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.Scanner;
import java.util.ArrayList;

public class Main {
	public static void main (String[] args) {
  Scanner sc = new Scanner(System.in);
  int h = sc.nextInt();
  int w = sc.nextInt();
  ArrayList<String> x = new ArrayList<String>();
  for(int i=0; i<h; i++){
    x.add(sc.next());
  }
  for(int j=0; j<h+2; j++){
    if(j==0 || j==h+1){
	for(int k=0; k<w+2; k++){
		System.out.print("#");
	}
        System.out.println("");
    }else{
	System.out.println("#" + x.get(j-1) + "#");
    }
}
}
}