





def 				_lowerCAmelCase			(	_a :       list[int]      )						->      int:

     # validate:
     if not isinstance(_a       , _a      ) or not all(
         isinstance(_a       , _a      ) and item >= 0 for item in citations      ):
          raise ValueError("""The citations should be a list of non negative integers."""      )

     citations.sort()
     lowerCAmelCase_       :							Optional[Any]			 =		len(_a      )

     for i in range(_a      ):
          if citations[len_citations - 1 - i] <= i:
               return i

     return len_citations


if __name__ == "__main__":
      import doctest

      doctest.testmod()







import numpy as np






def 				_lowerCAmelCase			(	_a :       Optional[int]       , _a :       str      )						->      Union[str, Any]:
     lowerCAmelCase_       :							int			 =		np.array(_a      )
     lowerCAmelCase_       :							str			 =		np.array(_a      )

     lowerCAmelCase_       :							Optional[Any]			 =		abs(predict - actual      )
     lowerCAmelCase_       :							Dict			 =		difference.mean()

     return score






def 				_lowerCAmelCase			(	_a :       Union[str, Any]       , _a :       int      )						->      Tuple:
     lowerCAmelCase_       :							int			 =		np.array(_a      )
     lowerCAmelCase_       :							int			 =		np.array(_a      )

     lowerCAmelCase_       :							Union[str, Any]			 =		predict - actual
     lowerCAmelCase_       :							Tuple			 =		np.square(_a      )

     lowerCAmelCase_       :							Tuple			 =		square_diff.mean()
     return score






def 				_lowerCAmelCase			(	_a :       Optional[Any]       , _a :       Tuple      )						->      Optional[int]:
     lowerCAmelCase_       :							Optional[Any]			 =		np.array(_a      )
     lowerCAmelCase_       :							Optional[Any]			 =		np.array(_a      )

     lowerCAmelCase_       :							int			 =		predict - actual
     lowerCAmelCase_       :							Any			 =		np.square(_a      )
     lowerCAmelCase_       :							Union[str, Any]			 =		square_diff.mean()
     lowerCAmelCase_       :							Optional[Any]			 =		np.sqrt(_a      )
     return score






def 				_lowerCAmelCase			(	_a :       Optional[Any]       , _a :       Optional[Any]      )						->      List[Any]:
     lowerCAmelCase_       :							Dict			 =		np.array(_a      )
     lowerCAmelCase_       :							List[Any]			 =		np.array(_a      )

     lowerCAmelCase_       :							str			 =		np.log(predict + 1      )
     lowerCAmelCase_       :							Any			 =		np.log(actual + 1      )

     lowerCAmelCase_       :							List[str]			 =		log_predict - log_actual
     lowerCAmelCase_       :							Dict			 =		np.square(_a      )
     lowerCAmelCase_       :							Optional[Any]			 =		square_diff.mean()

     lowerCAmelCase_       :							int			 =		np.sqrt(_a      )

     return score






def 				_lowerCAmelCase			(	_a :       str       , _a :       List[Any]      )						->      int:
     lowerCAmelCase_       :							Any			 =		np.array(_a      )
     lowerCAmelCase_       :							Optional[int]			 =		np.array(_a      )

     lowerCAmelCase_       :							Optional[int]			 =		predict - actual
     lowerCAmelCase_       :							str			 =		np.sum(_a      ) / len(_a      )
     lowerCAmelCase_       :							List[str]			 =		np.sum(_a      ) / len(_a      )
     # print(numerator, denumerator)
     lowerCAmelCase_       :							int			 =		float(_a      ) / denumerator * 1_00

     return score







def 				_lowerCAmelCase			(	_a :       Any       , _a :       Union[str, Any]      )						->      str:
     return np.mean(np.array(_a      ) == np.array(_a      )      )
