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.
t=int(input())

for _ in range(t):
    y=int(input())
    a=list(map(int,input().split()))
    positive=[]
    negative=[]
    
    for elem in a:
        if elem<0:
            negative.append(elem)
        else:
            positive.append(elem)
            
    positive.sort(reverse=True) # 4, 3, 2, 1
    negative.sort() # -3, -2, -1
    
    p=len(positive)
    n=len(negative)
    max_p=-10**20
    
    if p>=3 and n>=2:
        pr=positive[0]*positive[1]*positive[2]
        pr*=negative[0]*negative[1]
        max_p=max(max_p,pr)
    if p>=1 and n>=4:
        pr=positive[0]*negative[0]*negative[1]*negative[2]*negative[3]
        max_p=max(max_p,pr)
    if p>=5:
        pr=positive[0]*positive[1]*positive[2]*positive[3]*positive[4]
        max_p=max(max_p,pr)
    if 0 in negative:
        max_p=max(max_p,0)
  
    pr=1
    for i in range(5):
        if len(positive)*len(negative)!=0:
            if positive[-1]<=-negative[-1]:
                pr*=positive[-1]
                del(positive[-1])
            else:
                pr*=negative[-1]
                del(negative[-1])
        elif len(positive)!=0:
            pr*=positive[-1]
            del(positive[-1])
        else:
            pr*=negative[-1]
            del(negative[-1])
    max_p=max(max_p,pr)
    
    print(max_p)