#include <bits/stdc++.h>

using namespace std;
typedef long double ld;
const ld PI = acosl(-1);
ld cross(const pair<int, int>& p1, const pair<int, int>& p2) {
    return ld(p1.first * p2.second - p1.second * p2.first);
}

ld dot(const pair<int, int>& p1, const pair<int, int>& p2) {
    return ld(p1.first * p2.first + p1.second * p2.second);
}

pair<int, int> sub(const pair<int, int>& p1, const pair<int, int>& p2) {
    return make_pair(p1.first - p2.first, p1.second - p2.second);
}

int main() {
    int n;
    cin >> n;

    vector<pair<int, int>> pi(n);

    for (int i = 0; i < n; ++i) {
        cin >> pi[i].first >> pi[i].second;
    }
    ld ans = 0.0;
    const ld PI = acosl(-1.0);  

    for (int i = 0; i < n; ++i) {
        int prev = (i - 1 + n) % n;
        int cur = (i + 1) % n;
        int nxt = (i + 2) % n;

        pair<int, int> vector1 = sub(pi[prev], pi[i]);
        pair<int, int> vector2 = sub(pi[cur], pi[i]);
        pair<int, int> vector3 = sub(pi[nxt], pi[cur]);
        pair<int, int> vector4 = sub(pi[i], pi[cur]);

        ld len1 = sqrtl(dot(vector1, vector1));
        ld len2 = sqrtl(dot(vector2, vector2));
        ld len3 = sqrtl(dot(vector3, vector3));
        ld len4 = sqrtl(dot(vector4, vector4));

        ld angle1 = acosl(dot(vector1, vector2) / (len1 * len2));
        ld angle2 = acosl(dot(vector3, vector4) / (len3 * len4));

        ans += max(0.0L, PI - angle1 - angle2);
    }
    cout << fixed << setprecision(18) << ans / PI << endl;

    return 0;
}