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 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
		int H=scan.nextInt();
		int W=scan.nextInt();

		String[][] result = new String[H+2][W+2];

		for(int i=0;i<H+2;i++){
			for(int j=0;j<W+2;j++){

				result[i][j]="#";


			}
		}


		String[] sub = new String[H];
		for(int i=0;i<H;i++){
			sub[i]=scan.next();
			for(int j=0;j<W;j++){
				result[i+1][j+1]=sub[i].substring(j, j+1);
			}


		}

		for(int i=0;i<H+2;i++){
			for(int j=0;j<W+2;j++){

				System.out.print(result[i][j]);


			}
			System.out.println();
		}
	}

}