Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:

import java.util.*;
import java.io.*;

public class Solution2 {

    private void solve() throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();
        int[][] a = new int[n][m];
        int[] rown = new int[n];
        int[] colm = new int[m];
        Arrays.fill(colm, Integer.MAX_VALUE);

        for (int i = 0; i < n; i++) {
            int min = Integer.MAX_VALUE;
            for (int j = 0; j < m; j++) {
                a[i][j] = in.nextInt();
                if (a[i][j] < min) min = a[i][j];
            }
            for (int j = 0; j < m; j++) {
                if (a[i][j] < colm[j]) colm[j] = a[i][j];
            }
            rown[i] = min;
        }

        StringBuilder ans = new StringBuilder("");
        int c = 0;

        if (colm.length < rown.length) {
            for (int i = 0; i < colm.length; i++) {
                for (int j = 0; j < colm[i]; j++) {
                    for (int k = 0; k < rown.length; k++) {
                        if (a[k][i] - 1 < 0) {
                            System.out.println(-1);
                            return;
                        }
                        a[k][i]--;
                        rown[k] = Math.min(a[k][i], rown[k]);
                    }
                    ans.append("col ");
                    ans.append(i + 1);
                    ans.append("\n");
                    c++;
                }
            }
            for (int i = 0; i < rown.length; i++) {
                for (int j = 0; j < rown[i]; j++) {
                    for (int k = 0; k < colm.length; k++) {
                        if (a[i][k] - 1 < 0) {
                            System.out.println(-1);
                            return;
                        }
                        a[i][k]--;
                        colm[k] = Math.min(a[i][k], colm[k]);
                    }
                    ans.append("row ");
                    ans.append(i + 1);
                    ans.append("\n");
                    c++;
                }
            }
        }
        else {
            for (int i = 0; i < rown.length; i++) {
                for (int j = 0; j < rown[i]; j++) {
                    for (int k = 0; k < colm.length; k++) {
                        if (a[i][k] - 1 < 0) {
                            System.out.println(-1);
                            return;
                        }
                        a[i][k]--;
                        colm[k] = Math.min(a[i][k], colm[k]);
                    }
                    ans.append("row ");
                    ans.append(i + 1);
                    ans.append("\n");
                    c++;
                }
            }
            for (int i = 0; i < colm.length; i++) {
                for (int j = 0; j < colm[i]; j++) {
                    for (int k = 0; k < rown.length; k++) {
                        if (a[k][i] - 1 < 0) {
                            System.out.println(-1);
                            return;
                        }
                        a[k][i]--;
                        rown[k] = Math.min(a[k][i], rown[k]);
                    }
                    ans.append("col ");
                    ans.append(i + 1);
                    ans.append("\n");
                    c++;
                }
            }
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (a[i][j] > 0) {
                    System.out.println(-1);
                    return;
                }
            }
        }
        System.out.println(c);
        System.out.println(ans.toString());
    }

    private static String filename = "";
    private PrintWriter out;
    MyScanner in;

    private void run() throws IOException {
        in = new MyScanner();
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    private class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public MyScanner() throws IOException {
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }

        public MyScanner(String fileTitle) throws IOException {
            this.br = new BufferedReader(new FileReader(fileTitle));
        }

        public String nextLine() throws IOException {
            String s = br.readLine();
            return s == null ? "-1" : s;
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s == null) {
                    return "-1";
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        public Integer nextInt() throws IOException {
            return Integer.parseInt(this.next());
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(this.next());
        }

        public Double nextDouble() throws IOException {
            return Double.parseDouble(this.next());
        }

        public void close() throws IOException {
            this.br.close();
        }
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new Solution2().run();
    }
}