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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main{
	static final Scanner s=new Scanner(System.in);
	static IntStream REPS(int v){
		return IntStream.range(0,v);
	}
	static IntStream REPS(int l,int r) {
		return IntStream.rangeClosed(l,r);
	}
	static IntStream INS(int n) {
		return REPS(n).map(i->getInt());
	}
	static int getInt(){
		return Integer.parseInt(s.next());
	}
	
	static int h=getInt(),w=getInt(),f[][]=REPS(h).mapToObj(i->INS(w).toArray()).toArray(int[][]::new);
	static ArrayList<String> res=new ArrayList<>();
	public static void main(String[]__){
		if(h<w) {
			beet();
			uku();
		}else {
			uku();
			beet();
		}
		if(Arrays.stream(f).anyMatch(o->Arrays.stream(o).anyMatch(i->i>0))) {
			System.out.println(-1);
			return;
		}
		System.out.println(res.size());
		res.forEach(System.out::println);
	}
	private static void uku(){
		for(int j=0;j<w;j++) {
			final int J=j;
			int v=REPS(h).map(o->f[o][J]).min().getAsInt();
			if(v>0) {
				for(int i=0;i<v;i++)
					res.add("col "+(j+1));
				for(int i=0;i<h;i++)
					f[i][j]-=v;
			}
		}
	}
	private static void beet(){
		for(int i=0;i<h;i++) {
			int v=Arrays.stream(f[i]).min().getAsInt();
			if(v>0) {
				for(int j=0;j<v;j++)
					res.add("row "+(i+1));
				for(int j=0;j<w;j++)
					f[i][j]-=v;
			}
		}
	}
}