Permutation Making

A permutation of length $N$ is a sequence of $N$ natural numbers between $1$ and $N$ in which no number appears more than once.

You are given a permutation $A$ of length $N$.

Define the $i$-th element of a new sequence $P$ as follows. ($1 \le i \le N$)
$P_i = \left(\sum_{k=1}^{i}A_k\right)\ \bmod N$

Find any permutation $A$ for which the number of distinct values among the elements of $P$ is at most $\frac{N}{2} + 1$.

The first line contains $N$ ($1 \le N \le 100\,000$).

Print $A_1$ through $A_N$, separated by spaces.

A permutation $A$ satisfying the condition always exists.