Random Pair :)

Question:-

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 A_i + A_j 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 A_i + A_j. 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 ... A_N

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 ≤ A_i ≤ 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

Python Code:-

for _ in range(int(input())):
    n=int(input())
    a=[int(i) for i in input().split()]
    l=[]
    count=0
    sum=0.000000
    for i in range(n):
        for j in range(n):
            if i<j:
                count=count+1
                sum=a[i]+a[j]
                l.append(sum)
    n1=l.count(max(l))
    value=n1/count
    print('{:.8f}'.format(value))