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.
gans = []
INF = 100000000000000000000000000000000000000
for i in range(int(input())):
    n = int(input())
    inp = list(map(int, input().split()))
    if n == 5:
        ans = 1
        for i in range(n):
            ans *= inp[i]
        gans.append(ans)
        continue
    u = []
    w = []
    z = []
    for i in range(n):
        if inp[i] > 0:
            u.append(inp[i])
        elif inp[i] < 0:
            w.append(inp[i])
        else:
            z.append(inp[i])
    u.sort(reverse=1)
    w.sort()
    ans1 = ans2 = ans3 = ans4 = ans5 = -INF
    if len(u) > 0 and len(w) > 3:
        ans1 = u[0] * w[0] * w[1] * w[2] * w[3]
    if len(u) > 2 and len(w) > 1:
        ans2 = u[0] * u[1] * u[2] * w[0] * w[1]
    if len(u) > 4:
        ans3 = u[0] * u[1] * u[2] * u[3] * u[4]
    if len(z) > 0:
        ans5 = 0
    if len(w) > 4:
        ans4 = w[-1] * w[-2] * w[-3] * w[-4] * w[-5]
    gans.append(max(ans1, ans2, ans3, ans4, ans5))
if -INF in gans:
    print(1 / 0)
print('\n'.join(map(str, gans)))
    
