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.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
 
public class Test4 {
 
	public static void main(String[] args) {
            FastScanner fs=new FastScanner();
            int T=fs.nextInt();
            PrintWriter out=new PrintWriter(System.out);
            for (int tt=0; tt<T; tt++) {
                
            	int n=fs.nextInt();
            	int arr[] = new int[n];
            	long a = arr[0], b = arr[1];
            	long prod=1;
        		for(int i=0;i<n;i++) {
        			arr[i] = fs.nextInt();
        			
        		}
        		long min=Integer.MAX_VALUE;
        		for (int i = 0; i < n-1; i++)
        	          prod=Math.max(prod, arr[i]*arr[i+1]);
        		for (int i = n-1; i >=1; i--)
      	          prod=Math.max(prod, (long)arr[i]*(long)arr[i-1]);
        		System.out.println(prod);
            }
            out.close();
	}
	
	static class FastScanner {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st=new StringTokenizer("");
            public String next() {
            while (!st.hasMoreElements())
		try {
                    st=new StringTokenizer(br.readLine());
		} catch (IOException e) {
                    e.printStackTrace();
		}
		return st.nextToken();
            }
		
            int[] readArray(int n) {
            int[] a=new int[n]; 
            for (int i=0; i<n; i++) a[i]=nextInt();
		return a;
            }
            int nextInt () {
                return Integer.parseInt(next());
            }
	}
 
}