╳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀╳

⠀⣸⣿⣦⢆⠀⠀⢰⣵⢲⠀⠀⠇⠀⠇⠀⠀⠀⣀⡠⠤⢐⣂⠩⠤⠒⠊⡉⠀⠄⠐⠀⠀⠀⠀⠀⠀⡀⠠⠀⢂⠀⠄⠐⠀⠀⠀⠀⠀⠀
⣴⠟⠀⢹⡈⠢⣴⢢⢏⣼⡇⠀⠀⠀⢀⣒⡩⠥⠒⠒⢉⠁⠄⠐⠂⠈⠀⠀⠀⠀⢀⠀⠄⠐⣀⣩⡤⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠞⣁⡤⣚⣵⠟⢣⡗⣞⠚⠋⠉⠠⠀⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣥⣴⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠉⠩⠓⠊⣙⣀⣤⡄⢱⣎⣷⣄⠀⠀⠀⢀⠀⠀⢀⣀⣠⣥⣶⣶⣿⣿⣿⣿⣟⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡶⠂⣀⣤⣶⣿⣿⣿⣿⠷⢠⣿⣖⠑⢩⣷⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⣠⣶⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀
⣴⡾⠿⠿⠟⠛⠛⠉⠡⡴⢾⣹⣽⣸⡽⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢍⡠⠊⠉⠙⠻⢦⣀⠀⠀⠀⠀⠂⠀⠀⠀
⠭⠉⠒⠒⠒⠖⢺⣏⣵⢞⣯⡷⣾⣵⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⢿⣟⢾⠋⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀
⡻⠿⠶⢒⣀⡲⢟⣿⣿⠏⢳⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠻⣶⠀⠀⠀
⣭⡍⠩⢽⣵⣶⣿⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⡄⠀⠀
⣮⣴⡿⣿⣿⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉⠢⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⡀⠀
⣿⣏⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢑⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣏⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⢔⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠁⣧⡢⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⡈⠀
⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⡼⠾⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀
⠈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀
⠀⣽⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡴
⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⣠⢾⠄
⢀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡠⠚⠁⡾⠀
⢧⣿⣿⣿⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠸⡀⠀⠀⠻⠀
⣾⣿⠯⢉⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣀⠴⠳⡀⠀⠀⠀

╳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀╳