A8904. Lucky Permutation

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 $p_{pi}=n-i+1$ .

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

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

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.