Problem

Recently, the moon passed closer to the Earth than it ever has in decades. Hazel, set on seizing the opportunity, stayed up all night to watch the moon through her circular window. Unfortunately, there’s no guarantee that the moon and Hazel’s window perfectly aligned, making it possible that Hazel only saw part of the moon. Can you figure out how much of the moon she saw?

Input

Each test case begins with three integers $X_w, Y_w, R_w (1 \leq X_w, Y_w, R_w \leq 1000)$, representing a circle centered at $(X_w,Y_w)$ with radius $R_w$, the part of the sky that she could see through her window.

The next line contains three integers $X_w, Y_w, R_w (1 \leq X_w, Y_w, R_w \leq 1000)$, the position and radius of the moon in the sky.

Output

For each test case, output the area of the moon that was visible, rounded to two decimal places.

Sample Input 1

1 1 2
1 1 1

Sample Output 1

3.14

Sample Input 2

1 2 1
1 1 1

Sample Output 2

1.23

Editorial

Read only if you are stuck or have already solved the problem.