



'''simple docstring'''




from __future__ import annotations

from decimal import Decimal

from numpy import array



def    __lowerCamelCase						(      _lowercase	)   ->    list[list[float]]:
							UpperCAmelCase  :	Dict							  =	Decimal

							# Check if the provided matrix has 2 rows and 2 columns
							# since this implementation only works for 2x2 matrices
							if len(_lowercase	) == 2 and len(matrix[0]	) == 2 and len(matrix[1]	) == 2:
														# Calculate the determinant of the matrix
														UpperCAmelCase  :	Dict							  =	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
														UpperCAmelCase  :	int							  =	[[0.0, 0.0], [0.0, 0.0]]
														UpperCAmelCase  :	Any							  =	matrix[1][1], matrix[0][0]
														UpperCAmelCase  :	Any							  =	-matrix[1][0], -matrix[0][1]

														# Calculate the inverse of the matrix
														return [
														    [(float(d(_lowercase	)	) / determinant) or 0.0 for n in row] for row in swapped_matrix
														]
							elif (
							    len(_lowercase	) == 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
														UpperCAmelCase  :	Tuple							  =	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
														UpperCAmelCase  :	Optional[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	)],
														]
														UpperCAmelCase  :	List[str]							  =	(d(matrix[1][1]	) * d(matrix[2][2]	)) - (
														    d(matrix[1][2]	) * d(matrix[2][1]	)
														)
														UpperCAmelCase  :	int							  =	-(
														    (d(matrix[1][0]	) * d(matrix[2][2]	)) - (d(matrix[1][2]	) * d(matrix[2][0]	))
														)
														UpperCAmelCase  :	Optional[int]							  =	(d(matrix[1][0]	) * d(matrix[2][1]	)) - (
														    d(matrix[1][1]	) * d(matrix[2][0]	)
														)
														UpperCAmelCase  :	List[Any]							  =	-(
														    (d(matrix[0][1]	) * d(matrix[2][2]	)) - (d(matrix[0][2]	) * d(matrix[2][1]	))
														)
														UpperCAmelCase  :	Dict							  =	(d(matrix[0][0]	) * d(matrix[2][2]	)) - (
														    d(matrix[0][2]	) * d(matrix[2][0]	)
														)
														UpperCAmelCase  :	List[str]							  =	-(
														    (d(matrix[0][0]	) * d(matrix[2][1]	)) - (d(matrix[0][1]	) * d(matrix[2][0]	))
														)
														UpperCAmelCase  :	List[Any]							  =	(d(matrix[0][1]	) * d(matrix[1][2]	)) - (
														    d(matrix[0][2]	) * d(matrix[1][1]	)
														)
														UpperCAmelCase  :	List[Any]							  =	-(
														    (d(matrix[0][0]	) * d(matrix[1][2]	)) - (d(matrix[0][2]	) * d(matrix[1][0]	))
														)
														UpperCAmelCase  :	Union[str, Any]							  =	(d(matrix[0][0]	) * d(matrix[1][1]	)) - (
														    d(matrix[0][1]	) * d(matrix[1][0]	)
														)

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

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
														UpperCAmelCase  :	Dict							  =	array(_lowercase	)
														for i in range(3	):
																					for j in range(3	):
																												inverse_matrix[i][j] /= d(_lowercase	)

        # Calculate the inverse of the matrix
														return [[float(d(_lowercase	)	) 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



def    __lowerCamelCase						(      _lowercase	)   ->    bool:
							assert isinstance(_lowercase			,       _lowercase	) and (
							    number >= 0
							), "'number' must been an int and positive"

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

							UpperCAmelCase  :	str							  =	range(3			,       int(math.sqrt(_lowercase	) + 1	)			,       2	)
							return not any(not number % i for i in odd_numbers	)



def    __lowerCamelCase						(      _lowercase			,       _lowercase=1			,       **_lowercase	)   ->    Union[str, Any]:
							UpperCAmelCase  :	Optional[int]							  =	factor * value
							UpperCAmelCase  :	List[Any]							  =	value

							while not is_prime(_lowercase	):
														value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

							if value == first_value_val:
														return next_prime(value + 1			,       **_lowercase	)
							return value

