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.OutputStreamWriter;
import java.io.BufferedWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.readInt();
        IntArrayList[] a = new IntArrayList[n];
        for (int i = 0; i < n; i++) {
            a[i] = new IntArrayList();
        }
        for (int i = 0; i < n-1; i++) {
            int x = in.readInt() - 1;
            int y = in.readInt() - 1;
            a[x].add(y);
            a[y].add(x);
        }
        int[] init = IOUtils.readIntArray(in, n);
        int[] goal = IOUtils.readIntArray(in, n);
        IntArrayList toSwap = new IntArrayList();
        dfs(0, -1, a, init, goal, 0, false, false, toSwap);
        out.printLine(toSwap.size());
        for (int i = 0; i < toSwap.size(); i++) {
            out.printLine(toSwap.get(i) + 1);
        }
    }

    private void dfs(int x, int p, IntArrayList[] a, int[] init, int[] goal, int h, boolean b0, boolean b1, IntArrayList toSwap) {
        boolean needSwapX = false;
        if (h % 2 == 0) {
            if (b0) {
                if (goal[x] == init[x]) {
                    needSwapX = true;
                }
            } else {
                if (goal[x] != init[x]) {
                    needSwapX = true;
                }
            }
        } else {
            if (b1) {
                if (goal[x] == init[x]) {
                    needSwapX = true;
                }
            } else {
                if (goal[x] != init[x]) {
                    needSwapX = true;
                }
            }
        }
        if (needSwapX) {
            toSwap.add(x);
        }
        for (int i = 0; i < a[x].size(); i++) {
            int y = a[x].get(i);
            if (y == p) {
                continue;
            }
            boolean newB0 = (needSwapX && (h % 2 == 0)) ? !b0 : b0;
            boolean newB1 = (needSwapX && (h % 2 == 1)) ? !b1 : b1;
            dfs(y, x, a, init, goal, h + 1, newB0, newB1, toSwap);
        }
    }
}

class InputReader {

    private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	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 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 boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

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

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

class OutputWriter {
	private final PrintWriter writer;

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

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

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

    public void printLine(int i) {
		writer.println(i);
	}
}

class IntArrayList extends IntList {
	private int[] array;
	private int size;

	public IntArrayList() {
		this(10);
	}

	public IntArrayList(int capacity) {
		array = new int[capacity];
	}

	public IntArrayList(IntList list) {
		this(list.size());
		addAll(list);
	}

	public int get(int index) {
		if (index >= size)
			throw new IndexOutOfBoundsException();
		return array[index];
	}

    public int size() {
		return size;
	}

	public void add(int value) {
		ensureCapacity(size + 1);
		array[size++] = value;
	}

	public void ensureCapacity(int newCapacity) {
		if (newCapacity > array.length) {
			int[] newArray = new int[Math.max(newCapacity, array.length << 1)];
			System.arraycopy(array, 0, newArray, 0, size);
			array = newArray;
		}
	}

}

class IOUtils {

    public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

}

abstract class IntCollection {
	public abstract IntIterator iterator();
	public abstract int size();
	public abstract void add(int value);

    public void addAll(IntCollection values) {
		for (IntIterator it = values.iterator(); it.isValid(); it.advance()) {
			add(it.value());
		}
	}

}

interface IntIterator {
	public int value() throws NoSuchElementException;
	/*
	 * @throws NoSuchElementException only if iterator already invalid
	 */
	public void advance() throws NoSuchElementException;
	public boolean isValid();
}

abstract class IntList extends IntCollection implements Comparable<IntList> {

    public abstract int get(int index);

    public IntIterator iterator() {
		return new IntIterator() {
			private int size = size();
			private int index = 0;

			public int value() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				return get(index);
			}

			public void advance() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				index++;
			}

			public boolean isValid() {
				return index < size;
			}
		};
	}

    public int hashCode() {
		int hashCode = 1;
		for (IntIterator i = iterator(); i.isValid(); i.advance())
			hashCode = 31 * hashCode + i.value();
		return hashCode;
	}

	public boolean equals(Object obj) {
		if (!(obj instanceof IntList))
			return false;
		IntList list = (IntList)obj;
		if (list.size() != size())
			return false;
		IntIterator i = iterator();
		IntIterator j = list.iterator();
		while (i.isValid()) {
			if (i.value() != j.value())
				return false;
			i.advance();
			j.advance();
		}
		return true;
	}

	public int compareTo(IntList o) {
		IntIterator i = iterator();
		IntIterator j = o.iterator();
		while (true) {
			if (i.isValid()) {
				if (j.isValid()) {
					if (i.value() != j.value()) {
						if (i.value() < j.value())
							return -1;
						else
							return 1;
					}
				} else
					return 1;
			} else {
				if (j.isValid())
					return -1;
				else
					return 0;
			}
			i.advance();
			j.advance();
		}
	}

}