2010
Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
APPLICATION OF ANTS COLONY SYSTEM FOR
BANKRUPTCY PREDICTION OF COMPANIES
LISTED IN TEHRAN STOCK EXCHANGE
Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
Abstract
One of the most recent researches in financial field is using an Ant Colony System (ACS) in the
corporate bankruptcy prediction.
In this paper, the Ant Colony System is used to predict the bankruptcy of listed companies in Tehran
Stock Exchange. The research findings shows that model’s prediction power is about 59% with taking into
account the rations proposed by Altman (1968). After examining the causes of significant errors in model,
a proposed model is introduced. This model which is based on four financial ratios fits the economical
infrastructure of Iran. The results obtained from testing of the suggested model indicate that this model is
able to predict the corporate bankruptcy one year prior to bankruptcy with an accuracy of 93% for largesized firms and about 90% for small-sized ones, respectively.
Khodadadi V., Zandinia A., Npuri M. - Application of Ants Colony System for Bankruptcy Prediction of Companies listed in Tehran Stock Exchange
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Introduction
Ants’ behavior
Human foraging behavior always
seeks to approach an integrated set of
information and to discover relationships
between phenomena for the explanation
of these phenomena and the prediction of
their behaviors. These attempts extended to
financial field and have induced researchers
to discover relationships between financial
information in order to provide the financial
information users with more powerful
control tools.
A highly valuable effort made by
financial researches has been the application
of financial ratios in bankruptcy prediction.
The research conducted in this field
resulted in proposing numerous models
for the prediction of corporate bankruptcy.
The continuity of these researches led to
introduction of using artificial intelligence
(AI) and computer science techniques in the
field of finance.
One of the techniques introduced is
the application of Ant Colony System in
bankruptcy prediction (Milea, 2005). This
model was initially proposed by Dorigo
(1992) to solve the Traveling Salesman
Problem (TSP) (Dorigo and Stutzle, 2004).
Thereafter, researches tended to benchmark
this model to solve similar optimization
problems in their field of study. The
researchers of financial field were also to
test this model in order to find out a solution
for financial problems.
In this research, the applicability of
this model in the prediction of corporate
bankruptcy will be explained and the
coefficient of success of this model will be
tested. For this reason, the financial ratios
of corporate have filed in Tehran Stock
Exchange in the period 2001-2007 were
used.
In real world ants run more or less at
random around their colony to search for
food. Ants deposit a chemical substance
called pheromone along the travelled paths
(Dorigo and Caro, 1999). After rainfall,
these paths get white and become visible.
Other ants upon finding these paths would
follow the trail. Then, if they discover
food source they will return to the nest and
deposit another path along with the previous
one, and will be strengthened the preceding
path.
When it turns to select a path, ants
will prefer one containing high density of
pheromone, i.e. paths on which more ants
have travelled. Pheromone is gradually
evaporated. This evaporation is useful for
three reasons:
It makes the next trail less attractive for
following ants. Ants mostly take shorter
paths; hence, the shorter path between nest
and food source is highly strengthened and
any farther path is less strengthened.
Unless pheromone did not evaporate at
all, the paths having been passed many times
would become so attractive that the random
searching for food would be highly limited.
When food finished at the end of path,
evaporation of the remaining paths would
not mislead ants in their searching for that
track leading to food source.
Therefore, when an ant finds a shorter
(optimal) path from nest to food source, other
ants will more likely follow the same path
and, over time, the continuous strengthening
of the path and the evaporation of other trails
will make all ants become unidirectional
(Dorigo and Colorni, 1996).
This behavior in ants has a kind of swarm
intelligence having been recently considered
by scientists. But it should be reassured that
there is a major difference between swarm
intelligence and social intelligence. In social
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2010
Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
intelligence the agents have a degree of
intelligence. But, in swarm intelligence the
agents have random behavior and there is no
direct relationship between them and they
are in indirect contact with each other by
signals. This behavior was first studied by
Grassé, a French scientist. It was referred
to as Stigmergy which is a particular form
of indirect communication used by social
insects to coordinate their activities via
changes made in the local environment
(Dorigo et.al, 2000).
91
Probabilistic Transition Rule
A probabilistic transition rule pij (t) , the
probability that ant k will go from i to j at
iteration t, is used by the ants in building
their tours. This probability depends on
2 parameters: a heuristic measure of the
desirability of adding edge (i,j) to the current
tour, ηij, and the amount of pheromone
currently on edge (i,j), τij. Probabilistic
transition rule is given as (2) below:
k
(2)
Ant Behavior System
Ant Colony System was initially
proposed by Dorigo and Caro to solve the
Traveling Salesman Problem (TSP) and
with benchmarking of ants behavior he
designed a powerful algorithm for solving
optimization problems. In TSP the aim is to
find a closed tour of optimal path connecting
n cities (Dorigo and Stutzle, 2004).
Therefore, the path in TSP is a directional
graph, also referred to as Hamilton cycle.
An optimal tour in weighted directional
graph means a path with minimal length.
Thus, the TSP is, in fact, finding an optimal
tour for a weighted directional graph. Also,
the length of optimal tour does not depend
on the selection of Start vertex.
Pheromone in Ant Colony
System
In Ant Colony System, the quantity of
pheromone Oxijk (t) deposited by ant k on
each edge (i,j) of the tour Tk(t) is as follows:
(1)
Where Q is an adjustable parameter
and Lk is the length of the tour (Dorigo and
Stutzle, 2004).
Where α and β are adjustable parameters
and Jk(i) is the set of cities that remain to be
visited by ant k.
Because in the beginning of the simulation
the paths generated by the ants are mostly
random, pheromone evaporation should
take place, thus avoiding convergence to a
local optimum.
(3)
Where r is the coefficient of evaporation
(0 # t # 1) and Oxijk is given by:
(4)
Where m being the number of ants (Dorigo
and Stutzle, 2004). In Ant Colony System,
the parameters should take the values: α=1,
β=5 and ρ=0.5 (Aziz et.al, 1998).
Ant Colony System Algorithm
The algorithm for Ant Colony System is
as follows:
Khodadadi V., Zandinia A., Npuri M. - Application of Ants Colony System for Bankruptcy Prediction of Companies listed in Tehran Stock Exchange
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1. The initialization step:
In this step ants are placed in the initial
position and an amount of τ0 is taken for
initial pheromone.
2. Tour calculation:
Distance
calculated.
between
parameters
is
3. Model estimation:
If the system output is not satisfactory,
then ants will move to the next location
based on the probabilistic transition function
and pheromone is converged.
4. Repeating Criterion:
Procedure continues until the system
output reaches a satisfactory position
(Dorigo and Stutzle, 2004).
Literature Review
1. Classic Methods of Bankruptcy
Prediction
A primary study was made on bankruptcy
prediction by Whitaker and Smith in 1935.
They involved investigation about the
sufficiency of financial ratios as predictors of
financial failures. The two aforementioned
researches had been analyzing the average
procedure of 21 rations for 10 years since
then and concluded that “Working Capital/
Assets” has more stability and accuracy and
it is significant as an index to identify failure.
Merwin (1942) also examined several
ratios within first 6 years of the lifespan
of corporate with continuous activity and
those whose activity had been stopped.
He concluded that three ratios of Working
Capital/Total Assets; Net Equity/Debt and
Current Ratio are more effective than others
(Balcaen and Ooghe, 2006).
Followed by these studies, a great number
of researchers involved in examining
the prediction of corporate bankruptcy
based on financial ratios which resulted
in the presentation of four univariate
analysis methods, risk index model,
multiple discriminant analysis models
and conditional probability models for
bankruptcy prediction. In 1967, Beaver was
pioneer to examine the corporate bankruptcy
using univariate analysis method (Balcaen
and Ooghe, 2006).
Tamari in 1966 presented risk index
model to predict bankruptcy and thereafter
Moses and Liao (1987), also applied this
model to predict corporate bankruptcy.
In reference to studies made by Beaver,
Altman proposed a more accurate model to
predict firms’ risk of bankruptcy with using
Multiple Discriminant Analysis (MDA)
(Altman, 1968). After his work, some
extensive researches were also conducted
about bankruptcy prediction based on
financial ratios and applying multiple
discriminant analysis (MDA). Altman
(1968), Deakin (1972), Edmister (1972),
Blum (1974), Altman et al. (1977), Deakin
(1977), Taffler and Tisshaw (1977), Van
Frederikslust (1978), Bilderbeek (1979),
Dambolena and Khoury (1980), Taffler
(1982), Ooghe and Verbaere (1985), Taffler
(1983), Micha (1984), Betts and Belhoul
(1987), Gombola et al. (1987), Gloubos and
Grammatikos (1988), Declerc et al. (1991),
Laitinen (1992), Lussier and Corman
(1994), Altman et al. (1995) are among those
researchers who one after the other proposed
bankruptcy prediction models using multiple
discriminant analysis technique.
Beginning in the 1980s, the application
of Multiple Discriminant Analysis (MDA)
method was declined but it still remained
Business Intelligence Journal - July, 2010 Vol.3 No.2
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Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
as a standard accepted method and was
continuously applied for comparative
studies. Then, MDA technique was
substituted by other statistical techniques
such as Logit and Probit analysis and
linear probability modeling. These methods
resulted in the presentation of conditional
probability models including a combination
of variables which highly discriminated
bankrupted firms from non-bankrupted
ones (Balcaen and Ooghe, 2006). Ohelson
(1980); Zavgren (1983); Zmijewski (1984);
Gentry et al (1985); Zavgren (1985); Keasey
and Vatson (1987); Peel and Peel (1987);
.Swanson and Tybout (1988); Aziz et al.
(1988);Keasey and McGuinness (1990);
Platt and Platt (1990); Ooghe et al (1993);
Sheppard (1994); Lussier (1995); Mossman
et al. (1998); Chritou and Trigeorgis (2000);
Becchetti and Sierra (2002) as well as Chritou
et al. (2000) are among those researchers
involved in bankruptcy prediction based on
conditional probability models.
2. New Methods to predict Corporate
Bankruptcy
As science and technology advances, the
financial information users need to utilize
new and stronger models and methods for
decision making is raised. As described
above, an issue on which a proper and
accurate decision should be made is the
corporate bankruptcy prediction for the
purpose of right logical investment.
Artificial neural networks have been
considered as a proposed model for corporate
bankruptcy prediction and its application
in bankruptcy prediction proved that this
method is able to predict corporate financial
status with a very high accuracy. Odom and
Sharda (1990); Koster, Sandak and Bourbia
(1990); Cadden (1991); Coatsand Fant
(1993); Lee, Han and Kwon (1996) were
among those researchers who compared
Discriminant Analysis Models (ADM)
with artificial neural networks in terms of
bankruptcy prediction (Cybinski, 2001).
One of the most recent studies in the field
of bankruptcy prediction is the application
of Ant Colony System introduced by Dorigo
to solve the travelling salesman problem.
With application of this model to predict
the financial status of corporate for the first
time, Wang, Zhao and Kang, 2004, took a
new step to introduce artificial intelligence
to the field of financial researches. Then,
in 2005, Viorel Milea made some small
changes in Ant Colony System model to
predict firms’ bankruptcy and, then, he
compared this model with Altman’s classic
model. The choice for the financial ratios
used in this work is based on the study by
Altman. Results obtained in Milea research
showed that Ant Colony System is able to
predict firms’ bankruptcy with a coefficient
of success of 80% and it, as compared with
Altman model, provides a better prediction
in some of the studies. Thus, users are able
to predict firms’ financial status with having
very limited statistical data at hand and in
the shortest time possible (Milea, 2005).
Research Design
In this research we have decided to
predict the bankruptcy of listed companies
in Tehran Stock Exchange. This is done
by first running test data for measuring the
accuracy of the algorithm in separating
the known bankrupt firms from the nonbankrupt firms. To reach our goal we
fund that the current algorithm does not
fit our situation and should be modified to
have reasonable answer. In our modified
algorithm there is one point corresponding
to each firm. Therefore, in this research the
number of ants is as the same as the number
of the firm under the study.
Khodadadi V., Zandinia A., Npuri M. - Application of Ants Colony System for Bankruptcy Prediction of Companies listed in Tehran Stock Exchange
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R = {CX1, CX2, CX3, CX4, CX5}
(6)
Xki # CXi, i ! "1, 2, 3, 4, 5,
Where CXn represents the cut-point value
of financial ratio Xn for which the fitness
function is maximized. So, a firm with values
smaller or equal to R for each financial ratio
is predicted to go bankrupt otherwise not;
and k is the given firm (Milea, 2005).
Explanation of Bankruptcy
Concept in Iran
Research Findings
Application of Ant Colony System model
in the studied sample of large and small size
firms based on the five financial ratios of
sample firms led to the following results as
shown in Tables 1 and 2.
Table 1. Model’s Results in Large- sized firms
2007
(5)
2006
In Ant Colony System applied in present
research, ants, after running at random,
would find the shortest route among the
paths (financial parameters) to identify
bankruptcy. The resulting path will be
presented as a criterion to classify firms into
bankrupt and non-bankrupt as follows:
In this research three sample firms
consisted of 36 large-size firms, 36 smallsize firms and a control sample composed of
42 firms (21 bankrupt and 21 non-bankrupt
firms) are tested. The goal has been not only
to test the prediction power of the algorithm,
but to test its effectiveness on both small and
large size firms.
2005
Classification Rules
Studied Sample Firms
2004
Independent variables used in this model
and included in financial ratios applied by
Altman (1968) in his ZETA model are as
follows:
X1 = Working Capital/Total Assets,
X2 = Retained Earnings/Total Assets,
X3 = EBIT/Total Assets,
X4 = Market Value of Equity/Book Value
of Total Debt,
X5 = Sales/Total Assets
shall be obliged to call the shareholder’s
extraordinary general meeting to decide for
the survival or winding up of the company.
If the said meeting does not decide
for winding up of the company, it will be
required to decrease the company’s capital
by the current amount at the same meeting
in virtue of the regulations as stipulated in
article 6 of the Commercial Law of Iran.”
Otherwise firm considered as Bankrupt.
2003
Studied Variables
July
2002
94
Bankrupt
2
2
2
1
5
5
Non-Bankrupt
34
34
34
35
31
31
Bankrupt
0
0
0
0
2
1
Non-Bankrupt
36
36
36
36
34
35
Description (No.)
Actual
Situation
Model
Prediction
According to article 141 of commercial
law of Iran corporate are classified in two
groups of bankrupt and non-bankrupt firms
as follows:
“Where, due to incurred losses, the half of
corporate capital is lost the board of directors
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Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
2010
Proposed model
Actual
Situation
Model
Prediction
2007
2006
2005
2004
2003
Description (No.)
2002
Table 2. Model’s Results in Small- sized firms
Bankrupt
5
6
8
9
8
5
Non-Bankrupt
31
30
28
27
28
31
Bankrupt
0
0
1
1
1
0
Non-Bankrupt
36
36
35
35
35
36
The tables show that this model nearly is
not able to predict bankrupt firms, but it can
only predict non-bankrupt firms.
To be confident of the accuracy of the
obtained results and to examine whether
these results are affected by unequal number
of bankrupt and non-bankrupt firms or not,
we take a sample consisting of 42 bankrupt
and non-bankrupt firms (21 bankrupt and 21
non-bankrupt firms) as control sample and
the results are as shown in Table 3.
Table 3. Model’s Results in Control sample firms
Description (No.)
Bankrupt
NonBankrupt
Actual Situation
21
21
Model Prediction
4
38
Correct prediction
4
21
Percentage of correct
prediction
59.52%
The results of the tested sample show
that for even for equal number of bankrupt
and non-bankrupt samples the coefficient of
success of the model has reduced to 59.52%.
This result shows that the prediction power
concerning bankrupt firms is as low as 19%.
Therefore, it is concluded that the original
Ant Colony System model, based on the five
original financial rations cannot discriminate
bankrupt firms registered in Tehran stock
exchange above 59.52%.
The failure of the original model in
predicting the bankruptcy status of the
Tehran Stock Exchange, especially in the
case of small-size firms, forced us to closely
examine the model. We found out that in the
original model:
1. Non-fitness of bankruptcy identification
criterion in Iran with the ratio of Market
Value of Equity/ Book Value of Total
Debt:
As described in previous sections,
the bankruptcy of companies in Iran is
identified in article 141 of the Commercial
Law. Hence, the classification criterion to
identify firms into two groups of bankrupt
and non-bankrupt is the amount of firm’s
capital. With glancing over the concerned
independent variables in order to test Ant
Colony System for bankruptcy prediction we
will find out that this criterion has not been
considered in any of independent variables
and, instead, Market Value of Equity ratio
has been expressed in terms of fluctuation
which, in spite of firms’ belonging to
samples with equal sizes, would be high in
studied samples.
2. Inflation Impact on Sales/Book Value of
Total Assets:
In the calculation of Sales/Book Value of
total assets, sales at current value as well
as assets value are historical costs. Under
the Iran economic conditions with very
high inflation rate as well as instability of
economic conditions, sales are very inflated
rather than book value of total assets. In
order to make modifications to the influence
of inflation on Sales/Book Value of Total
Assets, revaluation of firms’ assets enabling
this ratio to express firms’ status in a more
Khodadadi V., Zandinia A., Npuri M. - Application of Ants Colony System for Bankruptcy Prediction of Companies listed in Tehran Stock Exchange
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Description (No.)
Bankrupt
NonBankrupt
Actual Situation
21
21
Model Prediction
21
21
Correct prediction
19
19
Percentage of correct
prediction
90.47%
The results displayed in Table 4 indicate
that this model is able to predict up to 90%
of corporate financial status.
After examining of proposed model in
control sample and being confident of the
model accuracy within the same sample,
we tested the new suggested model for two
main samples, i.e. sample of large- and
small-sized firms. The results obtained from
testing of proposed model are as shown in
Tables 5 and 6.
2007
2
2
1
5
5
34
34
35
31
31
Bankrupt
5
1
3
1
2
4
Non-Bankrupt
31
35
33
35
34
32
33
35
33
34
33
33
91.67
2006
2005
2
34
91.67
Model
Prediction
Bankrupt
Non-Bankrupt
94.44
Actual
Situation
91.67
Description (No.)
2004
Table 5: Proposed model’s Results in Large- sized
firms
2003
Thus, we examine Ant Colony System
model with new conditions for the samples
having been previously tested. The new
suggested model to predict the bankruptcy of
listed companies in Tehran Stock Exchange
is composed of four independent variables
as follows:
X1= Working Capital/Total Assets
X2= Retained Earnings/Total Assets
X3= EBIT/Total Assets
X4= Book Value of Equity/Book Value of
Total Debts
Due to unequal number of bankrupt and
non-bankrupt corporate in both studied
samples (large- and small-sized firms) and
in order to be confident that the proposed
model is not affected by unequal number
Table 4: Results of proposed model in Control
sample firms
97.22
1. Due to using amount of Capital for
classifying corporate into two groups
of bankrupt and non-bankrupt firms, we
have used Book Value of Equity/Book
Value of Total Debts instead of Market
Value of Equity/ Book Value of Total
Debts.
2. As a result of very highly inflated Sales/
Book Value of Total Assets as well as
lacking any legal obligation for Listed
Companies in Tehran Stock Exchange to
revaluate their assets and the monopoly
for some products, we eliminate this
ratio from the model.
of firms, we, firstly, test the model for the
control sample composed of 42 corporate
(21 bankrupt and 21 non-bankrupt firms).
The results obtained from control testing are
as shown in Table 4.
2002
reasonable manner is necessary. But, due
to lacking any legal obligation concerning
listed companies in Tehran Stock Exchange
to revaluate their assets, this ratio will
remain as a problematic parameter whenever
financial problems are to be solved. Also,
as a result of monopoly for some products
such as steel and automobile, the above ratio
cannot be an appropriate scale to compare
firms.
The following measures were taken to
resolve the above-mentioned issues:
July
91.67
96
Correct prediction (No.)
Percentage of correct
prediction
Average of correct
predictions per.
93.06%
The results of the test made on proposed
model indicate a coefficient of success of
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Vali Khodadadi, Abolfazl (Parviz) Zandinia and Marzieh Nouri
2010
93% for the model to predict the bankruptcy
of large-sized corporate.
After testing of proposed model in the
sample of large-sized firm, the model was
also tested for small-sized firms and the
following results were obtained:
2002
2003
2004
2005
2006
2007
Bankrupt
5
6
8
9
8
5
Non-Bankrupt
31
30
28
27
28
31
Bankrupt
3
5
5
4
7
1
Non-Bankrupt
33
31
31
32
29
35
34
35
33
29
33
30
94.44
97.22
91.67
80.56
91.67
83.33
Table 6: Proposed model’s Results in Small- sized
firms
Description (No.)
Actual
Situation
Model
Prediction
Correct prediction (No.)
Percentage of correct
prediction
Average of correct
predictions per.
89.82%
The results of the test made on proposed
model indicate a coefficient of success
of 89.82% for the model to predict the
bankruptcy of small-sized firms.
Upon comparison of the results of the test
made on proposed model we found out that
this system is slightly affected by corporate
size. So that the model’s coefficient of
success in large-sized corporate group is
about 93% while in small-sized corporate
group is about 90%, respectively.
Consequently, as the results of
investigations show, the proposed model is
able to predict the bankruptcy of corporate
one year prior to bankruptcy.
Conclusion and Summarization
This study aims at the application of Ant
Colony System for bankruptcy prediction
of corporate accepted in Tehran Stock
Exchange.
The primary variables used in this model
include Working Capital/Total Assets;
Retained Earnings/Total Assets; EBIT/Total
Assets; Market Value of Equity/Book Value
of Total Debts; Sales/Total Assets.
After these variables were tested in the
model we found out that this model is not
likely able to predict non-bankrupt firms
and its real prediction power is about 59%.
The investigations showed that the system
error was caused by the two ratios of Market
Value of Equity/Book Value of Total Debts
as well as Sales/Total Assets. In virtue
of article 141 of the Commercial Law of
Iran and choosing capital as a criterion for
corporate bankruptcy, using Market Value
of Equity is not logical. Moreover, this will
still remain as a problematic ratio because
of lacking any legal obligation for listed
companies in Tehran Stock Exchange for
assets revaluation. Also, as a result of very
high inflation rate in Iran, instable economic
situations as well as monopoly for some
products such as steel and automobile, the
ratio of Sales/Total Assets is very inflated
and may not be regarded as an appropriate
scale to compare firms.
In order to resolve above-mentioned
matters, we consider Book Value of Equity
instead of Market Value of Equity and, also,
Sales/Total Assets was omitted from among
variables. At last, a proposed model consisted
of four variables as described below was
proposed to predict the bankruptcy of listed
companies in Tehran Stock Exchange based
on Ant Colony System:
Working Capital/Total Assets; Retained
Earnings/Total Assets; EBIT /Total Assets;
Book Value of Equity/Book Value of Total
Debts.
The results produced by the testing of
new suggested model indicated that the
prediction power of this model within the
sample of large-sized firms is about 93%
and in the sample of small-sized firms is
about 90%, respectively. Therefore, this
model is able to predict the bankruptcy of
listed companies in Tehran Stock Exchange
with a very high coefficient of success and it
is slightly affected by corporate size.
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Suggestions and Prospective of
Future Researches
As the Ant Colony System is a dynamic
model having a very high coefficient of
accuracy to search the answer of optimization
problems, this model is recommended for
these types of problems. Also, in order to
be confident of the percentage of influence
made by the elimination of Sales/Total
Assets it is suggested to reconsider this
ratio within the model with considering the
assets revaluation problem. Also, it has been
proposed to investigate about the corporate
bankruptcy with using Ant Colony System
and applying phase rules in Iran.
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