Problem Description

Given a positive integer $n$. You need to construct a permutation $p$ of length $2n$ (i.e., each integer from $1$ to $2n$ appears exactly once) such that for all $i = 1, 2, \dots, n$:

$$|p_{2i-1} - p_{2i}| \equiv i \pmod{n}$$

That is, after pairing the elements into $n$ pairs, the absolute difference of the $i$-th pair modulo $n$ must be equal to $i$.

Please output any valid construction, or report that no such permutation exists.

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Input

The input contains a single integer $n$ ($1 \le n \le 10^5$).

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Output

If no such permutation exists, output a single line containing -1.

Otherwise, output a single line containing $2n$ integers $p_1, p_2, \dots, p_{2n}$, representing your constructed permutation. If there are multiple valid constructions, you may output any of them.

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Examples

Example 1

Input

3

Output

1 5 2 4 3 6

Explanation

Check the pairs:

• Pair 1: $|1-5| = 4 \equiv 1 \pmod{3}$ ✓
• Pair 2: $|2-4| = 2 \equiv 2 \pmod{3}$ ✓
• Pair 3: $|3-6| = 3 \equiv 0 \pmod{3}$ ✓

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Example 2

Input

4

Output

7 8 2 4 3 6 1 5

Explanation

Check the pairs:

• Pair 1: $|7-8| = 1 \equiv 1 \pmod{4}$ ✓
• Pair 2: $|2-4| = 2 \equiv 2 \pmod{4}$ ✓
• Pair 3: $|3-6| = 3 \equiv 3 \pmod{4}$ ✓
• Pair 4: $|1-5| = 4 \equiv 0 \pmod{4}$ ✓

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Example 3

Input

2

Output

-1

Explanation

When $n \equiv 2 \pmod{4}$ (here $n = 2$), no valid permutation exists, so we output -1.

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Constraints

• $1 \le n \le 10^5$