Computational Creativity Theory:
Inspirations behind the FACE and the IDEA models
Alison Pease1 and Simon Colton2
1 School of Informatics, University of Edinburgh, UK.
2Computational Creativity Group, Department of Computing,
Imperial College, London, UK. ccg.doc.ic.ac.uk
Abstract
We introduce two descriptive models for evaluating creative
software; the FACE model, which describes creative
acts performed by software in terms of tuples of
generative acts, and the IDEA model, which describes
how such creative acts can have an impact upon an audience.
We show how these models have been inspired
both by ideas in the psychology of creativity and by an
analysis of acts of human creativity.
Introduction
The Computational Creativity (CC) community needs concrete
measures of evaluation to enable us to make objective,
falsifiable claims about progress made from one version of a
program to another, or for comparing and contrasting different
software systems for the same creative task. There are
two notions of evaluation in CC: (i) judgements which determine
whether an idea or artefact is valuable, and (ii) judgements
to determine whether a system is acting creatively.
Our thesis is that ideas from the psychology of creativity
can help us to develop such measures, and we demonstrate
this via our two models, which form a framework to aid us in
the development and evaluation of creative software. Note
that while we draw on psychology and examples of human
creativity for inspiration, our goal lies squarely within CC –
to provide a means of formalising some aspects of computational
creativity – we by no means claim that our models
would be appropriate for evaluating human creativity. The
main test and value of such models lies in their applicability
to CC systems: we defer such application to a sister paper
[4].
The FACE model
The FACE model assumes eight kinds of generative acts, in
which both processes (p) and artefacts (g) are produced:
F
p
: a method for generating framing information
F
g
: an item of framing information for A/C/E p/g
A
p
: a method for generating aesthetic measures
A
g
: an aesthetic measure for process or product
C
p
: a method for generating concepts
C
g
: a concept
E
p
: a method for generating expressions of a concept
E
g
: an expression of a concept
Any particular creative episode can be expressed in terms
of at least one of these components (it may well be the case
that not all of the components will be present). In order
to cover as many creative acts as possible, we assume only
that there must be something new created for the question of
creativity to arise. This could be very small, a brush stroke
of an artist, an inference step by a mathematician, a single
note in a piece of music. Thus, we avoid the thorny issue
of where an act of creation starts and important questions
about where on the scale from basic to sophisticated an act
must be, to be judged creative, can be postponed. This position
is in line with the argument by Cardoso et al., that “To
achieve human levels of computational creativity, we do not
necessarily need to start big, at the level of whole poems,
songs, stories or paintings; we are more likely to succeed
if we are allowed to start small, at the level of simple but
creative phrases, fragments and images” [3, p. 17].
The IDEA model
In order to assess the impact of the creative acts performed
by software, we assume an (I)terative (D)evelopment-
(E)xecution-(A)ppreciation cycle within which software is
engineered and its behaviour is exposed to an audience. The
IDEA descriptive model recognises that in some creative
tasks, the invention of measures of value forms a part of the
creative act. Hence usual models of value are abandoned in
favour of describing the impact that creative acts can have.
The model introduces some simplifying assumptions about
the nature of (i) the software development process (ii) the
background information known in general, known by the
programmer, and given to the software, and (iii) the nature
of the audience who assess the impact of the creative acts
performed by the software. Using these simplifications, the
model comprises two branches. The first of these is a descriptive
model for the stage of development that software is
in, in terms of how close its creative acts are to those performed
by the programmer in engineering the software, and
how close they are to those that have been performed by
community members in the wider context in which the software
works. The second branch uses the notion of an ideal
audience who can perfectly assess both their personal hedonistic
value of a creative act, and the time they are prepared
to spend interpreting the act and its results. These measures
are used to capture certain notions that are usually associated
Proceedings of the Second International Conference on Computational Creativity 72
with impact. In particular, notions such as shock (when audience
members tend to take an instant dislike to a creative
act), acquired taste (when audience members tend to spend
a long time in eventually positively assessing a creative act)
and opinion splitting (when a creative act is particularly divisive)
are formally developed.
The creation of prime numbers
The many aspects which contributed to the creation and appreciation
of the concept of prime number have inspired our
development of the FACE model. These include inventing
the concept itself and inventing ways of developing new
concepts in number theory. Along with the concept definition
we find examples, or expressions, of the concept, in the
form of numbers which are either known to be prime (eg.
2, 3, 5, 7), known not to be prime (eg. 4, 6, 8, 9),1 or have
an unknown status (eg. 2
13466917 + 1) and algorithms for
determining whether a given number is prime have been developed,
such as the Sieve of Eratosthenes, as well as ways
of generating further primes. The concept of primes was
embedded into number theory by developing specialisations
(eg. Cuban, happy, illegal and lucky primes) and theorems
and conjectures (eg. the fundamental theorem of arithmetic);
and into the wider field of mathematics as uses for primes
have been found in group and ring theory, cryptography, and
so on, as well as its application to other areas of human experience
(eg. Messiaen used prime numbers to create ametrical
music). In addition to actually developing such concepts,
theorems and applications, we can create techniques for developing
them, eg. the use of analogical reasoning to create
analogous concepts in other areas of mathematics. We also
evaluate the concept (primes are considered to be the “basic
building blocks” of the natural numbers) and suggest new
ways in which to make such a judgement. We break this
complex story down into the FACE components below:
FACE Prime numbers
F
p
: Ways in which theorems involving primes can be found
F
g
: Theorems involving primes, which embed the concept
within the field of number theory
A
p
: Ways in which which we judge the value of concepts in
number theory (for instance, their applicability and use in
multiple mathematical domains)
A
g
: Judgements on the value of the concept of prime number
C
p
: Ways of finding new concepts in number theory
C
g
: The concept of a prime number
E
p
: Algorithms for determining whether a given number is
prime or not (for instance the Sieve of Eratosthenes)
E
g
: Numbers with an evaluation as to whether they are prime
The creation of upsidedowns
In [3], Cardoso et al. describe The Upsidedowns of Gustav
Verbeek. These are panels which tell a story up to a
half way point, the continuation of which then appears almost
magically when one turns the panels upside down. We
show another example of this type in Figure 1. In terms of
our model, starting with the artefact level, we could describe
1Whether 1 should be considered prime is still debated today.
the final piece of art as an expression of the concept Eg
;
the concept Cg
as the constraint that the picture must make
sense when upside down (and fit into the story); the aesthetic
Ag
as the idea of art having multiple meanings when
viewed from multiple perspectives; and the framing Fg being
the contextual history of this genre of art, the motivation,
justification, etc. At the process level, Ep
is the generation
of methods for producing expressions of art which have a
different meaning when viewed upside down (for example,
birds flying in the sky can double as waves in the sea, or a hat
on one’s head can double as a mouth on one’s face); Cp
represents
methods for generating new perspectives from which
the art might make sense (other examples include rotating
90◦
rather than 180◦
); methods for generating the aesthetic
of art having multiple meanings when viewed from multiple
perspectives would be Ap
(another example would be
the aesthetic of art having multiple meanings when viewed
from a single perspective); and Fp would be methods for
generating new motivations, justifications, and so on.
Figure 1: A man coming out of the water – turn upside down
to see the same man drowning.
Not all of these aspects may be present in a single act of
creativity, and they may be performed by different parties.
We can express the upsidedowns as follows:
FACE Upsidedowns
F
p
: Methods for generating the contextual history of this genre
of art
F
g
: The contextual history of this genre of art, motivation, justification,
etc.
A
p
: Methods for generating the idea of art having multiple
meanings when viewing from multiple perspectives
A
g
: The idea of art having multiple meanings when viewing
from multiple perspectives
C
p
: Methods for generating new perspectives from which the
art might make sense
C
g
: The constraint that a picture must make sense when upside
down
E
p
: Methods for generating expressions of art which have a different
meaning when viewed upsidedown
E
g
: Expressions of art which have a different meaning when
viewed upsidedown (see figure 1)
Lessons from psychology
There is much work on creativity and little cross-fertilization
between fields. In particular, the relationship between CC
and the psychology of creativity (in Europe at least) has
been oddly disjointed: this is a waste, and our models constitute
one attempt to embed various aspects of creativity
Proceedings of the Second International Conference on Computational Creativity 73
research from psychology into a CC context. Simonton
[22] identifies four perspectives in basic research in psychology
on the nature of creativity: cognitive psychologists are
concerned with mental operations which underlie the creative
process; developmental psychologists investigate circumstances
which contribute to creative growth; differential
psychologists focus on individual differences; and social
psychologists investigate sociocultural environments which
shape or favour creative activity. Of most relevance to CC
are Simonton’s first and final categories. The first is the most
obvious and much work in CC is motivated by giving a computational
representation of mechanisms which can underlie
creative behaviour: these may be cognitive or otherwise, depending
on the motivation of the CC researcher. The final
category is far less common in CC, although work such as
that by Saunders [21] has demonstrated its relevance to the
CC community. Our models are thus inspired by ideas in
these two areas.
Types of creativity
Despite being notoriously difficult to define, researchers
have distinguished different types of creativity. These often
include some sort of conceptual space, which is an area
of work defined culturally by a set of rules and approaches
into which individuals are socialised as they master the skills
of their field. Some individuals will produce work which
violates the rules but is considered by the community to
be highly creative, and new work produced according to
a new set of rules then becomes the standard for that domain.
Csikszentmihalyi [5] distinguishes between little-c
creativity which might be within a cultural paradigm and
includes everyday, mundane creativity which is not domainchanging,
and big-C creativity, which is a rare, eminent creativity
in which a problem is solved or an object created
that has a major impact on other people and changes the
field. Boden [2] draws a similar distinction in her view of
creativity as search within a conceptual space, where exploratory
creativity searches within the space, and transformational
creativity involves expanding the space by breaking
one or more of the defining characteristics. Boden also
distinguishes between psychological (P-creativity) and historical
creativity (H-creativity), concerning ideas which are
novel with respect to a particular mind, or the whole of human
history. In our FACE and IDEA models we have tried
to be sufficiently general so as to capture each of these three
types of creativity.
There are some controversies in creativity research regarding
how general creativity is. For instance, there is
disagreement over whether everyday creativity involves the
same processes as eminent creativity [11; 27]. Another
common debate (also heard at CC conferences) concerns
whether creativity is domain specific [1], and in particular
whether it is the same phenomenon in the arts as in science.
While most investigators assume that there are a small number
of cognitive operations which underlie creativity in diverse
domains, Simonton [22] notes that it is also possible
that no processes are unique to creativity, or that there are no
processes which are present in every instance of creativity.
There is also debate on where creativity starts, and which,
of the different types, is more creative. We occupy a comfortable
vantage point on the fence, attempting to create a
framework which is general enough to capture all aspects.
Specific claims can then be expressed and tested in terms of
our models.
The distinction between process and product
The distinction between a product or idea and the processes
used to create it is a common one in psychology. Torrance
argues that creativity is a combination of person, process and
product, seeing a fine line between studying processes and
product (reported in [25]). Maher et al. point out that “A
creative process is one in which the process that generates
the design is novel, and a creative product is when we evaluate
the result of the design process as being novel” [15].
Much work in creative cognition research seeks to understand
the mental representations and processes underlying
creative thought. Examples of processes include Finke et
al.’s Geneplore model [7], in which mental processes such
as retrieval, association, transformation, analogical transfer,
categorical reduction, and so on, might enter phases of creative
invention. Conceptual combination, in which concepts
are combined to yield emergent features, is another process
thought to be important for creative behaviour, and this process
is frequently mentioned in historical accounts of creative
accomplishments (see [13; 2]). Analogical reasoning,
in which structured knowledge from a familiar domain is applied
to a novel or less familiar one, is also thought to be a
process with a special link to creativity [10].
There is also justification from historical case studies of
creativity for considering a process to be the creative output
of interest. For example, consider young Euler’s discovery
of Arithmetic Series, in which he and his classmates were
told to add up all the numbers between 1 and 100. Other
pupils arrived at the answer 5050, but everyone except Euler
laboriously added each of the numbers individually. Euler
realised that if they were written in ascending order and then
underneath in descending order, the sum of each of the pairs
was 101, and there were 100 pairs. Therefore twice the required
sum was 10100, and the answer was 5050. As in the
example of the Basel problem described below, there are (at
least) two interesting creative outputs: the expression 5050
and the process by which the expression is generated, Sn =
sum to n terms =
n∗(f irst+last)
2
. This example shows the
importance of a generative process for evaluations of creativity
– much more so than the Basel problem, since the expression
π
2
6 was itself H-creative, whereas Euler’s solution
5050 was only P-creative. We can break it down as follows:
FACE Euler Problem
F
p
: –
F
g
: Embed into mathematics, eg. AP’s and GP’s
A
p
: –
A
g
: Proof that the solution is correct
C
p
: Ways of finding new problems
C
g
: Sum the numbers between 1 and 100
E
p
: Sum to n terms =
n∗(f irst+last)
2
E
g
: The solution 5050
Proceedings of the Second International Conference on Computational Creativity 74
In the CC literature, the focus is often on the product,
and virtually all systems in CC discuss the creation of artefacts,
rather than processes. One strong motivation behind
our development of the FACE model is to emphasize the importance
of the process by which an artefact is created in a
judgement of creativity. We have done this via our distinction
between process and product in each of the four aspects
of FACE.
Evaluation in creativity
In the introduction we noted two senses of evaluation which
are relevant to creativity: evaluating whether an idea or
product is valuable, and evaluating whether a person has
been creative. The former, which is judged both internally
by a creator and externally by a community, is an essential
component of creativity. This notion of evaluation of
products as being a key part of the creative process was introduced
early on by thinkers such as Wallas [26], who presented
one of the first models of the creative process, outlining
a four-stage model of creativity: (i) preparation, (ii)
incubation, (iii) illumination and (iv) verification. The fi-
nal stage, where an idea is consciously verified, elaborated,
and applied may be carried out by either the creator or by
the community. Similarly, Parnes [18] introduced evaluation
into the creative process in his theory that creativity is a
function of knowledge, imagination and evaluation, arguing
that the highly creative person must be able to make evaluative
judgements about his or her products. This kind of
evaluation is also linked to Williams’ divergent-productive
thinking (described in [16]) in which multiple solutions to a
problem are generated and then evaluated to select the best.
Mcgraw and Hofstadter account for evaluation in their twostage
model of guesswork and evaluation [17], and refer to
the “necessarily iterative process of guesswork and evaluation
as the ‘central feedback loop of creativity”’ [9, p. 451].
Additionally, Maher, Merrick and Macindoe point out that
there are numerous characteristics associated with creative
design in addition to simply producing novel material, including
aesthetic appeal, quality, unexpectedness, uncommonness,
peer-recognition, influence, intelligence, learning,
and popularity [15]. Thus, the twin processes of generation
and evaluation are firmly embedded into notions of creativity.
We maintain this distinction in our two complementary
models; FACE, which describes generative acts of creativity
and IDEA, which describes ways of evaluating the acts.
We further reflect notions of internal and external evaluation
of a product via our Aesthetic and Framing aspects of the
FACE model. The IDEA model complements these aspects
and provides a fine grained approach to evaluation.
Kreitler and Kreitler [14] distinguish between creators
and spectators of the creative products and argue that there
are two types of creative people, those who create art and
those who view it. They have developed a theory of experiencing
art consisting of two phases. In the first (perceptualcognitive)
phase, the spectator responds to the work of art,
and in the second (motivational) phase, the experience is
motivated by psychological tensions which exist in the spectator
independently of the current experience. These tensions
trigger new tensions in response to the work of art and
allow the spectator to give meaning to the art: such meaning
develops with the gradual unfolding of different aspects of
the artwork. This work has formed the inspiration behind
our IDEA model and our thoughts on the cognitive effort
required to understand a creative artwork.
Theories of creativity
In view of the difficulties of defining this nebulous concept,
some psychologists have moved on from considering ‘what
is creativity?’ to considering ‘where is creativity?’ Csikszentmihalyi
[5] answers this with his systems view of creativity.
He sees creativity as an interactive process between
three elements: an individual innovator, his or her knowledge
about a domain, and a field or community of experts
who decide which individuals and products are valued. Of
particular interest to us is Csikszentmihalyi’s emphasis on
the role of the community in which creators operate and how
it affects creative outcomes. Uzzi and Spiro [24] also emphasise
the role of a community in amplifying (or stifling)
creativity. They discuss work which traces the history of
key innovations and show that in nearly all cases the creator
is embedded in a network of artists or scientists who share
ideas and act as each other’s critics, creating an atmosphere
of cross-fertilisation of ideas. These theories have inspired
the social aspects of our model, in particular the framing aspect,
in which a creator embeds his or her creation within
a field. Attempts at framing may well inspire further innovations
in the field. Similarly, our IDEA model is based on
theories of how creative work is received. Noting the diffi-
culties experienced by psychologists when trying to define
creativity, the fine level of granularity of our models enables
us to pinpoint where creativity in a particular act has occurred,
without having to answer the question of what creativity
is.
Gardner [8] holds that an individual must be consistently
creative, in order to be considered to be creative. He argues
that “the creative individual is a person who regularly solves
problems, fashions products or defines new questions in a
domain in a way that is initially considered novel but that
ultimately becomes accepted in a particular cultural setting.”
[8, p. 35]. In order to accommodate this criterion, we have
designed our FACE model to be used in a cumulative way.
Creative acts and the FACE/IDEA models
We break down two further examples of creativity in order to
demonstrate the various aspects of our models. In an attempt
to avoid charges of cherry-picking examples which fit our
model, we analyse two very different examples in different
domains. The first is an example of big-C, transformational,
H-creativity in mathematics and the second concerns little-c,
P-creativity in general problem solving. It is difficult at this
stage to show generality: we invite the reader to similarly
decompose other creative acts in order to develop the FACE
and IDEA models. Recall that our models are intended to
help us to develop and evaluate creative software and are
inspired by, rather than models of, human creativity.
Proceedings of the Second International Conference on Computational Creativity 75
The Basel problem
Euler’s solution of the Basel problem in mathematics is a
seminal historical episode of human creativity. This is the
problem of finding the sum of the reciprocals of the squares
of the natural numbers, i.e. finding the exact value of the
infinite series 1 + 1
4 +
1
9 +
1
16 +
1
25 +
1
36 + . . . In Euler’s
time this was a difficult and well known problem. It had
been around at least since Pietro Mengoli posed it in 1650,
and had eluded efforts by Wallis, Leibniz and the Bernoulli
brothers: Sandifer refers to it as “the best known problem
of the time” [20, p. 58]. In 1734 Euler found the solution
π
2
6
, solving the problem in three different ways.2
In his third
solution, Euler drew an analogy between finite and infinite
series, and applied a rule about finite series to infinite series
to get what is referred to by Polya as an “extremely daring
conjecture” [19, p. 18]. Euler continued to evaluate this conjecture,
and his analogous rule. For instance, he used empirical
tests, calculating the value for more and more terms in
the series. He also applied the rule to other infinite series,
to form predictions which could then be tested: both series
with unknown solutions (eg. 1+ 1
16 +
1
81 +
1
256 + . . . =
π
4
90 )
and series where the solution was known (eg. Leibniz’s infi-
nite series 1 −
1
3 +
1
5 −
1
7 +
1
9 −
1
11 + . . . =
π
4
). In all tests
the conjecture and analogous rule held strong.
This creative episode involves several different aspects.
Firstly, finding the solution to the Basel problem was a major
result. This has inspired our Eg
, the expression of a concept.
Of even greater value was Euler’s discovery of the analogous
rule, and in general, ways of converting rules about
finite series to rules about infinite series, which – once con-
firmed – could be applied generally. This has inspired Ep
.
Euler’s proofs that his solution is consistent and sound have
inspired Ag
. While the modern mathematical concept of in-
finity was not developed in Euler’s time, the concept of in-
finite series was well established;3
therefore, his work with
infinite series had to fit with the structure already developed.
Euler’s extended work on the applications and limitations of
his analogy and his independent proofs of the solution inspire
our framing aspect, Fg
. We summarise these creative
acts in terms of our FACE model below.
FACE Basel Problem
F
p
: –
F
g
: Euler’s extended work on the applications and limitations
of his analogy; his independent proofs of the solution; general
ways in which analogies can be used in mathematics
A
p
: –
A
g
: Euler’s proofs that his solution was sound
C
p
: Ways to find problems such as the Basel problem
C
g
: The Basel problem (Pietro Mengoli)
E
p
: Ways which Euler discovered of converting rules about fi-
nite series to rules about infinite series
E
g
: The solution π
2
6
We see that, in describing how Euler solved the Basel
problem, authors such as Polya and Sandifer refer to other
2For excellent commentary on this work, see [20, pp. 157-165]
3
Infinite series have been around at least since Zeno.
creative acts in relevant mathematics communities. They
also describe the amount of time Euler took, and the effort he
went to in order to justify his result and his methods. They
use emotive terms such as “daring” to describe the results.
In effect, this is all an attempt to quantify and qualify the impact
this creative act had on mathematical society. This motivates
our emphasis on impact rather than just value judgement
in the IDEA model. In particular, by highlighting the
time taken, Polya and Sandifer indicate the level of development
Euler’s methods went through as he tried and failed
repeatedly to find a solution. They also highlight how diffi-
cult people had previously found the Basel problem, hence
how different Euler’s creative act(s) were to the sum of those
coming before him. These aspects of the description of impact
give us motivation for the branch of the IDEA model
that deals with the stage of development software is in, and
the utility of understanding exactly the background knowledge
available before, during and after the development and
execution of the software. In addition, the emotive descriptions
highlight that creative acts are intended to affect people’s
well being. Finally, the description of Euler going to
great lengths to justify his methods can be seen as motivation
for why we measure the level of cognitive effort that
audience members expend in understanding creative acts in
the IDEA model. Clearly, Euler was trying to convince people
to understand his approach and spend time appreciating
the implications it had for mathematics.
Duncker’s candle task
Duncker’s candle task [6] is a cognitive performance test
invented by the Gestalt psychologist Duncker, intended to
measure the influence of functional fixedness4 on a participant’s
problem solving capabilities, and has been used in
a variety of experiments concerning creative thinking. The
challenge in the candle task is to fix a lit candle on a wall
(a cork board) in such a way that the candle wax won’t drip
onto the table below. One may only use a book of matches,
a box of thumbtacks and the candle. The solution, to tack
the empty box of tacks onto the wall and sit the candle in the
box, is difficult since people typically see the box as a container
for the tacks rather than a piece of equipment for the
task. Some people find partial solutions, such as tacking the
candle to the wall or melting some of the candles wax and
using it to stick the candle to the wall. The task is interesting
for us since its solution is an example of everyday, little-c,
exploratory, P-creativity (other components surrounding the
task could be argued to be a different type of creativity, such
as Duncker’s invention of the problem, which could be seen
as H-creative and possibly big-C creativity). We show our
decomposition of various creative acts connected to this task
in terms of our FACE model below. Since we are interested
in the everyday, creative problem-solving aspects in this example
we do not consider the IDEA model: there is usually
no audience in such contexts.
4
Functional fixedness is a cognitive bias which limits a person
to using an object only in the way it is traditionally intended, for
instance a person with a hammer who needs a paper weight, but is
unable to see how the hammer could be used for such a purpose.
Proceedings of the Second International Conference on Computational Creativity 76
FACE Duncker’s candle task
F
p
: –
F
g
: An explanation as to how the task was completed
A
p
: –
A
g
: Evaluation of the solution
C
p
: Ways of finding problems like Duncker’s candle task
C
g
: Duncker’s candle task
E
p
: Techniques to overcome functional fixedness, eg. analogical
transfer, in which the problem is framed as an analogy,
or reorganization of mental categories
E
g
: Tack the box onto the wall and sit the candle in it
Further work and conclusions
While our FACE and IDEA models are not broad enough to
cover all potentially creative software systems, we believe
that they cover enough to guide and describe the first wave
of creative systems. These models constitute a start, rather
than endpoint, to our thinking about how to evaluate creativity
in machines. This project is ongoing, and we expect
to evaluate our two models principally by their utility in describing
creative systems: we begin this task in a companion
paper [4]. Philosophers of science can also help us to evaluate
and compare such measures: recent work has suggested
criteria which a good theory should satisfy.5
In their analysis of one hundred recent doctoral dissertations
on creativity, Wehner et al. found a “parochial isolation”
and no cross-disciplinary ideas (reported in [23]).
They compared the situation to the parable of the blind men
who attempt to understand an elephant by touching a different
part, thus each building a very different picture of it.
We hope that, by drawing inspiration from work in the psychology
of creativity, we will help to contribute to a fruitful
multidisciplinary approach.
Acknowledgements
We are very grateful to John Charnley for his thoughts on
the FACE and IDEA descriptive models. We would also
like to thank our three anonymous reviewers for their helpful
comments. This work is supported by EPSRC grants
EP/F035594/1 and EP/F036647/1.
<references_biblio/>
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