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.util.*;
import static java.lang.System.*;
import static java.lang.Math.*;
public class XorTree
{
	List<Integer> tree[];
	Set<Integer> set;
	int[] init,goal;
    void run() {
        int tc=1;
        StringBuilder sb = new StringBuilder();
        while(tc-->0) {
            int n=ni();
            tree = new ArrayList[n+1];
            set = new HashSet<>();
            init = new int[n+1];
            goal = new int[n+1];
            for(int i=1;i<=n;i++) tree[i] = new ArrayList<>();
            for(int i=0;i<n-1;i++) {
            	int u=ni(),v=ni();
            	tree[u].add(v);
            	tree[v].add(u);
            }
            tree[1].add(0);
            for(int i=1;i<=n;i++) init[i]=ni();
            for(int i=1;i<=n;i++) goal[i]=ni();

            dfs(1,0,true,0);
        	for(int child:tree[1]) if(child!=0) dfs(child,1,true,0);

        	sb.append(set.size()).append("\n");
        	Iterator<Integer> itr = set.iterator();
        	while(itr.hasNext()) sb.append(itr.next()).append("\n");
        }
        out.println(sb);
        out.flush(); 
        out.close();
    }

    void dfs(int cur, int par, boolean b, int d) {
    	if(d%2==0 && tree[cur].size()==1 && init[cur]!=goal[cur] && b) set.add(cur);
    	else if(d%2==0 && tree[cur].size()==1 && init[cur]==goal[cur] && !b) set.add(cur);
    	for(int child:tree[cur]) {
    		if(child!=par) {
    			if(init[cur]!=goal[cur] && b && d%2==0) {
    				set.add(cur);
    				dfs(child,cur,!b,d+1);
    			}
    			else if(init[cur]==goal[cur] && !b && d%2==0) { 
    				set.add(cur);
    				dfs(child,cur,true,d+1);
    			}
    			else dfs(child,cur,b,d+1);
    			// out.println(cur+" "+b);
    		}
    	}
    }

    public static void main(String[] args)throws Exception {
        try { 
            // new Thread(null, new XorTree()::run, "1", 1 << 26).start();
            new Thread(null, new XorTree("ONLINE_JUDGE")::run, "1", 1 << 26).start();
        } catch(Exception e) {}
    }

    FastReader sc=null;PrintWriter out = null;
    public XorTree()throws Exception {
        sc = new FastReader(new FileInputStream("input.txt"));
        out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    }
    public XorTree(String JUDGE) {
        sc = new FastReader(System.in);
        out = new PrintWriter(System.out);      
    }
    
    String ns() { return sc.next(); }
    int ni() { return sc.nextInt(); }
    long nl() { return sc.nextLong(); }
    int[] ni(int n) {
        int a[]=new int[n];
        for(int i=0;i<n;a[i++]=ni());
        return a;
    }
    long[] nl(int n) {
        long a[]=new long[n];
        for(int i=0;i<n;a[i++]=nl());
        return a;
    }
    
    int[][] ni(int n,int m) {
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++) 
            for(int j=0;j<m;j++)
                a[i][j]=ni();
        return a;
    }
    long[][] nl(int n,int m) {
        long a[][]=new long[n][m];
        for(int i=0;i<n;i++) 
            for(int j=0;j<m;j++)
                a[i][j]=nl();
        return a;
    }
    int gcd(int a, int b) {
        return b==0?a:gcd(b,a%b);
    }
    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;
        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }
        
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res = res*1L*10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res *1L* sgn;
        }
        
        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(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;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }
    }
}