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>
using namespace std;

string s[200];
int n, m;

int main(){
	cin>>n>>m;
	
	for(int i=1; i<=n; i++){
		cin>>s[i];
		s[i]="#"+s[i]+"#";
	}
	
	for(int i=0; i<=n+1; i++){
		if(i==0||i==n+1){
			for(int j=0; j<=m+1; j++) cout<<"#";
			cout<<endl;
		}
		else cout<<s[i]<<endl;
	}
}