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: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;

public class Main {
    static final class Edge {
        public final int src;
        public final int dest;
        public final long weight;
        public Edge(int src, int dest, long weight) {
            if (src < 0 || dest < 0) {
                throw new IllegalArgumentException();
            }
            this.src = src;
            this.dest = dest;
            this.weight = weight;
        }
        public int src() {
            return src;
        }
        public int dest() {
            return dest;
        }
        public long weight() {
            return weight;
        }
        public Edge reverse() {
            return new Edge(dest, src, weight);
        }
        @Override
        public int hashCode() {
            return Objects.hash(dest, src, weight);
        }
        @Override
        public boolean equals(Object obj) {
            if (this == obj) {
                return true;
            }
            if (obj == null) {
                return false;
            }
            if (!(obj instanceof Edge)) {
                return false;
            }
            Edge other = (Edge)obj;
            return dest == other.dest
                   && src == other.src
                   && weight == other.weight;
        }
        @Override
        public String toString() {
            return "Edge [src="
                   + src
                   + ", dest="
                   + dest
                   + ", weight="
                   + weight
                   + "]";
        }
        public static List<Edge> newEdges(int[] oneBasedSrc,
                                          int[] oneBasedDest,
                                          boolean directedGraph) {
            return newEdges(oneBasedSrc, oneBasedDest, null, directedGraph);
        }
        public static List<Edge> newEdges(int[] oneBasedSrc,
                                          int[] oneBasedDest,
                                          int[] weight,
                                          boolean directedGraph) {
            if (oneBasedSrc.length != oneBasedDest.length
                || (weight != null && oneBasedSrc.length != weight.length)) {
                throw new IllegalArgumentException();
            }
            List<Edge> result = new ArrayList<>(oneBasedSrc.length
                                                * (directedGraph ? 1 : 2));
            for (int i = 0; i < oneBasedDest.length; i++) {
                if (oneBasedSrc[i] <= 0 || oneBasedDest[i] <= 0) {
                    throw new IllegalArgumentException();
                }
                Edge e = new Edge(oneBasedSrc[i] - 1,
                                  oneBasedDest[i] - 1,
                                  weight == null ? 1 : weight[i]);
                result.add(e);
                if (!directedGraph) {
                    result.add(e.reverse());
                }
            }
            return result;
        }
        public static List<List<Edge>> newSrcToEdges(int vertexCount,
                                                     Collection<Edge> edges) {
            int[] edgeCount = new int[vertexCount];
            for (Edge e : edges) {
                edgeCount[e.src]++;
            }
            List<List<Edge>> result =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            for (int i = 0; i < vertexCount; i++) {
                result.set(i, new ArrayList<>(edgeCount[i]));
            }
            for (Edge e : edges) {
                result.get(e.src).add(e);
            }
            return result;
        }
        public static List<List<Edge>> newDestToEdges(int vertexCount,
                                                      Collection<Edge> edges) {
            int[] edgeCount = new int[vertexCount];
            for (Edge e : edges) {
                edgeCount[e.dest]++;
            }
            List<List<Edge>> result =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            for (int i = 0; i < vertexCount; i++) {
                result.set(i, new ArrayList<>(edgeCount[i]));
            }
            for (Edge e : edges) {
                result.get(e.dest).add(e);
            }
            return result;
        }
    }
    static void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        int u = in.nextInt();
        int v = in.nextInt();
        int[][] ab = in.nextVerticalIntArrays(2, n - 1);
        int[] a = ab[0];
        int[] b = ab[1];

        List<Edge> edges = Edge.newEdges(a, b, false);
        List<List<Edge>> srcToEdges = Edge.newSrcToEdges(n, edges);

        Set<Integer> takahashi = new HashSet<>();
        takahashi.add(u - 1);

        Set<Integer> aoki = new HashSet<>();
        aoki.add(v - 1);

        boolean[] seen = new boolean[n];
        seen[v - 1] = true;

        long ans = 0;
        while (!takahashi.isEmpty()) {
            Set<Integer> nextTakahashi = new HashSet<>();
            for (int p : takahashi) {
                if (aoki.contains(p)) {
                    continue;
                }
                for (Edge e : srcToEdges.get(p)) {
                    nextTakahashi.add(e.dest);
                }
            }
            takahashi = nextTakahashi;

            Set<Integer> nextAoki = new HashSet<>();
            for (int p : aoki) {
                if (takahashi.contains(p)) {
                    takahashi.remove(p);
                }
                for (Edge e : srcToEdges.get(p)) {
                    if (seen[e.dest]) {
                        continue;
                    }
                    seen[e.dest] = true;
                    nextAoki.add(e.dest);
                }
            }
            aoki = nextAoki;

            if (!takahashi.isEmpty()) {
                ans++;
            }
        }
        out.println(ans);
    }

    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }

    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;
        MyScanner(InputStream in) {
            this.in = in;
        }
        private byte readByte() {
            if (point < readLength) {
                byte result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(byte c) {
            return 33 <= c && c <= 126;
        }
        public char nextChar() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        public String next() {
            return next(16);
        }
        public String next(int n) {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        public long nextLong() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        public int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        public long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        public char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        public char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        public int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        public long[][] nextVerticalLongArrays(int arrayCount,
                                               int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        public char[][] nextVerticalCharArrays(int arrayCount,
                                               int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        public void joinAndPrintln(int[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(int[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(long[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(long[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(Iterable<?> iterable) {
            joinAndPrintln(iterable, " ");
        }
        public void joinAndPrintln(Iterable<?> iterable, String delimiter) {
            StringBuilder b = new StringBuilder();
            for (Iterator<?> i = iterable.iterator(); i.hasNext();) {
                b.append(i.next());
                while (i.hasNext()) {
                    b.append(delimiter).append(i.next());
                }
            }
            println(b.toString());
        }
    }
}