⣴⢡⠤⠄⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⡆⣢⡀⣀⡁⠀⠀⠀⠙⠒⡂⠂⢞⠄⡶⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡇⠀⢂⡧⠀⠀⠀⠀⠀⠀⡏⠉⠺⡆⡁⠂⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡂⠀⠈⡄⠆⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⡅⠀⠀⠇⠀⠀⠀⠀⠀⠈⠃⠀⢈⠅⠅⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⠀⠀⣇⡋⡔⡠⣄⡀⣠⡇⠀⢠⠅⡇⠀⣋⡀⡀⡀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢐⠅⡆⠀⠃⠁⠀⠉⠁⢈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣃⢄⡄⡒⣐⣐⣀⡆⡀⣸⣻⡀⣸⣥⡥⠶⠴⠔⡶⡀⡄⢞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠁⠁⠉⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⡶⡄⣀⣀⡀⠀⢀⡄⠤⠤⠄⠂⠂⠒⢲⠀⠀⡀⡀⠠⠐⠐⠐⡆⠀⠀⠀⡤⣄⡀⡀⡀⠀⠀⠀⠀
⠽⡅⠀⠀⡀⡀⡈⠈⢑⡇⡈⠀⡤⠄⠄⠄⠼⠤⠤⡇⠄⠀⡀⡀⠀⡇⠀⠀⠀⡍⠁⠁⠁⠉⠉⠁⠏⠁
⢉⡆⠀⠀⡧⡀⣇⣀⢈⠆⠄⠀⣇⣀⡀⠤⡄⠀⠀⡄⠀⠀⣇⡀⣉⡁⠀⠀⠀⠇⠀⠀⡏⠑⢤⠀⡅⠀
⢁⡅⠀⠀⠀⠤⡄⣄⣨⡃⠂⠀⠀⡀⠀⠀⡃⠀⠀⡄⠀⠀⠀⠀⠀⡃⠀⠀⠠⣉⠀⠀⠓⠒⠉⠀⡇⠀
⠩⠆⠀⠀⣙⠉⠈⠀⠉⠇⠂⠀⠀⡇⠤⠼⠤⠄⠀⡃⠀⢰⠆⠤⢄⡇⠀⠀⠄⣀⠀⠉⡃⠑⠛⠉⠀⠁
⠘⡅⠀⠀⣗⠀⠀⠀⠀⠆⡁⠀⠀⠅⠀⠀⠀⠀⡄⡃⠀⢸⡄⠤⠶⠅⠉⠉⣣⣋⠀⠀⡇⠀⠀⠀⠀⠀
⢘⡁⠀⠀⡃⠀⠀⠀⠀⡁⠂⠀⠀⠑⠋⠉⠉⠉⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⡁⠀⠀⠀⠀⠀
⠀⠃⠀⠀⡆⠀⠀⠀⠀⣢⠅⠀⡀⡀⡀⡀⡀⡀⡇⡃⠀⡀⣀⡄⡤⡖⣆⡖⠒⢳⠄⠤⡇⠀⠀⠀⠀⠀
⠁⠉⠂⠂⠃⠀⠀⠀⠀⠉⠈⠉⠁⠉⠉⠉⠉⠀⠀⠋⠁⠀⠀⠀⠀⠀