⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⢀⢀⢀⢀⢀⢀⢀⠀⡀⢀⢀⠀⡀⢀⠀⡀⡀⢀⢀⢀⢀⢀⢀⢀⢀⠀⡀⡀⡀⡀⢀⠀⡀⢀⠀⡀⡀⢀⠀⡀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⡀⠐⡀⠀⠀⠀⢐⢀⠀⠢⢠⠄⠀⠀⡒⢐⢅⢀⢀⠀⠀⠠⡱⡀⡸⢐⠀⠀⢀⡂⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⢌⠈⢦⢀⠀⠀⠀⢂⢂⠈⠂⠇⢆⠀⠇⠠⡐⠰⠸⡀⠠⢠⠁⠎⠨⡀⠀⢀⢂⠮⠸⠀⡀⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⢀⢀⢀⠘⢄⡑⠄⢅⠙⡐⠂⠢⢆⠂⠢⢀⠑⠍⡆⠀⠢⠀⠑⡱⣀⢜⠌⠆⠅⢣⡀⣂⠕⠨⠈⠁⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠂⠒⠐⠀⠂⠈⠈⠣⡂⠢⠠⠨⠠⡁⠂⢄⠀⠀⠑⠄⠐⠀⠀⠁⠁⠢⡑⢼⢄⢱⠑⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠂⡠⠂⠂⠈⠂⠆⢆⢄⡂⠠⢀⠀⠈⢢⠡⠈⠂⠌⡂⠀⠑⢄⠀⠌⠘⠀⠀⠀⠀⡀⠀⠀⢁⠪⠀⡃⠀⠀⠀⢀⡀⢀⠀⣄⠀⡀⢀⠀⠀⠀⠈⢲⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠄⠌⢄⠑⠠⠠⡠⡠⠠⠐⠒⠌⠢⢈⢀⠣⡂⠀⠑⠅⠄⠀⠐⢐⠀⠀⠑⡁⠢⠀⠀⠀⠐⢌⠀⠀⢐⠄⢀⠂⠀⠀⠀⠼⣧⢏⣞⣽⠼⢗⡏⢠⠀⠀⠀⠐⠅⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠈⠂⢅⠡⠅⢄⠐⢐⢨⠨⠠⠀⡐⠠⠢⠘⡄⠀⠀⠁⠀⠀⠀⠢⢀⠀⠈⠌⠈⠄⠀⠀⢢⠀⠀⢢⠂⠄⠀⠀⠀⠀⠃⠘⡘⡀⡉⢃⢘⠐⠃⠀⠀⠀⠨⡀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⢘⢘⢅⠢⠄⠄⡈⠈⠀⡂⠡⠀⠑⢑⠀⠀⠨⢀⠀⠀⠀⢃⠢⠀⢡⠣⡀⠀⢨⠌⠀⢈⠆⡐⠅⠀⠀⠀⠀⠀⠈⡽⠘⢁⡏⡥⠟⠀⠀⠀⠀⠨⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠂⡈⠐⠱⢐⢕⠠⡀⠀⡂⢆⠑⠀⠀⠑⠀⠐⡀⡂⠀⠀⠀⠅⢅⠸⠀⠁⠀⢠⠃⠠⠢⡰⡨⠈⠄⠀⠀⠀⠀⠚⠋⠀⡘⠋⠁⢀⠀⠀⠀⠀⠨⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⢄⠀⠀⠀⡠⠊⠂⠅⠅⢄⠈⠄⡀⠀⠈⠠⢀⠈⠄⠣⠁⠒⢄⢀⠀⠢⠨⡀⠀⠀⠈⠢⡁⠀⠀⠀⠠⠁⠄⠪⠢⡀⠄⡇⠀⠀⠀⢸⢣⣟⡼⣸⢱⣇⡮⠀⠀⠀⠀⢨⠂⠀⠀⢐⠀⠀⠀⠀
⠀⠨⡱⡀⡀⠪⡊⡈⡈⡈⠭⠑⠂⠁⡀⠀⠀⠄⠅⡑⡨⡢⡈⠠⡐⠐⢔⠀⠀⠨⡀⠀⠀⠀⠢⡀⠀⠀⠂⠀⠀⠀⠁⢊⠁⡧⠀⠀⠀⠙⠃⠛⠀⠃⠃⠘⠑⠃⠀⠀⠀⡈⠂⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠊⡌⢌⢄⢐⢔⢒⠰⡁⠅⠅⠒⠂⠀⠀⢀⠀⠁⠃⠑⡁⡂⡀⠀⠑⠑⠄⠀⠀⠀⠀⠀⠀⠔⠄⡀⠀⠀⠀⠀⢰⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠊⠢⢈⠂⡁⠢⡈⡊⠈⠀⡠⢐⠐⠈⠀⠀⠀⠀⠀⡀⢄⢂⢂⠂⠂⠂⠀⠀⡀⡀⠄⠌⠌⠈⠀⠀⠀⠀⠀⢸⠀⠨⡨⡈⠒⢄⡀⡀⡀⠀⠀⠀⡀⣀⡠⠆⡁⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡰⠨⢂⠨⠂⡀⠠⡊⢔⠌⠄⡐⠀⠀⠀⡠⢐⠑⠐⠀⠀⠀⠀⠀⠀⢔⠐⠐⢀⢑⠡⠀⠀⡀⠄⡢⠁⠀⠸⡀⠐⠄⢃⠂⡂⠈⡸⢔⠉⠉⢅⠈⠨⠨⡰⠒⠈⠉⠂⠀⢐⠀⠀⠀⠀
⠀⠀⠀⢄⠁⢄⠡⡑⠨⠈⡐⢐⠈⡀⡀⠌⠀⢀⠂⡂⠈⠀⠀⢀⢀⠀⡄⠔⢐⠀⠀⠀⡠⢂⠂⠁⠀⢀⢐⢁⢀⠐⠀⠀⠄⠀⢈⠌⠔⠀⠰⠁⡆⡂⡂⢐⢐⠈⢂⠱⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠨⡀⠁⡑⡉⠔⢸⠨⡐⢠⠑⢌⠌⠀⡠⡁⠪⢀⠀⡘⠀⠅⠂⡂⠀⡄⠃⠠⢐⠢⡑⠀⡀⠂⡠⢄⢂⠒⢀⡀⡂⠅⠰⠐⣌⠈⠀⠀⠈⠐⢘⢰⢨⠢⠠⢑⡀⢑⢱⠀⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠑⠀⠐⡐⠁⡄⠅⡱⠑⠡⡈⣂⠁⡰⡑⠄⠕⠠⡂⡐⡕⠀⡂⠰⠈⡀⠌⢔⠐⠨⡠⡂⠢⠑⠐⢔⠂⠠⠢⢑⠪⠠⠱⠡⡂⢐⢸⠀⡁⡣⢢⠀⡢⡈⡂⡀⢨⢄⡘⡄⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠊⡠⢨⢠⡪⢪⠨⡀⢅⠅⡪⠰⡡⡃⢑⢰⠀⡐⠌⠀⡄⠎⡈⡐⡜⠘⢐⡐⠡⡑⢅⠂⡐⠁⡑⢑⢌⠌⢌⢘⠆⡆⡐⠀⢌⢀⠊⠀⡢⠀⡆⢔⢸⠀⠨⠑⠀⠀⠀⢐⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠠⡪⠈⢈⢐⢐⠠⡱⡐⢥⠪⠂⡁⢊⠊⠢⡒�