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 i in range(t):
    n=int(input())
    arr=[int(i) for i in input().split()]
    arr=sorted(arr)
    pos=0
    neg=0
    point=n
    for i in range(n):
        if arr[i] >=0:
            pos+=1
        else:
            neg+=1
    ans=float('-inf')
    for j in range(n):
        if arr[j] >=0:
            point=j
            break
    if pos >= 5:
        prod=1
        for j in range(n-1,n-6,-1):
            prod*=arr[j]
        ans=max(ans,prod)
    if neg>=1 and pos>=4:
         prod=arr[point-1]
         prod=arr[point]*arr[point+1]*arr[point+2]*arr[point+3]*prod
         ans=max(ans,prod)
    if neg>=2 and pos>=3:
         prod=arr[0]*arr[1]
         prod=arr[-1]*arr[-2]*arr[-3]*prod
         ans=max(ans,prod)
    if neg>=3 and pos>=2:
        prod=arr[point-1]*arr[point-2]*arr[point-3]
        prod=prod*arr[-1]*arr[-2]
        ans=max(ans,prod)
    if neg>=4 and pos>=1:
        prod=1
        for j in range(4):
            prod*=arr[j]
        prod*=arr[-1]
        ans=max(ans,prod)
    if neg>=5:
         prod=1
         for j in range(point-1,point-6,-1):
             prod*=arr[j]
         ans=max(ans,prod)
    print(ans)
         
    


        
        
        
    
            
            
    
