lattice

Write a function P1:

• A point $(x,y)$ is called a lattice point iff both $x$ and $y$ are integers.

• input parameter: integers x1, y1, x2, y2, x3, y3

  • Three points (x1, y1), (x2, y2), (x3, y3) are not on a same straight line.
  • The absolute value of each input parameter is less than or equal to $2^{1024}$.

• return value: the number of the lattice points (including vertexes) on the perimeter of the triangle with three vertexes (x1, y1), (x2, y2), (x3, y3)

  • For example, if a triangle has vertexes $(0,0),(2,2),(3,0)$ then its perimeter has 6 lattice points: $(0,0),(1,1),(2,2),(3,0),(2,0),(1,0)$.