Background

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

Given a positive integer $n$.

We define, 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 $n$, $f(\{p_n\})\le f(\{q_n\})$, and output the constructed permutation $\{p_n\}$.

Input

A positive integer $n$.

Output

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

Any output that satisfies the conditions will be accepted.

Examples

Input 1

4

Output 1

1 4 2 3

Note 1

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

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

Constraints

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

This problem uses bundled testing.