单点时限: 2.0 sec
内存限制: 512 MB
Setsuna is an expert of Gluttonous Snake, and for that reason she started a Gluttonous Snake club!
One day she was inspired by an obscure group logo (below) and needed a few twisted snakes for her club’s logo.
She wants you to design an ideal association logo for her.And the logo should satisfy:
For example, the following diagrams are valid solutions for $n=3,4$.
Only one integer, $n$, indicating the number of snakes.
If no legal logo exists, output a line “0 0”.
Otherwise, output two integers $h$ and $w$ on the first line, separated by a space, indicating the number of rows and columns of the grids. The coordinate of the grid at the upper left corner is $(1,1)$, while the coordinate of the grid at the lower right corner is $(h,w)$.
Then follow $n$ rows, the $i$-th row contains $2i$ integers separated by spaces, indicating $i$ coordinates of the grids occupied by the $i$-th snake, from its head to tail (see the sample).
The answer is not unique, and you can output any valid solution. Your answer must satisfy all of the following conditions to be considered correct.
$h\times w=\frac{n\times (n+1)}{2}$
The $h\times w$ coordinates $(x_i,y_i)$ in output should be pairwise different and $1\le x_i \le h,1\le y_i \le w$.
For the $i$-th snake, its $i$ coordinates are $(x_1,y_1),(x_2,y_2),\cdots,(x_i,y_i)$, and for all $1\leq k < i$ needs to satisfy one of the following two conditions.
$|x_k-x_{k+1}|=1 \text{ and }\ y_k=y_{k+1}$
$x_k=x_{k+1}\text{ and }\ |y_k-y_{k+1}|=1$
The number of turns of the $i$-th snake is defined formally as $\sum\limits_{k=2}^{i-1}[\neg( |x_{k-1}-x_{k+1}|=2\vee\ |y_{k-1}-y_{k+1}|=2 )]$, whose parity is subject to the $5$-th restriction of the above description. (You can just refer it as the number of $90^\circ$ turns in logo.)
Note that
: Don’t print any extra space at the end of any line.
3
3 2 1 1 2 2 1 2 3 2 3 1 2 1
$1\leq n \leq 500$