

'''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

UpperCamelCase__  :      Optional[Any]			=    collections.namedtuple("_Datasets", ["train", "validation", "test"])

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


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Tuple       ):





    """simple docstring"""


    SCREAMING_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 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Any       ):





    """simple docstring"""


    print('Extracting' ,   f.name       )
    with gzip.GzipFile(fileobj=_SCREAMING_SNAKE_CASE       ) as bytestream:
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        if magic != 2_051:
            raise ValueError(
                'Invalid magic number %d in MNIST image file: %s' % (magic, f.name)       )
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        SCREAMING_SNAKE_CASE_									=						bytestream.read(rows * cols * num_images       )
        SCREAMING_SNAKE_CASE_									=						numpy.frombuffer(_SCREAMING_SNAKE_CASE ,   dtype=numpy.uinta       )
        SCREAMING_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 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		Dict       ):





    """simple docstring"""


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


@deprecated(_SCREAMING_SNAKE_CASE ,   'Please use tf.data to implement this functionality.'       )
def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		List[str] ,   _SCREAMING_SNAKE_CASE					:		Optional[Any]=False ,   _SCREAMING_SNAKE_CASE					:		Union[str, Any]=10       ):





    """simple docstring"""


    print('Extracting' ,   f.name       )
    with gzip.GzipFile(fileobj=_SCREAMING_SNAKE_CASE       ) as bytestream:
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        if magic != 2_049:
            raise ValueError(
                'Invalid magic number %d in MNIST label file: %s' % (magic, f.name)       )
        SCREAMING_SNAKE_CASE_									=						_readaa(_SCREAMING_SNAKE_CASE       )
        SCREAMING_SNAKE_CASE_									=						bytestream.read(_SCREAMING_SNAKE_CASE       )
        SCREAMING_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       __snake_case  :

  @deprecated(
      _A						,		'Please use alternatives such as official/mnist/_DataSet.py'
      ' from tensorflow/models.'						,		)
  def __init__(					self						,		_A						,		_A						,		_A=False						,		_A=False						,		_A=dtypes.floataa						,		_A=True						,		_A=None						,		):
      SCREAMING_SNAKE_CASE_							,			SCREAMING_SNAKE_CASE_									=						random_seed.get_seed(_A)
      # If op level seed is not set, use whatever graph level seed is returned
      numpy.random.seed(seeda if seed is None else seeda)
      SCREAMING_SNAKE_CASE_									=						dtypes.as_dtype(_A).base_dtype
      if dtype not in (dtypes.uinta, dtypes.floataa):
          raise TypeError('Invalid image dtype %r, expected uint8 or float32' % dtype)
      if fake_data:
          SCREAMING_SNAKE_CASE_									=						10000
          SCREAMING_SNAKE_CASE_									=						one_hot
      else:
          assert (
              images.shape[0] == labels.shape[0]
          ), f"""images.shape: {images.shape} labels.shape: {labels.shape}"""
          SCREAMING_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
              SCREAMING_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].
              SCREAMING_SNAKE_CASE_									=						images.astype(numpy.floataa)
              SCREAMING_SNAKE_CASE_									=						numpy.multiply(_A						,		1.0 / 255.0)
      SCREAMING_SNAKE_CASE_									=						images
      SCREAMING_SNAKE_CASE_									=						labels
      SCREAMING_SNAKE_CASE_									=						0
      SCREAMING_SNAKE_CASE_									=						0

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

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

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

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


  def 						lowerCAmelCase__     (					self						,		_A						,		_A=False						,		_A=True):
      if fake_data:
          SCREAMING_SNAKE_CASE_									=						[1] * 784
          SCREAMING_SNAKE_CASE_									=						[1] + [0] * 9 if self.one_hot else 0
          return (
              [fake_image for _ in range(_A)],
              [fake_label for _ in range(_A)],
          )
      SCREAMING_SNAKE_CASE_									=						self._index_in_epoch
      # Shuffle for the first epoch
      if self._epochs_completed == 0 and start == 0 and shuffle:
          SCREAMING_SNAKE_CASE_									=						numpy.arange(self._num_examples)
          numpy.random.shuffle(_A)
          SCREAMING_SNAKE_CASE_									=						self.images[perma]
          SCREAMING_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
          SCREAMING_SNAKE_CASE_									=						self._num_examples - start
          SCREAMING_SNAKE_CASE_									=						self._images[start : self._num_examples]
          SCREAMING_SNAKE_CASE_									=						self._labels[start : self._num_examples]
          # Shuffle the data
          if shuffle:
              SCREAMING_SNAKE_CASE_									=						numpy.arange(self._num_examples)
              numpy.random.shuffle(_A)
              SCREAMING_SNAKE_CASE_									=						self.images[perm]
              SCREAMING_SNAKE_CASE_									=						self.labels[perm]
          # Start next epoch
          SCREAMING_SNAKE_CASE_									=						0
          SCREAMING_SNAKE_CASE_									=						batch_size - rest_num_examples
          SCREAMING_SNAKE_CASE_									=						self._index_in_epoch
          SCREAMING_SNAKE_CASE_									=						self._images[start:end]
          SCREAMING_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
          SCREAMING_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 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Union[str, Any] ,   _SCREAMING_SNAKE_CASE					:		Dict ,   _SCREAMING_SNAKE_CASE					:		str       ):





    """simple docstring"""


    if not gfile.Exists(_SCREAMING_SNAKE_CASE       ):
        gfile.MakeDirs(_SCREAMING_SNAKE_CASE       )
    SCREAMING_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:
            SCREAMING_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 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		List[str] ,   _SCREAMING_SNAKE_CASE					:		Union[str, Any]=False ,   _SCREAMING_SNAKE_CASE					:		Optional[Any]=False ,   _SCREAMING_SNAKE_CASE					:		List[str]=dtypes.floataa ,   _SCREAMING_SNAKE_CASE					:		Dict=True ,   _SCREAMING_SNAKE_CASE					:		Tuple=5_000 ,   _SCREAMING_SNAKE_CASE					:		str=None ,   _SCREAMING_SNAKE_CASE					:		Dict=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       )

        SCREAMING_SNAKE_CASE_									=						fake()
        SCREAMING_SNAKE_CASE_									=						fake()
        SCREAMING_SNAKE_CASE_									=						fake()
        return _Datasets(train=_SCREAMING_SNAKE_CASE ,   validation=_SCREAMING_SNAKE_CASE ,   test=_SCREAMING_SNAKE_CASE       )

    if not source_url:  # empty string check
        SCREAMING_SNAKE_CASE_									=						DEFAULT_SOURCE_URL

    SCREAMING_SNAKE_CASE_									=						'train-images-idx3-ubyte.gz'
    SCREAMING_SNAKE_CASE_									=						'train-labels-idx1-ubyte.gz'
    SCREAMING_SNAKE_CASE_									=						't10k-images-idx3-ubyte.gz'
    SCREAMING_SNAKE_CASE_									=						't10k-labels-idx1-ubyte.gz'

    SCREAMING_SNAKE_CASE_									=						_maybe_download(
        _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   source_url + train_images_file       )
    with gfile.Open(_SCREAMING_SNAKE_CASE ,   'rb'       ) as f:
        SCREAMING_SNAKE_CASE_									=						_extract_images(_SCREAMING_SNAKE_CASE       )

    SCREAMING_SNAKE_CASE_									=						_maybe_download(
        _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   source_url + train_labels_file       )
    with gfile.Open(_SCREAMING_SNAKE_CASE ,   'rb'       ) as f:
        SCREAMING_SNAKE_CASE_									=						_extract_labels(_SCREAMING_SNAKE_CASE ,   one_hot=_SCREAMING_SNAKE_CASE       )

    SCREAMING_SNAKE_CASE_									=						_maybe_download(
        _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   source_url + test_images_file       )
    with gfile.Open(_SCREAMING_SNAKE_CASE ,   'rb'       ) as f:
        SCREAMING_SNAKE_CASE_									=						_extract_images(_SCREAMING_SNAKE_CASE       )

    SCREAMING_SNAKE_CASE_									=						_maybe_download(
        _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   source_url + test_labels_file       )
    with gfile.Open(_SCREAMING_SNAKE_CASE ,   'rb'       ) as f:
        SCREAMING_SNAKE_CASE_									=						_extract_labels(_SCREAMING_SNAKE_CASE ,   one_hot=_SCREAMING_SNAKE_CASE       )

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

    SCREAMING_SNAKE_CASE_									=						train_images[:validation_size]
    SCREAMING_SNAKE_CASE_									=						train_labels[:validation_size]
    SCREAMING_SNAKE_CASE_									=						train_images[validation_size:]
    SCREAMING_SNAKE_CASE_									=						train_labels[validation_size:]

    SCREAMING_SNAKE_CASE_									=						{'dtype': dtype, 'reshape': reshape, 'seed': seed}

    SCREAMING_SNAKE_CASE_									=						_DataSet(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   **_SCREAMING_SNAKE_CASE       )
    SCREAMING_SNAKE_CASE_									=						_DataSet(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   **_SCREAMING_SNAKE_CASE       )
    SCREAMING_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       )





def 					_UpperCAmelCase       (  ):





    """simple docstring"""


    for n in range(1 ,   1_000_000       ):
        yield n * (n + 1) // 2


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Tuple       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						1
    SCREAMING_SNAKE_CASE_									=						2
    while i * i <= n:
        SCREAMING_SNAKE_CASE_									=						0
        while n % i == 0:
            n //= i
            multiplicity += 1
        divisors_count *= multiplicity + 1
        i += 1
    if n > 1:
        divisors_count *= 2
    return divisors_count


def 					_UpperCAmelCase       (  ):





    """simple docstring"""


    return next(i for i in triangle_number_generator() if count_divisors(_SCREAMING_SNAKE_CASE       ) > 500       )


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


