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 check_n_and_p(a):
    n=[]
    p=[]
    for i in a:
        if i<0:
            n.append(i)
        else:
            p.append(i)
    return n,p

def main(neg,pos):
    if len(pos)+len(neg)==5:
        if len(pos)%2==0:
            res=1
            for i in range(len(pos)):
                res*=pos[i]
            for i in range(len(neg)):
                res*=neg[i]
            return res
    if len(pos)==0:
        res=neg[-1]*neg[-2]*neg[-3]*neg[-4]*neg[-5]
        return res
    else:
        len_neg,len_pos=len(neg),len(pos)
        res_1,res_2,res_3=0,0,0
        if len_pos>=5:
            res_1=pos[-1]*pos[-2]*pos[-3]*pos[-4]*pos[-5]
        if (len_neg>=2) and (len_pos>=3):
            res_2=neg[0]*neg[1]*pos[-1]*pos[-2]*pos[-3]
        if (len_neg>=4):
            res_3=neg[0]*neg[1]*neg[2]*neg[3]*pos[-1]
        return max([res_1,res_2,res_3])

t=int(input())
for i in range(t):
    len_a=int(input())
    
    a = [int(i) for i in input().split()]
    neg, pos= check_n_and_p(a)
    neg, pos= sorted(neg),sorted(pos)
    res=main(neg,pos)
    print(res)
