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 a[] = new String[h+2];
    String b = "";

    for (int j = 0; j < w+2; j++) {
      b += "#";
    }

    for (int i = 0; i < h+2; i++) {
      if (i == 0 || i == h+1) {
        a[i] = b;
      } else {
        a[i] = "#" + sc.next() + "#";
      }
    }

    for (int i = 0; i < (h+2); i++) {
      System.out.println(a[i]);
    }
  }  
}