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).
l = int(input())

t = [[] for _ in range(l)]


for i in range(l- 1):
    inp = list(map(int, input().strip().split()))
    t[inp[1] - 1].append(inp[0] - 1)

vals = list(map(int, input().strip().split()))
goal = list(map(int, input().strip().split()))


def getSos(i):

    sos = []

    if t[i] == []:
        return []

    for child in t[i]:
        sos.extend(t[child])
        sos.extend(getSos(child))

    return sos


def pick(i):

    if vals[i]:
        vals[i] = 0
    else:
        vals[i] = 1

    sos = getSos(i)

    for i in sos:
        if vals[i]:
            vals[i] = 0
        else:
            vals[i] = 1
    
    return


cnt = 0
picks = []

for i in range(l):
    if vals[i] != goal[i]:
        pick(i)
        picks.append(i)
        cnt += 1

print(cnt)

for pick in picks:
    print(pick + 1)

