⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⡀⡀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢅⠢⡈⡂⣂⠢⠂⠅⢂⠄
⠀⠀⠀⠀⠀⠀⠀⡌⡎⡌⡂⡂⡆⠈⠀⠁⠆⠮⢒⠪⠈⠄⡀
⠀⠀⠀⠀⠀⠀⣎⢎⢖⡑⡰⠁⠀⠀⠀⠀⠀⠀⠀⠠⢨⢔⢎⡢⡀
⠀⠀⠀⠀⠀⣪⢗⢧⠇⣂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁⢀⠂
⠀⠀⠀⠀⣘⣞⢽⣫⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢦⣃⠀
⠀⠀⠀⠀⣞⣞⣽⢕⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠪⢃
⠀⠀⠀⠨⣞⣯⢯⡂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⣸⡽⣺⣳⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢪⢧⡀
⠀⠀⠀⢲⡯⣯⢎⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⢃⠀
⠀⠀⠀⢝⡯⣻⢕⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀
⠀⠀⠀⢵⣏⢿⡜⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢺⠬⣳⡏⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀ ⠈⠦⢗⠅
⠀⠀⠀⢘⢽⡸⡫⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⡈⠄⠄⡂⠄⡁⡈ ⠀⢁⢂⠢
⠀⠀⠀⠐⡵⡹⣕⢌⠀⠀⠀⠀⠀⠀⠀⠄⡁⠄⡢⡑⢔⢅⢕⢔⢅⡂⡂⡡⠀ ⢦⣕⣇⠀
⠀⠀⠀⠈⢼⠸⡔⠆⡂⠀⠀ ⠀⠐⢈⢀⠢⡱⡸⣸⣵⣽⣮⣷⢵⣱⢱⠨⠠ ⠱⣻⣿⠀
⠀⠀⠀⠀⠌⡗⡪⡑⢄⠀⠀⠀⠀⠂⡐⡐⢅⠧⣯⣷⣿⣿⣿⣿⣿⢷⢕⢕⠅⠅ ⠝⢥⠡⠀
⠀⠀⠀⠀⠄⢣⠱⡑⠬⠀⠀⠀⠀⡁⢐⠨⡪⡝⣾⣿⣻⣿⣿⣿⣿⡯⡗⡕⡡⠡ ⢘⢐⣕⠀
⠀⠀⠀⠀⠀⠡⡑⠅⠅⡃⠀⠀⠀⠐⡀⠱⡐⡍⡷⣻⣟⣞⣿⣯⢷⡫⡫⡊⡢⠁⠄ ⣷⣻⡂
⠀⠀⠀⠀⠀⠁⠢⢑⢑⠨⠀⠀⠈⠀⠠⠁⡂⠕⡑⢕⢕⢳⢱⢹⢱⢑⠕⡐⠠⠁ ⠀⠟⣟⢃
⠀⠀⠀⠀⠀⠀⠡⡁⢂⠨⡀⠀⠀⠀⠀⠄⠂⠀⠡⢈⠂⡊⠔⠡⢊⠐⡐⠐⠀⠂⠂ ⠨⠸⣐
⠀⠀⠀⠀⠀⠀⠀⢂⠡⠐⢐⠀⠀⠀⠀⠀⠀⠈⠀⠠⠐⠀⢈⠀⠂⠀⠠⠀⠁⠀⠀ ⠀⢸⢼⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡐⢍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣘⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⣿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡍⡎⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⡞⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡓⡛⠌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⢀⢔⢼⢞⠢⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠒⠂⠊⠀⠀