Let $a, b, c, d, e, f, g,$ and $h$ be distinct elements in the set:
\[
\{-7, -5, -3, -2, 2, 4, 6, 13\}.
\]
Find the minimum possible value of:
\[
(a + b + c + d)^2 + (e + f + g + h)^2
\]

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