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;
public class Main {
    public static void main(String[] args) {
		try{
			Scanner sc = new Scanner(System.in);
			int H = sc.nextInt();
			int W = sc.nextInt();
			String[] result = new String[H+2];
			for(int i = 0 ; i < H+2; i++){
				if(i == 0 || i == H+1){
					StringBuilder str = new StringBuilder();
					for(int j = 0; j < W+2; j++){
						str.append("#");
					}
					result[i] = str.toString();
				}else{
					result[i] = "#" + sc.next() + "#";
				}
			}
			for(int i = 0; i < H+2; i++){
				System.out.println(result[i]);
			}
		}catch(Exception e){
			e.getMessage();
		}
	} 
}