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.util.*;
import java.io.*;

public class MaximalAreaQuadrilateral
{

	public static void main(String[] args)
	{
		JS scan = new JS();
		int n = scan.nextInt();
		Vec[] arr = new Vec[n];
		for(int i = 0; i < n; i++) arr[i] = new Vec(scan.nextLong(), scan.nextLong());
		double ans = 0;
		for(int i = 0; i < n; i++) {
			for(int j = i+1; j < n; j++) {
				long areaA = 0;
				long areaB = 0;
				for(int k = 0; k < n; k++) {
					if(k == i || k == j) continue;
					long r = triArea(arr[i], arr[j], arr[k]);
					if(r < 0) if(areaA > r) areaA = r;
					if(r > 0) if(areaB < r) areaB = r;
				}
				if(areaA == 0 || areaB == 0) continue;
				ans = Math.max(ans, areaB-areaA);
			}
		}
		System.out.println(ans*0.5);
	}
	
	static long triArea(Vec a, Vec b, Vec c) {
		Vec ab = b.sub(a);
		Vec ac = c.sub(a);
		return ab.cross(ac);
	}
	
	static class Vec implements Comparable<Vec> {
		long x, y;
		
		public Vec(long x, long y) {
			this.x=x;
			this.y=y;
		}
		
		public Vec sub(Vec v) {
			return new Vec(x-v.x, y-v.y);
		}
		
		public long cross(Vec v) {
			return x*v.y-y*v.x;
		}
		
		public long dot(Vec v) {
			return x*v.x+y*v.y;
		}
		
		//origin->q1, axes-> quadrant in ccw direction
		public int quadrant() {
			if (x==0||y==0) {
				if (y==0)
					if (x>=0)
						return 1;
					else
						return 3;
				else
					if (y>=0)
						return 2;
					else
						return 4;
			}
			if (x>0)
				if (y>0)
					return 1;
				else
					return 4;
			else
				if (y>0)
					return 2;
				else
					return 3;
		}
		
		public int compareTo(Vec o) {
			if (quadrant()==o.quadrant())
				return -Long.signum(cross(o));
			return Integer.compare(quadrant(), o.quadrant());
		}
	}
	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}