Area of Two Circles' Intersection

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Description

You are given two circles. Find the area of their intersection.

Input

The first line contains three integers x1, y1, r1 ( - 109 ≤ x1, y1 ≤ 109, 1 ≤ r1 ≤ 109) — the position of the center and the radius of the first circle.

The second line contains three integers x2, y2, r2 ( - 109 ≤ x2, y2 ≤ 109, 1 ≤ r2 ≤ 109) — the position of the center and the radius of the second circle.

Output

Print the area of the intersection of the circles. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Sample Input

Input
0 0 4
6 0 4
Output
7.25298806364175601379
Input
0 0 5
11 0 5
Output
0.00000000000000000000

Sample Output

None

Hint

None

Source

None

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