





import sys






def 	lowerCamelCase_		(							_UpperCamelCase					)						->		Tuple:






				"""simple docstring"""


				snake_case_		:       Union[str, Any]           =    len(_UpperCamelCase					)
				snake_case_		:       List[Any]           =    [[0 for x in range(_UpperCamelCase					)] for x in range(_UpperCamelCase					)]
				snake_case_		:       List[Any]           =    [[0 for x in range(_UpperCamelCase					)] for x in range(_UpperCamelCase					)]

				for chain_length in range(2					,							_UpperCamelCase					):
								for a in range(1					,							n - chain_length + 1					):
												snake_case_		:       Dict           =    a + chain_length - 1

												snake_case_		:       Tuple           =    sys.maxsize
												for c in range(_UpperCamelCase					,							_UpperCamelCase					):
																snake_case_		:       Dict           =    (
																    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
																)
																if cost < matrix[a][b]:
																				snake_case_		:       List[str]           =    cost
																				snake_case_		:       int           =    c
				return matrix, sol






def 	lowerCamelCase_		(							_UpperCamelCase					,							_UpperCamelCase					,							_UpperCamelCase					)						->		Any:






				"""simple docstring"""


				if i == j:
								print('''A''' + str(_UpperCamelCase					)					,							end=''' '''					)
				else:
								print('''('''					,							end=''' '''					)
								print_optiomal_solution(_UpperCamelCase					,							_UpperCamelCase					,							optimal_solution[i][j]					)
								print_optiomal_solution(_UpperCamelCase					,							optimal_solution[i][j] + 1					,							_UpperCamelCase					)
								print(''')'''					,							end=''' '''					)






def 	lowerCamelCase_		(							)						->		Union[str, Any]:






				"""simple docstring"""


				snake_case_		:       Tuple           =    [30, 35, 15, 5, 10, 20, 25]
				snake_case_		:       str           =    len(_UpperCamelCase					)
				# Size of matrix created from above array will be
				# 30*35 35*15 15*5 5*10 10*20 20*25
				snake_case_     ,				snake_case_		:       Optional[Any]           =    matrix_chain_order(_UpperCamelCase					)

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


if __name__ == "__main__":
	main()






'''simple docstring'''


def 						lowerCamelCase__   (				a							):
						assert (
						    isinstance(a    ,	a							) and number_of_steps > 0
						), f'number_of_steps needs to be positive integer, your input {number_of_steps}'
						if number_of_steps == 1:
												return 1
						__snake_case ,       __snake_case						 =   1, 1
						for _ in range(number_of_steps - 1							):
												__snake_case ,       __snake_case						 =   current + previous, current
						return current


if __name__ == "__main__":
	import doctest

	doctest.testmod()

