Canary islands Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠋⠀⠀⠀⠀⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⠛⠀⠀⠀⣴⣶⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣦⣴⣿⣿⣿⠋⠉⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠








⠁

⠀⠀⠀⠀⠀⠀⠀⣤⣶⣴⣼⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣀⡀⠀⠀⠉⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠉⠋⠉⠉⠙⠛⠻⢿⠿⢿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠛⠃⠀⠀⢠⣶⡆⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠐⠀⢀⠀⢀⠀⡀⡀⢀⠀⡀⡀⡀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠀⣀⡀⢀⠀⠀⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⢀⠀⠒⠒⠒⠒⠒⠒
⠀⠀⠘⠀⠊⠃⠋⠃⠊⠂⠚⠃⠛⠀⠀⠂⠑⠘⠀⠜⠣⠏⠇⠣⠚⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢤⡄⠤⠤⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡄⠈⠀⠀⠅⠁⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠄⠤⠤⠄⠀⣄
⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⢀⠀⡉⠑⠣⢲⣽
⠀⠀⠀⠀⡀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠒⠒⠀⢠⣔⣤⢾⡏
⠀⠀⠀⡀⠀⠀⣠⠄⡀⣀⣀⡀⠀⠀⢀⢀⢀⢀⠀⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⡱⣄⠏⠨⠜⠋⠙
⠀⠀⠀⠐⠂⢸⡐⠂⠀⢀⣀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠈⢀⣀⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣀⡀⣀⣀⣀⣀⣠⣀⣀⡀⢼⠙⡉⠉⠉
⠀⠀⠀⠀⠐⢁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⢔⣩⠶⡊⣀⡄⠠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣀⣀⢀⣐⢈⡂⠄⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣁⠀⡤⣀⣞⣄⢈⣁⡀⠈⠀⠀⠉⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢉⠲
⠀⠀⠀⠀⠐⠒⠒⠒⠀⠆⠌⠁⠠⠀⠀⠀⠳⣙⠉⣡⠇⠀⠠⠀⠀⠀⠀⠀⠁⠤⢮⣴⠀⣁⠀⢀⠀⡀⠀⠀⠀⠀⠈⢉⣀⠙⠂⢊⡑⠂⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠄⠓⠈⠣⣀⠀⠀⠀⠐⠀⠀⡶⠡⢆⣰⣿⡄⠀⠀⠀⠀⠐⠒⠒⠀⠂⠛⡉⠙⠢⠀⠀⠀⠉⠀⠀⠀⠐
⠀⠀⠀⠐⢁⡀⠀⠀⠐⠂⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠒⡂⠽⢷⣣⣽⠿⠉⢩⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠉
⠀⠀⠐⡀⠈⠁⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⠀⠀⠙⡗⠰⠖⠒⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠈⠉⠉⠉⡁⠈⠈⡉⠉⠉⠘
⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠄

⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠤⠤⠀⠤⠤




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡀⠀⣠⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣶⡶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠘⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢉⣙⠿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣻⣿⠟⢛⣻⣟⡛
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⡟⢛⠃⠓⠉⢝⠛⠓⢈⣛⣿⡿⠞⢿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭⣙⣻⣴⡶⢺⡦⠀⢻⣦⡷⢄⣾⠶⣼⣭⣴⣷⣶⣯⣹⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣟⣿⣽⣿⣿⣿⣟⢿⣏⣿⣷⣿⣿⣿⣿⣧⣽⣾⣻⣦⣬⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠃⠙⠈⠓⠋⠑⠀⠋⠘⠀⠛⠈⠃⠋⠉



⠀⢸
⠀⢸
⠀⣼
⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⡿⡿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣬⣕⣶⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣭⣽⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠻⡿⠃⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠔⠛⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠋⠙⠋⠙⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠒⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠦⠀⢀⠀⠀⠀⠀⠀⠠⠆⡀⠒⢀⠀⠀⣰⢀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢦⠀⠀⠀⠉⠉⠈⠁⠋⠉⠀⠀⠀⠇⠀⠨⠈⠁⠉⠉⠀⢀⡔⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠳⣄⠋⠋⠉⠘⠉⠃⠀⠀⠈⠁⠃⠋⠙⠉⠉⠋⠋⣠⠟⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡀⠹⣷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠏⠀⣿⣿⡄⢀⣠
⠀⠀⠀⠀⠀⠀⢰⣶⣾⣧⣄⣐⠉⠀⠠⢽⣿⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠒⠰⠿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠉⠀⢀⣴⣾⣿⡏⢈⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⠀⣼⣷⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠸⣿⣿⣥⣰⡿⣭⣿⣿⡿⢠⢹⣯⣭⣤⣄⠤⠒⠲⠚⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋⠉⠀⣻⣿⣟⣷⣿⣿⣿⣿⣿⣿⠛⠛⠛⠒⡎⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢣⠀⢷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠈⠀⢿⣿⣿⣿⡋⠘⣻⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⡄⠈⢻⣿⣿⣷⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠁⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⠐⠦⣀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⣤⣄⠀⠀⠀⣰⣿⣧⣾⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠋⠃⢠⣿⣿⣿⡛⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢁⣠⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⣴⠿⠟⠈⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠋⠁

⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠈⠻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠘⠀⠹⣿⣿⣿⣷⣄⢂⠀⠀⠀⠀⠸⣿⣶⣶⣿⣷⣿⣿⣿⣿⡟⠁⠀⠶⠓⠒⠲⠶⠋⠀⠀⢸⠏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠈⢿⣿⣿⣷⡄⢀⡀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣸⣦⣴⠶⠲⠀⡀⠀⠀⠩⠀⠀⠀⠳⢾⣿⣶⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⡛⠂⠶⠀⠀⠛⠛⠿⠿⠿⣿⣿⠀⠀⠠⢿⡟⢿⣦⠀⠀⠀⠀⣤⠀⠤⠴⢤⡀⠀⢴⣿⣦⣠⣾⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠻⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠶⣶⣶⣄⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⠠⠠⣤⡤⠤⠀⠤⣄⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠿
⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⢀⠖⠋
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⢀⠰⡄⠀⠒⠢⣄⣀⣀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠄⠀⠁⠀⠀⠘⢀⠀⢀⠀⠀⡀⢀⣤⠀⠀⣰⣯
⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠈⡭⠿⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⡋⠀⣄⣙⠀⠀⠀⠀⣉⡙⠢⢤⣤⡠⢄⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢠⣴⡆⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠠⠀⠻⠀⠄⢀⠀⠛⠁⠀⠀⠉⢶⣀⣸⣏⠚⣷⠶⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠁⠐⠀⠂⠐⠀⠸⠀⠀⠈⠄⠀⢀⠰⡀⠀⠀⠐⠀⠚⠗⠀⠉⠄⠈⠃⠩⣉⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠄⠀⠈⠋⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠂⠂⠛⠒⠒⠀⠐⠐⠓⠈⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡤⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠄⠀⡌⠂⢠⠀⡀⠀⠁⠐⠶⠖⠀⠀⠀⡀⠸⡆⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⢀⠀⠒⠀⠄⣀⣸⣛⠁⣹⡽⡛⢳⡀⠀⣤⡆⠠⡴⠊⢀⣽⣎⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠴⠃⢄⣉⠁⠀⠰⢖⣫⢞⠛⢻⡞⢻⣿⠷⠾⣶⣷⡉⢀⣲⠀⠐⣠⠟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠀⠀⠐⠋⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠇⢻⣿⠀⠒⠛⠛⠁⠐⠀⠑⠛⠀⠀⢒⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣫⣶⣰⣤⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⢯⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢿⡿⠋⡼⣿⡟⢸⠇⠙⠀⠀⠁⠀⠉⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⡠⣄⡀⠀⠀⠀⣀⣴⣿⣿⣪⣴⠋⢀⠞⣴⠋⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⣷⡿⠝⠛⢻⣶⣾⢟⡿⣻⣿⠟⠁⡴⠋⣼⠋⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⠺⣝⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣹⣏⣿⣷⣷⣤⣶⣿⣿⡿⣫⣾⣿⠁⢁⡜⢀⣾⣇⡆⢸⣿⣿⠀⢄⠀⠀⡆⠀⣿⣏⡆⠈⢦⡈⢻⣿⣦⡀
⠀⠀⠀⠀⠼⠿⣿⣿⣿⣾⣿⡿⢿⡟⠿⢿⣿⣿⣯⣾⠛⠹⠿⣶⡞⢀⠈⢿⣿⠁⣿⣿⣿⠀⢸⣄⣀⢱⢸⣿⠋⢹⢂⣤⣻⣮⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠻⠏⠉⠉⠀⠙⠲⣬⣟⠾⡟⠃⠀⠀⢠⣽⡿⠞⠀⠘⠉⠶⢽⣿⣿⠂⣿⣿⣿⡿⠟⠉⢦⠘⠋⢀⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠰⣤⠤⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣖⠼⠒⠼⣧⣄⢛⣤⣄⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣴⣿⡿⠞⠙⠳⣾⣯⠿⢿⡁⢀⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠻⡏⠀⠀⠀⡠⢨⣁⢀⣄⡇⡫⢾⣟⠅⠃⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣄⣤⣾⣴⣿⣿⣿⣿⣿⣷⠟⣡⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠄⠀⠚⠾⢭⣭⣿⣦⣶⡶⠶⠟⠛⠋⣡⢞⣁⠀⠀⠀⠀⢀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢶⠶⠶⠞⠛⣹⡿⣳⡙⠲⠦⠤⠄⠷⡟⠁⠀⠀⢼⠿⠋⠞⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠰⡏⠀⠉⠉⠳⣶⣄⡀⠀⣀⡶⠖⠒⠀⡀⣀⣀⣀⣠⠴⠖⠂
⠀⠀⠀⠀⠀⣠⣤⣥⣶⠶⠞⢓⠒⠒⠚⠛⠒⠢⢄⣷⡀⠀⠀⠀⢹⣿⣷⠞⠁⢀⣀⠴⠛⠋⠁⠀⠋⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⢀⡀⠀⣈⣻⣦⣤⣤⡿⠿⠑⠲⠾⢗⡀⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⠿⣻⠏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣸⠵⠛⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠖⠋⠁⠀⠀⠀⠀⠀⠀⡜⣀⣠⣤⣶⣴⡾⢥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠘⣸⠁⠀⢸⠧⡄⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠀⠈⠀⢶⣇⡀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡷⠆⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠠⢿⡵⠀⠀⠀⠀⠀⢋⣠⣄⣴⣤⣤⣤⣦⣴⡀⠀⢡⡄⠈⢉⠋⠀⠀⢠
⠀⠀⠀⠚⠿⣤⣤⡀⠀⠰⣾⣰⠼⠄⠘⠛⠃⠀⢈⣁⠀⠁⠉⠛⠀⠼⠅⠀⠸⢶⣰⠄⠘⠀⣸⠖
⠀⠀⠀⠀⠀⠘⠿⢷⣶⣄⠀⠉⠁⠀⣀⣀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⡿⠿⠟⠁⡀⢿⣧⡀⠚⠛⢿⣛⡛⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠚⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠠⠄⣠⢀⡆⠀⠀⠀⣍⡈⠙⠀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠼⠅⣠⡿⠿⠷⠷⠴⠶⠀⠠⠶⠟⠡⢬⢱⠾⢇⢀⣀⣿⣿⣿⣶⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠺⢇⣶⣾⢬⣼⣿⣿⡿⠟⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣶⣬⣿⡿⠀⠁⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡞⣿⣦⡙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣦⣿⡿⢩⣿⣿⣦⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡃⣼⣿⣿⣿⣦⢻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣯⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡃⠿⠿⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠦
⠀⠀⠀⠀⠶⠛⣻⠋⠓⢠⣀⠐⢻⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⡆⠀⠀⠛⠘⢿⣿⡛⣿⡟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠚⠃⠴⢂⣈⣥⣤⡬⠷⣿⡿⠟⠻⠉⠀⠀⢀⡟⠇⠀⠀⠀⠃⠀⠽⣷⡈⢷⡄⠁⠀⢿⠛⠻⠟⠋⠉⠛⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢵⠀⠴⡓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⣨⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢀⠀⠉⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⡆⠀⠀⠀⠀⡀⠀⠀⠄⠘⠁⠀⠀⠀⠛⢭⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣀⠀⡄
⠀⠘⠇⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⠀⢄⣀⣀⣀⣤⣀⣀⠑⠀⠀⠀⠀⢁⠀⠀⠀⠀⢠⠄⠈⠐⠂
⡀⠀⠃⠀⠰⠀⢨⡀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠿⡿⠛⠛⠉⠙⢻⣷⠀⠀⠀⠁
⡧⠬⣁⠀⠀⠀⢐⠁⠠⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠐⠳⠂⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⢿⠀⠈⠀⠂⠀⢸⡀⢀⠀⠀⠀⠀⠀⠘⣧⣴⡔⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠈⢀⠀⠀⠤⠂⠃
⣀⡧⢄⠈⠀⠀⠸⡆⢀⠤⠀⠀⠀⠀⠀⠈⣿⠃⡠⣶⠀⠀⠙⠀⢀⠠⠀⠠⣰⠧⠀⠀⠀⠠⡀⠒⡠⠄⠁
⠁⢠⣄⠃⠘⡀⢸⡦⣾⠀⠀⠀⠀⠀⠐⢢⠈⠆⣐⡅⢨⠄⡀⢠⡋⡄⢉⠀⣯⠆⠀⠀⠀⠀⠉⠲⣀⠀⠘
⠀⠋⠀⣧⠀⣁⣺⠀⡿⣧⠒⠀⠀⢀⢰⡆⣰⠀⠀⠀⠺⠄⠟⠒⠀⢦⠘⢜⠿⠀⠘⢄⡠⠀⠀⠀⠀⠀⡄
⡠⠀⠐⠬⠺⠅⢹⠠⠑⢫⡷⡄⢀⠈⡼⠁⠘⠦⡀⡈⢈⠀⠀⠈⠁⣮⣷⣄⡀⠀⢀⡨⢬⡤⠨⠀⠑
⠀⣦⠦⠤⣴⡟⢻⠖⠁⠸⡇⠰⠀⠶⣶⠂⡀⠪⠜⠏⢺⠉⠁⡰⠀⢐⣿⣄⠆⠀⣬⡀⣼⠎⠉⡀⠀⠐⢆
⣁⢰⣶⡄⠹⠧⣿⣧⠈⠐⡄⣄⣉⣿⣅⣐⠉⠁⠀⠀⣯⢄⡎⣸⡻⢸⠈⡎⠼⠠⠉⠀⠁⠈⠱⠎⢤⢶⣂
⡨⢶⢿⣾⠟⢷⠜⠃⠀⣀⢁⣟⣿⣿⣿⣻⠋⢄⡀⠩⡷⡿⠅⢿⢾⣾⠶⢀⠥⠛⠂⡄⣸⡶⣎⣠⣿⣄⠈
⠁⢼⣇⣤⡈⣉⡴⣷⣶⢭⣜⣏⠉⣴⡞⣿⣀⣴⠂⣴⣟⡆⢁⡘⠲⡗⠀⠘⡀⠶⡆⠺⠽⢣⣻⣽⢷⡻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢴⡁⠀⠀⠀⡀⠀⠃⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠋⠀⠀⠑⠄⢄⠀⠀⠑⢄⢤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⡀⠀⣄⡸⠀⠀⠀⢠⠞⠑⢤⣤⣶⣿⣶⣶⣷⡤⠤⠟⠀⢀⠀⠒⠒⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠛⠿⠟⢿⣿⣿⢿⣆⠀⢐⣉⡠⢀⣀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠉⠉⠁⠉⠝⢢⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡀⠻⣧⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠒⠀⠰⠀⠐⠊⠉⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣬⢷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢈⠥⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠽⣧⢳⡄⠀⠀⠀⣆⠁⠀⢀⣠⣠⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠻⣄⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠠⠀⠀⠈⢀⠃⡀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠀⠀⠀⠀⣠⢃⠁⠀⠀⢸⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠘⣦⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⣀⡴⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠻⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⣠⡟⠀⠀⠀⠀⢦⠀⠀⠀⠘⢆⠀⡀⠀⠀⠈⣝⡻⣝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣠⠾⠋⠐⠀⠀⠀⣠⣾⠟⠁⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡀⠈⠀⠱⠈⣿⣯⡓⣬⡳⣄
⠀⠀⠀⠀⠀⠀⡴⠟⢁⣴⠟⠁⢀⡜⠀⠀⣰⣾⠟⠁⠀⠀⠀⣀⣾⡟⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⢹⣦⣀⡀⠀⣸⣿⣿⣾⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠑⢾⣏⣁⣀⣠⡞⠀⣠⡾⠟⠁⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠲⢦⣴⣴⣾⣿⣿⣿⣤⣤⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠿⣶⣿⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⠛⠘⣿⣿⣾⣷⣮⣵⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⠁⣫⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣁⣴⣫⣾⣿⣿⣿⣿⣆⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣟⣣⡉⠇⠉⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⠋⠉⠈⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣞⣫⣴⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡿⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢿⣿⣿⡿⠛⠟⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠛⠟⠻⣻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢻⣿⣿⣥⣴⠟⠁⠀⠙⠳⢶⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⢀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⡿⢿⡿⠗⡤⣀⣀⡀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣧⣿⣿⣝⣏⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣫⢿⣿⣶⠔⠀⣴⣿⣿⣻⣷⡀⠀⠀⠀⠀⣾⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢶⠟⣽⣎⡷⣽⢦⣼⣟⠫⣏⠸⣿⣧⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⠸⡷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⠟⣤⣱⠟⡾⣿⠖⠀⣹⣧⡿⣿⣷⠀⢠⡿⣿⡏⢸⣿⢿⣿⣿⣿⣻⣿⣿⣿⣯⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⢻⣿⠃⢳⡀⢠⡄⢸⣿⣿⣿⣿⡀⣾⢃⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢮⣧⢀⣬⣵⣴⣿⣿⣿⣿⣿⠘⢫⡟⣾⣯⣝⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣴⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣧⣽⣿⣿⣟⣿⣿⡿⣿⠀⣼⡿⠉⣿⡷⣾⣧⣍⡩⠉⠙⠀⠨⣭⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠨⡸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣹⢀⡁⠃⠀⣾⣿⣿⣟⣋⢀⢉⣁⣬⣽⣿⣿⣹⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⡿⣿⠀⣿⣿⣿⢻⣿⢿⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢈⢻⣿⣿⢿⠿⠟⠿⠻⣿⣿⣿⣯⣿⣿⡞⢷⡿⠀⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿⣿⢻⡏
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣾⣿⣿⡿⠁⠄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠁⠀⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣶⣾⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⣮⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⠀⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠛⣯⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⡿⠀⢿⣿⣿⣏
⠀⠀⠀⢠⡄⢀⡀⠘⠛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠐⠀⠀⠀⢰⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⡗⠐⠀⠸⣿⡤⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇
⠀⠘⣆⣠⠓⠈⠠⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⡇⢸⣇⣟⣩⠁⠀⢤⠀⠀⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿
⠀⠀⢼⣿⢛⣷⣴⣆⠀⠀⢻⣿⣿⣿⢻⣿⣿⣿⡇⢈⣷⣾⣿⡶⠄⡀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏
⠀⠀⣈⣻⣿⣯⣀⣉⡀⠀⠸⣿⣿⣟⢸⣿⣿⡏⠀⢨⣭⣿⣿⣗⣀⠀⠀⠀⢸⣿⣿⠃⠀⠀⢸⣿⣿⠁
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣏⡁⠁⠀⢸⣿⣿⠀⠒⢦⣾⣿⡇⠀⠀⡀⠄⠄⠀⠀⢠⡄
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣤⣴⣾⣿⣿⣷⡀⣤⢀⡀⢠⡀⠀⠀⣁
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢛⠓⣒
⠀⠀⠀⠈⠛⠟⠻⠿⠿⠿⢿⣿⣿⣿⠿⢿⣿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⡯⢯⣿⣿⣿⠿⢿⡟⠿⠱⠏⠉⠓⠁
⣀⣀⣀⣀⣀⣀⣛⣋⣙⣂⣀⣀⣈⣙⣋⣀⣀⣈⣉⣉⣚⣒⣉⣙⣓⣛⣉⣋⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣒⣐⣀⣈⣁⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣦⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠤⠀⠠
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠴⠀⠀⢠⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡄
⠀⠀⠀⠰⠁⠀⠀⠛⠟⢫⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠃⠠⣆⠉⠋⢩⡀⣀⠈⢂
⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡧⠂⠀⢫⠁⠬⢴⣏⡠⢰⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠈⢥⠀⠀⠁⠉⠀⠾⢤⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠉⢩⠁⠴⢻⠓⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠗⠷⢽⣿⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡄⠀⠀⠉
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠈⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡉⠉⠀⠀⠒⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠒
⠀⢀⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⡀⠈⠁⠀⠤⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠢⠤⣤⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠁
⢤⢶⣆⠀⠀⠀⠀⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠄⠠
⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠢⠀⢨⡦⠀⢀⠄⠢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠢⠀⠀⣠⡶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣢⡄⢲⣄⣦⠀⣤⠎⢀⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡘⣢⡔⠵⡄⢁⡔⢨⡡⠂⢑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠶⠬⠑⠄⣀⡡⢊⠴⢂⡉⠉⡥⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢀⡉⠲⡐⢈⢁⠋⢠⠶⠅⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠐⠶⢂⠈⢣⡿⡿⣭⢀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣆⢀⣩⠀⣙⢾⣿⠥⢄⠛⠛⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⠖⢉⣠⢺⡇⡛⣄⢢⡉⠣⡁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡤⢊⡰⠋⣽⡅⠠⣌⠫⡀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠪⠉⠍⢁⡆⢸⣄⡓⠠⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠂⠘⡤⡏⢠⡑⢻⠸⢶⠈⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠃⢿⡼⢿⣄⢸⢹⡷⢂⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡘⠱⡎⠄⠇⠱⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢨⡁⣙⠲⣹⣯⣍⠰⡍⠶⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠃⡇⢘⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡺⢾⠝⢓⣽⢿⠿⣥⡞⢇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠧⡸⢻⠟⡎⣷⢳⠙⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⡔⡡⠾⠛⣤⠎⠏⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠎⢰⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠇⠀⡗⠚⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠓⠂⠠⢄⣀
⠀⠀⠀⠀⢀⠀⡠⠋⠉⠀⠀⠀⠓⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡸⠀⠀⠀⣀⡨⠉⢰
⠀⠀⠀⠐⠁⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠅⠐⢀⠩⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢔⡀⠉⠒⠠⢀⡀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⠀⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⠈⠒⠤⠀⣀⣀⠀⠈⠂⠀⠀⠉⠀⠈⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⢀⡴⠂⠉⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢢⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠧⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠈⠉⠁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡶⠎⢻⡄⠀⠀⠀⠀⠀⠀⢠⣾⠛⠙⠋⠿⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡙⠚⢻⣿⡄⢀⣠⣞⠟⠛⠛⠟⠀⢀⣀⣤⣤⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣧⣿⠙⠈⠀⢀⣰⣶⣾⣿⣿⢟⣿⣿⠃⢰⡖⣲⡤⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣿⠇⠀⡞⢡⣿⣿⡼⢂⣼⣿⣻⠿⢶⣼⣿⣿⣷⡿⢉⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡿⣿⠿⣿⣿⣿⡿⢋⣀⣉⠈⣿⣿⣿⣿⣿⣿⣏⠀⢄⠀⠘⠛⣿⣷⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢤⣤⣶⣿⣿⣿⣷⣿⣿⣿⣷⣤⣽⣿⣿⣯⣟⣹⡄⠀⣆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠛⢛⡿⠋⠉⠻⢿⣿⡿⠿⣿⣾⣿⣿⡟⠁⠀⡁⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠚⢃⣁⣄⡀⠀⢀⣀⠀⠶⠶⢾⣿⣶⣿⣷⣄⠀⡁⠈⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠈⠚⠹⡶⢿⠿⠿⣶⣄⢀⣿⣿⣿⣿⣟⡁⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠙⠂⠀⠀⠀⠠⠀⢠⣀⣈⣿⣿⡏⠸⠟⢿⡉⠑⠶⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⢤⣀⡀⠃⠀⠀⣠⣿⠿⣿⣿⣿⠄⠀⠀⠈⠙⠀⠀⠀⠀⣠⠴⢚⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠄⠉⠓⠄⢸⣿⣯⢰⡿⣿⣿⡄⠀⠀⣀⠀⢀⣤⡴⠟⢁⣼⠋⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⢠⡖⠁⢸⣿⣿⡟⣇⣿⣿⣷⡶⠿⠏⠀⣼⣿⠓⠀⣨⢁⡄⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢸⡅⢠⣾⣿⣷⣾⣯⣿⣿⣿⣤⡀⠀⠀⣿⣿⠂⢠⣇⡾⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢿⡦⢄⡸⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡄⠀⣿⣯⠕⣸⣏⠒⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣍⠁⢸⣿⣵⣦⣪⣿⣷⣿⣿⣿⣿⠋⣿⠈⠓⠘⣿⣆⠹⣿⡄⣿⣯⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣽⣿⣿⣿⣿⣶⣾⣿⠛⠛⠛⠁⠀⠋⠀⡤⠀⣬⣿⡄⠘⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⣩⣿⣿⡷⢹⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⣴⣖⠒⠶⣦⣀⠈⢛⣿⣿⣿⣷⣈⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠉⠻⣶⣤⡀⢹⡟⢿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⡌⠻⣦⡀⠀⠈⣿⡄⠀⠀⠙⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣂⠘⣻⣆⠀⠀⢷⠀⠀⠀⠀⢿⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⡸⣿⣷⠀⠘⡄⠀⠀⠀⢸⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣀⢻⣷⣄⣷⡀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣾⣿⣿⣿⣦⡀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠙⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠒⠀⠉⠀⠀⠀⠀⠐⢲⡤⠀⠀⠀⠀⠀⠀⠀⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢢⠀⠀⠀⠀⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠲⣦⠀⣷
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡀⣀⡀⠠⠀⠘⠀⢀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢇⡄⡀⠈⣠⠀⠈⢩⡔⠃⣀
⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠀⠆⠀⢀⠀⠀⠀⠈⠉⠀⠃⢉⡠⠏⠘⠉⠠⠴⠚⠁⠞⠃
⠀⠀⠀⠀⠀⢸⢻⣿⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⢠⣶⠀⠀⢸⠀⣿⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠤⡤⣤
⠀⠘⣿⠀⠀⢸⢠⣿⠀⠌⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣞⢷⡀
⠀⠀⣿⡄⠀⠘⢸⡿⢊⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠋⠀⢄⢸⢿⣧⣷⡀⠀⠀⣀⠀⣀
⠀⠀⢿⣧⠀⡞⢸⣿⠟⠁⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢺⡶⣋⡄⠀⣀⣼⠇⣾⣿⣛⢯⣿⣷⣾⣯⢁⠈⠢⣄
⠀⠀⠘⣿⣦⡗⢸⣿⠀⠀⢸⣼⡇⠀⣀⠀⠀⢀⠠⠀⢀⠎⠀⣼⡿⠋⠀⠀⡿⠋⢸⣧⡈⠛⢿⣿⡿⣿⣷⣿⣷⣀⣉⢻⡶⣦⣀
⠀⠀⠀⠘⢿⣇⢾⡏⢀⣄⢸⣿⠃⠀⠸⣷⡀⢉⡤⠚⠉⢀⡾⠋⠀⣰⣧⠞⠀⢼⠙⢿⣿⣦⡺⣿⣿⣮⣿⣿⣿⡿⠋⠻⣧⡿⣿⣿⣆
⠀⠀⢀⣶⠀⣿⢸⡇⢸⣿⢸⣿⡆⢀⣤⢿⡗⠉⠐⣠⡾⠋⠁⠀⣰⣿⢏⠄⡆⢠⠸⣄⠈⢿⣷⣿⣿⡿⠛⠉⠁⠀⠀⠀⣽⠿⣿⣄⡈
⠀⠀⠘⣿⣆⣿⣿⠁⣸⣿⣼⣿⡇⣿⣿⣿⣿⣶⠟⣫⣤⣶⠶⠋⠉⣠⠎⢀⡁⢸⡆⠨⣦⡈⠿⠟⠉⢰⢸⡇⠈⠁⠀⣰⣿⡀⠀⠉⠃⠑⠂
⠀⠰⣾⣿⣿⢿⣿⡇⠈⡻⣾⣿⠃⣤⠙⠿⠿⠗⠛⠛⢻⣃⣤⠈⣰⣟⣀⣾⡇⠘⠛⠀⠉⠀⠀⠀⣶⠸⢿⠁⣾⢠⣿⣿⡛⢻⣶⢤⡀
⠀⠀⠀⠀⣈⣿⣿⡇⠀⠙⢻⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣥⣾⣿⣷⠿⠋⠀⠀⠀⠀⢠⢠⣄⠀⢹⣄⣿⣰⠇⠈⠙⢻⣿⣿⣿⣿⣧
⠀⠀⢀⣈⣠⣿⣿⣿⡓⠶⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⡀⠀⠸⠿⠏⢠⡀⠀⠀⠀⠀⠀⠸⣇⣿⠀⠀⠙⡿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠻⠟
⢰⠂⠉⠉⠻⣛⡙⣉⣙⠓⠿⢿⣅⠀⠀⠀⠀⠨⠽⠟⠋⠀⠀⠀⠀⠈⣿⣦⣤⣀⣀⣤⣄⣸⣿⣤⡤⠼⢿⣶⣦⠙⢟⠗⣶⢷⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠒⣘⠛⠿⠿⢷⣶⣴⣦⣤⡀⠀⢀⣀⠀⠀⠙⠿⠟⠛⠀⡈⢙⣿⠋⠀⠀⠸⣿⡿⣷⡆⠀⢀⣀⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠉⣙⣯⠁⠀⠈⠛⢯⣤⣤⡤⠀⠀⠀⠀⠹⠿⡿⢦⣄⣤⢀⣿⠷⠛⠋⠙⠛⠿⠿⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⢠⣞⢁⡗
⠀⠙⣿⣿⣿⣿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣠⣄
⠀⠀⣾⣿⣿⣿⣴⣾⣋⣀⣀⣀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣧⣿⣷⡀⠀⣹⣿⣦
⠀⣿⣿⣿⣿⣿⡿⣛⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⠀⢸⣦⣀⣿⡀⢀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠉⡏⠁
⠀⣾⣿⣿⣯⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣦⣇
⠰⣿⣿⣿⣿⣿⣶⣤⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡌⠋⠉⠙⠉
⠀⣿⣿⣿⣿⣿⣿⣿⡖⡆⡀⢀⣴⣮⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣸⣿⣿⣿⣿⣧⣠⡤⣤⣤⡴
⠸⣿⣿⣿⣿⣿⣿⣿⣾⠙⣿⡿⠛⣿⡟⢅⣾⡿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟
⠀⣿⣿⣿⣿⣿⣽⣿⣷⣷⣦⣥⣼⠿⣿⣿⣿⠿⣿⣿⡿⠿⠿⢿⠿⢿⣯⠿⣿⣫⠭⠾⠿⢿⡥⠼⠿⠛⠟⠛
⠀⣿⡿⠿⠿⡟⠿⠋⠉⠙⠛⠛⠿⠿⢿⣿⣿⣶⣶⣤⣶⣶⣦⣦⣤⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠛⣃⣶⣶⡿⢿⡴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⢀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⢀⠀⣤⣤⣤⠐⠐⠓⣶⠿⠛⢿⣷⡖⠀⣰⡿⠳⡦⠒⠂⠐⠉⠙⠉⠉⠁⠦⣤⣤⠔⠂⠀⢹⣫⣎⡿⠂⠁⠀⢀⠀⠀⠀⢀⡀⠒
⠀⠀⠀⠙⠻⣦⣻⡏⠀⠀⢀⠤⠘⢢⡷⣤⣼⠀⡠⠟⠃⠀⠠⠤⡐⢢⠠⠀⠀⢀⡀⠰⠉⠁⠀⠀⠀⠀⢧⣙⠃⢠⠿⠰⡿⠛⠒⠀⠃⡘⠀⠀⡀
⠀⠀⠀⣀⠶⣞⣿⣾⣧⠂⠁⠂⠀⠘⠷⠿⠁⠀⢱⠀⣀⢠⡀⠤⣤⣿⡀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠘⠁⠀⠀⠀⠁⢀⠽⢋⡠⢠
⠀⠀⣾⠉⢈⣤⠛⣴⣿⠳⣄⠀⠀⠀⠀⢀⡁⠀⣁⠀⡘⠙⡒⠜⡅⠀⠅⠂⠀⠀⠂⠘⣶⣄⣀⣀⠀⠄⠀⠀⠀⠙⠈⠦⠀⢀⠴⡁⠐⠋⡐⠃
⠀⠀⠛⠟⢮⣥⡷⡜⣄⣾⠉⠁⠙⢄⡠⢎⠐⡀⠉⢸⣿⡁⠀⠠⠀⠀⠀⢀⠀⠀⠀⠉⣿⡇⠟⡋⠙⠃⠀⠀⠀⠀⢐⠛⠛⢷⣈⣁⣴⡌⠋⢰⣦
⠀⠀⠀⢀⠼⡉⣰⡄⠀⠙⠇⠀⠀⠛⠢⡉⣼⣧⠀⠐⢻⡗⠀⠀⠀⠀⠀⣰⠀⣀⣀⠌⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠹⠇⠈⠀⠀⣤⠈
⠀⢰⡿⡿⠀⢸⡿⢶⡤⠶⢮⡧⠄⣠⣶⠷⡈⢿⡆⠀⠘⢿⠿⠋⠉⠉⢿⡩⠆⢨⡏⢠⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠜⠂⠀⠀⢰⡧⢀⣀
⠀⠈⠰⣧⡄⠈⢰⠖⣄⢀⠀⠁⢀⣤⡿⠄⠸⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⠠⢹⡇⠄⠚⡿⠓⠀⠀⠀⠤⠄⠀⠂⠀⠀⢠⡈⠲⠀⠉⠱⣿
⠀⠀⣠⠀⠉⣶⣨⣠⡉⣂⣩⡏⡯⠂⠀⠀⠀⠀⠰⢥⢀⠀⠀⠀⠀⠀⠀⠉⣨⡠⠞⣡⣄⣻⡆⠔⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠿⠁⠀⠀⠀⠘
⠀⠀⠀⣤⢆⡍⣤⠀⠉⠛⡋⢅⡤⠀⠀⠠⠀⢀⣼⡇⠀⠀⠀⠐⠂⠀⠁⠀⠀⢁⣿⠵⡛⡋⠀⠐⠓⠲⢤⡀⠀⠀⠀⠀⠀⣟⡤⣠⢤⣤⣠⣤⡄
⠀⠀⢸⣿⡢⣴⣯⠀⢿⢋⡁⠀⠘⢶⣆⣐⡮⠘⢹⠦⠀⠀⠀⠀⠀⠐⠀⠀⠀⠨⢀⣰⡶⢣⠀⠀⠀⠀⠀⠉⠑⠐⠠⠠⠀⣹⣽⣿⣿⣾⣿⣿⠛
⠀⣠⣄⠉⡙⠋⡘⠷⢶⣾⠀⠀⠀⠀⠹⠘⢀⠀⠈⠀⠆⢄⡀⢄⠤⠀⠀⡀⣀⡸⠛⢯⠐⠖⠄⠄⠰⠄⢀⠀⠠⠀⡈⠂⣀⠀⠋⠉⠻⡿⠋⡁
⠀⠸⡟⠁⢠⠁⣌⡄⠹⣿⠀⠀⠀⠀⠀⡄⠙⠢⠖⠠⠦⣾⣷⣌⣸⠿⠿⠛⠁⣠⣰⡇⠀⠀⠀⠀⠀⢀⣼⣷⢤⡀⠀⠀⠈⡠⣼⣷⢀⣄⣈⣀
⠀⠀⠉⡐⠒⠊⠀⠂⠀⠀⡂⡀⠀⠀⢠⢦⡔⣌⣦⣔⡢⠤⢄⣀⣐⠀⢆⠡⢈⠕⠋⠉⠈⠙⠁⠀⡀⠊⠀⠉⠀⠸⣷⣗⢦⠀⠈⢋⠀⡾⠋⡝
⠀⠀⡄⠁⠈⠀⠀⠀⠀⠀⣤⠀⠉⠷⠚⠈⠻⢿⣿⣋⣉⠦⠄⣤⡤⣤⣤⠶⢟⠰⠆⠳⠀⠀⠀⠐⠁⠠⠀⠀⠀⠀⠈⣉⣂⣂⡀⣩⡤⠀⠤⠁
⠀⢀⣤⠀⠀⠄⠀⠀⠀⠀⠘⡀⠔⠢⣄⠀⠀⠈⠯⠍⠉⢠⠌⣁⠀⠊⠂⠀⠈⠳⡆⠀⠀⠀⠈⠀⠀⠀⠀⢠⡄⠀⠀⢻⡟⢁⠀⠎⠁⠄⠴⠾
⠀⠸⡧⠀⣀⣿⣄⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⡤⠀⡰⠃⠀⣝⢦⡀⠀⠀⠀⠀⠙⠷⣤⣦⡀⠀⠀⠀⣀⠛⠳⣠⠀⣈⠄⠈⢀⡐⢤⠄⠀⢀
⠀⢠⠀⠄⠁⠛⠉⢳⡤⠄⢄⡡⡄⠀⢀⣀⡀⣨⡄⠰⠁⢘⣧⢈⣺⣷⡄⠀⠀⠠⠀⢠⡘⣌⠣⣄⠀⣠⣀⠀⠋⠀⢈⣠⣾⣷⠟⠑⠄⢀⡸⠿⡇
⠀⣤⠮⠀⠀⠠⠀⠈⡃⠀⠿⢡⡶⢠⡬⡉⢴⣦⡀⠃⡻⣬⣿⣿⣿⣿⣿⣦⠀⠐⠡⠈⢧⡈⣦⠈⣿⣿⠏⠀⠀⠄⢛⠙⠙⠀⠀⠀⠲⡮
⠀⠙⠤⠀⡀⡀⢀⣴⠈⠈⣀⣀⣀⣬⡴⠟⠈⠉⠁⣋⡁⢸⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠄⠑⢈⠳⠸⡧⠀⡀⢀⣼⠀⠀⣀⠀⢀⠰⡇⢀⡀⠈
⠀⢠⣴⡶⣮⢦⡞⠵⠶⠟⠛⠋⠉⠉⠉⠙⠲⣶⢘⠀⠀⠘⠿⢿⣿⣿⠏⠀⠀⠀⢠⢰⠃⠀⠀⠱⠠⠀⠈⠁⢠⣿⡆⠀⢿⣀⠌⠠⠿⢿⠇
⠀⠠⣻⠵⣛⡌⠡⠂⠀⠀⠁⠀⠀⠀⠂⠀⠀⠁⣬⠱⠀⠀⠀⠀⠙⢿⣾⠏⡰⠟⠂⠀⠈⠁⠄⠀⢢⠁⢆⠲⠶⠍⣴⠗⠀⠀⠀⠀⠀⠐⠂⣰
⠀⠀⠁⢿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⢄⣀⢿⡄⢠⡐⠢⠤⠤⠬⡅⠀⠐⢠⡌⢣⡀⣀⠛⢀⡠⠑⢄⡁⠲⠆⢜⠀⠀⠀⠀⠀⠀⠋⠉⡋
⠀⠀⠀⠒⣼⡇⠀⣀⠀⢶⢤⣤⠂⢀⡙⣆⡀⠉⠊⣯⡼⠦⠄⡙⠛⠓⠀⣠⣤⣌⠀⢀⡈⢱⣤⢠⣟⡦⠀⢀⠁⣁⡙⢀⡀⢀⢠⣤⠀⠀⡤⠌⠂
⠀⠀⠀⠀⠀⠈⠈⣼⠷⢣⣾⣃⡈⢠⡰⠾⠛⢥⣤⣿⠆⡀⠀⠈⠠⣤⣶⣿⣿⡏⣀⣴⡧⠾⠿⠘⠾⢿⣿⡾⢱⣏⣠⣾⠿⠧⠀⠀⠀⢐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠠⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⣄⠑⢧⡄⠀⠀⠀⠀⢀⢉⣀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠃⢆⢳⡄⡠⢨⣀⡬⡉⠉⠀⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡄⠀⡄⠍⣑⢪⣾⡸⠾⠛⠑⠒⠛⠂
⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠁⡠⣴⡾⢿⣯⣿⣿⡧⡴⠖⠒⢏⢲⡢⡲⡠⡄⡀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡘⠻⠛⠟⣻⡏⣽⢁⣧⢀⠀⠀⠁⠀⠀⠈⠈⠃⠠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⠋⠠⡢⠊⠨⠇⡏⢸⠁⢋⠀⠘⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠁⠀⠀⢶⣇⠏⠀⠀⠘⠆⢠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠄⠀⠀⠀⠀⠀⡤⠤⠠⠤⠤⢤⣄⣤⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠒⠀⢰⡆⣸⡤⠄⠀⣀⡀⠀⠂⠋⠉⢉⣛⣉⣉⣉⣉⡩⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠁⠁⠉⠁⠈⠀⠀⠀⠁⠒⠢⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢹⠗
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠒⠀⠀⠂⠀⠤⠤⠤⠄⠶⠒⠚⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠶⢀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⣡⡞⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⡇⠠⠀⣀⠐⠆⠀⣤⢀⣂⠀⠀⠀⠀⢈⠁⠀⠘⠓⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⠲⠀⣠⣬⡿⠿⠿⠷⠤⠤⠶⠄⠀⠠⣤⣦⠉⣤⢀⡉⣤⣼⡁⠀⠀⠀⣤⣤⣶⣦⣀⣴⣤⡟⣿⣧⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢠⡮⢐⠉⣈⠠⠆⢶⣶⣾⣿⣿⣿⠏⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠘⢡⡼⠇⣅⠾⣶⣽⣟⣿⡻⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠡⢂⣀⣵⣿⡟⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠟⢿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⡈⠃⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠂⣿⣶⣀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢴⣶⡶⠃⢶⣿⣳⡀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢱⣿⡇⠃⠀⣿⣿⣿⣿⡀⠸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢛⡟⣱⣥⡟⣿⠀⠘⠻⡿⣿⣟⣿⡆⢹⣿⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⣼⠟⢚⣻⠞⣐⣿⣿⣷⣿⠀⢀⢰⣏⢹⣿⣿⣧⡌⢿⣿⣿⣝⣿⣶⣄⡀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠀⠁⠁⠀⢠⣚⠧⠼⠩⢈⢋⣵⣶⣿⣿⣿⣿⡇⠀⠈⣾⣿⡆⣿⣿⣝⡄⠸⣿⣯⣿⣧⣍⠻⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡴⣺⢶⡛⠃⡀⢈⡅⣵⣦⣶⣼⣯⣿⡟⠁⣶⠏⣸⠟⢳⣷⡘⢿⣿⣿⣦⠈⢿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⣀⣤⣴⡶⠀⢃⡀⠉⠊⢉⣀⠀⠌⠁⢸⣧⣿⣿⣿⣡⡿⣿⣥⣾⢃⠀⠋⠀⢸⡎⠹⢶⣝⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⡛⠛⠿⠶
⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠲⠤⠀⠠⠺⡿⢛⢡⣖⡥⣪⣿⣏⠐⠙⢫⢋⡆⠀⠈⠀⠀⠁⠀⠺⠻⣧⠹⣿⡝⠳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡻⣍
⠀⠀⠀⠀⠈⠙⠀⠐⠀⢀⣀⢠⣤⣤⢄⠠⣽⣫⡽⠿⠛⠍⠀⠀⠀⠀⢸⢠⠇⠀⠠⠀⠈⠇⠀⠐⣿⣆⠘⢷⡄⠈⠃⠈⡻⠿⠿⣿⣿⡟⠻⠿⠮⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠈⠄⢀⠀⠀⠀⠀⠀⠄⡀⣄⠐⡌⠉⠉⠑⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠐⠆⠀⠄⠈⠑⠈⠀⠈⠑⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠤⠤⠔⠒⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠿⣦⡀⢠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠎⠈⠁⠀⠀⠂⡀⣀⠀⠀⢀⢻⠀⠀⠱⠈⢏⡳⠤⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢴⠀⡰⠃⠀⢁⠊⠕⠁⠀⢠⠋⠀⠆⠀⠀⠐⠀⠀⠷⢀⠄⢡⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⣁⢀⠔⠇⠐⠂⠀⠀⡸⠀⠀⠃⠀⠀⣴⣄⠢⠠⠤⠐⠤⣠⡔⠢
⠀⠀⠀⢀⠐⠁⠀⠀⠀⣠⠋⠀⡁⠀⡘⣀⠀⠀⢠⠄⢸⠀⠀⠐⠂⡰⠓⣌⢢⠐⠶⠀⠀⠢⠀⣀⡤⣈⠶⢤⡀
⠀⠀⠀⠀⠃⠀⢀⠐⡈⢀⡰⣊⠀⠈⠉⠉⢀⡴⠁⠂⠘⠀⠀⠀⠀⠤⠀⠊⢸⠀⠰⠄⠀⠀⠀⠈⠁⠀⠀⠈⣙⢦⡁
⠀⠀⢠⠀⠀⠀⠀⢀⠡⠂⠀⠁⠀⠀⠀⣠⠎⠐⠆⠀⢑⠀⠀⠀⠀⠀⠀⠀⢬⠄⠀⠀⠀⣠⠀⠀⠀⠈⠓⠀⠀⡀⠍
⠀⠀⠂⡠⣤⣀⠈⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⣸⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠼⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⣆⡠⣄⢠⠀⠀⠅⢠⡄⠀⡀⠐⢀⠎⠁⠓⠤⣀⠂⢀⡰⠚⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠄⢀⡠⠤⠤⠥⠀⠂⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠠⢄⣀⢀
⠀⠀⠀⠀⠀⠀⢠⡖⠦⡀⠀⠀⠀⠀⠀⢰⠏⢀⣴⢱⡿⢛⡎⣑⢒⣳⣶⣾⣦⣴⢯⡠⡄
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⢶⡀⠀⠀⠀⠰⢬⢣⡄⠈⠹⢮⠑⣮⣿⣿⣿⣿⣿⣿⣦⡷⣿⠄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣾⣇⠀⠀⠀⢠⣡⢻⠙⢉⢳⣼⣀⠸⠉⠉⣿⣿⡟⠉⠻⢧⢿⣆⡴⣠⡄
⠀⠀⠀⠀⠀⠀⠠⣳⣶⣛⣿⠃⠀⠀⣀⡏⠙⠳⣄⣹⡆⠧⠬⣉⠙⠲⠣⢽⣿⣵⣶⡛⠛⣿⠃⣸⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠶⡄⠠⠀⠃⠈⣟⠻⠉⠛⣧⣰⠂⠈⠓⠀⠀⠀⠛⡻⠭⣤⣤⣿⣝⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣓⡛⣆⠉⢽⣿⣿⣧⣼⣏⣛⡉⡉⠈⠙⡷⣾⣻⣯⣽⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡀⢱⠀⠋⢿⡡⢩⡗⠂⠤⠄⠤⠋⢹⣿⣏⠛⢙⣿⣿⣿⢯⣠⠾⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⣿⣦⣶⡵⣿⡾⡫⠊⠐⠀⡤⠰⠒⠺⠛⠪⡟⡛⢿⣮⣍⣙⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⢌⣻⣵⣿⡭⠴⠂⢀⣶⠆⠀⠀⡆⠀⠀⢠⠤⠶⠯⢁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣷⡖⣦⣈⣿⠁⢀⠆⢰⣿⡔⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣆⡝⠀⠘⢁⣠⣴⡎⣩⠂⠀⠀⢢⠀⡀⠀⠀⢠⡞⣹⣋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢁⣀⣀⢹⣄⡇⣾⠿⠿⠛⢻⣀⣠⠘⣦⡰⠀⡠⣰⣿⣟⣫⠏⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠚⠻⠿⣗⠷⢦⣧⣀⢀⠀⠀⠘⢧⡅⠀⠀⠀⣿⣏⣇⠀⣼⡇⢰⠟⠋⢰⡍⢀⣰⣢⣤⣴⣾⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢶⣿⢷⣌⣄⠀⠀⠣⡀⠀⠀⡆⢿⡟⠀⣹⠠⠞⣶⣯⣾⣾⣫⠭⠥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡭⠷⠿⢿⣾⣴⣤⣈⡐⢤⡇⠘⡇⠔⠁⣠⣞⠋⣙⣻⣉⣴⣟⢂⣄⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⡤⠟⠊⠉⠉⠉⠉⠙⠻⢷⣛⣿⣛⠻⠛⠷⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠙⣷⡎⠀⠈⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠀⠀⠀⡠⠤⠽⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣶⣾⣄⡀⢀⣸⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢙⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠶⠚⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⢀⣴⣦⢀⡞⠀⠠⠤⡀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠄⢀⡴⢋⡀⣿⣼⠃⣴⣄⠀⢈⡀⠄⡈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣆⠀⢘⣚⡭⠚⠻⠄⣙⠋⡘⠉⢻⣷⣿⠿⠶⠤⢀⡀⠹⠷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⡿⠛⣿⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⡇⠀⠀⠀⠀⠈⠉⠉⠉⠙⢶⣄
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷
⠀⠀⠀⠓⠒⠛⠉⠳⣤⣴⣿⣦⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣀⡀⢀⣠⣤⣴⣶⣿⣷⣦⣴⠿⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⠈⠁⠀⠀⠉⠻⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠿⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢴⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣴⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣴⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡏⠛⣻⠿⣿⠿⠁⡿⠁⠀⠉
⠀⠀⠀⠀⣶⣾⣿⣿⠛⢿⡛⢉⣽⣷⣦⠰⠇⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠄⠠⠄⠠⠄⠠
⠀⣀⣰⣾⣦⣀⡄⢉⣠⣾⣿⣿⡿⣿⡟⠁⠀⠻⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢻⣿⢻⣿⣿⣿⣷⡀⠹⣿⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠘⢩⢷⣿⣿⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⣤⣴⣦⣴⣶⣶⣶⣤⣀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣠
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠙⠛⠋⠙⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠋⠁⠀⠀⠀⠈⠉⠉⠁

⠀⠀⣄⠀⠤⡀⠀⣴⣆⠀⢠⠆⠀⣸⣆⠀⠴⡄⠀⣴⣦⠀⢠⠤⠀⣰⣇⠀⠰⡄⠀⣰⣦⠀⢀⠤⠀⣠
⠀⠀⣿⠷⠾⢃⣾⡁⢈⣧⠘⠷⠾⣿⣿⠷⠾⢃⣼⡁⢈⣧⡘⠷⠾⣿⣿⠷⠾⠃⣼⡁⢈⣷⡘⠷⠾⣿
⠀⠀⣿⡛⢢⣞⠓⠀⠀⢚⣳⡐⢛⣿⣿⡛⢂⣞⠓⠀⠀⠚⣳⡐⢛⣿⣿⡛⢂⣞⡓⠀⠀⠚⣳⡔⢛⣿
⠀⠀⡿⣡⡟⣉⡉⠀⠀⢉⣉⢻⡌⢾⡷⢡⡟⣉⡉⠀⠀⢉⣉⢻⡌⢾⡷⢡⡞⢉⡉⠀⠀⢉⣉⢻⣌⢾
⠀⠀⣰⣿⣧⣽⣿⣆⣴⣿⣯⣾⣿⣎⣰⣿⣷⣽⣿⣆⣰⣿⣯⣾⣿⣎⣱⣿⣷⣽⣿⣦⣰⣿⣯⣼⣿⣆
⠀⠀⠻⣿⣟⢿⣿⢋⠹⣿⡟⣻⣿⠏⠻⣿⣟⢿⣿⢏⡹⣿⡿⣻⣿⠟⠹⣿⣟⢻⣿⠏⡙⣿⡿⣻⣿⠟
⠀⠀⠀⣈⣁⡾⢃⢿⡷⡘⣧⣉⣁⠀⠀⣈⣉⣼⢃⢾⡷⡘⣧⣉⣁⠀⠀⣈⣉⣼⢃⢾⡿⡘⢷⣈⣁
⠀⠀⠀⢬⡽⠡⣬⣿⣿⣥⠌⢯⡤⠀⠀⢤⡽⠡⣬⣿⣿⣥⠌⢯⡤⠀⠀⢤⡽⠡⣬⣿⣿⣥⠌⢯⡥
⠀⠀⢈⡟⢠⠶⣶⣿⣿⡶⢶⡌⢿⡁⢈⡟⢡⡶⢶⣿⣿⡶⢶⡌⢻⡁⢈⡟⢡⡶⢶⣿⣿⣶⠶⡄⢻⡁
⠀⠀⠏⠀⠘⠆⠀⢹⠏⠀⠒⠃⠀⠻⠟⠀⠘⠆⠀⢹⡏⠀⠐⠃⠀⠻⠟⠀⠘⠒⠀⠹⡏⠀⠐⠃⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣁⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠠⢀⣀⠔⣁⣠⠔⣀⠀⠀⣘⣻⣕⣤⣤⣄⡘⠄⠀⣃⣀⠀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠈⢦⡘⠂⡉⠻⢧⠀⠈⠳⡈⠈⠷⡀⠙⠓⠢⠄⠀⠀⠈⠂⣞⡁⠀⠀⠀⠨⠓⠨⠀⠀⠀⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠒⠂⠁⠐⠀⠓⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣥⣀
⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠂⠂⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠴⠀⡂⠄⠲⢀⡄⠈⠆⣰⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⡀⠐⣄⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠛⠒⠙⠚⠛⠛⠛⠉⠙⠛⠁⠀⢸⢿⠷⠀⢀⠘⠋⠀⠀⢋⠴⢙⠖⠀⠀⠈⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢠⡀⣠⣶⠶⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⡖⢾⣿⣿⣫⣤⣤⣤⣀⡈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠿⣿⣟⠶⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⣡⣾⠼⡈⢳⣄⠈⠙⠆⠳⡅⠀⠀⠀⣠⣼⣶⠒⠲⠦⠀⠀⣦⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣡⣠⢹⣿⡀⠛⢾⡿⢦⠀⠀⠀⠰⠀⠀⣩⢖⢻⣷⣄⠙⠦⣴⢞⣻⢿⠛⡛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠈⢿⠃⠀⠀⢿⡊⠀⠂⠀⠀⠀⢰⠛⠀⠀⡿⣽⣧⠀⠏⠸⠏⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢦⡄⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠒⢒⠂⢒⣒⣀⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⡀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠷⠶⢷⠷⠶⠾⠷⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣔⠀⠀⠈⠙⢦⣄⠀⢈⡷⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢄⠉⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠳⣷⡀⠀⠀⠻⡡⣌⡁⠻⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠤⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠦⢤⡵⠦⡙⣿⣤⢴⣎⣀⠚⠓⡦⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⠴⠾⠛⠉⢀⠄⠠⠞⠓⠲⢵⣬⣣⣿⠚⠻⢴⣿⣇⠨⠟⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣛⠂⠀⡰⠀⢠⡿⠋⡄⡆⣠⣿⣄⣻⣿⣮⣷⣄⣠⠀⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⣉⣴⢏⣴⣿⠅⣘⡁⡥⣸⣷⡿⣿⠿⠻⠿⠿⠿⠿⠟⢿⣶⡈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠛⠿⠿⡷⠾⠿⠷⠿⠋⠋⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⣀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣿⣦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠀⡠⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠰⠀⠀⢀⠀⠁⠀⠐⠃⠸⠀⠙⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⢀⣾⣿⡦⠄⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⡞⠀⠁⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⣤⠂⠀⠀⡴⠻⢷⡟⠀⣠⠀⠀⠀⠚⠉
⠀⠀⠀⠀⢀⡀⢀⠀⢀⢼⣿⠛⠁⠀⠀⢸⣦⣤⠈⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠋⢢⣴⠀⢀⡏⠁⠀⡐⠛⠹⠀⠀⠀⠀⣄⣴⣄⡀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡞⠀⠀⡼⠀⠀⡌⠀⠀⣤⣾⣿⡏⠉⢳⡄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⢰⣿⠋⠉⠀⡀⠀⠋⠀⠀⠐⠱⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡀⠰⠆⠀⢁⡠⣀⡀⠁⠀⠀⠀⠆⠘⠋⠀⠀⠀⡀⢀⣾⡄⠀⣳⡄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡁⠚⠃⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠙⠋⢠⣤⠾⡟⠂
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠰⠀⢻⠂⠀⢸⣷⢠⡄⠀⢀⠈⢀⠀⠀⠀⠀⠀⠁⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢰⠈⠙⠂⡀⢋⠀⠈⣇⢲⡿⠷⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢠⠉⢾⡀⠀⣏⡼⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠂⠀⣷⡄⡟⢀⣶⣧⠀⠀⠀⠐⠂⣤⣁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⣄⡄⣧⠉⡄⠸⣿⠋⡀⢀⣃⠀⠀⠛⠛⠋⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢳⣿⡅⢹⡀⠁⠀⠉⠀⠷⠏⣿⠏⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢻⠁⢸⡁⠀⠀⣀⣼⣶⣶⠠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠸⡇⣸⣵⣦⣾⠿⢋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠛⠓⠀⠀⣧⡟⣟⣉⣥⣶⣼⢿⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠀⠀⠀⠀⠀⢹⠇⣿⢀⢙⣿⣿⣿⣷⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠛⢦⣀⠀⠀⣿⡠⣿⠏⠿⠿⣿⣹⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠻⣦⠀⣿⣷⡇⠀⠀⠀⠈⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⢀⣧⣤⡄⠒⠒⠂⠐⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⠟⠁

⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⣠⠀⠂⠀⠂
⠀⠀⠀⠀⡆⠀⠀⡀⣴⠃⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠄⠀⡜⠀⠀⠾⠿⣟⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⠂⢨⡐⠶⠶⡀⠀⠠
⠀⠀⠀⠀⠀⡀⡄⠀⠃⠀⠀⠀⠆⠀⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡦⠊⠈⡗⢤⢠⣟⡡⢤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢊⡈⢥⡤⠈⢙⣁⠜⢧⡁⡃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⡍⠐⠻⠛⠄⠀⠀⠈⠀⠀⠘⠈⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢐⠀⠀⠀⠀⠀⠀⢠⡀⠠⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢘⠋⠁⠚⠓⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠐
⠀⢀⠂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠓⠀⠄⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠠⠞⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣀
⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠢⠤⣀
⠀⠉⠀⠀⠀⠀⣤⣀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠛⠛⠂⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⡀⠀⠀⠈
⢠⣤⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠀⠀⢁⣒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⣀⠀⢀⢸⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⣁⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣚⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣹⢉⡧⡁⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠐⠁⣸⡇⠀⢄⠀⢈⡑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⡠⠒⠀⣰⡀⡇⠀⠀⠑⠀⡽⣗⣬⣕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠚⡁⢈⣤⢂⡠⠂⠀⡀⠉⣇⠘⢂⡀⡈⠛⢷⣤⡀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⢀⣤⣒⣚⣯⣄⡉⣒⣁⣸⣿⣿⣃⣢⣖⣜⣀⡩⠵⠟⠋⠁⢀⣀⢍⡙⣝⣢⣤⣀⣀⠈⣙⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣦⣴⠟⠉⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢤⣀⡀⠀⢆⠀⠀⠠⠼⠛⠉⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠈⡩⠋⠙⣦⠞⠛⠲⠆⣤⣤⣴⣖⣋⣁⡀
⢀⣥⣤⣤⣶⣾⠀⠀⢀⠏⠀⣠⡤⠶⠻⣿⣿⣿⣿⡿⠟⠓⣀⣀⡀
⠐⢟⠋⠹⡏⣿⠀⠀⣮⢠⣾⡋⡠⡠⠑⠀⠀⠀⠀⣠⠴⠊⠀⠀⠠
⠀⠀⠑⣆⠁⡁⠀⠀⣧⣿⡿⣳⡞⠁⠀⠀⠀⢀⡞⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠸⣾⣿⣆⠀⡟⣻⣹⣟⡀⠀⠀⣀⡴⠋⢀⠄⠀⣸⡏⢀
⠀⠀⠀⠜⠻⢿⡟⠛⢻⣧⠟⠛⠛⠛⠛⠋⠀⠀⠀⢀⡀⢹⡇⠀⡓
⠀⠰⠀⠀⢀⡞⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⣰⣮⠀⠀⢣⠀⡇⠀⠀⢄
⠀⠀⣠⣾⠛⠻⠦⢀⡀⠀⠙⢷⡀⠀⠀⠀⠀⠀⣿⡃⠀⠀⢀⡀⢱⠀⠀⢸⣷⡀
⠀⠘⢿⠙⠛⠓⠂⢀⡠⠤⠤⠀⠙⢦⡀⡀⠀⠀⣾⣧⠀⢀⣼⠃⢨⣧⡀⣸⣿⣷⡀
⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⢧⡤⣄⣿⣿⡿⠊⠀⠀⢀⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢹⠇⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠀⠀⠀⣀⠈⠻⣿⢤⡀⠀⠀⠄⢧⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⠋⠁⠀⠀⠀⠀⠚⣿⡄⣀⢠⡝⢧⣂⣄⠉⠛⢹⠁⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣀⡐⠀⠠⠄⠀⢨⣿⣿⣇⠈⠀⠉⠳⢆⣤⣼⠀⠀⠀⠀⠈⠃⠀⠰⣴⡔⠀⠀⠁⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠴⠂⠙⠷⠀⠈⠀⠉⠙⠳⢾⣿⠋⣍⢹⣿⣶⣀⠀⠀⠈⠙⢿⣶⡀⠀⠀⠀⣠⡞⠳⣾⣧⠀⠀⠀⠸⣿⡏⠹
⠀⠀⠀⠀⠀⠀⠀⠤⠖⠚⠿⣶⣶⣤⣦⣾⣛⣿⣿⣾⠋⠈⠉⠙⠳⢦⣄⡀⠙⢿⢦⣀⠈⠉⠀⠀⠙⠋⠅⡀⠀⠀⢀⠹⣷
⠀⠀⠀⠀⠀⠀⠲⠗⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢀⡀⢈⠛⢦⣄⠳⡸⡆⠀⠀⡄⠀⠀⢀⣷⣀⠀⠈⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠉⠉⠉⠛⠿⣇⡻⣿⣄⠀⢸⣲⡴⣾⣿⣾⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⣻⠿⠿⠿⠿⠿⢿⣏⣽⡿⠀⠀⠀⠀⠀⠀⠈⠱⡝⠻⣆⡬⡛⣦⣼⣿⠛⣧⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣶⡾⠿⠶⢤⣀⠀⠀⠀⠀⠀⠀⣀⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢻⡄⠘⣽⡛⠿⣀⢩⣽⠞⠙
⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠈⠑⠐⠂⢀⣐⣂⣉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⡆⣷⠀⠈⢻⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⡿⡿⣿⣿⣿⡵⡶⠉⠁⠀⠀⢀⠄⠛⠋⢶⣦⣔⢸⡄⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠟⠉⠀⢠⣤⣤⡤⣴⡁⠀⠀⠀⠀⠈⢏⢸⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⠁⠀⠀⢠⣿⣿⣿⣽⠟⢳⡄⠀⠀⠀⠀⠘⣼⠁⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡏⠀⠀⡟⠀⠀⠀⠀⢳⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠛⠓⠶⠶⠶⠂⢺⣿⣿⣿⣿⠟⠀⠀⡰⠁⠀⠀⠀⢰⠿⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢿⣯⡤⠖⠋⠀⠀⠀⠀⠀⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠙⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⡍⠓⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢤⣀⡡⣟⣴⠀⢀⣴⠄⠀⠀⣾⡆
⠀⠀⢀⣰⢤⡀⣾⣟⣄⠀⠀⠐⠶⢝⣷⡿⠷⠀⣤⣭⣶⢰⣿⡿⠃
⠀⠚⠿⠋⢠⣥⡿⠛⠁⠀⠀⢰⡄⠈⠉⣐⣀⠸⡿⣿⠏
⠀⠀⠀⠲⢺⠇⢡⠀⠀⠰⠿⠀⠐⢀⣶⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠁⠚⠃⠀⠀⠀⠀⠀⠉⠀⠀⠛⠂





⣶⡶⠶⠶⠶⠶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⠾⣥⣵⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⣞⣿⣷⣿⡿⠿⡿⣻⠲⣖⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣩⣿⡗⣿⣿⣷⣶⣿⡟⠁⣶⣾⡧⣻⣄⢵⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢿⡿⣿⠿⣾⣿⣷⣜⣿⣷⢽⣶⣾⣿⣾⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣸⣿⣿⣷⢮⡉⠿⣿⠍⠿⠆⠾⠟⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢸⣿⠉⢗⣿⣕⢽⣦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠀⡀⠀⠀⠀⣸⣻⢻⠀⠘⣧⢿⣤⡈⢫⣮⣍⣿⣦⣀⡀
⠀⠀⢀⣠⣤⣄⣀⣀⠀⠀⣀⡾⠀⢰⠇⣴⡿⢱⠀⠀⠀⡟⣾⣿⣕⢶⣮⣿⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠛⠚⠛⠓⠋⠀⠉⠉⠉⠛⠋⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣰⠃⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢀⣴⠖⢣⣼⢋⣠⠟⣰⡇⣠⣄⠀⠠⣄⡀⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸
⣀⣤⠀⣤⣤⣤⣤⣤⣶⣿⣿⣿⣾⣿⣧⣾⣿⣵⠟⢃⣶⡿⣹⣏⣉⡠⡴⣠⢥⣭⣿⣿⣷⠶⣶⣶⠶⣦⢸
⠘⠛⠛⠒⠒⠲⠚⠇⠬⠭⠭⠯⠍⠿⢉⣙⣓⣛⢒⣛⣿⣅⡠⠤⠽⠿⠿⠿⠛⠛⠻⠛⠛⠛⠛⠉⠉⠉⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠓⠖⠛⠓⢦⣠⠤⠤⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠑⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠦⢤⠀⠀⠀⠀⠀⢀⣠⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠀⠁⠀⠀⠈⠓⠒⠦⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⣀⡠⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠶⠶⠶⠴⠒⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣀⠀⣄⣤⢀⣄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡟⢸⣿⠸⣿⠈⠙⢄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢰⣷⢻⣿⠀⢻⡳⣄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⣿⠃⠈⠁⠀⠀⠹⡜⡆⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣰⡿⠃⠀⠀⠀⠀⠀⠀⠓⠃⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⣼⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣙⣦
⠈⠉⠉⠉⠉⠁⠻⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⣀⣀⣤⠤⣤⣀⣀⡀⣸⠋⠉⠉⠉
⣦⣤⣤⣦⣦⣤⣤⣤⣤⣤⣤⣦⣬⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣽⣥⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣴⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣠⣴⠀⢀⣶⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠛⢿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢀⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠂
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣗⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢴⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣭⡄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆
⠀⢠⣾⣿⣿⣿⣿⣷⠈⢻⠋⠁⠉⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢩⣿⣿⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠄⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠐⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣴⣟⡁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠙⣿⣿⣿⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡟⢉⣝⣿⣿⠙⠂⣄⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡤⠞⠋⢹⣿⡟⣦⡌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⡁⢈⡼⢇⣻⣟⢧⡄⠘⢿⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣰⠟⠀⣰⡶⢀⢻⡏⠙⢇⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⢊⣷⢀⣿⣏⢣⠙⣦⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣴⢿⠇⢨⣿⠃⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢸⡟⠈⡎⠛⠷⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠠⠂⠛⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⣤⠴⠒⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⠀⡀⠀⠀⠼⢷⠔⠁⠀⠀⠀⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣠⠉⠀⠀⠠⠙⠂⠀⠀⢀⡀⠀⠀⡀⠀⠀⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠇⣿⣏⠀⠰⣆⣴⣶⠶⠀⠄⠼⢇⡀⠀⠠⡄⠀⣧⡧⠀⠂⢴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⣧⣴⡶⠉⢀⣀⠹⡟⠋⡁⠀⠀⠀⠠⢨⣧⠀⣰⡷⠿⣿⠟⠀⢶⣬⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢦⣄⢴⣦⣄⣼⣧⣤⣤⣠⣦⣾⣿⣿⣟⣀⣤⣧⡤⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠔⢊⣠⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠒⠺⠳⠦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀⢀⣀⣀⣤⠴⢋⣁⣋⣈⣉⡙⠋⠁⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠙⠚⠛⠉⠀⣠⣀⡉⠩⠤⠤⠚⠷⠤⠍⣉⠉⠉⠉⠁⢒⣪⣭⣩⠩⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢩⣭⣥⡤⠖⠠⣬⡍⠁⠀⠈⠉⠁⠒⠒⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣦⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠞⠋
⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠯⢻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠙⠉⠉⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠉⠀⠀⠀⠀⠼⠛⠓⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⢀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢈⣿⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣷⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠸⣿⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢐⡬⠃⠰⠀⠀⠀⠀⠀⠀⠀⠰⠆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠳⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣾⣀⣿⡀⠀⠀⠀⠀⠀⣠⠆⠀⡼⢃⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣤⣽⣯⡻⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⢠⣾⣿⣶⣿⣿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠛⠛⠿⠿⠿⣿⢿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠰⠿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⣴⠀⠀⠀⠀⣀⠀⣈⡨⠿⣿⣿⠿⠿⠌⠛⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠹⣿⣿⣿⣿⡦⠶⠿⠿⢿⠛⠙⢷⣄⠈⠛⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢴⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⣶⣶⠟⠀⠀⠀⠀⠀⢀⡾⠛⠋⠁⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣾⣷⣴⣶⣄⡀⠀⣠⣶⣾⣿⣋⣀⣀⣀⣼⠇⠀⠀⠀⠀⠀⢀⠐⣤⣻⣗⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⢸⡗⣯⣩⣿⡿⠀⠀⠀⠀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠟⢹⡿⢻⡟⠀⠉⠻⣿⡿⠻⣿⡿⠛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠛⠧⠾⠋⠁⠀⠀⢻⣿⣿⡄⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⢁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣿⣿⡶⠋⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⠶⠟⠻⠿⠿⠷⠀⠀⠿⣿⣦⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠆⢠⡟⠀⣿⣿⡇⣠⣾⠃
⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⡀⢉⡀⢀⣀⣀⡀⠺⢦⣠⣴⣿⡏⢀⣾⠏⠀⣰⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠉⢙⣿⠟⠛⠁⠀⠀⠀⠈⠛⠻⣇⢸⡏⠀⢰⣷⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⣄⡀⠀⠀⠀⠀⠀⠈⠀⢠⣾⠏⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠐⠁⠀⣸⣿⣿⣿⡷⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠚⢶⡾⠿⢿⡿⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠾⠞⠛⠃⠀⠀⠀⠀⠀⣠⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⢋⣉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⠿⠷⡄⠀⠀⣀⣴⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⣼⡿⠿⠛⣿⣿⣿⣿⡄⠀⠀⣰⣿⠃⣼⠏⠀⠀⠀⠀⠀⠀⠀⣤⠂⣲⣈⡶⢆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣤⣘⣋⠁⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢹⣂⣽⡋⠂⠌⠀⠀⠀⠀⠀⠀⠀⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⣿⣿⣿⡿⣿⣿⠻⢿⣿⡍⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠚⠿⠛⢋⣡⣾⡿⠋⠋⠀⡟⢹⣇⢀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠛⠁⠀⠀⠀⠀⢻⡈⣿⡈⠉⠉⣡⣾⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⣷⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣧⠀⠀⠀⠀⠈⠙⢛⣻⣶⣦⡄⣀⠀⠀⣀⣀⣠⠞⠁⠀⣰⡿⠃⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣆⠀⠀⠀⠰⠾⢿⣿⣿⠟⠰⠿⠿⠟⠛⣩⣵⣦⣀⠊⠉⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⢀⣠⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⡟⢹⡆⠀⠀⠀⠀⠀⣸⠏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠈⠀⠀⠀⠀⠀⢠⠏⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⢷⡄⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⢴⢔⡁⠃
⠀⠂⣄⠀⣧⡐⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⡀⠀⡀⠀⠍⢰⢟⠈⠉⠂
⠀⠐⠡⠈⡿⠙⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠻⠛⠀⠀⠤⠠⠀⢿⠴⡄⠀⠀⠂
⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⢰⠀⣠⡄⠌
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢾⣯⠀⠀⠀⠀⠈⠊⠙⠟⠿⠟⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⢠⠄
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡀⠀⠀⠀⠀⠐⠒⠀⠀⠉
⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠒⠂⠀⠠⠄⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⢠⣤⠀⠤⠤⠄⠀⠀⡀⠄⠠⠄⠤⠤⣤⣀⡤⠤⠀⣤⠀⣀⣠⣒⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠉⠁
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠈⠀⠀⠈⠙⠛⠦⠀⠀⠀⠀⠀⢀⣉⣀⠀⠀⠃⠀⠀⠉⠉⠀⠀⠀⠘⠋⠛⠉⠀⠀⠀⠀⠠⠤
⣤⠒⠀⠈⠉⠑⠂⠀⣀⠀⠀⠈⠉⠉⢀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢀⡀⠤⠤
⣀⣀⣉⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⣿⢛⡻⢛⡛⢻⡻⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠄⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠌⣴⣛⣿⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⡀
⠀⠀⠀⠀⡀⡀⠀⣀⠀⠀⠀⡎⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠰⠆⡐⠀⠀⠁
⠀⠀⠈⡲⢦⣷⢐⠁⠀⠀⢠⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢭⠤⠖⠒⠂⢸
⠀⠀⠀⠁⠀⡇⠀⠁⠀⠀⡼⠀⠀⢀⡀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠀⠙⡇⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠇⠀⠀⡠⢫⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡬
⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣄
⠀⠃⠀⠠⠤⢀⡄⠺⠃⢀⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠤⠀⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⢤⡤⢀⣤⣤⣤⠤⢀⢀⣀⡀⠀⣂⡀⠐⠖⠷⠖
⢀⣤⠀⠀⠀⡤⠚⠃⠀⢉⠀⣀⠀⠠⡄⠀⠀⠀⠀⠈⠉⠉⠁⣤⠉⠀⠀⠀⠺⣿⠛⠚⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠤⠉⠉⠝
⠀⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⢤⣒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣄⡀⠀⠈⠉⠉
⠀⣄⠨⠿⠷⢦⣴⡤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⠀⠀⠀⠀⠐⠀⠀⠈⡀⠀⠀⠉⠀⠠⠀⠀⠀⠒⠚⠋⣉⣀⣀⡀
⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠩⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⣶⣶⠬⠁⠀⠀⠀⠀⠤⠀⣀
⠀⠆⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠄⠀⠀⠀⠀⠀⠃⣀⣀⡤⠀⠀⠀⠀⠀⠨⠟⡒⠂
⠀⠓⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣬⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⢠⡄⠀⠀⠒⠂⠀⠀⠁⣋⠀⠠⡀
⠀⠀⢠⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⢻⠟⠋⠉⠀⠀⠀⠀⢀⡠⠤⢤⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠒⠒⠒
⠀⠁⠁⣴⠁⡀⠀⠀⠀⠀⠈⠇
⠀⠀⠱⠘⠷⠶⠆⠀⠀⣶⣄⠀⣀⡆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠉⠛⢻⣧⠄⠀⠘⠚⠀⠘⢋⢀⠀⢀
⠀⠀⠀⠀⠑⠬⠑⠚⠉⠉⠀⠀⣠⣽⣷⠖⠀⣰⣦⣀⠈⠁⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⠛⠋⠉⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⢶⡟⠁⢀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⢷⡄⡆
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣧⣄⡀
⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⡿⣞⢧⡙⢦⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣾⡤⢳⡜⣷⣟⢦⡑⢄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⡻⣿⣿⣷⠸⡇⢹⡜⣆⠙⣮⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠃⠀⠐⣰⣿⣿⣿⣿⢸⣷⣾⣄⠐⣌⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠑⣤⣶⣺⣼⣿⣿⣿⣽⡟⢻⣧⠙⢷⣿⠷⣄⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡿⠉⠀⢀⣀⣤⢿⣛⣿⣿⠿⣿⣿⣿⢿⡀⢻⣆⠀⠹⣄⠈⠳⢄⠛⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⡾⢿⣍⣀⣼⣿⣿⠁⠙⣿⢿⣿⣾⣇⠈⡌⢷⣦⣽⣆⠀⠀⠑⢄⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠋⣡⣽⡿⠟⠛⣻⢇⠀⢀⣿⣷⣿⣿⣿⡗⠛⢦⡈⠙⠻⢷⣤⣀⣀⠁⢀⡀⠙⠻⣦⡀
⠀⠀⢀⣀⣴⠿⢻⣿⣿⠟⡇⢠⣤⣾⣿⣿⢀⣴⣿⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⡀⠀⠙⠶⣄⠀⠹⣿⣿⠻⠶⠿⢦⣀⢻⣿⣶⣤⣀
⣀⣴⠟⠛⣇⣤⣿⣿⣟⣤⣾⡿⠛⣼⣿⠏⣾⡏⠑⠛⣔⣦⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠳⣦⡈⠙⢻⣦⣄⡀⠉⢧⣻⣿⣿⢻⣿
⣈⣤⣶⠾⣿⣿⣿⣿⠿⠛⢩⣶⣾⡿⠃⢠⣿⣿⠄⠀⠘⣿⣿⣯⣿⣿⣿⣿⡏⢿⣿⣷⡀⠀⠀⠙⣏⠀⠀⣿⡌⠙⠒⢤⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠢⠤⣀⡻⣍⣙⡻⠖⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡊⠭⠁⢒⣚⣉⣑⡒⠡⢴⠂⠘⠭⡀⣤⣉⡴⢊⣀⠬⠼⠓⠒⠢⢕⡌⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠡⠂⢁⡤⠒⡉⠍⠠⠆⠀⣠⢔⡒⠶⠿⠓⠚⠫⣄⡀⠛⠒⠖⠿⣀⣀⣤⠁⠋⡓⠉⣉⡒⡲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡽⢋⢔⡉⢠⡆⢀⡤⠚⠁⢸⠛⠦⣾⣀⣤⡀⠀⠉⠢⡀⠀⠀⢇⠀⠈⣹⠉⢹⠀⠢⡙⢦⡈⠒⠝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣁⠾⡥⠏⢹⠃⠀⡶⠴⣃⠀⣠⣧⣈⣩⡟⠛⠋⠉⠁⠀⠀⣴⠻⠟⢻⣄⢀⣧⠘⠀⠢⡙⣦⠷⣄⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣞⣠⠔⠁⠀⠀⠉⠈⢫⠉⣩⠿⡀⠀⠀⠀⡤⠚⢉⠢⣤⠇⠀⠀⠀⠳⣄⣆⠰⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠂⢘⡆⢠⢎⠑⢬⣀⠞⠀⠀⠀⠀⠀⠀⠈⠘⠢⢄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⢋⡱⡎⠢⣌⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⡠⢾⣀⣠⡇⢀⡀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⠉⡐⢊⣇⣹⢀⠊⡆⠀⠀⠀⠈⡄⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠂⠀⣀⡱⠚⠉⢀⠸⣤⡚⠁⣳⢹⢑⣀⠘⡄⠀⠀⠀⠸⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠋⠉⠡⠀⠀⠀⠀⠀⠀⠉⠁⠉⡛⠁⠀⠀⠁⠑⠀⠂⠀⠐⠀⠈⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢀⠀⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠂⡠⠬⠤⠔⠒⠚⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠛⠛⠉⠓⢄⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠚⠉⠀⠀⠉⠉⠁⠀⠀⠀⠁