#include <bits/stdc++.h>
using namespace std;
typedef double db;
const db EPS = 1e-9;
#define rep(i,j,k) for(int i = j;i < k;i++)
inline int sign(db a) { return a < -EPS ? -1 : a > EPS; }

inline int cmp(db a, db b){ return sign(a-b); }

struct P {
	db x, y;
	P() {}
	P(db _x, db _y) : x(_x), y(_y) {}
	P operator+(P p) { return {x + p.x, y + p.y}; }
	P operator-(P p) { return {x - p.x, y - p.y}; }
	P operator*(db d) { return {x * d, y * d}; }
	P operator/(db d) { return {x / d, y / d}; }
	
	bool operator<(P p) const { 
		int c = cmp(x, p.x);
		if (c) return c == -1;
		return cmp(y, p.y) == -1;
	}
	
	bool operator==(P o) const{
		return cmp(x,o.x) == 0 && cmp(y,o.y) == 0;
	}
	db alpha() { return atan2(y, x); }
	db dot(P p) { return x * p.x + y * p.y; }
	void read() { cin>>x>>y; }
	void write() {cout<<"("<<x<<","<<y<<")"<<endl;}
	db abs() { return sqrt(abs2());}
	db abs2() { return x * x + y * y; }
	P rot(db an){ return {x*cos(an) - y*sin(an),x*sin(an) + y*cos(an)}; }
};

#define cross(p1,p2,p3) ((p2.x-p1.x)*(p3.y-p1.y)-(p3.x-p1.x)*(p2.y-p1.y))
#define crossOp(p1,p2,p3) sign(cross(p1,p2,p3))

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cout << fixed << setprecision(10);
	int n;cin >> n;
	vector <P> a(n * 2);
	for(int i = 0;i < n;i++) {
		a[i].read();
		a[i + n] = a[i];
	}
	db ans = 0,pi = acos(-1);
	auto getdegree = [&] (P x,P y) {
		db deg = x.dot(y) / x.abs2() / y.abs2();
		return deg < 0 ? pi + acos(deg) : acos(deg);
	};
	for(int i = 1;i <= n;i++) {
		P x = a[i - 1] - a[i],y = a[i + 2] - a[i + 1],mid = a[i + 1] - a[i];
		db deg = acos(x.dot(y) / x.abs() / y.abs());
//		x.write();y.write();
//		cout << x.dot(y) << ' ' << x.abs() << ' ' << y.abs() << '\n';
		if(getdegree(x,mid) + getdegree(y,mid * (-1.0)) > pi) continue;
		if(deg < 0) continue;
		ans += deg;
//		cout << deg << ' ' << ans << ' ' << i << '\n';
	}
//	cout << acos(-1) << ' ';
	cout << ans / pi << '\n';
	return 0;
}