


"""simple docstring"""




import sys





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      len(lowercase__     )
			__lowerCamelCase          =      [[0 for x in range(lowercase__     )] for x in range(lowercase__     )]
			__lowerCamelCase          =      [[0 for x in range(lowercase__     )] for x in range(lowercase__     )]

			for chain_length in range(2,			lowercase__     ):
						for a in range(1,			n - chain_length + 1     ):
									__lowerCamelCase          =      a + chain_length - 1

									__lowerCamelCase          =      sys.maxsize
									for c in range(lowercase__,			lowercase__     ):
												__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       a_ (	lowercase__ :str,			lowercase__ :Optional[int],			lowercase__ :Dict     ):
			if i == j:
						print("""A""" + str(lowercase__     ),			end=""" """     )
			else:
						print("""(""",			end=""" """     )
						print_optiomal_solution(lowercase__,			lowercase__,			optimal_solution[i][j]     )
						print_optiomal_solution(lowercase__,			optimal_solution[i][j] + 1,			lowercase__     )
						print(""")""",			end=""" """     )





def       a_ (	):
			__lowerCamelCase          =      [30, 35, 15, 5, 10, 20, 25]
			__lowerCamelCase          =      len(lowercase__     )
			# 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(lowercase__     )

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


if __name__ == "__main__":
					main()








"""simple docstring"""




def       a_ (	lowercase__ :str,			lowercase__ :int     ):
			return [sentence[i : i + ngram_size] for i in range(len(lowercase__     ) - ngram_size + 1     )]


if __name__ == "__main__":
					from doctest import testmod

					testmod()




