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();
		String[] c = new String[H+1];

		for (int i = 0; i <= H; i++) {
			c[i] = "#" + sc.nextLine() + "#";
		}
		for (int i = 0; i <= W; i++) {
			System.out.print("#");
		}

		System.out.println("#");
		
		for (int i = 1; i <= H; i++) {
			System.out.println(c[i]);
		}
		
		for (int i = 0; i <= W+1; i++) {
			System.out.print("#");
		}

		sc.close();
	}
}