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).
from typing import List


def get_input():
    nodes_count: int = int(input())

    adj_list: List[List[int]] = [[] for i in range(nodes_count)]

    for _ in range(nodes_count - 1):
        u, v = map(int, input().split())
        adj_list[u - 1].append(v - 1)
        adj_list[v - 1].append(u - 1)

    current_state: List[int] = list(map(int, input().split()))
    desired_state: List[int] = list(map(int, input().split()))

    return nodes_count, adj_list, current_state, desired_state


def copy_2d_list(adj_list: List[List[int]]):
    copied_adj_list: List[List[int]] = []
    for u in range(len(adj_list)):
        copied_adj_list.append(adj_list[u][:])

    return copied_adj_list


def solve(nodes_count: int, adj_list: List[List[int]], current_state: List[int], desired_state: List[int]) -> List[int]:
    actions: List[int] = []

    def perform_dfs(source: int, parent: int, node_level: int = 0, odd_reverses: int = 0, even_reverses: int = 0):
        for node in adj_list[source]:
            if node == parent:
                continue
            if node_level % 2 == 0:
                if even_reverses % 2 == 0 and current_state[node] == desired_state[node]:
                    perform_dfs(node, source, node_level + 1, odd_reverses, even_reverses)

                elif even_reverses % 2 == 1 and current_state[node] != desired_state[node]:
                    perform_dfs(node, source, node_level + 1, odd_reverses, even_reverses)

                else:
                    actions.append(node + 1)
                    perform_dfs(node, source, node_level + 1, odd_reverses, even_reverses + 1)

            else:
                if odd_reverses % 2 == 0 and current_state[node] == desired_state[node]:
                    perform_dfs(node, source, node_level + 1, odd_reverses, even_reverses)

                elif odd_reverses % 2 == 1 and current_state[node] != desired_state[node]:
                    perform_dfs(node, source, node_level + 1, odd_reverses, even_reverses)

                else:
                    actions.append(node + 1)
                    perform_dfs(node, source, node_level + 1, odd_reverses + 1, even_reverses)

    perform_dfs(0, -1)
    return actions


def show(actions: List[int]):
    print(len(actions))
    for action in actions:
        print(action)


def main():
    nodes_count, adj_list, current_state, desired_state = get_input()
    actions: List[int] = solve(nodes_count, adj_list, current_state, desired_state)
    show(actions)


main()
