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.io.*;

public class Main{
  public static void main(String[] args){
    try{
      BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
      String[] t = r.readLine().split(" ");
	  int H = Integer.parseInt(t[0]);
      int W = Integer.parseInt(t[1]);
	  char[] c = new char[W+2];
      Arrays.fill(c, '#');
      StringBuilder sb = new StringBuilder();
      sb.append(String.valueOf(c)+"\n");
      for(int i = 0; i < H; i++){
        sb.append("#");
        sb.append(r.readLine());
        sb.append("#\n");
      }
      sb.append(String.valueOf(c));
      System.out.println(sb);
    } catch(IOException e){}
  }
}