Area of Two Circles' Intersection

题意翻译

分别给出两个圆的圆心坐标和半径（(x1,y1),r1和(x2,y2),r2），求两个圆相交部分的面积。

题目描述

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

输入输出格式

输入格式

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.

输出格式

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} $ .

输入输出样例

输入样例 #1

0 0 4
6 0 4

输出样例 #1

7.25298806364175601379

输入样例 #2

0 0 5
11 0 5

输出样例 #2

0.00000000000000000000