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 static java.util.Arrays.*;

import java.util.*;

public class Solution {

	public Solution () {
		int N = sc.nextInt();
		int [][] E = dec(sc.nextInts(N-1));
		G = graph(N, E);

		P = new int [N]; fill(P, -1);
		dfs(0);

		S = sc.nextInts();
		T = sc.nextInts();
		F = new boolean [N];
		V = new boolean [N];

		for (int i : rep(N))
			go(i);

		List<Integer> res = new ArrayList<>();
		for (int i : rep(N))
			if (F[i])
				res.add(i+1);

		print(res.size());
		println(res);
	}

	int [] P, S, T; boolean [] F, V; int [][] G;

	void dfs(int i) {
		for (int j : G[i])
			if (j != P[i]) {
				P[j] = i;
				dfs(j);
			}
	}

	void go(int i) {
		if (V[i]) return;
		V[i] = true;

		int g = -1;
		if (P[i] != -1)
			g = P[P[i]];

		if (g != -1) {
			go(g);
			F[i] = ((S[i] == T[i]) != (S[g] == T[g]));
		} else
			F[i] = S[i] != T[i];
	}

	private static int [][] dec(int [] ... E) {
		for (int [] e : E)
			for (int i = 0; i < e.length; ++i)
				--e[i];
		return E;
	}
	private static int [][][] dwgraph(int N, int [][] E) {
		int [] D = new int [N];
		for (int [] e : E)
			++D[e[0]];
		int [][][] res = new int [2][N][];
		for (int i = 0; i < 2; ++i)
			for (int j = 0; j < N; ++j)
				res[i][j] = new int [D[j]];
		D = new int [N];
		for (int [] e : E) {
			int x = e[0], y = e[1], z = e.length > 2 ? e[2] : 1;
			res[0][x][D[x]] = y;
			res[1][x][D[x]] = z;
			++D[x];
		}
		return res;
	}
	private static int [][] dup(int [][] E) {
		int [][] res = new int [2*E.length][];
		for (int i = 0; i < E.length; ++i) {
			res[2*i] = E[i].clone();
			res[2*i+1] = E[i].clone();
			res[2*i+1][0] = E[i][1]; res[2*i+1][1] = E[i][0];
		}
		return res;
	}
	private static int [][] graph (int N, int [][] E) { return wgraph(N, E)[0]; }
	private static int [] rep(int N) { return rep(0, N); }
	private static int [] rep(int S, int T) { if (T <= S) return new int [0]; int [] res = new int [T-S]; for (int i = S; i < T; ++i) res[i-S] = i; return res; }
	private static int [][][] wgraph(int N, int [][] E) { return dwgraph(N, dup(E)); }
	////////////////////////////////////////////////////////////////////////////////////
	private final static IOUtils.MyScanner sc = new IOUtils.MyScanner();
	private static void print (Object o, Object ... A) { IOUtils.print(o, A); }
	private static void println (Object o) { IOUtils.println(o); }
	private static class IOUtils {
		public static class MyScanner {
			public String next() { newLine(); return line[index++]; }
			public int nextInt() { return Integer.parseInt(next()); }
			public String nextLine() { line = null; return readLine(); }
			public String [] nextStrings() { return split(nextLine()); }
			public int [] nextInts() {
				String [] L = nextStrings();
				int [] res = new int [L.length];
				for (int i = 0; i < L.length; ++i)
					res[i] = Integer.parseInt(L[i]);
				return res;
			}
			public int [][] nextInts (int N) {
				int [][] res = new int [N][];
				for (int i = 0; i < N; ++i)
					res[i] = nextInts();
				return res;
			}
			//////////////////////////////////////////////
			private boolean eol() { return index == line.length; }
			private String readLine() {
				try {
					return r.readLine();
				} catch (Exception e) {
					throw new Error (e);
				}
			}
			private final java.io.BufferedReader r;
			private MyScanner () { this(new java.io.BufferedReader(new java.io.InputStreamReader(System.in))); }
			private MyScanner (java.io.BufferedReader r) {
				try {
					this.r = r;
					while (!r.ready())
						Thread.sleep(1);
					start();
				} catch (Exception e) {
					throw new Error(e);
				}
			}
			private String [] line;
			private int index;
			private void newLine() {
				if (line == null || eol()) {
					line = split(readLine());
					index = 0;
				}
			}
			private String [] split(String s) { return s.length() > 0 ? s.split(" ") : new String [0]; }
		}
		private static String build(Object o, Object ... A) { return buildDelim(" ", o, A); }
		private static String buildDelim(String delim, Object o, Object ... A) {
			StringBuilder b = new StringBuilder();
			append(b, o, delim);
			for (Object p : A)
				append(b, p, delim);
			return b.substring(delim.length());
		}
		//////////////////////////////////////////////////////////////////////////////////
		private static void start() { if (t == 0) t = millis(); }
		private static void append(StringBuilder b, Object o, String delim) {
			if (o.getClass().isArray()) {
				int len = java.lang.reflect.Array.getLength(o);
				for (int i = 0; i < len; ++i)
					append(b, java.lang.reflect.Array.get(o, i), delim);
			} else if (o instanceof Iterable<?>)
				for (Object p : (Iterable<?>) o)
					append(b, p, delim);
			else {
				if (o instanceof Double)
					o = new java.text.DecimalFormat("#.############").format(o);
				b.append(delim).append(o);
			}
		}
		private static java.io.PrintWriter pw = new java.io.PrintWriter(System.out);
		private static void print(Object o, Object ... A) { pw.println(build(o, A)); }
		private static void println(Object o) {
			if (o.getClass().isArray()) {
				int len = java.lang.reflect.Array.getLength(o);
				for (int i = 0; i < len; ++i)
					print(java.lang.reflect.Array.get(o, i));
			} else if (o instanceof Iterable<?>)
				for (Object p : (Iterable<?>) o)
					print(p);
			else
				print(o);
		}
		private static void err(Object o, Object ... A) { System.err.println(build(o, A)); }
		private static void exit() {
			IOUtils.pw.close();
			System.out.flush();
			err("------------------");
			err(IOUtils.time());
			System.exit(0);
		}
		private static long t;
		private static long millis() { return System.currentTimeMillis(); }
		private static String time() { return "Time: " + (millis() - t) / 1000.0; }
	}
	public static void main (String[] args) { new Solution(); IOUtils.exit(); }
}