






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







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     str:

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

					UpperCamelCase__      :       Tuple	    =  precision
					UpperCamelCase__      :       Dict	    =  ceil(precision / 14      )
					UpperCamelCase__      :       Any	    =  42_6880 * Decimal(1_0005      ).sqrt()
					UpperCamelCase__      :       Dict	    =  1
					UpperCamelCase__      :       Tuple	    =  1359_1409
					UpperCamelCase__      :       Tuple	    =  Decimal(lowerCamelCase__      )
					for k in range(1 ,   lowerCamelCase__      ):
										UpperCamelCase__      :       Tuple	    =  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     :							int    =50
	print(F"""The first {n} digits of pi is: {pi(n)}""")







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:
     assert isinstance(__lowerCAmelCase ,   __lowerCAmelCase      ), f'The input value of [n={number}] is not an integer'

     if number == 1:
          return 2
     elif number < 1:
          UpperCamelCase__      :       List[Any]	    =  f'The input value of [n={number}] has to be > 0'
          raise ValueError(__lowerCAmelCase      )
     else:
          UpperCamelCase__      :       Optional[Any]	    =  sylvester(number - 1      )
          UpperCamelCase__      :       str	    =  num - 1
          UpperCamelCase__      :       int	    =  num
          return lower * upper + 1


if __name__ == "__main__":
 print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")