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.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.StringTokenizer;


public  class Practice  {
	
	
	
	        public static void main(String[] args) {
		         FastReader sc=new FastReader();
		         int t=sc.nextInt();
		         while(t-->0) {
		        	int n=sc.nextInt();
		        	int[] arr=new int[n];
		        	for(int i=0;i<n;i++) {
		        		arr[i]=sc.nextInt();
		        	}
		        	long max=Integer.MIN_VALUE;
		        	for( int i=0;i<n-1;i++) {
		        		max=Math.max(max, (long)arr[i]*(long)arr[i+1]);
		        	}
		        	System.out.println(max);
		         }
	        }
	        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;
	            }
	        }
	     
	
	}
			
			