






from __future__ import annotations

import math
import random


def      lowerCamelCase__	(   lowercase  ,   lowercase  ,   lowercase ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE				:					List[str]		  =			d * e - 1
  SCREAMING_SNAKE_CASE				:					int		  =			0
  SCREAMING_SNAKE_CASE				:					str		  =			0
  while p == 0:
    SCREAMING_SNAKE_CASE				:					Any		  =			random.randint(2  ,   n - 1 )
    SCREAMING_SNAKE_CASE				:					List[str]		  =			k
    while True:
      if t % 2 == 0:
        SCREAMING_SNAKE_CASE				:					Dict		  =			t // 2
        SCREAMING_SNAKE_CASE				:					Union[str, Any]		  =			(g**t) % n
        SCREAMING_SNAKE_CASE				:					List[Any]		  =			math.gcd(x - 1  ,   lowercase )
        if x > 1 and y > 1:
          SCREAMING_SNAKE_CASE				:					Union[str, Any]		  =			y
          SCREAMING_SNAKE_CASE				:					int		  =			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()














import re


def      lowerCamelCase__	(   lowercase ):

  """simple docstring"""






  def docstring_decorator(lowercase ):
    SCREAMING_SNAKE_CASE				:					List[Any]		  =			fn.__doc__
    SCREAMING_SNAKE_CASE				:					Tuple		  =			func_doc.split("\n" )
    SCREAMING_SNAKE_CASE				:					Tuple		  =			0
    while i < len(lowercase ) and re.search(R"^\s*Examples?:\s*$"  ,   lines[i] ) is None:
      i += 1
    if i < len(lowercase ):
      SCREAMING_SNAKE_CASE				:					int		  =			example_docstring
      SCREAMING_SNAKE_CASE				:					Tuple		  =			"\n".join(lowercase )
    else:
      raise ValueError(
          F'''The function {fn} should have an empty \'Examples:\' in its docstring as placeholder, '''
          F'''current docstring is:\n{func_doc}''' )
    SCREAMING_SNAKE_CASE				:					int		  =			func_doc
    return fn

  return docstring_decorator






