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.Arrays;
import java.util.Scanner;

/**
 * Created by Christy on 8/8/2017.
 */
public class KarenAndGame {
    public static void main (String[] args) {
        Scanner scan = new Scanner(System.in);

        int r = scan.nextInt();
        int c = scan.nextInt();
        int count = 0;

        StringBuilder sb = new StringBuilder();

        int[][] arr = new int[r][c];

        for (int i = 0; i < r; i++) {
            for (int j = 0; j < c; j++) {
                arr[i][j] = scan.nextInt();
            }
        }

        out:
        while (!valid(arr)) {
           // System.err.println(".");
            //see if row can be changed
            if (r < c) {
                for (int i = 0; i < r; i++) {
                    boolean changeRow = true;
                    for (int j = 0; j < c; j++) {
                        if (arr[i][j] <= 0) {
                            //System.err.println("changeRow false at i = " + i + " j = " + j);
                            changeRow = false;
                            break;
                        }
                    }

                    if (changeRow) {
                        for (int j = 0; j < c; j++) {
                            arr[i][j]--;
                        }
                        sb.append("row " + (i + 1) + "\n");
                        count++;
                        continue out;
                    }
                }

                //see if column changed
                for (int j = 0; j < c; j++) {
                    boolean changeCol = true;

                    for (int i = 0; i < r; i++) {
                        if (arr[i][j] <= 0) {
                            changeCol = false;
                            break;
                        }
                    }

                    if (changeCol) {
                        for (int i = 0; i < r; i++) {
                            arr[i][j]--;
                        }
                        sb.append("col " + (j + 1) + "\n");
                        count++;
                        continue out;
                    }
                }

                System.out.print(-1);
                System.exit(0);
            }
            else {

                //see if column changed
                for (int j = 0; j < c; j++) {
                    boolean changeCol = true;

                    for (int i = 0; i < r; i++) {
                        if (arr[i][j] <= 0) {
                            changeCol = false;
                            break;
                        }
                    }

                    if (changeCol) {
                        for (int i = 0; i < r; i++) {
                            arr[i][j]--;
                        }
                        sb.append("col " + (j + 1) + "\n");
                        count++;
                        continue out;
                    }
                }

                for (int i = 0; i < r; i++) {
                    boolean changeRow = true;
                    for (int j = 0; j < c; j++) {
                        if (arr[i][j] <= 0) {
                            //System.err.println("changeRow false at i = " + i + " j = " + j);
                            changeRow = false;
                            break;
                        }
                    }

                    if (changeRow) {
                        for (int j = 0; j < c; j++) {
                            arr[i][j]--;
                        }
                        sb.append("row " + (i + 1) + "\n");
                        count++;
                        continue out;
                    }
                }

                System.out.print(-1);
                System.exit(0);
            }


        }

        System.out.println(count);
        System.out.println(sb.toString());
    }

    public static void print(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[0].length; j++) {
                System.err.print(arr[i][j] + " ");
            }
            System.err.println();
        }
    }

    public static boolean valid(int[][] arr) {
        //System.err.println("in valid...");
        //print(arr);
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[0].length; j++) {
                if (arr[i][j] != 0) {
                    //System.err.println("...false");
                    return false;
                }
            }
        }
        //System.err.println("true...");
        return true;
    }
}