Practice Geometry with the exercise "Disks intersection"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Geometry

Statement

Goal

Given centers and radius of two disks, you must determine their intersection area, rounded at a precision of 10^-2.
So if you think the area is 42.3371337, you must output 42.34 and if your answer is 41.78954719, you must print 41.79.

If these disks do not intersect, or intersect in one point, then the area is 0.00 .

Input

Line 1 : x1 y1 r1. x1 and y1 determine the position of the center of the first disk, and r1 its radius
Line 2 : x2 y2 r2. x2 and y2 determine the position of the center of the second disk, and r2 its radius

Output

The intersection area of the disks, rounded at a precision of 10^-2.

Constraints

-1000 < x1,y1,x2,y2 < 1000
1 ⩽ r1,r2 < 1000

Example

Input

0 10 1
10 0 1

Output

0.00

Solve it

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