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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskAA solver = new TaskAA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskAA {
        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;

            SimpleAdjListGraph g = new SimpleAdjListGraph(n);
            for (int i = 0; i < n - 1; i++) {
                int s = in.nextInt() - 1;
                int t = in.nextInt() - 1;
                g.addEdge(s, t);
                g.addEdge(t, s);
            }

            int[] d0 = g.bfs(u)[0];
            int[] d1 = g.bfs(v)[0];

            int ans = 0;
            for (int i = 0; i < n; i++) {
                if (d0[i] < d1[i]) {
                    ans = Math.max(ans, d1[i]);
                }
            }

            out.println(ans - 1);
        }

        class SimpleAdjListGraph {
            int m;
            int V;
            int E;
            int[] head;
            int[] next;
            int[] to;

            public SimpleAdjListGraph(int V) {
                this.V = V;
                this.E = V;
                head = new int[V];
                next = new int[E];
                to = new int[E];
                clear();
            }

            public void clear() {
                m = 0;
                Arrays.fill(head, -1);
            }

            public void addEdge(int s, int t) {
                if (m == next.length) {
                    int[] tmp = new int[Math.max(next.length + 5, next.length * 3 / 2)];
                    System.arraycopy(next, 0, tmp, 0, next.length);
                    next = tmp.clone();
                    System.arraycopy(to, 0, tmp, 0, to.length);
                    to = tmp;
                }

                next[m] = head[s];
                head[s] = m;
                to[m++] = t;
            }

            public int[][] bfs(final int src) {
                final int[] dist = new int[head.length];
                final int[] prev = new int[head.length];
                final int[] q = new int[2 * head.length + 10];
                int s = 0, t = 0;

                Arrays.fill(dist, -1);
                Arrays.fill(prev, -1);
                dist[src] = 0;
                q[t++] = src;
                while (s != t) {
                    final int v = q[s++];
                    for (int e = head[v]; e != -1; e = next[e]) {
                        final int u = to[e];
                        if (dist[u] == -1) {
                            dist[u] = dist[v] + 1;
                            prev[u] = v;
                            q[t++] = u;
                        }
                    }
                }
                return new int[][]{dist, prev};
            }

        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}