Two Circles - 2

In a plane, there are two circles with centers at points (O_1(X_1, Y_1)) and (O_2(X_2, Y_2)), and radii (R_1) and (R_2) respectively.

Determine how many distinct points with integer coordinates lie within both circles.

Input

You are given the coordinates of the centers and the radii of the circles: (X_1), (Y_1), (R_1), (X_2), (Y_2), (R_2). All input values are integers, each with an absolute value not exceeding (100).

Output

Output the number of such integer-coordinate points.

Examples