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 CPP):

Solution:
#include<stdio.h>
int main()
{
	int h,w,i,j;
	scanf("%d %d", &h, &w);
	char c;
	for(i=0; i<=h+1; i++)
	{
		for(j=0; j<=w+1; j++)
		{
			if(i==0 || i==h+1 || j==0 || j==w+1)
				printf("#");
			else
			{
				scanf(" %c", &c);
				printf("%c",c);
			}
		}
		puts("");
	}
	return 0;
}