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 P07 {
	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());
		}
		
		float nextFloat() {
			return Float.parseFloat(next());
		}
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			}catch(IOException e) {
				e.printStackTrace();
			}
			return str ;
		}
	}
	
 	public static  void main(String[] args)throws IOException {
		FastReader fs = new FastReader();
		int t = fs.nextInt();
		while(t-->0) {
			int n = fs.nextInt();
			long a[]= new long [n];
			long max =Long.MIN_VALUE;
			for(int i =0;i<n;i++) {
				a[i]= fs.nextLong();
			}
			for(int i =0;i<n-1;i++) {
				max=Math.max(max,a[i]*a[i+1]);
			}
			for(int i =n-1;i>0;i--) {
				max=Math.max(max,a[i]*a[i-1]);
			}
			System.out.println(max);
		}
		
    }
	private static int gcd(int i, int j) {
		if(j==0) {
			return i;
		}
		return gcd(j,i%j);
	}
	
}
