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 static System.Console;
using static System.Math;

class MainClass : Scanner
{
    static void Main()
    {
        var (N, u, v) = ReadStream<int,int,int>();
        u--;v--;
        var G = new Graph<int>(N);
        for (int i = 0; i < N-1; i++)
        {
            var r = RInts(x=>int.Parse(x)-1);
            G.Add(r[0],r[1]);
            G.Add(r[1], r[0]);
        }
        var usedt = Enumerable.Repeat(-1, N).ToArray();
        var useda = Enumerable.Repeat(-1, N).ToArray();


        var que = new Queue<(int n, int c)>();
        que.Enqueue((v, 0));
        useda[v] = 0;
        while (que.Count > 0)
        {
            var t = que.Dequeue();
            int n = t.n;
            int c = t.c;
            foreach (var i in G[n])
            {
                if (useda[i] != -1) continue;
                
                useda[i] = c + 1;
                que.Enqueue((i, c + 1));
            }
        }

        que = new Queue<(int n, int c)>();
        que.Enqueue((u, 0));
        usedt[u] = 0;
        while (que.Count > 0)
        {
            var t = que.Dequeue();
            int n = t.n;
            int c = t.c;
            foreach (var i in G[n])
            {
                if (usedt[i] != -1) continue;
                if (useda[i] ==c) continue;
                if(useda[i] == c + 1)
                {
                    usedt[i] = c + 1;
                    continue;
                }
                usedt[i] = c + 1;
                que.Enqueue((i, c + 1));
            }
        }
        int ans = 0;
        for (int i = 0; i < N; i++)
        {
            if (usedt[i]==-1) continue;
            int time = usedt[i];
            if (useda[i] - usedt[i] > 0) time += (useda[i] - usedt[i] - 1);
            ans = Math.Max(ans,time);
        }
        WriteLine(ans);
    }
}
class Graph<T>
{
    private List<T>[] G;
    public Graph(int size)
    {
        G = new List<T>[size];
        for (int i = 0; i < size; i++)
        {
            G[i] = new List<T>();
        }
    }

    public List<T> this[int i] => G[i];
    public void Add(int from, T to) => G[from].Add(to);
    public List<T>[] ToListArray() => G;
    public int Length => G.Length;
}
class Scanner
{
    public static int RInt() => int.Parse(Console.ReadLine());
    public static long RLong() => long.Parse(Console.ReadLine());
    public static string RString() => Console.ReadLine();
    public static double RDouble() => double.Parse(Console.ReadLine());

    public static int[] RInts() => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    public static int[] RInts(Func<string, int> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static long[] RLongs() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    public static long[] RLongs(Func<string, long> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static double[] RDoubles() => Array.ConvertAll(Console.ReadLine().Split(), double.Parse);
    public static double[] RDoubles(Func<string, double> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static string[] RStrings() => Console.ReadLine().Split();
    //public static string[] RStrings(Func<string, string> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static T1 ReadStream<T1>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        return r1;
    }
    public static (T1, T2) ReadStream<T1, T2>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        return (r1, r2);
    }
    public static (T1, T2, T3) ReadStream<T1, T2, T3>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        return (r1, r2, r3);
    }
    public static (T1, T2, T3, T4) ReadStream<T1, T2, T3, T4>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        var r4 = (T4)Convert.ChangeType(r[3], typeof(T4));
        return (r1, r2, r3, r4);
    }
}