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