⢀⡠⠤⢐⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢤⣶⣷⣶⡿⢿⣿⡿⡟⢽⣭⠦⢬⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⣺⠛⠁⠀⠀⠀⠀⠀⠈⠉⠒⠿⢶⣎⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣔⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀
⠀⠀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀
⠀⢀⣰⣿⠀⠀⡴⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣀⠀
⢠⠏⢠⣿⠀⠰⡇⠀⠀⠉⠀⠀⣶⡀⠀⠀⢀⡤⢄⠀⠈⣿⣷⠀⢳
⠘⠆⣼⣻⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⠀⠈⠇⠀⢸⣿⢀⠏
⠀⠀⠁⠘⡆⠀⠀⠀⠀⢀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢣⣀⣠⠏⠀⠀⠀⠀⠀⠀⣠⠏⠸⠇⠀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠃⠄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠏⢀⡀⠀⢀⢤⡀
⠀⠀⠀⣖⣦⠀⣀⡠⠄⠂⠉⢲⠂⠤⠔⠊⣹⡀⠀⠀⠀⠉⠉⣰⡃

⢀⡠⠤⢐⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢤⣶⣷⣶⡿⢿⣿⡿⡟⢽⣭⠦⢬⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⣺⠛⠁⠀⠀⠀⠀⠀⠈⠉⠒⠿⢶⣎⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣔⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀
⠀⠀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀
⠀⢀⣰⣿⠀⠀⡴⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣀⠀
⢠⠏⢠⣿⠀⠰⡇⠀⠀⠉⠀⠀⣶⡀⠀⠀⢀⡤⢄⠀⠈⣿⣷⠀⢳
⠘⠆⣼⣻⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⠀⠈⠇⠀⢸⣿⢀⠏
⠀⠀⠁⠘⡆⠀⠀⠀⠀⢀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢣⣀⣠⠏⠀⠀⠀⠀⠀⠀⣠⠏⠸⠇⠀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠃⠄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠏⢀⡀⠀⢀⢤⡀
⠀⠀⠀⣖⣦⠀⣀⡠⠄⠂⠉⢲⠂⠤⠔⠊⣹⡀⠀⠀⠀⠉⠉⣰⡃

⢀⡠⠤⢐⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢤⣶⣷⣶⡿⢿⣿⡿⡟⢽⣭⠦⢬⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⣺⠛⠁⠀⠀⠀⠀⠀⠈⠉⠒⠿⢶⣎⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣔⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⠀⠀⠀
⠀⠀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀
⠀⢀⣰⣿⠀⠀⡴⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣀⠀
⢠⠏⢠⣿⠀⠰⡇⠀⠀⠉⠀⠀⣶⡀⠀⠀⢀⡤⢄⠀⠈⣿⣷⠀⢳
⠘⠆⣼⣻⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⠀⠈⠇⠀⢸⣿⢀⠏
⠀⠀⠁⠘⡆⠀⠀⠀⠀⢀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢣⣀⣠⠏⠀⠀⠀⠀⠀⠀⣠⠏⠸⠇⠀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠃⠄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠏⢀⡀⠀⢀⢤⡀
⠀⠀⠀⣖⣦⠀⣀⡠⠄⠂⠉⢲⠂⠤⠔⠊⣹⡀⠀⠀⠀⠉⠉⣰⡃