#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005,INF=15<<26;

//幾何ライブラリ(整数)

class Point{
public:
    ll x,y;
    
    Point(ll x=0,ll y=0):x(x),y(y){}
    
    Point operator + (Point p){return Point(x+p.x,y+p.y);}
    Point operator - (Point p){return Point(x-p.x,y-p.y);}
    Point operator * (ll a){return Point(a*x,a*y);}
    
    double norm(){return x*x+y*y;}
    
    bool operator < (const Point &p)const{
        return x<p.x||(x==p.x&&y<p.y);
    }
    
    bool operator == (const Point &p)const{
        return x==p.x&&y==p.y;
    }
};

typedef Point Vector;

ll norm(Vector a){
    return a.x*a.x+a.y*a.y;
}

ll dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

ll cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

struct Segment{
    Point p1,p2;
};

bool isOrthogonal(Vector a,Vector b){
    return dot(a,b)==0;
}

bool isOrthogonal(Point a1,Point a2,Point b1,Point b2){
    return isOrthogonal(a1-a2,b1-b2);
}

bool isOrthogonal(Segment s1,Segment s2){
    return dot(s1.p2-s1.p1,s2.p2-s2.p1)==0;
}

bool isParallel(Vector a,Vector b){
    return cross(a,b)==0;
}

bool isParallel(Point a1,Point a2,Point b1,Point b2){
    return isParallel(a1-a2,b1-b2);
}

bool isParallel(Segment s1,Segment s2){
    return cross(s1.p2-s1.p1,s2.p2-s2.p1)==0;
}

//p0,p1,p2の順に見たときどうなるか？

static const int counter_clockwise=1;
static const int clockwise=-1;
static const int online_back=2;
static const int online_front=-2;
static const int on_segment=0;

int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    
    if(cross(a,b)>0) return counter_clockwise;
    if(cross(a,b)<0) return clockwise;
    if(dot(a,b)<0) return online_back;
    if(a.norm()<b.norm()) return online_front;
    
    return on_segment;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
    return(ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
    return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

bool overlap(Segment s1,Segment s2){
    int a=ccw(s1.p1,s1.p2,s2.p1),b=ccw(s1.p1,s1.p2,s2.p2);
    if(a&1||b&1) return 0;
    if(a==2){
        if(b==-2||(b==0&&!(s2.p2==s1.p1))) return 1;
        else return 0;
    }
    if(a==-2){
        if(b==2||(b==0&&!(s2.p2==s1.p2))) return 1;
        else return 0;
    }
    if(a==0){
        if(s1.p1==s2.p1){
            if(b!=2) return 1;
            else return 0;
        }
        else if(s1.p2==s2.p1){
            if(b!=-2) return 1;
            else return 0;
        }
        else return 1;
    }
    return 0;
}
//s1とs2の共通の線分(長さ0より大きい)があるかどうか

typedef Segment Line;

//ネットの適当を書いたのであってるか全く知りません→あってそう

class Circle{
public:
    Point c;
    ll r;
    Circle(Point c=Point(),ll r=0.0):c(c),r(r){}
};

typedef vector<Point> Polygon;

/*
 IN 2
 ON 1
 OUT 0
 */

int contains(Polygon g,Point p){
    int n=int(g.size());
    bool x=false;
    for(int i=0;i<n;i++){
        Point a=g[i]-p,b=g[(i+1)%n]-p;
        if(a.y>b.y) swap(a,b);
        if(a.y<=0&&0<b.y&&cross(a,b)<0) x=!x;
        if(abs(cross(a,b))<=0&&dot(a,b)<=0) return 1;
    }
    return (x?2:0);
}
//ayasii

Polygon andrewScan(Polygon s,bool ok){
    Polygon u,l;
    sort(all(s));
    
    if(int(s.size())<3) return s;
    int n=int(s.size());
    
    u.push_back(s[0]);
    u.push_back(s[1]);
    
    l.push_back(s[n-1]);
    l.push_back(s[n-2]);
    
    if(ok){
        for(int i=2;i<n;i++){
            for(int j=int(u.size());j>=2&&ccw(u[j-2],u[j-1],s[i])==counter_clockwise;j--){
                u.pop_back();
            }
            u.push_back(s[i]);
        }
        
        for(int i=int(s.size())-3;i>=0;i--){
            for(int j=int(l.size());j>=2&&ccw(l[j-2],l[j-1],s[i])==counter_clockwise;j--){
                l.pop_back();
            }
            l.push_back(s[i]);
        }
    }
    
    if(!ok){
        for(int i=2;i<n;i++){
            for(int j=int(u.size());j>=2&&ccw(u[j-2],u[j-1],s[i])!=clockwise;j--){
                u.pop_back();
            }
            u.push_back(s[i]);
        }
        
        for(int i=int(s.size())-3;i>=0;i--){
            for(int j=int(l.size());j>=2&&ccw(l[j-2],l[j-1],s[i])!=clockwise;j--){
                l.pop_back();
            }
            l.push_back(s[i]);
        }
    }
    
    reverse(all(l));
    
    for(int i=int(u.size())-2;i>=1;i--) l.push_back(u[i]);
    
    return l;
}//ok==1なら辺の上も含める

ll area(Polygon P){
    ll sum=0;
    for(int i=0;i<si(P);i++){
        sum+=cross(P[i],P[(i+1)%si(P)]);
    }
    return abs(sum);
}

// 倍

ll gcd(ll a,ll b){
    if(b==0) return a;
    return gcd(b,a%b);
}

pair<Point,Vector> perpendicular_bisector(Point a,Point b){
    Point c;
    c.x=(a.x+b.x)/2;
    c.y=(a.y+b.y)/2;
    Vector v=b-c;
    swap(v.x,v.y);
    v.x*=-1;
    
    Point p=c;
    if(v.x==0){
        v.y=1;
        p.y=0;
    }
    else if(v.y==0){
        v.x=1;
        p.x=0;
    }
    else{
        if(v.x<0){
            v.x*=-1;
            v.y*=-1;
        }
        ll g=gcd(abs(ll(v.x)),abs(ll(v.y)));
        v.x/=g;
        v.y/=g;
        if(p.x>=0){
            ll d=p.x/v.x;
            p=p-v*d;
        }else{
            ll d=abs(p.x)/v.x;
            p=p+v*d;
            
            if(p.x<0){
                p=p+v;
            }
        }
    }
    
    return mp(p,v);
}
//2倍するなりして整数にしておくこと


int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll N;cin>>N;
    if(N==3){
        cout<<1<<endl;
        return 0;
    }
    
    vector<Point> P(N);
    for(int i=0;i<N;i++) cin>>P[i].x>>P[i].y;
    
    double res=0;
    
    for(int i=0;i<N;i++){
        Point a=P[i],b=P[(i+1)%N],c=P[(i+2)%N],d=P[(i+3)%N];
        double sum=0;
        sum+=acos((double)(dot(a-b,c-b))/sqrt(norm(a-b))/sqrt(norm(c-b)));
        sum+=acos((double)(dot(b-c,d-c))/sqrt(norm(b-c))/sqrt(norm(d-c)));
        if(sum<acos(-1)) res+=acos(-1)-sum;
    }
    
    res/=acos(-1);
    
    cout<<fixed<<setprecision(25)<<res<<endl;
    
    return 0;
    
    /*
     
     mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
     
     while(1){
     ll N=rng()%100+1;
     vector<Point> P(N);
     for(int i=0;i<N;i++){
     ll x=abs(ll(rng()%200))-100,y=abs(ll(rng()%200))-100;
     P[i]={x,y};
     }
     P=andrewScan(P,0);
     N=si(P);
     /*
     P.resize(N);
     P[0]={0,0};
     P[1]={1,1};
     P[2]={1,2};
     P[3]={0,3};
     N=4;
     //if(N>=5) continue;
     if(N!=5) continue;
     ll s=0,t=0;
     
     vector<double> VV;
     for(ll q=0;q<10000;q++){
     ll x=abs((ll)(rng()%200000000))-100000000,y=abs((ll)(rng()%200000000))-100000000;
     if(x*x+y*y<=100000000LL*100000000){
     t++;
     vl S(N);
     for(int i=0;i<N;i++){
     Vector v=P[(i+1)%N]-P[i],vv={x,y};
     S[i]=abs(cross(v,vv));
     }
     sort(all(S));
     bool f=false;
     
     for(int bit=0;bit<(1<<N);bit++){
     ll sum=0;
     for(int i=0;i<N;i++){
     if(bit&(1<<i)) sum+=S[i];
     }
     if(sum%2==0&&binary_search(all(S),sum/2)) f=true;
     }
     
     if(f){
     s++;
     VV.pb(atan2(y,x));
     }
     }
     }
     //if(s==t||s==0) continue;
     double ss=0;
     for(int i=0;i<N;i++){
     Point a=P[i],b=P[(i+1)%N],c=P[(i+2)%N],d=P[(i+3)%N];
     Vector e=d-c,f=a-b;
     Vector O={0,0};
     int cc=ccw(e,O,f);
     if(cc==counter_clockwise){
     ss+=acos((double)(dot(f,e))/sqrt(norm(e))/sqrt(norm(f)));
     }
     }
     ss/=M_PI;
     cout<<N<<" "<<s<<" "<<t<<" "<<(double)(s)/t<<" "<<ss<<endl;
     continue;
     sort(all(VV));
     for(auto [a,b]:P) cout<<"("<<a<<","<<b<<")"<<endl;
     int i=0;
     while(i<si(VV)){
     int j=i;
     while(j+1<si(VV)&&VV[j+1]-VV[j]<=0.05) j++;
     cout<<VV[i]<<" "<<VV[j]<<endl;
     i=j+1;
     }
     //return 0;
     }
     
     */
}