⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠈⡐⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⡀⢂⠐⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⠀⡐⢀⠂⡂⠌⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⠀⠀⠂⠐⢈⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠠⡂⠕⡐⠡⢐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢌⢂⠅⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠁⠈⠀⡐⠀⡂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⠨⠠⠀⠀⠀⠀⠀⠀⠀⠈⢔⠡⢊⠌⢔⢐⠨⡐⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢕⠠⡡⠡⡡⡁⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠂⠄⠀⠀⠀⠀⠀⠠⠀⠡⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠂⠅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠨⠢⡑⢌⠢⡑⡐⡐⡀⠀⠀⠀⠀⠀⠀⠀⠨⠢⡑⢌⠪⡐⠐⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠌⠌⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⡈⡂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠁⡈⠂⠪⠠⡁⠀⠀⠀⠀⠀⠀⠈⠜⡨⠢⡃⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠪⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⢐⠌⢔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠡⡊⠅⡐⢈⠠⠐⢀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢑⠌⡂⢇⢢⠠⡀⠀⢀⠠⠀⠠⠀⢀⠀⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠢⡨⢂⢂⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⢀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠅⡁⠄⠂⠠⠁⢂⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⡡⡃⢕⠔⡑⠌⠂⠀⠠⠈⠠⠁⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠱⡐⡡⢢⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⢈⠀⠂⠄⢁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢐⠜⡌⢆⠆⡠⠀⠄⡠⠀⡀⢀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠑⡌⡢⡑⡄⠄⠀⠀⠀⠈⠀⠀⠂⠀⢀⠀⠂⠀⠠⠐⠀⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠁⠐⠀⠄⠁⠄⢁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡣⡪⡪⠪⡐⡅⢕⡐⡅⡌⡢⡨⢨⢐⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⡃⢆⢊⢆⠂⠠⠈⠀⠀⠂⠀⠀⠀⠀⢀⠀⠄⠀⠠⠀⠄⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠠⠀⠂⡈⠄⢌⢢⠠⠀⠀⠀⠀⠀⠀⠀⠐⢌⢪⢪⢸⠸⢐⢈⢂⠢⢑⠨⢂⠊⠆⠕⡌⡢⢡⠨⢐⠀⠄⠀⠀⠀⠀⠀⠀⡐⡐⠄⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠪⡢⢱⠰⡁⠀⠀⡀⠠⠐⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠅⡣⡱⡡⡑⠄⡀⠀⠀⠀⠀⠑⢅⡣⡣⡣⢫⠀⠀⠄⠂⠐⠀⠂⠨⠈⠂⢂⠨⠐⠈⡐⠈⠀⠀⠀⠀⠄⠠⢀⠢⢘⢌⠢⡡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⡪⢢⠣⣃⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⡀⠄⠂⠈⠀⠀⠐⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢅⠪⡸⣘⢜⢌⢢⢀⠀⠀⠀⠀⠈⠎⢎⢎⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠈⠐⠠⢈⠢⠢⡃⡪⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠰⢱⠸⡀⠀⠀⠀⠈⠀⠁⠀⠀⠄⠀⡀⠐⠈⠀⠀⠂⠀⠀⡀⠀⠀⠂⢁⠐⠈⠠⠈⠠⠈⡀⠄⠂⠀⠀⡀⠈⠀⢂⠑⢌⠢⡣⡣⡣⡱⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠈⡐⢌⢊⢎⢢⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⢍⢆⢇⢇⠂⡀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠄⠐⢈⠀⠀⠁⠀⠀⠀⠁⠄⡀⠈⠀⠈⠀⠄⠀⠄⠂⠈⡀⢀⠀⠀⠀⠈⠠⠑⢌⠪⠪⡪⡪⡣⡣⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢐⢑⠜⡌⡆⡣⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡣⡪⢢⢣⢃⠀⠄⠀⠀⠀⠀⠀⠀⠠⠈⠀⠠⠈⠀⠀⠀⠀⠀⠈⠀⡀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⢊⠢⡑⠕⡕⡕⡜⡜⡔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⡂⢇⡣⡱⡨⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⠜⡜⡜⡜⡔⡈⠐⡀⠀⡀⠠⠀⠂⡀⠌⡀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠢⡑⢕⢕⢕⢕⢭⢒⠤⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡂⢎⢎⢎⢎⢌⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢣⢣⢣⢣⡓⡆⡁⠄⠂⠀⡀⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠅⡀⠀⠀⠀⠄⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠜⡸⢸⢱⢹⡸⡸⡌⡆⡄⡄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⢔⢜⢜⢜⢜⢔⢐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠪⠪⠪⠪⠊⠀⠀⢀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠄⠂⠄⠀⠐⠀⠀⡀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡘⠜⢜⢪⢎⢮⢪⡪⡪⡢⡢⡢⢄⢤⢠⢠⢠⡐⡔⡔⡜⡌⣎⢮⢪⢣⠱⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠈⠠⠈⠄⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠂⠡⡀⠀⠂⠁⠄⡂⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠁⠣⠱⡱⡱⡹⢜⢎⢧⢣⡳⡱⡕⡵⡱⡕⣇⢇⢇⢇⠇⠕⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠨⠀⠅⠂⠁⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠂⠂⠅⠅⠀⠀⠀⠈⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠈⠈⠪⠘⠜⢌⢇⠝⡜⢜⠜⢜⢘⠌⡂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠌⠨⢀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠈⠀⠠⠐⠈⠀⠁⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠅⢂⢁⠂⡀⠄⠈⠀⡀⠁⠀⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⡀⡂⠄⠄⠂⠀⢀⠀⠂⠀⠄⠀⠂⠀⠀⠀⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢂⠐⢄⢑⠄⡁⠠⠀⢀⠐⠀⠄⢂⢐⠨⢐⠡⠨⢐⠨⢀⠢⡡⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡁⠄⡀⡂⡀⠀⠄⠂⠐⠀⠀⠀⠀⡀⢀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡂⠢⡑⡐⠠⠀⢀⠀⢐⠈⠄⠂⠌⡐⠨⠨⢐⠨⢐⠨⡪⢐⢐⢐⠨⢐⠡⢐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡢⢑⠔⢔⠄⡅⢌⢢⢑⠆⢅⢊⠢⠨⡂⡂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢑⠐⢌⠂⠌⠀⠀⡐⠠⢁⠡⢁⠀⠁⠈⠀⠐⠀⠨⡊⠀⠂⡂⠌⡐⠨⡐⠔⡐⡡⢂⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠄⠁⠘⡔⡝⡔⢕⠸⡘⡌⡆⢝⢐⠬⡈⡪⡢⡑⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠅⡅⡣⠡⠐⠀⠐⠈⠄⢌⠐⠌⠄⠅⢄⢁⠠⠐⢌⠀⠠⠀⠀⡀⠁⠀⠂⠂⠄⠡⠡⠑⠄⢅⠂⢄⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡊⡆⡆⡆⣜⢼⢘⠌⠐⠀⠂⢑⠨⢂⠢⢑⠌⢆⢕⢱⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠢⡑⢌⠪⠠⠀⠀⠈⠈⡐⠌⡌⠪⠨⡂⡢⢡⠡⡣⡊⢔⢐⠅⢄⠢⡐⠄⢄⢈⢐⢀⠡⠈⠄⡑⡐⢅⠡⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢑⢸⢸⢜⢜⢜⢐⠀⠀⠠⠈⠀⠌⡐⡀⢀⠄⠠⡐⢌⢆
⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠪⡪⠪⠀⠂⠀⠀⠀⠀⠈⠈⠑⠈⠊⠢⠡⢳⢡⢱⢨⢪⢨⠪⡨⡊⢆⠕⢔⢔⢡⠡⡑⢄⢂⢑⠌⠌⢔⠨⡐⡐⡀⡂⡐⠠⠐⠠⠠⠠⠐⠠⠠⠠⠠⠠⡘⡜⡜⣕⢕⢕⢄⢑⢐⠅⢅⠣⡱⡐⡸⠨⡘⢔⢱⠱
⠀⠀⠠⠐⠈⠄⠂⠄⢂⢐⠈⠄⠠⡁⠅⢂⠀⠀⠀⠀⠀⠀⠀⠈⠔⡱⡘⢜⠌⡀⢀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠐⠨⡀⠠⠐⠀⡁⠅⠡⢁⠑⡉⠊⡂⠣⠑⠕⠱⠨⠢⠅⠣⠅⠕⠌⠆⡪⢂⠪⡨⠌⡌⠢⡑⢌⠢⢑⠌⠔⡡⢂⠪⠪⠪⠪⡣⡣⡑⠁⠃⠡⠁⠕⠀⡪⠀⢪⢂⢪⠊
⠠⠨⠠⢁⠅⡡⠑⠨⠐⡠⠊⠌⡂⡂⠅⡂⠀⠀⢀⠠⠐⡈⡐⢐⠨⡂⡪⢪⢪⢐⠅⡂⡂⡀⠀⠐⠈⠀⠀⠠⠀⠀⢢⠀⠄⠂⠀⡐⢀⠐⢀⠐⠁⡀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠄⠄⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡌⠄⠀⢈⠈⠀⠜⢜⢜⢔⢜⠌
⢐⠡⢑⠐⠈⠀⠀⠀⠀⠀⠅⢕⢐⠔⠡⠀⡀⡂⡢⢈⢂⢂⢂⢂⢐⠱⡡⡣⡱⡱⡑⢔⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢀⠀⢀⠠⠀⡀⠁⡀⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠌⡢⢀⠀⠠⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢕⢄⠄⠀⢈⠢⡱⡑⡕⡅
⢂⠅⠅⠀⠀⠀⠀⠀⠀⢀⠅⢕⠐⡌⠄⠐⢅⠪⡐⡐⠔⠐⠐⠀⠄⠈⢎⢆⢧⢫⡪⡂⡢⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠄⠅⡑⢄⠀⠂⠀⠂⠀⠁⠌⠠⢀⠀⠀⠀⠀⠀⠣⡱⡡⠀⢰⢈⠢⡣⡣⡃
⢂⠅⢅⠀⠀⠀⠀⠀⠀⡂⢅⢅⠕⡐⡁⠌⡆⢃⠊⠀⠀⠀⠀⠨⠠⠁⢌⢲⣱⡳⡵⡑⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡐⢅⠕⢌⡀⠂⢈⠀⠀⠐⠀⠂⠀⠀⠀⠀⠐⢈⠸⠀⢈⢎⢎⢎⢮⢪
⢐⠅⢕⠠⠀⠀⠀⠀⢀⠪⢐⠔⡡⢂⠪⡘⢔⠀⠀⠀⠀⠀⠀⠌⡂⠁⡀⢧⣺⡪⣗⢧⠣⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡨⡢⢃⢕⢌⢆⠔⡀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠢⠐⠀⠈⠪⢪⢪⡣⡣
⡐⢌⢂⠢⠀⠀⠀⠀⠠⡑⡐⡑⢌⠢⡑⢜⠀⠀⠀⠀⠀⠠⠨⠢⠨⠀⡐⣜⣞⢞⢮⡳⡝⡜⢌⢌⢂⠅⡊⠔⡁⡢⢁⢂⢂⢂⠡⠀⠅⢅⢂⢂⠢⡢⡂⡢⢂⢑⠔⡠⢀⠀⠀⠀⠀⠀⡀⡂⡂⠄⠀⠀⠀⠀⠀⠁⠊⠪⠪⡪⡪⡢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⡑⠕⢭
⢐⠅⡂⢅⠀⠀⠀⠀⠠⡑⢌⠢⢡⢑⠌⢆⢂⠀⠀⢀⢀⠆⢕⠅⠅⠂⡂⡧⣳⢯⡳⣝⢞⢜⢌⠆⢆⠣⠪⡨⡂⡪⢐⢐⡐⢔⢨⢊⢪⢸⠸⠨⡪⡢⢪⢨⠢⣑⢌⠢⠡⡑⡐⡀⠀⠀⡂⠪⡐⡡⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⡂⡪⠨⡀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠄⠀⠌⠢
⢂⠅⡊⠄⠀⠀⠀⠀⡸⡈⡢⢡⢑⠰⡑⡅⢕⢐⢑⢌⢢⠩⠢⠂⢀⠌⡂⣏⢮⢯⢯⡺⣝⢎⢆⡣⡃⡉⠁⠑⡈⡊⣊⢲⢱⡱⡱⡑⡅⠇⡁⠁⠄⠂⠠⠀⠄⠀⠈⠘⠨⡂⡢⡈⡂⠀⢐⢁⢂⠪⡸⣐⢕⢌⠢⡁⡂⡂⠌⡀⠈⠜⢌⠪⡐⡀⠀⠀⠀⠀⠀⠨⠊⠀⡀⠀⠀⠀⠀⠡
⠢⡑⠀⠀⠀⠀⠀⢀⠪⡂⡪⡂⡅⢇⢕⠜⡔⢅⢕⠘⠀⠁⠀⢄⠅⢌⠢⢊⢳⠽⡮⣻⡪⡯⡳⣕⢵⣱⢱⡱⡸⡸⡰⡱⡣⡳⣝⢎⢎⠢⠂⠅⠂⠀⠂⠁⠀⠀⠀⠀⠂⠈⡐⡐⠠⠐⠀⡂⠢⠡⠪⡪⡪⡪⡪⢨⢂⠪⡐⠌⢄⠈⠐⡑⠔⡌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀
⠱⡀⠀⠀⠀⠀⠀⠀⠑⠕⠔⡌⠀⠀⠱⡱⡘⡌⠆⢕⢐⠆⡎⡢⡑⢔⠨⠠⠑⢝⢜⠕⡝⡞⣗⢽⣳⣳⣝⢮⡳⣝⡜⡮⡫⡳⡱⠁⠡⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠂⠌⠌⢌⢊⠢⠃⠁⠈⠀⠁⠁⠈⠈⠐⠈⠠⠈⠪⡈⡂⢅⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⡀⠀⠀⠀⠀⠀⠀⠀⢘⠄⢕⠀⠀⠀⠈⠘⠀⠌⢢⠱⡱⠱⠑⠘⠀⠕⡑⠩⠀⠕⠁⠈⢊⠊⠇⢗⠳⣝⢵⢝⢜⢜⢕⢝⢜⠌⠀⠀⢀⠠⠀⢂⢈⢐⢀⢂⠠⠀⠀⠀⠀⠀⠡⠀⠪⡨⡊⡪⡂⠆⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠨⡠⠡⠂⠌⠌⠄⠄⠀⠀⠀⠀⠀⠐
⠢⡂⠀⠀⠀⠀⠀⠀⠀⢐⠅⢒⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⢁⠂⠅⠨⠀⠀⠈⠀⠀⠀⢀⠀⢈⡪⣎⢎⢎⢎⢎⢎⠪⡀⠀⠄⠠⢈⠢⡪⡪⡸⣐⢅⢂⠠⠀⠀⠀⠀⠀⢑⢌⡊⡢⡑⢍⢂⠀⡀⠀⠀⡀⠠⠀⠁⠌⠀⠅⠈⠀⠀⢁⠢⠡⠡⠡⢈⠐⡈⠈⠠⠀⠀⠀⠀
⢘⠄⠀⠀⠀⠀⠀⠀⠀⢐⠅⢘⠀⠀⠀⠀⠠⠐⠀⠨⠀⢀⠀⠀⠄⢘⠄⢌⠠⡑⠀⠀⠀⠀⠀⠀⠀⢠⡺⡪⡮⢯⢷⢝⢮⢪⢪⠢⡡⡀⢕⢸⢸⡸⡜⣞⢼⢜⡐⠔⢀⠀⠀⠀⡈⠠⡂⡪⡐⠔⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠪⡨⠨⠠⠡⢀⠀⠀⠀⠀⠐⠀
⠠⡁⠀⠀⠀⠀⡀⠀⠄⢐⠅⠀⠥⠀⠀⠁⠀⠀⠀⢌⠊⠀⠀⠄⠀⠄⠁⠥⠁⠀⠀⠀⠀⠀⠀⠀⡰⡱⡱⡱⡍⡧⡫⠓⢵⡱⡕⣕⢜⢬⡢⣇⢧⢳⢹⢜⢮⢪⠪⡈⠄⠀⢂⢐⠀⡂⡪⡒⡌⠢⠀⠡⠐⠀⠂⠄⡀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠢⡡⢑⠨⢀⠀⠀⠀⠀⠀⠀
⠐⠄⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⢘⠀⠀⠂⠀⠁⠀⠰⡁⠄⠂⠀⠂⠀⡀⠪⠀⠀⠀⠀⠀⠀⠀⢢⡳⣕⢝⢮⢳⢽⠀⠀⠈⠺⡪⣎⢗⢵⣹⡪⣗⣝⣎⢮⡪⣪⡪⡰⡐⡅⢕⠠⢢⠱⢨⢪⢪⢱⢑⢔⢐⠅⡌⡂⡂⠅⡐⢐⠠⠀⠄⠠⢀⠁⠄⡂⢄⠑⢌⢂⠪⢐⠀⠀⠀⠀⠀⠀
⢈⠂⠀⠀⠀⠀⠠⠀⠠⠐⠅⠀⠀⡃⠀⠐⠈⠀⠈⠨⡂⠀⠀⡀⠂⠁⠀⠨⠀⠀⠀⢀⠂⠌⢄⢷⢝⢮⣫⢳⢝⠅⠀⠀⠀⠀⠀⡁⢉⠳⢕⣗⢕⢧⡳⡳⣝⠮⣎⠧⡣⡑⡔⢅⢃⠡⢸⢸⢸⢸⢰⠱⡡⡣⡒⢔⢈⢂⠂⠅⡂⡑⠨⢈⠔⡈⡂⡂⠢⡈⠄⢱⢈⠢⠑⠄⠀⠀⠀⠀
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⡅⠀⠠⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠢⢑⢑⢕⢯⡫⡗⡇⢇⢅⢀⢀⠠⠐⡈⢠⢀⠢⢈⠐⢌⢫⠳⣝⠮⣎⢧⡣⡫⡎⡎⡪⡐⢔⠨⡪⡪⡣⡣⡇⢀⠈⠊⢎⢆⠕⢄⠅⢅⠢⠐⠡⠂⠆⠢⠂⠈⠀⠀⠀⠀⢕⢌⢪⠨⡀⠀⠀⠀
⢈⠂⠀⠀⠀⠀⠠⠀⠀⠐⡄⠀⠀⠒⠀⠀⠀⠀⠀⢈⢂⠀⠀⠀⠀⠀⠁⢘⠀⠀⠄⠀⠡⠑⢝⢜⢕⢕⢕⢕⢕⢜⢔⡕⣕⣎⢆⡇⠕⠀⠈⠐⠨⡊⢮⠣⡊⠢⡑⢕⠱⡱⢱⢸⢰⢱⢹⢜⢕⢵⠡⠀⠄⢀⠀⠈⠪⢢⢑⢅⠪⡨⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠢⡣⠨⡀⠀⠀
⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡡⠀⠀⠀⠀⠠⠀⠸⡀⠀⠀⢀⠀⠄⠂⠀⠁⠑⠑⠕⡕⡕⡵⣹⡪⣮⡳⡝⡌⠄⡀⠀⠀⠂⢱⡁⠄⠁⠐⠀⠁⠈⠂⠕⢱⢱⢣⢏⢮⢺⠨⡐⠨⠠⢀⠁⠄⠠⠑⠌⡪⡸⡐⢔⢐⠄⡀⠀⠀⠀⠀⠀⠀⠈⡪⡂⢕⠨⡀⠀
⢈⠂⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⣄⡢⡔⣄⢇⢄⢀⠀⠀⠀⠀⠨⡂⠀⠀⠀⠀⠀⠐⠈⠀⢂⠐⡀⠢⢘⠸⡘⡞⣎⢯⡪⡪⢐⠄⠅⡂⡂⢬⢂⠀⠀⠀⡀⠀⠀⠀⠈⠔⡕⡕⡝⣜⠕⡕⡌⢜⠨⡀⢂⠐⡈⡀⢂⠈⠂⢎⢌⠢⡑⡐⠄⠄⠀⠀⠀⠀⠀⠰⠨⡐⠨⡐⡀
⠠⡃⠀⠀⠠⠀⠀⠠⠐⠀⡅⠀⠀⡠⡪⡺⡲⡜⣞⢼⡱⡣⣇⢇⢇⢄⡀⢈⡂⠀⠈⠀⠈⠀⠐⠈⡀⠂⡐⢐⠈⠄⠅⢕⠸⡸⣑⠑⠑⠅⡎⢌⠢⡘⡜⡔⠔⠄⢄⠀⠀⠀⠀⢐⢑⠜⡜⢜⠜⠌⡢⠪⢐⠅⡂⡂⡂⢐⠠⠐⢈⠐⠠⠘⢰⠨⡈⠪⡈⡂⠄⠀⠀⠀⠈⠂⡊⠌⡂⡐
⠨⡂⠀⠐⠀⢀⠀⠀⠀⠀⠆⢀⠪⡸⣜⢭⡳⣝⢮⢺⢜⣕⢧⡫⡮⡲⡱⣒⢆⠀⠀⠀⠐⠀⠁⠠⠐⢀⠂⡂⠌⡐⡁⠢⠡⡃⡧⡑⠀⠀⠀⠁⠑⠜⣜⢜⢅⠣⡑⢌⢐⠠⠀⠀⠂⠇⢕⠕⠡⢁⠂⠡⠐⠀⡂⢐⢀⠂⠂⠌⡀⠂⡁⠈⠄⡈⠢⡁⡂⠂⠅⡂⠄⠀⠀⠀⠠⢑⢐⠨
⠀⢪⠀⠂⠈⠀⠀⠀⠀⠀⡣⡢⡫⣊⠮⡺⣜⢮⢮⡳⡳⣕⢧⡳⣕⣝⢮⢳⢕⢅⠀⠀⠄⠀⠐⠀⢈⠠⠐⢀⢂⢐⠠⡑⢅⢇⢇⠢⠀⠀⠀⠀⠀⠀⠀⠁⠃⢇⢎⢆⠕⢌⠌⢔⠠⡀⢜⠄⠀⠂⠈⠀⠂⠁⠠⠐⠠⠨⠀⠅⡀⠂⠄⢁⠂⠠⠨⡂⠂⡁⠅⠂⠅⡂⠄⠀⠀⢂⠢⢈
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢣⢣⡓⡵⡱⡝⡮⢮⠓⠉⡏⠪⠳⣕⢗⡞⣜⢕⡇⡇⠌⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⠐⡐⢌⢆⢇⢇⢇⠂⠀⠀⠀⠀⠀⠀⠀⠠⠠⠨⡊⠮⡢⡣⡱⠨⢌⢆⢣⠀⠀⠀⠀⠈⠀⠄⠂⠁⠨⢀⠡⠐⠈⠠⠀⠂⠁⢸⠀⠠⠀⠂⢁⠨⢀⢂⠂⡀⠀⠊⢄
⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠨⡊⡎⣎⢧⢳⠩⢂⠐⠀⡎⡐⠀⡈⠕⢫⢪⢪⡺⡸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⡢⡣⡣⡳⡱⠁⠀⠀⠀⠀⠀⠀⠐⠈⠠⠑⢌⠪⡊⡊⢎⢇⢇⢕⢱⠡⡡⢀⠀⠀⠀⠀⠀⠐⠀⢂⠐⡈⠀⠅⢈⠈⠈⡰⠈⠀⢀⠀⠀⠠⠐⢀⠢⢐⠀⠈⠔
⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀⠪⡪⡪⡪⡪⡑⠄⠌⠐⣜⢀⠢⢐⠨⠠⠡⠁⢎⠄⠂⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠀⠄⡣⣫⢺⢸⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠅⢊⠢⠣⡣⢣⢣⢳⢘⢔⠡⡂⠄⠀⠀⠀⠀⠀⠄⠐⠈⠀⠂⠈⢐⠄⠀⠄⠀⠀⠀⠀⠐⠀⠌⠄⠌⡠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢅⢇⢇⢇⢏⠎⢌⠌⢌⢂⢵⠐⠅⢕⠨⡊⠌⢌⢪⠠⢐⠀⠄⢐⠀⠀⠂⠐⡀⡡⠠⡐⡐⡸⡸⡪⣣⢣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠠⠡⡑⢌⠢⡑⠕⢕⢅⢇⠢⡡⠂⠄⠀⠀⠀⠀⠀⠀⠁⠀⠄⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⢐⠐⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢕⢜⢬⢪⢪⢪⠪⢐⠨⢐⠐⡈⢪⠈⢂⠕⡐⠅⡂⢧⠑⢔⢱⢈⢂⢂⠡⢈⢐⢐⠜⡌⡆⡇⡎⡮⡣⡇⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⡡⠨⡢⡑⢌⢌⠢⡑⢕⢕⢌⠪⠨⡐⠠⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢂⠐
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠌⢆⢇⢇⢇⠇⢕⠡⠨⢐⢐⠐⠀⠂⠀⠌⠢⢑⠨⢸⠈⠄⡑⠕⢌⠢⢈⠪⡢⠢⣑⠱⡘⡜⡸⡸⡕⡇⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡊⢆⠪⡂⡆⠕⢌⠔⡈⠪⣊⢪⢐⢁⢂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠘⢐⠡⡊⡢⠀⠡⠐⠀⠈⠀⠀⠀⠈⡈⠄⠨⠸⠀⠁⠀⠐⠀⠁⢁⠂⠂⠁⠄⠣⡑⢜⢰⢱⢱⢱⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⢐⠌⡢⠑⠌⢌⠪⢐⠡⢊⢐⠁⢇⢖⢐⠄⠅⡂⢀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠁⡂⠑⢐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠠⠁⠢⢱⢱⠱⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢅⢅⠂⢅⠑⡐⠨⠐⡈⠄⠂⠌⢰⢑⠌⡜⡐⡄⠅⡀⠀⠀⡂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠠⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢇⢇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⡒⢔⢁⠢⢈⠐⢈⠀⡂⠌⠠⢁⠸⡐⠅⢊⠢⡪⠨⡂⡂⠀⠂⠀⠀⠀⠀⠄⠀⠐⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠡⠡⡑⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡪⢪⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⠱⠐⠄⠂⠐⢈⠠⠀⠄⢈⠀⡀⢈⢪⠀⠄⢑⢌⠪⡐⢄⠅⠠⠐⠀⠀⠀⠨⠀⠅⡂⡁⡀⠠⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠕⡠⢑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⡲⡐⢔⢀⠢⢑⠨⢂⠅⢅⠂⠀⠀⠀⠀⠡⡑⠰⡐⡐⢐⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⢂⠢⡁⠢⠑⠄⢅⠅⠀⠀⠀⠀⠄⠂⢈⠪⡐⠌⢔⠠⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⢈⠢⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⢒⢔⠢⡢⡂⡢⠠⡠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠨⠨⠨⠀⠀⠀⠀⠀⠐⠠⠈⠄⡊⢌⠪⡐⠌⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⢀⠂⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠪⠨⢂⠨⠈⠌⢐⢐⢐⠨⢐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠠⠈⠠⠁⠅⡂⠢⡑⠌⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⠐⠀⠅⠠⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠌⠄⠅⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠁⠄⠁⠅⢌⠢⠨⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⢂⠐⢈⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠠⠐⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠡⢁⠂⠅⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠠⢑⠐⡈⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠅⠕⡡⢁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠌⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡁⠂⡂⠌⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠁⡂⠂⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠂⠀⠀⡀⠠⠀⠂⠀⠈⠀⠀⠀⠠⢈⠜⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠠⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡂⡂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠄⠠⠠⠠⠠⡂⢄⠌⠀⠅⢊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⠄⠅⢅⠑⠄⠅⢌⢂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⢀⠠⠡⠡⡡⠡⠡⡑⠡⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⡂⠅⠅⡂⠅⠅⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠂⠡⠐⢈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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