Chessboard is a board of n × n squares arranged in two alternating colors (black and white). Top left square is white. You are given board size n. Output an image of a chessboard, with black and white squares marked with '#' and '.' characters, respectively.

Input

The only line of input contains an integer n (1 ≤ n ≤ 9).

Output

Output an image of n × n chessboard.

Examples

Input

4


Output

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

Source: codeforces | Difficulty: HARD


Solutions: