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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.

**Your Task:**

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(Log_{2}10^{9})

**Expected Auxillary Space: **O(1)

**Constraints:**

-10^{9 }≤ x-coordinate, y-coordinate ≤ 10^{9}

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Integral Points Inside Triangle

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