⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠙⣿⡅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⣿⣟⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠸⡁⠀⡘⠀⠀⠀
⠀⠀⠐⡈⠓⡟⠂⠤⢀⠊⠛⢙⣛⡿⠿⠶⠂⢀⢀⣀⡱⡾⠿⠿⠟⡟⡍⡐⠁⡃⠌⠀⠀⠀⠀
⠀⠀⠀⠈⠢⣁⠀⠀⠸⡀⠈⠘⠙⠐⢹⠈⠨⠀⠀⠐⡄⠀⠁⠊⠛⠁⢸⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠁⠁⠐⠈⠀⠀⠀⠀⠀⡅⠒⠂⠀⠂⠒⠂⠀⠀⠅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁⠂⠁⠈⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⠀⢀⡠⢄⣀⣀⠤⣀⠀⠂⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢀⣔⣉⣁⣀⡀⢄⣀⣀⣀⠱⢦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠔⠉⢆⠀⠀⠀⠀⠀⠀⠀⣀⠤⠋⠐⢄⠎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠑⠒⢐⢄⠒⠊⠉⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠁⠀⠀⠁⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⢀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠙⣿⡅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⣿⣟⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠸⡁⠀⡘⠀⠀⠀
⠀⠀⠐⡈⠓⡟⠂⠤⢀⠊⠛⢙⣛⡿⠿⠶⠂⢀⢀⣀⡱⡾⠿⠿⠟⡟⡍⡐⠁⡃⠌⠀⠀⠀⠀
⠀⠀⠀⠈⠢⣁⠀⠀⠸⡀⠈⠘⠙⠐⢹⠈⠨⠀⠀⠐⡄⠀⠁⠊⠛⠁⢸⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠁⠁⠐⠈⠀⠀⠀⠀⠀⡅⠒⠂⠀⠂⠒⠂⠀⠀⠅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁⠂⠁⠈⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⠀⢀⡠⢄⣀⣀⠤⣀⠀⠂⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢀⣔⣉⣁⣀⡀⢄⣀⣀⣀⠱⢦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠔⠉⢆⠀⠀⠀⠀⠀⠀⠀⣀⠤⠋⠐⢄⠎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠑⠒⢐⢄⠒⠊⠉⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠁⠀⠀⠁⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⢀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
