and Target Word Selection
Hyun Ah Lee yz
and Gil Chang Kim y
y
Dept.ofEECS,KoreaAdvanced InstituteofScienceandTechnology(KAIST),
373-1Kusong-DongYusong-GuTaejon305-701RepublicofKorea
z
DaumsoftInc.,Daechi-Dong946-12Kangnam-GuSeoul135-280RepublicofKorea
halee@csone.kaist.ac.kr,gckim@cs.kaist.ac.kr
Abstract
A word has many senses, and each sense can
bemapped into many target words. Therefore,
toselecttheappropriatetranslationwitha
cor-rectsense, thesenseofasourcewordshouldbe
disambiguated before selecting a target word.
Based onthisobservation,weproposeahybrid
method for translationselection that combines
disambiguationof a source word sense and
se-lectionofatarget word. Knowledgefor
transla-tion selection is extractedfrom a bilingual
dic-tionary and target language corpora. Dividing
translationselectioninto thetwosub-problems,
we can makeknowledgeacquisition
straightfor-wardandselectmoreappropriatetargetwords.
1 Introduction
In machine translation, translation selection is
aprocessthatselectsanappropriatetarget
lan-guagewordcorrespondingtoawordinasource
language. Like other problems in natural
lan-guage processing, knowledge acquisition is
cru-cial for translation selection. Therefore, many
researchers have endeavored to extract
knowl-edgefrom existingresources.
Asmassesoflanguageresourcesbecome
avail-able, statistical methods have been attempted
fortranslationselectionandshownpractical
re-sults. Someoftheapproacheshaveuseda
bilin-gualcorpusasaknowledgesourcebasedonthe
idea of Brown et al. (1990), but they are not
preferred in general since a bilingual corpus is
hardtocomeby. Thoughsomelatest
approach-eshaveexploitedwordco-occurrencethatis
ex-tracted from a monolingual corpus in a target
language(Daganand Itai,1994;Prescheretal.,
2000;KoehnandKnight,2001),those methods
oftenfailinselectingappropriatewordsbecause
theydonotconsidersenseambiguityofatarget
Inabilingualdictionary,sensesofawordare
classiedintoseveralsensedivisionsandalsoits
translationsaregrouped byeachsensedivision.
Therefore, when one looks up the translation
of a word in a dictionary, she/he ought to
re-solve the sense of a word ina source language
sentence,andthenchooseatarget wordamong
translationscorresponding to thesense. In this
paper, the fact that a word has many senses
and each sense can be mapped into many
tar-getwords(Leeetal.,1999)isreferredto asthe
`word-to-sense and sense-to-word' relationship,
basedonwhichweproposeahybridmethodfor
translationselection.
In ourmethod, translationselection is taken
as the combined problem of sense
disambigua-tionof a sourcelanguage wordand selection of
a target language word. To disambiguate the
sense of a source word, we employ both a
dic-tionary based method and a target word
co-occurrence based method. In order to select a
targetword,theco-occurrence basedmethodis
alsoused.
We introduce three measures for translation
selection: sense preference, sense probability
andwordprobability. In abilingual dictionary,
example sentences are listed for each sense
di-visionofasourceword. Thesimilaritybetween
thoseexamplesand aninputsentencecanserve
asameasureforsensedisambiguation,whichwe
deneassensepreference. In thebilingual
dic-tionary,target wordsare alsorecorded foreach
sensedivision. Since thesetof those words can
modeleachsense,wecancalculatethe
probabil-ity of the sense by applying the co-occurrence
based method to the set of words. We dene
the estimated probability as sense probability,
which is taken for the other measure of sense
prob-lationscan be calculated. We dene itasword
probability, which is a measure for word
selec-tion. Mergingsensepreference,sense
probabili-tyandwordprobability,wecomputepreference
for each translation, and then choose a target
word withthehighesttranslationpreference as
a translation.
2 Translation Selection based on
`word-to-sense and sense-to-word'
The`word-to-senseandsense-to-word'
relation-ship means that a word in a source language
couldhavemultiplesenses,eachofwhichmight
be mapped into various words in a target
lan-guage. As shown in examples below, a Korean
verb`meok-da'hasmanysenses(work,deaf,eat,
etc.). Also `kkae-da' has three senses (break,
hatch, wake), among which the break sense of
`kkae-da' is mapped into multiple words such
as `break', `smash' and `crack'. In that case, if
break
kkae-da
wake
hatch
break smash
hatch
wake_up
awake
(jeobsi-reul kkae-da)
⇒
(X) hatch a dish
⇒
(O) break a dish
⇒
(O) smash a dish
⇒
(O) crack a dish
crack
work
meok-da
eat
deaf
saw bite
cut
deaf
eat
take
….
dye
have
(jeomsim-eul meok-da)
⇒
(X) saw a lunch
⇒
(?) eat a lunch
⇒
(O) have a lunch
⇒
(O) take a lunch
`hatch'isselectedasatranslationof`kkae-da'in
a sentence `jeobsi-reul kkae-da', the translation
must be wrong because the sense of `kkae-da'
in the sentence is break rather than hatch. In
contrast, any word of the break sense of
`kkae-da' forms a well-translated sentence.
Howev-er, selecting a correct sense does not always
guarantee a correct translation. If the senseof
`meok-da' in`jeomsim-eul meok-da' is correctly
disambiguatedaseat butan inappropriate
tar-get word is selected, an improperorunnatural
translationwillbe produced like`eat a lunch'.
Therefore, in order to get a correct
transla-tion, such a target wordmust be selected that
has the right senseof a sourcewordand
form-s a proper target language sentence. Previous
approaches on translationselection usually try
totranslateasourceworddirectlyinto atarget
wordwithoutconsideringthesense. Thus,they
Target
Language
Corpus
Input
Sentence
Get
Sense
Preference
Get
Word
Probability
Sense Definition &
Example Sentence
Bilingual
Dictionary
Sense & Taget
Word Mapping
Word-level
Translation
Get
Sense
Probability
Combine
spf, sp, wp
Word-level
Translation
Get
Sense
Probability
Combine
spf, sp, wp
WordNet
Target Word
Cooccurrence
Sense
Disambiguation
Word
Selection
Figure1: Our process of translationselection
fer from the problem of knowledge acquisition
andincorrect selectionof translation.
In this paper, we propose a method for
translationselectionthatreects`word-to-sense
and sense-to-word' relationship. We dividethe
problem of translationselection into sense
dis-ambiguation of a source word and selection of
a target word. Figure 1 shows our process of
selecting translation. We introduce three
mea-suresfortranslationselection: sense preference
(spf)andsenseprobability(sp)forsense
disam-biguation, and word probability(wp) for word
selection.
Figure 2 shows a partof an
English-English-KoreanDictionary(EssEEK,1995) 1
. Asshown
inthe gure, example sentences and denition
sentences are listed for each sense of a source
word. In the gure, example sentences of the
destroysenseof`break'consist ofwords suchas
`cup',`piece',and`thread',andthoseforthe
vio-latesenseconsistofwordssuchas`promise'and
`contract', which can function asindicators for
the sense of `break'. We calculate sense
pref-erence of a word for each sense by estimating
similarity between words in an input sentence
andwordsinexampleand denitionsentences.
Each sense of a source word can be mapped
into a set of translations. Asshown in the
ex-ample, the break sense of `kkae-da' is mapped
intothesetf`break',`smash', `crack'g andsome
words in the set can replace each other in a
translated sentence like `break/smash/crack a
1
TheEnglish-English-KoreanDictionaryusedhereis
break
breik
G
v
UGO
broke, brok
"en
PG
vt
UG
1
Ow]S^P
cause (something) to come to
pieces by a blow or strain; destroy; crack; smash
UG
L bGbGbG
U
&
~ a cup
VG
~ a glass to [into] piece
VG
~ a thread
VG
~ one's arm
VG
~ a stick in two
VG
I heard the rope ~.
!" # $ %&
VG
The river broke its
bank.
'" ( )
UG
2
Ow]P
hurt; injure
UG
L
*+, -./.G0
UG
&
~ the skin
12 *+
UG
3
Ow]P
put (something) out of order; make useless by
rough handling, etc.
L 34bGG5 6.78-.G0
UG
&
~ a watch
9: 7
8
VG
~ a line
; <
VG
~ the peace
=> 34
UG
4
Ow]P
fail to keep
or follow; act against (a rule, law, etc) ; violate; disobey
UG
O?@"A BCP
VG
~
one's promise
DE
VG
~ a contract
:D CF0
UG
5 ….
Figure2: A partof an EEKDictionary
dish'. Therefore, we can expect the behavior
of those words to be alike or meaningfully
re-lated in a corpus. Based on this expectation,
we compute sense probability by applying the
target word co-occurrence based method to all
words inthesame sensedivision.
Wordprobabilityrepresentshowlikelya
tar-getwordisselectedfromthesetofwordsinthe
same sensedivision. In the example
`jeomsim-eul meok-da', the sense of `meok-da' is eat,
whichismappedintothreewordsf`eat', `have',
`take'g. Among them, `have' forms a natural
phrase while `eat' makes an awkward phrase.
We could judge the naturalness from the
fac-t that `have' and `lunch' co-occurs in a corpus
more frequentlythan `eat' and `lunch'. In
oth-er words, the level of naturalness or
awkward-ness of a phrase can be captured by word
co-occurrence. Based on this observation, we use
targetwordco-occurrencetogetword
probabil-ity.
3 Calculation of each measure
3.1 Sense Preference
Given a source word s and its k-th sense s k
,
we calculate sensepreference spf(s k
) usingthe
equation (1). In the equation, SNT is a set of
allcontent wordsexceptsinaninputsentence.
DEF
s k
isasetofallcontentwords indenition
sentencesof s k
,and EX
s k
isaset ofall content
wordsinexamplesentencesofs k
,bothofwhich
areextracted fromthe dictionary.
spf(s k )= X w i 2SNT max w d 2DEF s k sim(w i ;w d ) (1) + X wi2SNT max we2EX s k sim(w i ;w e )
Sensepreferenceisobtainedbycalculating
sim-ilaritybetweenwordsinSNTand wordsin DE-(w
i
2SNT),wesum up themaximum similarity
betweenw
i
and allcluewords(i.e. w
d and w
e ).
To get similarity betweenwords (sim(w
i ;w
j )),
we use WordNet and the metric proposed in
Rigauetal. (1997).
Senses in a dictionary are generally ordered
by frequency. To reect distribution of senses
in common text, we use a weight factor (s k
)
that is inversely proportionalto the order of a
sense s k
in a dictionary. Then, we calculate
normalized sense preference to combine sense
preferenceand senseprobability.
spf
w (s
k
)=(s k ) spf(s k ) P i spf(s i ) (2) spf norm (s k )= spf w (s k ) P i spf w (s i ) (3)
3.2 Sense Probability
Sense probability represents how likely target
wordswiththesame senseco-occurwith
trans-lationsofotherwordswithintheinputsentence.
Let us suppose that the i-th word in an input
sentence is s
i
and the k-th sense of s
i is s
k
i .
Then, sense probability sp(s k
i
) is computed as
follows: n(t k iq )= X (sj;m;c)2(si) m X p=1 f(t k iq ;t jp ;c) f(t k iq )+f(t
jp ) (4) sp(s k i )=p^
sense (s k i )= P q n(t k iq ) P x P y n(t x iy ) (5)
Intheequation,(s
i
) signiesa setof
word-s that co-occur with s
i
on syntactic relations.
In an element (s
j
;m;c) of (s
i ), s
j
is a word
that co-occurs with s
i
in an input sentences, c
is a syntactic relation 2 between s i and s j , and
misthenumberoftranslationsofs
j
. Provided
that the set of translations of a sense s k
i is T
k
i
anda memberofT k
i is t
k
iq
,thefrequencyof
co-occurring t k
iq and t
jp
with a syntactic relation
c is denoted as f(t k
iq ;t
jp
;c), which is
extract-ed from target language corpora. 3
Therefore,
2
We guess 37 syntactic relations in English
sen-tences based on verb pattern information in the
dic-tionary and the results of the memory based shallow
parser(Daelemansetal.,1999): subj-verb, obj-verb,
modifier-noun, adverb-modifiee, etc.
3
n(t
iq
) in the equation (4) represents how
fre-quentlyt k
iq
co-occurswithtranslationsofs
j . By
summingupn(t k
iq
)foralltargetwordsinT k
i ,we
obtainsenseprobabilityofs k
i .
3.3 Word Probability
Word probability represents how frequently a
target word in a sense division co-occurs in a
corpus with translations of other words within
theinputsentence. Wedenotewordprobability
as wp(t k
iq
) that is a probability of selecting t k
iq
from T k
i
. Using n(t k
iq
) in the equation (4), we
calculatewordprobabilityasfollows:
wp(t k
iq )=p^
word (t k iq )= n(t k iq ) P x n(t k ix ) (6)
3.4 Translation Preference
To select a target word among all translations
of a source word, we compute translation
pref-erence (tpf) by merging sense preference, sense
probability and word probability. We simply
sum up thevalue of sensepreference and sense
probability as a measure of sense
disambigua-tion,andthenmultiplyitwithwordprobability
asfollows:
tpf(t k
iq
)=(Æspf
norm (s
k
i
)+(1 Æ)sp(s k i )) (7) wp(t k iq )=(T k i )
In the equation, (T k
i
) is a normalizing factor
forwp(t k
iq )
4
,andÆisaweightingfactorforsense
preference. We select a target word with the
highest tpfasatranslation.
When allofthen(t k
iq
) intheequation (4)are
0,we usethefollowingequation forsmoothing,
which uses onlyfrequencyofa target word.
n(t k iq )= f(t k iq ) P p f(t k ip ) (8)
si, 4, verb-obj) in the example of `jeobsi-reul
kkae-da', and then the following frequencies will be used:
f(break,plate,verb-obj), f(break,dish, verb-obj),...,
f(crack,platter, verb-obj).
4
Because wp(t k
iq
) is a probability of t k iq within T k i , wp(t k iq
)becomes1whenT k
i
hasonlyoneelement. (T k
i )
isusedtomakethemaximumvalueofwp(t k iq )=(T k i )to
1. Hence, (T k
i
) =max
j wp(t
k
ij
). Using (T k
i
), we can
preventdiscountingtranslationpreferenceofaword,the
4 Evaluation
WeevaluatedourmethodonEnglish-to-Korean
translation. EssEEK(1995)wasusedasa
bilin-gual dictionary. We converted this
English-EnglishKoreandictionaryintoamachine
read-able form, which has about 43,000 entries,
34,000 unique words and 80,000 senses. From
the dictionary, we extracted sense
denition-s, example sentences and translations for each
sense. Co-occurrence of Korean was
extract-edfrom YonseiCorpus, KAISTcorpusand
Se-jongCorpususingthemethodproposedinYoon
(2001). Thenumberofextractedco-occurrence
isabout600,000.
To exclude any kind of human intervention
duringknowledgeextractionandevaluation,we
evaluatedourmethodsimilarlywithKoehnand
Knight (2001). English-Korean aligned
sen-tenceswerecollectedfromnovels,textbooksfor
highschoolstudentsandsentencesina
Korean-to-English bilingual dictionary. Among those
sentences,weextracted sentence pairsinwhich
words in the English sentence satisfy the
fol-lowingcondition: ifthepairedKoreansentence
contains a word that is dened in the
dictio-nary as a translation of the English word. We
randomlychose 945 sentences as an evaluation
set, in which 3,081 words in English sentences
satisfy the condition. Among them, 1,653 are
nouns, 990 are verbs, 322 are adjectives, and
116 areadverbs.
We used Brill's tagger (Brill, 1995) and
Memory-Based Shallow Parser (Daelemans et
al.,1999) to analyze English sentences. To
an-alyzeKorean sentences, we used a POS tagger
forKorean(Kim andKim,1996).
First, we evaluated the accuracies of sense
preference (spf) and senseprobability (sp). If
any target word of the sense with the highest
value is included in an alignedtarget language
sentence,weregarded itascorrect result.
The accuracy of sensepreference isshownin
Table 1. In the table, a w/o DEF row shows
theresult produced by removingthe DEF clue
in the equation (1), and a w/o ORDER row is
the result produced without the weight factor
(s k
)oftheequation(2). Asshowninthetable,
theresultwiththeweight factorand withouta
sensedenitionsentenceisbestforallcases. We
noun verb adj. adv. all
w/oORDER w/oDEF 59.23% 42.93% 45.03% 34.48% 52.47%
withDEF 57.65% 40.20% 49.07% 33.62% 51.14%
withORDER 5
w/oDEF 66.30% 48.48% 59.32% 44.83% 59.94%
withDEF 65.76% 45.56% 56.52% 42.24% 58.41%
Table 2: Accuracy of senseprobability(sp)
noun verb adj. adv. all
withallcoocword 52.49% 30.49% 38.94% 59.35% 46.52%
withcasecoocword 49.62% 31.33% 40.12% 60.98% 45.41%
Table3: Accuracy of translationselection
noun verb adj. adv. all
randomselection 11.11% 3.92% 7.41% 11.12% 6.77%
1sttranslationof1stsense 12.89% 12.12% 7.45% 2.59% 11.86%
mostfrequent 46.34% 27.58% 31.99% 37.93% 38.68%
spf 53.72% 38.18% 39.75% 44.83% 46.98%
with sp 42.88% 19.28% 26.25% 39.02% 35.04%
all wp 51.66% 31.41% 32.92% 46.55% 43.10%
cooc spwp 51.97% 31.92% 33.54% 50.00% 43.62%
word spfwp 55.23% 40.00% 41.30% 50.00% 50.17%
(spf+sp)wp 6
54.99% 34.55% 36.34% 50.86% 46.42%
with sp 38.90% 20.20% 25.96% 37.40% 33.05%
case wp 48.70% 34.04% 35.40% 45.69% 42.58%
cooc spwp 49.12% 33.74% 36.34% 50.86% 43.01%
word spfwp 53.60% 42.22% 42.86% 50.86% 49.93%
(spf+sp)wp 6
51.18% 36.46% 38.20% 53.45% 45.28%
Table2. Intheequation(4),weproposedtouse
syntactic relations to get sense probability. In
thetable,theresultobtainedbyusingwordson
asyntacticrelation(withcasecoocword)is
com-paredto thatobtainedbyusingall words
with-in a sentence (with all cooc word). As shown,
theaccuracy fornounsis higherwhenusingall
words in a sentence, whereas the accuracy for
others is higher when considering syntactic
re-lations.
Table 3 shows the result of translation
se-lection. 7
We set three types of baseline -
ran-dom selection, most frequent, 1st translation of
1st sense 8
. We conducted the experiment
al-5
Inthe case of (1st sense)=1.5, (2nd sense)=1.3,
(3rdsense)=1.15,and(remainder)=1
6
InthecaseofÆ=0.6,whichshowsthebestresultin
theexperiment.
7
Togetspf,weuseonlythebestcombinationofclues
-withtheweightfactorandwithoutsensedenition
sen-tences.
8
Result of selecting translation that is recorded at
tering the combination of spf, sp and wp. An
spfrowshowstheaccuracyofselectingtherst
translationofthesensewiththehighestspf,and
an sp row shows the accuracy of selecting the
rst translation of the sense with the highest
sp. A wp rowshows the accuracy of usingonly
wordprobability. In otherwords,itisobtained
through assuming all translations of a source
word to have the same sense. Therefore, the
result in a wp row can be regarded as a result
produced by the method that uses only target
wordco-occurrence. Anspwprowistheresult
obtained withoutspf
norm
, and an spfwp row
is the result obtained without sp in the
equa-tion (8). An (spf+sp)wp row is the result of
combiningall measures.
For the best case, the accuracy for nouns is
55.23%, that for verbs is 42.22% and that for
adjectives is42.86%. Althoughwe useasimple
methodforsensedisambiguation,ourresultsof
5 Discussion
We could summarize the advantage of our
method asfollows:
reductionof theproblem complexity
simplifyingknowledgeacquisition
selectionof more appropriatetranslation
useof amono-bilingualdictionary
integration of syntactic relations
guarantee ofrobustresult
The gure below shows theaverage numberof
senses and translations for an English word in
EssEEK (1995). The left half of the graph is
forall English words inthe dictionary,and the
right half is for the words that are marked as
frequent or signicant words in the dictionary.
Ontheaverage,a frequentlyappearingEnglish
word has 2.82 senses, each sense has 1.96
Ko-rean translations,and consequentlyan English
word has 5.55 Korean translations. Moreover,
inourevaluationset,awordhas6.86sensesand
awordhas14.78translations. Mostapproaches
on translationselection have tried to translate
a sourceworddirectly into a target word, thus
the complexity of their method grows
propor-tional to the number of translations per word.
In contrast, the complexity of our method is
proportional to only the number of senses per
word or the number of translations per sense.
Therefore, we could reduce the complexity of
translationselection.
Whenthedegreeofambiguityofasource
lan-guage is n and that of a target language is m,
0
1
2
3
4
5
6
7
all
noun
verb
adj
adv
all
noun
verb
adj
adv
all word
frequent word
sense per word
translation per sense
translation per word
Figure 3: The average number of senses and
translationsforan English word
Therefore,knowledgeacquisitionfortranslation
ismorecomplicatedthanotherproblemsof
nat-ural language processing. Although the
com-plexity of knowledge acquisition of the
meth-ods based on a target language corpus is
on-ly m, ignorance of a source language resultsin
selecting inappropriate target words. In
con-trast,bysplittingtranslationselection into two
sub-problems,ourmethodusesonlyexisting
re-sources-abilingualdictionaryandatarget
lan-guagemonolingualcorpus. Therefore, we could
alleviate the complexity of knowledge
acquisi-tionto around n+m.
Asshownintheprevioussection,ourmethod
could select more appropriate translationthan
themethodbasedontargetwordco-occurrence,
although we used coarse knowledge for sense
disambiguation. Itisbecause theco-occurrence
based method does notconsider sense
ambigu-ity of a target word. Consider the translation
oftheEnglishphrase`haveacar'. Aword`car'
is translated into a Korean word `cha', which
has many meanings including car and tea. A
word`have'hasmanysenses-posses,eat,drink,
etc.,amongwhichthedrinksenseismapped
in-to a Koreanverb `masi-da'. Because of thetea
senseof`cha',thefrequencyofco-occuring`cha'
and`masi-da'isdominantinacorpusoverthat
of all other translations of `car' and `have'. In
that case, the method that uses only word
co-occurrence (wp in our experiment) translated
`have acar' into an incorrectsentence `cha-reul
masi-da' that means `have a tea'. In contrast,
ourmethodproducedacorrecttranslation
`cha-reulkaji-da',becausewedisambiguatethesense
of`have'aspossesbyemployingsensepreference
before usingco-occurrence.
In the experiment, the combination spfwp
getshigheraccuracythan(spf+sp)wpformost
cases. Itisduetothelowaccuracyofsp, which
isalsocausedbytheambiguityofatargetword
as shown in the example of `have a car'.
Nev-ertheless,we do notthinkit meanssense
prob-abilityis useless. The accuracies of spwp are
almost better thanthose of wp, thereforesense
probabilitycan workasacountermeasurewhen
noknowledgeofasourcelanguageexistsfor
dis-ambiguating thesenseofa word.
dic-denitions in a source language and syntactic
patterns for the predicate. While previous
re-search on sense disambiguation that exploits
those kinds of information has shown reliable
results, inour experiment,theuseof sense
def-initionslowerstheaccuracy. Itislikelybecause
weusedsensedenitionstooprimitively.
There-fore, we expect that we could increase the
ac-curacybyproperlyutilizingadditional
informa-tion inthedictionary.
Many studies on translation selection have
concerned with translation of only nouns. In
particular, some of them use all co-occurring
wordswithinasentence,andothersuseafew
re-strictedtypesofsyntacticrelations. Evenmore,
eachsyntacticrelationisutilizedindependently.
In this paper, we proposed a statistical model
thatintegratesvarioussyntacticrelations,with
which the accuracies for verbs, adjectives, and
adverbs increase. Nevertheless, sincethe
accu-racy for nouns is higher when using all words
in a sentence, it seems that syntactic relations
maybe dierentlyusedforeach case.
The other advantage of our method is
ro-bustness. Since our method disambiguates the
sense of a source language word using reliable
knowledgeinadictionary,wecouldavoid
select-ingor generatingatarget wordthe meaningof
which is denitely improperin given sentences
like `hatch a dish' for 'jeobsi-reul kkae-da' and
`cha-reulmasi-da' for`havea car'.
6 Conclusion
Inthispaper, weproposeda hybridmethodfor
translation selection. By dividing translation
selection into sense disambiguationof a source
word and selection of a target word, we could
simplifyknowledge acquisition and select more
appropriatetranslation.
Acknowledgement
We are grateful to Sabine Buchholz, Bertjan
BusseratTilburgUniversityandprofessorW
al-terDaelemansat UniversityofAntwerpforthe
aid to use the Memory-Based Shallow Parser
(MBSP).
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