⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⢿⡹⣏⠿⢿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢯⡿⣹⡟⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⣯⡑⢎⡙⠈⠂⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⣭⠳⣏⠷⣹⣳⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⢣⠇⠀⠈⢳⠀⠈⠐⠄⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢈⠴⠁⠈⠓⡱⠻⣀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡌⠀⠀⡔⠠⢳⡀⠀⠀⠈⠐⢄⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠃⠀⠀⠀⠀⠀⡇⠈⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢏⡄⠀⠀⢄⠀⠱⠀⠀⠀⠀⠀⠑⠌⢣⡠⠔⠂⠉⠉⠉⠉⢣⡃⠀⠀⠀⢀⠠⠄⡇⡐⠀⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡈⠠⠀⠇⠄⠀⢀⠀⠀⠈⢂⠂⡀⠀⠀⠐⠀⠠⡌⡀⡠⠐⠉⠀⠀⠀⠇⠀⢈⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⡠⢠⠀⠸⠀⠀⠀⠀⠁⡠⠀⣰⣿⠏⠀⠀⠀⠀⠁⠊⡆⠀⠀⠀⠀⠀⢣⠀⠀⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠐⠀⠀⡐⠀⠀⠀⠀⠀⠙⢄⣻⣿⣦⣠⡀⢈⢦⠀⢰⠀⠀⠀⠀⠀⠀⠀⠣⡠⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⢷⣎⠂⠶⠈⣁⠉⠀⠀⠀⠀⠀⠀⠀⠘⢅⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠋⠀⠀⠀⣠⣴⣶⣷⣶⣤⡀⠀⠀⠀⣤⣿⠇⠀⠀⠀⠀⢠⣶⣿⠿⠛⢓⠀⠀⠀⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠈⠀⠀⠀⠀⠉⠀⡀⠰⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣓⠂⡈⠀⠀⠀⠀⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣄⠀⠀⠀⠀⠀⠑⢄⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⢁⠠⠁⠀⠀⠀⠀⢸⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠤⠶⠛⠉⠋⢯⠥⠄⠀⠀⠀⠀⠀⠈⠐⠚⠉⠉⠁⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠈⠙⠚⠒⠦⢄⡀⠀
⠀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⣀⡀⣀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠎⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠈⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀