Score : $1000$ points

Problem Statement

For an $n \times n$ grid, let $(r, c)$ denote the square at the $(r+1)$-th row from the top and the $(c+1)$-th column from the left. A good coloring of this grid using $K$ colors is a coloring that satisfies the following:

• Each square is painted in one of the $K$ colors.
• Each of the $K$ colors is used for some squares.
• Let us number the $K$ colors $1, 2, ..., K$. For any colors $i$ and $j$ ($1 \leq i \leq K, 1 \leq j \leq K$), every square in Color $i$ has the same number of adjacent squares in Color $j$. Here, the squares adjacent to square $(r, c)$ are $((r-1)\; mod\; n, c), ((r+1)\; mod\; n, c), (r, (c-1)\; mod\; n)$ and $(r, (c+1)\; mod\; n)$ (if the same square appears multiple times among these four, the square is counted that number of times).

Given $K$, choose n between 1 and 500 (inclusive) freely and construct a good coloring of an $n \times n$ grid using $K$ colors. It can be proved that this is always possible under the constraints of this problem,

Constraints

• $1 \leq K \leq 1000$

Input

Input is given from Standard Input in the following format:

$K$

Output

Output should be in the following format:

$n$

$c_{0,0}$ $c_{0,1}$ $...$ $c_{0,n-1}$

$c_{1,0}$ $c_{1,1}$ $...$ $c_{1,n-1}$

$:$

$c_{n-1,0}$ $c_{n-1,1}$ $...$ $c_{n-1,n-1}$

$n$ should represent the size of the grid, and $1 \leq n \leq 500$ must hold. $c_{r,c}$ should be an integer such that $1 \leq c_{r,c} \leq K$ and represent the color for the square $(r, c)$.

2

3
1 1 1
1 1 1
2 2 2

• Every square in Color $1$ has three adjacent squares in Color $1$ and one adjacent square in Color $2$.
• Every square in Color $2$ has two adjacent squares in Color $1$ and two adjacent squares in Color $2$.

Output such as the following will be judged incorrect:

2
1 2
2 2

3
1 1 1
1 1 1
1 1 1

9

3
1 2 3
4 5 6
7 8 9