Time Limit: 8000/4000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Nowadays, little $haha$ got a problem from his teacher.His teacher wants to design a big logo for the campus with some circles tangent with each other. And now, here comes the problem. The teacher want to draw the logo on a big plane. You could see the example of the graph in the $Figure 1$

At first, $ haha$'s teacher gives him two $big$ circles, which are tangent with each other. And, then, he wants to add more small circles in the area where is outside of the small circle, but on the other hand, inside the bigger one (you may understand this easily if you look carefully at the $Figure 1$.

Each small circles are added by the following principles.

* you should add the small circles in the order like $Figure 1$.

* every time you add a small circle, you should make sure that it is tangented with the other circles (2 or 3 circles) like $Figure 1$.

The teacher wants to know the total amount of pigment he would use when he creates his master piece.$haha$ doesn't know how to answer the question, so he comes to you.

$Task$

The teacher would give you the number of small circles he want to add in the figure. You are supposed to write a program to calculate the total area of all the small circles.

At first, $ haha$'s teacher gives him two $big$ circles, which are tangent with each other. And, then, he wants to add more small circles in the area where is outside of the small circle, but on the other hand, inside the bigger one (you may understand this easily if you look carefully at the $Figure 1$.

Each small circles are added by the following principles.

* you should add the small circles in the order like $Figure 1$.

* every time you add a small circle, you should make sure that it is tangented with the other circles (2 or 3 circles) like $Figure 1$.

The teacher wants to know the total amount of pigment he would use when he creates his master piece.$haha$ doesn't know how to answer the question, so he comes to you.

$Task$

The teacher would give you the number of small circles he want to add in the figure. You are supposed to write a program to calculate the total area of all the small circles.

The first line contains a integer $t (1 \leq t \leq 1200)$, which means the number of the test cases. For each test case, the first line insist of two integers $R_1$ and $R_2$ separated by a space ($1 \leq R \leq 100$), which are the radius of the two big circles. You could assume that the two circles are internally tangented. The second line have a simple integer $N$ ($ 1 \leq N \leq 10\ 000\ 000$), which is the number of small circles the teacher want to add.

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