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).
n = int(input())
adj_list = {i: [] for i in range(n)}

for edge in range(n - 1):
    a, b = list(map(int, input().split()))
    adj_list[a - 1].append(b - 1)
    adj_list[b - 1].append(a - 1)

initial = list(map(int, input().split()))
goal = list(map(int, input().split()))

ans = 0
queue = [[0, 0, 0, 0]]  # [node label, effect of even level flips, effect of odd level flips, current level]
visited = [0 for i in range(n)]
visited[0] = 1

moves = []

while len(queue) != 0:
    node, even, odd, level = queue.pop()
    if level == 0:
        if (even == 0 and initial[node] != goal[node]) or (even == 1 and initial[node] == goal[node]):
            ans += 1
            even = 1 - even
            moves.append(node + 1)
    else:
        if (odd == 0 and initial[node] != goal[node]) or (odd == 1 and initial[node] == goal[node]):
            ans += 1
            odd = 1 - odd
            moves.append(node + 1)
    level = 1 - level

    for son in adj_list[node]:
        if visited[son] == 0:
            visited[son] = 1
            queue.append([son, even, odd, level])

answer_str = str(ans) + '\n' + '\n'.join([str(x) for x in moves])
print(answer_str)
