Your task is to write a program, which, given two circles, calculates the area of their intersection with the accuracy of three digits after decimal point.

Input

In the single line of input file there are space-separated real numbers x₁ y₁ r₁ x₂ y₂ r₂. They represent center coordinates and radii of two circles.

Output

The output file must contain single real number — the area.

Samples