#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; template struct value_compression : vector { bool built = false; using VS = vector; using VS::VS; value_compression(vector v) : vector(move(v)) {} void build() { sort(this->begin(), this->end()); this->erase(unique(this->begin(), this->end()), this->end()); built = true; } template void convert(T first, T last) { assert(built); for (; first != last; ++first) *first = (*this)(*first); } int operator()(S x) { assert(built); return lower_bound(this->begin(), this->end(), x) - this->begin(); } void clear() { this->clear(); built = false; } }; } int main() { ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; vector

xy(n); value_compression vc_x, vc_y; for (auto& [x, y] : xy) cin >> x >> y, vc_x.emplace_back(x), vc_y.emplace_back(y); vc_x.build(); vc_y.build(); for (auto& [x, y] : xy) x = vc_x(x), y = vc_y(y); ll p = 0, q = 0, r = n * ll(n - 1) / 2, s = r; ranges::sort(xy, {}, [](const P& p) { return P(p.first, -p.second); }); fenwick_tree ft(n); for (auto [x, y] : xy) p += ft.sum(0, y), ft.add(y, 1); ranges::sort(xy, {}, [](const P& p) { return P(-p.first, -p.second); }); ft = fenwick_tree(n); for (auto [x, y] : xy) q += ft.sum(0, y), ft.add(y, 1); VI cntx(n), cnty(n); for (auto [x, y] : xy) r -= cntx[x]++, s -= cnty[y]++; auto res = (p - q) / sqrtl(__int128(r) * s); cout << fixed << setprecision(16) << res << '\n'; }