A12151 | Grid Sort

The first line contains two integers $n$ and $m$ ( $3 \leq n,m \leq 20$ ) — the dimensions of the grid.

Each of the next $n$ lines contains $m$ integers $x_{i,1}, x_{i,2}, \ldots, x_{i, m}$ ( $1 \leq x_{i,j} \leq nm$ ), denoting the values of the block in row $i$ and column $j$ .

It is guaranteed that all $x_{i,j}$ are distinct.

First, print a single integer $k$ , the number of operations ( $k \geq 0$ ).

On each of the next $k$ lines, print a cycle as follows:

$$$$s\ y_1\ y_2\ \ldots\ y_s $$ </p><p>Here, $s$ is the number of blocks to move ( $s \\geq 4$ ). Here we have block $y\_1$ moving to where block $y\_2$ is, block $y\_2$ moving to where block $y\_3$ is, and so on with block $y\_s$ moving to where block $y\_1$ is.</p><p>The sum of $s$ over all operations must be at most $10^5$$$.

The first sample is the case in the statement. Here, we can use the cycle in reverse order to sort the grid.