Problem: 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 <image>. The sign ai denotes the i-th element of permutation a. The modular equality described above denotes that the remainders after dividing ai + bi by n and dividing ci 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.

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:

  * <image>; 
  * <image>; 
  * <image>; 
  * <image>; 
  * <image>. 



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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = INT_MAX;
const long long INFL = LLONG_MAX;
const long double pi = acos(-1);
int isprime(int a) {
  if (a == 1) return 0;
  for (int d = 2; d * d <= a; d++)
    if (a % d == 0) return 0;
  return 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  cout.precision(15);
  cout << fixed;
  cout.tie(0);
  cin.tie(0);
  int N;
  cin >> N;
  vector<int> A;
  if (N <= 10) {
    for (int(i) = 0, j123 = N; (i) < j123; (i)++) {
      A.push_back(i);
    }
    do {
      set<int> s;
      for (int(i) = 0, j123 = N; (i) < j123; (i)++) s.insert((i + A[i]) % N);
      if (int(s.size()) == N) {
        for (int(i) = 0, j123 = N; (i) < j123; (i)++)
          cout << A[i] << (i + 1 == N ? '\n' : ' ');
        for (int(i) = 0, j123 = N; (i) < j123; (i)++)
          cout << i << (i + 1 == N ? '\n' : ' ');
        for (int(i) = 0, j123 = N; (i) < j123; (i)++)
          cout << (i + A[i]) % N << (i + 1 == N ? '\n' : ' ');
        return 0;
      }
    } while (next_permutation(A.begin(), A.end()));
  } else {
    if (N & 1) {
      for (int(i) = 0, j123 = N; (i) < j123; (i)++)
        cout << i << (i + 1 == N ? '\n' : ' ');
      for (int(i) = 0, j123 = N; (i) < j123; (i)++)
        cout << i << (i + 1 == N ? '\n' : ' ');
      for (int(i) = 0, j123 = N; (i) < j123; (i)++)
        cout << (i + i) % N << (i + 1 == N ? '\n' : ' ');
      return 0;
    }
  }
  cout << -1 << '\n';
}