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 product(a):
    ans=1
    for i in a:
        ans*=i
    return ans
for _ in range(int(input())):
    n=int(input())
    a=list(map(int, input().split()))
    a1=[i for i in a if i<0]
    a1.sort()
    a2=[i for i in a if i>=0]
    a2.sort(reverse=True)
    
    x1=len(a1)
    x2=len(a2)
    
    if n==5:
        print(product(a))
    else:
        
        ans=-float('inf')
        if x2>=5:
            p1=product(a2[:5])
            if p1>ans:
                
                ans=p1
        if x2>=3 and x1>=2:
            l=a2[:3]+a1[:2]
            p2=product(l)
            if p2>ans:
                ans=p2
                
        if x2>=1 and x1>=4:
            l=a2[:1]+a1[:4]
            p3=product(l)
            if p3>ans:
                ans=p3
        
        if x2==0 and x1>=5:
            l=a1[x1-5:]
            
            
            p4=product(l)
            
            if p4>ans:
                ans=p4
        
        print(ans)
            
    
    