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.*;
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int h = scan.nextInt();
        int w = scan.nextInt();
        char[][] array = new char[h+2][w+2];

        for(int i = 0;i < h+2;i++){
            Arrays.fill(array[i], '#');
        }
        for(int i = 0;i < h;i++){
            String s = scan.next();
            for(int j = 0;j < w;j++){
                array[i+1][j+1] = s.charAt(j);
            }
        }
        for(int i = 0;i < h+2;i++){
            for(int j = 0;j < w+2;j++){
                System.out.print(array[i][j]);
            }
            System.out.println();
        }
    }
}