See Russian translation

You have a polygon described by coordinates of its vertices. Can you find how many points with integer coordinates lay strictly inside it?

Input
The first line contains an integer N - number of vertices. Next N lines contain 2 space-separated integers each and describe polygon vertices in clockwise order. Note that polygon can be convex and non-convex as well.

Output
Output one integer - answer for the problem

Constraints

• 3 <= N <= 1000
• |x_i|, |y_i| <= 10⁶