Permutation of the Year 1

Let $N = 2026$. A permutation $(a_1,a_2,\cdots,a_N)$ of $(1, 2, \cdots, N)$ is called a permutation of the year if it satisfies the following condition.

• For every pair of integers $i,j$ ($1 \leq i < j \leq N$), $(i-j)^2+(a_i-a_j)^2$ is divisible by $N$.

Construct a permutation of the year.

The input is given in the following format.

$N$

Print a permutation of the year $a_1,a_2,\cdots,a_N$ on the first line, separated by spaces.

If there is more than one valid answer, print any of them.

• $N=2026$.