




def        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_,snake_case_,snake_case_,):
      _A							:  Dict    =		[redshift, radiation_density, matter_density, dark_energy]
      if any(p < 0 for p in parameters  ):
            raise ValueError("""All input parameters must be positive"""  )

      if any(p > 1 for p in parameters[1:4]  ):
            raise ValueError("""Relative densities cannot be greater than one"""  )
      else:
            _A							:  str    =		1 - (matter_density + radiation_density + dark_energy)

            _A							:  Tuple    =		(
                radiation_density * (redshift + 1) ** 4
                + matter_density * (redshift + 1) ** 3
                + curvature * (redshift + 1) ** 2
                + dark_energy
            )

            _A							:  int    =		hubble_constant * e_a ** (1 / 2)
            return hubble


if __name__ == "__main__":
  import doctest

  # run doctest
  doctest.testmod()

  # demo LCDM approximation
  _snake_case            = 0.3

  print(
      hubble_parameter(
          hubble_constant=6_8.3,
          radiation_density=1e-4,
          matter_density=matter_density,
          dark_energy=1 - matter_density,
          redshift=0,
      )
  )







def        lowerCAmelCase_			(  snake_case_ = 1000000  ):
      _A							:  Any    =		limit + 1
      _A							:  Tuple    =		[0] * limit
      for first_term in range(1,snake_case_  ):
            for n in range(snake_case_,snake_case_,snake_case_  ):
                  _A							:  Optional[int]    =		first_term + n / first_term
                  if common_difference % 4:  # d must be divisble by 4
                        continue
                  else:
                        common_difference /= 4
                        if (
                            first_term > common_difference
                            and first_term < 4 * common_difference
                        ):  # since x,y,z are positive integers
                              frequency[n] += 1  # so z>0 and a>d ,also 4d<a

      _A							:  List[str]    =		sum(1 for x in frequency[1:limit] if x == 10  )

      return count


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

