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:
// package Tree_Practice;
/**
 * Created by ankurverma1994
 * My code is awesome!
 */

import java.io.*;
import java.util.*;
import java.math.*;

public class R245Div1AXorTree {
    int[] initial, goal;
    ArrayList<Integer> ans;

    //------------> Solution starts here!!
    @SuppressWarnings("Main Logic")
    void solve() {
        int n = ii();
        int from[] = new int[n - 1];
        int to[] = new int[n - 1];
        for (int i = 0; i < n - 1; i++) {
            from[i] = ii() - 1;
            to[i] = ii() - 1;
        }
        g = packU(n, from, to, n - 1);
        initial = iia(n);
        goal = iia(n);
        ans = new ArrayList<>();
        dfs(0, -1, 0, 0, 0);
        out.println(ans.size());
        for (int i = 0; i < ans.size(); i++)
            out.println(ans.get(i) + 1);
    }

    void dfs(int v, int par, int level, int odd, int even) {
//        out.println("current node " + v);
        boolean flip = false;
        if (level % 2 == 1) { // current level is odd
            if (odd % 2 == 1)
                initial[v] = 1 - initial[v];
        } else { // current level is even
            if (even % 2 == 1)
                initial[v] = 1 - initial[v];
        }
        if (initial[v] != goal[v]) {
            ans.add(v);
            flip = true;
        }
        for (int i = 0; i < g[v].length; i++) {
            int u = g[v][i];
            if (u != par) {
                if (flip) {
                    if (level % 2 == 0)
                        dfs(u, v, level + 1, odd, even + 1);
                    else
                        dfs(u, v, level + 1, odd + 1, even);
                } else {
                    dfs(u, v, level + 1, odd, even);
                }
            }
        }
    }

    int g[][];

    // for undirected graph, max is length of from or to array
    public static int[][] packU(int n, int[] from, int[] to, int max) {
        /* This part of code is picked up from "uwi" previous submission */
        int[][] g = new int[n][];
        int[] p = new int[n];
        for (int i = 0; i < max; i++) p[from[i]]++;
        for (int i = 0; i < max; i++) p[to[i]]++;
        for (int i = 0; i < n; i++) g[i] = new int[p[i]];
        for (int i = 0; i < max; i++) {
            g[from[i]][--p[from[i]]] = to[i];
            g[to[i]][--p[to[i]]] = from[i];
        }
        return g;
    }

    //------------> Solution ends here!!
    InputStream obj;
    PrintWriter out;
    String check = "";

    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new R245Div1AXorTree().main1();
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (StackOverflowError e) {
                    System.out.println("RTE");
                }
            }
        }, "1", 1 << 26).start();
    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        // obj=check.isEmpty() ? new FileInputStream("/home/ankurverma1994/input.txt") : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }

    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) throw new InputMismatchException();
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) return -1;
        return inbuffer[ptrbuffer++];
    }

    String is() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
        {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int ii() {
        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();
        }
    }

    long il() {
        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();
        }
    }

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

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

    float nf() {
        return Float.parseFloat(is());
    }

    double id() {
        return Double.parseDouble(is());
    }

    char ic() {
        return (char) skip();
    }

    int[] iia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = ii();
        return a;
    }

    long[] ila(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) a[i] = il();
        return a;
    }

    String[] isa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) a[i] = is();
        return a;
    }

    double[][] idm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
        return a;
    }

    int[][] iim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = ii();
        return a;
    }
}