Camel

Define a new chess piece called camel-tone. It jumps two squares orthogonally to land three squares away, or one square diagonally to land two squares away. That is, from $(r, c)$ it can move to $(r \pm 3, c)$, $(r, c \pm 3)$, or $(r \pm 2, c \pm 2)$, whenever the destination lies on the board. There are 8 possible moves in total.

The board is a square of $N \times N$ cells, where $N$ is always a multiple of 5.

The piece starts on the top-left corner cell (row 1, column 1). Play consists of a sequence of moves that visits every cell exactly once, and after $N^2 - 1$ moves the piece is exactly one move away from its starting cell. Such a closed tour is called a camel-tone cycle.

Write a program camel that finds any such tour, or reports that the cycle is impossible.

One line is read from standard input, containing a single integer $N$.

Write one of the following to standard output.

• If the cycle is impossible, print NO on one line.

• Otherwise, print $N$ lines. Each line contains $N$ space-separated integers. These integers are the distinct integers from $1$ to $N^2$. The first number of the first line is $1$. The output represents the board, and each integer gives the visit order of its cell. The cells holding two consecutive numbers are one piece move apart, and the cell holding $N^2$ is one move away from the start cell holding $1$.

• $N$ is a multiple of 5.
• $5 \le N \le 1000$.

Each number in the output is the visit order of its cell. The cells holding $k$ and $k + 1$ are always one piece move apart, and so are the cells holding $N^2$ and $1$. The starting cell is always the top-left corner with value $1$.