Kattis

# Chuck

You are given an matrix of $R$ rows and $C$ columns. All elements of the matrix have absolute value smaller than or equal to $10^4$. You may perform the following operations:

 Operation Notation Example Rotate $i$-th row of the matrix $k$ elements right ($1 \leq i \leq R$, $1 \leq k < C$). $\mathrm{rotR}\ i\ k$ $\mathrm{rotR}\ 3\ 1$ $\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix} \mapsto \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 9 & 7 & 8 \\ 10 & 11 & 12 \end{pmatrix}$ Rotate $j$-th column of the matrix $k$ elements down ($1 \leq j \leq C$, $1 \leq k < R$). $\mathrm{rotS}\ j\ k$ $\mathrm{rotS}\ 3\ 1$ $\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix} \mapsto \begin{pmatrix} 1 & 2 & 12 \\ 4 & 5 & 3 \\ 7 & 8 & 6 \\ 10 & 11 & 9 \end{pmatrix}$ Multiply all elements in the $i$-th row by $-1$, if and only if none of them were multiplied before ($1 \leq i \leq R$). $\mathrm{negR}\ i$ $\mathrm{negR}\ 2$ $\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix} \mapsto \begin{pmatrix} 1 & 2 & 3 \\ -4 & -5 & -6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix}$ Multiply all elements in the $j$-th column by $-1$, if and only if none of them were multiplied before ($1 \leq j \leq C$). $\mathrm{negS}\ j$ $\mathrm{negS}\ 1$ $\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ 10 & 11 & 12 \end{pmatrix} \mapsto \begin{pmatrix} -1 & 2 & 3 \\ -4 & 5 & 6 \\ -7 & 8 & 9 \\ -10 & 11 & 12 \end{pmatrix}$
Table 1: Allowed operations

Using a limited number of these operations, you need to maximize the sum of all the elements of the matrix.

## Input

The first line of input contains two integers $R$ and $C$ ($1 \leq R, C \leq 100$), the number of rows and columns. The next $R$ lines contain $C$ integers each. All integers are by their absolute value smaller than $10^4$.

## Output

The first line of output should contain two integers, the maximal sum obtainable and the number of operations used. We shall call this number $T$, and it must hold that $T \leq 5RC$. The next $T$ lines should contain any sequence of operations leading to the sum. Each operation should follow the notation defined in Table 1. For details look at sample test cases.

Sample Input 1 Sample Output 1
3 4
1 -2 5 200
-8 0 -4 -10
11 4 0 100

345 2
rotS 2 1
negR 2

Sample Input 2 Sample Output 2
3 3
8 -2 7
1 0 -3
-4 -8 3

34 4
rotR 1 1
rotS 3 1
negR 2
negR 3