Description
Doraemon loves programming and overcomplicating things. Today, he wants to make a new carpet for Nobita's house, so he use his programming skill to design a cool pattern for the new carpet, and call it the "doracarpet"!
To have the carpet to be fit in all the rooms, we need it to be in a different size. The following are the rules of pattern for each size of the doracarpet, and we define a size-x doracarpet would be a square carpet with a side length equal to 4×2x-1, for example, a size-4 doracarpet is a square with a side length of 32.
The following is what the doracarpet in each size looks like:
Size-1 doracarpet looks like a plus sign.
Size-2 doracarpet is made of four size-1 doracarpet and arranged like the following figure.
Size-3 doracarpet, has a size-2 doracarpet in the center, and put four U shapes in four different directions and it looks like the following figure.
Size-4 doracarpet is made of four size-3 doracarpet and arranged like the following figure.
Size-5 doracarpet, has a size-4 doracarpet in the center, and put four U shapes in four different directions and it looks like the following figure.
So we discover that when x > 1, and:
- If we have a size-x doracarpet with x % 2 == 0, it would be made of four size-(x-1) doracarpet.
- If we have a size x doracarpet with x % 2 == 1, we would have a size-(x-1) doracarpet in the center and put four U shapes in four different directions.
Input
The input contains only an integer x, with 0 < x < 12.
Output
Output what a size-x doracarpet looks like, use '#' and '.' to represent the black and white block of it.
You may refer to the sample IO to know how to print the result, and don't forget to print a '\n' at the last line.