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();
		char[][] grid = new char[H][W];
		for (int i=0; i<H; i++) {
			char[] t = sc.next().toCharArray();
			grid[i] = t;
		}
		for (int i=-1; i<=H; i++) {
			StringBuffer sb = new StringBuffer();
			for (int j=-1; j<=W; j++) {
				if (i==-1) sb.append("#");
				else if (j==-1) sb.append("#");
				else if (i==H) sb.append("#");
				else if (j==W) sb.append("#");
				else sb.append(grid[i][j]);
			}
			System.out.println(sb.toString());
		}
	}
}