⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡰⣆⣼⣟⡀⣼⢇⠀⢸⡷⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⢰⣧⡪+⠿⣿⣿⣴⣃+⡀⣧⢸⣧⢿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀,⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿+⣟⣿⠟⠻⣯⡉⣹⣿⣿⣛⣿⣿⡏⢀⡔⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀*⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡿⣿⠿⣿⣒⣿⣿=⣿⣷⣾⣿⣿=⣿⠧⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀*⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣎⣹,⣿⣿⠟⠉⣹⣿⣿⣅⢨⣉⡿⠝⠦⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⣥⣀⠀⣿⡟⣤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠥⢿⠙⠳⡶⢿⣿⡃⠹⣇⢉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠟⢿⣷⣿⣿⣿⢻⣷⡄⠀⠀⢀⣞⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⣾⠁⠀⣿⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⣷⣟,⣦⣿⣿⠿⣿⡄⣼⡟⣷⣆⣾⡷⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀
⢻ ⣯⣿⣷⣿+⣿⣿⣿⣿⣶⣿⣛⣉⠤⠔⠊⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⢀⣤⣄⣿⣿⡄⣴⣶⣦⣿⣴⣶⠢⡄⠀⠀
⣟⡭⠽⣿⣿⣿,⣿⢿⣿⣿⢿⡇⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣇⣄⠀⠀⣾⡟⢿⣿⣿⣴⣫⣿⣿+⣿⠟⣻⣤⣧⠀⠀
⣷⣄⣴⡿-⢻⣿⣿⣿⣟⢙⢯⠀⠀⡀⠀⠂⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠪⢷⣴⣿⣿⣾=⢿⣿,⣿⣟⣽⠋⣏⣳⣿⣿⣟⠀⡀
⠙⣿⣿⡿⠛⢹⣿⣿⡛⢿⣦⣳⠈⡀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢄⣽⣿⡿⠛⢳⣿⣿⣿⡏⠉⣻⣹⣿⣿⣿⣁⣀
⠀⠉⣿⢀⠀⠘⣿⠂⠙⢻⡿⠭⠤⠀⠀⠁⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣶⣶⣿⣿⡏⢻⣷⡿⠻⠟⢻,⠈⠛⢧⠄
⠀⢠⡇⠀⠀⠀⢿⣦⠄⠀⠀⠀⠀⠃⠀⢣⣈⡇⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠻⠛⠛⠛⣿⠁⢸⡇⠀⠀⢀⣼⠀⠀⠀⠓