⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⣴⣶⣶⣶⣶⣶⣦⣤⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣿⣿⠁⠼⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠿⠛⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⢸⣿⡇⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠀⣾⣿⠁⣀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣷⣄⡀⠹⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⢰⣿⠿⠋⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠉⠻⣿⣿⣦⡈⠳⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠘⠁⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⡀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀ ⠀⠀⣰⣿⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣷⡀⢻⣿⣧⠀⠀ ⠀⢰⣿⡿⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⢴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡗⠀⢻⣿⣇⠀ ⢀⣿⣿⠃⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⣿⣿⡆ ⢸⣿⡏⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⣀⣤⣶⣄⠙⠿⣿⣷⣦⣀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠸⣿⣧ ⣾⣿⣷⣶⣤⣤⣤⣄⣠⣤⣤⣤⣴⣶⣿⣿⡿⠛⠉⠀⠀⠈⠛⠿⣿⠿⠂⢀⣴⣿⣿⠋⢀⣠⣤⣤⣶⣾⣿⣿ ⠀⠈⠙⠛⠻⠿⠿⣿⣿⠿⠿⠿⠟⠛⢉⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⢀⣴⣿⠿⠿⠿⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠉⠉⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⢰⣶⣶⣦⡀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⡈⠉⣻⣿⣷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠃⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣶⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀⣀⣀⠀⠀⠀⠀ ⠀⣴⣿⣿⠋⠁⠀⣀⡀⠀⠙⢿⣿⣿⣿⣿⡟⠁⢀⣴⣿⣿⣿⣿⣿⣶⡄⠀ ⢸⣿⣿⠁⠀⣴⣿⣿⣿⣷⣄⠀⢹⣿⣿⡟⠀⢀⣿⣿⡟⠁⡀⠈⠙⣿⣿⡆ ⢸⣿⣿⠀⠘⣿⣿⡅⠙⣿⣿⡀⠀⢿⣿⣇⠀⠘⣿⣿⣷⣿⣿⠇⠀⣿⣿⡇ ⠘⣿⣿⣆⠀⠉⠋⠁⣠⣿⣿⠃⠀⠘⣿⣿⣦⡀⠈⠛⠛⠛⠁⠀⣰⣿⣿⠃ ⠀⠘⢿⣿⣿⣶⣶⣾⣿⡿⠋⠀⠀⠀⠈⠻⣿⣿⣶⣤⣤⣤⣴⣾⣿⡿⠃⠀ ⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀