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: Wrong Answer)

using AtCoderBeginnerContest148.Questions;
using AtCoderBeginnerContest148.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoderBeginnerContest148.Questions
{
    public class QuestionF : AtCoderQuestionBase
    {
        List<int>[] nodes;
        int[] takahashiDistances;
        int[] aokiDistances;

        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nuv = inputStream.ReadIntArray();
            var nodeCount = nuv[0];
            var takahashiPosition = nuv[1] - 1;
            var aokiPosition = nuv[2] - 1;

            nodes = Enumerable.Range(0, nodeCount).Select(_ => new List<int>()).ToArray();
            takahashiDistances = new int[nodeCount];
            aokiDistances = new int[nodeCount];
            for (int i = 0; i < nodeCount - 1; i++)
            {
                var ab = inputStream.ReadIntArray().Select(j => j - 1).ToArray();
                var a = ab[0];
                var b = ab[1];
                nodes[a].Add(b);
                nodes[b].Add(a);
            }

            Search(aokiPosition, false);
            Search(takahashiPosition, true);

            yield return takahashiDistances.Max();
        }

        void Search(int initialNode, bool isTakahashi)
        {
            var seen = Enumerable.Range(0, nodes.Length).Select(i => i == initialNode).ToArray();
            var toDo = new Queue<int>();
            toDo.Enqueue(initialNode);

            while (toDo.Any())
            {
                var currentNode = toDo.Dequeue();

                foreach (var nextNode in nodes[currentNode].Where(n => !seen[n]))
                {
                    seen[nextNode] = true;
                    if (isTakahashi)
                    {
                        if (aokiDistances[nextNode] >= takahashiDistances[currentNode] + 1)
                        {
                            takahashiDistances[nextNode] = takahashiDistances[currentNode] + 1;
                        }
                    }
                    else
                    {
                        aokiDistances[nextNode] = aokiDistances[currentNode] + 1;
                    }

                    if (!isTakahashi || aokiDistances[nextNode] > takahashiDistances[nextNode])
                    {
                        toDo.Enqueue(nextNode);
                    }
                }
            }
        }
    }
}


namespace AtCoderBeginnerContest148
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionF();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtCoderBeginnerContest148.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

namespace AtCoderBeginnerContest148.Algorithms
{
    public static class BasicAlgorithm
    {
        public static long Gcd(long a, long b)
        {
            if (a <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(a), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (b <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(b), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (a < b)
            {
                var temp = a;
                a = b;
                b = temp;
            }

            while (b != 0)
            {
                var temp = a % b;
                a = b;
                b = temp;
            }
            return a;
        }

        public static long Lcm(long a, long b)
        {
            if (a <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(a), $"{nameof(b)}は正の整数である必要があります。");
            }
            if (b <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(b), $"{nameof(b)}は正の整数である必要があります。");
            }

            return a / Gcd(a, b) * b;
        }
    }
}
#region Extensions

    namespace AtCoderBeginnerContest148.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion