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<bits/stdc++.h>
#define r(i,n) for(int i=0;i<n;i++)
using namespace std;
int main(){
	int a,b,c,f=0,t=0;
	string s[102];
	cin>>a>>b;
	r(i,a){
		cin>>s[i+1];
		s[i+1]="#"+s[i+1]+"#";
	}
	r(i,b+2)s[0]+="#",s[a+1]+="#";
	r(i,a+2)cout<<s[i]<<endl;
}