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();
        String[] moji = new String[h+1];
        String moji2="";
        
        
        for(int i =0;i<w+2;i++){
             moji2+="#";
        }

        for(int i = 1;i<h+1;i++){
            moji[i] = "#"+sc.next()+"#";
        }

        for(int i = 0;i<h+2;i++){
            if(i==0){
                System.out.println(moji2);
            }else if(i==(h+1)){
                System.out.println(moji2);
            }else{
                System.out.println(moji[i]);
            }
        }
    }
}