⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠠⢠⢠⢀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⡘⠄⢅⢑⠩⢐⠁⠅⡊⡘⠌⠕⡱⡐⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠪⡪⠐⠄⠕⢐⠠⠈⠄⠌⢐⠀⡂⡁⠅⡐⠠⠁⡊⠨⠢⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡣⠣⡊⠌⠌⠌⠠⢂⠡⠡⠨⠐⡐⡀⡂⢂⠂⡡⢈⢐⢈⠐⡐⢈⠐⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⢫⠨⡐⡡⠡⠈⡂⢂⠐⠡⠨⢐⠐⡀⡂⠅⢂⠂⡂⢂⢐⢐⠐⡐⡈⠄⢂⠁⡑⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡪⡪⡪⣂⠢⡁⠢⢐⠐⠨⠨⢐⢐⢌⢔⢠⢑⢐⢐⠄⢅⢐⠠⠂⡂⠄⠅⡂⡂⡐⡀⡐⠨⡐⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⡯⡺⡸⡰⡱⢌⢌⠢⡌⠌⣊⢆⠇⡃⠅⠌⠪⡢⡑⡌⢔⢐⠌⡂⡢⠡⡁⠢⢐⢐⠠⢂⠡⢀⠂⠢⢑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢯⡺⡱⣝⢼⠱⠳⠙⢌⢪⠪⠨⢐⠠⢈⠈⠀⢸⠸⠸⡸⢔⢕⢕⡢⡣⢌⢪⢐⠔⡨⢐⢈⠄⠌⡐⠠⢁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡙⡉⠀⡀⡠⢠⠠⠨⢂⠁⠅⠂⠠⠀⠀⠠⢐⢅⢄⢄⠄⡀⠁⠑⠙⠱⠣⡇⣗⢜⢴⢰⡡⡱⡠⡡⡠⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⢆⠈⡀⡀⡀⡄⡄⡌⡢⢄⠀⠂⠀⢀⠄⢆⢅⢄⢄⣀⣀⢈⢈⠈⠈⠂⠢⠄⢄⢉⠊⠇⠗⡝⣜⢜⠜⠀⠈⠀⡀⡐⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⡀⡔⣒⡒⡆⡇⢇⠣⡑⡑⡘⡐⠍⡊⠜⡨⠨⡂⠪⡐⠅⢆⠪⡱⡑⡕⡖⢦⢢⢤⢠⠀⠑⠐⠄⠌⢈⠊⢀⢐⠄⠅⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡠⡪⠪⡊⡢⠨⠐⠐⠠⠈⠄⢂⠂⠌⡐⠨⢐⠠⠡⠨⠨⠂⢅⠕⡨⢐⠔⡨⠨⡊⡪⢪⢣⡳⣕⢔⢔⡨⡐⠈⡀⠄⠀⠄⠈⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠄⠰⡁⠀⠂⠨⡊⠈⡂⠌⠐⠄⡂⢁⠂⠡⠨⢐⠨⢐⠨⠨⢐⠨⠨⠨⠨⠨⡐⠨⠠⢑⠨⢐⢑⠌⢌⢢⠱⢱⢱⢹⢪⡪⡂⡁⠀⠄⠂⠐⠈⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠨⠀⠠⠐⠀⠐⠁⠢⠨⡈⡐⣀⠂⠌⡈⢂⠂⢌⢐⠨⠨⢐⠨⠈⠌⠌⠢⡨⠌⡊⡢⢊⢊⠢⡃⢕⢡⢡⢣⢣⠳⠑⡁⠄⠀⠂⠐⢀⠁⠄⠁⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠊⠄⠀⡀⠀⠀⠀⠀⠀⠈⠈⠐⠑⠑⠐⠒⠸⢐⢄⢆⢅⢆⢔⢅⢅⠥⡑⡄⡕⢌⠔⡅⢆⠕⠜⠔⠑⠑⠁⢁⠀⠂⠠⠀⡁⢈⠐⠀⠄⠂⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠈⡂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⢈⠈⡀⠁⠄⠐⠈⡀⠂⠠⠁⢈⠀⠄⢁⠐⠀⠄⠠⠀⡁⠄⠂⠈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢑⠄⠁⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠠⠀⠄⠠⠁⡀⠁⠄⠠⠈⢀⠂⠠⠐⠀⠄⡀⢁⠐⢀⠁⡀⠄⠈⠄⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⢀⠀⢂⠈⠠⢀⠐⠈⡀⠂⡈⢀⠐⠠⠈⡀⠂⠠⠀⠂⠠⠀⠄⠐⠈⠔⡈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⡀⠐⠀⠄⠁⠄⠠⠁⡀⠂⡀⠂⠐⡀⠂⠠⠈⡠⢈⠠⠁⠐⢀⠁⡌⠜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⢅⠑⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠄⠠⠈⢔⠨⢐⠡⡢⠐⠀⢂⠠⠈⠄⠐⢈⠀⡁⡈⢐⠐⡄⠁⠄⠌⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⢐⠄⠀⠀⠀⠀⠀⠁⡑⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠌⠊⢆⠣⠑⠠⢈⠐⠠⠐⢈⠀⠡⠀⢂⠠⠀⠆⠕⡌⡀⠅⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠡⠀⠡⠐⠨⢈⠐⠀⠂⡁⠐⡀⠌⢀⠡⠀⠄⠐⠀⢜⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠨⠂⠊⠀⠀⠐⠈⢀⠈⠄⢀⠂⠁⢁⠀⠂⠠⠐⠀⠀⠄⠐⠀⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠅⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠀⠠⠈⠀⠠⠀⠁⢀⠠⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢐⢀⠁⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⢄⠨⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠢⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⠢⡠⡀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⢐⠢⠪⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠑⠉⠊⠑⠐⠐⠂⠊⠈⠂