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.ArrayList;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;

/**
 * @SPOJ allow invoke method recursively deep up to 6K (http://www.spoj.com/PTIT/problems/P152PROC/)
 * @Codeforce: up to 1M (http://codeforces.com/contest/430/problem/C)
 */
public class P152PROC_TroChoiTrenCay {
    static InputStream is;
    static PrintWriter out;

    public static void main(String[] args) {

        long s = System.currentTimeMillis();
        is = System.in;
        out = new PrintWriter(System.out);

        solve();

        out.flush();

        // System.out.println();
        // System.out.println(System.currentTimeMillis() - s + "ms");
    }

    static ArrayList<ArrayList<Integer>> allEdges = new ArrayList<ArrayList<Integer>>();
    static boolean[] statuses;
    static boolean[] newStatuses;
    static boolean[] flips;

    static void solve() {
        int n = ni();
        statuses = new boolean[n];
        newStatuses = new boolean[n];
        flips = new boolean[n];

        for (int i = 0; i < n; i++) {
            allEdges.add(new ArrayList<Integer>());
        }

        for (int i = 0; i < n - 1; i++) {
            int u = ni() - 1;
            int v = ni() - 1;
            allEdges.get(u).add(v);
            allEdges.get(v).add(u);
        }
        for (int i = 0; i < n; i++) {
            statuses[i] = (ni() == 1);
        }
        for (int i = 0; i < n; i++) {
            newStatuses[i] = (ni() == 1);
        }
        int count = dfs(0, -1, false, false);
        System.out.println(count);
        StringBuilder bf = new StringBuilder();
        for (int i = 0; i < n; i++) {
            if (flips[i]) {
                bf.append((i + 1) + " ");
            }
        }
        System.out.println(bf.toString());
    }

    static int dfs(int node, int parentNode, boolean flipParent, boolean flipGrand) {
        int count = 0;
        if ((statuses[node] ^ newStatuses[node]) != flipGrand) {
            flips[node] = true;
            flipGrand = !flipGrand;
            count++;
        }
        for (int i : allEdges.get(node)) {
            if (i != parentNode) {
                count += dfs(i, node, flipGrand, flipParent);
            }
        }
        return count;
    }

    /*****************************************************************
     ******************** BASIC READER *******************************
     *****************************************************************/
    static byte[] inbuf = new byte[4096];
    static int lenbuf = 0, ptrbuf = 0;

    static int readByte() {
        if (lenbuf == -1)
            throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0)
                return -1;
        }
        return inbuf[ptrbuf++];
    }

    static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b))
            ;
        return b;
    }

    static double nd() {
        return Double.parseDouble(ns());
    }

    static char nc() {
        return (char) skip();
    }

    static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++)
            map[i] = ns(m);
        return map;
    }

    static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }

    static int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
}