You are given an array of integers a_1,a_2,…,a_n. Find the maximum possible value of a_ia_ja_ka_la_t among all five indices (i, j, k, l, t) (i<j<k<l<t).

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 2 ⋅ 10^4) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (5≤ n≤ 10^5) — the size of the array.

The second line of each test case contains n integers a_1,a_2,…,a_n (-3× 10^3≤ a_i≤ 3× 10^3) — given array.

It's guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, print one integer — the answer to the problem.

Example

Input


4
5
-1 -2 -3 -4 -5
6
-1 -2 -3 1 2 -1
6
-1 0 0 0 -1 -1
6
-9 -7 -5 -3 -2 1


Output


-120
12
0
945

Note

In the first test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ (-4)⋅ (-5)=-120.

In the second test case, choosing a_1,a_2,a_3,a_5,a_6 is a best choice: (-1)⋅ (-2) ⋅ (-3)⋅ 2⋅ (-1)=12.

In the third test case, choosing a_1,a_2,a_3,a_4,a_5 is a best choice: (-1)⋅ 0⋅ 0⋅ 0⋅ (-1)=0.

In the fourth test case, choosing a_1,a_2,a_3,a_4,a_6 is a best choice: (-9)⋅ (-7) ⋅ (-5)⋅ (-3)⋅ 1=945.

def solve(lst):
	lst = sorted(lst)
	neg = 0
	negs=[]
	ans=1
	pos=[]
	for i in range(len(lst)):
		if lst[i] <0:
			neg+=1
			negs.append(lst[i])
		else:
			pos.append(lst[i])
	if len(pos)==0:
		if len(negs)>5:
			negs=negs[::-1][0:5]
		for i in negs:
			ans*=i
		return ans
	pos=pos[::-1]
	if len(negs)>5:
		negs = negs[0:5]
	if len(pos) >5:
		pos = pos[0:5]
	maxed = -90210120921092190219090129
	end=len(pos)
	minus=5-end
	for x in range(len(pos)):
		if end+minus<5 or minus > len(negs):
			break
		p = 1
		for i in pos[0:end]:
			p*=i
		kl=0
		for i in negs[0:minus]:
			p*=i
		maxed=max(p,maxed)
		minus+=1
		end-=1
	return maxed
k = int(input())
for i in range(k):
	m = int(input())
	lst = list(map(int,input().split()))
	print(solve(lst))