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.io.*;
import java.util.*;
	
	public class CODEFORCES
	{
		private InputStream is;
		private PrintWriter out;
		int time = 0, DP[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7),
				arr[], weight[][], x[], y[], parent[];
		int MAX = 10000010, N, K;
		long red[];
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[][] pmp;
		boolean b[], boo[][];
		Pair prr[];
		HashMap<Pair, Integer> hm = new HashMap();
		long Dp[][][][] = new long[110][110][12][12];
	
		void soln()
		{
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			// out.close();
			out.flush();
			// tr(System.currentTimeMillis() - s + "ms");
		}
	
		public static void main(String[] args) throws Exception 
		{
			new Thread(null, new Runnable() 
			{
				public void run() 
				{
					try
					{
						// new CODEFORCES().soln();
					} catch (Exception e)
					{
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
			new CODEFORCES().soln();
		}
	
		int ans = 0, cost = 0, D[][];
		char ch[], ch1[];
		int hash = 29;
		TreeSet<Cell> ts;
		int prime[] = new int[100000];
		int dp[] = new int[50000];
		TreeSet<String> tset = new TreeSet<>();
		void solve() 
		{
			int n = ni();
			amp = (ArrayList<Integer>[]) new ArrayList[n];
			for(int i = 0; i < n ;i ++) amp[ i] = new ArrayList<>();
			buildGraph(n-1);
			arr = na(n);
			dist = na(n);
			b = new boolean[n];
			int b1 = 0, b2 = 0, lev = 0;
			dfs(0,b1, b2, lev);
			out.println(Aa.size());
			for(int i : Aa) out.println(i+1);
		}
		ArrayList<Integer> Aa = new ArrayList<>();
		void dfs(int x, int b1, int b2, int lev) {
			b[x] = true;
			if(lev%2==0) {
				if((arr[x]^b1)!=dist[x]) {
					b1 = (1-b1);
					Aa.add(x);
				}
			}
			else {
				if((arr[x]^b2)!=dist[x]) {
					b2 = (1-b2);
					Aa.add(x);
				}
			}
			for(int i : amp[x]) {
				if(!b[i]) dfs(i,b1,b2,lev+1);
			}
		}
		int calc(int x) {
			String s = Integer.toString(x);
			int ans = 0;
			for(char ch : s.toCharArray()) ans += (ch-'0');
			return ans;
		}
		boolean isCons(char ch){
			if(ch!='a' && ch!='e' && ch!='i' && ch!='o' && ch!='u' && ch!=' ') return true;
			return false; 
		}
		void seive(int x){
			b = new boolean[x+1];
			for(int i = 2;i*i<=x;i++){
				if(!b[i]){
					for(int j = 2*i;j<=x;j+=i) b[j] = true;
				}
			}
		}
		long[][] matMul(long a[][] , long b[][], int n)
		{
			long res[][] = new long[n][n];
			for(int i = 0;i<n;i++){
				for(int j = 0;j<n;j++){
					long sum = 0;
					for(int k = 0;k<n;k++){
						sum += (a[i][k]*1l*b[k][j]);
						sum %= MOD;
					}
					res[i][j] = sum;
				}
			}
			return res;
		}
		int min(int a, int b)
		{
			return (a<b)?a:b;
		}
		private class Cell implements Comparable<Cell>
		{
			int u, v, s;
			public Cell(int u, int v, int s) 
			{
				this.u = u;
				this.v = v;
				this.s = s;
			}
			public int hashCode() 
			{
				return Objects.hash();
			}
			public int compareTo(Cell other) 
			{
				return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u)))
						&((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(u, other.v)!=0?Long.compare(u, other.v):Long.compare(v, other.u))));
			}
			public String toString()
			{
				return this.u + " " + this.v;
			}
		}
	
		class Pair implements Comparable<Pair>
		{
			int u, v, i;
	
			Pair(int u, int v) 
			{
				this.u = u;
				this.v = v;
			}
	
			Pair() 
			{
	
			}
	
			Pair(int u, int v, int i) 
			{
				this.u = u;
				this.v = v;
				this.i = i;
			}
	
			public int hashCode()
			{
				return Objects.hash();
			}
	
			public boolean equals(Object o)
			{
				Pair other = (Pair) o;
				return (((u == other.v && v == other.u)));
			}
	
			public int compareTo(Pair other)
			{
				//return (((u == other.v && v == other.u)))?0:1;
				// return Integer.compare(val, other.val);
				return Long.compare(u, other.u);// != 0 ? (Long.compare(u, other.u)): (Long.compare(v, other.v));
						//&(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)): (Long.compare(v, other.u))));
			}
	
			public String toString()
			{
				return this.u + " " + this.v;
			}
		}
	
		int max(int a, int b) 
		{
			if (a > b)
				return a;
			return b;
		}
	
		static class FenwickTree 
		{
	
			int[] array; // 1-indexed array, In this array We save cumulative
							// information to perform efficient range queries and
							// updates
	
			public FenwickTree(int size) 
			{
				array = new int[size + 1];
			}
	
			public int rsq(int ind)
			{
				assert ind > 0;
				int sum = 0;
				while (ind > 0)
				{
					sum += array[ind];
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and decrementing ind by that
					// number
					ind -= ind & (-ind);
				}
				return sum;
			}
	
			public int rsq(int a, int b) 
			{
				assert b >= a && a > 0 && b > 0;
				return rsq(b) - rsq(a - 1);
			}
	
			public void update(int ind, int value)
			{
				assert ind > 0;
				while (ind < array.length) 
				{
					array[ind] += value;
					// Extracting the portion up to the first significant one of the
					// binary representation of 'ind' and incrementing ind by that
					// number
					ind += ind & (-ind);
				}
			}
	
			public int size() 
			{
				return array.length - 1;
			}
		}
		void buildGraph(int n) 
		{
			for (int i = 0; i < n; i++) 
			{
				int x1 = ni() - 1, y1 = ni() - 1;
				amp[x1].add(y1);
				amp[y1].add(x1);
			}
		}
		long modInverse(long a, long mOD2) 
		{
			return power(a, mOD2 - 2, mOD2);
		}
	
		long power(long x, long y, long m) 
		{
			if (y == 0)
				return 1;
			long p = power(x, y / 2, m) % m;
			p = (p * p) % m;
	
			return (y % 2 == 0) ? p : (x * p) % m;
		}
	
		public long gcd(long a, long b) 
		{
			if (b == 0)
				return a;
			return gcd(b, a % b);
		}
	
		static class ST1 
		{
			int arr[], st[], size;
	
			
			ST1(int a[]) 
			{
				arr = a.clone();
				size = 10 * arr.length;
				st = new int[size];
				build(0, arr.length - 1, 1);
			}
	
			void build(int ss, int se, int si) 
			{
				if (ss == se)
				{
					st[si] = arr[ss];
					return;
				}
				int mid = (ss + se) / 2;
				int val = 2 * si;
				build(ss, mid, val);
				build(mid + 1, se, val + 1);
				st[si] = Math.min(st[val], st[val + 1]);
			}
	
			int get(int ss, int se, int l, int r, int si) 
			{
				if (l > se || r < ss || l > r)
					return Integer.MAX_VALUE;
				if (l <= ss && r >= se)
					return st[si];
				int mid = (ss + se) / 2;
				int val = 2 * si;
				return Math.min(get(ss, mid, l, r, val),
						get(mid + 1, se, l, r, val + 1));
			}
		}
	
		static class ST 
		{
			int arr[], lazy[], n;
	
			ST(int a) 
			{
				n = a;
				arr = new int[10 * n];
				lazy = new int[10 * n];
			}
	
			void up(int l, int r, int val)
			{
				update(0, n - 1, 0, l, r, val);
			}
	
			void update(int l, int r, int c, int x, int y, int val)
			{
				if (lazy[c] != 0) {
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l > r || x > y || l > y || x > r)
					return;
				if (x <= l && y >= r) 
				
				{
					lazy[c] += val;
					return;
				}
				int mid = l + r >> 1;
				update(l, mid, 2 * c + 1, x, y, val);
				update(mid + 1, r, 2 * c + 2, x, y, val);
				arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
			}
	
			int an(int ind) 
			{
				return ans(0, n - 1, 0, ind);
			}
	
			int ans(int l, int r, int c, int ind) 
			{
				if (lazy[c] != 0) 
				{
					lazy[2 * c + 1] += lazy[c];
					lazy[2 * c + 2] += lazy[c];
					if (l == r)
						arr[c] += lazy[c];
					lazy[c] = 0;
				}
				if (l == r)
					return arr[c];
				int mid = l + r >> 1;
				if (mid >= ind)
					return ans(l, mid, 2 * c + 1, ind);
				return ans(mid + 1, r, 2 * c + 2, ind);
			}
		}
	
		public static int[] shuffle(int[] a, Random gen)
		{
			for (int i = 0, n = a.length; i < n; i++)
			{
				int ind = gen.nextInt(n - i) + i;
				int d = a[i];
				a[i] = a[ind];
				a[ind] = d;
			}
			return a;
		}
	
		long power(long x, long y, int mod) 
		{
			long ans = 1;
			while (y > 0) 
			{
				if (y % 2 == 0) 
				{
					x = (x * x) % mod;
					y /= 2;
				} else 
				{
					ans = (x * ans) % mod;
					y--;
				}
			}
			return ans;
		}
	
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	
		private 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++];
		}
	
		private boolean isSpaceChar(int c) 
		{
			return !(c >= 33 && c <= 126);
		}
	
		private int skip() 
		{
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	
		private double nd() 
		{
			return Double.parseDouble(ns());
		}
	
		private char nc() 
		{
			return (char) skip();
		}
	
		private String ns()
		{
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b)))
			{ // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	
		private 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);
		}
	
		private char[][] nm(int n, int m)
		{
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	
		private int[] na(int n)
		{
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	
		private 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();
			}
		}
	
		private 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();
			}
		}
	
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
		private void tr(Object... o) 
		{
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}