⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣶⣮⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣧⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⣿⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡿⠿⡿⢂⠀⠑⡀⠀⢀⣀⠀⠀⠀⠀⢸⠀⡟⠉⠉⠀⡄⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣎⡉⢁⣤⡀⣠⣰⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢀⣤⣀⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡄⠀⠀⡄⠀⠀⢠⣾⣺⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⡿⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⡇⠀⠀⢃⢀⣴⠞⢹⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠿⠛⢹⠋⠀⣴⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⢄⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⠀⢰⣿⡇⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠸⠀⠀⠀⢂⠀⢀⠼⠀⣼⠟⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⢀⠟⠉⠇⠀⠀⠀⠀⠀⡿⢳⡀⠀⢠⠀⠀⡄⠀⠀⢸⠂⠁⠰⣇⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⣬⣼⣤⣶⣸⣀⠀⠀⠀⢀⣇⣰⣾⣦⣬⣧⣧⡇⠀⠀⠀⠠⠪⠣⡏⡪⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⢸⠀⠀⣿⣿⡟⠛⠳⢄⠀⡘⠉⢸⣿⣿⣿⠛⢀⠁⠀⠀⢸⠀⠔⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⣾⠀⠀⢻⣿⣿⡏⠀⠀⠁⠀⠀⠘⣿⣿⣿⣿⡘⠀⠀⠀⡘⠁⠀⢰⢱⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡣⠂⢠⠀⠀⢹⠀⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⡑⡕⠊⠀⢠⠃⡇⠀⢈⢸⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢆⠀⠈⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢠⠃⡄⠇⠀⡟⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠘⣿⣿⣿⣷⣶⣶⣶⣲⢷⡶⣶⣿⣿⣿⠀⢀⣴⣧⠀⡇⠀⠀⠗⠀⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡑⠄⢹⣿⣿⡿⣿⠛⣿⡶⣯⣿⣯⡿⠟⣻⢀⣾⣿⢿⢰⠀⡈⢄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠀⠼⠞⠘⣿⣷⡙⢷⣌⣾⢿⠿⣋⣴⠾⠋⣾⣿⣏⠤⠃⡠⠁⠀⠑⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣼⣿⣿⣿⣦⣙⠏⡿⢛⣩⣤⣶⣿⣿⡎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⣽⣿⣿⣿⣎⠻⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣯⣟⣿⣿⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣫⣭⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠊⠽⢿⣿⣿⠇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣫⣭⣽⣿⣿⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀