




def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					return n * (2 * n - 1)







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					__magic_name__				:						Union[str, Any]     				=				(1 + 2_4 * n) ** 0.5
					return ((1 + root) / 6) % 1 == 0







def 		lowercase__ (		__A:						int = 1_4_4					):





					'''simple docstring'''






					__magic_name__				:						Dict     				=				start
					__magic_name__				:						str     				=				hexagonal_num(_A					)
					while not is_pentagonal(_A					):
										n += 1
										__magic_name__				:						Union[str, Any]     				=				hexagonal_num(_A					)
					return num


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







from typing import TYPE_CHECKING

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


A :       Optional[int]						=   {
    "configuration_mpnet": ["MPNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "MPNetConfig"],
    "tokenization_mpnet": ["MPNetTokenizer"],
}

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A :       List[Any]						=   ["MPNetTokenizerFast"]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A :       List[str]						=   [
        "MPNET_PRETRAINED_MODEL_ARCHIVE_LIST",
        "MPNetForMaskedLM",
        "MPNetForMultipleChoice",
        "MPNetForQuestionAnswering",
        "MPNetForSequenceClassification",
        "MPNetForTokenClassification",
        "MPNetLayer",
        "MPNetModel",
        "MPNetPreTrainedModel",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A :       Tuple						=   [
        "TF_MPNET_PRETRAINED_MODEL_ARCHIVE_LIST",
        "TFMPNetEmbeddings",
        "TFMPNetForMaskedLM",
        "TFMPNetForMultipleChoice",
        "TFMPNetForQuestionAnswering",
        "TFMPNetForSequenceClassification",
        "TFMPNetForTokenClassification",
        "TFMPNetMainLayer",
        "TFMPNetModel",
        "TFMPNetPreTrainedModel",
    ]


if TYPE_CHECKING:
    from .configuration_mpnet import MPNET_PRETRAINED_CONFIG_ARCHIVE_MAP, MPNetConfig
    from .tokenization_mpnet import MPNetTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_mpnet_fast import MPNetTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_mpnet import (
            MPNET_PRETRAINED_MODEL_ARCHIVE_LIST,
            MPNetForMaskedLM,
            MPNetForMultipleChoice,
            MPNetForQuestionAnswering,
            MPNetForSequenceClassification,
            MPNetForTokenClassification,
            MPNetLayer,
            MPNetModel,
            MPNetPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_mpnet import (
            TF_MPNET_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFMPNetEmbeddings,
            TFMPNetForMaskedLM,
            TFMPNetForMultipleChoice,
            TFMPNetForQuestionAnswering,
            TFMPNetForSequenceClassification,
            TFMPNetForTokenClassification,
            TFMPNetMainLayer,
            TFMPNetModel,
            TFMPNetPreTrainedModel,
        )

else:
    import sys

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


