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 *init*<sub class="lower-index">*i*</sub>, 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 *goal*<sub class="lower-index">*i*</sub>, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.
The first line contains an integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>). Each of the next *n* - 1 lines contains two integers *u*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i*</sub> (1 ≤ *u*<sub class="lower-index">*i*</sub>, *v*<sub class="lower-index">*i*</sub> ≤ *n*; *u*<sub class="lower-index">*i*</sub> ≠ *v*<sub class="lower-index">*i*</sub>) meaning there is an edge between nodes *u*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i*</sub>. 

The next line contains *n* integer numbers, the *i*-th of them corresponds to *init*<sub class="lower-index">*i*</sub> (*init*<sub class="lower-index">*i*</sub> is either 0 or 1). The following line also contains *n* integer numbers, the *i*-th number corresponds to *goal*<sub class="lower-index">*i*</sub> (*goal*<sub class="lower-index">*i*</sub> is either 0 or 1).
import queue

n = int(input())
graph=[]

for i in range(n):
    graph.append([i]) #in order to prevent list duplication
    graph[i].pop() 

for i in range(n-1):
    connection = list(map(int,input().split()))
    graph[connection[0]-1].append(connection[1]-1)
    graph[connection[1]-1].append(connection[0]-1)

initialColors = list(map(int,input().split()))
goalColors = list(map(int,input().split()))
isNodeUsed = [False for i in range(n)]
Recolor = [False for i in range(n)]
parentRecolor = [False for i in range(n)]
ans=[]

currentTargets = queue.Queue()

currentTargets.put(0) #index/to which graph
isNodeUsed[0]=True

while not currentTargets.empty():
    currentNode = currentTargets.get()
    if (initialColors[currentNode]==goalColors[currentNode])==Recolor[currentNode]:
        Recolor[currentNode]= not Recolor[currentNode]
        ans.append(currentNode+1)
    for i in graph[currentNode]:
        if not isNodeUsed[i]:
            currentTargets.put(i)
            isNodeUsed[i]=True
            Recolor[i] = parentRecolor[currentNode]
            parentRecolor[i] = Recolor[currentNode]
print(len(ans))
for i in ans:
    print(i)