






'''simple docstring'''
from random import shuffle

import tensorflow as tf
from numpy import array





def 	_a(					UpperCamelCase__			:  int,		UpperCamelCase__			:  Optional[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=int(UpperCamelCase__							)
      assert noofclusters < len(UpperCamelCase__							)

      # Find out the dimensionality
      SCREAMING_SNAKE_CASE__       :			Any													=len(vectors[0]							)

      # Will help select random centroids from among the available vectors
      SCREAMING_SNAKE_CASE__       :			Dict													=list(range(len(UpperCamelCase__							)							)							)
      shuffle(UpperCamelCase__							)

      # 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[Any]													=tf.Graph()

      with graph.as_default():
            # SESSION OF COMPUTATION

            SCREAMING_SNAKE_CASE__       :			str													=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__       :			Dict													=[
                tf.Variable(vectors[vector_indices[i]]							) for i in range(UpperCamelCase__							)
            ]
            ##These nodes will assign the centroid Variables the appropriate
            ##values
            SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=tf.placeholder('''float64''',		[dim]							)
            SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=[]
            for centroid in centroids:
                  cent_assigns.append(tf.assign(UpperCamelCase__,		UpperCamelCase__							)							)

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

            ##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__       :			List[str]													=tf.reduce_mean(UpperCamelCase__,		0							)

            ##Node for computing Euclidean distances
            # Placeholders for input
            SCREAMING_SNAKE_CASE__       :			Optional[int]													=tf.placeholder('''float''',		[dim]							)
            SCREAMING_SNAKE_CASE__       :			Any													=tf.placeholder('''float''',		[dim]							)
            SCREAMING_SNAKE_CASE__       :			str													=tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(UpperCamelCase__,		UpperCamelCase__							),		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__       :			Any													=tf.placeholder('''float''',		[noofclusters]							)
            SCREAMING_SNAKE_CASE__       :			List[Any]													=tf.argmin(UpperCamelCase__,		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__       :			Any													=tf.initialize_all_variables()

            # Initialize all variables
            sess.run(UpperCamelCase__							)

            ##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__       :			int													=1_0_0
            for _ in range(UpperCamelCase__							):
                  ##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(UpperCamelCase__							)							):
                        SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=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__       :			List[Any]													=[
                            sess.run(UpperCamelCase__,		feed_dict={va: vect, va: sess.run(UpperCamelCase__							)}							)
                            for centroid in centroids
                        ]
                        # Now use the cluster assignment node, with the distances
                        # as the input
                        SCREAMING_SNAKE_CASE__       :			Tuple													=sess.run(
                            UpperCamelCase__,		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(UpperCamelCase__							):
                        # Collect all the vectors assigned to this cluster
                        SCREAMING_SNAKE_CASE__       :			Any													=[
                            vectors[i]
                            for i in range(len(UpperCamelCase__							)							)
                            if sess.run(assignments[i]							) == cluster_n
                        ]
                        # Compute new centroid location
                        SCREAMING_SNAKE_CASE__       :			List[str]													=sess.run(
                            UpperCamelCase__,		feed_dict={mean_input: array(UpperCamelCase__							)}							)
                        # Assign value to appropriate variable
                        sess.run(
                            cent_assigns[cluster_n],		feed_dict={centroid_value: new_location}							)

        # Return centroids and assignments
            SCREAMING_SNAKE_CASE__       :			List[Any]													=sess.run(UpperCamelCase__							)
            SCREAMING_SNAKE_CASE__       :			str													=sess.run(UpperCamelCase__							)
            return centroids, assignments







'''simple docstring'''
def 	_a(					UpperCamelCase__			:  Optional[Any]=2_8_1_2_3							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			List[Any]													=[1] * (limit + 1)

      for i in range(2,		int(limit**0.5							) + 1							):
            sum_divs[i * i] += i
            for k in range(i + 1,		limit // i + 1							):
                  sum_divs[k * i] += k + i

      SCREAMING_SNAKE_CASE__       :			List[str]													=set()
      SCREAMING_SNAKE_CASE__       :			str													=0

      for n in range(1,		limit + 1							):
            if sum_divs[n] > n:
                  abundants.add(UpperCamelCase__							)

            if not any((n - a in abundants) for a in abundants							):
                  res += n

      return res


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