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Integral Points Inside Triangle
Medium Accuracy: 0.0% Submissions: 0 Points: 4

Given three non-collinear points whose co-ordinates are P(p1, p2), Q(q1, q2) and R(r1, r2) in the X-Y plane. Find the number of integral / lattice points strictly inside the triangle formed by these points.
Note - A point in X-Y plane is said to be integral / lattice point if both its co-ordinates are integral.

Example 1:

Input:
p = (0,0)
q = (0,5)
r = (5,0)
Output: 6
Explanation:
There are 6 integral points in the
triangle formed by p, q and r.

Example 2:

Input:
p = (62,-3)
q = (5,-45)
r = (-19,-23)
Output: 1129
Explanation:
There are 1129 integral points in the
triangle formed by p, q and r.

You don't need to read input or print anything. Your task is to complete the function InternalCount() which takes the three points p, q and r as input parameters and returns the number of integral points contained within the triangle formed by p, q and r.

Expected Time Complexity: O(Log2109)
Expected Auxillary Space: O(1)

Constraints:
-10≤ x-coordinate, y-coordinate ≤ 109