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.math.*;
import java.util.*;

public class Main {

    static final int MAX_N = 1000010;
    static final int INF = 0x3f3f3f3f;
    static final int mod = 1000000007;


    public static void main(String[] args) throws IOException {
        initReader(System.in);


        int T = nextInt();
        for (int i = 1; i <= T; i++)
        solve();


        pw.flush();
    }


    /*******************************************************************************************************************************/

    public static void solve() throws IOException {
        int n = nextInt();

        long[] a = new long[n];

        for (int i = 0; i < n; i++) a[i] = nextLong();

        long ans = 0;
        long Max = 0;

        for (int i = 0; i < n; i++) if (a[i] > Max) Max = a[i];

        boolean[] vis = new boolean[n];
        for (int i = 0; i < n; i++) {
            if (a[i] == Max) {
                if (i - 1 >= 0) ans = Math.max(ans, Max * a[i - 1]);
                if (i + 1 < n) ans = Math.max(ans, Max * a[i + 1]);
            }
        }

        pw.println(ans);
    }

    /*******************************************************************************************************************************/


    /*******************************************************************************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static PrintWriter pw;

    public static void initReader(InputStream input) throws IOException {
        reader = new BufferedReader(new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

//        reader = new BufferedReader(new FileReader("test.in"));
//        tokenizer = new StringTokenizer("");
//        pw = new PrintWriter(new BufferedWriter(new FileWriter("test1.out")));
    }

    public static boolean hasNext() {
        try {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (Exception e) {
            return false;
        }
        return true;
    }

    public static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    public static String nextLine() {
        try {
            return reader.readLine();
        } catch (Exception e) {
            return null;
        }
    }

    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public static char nextChar() throws IOException {
        return next().charAt(0);
    }

    public static short nextShort() throws IOException {
        return Short.parseShort(next());
    }

}

