Spiral Pattern

I decided to create a program that displays a "round and round pattern". The "round and round pattern" is as follows.

• If the length of one side is n, it is displayed as a character string with n rows and n columns.
• A spiral pattern that rotates clockwise with the lower left corner as the base point.
• The part with a line is represented by # (half-width sharp), and the blank part is represented by "" (half-width blank).
• Leave a space between the lines.

Create a program that takes an integer n as an input and outputs a "round and round pattern" with a side length of n.

Input

The input is given in the following format:

d n1 n2 :: nd

The number of datasets d (d ≤ 20) is given to the first line, and the side length ni (1 ≤ ni ≤ 100) of the i-th round pattern is given to each of the following d lines.

Output

Please output a round and round pattern for each data set. Insert a blank line between the datasets.

Example

Input

2 5 6

Output

#

#

##

#

#

inputFormat

input and

outputFormat

outputs a "round and round pattern" with a side length of n.

Input

The input is given in the following format:

d n1 n2 :: nd

The number of datasets d (d ≤ 20) is given to the first line, and the side length ni (1 ≤ ni ≤ 100) of the i-th round pattern is given to each of the following d lines.

Output

Please output a round and round pattern for each data set. Insert a blank line between the datasets.

Example

Input

2 5 6

Output

#

#

##

#

#

样例

2
5
6

#####

#
#



##
#
#
####

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