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 x-axis. 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 $n$ space-separated integers denoting the $x_i$ coordinates of the cameras.
- The third line of each test case contains two space-separated 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 1e-6 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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import math\r\n\r\ndef calLen(cam1, cam2, bird):\r\n    a = math.sqrt((cam1[0]-bird[0])**2 + (cam1[1]-bird[1])**2)\r\n    b = math.sqrt((cam2[0]-bird[0])**2 + (cam2[1]-bird[1])**2)\r\n    c = math.sqrt((cam1[0]-cam2[0])**2 + (cam1[1]-cam2[1])**2)\r\n\r\n    return a,b,c\r\n\r\ndef calculateAngle(a,b,c):\r\n    return math.acos((a**2 + b**2 - c**2)/(2*a*b))\r\n\r\n# def best_angle()\r\n\r\n# def brute(n,cams,bird):\r\n    # angles = []\r\n    # for i in range(n):\r\n    #     temp = [0]*n\r\n    #     angles.append(temp)\r\n    #     for j in range(i+1,n):\r\n    #         a,b,c = calLen(cams[i],cams[j],bird)\r\n    #         angles[i][j] = (calculateAngle(a,b,c))\r\n    # print(angles)        \r\n    # ans = 0\r\n    # for i in range(n):\r\n        \r\n    #     while \r\n\r\ndef angle2(cam1, cam2, bird):\r\n    a, b, c = calLen(cam1, cam2, bird)\r\n    return math.acos((a**2 + b**2 - c**2)/(2*a*b))\r\n\r\ndef backtrack(s, vertices, order):\r\n    global res\r\n\r\n    flag9 = 0\r\n    for a in range(0, len(vertices)):\r\n        if vertices[a] != 0:\r\n            flag9 = 1\r\n            break\r\n    if flag9==0:\r\n        # if s > res:\r\n\r\n        # print(order)\r\n        res = max(s, res)\r\n        return\r\n    for a in range(0, len(vertices)):\r\n        for b in range(0, len(vertices)):\r\n            if vertices[a] and vertices[b]:\r\n                n1 = vertices[a]\r\n                n2 = vertices[b]\r\n                vertices[a] = 0\r\n                vertices[b] = 0\r\n                backtrack(s + angle2(n1, n2, bird), vertices,order + [vertices[a],vertices[b]] )\r\n                vertices[a] = n1\r\n                vertices[b] = n2\r\n\r\nfrom random import randint\r\n\r\nfor h in range(int(input())):\r\n    n = int(input())\r\n    cams = list(map(lambda x: (int(x), 0), input().strip().split())) \r\n    # cams = [(randint(1,33),0) for a in range(0, n)]\r\n    cams1 = [i for i in cams]\r\n    # print(cams,cams1)\r\n    bird = list(map(int, input().strip().split()))\r\n    # bird = [randint(0,33),randint(1,33)]\r\n\r\n    # brute(n,cams,bird)\r\n\r\n    ans = 0\r\n    i = 0\r\n    i2 = [0,0]\r\n    i4 = [0,0]\r\n\r\n    while set(cams1) != {0}:\r\n\r\n        # print(set(cams1) )\r\n        i = 0\r\n        # i2 = [0,0]\r\n        for a in range(0, len(cams1)):\r\n            for b in range(a+1, len(cams1)):\r\n                if cams1[a] and cams1[b]:\r\n                    if abs( cams1[a][0] - cams1[b][0]) >= i:\r\n                        i = abs( cams1[a][0] - cams1[b][0])\r\n                        i2 = [cams1[a], cams1[b ]]\r\n                        i4=[a, b]\r\n                        # print(i2)\r\n        ans += angle2(i2[0],i2[1], bird)\r\n        cams1[i4[0]] = 0\r\n        cams1[i4[1 ]] = 0\r\n    print(ans)\r\n\r\n    res = 0\r\n    # backtrack(0,cams,[])\r\n    # print(res)\r\n\r\n\r\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14333