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.
# Fast IO (be careful about bytestring, not on interactive)

import os,io
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

INF = 10 ** 20

for _ in range(int(input())):
    n = int(input())
    a = list(map(int,input().split()))
    MINDP = [INF,INF,INF,INF,INF]
    MAXDP = [INF,INF,INF,INF,INF]
    for i in range(n):

        if MINDP[3] != INF and (MINDP[4] == INF or min(MINDP[3] * a[i], MAXDP[3] * a[i]) < MINDP[4]):
            MINDP[4] = min(MINDP[3] * a[i], MAXDP[3] * a[i])
        if MAXDP[3] != INF and (MAXDP[4] == INF or max(MINDP[3] * a[i], MAXDP[3] * a[i]) > MAXDP[4]):
            MAXDP[4] = max(MINDP[3] * a[i], MAXDP[3] * a[i])

        if MINDP[2] != INF and (MINDP[3] == INF or min(MINDP[2] * a[i], MAXDP[2] * a[i]) < MINDP[3]):
            MINDP[3] = min(MINDP[2] * a[i], MAXDP[2] * a[i])
        if MAXDP[2] != INF and (MAXDP[3] == INF or max(MINDP[2] * a[i], MAXDP[2] * a[i]) > MAXDP[3]):
            MAXDP[3] = max(MINDP[2] * a[i], MAXDP[2] * a[i])

        if MINDP[1] != INF and (MINDP[2] == INF or min(MINDP[1] * a[i], MAXDP[1] * a[i]) < MINDP[2]):
            MINDP[2] = min(MINDP[1] * a[i], MAXDP[1] * a[i])
        if MAXDP[1] != INF and (MAXDP[2] == INF or max(MINDP[1] * a[i], MAXDP[1] * a[i]) > MAXDP[2]):
            MAXDP[2] = max(MINDP[1] * a[i], MAXDP[1] * a[i])

        if MINDP[0] != INF and (MINDP[1] == INF or min(MINDP[0] * a[i], MAXDP[0] * a[i]) < MINDP[1]):
            MINDP[1] = min(MINDP[0] * a[i], MAXDP[0] * a[i])
        if MAXDP[0] != INF and (MAXDP[1] == INF or max(MINDP[0] * a[i], MAXDP[0] * a[i]) > MAXDP[1]):
            MAXDP[1] = max(MINDP[0] * a[i], MAXDP[0] * a[i])

        if MINDP[0] == INF or MINDP[0] > a[i]:
            MINDP[0] = a[i]
        if MAXDP[0] == INF or MAXDP[0] < a[i]:
            MAXDP[0] = a[i]

    print(MAXDP[4])
