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 maxmul(alist):
	alist.sort()
	nlist=[]
	plist=[]
	flist=[]
	for i in alist:
		if(i<0):
			nlist.append(i)
		else:
			plist.append(i)
	pos=len(plist)
	neg=len(nlist)

	if (pos>=5):
		res=plist[-5:]
		flist.append(res[0]*res[1]*res[2]*res[3]*res[4])
	if(pos>=4 and neg>=1):
		res=plist[:4]
		flist.append(nlist[neg-1]*res[0]*res[1]*res[2]*res[3])
	if(pos>=3 and neg>=2):
		res=plist[-3:]
		nes=nlist[:2]
		flist.append(nes[0]*nes[1]*res[0]*res[1]*res[2])
	if(pos>=2 and neg>=3):
		res=plist[:2]
		nes=nlist[-3:]
		flist.append(nes[0]*nes[1]*nes[2]*res[0]*res[1])
	if(pos>=1 and neg>=4):
		res=plist[-1:]
		nes=nlist[:4]
		flist.append(nes[0]*nes[1]*nes[2]*res[0]*nes[3])
	if(neg>=5):
		nes=nlist[-5:]
		flist.append(nes[0]*nes[1]*nes[2]*nes[4]*nes[3])

	print (max(flist))


t=int(input())
for it in range(t):
	n=int(input())
	x=input()
	alist = [int(i) for i in x.split()]
	maxmul(alist)






