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 collections

def dfs(tree, curNode, preNode, level, odd, even):
    global res
    if level & 1:
        if (init[curNode - 1] + odd) % 2 != goal[curNode - 1]:
            res.append(curNode)
            odd += 1
    else:
        if (init[curNode - 1] + even) % 2 != goal[curNode - 1]:
            res.append(curNode)
            even += 1
    for nxtNode in tree[curNode]:
        if nxtNode == preNode:
            continue
        dfs(tree, nxtNode, curNode, level + 1, odd, even)
if __name__ == '__main__':
    n = int(input())
    tree = collections.defaultdict(list)
    for i in range(n - 1):
        u, v = list(map(int, input().strip().split()))
        tree[u].append(v); tree[v].append(u)
    init = list(map(int, input().strip().split()))
    goal = list(map(int, input().strip().split()))
    global res; res = []
    dfs(tree, 1, 0, 1, 0, 0)
    cnt = len(res)
    print(cnt)
    for i in range(cnt):
        print(res[i])