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).
#!/usr/bin/env python3

from collections import defaultdict

children = defaultdict(list)
children[0] = []

parents = { }

n = int(input())
for _ in range(n - 1):
    u, v = tuple(map(int, input().split()))

    parent, child = None, None
    if u - 1 in children:
        parent = u - 1
        child = v - 1
    else:
        parent = v - 1
        child = u - 1

    children[parent].append(child)
    children[child] = []
    parents[child] = parent

current = list(map(bool, map(int, input().split())))
desired = list(map(bool, map(int, input().split())))

heights = { }
def set_height(x, h):
    heights[x] = h
    for y in children[x]:
        set_height(y, h + 1)
set_height(0, 0)

ops = []

ancestor = defaultdict(set)
def ans(x, y):
    """ check if x is ancestor of y """
    if not y in ancestor:
        z = y
        while z in parents and parents[z] in parents:
            z = parents[parents[z]]
            ancestor[y].add(z)

        ancestor[y].add(y)

    return x in ancestor[y]

def val(x):
    ch = heights[x]
    ht = ch % 2
    flipped = sum(1 for y in ops if ans(y, x)) % 2 != 0
    return flipped ^ current[x]

queue = [0]
while queue:
    x = queue.pop(0)
    if val(x) != desired[x]:
        ops.append(x)

    for y in children[x]:
        queue.append(y)

print(len(ops))
for x in ops:
    print(x + 1)
