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.*;
import java.lang.Math.*;
 
class Main{
  public static void main(String args[]){
    Scanner sc = new Scanner(System.in);
    int a = sc.nextInt();
    int b = sc.nextInt();
    
    String str[] = new String[a];
    for(int i=0;i<b+2;i++){
      System.out.print("#");
    }
    
    System.out.println();
    
    for(int i=0;i<a;i++){
      str[i] = sc.next();
      System.out.println("#" + str[i] + "#");
    }
    
    for(int i=0;i<b+2;i++){
      System.out.print("#");
    }
    
    System.out.println();
    
  }
}