Problem: Iahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees.

The game is played on a tree having n nodes, numbered from 1 to n. Each node i has an initial value initi, which is either 0 or 1. The root of the tree is node 1.

One can perform several (possibly, zero) operations on the tree during the game. The only available type of operation is to pick a node x. Right after someone has picked node x, the value of node x flips, the values of sons of x remain the same, the values of sons of sons of x flips, the values of sons of sons of sons of x remain the same and so on.

The goal of the game is to get each node i to have value goali, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.

Input

The first line contains an integer n (1 ≤ n ≤ 105). Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; ui ≠ vi) meaning there is an edge between nodes ui and vi. 

The next line contains n integer numbers, the i-th of them corresponds to initi (initi is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goali (goali is either 0 or 1).

Output

In the first line output an integer number cnt, representing the minimal number of operations you perform. Each of the next cnt lines should contain an integer xi, representing that you pick a node xi.

Examples

Input

10
2 1
3 1
4 2
5 1
6 2
7 5
8 6
9 8
10 5
1 0 1 1 0 1 0 1 0 1
1 0 1 0 0 1 1 1 0 1


Output

2
4
7

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

/**
 * Problem Cf430C
 */
public class Cf430C {

    int[] init;
    int[] goal;
    Map<Integer, Set<Integer>> map;
    List<Integer> moves;

    public void run() {
        int n = in.nextInt();
        init = new int[n+1];
        goal = new int[n+1];
        map = new HashMap<>();
        map.put(1, new HashSet<>());
        moves = new ArrayList<>();
        for(int i = 1; i < n; ++i){
            int a = in.nextInt();
            int b = in.nextInt();
            map.computeIfAbsent(a, key -> new HashSet<>()).add(b);
            map.computeIfAbsent(b, key -> new HashSet<>()).add(a);
        }
        direct(1);
        // print(1);
        for(int i = 1; i <= n; ++i) init[i]=in.nextInt();
        for(int i = 1; i <= n; ++i) goal[i]=in.nextInt();
        run(1,0,0);
        out.println(moves.size());
        for(int m : moves)
            out.println(m);
    }

    // void print(int i){
    //     out.println(i);
    //     for(int j : map.get(i)) print(j);
    // }

    void direct(int i){
        for(int j : map.get(i)){
            map.get(j).remove(i);
            direct(j);
        }
    }

    void run(int i, int p, int g){
        init[i]^=g;
        int moved = init[i]==goal[i] ? 0 : 1;
        if(moved==1) moves.add(i);
        for(int j : map.get(i)){
            run(j, (g+moved)%2, p);
        }
    }

    /***********************************************************
     *                      BOILERPLATE                        *
    /***********************************************************/
    public InputReader in = new InputReader(System.in);
    public PrintWriter out = new PrintWriter(System.out);
    public void close() {out.close();}
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokens = null;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);}
        private boolean prime() {
            while (tokens == null || !tokens.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if(line==null) return false; // EOF
                    tokens = new StringTokenizer(line);
                } catch (IOException e) {throw new RuntimeException(e);}
            } return true;}
        public boolean hasNext() {return prime();}
        public String next() {prime(); return tokens.nextToken();}
        public int nextInt() {return Integer.parseInt(next());}
        public long nextLong() {return Long.parseLong(next());}
        public double nextDouble() {return Double.parseDouble(next());}
    }
    public static void main(String[] args) {
        Cf430C task = new Cf430C(); task.run(); task.close();}
}