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:
/*
 *
 * @author Mukesh Singh
 *
 */

import java.io.*;
import java.util.*;
import java.text.DecimalFormat;
@SuppressWarnings("unchecked")
public class AB {	
	//solve test cases
	int n , m ; int[][] gr ; int[]s ; int[]t ;
	void solve() throws Exception {
		n = in.nextInt() ;
		int[]a = new int[n];
		int[]b = new int[n];
		int[]count = new int[n];
		for(int i = 0 ; i < n-1 ; ++i ) {
			a[i] = in.nextInt()-1 ;
			b[i] = in.nextInt() - 1 ;
			++count[a[i]];
			++count[b[i]];
		}
		s = new int[n];
		t = new int[n];
		for(int i = 0 ; i < n ; ++i ) s[i] = in.nextInt();
		for(int i = 0 ; i < n ; ++i ) t[i] = in.nextInt();
		gr = new int[n][];
		for(int i = 0 ; i < n ; ++i)gr[i] = new int[count[i]];
		for(int i = 0 ; i < n-1 ; ++i ){
			gr[a[i]][--count[a[i]]] = b[i] ;
			gr[b[i]][--count[b[i]]] = a[i] ;
		}
		LinkedList<Integer> res = new LinkedList<>();
		f(0,-1,0,0,res);
		System.out.println(res.size());
		for(int aa : res) System.out.println(aa+1);
	}
	void f(int node , int par , int val , int chVal , LinkedList<Integer> ls){
		if(s[node] == t[node] && val %2 == 0 ){
			for(int u : gr[node]) if(u != par) f(u,node,chVal , val,ls);
		}
		else if(s[node] != t[node] && val %2 == 1 ){
			for(int u : gr[node]) if(u != par) f(u,node,chVal , val,ls);
		}
		else if(s[node] == t[node] && val %2 == 1 ){//flip node
			ls.addLast(node);
			for(int u : gr[node]) if(u != par) f(u,node,chVal , 0,ls);
		}else{
			ls.addLast(node);
			for(int u : gr[node]) if(u != par) f(u,node,chVal , 1,ls);
		}
	}
	//@ main function
	public static void main(String[] args) throws Exception {
		new AB();
	}
	
	InputReader in;
	PrintStream out ;
	DecimalFormat df ;
	AB() {
		try {
			File defaultInput = new File("file.in");
			if (defaultInput.exists()) 
				in = new InputReader("file.in");
			else 
				in = new InputReader();
			defaultInput = new File("file.out");
			if (defaultInput.exists()) 
				out = new PrintStream(new FileOutputStream("file.out"));
			else
				out = new PrintStream(System.out);
			df = new DecimalFormat("######0.00");
			solve();
			out.close();
		} 
		catch (Exception e) {
			e.printStackTrace();
			System.exit(261);
		}
	}
	
	class InputReader {
		BufferedReader reader;
		StringTokenizer tokenizer;
		
		InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}
		
		InputReader(String fileName) throws FileNotFoundException {
			reader = new BufferedReader(new FileReader(new File(fileName)));
		}
		
		String readLine() throws IOException {
			return reader.readLine();
		}
		
		String nextToken() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
				tokenizer = new StringTokenizer(readLine());
			return tokenizer.nextToken();
		}
		
		boolean hasMoreTokens() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				String s = readLine();
				if (s == null)
					return false;
				tokenizer = new StringTokenizer(s);
			}
			return true;
		}
		
		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(nextToken());
		}
		
		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(nextToken());
		}
		
		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(nextToken());
		}
	}
}