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).
def main():
    n = int(input())
    odd_level = [1]
    even_level = []
    parity = {1:True}  # TRUE ODD, FALSE EVEN
    children = {i:[] for i in range(1, n+1)}
    for _ in range(n-1):
        u,v = map(int, input().split())
        if u in parity:
            v,u = u,v
        children[v].append(u)
        parity[u] = not parity[v]
        if parity[u]:
            odd_level.append(u)
        else:
            even_level.append(u)

    init = list(map(bool, map(int, input().split())))
    goal = list(map(bool, map(int, input().split())))
    picks = []

    adjacents = [1]
    visited = {1:True}
    while len(adjacents):
        i = adjacents.pop(0)

        init_i = init[i-1]
        goal_i = goal[i-1]
        if init_i != goal_i:
            picks.append(i)
            to_change = odd_level if parity[i] else even_level

            for j in to_change:
                if j not in visited:
                    init[j-1] = not init[j-1]
        adjacents.extend(children[i])
        for child in children[i]:
            visited[child] = True

    print(len(picks))
    print(*picks, sep="\n")

main()
	  		     					 				 		 	 	 	 	