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.*;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int H = sc.nextInt();
        int W = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for(int i=1;i<=W+2;i++) sb.append("#");
        System.out.println(sb.toString());
        for(int i=1;i<=H;i++){
            String cur = sc.next();
            StringBuilder now = new StringBuilder();
            now.append("#");
            now.append(cur);
            now.append("#");
            System.out.println(now.toString());
        }
        System.out.println(sb.toString());
    }
}