#include <stdio.h>
#include <random>
#include <queue>
#include <time.h>
std::mt19937_64 rng(time(0));
#include <math.h>
#include <time.h>
#include <assert.h>
#include <string.h>
#include <algorithm>
#include <vector>
#include <bitset>
#include <set>
#define int long long
#define ld(x) printf("%lld\n",x)
// #define int unsigned
using std::vector;
using vi=vector<int>;
using pi=std::pair<int,int>;
using vpi=vector<pi>;
#define x first
#define y second
const int mod=998244353;
inline int min(int a,int b){return a>b?b:a;}
inline int max(int a,int b){return a<b?b:a;}
inline int read()
{
    int num=0,f=1;char c=getchar();
    while(c<48||c>57){if(c=='-')f=-1;c=getchar();}
    while(c>47&&c<58)num=num*10+(c^48),c=getchar();
    return num*f;
}

typedef int arr[2000005];
int a[1234567],b[1234567];
double c[1234567];
double test(double x1,double y1,double x2,double y2,double x3,double y3)
{
	return acos(((x1-x2)*(x1-x3)+(y1-y2)*(y1-y3))/(hypot(x1-x2,y1-y2)*hypot(x1-x3,y1-y3)));
}
signed main()
{
	int n=read();
	for(int i=0;i<n;i++)a[i]=read(),b[i]=read();
	for(int i=0;i<n;i++)
	{
		c[i]=test(a[(i+1)%n],b[(i+1)%n],a[i],b[i],a[(i+2)%n],b[(i+2)%n]);
		// printf("%.12lf\n",c[i]/acos(-1));
	}
	double res=0,pi=acos(-1);
	for(int i=0;i<n;i++)
		res+=std::max(0.,pi-c[i]-c[(i+1)%n]);
	printf("%.12lf\n",res/pi);
	return 0;
}