Background

$1+2+3+\cdots+n=\dfrac {n\times (n+1)} 2$。

Problem Description

Given a positive integer $n$.

We define that, for a permutation $\{x_n\}$ of $1$ to $n$, $f(\{x_n\})=\max\limits_{i=1}^{n}(x_i+x_{(i \bmod n)+1})-\min\limits_{i=1}^{n}(x_i+x_{(i \bmod n)+1})$.

You need to construct a permutation $\{p_n\}$ of $1$ to $n$ such that for any permutation $\{q_n\}$ of $1$ to $n$, we have $f(\{p_n\})\le f(\{q_n\})$, and output the permutation $\{p_n\}$ you constructed.

Input Format

A positive integer $n$.

Output Format

Output $n$ integers, representing the permutation $\{p_n\}$ you constructed, separated by spaces.

Any output that satisfies the condition will be accepted.

4

1 4 2 3

Hint

Sample Explanation #1

$f(\{1,4,2,3\})=2$. It can be proven that for any permutation $\{q_n\}$ of $1$ to $n$, we have $f(\{1,4,2,3\})\le f(\{q_n\})$.

Of course, $\{1,3,2,4\}$, $\{3,1,4,2\}$, $\{4,1,3,2\}$, etc. are also valid permutations $\{p_n\}$.

Constraints

For all testdata, $3 \le n \le 10^6$.

This problem uses bundled tests.

Translated by ChatGPT 5