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.Collections;
import java.util.StringTokenizer;

public class A implements Runnable {

	public static void main(String[] args) throws Exception {

		new Thread(null, new A(), "SwapnilGanguly", 1 << 24).start();
	}

	public void run() {

		SwapScanner sc = new SwapScanner();
		PrintWriter pr = new PrintWriter(System.out);

		int T = sc.nextInt();

		while (T-- > 0) {

			int n = sc.nextInt();
			long ar[] = new long[n];

			for (int i = 0; i < n; i++)
				ar[i] = sc.nextLong();

			long maxVal = ar[0];

			for (int i = 1; i < n; i++)
				maxVal = Math.max(maxVal, ar[i]);

			long ans = 0;

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

				if (ar[i] == maxVal) {

					if (i == 0)
						ans = Math.max(ans, maxVal * ar[1]);

					else if (i == n - 1)
						ans = Math.max(ans, maxVal * ar[n - 2]);

					else {

						long pro1 = maxVal * ar[i - 1];
						long pro2 = maxVal * ar[i + 1];

						long pro = Math.max(pro1, pro2);
						ans = Math.max(ans, pro);
					}
				}
			}

			pr.println(ans);
		}

		pr.close();
	}

	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 class SwapScanner {

		BufferedReader br;
		StringTokenizer st;

		public SwapScanner() {

			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {

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

				try {

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

				catch (IOException e) {

					e.printStackTrace();
				}
			}

			return st.nextToken();
		}

		int nextInt() {

			return Integer.parseInt(next());
		}

		long nextLong() {

			return Long.parseLong(next());
		}

		double nextDouble() {

			return Double.parseDouble(next());
		}

		String nextLine() {

			String str = "";

			try {

				str = br.readLine();
			}

			catch (IOException e) {

				e.printStackTrace();
			}

			return str;
		}

		int[] readArray(int n) {

			int[] ar = new int[n];

			for (int i = 0; i < n; i++)
				ar[i] = nextInt();

			return ar;
		}
	}
}