⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⢿⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢲⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣯⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⢠⠤⢄⣈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡰⠛⣼⡀⠀⠀⠉⠛⣦⢄⡀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢰⡵⡿⡀⠀⢳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⠃⠀⠘⣇⠀⠀⠀⠀⠈⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⢰⠛⡶⠀⠀⡴⠁⠀⠀⠀⢠⠏⠀⢸⠃⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡌⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣀⣴⠇⠀⣿⢀⠎⠀⠀⠀⠀⣰⠃⠀⠀⠀⡇⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠊⠉⠢⣄⠀⢠⠃⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡇⠀⠀⠀⠀⣘⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠏⢀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠤⢛⣁⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡟⠀⠀⠀⢰⠃⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡸⠀⢰⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⢠⢫⠀⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⢳⢃⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣆⢣⠀⠈⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠊⣹⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠛⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⡞⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣷⣶⠒⠄⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠲⠤⠇⠀⠀⠀⠀⠓⠚⣁⣀⣠⣤⡤⠤⠤⠶⠶⣾⡤⡴⢋⣼⣹⠽⠔⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⠀⢸⡏⠈⠉⠉⠉⠉⣽⡗⢒⣶⠶⠀⠀⠀⠀⠀⢨⠉⣿⠁⣹⣿⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢧⡀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠸⣿⣼⣿⠀⢤⡦⡠⡤⠄⠈⠆⠹⣷⣿⠏⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣠⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⡐⢟⠁⠀⠀⠀⢀⡴⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡦⠰⣔⢴⢤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⡎⡢⠕⠀⠀⠈⠙⢦⡀⠀⠀