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.
from sys import stdin,stdout
from math import gcd,sqrt,inf
from collections import deque
input=stdin.readline
R=lambda:map(int,input().split())
I=lambda:int(input())
S=lambda:input().rstrip('\n')
L=lambda:list(R())
hg=lambda x,y:((y+x-1)//x)*x
pw=lambda x:1 if x==1 else 1+pw(x//2)
chk=lambda x:chk(x//2) if not x%2 else True if x==1 else False
M=inf
for _ in range(I()):
	n=I()
	N=[]
	P=[]
	*a,=R()
	for i in a:
		if i<0:
			N+=i,
		else:
			P+=i,
	ln1=len(N)
	ln2=len(P)
	if ln2==0 or ln1+ln2-ln1%2<5:
		sm=1
		N.sort()
		P.sort(reverse=True)
		for i in range(5):
			if not P:
				sm*=N.pop()
			elif not N:
				sm*=P.pop()
			elif abs(N[-1])<P[-1]:
				sm*=N.pop()
			else:
				sm*=P.pop()
		print(sm)
	else:
		a.sort(reverse=True,key=lambda x:abs(x))
		p=a[:5]
		a=a[5:]
		sm=1
		for i in p:sm*=i
		ans=sm
		if sum([1 if i<0 else 0 for i in p])%2:
				for i in range(4,-1,-1):
					sm=1
					for d in range(5):
						if d!=i:sm*=p[d]
					for j in a:
						ans=max(ans,sm*j)
		print(ans)