠋⠄⠀⠄⠉⠀⡀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡈⠀⣈⠒⠠⠄⠀⢰
⠀⠧⠀⠁⢁⠋⠀⠉⠉⠁⠀⠖⠀⢲⠀⠰⠀⠀⠀⠀⠀⠀⢀⣧⣀⣀⠀⠀⡄⠀⠀⢠⠀⠠⠃⠀⠁⣄⠐⠁⢀⠍⣉⣉⠀⠒⠆
⠀⣆⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠁⠀⠐⠀⠀⠀⠀⠀⠹⡻⡿⠿⠿⠏⠀⡀⠇⠂⡀⠥⠀⠀⠀⠨⠒⠀⣌⠀⠐⠤⠌
⠀⠀⠀⠀⠘⢄⠐⠀⠀⠀⠰⠁⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⡄⠀⢀⠀⠀⠙⠀⠈⠀⢀⠀⢀⣀⠜⡁⠀⠠⠀⠀⠁⠀⠐
⠀⠀⢈⠀⠂⠈⠀⡀⠀⠈⠀⠀⠀⢰⢿⡀⣿⠀⢀⡞⢳⡄⡶⠤⡄⣤⡄⠀⡶⣆⠀⢠⡿⡇⠀⠀⠈⢁⠄⠀⢂⡤⠀⠀⠈⠂
⠀⠐⠌⠀⠀⠀⡀⠉⠂⠀⣰⠂⢀⡟⢸⡇⣿⠀⢸⢃⣀⢸⡇⠀⠀⣇⡟⠀⣧⡞⠀⣾⣀⣧⠐⣋⡀⠀⠈⠀⢀⠔⠀⠀⢠
⢰⡆⠀⡀⢠⠄⠁⠀⠀⠀⠯⠀⢸⠗⢻⠇⡟⠀⢸⡀⣹⢸⠋⠃⢠⡟⠙⡆⡿⢧⠀⡏⠉⣿⠀⣋⣀⠐⠉⠠⠀⠒⠊⠀⠀⠀⡀
⠀⠀⡀⠀⠉⠀⠈⠀⠀⢠⢂⠀⠻⠀⠸⠀⠛⠒⠘⠷⠃⠸⢦⣤⠼⣇⣠⠇⡿⠸⠷⠇⠀⠙⠀⠐⠐⠀⡀⠀⠐⠄⢀⠀⠀⠀⠴
⠀⡀⡅⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠀⠐⢀⠠⠤⢀⠀⠀⢀⣤⣄⡤⣄⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠁⠃⡀⢀⠀⠀⠠⣴⠂
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠋⠀⡽⠀⠋⠀⠀⠀⠀⡀⠓⠃⠀⠀⠀⢠⠀⠇⠈⠀⠀⢀⢌⡉
⠀⠀⠀⠀⠀⠠⡵⡆⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠖⠀⡄⣠⣇⠀⡄⠀⠀⠒⠀⢀⡀⠀⠀⠄⠀⠸⠀⠁⠀⠀⠀⢀⡉⠁
⠀⠀⠄⠀⠀⠀⠀⠐⠄⠀⠀⢀⠀⠊⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠓⠈⠉⠍⠂⠴⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢄⠀⠐⡴⠠⠀⢀⡤⠀⠀⠀⠁⠂⠠⠀⠂⠀⠂⢀⣠⡤⣠⡀⠀⣰⠀⠀⠀⠀⢸⠈⠙⡂
⠀⢖⠒⠒⠒⠀⠀⠀⠀⠀⢂⠤⠀⠀⡔⠀⠀⠀⠀⠰⠏⠔⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡼⢁⡞⠙⠃⠆⠀⠀⠀⡄⠈⠒⠖
⠀⠀⡑⠀⠀⠀⠈⢆⠴⣂⠤⠀⢄⠀⠀⠀⠀⡔⠆⡤⠀⠀⠀⠀⠤⠂⠀⢀⡴⠀⠀⠀⡠⠞⢁⣺⣤⠀⠀⠸⡀⠀⢠⠁⢈⣓⠒
⠀⠮⠄⠀⠠⠀⠀⠈⢂⢃⠅⣀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠸⠛⢒⡶⠂⠀⠓⠀⠠⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠣⣀⠌⠀⠈⠓⠦
⠀⠀⠀⡄⠂⠀⠰⠂⠀⠣⡁⢀⠄⠂⢁⠂⠀⡐⠀⡤⠀⢀⡴⠋⢀⠀⢀⢀⠄⠀⢉⠁⠘⢀⠴⠋⡄⠀⠀⡀⠀⠀⠀⠀⠀⠠
⣀⣀⣀⣁⣀⣀⣀⣂⣀⣀⣉⣀⣀⣀⣀⣊⣈⣀⣁⣁⣐⣉⣙⣳⣛⣃⣀⣘⣀⣀⣓⣃⣀⣀⣈⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢶⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡀⢀⡷⠊⠀⠀⠀⢠⣴⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⢃⡞⠁⠀⠀⠀⠀⢾⣇⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⣒⠀⠀⠀⢀⣴⠋⠀⢠⣤⣤⡄⠀⠈⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣷⠀⠀⠐⠛⠀⠀⠀⠸⣏⠀⠀⠘⢻⣦⡄⠀⠀⠀⠀⢠⣶⡤
⠀⠀⠀⠀⠀⢀⣾⣀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣤⡄
⠀⢠⣴⣶⠀⠈⠉⠉⠛⠻⢷⣤⡀⠀⠀⠀⠀⠘⢦⡀⠀⢠⣿⠉⠉⠻⣦⡀⠀⣤⠶⣤⡀⠀⠀⠀⠀⠀⠰⠶⠆
⠀⠀⢾⡏⠀⠰⢦⡶⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠙⣦⣼⠏⠀⠀⠀⢸⡇⠈⢷⣤⡿⠃
⠀⠀⠀⠀⠀⠐⠟⠑⠂⠀⠀⠀⠀⠻⣷⣦⣄⡀⠀⣰⡟⠁⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⣄⣈⠙⠻⣶⡟⠀⠶⠀⣀⣼⡿⠖⠀⠀⠀⠀⠀⣰⠃⢠⣼⠿⠃
⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠰⣿⣧⠀⠀⠉⠙⠲⣿⣧⢀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⢠⡇⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣾⠛⢁⣀⣀⠀⢀⣾⡿⠓⠶⠌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠘⠓⢲⡒⢺⢧⡀⠀⠀⠀⢀⣶⢠⣿⡇⠀⣨⣿⣇⠀⢸⣿⠁⢀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯
⠀⢀⣤⣄⠀⠈⠐⠒⠈⠉⠉⠻⣛⣛⣷⣶⣿⠃⢸⣿⠁⠀⠀⠀⠀⢰⣿⣿⡾⠛⠁⠀⠀⠀⠀⠀⡀⢊⡠⠀⠂⣀⣀⡀⠈
⠀⢀⣺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠻⣷⣄⠨⣿⡇⠐⠦⣤⣴⣿⣟⣡⠶⢤⢤⣔⣒⠛⢈⣉⣁⠤⠛⠉⠉⠁⠀⠙⠁
⠀⠈⠉⠁⠀⠀⣰⣤⣴⡄⠀⠀⠀⣀⡀⠀⠉⠻⣷⣿⣿⣄⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠉⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⢼⡷⣿⠇⠀⠀⣰⡟⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠸⣿⣳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠔⠒⠒⠒⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠦⡀
⠀⠀⠀⠀⠀⠀⡴⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⢸⠁⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⣿⡆⡿⣿⣷
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣀⠀⠀⠀⢺⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⡤⠀⠀⠀⠇⠀⠀⠀⣿⡇⣏⣿⣿
⠀⠀⠀⠀⠀⢸⡇⣸⠀⠀⠀⠁⠀⡀⠀⢸⠀⣠⠠⠄⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⡇⣯⣿⣿
⠀⠀⠀⠀⠀⢸⠇⡏⠀⠀⢸⠀⠀⠀⠀⠈⠀⠂⠀⠀⠨⠄⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⡿
⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⣈⠀⠀⠀⠀⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠂⡐⠀⠀⠀⠀⠀⣿⢰⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡀⡀⠀⠀⠀⠀⠉⠀⠣⠔⠀⢠⠗⠐⠀⠀⣿⢸⠀⣿⡇
⠀⠀⠀⠀⠀⡏⢰⠆⠀⠴⠛⠀⠀⠀⢠⡟⠁⠸⡇⠦⣄⠀⠀⠸⠁⠂⠠⢀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⡇⠤⠊⠀⠀⡌⠀⠀⠀⠀⠀⠂⠄⡀⠀⢸⡇⢸⢸⣿⡇
⠀⠀⠀⠀⠀⡿⢸⠀⠤⠐⠰⠀⢀⣴⠂⠀⠀⠀⠁⢀⡤⣄⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⢸⡇⢸⢸⣿⡇
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠰⠁⠀⣨⠉⢠⣴⡄⠀⠀⢏⠀⢸⢀⠀⠀⠀⠀⠀⡠⡈⠀⡀⠀⢸⡇⢸⢸⣿⡇
⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠰⠟⠀⠐⠋⠋⠀⠀⠈⠀⠀⠸⠀⠀⠀⡠⠊⠐⢎⡜⢦⠀⢸⡇⢸⣸⣿
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⡟⠀⣀⢐⡄⣵⢶⠡⣏⣴⣶⠘⠒⡤⠊⠀⠀⠀⠊⠀⠛⠀⢸⡇⣬⢿⣿
⠀⠀⠀⠀⢸⡇⢰⠀⠀⠈⣽⠀⣰⣿⡏⣿⣿⣿⠐⢻⣿⣿⣠⠀⠀⠀⠀⣀⡀⢠⡔⠁⠀⢸⡇⡏⢸⣿
⠀⠀⠀⠀⢸⡇⢸⠀⠰⠾⠃⢠⠿⢉⣁⠾⢿⡿⣨⢺⡇⣿⣴⠿⠀⠀⠈⣹⠀⢸⠀⠀⠀⢸⡇⡇⢸⣿
⠀⠀⠀⠀⢸⠃⢸⠀⢀⠤⠄⠘⠀⠀⢀⡔⣤⢿⡇⡏⣜⣣⣴⣛⡆⠀⠀⠟⠀⠶⠀⠀⠀⢸⡇⡇⣼⣿
⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠄⠀⠀⠈⢿⣷⡏⣼⣷⢣⠜⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⣿
⠀⠀⠀⠀⢸⠀⣿⠀⠀⠰⠖⠊⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⣶⠶⢿⡇⡇⣿⣿
⠀⠀⠀⠀⢸⠀⠿⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⡶⠶⠾⠛⠻⡿⡿⡿⡟⠿⠯⠽⣦⣾⣷⡈⢣⣷⣿⣿
⠀⠀⠀⠀⠈⢶⣖⡲⢿⣿⣿⣻⣟⣯⣻⣽⡮⠷⠤⠤⣘⢻⡷⠶⠤⠤⠐⠒⢊⣉⣉⡿⠥⠤⢄⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠺⣿⣷⡝⢋⠭⠥⠄⠒⠒⣒⣛⣉⣩⣭⣄⣀⣀⣠⣤⣼⣷⣿⡷⠶⠾⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⣿⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠂⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⡠⠰⣦⠀⠑⠀⠀⠀⠀⡠⠒⢢⡀⢀⣤⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⢀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠄⠀⠀⠐⢂⠀⠀⠀⠀⠉⠙⠊⣠⡾⢋⠀⡰⠀⠀⠀⢾⣦⡀⠀⠈⠛⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⣀⢤⠼⠿⠀⠀⠈⠁⠓⠒⢒⢲⡄⠀⠀⠀⢾⡄⠀⠀⠄⠀⠀⣀⣀⡀⠼⠀⠀⠀⠀⠀⣔⡕⠁⢀⡤⠊⠁⠀⠀⠀⠀⢙⣿⠀⠀⠀⠀⠰⡋
⠀⠀⠀⠀⠀⣬⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠓⠐⠀⠈⠉⠀⠀⠠⠄⠠⡄⠀⠀⠀⠘⠿⢁⣀⠎⠀⠀⠀⠀⠀⢀⣴⠋⠁⠈⢀⣤⡀⠀⢑⢄
⠀⠀⠀⠀⠀⢰⣿⠀⣀⣠⣄⠀⠐⠀⡴⠒⠒⠚⠁⠀⠀⠀⠠⣶⠀⠀⠀⠀⠁⠀⠐⠀⢠⠇⠀⠀⠀⠰⡟⠡⢱⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠐⠁⠉⠳⢤⠤⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⠀⠂⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤
⠀⠀⠀⠀⠀⠀⣴⠖⡦⡀⠀⣠⣿⠏⡄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠉⣀⣀⣀⠀⠀⠀⠀⠀⣼⡅
⠀⠀⠀⠀⠀⠀⠫⣀⣡⠏⣼⡷⠃⡀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⡀⠀⠀⣾⠋⠒⠛⠀⠀⠛⠁⣈⠇⠀⠀⠀⠀⢹⡇⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡟⠁⠀⢁⠜⠀⠀⠀⠀⠀⠀⠀⣴⡶⠋⠙⢉⠉⢩⠀⠀⢀⠀⠀⢸⠀⠀⠉⠒⣦⡄⠀⠀⡀⢎⠁⠀⠀⠀⠀⠀⠈⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣣⠎⢠⠀⣠⠋⢀⡤⢤⡀⠀⠀⠀⠀⠱⣧⣀⣀⣀⣀⡀⠀⠤⠤⠤⠤⠼⠀⠀⠀⠘⢏⢀⡤⢶⣦⣈⠇⠀⠀⠀⠀⠀⠀⢿⣀⣀⡁
⠀⠀⠀⠀⠀⠀⣜⡴⠁⠀⢀⡔⠁⠀⠸⡄⠃⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠦⢄
⠀⠀⠀⠀⠀⠀⠈⠣⣄⡠⠊⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⣴⡶⠖⠢⢄⡀⠀⠀⠀⢀⢀⠋⠉⠆⠀⢰⣿⣄⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠐⢘⠆⠀⠀⠐⢿⡇⠀⠁⠒⠠⠀⣀
⠀⠀⢰⢩⠋⠀⡠⣤⠀⢱⡀⠀⠀⠈⣿⡆⢨⠀⠀⠀⠀⡿⡇⢸⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⢐⣠⠖⠁⠀⠀⠀⠀⠀⠈⠁⠒⢮⣄⡀⠈⢨⠆
⠀⠀⣇⡎⠀⡎⣰⣿⠃⢀⡇⠀⠀⡔⣟⠁⠎⠀⠀⠀⠀⢧⣆⠘⢂⠀⠀⠀⠀⠰⣿⡟⠁⠀⠀⢮⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠷⠋⢁⠔⠁
⠀⠀⢿⡇⠀⢶⠿⠋⠀⡼⠀⠀⠀⠀⣬⡆⢹⠀⠀⠀⠀⡏⡏⠀⡇⠀⠀⠀⠀⠀⠀⠉⠓⠮⢤⣀⠀⠍⠙⠒⣤⠀⠠⣾⠝⠋⠈⢀⠜⠁
⠀⠀⠀⠙⢤⣀⣀⠤⠚⠁⠀⠀⠀⠀⣿⡇⠺⢄⠀⠀⣴⡦⠃⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡴⠃⠀⠀⠘⣄⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠄⠀⠀⠙⠃⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠄⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠈⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠐⠢⣄
⠀⠀⢠⠀⠀⠊⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡆⠀⠓⠆
⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢲
⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢘
⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠘
⠀⠀⢸⠀⢸⠀⠀⠀⢀⠔⠚⠋⠀⠓⣄⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡀
⠀⠀⢸⠀⢸⠀⠀⡐⠁⡠⠂⠉⠆⠀⡤⠀⠀⠀⠀⠀⢰⠁⡰⠋⠀⠉⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡍⡇
⠀⠀⢸⠀⢸⠀⢰⣁⡴⠁⠀⣠⠃⣠⠃⢀⠀⠀⣀⠀⠀⠑⠁⠀⠀⡔⢁⡔⠀⢀⠤⣤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⢸⠀⢸⠀⠀⠀⠀⢀⡴⠁⡰⠁⠰⡉⠣⠔⠉⡳⠀⠀⠀⡠⠊⢀⠌⠀⠀⠘⠦⠤⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⢸⠀⢸⠀⠀⠀⣠⠊⠀⡜⠁⠀⢀⠜⠀⡀⠺⣄⠀⡠⠊⢀⠖⠁⠀⠀⠀⢰⠉⠓⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⢸⠀⠀⠀⠀⡰⠁⠀⡞⠀⠀⠀⠈⠳⠊⠉⠚⢁⠞⠁⡠⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠸⠀⠀⡇⢠⠃⠀⠮⠠⠤⠤⠤⠤⣄⠀⠀⠀⠼⠀⠐⠧⠀⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⡇
⠀⠀⠀⡀⠀⡇⠈⠦⠀⠴⠀⠤⠤⠄⠄⠸⠀⠀⠀⠱⠤⠤⠤⠤⠀⠀⠴⠤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇
⠀⠀⠀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⡇
⠀⠀⠀⢡⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⠃⠇
⠀⠀⠀⠀⠙⠢⠦⠲⣆⣂⣖⣲⣒⢲⠒⡆⢀⠀⣀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⡐⠒⡒⢒⡒⠒⣖⣒⣖⣲⣒⣢⣀⠢⠨⠭⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣤
⠀⠀⠀⠠⣤⣤⣶⣾⣧⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⣤⣴⣶⣶⣞⣋⣡⣾⣷⣦⣬⣽⠟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⡟⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⢹⣿⣧⠀⣸⡏⠘⡟⠉⠉⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⣦⡀
⠀⠀⢀⣀⣀⣠⠙⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣘⡮⣿⡔⠉⠆⢠⡇⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠈⠉⠛⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣆⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠦⡇⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢸⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣠⣿⣧⢀⣤⣤⣀⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣲⣛⣿⣿⡿⠿⢼⣿⡿⠤⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⣠⠙⠋⠛⣿⠁⠀⠀⣿⣧⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⡜⢀⠀⠀⢸⠁⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠃⠐⠀⢀⠃⠀⠀⠀⣶⣷⣿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢸⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⠀⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⡤⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣻⣋⣉⣍⣙⣙⣫⣭⣿⡋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠿⠛⠉⠉⡿⠛⠛⠛⠟⠏⠉⠙⠻⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⡠⠚⣳⠋⢱⣿⡦⣤⣀⠀⠀⠀⠀⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣤⡀⠀⠈⠀⢀⡇⠀⠀⣼⠂⠉⢹⣷⣄⣤⣤⣤⣤⣤⣤⣽⣶⡤
⠀⠀⠀⠀⠀⠀⠠⣤⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⠁⠀⠀⢻⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⢸⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⣦⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣴⣶⣴⣶⣶⣶⣦⣾⣿⣿⣿⣿⣷⣷⣶⣤⣤⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣆⣠⣠⣀⣀⣰⡆⠀⠀⠀⢸⢩⣭⣭⣭⡍⡆⠀⠀⠀⢰⠚⠚⠚⢳⣼⣿⠀⠀⠀⠀⠘⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡯⠭⢭⠭⣷
⠀⠀⡧⢼⣽⡥⠤⢼⡇⠀⠀⠀⢸⠠⠠⠠⢠⠄⡇⠀⠀⠀⢸⠀⠭⠭⢸⡇⣿⠀⠀⠀⠀⢠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⠈⠘⠘⣿
⠀⠀⡗⠺⠖⠒⠶⢺⡇⠀⠀⠀⢸⠨⠭⠬⠸⠇⡇⠀⠀⠀⢸⡀⠒⠒⢸⠝⡛⠀⠀⠀⠀⣦⣤⠀⠀⣴⣼⡀⠀⠀⠀⠀⡇⠀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⣠⠶⠶⢤⡀⠀⠀⠀⠀⠀⣠⠴⠶⢦⡀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠀⠀⣠⠴⠶⢦⡀
⠀⠀⣼⠁⣤⣤⡄⢻⠀⠀⠀⠀⢰⠇⣤⣷⣄⢹⡆⠀⠀⠀⠀⡏⠐⣦⡖⠈⡇⠀⠀⠀⠀⣾⢀⣼⣧⡀⣷⠀⠀⠀⠀⢸⠃⠶⠶⠆⢹⡄
⠀⠀⠸⣆⡀⢀⣠⠟⠀⠀⠀⠀⠈⢧⣀⠛⣀⡼⠁⠀⠀⠀⠀⠳⣌⡁⣉⡴⠃⠀⠀⠀⠀⠹⣄⡐⢂⣠⠏⠀⠀⠀⠀⠘⢦⣉⠉⣁⡞
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⣣⣼⠀⠀⠀⠀⠀⠀⣸⠛⢛⣟⡛⢻⡅
⠀⠀⢸⣇⣙⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⣀⠃⠺⣆⠀⠀⠀⠀⠀⣹⠀⠿⣬⠇⢸⡇
⠀⠀⠘⠛⠛⠋⠙⠃⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⠤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡜⢝⠂⡗⢩⢱⠀⠀⠀⠀⠀⢦⡞⠐⣆⣰⠀⠀⠀⠀⠀⠠⣿⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡄⣠⡞⠀⠀⠀⠀⢀⣀⠀⡟⠉⠉⠁
⠀⠀⢇⢠⠇⡧⠁⢸⠀⠀⠀⠀⠀⠋⠙⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢦⡄⠀⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⠃
⠀⠀⠀⠛⢤⠧⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠋⠓⠀⠀⠀⠀⠀⠘⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⢠⠶⢦⡀⠀⠀⠀⠀⠀⢠⡴⣤⡀⠀⠀⠀⠀⢀⣤⢰⡆⠀⠀⠀⠀⠀⠀⣴⠶⠶⠒⠂
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⠀⠠⣾⣥⣼⣇⣀⠀⠀⠀⠀⠘⠛⠛⢶⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴⣏⡀⠀⠀⠀⠀⠀⣀⣀⣀⣨⡿⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⢀⣄⡀⠀⢀⡾⠁
⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠙⠛⠋

⠀⠀⠀⠀⣤⠞⠛⠀⠀⠀⠀⠀⠖⠛⢻⡟⠀⠀⠀⠀⣠⠞⠛⠻⣆⠀⠀⠀⠀⢠⡶⠛⣻⡄⠀⠀⠀⠀⣠⠶⠛⢦⡀
⠀⠀⢀⣾⣥⣤⣄⡀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠙⠶⣦⣾⠃⠀⠀⠀⠀⢿⣤⡾⣿⠁⠀⠀⠀⣼⠃⠀⠀⠈⣷
⠀⠀⠸⣇⣀⣀⣼⠇⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢾⡁⢈⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣆⣀⣀⡼⠃
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⣠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠠⠶⢾⡷⠶⠒⠀⠀⠀⠤⠤⠶⠶⠶⠖⠀⠀⠀⠀⣨⣷⣟⠁⠀⠀⠀⠴⠶⠶⠶⠶⢤⠄⠀⠀⢈⣉⣉⣉⣉⡁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠙⠃⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⢈⣿⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⢀⣿⡹⣯⡀⠀⠀⠀⠀⠀⣤⣤⣼⣷⣿⣂⠀⠀⠀⠀⠀⣿⣴⣂⣀⡦⡄⠀⠀⠀⣴⣿⣿⠿⢻⣿⠶⠀⠀⠀⠀⢰⣿⣿⣿⢿⡀
⠀⠀⠘⠿⠶⠿⠃⠀⠀⠀⠀⠀⠛⠛⠷⠶⠋⠁⠀⠀⠀⠀⠤⠿⠿⠽⠿⠧⠤⠀⠀⠀⠀⠙⠿⠾⠿⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠾⠁

⠀⠀⢠⣶⣶⣶⡀⠀⠀⠀⠀⠀⢀⣠⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠶⡄⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖
⠀⠀⢸⣿⣿⣷⢲⡄⠀⠀⠀⠀⠾⢀⣞⠹⣿⠓⠀⠀⠀⠰⣟⣿⠀⠀⢸⣏⡷⠀⠀⠀⠀⣶⣒⣚⣛⣓⡂⠀⠀⠀⠀⠀⣰⣟⢽⣦
⠀⠀⠈⠙⠛⠙⠚⠁⠀⠀⠀⠀⠦⠌⠏⠠⠟⠁⠀⠀⠀⠀⠈⠁⠳⠶⠂⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⠯⠇⠀⠀⠀⠀⠀⠙⠿⠾⠋

⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⢾⣿⣾⣿⡧⠀⠀⠀⠀⠀⢰⣿⣿⣤⣤⠀⠀⠀⠀⠀⢀⡴⣤⡐⢀⠇⠀⠀⠀⠀⠀⣿⣿⣽⣭⣿⡛⠋⠀⠀⠀⢰⠀⣺⠀⢨
⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠘⠯⠿⠃⠁⠀⠀⠀⠀⠘⠛⠛⠒⠚⠓⠛⠁⠀⠀⠀⠀⠀⠂⠤⠄⠙⠁

⠸⠿⠿⡀⠀⠀⣶⡆⢀⡴⢺⣧⣭⡁⢳⣿⡏⠀⠀⠿⠀⠀⠀⠈⠛⠛⠉⠀⠙⠛⠋⠁⠈⠛⠒⠋⠀⠉⠛⠚⠃⠈⠓⠒⠂
⠀⣠⣤⢸⣶⣦⢀⡄⢸⣇⣨⣏⣈⣁⣈⣉⣁⡀⠀⠀⠀⠀⠰⠃⠘⣦⡞⠁⢱⡴⠁⠙⣦⡞⠀⢳⡞⠀⠙⣶⠋⠀⢷⠎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠈⢫⡌⠛⠋⠀⠀⣼⣿⣿⣿⣾⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢸⣷⠀⠀⣿⡇⠀⢸⣧⠀⠀⣿⡄⠀⣸⣇⠀⢀⢿⡄⠀⡀⢠⣤⣀⢀⡖
⠾⡿⠈⢱⣿⡆⠀⠘⣏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠋⠈⠀⠘⡅⠙⢀⠋⠈⠀⠈⠀⠙⠀⠁⠈⠀⠈⠀⠙⠈⠁⠸⣿⣿⣿⣿
⠐⠀⠀⠀⠈⠀⠀⠀⢈⠀⠀⠀⣀⣀⣀⢈⣁⠀⠀⠀⠀⠀⢀⠀⠘⠃⠀⠘⠁⠠⡄⢠⣵⣤⣼⣤⣄⡖⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⡋⠀⠠⠛⠿⡿⠟
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⣧⠀⠀⠀⠀⠠⠤⡀⠀⠈⠃⠰⢤⣠⣾⡿⡿⠻⢿⣷⣼⣷⣴⢂⣀⠀⣴⣶⣧⡀⢠⡆⢠⡀⢰⢰⠂⠠⠰
⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣯⢿⣿⢾⠀⠀⠀⠀⠀⢀⡁⠀⠃⠀⢀⢰⣿⣿⣿⡆⣰⣿⣮⢛⢿⣿⡇⠀⠀⠹⠿⠟⠀⠘⠇⠈⠁⠾⠿⢷⣶
⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠀⢀⠴⠶⠟⠫⡅⠀⢘⡷⠈⢭⣟⣻⣿⡟⢻⣿⣟⣶⣾⣿⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠰⢶
⣭⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡆⠠⣀⡀⢀⣀⡴⠀⠈⠀⠐⠊⣻⣿⣿⠾⣿⣿⣿⣿⣥⡼⠧⠀⠀⠈⠀⠀⠀⠀⠁⠀⠐⡞⠆⠀⠀⣈
⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣀⡜⠃⢠⠾⠛⠛⠓⠄⠀⠉⣂⠀⠈⠁⡹⠿⠿⣿⣿⠿⡟⠫⠀⠀⠀⠐⡂⠐⠦⠶⠛⠛⠂⠀⠉⠓⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠈⢳⡄⠠⣀⠀⣀⣀⡤⠀⠀⠀⠂⠀⢀⡁⠀⠀⠘⠈⠀⠘⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⠆⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣄⠀⠀⣸⠇⠠⠞⠛⠋⠓⠦⠀⠂⠀⣴⡶⢀⠀⠀⠀⣰⣶⣶⡀⠀⠀⢐⣾⠿⣿⣿⠿⠟⠋⠉⠀⣀⠛⠛⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠟⠓⢧⡀⠐⢦⣄⣠⡤⠖⠀⠀⠀⠠⠀⠘⠁⠀⠂⠙⠿⠟⠀⠀⠀⠉⠉⣉⣉⣀⡀⠀⣀⡄⠀⠙⢻⡷⠸⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢸⡇⠰⠚⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠂⢰⣦⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠁⠀⠀⠺⠇⠀⠗⠀⣁
⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠀⣀⣈⠀⠐⠤⠄⠀⠀⠀⠚⠃⠀⠀⡤⠀⠀⣴⣶⠆⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⣄⢀⠀⠄⠀⠐⠐⠂⠸⣿
⠀⠉⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠘⠛⠐⢿⣿⠲⠿⠀⣤⣤⡀⢘⣿⣿⣿⣇⣶⡆⠀⠉⠉⠁⢨⣿⣿⣿⣿⢶⠀⠀⠀⠰⡀⠀⠀⠑
⠀⠀⠂⠤⠄⣚⠳⣼⡑⢞⣿⠀⠀⠀⠀⠀⣀⠸⠷⠀⠛⣿⣇⠘⠿⠿⠇⠛⣿⠄⠘⠛⢀⡀⠹⣿⣿⣿⡿⡟⠀⠠⠀⠀⠈⠀⠀⠈⠀⠠⠴⠤⣄⠐
⠀⣴⡄⠀⠀⠀⢠⡿⢙⣫⡞⠀⢀⠀⠀⣿⣿⡗⠀⠀⣴⣿⣟⣤⣤⣄⡀⠀⢀⣰⢤⠀⠈⠁⣠⡈⠉⠛⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⢐⡀⠐⠀⠀⠇
⠄⢸⡇⠀⠀⢀⡘⣰⡾⣼⠇⠀⢈⠀⠿⠇⣽⣄⢸⣟⡸⠋⢿⠿⣯⡟⢤⠀⠀⢼⣻⠸⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠳⢽⠽⠃⠈⠉⠁⠘⠟⠀⣾⠁⠸⣿⣿⡀⠀⠁⠀⠙⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠒⠀⠀⠀⢸⡇⠻
⠑⡀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⡆⠀⠀⢻⣿⣷⡀⣶⠦⣾⡿⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠀⠺⠇
⠀⡆⠀⣉⠙⠛⠀⣀⠀⠀⢀⣾⢯⣿⣿⣷⣿⣧⠐⠈⢿⣿⣿⣟⢛⣁⡀⠀⠀⣴⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠸⣿⠇⠀⠄⣡⣴⣶⣷⣶⣤⡀⠆
⠘⡇⠈⠙⠃⢰⡆⠙⠀⠀⢸⣿⣿⣅⡸⢻⡿⣿⠠⠀⢠⣿⣏⣿⣽⡍⣿⣀⡀⠀⢀⠈⠀⠠⡆⠀⣾⣿⠆⢀⣤⡀⠠⠀⣼⣟⣹⣿⣿⣯⣽⣷⡌⠄
⠰⡇⠸⠿⠀⠘⠃⠘⣇⠀⠀⠛⢿⣭⣿⣿⣿⠟⠄⠀⢾⣿⣿⣿⣿⣟⠛⠻⠿⣀⡀⠀⣠⡀⠀⠀⣨⣇⠀⢀⣉⠀⠐⠰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐
⠀⣁⡠⠤⢄⣀⡤⢤⣍⠀⠀⠀⠀⠀⠙⠉⠈⠀⢠⣄⠀⣬⣉⡛⠻⠿⣿⠇⠸⣿⣿⡦⢈⣹⠿⠚⢿⡿⠃⠺⠿⠇⠈⠁⠻⣿⣽⣿⣿⣿⣵⡿⠁⠁
⣼⣿⠾⣧⣤⢩⡞⡯⢴⢩⠽⣖⠀⠀⠀⠀⢠⣤⠀⠙⠀⢀⡈⠉⠀⠀⠀⠀⠀⠈⠉⠐⠀⠉⠀⠀⣾⡆⠀⠘⠃⠸⠿⠀⠂⡈⠛⠛⡟⠛⠋⡀⠂⣠⣶
⡱⣿⣮⣗⡣⠒⠽⠣⠘⢜⣗⢾⠜⢀⣄⣤⣿⠃⠰⠇⢠⡟⠁⠘⠉⠉⢳⣤⠛⠉⠙⢲⡴⠛⠉⢳⣤⠞⠉⠙⠳⣴⠛⠋⠃⠀⠈⠀⠁⠈⠀⠀⠀⣯⠿
⢠⣦⣄⠀⠠⠶⠶⠆⠀⠀⠀⢠⣄⣼⣿⣿⣿⠀⠀⣄⠀⣤⠆⠀⠀⠀⣠⣏⡀⠀⢀⣼⣃⠀⠀⢀⣿⡀⠀⠀⣨⣇⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⣳⣧⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⢉⡱⠀⠀⠀⠀⡀⠀⠦⠄⠠⢒⣼⠒⢐⢚⣺⠀⣻⡃
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠥⠤⠄⠒⣒⢲⡂⢎⢫⣻⡦⠭⢯⠟⡖⠋⠉⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⡐⠀⡄⠀⠂⠀⣀⠀⠀⠀⠀⠓⠂⠋⠉⠉⠉⠁⠹⠀⠚⠚⠁⠀⠀⠖⠀⠀⠐⠨⢍⣀⠀⠀⢄
⠀⠀⠀⠤⢶⡤⠀⠀⠀⣠⠐⣲⣾⡞⠨⢵⣶⠅⠐⣖⣈⢥⡀⠶⢁⠁⠀⠀⢀⠀⠀⠀⢈⡐⢁⡢⣀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣈⣤⠴⠧
⠀⠀⠑⠤⡐⠀⠐⠀⢄⠙⠒⢋⣜⣿⣀⢘⣻⠤⢀⣰⣏⡿⣥⡀⠀⠁⢂⡐⠀⠌⣃⢠⠐⠀⠦⢄⠠⠑⠤⣏⣀⣈⣟⣶⡞⠉
⠀⠀⠀⠀⠈⠁⠠⡀⠀⢢⠄⠀⣠⠤⢉⣉⠩⢅⠀⠒⠾⣟⠉⠤⠴⠂⢀⡌⠀⢠⠈⠃⠄⢀⣀⡀⣰⡄⠴⠄⠵⢤⠶⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢡⣒⡶⠃⠀⠐⠁⠄⢬⡼⠿⣾⠷⣀⠀⠀⢉⡁⠀⡀⢀⣀⡀⣀⣠⣠⣜⣠⠒⠡⢶⡄⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡛⠉⠁⠀⠈⣿⣦⠟⠋⠛⠛⠋⠉⠀⠉⠁⠈⠀⠁⠀⠀⠌⠠⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣢⣀⡰⠆⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠴⠖⠚⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⡇⢹⡃⣸⢿⡇⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣹⡇⠉⠁⣿⣼⣧⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠶⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⢸⣿⣛⠃⢦⡆⣾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⡛⢹⡇⠞⠇⣿⢻⣧⢨⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠿⠾⠃⠀⠀⠻⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡗⠀⠀⣴⢶⡄⢀⡀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣬⡅⣸⡇⣿⣧⣭⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⣿⣼⡇⠀⠀⢿⣧⣿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣺⣿⣿⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⠘⠓⠒⠚⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠺⠿⠿⠷⠶⠾⠿⠿⠷⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠹⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣶⣶⡿⠿⠟
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣛⣫⣭⣷⠶⠛⠁
⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠛⠛⠛⠋⠉⠁
⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣤⣤⡄⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡤⠟⠉⠉⠁⠓⠶⠶⠦⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠂
⠀⢸⣿⣿⣿⣿⡿⠋⠁⠀⠈⠉⠻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂⢠⠆
⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⣿⣿⣷⣄⡀⠀⠀⣀⣴⣿⣿⡇⠀⠈⠋⠉⠉⠉⠉⠉⠉⠋⠙⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠢⠤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⣠⡤⠖⠛⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠛⣷⡀⢰⠏⠀⠀⠀⠀⢹⣀⡼⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣠⡶⠦⣤⣀⡀
⠀⠀⢀⣀⡤⣄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣀⡼⢳⣼⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠀⠀⠐⣟⡆⠀⠀⠀⠀⣿⢁⡇⠀⠀⠈⠉⢹⡆⢀⣤⣀⡀
⣶⠚⠉⠀⠀⢋⠓⢦⣄⠀⠀⢻⠀⠀⠀⠀⠏⠀⠀⠀⢻⠀⠀⢰⢦⠀⠀⠈⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢸⠃⠀⠀⠀⠀⠘⣇⡏⠀⠀⠉
⠘⡆⠀⠀⠀⠘⡄⠀⠈⠳⣄⡸⡆⠀⠀⠀⠘⠲⡄⠀⢸⠀⠀⠈⠉⠀⠀⠀⢸⡄⡏⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⠰⡀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢰⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢷⠀⠀⠀⠀⠳⠴⠀⠂⠉⢹⡆⠀⠀⠀⠀⠉⠉⢿⠀⠀⠀⢀⣦⠀⢀⣀⡀⢿⠀⠀⠀⡟⢆⠀⠀⠘⡆⢸⠇⠀⠀⢠⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡸⠈⡶⠁⠠⠌⢿⠤⠤⠤⠇⠀⠲⠤⠤⢽⣾⠀⠀⠀⡇⠱⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⣀⠸⠷⠤⠤⠒⠒⠒⢉⡉⠁⠀⢀⣤⣧⡘⠠⢊⣼⠦⣤⣤⣀⡶⣄⣀⣀⣤⠀⠈⠉⠚⢀⠀⢦⣀⠀⢀⡏
⠀⠀⠀⠀⢳⡀⢀⡠⠤⠒⠋⠉⠀⠀⣐⣶⠤⠶⠶⠶⠚⠙⠛⠋⠉⠁⠈⣯⠀⠸⡇⠀⠀⠀⠈⠀⠀⠈⠉⠉⠛⠛⠓⠶⠟⠳⣄⣈⣉⡿⠃
⠀⠀⠀⠀⠈⠻⢥⣀⣠⡤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠈⠷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠰⠂⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡖⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⢷⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡞⠈⣇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠇⠀⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡸⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⢀⡠⠒⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⣌⣙⠒⠦⠤⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠸⡤⠴⠖⢋⣁⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⡄⠀⠀⢘⡛⠛⠛⠛⢋⢙⡀⠀⠀⢢⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⢣⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣻⣿⡿⠟⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⡏⠠⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡏⡇⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢮⡷⣸⣢⣜⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣷⣷⣷⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣾⣷⣝⣫⣾⠿⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠐⠛⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡀⠐⠛⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⢀⣈⣻⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣟⣁⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢹⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠇


⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⢠⢦⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⣠⡀⣿⣿⣿⣄⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣉⣅⠀⠀⢨⣳⠀⠀⠀⣈⣉⣁
⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⢋⣿⣿⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣄⠉⣤⣤⣴⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣇⣿⣿⣿⣶⡆⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠀⠀⠀⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢻⠟⠛⢻⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣀⡼⢦⡀⢸⣿⡇⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀

⠀⢀⠔⠀⠐⡄⠀⠀⠀⠀⠀⢀⠔⢉⢉⠑⡄
⢠⡡⠊⠉⡆⡀⠀⠀⡎⠃⠀⠈⠒⠁⢠⢃⠇⢀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡖⠛⡄
⠀⠀⠀⡜⡰⠁⣖⣂⠃⢘⣒⡆⠀⡠⢃⠎⠀⢈⣉⣁⣈⡩⠖⢊⡩⠟⠋⠉⠉⠉⠉⠳⣄⠀⠀⠀⠸⡀⢱
⠀⣠⠊⡴⠁⠀⠀⠀⡁⡏⠉⠁⡰⢁⠎⠀⠀⠘⠒⠒⢺⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⢷⡈⡟⠓⠲⡄
⢴⣁⠚⠀⠤⢤⠀⠀⠉⠁⠀⠴⣀⣉⣐⠒⠀⡄⠀⠀⢸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠱⠇⠀⠀⠉⠳⡆
⠀⠀⠈⠉⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠤⠀⣠⡼⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠶⠚⠛⠋⠉⠙⠛⠛⠿⢤⣀⠀⢰⠇⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡴⠚⠁⣰⠉⠉⠋⠉⠉⠉⠉⠋⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠠⡀⢀⣀⠠⠤⢤⣀⡴⠀⠀⠀⠀⠸⡏⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠀⢠⡇
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⣇⠀⠀⠲⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠽⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⡏⢀⡠⠄⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⣷⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢿⠀⠀⠀⠀⠀⠀⡠⠊⠙⠒⠒⠒⠉⠁⠈⠂⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠛⠶⣦⣀⡀⠀⠀⣀⣀⣤⠶⠋⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⢹⠋⠉⠉⠉⡇⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠤⣴⣄⣀⣴⣤⠼⠇⠀⠀⠸⠧⢤⣦⣤⣤⠼⠦⠼⠃

⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⡷⣧⣤⣝⣶⠃⠀⠀⠀⠀⠀⠀⠀⣀⠛⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⠀⣰⣁
⢀⡜⠁⢰⣿⣞⠈⢦⡀⠀⠀⠀⠀⢐⣶⡿⠁⠀⠀⠀⠀⠈⠉⠙⢿⣷⣼⣿⡆⠀⠀⠀⠀⠀⠀⡼⡿⢿⠃⠀⠆
⠮⢴⣎⣀⣉⣀⣱⣆⣳⠀⠀⠀⢦⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢴⠦⠄
⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠀⠀⢆⠀⠀⠀⣄⠀⠀⠀⡠⠋⢹⣿⡟⠑⢄⠀⠀⠀⠀⠀⢀
⠘⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⠀⠀⡇⠀⡱⠀⠀⣀⠀⠀⠀⢁⣤⣄⣽⣡⣤⣌⡀⠀⠀⠀⠀⠸⣷⠆
⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠈⠑⠁⠈⠲⠀⠀⠁⠉⠀⠀⠀⠺⡿⠋⠀⠙⠿⡟⠀⠀⠀⠀⢀⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠊⠁⠀⠀⠀⠀⠸⠿⣿⡿⠗
⠀⠀⠀⠀⡄
⠀⠀⣶⠀⡄⠀⠔⡀⠀⠀⠀⢀⣘⠁⣤⠀⠀⠀⠴⠀⠀⠀⠀⠀⠐⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣷⠀⡇⠀⠰⠇⠀⠀⠀⠘⠛⢄⣀⠶⠀⡶⠀⡀⠀⠀⠀⠀⠰⠿⠿⢆⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣶⠦
⠀⠐⠛⠂⡃⠀⢰⡆⠀⠀⠀⢀⣤⠜⢻⠂⠘⠛⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣰⣄⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠉⢀⡘⠗⠀⠀⠁⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⡆
⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢶⣤⣴⣧⣄⠀⠀⠀⠀⠀⠀⢀⠉⢁⡘⠙⣀⠛⢃⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣆⠀⠀⠀⢀⢞⡟⠉⠉⢙⠲
⠀⢰⣏⣠⣟⣀⡀⠀⠀⠀⠀⠸⠉⠉⠉⠈⠉⠁⠘⡃⠀⠀⠀⠠⣾⣷⡇⠀⣸⣿⠀⠀⠀⣤⠞⠳⠄⠰⠚⠳⡇
⠀⠀⢉⣿⡋⢉⢹⠆⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠂⠂⢿⣿⣿⠿⠃⠀⠀⠀⠠⡀⡀⢸⡀⣠⠀⠄
⠀⠀⠀⠙⠛⢻⡟⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⠀⠀⠀⠀⠈⠛⠋⠉⠑⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣗⠀⢠⠆
⠀⠀⠀⠀⠀⣀⣴⣿⡟⠁⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡛⠻⢻⠛⠟⠛⢻⡟⠀⠀⠀⠀⠀⠀⠐⢄⢀⡡⠔⠒⠶⢍⡀⡤⠂
⠀⠀⠀⢀⡞⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⢰⠀⢸⡇⠀⠀⠀⠀⠀⠤⢤⢀⡞⠀⠀⠀⠀⠀⢳⡀⡤⠤
⠀⠀⠀⠸⡅⢿⣿⣿⠀⠀⠀⢀⣀⡤⠞⣡⠏⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⡁⢀⢸⠀⠀⣄⢸⡇⠀⠀⠀⠀⠀⣀⣀⠸⡇⠀⡤⠶⢤⠀⢸⠇⣀⣀
⠀⠀⠀⠀⠙⠦⣬⣉⣉⣉⣉⣉⡤⣴⠞⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⡗⠟⠛⠛⠃⠀⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⣠⠹⣄⢃⠀⡸⣠⠏⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠶⣞⠻⣶⣄⡀⣀⣾⡇⠀⠀⠀⠀⢠⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢣⠀⠀⠀⠀⠀⠉⠀⣰⢸⣾⣤⣷⡗⢆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⡗⢲⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣏⠉⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⢀⣤⠴⠶⣾⠇⣠⣤⠙⠿⠶⠶⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠃⢸⡇
⠀⠀⠀⠀⣠⢤⣰⡏⠁⠀⢹⡄⠀⠀⠀⢀⣹⣿⡧⠀⠀⠀⠀⢸⣇⠀⣠⡿⢁⡠⣤⡈⠐⣦⡀⢸⡿⠀⠀⠀⠀⢸⡇⢠⠄⢀⡀⣶⡷⠾⠤⠀⢸⡇
⠀⠀⠀⠀⠸⡌⣿⢷⣀⣤⣴⣷⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣴⠻⣯⣀⡇⢸⣤⣾⡿⠀⣄⣼⢿⡁⠀⠀⠀⠀⢸⡇⠘⠥⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠁⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠙⣷⣦⣉⣉⣤⠶⣛⣁⢈⣷⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣾⣿⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣻⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⢿⡟⠛⠙⠛⡾⢯⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠈⠛⠉⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠯⠼⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢀⡆⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣤⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⢸⣷⡖⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠿⢴⣶⠿⠷⢤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠋⢹⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⡿⢩⡍⠉⠉⠉⠉⠉⠉⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⠖⢾⡷⠲⣶⣾⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠈⠀⢰⠇⢀⡇
⠀⠀⠀⠀⠀⢀⣷⣬⣥⣤⣤⣤⣤⣤⣴⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⡏⣶⢹⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡤⠖⠋⢀⡞
⠀⠀⠀⠀⠀⠀⣟⣻⣋⡉⣩⣽⣯⣭⣭⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠙⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠧⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⣀⡀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠰⡂⠀⠐⠚⡠⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⡈⠀⠀⠠⠀⠀⣀⣱⠮⢀⠀⠓⠘⠓⠃⠀⠀⡀⢌⡃⠠⡆
⠀⠀⠀⠓⠓⠀⠀⠀⠠⠀⠢⢨⠀⠀⠀⢀⠀⠉⠀⠐⠸⡁⢐⠀⠁⠊⠀⠀⠀⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⠌⠀⢁⠂⠃⢸⡓⠃⠰⣀⠇
⠀⠀⠘⠀⠇⠀⠐⢀⠶⠀⠀⠈⠀⠀⢀⠀⠀⠀⠄⢀⠠⡤⠀⠠⠀⠀⠄⠀⡆⠀⢴⠀⢉⠀⠐⠀⠀⠀⠀⢄⠠⠁⠈⠄⠠⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠉⠔⡀⠢⠀⠂⠀⠀⠄⠀⠠⠀⠀⠄⠈⠈⣠⣀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢀⣀⠀⢀⠠⡁⢈⠆⢄⠀⠤⣄⠀⠀⢔⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⢴⠆⡄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠦⠘⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⣱⠀⠀⠀⠀⢀⠈⠠⠄⠈⢷⠀⠢⡤⠃
⠀⠀⠀⢾⡐⠁⠙⢀⡇⠀⠀⠖⠂⡀⠀⢐⡛⠆⠐⠶⣆⣶⡄⠀⠮⠆⠀⠌⣀⢂⡂⠀⠔⠢⠀⠸⠭⠭⠿⠿⠽⠇⠀⠌⠉⠈⢀⠅⠀⠀⠀⠐
⠀⠀⡀⠀⣅⡋⣀⠁⠁⠁⠀⠈⠀⠀⣲⢢⡀⠀⠀⠧⣍⠴⠀⠠⣄⠄⠑⠀⢻⠀⠈⠀⠀⠀⠀⠀⠉⠈⠚⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉
⠀⢀⠤⢌⠉⢠⠈⠉⠀⠠⠀⠀⠀⠀⠠⣉⠀⢻⠒⡄⢠⠀⠈⣡⢀⡐⠂⠠⠃⠀⠀⠀⠄⠀⡄⠁⠀⣤⠀⣴⡶⢿⠂⡀⢠⡀⠄⡀⠈⠉⣂⠈
⠀⡇⣀⠈⠀⠈⡀⠀⠀⠈⠁⠀⠀⣦⡄⠉⡀⠈⠒⠁⠀⠈⠃⠀⠀⠁⠤⠆⠀⠠⠀⠂⠀⠂⡄⠀⠘⠓⠛⣂⡅⠂⠀⠀⢀⢌⠉⢋⡀⠁⠄⠈
⠀⠑⠤⠜⠀⠀⠀⡀⠐⠀⠀⢀⠤⠤⠤⠀⠫⠀⠀⠀⠀⠰⢆⠀⢀⠀⠘⠂⠀⠜⣁⠀⢿⠆⠠⣛⠃⠰⠊⠁⣀⠋⡁⢀⣠⡃⣀⢀⠋⠤⢰⡄⠆
⠀⠀⣰⡆⠀⢀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠀⠠⡦⠀⠐⠀⠀⠀⢠⠀⠁⡠⠒⠢⡀⢀⠠⠢⡀⠀⠀⠀⠤⠀⣿⠀⠶⠀⡀⠀⣀⢄
⠀⠀⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠄⠀⠀⠀⠈⠀⠒⠉⠀⠀⠀⠀⠱⠄⢤⠃⠘⢈⠌⠀⡡⠀⢀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠃
⠀⢀⡀⣠⠀⠀⠄⠄⠂⠀⠠⠴⡏⠲⢀⠔⠁⠐⠄⠀⢠⠒⢸⣿⠷⠾⡀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠐⠀⠂⠀⢀⡞⠀⠀⡀⠀⠀⠀⠰⠁
⠀⠑⠸⠈⠈⠆⠀⠀⠀⠠⠀⠀⠇⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢟⡠⠀⠂⡄⠀⢬⣽⠀⣄⡠⠨⠀⡀⠐⢀⣁⠀⠂⠀⠂⠀⠁⡀
⠀⠒⢤⠈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠈⠀⠄⠀⢨⠾⡀⠀⠀⠀⡀⠀⠀⢸⠀⠐⠉⠁⠀⠀⣉⢀⠀⢈⡉⣍⠀⠂⠘⠄⡃⠉⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠈⠀⠐⠊⠀⠀⠂⠐⠀⠀⠀⠈⠀⠀⠑⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⢀⣞⢿⠀⠀⠀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢾⣽⣶⣶⢳⣶⣿⣿⡇⠀⡀⠀⠀⠀⠀⢀⣤⢾⠉⠁⣠⣄⣨⢽⡶⢄⠀⠀⠀⠀⠸⣟⣩⠇⠀⠀⠀⠀⠓⠈⢸⣀⣀⣀⣀⣀⣴⣭⠥⠚
⠀⠀⠀⢰⠀⠀⠀⣷⣭⠉⠉⠀⣘⣿⡇⠀⠉⠀⠀⠀⢠⢾⡵⡏⠀⠸⣿⣿⣿⢿⣧⡈⢳⠀⣄⡀⠀⠈⠁⠀⠀⠀⠀⣠⠶⠛⠋⠿⣌⠀⠀⡤⠀⣠⡀
⠀⠀⠀⠈⠀⠀⠀⡏⠙⠀⠀⠀⢸⣚⡇⠀⠀⠀⠀⠀⣞⣋⣤⡽⠀⠀⠿⢯⣔⣓⣠⠟⠀⡇⠈⠹⠀⠀⠀⢀⣀⡀⣀⠹⡀⠂⠈⠀⢈⠑⢄⠑⠀⠉⠰⠇
⠀⠀⠀⠀⠀⠀⡼⠉⢳⠀⠀⠀⠚⠃⣇⠀⠀⠀⠀⠀⢏⠁⢀⣴⡶⣤⡀⠀⠈⠉⢁⣴⣶⠇⠀⠀⠀⠀⠀⠘⠉⣁⣹⣅⣘⢦⡀⠀⡀⠠⡈⢧
⠀⠀⠀⠀⠀⢸⣡⣶⣷⣶⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⡜⢆⠻⣅⣴⣆⡇⠀⣠⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⠀⣀⠭⠛⢷⣤⣤⡤⠎⠲⠄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠂⠈⠓⢬⣻⡛⣃⣀⣿⡿⠟⠁⠀⠀⠀⠀⣀⣠⢠⠄⣷⣄⡀⠉⠄⠀⠨⠀⢱
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢖⣛⡲⡄⠀⠀⣀⣀⠉⠉⠉⠀⢀⠔⢤⠀⠀⠀⠀⠉⠁⣨⠷⠛⡉⠍⡻⣍⠙⠛⠛⠉⠀⢀
⠀⠀⠀⠀⠀⠻⣿⣛⣛⣻⣿⣿⣿⡿⠿⠋⣾⢼⠦⢇⡇⠀⠘⢥⡾⠃⠀⠀⠀⠈⠲⠛⠀⢠⡚⣦⠀⠊⠁⠂⠁⠀⠀⠀⢈⡇⠀⠀⠀⠟⠻⠰⠆⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⢀⣀⡀⠃⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡔⠉⠀⠀⣆⣀⡇⠀⣏⣉⠁⣰⡄⣴⡀⠀⡆⠀⢯⡉⠀⠉⣿⠉⢸⣠⠞⠀⠘⠞⠁⠀⠒⠒⢿⣷⣾⠆
⠀⠀⠀⠀⢠⣀⡄⢠⡀⣤⢀⠀⡀⢀⢉⠉⠀⠸⣀⢀⡀⠐⠇⠀⠸⠀⠻⠤⠀⠃⠛⠁⠃⠀⠇⠀⠰⠛⠀⠀⠙⠀⠘⠀⠉⠀⠀⠂⠀⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠸⠁⠇⠹⠀⠛⠘⠀⠉⣿⠻⠸⡇⣀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠐⠃⢠⡟⠛⡇⠀⠀⢸⠿⢷⠀⠃⠀⢸⠛⠛⡇⠙⠀⠀⠀⠀⠴⠀⣶⢻⡿⠿⠿⠟⠻⢷⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠁⠁⠭⢉⠳⣴⡒⢲⠄⠀⠀⠀⢸⡇⠀⡃⠀⠀⢸⠀⢸⠀⠀⠀⢸⣤⣤⡇⢀⠀⠀⠀⠀⠀⠀⡟⠉⡇⠀⠀⠠⡣⢼
⠀⠀⠀⠀⠀⢊⠘⢀⡎⠀⠀⠀⠀⠀⠀⣡⣴⣸⡖⠋⠀⠀⠀⡇⢰⣟⣿⡇⠀⠀⢸⣀⣸⠀⠀⠀⢨⣿⣿⡇⢸⡀⠀⢠⣄⡄⠀⣧⣄⡗⠀⠀⢀⡧⢸
⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢀⠠⠄⣂⡥⢖⢛⠽⡇⠀⠀⠀⠛⡟⠛⣿⣿⡿⠛⠛⠛⣿⣿⠛⠛⠛⢻⣿⣿⡟⢻⠋⠀⠈⠿⠁⠀⣇⣤⣧⣤⣶⣾⣶⣾
⠀⠀⠀⠀⠀⣰⢯⢻⣄⡬⠴⠒⠉⠁⠀⢰⢎⡼⠁⠀⠀⠀⠀⡇⠀⣿⣷⣇⠀⠀⠀⣿⣿⠀⠀⣀⣨⣿⣿⣇⣼⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠋⠉⠙⠦⣄⣀⣀⣀⣀⠴⠋⣠⣤⣤⡀⠀⠤⣿⠽⠿⠛⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠀⠀⠙⠀⠀⣴⡄⠀⠀⠉⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣉⣩⡀⠀⠀⣇⠻⣪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣹⠃⠀⢀⣀⡋⠉⣟⡆⠀⠀⡄⢀⡤⠴⠧⣄⣀⣀
⠀⠀⠀⠀⢀⡐⠀⠀⣤⠤⠶⣿⣛⣛⡟⠉⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢹⠀⠀⠀⠈⢁⡴⠞⠋⠤⣹⢦⢸⠀⠀⠠⢰⠋⣀⠀⡈⠜⣿⠤
⠀⠀⠀⠀⠀⠀⣠⢴⠷⠾⢷⠖⢾⠉⠀⠄⢹⠀⠀⠀⣸⠀⡤⠖⢦⣀⣤⣤⣴⡁⠀⣹⠃⠀⠋⠊⡼⠛⢀⡴⠚⢹⠁⢊⡇⠀⠀⠤⢼⠀⣏⡉⣹⢆⣼⠧
⠀⠀⠀⠀⠀⠀⣧⠘⠒⠖⠋⠀⢸⠀⠄⠀⢸⠀⠀⠀⠘⠲⣇⠀⢠⠟⠉⠁⠀⠙⠋⠁⠀⠀⠀⡼⠁⡰⠃⠀⣀⡇⠠⣿⠀⠀⠀⠐⠘⣆⢹⢣⣽⣼⠟⠄
⠀⠀⠀⠀⠀⠀⡗⠐⠂⠀⠀⠀⢸⠀⠁⡂⢸⠀⠘⣤⡆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⢸⠃⠀⠀⢿⡇⢸⡟⡿⠁⠀⠀⠁⠀⢻⣇⣿⠉⠂
⠀⠀⠀⠀⢀⠀⡇⠀⠒⠀⢀⡀⢸⡀⠀⠤⠈⡇⠀⠙⠀⢀⣴⣾⠇⠀⣠⣶⡆⠀⣀⣀⠀⠀⢸⡇⠈⢳⠤⣀⣀⣹⣋⠉⠀⠀⠀⠀⠀⠀⣼⣼⣿
⠀⠀⠀⠀⠚⠁⡇⠀⠀⠀⠀⠀⠸⡧⠴⠖⠚⠁⠀⢀⣤⣞⠛⠛⠒⠲⣿⡿⠤⠿⠾⠼⠁⠀⠘⣧⠸⣯⡇⠀⠀⠠⣭⢉⡇⠀⠀⠀⡀⣀⣿⣿⣿⠀⠄⠄
⠀⠀⠀⠀⠀⠀⣣⡤⠖⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠁⠹⣿⣷⡀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠷⢶⣦⣤⣤⣤⣼⠟⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⢀⣀⣀⣠⣀⠀⠀⣀⡀⢀⡀⠀⠠⢄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠈⠉⠉⠉⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠓⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠇⠀⠒⢀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢠⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣄
⠀⠠⡀⠀⠀⠘⠛⠻⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠒⠀⠀⠀⠁⠙⠘⢁⠐⠀⠐⠀⠀⠓⠃⠺⠿⠛⠋
⠀⠀⠹⢒⠤⠄⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⡀⣈⠁⠃⡀⢀⢀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠁⠀⠈⠀⡢⠀⠆⠐⠐⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠈⠀⠈⢡⠀⠀⢠⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣠⡀⠀⠙⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠄⠀⠐⠂⠰⠀⠀⠀⠈⣀⠀⠀⠀⠈⡊⠉⠉
⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⢠⣷⣄⠀⠀⠀⣠⣄⠀⠀⠀⠐⠘⠂⠀⣾⣻⡷⠀⠀⠀⠐⠆⠀⠀⠂⠀⠀⣤
⢀⠐⠈⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠐⠀⠊⠀⠀⠀⠈⠉⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠈⠐⢢⠀⢀⠀⠀⠤⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠈⠘⠀⠀⠀⠀⠀⠀⠅⠀⠠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠈⠛⠛⢁⠀⠀⠀⠀⠀⠀⢠⠲⡄⠀⠐⠀⠀⠀⠀⠀⢀⠒⢲
⠀⠀⠐⠀⠐⠈⡈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⣉⣈⠉⠀⣀⣴⣆⣀⠀⠀⠉⠀⠀⠂⠐⠂⣀⣤⡀⠀⢀
⠀⠀⢀⢀⢀⡀⠀⠀⢀⠠⠸⠐⠐⠀⠀⠀⠀⠀⢸⠯⡟⡧⠀⣿⣿⣿⣿⣿⣶⣶⠀⠁⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣒⣚⣉⣉⣉⣍⣉⣉⣙⣒⣒⣶⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⢞⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣷⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠓⠶⠤⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠤⠴⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⡶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⣴⡶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⡀⢠⠀⠀⠠⠄⠠⠀⠄⠠⠄⠠⠀⣉⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡾⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠎⠑⠠⢤⣤⣤⣤⣀⣀⣀⣀⣤⣤⡤⠤⠄⠀⠀⠈⢧⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠋⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡼⠁⠀⠀⠀⠀⢯⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⢦
⠀⠀⠀⠀⠀⠀⣠⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⡀
⠀⠀⠀⠀⠀⡰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢳⡀
⠀⠀⠀⠀⡼⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡱⡄
⠀⠀⢀⠞⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⣄
⠀⢠⢎⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣆
⠠⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠃
⣦⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠
⢯⠳⢭⣓⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⣋⡵⢫
⠀⠑⠦⣄⣉⠙⠒⠲⠮⠭⢭⣥⣒⣒⣒⣒⣒⣢⣤⠤⠤⠤⠤⠤⠤⠤⠒⠒⣒⣒⣒⣒⣒⣋⣩⣭⡭⠤⠶⠒⠚⣉⣠⠴⠋
⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⠤⠤⣤⣀⣀⣈⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣀⣠⡤⠤⠤⠶⠒⠚⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠒⠚⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠈⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⣿
⠀⠀⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣤⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠴⠧⠤⠶⠀⠀⠀⠀⠻⠤⠤⠤⠴⠶⠶⣦
⣠⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⠞⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡆⠀⠀⠀⣏⠀⠸⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⢸⡆⠀⠧⠤⠤⠤⠴⠖⠒⠒⠒⠒⠒⠚⠛⠛⣿⠃⠀⠀⠀⢹⡀⠀⠉⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡏⠉⠉⠉⠉⣩⠟⠁
⠀⢷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⠧⠤⠤⠤⠤⠴⢦⠀⠀⢸⠀⠀⠀⠀⢷⠖⠒⠒⠛⠁
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠓⠚⠛⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⠳⣤⡀⠀⠀⠀⠀⢀⡞⠁⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠈⢙⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⠲⣄⠀⣠⠏⠀⠀⠀⣠⢾⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣙⣶⣾⣯⣤⡤⠤⠴⠶⠶⠶⠶⠶⣆⠀⠀⠀⠀⠀⠀⡼⠉⠓⠦⣀⠀⠀⠀⠈⠙⠃⠀⠀⢀⡜⠁⣼
⠀⠀⣾⡏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⢰⣋⡠⠞⠁
⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡴⠃⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀
⢸⡁⠀⠹⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠚⠋⠉⠉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢠⠞⠲⢤⣀⠐⠀⠀⠀⠉⢹
⠈⣧⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⡰⠃⣀⡀⠀⠈⠑⠦⣀⠀⡠⣿
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣤⠞⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠢⡀⢀⡜⠁⡼⠋⠙⠲⣤⡀⠀⠈⣹⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠢⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠋⢀⡞⠁⠀⠀⠀⠀⠉⠓⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠲⡀⠈⡀⢀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⣀⣀⣠⣔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣤⣴⣿⣿⠃⠀⠀⠀⠈⢰⡇⣄⣀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣠⣤⠴⢿⣈⣿⡟⠉⠻⢿⡄⠀⠀⠠⡆⢸⣷⣿⠉⠈⣿⣿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠻⣯⠑⢛⡁⠂⠈⢻⣿⣷⠀⠀⡀⠀⢀⣤⡀⣷⣿⠿⣛⡆⣸⡿⢿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⢿⣿⣧⢠⣿⠀⠀⡿⠀⢉⡟⠀⠏⣸⣿⣄⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠡⠹⠆⠀⠀⠈⠀⠀⠘⢻⣿⣾⣧⠀⠰⢷⡄⠸⠷⠠⠂⢁⣾⣯⡿⠛⠿⠿⠿⢇⣤⣄
⠀⠀⠀⠀⠀⣀⣸⣤⣤⣄⡀⣠⠂⠀⠘⢿⣭⢿⣿⣷⠀⠀⣿⠀⠀⠀⠀⠀⠘⡿⠛⠁⠀⠀⠂⢀⣿⠹⠙⢷⡀
⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠁⠈⣀⠉⢿⣾⣿⣿⡀⠀⡽⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⢀⡴⠻⠁⠀⠀⠀⠁
⠀⠀⠀⠘⢷⠶⠦⠤⠂⠄⠀⠀⢂⣄⡈⠻⣾⣿⣿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠪
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⣻⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡈⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠰⣶⣬⣁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣷⢆⠄⠀⠀⠀⠀⠀⡐⢋
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣄⠀⠀⢠⣦⣰⣾⣴⢂⡤⠶⠦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⣀⣤⣀⣀⣀⣤⡶⠶⠖⠛⠛⠻⣿⣿⣧⣄⡀⠉⠉⠻⣿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⣾⠙⠛⠻⠿⠿⠿⠿⠛⠉⠀⠐⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⡄⠀⣶⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⢀⣤⡴⢊⡿⢳⣼⡟⣹⠟⡀⢹⡄⠀⢼⣁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣦⣤⣠⠤⠄⠀⠀⢀⣍⣸⡿⠋⢀⣬⣿⣷⡿⠟⡃⢸⣷⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠟⠉⠀⠀⣶⠋⠋⠀⣠⡾⠃⢸⡟⣆⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠇⠀⠀⠀⡰⠃⠀⠀⡄⠉⠀⠀⣿⠀⠘⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣼⠁⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐
⠀⠀⠀⠀⡶⠒⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠐⠒⠦⠖⢀⣤⠇⠀⠀⠀⠀⣀⣠⡖⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢁⠀⠛⡁
⠀⠀⠀⡀⠙⠀⠀⠸⠀⠀⠠⠃⠀⠀⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡾
⠀⠀⠀⠈⠉⠉⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠄⠀⠀⢀⣀⠈⠳⡄⠀⠑⠂⠤⠚⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⠀⣀⣠⡁⠀⠀⢀⠀⠀⠐⠦⠾⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠐⠚⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠞⠂⢈⠛
⠀⠀⠀⠀⠤⠤⠤⠀⠀⡤⠇⠀⠀⠀⠀⠀⣀⡤⠾⠀⠀⡀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠠⠤⠴⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠀⠀⢀⣉⡀⠀⡀⠀⠈⠉⠉⠉⡉⠁⠀⡀⠀⠀⢠⡂⠐⠂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⢁⠀⠀⡀⠘⠅⠉⠀⡽⠀⠀⠀⠀⠲⠁⠂⢀⡇⠀⠀⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⢸⠀⠀⠙⠢⠤⠴⠐⠁⠀⠀⠀⠀⢀⢀⡀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠢⠄⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠔⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⢀⡀⠠⡆⠀⠀⠀⠈⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣿⣸⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠡
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡙⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⢻⣷⡘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠹⡷⠈⠉⢀⢐⠂⠀⠀⠀⠀⢀⠀⠺⠇⠀⠀⠂⠀⠀⠀⠈⠉⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠒
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡔⠀⠀⠀⠀⠆⠀⠀⠀⠺⢠⣠⠔⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣐⠂⠁⠐⠚⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠂⠂⠐⠒⠁⠀⠀⢀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠂⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠳⠜⠜⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⡆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈
⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠲⠒⠂⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠠⠶⠀⠀⠀⠀⠀⡀⠀⣠
⡿⠋⢁⡄⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢠⠜⠀⠀⠀⠐⣠⣴⣿⣿
⠁⠀⠺⡤⠀⠀⢸⣿⣿⣿⡿⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡄⠀⠀⠤⠄⠀⣼⣿⡿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣶⣤⣤⣴⣾⡿⠋⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠄⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠈⠀⠁⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡐⠠⠈⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⡿⢋⠀⠀⠀⠑⠀⡀⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠀⠀⢀⠄⠀⠀⠀⠀⠀⢿⣿⣿
⠁⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠈⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠲⠄⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢄⣀
⡠⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⠖⠐⠀⠁⢀⠤⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲
⠀⠀⠀⠁⠀⠀⠀⡀⠀⣄⠀⠈⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⢓⡆⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡖⠀⠘⡅⠀⠀⠀⠀⠀⢉⠂⠐⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⠀⠉⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠒⠢⡁
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠿⢤⡀⣀⠠⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠄⣀⠫⠀⠀⡀⣀⡴⡃⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣠⡾⣿⢻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠛
⣇⠀⠀⠐⠀⠀⠀⠀⣀⣤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣀⣿⢸⣷⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘
⠀⠄⠀⠀⠀⠀⢠⣿⣯⢿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣾⣿⣶⣄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⡟⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠶⠶⠶⠤⢴⡷⠀⠀⠀⠀⠸⠾⠷⠶⠶⠶⢶⣄
⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣠⣤⣤⣤⣤⡄⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⢋⣰⡇
⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠚⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⠶⢶⡇⠀⠀⠀⠀⢸⠀⣾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣧⣤⣀⣠⣤⣤⣤⣤⣤⣶⣶⡶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠶⠶⠶⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠷⣤⡀⠀⠀⣠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠙⢶⡴⠋⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣞⣡⡾⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠶⠶⠶⠶⠶⠶⠶⠿⠛⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢙⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢀⡾⢁⣙⠳⢤⡀⠀⠀⢀⡞⣿
⠀⠀⠀⠀⠀⠀⢻⣶⣛⣛⣋⣩⣭⣭⣭⣥⣤⣤⣤⣤⣶⡶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⣰⠏⣴⠟⠛⠷⣦⡉⠳⠶⢋⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⢦⣤⠞⢁⣾⠋⠀⠀⠀⠈⠻⢶⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠒⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠘⠁⠀⢈⠂⠀⠀⠀⠀⠺⣿⣿⣿⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠿⠿⠇⡄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠐⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠣⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣷⣷⡄
⠀⠀⠀⣀⣀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣧⣦⣤⣤⡄⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⣿⣿⣿⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⣿⣿⣿⣿⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⠀⠀⠈⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡟⣾⣿⡇⠀⠠⣶⣶⣶⣶⣶⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⣠⣿⣿⣿⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠿⣿⣿⣧⣿⡿⠃⠀⠀⠙⠿⢿⠿⠟⠁⠀⠸⢿⣿⣿⣿⣿⣿⡿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠄⢤⣤⣤⠀⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⠀⠈⠉⢱⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣀⣸⣄⣼⣀⣸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⠀⢰⣤⣼⠀⢰⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢙⣉⣻⠋⢻⣉⣻⠋⡟⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⠿⢿⣿⣿⠿⢿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢸⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⠀⢸⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠀⢸⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⡂⢸⣿⣿⠀⢸⣿⡿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣶⣾⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣷⣶⣶⣿⣷⣶⣾⣿⣶⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⣀⢀⠀⣄⡐⠀⢀⢀⢀⠢⡐⠂⠀⠙⠙⠉⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠚⠀⠁⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠠⡀⠀⠐⠁⠢⠀⠀⠀⠁⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠀⠠⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⢈⠂⢀⠀⠀⠂⠐⠈⠀⠀⠀⠀⡀⠀⠀⡆⢀⠢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⢸⡇⡀⠀⠈⣤
⠀⠀⠀⠀⡀⠸⠮⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠠⠊⡀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠄⢸⡇⢰⣶⠀⣿
⠀⠁⠀⠀⠁⠃⠀⠀⣀⣤⠄⠀⠑⢄⡴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⠉⠉⠈⠉⡉⠉⢩⠉⢩⡍⠉⡏⠉⠃⠐
⠀⢠⣂⡀⠀⠀⠀⠀⠛⠁⠀⠀⡰⠋⡠⠒⡀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠉⠠⣉⠕⠊⠝⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠊⠀⢈⠁⠥⠐⠂⠃⠀⠀⢀⡡⠤⠔⠒⠓⠋⠀⣀⠀⠀⢀⠀⠰⠢⠀⠒⠀⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢁⢊⡀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠰⠉⠀⠀⡀⠀⠐⠀⠆⠀⠀⠠⠀⡀
⠀⠀⡠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠘⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠦⣀⠘⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣷⡄
⠀⠀⠃⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠁⠈⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠈⠻⣿⠄
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠻⠶⣲⠴⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠆⠑⠒⣀⣤⣧⡄
⠀⠀⠀⡀⠀⠀⠂⣀⠀⠃⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠐⠫⡨⠆⠀⠀⠀⠀⠀⠸⠄⠨⠜⠉⠛⠛⠁
⠀⠀⠰⠀⠐⠚⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⠀⠈⠃⠀⠀⠀⠀⠀⠰⠱⠀⠀⠀⠀⢀⡀⠀⢠⠀⣀⠀⠀⡀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠄⡒⠇⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠘⠀⠙⠃⠐⠂⠇⠘⠘⠃
⠀⠀⢠⠂⠀⠀⠀⠀⢸⠀⠀⠃⡀⠀⡜⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡰⢢⠕⠂⠀⠀⠀⠀⠀⠀⢀⡈⠀⡈⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠈⠒⠀⠀⠀⠀⠈⢸⠀⣦⠆⠀⡏⠀⠑⠀⣴⣁⣀⣩⠆⠀⡠⢊⠔⠁⠀⢀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⡂⠀⠀⠀⠐⠀⢀⣠⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠛⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⣀⠀⡰⠁⠀⠀⢠⢠⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠘⡀⡄⠀⠀⠀⠀⠀⣮⣤⣼⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⢀⠀⡠⡀⢠⡄⡄⠀⡄⢠⡄⠀⠀⠀⠀⠈⠱⠃⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⢀⡡⠶⠂⡀⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⢄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠀⡠⠔⠁⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠠⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠸
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⠐⠀⠀⠀⠈⢀⠈⡄⠀⠀⠀⠀⠀⠠⠈⠀⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⣠⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡄⠀⠀⠀⢀⡴⠖⠒⠒⠛⠒⠃⠀⠀⠀⠳⠒⠒⠒⠒⢲⡄
⠀⠀⠀⡞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢳⠀⢇⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⢤⡇⠀⠀⠘⡆⠀⠓⠂⠉⠉⠉⠙⠀⠀⠀⢠⠖⠒⠒⠒⣲⠏
⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠎⠀⠀⠀⠀⠳⠤⠤⠤⠤⢤⠀⠀⡇⠀⠀⠈⡶⠶⠒⠚⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢃⠀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣈⣉⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⡀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠲⣄⠀⠀⠀⢠⠞⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠽⠋⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡧⣀⠀⠀⠈⠙⠦⣴⠋⠀⠀⡠⢺⠁
⠀⠀⠀⠀⢠⡴⠖⠒⠒⠒⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⡇⠀⠀⠀⠀⢼⡀⠀⠑⠢⣄⠀⠀⠀⠀⢀⠞⣡⠞
⠀⠀⠀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠲⣄⣠⠎⠀⠀⠀⠀⠈⠛⠧⣄⡀
⠀⠀⠀⢾⠀⠘⠦⠤⠤⠤⠒⠒⠒⠒⠒⠒⠚⠉⢉⡽⠋⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⡰⠒⠢⢄⡀⠀⠀⠉⣹
⠀⠀⠀⠘⣦⠤⠤⠤⠤⠤⠤⠶⠖⢒⣶⡚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⢀⠞⣠⢤⣀⠀⠉⠲⢤⣔⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢏⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠙⠦⠊⡰⠃⠀⠈⠓⠦⣄⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⣠⠒⠛⢐⣤⣀⠀⠀⠀⢠⣴⣾⣿⣿⣶⡤⠀⠀⠀⠀⢀⣤⠤⢤⠠⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢻⣾⡿⣷⣿⠃
⠀⠀⠀⢾⣹⡇⠀⣿⣧⣿⠆⠀⠀⠀⢹⠀⢸⠀⢸⠀⠀⠀⠀⢰⣿⣷⣬⣿⣠⡾⠀⠀⠀⠀⢰⠾⣧⡿⢷⠀⠀⠀⠀⠀⢸⣯⡿⣯⣿
⠀⠀⠀⠀⠙⠄⣄⠬⠋⠉⠀⠀⠀⢀⣾⣄⣾⣄⣼⣄⠀⠀⠀⠘⠟⠛⠻⠻⠋⠀⠀⠀⠀⠘⠛⠒⠛⠓⠚⠛⠂⠀⠀⠀⠺⣿⣿⣿⣿⠆

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⣴⠹⡍⢩⠏⢦⡀⠀⠀⠀⢾⢉⢹⡄⢤⡄⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠈⣃⣜⢉⢟⡖⢤⠀⠀⠀⠀⢠⣤⠯⢧⣀
⠀⠀⢺⡇⣻⡇⣿⣿⠀⢸⡧⠀⠀⠀⢨⣧⣯⣵⣼⡄⠀⠀⠀⠑⣺⣿⣿⠀⣿⡒⠁⠀⠀⢺⠋⠀⢹⠺⠤⡎⠀⠀⠀⢶⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠉⠻⣰⣣⣞⣆⠞⠀⠀⠀⠀⢸⣿⣿⣿⣽⡇⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠈⠒⠐⠻⣄⡛⣤⠀⠀⠀⠀⠙⣿⠿⢿⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣤⣤⣤⣤⣶⣶⣄⠀⠀⠀⠀⠀⣸⣷⡆⠀⠀⠀⠀⠀⠀⢠⡿⠛⠿⣦⠀⠀⠀⠀⢠⠻⡈⢹⠐⢒⡆⠀⠀⠀⠀⣴⣶⣶⣶⣶⣤
⠀⠀⠀⣯⣽⣿⢺⢺⠾⡷⡇⠀⠀⠀⠂⠙⠛⡉⠛⠶⠄⠀⠀⠀⢘⠗⠀⠐⢟⠀⠀⠀⠀⠙⠒⠃⢸⠀⣎⣘⡄⠀⠀⠀⠘⢿⣿⣿⡿⠁
⠀⠀⠀⠛⠛⠛⠛⠿⠿⠋⠀⠀⠀⣠⣶⣶⡄⠂⠀⠀⠀⠀⠀⠠⣿⣿⣶⣾⣿⡧⠀⠀⠀⠀⠀⣀⣸⣀⡈⠁⠀⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠻⠛⠻⠂⠀⠀⠀⠀⡇⢴⡦⠀⣿⣻⣿⡇⠀⠀⢠⢝⢿⣿⡿⣆⡀⠀⠀⠀⢀⣀⣴⣒⣲⣆⣀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣷
⠀⠀⠀⠀⠀⠘⠂⠊⠀⠀⠀⠀⠀⣥⣤⣤⡄⠛⠛⠛⡁⠀⠀⠇⠀⠑⠀⠛⢩⡁⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣦⢸⡇⢿⣼⡿
⠀⠀⠀⠠⣾⣿⣾⣼⣿⡆⠀⠀⠀⣿⣯⣸⡇⠐⠟⠀⡇⠀⠀⠈⠢⢤⡄⢴⣿⣿⠂⠀⠀⠀⠿⠿⠷⠿⠿⠇⠀⠀⠀⠀⠉⠈⠁⢿⣾⠟
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⡀⠀⠀⠀⠀⠠⡆⠀⠚⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁
⠀⠀⠀⠀⠐⠁⣠⠀⠠⡌⠁⠀⠀⠀⠀⢀⣦⠈⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠠⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡂⠉⢂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠐⡐⢀⣀⡀
⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠸⠅⠀⢨⡀⠀⢠⠀⠀⠀⠀⠈⠉⡅⠒⢦
⠀⠀⢀⡄⠴⠥⠤⠤⠤⠤⠴⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠶⠃⠀⠀⠀⠀⠀⠘⠀⠀⠸⢧⡆
⠀⠀⠂⢵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⢸⡀⠀⠀⠀⣀⡴⠁⠀⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠈⠉⠀⠀⠀⠂⢀⡀
⠀⠀⠀⠨⠟⠀⠀⠈⠋⠀⠀⠀⠀⠴⠀⠀⠀⠀⠰⠀⢡⠀⠀⠀⠀⠀⠈⠁⠃⠙⠿⠶⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠘⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠁⠀⠀⠰⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣤⡤⠀⠀⠀⠀⢰⠁⣇⠀⠄⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢧⠀⠀⠀⠀⠀⠁⠁⣆⡆⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠀⠀⠀⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠲⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡀⢸⠀⡰
⢀⣴⣾⡟⠁⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠉⠉⠙⠉⢻⡇⠀⠀⠀⠀⠈⠓⡤⠓⠉⠑⠣⡔⠋
⡏⣿⣿⡇⠀⠀⠀⢀⣠⢇⠧⣄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠆⢸⡇⠀⠀⠀⠈⠉⢰⡇⠀⣀⡀⠀⡗⠈
⠙⠬⣙⣓⠒⣒⣋⣩⡴⠉⠀⢸⡀⠀⠀⠀⠀⠀⣿⠷⠶⠾⠀⠺⢿⡇⠀⠀⠀⠈⠉⣀⢣⡸⠀⡸⡰⢃⡉
⠀⠀⠀⠙⠛⠛⠲⣟⢷⣤⣀⣼⡇⠀⠀⠀⢠⠎⠉⠉⠉⠉⠉⠉⠉⠙⡆⠀⠀⠀⠈⠀⠔⣷⣧⣿⠗⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠣⡤⠤⠤⠤⠤⠤⢤⠴⠃⠀⠀⠀⠀⠀⠀⠻⣿⡿

⠀⠀⠀⠀⠀⠀⢀⣠⠤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⠲⡄⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⢀⣀⠤⣏⠁⠀⠀⠸⣿⣇⠀⠀⠀⢀⡴⠒⢲⡟⠤⠬⠛⠒⠲⣦⡀⠀⠀⠀⡿⠀⠀⠀⠀⡀⡠⠈⢸
⢰⣳⣼⡀⠀⢘⡄⣀⣠⠤⠿⠟⠀⠀⠀⢈⣷⡄⢺⢡⠒⣶⡄⠑⢤⡾⠁⠀⠀⠀⣟⢰⠅⠢⠘⠛⠓⠁⢸
⠀⠳⠃⠛⢹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡤⠛⢿⣌⡻⢛⣡⡶⠋⢹⡀⠀⠀⠀⣿⣀⣁⣀⣀⣀⣴⣶⣼
⠀⠀⠀⠀⡾⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠾⣿⠛⠛⢳⢯⡹⠛⠀⠀⠀⠀⠀⠀⠀⠈⡇⡏
⠀⠀⠀⠸⠃⠿⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿

⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡜⠉⠉⠛⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠪⠗⢀⡇⠀⠀⠀⠀⠀⠀⢸⠁⣹⠀⡄⠀⢸⠁⣹
⠀⠀⠀⢳⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠦⢴⣮⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣷⡏⢸⠉⢹
⠀⠀⡤⠤⠷⠤⠤⠴⠯⣤⣄⠀⠀⠀⠀⠀⠀⠀⣏⣉⣹⣏⣉⣹⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠃⢸⠀⡸
⠀⢀⣧⣿⣤⣤⣤⣤⣤⣯⣿⠀⠀⠀⠀⠀⠀⢠⣿⠁⠈⠁⢸⣫⢲⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⠤⠋⣠⠃
⠀⠈⣟⣟⣉⣹⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⢲⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢠
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡆⠀⢠⠄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⣦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠄⣀⢀⡀⠀⢠⠁⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣁⢀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⣣⠃⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⠁⠈⢀⠀⢀⠎⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⢤⡾⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠔⠁⡄⠀⠀⠂⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠢⠤⠤⠐⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣶⠶⣦⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢰
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣼⠟⣿⠖⣦⢶⣄⣴⠆⣶⡶⢼⣆⣴⠶⠆⣶⡶⠄⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⠀⡿⠀⡿⠈⣿⠏⠐⢯⡿⢾⡟⢷⣤⡔⢯⡿⠂⢀⡇⠀⠁⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠆⠀⠈⠄
⠀⠀⠀⢀⠀⠀⠀⠠⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠎⠀⠀⣀⠀⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠠⡄⠀⠀⢘
⠀⠀⠀⠀⠀⠈⠉⠠⠅⢘⠊⠛⠁⠀⠀⠀⠀⠂⠄⣀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣀⣀⣀⣀⣀⣀⣀⣲⠘⡣
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⣼⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⢤⣄⣀⣇⣀⡤⠔⠻
⠀⠀⠀⠈⠀⠐⠁⢠⠄⠀⠀⠊⠀⠈⠁⠀⠜⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⣲⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⣀⣀⣀⣤⣧⣄⣀⣀⠀⠀⡆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⢛⠉⠀⠀⠀⡇⠀⠀⠉⠙⠲⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢸⡗⠲⠘⡲⠖⠒⠐⡓⠒⠒⠒⠒⠒⣾⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⢬⣉⠁⠀⠀⠘⠃⠀⠀⣀⣠⠴⠃⠈⠇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢈⣉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡇⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⢃⠀⠀⠀⡠⠐⠉⠀⡀⠀⠀⢤⠀⠉⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢆⡔⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠠⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⢈⠀⠀⠘⡄⠁⠀⠒⠀⠀⠀⠀⠀⠆⠈⡂⡽⠒⢄⠐⠕⡠⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡸⢃⡀⠅⠹⣄⡔⣉⣂⣄⣢⣠⣠⣄⣱⣤⣇⣁⣀⢑⢿⣋⣡⣴
⠀⠀⠀⠀⠀⠀⡐⠠⠊⠬⠾⠤⠲⢵⢬⣔⠷⢦⢹⡉⠑⢁⡬⠆⠄⠀⠀⠸⡬⠐⠒⢔⠀⠀⣊⡴⠇⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠀⢀⡴⢻⠜⠣⡪⡧⢯⡁⢕⣙⠒⠲⣶⠀⢐⣌⡪⣐⣗⡡⠪⠂⢕⢇⠁
⠀⠀⠀⠀⡰⠀⠀⠀⠈⠂⠊⡤⣨⡂⢕⣕⣄⡪⢐⣎⡗⠻⣕⠀⠀⣀⠀⡋⠀⠉⠖⡡⢈⢔⢕⡽⠸
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⢍⠪⣺⣇⢠⡿⡊⣽⡿⣤⣷⡑⠉⢊⠤⡱⢂⢖⠭⡪⡱⢗⠵⡡⠁
⠀⠀⢠⠁⠀⠀⠀⠀⢅⠌⠀⠸⣋⣌⠞⡊⣕⠄⡪⢐⢡⣱⣹⡶⡋⢕⠅⡪⢚⢕⠈⣊⡔⢁⠔⠁
⠀⠀⠈⢔⠄⡀⠀⠀⠀⠀⠀⢨⠢⠐⠍⡪⠐⢅⢨⣲⡋⢇⡗⣬⣪⣕⡥⢪⠄⠵⠊⣉⠔⠁
⠀⠀⠀⠀⠈⠉⠀⠘⠁⠰⠶⠷⠾⠶⠿⠾⠿⠥⠉⠐⠊⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠠⡀⢀⠄⡀⢄⢠⠠⢀⠀⡀⡀⠄⠠⡀⢀⢀⠀⠀⠄⡀⠄⠀⡀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠁⠈⠀⠀⠁⠈⠐⠁⠊⠀⠑⠁⠊⠂⠅⠊⠐⠀⠐⠑⠨⠀⠅⠊⠔⡩⠂⠕⠨⢂⠕⠪⠐⠡⡪⠠⠃⠔⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⡠⠠⠠⡄⠀⠄⠀⠉⠀⠒⠂⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⡀⡀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠚⠀⠀⡀⠠⡄⠀⠁⠈⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠈⠁⠉⠉⠀⠑⠤⠂⠀⠀⠀⠀⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡂⠄⠀⠀⠀⠀⢐⣓⣒⣛⣒⣒⣳⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⢄⠀⢀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⡩⠘⠁⠄⡒⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠂⠠⠀⠀⠀⠀⠺⠂⠀⠀⠀⠈⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⡄⠛⠂
⠀⠀⠀⢠⢅⣠⠀⠀⠀⠀⠛⢠⡶⣆⠀⢶⠆⠀⡴⠶⣦⠀⣴⠀⠀⢀⡴⠲⣦⠀⣠⠖⠶⠄⠐⣆⠀⣴⠀⠀⠈⠢⠤⠚
⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢸⡷⣯⠀⢸⠀⢸⡇⠀⢸⠄⣿⠀⠀⢸⡇⠀⣹⠀⡿⠀⠰⡤⠀⠘⣾⠃⠀⠀⠠⠀⠠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠧⠞⠀⠾⠆⠈⠷⠶⠛⠀⠻⠶⠶⠈⠷⠶⠛⠀⠻⠶⠾⠃⠀⠰⠏⠀⠀⠀⠁⡀⠁⡀⠈⠁
⠀⠀⠀⠀⠐⠠⡁⠀⡀⠈⠀⠠⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠐⢀⢀⡘⠀⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠀⢼⠒⠂⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠠⢄⠀⠎⠀⠀⠄⠠
⠀⠀⠀⠀⠈⠠⢀⠀⠂⠀⡀⠀⢀⠔⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⢤⠀⠀⠀⠀⠰⠂⠀⠀⠀⡘⠀⠈⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠆⢠⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠦⠀⠀⠀⢶⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠖⠀⠆⢀⡄⠐⡠⠀⡄⠀⣐⠀⠠⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡈⠉⠐⠀⠀⠰⠒⠀⠀⠀⠰⡐⠒⠀⠰⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⣄⠀⠀⠀⠴⠂⠨⢦⡀⠀⠀⠀⠀⠁⠁⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⡤⠒⣆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⢻⣿⣿⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣷⣦⣤⣄⣀⣦⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠀⠀⠀⠀⣨⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⢿⣿⠏
⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣴⣾⡿⠿⣿⣷⣄⠀⠀⢀⣤⣶⣿⣿⠿⠛⠉⠀⠈⠃
⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣦⣄⣠⡾⠟⠋⠁⠀⠀⠈⠻⣿⣷⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣤⣀⣰⣿⡿⠋⡹⠿⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣤⣰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠆
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣔⠂⠘⠈⠓⠉⠐⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠁⣶⡖⢠⣆⣤⣆⠔⠒⠐⠃
⠀⠠⣎⠁⠀⡄⠀⠀⠀⠀⠐⠒⠀⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⣃⣋⣘⡘⠒⠃
⢠⠊⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠀⠀⠀⠀⠉⠉
⢸⠴⢃⠆⠈⠠⠀⠀⠀⠰⢄⠀⠀⠀⠀⢀⡔
⠀⠀⠃⡀⠀⠀⠀⠄⠀⡢⠔⠛⠒⠒⠒⡍
⠀⠀⠀⡇⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢰⠀⠀⢄⠀⡼
⠀⣀⠠⠄⠤⢄⠀⠀⠀⠀⠀⠀⠘⠽⠆⠀⠂
⠀⠀⢀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠨⠀⠍⠀⢀
⠀⡀⠀⠉⠁⣈⡺⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠉⠀⠀⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠈⠄⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠙⠋⠂⠀⠀⠀⠀⠈⠰⢄⠀⠐⠄⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠲⣤⣐⣀⣀⣀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠠⠸⠀⠀⠀⠀⠀⠀⠄
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠢⡊⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠒⠈⡁⠀⠀⠈
⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⢄⠀⠀⠀⣀⡀⡀⠀⠠⠤⠠⠤
⠀⠈⠀⠈⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠂⠤⠄⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⡀
⠀⠐⠀⠒⠃⠈⠁⠀⡀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠉⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠂⠈⠓⠒⠉⠉⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠲⣤⠀⢠⡄⠈⠢
⠂⠀⠀⡀⢀⡀⠀⠀⠀⠀⠈⠁⠁⠈⠑⠋⠂⠊⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠳⠀⠀⠜⡀⢀⠳⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐⠲⠦⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⠀⠂⠀⠀⠀⠀⡂⠘⠀⠀⠀⠀⠈
⠕⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠠
⠀⠐⢆⠀⠀⠀⠀⠀⠐⠂⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢊
⠀⠀⠀⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠄⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⡠⠃⠀⠀⠀⡐⠀⠀⢀⡀⠀⠉⠉⠙⠀⠀⠘⠀⠈⠆
⠀⠄⠀⠀⢀⠀⠀⢠⢀⡀⠀⠀⠈⠰⢤⡀⠈⠀⠀⠐⠀⠀⠀⢀⠉⠈⠓⠒⠛⠢⠤⢌⠀⠀⠀⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠂⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠁⠀⠈⠙⠦⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠃⠦⠉⠀⠰⠟⠛⠋⠁⠀⠀⠀⠀⠄⣀⠂⠀⠰⠊⠀⢀⢀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠀⠁⠰⠰⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠀⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠁⠀⠞⠀⠀⠀⠓⡀⠀⠀⠀⠀⠐⢺⡆⠀⠀⠀⠀⠚⠻⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⡀⡀⠀⢠⠆⠀⠀⠘⠀⠀⠄⢀⡀⢄⠀⠀⠀⠀⠀⠀⣴⣃
⠀⠀⣠⠀⠀⠀⢀⣀⠈⠋⠀⠀⡄⠀⠀⠀⢬⡻⣄⠔⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢶⡇⡘⣏
⠀⠀⠃⠀⣀⠈⠐⠀⠀⢀⠀⠉⠀⠀⠀⡐⢉⠥⠂⠠⠆⠀⠀⠀⣠⣀⠀⠀⠀⠀⠆⠀⢠⠀⢈⣩⣵⣵⠇
⠀⣸⠀⠀⠛⠀⠀⣀⠐⠈⠀⠄⠀⠀⢀⡁⠊⢀⡛⡀⠠⠆⠀⠘⠑⠀⠀⠀⡦⠀⠀⠀⠈⠀⠀⠀⠹⡏
⠀⣼⠀⠀⠀⠐⠀⠁⢀⡀⢀⠀⠐⠂⢣⡞⠄⣼⠃⢹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡄⠄⡀
⠀⠦⠀⡿⠇⠀⠀⠀⡀⠀⠌⠁⠀⢇⠁⢀⡾⡟⢎⡎⠀⠀⣀⡰⠄⠊⡷⠀⠀⠀⠈⠀⠂⠀⠀⠀⠰⢠⠁
⠀⣴⡔⢳⣦⣀⠀⠀⠐⠤⠀⠀⢀⠈⠣⡾⠈⠠⠌⠀⠀⠁⠻⢯⠆⠀⠁⠈⢀⣀⠈⠓⠒⣂⣸⡧⠄
⠀⠀⠀⠀⢋⠁⠀⢀⡀⠤⢒⡖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠏⠀⢰⠋⠁⠀⡇
⠲⣄⢠⡞⠀⠀⠀⢀⠖⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢠⠆⠀⠀⣀⣤⣼⡤⠴⠊⠀⠼⣆
⢰⡿⣆⡔⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⢈⡀⠀⠀⠀⠀⠁⡆⠀⠀⠀⣇⠀⣸⠇⠀⢀⠀⠀⠛
⠀⠙⡏⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⡒⠁⠀⠀⠀⡄⡀⠖⠀⠀⣰⠚⢻⡍⠁⠀⢰⣶⠧⠶⣄
⠀⢀⡄⠀⡀⠐⢀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠀⠨⠄⠀⠀⢑⠈⠀⢀⣻⠤⠞⠁⡀⠈⠉⡇⠀⠀⢉⠃
⠀⠘⠏⠀⠱⡀⠀⠀⠖⠀⠀⠒⠚⠉⠉⠉⠁⠀⣀⣀⣴⣶⡶⠆⠀⢀⣯⠟⠀⠀⠢⢏⠀⠀⠑⠧⡐⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣿⡏⠉⢹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⣤⣤⣤⣶⣤⣤⣤⠀⠀⠀⠀⠀⣀⣴⠺⣳⣤⡀
⠀⢻⡇⠀⢸⡿⠀⠀⠀⠀⠀⢀⣶⢶⡶⣶⡶⣿⠿⣷⠄⠀⠀⠀⣹⣷⢻⢺⡟⡞⡇⠀⠀⠀⠀⠈⣿⢹⡍⢹⡏⣿⠁
⡠⢼⣷⡖⣾⡧⢄⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢧⣿⢸⢸⡇⣇⡇⠀⠀⠀⠀⠀⣿⢸⠇⢸⡇⣿
⠑⠲⠤⠭⠥⠖⠊⠀⠀⠀⠀⠀⠿⠇⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠺⠼⠓⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠄


⠀⠀⢠⡄
⠀⣰⣿⣀⣙⣤⠄⠀⠀⠀⠀⠀⠀⡎⡉⠉⠉⢱⣀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣟⠂
⠀⣿⡏⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⢸⡿⠀⠀⠀⠀⢐⣖⢀⣼⣧⡀⣲⡀⠀⠀⠀⠀⠀⠀⠀⠠⣽⠇
⠀⣿⡗⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⠠⠀⠤⠄⣯⡇⠀⠀⠀⢠⣿⠙⣾⡧⣻⣷⠉⣿⡀⠀⠀⠀⠂⠉⠁⢐⣀⣰⠋⠉
⠰⠿⠷⠶⠾⠿⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠞⠀⠀⠀⠀⠈⠻⠟⠙⠿⠟⠋⠿⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⢁⡀
⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣄⣤⠀⠀⠀⠀⠀⠀⠾⠎⠀⠙⠛⠋
⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⢀⡴⣞⣵⠿⣾⣟⢦⣀⠀⠀⠀⠈⢶⡾⢷⡾⣷⡶⠁⠀⠀⠀⠀⠀⢀⣾⡀⣰⣇
⣿⣷⣿⣿⣷⣿⣿⡇⠀⠀⠀⠈⢸⣿⣧⡐⢺⣿⣷⠉⠀⠀⠀⠀⢸⡇⢸⡇⣾⣧⠀⠀⠀⠀⠀⣄⠜⣿⠻⣿⣿⢧⣤
⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⢸⣿⣧⣥⣾⣿⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⠸⡿⠀⣿⠀⢸⡏⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢠⣄⣠⡀⠂⣴⢄⣺⡫⢛⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀⠒⢀⣿⡟⠛⠏⣅⠨⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂⠡⠃⠘⠾⠀⠃⣀⢌⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠓⠄
⠀⠀⠀⠀⠀⠆⠄⠠⠀⡄⡌⠀⠂⠀⢀⡨⠁⠧⠀⠠⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⣠⣘⠻⠀⠀⠠
⠀⠀⠀⠀⠀⢷⢈⠂⠠⠈⠀⠀⣤⠐⠌⠱⠆⠀⠀⠀⠀⢄⠀⠀⠈⡠⠈⠃⡅⢷⢠⠈⡄⢁⠢⠂
⠀⠀⠀⠀⠀⡉⠴⢆⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣄⠈⢷⣄⠀⠘⣅⢎⠛⣿⡠⠖⣖⠂⠜⠁
⠀⠀⠀⠀⢠⠀⠄⡐⢦⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠁⠰⡌⠢⣚⠀⡈⠺⢷⡞⠁⠠⠀⠠⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠂⠬⠀⠀⠀⠀⠈⢶⡤⢀⡀⠀⠀⢀⡈⠠⠉⢤⡈⠀⡄⠛⣐⣈⣘⣐⣆⠴⠚⠁
⠀⠀⠀⠂⠀⠉⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠱⠏⠲⠂⠀⠀⠘⠄⠘⡄⠀⠨⢠⣌⠀⣈
⠀⠀⠀⠀⠀⢈⠀⠂⡤⠀⡀⠀⠀⠢⠄⠀⢀⠀⠀⠄⠢⢄⠀⢀⠀⠔⢰⠀⠉⠍⠀⡈⠀⢛⠉⠟⠒⠂
⠀⠀⠀⡀⢀⡄⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠐⠤⡈⣀⠏⠀⡀⠀⠀⠒⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⢂⡐⠙⠀⢁⠀⡀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠁⡋⠀⠄⠄⢀⠀⠠⢠
⠀⠀⠄⠀⢀⠈⠡⠀⢀⡜⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠄⠈⠈⠀⠀⡀⠀⠀⠀⢀⡀⠤⠆⠐
⠀⠀⠠⠀⠠⠐⡂⠐⢀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⠘⠀⠀⠁⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠆
⠀⠀⠀⠀⠀⡀⠁⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⢀⠀⠰⠂⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠁⠀⡆⠀⠀⠄⠁
⠀⠀⠀⠐⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠐⠀⢈
⠀⠀⠀⠠⠀⠀⠀⢸⠀⢇⢀⡀⠠⠔⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠹⣄⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⢈⠀⠀⠀⠡⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠁⠘⠀⠀⡀⠑⢀⠀⠀⠀⠀⠐

⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠀⠀⠉⠐
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠃⢀⠀⠀⡂⠁⠀⠈⡀⠅⠀⠀⠀⠀⠀⠛
⠀⠀⠉⢀⠈⠉⡁⠀⢉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠆⠀⠀⠐⠀⠈⠤⠀⠀⠊⠀⠀⠀⠀⠀⡀⡅
⠐⡘⠄⠀⠀⠀⠙⡀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠶⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠻⡁⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠂⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢠⠦⢸⡀⠀⠀⠀⠋
⠀⠘⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⣀⠈⠁
⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠓⣾⠎⠀⠀⠀⠠⠈⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⡄⢠⡆
⡌⠀⡀⠀⠀⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠠
⠀⠀⠈⠀⠀⠈⠀⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⡆⠀⠀⢀⡄⠠⠀⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⣂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠉⠀⠀⢀⠒
⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠀⢄⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⢀⣀⠈⠁⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⡀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⢤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠎⠐⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠄⢈⢤⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⠀⠀⠀⠂⠂⠂
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠠⡆⠀⠀⠀⠈⠈⠉⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡆⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠀⠀⠀⠀⡀
⠀⠀⠈⡁⠀⢀⠀⠀⠠⠄⠐⠀⣠⠀⡀⠀⠞⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢄
⠐⠀⠁⠢⣤⠋⠀⠀⠀⢠⠸⠈⠉⠀⠩⠄⠀⠐⠐⠚⠀⠀⠒⠀⡀⠀⢀⠘⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀⢀⠀⠀⠑⡄
⠀⠀⢀⢀⡄⡀⠀⠀⠀⢰⡀⠀⠄⢃⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠄⠠⠀⠀⠈
⠰⠀⠃⠀⠀⠀⠄⠠⠂⠀⠁⠀⠀⠀⢃⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠂⠀⠃⠀⣠⠄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⢡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⡀
⠀⠶⢤⣦⠂⠀⠀⠀⡈⠐⠲⠒⠂⢸⠀⠀⠀⠀⠁⠀⡠⠀⢀⡄⡀⢀⠉⠀⠠⠄⠀⠀⠀⠀⠒⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠐⠀⠀⠀⠀⢀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠂⠀⠀⠄⠀⠉⠐⠀⠀⠓⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀
⡠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠐⠀⣠⠀⣀⠀⠀⠀⠀⠩⠕

⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈
⡄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡐⠈⠁⠀⠁⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠕⠀⠐⠃
⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⡐⠀⡐⠠
⡇⠀⠀⠀⡰⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠜⢸⣧⠒⢄⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠠⠀⢁⠔⢢
⡇⠀⠀⠂⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢅⡴⠋⠳⢕⠉⡠⠢⡄⠀⠀⠀⠀⠀⠈⣆⠢⠀⢀⡌⠀⡀⡎
⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣁⠉⠢⡀⢸⠀⠃⢀⠇⠀⠀⡆⡇⠀⠀⡧⠙⡒⠋⠀⢠⠁⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⢀⢣⠀⠰⠀⠆⢰⠁⠢⠤⢣⠋⠀⠀⢀⠁⡆⠀⠀⢁⢀⡈⠀⠀⢸⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⣣⠁⠀⠀⠀⠀⠀⠀⢸⠀⠢⣀⠾⡀⢀⠑⢄⠀⣇⡀⠀⠀⠌⢰⠃⠀⠀⡉⠘⠀⠀⠀⠸⡇⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠀⠀⠀⠃⠸⠀⠀⠀⡔⠢⣀⡁⡸⠀⠀⣜⢀⠌⢠⠃⠀⠀⠀⢱⠆⠀⠀⠀⠐⠸⡀⢆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠐⠀⠸⠀⠀⠀⠈⢢⣀⠌⠀⠀⠀⡔⠁⡠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠱⡀⢢⠄
⡇⠀⠠⠄⣤⠀⠀⠀⠀⠀⠀⠀⡤⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⣸⣊⣁⣠⡀⠁⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⠈⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢡⠰⢈⠀⠀⣀⠀⠀⣄⡀⠤⠖⠶⠂⡤⠤⠼⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⡆⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⢢⠔⠂⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⣀⡄⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢡⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡂⠀⢸
⠀⠀⠀⠀⠀⠀⠐⢖⠚⡞⡒⠒⠒⠒⠒⠒⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠃⠀⠀⠀⠀⡂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣸⣀⣀⣀⣙⣇⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧⡤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡏⡇⠀⠉⣉⡉⢹⡇⠀⠀⠀⠀⠀⠀⣠⠴⠃⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢱⢡⠀⠀⠀⠆⢸⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⣤⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠘⡄⠈⣁⡁⢸⡇⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠤⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⣇⠀⠀⡃⢸⡇⠀⠀⠀⠀⠀⢿⢆⠀⠘⠝⣀⠺⢠⣿⠇⠀⠀⠀⠀⠀⠀⣿⣇⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣣⣤⣼⣧⣬⣭⣴⣪⠇⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣯⣶⠵⠃⠀⠀⠀⠀⠀⢀⣴⣻⣧⣤⣼⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠛⠛⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⣉⣉⣉⣉⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠒⠒⠒⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠒⠒⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠠⠬⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠚⢻⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠐⠒⢷⣻⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠉⠩⣇⣿⡄⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⢿⡉⢩⣍⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣺⡾⣷⠀⠀⠀⠀⠀⠀⠸⡿⡄⠈⠉⢀⣬⠁⣤⠀⠀⠀⠀⠀⢠⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀⠀⠀⠀⠹⣝⢄⣀⣀⣉⣀⣉⣀⣀⣀⣀⡴⣣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁

⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠈⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠅⠀⠀⣠⠂⠀⠀⠠⠎⠀⠈⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠐⠁⠀⠀⠁⠀⡠⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠄⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢄⡤⠀⡀⠈⠀⠀⠀⠀⠐⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠀⠀⡀
⠠⡀⠀⠀⠀⠐⠈⠁⠀⠄⢠⠀⠀⠀⡄⢰⣉⣃⣘⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⡄⣶⣹⣁⣛
⠀⠀⠀⢀⠤⢠⡄⠀⠀⠀⠈⠃⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡃⠀⢠⠤⢠⠄⠀⠀⠀⠈⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠉⠀⠀⠌⠀⠼⠀⢠⡄⠀⠂⠀⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠰⠃⠉⠁⠀⠀⠌⠠⠼⠀⢠⠄⠐⠂⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⡀⠀⠀⠀⠀⠄⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⣀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢢⡀⠀⢠⠄
⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠂⠰⠀⠊⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠂⡀⠄⠀⠀⠀⠀⢀⡐⠒⠢⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠠⢂⠐⠀⠂⠀⠀⠀⠀⠀⢀⠐⠒⠂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠄⢂
⠀⠠⠠⠞⠀⠀⠀⠈⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠉⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠈
⡀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟
⠀⠀⠀⠀⠉⠁⠐⠂⠀⢀⡀⠀⠀⠀⡀⢠⢰⡄⢲⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠁⠔⠀⠀⢀⡀⠀⠀⠀⠀⣠⢰⠄⡦
⠈⢢⠀⠀⡀⠀⡀⠀⠀⠀⠘⠆⠀⠀⠃⠜⠃⠒⠒⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠚⠄⠀⠀⠃⠟⠐⠒⠂
⠒⠊⠀⠠⠉⢩⠁⠠⠔⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠀⠀⢀⡂⠒⠒⠀⠀⠠⠉⢨⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⣠
⠀⠀⠀⠉⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⢂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠁⠀⠀⠰⠐⠈⣄⠃⠀⠘⠁⠀⡀⢀⠀⡄⠀⠀⠀⠀⠁⢁⠀⠀⠈⠁⠀⠀⠔⠀⠀⡌⠁⠀⠈⠀⠄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⡟⠀⠀⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢰⣶⣷⣶⡀⠈⠀⠀⠀⠀⠉⠉⠉⠀⢠⣧⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣏⢹⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡌⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⢷⣶⣶⣶⣶⡖⠀⢠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⡿⠁⠀⣷⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠰⡿



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⡞⠡⡼⣹⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⣽⢿⡍⣹⣿⣷⣸⣆
⠀⠀⠀⠀⠀⡠⢚⠙⢿⣿⡇⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡻⣿⡄⠀⠀⠀⠀⠀⠀⢸⣇⠉⠈⢿⣪⠟⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠃⣚⡠⣼⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡲⢍⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣔⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠒⠠⠤⠞⢡⣤⠀⠀⠀⠀⠀⠀⢰⡶⠒⡲⣒⣒⡲⡒⠲⣶⠀⠀⠀⠀⠀⢀⣾⠃⢸⣿⡦⠄⠛⠉
⠀⠀⠀⠀⠀⢠⣅⠐⣿⡇⣶⡆⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⠶⡹⣯⢜⡷⡱⠆⢸⠀⠀⠀⠀⠀⠘⠛⠃⠉⠈⡆
⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠸⠷⠤⣱⡯⠭⠷⠥⠴⠿⠀⠀⠀⠀⠀⠀⠀⡔⢪⠖⣩⡒⣴⢢
⠀⠀⠀⠀⠀⠈⠩⠤⠉⠡⠉⠡⠌⠩⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡺⣄⡞⣠⣟⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣄⡤⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠽⣋⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣶⣄⠁⣠⠟⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⢶⣿⣦⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠦⡝⢻⣿⣿⠃⠀⠀⠀⠀⣠⡞⠁⡘⠷⡧⣯⠞⠁⠻⣧⡄⠀⠀⠀⠀⣿⣿⣿⣿⡀⣫⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⣄⣁⣠⠞⡅⣿⣦⣴⡿⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠱⠚⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠚⠀⡀⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣎⣥⣶⣶⣮⣿⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⠋⠀⢈⣿⡿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⢁⡀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⡔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠊⠀⠈⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠁⠀⠠⠈⠀⣠⣤⣦⣀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣧⠄⠀⠀⠡⠼⣿⣿⣿⣿⣷⣬⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣽⣿⡍⢀⠀⠀⠀⠠⠄⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣀⣻⢤⣀⡐⣻⣿⠋⠀⠀⠐⠈⠐⠀⢀⡀⠀⠙⠻⣿⣿⣿
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡽⢟⡩⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠈⠻⣿
⠀⠲⣴⣤⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣤⣿⠿⠿⣾⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠉⠒⠶⠦⢔⢀⣂⣀⠄⠈⢁⡈⠉⠩⠻⠃⠀⡠⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡥⢔⡈⠀⠀⠠⡉⠀⡠⠚
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣻⠷⠚⠋⣰⠻⢅⠎⠀⡤⠄⣦
⠀⠀⠀⣀⣠⣾⡿⠟⠋⠁⠀⠀⢰⣟⣿⡇⠀⠀⠑⣖⠌⡆
⣷⣶⣬⡏⠉⠁⠀⠀⠀⠀⠀⠀⣿⣤⠟⠀⠀⠀⠀⠙⠲⢿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡔⣤⣐⢦⣄⡰⣥⣄⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠠⠤⠄⠐⠊⠀⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣣⠶⣿⡦⠾⣷⠶⣿⣤⡽⠞⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠁⠀⠆⠀⠀⠀⣁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢠⡿⠀⣼⠃⣰⡟⠀⠀⢀⣀⠀⠈⢙⣟⣂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠂⠀⠀⠀⠉⠀⠈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⣼⠇⣼⠇⣰⡟⠀⠀⠀⢟⣿⡇⠀⠀⢳⣍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠀⠀⠆⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⢴⣿⣴⡿⣶⡿⠐⢀⣀⠓⠀⡀⠀⠀⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠡⠇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣿⣵⣿⣶⣿⣴⣎⡍⠉⠙⢦⠈⠄⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠀⣤⠤⡤⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣽⢿⠿⣿⡇⠻⠿⠻⣿⣸⡇⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠄⢠⣠⣨⡜⠂⠑⠀⠀⠀⠀⠀⠀⢠⣻⣟⡯⣿⣿⣿⠏⠀⢻⣿⣦⣀⣘⣩⠟⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⡄⠈⠀⠇⢀⠐⠀⡄⠀⣀⠀⠀⠀⠒⢿⡿⠿⠿⣿⠃⠀⠀⣈⠉⠃⡄⠄⠀⣸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠊⠀⠀⠀⠀⡇⢠⠈⠀⢠⡆⠀⠀⠘⢉⠍⠉⠈⠱⠴⠅⠉⠉⢈⣭⠍⣭⡍⠉⠈⠉⠉⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠙⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠠⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⢠⢃⠀⠠⠀⡀⠀⠀⠀⠀⢠⣎⢊⣄⠈⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠨⠀⠆⠐⢠⡄⠀⢠⢠⠀⠀⡀⠀⠀⠀⡄⣄⠀⢠⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠰⡄⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⡄⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠂⠡⡂⠀⠀⠀⢘⠀⠀⢂⠀⣰⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⡇⠀⠀⠀⢈⡀⠀⠀⠀⡆⠀⠀⠀⠤⠀⠀⠤⠀⠄⠀⠀⠀⠠⠠⠀⠤⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠁⠡⠀⠀⠀⠁⠀⠨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠒⠒⠂⠒⠀⠂⠒⠐⠂⠐⠒⠒⠒⠀⠓⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠁⣉⢀⡉⠀⠈⡀⢈⠈⠉⢈⠀⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⠀⠀⠀⠀⢀⣆⣀⡀⠔⢠⣀⠀⠀⣀⠀⡀⠀⢀⡀⢀⢀⠀⣀⠀⡇⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠔⠀⠀⠀⠀⠘⠂⠀⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠


⣾⣿⣿⣶⣶⡷⢿⣾⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⢷⡿⠿⡿⢶⣶⣿⡿⠶⠶⢶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⡤
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠀⠀⣀⣀⡀⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⠇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠐⠂⠣⢄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⡇⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣷⣿⡿⠫⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣟⠉⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⣿⣿⣏⣿⣏⣿⣿⣿⣿⣿⣿⢯⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⠀⡠⠋⠊⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡠⠋
⡰⠋⠀⠀⠠⠔⣒⠒⠐⠄⠀⠀⠀⠀⠀⠀⠰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⢠⠔⣒⠒⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⢀⢾⣿⠶⠋
⠀⠀⠀⠀⠁⠠⣴⠄⠀⠀⠑⢄⠀⠀⠀⠀⠠⡠⢄⡀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠐⠁⠀⣴⠄⠀⠀⠁⠀⠀⠀⠀⠀⠘⡠⢄⡀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠙⢷⣾⡇⠀⠈
⡀⠀⠀⠀⠀⠈⠳⣄⣀⠐⢾⡰⣼⠀⠀⢀⠤⠒⠒⠉⠉⠉⠁⠀⠐⠤⡀⠀⠀⠀⠀⠀⠲⣄⣀⠐⢾⡴⡱⠀⠀⢀⠠⠂⠒⠉⠉⠉⠉⠀⠐
⠈⠢⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠁⠀⠀⢀⡀⠂⠄⠄⠤⢀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⢠⠃⠀⡀⢀⡀⠂⠤⠄⠤⢀
⠦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣯⠉⠁⠀⠀⠀⠀⠘⠢⣀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣯⠁⠁
⠲⡘⡂⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠲⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠳⣄⡀
⣿⠟⠛⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠶⠶⣶⣿⠟⠟⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠷⠶
⢀⣀⢌⣳⠋⠀⠀⠀⢀⠀⠠⠤⣤⣀⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣳⠋⠀⠀⠀⢀⠀⠤⠤⢤⣀⡀⠀⠀⠀⢀
⠭⠞⠋⠁⠀⢀⠔⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠉⠐⠢⠤⠬⠬⠬⠭⠖⠋⠁⠀⢀⠄⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠈⠐⠢⠤⠬⠤
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣹⠏⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢹⠇⠆⠈⡻
⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⡠⠋⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⡠⠫⠊⠀⢰⠏
⠀⠀⠀⠀⠄⢀⢾⣿⠶⠋⠀⠀⢀⡰⠃⠀⠀⡠⠒⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⢰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⡠⠒⠀⠀⠒⠄⡀
⠀⠀⠀⠰⡴⢄⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⢰⠁⠀⣴⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡰⢌⡀⠁⠀⢀⣀⠴⠊⠀⠀⠀⠀⠁⠀⣴⠆⠀⠀⠐⢄
⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⡄⠀⢠⠀⠈⢂⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠙⣿⣶⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡆
⠀⠀⢀⠄⠐⠚⠉⠁⠀⠉⠁⠒⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢐⣿⡴⡧⠀⠀⢀⠤⠒⠚⠉⠁⠀⠁⠀⠀⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢈⣮⡴
⠀⢠⠃⠀⠀⢀⡂⠒⠠⠄⠄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠓⠉⠀⠀⢀⠃⠀⠀⢀⡐⠒⠢⠄⠤⠀⠀⠈⠒⡀⠀⠀⠀⠀⠀⠉⠙⠓⠉
⠀⡆⠀⠀⠐⣿⠁⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣯⠈⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦
⠀⠠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠰⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠳⣌⢦⠀⣃
⠀⠀⠱⡀⠀⠀⠀⠀⠉⠓⠳⠶⢶⣿⠟⠛⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠛⠳⠶⢶⣿⠟⠓⢀⣸
⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡣⠃⠀⠀⠀⣀⠤⠀⠤⣄⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⡳⠋⠀⠀⠀⣀⠤⠀⠤
⡀⢛⡧⠀⠀⠀⠈⠒⠲⠤⠬⠬⠭⠽⠞⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀⡀⠌⢛⣦⠀⠀⠀⠈⠐⠲⠤⠤⠬⠬⠽⠚⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀
⠃⢈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣹⣇⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⡆
⠀⠀⠀⠀⠀⠀⠚⠂⠚⠛⠓⠀⠀⠀⠀⠐⠋⠉⣿⠀⠀⢸⠀⡇⠀⠀⠀⠉⠁⠀⣀⣀⣀⠀⣀
⠀⠀⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⢸⡇⠀⣻⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉
⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣿⢸⡇⢸⣋⣉⣻⢰⡟⢛⣛⣛⡛⢻⣇⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠐⠒⠂⢀⣾⠀⠀⢀⣀⣿⣸⣇⣸⣉⣉⣹⣖⡇⢈⣉⣉⣁⢸⡏⠙⠲⠦⣄⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣠⡴⣯⣽⡆⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠈⠉⠉⠁⢸⡇⠀⠀⠀⠀⠉⣷⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠘⡇⠙⢢⣼⠀⣟⣉⣉⣉⣉⣉⣿⢸⡇⢀⣀⣀⡀⢸⣇⡀⠀⠀⠀⠀⣿⡛⢻
⠀⠀⠀⠀⠀⠀⢰⣧⠞⠋⢸⠀⣉⣉⣉⣉⣉⣉⡁⢸⡇⢈⣉⣉⡁⢸⣏⣹⣇⡀⠀⠀⣷⣼⣿
⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢸⠀⣯⣉⣉⣉⣉⣉⡿⠘⡇⠈⠉⠉⠁⣼⠋⠁⠈⡙⣦⠀⣿⣳⣾
⠀⠀⠀⠀⠀⠃⢰⡖⢒⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡇⠀⠀⠀⡄⢸⠀⣿⢯⣹
⠀⠀⠀⠀⠀⡇⠈⠉⠉⠁⢸⠀⢸⡏⠉⠉⠉⢹⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠀⣿⠛⢻
⠀⠀⠀⠀⠚⣟⠒⢾⡙⠳⣟⠓⠚⠓⢶⠒⠒⠛⠓⢺⡟⠒⠒⠒⠚⣿⠒⠒⠚⠛⢻⡗⠛⠒⢻⠗
⠀⠀⠀⠀⠀⢹⡄⠀⠙⢦⡌⠳⢦⣀⡼⠛⠙⣦⠞⣋⣟⡳⣦⣤⣀⣿⠀⠀⠀⠀⣸⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢻⡖⠒⠛⣟⠳⣄⣉⡴⡞⠛⣏⠀⡳⢮⡅⢸⣦⣌⡙⠻⣿⣿⠛⣿⠒⢲⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠘⣦⠈⠉⠀⢻⣀⣙⣦⣙⣏⣥⣟⣀⣼⡙⢲⣤⡉⠁⠈⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡛⢿⡉⠉⠉⣯⠉⠉⢹⡏⠉⠉⣹⠋⠉⢻⡤⣤⣤⣤⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢽⣷⣄⡘⢧⡀⠘⡇⠀⣴⢋⣠⣴⣯⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠾⠷⠛⠛⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣾⣿⣿⡏⠛⠲⢤⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠙⢷
⠀⠀⠀⠀⠀⠙⣿⠛⠀⠀⠀⠀⠈⠛⠦⣄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⡇⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⣀⠀⠀⠀⠀⠀⠀⣀⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠳⣄⠀⠀⣠⠞⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢈⡵⢯⡁⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣄⣀⣤⣤⣤⢼⡧⢤⡴⠿⠤⠤⠿⢦⡤⢼⡧⣤⣤⣤⣀⣠⣞⡀⠀⠀⠀⢀⣀
⠀⠀⢀⣠⡤⠶⠒⠛⠉⠉⠉⠙⢧⡀⠀⠀⢸⡷⠋⠀⢀⣀⣄⡀⠀⠙⢾⡇⠀⠀⢀⡼⠋⠉⠉⠉⠛⢲⣿⣿⣷⡀
⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡴⢻⡇⠀⢰⣿⣿⣿⣿⡆⠀⠸⡟⢦⣴⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠳
⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠳⣼⠇⠀⠈⢿⣿⣿⡿⠁⠀⢸⣧⠞⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠓⠶⢤⣄⣀⡀⠀⠀⠀⢠⡞⠁⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⠈⢳⡄⠀⠀⠀⢀⣀⣠⡤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⡶⠛⠶⠶⠦⠤⢼⡧⣬⣷⣤⣤⣤⣤⣾⣥⢼⡧⠤⠴⠶⠶⠛⢶⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⢈⣷⣾⡁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡴⠋⠀⠀⠙⢦⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⢿⠉⠀⠀⠀⠀⠀⠀⠉⡿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣰⣿⣿⣶⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⢰⡇⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢧⣄⣀⣤⠴⠛⠿⠿⠃⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡄⠀⠞⠒⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢁⡴⠛⠁⠀⣆⣇⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀⡎⠉⠉⠉⠉⠉⠁⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠃⢀⠴⠊⢁⡤⠛⠁⠀⠀⠀⠀⠈⠁⠀⢴⢿⠆⠀⠀⣠⠀⡀⠀⠱⡀⠀⠀⠀⠀⢀⠜⠀⠀⠠⣳
⠀⠀⠀⠐⠈⠀⢿⣅⣠⠖⠉⠀⠀⣤⡄⠀⢠⠆⠀⡇⠀⠈⠉⠉⠀⠀⠁⠀⠇⠀⠀⠈⠒⣤⣴⠶⠁⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢠⡄⠈⠀⠀⢺⣀⣞⣀⣀⠀⠀⡄⢀⡀⠀⢠⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀
⠀⠀⠀⠀⠀⠘⠁⢰⣖⠤⣀⠀⢀⢀⠀⠀⠀⡟⢉⣁⣹⠃⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⠈⡕⠂⠉⠰⠦⠀⣀⢠⡯⠚
⠀⠀⠀⠀⠀⠀⢀⡮⠉⣻⠚⢁⠀⠂⠂⠀⠀⠙⠋⡼⢉⣹⠂⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡎
⠀⠀⠀⢀⡤⠒⠊⠁⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡹⠋⠉⢱⠄⠀⠀⠑⢄⠀⠀⠀⣀⠇⠀⠀⠀⢠⠀⣽⢒⡲
⠀⠀⠀⣿⣿⣶⣦⣄⠘⡆⠀⢰⡠⡇⡀⢰⠆⠀⠀⠀⢧⠄⠀⠉⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⣀⡀⠀⠸⡟⠉⠁
⠀⠀⠀⠙⢿⣿⣿⣿⣷⠇⠀⠘⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠘⣄⡜⠀⠊⠀⢀⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⠤⣶⣶⣶⣐⡦⠀⠟⠳⠄⠇⠀⠀⠀⢹⡀⠀⢀⣴⠷⣴⠁
⠀⠀⠀⢀⠠⡞⢶⠀⠀⠀⠀⢾⣁⣀⣀⡤⠆⠀⠀⠈⢺⢻⠟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⣴⠛⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠚⠋⠿⣅⠀⠀⠀⠀⠀⠀⠀⡞⣷⡏⢹⡄⠀⠀⠀⠀⠀⣤⠀⠀⠘⠂⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠠⠚⢧⠀⠀⠈⢛⣦⣄⣼⠆⠀⡀⠀⠀⠀⠀⢹⢻⣷⠘⣇⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⢾⣉⣁⣹⠀⠀⠘⠉⠈⠀⠀⠠⠈⡼⣿⡄⢿⠀⠋⠉⠹⡇⢱⠆⠀⠀⠀⠀⠀⠀⠘⠬⠜
⠀⠀⠀⢠⣄⠀⠀⢠⠖⠊⠛⢿⡉⠀⠀⠀⡤⠄⢤⠀⡀⠀⢣⢿⣷⣸⡇⠀⠀⠀⡸⢧⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠈⣁⠀⠀⠙⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠯⠚⠀⠀⠀⠘⠃⠀⢱⡄⠀⠰⣮⣭⣭⣵⠂
⠀⠀⠀⠘⠖⢃⣘⡛⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠇⡇⣀⡤⠒⠁⣠⣀⠀⢸⠀⠉⡇
⠀⠀⠀⠀⢐⠛⠉⠉⢹⠛⠉⡇⠀⠀⠀⠀⠀⠀⣀⡀⠤⠶⠶⠤⠤⣀⣀⣀⣀⣩⣤⡄⠀⠑⠋⣠⠜⠀⠀⠡⡀
⠀⠀⠀⠀⠈⡄⠀⠀⢸⠇⠀⢰⠀⠀⠛⠋⠉⠉⠙⠓⠤⠤⠤⠤⠜⠋⠉⠁⠀⠀⠀⠠⣶⠀⠀⣷⣶⣿⣿⣿⡟⢄
⠀⠀⠀⠌⠀⠉⠉⠹⠥⠤⠔⠚⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠄⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⢨⠽⠂⠀⠀⠀⠀⡝⠐⠀⠀⣠⠁
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠈⠂⡀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⡀⠀⠀⠠⠨⠈⠀⠀⠀⠀⠀⡀⠡⠮⠠⠀⡀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠧⠈⠀⠐⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢸⡀⠊⠀⠂⢸⠀⠀⢄⠠⠀⠀⠀⠀⢠
⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠈⠶⠠⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠀⢈⠠⠠⠘⠈⠀⠀⠀⠀⠀⠈⠂⠀⡆
⠀⠰⠰⠀⠀⠴⡆⣠⣄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠯⠭⢭⠭⠭⠭⠀⠀⠀⠀⠚⠁⡈⠑⠂⠀⠀⠀⠠⠁⠄
⠀⠀⠀⠀⠀⢆⣘⡠⠄⠀⠀⠐⠁⠐⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠄⠅⠐⠀⢀
⠀⡰⠒⠢⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⣶⠄⢠⡴⢦⡀⢰⠀⠀⢀⡴⢶⡄⠀⡴⠶⡄⠀⣦⠀⣴⠀⠀⠀⠀⠠⠁⠀⠈⡆⠒
⠀⠀⢀⠀⠆⠆⠸⠆⠃⠀⢸⡷⣇⠀⣿⠀⣿⠀⢸⡇⢸⠀⠀⢸⡇⠀⣿⢸⡇⠀⣦⠄⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠘⠷⠋⠐⠛⠂⠘⠶⠚⠁⠘⠓⠒⠈⠳⠞⠃⠈⠳⠶⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⣼⣃⣘⠿⠃⡋⠀⠀⠀⢀⠁⠀⠂
⠀⠘⠃⠀⠁⠀⠸⠂⠀⠀⠀⠐⠇⠀⠀⠀⢄⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⡀⡄⠀⠀⢀⡠⠔⠀⣠⠀⠀⠀⠁⠀⠀⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠐⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠃⠂⠇⠁⠑⠀⠀⠐⡂⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠨⠀⠀⠀⠀⢀⢀⠂⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠄⡀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⡐⠀⠃⡀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠀⠀⠀⢈⠐⠁⠀⠸⣀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡀⠀⠂⠀⠄⡐⠀⢂
⠀⠀⠀⠀⠀⡴⠁⠀⠠⠄⠀⠀⠀⠈⠸⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠁⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠹⠃⠀⡐⠄⠈⠁⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡷⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠄
⠀⠀⠀⠀⠀⠀⠀⡄⢤⡐⣮⢱⣆⡲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣘⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠰⡠⠀⠀⠈⠱⢾⠿⠉⠯⡉⠁⠀⠸⡄⠀⠀⠀⠄⠀⠀⠋⠀⢉⡇⠈⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠃⠀⠀⠀⠀⣀⠘⣷⠀⠀⠀⠠⠆⠁⠀⢀⠀⠆⠀⠀⠀⠀⣼⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠄⠟⠁
⠀⠀⠀⠀⠄⠐⠀⢿⡀⢂⠉⠀⠀⠐⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⣠⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡍⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠐⠂⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⠏
⠀⠀⡸⠀⠀⢹⠀⡁⢱⠀⣿⠁⢸⣿⡆⠀⠀⠀⠀⢀⢊⣾⣷⢢⣤⡤⠔⠀⠄⠄⠔⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠈⠀⡠⠋
⠀⠀⢻⡀⠀⠘⠀⠐⠋⠀⠷⠖⠘⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢵⣢⡀⢀⠜⠁
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⣠⠋
⠀⠀⠀⠀⠈⠙⠛⠶⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⢄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠅⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠂⡐⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠠⡀⠀⣖⠀⠹⠆⠀⠀⠀⠀⠀⠁⠀⠀⠈⣏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠁⢠⡖⠆⢱⣀⡉⣡⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣶⣦
⠀⠀⠀⠀⠀⠈⠣⣌⠁⣀⠞⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉