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 $0 \leq r \leq 10^5$. 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 $10^{-4}$.
| Sample Input 1 |
Sample Output 1 |
3 3 6
5 2
5 2
|
0.000000000000
|
| Sample Input 2 |
Sample Output 2 |
-5 4 5
-4 3
3 4
|
7.134954084936
|
| Sample Input 3 |
Sample Output 3 |
3 3 6
3 5
5 2
|
0.806169273811
|
| Sample Input 4 |
Sample Output 4 |
0 0 10
100 0
0 100
|
285.619449019234
|
| Sample Input 5 |
Sample Output 5 |
0 0 10000
10000 0
10000 1
|
314159265.358970978850
|
| Sample Input 6 |
Sample Output 6 |
0 0 10000
10000 1
10000 0
|
0.000008332768
|
