#include<iostream>

#include<cstdio>

#include<cmath>

#include<cstdlib>

#include<cstring>

#include<algorithm>

using namespace std;

#define ll long long

#define N 100010

#define vector point

#define double long double

char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<''||c>'')) c=getchar();return c;}

int gcd(int n,int m){return m==?n:gcd(m,n%m);}

int read()

{

    int x=,f=;char c=getchar();

    while (c<''||c>'') {if (c=='-') f=-;c=getchar();}

    while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();

    return x*f;

}

const double eps=1E-;

struct point

{

    double x,y;

    vector operator +(const vector&a) const

    {

        return (vector){x+a.x,y+a.y};

    }

    vector operator -(const vector&a) const

    {

        return (vector){x-a.x,y-a.y};

    }

    double operator *(const vector&a) const

    {

        return x*a.y-y*a.x;

    }

    vector operator *(const double&a) const

    {

        return (vector){x*a,y*a};

    }

}a[N];

struct line

{

    point a;vector p;

    bool operator <(const line&a) const

    {

        return atan2(p.x,p.y)>atan2(a.p.x,a.p.y);

    }

}b[N<<];

int n,m,head,tail;

point p[N<<];

line q[N<<];

double area;

bool onright(point a,line p)

{

    return (a-p.a)*p.p>=;

}

point cross(line a,line b)

{

    return a.a+a.p*((b.p*(b.a-a.a))/(b.p*a.p));

}

int main()

{

#ifndef ONLINE_JUDGE

    freopen("bzoj4445.in","r",stdin);

    freopen("bzoj4445.out","w",stdout);

    const char LL[]="%I64d\n";

#else

    const char LL[]="%lld\n";

#endif

    n=read();

    for (int i=;i<n;i++) a[i].x=read(),a[i].y=read();

    for (int i=;i<n;i++) area+=a[i]*a[(i+)%n];

    for (int i=;i<n;i++) m++,b[m].a=a[i],b[m].p=a[(i+)%n]-a[i];

    for (int i=;i<n;i++)

    {

        double A=(a[].y-a[].y+a[(i+)%n].y-a[i].y),B=(a[].x-a[].x+a[i].x-a[(i+)%n].x),C=(a[i]*a[(i+)%n]-a[]*a[]);

        m++;b[m].p=(vector){-B,A};

        if (fabs(B)>0.5) b[m].a=(point){,C/B};

        else b[m].a=(point){C/A,};

    }

    sort(b+,b+m+);

    head=tail=;q[]=b[];

    for (int i=;i<=m;i++)

    {

        while (head<tail&&onright(p[tail],b[i])) tail--;

        while (head<tail&&onright(p[head+],b[i])) head++;

        q[++tail]=b[i];

        if (fabs(q[tail].p*q[tail-].p)<eps)

        {

            tail--;

            if (onright(q[tail].a,b[i])) q[tail]=b[i];

        }

        if (head<tail) p[tail]=cross(q[tail],q[tail-]);

    }

    while (head<tail&&onright(p[tail],q[head])) tail--;

    p[head]=cross(q[head],q[tail]);

    double area2=;

    for (int i=head;i<tail;i++)

    area2+=p[i]*p[i+];area2+=p[tail]*p[head];

#undef double

    printf("%.4f",(double)(area2/area));

    return ;

}