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();
    
    for (int i = 0; i < h+2; i++) {
       String s = "";
       if (1 <= i && i <= h) {
         s = sc.next();
       }
       for (int j = 0; j < w+2; j++) {
         char c = '#';
         if (1 <= i && i <= h && 1 <= j && j <= w) {
            c = s.charAt(j-1);
         }
         System.out.print(c);
      }
      System.out.println();
    }
  }
}