Karen and Game

题意翻译

给你一个初始全为零的n*m的方格，每次操作可以使一行或一列全部加一，问最少要操作几步能使方格和输入一样 Translated by Dreamer丶杨

题目描述

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!

输入输出格式

输入格式

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 $ ).

输出格式

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.

输入输出样例

输入样例 #1

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1

输出样例 #1

4
row 1
row 1
col 4
row 3

输入样例 #2

3 3
0 0 0
0 1 0
0 0 0

输出样例 #2

-1

输入样例 #3

3 3
1 1 1
1 1 1
1 1 1

输出样例 #3

3
row 1
row 2
row 3

说明

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.