Snowfall Emojis & Symbols

⢀⡀⠄⠀⠀⠠⠀⠀⠈⠀⠀⡅⠀⠈⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡂⠄⣂⠄⡂
⢈⠁⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⡆⠄⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⡀⠆⠁⠂⠅⠂⢀⠀⠀⣀
⠀⠀⠀⠠⠀⠀⠀⡀⠀⠐⠀⠀⠀⠁⠂⠁⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⢠⠄⠀⠠⢀⠀⠅⢀⠠⠀⠀⠀⠀⠠⠀⠀⡀⠂⠀⠀⠄⠀⠀⠄⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠤⠀⠀⠈⠅⡢⠅⡂⠅⠀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠰⠄⠀⠀⠰⢀⡁⠄
⢄⡢⠀⠀⠀⠁⠀⡅⠀⠈⠀⠀⠀⠀⠠⠀⠁⠂⡁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠅⠂
⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠂⢨⠀⠂⠁⠀⢀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠂⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠁⠠⠀⠁⠄⠀⠈⠀⠀⢠⠀⠀⠘⠃
⠤⣀⠰⠀⣀⠄⠀⠀⠀⠠⠄⠂⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢘⠪
⠀⠠⠐⠂⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠅⠀⢠⠀⠀⠐⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠉⠀⠨⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⢐⠶⠀⠀⠀⠀⢈⠀⠆⢈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡃⠀⠈⠀⠀⠀⠀⠀⠈⠀⡂⠅⡂⠅⡂⠉
⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀⠄⡃⠅⡂⠄⣀
⠀⠀⠂⣅⠐⠀⠀⠀⠀⠤⢀⠠⢐⠠⢀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠐⠨⠐⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠠⢘⠸⢘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⢐⠠
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠆⠈⠐⢨⠐⠈⠐⠀⠀⢀⡀⠀⠠⢀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈
⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⢀⠠⠈⡃⠤⣀⠀⠀⠀⠀⠒⢈⠀⠂⠀⠀⠀⢀
⣉⠀⠀⠀⠈⢕⠪⠀⠀⠠⠀⠀⠀⠀⠰⠂⠀⡀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠠⠀⠃⠀⠀⠀⠀⢈⠐
⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠤⠀⠀⠀⠀⠀⠀⠠⢀⠀⠆⢀⠠⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠁⠀⢀⠠
⠀⠀⠀⠀⠴⠀⠐⠀⠀⠠⠀⠃⢠⠀⠀⠀⠰⠀⠀⠀⠄⠒⢠⠀⠀⠁⠀⠀⡀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠠⢠⠄⠄⠠⡀⠦⢐⢀⠦⢳⡁⠀⠀⠀⠀⢀⠀⣰⣎⢀⣶⡀⢀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠓⠆⡈⠀⠤⡌⠄⠌⠠⠆⠃⠀⠀⠀⠀⠀⢈⢤⠌⡠⠀⠈⣤⡌
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠌⠆⠮⠅⠐⠄⡄⡀⠀⠀⠀⠀⢠⠋⣡⡀⢂⣀⠉⢃⠀⠀⠀⠀⢀⠄
⠀⠀⢀⠀⠀⠀⠰⡉⡄⠊⡀⠊⢰⠎⠌⠔⠤⠁⠀⢀⠀⠀⠀⠀⠓⢇⠨⠛⠁⠈⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣖⢐⠅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣰⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢠⡄
⠀⠀⠀⠀⢀⠀⢊⠀⡡⠠⠄⠀⠀⠀⠀⠠⡨⢀⣈⠤⣄⡀⢇⠴⠀⠀⠀⢂⡌⠁⢉⠄⠠⡈⠱⠊⢀
⠀⠀⠀⠢⠀⡈⢀⡠⡁⠁⠄⠈⠀⠀⠀⠐⠁⠢⠬⠚⠣⢔⠈⠒⠀⠀⠀⢀⠂⠐⠀⡀⠀⠠⠀⡙
⠀⠀⠀⠀⠉⠔⠀⠠⠔⠀⠒⠱⡀⠀⠀⣈⠣⡑⠺⡉⠗⠊⡐⢉⠀⠀⠔⠈⣡⢀⡢⠀⠔⠀⠀⠚⡀
⠀⠀⠀⠐⠠⠀⠂⠆⠐⡌⠀⠀⠀⠀⠀⠀⠈⠁⠎⢲⠢⠀⠃⠀⠰⠂⠀⠀⠀⠈⠔⠀⠄⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⠀⠀⠀⠀⠀⠂⠀⠠⠤⠦⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⢀⠐⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣘⠋⠑⡊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡠⠞⡀⣀⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣉⠈⡑⠑⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⡷⢾⣀⡈⠡⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢘⡌⡉⣅⣉⠺⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⠁⢠⣤⢀⠀⢀⣀⠀⠈⣠⣂⠐⠐⠀⠸⣮⡥⢘⠋⠻⠛⠦⠐⠁⠐⠐⠂
⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠤⠉⠙⡚⡀⠛⠛⠀⠰⠾⠯⢿⠀⠈⠀⠘⢑⣙⠄⠅⠂⠒⢚⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠈⠺⠀⢈⢰⡉⠀⠀⠀⠀⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠑⠀⠂⠀⠂⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣾⣾⣿⣿⠿⣿⣿⣼⡷⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠉⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄⠂⠈⠁⠐⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠗⢘⠀⠓⠀⠀⢠⡄⠀⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡆⣶⠀⢀⣀⠀⠀⡄⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⣿⣿⡿⠋⡁⠀⠈⠀⠀⠈⠙⠛⢭⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡷⣿⣆⠈⠈⠁⠀⠀⠀⠀⠀⠉⠀⣼⣿⣷⣟⣮⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⣿⣷⣄⠀⠀⢰⣾⣾⣦⣤⣄⣀⡈⠉⠉⠉⠛⠙⠛⢿⣿⣿⡟⠉⠉⠀⢀⠀⠀⠀⠴⠂⠀⡰⢶⣿⣿⣿⢹⣿⣿⣿⡿⣿
⣿⣿⠛⠉⠁⠀⠀⠈⣿⣿⣷⣶⣿⣿⣿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠃⠀⠀⠈⢠⠁⠀⠸⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⣿⣿⣿⣿
⣿⣿⣶⠀⠀⠈⠀⠠⠙⠿⠟⠛⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣿⣿⣿⣿⣿
⣽⣿⣿⣦⣀⡁⠂⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⠄⠀⠠⠤⢄⡀⠐⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠚⠋⠄⠀⡀⠀⠀⠉⢀⠀⠀⠀⢈⣒⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡈⠀⠀⠀⠀⢀⠂⠁⠀⠈⠉⠀⢾⣿⣿⠿⣿⣿⣟⣿⣿
⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠐⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠒⢦⣠⣱⠆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠠⡄⠀⠑⢀⠀⠁⠂⠐⠀⠀⢠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠂⠀⠘⠉⠀⠀⠀⠀⠀⠔⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠜⠉⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⢸⣿⣿⣿⣿⣧⠀⢀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⢀⡠⠂⠀⠀⠀⡎⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⣤⣭⣥⡄⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠛⠛⠋⠉⠉
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣸⣿⣿⡿⠋
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢑⡆⠤⣤⣤⣤⣤⣤⣤⣴⠀⠉⠀⣶⣴⣶⣿⡿⠋⠤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠠⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠉⠉
⢸⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠁⠀⠀⠠⠁⠀⠊⠁⠀⠀⠈⠉⠉⠉⡡⠀⠀⠘⠢
⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠁⢀⣠⡄⠐⠛⠀⠉⠈⠉⠘⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⡀⠓⠀⠀⠄⠃⠢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣄⡀⠂⠀⠆
⢸⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠉⣓⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⣀⣀⣀⣀⣀⣀⡀⠀⣀
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠒⠒⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⣀⡤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣀⠰⡦⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⡈⠛⢄⣇⠜⠋⣠⠐⠒⠒⠒⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣉⠝⡟⢍⣉⠛⠀⠀⢠⣄⠙⡟⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢠⡧⡘⠋⠀⠀⢰⣄⣈⣶⣷⣋⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡴⠋⡏⢢⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠓⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢤⠀⢲⢲⠀⢃⣐⠊⡆⣂⠖⣯⡴⢲⠂⢠⣤⣖⠔⢤⢲⢀⢠⣇⡄⡰⠀⢀⠀⠀⠄⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡐⣤⡀⢦⡀⠓⠈⠇⣢⠂⡄⠙⡤⣽⠓⡹⢠⡋⠓⢦⠜⣭⢢⢄⣥⠞⢉⠈⢂⣇⣸⡃⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⠈⠀⣀⣢⡈⣯⠭⡥⢞⠛⡏⠱⠸⡄⠐⣉⢒⣣⢼⢊⣀⡤⣤⡄⠾⠐⡷⠦⣤⠐⠒⣛⢠⠎⠰⠁⣉⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤⠈⢉⠲⡉⠙⠉⢐⠞⢹⣣⡴⣌⣼⠏⡐⠱⣨⠳⡃⠐⢤⢠⢵⢱⡀⠾⡄⠙⠉⢑⣀⣈⣅⣠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠅⠒⢿⣿⣋⡂⡀⡋⡦⣝⣏⠡⢁⡆⢣⣿⢟⡧⢆⡐⢲⠭⠳⠍⡡⠈⠀⣄⣥⡟⢎⣥⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠮⣂⡎⢝⣀⣫⠁⡁⠽⢚⢹⡇⣩⠇⣥⣼⢛⠋⡈⠙⠌⠲⠋⠂⠑⠒⠫⣞⠊⢳⠉⡿⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠈⠢⠰⠶⠉⣭⡇⣹⡗⠆⢰⡗⢱⣿⢷⢿⡽⠇⠀⠓⣋⠡⠔⠡⠞⠅⣠⢝⡣⢬⢞⣁⡧⠋⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠄⠀⠈⢍⡉⠒⢂⢏⠉⠙⣅⡷⠬⢰⠓⢵⣍⠝⢤⠎⠑⠐⡠⠊⢰⡃⢎⡀⡩⠀⡛⢃⠀⣼⢀⡌⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠋⠐⠦⠰⠤⠓⠰⠎⣑⢮⠀⠀⣸⣀⠒⣰⠁⣠⠰⠀⣈⠛⢠⠤⣞⣋⣡⡓⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠐⠀⠁⠠⠌⡛⠃⠀⢋⡠⠔⡈⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠒⠕⠂⠀⠒⡒⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠉⠁⠤⠄⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⠀⠄⠀⠐⠠⡀
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⢀⠀⠀⠀⠀⠀⠀⢀⠀⢢⣼⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀⠔⠀⠀⠀⠀⠀⠀⢦⠀⠔⠀⠀⠀⠀⠀⠈⢀⠄⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣕⢪⠠⠠⠀⠀⠀⠐⠐⢒⠤⠐⠒⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢄⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⡄⠀⠀⠀⠀⠀⠀⠊⠀⠑
⠀⠀⠀⠔⢂⠓⢍⠁⠀⠀⠀⠀⠀⠀⠐⡄⠂⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠠⠤⢥⡌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⢄⣰⡠⠔
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠂⠱⠥⠄⠀⠀⠀⠀⠀⠊⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢂⢥⠐⠂⠀⠀⠀⠀⠠⢡⠄⠀⠩⠁⠀⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡅⠈⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢈⠰⠆⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⣤⢁⢀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠢⢌⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡘⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠔⠀⠀⠀⠀⠀⠀⢠⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⡀
⡐⢢⠀⠠⠀⠀⠀⠐⠐⢚⠬⡒⠒⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠊⠑⡀⠀⠀⠀⠀⠀⠀⠊⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠀⠀⠀⠐⠂⡃⠍⠁⠀⠀⠀⠀⠀⠀⠐⡄⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⡰⣠⠖⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⢽⡌⠀⠀⡀
⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⡂⠂⠱⠡⠄⠀⠀⠀⠀⠀⠊⠅⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠢
⠘⢇⢥⠐⠂⠀⠀⠀⠀⠠⢁⠄⢠⢅⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⠇⡇⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢨⣄⠀⠄⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⣉⣉⣉⠉⠛⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣁⡴⠞⠋⠉⠉⠁⠀⠀⠀⠀⠈⠛⣿⣦⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡿⠿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣀⣀⣤⣾⣷⣦⣄⣀⡀⠀⠀⠀⣀⣠⣴⣦⣄⡈⠉⠛⠛⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣛⡉⠁⠀⠉⠙⠛⠿⠿⠿⠿⠛⠛⠉⠉⠛⠿⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣄⠀⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠘⣿⣆⠀⠀⣰⣿⠋⢻⣷⡀⠀⠀⠠⣴⡆⠘⢿⠟⠀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠘⣿⣆⠀⣿⣇⠀⢀⣿⡇⠀⢀⠙⠛⠳⣄⢸⢀⣴⠟⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡄⠈⠻⠿⠿⠋⠀⠀⢼⣷⠶⠶⢾⣿⣿⠷⠶⢶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣴⠟⢹⠉⠳⣄⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡇⢀⣼⣄⠀⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣖⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣧⢄⠄⠀⠀⠀⠀⠀⠀⡀⠀⠓⣧⠛⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠾⣶⣆⢺⠗⣤⣶⠶⠁⠀⠀⠀⢒⣶⢘⠯⡥⣟⢼⣖⠀⠀⠀⠀⡴⢷⢔⡘⡷⢓⡢⡶⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⠿⠯⣭⣅⠀⠀⠀⠀⠐⢕⠲⢪⠑⡇⣭⢺⢪⠇⠀⠀⠀⡀⢨⢭⡭⡷⢭⡭⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠿⠛⠣⣺⣷⠉⠛⠿⠄⠀⠀⠀⠖⢛⣲⢎⡇⢷⠻⠓⠀⠀⠀⠀⠙⡟⠓⠴⣛⠜⠚⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠏⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠖⠟⠦

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⡶⢤⡄⠀⠀⠀⠀⠀⠀⢀⠤⢀⣆⠤⢄⠀⠀⠀⠀⠀⠀⠀⡤⠀⣖⢀⣤
⠀⠀⠀⠀⠀⠀⢀⣾⣧⢳⢭⡵⠆⣽⣧⡀⠀⠀⠀⢲⣤⠴⢮⡯⠦⣼⡴⠀⠀⠀⠀⠰⣴⡌⣮⣭⣶⢩⣴⠂
⠀⠀⠀⠀⠀⠀⢸⡥⡷⣋⠶⢆⡱⠶⢸⠆⠀⠀⢐⡃⠰⢎⡱⡷⣙⢾⠈⡇⠀⠀⠀⢞⠦⢾⣿⣿⣿⠶⠰⡳
⠀⠀⠀⠀⠀⠀⠈⢿⡟⡽⣚⡲⠏⢻⡟⠀⠀⠀⠀⠼⠛⠹⢖⣗⠯⢻⠳⠄⠀⠀⠀⠠⠿⣃⢟⣛⢿⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠷⠚⠃⠀⠀⠀⠀⠀⠀⠘⠒⠈⠏⠲⠚⠀⠀⠀⠀⠀⠀⠀⠓⠈⠿⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢰⡂⣠⡄⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⢦⣦⢴⡭⢵⡄⣧⠴⠀⠀⠀⠀⢠⣿⠽⢞⡏⡾⣼⣆⠀⠀⠀⠀⠠⣄⡄⠬⣟⠥⢠⣤
⠀⠀⠀⠀⠀⠀⠤⡊⠥⣧⣿⣷⣽⠌⢑⠤⠀⠀⠠⡫⢼⢜⣲⣧⣛⢼⢜⡇⠀⠀⠀⠀⠈⢝⣓⡶⣚⡫⠁
⠀⠀⠀⠀⠀⠀⢀⡼⡷⢵⠫⢷⠯⡾⢥⠀⠀⠀⠀⠹⣿⢩⡖⡗⣯⢺⡞⠀⠀⠀⠀⡰⠞⠏⠧⣗⠬⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢻⡛⠲⠇⠀⠀⠀⠀⠀⠀⠙⠿⠞⠓⠾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢄⡺⠟⠁⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣫⠟⡉
⠀⡀⢀⡀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠎⠁⠈⠃⠀⢀⣠⠖⠈⠀⠁⠀⠀⠀⠀⠈⠂⠀⠀⣶⠀⠀⢀⣿⢨⡵⣿⡄⠉
⣼⣟⠽⢁⣿⡀⢀⡀⠹⠖⠙⠄⠀⠈⢿⠀⠀⠈⠀⠙⠀⠀⠀⢀⠔⠀⠀⠀⢀⡄⠀⠠⣟⡄⠀⣾⢟⠷⡖⢋⠙⡟⠋⣼⡀
⣿⠕⡇⣻⢙⣿⣿⠄⠀⠲⠁⠓⡆⠀⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠄⠸⠛⢥⠨⠖⢛⣌⠺⣾⠧⡘⠲⣬⣷
⠷⢪⣽⢑⣮⡿⠇⠘⠶⠊⠓⠧⣙⢶⣤⣤⣠⣆⡄⢼⡧⣀⣠⣤⣴⣴⣷⣶⢉⣃⢺⠞⣙⢰⡡⠂⠻⣌⠻⣹⣦⢤⡀⠘⢿
⢶⡁⢸⡙⣧⡶⠺⢤⡞⠓⣭⣇⠙⠻⣿⣿⣿⣿⣏⠹⠏⣿⣿⣿⢃⣿⣿⡿⠚⣍⡉⠩⣌⢫⠤⠀⣻⣈⠶⣿⢿⡄⠙⠳⢿
⠉⣱⢾⣟⡥⠐⠂⡖⢃⡀⠎⠋⠑⢦⣻⣿⢿⡿⡰⢺⡀⡜⢿⣻⠁⠸⣿⠄⠈⣉⡉⠳⣷⡞⠈⠉⠀⢹⠢⢌⡄⠀⠢
⣾⣉⣾⡟⠁⠲⡋⢀⡞⠀⡀⠸⣤⠀⠉⡿⣟⠁⠀⠂⡏⠀⢈⡕⠀⣴⠃⣂⣸⢉⣭⡑⢻⣷⡴⢿⡀⢈⡷⣄⡙⢆⣠⠈⢻
⠈⠩⠋⠀⣀⡤⠜⠉⠀⠀⠙⣆⣸⠚⠓⠃⠘⠂⠊⠙⠓⠂⠀⠁⠀⠀⠁⠀⠈⠈⠀⠘⢋⠄⠀⡈⠁⠋⠀⠀⠉⠻⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠋⠢⠄⠀⠢⠴⠆⠈⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⠁⢀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⣫⡆⢐⢮⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠺⠂⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣤⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⣀⣤⣠⡋⠈⢩⣤⣶⣦⠄⠀⠀⠀⠀⠀⠐⠛⠢⣤⡤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠚⢈⡶⠭⢶⣁⠉⠀⠀⠀⠀⠀⠀⠀⣔⡶⠊⠉⠈⠐⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣠⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠂⠙⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣠⢀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠁⡀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣖⡴⠈⠪⠞⢱⢰⣲⠂
⠀⠀⠀⠀⠀⠀⠐⠷⡵⠄⡦⢱⡎⣥⢀⡴⣠⡀⠀⠀⠀⠀⠀⠀⠬⣖⣭⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⣓⠊⢑⡊⢰⠉⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠻⡂⠀⠘⠈⠀⠀⠀⠀⠀⡀⠶⠀⠔⠙⠂⠀⠶⠀⠀⠀⠀⠀⠀⣠⣖⢭⠃⣨⡁⢹⣱⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠠⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⡰⠲⠔⢦⢸⣷⠂⠀⠀⠀⠀⠀⠛⣨⣄⠀⠭⢀⣸⡀⠓⠀⠀⠀⠀⠀⠘⣂⣅⡀⠸⠇⣀⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣁⠀⠀⣁⡶⠈⠁⠀⠀⠀⠀⠀⢈⡀⢈⡹⣿⢎⠀⣀⡁⠀⠀⠀⠀⠀⠀⡀⢈⣉⠾⠦⣉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠳⢞⠦⠆⢰⠯⡄⠀⠀⠀⠀⠀⡤⢘⠇⢀⣖⠀⢸⠑⡴⠀⠀⠀⠀⠀⠠⠌⠋⠁⢸⡆⠉⠏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣸⣿⣧⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⣻⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⠀⠀⢸⣿⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡤⠾⢧⣄⠸⣿⣧⠀⣾⡁⡹⠃⠀⠀⠀⠀⢠⠶⢦⡀⠀⠀⠀⠀⢻⣤⠾⠀⠀⣀⣤⡾⢥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢀⡾⠉⠀⠀⠀⠀⠀⠀⠘⣦⡴⠃⠀⠀⠀⣀⣼⣤⣶⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣠⣴⣿⣿⠿⠟⠋⠁
⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢨⣉⡇⠀⠀⠀⢰⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⠿⠛⠛⠥⢤⡶⢤
⢯⣨⣷⣶⣶⣶⣶⣦⣤⣤⣄⣉⡑⡄⠀⠀⠈⠳⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⣁⡀⠀⠀⠀⠀⠑⠛
⠀⠀⠀⠀⠀⠈⠉⣙⠛⣿⢿⣿⣿⣿⣷⣶⣶⣶⣦⣬⣷⣄⣀⣀⡀⠀⠀⢀⡽⢤⣄⣀⣠⡶⠟⠋⠉⠙⠛⠻⢏⣙⣆
⠀⠀⠀⠀⠀⠀⢬⣉⡟⠁⠀⠀⠀⠀⠀⠉⢉⡿⠛⠛⠛⠛⠛⠋⠉⠓⣶⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠶⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠾⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣀⣀⣀⣠⣜⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡴⠞⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣷⠙⣿⣿⣧⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠟⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠿⣶⠈⠙⢯⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠹⡄⠀⠀⠀⠀⠀⠀⠸⣦⠞⠀⠀⠀⢹⢿⣿⣦⣀⣀⡠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣠⠤⣾⣿⠏⠀⢀⡽⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⠻⣿⣿⣌⠻⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠛⢀⣾⣿⡟⠀⠀⠀⠓⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⠟⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢁⡼⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢼⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣣⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢹⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⢺⠖⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠈⠣⣸⣀⠞⠀⠀⠀⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣢⠀⡄⠀⢆⠀⠀⠀⠻⣀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠟⠈⠀⠀⠰⠀⢠⠀⣔⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⣼⡀⠘⡀⠀⠀⠰⡿⡟⢦⣄⢸⡀⣠⡴⢻⢻⠆⠀⠀⢀⠃⢀⣧⠒⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣈⡱⠷⣀⠀⠀⣷⠘⣦⡈⢹⠋⣁⣴⠃⣾⠀⠀⣠⠾⢎⣁⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣲⢯⣸⠏⢏⢻⠋⡽⢹⢀⡹⣖⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣤⠖⣛⣁⡴⠚⡓⢬⣾⣾⡵⢚⠳⣤⣈⠛⠲⣤⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠛⠦⣥⡙⠳⣍⡡⢜⢿⢿⠣⢌⡠⠟⢉⣬⠴⠛⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠽⣞⢹⣀⠎⣸⣀⠳⣸⠉⣳⠯⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢉⡰⡶⠋⠁⠀⡿⢸⠟⢋⣸⣍⡙⠻⡄⢿⠀⠀⠙⢶⢆⡉⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡬⢻⠁⢠⠁⠀⠀⠐⣷⣧⠞⠋⢸⠁⠙⠳⣽⣾⠆⠀⠀⠘⡄⠉⡟⠥⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠋⠝⠀⠇⠀⠎⠀⠀⡀⣴⠁⠀⠀⠀⢸⡀⠀⠀⠀⠙⣦⢀⠀⠀⠱⠀⠸⠀⠫⠑⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡴⢹⠙⢆⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⢼⢆⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠰⠆⢴⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣴⢀⢙⠢⠌⣿⣠⠔⠃⢀⣤⣠⡶⠂⠀⠀⠀⠀⠀⢰⠞⣡⡂⡀⠠⢍⡟⠂⠈⢀
⠀⠀⠀⠀⠀⠀⡂⠀⠈⠈⠈⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠟⢬⣻⠉⣿⡋⣇⣤⠾⠛⠇⠀⠀⠀⠀⠀⠀⠀⠘⠈⠪⠛⠀⠂⠈⠀⠀⡄⣆⢱⠆
⠀⠀⡀⠀⠁⠀⠰⠅⠀⠀⠀⠀⠀⡡⠁⠀⠀⠁⡀⠀⠀⠀⠰⠶⣈⣎⠉⠈⡾⠡⠉⡻⢑⠤⠄⠀⠀⠀⠀⠀⠀⢀⡇⢄⢂⡀⠀⠀⠀⠀⠈⠫⠹⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣴⣤⢟⢻⢀⣯⣀⣟⠶⣤⣤⡄⠀⠀⠀⠀⠀⠄⠈⣗⠹⠩⠁⠀⢁⠀⠀⣤⢄⠀⡀
⠀⠀⠀⠀⠀⠀⢈⠁⠊⠀⠀⠌⠀⢁⠀⠀⠀⠀⠀⠀⠀⠶⠛⠺⠁⣨⠌⢃⣷⠚⢭⡀⠹⠟⠳⠦⠀⠀⠀⠀⠀⠠⠀⠃⡀⠠⣡⠗⠄⠐⠴⢛⠤⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⣿⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢢⡭⠤⠀⠒⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢢⣀⠀⢠⠀⢀⠀⠀⡠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⡀⠸⢽⣥⠋⠀⠈⠅⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠆⠀⠀⠈⠀⢰⠏
⠀⠀⠀⢀⡀⠉⠉⠃⡲⢀⠄⡤⢶⠆⠚⠚⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠄⠛⠀⠀⠀⠁⠃⠄⠀⠂
⠀⠀⢀⠀⠡⠄⣈⢵⠂⠀⠀⠀⠘⣡⠀⢀⡘⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢠⠀⠐⡀⣀⠀⠀⠤
⠀⠛⠓⠘⢫⡌⠻⡄⠀⠀⠈⠀⢤⡀⠿⠀⠶⠆⠥⠶⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠂⠐⠚⠕⢐⠀⠀⢀⡀⠮⡗⣀⠀⠀⠓⠪⠓⠒⠂
⠀⠀⠀⠀⠟⠀⠀⠐⣏⣠⡀⣀⠘⠑⠀⠈⢥⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠈⠑⢒⡌⣋⠀⠀⠀⣉⣔⡲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣈⠆⡄⠀⠀⠉⢎⡈⠀⠂
⠀⠀⠀⠀⠀⢲⡨⠃⠘⠆⠀⡞⠐⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠠⠀⠠⠀⠘⢶
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠟⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⣦⣀⠀⣿⠀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⣿⡆⠀⠀⣤⠄⠀⠀⠀⠈⣿⠁⠀⠀⠀⠙⠃⠀⠀⠀⢈⣿⠀⢀⣿⡋⢉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣸⣿⣀⠀⢿⡇⠀⠀⠀⢠⡄⠀⠀⠀⣿⠀⠀⠀⠸⠇⠀⠀⠀⠀⣸⣿⣶⠿⠛⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠛⢿⣿⣷⡀⠀⠀⠀⢠⣦⠀⠀⣿⠀⢀⣾⠆⠀⠀⣀⣤⣾⠿⠛⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠟⠛⠛⠻⢷⣦⣄⠀⠻⣧⡀⣿⢀⣾⢏⣠⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣿⣿⣿⣾⣿⣿⣋⣁⣀⣀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢴⠆⠰⠶⠶⠿⢿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠋⠀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⢩⣿⣿⣿⣯⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣶⣦⣤⣤⣶⠿⠛⠉⠀⣰⡿⠁⣿⡇⠻⣧⡀⠀⠉⠻⢷⣦⣤⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣤⡾⢿⣿⠃⠀⠀⠀⠀⠛⠁⠀⣿⡇⠀⠙⢃⠀⠀⠀⠀⠈⢿⡿⢷⣦⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⢹⣿⠁⠀⣿⠇⠀⠀⠀⠀⠟⠀⠀⠀⣿⡇⠀⠀⠙⠃⠀⠀⠀⠀⢸⣿⠀⠈⢻⣿⡉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⠀⠀⠀⠀⠾⠀⠀⠀⣰⣿⣧⡀⠀⠀⠘⠛⠀⠀⠀⢸⣿⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⡟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⣿⡇⠀⠙⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁

⠀⠠⠀⠀⠀⠀⢀⠶⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⣀⠀⠀⠀⠈⠀⠋⠐⠃⣦⡉⣡⢦⠙⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⢄⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠎⠀⠁⠀⠈⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⡁⠙⠁⢨⢷⣂⠀⠀⠀⠐⠃⠀⠀⠀⢀⢀⢢⠸⣫⣛⢦⢄
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡏⠆⠁⠀⠀⠃⠊⠷⣀⠀⠀⠀⠀⠀⠈⠉⠙⠙⣿⡛⡿⢓⣟⠺
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠠⠄⠀⠀⠀⣤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡜⠞⢽⡏
⠀⠀⠀⠀⠀⣀⣙⣤⢈⣀⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠇⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠞⠀⠀⠀⠈⢫
⠀⠀⠀⠀⠀⠀⡤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⠲⡬⣦⣡⠆⠴⠖⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠘⠚⠛⣂⠞⣿⣿⠛⣂⠘⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⢠⠏⠀⢦⢠⣶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢉⡀⢁⡎⢣⡈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠿⣏⠀⠀⣈⡿⠧⠤⠤⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀
⠃⠀⠈⣧⠈⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠐⠇⠀⢻⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⡄⠀⠀⠀⢻⡆⣸⠿⠁⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⠁
⢀⠀⡀⢸⡾⠴⠒⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⢶⢼⡦⠶⣷⠖⣿⡷⠰⡷⠦⢾⡷⡦⡦⢤⠀⠀⠀⠀⠀⠤⠤⠤⢷
⡃⠀⢸⡮⠄⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢀⣶⡁⠸⣦⡀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒
⣿⣻⢷⣀⣠⣋⣰⣃⣰⣂⡀⠀⠀⠀⠀⠀⢾⠲⣄⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⡀⠀⠀⢤⣤⢤⣼⠑⠀⠀⢉⣦⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⢳⡀⣦⣀
⣿⣻⡿⠁⠙⢧⠉⠳⣌⠃⠀⠀⠠⠀⠀⠀⠸⡀⠈⢳⠀⣿⡄⣠⠞⠁⡸⠀⠀⠀⠀⠀⠀⠀⢠⡾⠈⣇⠀⢠⠏⠘⣧⡀⠀⠀⠀⠀⠀⠀⠈⠙⠉⡽⢉⠟⠉
⡅⠀⣱⡦⠤⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣠⣀⠑⢦⡘⡆⠻⢠⡇⣀⠴⢁⡀⠀⠀⠀⡀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠈⠇⠀⠀⠀⠒⠂⠀⠀⠀⠘⠁⠀⠴⠖
⠙⠀⢁⡿⡖⠒⠒⠂⠀⠀⠀⠀⢀⣀⣀⣀⣉⠛⠢⡝⠋⠉⠛⣏⠵⠚⠏⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣛⡿
⠂⠀⡼⠀⡿⡓⠀⠀⠀⠀⠀⠛⠭⣄⣀⣀⣀⠩⠾⡀⠀⠀⠀⣸⢦⣛⡉⠉⠙⠲⣤⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠝⠳
⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣤⠶⢎⣹⡆⡤⢶⣏⠲⣦⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠛⠙⡴⠋⢠⠃⣷⢸⡄⠑⣄⠈⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⡄
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⢰⠁⣠⠞⠈⡿⠁⠻⣄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠱⡆⡀⠀⠸⠢
⡔⠀⠀⠀⠀⠀⠀⠹⠄⠰⠋⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠄⠺⠃⠸⡃⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠻⠇⠐⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠘⠁⠋⠞⢳⣀⣠⡚⠣⠈⠃⠉⠈⠁⠀⠀⠈⠀⠀⠀⠸⣖⡠⠀⠄⢠
⠀⠀⠈⠀⠀⠀⠀⠞⠀⠘⠆⠀⠀⠀⢠⡤⠀⠀⠀⢠⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠈⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⡥⢒⡼⠓
⣡⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣠⢋⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⠏⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⢴⢴⣴⢬⡦⢼⡄⠀⠀⢩⣇
⠙⠋⠉⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠲⣟⣟⠂⠺⠒⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠚⣤⡀⣤⠠⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀⡌⠡⠌⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢨⣽⠇⠉⢨⣶⠠
⠀⢠⡄⠀⠀⠀⠐⢃⠔⠀⠀⣄⠚⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠚⣯⡜⠀⠀⠘⣰⠯⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠂⢠⠄⡌⣦⢰⠄⡌⠀⢱⠤⠆⢴⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣈⣳⠜⠳⣴⣉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠁⠀⠀⣜⠂⢃⡀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠒⠶⡷⡷⢼⠦⣼⢠⣾⣷⠀⡮⢴⢥⡦⡤⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⣄⠀⠀⠀⣀⡤⠤⠶⠶⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡁⠀⠀⠀⠀⠀⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡤⠤⢤⣀
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣟
⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠟⣽⠛⠛⠻⣴⣟
⠀⠀⠧⣄⣀⣀⣀⣀⣀⡤⠴⠋⠙⠦⠤⠤⠤⣴⡏⠈⠷⣦⢤⣄⣀⣀⣤⡴⣯⢟⡴⢿⠀⠀⢀⡯⣉⡇⢀⣤⡀
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣗⠙⣒⣶⣾⠊⣳⡾⠋⢳⠿⠀⢚⣒⡋⣛⣒⡋⣘⣓⣒⣋⢘⣓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡜⢉⡿⢟⡜⠉⠉⣿⣭⢏⡶⡜⠯⣵⠟⠉⠳⡹⣄⡀⠈⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣾⣇⣀⣀⣹⢆⡼⠷⢧⣄⢿⡀⠀⣠⣧⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣨⠿⣭⢁⢯⠀⠀⠀⡼⣀⢩⡭⣅⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣣⢿⠎⢳⣶⡚⢱⡋⢧⠳⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡯⣠⢳⡈⠛⠋⠘⠛⠋⠁⢸⣃⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣸⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠇⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣶⡃⠀⠀⠀⠀⠰⣀⣠⣤⠶⡿⠲⠶⣤⣴⡃⠀⠀⣨⡿⠧⠤⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⠶⠞⠛⠉⠁⠀⠀⡇⠀⠀⠀⠈⠙⢳⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣆⢠⠁⠀⠀⠀⢳⡗⠃⠀⠀⢦⣴⠋⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣾⠁⠀⠼⠿⣄⢀⣀⣠⣼⣧⣤⣀⣴⠟⠉⠙⠀⢿⣤⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡀⠀⠀⢀⡼⠻⣅⠀⢸⡇⣠⠟⢹⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⣀⣠⣏⣀⣘⣆⣀⣾⣁⣀⣈⣷⣼⣿⣋⣀⣈⣇⣀⣤⣞⣀⣿⣀⣀⣀⣤⣶⡚⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠼⠋⠉⠹⣏⠉⠽⠋⠉⠙⢯⡉⢉⣽⢿⡿⣍⡉⣹⠏⠉⠹⠍⢩⡟⠉⠉⠉⠙⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣷⣞⠁⢸⡇⢈⣻⣯⣀⣀⠀⢠⡿⣄⡀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⡀⠒⢒⣿⡇⠈⠓⢾⡷⠋⠁⠈⠿⣦⣀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠏⠀⠃⠀⠰⢺⡗⠄⠀⢀⣠⠴⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠛⠲⣦⣤⣄⣸⣧⡴⠞⠛⢇⠀⠀⠀⠙⢶⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⣿⠏⠀⠀⠀⠠⠇⠀⠀⢹⡇⠀⠀⠀⠈⠀⠀⠀⠀⢸⠙⢧⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣿⠀⠀⠀⠀⠀⢀⡠⢾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠲⣄⡏⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠘⠇⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⡿⢿⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⠁⠀⠙



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

⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠠⠀⠀⠀⠘⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠴⠆⠀⠀⢼⣇⠀⠐⠒⢄⡀⠀⠀⠀⠀⠶⠀⠀⠀⣀⠀⠀⠀⠀⠀⡐⡁⣒⠪⢂⠀⠊⠉⢂⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣌⠌⠡⣅⠈⠒⠠⠬⢁⡒⡄⠀⠀⠀⠀⡰⡿⠀⠀⠛⠀⠀⠇⡅⠛⢁⢀⠀⠑⠒⠠⡁⠢⠀⢰⢷⠀⠣⠉⢐⢄
⠀⠀⠀⠀⢸⠀⠘⠃⢸⠀⢀⣀⢀⣤⣁⣶⠀⠀⡤⠴⢸⠤⠷⢤⡀⠐⡍⠥⠃⠀⠘⢜⣈⠆⢈⠀⣲⡅⢠⠏⠈⠧⢀⠠⡠⣿
⠀⢠⡆⠀⠘⢘⡃⣘⢘⣴⡿⣿⣿⡿⠈⢿⣀⣀⡇⢠⣆⢀⣦⠀⣦⣠⡇⡼⣵⢠⢿⡆⢠⣊⠕⢉⠙⠗⣴⣶⢳⣶⡕⠈⢎⠪⡆⠀⢀
⢐⢕⣿⠄⠀⢠⡄⡤⠸⠁⡀⠀⡀⠀⢘⠀⠁⣈⡀⠀⠀⠀⠀⠀⣠⡀⡇⠉⢉⡤⡍⠁⠈⠀⡀⠻⠃⡀⠹⣈⣉⣸⠰⠄⠀⠤⢠⡐⢛⣳⡄
⠀⡺⣷⡁⢴⡠⠄⠷⠀⠀⠛⠐⠋⠀⣈⠀⡆⠛⠃⡔⠂⠃⠒⡄⠉⠁⡇⠀⢸⣁⡇⠀⡇⢸⣿⠀⢸⣿⢀⠿⠿⢿⠀⠠⣶⠀⣈⠀⣶⡄⡄
⠨⢚⠣⡂⢽⡇⣶⣺⠀⡆⠷⠰⠇⢸⣉⡇⠁⠀⢘⠠⠂⡅⠄⢠⠀⢰⡧⢀⣞⣒⣣⡀⡇⠼⠻⠆⠼⡻⠄⣿⣭⢿⠀⠀⠛⠀⣿⠀⡭⡄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠰⣦⠀⠀⢺⣇⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⣤⢘⣇⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣆⠀⡐⡿⠁
⠀⠀⠀⠀⠰⠾⠾⠒⡒⣇⣪⡓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣟⢆⢸⢃⣤⡼⠞⠃
⠀⠀⠀⠀⠀⠀⣐⡶⠋⢐⣇⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⣨⡭⠝⡿⡗⠤⣶⣴⡄
⠀⠀⠀⠀⠀⠐⠋⠂⠀⢐⡗⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠁⣺⡇⠈⢶⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠
⠀⠀⠀⠀⠀⠀⢬⢵⠷⣛⠀⠀⠀⠀⠀⠀⠀⠠⡄⣆⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⢠⡥⠀⣀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⡺⡿⡖⠀⠀⠀⠀⢀⠀⠀⡘⠣⣀⣀⡔⠓⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠼⠉⠉⠉⢉⡽⠯⣉⠉⠋⠉⠙
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠋⢀⡆⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣥⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠀⢨⣇⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠉⡴⢰⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

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

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢄⡀⠀⡀⡃⢀⠀⢀⠄⠀⠀⠀⠀⠄⡀⠀⠀⡇⠀⠀⣀⠄⠀⠀⠀⠀⢀⡀⠀⠠⡇⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⣀
⠀⠀⠀⠀⠀⢈⠐⠆⣁⠴⢊⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠁⠔⠊⠁⠀⠀⠀⠀⠀⠀⠉⠃⠄⢢⢔⠋⠁⠀⠀⠀⠀⠀⠀⠉⡰⢈⡁⢆⠈
⠀⠀⠀⠀⢀⡠⠘⡃⠆⢙⠠⢄⠀⠀⠀⠀⠀⣀⠤⠒⠁⡆⠑⠢⣄⡀⠀⠀⠀⠀⢠⡴⠂⠑⡂⠑⠢⣄⠀⠀⠀⠀⠀⣀⠤⠈⠀⠄⠃⠠⣄
⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠉⠐⣤⢀⣃⠀⡄⠆⠁⠀⠀⠀⠀⠀⠀⢘⡃⠦⣛⠀⠀⠁⠀⠀⠀⠀⠑⢦⡄⠄⡣⡂⡴⠊⠁⠀⠀⠀⠈⠑⠢⣄⠀⠇⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⣀⠸⠿⠃⡀⠀⠀⠀⠀⠀⠀⠐⠗⠢⢄⢀⠄⠒⠓⠀⠀⠀⠀⠀⠀⣠⡨⡘⣟⠜⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⡃⢤⣀
⠀⠀⠀⠀⠒⠈⠀⠀⡂⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⡰⠃⠁⠳⡀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢑⡇⠁⠈⠑⠂⠀⠀⠀⠰⠘⠁⠀⠀⡇⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠰⢠⠀⠀⠀⡂⠀⠀⢠⡰⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⣀⠀⠀⠀⠀⠀⢄⡀⠰⠀⠃⡴⢀⣠⠄⠀⠀⠀⠐⣠⢀⠀⠀⡂⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠈⠐⠆⣅⠖⠈⠁⠀⠀⠀⠀⠀⠀⠈⢂⢰⣴⢀⠊⠀⠀⠀⠀⠀⠀⢀⣉⠐⢶⣧⠆⢈⡀⠀⠀⠀⠀⠀⠀⠉⠐⡄⢣⠒⠈
⠀⠀⠀⠀⢀⠰⠈⠉⠆⠉⠠⢄⡀⠀⠀⠀⠀⢠⠤⠂⠘⡙⠀⠢⢄⠀⠀⠀⠀⠀⣠⠤⢈⠍⠋⡁⠠⢤⡀⠀⠀⠀⠀⣀⠤⠙⠠⠇⠉⠰⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⡃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠀⢀⡄⠀⠀⠀⠀⠀⢼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠜⠓⠀⠀⠀⠀⢠⢾⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢈⣽⣅⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠒⢠⡤⡐⠀⠀⠀⢠⣾⡿⡄⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⢾⡣⠀⠀⠚⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⢉⣼⣿⡌⠂⠀⠀⢀⣾⣿⣧⠀⠀⠐⢨⡑⠀⠀⣼⣿⣿⠄⠀⠀⢀⣿⠀⠀⠀⠐⠾⣿⣿⡿⠒
⠀⠀⠀⠀⠀⢰⠖⠖⠂⠀⠀⠠⠋⣽⣿⡙⠦⡀⠀⣼⣿⣿⣿⣆⠀⢘⡱⣌⠂⠀⣰⣿⣷⣄⠀⠀⣼⣛⣇⠀⠀⠠⠾⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣽⣯⠳⢄⠀⣸⣿⣿⣿⣿⣿⡄⠋⣸⣌⠃⠘⢛⣿⣏⠉⠀⢰⣿⠼⣿⡄⣀⣤⣾⣿⣿⣟⠒⠂
⠀⠀⠀⠒⠂⠀⠀⡆⠀⠀⠀⡠⠞⠉⡏⠳⠀⢠⣿⣿⣿⣿⣿⣿⣿⠈⢁⠈⠀⢠⣾⣿⣿⣆⠀⣾⣿⠱⣿⣧⠀⢀⣴⣿⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⠀⠀⠉⠉⠭⠉⠉⠘⠛⠛⠛⠛⠛⠀⠉⠉⠩⡏⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠌⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣦⣄⠀⣿⠀⣠⣴⠞⠃⠀⠀⠀⣰⢤⡹⣽⢃⣤⡆⠈⠀⠀⠀⠀⠀⠀⠶⠀⠰⠇
⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⢉⣓⢾⣞⡉⠀⢐⠀⠀⠀⠀⢈⣛⣻⣿⣟⣋⡁⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠠⡷
⠀⠀⢂⠨⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣤⠾⠋⠁⣾⠀⠙⠻⢦⡀⠀⠀⠀⠻⠞⢱⣻⡜⠾⠇⠀⠀⠀⠀⠀⠀⢐⡴⠀⠰⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠤⣤⢠⣬⣼⣥⡤⢤⡤⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠄⠠⠀⠀⠀⢀⡀⢀⢀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠻⡦⠀⣴⠦⠄
⠀⠀⠘⢣⣿⣯⣝⣿⣿⡜⠁⠀⠀⠀⠀⠂⠀⠀⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡉⠀⢉⡤⠀⠀⠀⠀⠀⠘⠶⠖⠀⠀⠀⠉
⠀⠀⢰⣮⢟⣿⣽⣿⡿⢴⡆⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⡄⠡⢔⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⣰⠄⢀⡀⠘⠛⢧
⠀⠀⠉⠉⠀⠡⣭⡍⠀⠉⠉⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⠭⠘⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⢓⣿⢿⢠⡄⣠⡄
⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠑⢣⣄⣻⣠⡄⠪⡥⠀⠀⠀⠀⠀⠠⠠⠡⠀⠀⠀⠀⠀⠀⠀⢩⢻⡶⣍⣹⣩⡶⣟⣯⠁
⠀⠀⠀⠀⠠⠘⠛⠣⠀⠀⠀⠀⠀⠀⠴⢄⡠⠜⢻⠳⢆⡠⠦⠀⠀⠀⠀⠀⠀⠡⠡⠌⠀⠀⠀⠀⠀⠀⠰⣰⣥⠞⣿⠳⣮⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠆⡀⢭⢀⠰⠮⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠫⠆⡹⣿⢾⠱⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠍
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠰⣶⢫⠧⣩⠉⣏⠴⡜⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠢⣤⣾⢾⣆⣤⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢙⡛⢴⢽⣿⡯⡦⢚⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣽⣻⣯⣿⠋⠀⠀⠀⠀⠀⡀
⠀⢀⣮⣱⡄⠾⠭⠗⣀⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠷⢾⣹⡷⢿⣑⣄
⠀⠀⠉⠉⠁⢏⣒⡟⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡄⠀⠀⠀⠀⠀⢀⣀⠀⢀⡄⡀⡀
⠀⠀⠀⠀⠀⡧⢰⣆⡠⠄⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢠⣬⠾⣷⣦⣦⡥⠋⣀⠀⠀⠀⠀⠀⣐⠶⣤⣰⡀
⠀⠀⠀⠀⢀⠀⠀⠈⠘⠂⠀⠀⠀⠀⠊⢡⠀⠀⠀⠐⠢⠿⡏⢩⡍⠉⡱⠣⢼⡃⠀⠀⠀⠀⠠⠀⠸⡋⠈⠂
⠀⠀⠀⢠⠋⠉⠓⠠⠀⠀⠀⠀⠀⢰⡄⠶⠆⠀⠀⠀⠀⠀⠈⠙⣇⠈⠁⢀⢈⡀⠀⠐⠒⠒⠒⠒⠒⠑⠚
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⣈⠵⠁⠀⠀⠀⠶⡀⢀⡇⠀⢠⠞⠈
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣁⠠⠄⠩⡭⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠑⠠⠤⠄⠀⠀⠀⣠⡤⠠⠀⠀⠂⠀⡞⠀⠀⠀⠀⠀⢠⡴⠊⣱⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⡀⠉⠀⠀⠖⢀⠐⠂⠀⠀⡤⠜⠁⠀⠀⠁⠀⠀⠠⡤⠤⠤⠤⠤⠤⡤⠼⡇
⠀⠀⠠⣄⠀⢠⠀⠐⠀⢠⡀⠀⠀⠀⣼⣃
⠀⠀⣠⣀⣠⣄⣀⣾⣀⢘⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠠⠄⣀⣴⠁⠀⢳⠤⢁⡠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡁⠀⢀
⠀⠀⡐⠀⢀⠀⠀⢀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠐⡄
⠀⠀⠁⢀⠙⠀⠀⠐⠁⡀⠃⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠠⣂⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠤⠤⠤⣤⡀
⠀⠀⠇⠁⠴⠄⠠⠤⠀⠈⠀⠀⠀⠀⠂⠐⠀⠈⠁⠀⠈⠀⠐⠂⠀⠁⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠸⠗⠀⠀⣠⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⠀⣄⡸⢎⠛⠁⣃⣸⠋⡘⣠⣤⠀⠀⢀⣀⣀⡴⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢈⡥⡈⣉⢹⡄⣹⢛⣤⠙⠈⠁⠀⠀⠀⠀⢭⢛⠻⣶⣞⡡⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡍⣠⡞⣷⡄⠀⠀⠙⠈⠛⠁⠀⠀⠀⠂⠀⠀⠀⠸⢸⢹⠸⠳⣶⡩⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠁⣀⠠⢀⡈⠀⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠘⠀⡆⡇⡿⣖⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡷⣠⠏⠀⠀⠀⢷⠀⠀⠀⣰⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⡏⢳⣖⣊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣸⠇⠀⠀⠀⠀⢸⡇⠀⢠⡏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⢘⠀⣿⠀⠀⠀⠀⠀⢸⠃⠀⣼⢁⠞⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠀⡁⣀⠉⠠⢁⠀⠀⠀⠀⠀⣿⠀⠀⣿⠊⢠⡞⣳⠂⠀⢸⡇⢀⡆⢸⡇⢠⡖⢰⠆⠠⡆⠀⠀⠀⠀⠀⠈⣶⠤⠤⡄
⠀⠀⠀⠀⠄⠀⠐⠂⠘⢲⣶⡄⠐⠇⠒⠂⠈⠠⠀⠀⠠⣿⠔⠈⣿⠀⠸⠇⢹⡀⠀⢿⠁⠞⠁⣾⠠⠞⠀⠸⠀⢰⡇⠀⠀⠀⠀⠀⡴⠁⢳⡀⡣
⠀⠀⠀⠉⠀⠀⠈⠁⠀⢈⣿⣿⡷⠄⠉⠀⠀⠀⠉⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠂⡼⠀⠀⠀⠀⠀⠀⢸⠀⢨⠁⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⡴⠒⠂⢲⡄⠀⠀⠀⢨⠞⢀⠆⠀⠀⢠⠎⢸⠀⠀⠀⠀⠀⢀⡞⢀⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠳⡀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣠⠏⠀⠀⠀⠀⣷⠀⠀⢠⡏⠀⡜⠀⠀⢠⡏⢀⡞⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⣀⡑⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢡⡟⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⡼⠁⠀⠀⣼⠁⡞⠀⠀⠀⠀⠀⢸⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣿⠀⢠⣏⡜⢁⠀⠀⠀⣿⠜⠀⠀⠠⠀⠀⠀⣿⠜⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⣀⡸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡇⢀⢸⡏⠀⣿⠄⡷⠘⣇⠀⠀⢀⣿⢀⡾⢩⣿⠀⠀⠀⣴⠋⠟⠀⡏⠀⢸⡇⠀⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⣯⢀⢄⠀⠀⢸⡏⠀⢸⡇⠀⠙⠀⠁⠀⣿⠀⠀⠌⠋⠈⠓⠀⣿⠀⠀⡰⠛⠀⠴⠀⠃⡔⢸⠇⡔⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢧⢀⢶⠀⠈⠇⠀⠀⠇⠀⠀⠀⠀⠀⠙⠆⠈⠀⠀⠀⠀⠀⠘⠇⠀⠁⠀⠀⠀⠀⢸⢀⡿⠀⠀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡎⢿⡜⠘⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢫⣥⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢷⣌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣯⣋⣡⠐⢂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠉⢀⣄⢀⡄⠻⢷⢠⡄⠀⠀⢠⣤⠀⣀⠀⠀⢠⣤⠀⠀⠠⠈⠁⢀⠐⠛⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡕⠓⣰⠿⢇⣘⡿⠰⠠⡿⡞⠛⠰⠂⠈⠉⢀⠀⠀⠀⣀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠰⢆⣤⡔⣋⢣⣤⠅⣼⣁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠉⢀⡔⣉⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣠⡶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡂⠀⣯⡰⢀⣠⣶⡿⠋⠁⠀⠀⠀⠀⢀⡤⠀⠀⠀⢬⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⢀⠀⠀⠠⣅⢀⠀⠼⠻⠣⠞⡿⢞⣏⠘⢋⠀⠀⠀⢀⡤⠐⠉⠊⠀⢶⠄⠀⣶⢻⣤⠀⠀⠠⡷⠀⠀⠀⣭⡠⢶⡅⣬⣧⢸
⢰⣦⠿⡆⣶⢬⡩⣼⣷⢾⠾⡖⠾⣇⠈⠙⠀⠁⠀⠒⠘⠿⠀⠀⠀⠀⣘⣿⢃⠐⠻⡾⢆⡀⠀⠒⣷⠗⡄⢸⣏⡷⢆⠘⡿⣼⣼
⢸⣿⡟⢿⡷⠚⠃⠞⢧⡏⣰⣟⡠⢻⣴⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣼⠘⡓⣺⡿⣬⠁⠘⢛⣿⢬⠑⢈⣿⡶⢛⠚⢷⣧⣰
⣸⣯⣷⡟⠖⠊⢱⡓⠻⣿⣿⣿⣥⣾⣿⣄⣷⣧⣿⣤⣦⣦⣄⣀⣄⡤⢟⣸⣝⣓⡀⡀⠀⢀⣌⠉⣍⣠⠺⡠⣭⣷⣿⣷⣼⣞⢸
⢸⣿⣿⡗⠞⣠⡞⠳⡶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣳⣾⣿⣊⢽⠉⣯⡙⣝⣿⣟⠑⠫⣿⠒⢣⠒⡖⠸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠆⢴⠀⢰⣄⣻⡬⠇⠙⠙⣿⠈⠙⠛⠛⠁⠉⠈⠛⠛⠿⡏⠅⠺⠃⠠⠿⠉⣟⠹⡊⡁⠘⢵⠊⣰⠙⣬⡟⣿⠟⠉⠉⠻
⠀⢀⣙⡒⢉⡉⢠⠄⠀⠛⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⠂⠉⠀⠀⠀⠀⠀⠙⠉⠀⠀⠂⠐⠲⠂

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢰⡀⣶⡿⠴⣀⣦⣀⡰⣂⣀⣾⠀⠀⠀⢤⣀⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢨⣧⡽⣿⣄⣀⢀⠀⠀⠀⣘⠀⠀⢠⢐⣷⠀⡀
⠀⣫⡿⠐⡷⢄⣹⣿⣿⣷⠛⠟⢴⠸⣿⣻⡭⡾⣶⣖⣸⣩⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⢷⡀⡞⢿⠻⣽⣌⠤⣿⣤⣶⢿⢈⡗⢻⡞⠾⣿⠠⣷
⠀⣭⢗⡎⠰⣀⡝⡻⣏⠬⡇⢀⣲⢃⣿⠁⣷⡁⡿⠁⠢⠼⠲⡃⢤⣄⣤⣀⣰⣧⡀⣀⣤⣴⣤⢛⣑⡖⣋⣍⠐⠯⠑⠿⡬⣖⠘⣿⣏⢃⡌⠣⣍⣷⠲⢹⡟⠻⡆
⠀⡟⡈⢹⡦⡟⢱⠇⢹⣴⢿⣋⣽⢠⣵⢇⣸⡹⠖⡙⣖⠉⣿⣍⠘⣿⠏⢿⣃⠋⢿⣿⣷⢿⡟⣸⣯⣁⡌⣗⣠⣷⡔⢻⠷⢌⢛⠻⣿⡅⠊⢲⠈⢹⡉⣸⠺⡿⠃
⠠⠊⢀⣾⡤⠁⣻⠦⡞⠟⣢⠂⣵⡬⢂⠚⣻⡗⣋⠎⢁⢿⠀⣆⠙⢫⣧⠊⠡⠲⠉⢿⢵⡽⢧⡠⢒⠈⢿⢅⣷⠀⣯⡘⢧⠈⠷⣴⣧⣀⢽⠀⢋⠘⣤⡯⠰⣙⡇
⠀⠀⠀⢈⠃⠒⠷⢄⠙⣀⠀⠀⠈⠐⠋⠙⠁⣤⣌⣻⡇⠀⢳⣸⡟⠲⠈⠒⠒⠒⠀⠈⠀⠀⠀⠁⠈⠐⣋⠋⢈⠱⠗⣈⡑⢯⣀⣌⠸⠓⠴⠀⠸⠢⣮⠔⠀⣌⠁
⠀⠀⠠⠯⠐⠚⠠⠈⠑⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡀⢹⣆⡀⡘⡟⠢⢩⡍⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡜⠈⢇⠀⠤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⡦⠀⠀⠀⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡤⠊⠓⣤⡆⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠞⠀⠆⡼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣤⣄⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠘⢃⣡⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⢠⡄⢀⣿⠂⠀⠀⠀⠀⣶⣤⠶⠶⠦⠤⠤⠞⠋⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣷⠀⠀⠀⠀⢀⡀⢠⣄⢸⣿⣼⣿⢁⣾⡇⣸⣿⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣿⢁⡟⠀⠀⠀⠀⣸⣇⣿⡏⣸⣿⠘⣿⣾⠛⠿⢿⡏⠀⠀⠀⢀⣠⠞⠀⠀⡰⠤⠤⣀⣤⠤⠴⠞⠛⠀⠒
⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⡟⠀⢸⣷⠊⢠⣿⢿⣷⠀⣿⡟⣿⣁⣿⡇⠀⠀⠁⠀⠀⣼⠃⠀⢠⣄⣸⡇⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠁
⠀⠀⠀⣠⡶⠟⠉⠁⠀⢸⠃⡠⢾⡇⠀⣾⡏⢸⡏⣸⣿⠃⠈⠉⢹⠀⠀⠀⠳⣤⣾⠏⠀⠀⠀⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣠⠞⠁⠀⠀⠀⠀⠀⣾⠂⠀⢻⡇⢀⣿⣧⣿⠟⢩⡟⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⣰⠃⠀⠀⠀⠀⠀⠠⣾⡟⠀⠀⠘⢷⡾⠁⠉⠁⠀⠸⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣀⢸⣷⣄⡀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⢰⡷⠀⣿⣿⡆⠀⣰⣿⣿⣿⣆
⣇⡀⠀⠀⠀⠀⣀⢡⡿⠁⢰⣿⡆⠀⠀⣰⡆⠀⣠⣶⣦⡀⠀⠀⢻⣿⠀⠀⠀⠘⢻⣿⠻⠆⣻⣿⠿⣦⡀⠀⠀⠀⣿⣿⡗⠀⠀⢸⡇⢸⣿⣿⠃⢠⣿⣿⡟⢹⣿
⠈⠉⠀⠀⠀⠀⠲⠟⠁⠀⢸⣿⡇⠀⠀⣿⡇⢰⣿⡏⠙⣿⡄⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⣾⡇⠀⠈⢿⡄⠀⠀⣿⣿⣧⠀⠀⠸⣧⣿⣿⣿⠀⢸⣿⣿⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠶⢾⣿⡇⣿⣿⠇⠀⣿⣧⠀⣾⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⣿⣿⣿⣤⣤⡄⠈⠉⣿⡟⠀⠀⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿⡇⢻⣿⡆⢰⣿⡿⠀⣿⣷⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢀⣿⠇⠀⢾⣿⠟⢻⣏⠉⠁⠀⢠⣿⡇⣤⣄⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠘⢿⣷⣿⣿⡷⠀⣿⣿⣾⣿⣷⠴⣿⣿⡄⠀⢿⣷⣴⡿⠋⠀⠀⣸⣿⠀⠈⣿⡀⠀⠀⣿⣿⡇⠙⣿⣦⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠻⠇⠀⠈⠛⠿⠿⠃⠀⠈⠛⠁⠀⠀⠀⠙⠻⠟⠀⠀⠈⠁⠀⠀⠀⢾⣿⣧⠀⠀⠘⠷⠀⠀⠙⠿⠗⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⣄⠠⠀⠀⠀⠀⠀⠀⠈⡁⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣔⣿⠞⢡⠀⠀⠀⠀⠀⠀⠈⠁⠠⢀⡁⠀⡀⠀⠀⣠⠄⢠⠒⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠒⠈⡅⠀⠀⠀⠀⠀⠐⣤⠐⠈⠊⠄⠈⠁⠀⠀⠀⢲⠈⠐⠛⠙⠷⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠁⠀⣀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠋⠉⡇⠀⠀⠀⠳⣄⣀⣠⠔⠀⠀⠀⠀⠀⠀⣆⣘⡀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣴⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⣀⡆⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠠⢿⣴⡹⡟⣱⡾⠤⠀⠀⢀⡀⣙⢿⣁⡿⢃⢀⡀⠀⠀⢠⢷⣦⣻⣟⣰⡼⣄⠀⠀⠀⢴⣦⡔⣿⢣⣴⡶⠄
⠀⢀⣸⣥⠿⡿⢤⣍⣀⠀⠀⠀⠟⢟⣻⠧⣟⡻⠻⠄⠀⠀⢀⣨⣭⢿⡿⣯⣍⡀⠀⠀⠀⢀⣭⡽⣭⢯⣭⡀
⠀⠀⠛⠉⣺⣟⠊⠙⠀⠀⠀⠀⠀⠾⡟⠓⢻⠧⠀⠀⠀⠀⠀⠻⠙⢺⣗⠈⠹⠁⠀⠀⠀⠙⠋⠑⣿⡊⠙⠛
⠀⠀⠀⠀⠉⠈⠀⠀⠰⢦⣿⡴⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡉⠈⠀⠀⢀⣶⣶⣀⠀⠀⠀⠉
⠀⠀⠀⠀⣤⠀⠀⠀⠐⠋⡿⠙⠂⠀⢶⣖⣿⣲⡾⠄⠀⠀⠠⣦⣾⣷⣴⠆⠀⠈⠟⠻⠁⠀⠀⡀⣶⠄⡀
⠀⠰⣶⣌⣿⣱⣶⠇⠀⠀⠀⠀⠀⠠⣼⢞⣷⣳⣧⠄⠀⠀⠠⠿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠻⣦⣎⣿⣳⣶⠿⠂
⠀⣀⣴⡿⣿⢷⣶⣀⠀⠀⠀⢠⣦⠀⠀⠀⠛⠂⠈⣀⣰⣀⡀⠀⠘⠃⠀⠀⢠⡤⠀⠀⠀⣉⣲⡶⣻⢳⣞⣉
⠀⠈⠁⠘⣿⠁⠈⠁⢰⣦⣠⠺⡿⢢⣤⣦⠄⠀⠀⠼⢿⠿⠄⠀⠀⢠⣦⡤⢝⣟⢄⣤⣆⠉⠁⠊⣽⡑⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣿⣉⣏⣳⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣹⢹⣿⣿⣏⢏⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠰⠿⠙⠴⣷⠜⠹⠷⠀⠀⠀⠀⡸⣂⠀⠀⠀⠙⠟⠃⣫⣏⠎⠟⡞⢀⠀⠀⠀⠀⡀
⠀⠀⠐⣶⣌⣅⣶⡆⠀⠀⠀⠘⠟⠀⠀⠀⠰⢆⣆⡄⢽⠵⣀⣤⠴⠆⠀⠀⠘⠓⠀⠀⠀⢯⣹⢠⡔⣏⡇
⠀⣈⡑⣶⣬⣯⡼⢗⣍⡀⠀⠀⠀⠀⠀⠀⠀⠉⣚⣻⡞⣶⣛⡊⠁⠀⠀⠀⠀⠀⠀⣀⢤⡒⣞⣯⣿⣷⣃⡤⣀
⠀⢙⠫⣶⢛⣟⠳⠿⢋⠁⠀⠀⣄⣤⠀⠀⣤⠝⠞⢣⢼⠌⠟⡞⣥⠀⠀⣄⣶⣠⠄⠙⠚⢩⢯⣿⣿⡿⠭⠓⠉
⠀⠈⠠⢿⠏⣋⢿⠧⠈⠀⠀⠘⡿⣿⠃⠀⠀⠀⠀⠐⣫⠃⠀⠀⠀⠀⠀⠞⣿⠳⠀⠀⠀⢶⣻⠘⠣⣏⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠷⠀⠫⠾⠒⠻⠘⠴⠐⢿⠘⠻⠴⠀⠺⠧⠶⠆⠐⠕⠗⠋⠺⠺⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣠⡞⢛⡛⡶⢤⣤⡶⠆⠀⠀⠀⢠⣤⡤⣜⣿⣳⢤⣤⡤⠀⠀⣀⡀⣀⣠⠾⣿⠵⣦⣀⡀⣀⡀⠀⠀⠹⣶⠀⢰⡿
⠀⠀⠀⠹⢳⣿⣬⣿⣞⣿⣷⣶⣹⡇⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣯⡝⠁⠀⠀⠙⣿⣫⣜⡟⠾⠚⣧⢷⣻⠉⠀⠀⣠⣀⣈⣷⣮⢡⣤⣦⠤⠄
⠀⠀⠀⠀⠀⣷⡾⣗⢿⣻⣿⣯⣍⣧⡀⠀⠀⠀⢀⣾⣶⣻⢿⢿⣷⣾⣦⠀⠀⠀⣹⠲⢏⡩⢿⢯⣭⢗⣺⠀⠈⠉⠉⠋⢁⡽⠻⣤
⠀⠀⠀⠀⢀⣾⣾⢋⣿⢷⠟⣳⠼⠟⠻⠂⢀⡄⠈⠉⠉⠐⢿⡟⠀⠀⠀⠀⠀⣠⣽⣞⣋⡧⣺⡲⣏⣟⡾⣤⡀⠀⠀⠀⡿⠃⠀⠛⢧⡀
⠀⠀⠀⠀⠚⠃⠁⠉⠛⠾⡿⠁⠀⠀⠀⠀⢰⣧⡀⠀⠀⢀⠈⠀⠀⠀⢠⡄⠀⠉⠀⠈⠉⠾⢽⠵⠋⠉⠀⠀⠀⠀⠀⠈⠁⠀⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠋⠀⠘⠳⣶⣆⣽⡿⣤⡵⡞⠋⠀⡀⠀⠀⠸⡧⠀⢀⣠⠆⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣻⣿⣶⢿⠁
⠀⢀⠀⠀⠀⡐⣿⡗⣀⢠⣤⠞⠂⠀⡌⣸⣽⣿⣽⣬⡅⠀⠀⠉⠻⠶⢄⣯⡴⠛⠃⠀⠀⠀⠀⠒⠠⠁⡐⡈⡀⢀⠀⠈⠙⣿⣿⣿⣿⣯⣦⡀
⠀⠈⠛⢷⣷⣽⣾⣽⡿⣟⡛⠀⠠⠶⠛⠋⢽⣿⠅⠛⠛⠶⠀⠀⢠⣤⠞⢹⠙⢳⠶⣄⠀⠀⢀⠰⠣⡠⡞⣀⡠⠤⢀⠀⢀⡷⠯⢿⣯⠋⠁
⠀⠀⠀⢀⣒⣿⣿⣿⣷⢿⣴⣄⠀⠀⠀⠀⠀⣟⠀⠀⢀⠀⠀⠐⠋⠀⠀⢺⡇⠀⠀⠀⠀⠐⢀⠄⠵⢺⡿⢍⢀⠰⠀⠀⠀⠀⠀⠀⠙
⠀⠀⣀⡴⠟⠫⠏⣿⣍⠂⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⡈⣦⡀⢠⡞⠁⠀⠈⠃⠀⠀⠀⠀⠀⠠⠠⠄⠼⠌⣀⠁⠂⠃⠀⠀⠠⡄
⠀⠀⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡀⠀⠀⠀⠀⠦⠴⢴⣿⣿⣷⣀⡀⡀⠀⠠⣦⠀⠀⠀⢠⡄⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⣿⡆⠀⣤⡴⠃
⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⢀⣠⣺⣗⡦⣤⡴⠂⠀⠀⣨⠟⠿⡏⠌⠉⠉⠀⠀⠸⣦⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣶⣤⣾⣿⣷⡏⠁
⠀⠀⢰⣦⣔⣿⣄⡀⠀⠉⡿⣾⣯⣯⡿⣯⡇⠀⠀⠰⠁⠀⠀⢳⠀⠀⠶⠤⣶⡤⢝⡼⣥⣤⣄⣀⡀⠀⠀⡀⠀⠀⠀⠀⢁⣘⣿⣿⣿⠻⡾⠦⡤
⠀⢀⣬⣻⣿⣿⣾⠟⠁⠀⢨⣽⣾⣿⣽⣟⡾⠤⠀⢤⣤⣾⣤⣀⠀⠀⠀⠀⠀⣠⡟⠸⣆⠀⠀⠈⠡⣀⡀⠗⣠⠔⠀⢀⡼⠛⠀⠸⣷
⠀⠈⠉⢩⣿⠛⠿⠇⠀⠐⠋⠉⠙⢾⡗⠁⠀⠀⠀⣸⣯⣷⣽⡇⠀⠀⠀⠀⣴⠋⠀⠀⢹⣄⠀⠀⠀⢀⡬⢻⠳⠤⡀⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡯⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣙⣳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡙⠿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣋⣤⣴⣿⣷⣆⠈⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠟⢻⣿⠿⣿⣿⣿⣿⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣠⠴⠛⠃⣤⣾⣿⣿⣿⣬⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣧⠄⢀⣴⣿⣅⢀⣿⣿⣍⡻⡟⣳⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢆⢀⡷⣼⣿⣿⡿⠟⢁⡰⠎⣩⣿⣿⠏⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢿⣿⢿⣿⣿⡟⠉⣃⢲⡛⠛⠛⠻⢆⣈⣤⣤⠴⠋⣹⠇⠀⠀⢀⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢀⢉⡼⠋⠁⢠⣾⣿⣯⠝⢶⡤⡴⠾⠿⠟⢽⢳⣾⣥⣤⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⠞⠛⣿⡀⢀⡀⣀⣾⣿⣿⣿⣶⣤⣤⣤⣷⣶⣶⡘⣟⣿⢿⣿⠿⢿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣁⢀⣤⠂⠀⢀⣨⣷⣨⣿⣿⣿⣽⣿⣿⣿⡇⠀⢹⣿⡟⠿⡿⢧⣿⣶⣤⣴⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣒⠉⠙⠓⠲⠧⢬⣁⠛⠉⣫⣼⣄⡠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠛⢹⢿⣻⣽⠟⠋⢱⣾⠿⢿⣦⡽⠟⠛⠿⣿⡷⣶⡄⢠⡼⢋⢀⡀⠀⣠⣶⢶⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡂⣀⠠⣦⠰⠟⠉⠀⣀⣠⣾⣿⣄⣼⣿⣖⠶⢤⣤⡬⢿⣶⠊⠁⠙⠿⣿⣿⣶⣟⣁⣾⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣉⢩⣅⠀⠀⠘⣧⡀⣠⣾⠟⠛⠋⣠⣦⠀⠛⢿⣦⣆⡀⠀⠀⠙⠿⣷⣠⣤⣀⠈⠉⣉⠉⣭⣁⣴⣶⣾⠇
⠀⠀⠀⠀⠀⡸⢸⣿⣿⣦⡆⠀⠙⠣⣾⠟⣿⡷⢀⣷⣷⡟⠾⠁⣀⣴⣿⠧⣿⣷⡀⠀⠙⣿⣿⠂⠀⠀⡖⠉⢻⡟⣿⣿⣶⣿⣶⡏⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠐⣷⣾⡿⢣⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⢻⣿⣥⣿⠒⢿⣿⡇⠀⠀⠈⢿⡿⣿⣇⠰⢲⠞⠀⠀⠙⢿⣇⡁⠀⠀⠀⠀⠀⣠⡄⢰⣞
⠀⠀⠀⠀⢀⡿⠙⢱⡟⠀⣴⣶⣶⣶⠀⣠⣴⠿⠋⢀⡰⣷⣾⣿⣿⠿⢿⠦⢾⣿⣷⣶⠀⢀⠈⠙⠻⢿⣿⣛⢿⡷⢦⣄⣠⣈⢉⠓⢦⣤⣤⣾⢣⢿⣼⣿⡇
⠀⠀⠀⠀⢸⠃⠀⡾⢸⣿⡘⣿⣿⣿⡟⢉⠀⠀⣰⣿⣷⡸⣿⣷⣿⣤⣴⣄⣴⣿⣟⣻⣾⣿⡆⢰⣶⣾⣯⠉⠳⣄⠸⠟⠛⠛⢾⣿⣤⣦⣤⣿⣿⡜⠛⡿⠤⠴⠂
⠀⠀⠀⠀⢸⡆⢸⡇⠀⣿⣧⠹⣿⣿⣿⡘⢷⣿⠟⢛⣉⢷⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⣿⠇⣾⣿⣿⡟⢀⡼⠋⣀⣀⠀⠀⠀⣽⢻⡽⠿⣿⡍⠀⢸⠷⠿⠂
⠀⠀⠀⠀⢸⣇⠈⢷⡖⠛⡿⠃⠉⣀⣀⣰⣞⢳⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⢀⣤⣤⣄⢸⠟⠀⠿⢿⣿⣧⣾⣵⣿⠟⠻⣿⡆⠀⣷⢰⣇⣴⡟⣠⢆⡇
⠀⠀⢀⡴⠾⣷⡀⠈⢿⡾⣧⣴⣿⣿⠋⠉⣿⣿⣿⣿⡇⠀⠀⠸⡏⢿⡇⣰⠿⠋⠉⢻⡟⠶⠦⠶⣦⣿⣿⣿⣿⠀⠀⠀⢹⣿⢠⡷⠖⢛⣫⣾⣡⣾⣀⡀
⠀⠀⠈⢰⣿⣿⠧⡀⢨⢷⣿⣿⠷⠛⠀⠀⣸⣿⣿⡏⠤⠀⠀⠀⣿⡘⣹⣿⠀⠀⠀⣼⠀⠁⠀⠀⣜⢹⣿⠟⣿⠄⠰⠆⣼⣾⣯⠶⢒⣻⣿⣟⣥⣤⢀⡉⠁⣀
⠀⠀⠀⠀⠉⠃⠀⢻⣿⣼⣟⢣⣀⠐⣠⢤⣿⣿⣿⣿⠔⣄⠶⢰⣿⠇⢻⣿⠣⡜⠃⠻⡇⠶⠀⠀⠉⣻⣟⢦⡀⠶⣤⠴⠂⣠⢿⣾⡟⠋⢠⡅⠈⡿⠏⠛⠃
⠀⠀⠀⠀⠀⣼⢻⡏⠙⢯⠙⠿⢿⣯⣤⡞⠁⣉⣿⡀⠀⠀⠑⠉⠉⠀⣸⡈⣳⣶⣶⡾⠿⢆⠰⡶⠚⢿⣿⣿⣿⣶⣦⣀⠶⠋⣀⠬⠛⢁⡾⠶
⠀⠀⠀⠀⢰⡇⡀⠃⣀⢈⣷⣀⣀⠈⢩⡙⠚⠻⠿⣷⣤⣀⣀⣀⣄⣰⣿⣿⣯⢿⣿⣇⢀⡜⠉⢱⣄⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣸⣧⣄⠀⠈⡄
⠀⠀⠀⠀⣸⢟⣡⠋⣹⣿⣿⣿⡿⢣⢸⡏⡷⣶⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⡧
⠀⠀⠀⢀⡾⢹⡇⠀⢿⢻⠝⡏⠀⠀⢸⡇⡇⣿⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠆⢶⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣠⡄⣲⠴⢷⠀⣸⡿⢥⣠⠔⠋
⠀⠀⠀⢘⣷⠟⢳⡀⢀⡟⣰⠀⠀⠀⠘⠃⠗⠿⢸⡏⢸⡇⢸⡇⢰⡆⡆⠀⣿⠀⠀⢼⠐⡆⣷⠁⣷⠛⣤⣿⢸⣿⣿⠷⠟⠃⠈⢠⡏⠀⢠⡗
⠀⠀⠀⢸⡏⠀⢸⣿⣼⠁⠈⠉⠛⠲⠦⠤⣤⣀⣀⡀⠈⠁⠈⠃⠈⠃⡇⠀⠙⠀⠀⠚⠚⠃⠛⠀⠉⠀⠉⠀⠀⠀⣀⣀⠤⠤⠒⠉⢷⣠⠟
⠀⠀⠀⠈⢿⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢴⡦⠶⠶⠖⠙⠃⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢠⣾⣎⣻⣏⣿⣦⠀⠀⠀⠀⣴⣆⢹⡏⣰⣦⠀⠀⠀⠀⣴⣆⣙⡏⣠⣶⡄⠀⠀⠀⢠⣶⡙⣿⢡⣷⡄
⠀⠀⠀⢨⣭⣽⣿⣿⣭⣭⠀⠀⠀⠀⣥⣬⢿⡿⣥⣬⠀⠀⠀⠀⣭⣬⢿⡿⣯⣬⡀⠀⠀⠀⢭⣭⡽⣿⢯⣭⡅
⠀⠀⠀⠈⠛⢣⣾⣧⠟⠋⠀⠀⠀⠀⠙⠃⣼⣧⠘⠋⠀⠀⠀⠀⠙⠃⣴⣷⠈⠛⠀⠀⠀⠀⠈⠛⢴⣿⡌⠛⠁

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣶⣎⣻⣏⣴⣦⠀⠀⠀⠀⣴⣞⢻⡟⣷⣦⠀⠀⠀⠀⢤⣆⠙⡟⢡⣦⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⡄
⠀⠀⠀⢀⣍⣽⣿⣿⣍⣭⠀⠀⠀⠀⣯⣽⣿⣿⣯⣽⠀⠀⠀⠀⢍⣉⡽⡿⣍⣩⠁⠀⠀⠀⢼⣯⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠻⢃⣾⣧⠹⠛⠀⠀⠀⠀⠻⢯⣼⣷⡽⠟⠀⠀⠀⠀⠈⠏⡴⣧⡘⠏⠀⠀⠀⠀⠙⠻⣷⣿⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⡾⢾⡗⣶⣤⠀⠀⠀⠀⣄⡖⢺⡗⢲⣀⠀⠀⠀⠀⢠⡄⠙⡟⢀⣤⠀⠀⠀⠀⢠⣦⠙⡟⠁⣦⡀
⠀⠀⠀⠀⣟⣹⣿⣿⣙⡷⠀⠀⠀⠀⢾⣉⣾⣷⣉⡷⠀⠀⠀⠀⣉⢉⣳⣷⣋⢉⠀⠀⠀⠀⣈⣉⣳⣿⣏⢉⡃
⠀⠀⠀⠀⠛⢯⣼⣧⡿⠓⠀⠀⠀⠀⠊⢧⢴⡧⡼⠑⠀⠀⠀⠀⠚⠏⢠⣇⠈⠟⠀⠀⠀⠀⠘⠿⣀⣧⡈⠟⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠲⠀⢠⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠆⠀⡀⠀⠀⠀⠀⠀⡀⠀⠖⠀⢀
⠀⠀⠀⠀⠈⠁⢰⠄⠉⠀⠀⠀⠀⠀⠄⠁⠠⡄⠈⠠⠀⠀⠀⠀⠈⠁⡠⡦⠈⠁⠀⠀⠀⠀⠀⠉⠀⡤⠂⠉
⠀⠀⠀⠀⠈⠁⣠⡀⠹⠀⠀⠀⠀⠀⠀⢁⠠⠄⡈⠀⠀⠀⠀⠀⠈⠃⢀⡄⠈⠋⠀⠀⠀⠀⠀⠃⠀⣀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠛⢽⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢺⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⢾⡛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣦⣄⣤⠤⡄⠀⠀⠀⠀⠤⠟⣺⣠⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⢾⠀⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣼⠗⠀⢠⡶⣻⣿⢹⣮⣿⣦⣀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡻⢾⣹⣇⣀⢡⣛⣬⢙⣛⣿⣷⣏⣑⣄
⠀⠀⠀⠠⣀⡀⠑⣺⡃⠄⠐⠠⠄⠀⢀⣄⣤⢟⠟⢫⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⡿⢿⢀
⠀⠀⠀⠘⠟⠲⠒⠛⣷⡔⢲⡀⠀⠈⠁⣨⣿⣣⠖⣈⣿⣟⣙⣫⢿⣩⢿⣿⣿⣿⣧⣶⣿⣼⣧
⠀⠀⠀⠀⠈⣵⠛⠋⠽⢿⡁⠉⡛⠿⢃⣿⡿⣋⠀⢀⣼⠿⣿⣷⣾⣏⣿⣳⣿⣿⣿⣴⣿⢩⣵⣧
⠀⠀⠀⠀⠀⠘⣷⢤⣠⠜⣿⣿⣫⣴⣏⣿⢯⣟⣰⢿⣿⡶⠛⣻⡿⣿⣿⣿⣿⡟⣿⣏⣿⣾⣯⡟⡄
⠀⠀⠀⠀⠀⠀⠘⣷⣿⣾⡽⣟⣿⣿⣿⣯⡿⣾⡤⣼⣍⣷⣌⣧⣶⣴⣯⣾⣽⣛⣿⣍⣛⣤⣿⣟⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢾⣟⣴⣿⢿⠿⣿⣿⣿⣿⣿⣽⡟⣻⢿⡷⢋⢛⣣⣾⣻⠟⣛⣟⣻⣿⣻⣩⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣯⣿⣿⣳⢬⡟⢷⣾⣛⣿⣿⣿⣿⣯⣼⡿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣭⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⢿⣵⣿⣿⣿⣿⣏⣽⣿⣿⣿⣧⣤⣧⣄⣿⣇⠈⣼⠿⣿⠿⣛⣫⢿⣿⣿⢿⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣹⣷⣻⣍⣿⡾⣿⣿⣿⣿⣿⣯⣛⣿⣻⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣼⣿⣿⣯⡄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⣿⣿⢟⣿⣏⣽⢿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣻⣟⣩⣟⣛⣿⣟⣧⡾⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⣿⣿⣿⣿⡤⠒⣛⣷⣫⣞⣿⣿⣯⠈⠛⠿⠟⠿⣿⣿⢿⢿⡙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠁⠉⠿⣿⣿⣽⣧⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠻⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⣶⠉⠈⠀⠀⠀⠀⠀⠈⠻⢿⠟⠙⠻⠻⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠾⠛⠃⠀⠀⢠⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⣿⣡⠄⢄⢸⣇⡤⠀⠀⠀⡆⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠑⢄⠀⢹⡏⢀⡴⠃⢀⡿⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⢰⠈⠀⣤⠑⢼⡷⢋⣄⠀⠈⡆⠀⢰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢤⣠⠀⡄⠠⠤⠷⢇⠀⢸⠀⠘⣿⠇⣸⣇⠸⡿⠀⠀⡇⢀⡼⠯⠤⠄
⠀⠀⠀⠀⠀⠀⢘⣛⣷⣇⢀⣀⣀⣠⣵⣾⠀⠀⡠⠊⢸⡏⠳⣄⠀⢀⣷⣋⣀⣀⣀⡀⠀⢀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⡱⢎⠀⢠⢾⣧⡀⢈⡵⢏⠀⠀⠀⣀⠀⠐⠚⡻⣟⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠳⣄⠺⠿⠗⣠⠞⠁⢀⡝⢇⢸⣇⡽⠫⡀⠀⠑⢄⠻⠿⠛⣠⠊⠀⡨
⠀⠀⠀⠀⠀⠰⠶⠾⡷⠶⠾⡷⠶⢾⠷⠶⢶⡷⠶⢶⣿⣿⠶⠶⣾⠷⠶⢾⡷⠶⢾⡶⠶⢾⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⡊⠀⡠⠋⣤⣶⣦⠑⢄⠀⢉⡶⣋⢸⡇⢱⣞⠁⢀⡴⠋⢴⣾⡦⠙⢦⡀⠙
⠀⠀⠀⠀⢀⣀⣦⣽⣮⡤⠀⠀⠉⠀⠀⢀⡵⢋⡀⠈⢻⡷⠃⠀⡱⢎⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠋⠜⠁⠀⠈⠉⠉⢉⡽⣿⠀⠀⠙⢦⣸⣇⡠⠊⠀⠀⡟⢏⠉⠉⠉⠀⢹⢿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡿⡏⠀⢹⠀⠀⣾⡆⢹⡏⢰⣿⡄⠀⡇⠀⣷⢖⠒⠂⠘⠀⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠇⠀⠘⡀⠀⠙⣡⢾⡗⣄⠛⠀⠀⠇⠀⠸⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣾⠁⢠⠞⠁⣸⣇⠀⠑⢄⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠸⠀⠀⠀⠚⢹⡇⠑⠐⢋⣿⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸

⠀⠀⠰⢦⣤⣤⡀⠀⡀
⠀⠀⢀⠀⠀⠀⠄⠲⠞⠛
⠀⢰⠛
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⢤⣤
⣷⢀⡀⠈⢿⣿⠀⠀⢀⠀⢀⣄⠀⠀⠀⣠⠀⣤⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉
⣿⠙⣿⣿⡆⠀⢀⣠⡿⠞⠛⠉⠈⠀⠀⠉⡄⠘⡿⣿⣆⠀⠀⠔⠀⣀⠀⣀⣀⠀⢠⣀⠑⠀⠀⠀⢀
⣿⡿⡟⠙⢃⣤⠠⠠⠑⠂⠄⠀⠀⡆⠀⣀⠀⠈⠀⠈⠙⠛⣄⡀⠀⠈⠁⠉⠲⣶⣤⣍⠻⢷⣶⣆⠸⠆
⠛⠛⢧⣞⡳⠛⠂⣀⠐⠈⣂⣀⠐⠚⠀⠙⠿⢧⣤⣠⣄⡀⠀⠀⡀⠀⣤⣀⠀⠈⢙⡛⠟⠒⣯⣿⡀⠀⢠
⠀⠀⣼⢿⡶⠾⣾⣿⣿⣛⡝⠋⠀⠀⠀⠀⠀⠀⠀⠁⢙⡇⣶⡄⠁⠚⢟⣃⣀⠀⠈⢋⠐⠀⢿⣿⣿⣷⣾
⣀⣶⡷⣶⣆⣤⣸⡭⢛⠏⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠤⣤⣝⡻⣇⣊⠙⠛⠃⢶⠀⠳⣄⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⠃⠙⠇⢰⠠⠘⠁⠐⣜⣶⣿⠛⢿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢀⠴⠚⡗⠒⠀⣡⠴⠒⠒⠀⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⢰⠃⡀⠀⢏⡀⠠⠁⢀⠎⢀⡀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡗⠁⢀⡟⠀⢈⡆⠀⠀⠀⡀⠀⠢⠁⠀⠀⠀⡀⠈⢳⣀⡰⠃
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢸⠃⠀⢸⣧⠶⠋⠀⣶⢀⡀⣷⠠⡄⢶⠀⡆⠀⣈⡒⣺⡋
⠀⠀⠀⠀⠀⠘⠁⡔⠒⢦⢸⣀⡴⣿⢁⡖⢸⠀⣿⢀⡇⣿⢰⠇⠻⢼⡇⢰⠁⡠⡃⠘⡆⢠⠖⠚⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠐⠀⠑⠀⢊⣾⠋⠀⣿⠈⠓⠛⠂⡿⠈⠁⣿⠀⠀⡀⣼⠐⠚⠻⠐⣡⢶⠗⠷⣄⡜⠉⠗⠀⣼
⠀⠀⠀⠀⢀⡤⠤⢀⢀⡞⣿⠀⠀⢻⠀⠈⣳⠀⠇⠀⣀⢩⡔⠃⠀⡦⣄⠀⠀⣸⡵⠋⠀⠣⠞⠘⠢⠤⠔⠃
⠀⠀⠀⠀⡏⠀⠀⠼⠀⣰⠇⠀⣀⡈⠓⠐⠁⣠⠖⠉⠀⠘⠧⠤⠞⢀⡈⢳⡄⠇⠀⠀⢀⠤⠒⠒⠂⣄
⠀⠀⠀⠀⠳⢤⣀⡤⠶⠋⠀⡼⣡⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⡇⠘⢦⣠⣃⡰⠀⠀⢐⣹⠉⠑⣆
⠀⠀⠀⡴⠒⠐⠲⢄⢀⡠⢴⡏⠁⠀⢠⠏⡀⡀⠀⢀⠄⠀⢄⠀⠈⠢⠀⠐⠁⠀⠀⡏⠈⠀⠀⠀⢀⠔⢢⠀⣸
⠀⠀⠀⠓⠀⠀⡠⠚⢳⠀⢸⡇⠀⢠⡏⠈⢃⡇⢰⠁⢀⠀⣼⢀⡄⠀⠀⠀⠀⠀⠀⢣⣀⡀⠀⠀⠘⢤⣩⠴⠃
⠀⠀⠀⠀⢀⡞⢀⡴⢺⢄⢸⡇⠀⣸⠁⣠⠞⠀⣾⣀⡭⠞⠁⢸⡇⣠⢴⡄⢲⠘⡇⡓⢬⠁⢀⡠⠄⠤⡀
⠀⠀⠀⠀⢸⠀⠀⠉⠁⢠⢸⡇⣠⣿⠚⢁⡀⡉⡏⠀⡇⠀⡏⢘⡇⠿⡼⠇⠘⠚⡇⠈⢉⡔⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠳⠤⡤⢴⡧⢾⡏⠁⡇⠀⢺⣀⡟⢷⡄⢳⣄⣙⣉⣍⣀⣀⣀⣀⣰⣇⣠⣋⣀⣀⣠⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢸⡇⠀⣷⠀⠀⠁⠀⣰⠚⠉⠁⠀⠀⠀⠀⠀⠀⡴⠋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡂⣹⢳⠀⢻⡀⠀⠀⠀⠱⢄⣀⠀⢀⣀⣀⡤⠔⣋⣀⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠠⣍⠉⢡⠴⠚⢉⡴⢋⡤⠄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⠃⢅⡤⠖⠋⠀⠘⢤⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⢿⣦⣾⢇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣉⣿⠀⣿⡇⢸⣏⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣷⣿⣷⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠈⣿⡇⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⣿⡇⢀⣴⠟⠁
⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣷⡟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⢠⣤⢰⣿⣙⣿⠂⠀⣠⡄⠀⠀⠀⠀⢸⣿⢷⣤⡀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣠⣶⢿⣿⠀⠀⠀⠀⠀⣤⠀⠀⢿⣏⣹⣷⢠⣤
⣀⣤⣿⣄⡙⢿⡇⠀⠀⠸⣧⠀⠀⠀⠀⠘⣿⠀⠈⠻⢷⣤⡀⠀⠀⣿⡇⠀⠀⣠⣴⠿⠋⠀⢸⡇⠀⠀⠀⠀⢰⡿⠀⠀⠀⣿⠋⣡⣾⣧⣄
⢈⣵⣤⣉⣻⣿⣿⣀⠀⠀⢿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠻⣶⣄⣿⣇⣴⡾⠋⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⣾⠇⠀⢀⣼⣿⣿⣋⣡⣼⡍
⢾⣯⣹⡿⠋⠉⠉⠛⠿⣦⣼⣷⠀⠀⠀⠀⣿⡇⠀⢰⣶⣄⠀⠀⠙⣿⡟⠁⠀⢀⣴⣶⠀⠀⣿⠇⠀⠀⠀⢸⣿⣴⡾⠟⠉⠉⠉⠻⣿⣨⣿
⠀⠉⠛⠀⠀⣀⣀⣤⣤⡶⠿⠿⢷⣤⣀⠀⢸⡇⠀⠘⣿⠙⠿⣦⣄⣿⣇⣤⡾⠟⢹⡏⠀⠀⣿⠀⢀⣠⣴⠿⠿⢷⣦⣤⣄⣀⡀⠀⠙⠋⠁
⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠛⢷⣾⣧⡀⠀⣿⠀⠀⠈⠙⣿⡟⠉⠀⠀⣸⡇⠀⣰⣿⣾⠟⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠙⠻⣶⣿⡇⠀⠀⠀⣿⡇⠀⠀⢀⣿⣷⠿⠛⠉⠛⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠋⠁⠀⢀⣠⣴⠾⠟⠋⠛⠷⣦⣄⣿⣇⣤⡶⠟⠋⠛⠿⣶⣤⣀⠀⠀⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠿⣿⣭⣀⠀⠀⠀⠀⠺⢿⣯⣀⠀⠀⠀⠀⠀⣨⣽⣿⣿⣭⡀⠀⠀⠀⠀⣀⣨⣿⠿⠂⠀⠀⠀⢀⣨⣽⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣦⣄⡀⠀⠈⠙⠻⣶⣦⡶⠟⠋⠁⣿⡇⠉⠛⢷⣦⣶⠿⠛⠉⠀⠀⣀⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣴⡾⠛⣿⠇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡟⠿⣶⣤⣶⠟⠋⠉
⠀⠀⠀⠀⠶⣶⣤⣤⣀⡀⠀⠀⢀⣠⣶⠟⢻⡏⠀⠀⣿⠀⠀⣠⣴⣿⣷⣤⡀⠀⢹⡇⠀⠘⣿⠻⢷⣤⣀⠀⠀⢀⣀⣠⣤⣴⡶⠆
⢀⣤⣶⡀⠀⠀⠀⠉⠉⣛⣿⣿⠟⠉⠀⠀⣸⡇⠀⢰⣿⣴⠿⠋⠁⣿⡇⠉⠻⢶⣼⣧⠀⠀⣿⠀⠀⠈⠙⢿⣿⣟⡋⠉⠁⠀⠀⠀⣴⣦⣀
⢻⣯⣼⣿⣦⣤⣤⣴⠿⠋⢹⡟⠀⠀⠀⠀⣿⠇⠀⠘⠛⠁⠀⣀⣴⣿⣷⣄⡀⠀⠙⠛⠀⠀⣿⡇⠀⠀⠀⠸⣿⠉⠻⢶⣤⣤⣤⣾⣿⣨⣿
⢠⣝⣉⣤⡾⢿⡿⠀⠀⠀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⡾⠛⠁⣿⡇⠙⠻⣦⣄⠀⠀⠀⢹⡇⠀⠀⠀⠀⢻⡇⠀⠀⠹⣿⠿⣦⣌⣙⣥
⠀⢉⣿⢁⣴⣿⣇⠀⠀⣸⡏⠀⠀⠀⠀⢰⣿⢀⣤⡾⠟⠁⠀⠀⠀⣿⡇⠀⠀⠈⠙⠿⣦⣀⢸⣇⠀⠀⠀⠀⠘⣿⠀⠀⢀⣿⣦⣌⢻⣏⠁
⠀⠈⠉⠘⣿⣴⡿⠂⠀⠈⠁⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠻⣧⣼⡟⠈⠉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣿⡇⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣠⣿⣇⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⠟⣿⡟⢿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣤⣿⢀⣿⣇⢸⣧⣼⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢷⡔⣻⠀⣠⠒⣄⠀⢰⠀⡠⣄⠀⣦⠔⢲⣄⣼⠁⢀⡆⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⢿⡠⠷⠴⡇⠀⣼⡼⢀⣼⢉⡏⢠⢺⠇⠣⠀⢸⡇⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⡄⠀⠀⠀⠀⢀⠉⠁⢸⠁⠓⠁⢰⡇⠈⠁⡠⠖⠂⢸⠋
⠀⠀⠀⠀⠀⠀⢰⡇⠤⠚⠁⠀⠀⠀⣰⠩⠃⠀⠘⠀⢀⡄⠀⠀⠀⢸⡀⠀⣠⠏
⠀⠀⠀⠀⠀⡤⢺⠀⠀⠀⣾⠛⢦⣰⠇⠁⣀⠀⠀⣀⡾⠀⢀⣀⠀⠀⣉⠉⠀⢀⡔⣦⠀⢤
⠀⠀⠀⠀⠸⠇⢸⡌⢹⠆⢸⠉⡹⢼⠀⢠⠆⢠⡏⢹⠃⢠⡏⣸⠂⢰⠇⠀⡴⠘⣇⠡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠁⢿⣀⠛⠒⠁⠘⠒⠹⠄⠜⠓⢹⣀⡸⠋⠹⠄⠘⢓⡾⢱⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠈⠀⠀⠀⠀⢠⠞⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠉⠙⠓⠶⣤⣴⡕⠒⠐⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠄⠒⠈⡜⢩⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⡀⡀⢠⠐⠦⣹⡴⠂⡤⢠⢀⡀⠀⠀⠀⠀⣠⠀⢀⠀⡀⠲⡗⢀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠐⣮⠄⣉⡀⣴⡂⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢛⣺⣌⠗⣹⠸⣣⣧⡚⠃⠀⠀⠀⠀⠀⠀⠨⠾⢤⣭⠓⠓⢹⡠⠿⠆⠀⠀⠀⠀⠀⠀⠙⠛⢠⣜⡫⠟⠝⣳⡤⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣁⡒⢂⡽⣉⣯⡰⢖⣈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢮⣁⢮⡽⢈⡵⠆⠀⠀⠀⠀⠀⠀⠀⠸⠾⢾⢨⠰⣍⡗⣅⡗⠿⠮
⠀⠀⠀⠀⠀⠀⠀⣰⡤⢻⢣⠖⣨⢲⡌⡟⢤⣆⠀⠀⠀⠀⠀⣀⠨⢷⠋⣽⠴⡦⣼⠉⡶⠅⣀⠀⠀⠀⠀⠀⣤⡴⠘⣋⡬⣲⡩⣜⡃⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠊⣭⠑⠄⠁⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠴⡧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠐⠻⠃⣭⠀⠹⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣺⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⢸⡇⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢻⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣴⠸⡳⡍⡔⡏⣤⠶⠚⠁⠀⠀⠀⠀⠀⠲⣤⠀⡅⠒⡖⠨⡀⣴⠶⠀⠀⠀⠀⠀⠀⠻⠷⣄⡙⣧⣬⣼⠟⣠⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣒⡬⣒⠭⣖⣤⠥⠀⠀⠀⠀⠀⠀⠠⣴⠄⡊⠑⢰⡦⠊⠙⠠⣴⠄⠀⠀⠀⠀⠀⠠⣤⣤⣽⢳⠊⡊⣫⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⢠⣚⠍⣗⡄⠶⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠙⠏⢀⡄⠘⠏⢤⣄⠀⠀⠀⠀⠀⠀⢀⣤⠴⢊⡧⢭⢵⡓⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠡⣺⠎⠓⠀⠀⠙⠁⠀⠀⠀⠀⠀⠉⠁⢰⠆⢁⡌⢰⣶⠀⠉⠀⠀⠀⠀⠀⠀⠛⠉⠀⠿⠃⣸⠈⠿⠄⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠿⡄⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⣗⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢄
⠀⠀⠀⠀⠀⠀⠀⠰⡤⢬⡻⡌⣲⢃⠟⡡⢤⡴⠀⠀⠀⠀⠀⠀⣤⣀⡨⢶⠉⡏⡳⠡⣄⣤⠀⠀⠀⠀⠀⠀⠴⣠⠰⠀⣌⢲⢫⡄⡄⣤⠶
⠀⠀⠀⠀⠀⠀⢀⢀⣌⣚⣳⣾⠟⣿⣖⢓⣪⡀⣀⠀⠀⠀⠀⠀⢀⣯⣙⡢⡵⢧⡕⣊⣙⢂⠀⠀⠀⠀⠀⠀⠀⠐⢚⣓⢯⡽⡭⣖⣓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡩⠦⡼⣿⣶⣿⠧⡤⢝⠀⠀⠀⠀⠀⠀⠀⠀⢯⡤⢖⡓⡞⡓⢤⣭⠄⠀⠀⠀⠀⠀⠀⠀⡐⠤⡽⣮⣳⣱⠫⡥⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠓⠩⣴⢡⠾⡌⣦⠅⠚⠓⠀⠀⠀⠀⠀⠀⠛⠙⢓⠺⣠⣇⠽⡂⠋⠛⠂⠀⠀⠀⠀⠀⠒⠘⠘⠀⢡⠞⢌⠁⠃⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣶⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣿⡇⠀⠀⢸⣿⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠙⢿⡇⠀⠀⢸⡿⠋⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢻⣷⡄⠀⠈⠃⠀⠀⠘⠁⠀⢠⣾⠟⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⣿⠟⠉⠻⣿⡄⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢠⣿⠟⠉⠻⣿⠀⣀⣤⣤⣀
⠀⠀⠀⠀⣼⡿⠋⠙⠻⢿⣿⣧⠀⠀⠹⣿⡄⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⡿⠟⠋⠙⢿⣧
⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠈⠛⠦⠀⠀⠹⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠏⠀⠀⠴⠛⠁⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⠈⣹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣏⠁
⠀⠀⠀⠀⠀⣼⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣿⡇⠀⠀⢸⣿⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣇
⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣦⣀⠀⠀⠈⠙⠻⡇⠀⠀⢸⠟⠋⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣤⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⠿⣶⣶⣶⣶⣶⡿⠛⠉⠀⠀⢀⣠⡆⠀⠀⢰⣄⡀⠀⠀⠉⠛⢿⣶⣶⣶⣶⣶⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⢺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⣿⡇⠀⠀⢸⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗
⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠙⠻⣿⡄⠀⠀⠀⠀⠀⠻⢿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⣀⡄⠀⠀⢠⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡄⠀⠀⢤⣀⠀⠀⠈⠙⠿⣷⡄
⠀⠀⠀⠀⢿⣇⡀⢀⣠⣴⣿⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⢿⣦⠀⠀⠀⠀⠹⣿⡄⠀⠀⢿⣷⣦⣄⡀⢀⣼⡿
⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉⣿⣇⠀⣠⣿⠏⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⣨⣿⠉⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⣰⣿⠋⠀⠀⡀⠀⠀⢀⠀⠀⠹⣿⣆⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⢀⣼⡇⠀⠀⢸⣧⡀⠀⢘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡿⣿⡇⠀⠀⢸⣿⢿⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢿⣿⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⠙⢿⣦⣿⣿⣴⡿⠋⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠙⣿⣿⠋⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣻⣿⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⣾⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣤⣈⣿⡇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢸⣿⣁⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣄⡀⢿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⣠⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠉⠉⠛⣿⣿⣿⣾⠿⢿⣶⡄⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⢠⣶⡿⠿⣷⣿⣿⣿⠛⠉⠉⠛⠛⠿⠿
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⡿⠿⢻⣿⠁⠀⠀⢹⣿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣿⡏⠀⠀⠈⣿⡟⠿⢿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁⠀⠀⠀⠈⠻⣷⣦⣶⡿⢿⣶⣤⣠⣴⣿⣿⣦⣄⣤⣶⡿⢿⣶⣤⣾⠿⠁⠀⠀⠀⠈⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⢹⣿⠋⠀⠀⠙⣿⡏⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣼⣿⣄⠀⠀⣠⣿⣧⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣤⣄⣀⡀⠀⠀⠀⢀⣾⡿⠛⠻⣿⣾⠿⠛⠙⠻⣿⣿⠟⠋⠛⠿⣷⣿⠟⠛⢿⣷⡀⠀⠀⠀⢀⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣷⣶⣾⣿⡀⠀⠀⣸⡿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⣇⠀⠀⢀⣿⣷⣶⣾⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢶⣶⣦⣤⣄⣀⣴⣿⣿⣿⢿⣶⣾⠟⠁⠀⠀⢠⣴⣿⣿⣦⡄⠀⠀⠈⠻⣷⣶⡿⣿⣿⣿⣦⣀⣠⣤⣴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⠋⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠙⣿⣿⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠺⠿⠛⢉⣿⡇⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⣿⡈⠛⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⣿⣿⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣿⣿⣄⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣠⣾⠟⣻⣿⠻⣷⣄⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⣿⣿⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⣀⣜⣿⣟⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢦⣿⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡂
⠀⠀⠀⣽⢿⣿⡈⢹⠋⣸⣿⢿⡅⠀⠀⠀⢻⣿⣶⣨⣿⣅⣰⣿⣿⠂⠀⠀⠀⢳⣾⣄⠀⣿⢀⣠⣷⡚⠀⠀⠀⠈⡿⣷⣆⢉⣏⢁⣶⡿⡟
⠀⠀⠀⠰⣏⣁⣹⣿⣿⣁⣉⡷⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣏⣉⠀⠀⠀⠀⠀⣍⠀⣈⣽⣿⣯⡁⢀⣉⠀⠀⠀⠀⠀⣍⣈⣿⣩⣏⣀⡅
⠀⠀⠀⠽⣿⣿⢁⣼⣄⢸⣿⡾⠅⠀⠀⠀⡼⣿⠿⢙⣿⣍⠹⢿⢿⠄⠀⠀⠀⠼⢿⠉⠀⣿⠀⢙⡿⠧⠀⠀⠀⠠⢿⡟⠏⣀⣇⡀⠿⣷⠧
⠀⠀⠀⠀⠁⠈⠩⢾⠮⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⢤⡀⣦⠙⢾⠞⢡⣆⣠⠄⠀⠀⠀⣴⡆⢿⠶⣿⡴⣿⢀⣦⠄⠀⠀⠠⣤⣴⠀⢙⣿⠋⢀⣆⣤⠀⠀⠀⠠⣤⣄⠀⣸⣿⡁⢀⣤⣤
⠀⠀⠀⢠⠽⠛⣦⠞⢦⡞⠻⢥⠀⠀⠀⠀⣉⡽⠿⢦⣿⡤⠿⢯⣉⠁⠀⠀⠀⠹⠛⣷⢯⣿⡽⡾⠛⠏⠀⠀⠀⠀⠙⠛⡿⣬⣯⡼⢿⠛⠁
⠀⠀⠀⠘⣳⣶⠛⢶⠞⢳⣶⡚⠀⠀⠀⠀⣍⣹⣶⠚⣿⠙⣶⣟⣉⡀⠀⠀⠀⣰⣤⡿⣟⣿⣻⢷⣴⣆⠀⠀⠀⠀⣠⣼⢷⢛⣟⢳⢿⣤⡄
⠀⠀⠀⠉⠁⠟⡤⢾⠶⡌⠇⠉⠁⠀⠀⠀⠛⠃⣾⠞⣿⠳⢿⠈⠟⠁⠀⠀⠈⠛⠛⠀⣠⣿⣄⠀⠋⠛⠀⠀⠀⠈⠉⠉⠀⢩⣿⡁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⢐⢼⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⠄⠀⠐⣼⠠⠄
⠀⠀⠀⠀⠀⠀⠙⡛⢦⣄⡀⢐⣽⠇⢀⡀⣰⣤⠦⠀⠀⠀⠀⠀⠀⢄⠘⢃⢶⠨⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⢋⢹⡌⢱⠞⠫⠑⠈⠀⠀⠀⠀⠰⢦⣤⣙⣓⣌⣴⣅⣚⣃⣄⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢻⢺⣵⠺⠣⢔⡠⡀⠀⠀⠀⠀⠈⠀⠁⡤⠖⡘⠹⡑⢤⣄⡁⠙
⠀⠀⠀⠀⠀⠈⠏⠃⠂⠀⠀⣲⡣⠀⠀⠀⠙⠲⣤⠀⠀⠀⠀⠀⠀⢄⡎⠃⠿⢡⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠻⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣟⠕⠀⢀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠰⡄⠀⠁⢠⢀⠼⣃
⠀⠀⠀⠀⠀⢀⡶⣤⣤⡀⢀⡆⠄⡠⢔⠪⡣⢀⠀⠀⠀⢀⡭⠛⠂⠠⠄⢈⡤⣤⢐⣁⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠨⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠘⣦⢼⠂⠠⣤⣒⠅
⠀⠀⠀⠀⠀⠀⠀⠄⢒⠶⠁⠐⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠡⠌⠸⠀⠑⠄⠘⠕⠁
⠀⠀⠀⠀⠀⠀⠈⠝⢋⠄⠀⠀⠐⡹⠫⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢐⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⢰⣾⣇⣀⡀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣶⠆⠀⠀⠠⣶⣿⡿⡆⠀⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⢀⣾⣦
⠀⠀⠀⠀⣸⣿⣿⣿⡿⠇⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠈⠙⠀⠇⠀⠀⠀⠀⣀⣹⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⣤⡤⠀⠀⠀⢀⣤
⠀⠀⠀⠀⣸⣿⣿⣿⣷⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠸⣿⣶⣿⠃
⠀⠀⠀⠀⠛⠛⠿⠿⠟⠻⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠾⠿⠇⠀⠀⠀⠐⠿⠿⠿⠿⠂⠀⠀⠀⠈⠛⠻⠷

⠀⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⡁⠀⠀⢀⣶⠟⠻⣦⠀⠀⠀⠀⠀⣴⣾⠃⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀⣤⣸⣧⠀⠀⠀⠀⢴⣤⡀
⠀⠀⣐⠀⠿⣷⣶⣿⣿⣿⣿⠏⠀⠀⠘⣿⣄⣠⡿⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⣤⠿⡿⠇⠀⠀⠀⠀⣷⣿⣿⡇
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⢸⣦⣀⣀⣤⣿⣿⣿⡿⠀⠀⠀⠳⣿⡿⠒⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⣰⣿⣿⣻⡀
⠀⠑⠍⠈⠻⠿⠟⠛⠛⠻⠟⠁⠄⠀⠀⠴⠟⠻⠆⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠄⠀⠀⠸⠿⠿⠿⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⡀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠈⡄⢠⠂⠀⠀⠐⠀⠀⠁⣀⢐⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⡀⠈⢦⣱⡎⠀⠀⠀⠀⠀⠀⢀⢀⠉⠀⠚⠍⡅⠀⠀⠁⠀⠀⠠⠀⠳⣀⡞⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⠆⡀⠐⠬⠽⢁⢱⣿⣵⠦⠀⠀⠀⠀⠀⠀⠀⠗⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠋⠉⠁⠐⠒⠒⠐⠚⠋⠀⠀⠁⠀⠀⣀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢠⠀⠀⠂⠀⠀⠀⢀⣀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠊⠘⠛⢯⡁⠤⠀⠂⢀⡀⢣⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠂⡀⢀⡴⠺⡅⠁⠀⢈⡼⠱⣠⠁⠂⣀⠔⠋⠀⠀⠀⠀⠠⡀⠀⠀⠒⠛⠛⠣⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠄⠀⠀⠐⠀⠀⠠⢀⡘⡄⠀⢸⠁⠁⠉⠒⠉⠀⢠⡞⠉⠀⠀⠁⠀⠤⣀⠀⡀⣒⡈⠒⠦⠛⠲
⠀⠀⠀⠀⠀⠠⣤⣀⣠⣄⠠⢴⡰⢧⣦⠴⠀⠀⠀⠀⠀⠀⠁⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⢉⠉⠉⡑⢦⣦⣆⣤⣠⣌
⠀⠀⠀⠀⠀⢠⣍⣉⣉⣡⣄⣴⡴⣠⢌⣅⠠⠀⠠⠀⠀⠀⠀⢴⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠚⠛⠙⢧⣄⡀⣀⣈⡁⡂⡄⠀⠂
⠀⠀⠀⠀⢀⡈⢁⠉⡀⣙⣠⢄⡄⣀⠀⡈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠁⠵⠦⠆⠶⠖⢖⡟⠓⢈⠉⠙⠢⡀
⠀⠀⠀⠀⠠⠒⠋⠚⠙⠻⠌⠉⠓⠉⠁⠈⠣⠀⠀⠈⠠⣀⠀⠘⠵⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠘⣤⣆⣤⢠⣦⡠⣠⡉⣷⠀⠂⠁⠁
⠀⠀⠀⠀⠉⠖⠓⠊⠶⢿⡡⣖⡴⣆⡰⢴⣦⠎⠀⠀⠀⠀⠉⠂⠄⠠⢀⠀⠀⠄⠄⠊⠁⠀⠀⠀⠀⠀⠠⢤⠠⢄⠠⢀⠈⡙⢻⠆⠀⠀⠁⡀
⠀⠀⠀⠀⠐⠐⢤⡆⠠⢠⠄⠀⢀⡀⢀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠹⠂⠀⠐⠀⠤⢬⡐
⠀⠀⠀⠀⠀⠀⣸⡧⢀⠀⠀⠀⠘⣿⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⠘⠐⠒⠀⢀⢀⢀⠠⠀⠉⠲⠀⠄
⠀⠀⠀⠀⣀⡀⢄⣀⡀⠈⠀⠐⠲⠼⠁⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠀⠘⠲⠁⠀⠈⠀⠀⠀⠲⠨⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠀⠜⠐⠀⠀⢀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⢀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠒⠚⠒⠺⠡⠟⠈⡀⠈⠐⠄⠀⠤⠈⠀⠈⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⢀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡆⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠂⠀⠀⠀⠀⠀⠀⠄⡰⠂⠀⠀⠀⠀⠀⢀⡄⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢆⡠⠀⠠⠀⠀⠀⠀⠉⡁⢀⠒⠂
⠀⠀⠀⠐⠆⡘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠄
⠀⠀⠀⠊⢡⠑⠄⠀⠀⠀⠀⠀⠀⠀⢡⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠒⠟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠬⡔⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠨⠌⠀⢁⢂⠀⠀⠀⢀⠀⠁⠡
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠔⢁⠀⠀⠀⠀⠀⠂⠖⡄⠂⠂
⠀⠀⠀⠀⠈⠀⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⠀⠂⢙⠁⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠰⠀⠀⠀⠀⠀⠀⠐⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠕⠈⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡹⠃⠂⠂⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⣀⡔⠀⠀⠀⠀⠀⠀⡤⠅⠊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠑⠪⠀⠈⠀⠀⠀⠀⠠⠂⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠅⢆⠒⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠⢀⡠⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠄⡀⣐⣄⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠠⠈⠄⡀⠀⠀⠀⠀⠀⠅⠃⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠀⠁
⠐⢄⢀⠔⠀⠀⠀⠀⠀⠨⢁⠀⣐⡐⠀⠀⠀⠐⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠐⠈⡇⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⢨⣤⠀⠄⠀⠀⠀⠀⠐⠀⠁⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡽⠋⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢊⡹⠋⠉
⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠔⠁⠐⠻⠀⠀⠀⢀⣠⠔⠈⠐⠃⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣦⠀⠀⠀⢸⡇⢀⣏⣵⣎⠙⠒
⣠⣧⣼⣯⡇⣦⠀⠀⠀⠐⢋⠁⠲⠀⠀⠀⠤⢤⠀⠁⠠⠔⠂⢿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⣾⣿⣈⣉⡙⠟⣶⠦⠦⢀⡄
⣻⣿⣿⢻⣷⣟⣰⣠⠔⢂⡉⠁⠄⣁⢀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣧⠀⠀⢸⣭⠃⠀⠜⠛⡅⢙⣳⠀⣀⠸⣇⡀⠾⣷⣀
⢸⣿⠄⡘⣿⣿⣿⣿⠖⡃⠁⢉⠀⠈⠋⣀⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⠀⠀⢣⣈⠲⣄⡴⠂⡴⢦⣹⣏⠈⠳⡈⠻⣶⣼⣿
⢈⣹⠾⠇⣸⣿⡿⠏⢐⠁⠂⠊⠀⠊⠤⠘⣿⣿⣦⣿⣤⣀⣆⣄⠀⠀⠀⢀⣀⣀⣰⣆⣀⣜⣡⣁⠀⠷⠋⢁⠐⣩⠗⠛⠀⠀⠹⣷⠀⠀⠀⡀⠈⠹⣿
⢀⡅⠠⠆⢺⣁⣤⠴⠅⣤⠞⠀⠀⠀⠀⠢⣿⣿⢿⡿⢿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠺⣁⠈⢻⣡⡴⠚⣡⣀⢢⣍⡀⠀⠀⠙⠶⢶⣿
⢸⣧⠀⢢⠾⠋⢀⡤⢀⣤⡀⠀⣴⣟⠒⢄⡘⠿⣚⠓⢛⣟⣹⡿⠛⠉⠁⠀⠈⠉⠙⢿⡏⢀⠀⠋⠲⣶⡌⢆⣸⠧⠤⠊⠀⠳⣄⠙⠆⠀⠀⢄⠀⠀⠙
⠀⠀⠀⠉⡿⠋⠀⣀⠈⠀⡘⠳⣇⠘⡤⠀⠙⠛⠛⠚⢹⠉⣁⠴⣎⣹⣦⣄⡀⣀⣀⣀⠉⠀⠀⠔⠀⠤⣙⣾⣗⡴⢠⡄⠀⠐⣄⠉⠑⢆⡀⠈⠁⢤⣘
⠀⠀⢀⡾⠂⠈⠁⠧⣀⠼⠁⠀⢀⡓⠛⡆⣠⡀⡄⠀⠀⠈⠷⠾⠿⠴⠷⠾⠿⠿⠟⠅⠨⠤⠒⠀⡼⠦⣤⣹⠿⠆⠁⡷⡀⣠⠿⠇⠀⣌⣣⣴⠀⠀⢻
⠀⠠⠏⠀⢀⣠⡴⠶⢅⠀⠀⠀⠈⢳⣠⠓⢎⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⢀⣀⠀⠃⠐⡄⠠⡀⠘⣧⡀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠐⠊⠉⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⡤⠄⠚⠉⠠⠤⡀⠰⠤⠵⠄⠀⠿⠯⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈
⣿⠿⠿⠿⡿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣟⣿⣿⣻⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⣆⣄⠀⠀⠀⠀⣀⡠⡦⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠏⠹⢿⣿⣿⣿⣿⠿⣟⢹⡿⣿⣿⣿
⠀⠀⠰⢦⣷⠀⠙⡏⠀⢸⣧⠆⠀⢨⡵⡷⣭⡀⠀⠀⢸⣿⣿⣏⡛⠸⣿⡆⢰⣿⡇⠛⣻⣿⠷⣎⢈⠖⣿⣿⣿
⠀⠀⠐⠋⠉⢻⡟⠛⡞⠋⠙⠂⠀⠀⠐⠗⠈⠀⠀⠀⢸⣿⣿⣯⣴⣶⡌⣵⣦⢡⣶⣦⣽⣿⣿⣯⣼⣿⣿⣿⣿
⠀⠀⢈⣿⣶⠋⢻⡟⠙⢶⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠈⢩⣴⡎⢡⣦⡉⠡⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠋⢠⢾⡷⡄⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⡟⡁⢈⢻⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⠻⠀⠟⢋⡽⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣋⠳⠿⠸⠷⠊⣹⢀⣤⡀
⠀⠀⠀⠀⣀⠀⡏⢹⢀⣠⡖⠮⣷⠀⣾⠵⢲⣄⡀⡏⢹⠀⣀⠀⠀⠀⠀⢠⠶⢤⡇⢸⢠⠬⣕⣦⢠⣖⡫⢤⢸⡀⣧⡴⢦
⠀⠀⠀⠘⢏⡙⠃⢸⣸⠀⡟⠲⣤⠀⣠⠖⢻⠀⣇⡇⠘⢋⡹⠇⠀⠀⠀⣈⡷⠄⠀⢿⡞⢠⣄⡉⠈⣉⣤⠘⣯⠇⠀⠴⣏⡀
⠀⠀⠀⣴⠚⣡⠴⣦⡉⠀⢧⣄⣸⠀⣇⣠⠼⠀⠉⣴⠦⣌⠓⣦⠀⠀⠘⠥⠴⣚⡽⠆⠀⠸⡤⠿⠘⢧⡼⠀⠀⠾⣝⡲⠤⠽
⠀⠀⠀⠈⠉⠱⣏⣡⠖⠛⠲⣌⡙⠀⢋⣡⠖⠛⠲⣌⣹⠎⠉⠁⠀⠀⣞⠳⣄⢧⡀⢾⣉⡗⠀⠀⠀⠀⠐⣏⣹⠆⣠⢇⡴⢛⡆
⠀⠀⠀⣠⢤⣘⢧⣉⠓⠶⠚⣉⣤⠀⣤⣉⠓⠶⠚⣉⡼⣃⡤⣄⠀⢀⡬⠷⠈⠛⣋⠀⢩⣤⠀⠀⠀⠀⢠⣬⠁⢈⠓⠋⠰⠯⣄
⠀⠀⠀⠙⢦⣌⠙⢋⣡⠀⡟⠁⢸⠀⡇⠈⢹⠀⣌⡙⠋⢡⡴⠋⠀⠘⠲⢲⠂⡾⡽⠀⠷⠼⠃⡴⠶⡄⠻⠤⠇⠸⡽⡆⢲⠲⠚
⠀⠀⠀⠰⣏⡤⡆⢸⢹⣀⡷⠞⣉⠀⣉⠓⢾⣀⡏⡇⢰⢦⣹⠆⠀⠀⠀⠻⠴⢃⣙⣒⣲⠂⣤⠙⠞⢡⡄⢲⣒⣚⣁⠳⡼⠃
⠀⠀⠀⠀⠀⠀⢧⡼⠀⠉⢓⣫⠽⠀⠿⣝⡚⠉⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢯⣥⣤⠀⡈⢯⡳⠴⣫⠏⠀⢠⣬⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡤⢶⠀⡶⢤⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡼⠳⣄⣳⢰⣃⡴⠳⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⢼⠉⣧⠶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣙⠾⠹⢚⣩⠇
⠀⠀⠀⠀⠀⢠⡶⣴⢋⣇⣠⢽⣶⠀⣶⡯⣅⣸⡝⣧⢶⡄⠀⠀⠀⠀⠀⠀⡴⣄⢠⣄⠰⣟⠻⢿⢰⠿⢚⡽⠀⣀⢠⡤⡄
⠀⠀⠀⠀⢠⡴⢛⣀⡸⡿⣸⠓⢮⠀⡵⠚⣇⢻⠇⣀⡛⢦⡄⠀⠀⠀⠀⡴⠇⣿⣿⢸⣀⡬⠟⣂⢀⡚⠯⣄⣸⢹⣿⡆⠷⣄
⠀⠀⠀⠀⣀⠉⣹⣛⣋⣤⡻⣄⢸⠀⡇⣠⠞⣠⣘⣛⣯⠉⣁⠀⠀⢀⡴⢋⣤⣬⠋⠘⣩⡖⠋⢹⢸⡏⠓⣮⡙⠈⢫⣤⣌⡓⣦
⠀⠀⠀⣘⣏⢳⣧⡹⣄⣀⣙⣮⡻⠀⢟⣡⣊⣀⣠⠏⣼⡾⣹⣃⠀⠀⠉⢹⣋⡵⣶⢰⠦⣝⠲⢾⢸⠷⢚⡥⢶⢰⡶⢍⣳⡍⠁
⠀⠀⠘⠯⡭⢠⣭⢄⡬⠭⠭⣭⠅⠀⡨⣭⠭⠭⢥⡠⣭⡄⢭⠽⠃⠀⠀⣠⢤⣀⣿⢸⣀⡤⠟⣂⢀⡚⠯⣄⣸⢸⣇⣠⣥
⠀⠀⠀⠸⠥⠋⣯⠾⣤⣠⢞⡵⢻⠀⡟⢮⡳⣄⣤⠷⣽⠙⢮⠇⠀⢠⡶⢼⣶⣬⠋⠘⣭⡖⠋⢹⢸⡍⠓⣮⡝⠈⢫⣴⣾⠖⡦
⠀⠀⠀⠀⢠⣖⠾⠿⢖⡀⢿⠀⣸⠀⣇⠀⡿⢀⡲⡾⠷⢲⡄⠀⠀⠀⠉⣗⡈⣱⣶⢰⠦⣝⡲⢾⢸⠷⢚⡥⢶⢰⣶⡍⣐⡏⠁
⠀⠀⠀⠀⠀⢩⣟⣤⢸⡿⣼⣋⣥⠀⣬⣙⣧⢿⡇⣤⣻⡍⠀⠀⠀⠀⠀⠉⣇⣹⠻⠼⢀⡤⠟⣂⢀⡘⠧⣄⠸⣼⢿⣇⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠘⠷⠇⢠⢟⣫⠀⣝⡻⡄⠸⠶⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢒⡿⠟⠘⠻⣷⡋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠶⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠞⠛⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢸⡇⠀⢀⣴⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⡶⠟⠁⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣤⠀⠀⠀⠈⣷⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠿⣧⡀⠀⠀⠀⠀⠀⠐⢦⣾⣇⣤⠆⠀⠀⢻⡀⠀⣠⡾⠋⠉⠛⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠻⣦⡀⠀⠀⣧⠀⠀⣻⡏⠀⠀⠀⠀⠸⣧⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣦⣀⡿⠀⠀⢸⡇⠀⠀⠀⣠⡾⠋⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠛⠻⣷⣄⠀⢸⡇⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⢷⣼⣷⡾⠋⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠶⠶⠶⠾⠿⠿⣿⣿⠿⠿⠿⠿⢷⣾⣿⣿⣶⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⢀⣴⡾⠋⢸⡏⠙⢷⣄⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡿⠋⠀⠀⢸⡇⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⠏⠀⠀⢀⣴⢿⣿⣆⠀⠀⠀⠙⣶⣶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⡟⠀⠀⠐⠋⠀⢸⣷⠘⢷⡀⠀⠀⣿⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠁⠀⠀⠉⠀⠀⠙⢷⣄⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣽⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢹⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠸⠟⠈⢻⣆⠀⠀⠀⠀⠀⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢻⡆




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⡀⠀⠀⠀⠘⠀⠃⠀⠀⠀⢀⠀⢔⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⡛⠀⢀⠀⠀⠅⠀⠀⢚⣥⠒
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠊⡄
⠀⠀⠀⠀⠤⠀⢀⠄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠁⠐⠀⠢⠄⡀⢁⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠈⠤⠛⠀⠀⠈⠀⠠⠔⠀⠳⠠⢁⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⠋⠡⠄⢀⠀⠀⠀⠀⠂
⠀⠀⢀⣢⣀⠀⠀⠀⢀⢰⡀⠀⠀⠀⣀⣐⠄⠂⠀⠀⠀⠀⠠⠠⢤⡂⠆⠂⠈⠁⢠⠀⠀⠀⠋⠐⠤⠤⢣⠄
⠀⠀⠀⠀⠉⠐⣰⠄⣀⠈⣀⠰⣂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⢠⡀⠀⢾⡀⣰⠶⠂⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠓⢒⣉⠡⢴⣄⠀⠰⠦⠄
⠀⠀⠀⠀⣀⠠⠻⠀⠉⡀⠁⠰⠏⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠠⠶⠋⠀⣷⠀⠈⠁⠀⣆
⠀⠀⠀⠍⠁⠀⠀⠀⠈⠏⠁⠀⠀⠀⠉⠹⠄⠀⠀⠀⠀⠀⠀⠀⢪⠔⠃⠆⢠⠀⠀⠀⠃⠀⣀⠰⠰⠎⣟⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢠⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠠⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⠐⡀⠀⠀⠀⠠⠐⠐⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠐⢠⠀⠀⠀⠈⢅⠙⢆⢔⠀⢀⠄⢃⡴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣈⠀⠀⡀⢅⡀⠀⠠⠂⢆⠄⠈⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠡⠀⠀⠀⠀⡀⢠⠀⠄⣀⠀⠀⠐⡀⠀⠄⠄⠀⠜⠀⠨⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠠⢎⠀⠀⠀⢀⠊⠐⠄⠀⠁⠀⠈⠞⠋⢀⠂
⠀⠀⠠⡀⢀⠀⡀⠐⠀⠂⣑⡁⠄⠐⠀⢈⠁⠀⠑⠀⣀⠁⠄⠐⠘⡀⠀⠤⠀⠐⠈
⠀⠀⠐⠁⠀⠀⠁⠠⠀⠄⡩⡡⡂⡠⠀⢈⡀⠀⡠⠀⠉⡀⠂⠠⢠⠁⠀⠒⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠰⢎⠀⠀⠀⠀⢄⠠⠂⠀⡀⠀⠀⢦⣄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡐⠀⠀⠀⠀⠁⠙⠀⠢⡈⢠⠠⠤⠅⠰⠂⠦⢦⢦⠠⣴⣔⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⢉⠠⠀⠁⠊⠀⠀⠀⠄⠌⢢⡇⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠘⠀⠀⠀⢀⠀⣠⠀⠪⠀⠈⠈⠍⠻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠠⠁⠀⠀⠀⠘⠠⠠⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠑⠀⠀⠀⠀⠀⠀⠐⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠁⠈⠁⠀⢰⣄⠀⠉⠉⠉⠉⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣸⡇⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⣿⣿⣾⡿⢠⣿⣿⣷⡀
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡟⡜⠉⢰⣿⣿⣿⣿⣷⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢀⢀⣿⡏⣿⠖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣒⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⡔⢫⠆⢸⠟⡼⢋⣀⠀⣫⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⠀⣀⠈⠉⠉⠙⠛⢃⣴⠞⠀⠋⢀⣄⢞⣴⡿⠁⣽⣛⣴⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠘⠀⠂⠀⡀⠀⣠⠞⡱⠀⡰⠀⣾⣧⣾⡿⢳⠿⡿⠛⠁⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣄⠀⠐⠀⢀⡞⠁⠔⠀⠈⢀⣀⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣀⠰⠊⠀⠀⠀⠀⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⣋⢀⣽⣿
⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⠆⠁⠚⠳⠳
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣶⣽⡋⠉
⠁⠀⢐⣾⣿⠿⠋⠀⢘⣧⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣀
⣷⣶⣦⣥⣤⣶⣶⠶⠊⢛⣿⣦⢀⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣝⠻⢿⣿⣿⣿⣷⣶⡾⠷⠒⣀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠈⠉⠻⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣶⣴⣮⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠓⠦⢄⡀⠀⠀⠀⠀⠀⠉⠻⢯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠉⠙⠛⠛⠂
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠂⠉⠓⠂⠀⢀⠀⠀⠠⢄⣀⠈⠉⠉⠉⠉⠛⠛⠻⠻⠿⢷⣦⣄⣀
⠀⠈⠛⠻⣿⣿⣿⣿⡿⠿⠟⠋⣩⣿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣤⡀⠐⠲⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀
⠀⣆⠀⠀⠀⠉⠉⠀⠈⠀⠒⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣆⠐⠚⠋⠁
⣦⣿⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⣿⣿⣿⣿⣮⡳⢯⣛⢿⣷⣿⣿⣿⣿⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣄⡀⢸
⣿⣿⣦⡀⠀⢠⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣤⣍⠳⢮⡙⠻⢿⣿⣿⣿⣤⣿⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⣎
⡿⣿⣿⣷⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣍⡺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⢿⣿⠻⢿⡃⠙⢿⢿⣟⢮
⣿⣵⣏⣛⠿⣿⣷⣾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣀⠀⠀⠀⠈⠓
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠆⢀⣤⣶⣀⠀⠀⠀⠀⣨⡑⢌⡛⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣤⣉⠙⠛⠂
⣿⣿⣿⣿⣿⣛⠿⣿⣷⣦⣤⣶⣿⣿⣿⠁⣀⣤⣴⣾⣿⣿⡤⣌⡑⢦⣍⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠓⠲⠆⠀⠀⣀
⣿⣿⣿⡿⣿⣿⣿⣦⣭⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠳⢼⣟⣶⡄⠙⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠺⢿
⣿⣿⣿⣿⣄⣾⡽⣻⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠉⠻⢿⣶⣦⣴⣿⠻⢿⣿⣿⣿⣿⣿⣿⣦⣀
⣿⣿⣿⡿⢿⣿⣗⣿⡇⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠠⣴⡌⠛⠻⣷⣦⠀⠉⠛⠿⠟⠻⢿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠐⠠⠄⠈⠑⠠⢄⡀⡀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⢸⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠲⣦⠀⠀⠀⠀⠉⠂⣄⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢴⡆⠀⠀⣽⣿⣿⡧⢼⣿⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⣸⣷⠀⢴⣿⣿⣿⣿⣿⣿⡆⢀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⡽⠁⡠⠈⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡞⢀⡜⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡏⠀⠀⠀⠀⡴⠀⣦⠀⢠⠀⣦⠀⢠⡄⢠⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡞⠀⡞⠀⢠⠂⠀⣼⠁⣸⠁⢀⡞⢰⠃⠀⡼⢡⠏⠀⡾⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠎⠀⢀⣇⣀⠘⠒⠀⠛⢠⠟⠃⠀⢀⠏⠃⠀⠀⠘⠂⢰⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠔⢁⡔⠊⠀⢣⡀⠈⡱⠀⢀⡎⠀⠀⠀⢸⠀⠀⣠⠔⠀⢀⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠝⠀⣠⢤⠀⠸⣀⡰⣀⢤⡄⠁⠀⢀⡞⠀⢳⠠⡀⢸⢀⠞⡡⠲⢦⠊⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⡽⠁⠀⡠⠊⢀⡞⠀⠀⢀⡔⠁⢸⠃⠷⠴⠋⠀⢀⡞⢸⡇⣸⡏⠀⠁⠀⣪⠂⠀⠲⣤
⠀⠀⠀⠀⠀⠀⠰⠋⠀⡀⢀⡞⠀⣠⠊⢀⡴⠋⠀⠀⢀⡞⠀⢠⠏⣀⠰⣧⣠⠴⠋⢀⡞⢀⡏⠀⠐⠖⠋⠁⠀⣠⠖⠛⣿⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠐⠒⠊⢡⡟⢀⣴⠥⠖⠉⠀⠀⠀⠀⡼⠁⡠⠀⠀⠉⠀⠀⠀⠀⠀⡞⠀⠈⠛⠊⠀⠀⠀⠀⠀⢯⡀⠠⠃⢀⠀⠈⢆
⠀⠀⠀⠀⢀⡠⠄⠒⢨⠏⠉⣼⠃⠀⢀⡴⠃⢈⡆⢰⠇⠊⠀⢀⡞⠁⠀⡀⠀⠀⡿⠁⠀⡀⠀⠀⣹⠛⠀⣸⠃⠀⣰⠃⠀⢿⠀⠀⢸
⠀⠀⣠⠖⠁⠀⠀⢠⠏⠀⢰⠇⠀⢠⡟⠀⠀⡼⠁⡏⠀⠀⠀⣼⠁⢀⡞⠀⠀⣰⠃⠀⡼⠁⠀⢠⡏⠀⣰⠏⠀⢰⠏⠀⠀⠈⣇
⢀⡼⠁⠀⠀⠀⢠⠏⠀⠀⣿⠀⠀⠸⡇⠀⠈⠀⠀⠷⡄⠀⠀⠷⠔⠸⣧⠄⠀⢿⠄⠀⢧⠤⠀⢸⠤⠀⠿⠄⢀⣾⠀⠀⢰⡥⠋
⢸⠁⠀⠀⠀⡠⠋⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⠃
⠘⢦⣄⠤⠊⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⣀⡠⠴⠒⠉⠉⠁⠀⣀⠬⠛⢿⠉⠙⠛⠳⢦⣄⡀⢀⡤⠀⠀⠀⢠⠏⠀⡴⠋⠉⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣸⠂⠀⠀⠀⠀⠈⣿⢯⣄⠀⠀⢠⠏⠀⠸⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡤⠞⠁⠀⠀⠀⠀⢀⡾⠁⠀⠙⠳⣶⣇⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⠄⠀⠈⠙⠓⠲⠦⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠔⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣦⣻⣟⣴⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⡀⢀⡈⢻⡟⢁⡀⢀⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢿⣿⣿⣧⢸⡇⢸⡇⢸⡇⣼⣿⣿⡿⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⢀⣈⣉⣻⣿⣇⢸⡇⣸⣿⣟⣉⣁⡀⠀⠀⠀⢀⣴⣿⣿
⠘⢿⣿⣿⣷⡄⢸⣆⠀⠀⢿⣿⣿⡇⣀⡀⣶⣤⡉⠉⠉⠉⠻⣿⣿⠟⠉⠉⠉⢉⣠⣶⢀⣀⠸⣿⣿⡿⠀⠀⣰⡇⢠⣾⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣮⣿⡀⣴⣄⡻⣿⣰⡿⠁⢸⣿⣿⣶⠀⢀⠀⢸⡇⠀⡀⠀⣶⣿⣿⡇⠈⢿⣆⣿⢟⣠⣦⢀⣿⣵⣿⣿⣿⠟⠁
⠀⠀⠀⢠⣴⡶⠿⠛⠿⣦⣍⡛⢿⡟⠀⠀⠘⠻⣿⣿⣀⣿⠁⢸⡇⠈⣿⡀⣿⣿⠟⠃⠀⠀⢻⡿⢛⣩⣴⠿⠛⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣝⣻⣾⣿⣀⠀⠰⢶⣮⣿⣿⡏⠀⢸⡇⠀⢹⣿⣿⣵⡶⠆⠀⣀⣿⣷⣟⣫⣴⠾⠛
⠀⠀⠀⢀⣴⣾⣿⣿⣷⢿⣿⠟⠉⠉⠛⠷⣦⣄⡀⠈⠹⣷⡀⢸⡇⢀⣾⠏⠁⢀⣠⣴⠾⠛⠉⠉⠻⣿⡿⣾⣿⣿⣷⣦⡀
⠀⠀⠐⠛⠛⠻⠿⠟⢡⣾⠃⠀⠀⠀⢶⣄⠀⠙⠻⢶⣤⡘⣷⣼⣧⣾⢃⣤⡶⠟⠋⠁⣠⡶⠀⠀⠀⠘⣷⡌⠻⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⣾⣿⣷⣦⣽⣷⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣾⣯⣴⣾⣿⣷⣦⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠙⠻⠿⠟⢋⣽⠟⠉⠉⢉⣭⡿⣿⣿⣿⣿⢿⣭⡉⠉⠉⠻⣯⡙⠻⠿⠟⠋⣩⡀
⠀⠀⠐⢶⣶⣾⣿⣷⣌⢻⣆⠀⠀⠀⠛⠁⣀⣴⡾⠛⠉⣰⡟⢹⡏⢻⣆⠉⠛⢷⣦⣄⠈⠛⠀⠀⠀⣰⡟⣡⣾⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠙⠻⠿⠿⠟⣿⣿⣷⣤⣤⣶⠟⠋⢁⣀⣠⣼⡟⠀⢸⡇⠀⢻⣧⣄⣀⡈⠙⠻⣶⣤⣤⣾⣿⣿⠻⠿⠿⠟⠋
⠀⠀⠀⢀⣀⡀⠀⠶⠟⣋⣵⡾⢻⡿⠀⠀⠘⠛⣫⣿⣿⣧⠀⢸⡇⠀⣼⣿⣿⣝⠛⠃⠀⠀⢿⡟⢷⣮⣙⠻⠦⠀⢀⣀⡀
⠀⠀⠀⢈⣙⣛⣿⣶⡿⣋⣥⡶⣿⣷⡀⠀⢰⣾⣿⣿⠀⢿⠄⢸⡇⠠⡿⠀⣿⣿⣷⡆⠀⢀⣾⣿⢶⣬⣙⢿⣶⣿⣛⣋⣁
⠀⢠⣾⣿⣿⡿⢫⣿⠀⠙⢁⣾⣿⠘⣷⡄⣸⣿⡿⠛⠀⠀⠀⣸⣇⠀⠀⠀⠛⢿⣿⣇⢠⣾⠃⣿⣷⡈⠋⠀⣿⡝⢿⣿⣿⣷⡄
⠰⠿⠿⠿⠟⠁⠸⠃⠀⠀⣿⣿⣿⡇⠀⠀⠛⢉⣤⣤⣤⣤⣾⢿⡿⣷⣤⣤⣤⣤⡉⠛⠀⠀⢸⣿⣿⣿⠀⠀⠘⠇⠈⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⢀⣠⣤⣾⢿⡗⢸⡇⢸⡿⣷⣤⣄⡀⠀⠀⠀⠀⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⣿⣿⡟⢸⡏⢸⡇⢸⡇⢻⣿⣿⣿⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠋⠀⠀⣠⣾⣷⣄⠀⠀⠙⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⣾⣷⡙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣌⢹⡆⣿⢩⣤⣀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢦⣄⠀⠀⠀⠻⣄⠈⠻⠇⠛⠋⣠⡟⠀⠀⠀⠀⡼⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⣆⠀⠀⠀⠈⠙⢦⠀⣴⠛⠁⠀⠀⠀⢀⡾⠁⣼⠃
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣆⠀⢰⡖⢦⣽⠀⣿⡴⠲⣆⠀⢀⡾⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⣾⡛⠙⠛⢶⡄⢰⡟⢦⡀⠀⠀⠀⠘⣧⠀⠘⣆⠘⠳⣄⠉⠀⠋⢀⡴⠇⢀⡞⢁⡼⠁⠀⠀⠀⣠⢶⣄⠀⣴⠟⠉⠉⣿⡟
⠀⠙⢷⣄⣀⣈⡳⠾⡇⠸⡇⠀⣴⢦⡀⠘⢧⠀⠘⣦⠀⠈⢳⡄⣴⠋⠀⢀⡞⢀⡾⢁⡴⠶⡄⠀⡿⠀⣿⡶⢋⣠⣤⡾⠟
⠀⠀⠀⠙⢋⣭⠿⠶⠀⠀⠻⣄⣻⠀⢹⡆⠈⢧⣀⣸⡁⠀⢸⡇⣿⠀⠀⣸⢠⡞⠀⢸⡇⢠⣏⡴⠇⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠾⢦⣤⡴⠞⠛⢳⣦⡉⠀⠘⣇⠀⠀⠉⢳⡳⡄⢸⡇⣿⠀⡼⣳⠋⠀⢀⣾⠀⠈⢩⡴⠛⠛⠲⠦⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢁⣠⡤⠶⢬⣛⠶⣤⡀⢳⡹⣼⡇⣿⣼⡷⢃⣤⠶⣋⡥⠦⣤⣈⠉⢻⡄
⠀⠀⠀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⠀⠉⠛⠶⣝⡳⢷⣹⡇⠿⡽⠟⣩⠴⠚⠉⠀⢀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣄⣤⣄
⠀⠀⠺⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣛⣂⠉⠀⠀⢀⣻⣿⣿⣿⣭⣽⣭⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⠁⠀⠀⢀⣤⠖⣫⢵⡆⡀⣤⢤⣍⡳⢦⣄⡀⠀⠀⣀⣤⠦⢤⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠛⢶⣄⣠⡴⢞⡭⠖⠋⢁⣞⣼⡇⣿⣜⣦⠙⠳⢮⡉⠓⠛⠉⠀⣀⡼⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠸⣟⠛⠳⢦⣈⣹⡶⠀⠈⣵⠞⠉⠀⠀⢠⢏⡞⢸⡇⣿⠘⣎⢧⠀⠀⢹⡆⠀⣘⣿⢥⡤⠖⠋⠉⢨⡟

⠀⠀⠀⠀⠀⠈⢙⣦⠀⠈⣠⠖⣷⠀⣿⠀⠀⠀⡴⠋⡞⠀⢸⡇⣿⠀⠘⣾⢧⡄⠀⣷⠀⣿⠙⣧⠀⣀⡲⣿⡉⣀
⠀⢀⣴⠞⠛⠚⢋⣥⡄⠀⡟⠀⢿⣀⣿⠀⢀⡼⠁⣼⠃⢀⡼⠇⢿⡀⠀⢿⡀⠹⣆⠸⣄⣸⡆⢹⡄⢹⡟⢻⣍⠉⠛⢶⣄
⠀⣸⣇⠀⢀⣸⠏⢸⡇⢠⡿⠀⠀⠉⠁⢀⡾⠁⡼⣡⠶⠋⢀⠀⢀⠙⠶⣄⠹⡄⠹⣆⠈⠉⠀⠘⢧⣰⡇⠀⠙⢶⣄⣠⣿
⠀⠉⠉⠛⠋⠁⠀⠀⠙⠟⠀⠀⠀⠀⢀⡞⢁⡾⣹⣃⣀⡴⢻⡇⣿⠳⣄⣸⣇⠹⡄⠙⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡞⠀⠈⠉⢉⡴⠟⠁⠙⢷⡈⠉⠉⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠀⠀⢠⡶⠋⠀⣠⡄⣶⣄⠙⢳⣄⠀⠀⠹⢶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠋⣽⠇⢯⡈⠷⠾⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀
⠀⠀⠀⠀⠀⠠⢂⡀⣸⣃⢀⡐⠄⠀⠀⠀⠀⠠⣀⡀⠈⠃⢀⣤⠄⠀⠀⠀⠀⠀⢐⡀⠀⡇⢀⣰⡀
⠀⠀⠀⠀⠀⠀⢈⢹⠀⠀⣇⡁⠀⠀⠀⠀⠀⠀⠀⢈⢾⡷⡁⠀⠀⠀⠀⠀⠀⢈⠀⣈⡁⠆⣉⠀⠈
⠀⠀⠀⠀⠀⠘⠌⠁⢩⡍⠈⠱⠂⠀⠀⠀⠀⠐⠛⠁⢀⡄⠈⠋⠂⠀⠀⠀⠀⠈⠹⠁⠀⡇⠀⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⢠⡀⠀⠄⡀⠀⠀⠀⠀⠀⡄⠀⠀⡂⢀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⣀
⠀⠀⠀⠀⠀⠐⠈⠂⢤⡤⠐⠁⠀⠀⠀⠀⠀⠈⠉⠒⢄⡠⠐⠉⠁⠀⠀⠀⠀⠀⠈⠒⢤⠣⠔⠃
⠀⠀⠀⠀⠀⢀⠰⠂⢈⠁⠐⠀⡀⠀⠀⠀⠀⢠⡤⠂⠁⠊⠑⢤⡄⠀⠀⠀⠀⢀⠀⠚⠁⡆⠑⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⡖⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⢀
⠀⠀⠀⠀⠀⠈⠲⢤⣨⣄⡠⠖⠁⠀⠀⠀⠀⠠⠓⣴⠚⠓⣦⠚⠤⠀⠀⠀⠀⠈⠐⠀⡢⠠⡂⠐⠈
⠀⠀⠀⠀⠀⠀⣠⠔⠻⠟⠢⣀⠀⠀⠀⠀⠀⠤⣀⢷⣈⣁⠾⣀⠤⠀⠀⠀⠀⠈⢁⠉⡣⠵⡉⢀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⡨⢇⠀⠘⠀⠀⠀⠀⠀⠈⠀⠐⠀⠄⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠚⠁⡠⠆⠀⠀⡴
⠀⠀⢠⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⢀⡄⠀⠸
⠀⢻⣿⣿⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢈⠀⠀⠀⠘
⠀⠈⣰⡉⠀⠀⠀⠀⢀⣾⣿⣆⠀⠀⠀⠀⠀⠀⣼⠟⣦⠀⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⣼⣇⠀⣀⡀
⠀⠀⣿⡇⠀⠀⠀⠘⣻⣿⣷⣿⡛⠂⠀⠀⠀⢸⠃⠘⢙⡀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⢞⡟⠂⠀⠻⠏⠀⢹⡇
⠀⢸⣿⣿⠀⠀⠀⢘⣿⣿⣿⡿⣯⣒⠀⠀⠀⢃⡎⠸⣸⢴⠀⠀⠀⠾⣿⣿⣿⠃⠀⠀⠀⣈⠵⡯⢽⠀⠀⠀⣠⣾⣷
⠀⣾⣿⣿⣇⠀⡛⣻⣿⣿⣿⣿⣶⠍⠁⠀⡰⡋⢈⡅⢀⢢⡡⢀⣴⣾⣿⣿⣿⣿⣦⠀⠐⢛⡩⡯⣓⡂⠀⠘⣻⣿⣿
⢠⣿⣿⣿⣿⡄⠬⣷⣿⣿⣿⣿⣿⣟⠂⢰⡵⡧⢏⡱⠜⠢⠗⣇⣩⣽⣿⣿⣿⣿⡄⡀⢨⡭⢒⣷⠆⢤⢀⣼⣿⣿⣿
⣸⣿⣿⣿⣿⣗⠻⢿⣿⣿⣾⣿⣿⣿⣿⣟⣠⢸⣀⢀⣴⡐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣊⠭⡧⠙⡙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣯⠷⣽⣏⡏⠉⠞⣼⠳⠉⣩⣤⣿⣿⣿⣿⣿⣿⣷⣾⡅⠶⠊⡏⠒⣲⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣮⣟⡶⠶⠆⡠⣤⣾⣤⡜⠛⠛⠛⠛⠻⡿⠛⠿⠿⠿⠟⠀⣤⠷⣾⣟⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠯⠴⠞⠃⣿⣷⠈⣙⣛⣛⣋⠁⣿⣤⣿⠀⣾⣿⣧⠀⠀⡇⢠⣶⣾⣶⡆⠀⣿⣿⡇⠉⠙⠛⠿⢿⣿
⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣷⣿⠀⠈⠉⠁⠀⠿⠿⠟⠀⠀⠁⠘⠿⠿⠿⠇⠀⠛⠋⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡄⠀⢠⣦⠀⢸⡇⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⠀⠀⠀⠀⢸⡁⣀⡀⠉⢸⡇⠀⠈⣿⠀⢸⡇⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠸⣿⠀⢀⡞⠁⠈⠉⢹⡇⠀⠀⢿⡀⠀⠘⢧⠄⡇⠀⠀⠉⣿⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠆⠀⢻⡆⠀⣿⡀⢸⡇⠀⠀⢀⠈⢧⣀⠀⠈⠛⠀⠀⠀⡸⠃⠀⣠⠞⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢷⡀⠘⣷⡈⠳⠤⠤⠂⢠⡄⣤⠀⠰⠏⠀⠀⠀⠀⢐⡍⣴⠄⡆⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⠄⠀⠈⠇⠀⠈⠻⠦⣀⠀⠀⠀⠁⣿⠂⢀⡀⣀⠠⣤⠀⣾⠁⢸⡇⠙⢶⣄⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠖⠊⢀⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢹⡇⢸⡇⢹⡀⢿⡀⢸⡇⠘⢧⡤⠀⢹⠆⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠰⡷⢸⡇⠀⢸⠁⣀⠀⠀⣭⠀⠱⣦⡀⢸⡇⢸⡇⢸⡇⢸⡇⠀⠉⠁⠀⠐⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣇⠴⣌⠉⣿⡄⠀⣿⠀⢀⠀⣻⢸⡇⠈⠃⠀⠀⠘⠷⠀⠀⠀⠀⠀⢠⢀⢀⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⡏⠀⢻⡀⠸⣇⡀⢻⡄⠘⠒⠋⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠮⠦⢠
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠐⢷⠀⢸⡇⠀⠈⠀⠈⠳⠂⠀⠀⡀⠀⠀⡀⣀⢀⠀⡀⣀⠀⠀⡀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢀⠇⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡶⣜⡇⠟⠎⠛⠀⣇⣿⢸⣶⠁⠹⠬⢀⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠙⠂⠀⠀⠀⠛⠛⠀⠉⠀⠈⠑⠈⠙⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢬⡥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢬⣙⣋⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐⠠⠀⠑⠢⢬⡥⠔⠊⢀⠀⠂⠀⠀⠀⠀⠀⢀⢠⠊
⠀⠀⠀⠀⠀⠀⠂⠤⠜⡳⢄⡄⡆⢀⢀⠀⠀⠀⠀⠰⠀⢸⠁⠀⠆⠀⠀⠀⠀⠀⡀⢠⢠⡬⢞⠣⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠜⣳⠶⣸⡀⠀⡐⠀⠀⠀⠈⠀⠀⠀⠀⢒⠀⢀⣧⠶⣎⠃⢍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠒⠉⢉⠲⢄⡁⠄⢈⡢⠔⡀⠠⢈⡤⠒⡉⠉⠒⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠂⠁⠂⠀⣊⠀⠁⠀⠁⠐⠀⠐⠈⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⡀⠄⠀⢄⢀⠀⢀⠀⡩⠀⠠⢀⠠⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠤⣀⣈⠤⠊⡁⠂⢈⠔⠪⡁⠐⢈⠑⠦⣁⣀⠤⠂⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢠⡹⠶⢻⠁⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡏⠶⢏⡔⡊⠄
⠀⠀⠀⠀⠀⠀⠄⠒⢢⡴⡚⠃⠃⠀⠀⠀⠀⠀⠀⠰⠐⢀⡀⠂⠆⠀⠀⠀⠀⠁⠀⠸⠘⢑⢮⡔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠁⠀⠀⠀⠀⠀⠰⠀⠁⡠⠔⢚⡓⠢⢄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢚⣩⣍⡓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢚⡓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣟⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠙⢦⣿⡾⠋⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⣏⡴⠂
⠀⠀⠀⠀⠀⠀⢘⣾⣧⡘⣇⠀⠀⠀⠀⣯⠀⠀⠀⠀⣾⣀⣾⣞⡃⠀⠀⠀⠀⠀⠀⢻⠿⣼⡆⢷⠀⠀⠀⠈⡟⠀⠀⠀⢰⠇⣾⡼⠿⠃
⠀⠀⠀⠀⠀⠀⠈⢀⣤⠽⠿⢦⣀⠀⠀⡷⠀⢀⣠⡴⠿⠯⣤⡈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣉⣹⡿⢦⣀⡤⠞⡟⠶⣄⣠⠾⣿⣍⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣿⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⣶⣧⡖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⣠⡴⠞⠉⣯⠙⠳⣤⣀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣠⣿⣞⠉⡏⢙⣾⣧⣀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠠⣤⣤⠿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠙⣿⠯⣤⣤⠄⠀⠀⠀⠀⠀⠀⢀⣐⣶⡾⣻⠁⠀⠈⠙⡟⠋⠀⠀⢻⡛⣶⣖⣀
⠀⠀⠀⠀⠀⠀⠘⠻⠇⠸⠇⠀⠀⠀⣠⣿⡀⠀⠀⠀⠹⠀⠻⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠘⠁⠋⠀⠀⢀⡴⣷⣄⠀⠀⠈⠃⠙⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⣯⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣷⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣯⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣟⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⡷⢃⡀
⠀⠀⠀⠀⠀⠀⣤⣰⡄⢰⡄⠀⣆⣠⠙⣿⠃⣄⡴⠀⢰⠆⢰⣆⡄⠀⠀⠀⠀⠀⠀⣤⣤⢀⡀⣀⠀⠀⠈⢷⣷⠟⠁⠀⢀⡀⢀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠲⠛⠓⢦⣧⠘⠛⢧⣀⣿⣀⡟⠛⢁⣿⡴⠛⠛⠆⠀⠀⠀⠀⠀⠀⠘⢫⡿⢧⣽⡀⠀⣠⠴⡷⢤⡀⠀⣸⣧⠿⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⡉⠙⢶⣟⣧⣿⣟⣷⡞⠋⣩⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⢻⠿⣵⡚⣟⣲⡽⢿⠋⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡿⠒⢿⣺⣿⣿⣿⣚⡗⠚⢿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣯⠿⡿⢧⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠘⠲⣦⣤⠖⠋⣳⢯⣯⠷⡟⠛⢶⣤⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣳⣶⠞⠻⣍⡓⡟⣋⡽⠛⢶⣶⣛⣁
⠀⠀⠀⠀⠀⠀⣹⣷⡞⢩⡏⠰⣺⣇⠀⣿⠀⡿⡖⠂⢿⠙⢷⣿⡁⠀⠀⠀⠀⠀⠀⣰⣶⢻⠏⡾⠀⠀⠀⢉⣏⠁⠀⠀⠸⡎⢿⢳⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠁⠀⠁⢈⡶⡿⢦⡁⠉⠀⠈⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣤⡀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣠⠴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣏⠀⠀⠙⠳⣄⡀⡇⠀⠀⡇⣠⠴⠋⠁⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⢲⠀⠀⠀⠙⠦⣄⠀⠀⠙⠃⠀⠀⠋⠁⠀⣀⡴⠚⠁⠀⠀⢰⠚⠋⡏
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠋⠈⠛⠦⣄⡀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⣀⡤⠞⠉⠈⢧⡀
⠀⠀⠀⠀⠘⠳⢤⡀⠀⠀⠈⠙⠲⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠷⠚⠉⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⢀⣠⠴⠚⠉⠛⠦⣄⡀⠀⠈⠙⠲⣄⣀⡇⠀⠀⡇⣠⡴⠚⠉⠀⠀⣀⡤⠞⠉⠙⠲⢤⣀⠀⠀⠉⠓⢦⡄
⠀⠀⠀⠀⠀⠈⢧⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠉⠃⠀⠀⠋⠁⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⠄⠀⠀⠀⠀⢤⣞⠉
⠀⠀⠀⠀⠀⠀⡴⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⡀⠀⠀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⡄
⠀⠀⠀⠀⠀⢾⣁⠀⠀⠉⠛⠦⢄⡀⠀⢀⣠⠖⠋⠁⠀⢀⣠⠴⠛⡇⠀⠀⡟⠲⢤⡀⠀⠀⠉⠓⢦⣀⠀⢀⣠⠴⠞⠋⠁⠀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠉⠛⠉⠀⠀⢀⣤⠖⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠉⠳⢦⣀⠀⠀⠈⠙⠉⠁⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣠⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣤⡀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠖⠋⠁⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠉⠓⢦⣀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠳⢦⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠈⠙⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣸⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⠀⠀⡀⠀⠈⠓⢦⣀⠀⠀⠀⢹⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠠⡖⠋⠀⢀⣠⠴⠛⡇⠀⠀⡟⠳⢤⡀⠀⠈⠓⡦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠶⠋⠁⠀⠐⡇⠀⠀⡇⠀⠀⠉⠳⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⢀⣸⣇⡀⣄⣤⠆⠀⠀⠠⣼⡆⢹⡟⢁⣿⡤⠀⠀⠰⣤⣆⢶⣼⣇⡶⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠋⠙⣿⡍⠀⠀⠀⠀⣛⡋⣙⣿⣿⣟⢉⣛⡀⠀⠀⠨⣭⣿⣿⣿⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠷⡾⠟⡶⣤⡀⠀⠀⠸⢿⡏⢹⣇⠉⣿⠏⠀⠀⢀⣴⡶⣻⡿⡿⣟⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠏⠓⠈⠀⠀⠀⠀⠀⠀⠉⢼⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠦⣽⠴⣀⣴⡶⠀⠀⠲⣤⣀⠀⣹⡁⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣳⣾⣞⣛⠌⠀⠀⠀⠀⠀⠉⣛⣾⣶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⡇⣿⢬⡛⣶⣦⠀⠀⣠⡶⠞⠉⢺⠒⠉⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠘⡏⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣷⡚⠉⠁
⠀⠚⠒⠂⠒⠂⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⡇⠉⢻⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡄⣀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠪⢽⡯⠔⠁⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⠀⠰⠔⠀⠀⣸⣠⡆⠀⠀⠀⠀⠀⠀⠀⡀⠇⢂⠀⠀⠈⠒⣗⠁⠀⠀⡄⢸⣸⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣰⠀⢸⢰⠄⣀⠴⠊⠉⠁⠒⠀⠀⠀⠀⠀⠀⢀⡬⠛⡶⢴⣆⡀⢢⣸⡠⢃⡠⠞⢮⡓⢌⡒⢄
⠀⠀⠀⠀⠀⠀⢀⡢⣀⠀⢀⣀⣀⣈⣑⣼⣷⠊⢴⠀⢴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠉⠀⣉⡉⣿⣿⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠘⠫⠋⠉⠉⠀⣤⠜⣹⢫⣄⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠰⡎⢳⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠈⢠⠃⠀⠙⠁⠀⠀⠈⠒⣶⡯⡀⠀⠀⠀⠀⠀⠀⠠⣄⣒⣲⠞⠳⠀⠀⠀⠞⡽⣖⣒⡂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠐⠵⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⡐⠀⠀⠀⠀⠐⢡⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡔⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢾⢊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⠲⡶⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⢦⠀⠀⢠⡄⢀⠀⡾⠂⣧⣞⠁⠒⠀⠀⠀⠀⠀⠀⢐⣧⣱⡀⠐⠄⢄⠀⡈⣄⠄⠀⢀⣞⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠞⠋⠑⠒⠤⢝⣮⣠⡇⠊⢠⡶⠀⠀⠒⠒⠀⠀⠀⠀⠀⠔⠚⠉⠒⠬⣙⣆⣾⣁⠤⠒⡉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠘⢓⡠⢻⠿⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠔⢺⠿⢏⡉⠙⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⢠⡇⠸⠈⠶⠀⠉⡟⢳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡴⢁⣤⡀⠙⠢⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢶⠋⠇⠀⠀⠀⠀⠀⢇⠀⠀⠠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⢿⠀⠀⢠⠀⠀⠀⡏⣷⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠠⢛⡒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣹⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠘⢦⣸⣇⡴⠁⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣰⡀⡄⢠⠀⠘⠻⡇⠀⠀⢹⡏⠀⠀⣸⠟⠃⠀⡄⢠⢀⣆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣱⠿⣌⣇⠀⠀⢸⣦⣦⢼⣧⡤⣴⡃⠀⠀⣸⣡⠾⣎⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⠲⣴⡟⠛⢇⢸⡇⡼⠓⢿⡤⠖⠛⠓⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⡴⣻⠈⠓⢮⣿⣾⡵⠚⢉⡟⣆⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠉⢯⣹⢉⡩⢟⣿⣿⡻⢍⣉⣏⠟⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢤⣤⠴⢻⡧⣤⡎⢸⡇⢳⡤⢾⠟⠦⣤⡤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡻⣶⢋⡟⠀⠀⢱⠯⠽⢾⡿⠭⠵⡏⠀⠀⢻⠙⣶⢞⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠹⠡⠇⠘⠀⢠⣴⡇⠀⠀⣸⣇⠀⠀⢹⣦⡄⠀⠃⠸⠌⠏⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⠞⢹⡍⢣⡀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣏⠂

⠀⠀⠀⠀⣀⣀⣠⠒⢦⠀⠀⣀⣀⢀⡤⠤⢄⡔⠒⣒⠲⣎⠱⡤⠤⡄
⠀⠀⠀⠸⡄⠀⠻⠀⠈⢳⣸⠀⡈⢿⡀⠘⠂⣹⠀⢀⠴⢋⠆⡴⠒⠁
⠀⠀⠀⠀⢳⠀⢀⣄⠀⠸⣏⢠⢦⣘⣇⣠⣏⣈⠒⣺⠤⣈⡶⢅⢀⣠⣀⠤⢄⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠈⣆⣀⡟⠶⡶⢯⡁⣔⠛⢉⣿⠀⣤⢹⠇⠀⠘⡷⡌⢁⠤⣧⣀⠐⢏⠀⠀⣸⠁⠘⡆
⡠⠤⣴⠉⠳⣀⠞⢉⡑⣇⠀⣇⣈⠇⠸⣽⣀⣉⣼⣀⡖⣆⡹⢧⡼⠀⠧⣀⣀⠜⡞⠉⠻⠀⠀⠗⠓⣦
⢳⠀⠈⠁⠀⢸⡄⠘⠇⣸⣀⡤⠼⠒⠒⠉⠉⢀⡖⠢⣄⣀⠴⠲⡄⠀⠀⣤⠴⠶⠟⠒⠂⠂⠐⠐⠚⠓⠒
⠈⢧⠀⢿⣄⣈⡟⠒⢚⠁⠀⠀⠀⠀⠀⡤⠤⠼⠧⠤⠊⠙⠤⠀⠷⠶⡄⣿⠀⠀⠀⠀⡇⠀⠀⠐
⠀⠘⠒⠊⢈⣄⡞⢳⠏⣷⢚⡆⠀⠀⠀⣟⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣼⣄⠹⣸⢰⣃⣞⣽⣀⣠⣄⢻⠀⠀⠀⢰⠀⠁⣸⡄⠀⠀⡇⢸⠀⠀⠀⠀⠠
⠀⠀⢠⠖⠚⠛⠛⠉⠁⠈⠉⠀⠀⠀⣸⢸⡀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⡤⠀⠄⠀⠂⠀⠀⠒⠂⠀⠀⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠟⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⢿⣠⠟⢠⠀⠀⢠⠏⠹⣄⠀⠀⡀⠻⣄⡿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠛⢯⣠⠏⠀⣰⠏⢰⡆⠙⣆⠀⠹⣄⡽⠛⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣀⣀⠀⠈⠉⠛⣇⠀⣰⠃⠀⢸⡇⠀⠘⣆⠀⣸⠛⠉⠉⠀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣤⡉⠙⠓⠶⠦⣼⣶⣧⠀⡀⣾⣷⢀⠀⣼⣶⣧⠴⠶⠚⠋⢉⣤⢀⡟
⠀⠀⠀⠀⡄⢠⡀⢀⠀⠈⣇⠈⠻⣦⣄⠀⣀⡙⠻⣇⡼⠁⡏⢹⠈⢧⣸⠟⢛⣀⠀⣀⣴⠟⠁⣸⠁⠀⡀⢀⡄⢠
⠀⠀⠀⢲⣿⣄⣧⠘⡇⠀⢹⡄⠀⠘⢯⡳⣌⡉⢛⢻⣡⠆⡇⢸⠰⣌⡟⠛⢉⣡⢞⡽⠁⠀⢠⡏⠀⢸⠃⣼⣠⣿⡖
⠀⠀⠀⠉⡤⠞⠋⣻⠿⢤⣀⣧⣤⠘⡆⠙⢆⠙⢮⡙⢻⢸⡇⢸⡇⡿⢋⡵⠋⡰⠋⢰⠃⣤⣼⣀⡤⠿⣟⠙⠳⢤⠉⠁
⠀⠀⠀⠀⠀⠐⠉⠀⢀⣠⠾⣿⠟⢶⣿⣀⣎⠳⣄⠉⠻⣿⢡⡌⣿⠟⠉⣠⠞⣱⣀⣿⡶⠻⣿⠷⣄⡀⠀⠉⠂
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠠⠖⠋⠁⣞⣋⣓⣾⣦⣙⣾⣿⣿⣷⣋⣴⣷⣚⣙⣳⠈⠙⠲⠄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠶⣏⡁⠰⠶⠶⠶⠿⢿⣭⣭⣉⣉⣉⣀⣀⠶⣺⣿⣿⣿⣿⣷⠲⣀⣈⣉⣉⣉⣭⣭⠿⠿⠶⠶⠶⠆⢈⣹⠶
⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠐⠶⣄⡀⣲⣬⠽⣻⠟⡵⢻⢿⡿⡟⢮⠻⣿⠯⣥⣖⢀⣠⠶⠂⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠠⣄⡀⠈⠙⢲⣽⣶⠖⣿⠉⢏⡴⠃⣠⢶⣿⡘⢃⣿⡶⣄⠘⢧⡹⠉⣿⠲⣶⣯⡖⠋⠁⢀⣠⠄
⠀⠀⠀⣄⡙⢲⣤⡽⣷⠛⠉⡟⠋⢰⠇⡰⢋⡤⢞⣥⣾⢸⡇⢸⡇⣷⣬⡳⢤⡙⣆⠸⠆⠛⢻⠉⠛⣾⢯⣤⡖⢋⣠⠄
⠀⠀⠀⠞⣿⢉⡟⢠⠇⠀⣸⠃⠀⣠⣾⡵⣋⣠⡤⣾⡉⠃⡇⢸⠘⢉⣷⢤⣄⣙⢮⣳⡄⠀⠘⣇⠀⠸⡄⢻⠉⣿⠳
⠀⠀⠀⠀⠁⠈⠁⠈⠀⢠⡏⢀⣴⠟⠁⠀⠈⣤⣼⡇⢳⡀⣇⣼⢀⡞⢸⣧⢤⠉⠀⠈⠻⣦⡀⢸⡄⠀⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢉⣀⣤⠴⠖⠚⢻⠿⡝⠀⠁⢿⡿⠈⠀⢫⠿⡟⠓⠲⠦⣤⣀⡉⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⢀⣀⣠⣤⣏⠀⠹⣄⠀⢸⡇⠀⣰⠏⠀⣹⣤⣄⣀⡀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣡⣤⣞⠘⣆⠀⠙⣆⠸⠇⣰⠋⠀⣰⠃⣻⣤⣌⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠈⢧⠈⠀⠀⠘⣆⣰⠃⠀⠀⠁⡼⢁⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠉⠃

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿