CF815A.Karen and Game

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!

上学路上，凯伦被手机上的益智游戏深深吸引住了！

游戏规则如下：每一关中，你面对一个具有 $n$ 行 $m$ 列的网格，每个格子初始值均为 $0$。

一次操作定义为：选择某一行或某一列，并将该行或该列中所有格子的数值加 $1$。

当所有操作完成后，若第 $i$ 行第 $j$ 列的格子中的数值恰好等于 $g_{i,j}$，则该关卡获胜。

凯伦卡在了某一关，她想知道如何以最少的操作次数通关。请帮她解决这个问题！

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).

输入的第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 100$），分别表示网格的行数和列数。

接下来的 $n$ 行，每行包含 $m$ 个整数。特别地，第 $i$ 行中的第 $j$ 个整数为 $g_{i,j}$（$0 \leq g_{i,j} \leq 500$）。

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.

如果存在错误，实际上无法通关该关卡，则输出单个整数 $-1$。

否则，在第一行输出单个整数 $k$，表示通关该关卡所需的最少操作步数。

接下来的 $k$ 行每行应包含以下之一，按执行顺序描述各步操作：

• row x（其中 $1 \leq x \leq n$），表示操作“选择第 $x$ 行”；
• col x（其中 $1 \leq x \leq m$），表示操作“选择第 $x$ 列”。

若存在多个最优解，输出任意一个即可。

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 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:

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

在第一个测试用例中，Karen 有一个 3 行 5 列的网格。她可以通过以下 4 步操作通关：

在第二个测试用例中，Karen 有一个 3 行 3 列的网格。显然，无法通关；因为任何一步操作都会使网格中出现三个 1，但题目要求最终仅在中心位置存在一个 1。

在第三个测试用例中，Karen 有一个 3 行 3 列的网格。她可以通过以下 3 步操作通关：

注意：这并非唯一解；其他可行解之一（还有更多）是：列 1、列 2、列 3。