Finding a Dongga Sequence

A dongga sequence of length $N$ is a sequence that satisfies the following two conditions.

• It consists of integers from $1$ to $N$, and all elements are distinct.
• The difference between adjacent elements is at least $\lfloor \frac{N}{2} \rfloor$.

Find any one dongga sequence of length $N$. For every valid input, a dongga sequence always exists.

The first line contains $N$ ($1 \le N \le 5\,000$), the length of the dongga sequence to find.

On the first line, print any one dongga sequence of length $N$. Separate the elements with spaces.

$\lfloor x \rfloor$ is the largest integer not greater than $x$.

$\lfloor {3.7} \rfloor$ $=$ $3$

$\lfloor {4} \rfloor$ $=$ $4$