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.io.*;
import java.util.*;

public class Main{
	public static void main(String[] args)throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] s = br.readLine().split(" ");
		int Y = Integer.parseInt(s[0]);
		int X = Integer.parseInt(s[1])+2;
		String line =  "";
		for(int i = 0;i<X;i++){
		    line = line + "#";
		}
		System.out.println(line);
	    
	    for(int i = 0;i<Y;i++){
	        System.out.println("#" + br.readLine() + "#");
	    }
	    System.out.println(line);
	}
	
}