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) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		int y = sc.nextInt();
		String[] m =new String[x];
		String tmp ="";
		for (int i=0;i<m.length;i++){
			m[i] = sc.next();
		}
		for (int i=0;i<x+2;i++){
			if(i>0&&i<x+1){
				tmp = m[i-1];
			}
			for (int j=0;j<y+2;j++){
				if(i==0||i==x+1){
					System.out.print("#");
				}
				else if (j==0||j==y+1){
					System.out.print("#");
				}
				else System.out.print(tmp.charAt(j-1));
			}
			System.out.println();
		}
	}

}