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 javax.swing.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class A {
    static ArrayList<Integer> [] adj;
    static ArrayList<Integer> temp;
    static int mod = (int) 1e9+7;
    static boolean[] vis = new boolean[(int)1e5];

    public static void main(String[] args) throws IOException {
        FastScanner s=new FastScanner();
        int t = s.nextInt();
//        int t = 1;
        while(t-->0){
            int n = s.nextInt();
            int[] a = s.readArray(n);
            int[] max = new int[n];
            int[] min = new int[n];
            int[] max1 = new int[n];
            int[] min1 = new int[n];
            max[0] = a[0];
            min[0] = a[0];
            long ans=0;
            for(int i=1;i<n;i++){
                max[i] = Math.max(max[i-1],a[i]);
                min[i] = Math.min(min[i-1],a[i]);
                ans = Math.max(ans,max[i]*(long)min[i]);
            }
            max1[n-1]=a[n-1];
            min1[n-1]=a[n-1];
            for(int i=n-1;i>0;i--){
                max1[i] = Math.max(max1[i-1],a[i]);
                min1[i] = Math.min(min1[i-1],a[i]);
                ans = Math.max(ans,max1[i]*(long)min1[i]);
            }
            for(int i=1;i<n;i++){
                ans=Math.max(a[i]*(long)a[i-1],ans);
            }
            System.out.println(ans);
        }
    }
//Important
//Dont't stick on same approach
//Check long




    static void dfs(int i){
        vis[i]=true;
        temp.add(i);
        List<Integer> Y = adj[i];
        for(int x:Y){
            if(!vis[x])dfs(x);
        }
    }

    static long gcd(long a, long b) throws IOException {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcd(int a, int b) throws IOException {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static void sortr(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}