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 JAVA):

Solution:
import java.util.*;
public class Main
{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int H = sc.nextInt();
		int W = sc.nextInt();
		
		char c[][] = new char[H+2][W+2];
		
		int i;
		int j;
		String s;
		
		for(i=0; i<H+2; i++){
			for(j=0; j<W+2; j++){
				c[i][j]='#';
			}
		}
		for(i=1; i<H+1; i++){
			s=sc.next();
			for(j=1; j<W+1; j++){
				c[i][j]=s.charAt(j-1);
			}
		}
		
		
		for(i=0;i<H+2;i++){
			System.out.println(c[i]);
		}
	}
}