A permutation $*p*$ of size $*n*$ is the sequence $*p*_{1}, *p*_{2}, ..., *p*_{*n*}$, consisting of $*n*$ distinct integers, each of them is from $1$ to $*n*$ $(1 ≤ *p*_{*i*} ≤ *n*)$.

A lucky permutation is such permutation $*p*$, that any integer $*i*$ $(1 ≤ *i* ≤ *n*)$ meets this condition $*p*_{*p*_{*i*}} = *n* - *i* + 1$.

You have integer $*n*$. Find some lucky permutation $*p*$ of size $*n*$.

Input

The first line contains integer $*n*$ ($1 ≤ *n* ≤ 10^{5}$) — the required permutation size.

Output

Print "-1" (without the quotes) if the lucky permutation $*p*$ of size $*n*$ doesn't exist.

Otherwise, print $*n*$ distinct integers $*p*_{1}, *p*_{2}, ..., *p*_{*n*}$ $(1 ≤ *p*_{*i*} ≤ *n*)$ after a space — the required permutation.

If there are multiple answers, you can print any of them.