Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices. The i-th edge connects Vertex A_i and B_i bidirectionally.

Takahashi is standing at Vertex u, and Aoki is standing at Vertex v.

Now, they will play a game of tag as follows:

1. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Takahashi moves to a vertex of his choice that is adjacent to his current vertex.

2. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Aoki moves to a vertex of his choice that is adjacent to his current vertex.

3. Go back to step 1.

Takahashi performs his moves so that the game ends as late as possible, while Aoki performs his moves so that the game ends as early as possible.

Find the number of moves Aoki will perform before the end of the game if both Takahashi and Aoki know each other's position and strategy.

It can be proved that the game is bound to end.

Constraints

2 \leq N \leq 10^5

1 \leq u,v \leq N

u \neq v

1 \leq A_i,B_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N u v
A_1 B_1
:
A_{N-1} B_{N-1}

Output

Print the number of moves Aoki will perform before the end of the game.

Sample Input 1

5 4 1
1 2
2 3
3 4
3 5

Sample Output 1

2

If both players play optimally, the game will progress as follows:

Takahashi moves to Vertex 3.

Aoki moves to Vertex 2.

Takahashi moves to Vertex 5.

Aoki moves to Vertex 3.

Takahashi moves to Vertex 3.

Here, Aoki performs two moves.

Note that, in each move, it is prohibited to stay at the current vertex.

Sample Input 2

5 4 5
1 2
1 3
1 4
1 5

Sample Output 2

1

Sample Input 3

2 1 2
1 2

Sample Output 3

0

Sample Input 4

9 6 1
1 2
2 3
3 4
4 5
5 6
4 7
7 8
8 9

Sample Output 4

5

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
    static void Solve()
    {
        N = sc.ReadInt();
        U = sc.ReadInt();
        V = sc.ReadInt();
        U--; V--;
        G = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            G[i] = new List<int>();
        }
        var dij = new Dijkstra(N);
        for (int i = 0; i < N - 1; i++)
        {
            var a = sc.ReadInt();
            var b = sc.ReadInt();
            a--; b--;
            G[a].Add(b);
            G[b].Add(a);
            dij.Add(a, b);
            dij.Add(b, a);
        }
        // Vからの距離
        var dist = dij.Calc(V);
        // UからVにできる限り近づいたときの頂点をもとめる
        var rem = (dist[U] - 1) / 2;
        var x = Rec(U, -1, rem, dist);

        // Uからできるだけ遠ざかるときの距離と先に移動した距離、微調整
        var ans = Rec2(x, -1, dist) + rem + (dist[U] % 2 ^ 1);
        Console.WriteLine(ans);
    }
    static int N, U, V;
    static List<int>[] G;

    static int Rec2(int now, int prev, long[] dist)
    {
        var res = 0;

        foreach (var next in G[now])
        {
            if (next == prev) continue;
            // 近づかない
            if (dist[next] != dist[now] + 1) continue;

            var x = Rec2(next, now, dist) + 1;
            res = Math.Max(res, x);
        }

        return res;
    }

    static int Rec(int now, int prev, long rem, long[] dist)
    {
        if (rem <= 0) return now;

        foreach (var next in G[now])
        {
            if (prev == next) continue;
            // より近づく方向へ進む
            if (dist[next] == dist[now] - 1)
            {
                return Rec(next, now, rem - 1, dist);
            }
        }
        // ここには来ない
        throw new Exception();
    }

    class Dijkstra
    {
        public const long INF = long.MaxValue / 2;
        public int V { get; set; }
        public int E { get; set; }
        public List<Edge>[] G { get; set; }
        public Dijkstra(int n)
        {
            this.V = n;
            this.G = new List<Edge>[V];
            for (int i = 0; i < V; i++)
            {
                this.G[i] = new List<Edge>();
            }
        }
        public void Add(int a, int b, long cost = 1)
        {
            this.G[a].Add(new Edge(b, cost));
            this.E++;
        }
        public long GetMinCost(int start, int goal)
        {
            var cost = new long[V];
            for (int i = 0; i < V; i++) cost[i] = INF;
            cost[start] = 0;

            var capacity = Math.Max(1, E);
            var q = new PriorityQueue<P>(false);
            q.Enqueue(new P(start, 0));

            while (q.Count > 0)
            {
                var p = q.Dequeue();
                if (p.Cost != cost[p.A]) continue;
                foreach (var e in this.G[p.A])
                {
                    if (cost[e.To] > p.Cost + e.Cost)
                    {
                        cost[e.To] = p.Cost + e.Cost;
                        q.Enqueue(new P(e.To, cost[e.To]));
                    }
                }
            }
            return cost[goal] == long.MaxValue ? -1 : cost[goal];
        }
        public long[] Calc(int start)
        {
            var visited = new bool[V];
            var cost = new long[V];
            for (int i = 0; i < V; i++) cost[i] = INF;
            cost[start] = 0;

            var capacity = Math.Max(1, E);
            var q = new PriorityQueue<P>(false);
            q.Enqueue(new P(start, 0));

            while (q.Count > 0)
            {
                var p = q.Dequeue();
                visited[p.A] = true;
                if (p.Cost != cost[p.A]) continue;
                foreach (var e in this.G[p.A])
                {
                    if (cost[e.To] > p.Cost + e.Cost && !visited[e.To])
                    {
                        cost[e.To] = p.Cost + e.Cost;
                        q.Enqueue(new P(e.To, cost[e.To]));
                    }
                }
            }
            return cost;
        }
        public struct Edge
        {
            public int To;
            public long Cost;
            public Edge(int to, long cost)
            {
                this.To = to;
                this.Cost = cost;
            }
        }
        public struct P : IComparable<P>
        {
            public int A;
            public long Cost;
            public P(int a, long cost)
            {
                this.A = a;
                this.Cost = cost;
            }
            public int CompareTo(P other)
            {
                return this.Cost.CompareTo(other.Cost);
            }
        }
        class PriorityQueue<T>
        {
            public int Count;
            private int Capacity;
            private bool IsMaxHeap;
            private T[] Buffer;
            private IComparer<T> Cmp;
            public PriorityQueue(bool isMaxHeap = true, IComparer<T> cmp = null)
            {
                Count = 0;
                Capacity = 1 << 10;
                IsMaxHeap = isMaxHeap;
                Buffer = new T[Capacity];
                if (cmp != null) Cmp = cmp;
                else Cmp = Comparer<T>.Default;
            }
            public PriorityQueue(int capacity, bool isMaxHeap = true, IComparer<T> cmp = null)
            {
                Count = 0;
                Capacity = Math.Max(16, capacity);
                IsMaxHeap = isMaxHeap;
                Buffer = new T[Capacity];
                if (cmp != null) Cmp = cmp;
                else Cmp = Comparer<T>.Default;
            }
            private void Resize()
            {
                Capacity <<= 1;
                Array.Resize(ref Buffer, Capacity);
            }
            public void Enqueue(T value)
            {
                if (Count == Capacity) Resize();
                Buffer[Count] = value;
                Count++;
                UpHeap();
            }
            public T Dequeue()
            {
                var res = Buffer[0];
                Swap(0, Count - 1);
                Count--;
                DownHeap();
                return res;
            }
            public T Peek() { return Buffer[0]; }
            private void Swap(int i, int j)
            {
                var tmp = Buffer[i];
                Buffer[i] = Buffer[j];
                Buffer[j] = tmp;
            }
            private void UpHeap()
            {
                var n = this.Count - 1;
                while (n != 0)
                {
                    var parent = (n - 1) / 2;
                    if (Compare(Buffer[n], Buffer[parent]) > 0)
                    {
                        Swap(n, parent);
                        n = parent;
                    }
                    else break;
                }
            }
            private void DownHeap()
            {
                var parent = 0;
                while (true)
                {
                    var child = 2 * parent + 1;
                    if (child > this.Count - 1) break;
                    if (child < Count - 1 && Compare(Buffer[child], Buffer[child + 1]) < 0)
                    {
                        child += 1;
                    }
                    if (Compare(Buffer[parent], Buffer[child]) < 0)
                    {
                        Swap(parent, child);
                        parent = child;
                    }
                    else break;
                }
            }
            private int Compare(T x, T y)
            {
                var res = Cmp.Compare(x, y);
                if (!IsMaxHeap) res *= -1;
                return res;
            }
        }
    }
    static Scanner sc = new Scanner();
}
class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}