What the Equation

You are given the sum (S) of five numbers. Let numbers be v,w,x,y,z. Three new numbers namely a,b,c are formed from these numbers as follows: - $a = (vwz)^2 + 2vx(wz)^2$ - $b = (wxz)^2 + 2wy(xz)^2$ - $c = (xyz)^2 + 2vwxyz^2$, What is the maximum sum possible of a,b and c ? ###Input: - First-line will contain $T$, the number of test cases. Then the test cases follow. - Each test cas