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