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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.*;
import java.math.*;
import static java.lang.Math.min;
import static java.lang.Math.max;
import static java.lang.Math.abs;

/* https://codeforces.com/contest/1554/problem/A*/
public class A {
    static Node st[];
    static FastScanner fs = new FastScanner();
    static PrintWriter fop = new PrintWriter(System.out);
    static StringBuilder sb = new StringBuilder();

    public static void main(String[] args) {
        try {
            solve();
        } catch (Exception e) {
            return;
        }
        // solve();
    }

    static void solve() throws IOException {

        int T = fs.nextInt();
        while (T-- > 0) {
            long ans = 0,nans = 0;
            int n = fs.nextInt();
            int a[] = fs.readArray(n);
            for (int i = 0; i < n - 1; i++) {
                nans = (long)a[i] * a[i + 1];
                ans = nans>ans?nans:ans;
            }
            fop.println(ans);
        }
        fop.flush();
        fop.close();

    }

    static class Node {
        int min;
        int max;
    }

    static Node MaxMinUtil(Node st[], int ss, int se, int qs, int qe, int index) {
        Node temp = new Node();
        Node left, right;
        if (qs <= ss && qe >= se)
            return st[index];
        if (se < qs || ss > qe) {
            temp.min = Integer.MAX_VALUE;
            temp.max = Integer.MIN_VALUE;
            return temp;
        }
        int mid = ss + (ss + se) / 2;
        left = MaxMinUtil(st, ss, mid, qs, qe, 2 * index + 1);
        right = MaxMinUtil(st, mid + 1, se, qs, qe, 2 * index + 2);
        temp.min = min(left.min, right.min);
        temp.max = max(left.max, right.max);
        return temp;
    }

    static Node MaxMin(Node[] st, int n, int qs, int qe) {
        return MaxMinUtil(st, 0, n - 1, qs, qe, 0);
    }

    static void constructSTUtil2(int[] arr, int ss, int se, Node[] st, int si) {
        if (ss == se) {
            st[si].min = arr[ss];
            st[si].max = arr[ss];
            return;
        }

        int mid = ss + (ss + se) / 2;
        constructSTUtil2(arr, ss, mid, st, si * 2 + 1);
        constructSTUtil2(arr, mid + 1, se, st, si * 2 + 2);
        st[si].min = min(st[si * 2 + 1].min, st[si * 2 + 2].min);
        st[si].max = min(st[si * 2 + 1].max, st[si * 2 + 2].max);
        // return st[si];
    }

    static void constructST(int arr[], int n) {
        int h = (int) (Math.ceil(Math.log(n) / Math.log(2)));

        int max_size = 2 * (int) Math.pow(2, h) - 1;
        st = new Node[max_size];
        constructSTUtil2(arr, 0, n - 1, st, 0);
        // return st;
    }
    // above function for both ^^^

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

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

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

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

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