CodeForces 304C

E - E

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 304C

Description

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 ≤ 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.

Sample Input

Input

5

Output

1 4 3 2 0
1 0 2 4 3
2 4 0 1 3

Input

2

Output

-1

Hint

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.

#include<iostream>
#include<stdio.h>
using namespace std;
int main()
{
    int n;
    scanf("%d",&n);
    if(n==)
    {
        printf("%d\n%d\n%d\n",,,);
        return ;
    }
    if(!(n&))
    {
        printf("-1\n");
        return ;
    }
    for(int i=;i<n;i++)
    {
        printf("%d ",i);
    }
    printf("\n");
    for(int i=;i<n;i++)
    {
        printf("%d ",i);
    }
    printf("0\n");
    for(int i=;i<n;i++)
        printf("%d ",(i+i+)%n);
    return ;
}

http://www.voidcn.com/blog/theArcticOcean/article/p-4944592.html

这个大神讲解的挺好的。