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.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.StringTokenizer;

/**
 *
 *
 * 10 5 8 1 10 3 6 2 9 7 4 4 2 6 3 1 9 10 5 8 7
 *
 * @author pttrung
 */
public class C {

    //   public static long x, y, gcd;
    public static int Mod = 1000000007;
    public static PrintWriter out;
    public static ArrayList<Integer> re = new ArrayList();

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner();
        out = new PrintWriter(System.out);
        //   System.out.println(Integer.MAX_VALUE);
        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        int n = in.nextInt();
        ArrayList<Integer>[] map = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            map[i] = new ArrayList();
        }
        for (int i = 0; i < n - 1; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            map[a].add(b);
            map[b].add(a);
        }
        int[] org = new int[n];
        int[] goal = new int[n];
        for (int i = 0; i < n; i++) {
            org[i] = in.nextInt();

        }
        for (int i = 0; i < n; i++) {
            goal[i] = in.nextInt();
        }
        int val = cal(0, -1, org, goal, map);
        out.println(val);
        for (int i : re) {
            out.println(i);
        }
        out.close();
    }

    public static int cal(int node, int pa, int[] data, int[] goal, ArrayList<Integer>[] map) {
        int result = 0;
        if (data[node] != goal[node]) {
            re.add(node + 1);
            result++;
            result += update(node, pa, data, goal, true, map);
        }
        for (int i : map[node]) {
            if (i != pa) {
                result += cal(i, node, data, goal, map);
            }
        }
        return result;
    }

    public static int update(int node, int pa, int[] data, int[] goal, boolean flip, ArrayList<Integer>[] map) {
        int result = 0;
        if (flip) {
            data[node] = 1 - data[node];

            if (data[node] != goal[node]) {
                re.add(node + 1);
                result++;
                data[node] = 1 - data[node];
                return result;
            }
        }
        for (int i : map[node]) {
            if (i != pa) {
                result += update(i, node, data, goal, !flip, map);
            }
        }
        return result;
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            if (x != o.x) {
                return x - o.x;
            } else {
                return y - o.y;
            }
        }
    }
//    public static void extendEuclid(long a, long b) {
//        if (b == 0) {
//            x = 1;
//            y = 0;
//            gcd = a;
//            return;
//        }
//        extendEuclid(b, a % b);
//        long x1 = y;
//        long y1 = x - (a / b) * y;
//        x = x1;
//        y = y1;
//
//    }

    public static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        public void update(int index, int value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public int get(int index) {
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}