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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 2010-2022 Mike Mirzayanov

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