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

```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 = 'for _ in range(int(input())):\n N = int(input())\n L = list(map(int, input().split()))\n \n L_copy = L.copy()\n N1 = max(L_copy)\n L_copy.remove(N1)\n N2 = max(L_copy)\n \n req_out = 0\n for i in range(N):\n  for j in range(N):\n   if i != j and ((L[i]==N1 and L[j]==N2) or (L[i]==N2 and L[j]==N1)):\n    req_out += 1\n \n tot_out = N * (N-1) / 2\n \n print(req_out / (2 * tot_out))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13293