⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣳⢷⣻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⢱⠸⡘⡽⡽⣽⣳⣻⣺⣻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⡑⡑⢕⠬⣑⠳⣳⡳⣝⢷⢽⢝⣖⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⢃⠇⡭⡢⡹⡱⣫⡳⣕⢯⡳⣝⢖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡮⠫⠩⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠐⠨⢒⢜⠰⡙⡸⠱⡝⡮⡳⡱⣝⢵⢤⡀⠀⠀⠀⠀⠀⣔⠵⡎⠊⡈⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⠂⡑⠅⠕⠡⢘⢎⢏⢗⢕⡳⡱⡩⡓⡆⡄⡀⢜⡜⡼⢈⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⢂⠀⠨⠈⡂⡪⡊⢆⠣⡱⠱⡱⡑⡕⡕⡕⣕⠳⡸⠨⢂⢈⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡔⠙⠐⠁⢂⠀⠈⠐⠨⢢⠱⡨⢊⠢⡱⡑⢕⠸⡰⡳⡁⢑⠀⡀⢂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⢂⠁⡈⠄⠂⠀⠁⠠⡁⠥⡑⢌⠪⡨⢒⠨⠪⢸⢘⢜⠔⢀⠁⠠⠐⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢖⡢⠆⠆⡆⢄⢀⠁⠕⡀⡀⠂⢀⢁⢔⠱⢘⢌⢊⠢⠑⢌⢂⠪⢐⢸⢨⢂⢅⢂⢐⠠⢈⠐⠀⠀⠂⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠆⠕⠊⡈⠄⠂⠐⠀⡀⠀⠈⠐⠅⡄⡁⡀⡰⡑⡐⡐⠨⡈⡐⠄⡑⡐⢸⢰⠱⢰⢡⢂⢔⠠⢁⠀⠈⠀⠄⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠈⠄⠄⠂⡈⢀⠂⠀⠄⠁⡀⠀⡀⠊⢔⠕⢌⠢⡊⡂⢆⠢⡑⡐⡐⢸⢸⢸⠸⡈⡆⢇⠌⠠⢂⠀⢁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢲⢵⢢⠂⠀⠄⠀⠠⠀⠁⠄⢁⠠⠀⠠⢀⠣⡑⡡⢂⠊⠌⡢⠣⡱⢨⢂⢪⢪⢒⢅⢗⢜⠔⢅⠕⠠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠝⢌⠊⠂⠑⢀⠐⠀⠄⢀⠀⠄⠀⠐⢈⢠⠪⠨⡂⢪⢐⠅⡑⡠⠡⢈⠐⠀⡇⡇⡇⡇⢜⠌⢜⠆⡈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠈⠠⠁⡀⠌⢀⠂⠠⠐⠀⠄⠀⢌⠢⡡⢃⠪⠰⢐⠨⠢⠢⢑⠠⠈⠀⡕⡕⡕⢕⠅⡍⡢⢑⠀⠌⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡤⡔⡄⢄⠀⠄⠂⢀⠂⠁⡀⢁⠆⢕⠨⢂⠊⠌⠔⡡⠡⡡⠡⠨⠀⠀⡳⡕⢕⠱⡡⠸⡨⠀⡀⢂⢂⢂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠭⡃⢑⠈⠠⠁⠄⡀⠀⠀⠁⠐⢅⠕⡡⢊⠄⢅⠣⡑⡐⠅⡂⠅⠅⢀⠀⢕⢕⢕⠱⡨⢂⠱⠠⢈⠐⡀⡀⠂⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠠⠐⡀⠡⠐⢈⠌⢆⢀⠰⡁⡪⢐⠅⡊⠢⡑⡐⢌⠢⢘⠨⢈⠀⠀⢕⢕⢅⠇⢌⠢⡈⢎⠠⡀⡂⠄⠅⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⢂⠀⢊⠀⡢⡣⡂⡪⢐⠌⢌⠂⢆⠊⢔⠡⡑⠨⠀⠀⢀⠪⡸⡐⢕⢐⠡⢂⠘⠠⠀⠄⠁⠌⠀⠅⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⢀⠂⠅⡪⠨⡊⡎⠪⠐⠡⢑⠨⢂⢑⠌⡈⠀⠈⡀⢌⢪⠪⡂⡂⢅⠢⠡⢁⠈⠄⠡⢁⠈⠨⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠡⢘⠄⠅⠀⠄⠠⠀⡁⠐⡀⠄⡀⡢⡸⡌⡢⡑⢌⢂⠢⠨⠨⠠⠱⠈⠐⡀⠂⡐⠠⠨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⡨⠈⢄⠡⡀⣅⢄⡆⣖⢕⢇⢇⢇⢎⠢⡱⠨⡈⠌⠐⠄⠣⢁⠐⡀⠂⠡⠈⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢕⢆⢗⢝⢜⢎⢞⢜⢜⢜⢜⢌⠪⡪⡨⠢⡂⠪⢐⠑⠨⡂⡐⡀⠅⢀⢁⠡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡪⡪⡲⡹⡸⡑⡕⡝⡜⡜⡔⢕⢅⠪⡸⠨⡂⢕⢠⠡⢑⢐⠠⠠⡊⢄⠄⠨⢐⢔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢪⠪⡪⡪⡪⢪⠪⡪⡘⢌⠢⡡⢣⢘⢜⠜⡈⡢⠨⡂⡂⡪⡘⡌⠄⢨⠨⡘⠸⣜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠣⠪⡨⠢⢑⠔⡈⡢⡱⢘⠜⡐⢔⠜⠌⢌⢌⢢⠱⡡⡑⡠⡡⡑⢌⠪⠐⠄⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠡⠂⠅⡂⠌⡂⢊⠐⠔⡨⠨⡂⠅⡅⢕⢜⢌⠎⡆⢕⠰⡑⡌⡔⡜⡌⡇⡕⢔⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢂⢂⠂⢂⠐⡈⠔⢌⢊⠔⡑⡜⢌⢆⠣⣑⢬⡲⣝⢜⡜⠜⠘⢈⠐⢀⠂⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡂⢌⠪⢂⠢⡑⡑⡌⣆⢕⣝⡼⢕⠋⠌⡀⠄⠠⢁⠠⠐⡀⠌⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⡑⢅⠅⡇⡕⡕⡵⠵⠝⡨⢰⢰⢱⢑⢆⢕⢅⠣⡊⡢⢂⠅⡢⠠⠀⠀⠀⠀⠀⠀