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.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.StringTokenizer;

public class MaximalAreaQuadrilateral {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        
        int N = sc.nextInt();
        
        int[] X = new int[N];
        int[] Y = new int[N];
        for (int i = 0; i < N; i++) {
            X[i] = sc.nextInt();
            Y[i] = sc.nextInt();
        }
        
        int maxArea = 0;
        for (int i = 0; i < N; i++) {
            for (int j = i + 1; j < N; j++) {
                int maxTop = -1;
                int maxBot = -1;
                int dx1 = X[j] - X[i];
                int dy1 = Y[j] - Y[i];
                for (int k = 0; k < N; k++) {
                    if (i == k || j == k) {
                        continue;
                    }
                    int dx2 = X[k] - X[i];
                    int dy2 = Y[k] - Y[i];
                    int prod = cross(dx1, dy1, dx2, dy2);
                    if (prod > 0) {
                        maxTop = Math.max(maxTop, prod);
                    } else {
                        maxBot = Math.max(maxBot, -prod);
                    }
                    if (maxTop > 0 && maxBot > 0) {
                        maxArea = Math.max(maxArea, maxTop + maxBot);
                    }
                }
            }
        }
        System.out.println(maxArea / 2.0);
    }
    
    public static int cross(int dx1, int dy1, int dx2, int dy2) {
        return (dx1 * dy2) - (dy1 * dx2);
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        int nextInt() {
            return Integer.parseInt(next());
        }
        
        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

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

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String str = "";
            try { str = br.readLine(); }
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
    }
}