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 scan = new Scanner(System.in);
        int h = scan.nextInt();
        int w = scan.nextInt();
        String[] str = new String[h+1];
        for(int i=0; i<h+1; i++) {
            str[i] = scan.nextLine();
        }

            for(int j=0; j<w+2; j++) {
                System.out.print("#");
            }
            System.out.println();

            for(int k=1; k<h+1; k++) {
                System.out.println("#" + str[k] + "#");
            }

            for(int j=0; j<w+2; j++) {
                System.out.print("#");
            }
        System.out.println();


    }

}