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~