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 A429 
{
    public static void main(String args[])throws IOException
    {
        Reader sc=new Reader();
        int n=sc.nextInt();
        HashMap<Integer,ArrayList<Integer>> map=new HashMap<>();
        for(int i=1;i<=n;i++)
        {
            map.put(i,new ArrayList<>());
            
        }
        for(int i=1;i<n;i++)
        {
            int x=sc.nextInt();
            int y=sc.nextInt();
            map.get(x).add(y);
            map.get(y).add(x);
        }
        int arr[]=new int[n+1];
        int goal[]=new int[n+1];
        for(int i=1;i<=n;i++)
        {
            arr[i]=sc.nextInt();
        }
        for(int i=1;i<=n;i++)
        {
            goal[i]=sc.nextInt();
        }
        int tot=0;
        int curr[]=new int[n+1];
        int par[]=new int[n+1];;
        boolean vis[]=new boolean[n+1];
        Stack st=new Stack();st.push(1);
        vis[1]=true;
        List<Integer> list=new ArrayList<>();
        if(goal[1]!=arr[1])
        {
            curr[1]=1;tot++;
            list.add(1);
        }
        //List<Integer> list=new ArrayList<>();
        //System.out.println(map+" "+tot);
        while(st.size()!=0)
        {
            int a=(Integer)st.pop();
            for(int i:map.get(a))
            {
                if(!vis[i])
                {
                    par[i]=a;
                    if((curr[par[a]]+arr[i])%2!=goal[i])
                    {
                        tot++;
                        curr[i]=curr[par[a]]+1;
                        list.add(i);
                    }
                    else
                        curr[i]=curr[par[a]];
                    vis[i]=true;
                    st.push(i);
                }
            }
        }
        System.out.println(tot);
        for(int i:list)
        {
            System.out.println(i);
        }
    }
}
class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte [] buffer;
		private int bufferPointer, bytesRead;
		
		public Reader () {
			din = new DataInputStream (System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		
		public Reader (String file_name) throws IOException {
			din = new DataInputStream (new FileInputStream (file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
		
		public String readLine () throws IOException {
			byte [] buf = new byte[1024];
			int cnt = 0, c;
			while ((c = read ()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String (buf, 0, cnt);
		}
		
		public int nextInt () throws IOException {
			int ret = 0;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		
		public long nextLong () throws IOException {
			long ret = 0;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		
		public double nextDouble () throws IOException {
			double ret = 0, div = 1;
			byte c = read ();
			while (c <= ' ')
				c = read ();
			boolean neg = (c == '-');
			if (neg)
				c = read ();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read ()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read ()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}
		
		private void fillBuffer () throws IOException {
			bytesRead = din.read (buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
		
		private byte read () throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer ();
			return buffer[bufferPointer++];
		}
		
		public void close () throws IOException {
			if (din == null)
				return;
			din.close ();
		}
	}