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 $\text{[math]}$ . 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 ≤ 10⁵).

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:

$\text{[math]}$ ;
$\text{[math]}$ ;
$\text{[math]}$ ;
$\text{[math]}$ ;
$\text{[math]}$ .

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

Idx	Name	Rating
A	Lucky Permutation Triple	1300
B	Rectangle Puzzle II	1700
C	Minimum Modular	2400
D	Rotatable Number	2600
E	Random Ranking	3000

Codeforces Round 183 (Div. 1)