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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.LinkedList;

public class XorTree {

	static LinkedList<Integer> adj[];
	static boolean visited[];
	static int[] init, goal;
	static ArrayList<Integer> q = new ArrayList<>();

	static int dfs(int s, int skip, int flag) {
		int count = 0;
		if (visited[s] == true) {
			return 0;
		}
		if (skip == 1) {
			visited[s] = true;
			for (int it : adj[s]) {
				count += dfs(it, 0, flag);
			}
		} else {
			visited[s] = true;
			if ((goal[s] ^ flag) == init[s]) {
				for (int it : adj[s]) {
					count += dfs(it, 1, flag);
				}
			} else {
				count++;
				q.add(s + 1);
				// System.out.println(s);
				for (int it : adj[s]) {
					count += dfs(it, 1, 1 ^ flag);
				}
			}
		}
		return count;
	}

	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		OutputWriter out = new OutputWriter(System.out);
		int n = in.readInt();
		int ans = 0;
		int j = 0;
		int u, v;
		adj = new LinkedList[n];
		for (int i = 0; i < n; i++) {
			adj[i] = new LinkedList<Integer>();
		}
		visited = new boolean[n];
		while (j < n - 1) {
			u = in.readInt() - 1;
			v = in.readInt() - 1;
			adj[u].add(v);
			adj[v].add(u);
			j++;
		}
		init = new int[n];
		goal = new int[n];
		for (int i = 0; i < n; i++) {
			init[i] = in.readInt();
		}
		for (int i = 0; i < n; i++) {
			goal[i] = in.readInt();
		}
		ans += dfs(0, 0, 0);
		// System.out.println(ans);
		visited = new boolean[n];
		visited[0] = true;
		for (int it : adj[0]) {
			ans += dfs(it, 0, 0);
		}
		System.out.println(ans);
		StringBuilder s = new StringBuilder();
		for (int i : q) {
			s.append(i);
			s.append("\n");
		}
		System.out.println(s);
		out.close();
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(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 long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			long sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long 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 int readInt() {
			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 String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		static boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public String next() {
			return readString();
		}
	}

	private static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(outputStream);
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}
	}
}