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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws Exception {
        int t = readInt();
        while(t-->0) {
            int n = readInt();
            long[] a = readLongArray();
            Arrays.sort(a);
            long ans = Long.MIN_VALUE;
            for(int l=0 ; l<=5 ; l++) {
                long p=1;
                for (int i = 0; i < l; i++) {
                    p = p*a[i];
                }
                for (int i = n-1; i >= (n-(5-l)) ; i--) {
                    p = p*a[i];
                }
                ans = Math.max(p,ans);
            }
            System.out.println(ans);
        }
    }


    private static String readString() throws Exception {
        return br.readLine();
    }

    private static int readInt() throws Exception{
        return Integer.parseInt(readString());
    }

    private static long readLong() throws Exception{
        return Long.parseLong(readString());
    }

    private static double readDouble() throws Exception{
        return Double.parseDouble(readString());
    }

    private static String[] readStringArray() throws Exception {
        return br.readLine().split(" ");
    }

    private static List<String> readStringList() throws Exception {
        return Arrays.asList(readStringArray());
    }

    private static List<Integer> readIntList() throws Exception {
        return readStringList().stream().map(s -> Integer.parseInt(s)).collect(Collectors.toList());
    }

    private static int[] readIntArray() throws Exception {
        return readIntList().stream().mapToInt(i -> i).toArray();
    }

    private static List<Long> readLongList() throws Exception {
        return readStringList().stream().map(s -> Long.parseLong(s)).collect(Collectors.toList());
    }

    private static long[] readLongArray() throws Exception {
        return readLongList().stream().mapToLong(i -> i).toArray();
    }

    private static List<Double> readDoubleList() throws Exception {
        return readStringList().stream().map(s -> Double.parseDouble(s)).collect(Collectors.toList());
    }

    private static double[] readDoubleArray() throws Exception {
        return readDoubleList().stream().mapToDouble(i -> i).toArray();
    }
}