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.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	/** 囲む文字 */
	private static final char BORDER = '#';

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int h = scanner.nextInt(), w = scanner.nextInt();
			String[] a = IntStream.range(0, h).mapToObj(i -> scanner.next()).toArray(String[]::new);
			char[] border = new char[w + 2];
			Arrays.fill(border, BORDER);
			System.out.println(border);
			IntStream.range(0, h).forEach(i -> System.out.println(BORDER + a[i] + BORDER));
			System.out.println(border);
		}
	}
}