

from __future__ import annotations

import math
import random





def  _snake_case		(snake_case_					:     Optional[Any]    ,       snake_case_					:     Optional[int]    ,       snake_case_					:     str  )							->		list[int]:
  __UpperCAmelCase	:  Optional[Any]		=     d * e - 1
  __UpperCAmelCase	:  Optional[Any]		=     0
  __UpperCAmelCase	:  int		=     0
  while p == 0:
    __UpperCAmelCase	:  Any		=     random.randint(2    ,       n - 1  )
    __UpperCAmelCase	:  int		=     k
    while True:
      if t % 2 == 0:
        __UpperCAmelCase	:  List[Any]		=     t // 2
        __UpperCAmelCase	:  Tuple		=     (g**t) % n
        __UpperCAmelCase	:  Dict		=     math.gcd(x - 1    ,       SCREAMING_SNAKE_CASE_  )
        if x > 1 and y > 1:
          __UpperCAmelCase	:  int		=     y
          __UpperCAmelCase	:  List[str]		=     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()












def        A__						(							SCREAMING_SNAKE_CASE_ = 1_0_0_0		) ->  int:
		lowerCamelCase :			Dict    		=[]
		lowerCamelCase :			Dict    		=[]
		lowerCamelCase :			Union[str, Any]    		=3
		lowerCamelCase :			List[str]    		=5
		lowerCamelCase :			Union[str, Any]    		=1
		while True:
				lowerCamelCase :			Dict    		=z * temp
				if result < n:
						zmulti.append(SCREAMING_SNAKE_CASE_		)
						temp += 1
				else:
						lowerCamelCase :			List[Any]    		=1
						break
		while True:
				lowerCamelCase :			Optional[Any]    		=x * temp
				if result < n:
						xmulti.append(SCREAMING_SNAKE_CASE_		)
						temp += 1
				else:
						break
		lowerCamelCase :			str    		=list(set(xmulti + zmulti		)		)
		return sum(SCREAMING_SNAKE_CASE_		)


if __name__ == "__main__":
				print(F"""{solution() = }""")

