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Two points A (x1, y1, z1) and B
(x2, y2, z2) are placed on the surface of parallelepiped
P = {(x, y, z): 0<=x<=L,
0<=y<=W, 0<=z<=H} with
L*W*H dimensions (see figure). These two points can be
linked with various curves lying on the surface of P. You are to find out
the square of the shortest curve length.
Parallelepiped dimensions L, W, H and coordinates of the points are integers, 0<=L,W,H<=1000.
Input data
Input data begins with a positive number - number of data sets. Each data set consists of 9 integers (in indicated order): L, W, H, x1, y1, z1, x2, y2, z2. The numbers are separated with spaces and end-of-line characters.
Output data
For each data set write to the output a line containing the square of the shortest curve length between points A and B on the surface of P.
Input data example:
1 5 5 2 3 1 2 3 5 0
Output data for our example:
36