⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡓⣾⢷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣂⣕⣺⣿⣿⣿⣿⣿⣷⣦⣤⣤⢤⣀⢆⠘⡦⡑⢳⣸⣟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⠺⢉⠚⠻⢞⠪⠫⢻⡹⡿⣿⠹⡷⠉⠩⠋⠝⠩⣹⣿⣦⡲⠈⢻⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠋⠀⠀⠀⠀⠀⠀⣴⢣⠢⠓⠀⠀⠀⠀⠀⠀⢁⠈⠁⢍⠂⡈⠐⠀⠀⡀⠀⠁⠹⢝⣿⣌⠻⠼⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⡿⠁⠀⠀⠀⠀⠀⠠⡨⢙⣀⠁⡠⠀⢂⣀⡒⠂⢤⡀⠐⠐⣒⣦⠈⡐⡐⣁⡤⠤⣄⠀⠀⠈⢿⡄⠉⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⣀⠊⠀⠈⠁⠉⣈⠓⡄⢀⠁⠀⠁⣿⣄⡔⠀⠁⠠⠢⠀⠁⠐⡄⢝⡇⠀⠀⠂⡔⣉⠖⡀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⢂⠀⠀⢀⠈⡀⠀⠈⣪⠀⣜⠠⣿⣿⣷⠀⣀⣀⣀⣠⣾⣦⣱⣼⡇⠀⠀⠀⠴⠑⢺⠁⢆⡀⠀⠀⠁⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⡤⡿⣆⣀⣐⣂⣖⡻⣷⡅⢆⢻⣧⣻⠿⣯⣿⡒⡠⡮⣷⣻⣿⣿⣿⡇⠀⠀⠀⠂⢈⠠⠈⡌⢆⡍⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡺⣜⢾⡯⠵⣟⡭⢕⣡⢖⠈⡑⢭⣸⣷⣘⣿⣿⣿⣵⡿⣿⣿⣿⣿⠀⠀⢀⠆⡀⠂⠐⠠⠤⢍⡲⣇⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣨⠻⡾⣎⡐⢡⡾⠡⣰⢾⡆⠀⠙⠛⠿⣿⠛⢯⢿⣿⡨⣿⣿⣿⠀⠀⠒⠈⣇⠀⠀⠀⡁⠈⠔⠂⠉⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠅⡙⠁⣘⠐⠀⣨⣏⣿⣇⠀⠀⠀⢀⡁⡀⢠⣿⣿⣿⡼⠟⣛⠀⠀⠀⠁⠘⣮⠄⢀⠐⠤⠀⡀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠫⠁⢀⠭⢾⣿⣿⣤⣀⠀⢈⣿⣾⣿⣿⣿⣿⣿⣸⣆⠀⠀⠀⠀⠂⠼⡖⣀⠀⠀⠡⠈⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠙⠨⣛⣿⣟⡛⡦⣜⢿⣿⣿⣿⣿⣿⣿⣯⡣⠀⠀⠀⠀⠀⠀⡔⢫⡷⢨⢄⠡⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠠⠀⠁⡉⣪⠫⡃⠻⡎⢣⠽⢻⠙⢻⡉⣟⢺⣱⣿⣷⠀⠐⢄⠀⠂⠄⠘⢨⠻⡡⢎⡍⠱⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠡⢉⡐⠍⠸⡸⣈⠮⠀⠠⠁⣘⣐⣅⢧⣶⣞⢵⣟⣿⡖⠀⠐⡀⠄⢡⠀⡀⠐⠠⠀⠌⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⡈⡌⢁⠀⣵⢈⢰⠃⣽⣯⣿⣽⣾⣾⣶⣿⣯⣃⠏⠀⠀⠈⢁⠕⠄⠀⠀⠀⠀⠀⠈⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠄⠂⠀⠀⠁⡀⠖⢲⠨⠺⠹⢛⣻⣏⣛⣽⣯⣾⣿⢷⠁⠀⠀⠈⢀⠈⠡⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡐⠑⠶⠶⠵⠶⠲⠞⠹⠟⡻⠻⠍⠛⠊⠠⣾⣿⡯⡲⡀⠀⠀⠈⠂⡀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⡇⢽⣿⣿⠱⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⡒⠀⠀⡈⠂⠄⠀⠀⠀⢹⠀⠜⣻⡷⡿⡺⡏⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠁⠀⠄⠀⠀⠂⠠⡜⣊⢁⡌⡪⠳⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠘⡀⢀⠐⠆⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀