Shortest 8-Directional Clear Path Across a Binary Grid

You are given an `n x n` grid in which every cell is `0` (open) or `1` (blocked). Return the length of the shortest clear path from the top-left cell `(0, 0)` to the bottom-right cell `(n - 1, n - 1)`, or `-1` if no clear path exists. A clear path is a sequence of open cells that starts at `(0, 0)` and ends at `(n - 1, n - 1)`, in which every two consecutive cells are 8-directionally adjacent: they share an edge or a corner. The length of a path is the number of cells it visits, counting both endpoints. ### Function Signature ```python def shortest_clear_path(grid: list[list[int]]) -> int: ``` ### Rules - From cell `(r, c)` a path may move to any of the up to eight cells `(r + dr, c + dc)` with `dr` and `dc` each in `{-1, 0, 1}`, not both `0`, as long as the target cell is inside the grid and open. - A diagonal move is allowed even when both cells that share an edge with the two cells involved are blocked; touching at a corner is enough. - If `grid[0][0]` or `grid[n - 1][n - 1]` is `1`, return `-1`. - If `n = 1` and the only cell is open, return `1`. ### Constraints - `1 <= n <= 500`, where `n = len(grid)` and `len(grid[i]) == n` for every row `i` - Every cell is `0` or `1`. - Any answer other than `-1` is at most `n * n = 250,000`, which fits in a 32-bit signed integer. ### Examples **Example 1** ```text Input: grid = [[0, 1, 1], [1, 0, 1], [1, 1, 0]] Output: 3 ``` The path `(0, 0) -> (1, 1) -> (2, 2)` moves diagonally twice, even though every cell beside those moves is blocked. **Example 2** ```text Input: grid = [[0, 0, 1, 0], [1, 1, 0, 1], [1, 1, 1, 0], [1, 1, 1, 0]] Output: 5 ``` The path `(0, 0) -> (0, 1) -> (1, 2) -> (2, 3) -> (3, 3)` visits 5 cells. A 4-cell path would need three diagonal moves through `(1, 1)` and `(2, 2)`, which are blocked. **Example 3** ```text Input: grid = [[0, 0, 0], [1, 1, 1], [0, 0, 0]] Output: -1 ``` The middle row is entirely blocked, so no path can cross it.