⠀⠀⢀⣀⠀⡆⠀⢆⣀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿ ⠀⢀⣬⡉⠉⡇⠀⠈⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠛⠻⣶⣅⣰⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣷⡀⠀⢘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠛⠛⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣦⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣠⣾⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⢀⣴⡿⠃⠀⣿⣷⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⣿⠟⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⢀⣴⣿⣿⣥⣤⣴⠶⠶⢾⣿⣧⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣾⡿⠃⠶⠶⠶⠶⣶⣤⣼⣿⣤⡄⠀⠀⠀⠻⣧⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣠⣶⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠉⢿⣦⠀⠀⠀⢿⣿⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣿⡲⠶⠄⠀⠹⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⣶⣦⣴⣿⣿⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⠸⣿⣇⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠸⣷⣄⠀⣿⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⣸⡿⠿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠘⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⢷⣤⡀⠈⢻⣶⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⣴⣿⠇⠀⠀⣿⣿⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⣷⣄⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠈⠉⠻⢷⠙⣿⠀⠀⠀⠀⠀ ⣶⠀⣼⣿⣿⠀⠀⠀⠹⣿⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀ ⣧⣴⣿⣿⡇⠀⠀⠀⢠⣿⠀⠀⠀⠙⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣤⣤⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀ ⣧⣼⣿⡿⠃⠀⠀⠀⣿⣿⡆⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠛⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠉⠻⢿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀ ⢹⣿⢸⡇⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢀⣴⣶⣆⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀ ⢸⠁⢸⡇⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⣴⣿⡿⣿⣿⣷⣤⣠⣤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀ ⠈⠀⣼⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠟⠀⠀⠘⠿⢿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⣿⣇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼ ⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣿ ⠀⢸⣿⣿⣧⠀⠀⢸⣿⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⣰⣿⠟ ⠀⢸⣿⠀⢻⣄⠀⢸⣿⡇⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀ ⠀⠀⣿⠀⠈⢿⣦⠸⣿⡏⠀⠈⠙⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡿⠟⠁⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀ ⠀⠀⣿⡀⠀⠀⠙⢷⣿⣇⠀⠀⠀⠀⠈⠙⠛⠻⠷⠶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⡶⠶⠿⣛⣿⡿⠋⠀⠀⠀⣀⣤⣶⠿⠛⣿⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⣛⣻⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣤⣀⢤⡄⠰⠿⠛⠁⢀⣠⣴⡿⠟⠛⠋⠀⠀⢼⡿⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠙⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⡿⠁⢀⠀⠀⡀⠀⢀⠀⠀⠈⠉⠙⠿⣿⣿⣷⣀⣀⣠⣶⡏⣁⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀