⠀⣿⡻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⢻⣿⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠈⠙⠷⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣴⣶⠿⠛⠛⠉⢀⠀⢠⣿⠇⠀⠀ ⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠀⣀⣤⡶⠛⠁⢠⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡛⠁⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡵⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⢹⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣀⡀⢰⣿⠀⠀⠀⠉⠙⠛⠀⠀⠤⠄⢀⣤⠻⠿⢿⠿⠇⣀⠀⢀⠠⠀⡄⠀⢀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢹⣿⠶⠤⣄⡀⠀⣠⣤⣀⡈⠙⠘⠿⠐⠳⠘⠞⠻⠸⠒⠘⢀⠡⠿⠨⠓⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠲⠤⢼⣿⠤⠤⠄⠀⠄⠹⣤⠾⠃⠀⣀⠀⠀⠀⠠⠤⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣠⠤⠤⠒⡀⢃⣏⠀⠒⠀⢀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠉⠉⢹⡿⠀⠀⠀⠀⣴⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉⠓⠒⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠓⠲⠾⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣻⣿⣿⣧⣤⣤⣤⣤⣀⣀⡀ ⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀; ⠀⣿⡻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⢻⣿⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠈⠙⠷⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣴⣶⠿⠛⠛⠉⢀⠀⢠⣿⠇⠀⠀ ⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠀⣀⣤⡶⠛⠁⢠⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡛⠁⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡵⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⢹⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣀⡀⢰⣿⠀⠀⠀⠉⠙⠛⠀⠀⠤⠄⢀⣤⠻⠿⢿⠿⠇⣀⠀⢀⠠⠀⡄⠀⢀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢹⣿⠶⠤⣄⡀⠀⣠⣤⣀⡈⠙⠘⠿⠐⠳⠘⠞⠻⠸⠒⠘⢀⠡⠿⠨⠓⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠲⠤⢼⣿⠤⠤⠄⠀⠄⠹⣤⠾⠃⠀⣀⠀⠀⠀⠠⠤⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣠⠤⠤⠒⡀⢃⣏⠀⠒⠀⢀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠉⠉⢹⡿⠀⠀⠀⠀⣴⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉⠓⠒⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠓⠲⠾⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣚⣻⣿⣿⣧⣤⣤⣤⣤⣀⣀⡀ ⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀