namespace AtCoder; #nullable enable using System.Numerics; class WaveletMatrix where T : IAdditionOperators, ISubtractionOperators, IAdditiveIdentity { const int d = 32; uint[,] Rank0 { get; init; } T[,] Sum { get; init; } int Length => Rank0.GetLength(1) - 1; public WaveletMatrix((uint, T)[] array) { var n = array.Length; var ranks = new uint[d, n + 1]; var sum = new T[d, n + 1]; var a = array.AsSpan(); var b = new (uint, T)[n].AsSpan(); var a0 = new (uint, T)[n].AsSpan(); var a1 = new (uint, T)[n].AsSpan(); for (var i = d - 1; i >= 0; i--) { var (i0, i1) = (0, 0); for (var j = 0; j < n; j++) { ranks[i, j + 1] += ranks[i, j]; var v = a[j]; if ((v.Item1 & (1U << i)) > 0) { ranks[i, j + 1]++; a1[i1++] = v; } else a0[i0++] = v; } for (var j = 0; j < i0; j++) b[j] = a0[j]; for (var j = 0; j < i1; j++) b[j + i0] = a1[j]; sum[i, 0] = T.AdditiveIdentity; for (var j = 0; j < n; j++) sum[i, j + 1] = sum[i, j] + b[j].Item2; var tmp = a; a = b; b = tmp; } for (var i = 0; i < d; i++) for (var j = 1U; j <= n; j++) ranks[i, j] = j - ranks[i, j]; (Rank0, Sum) = (ranks, sum); } public T Frequency(uint l, uint r, uint upper) // [l, r), [0, upper) { var (n, rank0, sum) = (Length, Rank0, Sum); var res = T.AdditiveIdentity; for (var i = d - 1; i >= 0; i--) { if (l >= r) break; var (l0, r0) = (rank0[i, l], rank0[i, r]); if ((upper & (1U << i)) > 0) { res += sum[i, r0] - sum[i, l0]; var zeros = rank0[i, n]; l += zeros - l0; r += zeros - r0; } else (l, r) = (l0, r0); } return res; } } class PointMap { readonly WaveletMatrix matrix; readonly uint[] xs; public PointMap((uint, uint, long)[] points) { var sorted = points.OrderBy(e => e.Item1); var xs = sorted.Select(e => e.Item1); var ys = sorted.Select(e => (e.Item2, e.Item3)); matrix = new WaveletMatrix(ys.ToArray()); this.xs = xs.ToArray(); } public long Sum((uint, uint) lowerLeft, (uint, uint) upperRight) // [lx, rx), [ly, ry) { var (lx, ly) = lowerLeft; var (rx, ry) = upperRight; if (lx > rx || ly > ry) return 0; return Sum(lx, ly, rx - lx, ry - ly); } public long Sum(uint x, uint y, uint dx, uint dy) // [x, x + dx), [y, y + dy) { var ux = uint.MaxValue; if (x <= ux - dx) ux = x + dx; var uy = uint.MaxValue; if (y <= uy - dy) uy = y + dy; var l = MinIndex(x); var r = MinIndex(ux); return matrix.Frequency(l, r, uy) - matrix.Frequency(l, r, y); } uint MinIndex(uint x) { var xs = this.xs; var (l, r) = (-1, xs.Length); while (r - l > 1) { var m = (l + r) >> 1; if (xs[m] < x) l = m; else r = m; } return (uint)r; } } static class Extensions { public static T[] Repeat(this int time, Func F) => Enumerable.Range(0, time).Select(_ => F()).ToArray(); } class AtCoder { object? Solve() { var n = Int(); var xy = new Dictionary(); var yx = new Dictionary(); var points = new (uint, uint, long)[n]; PointMap map; { for (var i = 0; i < n; i++) { var x = (uint)(Input() + int.MaxValue - 1); var y = (uint)(Input() + int.MaxValue - 1); points[i] = (x, y, 1); if (xy.TryGetValue(x, out var vx)) xy[x] = vx + 1; else xy[x] = 1; if (yx.TryGetValue(y, out var vy)) yx[y] = vy + 1; else yx[y] = 1; } map = new(points); } var p = 0L; var q = 0L; var r = (long)n * (n - 1) / 2; var s = r; var u = uint.MaxValue; foreach (var (x, y, _) in points) { p += map.Sum(0, 0, x, y) + map.Sum(x + 1, y + 1, u, u); q += map.Sum(x + 1, 0, u, y) + map.Sum(0, y + 1, x, u); } foreach (var (_, v) in xy) r -= (long)v * (v - 1) / 2; foreach (var (_, v) in yx) s -= (long)v * (v - 1) / 2; var ans = (p - q) / (Math.Sqrt(r) * Math.Sqrt(s)); return ans / 2; } public static void Main() => new AtCoder().Run(); public void Run() { var res = Solve(); if (res != null) { if (res is bool yes) res = yes ? "Yes" : "No"; sw.WriteLine(res); } sw.Flush(); } string[] input = Array.Empty(); int iter = 0; readonly StreamWriter sw = new(Console.OpenStandardOutput()) { AutoFlush = false }; string String() { while (iter >= input.Length) (input, iter) = (Console.ReadLine()!.Split(' '), 0); return input[iter++]; } T Input() where T : IParsable => T.Parse(String(), null); int Int() => Input(); void Out(object? x, string? separator = null) { separator ??= Environment.NewLine; if (x is System.Collections.IEnumerable obj and not string) { var firstLine = true; foreach (var item in obj) { if (!firstLine) sw.Write(separator); firstLine = false; sw.Write(item); } } else sw.Write(x); sw.WriteLine(); } }