⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠔⠠⠂⠴⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⡀⠄⠢⠀⡀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢐⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠁⠒⠠⠄⢰⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠁⠀⠀⠄⠀⠀⠀⠀⠄⠒⢄⠀⠀⠀⠀⡌⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠌⣴⠀⠀⠀⠜⡀⠃⠈⠀⠀⠀⠀⠈⠀⠂⡐⢄⠀⠀⢀⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⣿⣆⠠⠂⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⣀⣼⣿⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⣿⣿⣦⡀⠀⠀⢦⠀⠂⠁⠀⠁⠂⠄⠆⠀⠀⢠⣾⣿⣿⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⣿⠙⢿⣷⣤⡀⠀⢂⠀⠀⠀⠀⠀⠊⠈⣀⣴⣿⠿⢹⣿⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⣿⡆⠀⠙⢿⣷⣄⠀⢄⠠⠒⠄⡌⢀⣴⣿⠟⠉⠀⣸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⣧⡀⠀⠀⠈⠻⣿⣄⢂⡀⢌⣰⡿⠋⠁⠀⠀⢠⣿⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢿⣷⣤⣀⣀⣤⣼⠿⣁⠐⡹⢿⣦⣄⣀⣠⣴⣿⠟⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠊⠻⠿⠿⠛⡁⠐⠀⠀⠐⡀⠘⠻⠿⠿⢋⠂⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢐⠁⠂⢀⠀⠀⠃⠐⠂⠀⠃⠀⠀⠠⠀⢁⠢⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠐⡀⠀⠠⡐⢀⠀⡀⢀⠐⡠⠊⠀⡠⠂⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣦⡈⠢⢀⠁⠀⠀⠀⠀⠀⢡⠀⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣿⠄⠘⣷⣄⡙⠀⠀⠀⠂⠀⠁⠐⣃⣴⣿⣿⢿⡗⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⢡⠄⠀⢾⠈⠡⠘⣿⣷⣤⣀⣀⣀⣀⣠⣴⣿⣿⣿⠏⢸⡇⠀⢤⡉⠙⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠉⠁⢀⠨⠔⠈⠀⠐⣠⠟⢂⠄⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣐⠘⢧⡠⠀⠀⠐⠤⢀⠀⠉⠙⠛⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡶⢟⠉⠁⠀⠀⡀⠐⠢⢈⠀⠀⠀⢰⣠⠚⠁⠀⣤⠓⠠⠀⠌⢿⣿⣿⣿⣿⣿⣿⠿⠁⠐⠡⡄⠀⠉⠒⣤⠁⠀⠀⠀⡰⠘⠀⠀⠀⠀⠉⢙⠻⣦⣄⠀⠀⠀⠀
⠀⠀⢠⡾⠋⠀⠀⠈⡄⢐⠁⠀⠀⠀⠀⢢⠤⠊⡁⠀⠈⠀⡴⠁⡉⠒⠠⠄⠈⢻⣿⣿⣿⠿⠁⣘⠀⠊⡁⠱⣄⠈⠀⠀⢉⠢⢄⠂⠀⠀⠀⠀⢁⠠⡄⠁⠀⠈⠙⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⢀⡀⠔⠁⠀⠀⠀⠁⢄⠜⠀⠀⠀⠑⠤⠐⠠⠀⠈⡉⢀⠠⠐⠠⠔⠀⠀⠀⡈⢆⡠⠈⠀⠀⠀⠉⢄⡀⠄⠊⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠂⠄⣀⠂⠀⠀⠈⠐⢠⠆⠠⠄⡀⠀⠉⠀⡀⠤⠀⢆⠐⠁⠀⠀⠀⠑⣀⠠⠂⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⢠⠁⠀⠀⠁⠐⠠⣈⠀⣀⠀⠀⠁⠋⠀⠀⣀⠀⡈⡄⠀⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠠⠄⡀⠀⠃⠀⠀⠀⠁⠐⠒⠈⠀⠀⠀⠀⢁⠀⡀⠄⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⠐⠀⠀⠀⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀