⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠀⡀⠨⡀⢄⡐⠌⠀⡀⠀⠄⠈⠀⢀⠀⠀⠎⢀⢀⠀⠀⢀⠠⠀⡐⠄⡀⠀⠘⢼⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠘⠠⠐⡀⠅⠀⠠⠐⠀⠀⢐⠀⢂⠈⠀⠀⡀⢀⠀⠀⢀⠈⡀⡠⠁⠀⠁⠀⠠⠀⢸⢜⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠈⠀⠐⡀⠄⡐⠁⠂⠁⠀⠐⡀⠄⢀⠠⠐⡈⠐⠈⠀⠀⠀⠀⠂⠁⠀⠠⠈⠓⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠄⠁⠀⠀⠀⠀⢀⠠⠁⠂⠁⠐⠠⠀⠀⠀⠀⠐⠀⠀⢂⠅⠂⠁⠀⠀⢀⠀⠂⠁⠠⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡅⠀⠄⠂⠀⠀⠄⠐⢀⠌⠀⠀⡀⠠⠀⠄⠀⠈⠂⢌⢀⠀⠄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠌⠂⠀⡀⠈⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⢂⠄⢀⠀⠠⠀⢀⡐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠄⢂⠐⠀⠅⠀⠀⢀⠀⠀⠀⢀⠠⠈⠠⠁⠠⠀⠀⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡢⡣⣐⠠⠀⠄⢢⠂⠀⡀⠀⡀⠀⢐⠀⠌⡈⠠⠀⠀⠀⠄⠀⠀⡀⠀⡀⠈⠀⠀⡠⠁⠀⡀⠀⠠⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⢰⢱⢱⢨⢌⢔⢀⢂⢂⠄⡅⡢⢊⠌⡂⠁⠀⡀⠄⠂⠀⢀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⡀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡣⡱⡘⢔⢑⠔⠈⡀⠀⢀⠂⠀⠀⠀⠅⠀⢁⠄⠀⡀⠂⠁⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⢢⠣⡡⠐⡈⠠⠀⠀⠈⠀⠄⠡⠂⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠹⢝⢮⣎⢮⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡢⡂⡊⠀⠀⠂⠀⢈⠁⢀⠐⠈⠀⠀⡀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢷⢝⣎⡗⣝⢮⡪⡮⡺⡼⣜⡜⡮⡂⠀⠀⠄⠀⠀⡂⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡣⡣⡣⡫⡪⡳⣝⢮⣻⣺⡲⣽⣹⠀⠀⠄⠀⠠⠀⡂⠀⠀⠄⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢮⢪⡪⡪⡪⡪⡣⡳⡕⣝⢞⣞⠀⠀⠄⠀⡀⠠⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⢕⢕⢕⢝⢜⢎⢮⢪⡪⡪⡪⡪⡀⠂⠀⡀⠀⠂⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢝⢜⢎⠆⠀⠂⠀⡄⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢜⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢬⡰⡝⡵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡪⡣⡳⡱⡕⣕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⢝⢮⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡪⡪⡪⡪⡪⡪⡪⡣⡳⡱⡕⣕⢕⢕⢕⢕⢕⢅⢇⢇⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⡺⡜⡮⣪⢪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡪⡣⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢎⣗⢽⢜⣕⢝⣎⢗⢝⢮⡪⡪⣎⢮⢪⠪⠊⠀⠀⠀⠀⠀⠁⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣳⢳⡳⡵⣕⢧⡳⡹⣕⢕⢝⢮⡪⡎⠃⠀⢀⠠⠐⠀⠐⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡳⣝⡞⡮⡳⣝⢮⡪⡳⣕⢧⡫⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢻⡺⡪⡯⡺⣜⢵⡹⡪⡮⡓⠠⠐⠀⠀⠠⠀⠠⠀⠁⠀⢀⠠⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⡮⡫⡮⡫⣎⢗⣝⣝⠎⠄⢁⠀⠠⠐⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠘⡝⡮⡯⣪⡳⣕⠇⠅⠁⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⠁⢈⢹⣺⣺⣺⡺⠈⠀⠀⠂⠁⠀⠀⠠⠀⢀⠈⠀⠀⠁⠀⡀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠌⠀⠄⡘⣞⠎⠀⢀⠀⠁⡀⠠⠀⠂⠀⡀⠀⡀⠀⠁⠀⠁⠀⢀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⢁⢁⠂⠄⡌⠠⠈⠀⡀⠂⠀⢀⠀⠄⠀⡀⢀⠀⢀⠁⠀⠂⠈⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⡐⡈⡐⠀⠄⠂⠁⠀⡀⠈⠀⡀⠄⠂⠀⡀⠄⠀⠄⢈⢀⠡⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀