⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⢀⠀⠠⠀⡀⠂⡀⠂⠐⠀⠈⠀⠄⠁⢈⠠⠈⠀⠂⠁⠀⠂⠐⠀⠂⠠⠠⢀⠀⠠⠀⠀⠠⠐⠀⠀⠐⠀⠀⠐⠀⠀⠂⠀⠂⠈⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠄⠂⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⠀⠀⠄⠀⠀⠄⠀⠠⠀⠀⠄⠀⠄⠀⠄⠂⠀⠐⠀⠀⠂⠀⠁⠀⠁⠀⠀⠀⠀⡀⢀⠠⠈⡀⠄⠂⠀⢄⠅⠀⠄⠁⠀⠀⡁⠀⠂⠀⠀⠄⠁⡀⠁⡈⠀⠂⠐⠀⠁⠐⠀⠌⢐⠐⡀⢂⠠⢀⢀⠀⡀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠄⢂⠌⠀⠄⠀⠀⠔⠀⠠⠀⠠⠐⠡⡂⡐⢈⠀⠀⠀⢈⠠⠈⠀⡀⠀⠀⠀⠄⠂⠈⡀⠈⡀⠁⠄⠐⠠⠐⠐⡐⠨⡐⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠂⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠀⡠⢃⢐⢕⠀⡂⢐⠀⠈⡪⠠⠈⠐⢄⠑⢄⠈⠊⠦⣈⠂⠄⠀⠐⢀⠁⢀⠀⠁⠄⠀⠄⠀⡀⠐⠀⠂⡈⢈⠐⢀⠁⠂⡁⠌⢐⠀⠑⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⡃⡂⢌⢳⡀⠢⠀⠑⡀⠈⠅⠡⠀⠀⠈⠀⡁⠅⢄⠀⠁⠅⠨⠀⡀⠀⠂⠀⠁⡀⠄⠀⠁⠠⠀⢁⠠⠀⡀⠀⠂⠠⠀⠀⠀⠀⠀⠁⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⡐⡐⢈⠲⡐⡀⢀⠈⠂⡐⠀⠀⠠⠀⠀⠂⠠⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠂⠠⠀⠁⠀⠀⠂⠁⠠⠀⡀⠀⠀⠀⠈⠀⠂⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠄⠀⠁⠀⠀⠀⠁⠀⠀⠄⠀⠀⠂⠁⠀⠀⠂⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠠⠐⠄⡈⠂⠄⢄⠀⠄⢀⠀⠀⠁⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠈⠀⠂⠐⠠⢀⢀⠀⠑⠐⠄⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⠀⠈⠂⢄⢀⠀⠈⠀⠈⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⠐⢄⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠈⠀⠈⠀⠁⠠⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠁⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⡂⢀⠀⠀⣠⣄⠀⠀⡀⡀⡤⢂⢀⢐⢁⠀⠄⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠂⢀⠀⠀⠑⠑⣈⣄⣴⠈⢀⠀⢁⡀⡢⢄⣀⠀⠁⢂⠢⡤⣀⠐⠱⣲⢨⣪⡪⡭⡣⣕⢖⢬⢔⢤⡐⡀⢂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠂⠀⠐⠔⣜⣜⢝⡬⣪⡢⣆⢮⡺⣪⡫⣓⡆⠡⢉⠪⢯⡲⣔⣕⢧⡫⡮⡫⡮⡳⣝⢕⡗⡽⣸⠀⡆⠈⠄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡲⢤⡨⣘⠱⡝⡮⡺⣜⢵⡹⣜⢞⢮⡺⡌⡀⢂⠂⡉⢖⢧⡳⡝⣎⢯⢮⢳⢕⣗⢝⢞⢮⡣⡃⡌⢐⠀⢐⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⢵⡹⡪⡯⣎⢯⡺⣪⡳⡝⡮⡓⢗⣅⠂⡐⢀⠂⣂⢔⢗⡝⡞⣎⢗⢵⢝⢵⠵⣝⢽⢜⢮⡪⠂⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⣝⣜⢮⡺⡪⡮⡳⡝⡮⣳⣪⡺⣒⡖⠽⡸⠕⢗⠽⢝⠼⡭⡳⣝⢵⢝⢮⢮⢳⠣⠁⡀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠚⠼⣪⢏⡮⡳⣝⢎⡥⡢⡦⢦⠲⠕⠗⠝⡎⣞⢖⢵⢝⢞⢎⡗⣝⠵⠓⠁⡁⡐⡀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠽⢜⡵⣝⢮⡫⣲⣓⢮⡪⡮⡳⡵⣝⢵⢝⣕⢗⠝⠊⠈⡀⢂⠐⠠⠀⠂⢀⠄⠅⠂⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⡡⠀⠀⠀⢢⢬⡈⡓⠝⢜⡮⣺⢪⡫⡮⡳⡵⡝⠞⠈⠠⠀⡂⠡⠐⠠⠈⠌⠀⡁⠂⠄⠅⠠⡂⢅⢂⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⡀⡀⡀⡀⠄⢄⠂⡠⡂⡣⡱⠀⣿⣳⢴⡀⠂⠀⠑⠽⡜⣆⡂⠄⠅⡉⢉⠉⠉⢀⠀⠄⢂⢁⠂⠄⠡⠨⠠⠁⠅⠀⠠⠡⠈⢠⠑⢌⢂⠢⢑⠄⠀⠐⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠀⠄⡐⠀⠄⠠⠠⢀⠢⢐⢐⠡⠡⡑⢌⢂⠢⡐⠔⠌⢀⠱⠀⡔⡑⢌⢆⢪⢀⣟⡾⡽⡽⣮⣢⢀⢀⠹⢜⢮⢳⣢⣐⠠⡈⠌⠠⢈⠐⡀⢂⠨⠈⠄⠡⠈⠄⠁⡀⠅⠌⠠⡑⠌⡂⡢⠡⡑⠌⠀⢈⠀⡁⠐⢀⠈⠈⠈⠒⠢⢢⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⢀⠈⠀⡐⠈⠠⢀⠡⠈⠄⠅⡂⠌⡐⡐⡈⠢⡈⡂⠢⠑⠌⢌⢐⠌⡀⡊⣂⠪⡂⢆⠅⣴⡳⡯⣯⣻⣺⣺⡳⡦⠂⠂⠍⠓⠵⡵⡝⡮⡲⡅⣆⡐⡐⡀⡂⠡⠈⠄⠡⠁⡀⡐⠨⡐⡡⢊⠌⢔⠐⠅⡌⠠⠀⠠⠀⠄⢈⠀⡀⢈⠠⠈⠀⡐⠀⡁⠣⠱⡠⡀⠄⡄⣀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠐⠀⠀⠂⡀⠈⠄⠂⠠⠁⠌⡀⢂⠡⠐⡀⡂⠅⡂⠌⠌⠌⠌⢂⠡⢂⠢⡑⠄⠕⢌⠂⣰⡳⣝⣝⣞⢞⣞⠎⠋⠀⠀⠡⡑⡐⠄⠌⠓⡝⣎⢗⢵⡹⣪⡺⠁⠅⡁⣁⠤⠥⠔⠤⠕⠴⢔⠴⢔⠖⠼⠔⠖⠖⠲⡒⢖⠲⠔⠖⢔⠦⡒⠖⠲⢐⠢⠂⠒⢀⠈⡘⢌⢆⢌⠊⢎⠕⡕⡒⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠁⠀⠀⢀⠈⡀⠄⢈⠠⠈⠠⠁⡐⠀⡂⠄⠡⠐⡀⢂⠂⢁⠡⢐⠨⢐⢈⠂⠅⠌⢌⢊⠂⢰⡣⡯⡺⠜⢎⣩⢔⢶⡀⠀⠀⠀⠐⠈⠌⢂⠢⠈⠨⢑⣁⡩⡤⣢⡪⡬⡢⡖⠮⢮⢳⢕⡬⡢⡤⣨⣀⢌⡠⡡⡈⡈⡀⠠⠀⠄⢁⠈⡀⠠⠀⢈⠠⠀⡀⠂⢈⠀⠄⠠⠀⠐⠅⡍⢆⠣⡪⡨⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠠⠀⠀⢀⠀⠠⠀⠄⠠⠈⡀⠁⠄⠁⠄⠨⠀⠅⢐⠠⠀⠄⡈⢀⠈⠀⠂⠁⠁⡁⠅⡂⢀⢃⠉⠄⣲⡹⣕⢗⢽⢕⡯⡶⠴⠄⣀⡠⠤⡔⣆⢗⡝⡵⣱⢱⢭⡢⡮⣲⢲⢤⢅⣂⢂⠁⠌⠉⢉⠊⠊⡑⢉⠊⡑⢙⠘⠕⡓⢖⢆⢦⢄⡄⡂⠀⠠⠀⠄⠂⠠⠀⠂⠐⠈⠠⢐⢌⠪⡊⢆⢕⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠠⠐⠈⡀⠅⠈⠄⠨⠐⠀⠂⠁⠂⡂⡀⡁⠡⠁⠔⢀⢀⢄⢠⡁⡌⡤⡰⠤⠨⢀⡉⡍⡥⢥⢒⢎⢇⢇⢗⢝⢎⡞⣜⢎⢗⠵⣝⢎⢮⡩⡊⢑⠉⡓⠕⠝⠭⢧⢳⢲⢤⢥⢤⣀⣂⡐⠀⠂⠅⠄⠄⠂⢀⠡⠡⠙⠕⡖⢤⣐⡈⡀⠄⢁⠀⢅⢜⠰⡡⡱⢡⢃⢎⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠄⠀⠈⡀⢀⠁⠄⠂⠐⠀⠄⠐⠀⡂⠐⡈⠠⢁⠁⠅⡀⠂⠄⠅⠁⢄⢣⠱⡑⡕⡜⡜⡊⢄⢇⢝⢜⢜⢜⢜⢜⢕⢕⢝⢜⡕⡭⣣⢫⡪⡳⣹⢹⢜⣕⢗⡝⡮⣲⢢⢔⣐⠨⠦⢦⣤⣢⣄⣂⡁⠌⢘⠘⠝⡲⢤⣀⡠⠀⠄⠀⠄⢀⠡⡈⢄⢄⠨⡠⡐⢅⢕⠱⡐⢕⢑⢌⢆⠣⡢⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⡀⠀⠄⠐⠀⡁⠐⢀⠡⠐⠀⢂⠐⡀⠂⠄⠡⠀⠅⠈⠠⡨⡊⢆⢣⠣⡣⡱⡁⠠⡑⡅⢇⢕⠕⡕⢕⢕⢕⢕⢝⡜⡜⠮⠪⡚⡘⠩⠨⠨⠈⠄⠅⠅⠙⠘⠕⠳⠵⢝⢕⣖⢤⢕⡹⣞⠽⠑⠠⡢⠡⡀⡂⠐⠨⠙⡒⠦⡌⣌⠪⡘⢔⠢⣃⠲⡘⢔⢅⢣⠱⡡⡃⢎⠢⡣⡊⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠂⠀⠈⠀⠀⡀⠁⢀⠀⠂⢀⠁⠠⠈⡀⠄⠂⠁⠄⠠⠐⢈⠠⠁⠌⠀⢌⠢⠪⡨⡊⢆⢣⠱⡱⠀⠐⡈⠌⠨⢈⠨⠈⠌⠨⢈⠊⠐⠨⠀⡁⣁⣠⡠⡔⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡂⠨⠑⣗⢵⡀⢅⠅⡘⢌⢪⢘⢌⢎⠢⡢⡠⡂⡄⠤⡐⢈⢎⢊⢆⠣⡑⢕⠌⡆⡣⠪⡘⡌⡪⡂⢎⠢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠈⠀⠀⠀⡀⠈⠀⠠⠀⠠⠀⠠⠈⠀⠀⠂⠠⠀⢀⠈⠀⠁⢀⠈⠀⠄⠁⡀⠅⡢⡑⡑⢌⠪⡘⡌⢎⠪⠀⡁⠠⢀⢂⢐⠀⡰⡢⣂⠂⡂⡑⢳⡹⣝⢞⡞⣾⠁⣟⣞⣞⣝⠷⣲⢤⣀⠀⠀⠀⠀⠈⠀⠁⠐⢕⢗⣄⠀⡎⡊⢆⠕⢔⠅⡕⡢⡒⢌⠜⠌⠀⡀⠂⡑⡌⡪⠸⡐⢕⢌⠪⡘⢔⢑⢔⠸⡐⡑
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠁⠀⠀⠀⠠⠀⠀⢀⠈⠀⠀⠄⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠐⠐⠨⠘⠐⠁⡂⠐⡀⠌⡀⠠⢁⠐⠠⢀⠐⠸⡸⡜⣕⢖⢤⡁⠍⠺⢵⢝⢾⢨⡳⣳⢵⣝⢷⢔⣅⠙⢄⠀⠀⡀⠀⠀⠀⠀⠀⠑⠁⠧⡌⢊⢢⢑⠅⡕⢌⠢⡊⠆⠁⠄⠂⡠⡊⡢⡑⡌⠕⢅⠕⢔⠡⡑⡑⢌⠢⡑⢌⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠐⠀⠐⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠂⠐⢈⠀⡁⠄⠂⠀⠂⡀⠂⢀⢈⠐⠠⢈⢐⠈⠪⡪⡪⣣⢫⢳⡱⡌⣍⠺⢆⢹⠎⣓⠕⢯⡳⡽⣕⢶⢄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⢑⠌⠀⠂⡐⢌⠢⡂⡪⡂⡪⡊⡢⡑⢅⠀⢕⢘⠔⡑⢌⢂⠂
⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⡀⠄⠀⠀⠀⠀⠀⠄⠡⠠⢁⢂⠐⠄⠈⠄⠐⡈⢐⠠⠉⢎⢎⢇⢧⢫⡪⡝⡵⡐⢝⡲⡕⡗⣝⢮⡪⡳⡳⡹⣕⢤⡀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠕⠌⡂⡢⡂⢆⠢⢊⠂⠀⠐⠔⠑⠈⠂⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⡀⠐⠀⡀⢀⠀⢀⠀⠄⢀⠂⡈⠠⠁⠌⠠⠐⡈⠌⠄⠈⡀⢂⠐⡀⠅⠂⡑⡕⡕⡕⡕⡕⡕⡝⡄⢳⢹⢸⢸⢸⢸⢱⢹⢸⢜⢜⢜⡲⣀⠀⢀⠀⠀⠀⠀⠀⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⢀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠠⠀⠁⢀⠀⠄⠂⠀⠠⠀⠄⠐⠀⠄⠠⠀⠂⡈⠐⢈⠠⠐⢀⠁⠅⡀⠠⠐⠀⠄⠁⠄⡪⡘⡌⢎⠪⡊⡎⡲⠈⢎⠎⡎⢎⢎⢎⢎⠎⡎⢎⠎⡎⡪⡒⡄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⢈⠂⠅⡂⡂⡂⡂⡂⡂⠅⠅⠅⠌⡂⠄⠀⡀⠐⡁⠂⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠠⠐⠀⠠⠀⠂⠁⠀⠂⠈⡀⠄⠐⠀⡀⠌⠠⠐⠀⠂⠄⠀⠁⠄⠁⠌⡂⡪⠨⠢⡑⡑⢌⠜⠀⡪⢘⠌⡢⡑⠔⢅⠕⡘⢌⠪⡨⠢⡑⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢐⢀⢂⢐⢀⠂⡂⠅⠌⠨⠐⠠⠡⠀⠀⡀⠀⠡⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⠀⠄⠀⠂⠁⠀⠁⠀⡀⠂⠁⢀⠀⠄⠈⡀⠁⠄⢁⠀⠐⠀⡈⠐⠄⢅⢑⠐⠌⠄⠅⢐⠡⠂⠅⠢⠨⠨⢂⢑⢈⠢⢁⠢⠑⡈⠌⠀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠌⠠⠁⠌⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠄⠈⠀⢀⠀⠠⠐⠀⠀⠠⠀⢀⠐⠀⠠⠀⠀⠂⠀⡀⠁⠐⠠⠈⠌⡈⠀⡂⠌⠨⠈⠌⠈⢈⠀⠠⠀⠄⠄⢂⠡⠠⠑⡀⠠⠀⠂⢁⠐⠀⠀⠀⠂⡁⢈⠀⡁⢈⠀⡁⢈⠀⠡⠐⠀⠄⢀⠀⡀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⡀⠐⠀⢀⠀⢀⠀⠂⠀⠁⠀⠀⠀⠂⠐⠀⡈⠀⠀⠀⠀⢂⠠⠀⠄⢀⠀⢀⠠⠐⠀⠈⠀⠐⠀⡁⠄⠀⠂⠁⢀⠀⠁⠀⠁⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠁⡀⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠀⠠⠀⡀⠀⠀⠁⠀⠄⠀⠀⠐⠀⠄⠂⠀⠄⠀⠂⠈⠠⠈⠀⠄⠐⠀⠀⠈⠀⠀⠁⠀⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠂⠀⠠⠀⠠⠀⠁⠀⠀⠂⠀⠀⠀