




"""simple docstring"""




import math






def  snake_case(    __magic_name__   )			->							Optional[Any]:





     '''simple docstring'''


     if not isinstance(__lowerCamelCase			,		__lowerCamelCase   ):
          lowercase :       Optional[int]       =			F"""Input value of [number={number}] must be an integer"""
          raise TypeError(__lowerCamelCase   )

     if number < 1:
          lowercase :       Optional[int]       =			F"""Input value of [number={number}] must be > 0"""
          raise ValueError(__lowerCamelCase   )
     elif number == 1:
          return 3
     elif number == 2:
          return 5
     else:
          lowercase :       Dict       =			int(math.log(number // 3			,		2   )   ) + 2

          lowercase :       str       =			[3, 5]
          lowercase :       Union[str, Any]       =			2
          lowercase :       Any       =			3
          for block in range(1			,		__lowerCamelCase   ):
               for _ in range(__lowerCamelCase   ):
                    proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]   )
                    proth_index += 1
               increment *= 2

     return proth_list[number - 1]


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 for number in range(11):
  lowerCAmelCase_						=			0
  try:
   lowerCAmelCase_						=			proth(number)
  except ValueError:
   print(f'''ValueError: there is no {number}th Proth number''')
   continue

  print(f'''The {number}th Proth number: {value}''')





from sklearn.metrics import mean_squared_error

import datasets


lowerCAmelCase_						=			'\\n@article{scikit-learn,\n title={Scikit-learn: Machine Learning in {P}ython},\n author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n journal={Journal of Machine Learning Research},\n volume={12},\n pages={2825--2830},\n year={2011}\n}\n'

lowerCAmelCase_						=			'\\nMean Squared Error(MSE) is the average of the square of difference between the predicted\nand actual values.\n'


lowerCAmelCase_						=			'\nArgs:\n    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Estimated target values.\n    references: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Ground truth (correct) target values.\n    sample_weight: array-like of shape (n_samples,), default=None\n        Sample weights.\n    multioutput: {"raw_values", "uniform_average"} or array-like of shape (n_outputs,), default="uniform_average"\n        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.\n\n        "raw_values" : Returns a full set of errors in case of multioutput input.\n\n        "uniform_average" : Errors of all outputs are averaged with uniform weight.\n\n    squared : bool, default=True\n        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.\n\nReturns:\n    mse : mean squared error.\nExamples:\n\n    >>> mse_metric = datasets.load_metric("mse")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.375}\n    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)\n    >>> print(rmse_result)\n    {\'mse\': 0.6123724356957945}\n\n    If you\'re using multi-dimensional lists, then set the config as follows :\n\n    >>> mse_metric = datasets.load_metric("mse", "multilist")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.7083333333333334}\n    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput=\'raw_values\')\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {\'mse\': array([0.41666667, 1. ])}\n'
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION      ,       _KWARGS_DESCRIPTION				)
class 						_A (  datasets.Metric				):






  def  __a      (  self		:     List[Any]				)		->   Optional[Any]:






       """simple docstring"""







       return datasets.MetricInfo(
           description=_DESCRIPTION				,						citation=_CITATION				,						inputs_description=_KWARGS_DESCRIPTION				,						features=datasets.Features(self._get_feature_types()				)				,						reference_urls=[
               '''https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html'''
           ]				,						)






  def  __a      (  self		:     List[Any]				)		->   int:






       """simple docstring"""







       if self.config_name == "multilist":
            return {
                "predictions": datasets.Sequence(datasets.Value('''float'''				)				),
                "references": datasets.Sequence(datasets.Value('''float'''				)				),
            }
       else:
            return {
                "predictions": datasets.Value('''float'''				),
                "references": datasets.Value('''float'''				),
            }






  def  __a      (  self		:     Any				,						_A		:     Dict				,						_A		:     Any				,						_A		:     Any=None				,						_A		:     Any="uniform_average"				,						_A		:     Optional[Any]=True				)		->   Dict:






       """simple docstring"""







       lowercase :       Any       =			mean_squared_error(
           _A				,						_A				,						sample_weight=_A				,						multioutput=_A				,						squared=_A				)

       return {"mse": mse}