





"""simple docstring"""



from __future__ import annotations

from decimal import Decimal

from numpy import array







def 		__lowercase					(       snake_case_  :  list[list[float]]						)       ->list[list[float]]:



    '''simple docstring'''







    __A   :						str									=					Decimal

    # Check if the provided matrix has 2 rows and 2 columns
    # since this implementation only works for 2x2 matrices
    if len(snake_case_						) == 2 and len(matrix[0]						) == 2 and len(matrix[1]						) == 2:
        # Calculate the determinant of the matrix
        __A   :						Union[str, Any]									=					float(
            d(matrix[0][0]						) * d(matrix[1][1]						) - d(matrix[1][0]						) * d(matrix[0][1]						)						)
        if determinant == 0:
            raise ValueError('''This matrix has no inverse.'''						)

        # Creates a copy of the matrix with swapped positions of the elements
        __A   :						Union[str, Any]									=					[[0.0, 0.0], [0.0, 0.0]]
        __A   :						Dict									=					matrix[1][1], matrix[0][0]
        __A   :						Union[str, Any]									=					-matrix[1][0], -matrix[0][1]

        # Calculate the inverse of the matrix
        return [
            [(float(d(snake_case_						)						) / determinant) or 0.0 for n in row] for row in swapped_matrix
        ]
    elif (
        len(snake_case_						) == 3
        and len(matrix[0]						) == 3
        and len(matrix[1]						) == 3
        and len(matrix[2]						) == 3
    ):
        # Calculate the determinant of the matrix using Sarrus rule
        __A   :						Any									=					float(
            (
                (d(matrix[0][0]						) * d(matrix[1][1]						) * d(matrix[2][2]						))
                + (d(matrix[0][1]						) * d(matrix[1][2]						) * d(matrix[2][0]						))
                + (d(matrix[0][2]						) * d(matrix[1][0]						) * d(matrix[2][1]						))
            )
            - (
                (d(matrix[0][2]						) * d(matrix[1][1]						) * d(matrix[2][0]						))
                + (d(matrix[0][1]						) * d(matrix[1][0]						) * d(matrix[2][2]						))
                + (d(matrix[0][0]						) * d(matrix[1][2]						) * d(matrix[2][1]						))
            )						)
        if determinant == 0:
            raise ValueError('''This matrix has no inverse.'''						)

        # Creating cofactor matrix
        __A   :						Union[str, Any]									=					[
            [d(0.0						), d(0.0						), d(0.0						)],
            [d(0.0						), d(0.0						), d(0.0						)],
            [d(0.0						), d(0.0						), d(0.0						)],
        ]
        __A   :						str									=					(d(matrix[1][1]						) * d(matrix[2][2]						)) - (
            d(matrix[1][2]						) * d(matrix[2][1]						)
        )
        __A   :						Tuple									=					-(
            (d(matrix[1][0]						) * d(matrix[2][2]						)) - (d(matrix[1][2]						) * d(matrix[2][0]						))
        )
        __A   :						Union[str, Any]									=					(d(matrix[1][0]						) * d(matrix[2][1]						)) - (
            d(matrix[1][1]						) * d(matrix[2][0]						)
        )
        __A   :						Any									=					-(
            (d(matrix[0][1]						) * d(matrix[2][2]						)) - (d(matrix[0][2]						) * d(matrix[2][1]						))
        )
        __A   :						List[str]									=					(d(matrix[0][0]						) * d(matrix[2][2]						)) - (
            d(matrix[0][2]						) * d(matrix[2][0]						)
        )
        __A   :						Optional[Any]									=					-(
            (d(matrix[0][0]						) * d(matrix[2][1]						)) - (d(matrix[0][1]						) * d(matrix[2][0]						))
        )
        __A   :						Dict									=					(d(matrix[0][1]						) * d(matrix[1][2]						)) - (
            d(matrix[0][2]						) * d(matrix[1][1]						)
        )
        __A   :						str									=					-(
            (d(matrix[0][0]						) * d(matrix[1][2]						)) - (d(matrix[0][2]						) * d(matrix[1][0]						))
        )
        __A   :						List[str]									=					(d(matrix[0][0]						) * d(matrix[1][1]						)) - (
            d(matrix[0][1]						) * d(matrix[1][0]						)
        )

        # Transpose the cofactor matrix (Adjoint matrix)
        __A   :						List[Any]									=					array(snake_case_						)
        for i in range(3						):
            for j in range(3						):
                __A   :						Union[str, Any]									=					cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
        __A   :						Union[str, Any]									=					array(snake_case_						)
        for i in range(3						):
            for j in range(3						):
                inverse_matrix[i][j] /= d(snake_case_						)

        # Calculate the inverse of the matrix
        return [[float(d(snake_case_						)						) or 0.0 for n in row] for row in inverse_matrix]
    raise ValueError('''Please provide a matrix of size 2x2 or 3x3.'''						)











"""simple docstring"""



import math
from collections.abc import Iterator
from itertools import takewhile







def 		__lowercase					(       snake_case_  :  int						)       ->bool:



    '''simple docstring'''







    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5    ,int(math.sqrt(snake_case_						) + 1						)    ,6						):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def 		__lowercase					(       )       ->Iterator[int]:



    '''simple docstring'''







    __A   :						int									=					2
    while True:
        if is_prime(snake_case_						):
            yield num
        num += 1







def 		__lowercase					(       snake_case_  :  int = 2000000						)       ->int:



    '''simple docstring'''







    return sum(takewhile(lambda snake_case_						: x < n    ,prime_generator()						)						)


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




