⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣟⣛⣛⣻⣟⣛⣁⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣛⣛⣛⣛⣛⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴
⠉⠛⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠛
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣀⣠⠤⢶⣤⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠘⣦⡄⠀⠀⢀⡀⠀⠀⠀⠀⢀⣿⣿⡇⠀
⠀⠀⠀⣿⣿⡄⠀⠀⠀⢀⠋⠈⠀⣨⣿⡏⢳⡀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣹⢿⡀⠀⠀⠙⣦⠀⠀⠀⢸⣿⣿⠁⠀
⠀⠀⠀⢿⣿⣇⠀⠀⠀⣾⣀⠄⡐⣿⣿⣿⣸⡇⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⣤⣴⣿⣼⣷⡄⡄⢀⣼⠀⠀⢸⣿⡿⠀⠀
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠙⢿⣀⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⡟⠻⣿⣿⣷⡀⠀⠈⢿⣿⣿⣿⣷⣧⡾⠃⠀⢠⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣦⣀⠀⠀⠉⠛⠛⠉⠁⠀⣀⣴⣿⣿⠟⠀⠀⠘⢿⣿⣷⣄⠀⠀⠉⠙⠛⠋⠉⠀⣠⣶⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⣽⠻⢿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠛⢿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢲⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀ ⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀.⠀⠀⠀⠀⠀⠀⣾⣿⠖⠲⠶⢶⣶⣶⠖⠶⣿⣷⠂⠀⠀⠀⠀⠀ ⠀ ⣼⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀.⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀.⠀⠀ ⣠⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⠤⠤⠤⠤⠴⠾⠋⠀⠀⠀⠀⠀ ⠀ ⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⣀⣴⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀