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())
edges = [set() for _ in range(n)]
for _ in range(n - 1):
    u, v = [int(i) - 1 for i in input().split()]
    edges[u].add(v)
    edges[v].add(u)


inits = [int(i) for i in input().split()]
goals = [int(i) for i in input().split()]
require_change = set()
for index, init, goal in zip(range(n), inits, goals):
    if init != goal:
        require_change.add(index)


results = []
discovered = set()


def discover(index: int, remain_self: bool = True) -> None:
    if index in discovered:
        return

    discovered.add(index)
    if any((remain_self and index in require_change, not remain_self and index not in require_change)):
        global results
        results.append(index)
        remain = not remain_self
    else:
        remain = remain_self

    for edge in edges[index]:
        discover(edge, remain)


discover(0)
print(len(results))
print("\n".join(str(r + 1) for r in results))
