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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
 
public class cf2{
    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;
    
        public FastReader() {
          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;
        }
    
      }
        
    public static void main(String[] args) {
        FastReader fr = new FastReader();
        int t = fr.nextInt();
        while(t-->0){
            int n = fr.nextInt();
          long [] arr =  new long[n];
          for(int i=0;i<n;i++){
              arr[i] = fr.nextInt();
          }
          
          long ans = 0;
          for(int i=0;i<(n-1);i++){
            long n1 =arr[i];
            long n2  = arr[i+1];
            if((n1*n2)> ans){
                ans=(n1*n2);
            }
          }
          
            System.out.println(ans);  
        }
        return;
        
    }
}
// 381274500335
// 1784478530