⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢔⢐⢐⠔⢄⠢⡐⢄⠄⡄⢄⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⠠⡂⠄⡠⡐⢄⠪⡐⢅⠪⠘⠄⡑⡐⠡⠡⡃⠌⡀⠂⠈⠄⠑⠌⠌⢌⢂⠄⢄⠀⡄⠄⠔⠐⡀⠌⠄⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡨⡊⢆⢍⠆⢕⢌⠢⠈⡈⠀⠀⠀⠁⠕⡀⠂⠀⠀⠀⠀⠈⠈⠌⡂⡢⠡⡑⠨⡪⢂⠂⠡⡐⢁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡪⡨⠢⡑⡱⢐⠁⡁⠄⢀⠀⠠⠀⠡⠀⠈⠀⠀⠐⠈⠀⠀⠅⠪⡐⢅⢊⢂⢊⠂⠌⠌⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠢⡪⠡⡃⣪⣦⣶⡠⡡⠀⠄⠀⠀⠄⠀⠀⠄⠁⠄⠡⡀⣄⡨⢐⠠⠡⠂⢅⠢⠨⠨⢀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠜⢌⢪⠨⡢⣟⣯⣿⣽⡮⡂⠠⠀⠂⠀⠀⠠⠐⢨⣨⡞⣾⢿⣾⡦⢈⠈⠌⠠⢊⠨⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠡⢑⢐⢐⠁⢆⠻⢯⠷⢻⠉⡀⠀⠀⡀⠀⠐⠀⢀⠣⡯⡧⡿⡿⣗⢏⠐⠀⠁⠈⢀⠐⠈⠄⢂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠅⠅⡂⡐⠠⢈⠢⠩⠢⠡⠁⠄⠀⡀⠁⠀⠠⠀⠀⠀⠠⠈⠌⢊⢘⠐⡁⠐⠈⠀⠀⠄⠀⠠⠈⠄⡂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡊⠐⠄⡊⠌⠄⢌⠨⠈⠠⠁⠀⠄⠐⠈⠄⡁⠄⠈⠀⢀⠀⠀⠀⠄⠁⠐⠀⡀⠐⠀⢀⠀⠀⠌⠐⡠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄⠡⠡⠨⡊⢎⠢⡐⠨⠐⡀⡡⣠⡡⣅⢥⠠⠀⢀⠠⠀⠀⠐⠀⢀⠈⡀⢁⠠⠐⠈⠀⠀⠀⠄⠂⡐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⡂⠆⡊⡐⠅⡇⢇⡃⠅⢢⣾⣽⡺⣜⠮⡭⣫⢮⡀⠀⠀⠀⡁⠐⠠⢀⢂⢂⢂⠐⠀⠠⠀⠂⠀⢂⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡢⡱⡐⡁⡂⠪⡨⢊⢜⢐⢈⢾⣽⣿⡿⣾⣿⣿⣽⡳⡕⢀⠀⢁⠠⠡⡑⢅⠪⢐⠐⡈⠀⠂⠠⠐⠈⠠⡊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡌⡖⡢⢂⠈⡂⠌⠆⢇⠆⡅⡳⣻⣽⣿⣿⣿⣽⣵⢫⠂⠄⡂⠄⡐⡡⠨⠠⠁⠅⠐⠀⠁⢈⠀⠠⠨⢨⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡱⡱⡸⡠⠂⡐⠡⡑⡑⡕⡜⣜⣜⠽⡽⣟⡯⣻⢸⡐⢅⢂⠢⡂⡕⡌⢌⠂⠅⠨⠀⠁⠈⠀⢀⠐⡨⢂⠕⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢆⢇⢇⢎⢂⠂⢅⠢⢑⠌⢞⢪⣮⣯⣾⣵⣽⡼⣕⣎⢦⢣⢣⡪⡎⢎⠔⠨⠀⢁⠀⠁⠄⠈⡀⠔⢌⢂⢊⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢐⠸⡰⡑⠥⡑⡑⢔⠡⡡⠪⡨⢢⢣⢺⢕⢯⣳⡫⣳⢱⡹⡸⡱⢡⠡⠡⡈⠐⠈⢀⠀⢂⠐⡀⠂⢜⢐⠅⡢⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢎⠔⠡⡊⡪⡑⡅⢕⢅⢇⠢⡑⢌⢆⢣⢣⢫⡳⡵⣝⢼⢱⠱⡑⠅⠅⡊⡐⡈⡈⠄⠂⡐⠀⡂⢄⢑⠕⡐⢅⠢⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣜⠌⡂⢌⠢⡊⡌⢆⢕⢜⢜⠌⡆⡪⢢⢃⢇⢏⢎⢎⢎⠪⠨⠠⠡⡁⡂⡂⠔⠠⢂⠡⠠⡡⢢⠢⡑⡅⠕⠡⡈⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡺⡜⡌⠔⠠⢁⠆⡊⢆⠕⡜⢔⢣⢣⢪⠪⣊⢎⢎⢎⢆⠕⡌⡌⢌⢂⢆⢒⢌⢌⡊⡢⠡⡑⠨⡢⢑⢑⠌⠌⠂⢌⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡑⡕⡇⢕⠡⡁⢂⠂⢅⠅⡕⢌⢪⠸⡘⡬⡣⡣⡣⡫⣣⡫⡺⡸⡸⡸⡰⡡⠣⡊⡢⢑⠌⡂⡊⢌⠢⠑⡐⠀⠂⡁⣒⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢪⠪⢂⢑⠔⡠⠡⡑⢌⠢⡑⢅⢣⠣⡃⢇⢕⢕⠭⡒⡕⡕⡕⡕⢕⢌⠆⡃⡑⢄⠅⡂⠢⢐⠐⡈⠄⠀⠂⢁⢌⢢⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢱⠍⡂⡂⡑⠌⢌⠢⡑⢌⠪⡘⢔⠱⡑⡕⢜⠰⡑⢅⠕⢅⢃⠇⡕⢅⢣⢊⠔⠡⢂⢂⠡⠐⡀⠄⢀⠁⡈⡐⡌⡆⠂⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡱⡱⡱⡐⡐⡨⢘⢐⠅⡪⢐⢑⢌⠪⡨⠢⡑⢕⠱⡑⢅⢎⠢⡑⡬⡨⡊⡪⠢⡑⠅⡂⠐⡀⠁⠄⡐⠀⠄⠠⡂⢇⢎⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⢎⢎⠢⡂⡢⢑⠔⢅⠢⡑⡰⠐⢅⠢⡑⠌⡂⠅⡊⠔⠡⠡⢑⠐⡂⡊⡐⠡⠊⡈⠄⠅⡐⠈⠄⠂⠐⠀⢅⢪⢪⠪⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⢳⢱⢱⠨⡂⢕⠨⡊⢎⢆⢆⢅⠅⠢⢈⠐⡀⠂⠄⠂⠁⡈⠄⠂⠐⠐⠀⠅⠂⡐⠠⠁⠂⡁⠐⠈⡀⠅⢕⢅⢇⢃⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⢢⢑⢕⢵⢱⠡⡑⠬⡘⡜⡌⡎⡎⠮⡌⡄⠄⠠⠀⠠⠀⠂⠀⠀⠈⠀⡈⠠⠀⢁⠠⠀⡁⠄⠠⠁⢂⢐⢅⢇⠕⡌⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢨⠢⡣⢣⢣⠣⡑⡅⢇⢪⢸⢨⢪⢱⢱⢱⢹⢰⠡⠠⡀⡀⢀⠈⠀⠄⠠⡀⢔⢠⢐⠔⡐⡁⢂⠅⠢⡑⡌⠆⠕⠀⠀⠀⠀⠀⠀⠀⠀