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.*;
public class s1 {
	public static void main(String[] args) throws Exception {
		FastScanner scan=new FastScanner(System.in);
		PrintWriter out=new PrintWriter(System.out);

//		int T=1;
		int T=scan.nextInt();
		while(T-->0) {

			int n=scan.nextInt(),maxIndex=0;
			int[] a=new int[n];
			for(int i=0;i<n;i++) {
				a[i]=scan.nextInt();
				if(a[i]>a[maxIndex]) maxIndex=i;
			}

			long best=Long.MIN_VALUE,min=a[maxIndex];
			for(int i=maxIndex-1;i>=0;i--) {
				if(a[i]<min) min=a[i];
				if((long)a[maxIndex]*min>best) {
					best=(long)a[maxIndex]*min;
				}
			} min=a[maxIndex];
			for(int i=maxIndex+1;i<n;i++) {
				if(a[i]<min) min=a[i];
				if((long)a[maxIndex]*min>best) best=(long)a[maxIndex]*min;
			}
			out.println(best);

		} out.close();
	}
}

class Pair {
	Integer a,b;
	Pair(int a,int b) {
		this.a=a;
		this.b=b;
	}
}

class FastScanner {
	private InputStream stream;
	private byte[] buf=new byte[1024];
	private int curChar;
	private int numChars;

	public FastScanner(InputStream stream) { this.stream=stream; }

	int read() {
		if(numChars==-1) throw new InputMismatchException();
		if(curChar>=numChars) {
			curChar=0;
			try { numChars=stream.read(buf); }
			catch(IOException e) { throw new InputMismatchException(); }
			if(numChars<=0) return -1;
		} return buf[curChar++];
	}

	boolean isSpaceChar(int c) { return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1; }

	boolean isEndline(int c) { return c=='\n'||c=='\r'||c==-1; }

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

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

	double nextDouble() { return Double.parseDouble(next()); }

	String next() {
		int c=read();
		while(isSpaceChar(c)) c=read();
		StringBuilder res=new StringBuilder();
		do {
			res.appendCodePoint(c);
			c=read();
		} while(!isSpaceChar(c));
		return res.toString();
	}

	String nextLine() {
		int c=read();
		while(isEndline(c)) c=read();
		StringBuilder res=new StringBuilder();
		do {
			res.appendCodePoint(c);
			c=read();
		} while(!isEndline(c));
		return res.toString();
	}
}