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 java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Main {
    static int mod = (int)1e9 + 7;


    private static final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) throws IOException {

        int [] choice = new int[]{4,2,0,1,3,5};
        int t = sc.nextInt();
        while (t-- > 0)
        {
            int n = sc.nextInt();
            Integer[]arr = new Integer[n];

            for (int i = 0 ; i < n ; i++) arr[i] = sc.nextInt();

            Arrays.sort(arr);
            long max = Long.MIN_VALUE;
            for (int c = 0; c < choice.length ; c++)
            {
                long tmp = 1;
                for (int i = 0; i < choice[c] ; i++)
                    tmp= 1l * tmp *arr[i];
                for (int i = ( 5 - choice[c] ), j = n - 1 ; i > 0;i--,j--  )
                    tmp= 1l*tmp*arr[j];
                max = Math.max(max, tmp);
            }
            System.out.println(max);
        }
        

     }
}
