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.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分