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.Scanner;
public class Main {
public static void main(String[]srgs) {
	Scanner scan=new Scanner(System.in);
	int a=scan.nextInt();
	int b=scan.nextInt();
	String an[]=new String[a];
	for(int i=0;i!=a;i++) {
		an[i]=scan.next();
	}
	for(int i=0;i!=b+2;i++) {
		System.out.print("#");
	}
	System.out.println();
	for(int i=0;i!=a;i++) {
		System.out.println("#"+an[i]+"#");
	}
	for(int i=0;i!=b+2;i++) {
		System.out.print("#");
	}
	System.out.println();
	
}
}