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{}.
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