





'''simple docstring'''


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







def    _lowerCamelCase  (__lowerCamelCase  :     int     )   ->    str:

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

			a__     = precision
			a__     = ceil(precision / 14     )
			a__     = 42_6880 * Decimal(1_0005     ).sqrt()
			a__     = 1
			a__     = 1359_1409
			a__     = Decimal(__lowerCamelCase     )
			for k in range(1					,  __lowerCamelCase     ):
						a__     = factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCamelCase     ) ** 3)
						linear_term += 5_4514_0134
						exponential_term *= -26_2537_4126_4076_8000
						partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
			return str(constant_term / partial_sum     )[:-1]


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










'''simple docstring'''


def    _lowerCamelCase  (__lowerCamelCase  :     int = 400_0000     )   ->    int:
			a__     = [0, 1]
			a__     = 0
			while fib[i] <= n:
						fib.append(fib[i] + fib[i + 1]     )
						if fib[i + 2] > n:
									break
						i += 1
			a__     = 0
			for j in range(len(__lowerCamelCase     ) - 1     ):
						if fib[j] % 2 == 0:
									total += fib[j]

			return total


if __name__ == "__main__":
		print(f"""{solution() = }""")



