Splitting Integers into Arrays

Time limit2sMemory limit256 MB

Summary

Split the integers 1 to 3n into three arrays of length n so that a_i + b_i = c_i for every i, or report -1 if no split exists.

Level: Medium5 of 10
Topics: Array, Math, Implementation
Solved: No attempts yet

Problem

Split the integers from 1 to $3n$ into three arrays $a$ , $b$ , and $c$ , each of length $n$ , so that for every $i$ from 1 to $n$ , $a_i + b_i = c_i$ holds.

Input

A single integer $n$ ( $1 \le n \le 23$ ).

Output

If no solution exists, print -1 on the first line. Otherwise, print three lines of $n$ integers each, separated by spaces: the elements of array $a$ on the first line, the elements of $b$ on the second, and the elements of $c$ on the third. Each integer from 1 to $3n$ must be printed exactly once.

Examples1

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