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
# -*- coding: utf-8 -*-
H,W = map(int,raw_input().split(" "))

lista = []
for i in range(H):
	lista.append([map(str,raw_input().split(" "))])

result = []
stre = ""
for i in range(W+2):
	stre = stre + "#"

print stre

for i in lista:
	stre1 = "#"
	for k in i:
		stre1 = stre1 + k[0]
	stre1 = stre1 + "#"
	print stre1

print stre