from math import factorial

_lowerCAmelCase  :dict[str, int]  				=    {str(digit): factorial(digit) for digit in range(10)}


def     __lowerCAmelCase						(       a_		)      ->	int:





     '''simple docstring'''





     if not isinstance(__lowerCAmelCase       ,      __lowerCAmelCase		):
          raise TypeError('Parameter number must be int'		)

     if number < 0:
          raise ValueError('Parameter number must be greater than or equal to 0'		)

     # Converts number in string to iterate on its digits and adds its factorial.
     return sum(DIGIT_FACTORIAL[digit] for digit in str(__lowerCAmelCase		)		)


def     __lowerCAmelCase						(       a_ = 60       ,      a_ = 100_0000		)      ->	int:





     '''simple docstring'''





     if not isinstance(__lowerCAmelCase       ,      __lowerCAmelCase		) or not isinstance(__lowerCAmelCase       ,      __lowerCAmelCase		):
          raise TypeError('Parameters chain_length and number_limit must be int'		)

     if chain_length <= 0 or number_limit <= 0:
          raise ValueError(
              'Parameters chain_length and number_limit must be greater than 0'		)

     # the counter for the chains with the exact desired length
     SCREAMING_SNAKE_CASE					:			str    	=       0
     # the cached sizes of the previous chains
     SCREAMING_SNAKE_CASE					:			dict[int, int]    	=       {}

     for start_chain_element in range(1       ,      __lowerCAmelCase		):
          # The temporary set will contain the elements of the chain
          SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       set()
          SCREAMING_SNAKE_CASE					:			List[str]    	=       0

          # Stop computing the chain when you find a cached size, a repeating item or the
          # length is greater then the desired one.
          SCREAMING_SNAKE_CASE					:			str    	=       start_chain_element
          while (
              chain_element not in chain_sets_lengths
              and chain_element not in chain_set
              and chain_set_length <= chain_length
          ):
               chain_set.add(__lowerCAmelCase		)
               chain_set_length += 1
               SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       digit_factorial_sum(__lowerCAmelCase		)

          if chain_element in chain_sets_lengths:
               chain_set_length += chain_sets_lengths[chain_element]

          SCREAMING_SNAKE_CASE					:			str    	=       chain_set_length

          # If chain contains the exact amount of elements increase the counter
          if chain_set_length == chain_length:
               chains_counter += 1

     return chains_counter


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f"""{solution()}""")




'''simple docstring'''





from typing import Optional

import torch
import torch.utils.checkpoint
from torch import Tensor, nn
from torch.nn import BCEWithLogitsLoss, CrossEntropyLoss, MSELoss

from ...activations import ACTaFN
from ...file_utils import add_code_sample_docstrings, add_start_docstrings, add_start_docstrings_to_model_forward
from ...modeling_outputs import (
    BaseModelOutputWithNoAttention,
    BaseModelOutputWithPoolingAndNoAttention,
    ImageClassifierOutputWithNoAttention,
)
from ...modeling_utils import PreTrainedModel
from ...utils import logging
from .configuration_regnet import RegNetConfig


_lowerCAmelCase  :List[Any]  				=    logging.get_logger(__name__)

# General docstring
_lowerCAmelCase  :Optional[Any]  				=    """RegNetConfig"""

# Base docstring
_lowerCAmelCase  :int  				=    """facebook/regnet-y-040"""
_lowerCAmelCase  :Any  				=    [1, 1_088, 7, 7]

# Image classification docstring
_lowerCAmelCase  :Optional[Any]  				=    """facebook/regnet-y-040"""
_lowerCAmelCase  :Optional[int]  				=    """tabby, tabby cat"""

_lowerCAmelCase  :List[Any]  				=    [
    """facebook/regnet-y-040""",
    # See all regnet models at https://huggingface.co/models?filter=regnet
]






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__ = 3    ,							lowercase__ = 1    ,							lowercase__ = 1    ,							lowercase__ = "relu"    ,							)							-> Any:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			List[str]    	=       nn.Convad(
             lowercase__    ,							lowercase__    ,							kernel_size=lowercase__    ,							stride=lowercase__    ,							padding=kernel_size // 2    ,							groups=lowercase__    ,							bias=lowercase__    ,							)
         SCREAMING_SNAKE_CASE					:			Dict    	=       nn.BatchNormad(lowercase__ )
         SCREAMING_SNAKE_CASE					:			int    	=       ACTaFN[activation] if activation is not None else nn.Identity()






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> List[Any]:
         SCREAMING_SNAKE_CASE					:			int    	=       self.convolution(lowercase__ )
         SCREAMING_SNAKE_CASE					:			List[str]    	=       self.normalization(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self.activation(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> str:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       RegNetConvLayer(
             config.num_channels    ,							config.embedding_size    ,							kernel_size=3    ,							stride=2    ,							activation=config.hidden_act )
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       config.num_channels






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> str:
         SCREAMING_SNAKE_CASE					:			Dict    	=       pixel_values.shape[1]
         if num_channels != self.num_channels:
              raise ValueError(
                  'Make sure that the channel dimension of the pixel values match with the one set in the configuration.' )
         SCREAMING_SNAKE_CASE					:			str    	=       self.embedder(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__ = 2 )							-> Optional[int]:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       nn.Convad(lowercase__    ,							lowercase__    ,							kernel_size=1    ,							stride=lowercase__    ,							bias=lowercase__ )
         SCREAMING_SNAKE_CASE					:			Dict    	=       nn.BatchNormad(lowercase__ )






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Tensor:
         SCREAMING_SNAKE_CASE					:			int    	=       self.convolution(lowercase__ )
         SCREAMING_SNAKE_CASE					:			int    	=       self.normalization(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__ )							-> List[str]:
         super().__init__()

         SCREAMING_SNAKE_CASE					:			Any    	=       nn.AdaptiveAvgPoolad((1, 1) )
         SCREAMING_SNAKE_CASE					:			Tuple    	=       nn.Sequential(
             nn.Convad(lowercase__    ,							lowercase__    ,							kernel_size=1 )    ,							nn.ReLU()    ,							nn.Convad(lowercase__    ,							lowercase__    ,							kernel_size=1 )    ,							nn.Sigmoid()    ,							)






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Dict:
         # b c h w -> b c 1 1
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.pooler(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.attention(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       hidden_state * attention
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ = 1 )							-> Tuple:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       in_channels != out_channels or stride != 1
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       max(1    ,							out_channels // config.groups_width )
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       (
             RegNetShortCut(lowercase__    ,							lowercase__    ,							stride=lowercase__ ) if should_apply_shortcut else nn.Identity()
         )
         SCREAMING_SNAKE_CASE					:			Any    	=       nn.Sequential(
             RegNetConvLayer(lowercase__    ,							lowercase__    ,							kernel_size=1    ,							activation=config.hidden_act )    ,							RegNetConvLayer(lowercase__    ,							lowercase__    ,							stride=lowercase__    ,							groups=lowercase__    ,							activation=config.hidden_act )    ,							RegNetConvLayer(lowercase__    ,							lowercase__    ,							kernel_size=1    ,							activation=lowercase__ )    ,							)
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       ACTaFN[config.hidden_act]






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Any:
         SCREAMING_SNAKE_CASE					:			Tuple    	=       hidden_state
         SCREAMING_SNAKE_CASE					:			str    	=       self.layer(lowercase__ )
         SCREAMING_SNAKE_CASE					:			int    	=       self.shortcut(lowercase__ )
         hidden_state += residual
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       self.activation(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ = 1 )							-> str:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			Dict    	=       in_channels != out_channels or stride != 1
         SCREAMING_SNAKE_CASE					:			int    	=       max(1    ,							out_channels // config.groups_width )
         SCREAMING_SNAKE_CASE					:			int    	=       (
             RegNetShortCut(lowercase__    ,							lowercase__    ,							stride=lowercase__ ) if should_apply_shortcut else nn.Identity()
         )
         SCREAMING_SNAKE_CASE					:			Tuple    	=       nn.Sequential(
             RegNetConvLayer(lowercase__    ,							lowercase__    ,							kernel_size=1    ,							activation=config.hidden_act )    ,							RegNetConvLayer(lowercase__    ,							lowercase__    ,							stride=lowercase__    ,							groups=lowercase__    ,							activation=config.hidden_act )    ,							RegNetSELayer(lowercase__    ,							reduced_channels=int(round(in_channels / 4 ) ) )    ,							RegNetConvLayer(lowercase__    ,							lowercase__    ,							kernel_size=1    ,							activation=lowercase__ )    ,							)
         SCREAMING_SNAKE_CASE					:			Tuple    	=       ACTaFN[config.hidden_act]






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Union[str, Any]:
         SCREAMING_SNAKE_CASE					:			int    	=       hidden_state
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.layer(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Tuple    	=       self.shortcut(lowercase__ )
         hidden_state += residual
         SCREAMING_SNAKE_CASE					:			int    	=       self.activation(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ = 2    ,							lowercase__ = 2    ,							)							-> Any:
         super().__init__()

         SCREAMING_SNAKE_CASE					:			Tuple    	=       RegNetXLayer if config.layer_type == 'x' else RegNetYLayer

         SCREAMING_SNAKE_CASE					:			str    	=       nn.Sequential(
             # downsampling is done in the first layer with stride of 2
             layer(
                 lowercase__    ,							lowercase__    ,							lowercase__    ,							stride=lowercase__    ,							)    ,							*[layer(lowercase__    ,							lowercase__    ,							lowercase__ ) for _ in range(depth - 1 )]    ,							)






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> List[Any]:
         SCREAMING_SNAKE_CASE					:			Tuple    	=       self.layers(lowercase__ )
         return hidden_state






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> Dict:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			Dict    	=       nn.ModuleList([] )
         # based on `downsample_in_first_stage`, the first layer of the first stage may or may not downsample the input
         self.stages.append(
             RegNetStage(
                 lowercase__    ,							config.embedding_size    ,							config.hidden_sizes[0]    ,							stride=2 if config.downsample_in_first_stage else 1    ,							depth=config.depths[0]    ,							) )
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       zip(config.hidden_sizes    ,							config.hidden_sizes[1:] )
         for (in_channels, out_channels), depth in zip(lowercase__    ,							config.depths[1:] ):
              self.stages.append(RegNetStage(lowercase__    ,							lowercase__    ,							lowercase__    ,							depth=lowercase__ ) )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = False    ,							lowercase__ = True )							-> BaseModelOutputWithNoAttention:
         SCREAMING_SNAKE_CASE					:			str    	=       () if output_hidden_states else None

         for stage_module in self.stages:
              if output_hidden_states:
                   SCREAMING_SNAKE_CASE					:			Any    	=       hidden_states + (hidden_state,)

              SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       stage_module(lowercase__ )

         if output_hidden_states:
              SCREAMING_SNAKE_CASE					:			int    	=       hidden_states + (hidden_state,)

         if not return_dict:
              return tuple(v for v in [hidden_state, hidden_states] if v is not None )

         return BaseModelOutputWithNoAttention(last_hidden_state=lowercase__    ,							hidden_states=lowercase__ )






class 				UpperCAmelCase (       _SCREAMING_SNAKE_CASE ):




    '''simple docstring'''







    snake_case__							:   Any							=						RegNetConfig
    snake_case__							:   List[str]							=						"regnet"
    snake_case__							:   List[Any]							=						"pixel_values"
    snake_case__							:   Optional[Any]							=						True






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Any:
         if isinstance(lowercase__    ,							nn.Convad ):
              nn.init.kaiming_normal_(module.weight    ,							mode='fan_out'    ,							nonlinearity='relu' )
         elif isinstance(lowercase__    ,							(nn.BatchNormad, nn.GroupNorm) ):
              nn.init.constant_(module.weight    ,							1 )
              nn.init.constant_(module.bias    ,							0 )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__=False )							-> Tuple:
         if isinstance(lowercase__    ,							lowercase__ ):
              SCREAMING_SNAKE_CASE					:			Tuple    	=       value






_lowerCAmelCase  :Optional[Any]  				=    R"""
    This model is a PyTorch [torch.nn.Module](https://pytorch.org/docs/stable/nn.html#torch.nn.Module) subclass. Use it
    as a regular PyTorch Module and refer to the PyTorch documentation for all matter related to general usage and
    behavior.

    Parameters:
        config ([`RegNetConfig`]): Model configuration class with all the parameters of the model.
            Initializing with a config file does not load the weights associated with the model, only the
            configuration. Check out the [`~PreTrainedModel.from_pretrained`] method to load the model weights.
"""

_lowerCAmelCase  :Optional[Any]  				=    R"""
    Args:
        pixel_values (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)`):
            Pixel values. Pixel values can be obtained using [`AutoImageProcessor`]. See
            [`ConvNextImageProcessor.__call__`] for details.

        output_hidden_states (`bool`, *optional*):
            Whether or not to return the hidden states of all layers. See `hidden_states` under returned tensors for
            more detail.
        return_dict (`bool`, *optional*):
            Whether or not to return a [`~file_utils.ModelOutput`] instead of a plain tuple.
"""






@add_start_docstrings(
    "The bare RegNet model outputting raw features without any specific head on top."   ,    _SCREAMING_SNAKE_CASE   ,    )
# Copied from transformers.models.resnet.modeling_resnet.ResNetModel with RESNET->REGNET,ResNet->RegNet
class 				UpperCAmelCase (       _SCREAMING_SNAKE_CASE ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> Union[str, Any]:
         super().__init__(lowercase__ )
         SCREAMING_SNAKE_CASE					:			str    	=       config
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       RegNetEmbeddings(lowercase__ )
         SCREAMING_SNAKE_CASE					:			List[str]    	=       RegNetEncoder(lowercase__ )
         SCREAMING_SNAKE_CASE					:			int    	=       nn.AdaptiveAvgPoolad((1, 1) )
         # Initialize weights and apply final processing
         self.post_init()






    @add_start_docstrings_to_model_forward(lowercase__ )
    @add_code_sample_docstrings(
        checkpoint=_CHECKPOINT_FOR_DOC    ,							output_type=lowercase__    ,							config_class=_CONFIG_FOR_DOC    ,							modality='vision'    ,							expected_output=_EXPECTED_OUTPUT_SHAPE    ,							)
    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = None    ,							lowercase__ = None )							-> BaseModelOutputWithPoolingAndNoAttention:
         SCREAMING_SNAKE_CASE					:			Dict    	=       (
             output_hidden_states if output_hidden_states is not None else self.config.output_hidden_states
         )
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       return_dict if return_dict is not None else self.config.use_return_dict

         SCREAMING_SNAKE_CASE					:			List[str]    	=       self.embedder(lowercase__ )

         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       self.encoder(
             lowercase__    ,							output_hidden_states=lowercase__    ,							return_dict=lowercase__ )

         SCREAMING_SNAKE_CASE					:			Dict    	=       encoder_outputs[0]

         SCREAMING_SNAKE_CASE					:			Dict    	=       self.pooler(lowercase__ )

         if not return_dict:
              return (last_hidden_state, pooled_output) + encoder_outputs[1:]

         return BaseModelOutputWithPoolingAndNoAttention(
             last_hidden_state=lowercase__    ,							pooler_output=lowercase__    ,							hidden_states=encoder_outputs.hidden_states    ,							)






@add_start_docstrings(
    "\n    RegNet Model with an image classification head on top (a linear layer on top of the pooled features), e.g. for\n    ImageNet.\n    "   ,    _SCREAMING_SNAKE_CASE   ,    )
# Copied from transformers.models.resnet.modeling_resnet.ResNetForImageClassification with RESNET->REGNET,ResNet->RegNet,resnet->regnet
class 				UpperCAmelCase (       _SCREAMING_SNAKE_CASE ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> Dict:
         super().__init__(lowercase__ )
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       config.num_labels
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       RegNetModel(lowercase__ )
         # classification head
         SCREAMING_SNAKE_CASE					:			int    	=       nn.Sequential(
             nn.Flatten()    ,							nn.Linear(config.hidden_sizes[-1]    ,							config.num_labels ) if config.num_labels > 0 else nn.Identity()    ,							)
         # initialize weights and apply final processing
         self.post_init()






    @add_start_docstrings_to_model_forward(lowercase__ )
    @add_code_sample_docstrings(
        checkpoint=_IMAGE_CLASS_CHECKPOINT    ,							output_type=lowercase__    ,							config_class=_CONFIG_FOR_DOC    ,							expected_output=_IMAGE_CLASS_EXPECTED_OUTPUT    ,							)
    def       _UpperCamelCase    (       self    ,							lowercase__ = None    ,							lowercase__ = None    ,							lowercase__ = None    ,							lowercase__ = None    ,							)							-> ImageClassifierOutputWithNoAttention:
         SCREAMING_SNAKE_CASE					:			List[str]    	=       return_dict if return_dict is not None else self.config.use_return_dict

         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       self.regnet(lowercase__    ,							output_hidden_states=lowercase__    ,							return_dict=lowercase__ )

         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       outputs.pooler_output if return_dict else outputs[1]

         SCREAMING_SNAKE_CASE					:			List[Any]    	=       self.classifier(lowercase__ )

         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       None

         if labels is not None:
              if self.config.problem_type is None:
                   if self.num_labels == 1:
                        SCREAMING_SNAKE_CASE					:			List[Any]    	=       'regression'
                   elif self.num_labels > 1 and (labels.dtype == torch.long or labels.dtype == torch.int):
                        SCREAMING_SNAKE_CASE					:			int    	=       'single_label_classification'
                   else:
                        SCREAMING_SNAKE_CASE					:			str    	=       'multi_label_classification'
              if self.config.problem_type == "regression":
                   SCREAMING_SNAKE_CASE					:			List[Any]    	=       MSELoss()
                   if self.num_labels == 1:
                        SCREAMING_SNAKE_CASE					:			Any    	=       loss_fct(logits.squeeze()    ,							labels.squeeze() )
                   else:
                        SCREAMING_SNAKE_CASE					:			Any    	=       loss_fct(lowercase__    ,							lowercase__ )
              elif self.config.problem_type == "single_label_classification":
                   SCREAMING_SNAKE_CASE					:			Any    	=       CrossEntropyLoss()
                   SCREAMING_SNAKE_CASE					:			int    	=       loss_fct(logits.view(-1    ,							self.num_labels )    ,							labels.view(-1 ) )
              elif self.config.problem_type == "multi_label_classification":
                   SCREAMING_SNAKE_CASE					:			Optional[int]    	=       BCEWithLogitsLoss()
                   SCREAMING_SNAKE_CASE					:			Tuple    	=       loss_fct(lowercase__    ,							lowercase__ )

         if not return_dict:
              SCREAMING_SNAKE_CASE					:			List[str]    	=       (logits,) + outputs[2:]
              return (loss,) + output if loss is not None else output

         return ImageClassifierOutputWithNoAttention(loss=lowercase__    ,							logits=lowercase__    ,							hidden_states=outputs.hidden_states )



