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 java.math.*;

/**
 * Moonsorrow - Jaasta Syntynyt / Varjojen Virta.
 * 
 * @author Gorokhov Nikita (wackloner@gmail.com)
 */

public class A implements Runnable {
	
	void solve() {
		int n = nextInt();
		ArrayList<Integer>[] g = new ArrayList[n];
		for (int i = 0; i < n; i++)
			g[i] = new ArrayList<Integer>();
		for (int i = 0; i < n - 1; i++) {
			int x = nextInt() - 1, y = nextInt() - 1;
			g[x].add(y);
			g[y].add(x);
		}
		int[] init = new int[n], goal = new int[n];
		for (int i = 0; i < n; i++)
			init[i] = nextInt();
		for (int j = 0; j < n; j++)
			goal[j] = nextInt();
		ArrayList<Integer> ans = new ArrayList<Integer>();
		dfs(0, -1, g, init, goal, false, false, ans);
		println(ans.size());
		for (int i : ans)
			println(i + 1);
	}
	
	void dfs(int v, int p, ArrayList<Integer>[] g, int[] init, int[] goal, boolean cur, boolean prev, ArrayList<Integer> ans) {
		boolean now = false;
		if (cur)
			init[v] = 1 - init[v];
		if (goal[v] != init[v]) {
			ans.add(v);
			now = true;
		}
		cur ^= now;
		for (int to : g[v])
			if (to != p)
				dfs(to, v, g, init, goal, prev, cur, ans);
	}
	
	public static void main(String[] args) throws IOException {
		new A().run();
	}
	
	A() {
		this.stream = System.in;
		this.writer = new PrintWriter(System.out);
	}
	
	A(String input, String output) throws IOException {
		File inputFile = new File(input);
		inputFile.createNewFile();
		stream = new FileInputStream(inputFile);
		File outputFile = new File(output);
		outputFile.createNewFile();
		writer = new PrintWriter(outputFile);
	}
	
	public void run() {
		solve();
		writer.close();
	}
	
	void halt() {
		writer.close();
		System.exit(0);
	}
	
	PrintWriter writer;;
	
	void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	
	void println(Object... objects) {
		print(objects);
		writer.println();
	}
	
	void printArray(int[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0) writer.print(' ');
			writer.print(array[i]);
		}
		writer.println();
	}
	
	void printArray(long[] array) {
		for (int i = 0; i < array.length; i++) {
			if (i != 0) writer.print(' ');
			writer.print(array[i]);
		}
		writer.println();
	}
	
	void printMatrix(int[][] matrix) {
		for (int i = 0; i < matrix.length; i++)
			printArray(matrix[i]);
	}
	
	void printMatrix(long[][] matrix) {
		for (int i = 0; i < matrix.length; i++)
			printArray(matrix[i]);
	}
	
	/**
	 * Pure Egor's code is straight ahead.
	 */
	
	InputStream stream;
	byte[] buf = new byte[1024];
	int curChar, numChars;
	
	int nextInt() {
		int c = next();
		while (isWhitespace(c))
			c = next();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = next();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = next();
		} while (!isWhitespace(c));
		return res * sgn;
	}
	
	long nextLong() {
		int c = next();
		while (isWhitespace(c))
			c = next();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = next();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = next();
		} while (!isWhitespace(c));
		return res * sgn;
	}
	
	double nextDouble() {
		int c = next();
		while (isWhitespace(c))
			c = next();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = next();
		}
		double res = 0;
		while (!isWhitespace(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, nextInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = next();
		}
		if (c == '.') {
			c = next();
			double m = 1;
			while (!isWhitespace(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = next();
			}
		}
		return res * sgn;
	}
	
	BigInteger nextBigInteger() {
		try {
			return new BigInteger(nextString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}
	
	int next() {
		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++];
	}
	
	String nextString() {
		int c = next();
		while (isWhitespace(c))
			c = next();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = next();
		} while (!isWhitespace(c));
		return res.toString();
	}
	
	String nextLine() {
		StringBuilder buf = new StringBuilder();
		int c = next();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = next();
		}
		return buf.toString();
	}
	
	boolean EOF() {
		int value;
		while (isWhitespace(value = peek()) && value != -1)
			next();
		return value == -1;
	}
	
	int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}
	
	boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
}