// https://www.youtube.com/watch?v=R0P_f0gXXqs
// I could feel your heartbeat
// I could feel somewhere you’re looking down
// ‘Cause it’s you who I’m loving
// And it’s you that I want in need

#ifndef ONLINE_JUDGE
#include "templates/debug.hpp"
#else
#define debug(...)
#endif

#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using u64 = uint64_t;

void solve() {
    int n; cin >> n;
    double ans = 0.0;
    vector<pair<int, int>> p(n);
    for (int i = 0; i < n; i++) {
        cin >> p[i].first >> p[i].second;
    }
    vector<double> angles(n);
    for (int i = 0; i < n; i++) {
        double x1 = p[(i-1+n)%n].first - p[i].first;
        double y1 = p[(i-1+n)%n].second - p[i].second;
        double x2 = p[(i+1)%n].first - p[i].first;
        double y2 = p[(i+1)%n].second - p[i].second;
        angles[i] = abs(atan2(y2, x2) - atan2(y1, x1));
    }
    using numbers::pi;
    for (int i = 0; i < n; i++) {
        double a = angles[i], b = angles[(i+1)%n];
        if (a + b < pi) {
            ans += (pi - a - b) / pi;
        }
    }
    cout << fixed << setprecision(10) << ans << endl;
}

// Make bold hypotheses and verify carefully
int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    };
}