Problem:
Score : 800 points

Problem Statement

There is a tree with N vertices numbered 1 through N.
The i-th edge connects Vertex x_i and y_i.
Each vertex is painted white or black.
The initial color of Vertex i is represented by a letter c_i.
c_i = W represents the vertex is white; c_i = B represents the vertex is black.

A cat will walk along this tree.
More specifically, she performs one of the following in one second repeatedly:

Choose a vertex that is adjacent to the vertex where she is currently, and move to that vertex. Then, invert the color of the destination vertex.

Invert the color of the vertex where she is currently.

The cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex.
At least how many seconds does it takes for the cat to achieve her objective?

Constraints

1 ≤ N ≤ 10^5

1 ≤ x_i,y_i ≤ N (1 ≤ i ≤ N-1)

The given graph is a tree.

c_i = W or c_i = B.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}
c_1c_2..c_N

Output

Print the minimum number of seconds required to achieve the objective.

Sample Input 1

5
1 2
2 3
2 4
4 5
WBBWW

Sample Output 1

5

The objective can be achieved in five seconds, for example, as follows:

Start at Vertex 1. Change the color of Vertex 1 to black.

Move to Vertex 2, then change the color of Vertex 2 to white.

Change the color of Vertex 2 to black.

Move to Vertex 4, then change the color of Vertex 4 to black.

Move to Vertex 5, then change the color of Vertex 5 to black.

Sample Input 2

6
3 1
4 5
2 6
6 1
3 4
WWBWBB

Sample Output 2

7

Sample Input 3

1
B

Sample Output 3

0

Sample Input 4

20
2 19
5 13
6 4
15 6
12 19
13 19
3 11
8 3
3 20
16 13
7 14
3 17
7 8
10 20
11 9
8 18
8 2
10 1
6 13
WBWBWBBWWWBBWWBBBBBW

Sample Output 4

21

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        graph = buildGraph(in, n, n-1);
        char[] s = in.nextToken().toCharArray();
        color = new int[n];
        for (int i = 0; i < n ; i++) {
            color[i] = s[i] == 'W' ? 0 : 1;
        }

        out.println(solve());
        out.flush();
    }

    static void cutBlackLeaf() {
        int n = graph.length;
        available = new boolean[n];
        Arrays.fill(available, true);

        int[] deg = new int[n];
        int[] que = new int[n];
        int qh = 0;
        for (int i = 0; i < n ; i++) {
            deg[i] = graph[i].length;
            if (deg[i] == 1) {
                if (color[i] == 1) {
                    que[qh++] = i;
                }
            }
        }
        int qt = 0;
        while (qt < qh) {
            int now = que[qt++];
            available[now] = false;
            for (int to : graph[now]) {
                deg[to]--;
                if (deg[to] == 1 && color[to] == 1 && available[to]) {
                    que[qh++] = to;
                }
            }
        }

        for (int i = 0; i < n ; i++) {
            if (available[i]) {
                int de = 0;
                int[] cp = graph[i].clone();
                for (int to : cp) {
                    if (available[to]) {
                        de++;
                    }
                }
                graph[i] = new int[de];
                for (int to : cp) {
                    if (available[to]) {
                        graph[i][--de] = to;
                    }
                }
            } else {
                graph[i] = null;
            }
        }

    }

    static int solve() {
        int n = graph.length;


        if (n == 1) {
            return color[0]^1;
        }

        available = new boolean[n];
        cutBlackLeaf();

        int root = -1;
        int vc = 0;
        for (int i = 0; i < n ; i++) {
            if (available[i]) {
                vc++;
                if (graph[i].length >= 2) {
                    root = i;
                }
            }
        }
        if (vc <= 1) {
            // W or nothing
            return vc;
        }
        if (root == -1) {
            // W-W
            return 2;
        }

        int total = 0;
        for (int i = 0; i < n ; i++) {
            if (available[i]) {
                int gd = graph[i].length;
                color[i] ^= gd % 2;
                total += color[i] ^ 1;
            }
        }
        return (vc - 1) * 2 + total - find(root) * 2;
    }

    static int find(int rt) {
        int[] x = dfs0(rt, -1);
        int[] y = dfs0(x[1], -1);
        return y[0];
    }

    static int[] dfs0(int now, int par) {
        int[] best = new int[]{-1, -1};
        for (int to : graph[now]) {
            if (to == par || !available[to]) {
                continue;
            }
            int[] t = dfs0(to, now);
            if (best[0] < t[0]) {
                best = t.clone();
            }
        }
        if (best[0] == -1) {
            return new int[]{0, now};
        }
        best[0] += color[now] ^ 1;
        return best;
    }

    static boolean[] available;

    static int[] color;
    static int[][] graph;

    static int[][] buildGraph(InputReader in, int n, int m) {
        int[][] edges = new int[m][];
        int[][] graph = new int[n][];
        int[] deg = new int[n];
        for (int i = 0 ; i < m ; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            deg[a]++;
            deg[b]++;
            edges[i] = new int[]{a, b};
        }
        for (int i = 0 ; i < n ; i++) {
            graph[i] = new int[deg[i]];
        }
        for (int i = 0 ; i < m ; i++) {
            int a = edges[i][0];
            int b = edges[i][1];
            graph[a][--deg[a]] = b;
            graph[b][--deg[b]] = a;
        }
        return graph;
    }

    public static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}