Recently, the moon has passed closer to the Earth than it has in decades. Hazel, set on seizing the opportunity, stayed up all night to watch the moon through her circular window. Unfortunately, the moon and Hazel's window did not perfectly align, and Hazel could only see 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 \le X_w, Y_w, R_w \le 1~ ~000)~, 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_m, Y_m, R_m~ ~(1 \le X_m, Y_m, R_m \le 1~ ~000)~, the position of the moon in the sky.

Output

For each test case, output the area of the moon that was visible. Your answer will be counted as correct if it is within a relative or absolute error of ~10^{-4}~ from the judge's answer.

Sample Input

1 1 2
1 1 1

Sample Output

3.1415926536

Sample Input

1 2 1
1 1 1

Sample Output

1.2283696986