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 = "import sys\n\n\ndef dfs(tree, root, priv_root, cur_lvl, priv_lvl, diff, pick_list):\n    # if tree is 1 or less nodes just return nothing\n    if not tree:\n        return\n    stack = [(root, priv_root, cur_lvl, priv_lvl)]\n    while stack:\n        (root, priv_root, cur_lvl, priv_lvl) = stack.pop()\n        # set level to account for only evens where a difference exists\n        if cur_lvl ^ diff[root]:\n            cur_lvl ^= 1\n            pick_list.append(str(root))\n        # add to the queue all cases where a vertex exists\n        stack += [(vertex, root, priv_lvl, cur_lvl)\n                for vertex in tree[root] if vertex != priv_root]\n\ndef main():\n    n = int(input())\n    tree = dict()\n    for _ in range(n - 1):\n        u, v = [int(x) for x in input().split()]\n        tree[u] = tree.get(u, set()) | set([v])\n        tree[v] = tree.get(v, set()) | set([u])\n    init = [0] + [int(x) for x in input().split()]\n    goal = [0] + [int(x) for x in input().split()]\n    # find numbers that don't match that need to be accounted for\n    diff = [i ^ j for (i, j) in zip(init, goal)]\n    pick_list = list()\n\n    dfs(tree, 1, 0, 0, 0, diff, pick_list)\n\n    num = len(pick_list)\n    print(num)\n    if num:\n        print('\\n'.join(pick_list))\n\ndef __starting_point():\n    return(main())\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14541