⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣶⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠉⣹⣿⣿⣿⣿⣿⣿⠾⠿⠿⠿⠿⠿⢿⠛⣿⣿⣯⣿⣿⡇⠀⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡿⣧⣿⣟⣷⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣛⢶⡟⢻⣿⣿⡿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣿⡟⢿⣾⡿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣯⣽⣿⣿⡯⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣽⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠿⣿⣿⣿⡟⠳⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣷⣧⣷⣰⣾⡤⠶⠶⣦⡤⣤⣀⠀⠀⠀⣠⣴⣶⡶⣶⣄⣿⡏⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡿⣿⣞⣿⣿⠏⣀⣤⣤⣤⣴⣌⠙⠄⣤⢸⢉⣥⣤⣤⣤⣿⣿⢹⣿⣿⡿⣿⣿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠛⠛⣿⣿⣾⣿⡻⣿⠿⣿⣥⣼⣿⣿⣿⠶⠀⢻⢸⣏⡉⣿⣿⣿⡟⣿⣿⣿⣿⣷⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⡿⣿⣿⣷⠀⠉⠒⠈⠁⠀⠊⠰⣴⣦⡏⠓⠈⠽⠿⠿⠃⢻⣿⣿⣿⣾⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢻⣿⣗⢻⣟⣿⠀⠀⠀⠀⠀⢠⣀⣴⣄⠀⣉⣑⡄⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣾⣿⣿⣀⠀⠀⠀⠀⠈⠷⠌⠉⠠⠴⠋⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣠⣤⣤⣶⣶⣾⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢼⣿⣿⣿⠋⣵⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⡿⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢿⣿⣿⡿⣰⣿⠥⠤⠤⠤⠴⠤⠤⠤⠤⢄⣀⣀⣀⣀⣹⣿⡌⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠉⠉⠀⠂⠀⠀⠤⢿⣧⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠼⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⡶⣶⣶⢿⣿⣿⣿⠿⣷⡒⡲⡶⣶⠾⠿⠋⢟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⣿⣟⣓⣸⣿⡾⠀⠀⣿⠸⠁⠘⡌⠛⣶⡈⢘⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣭⣭⣿⣿⣷⣮⣥⣴⣿⣦⣤⣤⣴⣤⣴⣽⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣒⡦⡤⠄⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠤⠤⠤⠤⣼⡋