⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣴⡾⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣴⡾⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡟⠁⠈⠻⣿⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣷⡀⠀⠀⢻⠃⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠈⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣿⠋⠀⠈⢻⣆⣀⣤⠶⠿⠷⣦⣄⠀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡇⠀⠀⠀⠈⣿⠋⠁⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠘⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢻⣆⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣆⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡄⠐⠚⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⣤⣀⡀⠀⢀⣠⣤⣄⡀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⠟⠉⠉⠙⢿⣶⡿⠋⠉⠙⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢀⣿⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⡄⠀⠀⠀⠀⠻⠇⠀⠀⠼⢇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠻⣦⣀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠁⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⣰⡿⠋⠉⠛⢷⡄⢀⣠⣴⣶⣤⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠃⠀⠀⠀⢘⣿⠟⠉⠁⠀⠉⢿⣆⠀
⠀⠀⠀⠀⠀⠀⢸⣧⠀⢻⡇⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠸⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠘⣿⡄⠀⠀⠛⠁⠀⠀⠀⠀⠀⣰⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⢿⣆⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⡄⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣾⠿⠻⢷⣦⣼⡟⠉⠙⣷⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢾⡇⠀⠀⠀⠹⣿⡄⠀⠀⣿⠇⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣄⠀⠀⠀⠙⠓⠀⢠⡿⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣧⣀⠀⠀⠀⠀⠀⣿⣣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠳⠦⠤⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠙⢻⣦⣀⣤⡶⠶⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⣿⡇⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠄⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀