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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int rows, cols, r, c, t, ans1 = 0, ans2 = 0;
  vector<int> tmp, rows_vec, cols_vec, rows_vec2, cols_vec2;
  vector<vector<int>> grid;
  scanf("%d %d", &r, &c);
  for (int i = 0; i < r; i++) {
    tmp.clear();
    for (int j = 0; j < c; j++) {
      scanf("%d", &t);
      tmp.push_back(t);
    }
    grid.push_back(tmp);
  }
  for (int i = 0; i < r; i++) {
    int mini = 1000;
    for (int j = 0; j < c; j++) {
      mini = min(mini, grid[i][j]);
    }
    rows_vec.push_back(mini);
    ans1 += mini;
  }
  for (int i = 0; i < c; i++) {
    cols_vec.push_back(grid[0][i] - rows_vec[0]);
    ans1 += (grid[0][i] - rows_vec[0]);
  }
  for (int i = 0; i < c; i++) {
    int mini = 1000;
    for (int j = 0; j < r; j++) {
      mini = min(mini, grid[j][i]);
    }
    cols_vec2.push_back(mini);
    ans2 += mini;
  }
  for (int i = 0; i < r; i++) {
    rows_vec2.push_back(grid[i][0] - cols_vec2[0]);
    ans2 += (grid[i][0] - cols_vec2[0]);
  }
  for (int i = 0; i < r; i++) {
    for (int j = 0; j < c; j++) {
      if (grid[i][j] != (rows_vec[i] + cols_vec[j])) {
        cout << -1 << endl;
        return 0;
      }
    }
  }
  if (ans1 <= ans2) {
    cout << ans1 << endl;
    for (int i = 0; i < r; i++) {
      for (int ii = 0; ii < rows_vec[i]; ii++) cout << "row " << i + 1 << endl;
    }
    for (int i = 0; i < c; i++) {
      for (int ii = 0; ii < cols_vec[i]; ii++) cout << "col " << i + 1 << endl;
    }
  } else {
    cout << ans2 << endl;
    for (int i = 0; i < r; i++) {
      for (int ii = 0; ii < rows_vec2[i]; ii++) cout << "row " << i + 1 << endl;
    }
    for (int i = 0; i < c; i++) {
      for (int ii = 0; ii < cols_vec2[i]; ii++) cout << "col " << i + 1 << endl;
    }
  }
  return 0;
}