⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠠⡀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⢀⢂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⢀⠐⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡌⡐⠀⠀⠀⠅⠄⡈⠀⠠⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠠⢀⠅⡀⠀⠄⡪⢌⠀⠀⠀⠀⢀⠀⠠⡀⠄⢂⢇⠇⢌⠀⠠⠁⡑⡅⠂⠀⠁⠔⡀⠂⠅⡀⠂⠀⠀⠈⠀⠀⡀⠁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢈⠨⠠⡁⠄⠌⡪⡺⠄⠀⠀⠀⢐⢐⢈⠔⡐⡐⡨⡣⡣⠡⡀⠄⠨⡘⡆⠁⠀⠌⢠⢑⢁⢂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢄⠥⠡⡐⡌⢢⡣⡯⠀⠀⠀⠐⡔⡬⢰⠡⡃⡢⢑⢧⠣⡃⡆⠌⡂⡣⡣⠐⠀⠂⡡⢑⢅⢐⠠⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣣⢅⠊⡢⡕⢔⢧⢳⠀⠀⠠⠘⡔⣽⢸⢕⡧⠨⡢⡣⡣⡂⢅⠐⡌⡎⡂⡐⠀⡐⡅⡢⡱⢀⢅⠀⠁⠀⢀⠀⠄⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⡞⡠⠸⣼⣪⣻⢜⢪⠀⠀⠈⢌⡇⡿⡸⣕⢯⢊⢢⢑⢕⠅⡣⢡⢣⠣⡐⠄⠅⡂⣳⠑⡎⠢⡐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢘⠄⢕⣿⣜⡮⡯⠐⡀⢈⠀⢢⢇⣿⢸⢮⢏⢊⠰⡐⡇⡕⡜⡜⡸⢡⠘⢌⠢⢅⢗⢕⡍⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢜⠤⠁⣞⣿⡲⡳⡕⠄⠡⠀⠈⢔⢕⢵⠍⢗⢽⠀⡪⢌⢎⢢⢳⠵⢅⠢⢸⢐⠁⣗⢽⠰⣑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡪⡀⠈⢮⣿⡣⡇⢏⠢⢑⠀⠀⢼⢱⢩⡣⠕⣝⠀⡣⠱⡐⣼⣱⠫⢀⠨⠨⢂⠁⡪⡇⡇⡢⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠸⢸⡿⡆⠌⠆⢕⠈⠄⠀⢍⡾⣸⡪⡨⢪⢐⠨⢡⢣⣗⡳⡡⢐⠈⡨⠀⠀⠐⢌⢇⠪⡐⡀⠀⠀⠀⠀⠀⠂⠁⠠⠈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡁⠈⢌⢯⡏⡐⠁⠕⡜⡅⠐⢨⢚⣎⢷⠈⡎⠐⠀⡊⣗⣗⠕⡂⠐⠀⠂⠀⠀⠀⡂⢇⡑⡰⢨⢂⠀⠀⠀⠀⠂⠁⠌⡐⠠⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢌⠀⢨⡫⣗⢀⠁⡨⢪⣂⢊⢰⠸⡸⡹⡂⢕⠁⠀⡹⡝⢆⢃⠂⠀⠠⠀⠀⠀⠀⢐⢑⢎⡺⣸⢧⡣⡀⠀⠀⠀⠁⠐⡈⠄⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢁⠂⠀⣗⢺⢠⢀⠀⠠⢓⢄⢏⡆⡱⢵⠐⢔⢈⠀⢪⢊⠎⠄⠂⠀⠀⠀⠀⠀⠠⡱⣱⣳⢽⣺⢯⣟⡶⣐⠀⠀⠀⠁⠀⠈⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⡁⣂⠐⡱⡕⡐⠀⠀⠡⢑⢌⢆⠪⡪⢂⠕⡐⠀⢱⠡⢘⠨⠀⢁⠀⡠⢀⢢⢱⢵⣻⣽⣯⣯⣟⡾⣝⢷⡆⡂⠀⠀⠀⠀⠨⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠌⣦⠀⠡⠣⠣⡡⠀⠀⠂⡡⡑⡅⢝⠐⢌⢂⠨⢀⠧⣕⣎⢧⢱⡸⡴⣵⣳⡽⣯⣿⢷⣟⣾⣺⢽⡫⣛⢊⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡪⠠⠈⠨⠑⡬⢐⠀⠀⠀⢐⢘⢜⢌⢂⠣⠀⠐⢝⢷⣻⣿⣯⣿⣻⣽⣾⣻⣽⣾⢿⣯⢷⢝⢕⠁⠂⢀⠀⢀⢀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠀⠈⢐⠘⡌⠄⠀⠀⠀⠀⢇⢕⢔⠨⠐⢀⠑⡝⣽⣳⣿⣽⣿⣻⣽⣿⣽⣟⣯⡿⣽⣇⣇⡦⡵⣵⣪⢂⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⢂⢑⢁⠀⠀⠀⠀⢇⠧⡑⠠⠀⠐⠨⢢⢳⢳⢟⡾⡯⣷⢿⢾⣯⡷⣿⣗⣿⣞⣯⣟⠷⠝⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠐⡀⠂⠀⠀⢀⠑⡨⢀⠡⠀⡈⢐⠅⢇⢏⢎⢯⡺⡽⣯⢷⣟⣿⢾⣷⣻⢗⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠠⠁⠀⠀⠀⡀⠀⠠⢈⠐⠠⡊⢌⠪⡪⡪⡪⣏⡯⣯⢿⡾⡿⡾⡝⠅⠀⠠⠀⡂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠁⠀⠄⠀⠂⡀⠀⠨⠐⡈⢂⠕⡸⢸⢸⢘⢮⢯⢿⢽⠯⡣⢅⢢⢪⠌⡂⠄⡁⡐⢄⢂⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠂⠀⠄⠠⠀⠐⠐⠈⠌⡂⠣⠅⡇⠇⡇⡗⡝⡔⡜⡜⡪⡂⡢⢡⠢⡊⡦⡑⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠠⠀⠀⠀⠈⠠⠀⡀⠂⠄⠀⠁⠀⠄⠁⠡⠨⠈⢂⠑⡈⠐⠐⢑⢈⠢⠡⢑⠁⢇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⢁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡅⡪⡳⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢑⢴⢱⠐⠀⠀⠀⠄⠀⠀⠀⠈⠀⠄⠀⠁⠠⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡂⡎⡆⡧⡯⣗
⠀⠀⠀⠐⠀⠀⠀⠀⢀⠢⣑⡵⣝⢎⠎⠄⠀⠀⠀⠀⠀⠀⠈⢀⢀⢁⠀⠠⠁⠠⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣳⢕⣕⢯⡯⣟
⠀⡈⠅⠐⠀⠀⠀⠠⡱⣱⣼⣗⣗⣇⢏⢌⠀⠀⠀⠀⠀⠀⡀⠀⠄⢀⠂⠠⠀⡀⠂⠁⡀⠁⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣳⣽⣯⢿⣽