Circular area

The two circles are given coordinates of the centers in a rectangular Cartesian coordinate system and radius. Find the area of their intersection.

Input

In the first row there are six real numbers by a space - the coordinates of the centers and radii of two circles: x_1, y_1, r_1, x_2, y_2, r_2. All numbers are real and do not exceed 1000.

Output

Print a single real number with two characters after the decimal point - the area of intersection of circles.

Examples