⠀⠀⠀⣠⡪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣪⡪⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡨⡪⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡢⡪⡪⡪⡪⡪⣪⡺⣪⡺⣢⡢⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡺⡪⡺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡂⠀⡀⠀⠀⠀⡀⠀⡢⡪⡢⡪⡢⡪⡢⡪⡪⡪⡪⡪⡪⡪⣪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣪⡂⡪⡂⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣢⡊⡀⠀⡀⠀⠀⠀⠀⠀⡀⡂⡢⡊⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡪⡪⡪⡪⣪⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡨⡪⡂⠊⡂⠀⠀⠀⠀⠀⠀⡠⣪⡪⡢⡂⡀⠀⡀⠀⡀⠀⡀⠀⡢⡊⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡪⡪⣪⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡪⡢⡂⡀⡢⡀⠀⡀⡺⡪⡪⡢⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡪⡪⣪⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣪⡪⡂⠀⡪⡪⡪⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡪⡺⡂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⣺⣻⡢⡪⡢⡪⡢⡪⡢⡪⣺⣻⡢⡊⡢⡊⡢⡊⡢⡊⡢⡊⡢⡊⡢⡊⡢⡊⡢⡪⡪⡂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡢⡂⡢⡊⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂⡂⡂⡂⡂⡂⡂⡢⡂⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡪⡢⡪⡢⡪⡢⡪⡢⡊⡢⡊⡢⡊⡢⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡂⡂⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡪⡢⡪⡢⡊⡢⡊⡢⡊⡢⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡪⡢⡊⡢⡊⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡊⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡪⡢⡪⡢⡊⡢⡂⡂⡂⡂⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡊⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡪⡢⡂⡂⡂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⡂⡀⡂⡂⡊⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡪⡢⡂⡂⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⡂⡀⡂⡢⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡢⡂⡀⡂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⡂⡀⡂⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡢⡢⡂⡀⡂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⡂⡀⡢⡢⡪⡂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡊⡢⡂⡢⡂⡢⡂⡀⡂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⠂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡂⡢⡂⡢⡊⡪⡪⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡊⡢⡢⡢⡂⡀⡂⡀⡂⡀⡂⡀⡂⡀⡂⡂⡂⡢⡂⡢⡂⡢⡊⡢⡂⡢⡂⡢⡪⣪⡪⡂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⣪⡪⡢⡂⡢⡂⡢⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡪⡢⡪⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡪⣪⡪⡢⡪⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⡪⡢⡪⣪⡪⡪⡪⡊⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠊⡊⠊⡊⠊⡪⠊⡊⠊⡂⠂⠀