⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⢶⡄⠀⠀⢀⣴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠀⡿⠀⠀⡟⠀⠀⡘⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢠⡇⠀⢸⠃⠀⢀⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡾⠀⢀⡞⠀⠀⢸⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢰⠇⢀⡞⠁⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⣾⣠⠏⠀⠀⠀⢰⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⣠⣤⠤⠒⠛⠛⣤⡀⠀⠒⠌⣿⠂⣸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠒⠂⠰⠿⣔⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡾⠀⠀⠀⠀⠀⢰⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠄⠒⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡾⢙⠓⠶⠶⠶⠒⠋⠙⠓⠒⠧⢤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠉⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢃⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠀⠀⠀⠀⢿⡿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⢸⣇⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠹⣦⡀⠀⠀⠀⠀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀
⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀
⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀
⠀⠀⠀⠈⠙⣦⣀⡀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠀⠀⢰⡇⢣⠩⣷⣤⡀⠀⣧⠀⢦⠀⠀⠀⠀⠀⢀⣠⠴⢊⡽⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠈⣇⠘⣇⠀⠉⠑⠲⣿⡇⠘⠷⠶⠶⣶⣿⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⢻⡄⢹⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡇
⠀⠀⣀⣄⣀⣈⣿⣬⣧⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀
⢠⣞⢉⡁⡀⠀⣀⣀⣽⡄⠀⠀⢸⡇⠀⠀⠀⢸⣤⡀⠀⠈⠁⢀⣀⣤⣤⣤⣀⡀⠀⠠⠒⢉⣠⡴⠟⠀⠀
⠀⠉⠉⠙⠉⠉⠉⠉⠹⣧⣀⣀⣼⣇⠀⠀⢀⣼⠈⠉⠛⠛⠛⢿⣀⣀⣀⣀⣈⣻⡦⠶⠞⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀