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.

Difficulty: UNKNOWN_DIFFICULTY

Solutions:
inp = input
import math
for _ in range(int(input())):
	n = int(input())
	arr = list(map(int, input().split()))
	(p, q) = map(int, input().split())
	ans = 0
	arr.sort()
	for i in range(n // 2):
		(mn, mx) = (arr[i], arr[n - i - 1])
		if mx == p or mn == p:
			adj = q
			opp = mx - mn
			val = math.atan2(opp, adj)
		elif mn < p and mx > p:
			adj = q
			opp = p - mn
			valA = math.atan2(opp, adj)
			opp = mx - p
			valB = math.atan2(opp, adj)
			val = valA + valB
		elif p < mn:
			adj = abs(mx - p)
			opp = q
			valA = math.atan2(opp, adj)
			adj = abs(mn - p)
			valB = math.atan2(opp, adj)
			val = valA - valB
		else:
			adj = abs(p - mn)
			opp = q
			valA = math.atan2(opp, adj)
			adj = abs(p - mx)
			valB = math.atan2(opp, adj)
			val = valA - valB
		val = abs(val)
		ans += val
	print('%.12f' % ans)


import math
for _ in range(int(input())):
	n = int(input())
	arr = list(map(int, input().split()))
	(p, q) = map(int, input().split())
	k = []
	for i in range(n):
		if p == arr[i]:
			k.append(0)
		else:
			k.append(math.atan((p - arr[i]) / q))
	k = sorted(k)
	print(round(abs(sum(k[:n // 2]) - sum(k[n // 2:])), 12))