Little Petya is now fond of data compression algorithms. He has already studied gz, bz, zip algorithms and many others. Inspired by the new knowledge, Petya is now developing the new compression algorithm which he wants to name dis.

Petya decided to compress tables. He is given a table a consisting of n rows and m columns that is filled with positive integers. He wants to build the table a' consisting of positive integers such that the relative order of the elements in each row and each column remains the same. That is, if in some row i of the initial table ai, j < ai, k, then in the resulting table a'i, j < a'i, k, and if ai, j = ai, k then a'i, j = a'i, k. Similarly, if in some column j of the initial table ai, j < ap, j then in compressed table a'i, j < a'p, j and if ai, j = ap, j then a'i, j = a'p, j. 

Because large values require more space to store them, the maximum value in a' should be as small as possible.

Petya is good in theory, however, he needs your help to implement the algorithm.

Input

The first line of the input contains two integers n and m (<image>, the number of rows and the number of columns of the table respectively.

Each of the following n rows contain m integers ai, j (1 ≤ ai, j ≤ 109) that are the values in the table.

Output

Output the compressed table in form of n lines each containing m integers.

If there exist several answers such that the maximum number in the compressed table is minimum possible, you are allowed to output any of them.

Examples

Input

2 2
1 2
3 4


Output

1 2
2 3


Input

4 3
20 10 30
50 40 30
50 60 70
90 80 70


Output

2 1 3
5 4 3
5 6 7
9 8 7

Note

In the first sample test, despite the fact a1, 2 ≠ a21, they are not located in the same row or column so they may become equal after the compression.
import java.io.*;
import java.util.*;

public class Main {

    private static InputStream inputStream;
    private static OutputStream outputStream;
    private static PrintWriter writer;
    private static InputReader reader;

    public static void main(String[] args) {
        inputStream = System.in;
        outputStream = System.out;
        reader = new InputReader(inputStream);
        writer = new PrintWriter(outputStream);
        new Main().main();
        writer.close();
    }


    static int[][] a;
    static int[] father;
    static ArrayList<Integer>[] edges;
    static int[] degrees;
    static int[] distances;

    int find(int n) {
        if (father[n] == n) {
            return n;
        }
        return father[n] = find(father[n]);
    }

    void union(int x, int y) {
        x = find(x);
        y = find(y);
        if (x != y) {
            father[x] = y;
        }
    }

    private void main() {
        int n, m, cnt = 0;
        n = reader.nextInt();
        m = reader.nextInt();
        a = new int[n][m];
        father = new int[n * m + 1];
        edges = new ArrayList[n * m + 1];
        degrees = new int[n * m + 1];
        distances = new int[n * m + 1];
        int total = edges.length;
        for (int i = 0; i < total; ++i) {
            edges[i] = new ArrayList<>();
            father[i] = i;
        }
        ArrayList<Node>[] rows = new ArrayList[n];
        ArrayList<Node>[] columns = new ArrayList[m];
        for (int i = 0; i < n; ++i) {
            rows[i] = new ArrayList<>();
            for (int j = 0; j < m; ++j) {
                a[i][j] = reader.nextInt();
                rows[i].add(new Node(a[i][j], i * m + j));
                ++cnt;
            }
            shrink(rows[i]);
        }
        for (int i = 0; i < m; ++i) {
            columns[i] = new ArrayList<>();
            for (int j = 0; j < n; ++j) {
                columns[i].add(new Node(a[j][i], j * m + i));
            }
            shrink(columns[i]);
        }

        for (int i = 0; i < n; ++i) {
            addEdge(rows[i]);
        }
        for (int i = 0; i < m; ++i) {
            addEdge(columns[i]);
        }

        topSort(n, m);
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                int k = find(i * m + j);
                writer.print(distances[k]);
                writer.print(' ');
            }
            writer.println();
        }
    }

    private void shrink(ArrayList<Node> list) {
        int n = list.size();
        Collections.sort(list);
        for (int i = 1; i < n; ++i) {
            Node node = list.get(i);
            Node pre = list.get(i - 1);
            int x = find(node.tag);
            int y = find(pre.tag);
            if (node.value == pre.value) {
                union(x, y);
            }
        }
    }

    private void addEdge(ArrayList<Node> list) {
        int n = list.size();

        for (int i = 1; i < n; ++i) {
            Node node = list.get(i);
            Node pre = list.get(i - 1);
            int x = find(node.tag);
            int y = find(pre.tag);
            if (node.value != pre.value) {
                edges[y].add(x);
                degrees[x]++;
            }
        }
    }

    private void topSort(int n, int m) {
        int front = 0, rear = 0;
        int total = n * m;
        boolean[] visit = new boolean[n * m];
        int[] queue = new int[total + 1];
        for (int i = 0; i < total; ++i) {
            int k = find(i);
            if (degrees[k] == 0 && !visit[k]) {
                queue[rear++] = k;
                visit[k] = true;
                distances[k] = 1;
            }
        }
        while (front < rear) {
            int u = queue[front++];
            int distance = distances[u];
            for (Integer vertex : edges[u]) {
                degrees[vertex]--;
                if (degrees[vertex] == 0) {
                    distances[vertex] = distance + 1;
                    queue[rear++] = vertex;
                }
            }
        }
    }

    class Node implements Comparable<Node> {
        int value;
        int tag;

        public Node(int value, int tag) {
            this.value = value;
            this.tag = tag;
        }


        @Override
        public int compareTo(Node obj) {
            return value - obj.value;
        }
    }
}


class InputReader {
    private StringTokenizer tokenizer;
    private BufferedReader reader;

    public InputReader(InputStream inputStream) {
        tokenizer = null;
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }
}