Question 122
666 fields line up in a row, with each field being a wheat field or a rice field. Rose the hen lays an egg on each of the $W$ wheat fields and $R$ rice fields, so that for each egg, there is at most one field without egg between it and the closest egg to its right. Find the largest positive integer $S$ so that, regardless of the distribution of the wheat fields and rice fields, Rose can always make $|W - R|$ be at least $S$.