


'''simple docstring'''



from sklearn.metrics import mean_absolute_error

import datasets


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

A__		: Union[str, Any]												=  """\
Mean Absolute Error (MAE) is the mean of the magnitude of difference between the predicted and actual
values.
"""


A__		: Optional[int]												=  """
Args:
    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Estimated target values.
    references: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Ground truth (correct) target values.
    sample_weight: array-like of shape (n_samples,), default=None
        Sample weights.
    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"
        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.

                 \"raw_values\" : Returns a full set of errors in case of multioutput input.

                 \"uniform_average\" : Errors of all outputs are averaged with uniform weight.

Returns:
    mae : mean absolute error.
        If multioutput is \"raw_values\", then mean absolute error is returned for each output separately. If multioutput is \"uniform_average\" or an ndarray of weights, then the weighted average of all output errors is returned.
        MAE output is non-negative floating point. The best value is 0.0.
Examples:

    >>> mae_metric = datasets.load_metric(\"mae\")
    >>> predictions = [2.5, 0.0, 2, 8]
    >>> references = [3, -0.5, 2, 7]
    >>> results = mae_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mae': 0.5}

    If you're using multi-dimensional lists, then set the config as follows :

    >>> mae_metric = datasets.load_metric(\"mae\", \"multilist\")
    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
    >>> references = [[0, 2], [-1, 2], [8, -5]]
    >>> results = mae_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mae': 0.75}
    >>> results = mae_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
    >>> print(results)
    {'mae': array([0.5, 1. ])}
"""





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





    """simple docstring"""






    def 				lowercase_    (							self     )    ->					int:
         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_absolute_error.html'
             ]      ,					)







    def 				lowercase_    (							self     )    ->					Dict:
         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 				lowercase_    (							self      ,					SCREAMING_SNAKE_CASE_      ,					SCREAMING_SNAKE_CASE_      ,					SCREAMING_SNAKE_CASE_=None      ,					SCREAMING_SNAKE_CASE_="uniform_average"     )    ->					Optional[Any]:
         __lowerCamelCase       :     Union[str, Any]        =		mean_absolute_error(SCREAMING_SNAKE_CASE_      ,					SCREAMING_SNAKE_CASE_      ,					sample_weight=SCREAMING_SNAKE_CASE_      ,					multioutput=SCREAMING_SNAKE_CASE_     )

         return {"mae": mae_score}










'''simple docstring'''



import math
from itertools import permutations



def       UpperCAmelCase__ (     UpperCAmelCase_   :    int							)					->		bool:

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5				,   int(math.sqrt(UpperCAmelCase_							) + 1							)				,   6							):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True



def       UpperCAmelCase__ (     UpperCAmelCase_   :    int				,   UpperCAmelCase_   :    list							)					->		bool:
     __lowerCamelCase    ,	__lowerCamelCase       :     str        =		0, len(UpperCAmelCase_							) - 1
     while left <= right:
          __lowerCamelCase       :     Optional[Any]        =		(left + right) // 2
          if prime_list[middle] == target:
               return True
          elif prime_list[middle] < target:
               __lowerCamelCase       :     Union[str, Any]        =		middle + 1
          else:
               __lowerCamelCase       :     Union[str, Any]        =		middle - 1

     return False



def       UpperCAmelCase__ (     )					->		List[str]:
     __lowerCamelCase       :     Tuple        =		[n for n in range(10_01				,   1_00_00				,   2							) if is_prime(UpperCAmelCase_							)]
     __lowerCamelCase       :     Any        =		[]

     for number in prime_list:
          __lowerCamelCase       :     Optional[int]        =		[]

          for prime_member in permutations(list(str(UpperCAmelCase_							)							)							):
               __lowerCamelCase       :     int        =		int(''.join(UpperCAmelCase_							)							)

               if prime % 2 == 0:
                    continue

               if search(UpperCAmelCase_				,   UpperCAmelCase_							):
                    tmp_numbers.append(UpperCAmelCase_							)

          tmp_numbers.sort()
          if len(UpperCAmelCase_							) >= 3:
               candidates.append(UpperCAmelCase_							)

     __lowerCamelCase       :     int        =		[]
     for candidate in candidates:
          __lowerCamelCase       :     Union[str, Any]        =		len(UpperCAmelCase_							)
          __lowerCamelCase       :     Optional[Any]        =		False

          for i in range(UpperCAmelCase_							):
               for j in range(i + 1				,   UpperCAmelCase_							):
                    for k in range(j + 1				,   UpperCAmelCase_							):
                         if (
                             abs(candidate[i] - candidate[j]							)
                             == abs(candidate[j] - candidate[k]							)
                             and len({candidate[i], candidate[j], candidate[k]}							) == 3
                         ):
                              passed.append(
                                  sorted([candidate[i], candidate[j], candidate[k]]							)							)
                              __lowerCamelCase       :     List[str]        =		True

                         if found:
                              break
                    if found:
                         break
               if found:
                    break

     __lowerCamelCase       :     List[Any]        =		set()
     for seq in passed:
          answer.add(''.join([str(UpperCAmelCase_							) for i in seq]							)							)

     return max(int(UpperCAmelCase_							) for x in answer							)


if __name__ == "__main__":
      print(solution())






