





'''simple docstring'''

__lowerCamelCase : str											=			8.314_4598







def 							UpperCAmelCase_    (	lowerCAmelCase_		,							lowerCAmelCase_							):

				"""simple docstring"""






				if temperature < 0:
								raise Exception("Temperature cannot be less than 0 K"							)
				if molar_mass <= 0:
								raise Exception("Molar mass cannot be less than or equal to 0 kg/mol"							)
				else:
								return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
			import doctest

			# run doctest
			doctest.testmod()

			# example
			__lowerCamelCase : Optional[Any]											=			300
			__lowerCamelCase : Tuple											=			28
			__lowerCamelCase : str											=			rms_speed_of_molecule(temperature, molar_mass)
			print(f"Vrms of Nitrogen gas at 300 K is {vrms} m/s")











'''simple docstring'''

import functools







def 							UpperCAmelCase_    (	lowerCAmelCase_		,							lowerCAmelCase_							):

				"""simple docstring"""






				if not isinstance(lowerCAmelCase_		,							lowerCAmelCase_							) or not all(isinstance(lowerCAmelCase_		,							lowerCAmelCase_							) for day in days							):
								raise ValueError("The parameter days should be a list of integers"							)

				if len(lowerCAmelCase_							) != 3 or not all(isinstance(lowerCAmelCase_		,							lowerCAmelCase_							) for cost in costs							):
								raise ValueError("The parameter costs should be a list of three integers"							)

				if len(lowerCAmelCase_							) == 0:
								return 0

				if min(lowerCAmelCase_							) <= 0:
								raise ValueError("All days elements should be greater than 0"							)

				if max(lowerCAmelCase_							) >= 366:
								raise ValueError("All days elements should be less than 366"							)

				lowercase         = set(lowerCAmelCase_							)

				@functools.cache
				def dynamic_programming(lowerCAmelCase_							) -> int:
								if index > 365:
												return 0

								if index not in days_set:
												return dynamic_programming(index + 1							)

								return min(
								    costs[0] + dynamic_programming(index + 1							)		,							costs[1] + dynamic_programming(index + 7							)		,							costs[2] + dynamic_programming(index + 30							)		,							)

				return dynamic_programming(1							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()




