EIT
To simplify the external independent testing (EIT) in literature, it was decided to include only questions with «yes» or «no» answers. The answer sheet is a grid with N rows and M columns, where each cell corresponds to a question. Students need to mark diagonally the cells they believe correspond to questions with a «no» answer (marking can be done along either of the two diagonals). To prevent scanning errors, no two diagonals should "merge," meaning they should not share an endpoint.
The authors of the variant need to determine the maximum number of questions with a «no» answer that can be included in the variant so that the answer sheet with correct answers can be accurately recognized by the computer.
Input
You will be given two natural numbers — the number of rows N and the number of columns M. The number of questions in the variant does not exceed 100, i.e., 1 ≤ N ∙ M ≤ 100.
Output
In the first line, output one number — the maximum number of questions with a «no» answer that can be included in the variant. In the next N lines, output M characters each — an example of such an answer sheet with correct answers that can be accurately recognized by the computer. No two diagonals should share endpoints. Use the following notations: . (dot) — an empty cell corresponding to a «yes» answer; / or \ — cells marked diagonally from right to left or left to right, corresponding to a «no» answer. If there are multiple ways to fill out the sheet, output any.