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.
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.
K — the required number of points without leading zeros.