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.util.*;
  import java.io.*;
  import java.math.*;
  import java.lang.*;
  
  public class RobotFactory {
      
      // static int mod = 998244353;
      static int mod = 1000000007;
  
      public static class Reader {
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
   
          public Reader()
          {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
   
          public Reader(String file_name) throws IOException
          {
              din = new DataInputStream(
                  new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
   
          public String readLine() throws IOException
          {
              byte[] buf = new byte[64]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n') {
                      if (cnt != 0) {
                          break;
                      }
                      else {
                          continue;
                      }
                  }
                  buf[cnt++] = (byte)c;
              }
              return new String(buf, 0, cnt);
          }
   
          public int nextInt() throws IOException
          {
              int ret = 0;
              byte c = read();
              while (c <= ' ') {
                  c = read();
              }
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
   
              if (neg)
                  return -ret;
              return ret;
          }
   
          public long nextLong() throws IOException
          {
              long ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg)
                  return -ret;
              return ret;
          }
   
          public double nextDouble() throws IOException
          {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
   
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
   
              if (c == '.') {
                  while ((c = read()) >= '0' && c <= '9') {
                      ret += (c - '0') / (div *= 10);
                  }
              }
   
              if (neg)
                  return -ret;
              return ret;
          }
   
          private void fillBuffer() throws IOException
          {
              bytesRead = din.read(buffer, bufferPointer = 0,
                                   BUFFER_SIZE);
              if (bytesRead == -1)
                  buffer[0] = -1;
          }
   
          private byte read() throws IOException
          {
              if (bufferPointer == bytesRead)
                  fillBuffer();
              return buffer[bufferPointer++];
          }
   
          public void close() throws IOException
          {
              if (din == null)
                  return;
              din.close();
          }
      }
  
      public static void main(String[] args) throws Exception {
          Reader scn = new Reader();
          PrintWriter pw = new PrintWriter(System.out);
          int t = 1;
          outer : while(t-->0){
              int n = scn.nextInt();
              int m = scn.nextInt();
              int V = n * m;
              ArrayList<Integer>[] graph = new ArrayList[V];
  	        for(int i=0; i<graph.length; i++){
  	        	graph[i] = new ArrayList<>();
  	        }
  	        for(int i=0; i<n; i++){
  	        	for(int j=0; j<m; j++){
  	        		int no = scn.nextInt();
  	        		int temp = no, pos = 0, u = i*m + j;
  	        		while(pos != 4){
  	        			if((temp & 1) == 0){
  	        				if(pos == 0){
  	        					int v = i*m + j - 1;
  	        					addEdge(graph, u, v);
  	        				}else if(pos == 1){
  	        					int v = (i+1)*m + j;
  	        					addEdge(graph, u, v);
  	        				}else if(pos == 2){
  	        					int v = i*m + j + 1;
  	        					addEdge(graph, u, v);
  	        				}else if(pos == 3){
  	        					int v = (i-1)*m + j;
  	        					addEdge(graph, u, v);
  	        				}
  	        			}
  	        			pos++;
  	        			temp >>= 1;
  	        		}
  	        	}
  	        }
  	        ArrayList<Integer> list = new ArrayList<>();
  	        gcc(graph, list);
  	        reverseSort(list);
  	        for(int val : list){
  	        	pw.print(val + " ");
  	        }
          }
          pw.close();
      }
  
      private static int dfs(ArrayList<Integer>[] graph, int src, boolean[] visited){
          visited[src] = true;
          int size = 1;
          for(int v : graph[src]){
              if(visited[v] == false){
                  size += dfs(graph, v, visited);
              }
          }
          return size;
      }
  
      private static void gcc(ArrayList<Integer>[] graph, ArrayList<Integer> list){
          int V = graph.length;
          boolean[] visited = new boolean[V];
          for(int i=0; i<graph.length; i++){
              if(visited[i] == false){
                  int size = dfs(graph, i, visited);
                  list.add(size);
              }
          }
      }
  
      private static void addEdge(ArrayList<Integer>[] graph, int u, int v){
          graph[u].add(v);
      }
  
      public static class Pair{
          int x;
          int y;
  
          Pair(int x, int y){
              this.x = x;
              this.y = y;
          }
      }
  
      private static void sort(int[] arr) {
          List<Integer> list = new ArrayList<>();
          for (int i=0; i<arr.length; i++){
              list.add(arr[i]);
          }
          Collections.sort(list); // collections.sort uses nlogn in backend
          for (int i = 0; i < arr.length; i++){
              arr[i] = list.get(i);
          }
      }
  
      private static void sort(long[] arr) {
          List<Long> list = new ArrayList<>();
          for(int i=0; i<arr.length; i++){
              list.add(arr[i]);
          }
          Collections.sort(list); // collections.sort uses nlogn in backend
          for (int i = 0; i < arr.length; i++){
              arr[i] = list.get(i);
          }
      }
  
      // private static void sort(Pair[] arr) {
      //     List<Pair> list = new ArrayList<>();
      //     for(int i=0; i<arr.length; i++){
      //         list.add(arr[i]);
      //     }
      //     Collections.sort(list); // collections.sort uses nlogn in backend
      //     for (int i = 0; i < arr.length; i++){
      //         arr[i] = list.get(i);
      //     }
      // }
  
      private static void reverseSort(int[] arr){
          List<Integer> list = new ArrayList<>();
          for (int i=0; i<arr.length; i++){
              list.add(arr[i]);
          }
          Collections.sort(list, Collections.reverseOrder()); // collections.sort uses nlogn in backend
          for (int i = 0; i < arr.length; i++){
              arr[i] = list.get(i);
          }
      }
  
      private static void reverseSort(long[] arr){
          List<Long> list = new ArrayList<>();
          for (int i=0; i<arr.length; i++){
              list.add(arr[i]);
          }
          Collections.sort(list, Collections.reverseOrder()); // collections.sort uses nlogn in backend
          for (int i = 0; i < arr.length; i++){
              arr[i] = list.get(i);
          }
      }
  
      private static void reverseSort(ArrayList<Integer> list){
          Collections.sort(list, Collections.reverseOrder());
      }
  
      private static int lowerBound(int[] arr, int x){
          int n = arr.length, si = 0, ei = n - 1;
          while(si <= ei){
              int mid = si + (ei - si)/2;
              if(arr[mid] == x){
                  if(mid-1 >= 0 && arr[mid-1] == arr[mid]){
                      ei = mid-1;
                  }else{
                      return mid;
                  }
              }else if(arr[mid] > x){
                  ei = mid - 1; 
              }else{
                  si = mid+1;
              }
          }
          return si; 
      }
  
      private static int upperBound(int[] arr, int x){
          int n = arr.length, si = 0, ei = n - 1;
          while(si <= ei){
              int mid = si + (ei - si)/2;
              if(arr[mid] == x){
                  if(mid+1 < n && arr[mid+1] == arr[mid]){
                      si = mid+1;
                  }else{
                      return mid + 1;
                  }
              }else if(arr[mid] > x){
                  ei = mid - 1; 
              }else{
                  si = mid+1;
              }
          }
          return si; 
      }
  
      private static int upperBound(ArrayList<Integer> list, int x){
          int n = list.size(), si = 0, ei = n - 1;
          while(si <= ei){
              int mid = si + (ei - si)/2;
              if(list.get(mid) == x){
                  if(mid+1 < n && list.get(mid+1) == list.get(mid)){
                      si = mid+1;
                  }else{
                      return mid + 1;
                  }
              }else if(list.get(mid) > x){
                  ei = mid - 1; 
              }else{
                  si = mid+1;
              }
          }
          return si; 
      }
  
      // (x^y)%p in O(logy)
      private static long power(long x, long y){
          long res = 1; 
          x = x % mod;
          while(y > 0){
              if ((y & 1) == 1){
                  res = (res * x) % mod;
              }
              y = y >> 1; 
              x = (x * x) % mod;
          }
          return res;
      }
  
      public static boolean nextPermutation(int[] arr) {
          if(arr == null || arr.length <= 1){
              return false;
          }
          
          int last = arr.length-2;
          while(last >= 0){
              if(arr[last] < arr[last+1]){
                  break;
              }
              last--;
          }
  
          if (last < 0){
                return false;
          }
          
          if(last >= 0){
              int nextGreater = arr.length-1;
              for(int i=arr.length-1; i>last; i--){
                  if(arr[i] > arr[last]){
                      nextGreater = i;
                      break;
                  }
              }
              swap(arr, last, nextGreater);
          }
          
          reverse(arr, last+1, arr.length-1);
          return true;
      }
      
      private static void swap(int[] arr, int i, int j){
          int temp = arr[i];
          arr[i] = arr[j];
          arr[j] = temp;
      }
      
      private static void reverse(int[] arr, int i, int j){
          while(i < j){
              swap(arr, i++, j--);
          }
      }
  
      private static String reverseStr(String s){
          StringBuilder sb = new StringBuilder(s);
          return sb.reverse().toString();
      }
  
      // TC- O(logmax(a,b))
      private static int gcd(int a, int b) {
          if(a == 0){
              return b;
          }
          return gcd(b%a, a);
      }
  
      private static long gcd(long a, long b) {
          if(a == 0L){
              return b;
          }
          return gcd(b%a, a);
      }
  
      private static long lcm(long a, long b) {
          return a / gcd(a, b) * b;
      }
  
      // TC- O(logmax(a,b))
      private static int lcm(int a, int b) {
          return a / gcd(a, b) * b;
      }
  
      private static long inv(long x){
          return power(x, mod - 2);
      }
  
      private static long summation(long n){
          return (n * (n + 1L)) >> 1;
      } 
  }