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 {

    private static Scanner scan = new Scanner(System.in);

    public static void main(String[] args) {
	int H = Integer.parseInt(scan.next());
	int W = Integer.parseInt(scan.next());

	StringBuilder str = new StringBuilder();
	for (int i = 0; i < W+2; i++) {
	    str.append("#");
	}
	str.append("\n");
	for (int i = 0; i < H; i++) {
	    str.append("#");
	    str.append(scan.next());
	    str.append("#\n");
	}
	for (int i = 0; i < W+2; i++) {
	    str.append("#");
	}
	System.out.println(str.toString());
	scan.close();
    }
}