On the way to school, Karen became fixated on the puzzle game on her phone!

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 $*g*_{*i*, *j*}$.

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 $*g*_{*i*, *j*}$ ($0 ≤ *g*_{*i*, *j*} ≤ 500$).

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.

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:

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 $1$s 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:

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.