C. Magic Grid
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Let us define a magic grid to be a square matrix of integers of size $$$n \times n$$$, satisfying the following conditions.

  • All integers from $$$0$$$ to $$$(n^2 - 1)$$$ inclusive appear in the matrix exactly once.
  • Bitwise 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 $$$n \times n$$$.

Input

The only line of input contains an integer $$$n$$$ ($$$4 \leq n \leq 1000$$$). 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 $$$60$$$.