






"""simple docstring"""






from math import isqrt



def       _A    (__a							)				-> list[int]:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	[True] * max_number
    for i in range(2					,       isqrt(max_number - 1							) + 1							):
        if is_prime[i]:
            for j in range(i**2					,       __a					,       __a							):
                SCREAMING_SNAKE_CASE_   :						Tuple							=	False

    return [i for i in range(2					,       __a							) if is_prime[i]]



def       _A    (__a = 10**8							)				-> int:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_   :						Any							=	calculate_prime_numbers(max_number // 2							)

    SCREAMING_SNAKE_CASE_   :						List[str]							=	0
    SCREAMING_SNAKE_CASE_   :						Any							=	0
    SCREAMING_SNAKE_CASE_   :						List[str]							=	len(__a							) - 1
    while left <= right:
        while prime_numbers[left] * prime_numbers[right] >= max_number:
            right -= 1
        semiprimes_count += right - left + 1
        left += 1

    return semiprimes_count


if __name__ == "__main__":
  print(f'''{solution() = }''')










"""simple docstring"""






from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst



def       _A    ()				-> Union[str, Any]:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_   :						Tuple							=	9, 14  # noqa: F841
    SCREAMING_SNAKE_CASE_   :						Tuple							=	[
        [0, 1, 4],
        [0, 7, 8],
        [1, 2, 8],
        [7, 8, 7],
        [7, 6, 1],
        [2, 8, 2],
        [8, 6, 6],
        [2, 3, 7],
        [2, 5, 4],
        [6, 5, 2],
        [3, 5, 14],
        [3, 4, 9],
        [5, 4, 10],
        [1, 7, 11],
    ]

    SCREAMING_SNAKE_CASE_   :						Dict							=	defaultdict(__a							)
    for nodea, nodea, cost in edges:
        adjancency[nodea].append([nodea, cost]							)
        adjancency[nodea].append([nodea, cost]							)

    SCREAMING_SNAKE_CASE_   :						Any							=	mst(__a							)

    SCREAMING_SNAKE_CASE_   :						Optional[int]							=	[
        [7, 6, 1],
        [2, 8, 2],
        [6, 5, 2],
        [0, 1, 4],
        [2, 5, 4],
        [2, 3, 7],
        [0, 7, 8],
        [3, 4, 9],
    ]

    for answer in expected:
        SCREAMING_SNAKE_CASE_   :						Dict							=	tuple(answer[:2]							)
        SCREAMING_SNAKE_CASE_   :						Optional[int]							=	tuple(edge[::-1]							)
        assert edge in result or reverse in result


