Problem: Iahub has drawn a set of n points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. 

Input

The first line contains integer n (4 ≤ n ≤ 300). Each of the next n lines contains two integers: xi, yi ( - 1000 ≤ xi, yi ≤ 1000) — the cartesian coordinates of ith special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. 

Output

Output a single real number — the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10 - 9.

Examples

Input

5
0 0
0 4
4 0
4 4
2 3


Output

16.000000

Note

In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4·4 = 16.

Solution (in JAVA):

Solution:


import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.InputStream;
import java.util.ArrayList;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        B solver = new B();
        int testCount = 1;
        for (int i = 1; i <= testCount; i++) {
            solver.solve(i, in, out);
        }
        out.close();
    }
}

class B {

    public void solve(int testNumber, InputReader in, OutputWriter out) {
       
        int n = in.readInt();
        
        int[] x = new int[n];
        int[] y = new int[n];
        
        for( int i = 0; i < n; i++){
          x[i] = in.readInt();
          y[i] = in.readInt();
        }
        
        int[][][] len = new int[n][n][n];
        
        double res = -1;  int a1;
        
        for( int i = 0; i < n; i++){
          for(int j = i+1; j < n; j++){
             int mx1 = -1;
             int mx2 = -1;
             for( int k = 0; k < n; k++){
                 if( k != i && k != j){
                    
                    if(len[i][j][k] == 0){
                          a1 = area(x[i],x[j],x[k],y[i],y[j],y[k]);
                          len[i][j][k] = a1;
                    }
                    else{
                       a1 = len[i][j][k];
                    }
                        
                    if( a1 < 0){
                      mx1 = Math.max(-a1, mx1);
                    }
                    else
                      mx2 = Math.max(a1, mx2); 
                 }                         
             }
             
             if( mx1 >= 0 && mx2 >= 0)
                 res = Math.max(res, mx1+mx2);
          }
        }
        
        out.printLine(res/2.0); 
        
    }
    
    public int area( int x1 , int x2, int x3, int y1 ,  int y2 , int y3){
           
        int abx = (x2-x1);
        int aby = (y2-y1);
        int acx = (x3-x1);
        int acy = (y3-y1);
        
        return abx*acy - acx*aby;
    }
}

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 readInt() {
        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 readString() {
        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 isWhitespace(c);
    }

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

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

    public interface SpaceCharFilter {

        public boolean isSpaceChar(int ch);
    }
}

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]);
        }
    }

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

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

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.readInt();
        }
        return array;
    }
}