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)
parents = { }

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

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

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

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

scoring = { }
def score(x):
    if x in scoring:
        return scoring[x]

    count = 0
    if current[x] == desired[x]:
        count = -1
    else:
        count = 1

    for y in children[x]:
        for z in children[y]:
            count += score(z)

    scoring[x] = count
    return count

def zero(x):
    current[x] = not current[x]
    del scoring[x]

    for y in children[x]:
        for z in children[y]:
            zero(z)

ops = []

while True:
    s, x = max((score(i), i) for i in range(n))
    if s <= 0:
        break
    ops.append(x)
    zero(x)

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