⠀⠀⠀⠀⠀⠀⣀⣀⢀⠤⠠⠦⠄⠄⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠖⠁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀
⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀
⠀⠀⠸⠅⢀⠔⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀
⠀⠀⠀⠉⠎⠀⠀⠀ ⠉⠠⣶⡄⢰⣦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀
⠀⠀⢀⣤⠖⠉⠉⠒⠤⠒⠂⠒⠄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡑⠀
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠑⠢⣀⣧⠀⠀⠀⠀⣠⠃⠀
⠀⠀⠘⢾⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠈⠓⣖⠒⢊⠁⠀⠀
⠀⠀⠀⠀⢘⠢⡀⠀⠀⠀⣠⠛⠂⠀⠀⠀⠀⠀⠀⠘⣆⡏⢣⠀⠀
⠀⠀⠀⠀⠘⡃⠈⠙⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡜⠀

⡠⠒⠒⠦⣄⠀⠀
⢧⠀⠀⠀⠀⠑⢄⠀⣀⣀⡀
⠀⠑⠤⡀⠀⠀⡼⠋⠀⠀⠈⢣
⠀⠀⠔⠚⠓⢚⡅⠀⢀⡴⠁⠈⡆
⠀⢀⢎⣈⠤⠨⠊⠉⠁⠀⠀⠀⠱⡀
⠀⢸⢀⢔⣒⠒⠒⠒⠤⣀⠀⠀⠀⢱
⠀⠘⢥⠘⠋⠀⣤⠀⠀⣶⠑⡄⠀⡜
⠀⠠⠖⢻⠁⢪⠭⣀⣀⣀⣠⠧⠊⠀
⠀⠈⣗⠕⡐⢰⣉⡁⢲⣃⣀⠀⠀⠀
⠀⠀⡄⢸⠉⠀⠀⠉⠁⣇⣨⠀
⠀⠀⠑⠚⠢⠤⠄⠒⠊

⢀⣤⣄⡀ ⁺
⣇⠈⠙⠿⣦⣀⣀⣀⣤⡴⠶⠛⢓⡄
⠈⠛⠛⠛⢋⡿⠋⠻⣯⡑⠒⠛⠋
⠀ ⁺⠀⢠⡟⠀⠀⠀⠘⣿⣆⠀ ⁺
⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿
⠀⠀⠀⣿⣷⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢸⣿⡄⠀⠀⠀⢷⣄
⟡⠀⠀⢸⣿⠃⠀⠀⠀⠀⠉⠀⠀⁺
⠀⠀⠠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⣠⣾⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀
⠀⣶⣿⣦⣜⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⣴⣺⣦⣙⣿⣷⣄⠀⠀⠀
⠀⣯⡇⣻⣿⣿⣿⣿⣷⣾⣿⣬⣥⣭⣽⣿⣿⣧⣼⡇⣯⣇⣹⣿⣿⣿⣿⣧⠀⠀
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⢀⠠⠤⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠐⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠀⠀:¨ ·.· ¨:
⠀⠀⠀⠀⢰⡿⠉⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⠃.⠀⠀`· . ꔫ⠀
⠀⠀⠒⠒⠸⣿⣄⢀⣃⣿⣿⡟⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠚⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠘⠠⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠁⠀⠒⠤⠀⠀⠀⠀
⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀
⠁⠃⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣦⣀⠀⠘⠛⠛⠃⠸⠿⠟⣫⣴⣶⣾⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠹⣿⣶⡾⠛⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠈⠉⣀⡀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠀⠀⢠⣾⠟⠃⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀
⠀⢀⣠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀
⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠋⠀⠀⠀