⠀⠀⠀⠀⠀⠀⠀Actually, it's a Cthulhu... But now it looks like a headless, winged Ursula with big boobs...
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠉⠉⠉⠉⠉⠑⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡇⠀⠀⠘⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠀⢇⠀⠀⠀⠀⠘⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡎⠀⠀⠀⠀⠈⡜⠢⢈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠊⠀⠸⢸⠀⠀⠀⠀⠀⠘⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⠃⠀⠀⠀⠀⠀⡇⠃⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠇⡈⡀⠀⠀⠀⠀⠀⠱⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠇⠐⠀⠀⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡜⠀⠇⡇⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢸⢸⢆⢀⠀⠀⠀⠀⠑⢌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⠂⠀⠀⠀⠀⠀⠰⠀⠀⠸⠸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⢇⠀⠀⡎⡆⠈⠄⠄⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⠀⠀⢠⠃⠁⠀⠀⠡⢣⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⡘⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⠀⡜⠜⠀⠀⠘⡌⠄⠀⠀⣀⠀⠀⠀⠁⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⡁⠁⡠⠔⠊⠁⠀⢹⣄⠃⠀⠀⠀⠀⠀⠑⣷⡀⠀⢹⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⢀⠊⠀⠀⢄⠀⢐⠀⠀⠀⡰⠀⢀⡜⢁⠼⠊⠀⠀⠀⠀⠘⠜⡀⠏⠀⠉⠑⠢⢄⡈⢎⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⣑⠔⠋⠀⠀⠀⠀⠀⢸⠏⢁⡠⠤⠒⠒⠢⠤⣈⠛⢦⣈⢣⡀⠀⠀⠀⠈⢄⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠁⣟⡀⢀⣐⠅⢠⣮⡴⠛⣀⡤⠴⠒⠒⠒⠒⠚⠛⠃⠤⡀⠀⠀⠀⠙⠢⣢⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⡕⠁⠀⠀⠀⠀⠀⣀⠤⠘⠓⠛⠒⠒⠢⢤⡀⢀⠔⠛⠒⠬⢙⠓⡄⠀⠀⠀⠁⠚⠒⠊⠺⠀⠀⠀⠀⠀⠀⠀⢉⢌⠉⠀⢠⢛⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠈⠣⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠈⠚⢆⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⣀⣀⠴⠁⠀⠈⠰⡀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⢏⠂⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠨⢊⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠮⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠂⢩⠋⠉⠑⢦⣀⠀⠘⡄⠀⠀⠀⠀⠡⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠋⠈⠣⡀⠈⢆⠀⠀⠀⠀⠡⡀⢈⡉⠦⢄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠐⠰⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⠈⢄⠀⠣⡀⠀⠀⠀⠙⡀⠀⠀⠀⠉⠐⠂⠤⠄⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠀⢡⠔⠈⠢⡀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠠⢣⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠸⡀⢀⡇⠀⠀⠀⠀⢀⠃⠀⡴⠋⠀⠈⢢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠑⢄⠀⠀⠘⢄⠤⠐⠂⠉⠀⠀⢈⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⢸⠀⡜⠀⡠⢢⠀⠈⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠣⡀⠀⠈⠄⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⢸⠀⡇⡜⠀⢸⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢇⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠰⡄⠀⠘⡄⠀⠀⠀⡌⠀⠘⡀⠀⠀⠀⠀⠀⢸⡗⢄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡟⡀⠀⠀⠀⠀⢸⠀⠣⠃⠀⡸⠀⢠⠁⠀
⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠸⡀⠀⠌⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠰⡀⠀⠰⡀⠀⡘⡄⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⡜⠱⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⢇⠀⠀⠀⠀⠈⠫⡑⢄⠔⠁⢠⠃⠀⠀
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠇⡌⠀⠀⠀⠀⠀⠠⠊⡇⠀⠀⠀⠀⠀⢠⠀⢃⠀⠀⠇⠰⠁⠘⡄⠀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠈⢄⠱⡴⠃⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠈⡆⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠁⠀⠇⡆⠀⠀⠀⠀⠸⠀⢸⠀⠀⣀⠃⠀⠀⢰⠀⠇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠑⢄⣀⠀⢀⣀⠼⡆⠰⡀⠀⠀⠀
⠀⢀⣀⠀⠀⢃⠀⢳⡀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⢀⢧⠀⠀⠀⠀⠀⡇⡸⠀⢠⡙⠀⢀⡠⠊⡜⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠁⠀⠀⢹⠀⢡⠀⠀⠀
⠀⡌⠈⠀⠀⠈⢆⠀⠑⠤⣀⣀⡠⠞⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⣼⠎⠈⡄⠀⠀⠀⡠⠞⢁⠔⠁⣃⠔⠉⠀⣰⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀
⠀⡇⠀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢧⠀⠀⠀⠀⢇⢰⠃⠀⠀⠰⠀⠀⠀⠁⠈⡅⠀⢸⠁⠀⠀⢠⡧⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠀⠀⠀
⠀⡇⠀⢇⠀⠀⠀⠀⠈⠓⠢⠤⠤⠒⠋⠀⠀⡸⠀⢢⠀⠀⠀⠈⢇⠀⠀⠀⠀⢃⠀⠀⠀⠀⢡⠀⢸⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢠⠇⠀⠀⡸⡀⠀⢰⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠀⠀⠀
⠀⢱⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠱⡀⠀⠀⠈⢢⠀⠀⠀⠈⡄⠀⠀⠀⠸⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⠁⠀⠀⠀⡼⠀⠀⢰⠁⢣⠀⠈⡄⢣⠀⠀⠑⠤⣀⣀⡠⠔⠁⠀⠀⠀⡎⠀⠀⠀
⠀⠀⠣⡀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⢀⠜⣄⠀⠀⠀⠡⡀⠀⡠⡅⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⡇⠀⠀⠀⢰⠃⠀⢠⠃⠀⠀⠳⡀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀
⠀⠀⠀⠑⢄⠀⠀⠉⠓⠒⠠⠒⠒⠉⠀⠀⠀⠀⣀⠔⠉⡰⠉⢢⠀⠀⠀⠑⡜⠁⡏⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠠⢲⠋⡄⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⡎⠀⠀⠀⠀⠈⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠈⣦⢄⣀⠀⠀⠀⠀⢀⣀⡠⠔⠊⠀⠀⡴⠁⠀⠀⠳⡀⠀⠀⠘⡄⡇⢠⠊⠀⠀⠀⠀⣀⠔⠊⠁⠀⡎⠀⢧⠀⠀⠀⠀⢣⠀⠀⢸⠁⠀⢸⠁⠀⠀⠀⠀⢠⠃⠀⡏⠁⠒⠒⠂⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠈⢦⡀⠈⠉⠉⠉⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⢣⠀⠀⠀⢹⢠⠃⠀⠀⢀⡤⠊⡇⠀⡠⠔⠒⠁⠒⡜⡄⠀⠀⠀⠘⡀⠀⣾⠀⠀⡎⠀⠀⠀⠀⣠⠋⠀⢠⡝⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠀⠙⠢⣄⣀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀⡠⠎⠀⢸⠀⠀⠀⠀⡇⠀⠀⢠⠊⠀⠀⢳⠎⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⢣⠀⢇⠀⠀⣇⣀⣀⠤⠚⠁⠀⢠⢳⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⣀⠎⠀⠀⠀⢰⠀⠀⢀⠇⠀⠀⠀⢸⠀⢠⠊⢹⠀⠀⢸⠈⡆⠀⠀⠀⠈⢆⠸⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⢤⡤⠴⠒⠛⠒⠒⠒⠒⠊⠁⠀⠀⠀⡠⢻⠀⠀⢸⡄⠀⠀⠀⠸⡀⢈⠀⡜⠀⠀⡎⠀⠸⡄⠀⠀⠀⠈⢢⠣⣀⠀⢀⣀⡤⠒⠁⠀⡜⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢤⠄⠊⠀⡔⡄⠀⠘⣧⠀⠀⠀⢠⠉⢉⠞⠀⠀⡰⠈⢆⠀⠹⡄⠀⠀⠀⠀⠑⢌⠉⠉⠀⠀⠀⢀⠜⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠎⠀⠱⡀⠀⠈⠒⠤⠤⠼⠒⠁⠀⢀⡜⠀⠀⠈⢣⠀⠘⢆⠀⠀⠀⠀⠀⠉⠒⠠⠒⠊⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣠⠃⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⣀⠔⠁⠘⢄⠀⠀⠀⢣⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡰⠃⠀⠀⠀⠀⠀⠀⢸⠋⠐⠒⠎⠉⠀⠀⠀⠀⠈⢂⠀⠀⠀⢣⠀⠀⠀⠑⠢⢤⣀⣀⣀⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠎⠀⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠉⠉⠉⠉⠉⠑⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡇⠀⠀⠘⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠀⢇⠀⠀⠀⠀⠘⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡎⠀⠀⠀⠀⠈⡜⠢⢈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠊⠀⠸⢸⠀⠀⠀⠀⠀⠘⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⠃⠀⠀⠀⠀⠀⡇⠃⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠇⡈⡀⠀⠀⠀⠀⠀⠱⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠇⠐⠀⠀⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡜⠀⠇⡇⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢸⢸⢆⢀⠀⠀⠀⠀⠑⢌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡡⠂⠀⠀⠀⠀⠀⠰⠀⠀⠸⠸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⢇⠀⠀⡎⡆⠈⠄⠄⠀⠀⠀⠀⠀⠑⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⠀⠀⢠⠃⠁⠀⠀⠡⢣⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⡘⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⠀⡜⠜⠀⠀⠘⡌⠄⠀⠀⣀⠀⠀⠀⠁⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⡁⠁⡠⠔⠊⠁⠀⢹⣄⠃⠀⠀⠀⠀⠀⠑⣷⡀⠀⢹⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⢀⠊⠀⠀⢄⠀⢐⠀⠀⠀⡰⠀⢀⡜⢁⠼⠊⠀⠀⠀⠀⠘⠜⡀⠏⠀⠉⠑⠢⢄⡈⢎⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⣑⠔⠋⠀⠀⠀⠀⠀⢸⠏⢁⡠⠤⠒⠒⠢⠤⣈⠛⢦⣈⢣⡀⠀⠀⠀⠈⢄⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠁⣟⡀⢀⣐⠅⢠⣮⡴⠛⣀⡤⠴⠒⠒⠒⠒⠚⠛⠃⠤⡀⠀⠀⠀⠙⠢⣢⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⡕⠁⠀⠀⠀⠀⠀⣀⠤⠘⠓⠛⠒⠒⠢⢤⡀⢀⠔⠛⠒⠬⢙⠓⡄⠀⠀⠀⠁⠚⠒⠊⠺⠀⠀⠀⠀⠀⠀⠀⢉⢌⠉⠀⢠⢛⡩⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠈⠣⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠈⠚⢆⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⣀⣀⠴⠁⠀⠈⠰⡀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⢏⠂⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠨⢊⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠮⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠂⢩⠋⠉⠑⢦⣀⠀⠘⡄⠀⠀⠀⠀⠡⠠⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠋⠈⠣⡀⠈⢆⠀⠀⠀⠀⠡⡀⢈⡉⠦⢄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠐⠰⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⠈⢄⠀⠣⡀⠀⠀⠀⠙⡀⠀⠀⠀⠉⠐⠂⠤⠄⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠀⢡⠔⠈⠢⡀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠠⢣⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠸⡀⢀⡇⠀⠀⠀⠀⢀⠃⠀⡴⠋⠀⠈⢢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠑⢄⠀⠀⠘⢄⠤⠐⠂⠉⠀⠀⢈⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⢸⠀⡜⠀⡠⢢⠀⠈⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠣⡀⠀⠈⠄⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⢸⠀⡇⡜⠀⢸⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢇⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠰⡄⠀⠘⡄⠀⠀⠀⡌⠀⠘⡀⠀⠀⠀⠀⠀⢸⡗⢄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⡟⡀⠀⠀⠀⠀⢸⠀⠣⠃⠀⡸⠀⢠⠁⠀
⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠸⡀⠀⠌⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠰⡀⠀⠰⡀⠀⡘⡄⠀⠀⡇⠀⠀⠀⠀⠀⠘⡇⡜⠱⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⢇⠀⠀⠀⠀⠈⠫⡑⢄⠔⠁⢠⠃⠀⠀
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠇⡌⠀⠀⠀⠀⠀⠠⠊⡇⠀⠀⠀⠀⠀⢠⠀⢃⠀⠀⠇⠰⠁⠘⡄⠀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠈⢄⠱⡴⠃⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠈⡆⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠁⠀⠇⡆⠀⠀⠀⠀⠸⠀⢸⠀⠀⣀⠃⠀⠀⢰⠀⠇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠑⢄⣀⠀⢀⣀⠼⡆⠰⡀⠀⠀⠀
⠀⢀⣀⠀⠀⢃⠀⢳⡀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⢀⢧⠀⠀⠀⠀⠀⡇⡸⠀⢠⡙⠀⢀⡠⠊⡜⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠁⠀⠀⢹⠀⢡⠀⠀⠀
⠀⡌⠈⠀⠀⠈⢆⠀⠑⠤⣀⣀⡠⠞⠀⠀⢀⢿⠀⠀⠀⠀⠀⠀⠀⣼⠎⠈⡄⠀⠀⠀⡠⠞⢁⠔⠁⣃⠔⠉⠀⣰⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀
⠀⡇⠀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢧⠀⠀⠀⠀⢇⢰⠃⠀⠀⠰⠀⠀⠀⠁⠈⡅⠀⢸⠁⠀⠀⢠⡧⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠀⠀⠀
⠀⡇⠀⢇⠀⠀⠀⠀⠈⠓⠢⠤⠤⠒⠋⠀⠀⡸⠀⢢⠀⠀⠀⠈⢇⠀⠀⠀⠀⢃⠀⠀⠀⠀⢡⠀⢸⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢠⠇⠀⠀⡸⡀⠀⢰⢀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠀⠀⠀
⠀⢱⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠱⡀⠀⠀⠈⢢⠀⠀⠀⠈⡄⠀⠀⠀⠸⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⠁⠀⠀⠀⡼⠀⠀⢰⠁⢣⠀⠈⡄⢣⠀⠀⠑⠤⣀⣀⡠⠔⠁⠀⠀⠀⡎⠀⠀⠀
⠀⠀⠣⡀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⢀⠜⣄⠀⠀⠀⠡⡀⠀⡠⡅⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⡇⠀⠀⠀⢰⠃⠀⢠⠃⠀⠀⠳⡀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀
⠀⠀⠀⠑⢄⠀⠀⠉⠓⠒⠠⠒⠒⠉⠀⠀⠀⠀⣀⠔⠉⡰⠉⢢⠀⠀⠀⠑⡜⠁⡏⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠠⢲⠋⡄⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⡎⠀⠀⠀⠀⠈⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠈⣦⢄⣀⠀⠀⠀⠀⢀⣀⡠⠔⠊⠀⠀⡴⠁⠀⠀⠳⡀⠀⠀⠘⡄⡇⢠⠊⠀⠀⠀⠀⣀⠔⠊⠁⠀⡎⠀⢧⠀⠀⠀⠀⢣⠀⠀⢸⠁⠀⢸⠁⠀⠀⠀⠀⢠⠃⠀⡏⠁⠒⠒⠂⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠈⢦⡀⠈⠉⠉⠉⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⢣⠀⠀⠀⢹⢠⠃⠀⠀⢀⡤⠊⡇⠀⡠⠔⠒⠁⠒⡜⡄⠀⠀⠀⠘⡀⠀⣾⠀⠀⡎⠀⠀⠀⠀⣠⠋⠀⢠⡝⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠀⠙⠢⣄⣀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀⡠⠎⠀⢸⠀⠀⠀⠀⡇⠀⠀⢠⠊⠀⠀⢳⠎⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⢣⠀⢇⠀⠀⣇⣀⣀⠤⠚⠁⠀⢠⢳⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⣀⠎⠀⠀⠀⢰⠀⠀⢀⠇⠀⠀⠀⢸⠀⢠⠊⢹⠀⠀⢸⠈⡆⠀⠀⠀⠈⢆⠸⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⢤⡤⠴⠒⠛⠒⠒⠒⠒⠊⠁⠀⠀⠀⡠⢻⠀⠀⢸⡄⠀⠀⠀⠸⡀⢈⠀⡜⠀⠀⡎⠀⠸⡄⠀⠀⠀⠈⢢⠣⣀⠀⢀⣀⡤⠒⠁⠀⡜⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢤⠄⠊⠀⡔⡄⠀⠘⣧⠀⠀⠀⢠⠉⢉⠞⠀⠀⡰⠈⢆⠀⠹⡄⠀⠀⠀⠀⠑⢌⠉⠉⠀⠀⠀⢀⠜⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠎⠀⠱⡀⠀⠈⠒⠤⠤⠼⠒⠁⠀⢀⡜⠀⠀⠈⢣⠀⠘⢆⠀⠀⠀⠀⠀⠉⠒⠠⠒⠊⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣠⠃⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⣀⠔⠁⠘⢄⠀⠀⠀⢣⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡰⠃⠀⠀⠀⠀⠀⠀⢸⠋⠐⠒⠎⠉⠀⠀⠀⠀⠈⢂⠀⠀⠀⢣⠀⠀⠀⠑⠢⢤⣀⣀⣀⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠎⠀⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
