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;
string func(vector<vector<int>> arr, bool tp, int& ans) {
  long long int i, j;
  int r = arr.size();
  int c = arr[0].size();
  vector<int> rowmin(r);
  for (i = 0; i < r; ++i) {
    rowmin[i] = *(min_element(arr[i].begin(), arr[i].end()));
    ans += rowmin[i];
  }
  vector<int> clans(c);
  vector<int> cd(r);
  for (j = 0; j < c; ++j) {
    for (i = 0; i < r; ++i) {
      cd[i] = arr[i][j] - rowmin[i];
    }
    int mx = *max_element(cd.begin(), cd.end());
    int mn = *min_element(cd.begin(), cd.end());
    if (mx != mn) {
      ans = -1;
      return "";
    } else {
      ans += cd[0];
      clans[j] = cd[0];
    }
  }
  string sa = "";
  for (i = 0; i < r; ++i) {
    while (rowmin[i]--) {
      if (tp)
        sa += "col " + to_string(i + 1) + "\n";
      else
        sa += "row " + to_string(i + 1) + "\n";
    }
  }
  for (i = 0; i < c; ++i) {
    while (clans[i]--) {
      if (tp)
        sa += "row " + to_string(i + 1) + "\n";
      else
        sa += "col " + to_string(i + 1) + "\n";
    }
  }
  return sa;
}
int main() {
  long long int n, atl, q, i, l, j, ans = 0;
  int r, c;
  cin >> r >> c;
  vector<vector<int>> arr(r, vector<int>(c));
  vector<vector<int>> tps(c, vector<int>(r));
  for (i = 0; i < r; ++i) {
    for (j = 0; j < c; ++j) {
      cin >> arr[i][j];
      tps[j][i] = arr[i][j];
    }
  }
  int ar = 0, ac = 0;
  string sr = func(arr, 0, ar);
  string sc = func(tps, 1, ac);
  if (ac == -1 || ar == -1) {
    cout << -1 << endl;
    return 0;
  }
  if (ar < ac) {
    cout << ar << endl << sr << endl;
  } else {
    cout << ac << endl << sc << endl;
  }
  return 0;
}