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: 
  import java.io.*;
  import java.util.*;
  
  public final class Main {
  
      static PrintWriter out = new PrintWriter(System.out);
      static FastReader in = new FastReader();
      static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(0, 1), new Pair(1, 0), new Pair(0, -1)};
      static int mod = (int) (1e9 + 7);
      static int mod2 = 998244353;
  
      public static void main(String[] args) {
          int tt = 1;
          while (tt-- > 0) {
              solve();
          }
          out.flush();
      }
  
      static List<Integer> ans = new ArrayList<>();
  
      public static void solve() {
          int n = i();
          int m = i();
          int[][] mat = new int[n][m];
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < m; j++) {
                  mat[i][j] = i();
              }
          }
          boolean[][] vis = new boolean[n][m];
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < m; j++) {
                  int dfs = dfs(i, j, vis, mat);
                  if (dfs > 0) {
                      ans.add(dfs);
                  }
              }
          }
  
          Collections.sort(ans);
          for (int i = ans.size() - 1; i >= 0; i--) {
              out.print(ans.get(i) + " ");
          }
          out.println();
          ans.clear();
      }
  
      private static int dfs(int i, int j, boolean[][] vis, int[][] mat) {
          if (vis[i][j]) {
              return 0;
          }
          vis[i][j] = true;
  
          int cur = mat[i][j];
          int d = 1;
          for (int k = 0; k < 4; k++) {
              if ((cur & (1 << k)) == 0) {
                  int nx = i + moves[3 - k].i;
                  int ny = j + moves[3 - k].j;
                  d += dfs(nx, ny, vis, mat);
              }
          }
          return d;
      }
  
  
      static long[] pre(int[] a) {
          long[] pre = new long[a.length + 1];
          pre[0] = 0;
          for (int i = 0; i < a.length; i++) {
              pre[i + 1] = pre[i] + a[i];
          }
          return pre;
      }
  
      static void print(char A[]) {
          for (char c : A) {
              out.print(c);
          }
          out.println();
      }
  
      static void print(boolean A[]) {
          for (boolean c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(int A[]) {
          for (int c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(long A[]) {
          for (long i : A) {
              out.print(i + " ");
          }
          out.println();
      }
  
      static void print(List<Integer> A) {
          for (int a : A) {
              out.print(a + " ");
          }
      }
  
      static int i() {
          return in.nextInt();
      }
  
      static long l() {
          return in.nextLong();
      }
  
      static String s() {
          return in.nextLine();
      }
  
      static int[][] inputWithIdx(int N) {
          int A[][] = new int[N][2];
          for (int i = 0; i < N; i++) {
              A[i] = new int[]{i, in.nextInt()};
          }
          return A;
      }
  
      static int[] input(int N) {
          int A[] = new int[N];
          for (int i = 0; i < N; i++) {
              A[i] = in.nextInt();
          }
          return A;
      }
  
      static long[] inputLong(int N) {
          long A[] = new long[N];
          for (int i = 0; i < A.length; i++) {
              A[i] = in.nextLong();
          }
          return A;
      }
  
      static int GCD(int a, int b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long GCD(long a, long b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long LCM(int a, int b) {
          return (long) a / GCD(a, b) * b;
      }
  
      static long LCM(long a, long b) {
          return a / GCD(a, b) * b;
      }
  
      static void shuffleAndSort(int[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static void shuffleAndSort(int[][] arr, Comparator<? super int[]> comparator) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int[] temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr, comparator);
      }
  
      static void shuffleAndSort(long[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              long temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static boolean isPerfectSquare(double number) {
          double sqrt = Math.sqrt(number);
          return ((sqrt - Math.floor(sqrt)) == 0);
      }
  
      static void swap(int A[], int a, int b) {
          int t = A[a];
          A[a] = A[b];
          A[b] = t;
      }
  
      static long pow(long a, long b, int mod) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow = (pow * x) % mod;
              }
              x = (x * x) % mod;
              b /= 2;
          }
          return pow;
      }
  
      static long pow(long a, long b) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow *= x;
              }
              x = x * x;
              b /= 2;
          }
          return pow;
      }
  
      static long modInverse(long x, int mod) {
          return pow(x, mod - 2, mod);
      }
  
      static boolean isPrime(long N) {
          if (N <= 1) {
              return false;
          }
          if (N <= 3) {
              return true;
          }
          if (N % 2 == 0 || N % 3 == 0) {
              return false;
          }
          for (int i = 5; i * i <= N; i = i + 6) {
              if (N % i == 0 || N % (i + 2) == 0) {
                  return false;
              }
          }
          return true;
      }
  
      public static String reverse(String str) {
          if (str == null) {
              return null;
          }
          return new StringBuilder(str).reverse().toString();
      }
  
      public static String repeat(char ch, int repeat) {
          if (repeat <= 0) {
              return "";
          }
          final char[] buf = new char[repeat];
          for (int i = repeat - 1; i >= 0; i--) {
              buf[i] = ch;
          }
          return new String(buf);
      }
  
      public static int[] manacher(String s) {
          char[] chars = s.toCharArray();
          int n = s.length();
          int[] d1 = new int[n];
          for (int i = 0, l = 0, r = -1; i < n; i++) {
              int k = (i > r) ? 1 : Math.min(d1[l + r - i], r - i + 1);
              while (0 <= i - k && i + k < n && chars[i - k] == chars[i + k]) {
                  k++;
              }
              d1[i] = k--;
              if (i + k > r) {
                  l = i - k;
                  r = i + k;
              }
          }
          return d1;
      }
  
      public static int[] kmp(String s) {
          int n = s.length();
          int[] res = new int[n];
          for (int i = 1; i < n; ++i) {
              int j = res[i - 1];
              while (j > 0 && s.charAt(i) != s.charAt(j)) {
                  j = res[j - 1];
              }
              if (s.charAt(i) == s.charAt(j)) {
                  ++j;
              }
              res[i] = j;
          }
          return res;
      }
  }
  
  class Pair {
  
      int i, j;
  
      Pair(int i, int j) {
          this.i = i;
          this.j = j;
      }
  
      @Override
      public boolean equals(Object o) {
          if (this == o) {
              return true;
          }
          if (o == null || getClass() != o.getClass()) {
              return false;
          }
          Pair pair = (Pair) o;
          return i == pair.i && j == pair.j;
      }
  
      @Override
      public int hashCode() {
          return Objects.hash(i, j);
      }
  }
  
  class FastReader {
  
      BufferedReader br;
      StringTokenizer st;
  
      public FastReader() {
          br = new BufferedReader(new InputStreamReader(System.in));
      }
  
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
  
      int nextInt() {
          return Integer.parseInt(next());
      }
  
      long nextLong() {
          return Long.parseLong(next());
      }
  
      double nextDouble() {
          return Double.parseDouble(next());
      }
  
      String nextLine() {
          String str = "";
          try {
              str = br.readLine();
          } catch (IOException e) {
              e.printStackTrace();
          }
          return str;
      }
  }
  
  class Node {
  
      int data, open, close;
  
      Node() {
          this(0, 0, 0);
      }
  
      Node(int data, int open, int close) {
          this.data = data;
          this.open = open;
          this.close = close;
      }
  }
  
  class ST {
  
      int n;
      Node[] st;
  
      ST(int n) {
          this.n = n;
          st = new Node[4 * Integer.highestOneBit(n)];
      }
  
      void build(Node[] nodes) {
          build(0, 0, n - 1, nodes);
      }
  
      private void build(int id, int l, int r, Node[] nodes) {
          if (l == r) {
              st[id] = nodes[l];
              return;
          }
          int mid = (l + r) >> 1;
          build((id << 1) + 1, l, mid, nodes);
          build((id << 1) + 2, mid + 1, r, nodes);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      void update(int i, Node node) {
          update(0, 0, n - 1, i, node);
      }
  
      private void update(int id, int l, int r, int i, Node node) {
          if (i < l || r < i) {
              return;
          }
          if (l == r) {
              st[id] = node;
              return;
          }
          int mid = (l + r) >> 1;
          update((id << 1) + 1, l, mid, i, node);
          update((id << 1) + 2, mid + 1, r, i, node);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      Node get(int x, int y) {
          return get(0, 0, n - 1, x, y);
      }
  
      private Node get(int id, int l, int r, int x, int y) {
          if (x > r || y < l) {
              return new Node();
          }
          if (x <= l && r <= y) {
              return st[id];
          }
          int mid = (l + r) >> 1;
          return comb(get((id << 1) + 1, l, mid, x, y), get((id << 1) + 2, mid + 1, r, x, y));
      }
  
      Node comb(Node a, Node b) {
          if (a == null) {
              return b;
          }
          if (b == null) {
              return a;
          }
          int min = Math.min(a.open, b.close);
          return new Node(a.data + b.data + min * 2, a.open + b.open - min, a.close + b.close - min);
      }
  }