#line 1 "main.cpp" #include using namespace std; // #pragma GCC target("avx,avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vul = vector; using vpii = vector; using vvpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){return *min_element(all(a));} template auto max(const T& a){return *max_element(all(a));} template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;} void Yes() {cout << "Yes\n";return;} void No() {cout << "No\n";return;} void YES() {cout << "YES\n";return;} void NO() {cout << "NO\n";return;} template T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);} template T ceil(T x, T y) {return floor(x + y - 1, y);} template T bmod(T x, T y) {return x - y * floor(x, y);} template pair divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack constexpr long double PI = 3.141592653589793238462643383279L; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; constexpr int mod = 998244353; //constexpr int mod = 1000000007; #line 2 "library/segtree/segtree.hpp" template struct segtree { int N; int size; vector seg; const OP op; const T I; segtree(OP _op, const T I_) : N(0), size(0), op(_op), I(I_) {} explicit segtree(int _N, const OP _op, const T I_) : op(_op), I(I_) { init(_N); } explicit segtree(const vector &v, const OP _op, const T I_) : op(_op), I(I_) { init(v.size()); for (int i = 0; i < (int)v.size(); i++) { seg[i + size] = v[i]; } build(); } void init(int _N) { N = _N; size = 1; while (size < N) size <<= 1; seg.assign(2 * size, I); } void build() { for (int k = size - 1; k > 0; k--) { seg[k] = op(seg[2 * k], seg[2 * k + 1]); } } void set(int p, T x) { assert(0 <= p && p < N); p += size; seg[p] = x; while (p >>= 1) { seg[p] = op(seg[2 * p], seg[2 * p + 1]); } } void add(int p, T x) { assert(0 <= p && p < N); p += size; seg[p] += x; while (p >>= 1) { seg[p] = op(seg[2 * p], seg[2 * p + 1]); } } T get(int p) const { assert(0 <= p && p < N); return seg[p + size]; } // query to [l, r) T prod(int l, int r) { assert(0 <= l && l <= r && r <= N); T L = I, R = I; for (l += size, r += size; l < r; l >>= 1, r >>= 1) { if (l & 1) L = op(L, seg[l++]); if (r & 1) R = op(seg[--r], R); } return op(L, R); } T all_prod() {return seg[1];} // check(a[l] * ... * a[r-1]) が true となる最大の r // (右端まですべて true なら N を返す) template int max_right(int l, C check) { assert(0 <= l && l <= N); assert(check(I) == true); if (l == N) return N; l += size; T sm = I; do { while (l % 2 == 0) l >>= 1; if (!check(op(sm, seg[l]))) { while (l < size) { l = (2 * l); if (check(op(sm, seg[l]))) { sm = op(sm, seg[l]); l++; } } return l - size; } sm = op(sm, seg[l]); l++; } while ((l & -l) != l); return N; } // check(a[l] * ... * a[r-1]) が true となる最小の l // (左端まで true なら 0 を返す) template int min_left(int r, C check) { assert(0 <= r && r <= N); assert(check(I) == true); if (r == 0) return 0; r += size; T sm = I; do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!check(op(seg[r], sm))) { while (r < size) { r = (2 * r + 1); if (check(op(seg[r], sm))) { sm = op(seg[r], sm); r--; } } return r + 1 - size; } sm = op(seg[r], sm); } while ((r & -r) != r); return 0; } }; #line 100 "main.cpp" using T = int; T op(T x,T y) {return x + y;} T e() {return 0;} int main() { INT(n); vi x(n),y(n); rep(i,n) cin >> x[i] >> y[i]; ll r = 1LL * n * (n - 1) / 2; ll s = r; map mpx,mpy; rep(i,n) { r -= mpx[x[i]]; ++mpx[x[i]]; s -= mpy[y[i]]; ++mpy[y[i]]; } map mp; rep(i,n) mp[x[i]].emplace_back(i); ll p = 0,q = 0; vi Y = y; sort(all(Y)); Y.erase(unique(all(Y)),Y.end()); segtree seg(Y.size(),op,e()); for(auto &[_,v]:mp) { rep(i,v.size()) { int id = lower_bound(all(Y),y[v[i]]) - Y.begin(); p += seg.prod(0,id); q += seg.prod(id+1,Y.size()); } rep(i,v.size()) { int id = lower_bound(all(Y),y[v[i]]) - Y.begin(); seg.add(id,1); } } cout << (p - q) / sqrt(r * s) << '\n'; }