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.
The first input line has an integer $n$ : the number of vertices.
After this, there are $n$ lines that describe the vertices. The $i$ th such line has two integers $x_i$ and $y_i$ .
You may assume that the polygon is simple, i.e., it does not intersect itself.
Print two integers: the number of lattice points inside the polygon and on its boundary.