Problem: Let us define a magic grid to be a square matrix of integers of size n × n, satisfying the following conditions. 

  * All integers from 0 to (n^2 - 1) inclusive appear in the matrix exactly once. 
  * [Bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all elements in a row or a column must be the same for each row and column. 



You are given an integer n which is a multiple of 4. Construct a magic grid of size n × n.

Input

The only line of input contains an integer n (4 ≤ n ≤ 1000). It is guaranteed that n is a multiple of 4.

Output

Print a magic grid, i.e. n lines, the i-th of which contains n space-separated integers, representing the i-th row of the grid.

If there are multiple answers, print any. We can show that an answer always exists.

Examples

Input


4


Output


8 9 1 13
3 12 7 5
0 2 4 11
6 10 15 14

Input


8


Output


19 55 11 39 32 36 4 52
51 7 35 31 12 48 28 20
43 23 59 15 0 8 16 44
3 47 27 63 24 40 60 56
34 38 6 54 17 53 9 37
14 50 30 22 49 5 33 29
2 10 18 46 41 21 57 13
26 42 62 58 1 45 25 61

Note

In the first example, XOR of each row and each column is 13.

In the second example, XOR of each row and each column is 60.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long double inf = 1e9;
long long mod = 1e9 + 7;
void solve() {
  long long n;
  cin >> n;
  long long it = 0;
  vector<vector<long long>> ans(n);
  for (long long i = 0; i < n * n / 16; ++i) {
    if (i % (n / 4) == 0 && i != 0) {
      it += 4;
    }
    ans[it].push_back(i * 16 + 0);
    ans[it].push_back(i * 16 + 1);
    ans[it].push_back(i * 16 + 2);
    ans[it].push_back(i * 16 + 3);
    ans[it + 1].push_back(i * 16 + 4);
    ans[it + 1].push_back(i * 16 + 5);
    ans[it + 1].push_back(i * 16 + 6);
    ans[it + 1].push_back(i * 16 + 7);
    ans[it + 2].push_back(i * 16 + 8);
    ans[it + 2].push_back(i * 16 + 9);
    ans[it + 2].push_back(i * 16 + 10);
    ans[it + 2].push_back(i * 16 + 11);
    ans[it + 3].push_back(i * 16 + 12);
    ans[it + 3].push_back(i * 16 + 13);
    ans[it + 3].push_back(i * 16 + 14);
    ans[it + 3].push_back(i * 16 + 15);
  }
  for (long long i = 0; i < n; ++i) {
    for (long long j = 0; j < n; ++j) {
      cout << ans[i][j] << ' ';
    }
    cout << endl;
  }
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  solve();
  return 0;
}