Problem Statement 
 Dissatisfied with the inconvenient spherical shape of the Earth, a group of
mapmakers have gone to Magrathea to obtain a custombuilt planet. They
decided to design their new planet to be flat and in the shape of a polygon.
All coordinates will be in the Cartesian (x, y) plane.
In order to provide everyone on the planet with internet access, a wireless
router will be placed at every lattice point that is inside the polygon (a
lattice point is a point with integer coordinates). The mapmakers decided to
keep their job simple by choosing a polygon with no lattice points on its
boundary.
Because the mapmakers are highly rational people, they decided that the coordinates of all the
vertices of the polygon would be fractions with a common denominator. The vertices of the
polygon (in order), are given by the int[]s x and y, and by the
common denominator denom. The ith vertex is
(x[i]/denom, y[i]/denom).
Calculate and return the number of routers required.


Definition 
 Class:  WifiPlanet  Method:  routersNeeded  Parameters:  int[], int[], int  Returns:  long  Method signature:  long routersNeeded(int[] x, int[] y, int denom)  (be sure your method is public) 




Constraints 
  x and y will contain the same number of elements. 
  x and y will each contain between 3 and 50 elements, inclusive. 
  Each element of x and y will be between 1 and 10^9, inclusive. 
  No two vertices of the polygon will be the same. 
  No two edges of the polygon (including their endpoints) will intersect, with the exception that adjacent edges will intersect at their common endpoint. 
  No lattice point will lie on the boundary of the polygon. 
  denom will be between 2 and 10^9, inclusive. 

Examples 
0)  
  Returns: 2  This is illustrated in the image below:



1)  
 {3,3,4,4,5,6,10,10,11,11,10,10,9,9}  {1,2,2,6,3,8,8,9,9,3,3,2,2,1}  3 
 Returns: 4  

2)  
 {50,1000050,1000049}  {2,1000002,1000003}  100 
 Returns: 0  

3)  
 {32,32,64,8,15,1000,999}  {1,10,10,48,48,47,1}  16 
 Returns: 120  

4)  
 {1,1000000000,1000000000,1}  {1,1,1000000000,1000000000}  3 
 Returns: 111111110888888889  
