"""simple docstring"""




from random import shuffle

import tensorflow as tf
from numpy import array







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__     ):





		"""simple docstring"""




		lowerCAmelCase__        =   int(lowerCamelCase__     )
		assert noofclusters < len(lowerCamelCase__     )

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

		# Will help select random centroids from among the available vectors
		lowerCAmelCase__        =   list(range(len(lowerCamelCase__     )     )     )
		shuffle(lowerCamelCase__     )

		# 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.

		lowerCAmelCase__        =   tf.Graph()

		with graph.as_default():
				# SESSION OF COMPUTATION

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

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

				##Now lets construct the node that will compute the mean
				# The placeholder for the input
				lowerCAmelCase__        =   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
				lowerCAmelCase__        =   tf.reduce_mean(lowerCamelCase__			,  0     )

				##Node for computing Euclidean distances
				# Placeholders for input
				lowerCAmelCase__        =   tf.placeholder("""float"""			,  [dim]     )
				lowerCAmelCase__        =   tf.placeholder("""float"""			,  [dim]     )
				lowerCAmelCase__        =   tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(lowerCamelCase__			,  lowerCamelCase__     )			,  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
				lowerCAmelCase__        =   tf.placeholder("""float"""			,  [noofclusters]     )
				lowerCAmelCase__        =   tf.argmin(lowerCamelCase__			,  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.
				lowerCAmelCase__        =   tf.initialize_all_variables()

				# Initialize all variables
				sess.run(lowerCamelCase__     )

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

        # Return centroids and assignments
				lowerCAmelCase__        =   sess.run(lowerCamelCase__     )
				lowerCAmelCase__        =   sess.run(lowerCamelCase__     )
				return centroids, assignments





"""simple docstring"""




import os







def 							_UpperCAmelCase		(       ):





		"""simple docstring"""




		lowerCAmelCase__        =   os.path.dirname(os.path.realpath(lowerCamelCase__     )     )
		lowerCAmelCase__        =   os.path.join(lowerCamelCase__			,  """triangle.txt"""     )

		with open(lowerCamelCase__     ) as f:
				lowerCAmelCase__        =   f.readlines()

		lowerCAmelCase__        =   []
		for line in triangle:
				lowerCAmelCase__        =   []
				for number in line.strip().split(""" """     ):
						numbers_from_line.append(int(lowerCamelCase__     )     )
				a.append(lowerCamelCase__     )

		for i in range(1			,  len(lowerCamelCase__     )     ):
				for j in range(len(a[i]     )     ):
						lowerCAmelCase__        =   a[i - 1][j] if j != len(a[i - 1]     ) else 0
						lowerCAmelCase__        =   a[i - 1][j - 1] if j > 0 else 0
						a[i][j] += max(lowerCamelCase__			,  lowerCamelCase__     )
		return max(a[-1]     )


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




