P7812 [JRKSJ R2] Dark Forest

**This is an output-only problem.**

You are given a sequence $a$ of length $n$. Define the weight of a permutation $p$ of $1 \dots n$ as $$\sum_{i=1}^n p_i a_{p_{i-1}} a_{p_i}a_{p_{i+1}}$$ You may treat this permutation as a cycle, i.e., $p_{0}=p_n, p_{n+1}=p_1$. Please construct a permutation of $1 \dots n$ with the weight as **large as possible**.

The first line contains an integer $n$. The second line contains $n$ integers representing the sequence $a$.

Output one line with $n$ integers representing the permutation.

Note that it is `a[p[i-1]] a[p[i+1]]`. The testdata has some gradation. ### Constraints For $100\%$ of the testdata, $1 \le n, a_i \le 10^3$. ### Sample Explanation The weight of this permutation is $1\times2\times1\times3+3\times1\times3\times5+5\times3\times5\times4+2\times5\times4\times2+4\times4\times2\times1=463$. It can be proven that this is one of the optimal permutations. ### Scoring **This problem uses Special Judge.** Each test point has $10$ parameters $v_1, v_2, \dots v_{10}$. If the weight of your output is $V \ge v_i$, then on that test point you will get at least $i$ points. In particular, if your output is not a permutation of $1 \dots n$, you will get $0$ points on that test point. The scoring parameters have been provided in the attachment. Translated by ChatGPT 5