



'''simple docstring'''

from __future__ import annotations

from functools import lru_cache
from math import ceil

snake_case_      =  100

snake_case_      =  set(range(3, NUM_PRIMES, 2))
primes.add(2)
snake_case_      =  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    __lowercase	(_SCREAMING_SNAKE_CASE   :str							):
				if number_to_partition < 0:
								return set()
				elif number_to_partition == 0:
								return {1}

				SCREAMING_SNAKE_CASE	:    set[int]          =			set()
				SCREAMING_SNAKE_CASE	:    int
				SCREAMING_SNAKE_CASE	:    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    __lowercase	(_SCREAMING_SNAKE_CASE   :Optional[Any] = 50_00							):
				for number_to_partition in range(1     ,						_A							):
								if len(partition(_A							)							) > number_unique_partitions:
												return number_to_partition
				return None


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












"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_lowerCAmelCase            =	{
    'configuration_mobilebert': [
        'MOBILEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'MobileBertConfig',
        'MobileBertOnnxConfig',
    ],
    'tokenization_mobilebert': ['MobileBertTokenizer'],
}

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase            =	['MobileBertTokenizerFast']

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase            =	[
				    'MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'MobileBertForMaskedLM',
				    'MobileBertForMultipleChoice',
				    'MobileBertForNextSentencePrediction',
				    'MobileBertForPreTraining',
				    'MobileBertForQuestionAnswering',
				    'MobileBertForSequenceClassification',
				    'MobileBertForTokenClassification',
				    'MobileBertLayer',
				    'MobileBertModel',
				    'MobileBertPreTrainedModel',
				    'load_tf_weights_in_mobilebert',
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase            =	[
				    'TF_MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'TFMobileBertForMaskedLM',
				    'TFMobileBertForMultipleChoice',
				    'TFMobileBertForNextSentencePrediction',
				    'TFMobileBertForPreTraining',
				    'TFMobileBertForQuestionAnswering',
				    'TFMobileBertForSequenceClassification',
				    'TFMobileBertForTokenClassification',
				    'TFMobileBertMainLayer',
				    'TFMobileBertModel',
				    'TFMobileBertPreTrainedModel',
				]


if TYPE_CHECKING:
				from .configuration_mobilebert import (
				    MOBILEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    MobileBertConfig,
				    MobileBertOnnxConfig,
				)
				from .tokenization_mobilebert import MobileBertTokenizer

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_mobilebert_fast import MobileBertTokenizerFast

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_mobilebert import (
								    MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
								    MobileBertForMaskedLM,
								    MobileBertForMultipleChoice,
								    MobileBertForNextSentencePrediction,
								    MobileBertForPreTraining,
								    MobileBertForQuestionAnswering,
								    MobileBertForSequenceClassification,
								    MobileBertForTokenClassification,
								    MobileBertLayer,
								    MobileBertModel,
								    MobileBertPreTrainedModel,
								    load_tf_weights_in_mobilebert,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_mobilebert import (
								    TF_MOBILEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
								    TFMobileBertForMaskedLM,
								    TFMobileBertForMultipleChoice,
								    TFMobileBertForNextSentencePrediction,
								    TFMobileBertForPreTraining,
								    TFMobileBertForQuestionAnswering,
								    TFMobileBertForSequenceClassification,
								    TFMobileBertForTokenClassification,
								    TFMobileBertMainLayer,
								    TFMobileBertModel,
								    TFMobileBertPreTrainedModel,
								)

else:
				import sys

				_lowerCAmelCase            =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
