169 is a square and it is a sum of squares ($169 = 12^2 + 5^2$).

But its square can also be written as the sum of two squares. Let
$\large 169^2 = a^2 + b^2$
with $a > b > 0$ and $\gcd(a,b)=1$.
Without using a calculator, find $a + b$.

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