Anti-Diagonal Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$, print an $n$-by-$n$ grid, 1-indexed. Print # exactly when $i+j=n+1$ and . elsewhere, without any spaces.

Input

One line contains integer $n$.

Output

Print $n$ rows, each containing exactly $n$ 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:

4

Output:

...#
..#.
.#..
#...

Explanation:

The marked cell in row i is at column n+1-i. For this sample, the input is 4; 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.