⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢎⠪⡂⢕⠡⡃⢆⠱⡠⢃⠜⢄⠕⡡⢊⠜⡠⠣⡨⢊⠜⠜⡰⢂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⢅⠪⡐⠅⠪⡐⢌⠢⡑⠌⡢⢑⠌⠢⡑⠌⡢⠑⢌⠢⠑⡌⠰⡁⡣⢘⠵⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢍⠊⠔⠡⡈⠜⡠⠑⠄⢅⠌⡂⠢⡁⢊⠢⠘⢄⠊⢌⠂⢅⢑⢈⠢⡨⠠⡑⠨⠢⡫⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢅⠑⡁⡑⠠⠊⡀⡑⠌⠐⠄⢊⠐⡨⠀⢅⠊⡠⠊⠠⠊⡠⠂⡁⠢⠐⡐⢈⠂⡑⢄⢙⢇⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡑⢌⠐⠄⢌⠐⡁⠔⢀⠊⡨⠠⢁⠢⢀⠑⠠⢂⠐⠌⡐⢁⠄⠌⠠⢁⠌⠠⠁⠔⢀⠢⢀⠣⢳⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠫⡂⠔⢁⠂⠢⠐⡀⢊⠠⠂⡐⢐⠀⡂⢁⠈⠢⠠⡈⠄⠢⡀⢆⢨⢂⠔⡀⢅⠈⠂⠔⢁⠊⢈⡜⣥
⠀⠀⠀⠀⠀⠀⠀⢀⢏⠪⢀⠊⡠⠈⢄⠡⠐⡀⠢⢈⠠⠂⠨⢀⠂⡁⡊⣐⢄⣳⠕⠯⠚⠓⠛⠚⠶⣄⠅⡡⠈⢄⢂⡈⢮⡀
⠀⠀⠀⠀⠀⠀⠀⣜⠥⡑⠠⠂⡐⠈⠄⠄⡡⠠⢁⠂⠄⡑⠠⢁⢌⢔⢮⠎⠋⠁⠀⠀⠀⠀⠀⠀⠀⠑⢧⠐⡡⠠⢈⠂⢎⡇⠀
⠀⠀⠀⠀⠀⠀⠰⣝⢆⠢⠁⠂⠌⠠⠑⡀⢂⠐⠄⡈⡐⢀⠑⢤⡳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡬⡀⠂⠔⢀⠢⢖
⠀⠀⠀⠀⠀⠀⢘⢮⡣⡂⠡⢁⠊⠠⠁⠔⢀⠁⠢⠐⡀⢅⠈⡲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡨⠨⡀⠅⠄⢪⢖⠀
⠀⠀⠀⠀⠀⠀⠈⡮⡳⡕⡡⢀⠊⠠⠑⠈⢄⠁⡊⢀⠢⠠⢈⠌⠳⡔⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢕⢄⠢⡁⢯⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡮⡹⣖⠤⡁⢊⠠⠑⡀⠂⠔⢀⠂⠢⠠⢈⠂⠔⠠⡑⠝⢖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢝⣜⠵⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡢⡊⡛⢼⢔⡄⡡⠠⢁⠌⠠⡈⢄⠁⠂⠌⠠⡁⠔⢈⠂⡙⢕⠢⠲⠪⡚⠪⠪⡋⢚⠕⡫⡲⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡨⢂⠡⠊⡱⠳⠶⣄⣊⠠⠂⠄⢊⠈⢄⠡⠐⡀⠅⡈⠄⢂⠁⡑⠄⠌⡐⠁⠌⠐⠄⡊⢨⡛⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⠔⡀⠊⠠⡈⠢⡑⢍⡳⣳⢜⡤⣌⠠⢂⠂⠔⢀⠢⠈⠄⢂⠐⡈⠄⠨⡀⠅⠑⡠⢈⢆⡽⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢆⠌⡈⠐⠄⠡⠐⡡⢪⢗⢽⠆⠉⠙⠣⠷⣜⡤⡢⡡⡨⡀⡢⢐⢈⠔⡠⣊⢦⣪⠖⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡨⡀⡑⢈⠂⡡⠐⢌⡷⣙⢖⣄⠀⠀⠀⠀⠈⠉⠙⠚⠚⠪⠳⠓⠋⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⠄⠢⠐⠠⠂⢌⠠⢛⢮⡪⡜⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢐⠡⢈⠂⠢⠐⡁⢝⢮⡪⡢⡹⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⠡⢂⢈⠐⡁⠔⠠⢓⢵⡪⢢⠑⡝⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡢⠄⢌⢀⠊⡐⠡⢊⢷⡑⡌⡐⠡⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡔⢢⢀⠊⢄⠑⠔⡡⢻⡔⢌⠂⡕⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⡡⡨⠠⡑⠌⡢⢑⠽⣪⡪⣢⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⢐⠅⠢⡑⠨⡢⣙⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⡕⡡⢊⠒⢔⢌⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⡵⣩⡲⡕⠃