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).
#include <bits/stdc++.h>
using namespace std;

vector<vector<int>>graph;
vector<int>initial,goal,ans;

void dfs(int node, int par, int level, int even, int odd){
  if(level&1) initial[node] = (odd&1) ? !initial[node] : initial[node];
  else initial[node] = (even&1) ? !initial[node] : initial[node];
 
  if(initial[node]!=goal[node]){
    initial[node]=goal[node];
    ans.push_back(node);
    if(level&1) odd++;
    else even++;
  }
 
  for(int& x : graph[node])
    if(x!=par)
      dfs(x,node,level+1,even,odd);
}

int main() {
    int n,u,v;
    cin >> n;
    graph.resize(n);
    initial.resize(n);
    goal.resize(n);
    
	for(int i=0;i<n-1;i++){
		cin >> u >> v;
		graph[u-1].push_back(v-1);
		graph[v-1].push_back(u-1);
	}
	for(int i=0;i<n;i++) cin >> initial[i];
	for(int i=0;i<n;i++) cin >> goal[i];
	dfs(0,-1,0,0,0);
	cout<<ans.size()<<endl;
	for(auto x:ans) cout<<++x<<endl;
    return 0;
}
