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;
template <class T>
string toString(T n) {
  ostringstream ost;
  ost << n;
  ost.flush();
  return ost.str();
}
int toInt(string s) {
  int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
long long toLInt(string s) {
  long long r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
vector<string> parse(string temp) {
  vector<string> ans;
  ans.clear();
  string s;
  istringstream iss(temp);
  while (iss >> s) ans.push_back(s);
  return ans;
}
template <typename T>
inline unsigned long long dist(T A, T B) {
  unsigned long long res =
      (A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y);
  return res;
}
template <typename T>
inline double cosAngle(T a, T b, T c) {
  double res = a * a + b * b - c * c;
  res = res / (2 * a * b);
  res = acos(res);
  return res;
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
template <class T>
inline T lcm(T a, T b) {
  if (a < 0) return lcm(-a, b);
  if (b < 0) return lcm(a, -b);
  return a * (b / gcd(a, b));
}
template <class T>
inline T power(T b, T p) {
  if (p < 0) return -1;
  if (b <= 0) return -2;
  if (!p) return 1;
  return b * power(b, p - 1);
}
template <class T>
int bit_count(T no) {
  int cnt = 0;
  while (no) {
    no = no >> 1;
    cnt++;
  }
  return cnt;
}
void seive(int lm, int arr[]) {
  for (int i = 2; i * i <= lm; i++)
    if (arr[i] == 0)
      for (int j = 1; j * i <= lm; j++) arr[i * j] = 1;
}
template <class T>
void showBit(T N) {
  T zero = 0, one = 1;
  if (N == zero) return;
  showBit(N >> 1);
  printf("%d", N & one);
}
long long binToDec(string s) {
  int ln = s.length();
  long long sum = 0;
  for (int i = ln - 1, k = 0; i >= 0; i--, k++)
    sum = sum + (s[i] - '0') * (1 << k);
  return sum;
}
string rev(string s) {
  string rs = "";
  int l = s.length();
  for (int i = l - 1; i >= 0; i--) rs = rs + s[i];
  return rs;
}
template <typename T>
string decToBin(T n, int dg) {
  string s = "";
  int td = 0;
  while (n) {
    int cb = n & 1;
    s = s + (char)(cb + '0');
    n = n >> 1;
    td++;
  }
  string as = "";
  while (td != dg) {
    as = as + "0";
    td++;
  }
  as = as + rev(s);
  return as;
}
void combination(long long com[][1005]) {
  com[0][0] = 1;
  int sz = 1000;
  for (int i = 1; i <= sz; i++) {
    com[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      com[i][j] = com[i - 1][j] + com[i - 1][j - 1];
      com[i][j] = com[i][j] % 1000000007;
    }
  }
}
template <class T>
T bigmod(T bs, T p, T mod) {
  if (mod <= 0) {
    printf("Exception");
    return 0;
  }
  T ans = 1;
  T k = bs;
  while (p) {
    if (p & 1) {
      ans = ans * k;
      ans %= mod;
    }
    k *= k;
    k %= mod;
    p = p >> 1;
  }
  return ans;
}
void insert_ind(int cs, int ci, int s, int e) {
  if (s == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ci <= mid)
    insert_ind(2 * cs, ci, s, mid);
  else
    insert_ind(2 * cs + 1, ci, mid + 1, e);
}
void update_ind(int cs, int ci, int s, int e, int val) {
  if (s == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ci <= mid)
    update_ind(2 * cs, ci, s, mid, val);
  else
    update_ind(2 * cs + 1, ci, mid + 1, e, val);
}
void update_seg(int cs, int ds, int de, int s, int e, int val) {
  if (ds == s && de == e) {
    return;
  }
  int mid = (s + e) / 2;
  if (ds <= mid) update_seg(2 * cs, ds, min(mid, de), s, mid, val);
  if (de > mid) update_seg(2 * cs + 1, max(mid + 1, ds), de, mid + 1, e, val);
}
void pattern_match(char pat[], const int len, int pi[]) {
  pi[0] = 0;
  for (int i = 1; i < len; i++) {
    int ch = pi[i - 1];
    while (pat[ch] != pat[i]) {
      if (ch == 0) {
        ch = -1;
        break;
      }
      ch = pi[ch - 1];
    }
    pi[i] = ch + 1;
  }
}
void pattern_match(char pat[], int pi[], char tar[], const int len1, int gi[]) {
  if (pat[0] == tar[0]) gi[0] = 1;
  for (int i = 1; i < len1; i++) {
    int st = gi[i - 1];
    while (pat[st] != tar[i]) {
      if (st == 0) {
        st = -1;
        break;
      }
      st = pi[st - 1];
    }
    if (st == -1)
      gi[i] = 0;
    else
      gi[i] = st + 1;
  }
}
struct myArray {
  int mat[10][10];
};
myArray matrix_mul(myArray mat1, myArray mat2, const int sz) {
  int tmp[sz][sz];
  memset((tmp), 0, sizeof((tmp)));
  for (int r = 0; r < sz; r++)
    for (int c = 0; c < sz; c++)
      for (int cr = 0; cr < sz; cr++)
        tmp[r][c] += mat1.mat[r][cr] * mat2.mat[cr][c];
  myArray res;
  for (int r = 0; r < sz; r++)
    for (int c = 0; c < sz; c++) res.mat[r][c] = tmp[r][c];
  return res;
}
myArray unit_matrix(const int sz) {
  myArray ma;
  memset((ma.mat), 0, sizeof((ma.mat)));
  for (int i = 0; i < sz; i++) ma.mat[i][i] = 1;
  return ma;
}
myArray matrix_expo(int p, myArray mat, const int sz) {
  if (p == 0) {
    return unit_matrix(sz);
  }
  if (p & 1) return matrix_mul(mat, matrix_expo(p - 1, mat, sz), sz);
  myArray tmp = matrix_expo(p >> 1, mat, sz);
  return matrix_mul(tmp, tmp, sz);
}
map<string, int> msi;
void cal_state(string s, int tran[][30]) {
  int ln = s.length();
  string s1 = s;
  for (int i = 0; i < ln; i++) {
    msi[s1] = ln - i;
    s1 = s1.substr(0, ln - i - 1);
  }
  s1 = "";
  for (int i = 0; i < ln; i++) {
    string ts = s1;
    for (int j = 0; j < 26; j++) {
      s1 = ts + (char)('a' + j);
      int tln = i + 1;
      while (msi[s1] == 0) {
        s1 = s1.substr(1);
        tln--;
        if (tln == 0) break;
      }
      if (tln == 0) s1 = "";
      tran[i][j] = msi[s1];
    }
    s1 = s.substr(0, i + 1);
  }
}
double distance(double x1, double y1, double x2, double y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
int X[] = {0, 0, 1, -1};
int Y[] = {1, -1, 0, 0};
const int dx[8] = {-1, 1, -2, 2, -1, 1, -2, 2};
const int dy[8] = {2, 2, -1, -1, -2, -2, 1, 1};
int n, m, k, k1;
vector<int> V[100005], ans;
int init[100005], goal[100005], chp[100005], p[100005], col[100005];
void dfs(int cn) {
  init[cn] ^= (chp[p[p[cn]]] & 1);
  chp[cn] ^= chp[p[p[cn]]];
  col[cn] = true;
  if (goal[cn] != init[cn]) {
    chp[cn] ^= 1;
    ans.push_back(cn);
  }
  for (int i = 0; i < V[cn].size(); i++)
    if (!col[V[cn][i]]) {
      p[V[cn][i]] = cn;
      dfs(V[cn][i]);
    }
}
int main() {
  scanf("%d", &n);
  for (int i = (0); i < (n - 1); ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    V[u].push_back(v);
    V[v].push_back(u);
  }
  for (int i = (0); i < (n); ++i) scanf("%d", &init[i + 1]);
  for (int i = (0); i < (n); ++i) scanf("%d", &goal[i + 1]);
  p[1] = 0;
  dfs(1);
  cout << ans.size() << endl;
  for (int i = (0); i < (ans.size()); ++i) printf("%d\n", ans[i]);
  printf("\n");
  return 0;
}