import itertools as it
from typing import Any, Iterator

from ..base import BaseSolver


def process(
    grid: list[list[int]], current: tuple[int, int]
) -> set[tuple[tuple[int, int], ...]]:
    row, col = current
    value = grid[row][col] + 1

    if grid[row][col] == 9:
        return {((row, col),)}

    return {
        ((row, col),) + path
        for i, j in ((row - 1, col), (row, col + 1), (row + 1, col), (row, col - 1))
        if 0 <= i < len(grid) and 0 <= j < len(grid[i]) and grid[i][j] == value
        for path in process(grid, (i, j))
    }


class Solver(BaseSolver):
    def solve(self, input: str) -> Iterator[Any]:
        grid = [[int(col) for col in row] for row in input.splitlines()]

        paths = {
            (i, j): process(grid, (i, j))
            for i, j in it.product(range(len(grid)), range(len(grid[0])))
            if grid[i][j] == 0
        }

        yield sum(len({path[-1] for path in paths[head]}) for head in paths)
        yield sum(len(paths_of) for paths_of in paths.values())