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 -*-

import Queue

def output_frame(w):
    f = ""
    for i in range(w+2):
        f += "#"
    return f

H,W = map(int, raw_input().split())
q_str = Queue.Queue()
for i in range(H):
    q_str.put(raw_input())

print output_frame(W)
while not q_str.empty():
    print "#" + q_str.get() + "#"
print output_frame(W)