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