Polygon Lattice Points

Given a polygon, your task is to calculate the number of lattice points inside the polygon and on its boundary. A lattice point is a point whose coordinates are integers. The polygon consists of n vertices (x_1,y_1),(x_2,y_2),\dots,(x_n,y_n). The vertices (x_i,y_i) and (x_{i+1},y_{i+1}) are adjacent for i=1,2,\dots,n-1, and the vertices (x_1,y_1) and (x_n,y_n) are also adjacent. Input The first