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

stack = deque()

n = int(input())
links = [tuple(map(lambda x:int(x)-1, input().split())) for i in range(n-1)]

linked_to = [[] for i in range(n)]

for x, y in links:
    linked_to[x].append(y)
    linked_to[y].append(x)

init = list(map(lambda x:x=="1", input().split()))
goal = list(map(lambda x:x=="1", input().split()))

#print(init)
#print(goal)

stack.append(0)
ops = 0

visited = [False] * n
parent = [n] * (n+1)
was_swapped = [False] * (n+1)

visited[0] = True

def xor(x, y):
    return x != y

def get_chld(i):
    for e in linked_to[i]:
        if e != parent[i]:
            yield e

while len(stack) > 0:
    c = stack.pop()
    for l in linked_to[c]:
        if not visited[l]:
            visited[l] = True
            parent[l] = c
            stack.append(l)

chosen = []

stack.append(0)

while len(stack) > 0:
    c = stack.pop()
    stack.extend(get_chld(c))
    was_swapped[c] = was_swapped[parent[parent[c]]]
    if xor(xor(init[c], goal[c]), was_swapped[c]):
        was_swapped[c] = not was_swapped[c]
        ops += 1
        chosen.append(c+1)

print(ops, *chosen, sep='\n')

