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.StringTokenizer;

public class Main {

    static long solve(int n, int[] arr) {
        long ret = 0;

        for (int i = 1; i < n; i++) {
            ret = Math.max(ret, (long) arr[i - 1] * arr[i]);
        }

        return ret;
    }

    public static void main(String[] args) throws IOException {
//        System.out.println("===== input =====");
//        BufferedReader br = new BufferedReader(new FileReader("input/input1.txt"));
//        BufferedReader br2 = new BufferedReader(new FileReader("input/input1.txt"));
//        String s;
//        while ((s = br2.readLine()) != null) {
//            System.out.println(s);
//        }
//        System.out.println("===== output =====");
         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        StringBuilder out = new StringBuilder();
        int T = Integer.parseInt(st.nextToken());
        while (T-- > 0) {
            int N = Integer.parseInt(br.readLine());
            int[] arr = new int[N];

            st = new StringTokenizer(br.readLine());
            for (int i = 0; i < N; i++) {
                arr[i] = Integer.parseInt(st.nextToken());
            }

            out.append(solve(N, arr)).append("\n");
        }
        System.out.println(out);
    }
}