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 = "def main():\n    n = int(input())\n    l = [[] for _ in range(n + 1)]\n    for _ in range(n - 1):\n        u, v = list(map(int, input().split()))\n        l[u].append(v)\n        l[v].append(u)\n    sw = [a != b for a, b in zip(input()[::2], input()[::2])]\n    root = (1, False, False)\n    nxt, res, avail = [root], [0], [True] * (n + 1)\n    while nxt:\n        cur, nxt = nxt, []\n        for v, a, b in cur:\n            if sw[v - 1] != a:\n                a = not a\n                res.append(v)\n            avail[v] = False\n            for u in l[v]:\n                if avail[u]:\n                    nxt.append((u, b, a))\n    res[0] = len(res) - 1\n    print('\\n'.join(map(str, res)))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14443