





"""simple docstring"""



from __future__ import annotations







def 		__lowercase					(       snake_case_  :  int						)       ->list[int]:



    '''simple docstring'''







    __A   :						List[str]									=					2
    __A   :						Union[str, Any]									=					[]
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(snake_case_						)
    if n > 1:
        factors.append(snake_case_						)
    return factors


if __name__ == "__main__":
       import doctest

       doctest.testmod()











"""simple docstring"""



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







def 		__lowercase					(       snake_case_  :  int						)       ->str:



    '''simple docstring'''







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

    __A   :						int									=					precision
    __A   :						Tuple									=					ceil(precision / 14						)
    __A   :						Dict									=					426880 * Decimal(10005						).sqrt()
    __A   :						Optional[Any]									=					1
    __A   :						int									=					13591409
    __A   :						Optional[int]									=					Decimal(snake_case_						)
    for k in range(1    ,snake_case_						):
        __A   :						int									=					factorial(6 * k						) // (factorial(3 * k						) * factorial(snake_case_						) ** 3)
        linear_term += 545140134
        exponential_term *= -262537412640768000
        partial_sum += Decimal(multinomial_term * linear_term						) / exponential_term
    return str(constant_term / partial_sum						)[:-1]


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




