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.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
 public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 1000000007;
    long fac[]= new long[1000001];
    long inv[]=new long[1000001];
    public  void solve() throws IOException 
    {

        
         int t = readInt();

        for(int f =0;f<t;f++)
        {
             int n = readInt();
             long arr[]=new long[n];
             for(int i =0;i<n;i++)
                arr[i]= readInt();
             long max = arr[0]*arr[1];
             for(int i=1;i<n-1;i++)
             {
                max=Math.max(max,arr[i]*arr[i+1]);
             }
             out.println(max);
        }

        



    }
    
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v;
    
    edge(int  u, int v)
    {
       this.u=u;
       this.v=v;
    }
    public int compareTo(edge e)
    {
        return this.v-e.v;
    }
}