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 scanner = new Scanner (System.in);
    
    int H = scanner.nextInt();
    int W = scanner.nextInt();
    String[] list = new String[H];
    
    scanner.nextLine();
    for(int i=0; i<H; i++){
      String temp = scanner.nextLine();
      list[i] = temp;
    }
    
    for(int i=0; i<W+2; i++){
      System.out.print("#");
    }
    System.out.println();
    
    for (int i=0; i<H; i++){
      System.out.print("#");
      System.out.print(list[i]);
      System.out.println("#");
    }
    for(int i=0; i<W+2; i++){
      System.out.print("#");
    }
    System.out.println();
  }
}