





_UpperCAmelCase       : Dict     =       "0.18.2"

from .configuration_utils import ConfigMixin
from .utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_onnx_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    logging,
)


try:
    if not is_onnx_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_onnx_objects import *  # noqa F403
else:
    from .pipelines import OnnxRuntimeModel

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_pt_objects import *  # noqa F403
else:
    from .models import (
        AutoencoderKL,
        ControlNetModel,
        ModelMixin,
        PriorTransformer,
        TaFilmDecoder,
        TransformeraDModel,
        UNetaDModel,
        UNetaDConditionModel,
        UNetaDModel,
        UNetaDConditionModel,
        VQModel,
    )
    from .optimization import (
        get_constant_schedule,
        get_constant_schedule_with_warmup,
        get_cosine_schedule_with_warmup,
        get_cosine_with_hard_restarts_schedule_with_warmup,
        get_linear_schedule_with_warmup,
        get_polynomial_decay_schedule_with_warmup,
        get_scheduler,
    )
    from .pipelines import (
        AudioPipelineOutput,
        ConsistencyModelPipeline,
        DanceDiffusionPipeline,
        DDIMPipeline,
        DDPMPipeline,
        DiffusionPipeline,
        DiTPipeline,
        ImagePipelineOutput,
        KarrasVePipeline,
        LDMPipeline,
        LDMSuperResolutionPipeline,
        PNDMPipeline,
        RePaintPipeline,
        ScoreSdeVePipeline,
    )
    from .schedulers import (
        CMStochasticIterativeScheduler,
        DDIMInverseScheduler,
        DDIMParallelScheduler,
        DDIMScheduler,
        DDPMParallelScheduler,
        DDPMScheduler,
        DEISMultistepScheduler,
        DPMSolverMultistepInverseScheduler,
        DPMSolverMultistepScheduler,
        DPMSolverSinglestepScheduler,
        EulerAncestralDiscreteScheduler,
        EulerDiscreteScheduler,
        HeunDiscreteScheduler,
        IPNDMScheduler,
        KarrasVeScheduler,
        KDPMaAncestralDiscreteScheduler,
        KDPMaDiscreteScheduler,
        PNDMScheduler,
        RePaintScheduler,
        SchedulerMixin,
        ScoreSdeVeScheduler,
        UnCLIPScheduler,
        UniPCMultistepScheduler,
        VQDiffusionScheduler,
    )
    from .training_utils import EMAModel

try:
    if not (is_torch_available() and is_scipy_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
    from .schedulers import LMSDiscreteScheduler

try:
    if not (is_torch_available() and is_torchsde_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
    from .schedulers import DPMSolverSDEScheduler

try:
    if not (is_torch_available() and is_transformers_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
    from .pipelines import (
        AltDiffusionImgaImgPipeline,
        AltDiffusionPipeline,
        AudioLDMPipeline,
        CycleDiffusionPipeline,
        IFImgaImgPipeline,
        IFImgaImgSuperResolutionPipeline,
        IFInpaintingPipeline,
        IFInpaintingSuperResolutionPipeline,
        IFPipeline,
        IFSuperResolutionPipeline,
        ImageTextPipelineOutput,
        KandinskyImgaImgPipeline,
        KandinskyInpaintPipeline,
        KandinskyPipeline,
        KandinskyPriorPipeline,
        KandinskyVaaControlnetImgaImgPipeline,
        KandinskyVaaControlnetPipeline,
        KandinskyVaaImgaImgPipeline,
        KandinskyVaaInpaintPipeline,
        KandinskyVaaPipeline,
        KandinskyVaaPriorEmbaEmbPipeline,
        KandinskyVaaPriorPipeline,
        LDMTextToImagePipeline,
        PaintByExamplePipeline,
        SemanticStableDiffusionPipeline,
        ShapEImgaImgPipeline,
        ShapEPipeline,
        StableDiffusionAttendAndExcitePipeline,
        StableDiffusionControlNetImgaImgPipeline,
        StableDiffusionControlNetInpaintPipeline,
        StableDiffusionControlNetPipeline,
        StableDiffusionDepthaImgPipeline,
        StableDiffusionDiffEditPipeline,
        StableDiffusionImageVariationPipeline,
        StableDiffusionImgaImgPipeline,
        StableDiffusionInpaintPipeline,
        StableDiffusionInpaintPipelineLegacy,
        StableDiffusionInstructPixaPixPipeline,
        StableDiffusionLatentUpscalePipeline,
        StableDiffusionLDMaDPipeline,
        StableDiffusionModelEditingPipeline,
        StableDiffusionPanoramaPipeline,
        StableDiffusionParadigmsPipeline,
        StableDiffusionPipeline,
        StableDiffusionPipelineSafe,
        StableDiffusionPixaPixZeroPipeline,
        StableDiffusionSAGPipeline,
        StableDiffusionUpscalePipeline,
        StableUnCLIPImgaImgPipeline,
        StableUnCLIPPipeline,
        TextToVideoSDPipeline,
        TextToVideoZeroPipeline,
        UnCLIPImageVariationPipeline,
        UnCLIPPipeline,
        UniDiffuserModel,
        UniDiffuserPipeline,
        UniDiffuserTextDecoder,
        VersatileDiffusionDualGuidedPipeline,
        VersatileDiffusionImageVariationPipeline,
        VersatileDiffusionPipeline,
        VersatileDiffusionTextToImagePipeline,
        VideoToVideoSDPipeline,
        VQDiffusionPipeline,
    )

try:
    if not (is_torch_available() and is_transformers_available() and is_invisible_watermark_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_transformers_and_invisible_watermark_objects import *  # noqa F403
else:
    from .pipelines import StableDiffusionXLImgaImgPipeline, StableDiffusionXLPipeline

try:
    if not (is_torch_available() and is_transformers_available() and is_k_diffusion_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_transformers_and_k_diffusion_objects import *  # noqa F403
else:
    from .pipelines import StableDiffusionKDiffusionPipeline

try:
    if not (is_torch_available() and is_transformers_available() and is_onnx_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_transformers_and_onnx_objects import *  # noqa F403
else:
    from .pipelines import (
        OnnxStableDiffusionImgaImgPipeline,
        OnnxStableDiffusionInpaintPipeline,
        OnnxStableDiffusionInpaintPipelineLegacy,
        OnnxStableDiffusionPipeline,
        OnnxStableDiffusionUpscalePipeline,
        StableDiffusionOnnxPipeline,
    )

try:
    if not (is_torch_available() and is_librosa_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_torch_and_librosa_objects import *  # noqa F403
else:
    from .pipelines import AudioDiffusionPipeline, Mel

try:
    if not (is_transformers_available() and is_torch_available() and is_note_seq_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_transformers_and_torch_and_note_seq_objects import *  # noqa F403
else:
    from .pipelines import SpectrogramDiffusionPipeline

try:
    if not is_flax_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_flax_objects import *  # noqa F403
else:
    from .models.controlnet_flax import FlaxControlNetModel
    from .models.modeling_flax_utils import FlaxModelMixin
    from .models.unet_ad_condition_flax import FlaxUNetaDConditionModel
    from .models.vae_flax import FlaxAutoencoderKL
    from .pipelines import FlaxDiffusionPipeline
    from .schedulers import (
        FlaxDDIMScheduler,
        FlaxDDPMScheduler,
        FlaxDPMSolverMultistepScheduler,
        FlaxKarrasVeScheduler,
        FlaxLMSDiscreteScheduler,
        FlaxPNDMScheduler,
        FlaxSchedulerMixin,
        FlaxScoreSdeVeScheduler,
    )


try:
    if not (is_flax_available() and is_transformers_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_flax_and_transformers_objects import *  # noqa F403
else:
    from .pipelines import (
        FlaxStableDiffusionControlNetPipeline,
        FlaxStableDiffusionImgaImgPipeline,
        FlaxStableDiffusionInpaintPipeline,
        FlaxStableDiffusionPipeline,
    )

try:
    if not (is_note_seq_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from .utils.dummy_note_seq_objects import *  # noqa F403
else:
    from .pipelines import MidiProcessor












from __future__ import annotations

from collections.abc import Generator


def  SCREAMING_SNAKE_CASE   ( )    ->  Generator[int, None, None]:
    lowerCamelCase__					:   dict[int, int]      				=	{}
    lowerCamelCase__					:   Union[str, Any]      				=	2
    while True:
        lowerCamelCase__					:   Optional[int]      				=	factor_map.pop(_UpperCAmelCase		,			_UpperCAmelCase				)
        if factor:
            lowerCamelCase__					:   Optional[Any]      				=	factor + prime
            while x in factor_map:
                x += factor
            lowerCamelCase__					:   Optional[Any]      				=	factor
        else:
            lowerCamelCase__					:   Union[str, Any]      				=	prime
            yield prime
        prime += 1


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 1e10				)    ->  int:
    lowerCamelCase__					:   Tuple      				=	sieve()

    lowerCamelCase__					:   Dict      				=	1
    while True:
        lowerCamelCase__					:   List[Any]      				=	next(_UpperCAmelCase				)
        if (2 * prime * n) > limit:
            return n
        # Ignore the next prime as the reminder will be 2.
        next(_UpperCAmelCase				)
        n += 2


if __name__ == "__main__":
    print(solution())





