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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.Scanner;
import java.util.TreeMap;

public class Solution{
	
	///////////////////////////////////////////////////////////////////////////
	static class FastScanner{
		BufferedReader s;
		StringTokenizer st;
		
		public FastScanner(){
			st = new StringTokenizer("");
			s = new BufferedReader(new InputStreamReader(System.in));
		}
		
		public FastScanner(File f) throws FileNotFoundException{
			st = new StringTokenizer("");
			s = new BufferedReader (new FileReader(f));
		}
		
		public int nextInt() throws IOException{
			if(st.hasMoreTokens())
				return Integer.parseInt(st.nextToken());
			else{
				st = new StringTokenizer(s.readLine());
				return nextInt();
			}
		}
		
		public double nextDouble() throws IOException{
			if(st.hasMoreTokens())
				return Double.parseDouble(st.nextToken());
			else{
				st = new StringTokenizer(s.readLine());
				return nextDouble();
			}
		}
		
		public long nextLong() throws IOException{
			if(st.hasMoreTokens())
				return Long.parseLong(st.nextToken());
			else{
				st = new StringTokenizer(s.readLine());
				return nextLong();
			}
		}
		
		public String nextString() throws IOException{
			if(st.hasMoreTokens())
				return st.nextToken();
			else{
				st = new StringTokenizer(s.readLine());
				return nextString();
			}
			
		}
		public String readLine() throws IOException{
			return s.readLine();
		}
		
		public void close() throws IOException{
			s.close();
		}
		
	}
	
	////////////////////////////////////////////////////////////////////
	//		Number Theory
	
	public static int divisor(int x){
	    int limit = x;
	    int numberOfDivisors = 0;

	    for (int i=1; i < limit; ++i) {
	        if (x % i == 0) {
	            limit = x / i;
	            if (limit != i) {
	                numberOfDivisors++;
	            }
	            numberOfDivisors++;
	        }
	    }

	    return numberOfDivisors;
    }
	
	
	public static long gcd(long a, long b){
		return b == 0 ? a : gcd(b,a%b);
	}
	
  
	public static long lcm(long a,long b, long c){
		return lcm(lcm(a,b),c);
	}
	
	public static long lcm(long a, long b){
		return a*b/gcd(a,b);
	}
	
	
	////////////////////////////////////////////////////////////////////
	
	
//	  private static  	FastScanner s = new FastScanner(new File("input.txt"));
//	  private static PrintWriter ww = new PrintWriter(new FileWriter("output.txt"));
	  private static FastScanner s = new FastScanner();   
      private static PrintWriter ww = new PrintWriter(new OutputStreamWriter(System.out));
//    private static Scanner s = new Scanner(System.in);
      @SuppressWarnings("unused")
	private static Map<Integer,Integer> mm = new HashMap<Integer,Integer>();
      @SuppressWarnings("unused")
	private static Map<Integer,node> mn = new HashMap<Integer,node>();
	@SuppressWarnings("unused")
	private static int[][] states = { {-1,0} , {1,0} , {0,-1} , {0,1} };
	
      
    //////////////////////////////////////////////////////////////////// 
      
     static class node{
      	int l;
      	int r;
      	int d;
      	public node(int x, int y, int z){
      		this.l  = x;
      		this.r = y;
      		this.d = z;
      	}
      }
    
    public static void main(String[] args) throws IOException{
 		Solution so = new Solution();
 		so.solve();
 	}
     
    ////////////////////////////////////////////////////////////////////
     
    ArrayList<Integer>[] arr = new ArrayList[100009];
    int[] src;
    int[] dsc;
    boolean[] vis;
    List<Integer> li = new ArrayList<Integer>();
    
   void dfs(int x , int curLevel, int nextLevel){
	   
	   vis[x] = true;
	   int sr = ((src[x]^curLevel)&1);
	   int ds = dsc[x];
	   
	   if(sr != ds){
		   li.add(x);
		   curLevel++;
	   }
	   
	   for(int to : arr[x]){
		   if(!vis[to])
			   dfs(to,nextLevel,curLevel);
	   }
   }
    
     void solve() throws IOException{
    	
    	int n = s.nextInt();
    	src = new int[n+1];
    	dsc = new int[n+1];
    	vis = new boolean[n+1];
    	for(int i=0;i<=n;i++) arr[i] = new ArrayList<Integer>();
    	
    	for(int i=1;i<n;i++){
    		int a = s.nextInt();
    		int b = s.nextInt();
    		arr[a].add(b);
    		arr[b].add(a);
    	}
    	
    	for(int i=1;i<=n;i++) src[i] = s.nextInt();
    	for(int i=1;i<=n;i++) dsc[i] = s.nextInt();
    	
    	dfs(1,0,0);
    	
    	ww.println(li.size());
    	Iterator<Integer> it = li.iterator();
    	while(it.hasNext())
    		ww.println(it.next());
    	
        s.close();
 	    ww.close(); 
     }
    
}