





'''simple docstring'''






import sys






def      __A						(							a_						:  Dict	):
		lowerCAmelCase     :    int						=   len(a_	)
		lowerCAmelCase     :    Any						=   [[0 for x in range(a_	)] for x in range(a_	)]
		lowerCAmelCase     :    Optional[Any]						=   [[0 for x in range(a_	)] for x in range(a_	)]

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

						lowerCAmelCase     :    Any						=   sys.maxsize
						for c in range(a_      ,a_	):
								lowerCAmelCase     :    int						=   (
								    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
								)
								if cost < matrix[a][b]:
										lowerCAmelCase     :    Optional[int]						=   cost
										lowerCAmelCase     :    Optional[Any]						=   c
		return matrix, sol






def      __A						(							a_						:  List[str]      ,a_						:  Any      ,a_						:  Optional[Any]	):
		if i == j:
				print("A" + str(a_	)      ,end=" "	)
		else:
				print("("      ,end=" "	)
				print_optiomal_solution(a_      ,a_      ,optimal_solution[i][j]	)
				print_optiomal_solution(a_      ,optimal_solution[i][j] + 1      ,a_	)
				print(")"      ,end=" "	)






def      __A						(							):
		lowerCAmelCase     :    str						=   [3_0, 3_5, 1_5, 5, 1_0, 2_0, 2_5]
		lowerCAmelCase     :    str						=   len(a_	)
		# Size of matrix created from above array will be
		# 30*35 35*15 15*5 5*10 10*20 20*25
		lowerCAmelCase     :    Union[str, Any]						=   matrix_chain_order(a_	)

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


if __name__ == "__main__":
			main()










'''simple docstring'''






from __future__ import annotations






def      __A						(							a_						:  float      ,a_						:  float      ,a_						:  float      ,):
		if (stress, tangential_force, area).count(0	) != 1:
				raise ValueError("You cannot supply more or less than 2 values"	)
		elif stress < 0:
				raise ValueError("Stress cannot be negative"	)
		elif tangential_force < 0:
				raise ValueError("Tangential Force cannot be negative"	)
		elif area < 0:
				raise ValueError("Area cannot be negative"	)
		elif stress == 0:
				return (
				    "stress",
				    tangential_force / area,
				)
		elif tangential_force == 0:
				return (
				    "tangential_force",
				    stress * area,
				)
		else:
				return (
				    "area",
				    tangential_force / stress,
				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()



