For a non-negative integer $K$, we define a level-$K$ carpet as follows:

-   A level-$0$ carpet is a $1 \times 1$ grid consisting of a single black cell.
-   For $K > 0$, a level-$K$ carpet is a $3^K \times 3^K$ grid. When this grid is divided into nine $3^{K-1} \times 3^{K-1}$ blocks:
    -   The central block consists entirely of white cells.
    -   The other eight blocks are level-$(K-1)$ carpets.

You are given a non-negative integer $N$.  
Print a level-$N$ carpet according to the specified format.

The input is given from Standard Input in the following format:

```
$N$
```

Print $3^N$ lines.  
The $i$-th line ($1 \leq i \leq 3^N$) should contain a string $S_i$ of length $3^N$ consisting of `.` and `#`.  
The $j$-th character of $S_i$ ($1 \leq j \leq 3^N$) should be `#` if the cell at the $i$\-th row from the top and $j$\-th column from the left of a level-$N$ carpet is black, and `.` if it is white.

-   $0 \leq N \leq 6$
-   $N$ is an integer.

###
#.#
###

A level-$1$ carpet is a $3 \times 3$ grid as follows:

When output according to the specified format, it looks like the sample output.

#########
#.##.##.#
#########
###...###
#.#...#.#
###...###
#########
#.##.##.#
#########

A level-$2$ carpet is a $9 \times 9$ grid.