

'''simple docstring'''



from __future__ import annotations

from decimal import Decimal

from numpy import array
def 						__lowerCamelCase	(       __snake_case					:		list[list[float]]	)	->							list[list[float]]:






						"""simple docstring"""





						A__					:       List[Any]     =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__					:       List[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__					:       Optional[Any]     =[[0.0, 0.0], [0.0, 0.0]]
												A__					:       List[Any]     =matrix[1][1], matrix[0][0]
												A__					:       Optional[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__					:       Optional[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__					:       List[str]     =[
												    [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__					:       int     =(d(matrix[1][1]	) * d(matrix[2][2]	)) - (
												    d(matrix[1][2]	) * d(matrix[2][1]	)
												)
												A__					:       Any     =-(
												    (d(matrix[1][0]	) * d(matrix[2][2]	)) - (d(matrix[1][2]	) * d(matrix[2][0]	))
												)
												A__					:       str     =(d(matrix[1][0]	) * d(matrix[2][1]	)) - (
												    d(matrix[1][1]	) * d(matrix[2][0]	)
												)
												A__					:       Optional[Any]     =-(
												    (d(matrix[0][1]	) * d(matrix[2][2]	)) - (d(matrix[0][2]	) * d(matrix[2][1]	))
												)
												A__					:       Tuple     =(d(matrix[0][0]	) * d(matrix[2][2]	)) - (
												    d(matrix[0][2]	) * d(matrix[2][0]	)
												)
												A__					:       Tuple     =-(
												    (d(matrix[0][0]	) * d(matrix[2][1]	)) - (d(matrix[0][1]	) * d(matrix[2][0]	))
												)
												A__					:       str     =(d(matrix[0][1]	) * d(matrix[1][2]	)) - (
												    d(matrix[0][2]	) * d(matrix[1][1]	)
												)
												A__					:       List[Any]     =-(
												    (d(matrix[0][0]	) * d(matrix[1][2]	)) - (d(matrix[0][2]	) * d(matrix[1][0]	))
												)
												A__					:       Optional[int]     =(d(matrix[0][0]	) * d(matrix[1][1]	)) - (
												    d(matrix[0][1]	) * d(matrix[1][0]	)
												)

												# Transpose the cofactor matrix (Adjoint matrix)
												A__					:       Dict     =array(__snake_case	)
												for i in range(3	):
																		for j in range(3	):
																								A__					:       Tuple     =cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
												A__					:       Optional[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'''



from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors
def 						__lowerCamelCase	(       __snake_case					:		int	)	->							int:






						"""simple docstring"""





						A__					:       List[Any]     =prime_factors(__snake_case	)
						if is_square_free(__snake_case	):
												return -1 if len(__snake_case	) % 2 else 1
						return 0


if __name__ == "__main__":
		import doctest

		doctest.testmod()

