⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⡰⡸⡸⡸⡸⡱⡱⡰⡰⣘⠌⡂⡑⠠⠁⢌⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⠪⠪⠒⠍⠲⢠⢁⢁⠢⢂⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡱⡱⡱⡱⡱⡱⡱⠑⢁⠄⠂⢀⠨⠠⠨⠠⠀⠁⠣⡌⡜⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⡪⡪⡪⡪⡈⠌⠠⠈⠀⠄⠀⠀⠀⠀⠀⠁⠁⠂⡀⠀⢑⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⡣⡣⡣⢂⠌⠨⠢⠡⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⡣⡣⡣⠀⡌⡘⠌⢌⢀⢂⠀⠀⣀⢠⢰⠠⠁⠠⠀⠀⠀⢀⢂⢐⠕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡜⠄⡜⡰⢨⢪⢢⢢⠢⡊⠔⠨⠐⠱⡑⢡⠀⠀⠀⠜⢀⢂⠢⡈⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢎⠊⡜⡜⡜⠜⠄⠀⠀⡀⠀⠀⠀⠀⠀⠁⠌⡐⡀⢂⠂⢅⢂⢂⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠕⡨⡘⢌⠬⠈⠪⠸⠨⠪⢪⠰⡠⢀⠀⢨⡐⡌⠄⠌⡂⡂⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠠⠋⣆⠑⢥⢈⡊⠢⠊⢆⠱⡁⠄⡂⡁⡘⠐⠨⠨⡐⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡫⡌⢌⠐⢕⢢⢑⠱⢱⢐⢄⠂⠅⠅⡂⡂⠆⠅⠅⡂⠄⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠘⡔⡑⢕⢅⡢⢁⠣⡪⢄⢅⢑⢑⢑⠩⢠⠑⠈⠨⠨⠠⠡⢁⠀⢄⡂⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢀⢠⢠⢠⢠⢠⢠⢠⢠⢢⢪⢪⠀⠀⠈⠐⠥⡑⢜⢔⢔⣐⡁⡃⢑⠂⠆⠪⢐⠨⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢄⢄⢔⢢⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢃⠀⠀⢀⠠⠐⢅⠅⠣⡒⠕⡕⡤⡡⠡⠱⡡⠁⡀⠀⠀⠀⠀⠀⠀⢀⠔⣈⢢⢨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⠥⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⢣⢣⢣⢣⢣⠀⠀⠀⠀⠀⠑⡕⡕⢔⢁⢂⢐⢈⠪⢑⠀⠀⠀⢢⠠⠀⠀⠀⢀⠢⢣⢣⢣⢪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⠕⠡⢱⢱⢱⢱⢁⠀⠠⢁⢇⡀⠘⢜⢢⢂⢂⠢⠡⠑⢀⠀⠀⠀⠰⡡⢡⠱⡠⢐⢨⢢⢂⢇⢇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⠡⢣⢣⢣⢣⢣⠀⠠⢀⠁⠘⠰⠢⡀⡂⠂⠁⠁⢄⠁⠀⠀⠀⠈⠎⡄⠣⠘⡢⡘⡘⡘⢜⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢌⢪⢪⢪⢐⠱⡱⡱⡱⡱⡡⢑⠐⢄⠀⠀⠀⠁⠑⠱⡱⡡⢂⠀⠀⠀⠀⠀⠡⢈⠄⢁⢆⠂⡢⡨⡊⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢜⢜⢜⢔⠅⢕⢕⢕⢜⢔⠸⡸⡱⢄⠀⠀⠀⠀⠀⠈⢪⢢⠀⠀⠀⠀⠀⠈⡀⡐⠨⡐⠕⡆⡇⡇⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢕⢕⢕⢕⢕⢕⢅⢇⢕⢎⢎⢎⢎⢎⢎⢎⢎⠸⡸⡸⡸⡸⡨⢪⢪⢪⢢⠀⠀⠀⠀⠀⡇⡕⡱⠠⠀⠀⠀⠀⢀⠂⠅⡂⠅⠊⠜⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⢕⢕⢕⢕⢕⠌⡎⡎⡎⡎⡆⡣⡣⡣⡣⡢⠀⠀⠀⠀⠪⢸⠘⠌⡂⠄⠀⠀⠀⢪⠢⠨⠨⡂⠅⠢⡁⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡢⡣⡣⡣⢪⢪⢪⢪⢪⢨⢪⢪⢪⢪⢂⠀⠀⠀⠈⡂⡡⠱⢐⢁⠂⠀⠀⠢⡙⣌⢂⠑⢅⠅⡂⠢⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀