





import unittest

from transformers.testing_utils import CaptureStdout
from transformers.tools.python_interpreter import evaluate




def 	lowerCAmelCase_					(						__UpperCAmelCase:    List[Any]   )   ->			Optional[Any]:
    return x + 2






class 					lowercase__ (			unittest.TestCase       ):

   '''simple docstring'''


   def    UpperCamelCase__						(					self							)				->   Union[str, Any]:






       """simple docstring"""
       UpperCamelCase__							:       str      =   '''x = 3'''
       UpperCamelCase__							:       str      =   {}
       UpperCamelCase__							:       Any      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       assert result == 3
       self.assertDictEqual(__magic_name__,	{'''x''': 3}							)

       UpperCamelCase__							:       str      =   '''x = y'''
       UpperCamelCase__							:       Any      =   {'''y''': 5}
       UpperCamelCase__							:       str      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       # evaluate returns the value of the last assignment.
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 5, '''y''': 5}							)




   def    UpperCamelCase__						(					self							)				->   Union[str, Any]:






       """simple docstring"""
       UpperCamelCase__							:       str      =   '''y = add_two(x)'''
       UpperCamelCase__							:       List[Any]      =   {'''x''': 3}
       UpperCamelCase__							:       str      =   evaluate(__magic_name__,	{'''add_two''': add_two},	state=__magic_name__							)
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''y''': 5}							)

       # Won't work without the tool
       with CaptureStdout() as out:
           UpperCamelCase__							:       Optional[Any]      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       assert result is None
       assert "tried to execute add_two" in out.out




   def    UpperCamelCase__						(					self							)				->   List[Any]:






       """simple docstring"""
       UpperCamelCase__							:       int      =   '''x = 3'''
       UpperCamelCase__							:       Dict      =   {}
       UpperCamelCase__							:       Tuple      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       assert result == 3
       self.assertDictEqual(__magic_name__,	{'''x''': 3}							)




   def    UpperCamelCase__						(					self							)				->   str:






       """simple docstring"""
       UpperCamelCase__							:       Optional[int]      =   '''test_dict = {\'x\': x, \'y\': add_two(x)}'''
       UpperCamelCase__							:       Optional[Any]      =   {'''x''': 3}
       UpperCamelCase__							:       str      =   evaluate(__magic_name__,	{'''add_two''': add_two},	state=__magic_name__							)
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''y''': 5}							)
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''test_dict''': {'''x''': 3, '''y''': 5}}							)




   def    UpperCamelCase__						(					self							)				->   Any:






       """simple docstring"""
       UpperCamelCase__							:       Any      =   '''x = 3\ny = 5'''
       UpperCamelCase__							:       Optional[int]      =   {}
       UpperCamelCase__							:       List[Any]      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       # evaluate returns the value of the last assignment.
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''y''': 5}							)




   def    UpperCamelCase__						(					self							)				->   Dict:






       """simple docstring"""
       UpperCamelCase__							:       List[Any]      =   '''text = f\'This is x: {x}.\''''
       UpperCamelCase__							:       Dict      =   {'''x''': 3}
       UpperCamelCase__							:       Optional[int]      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       # evaluate returns the value of the last assignment.
       assert result == "This is x: 3."
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''text''': '''This is x: 3.'''}							)




   def    UpperCamelCase__						(					self							)				->   Optional[int]:






       """simple docstring"""
       UpperCamelCase__							:       str      =   '''if x <= 3:\n    y = 2\nelse:\n    y = 5'''
       UpperCamelCase__							:       int      =   {'''x''': 3}
       UpperCamelCase__							:       str      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       # evaluate returns the value of the last assignment.
       assert result == 2
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''y''': 2}							)

       UpperCamelCase__							:       Optional[int]      =   {'''x''': 8}
       UpperCamelCase__							:       List[Any]      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       # evaluate returns the value of the last assignment.
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 8, '''y''': 5}							)




   def    UpperCamelCase__						(					self							)				->   Optional[Any]:






       """simple docstring"""
       UpperCamelCase__							:       Tuple      =   '''test_list = [x, add_two(x)]'''
       UpperCamelCase__							:       Tuple      =   {'''x''': 3}
       UpperCamelCase__							:       Any      =   evaluate(__magic_name__,	{'''add_two''': add_two},	state=__magic_name__							)
       self.assertListEqual(__magic_name__,	[3, 5]							)
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''test_list''': [3, 5]}							)




   def    UpperCamelCase__						(					self							)				->   List[str]:






       """simple docstring"""
       UpperCamelCase__							:       List[Any]      =   '''y = x'''
       UpperCamelCase__							:       Any      =   {'''x''': 3}
       UpperCamelCase__							:       Dict      =   evaluate(__magic_name__,	{},	state=__magic_name__							)
       assert result == 3
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''y''': 3}							)




   def    UpperCamelCase__						(					self							)				->   Dict:






       """simple docstring"""
       UpperCamelCase__							:       Tuple      =   '''test_list = [x, add_two(x)]\ntest_list[1]'''
       UpperCamelCase__							:       Dict      =   {'''x''': 3}
       UpperCamelCase__							:       List[str]      =   evaluate(__magic_name__,	{'''add_two''': add_two},	state=__magic_name__							)
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''test_list''': [3, 5]}							)

       UpperCamelCase__							:       str      =   '''test_dict = {\'x\': x, \'y\': add_two(x)}\ntest_dict[\'y\']'''
       UpperCamelCase__							:       Tuple      =   {'''x''': 3}
       UpperCamelCase__							:       List[str]      =   evaluate(__magic_name__,	{'''add_two''': add_two},	state=__magic_name__							)
       assert result == 5
       self.assertDictEqual(__magic_name__,	{'''x''': 3, '''test_dict''': {'''x''': 3, '''y''': 5}}							)




   def    UpperCamelCase__						(					self							)				->   Union[str, Any]:






       """simple docstring"""
       UpperCamelCase__							:       Tuple      =   '''x = 0\nfor i in range(3):\n    x = i'''
       UpperCamelCase__							:       Dict      =   {}
       UpperCamelCase__							:       Optional[int]      =   evaluate(__magic_name__,	{'''range''': range},	state=__magic_name__							)
       assert result == 2
       self.assertDictEqual(__magic_name__,	{'''x''': 2, '''i''': 2}							)








from __future__ import annotations

from math import gcd




def 	lowerCAmelCase_					(						__UpperCAmelCase:    int	,     __UpperCAmelCase:    int = 2	,     __UpperCAmelCase:    int = 1	,     __UpperCAmelCase:    int = 3	,     )   ->			int | None:
    # A value less than 2 can cause an infinite loop in the algorithm.
    if num < 2:
        raise ValueError('''The input value cannot be less than 2'''   )

    # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
    # algorithm struggles to find factors that are divisible by two.
    # As a workaround, we specifically check for two and even inputs.
    #   See: https://math.stackexchange.com/a/2856214/165820
    if num > 2 and num % 2 == 0:
        return 2

    # Pollard's Rho algorithm requires a function that returns pseudorandom
    # values between 0 <= X < ``num``.  It doesn't need to be random in the
    # sense that the output value is cryptographically secure or difficult
    # to calculate, it only needs to be random in the sense that all output
    # values should be equally likely to appear.
    # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
    # However, the success of Pollard's algorithm isn't guaranteed and is
    # determined in part by the initial seed and the chosen random function.
    # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
    # where ``C`` is a value that we can modify between each attempt.
    def rand_fn(__UpperCAmelCase:    int	,     __UpperCAmelCase:    int	,     __UpperCAmelCase:    int   ) -> int:
        return (pow(__UpperCAmelCase	,     2   ) + step) % modulus

    for _ in range(__UpperCAmelCase   ):
        # These track the position within the cycle detection logic.
        UpperCamelCase__							:       List[Any]      =   seed
        UpperCamelCase__							:       List[str]      =   seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       List[str]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )

            # At some point both the tortoise and the hare will enter a cycle whose
            # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
            # the tortoise and hare will end up on the same value modulo ``p``.
            # We can detect when this happens because the position difference between
            # the tortoise and the hare will share a common divisor with ``num``.
            UpperCamelCase__							:       Optional[int]      =   gcd(hare - tortoise	,     __UpperCAmelCase   )

            if divisor == 1:
                # No common divisor yet, just keep searching.
                continue
            else:
                # We found a common divisor!
                if divisor == num:
                    # Unfortunately, the divisor is ``num`` itself and is useless.
                    break
                else:
                    # The divisor is a nontrivial factor of ``num``!
                    return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
        UpperCamelCase__							:       List[str]      =   hare

        # The new step value for the random function can just be incremented.
        # At first the results will be similar to what the old function would
        # have produced, but the value will quickly diverge after a bit.
        step += 1

    # We haven't found a divisor within the requested number of attempts.
    # We were unlucky or ``num`` itself is actually prime.
    return None


if __name__ == "__main__":
  import argparse

  UpperCAmelCase_  							=				argparse.ArgumentParser()
  parser.add_argument(
      'num',
      type=int,
      help='The value to find a divisor of',
  )
  parser.add_argument(
      '--attempts',
      type=int,
      default=3,
      help='The number of attempts before giving up',
  )
  UpperCAmelCase_  							=				parser.parse_args()

  UpperCAmelCase_  							=				pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F'''{args.num} is probably prime''')
  else:
    UpperCAmelCase_  							=				args.num // divisor
    print(F'''{args.num} = {divisor} * {quotient}''')

