import std; void main () { int N = readln.chomp.to!int; auto x = new int[](N); auto y = new int[](N); foreach (i; 0..N) readln.read(x[i], y[i]); // PとQをどう求めるかが最も難しい。 // Pについて考える。 // 面倒なので、片方の大小関係は異なるとして考えたい。 // xj < xiを仮定する。この時、yj < yiが必要十分条件。xの昇順にデータを追加することを考えると、rectangle sumの特殊ケースに帰着する。これは平面走査で解ける。 // Qも不等号の向きを反転させればよい。 long P = () { long res = 0; auto index = iota(N).array.sort!((i, j) => x[i] < x[j]).array; auto rsq = new DynamicSegmentTree!(int, (int a, int b) => a + b, () => 0)(10L ^^ 10); const int pad = 10 ^^ 9; int L = 0, R = 0; while (L < N) { while (R < N) { if (x[index[L]] != x[index[R]]) break; R++; } foreach (U; L..R) { res += rsq.prod(0, y[index[U]] + pad); } // 追加 foreach (U; L..R) { rsq.set(y[index[U]] + pad, rsq.get(y[index[U]] + pad) + 1); } L = R; } return res; }(); long Q = () { long res = 0; auto index = iota(N).array.sort!((i, j) => x[i] < x[j]).array; auto rsq = new DynamicSegmentTree!(int, (int a, int b) => a + b, () => 0)(10L ^^ 10); const int pad = 10 ^^ 9; int L = 0, R = 0; while (L < N) { while (R < N) { if (x[index[L]] != x[index[R]]) break; R++; } foreach (U; L..R) { res += rsq.prod(y[index[U]] + pad + 1, 10L ^^ 10); } // 追加 foreach (U; L..R) { rsq.set(y[index[U]] + pad, rsq.get(y[index[U]] + pad) + 1); } L = R; } return res; }(); long R = () { long res = 0; auto index = iota(N).array.sort!((i, j) => x[i] < x[j]).array; int L = 0, R = 0; while (L < N) { while (R < N) { if (x[index[L]] != x[index[R]]) break; R++; } res += 1L * (R - L) * (N - (R - L)); L = R; } return res / 2; }(); long S = () { long res = 0; auto index = iota(N).array.sort!((i, j) => y[i] < y[j]).array; int L = 0, R = 0; while (L < N) { while (R < N) { if (y[index[L]] != y[index[R]]) break; R++; } res += 1L * (R - L) * (N - (R - L)); L = R; } return res / 2; }(); double ans = (P - Q) / sqrt(R.to!double) / sqrt(S.to!double); writefln("%.10f", ans); } void read (T...) (string S, ref T args) { import std.conv : to; import std.array : split; auto buf = S.split; foreach (i, ref arg; args) { arg = buf[i].to!(typeof(arg)); } } import std.traits : ReturnType, isCallable, Parameters; import std.meta : AliasSeq; class DynamicSegmentTree (T, alias op, alias e) { // TODO: assertのメッセージを表示 static assert(isCallable!(op)); static assert(isCallable!(e)); static assert(is (ReturnType!(op) == T)); static assert(is (ReturnType!(e) == T)); static assert(is (Parameters!(op) == AliasSeq!(T, T))); static assert(is (Parameters!(e) == AliasSeq!())); // 内部が1-indexedで動的な完全二分セグメント木 import std.format : format; public: this (long N_) in { assert(1 <= N_, format("Dynamic SegmentTree: N = %s does not satisfy constraints. N must be in range of [1, %s]", 4 * 10L^^18)); } do { length = N_; // N_以上の2冪に設定 N = 1; while (N < N_) N *= 2; } void set (long idx, T val) in { assert(0 <= idx && idx < length, format("Dynamic SegmentTree: idx = %s does not satisfy constraints. idx must be in range of [0, %s)", idx, length)); } do { idx++; internal_set(root, idx, val, 1, N + 1); } T get (long idx) in { assert(0 <= idx && idx < length, format("Dynamic SegmentTree: idx = %s does not satisfy constraints. idx must be in range of [0, %s)", idx, length)); } do { idx++; return internal_get(root, idx, 1, N + 1); } T prod (long l, long r) in { assert(0 <= l && l < length, format("Dynamic SegmentTree: l = %s does not satisfy constraints. l must be in range of [0, %s)", l, length)); assert(0 <= r && r <= length, format("Dynamic SegmentTree: r = %s does not satisfy constraints. r must be in range of [0, %s]", r, length)); assert(l <= r, format("Dynamic SegmentTree: l = %s, r = %s does not satisfy constraints. l <= r must be satisfied.", l, r)); } do { l++, r++; if (l == r) return e(); return internal_prod(root, l, r, 1, N + 1); } T all_prod () { return internal_prod(root, 1, N + 1, 1, N + 1); } private: struct node { long index; T value, product; node *left = null, right = null; } void node_update (node *n) { n.product = op( op((n.left == null ? e() : n.left.product), n.value), (n.right == null ? e() : n.right.product) ); } node *root = null; long N = 0; long length = 0; // [l, r) : 今見ている部分木が管理する範囲 node *internal_set (ref node *cur, long idx, T val, long l, long r) { if (cur == null) { return cur = new node(idx, val, val, null, null); } if (cur.index == idx) { cur.value = val; node_update(cur); return cur; } // 既に部分木管理ノードが存在するときの処理 import std.algorithm : swap; long mid = (l + r) / 2; if (idx < mid) { // 今いる人を押しのける if (cur.index < idx) { swap(cur.value, val); swap(cur.index, idx); } cur.left = internal_set(cur.left, idx, val, l, mid); } else { if (idx < cur.index) { swap(cur.value, val); swap(cur.index, idx); } cur.right = internal_set(cur.right, idx, val, mid, r); } node_update(cur); return cur; } T internal_get (const node *cur, long idx, long l, long r) { if (cur == null) return e(); if (cur.index == idx) return cur.value; long mid = (l + r) / 2; if (idx < mid) return internal_get(cur.left, idx, l, mid); return internal_get(cur.right, idx, mid, r); } // [a, b) = 要求区間 T internal_prod (const node *cur, long a, long b, long l, long r) { if (cur == null || b <= l || r <= a) return e(); if (a <= l && r <= b) return cur.product; long mid = (l + r) / 2; T res = internal_prod(cur.left, a, b, l, mid); if (a <= cur.index && cur.index < b) res = op(res, cur.value); res = op(res, internal_prod(cur.right, a, b, mid, r)); return res; } }