Area of Two Circles' Intersection

Description:

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:

0 0 4
6 0 4

Sample Output:

7.25298806364175601379

Sample Input:

0 0 5
11 0 5

Sample Output:

0.00000000000000000000