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.
import sys
input=sys.stdin.readline
for _ in range(int(input())):
    n=int(input())
    ar=list(map(int,input().split()))
    pos=[]
    neg=[]
    zer=[]
    for i in ar:
        if(i>0):
            pos.append(i)
        elif(i<0):
            neg.append(i)
        else:
            zer.append(i)
    if(len(pos)==0):
        if(len(zer)!=0):
            ans=0
        else:
            ar.sort(key=lambda x:abs(x))
            ans=1
            for i in range(5):
                ans*=ar[i]
    else:
        ans=max(pos)
        pos.remove(ans)
        le1=len(pos)
        le2=len(neg)
        le3=len(zer)
        a1=[]
        if(le1>=2):
            pos.sort(reverse=True)
            for i in range(1,le1,2):
                a1.append(pos[i]*pos[i-1])
        if(le2>=2):
            neg.sort()
            for i in range(1,le2,2):
                a1.append(neg[i]*neg[i-1])
        if(len(a1)>=2):
            a1.sort(reverse=True)
            for i in range(2):
                ans*=a1[i]
        else:
            if(le3!=0):
                ans=0
            else:
                ar.sort(key=lambda x:abs(x))
                ans=1
                for i in range(5):
                    ans*=ar[i]
    print(ans)
            
                