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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Random;

/**
 * @author Ivan Pryvalov (ivan.pryvalov@gmail.com)
 */
public class Codeforces_R245_Div1_A implements Runnable{

	boolean debug = false;
	
	int N;
	List<Integer>[] adj;
	int[] init;
	int[] goal; 
	int[] visited;
	int level;
	int[] path;
	int[] xor;
	List<Integer> result;
	
	private void solve() throws IOException {
		N = scanner.nextInt(); //10^5
		adj = new List[N]; 
		for (int i = 0; i < adj.length; i++) {
			adj[i] = new ArrayList<>();
		}
		for (int i = 0; i < N-1; i++) {
			int u = scanner.nextInt()-1;
			int v = scanner.nextInt()-1;
			adj[u].add(v);
			adj[v].add(u);
		}
		init = scanner.loadIntArray(N);
		goal = scanner.loadIntArray(N);
		//solve
		visited = new int[N];
		level = 0;
		path = new int[N];
		xor = new int[N];
		
		result = new ArrayList<>();
		go(0);
		
		out.println(result.size());
		for(int x:result){
			out.println(x+1);
		}
	}

	private void go(int u) {
		visited[u] = 1;
		path[level] = u;
		if (level>=2){
			xor[u] = xor[path[level-2]];
		}
		if ((init[u]^xor[u]) != goal[u]){
			xor[u] = 1-xor[u];
			result.add(u);
		}
		
		level++;
		for(int v: adj[u]) if (visited[v]==0){
			go(v);
		}
		level--;
	}

	/////////////////////////////////////////////////
	final int BUF_SIZE = 1024 * 1024 * 8;//important to read long-string tokens properly
	final int INPUT_BUFFER_SIZE = 1024 * 1024 * 8 ;
	final int BUF_SIZE_INPUT = 1024;
	
	final int BUF_SIZE_OUT = 1024;
	
	boolean inputFromFile = false;
	String filenamePrefix = "A-small-attempt0";
	String inSuffix = ".in";
	String outSuffix = ".out";
	
	PrintStream out;
	ByteScanner scanner;
	ByteWriter writer;
	
//	@Override
	public void run() {
		try{
			InputStream bis = null;
			OutputStream bos = null;
			if (inputFromFile){
				File baseFile = new File(getClass().getResource("/").getFile());
				bis = new BufferedInputStream(
						new FileInputStream(new File(
								baseFile, filenamePrefix+inSuffix)),
								INPUT_BUFFER_SIZE);
				bos = new BufferedOutputStream(
						new FileOutputStream(
								new File(baseFile, filenamePrefix+outSuffix)));
				out = new PrintStream(bos);
			}else{
				bis = new BufferedInputStream(System.in, INPUT_BUFFER_SIZE);
				bos = new BufferedOutputStream(System.out);
				out = new PrintStream(bos);
			}
			scanner = new ByteScanner(bis, BUF_SIZE_INPUT, BUF_SIZE);
			writer = new ByteWriter(bos, BUF_SIZE_OUT);
			
			solve();
			out.flush();
		}catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	
	public interface Constants{
		final static byte ZERO = '0';//48 or 0x30
		final static byte NINE = '9';
		final static byte SPACEBAR = ' '; //32 or 0x20
		final static byte MINUS = '-'; //45 or 0x2d	
		
		final static char FLOAT_POINT = '.';
	}
	
	public static class EofException extends IOException{
	}
	
	public static class ByteWriter implements Constants {
		
		int bufSize = 1024;
		byte[] byteBuf = new byte[bufSize];
		OutputStream os;
		
		public ByteWriter(OutputStream os, int bufSize){
			this.os = os;
			this.bufSize = bufSize;
		}
		
		public void writeInt(int num) throws IOException{
	         int byteWriteOffset = byteBuf.length;
	         if (num==0){
	        	 byteBuf[--byteWriteOffset] = ZERO;
	         }else{
	        	 int numAbs = Math.abs(num);
	        	 while (numAbs>0){
	        		 byteBuf[--byteWriteOffset] = (byte)((numAbs % 10) + ZERO);
	        		 numAbs /= 10;
	        	 }
	        	 if (num<0)
	        		 byteBuf[--byteWriteOffset] = MINUS;
	         }
	         os.write(byteBuf, byteWriteOffset, byteBuf.length - byteWriteOffset);
		}
		
		/**
		 * Please ensure ar.length <= byteBuf.length!
		 * 
		 * @param ar
		 * @throws IOException
		 */
		public void writeByteAr(byte[] ar) throws IOException{
			for (int i = 0; i < ar.length; i++) {
				byteBuf[i] = ar[i];
			}
			os.write(byteBuf,0,ar.length);
		}
		
		public void writeSpaceBar() throws IOException{
			byteBuf[0] = SPACEBAR;
			os.write(byteBuf,0,1);
		}
		
	}
	
	public static class ByteScanner implements Constants{
		
		InputStream is;
		
		public ByteScanner(InputStream is, int bufSizeInput, int bufSize){
			this.is = is;
			this.bufSizeInput = bufSizeInput;
			this.bufSize = bufSize;
			
			byteBufInput = new byte[this.bufSizeInput];
			byteBuf = new byte[this.bufSize];
		}
		
		public ByteScanner(byte[] data){
			byteBufInput = data;
			bufSizeInput = data.length;
			bufSize = data.length;
			byteBuf = new byte[bufSize];
			byteRead = data.length;
			bytePos = 0;
		}
		
		private int bufSizeInput;
		private int bufSize;
		
		byte[] byteBufInput;
		byte by=-1;
		int byteRead=-1;
		int bytePos=-1;

		byte[] byteBuf;
		int totalBytes;
		
		boolean eofMet = false;
		
		private byte nextByte() throws IOException{
			
			if (bytePos<0 || bytePos>=byteRead){
				byteRead = is==null? -1: is.read(byteBufInput);
				bytePos=0;
				if (byteRead<0){
					byteBufInput[bytePos]=-1;//!!!
					if (eofMet)
						throw new EofException();
					eofMet = true;
				}
			}
			return byteBufInput[bytePos++];
		}
		
		/**
		 * Returns next meaningful character as a byte.<br>
		 * 
		 * @return
		 * @throws IOException
		 */
		public byte nextChar() throws IOException{
			while ((by=nextByte())<=0x20);
			return by;
		}
		
		/**
		 * Returns next meaningful character OR space as a byte.<br>
		 * 
		 * @return
		 * @throws IOException
		 */
		public byte nextCharOrSpacebar() throws IOException{
			while ((by=nextByte())<0x20);
			return by;
		}
		
	    /**
	     * Reads line.
	     * 
	     * @return
	     * @throws IOException
	     */
	    public String nextLine() throws IOException {
            readToken((byte)0x20);
            return new String(byteBuf,0,totalBytes);
	    }
	    
	    public byte[] nextLineAsArray() throws IOException {
            readToken((byte)0x20);
            byte[] out = new byte[totalBytes];
            System.arraycopy(byteBuf, 0, out, 0, totalBytes);
            return out;
	    }
	    
		
	    /**
	     * Reads token. Spacebar is separator char.
	     * 
	     * @return
	     * @throws IOException
	     */
	    public String nextToken() throws IOException {
            readToken((byte)0x21);
            return new String(byteBuf,0,totalBytes);
	    }
	    
	    /**
	     * Spacebar is included as separator char
	     * 
	     * @throws IOException
	     */
	    private void readToken() throws IOException {	    	
            readToken((byte)0x21);
	    }
	    
	    private void readToken(byte acceptFrom) throws IOException {
            totalBytes = 0;
            while ((by=nextByte())<acceptFrom);
            byteBuf[totalBytes++] = by;
            while ((by=nextByte())>=acceptFrom){
                byteBuf[totalBytes++] = by;
            }
	    }
		
	    public int nextInt() throws IOException{
			readToken();
			int num=0, i=0;
			boolean sign=false;
			if (byteBuf[i]==MINUS){
				sign = true;
				i++;
			}
			for (; i<totalBytes; i++){
				num*=10;
				num+=byteBuf[i]-ZERO;
			}
			return sign?-num:num;
		}
		
		public long nextLong() throws IOException{
			readToken();
			long num=0;
			int i=0;
			boolean sign=false;
			if (byteBuf[i]==MINUS){
				sign = true;
				i++;
			}
			for (; i<totalBytes; i++){
				num*=10;
				num+=byteBuf[i]-ZERO;
			}
			return sign?-num:num;
		}
		
		/*
		//TODO test Unix/Windows formats
		public void toNextLine() throws IOException{
			while ((ch=nextChar())!='\n');
		}
		*/
		
		public double nextDouble() throws IOException{
			readToken();
			char[] token = new char[totalBytes];
			for (int i = 0; i < totalBytes; i++) {
				token[i] = (char)byteBuf[i];
			}
			return Double.parseDouble(new String(token));
		}
		
		public int[] loadIntArray(int size) throws IOException{
			int[] a = new int[size];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
			return a;
		}
		
		public long[] loadLongArray(int size) throws IOException{
			long[] a = new long[size];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
			return a;
		}
	    
	}
	
	public static abstract class Timing{
		private static int counter = 0;
		protected String name = "Timing"+(++counter);
		private boolean debug;
		
		public Timing(boolean debug) {
			super();
			this.debug = debug;
		}
		
		public abstract void run();
		public void start(){
			long time1 = System.currentTimeMillis();
			run();
			long time2 = System.currentTimeMillis();
			if (debug)
				System.out.println(name+" time = "+(time2-time1)/1000.0+" s.");
		}
		
	}
	
	public static class TimeMonitor{
		public boolean printNow = true;
		String name;
		public TimeMonitor(String name, boolean printNow) {
			super();
			this.name = name;
			this.printNow = printNow;
		}
		long time1 = 0, time2 = 0;
		public TimeMonitor start(){
			time1 = System.currentTimeMillis();
			return this;
		}
		public void stop(){
			time2 = System.currentTimeMillis();
			if (printNow) printStat();
		}
		public void printStat(){
			if (time2==0){
				System.out.println("['"+name+"' is still running..."+"]");
			}else{
				System.out.println("['"+name+"', time = "+(time2-time1)/1000.0+" s."+"]");
			}
		}
	}
	
	public static class Alg{
		public static interface BooleanChecker{
			public boolean check(long arg);
		}
		
		public static class BinarySearch{
					
			/**
			 * This check returns boolean value, result of function.
			 * It should be monotonic.
			 * 
			 * @return
			 */
			public BooleanChecker bc;
			
			
			/**
			 * Returns following element: <pre> 0 0 [1] 1 1</pre>
			 */
			public long search(long left, long right){
				while (left<=right){
					long mid = (left+right)/2;
					if (bc.check(mid)){
						right = mid-1;
					}else{
						left = mid+1;
					}
				}
				return left;
			}
			
			/**
			 * Optional.<br>
			 * Returns following element: <pre> 1 1 [1] 0 0</pre>
			 */
			public long searchInverted(long left, long right){
				while (left<=right){
					long mid = (left+right)/2;
					if (!bc.check(mid)){
						right = mid-1;
					}else{
						left = mid+1;
					}
				}
				return left - 1; 
			}
		}
	}
	
	public static class Modulo{
		long mod = (long)1e9+7;
		
		public Modulo(long mod) {
			super();
			this.mod = mod;
		}

		public long inv(long a) {
			long res =  pow(a, mod-2);
			return res;
		}

		public long pow(long a, long x) {
			if (x==0)
				return 1;
			long part = 1;
			if ((x&1)!=0)
				part = a;
			return (part * pow((a*a)%mod, x>>1)) % mod;
		}
		
		public long c(long n, long m){
			long res = 1;
			for(int i=1; i<=m; i++){
				res = (res * (n-m+i)) % mod;
				res = (res * inv(i)) % mod;
			}
			return res;
		}
		
	}
	
	
	/**
	 * Added 26.04.2013. 
	 * See KROK 2013, Round 1, Problem D.
	 */
	static class DisjointUnionSet implements Cloneable{
		
		int[] rank;
		int[] parent;
		
		protected DisjointUnionSet clone(){
			DisjointUnionSet cloned = new DisjointUnionSet(parent.length);
			for(int i=0; i<parent.length; i++){
				cloned.parent[i] = parent[i];
				cloned.rank[i] = rank[i];
			}
			return cloned;
		}

		public DisjointUnionSet(int n) {
			rank = new int[n];
			parent = new int[n];
			
			for (int i = 0; i < n; i++) {
				parent[i] = i;
			}
		}
		
		@Override
		public String toString() {
			return "disj [parents=" + Arrays.toString(parent) + "]";
		}

		/**
		 * Problem specific or general?
		 * O(N * alpha)
		 * 
		 * @param set2
		 */
		public void union(DisjointUnionSet set2){
			for(int i=0; i<parent.length; i++){
				parent[find(i)] = parent[find(set2.find(i))];
			}
		}
		
		
		/**
		 * @param index1 range 0..n-1
		 * @param index2
		 */
		public void union(int index1, int index2){
			int p1 = find(index1);
			int p2 = find(index2);
			
			if (rank[p1] > rank[p2]){
				parent[p2] = p1;
			}else if (rank[p2] > rank[p1]){
				parent[p1] = p2;
			}else{
				parent[p2] = p1;
				rank[p1]++;
			}
		}

		/**
		 *  O(alpha(n)) 
		 * 
		 * @param index
		 * @return
		 */
		private int find(int index) {
			if (parent[index] != index)
				parent[index] =  find(parent[index]);
			return parent[index];
		}
		
		/**
		 * O(N alpha(N)) ==> see find()
		 * 
		 * @return
		 */
		public int getCountDisjointSets(){
			int[] used = new int[parent.length];
			for(int i=0; i<parent.length; i++){
				used[find(i)] = 1;
			}
			int res = 0;
			for(int i=0; i<parent.length; i++){
				res += used[i];
			}
			return res;
		}
	}

	private static Random rnd = new Random();
	public static class ArrayUtils{
		public static void shuffle(int[] a){
			for(int j=a.length-1; j>=1; j--){
				int i = rnd.nextInt(j+1);
				swap(a, i, j);
			}
		}
		
		public static void swap(int[] a, int i, int j){
			int tmp = a[i];
			a[i] = a[j];
			a[j] = tmp;
		}
	}
	
	public static void main(String[] args) {
		new Codeforces_R245_Div1_A().run();
	}
	
}