

'''simple docstring'''





import sys







def   _UpperCamelCase	(		__UpperCamelCase	)       ->			Optional[Any]:
					lowerCamelCase_  				=      len(__UpperCamelCase	)
					lowerCamelCase_  				=      [[0 for x in range(__UpperCamelCase	)] for x in range(__UpperCamelCase	)]
					lowerCamelCase_  				=      [[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	):
															lowerCamelCase_  				=      a + chain_length - 1

															lowerCamelCase_  				=      sys.maxsize
															for c in range(__UpperCamelCase    ,__UpperCamelCase	):
																				lowerCamelCase_  				=      (
																				    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
																				)
																				if cost < matrix[a][b]:
																									lowerCamelCase_  				=      cost
																									lowerCamelCase_  				=      c
					return matrix, sol







def   _UpperCamelCase	(		__UpperCamelCase    ,__UpperCamelCase    ,__UpperCamelCase	)       ->			Optional[int]:
					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   _UpperCamelCase	(		)       ->			Optional[int]:
					lowerCamelCase_  				=      [30, 35, 15, 5, 10, 20, 25]
					lowerCamelCase_  				=      len(__UpperCamelCase	)
					# Size of matrix created from above array will be
					# 30*35 35*15 15*5 5*10 10*20 20*25
					lowerCamelCase_				,lowerCamelCase_  				=      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()









def lowercase    (  SCREAMING_SNAKE_CASE )			->							int:


			'''simple docstring'''







			if not numbers:
						return 0

			if not isinstance(SCREAMING_SNAKE_CASE       ,    (list, tuple) ) or not all(
			    isinstance(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE ) for number in numbers ):
						raise ValueError('numbers must be an iterable of integers' )

			SCREAMING_SNAKE_CASE_								=						SCREAMING_SNAKE_CASE_								=						SCREAMING_SNAKE_CASE_								=						numbers[0]

			for i in range(1       ,    len(SCREAMING_SNAKE_CASE ) ):
						# update the maximum and minimum subarray products
						SCREAMING_SNAKE_CASE_								=						numbers[i]
						if number < 0:
									SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						min_till_now, max_till_now
						SCREAMING_SNAKE_CASE_								=						max(SCREAMING_SNAKE_CASE       ,    max_till_now * number )
						SCREAMING_SNAKE_CASE_								=						min(SCREAMING_SNAKE_CASE       ,    min_till_now * number )

						# update the maximum product found till now
						SCREAMING_SNAKE_CASE_								=						max(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )

			return max_prod
