"""simple docstring"""




import numpy as np

import datasets


__lowerCamelCase											=  "\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n"

__lowerCamelCase											=  "\\n@article{de2000mahalanobis,\n  title={The mahalanobis distance},\n  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},\n  journal={Chemometrics and intelligent laboratory systems},\n  volume={50},\n  number={1},\n  pages={1--18},\n  year={2000},\n  publisher={Elsevier}\n}\n"

__lowerCamelCase											=  "\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {'mahalanobis': array([0.5])}\n"




@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,						_KWARGS_DESCRIPTION )
class     UpperCamelCase__(			datasets.Metric ):





						def 				snake_case__	(       self     )					->				Tuple:
													return datasets.MetricInfo(
													    description=_DESCRIPTION		,citation=_CITATION		,inputs_description=_KWARGS_DESCRIPTION		,features=datasets.Features(
													        {
													            'X': datasets.Sequence(datasets.Value('float'		,id='sequence'     )		,id='X'     ),
													        }     )		,)





						def 				snake_case__	(       self		,__UpperCAmelCase		,__UpperCAmelCase     )					->				str:
													# convert to numpy arrays
													A__	     =							np.array(lowercase_     )
													A__	     =							np.array(lowercase_     )

													# Assert that arrays are 2D
													if len(X.shape     ) != 2:
																				raise ValueError('Expected `X` to be a 2D vector'     )
													if len(reference_distribution.shape     ) != 2:
																				raise ValueError('Expected `reference_distribution` to be a 2D vector'     )
													if reference_distribution.shape[0] < 2:
																				raise ValueError(
																				    'Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension'     )

													# Get mahalanobis distance for each prediction
													A__	     =							X - np.mean(lowercase_     )
													A__	     =							np.cov(reference_distribution.T     )
													try:
																				A__	     =							np.linalg.inv(lowercase_     )
													except np.linalg.LinAlgError:
																				A__	     =							np.linalg.pinv(lowercase_     )
													A__	     =							np.dot(lowercase_		,lowercase_     )
													A__	     =							np.dot(lowercase_		,X_minus_mu.T     ).diagonal()

													return {"mahalanobis": mahal_dist}






"""simple docstring"""




def   UpperCAmelCase					(	UpperCamelCase__				):






							"""simple docstring"""





							if len(UpperCamelCase__				) <= 1:
														return [tuple(UpperCamelCase__				)]

							A__	     =							[]

							def generate(UpperCamelCase__       ,    UpperCamelCase__				):
														if k == 1:
																					res.append(tuple(arr[:]				)				)
																					return

														generate(k - 1       ,    UpperCamelCase__				)

														for i in range(k - 1				):
																					if k % 2 == 0:  # k is even
																												A__     ,  A__	     =							arr[k - 1], arr[i]
																					else:  # k is odd
																												A__     ,  A__	     =							arr[k - 1], arr[0]
																					generate(k - 1       ,    UpperCamelCase__				)

							generate(len(UpperCamelCase__				)       ,    UpperCamelCase__				)
							return res


if __name__ == "__main__":
				__lowerCamelCase											=  input("Enter numbers separated by a comma:\n").strip()
				__lowerCamelCase											=  [int(item) for item in user_input.split(",")]
				print(heaps(arr))





