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:
#!/usr/bin/env/ python

H,W=map(int,raw_input().split())
arr=[['#']*W]*H
for i in range(H):
    line=map(str,raw_input())
    line.insert(0,'#')
    line.append('#')
    arr[i]=line

print '#'*(W+2)
for i in range(H):
    print "".join(arr[i])
print '#'*(W+2)