description: You have received data from a Bubble bot. You know your task is to make factory facilities, but before you even start, you need to know how big the factory is and how many rooms it has. When you look at the data you see that you have the dimensions of the construction, which is in rectangle shape: N x M. 
  
  Then in the next N lines you have M numbers. These numbers represent factory tiles and they can go from 0 to 15. Each of these numbers should be looked in its binary form. Because from each number you know on which side the tile has walls. For example number 10 in it's binary form is 1010, which means that it has a wall from the North side, it doesn't have a wall from the East, it has a wall on the South side and it doesn't have a wall on the West side. So it goes North, East, South, West. 
  
  It is guaranteed that the construction always has walls on it's edges. The input will be correct. 
  
  Your task is to print the size of the rooms from biggest to smallest. 
  
  Input
  
  The first line has two numbers which are N and M, the size of the construction. Both are integers: 
  
  n (1 ≤ n ≤ 10^3)
  
  m (1 ≤ m ≤ 10^3)
  
  Next N x M numbers represent each tile of construction.
  
  Output
  
  Once you finish processing the data your output consists of one line sorted from biggest to smallest room sizes. 
  
  Example
  
  Input
  
  
  4 5
  9 14 11 12 13
  5 15 11 6 7
  5 9 14 9 14
  3 2 14 3 14
  
  
  Output
  
  
  9 4 4 2 1 
solution: #include <bits/stdc++.h>
  using namespace std;
  const long double pi = acos(-1.0);
  const long double eps = 1e-6;
  const long long int mod = 1e9 + 7;
  const long long int mod2 = 998244353;
  const long long int inf = 2e18;
  const long long int inf2 = (1LL << 60);
  const long long int maxn = 2e5 + 10;
  void _print(long long int t) { cerr << t; }
  void _print(string t) { cerr << t; }
  void _print(char t) { cerr << t; }
  void _print(float t) { cerr << t; }
  void google(long long int t) { cout << "Case #" << t << ": "; }
  template <class T, class V>
  void _print(pair<T, V> p);
  template <class T>
  void _print(vector<T> v);
  template <class T>
  void _print(set<T> v);
  template <class T, class V>
  void _print(map<T, V> v);
  template <class T>
  void _print(multiset<T> v);
  template <class T, class V>
  void _print(pair<T, V> p) {
    cerr << "{";
    _print(p.first);
    cerr << ",";
    _print(p.second);
    cerr << "}";
  }
  template <class T>
  void _print(vector<T> v) {
    cerr << "[ ";
    for (T i : v) {
      _print(i);
      cerr << " ";
    }
    cerr << "]";
  }
  template <class T>
  void _print(set<T> v) {
    cerr << "[ ";
    for (T i : v) {
      _print(i);
      cerr << " ";
    }
    cerr << "]";
  }
  template <class T>
  void _print(multiset<T> v) {
    cerr << "[ ";
    for (T i : v) {
      _print(i);
      cerr << " ";
    }
    cerr << "]";
  }
  template <class T, class V>
  void _print(map<T, V> v) {
    cerr << "[ ";
    for (auto i : v) {
      _print(i);
      cerr << " ";
    }
    cerr << "]";
  }
  long long int power(long long int a, long long int y, long long int m) {
    long long int res = 1;
    a = a % m;
    while (y > 0) {
      if (y & 1) res = (res * a) % m;
      y = y >> 1LL;
      a = (a * a) % m;
    }
    return res;
  }
  long long int inverse(long long int n, long long int m) {
    return power(n, m - 2, m);
  }
  long long int mod_add(long long int a, long long int b, long long int m) {
    a = a % m;
    b = b % m;
    return (((a + b) % m) + m) % m;
  }
  long long int mod_mul(long long int a, long long int b, long long int m) {
    a = a % m;
    b = b % m;
    return (((a * b) % m) + m) % m;
  }
  long long int mod_sub(long long int a, long long int b, long long int m) {
    a = a % m;
    b = b % m;
    return (((a - b) % m) + m) % m;
  }
  long long int mod_div(long long int a, long long int b, long long int m) {
    a = a % m;
    b = b % m;
    return (mod_mul(a, inverse(b, m), m));
  }
  void IOS() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    cout.precision(20);
    cout.setf(ios::fixed);
    freopen("Error.txt", "w", stderr);
  }
  vector<pair<long long int, long long int> > adj[1005][1005];
  bool vis[1005][1005];
  void addEdges(long long int x, long long int y, long long int xx,
                long long int yy) {
    adj[x][y].push_back({xx, yy});
    adj[xx][yy].push_back({x, y});
  }
  long long int val;
  void dfs(long long int x, long long int y) {
    val++;
    vis[x][y] = true;
    for (auto &node : adj[x][y])
      if (!vis[node.first][node.second]) dfs(node.first, node.second);
  }
  void solve() {
    long long int n, m;
    cin >> n >> m;
    long long int arr[n][m];
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < m; j++) {
        vis[i][j] = false;
        adj[i][j].clear();
        cin >> arr[i][j];
      }
    }
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < m; j++) {
        if (!(arr[i][j] & 1))
          if (j > 0) addEdges(i, j, i, j - 1);
        if (!(arr[i][j] & 2))
          if (i < n - 1) addEdges(i, j, i + 1, j);
        if (!(arr[i][j] & 4))
          if (j < m - 1) addEdges(i, j, i, j + 1);
        if (!(arr[i][j] & 8))
          if (i > 0) addEdges(i, j, i - 1, j);
      }
    }
    vector<long long int> ans;
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < m; j++) {
        if (!vis[i][j]) {
          val = 0;
          dfs(i, j);
          ans.push_back(val);
        }
      }
    }
    sort((ans).rbegin(), (ans).rend());
    for (auto &i : ans) cout << i << " ";
    cout << "\n";
  }
  int32_t main() {
    IOS();
    long long int ttc = 1;
    while (ttc--) {
      auto start_time = chrono::high_resolution_clock::now();
      solve();
      cerr << "Executed in "
           << chrono::duration_cast<chrono::milliseconds>(
                  chrono::high_resolution_clock::now() - start_time)
                  .count()
           << "ms."
           << "\n";
    }
    return 0;
  }
  