





'''simple docstring'''




from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


__SCREAMING_SNAKE_CASE     :Union[str, Any]       =				logging.get_logger(__name__)


__SCREAMING_SNAKE_CASE     :Union[str, Any]       =				TypeVar('''DatasetType''', Dataset, IterableDataset)
def 	UpperCAmelCase_							(					__lowercase							:      List[DatasetType]			,     __lowercase							:      Optional[List[float]] = None			,     __lowercase							:      Optional[int] = None			,     __lowercase							:      Optional[DatasetInfo] = None			,     __lowercase							:      Optional[NamedSplit] = None			,     __lowercase							:      Literal["first_exhausted", "all_exhausted"] = "first_exhausted"			,     )		->       DatasetType:


     '''simple docstring'''



     from .arrow_dataset import Dataset
     from .iterable_dataset import IterableDataset

     if not datasets:
          raise ValueError("Unable to interleave an empty list of datasets."       )
     for i, dataset in enumerate(__lowercase       ):
          if not isinstance(__lowercase			,     (Dataset, IterableDataset)       ):
               if isinstance(__lowercase			,     (DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             f'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '
                             "is an empty dataset dictionary."       )
                    raise ValueError(
                        f'Dataset at position {i} has at least one split: {list(__lowercase       )}\n'
                        f'Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(__lowercase       )       )}\']'       )
               raise ValueError(
                   f'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__lowercase       ).__name__}.'       )
          if i == 0:
               _UpperCAmelCase							,  _UpperCAmelCase     							=   (
                   (Dataset, IterableDataset) if isinstance(__lowercase			,     __lowercase       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__lowercase			,     __lowercase       ):
               raise ValueError(
                   f'Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'       )
     if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
          raise ValueError(f'{stopping_strategy} is not supported. Please enter a valid stopping_strategy.'       )
     if dataset_type is Dataset:
          return _interleave_map_style_datasets(
              __lowercase			,     __lowercase			,     __lowercase			,     info=__lowercase			,     split=__lowercase			,     stopping_strategy=__lowercase       )
     else:
          return _interleave_iterable_datasets(
              __lowercase			,     __lowercase			,     __lowercase			,     info=__lowercase			,     split=__lowercase			,     stopping_strategy=__lowercase       )






def 	UpperCAmelCase_							(					__lowercase							:      List[DatasetType]			,     __lowercase							:      Optional[DatasetInfo] = None			,     __lowercase							:      Optional[NamedSplit] = None			,     __lowercase							:      int = 0			,     )		->       DatasetType:


     '''simple docstring'''



     if not dsets:
          raise ValueError("Unable to concatenate an empty list of datasets."       )
     for i, dataset in enumerate(__lowercase       ):
          if not isinstance(__lowercase			,     (Dataset, IterableDataset)       ):
               if isinstance(__lowercase			,     (DatasetDict, IterableDatasetDict)       ):
                    if not dataset:
                         raise ValueError(
                             f'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '
                             "is an empty dataset dictionary."       )
                    raise ValueError(
                        f'Dataset at position {i} has at least one split: {list(__lowercase       )}\n'
                        f'Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(__lowercase       )       )}\']'       )
               raise ValueError(
                   f'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__lowercase       ).__name__}.'       )
          if i == 0:
               _UpperCAmelCase							,  _UpperCAmelCase     							=   (
                   (Dataset, IterableDataset) if isinstance(__lowercase			,     __lowercase       ) else (IterableDataset, Dataset)
               )
          elif not isinstance(__lowercase			,     __lowercase       ):
               raise ValueError(
                   f'Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'       )
     if dataset_type is Dataset:
          return _concatenate_map_style_datasets(__lowercase			,     info=__lowercase			,     split=__lowercase			,     axis=__lowercase       )
     else:
          return _concatenate_iterable_datasets(__lowercase			,     info=__lowercase			,     split=__lowercase			,     axis=__lowercase       )










from __future__ import annotations

from math import gcd

def 					UpperCAmelCase_							(      __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.
            SCREAMING_SNAKE_CASE_							=			seed
            SCREAMING_SNAKE_CASE_							=			seed

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  SCREAMING_SNAKE_CASE_							=			rand_fn(__UpperCAmelCase			,			__UpperCAmelCase			,			__UpperCAmelCase							)
                  SCREAMING_SNAKE_CASE_							=			rand_fn(__UpperCAmelCase			,			__UpperCAmelCase			,			__UpperCAmelCase							)
                  SCREAMING_SNAKE_CASE_							=			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``.
                  SCREAMING_SNAKE_CASE_							=			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.
            SCREAMING_SNAKE_CASE_							=			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

   lowerCamelCase__ :   List[str]					=							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',
   )
   lowerCamelCase__ :   Tuple					=							parser.parse_args()

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