Score : $250$ points

问题陈述

对于一个非负整数 $K$，我们定义一个 $K$ 级地毯如下：

• 一个 $0$ 级地毯是一个 $1 \times 1$ 的网格，由一个单独的黑色单元格组成。
• 对于 $K > 0$，一个 $K$ 级地毯是一个 $3^K \times 3^K$ 的网格。当这个网格被划分为九个 $3^{K-1} \times 3^{K-1}$ 的区块时：
  • 中心区块完全由白色单元格组成。
  • 其他八个区块是 $(K-1)$ 级地毯。

你给定一个非负整数 $N$。 请按照指定的格式打印一个 $N$ 级地毯。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

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.

Constraints

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

Input

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

$N$

Output

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.

Sample Input 1

1

Sample Output 1

###
#.#
###

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.

Sample Input 2

2

Sample Output 2

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

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