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 cin = new Scanner(System.in);

		int H = cin.nextInt();
		int W = cin.nextInt();
		String tmp = "";
		char graph[][] = new char[H+2][W+2];

		for(int i=0;i<H+2;i++){
			if(i!=0&&i!=H+1){
				tmp = cin.next();
			}
			for(int j=0;j<W+2;j++){
				if(i!=0&&i!=H+1){
					if(j!=0&&j!=W+1){
						graph[i][j] = tmp.charAt(j-1);
					}else{
						graph[i][j] = '#';
					}
				}else{
					graph[i][j] = '#';
				}
			}
		}

		for(int k=0;k<H+2;k++){
			for(int l=0;l<W+2;l++){
				System.out.print(graph[k][l]);
			}
			System.out.println("");
		}
	}
}