⠀⠀⠀⠀⢀⣴⣶⠿⠟⠻⠿⢷⣦⣄⠀⠀⠀
⠀⠀⠀⠀⣾⠏⠀⠀⣠⣤⣤⣤⣬⣿⣷⣄⡀
⠀⢀⣀⣸⡿⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠙⣷
⢸⡟⠉⣽⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿
⣾⠇⠀⣿⡇⠀⠀⠘⠿⢶⣶⣤⣤⣶⡶⣿⠋
⣿⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⢿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀
⠘⠻⠷⢿⡇⠀⠀⠀⣴⣶⣶⠶⠖⠀⢸⡟⠀
⠀⠀⠀⢸⣇⠀⠀⠀⣿⡇⣿⡄⠀⢀⣿⠇⠀
⠀⠀⠀⠘⣿⣤⣤⣴⡿⠃⠙⠛⠛⠛⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠙⣿⣧⠀⣤⣶⣄⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣴⣮⡿⣿⡟⠛⠁⣙⠿⠿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⣿⣿⣾⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⡇⢿⣿⡇⠈⠉⠻⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠧⠿⠿⠇⠀⠀⠀⠀⠿⠿⠿⠿⠗

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀
⣤⣶⣶⡿⠿⠿⠿⠿⠿⣶⣶⣶⠄⠀⠀⠐⢶⣶⣶⣿⡿⠿⠿⠿⠿⢿⣷⠦⠀
⠙⠏⠁⠀⣤⣶⣶⣶⣶⣒⢳⣆⠀⠀⠀⠀⢠⡞⣒⣲⣶⣖⣶⣦⡀⠀⠉⠛⠁
⠀⠀⠴⢯⣁⣿⣿⣿⣏⣿⡀⠟⠀⠀⠀⠀⠸⠀⣼⣋⣿⣿⣿⣦⣭⠷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠁⢀⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡗⠶⠶⠶⠶⠶⠖⠚⠛⠛⠋⠉⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.

⣽⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣧⣤⣤⣤ ⡇⢸⣿⡇⢸⣿⠀⣿⠟⠁⣿⡇⢸⡟⢀⣿⠀⣿⡿⠁⢸⣤⡄⢠⣤⣿⠃⡀⢿⣿ ⡇⢠⣤⡄⢸⣿⠀⠋⣰⠀⣿⡇⢨⡀⢺⣿⠀⠟⣠⡇⢸⣿⡇⢸⣿⡏⠰⠧⠈⣿ ⣇⣸⣿⣇⣸⣿⣀⣾⣿⣀⣿⣇⣸⣿⣀⣻⣀⣴⣿⣇⣸⣿⣇⣸⣿⣀⣿⣿⣆⣸

⣿⡇⠀⢸⣿⠀⢠⣿⣿⡄⠀⣠⣾⣿⣿⠀⣿⡿⢿⣷⠀⢠⣿⣿⡄⠀⠀⠀⣿⣿⣿ ⣿⡟⠛⢻⣿⢸⣿⣤⣤⣿⢸⣿⡄⠀⠀⠀⣿⡿⠿⠛⢸⣿⣤⣤⣿⠀⠀⣸⡿⠀⣿ ⣿⡇⠀⢸⣿⢸⣿⠉⠉⣿⡇⠙⢿⣿⣿⠀⣿⡇⠀⠀⢸⣿⠉⠉⣿⡇⣶⡿⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠃⠀⣤⡄⠀⠠⣤⠀⠀⢤⡄⡠⠤⣤⡀⡠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⢸⡏⠀⠀⢸⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⢀⠄⠀⢿⡇⠀⢀⣿⡀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠊⠁⠀⠀⠈⠛⠒⠁⠛⠃⠐⠚⠛⠂⠐⠚⠓⠂⠐⠛⠓⠂⠀⠀