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())

g = {}
for _ in range(n-1):
    u, v = map(int, input().split())
    if u not in g: g[u] = []
    if v not in g: g[v] = []
    g[u].append(v)
    g[v].append(u)

p = list(map(int, input().split()))
goal = list(map(int, input().split()))
cnt = 0
ng = {i: [] for i in range(1, n + 1)}


def search(u, parity, np):
    for i in np[parity]:
        ng[i].append(u)
    np[parity].append(u)
    if u not in g:
        return [u]
    for v in g[u]:
        g[v].remove(u)
        search(v, not parity, [np[0][:], np[1][:]])


search(1, 0, [[], []])
o = []


def count(u=1):
    global cnt
    if p[u-1] != goal[u-1]:
        o.append(u)
        for i in ng[u]:
            p[i-1] = not p[i-1]
        cnt += 1


for i in range(1, n + 1):
    count(i)
print(cnt)
for i in o:
    print(i)
