





'''simple docstring'''



from math import factorial

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




def 				snake_case_      (		SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  if not isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):
    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(SCREAMING_SNAKE_CASE__       )       )




def 				snake_case_      (		SCREAMING_SNAKE_CASE__ = 60					,	SCREAMING_SNAKE_CASE__ = 1_00_00_00       ):







  '''simple docstring'''



  if not isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ) or not isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):
    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
  _snake_case     		=				0
  # the cached sizes of the previous chains
  _snake_case     		=				{}

  for start_chain_element in range(1					,	SCREAMING_SNAKE_CASE__       ):
    # The temporary set will contain the elements of the chain
    _snake_case     		=				set()
    _snake_case     		=				0

    # Stop computing the chain when you find a cached size, a repeating item or the
    # length is greater then the desired one.
    _snake_case     		=				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(SCREAMING_SNAKE_CASE__       )
      chain_set_length += 1
      _snake_case     		=				digit_factorial_sum(SCREAMING_SNAKE_CASE__       )

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

    _snake_case     		=				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'''



import collections
import gzip
import os
import urllib

import numpy
from tensorflow.python.framework import dtypes, random_seed
from tensorflow.python.platform import gfile
from tensorflow.python.util.deprecation import deprecated

__magic_name__   :						Union[str, Any]    =			collections.namedtuple("""_Datasets""", ["""train""", """validation""", """test"""])

# CVDF mirror of http://yann.lecun.com/exdb/mnist/
__magic_name__   :						int    =			"""https://storage.googleapis.com/cvdf-datasets/mnist/"""




def 				snake_case_      (		SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  _snake_case     		=				numpy.dtype(numpy.uintaa       ).newbyteorder(">"       )
  return numpy.frombuffer(bytestream.read(4       )					,	dtype=SCREAMING_SNAKE_CASE__       )[0]




@deprecated(SCREAMING_SNAKE_CASE__					,	"Please use tf.data to implement this functionality."       )
def 				snake_case_      (		SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  print("Extracting"					,	f.name       )
  with gzip.GzipFile(fileobj=SCREAMING_SNAKE_CASE__       ) as bytestream:
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    if magic != 20_51:
      raise ValueError(
          "Invalid magic number %d in MNIST image file: %s" % (magic, f.name)       )
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    _snake_case     		=				bytestream.read(rows * cols * num_images       )
    _snake_case     		=				numpy.frombuffer(SCREAMING_SNAKE_CASE__					,	dtype=numpy.uinta       )
    _snake_case     		=				data.reshape(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	1       )
    return data




@deprecated(SCREAMING_SNAKE_CASE__					,	"Please use tf.one_hot on tensors."       )
def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  _snake_case     		=				labels_dense.shape[0]
  _snake_case     		=				numpy.arange(SCREAMING_SNAKE_CASE__       ) * num_classes
  _snake_case     		=				numpy.zeros((num_labels, num_classes)       )
  _snake_case     		=				1
  return labels_one_hot




@deprecated(SCREAMING_SNAKE_CASE__					,	"Please use tf.data to implement this functionality."       )
def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__=False					,	SCREAMING_SNAKE_CASE__=10       ):







  '''simple docstring'''



  print("Extracting"					,	f.name       )
  with gzip.GzipFile(fileobj=SCREAMING_SNAKE_CASE__       ) as bytestream:
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    if magic != 20_49:
      raise ValueError(
          "Invalid magic number %d in MNIST label file: %s" % (magic, f.name)       )
    _snake_case     		=				_readaa(SCREAMING_SNAKE_CASE__       )
    _snake_case     		=				bytestream.read(SCREAMING_SNAKE_CASE__       )
    _snake_case     		=				numpy.frombuffer(SCREAMING_SNAKE_CASE__					,	dtype=numpy.uinta       )
    if one_hot:
      return _dense_to_one_hot(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       )
    return labels


class       __SCREAMING_SNAKE_CASE	:



     '''simple docstring'''






     @deprecated(
         lowerCamelCase						,   "Please use alternatives such as official/mnist/_DataSet.py"
         " from tensorflow/models."						,   )
     def __init__(					self						,   lowerCamelCase						,   lowerCamelCase						,   lowerCamelCase=False						,   lowerCamelCase=False						,   lowerCamelCase=dtypes.floataa						,   lowerCamelCase=True						,   lowerCamelCase=None						,   ):
       _snake_case		,		_snake_case     		=				random_seed.get_seed(lowerCamelCase	)
       # If op level seed is not set, use whatever graph level seed is returned
       numpy.random.seed(seeda if seed is None else seeda	)
       _snake_case     		=				dtypes.as_dtype(lowerCamelCase	).base_dtype
       if dtype not in (dtypes.uinta, dtypes.floataa):
         raise TypeError("Invalid image dtype %r, expected uint8 or float32" % dtype	)
       if fake_data:
         _snake_case     		=				10_000
         _snake_case     		=				one_hot
       else:
         assert (
             images.shape[0] == labels.shape[0]
         ), F'''images.shape: {images.shape} labels.shape: {labels.shape}'''
         _snake_case     		=				images.shape[0]

         # Convert shape from [num examples, rows, columns, depth]
         # to [num examples, rows*columns] (assuming depth == 1)
         if reshape:
           assert images.shape[3] == 1
           _snake_case     		=				images.reshape(
               images.shape[0]						,   images.shape[1] * images.shape[2]	)
         if dtype == dtypes.floataa:
           # Convert from [0, 255] -> [0.0, 1.0].
           _snake_case     		=				images.astype(numpy.floataa	)
           _snake_case     		=				numpy.multiply(lowerCamelCase						,   1.0 / 255.0	)
       _snake_case     		=				images
       _snake_case     		=				labels
       _snake_case     		=				0
       _snake_case     		=				0

     @property
     def 	UpperCamelCase(					self	):
       return self._images

     @property
     def 	UpperCamelCase(					self	):
       return self._labels

     @property
     def 	UpperCamelCase(					self	):
       return self._num_examples

     @property
     def 	UpperCamelCase(					self	):
       return self._epochs_completed






     def 	UpperCamelCase(					self						,   lowerCamelCase						,   lowerCamelCase=False						,   lowerCamelCase=True	):
       if fake_data:
         _snake_case     		=				[1] * 784
         _snake_case     		=				[1] + [0] * 9 if self.one_hot else 0
         return (
             [fake_image for _ in range(lowerCamelCase	)],
             [fake_label for _ in range(lowerCamelCase	)],
         )
       _snake_case     		=				self._index_in_epoch
       # Shuffle for the first epoch
       if self._epochs_completed == 0 and start == 0 and shuffle:
         _snake_case     		=				numpy.arange(self._num_examples	)
         numpy.random.shuffle(lowerCamelCase	)
         _snake_case     		=				self.images[perma]
         _snake_case     		=				self.labels[perma]
       # Go to the next epoch
       if start + batch_size > self._num_examples:
         # Finished epoch
         self._epochs_completed += 1
         # Get the rest examples in this epoch
         _snake_case     		=				self._num_examples - start
         _snake_case     		=				self._images[start : self._num_examples]
         _snake_case     		=				self._labels[start : self._num_examples]
         # Shuffle the data
         if shuffle:
           _snake_case     		=				numpy.arange(self._num_examples	)
           numpy.random.shuffle(lowerCamelCase	)
           _snake_case     		=				self.images[perm]
           _snake_case     		=				self.labels[perm]
         # Start next epoch
         _snake_case     		=				0
         _snake_case     		=				batch_size - rest_num_examples
         _snake_case     		=				self._index_in_epoch
         _snake_case     		=				self._images[start:end]
         _snake_case     		=				self._labels[start:end]
         return (
             numpy.concatenate((images_rest_part, images_new_part)						,   axis=0	),
             numpy.concatenate((labels_rest_part, labels_new_part)						,   axis=0	),
         )
       else:
         self._index_in_epoch += batch_size
         _snake_case     		=				self._index_in_epoch
         return self._images[start:end], self._labels[start:end]







@deprecated(SCREAMING_SNAKE_CASE__					,	"Please write your own downloading logic."       )
def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       ):







  '''simple docstring'''



  if not gfile.Exists(SCREAMING_SNAKE_CASE__       ):
    gfile.MakeDirs(SCREAMING_SNAKE_CASE__       )
  _snake_case     		=				os.path.join(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       )
  if not gfile.Exists(SCREAMING_SNAKE_CASE__       ):
    urllib.request.urlretrieve(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__       )  # noqa: S310
    with gfile.GFile(SCREAMING_SNAKE_CASE__       ) as f:
      _snake_case     		=				f.size()
    print("Successfully downloaded"					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	"bytes."       )
  return filepath




@deprecated(
    SCREAMING_SNAKE_CASE__					,	"Please use alternatives such as:" " tensorflow_datasets.load('mnist')"       )
def 				snake_case_      (		SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__=False					,	SCREAMING_SNAKE_CASE__=False					,	SCREAMING_SNAKE_CASE__=dtypes.floataa					,	SCREAMING_SNAKE_CASE__=True					,	SCREAMING_SNAKE_CASE__=50_00					,	SCREAMING_SNAKE_CASE__=None					,	SCREAMING_SNAKE_CASE__=DEFAULT_SOURCE_URL					,	):







  '''simple docstring'''



  if fake_data:

    def fake():
      return _DataSet(
          []					,	[]					,	fake_data=SCREAMING_SNAKE_CASE__					,	one_hot=SCREAMING_SNAKE_CASE__					,	dtype=SCREAMING_SNAKE_CASE__					,	seed=SCREAMING_SNAKE_CASE__       )

    _snake_case     		=				fake()
    _snake_case     		=				fake()
    _snake_case     		=				fake()
    return _Datasets(train=SCREAMING_SNAKE_CASE__					,	validation=SCREAMING_SNAKE_CASE__					,	test=SCREAMING_SNAKE_CASE__       )

  if not source_url:  # empty string check
    _snake_case     		=				DEFAULT_SOURCE_URL

  _snake_case     		=				"train-images-idx3-ubyte.gz"
  _snake_case     		=				"train-labels-idx1-ubyte.gz"
  _snake_case     		=				"t10k-images-idx3-ubyte.gz"
  _snake_case     		=				"t10k-labels-idx1-ubyte.gz"

  _snake_case     		=				_maybe_download(
      SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	source_url + train_images_file       )
  with gfile.Open(SCREAMING_SNAKE_CASE__					,	"rb"       ) as f:
    _snake_case     		=				_extract_images(SCREAMING_SNAKE_CASE__       )

  _snake_case     		=				_maybe_download(
      SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	source_url + train_labels_file       )
  with gfile.Open(SCREAMING_SNAKE_CASE__					,	"rb"       ) as f:
    _snake_case     		=				_extract_labels(SCREAMING_SNAKE_CASE__					,	one_hot=SCREAMING_SNAKE_CASE__       )

  _snake_case     		=				_maybe_download(
      SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	source_url + test_images_file       )
  with gfile.Open(SCREAMING_SNAKE_CASE__					,	"rb"       ) as f:
    _snake_case     		=				_extract_images(SCREAMING_SNAKE_CASE__       )

  _snake_case     		=				_maybe_download(
      SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	source_url + test_labels_file       )
  with gfile.Open(SCREAMING_SNAKE_CASE__					,	"rb"       ) as f:
    _snake_case     		=				_extract_labels(SCREAMING_SNAKE_CASE__					,	one_hot=SCREAMING_SNAKE_CASE__       )

  if not 0 <= validation_size <= len(SCREAMING_SNAKE_CASE__       ):
    _snake_case     		=				(
        "Validation size should be between 0 and "
        f'''{len(SCREAMING_SNAKE_CASE__       )}. Received: {validation_size}.'''
    )
    raise ValueError(SCREAMING_SNAKE_CASE__       )

  _snake_case     		=				train_images[:validation_size]
  _snake_case     		=				train_labels[:validation_size]
  _snake_case     		=				train_images[validation_size:]
  _snake_case     		=				train_labels[validation_size:]

  _snake_case     		=				{"dtype": dtype, "reshape": reshape, "seed": seed}

  _snake_case     		=				_DataSet(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	**SCREAMING_SNAKE_CASE__       )
  _snake_case     		=				_DataSet(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	**SCREAMING_SNAKE_CASE__       )
  _snake_case     		=				_DataSet(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	**SCREAMING_SNAKE_CASE__       )

  return _Datasets(train=SCREAMING_SNAKE_CASE__					,	validation=SCREAMING_SNAKE_CASE__					,	test=SCREAMING_SNAKE_CASE__       )


