


from __future__ import annotations






def 							__lowercase     (				__lowerCAmelCase							:       Union[str, Any]      ,					__lowerCAmelCase							:       Optional[Any]      ,					__lowerCAmelCase							:       Dict      ,					):
							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()








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






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

							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 / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


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




