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