Jorge, as a mathematics enthusiastic, likes to learn about fractals. He learned recently about the Vicsek Fractal. The Vicsek fractal, also known as the Vicsek snowflake, is a self-similar fractal named after the Hungarian physicist Tamás Vicsek. It is generated by repeatedly arranging smaller copies of the same figure according to a fixed pattern. Despite this simple construction rule, increasingly complex patterns emerge as the process is repeated.

In this problem, Jorge represents the Vicsek fractal using * and . characters.

The fractal of level $$$0$$$ consists of a single *:

*

For every $$$n \ge 1$$$, the fractal of level $$$n$$$ is constructed from the fractal of level $$$n-1$$$. Since the previous fractal has size $$$3^{n-1} \times 3^{n-1}$$$, consider a $$$3 \times 3$$$ arrangement of square blocks, where each block has size $$$3^{n-1} \times 3^{n-1}$$$. Place an exact copy of the level $$$n-1$$$ fractal in the four corner blocks and in the center block. Every position in the remaining four blocks is filled with . characters. In other words, if F represents the complete fractal of level $$$n-1$$$, and E represents an equally sized block containing only . characters, the construction is:

F E F
E F E
F E F

where adjacent blocks are printed without spaces between them.

For example, the fractal of level $$$1$$$ is:

*.*
.*.
*.*

and the fractal of level $$$2$$$ is:

*.*...*.*
.*.....*.
*.*...*.*
...*.*...
....*....
...*.*...
*.*...*.*
.*.....*.
*.*...*.*

This construction is applied recursively for every higher level. More precisely, to construct the fractal of any level $$$n \ge 2$$$, divide its $$$3^n \times 3^n$$$ grid into nine equal square regions of size $$$3^{n-1} \times 3^{n-1}$$$. The regions in the top-left, top-right, center, bottom-left, and bottom-right positions must each contain an exact copy of the level $$$n-1$$$ fractal. The top-center, middle-left, middle-right, and bottom-center regions contain only . characters. Thus, every level is completely determined by the previous one, and the resulting fractal of level $$$n$$$ always has exactly $$$3^n$$$ rows and $$$3^n$$$ columns.

Given an integer $$$n$$$, help Jorge to print the Vicsek fractal of level $$$n$$$.