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.Arrays;
import java.util.Scanner;
public class BT {
    public static void swap(long a[], int x, int y) {
        long tg = a[x];
        a[x] = a[y];
        a[y] = tg;
    }
    public static long max(long a,long b){
        if(a>=b){
            return a;
        }
        else return b;
    }
    public static void quicksort(long a[],int l,int r){
        int i=l;
        int j=r;
        long piv=a[(l+r)/2];
        while(i<=j){
            while(a[i]<piv){
                i++;
            }
            while(a[j]>piv && j>0){
                j--;
            }
            if(i<=j){
                swap(a,i,j);
                i++;
                j--;
            }
        }
        if(l<j){
            quicksort(a,l,j);
        }
        if(r>i){
            quicksort(a,i,r);
        }
    }
    public static void main(String[] args) {
        int m;
        int n;
        Scanner sc=new Scanner(System.in);
        m=sc.nextInt();
        while(m>0){
            n=sc.nextInt();
            long []a=new long[n];
            for(int i=0;i<n;i++){
                a[i]=sc.nextInt();
            }
            quicksort(a,0,n-1);
            System.out.println(max(max(a[0]*a[1]*a[n-1]*a[n-2]*a[n-3],a[n-5]*a[n-4]*a[n-1]*a[n-2]*a[n-3]),a[0]*a[1]*a[2]*a[3]*a[n-1]));
            m--;
        }
    }
}
