⠀⠀⠀⠀⠀⠀⠀⢠⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⣿⡇⠀⢀⣠⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡥⠒⠛⢿⣿⣿⠿⢿⡅⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢶⡚⣹⣿⠿⣿⡿⣿⣶⣶⡾⢷⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀
⠀⠀⠀⠈⢳⣏⣤⣶⣷⡇⣹⣾⣶⣶⣶⣿⠏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⠄
⠀⠀⠀⠀⣾⣾⢿⣟⠜⠁⠀⠀⠛⣽⣿⡿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀
⠀⠀⠀⠀⠋⢾⣶⣿⣦⣄⣀⡠⣴⣿⣷⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀
⠀⠀⠀⠀⠀⢀⡀⣹⣏⠫⣤⣊⢽⣿⡌⡄⠈⠉⠐⠂⠤⠄⠀⣀⣀⠀⠀⡰⢠⡄
⠀⠀⠀⠀⠀⣿⣷⢰⣿⡀⠿⠯⠀⣹⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢊⠀⣠⠣
⠀⠀⠀⠀⠀⢸⠈⢾⠃⠙⠒⠙⢉⡧⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⡇⠀
⠀⠀⠀⠀⠀⡎⠀⢸⡆⡀⠀⠀⠀⣿⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓⢶⣤⣴⣿⠿⠿⣿⡵⢕⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠎⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⢸⣿⣿⣀⠛⣄⠀⠉⠁⠀⠉⠁⠀⠀⠀
⠀⠀⠀⠌⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠘⡷⣿⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡌⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⡁⣿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠚⢠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣿⣧⣰⣶⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⠟⢻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢳⡶⠦⢤⣀⣀⣀⣀⣼⣿⣠⠟⠀⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠉⠃⠤⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠐⢉⣇⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠔⠁⠀⠁⠂⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠁⠀⠑⡀⠀⠀⠀⠀⠀⠀
⠘⠢⠀⣀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀