A9036. Lucky Permutation Triple

Bike is interested in permutations. A permutation of length $n$ is an integer sequence such that each integer from 0 to $(n-1)$ appears exactly once in it. For example, $[0,2,1]$ is a permutation of length 3 while both $[0,2,2]$ and $[1,2,3]$ is not.

A permutation triple of permutations of length $n$ $(a,b,c)$ is called a Lucky Permutation Triple if and only if . The sign $a_{i}$ denotes the $i$ -th element of permutation $a$ . The modular equality described above denotes that the remainders after dividing $a_{i}+b_{i}$ by $n$ and dividing $c_{i}$ by $n$ are equal.

Now, he has an integer $n$ and wants to find a Lucky Permutation Triple. Could you please help him?

The first line contains a single integer $n$ $(1<=n<=10^{5})$ .

If no Lucky Permutation Triple of length $n$ exists print -1.

Otherwise, you need to print three lines. Each line contains $n$ space-seperated integers. The first line must contain permutation $a$ , the second line — permutation $b$ , the third — permutation $c$ .

If there are multiple solutions, print any of them.

In Sample 1, the permutation triple $([1,4,3,2,0],[1,0,2,4,3],[2,4,0,1,3])$ is Lucky Permutation Triple, as following holds:

- ;
- ;
- ;
- ;
- .

In Sample 2, you can easily notice that no lucky permutation triple exists.