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

/**
*@author Julian Avenda�o
*Version 12-06-2014 
**/

public class XorTree {
	
	//configuration initial of problem
	static int[] initial;
	//configuration goal of problem
	static int[] end;
	//Array of booleans by determinate if n-node have parent
	static boolean[] parents;
	//Nodes of the tree
	static int nodes;
	//List of List<Integer> any element of list represent n-node and his childs 
	static List<List<Integer>> edges;
	//List of nodes changes 
	static List<Integer> changes = new ArrayList<Integer>();
	//Total moves
	static int moves;

	public static void initialVariable(){
		Scanner sc = new Scanner( System.in );
		//Initialize variables
		moves = 0;
		nodes = sc.nextInt();
		//nodes+1 by manage any index from 1 to nodes
		initial = new int[nodes + 1];
		end = new int[nodes + 1];
		parents = new boolean[nodes + 1];
		//Root don�t have parent by he will be parent
		parents[1] = true;
		//Fill array parents with false  
		if (nodes > 1)
			Arrays.fill(parents, 2, nodes, false);
		//Initialize any list of child by each node
		edges = new ArrayList<List<Integer>>();
		edges.add(new ArrayList<Integer>());
		for (int i = 1; i <= nodes; i++)
			edges.add(new ArrayList<Integer>());
		for (int i = 1; i < nodes; i++){
			int u = sc.nextInt();
			int v = sc.nextInt();
			//If u have parent, v have that be son of u 
			if (parents[u]){
				edges.get(u).add(v);
				parents[v] = true;
			} else{ //Else u have that be son of u
				edges.get(v).add(u);
				parents[u] = true;
			}
		}
		//Initialize configuration initial and goal 
		for(int i = 1; i <= nodes; i++)
			initial[i] = sc.nextInt();
		for (int i = 1; i <= nodes; i++)
			end[i] = sc.nextInt();
	}
	
	//Boolean v1 represent if node was change
	//Boolean v2 represent if node son was change
	public static void solveProblem(int node, boolean v1, boolean v2){
		if( initial[node] != end[node] ){
			//If configuration initial[i] != end[i] and node don�t was change before, change node
			if(!v1){
				// Add node List of changes
				changes.add(node);
				moves++;
				v1 = true;
			}
		}else if(initial[node] == end[node] && v1){
			//If configuration initial[i] = end[i] and node was change before, change node
			// Add node List of changes
			changes.add(node);
			moves++;
			v1 = false;
		}
		//Analyze nodes son of each node 
		for(Integer son: edges.get(node))
			//v2 is now state of node son and v1 is state of node grandson 
			solveProblem(son, v2, v1);
	}

	public static void main(String arg[]){
		initialVariable();
		solveProblem(1,false,false);
		System.out.println(moves);
		for(Integer change: changes)
			System.out.println(change);
	}

}