#include "bits/stdc++.h"

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i < (n); ++i)
#define rep1n(i, n) for (int i = 1; i <= (n); ++i)
#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
#define pb push_back
#define eb emplace_back
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define each(x, a) for (auto &x : a)
#define ar array
#define vec vector
#define range(i, n) rep(i, n)

using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;

using vi = vector<int>;
using vl = vector<ll>;
using vpi = vector<pair<int, int>>;
using vvi = vector<vi>;

int Bit(int mask, int b) { return (mask >> b) & 1; }

template<class T>
bool ckmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool ckmax(T &a, const T &b) {
    if (b > a) {
        a = b;
        return true;
    }
    return false;
}

// [l, r)
template<typename T, typename F>
T FindFirstTrue(T l, T r, const F &predicat) {
    --l;
    while (r - l > 1) {
        T mid = l + (r - l) / 2;
        if (predicat(mid)) {
            r = mid;
        } else {
            l = mid;
        }
    }
    return r;
}


template<typename T, typename F>
T FindLastFalse(T l, T r, const F &predicat) {
    return FindFirstTrue(l, r, predicat) - 1;
}

const ll INF = 2e18;
const int INFi = 1e9;
const int LG = 49;
const int N = 1e4 + 4;

template<typename T>
int normalize(T value, int mod) {
    if (value < -mod || value >= 2 * mod) value %= mod;
    if (value < 0) value += mod;
    if (value >= mod) value -= mod;
    return value;
}

template<int mod>
struct static_modular_int {
    using mint = static_modular_int<mod>;

    int value;

    static_modular_int() : value(0) {}

    static_modular_int(const mint &x) : value(x.value) {}

    template<typename T, typename U = std::enable_if_t<std::is_integral<T>::value>>
    static_modular_int(T value) : value(normalize(value, mod)) {}

    template<typename T>
    mint power(T degree) const {
        degree = normalize(degree, mod - 1);
        mint prod = 1, a = *this;
        for (; degree > 0; degree >>= 1, a *= a)
            if (degree & 1)
                prod *= a;

        return prod;
    }

    mint inv() const {
        return power(-1);
    }

    mint &operator=(const mint &x) {
        value = x.value;
        return *this;
    }

    mint &operator+=(const mint &x) {
        value += x.value;
        if (value >= mod) value -= mod;
        return *this;
    }

    mint &operator-=(const mint &x) {
        value -= x.value;
        if (value < 0) value += mod;
        return *this;
    }

    mint &operator*=(const mint &x) {
        value = int64_t(value) * x.value % mod;
        return *this;
    }

    mint &operator/=(const mint &x) {
        return *this *= x.inv();
    }

    friend mint operator+(const mint &x, const mint &y) {
        return mint(x) += y;
    }

    friend mint operator-(const mint &x, const mint &y) {
        return mint(x) -= y;
    }

    friend mint operator*(const mint &x, const mint &y) {
        return mint(x) *= y;
    }

    friend mint operator/(const mint &x, const mint &y) {
        return mint(x) /= y;
    }

    mint &operator++() {
        ++value;
        if (value == mod) value = 0;
        return *this;
    }

    mint &operator--() {
        --value;
        if (value == -1) value = mod - 1;
        return *this;
    }

    mint operator++(int) {
        mint prev = *this;
        value++;
        if (value == mod) value = 0;
        return prev;
    }

    mint operator--(int) {
        mint prev = *this;
        value--;
        if (value == -1) value = mod - 1;
        return prev;
    }

    mint operator-() const {
        return mint(0) - *this;
    }

    bool operator==(const mint &x) const {
        return value == x.value;
    }

    bool operator!=(const mint &x) const {
        return value != x.value;
    }

    bool operator<(const mint &x) const {
        return value < x.value;
    }

    template<typename T>
    explicit operator T() {
        return value;
    }

    friend std::istream &operator>>(std::istream &in, mint &x) {
        std::string s;
        in >> s;
        x = 0;
        for (const auto c: s)
            x = x * 10 + (c - '0');

        return in;
    }

    friend std::ostream &operator<<(std::ostream &out, const mint &x) {
        return out << x.value;
    }

    static int primitive_root() {
        if constexpr (mod == 1'000'000'007) return 5;
        if constexpr (mod == 998'244'353) return 3;
        if constexpr (mod == 786433) return 10;

        static int root = -1;
        if (root != -1)
            return root;

        std::vector<int> primes;
        int value = mod - 1;
        for (int i = 2; i * i <= value; i++)
            if (value % i == 0) {
                primes.push_back(i);
                while (value % i == 0)
                    value /= i;
            }

        if (value != 1) primes.push_back(value);
        for (int r = 2;; r++) {
            bool ok = true;
            for (auto p: primes) {
                if ((mint(r).power((mod - 1) / p)).value == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return root = r;
        }
    }
};

constexpr int MOD = 1'000'000'007;
// constexpr int MOD = 998'244'353;
using mint = static_modular_int<MOD>;

const ld PI = atan2(0, -1);

ld normalize(ld ang) {
    while (ang < 0) ang += 2 * PI;
    while (ang >= 2 * PI) ang -= 2 * PI;
    return ang;
}

void solve() {
    int n; cin >> n;
    vector<pair<ll, ll>> a(n);
    rep(i, n) cin >> a[i].first >> a[i].second;
    vector<pair<ll, ll>> pts(n);
    vector<ld> ang(n);
    rep(i, n) {
        pts[i] = {a[(i + 1) % n].first - a[i].first, a[(i + 1) % n].second - a[i].second};
        ang[i] = atan2(pts[i].second, pts[i].first);
    }
    sort(all(ang));
    ld ans = 0;
    rep(i, n) {
        ld R = normalize(ang[(i + 1) % n] - ang[i]);
        ld L = normalize(ang[i] - ang[(i + n - 1) % n]);
        R -= PI / 2;
        R = min(R, PI / 2);
        L -= PI / 2;
        L = min(L, PI / 2);
        if (-L <= R) {
            ans += (R + L);
        }
    }
    cout << ans / PI << '\n';
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(12) << fixed;
    int t = 1;
//    cin >> t;
    rep(i, t) {
        solve();
    }
    return 0;
}