⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠝⠛⢩⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⠴⠞⠙⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠯⠭⠍⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣏⣀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣶⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣷⣦⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣌⠑⠤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣄⠉⠓⢤⡀⠀⠀⠀
⠀⠀⡇⣷⡀⠀⠀⣀⣀⣀⣠⣄⣠⣤⣄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠈⢦⡀⠀
⠀⠀⠸⡌⢿⣄⡀⠈⠙⠛⠛⠛⠛⠛⠛⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢂⠀⠙⡇
⠀⠀⠀⠈⠑⠪⣑⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠒⠻⠭⠭⠭⠭⠭⠭⠛⠛⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⠤⠤⢤⠖⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡮⣗⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⡾⠀⠀⠀⠀
⠀⠀⡀⡒⡲⠔⠴⠰⢀⠆⢔⣄⢆⠰⣀⠜⣉⡙⣉⣍⡉⡩⡭⡍⠛⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠑⠀⠑⠀⠚⠀⠬⠎⠽⠭⠇⠒⠠⡄⠀