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.*;
import java.io.*;
import java.math.*;
import java.util.LinkedList;
public class Main
{
 
    public static void process()throws IOException
    {
     int n=ni();
     long arr[]=larr(n);
     long max=Long.MIN_VALUE;
     int idx=0;
     long ans=0l;
     for(int i=0;i<n;i++)
     {
      if(max<arr[i])
      {
        max=arr[i];
        idx=i;
        if(idx==0)
      ans=(max*arr[idx+1]);
    else if(idx==n-1)
      ans=(max*arr[idx-1]);
    else
      ans=(Math.max((max*arr[idx+1]),(max*arr[idx-1])));

      }
      else if(max==arr[i])
      {
        long ans2=0l;
        if(i==0)
      ans2=(arr[i]*arr[i+1]);
    else if(i==n-1)
      ans2=(arr[i]*arr[i-1]);
    else
      ans2=(Math.max((arr[i]*arr[i+1]),(arr[i]*arr[i-1])));

      if(ans2>ans)
      {
        idx=i;
        ans=ans2;
        max=ans;
      }
      }
     }

     pn(ans);
    }
    
     
    
    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

           //PrintWriter out=new PrintWriter("output");
        //oj = System.getProperty("ONLINE_JUDGE") != null;
        //if(!oj) sc=new AnotherReader(100);
    //int T=ni(); while(T-->0)
      //process();
 //   int i=1;
      int T=ni();
 while(T-->0)
 //     {
 //      p("Case #"+i+": ");
            process();
    //         i++;
    // }
        long s = System.currentTimeMillis();
      
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
    static void sort(long arr[],int n)
    {
    shuffle(arr,n);
    Arrays.sort(arr);
    }
    static void shuffle(long arr[],int n)
    {
        Random r=new Random();
        for(int i=0;i<n;i++)
        {
          long temp=arr[i];
          int pos=i+r.nextInt(n-i);
          arr[i]=arr[pos];
          arr[pos]=temp;
        }
    }
 
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static String nn()throws IOException{return sc.next();}
    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 long bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static int[] iarr(int N)throws IOException{int[]ARR=new int[N];for(int i=0;i<N;i++){ARR[i]=ni();}return ARR;}
    static long[] larr(int N)throws IOException{long[]ARR=new long[N];for(int i=0;i<N;i++){ARR[i]=nl();}return ARR;}
    static boolean multipleTC=false;
            
 
/////////////////////////////////////////////////////////////////////////////////////////////////////////
    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
 
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}