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.