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:
# coding: utf-8

h, w = map(int, raw_input().split())

pic = [["#" for _j in xrange(w+2)] for _i in xrange(h+2)]

for i in xrange(h):
    aij = raw_input()

    for j in xrange(len(aij)):
        pic[i+1][j+1] = aij[j]

for p in pic:
    print "".join(p)