Count Straight-Line Occurrences of a Word in a Letter Grid, Rows and Columns Only

You are given a rectangular grid of lowercase letters and a target word. Count how many times the word appears in the grid when read in a straight line, either horizontally along a row or vertically down a column. Unlike the classic word-search puzzle, a match may not turn: all letters of one occurrence lie in consecutive cells of a single row or of a single column. ### Function Signature ```python def count_word_occurrences(grid: list[str], word: str) -> int: ``` ### Rules - `grid[i][j]` is the letter in row `i`, column `j`. Rows are numbered from the top and columns from the left. - An occurrence is a starting cell together with a direction, either rightward along the row or downward along the column, such that the `len(word)` consecutive cells read from the start in that direction spell `word` exactly. - Only left-to-right and top-to-bottom readings count. Reversed readings (right to left, bottom to top) and diagonals do not. - Occurrences may overlap and share cells. Each distinct pair of starting cell and direction counts once; for example, `"aa"` occurs twice in a row that reads `"aaa"`. - If `word` has exactly one letter, the rightward and downward readings from a cell are the same single cell, so each cell equal to that letter counts exactly once. - A reading that would run past the edge of the grid is not an occurrence. ### Constraints - `1 <= len(grid) <= 300` - `1 <= len(grid[i]) <= 300`, and every row has the same length. - `1 <= len(word) <= 300` - `grid` and `word` contain only lowercase English letters `a` to `z`. - The result is an integer from `0` to `2 * len(grid) * len(grid[0])`, so at most `180000`, and it is uniquely determined by the input. ### Examples **Example 1** - Input: `grid = ["cat", "abx", "tat"]`, `word = "cat"` - Output: `2` - Explanation: Row 0 reads `"cat"` from its first cell, and column 0 reads `c`, `a`, `t` downward from the same cell. They are different directions, so both count. No other row or column contains `"cat"`. **Example 2** - Input: `grid = ["aaa", "aab"]`, `word = "aa"` - Output: `5` - Explanation: Row 0 contains `"aa"` starting at columns 0 and 1, and row 1 contains it starting at column 0, for 3 horizontal occurrences. Columns 0 and 1 each read `a`, `a` downward, for 2 vertical occurrences. Column 2 reads `a`, `b`. **Example 3** - Input: `grid = ["ab", "dc"]`, `word = "abc"` - Output: `0` - Explanation: The letters `a`, `b`, `c` can be visited in order only by moving right and then down, which is a turn. Every row and column has just two cells, too short for a three-letter word.