

from random import shuffle

import tensorflow as tf
from numpy import array

def 						UpperCamelCase					(lowercase_: Any    ,      lowercase_: Union[str, Any]					)     ->      List[Any]:
	A__							:    List[Any]        =		int(lowercase_					)
	assert noofclusters < len(lowercase_					)

	# Find out the dimensionality
	A__							:    Tuple        =		len(vectors[0]					)

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

	# 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.

	A__							:    List[str]        =		tf.Graph()

	with graph.as_default():
		# SESSION OF COMPUTATION

		A__							:    List[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
		A__							:    str        =		[
		    tf.Variable(vectors[vector_indices[i]]					) for i in range(lowercase_					)
		]
		##These nodes will assign the centroid Variables the appropriate
		##values
		A__							:    Dict        =		tf.placeholder("""float64"""    ,      [dim]					)
		A__							:    Any        =		[]
		for centroid in centroids:
			cent_assigns.append(tf.assign(lowercase_    ,      lowercase_					)					)

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

		##Now lets construct the node that will compute the mean
		# The placeholder for the input
		A__							:    Optional[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
		A__							:    List[Any]        =		tf.reduce_mean(lowercase_    ,      0					)

		##Node for computing Euclidean distances
		# Placeholders for input
		A__							:    Optional[int]        =		tf.placeholder("""float"""    ,      [dim]					)
		A__							:    Optional[Any]        =		tf.placeholder("""float"""    ,      [dim]					)
		A__							:    Dict        =		tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(lowercase_    ,      lowercase_					)    ,      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
		A__							:    Dict        =		tf.placeholder("""float"""    ,      [noofclusters]					)
		A__							:    str        =		tf.argmin(lowercase_    ,      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.
		A__							:    Tuple        =		tf.initialize_all_variables()

		# Initialize all variables
		sess.run(lowercase_					)

		##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.
		A__							:    int        =		100
		for _ in range(lowercase_					):
			##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(lowercase_					)					):
				A__							:    Dict        =		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.
				A__							:    Any        =		[
				    sess.run(lowercase_    ,      feed_dict={va: vect, va: sess.run(lowercase_					)}					)
				    for centroid in centroids
				]
				# Now use the cluster assignment node, with the distances
				# as the input
				A__							:    List[Any]        =		sess.run(
				    lowercase_    ,      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(lowercase_					):
				# Collect all the vectors assigned to this cluster
				A__							:    List[str]        =		[
				    vectors[i]
				    for i in range(len(lowercase_					)					)
				    if sess.run(assignments[i]					) == cluster_n
				]
				# Compute new centroid location
				A__							:    Union[str, Any]        =		sess.run(
				    lowercase_    ,      feed_dict={mean_input: array(lowercase_					)}					)
				# Assign value to appropriate variable
				sess.run(
				    cent_assigns[cluster_n]    ,      feed_dict={centroid_value: new_location}					)

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






from math import factorial

def 						UpperCamelCase					(lowercase_: int = 20					)     ->      int:
	A__							:    Union[str, Any]        =		2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
	# 2, 3,...
	A__							:    Tuple        =		n // 2

	return int(factorial(lowercase_					) / (factorial(lowercase_					) * factorial(n - k					))					)


if __name__ == "__main__":
	import sys

	if len(sys.argv) == 1:
		print(solution(20))
	else:
		try:
			A_       : List[str]         =			int(sys.argv[1])
			print(solution(n))
		except ValueError:
			print('Invalid entry - please enter a number.')



