


'''simple docstring'''




class 		UpperCAmelCase_      :





     def __init__( self       :      List[str]    ,      UpperCAmelCase__       :      list[int]    )				->  None:
        lowerCAmelCase     =			len(UpperCAmelCase__    )
        lowerCAmelCase     =			[0] * len_array

        if len_array > 0:
           lowerCAmelCase     =			array[0]

        for i in range(1    ,      UpperCAmelCase__    ):
           lowerCAmelCase     =			self.prefix_sum[i - 1] + array[i]





     def 							__UpperCAmelCase      ( self       :      Optional[Any]    ,      UpperCAmelCase__       :      int    ,      UpperCAmelCase__       :      int    )				->  int:
        if start == 0:
           return self.prefix_sum[end]

        return self.prefix_sum[end] - self.prefix_sum[start - 1]





     def 							__UpperCAmelCase      ( self       :      int    ,      UpperCAmelCase__       :      int    )				->  bool:
        lowerCAmelCase     =			{0}
        for sum_item in self.prefix_sum:
           if sum_item - target_sum in sums:
              return True

           sums.add(UpperCAmelCase__    )

        return False


if __name__ == "__main__":
       import doctest

       doctest.testmod()













"""simple docstring"""





from math import pow, sqrt







def      lowerCamelCase__       (							*_lowerCamelCase       :		float )      ->				bool:
  lowerCamelCase_         =						len(_lowerCamelCase ) > 0 and all(value > 0.0 for value in values )
  return result







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase )
      else ValueError('Input Error: Molar mass values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,				2 )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,				2 ) / molar_mass		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )




