⠀⠀⢠⢀⠐⠀⡀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣴⣄⢴⣶⣤⣦⣤⣤⣤⠄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⠀⠀⠀⠉⡈⠠⠀⢸⣇⠀⠀⠀⠀⠀⠀⠐⣿⣽⣿⣮⣿⣿⣿⣿⢬⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⣿⣷⣀⣀⣀⠀⠂⠂⠈⣻⠀⠀⠀⠀⠀⠀⠀⠨⣷⣿⣿⣿⣿⣿⡯⣿⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣈⣧⣬⣄⣀⣀⠲⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣶⣶⡦⣼⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⣿⣿⣾⣕⠂⠙⡄⠘⣇⡀⠀⠀⠀⠀⠀⣄⣼⡿⣿⣿⣿⣿⣿⡿⠷⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⠆⠈⠓⠀⢻⣷⣦⣴⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠽⣿⣿⣿⣿⣿⣆⠁⡁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⡿⣯⢇⡀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣟⣵⣯⠏⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⢃⣶⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣫⣙⡻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠸⣿⣟⢋⣼⣻⣿⣛⣟⣿⡻⠋⠀⠀⠀⠉⠉⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠆⠙⠲⠍⠉⠁⡁⣻⣻⢿⡏⡀⡀⠠⠄⠀⠀⠨⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠞⠈⠀⠀⠀⠀⠚⣿⣿⣶⣄⠀⠀⠀⢀⠀⠄⠸⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠹⠁⠀⠀⠀⠀⠁⡾⣛⣿⣿⣿⣿⡀⢀⢀⡀⢰⡳⠄⡁⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡘⢿⣦⣼⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⡇⠀⠀⠀⠀⣀⠸⣿⣿⣿⢟⣵⣿⠿⠿⣤⣤⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣿⣿⠂⢠⣤⣼⣿⣤⣿⠿⠀⠙⠙⠁⠀⠠⡮⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣘⣿⠦⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⣿⣽⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡆⠀⠀⠀⠙⣿⣿⣷⣀⠸⠀⠀⠀⠀⠀⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢻⣷⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠤⣠⠄⠀⣰⠞⠁⣤⡾⠟⠀⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⢀⣤⣶⣶⣦⡄
⠀⢀⣀⣴⠿⠛⢯⡝⠃⣠⣾⣿⣧⣃⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠂⠀⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡇
⠀⠈⠛⠃⠄⠁⠛⠀⠼⠛⠟⠞⠟⠓⠟⠒⠶⠤⠤⠤⠠⠒⠺⠧⠀⠃⠈⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠁⠀