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);
    
		// 整数の入力
		int h = sc.nextInt();
		int w = sc.nextInt();
        String edge = "";
        for(int i = 0; i < w + 2; i++) {
          edge += "#";
        }
        // 出力
		System.out.println(edge);
       
        for(int i = 0; i < h; i++) {
          // 文字列の入力
		  String s = sc.next();
          String ans = "#";
          ans += s + "#";
          // 出力
		  System.out.println(ans);
        }
      
        // 出力
		System.out.println(edge);
	}
}