.⣠⣤⣤⣤⡀⠀⠀⢀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣻⣻⣻⣻⡿⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⣴⣻⣻⣻⣷⣄
⢸⣻⣻⣻⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣻⣻⣻
⠀⠻⣻⣻⠏⠀⠀⠀⠀⣶⠿⠿⢿⣷⣄⢠⡿⠿⠶⠦⠀⢹⣻⣻⣻
⠀⠀⢈⡏⠀⠀⠀⠀⠈⠑⠺⣻⠟⠉⠁⠈⠛⢿⠆⠀⠀⠀⢻⠋⠁
⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠂⠀⢀⠀⢠⡄⠀⠀⠀⢸⡀⠀
⢀⣴⡇⠀⠀⠀⠀⠀⠀⠶⢿⣻⣉⣛⣻⣻⣛⣉⡻⣦⠀⠀⠀⣇⠀
⣾⣻⡇⠀⠀⠀⠀⠀⠀⠄⢸⡟⢿⣯⣭⣭⣽⣻⠃⠈⠀⠀⠀⣻⣧
⣻⣻⣻⣦⡀⠀⠀⠀⠀⠈⠿⠶⣭⣭⣬⡭⠁⠀⠀⠀⢀⣼⣻⣻⣧
⣻⣻⣻⣻⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣻⣻⣻⣻⣻
⣻⣻⣻⣻⣻⣻⣻⣻⣻⣷⣶⣶⣶⣶⣶⣾⣻⣻⣻⣻⣻⣻⣻⣻⣻
⠀⣾⣻⣻⣻⣻⡿⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⣴⣻⣻⣻⣷⣄
⢸⣻⣻⣻⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣻⣻⣻
⠀⠻⣻⣻⠏⠀⠀⠀⠀⣶⠿⠿⢿⣷⣄⢠⡿⠿⠶⠦⠀⢹⣻⣻⣻
⠀⠀⢈⡏⠀⠀⠀⠀⠈⠑⠺⣻⠟⠉⠁⠈⠛⢿⠆⠀⠀⠀⢻⠋⠁
⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠂⠀⢀⠀⢠⡄⠀⠀⠀⢸⡀⠀
⢀⣴⡇⠀⠀⠀⠀⠀⠀⠶⢿⣻⣉⣛⣻⣻⣛⣉⡻⣦⠀⠀⠀⣇⠀
⣾⣻⡇⠀⠀⠀⠀⠀⠀⠄⢸⡟⢿⣯⣭⣭⣽⣻⠃⠈⠀⠀⠀⣻⣧
⣻⣻⣻⣦⡀⠀⠀⠀⠀⠈⠿⠶⣭⣭⣬⡭⠁⠀⠀⠀⢀⣼⣻⣻⣧
⣻⣻⣻⣻⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣻⣻⣻⣻⣻
⣻⣻⣻⣻⣻⣻⣻⣻⣻⣷⣶⣶⣶⣶⣶⣾⣻⣻⣻⣻⣻⣻⣻⣻⣻