

def 					__lowercase      (     _A						,    _A						,    _A						,    _A						,    _A						,    )     ->						float:
						SCREAMING_SNAKE_CASE :      Optional[int]       =   [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:
												SCREAMING_SNAKE_CASE :      Tuple       =   1 - (matter_density + radiation_density + dark_energy)

												SCREAMING_SNAKE_CASE :      str       =   (
												    radiation_density * (redshift + 1) ** 4
												    + matter_density * (redshift + 1) ** 3
												    + curvature * (redshift + 1) ** 2
												    + dark_energy
												)

												SCREAMING_SNAKE_CASE :      Union[str, Any]       =   hubble_constant * e_a ** (1 / 2)
												return hubble


if __name__ == "__main__":
		import doctest

		# run doctest
		doctest.testmod()

		# demo LCDM approximation
		UpperCAmelCase__ :     Optional[int]				    =    0.3

		print(
		    hubble_parameter(
		        hubble_constant=68.3,
		        radiation_density=1E-4,
		        matter_density=matter_density,
		        dark_energy=1 - matter_density,
		        redshift=0,
		    )
		)







def 					__lowercase      (     _A						,    _A			)     ->						int:
      assert x is not None
      assert y is not None

      SCREAMING_SNAKE_CASE :      int       =   len(_A			)
      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   len(_A			)

      # declaring the array for storing the dp values
      SCREAMING_SNAKE_CASE :      Tuple       =   [[0] * (n + 1) for _ in range(m + 1			)]  # noqa: E741

      for i in range(1						,    m + 1			):
            for j in range(1						,    n + 1			):
                  SCREAMING_SNAKE_CASE :      List[Any]       =   1 if x[i - 1] == y[j - 1] else 0

                  SCREAMING_SNAKE_CASE :      int       =   max(l[i - 1][j]						,    l[i][j - 1]						,    l[i - 1][j - 1] + match			)

      SCREAMING_SNAKE_CASE :      int       =   """"""
      SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      int       =   m, n
      while i > 0 and j > 0:
            SCREAMING_SNAKE_CASE :      Tuple       =   1 if x[i - 1] == y[j - 1] else 0

            if l[i][j] == l[i - 1][j - 1] + match:
                  if match == 1:
                        SCREAMING_SNAKE_CASE :      List[Any]       =   x[i - 1] + seq
                  i -= 1
                  j -= 1
            elif l[i][j] == l[i - 1][j]:
                  i -= 1
            else:
                  j -= 1

      return l[m][n], seq


if __name__ == "__main__":
  UpperCAmelCase__ :     str				    =    """AGGTAB"""
  UpperCAmelCase__ :     Optional[int]				    =    """GXTXAYB"""
  UpperCAmelCase__ :     Tuple				    =    4
  UpperCAmelCase__ :     Dict				    =    """GTAB"""

  UpperCAmelCase__    ,   UpperCAmelCase__ :     Optional[int]				    =    longest_common_subsequence(a, b)
  print("""len =""", ln, """, sub-sequence =""", subseq)
  import doctest

  doctest.testmod()




