Chefu is Chef's little brother, he is 12 years old and he is new to competitive programming.
Chefu is practicing very hard to become a very skilled competitive programmer and win gold medal in IOI.
Now Chefu is participating in a contest and the problem that he is trying to solve states:
Given an array A of N integers, find any i, j such that i <  j 
and Ai + Aj is maximum possible 
unfortunately, there's no much time left before the end of the contest, so Chefu doesn't have time to think of correct solution, so instead, he wrote a solution that selects a random pair (i,  j) (i <  j) and output Ai + Aj. each pair is equiprobable to be selected.
Now Chefu wants your help to calculate the probability that his solution will pass a particular input.
-----Input-----
First line contains an integer T denoting the number of test-cases.
First line of each test-case contains a single integer N
Second line of each test-case contains N space-separated integers A1 A2 ... AN
-----Output-----
For each test-case output a single line containing a single number denoting the probability that Chefu's solution to output a correct answer. your answer will be accepted if the absolute difference between it and correct answer is less than 1e-6
-----Constraints-----
- 1 ≤ T ≤ 100
- 2 ≤ N ≤ 100
- 1 ≤ Ai ≤ 1,000
-----Example-----
Input:
3
4
3 3 3 3
6
1 1 1 2 2 2
4
1 2 2 3
Output:
1.00000000
0.20000000
0.33333333
# cook your dish here
try:
 T=int(input())
 for _ in range(T):
  N=int(input())
  A=list(map(int,input().split()))
  c=0
  d=[]
  for i in range(N):
   for j in range(i+1,N):
    d.append(A[i]+A[j])
  ans=d.count(max(d))/len(d)
  print('%0.8f'%ans)
except:
 pass
# cook your dish here
try:
 T=int(input())
 for _ in range(T):
  N=int(input())
  A=list(map(int,input().split()))
  c=0
  d=[]
  for i in range(N):
   for j in range(i+1,N):
    d.append(A[i]+A[j])
  ans=d.count(max(d))/len(d)
  print('%0.8f'%ans)
except:
 pass