LG4250

#include<bits/stdc++.h>

using namespace std;

#define gc c=getchar()
#define r(x) read(x)
#define db double

template<typename T>
inline void read(T&x){
    x=0;T k=1;char gc;
    while(!isdigit(c)){if(c=='-')k=-1;gc;}
    while(isdigit(c)){x=x*10+c-'0';gc;}x*=k;
}

const int N=2e5+7;
const db eps=1e-10;
inline int dcmp(const db &a){
    if(fabs(a)<eps)return 0;
    return a<0?-1:1;
}

struct Point{db x,y;};
#define Vec Point
inline Vec operator +(const Vec &a,const Vec &b){return Vec{a.x+b.x,a.y+b.y};}
inline Vec operator -(const Vec &a,const Vec &b){return Vec{a.x-b.x,a.y-b.y};}
inline Vec operator *(const Vec &a,const db &b){return Vec{a.x*b,a.y*b};}
inline db operator *(const Vec &a,const Vec &b){return a.x*b.y-a.y*b.x;}
inline db Angle(const Vec &a){return atan2(a.y,a.x);}

struct Line{
    Point S;
    Vec V;
    db ang;
    inline Line (){}
    inline Line (const Point &s,const Point &v):S(s),V(v),ang(Angle(v)){}
};

inline bool operator < (const Line &a,const Line &b){
    double alpha=a.ang-b.ang;
    if(dcmp(alpha))return dcmp(alpha)==-1;
    return dcmp(a.V*(b.S-a.S))==-1;
}

inline Point cross(const Line &a,const Line &b){
    Vec u=a.S-b.S;
    db t=(u*b.V)/(b.V*a.V);
    return a.S+a.V*t;
}

inline bool OnRight(const Line &a,const Point &b){
    return dcmp((b-a.S)*a.V)==1;
}

int head,tail;
Line Q[N];

inline int Half(Line *A,int n,Point *B){
    sort(A+1,A+n+1);
    Q[head=tail=0]=A[1];
    for(int i=2;i<=n;++i){
        if(!dcmp(A[i].ang-A[i-1].ang))continue;
        while(head<tail&&OnRight(A[i],cross(Q[tail],Q[tail-1])))
        --tail;
        while(head<tail&&OnRight(A[i],cross(Q[head],Q[head+1])))
        ++head;
        Q[++tail]=A[i];
    }
    while(head<tail&&OnRight(Q[head],cross(Q[tail],Q[tail-1])))
    --tail;
    while(head<tail&&OnRight(Q[tail],cross(Q[head],Q[head+1])))
    ++head;
    int m=0;
    for(int i=head;i<tail;++i){
        B[m++]=cross(Q[i],Q[i+1]);
    }
    B[m++]=cross(Q[head],Q[tail]);
    return m;
}

Line L[N];
Point P[N];

int main(){
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    int n,tot=0;r(n);
    for(int i=0;i<n;++i){
        r(P[i].x),r(P[i].y);
    }
    db sum=0;
    for(int i=2;i<n;++i){
        sum+=(P[i-1]-P[0])*(P[i]-P[0]);
    }
    P[n]=P[0];
    for(int i=0;i<n;++i){
        L[++tot]=Line(P[i],P[i+1]-P[i]);
    }
    for(int i=1;i<n;++i){
        db a=P[0].y-P[1].y-P[i].y+P[i+1].y;
        db b=P[1].x-P[0].x+P[i].x-P[i+1].x;
        db c=P[0].x*P[1].y-P[0].y*P[1].x-P[i].x*P[i+1].y+P[i].y*P[i+1].x;
        if(dcmp(b))L[++tot]=Line(Point{0,-c/b},Vec{-b,a});
        else if(dcmp(a))L[++tot]=Line(Point{-c/a,0},Vec{-b,a});
        else if(c>0)return puts("0.0000"),0;
    }
    n=Half(L,tot,P);
    db ans=0;
    for(int i=2;i<n;++i){
        ans+=(P[i-1]-P[0])*(P[i]-P[0]);
    }
    printf("%.4lf",ans/sum);
    return 0;
}