⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢒⡛⠍⠛⠀⠀⠀⠀⠀⠀⠈⠋⠶⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠊⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣙⡄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣴⣾⡄⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⣠⠤⣿⠃⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁⢸⠀⣤⣶⣿⠟⠉⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⡞⠁⠀⢸⡇⠀⠀⠀⠀⡠⠒⠀⠐⢢⡀⠀⠀⠸⠀⠻⣟⠥⠀⠀⢲⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⢁⠀⠀⠈⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠠⠐⠁⠀⠸⣇⠀ ⠀⠀⠀⠀⠀⠘⣕⠂⠄⢿⠆⠀⠀⠀⠣⡀⠀⢀⢼⣝⣃⣇⠤⢤⣤⢤⡁⠉⠉⠉⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⡞⡀⠀⠀⠀⠀⠀⠠⠚⠭⠼⠿⠃⠙⠉⠒⠠⠤⠤⠀⣰⣄⡈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠀⠀⢀⠤⡀⡀⠀⠀⠀⠀⣀⣤⠴⡒⠆⠊⠉⠀⠀⢠⢳⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⡀⢱⣉⣈⣠⣤⠖⠚⠿⠁⢸⠇⠀⠀⠀⠀⠀⢠⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣄⡀⠀⠀⠀⠓⠡⠄⠘⠉⠀⠀⠀⢀⣠⣶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣀⣀⣀⣀⣀⣠⠤⠶⠞⠋⠁⠀⠀⠀⠀ ⢸⣿⣷⣿⢿⢿⡇⣸⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠴⣄⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢒⡛⠍⠛⠀⠀⠀⠀⠀⠀⠈⠋⠶⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠊⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⢀⣙⡄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣴⣾⡄⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⣠⠤⣿⠃⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁⢸⠀⣤⣶⣿⠟⠉⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⡞⠁⠀⢸⡇⠀⠀⠀⠀⡠⠒⠀⠐⢢⡀⠀⠀⠸⠀⠻⣟⠥⠀⠀⢲⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⢁⠀⠀⠈⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠠⠐⠁⠀⠸⣇⠀ ⠀⠀⠀⠀⠀⠘⣕⠂⠄⢿⠆⠀⠀⠀⠣⡀⠀⢀⢼⣝⣃⣇⠤⢤⣤⢤⡁⠉⠉⠉⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⡞⡀⠀⠀⠀⠀⠀⠠⠚⠭⠼⠿⠃⠙⠉⠒⠠⠤⠤⠀⣰⣄⡈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠀⠀⢀⠤⡀⡀⠀⠀⠀⠀⣀⣤⠴⡒⠆⠊⠉⠀⠀⢠⢳⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⡀⢱⣉⣈⣠⣤⠖⠚⠿⠁⢸⠇⠀⠀⠀⠀⠀⢠⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣄⡀⠀⠀⠀⠓⠡⠄⠘⠉⠀⠀⠀⢀⣠⣶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣀⣀⣀⣀⣀⣠⠤⠶⠞⠋⠁