#include<bits/stdc++.h>
#define endl '\n'
using namespace std;
#define int long long

const int N=1e6+5;
#define double long double
struct Point{
    int x,y;
    int dis2(const Point&a)const{
        return (x-a.x)*(x-a.x)+(y-a.y)*(y-a.y);
    }
    double dis(const Point&a)const{
        return sqrt(dis2(a));
    }
}p[N];
const double pi=acos(-1);
double ang[N];
void solve(){
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>p[i].x>>p[i].y;
    }
    for(int i=0;i<n;i++){
        int a2=p[i].dis2(p[(i-1+n)%n]),b2=p[i].dis2(p[(i+1)%n]),c2=p[(i-1+n)%n].dis2(p[(i+1)%n]);
        double a=sqrt(a2),b=sqrt(b2);
        ang[i]=acos((a2+b2-c2)/(2.0l*a*b));
    }
    double ans=0;
    for(int i=0;i<n;i++){
        ans+=max(0.l,pi-ang[i]-ang[(i+1)%n]);
    }
    cout<<fixed<<setprecision(10)<<ans/pi<<endl;
}

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int Te=1;
//    cin>>Te;
    while(Te--){
        solve();
    }
}