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

-----Input-----

The first line contains three integers x_1, y_1, r_1 ( - 10^9 ≤ x_1, y_1 ≤ 10^9, 1 ≤ r_1 ≤ 10^9) — the position of the center and the radius of the first circle.

The second line contains three integers x_2, y_2, r_2 ( - 10^9 ≤ x_2, y_2 ≤ 10^9, 1 ≤ r_2 ≤ 10^9) — 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}.

-----Examples-----

Input 0 0 4 6 0 4

Output 7.25298806364175601379

Input 0 0 5 11 0 5

Output 0.00000000000000000000