⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠤⠖⠈⠀⠀⢀⡜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⠲⢤⣸⠒⣊⣭⠛⠉⠀⠀⠀⠀⠀⢀⣠⢿⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣹⠎⠀⠀⠑⡄⠀⢀⡠⠔⢊⡥⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣾⠋⠁⣠⠞⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡠⠊⡜⠁⠀⠀⠀⢀⡊⠁⠁⠀⢊⡀⠀⠀⠀⣀⣉⣓⣦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠊⠁⠸⠀⠀⠀⡠⡖⡝⠀⠀⠀⠀⠀⠈⢉⡩⠭⠒⢋⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠑⠒⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠀⠀⠀⡰⠚⢧⠉⠒⠒⠮⠽⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⡠⣖⠂⠀⠀⠀⡠⠋⠉⠀⡀⠀⠀⢀⡴⠁⠀⠸⡄⠀⠀⠀⠀⡇⠙⢌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠐⠁⣀⡠⠔⠋⣀⣀⡴⠚⠓⡶⣞⣉⣀⣀⡠⢤⠇⠀⠀⠀⢰⣃⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣠⡊⠁⡀⣠⠞⠁⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣿⠀⠈⠑⢄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⢻⡏⠁⠀⠀⠀⢀⠞⠑⠦⠤⠤⠤⠄⡸⠁⠀⠀⠀⢸⠉⣆⠀⠀⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠃⠀⠀⠀⢀⢏⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⠀⠘⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠦⠤⠤⠄⢲⠁⠀⠀⠀⠀⠀⠘⣆⣀⣹