⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡤⠶⢶⣄⡀⡀⣠⠶⠒⣦⡀⡀⡀⣠⠖⠶⣴⡀⠲⣶⡖⠂⡀⠒⣶⠒⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣠⣶⢀⣴⣶⣄⡀⡀
⡀⣿⣀⣀⣀⣿⣇⡀⠿⡀⡀⢸⣿⡀⡀⣷⡀⡀⢸⡀⡀⠸⣷⡀⡀⢀⠏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠁⡀⡀⣿⡀⡀
⡀⣿⡀⡀⡀⡀⡀⡀⢀⡴⠛⢹⣿⡀⡀⠙⠿⣿⣤⡀⡀⡀⢻⣧⡀⡿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⣿⡀⡀
⡀⣿⣦⡀⡀⢀⠇⡀⣿⡀⡀⢸⣿⡀⠐⡀⡀⡀⢻⡇⡀⡀⡀⢿⣴⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⣿⡀⡀
⡀⡀⠛⠿⠿⠋⡀⡀⠻⠿⠛⠘⠿⠋⠠⠻⠶⠴⠋⡀⡀⡀⡀⢈⠇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠠⠼⠿⠤⠠⠴⠿⠦⠄
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡾⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠘⠿⠛⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⣀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⡀⡀⣀⡀⡀⡀⣀⡀⢀⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣀⡀⡀⡀⡀
⡀⡀⡀⣿⡄⡀⡀⣿⡄⡀⡀⣸⡀⠈⢹⣿⡀⠈⢹⣿⠞⠉⠹⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣾⠁⡀⠙⣿⡀⡀
⡀⡀⡀⠘⣿⡀⡀⠟⣿⡀⢀⠃⡀⡀⢸⣿⡀⡀⢸⣿⡀⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣾⡇⡀⡀⡀⢹⣿⡀
⡀⡀⡀⡀⢻⡇⡾⡀⢻⣇⡟⡀⡀⡀⢸⣿⡀⡀⢸⣿⡀⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⣷⡀⡀⡀⢸⡿⡀
⡀⡀⡀⡀⡀⣿⡀⡀⡀⣿⡀⡀⡀⡀⢸⣿⡀⡀⢸⣿⡀⡀⢀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠿⣦⣀⣀⠟⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⣰⠋⠉⢿⡆⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⠘⠋⣿⠙⠛⡀⢀⡶⠛⠛⣶⡀⡀⠤⣾⢁⠾⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣴⠚⠛⢷⣄⡀⡀
⡀⡀⡀⡀⡀⡀⣿⡀⡀⢀⣿⡀⡀⡀⠘⣿⡀⡀⣿⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣾⡇⡀⡀⡀⣿⡆⡀
⡀⡀⡀⡀⡀⡀⣿⡀⡀⢸⣿⡀⡀⡀⡀⣿⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡇⡀⡀⡀⣹⡟⡀
⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⢿⣆⡀⡀⢠⡟⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠹⣿⡀⡀⡀⣿⠁⡀
⡀⡀⡀⡀⠐⠚⠛⠓⠒⡀⡀⠉⠛⠛⠁⡀⡀⠒⠛⠛⠒⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠛⠛⠉⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣠⣶⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⣀⣤⡀⣠⣤⡀⡀⣠⣤⡀⡀⡀⡀⣀⣤⣤⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⣠⣤⡀⡀⡀
⡀⡀⡀⡀⡀⢸⣷⠉⡀⠙⣿⠋⡀⠈⣿⡀⡀⣼⠁⡀⡀⣿⣇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠋⡀⠙⣿⡆⡀
⡀⡀⡀⡀⡀⢸⣿⡀⡀⡀⣿⡀⡀⡀⣿⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⢸⣿⡀
⡀⡀⡀⡀⡀⢸⣿⡀⡀⡀⣿⡀⡀⡀⣿⡀⡀⣿⣆⡀⡀⡀⡞⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀⡀⣼⠇⡀
⡀⡀⡀⡀⣀⣼⣿⣀⢀⣠⣿⣀⡀⣀⣿⣄⡀⠈⠿⣿⣿⠟⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠿⣦⣤⠴⠋⡀⡀