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 org.omg.CORBA.MARSHAL;

import java.awt.event.InputEvent;
import java.awt.image.AreaAveragingScaleFilter;
import java.io.*;
import java.net.CookieHandler;
import java.util.*;
import java.math.*;
import java.lang.*;


public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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

        public int read() {
            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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }

    static long gcd(long a,long b){ if(b==0)return a;return gcd(b,a%b); }
    static long modPow(long a,long p,long m){ if(a==1)return 1;long ans=1;while (p>0){ if(p%2==1)ans=(ans*a)%m;a=(a*a)%m;p>>=1; }return ans; }
    static long modInv(long a,long m){return modPow(a,m-2,m);}

    ArrayList<Integer> ans;
    int count=0;
    void dfs(int u,int par,int freLevel0,int freLevel1,int curLevel,ArrayList<Integer> l[],int want[],int initial[]){

        if(curLevel==0){
            if(freLevel0==0){
                if(want[u]!=initial[u]){
                    count++;
                    ans.add(u+1);
                }
            }
            else{
                if(want[u]!=(initial[u]^1)){
                    count++;
                    ans.add(u+1);
                }
            }
        }
        else{
            if(freLevel1==0){
                if(want[u]!=initial[u]){
                    count++;
                    ans.add(u+1);
                }
            }
            else{
                if(want[u]!=(initial[u]^1)){
                    count++;
                    ans.add(u+1);
                }
            }
        }

        for(int v:l[u]){
            if(v==par)continue;
            if(curLevel==0){
                if(freLevel0==0){
                    if(want[u]!=initial[u]){
                        dfs(v,u,freLevel0^1,freLevel1,curLevel^1,l,want,initial);
                    }
                    else{
                        dfs(v,u,freLevel0,freLevel1,curLevel^1,l,want,initial);
                    }
                }
                else{
                    if(want[u]!=(initial[u]^1)){
                        dfs(v,u,freLevel0^1,freLevel1,curLevel^1,l,want,initial);
                    }
                    else{
                        dfs(v,u,freLevel0,freLevel1,curLevel^1,l,want,initial);
                    }
                }
            }
            else{
                if(freLevel1==0){
                    if(want[u]!=initial[u]){
                        dfs(v,u,freLevel0,freLevel1^1,curLevel^1,l,want,initial);
                    }
                    else{
                        dfs(v,u,freLevel0,freLevel1,curLevel^1,l,want,initial);
                    }
                }
                else{
                    if(want[u]!=(initial[u]^1)){
                        dfs(v,u,freLevel0,freLevel1^1,curLevel^1,l,want,initial);
                    }
                    else{
                        dfs(v,u,freLevel0,freLevel1,curLevel^1,l,want,initial);
                    }
                }
            }
        }
    }

    public void run() {
        Scanner  sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        ArrayList<Integer> l[]=new ArrayList[n];
        for (int i = 0; i <n ; i++) {
            l[i]=new ArrayList<>();
        }
        for (int i = 0; i <n-1 ; i++) {
            int u=sc.nextInt()-1;
            int v=sc.nextInt()-1;
            l[v].add(u);
            l[u].add(v);
        }
        int initial[]=new int[n];
        int want[]=new int[n];
        for (int i = 0; i <n ; i++) {
            initial[i]=sc.nextInt();
        }
        for (int i = 0; i <n ; i++) {
            want[i]=sc.nextInt();
        }
        ans=new ArrayList<>();
        dfs(0,-1,0,0,0,l,want,initial);
        out.println(count);
        for (int i = 0; i <ans.size() ; i++) {
            out.println(ans.get(i));
        }

        out.close();
    }


}