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();
		
		double[] X = new double[N];
		double[] Y = new double[N];
		for (int i = 0; i < N; i++) {
			X[i] = sc.nextInt();
			Y[i] = sc.nextInt();
		}
		
		double maxArea = 0;
		for (int i = 0; i < N; i++) {
			for (int j = i + 1; j < N; j++) {
				double maxTop2 = -1;
				double maxBot2 = -1;
				double diag = getLength(X[i], Y[i], X[j], Y[j]);
				for (int k = 0; k < N; k++) {
					if (i == k || j == k) {
						continue;
					}
					boolean topSide = true;
					if (X[i] != X[j]) {
						double m = (Y[j] - Y[i]) / (X[j] - X[i]);
						double yDiag = m * (X[k] - X[i]) + Y[i];
						topSide = (Y[k] > yDiag);
					} else {
						topSide = (X[k] > X[i]);
					}
					double s1 = getLength(X[i], Y[i], X[k], Y[k]);
					double s2 = getLength(X[j], Y[j], X[k], Y[k]);
					if (topSide) {
						maxTop2 = Math.max(maxTop2, getTriangleArea2(s1, s2, diag));
					} else {
						maxBot2 = Math.max(maxBot2, getTriangleArea2(s1, s2, diag));
					}
					if (maxTop2 > 0 && maxBot2 > 0) {
						maxArea = Math.max(maxArea, Math.sqrt(maxTop2) + Math.sqrt(maxBot2));
					}
				}
			}
		}
		System.out.println(maxArea);
	}
	
	public static double getLength(double x1, double y1, double x2, double y2) {
		double dx = x2 - x1;
		double dy = y2 - y1;
		return Math.sqrt(dx * dx + dy * dy);
	}
	
	public static double getTriangleArea2(double a, double b, double c) {
		double s = (a + b + c) / 2;
		return (s * (s - a) * (s - b) * (s - c));
	}

	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;
		}
	}
}