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.
T = int(input())
for _ in range(T):
    N = int(input())
    A = list(map(int,input().split()))
    pos = []
    neg = []
    zero = 0
    for a in A:
        if a > 0:
            pos.append(a)
        elif a < 0:
            neg.append(a)
        else:
            zero += 1
    pos.sort()
    neg.sort()
    ans = -float('inf')
    for i in range(6):
        if i > len(pos): continue
        for j in range(6-i):
            if j > len(neg): continue
            for k in range(6-i-j):
                if i+j+k != 5: continue
                if k > zero: continue
                tmp = 1
                if i:
                    for p in pos[-i:]:
                        tmp *= p
                if j:
                    if j%2:
                        for n in neg[-j:]:
                            tmp *= n
                    else:
                        for n in neg[:j]:
                            tmp *= n
                if k:
                    tmp = 0
                ans = max(ans, tmp)
    print(ans)
