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.util.*;
import java.io.*;
    public class Main {
        public static long mod= (long) (1e9 +7);
        static int arr1[];
        static int arr2[];
        static boolean visited1[];
        static boolean visited2[];
        static ArrayList<ArrayList<Integer>> node= new ArrayList<ArrayList<Integer>>();
        static int odd[];
        static int even[];
        static int level[];
        static ArrayList<Integer> count= new ArrayList<Integer>();
        public static void main(String args[]){
            InputReader s= new InputReader(System.in);
            OutputStream outputStream= System.out;
            PrintWriter out= new PrintWriter(outputStream);
            int n= s.nextInt();
            for(int i=0;i<=n;i++)
                node.add(new ArrayList<Integer>());
            for(int i=0;i<n-1;i++){
                int u= s.nextInt();
                int v= s.nextInt();
                node.get(u).add(v);
                node.get(v).add(u);
            }
            arr1= new int[n+1];
            arr2= new int[n+1];
            for(int i=1;i<=n;i++)
                arr1[i]= s.nextInt();
            for(int i=1;i<=n;i++){
                arr2[i]= s.nextInt();
            }
            //out.println(node.get(1));
            //out.println(node.get(2));
            Queue<Integer> queue= new LinkedList<>();
            queue.add(1);
            level= new int[n+1];
            visited1= new boolean[n+1];
            while(!queue.isEmpty()){
                int u= queue.remove();
                visited1[u]= true;
                if(u==1) level[1]= 1;
                for(int i=0;i<node.get(u).size();i++){
                    if(!visited1[node.get(u).get(i)]){
                        queue.add(node.get(u).get(i));
                        level[node.get(u).get(i)]= level[u]+1;
                    }
                }
            }
            odd= new int[n+1];
            even= new int[n+1];
            visited2= new boolean[n+1];
            dfs(1);
            /*for(int i=1;i<=n;i++){
                out.print(level[i]+" ");
            }*/
            out.println(count.size());
            for(int i=0;i<count.size();i++){
                out.println(count.get(i));
            }
            out.close();
        }
        static void dfs(int curr){
        //  System.out.println(curr+" "+even[curr]+" "+odd[curr]);
            visited2[curr]= true;
            if(arr1[curr]!= arr2[curr]){
                if(level[curr]%2!=0){
                    if(odd[curr]%2==0){
                        count.add(curr);
                        odd[curr]++;
            //          System.out.println("fsd");
                    }
                }
                else{
                    if(even[curr]%2==0){
                        count.add(curr);
                        even[curr]++;
                    }
                }
            }
            else{
                if(level[curr]%2!=0){
                    if(odd[curr]%2!=0){
                        odd[curr]++;
                        count.add(curr);
                    }
                }
                else{
                    if(even[curr]%2!=0){
                        even[curr]++;
                        count.add(curr);
                    }
                }
            }
            for(int i=0;i<node.get(curr).size();i++){
            //  System.out.println("fdg");
                if(visited2[node.get(curr).get(i)]== false){
                    //System.out.println("das");
                    even[node.get(curr).get(i)]= even[curr];
                    odd[node.get(curr).get(i)]= odd[curr];
                    dfs(node.get(curr).get(i));
                }
            }
        }
        static class InputReader {
    
            public BufferedReader reader;
            public StringTokenizer tokenizer;
     
            public InputReader(InputStream inputstream) {
              reader = new BufferedReader(new InputStreamReader(inputstream));
              tokenizer = null;
            }
            
            public String nextLine(){
                String fullLine=null;
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    try {
                      fullLine=reader.readLine();
                    } catch (IOException e) {
                      throw new RuntimeException(e);
                    }
                    return fullLine;
                  }
                  return fullLine;
            }
            public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                  tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                  throw new RuntimeException(e);
                }
              }
              return tokenizer.nextToken();
            }
            public long nextLong() {
                  return Long.parseLong(next());
                }
            public int nextInt() {
              return Integer.parseInt(next());
            }
          }
        static class Pair implements Comparable<Pair>
        {
            long f,s;
            Pair(long ii, long cc)
            {
                f=ii;
                s=cc;
            }
            
            public int compareTo(Pair o) 
            {
                return Long.compare(this.f, o.f);
            }
            
        }
        public static int gcd(int number1, int number2) {  
            if(number2 == 0){
                return number1;
            } 
            return gcd(number2, number1%number2); 
        }
        public static int combinations(int n,int r){
            if(n==r) return 1;
            if(r==1) return n;
            if(r==0) return 1;
            return combinations(n-1,r)+ combinations(n-1,r-1);
        }
        public static long binomialCoeff(int n, int k)
        {
            long C[][]= new long[n+1][k+1];
            int i, j;
         
            // Caculate value of Binomial Coefficient in bottom up manner
            for (i = 0; i <= n; i++)
            {
                for (j = 0; j <= Math.min(i, k); j++)
                {
                    // Base Cases
                    if (j == 0 || j == i)
                        C[i][j] = 1;
         
                    // Calculate value using previosly stored values
                    else
                        C[i][j] = C[i-1][j-1] + C[i-1][j];
                }
            }
         
            return C[n][k];
        }
        public static int expo(int a, int b){
            if (b==1)
                return a;
            if (b==2)
                return a*a;
    
            if (b%2==0){
                    return expo(expo(a,b/2),2);
            }
            else{
                return a*expo(expo(a,(b-1)/2),2);
            }
        }
        
        public static void sieve(int N){
            int arr[]= new int[N+1];
            for(int i=2;i<Math.sqrt(N);i++){
                if(arr[i]==0){
                    for(int j= i*i;j<= N;j= j+i){
                        arr[j]=1;
                    }
                }
            }
            // All the i for which arr[i]==0 are prime numbers.
        }
    }