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 sc = new Scanner(System.in);

		int H = sc.nextInt();
		int W = sc.nextInt();
		sc.nextLine();
		String[] img = new String[H];
		char sp = '#';

		for(int h = 0; h < H; h++){
			img[h] = sc.nextLine();
		}
		sc.close();

		StringBuilder sb = new StringBuilder();
		for(int w = 0; w < W+2; w++){
			sb.append(sp);
		}
		String sharpLine = sb.toString();
		System.out.println(sharpLine);
		for(int h = 0; h < H; h++){
			System.out.print(sp);
			System.out.print(img[h]);
			System.out.println(sp);
		}
		System.out.println(sharpLine);
	}

}