IMAS 2015/2016 Junior Round 2 Question 8

Let $a,b,c,d$ be real numbers such that $|a+b|$, $|a-b|$, $|c+d|$ and $|c-d|$ are 6, 7, 8 and 9 in some order. What is the value of $a^2+b^2+c^2+d^2$?