⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⣤⣤⡄⡠⢤⢠⠠⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⠀⡱⡢⢇⠣⠼⢹⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⣀⣤⣤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢯⡀⠐⣮⠁⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠙⠲⢜⣦⠀⠀⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⢠⣑⢴⠣⡀⠀⢀⢏⣬⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡇⠀⢸⠁⣾⣷⠈⠲⠬⠊⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢘⡆⠙⠋⡠⠀⢠⡀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⡉⣠⠤⡈⠙⢧⣩⡯⠢










⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣱⣿⠀⠀⢎⡱⠇⢸⢹⣸⠐⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠟⠀⠀⠫⠓⠣⠘⠚⠸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⠒⠶⣒⡒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢚⣃⠀⠈⠀⠀⠀⠉⠳⡄⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⢤⣀⠈⠧⣄⣀⠀⣠⢦⣀⣀⣧⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡖⠃⠀⠈⠙⣶⠒⠃⠐⡇⣶⣶⡆⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢧⡀⠀⣎⡗⢋⣓⠒⠒⠓⠉⢉⡁⠸⠔⡆⠀⢀⢳⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠸⡅⢿⡿⠂⠀⢰⣄⣠⠇⠀⢀⡇⡄⡴⠀⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠹⡄⠀⢙⣲⠄⠘⠒⠚⠿⠋⠀⠀⠸⠔⠙⠒⠦⡀⠳⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠧⣏⠳⠭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢹⠀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢆
⠀⠀⠀⠀⢄⣀⡴⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈