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:
from __future__ import division
import math


def get_min(w, h):
    m = 1e11
    for x in [w // 3, w // 3 + 1]:
        if x == 0: continue
        a = [x*h, (w-x)*(h//2), (w-x)*(h - h//2)]
        print a
        m = min(m, max(a) - min(a))
    return m

digits = raw_input()
a, b = [int(x) for x in digits.split(' ')]
m = []
for i in range(a):
    s = raw_input()
    m.append(s)
print ''.join(['#'] * (b + 2))
for i in range(a):
    print '#' + m[i] + '#'
print ''.join(['#'] * (b + 2))