
"""simple docstring"""
from random import shuffle

import tensorflow as tf
from numpy import array





def  _lowerCAmelCase     (  lowerCamelCase__				:				int,    lowerCamelCase__				:				Union[str, Any]					)	->     str:
  _SCREAMING_SNAKE_CASE :					Tuple				     =			int(a__					)
  assert noofclusters < len(a__					)

  # Find out the dimensionality
  _SCREAMING_SNAKE_CASE :					int				     =			len(vectors[0]					)

  # Will help select random centroids from among the available vectors
  _SCREAMING_SNAKE_CASE :					int				     =			list(range(len(a__					)					)					)
  shuffle(a__					)

  # GRAPH OF COMPUTATION
  # We initialize a new graph and set it as the default during each run
  # of this algorithm. This ensures that as this function is called
  # multiple times, the default graph doesn't keep getting crowded with
  # unused ops and Variables from previous function calls.

  _SCREAMING_SNAKE_CASE :					Optional[int]				     =			tf.Graph()

  with graph.as_default():
    # SESSION OF COMPUTATION

    _SCREAMING_SNAKE_CASE :					Any				     =			tf.Session()

    ##CONSTRUCTING THE ELEMENTS OF COMPUTATION

    ##First lets ensure we have a Variable vector for each centroid,
    ##initialized to one of the vectors from the available data points
    _SCREAMING_SNAKE_CASE :					Tuple				     =			[
        tf.Variable(vectors[vector_indices[i]]					) for i in range(a__					)
    ]
    ##These nodes will assign the centroid Variables the appropriate
    ##values
    _SCREAMING_SNAKE_CASE :					List[str]				     =			tf.placeholder("float64",    [dim]					)
    _SCREAMING_SNAKE_CASE :					Dict				     =			[]
    for centroid in centroids:
      cent_assigns.append(tf.assign(a__,    a__					)					)

    ##Variables for cluster assignments of individual vectors(initialized
    ##to 0 at first)
    _SCREAMING_SNAKE_CASE :					List[Any]				     =			[tf.Variable(0					) for i in range(len(a__					)					)]
    ##These nodes will assign an assignment Variable the appropriate
    ##value
    _SCREAMING_SNAKE_CASE :					Dict				     =			tf.placeholder("int32"					)
    _SCREAMING_SNAKE_CASE :					Optional[int]				     =			[]
    for assignment in assignments:
      cluster_assigns.append(tf.assign(a__,    a__					)					)

    ##Now lets construct the node that will compute the mean
    # The placeholder for the input
    _SCREAMING_SNAKE_CASE :					int				     =			tf.placeholder("float",    [None, dim]					)
    # The Node/op takes the input and computes a mean along the 0th
    # dimension, i.e. the list of input vectors
    _SCREAMING_SNAKE_CASE :					Optional[int]				     =			tf.reduce_mean(a__,    0					)

    ##Node for computing Euclidean distances
    # Placeholders for input
    _SCREAMING_SNAKE_CASE :					Any				     =			tf.placeholder("float",    [dim]					)
    _SCREAMING_SNAKE_CASE :					Optional[int]				     =			tf.placeholder("float",    [dim]					)
    _SCREAMING_SNAKE_CASE :					Union[str, Any]				     =			tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(a__,    a__					),    2					)					)					)

    ##This node will figure out which cluster to assign a vector to,
    ##based on Euclidean distances of the vector from the centroids.
    # Placeholder for input
    _SCREAMING_SNAKE_CASE :					Tuple				     =			tf.placeholder("float",    [noofclusters]					)
    _SCREAMING_SNAKE_CASE :					Dict				     =			tf.argmin(a__,    0					)

    ##INITIALIZING STATE VARIABLES

    ##This will help initialization of all Variables defined with respect
    ##to the graph. The Variable-initializer should be defined after
    ##all the Variables have been constructed, so that each of them
    ##will be included in the initialization.
    _SCREAMING_SNAKE_CASE :					Union[str, Any]				     =			tf.initialize_all_variables()

    # Initialize all variables
    sess.run(a__					)

    ##CLUSTERING ITERATIONS

    # Now perform the Expectation-Maximization steps of K-Means clustering
    # iterations. To keep things simple, we will only do a set number of
    # iterations, instead of using a Stopping Criterion.
    _SCREAMING_SNAKE_CASE :					Any				     =			1_0_0
    for _ in range(a__					):
      ##EXPECTATION STEP
      ##Based on the centroid locations till last iteration, compute
      ##the _expected_ centroid assignments.
      # Iterate over each vector
      for vector_n in range(len(a__					)					):
        _SCREAMING_SNAKE_CASE :					Tuple				     =			vectors[vector_n]
        # Compute Euclidean distance between this vector and each
        # centroid. Remember that this list cannot be named
        #'centroid_distances', since that is the input to the
        # cluster assignment node.
        _SCREAMING_SNAKE_CASE :					Tuple				     =			[
            sess.run(a__,    feed_dict={va: vect, va: sess.run(a__					)}					)
            for centroid in centroids
        ]
        # Now use the cluster assignment node, with the distances
        # as the input
        _SCREAMING_SNAKE_CASE :					Optional[int]				     =			sess.run(
            a__,    feed_dict={centroid_distances: distances}					)
        # Now assign the value to the appropriate state variable
        sess.run(
            cluster_assigns[vector_n],    feed_dict={assignment_value: assignment}					)

      ##MAXIMIZATION STEP
      # Based on the expected state computed from the Expectation Step,
      # compute the locations of the centroids so as to maximize the
      # overall objective of minimizing within-cluster Sum-of-Squares
      for cluster_n in range(a__					):
        # Collect all the vectors assigned to this cluster
        _SCREAMING_SNAKE_CASE :					Optional[int]				     =			[
            vectors[i]
            for i in range(len(a__					)					)
            if sess.run(assignments[i]					) == cluster_n
        ]
        # Compute new centroid location
        _SCREAMING_SNAKE_CASE :					List[Any]				     =			sess.run(
            a__,    feed_dict={mean_input: array(a__					)}					)
        # Assign value to appropriate variable
        sess.run(
            cent_assigns[cluster_n],    feed_dict={centroid_value: new_location}					)

        # Return centroids and assignments
    _SCREAMING_SNAKE_CASE :					Tuple				     =			sess.run(a__					)
    _SCREAMING_SNAKE_CASE :					int				     =			sess.run(a__					)
    return centroids, assignments






'''simple docstring'''



from math import isqrt







def   a__			(    a__		):




     """simple docstring"""


     return all(number % divisor != 0 for divisor in range(2 ,       isqrt(a__		) + 1		)		)







def   a__			(    a__ = 10**6		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = 0
     __SCREAMING_SNAKE_CASE      = 1
     __SCREAMING_SNAKE_CASE      = 7
     while prime_candidate < max_prime:
          primes_count += is_prime(a__		)

          cube_index += 1
          prime_candidate += 6 * cube_index

     return primes_count


if __name__ == "__main__":
  print(f"""{solution() = }""")






