1554_A. Cherry_114
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.util.*;


public class A {

	public static void main(String[] args) {
		sc = new MyScanner();
		out = new PrintWriter(new BufferedOutputStream(System.out));

		// solution
		int t = sc.nextInt();
		
		while (t != 0) {
			
			int n = sc.nextInt();
			int[] arr = new int[n];
			
			for (int i = 0; i < n; ++i) {
				arr[i] = sc.nextInt();
			}
			
			int minIndex = 0;
			int maxIndex = 1;
			
			if (arr[1] < arr[0]) {
				minIndex = 1;
				maxIndex = 0;
			}
			long res = (long)arr[minIndex] * (long)arr[maxIndex];
			
			/*for (int i = 2; i < n; ++i) {
				if (arr[i] > arr[minIndex] && arr[i] < arr[maxIndex]) {
					minIndex = i;
				} else if (arr[i] >= arr[maxIndex]) {
					maxIndex = i;
				}
				res = Math.max(res, (long)arr[minIndex] * (long)arr[maxIndex]);
			} */
			
			for (int i = 2; i < n; ++i) {
				res = Math.max(res, (long)arr[i] * (long)arr[i - 1]);
			}
			
			
			
			
			
			
			out.println(res);
			
			
			
			--t;
		}
		
		out.close();
	}

	// -----------------------------------------------------------------

	public static MyScanner sc;
	public static PrintWriter out;

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			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;
		}
	}

}
