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.beans.IntrospectionException;
        import java.io.*;
        import java.lang.reflect.Array;
        import java.util.*;
        import java.lang.*;
        import static java.lang.Math.*;
        public class main implements Runnable {

            static ArrayList<Integer> adj[];

            static void Check2(int n) {
                adj = new ArrayList[n + 1];
                for (int i = 0; i <= n; i++) {
                    adj[i] = new ArrayList<>();
                }

            }
            static void add(int i, int j)
            {
                adj[i].add(j);
                adj[j].add(i);
            }



            public static void main(String[] args) {
                new Thread(null, new main(), "Check2", 1 << 26).start();// to increse stack size in java
            }
            static long mod = (long) (1e9 + 7);
            public void run() {
                InputReader in = new InputReader(System.in);
                PrintWriter w = new PrintWriter(System.out);

                int n=in.nextInt();
                Check2(n);
                for(int i=0;i<n-1;i++){

                    int c=in.nextInt();
                    int d=in.nextInt();
                    add(c,d);
                }
                init=new int[n+1];
                des=new int[n+1];
                list=new ArrayList<>();
                for(int i=1;i<=n;i++)init[i]=in.nextInt();
                for(int i=1;i<=n;i++)des[i]=in.nextInt();

                dfs(1,new int[n+1],false,false,0);

                w.println(list.size());
                for(Integer ne:list)w.println(ne);


                    w.close();

            }

            static int init[],des[];
            static ArrayList <Integer> list;
            static void dfs(int i,int v[],boolean isflip,boolean isflip2,int lvl)
            {
                if(v[i]==1)return;

                v[i]=1;
                int val=init[i];
                if(lvl%2==0) {
                    if (isflip) val = val ^ 1;
                }
                else {
                    if (isflip2) val = val ^ 1;
                }
                if(val!=des[i]){
                    list.add(i);
                           if(lvl%2==0){

                        isflip=!isflip;

                    }
                    else{

                        isflip2=!isflip2;

                    }

                }

                for(Integer ne:adj[i])
                {
                    dfs(ne,v,isflip,isflip2,lvl+1);
                }

            }
            static void diji(int s,long dist[],ArrayList <pair> adj[]){
                dist[s]=0;
                PriorityQueue <pair> q=new PriorityQueue<>(new cmp());
                q.add(new pair(s,0));
                while (!q.isEmpty())
                {
                    pair p1=q.poll();
                    for(pair ne:adj[p1.a]){

                        if((long)p1.b+(long)ne.b<dist[ne.a]){
                            dist[ne.a]=(long)p1.b+(long)ne.b;
                            pair p2=new pair(ne.a,dist[ne.a]);
                            q.add(p2);
                        }

                    }
                }

            }
            static class cmp implements Comparator<pair>{

                public  int compare(pair o1,pair o2)
                {
                    return o1.b<o2.b?-1:o1.b>o2.b?1:0;
                }

            }

            static class pair {
                int a;
                long b;
                pair(int a,long b){
                    this.a=a;
                    this.b=b;
                }
                        public boolean equals(Object obj) {      //  override equals method for object to remove tem from arraylist and sets etc.......
                            if (this == obj)
                                return true;
                            if (obj == null)
                                return false;
                            if (getClass() != obj.getClass())
                                return false;
                            pair other = (pair) obj;
                            if (b!= other.b||a!=other.a)
                                return false;
                            return true;
                        }
            }

            static long modinv(long a,long b)
            {
                long p=power(b,mod-2);

                p=a%mod*p%mod;
                p%=mod;

                return p;

            }

            static long power(long x,long y){
                if(y==0)return 1%mod;
                if(y==1)return x%mod;


                long res=1;
                x=x%mod;
                while(y>0){


                    if((y%2)!=0){
                        res=(res*x)%mod;
                    }


                    y=y/2;
                    x=(x*x)%mod;
                }


                return res;

            }
            static  int gcd(int a,int b){

                if(b==0)return a;
                return gcd(b,a%b);
            }

            static  void sev(int a[],int n){

                for(int i=2;i<=n;i++)a[i]=i;
                for(int i=2;i<=n;i++){

                    if(a[i]!=0){
                        for(int j=2*i;j<=n;){

                            a[j]=0;
                            j=j+i;
                        }
                    }

                }

            }



            static class node{

                int y;
                int val;

                node(int a,int b){

                    y=a;
                    val=b;

                }


            }

            static class InputReader
            {
                private InputStream stream;
                private byte[] buf = new byte[1024];
                private int curChar;
                private int numChars;
                private SpaceCharFilter filter;

                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()
                {
                    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                    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);
                }
            }







        }