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.*;

public class Main {
    static int checked[];//arreglos revisados
    static int ini[];//arreglo inicial
    static int fin[];//arreglo final
    static int mod[];//modificados
    static ArrayList <Integer> un[];//uniones
    static int n, count;
    
     
    
    public static void dfs (int checked[], int level, int odd_mod, int even_mod, int index){
        if(checked[index]==0){//no ha sido visitado
            checked[index]=1;//lo cambia a visitado
            
            if(level%2==0){//nivel par
                if(even_mod%2 != 0){//si se ha cambiado un # impar de veces
                        if(ini[index]==0)
                            ini[index]=1;
                        else
                            ini[index]=0;
                }
            }
            else{
                if(odd_mod%2 != 0){
                        if(ini[index]==0)
                            ini[index]=1;
                        else
                            ini[index]=0;
                }
            }
            if(ini[index] != fin[index]){// si el valor en el indicees diferente
                mod[index] = 1;//modificado activado
                count+=1;// aunmenta la cuenta
                if(level%2 == 0)//que va a modificar
                    even_mod+=1;
                else
                    odd_mod+=1;
            }
            for(int i=0;i<un[index].size();i++){// Repite el proceso el numero de conexiones que tenga el nodo
                dfs(checked,level+1,odd_mod, even_mod,un[index].get(i));//repetir el numero uniones que se han ingresado
            }
        }
    }
    public static void main(String args []) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        un=new ArrayList[n+1];//arreglo de conexiones
        checked =new int[n+1];
        for(int i=0;i<=n;i++)//inicia todas los arreglos de nodos
            un[i]=new ArrayList<Integer>();
        int l=n;        
        while(l-->1){
            String s=br.readLine();
            String str[]=s.split(" ");// lee las posiciones separadas por un espacio
            int x=Integer.parseInt(str[0]);//ingresa el primer valor en x
            int y=Integer.parseInt(str[1]);//segundo valor en y
            un[x].add(y);//guarda en cada nodo x el valor de y(guarda sus conexiones)
            un[y].add(x);//guarda en cada nodo y el valor de x(guarda sus conexiones)

        }
                
        count=0;
        ini=new int[n+1];// inicia el arreglo (como el numero de conexiones es 1 menos que el de nodos se suma 1)
                fin=new int[n+1];//arreglo final
        mod=new int[n+1];// arreglo de los cambios hechos
        String s=br.readLine();
        String str[]=s.split(" ");
        String s1=br.readLine();
        String str1[]=s1.split(" ");
        for(int i=1;i<=n;i++){
            ini[i]=Integer.parseInt(str[i-1]);//guarda en el primero    
            fin[i]=Integer.parseInt(str1[i-1]);// guarda en el segundo
        }
        dfs(checked,0,0,0,1);// hace una dfs iniciando del nodo raiz
        System.out.println(count);//mostrar la cuenta
        for(int i=1;i<=n;i++){
            if(mod[i]==1)
                System.out.println(i);// imprimir las posiciones q tienen cambio
        }
    }
}