Integral Points In Triangle
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  Difficulty: Easy   Marks: 2

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 six integers (p1  p2),( q1  q2),( 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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