⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣆⣰⠿⣤⣿⢷⣼⠿⣧⡼⢿⣄⣴⣧⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠈⠋⠀⠙⠁⠈⠉⠀⠉⠃⠘⠛⠁⢻⡿⠙⣧⠾⣇⣠⡄⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⣿⠃⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀
⠀⠀⣴⢋⣀⣁⣀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀
⠀⣠⡿⠛⠉⠈⠉⠛⣶⡿⠛⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⢰⡏⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠰⡿⢸⠀⠀⠀⠀⠰⡿⠆⠀⢈⡗⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀
⠹⣧⡀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣿⠊⠀⠀⠀⠀⠀
⠀⢈⡷⢶⣤⣤⣤⡶⠛⠻⢶⣤⣤⣤⡾⠟⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀
⠀⣾⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠻⣦⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠻⣟⣛⡛⠛⠉⠉⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣤⣶⠾⠟⠋⠁⠹⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣾⠗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡉⠙⠟⠛⢻⠛⢿⠛⠛⠛⠛⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⣼⡇⢸⠀⠀⠀⠀⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣦⣉⣉⣉⣉⣉⣷⠿⣦⣥⣤⣤⠿⢦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⠉⢻⡿⠛⣿⣿⣷⣤⣤⣤⣴⣶⣿⡀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣏⣀⣎⣀⣀⣀⣸⣷⡾⣫⠖⠉⠈⠉⠉⠉⠀⠘⣿⠀
⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣭⣉⣉⣉⣹⣯⣴⣅⣀⣀⣀⣠⣀⣠⣤⣶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠬⠉⠉⢉⠉⠉⠭⠤⠤⠴⠒⠁