⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣦⠀⠀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡀⠀⠀⠀⠘⠿⠟⠀⣀⡀⠀⢀⣀⠀⠻⠿⠇⠀⠀⠀⢠⣿⠇⠀
⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠛⠶⠾⠛⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀
⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣶⣎⠉⠉⠓⠦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠙⠻⢆⠀⠀⠀⣹⡄⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⢾⠟⠀⠀
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⣔⣿⠗⠀⠀⠀
⠀⠀⠀⡮⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⡟⠁⠀⠀⠀⠀
⠀⠀⡞⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡯⡞⠁⠀⠀⠀⠀⠀⠀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡱⡽⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡀⠀⠀⠀⠀⡠⡠⠦⢧⢯⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⢷⣧⠭⢝⡻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⠀⢀⠔⠁⢠⡿⠀⡠⠈⠀⡘⢻⣧⠀⡸⠀⢠⡿⠁⠀⠀⢰⣿⠀⢀⠔⠁⢠⡿⠀⢀⣿⠃⠈⣿⡆⠀⣾⠇⠀⠀⠀⣾⡇⠀⡠⠊⠀⣾⠇⢀⣶⠋⠀⠀⠙⠀⣾⠇⠀
⢸⣿⠔⠁⠀⠀⣾⠋⠉⠃⠀⢠⠁⠀⠹⣧⠁⢀⣾⠃⠀⠀⠀⢸⣿⠔⠁⠀⢀⣾⠃⠀⣼⡏⠀⢠⡿⠃⣰⡟⠀⠀⠀⠀⣿⡧⠊⠀⠀⣸⡟⠀⢾⡏⠀⠀⠀⠀⣸⡟⠀⠀
⠘⠁⠀⠀⠐⠚⠛⠒⠒⠋⠐⠒⠂⠀⠀⠁⠐⠚⠛⠂⠀⠀⠀⠘⠁⠀⠀⠐⠚⠛⠂⠚⠛⠒⠊⠉⠀⠒⠛⠓⠀⠀⠀⠀⠋⠀⠀⠀⠒⠛⠓⠀⠀⠙⠒⠂⠁⠒⠛⠓⠀⠀