A Generalised Structural Model of Structured and ObjectOriented Programs for Software Metrics Defini

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A Generalised Structural Model of Structured and
Object-Oriented Programs for Software Metrics
Definition
Boris Cogan Department of Computing, Multimedia
Technology, and Mathematics London Metropolitan
University, London, UK Elena Shalfeeva Institute
for Automation and Control Processes Russian
Academy of Sciences, Vladivostok, Russia
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Contents

• What was before us
• General Task and two Subtasks
• Language-Oriented Approach
• Basic Generalised Model of a Structured Program
• Generalised Model of a Program Unit
• Generalised Model of a Structured Program
• Basic Generalised Model of an Object-Oriented
  Program
• Generalised Class Inheritance Model
• Generalised Class Interaction Model
• Conclusions
• Future Work
• Publications

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1. What was before us

• Many models and hundreds of metrics

• We considered only those metrics that are used in
  software development practice

• Some metrics were and are used for both main
  kinds of programs

Hierarchical models and metrics
Object-oriented models and metrics
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2.1 The Task and two Subtasks

• We may use many model to explain metrics
• Too many models are impractical for developing
  program measurement tools
• Our general task is development of a generalised
  structural model and then redefinition all
  metrics for this new model
• This model for measurement tools only!

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2.2 The Task and two Subtasks

• Two subtasks for hierarchical and
  object-oriented models

Generalised Structural Program Model
Generalised Structural Model of Structured
Programs
Generalised Structural Model of Object-Oriented
Programs
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3.1 Language-Oriented Approach First stage

• First stage of program measurement
• Language Measuring Model
• PMM a set of relational tables

Program Measuring Model (PMM)
Program
Measuring Language Processor
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3.2 Language-Oriented Approach Second stage

• A language to describe treatment of PMMs in terms
  of product models and product metrics

• Its implementation is a general-purpose processor

Program Measuring Model (PMM)
Models
Metric values
Metric Evaluator
Model Constructor
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4.1 Models for Structured Programs
Structural Model of Structured Programs
Generalised Graph Model of a Program Unit
Generalised Graph Model of a Structured Program
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4.2 A Basic Generalised Model

• A generalised structural model has to cover
  combinations of functional and informational
  program components and/or elements as well as
  relationships among them.
• The model can be used to redefine
• software metrics defined using the particular
  models
• all widely-used 'particular' structural program
  models by means of specifying values of the model
  parameters.

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4.3 The Basic Generalised Model

• The Generalised Graph Model (GGM) of a
  component of a program is a directed multigraph
  G (N, E) consisting of a set of nodes N and a
  set of edges E.
• Any node n ? N corresponds to a computer memory
  fragment with 'information' or functions.
• Any directed edge e ? E reflects a relationship
  between two 'memory fragments' by information or
  control.
• GGM (Node, Edge).

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4.4 The Basic Generalised Model

• Node (Node name,
• Program component type,
• Component attributes)
• Edge (N-1 name,
• N-2 name,
• Relationship type,
• Relationship characteristics)

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4.5 Useful Characteristics of the Basic
Generalised Model

• The model has the characteristics used to define
  software quality metrics
• The number of nodes with a specific value of
  Program component type
• The number of edges with a specific value of
  Relationship type
• Fan-in/fan-out for a graph node (for the edges
  with a specific value of Relationship type)
• The number of loops in a graph

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5.1 A Basic Model Specification for a Program
Unit

• The practical experience has shown that
  properties of control and information flows
  inside any program unit affect properties of the
  complete program.
• Use of many models it is inconvenient for the
  development of software measurement tools.
• The model for a program unit implies
  consideration of main blocks, statements,
  variables and relationships among them.
• The control flow graph and the variable
  dependence graph are sub-graphs of the model.

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5.2 A Model for a Program Unit

• A Generalised Graph Model for a program unit is
  a directed multigraph G (N, E) consisting of a
  set of nodes N and a set of edges E.
• Any node n ? N corresponds to a simple (s-)
  statement, a main block or a variable used in the
  program unit (local or non-local including global
  and a formal parameter) and a function
  invocation.
• Any edge e ? E reflects a relationship between
  two s-statements by control or using
  variables in s-statements or
  modification variable values in the s-statements.

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5.3 A Model for a Program Unit A Node

• Node (Node name,
• Program component type,
• Component attributes)
• Program component type s-statement ? variable
• Component attributes (Node type, Node location)
• Node type S-statement-node type ? Variable
  scope
• S-statement-node type predicate ? procedure
• Variable scope parameter ? local ? non-local
• Node location first ? internal ? last

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5.4 A Model for a Program Unit An Edge

• Edge (N-1 name,
• N-2 name,
• Relationship type,
• Relationship characteristics)
• Relationship type control ? data
• Relationship characteristics
• Characteristic
• Relationship characteristics,
  Characteristic
• Characteristic value t f Ø

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5.5 A Program Unit and its Generalised
Structural Graph Model
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5.6 Useful Characteristics of the Basic Program
Unit Model

• The characteristics of the model a program unit
  can be expanded and used to define software
  quality metrics

• The set of variable-nodes and the set of data
  flow paths from a particular variable-node to
  nodes of the set
• The set of variable-nodes for non-local variables
  and the set of incoming and outgoing edges for
  these nodes
• The number of linearly independent control paths
  in the corresponding sub-graph (as well as simple
  paths, visit-each-loop paths etc.)
• ...

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5.7 The Control Flow Graph

• Node Node (Node name, Program component type,
• Component attributes)
• Program component type s-statement
• Component attributes (Node type, Node location)
• Node type Statement-node type
• Statement-node type predicate ? procedure
• Node location first ? internal ? last
• Edge (N-1 name, N-2 name, Relationship type,
• Relationship characteristics)
• Relationship type control
• Relationship characteristics Characteristic
• Relationship characteristics,
  Characteristic
• Characteristic value t f Ø

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5.8 The Control Flow Graph for the Previous
Program Example

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5.9 A Possible Representation of the Control Flow
Graph of 5.8
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5.10 An example of a Program Unit Metric

• McCabe's cyclomatic complexity measure
• The definition in the literature For a program
  unit with flowgraph F, the cyclomatic number is
  calculated as v(F) e n 2, where F has
  e edges and n nodes.
• In terms of the generalised model McCabe's
  cyclomatic complexity of a program unit is
  calculated by the formula e n 2, where
  e is the number of edges with the value control
  of the attribute Relationship type, and n is the
  number of nodes with the value s-statement of the
  attribute Program component type of the
  generalised program unit model.

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6.1 A Generalised Model Specification for a
Program

• Graph models used in the software assessment
  practice cover different structural properties of
  structured programs.
• All the models represent the same object, a
  program, and consider the program as a
  combination of all its components and a set of
  relationships among them.
• The specification of the generalised model covers
  all structural properties of a structured program
  and takes into account needs of the software
  assessment practice.

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6.2 A Generalised Model of a Traditional Program

• The Generalised Graph Model of a structured
  program is a directed multigraph G (N, E)
  consisting of a set of nodes N and a set of edges
  E.
• Any node n ? N corresponds to a program unit, a
  non-local variable or a file.
• Any node has the name of a corresponding program
  unit, a non-local variable or a file.
• Any edge e ? E reflects a relationship between
  two program units by control or by a parameter or
  using a non-local variable or a file by a program
  unit.

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6.3 A Generalised Model of a Traditional
Program A Node

• Node (Node name,
• Program component type,
• Component attributes).
• Program component type p-unit ? n-variable ?
  file
• Component attributes Reusability ?
  Structuredness
• Reusability new ? reusable
• Structuredness simple ? complex

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6.4. A Generalised Model of a Traditional
Program An Edge

• Edge (N-1 name, N-2 name,
• Relationship type, Relationship
  characteristics)
• Relationship type control ? data
• Relationship characteristics Number of
  relationships
• (Number of relationships, Dependence of N-2
  from N-1)
• Number of relationships integer
• Dependence of N-2 from N-1
• (Data role, Parameter structuredness)
• Data role controlling processed
• Parameter structuredness simple Structural
• Structural set of values

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6.5 An Example of a Generalised Model of a
Traditional Program
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6.6 An Example of Widely Used Program Models

• Call graph
• Node Node (Node name, Program component type,
• Component attributes)
• Component attributes Reusability
• Reusability new ? reusable
• Edge (N-1 name, N-2 name,
• Relationship type, Relationship
  characteristics)
• Program component type p-unit
• Relationship type control

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6.7 An Example of the Program Call Graphs
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6.8 A Possible Representation of the Call Graph
of 6.7
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6.9 An Example of Program Metrics

• Call depth. In the literature "the length of the
  longest path from the root node to a leaf node".
• In terms of the model the length of the longest
  control flow path in the generalised graph model
  of a program. These conditions have to be met for
  control paths
• All nodes Ni of each path have the value p-unit
  of the attribute Program component type
• The first node of any path N1 has no incoming
  edge with the value control of its attribute
  Relationship type
• Any edge of the path has the value control of its
  attribute Relationship type, and it is not a loop
  (N-2 name ? N-1 name)
• The last node of any path has no outgoing edge
  with the value control of its attribute
  Relationship type except a loop (i.e., it may
  have that edge with N-2 name N-1 name).

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7.1 Models for Object-Oriented Programs
Generalised Structural Model of Object-Oriented
Programs
Generalised Model of Class Inheritance
Generalised Model of Class Interaction
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7.2 The Basic Generalised Model

• The Generalised Graph Model of an object-oriented
  program (OO-GGM) is a directed multigraph G (N,
  E) consisting of a set of nodes N and a set of
  edges E.
• Any node n ? N corresponds to a class
• Any directed edge e ? E reflects a relationship
  between two classes by information or control
• OO-GGM (Node, Edge).

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7.3 The Basic Generalised Model

• Node (Node name,
• Program component type,
• Program component
  attributes)
• Edge (N-1 name,
• N-2 name,
• Relationship type,
• Relationship characteristics)

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8.1 A Generalised Model for Class Inheritance

• A Generalised Class Inheritance Model is a
  directed multigraph G (N, E) consisting of a
  set of nodes N and a set of edges E.
• Any node n ? N corresponds to a class.
• Any edge e ? E reflects a relationship between
  two classes by inheritance (a relationship
  between superclass attributes and subclass ones,
  superclass methods and subclass ones).

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8.2 A Node of the Generalised Model for Class
Inheritance

• Node (Node name,
• Program component type,
• Program component attributes)
• Program component type class
• Program component attributes
• (Node type, Node location,
• List of fields, List of
  methods)
• Node type abstract specific
• Node location root intermediate end
• List of fields Field List of fields, Field

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8.3 A Node of the Generalised Model for Class
Inheritance

• Field (Field name, Membership, Access type)
• Membership class instance
• Access type public private protected
• List of methods Method List of methods,
  Method
• Method (Method name, Method type,
• Access type, Membership,
  Complexity)
• Method type procedure function
• Complexity integer

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8.4 An Edge of the Generalised Model for Class
Inheritance

• Edge (N-1 name,
• N-2 name,
• Relationship type,
• Relationship characteristics)
• Relationship type inheritance
• Relationship characteristics
• Dependence of Node N2 from
  Node N1

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8.5 An Edge of the Generalised Model for Class
Inheritance

• Dependence of Node N2 from Node N1
• (Dependence specification,
• Extent of inheritance)
• Dependence specification
• (Component name from N1,
• Component name from N2)
• Extent of inheritance field inheritance
• method inheritance
• field redefinition
• method redefinition
• method implementation

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8.6 An Example of the Generalised Inheritance
Model

•   .

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8.7 Metrics defined on this Generalised
Inheritance Model

• The characteristics of the generalised
  inheritance model can be used to define software
  quality metrics
• The graph width (the width of the inheritance
  hierarchy)
• The maximum path length in the graph (the maximum
  inheritance hierarchy level (depth))
• The average path length from roots to end nodes
  (leaves)
• Presence of nodes with more than one incoming
  edge (i.e., presence of the multiple
  inheritance)
• ...

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8.8 Inheritance Hierarchy Model

• Node (Node name,
• Program component type,
• Program component attributes)
• Program component type class
• Program component attributes
• (Node type, Node location,
• List of fields, List of
  methods)
• Node location root intermediate end
• Values of the node attributes Node type, List of
  fields, List of methods are not considered here.

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8.9 An Example of Inheritance Hierarchy Model

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8.10 A Possible Representation of the Model of 8.9
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8.11 An Example of Metrics defined on the
Inheritance Model

• Depth of inheritance tree of a class (DIT)

• A definition in the literature Depth of
  inheritance tree of a class (DIT) is length of
  maximal path from the node to the root of the
  tree.

• In terms of the generalised model DIT of the
  class C is the length of the path from the node
  with the values root of the attribute Node
  location to the node with the value C of the
  attribute Node name .

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9.1 A Generalised Component Interaction Model

• Methods are actually parts of classes (not of
  objects), it is usual to develop model that,
  first, include classes and then their methods.
• There are not generally accepted names for these
  models. Those static models consider interactions
  of objects of different classes and/or of the
  same class.
• A method of a class can send messages to other
  methods of different classes or to itself (i.e.,
  can invoke the methods) besides it can access
  fields (variables) of objects of its own or
  different classes or fields of the classes
  themselves.

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9.2 Specification of the Generalised Component
Interaction Model

• The Generalised Component Interaction Model of an
  object-oriented program is a directed multigraph
  G (N, E) consisting of a set of nodes N and a
  set of edges E.

• Any node n ? N corresponds to a class.

• Any edge e ? E reflects a relationship between
  two classes by interaction.

• Two types of relationships between classes
  messaging between a method of a classsender and
  a method of a classreceiver and accessing by a
  method of a class-sender (a client) to a field of
  an object of a class-receiver or a field of a
  class-receiver itself.

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9.3 A Node of the Component Interaction Model

• Node (Node name,
• Program component type,
• Program component attributes)
• Program component type class
• Program component attributes
• (Node type, Reuse,
• List of fields, List of
  methods)
• Node type abstract specific
• Reuse new library

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9.4 A Node of the Component Interaction Model

• List of fields Field List of fields, Field
• List of methods Method List of methods,
  Method
• Field (Field name, Structuredness)
• Field name identifier
• Structuredness simple Structured
• Structured set of values
• Method (Method name,
• Method parameter list length)
• Method parameter list length integer

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9.5 An Edge of the Component Interaction Model

• Edge (N-1 name,
• N-2 name,
• Relationship type,
• Relationship characteristics)
• Relationship type
• transfer of control data
  transfer
• Relationship characteristics
• The number of relationships
• Dependence of N-2 from N-1

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9.6 An Edge of the Component Interaction Model

• The number of relationships integer
• Dependence of N-2 from N-1
• Node relationship elaboration
• Node relationship elaboration
• (N-1 component name,
• N-2 component name)

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9.7 An Example of the Model of Interaction of two
Classes
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9.8 Metrics defined on this Generalised
Interaction Model

• The characteristics of the Generalised
  Interaction Model can be used to define software
  quality metrics, for example

• The number of node couples connected at least by
  an edge
• The number of nodes with at least one incoming
  edge that goes out from a particular node
  (interpreted as the number of program classes
  accessed (used) by a particular class)
• The number of nodes with at least one outgoing
  edge that comes in a particular node (interpreted
  as the number of program classes accessing
  (using) a particular class)

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9.9 The Model of Collaborating Classes

• Node (Node name,
• Program component type,
• Program component attributes)
• Program component type class
• Program component attributes
• (Node type, Reuse,
• List of fields, List of
  methods)
• Values of the node attributes Node type, List of
  fields, List of methods are not considered here.
• Edge (N-1 name, N-2 name,
• Relationship type, Relationship
  characteristics)
• Values of the node attributes Relationship type
  and Relationship characteristics are not
  considered here.

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9.10 An Example of the Model of Collaborating
Classes
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9.11 A Possible Representation of the Model of
9.10
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9.12 An Example of the Model of Message Passing
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9.12 A Possible Representation of the Model of
9.11
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9.13 An Example of Metrics defined on the
Interaction Model

• Fan-out of a class

• A definition in the literature Fan-out is the
  number of other collaborating classes
  irrespective of the number of references.

• In terms of the generalised model The fan-out of
  the class C is the number of nodes in the program
  generalised component interaction model with
  incoming edges having the following properties
• (1) the value of the N-2 name attribute is C
  and
• (2) the value of the Relationship type
  attribute is transfer of control .

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10.1 Conclusions

• A generalised graph model of a program written in
  a traditional algorithmic or object-oriented
  programming language is presented. This model
  covers all informational and control
  relationships between program elements and
  components.
• As a matter of fact, there are four generalised
  models a model for a program unit,
  a model for a
  structured program,
  a model for class inheritance, and
  a model for class
  interaction.

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10.1 Conclusions
Generalised Structural Program Model
Generalised Structural Model of Structured
Programs
Generalised Structural Model of Object-Oriented
Programs
Generalised Graph Model of a Program Unit
Generalised Graph Model of a Structured Program
Generalised Graph Model of Inheritance
Generalised Graph Model of Class Interaction
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10.3 Conclusions

• For any particular program, these models may be
  generated by texts of compilation units of the
  program.
• A model comprises two tables, the table of nodes
  and the table of edges, with all attribute values
  that could be used for structure metric value
  calculation.

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10.4 Conclusions

• Node
• Edge

__ __ (_, _, ((_,_,_), ), ((_,_,_,_,_), )))
__ __ __ (_,_)
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10.5 Conclusions

• Any function of metric value calculation is a
  function of extraction of attribute values from
  the tables of nodes and edges and then making
  simple calculations on these sets of values.

Program Measuring Model (PMM)
Models (N E)
Metric values
Metric Evaluator
Model Constructor
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11 Future Work

• No future work!
• All structural models of structured and
  object-oriented programs have been covered in
  this research!

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13 Publications

• Cogan B.I., Shalveeva E.A. Generalised structural
  models of structured programs to define quality
  metrics Research Report 35-2002. IACP FEB RAN,
  2002 (in Russian)
• Cogan B.I., Shalfeeva E.A. A generalised
  structural model of structured programs for
  software metrics definition, Proceedings of SQM
  2002, pp 203-218, Limerick, 2002
• Cogan B.I., Shalfeeva E.A. (2002). A generalised
  structural model of structured programs for
  software metrics definition. Software Quality
  Journal, 10, 147-165
• Cogan B.I., Shalfeeva E.A. A generalised
  structural model of object-oriented programs for
  software metrics definition Research Report
  1-2003. IACP FEB RAN, 2003 (in Russian)
• Cogan B.I., Shalfeeva E.A. A generalised
  structural model of object-oriented programs for
  software metrics definition, Proceedings of SQM
  2004, pp 299-316, Canterbury, 2004  

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