




import math




def 							_UpperCAmelCase  (UpperCamelCase_ : int       ):
				'''simple docstring'''
				assert isinstance(UpperCamelCase_      ,    UpperCamelCase_       ) 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

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





def 							_UpperCAmelCase  (UpperCamelCase_ : Any      ,    UpperCamelCase_ : Union[str, Any]=1      ,    **UpperCamelCase_ : int       ):
				'''simple docstring'''
				_lowerCAmelCase    :    Tuple										=      factor * value
				_lowerCAmelCase    :    Any										=      value

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

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







from __future__ import annotations

from decimal import Decimal

from numpy import array




def 							_UpperCAmelCase  (UpperCamelCase_ : list[list[float]]       ):
				'''simple docstring'''
				_lowerCAmelCase    :    int										=      Decimal

				# Check if the provided matrix has 2 rows and 2 columns
				# since this implementation only works for 2x2 matrices
				if len(UpperCamelCase_       ) == 2 and len(matrix[0]       ) == 2 and len(matrix[1]       ) == 2:
								# Calculate the determinant of the matrix
								_lowerCAmelCase    :    Optional[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
								_lowerCAmelCase    :    Union[str, Any]										=      [[0.0, 0.0], [0.0, 0.0]]
								_lowerCAmelCase					,    _lowerCAmelCase    :    Any										=      matrix[1][1], matrix[0][0]
								_lowerCAmelCase					,    _lowerCAmelCase    :    Optional[Any]										=      -matrix[1][0], -matrix[0][1]

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

								# Transpose the cofactor matrix (Adjoint matrix)
								_lowerCAmelCase    :    List[str]										=      array(UpperCamelCase_       )
								for i in range(3       ):
												for j in range(3       ):
																_lowerCAmelCase    :    List[Any]										=      cofactor_matrix[j][i]

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

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

