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.*;
//267630EY
public class Main429A
{
  static PrintWriter out=new PrintWriter(System.out);
  static Vector<Integer>[] g;
  static int[] init;
  static int[] fi;
  static boolean[] marked;
  static int ans=0;
  static Vector<Integer> sol;
  
  static void dfs(int even,int odd,int level,int s,int in)
  {
    marked[s]=true;
    if(in!=fi[s])
    {
      //System.out.println(s);
      if(level%2==0)
      {
        even++;
      }else
        odd++;
      ans++;
      sol.add(s);
    }
    //else
      
    for(int i:g[s])
    {
      if(!marked[i])
      {
        if(level%2==0)
        {
          dfs(even,odd,level+1,i,(init[i]+odd)%2);
        }
        else
          dfs(even,odd,level+1,i,(init[i]+even)%2);
      }
    }
  }
      
    
  
  
  public static void main(String[] args) throws IOException
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    g=(Vector<Integer>[]) new Vector[n];
    for(int i=0;i<n;i++)
      g[i]=new Vector<Integer>();
    for(int i=0;i<n-1;i++)
    {
      int u=sc.nextInt();
      int v=sc.nextInt();
      u--;
      v--;
      g[u].add(v);
      g[v].add(u);
      //if(u<v) g[u].add(v);
      //else g[v].add(u);
    }
    init=new int[n];
    fi=new int[n];
    marked=new boolean[n];
      
    init=sc.nextIntArray(n);
    fi=sc.nextIntArray(n);
    ans=0;
    sol=new Vector<Integer>();
    dfs(0,0,0,0,init[0]);
    out.println(ans);
    for(int j:sol)
      out.println(j+1);
    out.flush();
    
    
    
    
    
  }
  static class Scanner
  {
    BufferedReader br;
    StringTokenizer tk=new StringTokenizer("");
    public Scanner(InputStream is) 
        {
      br=new BufferedReader(new InputStreamReader(is));
    }
        public int nextInt() throws IOException
        {
          if(tk.hasMoreTokens())
                return Integer.parseInt(tk.nextToken());
          tk=new StringTokenizer(br.readLine());
          return nextInt();
        }
        public long nextLong() throws IOException
        {
            if(tk.hasMoreTokens())
              return Long.parseLong(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextLong();
        }
        public String next() throws IOException
        {
          if(tk.hasMoreTokens())
            return (tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return next();
        }
        public String nextLine() throws IOException
        {
          tk=new StringTokenizer("");
          return br.readLine();
        }
        public double nextDouble() throws IOException
        {
            if(tk.hasMoreTokens())
              return Double.parseDouble(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextDouble();
        }
        public char nextChar() throws IOException
        {
            if(tk.hasMoreTokens())
              return (tk.nextToken().charAt(0));
            tk=new StringTokenizer(br.readLine());
            return nextChar();
        }
        public int[] nextIntArray(int n) throws IOException
        {
            int a[]=new int[n];
            for(int i=0;i<n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArray(int n) throws IOException
        {
          long a[]=new long[n];
            for(int i=0;i<n;i++)
              a[i]=nextLong();
            return a;
        }
        public int[] nextIntArrayOneBased(int n) throws IOException
        {
          int a[]=new int[n+1];
            for(int i=1;i<=n;i++)
              a[i]=nextInt();
            return a;
        }
        public long[] nextLongArrayOneBased(int n) throws IOException
        {
          long a[]=new long[n+1];
          for(int i=1;i<=n;i++)
                a[i]=nextLong();
          return a;
        }
  }
}