




from random import shuffle

import tensorflow as tf
from numpy import array







def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Tuple	,					__UpperCamelCase      :						List[str]				)  ->							Tuple:
    UpperCAmelCase_										=					int(__UpperCamelCase				)
    assert noofclusters < len(__UpperCamelCase				)

    # Find out the dimensionality
    UpperCAmelCase_										=					len(vectors[0]				)

    # Will help select random centroids from among the available vectors
    UpperCAmelCase_										=					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.

    UpperCAmelCase_										=					tf.Graph()

    with graph.as_default():
        # SESSION OF COMPUTATION

        UpperCAmelCase_										=					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
        UpperCAmelCase_										=					[
            tf.Variable(vectors[vector_indices[i]]				) for i in range(__UpperCamelCase				)
        ]
        ##These nodes will assign the centroid Variables the appropriate
        ##values
        UpperCAmelCase_										=					tf.placeholder('''float64'''	,					[dim]				)
        UpperCAmelCase_										=					[]
        for centroid in centroids:
            cent_assigns.append(tf.assign(__UpperCamelCase	,					__UpperCamelCase				)				)

        ##Variables for cluster assignments of individual vectors(initialized
        ##to 0 at first)
        UpperCAmelCase_										=					[tf.Variable(0				) for i in range(len(__UpperCamelCase				)				)]
        ##These nodes will assign an assignment Variable the appropriate
        ##value
        UpperCAmelCase_										=					tf.placeholder('''int32'''				)
        UpperCAmelCase_										=					[]
        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
        UpperCAmelCase_										=					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
        UpperCAmelCase_										=					tf.reduce_mean(__UpperCamelCase	,					0				)

        ##Node for computing Euclidean distances
        # Placeholders for input
        UpperCAmelCase_										=					tf.placeholder('''float'''	,					[dim]				)
        UpperCAmelCase_										=					tf.placeholder('''float'''	,					[dim]				)
        UpperCAmelCase_										=					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
        UpperCAmelCase_										=					tf.placeholder('''float'''	,					[noofclusters]				)
        UpperCAmelCase_										=					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.
        UpperCAmelCase_										=					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.
        UpperCAmelCase_										=					100
        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				)				):
                UpperCAmelCase_										=					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.
                UpperCAmelCase_										=					[
                    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
                UpperCAmelCase_										=					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
                UpperCAmelCase_										=					[
                    vectors[i]
                    for i in range(len(__UpperCamelCase				)				)
                    if sess.run(assignments[i]				) == cluster_n
                ]
                # Compute new centroid location
                UpperCAmelCase_										=					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
        UpperCAmelCase_										=					sess.run(__UpperCamelCase				)
        UpperCAmelCase_										=					sess.run(__UpperCamelCase				)
        return centroids, assignments











def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						Dict=2_8123				)  ->							str:
    UpperCAmelCase_										=					[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

    UpperCAmelCase_										=					set()
    UpperCAmelCase_										=					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())





