⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⡪⠣⠐⡐⢐⠀⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠠⡌⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠡⠨⠨⢈⣖⢵⡹⢁⠂⢂⠂⠅⠅⢊⢂⠢⡨⢠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢜⠽⡈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠅⠂⡁⢂⢱⢕⢧⢃⠐⠡⠀⠂⠂⠡⠐⠰⠨⢈⠢⡑⠔⢅⠀⠄⠀⠀⠀⠀⢀⡠⡤⡺⣪⡫⠑⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⢂⠡⠨⠐⠠⡑⢜⡕⡇⡅⠀⢀⠀⠄⠂⠁⠌⢐⠈⡀⢂⠁⡙⢌⠪⣈⢄⢲⣒⢖⢵⡳⣹⡹⡜⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢅⢃⢐⠨⢈⠌⠀⠈⠐⡝⠔⠪⠈⠂⡁⠄⠡⠈⡐⠠⠈⠌⠒⡠⡀⠂⠄⢡⢳⢕⡳⣝⢵⢝⠮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢅⠅⡂⠌⠠⢂⠅⠅⠠⠈⠄⠡⠈⠄⠀⡂⢁⠐⠀⠂⠁⠄⠡⠐⡈⠪⠢⡂⠰⡱⢕⠓⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠈⠠⠡⡑⡐⠌⠐⢌⠂⡈⠌⡈⠄⡈⡂⠁⢄⠂⡂⢈⠠⠈⠠⠈⠄⠅⠠⠈⠨⢊⢢⢘⢄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠈⡨⠨⢐⠐⡁⠁⠅⡂⢂⢡⠂⡐⠠⠐⠈⡂⡀⡂⠄⢂⠐⢈⠠⠡⠈⠄⠐⡀⠡⡑⡌⡂⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡐⢥⠑⠠⠨⠀⢅⠅⢆⠦⢒⢐⠤⢑⠅⢜⠔⡀⠄⠌⠄⢂⢐⠨⢐⠁⢌⠐⢄⢑⠐⢌⠪⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢂⠪⢪⠀⡂⡑⠡⡨⠢⠑⠀⡐⠅⡌⡒⢌⠢⢂⢐⠈⢌⢐⢀⢂⠕⡐⠨⢐⠨⠐⡔⡡⡡⢣⠨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⢽⠠⠠⢘⠄⡣⣑⡈⡀⠠⡁⠢⠪⡔⡱⡐⡐⠨⡐⡐⡐⡨⢂⠌⢌⠄⢅⢕⠅⡇⡌⡢⡃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⢨⠐⡒⡸⠀⠌⡐⣡⠣⣹⢸⠚⡽⡺⡮⢷⢱⠐⠕⠌⡂⢅⢂⠢⡪⢂⠥⢑⠨⠢⡑⡱⡱⡐⢌⠢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢁⠡⠀⢸⠀⢐⢸⠈⡐⠨⢰⢑⠈⠑⠒⠢⠌⠎⠀⠈⠀⠁⠇⡂⡂⡢⢑⠔⡑⠜⡢⠱⠡⡃⠅⣳⢈⢂⠃⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠂⢸⠀⢘⠀⢐⠸⠀⠄⡁⢂⠢⠂⠁⡐⠀⠄⠀⠂⠁⢀⠁⠀⠂⠈⠄⠣⠩⡚⡛⡚⠵⡱⢬⡌⢸⠠⡱⢠⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠐⢘⠀⠀⡊⡀⠱⠀⡁⠄⠂⠕⠀⡁⢀⠂⢈⠀⠁⠐⠀⢀⠁⡈⠀⠀⠂⡈⠐⠨⠘⠤⢴⡰⡛⣜⢐⠅⢔⢑⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠁⢀⠂⠄⡂⢍⢢⠐⡀⢂⠨⠨⠀⡀⠄⠀⠄⢀⠈⠀⠈⠀⡀⠀⠄⠈⠀⡀⠂⢐⠀⢂⠐⡐⡌⡇⡢⢣⢑⠅⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡊⠀⠠⡃⠡⡀⡣⢑⠐⠔⠀⡐⠡⠀⢀⠀⠄⠀⠄⠄⠌⠀⠄⡀⠄⠀⠄⠁⠀⠐⢀⠈⠠⢀⡇⡕⡇⡕⠡⡣⡁⢜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢀⠀⠀⡇⢑⡐⢌⢢⢘⠄⡁⠄⡑⠀⡀⠀⠠⢠⡳⠁⡤⣂⡀⠀⡁⢀⠠⠀⠈⢀⠠⠀⠁⡜⡜⡘⡎⠜⡌⡢⢥⢊⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠀⠀⠀⡇⢌⠢⢂⠪⡂⠂⠄⠅⡂⢀⠀⠐⠐⠱⡹⡑⡎⡳⡹⢥⡀⢀⠁⠄⠈⠀⠀⡀⢮⡊⡎⡪⡘⠄⡣⢊⢆⠅⡣⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠁⠀⠀⠅⢸⢈⠢⡱⠅⠡⢁⢱⢔⠀⠠⠐⠀⠁⠹⢸⢨⢊⠎⡎⣮⠠⢀⠈⠄⠂⢅⠪⢺⡐⢕⠌⡎⢢⠱⠨⡢⡂⢎⠬⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠸⠀⣓⠨⢐⢸⢨⠈⠄⢺⠂⢍⠆⡀⠄⠈⠀⡠⠈⢘⠈⢊⢀⢈⢂⠐⢈⠘⡌⢎⢜⡌⢆⠣⡃⢜⢜⢌⢒⢌⠔⡱⡨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⠠⠀⠀⡀⠨⠂⠨⢐⢸⢸⠨⡈⢸⢌⠢⠨⠨⡑⢈⠈⠄⠂⠠⠀⡀⢀⠀⢀⠀⠂⠄⠈⠒⠸⢊⠢⡃⢆⠸⡂⠍⠠⡁⠌⠠⠒⡄⢂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠅⠀⠡⡁⡂⡑⡐⡕⢽⠨⡐⢸⡁⠪⡨⢌⢐⢐⠨⠨⠪⠬⢔⢢⢢⠲⢀⠐⠀⠀⠂⠀⠂⠀⠣⢑⢱⠀⡆⡁⡁⠄⢈⠀⢂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⢈⠈⢠⢑⢐⠔⢌⢇⢯⢘⠄⢪⠪⠨⡂⡂⡢⠡⢊⢜⢈⠠⠀⠄⢀⠂⠠⠈⠠⠈⠀⡀⠁⠀⠂⠈⠪⠠⡁⡂⠠⠀⠄⠐⠀⠐⡀⠐⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⢀⢐⠔⠅⡌⡎⡲⣱⢑⠨⠠⡣⢑⠰⠨⡐⠡⠢⠃⠠⠐⠀⠂⡀⠄⠀⠄⠀⠄⠁⠀⠀⠁⢀⠈⠀⠉⠲⠐⡀⠐⠀⠐⠈⠀⠀⠂⠈⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠌⡐⢔⢘⢌⢆⢇⢇⢺⢨⠨⢘⠀⢄⠅⠕⢨⠊⠌⡈⡂⠍⡉⠒⠄⠤⡀⠐⠀⠄⠐⠀⠁⠠⠀⢀⠈⠀⠄⠂⠐⢈⠀⠂⠐⠈⠀⡁⠄⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⡀⢪⠨⡂⡇⡢⡣⠕⠡⡑⠌⠄⡇⡂⠅⠅⠅⢆⠑⠄⡂⡂⠂⠅⠡⢑⠌⡢⠅⡐⠈⡀⢈⠀⠄⠀⡀⠂⠀⠄⠈⠈⡠⠈⠀⠂⡀⠄⠠⠀⠁⠀⠀⠀⠀
⠀⠀⠀⢀⠂⠌⠐⠁⡁⢁⠀⠀⠠⡃⡅⠅⡊⢐⢀⠈⢀⠈⠠⠡⡑⡐⠄⠅⠡⠨⢐⠨⠠⢑⠨⢂⠆⢄⡐⡀⠂⡀⠄⢁⠐⠈⡀⠰⢈⠀⡁⢀⠐⠠⠀⢈⠀⠀⠀⠀
⠀⠀⠠⠀⠀⡀⠂⠡⠀⡀⠄⠈⡀⠡⡂⠅⠢⠐⠄⠀⠄⠀⠄⠂⢈⠢⡑⡁⡅⠅⠁⢀⠀⡐⠌⡂⡊⠔⡠⠱⡁⡀⠄⠠⠀⡁⠀⠄⢋⠆⢊⠄⡐⡐⠠⠐⢐⠀⠀