


from math import factorial

class 							a						:




							"""simple docstring"""


							def __init__(				self			:    Any       ,      lowerCamelCase			:    Dict       ,      lowerCamelCase			:    Optional[Any]							)      ->       Any:
														__snake_case						:     Optional[Any]									=  real
														if isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					__snake_case						:     List[str]									=  [1] * rank
														else:
																					__snake_case						:     List[str]									=  rank

							def __repr__(				self			:    Optional[int]							)      ->       List[str]:
														return (
														    F'{self.real}+'
														    F'{"+".join(str(lowerCamelCase							)+"E"+str(n+1							)for n,dual in enumerate(self.duals							)							)}'
														)

							def        __snake_case   (				self			:    Any							)      ->       Dict:
														__snake_case						:     Optional[int]									=  self.duals.copy()
														while cur[-1] == 0:
																					cur.pop(-1							)
														return Dual(self.real       ,      lowerCamelCase							)

							def __add__(				self			:    Any       ,      lowerCamelCase			:    int							)      ->       Dict:
														if not isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					return Dual(self.real + other       ,      self.duals							)
														__snake_case						:     Dict									=  self.duals.copy()
														__snake_case						:     Tuple									=  other.duals.copy()
														if len(lowerCamelCase							) > len(lowerCamelCase							):
																					o_dual.extend([1] * (len(lowerCamelCase							) - len(lowerCamelCase							))							)
														elif len(lowerCamelCase							) < len(lowerCamelCase							):
																					s_dual.extend([1] * (len(lowerCamelCase							) - len(lowerCamelCase							))							)
														__snake_case						:     int									=  []
														for i in range(len(lowerCamelCase							)							):
																					new_duals.append(s_dual[i] + o_dual[i]							)
														return Dual(self.real + other.real       ,      lowerCamelCase							)

							__UpperCAmelCase       :				Tuple	    =    __add__

							def __sub__(				self			:    Union[str, Any]       ,      lowerCamelCase			:    int							)      ->       List[Any]:
														return self + other * -1

							def __mul__(				self			:    Any       ,      lowerCamelCase			:    Optional[Any]							)      ->       Any:
														if not isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					__snake_case						:     Tuple									=  []
																					for i in self.duals:
																												new_duals.append(i * other							)
																					return Dual(self.real * other       ,      lowerCamelCase							)
														__snake_case						:     Union[str, Any]									=  [0] * (len(self.duals							) + len(other.duals							) + 1)
														for i, item in enumerate(self.duals							):
																					for j, jtem in enumerate(other.duals							):
																												new_duals[i + j + 1] += item * jtem
														for k in range(len(self.duals							)							):
																					new_duals[k] += self.duals[k] * other.real
														for index in range(len(other.duals							)							):
																					new_duals[index] += other.duals[index] * self.real
														return Dual(self.real * other.real       ,      lowerCamelCase							)

							__UpperCAmelCase       :				Union[str, Any]	    =    __mul__

							def __truediv__(				self			:    int       ,      lowerCamelCase			:    str							)      ->       Optional[Any]:
														if not isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					__snake_case						:     Optional[Any]									=  []
																					for i in self.duals:
																												new_duals.append(i / other							)
																					return Dual(self.real / other       ,      lowerCamelCase							)
														raise ValueError

							def __floordiv__(				self			:    Tuple       ,      lowerCamelCase			:    Any							)      ->       Optional[Any]:
														if not isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					__snake_case						:     str									=  []
																					for i in self.duals:
																												new_duals.append(i // other							)
																					return Dual(self.real // other       ,      lowerCamelCase							)
														raise ValueError






							def __pow__(				self			:    Optional[int]       ,      lowerCamelCase			:    List[Any]							)      ->       int:
														if n < 0 or isinstance(lowerCamelCase       ,      lowerCamelCase							):
																					raise ValueError("power must be a positive integer"							)
														if n == 0:
																					return 1
														if n == 1:
																					return self
														__snake_case						:     Dict									=  self
														for _ in range(n - 1							):
																					x *= self
														return x







def 							lowerCAmelCase_	(   __lowerCamelCase				,      __lowerCamelCase				,      __lowerCamelCase      ):
							if not callable(__lowerCamelCase      ):
														raise ValueError("differentiate() requires a function as input for func"      )
							if not isinstance(__lowerCamelCase				,      (float, int)      ):
														raise ValueError("differentiate() requires a float as input for position"      )
							if not isinstance(__lowerCamelCase				,      __lowerCamelCase      ):
														raise ValueError("differentiate() requires an int as input for order"      )
							__snake_case						:     Optional[Any]									=  Dual(__lowerCamelCase				,      1      )
							__snake_case						:     Optional[int]									=  func(__lowerCamelCase      )
							if order == 0:
														return result.real
							return result.duals[order - 1] * factorial(__lowerCamelCase      )


if __name__ == "__main__":
			import doctest

			doctest.testmod()







			def 							lowerCAmelCase_	(   __lowerCamelCase      ):
										return y**2 * y**4

			print(differentiate(f, 9, 2))








'''simple docstring'''




from . import (
    albert,
    align,
    altclip,
    audio_spectrogram_transformer,
    auto,
    autoformer,
    bark,
    bart,
    barthez,
    bartpho,
    beit,
    bert,
    bert_generation,
    bert_japanese,
    bertweet,
    big_bird,
    bigbird_pegasus,
    biogpt,
    bit,
    blenderbot,
    blenderbot_small,
    blip,
    blip_a,
    bloom,
    bridgetower,
    byta,
    camembert,
    canine,
    chinese_clip,
    clap,
    clip,
    clipseg,
    codegen,
    conditional_detr,
    convbert,
    convnext,
    convnextva,
    cpm,
    cpmant,
    ctrl,
    cvt,
    dataavec,
    deberta,
    deberta_va,
    decision_transformer,
    deformable_detr,
    deit,
    deprecated,
    deta,
    detr,
    dialogpt,
    dinat,
    distilbert,
    dit,
    donut,
    dpr,
    dpt,
    efficientformer,
    efficientnet,
    electra,
    encodec,
    encoder_decoder,
    ernie,
    ernie_m,
    esm,
    falcon,
    flaubert,
    flava,
    fnet,
    focalnet,
    fsmt,
    funnel,
    git,
    glpn,
    gpta,
    gpt_bigcode,
    gpt_neo,
    gpt_neox,
    gpt_neox_japanese,
    gpt_swa,
    gptj,
    gptsan_japanese,
    graphormer,
    groupvit,
    herbert,
    hubert,
    ibert,
    imagegpt,
    informer,
    instructblip,
    jukebox,
    layoutlm,
    layoutlmva,
    layoutlmva,
    layoutxlm,
    led,
    levit,
    lilt,
    llama,
    longformer,
    longta,
    luke,
    lxmert,
    mam_aaa,
    marian,
    markuplm,
    maskaformer,
    maskformer,
    mbart,
    mbartaa,
    mega,
    megatron_bert,
    megatron_gpta,
    mgp_str,
    mluke,
    mobilebert,
    mobilenet_va,
    mobilenet_va,
    mobilevit,
    mobilevitva,
    mpnet,
    mra,
    mta,
    musicgen,
    mvp,
    nat,
    nezha,
    nllb,
    nllb_moe,
    nystromformer,
    oneformer,
    open_llama,
    openai,
    opt,
    owlvit,
    pegasus,
    pegasus_x,
    perceiver,
    phobert,
    pixastruct,
    plbart,
    poolformer,
    prophetnet,
    qdqbert,
    rag,
    realm,
    reformer,
    regnet,
    rembert,
    resnet,
    roberta,
    roberta_prelayernorm,
    roc_bert,
    roformer,
    rwkv,
    sam,
    segformer,
    sew,
    sew_d,
    speech_encoder_decoder,
    speech_to_text,
    speech_to_text_a,
    speechta,
    splinter,
    squeezebert,
    swiftformer,
    swin,
    swinasr,
    swinva,
    switch_transformers,
    ta,
    table_transformer,
    tapas,
    time_series_transformer,
    timesformer,
    timm_backbone,
    transfo_xl,
    trocr,
    tvlt,
    umta,
    unispeech,
    unispeech_sat,
    upernet,
    videomae,
    vilt,
    vision_encoder_decoder,
    vision_text_dual_encoder,
    visual_bert,
    vit,
    vit_hybrid,
    vit_mae,
    vit_msn,
    vivit,
    wavaveca,
    wavaveca_conformer,
    wavaveca_phoneme,
    wavaveca_with_lm,
    wavlm,
    whisper,
    x_clip,
    xglm,
    xlm,
    xlm_prophetnet,
    xlm_roberta,
    xlm_roberta_xl,
    xlnet,
    xmod,
    yolos,
    yoso,
)

