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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Locale;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    long prevTime = System.currentTimeMillis();
                    new Main().run();
                    System.err.println("Total time: "
                            + (System.currentTimeMillis() - prevTime) + " ms");
                    System.err.println("Memory status: " + memoryStatus());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }, "1", 1L << 24).start();
    }

    void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        Object o = solve();
        if (o != null)
            out.println(o);
        out.close();
        in.close();
    }
    int[] value;
    int[] req;
    List<Integer>[] tree;
    List<Integer> ret = new ArrayList<Integer>();

    private Object solve() throws IOException {
        int n = ni();
        tree = new List[n];
        for(int i =0;i<n;i++)
            tree[i]= new ArrayList<Integer>();
        for(int i =0;i<n-1;i++){
            int u = ni()-1;
            int v = ni()-1;
            tree[u].add(v);
            tree[v].add(u);
        }
        value = nia(n);
        req= nia(n);
        
        go(-1,0, 0, 0);
        Collections.sort(ret);
        pln(ret.size());
        for(int a : ret)
            pln(a);
        
        return null;
    }

    private void go(int prev, int u, int par, int impar) {
        int curr = value[u]^par;
        if(curr!= req[u]){
            ret.add(u+1);
            par^=1;
        }
        for(int v : tree[u])
            if(v!=prev)
                go(u,v,impar,par);
    }
    
    
    BufferedReader in;
    PrintWriter out;
    StringTokenizer strTok = new StringTokenizer("");

    String nextToken() throws IOException {
        while (!strTok.hasMoreTokens())
            strTok = new StringTokenizer(in.readLine());
        return strTok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nl() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nd() throws IOException {
        return Double.parseDouble(nextToken());
    }

    int[] nia(int size) throws IOException {
        int[] ret = new int[size];
        for (int i = 0; i < size; i++)
            ret[i] = ni();
        return ret;
    }

    long[] nla(int size) throws IOException {
        long[] ret = new long[size];
        for (int i = 0; i < size; i++)
            ret[i] = nl();
        return ret;
    }

    double[] nda(int size) throws IOException {
        double[] ret = new double[size];
        for (int i = 0; i < size; i++)
            ret[i] = nd();
        return ret;
    }

    String nextLine() throws IOException {
        strTok = new StringTokenizer("");
        return in.readLine();
    }

    boolean EOF() throws IOException {
        while (!strTok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            strTok = new StringTokenizer(s);
        }
        return false;
    }

    void printRepeat(String s, int count) {
        for (int i = 0; i < count; i++)
            out.print(s);
    }

    void printArray(int[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i > 0)
                out.print(' ');
            out.print(array[i]);
        }
        out.println();
    }

    void printArray(long[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i > 0)
                out.print(' ');
            out.print(array[i]);
        }
        out.println();
    }

    void printArray(double[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i > 0)
                out.print(' ');
            out.print(array[i]);
        }
        out.println();
    }

    void printArray(double[] array, String spec) {
        for (int i = 0; i < array.length; i++) {
            if (i > 0)
                out.print(' ');
            out.printf(Locale.US, spec, array[i]);
        }
        out.println();
    }

    void printArray(Object[] array) {
        boolean blank = false;
        for (Object x : array) {
            if (blank)
                out.print(' ');
            else
                blank = true;
            out.print(x);
        }
        out.println();
    }

    @SuppressWarnings("rawtypes")
    void printCollection(Collection collection) {
        boolean blank = false;
        for (Object x : collection) {
            if (blank)
                out.print(' ');
            else
                blank = true;
            out.print(x);
        }
        out.println();
    }

    static String memoryStatus() {
        return (Runtime.getRuntime().totalMemory()
                - Runtime.getRuntime().freeMemory() >> 20)
                + "/" + (Runtime.getRuntime().totalMemory() >> 20) + " MB";
    }

    public void pln() {
        out.println();
    }

    public void pln(int arg) {
        out.println(arg);
    }

    public void pln(long arg) {
        out.println(arg);
    }

    public void pln(double arg) {
        out.println(arg);
    }

    public void pln(String arg) {
        out.println(arg);
    }

    public void pln(boolean arg) {
        out.println(arg);
    }

    public void pln(char arg) {
        out.println(arg);
    }

    public void pln(float arg) {
        out.println(arg);
    }

    public void pln(Object arg) {
        out.println(arg);
    }

    public void p(int arg) {
        out.print(arg);
    }

    public void p(long arg) {
        out.print(arg);
    }

    public void p(double arg) {
        out.print(arg);
    }

    public void p(String arg) {
        out.print(arg);
    }

    public void p(boolean arg) {
        out.print(arg);
    }

    public void p(char arg) {
        out.print(arg);
    }

    public void p(float arg) {
        out.print(arg);
    }

    public void p(Object arg) {
        out.print(arg);
    }

}