Capturing Bird in A Camera

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Nature photographing may be fun for tourists, but it is one of the most complicated things for photographers. To capture all the facets of a bird, you might need more than one cameras. You recently encountered such a situation. There are $n$ photographers, so there are $n$ cameras in a line on the xaxis. All the cameras are at distinct coordinates. You want to pair up these cameras ($n$ is even) in such a way that the sum of angles subtended on the bird by the pair of cameras is maximized. Formally, let A, B be two cameras, and let P be the bird to be captured by these two cameras. The angle will APB. Note: All angles are in radians. ### Input  The first line of the input contains an integer $T$ denoting the number of test cases. The description of the test cases follows.  The first line of each test case contains an integer $n$.  The second line of each test case contains $n$ spaceseparated integers denoting the $x_i$ coordinates of the cameras.  The third line of each test case contains two spaceseparated integers $P, Q$ denoting the x and y coordinates of the bird respectively. ### Output For each test case, output your answer in a single line. Your answer would be considered correct if its absolute error is less than or equal to 1e6 of the actual answer. ###Constraints  $1 \le T \le 10$  $2 \le n \leq 100$  $1 \le x_i \leq 300$  $0 \le P \leq 300$  $1 \le Q \leq 300$ ### Example Input ``` 2 2 0 1 0 1 2 0 1 100 1 ``` ### Example Output ``` 0.785398163397 0.000100999899 ``` ###Explanation **Note**: $1 \leq x_i$ is not being satisfied by the sample input, but will be satisfied in the actual test data. **Testcase 1**: There are only 2 cameras, so they have to paired up with each other. And the angle subtended by then is 45 degrees. Converting this to radians gives the output.Author:  admin2 
Tags  admin2 
Date Added:  13122018 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, kotlin 
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