For a positive integer n, let P_{n} be the set of sequences of 2 n elements, each 0 or 1 , where there are exactly n 1's and n 0's. I choose a sequence uniformly at random from P_{n}. Then, I partition this sequence into maximal blocks of consecutive 0's and 1's. Define f(n) to be the expected value of the sum of squares of the block lengths of this uniformly random sequence. What is the largest integer value that f(n) can take on?