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).
import sys


def dfs(tree, root, priv_root, cur_lvl, priv_lvl, diff, pick_list):
    # if tree is 1 or less nodes just return nothing
    if not tree:
        return
    stack = [(root, priv_root, cur_lvl, priv_lvl)]
    while stack:
        (root, priv_root, cur_lvl, priv_lvl) = stack.pop()
        # set level to account for only evens where a difference exists
        if cur_lvl ^ diff[root]:
            cur_lvl ^= 1
            pick_list.append(str(root))
        # add to the queue all cases where a vertex exists
        stack += [(vertex, root, priv_lvl, cur_lvl)
                for vertex in tree[root] if vertex != priv_root]

def main():
    n = int(input())
    tree = dict()
    for _ in range(n - 1):
        u, v = [int(x) for x in input().split()]
        tree[u] = tree.get(u, set()) | set([v])
        tree[v] = tree.get(v, set()) | set([u])
    init = [0] + [int(x) for x in input().split()]
    goal = [0] + [int(x) for x in input().split()]
    # find numbers that don't match that need to be accounted for
    diff = [i ^ j for (i, j) in zip(init, goal)]
    pick_list = list()

    dfs(tree, 1, 0, 0, 0, diff, pick_list)

    num = len(pick_list)
    print(num)
    if num:
        print('\n'.join(pick_list))

if __name__ == '__main__':
    sys.exit(main())