If it is impossible to obtain the desired configuration of numbers on the cubes from the initial one, print a single integer $-1$.

Otherwise, in the first line, print a single integer $k$~--- the number of swaps in your sequence ($0 \le k \le 20\,000$).

In the second line, print $k$ integers $s_1, s_2, \ldots, s_k$ describing the operations in order ($1 \le s_i \le n - 1$). Integer $s_i$ stands for ``swap the $s_i$-th cube from the left with the $(s_i + 1)$-th cube from the left''.

You do not have to find the shortest solution. Any solution satisfying the constraints will be accepted. 