Problem: 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 initi, 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 goali, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.

Input

The first line contains an integer n (1 ≤ n ≤ 105). Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; ui ≠ vi) meaning there is an edge between nodes ui and vi. 

The next line contains n integer numbers, the i-th of them corresponds to initi (initi is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goali (goali is either 0 or 1).

Output

In the first line output an integer number cnt, representing the minimal number of operations you perform. Each of the next cnt lines should contain an integer xi, representing that you pick a node xi.

Examples

Input

10
2 1
3 1
4 2
5 1
6 2
7 5
8 6
9 8
10 5
1 0 1 1 0 1 0 1 0 1
1 0 1 0 0 1 1 1 0 1


Output

2
4
7

Solution (in PYTHON3):

Solution:
# cook your dish here
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush
from math import *
from collections import defaultdict as dd, deque, Counter as C
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect
from time import perf_counter
from fractions import Fraction
import copy
import time
starttime = time.time()
mod = int(pow(10, 9) + 7)
mod2 = 998244353
# from sys import stdin
# input = stdin.readline
def data(): return sys.stdin.readline().strip()
def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
def L(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
try:
    # sys.setrecursionlimit(int(pow(10,7)))
    sys.stdin = open("input.txt", "r")
    # sys.stdout = open("../output.txt", "w")
except:
    pass
def pmat(A):
    for ele in A:
        print(*ele,end="\n")
def seive():
    prime=[1 for i in range(10**6+1)]
    prime[0]=0
    prime[1]=0
    for i in range(10**6+1):
        if(prime[i]):
            for j in range(2*i,10**6+1,i):
                prime[j]=0
    return prime




# exit()
n=L()[0]
A=[L() for i in range(n-1)]
g=[[] for i in range(n+1)]
for x,y in A:
    g[x].append(y)
    g[y].append(x)
curr=L()
target=L()
q=deque()
q.append([1,0,int(curr[0]!=target[0])])
vis=[0 for i in range(n+1)]
vis[1]=1
turns=[]
if curr[0]!=target[0]:
    turns.append(1)
while(q):
    node,l2,l1=q.popleft()
    for neigh in g[node]:
        if vis[neigh]:
            continue
        vis[neigh]=1
        if (curr[neigh-1]+l2)%2!=target[neigh-1]:
            turns.append(neigh)
            q.append([neigh,l1,(l2+1)%2])
        else:
            q.append([neigh,l1,l2])
print(len(turns))
for ele in turns:
    print(ele)





endtime = time.time()
# print(f"Runtime of the program is {endtime - starttime}")