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:

<image>

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 grd[109][109], minn[109], minm[109];
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < 109; i++) {
    minn[i] = minm[i] = 999;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      cin >> grd[i][j];
      minn[i] = min(minn[i], grd[i][j]);
      minm[j] = min(minm[j], grd[i][j]);
    }
  }
  int flag = 0, k = 0, aro[109], aco[109];
  if (n <= m) {
    for (int i = 1; i <= n; i++) {
      aro[i] = minn[i];
      k += aro[i];
      if (minn[i] > 0) {
        for (int j = 1; j <= m; j++) {
          grd[i][j] -= minn[i];
        }
      }
    }
    for (int j = 1; j <= m; j++) {
      minm[j] = grd[1][j];
      for (int i = 2; i <= n; i++) {
        if (grd[i][j] != grd[i - 1][j]) flag++;
      }
      aco[j] = minm[j];
      k += aco[j];
    }
  } else {
    for (int j = 1; j <= m; j++) {
      aco[j] = minm[j];
      k += aco[j];
      if (minm[j] > 0) {
        for (int i = 1; i <= n; i++) {
          grd[i][j] -= minm[j];
        }
      }
    }
    for (int i = 1; i <= n; i++) {
      minn[i] = grd[i][1];
      for (int j = 2; j <= m; j++) {
        if (grd[i][j] != grd[i][j - 1]) flag++;
      }
      aro[i] = minn[i];
      k += aro[i];
    }
  }
  if (flag > 0) {
    cout << -1 << endl;
    return 0;
  }
  cout << k << endl;
  int r = 1;
  while (r < n + 1) {
    while (aro[r] > 0) {
      cout << "row " << r << endl;
      aro[r]--;
    }
    r++;
  }
  int c = 1;
  while (c < m + 1) {
    while (aco[c] > 0) {
      cout << "col " << c << endl;
      aco[c]--;
    }
    c++;
  }
  return 0;
}