


from __future__ import annotations

from decimal import Decimal

from numpy import array






def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		lowerCAmelCase__       :      Optional[int]   					= Decimal

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

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

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

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

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



from __future__ import annotations






def 					lowerCamelCase_   (	_a     ,       _a     ,       _a     ,       _a	):  # noqa: E741




		"""simple docstring"""






		while r - l > 1:
				lowerCAmelCase__       :      Any   					= (l + r) // 2
				if v[m] >= key:
						lowerCAmelCase__       :      int   					= m
				else:
						lowerCAmelCase__       :      Tuple   					= m  # noqa: E741
		return r






def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		if len(_a	) == 0:
				return 0

		lowerCAmelCase__       :      Optional[int]   					= [0] * len(_a	)
		lowerCAmelCase__       :      List[Any]   					= 1

		lowerCAmelCase__       :      int   					= v[0]

		for i in range(1     ,       len(_a	)	):
				if v[i] < tail[0]:
						lowerCAmelCase__       :      str   					= v[i]
				elif v[i] > tail[length - 1]:
						lowerCAmelCase__       :      Any   					= v[i]
						length += 1
				else:
						lowerCAmelCase__       :      int   					= v[i]

		return length


if __name__ == "__main__":
		import doctest

		doctest.testmod()




