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;
template <class II, class SZ, class OI>
OI cpy_n(II _i, SZ _s, OI _o) {
  for (int_fast64_t _j = 1; _j <= _s; _j++) {
    *(_o++) = *_i;
    if (_j != _s) {
      _i++;
    }
  };
  return _o;
}
template <class T>
void slurp(vector<T>& v, int_least32_t n = 1000000000) {
  istream_iterator<T> i(cin);
  istream_iterator<T> eoi;
  ;
  if (n == 1000000000) {
    copy((i), (eoi), back_inserter((v)));
  } else {
    v.reserve(n);
    cpy_n(i, n, back_inserter((v)));
  }
}
template <class T, class U>
void slurp2(vector<T>& va, vector<U>& vb, int_least32_t n = 1000000000) {
  istream_iterator<T> a(cin);
  istream_iterator<T> eoa;
  ;
  istream_iterator<U> b(cin);
  istream_iterator<U> eob;
  ;
  if (n != 1000000000) {
    va.reserve(n);
    vb.reserve(n);
  }
  auto ao = back_inserter((va));
  auto bo = back_inserter((vb));
  for (int_fast64_t i = 1; i <= n; i++) {
    if (a == eoa) break;
    *(ao++) = *a;
    *(bo++) = *b;
    if (i != n) {
      a++;
      b++;
    }
  }
}
chrono::time_point<chrono::system_clock> start_time;
void do_it() {
  int_fast64_t n;
  cin >> n;
  if (n % 2 == 0) {
    cout << "-1";
  } else {
    for (int_fast64_t zzz = 1; zzz <= 2; zzz++) {
      for (int_fast64_t i = (0); i <= (n - 1); i++) {
        cout << i << " ";
      }
      cout << endl;
    }
    for (int_fast64_t i = (0); i <= (n - 1); i++) {
      cout << (i * 2) % n << " ";
    }
  }
}
void start() { start_time = chrono::system_clock::now(); }
void end() {
  chrono::time_point<chrono::system_clock> end_time;
  end_time = chrono::system_clock::now();
  chrono::duration<double> diff = end_time - start_time;
  cerr << fixed << setprecision(4) << diff.count() << "s" << endl;
}
void do_mult() {
  int_least32_t times;
  cin >> times;
  for (int_fast64_t i = 1; i <= times; i++) {
    do_it();
    cout << endl;
  }
}
int main(int argc, char* argv[]) {
  ios::sync_with_stdio(false);
  start();
  do_it();
  cout << endl;
  end();
  return 0;
}