
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     bool:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				int(number**0.5						)
   return number == sq * sq
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     tuple[int, int]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
   _SCREAMING_SNAKE_CASE      =				x_den * y_den * z_den
   _SCREAMING_SNAKE_CASE      =				gcd(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
   top //= hcf
   bottom //= hcf
   return top, bottom
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_ = 35						)     ->     int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				set()
   _SCREAMING_SNAKE_CASE      =				42
   _SCREAMING_SNAKE_CASE      =				Fraction(0						)
   _SCREAMING_SNAKE_CASE      =				42

   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
               _SCREAMING_SNAKE_CASE      =				x_num * y_den + x_den * y_num
               _SCREAMING_SNAKE_CASE      =				x_den * y_den
               _SCREAMING_SNAKE_CASE      =				gcd(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
               z_num //= hcf
               z_den //= hcf
               if 0 < z_num < z_den <= order:
                  _SCREAMING_SNAKE_CASE      =				add_three(
                      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                  unique_s.add(SCREAMING_SNAKE_CASE_						)

               # n=2
               _SCREAMING_SNAKE_CASE      =				(
                   x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
               )
               _SCREAMING_SNAKE_CASE      =				x_den * x_den * y_den * y_den
               if is_sq(SCREAMING_SNAKE_CASE_						) and is_sq(SCREAMING_SNAKE_CASE_						):
                  _SCREAMING_SNAKE_CASE      =				int(sqrt(SCREAMING_SNAKE_CASE_						)						)
                  _SCREAMING_SNAKE_CASE      =				int(sqrt(SCREAMING_SNAKE_CASE_						)						)
                  _SCREAMING_SNAKE_CASE      =				gcd(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                  z_num //= hcf
                  z_den //= hcf
                  if 0 < z_num < z_den <= order:
                     _SCREAMING_SNAKE_CASE      =				add_three(
                         SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                     unique_s.add(SCREAMING_SNAKE_CASE_						)

                    # n=-1
               _SCREAMING_SNAKE_CASE      =				x_num * y_num
               _SCREAMING_SNAKE_CASE      =				x_den * y_num + x_num * y_den
               _SCREAMING_SNAKE_CASE      =				gcd(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
               z_num //= hcf
               z_den //= hcf
               if 0 < z_num < z_den <= order:
                  _SCREAMING_SNAKE_CASE      =				add_three(
                      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                  unique_s.add(SCREAMING_SNAKE_CASE_						)

               # n=2
               _SCREAMING_SNAKE_CASE      =				x_num * x_num * y_num * y_num
               _SCREAMING_SNAKE_CASE      =				(
                   x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
               )
               if is_sq(SCREAMING_SNAKE_CASE_						) and is_sq(SCREAMING_SNAKE_CASE_						):
                  _SCREAMING_SNAKE_CASE      =				int(sqrt(SCREAMING_SNAKE_CASE_						)						)
                  _SCREAMING_SNAKE_CASE      =				int(sqrt(SCREAMING_SNAKE_CASE_						)						)
                  _SCREAMING_SNAKE_CASE      =				gcd(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                  z_num //= hcf
                  z_den //= hcf
                  if 0 < z_num < z_den <= order:
                     _SCREAMING_SNAKE_CASE      =				add_three(
                         SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
                     unique_s.add(SCREAMING_SNAKE_CASE_						)

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

   return total.denominator + total.numerator


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








'''simple docstring'''



from sklearn.metrics import matthews_corrcoef

import datasets


UpperCamelCase__      :		List[str]       							=  "\nCompute the Matthews correlation coefficient (MCC)\n\nThe Matthews correlation coefficient is used in machine learning as a\nmeasure of the quality of binary and multiclass classifications. It takes\ninto account true and false positives and negatives and is generally\nregarded as a balanced measure which can be used even if the classes are of\nvery different sizes. The MCC is in essence a correlation coefficient value\nbetween -1 and +1. A coefficient of +1 represents a perfect prediction, 0\nan average random prediction and -1 an inverse prediction.  The statistic\nis also known as the phi coefficient. [source: Wikipedia]\n"

UpperCamelCase__      :		List[Any]       							=  "\nArgs:\n    predictions (list of int): Predicted labels, as returned by a model.\n    references (list of int): Ground truth labels.\n    sample_weight (list of int, float, or bool): Sample weights. Defaults to `None`.\nReturns:\n    matthews_correlation (dict containing float): Matthews correlation.\nExamples:\n    Example 1, a basic example with only predictions and references as inputs:\n        >>> matthews_metric = datasets.load_metric(\"matthews_correlation\")\n        >>> results = matthews_metric.compute(references=[1, 3, 2, 0, 3, 2],\n        ...                                     predictions=[1, 2, 2, 0, 3, 3])\n        >>> print(round(results['matthews_correlation'], 2))\n        0.54\n\n    Example 2, the same example as above, but also including sample weights:\n        >>> matthews_metric = datasets.load_metric(\"matthews_correlation\")\n        >>> results = matthews_metric.compute(references=[1, 3, 2, 0, 3, 2],\n        ...                                     predictions=[1, 2, 2, 0, 3, 3],\n        ...                                     sample_weight=[0.5, 3, 1, 1, 1, 2])\n        >>> print(round(results['matthews_correlation'], 2))\n        0.1\n\n    Example 3, the same example as above, but with sample weights that cause a negative correlation:\n        >>> matthews_metric = datasets.load_metric(\"matthews_correlation\")\n        >>> results = matthews_metric.compute(references=[1, 3, 2, 0, 3, 2],\n        ...                                     predictions=[1, 2, 2, 0, 3, 3],\n        ...                                     sample_weight=[0.5, 1, 0, 0, 0, 1])\n        >>> print(round(results['matthews_correlation'], 2))\n        -0.25\n"

UpperCamelCase__      :		Any       							=  "\\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"

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





       """simple docstring"""




       def        UpperCamelCase				(							self      )    ->			Optional[Any]:
          return datasets.MetricInfo(
              description=_DESCRIPTION       ,							citation=_CITATION       ,							inputs_description=_KWARGS_DESCRIPTION       ,							features=datasets.Features(
                  {
                      """predictions""": datasets.Value("""int32"""      ),
                      """references""": datasets.Value("""int32"""      ),
                  }      )       ,							reference_urls=[
                  """https://scikit-learn.org/stable/modules/generated/sklearn.metrics.matthews_corrcoef.html"""
              ]       ,							)






       def        UpperCamelCase				(							self       ,							A__       ,							A__       ,							A__=None      )    ->			List[str]:
          return {
              "matthews_correlation": float(matthews_corrcoef(A__       ,							A__       ,							sample_weight=A__      )      ),
          }






