Problem I
Circular Segment Area

You are given a circular segment, represented by a circle at $x,y$ with radius $r$ and two rays from the center of the circle with directions $x_a,y_a$ and $x_b,y_b$, respectively. The rays intersect the circle at two not necessarily distinct points, $x_p,y_p$ and $x_q,y_q$, forming both a chord between the points and an arc on the circle. The arc is the one from $x_p,y_p$ to $x_q,y_q$ clockwise. Determine the area that lies between the chord and the arc.

Input

The first line contains three integers $x,y,r$, where $0\le r\le {10}^5$. The second line contains two integers $x_a,y_a$. The third line contains two integers $x_b,y_b$.

All coordinates are between $-{10}^5$ and ${10}^5$, inclusive.

Output

Output the area between of the circular segment. Your output is considered correct if it has at most an absolute or relative error of ${10}^{-4}$.

3 3 6
5 2
5 2

0.000000000000

-5 4 5
-4 3
3 4

7.134954084936

3 3 6
3 5
5 2

0.806169273811

0 0 10
100 0
0 100

285.619449019234

0 0 10000
10000 0
10000 1

314159265.358970978850

0 0 10000
10000 1
10000 0

0.000008332768