Count OPTIVER in a Letter Grid Across Rows, Columns and Reversed Readings

Given a rectangular grid of uppercase English letters, count how many times the word `OPTIVER` appears when read along a straight line of consecutive cells in any of these four directions: - left to right along a row; - right to left along a row (the word appears reversed in that row); - top to bottom along a column; - bottom to top along a column (the word appears reversed in that column). The grid is given as a list of strings: each string is one row, and all rows have the same length. ### Function Signature ```python def count_optiver(grid: list[str]) -> int: ``` ### Rules - An occurrence is a run of 7 consecutive cells in one row or one column whose letters, read in one of the four directions above, spell `OPTIVER` exactly. - Diagonal readings do not count, and a reading may not bend or wrap around the edge of the grid. - Occurrences are counted independently. The same cell may be part of several occurrences, for example a horizontal one and a vertical one that share the letter `O`. - An occurrence is identified by its starting cell (the cell holding `O`) and its direction. Because `OPTIVER` is not a palindrome, the same 7 cells can never match in both of their two opposite reading directions. - Return the total number of occurrences, or `0` if there are none (in particular whenever the grid has fewer than 7 rows and fewer than 7 columns). ### Constraints - `1 <= R <= 1000`, where `R = len(grid)` - `1 <= C <= 1000`, where `C = len(grid[i])` for every row `i` - Every character is an uppercase letter from `A` to `Z`. - The answer is at most `4 * R * C` (at most 4,000,000), which fits in a 32-bit signed integer. ### Examples **Example 1** ```text Input: grid = ["OPTIVERXREVITPO"] Output: 2 ``` Columns 0 through 6 read `OPTIVER` left to right, and columns 14 down to 8 read `OPTIVER` right to left. The grid has a single row, so no vertical occurrence is possible. **Example 2** ```text Input: grid = [ "OPTIVER", "PAAAAAA", "TAAAAAA", "IAAAAAA", "VAAAAAA", "EAAAAAA", "RAAAAAA" ] Output: 2 ``` Row 0 read left to right and column 0 read top to bottom both spell `OPTIVER`. They share the `O` in the top-left cell and count as two occurrences. Reading row 0 right to left, or column 0 bottom to top, gives `REVITPO`, which does not count. **Example 3** ```text Input: grid = [ "OXXXXXX", "XPXXXXX", "XXTXXXX", "XXXIXXX", "XXXXVXX", "XXXXXEX", "XXXXXXR" ] Output: 0 ``` The word appears only along the main diagonal, which is not one of the four allowed directions.