⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠤⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡼⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣲⡴⣗⣲⡦⢤⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠓⠛⠿⢷⣶⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠳⡄⠀⢀⣀⣀⡀⠀⣸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠰⠆⣿⡞⠉⠀⠀⠉⠲⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣀⡴⠛⡇⠀⠈⠃⠀⠀⡗⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠃⡴⠙⠢⠤⣀⠤⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⡼⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣉⣀⡴⠙⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠤⠚⣶⡀⢠⠄⡰⠃⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⠔⣋⣷⣠⡞⠀⠉⠙⠛⠋⢩⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀
⠀⡏⢴⠋⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⣹⢦⣶⡛⠳⣄⠀⠀⠀⠀⠀
⠀⠙⣌⠳⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠳⡌⣦⠀⠀⠀⠀
⠀⠀⠈⢳⣈⣻⡇⠀⠀⠀⠀⠀⠀⢰⣇⣀⡠⠴⢊⡡⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠳⢿⡇⠀⠀⠀⠀⠀⠀⢸⣻⣶⡶⠊⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠟⠙⠓⠒⠒⠒⠒⢾⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠏⠀⣸⠏⠉⠉⠳⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡰⠃⠀⡴⠃⠀⠀⠀⠀⠈⢦⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⠳⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡤⢯⡀⠀⠀⠀⠀⠀⠀
⠀⠐⡇⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢳⠀⠀⠀⠀⠀⠀
⠀⠀⠹⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠹⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡤⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠚⣆⠀⠀⠀⠀
⠀⠀⠀⡠⠊⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠉⠀⠙⢦⡀⠀
⠀⠀⠾⠤⠤⠶⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⠽⠀