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.util.concurrent.LinkedBlockingDeque;
import java.io.*;
import java.lang.*;
	
	public class graph1
	{
		public static int n;
		public static ArrayList<Integer> adj[];
		public static ArrayList<Integer> adj2[];
		
		public static ArrayList<Integer> child[];
		public static boolean[] vis;
		public static ArrayList<Integer> pair;
		public static int[] par;
		public static int[] level;
		public static int[] set;
		public static int[] a;
		public static int[] ans;
		public static int[] init;
		public static int[] goal;
		
		public static int count;
		
		public static long INF = Long.MAX_VALUE/100;
		
		
		public static void main(String[] args)
		{
			InputReader in = new InputReader(System.in);
			PrintWriter pw = new PrintWriter(System.out);
	
	//		n = in.nextInt();
			n = in.nextInt();
			//int m = in.nextInt();
			//int s = in.nextInt();
			
			
			//children = new ArrayList[n+1];
			vis = new boolean[n+1];
			par = new int[n+1];
			set = new int[n+1];
			level = new int[n+1];
			init = new int[n+1];
			goal = new int[n+1];
			pair = new ArrayList<>();
			adj = new ArrayList[n+1];
			adj2 = new ArrayList[n+1];
			for(int i=0; i<=n; i++)
			{
				vis [i] = false;
				par[i] = -1;
			}
			
			
			
			for(int i=0;i<=n;i++)
			{
				adj[i] = new ArrayList<Integer>();
				adj2[i] = new ArrayList<Integer>();
				
			}
			
			
			for(int i=0; i<n-1; i++)
			{
				int u = in.nextInt();
				int v = in.nextInt();
				adj[u].add(v);
				adj[v].add(u);
				
			
			}
			
			for(int i=1; i<=n; i++)
				init[i] = in.nextInt();
			for(int i=1; i<=n; i++)
				goal[i] = in.nextInt();
			
			
			
			bfs(1);
			Queue<Integer> que = new LinkedList<>();
			que.add(1);
			for(int i=0; i<=n; i++)
			{
				vis [i] = false;
				par[i] = -1;
			}
			
			recbfs(1, 0, 0, que);
			pw.println(count);
			for(int p: pair)
				pw.println(p);
			
			
			
			//code ends....
			pw.flush();
			pw.close();
		}
		
		
		public static void recbfs(int last, int odd, int even, Queue<Integer> que)
		
		{
			
			//if(que.isEmpty())
				//return ;
		
			//int last = que.poll();
			//System.out.println(vis[last]);
			//if(vis[last])
				//return;
			
			int curr = (init[last]);
			if(level[last]%2==0)
				curr += even;
			else
				curr += odd;
			
			//System.out.println(last+" "+even+" "+odd+" "+level[last]+" "+goal[last]+" "+curr);
			
			if(goal[last]%2!=curr%2)
			{
				if(level[last]%2==0)
					even++;
				else
					odd++;
				count++;
				pair.add(last);
				
			}
			
			for(int p : adj2[last])
				{
					if(!vis[p])
					{
					//	que.add(p);
						vis[p] = true;
						recbfs(p, odd, even, que);
					}
				}
			
			
			//recbfs(odd, even, que);
			
		}
		
		
		
		
		public static int bfs(int x)
		{
			Queue<Integer> queue = new LinkedList<>();
			queue.add(x);
			level[x] = 0;
			int c = 0;
			//parent[x] = 0;
			boolean[] vis = new boolean[n+1]; 
			vis[x] = true;
			while(!queue.isEmpty())
			{
				int last = queue.poll();
				for(int p : adj[last])
				{
					if(!vis[p])
					{
							//	children[last].add(a);
						queue.add(p);
					adj2[last].add(p);
						vis[p] = true;
						c++;
					//	parent[a] = last;
						level[p] = level[last]+1;
						
					}
				}
			}
			return c;
		}
		
		public static int fbfs(int x)
		{
			Queue<Integer> queue = new LinkedList<>();
			queue.add(x);
			//level[x] = 1;
			int c = 0;
			//parent[x] = 0;
			//boolean[] vis = new boolean[n+1]; 
			vis[x] = true;
			while(!queue.isEmpty())
			{
				int last = queue.poll();
				for(int p : adj[last])
				{
					if(!vis[p])
					{
							//	children[last].add(a);
						queue.add(p);
					//	System.out.println(p+" ");
						vis[p] = true;
						c++;
					//	parent[a] = last;
						//level[a] = level[last]+1;
						
					}
				}
			}
			return c;
		}
		
		
		/*
		
		
		public static void fun(int s)
		{
			
			if(vis[s])
				return;
			set[s] = count;
			vis[s] = true;
			fun(a[s]);
			
		}
		

		public static int dfs(int s)
		{
			for(int i=0; i<=n; i++)
			{
				vis [i] = false;
				par[i] = -1;
				level[i] = 0;
				
			}
			Stack<Integer> stk = new Stack<>();
	 		stk.add(s);
			par[s] = 0;
			vis[s] = true;
			
			while(!stk.isEmpty())
			{
				int last = stk.pop();
			///	System.out.println(last);
				boolean f = false;
				for(int a : adj[last])
				{
					if(!vis[a])
					{
						//child[last].add(a);
						stk.add(a);
						par[a] = last;
						level[a] = level[last] +1;
						vis[a] = true;
					}
				}
			
			}
			int max = 0;
			int maxi = 0;
			for(int i=1; i<=n; i++)
			{
				if(level[i]>max)
				{
					max = level[i];
					maxi = i;
				}
				
			}
			return maxi;
		}
				
		 */
	
		
/*		public static void dfsrec(int s)
		{
			if(vis[s])
				return;
			
			vis[s] = true;
			int k = 0;
			for(int p: adj[s])
			{
				boolean f2 = false;
				if(!vis[p])
				{
					k++;
					dfsrec(p);
				}
				
			}
			par[s] = k;
			
		}
		
		public static int find(int i) {
			
			
			if(par[i]==-1)
				return i;
			else
				return find(par[i]);
				
		}
		
		 public static void union( int x, int y)
		    {
		        int xset = find( x);
		        int yset = find(y);
		        par[xset] = yset;
		    }

	 */
		
		
	/*	 public static boolean cycle(HashSet<pair> set) {
			 
			 
			 for(pair p: set)
			 {
				 int x = find(p.x);
				 int y = find(p.y);
				 if(x==y)
					 return true;
		
				 union(x, y);
				 
			 }
			 
			 return false;
		 }
		 */
		
		
		
		
		
		
		static class pair implements Comparable<pair>
		 
		{
			Long x;
			Integer y;
			pair(long adj,int y)
			{
		
				this.x=adj;
				this.y=y;
			}
			
			public int compareTo(pair o) {
				//int result = x.compareTo(o.x);
				//if(result==0)
					int result = -y.compareTo(o.y);
				
				return result;
			}  
			
			public String toString()
			{
				return x+" "+y;
			}
			
			public boolean equals(Object o)
			{
				if (o instanceof pair)
			    {
					pair p = (pair)o;
					return p.x == x && p.y == y ;
				}
				return false;
			}
			
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode();
			}
		}
	
	
		static class triplet implements Comparable<triplet>
		{
			Integer x,y,z;
			triplet(int x,int y,int z)
			{
				this.x = x;
				this.y = y;
				this.z = z;
			}
			
			public  int compareTo(triplet o)
			{
				int result = x.compareTo(o.x);
				if(result==0)
					result =  y.compareTo(o.y);
				if(result==0)
					result = z.compareTo(o.z);
	
				return result;
			}
			
			public boolean equlas(Object o)
			{
				if(o instanceof triplet)
				{
					triplet p = (triplet)o;
					return x==p.x && y==p.y && z==p.z;
				}
				return false;
			}
			
			public String toString()
			{
				return x+" "+y+" "+z;
			}
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode() + new Long(z).hashCode(); 
			}
		}
		
	
		
		
		
		static class InputReader 
		{
			 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) 
			{
				this.stream = stream;
			}
	 
			public int snext() 
			{
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) 
				{
					curChar = 0;
					try 
					{
						snumChars = stream.read(buf);
					} 
					catch (IOException e) 
					{
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public int nextInt() 
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-')
			    {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) 
			{
				int a[] = new int[n];
				for (int i = 0; i < n; i++) 
				{
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() 
			{
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}
	 
			public boolean isSpaceChar(int c) 
			{
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) 
			{
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter
		    {
				public boolean isSpaceChar(int ch);
			}
		}
		
		public static long mod = 1000000007;
		public static int d;
		public static int p;
		public static int q;
		
		public static int[] suffle(int[] a,Random gen)
		{
			int n = a.length;
			for(int i=0;i<n;i++)
			{
				int ind = gen.nextInt(n-i)+i;
				int temp = a[ind];
				a[ind] = a[i];
				a[i] = temp;
			}
			return a;
		}
		
		public static void swap(int a, int b){
			int temp = a;
			a = b;
			b = temp;
		}
		
		public static HashSet<Integer> primeFactorization(int n)
		{
			HashSet<Integer> a =new HashSet<Integer>();
			for(int i=2;i*i<=n;i++)
			{
				while(n%i==0)
				{
					a.add(i);
					n/=i;
				}
			}
			if(n!=1)
				a.add(n);
			return a;
		}
		
		public static void sieve(boolean[] isPrime,int n)
		{
			for(int i=1;i<n;i++)
				isPrime[i] = true;
			
			isPrime[0] = false;
			isPrime[1] = false;
			
			for(int i=2;i*i<n;i++)
			{
				if(isPrime[i] == true)
				{
					for(int j=(2*i);j<n;j+=i)
						isPrime[j] = false;
				}
			}
		}
		
		public static int GCD(int a,int b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static long GCD(long a,long b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static void extendedEuclid(int A,int B)
		{
			if(B==0)
			{
				d = A;
				p = 1 ;
				q = 0;
			}
			else
			{
				extendedEuclid(B, A%B);
				int temp = p;
				p = q;
				q = temp - (A/B)*q;
			}
		}
		
		public static long LCM(long a,long b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int LCM(int a,int b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int binaryExponentiation(int x,int n)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long binaryExponentiation(long x,long n)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modularExponentiation(int x,int n,int M)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long modularExponentiation(long x,long n,long M)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modInverse(int A,int M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		public static long modInverse(long A,long M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		
		
		
		
		public static boolean isPrime(int n)
		{
		    
		    if (n <= 1)  return false;
		    if (n <= 3)  return true;
		    
		    if (n%2 == 0 || n%3 == 0) 
		    	return false;
		 
		    for (int i=5; i*i<=n; i=i+6)
		    {
		        if (n%i == 0 || n%(i+2) == 0)
		           return false;
		    }
		    
		    return true;
		}
		
		
	}