Multi criteria decision making (MCDM) techniques in today’s organizations, as a key to performance measurement comes more to the foreground with the advancement in the high technology. During recent years, many studies have been conducted to obtain a ranking among many alternatives via measuring performance of each of them against many criteria. Managerial decision making problems like supplier selection, weapon selection, project selection, site selection etc are dealt with many multi criteria decision making methods like TOPSIS, AHP-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation), ELECTRE, VIKOR etc in crisp throughout the literature. In this work, we first compare several MCDM methodologies to validate the consistency of them on a standard dataset of plant layout problem. We proposed M-TOPSIS, A-TOPSIS procedure to select a suitable layout for the comparative study. Results of M-TOPSIS and A-TOPSIS have been employed to build an unsupervised artificial neural network (ANN) to obtain a new ranking of alternatives. This study proposes an approach of deriving the rank value, in order to get optimal configuration, from the average of more than one set of rank results obtained through the deployment of MCDM methodologies

1. International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online), Volume 5, Issue 3, May- June (2014), pp. 13-23 © IAEME
INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING
RESEARCH AND DEVELOPMENT (IJIERD)
ISSN 0976 – 6979 (Print)
ISSN 0976 – 6987 (Online)
Volume 5, Issue 3, May - June (2014), pp. 13-23
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13
IJIERD
© I A E M E
AN INTELLIGENT HYBRID MULTI CRITERIA DECISION MAKING
TECHNIQUE TO SOLVE A PLANT LAYOUT PROBLEM
Indranil Ghosh
Calcutta Business School, West Bengal, India
ABSTRACT
Multi criteria decision making (MCDM) techniques in today’s organizations, as a key
to performance measurement comes more to the foreground with the advancement in the high
technology. During recent years, many studies have been conducted to obtain a ranking
among many alternatives via measuring performance of each of them against many criteria.
Managerial decision making problems like supplier selection, weapon selection, project
selection, site selection etc are dealt with many multi criteria decision making methods like
TOPSIS, AHP-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution),
PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation),
ELECTRE, VIKOR etc in crisp throughout the literature. In this work, we first compare
several MCDM methodologies to validate the consistency of them on a standard dataset of
plant layout problem. We proposed M-TOPSIS, A-TOPSIS procedure to select a suitable
layout for the comparative study. Results of M-TOPSIS and A-TOPSIS have been employed
to build an unsupervised artificial neural network (ANN) to obtain a new ranking of
alternatives. This study proposes an approach of deriving the rank value, in order to get
optimal configuration, from the average of more than one set of rank results obtained through
the deployment of MCDM methodologies.
Keywords: TOPSIS, M-TOPIS, VIKOR, Crisp, ANN.
1. INTRODUCTION
Due to ever increasing complexity of performance measurements which is one of the
most important processes in management literature and as its measurement is critical for
judging the success or failure of a firm, multi criteria decision making (MCDM) techniques

2. International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online), Volume 5, Issue 3, May- June (2014), pp. 13-23 © IAEME
have recently been in the limelight of research. MCDM techniques are tailor made to cater a
systematic and deterministic approach to tackle complex real world decision making
problems composed of several intertwining and incommensurate criteria. Roy (1990)[1]
argues that solving MCDM problems and searching for an optimal solution are clearly two
distinct measures, prime focus of MCDM is to assist Decision makers (DMs) evaluate the
complex judgments and to carefully analyze data involved in their problems and advance
towards an acceptable solution. The entire process is subdivided in three parts, a set of
alternatives, A, is evaluated to produce a final decision result:
Sorting- Sort the alternatives of A into relatively homogeneous groups in a preference order.
Ranking- Rank the alternatives of A from best to worst.
14
Choice- Choose the best alternative from A.
Unlike many off-the-shelf recipes that can be applied to every problem regardless of
their constraints MCDM techniques have often beendictated by the essence of real-life
problems.Several MCDM techniques like TOPSIS, AHP, combined AHP-TOPSIS [2],
VIKOR [3], PROMETHEE [4], ELECTRE [5] etc. have been successfully applied by many
researchers addressing many MCDM problems. Artificial neural network (ANN), an
evolutionary optimization based algorithm had been developed in [6, 7], and [8]. ANN based
algorithms are claimed to be helpful for practical industrial applications especially for
dynamic situations. ANN is categorized in two sections- Supervised ANN Unsupervised
ANN which we discuss in section 4. ANN has been successfully applied in many real life
industrial problems including MCDM problems too [9, 10]. One famous work of Kumar
Roy [11] deploys an Unsupervised artificial neural network to evaluate rank of suppliers.
This work avails the model of to rank the layouts based on the results of M-TOPSIS A-TOPSIS.
The remainder of the paper is organized is as follows section 2 outlines the plant
layout problem, section 3 depicts the mathematical steps involved with TOPSIS, A-TOPSIS,
M-TOPSIS respectively, section 4 presents the unsupervised ANN model and algorithm to
generate composite ranking, section 5 presents the comparative analysis of results and
proposed methods and results of Yang Hung [12] an approach of deriving the rank value,
in order to get optimal configuration.
2. PLANT LAYOUT
Designing and implementation of plant or facility layout is the most critical phase of
setting up new facility in existing unit both in manufacturing and service sectors. It directly
affects the performance of an entire unit. Layout design can influence quality of
manufactured products or service delivery as checking or testing locations needs to be
incorporated in the integrated system in most befitting manner besides the fact that in certain
situations material damages are obviated by reducing its handling requirement. So choosing
an appropriate layout among several layout configurations that can be generated by software
such as ARENA, CORLAP, CRAFT etc is indeed a typical MCDM problem which contains
several conflicting criteria associated with possible alternatives (plant configurations). A
good layout design ensures increase in productivity reducing overheads. Some notable works
on this domain include Karray et al[13] where he proposed an integrated methodology using

3. International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online), Volume 5, Issue 3, May- June (2014), pp. 13-23 © IAEME
the fuzzy set theory and genetic algorithms to investigate the layout of temporary facilities in
relation to the planned buildings in a construction site, (TOPSIS) and fuzzy TOPSIS[12,
14](Yang and Hung ,2007, Grey Relational Analysis(Kuo, Yang, and Huang, 2008). Yang
and Hung [12] mentioned six criteria out of which three are quantitative and rest are
qualitative. Thequantitative criteria included material handling distance(in ‘meters’),
adjacency score and shape ratio, which are thedirect outputs of Spiral. The handling distance
is calculated by the sum of the products of flow volume and rectilinear distance between the
centroids of two departments. The adjacency score is the sum of all positive relationships
between adjacent departments. Whereas, shape ratio is defined as the maximum of the depth-to
15
width and width-to-depth ratio of the smallest rectangle that completely encloses the
department. For a layout design problem, it is needed to minimize both the shape ratio and
flow distance, while maximizing adjacency score. There are three qualitative attributes are
flexibility, accessibilityand maintenance. These are the six attributes chosen by Yang and
Hung to evaluate their 18 alternatives.
3. MCDM METHODOLOGIES
3.1 TOPSIS: The TOPSIS (technique for order performance by similarity to ideal solution)
method [15](Hwang Yoon, 1981) constitutes a usefultechnique in solving ranking
problems. The basic idea of the TOPSISis simple and intuitive: measure alternatives’
distances to predefinedideal and anti-ideal points first and, then, aggregate theseparate
distance information to reach overall evaluation results.Some features of TOPSIS, as
summarized in [16] (Kim, Park, and Yoon(1997)) and [17] (Shih, Shyur, and Lee (2007),
include clear and easilyunderstandable geometric meaning, simultaneously considerationfrom
both best and worst points of view, and convenient calculationand implementation. The
procedural steps of TOPSIS are mentioned below:
3.1.1 Construct a matrix based on the priority scoresassigned to each alternative simulator on
each attributedenoted by
X = (xij)nxm (1)
3.1.2 Determine the importance weight (wj) of the attributes such that:
= 1, j=1, 2, 3,……m. (2)
3.1.3 Obtain the normalized decision matrix:
= / (

4. )0.5 j = 1, 2,…m; i = 1, 2, ….n. (3)
3.1.4 Obtain the weighted normalized decision matrix,
= ; j = 1, 2, …., m; i = 1, 2, ….., n. (4)
3.1.5 Determine the PIS and NIS:
= (

5. ) = {( { }| j B ), ( { | j C)} , (5)

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= (

7. ) = {( { }| j B ), ( { | j C)} .
3.1.6 Calculate the separation measures of each alternative simulator from the PIS and NIS is
calculated by the Euclidean distance:
!#$
; i = 1, …., n, (6)
!#$
; i = 1, …., n. (7)
3.1.7 The relative closeness of a particular alternative simulator to the ideal simulator, Ti, can
be expressed in this step as follows:
(
% '
)'
*'
(+
(8)
3.1.7 A set of alternative simulators is generated in the descending order based on the value
of Ti indicating the most preferred and least preferred feasible solutions.
Apparently these computation steps are very simple and logical and produce feasible
solutions however one drawback that it and many other MCDM techniques suffer from is the
rank reversal phenomenon. Literature reports many such evidence of it. As the scarcity of
works carried out to betray the comparative of results of different techniques on same
problem instance is high, justification of consistency of methods in most of the occasion is
not rigid in full extent. Ren et al. (2007) [18] has introduced a modified synthetic evaluation
method (M-TOPSIS) based on the concept of the conventional TOPSIS to avoid rank
reversals. M-TOPSIS considers the evaluation failure that often occurs in the conventional
TOPSIS. In this study we intend to the compare the convention TOPSIS with M-TOPSIS and
another technique A-TOPSIS presented by Deng et al. (2000) [19] applying weighted
Euclidean distances, rather than creating a weighted decision matrix to observe the results
and measure the degree of rank of reversal which could affect the organization in future. The
steps of M-TOPSIS and A-TOPSIS described below.
3.2 M-TOPSIS: Steps 3.2.1–3.2.6 for M-TOPSIS is identical to steps 3.1.1–3.1.6 for the
conventional TOPSIS method described in Section 3.1.
3.2.7 Determine the ideal reference point (S):
S = , - )
+ ; i = 1, …, n. (9)
and
3.2.8 Determine the Euclidean distance between
for each alternative simulator and
point S:
%
. /0
1 2 0
10.5 (10)
3.3 A-TOPSIS: Steps 3.3.1–3.3.3 for A-TOPSIS is similar to steps 3.1.1–3.1.3 for the
conventional TOPSIS method described in Section 3.1.

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3.3.4 In A-TOPSIS, the PIS (A+) and NIS (A_), which are not dependent on the weighted
decision matrix, are defined as:
= (
17

9. ) = {( { }| j B ), ( { | j C)} , (11)
= (

10. ) = {( { }| j B ), ( { | j C)} . (12)
3.3.5 The weighted Euclidean distances are calculated as:
!#$
; i = 1, …., n, (13)
!#$
; i = 1, …., n. (14)
3is expressed as:
3.3.6 The relative closeness of a particular alternative to the ideal solution %
3 '
%
(
)'
*'
(+
(15)
4. ARTIFICIAL NEURAL NETWORK MODEL
The concept of neural networks started in the late-1800s and traditionally, the term
neural network had been used to refer to a network or circuit of biological neurons. Kumar
and Roy [11] in their hybrid AHP-neural network model to solve supplier selection problem
used the weights of criterion obtained from AHP as weights of neuron to yield the assessment
of vendors. In our work, the Unsupervised ANN is trained with composite scores generated
by M-TOPSIS and A-TOPSIS individually. Basic definition regarding unsupervised learning
is described below.
Unsupervised learning: In unsupervised learning with a given input data x, sigmoid function
[1 / (1 + e-(xiwi))] is to be minimized which can be anyfunction of x is related to the
network's output, y=f (w, x), wherew is the matrix of all weight vectors.
Yang and Hung [12] considered the weight of these six criteria to be (0:20; 0:20; 0:15; 0:10;
0:20; 0:15) which we incorporated for experiment and analysis. The algorithm to assess the
rankings of layout is listed below.
Step 1- Input: Select the number of criteria to be decided.
Input: The number of alternatives to be evaluated.
Step 2- Generate the comparison matrix for layouts with respect to givencriteria.
Create this matrix of alternative-criteria (i.e. reviewed from experts) by questionnaire.
Step 3- Apply M-TOPSIS/A-TOPSIS to compute the composite scores of each alternative
against all the criteria to find the weighted normalized decision matrix.
Step 4- Apply ANN model to create a matrix for hidden on criteria weight.

11. International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
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Step 5- Output value for hidden layer Yci = 1 / (1 + e-(XiWci) )
Step 6- Create a matrix for output layer by using following formula:
Value for output layer Yvi = 1 / (1 + e-(YciWvi) )
Step 7- Rank each layout according to their score in descending order from the matrix.
For step 2, dataset used by Yang and Kuo[19] score of each alternative against each attribute
is applied for this study which is mentioned in table-1 of section 5.
5. COMPUTATIONAL RESULTS AND ANALYSIS
18
Yvi = Total score of corresponding layout.
Stop.
Dataset of Yang and Kuo [20] has been adopted for all the computation and
comparative study, we first compare results of our methods with TOPSIS method proposed
by Yang and Hung [12].
Table 1: Quantitative measures of different criteria for the alternative layouts
(Yang Kuo, 2003)
Alternati
ves Distance Adjacency Shape ratio Flexibility Accessibility Maintenance
A1 185.95 8 8.28 0.0494 0.0294 0.013
A2 207.37 9 3.75 0.0494 0.0147 0.0519
A3 206.38 8 7.85 0.037 0.0147 0.0519
A4 189.66 8 8.28 0.037 0.0147 0.0519
A5 211.46 8 7.71 0.0617 0.0147 0.039
A6 264.07 5 2.07 0.0494 0.0147 0.0519
A7 228 8 14 0.0247 0.0735 0.0649
A8 185.59 9 6.25 0.037 0.0441 0.039
A9 185.85 9 7.85 0.0741 0.0441 0.0519
A10 236.15 8 7.85 0.0741 0.0588 0.0649
A11 183.18 8 2 0.0864 0.1029 0.0909
A12 204.18 8 13.3 0.037 0.0588 0.026
A13 225.26 8 8.14 0.0247 0.0735 0.0519
A14 202.82 8 8 0.0247 0.0588 0.0519
A15 170.14 9 8.28 0.0864 0.1176 0.1169
A16 216.38 9 7.71 0.0741 0.0735 0.0519
A17 179.8 8 10.3 0.0988 0.1324 0.0909
A18 185.75 10 10.16 0.0741 0.0588 0.039
MAX 264.07 10 14 0.0988 0.1324 0.1169
MIN 170.14 5 2 0.0247 0.0147 0.013
BF/NBF NBF BF NBF BF BF BF

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Yang and Hung [6] considered the weight of these six criteria to be (0:20; 0:20; 0:15; 0:10;
0:20; 0:15), which is used for this work to compare their TOPSIS based result with M-TOPSIS
. Final ranking
19
and A-TOPSIS. Table 2 and Table 3 displayed the results of A-TOPSIS and M-TOPSIS
respectively.
Table 2: Result of A-TOPSIS:
Alternatives
%
3 Final Ranking
A1 0.163620.1708860.51086 A11 (1)
A2 0.1607690.1759770.522581 A6 (2)
A3 0.1723760.1871010.520482 A14 (3)
A4 0.1913970.2134220.527204 A4 (4)
A5 0.1726220.184820.517063 A15 (5)
A6 0.1629620.1830930.529087 A10 (6)
A7 0.202204 0.2016510.499316 A17 (7)
A8 0.1592590.1667560.511497 A2 (8)
A9 0.1625180.1714590.513386 A16 (9)
A10 0.2073850.2290880.524862 A3 (10)
A11 0.2513220.2868760.53303 A5 (11)
A12 0.1990720.203340.505303 A18 (12)
A13 0.174470.1841380.51348 A13 (13)
A14 0.1854770.2072230.527688 A9 (14)
A15 0.2671910.2972190.526601 A8 (15)
A16 0.1873570.20440.521752 A1 (16)
A17 0.1867230.2045240.522749 A12 (17)
A18 0.18733 0.1998840.516211 A7 (18)
Table 3: Result of M-TOPSIS
Alternatives %
A1 0.005546 A11 (1)
A2 0.004624 A15 (2)
A3 0.004851 A10 (3)
A4 0.003912 A4 (4)
A5 0.005124 A6 (5)
A6 0.00408 A14 (6)
A7 0.006363 A17 (7)
A8 0.005371 A16 (8)
A9 0.005371 A2 (9)
A10 0.003701 A3 (10)
A11 0.0009 A18 (11)
A12 0.005818 A5 (12)
A13 0.005314 A13 (13)
A14 0.004011 A8 (14)
A15 0.001 A9 (15)
A16 0.004472 A1 (16)
A17 0.004295 A12 (17)
A18 0.004934 A7 (18)

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The rank of alternatives obtained from M-TOPSIS and A-TOPSIS method is hence
compared with output of TOPSIS method proposed by Yang and Hung to demonstrate the
comparative results of different MCDM technique. It is very evident that different MCDM
methodologies can give different answers to the same problem. However to proper analysis
and justification of their consistency it is essential to carry out a comparative study which is
shown in Table-4.
Table 4: Comparative study of three methods
Alternative M-TOPSIS A-TOPSIS TOPSIS
Yang and Hung
(2007)
Average
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
A17
A18
16
9
10
4
12
5
18
14
14
3
1
17
13
6
2
8
7
11
16
8
10
4
11
2
18
15
14
6
1
17
13
3
5
9
7
12
16
9
10
4
12
6
18
13
15
3
1
17
14
5
2
8
7
11
16
8.667
10
4
11.667
4.333
18
14
14.333
4
1
17
13.333
4.667
3
8.667
7
11.333
The study reveals that A11 is chosen as the most suitable candidate by all 3 methods
and A7 as the most ineffective candidate. To add to more justification we have also computed
the average of all proposed and existing methodologies which demonstrate over the same
problem. Calculating the average value by combining all of the proposed and existing
methodologies, it is seen that the alternative having the minimum average value (A11) is the
best optimal facility layout design alternative.
As all the MCDM methodologies can give different answers to the same problem, we
mentioned to determine the best alternative it is required to compute the average value of the
order of the rank from the available rank order obtained by using more than one
methodology. However 2 methods are shown to maintain concrete consistency in order to
determine the best feasible alternatives and discarding the worst ones.
Now we apply the unsupervised ANN model, described in section 4 to further find the
composite ranking based on the results of M-TOPSIS and A-TOPSIS. The steps are described
in table 4 and table 5.

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Table 4: Output values for hidden layer
Criteria
Weight
Input value
Xi
XiWCi) Output value for hidden
layer Yci
C1
C2
C3
C4
C5
C6
0.20
0.20
0.15
0.10
0.20
0.15
0.0556
0.22
0.22
0.17
0.12
0.22
0.17
0.5548
0.5548
0.5424
0.5300
0.5548
0.5424
XiWC1= .0556x.22 + .0556x.22 +.0556x.17 +.0556x.12+ .0556x.22+. 0556x.559+ .0556x.559+1x .2 =.760
Input value for all bias neuron, weight for all bias neuron and learning rate () was
chosen same as of [], i.e. 1, 0.2 and 1 respectively.
Xi = Input value for input layer = 1/18 = 0.0556
WCi = Weight of criteria
Yci= Output value for hidden layer = 1 / (1 + e-(XiWci)) = Inputvalue for output layer
Yc1= .5548
Now we apply the algorithm mentioned in section 4 on normalized decision matrix
obtained by both M-TOPSIS and A-TOPSIS which is shown in table 6.
Table 6: Output of ANN
Alternati
ves
Yc1= Yc2= Yc3= Yc4= Yc5= Yc6= YciWVi Yvi
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
A17
A18
0.0427
0.0427
0.0474
0.0436
0.0486
0.0607
0.0524
0.0427
0.0427
0.0543
0.0421
0.0469
0.0518
0.0466
0.0391
0.0497
0.0413
0.0427
0.0455
0.0512
0.0455
0.0455
0.0455
0.0285
0.0455
0.0512
0.0512
0.0455
0.0455
0.0455
0.0455
0.0455
0.0512
0.0512
0.0455
0.0569
0.0347
0.0157
0.0329
0.0347
0.0323
0.0087
0.0586
0.0262
0.0329
0.0329
0.0084
0.0557
0.0341
0.0335
0.0347
0.0323
0.0431
0.0425
0.0047
0.0236
0.0283
0.0283
0.0283
0.0142
0.0189
0.0189
0.0142
0.0236
0.0378
0.0142
0.0283
0.0142
0.0378
0.0189
0.0189
0.0236
0.0196
0.0196
0.0390
0.0586
0.0293
0.0390
0.0293
0.0098
0.0196
0.0586
0.0880
0.0293
0.0293
0.0586
0.0880
0.0390
0.0586
0.0390
0.0416
0.0346
0.0208
0.0277
0.0277
0.0416
0.0139
0.0346
0.0346
0.0416
0.0554
0.0346
0.0208
0.0346
0.0554
0.0416
0.0208
0.0208
0.103684
0.105535
0.117304
0.130789
0.116005
0.105934
0.119912
0.100528
0.107108
0.140797
0.152062
0.124024
0.115014
0.128072
0.167825
0.127717
0.125344
0.123737
0.525898
0.526359
0.529292
0.532651
0.528969
0.526459
0.529942
0.525111
0.526751
0.535141
0.537942
0.530966
0.528722
0.531974
0.541858
0.531886
0.531295
0.530895

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22
This particular table is composed of scores of each alternative layout deducted from
both M-TOPSIS and A-TOPSIS via ANN modeling, according to step 7 of algorithm, the
rankings of alternatives are depicted in table 7.
Table 7: Composite score and final ranking
Alternatives Yvi Ranks
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
A17
A18
0.525898
0.526359
0.529292
0.532651
0.528969
0.526459
0.529942
0.525111
0.526751
0.535141
0.537942
0.530966
0.528722
0.531974
0.541858
0.531886
0.531295
0.530895
A15
A11
A10
A4
A14
A16
A17
A12
A18
A7
A3
A5
A13
A9
A6
A2
A1
A8
According to ANN model choice of layouts would be in order of:-
A15A11A10A4A14A16A17A12A18A7A3A5A13A9A6A2A1.
6. CONCLUSION
This work reveals that the most of the MCDM methods are consistent enough to
determine the top alternatives regardless of the complexity of the problem if modeled
properly in most of the occasions. It is always a good practice to apply multiple
methodologies to validate the result and detect anomaly if found in large proportion.
Averaging ranks obtained from multiple procedures can be used in such scenarios. It also
suggests a soft computing based (ANN) approach could be undertaken to reduce the anomaly
ratio and generate a composite ranking. Overall findings suggest that MCDM methodologies
along with artificial intelligent based methods should not be restricted to only manufacturing
problems, they could well be deployed in service industry also which also involves in key
managerial decision making problems like vendor selection, recruitment procedure etc. More
research work should be carried out in this domain to better tackle the problems in uncertain
environment, generate a composite ranking if results vary drastically from multiple methods.
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