Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Lucky Permutation Triple

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBike 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.

Examples

Input

5

Output

1 4 3 2 0

1 0 2 4 3

2 4 0 1 3

Input

2

Output

-1

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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/25/2019 22:13:51 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|