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

public class Main {
	
	static class FastScanner {
		BufferedReader s;
		StringTokenizer st;

		public FastScanner(InputStream InputStream) {
			st = new StringTokenizer("");
			s = new BufferedReader(new InputStreamReader(InputStream));
		}

		public FastScanner(File f) throws FileNotFoundException {
			st = new StringTokenizer("");
			s = new BufferedReader(new FileReader(f));
		}

		public int nextInt() throws IOException {
			if (st.hasMoreTokens())
				return Integer.parseInt(st.nextToken());
			else {
				st = new StringTokenizer(s.readLine());
				return nextInt();
			}
		}

		public BigInteger big() throws IOException {
			if (st.hasMoreTokens())
				return new BigInteger(st.nextToken());
			else {
				st = new StringTokenizer(s.readLine());
				return big();
			}
		}

		public double nextDouble() throws IOException {
			if (st.hasMoreTokens())
				return Double.parseDouble(st.nextToken());
			else {
				st = new StringTokenizer(s.readLine());
				return nextDouble();
			}
		}

		public long nextLong() throws IOException {
			if (st.hasMoreTokens())
				return Long.parseLong(st.nextToken());
			else {
				st = new StringTokenizer(s.readLine());
				return nextLong();
			}
		}

		public String next() throws IOException {
			if (st.hasMoreTokens())
				return st.nextToken();
			else {
				st = new StringTokenizer(s.readLine());
				return next();
			}

		}

		public String nextLine() throws IOException {
			return s.readLine();
		}

		public void close() throws IOException {
			s.close();
		}

	}

	public static void main(String[] args) throws java.lang.Exception {
		FastScanner in = new FastScanner(System.in);
		int n = in.nextInt();
		ArrayList<Integer>[] graph = new ArrayList[n + 1];
		for(int x = 0; x <= n; x++)
			graph[x] = new ArrayList();
		for(int x = 1; x < n; x++) {
			int u = in.nextInt(), v = in.nextInt();
			graph[u].add(v);
			graph[v].add(u);
		}
		int init[] = new int[n + 1];
		int goal[] = new int[n + 1];
		for(int x = 1; x <= n; x++) {
			init[x] = in.nextInt();
		}
		for(int x = 1; x <= n; x++) {
			goal[x] = in.nextInt();
		}
//		Set<Integer> set1 = new HashSet();
//		Set<Integer> set2 = new HashSet();
		boolean[] vis = new boolean[n + 1];
//		dfs(set1, set2, true, graph, 1, vis);
		List<Integer> list = new ArrayList();
		changes(graph, init, goal, 1, true, true, 0, vis, list);
		StringBuilder sb = new StringBuilder("");
		sb.append(list.size() + "\n");
		for(int ele : list)
			sb.append(ele + "\n");
		System.out.print(sb);
	}

	private static void changes(ArrayList<Integer>[] graph, int[] init, 
								int[] goal, int i, boolean flag0, boolean flag1,
								int j, boolean[] vis, List<Integer> list) 
	{
		if(j == 0) {
			if(flag0) {
				if(init[i] != goal[i]) {
					list.add(i);
					flag0 = !flag0;
				}
			} else {
				if(init[i] == goal[i]) {
					list.add(i);
					flag0 = !flag0;
				}
			}
		} else {
			if(flag1) {
				if(init[i] != goal[i]) {
					list.add(i);
					flag1 = !flag1;
				}
			} else {
				if(init[i] == goal[i]) {
					list.add(i);
					flag1 = !flag1;
				}
			}
		}
		vis[i] = true;
		for(int ele : graph[i]) {
			if(vis[ele] != true) {
				changes(graph, init, goal, ele, flag0, flag1, (j ^ 1), vis, list);
			}
		}
		
	}
	
}