AQT is studying circles and he has encountered the following problem. Two circles $C_1$ and $C_2$ have their centres located at $(0,0)$ on a coordinate plane. Circle $C_1$ and $C_2$ have radii $R_1$ and $R_2$ $(R_1\le R_2)$, respectively. AQT decides to add another circle $C_3$ with radius $R_3$ $(R_3<R_2)$ and a centre that is located at $(x,y)$, where $x$ and $y$ are real numbers. The location of circle $C_3$ is random but it follows the condition that it is completely inside circle $C_2$. Formally, $x^2+y^2<(R_2-R_3{)}^2$. A position of circle $C_3$ is called valid if the circumference of circle $C_3$ has $0$ intersection points with the circumference of circle $C_1$. AQT wants to know the probability that the position of circle $C_3$ is valid. AQT is given $T$ of these problems. Can you help AQT solve all of them?

Constraints

In all subtasks,

$1\le T\le 2\cdot {10}^5$

$1\le R_1\le R_2\le {10}^3$

$1\le R_3<R_2$

It is guaranteed that $R_1$, $R_2$, and $R_3$ are integers.

Subtask 1 [10%]

$R_1=R_2$

Subtask 2 [15%]

$0\le R_2-R_1\le 2$

$R_3<R_1$

Subtask 3 [75%]

No additional constraints.

Input Specification

The first line contains $T$, the number of problems you need to help AQT solve.

The next $T$ lines each contain the radii of the three circles: $R_1$, $R_2$, and $R_3$.

Output Specification

Output $T$ lines. In the $i$-th line, output the answer to the $i$-th problem. Your answer will be considered correct if it differs from the correct answer by at most ${10}^{-3}$.

Sample Input

2
2 3 1
5 10 2

Sample Output

0.25
0.375

Explanation

For the first test case, circle $C_1$ and $C_2$ are represented by the blue circle and the red circle, respectively. The green circles represent possible valid positions for circle $C_3$.

This region represents the set of all possible centres for circle $C_3$ and has an area of $4\pi$

This region represents the set of all valid centres for circle $C_3$ and has an area of $\pi$

The probability is $\frac{\pi }{4\pi }=0.25$