Entire

Polygon on the plane is given coordinates of its vertices. Required to count the number of points with integer coordinates that lie strictly within it.

Input

The first line contains N (3 ≤ N ≤ 1000) — the number of vertices of the polygon. Next come the coordinates (X_i, Y_i) of vertices in the order of traversal in a clockwise direction. X_i and Y_i — integers and do not exceed 1000000.

Output

K — the required number of points without leading zeros.

Examples