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.
//package com.amoghghadge.compProgramming.CodeforcesUnder1100;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class Cherry {

    public static void main(String[] args) {
        
        FastReader in = new FastReader();
        StringBuffer sb = new StringBuffer();

        int t = in.nextInt();
        
        while (t > 0) {

            int n = in.nextInt();
            ArrayList<Long> nums = new ArrayList<Long>();
            long maxValue = Long.MIN_VALUE;

            for (int i = 0; i < n; i++) {

                nums.add(in.nextLong());

            }

            for (int i = 0; i < n - 1; i++) {

                if (nums.get(i) * nums.get(i + 1) > maxValue) {

                    maxValue = nums.get(i) * nums.get(i + 1);

                }

            }

            sb.append(maxValue + "\n");

            t--;

        }

        System.out.println(sb);

    }

    static int gcd (int a, int b) {
        
        if (b == 0) {

            return a;

        } else {

            return gcd(b, a % b);

        }

    }
 
    static long gcd (long a, long b) {
        
        if (b == 0) {

            return a;

        } else {

            return gcd(b, a % b);

        }

    }
 
    static long lcm (int a, int b) {

        return (long) a / gcd(a, b) * b;

    }
 
    static long lcm (long a, long b) {

        return a / gcd(a, b) * b;

    }

    public static int search (int l, int r, int[] a, int key) {

        while (l <= r) {

            int middle = ((r - l) / 2) + l;

            if (a[middle] == key) {

                return middle;

            } else if (a[middle] < key) {

                l = middle + 1;

            } else {

                r = middle - 1;

            }

        }

        return -1;

    }

    public static void sort (int[] a) {

		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
        
	}

    public static void sort (long[] a) {

		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);

	}

    public static class FastReader {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        public String next() {

            while (st == null || !st.hasMoreElements()) {

                try {

                    st = new StringTokenizer(br.readLine());

                } catch (IOException e) {

                    e.printStackTrace();

                }

            }

            return st.nextToken();

        }

        public int nextInt() {

            return Integer.parseInt(next());

        }

        public long nextLong() {

            return Long.parseLong(next());

        }

        public double nextDouble() {

            return Double.parseDouble(next());

        }

        public String nextLine() {

            String str = "";

            try {

                str = br.readLine();

            } catch (IOException e) {

                e.printStackTrace();

            }

            return str;

        }

        public int[] readArray(int n) {

			int[] a = new int[n];

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

            return a;

		}

        public long[] readArrayLong(long n) {

			long[] a = new long[(int) n];

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

            return a;

		}

    }

}