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.math.BigInteger;
import java.util.*;

import static java.lang.Math.min;
import static java.lang.Math.max;

public class Main {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {

        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

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

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Main().run();
        // Sworn to fight and die
    }

    public static void mergeSort(int[] a) {
        mergeSort(a, 0, a.length - 1);
    }

    private static void mergeSort(int[] a, int levtIndex, int rightIndex) {
        final int MAGIC_VALUE = 2;
        if (levtIndex < rightIndex) {
            if (rightIndex - levtIndex <= MAGIC_VALUE) {
                insertionSort(a, levtIndex, rightIndex);
            } else {
                int middleIndex = (levtIndex + rightIndex) / 2;
                mergeSort(a, levtIndex, middleIndex);
                mergeSort(a, middleIndex + 1, rightIndex);
                merge(a, levtIndex, middleIndex, rightIndex);
            }
        }
    }

    private static void merge(int[] a, int levtIndex, int middleIndex,
                              int rightIndex) {
        int length1 = middleIndex - levtIndex + 1;
        int length2 = rightIndex - middleIndex;
        int[] levtArray = new int[length1];
        int[] rightArray = new int[length2];
        System.arraycopy(a, levtIndex, levtArray, 0, length1);
        System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
        for (int k = levtIndex, i = 0, j = 0; k <= rightIndex; k++) {
            if (i == length1) {
                a[k] = rightArray[j++];
            } else if (j == length2) {
                a[k] = levtArray[i++];
            } else {
                a[k] = levtArray[i] <= rightArray[j] ? levtArray[i++]
                        : rightArray[j++];
            }
        }
    }

    private static void insertionSort(int[] a, int levtIndex, int rightIndex) {
        for (int i = levtIndex + 1; i <= rightIndex; i++) {
            int current = a[i];
            int j = i - 1;
            while (j >= levtIndex && a[j] > current) {
                a[j + 1] = a[j];
                j--;
            }
            a[j + 1] = current;
        }
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    class LOL implements Comparable<LOL> {

        long x;
        int y;

        public LOL(long x, int y) {
            this.x = x;
            this.y = y;

        }

        @Override
        public boolean equals(Object object) {
            boolean sameSame = false;

            if (object != null && object instanceof LOL) {
                sameSame = ((this.x == ((LOL) object).x) && (this.y == ((LOL) object).y));
            }

            return sameSame;
        }

        @Override
        public int compareTo(LOL o) {
            if (x > o.x) return 1;
            if (x < o.x) return -1;
            return 0;
            // return o.x * o.y - x * y; // <----
        }

    }


    Map <Integer, ArrayList<Integer>> g;
    int [] initVals;
    int [] goalVals;
    ArrayList<Integer> result;
    public void dfs(int v, int prevV, int currPar, int othPar) {

        initVals[v] ^= currPar;

        if (initVals[v] != goalVals[v]) {
            result.add(v);
            currPar ^= 1;
        }

        for (int i = 0; i < g.get(v).size(); i++) {
            int temp = g.get(v).get(i);
            if (temp != prevV) {
                dfs(temp, v ,othPar, currPar);
            }
        }

    }






    public void solve() throws IOException {
        int n = readInt();
        g = new HashMap<Integer, ArrayList<Integer>>();

        for (int i = 1; i <= n; i++) {
            g.put(i, new ArrayList<Integer>());
        }

        for (int i = 0; i < n - 1; i++) {
            int temp1 = readInt();
            int temp2 = readInt();

            if (!g.containsKey(temp2)) {
                g.put(temp2, new ArrayList<Integer>());
            }

            if (!g.containsKey(temp1)) {
                g.put(temp1, new ArrayList<Integer>());
            }


            g.get(temp1).add(temp2);
            g.get(temp2).add(temp1);

        }

        initVals = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            initVals[i] = readInt();
        }

        goalVals = new int[n + 1];

        for (int i = 1; i <= n; i++) {
            goalVals[i] = readInt();
        }

        result = new ArrayList<Integer>();
        dfs(1, 0, 0, 0);

        out.println(result.size());

        for (Integer val: result) {
            out.println(val);
        }

    }


}