

"""simple docstring"""
import argparse
from collections import defaultdict

import yaml


_A							=  """docs/source/en/_toctree.yml"""




def 					a__						(						lowerCAmelCase    )	-> Any:
      UpperCAmelCase__			:							str							=    defaultdict(lowerCAmelCase    )
      for doc in model_doc:
            counts[doc["local"]] += 1
      UpperCAmelCase__			:							Any							=    [key for key, value in counts.items() if value > 1]

      UpperCAmelCase__			:							List[str]							=    []
      for duplicate_key in duplicates:
            UpperCAmelCase__			:							List[Any]							=    list({doc["""title"""] for doc in model_doc if doc["""local"""] == duplicate_key}    )
            if len(lowerCAmelCase    ) > 1:
                  raise ValueError(
                      F"""{duplicate_key} is present several times in the documentation table of content at """
                      """`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the """
                      """others."""    )
            # Only add this once
            new_doc.append({"""local""": duplicate_key, """title""": titles[0]}    )

      # Add none duplicate-keys
      new_doc.extend([doc for doc in model_doc if counts[doc["""local"""]] == 1]    )

      # Sort
      return sorted(lowerCAmelCase			,	key=lambda lowerCAmelCase    : s["title"].lower()    )




def 					a__						(						lowerCAmelCase=False    )	-> Any:
      with open(lowerCAmelCase			,	encoding="""utf-8"""    ) as f:
            UpperCAmelCase__			:							Tuple							=    yaml.safe_load(f.read()    )

      # Get to the API doc
      UpperCAmelCase__			:							Optional[int]							=    0
      while content[api_idx]["title"] != "API":
            api_idx += 1
      UpperCAmelCase__			:							List[Any]							=    content[api_idx]["""sections"""]

      # Then to the model doc
      UpperCAmelCase__			:							int							=    0
      while api_doc[model_idx]["title"] != "Models":
            model_idx += 1

      UpperCAmelCase__			:							List[Any]							=    api_doc[model_idx]["""sections"""]

      UpperCAmelCase__			:							Optional[Any]							=    [(idx, section) for idx, section in enumerate(lowerCAmelCase    ) if """sections""" in section]
      UpperCAmelCase__			:							Optional[Any]							=    False
      for idx, modality_doc in modalities_docs:
            UpperCAmelCase__			:							List[str]							=    modality_doc["""sections"""]
            UpperCAmelCase__			:							int							=    clean_model_doc_toc(lowerCAmelCase    )

            if old_modality_doc != new_modality_doc:
                  UpperCAmelCase__			:							Optional[Any]							=    True
                  if overwrite:
                        UpperCAmelCase__			:							Optional[Any]							=    new_modality_doc

      if diff:
            if overwrite:
                  UpperCAmelCase__			:							Any							=    model_doc
                  UpperCAmelCase__			:							Optional[Any]							=    api_doc
                  with open(lowerCAmelCase			,	"""w"""			,	encoding="""utf-8"""    ) as f:
                        f.write(yaml.dump(lowerCAmelCase			,	allow_unicode=lowerCAmelCase    )    )
            else:
                  raise ValueError(
                      """The model doc part of the table of content is not properly sorted, run `make style` to fix this."""    )


if __name__ == "__main__":
    _A							=  argparse.ArgumentParser()
    parser.add_argument("""--fix_and_overwrite""", action="""store_true""", help="""Whether to fix inconsistencies.""")
    _A							=  parser.parse_args()

    check_model_doc(args.fix_and_overwrite)




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

from functools import lru_cache
from math import ceil

_A							=  1_00

_A							=  set(range(3, NUM_PRIMES, 2))
primes.add(2)
_A							=  42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
    if prime not in primes:
        continue
    primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))




@lru_cache(maxsize=1_00    )
def 					a__						(						lowerCAmelCase    )	-> set[int]:
      if number_to_partition < 0:
            return set()
      elif number_to_partition == 0:
            return {1}

      UpperCAmelCase__			:							set[int]							=    set()
      UpperCAmelCase__			:							int
      UpperCAmelCase__			:							int

      for prime in primes:
            if prime > number_to_partition:
                  continue
            for sub in partition(number_to_partition - prime    ):
                  ret.add(sub * prime    )

      return ret




def 					a__						(						lowerCAmelCase = 50_00    )	-> int | None:
      for number_to_partition in range(1			,	lowerCAmelCase    ):
            if len(partition(lowerCAmelCase    )    ) > number_unique_partitions:
                  return number_to_partition
      return None


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

