Integral Points In Triangle
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Given three non-collinear coordinates P(p1,p2), Q(q1,q2) and R(r1,r2) of a triangle in X-Y plane, find the number of integral / lattice points inside this triangle.(A point in XY plane is said to be integral / lattice point if both its co-ordinates are integral)

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains an two integers (p1  p2), second line of the testcase contains ( q1  q2) and the third line of the testcase contains ( r1 & r2) denoting the coordinates P, Q, R respectively.

Output:
Print out the count of integral points lying inside the triangle .

Constraints:
1 <= T <= 100
-100 <= P, Q, R <=100

Examples:
Input:
2
0 0
0 5
5 0
62 -3
5 -45
-19 -23

Output:
6
1129

#### ** For More Input/Output Examples Use 'Expected Output' option **

Author: Rohan Malhotra

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