
from collections import OrderedDict

from ...utils import logging
from .auto_factory import _BaseAutoModelClass, _LazyAutoMapping, auto_class_update
from .configuration_auto import CONFIG_MAPPING_NAMES


_A   =			logging.get_logger(__name__)


_A   =			OrderedDict(
    [
        # Base model mapping
        ("albert", "FlaxAlbertModel"),
        ("bart", "FlaxBartModel"),
        ("beit", "FlaxBeitModel"),
        ("bert", "FlaxBertModel"),
        ("big_bird", "FlaxBigBirdModel"),
        ("blenderbot", "FlaxBlenderbotModel"),
        ("blenderbot-small", "FlaxBlenderbotSmallModel"),
        ("clip", "FlaxCLIPModel"),
        ("distilbert", "FlaxDistilBertModel"),
        ("electra", "FlaxElectraModel"),
        ("gpt-sw3", "FlaxGPT2Model"),
        ("gpt2", "FlaxGPT2Model"),
        ("gpt_neo", "FlaxGPTNeoModel"),
        ("gptj", "FlaxGPTJModel"),
        ("longt5", "FlaxLongT5Model"),
        ("marian", "FlaxMarianModel"),
        ("mbart", "FlaxMBartModel"),
        ("mt5", "FlaxMT5Model"),
        ("opt", "FlaxOPTModel"),
        ("pegasus", "FlaxPegasusModel"),
        ("regnet", "FlaxRegNetModel"),
        ("resnet", "FlaxResNetModel"),
        ("roberta", "FlaxRobertaModel"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormModel"),
        ("roformer", "FlaxRoFormerModel"),
        ("t5", "FlaxT5Model"),
        ("vision-text-dual-encoder", "FlaxVisionTextDualEncoderModel"),
        ("vit", "FlaxViTModel"),
        ("wav2vec2", "FlaxWav2Vec2Model"),
        ("whisper", "FlaxWhisperModel"),
        ("xglm", "FlaxXGLMModel"),
        ("xlm-roberta", "FlaxXLMRobertaModel"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for pre-training mapping
        ("albert", "FlaxAlbertForPreTraining"),
        ("bart", "FlaxBartForConditionalGeneration"),
        ("bert", "FlaxBertForPreTraining"),
        ("big_bird", "FlaxBigBirdForPreTraining"),
        ("electra", "FlaxElectraForPreTraining"),
        ("longt5", "FlaxLongT5ForConditionalGeneration"),
        ("mbart", "FlaxMBartForConditionalGeneration"),
        ("mt5", "FlaxMT5ForConditionalGeneration"),
        ("roberta", "FlaxRobertaForMaskedLM"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForMaskedLM"),
        ("roformer", "FlaxRoFormerForMaskedLM"),
        ("t5", "FlaxT5ForConditionalGeneration"),
        ("wav2vec2", "FlaxWav2Vec2ForPreTraining"),
        ("whisper", "FlaxWhisperForConditionalGeneration"),
        ("xlm-roberta", "FlaxXLMRobertaForMaskedLM"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Masked LM mapping
        ("albert", "FlaxAlbertForMaskedLM"),
        ("bart", "FlaxBartForConditionalGeneration"),
        ("bert", "FlaxBertForMaskedLM"),
        ("big_bird", "FlaxBigBirdForMaskedLM"),
        ("distilbert", "FlaxDistilBertForMaskedLM"),
        ("electra", "FlaxElectraForMaskedLM"),
        ("mbart", "FlaxMBartForConditionalGeneration"),
        ("roberta", "FlaxRobertaForMaskedLM"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForMaskedLM"),
        ("roformer", "FlaxRoFormerForMaskedLM"),
        ("xlm-roberta", "FlaxXLMRobertaForMaskedLM"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Seq2Seq Causal LM mapping
        ("bart", "FlaxBartForConditionalGeneration"),
        ("blenderbot", "FlaxBlenderbotForConditionalGeneration"),
        ("blenderbot-small", "FlaxBlenderbotSmallForConditionalGeneration"),
        ("encoder-decoder", "FlaxEncoderDecoderModel"),
        ("longt5", "FlaxLongT5ForConditionalGeneration"),
        ("marian", "FlaxMarianMTModel"),
        ("mbart", "FlaxMBartForConditionalGeneration"),
        ("mt5", "FlaxMT5ForConditionalGeneration"),
        ("pegasus", "FlaxPegasusForConditionalGeneration"),
        ("t5", "FlaxT5ForConditionalGeneration"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Image-classsification
        ("beit", "FlaxBeitForImageClassification"),
        ("regnet", "FlaxRegNetForImageClassification"),
        ("resnet", "FlaxResNetForImageClassification"),
        ("vit", "FlaxViTForImageClassification"),
    ]
)

_A   =			OrderedDict(
    [
        ("vision-encoder-decoder", "FlaxVisionEncoderDecoderModel"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Causal LM mapping
        ("bart", "FlaxBartForCausalLM"),
        ("bert", "FlaxBertForCausalLM"),
        ("big_bird", "FlaxBigBirdForCausalLM"),
        ("electra", "FlaxElectraForCausalLM"),
        ("gpt-sw3", "FlaxGPT2LMHeadModel"),
        ("gpt2", "FlaxGPT2LMHeadModel"),
        ("gpt_neo", "FlaxGPTNeoForCausalLM"),
        ("gptj", "FlaxGPTJForCausalLM"),
        ("opt", "FlaxOPTForCausalLM"),
        ("roberta", "FlaxRobertaForCausalLM"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForCausalLM"),
        ("xglm", "FlaxXGLMForCausalLM"),
        ("xlm-roberta", "FlaxXLMRobertaForCausalLM"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Sequence Classification mapping
        ("albert", "FlaxAlbertForSequenceClassification"),
        ("bart", "FlaxBartForSequenceClassification"),
        ("bert", "FlaxBertForSequenceClassification"),
        ("big_bird", "FlaxBigBirdForSequenceClassification"),
        ("distilbert", "FlaxDistilBertForSequenceClassification"),
        ("electra", "FlaxElectraForSequenceClassification"),
        ("mbart", "FlaxMBartForSequenceClassification"),
        ("roberta", "FlaxRobertaForSequenceClassification"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForSequenceClassification"),
        ("roformer", "FlaxRoFormerForSequenceClassification"),
        ("xlm-roberta", "FlaxXLMRobertaForSequenceClassification"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Question Answering mapping
        ("albert", "FlaxAlbertForQuestionAnswering"),
        ("bart", "FlaxBartForQuestionAnswering"),
        ("bert", "FlaxBertForQuestionAnswering"),
        ("big_bird", "FlaxBigBirdForQuestionAnswering"),
        ("distilbert", "FlaxDistilBertForQuestionAnswering"),
        ("electra", "FlaxElectraForQuestionAnswering"),
        ("mbart", "FlaxMBartForQuestionAnswering"),
        ("roberta", "FlaxRobertaForQuestionAnswering"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForQuestionAnswering"),
        ("roformer", "FlaxRoFormerForQuestionAnswering"),
        ("xlm-roberta", "FlaxXLMRobertaForQuestionAnswering"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Token Classification mapping
        ("albert", "FlaxAlbertForTokenClassification"),
        ("bert", "FlaxBertForTokenClassification"),
        ("big_bird", "FlaxBigBirdForTokenClassification"),
        ("distilbert", "FlaxDistilBertForTokenClassification"),
        ("electra", "FlaxElectraForTokenClassification"),
        ("roberta", "FlaxRobertaForTokenClassification"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForTokenClassification"),
        ("roformer", "FlaxRoFormerForTokenClassification"),
        ("xlm-roberta", "FlaxXLMRobertaForTokenClassification"),
    ]
)

_A   =			OrderedDict(
    [
        # Model for Multiple Choice mapping
        ("albert", "FlaxAlbertForMultipleChoice"),
        ("bert", "FlaxBertForMultipleChoice"),
        ("big_bird", "FlaxBigBirdForMultipleChoice"),
        ("distilbert", "FlaxDistilBertForMultipleChoice"),
        ("electra", "FlaxElectraForMultipleChoice"),
        ("roberta", "FlaxRobertaForMultipleChoice"),
        ("roberta-prelayernorm", "FlaxRobertaPreLayerNormForMultipleChoice"),
        ("roformer", "FlaxRoFormerForMultipleChoice"),
        ("xlm-roberta", "FlaxXLMRobertaForMultipleChoice"),
    ]
)

_A   =			OrderedDict(
    [
        ("bert", "FlaxBertForNextSentencePrediction"),
    ]
)

_A   =			OrderedDict(
    [
        ("speech-encoder-decoder", "FlaxSpeechEncoderDecoderModel"),
        ("whisper", "FlaxWhisperForConditionalGeneration"),
    ]
)

_A   =			OrderedDict(
    [
        ("whisper", "FlaxWhisperForAudioClassification"),
    ]
)

_A   =			_LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_MAPPING_NAMES)
_A   =			_LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_PRETRAINING_MAPPING_NAMES)
_A   =			_LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_MASKED_LM_MAPPING_NAMES)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING_NAMES)
_A   =			_LazyAutoMapping(CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_CAUSAL_LM_MAPPING_NAMES)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING_NAMES
)
_A   =			_LazyAutoMapping(
    CONFIG_MAPPING_NAMES, FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING_NAMES
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							int									=		FLAX_MODEL_MAPPING


_A   =			auto_class_update(FlaxAutoModel)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Optional[Any]									=		FLAX_MODEL_FOR_PRETRAINING_MAPPING


_A   =			auto_class_update(FlaxAutoModelForPreTraining, head_doc="pretraining")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Any									=		FLAX_MODEL_FOR_CAUSAL_LM_MAPPING


_A   =			auto_class_update(FlaxAutoModelForCausalLM, head_doc="causal language modeling")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Any									=		FLAX_MODEL_FOR_MASKED_LM_MAPPING


_A   =			auto_class_update(FlaxAutoModelForMaskedLM, head_doc="masked language modeling")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							List[str]									=		FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForSeqaSeqLM, head_doc="sequence-to-sequence language modeling", checkpoint_for_example="t5-base"
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							List[str]									=		FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForSequenceClassification, head_doc="sequence classification"
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							List[str]									=		FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING


_A   =			auto_class_update(FlaxAutoModelForQuestionAnswering, head_doc="question answering")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Dict									=		FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForTokenClassification, head_doc="token classification"
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Optional[int]									=		FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING


_A   =			auto_class_update(FlaxAutoModelForMultipleChoice, head_doc="multiple choice")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Any									=		FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForNextSentencePrediction, head_doc="next sentence prediction"
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Dict									=		FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForImageClassification, head_doc="image classification"
)







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Dict									=		FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING


_A   =			auto_class_update(FlaxAutoModelForVisionaSeq, head_doc="vision-to-text modeling")







class 					lowerCamelCase		(  _BaseAutoModelClass  ):
					UpperCAmelCase__    :							Union[str, Any]									=		FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING


_A   =			auto_class_update(
    FlaxAutoModelForSpeechSeqaSeq, head_doc="sequence-to-sequence speech-to-text modeling"
)



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def 						lowercase_      (       A__		)							->							bool:
    """simple docstring"""

    snake_case								= int(number**0.5		)
    return number == sq * sq



def 						lowercase_      (       A__			,		A__			,		A__			,		A__			,		A__			,		A__		)							->							tuple[int, int]:
    """simple docstring"""

    snake_case								= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    snake_case								= x_den * y_den * z_den
    snake_case								= gcd(A__			,		A__		)
    top //= hcf
    bottom //= hcf
    return top, bottom



def 						lowercase_      (       A__ = 35		)							->							int:
    """simple docstring"""

    snake_case								= set()
    snake_case								= 42
    snake_case								= Fraction(0		)
    snake_case								= 42

    for x_num in range(1			,		order + 1		):
        for x_den in range(x_num + 1			,		order + 1		):
            for y_num in range(1			,		order + 1		):
                for y_den in range(y_num + 1			,		order + 1		):
                    # n=1
                    snake_case								= x_num * y_den + x_den * y_num
                    snake_case								= x_den * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= (
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    snake_case								= x_den * x_den * y_den * y_den
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

                    # n=-1
                    snake_case								= x_num * y_num
                    snake_case								= x_den * y_num + x_num * y_den
                    snake_case								= gcd(A__			,		A__		)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case								= add_three(
                            A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                        unique_s.add(A__		)

                    # n=2
                    snake_case								= x_num * x_num * y_num * y_num
                    snake_case								= (
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= add_three(
                                A__			,		A__			,		A__			,		A__			,		A__			,		A__		)
                            unique_s.add(A__		)

    for num, den in unique_s:
        total += Fraction(A__			,		A__		)

    return total.denominator + total.numerator


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

