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

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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:

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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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class C {
	
	
	static int [][] transpose(int [][] T, int R, int C) {
		int [][] transposed = new int[C][R];
		
		for(int r = 0; r < R; r++) {
			for(int c = 0; c < C; c++) {
				
				transposed[c][r] = T[r][c];
			}
		}
		
		return transposed;
	}
	static ArrayList<String> minMoves(int [][] board, int R, int C, boolean transposed) throws IOException {
		int [] colCount = new int[C];
		
		while(true) {
			int numRowsSame = 0;
			for(int r = 0; r < R; r++) { 
				int min_ind = getMinInd(board[r],colCount);
				int min = getCurrNumber(board, r, min_ind, colCount);	
			
				if(min  < 0) {
					return null;
				}
				int numSame = 0;
	
				for(int c = 0; c < C; c++) {
					if(c == min_ind) {
						numSame++;
						continue;
					}
					int currNumber = getCurrNumber(board, r, c, colCount);
	
					if(currNumber == min) numSame++;
					else colCount[c] += currNumber - min;

				}
				if (numSame == C) numRowsSame++;
			}
			
			if(numRowsSame == R) {
				return generateSolution(board, colCount, R, C, transposed);
			}
		}
		
		
	}
	
	static ArrayList<String> generateSolution(int [][] board, int [] colCount, int R,int C, boolean transposed) {
		ArrayList<String> sol = new ArrayList<String>();
		for(int c = 0; c < C; c++) {
			for(int k = 0; k < colCount[c]; k++) {
				
				String add = transposed?"row ":"col ";
				sol.add(add + (c+1));
			}
		}
		for(int r = 0; r < R; r++) {
			int numRows = getCurrNumber(board, r, 0, colCount);
			for(int k = 0; k < numRows; k++) {
				String add = transposed?"col ":"row ";
				sol.add(add + (r+1));
			}
		}
		return sol;
	}

	static int getCurrNumber(int [][] board, int r, int c, int [] colCount) {
		return board[r][c] - colCount[c];
	}

	 static int getMinInd(int [] board_row, int [] colCount) {
		int min_ind = 0;
		int min = board_row[0] - colCount[0];
		for(int c = 1; c < board_row.length; c++) {
			if(board_row[c] - colCount[c] < min) {
				min_ind = c;
				min = board_row[c] - colCount[c];
			}
		}
		return min_ind;
	}

	
	public static void main(String [] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tokenizer = new StringTokenizer(br.readLine());
		
		int R = Integer.parseInt(tokenizer.nextToken());
		int C = Integer.parseInt(tokenizer.nextToken());
		
		int [][] board = new int[R][C];
		
		for(int i = 0; i < R; i++) {
			tokenizer = new StringTokenizer(br.readLine());
			for(int j = 0; j < C; j++) {
				board[i][j] = Integer.parseInt(tokenizer.nextToken());
			}
			
		}
		ArrayList<String> t1 = minMoves(board, R, C, false);
		ArrayList<String> t2 = minMoves(transpose(board, R,C), C, R, true);
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));		

		if(t1 == null && t2 == null) { 
			bw.write("-1");
			bw.newLine();
			bw.close();
			return;
		}
		
		ArrayList<String> sol = t1;
		
		if(t2.size() < t1.size()) {
			sol = t2;
		}
		bw.write("" + sol.size());
		bw.newLine();
		for(String s : sol) { 
			bw.write(s);
			bw.newLine();
		}
		bw.close();
	}

}