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 CPP):

Solution:
#include<iostream>
using namespace std;
int main()
{ int a,b,i,j;
cin>>a>>b;
char c[a][b+1];
for(i=0; i<a; i++)
cin>>c[i];

for(i=0; i<a+2; i++)
{
for(j=0; j<b+2; j++)
{
if(i==0 || i==a+1)
cout<<"#";
}
if(i==0 || i==a+1)
cout<<endl;
if(i>0 && i<a+1)
cout<<"#"<<c[i-1]<<"#"<<endl;
}
}