Magic Grid
Description
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 $n \times n$.
The only line of input contains an integer $n$ ($4 \leq n \leq 1000$). It is guaranteed that $n$ is a multiple of $4$.
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.
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.
Samples
4
8 9 1 13
3 12 7 5
0 2 4 11
6 10 15 14
8
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 $60$.