⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⡀⠄⠠⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠔⠠⠠⠠⠠⠠⠠⠠⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠐⢀⠡⢈⠐⡀⡂⡂⠢⠠⠡⡁⡢⠡⠡⡡⠡⡡⢑⠅⢅⠕⡡⠡⠡⠡⠡⠡⠡⠡⠡⠡⠡⠡⠀⠂⠁⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠂⠨⢀⢐⢐⠨⢐⢐⠨⠨⡨⢂⢂⠢⡡⢑⠌⢌⠢⡑⢌⠢⡑⡐⠅⠕⡡⠡⠡⠡⢁⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀
⡐⢈⠌⡐⡐⡐⢌⢂⠢⡡⡑⢌⠢⠢⡑⢌⠢⡑⢅⠕⢌⠢⡑⠔⠨⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠁⢀⠐⠀⢀⠠⠀⠀⡀⠀
⡂⠅⡂⡂⡢⢊⠔⡡⡑⢔⢌⠢⡑⢕⢌⢢⠱⡨⡂⡇⠅⠕⠈⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠐⠀⡀⠄⠀⠀⡀⠀⠀⠀
⡂⢕⢐⢌⠢⡑⢌⢆⢪⠢⡑⡕⢜⢔⢱⢘⢌⠆⠣⠈⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠈⠀⡀⠀⠁⠀
⡪⡐⢅⠢⡑⡜⢔⢅⢇⢕⢕⢜⢜⢜⢜⢜⢔⠈⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⠀⠂⠀
⡢⡊⢆⢣⢱⢸⢸⢸⢸⢸⢸⢸⢸⢸⢸⢘⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠂⠁⢀⠠⠀⠠⠀
⡢⢣⢱⢡⢣⢱⢱⢱⢱⢱⢱⢱⢱⢑⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠈⢀⠀⠠⠀⠀
⢕⢅⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⠃⠀⠄⠀⢀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠠⠁⡈⠀⠄⠂⠀⠁
⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢅⠈⠠⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⡂⠐⠈⡀⠐⠈⠀
⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡄⠠⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡁⢂⠀⢂⠀⠁
⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡔⡌⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠐⠈⠀⠀⠀⠀⠂⢈⠨⢀⠐⡀⠌⢀⠀⠁
⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡝⡜⡜⡜⡆⠀⠀⠀⠠⠀⠀⢮⠊⠈⢑⢆⠀⠀⠀⠀⠀⠀⠀⠠⢸⠂⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⢐⠠⢂⠐⡀⢂⠐⠀⠄⠁
⡇⡇⡇⡇⡇⡇⡇⡇⡗⡕⡕⡕⡝⡮⡪⡪⡪⡪⡊⠀⠀⠀⠀⠀⠈⠈⠀⠠⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⢐⠐⡐⠠⢈⠐⠀⠂
⡇⡇⡇⡇⡇⡇⡇⡧⡳⡱⡱⡹⡜⡮⡪⡪⡪⡪⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⢐⠐⠠⠁⠔⠈⡀⠁
⡇⡇⡇⡇⡇⡇⡏⣎⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⢀⠠⠀⢐⠐⡐⠨⠈⠄⡁⢂⠐⠀
⡇⡇⡇⡇⣇⢇⢏⢎⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⢊⢀⢀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠐⡀⡂⠅⠡⡁⡐⢀⠂⠁
⡇⡇⡇⡇⡇⡧⡣⡣⡣⡫⡪⡪⡪⡪⡪⡪⡪⡰⣘⠠⡠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡂⠡⠠⠐⡈⡐⡀⡂⡐⢀⠁
⡇⡇⡇⡇⣇⢧⢫⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡲⡐⡕⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠰⢀⢂⠡⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⡀⡂⠔⡀⡂⡐⢀⠂⡀
⡇⡇⡇⡇⡇⡧⡣⡫⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡢⡣⡂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠡⡁⡂⡂⡂⠅⡂⡐⡀⠂⠄⠀
⡇⡇⡇⡇⣇⢗⢝⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡢⠀⠀⠀⠀⠀⠁⠀⠁⠂⠂⠐⠨⠐⠅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠢⢂⢂⠂⢅⢐⢀⠂⡁⠌⠀
⡇⡇⡇⡇⡇⡇⡧⡣⡫⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡊⠌⠕⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠁⠀⢐⢐⠅⡊⠔⡠⠑⡐⠠⠂⡐⠠⠐⠀
⡇⡇⡇⡇⡇⡏⡎⣎⢎⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⢊⠨⡐⢬⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢕⢐⢅⢊⠔⡠⢁⠂⠅⢂⠐⡀⠂⠁
⡇⡇⡇⡇⡇⡇⡇⡇⡧⡣⡳⡱⡱⡹⡜⣎⢎⢎⢎⢎⢎⢆⠢⠑⠁⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠊⠆⢕⢐⠅⡂⡂⡂⠅⠌⠠⠐⢀⠐⠀
⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⢇⠇⠇⠃⠁⠀⠀⠀⡀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠐⢐⠠⠡⢈⠐⠈⢀⠀⠄
⡇⡇⡇⡇⡇⡇⡇⡇⡇⡇⡇⠇⠇⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠄⢀⠐⡈⠄⠠⢁⠀⠀⠀⡀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠁⠄⢀⠀
⢕⢕⢕⢕⢕⢕⢕⠕⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡐⠨⡨⢂⢂⠂⠁⠢⠠⢑⠀⡀⢀⠐⡀⠄⠀⡀⠠⠐⠀⢁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡣⡣⡣⡣⡣⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠅⢌⠢⡱⡨⡨⠠⠁⠄⠄⠄⡂⠔⡀⠐⢀⠠⠀⠄⠂⡀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀
⡪⡪⡪⡪⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠌⡎⡪⠨⡨⠨⡨⢪⠨⢂⠠⠈⡀⠐⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⡪⡸⡸⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⠈⠘⠜⠜⠜⠌⠄⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠀⠀⠀⠀⠀