1988 AIME Problem 2

For any positive integer k, let f_1(k) denote the square of the sum of the digits of k. For n \ge 2, let f_n(k) = f_1(f_{n - 1}(k)). Find f_{1988}(11).

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.