//Date: 2024-09-07 16:47:13
#include<bits/stdc++.h>
using namespace std;
#define int long long
inline int rd() {
    int s=0,m=0;char ch=getchar();
    while(!isdigit(ch)) {if(ch=='-')m=1;ch=getchar();}
    while( isdigit(ch)) s=(s<<3)+(s<<1)+(ch^48),ch=getchar();
    return m?-s:s;
}
bool MBE;
namespace SOLVER {
const double pi=acos(-1);
int n,x[200005],y[200005];double a[200005],b[200005],ans;
void MAIN() {
    cin>>n;for(int i=0;i<n;i++) x[i]=rd(),y[i]=rd();x[n]=x[0],y[n]=y[0];
    for(int i=0;i<n;i++) a[i]=atan2(y[i+1]-y[i],x[i+1]-x[i]);a[n]=a[0];
    if(a[0]-atan2(y[n-1]-y[0],x[n-1]-x[0])<0) {//逆时针
        for(int i=0;i<n;i++) {
            b[i]=a[(i+n-1)%n]-a[i];
            while(b[i]<=0) b[i]+=pi;
            while(b[i]>pi) b[i]-=pi;
            // printf("%.12lf\n",b[i]);
        }
        for(int i=0;i<n;i++) ans+=max(0.0,pi-b[(i+n-1)%n]-b[i]);
        printf("%.12lf\n",ans/pi);
    }
    else {//顺时针
        for(int i=0;i<n;i++) {
            b[i]=a[i]-a[(i+n-1)%n];
            while(b[i]<=0) b[i]+=pi;
            while(b[i]>pi) b[i]-=pi;
            // printf("%.12lf\n",b[i]);
        }
        for(int i=0;i<n;i++) ans+=max(0.0,pi-b[(i+n-1)%n]-b[i]);
        printf("%.12lf\n",ans/pi);
    }
}
}
bool MED;
signed main() {
    //freopen(".in","r",stdin);freopen(".out","w",stdout);
    for(int tt=1;tt;tt--) SOLVER::MAIN();
    cerr<<(&MBE-&MED)/1024<<" KB, "<<1000*clock()/CLOCKS_PER_SEC<<" ms\n";
    return 0;
}