"""simple docstring"""







import functools


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





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

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

	if len(__UpperCAmelCase			) == 0:
		return 0

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

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

	_lowercase :    List[Any]							=							set(__UpperCAmelCase			)

	@functools.cache
	def dynamic_programming(__UpperCAmelCase			) -> 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()




"""simple docstring"""







from decimal import Decimal, getcontext
from math import ceil, factorial


def      __lowerCAmelCase(		__UpperCAmelCase			):






	"""simple docstring"""





	if not isinstance(__UpperCAmelCase     ,__UpperCAmelCase			):
		raise TypeError('Undefined for non-integers'			)
	elif precision < 1:
		raise ValueError('Undefined for non-natural numbers'			)

	_lowercase :    Optional[Any]							=							precision
	_lowercase :    Dict							=							ceil(precision / 14			)
	_lowercase :    int							=							426_880 * Decimal(10_005			).sqrt()
	_lowercase :    Optional[Any]							=							1
	_lowercase :    Union[str, Any]							=							13_591_409
	_lowercase :    Optional[int]							=							Decimal(__UpperCAmelCase			)
	for k in range(1     ,__UpperCAmelCase			):
		_lowercase :    List[str]							=							factorial(6 * k			) // (factorial(3 * k			) * factorial(__UpperCAmelCase			) ** 3)
		linear_term += 545_140_134
		exponential_term *= -262_537_412_640_768_000
		partial_sum += Decimal(multinomial_term * linear_term			) / exponential_term
	return str(constant_term / partial_sum			)[:-1]


if __name__ == "__main__":
						SCREAMING_SNAKE_CASE									=						50
						print(f"""The first {n} digits of pi is: {pi(n)}""")



