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())
    l = list(map(int,input().split()))
    l.sort()
    ans = 1
    if l[0]>=0 or (l[0]<0 and l[1]>=0) or l[-1]<=0:
        for i in range(n-1,n-6,-1):
            ans *= l[i]
    else:
        if l[0]*l[1]>=l[n-1]*l[n-2]:
            ans *= l[0]*l[1]
            if l[2]*l[3] >= l[n-1]*l[n-2] or l[n-3]<0: ans *= l[2]*l[3]*l[n-1]
            else: ans *= l[n-1]*l[n-2]*l[n-3]
        else:
            ans *= l[n-1]*l[n-2]
            if l[0]*l[1] >= l[n-3]*l[n-4] or l[n-5]<0: ans *= l[0]*l[1]*l[n-3]
            else: ans *= l[n-3]*l[n-4]*l[n-5]
        a2 = l[0]*l[1]*l[n-3]*l[n-2]*l[n-1]
        ans = max(a2,ans)
        a1 = l[0]*l[1]*l[2]*l[3]*l[n-1]
        ans = max(ans,a1)
    print(ans)