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232 lines
8.2 KiB
Python
232 lines
8.2 KiB
Python
# Natural Language Toolkit: K-Means Clusterer
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#
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# Copyright (C) 2001-2020 NLTK Project
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# Author: Trevor Cohn <tacohn@cs.mu.oz.au>
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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import copy
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import random
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import sys
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try:
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import numpy
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except ImportError:
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pass
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from nltk.cluster.util import VectorSpaceClusterer
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class KMeansClusterer(VectorSpaceClusterer):
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"""
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The K-means clusterer starts with k arbitrary chosen means then allocates
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each vector to the cluster with the closest mean. It then recalculates the
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means of each cluster as the centroid of the vectors in the cluster. This
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process repeats until the cluster memberships stabilise. This is a
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hill-climbing algorithm which may converge to a local maximum. Hence the
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clustering is often repeated with random initial means and the most
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commonly occurring output means are chosen.
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"""
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def __init__(
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self,
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num_means,
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distance,
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repeats=1,
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conv_test=1e-6,
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initial_means=None,
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normalise=False,
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svd_dimensions=None,
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rng=None,
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avoid_empty_clusters=False,
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):
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"""
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:param num_means: the number of means to use (may use fewer)
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:type num_means: int
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:param distance: measure of distance between two vectors
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:type distance: function taking two vectors and returing a float
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:param repeats: number of randomised clustering trials to use
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:type repeats: int
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:param conv_test: maximum variation in mean differences before
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deemed convergent
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:type conv_test: number
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:param initial_means: set of k initial means
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:type initial_means: sequence of vectors
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:param normalise: should vectors be normalised to length 1
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:type normalise: boolean
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:param svd_dimensions: number of dimensions to use in reducing vector
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dimensionsionality with SVD
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:type svd_dimensions: int
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:param rng: random number generator (or None)
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:type rng: Random
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:param avoid_empty_clusters: include current centroid in computation
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of next one; avoids undefined behavior
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when clusters become empty
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:type avoid_empty_clusters: boolean
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"""
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VectorSpaceClusterer.__init__(self, normalise, svd_dimensions)
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self._num_means = num_means
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self._distance = distance
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self._max_difference = conv_test
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assert not initial_means or len(initial_means) == num_means
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self._means = initial_means
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assert repeats >= 1
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assert not (initial_means and repeats > 1)
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self._repeats = repeats
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self._rng = rng if rng else random.Random()
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self._avoid_empty_clusters = avoid_empty_clusters
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def cluster_vectorspace(self, vectors, trace=False):
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if self._means and self._repeats > 1:
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print("Warning: means will be discarded for subsequent trials")
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meanss = []
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for trial in range(self._repeats):
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if trace:
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print("k-means trial", trial)
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if not self._means or trial > 1:
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self._means = self._rng.sample(list(vectors), self._num_means)
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self._cluster_vectorspace(vectors, trace)
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meanss.append(self._means)
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if len(meanss) > 1:
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# sort the means first (so that different cluster numbering won't
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# effect the distance comparison)
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for means in meanss:
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means.sort(key=sum)
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# find the set of means that's minimally different from the others
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min_difference = min_means = None
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for i in range(len(meanss)):
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d = 0
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for j in range(len(meanss)):
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if i != j:
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d += self._sum_distances(meanss[i], meanss[j])
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if min_difference is None or d < min_difference:
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min_difference, min_means = d, meanss[i]
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# use the best means
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self._means = min_means
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def _cluster_vectorspace(self, vectors, trace=False):
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if self._num_means < len(vectors):
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# perform k-means clustering
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converged = False
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while not converged:
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# assign the tokens to clusters based on minimum distance to
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# the cluster means
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clusters = [[] for m in range(self._num_means)]
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for vector in vectors:
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index = self.classify_vectorspace(vector)
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clusters[index].append(vector)
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if trace:
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print("iteration")
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# for i in range(self._num_means):
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# print ' mean', i, 'allocated', len(clusters[i]), 'vectors'
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# recalculate cluster means by computing the centroid of each cluster
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new_means = list(map(self._centroid, clusters, self._means))
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# measure the degree of change from the previous step for convergence
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difference = self._sum_distances(self._means, new_means)
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if difference < self._max_difference:
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converged = True
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# remember the new means
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self._means = new_means
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def classify_vectorspace(self, vector):
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# finds the closest cluster centroid
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# returns that cluster's index
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best_distance = best_index = None
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for index in range(len(self._means)):
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mean = self._means[index]
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dist = self._distance(vector, mean)
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if best_distance is None or dist < best_distance:
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best_index, best_distance = index, dist
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return best_index
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def num_clusters(self):
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if self._means:
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return len(self._means)
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else:
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return self._num_means
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def means(self):
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"""
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The means used for clustering.
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"""
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return self._means
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def _sum_distances(self, vectors1, vectors2):
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difference = 0.0
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for u, v in zip(vectors1, vectors2):
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difference += self._distance(u, v)
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return difference
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def _centroid(self, cluster, mean):
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if self._avoid_empty_clusters:
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centroid = copy.copy(mean)
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for vector in cluster:
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centroid += vector
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return centroid / (1 + len(cluster))
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else:
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if not len(cluster):
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sys.stderr.write("Error: no centroid defined for empty cluster.\n")
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sys.stderr.write(
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"Try setting argument 'avoid_empty_clusters' to True\n"
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)
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assert False
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centroid = copy.copy(cluster[0])
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for vector in cluster[1:]:
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centroid += vector
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return centroid / len(cluster)
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def __repr__(self):
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return "<KMeansClusterer means=%s repeats=%d>" % (self._means, self._repeats)
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#################################################################################
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def demo():
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# example from figure 14.9, page 517, Manning and Schutze
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from nltk.cluster import KMeansClusterer, euclidean_distance
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vectors = [numpy.array(f) for f in [[2, 1], [1, 3], [4, 7], [6, 7]]]
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means = [[4, 3], [5, 5]]
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clusterer = KMeansClusterer(2, euclidean_distance, initial_means=means)
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clusters = clusterer.cluster(vectors, True, trace=True)
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print("Clustered:", vectors)
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print("As:", clusters)
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print("Means:", clusterer.means())
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print()
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vectors = [numpy.array(f) for f in [[3, 3], [1, 2], [4, 2], [4, 0], [2, 3], [3, 1]]]
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# test k-means using the euclidean distance metric, 2 means and repeat
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# clustering 10 times with random seeds
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clusterer = KMeansClusterer(2, euclidean_distance, repeats=10)
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clusters = clusterer.cluster(vectors, True)
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print("Clustered:", vectors)
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print("As:", clusters)
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print("Means:", clusterer.means())
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print()
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# classify a new vector
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vector = numpy.array([3, 3])
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print("classify(%s):" % vector, end=" ")
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print(clusterer.classify(vector))
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print()
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if __name__ == "__main__":
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demo()
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