from __future__ import annotations

from functools import lru_cache
from math import ceil

UpperCamelCase  							=						100

UpperCamelCase  							=						set(range(3, NUM_PRIMES, 2))
primes.add(2)
UpperCamelCase  							=						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=100)
def 			lowercase_				(			_lowerCamelCase							:       Any):
    if number_to_partition < 0:
        return set()
    elif number_to_partition == 0:
        return {1}

    lowercase__ :   List[Any]    					=				set()
    lowercase__ :   Any    					=				42
    lowercase__ :   Union[str, Any]    					=				42

    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_				(			_lowerCamelCase							:       Optional[Any] = 5000):
    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_torch_available


lowercase    :							Tuple      =					{
    "configuration_xlm": ["XLM_PRETRAINED_CONFIG_ARCHIVE_MAP", "XLMConfig", "XLMOnnxConfig"],
    "tokenization_xlm": ["XLMTokenizer"],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowercase    :							int      =					[
					    "XLM_PRETRAINED_MODEL_ARCHIVE_LIST",
					    "XLMForMultipleChoice",
					    "XLMForQuestionAnswering",
					    "XLMForQuestionAnsweringSimple",
					    "XLMForSequenceClassification",
					    "XLMForTokenClassification",
					    "XLMModel",
					    "XLMPreTrainedModel",
					    "XLMWithLMHeadModel",
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowercase    :							Tuple      =					[
					    "TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST",
					    "TFXLMForMultipleChoice",
					    "TFXLMForQuestionAnsweringSimple",
					    "TFXLMForSequenceClassification",
					    "TFXLMForTokenClassification",
					    "TFXLMMainLayer",
					    "TFXLMModel",
					    "TFXLMPreTrainedModel",
					    "TFXLMWithLMHeadModel",
					]


if TYPE_CHECKING:
					from .configuration_xlm import XLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMConfig, XLMOnnxConfig
					from .tokenization_xlm import XLMTokenizer

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_xlm import (
										    XLM_PRETRAINED_MODEL_ARCHIVE_LIST,
										    XLMForMultipleChoice,
										    XLMForQuestionAnswering,
										    XLMForQuestionAnsweringSimple,
										    XLMForSequenceClassification,
										    XLMForTokenClassification,
										    XLMModel,
										    XLMPreTrainedModel,
										    XLMWithLMHeadModel,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_xlm import (
										    TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TFXLMForMultipleChoice,
										    TFXLMForQuestionAnsweringSimple,
										    TFXLMForSequenceClassification,
										    TFXLMForTokenClassification,
										    TFXLMMainLayer,
										    TFXLMModel,
										    TFXLMPreTrainedModel,
										    TFXLMWithLMHeadModel,
										)

else:
					import sys

					lowercase    :							Union[str, Any]      =					_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

