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.*;
import java.io.IOException;
import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;
 
 
 
//import sun.net.www.content.audio.wav;
 
import java.text.DecimalFormat;
 
public class Codeforces {
    
    public static long mod = (long)Math.pow(10, 9)+7 ;
    public static double epsilon=0.00000000008854;//value of epsilon
    public static InputReader sc = new InputReader(System.in);
    public static PrintWriter pw = new PrintWriter(System.out);
    
    public static void diji(PriorityQueue<Pair> q,ArrayList<ArrayList<Pair>> a){
        //int vis[]=new int[a.size()];
        boolean vis[]=new boolean[a.size()];
        //vis[0]=1;
        Arrays.fill(vis, false);
        int n=a.size();
        long val[]=new long[n];
 
        long inf=Long.MAX_VALUE;
        Arrays.fill(val, inf);
        q.add(new Pair(0, 0));
        val[0]=0;
        int p[]=new int[n];
        p[0]=-1;
        while(q.size()>0){
            Pair r=q.remove();
            if(vis[r.i])
            continue;
            vis[r.i]=true;///removed
            int u=r.i;
            for(int i=0;i<a.get(u).size();i++){
 
                int v=a.get(u).get(i).i;
                long w=a.get(u).get(i).j;
                    if(val[v]>r.j+w){
                        p[v]=u;
                        val[v]=r.j+w;
                        q.add(new Pair(v, val[v]));
                    }
            }
        }
        //pw.println(Arrays.toString(p));
        int i=n-1;
        Stack<Integer> st=new Stack<>();
        if(val[i]==inf)
        {
            pw.println(-1);
            return;
        }
        while(i!=-1){
            st.add(i+1);
            i=p[i];
        }
        while(st.size()>0){
            pw.print(st.pop()+" ");
        }
        
 
    }
    public static int countSet(int a){
        int c=0;
        while(a>0){
            a&=(a-1);
            c++;
        }
        return c;
    }
    public static void Zfunction(String s){
        int n=s.length();
        int a[]=new int[n];
        int r1=0,r2=1;
        for(int i=1;i<n;){
            int f=0;
            while(r2<n&&s.charAt(r1)==s.charAt(r2)){
                r1++;
                r2++;
            }
            a[i]=r1;
            i++;
            int l2=1;
            for(;i<r2;i++){
                if(i+a[l2]<r2)
                a[i]=a[l2++];
                else{
                    f=1;
                    r1=r2-i;
                    break;
                }
            }
            if(f==0){
                r2=i;
                r1=0;
            }
 
        }
        pw.println(Arrays.toString(a));
    }
    public static void hieghtBfs(int r,int h[],ArrayList<ArrayList <Integer>> a,int p[],int vis[]){/// top to bottom
		Deque<Integer> q=new LinkedList<>();
		q.add(r);
		int c=0;
		p[r]=-1;
		vis[r]=1;
		while(q.size()>0){
			int l=q.size();
			while(l-->0){
				int v=q.remove();
				h[v]=c;
				for(int i=0;i<a.get(v).size();i++){
                    int u=a.get(v).get(i);
                    
					if(vis[u]==0){
                        //pw.print(u+" ");
						p[u]=v;
						vis[u]=1;
						q.add(u);
					}
				}
            }
            //pw.print("\n");
			c++;
		}
    }
    
    public static int hieght(int r,int h[],ArrayList<ArrayList <Integer>> a,int vis[],int cur,int max,int m){//bottom Up
        vis[r]=1;
        int e=0;
        if(h[r]==1)
        cur++;
        else cur=0;
        int num=0;
        max=Math.max(cur, max);
		for(int i=0;i<a.get(r).size();i++){
            int v=a.get(r).get(i);
			if(vis[v]==0){
                e++;
				num+=hieght(v, h, a, vis, cur, max, m);
			}
        }
        if(e==0&&max<=m){
            num++;
        }
        return num;
	}
    public static ArrayList<ArrayList <Integer>> GetGraph(int n,int m){
        ArrayList<ArrayList <Integer>> a=new ArrayList<>();
        for(int i=0;i<n;i++){
            a.add(new ArrayList<>());
        }
        for(int i=0;i<m;i++){
            int u=sc.nextInt()-1;
            int v=sc.nextInt()-1;
            a.get(u).add(v);
            a.get(v).add(u);
        } 
        return a;
    }
    public static long fun(int n,int k,int d,long dp[][][],int v){
        long c=0;
        for(int i=1;i<=k;i++){
            fun(n-i, k, d, dp, v);
        }
        return c;
    }
    public static int h(String s,int r[]){
        if(r[0]>=s.length())
        return 0;
        if(s.charAt(r[0])=='l'){
            r[0]++;
            return 0;
        }
        r[0]++;
        return 1+Math.max(h(s,r), h(s,r));
    }
    public static void dfs(int r,ArrayList<ArrayList<Integer>> a,int vis[],int there[],int todo[],int odd,int even,int i,ArrayList<Integer> ans){
        if((i%2==0&&even==1)||(i%2>0&&odd==1)){
            there[r]^=1;
        }
        if(there[r]!=todo[r]){
            ans.add(r+1);
            there[r]=todo[r];
            if(i%2>0){
                odd^=1;
            }
            else{
                even^=1;
            }
        }
        i++;
        vis[r]=1;
        for(int j=0;j<a.get(r).size();j++){
            int v=a.get(r).get(j);
			if(vis[v]==0){
				dfs(v, a, vis, there, todo, odd, even, i, ans);
			}
        }
    }
    
    public static void main(String[] args) {
        // code starts..
        int n=sc.nextInt();
        ArrayList<ArrayList<Integer>> a=GetGraph(n, n-1);
        int there[]=scanArray(n);
        int todo[]=scanArray(n);
        ArrayList<Integer> ans=new ArrayList<>();
        dfs(0, a, new int[n], there, todo, 0, 0, 1, ans);
        pw.println(ans.size());
        for(int i=0;i<ans.size();i++){
            pw.println(ans.get(i));
        }
    
        // Code ends...
        pw.flush();
        pw.close();
    }
    public static Comparator<Integer> C(){
        return 
        new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return o2.compareTo(o1);//for descending
            }
        };
    }
    public static Comparator<Pair> di(){
        return 
        new Comparator<Pair>() {
            @Override
            public int compare(Pair o1, Pair o2) {
                Long a=o1.j;
                Long b=o2.j;
                return a.compareTo(b);//ascending
            }
        };
    }
    static class tripletL implements Comparable<tripletL> {
        Long x, y, z;
 
        tripletL(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }
 
        public int compareTo(tripletL o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);
 
            return result;
        }
 
        public boolean equlas(Object o) {
            if (o instanceof tripletL) {
                tripletL p = (tripletL) o;
                return (x - p.x == 0) && (y - p.y ==0 ) && (z - p.z == 0);
            }
            return false;
        }
 
        public String toString() {
            return x + " " + y + " " + z;
        }
 
        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }
    public static String Doubleformate(double a,int n){
        String s="";
        while(n-->0){
            s+='0';
        }
        DecimalFormat f =new DecimalFormat("#0."+s);
        return f.format(a);
    }
 
    public static Comparator<Integer[]> column(int i){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
                return o1[i].compareTo(o2[i]);//for ascending
                //return o2[i].compareTo(o1[i]);//for descending
            }
        };
    }
    public static Comparator<Long[]> column1(int i){
        return 
        new Comparator<Long[]>() {
            @Override
            public int compare(Long[] o1, Long[] o2) {
                return o1[i].compareTo(o2[i]);//for ascending
                //return o2[i].compareTo(o1[i]);//for descending
            }
        };
    }
    public static Comparator<Integer[]> pair(){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
                int result=o1[0].compareTo(o2[0]);
                if(result==0)
                result=o1[1].compareTo(o2[1]);
                return result;
            }
        };
    }
    public static Comparator<Integer[]> Triplet(){
        return 
        new Comparator<Integer[]>() {
            @Override
            public int compare(Integer[] o1, Integer[] o2) {
            
                    for(int i=0;i<3;i++){
                        for(int j=i+1;j<3;j++){
                            for(int k=0;k<3;k++){
                                for(int p=k+1;p<3;p++){
                                    if((o1[i]==o2[k]&&o1[j]==o2[p])||(o1[j]==o2[k]&&o1[i]==o2[p])){
 
                                    }
                                }
                            }
                        }
                    }
                    int result=o1[0].compareTo(o2[0]);
                    if(result==0)
                    result=o1[1].compareTo(o2[1]);
                    if(result==0)
                    result=o1[2].compareTo(o2[2]);
                    return result;
            }
        };
    }
    
    
    public static String reverseString(String s){
        StringBuilder input1 = new StringBuilder(); 
        input1.append(s);  
        input1 = input1.reverse();
        return input1.toString();
    }
    public static int[] scanArray(int n){
        int a[]=new int [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextInt();
 
        return a;
    }
    public static long[] scanLongArray(int n){
        long a[]=new long [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextLong();
 
        return a;
    }
    public static String [] scanStrings(int n){
        String a[]=new String [n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextLine();
 
        return a;
    }
     
}
class Pair{
    int i;
    long j;
    Pair(int a,long b){
        i=a;
        j=b;
    }
}
class InputReader {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }