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.util.*;
import java.io.*;
import java.math.*;
public class a{
	static List<Integer> [] al;
	public static void main( String [] args) throws IOException{
		FastScanner sc=new FastScanner();
		int n=sc.nextInt();
		al=new ArrayList[n];
		for(int i=0;i<n;i++)al[i]=new ArrayList<>();
		for(int i=0;i<n-1;i++){
			int u=sc.nextInt()-1;
			int v=sc.nextInt()-1;
			al[u].add(v);
			al[v].add(u);
		}
		int [] init=sc.nextIntArray(n);
		int [] goal=sc.nextIntArray(n);

		int [] parent=new int[n];
		int [] changes=new int[n];
	
		ArrayList<Integer> list=new ArrayList<>();
		Queue<Integer> q=new LinkedList<>();

		q.add(0);
		parent[0]=-1;
		int cnt=0;

		while(!q.isEmpty()){
			int u=q.poll();
			int p=parent[u];

			if(p!=-1){
				int gp=parent[p];
				if(gp!=-1){
					changes[u]+=changes[gp];
				}
			}
			init[u]=(init[u]+changes[u]%2)%2;
			if(init[u]!=goal[u]){
				cnt++;
				list.add(u+1);
				changes[u]+=1;
			}
			for(int v : al[u]){
				if(v!=p){
					parent[v]=u;
					q.add(v);
				}
			}
		}
		StringBuilder sb=new StringBuilder("");
		System.out.println(cnt);
		for(int x : list)sb.append(x+"\n");
		System.out.println(sb.toString().trim());
	}
}






















































































class FastScanner{	
	 private int BUFFER_SIZE = 1 << 16;
	
	private  DataInputStream din;
	
	private  byte[] buffer;
	
	private int bufferPointer, bytesRead;
	
	public FastScanner() {
		din = new DataInputStream(System.in);
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}

	public FastScanner( String file_name) throws IOException {
		din = new DataInputStream(new FileInputStream(file_name));
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
    }
    
	public String readLine() throws IOException {
		 byte[] buf = new byte[64];
		int cnt = 0, c;
		while ((c = read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}
    
    public String next() throws IOException{

		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		
		 StringBuilder builder = new StringBuilder();
		builder.append((char)c);
		c = read();
		while(!Character.isWhitespace(c)){
			builder.append((char)c);
			c = read();
		}
		
		return builder.toString();
	}

	public int nextInt() throws IOException {
		int ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (neg)
			return -ret;
		return ret;
	}
	
	public int[] nextIntArray( int n) throws IOException {
		 int arr[] = new int[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextInt();
		}
		return arr;
	}

	public long nextLong() throws IOException {
		long ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}
	
	public long[] nextLongArray( int n) throws IOException {
		 long arr[] = new long[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextLong();
		}
		return arr;
	}

	public char nextChar() throws IOException{
		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		return (char) c;	
	}
	
	public double nextDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg)
			return -ret;
		return ret;
    }
    
	public double[] nextDoubleArray( int n) throws IOException {
		 double arr[] = new double[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextDouble();
		}
		return arr;
	}

	private void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private byte read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	public void close() throws IOException {
		if (din == null)
			return;
		din.close();
	}

}