⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣾⠿⠛⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣿⠟⠁⣀⡀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣀⡀⠙⢿⣷⡀⠀⠀⠀
⠀⠀⣾⡿⠁⢰⡿⠿⣿⣇⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⡿⢿⣆⠀⢹⣿⡀⠀⠀
⠀⠀⢻⣧⠀⠀⠀⠀⠘⣿⡆⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢀⣿⡟⠀⠀⠀⠀⠀⢿⣷⠀⠀
⠀⠀⠈⣿⣦⠀⠀⠀⠀⢹⣿⡀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⣼⣿⠁⠀⠀⠀⠀⠀⠈⣿⡇⠀
⣰⣶⣶⣿⡿⠀⠀⠀⠀⠘⣿⣧⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀
⣿⣿⠉⠁⠀⠀⠀⢀⣤⣶⣼⣿⣆⠀⠙⣿⣆⠀⠀⣠⣴⣷⠟⠁⠀⠀⠀⠀⠀⠹⣾⣷⣤⡀⠀⢠⣾⡟⠀⢠⣾⣿⣴⣤⡀⠀⠀⠀⠀⠀⢸⣿⠀
⣿⣯⠀⠀⠀⠀⠀⢸⣿⡍⠉⠙⢿⣦⣴⣾⣿⣷⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢻⣶⣿⣿⣶⣰⣿⠟⠉⠉⣿⡿⠀⠀⠀⡀⠀⢸⣿⠀
⢻⣿⠀⠈⣧⠀⠀⠀⠙⠻⠀⠀⣸⡿⣿⠿⠾⠛⢿⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢼⠟⠹⠿⣿⢿⣯⡀⠀⠺⠛⠁⠀⠀⢠⡇⠀⢸⣿⠀
⢸⣿⡆⠀⠉⣀⠀⠀⠀⠀⠀⠈⠛⣻⡿⠁⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⠛⠋⠀⠀⠀⠀⠀⢀⡌⢀⣤⣾⡟⠀
⠈⣿⣧⠀⠀⠘⠷⣦⣤⣤⣤⣴⣶⣿⣶⠀⠀⠀⠀⠀⢠⠀⠀⢻⣶⡄⠀⣾⡾⠁⠀⠀⠀⠀⠀⠀⢰⣾⣷⣦⣤⣤⣤⣤⡶⠋⣠⡺⣧⡙⢧⠀
⠀⠈⢿⣷⣄⡀⠀⠀⠉⢉⣉⣭⣼⣿⣿⠀⡀⠀⢄⠀⢸⡀⠄⡄⠘⣧⣰⠟⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣬⣉⣉⠉⠁⠀⢸⣿⣿⣿⣿⣄⡷
⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠛⠉⠉⣿⡇⠀⠐⢦⡸⣦⣿⣗⣾⢦⡴⠉⠉⠀⠀⠀⠀⠀⣼⡇⠀⠀⠈⣿⡟⠋⠛⠛⠿⠿⠿⠿⢿⣿⡷⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠈⡿⣿⣿⣿⣏⡹⠀⡀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⣽⣏⢸⡷⢬⠟⡁⠀⢀⣀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⡙⠿⠿⡷⣶⣧⡁⠀⠀⠙⠻⣿⣾⣿⣧⣀⣀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣃⡚⠳⡷⢀⣿⢋⠀⠀⠀⠀⢰⣿⡟⠉⠉⠉⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⠈⠉⠛⠳⣷⠟⠋⠈⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢀⣠⣤⠄⠀⢻⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⠾⣦⡀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⣼⣿⠃⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣄⠈⢿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⠃⠀⣼⡿⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⣷⠀⠙⣦⣼⣿⡟⠀⠀ RAT$! ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣿⡇⠀⣠⣾⣿⣛⣙⣻⣿⣦⠀⠀⣿⣦⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠉⠛⢿⣿⠛⠋⠀⢀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠰⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⠀⢰⡇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀