Problem: 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#

Solution (in PYTHON):

Solution:
import sys
H, W = map(int, raw_input().split())
a = [raw_input() for _ in range(H)]
for i in range(H + 2):
    for j in range(W + 2):
        if i == 0 or j == 0 or i == H + 1 or j == W + 1:
            sys.stdout.write('#')
        else:
            sys.stdout.write(str(a[i - 1][j - 1]))
    print("")