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 
6 1
13
5
7
15
13
7

3 2 1 
/*
⠀⠀⠀⠀⣠⣶⡾⠏⠉⠙⠳⢦⡀⠀⠀⠀⢠⠞⠉⠙⠲⡀⠀
⠀⠀⠀⣴⠿⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀⡏⠀⠀Y⠀⠀⢷
⠀⠀⢠⣟⣋⡀⢀⣀⣀⡀⠀⣀⡀⣧⠀⢸⠀⠀A⠀⠀ ⡇
⠀⠀⢸⣯⡭⠁⠸⣛⣟⠆⡴⣻⡲⣿⠀⣸⠀⠀S⠀  ⡇
⠀⠀⣟⣿⡭⠀⠀⠀⠀⠀⢱⠀⠀⣿⠀⢹⠀⠀H⠀⠀ ⡇
⠀⠀⠙⢿⣯⠄⠀⠀⠀⢀⡀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠹⣶⠆⠀⠀⠀⠀⠀⡴⠃⠀⠀⠘⠤⣄⣠⠞⠀
⠀⠀⠀⠀⠀⢸⣷⡦⢤⡤⢤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣴⣿⣏⠁⠀⠀⠸⣏⢯⣷⣖⣦⡀⠀⠀⠀⠀⠀⠀
⢀⣾⣽⣿⣿⣿⣿⠛⢲⣶⣾⢉⡷⣿⣿⠵⣿⠀⠀⠀⠀⠀⠀
⣼⣿⠍⠉⣿⡭⠉⠙⢺⣇⣼⡏⠀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣀⣿………⣀⣰⣏⣘⣆⣀⠀⠀
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter; // System.out is a PrintStream
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.Collections;


public class J1600 {
    private static int MOD = (int)1e9 + 7, mod = 99_82_44_353;
    private static double PI = 3.14159265358979323846;

    public static void main(String[] args) throws IOException {
        FasterScanner scn = new FasterScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = scn.nextInt(), M = scn.nextInt();
        int[][] arr = new int[N][M];
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < M; j++) {
                arr[i][j] = scn.nextInt();
            }
        }
        ArrayList<Integer> al = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < M; j++) {
                if (arr[i][j] < 0) continue;
                int val = dfs(i, j, arr, N, M);
                al.add(val);
            }
        }
        Collections.sort(al);
        for (int i = al.size() - 1; i >= 0; i--) {
            out.print(al.get(i) + " ");
        }
        out.println();
        out.close();
    }

    private static int dfs(int r, int c, int[][] arr, int N, int M) {
        if (r < 0 || c < 0 || r >= N || c >= M || arr[r][c] < 0) {
            return 0;
        }
        int val = arr[r][c], count = 1;
        arr[r][c] = -1;
        if ((val & 0b1000) == 0) {
            count += dfs(r - 1, c, arr, N, M);
        }
        
        if ((val & 0b0100) == 0) {
            count += dfs(r, c + 1, arr, N, M);
        }

        if ((val & 0b0010) == 0) {
            count += dfs(r + 1, c, arr, N, M);
        }

        if ((val & 0b0001) == 0) {
            count += dfs(r, c - 1, arr, N, M);
        }
        return count;
    }

    /* ------------------- Sorting ------------------- */
    private static void ruffleSort(int[] arr) {
        // int N = arr.length;
        // Random rand = new Random();
        // for (int i = 0; i < N; i++) {
        //     int oi = rand.nextInt(N), temp = arr[i];
        //     arr[i] = arr[oi];
        //     arr[oi] = temp;
        // }
        // Arrays.sort(arr);
    }
        
    /* ------------------- Sorting ------------------- */
    
    private static boolean isPalindrome(String str) {
        for (int i = 0, j = str.length() - 1; i < j; i++, j--) {
            if (str.charAt(i) != str.charAt(j)) {
                return false;
            }
        }
        return true;
    }
    
    private static boolean isPalindrome(char[] str) {
        for (int i = 0, j = str.length - 1; i < j; i++, j--) {
            if (str[i] != str[j]) {
                return false;
            }
        }
        return true;
    }
    
    /* ------------------- Pair class ------------------- */
    private static class Pair implements Comparable<Pair> {
		int x, y;
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public int compareTo(Pair o) {
			return this.x == o.x ? this.y - o.y : this.x - o.x;
		}
	}

    /* ------------------- HCF and LCM ------------------- */
    private static int gcd(int num1, int num2) {
        int temp = 0;
        while (num2 != 0) {
            temp = num1;
            num1 = num2;
            num2 = temp % num2;
        }
        return num1;
    }
    
    private static int lcm(int num1, int num2) {
        return (int)((1L * num1 * num2) / gcd(num1, num2));
    }
    
    /* ------------------- primes and prime factorization ------------------- */
    private static boolean[] seive(int N) {
        // true means not prime, false means is a prime number :)
        boolean[] notPrimes = new boolean[N + 1];
        notPrimes[0] = notPrimes[1] = true;
        for (int i = 2; i * i <= N; i++) {
            if (notPrimes[i]) continue;
            for (int j = i * i; j <= N; j += i) {
                notPrimes[j] = true;
            }
        }
        return notPrimes;
    }

	/*
    private static TreeMap<Integer, Integer> primeFactors(long N) {
		TreeMap<Integer, Integer> primeFact = new TreeMap<>();
		for (int i = 2; i <= Math.sqrt(N); i++) {
            int count = 0;
            while (N % i == 0) {
                N /= i;
                count++;
            }
            if (count != 0) {
                primeFact.put(i, count);
            }
		}
		if (N != 1) {
            primeFact.put((int)N, 1);
        }
		return primeFact;
	}
    */

    /* ------------------- Binary Search ------------------- */
    private static long factorial(int N) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans *= i;
        }
        return ans;
    }

    private static long[] factorialDP(int N) {
        long[] factDP = new long[N + 1];
        factDP[0] = factDP[1] = 1;
        for (int i = 2; i <= N; i++) {
            factDP[i] = factDP[i - 1] * i;
        }
        return factDP;
    }

    private static long factorialMod(int N, int mod) {
        long ans = 1L;
        for (int i = 2; i <= N; i++) {
            ans = ((ans % mod) * (i % mod)) % mod;
        }
        return ans;
    }

    /* ------------------- Binary Search ------------------- */
    private static int floorSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] <= tar) {
                ans = mid;
                st = mid + 1;
            } else {
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    private static int ceilingSearch(int[] arr, int st, int ed, int tar) {
        int ans = -1;
        while (st <= ed) {
            int mid = ((ed - st) >> 1) + st;
            if (arr[mid] < tar) {
                st = mid + 1;
            } else {
                ans = mid;
                ed = mid - 1;
            }
        }
        return ans;
    }
    
    /* ------------------- Power Function ------------------- */
    public static long pow(long x, long y) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x);
				y--;
			}
			x = (x * x);
			y >>= 1;
		}
		return res;
	}
    
	public static long powMod(long x, long y, int mod) {
        long res = 1;
		while (y > 0) {
            if ((y & 1) != 0) {
                res = (res * x) % mod;
				y--;
			}
			x = (x * x) % mod;
			y >>= 1;
		}
		return res % mod;
	}

    /* ------------------- Disjoint Set(Union and Find) ------------------- */
    private static class DSU {
		public int[] parent, rank;
		DSU(int N) {
			parent = new int[N];
			rank = new int[N];
			for (int i = 0; i < N; i++) {
				parent[i] = i;
                rank[i] = 1;
            }
		}
		public int find(int a) {
			if (parent[a] == a) {
				return a;
            }
            return parent[a] = find(parent[a]);
		}
		public boolean union(int a, int b) {
			int parA = find(a), parB = find(b);
			if (parA == parB) return false;
			if (rank[parA] > rank[parB]) {
                parent[parB] = parA;
            } else if (rank[parA] < rank[parB]) {
                parent[parA] = parB;
            } else {
                parent[parA] = parB;
                rank[parB]++;
            }
            return true;
		}
	}
    
    /* ------------------- Scanner class for input ------------------- */
    
    private static class FasterScanner {
		private InputStream stream;
		private byte[] buffer = new byte[1024];
		private int curChar, numChars;
		private SpaceCharFilter filter;

		public FasterScanner() {
            // default
			this.stream = System.in;
		}

		public FasterScanner(InputStream stream) {
			this.stream = stream;
		}

		private int readChar() {
			if (numChars == -1) {
				throw new InputMismatchException();
            }
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException(e.getMessage());
				}
				if (numChars <= 0) {
					return -1;
                }
			}
			return buffer[curChar++];
		}

		private boolean isWhiteSpace(int c) {
			if (filter != null) {
				return filter.isWhiteSpace(c);
            }
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isNewLine(int ch) {
			if (filter != null) {
				return filter.isNewLine(ch);
            }
			return ch == '\r' || ch == '\n' || ch == -1;
		}

        public char nextChar() {
            int ch = readChar();
            char res = '\0';
            while (isWhiteSpace(ch)) {
                ch = readChar();
            }
            do {
                res = (char)ch;
                ch = readChar();
            } while (!isWhiteSpace(ch));
            return res;
        }

		public String next() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			while (isWhiteSpace(ch)) {
				ch = readChar();
            }
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isWhiteSpace(ch));
			return res.toString();
		}

		public String nextLine() {
			int ch = readChar();
            StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(ch);
				ch = readChar();
			} while (!isNewLine(ch));
			return res.toString();
		}

		public int nextInt() {
			int ch = -1, sgn = 1, res = 0;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (res * 10) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));
            
			return res * sgn;
		}

		public long nextLong() {
			int ch = -1, sgn = 1;
            long res = 0L;
            do {
                ch = readChar();
            } while (isWhiteSpace(ch));
			if (ch == '-') {
				sgn = -1;
				ch = readChar();
			}
			do {
				if (ch < '0' || ch > '9') {
					throw new InputMismatchException("not a number");
                }
				res = (10L * res) + (ch - '0');
				ch = readChar();
			} while (!isWhiteSpace(ch));

			return 1L * res * sgn;
		}

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        /* for custom delimiters */
		public interface SpaceCharFilter {
			public boolean isWhiteSpace(int ch);
			public boolean isNewLine(int ch);
		}
	}
}
