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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author dipankar12
 */
import java.io.*;
import java.util.*;
public class r245a {
    private ArrayList<Integer> adj[];
    static int count=0;
    
    public r245a(int n)
    {
        adj=new ArrayList[n+1];
        for(int i=0;i<=n;i++)
            adj[i]=new ArrayList<Integer>();
    }
    void setEdge(int u,int v)
    {
        adj[u].add(v);
    }
    void dfs(int src,int p,int changes[],int level,int y,int flag)
    {
        //System.out.println(src+" "+level);
        if(level==2)
        {
            if(p!=-1)
                changes[src]+=y;
            if(flag==1)
                changes[src]++;
            return;
        }
        
        Iterator<Integer> it=adj[src].iterator();
        while(it.hasNext())
        {
            int x=it.next();
            if(x!=p)
                dfs(x,src,changes,level+1,y,flag);
        }
    }
    void bfs(int goal[],int val[],int changes[],int p[])
    {
        ArrayList<Integer> al=new ArrayList<Integer>();
        int parent[]=new int[adj.length];
        parent[1]=-1;
        al.add(1);
        
        while(!al.isEmpty())
        {
            int x=al.get(0);
            al.remove(0);
            //System.out.println(x+" "+goal[x]+" "+val[x]+" "+changes[x]);
            if(goal[x]!=val[x]&&changes[x]%2==0)
            {
                dfs(x,parent[x],changes,0,changes[x],1);
                p[x]=1;
                count++;
            }
            else if(goal[x]==val[x]&&changes[x]%2!=0)
            {
                dfs(x,parent[x],changes,0,changes[x],1);
                p[x]=1;
                count++;
            }
            else
                dfs(x,parent[x],changes,0,changes[x],0);
            Iterator<Integer> it=adj[x].iterator();
            while(it.hasNext())
            {
                int y=it.next();
                if(parent[x]!=y)
                {
                    al.add(y);
                    parent[y]=x;
                }
            }
        }
    }
    public static void main(String args[])
    {
        fastio in=new fastio(System.in);
        PrintWriter pw=new PrintWriter(System.out);

        int n=in.nextInt();
        r245a ob=new r245a(n);
        for(int i=0;i<n-1;i++)
        {
            int u=in.nextInt();
            int v=in.nextInt();
            ob.setEdge(u, v);
            ob.setEdge(v, u);
        }
        
        int val[]=new int[n+1];
        for(int i=1;i<=n;i++)
            val[i]=in.nextInt();
        
        int goal[]=new int[n+1];
        for(int i=1;i<=n;i++)
            goal[i]=in.nextInt();
        
        int changes[]=new int[n+1];
        int p[]=new int[n+1];
        ob.bfs(goal, val, changes, p);
        
        StringBuilder sb=new StringBuilder();
        sb.append(count+"\n");
        for(int i=1;i<n+1;i++)
            if(p[i]==1)
                sb.append(i+"\n");
        
        pw.println(sb);
        pw.close();
    }

    static class fastio {
     
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int cchar, snchar;
            private SpaceCharFilter filter;
     
            public fastio(InputStream stream) {
                this.stream = stream;
            }
     
            public int nxt() {
                if (snchar == -1)
                    throw new InputMismatchException();
                if (cchar >= snchar) {
                    cchar = 0;
                    try {
                        snchar = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snchar <= 0)
                        return -1;
                }
                return buf[cchar++];
            }
     
            public int nextInt() {
                int c = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = nxt();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = nxt();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
     
            public long nextLong() {
                int c = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = nxt();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = nxt();
                } 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 = nxt();
                while (isSpaceChar(c)) {
                    c = nxt();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = nxt();
                } while (!isSpaceChar(c));
                return res.toString();
            }
     
            public String nextLine() {
                int c = nxt();
                while (isSpaceChar(c))
                    c = nxt();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = nxt();
                } 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);
            }
        }
    

}