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.* ;
import java.util.* ;


 
public class App {
    public static void main (String[] args) throws java.lang.Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        //reader = new BufferedReader(new FileReader(new File("C:\\Users\\Anjali\\Desktop\\projects\\HelloWorld\\src\\input.txt")));
		BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        //writer = new BufferedWriter(new FileWriter(new File("C:\\Users\\Anjali\\Desktop\\projects\\HelloWorld\\src\\output.txt")));
		//int tests = Integer.parseInt(reader.readLine());
        int tests = 1;
		//StringBuilder sb = new StringBuilder(tests);
		while (tests-- > 0){
		    solve(reader, writer);
            writer.write("\n");
		}
		reader.close();
        writer.flush();
        writer.close();
    }

 
    static void solve(BufferedReader reader, BufferedWriter writer) throws  IOException {
		int tests = Integer.parseInt(reader.readLine());
		for (int i = 0; i < tests; i++) {
			int n = Integer.parseInt(reader.readLine());
			int[] a = new int[n];
			long product = 0;
			String[] input = reader.readLine().split(" ");
			for(int j = 0; j < n; j++) {
				a[j] = Integer.parseInt(input[j]);
			}
			for(int j = 1; j < n; j++) {
				product = Math.max(product, (long)a[j] * a[j - 1]);
			}
			writer.write(product + "\n");
		}
	}
}
