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();

        String[] a = new String[H];
        for (int i = 0; i < H ; i++) {
            a[i] = sc.next();
        }

        for (int i = 0; i <= H + 1; i++) {
            if (i == 0 || i == H + 1) {
                for (int j = 0; j <= W + 1; j++) {
                    System.out.print("#");
                }
                System.out.println();
            }else{
                System.out.println("#" + a[i - 1] + "#");
            }
        }
    }
}