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.
from collections import Counter
t=int(input())
for  _ in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    neg=[]
    pos=[]
    z=0
    for i in a:
        if i>0:
            pos.append(i)
        elif i==0:
            z+=1
        else:
            neg.append(i)
    pos.sort(reverse=True)
    neg.sort()
    if z>0:
        ans=0
    else:
        ans=-float('inf')
    lp=len(pos)
    ln=len(neg)
    if 5<=lp:
        c=1
        for i in range(5):
            c*=pos[i]
        ans=max(ans,c)
    if 3<=lp and 2<=ln:
        c=1
        for i in range(3):
            c*=pos[i]
        for i in range(2):
            c*=neg[i]
        ans=max(ans,c)
    if 1<=lp  and 4<=ln:
        c=1
        for i in range(1):
            c*=pos[i]
        for i in range(4):
            c*=neg[i]
        ans=max(ans,c)
    if 4<=lp and 1<=ln:
        c=1
        for i in range(lp-1,lp-1-4,-1):
            c*=pos[i]
        for i in range(ln-1,ln-1-1,-1):
            c*=neg[i]
        ans=max(ans,c)
    if 2<=lp and 3<=ln:
        c=1
        for i in range(lp-1,lp-1-2,-1):
            c*=pos[i]
        for i in range(ln-1,ln-1-3,-1):
            c*=neg[i]
        ans=max(ans,c)
    if 5<=ln:
        c=1
        for i in range(ln-1,ln-1-5,-1):
            c*=neg[i]
        ans=max(ans,c)
    print(ans)