

import sys
def 						_snake_case(    SCREAMING_SNAKE_CASE__			:	Optional[Any]      )							->      Union[str, Any]:





    '''simple docstring'''






    A__          =   len(SCREAMING_SNAKE_CASE__      )
    A__          =   [[0 for x in range(SCREAMING_SNAKE_CASE__      )] for x in range(SCREAMING_SNAKE_CASE__      )]
    A__          =   [[0 for x in range(SCREAMING_SNAKE_CASE__      )] for x in range(SCREAMING_SNAKE_CASE__      )]

    for chain_length in range(2    ,			SCREAMING_SNAKE_CASE__      ):
        for a in range(1    ,			n - chain_length + 1      ):
            A__          =   a + chain_length - 1

            A__          =   sys.maxsize
            for c in range(SCREAMING_SNAKE_CASE__    ,			SCREAMING_SNAKE_CASE__      ):
                A__          =   (
                    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
                )
                if cost < matrix[a][b]:
                    A__          =   cost
                    A__          =   c
    return matrix, sol
def 						_snake_case(    SCREAMING_SNAKE_CASE__			:	Optional[Any]    ,			SCREAMING_SNAKE_CASE__			:	str    ,			SCREAMING_SNAKE_CASE__			:	int      )							->      Dict:





    '''simple docstring'''






    if i == j:
        print('A' + str(SCREAMING_SNAKE_CASE__      )    ,			end=' '      )
    else:
        print('('    ,			end=' '      )
        print_optiomal_solution(SCREAMING_SNAKE_CASE__    ,			SCREAMING_SNAKE_CASE__    ,			optimal_solution[i][j]      )
        print_optiomal_solution(SCREAMING_SNAKE_CASE__    ,			optimal_solution[i][j] + 1    ,			SCREAMING_SNAKE_CASE__      )
        print(')'    ,			end=' '      )
def 						_snake_case(    )							->      Tuple:





    '''simple docstring'''






    A__          =   [30, 35, 15, 5, 10, 20, 25]
    A__          =   len(SCREAMING_SNAKE_CASE__      )
    # Size of matrix created from above array will be
    # 30*35 35*15 15*5 5*10 10*20 20*25
    A__      ,						A__          =   matrix_chain_order(SCREAMING_SNAKE_CASE__      )

    print('No. of Operation required: ' + str(matrix[1][n - 1]      )      )
    print_optiomal_solution(SCREAMING_SNAKE_CASE__    ,			1    ,			n - 1      )


if __name__ == "__main__":
     main()




def 						_snake_case(    SCREAMING_SNAKE_CASE__			:	float    ,			SCREAMING_SNAKE_CASE__			:	float    ,			SCREAMING_SNAKE_CASE__			:	float    ,			SCREAMING_SNAKE_CASE__			:	float    ,			SCREAMING_SNAKE_CASE__			:	float    ,			)							->      float:





    '''simple docstring'''






    A__          =   [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__          =   1 - (matter_density + radiation_density + dark_energy)

        A__          =   (
            radiation_density * (redshift + 1) ** 4
            + matter_density * (redshift + 1) ** 3
            + curvature * (redshift + 1) ** 2
            + dark_energy
        )

        A__          =   hubble_constant * e_a ** (1 / 2)
        return hubble


if __name__ == "__main__":
     import doctest

     # run doctest
     doctest.testmod()

     # demo LCDM approximation
     lowercase_       		=  0.3

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

