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 = Integer.parseInt(sc.next()) + 2;
		int w = Integer.parseInt(sc.next());
		StringBuffer s = new StringBuffer();
		for (int i = 0; i < w; i++)
			s.append("#");
		String t = s.toString();
		String[][] ans = new String[h][3];
		for (int i = 0; i < h; i++) {
			ans[i][0] = "#";
			ans[i][2] = "#";
			if (i == 0 || i == h - 1)
				ans[i][1] = t;
			else
				ans[i][1] = sc.next();
		}
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < 3; j++)
				System.out.print(ans[i][j]);
			System.out.println("");
		}
	}
}