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.*;
 
public class SolutionA{
       public static void main(String[] args) throws Exception{
               Fast sc=new Fast();
      PrintWriter out=new PrintWriter(System.out);
       int t=sc.nextInt();
       while(t-->0)
       {
            int n=sc.nextInt();
            long ans=0;
            long ti=0;
            long[] ar=new long[n];
            for(int i=0;i<n;i++){
              ar[i]=sc.nextLong();
            }
            long max=ar[0];
            long min=ar[0];
            for(int i=1;i<n;i++){
              max=Math.max(max,ar[i]);
              min=Math.min(min,ar[i]);
              ans=Math.max(ans,min*max);
              ans=Math.max(ans,ar[i]*ar[i-1]);
            }
            out.println(ans);
                  
       }
    out.close();
}

static void Sort(int[] ar){
    ArrayList<Integer> al=new ArrayList<>();
    for(int i=0;i<ar.length;i++){al.add(ar[i]);}
    Collections.sort(al);
    for(int i=0;i<al.size();i++)ar[i]=al.get(i);
  }
static long gcd(long a,long b){
    if(b==0) return a;
    else return  gcd(b,a%b);
}
}
class Pair{
    int x, y;
     Pair(int x,int y){
        this.x=x;
        this.y=y;
     }
}
class Fast{
  BufferedReader br; 
  StringTokenizer st;
  public Fast(){ br=new BufferedReader(new InputStreamReader(System.in)); }
  String next() 
        {  while (st == null || !st.hasMoreElements()) 
            {   try
                {     st = new StringTokenizer(br.readLine()); } 
                catch (IOException  e) 
                {    e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        }
  int nextInt(){  return Integer.parseInt(next()); }
  long nextLong(){     return Long.parseLong(next()); } 
  double nextDouble() {     return Double.parseDouble(next()); } 
  String nextLine() 
        { 
            String str = ""; 
            try{      str = br.readLine(); } 
            catch (IOException e)  {  e.printStackTrace(); } 
            return str; 
        } 
}
    
