#include <bits/stdc++.h>
using namespace std;
using ui = unsigned int;
using ull = unsigned long long;
using ll = long long;
#define endl '\n'
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int maxn = 2e5 + 10;
const int mod = 1000000007;
#define inl inline
#define fr(i, a, b) for (int i = a; i <= b; i++)
#define ford(i, a, b) for (int i = a; i >= b; i--)
#define forall(i, a) for (auto &i : a)

/**
   ____         ___ _____
  / ___| _   _ / _ \___ /
  \___ \| | | | | | ||_ \
   ___) | |_| | |_| |__) |
  |____/ \__, |\___/____/
         |___/
*/
istream &operator>>(istream &in, vector<int> &v)
{
    for (auto &i : v)
        in >> i;
    return in;
}
ostream &operator<<(ostream &out, vector<int> &v)
{
    for (auto &i : v)
        out << i << " ";
    return out;
}
bool _output = 0;

using db = long double;
db make(pii a, pii b)
{
    db len_a = sqrt(a.first * a.first + a.second * a.second);
    db len_b = sqrt(b.first * b.first + b.second * b.second);
    db dot = a.first * b.first + a.second * b.second;
    db cos = dot / (len_a * len_b);
    // cout << cos << endl;
    return acos(cos);
}
pii get(pii a, pii b)
{
    return {a.first - b.first, a.second - b.second};
}
void solve()
{
    int n;
    cin >> n;
    using pdd = pair<db, db>;
    vector<pdd> a(n);
    for (auto &i : a)
        cin >> i.first >> i.second;
    db ans = 0;
    vector<db> b(n);
    for (int i = 0; i < n; i++)
    {
        auto p1 = a[i];
        auto p2 = a[(i + 1) % n];
        auto p3 = a[(i + 2) % n];
        auto t1 = get(p1, p2);
        auto t2 = get(p3, p2);
        b[i] = make(t1, t2);
    }
    const db PI = acos(-1);
    for (int i = 0; i < n; i++)
    {
        db p1 = b[i], p2 = b[(i + 1) % n];
        if (p1 + p2 < PI)
        {
            ans += PI - p1 - p2;
        }
    }
    ans /= PI;
    cout << fixed << setprecision(10) << ans << endl;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int _ = 1;
    if (_output)
        cin >> _;
    while (_--)
        solve();
    return 0;
}