//Author: Kevin5307
#include<bits/stdc++.h>
//#pragma GCC optimize("O2")
using namespace std;
#define ll long long
#define ull unsigned ll
#define pb emplace_back
#define mp make_pair
#define ALL(x) (x).begin(),(x).end()
#define rALL(x) (x).rbegin(),(x).rend()
#define srt(x) sort(ALL(x))
#define rev(x) reverse(ALL(x))
#define rsrt(x) sort(rALL(x))
#define sz(x) (int)(x.size())
#define inf 0x3f3f3f3f
#define pii pair<int,int>
#define lb(v,x) (int)(lower_bound(ALL(v),x)-v.begin())
#define ub(v,x) (int)(upper_bound(ALL(v),x)-v.begin())
#define uni(v) v.resize(unique(ALL(v))-v.begin())
void die(string S){puts(S.c_str());exit(0);}
const long double pi=acosl(-1);
int x[200200],y[200200];
long double angle[200200];
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int n;
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>x[i]>>y[i];
	x[n+1]=x[1];
	y[n+1]=y[1];
	x[0]=x[n];
	y[0]=y[n];
	long double ans=0.0;
	for(int i=1;i<=n;i++)
	{
		int ax=x[i-1]-x[i];
		int ay=y[i-1]-y[i];
		int bx=x[i+1]-x[i];
		int by=y[i+1]-y[i];
		ll prod=(1ll*ax*bx+1ll*ay*by);
		long double lena=sqrtl(1ll*ax*ax+1ll*ay*ay);
		long double lenb=sqrtl(1ll*bx*bx+1ll*by*by);
		long double cosv=prod/lena/lenb;
		angle[i]=acosl(cosv);
	}
	angle[0]=angle[n];
	for(int i=1;i<=n;i++)
		if(angle[i-1]+angle[i]<pi)
			ans+=(pi-angle[i]-angle[i-1]);
	cout<<fixed<<setprecision(15)<<ans/pi<<endl;
	return 0;
}