Let $b$ and $c$ be non-zero integers satisfying ${ 37 }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$. Denote $Z$ as the number of different triplets $(37,b,c)$ that satisfy these constraints, and denote $C$ as the sum of all possible values of $c$. Find $Z+C$.

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