Litusiano was reading a book called Rich Dad Poor Dad when he came across the following problem:

You are given an integer $$$n$$$ and an array $$$a$$$ of length $$$n$$$. Your task is to find a permutation $$$p$$$ of length $$$n$$$ (i.e., an arrangement of the numbers from $$$1$$$ to $$$n$$$) that satisfies the following conditions:

1. For every index $$$i$$$ ($$$1 \leq i \leq n$$$): - Let $$$a_i$$$ be the smallest index greater than $$$i$$$ ($$$i \lt a_i \leq n$$$) such that $$$p_i \lt p_{a_i}$$$, or $$$a_i = -1$$$ if no such index exists. 2. The permutation $$$p$$$ must be the lexicographically smallest one that satisfies this property, or it must be determined that no such permutation exists.

Note on lexicographical order:

Lexicographical order (or lexicographically smallest) means that, given two arrays $$$x$$$ and $$$y$$$ of the same length, $$$x$$$ is smaller than $$$y$$$ in this order if at the first position $$$k$$$ where they differ, $$$x_k \lt y_k$$$. For example: - $$$[1, 2, 3]$$$ is smaller than $$$[1, 3, 2]$$$ because at the second position, $$$2 \lt 3$$$. - $$$[2, 1, 3]$$$ is greater than $$$[1, 3, 2]$$$ because at the first position, $$$2 \gt 1$$$.

If no permutation satisfying the given property exists, it should be explicitly stated.