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())

tree = {}
for i in range(n-1):
    u, v = list(map(int, input().split(" ")))
    if v in set(tree.keys()):
        tree[v].append(u)
    else:
        tree[v] = [u]

#print(tree)
keys = set(tree.keys())

init = list(map(int, input().split(" ")))
goal = list(map(int, input().split(" ")))
#print("initial init", init)
#print("goal", goal)

def flip(root, change=True):
    if change:
        init[root-1] = abs(init[root-1]-1)
        if root in keys:
            for vertex in tree[root]:
                flip(vertex, change=False)
    else:
        if root in keys:
            for vertex in tree[root]:
                flip(vertex, change=True)


ans = []
for i in range(n):
    if init[i] != goal[i]:
        flip(i+1)
        ans.append(i+1)

        #print("changed", i+1)
        #print("init", init)

print(len(ans))
for a in ans:
    print(a)
