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?

Input

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

Output

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.

Note

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.