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.
import sys
input= sys.stdin.buffer.readline
def print(val):
    sys.stdout.write(str(val) + '\n')
def prog():
    for _ in range(int(input())):
        n = int(input())
        a = list(map(int,input().split()))
        dp = [[[0]*2 for i in range(6)] for i in range(n + 1)]
        dp[0][0][0] = 1
        for i in range(1,n+1):
            for j in range(6):
                dp[i][j][0] = dp[i-1][j][0]
                dp[i][j][1] = dp[i-1][j][1]
                if j:
                    if a[i-1] < 0:
                        dp[i][j][0] = max(dp[i][j][0], -dp[i-1][j-1][1]*a[i-1])
                        dp[i][j][1] = max(dp[i][j][1], -dp[i-1][j-1][0]*a[i-1])
                    else:
                        dp[i][j][1] = max(dp[i][j][1], dp[i-1][j-1][1]*a[i-1])
                        dp[i][j][0] = max(dp[i][j][0], dp[i-1][j-1][0]*a[i-1])

        
        dp2 = [[[10**18]*2 for i in range(6)] for i in range(n + 1)]
        dp2[0][0][0] = 1
        for i in range(1,n+1):
            for j in range(6):
                dp2[i][j][0] = dp2[i-1][j][0]
                dp2[i][j][1] = dp2[i-1][j][1]
                if j:
                    if a[i-1] < 0:
                        dp2[i][j][0] = min(dp2[i][j][0], -dp2[i-1][j-1][1]*a[i-1])
                        dp2[i][j][1] = min(dp2[i][j][1], -dp2[i-1][j-1][0]*a[i-1])
                    else:
                        dp2[i][j][1] = min(dp2[i][j][1], dp2[i-1][j-1][1]*a[i-1])
                        dp2[i][j][0] = min(dp2[i][j][0], dp2[i-1][j-1][0]*a[i-1])
        in_a = (0 in a)
        if in_a:
            print(dp[n][5][0])
        else:
            if dp[n][5][0] == 0:
                print(-dp2[n][5][1])
            else:
                print(dp[n][5][0])
prog()

