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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net.NetworkInformation;
using CompLib.Util;

public class Program
{
    int N;
    int U, V;
    List<int>[] E;
    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        U = sc.NextInt() - 1;
        V = sc.NextInt() - 1;
        E = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            E[i] = new List<int>();
        }

        for (int i = 0; i < N - 1; i++)
        {
            int a = sc.NextInt() - 1;
            int b = sc.NextInt() - 1;
            E[a].Add(b);
            E[b].Add(a);
        }

        // vの根付き木
        // 
        // u できるだけ上がって一番深い頂点に向かう

        // vよりuが早い一番深いとこ
        // 

        var distV = Go(V);
        var distU = Go(U);

        var sorted = new int[N];
        for (int i = 0; i < N; i++)
        {
            sorted[i] = i;
        }

        Array.Sort(sorted, (l, r) => distV[r].CompareTo(distV[l]));

        foreach (var i in sorted)
        {
            if (distU[i] < distV[i])
            {
                Console.WriteLine(distV[i] - 1);
                return;
            }
        }
    }

    int[] Go(int r)
    {
        int[] result = new int[N];
        for (int i = 0; i < N; i++)
        {
            result[i] = int.MaxValue;
        }

        var q = new Queue<int>();
        q.Enqueue(r);
        result[r] = 0;

        while (q.Count > 0)
        {
            var d = q.Dequeue();
            foreach (var to in E[d])
            {
                if (result[to] <= result[d] + 1) continue;
                result[to] = result[d] + 1;
                q.Enqueue(to);
            }
        }
        return result;
    }

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            if (_index >= _line.Length)
            {
                string s;
                do
                {
                    s = Console.ReadLine();
                } while (s.Length == 0);

                _line = s.Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public string ReadLine()
        {
            _index = _line.Length;
            return Console.ReadLine();
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            string s = Console.ReadLine();
            _line = s.Length == 0 ? new string[0] : s.Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}