Parallelepiped Walk

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

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

The input consists of a series of lines with each line containing 9 integers (in indicated order): L, W, H, x1, y1, z1, x2, y2, z2. The numbers are separated with spaces.


Output

For each line of input there will be one line of output, which should contain the square of the shortest curve length between points A and B on the surface of P.


Sample Input

5 5 2 3 1 2 3 5 0
300 600 900 300 550 0 0 550 900

Sample Output

36
970000

Hint

None

Source

Northeastern Europe 1996

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