DivideByNineMethod
China
Difficult
Let $n$ be a positive integer and function $S_1(n)$ return the square of the sum of $n$'s digits. Additionally, let $S_{k+1}(n)=S_1\left(S_k(n)\right)$, where $k$ is a positive integer. Find the value of $S_{1991}(2^{1990})$.
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