⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⢀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡘⢀⢧⠃⢀⣀⣰⠢⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣴⠤⡤⣀⠐⢧⣃⠸⡸⣜⢵⡑⠁⠀⠀⡠⡲⠙⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡈⣷⢱⢕⡖⣍⢫⡒⢧⡣⢛⢜⡀⡀⡀⡜⡜⠀⠀⠀⠀⣀⢜⢕⠎⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠗⡕⠕⣗⢝⢮⡲⡵⣕⢕⡷⢒⠑⢵⠑⠱⠭⢕⡪⡪⣍⢆⣇⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢐⠀⢏⠧⣫⡺⣪⢻⡺⢕⢷⣻⢢⢤⠀⠀⠀⠀⠀⠘⢜⠬⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⠀⡳⡳⡕⡇⡇⢇⡓⡲⡱⡓⡦⢤⠢⢤⢠⣀⠉⠒⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦⢳⢽⣪⢇⠇⡇⡎⢎⢪⢸⢪⢣⢹⢨⡲⡪⢭⢱⠲⡲⡲⢲⠲⡲⡲⢲⠲⡲⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢮⡳⣗⡕⡕⡜⢜⠜⣜⢜⢜⢬⢺⢜⢕⠕⡅⡇⢇⢎⢎⢾⣪⢪⢊⢎⢪⠪⡒⡌⠂⠤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢎⡎⡮⡳⡵⣕⡕⣕⣗⢇⡳⡹⡕⡅⡇⡣⡪⡪⢢⠣⡪⡚⣯⢺⢸⢨⠪⡪⡸⡀⢄⠈⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣮⡪⡺⡮⣎⢳⣑⢕⡭⣫⢎⢎⢪⢊⢆⢇⢣⠣⡣⢪⢪⡫⣎⢎⢪⢪⠸⡀⢐⡍⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⢧⣣⢳⢣⡳⣝⢮⢳⣻⢜⢌⢎⢆⢇⢕⢕⢕⣕⢗⢝⣜⢮⡪⡢⡣⠭⢐⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⢕⢇⡏⢯⢺⢜⡵⣯⢫⡣⡧⡳⣪⡺⡪⡣⡣⡣⡳⡕⣗⢽⡸⣜⢼⢰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡧⡥⡹⡕⡽⣱⣣⠗⠧⠯⠮⠯⠮⠮⠚⢞⢮⠾⠮⣞⡪⡇⡯⣎⢗⡭⣃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⢼⠵⠝⠚⡗⣝⢎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡪⠨⠂⢝⠘⠮⣪⢱⢝⡜⣆⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣹⡁⠀⠀⢠⢫⢎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⣊⢈⢂⠦⡀⠉⠒⡕⡗⣗⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣗⡄⠀⡮⣳⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢱⠯⠃⠀⠀⠈⢞⢜⢮⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⣷⢝⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⡏⠀⠀⠀⠀⠀⠀⢫⣺⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡵⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⠏⠀⠀⠀⠀⠀⠀⠀⢸⢸⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣪⡁⠀⠀⠀⠀⠀⠀⠀⢰⢱⣣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⣺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡏⠀⠀⠀⠀⠀⠀⡠⣣⠏⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣵⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀