You are given n integers a_1, a_2, …, a_n. Find the maximum value of max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r) over all pairs (l, r) of integers for which 1 ≤ l < r ≤ n.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print a single integer — the maximum possible value of the product from the statement.

Example

Input


4
3
2 4 3
4
3 2 3 1
2
69 69
6
719313 273225 402638 473783 804745 323328


Output


12
6
4761
381274500335

Note

Let f(l, r) = max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r).

In the first test case, 

  * f(1, 2) = max(a_1, a_2) ⋅ min(a_1, a_2) = max(2, 4) ⋅ min(2, 4) = 4 ⋅ 2 = 8. 
  * f(1, 3) = max(a_1, a_2, a_3) ⋅ min(a_1, a_2, a_3) = max(2, 4, 3) ⋅ min(2, 4, 3) = 4 ⋅ 2 = 8. 
  * f(2, 3) = max(a_2, a_3) ⋅ min(a_2, a_3) = max(4, 3) ⋅ min(4, 3) = 4 ⋅ 3 = 12. 



So the maximum is f(2, 3) = 12.

In the second test case, the maximum is f(1, 2) = f(1, 3) = f(2, 3) = 6.
import java.util.*;

public class Cherry {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();

        for (int i=0; i<k; i++) {
            int n = sc.nextInt();
            int[] arr = new int[n];
            for(int j=0; j<n; j++){
                arr[j] = sc.nextInt();
            }

            int l = 0;
            int r = l + 1;
            int[] arr2 = new int[n-1];
            for (int j=0; j<n-1; j++){
                arr2[j] = arr[l]*arr[r];
            }
            System.out.println(Arrays.stream(arr2).max().getAsInt());
        }
    }
}
































           
























           







        /*Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        

        for (int i=0; i<k; i++) {

            int n = sc.nextInt();
            int[] dummekackzahlen = new int[n];
            for (int j=0; j<n; j++){
                dummekackzahlen[j] = sc.nextInt();
            }

            BigInteger momentanderkingindembiz= BigInteger.valueOf(0);
            for (int x=0; x<n-1; x++){
                for (int y=x+1; y<n; y++){
                    momentanderkingindembiz = (f(dummekackzahlen,x,y).compareTo(momentanderkingindembiz)==1)?f(dummekackzahlen,x,y):momentanderkingindembiz;
                }
            } 
            
            System.out.println(momentanderkingindembiz);
        }
    }


    public static int max(int[] a, int links, int rechts){
        int max=0;
        for (int i=links; i<=rechts; i++){
            max = max<a[i]?a[i]:max;
        }
        return max;
    }

    public static int min(int[] a, int links, int rechts){
        int min=a[links];
        for (int i=links; i<=rechts; i++){
            min= min>a[i]?a[i]:min;
        }
        return min;
    }

    public static BigInteger f(int[] a, int links, int rechts){
        return BigInteger.valueOf(max(a,links,rechts)).multiply(BigInteger.valueOf(min(a,links,rechts))); */












           
                 
/*Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for (int i=0; i<n; i++) {
            int z = sc.nextInt();
            int[] xa = new int[z];
            int l = 0;
            int r = l+1;
            int[] xc = new int[z];
                for (int m=0; m<z; m++) {
                
                    int k = sc.nextInt();
                    xa[m] = k;
                }
                for (int u=0; u<z; u++){
                    int[] xb = new int[r-l+1];
                    for (int s=0; s<(r-l); s++){
                        xb[s] = xa[s];
                    }
                    int min = Arrays.stream(xb).min().getAsInt();
                    int max = Arrays.stream(xb).max().getAsInt();
                    xc[u] = min * max;
                }
                System.out.println(Arrays.stream(xc).max().getAsInt());
                System.out.println("Max mutter, die olle fotze stinkt")
            }
            */  