Target

Here at [topcoder], we call a contestant a "target" if their rating is 3000 or more. In the arena, the targets have a red icon with a small target on it. Do you want to become a target as well? Sure you do. But before you get there, let's start with something easier: drawing a target.


The target you need to draw consists of nested squares. The innermost square is just a single '#' character. The larger squares use alternatingly the character ' ' (space) and the character '#'. Here is an example in which the side of the largest square is n = 5:

#####
#   #
# # #
#   #
#####

And here is an example for n = 9:

#########
#       #
# ##### #
# #   # #
# # # # #
# #   # #
# ##### #
#       #
#########

You will be given an int n. Your method must return a String[] which contains a drawing of the target with side n. More precisely, each element of the returned String[] must be one row of the drawing, in order. Therefore, the returned String[] will consist of n elements, each with n characters. (See the examples below for clarification.)


The value of n will be such that a target like the ones above can be drawn: 5, 9, 13, and so on. Formally, n will be of the form 4k+1, where k is a positive integer.