






"""simple docstring"""
from __future__ import annotations

import math
import random






def        lowerCamelCase_  (						_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase				):
 lowerCamelCase__     :			str     				=						d * e - 1
 lowerCamelCase__     :			List[str]     				=						0
 lowerCamelCase__     :			Any     				=						0
 while p == 0:
  lowerCamelCase__     :			List[Any]     				=						random.randint(2			,   n - 1				)
  lowerCamelCase__     :			Union[str, Any]     				=						k
  while True:
   if t % 2 == 0:
    lowerCamelCase__     :			Optional[Any]     				=						t // 2
    lowerCamelCase__     :			str     				=						(g**t) % n
    lowerCamelCase__     :			str     				=						math.gcd(x - 1			,   _lowerCamelCase				)
    if x > 1 and y > 1:
     lowerCamelCase__     :			Tuple     				=						y
     lowerCamelCase__     :			List[Any]     				=						n // y
     break  # find the correct factors
   else:
    break  # t is not divisible by 2, break and choose another g
 return sorted([p, q]				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()


"""simple docstring"""


def 			lowerCamelCase_ (					__lowerCAmelCase				)							->					str:




						'''simple docstring'''



						lowerCamelCase__					=1
						lowerCamelCase__					=0
						lowerCamelCase__					=1
						lowerCamelCase__					=1
						lowerCamelCase__					=3
						lowerCamelCase__					=3
						lowerCamelCase__					=limit
						lowerCamelCase__					=0

						lowerCamelCase__					=""
						while counter != decimal + 1:
												if 4 * q + r - t < n * t:
																		result += str(__lowerCAmelCase				)
																		if counter == 0:
																								result += "."

																		if decimal == counter:
																								break

																		counter += 1
																		lowerCamelCase__					=10 * (r - n * t)
																		lowerCamelCase__					=((10 * (3 * q + r)) // t) - 10 * n
																		q *= 10
																		lowerCamelCase__					=nr
												else:
																		lowerCamelCase__					=(2 * q + r) * l
																		lowerCamelCase__					=(q * (7 * k) + 2 + (r * l)) // (t * l)
																		q *= k
																		t *= l
																		l += 2
																		k += 1
																		lowerCamelCase__					=nn
																		lowerCamelCase__					=nr
						return result





def 			lowerCamelCase_ (					)							->					None:




						'''simple docstring'''



						print(F'''{calculate_pi(50				) = }'''				)
						import doctest

						doctest.testmod()


if __name__ == "__main__":
	main()


