⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡄⡠⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀$⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⡕⡕⡕⡕⡜⡼⣜⢼⣪⡲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⣪⡳⣹⢸⢸⢘⢜⢮⡪⣳⢕⢗⢵⢕⡀⠀⠀ ⠀$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡯⣻⣺⣺⡺⡜⡜⢜⢜⢎⢞⢪⠫⣪⡫⡳⢅⠀⠀⠀⠀⠀ ⠀ ⠀⠀ $
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢯⢺⢪⡪⡪⡪⡊⢆⢳⢕⣕⡱⣕⡜⣎⢎⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡎⡎⡎⡎⢎⢪⢘⢌⢪⢣⡳⡝⡮⡺⡜⡮⡪⡃⠀ ⠀$⠀⠀⠀⠀ $
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠪⡊⢎⢊⠎⢜⢐⡑⡌⡎⡎⡎⡎⡗⣕⢇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡪⢨⠢⡑⡑⠔⢌⠢⡣⡣⡳⡱⡡⡢⡪⠂⠀⠀⠀⠀⠀⠀ ⠀$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⡌⡢⡑⡐⠌⡊⠢⡑⢜⢸⢰⢌⢆⢥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀$
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢌⠆⡆⠪⡐⢌⠨⠐⠡⠪⢸⢸⢹⡱⠀⠀⠀⠀⠀ ⠀⠀$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⢣⠱⡑⢌⢂⠪⡠⠡⠈⠄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀$⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⢆⢇⠕⡅⢕⢑⠌⠌⡔⠀⠀⠀⠀⠀⠀⠀⠀$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠠⠐⠀⠄⠂⢀⠁⢇⢇⢇⠕⢅⡇⣿⡆⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀$⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠠⠐⠠⢁⠐⠠⠈⠄⠄⠂⠐⠈⠀⡀⠈⠳⣷⣭⡺⠾⣿⡇⠁⠅⢐⠀⡂⠄⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⠀$⠀⠀⠀
⠀⠠⡈⠄⠂⠁⢈⠠⠈⠄⡁⢂⠁⠄⠡⠈⠠⠀⡈⠀⠊⢒⢪⢪⢈⠃⠌⠨⢀⠂⡐⠈⠄⠡⢁⠢⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡂⡂⢐⠀⡁⠄⠀⠂⠁⠄⠂⡐⠀⡁⠄⢁⠂⠄⠈⠄⠂⡁⢗⢽⠌⡈⡐⡀⠂⠄⡈⠄⡁⠂⠄⠅⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠌⠄⠠⠀⠄⠡⠈⡐⢀⠡⠀⠂⡀⠀⢐⠠⠁⠌⠠⢀⠐⠈⠣⡃⠄⠂⠄⡁⠂⠄⠂⠄⡁⢂⠡⠐⠠⠀⠀⠀⠀⠀$⠀⠀⠀⠀
⠀⠀⢕⠡⠡⠐⠀⠐⡀⠐⡀⢐⠀⠁⠄⠀⠠⠐⢈⢀⠡⠀⢂⠁⠌⢐⠈⠄⠡⠀⠅⠂⡁⢂⠀⢂⠐⢈⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢅⢌⠔⠠⠈⢀⢀⠁⠄⠂⡈⠄⠂⠁⠀⠄⠂⠠⠐⡈⠠⠐⢈⠠⠠⠁⠌⠠⠁⡂⢐⠠⠈⢀⠂⠐⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠔⡈⠄⢂⠠⠀⠂⠂⡁⠠⠐⢀⠀⠄⠀⠂⢁⠐⠀⠅⠂⢂⠐⠀⠅⠨⢀⠡⠀⡂⢐⠀⠐⢀⠁⠡⠀⠅⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⡢⡂⠅⢂⠠⠈⠄⠡⠐⡀⣦⡐⠀⠀⡀⠁⠄⠂⢁⠈⡈⡀⠂⠂⠁⠁⠄⠐⡀⢂⠐⡀⢈⠀⠠⠁⠌⢐⠠⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠒⢌⠪⠠⠐⠀⠂⢁⠐⠠⠈⠞⢦⠀⠀⡂⠐⠈⠀⠄⠠⢀⠁⠅⡈⢀⠀⠁⠄⢂⠐⠠⠀⠀⠐⠈⡀⢂⠂⡂⠄⠀⠀⠀⠀
⠀⠀⠀⠈⠆⢕⠨⠐⡁⢁⠠⠐⠀⡁⠄⠂⠨⠀⠂⠌⠄⡁⢂⠡⢀⢂⢐⢀⠂⠄⡐⡀⡂⢪⣔⢄⣀⠁⠐⠀⠂⠐⠐⠈⠄⠀⠀⠀
⠀⠀⠀⠀⠁⠱⡈⡢⠨⠀⠄⠐⢀⠠⠀⠡⠈⢀⠁⠂⢂⠐⡀⢂⠐⠠⠐⠠⠈⠄⠂⡀⠂⠌⢷⡯⡮⡢⢁⠈⠄⠡⠈⠄⠡⠀⠀⠀
⠀⠀⠀⠀⠀⠡⠐⠄⠅⠅⠂⢁⠀⠄⢈⠀⠂⠠⠈⡈⠠⠐⠀⠂⡈⠠⠈⠠⠁⢂⠁⠄⠡⠈⠌⡊⠳⠉⠄⢂⠨⠀⡂⠁⠌⠐⡀⠀
⠀⠀⠀⠀⠀⠀⠈⢌⠪⠠⡁⠄⢀⠐⠀⠈⡀⠁⠄⠐⡀⠌⢀⠡⠀⢂⠡⢈⠐⠠⠈⠄⡁⠅⢂⠠⠐⠈⠠⢀⠂⡁⠄⠡⠈⠄⠄⠀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠁⠄⠂⡀⠀⠄⠁⠀⠐⠀⠁⠠⠐⠀⡐⠈⡀⠄⠠⠈⡀⠡⠐⠀⠂⠄⠂⡈⠄⠡⠀⢂⠀⡂⢈⠀⠡⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠐⠀⠀⠀⠂⢐⢀⢁⢀⢀⢀⢀⠄⠀⠀⠐⠀⠠⠀⠈⠈⡀⠂⢁⠀⠠⠐⠈⡀⠠⠀⠂⡈⢀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⢌⠀⢀⠠⠐⠀⠀⠠⠀⠀⠀⠈⠀⠑⠈⠪⠐⡡⠀⢀⠠⠀⠀⠠⠀⠁⠀⠈⠀⠈⠀⡁⠐⠀⠂⠁⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⠂⠀⠄⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⡀⠂⠁⡀⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠄⠁⠄⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠄⠂⠀⠁⠀⡀⠄⠀⢀⠐⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⡀⠄⠀⠄⠂⠀⠐⠀⠈⠀⡀⠈⠀⠀⠀⠀⠀⠄⠠⠐⠀⢅⢂⠀⡈⢀⠠⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⡀⠀⡀⠄⠂⠀⠂⠁⠀⠀⠠⠀⠠⠀⠀⠄⠀⠠⠀⠢⡂⠅⠀⠄⢀⠂⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀