Sequences

Time limit2sMemory limit1024 MB

Summary

Choose 2n fighters from two copies of each strength 1 to n+1 so that each chosen strength's copies sit x apart, or report -1.

Level: Medium7 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

A decisive battle is coming. Professor X knows the odds are poor, but he will use every chance he gets. The X-Men army has $2 \cdot (n+1)$ fighters, and for every strength $x$ from $1$ to $n+1$ , exactly two fighters have that strength. To win, the X-Men must choose $2 \cdot n$ fighters and line them up so that if a fighter with strength $x$ is in the line, the other fighter with strength $x$ is also in the line, with exactly $x-1$ other fighters standing between them. Both fighters with the same strength must stay in reserve so they can help at the right moment.

Help Professor X find such a lineup, or report that none exists.

Input

The only line of input contains one integer $n$ ( $1 \le n \le 100$ ), which is half the length of the required lineup.

Output

If no such lineup exists, print one number $-1$ . Otherwise, print the $2 \cdot n$ numbers of the lineup.

Examples2

Example 1
Input
```
1
```
Expected output
```
1 1
```
Example 2
Input
```
3
```
Expected output
```
2 4 2 1 1 4
```