#include<bits/stdc++.h>
using std::cin;
using std::cout;
using namespace std::ranges;
using u64 = unsigned long long;
const int N = 500005;
const int mod = 998244353;
using ll = long long;
using cp = std::complex<ll>;
using db = long double;
const db pi = std::acos(-1);
int n;
cp a[N], b[N];
struct frac {
	cp x, y; int id;
};
bool operator == (const frac & x, const frac & y) {
	return x.x * y.y == x.y * y.x;
}

frac A[N]; int cnt;
int lcp[N];
void push(cp * a, int rev = 0) {
	std::vector<cp> d(n);
	for(int i = 0;i < n;++i) {
		d[i] = a[(i + 1) % n] - a[i];
	}
	for(int i = 0;i < n;++i) {
		A[++cnt] = {d[(i + 1) % n], d[i], rev ? n - 1 - i : i};
	}
}
int main() {
	std::ios::sync_with_stdio(false), cin.tie(0);
	cin >> n;

	for(int i = 0;i < n;++i) {
		ll x, y; cin >> x >> y;
		a[i] = cp(x, y);
	}
	for(int i = 0;i < n;++i) {
		b[i] = std::conj(a[i]);
	}
	std::reverse(b, b + n);
	push(a); push(b, 1); push(b, 1);
	int mx = 1, pt = 1;
	lcp[1] = cnt;
	
	for(int i = 2;i <= cnt;++i) {
		if(i <= mx) lcp[i] = std::min(lcp[i - pt + 1], mx - i +1);
		while(i + lcp[i] <= cnt &&  A[i + lcp[i]] == A[1 + lcp[i]]) ++ lcp[i];
		if(i + lcp[i] - 1 > mx) pt = i, mx = i + lcp[i] - 1;
	}
	std::vector<std::pair<int, int>> v;
	for(int i = 1;i <= n;++i) {
		if(lcp[i + n] >= n) {
			v.emplace_back(A[1].id, A[i + n].id);
		}
	}
	db sx = 0, sy = 0;
	for(int i = 0;i < n;++i) {
		sx += a[i].real();
		sy += a[i].imag();
	}
	sx /= n;
	sy /= n;
	if(v.size() >= 2) {
		db r = 0;
		for(int i = 0;i < n;++i) {
			db x = a[i].real() - sx;
			db y = a[i].imag() - sy;
			r = std::max(r, std::sqrt(x * x + y * y));
		}
		printf("%.10Lf\n", 4 * pi / 3 * r * r * r);
	} else if(v.size() == 1) {
		auto [X, Y] = v[0];
		db tx = 0, ty = 0;
		for(int i = 0;i < n;++i) {
			cp z = a[(X + i) % n] + a[(Y + n - i) % n];
			db dx = db(z.real()) / 2 - sx;
			db dy = db(z.imag()) / 2 - sy;
			db ab = std::sqrt(dx * dx + dy * dy);
			if(ab > 1e-6) {
				tx = dx / ab;
				ty = dy / ab;
				break;
			}
		}
		db rx = -ty, ry = tx;

		db H = rx * sx + ry * sy;

		db ans = 0;
		for(int i = 0;i < n;++i) {
			auto get = [&](cp x) {
				db X = x.real(), Y = x.imag();
				return std::make_pair(tx * X + ty * Y, rx * X + ry * Y - H);
			};
			auto [lx, hx] = get(a[i]);
			auto [ly, hy] = get(a[(i + 1) % n]);
			auto eval = [&](db p) {
				return p * p * pi;
			};
			ans += (eval(hx) + eval(hy) + eval((hx + hy) / 2) * 4) / 6 * std::abs(lx - ly);
		}

		printf("%.10Lf\n", ans / 2);
	} else {
		puts("0");
	}
}