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);
		StringBuilder sb;
		int rr = sc.nextInt();
		int cc = sc.nextInt();
		sc.nextLine();
		char[][] res = new char[rr+2][cc+2];
		String temp = "";
		for(int i=0; i<rr+2; i++) {
			sb = new StringBuilder();
			if(i>0 && i<rr+1) temp = sc.nextLine();
			for(int j=0; j<cc+2; j++) {
				if(i==0 || j==0 || i==rr+1 || j==cc+1) {
					sb.append('#');
				}
				else {
					sb.append(temp.charAt(j-1));
				}
			}
			System.out.println(sb.toString());
		}
	}
}