UVA 10173

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define min(x,y) ((x)<(y)?(x):(y))
using namespace std;

struct point
{
    double x,y;
}p[1005];

int ans[1005],st[1005],stop,cnt,n;

int DB (double d){
	if (fabs(d)<1e-8)
		return 0;
	return d>0?1:-1;
}
double cross (point a,point b,point c){
	return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);
}
double dot(point a,point b,point c){
    return (a.x-c.x)*(b.x-c.x)+(a.y-c.y)*(b.y-c.y);
}
bool cmp(point A,point B){
	if(A.y<B.y) return true;
	else if(A.y==B.y){
		if(A.x<B.x)return true;
	}
	return false;
}

void forTU(){
	stop=cnt=0;
	st[stop++]=0; st[stop++]=1;
	for(int i=2;i<n;i++){
		while(stop>1&&cross(p[i],p[st[stop-1]],p[st[stop-2]])>=0) stop--;
		st[stop++]=i;
	}
	for(int i=0;i<stop;i++)
	ans[cnt++]=st[i];
	stop=0; st[stop++]=n-1; st[stop++]=n-2;
	for(int i=n-3;i>=0;i--){
		while(stop>1&&cross(p[i],p[st[stop-1]],p[st[stop-2]])>=0) stop--;
		st[stop++]=i;
	}
	for(int i=1;i<stop;i++){
		ans[cnt++]=st[i];
	}
}

double roating(){
	cnt--;
    if(n<3) return 0;
    int i,m=1,q=1,r;
    double anst=1e10,a,b,c;
    for(i=0;i<cnt;i++){
		while (DB(cross(p[ans[(i+1)]],p[ans[(m+1)]],p[ans[i]])-cross(p[ans[(i+1)]],p[ans[m]],p[ans[i]])) >0)
  		m=(m+1)%cnt;
        while (DB(dot(p[ans[(q+1)]],p[ans[(i+1)]],p[ans[i]])-dot(p[ans[q]],p[ans[(i+1)]],p[ans[i]])) >0)
        q=(q+1)%cnt;
        if (i==0)
		r=q;
        while(DB(dot(p[ans[(r+1)]],p[ans[(i+1)]],p[ans[i]])-dot(p[ans[r]],p[ans[(i+1)]],p[ans[i]])) <= 0)
        r=(r+1)%cnt;
        a=cross(p[ans[(i+1)]],p[ans[m]],p[ans[i]]);
        b=dot(p[ans[q]],p[ans[(i+1)]],p[ans[i]])-dot(p[ans[r]],p[ans[(i+1)]],p[ans[i]]);
        c=dot(p[ans[(i+1)]],p[ans[(i+1)]],p[ans[i]]);
        anst=min(anst,a*b/c);
    }
    return anst;
}

int main (){  
    while (scanf("%d",&n) && n!=0) {  
        for (int i=0;i<n;i++)
		scanf("%lf%lf",&p[i].x,&p[i].y);
		sort(p,p+n,cmp);   
        forTU();  
        printf("%.4lf\n",roating());  
    }  
    return 0;  
}