Problem: 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 initi, 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 goali, 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 ≤ 105). Each of the next n - 1 lines contains two integers ui and vi (1 ≤ ui, vi ≤ n; ui ≠ vi) meaning there is an edge between nodes ui and vi. 

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

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:2000000")
#pragma comment(linker, "/HEAP:2000000")
using namespace std;
void print_width(long long x) {
  std::cout << std::fixed;
  std::cout << std::setprecision(x);
}
long long power(long long x, long long y, long long p = 1000000007) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void printArr(long long a[], long long n) {
  for (long long i = 0; i < n; i++) cout << a[i] << " ";
  cout << '\n';
}
void printVector(std::vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << '\n';
}
void printVectorPair(std::vector<pair<long long, long long>> v) {
  for (long long i = 0; i < v.size(); i++)
    cout << v[i].first << " " << v[i].second << '\n';
  ;
  cout << '\n';
}
long long Min(long long a, long long b, long long c) {
  if (a < b and a < c) return a;
  if (b < c) return b;
  return c;
}
void initialize(long long arr[], long long n) {
  for (long long i = 0; i <= n; i++) arr[i] = i;
}
long long root(long long arr[], long long i) {
  while (arr[i] != i) {
    arr[i] = arr[arr[i]];
    i = arr[i];
  }
  return i;
}
void Union(long long arr[], long long a, long long b) {
  long long root_a = root(arr, a);
  long long root_b = root(arr, b);
  arr[root_a] = root_b;
}
long long gcd(long long a, long long b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long power_wm(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
long double dpower(long double x, long long y) {
  long double res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
std::vector<long long> vsum(std::vector<long long> a) {
  std::vector<long long> s(a.size());
  s[0] = a[0];
  for (long long i = 1; i <= a.size() - 1; i++) {
    s[i] = s[i - 1] + a[i];
  }
  return s;
}
bool comp(pair<long long, long long> a, pair<long long, long long> b) {
  long long x = a.second * b.first;
  long long y = a.first * b.second;
  if (x <= y)
    return false;
  else
    return true;
}
bool is_cap(char a) {
  if (a <= 'Z' and a >= 'A')
    return true;
  else
    return false;
}
bool is_small(char a) {
  if (a <= 'z' and a >= 'a')
    return true;
  else
    return false;
}
string findSum(string str1, string str2) {
  string str = "";
  if (str1.size() > str2.size()) {
    swap(str1, str2);
  }
  int n1 = str1.size(), n2 = str2.size();
  reverse(str1.begin(), str1.end());
  reverse(str2.begin(), str2.end());
  int carry;
  carry = 0;
  for (int i = 0; i < n1; i++) {
    int sum;
    sum = ((str1[i] - '0') + (str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  for (int i = n1; i < n2; i++) {
    int sum;
    sum = ((str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  if (carry) str.push_back(carry + '0');
  reverse(str.begin(), str.end());
  return str;
}
bool mcomp(long long a, long long b, long long c, long long d) {
  if (a == b and b == c and c == d)
    return true;
  else
    return false;
}
long long c2(long long n) { return (n * (n - 1)) / 2; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  vector<vector<long long>> g(n + 1, vector<long long>(0));
  ;
  for (long long i = 0; i < n - 1; i++) {
    long long a, b;
    cin >> a >> b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  std::vector<long long> a(n + 1);
  std::vector<long long> b(n + 1);
  for (long long i = 0; i < n; i++) cin >> a[i + 1];
  for (long long i = 0; i < n; i++) cin >> b[i + 1];
  std::vector<long long> prop(n + 1, 0);
  queue<long long> q;
  q.push(1);
  std::vector<long long> vis(n + 1, 0);
  vis[1] = 1;
  std::vector<long long> parent(n + 1, 0);
  long long ans = 0;
  std::vector<long long> av;
  while (!q.empty()) {
    long long x = q.front();
    q.pop();
    long long px = parent[x];
    long long pv = prop[px];
    if (prop[px] % 2 == 0 and a[x] == b[x]) {
    } else if (prop[px] % 2 == 1 and a[x] != b[x]) {
    } else {
      pv = pv + 1;
      ans++;
      av.push_back(x);
    }
    for (long long i = 0; i < g[x].size(); i++) {
      long long y = g[x][i];
      if (vis[y] == 0) {
        parent[y] = x;
        prop[y] = pv;
        vis[y] = 1;
        q.push(y);
      }
    }
  }
  cout << ans << '\n';
  for (long long i = 0; i < av.size(); i++) cout << av[i] << '\n';
  ;
  return 0;
}