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.
for _ in range(int(input())):
    n=int(input())
    pos=[]
    neg=[]
    all=[]
    ans=1
    flag=0

    for x in list(map(int,input().split())):
        ans*=x
        if x==0:
            flag=1
        if x<0:
            neg.append(-x)
        else:
            pos.append(x)
        all.append(abs(x))
    ans=[]
    pos.sort(reverse=True)
    neg.sort(reverse=True)
    all.sort()
    if len(pos)>=5:
        tmp=1
        for i in range(5):
            tmp*=pos[i]
        ans.append(tmp)
    if len(pos)>=2:
        tmp=1
        for i in range(5):
            tmp*=all[i]
        ans.append(-tmp)
    if len(pos)>=3:
        tmp=1
        for i in range(3):
            tmp*=pos[i]
        if (len(neg)>=2):
            tmp=tmp*neg[0]*neg[1]
            ans.append(tmp)
    if len(pos)>=1:
        tmp=pos[0]
        if len(neg)>=4:
            for i in range(4):
                tmp*=neg[i] 
            ans.append(tmp)
    tmp=1
    for i in range(5):
        tmp*=all[i]
    ans.append(-tmp)
    ans.sort(reverse=True)
    if flag==1:
        ans[0]=max(ans[0],0)
    print(ans[0])