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.
ansl = []
for _ in range(int(input())):
    n = int(input())
    al = list(map(int, input().split()))
    al.sort()
    alm = []
    alp = []
    zero = 0
    for a in al:
        if a > 0: alp.append(a)
        elif a < 0: alm.append(-a)
        else: zero += 1

    if alp: alp.sort(reverse=True)
    ans = (-1)*(10**18)
    if len(alm) >= 4 and len(alp) >= 1:
        v = alm[0]*alm[1]*alm[2]*alm[3] *alp[0]
        ans = max(ans,v)
    if len(alm) >= 2 and len(alp) >= 3:
        v = alm[0]*alm[1] *alp[0]*alp[1]*alp[2]
        ans = max(ans,v)
    if len(alp) >= 5:
        v = alp[0]*alp[1]*alp[2]*alp[3]*alp[4]
        ans = max(ans,v)

    if zero > 0: ans = max(ans,0)

    if len(alm) >= 5:
        v = alm[-1]*alm[-2]*alm[-3]*alm[-4]*alm[-5]
        ans = max(ans,-v)
    if len(alm) >= 3 and len(alp) >= 2:
        v = alm[-1]*alm[-2]*alm[-3] *alp[-1]*alp[-2]
        ans = max(ans,-v)
    if len(alm) >= 1 and len(alp) >= 4:
        v = alm[-1] *alp[-1]*alp[-2]*alp[-3]*alp[-4]
        ans = max(ans,-v)

    ansl.append(ans)

for a in ansl: print(a)

