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.BigInteger;

public class A {

	static class pair implements Comparable<pair> {
		int x;
		int y;

		public pair(int d, int k) {
			x = d;
			y = k;
		}

		@Override
		public int compareTo(pair arg0) {
			// TODO Auto-generated method stub
			if (x == arg0.x) {
				return y - arg0.y;
			}
			return x - arg0.x;
		}
	}

	static PrintWriter pw;
	static int n;
	static int m;

	static int[] a;

	static int bin(int num) {
		int s = 0;
		int e = a.length - 1;
		int ans = -1;
		while (s <= e) {
			int mid = (s + e) / 2;
			if (a[mid] <= num) {
				s = mid + 1;
				ans = mid;
			} else
				e = mid - 1;
		}
		return ans;
	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());

		g = new ArrayList[n];
		for (int i = 0; i < g.length; i++) {
			g[i] = new ArrayList<>();
		}

		for (int i = 0; i < n - 1; i++) {
			st = new StringTokenizer(br.readLine());
			int u = Integer.parseInt(st.nextToken()) - 1;
			int v = Integer.parseInt(st.nextToken()) - 1;
			g[u].add(v);
			g[v].add(u);
		}
		st = new StringTokenizer(br.readLine());
		sta = new int[n];
		for (int i = 0; i < sta.length; i++) {
			sta[i] = Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(br.readLine());
		end = new int[n];
		for (int i = 0; i < sta.length; i++) {
			end[i] = Integer.parseInt(st.nextToken());
		}
		vis = new boolean[n];
		r = new ArrayList<>();
		vis[0] = true;
		bfs(0);
		pw.println(r.size());
		for (int x : r) {
			pw.println(x);
		}
//		int t = Integer.parseInt(br.readLine());
//		StringTokenizer st = new StringTokenizer(br.readLine());
//		int n = Integer.parseInt(st.nextToken());
//		int m = Integer.parseInt(st.nextToken());
//
//		g = new ArrayList[n];
//		hs = new HashSet[n];
//		for (int i = 0; i < g.length; i++) {
//			g[i] = new ArrayList<>();
//			hs[i] = new HashSet<>();
//		}
//		triple[] pq = new triple[m];
//		for (int i = 0; i < m; i++) {
//			st = new StringTokenizer(br.readLine());
//			int u = Integer.parseInt(st.nextToken()) - 1;
//			int v = Integer.parseInt(st.nextToken()) - 1;
//			g[u].add(v);
//			g[v].add(u);
//			pq[i] = new triple(Math.min(u+1, v+1), Math.max(u+1, v+1));
//		}
//		boolean f = true;
//		for (int i = 0; i < g.length; i++) {
//			if (g[i].size() == 1)
//				f = false;
//		}
//		if (f) {
//			p = new ArrayList<A.triple>();
//			vis = new boolean[n];
//			dfs(0);
//			HashSet<triple> hp = new HashSet<>();
//			for (triple x : p) {
//				pw.println(x.x + " " + x.y);
//				hp.add(new triple(Math.min(x.x, x.y), Math.max(x.x, x.y)));
//			}
////			for (int i = 0; i < pq.length; i++) {
////				if (!hp.contains(pq[i])) {
////					pw.println(pq[i].x + " " + pq[i].y);
////				}
////			}
//		} else
//			pw.println(0);

		pw.flush();
		pw.close();

	}

	static boolean check(String s, int h, int m) {
		String s2 = reversString(m + "") + ":" + reversString(h + "");
		return s2.equals(com(h, m));

	}

	static String com(int h, int m) {
		String s = "";
		if (h < 10)
			s += "0" + h;
		else {
			s += h;
		}
		s += ":";
		if (m < 10)
			s += "0" + m;
		else {
			s += m;
		}
		return s;
	}

	static String reversString(String x) {
		int y = Integer.parseInt(x);
		if (y < 10)
			return x + "0";
		else
			return x.charAt(1) + "" + x.charAt(0);
	}

	static boolean[] vis;
	static ArrayList<Integer>[] g;
	static ArrayList<Integer> r;
	static int[] sta;
	static int[] end;

//	static void dfs(int n) {
//		vis[n] = true;
//		for (int v : g[n]) {
//			boolean f = false;
//			if (!vis[v]) {
//				p.add(new triple(n + 1, v + 1));
//				f = true;
//				dfs(v);
//				break;
//			}
//			if (!f) {
//				p.add(new triple(n + 1, g[n].get(0) + 1));
//			}
//		}
//	}

	static void bfs(int s) {
		Queue<triple> q = new LinkedList<triple>();
		q.add(new triple(s, 1,0,0));
		vis[s] = true;
		while (!q.isEmpty()) {
			triple p = q.remove();
			int u = p.x;
			int c = p.y;
			int even = p.z;
			int odd = p.w;
//			System.out.println(odd + " " + even);
			if (c == 0) {
				int l = even % 2 == 1 ? 1 - sta[u] : sta[u];
				if (l == end[u]) {
					for (int v : g[u]) {

						if (!vis[v]) {
							vis[v] = true;
							q.add(new triple(v, 1 - c,even,odd));
						}
					}

				} else {
					r.add(u + 1);
					even = 1 - even;
					for (int v : g[u]) {

						if (!vis[v]) {
							vis[v] = true;
							q.add(new triple(v, 1 - c,even,odd));
						}
					}
				}

			} else {
				int l = odd % 2 == 1 ? 1 - sta[u] : sta[u];
				if (l == end[u]) {
					for (int v : g[u]) {

						if (!vis[v]) {
							vis[v] = true;
							q.add(new triple(v, 1 - c,even,odd));
						}
					}

				} else {
					r.add(u + 1);
					odd = 1 - odd;
					for (int v : g[u]) {

						if (!vis[v]) {
							vis[v] = true;
							q.add(new triple(v, 1 - c,even,odd));
						}
					}
				}
			}
		}

	}

	static class triple implements Comparable<triple> {
		int x;
		int y;
		int z;
		int w;

		public triple(int a, int b, int c, int d) {
			x = a;
			y = b;
			z = c;
			w = d;
		}

		@Override
		public int compareTo(triple o) {
			// TODO Auto-generated method stub
			return y - o.y;
		}
	}

	static long pow(long a, long e) // O(log e)
	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res *= a;
			a *= a;
			e >>= 1;
		}
		return res;
	}

	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

}