Dairy product Emojis & Symbols

⠀⠀⠀⢀⡀⠀⠀⣀⠀⣀⠀⠀⠔⠒⠒⠒⠲⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠠⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠊⠀⠀⠀⠠⣀⠈⢠⠀⡀⢀⠀⢀⣀⣀⣴⠋
⠀⠀⠀⠀⠀⠐⠶⠛⠛⠁⠀⠀⠀⠀⠀⣀⣃⡄⠀⠀⠀⠀⠀⠉⠀⠘⠁⠀⠀⠀⠀⠀⠐⠤⠈⠻⠄⢆⠀⠀⠈⠛⠛⠓⠊
⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢤⣀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠷
⠀⠀⠀⠀⠀⠀⠭⠧⡐⣠⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⡼⢬⣧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠨⠍⢉⠀⣠⢤⣍⣧⠌⠁⢼⣳⣶⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⣧⡼⠿⢭⡟⠛⠯⠑⠚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⣾⣖⣀⡄⠀⠁⠘⠁⠀⠀⠀⠀⠀⠠⣕⡦⣤⣥⡀⠠⠠⢬⡀⠠⢤⠀⠀⠀⠄⣀⠰⠿⠖⠉
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠿⠀⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠈⢲⣖⣘⡃⠌⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠁⡄⢹⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠈⠦⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠈⠿⠃
⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⡀⠐⠒⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢧
⠀⠀⣰⠁⣀⠀⢀⡀⠀⠀⠀⢀⠎⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠩⠤⢅⣀⣀⣀⣙⣐⣶⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⡀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠄⢀⠀⠀⢄⣤⣤⣼⣄⡀⠧⠔⠁⠀⠀⠀⠀⠂⠀⣠⣄⠀⠠⣤⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠠⠴⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡠⣂⣉⡐⢀⡀
⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠔⢦⡁⢀⡀⠜⠉⠀⣀⣈⠓⠄⣍⠑⠦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡐⠀⢂⠀⠀⠐⠐⠆⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠠⠆⠀⠀⡆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠐⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡠⠶⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢽⣏⡈⢧⣶⢠⡶⣦⢰⣴⡀⢠⣶⡴⣦⢠⡲⣤⣿⣰⣴⢠⣂⣿⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠙⠀⠸⠇⠀⠀⠀⠁⠈⠈⠀⠈⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠔⠉⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠰⠶⣦⠘⠀⢀⢀⠄⠍⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠔⠂⢠⠀⡜⠀⠀⠠⠂⠀⠀⠐⠂⠡⡀⠀⠀⠀⠠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠢⡀⠀⠃⠀⠀⠀⠻⠄⠐⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⡄⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⣴⣿⢿⣷⠀⣀⣀⡀⠀⣋⠀⡀⢀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠆⠘⠀⡀⠀⠀⠀⣿⡇⢨⣿⠛⣋⣹⣷⢸⣿⢸⣿⠛⠛⣿⡇⢸⣷⠀⠀⠰⠦⠔⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠡⠀⠁⠀⠈⠀⡀⠀⠀⠊⠀⠀⢀⠀⠀⠀⠀⣿⣷⠿⠋⠸⣿⣽⣿⠸⡿⢸⣿⠀⠀⠻⣿⢿⣿⠀⠀⠣⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⢠⣄⣼⡏⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⡆⣀⠀⡀⠀⣀⣀⠀⢀⣀⣸⡇⢀⡀⢀⠀⠀⣀⣀⢀⣸⣇⡀⢀⣤⡀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠋⣿⡟⠛⣺⡟⢻⣇⣾⠟⣿⡇⣾⡇⢸⣇⣼⡟⠿⠛⣿⡟⠁⣿⣏⠀⠀⠀⠀⠀⠇⠃⡐⠄
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⠀⠀⢹⣧⣼⠏⢿⣦⣾⡇⢻⣧⣾⡏⢿⣧⣴⠀⣿⣇⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⢃⡀⠀⠀⠀⠁⠂⠀⠂⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⢐⡼⠋⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⠀⠀⠸⠛⣀⠃⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣠⠤⠖⠂⣤⣄⣀⠀⠀⠀⣀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢄⡀⠀⣰⠄⠀⠀⣭⣾⣧⠀⣠⡟⠉⠁⠀⠀⠈⡗⠛⠼⣿⣿⡇
⠀⠀⠀⢠⣷⣿⠀⠀⢀⣤⣶⣿⣿⠆⣀⣴⢿⣿⣷⡧⠀⠀⣼⣿⣿⣿⠀⣿⠁⠀⠀⠀⠀⠀⠶⠀⠀⢉⣛⡇
⠀⠀⠀⠀⢹⢿⣤⡀⢘⠟⠉⠿⠟⠀⠀⣧⣾⠿⣿⣧⣴⣿⣿⣿⠟⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⢰⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃⠰⣿⠀⢿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠘⡇
⠀⠀⢠⣽⡇⠛⠀⡴⠂⢠⡄⠀⠀⠀⠛⠉⢀⣠⣿⠀⠶⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠘⡿⠛⠀⣸⢧⠔⠀⠀⠀⠀⠀⠀⠉⠁⠉⣹⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠁
⠀⠀⠀⠀⠠⣠⡐⢼⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣄⢠⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠞⢰⢸⢰⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠈⠈⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠠⠬⠂
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⡔⠈⣾⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠨⡀⠙⠐⠂⠀⢤⠀⠀⠀⣀⣴⣶⣶⣴⣶
⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⣠⣶⠟⠋⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠴⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠑⠂
⠀⠀⠠⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣾⣶⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⢀⣀⣠⡀⠀⠀⠠⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠠⠆⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡟⠥⢄⣀⠀⠀⠀⢀⠆⢰⢄⢀⣀⣀⣠⡤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠈⠉⠐⡆⠀⠀⢸⠀⢀⢀⠀⢠⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⡀⠀⡇⠀⠀⣿⠀⠈⠀⠥⠀⠤⠤⠤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠪⠀⠈⠦⠤⣄⣀⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⣿⠠⡀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢰⣾⣦⡁⠀⡴⠀⠀⠀⠀⠀⡾⠀⠀⠀⣀⠀⠲⠦⠤⠤⣤⣀⣀
⣀⠀⠀⠀⠀⠂⣿⠀⠀⠀⠀⠃⠀⡇⠀⠀⠇⠀⠷⠿⠿⢡⠐⡄⠀⠀⠀⠀⢀⡇⠀⠀⠸⠇⠀⠀⡀⠀⠀⠀⠀⠉⠙⡲
⢩⠉⠀⠀⠀⠀⢹⠰⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⢤⠒⠋⢸⢀⡴⠻⣍⠲⠞⠀⠘⢦⠀⠀⠀⠀⢰⡷
⠀⢈⠉⠁⠀⠀⢸⡆⠀⠀⠀⠉⠁⠀⡆⣀⠀⠀⠀⡀⢸⠀⠇⠰⠀⠀⠀⢀⡴⠫⡄⠀⠈⢳⡀⠠⠄⠀⡇⠀⠀⠀⢸⠣⣤⣄⣀⣀
⠀⠈⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⢃⡏⠀⠠⣈⡀⠀⠀⠠⠂⠀⠀⠀⠀⠘⢦⡀⠀⠀⠉⡀⠠⠤⠽⢐⡂⠀⢉⡉⢉
⠀⠀⠈⠙⠛⠋⠁⠐⠩⠜⡐⡂⠦⢀⢸⡀⠀⠀⠀⣼⠀⠀⠀⢠⠔⠒⢁⣀⣀⠀⠰⠆⠀⠀⠀⠻⡄⠣⠆⢱⠐⠤⠤⠀⠀⠀⢉⣴⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⢰⠇⠀⠀⠀⠘⢦⣀⠀⠈⠉⠛⠷⠶⣤⣄⡀⠀⢁⢀⠴⠚⠁⠐⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣄⣀⣀⡈⠉⠓⠀⠁⣀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠚⠉⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠠⠔⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠶⠚⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄⠠⠔⠀⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠐⠋⢁⣀⡤⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⠀⢂
⠀⠘⠀⠑⠀⠠⠀⢒⠉⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠆⠃⠠⠀⠀⠀⢸⠀⠀⠓⠂⠉⠂⠉⢀
⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠊⠀⢸⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⡀⢀⠀⠀⠀⢈⡤⠤⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⢠⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠈⠘⠒⠘⠻
⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄
⠀⠀⡰⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⢀⡀⠈⠐⠀⠀⢰⠀⠀⠀⠀⠀⢀⡴⠒⢢⣄⠀⠀⠨⠀⠀⠀⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠃⣈⠁⠉⣈⠌⠀⠸⠀⠀⠀⡐⠢⠄⠭⠭⠬⠥⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠐⠒⠀⡒⠤⢄⡀
⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠐⡠⠰⠄⠒⠐⡠⢀⡇⠀⠀⠀⠀⠘⠢⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡈⢀⠀⣄⠄⢰
⠀⢀⠀⠀⠘⠑⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠄⠀⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠑⠒⠒⠒⠉⠁⣠
⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢶⣵⣤⠠⠦⠶⠀⠀⠈⢉⣓⠒⠤⢀⡀⠘⠤⠎⢀⠤⠤⠤⠤⠤⠤⡀⠀⢠⠒⠒⡄⠀⠀⠀⣳⣀⣀⣐⣎
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣾⣥⡄⢠⡄⣠⠄⠀⠀⢀⡄⢠⡜⠍⠄⠒⠈⢹⠀⠀⠀⡜⢀⢦⣤⠂⠒⢰⢇⠀⠀⠑⠞⠁⢀⠴⠊⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⢀⣁⣀⣭⠭⠑⠒⠊⠉⠙⠤⠊⠁⣠⡄⠀⠀⢸⠀⢀⡎⠀⠣⣠⡾⠃⣠⠋⢀⣂⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⢠⡴⠬⣔⠃⣸⢍⠉⠀⢠⠋⠁⣳⠒⢳⡀⠀⠀⠀⠀⠀⠈⠁⠀⣤⣼⠀⢸⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⢣
⠀⠀⠈⡆⡀⠈⡋⠀⣠⠆⠀⠀⠑⠒⢹⠖⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢱⠀⡆
⠀⠀⠀⠃⢁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠐⠦⠞⠀⠔⣴⣲⣦⠤⠔⠒⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠸⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠖⠒⠚⠉⠁⠀⠀⠀⡔⠋⠒⠊⠲⡀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⢧⣇⡤⠤⠄⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠜⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⣄⣀⠀⠙⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⡼⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠈⠉⢙⣛⢒⠶⠐⠒⠒⠒⠒⠒⠂⠉⠈⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣤⣤⣤⣤⣤⣤⣬⣥⣠⣬⣍⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣞⠏⠩⣩⣫⡇⠀⠀⠀⠀⠀⠀⠀⢸⠢⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⣤⢀⡄⣀⣠⠀⢠⣀⠄⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠓⠙⠳⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⡨⠓⠤⡀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠿⠛⠇⠿⠻⠤⠼⠻⠆⢰⡇⠀⡇
⠀⠀⠀⠀⠀⢀⠧⠄⣀⣀⠀⢀⡀⠀⠀⠈⠢⣀⠀⠀⣀⣀⠠⢼⠞⠁⠀⢠⠇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠁⡠⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢩⠏⠉⠉⠉⠉⠉⠻⢄⠀⠀⢀⣎⣀⠀⢠⠃⠀⠘⠤⠤⠤⠤⠤⠤⠧⠤⠤⠔⠀⠀⠈⠒⠢⠤⠤⠠⠤⠤⠤⠤⠤⠤⠄⠚⠁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣽⣥⣈⣶⠁⠀⠀⠀⠀⠀⢠⠤⠤⠤⢤⡄⠀⠀⢠⡤⠤⠤⠤⣤⠀⠀⠀⣤⠤⠤⠤⣤
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⢆⠀⢰⡑⡲⠀⢨⣥⣤⣤⣽⠀⠀⠀⠀⣯⣤⣤⣬⡇⠀⠀⠀⢸⣥⣤⣤⣯
⠀⠀⢰⣥⡀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡄⠀⠉⠀⠀⢰⣤⣀⣀⣨⡀⠀⠀⠀⣧⣀⣀⣠⡇⠀⠀⠀⣨⣄⣀⣀⣴
⠀⠀⢸⠀⠉⠑⠂⠤⢤⣇⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠐⠊⠁⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⢇⠀⠀⣸⠀⠀⠀⠀⠸⠀⠀⠀⠇⠀⠀⠀⠈⡆
⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠒⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣸⠀⠀⠀⠀⠀⠸⣀⣀⠇⠀⠀⠀⠀⠀⢇⣀⡘⠀⠀⠀⠀⠀⢰⣀⣀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡧⠤⠧⠤⠤⠤⠤⠤⠤⠼⠶⠤⠤⠤⠤⠤⠤⠼⠾⠤⠤⠤⠤⠤⠤⠤⠶⠤⡇
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠐⡆⠂⠀⠀⠀⠀⠀⢲⠒⠒⠀⠀⠀⠀⠀⢰⢲⠒⠂⠀⠀⠀⠀⠀⡖⠘⠁
⠀⠀⠈⠓⢤⣀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠀⠀⣠⠤⠧⠤⠤⠤⠤⠤⠤⠼⠤⠠⠤⠠⠤⠤⡤⠬⠼⠄⠤⢤⠤⠤⠤⠤⠤⢠⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠂⠠⠤⠤⠤⠤⠄⠀⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃

⠀⣀⣠⣤⣶⣶⣶⣶⣶⣦⠤⣄⡀⠀⣤⠤⢴⣶⣒⣒⣒⠒⠒⠦⠤⠤⢀⣀⣀⣀
⢸⠙⠛⠛⠒⠒⠒⠒⠒⠛⠛⣁⡇⠀⢳⠦⢤⣤⣀⣀⣉⠉⠉⠙⢳⠈⠁⢀⡼⢻
⠨⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⢨⠀⠀⢸⠀⠀⢰⣤⠤⣩⠉⠉⠉⢹⡚⠉⠉⠀⢸⢀⣀⣠⠤⠤⠤⢤⡀
⠠⡆⠀⢀⣠⣤⣤⣤⣄⡀⠀⢸⠀⠀⠰⠀⢰⣬⣌⣝⡛⡂⠀⠀⢸⠀⠀⠀⢀⣼⡇⠇⠀⠐⠒⠀⠘⢅
⠀⡇⢰⣿⣿⣭⣿⣼⣿⣿⣆⢸⠀⠀⠘⠒⠤⢍⣉⣛⠃⠿⠇⠀⢸⠀⣀⠔⡻⡫⠂⠈⣆⠀⠀⠀⠀⠈⢳
⠀⠃⠸⣾⣧⣤⣿⣬⣤⣼⠇⣸⠤⣴⣶⠶⠶⠶⠶⢾⡏⠹⢒⠲⠾⠊⠁⠎⠘⠓⠒⠂⠘⠀⠄⠀⠐
⠀⢸⠀⠈⠙⠛⠛⠛⠋⢱⡛⠲⠤⠤⠤⠤⠤⠤⠤⠲⠒⣲⣏⠗⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠘⢧⣴⣂⣠⣤⣤⢴⡦⣟⠙⠛⠛⠛⠚⠛⠛⠓⠊⠉⠉⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣳⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⢠⡇⠀⣀⣀⣀⡇⠀⠀⠀⠀⢸⠀⠈⠉⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠉⠉⠉⠉⠁⠁⠀⢸⢁⡟⠉⣉⣉⣙⣟⡆⠀⠀⢸⠀⠰⢟⣛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⢤⣤⣤⣤⣤⠤⠴⠃⢨⠀⢀⣀⣈⣉⠀⡇⠀⠀⡼⠀⢘⣛⣩⠀⢸
⠀⠀⠀⠀⠀⠀⢰⠙⣛⡉⢛⡋⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⠤⠤⠒⣿⠀⠀⡇⠀⠘⣻⡧⠀⡾
⠀⠀⠀⠀⢀⡠⠃⠀⠈⠉⠉⣴⡷⢄⠠⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇⠀⠾⠿⠖⢀⡇
⠀⠀⠀⠀⠊⠐⠠⠤⠤⠄⠨⠾⠤⠒⠃⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣇⠀⢸⠀⠀⢀⣀⣤⠼⠁
⠀⠀⠀⠀⢰⠀⠤⣄⣀⡀⡆⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⠲⠶⣶⡶⣶⠾⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠈⣄⣀⠀⠀⠀⢠⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⣤⠒⢲⢆⠈⠉⠉⠉⠉⠉⠉⠉⢰
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠚⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠃⠳⡌⠀⠚⢒⣛⣘⣙⣻⣤⣼⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣭⡭⠽⠿⠿⡿⡭⠭⠭⠭⠭⣭⣭⠥⠴⠋
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠘⠦⠀⠒⠒⠒⠚⠊⠙⠑⠐⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣯⣭⣉⣉⣉⠉⠉⢹⠀⠀⠀⠀⣤⣀⣐⣒⡒⣒⣒⣒⣂⣐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡿⢾⣭⣽⣭⣙⣿⡏⠀⠀⠀⠀⢳⠛⠼⠯⠯⠯⠭⠿⠿⠓⢻⠃
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⣼⢠⢠⣤⢤⢠⢠⣠⣠⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⠷⠾⠟⠛⠀⠀⠀⠀⠀⢹⠀⢠⢠⢤⣤⡄⣤⡄⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⡸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⠉⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠒⠲⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡀⠀⠄⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢉⣡⣶⣖⠒⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠈⠳⣌⠳⡄⠀⠀⠀⠀⠀⡠⠋⠠⣿⠤⢶⣿⠀⣼⠷⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⠶⡄⠀⠀⠀⠀⠀⠀⢸⡄⢀⠀⠑⠀⠀⠀⠀⠆⠈⠳⣌⢢⠀⠀⠀⡼⠷⠶⠤⠭⣍⣉⣀⣰⡯⠖⠊⢹
⠀⠀⠀⠀⠀⠀⠀⣼⠷⠶⠶⠒⠲⠶⠤⢽⡄⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⡟⠲⠶⠤⠤⠤⠤⠴⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠺⣉⠉⠑⠲⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠹⡓⠶⣟⣛⣚⣓⣒⣦⣼⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢠⡶⠛⠲⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠦⠤⠀⠀⠈⡏⠙⢦⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⡋⣉⣙⡿⡇⠀⢸⡇⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠉⠉⠉⠀⠀⢹⡄⢸⡇⣿⠀⠀⠘⣧⣀⣀⠀⠀⠀⠀⢸⠀⠀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠹⣄⠻⠇⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⠼⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣰⠇
⠀⠀⠀⠀⠀⠀⢀⣴⢶⣖⣒⡒⠒⠀⢀⡀⠀⠀⢠⡦⣄⠀⠀⠻⢦⣀⣀⠀⠀⠀⠀⣀⣨⠔⠃⠀⠀⠀⠀⠀⠀⠀⢶⣿⣏⣉⣉⣉⣉⣉⣭⣵⡆
⠀⠀⠀⠀⠀⠀⢸⠙⠒⠀⠙⠛⠓⠊⠁⢸⠀⠀⠈⠳⣜⢳⡀⠀⠀⠙⠻⠯⠭⠭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠍⠀⠨⠀⠤⣤⡇
⠀⠀⠀⠀⠀⠀⡞⠀⢰⣋⡇⠀⢸⠀⠀⢸⡄⠀⠀⠀⠈⠢⡳⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡍⢙⠒⡛⠒⡛⠒⡏⢹⠃
⠀⠀⠀⠀⠀⢠⡇⠺⠆⠉⠀⠀⢸⢙⡆⠀⡇⠀⠀⠀⢀⡴⠻⣿⡀⠀⣀⡀⣠⠴⢤⡀⣀⠉⢉⣓⠦⣄⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠁⠀⠃⣼
⠀⠀⠀⢰⠮⣍⡛⠒⠶⠤⣄⡀⣾⣯⠶⠚⠳⢤⡀⠀⠸⣦⣴⠿⠉⠙⠁⠈⠓⠀⠀⠉⠉⠿⠋⠉⠹⣎⣷⠀⠀⠀⠀⣧⠀⠀⠇⠀⡄⠀⠀⣿
⠀⠀⠀⢸⠀⠀⢉⠙⢲⡦⣤⣈⣉⣠⠤⣶⠞⣩⡇⠀⠀⢿⡏⣟⢛⠲⠶⠶⠶⡤⡤⠤⠴⠶⠶⠒⠋⣡⠇⠀⠀⠀⠀⣿⠀⡀⡅⠀⡇⢸⠀⣿
⠀⠀⠀⠸⣤⣀⠘⠃⠀⣙⠁⢀⣸⠀⠀⠶⠘⣧⡇⠀⠀⠈⢿⣿⡾⣧⣧⢼⣤⣦⣥⣤⢤⢴⢶⢺⣿⠏⠀⠀⠀⠀⠀⢸⣤⣇⣽⣀⣇⣸⠄⣿
⠀⠀⠀⠀⠀⠈⠙⠓⠦⣍⣀⠸⣽⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠙⢿⣿⣼⡌⣇⣇⢃⣄⣌⣶⣧⠟⠁⠀⠀⠀⠀⠀⠀⢺⣆⣉⡉⠀⢀⣀⣲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣶⣶⣶⣶⣦⡀⠀⠀⢠⣶⣶⣶⣄⠀⠀⢰⣶⠀⢠⣶⣶⣶⣶⣦⡀⢰⣶⣄⠀⢀⣴⣶⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠈⢿⣷⠀⠀⣿⡿⠀⢻⣿⡀⠀⢸⣿⠀⢸⣿⣧⣀⣨⣿⡗⠀⠙⣿⣷⣿⡟⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⣼⣿⠀⢰⣿⣷⣶⣾⣿⡇⠀⢸⣿⠀⢸⣿⡟⢻⣿⣏⠀⠀⠀⠈⣿⡏⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣶⣾⣿⠋⠀⢸⣿⠉⠉⠉⣿⣷⠀⢸⣿⠀⢸⣿⡇⠀⠹⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠈⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁⠀⢀⣴⣿⠟⠁⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠈⠻⣿⣦⡀⠀⠉⠻⢿⣷⣦⣀
⠀⠀⠀⠀⣠⣴⣿⣿⣟⣁⣀⣀⣀⣴⣿⣟⣁⣀⣀⣀⣀⣾⣿⣁⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣈⣿⣷⣀⣀⣀⣀⣈⣻⣿⣦⣄⣀⣀⣈⣻⣿⣷⣦⣄
⠀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠛⠛⣿⣿⠟⠛⠛⠛⠛⠛⢻⣿⡿⠛⠛⠛⠛⠛⠛⣿⣿⠟⠛⠛⠛⠛⠛⢿⣿⡿⠛⠛⠛⠛⠛⠛⣿⣿⠟⠛⠛⠛⠛⠛⢿⣿
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠙⢿⣷⣤⣀⣠⣤⣾⡿⢿⣿⣦⣄⣀⣤⣴⣿⠿⣿⣷⣤⣀⣠⣤⣾⡿⢿⣿⣦⣄⣀⣤⣶⣿⠿⣿⣷⣤⣀⣠⣤⣾⡿⢿⣷⣤⣄⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⠛⠉⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠉⠛⠛⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⡄⠀⠀⢸⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡄⠀⢸⣿⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡋⠉⠀⠀⢸⣿⠀⠀⢀⣾⡿⠛⠉⠉⠉⠙⢿⣷⡄⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⢸⣿⣤⣤⣾⣿⠁⠀⣴⣶⣦⠀⠀⢻⣿⣤⣤⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠛⠛⠛⠋⠀⣾⡿⠛⣿⣷⠀⠈⠛⠛⠛⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣺⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⠂⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣷⣤⣾⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣿⣧⣀⣀⣀⣀⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄
⠀⠀⠀⠀⢠⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡄
⠀⠀⠀⠀⠸⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⠇
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠰⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠉⠉⠉⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⡀⠀⠀⠀⠉⠉⠉⠉⢦⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠤⢤⣤⣤⣄⣀
⠀⠀⢸⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣈⣷⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠶⠟⠁
⠀⢀⡞⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡄⠀⠈⢻⡟⠋⠉⠉⠉⠉⠉⠁⣽⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⣤⡀
⢀⡾⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠒⢄⠙
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡆
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⡇
⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣠⠟⡐
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠸⠠⠃⠇⠀⠈⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠁⠈
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠻⢷⣶⣶⣾⠿⠋⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⣧⡀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠹⣿⣦⣤⣄⣀⣠⣤⣴⡿⠃⠀⠀⠈⠙⢶⣄⣀⣀⣠⣤⣴⠶⠾⠛⠋⠀⠀⠀⠀⠀⠀⣀⠠⠀⠐⠊⠉⠉⠳⢦⣀⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣲⠂
⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌
⠀⣠⠶⠛⠛⠓⠦⠤⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠲⠤⣄⣀⠀⠀⠀⡿⠛⠳⢦⣄⡀⠀⣀⣤⠶⠿⢿⠁
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠃⠀⠀⠻⠮⠃⠀⣠⡤⠈⠙⡆⠀⢃⠀⠀⠀⠈⡟⠛⠋⠀⠀⠀⠸
⢸⡃⠀⠀⠀⡀⠀⠀⠀⠘⢸⡇⠀⠀⢀⡴⠋⢀⣀⣤⡤⠶⠖⠛⠉⠉⠊⠁⢰⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⢸⡇⠠⡆⠠⡀⠀⠀⢨⠀⢸⡇⠀⣴⠿⠚⠛⠉⠉⠀⢀⡀⠀⢰⣏⣴⠇⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢷⡀⠀⠀⠉⠁⠀⢰⠁⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠿⣴⠟⠀⠉⠁⠀⠀⢸⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠙⠳⢤⣀⠀⠀⠉⠀⠸⡇⠀⢸⣠⡤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠟⠀⠀⠀⠀⠻⢦⣤⣀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠤⠀⠀⠀⠀⠘⠙⠓⠀⢀⡴⠦⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣠⠞⢉⡞⢁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢿⡞⠡⠁⠘⠛⠉⢉⠉⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠲⣤⡀⠀⠀⢰⠏⠀⠆⠈⠀⠃⡠⠐⠈⠀⠀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⢦⡀⣿⠀⠀⡄⢀⠔⠉⠂⠀⠀⠀⠘⠛⢒⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣿⠍⠛⠳⢦⣄⠙⢦⡙⣿⠀⠀⡴⠡⠄⠀⠀⠀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢾⣯⠁⠀⠠⠀⡀⠀⠉⠂⠈⠳⣄⠹⡌⢧⣈⡤⠶⣤⡴⠶⣄⣈⣩⠿⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠂⢈⠀⠁⠀⠀⡨⠓⢢⡼⢧⡟⠉⠛⣆⠀⡏⠀⠀⢸⡏
⠀⠀⠀⠀⢠⣏⣤⡤⢤⡄⠀⠁⡀⠀⠀⠁⡴⠶⠿⣤⣸⡄⠀⠀⢸⣦⣷⣀⣀⣼⣁
⠀⠀⠀⠀⠈⠀⠀⢰⣯⠤⠶⣺⠏⣀⣠⡼⡇⠀⠀⠈⢻⣷⣦⣤⣿⠁⠀⠙⡿⠁⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⣽⢦⣄⣠⣾⠀⠈⢹⣿⣄⣀⣠⣧⡀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⣿⣿⣦⣤⣼⠋⠉⠹⣿⠟⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡶⠃⡴⠛⠛⢿⡀⠀⢀⣟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣇⠀⠀⠀⣿⣶⣾⡿⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡶⠖⠛⢻⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⣷⣄⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡟⠉⠩⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢵⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢠⣧⠤⣤⣦⡽⠃⠀⠀⢶⣀⠀⠀⠀⠐⢠⡐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠐⠒⠻⡾⠀⠀⠀⠀⠈⣋⠀⠐⢦⣾⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠇⠀⠀⠀⠀⣻⡀⠀⠀⠀⢠⠇⠀⠀⢠⡆⠀⠀⠱⡶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⢨⡖⠐⢢⡀⠀⠀⢀⠜⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠞⠋⢿⠁⠀⡌⠀⠀⠀⣹⣿⣿⣷⣄⣀⣀⣤⡾⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢆⡀⢀⡀⠀⠰⠒⣉⠛⠉⠈⠉⠛⠉⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠑⠶⠶⠾⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣿⠀⠀⠀⠀⠀⢀⠿⢶⡞⢃⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠢⣄⣀⣠⠄⠋⠃⠀⠹⡿⠋⠛⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡄⢸⣦⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆⠀⠀⠀⢀⡞⠟⠛⠶⡤⣤⡖⠛⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⣴⠛⠁⠀⠀⡀⢠⡌⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠛⠁⠙⢄⠠⢀⠰⠀⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣭⠴⣧⠀⠀⠑⢲⡶⡞⠀⠘⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢛⣧⣤⣠⣬⡌⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠋⠀⠘⠇⢹⣶⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⡀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠐⠫⠹⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣀⠀⠀⠀⠀⣿⣶⣄⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⠓⢦⣀⠀⠀⢀⡀
⠛⠿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢭⡉⠛⠒⠚⠀⠀⣌⠓⠒⠋⠙⡆
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠉⠓⢤⣸⡄⠀⠀⡀⢿⠀⠀⠀⣠⣤⡀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣴⣿⣿⣮⡷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠤⠤⢤⣌⣳⡄⠀⡇⢸⢀⡤⠞⠙⢦⣹⠆
⠀⠀⠘⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣒⣦⡀⠀⠀⠈⠙⣦⠇⣸⠟⠀⢀⣴⣞⡁
⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡴⠋⠉⠉⢉⡷⠚⠛⠛⠻⣴⠃⢀⡴⢻⡶⣈⡉⢩⣝⢲
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣧⣤⣿⣏⣈⣿⡷⢹⣿⡇⠀⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡷⠻⢦⣾⢸⣅⣹⢸⠏⣧
⠀⣰⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠟⢁⣼⣿⠃⠀⢀⡞⢧⡀⠀⠀⢻⣄⡤⠤⣤⡀⣠⠇⠀⠀⠙⡷⠮⠶⠋⣠⢏
⠀⢿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣧⣷⣴⣿⠀⠀⠀⠘⠛⠁⠀⠀⠸⣇⣠⠭⠿⣶⡟⠁⠀⠀⠀⠙⣧⠀⠀⠀⢀⡇⠀⠀⠀⠛⠋
⠀⣼⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⣸⣤⣤⠴⢿⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢳⣤⣀⣀⣀⡴⣇⠀⠀⠀⠀⣿
⠀⠙⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣠⡟⠀⠈⠉⠀⠀⢸⡆⠀⠀⣠⠏
⠀⢰⣿⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠉⠀⢷⡀⠀⠀⠀⠀⣸⠓⠒⠛⠁
⠀⠸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣹⠶⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡀⠀⢀⢀⡀⣀⣵⣺⣣⢒⡒⡢⢀⣀⣯⣿⣭⣽⣽⣟⣫⣽⣿⣶⣶⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⢚⣉⣦⣖⣍⣯⣸⣳⣦⣦⣶⣎⣴⣽⠉⢉⣯⡭⠀⠉⠀⠉⠉⠉⠁⢩⠀⢻⡿⡟⢁
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣧⣿⣿⣿⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⢳⠇⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⣷⡂⡡⠄⢀⡀
⠀⠀⠀⠀⢀⣄⣶⣶⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠹⣷⡃⠘⠊
⠀⠀⠀⠀⠰⣻⢿⣿⣿⣿⠁⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⢲⣞⣥
⠀⠀⠀⠀⠈⣻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣸⡇⠀⢰⣾⣶⣶⣶⣶⣶⣶⣶⣿⣷⠀⣿⡆⠀⣺⣿⣏⣻⣒⢀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⠁⠀⢀⣤⡀⠀⠀⠀⢹⣿⣿⣿⣿⢹⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠁⠀⣻⣿⣿⣿⡇
⠀⠀⠀⠀⢐⣺⣿⣿⡇⠀⠀⠀⠘⠀⢀⠀⢰⣴⡅⠈⣿⣿⢸⣿⣟⡄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⢀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⡨⡿⣿⣿⠀⣤⠀⠀⠀⠀⠁⠀⠀⠀⣥⠀⢿⣿⣇⢻⣿⣷⡹⣻⣿⣿⣿⣿⣿⣿⣿⣟⣼⣏⡼⣰⣿⣿⣿⣿⣾⠂
⠀⠀⠀⢼⣭⣿⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⠠⠚⠯⣄⣨⣿⣿⣯⡿⣿⣿⣷⣾⣿⠛⢻⣿⣿⣿⣾⣿⣿⣽⣿⣿⣯⢛⢟⣴⠕
⠀⠀⠠⣴⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⠻⣷⣿⣓⣐⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⡩⠶⠄
⠀⠀⢴⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⡿⢿⣿⣿⣿⣭⣛⠻⣿⡿⠿⢛⣟⣽⣿⣿⣿⣿⣿⣿⣿⣻⢏⡑⠉
⠀⢠⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⡀⠐⠘⠁⠈⢻⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠐
⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠠⠡⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠃⠀⠌⠀⠀⠀⠀⠀⠀⢿⣻⡉⠻⣿⣿⣿⣏⠀⠳⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣅
⠀⢼⣿⣿⣿⡇⠆⠒⡄⠀⠀⠀⠀⠀⠁⠸⡗⣠⠤⠀⡀⠀⠀⠀⠀⡘⣠⡾⢻⠉⣿⣇⣽⣶⣶⣿⠭⢉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⣾⣿⣿⣿⠏⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢋⡇⠀⠀⡁⠀⠀⠀⣞⠀⣻⣧⣈⣀⣿⣿⠘⠻⡇⠀⠀⠀⠡⣴⡿⢻⡏⠙⠻⣿⣿⣿⣿⣿⣧⡀
⠀⣿⣿⣿⡟⠀⠀⠜⠁⠀⠀⠀⠀⠀⠲⠀⠈⠀⠀⠠⢶⠀⠀⢸⣧⣿⣷⣿⠿⣧⣾⣿⣶⣶⣿⠦⠤⣤⣶⣾⡇⠈⠃⣀⡀⣿⣿⣿⣿⣿⣿⣷⣀
⠀⣿⣿⣿⠏⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠈⣿⠖⠉⡀⠈⠀⠀⠀⠙⣿⢿⣿⣧⣻⣿⣿⡇⣿⢁⣁⢀⡽⠟⢻⣹⣷⡜⠻⡇⠈⢻⠿⠉⠙⢿⣿⣿⣶⣆
⠀⣽⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡟⠀⠀⠻⡆⠀⠀⠀⢀⣻⣿⣿⣿⣿⣟⣿⣜⣿⣶⣿⣿⠀⢡⣤⠛⠛⢇⠀⠐⢠⣿⠋⠉⠀⣼⠛⠛⠿⡿⣷
⠀⠹⠿⠿⠷⢦⢤⣤⣀⣀⡀⢀⠀⢀⣤⣽⡇⠀⠀⠀⠁⢀⣀⣀⣨⣿⣿⣿⡿⣿⠇⣿⡿⣿⣿⣿⣿⡄⡇⠘⠄⠀⢸⣖⠶⢶⠉⠇⠀⠀⣟⠒⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⡛⠟⠛⠋⠙⡛⠛⠉⣉⣁⣯⠞⠻⣾⣿⣍⣝⢯⣿⣿⣿⣿⣦⣤⣤⣾⣿⡿⡿⣷⢦⡴⢾⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣒⣶⣒⣒⣒⣒⡒⢰⣶⣿⣿⣍⡀⠓⢋⣶⣷⣐⠞⠳⠞⠛⣛⣿⠾⠁⠙⠛⠻⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠈⠉⠉⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⠀⠤⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡆⠀⠰⠃⢀⠠⠀⠀⠈⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢠⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣜⣰⠟⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣀⠄⡤⠤⣀⣀⢀⣇⡼⠋⠁⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠊⠙⢻⡷⣿⠛⣛⠿⡟⢿⣛⠛⠉⠉⠁⠀⠀⠀⠴⠶⣭⡀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀
⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠂⠀⠀⢘⣘⣇⢿⠟⠁⣰⡇⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⢰⠁⠀⢀⠄⠠⠂⠘⣋⠟⢹⡈⠀⣠⠾⡄⠀⠜⢸⡟⣿⣙⠃⠁⠀⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠸
⠀⠀⠀⠀⢰⡇⠀⠈⢁⠀⠀⠒⠈⠉⠐⠈⡇⣾⡻⠀⢴⠀⠀⠐⣇⠸⡟⣷⣤⣀⣀⡀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠊⡘⠃⠐⠚⠦
⠀⠀⠀⠀⢠⢁⠀⠀⠀⢄⣱⠆⠀⠀⠀⢸⠇⠹⡎⢴⠘⢧⠀⠈⠏⢈⡾⣻⠍⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠂
⠀⠀⠀⢀⡤⠚⠲⣦⣀⣴⠿⠴⠮⣄⡡⢞⣴⢠⡳⣿⡀⡠⣡⠀⣀⠀⣐⣿⡧⣤⣽⣦⠤⣈⡚⠋⠃⠀⠀⠀⠀⠀⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠲⠶⠶⢼⣿⢟⠌⡟⢟⣶⠎⠀⠀⠀⠙⢋⡿⠁⠀⠀⠈⠑⡄⠀⠘⣦⡲⠒⠖⠀⠀⠀⠈⢀
⠀⠀⠀⢇⠀⠀⠀⢀⣜⠃⠀⠀⠀⢸⡏⠛⢶⡇⣎⠸⢂⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡄⠀⢠⣯⠙⢶⣤⡥⠀⠀⠀⠹⡀
⠠⠂⠉⠙⠳⣦⠎⠁⠀⠈⠳⡀⠠⠜⠀⠀⠀⣿⣁⡽⠗⠒⠠⣠⣾⠭⠦⣀⢀⡀⣠⠴⠶⢾⠉⠸⡇⠀⡛⡳⢤⣐⠀⠒⡟
⣧⠀⠀⠀⢰⣥⠀⠀⠀⠀⠀⡿⢑⣲⢄⣀⣀⣿⣽⣃⠀⠀⠀⠀⡀⠀⠀⠈⢯⢍⡵⠒⠐⠚⠢⡀⢹⡀⠸⣇⠈⠛⣦⢀⠘⢆
⢸⠷⠀⠐⣪⣵⣄⡀⣀⢀⡠⠃⠀⠈⠻⣷⠏⠀⠀⠈⠱⠀⣠⣘⣃⠀⠀⢀⣞⠾⠂⠀⠀⠀⠀⠙⣄⠀⡄⠌⢤⣀⣟⣑⠢⢄⠣
⢸⠀⢀⡞⠁⠀⠈⢻⣿⡛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡆⠁⠉⠀⠙⢶⠎⠉⠙⣧⡀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢳⡞⠁⠀⠀⠀⢸⡍⠣⢄⣤⣤⣶⣿⡿⣦⣴⣠⣴⣿⠀⠀⠀⣠⠤⠘⠦⡤⠤⣷⠓⠙⡋⠉
⠀⠀⠛⢄⠀⠀⡠⡎⠀⠐⡞⠁⠀⠀⠉⣿⣿⣿⡿⠿⣿⣷⣧⣼⠁⠀⠀⠀⢸⠀⠈⣆⠔⠁
⠀⠀⠀⠀⠙⣄⠀⣹⣦⣤⡇⠀⠀⠀⢀⣿⣿⣿⡗⠀⣀⠴⠛⠛⠦⡀⠀⢀⣼⠀⣠⡷⢄
⠀⠀⠀⠀⠀⠀⠉⡔⠀⠀⢑⠦⠠⠴⠋⠀⠀⠘⣇⡰⠉⠀⠀⠀⠀⠘⡷⠃⠀⠀⠀⠈⡆⡇
⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠑⠠⣆⠀⠀⠀⢀⣼⣧⠁⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⣤⠚⠉⣱⠖⠒⠉⠛⢿⣦⣄⣀⣀⣀⣾⣷⠖⠛⠛⢶⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⡀⢰⡃⠀⠀⠀⢠⠊⠀⠈⠉⢻⣿⣿⡏⠀⠀⠀⢈⠁⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠚⢷⣄⣀⣀⣼⡀⠀⠀⠀⣸⠟⠛⠻⢦⣤⡴⠎⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣈⣽⠉⠀⠉⠒⠲⣾⡇⠀⠀⠀⢈⣿⡷⠶⠶⠦⣤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣰⡿⠷⣄⣀⢀⣼⡿⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢻⠃⠀⠀⠈⢹⡟⠋⢹⣄⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⢀⡞⠀⠀⠀⠉⡛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⣀⣀⢀⠴⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢠
⠀⠀⠀⣆⣀⠈⠀⠀⢈⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣧⣀⣀⣀⣛⣀⡼⡀
⠀⠀⠀⢿⣿⡟⠀⠘⣿⣿⠇⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⣶⠀⢠⣶⣶⣿⠂⠀⠸⡇⠀⠉⠉⠀⠀⠀⠇
⠀⠀⠀⠈⢿⣿⠄⢸⣿⠟⠀⠀⠀⢿⡞⠒⠲⠶⠶⠶⠶⠶⠖⠒⠒⠉⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⢰⣿⡿⠃⠀⠀⠀⠳⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠣⠽⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠐⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠃⠀⠦⣈⣀⣈⡠⠞⣁⠀⢸⡇⠀⠀⠀⠨⣅⣀⣀⡠⠽⢡⠀⠀⠀⣿⠀⠘⠀⠀⠀⡷⡍⣁⣀⣩⡵⠀⢹⠀⠸⠀⠀⠸⢯⣀⣀⣈⡭⣇
⠀⠀⠀⡆⡀⣾⠀⠰⠀⠀⠈⢀⢸⠇⠀⠠⣦⠀⠀⢸⡇⠀⠀⠈⠉⠀⠀⡇⠀⠘⠔⠀⠀⣇⠂⠀⠀⠀⠁⠀⢸⠀⠀⠠⣤⠀⠘⢸⠃⠀⠀⠉
⠤⠤⠀⠤⠧⡿⡤⠤⠼⠀⠤⠼⠼⣤⣤⣤⢤⣥⠤⡼⠧⠄⠠⠤⠴⠤⢠⡧⠄⠄⠠⠼⣶⠿⠤⠴⠧⠠⠤⠦⠼⣤⣤⡤⠼⢤⠤⡼⠤⠄⠤⠤⠧⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠠⠅⠀⣠⠄⡂⠀⠀⠀⠅⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⡃⠘⠀⠘⣛⣛⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣉⣉⣉⣉⣉⡅⠠⠂⢸⣿⣿⠇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠈⠁⢠⡆⣼⣿⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠆⠨⣤⠄⣀⣴⣪⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣌⢛⠋⣡⠎⠙⡽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢴⠃⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠀⠀⣀⣼⣿⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⠋⢹⡏⠐⠛⠉⡿⠿⠧⣤⣄⣰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣞⣹⡂⣀⢀⡀⠀⢸⡇⠀⣇⠀⢸⡇⢀⠀⠀⠀⠠⠀⠈⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⣠⣾⣿⢛⣿⡿⠿⣾⣿⣽⣦⣯⣼⣇⣿⣿⠀⣿⣿⡈⠀⠀⠀⠀⠀⠀⡀⠈⠹⣷⠜⠛⢦⣾⣄⡤⡄
⠀⠀⠀⢀⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣿⡿⡧⢱⣟⠇⠀⠀⢐⣦⡀⠀⣀⠀⢸⣿⡟⠲⣾⠁⢻⡌⢶⠚⠀⠀⡀
⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣶⡿⢻⣾⣿⠟⣿⣋⠏⠃⢆⠀⠀⠀⠟⠒⠶⠆⢀⣡⣂⣠⣤⡼⠛⢏⡉⠿⠉⣹⡟⢢⣼⡷⠒⢡⣾⡅
⠀⠈⠛⠻⣿⣿⣿⣿⣹⣿⣼⣿⣶⣿⣿⣿⡏⠋⣐⣶⣨⣤⡀⠈⠛⠛⣙⣿⣿⣿⡟⠁⠉⣿⣿⠈⠁⣄⣸⡉⣳⡋⢻⣷⢦⣾⡿⠁
⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣿⣿⣦⣿⣬⣄⣁⣀⣀⡐⣀⣉⣉⣰⡟⠹⣿⣿⣿⣿⡷⠠⣾⣿⣿⣦⣤⣷⣾⣭⣿⣯⣽⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠉⠛⠃⠉⠉⠉⢩⢀⠁⠉⠩⠤⠖⠌⠻⠄⠰⠶⠂⠲⠛⠛⠛⠏⠡⠤⢿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠁⠀⢀⠤⠀⠀⢀⡠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠈⠀⠀⠀⠈⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠁⠐⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠯⡈⠑⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⣀
⠀⠀⠀⠀⠀⠀⠱⡀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠴⠋⠀⠀⠑⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠑⡄⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠡⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡷⠚⠉⠙⠲⢤⡀⣠⡤⠴⢧⡈⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡴⠛⠉⠓⠦⣶⡁⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠙⡆⠀⠄⠀⠀⠀⠢⠀⠀⠀⠀⠀⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⡤⠒⠻⣄⠀⠀⠀⣀⣀⣈⠓⣤⠤⠤⣄⠀⠀⡼⠀⠀⢀⡿⠋⠁⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠠⠖⠊⠁⠀⠈
⠀⢸⡃⠀⠀⠈⠑⢲⠞⠁⠀⠀⡟⠀⠀⠀⠀⠙⢏⡔⠋⠉⠉⠓⢄⠀⠀⠀⠀⣷⠤⣄⠀⠀⠀⠠⠀⠄⠋⠁⠀⠁
⢀⡤⠛⠉⠉⠉⠉⢿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣧⣀⣠⠔⠃⠀⠈⢳⠀⣀
⢸⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⠓⢤⣀⣀⡤⠞⣄⠀⣀⣀⠀⢀⣿⠤⠤⣄⣀⠀⢀⡼⠀⠀⠆
⠸⣄⠀⠀⢀⡴⠖⠋⠉⠉⠁⠀⣠⠊⠀⠀⠀⠀⠀⡼⠋⠉⠈⠙⢾⡁⠀⠀⠀⠈⠑⢯⡄⠠⠀⠄⠰
⢠⠞⠓⠒⣾⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⢻
⡟⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⡸
⢷⡀⠀⠀⠀⣨⠿⠒⠒⠒⠒⠀⠈⠓⠢⠄⠒⠀⠀⠀⠙⠢⠤⢶⡋⠀⠈⠙⠒⠲⡖⠋⠁
⠈⠳⠦⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⢸⠶⠤⠴⠚
⠀⠀⠀⠀⢹⣦⣀⣀⣠⡴⠋⠀⠻⣄⡀⢀⣠⠋⣨⠷⢦⣄⣀⣀⣠⡞
⠀⠀⠀⢰⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠇⠀⠀⠀⠈⠁⠀⠘⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠈⢷⣄⠀⠀⠀⢸⣄⠀⠀⠀⠀⡠⢆⠠⠊⠉⠁⠲⢤⣤⠴⠟
⠀⠀⠀⠀⠀⠈⢩⡟⠋⠉⠈⣱⠒⠊⠛⢦⢰⠃⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠘⠦⣄⡀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⣹⡀⠀⠀⠀⢀⣎⠀⠀⠀⠙⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠙⣦⠤⠖⠋⠀⠙⡄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣰⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣤⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠤⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⠄⠀⠈⢄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠢⠀⠀⢂⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠐⠄⠀⠀⠑⢄⠀⠁⢀⠀⠢⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠢⢄⠀⠑⢄⠀⠢⡀⠡⠀⢂⠀⠄⠀⠀⠀⠈⠠⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⠑⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠢⠤⠤⠄⣾⣄⣤⣤⢤⠦⡤⠴⡼⠇⠀⢀⠀⠀⠀⠀⠀⢸⠀⠐⠖⠰⠤⠴⠤⠦⠂⠒⠒⠚⡅⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢣⠀⠀⠀⠀⢻⡳⠤⣤⣠⣄⣤⣀⣄⣤⣠⡤⣠⠤⡔⡆⠀⠈⠀⠐⠂⠀⠀⠘⠓⠆⢤⠀⠀⡘⠇⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦⡜⣧⠀⠀⠁⠈⡒⠉⠠⠀⠀⠐⢌⠲⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠰⠀⡄
⠀⢀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠠⠤⣼⣧⡀⠈⠀⠁⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⢀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⣀⣠⠬⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⡇⠀⠈⠐⠂
⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⢦⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⢀⡀⠀⣨⠤⠀⠈⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠁⠉⠉⡁⠀⠐⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠶⠿⠛⠛⠛⠛⠛⠛⠿⠶⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣀⣠⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢰⠂⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⡆
⠀⠀⠀⠀⠀⢸⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠘⡄
⠀⠀⠀⠀⠀⢰⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣴⠃
⠀⠀⠀⠀⠀⢼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⢀⣠⣧⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣼⡅⢛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⡆
⠀⠀⢀⣿⢱⣿⣿⢻⣿⣿⣿⡄⠀⠀⠀⣼⠃⣿⡇⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠟⢁⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠊⢹⡆⡀
⠀⠀⢸⡏⢸⣿⣿⣸⣿⣿⡟⡇⠀⠀⠀⣿⣄⣿⠇⢤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⣾⣦⣼⣷⣧
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠄⠀⠀⠀⠀⠛⣿⣿⡄⠀⠀⠀⠀⠀⣼⢳⣿⣷⢸⣿⣿⣇
⠀⠀⠸⠇⠘⠛⠛⠻⠟⠿⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⣸⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⣸⠃⢸⣿⣿⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣤⣀⣿⣀⣤⣿⣿⣿⡤⠀⠀⠀⡿⠀⢸⣿⣿⢈⣹⣿⣿⣧
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⡟⢸⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣶⣶⣤⣤⣤⣤⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠀⠛⠛⠃⠒⠛⠛⠛⠛
⠀⠀⢸⡇⢸⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⢸⣿⣿⣾⣿⣿⣿⣿⠀⠀⢶⣤⣤⢀⣀⣀⣀⣀⣀⣤⣤⣵⠂
⠀⠀⢸⡇⣺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣾⣿⣿⣠⣿⣿⣿⣿⠀⠀⢸⣿⡃⠀⢙⣟⡓⠀⢹⣿⣿⣿
⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⣀⣿⣥⣀⣸⣿⣿⡇
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠘⠷⣶⣤⣤⣤⣤⣤⣤⣶⠾⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⠈⠍⠈⠉⠙⠿⠿⣿⣛⠃⠉⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠒⠊⠡⠤⠤⠍⣤⣥⣄⣠⡤⠤⣤⣤⣀⣀⣀⣈⢀⢀⣠⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠂⣉⣁⣐⣀⣀⣈⣀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠃⠀⠀⠏⡁⡀⠀⢀⣽⡿⢋⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⠈⠉⠉⠩⢉⣿⣿⡟⢿⣿⡿⡿⣿⠛⢲⠒⠲⢐⠀⠀⠀⣠⣤⣿⣿⠿⠟⣋⠥⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⠃⠀⠙⠀⣢⣤⣶⣧⣤⣬⡖⠻⠶⠟⣛⠭⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⣀⣀⠠⠀⠰⠆⠈⠻⣿⣿⣿⡿⠟⢁⡠⠄⠒⠉
⠀⠀⠀⠀⢀⠔⠁⠀⠐⣀⣠⣀⣀⣄⣤⣄⣰⣠⢴⠶⠻⠿⢠⣠⢀⢠⣶⣷⠶⠖⢛⣫⠵⠚⠉⠁
⠀⠀⠀⡰⣃⠀⠀⢠⣾⡿⣿⡝⠛⢻⣿⣟⣙⣧⣦⣦⣧⣷⣿⡿⠜⠌⣉⠥⠖⠊⠁
⠀⠀⠀⣷⣿⣿⣿⣠⣽⣾⣿⣿⣶⣾⣿⣿⣷⣿⣿⡿⠿⢛⡯⠗⠊⠉
⠀⠀⠀⠙⠿⣛⡿⠿⣿⣿⣿⣿⣿⣿⠻⡟⢛⡭⠷⠒⠉
⠀⠀⠀⠀⠀⠀⠉⠘⠒⠒⠒⠒⠒⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠤⠤⠴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠙⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠆⠀⠒⠛⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣶⣶⡟⠒⠀⠀⡀⠀⠀⠀⣴⢯⠘⡍⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⠟⠣⠄⢂⠀⠄⠀⠀⠀⠾⣞⣾⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢈⣙⠧⠻⣀⠀⠀⣿⣷⡆⠀⠀⠀⠀⣌⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⣸⡿⠿⢤⡄⣡⢐⣿⣿⣿⡀⠀⠀⠀⠀⠈⢈⣁⠁
⠀⠀⠀⠀⠀⠀⢀⣷⠾⠿⡁⠉⠀⢹⣶⠂⢹⣿⣽⣏⠀⠁⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⣾⠻⠆⠀⢷⡎⠐⠛⠫⣴⣿⣟⠁⢭⣤⡃⠀⢸⠋⠀⠀⠀⠀⢀⣠⣶⡿⠈⢀
⠀⠰⠐⠀⣦⠛⠁⢹⣄⢸⣿⠧⠀⠠⣤⡿⡧⣭⡤⠓⢩⢧⠀⠀⠀⠀⠀⠀⠐⠛⠉⡅⠂⠀⠀⠀⠀⢲⠒⠀⠂
⠀⠀⠀⠀⡇⠁⠀⠉⠙⢻⠉⠓⢶⠈⢈⡏⠉⠉⠁⠀⢸⠀⠘⠖⠀⡄⠤⠀⠀⠢⢠⡄⣰⣷⣶⣤⣄⡘⠈⠁
⣀⣂⣒⣛⢓⣒⣒⣐⠒⠚⠒⣒⣒⣒⣚⣓⣀⣒⣒⡂⣖⣀⣀⡐⣚⣓⣒⣓⡐⠚⠚⠒⣓⣛⣛⣛⣓⣀⣒⣒⣂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣶⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⢜⠀⠀⠀⠠⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠳⠐⠊⠁⠀⢸⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣈⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣟⣿⣿⣿⣿⣿⣿⠻⢻⣾⣿⣟⣡⣤⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠻⠟⠉⠉⠉⠉⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⡀⣾⣿⣿⠈⣻⣿⣋⡙⠿⠟⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⡄⠋⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢛⣿⣿⣿⣉⣿⣷⣤⠹⣿⣿⡗
⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠙⢿⣿⣿⢆⢛⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠁⠀⠀⣷⡄⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄⢰⣿⣿⣦⢾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⣦⠀⠘⠿⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⣿⣶⣾⢿⣿⣟⢠⣭⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⣻⣤⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠻⣿⠟⢠⣿⣿⣧⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠉⣿⡟⠀⠈⠙⡃⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⣾⣷⡆⣘⣿⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⣀⡀⠀⠀⠀⠀⠄⠀⠐⠛⠃⡀⠀⢠⡟⠒⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣼⣿⣿⡄⣾⡧⣽⣧
⠀⠀⠀⠀⠀⠀⠘⢀⡞⣁⠠⠃⠀⠀⠈⠀⠠⠘⡇⠀⣠⡟⠀⠀⠸⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢟⣀⣿⢾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠈⢳⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠆⠀⠀⠀⠀⠀⠈⠄⠠⠋⠀⠀⢰⠁⢰⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡍⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠙⡃⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣶⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⡛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡏⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠋⢳⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣿⣿⣿⣿⣟⣿⣿⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⢀⠄⡀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠻⣄⠈⠁⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠿⠛⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⢰
⠀⠀⠴⢲⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠤⠴⠶⠚⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠤⠤⠄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⢀⠀⠐⢦⡀⣀⢸⠀⠀⠀⠀⠀⠃⣠⠖⠉⠀⣀⢀⣀⠀⠀⠢⡄⣠
⠀⢠⡇⠀⣀⠀⠤⠤⠄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢰⠋⢧⡀⠀⠀⠀⠀⠀⠀⠉⣀⡼⢺⠀⠀⠀⠀⠀⠀⠳⠄⡀⠀⠀⠀⠀⠗⠠⢀⣷⡏
⠀⢸⣷⠋⡀⠛⠀⠀⢂⡴⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠛⠓⠒⠒⠒⠚⠋⠉⠀⡾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠤⣐⣽⠟
⠀⠈⢿⡋⠃⠜⠀⠒⠒⠈⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠦⣌⣙⠒⠚⠛⣋⣡⢄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠶⠲⠶⡛⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢭⣭⣭⣽⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠐⠂⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⡸⡄
⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⣀⡀⠀⠠⠚⠁⠁⠀⠮⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠦
⠘⠁⣬⠁⠀⠀⠀⠀⠀⠀⠘⠮⣏⠄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠚⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠔⡁⠈⠃
⠀⠀⠀⠒⠲⠶⠶⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠤⠴⠖⠋

⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⢀⢻⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠉⠁⠀⠀⠀⠀⡀
⠀⠀⡳⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⣾⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⡿⠻⣶⡀⡀⠀⠀⠀⠀⠘⡇
⠀⢰⣾⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⢾⣈⣻⣿⡀⠀⠀⠀⠻
⠀⡞⢯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣅⠀⠀⠀⠈⠻⣙⠁⠀⠀⠆⠇
⠀⣻⣶⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⡜
⠀⡶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⡟⣺⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀
⠀⣛⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠮⠈⠻⡙⢻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢭⣤⣀⠈⠙⢷⡄
⠀⣫⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠁⠢⣄⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣀⣀⡀⠈⠙⠓⠂⠹⣿
⠀⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⠀⠀⠀⠀⠀⠀⠈⢷⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠻⣭⣉⠃⠀⣀⠀⠠⣿
⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠉⠛⠛⠛⠃⠀⣸
⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡼⣏⠈⠟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⣯⠛⠳⢤⣀⠀⠀⠀⠀⢹
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠑⠙⠣⠘⠽⠿⣷⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠈⠳⠶⣤⣠⣥⣤⠄⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⣀⣀⠀⠀⠁⠀⠀⠸⣿
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡅⣀⠀⠀⠀⠀⠀⠀⠈⢫⣻⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢬⣉⣉⣀⣆⣀⠀⢸⣿
⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠉⠉⠉⠉⠉⢠⣾⠏
⠀⠀⠀⠈⠀⠀⠀⠀⢠⡌⣿⡜⢻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡷⢤⣴⣶⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠘⣧⡜⠣⣽⣧⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠻⣄⠘⣿⣧⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢀⠻⡀⠀⠀⠀⠀⠈⠳⣏⣿⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⣾⣧⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⣴⡗⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀
⠀⠀⠀⠀⠀⣼⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢀⣴⣴⣿⣶⣶⣤⣤⡀⠀⠈⢦⡀
⠀⠀⠀⠀⢀⠱⣿⡔⡽⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠀⢀⣰⡿⠋⠀⠀⠀⠈⠙⣿⣷⡄⠀⢺⣷
⠀⠀⠀⠀⣰⠄⠙⢧⡀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡁⠀⢘⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠰⣻⠇
⠀⠀⠀⢰⣧⠀⠀⠀⠈⠲⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢲⣿⠇
⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠄⠀⢿⣧⣄⡀⡀⠀⣀⣠⣾⠏⠀⠠⣿⣿
⠀⠀⠀⣦⠘⢳⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⣄⠀⠘⠛⠛⠟⢿⠟⠭⠉⠀⣠⣬⣿⠃
⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣹⣷⣤⣄⣄⡀⠀⡀⢀⠀⣤⣤⣿⠟⠁
⠀⠀⠀⠘⠫⢷⠆⡤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠳⠿⠷⠷⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⣀⣬⣭⣿⣿⣿⣿⣧⣤⣄⣀⠈⠥⢜⢇⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⣼⣭⣻⣿⣿⣿⣿⠀⠐⣶⠮⠁⠈⠉⠒⠀⠀⠒⠈
⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⡟⣿⣿⠟⡟⢻⡓⢠⡄⠈⢠⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠙⢡⣾⣿⣿⢹⢟⢣⣶⠈⠈⠇⢸⣟⠳⣾⡆⠀⣿⡀⣰
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⠀⣀⣿⣆⠀⣀⣼⣿⢠⣾⠟⠛⢻⡞⠛⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢃⣤⣿⣯⣌⣾⣿⣿⣄⠀⢘⣄⣀⣄⣿⣆⣴
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⣿⣿⣛⣿⣿⣿⡿⢿⣿⡌⠁⢻⣿⡿⠛⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⢹⡏⠀⠀⢨⣿⣦⣎⠈⢿⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⠿⠾⢷⠋⠀⢸⣿⠷⣿⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣤⣼⠷⠒⠻⠃⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⢿⣷⣠⣼⡟⢻⣷⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣾⠋⠉⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⡿⣦⣠⠜⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢦⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⠁⠀⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡭⢲⣄⡠⠞⠓⠛⠒⠚⠓⠺⣄⢀⡔⠊⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣁⢀⡠⡟⠀⠀⠀⠀⠀⢰⣷⢄⣼⣷⠛⠉⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⣦⠀⠀⢼⠆⢿⠀⣰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡉⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢟⡃⠢⠠⠤⠤⠶⠶⠶⢦⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣔⣢⠀⣔⢲⠀⠀⠀⠀⣷⠀⢠⢲⣥⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠈⣁⠤⠔⠒⠒⢿⠐⠻⣽⠿⣟⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢆⣀⣠⣶⠉⠀⠀⠀⠀⣀⠆⠀⠀⠉⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⡴⣦⡬⠭⣤⠠⡴⠶⠖⠚⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢿⣿⠏⠀⠀⠀⠀⣾⣶⣦⠀⠀⣠⣼⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣄⢒⣒⣒⠒⣒⣒⣢⡤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠉⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠉⣿⠁⠈⠉⢉⡉⠭⠀⠉⢉⡿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠑⠢⢀⡙⠋⢀⣀⣤⣎⡇⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢾⠆⠀⠀⠀⠀⠙⢹⡃⢸⡿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣧⠀⢀⣤⡤⠶⠤⠄⠰⠢⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢰⡶⠀⠀⣸⠿⠀⠀⣴⡇⠀⠀⠀⠀⡜⠉⠉⠳⡀⠀⠀⢸⠀⣾⣷⢸⣾⡇⠤⠴⡞⢉⢉⣑⠒⢒⣢⡤⢼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠸⡯⣶⣶⣾⣿⣿⠀⠀⠀⢰⡇⠀⠀⠀⣧⠀⠀⢸⠀⠙⠋⠀⢧⣷⠻⠇⠀⠀⠀⠀⢸⡏⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢰⣶⠀⣀⣀⠻⣿⣿⣿⣿⣇⠀⠀⠸⡇⠀⣠⠄⢿⠀⠀⢸⠀⠀⠀⠀⢸⢿⠳⣄⠀⠴⠆⠀⠀⠀⣠⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠛⢻⢀⣿⣿⣿⣿⣿⡀⠀⠀⣇⡜⠁⠀⣿⠀⠀⡜⣇⠀⠀⠀⢸⢸⡄⣨⣍⠒⠒⠒⢀⡉⠈⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢿⣿⣿⣿⣿⢇⠀⠀⠸⡇⠀⠀⡇⠀⢠⠃⡏⠀⠀⠀⠸⡈⣇⠈⠁⠀⠀⠀⠻⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠀⠈⢆⣀⣠⣇⠀⢰⣧⣤⡿⡴⢋⠀⣀⣀⠀⠉⢻⣶⠄⠀⣠⡄⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠀⠀⡴⠁⠉⠑⠒⠠⢾⡿⠷⠟⠢⠿⠿⠿⠓⠞⠈⠉⠀⠀⠳⡄⣠⣿⣦⣄⠉⠁⢀⣄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠚⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢚⣛⣛⠒⠲⠦⢤⣄⣀⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠾⠷⠶⠤⣤⣄⣀⠀⠀⠈⠉⠒⠠⢄⡉⠛⠶⣄⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠉⠉⠀⠀⠀⠒⠠⠄⢀⣀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠀⠉⠐⠈⠓⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠴⠟⠛⠛⠛⠛⠛⠛⠲⠦⣤⣀⠀⠀⠀⠈⠀⠀⠠⠄⣈⣙⣦⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⢠⠚⠓⠒⠈⠁⠀⠀⠈⠀⠈⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⡰⠁⣀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠊⠁
⠀⠀⠀⡇⠛⠉⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉
⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠉⠒⠒⠐⠒⠒⠒⠒⠒⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⡾⠋⠡⠁⢈⢹⠆⠀⠀⠀⠀⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⡇⢻⣿
⠀⠀⢰⡦⠤⠴⢶⡆⠀⠀⡘⠀⠈⠈⠉⠙⢇⠀⠀⠀⠀⠀⠀⣩⣗⡢⢀⡝⣈⠔⠲⣄⠀⠀⣿⣿⣨⠇⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⢸⡇⠂⠺⢻⡇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⠾⠀⣠⡶⢻⡃⠸⣿⠟⠺⠄⠀⡏⠛⠸⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿
⠀⠀⠘⣇⠀⠀⣸⠁⠀⠸⣄⡀⠀⠀⣀⣀⣸⠃⠀⠀⢠⡏⡀⠚⠿⠁⠘⣿⣶⢿⣁⠌⠀⠀⡄⢸⢸⠀⠀⠀⠀⠀⠀⣠⣧⣼⣿⣄
⠀⠀⠀⠙⢷⣾⠃⠀⠀⠀⠙⠷⠶⣶⣾⡿⠋⠀⠀⠀⠸⠏⠀⠀⠀⠀⠒⠈⢳⠴⠋⠀⠀⠀⡅⢸⠠⠀⠀⠀⠀⢀⡾⠋⢉⣿⣿⡟⣳⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⢀⠒⢋⣦⡀⠀⠀⠀⠀⣠⡴⢴⡦⢔⠀⠀⠀⠀⡇⣿⠘⡀⠀⠀⠀⢸⠁⠀⣼⣿⣿⡇⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠢⢾⠉⢙⠇⠀⠀⢤⣐⢃⠎⢹⡖⠁⠀⠀⣸⠷⢿⠔⢧⠀⠀⠀⢸⠀⠀⠻⠿⣿⡗⠛⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹⡆⢱⡞⢀⠀⠀⢰⣇⠀⢠⠀⠈⣆⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠰⢿⣭⣷⠂⠀⠀⠀⠀⠀⠠⣤⡄⠀⠁⠀⠈⠀⠀⠀⢠⣯⣿⡆⢸⡇⠀⢹⣆⠀⢸⠀⠀⠀⠀⣙⠀⠀⣿
⠀⠀⠀⠘⠯⠿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣠⠀⣚⣫⡽⣧⡆⡀⠀⠀⠀⠀⣸⣿⣇⣙⣿⡏⠀⠈⣿⠀⢸⠀⠀⠀⠀⢩⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⢬⠴⣚⡿⡬⢇⣰⡼⡵⢫⠇⠀⠀⠀⣿⡿⠉⠀⢸⡏⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡄⢐⡆⠀⠠⠼⠃⠀⠀⠀⠀⢰⣟⣺⣽⡫⢞⣸⢛⣿⣉⣻⢤⣟⢷⣀⠀⠀⠀⣿⣇⠀⠀⢸⡇⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣩⠗⢣⣎⣸⣶⣾⣉⣻⡷⣦⣉⣗⣆⠮⣭⡶⠀⠀⣿⣿⠦⣤⣼⡇⠀⠀⣿⠀⢸⡇⠀⢺⣿⣿⡟⣿⢷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣛⡶⠷⠳⢲⡳⢾⢭⠷⣿⣧⡶⠏⢿⣭⡮⢽⣒⡿⠿⠧⠀⣿⣿⣠⣴⣾⡷⣄⣰⣿⠀⢸⡇⠀⢸⣿⣿⣇⢿⣿
⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠁⠀⠮⠗⠑⠚⠣⣇⣶⣷⠞⠛⠙⠻⠦⠀⠀⢿⣿⣿⣿⣼⡇⠈⢻⣿⠀⢸⣇⣀⣸⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠒⠛⠉⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠠⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇
⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣇
⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣆
⠀⠀⠀⠀⠀⡠⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⡀⠀⠀⠀⠀⡀⠀⠀⠈⢳⡘⣧
⠀⠀⠀⡀⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⡦⠶⠶⠦⣤⡀⠀⣠⡶⠛⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⢦⣀⡾⠋⠀⠀⠀⠀⠈⢻⣤⣿⣤⣀⠀⠀⠀⣨⣧⣀⡀
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠉⠻⣦⠟⠉⠀⠈⠙⠳⣄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣿⠀⠀⠀⣠⡶⠋⠉⠉⠛⢦⠀⣠⣤⠤⠼⣧⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠹
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⢧⣀⣠⡏⠀⠀⠀⠀⠀⠈⡟⠉⠀⠀⠀⠀⠙⢧⡀⠀⢀⡇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣧⠀⢀⡴⠋⠀⠘⣇⠀⠀⠀⣀⣠⣄⡁⠀⠀⠀⠀⠀⠀⠈⣧⠴⠾⠷⠦⣄⠀⠀⠀⢠
⠀⠀⠁⠀⢀⠀⠀⠠⠠⠄⠂⠂⠒⠂⠉⠀⣀⠀⠀⠀⠀⠙⢦⣼⠁⠀⠀⠀⠈⠳⣴⠛⠁⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣤⠶⠋
⠴⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠄⢻⡄⠀⠀⣠⡤⣼⡇⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣄⣼⡃⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠂⠀⠀⠀⠀⠙⢳⠞⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠈⠙⢷⡄⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⡋⠙⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡴⠖⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⣀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⣴⠞⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢛⣡⣤⣤⣀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⢻⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⣀⠀⣀⡀⠀⠚⠉⠛⠦⠀⠀⠀⠀⣤⣾⣁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⠞⠉⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⣤⠴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣤⠶⠛⢉⡿⠒⠛⠁⠀⠀⠀⢤⠀⠰⠞⠳⢤⡀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣹⠷⣄⣀⣀⣀⣴⢿⡄⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⡟⠀⠀⠉⠉⠉⠀⠀⢹⡶⣴⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⣀⣀⣤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⡖⠳⡄⠚⢭⠀⣼⠍⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⢧⠀⠑⠚⢀⣈⣉⣀⣉⠁⠀⠀⠼⠓⠁⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠣⠔⠀⣠⡴⠚⠋⠉⠉⠉⠉⠉⠉⠛⠶⣤⡀⠘⢹⠊⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠉⢀⡴⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠉⠳⣄⠐⠏⠂⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⠂⠀⠻⣤⡀⠀⠀⠀⠀⢯⣤⣤⠀⣬⠇⠀⠀⠀⠀⠀⠈⢧⡀⢲⠻⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⠶⣄⠀⠀⣸⡧⠤⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠓⣶⠏⣤⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡏⣸⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⣤⡀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⣄⠀⢀⡾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠀⠀⠘⢦⡀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠈⠳⠞⢀⠘⠾⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣚⠇⠀⠙⢦⣀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣠⠄⠀⠀⢁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠊⠓⢀⡉⠛⠶⠤⣤⣀⣀⣀⣠⣤⠴⠞⠋⡁⠰⣍⢧⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢠⠏⠁⡤⢤⡀⢀⣤⠀⣠⠤⠀⠀⠹⡔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁⢈⣳⠄⠸⠭⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡠⠊⢸
⠀⠀⠀⠀⠀⠀⠀⣎⡁⣅⣀⡸⠛⠢⡤⠻⡇⠀⢢⠀⠠⠀⠀⠀⠀⠀⢀⠄⢘⠤⠠⢁⠀⠦⣮⠆⠑⢼⡄
⠀⠀⠀⠀⠀⠀⡆⠀⡌⠀⠀⢱⠀⢀⡿⠀⠁⢤⠐⢢⠀⠁⠀⠀⢀⠎⢘⠄⣎⠀⠀⡎⠀⠀⢘⡆⠀⢲⠋⠀⠀⢆
⠀⠀⠀⠀⠀⢄⢸⠁⠀⡤⠤⣞⠀⠈⠻⠄⣠⠞⠀⡜⢢⠀⠀⠀⠀⠁⠺⡀⢸⠁⠀⠈⢠⠤⠎⣇⠀⢀⡇⢀⢀⠎⠀⢱
⠀⠀⠀⠀⠀⡆⢠⠃⠺⣀⠀⣸⠆⠐⢄⣠⠿⣄⠠⣇⠰⠀⠀⠀⠀⠀⠀⠀⢈⠄⡀⠠⡆⠀⠀⢹⠁⢹⡄⢨⡇⠀⣱⠁
⠀⠀⠀⠀⠘⡀⡨⠒⠞⠁⠙⣧⡀⢀⣸⣁⣀⢼⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢣⢰⡁⠀⠑⡄⠄⠃⢠⠈⠀⠣⢱⠐⠁
⠀⠀⠀⠀⠀⠀⡱⢤⠊⠀⣾⠁⠈⡟⠁⠈⡧⠰⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡐⠁⠀⢢⠠⠎⣀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⢇⣀⡦⢴⠁⠀⣏⡩⠄⡈⢹⠖⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠒⢧⠀⠀⠜⠀⠀⡸⠘
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡓⠂⠑⣄⢀⡏⢹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣰⠋⠈⢹⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠱⠄⠰⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡢⠀⢻⠄⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠂⠺⣀⢠⡏⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⡁⠀⡸⢀⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⣸⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡸⠀⢤⠎⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⡟⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠓⣦⠀⠀⢀⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡏⢀⠖⠉⢰⠁⠀⢀⣠⠖⠛⠉⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⡇⠀⢀⣷⠋⠀⠀⢸⢀⡴⠋⠀⠀⠀⣠⠏
⠀⠀⢀⡶⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢳⡀⠀⠀⠀⢰⠃⠀⢸⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⡰⠃
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⡜⠀⠀⠀⢧⠀⠀⠀⣼⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡠⠤⢄⣀⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢀⠇⠀⠀⠀⢸⠀⢀⡞⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⣤⠋⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠉⠉⠓⠦⣼⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢄⣀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠉⠓⢴⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⢀⣀⣀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢳⣄⣤⠤⢤⣄⣀⠀⠀⠀⢳⡄
⡴⠖⠒⠚⠛⠋⠉⣡⠖⠋⠉⠉⠉⠉⠙⡇⠀⠀⣠⡤⠴⠶⠦⢤⣀⠀⠀⠀⢸⣆⣀⣀⣀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⣷
⠘⢦⣀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢧⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⢦⡔⠋⠉⠉⠉⠉⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⣿
⠀⠀⠀⠉⠑⡞⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢷⠃
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣸⠓⠦⡀
⠀⠀⣠⠞⠉⢧⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⢦
⠀⡼⠁⠀⠀⠈⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣠⠎
⢰⠃⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠤⢤⡤⠖⠋⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠒⠊⠁⠀⠑⠦⣄⣀⣀⣀⣀⠴⠚⠁⠀⠀⠀⠈⡇
⠀⢧⠀⠀⠀⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠣⡀⠀⠀⠀⢀⡞⠀⠀⠙⠲⠤⣤⣀⣤⠤⠖⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡷⢤⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠈⠓⠢⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢀⣀⠴⠋⠲⠤⣄⣀⣀⣠⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⠉⢙⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⣤⠒⠊⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣄⣀⣀⣀⡠⠴⠊⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⠀⠀⣀⡤⠷⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠁⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠑⠦⣄⣀⣀⣀⣀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠖⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣀⠤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⠟⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣛⠿⢿⣿⣿⣿⣯⣭⡵⠶⢛⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣄⠀⢤⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣉⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠶⠒⠋⠐⠒⠂⣨⡿⠷⠖⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠶⠶⠶⠶⠶⠖⠛⠛⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠚⠛⠒⠒⠒⠒⠲⢄
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⡏⠀⠐⠤⣀⠀⠀⠀⠑⠢⢀⡀⠀⠀⢀⠀⠉⠢⣄⡀⠐⡄⠀⠀⠁⠂⠀⢑⣀⣀⣠⠤⠔⠋
⠀⠀⠀⠀⠀⠑⠦⠤⠤⠬⣭⣤⣤⣄⣀⣤⣤⣤⣬⡥⠤⠤⠤⠴⠒⠓⠒⠒⠛⠋⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠶⣄⠀⠀⢰⠚⠑⠲⠤⠤⢤⣠⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⠀⠈⡆⠀⡜⠀⠄⡀⠀⠀⠀⠀⠀⠈⠉⠉⡉⠝⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡺⠋⠁⠀⠀⠤⠊⠀⠐⠀⢀⡇⠀⢇⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⣠⠔⠋⡠⠊⠀⠀⠑⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠉⠉⠉⠑⠒⠒⠒⠢⠤⠤⠤⠤⠄⠐⠒⠁
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉
⠀⠀⠀⠘⣄⣀⣀⣠⠤⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⠤⠤⠄⠀⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣢⡥⠖⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣊⠒⠊⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠑⠣⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡚⠁⠀⣀⠀⠀⠀⠀⠀⠸⡀⠂⠀⠊⠄⠂⠀⠀⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣇⠈⠐⠂⢄⡀⠀⠀⢀⢀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢐⡀⠢⠀⠀⠀⠈⠂⠀⢂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠺⣦⣠⡀⢠⡈⠑⡦⠁⠀⠀⠀⠀⠀⢀⠘⣤⠐⠀⠀⢀⠀⢀⠀⠡⠀⠀⠀⠀⠈⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⠠⢈⡙⠷⣤⡀⡱⠁⠔⠀⠀⠀⢀⠘⡉⠁⠈⠏⠉⢡⠈⠂⠀⠂⠀⡀⠀⠀⠀⠀⠘⡌⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠍⣒⠢⠀⠀⠜⠿⣧⢀⠀⠀⡠⢀⠀⡢⡘⠀⠹⢠⠄⠀⠃⠙⡀⠈⠀⠠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠈⢃⠀⠀⠀⠃⠈⠛⣷⣎⠀⠅⠠⠊⠄⠂⢸⠸⠂⠀⠄⠙⠅
⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠐⠀⠄⣀⠁⠒⢰⠂⠀⠀⠄⠙⢿⣦⣀⢀⠕⠂⢐⠰⠒⠉⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆
⠀⠀⠀⢐⠀⡀⠀⠀⠁⡀⡐⠈⠈⠀⠀⠄⣁⢈⠀⠀⠀⠀⠊⠀⠙⢿⣷⣔⠀⢸⢸⠀⡊⡀⢲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢈⠖⠒⠀⢄⣀⣸⠀⠀⢐⠀⠀⠀⠔⠁⢝⢿⣧⣼⠸⢧⢃⣠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠔⠀⠀⢠⠉⣙⠀⠀⠌⠀⠔⠐⢀⠀⢐⠄⠀⢻⣿⡍⠀⠀⢉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢢⣤⣥⠐⡀⠑⢛⠀⠀⡀⠀⠀⠂⢀⠔⠑⠀⠀⢸⢸⣷⣧⣤⠸⢂⡄⠀⠀⠀⠀⠀⡀⠀⣤⡤
⠀⠀⠀⠀⠀⢢⠀⠀⢀⠔⠁⢀⠀⢀⡀⠈⠫⠉⠀⠀⠀⠀⡀⢠⠔⠀⠔⠀⡄⢸⢀⣀⣈⠩⣤⣬⠀⠀⠀⠀⠀⠀⠁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⢖⢀⠁⠀⠰⠀⠀⠀⠈⠄⠀⠘⠀⠀⠀⠀⠠⠃⠀⠠⠀⠀⠢⢼⢤⡆⠀⢶⣧⡲⢶⣶⠰⠶⢤⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢄⠸⡀⠈⠀⠀⡀⠀⠑⠀⠄⠀⢀⣺⢀⡒⠀⠀⠀⠀⠈⠙⢷⡂⠐⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⡀⢄⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠄⠀⠈⠄⠀⢀⣠⠌⠁⠈⠀⠀⠀⠀⠀⠀⡡⡆⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢐⠠⠀⠀⡀⠀⠈⠀⠈⠑⠒⠐⠒⠒⠚⠉⠉⢀⠠⠠⠈⠀⠀⢀⣠⠔⠺⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠠⡠⠒⡀⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠘⠁⠒⠤⢤⢀⣀⣀⣌⡁⣠⢄⡄⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡞⠀⠀⠀⠀⠌⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠈⢦⣈⢢⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠳⠾⡥⠄⢀⠀⠀⠀⠀⣀⠀⠴⠶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠛⠁⠀⠀⢀⡐⣶⣵⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⢷⡀⠠⢀⠀⠀⠀⠀⠛⠷⢮⣇⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡂⠀⠙⠄⠀⠈⠀⠀⠀⠛⠲⡂⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢦⡀⠉⡦⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠈⣷⣦⠀⠀⠀⢠⣿⠀⢰⠀⠀⠀⠈⣍⠀⠈⠃⢁⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣿⣿⣷⠀⠀⢘⣿⣦⠈⠀⠀⠐⠀⠈⣦⡦⢠⡀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣈⣿⡇⠘⣃⡤⠞⢹⣿⣧⣤⣀⠀⠀⠀⠀⠑⠥⣻⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⢤⣤⠤⢿⣷⡀⠉⠀⠀⠀⢚⣿⣟⣿⣧⡶⢦⣀⡀⠈⢀⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⠏⠀⠀⠀⣘⣷⣦⣄⣀⣀⣠⣿⣾⠩⣦⣀⣠⣩⣿⡷⣎⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠸⣤⣀⣴⠏⠉⠀⠈⠙⢿⣭⡿⠉⠀⠀⢀⢻⣿⣿⠛⢿⣷⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⣰⠟⣿⠉⠀⠀⠀⠀⠀⢢⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢻⠀⠀⠀⠀⠀⢰⠋⣿⡀⠀⠀⠀⣸⣤⣿⣽⡄⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠳⣄⠀⠀⢈⣰⢏⡡⢿⣦⣄⣠⣼⣿⢾⠿⡤⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣆⣐⣩⠿⠉⠉⢿⣿⡿⠁⠀⢨⣍⢿⣷⡄⠀⣀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠰⣾⡟⠀⠀⠀⠀⢸⣶⣿⡵⢧⣾⣯⠿⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⡀⢿⣷⠀⠀⠀⣀⡿⠋⠀⠀⠀⠀⠉⢶⡀⠀⠈⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣀⣘⣚⣵⠷⠦⢄⣿⠁⠀⠀⠀⠀⠀⠀⣼⣥⡀⣢⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠁⠀⢀⠈⢿⣇⠀⠀⢀⢀⣤⢸⣿⣿⣿⣿⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡶⣿⣶⣤⣤⣼⣤⣟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⣽⣿⠏⠈⠉⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣼⣿⣿⡇⠀⠀⠀⠀⢀⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⠉⠳⣄⣄⣀⣴⣿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣶⣷⣾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠉⠉⠉⠉⠉⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢰⣿⣿⣿⣿⣿⡗⠀⠀⠀⠉⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⠟⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣤⣾⠟⠁⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⢿⣧⠁⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣠⣾⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣠⣾⠟⠁⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧⡀⠀⠈⠻⠶⠶⠶⠶⠶⠾⠃⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣤⣄⣀⣀⣀⣠⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⣶⡀⢠⠒⠲⠐⣶⠒⡴⠒⢦⢠⡒⠦⢰⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠼⠒⢧⠸⣄⡤⠀⠾⠀⠳⣀⡼⠠⣍⡷⢸⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠂⡴⠲⡄⡖⠒⢰⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⡟⠻⡄⣏⣉⢸⣉⡁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⡂⠀⢃⠀⠀⠀⠀⠀⢀⠐⠍⠻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢁⢄⣄⢊⡄⠀⠀⠀⠀⢸⠸⡓⢦⠈⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⠁⢘⢩⢂⠀⠀⠀⠀⠘⠃⠻⢅⡡⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡏⡠⠊⡀⠘⠀⠀⠀⠀⠀⢷⣩⡢⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠏⡠⣢⠂⠈⣀⠃⠀⠀⠀⢸⣃⠙⠦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠞⢁⠀⠘⠉⠀⠀⠀⠀⠀⡹⣮⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡰⡋⢔⢁⡔⡃⠀⠀⠀⠀⠀⠆⣅⣈⡛⠮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢔⡵⠋⡠⠁⠇⠀⠀⠀⢀⣁⡙⣷⣄⣝⡤⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠋⡠⠞⣀⡄⠀⠀⠀⠀⢠⢉⠸⠗⢠⣤⢴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⢀⡶⠹⠁⢀⠀⠀⠀⢠⢈⣀⠀⠀⠋⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡴⠋⡐⠁⠼⠈⠀⠀⠀⠘⢀⠉⣁⣤⡤⠄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠐⠋⣠⡤⡄⠀⠀⠀⠀⠀⠀⠃⠸⠏⠀⢈⡯⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⠞⠅⡐⠀⠄⠀⠀⠀⠀⠀⠿⢁⣀⣤⡀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠏⢀⠌⠐⠀⠀⠀⠀⠀⠈⠀⣤⡈⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠑⢋⡶⠢⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣤⡀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢀⠞⠡⠂⠂⠀⠀⠀⠀⠀⠃⡴⣶⠾⠛⢀⠹⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⣀⣱⠀⠇⠀⠀⠀⠀⠀⢸⢻⠆⠈⣡⣽⣯⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⣎⡿⢠⠀⠀⠀⠀⠀⠀⢸⣶⠶⠦⢶⣶⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡄⢀⠌⠀⠀⠀⠀⠀⠀⢸⡆⢀⣃⢀⣤⣄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠒⠊⠉⠉⠉⡉⣉⢉⠉⡉⠉⢒⠒⠒⠠⠤⢄⣀⡀
⢀⢶⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠕⠘⠚⠻⠲⠀⠀⡹⡆
⢸⠏⠑⠫⢔⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧
⣿⠀⠀⠀⠀⠈⣑⠊⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢟⡸⣧
⢻⡄⢀⡀⠀⢸⡹⡷⡀⠀⠉⠑⠫⠖⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⡆⣡⣿
⠀⡇⠘⠗⠀⠈⠧⣀⡅⠀⠀⠀⠀⣠⡀⠉⠑⠛⠵⣖⡤⣀⡀⡰⣵⣝⣷⡛⣿⣿
⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠁⠀⣠⢲⡶⣄⠈⠙⠺⣻⡇⢹⡿⢁⡿⣿
⢸⡆⠀⣠⣤⡀⠀⠀⣾⣹⠼⠟⡆⠀⠀⢸⣷⠅⠀⢈⠀⠀⠀⣿⣼⡎⠟⢛⢳⣿⡶⢶⣖⠒⠂⠠⠤⠤
⢸⡇⢸⣿⡟⠚⡆⠀⠙⢇⣀⠰⠁⠀⠀⠀⠙⠤⠴⠊⠀⣠⠶⡿⠙⡕⡀⣸⠛⣿⡛⢉⣉⠉⣉⣉⣈⡁⠉
⢸⡧⡀⠙⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠠⣷⣵⠂⢸⣷⡟⣏⣿⡿⠔⠀⠤⠦⠤⠔⠂
⠀⠙⠪⣕⡤⣀⠀⠀⠀⣴⢦⠀⠀⠀⣾⣶⡵⠛⠆⠀⠀⠉⠓⣔⣳⣿⣷⣿⣿⣃⣉⣉⣉⣭⡭
⠀⠀⠀⠀⠙⠳⢽⣦⣀⠈⠊⠀⠀⠀⠙⢏⡀⣀⠇⠀⠀⠀⠀⣿⠄⠦⢶⡿⠷⠺⠿⠖⢳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⢿⡏⣿⠍⠉⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣒⣄⡀⠀⠀⢠⡶⡄⠰⣷⢁⣼⣽⡯⠍⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⣤⡀⠉⠀⠀⠈⡿⣿⣟⣓⣒⣐⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣦⢄⡀⠀⣧⡯⠌⠥⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣿⠛⠛⡏⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠠⠄⠤⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡜⠁⠉⠁⠀⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢠⢤⠄⠂⠀⠀⠀⠀⠀⠂⠀⠀⠠⡀⢤
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⠀⠀⠀⠸⣶⣤⣤⣤⣆⣀⣀⣀⣐⣒⣒⣀⣀⣀⣀⣾⣼⣿
⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⢿⣿⣿⡏⠛⠋⠉⠉⠿⠩⠭⠉⠉⠈⣽⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠑⡣⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣷⣴⣇⠀⠀⠀⠁⠀⠀⠐⣰⡟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⡛⠆⠀⠀⢀⠀⢶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣧⣵⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⡷
⠀⠀⠀⠀⠀⢀⡀⠂⢠⠊⠇⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡄⢀⣡⡐⢀
⠀⠀⠀⠀⠘⠶⣽⣶⣊⣝⣶⡀⠈⣁⣒⣂⣭⡴⠂⠀⠀⠀⠀⠀⠐⠦⣀⢀⣉⠀⠀⠀⠀⢀⣀⣁⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠈⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠐⠄⠲⠾⠿⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⢠⣄⣈⣵⣔⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⢰⡴⣦⣤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠈⠉⠀⠈⠉⠉⠀⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡶⠠⠀⠀⠈⠑⠋⠈⠻⠟⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢿⣄⡀⠀⠀⠀⠀⠀⠠⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣥⣀⠀⠀⠓⠛⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣰⣶⢴⡖⢰⣆⢰⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⣦⣄⡀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠄




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢂⢄⠈⢰⡏⠀⠀⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣄⠀⠠⠜⠀⠀⠀⠀⣼⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⣾⡈⢳⣼⣷⢖⠀⠐⣉⡠⠘⠇⠀⠄
⠀⠀⠀⠀⠀⣀⠤⠀⠁⠀⠀⠀⠀⠑⣦⠀⠀⡀⢦⣴⡟⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠾⠻⠺⣿⠟⠁⠠⢚⡡⠑⠒⠂⠀⠘⠠⡄
⠀⠀⠀⠠⠀⠁⢀⣠⣠⣄⡀⠀⠀⠐⠈⠃⠄⠁⢻⣿⣅⢀⣠⠀⣮⣴⠂⠘⠛⣥⣄⣁⣠⣵⣶⣧⣤⣴⣄⣤⣤⣤⣤⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢶⣦⣄⡀⠀⠀⠀⢸⠏⠁⣤⡖⠛⢒⠚⠙⠛⢛⣿⣅⣤⠖⠻⡿⠝⠿⣧⣍⠫⡙⠛⢅⣹⠤⠀⢀⠀⠁
⠀⠀⠀⠀⠣⢀⠀⠀⢀⠀⠀⠀⠀⠉⢿⠟⢷⣦⣼⣶⣾⠞⣁⡀⠈⠙⣣⣬⣿⠿⠋⠀⠀⢼⣷⡀⠀⠘⢿⣿⣦⡌⠓⠂⠿⡖⠉
⠀⠀⠀⠀⠀⠈⠀⢠⡄⠴⠆⠐⠀⠁⣠⣴⣾⢿⠟⠉⡏⠈⣡⡴⠛⢋⡟⠫⠀⣀⠆⠀⠀⣼⠃⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣶⣿⣿⠟⠁⡈⠀⡆⠀⠚⠁⠀⠀⠀⠀⢀⣴⢋⡴⠁⢰⡿⠀⠀⠀⡅⠀⠀⠉⠻⣿⡀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠁⡀⠘⣥⣀⣧⣤⡄⢴⠸⠿⢾⡴⡿⠁⠁⠀⢀⣿⠁⠀⠀⠀⣧⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠆⠀⠀⠀⣠⣶⠛⠋⠀⠀⢀⡰⠁⢠⠟⠛⠿⢿⣧⣀⣀⣠⠎⠰⡇⠈⠀⢀⣼⡇⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠄⣾⠁⠂⡀⠀⠀⡀⠀⠙⠿⢿⣿⠀⠀⣅⠀⠀⠘⡟⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠤
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⢿⡅⠀⢳⣤⣴⣥⠀⠀⢀⡴⠛⠚⠲⣾⣿⠀⠀⠀⠀⠀⣰⣿⠻⣿⠁⠖⢠⠀⠀⠀⢻⡀
⠀⠀⠀⠐⠁⠀⠋⠒⠈⠁⠘⠈⠀⢀⡇⠀⠀⠉⠛⠻⣿⣿⠃⠀⠀⠀⠀⣼⠉⠳⡀⢀⣤⣿⣿⡟⢸⣿⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢶⡀⠀⠀⡠⠚⡋⡀⠀⠀⢀⣼⡿⠀⠀⢩⣿⡇⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⠃⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠸⢿⣿⣿⠁⠀⠸⣶⣶⣶⣾⣿⣇⣄⣤⣼⡿⠁⣿⣿⠉⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠇⠀⠀⠀⠉⠉⠋⠉⢀⣿⡿⣿⣛⢁⣠⣿⡏⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢾⣶⣿⠀⠀⠀⠀⣼⣿⠇⢹⣿⡿⠿⢿⣷⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣄⣤⣿⠟⠳⣷⣾⣾⣿⡟⠀⠀⣿⡇⠀⢘⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣣⡀⠀⣨⠋⠉⠁⢰⣤⣶⣿⣷⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⣹⣿⠛⣿⣆⠁⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢀⢀⡈⠉⢰⡠⢀⣤⣾⡏⠀⢿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⠀⠀⢹⠿⠛⠋⢠⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣶⣶⣿⠀⠀⠀⢸⣿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠉⢡⢀⣀⣤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠙⠛⠻⢿⣿⠉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣴⣶⣿⣧⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⢿⡏⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣻⡟⠛⠛⠛⠃⠀⠀⠀⠙⢿⣷⣄⠀⠀⢸⣿⣿⠀⠀⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⢸⣿⡏⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠘⠿⠷⣄⡀⠀⠀⠀⠹⡄⠀⠀⢀⣀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⢀⣹⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠙⢦⡀⠀⠀⣧⣤⠾⠛⠉⢁⣀⣀⡀⠉⠻⢷⡄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⠀⢠⡟⢁⣤⠶⠛⣻⣿⠟⠛⠷⢦⡀⠹⣆
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⠀⢀⣴⠟⠉⠈⠙⢿⡄⠀⣼⠃⠀⠀⠀⢀⡴⠋⠀⣼⣴⠟⠁⠀⣼⡿⢁⣤⣶⣤⡄⢹⡄⢹
⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⢋⣉⡉⠛⢿⣷⣾⠃⠀⠚⠛⢳⡄⢻⣼⡇⠀⣀⡤⠞⠋⠀⣠⣾⡿⠁⠀⠀⢀⣿⠃⢿⣿⣀⣈⣀⣼⠇⢸
⠀⣼⡟⠀⠀⣀⣀⡀⠀⠀⣾⠋⠀⠀⠀⠉⠻⠆⠀⢻⣿⠀⠀⠀⠀⠀⠁⢸⣿⡟⠋⣁⣠⠴⠶⠿⢿⣿⡄⠀⠀⠀⠘⣿⣄⠀⠛⠿⠿⠿⢋⣠⣾
⢠⣿⣶⡾⠿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠈⠻⣿⣶⣶⣶⣾⠿⠛⠁
⠚⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣄⡀⠀⠀⠀⠀⣠⡾⠋⢹⣧⣄⠀⢀⣀⣴⠋⠁⢀⡀⠙⢧⡀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠛⠛⠶⣿⣿⡟⠀⠀⠀⠉⠛⠻⣿⣿⠃⠀⠚⠛⠛⢷⡄⢻⣶⣤⣤⣾⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠇⢸⣿⡟⠁⠀⣀⣉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀⢀⣠⣤⣄⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠈⠉⠉⣧⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⢸⣿⣴⡿⠋⠉⠉⠛⢿⣿⣆⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⣠⣿⣿⡏⠠⠾⠿⠿⣶⡌⢿⣿⡷⣶⣶⣶⡿⠛⠛⠿⣆⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⠀⠀⠀⠀⠀⠈⡇⢸⣿⠀⠀⠻⣿⡇⠀⠀⠀⠈⢳⣄⣀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠁⣸⡇⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⣰⣿⣀⠀⣀⠜⠋⠉⠛⢦⣄⣀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣤⣶⣿⣿⠿⠻⣿⠏⠀⠞⠛⠳⣆⢻⡉⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⠀⣷⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣾⣯⣀⡀⢀⡞⠉⣉⣉⡛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⢻⣿⡶⠒⠛⢿⣿⣿⠿⠻⢧⣜⠉⠉⠉⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣿⣿⠋⠀⠀⠀⠈⣿⠁⠈⠛⢷⣌⢳⡀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢳⣤⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⢀⣼⣿⣧⡀⠀⠀⠀⠀⠈⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣶⣿⣿⠇⠙⢿⣤⡀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠙⠻⢶⣶⣿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠻⣦⡀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⠻⣦⡀⠀⢀⣼⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⣠⣾⣋⣈⣻⣧⣀⣀⣀⣀⣀⣀⣀⣙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣄⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣦⡀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⠈⠻⣦⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣤⣤⣀⠀⠈⠉⠑⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢸⣵⣿⣿⣿⢇⠀⢰⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⣤⣤⡀⠀⠉⠹⠿⠗⠃⠀⠘⣞⢷⣝⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⢴⣶⣤⡀⠈⠉⠁⢀⣤⠶⠶⠶⢦⣄⠀⠈⠙⠚⠭⠉⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠘⠻⣿⡿⠏⠀⠀⢰⣿⣶⣿⣿⣿⣿⣿⣷⠒⠒⢒⣛⡉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣠⠔⣋⣀⣀⣀⣤⠤⠤⠴⠖⠒⠒⠋⠉⠉⠻⢿⣿⣿⣿⣿⠿⣫⠂⠀⢿⣿⣷⡄⠀⢸
⠀⠀⠀⠀⠀⣾⠉⠉⣽⣂⡀⠀⠀⣠⢖⣒⣒⡂⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠀⠀⠀⠈⠙⠋⣀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠿⠇⠀⠘⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢔⣂⡀⠀⠀⢀⡴⣫⢷⣶⣿
⠀⠀⠀⠀⠀⣿⣀⣀⡠⢄⡀⠀⠀⢿⣿⣿⣿⢿⡟⠀⢀⡤⢤⠤⠀⠀⠀⣿⣿⣿⡆⠀⡞⡾⣱⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣝⢦⠀⠀⠙⠛⠚⠋⠀⠀⠋⣾⣿⣿⣷⡀⠀⠙⠒⠋⠀⠀⡜⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⢀⣀⣀⣀⡤⠬⠥⠤⠶⠒⠒⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⠿⠓⠒⠒⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠈⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠘⣧⡀⠀⠀⠀⠀⢀⡴⠋⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⢷⡀⠀⢀⡴⠋⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⢿⡔⠋⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡿⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠹⣧⡀⠀⢀⡴⠂⢻⣄⠀⠀⠀⠀⣀⣤⠾⠋⢀⡾⠁⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠉⠀⠀⠈⢷⣶⠋⠀⠀⠀⠙⠷⣤⣀⣀⣈⣀⣤⡶⠛⠁⠀⠀⠀⣠⡾⠋⢠⣎⣰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣤⠴⡶⠀⠉⠳⣦⣀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣀⣤⠾⠋⢠⡞⢁⡌⠳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⢁⡴⠒⢦⣀⠉⠛⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠛⠋⣁⣤⠞⣶⠙⢧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢨⡟⠓⣤⠤⣄⢀⣀⣀⢀⣤⡤⠀⠰⣏⣥⠘⢿⡙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢸⣇⢀⣿⠘⠷⣤⠘⡷⠖⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠒⠋⠀⠛⠉⠁




⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⡿⣥⡧⠴⠛⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⡘⢿⣽⣯⣽⠾⠶⠖⠜⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣌⣾⠻⡿⡶⣿⣴⠊⡖⠠⢥⣔⢤⠤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠉⠀⠉⠃⣀⠐⣹⡇⠈⠘⣿⣦⡁⠀⠩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⢋⡀⠴⠷⠀⠊⢒⠠⠈⢽⠂⠀⠐⠆⠈⠙⣦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠊⠀⠀⠀⠀⠀⠀⠈⠂⡀⢺⠂⠹⠂⠀⠒⠦⢴⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⢤⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⣉⣝⢀⡲⣾⣿⡶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⠉⣼⣁⣔⣚⣵⣿⣶⢋⣹⡿⢷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⡇⣐⣿⡗⠀⣘⣧⣿⡟⠳⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⣾⣷⣷⣴⣿⡷⢿⣿⣽⢟⣽⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠸⣿⣷⣿⣿⣽⣯⣽⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣿⢾⣷⣾⣿⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣿⠟⡉⣽⢿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠻⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣰⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⡿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠄⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠊⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⣁⠄⠒⠁⠀⠀⡠⠊⠉⠆⠀⠀⠀⠀⠀⠀⣠⠮⠐⠂⢀⡜⠀⠀⠀⠀⠀⢀⣠⢤
⠀⠀⠀⠀⠀⠀⢀⠔⡡⠚⠁⠀⠀⠀⢀⡀⠈⠀⠀⢀⡄⠀⠀⠀⢀⣰⢊⠤⠔⠊⣠⠞⠀⠀⢀⠄⢀⡞⠉⠀⢠⠇⠀⠒⠠⠤⠀⡀
⠀⠀⠀⠀⠀⡐⠡⠊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⣴⡏⣥⠄⠀⠀⡤⠋⠀⢀⠔⢁⣰⡯⠄⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⠈⠀⠀⠀⠀⠀⣀⡼⠋⠀⢀⡴⠋⠀⠀⠄⠂⣵⠋⠀⠀⠀⠁⢀⣈⠀⠤⠂⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⡷
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁⠀⠀⣠⣞⣉⠉⠁⠀⢠⠟⠁⠀⠠⠊⠀⡴⠉⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠠⠻⠁
⠀⠀⠀⠀⠈⠓⠲⠴⠶⠖⠚⠋⠁⠀⠀⠀⠀⡠⠚⠉⠀⣀⠄⢀⡼⠁⠀⢀⠀⠀⢀⠾⠐⠂⣉⠕⢁⡼⠁⠀⠀⠀⠀⠀⠀⠠⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣁⡤⠖⠉⠠⡾⠋⠀⠀⠀⠁⠀⠠⠇⠖⠒⠊⣁⢰⠞⠀⠀⠀⠀⠀⠀⠀⡀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠠⠀⠀⠀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⣀⣈⠎⠀⠀⠀⠀⠀⠀⠀⡐⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⢀⣀⠠⠂⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠉⠀⢢⠀⠀⠀⠀⠀⠀⠀⠄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠃⠈⠁⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣄⡀⠳⠦⠴⣆⣠⠴⠃⠀⠀⠀⠀⠀⢀⢮⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠉⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡴⠶⠞⠁⠀⠀⠀⠀⠀⠀⠠⢣⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠤⠜⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡵⠁
⠀⠀⠀⠀⠀⠀⠰⠃⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠯⣐⠢⠄⣀⣀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⢪⠞
⠀⠀⠀⠀⠀⠀⠈⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠬⢭⣀⣁⣀⣐⣒⣒⣀⣈⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠤⠤⣒⠋⠀⠀⠀⠀⠀⠈⠉⢁⡒⠀⠀⠀⠑⠒⠬⠉⠂⠀⠀⠈⠳⢍⡉⠉⠉⠉⠀⠀⠠
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠉⠉⠐⠒⠠⠠⠠⠀⠀⠀⠉⠒⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⣀⣀⣀⡤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢠⡤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠰⠀⡇⠀⠀⠀⠀⠀⢨⡄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⠢⡀⠀⠀⠀⢀⡤⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡉⠉⠉⣿⣿⣿⣿⣿⡉⠉⢁⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣄⣀⣠⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠉⠉⢿⣿⣿⣿⣿⠋⠉⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⣤⣿⣿⣿⣿⣿⣤⣀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠈⣿⣿⣿⣿⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠁⠀⠀⠿⠿⠿⠿⠿⠁⠀⠈⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⢈⣹⠶⣏⢹⡏⢢⣠⠔⠒⠒⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⠋⠀⠀⠈⢿⡗⠉⠈⠳⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⢣⡀⠀⠀⢀⠤⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡡⠚⢩⠇⠀⡸⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠔⠁⠀⢠⠃⠀⢸⠙⢦⢠⠿⣄⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡴⠀⠀⢀⡤⢼⣄⡎⠳⡀⠈⢲⣄⣧⠙⢆⠀⠀⠀⢾⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⠟⢄⠀⠈⣳⠤⠝⡖⠈⢇⠀⠀⣼⠓⠉⢂⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣼⠀⢸⠉⠉⠹⡀⠀⡸⠄⢨⡝⠉⠀⣇⠀⠀⠑⠪⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢉⢦⠜⠦⣤⡤⠎⢻⡀⠀⣠⣇⢀⡰⠋⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡇⠘⣆⠀⠀⣦⡀⠀⡹⠛⣅⠀⢀⡇⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⢴⠋⢹⠀⠈⠉⢄⣀⣨⡏⠁⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⢆⣈⣳⡤⠤⢮⠈⠀⠑⡦⠴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⢺⡀⠀⢧⡀⠀⡹⠒⢺⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣹⡗⠋⠹⡉⠁⢀⡼⣤⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡟⠦⠤⢏⠉⠉⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠣⣀⣀⡸⠋⠙⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠊⠙⢦⣤⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⡠⠂

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿