⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣄⡀⠀⠀⢀⣴⣿⠛⣏⠻⣦⡀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡉⣯⣙⡻⣶⡿⠛⠁⠀⠹⣆⢈⣻⣷⠿⠛⠛⢉⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠟⠃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠹⠛⠁⠀⠀⠀⢀⡾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⡴⢋⣽⣿⣮⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⣀⠄⠀⢡⣿⡿⠛⠙⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠰⠚⠁⠀⣰⣿⠟⠀⠀⠀⠀⠙⣿⣿⣶⣦⣤⣤⣶⣦⣾⣿⠋⠁⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀ ⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⢉⣉⠉⢉⣉⠙⢻⣿⡛⠁⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀ ⠀⠀⠀⣿⡏⣧⡀⠀⠀⣾⣷⣦⣤⣿⠏⠀⠀⠀⠀⠀⠀⢠⣟⡏⢀⣾⡟⠀⣞⡟⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀ ⠀⢀⣠⣿⣇⣎⠙⠳⣦⣀⣉⣻⣿⡟⠀⢠⣤⣀⠀⠀⠀⠈⠉⠀⠘⠋⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣠⣾⣷⠀⠀⠀⢀⢸⣧⠀⠀ ⣰⡿⠟⠉⠻⣿⡆⠀⠸⣿⠿⢿⣿⠇⠀⠈⣻⣿⣷⠀⢀⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⢿⣿⠿⠛⠁⠀⠀⣀⣼⡇⣿⠀⠀ ⢹⣧⡀⠀⠀⣽⡷⡀⠀⠀⠀⢾⡁⠀⠀⠸⡿⠛⠉⠀⠸⣿⣶⣾⣿⣷⣦⣴⣶⠀⢰⣾⣿⠻⠁⠀⠀⠀⢀⣼⣿⣤⣤⣦⠗⠛⢡⣘⣷⡿⠀⠀ ⠀⠙⠻⣶⣶⡟⠀⡇⠀⠀⢦⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠈⣿⣿⠋⠀⠈⠛⢿⣿⡆⠀⠀⠤⠦⣿⡏⠉⠉⠙⠀⢰⣿⡿⠟⠻⢷⡄ ⠀⠀⠀⢹⣷⡤⢤⡀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣤⣀⣀⠀⠀⠻⣿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣼⠇⠀⠀⣧⠘⢿⣯⠀⠀⠀⣼⡇ ⠀⠀⠀⠀⢻⣧⡈⠁⠀⠀⠀⠀⠀⠀⠈⠓⠉⠭⣝⡛⠻⠿⠿⣿⣾⣿⣿⣴⣶⣦⣶⣶⣶⣶⣶⡾⠿⣯⡿⠁⠀⠀⠀⠸⡆⠈⠛⠳⣶⡾⠋⠀ ⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⢰⠀⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⢻⡀⢠⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠄⠀⠀⢠⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠉⠉⢿⣦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢈⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣷⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠟⠋⠀⠉⠉⠉⠛⠛⠛⠛⠻⠷⠶⠶⠶⠶⠶⠿⠷⠶⢾⡿⠟⠁⠀⢠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀