Secondary Diagonal Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$, print an $n$-by-$n$ grid. Row and column indices start at 1. Print # if $i+j=n+1$ and . otherwise, with no spaces between characters.

Input

One line contains integer $n$.

Output

Print $n$ lines of $n$ characters.

Subtasks

• Subtask 1 (20%): $1\le n\le 3$.

• Subtask 2 (30%): $1\le n\le 9$.

• Subtask 3 (50%): $1\le n\le 30$.

Examples

Example 1

Input:

3

Output:

..#
.#.
#..

Explanation:

The marked cell in row i is at column n+1-i. For this sample, the input is 3; the displayed rows follow these rules exactly.

Example 2

Input:

1

Output:

#

Explanation:

The marked cell in row i is at column n+1-i. For this sample, the input is 1; the displayed rows follow these rules exactly.