Snack food Emojis & Symbols

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄
⠀⠠⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠄⠈⠰⢁⡅⠀⠀⠀⠀⠀⠀⣈⣰⢄⠑⠀⠀⠀⠀⠀⠀⠀⣤⣝⢸⠸⠂⠀⠀⠀⠀⠀⠀⠀⡀⢈⠻
⠀⠰⠈⠤⠀⠀⠤⠑⠆⠀⠀⠀⠀⠌⠀⡀⡂⠉⠅⠀⠀⠀⠀⠀⠰⣇⠉⢂⡁⡈⠀⠀⠀⠀⠀⠘⠉⠛⠛⠉⠇⠀⠀⠀⠀⠀⡠⣤⠔⠫⠂⢀
⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⡀⠀⠄⠀⠀⠀⠀⠀⠀⠲⢞⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠐⠁

⠀⠀⡤⠤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠁⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠻⠆⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⢀⡒⣦⢜⡄
⠀⠀⠀⠄⠀⠘⡁⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⡶⠀⠀⠀⠀⠀⠀⠀⣌⠣⣈⠉⠀⠀⠀⠀⠀⠀⡒⠶⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡠⢉⠊⠐⠁
⠀⠀⠆⠀⠐⠂⠀⠢⠀⠀⠀⠀⠀⠀⢡⡶⡄⠀⠀⠀⠀⠀⠀⠈⠳⡭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⠁⠈⠁

⠀⠀⡀⠀⣀⣀⠠⢠⠀⠀⠀⠀⠀⡠⢂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡀⣄⣤⣄⡀
⠀⠀⠠⢊⠀⢀⢑⠄⠀⠀⠀⠀⠀⠡⠦⠬⠧⠤⢦⠀⠀⠀⠀⠀⠀⢰⢄⠀⢐⡄⠀⠀⠀⠀⠈⠀⡐⠒⠒⠈⠠⠃⠀⠀⠀⠀⠈⠿⠁⠀⠀⠈⠂
⠀⠀⠀⠐⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⠀⠀⠀⠀⠀⠀⢠⢹⢸⣩⠥⠌⠀⠀⠀⠀⠀⠀⠀⠏⠨⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠠⠭⠭⠥⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠠⠝⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤

⠀⢀⣐⡂⡂⢐⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣀⠀⠀⠀⠀⠀⠀⣤⣰⣶⣠⡀⠀⠀⠀⠀⠀⠀⣐⡀⢀⡂⡄
⠀⢸⡇⠀⡆⢠⣾⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⢀⠐⠃⠀⠀⠀⠀⠀⡅⢀⡀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⢉
⠀⠀⢈⡀⠀⢀⠂⠊⠀⠀⠀⠀⠀⠀⢈⠀⡀⡂⠀⠀⠀⠀⠀⠠⡐⠁⠒⠞⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠀⠁⢀⢀⣸
⠀⠀⠻⠟⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠁⠀⠀⠀⠀⠀⠠⠤⠄⠠⠤⠤

⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣀
⠀⠀⠀⠀⠀⠈⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⢻⡿⠇⠀⠀⠀⠀⠀⢠⡞⢋⡿⣿⠛⣦⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⠀⠀⠀⠀⠀⠀⠘⣧⠀⣳⡏⢠⡿⠀⠀⠀⠀⠀⣴⡿⢿⣿⡿⢿⣦
⠀⠀⠀⠀⠀⢸⢿⢿⢿⠿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣬⢊⡵⠁⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⠟⡄⠀⠀⠀⠀⠀⠀⢸⡿⣿⠅⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⢿⣿⣧
⠀⠀⠀⠀⠀⠠⡾⣿⣿⡷⠊⠀⠀⠀⠀⠀⢰⡷⣶⣶⣛⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠺⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻


⠀⠀⠀⠀⠀⠀⣠⣶⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆
⠀⠀⠀⠀⠀⣼⣷⣿⣻⣿⣻⣇⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⢻⣯⣿⢿⣽⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢿⠆⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⠿⠶⠂⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢴⣦⣀⣠⣶⡆⠀⠀⠀⠀⠀⠀⢠⢩⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠷⠽⠳⠽⠻⠼⠄⠀⠀⠀⠀⠀⠸⣿⡋⣻⣿⠀⠀⠀⠀⠀⠀⢀⣻⣿⡧⠐⠉⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠉⠋⠁

⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠦⠀⠀⠀⢀⠀⠀⠀⠐⠂⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢢⠀⠀⠀⠀⠀⠈⠀⠅
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢋⠀⢱⢸⡆⠀⠀⢀⡆
⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠤⠬⠼⠥⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠠⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢁⢠⡀⠀⠀⠀⠀⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠠⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⡀⠐⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠄⡄
⠑⠄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢰⡇⢀⣀⠀⢂⢀⠀⠀⠀⣀⡈⢢⡀⠀⠀⠐⠄⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠠⠀⠀⣠
⠌⡞⠁⠀⠇⠀⠀⠀⠀⢺⣅⡷⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠐⠂⠈⠀⠄⡀⣐⣠⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⢀⢌⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠂⢣⠐⠉⠉⠀⠁⠈⠁⠀⠈⠁⠐⢰⠰⡀⠀⠀⠀⠀⠀⠀⡇⠄⠂⠒⠀⢄⠀⠃⠂⠀⠤⡀⠀⠈⠐⠀⠁⠒⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠑⠄⣠
⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠔⠁⠀⢀⡀⠀⠁⠀⠙⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠢⢄⡀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⣀⠁⠈⠉⠂⢄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠀⠀⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠂⠂⠀⠀⢁⠀⠀⠄⠀⠀⠀⠈⠀⠁⠐⠀⠠⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡀⠀⠠⠌⠀⠀⠀⠄⠠⠄⠂⡐⠂⠀⡀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡁⠤⠂⣀⣀⣀⡠⠴⠖⠒⠊⠉⠀⠀⠀⠅⠈⠀⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠆⠀⠁⠂⠤⠀⠀⠠⠂⠀⠀⠐⡀⠀⠑⠀⠀⠀⠀⠄⠀⠜⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠃
⣀⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠐⠀⣈⠡⠏⡴⢀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠈⠦⣀⡀⠀⠀⠀⠀⠀⢀⣀⠴
⢇⠀⠀⠀⢀⡠⠄⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠰⢁⡀⠃⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⠐⡀⠀⠈⠑⠀⠀⠀⢉⠉⠁⢀
⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠄⡀⠀⠐⡈⠒⠄⠒⠂⠉⢀⣀⡀⠤⠐
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠠⠐⠀⠀⠀⠠⠁⠀⠀⠀⠀⠢⠀⠐⠒⠀⠰⢴⣉⣉⠄⠄⠐⠚
⠀⠁⠀⠀⠀⠀⠀⠀⠖⠁⠀⠌⢠⠃⠀⠀⠀⠀⠀⠈⠂⢄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠃
⠀⠣⣀⡠⠤⠄⠀⠀⠀⠇⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠤⠀⠀⠀⠐
⠀⠀⠉⠂⠤⠀⠀⠤⠄⠒⠁⠀⠀⠀⠂⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⣠⠂⡠⢀⠤⠤⡀⠀⠐⢄⠀⠀⠁⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡞⠁⠀⠁⠀⣀⢀⡸⠀⣀⡀⠱⣄⠀⠀⠀⠈⠒⢌⠂⠄⠀⠀⠀⠀⠀⢠⠎
⠂⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⡸⠀⠀⠀⠀⢳⠊⠀⠱⠀⠈⠈⠁⠘⣧⣽⠂⠈⠂⠀⠀⠀⠀⠈⣆⠀⠂⠀⠀⠀⢠⠂⠀⠂
⢠⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢀⠀⡇⠀⠀⠀⠁⠐⠤⠀⠂⠀⠀⢀⠂⡔⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠁
⠀⠀⢀⠜⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣤⠀⠑⢄⠀⣰⡤⠰⡄⡚⠚⠀⠈⠉⠉⠀⠀⠉⠉⠀⠇⢱⠀⠀⢀⡀⠤⠠⡄⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠁⠒⠢⠤⠤⠤⠄⠒⡈⠁⢀⠤⣛⠄⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠐⠠⠤⠤⠰⠐⠁⠀⠀⠀⡀⢨⠁
⢀⡤⠀⠂⠀⠁⠐⠀⠀⠀⠔⠂⠀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠘⠀⠀⠀⢀⠄⠠⠀⠀⠀⠢⠜
⠠⠃⠀⠀⠀⠐⠄⣀⠈⠀⡰⠊⣋⡄⡢⠐⠊⠀⣀⡀⠤⠤⠀⡄⠀⠰⢊⠠⠤⠔⠀⢀⠊
⠠⡇⠀⠂⠀⠀⢈⡀⠀⠈⠉⠉⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠄
⠀⢀⡔⠁⠄⠠⠤⠤⡁⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠸⠂⠰⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠶⠐⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣾⣯⣻⣷⡀⠀⠀⠀⠀⠀⠀⢠⡤⢋⡀⣤⣔⣶⣶⣾⣯⡱⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣺⣻⣿⣹⣯⠭⢟⣽⣿⠄⠀⠀⠀⠀⠀⡚⠄⣽⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡰⣾⣻⣯⡶⠿⣟⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣀⠐⣽⡿⢻⣯⣿⠿⣥⠶⠏⠻⠞⠀⠀⠀⠀⠀⢠⣯⡿⣿⣿⣿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠰⠟⣿⣿⣷⣾⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠴⠆⠼⠖⠛⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⢿⣏⣽⡞⣫⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠟⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡍⢻⡟⢻⣷⠹⡿⠁
⠀⠀⠀⠀⠘⢫⣿⣿⣿⡿⠿⣿⣟⡿⢛⡛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢊⣽⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣦⡉⢾⡇⣿⣷⣽⣶⡟
⠀⠀⠀⠀⠘⠻⠿⣾⣿⣿⣷⣟⣻⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋⠁⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣛⣻⣷⡄
⠀⠀⠀⠀⠀⣰⣿⡏⣿⣿⣿⡻⣸⣟⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣿⣿⣾⣿⠟⡁⢀⣿⣿⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣿⣶⡹⢾⣶⡿⠻⢯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⠿⠟⠕⠚⠁⠛⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣷⣶⡾⣿⠶⢶⣞⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡻⣛⣯⣽⣟⡀
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣟⣻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⠛⢻⠿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢈⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣀⢸⣿⣯⣈⣯⣿⡿⣰⣿⣿⡏⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠐⣿⣿⡿⢿⣿⣛⡿⣃⣝⣛⣫⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢹⠀⡶⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡉⠀⠀⠂⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠠⠘⠀⠐⠖⠂
⠀⠀⠀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠒⠃⠤⣄⣠⣨⣠⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣿⣭⣿⣿⣿⣿⣻⣿⣯⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⡉⣙⠛⡒⠻⢿⡿⠿⣷⣏⣽⣴⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠸⣿⣿⠓⠋⠈⠉⠉⠈⠉⠁⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠖⠀⠀⠀⠄
⠀⠀⠀⠀⢀⣆⣠⣄⣐⠲⢶⢤⣤⢤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣇⢰⣄⣀⣰⢠⠆⠐⡀
⠀⠀⠀⠀⢹⣾⢣⣛⢢⠁⠈⢛⡩⣭⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢄⡀⢀⣀⡜⠉⠂⡰⠐⠊⣱⠒
⠀⠀⠀⠀⠰⣇⢈⡙⠰⣏⠉⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⣭⠈⠁⢠⣌⡀⠿⣠⡬⣡⡀⢠
⠀⠀⠀⠀⠀⢸⡃⠠⣀⡴⠏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣏⠙⣿⣣⣌⠿⡎⠹⣿⣉⣹⠓⡟
⠀⠀⠀⠀⠀⠀⠣⡀⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠿⠞⣳⠧⡼⣿⡬⢽⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠈⠑⠂⠑⠂

⠀⠀⠑⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠁⡆⠡⠤⠂
⠀⠀⠀⠰⡅⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠙⠓⠄
⠀⠀⠀⠀⠘⠡⢀⠔⢀⠀⠀⠀⠀⠀⠀⢨⠀⠘⠰⠗⠒⠀⠌⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠞⠃⠶⢲⢀⠒⠀⠀⠀⣤⠀⠐⠒⠓⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠈⠤⠈⠁⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠔⣹⠔⠑⠄⢀⡠⡔⠈⠉⠀⠀⠀⠀⠈⠀⠘⠂⠈⠓⠀⠈⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤
⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠱⢄⣀⡀⢤⡤⠄⠀⠀⠀⠀⠀⢀⠄⠁⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠈⠀⠒⠚⠄
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡤⠃⠔⢂⡌⠀⠀⠀⠀⠀⣬⠀⠂⠁⠤⠀⠘⠁⠀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⠀⠀⠀⠀⠀⠀⠁⡄⠓⠠⠂⠴⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠶⠢⠀⠀⠀⠀⠐⠲⠆⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠖⠀⡁⠀⠀⠠⠴⠀⡄⠀⠀⠀⠀⢡⣇⠀⠀⠀⠀⠀⠀⣨⡌⠀⠀⠀⠀⠈⢀⠀⡀⢀⠀⡀⡁⠀⠀⠀⠀⠀⢜⡁⢒⠀⣀⡀⣐⢈⡃
⠀⠀⠂⠀⠀⠀⠀⣤⢤⠂⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠈⢨⠈⠁⠈⠁⣨⠁⠀⠀⠀⠀⠀⢈⡥⠄⠤⠄⠤⠄⢬⡁
⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠤⡈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠦⠄⠲⠀⡈⠁⠀⠀⠀⠀⢀⠀⣤⣀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⡁⠠⠀⠤⠓⠘⠁⠀⠀⠀⠀⠀⠈⡀⠛⠁⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡤
⠀⠀⠀⢀⠂⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡶⣆⡹⠀⠀⠀⠀⠀⠀⠀⠜⣠⡀⠚⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠘⡠⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠰⣚⣳⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⠀⠀⠀⠀⠀⠀⠀⢠⠠⢤⣄⡄⢠⠀⠄
⠀⠀⠀⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠭⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠀⠀⠀⠀⠀⠀⠈⠀⠲⠒⠶⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀
⠀⠀⢀⡈⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠑⢀
⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠆⠠⠤⠄⠤⠀⠠⠀⠀⠀⠀⢀⡀⠶⠂⠠⠴⠅⠂⠀⢀⠀⠀⠀⠀⢂⠀⡁⠀⡀⢀⡑⢈⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠀⠀⠀⠤⡤⠔⠂⢈⠀⠀⠀⠀⢨⠀⠙⠀⠒⠒⠒⠙⠁⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⡀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠱⠂⠒⠒⠒⠀⠂⠌⠉⠀⠀⠀⠀⠈⠄⠐⢉⣁⣉⣉⠉⠀⠷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⠙⠁⠀⠄⣀⠀⠀⠀⠀⢸⡁⣧⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠈⠉⠁⠘⠋⠃⠀⠐⠒⠒⠋⠀⠀⠈⣗⠈⣀⠜⠀⠀⠐⠒⢀⠀⠀⠘⠾⣽⠟⠀⠀⠀⠀⠀⠸⠧⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⢚⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠛⠿⠟⠃⠀⠀⢂⡁⠂⢤⠀⠀⠰⢷⣾⠿⠄
⠀⠀⠀⢰⠄⠀⠀⢠⠐⠐⢃⠀⠀⠀⢀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠠⠄⠰⠋⠐⣂⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⣈⠁⢲⠄⡀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠠⣦⡤⠀⠰⠁⠀⠀⠀⠺⠀⠈⠁⠀⠀⠀⠀⢠⣀⣀⣤⡄⠀⠀⠙⢀⣀⠀⠀⠀⠀⠀⠀⠒⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈
⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⢀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⠀⣄⡸⠀⠠⠤⠤⠂⠁⠀⠠⠄⠄⢀⡀⠀⠀⠐⠄⠁⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡀⣂⢠⡀
⠀⠀⠀⠀⠀⠒⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠿⠜
⠀⠀⠀⠓⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⢠⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢤⣤⣀⣠⡤⠀⠐⠿⣵⣦⠽⠀⠀⠀⠊⠂⠀⠀⠀⠉⠁⠀⠉⠁⠀⠰⢁⢶⠶⣔⠢⡀⠾⢏⡹
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⣀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠟⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⣠⡆⠀⠠⠄⠄⠒⠈⠀⠀⣀⣷⣌⡓⠀⠀⠀⢀⠀⢢⡀⠀⠀⠀⠀⠛⠃⠀⠀⢀⡤⡤⢠⠄
⠀⠀⠂⠘⠀⠐⠀⠀⢀⣀⠀⠀⠀⠠⠝⠹⠈⠗⠀⠀⢐⡘⢑⡋⠀⠀⠘⠛⣤⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠆⣀⡀⠀⠀⢀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠄⠂⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⢃⠀⢴⢂⡄
⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢀⠀⠿⠁⠀⢀⣶⠤⠼⠦⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣧⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⡒⡒⠍⠍⠉⠉⠙⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⡠⢒⠡⠐⠀⠰⡳⠄⠀⠀⢰⣒⡄⠀⣠⠉⠋⠟⡲⢦⠔⡊⠅⠂⠃⠱⠵⠀⠀⠀⠀⠀⢰⣒⡦⠀⠀⠈⠕⡦⡀
⠀⠀⠀⡠⠊⢀⠀⢠⢢⠄⠀⢀⢠⣰⣠⢀⠀⠀⠀⠀⣠⡀⢀⣞⡀⠂⣤⡄⣀⢠⠠⡄⡄⡐⠰⢠⢀⠀⠀⠀⠀⠐⠿⠂⠈⣽⣳⣄
⠀⠀⡔⣡⠁⡛⠁⠀⠀⢴⡴⡘⡸⣣⣾⣸⣸⢰⢠⢀⢉⢠⠋⠉⠀⠀⠨⡙⣬⠖⡇⡇⡄⣇⣀⣸⣘⣸⣰⢠⢠⢀⠀⠀⠀⠓⠻⠭⠷⡀
⠀⠰⠘⠋⠉⠋⠀⠀⢌⢆⡧⠛⠉⠉⠀⠈⠉⠛⠾⠼⣼⣸⠘⠝⠀⠀⣐⢜⣜⣽⣽⠛⠋⠉⠉⠉⠉⠉⠉⠙⠳⢌⠳⡀⡤⡄⠀⢭⣭⢿⣆
⢀⠃⠀⠸⠭⠵⢤⡙⢪⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⢠⣾⣽⠿⠏⣓⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡎⠈⠀⠀⢰⢚⣝⡺⡆
⡈⠘⠃⠀⠀⠀⣐⠪⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⡴⠛⠁⠐⠽⢖⢪⣟⢶⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢣⠁⣀⠀⠀⠩⣓⢌⢻
⡇⠀⣠⣀⠀⠀⠬⢑⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⡀⠈⠃⠀⠀⢰⢮⡢⣹⣯⡎⠀⣎⣹⠏⠲⣄⠀⠀⠀⠀⢸⠀⠓⠃⠀⢸⣮⠱⣝⡆
⡇⠀⠉⠁⠀⣶⡍⢯⣽⠀⠀⠀⠀⢀⡴⠚⠱⠶⠄⠀⡀⡘⡛⡄⡆⡎⢏⢂⣱⣽⢹⡸⡌⡔⢠⣀⠀⠛⠋⠳⡄⠀⠀⣾⠀⠀⠀⠀⢙⡻⡱⡘⡇
⢠⢀⠀⠀⠀⠀⠩⠭⢽⣆⠀⠀⡠⠋⣂⠀⡀⡄⠆⢳⢿⢣⣡⣥⠧⠿⠚⠉⠀⠉⠉⠉⠓⠣⢮⡟⡖⡀⠀⠀⠈⠢⣼⣗⠀⠀⠀⡠⢧⡱⡔⣜⠃
⠘⡠⡀⠀⢀⡄⡈⠥⣠⣭⣧⠞⠁⡀⢻⢹⡼⠗⠚⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣡⡀⠶⠍⠂⠉⠢⡀⠀⢝⠺⡑⡘⣼
⠀⢱⠠⠀⠈⠒⠃⢈⠶⠚⠁⠠⠀⣁⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣗⣤⠀⡀⣀⢤⢧⠀⢢⠱⡱⣰⠇
⠀⠀⢳⢰⡀⠀⢰⠃⢀⢀⠂⠡⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠟⠋⠙⠛⣹⢯⡙⣆⢷⢳⡿
⠀⠀⠀⠣⡑⣆⢈⠢⣍⣈⣂⡵⠿⠛⠫⠋⠓⠦⢄⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠤⠴⠒⣚⡀⠀⠀⠀⠊⡙⠀⠀⢈⡩⡝⣦⣷⡸⡌⣷⠁
⠀⠀⠀⠀⠙⢬⢿⡆⡀⠀⠀⠀⠀⠰⣋⣇⠀⠈⠂⠀⠨⡭⠉⠉⠉⠛⣁⡀⠀⠀⡤⣄⠀⠑⠃⠀⠰⠶⠀⢀⠀⡐⡄⢳⡘⡍⡏⢣⡽⠁
⠀⠀⠀⠀⠀⠀⠑⢞⡧⠁⡆⡄⠀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⡀⠀⠉⠉⠀⠀⠈⠀⢀⢀⠀⡀⡀⢄⢢⣜⣱⢧⠘⡄⢇⢱⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢧⣇⡇⡇⠆⢠⢠⢠⠀⣠⡄⡀⠘⠒⢃⢀⠀⡄⡆⣟⣹⠻⠘⡌⡆⢳⠘⡌⢆⢣⢹⠈⢇⣳⠼⠊⠁
⠀⠀⠀⠀⢔⠤⣒⠤⣀⠴⢀⠬⢛⠾⣼⣜⡜⡌⡎⡏⢃⢣⢹⠘⡜⡆⣇⢣⢱⡸⡌⢇⢣⠱⡈⢆⠳⡙⡜⣎⣧⠗⡋⠁
⠀⠀⠀⠈⠀⠊⠐⠊⠐⠊⠡⠊⠡⠊⠕⢋⠝⣻⠞⡾⢮⣮⣧⣳⣱⣘⣜⣮⢣⣱⣘⣌⣦⡵⣽⢆⠗⡫⢋⢕⡥⡪⢊⠕⣡⠞⡡⢢⠖⡰⢠⢄⢄⢔⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠺⠃
⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⢰⢲⠀⠀⢀⢀⡀⢠⠈⡀⠀⣀⠀⡀⠸⠀⠀⠀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠰⣇⠀⠛⣄⣱⠄⠀⠈⡄⢲⠰⠼⠜⠛⠐⠒⠐⠓⠒⠺⠁⠋⣇⡖⣠⠃⡊⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⢶⣟⣫⡴⠂⠀⠑⠈⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠃⠀⠀⠀⡢⠥⡞⠉⣐⡄
⠀⠸⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⡾⣾⢿⡶⢶⡆⠀⠀⢀⣠⡄⠀⠐⠀⠀⡁⣀⡴⠒⠋⠁
⠀⣀⠀⠀⠀⠀⠀⡠⠀⠒⢦⣄⠀⠀⠀⣿⣙⣅⣿⣿⣯⣻⣿⣿⠀⠀⠉⠉⢀⠀⠀⠀⠀⠈⠉⠀⠀⠄
⣼⣿⣿⡄⠀⠀⠀⣷⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⢀⠀⠈⠉⣳⣄⠀⠀⠀⠀⠋⠛
⠱⢿⡿⠃⠀⠀⠀⢦⣨⣿⣿⡿⠀⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣛⣿⡿⠀⠀⢀⣀
⠀⠀⠀⠀⠞⠀⠀⠀⠀⠉⠉⠀⠀⣀⣽⣅⠀⠀⢠⣶⠀⢠⡟⠀⠀⡀⠈⠚⠛⠿⠟⠃⠀⠠⢺⣿⠾⡿⠂
⠀⡀⡀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠹⠟⠁⡾⠀⠀⠐⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠁⠀⠀⣀⠀⠐⢂⣤⡆⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠃⠀⣀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠈⠐⠒⠄
⠀⠀⠀⠀⠀⠽⠻⠲⣿⣿⡇⠀⢠⠎⠀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢦⣜⠛⣿⡶⢆⣤
⠀⠐⣄⠀⠀⠀⠀⠘⠛⠉⢀⡴⠁⠀⠀⠙⠶⢶⣭⣽⣶⣦⡄⠀⠀⠑⠄⠀⠈⠳⢦⣾⠟⠋⠀⣶⣀⣶⡀
⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣵⣾⣶⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣿⣿⣇
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⡴⠚⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠿⠋⠀⠉⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠀⣀⣶⠷⢶⡀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠦⣶⣾⣭⣿⡋
⠀⠀⠀⠀⠀⢰⣦⣷⣬⠷⣠⠖⣲⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠾⠋⠁⠀⠈⠁⠀⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣝⠳⣿⣯⣽⡟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠛⠛⠛⠛⠛⠛⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣛⣻⣶⣶⠶⣿⡀
⠀⠀⠀⠀⣠⣿⣿⣄⣀⣙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣴⣶⣶⣶⣶⡄⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣩⣾⣿
⠀⠀⠀⣘⣿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠉⠙⠛⠋⠉⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣤⣀⣀⣙⣿⠇
⠀⠀⠈⠉⠉⠻⢶⣯⣽⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⣀⣀⣀⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⣯⣽⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠶⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢲⣄⣄⡀
⠀⠀⠀⠀⣰⡟⠉⠙⠃⠉⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠐⠀⠐⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢖⣫⣤⣶⣾⣿⣿⣿⡿
⠀⠀⠀⢰⡟⠛⠀⣶⠆⣀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢦⣀⠀⠀⠀⠀⢀⣠⠖⡋⠀⠀⠀⠀⠀⠀⢀⣾⣥⣶⣿⡿⠿⠋⠉⠀⠀⠈⣿
⠀⠀⠀⠘⣷⡶⠀⣤⡾⢩⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣬⡛⢦⣤⠶⣫⣵⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠠⠄⠠⠀⠀⣠⡿
⠀⠀⠀⠀⠈⠻⢦⣬⣿⠀⠁⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠿⣿⡻⣷⣶⠾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⢻⣌⠀⠂⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠈⠛⠛⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡺⠂
⠀⠀⠀⠀⠺⢿⣶⣦⣄⠙⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⣦⣄⣿⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡶⢾⡇⢸⡀⣿⠀⣿⠃⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣦⣤⣤⡄
⠀⠀⠀⢰⣶⣾⣿⣿⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣣⣬⣶⣯⣤⣟⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⣹
⠀⠀⠀⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⣾⣷⣀⣀⡿
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠋⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠿⠟⠀⢸⡇
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣤⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣼
⣀⣀⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠉⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡎⠂⣾⡁⢸⠤⣤⠖⢂
⠀⠀⢀⠴⠒⠂⠠⢀⡀⢀⠔⠁⢀⡤⠖⠒⢤⠀⢹⠀⠀⠀⠀⣀⠉⢳⡼⠀⢸⣷⣀⠓⣇⠀⠀⠊⠠⠁
⠀⢠⡏⠀⣀⣀⣀⠀⠈⠃⠀⡰⠋⠀⠀⠀⠈⡇⢸⡇⠀⡠⢼⣄⠑⠌⠑⠂⠀⡿⣷⠀⠈⡄⠀⠀⢦
⠀⢸⡀⠐⡅⠀⠈⠉⢻⠀⠰⠁⡄⠀⠀⠀⢰⠁⢸⠇⠀⠑⢦⡙⠇⠀⠀⠀⠀⠐⡽⠄⠀⠀⠀⠀⠈⡄
⠀⠈⣇⠀⠰⡀⠀⠀⠘⡄⠀⢠⡀⠀⠀⠀⡌⠀⣸⠀⠀⠀⠀⠉⢢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠘⢆⠀⠹⣄⢠⠖⠀⣠⡂⠉⠒⢄⡰⠁⢠⠇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡆
⠀⠀⠀⠈⠳⡀⠈⠁⠀⡴⠁⠈⠢⡀⠀⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠘⢆⣠⠊⠑⠢⠤⠖⠉⢂⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢀⡠⠄⠲⠊⠉⠉⠉⠩⠉⠉⠛⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡴⠊⠉⠉⠉⠉⠉⠉⠉⠑⠒⠤⣀⡀
⠀⠀⢠⠏⠉⠈⠉⠈⠉⠁⠁⠈⠉⠉⠉⠈⠉⠁⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⢨⠧⢀⠄⠀⠀⠀⢀⠀⠀⣀⠀⢀⡀⣀⣀⠀⠀⢺⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠠⠤⠀⠀⠀⠈⢧
⠀⠠⡚⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠀⠀⠀⢹⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠧⡄⢀⡠⠬⡈⢀⡀⠀⠀⠁⣀⣁⢈⣐⠀⣠⠌⣹⠋⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠑⠤⣀⣀⣀⠀⠀⡀⠀⠊⠀⠀⢀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠃⠠⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠞⠁⠣⠢⠄⠀⠀⠀⠠⠀⢀
⠀⠀⠂⠀⠉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠆⠃⠈⠔⠁⠀⠀⠀⠀⠁
⠀⠰⠀⠀⢀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⢀⠀⡀
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⢃⣌⢏⢀
⠀⠀⢠⠀⠀⠌⠀⠀⢀⡘⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠀⠊
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡃⠦⠀⠒⠀⠈⣀⠤⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⢇⢵⠄⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠁⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰⠦⠶⠴⠆⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠆⠀⠀⣀⣀⡀⠀⠠
⠀⣠⣴⣾⠟⣿⡇⠀⠀⠀⠈⠀⠀⠆⠀⠑⠒⠚⠂⠚⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐
⠀⣿⣬⡼⠶⠛⠃⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢀⣠⣞⡇⠈⠀⠫⠩⠥⠼⠃⡀⠀⣶⣳⠐⠂
⠀⠉⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠔⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣣⠟⠁⠀⠀⠀⠰⠇⠀⠀⠀⠀⠘⠋
⠀⢀⠀⠀⠀⢀⡀⠀⠀⣰⣂⣂⣲⣀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⢸⠟⢁⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠻⠭⠿⠭⠝⠇⠀⠰⡏⣋⣹⣷⣽⠇⠀⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠁⠐⠀⢀⠀⠀⠀⢀⠀⠀⠦⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠩⢐⠀⠀⢨⠀⠀⠀⠀⠸
⠀⠀⠴⠀⠀⠀⣈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⢨⣲⠀⢨⠀⠀⢄⣀⠈
⠀⠠⠀⠀⠀⠀⢀⣈⠔⠀⠀⠀⢰⡶⠶⠄⠀⠀⠀⠀⠀⢠⡤⣤⣤⠀⠀⠀⠁⠀⠈⣤⡤⠆⠀⠀⠀⠀⠀⠈⠐⠀⠐⠌
⠀⠀⠀⠀⠀⠁⢉⠄⠐⠀⠀⠀⣼⣇⠀⠲⠤⠤⠄⠀⠤⠘⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣽⣉⣁⣄⣀⣀⣀⣀⣀⣁⣀⣀⣙⠀⠀⠀⠀⠀⠀⡈⢲⣠⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⡏⣠⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠤⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⢿⡟⠃⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⡶⡢⡀⠀⠁⠂⠐⠒⠀⠀⢀⢀⠀⠀⠀⡀⡀⡀⠀⣰⠖⠀⠒⠀⠐⠐
⠀⠈⠀⠀⠀⠝⠂⠀⠀⠀⠀⠀⠀⡎⣭⢉⣑⢂⣜⣣⡥⠏⠀⡄⡀⠀⠀⠘⠀⠛⠘⠀⠂⠀⠃⠓⠃⣼⡏
⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠛⠾⠿⠿⠛⠋⣽⣀⣠⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⣀⠀⣀⣀⣀⣐⣒⣀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢡⠐⡴⣆⠀⠍⠠⢂⢠⠀⠀⠀⠀⠀⠀⠀⠇⠇⠀⠄⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⡂⡤⡒⠂⠀⠂⠄⠀⢂⢢⠀⠂⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠤
⠀⠀⠀⠀⢠⡀⠤⠀⠀⠀⠀⠀⣀⠁⠀⠁⠁⠀⠁⠀⠀⠁⢀⡀⠀⠈⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠓⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠶⢶⡄⠆
⠀⠀⠀⠠⢠⠀⠀⡠⠀⠀⠀⠀⠀⠀⣾⣿⣭⣽⣽⣽⣿⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠂
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⡀⢀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠐⠀⠀⠁⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡤⠖⢚⣋⣉⣉⣉⣉⣀⣠⣤⣤⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⣷⣶⣤⣀
⠀⠐⣏⠛⢛⣻⣿⣿⡿⠿⠿⠿⠿⠿⢯⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⠥⠤⠤⠤⠤⣤⣬⡉⢧
⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠟
⠀⠀⠀⠈⠲⠿⠶⠒⠒⠒⠶⠞⣶⣄⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⣶⢄⡠⠶⢶⠻⠋
⠀⠀⠀⠀⢀⠀⣨⠿⢟⣿⠿⠿⢿⡿⠯⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⠝⠋⠀⠂⢸
⠀⠀⠀⠀⡾⡜⢡⠖⠉⠀⠀⠀⢸⣷⠃⣀⡬⠓⢦⠀⠀⠀⠀⠀⣠⠔⢋⣩⠽⠋⠁⢠⣤⢀⠀⢸⡷⣄⡀
⠀⠀⠀⢰⢇⣷⠃⠀⠠⠴⠶⣦⢼⠿⠋⠀⠀⠀⠈⢳⡀⠀⠀⣴⣧⠴⠋⠁⠀⠀⠀⠈⠁⠘⠃⠘⡇⠀⠙⢆
⠀⠀⠀⣸⢸⡇⠀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠚⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠃
⠀⠀⠀⡏⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⢸⣠⠾⠃
⠀⠀⠀⡇⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡤⣴⡄⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡦⢾⣿⡆
⠀⠀⢰⡇⡏⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣹⣍⡉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣠⣿⣤⣼⢸⠁
⠀⠀⠈⢧⢧⡀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⣿⢯⣙⠓⠒⠚⠛⠛⣉⣭⣿⣟⣛⠻⢧⣤⣄⣸⣺
⠀⠀⠀⠈⢳⠬⣝⣛⣛⣓⣒⣒⣒⣒⡿⣺⣥⣄⡏⠈⠳⠈⠙⠓⣖⣚⠉⢁⡾⣍⣛⣿⢻⡽⢯⣉⡏⡧
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠉⠉⠉⢹⣿⠁⠘⢾⣶⣠⣶⣤⣴⣚⣁⣘⣞⣉⣀⣉⣩⣯⠬⠤⠚⡽
⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣄⣀⣀⣘⣋⣀⣀⣀⣀⣉⣀⣀⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⡀⢠⠀⠀⢄⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠠⠐⠀⣀⢡⡀⠆⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⡄⠀⠸⠀⠔⠘⠘⠊⠄⠀⠉⠀⠀⠡⠀⠀⠀⠀⠀⡀⡀⣧⡄⣧⡗⡠⡐⠳⡘⠆⡅⠄⣦⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡈⠁⠀⠀⠀⠀⠀⠁⠆⠋⣁⠘⡰⢇⠉⠆⠙⢸⠀⠄⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠳⠾⣄⣅⠣⠈⣤⠆⣻⡼⢢⡄⢠⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⡀⢠⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠴⠥⡌⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣷⠀⠀⠀⠀⢸⠀⠐⠠⠄⠀⠔⣠⠀⡄⣶⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠀⠐⠲⠶⠶⠞⠴⠟
⠀⠀⠀⡈⠓⠠⠤⢄⠀⣀⣀⣀⠀⠀⠰⠞⠃⣈⣾⠀⠀⠀⠀⠀⢇⠀⠁⠀⠁⠈⠉⠉⠁⠒⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⡖⠒⢤⣀⡀⢀⡀⠀⠀⠀⠀⢀⡄⠉⠭⣲⠆⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⢠⠉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣰
⠀⠀⠀⡗⢦⡈⠉⡀⠀⠀⠁⠈⠉⠊⠉⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⢀⠘⠷⠤⠀⠀⠀⠠⠴⠔⠒⠀⡠⠖⠁⠀⠀⠀⠀⠀⡄⠈⡀⠀⠀⠄⣄⠀⠠⠃⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠠⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠃⠂⠘⠂⠒⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠄⣠⣄⠐⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⠙⠲⠄⠀⠢⠴⠀⠀⢫⣙⢃⠀⠑⠒⠶⠆⠀⠀⠢⠐⣦⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠓⠋
⠀⠀⠀⠀⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠂⠈⠠⠔⠠⠄⠩⠗⠠⠔⠰⠒⢠⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠊⠀⠒
⠀⠀⠀⠀⠀⠀⠉⠾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠋⠀⠐⠁⠀⠀⠀⠠⠘⠁⠀⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⡽⠛⠋⠛⠛⠓⠶⢤⣄⣀⢀⣀⣠⣤⠶⠶⠶⢦⣄⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣰⣦⠀⠀⠙⢦⠀⠀⠀⠙⢷⣄⣀⠤⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡿⠀⠀⠀⢸⣾⡿⠀⠀⠀⣄⢠⡄⠀⠀⠈⠛⠛⠀⠀⠀⠈⢷⣄⢀⡤⣾⡁⢠⣤⡄⠛⠉⢀⣠⡍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⡯⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠿⠗⢈⣥⡄⢀⠾⠶⠀⠾⠿⠀⠰⠿⠉⢢⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠞⠃⠀⣀⣠⣤⣤⣤⣴⠶⠦⢤⣄⠀⠀⠨⣧⠀⡼⠁⠰⠶⠆⢡⣗⠀⠶⡶⢀⣴⡌⠛⠓⠰⣿⠀⢳
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⣡⡴⠚⠛⠉⠉⠙⠛⠲⢬⣳⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⢷⡀⢸⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⢀⣀⠈⠃⠘⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢸⡇⠀⣾⠀⠀⠚⠛⠉⠀⠀⠀⠹⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣶⠒⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠁
⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠀⠛⠳⠆⠘⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠨⡆⠘⠤⠊⠉⠓⠤⠤⢤⡀⠀⠀⠀⣠⠖⠦⣀⠀⠀⡰⠋⢸
⠀⠀⠀⠀⠸⡆⢿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⣤⠤⠶⠋⠁⠀⡀⣣⠀⠀⠀⠀⠀⣠⣀⠀⢧⡀⢀⡴⠃⢀⣄⡀⠉⠉⠀⠀⡎
⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠈⠻⠂⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠛⡿⣿⠀⠀⢦⠀⠘⢷⡿⠀⠀⢌⡤⠀⠀⢿⡿⠇⠀⢰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⣴⠇⠀⠀⠀⠘⠷⠀⠀⢸⠇⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠙⠲⠶⢤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⣆⢀⣀⡀⢀⡟⠀⠀⢹⡀⣈⣄⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠙⠾⠤⣴⠚⠺⠏⠉⠉⢧⠀⠸⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣝⣓⣲⠒⠚⠋⠁⠙⣦⣀⠀⢀⣠⠾⢦⣀⣀⣀⡴⠛⠒⠒⠀⠤⠤⠤⠀⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣀⣰⠋⢳
⠀⠀⠀⢀⡼⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⣠⢬⣇⢀⣏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⢀⣠⠴⠒⣆
⠀⣠⢦⣉⣻⡁⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠉⣵⠒⣯⣛⣻⢷⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⣉⣀⡀⠀⢸⡀
⠴⠧⡞⠁⠉⠳⣄⡀⠀⠈⠙⠒⢲⢲⠀⠀⠀⡿⢷⣯⣏⣉⣹⡼⠃⠈⣇⠀⠀⠀⠀⠀⠙⣦⠀⡞⠁⠀⠈⣧⠀⠙⢦⡀
⠀⠀⠳⣄⠀⠀⠀⠙⠓⠶⠶⣖⣉⡛⠀⠀⠀⢱⡀⠀⠌⢉⡝⠡⠀⠀⠸⡄⠀⠀⠀⢀⠔⠃⠀⢧⣀⠀⣀⠏⠀⠀⠀⡇
⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣀⣰⣏⡇⠀⠀⠀⠀⠳⡀⢀⡞⠀⠀⠠⠀⠀⢳⠀⠀⠀⣏⠀⠀⠀⠀⣈⣉⡁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠒⠖⠚⠉⠁⠈⠉⠙⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⡆⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈⠣⣄⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢣⣴⠲⣇⣸⣁⣀
⠀⠀⠀⣀⣀⣀⣟⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣎⣈⣧⡄⠀⢰⡇⡖⠀⠀⠀⣠⣾⠀⠀⢠⣄⣹⡏⢩⢿⢙⣇⠙⣽⠂
⠀⠼⣭⠭⠭⠭⠤⠤⠤⠤⢤⠿⠀⠀⠀⠀⢀⡷⠲⠒⠶⢇⡀⠀⡇⠃⡞⠛⠾⡟⠁⠀⠀⠘⠒⢦⡍⠻⣼⢸⠟⣆⠘⣆⡀
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢹⠀⡵⠒⢿⣦⣤⠇⠀⠀⠀⠀⢻⡛⠻⠦⠼⠿⠾⠛⠊⡽
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣸⣤⣷⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣷⣀⠈⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢾⠁⠈⠙⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠒⠒⠒⠒⠚⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠛⠒⣲⡾⠷⠥⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⠤⡤⢤⣤⣄⣠⣄⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠉⠉⠛⠲⠤⣄
⠀⠀⡰⠛⠉⠍⠉⠲⢼⡒⣿⢶⡲⢤⡀⠀⠀⠀⠀⣠⠖⣋⡉⡉⠫⢙⡳⢤⡀⠀⠀⠀⠀⠀⣿⡚⠲⠤⣞⡀⠀⠈⠙⢦⡀
⠀⢸⠁⠀⠀⠀⠓⠀⡀⠙⣍⢳⣗⡦⢳⠀⠀⠀⢸⡃⠖⠀⠁⠉⡠⠈⠤⠆⢳⡀⠀⠀⠀⠀⣿⡙⣦⠀⠤⠉⠻⢤⣠⠄⠙
⠀⠈⠣⣁⠀⠂⠀⠀⠀⠰⠘⣎⢹⣿⢺⠀⠀⠀⠀⣟⣓⣒⡒⠒⣒⣲⣒⢒⣾⡃⠀⠀⠀⠀⣿⠕⠃⡴⣫⣭⣿⣳⣽⠶⠒
⠀⠀⠀⠈⠓⠦⣀⠈⠀⢠⠀⢸⣼⢼⡏⠀⠀⠀⠘⢯⣭⡤⠭⢿⣥⡤⠬⠭⢴⡏⠀⠀⠀⠀⡧⢄⠘⣏⡷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀⣧⠎⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣙⣶⡤⠞⠀⠀⠀⠀⠀⡧⠞⠋⠁
⣾⣷⠿⠿⠾⣿⣿⣿⣿⣾⣶⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠄⡀⠀⣤⣠⡦⢴⣏⣳⣀⡤
⠀⠀⠀⠀⠠⠔⣟⡨⠛⠁⣇⠀⡿⡄⡇⢰⡇⣾⢈⠟⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠴⠾⡷⢒⡲⠖⣇⣠⠃⢱⡇⠘⠃⢈⣁⣰⡀⢠⠀⢀⣞⢕⡅
⠀⠀⠀⠀⢀⡤⡟⠉⠀⠀⠉⠀⣴⣀⢸⣤⡞⣾⠓⠛⠉⠁⠀⠈⠁⠁⠀⢠⣀⣀⡤⡄
⠀⠀⠀⠀⠁⣀⠀⣀⣀⣤⣦⠛⣿⠿⠺⠖⠀⣀⣀⣠⡤⠶⢖⡈⢉⠑⠢⢇⠁⠁
⠀⠀⠀⠀⢀⢸⠟⡿⠋⠈⠏⠁⠁⣀⠤⠔⠁⠀⠘⢾⣶⣞⢨⡓⡄⢱⡤⣄⠑⠢⡀
⠀⠀⠀⠀⢇⠞⠀⠁⢀⡠⠔⢺⠿⣆⡐⠀⡀⠤⠀⢄⠞⠉⠙⢭⢇⣎⡑⡈⣇⢤⣈⠓⢄⡀
⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⢀⠠⠀⠁⠌⠒⢤⣦⡀⠈⠀⠀⣀⡀⢛⡲⠻⢜⠕⡼⠡⣄⠀⡌⠢⡀
⠀⠀⠀⠀⢰⡗⠾⣆⠀⠄⠒⠁⠀⠀⠘⡐⠀⠈⠛⢄⣸⠀⠀⢰⠊⠀⠀⠀⢻⣡⡔⡡⣺⡢⠗⡇
⠀⠀⠀⠀⢸⠑⢦⣸⠨⠤⠀⢔⢨⠢⠑⠈⣠⡟⢛⠧⠨⢟⢧⡃⢰⢁⣀⠈⣀⠧⠗⠋⠁⠀⢠⠇
⠀⠀⠀⠀⢸⠀⠀⠈⠲⣄⣐⢬⠞⢳⠞⠉⠀⢉⠋⡤⠠⡀⣆⣈⡺⠞⠛⠉⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠉⠲⢄⣜⣠⡊⣱⣸⡼⠤⠒⠋⠉⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠩⠉⠁⠀⠀⠀⠈⠀⢀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⢀⠀⣄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠚⠉⠁⠀⠀⠀⠀⢰⠻⠆⠟⠙⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡶⠖⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠖⠛⣏⠉⠙⣇⣀⣀⣷⣤⠴⠿⣦⡀
⠀⠀⢀⣀⣤⢶⡞⠛⢻⠁⠀⢹⣀⣤⠼⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠙⣦⡀
⢰⡟⠋⢯⠀⢀⣧⣤⠼⠗⠛⠋⠁⠀⠀⠀⠀⠀⡀⣄⠰⣄⠀⠀⠀⠀⠈⠻⣄
⠈⣷⡴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠉⠈⠂⢀⣀⡤⠴⠒⠛⣦
⢰⠿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠸⣆
⣿⠀⣿⠈⢳⡄⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣿⠀⠸⡇⠀⢻⣄⡠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣿⠀⠀⢿⠀⠀⢷⠀⢠⠞⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣧
⢸⡄⠀⠸⡇⠀⠘⣧⠀⠚⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡀⢹⡄
⠈⣧⠀⠀⢿⡀⠀⢹⡆⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⣤⠀⣿⣁⠀⢷⡀
⠀⢹⡆⠀⠘⣇⠀⠀⢿⡀⠀⣟⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠏⠁⠈⣿⣦⠀⢉⡇⠘⣧
⠀⠀⢷⠀⠀⢻⡄⠀⠈⣧⠀⠈⠓⢦⣄⠀⠀⢀⡀⠀⣼⠋⢹⣆⠘⠷⠤⠆⠈⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠸⣇⠀⠈⣷⠀⠀⠸⡆⠀⠀⠀⠉⢷⢹⡏⠻⣆⠻⠦⠾⠙⠀⠀⠀⣀⣠⠴⠒⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢻⡀⠀⢸⡆⠀⠀⢻⡀⠀⠀⠀⣸⠇⠓⠀⠙⠀⢀⣀⡤⠖⠚⠉⠁⠀⢀⡀⢠⠀⠀⠀⠈⣧
⠀⠀⠀⠈⣧⠀⠀⢻⡀⠀⠈⣧⠀⠈⠛⠉⠀⠠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⢸⠇⠀⠀⠸⡆
⠀⠀⠀⠀⢸⡆⠀⠈⣧⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠹⡇
⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡆⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⡀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⣷⠀⠘⣧⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠸⣇⠀⢻⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⡖⠛⣏⢁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢻⡄⢸⡇⠀⣓⢌⠑⠆⠀⠀⠀⣀⣀⣤⢶⡞⠛⠹⡅⢀⣠⣷⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣷⢸⡇⠀⠈⢁⣠⣤⢶⠞⠛⠙⣇⠀⢀⣧⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡤⢶⡟⠙⡇⠀⠀⣧⣠⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣷⠴⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠉⠉⠉⠈⠉⠉⠐⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠉⢉⣙⠛⠷⢶⣤⣀⠀⠀⠈⠑⢄
⠀⠀⣤⢠⣄⣤⣤⡄⠀⠀⠀⠀⡠⠊⠀⠀⣠⣴⣿⠕⠊⠉⠉⡉⠉⣒⢄⡰⠁⠀⠉⢦⡀⠈⠙⠳⣦⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡴⢄
⠀⠀⢽⣿⣿⣿⢹⡇⠀⠀⠀⡜⠀⠀⢀⣴⢟⠟⠀⠀⠀⠀⠘⠜⠈⠊⠈⢟⠀⠀⠀⢠⠊⠙⢷⡖⢁⠙⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⡇⠀⠱⡀
⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⡞⠀⠀⢀⡾⢃⠎⠀⠀⠀⠀⠀⠓⠀⠚⠐⠗⡟⠀⠀⠀⠀⠑⡬⠷⢵⡦⠼⠚⠿⡄⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⢱
⠀⠀⠈⢿⠻⢛⡟⠀⠀⡸⠀⠀⢀⣾⠁⡎⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⣇⣀⠤⠄⠠⢄⣥⠒⠀⣷⡛⡤⠔⢻⣆⠀⠀⢱⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⢹⡇⠀⠀⢀⠃⠀⠀⣸⠇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⢤⠀⡯⠇⡒⡌⢉⠛⣿⡟⠃⠀⠀⢻⡄⠀⠀⡇⠀⠀⡇⠀⡠⠃
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡿⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⢌⢉⡸⠝⠀⡬⡠⠚⠓⠖⠓⠒⠒⢄⠘⣧⠀⠀⢰⠀⠀⢧⡔⠁
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡀⣨⢇⣰⡎⡤⡔⠋⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⣯⠜⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⣘⠚⠉⢉⢕⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⠀⠀⢸⠀⠀⡘⡇
⠀⠀⠀⠀⢸⢰⠀⠀⠈⡄⠀⠰⣁⣄⠀⠀⠀⢠⠊⢀⠤⣄⠸⡡⠀⠉⢢⡈⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠀⠀⡆⠀⠀⡇⡇
⠀⠀⠀⠀⠸⢸⠀⠀⠀⢱⠀⢀⣸⡟⢢⠖⠤⠃⢀⠓⠀⣈⠀⡱⣮⢄⣀⠗⠀⣘⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣾⠃⠀⢰⠁⠀⠀⡇⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢣⢇⣀⡀⠘⡄⠀⠀⢸⠀⠀⣼⢸⠄⠉⡆⠀⢰⡩⢃⠵⠈⣉⣢⣀⠀⠀⢀⠔⢁⣾⠃⠀⢠⠃⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠣⡀⠑⠚⢷⣄⠀⠘⠮⠔⠁⠸⡠⠈⡇⠀⠘⢾⡴⠞⠋⠑⣬⢧⠉⠉⠀⣴⡟⠁⠀⡠⠃⠀⠀⠀⢸⠀⠁
⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⢷⣄⡀⠀⠀⠀⠑⠜⠁⢠⠻⡄⢙⡆⠛⠭⠿⠃⣀⣴⠟⠉⠀⢀⠔⠁⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠈⠺⣬⡖⣁⣠⣤⡶⠟⠋⠁⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠉⠉⠛⠛⠛⠓⠚⠛⠉⠉⠀⠀⢀⡠⠔⠊
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠐⠉⠁⠈⠈⠁⠀⠒⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣀⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⡉⣉⣁⣀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠛⠛⠛⡿⢿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠻⢲⣄⠀⠀⠈⠙⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢢⣄⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠳⣶⣶⣤⣄⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⠏⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠶⠚⠉⠁⠀⠀⠀⠈⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠖⠀⠀⠊⢹⣦
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣚⡏
⠀⠀⠀⠀⠀⠀⠛⠿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠋⢀⡤⠀⠀⠀⠀⢴⡇
⠀⠀⢰⣄⡀⠀⠀⠀⠀⠉⠛⠺⠿⢏⣻⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠢⠄⠀⠀⠈⠀⣀⡠⠎⠀⠀⠀⣞⠀⠀⠀⣾⠇⠀⠀⠀⢀⣾
⠀⠀⠸⠿⣽⣲⢤⣄⣀⣀⠀⠀⣦⣀⣠⣬⣤⣿⠋⠉⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠈⠁⠀⠀⣀⣠⡤⠒⠋⠁⠀⠀⣠⠺⠇⢳⣤⢀⡤⠂⠀⠀⠀⠀⣰⠏
⠀⠘⣦⣤⣀⠀⠉⠁⠘⠻⠁⢀⣟⠀⠀⠘⠉⠀⠀⠀⠀⠀⠒⠒⠦⠄⠀⠀⠀⠀⠀⡀⠴⠒⠉⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠉⢾⠁⠀⠀⠀⢀⣰⠁
⠀⠀⠈⠙⠛⠿⠇⢰⢦⣤⠀⠼⠃⠀⠀⠀⢀⡀⠀⠉⠉⠓⠀⠀⠀⢀⣤⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⣠⠖⠂⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢹⡞⠸⡇⠀⠀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⢀⣴⡾⠓⠂⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⠀⠀⠀⠀⠀⠹⣹⡧⠀⣀⣠⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣦⣄⣀⠀⠀⠀⠀⡀⠀⠐⠛⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠉⠛⠿⣷⣶⣌⣉⡳⠶⠂⠈⠀⣀⣠⡾⠃⠀⠀⠀⠀⣀⡀⠺⠋⠀⠀⠀⠈⠙⢆⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣤⣴⠷⠚⠁⠀⠀⠀⠀⠀⢀⠚⠁⠀⠙⣶⣤⣄⣀⣀⣠⠞⠛⢧⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠊⠉⠁⠽⣍⣹⡥⠀⠀⢘⡇
⠀⠀⠀⠘⢦⣄⣀⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣴⠋⠀⠀⠀⠀⠀⠓⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣠⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⣤⣈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢤⣄⡀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡀⠀⢀⡀⠓⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⡤⣼⠟⣱⣛⣆⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠴⠚⣫⠝⠁⠀⠀⠀⠀⡾⣠⡆⡰⣹⢠⡏⣹⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢹⣠⣴⠯⠴⠒⢶⠀⢰⣿⡾⣿⠫⡿⠁⡿⠀⠉⠁⠀⡆⢀⡿⠀⠀⢀⡀
⠀⠀⠀⠀⣠⣖⣫⠔⠋⠀⢸⠁⠀⠀⣀⡴⠃⠐⠻⠜⢁⠁⠀⢀⠀⣀⠀⣇⡶⣼⣧⢞⡇⠀⠰⢋⡁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⣆⣤⠞⠁⠀⠀⠀⠀⠀⣼⠀⣾⢾⡵⣿⣰⠻⡴⢻⠃⠸⠇⠀⠀⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡏⠀⠀⠀⢀⣀⡄⠀⠀⡟⠀⣉⠈⢡⡏⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠈⠁⠀⠀⠈⢩⢿⠀⠀⠰⠷⠛⠁⠀⠈⠁⠀⠀⢀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⢉⣹⠁⢄⣑⡢⣍⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠀⠀⠀⠀⢀⣀⣤⢶⡚⠉⡕⠁⠀⠀⡄⠂⢣⣀⡀⡀⡇⠈⠂⠀⠆⣙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⢀⢄⣰⠛⠶⠃⠈⠉⠱⣈⡛⠦⣐⠚⠉⡠⠊⠁⠀⣀⠨⢃⡐⡠⠞⢉⠤⣖⣂⡌⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠙⠊⠀⠁⠀⠀⠀⠀⠠⠢⠄⢆⠀⣀⢙⠾⢤⠐⠒⣉⠕⢂⡩⠭⢕⠢⡈⠂⠇⠊⣀⡤⠞⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠒⠀⠀⠀⠀⠀⣀⣸⠉⠀⠀⡔⠊⠀⠁⣳⠐⢍⡺⢥⡐⠥⣘⣈⠼⢃⣨⠷⠒⠋⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡟⠦⣀⠀⠀⠀⢀⠤⠒⠛⠯⡀⢀⢀⢁⡠⠖⠚⠻⡇⠀⠐⡇⢈⣳⡦⠖⠚⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠙⠲⢴⣡⠀⠀⠀⣠⠞⠛⠛⢯⡀⠀⠀⢀⣸⠤⠖⠛⠉⠀⡠⠄⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠉⠓⠦⣴⣁⣆⢀⣀⣠⠷⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠭⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠀⣠⡴⠶⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡂⢄⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠠⠆⢩⠁⠀⠀⠀⢠⣴⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⢀⠈⡄⠀⠀⠀⠠⢠⣉⣩⠝⠀⣤⠤⠛⠂⡀
⠀⠀⠀⠈⠃⠁⠀⠀⠀⠗⠀⠁⠀⠀⠀⠙⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠻⣶⣦⣟⣀⣴⡾⠃⠀⠀⠤⠾⢖⡽⠇⠀⠌⠇⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃

⠀⢀⣤⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣡
⠀⠈⢯⣽⣿⠏⣹⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣤⡁⣤⠀⣴⡀⢠⡤⣄⢠⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢫⠸⠀⣾⣿⡏
⠀⠀⠈⢻⠙⠛⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡷⣿⠻⣿⣰⠿⢷⠻⣤⡤⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢹⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢺⢿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⡀
⠀⠀⠀⠀⠈⠁⣀⣀⢤⣶⣀⠀⠀⠂⢀⡤⠀⠐⢯⠿⠀⠶⡆⠀⠀⠀⠘⠛⠈⠉⠉⠃⡀⠈⠓⠢⠬⠅⠀⠀⠠⠄⠐⠀⡀
⠀⠀⠀⠀⢸⠯⠛⢟⠋⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠀⣠⣤
⠀⠀⠀⠀⠘⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠄⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢘⡃⠃⠙⠈
⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡤⣠⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣍⣀⣀⣩⡄
⠀⠀⠀⠂⠀⠓⠒⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢀⡉⣤⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

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

⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠄⠠⢈⡐⠁⠷⢀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠡⠄⢘⠑⠂⠗⢸⠁⠀⠀⠀⠁⠛⠋⠘⠛⠛⣮⣂⠀⠀⠠⠀⣀⠀⠀⠀⣀⠀⠴⠃⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠘⠁⠘⢆⡈⠡⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡇⠰⢆⡆⢠⠀⠤⢤⠤⡄⢠⡄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠂⠌⡃⠛⠉⡀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠈⠙⠻⠶⠧⠴⠦⠛⠊⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢄⡘⣆⠀⠀⣠⣿⣿⡿⠀⠀⠀⠠⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣞⣿⣿⣿⠃⠀⠀⠰⠀⠉⠉⣠⠀⠀⡘⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠰⠊⠹⣶⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠲⠤⠤⠊⠀⣰⠁⠀⢰⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⢰⢦⠀⠀⠀⠀⣶⣀⣀⣠⣶⢀⡀⠀⠀⠀⠐⠛⡇⠀⠀⠀⠑⢶⣴⣿⠾⠟⠁
⠀⠀⠀⠀⠃⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠛⢟⣣⠞⠁⠀⢀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⢸⡏⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⣠⡀⢰⠀⢠⣦⡏⢀⠄⢦⣶⣹⣧⣤⣄⠀⠀⠀⣸⠁⠀⠘⢷⣀⠀⠀⠀⣠⣀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠛⠛⠋⠁⠀⠄⠊⠙⢻⠉⠀⠈⠻⣧⠀⠁⠹⡄⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⢤⡆⠀⠈⠢⣀⣀⣀⣶⣶⠾⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠰⠶⠛⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣄⣀⣠⣶⠀⠀⢰
⠀⠀⠀⠀⠀⣴⣾⣶⣶⣶⣶⡊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⡸⠀⠀⠀⠀⠠⠛⠃⠹⠀⠇⠠⠄
⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⡛⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣦⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⡀⢀⠠⠄⢀
⠀⠀⠀⡀⠀⠀⠀⡀⠀⠠⠀⢉⠑⢆⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡁⠀⢁⠀⢀⠀⢠⡀⠠⠀⠈⠁⢆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠢
⠀⠀⠀⠘⠀⠈⠀⠀⡀⠠⠀⠐⠄⠁⡀⢨⡀⠀⠀⠀⣄⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠸⢀⠈⠀⢀⣀⢀⣠⠊⠓⢀⠀⠜⠁⠀⠀⠀⠈⠂⢀⡀⠁⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠈⠀⠉⠀⠉⢄⡀⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⢄⡂⠐⣈⣖⡓⢼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉
⠀⠀⠐⠀⠀⠒⠀⣱⠠⢆⡡⢉⣡⡀⠃⡴⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠁⠈⠀⠈⡉⠂⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⢈⠂⠀⡘⠁⠀⠀⠹⠄⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠼⠄⣀⣀⡠⡀⠀⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠈⠉⢀⠣⡀⠀⠒⠂⠀⠀⠀⠃⠠⠆⠀⣠⣬⡄⠀⢥⣶⠆⡞
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣅⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣤⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠁⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠔⣀⡀⢈⣙⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠺⠶⠷⠶⠤⠿⠤⠀⠔⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⢈⠕⢢⡀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢡⠀⠀⠀⡀⠀⠐⢹⠄⠀⠀⠀⠀⠀⠀⡠⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠢⠀⠀⡄⠀⠂⠁⠀⠀⠀⠀⠀⠀⢰⠐⣐⠨⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠈⠉⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣄⠀⠀⠀⠀⢀⣀⣤⠄⠀⠠⠔⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠈⠛⡶⢶⠶⢞⣁⣀⣀⣠⡴⠊⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡤⣶⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⡷⠖⠂⠀⠀⠀⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⠶⠆⠀⠠⠄⠘⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠟⠀⢒⠶⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⠆⠈⠀⠈⠀⠛⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⣠⣤⣴⣶⡿⣿⣷⡀⠀⠈⠀⠈⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠲⢼⣷⣌⠛⣄⢠⣤⠴⢪⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⢅⣠⡆⠁⠀⠈⠓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠀⠾⠿⠃⠀⠀⠀⠀⠀⠙⠶⣤⡀
⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡀⠀⠀⢀⡀⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠙⡆
⠀⠀⠀⣠⠞⠀⠠⠤⠤⣄⡀⢻⡄⣀⢀⢶⣈⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣶⡄⠀⢹
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢷⣼⢃⣿⠶⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠸⡆
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢻⡎⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⢻⡆⠀⢰⠀⠀⠀⠀⠀⠹⣦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡟⠘⠁⠀⠀⡧
⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣨⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠐⠂⠀⢀⣾⠁⠀⠈⠳⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⡀⠀⠠⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⢀⣾⡇⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠒⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⠇⠀⡀⠠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⢦⠀⠀⢸⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠤⢄⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣠⣤⣼⡇⢸⡀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢀⡀⠀⠀⢡⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠅⠸⣇⢸⣿⣦⠀⠀⠀⠰⢶⣤⡶⢢⡟⣱⡦⡄⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠦⠂⢈⣎⢻⡄⣿⣍⠐⡰⠟⡉⠄⣈⡜⠢⠗⢸⣾⣶⠏
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠻⢛⣥⣠⣦⣄⡈⠙⢷⣌⢿⣿⣧⡁⠈⠛⠳⣽⠿⠷⠾⠿⠿⠿⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠋⡹⠀⠀⠛⢷⣝⠻⢿⣦⡀⣀⠈⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠸⣿⣿⣦⣍⣉⣾⣿⣷⣿⣾⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣇⠈⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠾⠞⠛⠛⠛⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠉⠀⠠⠔⠆⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠰
⠀⠀⠀⠀⡄⠀⠠⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⣀⡄⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠑⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣀⢀
⠀⠀⠀⠀⠐⠒⠃⣀⡩⠀⠀⠂⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⡀
⠀⠘⢀⡃⠀⠂⠰⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⢉⡀⠉⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⢀⠀⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠋⠉⠀⠀⠀⡂⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠠⠀⠣⠄⢶
⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠆
⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠒⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠁⢀⠀⢐⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢠⠀⠤⠀⠠⠠⠀⠀⠀⠀⠀⡀⠀⠞⠉⠱⠆⢀⡀⠀⠀⠀⠀⠀⠔⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠐⠂⠀⠐⠁⠀⠀⠀⠀⢰⠈⠁⢉⠉⡍⠉⠉⠱⠀⠀⠀⠀⢀⢠⠀⠨⡤⠀⠀⠀⠀⠀⠀⠐⠉⠀⠠⠐⠈⠑⢢
⠀⠀⠀⠐⠆⠀⠀⠀⡠⠀⠀⠈⠂⠈⠈⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣀⡁⠈⠈⡰
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠢⠤⠤⠔⠊⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⡄
⠀⠁⠀⠀⠀⢈⠀⠀⠀⠀⡄⠀⠠⠀⠰⠟⠛⠚⠆⠀⠀⠀⠀⠠⠅⠀⡤⠈⠀⠐⠤⠀⠀⠀⠀⠀⠠⠆⠁
⠀⣤⣶⢿⢻⣻⠀⠀⠀⠀⠉⠑⠚⠀⠘⠛⠛⠃⠛⠀⠀⠀⠎⠀⠀⡀⠈⠀⢀⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠠⡶
⠀⣿⡮⠿⠛⠛⠀⠀⡈⠁⠀⠀⠀⠀⠀⣀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⣠⡶⣿⡇⠁⠉⠃⢻⠿⠋⠀⠀⣼⣽⡀⠂
⠀⠁⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠰⠀⠇⠐⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⠾⠋⠀⠀⠀⠈⠛⠄⠀⠀⠀⠉⠉⠀⠐
⠀⣤⣀⣀⣀⣠⠀⠀⢠⣯⣿⣿⢧⡄⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠘⠁⠴⠄⠀⠀⠂⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰
⠀⠉⠚⠛⠒⠹⠀⠀⠻⣽⣷⣿⣿⠟⠀⠀⠀⠚⠉⠀⠁⠀⠀⠠⡀⠀⢀⠠⠀⠀⢀⠀⠀⢀⢤⡀⠀⠀⡄⠀⠀⠀⢈
⠀⠀⠀⠀⢀⠤⠰⠀⠂⠄⠀⠀⠠⠐⠀⠂⠄⠀⠀⠠⠂⠀⠉⠐⠀⠦⠀⠀⠀⠄⠂⠄⡀⠀⠣⠅⠀⠰⠀⠀⠀⠀⠘
⠀⠀⠉⢀⠀⠄⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠄⠀⢀⡀⠀⠈⠭⠂⠰⣲⠉⢑⢠
⠀⠘⠐⠀⠠⠀⠴⠞⡈⠀⠀⢨⡿⠉⢙⠀⠀⠀⠀⠀⢸⠛⢿⣿⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠁⠉⡀
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠸⡿⠤⠈⠉⠉⠉⠀⠉⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠜⡑⠐⠀⠖⠀⠤⠠⠤⠠⠄⠐⡇
⠀⠀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠘⠓⠖⠚⠒⠒⠒⠒⠒⠶⠳⠒⠂⠀⠀⢀⡀⠀⠐⠀⠳⠋⠀⠀⢄⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⣾⣥⠋⢀⠀⠀⠆⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⡄⠀⡀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠀⣀⠠
⠀⠠⠀⠀⢀⣿⠡⠐⠀⠀⠀⠃⢠⢳⠻⠛⡝⠫⢯⠖⡷⠀⡃⠀⠀⠀⢐⠰⡆⠄⢠⠀⢸⠰⡸⢀⣾⠋
⠀⠠⡄⢠⠀⠠⠀⠄⠀⢠⠀⡀⠹⣭⣶⣾⣶⠿⢟⣋⣁⠀⡇⠂⠒⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠅⠦⠀⠀⠤⠴⠤⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⢃⠠⣭⡢⠖⡲⣠⡆⡆⠀⠀⠀⠀⠀⠀⢌⣒⠀⢱⢱
⠀⠋⠉⠉⠉⠉⠉⠉⠉⠓⠀⢀⠠⢀⠠⢄⠀⡤⠀⠐⠤⢄⠈⠄⠙⠛⠐⠛⠒⢁⠃⡀⠀⠀⠐⠂⠄⢀⡀⠁⠀⣀
⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠈⠈⠀⠈⠊⠀⠑⠑⠀⠊⠈⠀⠀⠐⠄⣀⡠⠒⠁⠨⠀⠀⠂⠀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠌⠈⠤⠀⠀⠀⠀⠈⠉⠁⢀⣀⣀⣀⣀⡀⠀⠈⠁⠀⠧⠀⠀⡀⢴⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⡤⣤⣄⡄
⠀⠀⠀⢄⡀⢀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣟⣽⣻⣭⣿⠀⠀⠀⠀⡄⠁⠀⠁⠐⠀⠀⠀⠀⡀⠀⠀⡀⡎⠛⠶⠞⠃⠂
⠀⡀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠀⢀⠄⠀⡀⢀⣛⠃⢰⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠀⠀⢀⡅
⠀⠣⠤⠤⠤⠤⠤⠤⠤⠽⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠃⠀⠀⠄⠀⠄⠊⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣴⣿⣿⡿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⢸⡟⠛⠛⠃⠈⢿⡇⠀⠀⠀⠀⠀⠀⡠⢸⠁⠀⠀⠀⠀⠀⡍⢰⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣿⡆
⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠘⠀⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠋⠀⠙⢿⠇
⠀⠀⠀⠠⠠⠙⠋⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠆⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⣀⣀⡄
⠀⠀⠀⠠⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣅⠎⠀⠀⡀⠂
⠀⠀⠀⠀⠚⠀⠀⠀⠒⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⣀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠠⠜
⠀⠀⠀⠠⠈⠉⠑⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡁⣠⠤⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠐⠐⠒⠠
⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⣶⣄⠀⠀⠀⢀⣠⠖⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠁⠘⣿⠀⠀⢀⢸⠡⠤⠀⠀⠀⠀⡉⢲⠀⠀⢰⣿⣿⣿⡿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠀⠀⠸⠘⠀⠀⠀⠀⠀⠈⠃⠸⠀⠀⠻⠟⠙⠛⠁⠘⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠒⠒⠒⢦⠀⠀⠀⠀⠀⢀⠶⡆⠄⠰⡀⠀⠀⠀⠀⠀⢂⣀⢀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⠀⢃⠀⠀⠀⠀⠮⠄⠀⠀⠀⠑⡀⠀⠀⠀⠠⣨⡰⠁⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠢⡭⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠃⠀⠀⠀⠐⠀⠁⠀⠀⠃⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠑⠒⠠⠤⡆⠀⠀⠀⡄⣈⡁⣀⠤⠠⠁⠀⠀⠀⠀⢈⠄⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⢤⠀⣤⠑⢦⠀⠀⢧⣀⡅⡴⠢⠊⠀⢀⠴⠒⠀⠺⣠⠀⡘⠄⠀⠒⡄⠀⢠⠋⣧⠀⢰⠋⠙⠲⢍⡉⠓⠦⢤⣀⣀
⠀⠀⢀⢁⠨⣧⣽⡤⠊⣀⠠⠤⣀⠀⠑⠀⠊⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠩⢨⡆⠈⡷⠃⢠⠏⠀⠀⠀⠀⠈⠉⢳⡄⠀⢠⠇
⠀⠀⠀⠐⢋⠙⢀⠔⠉⠀⠀⠀⠀⠉⠒⢤⡀⠀⢸⢏⠉⠐⠒⠀⠐⠒⠀⠒⠂⢙⡆⠀⠁⣠⠏⠀⠀⠀⠀⠀⠀⡤⢺⠃⢀⡏⡄
⠀⠀⠀⠑⠁⡔⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⡆⠘⠳⠭⢀⣀⣀⣀⡀⠀⢂⣀⠹⠂⠀⢸⡁⠀⠀⠠⠀⠀⢀⡞⡔⠁⠀⢸⡸
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠉⠉⠳⡄⠀⡽⢀⡴⠶⣦⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠈⠻⢵⣲⣤⣀⠀⡜⣸⣁⣀⣠⠇⡇
⠀⠀⣰⢤⡀⠘⠦⣄⠀⠀⢷⡀⣀⡠⢢⠇⢠⠇⢸⠀⢀⡾⠀⢰⠊⠓⢦⠀⠀⢈⣧⣀⣀⣀⣀⣀⡙⠪⢿⠕⠛⠒⠒⠒⠚⠁
⠀⢰⡇⠀⠘⠢⡀⠈⢢⡀⠀⠙⠒⠚⠉⣠⠎⠀⠈⣉⣉⣀⡀⠈⠳⠤⢾⠀⢸⠿⠼⣧⠤⠶⠒⠚⡃⠀⠀⠀⠀⣠⠊⠉⠳⡀
⠀⠈⣿⡀⠀⠀⠈⠓⢤⡑⠢⠤⠤⠴⠞⣡⠖⠋⠉⠉⠀⠉⠉⢙⡆⡀⠀⠀⢸⡄⠀⢹⡄⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⢠⢃
⠀⠀⢸⣧⠀⢰⠋⢓⢦⠈⠳⡀⠀⢀⡜⠈⣇⠰⠀⠀⠀⠀⠀⣸⠀⠈⠳⣄⠀⣷⠭⣭⣿⡭⠭⠿⡇⠀⠀⠀⡟⠦⠤⠤⠤⠜⡃
⠀⠀⠸⡌⣇⠈⢦⣀⣹⠇⢀⡇⠀⢸⣔⠄⠘⡆⠀⠤⠄⠀⢀⣇⠀⠐⣡⠻⡀⢱⠀⠀⠈⣧⠀⢰⠇⠀⠀⠀⠙⢾⣤⣀⣠⠞⠁
⠀⠀⠀⠳⣌⠳⢤⣀⣀⣠⡾⠁⠀⣇⢊⡷⠴⠛⠋⠉⠉⠉⠉⠈⠙⠚⣅⣀⡇⠘⢆⣀⣀⣘⣀⡼⠀⣏⠹⡀⠀⣀⡬⠉⢤⣀
⠀⠀⠀⠀⠈⠙⠒⢚⣛⣉⣠⢤⣀⠈⡩⢄⠀⠀⠀⢻⡲⣦⣄⠀⠀⠀⠀⠁⢀⣴⣦⣍⣉⣁⣀⣀⣀⠈⠛⠧⣌⣓⠒⠒⠒⠋
⠀⠀⠀⣮⠐⣾⢍⠁⠤⠤⠀⠀⠈⠻⡀⠸⡀⠀⢀⠴⡛⠛⠿⠴⠒⠒⢦⡀⠸⣯⣝⣻⠶⠦⣥⣤⣭⣭⣓⠦⣀⠀⠉⠲⣄
⠀⠀⠀⣹⡆⠈⢳⣿⢶⣤⡀⠂⠀⠀⠱⡀⣇⠀⡏⠈⠀⠀⠀⠀⠀⠀⠂⢳⠀⢈⣛⠻⠿⠿⠿⠶⠶⣾⣭⡳⣮⠇⠀⠀⠸⡆
⠀⠀⠀⠻⣉⢝⡂⠻⠦⢯⠛⠷⣦⣄⡀⠘⢎⠀⢳⠀⠀⠀⣰⠠⡄⠀⠀⡜⠀⢸⣯⣭⣉⣒⣒⣒⡒⠤⢍⠛⠃⠀⢠⠶⠚⠣⡄
⠀⠀⠈⠲⡈⠙⠪⣗⢤⡈⠒⢢⠈⠙⠫⢕⠞⠀⠈⢧⣠⡀⠀⠀⢀⠀⣰⠃⠀⠸⢾⣭⡭⣤⣤⡭⠍⡑⢢⡇⠀⢀⡾⡤⠤⣼⡇
⠀⠀⠀⢺⣷⣤⡤⢤⠑⠮⡓⢤⣁⣉⠖⠀⠀⣀⠀⠀⠑⠚⠒⠲⠶⠚⠁⢀⣠⡤⠤⠤⠭⢭⣉⠉⠳⢤⣸⡄⠀⠸⠵⣦⣼⣟⡇
⠀⢀⣴⡿⠋⠉⠐⠉⠀⠀⠈⠑⠒⠁⣠⠔⠋⠀⠉⠓⠦⣄⡀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠨⠳⡀⠀⠀⢀⣀⣀⣀⣀⠀⠁
⠀⠀⣀⣴⣒⣒⣠⣤⣴⣶⣒⣤⠀⢸⣓⠒⠒⠒⠲⣒⡶⠤⢬⣑⣢⠀⢿⢄⠀⠀⠀⠀⠀⠀⠰⡔⠁⣠⠞⣹⠃⠈⠀⠈⠑⣄
⠀⠘⡄⣧⢹⠉⠉⠉⠉⠉⠀⡔⠀⢀⡼⠃⢠⢤⡀⠀⠀⠀⠀⠀⡜⠀⠈⠪⡝⣆⠀⠀⠀⠀⠀⡆⢰⡇⢘⠆⣴⠋⢻⣆⠀⠘⡄
⠀⠀⠈⡻⣆⠀⠀⠀⠀⠀⣴⡁⠀⠈⡷⠀⠀⠉⠀⠀⣏⣿⠀⠀⢸⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⢳⠘⡇⡇⠀⠙⠦⠾⢃⡤⣸⠁
⠀⠀⠀⠙⠺⢷⣶⣶⣶⠾⠓⠁⠀⠀⠷⠤⠤⠤⠤⠔⠦⠤⠤⠤⠼⠀⠀⠀⠘⢮⣇⣀⣀⣀⣀⡼⠀⠙⠮⣍⣙⠒⣉⣻⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⢤⣤⡤⠴⠒⠈⣨⠤⢆⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⡦⢰⣯⡤⠴⠒⠋⠁⠈⣉⣛⣳⡄⢦⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠛⠉⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠛⠶⠶⠦⡠⡖⠛⠉⣙⣉⣁⣹⡌⢣⣬⣉⣭⡙⣦
⠀⠀⠀⠀⠀⡠⡶⠛⠉⠁⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣍⣛⣛⣛⠛⠛⠛⠻⣿⣿⠯⠭⢶⠋
⠀⠀⠀⠀⠀⡄⠈⠓⠲⠶⠤⣴⣎⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠙⣇⠀⠀⠠⠤⠤⠤⠤⠤⠤⠔⠂⡾
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠶⠲⡒⠋⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣁⣀⣀⣀⣀⣠⠴⠚⠹⡇⠀⠀⠤⠤⠄⣤⠾⠛⠓⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⣳⡶⠛⠉⢁⢄⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⣟⠛⠶⠶⠦⢤⣼⣥⣄⣀⣀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠈⢦⠱⡄⠀⠀⠀⠀⠀⠀⢀⡴⢻⣀⣤⠶⠶⣾⠒⠒⠶⢬⡉⠉⠉⢓⠦
⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢳⡝⣆⠀⠀⣠⠴⢚⣩⣶⡟⠋⠀⠀⠁⠲⠚⠀⠀⠀⢹⣦⠴⠋⢸
⠀⠀⠀⠀⢠⡾⣏⣁⣹⣤⣈⣉⣙⡛⠛⠛⠲⠶⠶⠶⠶⣿⢌⡄⢪⡵⠚⣛⣿⡏⡰⠁⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⠶⠶⣶⣶⣶⣿⣿⣟⣁⣼⣞⣣⡼⡇⠁⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⠉⣍⢳⡄⠀⠀⠀⠀⢀⣈⣉⣉⠉⠛⠛⠳⠷⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼
⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢠⠚⠁⡼⠁⠈⠀⠀⠀⠀⠀⢀⡔⠐⣼⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠙⠶⠤⣤⣰⢡⠀⠘⢇⣀⣀⣀⣀⠀⢀⣠⡞⠁⣰⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣒⣒⣀⡀⠀⠀⠉⠉⢁⣠⡾⢃⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠋⠁⠀⠀⠉⠉⠙⠓⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠤⣄⠃
⠀⠀⠀⠀⠀⠀⠴⣱⣤⡄⠉⠀⠐⠀⡰⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠩⠀⠀⢇⣀⡸⠀⠂⡠⠄⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⠑⠤⠜⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢲⡁⠀⠄⠀⠐⠈⠒⠠⠢⠀⠂
⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⣀⢀⠀⠀⠂⡀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠁⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⡿⠃⠋⠉⠘⠈⠁⠁⠁⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠴⠀⢀⣐⡀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠈⠁⢈⣡⡀⣠⠤⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣚⢪⡟⠐⡋⠩⠄⠂⠄⢄⡀
⠀⠀⠀⠀⠀⠀⡜⢗⣘⡤⠌⡉⣤⡤⣖⣯⣷⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠌⣒⣒⠒⠈⠑⠂⠀⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠀⠁⠷⠧⠼⠚⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡦⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣖⡀⠀⠀⣤⠈⠐⠊⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⢀⢀⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣣⠄⠀⠀⠁⠈⠉⠃⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢒⠶⣶⣶⠶⠒⣢⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⣷⠿⠯⠽⠛⡿⣿⡿⠟⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⣠⠤⠒⠂⢼⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠑⠦⠤⣤⡯⠤⠖⠁⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣤⣤⣀⣀⣤⣤⡴⠶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠤⠤⣀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⡀⠀⢠⠀⠀⠁⠀⢀⠀⠀⠉⠲⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣄⣀⠀⠀⠀⠤⠀⠀⠉⠀⠘⠀⠀⠈⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠬⠤⠤⠤⣤⣄⣠⣤⣤⣀⣠⣤⣤⣤⣀⣀⡤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠳⢶⣤⣭⣿⣍⣀⣀⣀⣠⣴⢦⣤⣤⡶⠂⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡀⠉⠉⠉⠉⠉⠉⠁⣉⣠⣴⠖⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⣿⡀⠀⠉⠉⠛⠓⠚⠛⠛⠛⠉⠁⢀⣠⠄⠀⠀⠀⠈⠻⠷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠈⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⠶⠞⠋⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣠⠤⠒⠛⠋⠉⠉⠉⠉⠛⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣁⣀⣀⣀⠠⢤⣤⣄⣀⣀⡀⠀⠀⠀⣸⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⣀⣈⣙⠛⠛⠛⠉⠻⢶⣄⡈⠉⠉⠁⠀⠀⢠⣿⣿
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢶⣶⣤⣈⠉⠛⠿⣷⣦⣄⠀⠀⠉⠻⠷⠄⠀⠀⢀⣾⣿⠇
⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⣴⠟⠁⠘⠳⢦⣄⡉⠛⠿⢷⣦⣄⡉⠛⠿⣶⣄⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠀⠈⡙⠷⣤⣀⠈⠙⠻⢷⣦⠈⠙⠋⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠛⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡠⢖⡛⣈⣀⣉⠀⠁⣀⣁⣈⣁⣉⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠚⠀⠧⠭⠤⠧⠬⠥⠼⠼⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢰⠀⠀⢀⠴⢄⡠⠒⠢⡔⠁⠀⠀⢰
⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠁⠈⠉⠉⠛⠛⠲⠶⢦⣤⡤⠄⠀⠀⠐⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢘⠛⠷⢦⡄⠤⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣤⠞⢦⣤⣄⣀⣀⣒⡒⠀⠀⠀⠀⢀⣒⣒⣒⣒⣨⣥⣤⠚
⠀⠀⠀⠀⠀⠙⠐⡚⠆⠐⠤⠀⡿⠛⠓⠲⠾⠛⠛⡃⠐⠲⢐⠈⠩⠽⠏⠉⠉⣯⠉⠁⣀⣈⠤⢬⡁⠤⠭⠀⠀⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⡃⠈⢁⡀⡀⢢⠀⠠⠇⠀⠉⠠⣄⡭⣗⣖⣒⢶⣢⠶⣀⡉⠉⠉⣁⠰⠒⠒⠒⠚⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠚⠍⠑⠌⠾⠀⢨⠂⠒⠒⠞⣂⠎⢉⣳⣁⢋⣠⣄⠀⠙⠀⢀⡠⠄⢀⠬⠄⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠐⠀⠀⠖⢹⠆⠉⡄⠉⠀⠄⢸⣽⠡⠦⣌⢙⠐⠛⣛⣁⢉⣙⢀⣤⡠⢿⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⣼⡄⠸⢀⣠⠤⠔⠂⠉⠀⠳⠤⣄⣀⡉⠚⠟⢩⡟⠛⠉⠘⠉⠀⢒⣒⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⡀⢤⠀⠴⢦⣴⡀⠄⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⡤⠦⠀⠀⡰⢀⡀⠐⢠⠊⠱⠗⣠⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣂⠼⡁⠀⢈⡩⣼⡵⣼⡷⣐⢀⡣⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠘⠁⠨⡽⠀⠉⠛⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠕⠁⠒⠀⠀⣰⠄
⠀⠀⠀⡀⠀⠈⠢⠀⢄⠀⢠⠊⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⣀⣀⠀⠴⠚⢱⠞⠒⠞⠦⠤⠖⢠⣆⣶⢿⡦⠀⣀⣀⡤⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠈⢡⢦⠀⡠⠐⠉⠁⠀⢈⡖⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢙⠘⢂⣀⡉⢙⣛⣚⣉⡷⢏⠉
⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⣀⠒⠣⠀⢀⠠⢠⢾⣼⠄⠀⣀⡆⠀⢀⣴⠮⠲⡚⠀⠀⠀⣄⣙⢢⢴⢉⠩⠀⠈
⠀⠀⠀⠀⠀⠰⠔⠀⠁⠚⠀⠀⠀⠀⠀⠐⠒⢋⠁⣐⡬⠖⠁⠀⠈⠠⢰⣐⣇⣧⡴⠆
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠼⠓⠋⠁⠀⠀⠀⠀⠀⠠⢀⠈⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀
⠀⠀⢀⢤⡯⠴⠚⠛⢿⠄⠀⠀⠀⣀⠋⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⡠⢤⡀⠀⣤⣀⢀⠀⠀⠠⣤⣤⡄
⠀⠀⢸⡅⠉⠈⣀⣀⠈⣧⠀⠠⠊⠀⠀⠀⠀⠀⠀⢢⢣⠀⠀⢀⠔⠲⡢⡀⠀⠀⠀⢸⡆⠸⠀⠘⡇⠀⡻⢯⡟⠀⠀⠀⡇⠀⡆
⠀⠀⠀⢷⠈⠥⠀⠒⢂⠺⡄⠀⢄⠀⠀⠀⠀⠀⠀⢘⡼⠀⢠⠊⡀⡀⠘⢴⡄⠀⢐⠀⡇⠀⢑⠊⠀⠀⠑⡔⠁⠀⠀⢀⠇⠀⡇
⠀⠀⠀⢫⠔⣈⠉⠩⢤⡸⠇⠀⠀⠙⠀⡆⠒⢐⠘⠉⠀⠰⠁⠀⠈⠉⠀⠈⢳⠀⠘⢲⠚⠀⠀⢘⠀⠀⠃⡄⠀⠀⢠⠊⠀⠀⠸⢢
⠀⠀⠀⠈⠍⠀⠬⠅⠒⠂⠁⠀⠀⠀⡖⠒⠲⠖⢲⡆⠀⠁⠛⠛⠛⠛⠛⠋⠊⠁⠀⠀⠒⠀⠐⠊⠀⠀⠑⠁⠀⠀⡘⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠭⡭⡭⠭⠭⠭⠭⢭⠭⠭⠭⠕⠀⠀⡇⠀⠟⠑
⠀⠀⠀⢀⠔⡉⠤⠒⠨⢕⠢⡀⠀⠀⠀⠀⢀⡠⠐⠚⠓⠂⢄⠀⠀⠀⠀⢰⠸⠷⠃⣠⡤⣄⡹⠿⢤⠆⠀⠀⠀⠀⠋⠈⠉⠈⠁⢩
⠀⠀⢠⢡⢊⠤⡀⠀⠀⠀⠱⠰⡀⠀⠀⠰⡑⠁⡎⠀⠀⠀⠀⠑⠄⠀⠀⢸⠈⠀⡾⣥⡄⡀⣿⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⢈⢰⡃⠀⢟⠸⢸⣳⡇⠇⠅⠀⣀⣃⣀⣈⣁⣠⣤⣤⣤⣤⣸⣀⠀⢰⠀⠀⠙⣿⣁⣻⠟⠀⢸⡇⠀⡎⣤⣠⣤⢠⡄⣤⠠⢼⡆
⠀⠀⠈⢌⠓⡔⠁⠘⣍⣩⠞⡸⠀⠘⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠃⠸⠴⠤⠄⠉⠀⠈⠀⠤⠎⠇⠠⠁⠉⠀⡁⠉⠈⠈⠈⠵⠒
⠀⠀⠀⢀⠁⠯⠐⡂⠇⡀⠊⣠⣖⡒⢦⠀⠀⠀⣀⣀⣀⡀⠤⢀⠢⡄⠀⠀⣠⠀⠐⠒⢂⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠜⠀⠀⠀⢅⠅⠀⠟⢶⠲⠽⠀⠀⡎⢠⢢⢀⠠⡀⠑⢁⠿⠀⠀⣇⣤⠬⢤⣤⣴⠀⠀⡠⣴⣡⣤⣤⣤⣤⣤⣤⣌⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠀⠀⡄⠀⠀⣧⢄⣈⣘⣀⣡⢰⡩⠋⠀⠀⢸⠇⣀⡾⠿⡾⠀⠀⢠⠊⣠⠲⣠⣦⢴⠂⣦⣤⠙⢺
⠀⠀⠀⡤⠀⠒⠀⢠⡀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠚⠚⠂⠉⠁⠀⠀⠀⠀⠘⣎⠛⣃⣠⡇⠀⠀⡌⠣⠙⠚⠙⠁⠘⠂⠃⠋⠴⢺
⠀⠀⠠⢉⡀⠠⢀⣈⡅⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⣀⡀⢀⠀⠀⠀⠀⠀⡠⡀⠈⠉⠈⠉⣀⠀⣀⡈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁
⠀⠀⢰⠜⠉⠉⠁⠨⡄⠀⠀⡇⡧⣒⣒⣒⣒⣓⣒⣚⣓⣚⣒⣒⣒⣒⡂⡇⡇⠀⠀⣊⡉⡤⠁⠀⠨⠍⡂⠳⢢⣀⠀⠀⠤⠤⢄
⠀⠀⠀⠪⣂⠄⣐⠕⠁⠀⠀⡇⠧⠤⠤⢄⠀⠀⠀⠀⠁⠀⠀⢠⠤⠠⠤⠇⡇⠀⢰⠉⠂⡇⢸⠈⢨⠀⡌⢑⡞⠉⠀⢸⣁⣀⡌⡇
⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⡇⡏⠉⢹⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡇⡇⠀⠰⢗⠤⣇⣈⣈⣈⠤⣐⠇⠘⠦⠀⢘⠀⠇⠃⡇
⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠧⠇⠀⠸⠼⠀⠀⠀⠄⠆⠀⢀⡸⠼⠀⠀⠣⠇⠀⠀⠀⠉⠑⠂⠐⠊⠈⠀⠀⠀⠀⠀⠘⠦⠤⠦⠃
⠀⠀⡀⡀⡀⠀⣀⠀⣀⣤⣤⠦⠖⠀⠀⠀⣀⠠⠤⠤⣤⠄⢮⠘⠀⠀⠀⠀⠀⠀⢀⣠⣤⢄⠤⢒⡸⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⣘⣀⣘⣙⣀⣀⣋⣀⠀⠀⠀⠀⡠⢊⠔⠆⠀⡜⠀⠀⡰⢢⠀⠀⠀⠀⠀⠀⠀⣻⣷⠜⠀⠀⠀⠀⠀⠀⠀⢠⠒⠯⠽⠒⢤⡀
⠀⠘⡀⡄⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡁⢸⠈⠦⡄⠈⠒⢋⠔⡸⠀⠀⠀⠀⡠⣶⣲⣾⣷⣖⣶⣄⠀⠀⠀⠀⠀⣮⠤⠒⢊⡍⠴⡆
⠀⠀⣸⠮⡂⣀⠀⡠⠴⡅⠀⠀⠰⡀⣓⣀⣓⣒⡃⣐⣈⣐⣚⣀⠄⠠⡄⠴⠿⠿⠻⠿⠿⠞⠿⠿⠦⠤⡤⠀⢸⡒⣒⣉⡩⠄⠒⠁
⠀⠀⠀⠁⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⡤⢤⣀⢀⣀⣀⣀⣀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠚⡵⠓⢄⣈⠓⢤⣀⠀⠈⠉⠓⠦⣄⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⠎⢠⠊⢰⣓⠒⢮⡳⢄⠈⠑⣦⡀⠀⠀⠀⠑⢆⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⡴⠡⣞⡡⣞⠒⠺⢭⠉⣀⠞⣠⠞⣠⠟⠀⠀⠀⠀⠀⢳⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⠇⠸⢍⡑⠨⢉⠪⢕⡒⢚⡽⣡⠞⣡⠎⡝⡟⣩⣉⣉⣉⣑⣚⠓⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣿⣥⠢⢍⡲⢝⣋⡔⣡⠜⠁⢀⢁⡇⡇⢀⡖⣶⡄⢹⢱⠃⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⢠⢏⣴⠃⢰⠦⣍⠓⠿⠔⠁⠀⠀⢸⢸⢀⠇⠀⣙⠋⠁⡜⡞⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠹⡜⣎⢻⡀⠀⢣⡀⠩⣒⡒⠒⢲⠆⡞⣸⢨⠀⠸⣙⣿⠆⡇⡇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠛⠙⢦⣀⠉⠒⠒⠒⠊⣁⡄⣇⣿⣘⠒⢤⡤⠤⠤⢇⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢮⡉⢉⣩⣉⡜⠁⠛⠓⠬⠭⢭⣭⣭⡍⠩⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣈⡉⠉⠉⠉⠉⠙⠛⠉⠉⠉⣀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⡀⠄⠤⡀⠀⢀⠄⠀⠐⢒⠒⠤⡀⢠⢄⢀⠒⠂⠐⠀⠐⢦⠀⣀⠀⢀⣤⡶⠶⣀⠄
⠀⠀⠀⠀⢰⠁⠀⠀⢸⡐⠁⠘⢀⠤⠨⡁⡄⠑⠘⠉⠀⠍⢣⠲⠢⢴⡞⠀⠓⠀⣺⡿⡯⠑⣶⡇⡁
⠀⠀⠀⠀⠀⠑⠀⠔⠃⢃⠀⡄⠈⢄⠀⡐⠀⡐⢠⠁⢉⠈⢐⠈⡼⢮⠤⡀⣄⠀⣿⣯⣚⣎⣿⣷⠃
⠀⠀⠀⠀⠀⢀⠄⠀⢠⠈⢆⠀⠠⠀⠀⢚⠐⠁⠸⣀⡒⢠⠏⠀⡇⠀⠀⠸⣸⠀⠙⠛⠓⡿⠟⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⢁⡀⠀⠈⠀⠀⠤⡄⠀⠀⡀⡀⠈⠮⠶⠴⠮⠟⠀⢖⠀⠀⡇⢰⠓⠇
⠀⠀⠀⠀⠀⡡⠴⠖⠒⠦⣤⠘⠀⠀⠀⠀⠀⠀⡗⠒⡌⠣⡀⠡⠀⣂⣆⠀⣤⠠⢠⡄⠀⠇⠈⠈
⠀⠀⠀⠀⠘⠆⠀⠀⠈⠀⠇⠸⡉⠥⢀⡁⠄⣀⡃⡰⢰⠀⠈⠁⣏⣀⣉⣉⣁⢈⣧⣶⠘⠄⢀⢄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⠐⠁⠁⢣⠀⠀⠀⠀⡜⠁⠐⢁⠀⢀⡀⠙⠉⠋⡉⠉⠉⠛⠁⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠈⢆⠀⠤⠠⠀⡀⡀⠉⠀⢀⡅⡆⣄⠀⡴⠤⠤⢤⣭⢀⠁⣦⠑⠂⡍⠑⠀⠀⡤⠤⢄
⠀⠀⠀⠀⠀⢴⡀⢰⠢⠀⠀⠒⠁⠀⠀⢥⠼⢿⣼⠀⠑⠢⠀⠐⠁⡈⡀⣄⠀⡘⠁⡜⠀⠀⣟⣻⠁
⠀⠀⠀⠀⠀⠑⠀⢐⠉⢄⠀⠶⢧⣈⠐⢌⠑⠉⢠⡂⠐⠒⠀⠐⣂⠀⠑⠄⠀⠡⢊⢄⠀⠀⡃⢰
⠀⠀⠀⠀⠀⠀⢱⠀⡁⢠⠠⠈⠢⣉⠛⣦⠆⠀⢀⠀⠀⠉⠉⠁⢸⡒⠢⠀⢠⠊⠉⡷⠃⠀⡇⢨
⠀⠀⠀⠀⠀⠂⠘⠀⠃⠁⢐⠍⠵⠀⡠⡀⠀⠀⠸⠀⠀⠀⠀⠀⣠⣬⡠⠠⡊⠀⢈⠁⠀⠀⠯⠽⠄
⠀⠀⠀⠀⠐⣧⣴⣦⣆⣇⣈⡒⠀⠊⠀⠈⠢⠠⠀⠑⠠⠤⠤⠐⠁⠀⠀⠀⡌⠲⡁⠀⠀⡠⡄⢤
⠀⠀⠀⠀⠀⠇⠀⠀⣀⡃⡆⡅⠀⢁⣈⡀⣨⠤⢄⠀⠈⠚⠋⠟⢋⠂⣰⠁⣋⢉⣋⡂⠀⠈⣿⡊
⠀⠀⠀⠀⠀⢈⠉⠘⠉⠟⠒⠀⢸⠀⠀⠀⡁⢐⣼⡇⠆⡞⡇⠷⢾⠀⠇⢀⠀⠀⡈⡑⢀⠎⠀⠱⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠉⠁⠉⠉⠈⠀⠀⠐⠙⠑⠛⠈⠀⠈⠒⠄⠀⠐⠁⠈⠂⠠⠬⠁

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

⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⢖⢢⡵⠦⠶⣂⢆⣠⢀⠀⠀⠀⠀⠶⠤⠈⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠠⠄⣐⣇⣬⣥⣽⠖⣃⣿⣿⡾⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣶⣬⣍⡣⣛⣯⣾⡷⠖⠛⠉⠀⣠⡴⠎
⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⣦⠀⠀⠈⠘⠛⠋⠉⠁⣀⣠⡄⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⣀⠀⠄⠈⠀⠀⠀⢠⠀⠀⠀⠈⠛⠳⢤⡀⡀⣶⠾⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠀⠆⠀⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠡⣀
⠀⠀⠀⠠⠀⠑⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢇⠀⠃⢄⠁
⠀⠀⠘⠢⢀⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠤⠆⠘⠃⠀⠀⠠⠄
⠀⠀⠀⠀⠘⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠁⠀⠒
⠀⢀⠄⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠠⢄⡀⠀⠈⠀⠤⠀⠀⠐⠒⠃⠀⠀⠠⢀
⠀⠃⣔⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠃⠒⢄⠀⣠⢄⠀⠀⠀⠀⢀⡠⠄⠠⠂⠁
⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠈⠂⠈

⠠⢹⡀⢀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠉⠐⠠⡀⠀⠈⡁⠈⠀⡠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠀⠲⡀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿
⡄⠠⡀⠙⠀⢠⠁⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⣀⠀⢀⡀⠄⠀⠀⠀⠀⠀⡰⠀⠘⢧⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡄
⠠⠀⠀⠀⠀⠈⡀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠄⠙⠳⠶⠶⠶⠞⠉⠀⠀⠀⠒⠀⠀⡇
⠀⠣⡀⠀⠀⠀⠑⢄⠀⠀⠀⠠⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠉⠂⣄⠀⠀⠀⠉⠒⠂⠤⠤⠀⠐⠊⠔⠈⠉⠉⠍⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠄⢀⡤⠚⠈⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠜⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠂⠀⠀⡇
⠰⡉⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡘⠀⠠⡀⠁⠑⠠⠄⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⢤⡀⠀⢀⠴⠊
⠀⠈⠄⠀⠀⠀⡠⠔⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠈⠐⠂⠤⠤⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸
⠀⠀⠈⢀⡴⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠛⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⢠⡾⠋⠙⢷⡄⣴⠟⠉⠻⣦⠀⣿⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠸⣇⠀⢀⣼⠇⢿⣀⠀⢀⡿⠀⣿⢀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠉⠛⠛⠁⠀⠀⠙⠛⠋⠁⠀⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡦⠀⣰⣧⠀⣰⠚⠓⠀⣶⡴⠂⣰⠚⠓⠂⢰⣛⡆⣰⠚⠳⡄⢰⠀⡆⢰⣦⢰⡆⣾⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠠⠟⠙⠇⠘⠦⠴⠂⠿⠱⠄⠙⠮⠽⠃⠸⠻⠄⠙⠦⠴⠃⠸⠶⠇⠸⠆⠻⠇⠻⠴⠏


⡀⠀⡖⠒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠈⢂⠹⡉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠔⠁⣠⠎⠑
⠄⠘⠀⠇⠀⢡⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⡔⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠴⠋⠁⠀⠀⠘⢄
⠀⠰⢀⠆⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⠈⢉⠳⠠⡄⡀⠈⠑⠆⠀⢸⠀⠀⠀⠀⠀⠀⢀⢀⠀⠁⠀⡄⠀⠀⠈⠢⢄⠀⠀⠀⠀⣠
⠔⠚⠁⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠢⠀⠈⠉⠀⠀⠁⢨⣀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠡⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠑⠤⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠁⣒⠂⠀⠀⢈⡠⢃⡠⠄⠀⠐⠦⠤⣀⡀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡜⠁⠀⠀⠀⠁⠀⠀⠀⠈⢢⠀⠀⠀⠀⠑
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠠⡀⡠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠐⢤⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⡴⠋⠁⠀⠀⠈⠙⢷⣄⠀⢸⠃⠀⠀⠀⠀⠀⠔⠂⠉⠁⠒⠄⠀⠄⠀⢃⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⡜⠀⢱⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠀⡀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠀⢀⠀⢁⠀⠀⠑⠤⣀⠀⠀⠀⣀⠤⠞⠁⠀⠀⠈⠀⠹

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠒⠉⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⡖⠀⠠⢄⡀⢀⠀⠂⠙⡏⠀⠀⠀⠠⠫⠋⠀⠀⠀⠀⠀⢠⠛⠒⠀⠉⠁⠀⠛⠋⠇
⠀⢰⡥⠒⠂⠠⠤⣀⣀⠙⢆⠀⠀⠀⠀⠀⠈⠒⠤⣂⢀⣀⣀⡠⠀⠀⠀⠀⢠⢁⠄⡌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⢀⢰
⠀⢸⢠⠀⣁⠀⠘⠁⠀⠢⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡹⡅⠀⠀⠀⠀⠀⢁⠈⡰⠀⠀⠐⠁⠀⠐⠀⠂⡈⢀⠡⡀⠀⢠⡘
⠀⠈⠒⠠⠁⠅⠀⠉⠃⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⡅⡔⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠆⡂⠐⠀⠀⠁⠠⠙⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⣽
⠀⠀⠀⠀⣀⠞⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡀⠀⠀⠀⠟⠀⠀⠀⠠⠬⠅⠊
⠀⠀⠀⢈⡒⠲⠿⣐⠀⠄⡀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠐⢖⡈⣠⠀⠐⡌⠑⠠⣄⡱⡄⠀⠈⠀⠉⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈
⠀⠀⠀⠈⢣⠑⢄⠈⠳⡀⠈⡢⠃⠀⠀⠀⠀⡀⠠⠤⠴⠀⠒⠂⠀⠈⠉⢉⡉⠀⠐⠒⢀⠀⠀⠀⠀⠀⠔⠈⠠⡈⠂
⠀⠀⠀⠈⡀⠱⡄⠑⡀⠈⠉⠀⠀⠀⠀⠎⠀⠀⣴⠂⠀⡴⢠⡖⣰⡆⠀⡜⣧⠀⠀⠀⢈⠀⠀⠀⠀⠀⡠⠄⠂⠐⠉⢄
⠀⠀⠀⠀⠹⡀⠸⢀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⣼⠟⠓⠈⠁⠈⠁⢀⡉⠉⠀⠀⠀⣨⠀⠀⠀⠐⠀⠀⢀⠀⠂⠀⠘⠮⠨⠃
⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠈⠁⠀⠀⡀⠀⡀⠀⡀⢰⡄⡤⣀⢠⡖⣺⣧⡆⢌⡶⢀⠇⠀⠀⡄⠀⠀⠀⢬⠀⠀⠀⠁
⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢡⠀⣹⠞⠛⢾⠜⠓⠿⠈⠉⠈⠋⠉⠀⡠⠊⠀⠀⠀⠀⠁⠁⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢔⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀⣄
⠀⠀⠀⠀⠘⠀⠀⠀⢀⢄⠄⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠉⠁⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠌⡀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢤⡆⢄⣀⢄⢤⡎⡄
⠀⠀⡐⠁⠊⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠡⠀⢐⠀⠀⠀⠀⠀⠠⠌⠏⠀⡄⠀⠊⠀⠈⠁⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠖⠂⠀⠂⠀⠀⠀⠀⢈⡠⠁⠀⠐⠋⠁⠠⠀⠀⠀⠀⠀⠀⠪⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡠⠒⢒⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢄
⠀⢘⢀⠎⣀⢨⠏⢲⠨⡈⢆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡌⢀⠂⠙⢓⡄⠀⡃⠢
⠀⠈⢌⠲⡄⠠⣖⠫⣀⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕⠀⠀⠀⠀⠐⡠⠈⠀⠀⠈⠁⠀⠀⠀⡆⢀⣤⡴⠟⠡⣠⠗⠀⡅
⠀⠀⠈⠣⢍⠢⠬⢓⡣⠞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⢔⠊⢉⡠⠎
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠎⠀⠰⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⠀⠀⠀⠀⠈⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠁⠀⣠⣤⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡜⠁⠀⠀⠻⠋⠀⠀⠀⢸⣷⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⣶⡆⠀⠀⠀⠈⠉⠀⠀⢀⣦⡀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢣
⠀⠀⠀⠀⠀⢀⠞⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⡠⠷⡀
⠀⠀⠀⠀⢠⣿⣷⣄⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⣀⣴⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⣀⠈⠉⠑⠒⠒⠒⠠⠤⠤⠤⠔⠒⠒⠒⠊⠉⠀⣀⣤⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠐⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠒⠋⠉⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠠
⠀⠀⠀⢤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠙⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡀⠀⠀⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠐⠒⠐
⠀⡀⠀⠀⠀⠈⠄⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⡄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠁⠀⠀⠀⣤
⠀⢁⠠⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⢀⡂⠀⠀⠀⠀⡁⠀⢀⡀⣄⡤⢠⠠⠀⠁
⠀⠈⠠⠬⠀⠈⢀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠀⠘⡁⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠁⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⡉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠂⢀⡀⠸⣁⠘⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⢀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠆⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠠⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠇⠘⠓⠂⢂⠀⠀⠀⠀⠀⠀⠤⠄⢙⣒⣂⣉⡠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠈⠀⠁⠀⠀⡀⠀⠀⠐⠀⣀⠤⠀⠠⠠⠤⣀
⠀⠀⠀⠁⠠⠀⠁⠀⠀⠀⠀⠀⠸⡀⠖⣀⣄⠲⠐⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠺⠂⠀⠀⠀⠀⠀⢀⡈⠀⣀⡀⢃⡁⣀⣀⢱
⠀⠀⠀⠈⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠈⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣠
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠂⠀⠀⠁