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.*;
import java.io.*;
import java.math.*;
public class Main{
    public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter ou = new PrintWriter(System.out);
		int h = Integer.parseInt(sc.next());
		int w = Integer.parseInt(sc.next());
		char[][] a = new char[h + 2][w + 2];
		for(int i = 0 ; i < h + 2 ; i++) Arrays.fill(a[i] , '#');
		for(int i = 1 ; i < h + 1 ; i++){
			String s = sc.next();
			for(int j = 1 ; j < w + 1 ; j++){
				a[i][j] = s.charAt(j - 1);
			}
		}
		for(int i = 0 ; i < h + 2 ; i++){
			for(int j = 0 ; j < w + 2 ; j++){
				ou.print(a[i][j]);
			}
			ou.println();
		}
		ou.flush();
	}
}