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
import threading
from collections import defaultdict
n = int(input())
adj = defaultdict(list)
for i in range(n-1):
    x,y = map(int,input().split())
    adj[x].append(y)
    adj[y].append(x)
intial = list(map(int,input().split()))
target = list(map(int,input().split()))
# final = list(zip(intial,target))

# flip_count = 0
flip_node = []
global grandflip
grandflip=False
def dfs(node,par,grandParentFlip,parentFlip):
    global grandflip
    grandflip =False
    if intial[node-1]!=target[node-1]:
        if grandParentFlip%2==0:
            flip_node.append(node)
            grand_flip=True
    else:
        if grandParentFlip%2!=0:
            flip_node.append(node)
            grand_flip = True
    for i in range(len(adj[node])):
        if adj[node][i]!=par:
            if grandflip==True:
                dfs(adj[node][i],node,grandParentFlip+1,parentFlip)
            else:
                dfs(adj[node][i],node,grandParentFlip,parentFlip+1)
def main():
    par = 0
    grandParentFlip = 0
    parentFlip = 0
    dfs(1,par,grandParentFlip,parentFlip)
    print(len(flip_node))
    for i in flip_node :
        print(i,end="\n")
if __name__=="__main__":
    sys.setrecursionlimit(10**6)
    threading.stack_size(10**8)
    t = threading.Thread(target=main)
    t.start()
    t.join()