'''simple docstring'''


from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def  _lowerCamelCase   (				lowerCamelCase_ :							int       ):



     """simple docstring"""





     UpperCAmelCase_							:       int       =				int(number**0.5       )
     return number == sq * sq


def  _lowerCamelCase   (				lowerCamelCase_ :							int     ,					lowerCamelCase_ :							int     ,					lowerCamelCase_ :							int     ,					lowerCamelCase_ :							int     ,					lowerCamelCase_ :							int     ,					lowerCamelCase_ :							int       ):



     """simple docstring"""





     UpperCAmelCase_							:       int       =				x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     UpperCAmelCase_							:       int       =				x_den * y_den * z_den
     UpperCAmelCase_							:       int       =				gcd(UpperCAmelCase__     ,					UpperCAmelCase__       )
     top //= hcf
     bottom //= hcf
     return top, bottom


def  _lowerCamelCase   (				lowerCamelCase_ :							int = 35       ):



     """simple docstring"""





     UpperCAmelCase_							:       set       =				set()
     UpperCAmelCase_							:       int
     UpperCAmelCase_							:       Fraction       =				Fraction(0       )
     UpperCAmelCase_							:       tuple[int, int]

     for x_num in range(1     ,					order + 1       ):
          for x_den in range(x_num + 1     ,					order + 1       ):
               for y_num in range(1     ,					order + 1       ):
                    for y_den in range(y_num + 1     ,					order + 1       ):
                         # n=1
                         UpperCAmelCase_							:       Union[str, Any]       =				x_num * y_den + x_den * y_num
                         UpperCAmelCase_							:       int       =				x_den * y_den
                         UpperCAmelCase_							:       List[Any]       =				gcd(UpperCAmelCase__     ,					UpperCAmelCase__       )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              UpperCAmelCase_							:       Optional[Any]       =				add_three(
                                  UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__       )
                              unique_s.add(UpperCAmelCase__       )

                         # n=2
                         UpperCAmelCase_							:       Any       =				(
                             x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                         )
                         UpperCAmelCase_							:       Union[str, Any]       =				x_den * x_den * y_den * y_den
                         if is_sq(UpperCAmelCase__       ) and is_sq(UpperCAmelCase__       ):
                              UpperCAmelCase_							:       Optional[Any]       =				int(sqrt(UpperCAmelCase__       )       )
                              UpperCAmelCase_							:       Dict       =				int(sqrt(UpperCAmelCase__       )       )
                              UpperCAmelCase_							:       Any       =				gcd(UpperCAmelCase__     ,					UpperCAmelCase__       )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   UpperCAmelCase_							:       Any       =				add_three(
                                       UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__       )
                                   unique_s.add(UpperCAmelCase__       )

                    # n=-1
                         UpperCAmelCase_							:       List[str]       =				x_num * y_num
                         UpperCAmelCase_							:       Optional[Any]       =				x_den * y_num + x_num * y_den
                         UpperCAmelCase_							:       Dict       =				gcd(UpperCAmelCase__     ,					UpperCAmelCase__       )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              UpperCAmelCase_							:       List[str]       =				add_three(
                                  UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__       )
                              unique_s.add(UpperCAmelCase__       )

                         # n=2
                         UpperCAmelCase_							:       Optional[Any]       =				x_num * x_num * y_num * y_num
                         UpperCAmelCase_							:       Optional[Any]       =				(
                             x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                         )
                         if is_sq(UpperCAmelCase__       ) and is_sq(UpperCAmelCase__       ):
                              UpperCAmelCase_							:       List[str]       =				int(sqrt(UpperCAmelCase__       )       )
                              UpperCAmelCase_							:       Optional[int]       =				int(sqrt(UpperCAmelCase__       )       )
                              UpperCAmelCase_							:       Dict       =				gcd(UpperCAmelCase__     ,					UpperCAmelCase__       )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   UpperCAmelCase_							:       Union[str, Any]       =				add_three(
                                       UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__     ,					UpperCAmelCase__       )
                                   unique_s.add(UpperCAmelCase__       )

     for num, den in unique_s:
          total += Fraction(UpperCAmelCase__     ,					UpperCAmelCase__       )

     return total.denominator + total.numerator


if __name__ == "__main__":
 print(f"""{solution() = }""")







'''simple docstring'''


from sklearn.metrics import fa_score

import datasets


snake_case__					:      str				      =  '''
The F1 score is the harmonic mean of the precision and recall. It can be computed with the equation:
F1 = 2 * (precision * recall) / (precision + recall)
'''


snake_case__					:      int				      =  '''
Args:
    predictions (`list` of `int`): Predicted labels.
    references (`list` of `int`): Ground truth labels.
    labels (`list` of `int`): The set of labels to include when `average` is not set to `\'binary\'`, and the order of the labels if `average` is `None`. Labels present in the data can be excluded, for example to calculate a multiclass average ignoring a majority negative class. Labels not present in the data will result in 0 components in a macro average. For multilabel targets, labels are column indices. By default, all labels in `predictions` and `references` are used in sorted order. Defaults to None.
    pos_label (`int`): The class to be considered the positive class, in the case where `average` is set to `binary`. Defaults to 1.
    average (`string`): This parameter is required for multiclass/multilabel targets. If set to `None`, the scores for each class are returned. Otherwise, this determines the type of averaging performed on the data. Defaults to `\'binary\'`.

        - \'binary\': Only report results for the class specified by `pos_label`. This is applicable only if the classes found in `predictions` and `references` are binary.
        - \'micro\': Calculate metrics globally by counting the total true positives, false negatives and false positives.
        - \'macro\': Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account.
        - \'weighted\': Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters `\'macro\'` to account for label imbalance. This option can result in an F-score that is not between precision and recall.
        - \'samples\': Calculate metrics for each instance, and find their average (only meaningful for multilabel classification).
    sample_weight (`list` of `float`): Sample weights Defaults to None.

Returns:
    f1 (`float` or `array` of `float`): F1 score or list of f1 scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher f1 scores are better.

Examples:

    Example 1-A simple binary example
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0])
        >>> print(results)
        {\'f1\': 0.5}

    Example 2-The same simple binary example as in Example 1, but with `pos_label` set to `0`.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], pos_label=0)
        >>> print(round(results[\'f1\'], 2))
        0.67

    Example 3-The same simple binary example as in Example 1, but with `sample_weight` included.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], sample_weight=[0.9, 0.5, 3.9, 1.2, 0.3])
        >>> print(round(results[\'f1\'], 2))
        0.35

    Example 4-A multiclass example, with different values for the `average` input.
        >>> predictions = [0, 2, 1, 0, 0, 1]
        >>> references = [0, 1, 2, 0, 1, 2]
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="macro")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="micro")
        >>> print(round(results[\'f1\'], 2))
        0.33
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="weighted")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=None)
        >>> print(results)
        {\'f1\': array([0.8, 0. , 0. ])}
'''


snake_case__					:      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}
}
'''






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







  '''simple docstring'''






  def _UpperCamelCase					(			self						):




       '''simple docstring'''

       return datasets.MetricInfo(
           description=_DESCRIPTION				,		citation=_CITATION				,		inputs_description=_KWARGS_DESCRIPTION				,		features=datasets.Features(
               {
                   'predictions': datasets.Sequence(datasets.Value('int32'						)						),
                   'references': datasets.Sequence(datasets.Value('int32'						)						),
               }
               if self.config_name == 'multilabel'
               else {
                   'predictions': datasets.Value('int32'						),
                   'references': datasets.Value('int32'						),
               }						)				,		reference_urls=['https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html']				,		)






  def _UpperCamelCase					(			self				,		snake_case_				,		snake_case_				,		snake_case_=None				,		snake_case_=1				,		snake_case_="binary"				,		snake_case_=None						):




       '''simple docstring'''

       UpperCAmelCase_							:       Optional[int]       =				fa_score(
           snake_case_				,		snake_case_				,		labels=snake_case_				,		pos_label=snake_case_				,		average=snake_case_				,		sample_weight=snake_case_						)
       return {"f1": float(snake_case_						) if score.size == 1 else score}






