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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        private static final int INF = (int) 1e9;
        int n;
        int m;
        int[] minRow;
        int[] minCol;
        int[][] rowRes;
        int[][] colRes;
        int[][] grid;
        HashSet<Integer> rowBlock;
        HashSet<Integer> colBlock;
        int rowAns;
        int colAns;
        StringBuilder rans;
        StringBuilder cans;
        boolean rpossible;
        boolean cpossible;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();

            grid = new int[n][m];
            minRow = new int[n];
            minCol = new int[m];

            Arrays.fill(minRow, INF);
            Arrays.fill(minCol, INF);

            rowBlock = new HashSet<>();
            colBlock = new HashSet<>();

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    grid[i][j] = in.nextInt();
                    if (grid[i][j] == 0) {
                        rowBlock.add(i);
                        colBlock.add(j);
                    }
                    minRow[i] = Math.min(minRow[i], grid[i][j]);
                    minCol[j] = Math.min(minCol[j], grid[i][j]);
                }
            }

            rowRes = new int[n][m];
            colRes = new int[n][m];

            rowAns = 0;
            colAns = 0;

            rans = new StringBuilder();
            cans = new StringBuilder();

            rpossible = true;
            cpossible = true;

            for (int row = 0; rpossible && row < n; ++row) {
                int val = minRow[row];
                for (int i = 0; rpossible && i < val; ++i) {
                    if (rowBlock.contains(row)) {
                        rpossible = false;
                    }
                    incRow(row, rowRes, rans);
                    rowAns++;
                }
            }
            for (int col = 0; cpossible && col < m; ++col) {
                int val = minCol[col];
                for (int i = 0; cpossible && i < val; ++i) {
                    if (colBlock.contains(col)) {
                        cpossible = false;
                    }
                    incCol(col, colRes, cans);
                    colAns++;
                }
            }

            for (int row = 0; rpossible && row < n; ++row) {
                for (int col = 0; rpossible && col < m; ++col) {
                    while (rpossible && rowRes[row][col] < grid[row][col]) {
                        if (colBlock.contains(col)) {
                            rpossible = false;
                        }
                        incCol(col, rowRes, rans);
                        rowAns++;
                    }
                }
            }
            for (int row = 0; cpossible && row < n; ++row) {
                for (int col = 0; cpossible && col < m; ++col) {
                    while (cpossible && colRes[row][col] < grid[row][col]) {
                        if (rowBlock.contains(row)) {
                            cpossible = false;
                        }
                        incRow(row, colRes, cans);
                        colAns++;
                    }
                }
            }

            for (int row = 0; rpossible && row < n; ++row) {
                for (int col = 0; rpossible && col < m; ++col) {
                    if (rowRes[row][col] != grid[row][col]) {
                        rpossible = false;
                    }
                }
            }
            for (int row = 0; cpossible && row < n; ++row) {
                for (int col = 0; cpossible && col < m; ++col) {
                    if (rowRes[row][col] != grid[row][col]) {
                        cpossible = false;
                    }
                }
            }

            if (!rpossible) {
                if (cpossible) {
                    out.println(colAns);
                    out.println(cans);
                } else {
                    out.println(-1);
                }
            } else if (!cpossible) {
                if (rpossible) {
                    out.println(rowAns);
                    out.println(rans);
                } else {
                    out.println(-1);
                }
            } else if (cpossible && rpossible) {
                if (rowAns > colAns) {
                    out.println(colAns);
                    out.println(cans);
                } else {
                    out.println(rowAns);
                    out.println(rans);
                }
            }
        }

        private void incCol(int col, int[][] res, StringBuilder ans) {
            for (int row = 0; row < n; ++row) {
                res[row][col]++;
            }
            ans.append("col " + (col + 1) + "\n");
        }

        private void incRow(int row, int[][] res, StringBuilder ans) {
            for (int col = 0; col < m; ++col) {
                res[row][col]++;
            }
            ans.append("row " + (row + 1) + "\n");
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }
}