Description

Given one triangle and one circle in the plane. Your task is to calculate the common area of these two figures.

Input

The input will contain several test cases. Each line of input describes a test case. Each test case consists of nine floating point numbers, x₁, y₁, x₂, y₂, x₃, y₃, x₄, y₄ and r, where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the three vertices of the triangle and (x₄, y₄) is the center of the circle and r is the radius. We guarantee the triangle and the circle are not degenerate.

Output

For each test case you should output one real number, which is the common area of the triangle and the circle, on a separate line. The result should be rounded to two decimal places.

0 20 10 0 -10 0 0 0 10

144.35

Source

POJ Monthly--2006.08.27, Rainer