Problem Statement

You are given a positive integer $N$. Freely choose positive integers $H, W$ and construct a grid with $H$ rows and $W$ columns that satisfies all of the following conditions.
Here, the cell in the $i$-th row from the top ($1 \leq i \leq H$) and the $j$-th column from the left ($1 \leq j \leq W$) is denoted by cell $(i,j)$.

• $1 \leq H \leq 2\,000$
• $1 \leq W \leq 2\,000$
• Each cell is painted white or black.
• There are exactly $N!$ paths from cell $(1,1)$ to cell $(H,W)$ that repeatedly move $1$ cell to the right or down, passing only through cells painted white.
• More formally, there are $N!$ sequences of cells $(x_1, y_1), (x_2, y_2), \dots, (x_{H+W-1}, y_{H+W-1})$ that satisfy all of the following conditions.
• $(x_1,y_1)=(1,1)$
• $(x_{H+W-1},y_{H+W-1})=(H,W)$
• For each $i \ (1 \leq i \leq H + W - 1)$, cell $(x_i, y_i)$ is painted white.
• For each $i \ (1 \leq i \leq H + W - 2)$, $(x_{i+1}, y_{i+1})$ is either $(x_i+1, y_i)$ or $(x_i,y_i+1)$.
• Here, $2$ sequences of cells are considered different if there exists some $i \ (1 \leq i \leq H+W-1)$ for which $(x_i, y_i)$ differs.

Input

The input is given from standard input in the following format.

$N$

Output

Print to standard output in the following format.

$H$ $W$
$S_{1,1}S_{1,2} \cdots S_{1,W}$
$S_{2,1}S_{2,2} \cdots S_{2,W}$
$\vdots$
$S_{H,1}S_{H,2} \cdots S_{H,W}$

Constraints

The input satisfies the following constraints.

• $1 \leq N \leq 400$
• $N$ is an integer.

Sample

3

3 3
...
...
...

5

6 6
....#.
......
..#...
......
#.....
......

1

3 4
..##
#..#
##..