Circular area#874

Circular area

1 second
64 megabytes
Easy

Two circles are given by the coordinates of their centers in a rectangular Cartesian coordinate system and their radii. Find the area of their intersection.

Input

In the first row there are 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 in absolute value.

Output

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

Examples

Example 1

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