Background

This is an output-only problem.

Problem Description

You are given a sequence $a$ of length $n$. Define the weight of a permutation $p$ of $1 \dots n$ as

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.

Input Format

The first line contains an integer $n$.

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

Output Format

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

5
1 4 3 2 5

1 3 5 2 4

Hint

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