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[] args){
	Scanner scan = new Scanner(System.in);

	int h = scan.nextInt();
	int w = scan.nextInt();
	String[] s = new String[h+2];
	for(int i = 1; i < h+1; i++){
	    s[i] = scan.next();
	}

	/* 上端と下端 */
	s[0] = "#";
	s[h+1] = "#";

	/* '#'追加操作 */
	for(int i = 0; i < h+2; i++){
	    if(i == 0 || i == h+1){
		for(int j = 0; j < w+1; j++){
		    s[i] += "#";
		}
	    }else{
		s[i] = "#"+s[i]+"#";
	    }
	}

	/* 出力 */
	for(int i = 0; i < h+2; i++){
	    System.out.println(s[i]);
	}
    }
}