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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.*;


 
 
public class ck {

	private static InputStream stream;
	private static PrintWriter pw;
	
	
	
//	static int a;
//	static int b;
	static int f = 0;
	static int n;
	static int init[];
	static int goal[];
	static ArrayList<Integer> ans;
//	static int m;
//	static int arr[][];
//	static int arr[];
	static int[] visited;
	static ArrayList<Integer> arr[];

	
	public static void main(String[] args) throws NumberFormatException, IOException{
		//InputReader(System.in);
		//pw = new PrintWriter(System.out);
		
		Scanner in = new Scanner(System.in);
		
		n = in.nextInt();
		in.nextLine();
		
		goal = new int[n];
		init = new int[n];
		
		visited = new int[n];
		arr = new ArrayList[n];
		ans = new ArrayList();
		
		for(int i = 0;i<n;i++){
			arr[i] = new ArrayList();
		}
	
		//pw.println("kishan");
		for(int i = 0;i<n-1;i++){
			int a = in.nextInt();
			int b = in.nextInt();
			
			arr[a-1].add(b-1);
			arr[b-1].add(a-1);
		}
		
		for(int i = 0;i<n;i++){
			init[i] = in.nextInt();
		}
		
		for(int i = 0;i<n;i++){
			goal[i] = in.nextInt();
		}
		
		
		dfs(0,0,0,0);
		
		System.out.println(ans.size());
		
		for(int i = 0;i<ans.size();i++){
			int a = ans.get(i) + 1;
			System.out.println(a);
		}
		
		
}

	
	
	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}
	
//	public static void bfs(int s){
//		
//	
//		if(visited[s] == 1){
//			return;
//		}
//		c++;
//		visited[s] = 1;
//		Queue<Integer> q=new LinkedList<Integer>();
//    	q.add(s);
//  
//    	while(!q.isEmpty()){
//    		int top=q.poll();
//    		v++;
//    		Iterator<Integer> i= adj[top].listIterator();
//    		while(i.hasNext()){
//    			int n=i.next();
//    			if(visited[n] == 0){
//    				q.add(n);
//    				visited[n]=1;
//    				
//    			}
//    		}
//    	}
//		
//		
//	}
//	
//	
//	
	public static void dfs(int i,int odd,int even,int level){
		
		if(visited[i] == 1){
			return;
		}
		
		visited[i] = 1;
		
		
		if(level % 2 == 0){
			init[i] = (init[i] + even)%2;
		}else{
			init[i] = (init[i] + odd)%2;
		}
		
	//	System.out.println(i+1 + " " + init[i]);
			
		if(init[i] != goal[i]){
			if(level%2 == 0){
				for(int j = 0;j<arr[i].size();j++){
					dfs(arr[i].get(j),odd,even+1,level+1);
				}
			}else{
				for(int j = 0;j<arr[i].size();j++){
					dfs(arr[i].get(j),odd+1,even,level+1);
				}
			}
		
		ans.add(i);	
		}else{
			for(int j = 0;j<arr[i].size();j++){
				dfs(arr[i].get(j),odd,even,level+1);
			}
		}
		
		
		
	}
	
	
	
	
	public static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip 
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
	
	
	
	public static void Range(int[] numbers, int target) {
	    if (numbers == null)
	        return;

	    int low = 0, high = numbers.length - 1;
	    // get the start index of target number
	    int startIndex = -1;
	    while (low <= high) {
	        int mid = (high - low) / 2 + low;
	        if (numbers[mid] > target) {
	            high = mid - 1;
	        } else if (numbers[mid] == target) {
	            startIndex = mid;
	            high = mid - 1;
	        } else
	            low = mid + 1;
	    }

	    // get the end index of target number
	    int endIndex = -1;
	    low = 0;
	    high = numbers.length - 1;
	    while (low <= high) {
	        int mid = (high - low) / 2 + low;
	        if (numbers[mid] > target) {
	            high = mid - 1;
	        } else if (numbers[mid] == target) {
	            endIndex = mid;
	            low = mid + 1;
	        } else
	            low = mid + 1;
	    }

	    if (startIndex != -1 && endIndex != -1){
	        for(int i=0; i+startIndex<=endIndex;i++){
	            if(i>0)
	                System.out.print(',');
	            System.out.print(i+startIndex);
	        }
	    }
	}
	
	 // union code starts	
	
	 private static void initialize( int Arr[ ],int size[], int N)
	    {
	        for(int i = 0;i<N;i++)
	        {
	        	Arr[ i ] = i ;
	        	size[ i ] = 1;
	        }
	    }
	 
	 private static int root(int Arr[ ],int i)
	    {
	        while(Arr[ i ] != i)           //chase parent of current element until it reaches root
	        {
	            Arr[ i ] = Arr[ Arr[ i ] ] ; 
	            i = Arr[ i ];
	        }
	        return i;
	    }
	 
	 private static void union(int Arr[ ],int size[ ],int A,int B)
	    {
	        int root_A = root(Arr,A);
	        int root_B = root(Arr,B);
	     
	        if(root_A != root_B){
	        	 if(size[root_A] < size[root_B ])
	 	        {
	        		 Arr[ root_A ] = Arr[root_B];
	        		 size[root_B] += size[root_A];	 	
	 	        }
	 	        else
	 	        {   	
	 	        	Arr[ root_B ] = Arr[root_A];
	 	        	size[root_A] += size[root_B];	 	   
	 	        }	
	        }
	    }
	 
	 private static boolean find(int Arr[],int A,int B)
	    {
	        if( root(Arr,A)==root(Arr,B) )       //if A and B have the same root, it means that they are connected.
	        return true;
	        else
	        return false;
	    }
	 
	 
	 // union code ends
	
	
	 
//	 // Segment tree code begins
//	 
//	 
//	 static void build(int node,int start,int end)
//	 {
//	 if(start==end)
//	 tree[node]=a[start];
//	 else
//	 {
//	 int mid=(start+end)/2;
//	 build(2*node,start,mid);
//	 build(2*node+1,mid+1,end);
//	 if(tree[2*node]<tree[2*node+1])
//	 tree[node]=tree[2*node];
//	 else
//	 tree[node]=tree[2*node+1];
//	 }
//	 }
//	 
//	 
//	 static void update(int node,int start,int end,int idx,int val)
//	 {
//	 if(start==end)
//	 {
//	 a[idx]=val;
//	 tree[node]=val;
//	 }
//	 else
//	 {
//	 int mid=(start+end)/2;
//	 if(idx>=start&&idx<=mid)
//	 update(2*node,start,mid,idx,val);
//	 else
//	 update(2*node+1,mid+1,end,idx,val);
//	 if(tree[2*node]<tree[2*node+1])
//	 tree[node]=tree[2*node];
//	 else
//	 tree[node]=tree[2*node+1];
//	 }
//	 }
//	 
//	 static int query(int node,int start,int end,int l,int r)
//	 {
//	 if(l>end||start>r)
//	 return 100005;
//	 if(l<=start&&r>=end)
//	 return tree[node];
//	 int p1,p2;
//	 int mid=(start+end)/2;
//	 p1=query(2*node,start,mid,l,r);
//	 p2=query(2*node+1,mid+1,end,l,r);
//	 if(p1<p2)
//	 return p1;
//	 else
//	 return p2;
//	 }
//	 
//	 
//	 
//}

}

class Node{
	int a;
	int b;
}


class MyComp2 implements Comparator<Node>{
    
	@Override
	public int compare(Node o1, Node o2) {
		if(o1.b>o2.b){
			return 1;
		}else if(o1.b<o2.b){
			return -1;
		}else{
			return 0;
			
			
		}
		
		
	}
}