815_A. Karen and Game
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.
```python
from itertools import product

n, m = map(int, input().split())
matr = []
for i in range(n):
    matr.append([int(num) for num in input().split()])


def walker(start_row, start_col, dif_row, dif_col):
    row = start_row
    col = start_col
    while 0 <= row < n and 0 <= col < m:
        yield row, col
        row += dif_row
        col += dif_col


def walker_row(row):
    return walker(row, 0, 0, 1)


def walker_col(col):
    return walker(0, col, 1, 0)


def get_min(line):
    res = float('inf')
    for row, col in line:
        res = min(res, matr[row][col])
    return res


def subtract(line, diff):
    for row, col in line:
        matr[row][col] -= diff


def resolve_rows():
    for row in range(n):
        min_num = get_min(walker_row(row))
        if min_num > 0:
            subtract(walker_row(row), min_num)
            step = 'row {}'.format(row + 1)
            for i in range(min_num):
                ans.append(step)


def resolve_cols():
    for col in range(m):
        min_num = get_min(walker_col(col))
        if min_num > 0:
            subtract(walker_col(col), min_num)
            step = 'col {}'.format(col + 1)
            for i in range(min_num):
                ans.append(step)


ans = []
if n > m:
    resolve_cols()
    resolve_rows()
else:
    resolve_rows()
    resolve_cols()


cant = False
for row, col in product(range(n), range(m)):
    cant |= matr[row][col] > 0

if cant:
    print(-1)
else:
    print(len(ans))
    print('\n'.join(ans))

```