Picture Frame

You are given a image with a height of H pixels and a width of W pixels. Each pixel is represented by a lowercase English letter. The pixel at the i-th row from the top and j-th column from the left is a_{ij}.

Put a box around this image and output the result. The box should consist of # and have a thickness of 1.

Constraints

• 1 ≤ H, W ≤ 100
• a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W a_{11} ... a_{1W} : a_{H1} ... a_{HW}

Output

Print the image surrounded by a box that consists of # and has a thickness of 1.

Examples

Input

2 3 abc arc

Output

#abc# #arc#

Input

1 1 z

Output

z#

inputFormat

outputFormat

output the result. The box should consist of # and have a thickness of 1.

Constraints

• 1 ≤ H, W ≤ 100
• a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W a_{11} ... a_{1W} : a_{H1} ... a_{HW}

Output

Print the image surrounded by a box that consists of # and has a thickness of 1.

Examples

Input

2 3 abc arc

Output

#abc# #arc#

Input

1 1 z

Output

z#

样例

2 3
abc
arc

#####
#abc#
#arc#
#####

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