Integral Points

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You are given a triangle where the vertices are and . All three vertices have integral coordinates. An integral point is defined as the point with both and coordinates as integers. Cay you find the number of integral points inside the triangle using Pick's theorem?

Input Format

The first line of input contains i.e. number of test cases.
The next lines will contain integers .

Constraints

Output Format

Print lines each containing the number of integral points in that triangle.

Sample Input

2
0 0 0 2 2 0
0 0 3 0 0 3

Sample Output

0
1

Explanation

In the second test case, is the only integral point inside the triangle.

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