#include <bits/stdc++.h>

using namespace std;

const long double PI = acos(-1);

typedef pair<int, int> pi;
typedef long long ll;
typedef long double ld;

pi operator -(const pi &a, const pi &b) {
    return {a.first - b.first, a.second - b.second};
}

int main() {
    int n;
    cin >> n;
    vector<pi> points(n);
    for (auto& point : points) {
        cin >> point.first >> point.second;
    }

    ld ans = 0.0;
    for (int i = 0; i < n; ++i) {
        int prev = (i - 1 + n) % n;
        int nxt1 = (i + 1) % n;
        int nxtt = (i + 2) % n;

        pi vector1 = points[prev] - points[i];
        pi vector2 = points[nxt1] - points[i];
        pi vector3 = points[nxtt] - points[nxt1];
        pi vector4 = points[i] - points[nxt1];

        ll dot1 = ll(vector1.first) * vector2.first + ll(vector1.second) * vector2.second;
        ll dot2 = ll(vector3.first) * vector4.first + ll(vector3.second) * vector4.second;
        ld length1 = sqrtl(ll(vector1.first) * vector1.first + ll(vector1.second) * vector1.second);
        ld length2 = sqrtl(ll(vector2.first) * vector2.first + ll(vector2.second) * vector2.second);
        ld length3 = sqrtl(ll(vector3.first) * vector3.first + ll(vector3.second) * vector3.second);
        ld length4 = sqrtl(ll(vector4.first) * vector4.first + ll(vector4.second) * vector4.second);

        ld angle1 = acos(dot1 / (length1 * length2));
        ld angle2 = acos(dot2 / (length3 * length4));

        ans += max((ld)0, PI - (angle1 + angle2));
    }

    cout << fixed << setprecision(18) << ans / PI << '\n';

    return 0;
}