⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣿⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⡏⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠷⠶⠶⠶⠲⠟⢶⡄⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⠿⠛⠛⠛⠛⠛⠛⠛⠻⣷⣶⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⣿⡁⠶⣶⠲⠦⢤⣤⣀⣀⡀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠘⢿⣿⣿⣀⣀⡀⠀⠀ ⠈⢿⣦⠈⢻⣄⠀⠀⠈⠉⢙⣿⠟⠁⠀⠀⠀⢰⡀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠶⣿⠘⠙⣛⠛⠛⢫⡇⠀⠀ ⠀⠀⠹⣷⡄⠈⠳⣄⠀⠀⣿⠋⠀⠀⠀⠀⢠⣼⡇⠹⠀⠀⠀⠀⠀⠀⠘⢿⣧⣼⠋⠁⠈⠻⣿⣿⡟⠃⠀⠀ ⠀⠀⠀⠈⠿⣦⡀⠛⣷⡾⠁⠀⠀⠀⠀⠀⢸⡟⠃⠀⠠⣶⣶⣦⣀⠀⠀⠀⠀⠉⠙⠳⠶⣦⣄⣙⣧⠀⠀⠀ ⠀⠀⠀⠀⣀⡼⠿⠿⠋⠀⠀⠁⠀⠀⠀⠀⠈⢡⣤⠶⠛⠉⢉⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⡄⠀ ⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣶⣏⡠⠀⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠏⣿⡄ ⠀⢠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⣇⢀⣿⠇ ⠀⣾⣟⣉⣁⣀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣴⣾⠟⠀ ⠀⠈⠻⢿⣿⣧⣶⣶⣶⡀⠀⡀⠊⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢀⣤⣴⢶⣶⣶⣶⠶⣶⣶⠶⠞⠛⠛⠁⠀⠀ ⠀⠀⠀⠀⠙⢻⣿⣿⡟⠛⣾⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠉⠁⠀⢹⣿⣧⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣡⣾⣿⣿⠀⣀⣶⣶⢀⠀⠀⢸⣄⠀⠀⠀⠀⠀⣸⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣼⢻⣽⣿⠀⠙⠀⠈⣿⠀⠀⠀⠀⠀⢉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⠈⠻⣿⣀⢀⡀⠀⢿⠣⣄⠀⠀⠀⣿⠁⠙⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠉⠉⠛⠂⠿⣷⣌⢷⡀⠀⣏⠀⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣿⣄⡀⢠⣀⣀⣀⠈⠙⢿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠿⡿⢿⣾⣿⣿⣿⡿⢿⣶⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⢣⡜⣷⡘⢿⣿⡅⠀⠀⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡀⠸⣇⣈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀⠀⠀⢸⣿⣿⢿⣿⣿⣦⣄⢹⣼⡟⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢙⡻⠿⣷⣶⣾⣿⡇⠀⣍⠙⣿⣿⣿⣿⣿⣯⣿⣿⡆⠀⠀⠀⠀