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>
using namespace std;
namespace io {
string separator = " ";
}
template <typename T>
inline void write(T x) {
  cout << x << io::separator;
}
template <typename T, typename... Args>
inline void write(T x, Args... args) {
  write(x);
  write(args...);
}
inline void writeln() { cout << '\n'; }
template <typename... Args>
inline void writeln(Args... args) {
  write(args...);
  writeln();
}
template <typename T>
inline void read(T& x) {
  cin >> x;
}
template <typename T, typename... Args>
inline void read(T& x, Args&... args) {
  cin >> x;
  read(args...);
}
template <typename T>
inline void writec(T x) {
  for (auto i = x.begin(); i != x.end(); i++) write(*i);
  writeln();
}
template <typename TL, typename TR>
inline TL GCD(TL a, TR b) {
  TL c;
  while (b) {
    c = b;
    b = a % b;
    a = c;
  }
  return a;
}
template <typename TL, typename TR>
inline TL LCM(TL a, TR b) {
  return a / GCD(a, b) * b;
}
template <typename TL, typename TR>
inline TL MAX(TL a, TR b) {
  return a > b ? a : b;
}
template <typename T, typename... Args>
inline T MAX(T a, Args... args) {
  return MAX(a, MAX(args...));
}
template <typename TL, typename TR>
inline TL MIN(TL a, TR b) {
  return a < b ? a : b;
}
template <typename T, typename... Args>
inline T MIN(T a, Args... args) {
  return MIN(a, MIN(args...));
}
inline int64_t fac(int16_t n) {
  static vector<int64_t> f(1, 1);
  for (auto i = f.size(); i <= n; i++) f.push_back(f.back() * i);
  return f[n];
}
inline int64_t suma(int32_t a1, int32_t d, int32_t n) {
  return n * (2 * a1 + (n - 1) * d) / 2;
}
inline int32_t factor(int32_t n) {
  static vector<int32_t> d(2, 2), prime;
  if (n + 1 > d.size()) {
    int32_t np = d.size() - 1;
    int32_t nn = d.size();
    while (n > nn - 1) nn *= 2;
    nn--;
    d.resize(nn + 1);
    for (auto i = 2; i <= nn; i++) {
      if (!d[i]) {
        d[i] = i;
        prime.push_back(i);
      }
      int64_t x;
      for (int32_t j = 0; prime[j] <= d[i] && j < prime.size() &&
                          (x = (int64_t)i * prime[j]) <= nn;
           j++)
        d[x] = prime[j];
    }
  }
  return d[n];
}
inline bool isprime(int32_t n) { return (factor(n) == n); }
inline int32_t prime(int32_t n) {
  static vector<int32_t> p(1, 2);
  if (n + 1 > p.size()) {
    int32_t np = p.size() - 1;
    int32_t nn = p.size();
    while (n > nn - 1) nn *= 2;
    factor(nn * (log(nn) + log(log(nn))));
    nn--;
    p.resize(nn + 1);
    int32_t x = p[np] + 1;
    for (auto i = np + 1; i <= nn; i++) {
      while (!isprime(x)) x++;
      p[i] = x++;
    }
  }
  return p[n];
}
int32_t MOD = 1e9 + 7;
inline int32_t SUM(int32_t x, int32_t y) { return (x + y) % MOD; }
inline int32_t MUL(int32_t x, int32_t y) { return (int64_t)x * y % MOD; }
inline int32_t POW(int32_t x, int32_t n) {
  int32_t y = 1;
  while (n) {
    if (n % 2) y = MUL(y, x);
    x = MUL(x, x);
    n /= 2;
  }
  return y;
}
inline int32_t INV(int32_t x) { return POW(x, MOD - 2); }
inline int32_t DIV(int32_t x, int32_t y) { return MUL(x, INV(y)); }
inline int32_t P(int32_t l, int32_t r) {
  int32_t x = 1;
  for (auto i = l; i <= r; i++) x = MUL(x, i);
  return x;
}
inline int32_t FAC(int32_t n) { return P(2, n); }
inline int32_t C(int32_t n, int32_t k) { return DIV(P(k + 1, n), P(2, n - k)); }
void solve();
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  solve();
}
vector<int16_t> init, goal;
vector<vector<int32_t>> e(0, vector<int32_t>(0));
vector<int32_t> ans;
inline void dfs(int32_t curr, int32_t prev, int16_t ths, int16_t oth) {
  if (init[curr] ^ ths != goal[curr]) {
    ans.push_back(curr + 1);
    ths ^= 1;
  }
  for (auto i : e[curr])
    if (i != prev) dfs(i, curr, oth, ths);
}
inline void solve() {
  int32_t n;
  read(n);
  e.resize(n);
  for (auto i_ = n - 1; i_--;) {
    int32_t u, v;
    read(u, v);
    u--;
    v--;
    e[u].push_back(v);
    e[v].push_back(u);
  }
  init.resize(n);
  goal.resize(n);
  for (auto i = init.begin(); i != init.end(); i++) read(*i);
  for (auto i = goal.begin(); i != goal.end(); i++) read(*i);
  dfs(0, -1, 0, 0);
  writeln(ans.size());
  for (auto x : ans) writeln(x);
}