Lina is playing with $n$ cubes placed in a row. Each cube has an integer from $1$ to $n$ written on it. Every integer from $1$ to $n$ appears on exactly one cube.

Initially, the numbers on the cubes from left to right are $a_1, a_2, \ldots, a_n$. Lina wants the numbers on the cubes from left to right to be $b_1, b_2, \ldots, b_n$.

Lina can swap any two adjacent cubes, but only if the difference between the numbers on them is at least~$2$. This operation can be performed at most $20\,000$ times.

Find any sequence of swaps that transforms the initial configuration of numbers on the cubes into the desired one, or report that it is impossible.