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.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;
import java.text.*;

public class Main {

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);








    public static void main(String[] args)
            throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        BufferedReader br = new BufferedReader(
                new InputStreamReader(System.in));
        int t = i();
        PrintWriter out = new PrintWriter(System.out);
        while (t > 0) {

            int n=i();
            int arr[]=new int[n];
            for(int i=0;i<n;i++) {
                arr[i]=i();
            }

            long ans=0L;
            for(int i=0;i<n-1;i++) {
                ans=Math.max(ans, arr[i]*(long)arr[i+1]);
            }
            System.out.println(ans);







            t--;

        }
        out.close();

        //      long l=l();
        //      String s=s();     //    ONLY BEFORE SPACE IN STRING , ELSE USE BUFFER-READER

    }

    public static long pow(long a, long b) {
        long m = 1000000007;
        long result = 1;
        while (b > 0) {
            if (b % 2 != 0) {
                result = (result * a) % m;
                b--;
            }
            a = (a * a) % m;
            b /= 2;
        }
        return result % m;
    }

    public static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    public static long lcm(long a, long b) {
        return a * (b / gcd(a, b));
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static void pln(String value) {
        System.out.println(value);
    }

    public static int i() {
        return in.Int();
    }

    public static String s() {
        return in.String();
    }

}

class pair {
    int x, y;

    pair(int x, int y) {
        this.x = x;
        this.y = y;
    }
}

class CompareValue {

    static void compare(pair arr[], int n) {
        Arrays.sort(arr, new Comparator<pair>() {
            public int compare(pair p1, pair p2) {
                return p1.y - p2.y;
            }
        });
    }
}

class CompareKey {
    static void compare(pair arr[], int n) {
        Arrays.sort(arr, new Comparator<pair>() {
            public int compare(pair p1, pair p2) {
                return p2.x - p1.x;
            }
        });
    }
}

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

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

    public 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++];
    }

    public int Int() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

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

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public String next() {
        return String();
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') {
                return res * Math.pow(10, Int());
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, Int());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
        writer.flush();
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
        writer.flush();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }
}

class IOUtils {
    public static int[] readIntArray(InputReader in, int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++)
            array[i] = in.Int();
        return array;
    }
}

