JJ loves playing with averages. He has an array A of length N. He wants to divide the array A into two non-empty subsets P and Q such that the value of mean(P) + mean(Q) is as large as possible. (Note that each A_{i} must belong to either subset P or subset Q).

Help him find this maximum value of mean(P) + mean(Q).

As a reminder, the mean of a subset X of size M is defined as: mean(X) = \dfrac{\sum_{i = 1}^{M} X_{i}}{M}. 

For example, mean([3, 1, 4, 5]) = \frac{3 + 1 + 4 + 5}{4} = 3.25.

------ Input Format ------ 

- The first line contains T - the number of test cases. Then the test cases follow.
- The first line of each test case contains an integer N - the size of the array A.
- The second line of each test case contains N space-separated integers A_{1}, A_{2}, \dots, A_{N} denoting the array A.

------ Output Format ------ 

Output the largest value of mean(P) + mean(Q).

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}.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$2 ≤ N ≤ 1000$
$1 ≤ A_{i} ≤ 10^{6}$

----- Sample Input 1 ------ 
2
2
4 5
5
2 2 2 2 2

----- Sample Output 1 ------ 
9.000000
4.000000

----- explanation 1 ------ 
*Test case-1:* We can divide the two elements into two non-empty subsets $P$ and $Q$ as follows: $P = [4]$, $Q = [5]$. 

Therefore, $mean(P) + mean(Q) = 9$.

*Test case-2:* In whatever way we divide the elements of the array, mean of both the subsets will always be $2$.

Therefore, $mean(P) + mean(Q) = 4$.

Difficulty: MEDIUM

Solutions:
t = int(input())
while t != 0:
	n = int(input())
	l = list(map(int, input().split()))
	m = max(l)
	l.remove(m)
	s = 0
	for i in l:
		s = s + i
	print('{:.6f}'.format(m + s / (n - 1)))
	t = t - 1


def soln(n, arr):
	maxm = max(arr)
	m_sum = sum(arr) - maxm
	return maxm + m_sum / (n - 1)
for _ in range(int(input())):
	n = int(input())
	arr = list(map(int, input().split()))
	print(f'{soln(n, arr):.6f}')


for _ in range(int(input())):
	n = int(input())
	arr = list(map(int, input().lstrip().split()))
	arr.sort()
	ans = 0
	if n == 2:
		ans += sum(arr)
		print('{:.6f}'.format(ans))
	else:
		ans += sum(arr[:n - 1]) / (n - 1) + arr[n - 1]
		print('{:.6f}'.format(ans))


for _ in range(int(input())):
	n = int(input())
	x = list(map(int, input().split()))
	y = max(x)
	z = []
	s = []
	x.sort()
	print('{:.6f}'.format((sum(x) - x[-1]) / (len(x) - 1) + x[-1]))


for i in range(int(input())):
	x = int(input())
	c = list(map(int, input().split(' ')))[:x]
	c.sort()
	p = []
	for i in range(x):
		if i != x - 1:
			y = c[:i + 1]
			z = c[i + 1:]
			p.append(sum(y) / len(y) + sum(z) / len(z))
	print('{:.6f}'.format(max(p)))


for i in range(int(input())):
	x = int(input())
	c = list(map(int, input().split(' ')))[:x]
	c.sort()
	print('{:.6f}'.format((sum(c) - c[-1]) / (len(c) - 1) + c[-1]))


def main():
	tsc = int(input())
	for i in range(0, tsc):
		length = int(input())
		string = input()
		List = []
		string = string.split()
		for word in string:
			List.append(float(word))
		List.sort()
		A = List.pop()
		B = List
		a = A + mean(B)
		print(format(a, '.6f'))

def mean(x):
	sum = 0
	for index in range(0, len(x)):
		sum += x[index]
	lmean = sum / len(x)
	return lmean
main()


for _ in range(int(input())):
	n = int(input())
	k = list(map(int, input().split()))
	k.sort()
	x = max(k) + sum(k[:n - 1]) / (n - 1)
	print('%.6f' % x)


t = int(input())
for _ in range(t):
	n = int(input())
	l = list(map(int, input().split()))
	l.sort()
	s = 0
	for i in range(n - 1):
		s = s + l[i]
	z = s / (n - 1) + l[n - 1]
	print('%0.6f' % z)


for _ in range(int(input())):
	N = int(input())
	A = sorted(list(map(int, input().split(' '))))
	S = 0
	for i in range(N - 1):
		S += A[i]
	print('%.6f' % (A[-1] + S / (N - 1)))


t = int(input())
while t:
	n = input()
	n = int(n)
	list = [int(x) for x in input().split()]
	list = sorted(list)
	x = list[n - 1]
	list.remove(list[n - 1])
	mean = float(sum(list) / len(list))
	print('%.6f' % (mean + x))
	t -= 1


for i in range(int(input())):
	n = int(input())
	l = [int(j) for j in input().split()]
	k = sorted(l)[::-1]
	s = k[0]
	k.remove(s)
	d = s + sum(k) / len(k)
	print('{:.6f}'.format(d))


def sol(l, n):
	if n < 3:
		return '{0:.6f}'.format(sum(l))
	elif len(set(l)) == 1:
		return '{0:.6f}'.format(sum(l[:2]))
	l.sort()
	s = sum(l[:n - 1]) / (n - 1)
	return '{0:.6f}'.format(s + l[n - 1])
for _ in range(int(input())):
	n = int(input())
	l = list(map(int, input().split()))
	print(sol(l, n))