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 sc = new Scanner(System.in);
        int h=sc.nextInt();
        int w=sc.nextInt();
        System.out.println(charp(w+2));
        for(int i=0;i<h;i++){
            System.out.println("#"+sc.next()+"#");
        }
        System.out.println(charp(w+2));
    }
    static String charp(int input){
        String output="";
        for(int i=0;i<input;i++){
            output+="#";
        }
        return output;
    }
}