⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⡲⡒⠒⠒⠀⠂⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠖⠂⠀⠀⡦⠖⣹⢀⠀⠀⠀⠂⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎⢀⠀⠀⠠⠙⣃⠘⡈⢜⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠌⣦⣤⢊⡔⡐⡀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡵⠀⠀⡰⠀⡉⠞⡑⣱⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠂⠨⠔⠗⢂⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⢄⠀⡨⣜⠨⠂⠄⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠶⠞⠁⠀⣁⡆⠀⠀⠀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠠⠤⠀⠄⠠⠀⠀⠀⠀⠀⠀⠊⠀⠀⠖⠀⡃⡩⠘⠀⠀⠀⠀⠈⠀⠐⠐⠂⠐⠐⠐⠐⠂⠂⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⡂⠂⠀⣇⠤⡡⠀⠀⡡⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⡧⠁⠄⠅⢱⠃⠀⠄⢠⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠀⢂⢈⠀⢀⠀⠐⢤⠰⠂⠀⠀⡣⠀⠀⠐⣴⣄⣤⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠖⠈⠃⠠⠄⠀⡈⡚⠀⠀⡌⠐⠴⠐⢇⡼⡐⠁⣀⠅⠈⣗⢀⠀⠖⣠⠘⠄⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢂⠠⠁⠀⠀⠙⠲⣂⠄⣉⠀⠃⠐⠀⡀⡈⠘⠁⣃⢂⠉⢀⣐⡶⠀⡙⠎⢒⠁⣈⡀⠬⠍⡤⢲⢮⣡⠰⠀⠆⢀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠜⣗⡆⠋⠀⠠⡀⢐⢂⠀⠊⠘⠒⠢⢤⣶⡄⡄⠀⠣⢀⠀⢎⠴⠃⢀⠀⠀⣤⠽⠐⢁⡀⠀⠠⠝⡥⠉⢰⠡⢊⢴⠠⠂⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠲⢲⠤⡋⡢⢀⢅⡉⠐⡨⠀⠂⠈⠉⡁⠠⢤⡀⠀⠀⠀⠀⠂⠀⢀⣐⠗⠄⠞⠋⠈⠋⡁⢠⣤⠧⡒⠔⠨⡊⢔⠔⢌⠄⢔⠰⠴⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡲⢀⠐⠀⠛⠀⠉⠂⠀⠀⠄⢨⠢⢂⡂⠕⠒⠐⢀⡠⠀⡀⡀⠁⠂⠀⠀⢀⠔⠼⠍⠁⡉⢈⠨⠀⡐⢄⡂⠣⢑⢀⢋⡃⣪⠸⢢⠁⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡈⢡⢠⠀⡀⠠⡸⢊⠰⠣⢉⢀⠀⠀⢉⣁⠘⠨⢀⢤⣅⡠⠁⠀⢠⢀⡀⡐⠁⢘⠠⠲⠐⠍⡒⠐⠃⠥⣁⡁⠝⢯⣜⡂⡆⠀⠀⠂⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠠⠀⠀⠘⢎⣀⡌⡌⠀⠤⠩⣂⡌⠠⣔⡠⠢⠚⢁⠀⠄⠀⠑⣃⠵⡋⢅⠐⠀⢒⠂⡲⠨⣆⠪⢰⠂⡠⠈⠈⠀⠤⠄⢀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠈⠀⢀⠲⡚⣐⡒⠠⠑⡐⠪⢀⢆⠁⡤⡓⠢⡜⠀⠁⠈⠀⡀⠁⠍⠉⠠⠀⠈⠠⡜⠃⣢⠀⢓⠊⡠⠁⠀⠀⠠⠠⠄⠐⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠔⠁⢾⢸⢵⠂⠊⠀⠲⠂⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠂⠓⠈⠀⠄⠈⠀⠁⠀⠀⠀⠀⠀⠀⠘⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀