A. Ezzat and Two Subsequencestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputEzzat 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.InputThe first line contains a single integer t (1 \le t \le 10^3)— the number of test cases. Each test case consists of two lines.The first line contains a single integer n (2 \le n \le 10^5).The second line contains n integers a_1, a_2, \ldots, a_n (-10^9 \le a_i \le 10^9).It is guaranteed that the sum of n over all test cases does not exceed 3\cdot10^5.OutputFor 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|)}} \le 10^{-6}.ExampleInput
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
NoteIn 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.
4
3
3 1 2
3
-7 -6 -6
3
2 2 2
4
17 3 5 -3

4.500000000 -12.500000000 4.000000000 18.666666667 
['brute force', 'math', 'sortings', '*800']