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.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class _1554_A {

    private static final FastScanner in = new FastScanner();
    private static final PrintWriter out = new PrintWriter(System.out);
    private static final PrintWriter err = new PrintWriter(System.err);

    public static void solve() {
        int n = in.nextInt();
        long[] arr = in.nextLongArray(n);
        long max = arr[0] * arr[1];
        for (int i = 1; i < n - 1; i++) {
            if (arr[i] * arr[i+1] > max) {
                max = arr[i] * arr[i+1];
            }
        }

        out.println(max);
    }

    // Boilerplate
    public static void main(String[] args) {
        int t = in.nextInt();
        while (t-- > 0) {
            solve();
        }

        err.close();
        out.close();
    }

    @SuppressWarnings("unused")
    static class FastScanner {

        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        FastScanner() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (!tok.hasMoreElements()) {
                try {
                    tok = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tok.nextToken();
        }

        String nextLine() {
            String line;
            try {
                line = in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        List<Integer> nextIntegerList(int n) {
            ArrayList<Integer> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        List<Long> nextLongList(int n) {
            ArrayList<Long> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        ArrayList<Integer>[] nextGraph(int n, int m) {
            @SuppressWarnings("unchecked")
            ArrayList<Integer>[] adj = (ArrayList<Integer>[]) new ArrayList[n];

            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }

            for (int i = 0; i < m; i++) {
                int v = nextInt();
                int t = nextInt();
                adj[v - 1].add(t - 1);
                adj[t - 1].add(v - 1);
            }

            return adj;
        }
    }
}