⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣩⣄⣤⣹⣧⠀⠀⠀⢀⣠⣴⣶⣄⡀⠀⠀⠀⢀⣀⣀⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⡵⠋⠁⠈⠉⠙⠻⣶⣤⣴⣟⠋⠀⠀⠙⣿⣶⠾⠟⠛⠋⠉⠉⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⠋⠀⠀⠀⠀⠀⠀⣴⡟⠋⠉⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⠛⠦⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠸⣇⣠⣴⡶⠶⣶⣦⣄⠘⡇⠀⣀⣤⣤⣤⣤⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⡤⠞⠋⢀⡶⠟⠉⠀⠀⠀⠀⠀⠙⣿⣿⡾⠋⠁⠀⠀⠀⠀⠉⠛⢷⣄⠀⠰⠶⠶⠾⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⢾⣏⣁⣀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠙⣿⡆⣧⠀⢠⣄⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠰⡦⠀⠀⠀⠀⠀⠀⣼⣇⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⣸⡏⠓⠦⠥⣤⣤⣤⣴⡶⢋⣠⠼⠛⠛⠶⣤⣤⣤⣤⣴⠶⡞⢻⣿⡿⠿⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣯⠴⠞⣿⣷⠀⠤⠴⣶⠟⠛⢋⣉⣭⣴⣶⣿⣶⣤⣿⣿⣿⣍⠉⣯⠁⣼⣿⣃⣀⣀⣈⣽⣷⣦⣠⣤⣤⣤⣄⣀⠀⠀ ⠙⠋⠁⠀⣼⠻⣿⣦⠀⠀⠙⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣴⣿⣿⣿⠛⠉⠉⠁⣰⡿⠋⠉⠀⠈⠉⢻⣧⡀ ⠀⠀⠀⣼⢃⣴⣿⣿⣷⣄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣽⣶⣴⡶⢾⣟⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⢸⣿⠟⠁⠟⣻⡏⠙⢷⣦⣀⠀⠙⣿⣿⣿⣯⣿⣾⣷⣿⣽⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⣠⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢰⡏⠙⠛⢻⣿⢿⣿⣿⣷⣿⣿⠾⠋⠙⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣤⣴⡾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⡄⠀⠀⠈⠻⠶⠦⠤⠤⠤⣤⠤⠴⠞⠛⢉⡀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠁⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣀⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⣀⣤⣤⠶⠶⠷⠾⢷⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣴⠾⠛⠋⠉⠀⢀⣠⣴⠾⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⠟⣉⣀⣤⣤⡴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣻⣿⣻⣿⣻⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣻⣿⣿⣟⣿⡿⣟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣦⣼⡿⠁⠀⠀⠀⠀⠀⣴⣦⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀