namespace AtCoder; #nullable enable using System.Numerics; static class Extensions { public static T[] Repeat(this int time, Func F) => Enumerable.Range(0, time).Select(_ => F()).ToArray(); } abstract class SelfBalancingTreeBase { protected class Node { public required T Data { get; set; } public Node? L { get; set; } public Node? R { get; set; } public int Height { get; set; } = 1; public int Size { get; set; } = 1; public Node? this[bool right] { get => right ? R : L; set { if (right) R = value; else L = value; } } } protected static Node At(Node? node, int index) { while (node != null) { var ls = Size(node.L); if (index == ls) return node; var right = index > ls; if (right) index -= ls + 1; node = node[right]; } throw new IndexOutOfRangeException(); } protected Node? Root { get; set; } protected static int Size(Node? node) => node?.Size ?? 0; protected static int Height(Node? node) => node?.Height ?? 0; protected static int HeightDiff(Node node) => Height(node.R) - Height(node.L); protected static void Update(Node node) { node.Height = Math.Max(Height(node.L), Height(node.R)) + 1; node.Size = Size(node.L) + Size(node.R) + 1; } protected static Node? DeleteMin(Node node, Node swap) { if (node.L == null) { swap.Data = node.Data; return node.R; } node.L = DeleteMin(node.L, swap); return Balance(node); } protected static Node Balance(Node node) { var diff = HeightDiff(node); if (diff < -1 || 1 < diff) { var right = diff > 0; var next = node[right]!; if (HeightDiff(next) * diff < 0) node[right] = Rotate(next, right); return Rotate(node, !right); } Update(node); return node; } protected static Node Rotate(Node node, bool right) { var n0 = node[!right]!; node[!right] = n0[right]; Update(node); n0[right] = node; Update(n0); return n0; } public bool DeleteAt(int index) => Size(Root) != Size(Root = DeleteAt(Root, index)); static Node? DeleteAt(Node? node, int index) { if (node == null) return null; var ls = Size(node.L); if (index == ls) { if (node.R == null) return node.L; node.R = DeleteMin(node.R, node); } else { var right = index > ls; node[right] = DeleteAt(node[right], right ? index - 1 - ls : index); } return Balance(node); } protected IEnumerator GetEnumerator() { var stack = new Stack(); var lastR = Root; while (lastR != null || stack.Count > 0) { while (lastR != null) { stack.Push(lastR); lastR = lastR.L; } var last = stack.Pop(); yield return last.Data; lastR = last.R; } } public int Count { get => Size(Root); } } abstract class SelfBalancingTree : SelfBalancingTreeBase> where TKey : IComparable { public int MaxIndex(TKey key, bool include) => Bound(Root, key, true, include).Item1; public int MinIndex(TKey key, bool include) => Bound(Root, key, false, include).Item1; protected static (int, Node?) Bound(Node? node, TKey key, bool max, bool include) { var index = max ? -1 : 0; Node? res = null; while (node != null) { var comp = key.CompareTo(node.Data.Key); var left = comp < 0 || comp == 0 && (max ^ include); if (!left) index += Size(node.L) + 1; if (max ^ left) res = node; node = left ? node.L : node.R; } return (index, res); } public int CountKey(TKey key) => MaxIndex(key, true) - MaxIndex(key, false); public ValueTuple? MaxKey(TKey key, bool include) => ToOptionalKey(Bound(Root, key, true, include).Item2); public ValueTuple? MinKey(TKey key, bool include) => ToOptionalKey(Bound(Root, key, false, include).Item2); static ValueTuple? ToOptionalKey(Node? node) => node == null ? null : new(node.Data.Key); protected static Node? Find(Node? node, TKey key) { var res = Bound(node, key, false, true).Item2; return res != null && key.CompareTo(res.Data.Key) == 0 ? res : null; } protected static KeyValuePair CreateData(TKey key, TValue value) => new(key, value); protected void Insert(KeyValuePair data) => Root = Insert(Root, data); static Node Insert(Node? node, KeyValuePair data) { if (node == null) return new Node{ Data = data }; var right = data.Key.CompareTo(node.Data.Key) >= 0; node[right] = Insert(node[right], data); return Balance(node); } public bool Delete(TKey key) => Size(Root) != Size(Root = Delete(Root, key)); static Node? Delete(Node? node, TKey key) { if (node == null) return null; var comp = key.CompareTo(node.Data.Key); if (comp == 0) { if (node.R == null) return node.L; node.R = DeleteMin(node.R, node); } else { var right = comp > 0; node[right] = Delete(node[right], key); } return Balance(node); } } class OrderedMultiSet : SelfBalancingTree where T : IComparable { public bool Contains(T key) => Find(Root, key) != null; public T At(int index) => At(Root, index).Data.Key; public void Insert(T key) => Insert(CreateData(key, ValueTuple.Create())); public new IEnumerator GetEnumerator() { using var e = base.GetEnumerator(); while (e.MoveNext()) yield return e.Current.Key; } } class AtCoder { object? Solve() { var n = Int(); var zz = n.Repeat(() => (Int(), Int())); var pz = new int[n]; for (var i = 0; i < n; i++) pz[i] = i + 1; bool F(int x) { var cz = new OrderedMultiSet<(int, int)>(); var evs = new List<(int, int, int)>(); for (var i = 0; i < n; i++) { var (l, r) = zz[i]; r -= x; if (r < l) return false; evs.Add((l, 3, r)); evs.Add((r, 30, l)); } foreach (var t in pz) evs.Add((t, 10, 0)); evs.Sort(); foreach (var (t, kind, v) in evs) { if (kind == 3) { cz.Insert((t, v)); } else if (kind == 30) { cz.Delete((v, t)); } else { if (cz.Count == 0) { return false; } var (h, jdx) = cz.At(0); if (h <= t) { cz.Delete((h, jdx)); continue; } return false; } } return true; } int BinarySearch(int pass, int fail) { while (Math.Abs(pass - fail) > 1) { var middle = (pass + fail) >> 1; if (F(middle)) pass = middle; else fail = middle; } return pass; } var rb = BinarySearch(-1, int.MaxValue / 2) + 1; for (var i = 0; i < n; i++) pz[i] *= -1; Array.Sort(pz); for (var i = 0; i < n; i++) { var (l, r) = zz[i]; zz[i] = (-r, -l); } var lb = BinarySearch(-1, int.MaxValue / 2) + 1; var ans = rb + lb; return ans; } 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 }; #pragma warning disable IDE0051 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(); } #pragma warning restore IDE0051 }