#include <bits/stdc++.h>
using namespace std;
int T;
int a[300100];
int main() {
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    long long sum = 0;
    for (int i = 1; i <= n; i++) cin >> a[i], sum += a[i];
    sort(a + 1, a + n + 1);
    double ans = -1e18;
    long long now = 0;
    for (int i = n; i > 1; i--) {
      now += a[i];
      ans = max(ans, now * 1.0 / (n - i + 1) + (sum - now) * 1.0 / (i - 1));
    }
    printf("%0.8lf\n", ans);
  }
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

Ezzat has an array of n integers (maybe negative). He wants to split it into two non-empty subsequences a and b, such that every element from the array belongs to exactly one subsequence, and the value of f(a) + f(b) is the maximum possible value, where f(x) is the average of the subsequence x. 

A sequence x is a subsequence of a sequence y if x can be obtained from y by deletion of several (possibly, zero or all) elements.

The average of a subsequence is the sum of the numbers of this subsequence divided by the size of the subsequence.

For example, the average of [1,5,6] is (1+5+6)/3 = 12/3 = 4, so f([1,5,6]) = 4.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^3)— the number of test cases. Each test case consists of two lines.

The first line contains a single integer n (2 ≤ n ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (-10^9 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 3⋅10^5.

Output

For each test case, print a single value — the maximum value that Ezzat can achieve.

Your answer is considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Example

Input


4
3
3 1 2
3
-7 -6 -6
3
2 2 2
4
17 3 5 -3


Output


4.500000000
-12.500000000
4.000000000
18.666666667

Note

In the first test case, the array is [3, 1, 2]. These are all the possible ways to split this array: 

  * a = [3], b = [1,2], so the value of f(a) + f(b) = 3 + 1.5 = 4.5. 
  * a = [3,1], b = [2], so the value of f(a) + f(b) = 2 + 2 = 4. 
  * a = [3,2], b = [1], so the value of f(a) + f(b) = 2.5 + 1 = 3.5. 

Therefore, the maximum possible value 4.5.

In the second test case, the array is [-7, -6, -6]. These are all the possible ways to split this array: 

  * a = [-7], b = [-6,-6], so the value of f(a) + f(b) = (-7) + (-6) = -13. 
  * a = [-7,-6], b = [-6], so the value of f(a) + f(b) = (-6.5) + (-6) = -12.5. 

Therefore, the maximum possible value -12.5.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int T;
int a[300100];
int main() {
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    long long sum = 0;
    for (int i = 1; i <= n; i++) cin >> a[i], sum += a[i];
    sort(a + 1, a + n + 1);
    double ans = -1e18;
    long long now = 0;
    for (int i = n; i > 1; i--) {
      now += a[i];
      ans = max(ans, now * 1.0 / (n - i + 1) + (sum - now) * 1.0 / (i - 1));
    }
    printf("%0.8lf\n", ans);
  }
  return 0;
}

```