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) {
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		for(int i =0;i < h+2;i++) {
			StringBuilder sb = new StringBuilder();
			for(int j =0;j < w+2;j++) {
				if(i ==0 || i ==h+1 || j ==0 || j == w+1) {
					sb.append("#");
				}else {
					sb.append(sc.next());
					j+=w-1;
				}
			}
			System.out.println(sb);
		}
	}
}