Triangle and Points

You are given the coordinates of a triangle with three vertices:

• (x1, y1)
• (x2, y2)
• (x3, y3) Additionally, you are provided the coordinates of two points:
• Point p: (xp, yp)
• Point q: (xq, yq) Your task is to determine the following:
• Print '1' if the triangle cannot be formed.
• Print '2' if both p and q lie inside the triangle.
• Print '3' if only point p lies within the triangle.
• Print '4' if only point q lies within the triangle.
• Print '5' if neither point lies inside the triangle. Input Format:
• Coordinates of the triangle vertices: x1, y1, x2, y2, x3, y3
• Coordinates of the points p and q: p(xp, yp), q(xq, yq)

Example 1

Input:

x1 = 0
y1 = 0
x2 = 5
y2 = 0
x3 = 0
y3 = 5
xp = 1
yp = 1
xq = 6
yq = 6

Output:

3

Explanation: Only point p lies inside the triangle.