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.
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.
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)
-109 ≤ x-coordinate, y-coordinate ≤ 109
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