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,threading
from collections import defaultdict

sys.setrecursionlimit(200000)
threading.stack_size(2**24)

graph = defaultdict(list)
n = int(input())

for i in range(n-1):
    u,v = map(int,input().split())
    graph[u].append(v)
    graph[v].append(u)
    
init = list(map(int,input().split()))
goal = list(map(int,input().split()))

    
visited = [False]*(n+1)
res = [ ]

def dfs(v,even_times, odd_times, level):
    visited[v] = True
    
    
    if level % 2==0:
        current_value = (init[v-1] + even_times) % 2
    else:
        current_value = (init[v-1] + odd_times) % 2
        
    flip = goal[v-1] != current_value
    if flip:
        res.append(v)

    for u in graph[v]:
        if not visited[u]:
            if flip:
                if level % 2==0:
                    dfs(u, even_times+1 ,odd_times, level+1)
                else:
                    dfs(u, even_times, odd_times+1 , level+1)
            else:
                dfs(u, even_times, odd_times , level+1)


dfs(1,0,0,1)


print(len(res))
for i in res:
    print(i)