For any positive integer $k$, define $f_1(k)$ as the square of the digital sum of $k$ in the decimal system. For $n > 1$, define $f_{n}(k)=f_1(f_{n-1}(k))$. Compute $f_{1992}(2^{1991})$.

Let's think step by step and output the final answer within \boxed{}.
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