⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⢂⠐⡀⡂⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠐⡀⢂⢐⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠐⡐⢄⢊⠔⡐⠔⡐⢄⠂⡂⡐⢐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⡂⠌⢔⢐⠔⡐⡐⡐⡈⠄⠄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠢⡨⢂⠅⡢⠑⠌⢌⠢⢑⠌⢔⢀⠂⡂⠄⡀⠀⠀⠀⠀⠀⠀⠌⠨⡈⡢⢊⠌⡂⡢⢑⢐⠌⢔⠨⢂⠅⡐⢀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠢⡑⡐⢅⢊⠔⡡⢑⠡⢊⠔⡨⢂⠢⠡⠐⡐⠠⠀⠀⠀⠀⠀⠅⠡⡁⡢⢊⠔⡨⢂⠌⡂⡢⢑⢐⠅⡑⠌⠔⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠄⢕⠐⢌⢂⠢⡑⡐⢅⢊⠔⡨⢐⠡⢊⠌⡂⠄⠅⢂⠀⡀⠠⠈⠌⡐⡐⢌⢂⠪⡐⡡⢊⠔⡨⢂⠢⡑⠌⢌⢊⠌⢐⠀⠀⠀
⠀⠀⠀⠀⠅⢕⠨⢂⠢⡑⡐⢌⢂⠢⡑⡐⠅⢊⢀⢂⢐⢈⠐⡐⢐⠠⠁⠅⠡⠐⡀⢂⢂⠑⢔⠨⢂⢊⠄⢕⠨⡐⢅⢑⢐⠌⡀⠀⠀⠀
⠀⠀⠀⠀⢁⠢⠡⡑⠌⢔⠨⢂⠢⡑⡐⠠⢁⢂⢐⢀⢂⠐⡐⢐⢀⢂⠡⠨⠠⢁⠂⡂⡐⡈⠄⠅⢕⠠⡑⡐⠅⢌⢂⠢⡁⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠌⠌⡢⠡⡑⢌⠢⡑⡀⡂⡁⡂⡐⡀⡂⡐⢐⠐⡀⡂⡐⠠⠡⠈⠄⢂⢐⢀⠂⠌⡐⠠⢑⢐⠌⢌⢂⠢⠑⡀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠂⡑⠌⢔⠨⢀⢂⢐⢀⢂⢐⢀⢂⠐⡐⢐⢀⠂⠄⠅⠌⠨⠈⠄⢂⠐⡈⡐⠠⢁⠂⢅⠪⢐⠐⡁⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡂⢂⢐⢀⢂⢐⢀⢂⠐⡐⢐⢀⠂⠌⠄⠅⠌⠨⠈⠌⡀⡂⡐⠠⢁⠂⠌⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⡂⡐⡀⡂⡐⡀⢂⠂⡂⡐⡈⠄⠡⠈⠌⠨⢈⢐⢀⠂⠄⠅⠂⠌⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⢐⢀⢂⢐⢠⢦⢦⠂⡐⡀⡂⠌⠨⠈⠌⠨⢀⢦⢴⡌⠠⠁⠅⠡⠡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⢂⠐⡀⡯⡯⣯⡃⠄⢂⠐⡈⠌⠨⠈⠌⢸⣝⢷⢽⠀⠅⠡⠡⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠐⡈⠠⠙⠝⠞⠠⠨⢀⢂⢐⠨⠠⠡⠨⢀⠫⠯⠃⠨⠠⠡⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠠⠡⠨⠠⠡⠨⠐⡀⡢⢐⠄⠅⢌⠐⡀⡂⠄⠅⠡⠨⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠄⠢⡐⡐⠄⢕⠨⠠⠡⠨⠐⠨⡐⡡⢊⠌⡂⢂⢂⠐⡈⡢⢑⠨⡐⠄⡢⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⡂⠕⡈⠌⡐⠐⠌⠢⠑⡐⡀⡂⠅⡢⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡐⠌⠂⠊⠈⠀⠀⠐⠐⠠⠡⠨⠠⠡⠐⠀⠀⠀⠀⠁⠁⠊⠔⡠⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀