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C. Lucky Permutation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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*.

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.

Examples

Input

1

Output

1

Input

2

Output

-1

Input

4

Output

2 4 1 3

Input

5

Output

2 5 3 1 4

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