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.Scanner;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;


public class Xortree {
    
//estado inicial 
static int[] ini ;
// estado final 
static int[] fini ;
//numero de nodos 
static  int nodos;
//coneciones 
static  List<List<Integer>> ramitas ;
//padres 
static  boolean[] papa;
//resultado cambios 
static List<Integer> cambios = new ArrayList<>() ;
//resultado movimientos 
static int movi;

static void armando () {
       //escanea lo que meto por consola XD
       Scanner sc = new Scanner( System.in );
       // inicializar variables 
       movi=0;
       nodos = sc.nextInt();
       ini = new int[nodos+1];
       fini = new int[nodos+1];
       papa = new boolean[nodos+1];
       
       papa[1]=true ;     
      //llenado con false 
       if (nodos > 1)
       Arrays.fill(papa, 2, nodos, false);   
       
       
       ramitas = new ArrayList<List<Integer>>();
       //primera rama 
       ramitas.add(new ArrayList<Integer>() );
       //creo ramitas listas de listas  
       for (int i=1;i<= nodos;i++ )
       ramitas.add(new ArrayList<Integer>() );
       for (int i=1;i< nodos ; i++ ){
           //escaneo las cuplas de las uniones de las ramas 
           int u = sc.nextInt();
           int v = sc.nextInt();
            // miro  si es un tronco o no (raiz o si ya lo use )   
           if (papa[u])    {           
               ramitas.get(u).add(v);
               papa[v]=true;    
           }
           else {
               ramitas.get(v).add(u);
               papa[u]=true; 
           }
       }
       // se llenan con los estados de partida 
        for(int i=1;i<=nodos;i++)
            ini[i] = sc.nextInt();
        //estados de llegada 
        for(int i=1;i<=nodos;i++)
            fini[i] = sc.nextInt();
}

        public static void solucito (int nodo, boolean valyo, boolean valhijo){
            // valyo me muestra el valos de donde estoy parado 1 o 0 es decir falso o verdadero 
		if( ini[nodo] != fini[nodo] && !valyo){
	                        cambios.add(nodo);
				movi++;
				valyo = true;
                                
		}else if(ini[nodo] == fini[nodo] && valyo){
			
			cambios.add(nodo);
			movi++;
			valyo = false;
		}
		
		for(Integer son: ramitas.get(nodo))
			//como al cambiar un abuelo cambia el nieto el valyo sera el val de mi nieto mas no es de mi hijo 
			solucito(son, valhijo, valyo );
	}

	public static void main(String arg[]){
		armando();
		solucito(1,false,false);
		System.out.println(movi);
		for(Integer change: cambios)
			System.out.println(change);
	}       
           
           
}