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())
while(t>0):
    t-=1
    n=int(input())
    lst=list(map(int,input().split()))
    pos=[]
    neg=[]
    for i in range(n):
        if(lst[i]<0):
            neg.append(lst[i])
        else:
            pos.append(lst[i])
    ans=-11000000000000000000000000000007
    neg.sort()
    pos.sort()
    if(len(neg)>=5):
        ans=max(ans,neg[-1]*neg[-2]*neg[-3]*neg[-4]*neg[-5])
    if(len(pos)>=4 and len(neg)>=1):
        ans=max(ans,neg[-1]*pos[0]*pos[1]*pos[2]*pos[3])
    if(len(neg)>=2 and len(pos)>=3):
        ans=max(ans,neg[0]*neg[1]*pos[-1]*pos[-2]*pos[-3])
    if(len(neg)>=3 and len(pos)>=2):
        ans=max(ans,neg[-1]*neg[-2]*neg[-3]*pos[0]*pos[1])
    if(len(neg)>=4 and len(pos)>=1):
        ans=max(ans,neg[0]*neg[1]*neg[2]*neg[3]*pos[-1])
    if(len(pos)>=5):
        ans=max(ans,pos[-1]*pos[-2]*pos[-3]*pos[-4]*pos[-5])
    if(ans<0 and len(pos)>0 and pos[0]==0):
        ans=0
    print(ans)
    