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:
/*
 * Remember a 7.0 student can know more than a 10.0 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 */
import java.util.*;
import java.util.Map.Entry;
import java.io.*;
import java.text.*;

import static java.lang.System.out;
import static java.util.Arrays.*;
import static java.lang.Math.*;
public class ContestMain {
	private static Reader in=new Reader();
	private static StringBuilder ans=new StringBuilder();
	private static long MOD=1000000007;//10^9+7 
	private static final int N=100000+7; //10^5
//	private static final int LIM=26;
//	private static final double PI=3.1415;
	private static ArrayList<Integer> v[]=new ArrayList[N];
	private static int color[]=new int[N];
	private static boolean mark[]=new boolean[N];
//	private static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	private static int init[];
	private static int goal[];
	private static int cnt=0;
	private static void dfs(int node,int a,int b){
		mark[node]=true;
		if(goal[node]!=init[node]){
			if(a==0){
				cnt++;
				ans.append(node+"\n");
			}
			a=b;
			b=1;
		}
		else{
			if(a==1){
				ans.append(node+"\n");
				cnt++;
			}
			a=b;
			b=0;
		}
		for(int x:v[node]){
			if(!mark[x]){
				dfs(x,a,b);
			}
		}
	}
	private static long powmod(long x,long n,long m){
		if(n==0)return 1;
		else if(n%2==0)return(powmod((x*x)%m,n/2,m));
		else return (x*(powmod((x*x)%m,(n-1)/2,m)))%m;
	}
//	private static void shuffle(long [] arr) {
//		for (int i = arr.length - 1; i >= 2; i--) {
//			int x = new Random().nextInt(i - 1);
//	        long temp = arr[x];
//	        arr[x] = arr[i];
//	        arr[i] = temp;
//	    }
//	 }
//	private static long gcd(long a, long b){
//		if(b==0)return a;
//		return gcd(b,a%b);
//	}
//	private static boolean check(int x,int y){
//		if((x>=0&&x<n)&&(y>=0&&y<m)&&mat[x][y]!='X'&&!visited[x][y])return true;
//		return false;
//	}
	public static void main(String[] args) throws IOException{
		int n=in.nextInt();
		init=new int[n+1];
		goal=new int[n+1];
		int x,y;
		for(int i=1;i<=n;i++)v[i]=new ArrayList();
		for(int i=0;i<n-1;i++){
			x=in.nextInt();
			y=in.nextInt();
			v[x].add(y);
			v[y].add(x);
		}
		for(int i=1;i<=n;i++)
			init[i]=in.nextInt();
		for(int i=1;i<=n;i++)
			goal[i]=in.nextInt();
		dfs(1,0,0);
		out.println(cnt+"\n"+ans);
	}
	static class Pair<T> implements Comparable<Pair>{
		int l;
		int r;
		int c;
		Pair(){
			l=0;
			r=0;
		}
		Pair(int k,int v,int p){
			l=k;
			r=v;
			c=p;
		}
		@Override
		public int compareTo(Pair o) {
			if(o.l!=l)return (int) (l-o.l);
			else return (r-o.r);
		}
		
	}
	static class Reader{
        BufferedReader br;
        StringTokenizer st;
        public Reader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
     
                	st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}