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).
from collections import deque, defaultdict
gph, n = defaultdict(set), int(input())
for i in range(n - 1):
    u, v = map(int, input().split())
    gph[u].add(v)
    gph[v].add(u)
value = [0] + list(map(int, input().split()))
goal = [0] + list(map(int, input().split()))
parent = [None] * (n + 1)
parent[1] = (None, 0)
f, queue = [], deque([1])
while queue:
    x = queue.popleft()
    p, n = parent[x]
    z = 0 if p is None else parent[p][1]
    if z % 2:
        value[x] = 1 - value[x]
    if value[x] != goal[x]:
        value[x] = 1 - value[x]
        f.append(str(x))
        z += 1
    for c in gph[x]:
        if not parent[c]:
            parent[c] = (x, z)
            queue.append(c)
print(len(f))
print('\n'.join(f))