⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⢔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢀⢔⣵⡿⣷⣕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣠⣴⣶⣾⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⡆⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⣾⠀⠀⢪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⡾⠋⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⣸⣿⠀⠀⠘⢿⣮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣾⠋⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠁⠀⣼⣿⡏⠀⢰⣿⣿⠀⠀⠀⠀⠙⢿⣮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⣪⣾⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⠂⠀⣸⣿⡟⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⢷⣜⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⣪⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠌⠀⢰⣿⣿⠁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⠀⠀⠀⠀⠀
⠀⠀⢠⢪⣾⡟⠁⠀⡄⢀⡀⣄⣄⠀⠀⠀⢸⣿⣿⠀⠀⡜⠀⢠⣿⣿⠃⠀⠀⠀⢸⣿⣿⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠙⢷⣝⢄⠀⠀⠀
⠀⠀⠀⠑⢝⢿⣦⡀⠀⠀⠁⠈⠉⠀⠀⠀⢸⣿⣿⠀⡰⠁⠀⣾⣿⠏⠀⠀⠀⠀⢸⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⡿⡫⠊⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢝⢿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣰⠃⠀⣼⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡫⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⢝⢷⣄⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⡫⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡙⢷⣄⠀⠀⠀⢸⣿⡟⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡾⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢷⡄⠀⢸⡿⠁⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⡾⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠸⠃⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢘⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢡⣿⣷⣶⣤⣴⣶⣿⣿⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠟⠋⠁⢸⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⢀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡻⢟⡵⠃⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀