zzq is writing a renderer and has set up the following scene: there is a point light source at $(x_{1}, y_{1}, z_{1})$, a sphere with radius $r$ at $(x_{2}, y_{2}, z_{2})$, and a plane described by $a x+b y+c z+d=0$. It is guaranteed that the sphere, the point light source, and the plane do not intersect each other (the intersection set is empty).
To verify if the renderer is correct, he needs to calculate the area of the shadow formed on the plane by the sphere being illuminated by the point light source. zzq guarantees that this value is greater than 0 and finite. Your output must have an absolute or relative error no greater than $10^{-6}$ compared to the standard output.
Input
The first line contains a positive integer $T$, representing the number of test cases. The next $T$ lines each contain integers $x_{1}, y_{1}, z_{1}, x_{2}, y_{2}, z_{2}, r, a, b, c, d$ separated by spaces.
Output
Output $T$ lines, each containing a decimal number representing the shadow area.
Examples
Input 1
4 0 0 5 0 0 2 1 0 0 1 1 2 3 6 0 0 2 2 1 1 10 30 8 7 6 5 4 3 2 1 0 1 2 9 9 9 5 5 5 4 3 2 1 0
Output 1
14.1371669412 88.0769231962 147.2623403467 469.7668717193
For the first test case, it can be proven that the shadow area is $4.5 \pi$.
For the second test case, the rendered image is as follows. The goal is to find the area of the black shadow.
Note
$\left|x_{1}\right|,\left|y_{1}\right|,\left|z_{1}\right|,\left|x_{2}\right|,\left|y_{2}\right|,\left|z_{2}\right|,|a|,|b|,|c|,|d| \leq 10^{4}, 1 \leq r \leq 10^{4}, 1 \leq T \leq 30$.
- Subtask 1 (30pts): $x_{1}=y_{1}=x_{2}=y_{2}=0, a=b=d=0, c=1$.
- Subtask 2 (30pts): $x_{1}=x_{2}=0, a=b=d=0, c=1$.
- Subtask 3 (20pts): $a=b=d=0, c=1$.
- Subtask 4 (20pts): No special restrictions.