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.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Sorting {
    static int sign(int x){
        if((x &1)==1)
            return -1;
        return 1;
    }
    static long biggestMUL(ArrayList<Integer> v, int x){
        long ret = 1;
        for(int i = 0; i < x; i++){
            ret *= v.get(v.size() - i - 1);
        }
        return ret;
    }
    static long smallestMUL(ArrayList<Integer> v, int x){
        long ret = 1;
        for(int i = 0; i < x; i++){
            ret *= v.get(i);
        }
        return ret;
    }

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        while (t-- > 0) {
            ArrayList<Integer> pos = new ArrayList<Integer>();
            ArrayList<Integer> neg = new ArrayList<Integer>();
            boolean zero = false;
            int n = input.nextInt();
            for (int i = 0;i < n;i++) {
                int x = input.nextInt();
                if (x > 0) pos.add(x);
                else neg.add(Math.abs(x));
                zero |= (x == 0);
            }
            Collections.sort(pos);
            Collections.sort(neg);
            long ans = (long) -1e18;
            if (zero) {
                ans = 0;
            }
            for (int x = 0;x <= 5;x++) {
                int y = 5 - x; //odd
                if (x <= pos.size()) {
                    long BiggestXPosNumber = biggestMUL(pos, x);
                    long smalledXPosNumber = smallestMUL(pos, x);
                    if (y <= neg.size()) {
                        long BiggestYNegNumber = biggestMUL(neg, y);
                        long smallestYNegNumber = smallestMUL(neg, y);
                        ans = Math.max(ans, BiggestXPosNumber * BiggestYNegNumber * sign(y));
                        ans = Math.max(ans, smalledXPosNumber * smallestYNegNumber * sign(y));

                    }
                }

            }
            System.out.println(ans);
        }
      }
    }