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_{i}, 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_{i}, 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 ≤ 10^5). Each of the next n - 1 lines contains two integers u_{i} and v_{i} (1 ≤ u_{i}, v_{i} ≤ n; u_{i} ≠ v_{i}) meaning there is an edge between nodes u_{i} and v_{i}. 

The next line contains n integer numbers, the i-th of them corresponds to init_{i} (init_{i} is either 0 or 1). The following line also contains n integer numbers, the i-th number corresponds to goal_{i} (goal_{i} 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 x_{i}, representing that you pick a node x_{i}.


-----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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from collections import deque\n\nstack = deque()\n\nn = int(input())\nlinks = [tuple(map(lambda x:int(x)-1, input().split())) for i in range(n-1)]\n\nlinked_to = [[] for i in range(n)]\n\nfor x, y in links:\n    linked_to[x].append(y)\n    linked_to[y].append(x)\n\ninit = list(map(lambda x:x=="1", input().split()))\ngoal = list(map(lambda x:x=="1", input().split()))\n\n#print(init)\n#print(goal)\n\nstack.append(0)\nops = 0\n\nvisited = [False] * n\nparent = [n] * (n+1)\nwas_swapped = [False] * (n+1)\n\nvisited[0] = True\n\ndef xor(x, y):\n    return x != y\n\ndef get_chld(i):\n    for e in linked_to[i]:\n        if e != parent[i]:\n            yield e\n\nwhile len(stack) > 0:\n    c = stack.pop()\n    for l in linked_to[c]:\n        if not visited[l]:\n            visited[l] = True\n            parent[l] = c\n            stack.append(l)\n\nchosen = []\n\nstack.append(0)\n\nwhile len(stack) > 0:\n    c = stack.pop()\n    stack.extend(get_chld(c))\n    was_swapped[c] = was_swapped[parent[parent[c]]]\n    if xor(xor(init[c], goal[c]), was_swapped[c]):\n        was_swapped[c] = not was_swapped[c]\n        ops += 1\n        chosen.append(c+1)\n\nprint(ops, *chosen, sep=\'\\n\')\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15255