⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣛⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣮⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠺⣷⣀⣹⣟⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⡰⠋⣭⡿⣿⣿⠈⠉⢻⡙⣦⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡭⠊⠉⠚⠀⠀⣻⣿⣽⣿⣧⡀⣼⣇⣬⣧⣴⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠸⡄⠀⠀⢀⡤⠋⢸⡉⢿⣦⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡨⠕⢲⢿⣇⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⢧⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⢶⣏⣼⣿⣿⣿⣿⣿⣿⡿⣿⡯⠀⠂⠈⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠩⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠉⠉⣉⠿⠿⡿⣿⣟⠻⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣠⠞⠁⠀⠀⠀⠀⢈⢳⡙⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡔⣽⠟⠀⠀⠀⢀⣀⣤⣤⣤⣀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⡟⠀⡇⠀⠀⠀⣤⣿⠛⠻⣿⣿⣿⣧⡈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⡿⠋⠀⢸⠅⠀⠀⣠⣿⠏⠀⠀⠹⣿⣿⣿⣦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⢔⡵⠋⠀⠀⠀⠀⣼⠀⠀⠀⣽⡟⠀⠀⠀⠀⠻⣿⣿⣿⣇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣼⡷⠋⠂⠀⠀⠀⠀⢠⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠠⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣟⡉⢀⡄⠀⠀⠀⠀⢰⡿⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠐⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢴⣟⠋⡸⢅⢭⠀⠀⠀⠀⠀⠸⣶⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠙⠚⢧⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠉⠛⠉⠀⠀⢸⣿⣿⠉⠉⠙⠒⠒⠒⠀⠤⠤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀