Main Diagonal Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$, print an $n$-by-$n$ grid. The cell $(i,j)$ is # when $i=j$ and . otherwise. Indices begin at 1 and characters have no separating spaces.

Input

One line contains integer $n$.

Output

Print $n$ lines each 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:

Exactly the positions with equal row and column numbers are marked. For this sample, the input is 3; the displayed rows follow these rules exactly.

Example 2

Input:

1

Output:

#

Explanation:

Exactly the positions with equal row and column numbers are marked. For this sample, the input is 1; the displayed rows follow these rules exactly.