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Multi-Perspective Comparison of Business Process
Variants Based on Event Logs
Hoang Nguyen1, Marlon Dumas2, Marcello La Rosa3, and Arthur H.M. ter Hofstede1
1Queensland University of Technology
huanghuy.nguyen@hdr.qut.edu.au, a.terhofstede@qut.edu.au
2University of Tartu
marlon.dumas@ut.ee
3University of Melbourne
marcello.larosa@unimelb.edu.au
Abstract. A process variant represents a collection of cases with certain shared
characteristics, e.g. cases that exhibit certain levels of performance. The com-
parison of business process variants based on event logs is a recurrent operation
in the field of process mining. Existing approaches focus on comparing variants
based on directly-follows relations such as “a task directly follows another one”
or a “resource directly hands-offto another resource”. This paper presents a more
general approach to log-based process variant comparison based on so-called per-
spective graphs. A perspective graph is a graph-based abstraction of an event log
where a node represents any entity referred to in the log (e.g. task, resource, lo-
cation) and an arc represents a relation between these entities within or across
cases (e.g. directly-follows, co-occurs, hands-offto, works-together with). Sta-
tistically significant differences between two perspective graphs are captured in
a so-called differential perspective graph, which allows us to compare two logs
from any perspective. The paper illustrates the approach and compares it to an
existing baseline using real-life event logs.
Keywords: Process mining, variant analysis, comparison, multi-perspective.
1 Introduction
The performance of a business process may vary over time, geographically, or across
business units, products, or customer types. And even within a given time period, place,
business unit, product, and customer type, there are usually performance variations be-
tween cases of a process. Some cases lead to a positive outcome (e.g. on-time com-
pletion), while others lead to negative outcomes. A typical question that arises in this
setting is: “What differentiates the positive and the negative cases?”, or more broadly:
“What (statistically) significant differences exist between two variants of a process?”
Recently, several approaches for comparing variants of a process based on their
event logs have been proposed [1–4]. Given two event logs L1 and L2 corresponding to
two variants of a business process, these techniques allow us to identify characteristics
that are commonly found in the cases in L1, but are rare or non-existent in L2 and vice-
versa. These approaches are restricted to identifying differences in the directly-follows
relations, such as “task A always directly follows task B in one variant but never in the
other” or “resource X often hands-offwork to resource Y in one variant but rarely in
the other”. However, events in a log may carry a richer set of attributes besides tasks
and resources – e.g. customer attributes, location attributes, product-related attributes,
etc. Differences between two event logs may be found along any of these attributes.
This paper presents an approach for comparing process variants from multiple per-
spectives corresponding to arbitrary sets of attributes. Specifically, the paper introduces
a graph-based abstraction of an event log, namely a perspective graph, where a node
represents any entity referenced in an attribute of the event log (task, resource, location,
etc.) and an arc represents an arbitrary relation between entities (e.g. directly-follows,
2 H. Nguyen et al.
co-occurs, hands-offto, works-together with, etc.) within or across cases. Statistically
significant differences between two perspective graphs are captured in a so-called dif-
ferential perspective graph, which allows a user to visually compare two event logs
from any given perspective using either a graphical or a matrix representation.
The proposed approach has been implemented as a proof-of-concept prototype in
the ProM open-source process mining toolset. The paper illustrates the capabilities pro-
vided by differential perspective graphs using two real-life event logs, and compares
them against an existing state-of-the-art approach for process variant analysis.
The paper is structured as follows. Section 2 discusses existing process variant anal-
ysis approaches. Section 3 presents the proposed approach, while Section 4 discusses its
evaluation. Section 5 summarizes the contributions and outlines future work directions.
2 Related Work
Existing approaches to log-based process variant comparison can be classified into
indicator-based, graph-based, and model-based. Indicator-based approaches extract per-
formance indicators from two input logs and compare these indicators using visualiza-
tion techniques (e.g. bar charts), e.g. risk indicators [5], performance indicators [6], and
resource behavior indicators [7]. These approaches allow one to determine how two
variants perform relative to each other on an aggregate basis or at a task- or resource
level. For example, these techniques allow us to determine which tasks have higher
cycle time in one variant than in the other. However, they do not allow us to identify
behavioral differences and their impact on performance.
Graph-based approaches rely on pairwise differencing of graphs, such as event
structures [2], directly-follows graphs [8], or transition systems [4]. For example, the
approach in [4] abstracts a process as a transition system where each state represents an
equivalence class of trace prefixes, e.g. a state may represent all prefixes that coincide
on their last nevents. Each transition is labeled with an event label or event attribute
value. Transition systems are contrasted and differences are visually highlighted. The
approach in [4] is integrated with a Process Cube approach for log slicing and dicing to
generate sublogs for comparison [9]. Our technique falls into this category. In particular,
the technique in [4] is used as a baseline in our evaluation.
Other related techniques take as input process models and enrich them with per-
formance measures extracted from event logs, such as occurrence frequency or cycle
time [3]. These techniques assume that a process model is available, which captures the
dominant behaviors of the process variants. In contrast, in this paper we assume that
no models are given a priori. Instead, the comparison of variants is conducted on an
exploratory basis, from multiple perspectives, and purely based on event logs.
3 Approach
Given two event logs as input, each representing a variant of the same business process,
our approach mines two perspective graphs, one from each log. Next, it compares the
two graphs and visualizes their statistically significant differences using a differential
graph. In the remainder, we define all ingredients of our approach: event logs, process
abstraction, perspective graphs, and differential graphs.
3.1 Event Logs and Process Abstraction
An event log consists of cases where each case has a number of associated events. Cases
and events can have various attributes. An example log is shown in Table 1. Rows are
events and columns are event attributes. The format of event logs has been standardized
in the eXtensible Event Stream by the IEEE CIS Task Force on Process Mining [10].
Table 1 provides an example of a log schema. Our technique can work with any log
schema.
Multi-Perspective Comparison of Business Process Variants 3
Let Ωbe a universe of values, Ebe a universe of events and Abe a universe of
attribute names, where for each A∈ A,A:E → Ω.
Definition 1 (Event Log) An event log L over a schema S ={A1,A2,...,An} ⊂ A is a
set of events, i.e. a subset of E.
CaseID EventID Timestamp Activity Resource Department Location
c1e101.10 10:00:00 a1r1d1l1
c1e202.10 10:00:00 a2r2d1l1
c1e303.10 10:00:00 a3r3d2l1
c1e404.10 10:00:00 a1r3d2l2
c1e505.10 10:00:00 a2r1d1l2
c2e602.10 10:00:00 a3r1d1l1
c2e704.10 10:00:00 a1r2d1l2
c2e806.10 10:00:00 a3r4d2l2
c2e908.10 10:00:00 a2r2d1l1
Table 1. Event log example
Assume that events in a case occur
sequentially as shown in Table 1. Based
on the event sequence in each case, Fig. 1
shows an example of event clusterings
in each case along the time line accord-
ing to the Department and Location at-
tributes. For example, in Fig. 1a, events
e1and e2share the same department at-
tribute d1, and the next occurring events
e3and e4share the same department
d2. This is followed by event e5which
has occurred with department attribute d1
again. Fig. 1a and Fig. 1b each is seen as
an abstraction of the process in Table 1.
This method of process abstraction is formalized as follows.
87
e1 e2 e5
d1 d1
d1
c1:
c2:
Abstraction (Location)
e3 e4
d2
d2
e6 e7
e1 e2 e3
l1
l1
c1:
c2:
Abstraction (Department)
e4 e5
l2
e6 e7 e8
l2
e8
e9
l1
e9
d1
r1,a1 r2,a2 r3,a3 r3,a1 r1,a2
r1,a3 r2,a1 r4,a3 r2,a2
r1,a1 r2,a2 r3,a3 r3,a1 r1,a2
r1,a3 r2,a1 r4,a3 r2,a2
(a)
87
e1 e2 e5
d1 d1
d1
c1:
c2:
Abstraction (Location)
e3 e4
d2
d2
e6 e7
e1 e2 e3
l1
l1
c1:
c2:
Abstraction (Department)
e4 e5
l2
e6 e7 e8
l2
e8
e9
l1
e9
d1
r1,a1 r2,a2 r3,a3 r3,a1 r1,a2
r1,a3 r2,a1 r4,a3 r2,a2
r1,a1 r2,a2 r3,a3 r3,a1 r1,a2
r1,a3 r2,a1 r4,a3 r2,a2
(b)
Fig. 1. Abstraction by (a) Department,
(b) Location
Let Lbe a log over schema S,CaseID the
CaseID attribute of events, timestamp the times-
tamp attribute of events, CIDLthe set of CaseIDs
in L, and T⊆Sa schema with T6=∅and
timestamp /∈T. We assume that all timestamps
are different.
First, we define a number of relations between
events as the basis for our later formalisation.
Events can be related in terms of timestamp,Ca-
seID, and other attributes. Given two events, first
they can be ordered based on their timestamps,
i.e. e1<e2ifftimestamp(e1)<timestamp(e2).
Second, they are case-related if they occur in
the same case, i.e. e1
.
=e2iffCaseID(e1)=
CaseID(e2). Finally, in terms of a schema T⊆S,
they are T-equal if they share values for all at-
tributes in T, i.e. e1=Te2iff∀t∈T[t(e1)=
t(e2)]; otherwise, they are T-unequal, i.e. e16=Te2.
Based on the above relations, two events are case-ordered iffthey are ordered and
case-related, i.e. e1le2iffe1<e2∧e1
.
=e2. Further, two events are T-case-ordered
iffthey are case-ordered and T-unequal or case-ordered,T-equal but separated in time
from each other by another case-related but T-unequal event, i.e. e1lTe2iff(e1le2∧
e16=Te2)∨(e1le2∧e1=Te2∧ ∃e3∈L[e1le3∧e3le2∧e36=Te1]).
The T-case-ordered relation lTcan be observed in Table 1. In case c1, in terms of
schema T={Department}, events e1and e3are T-case-ordered because they are ordered
and T-unequal; events e1and e5are also T-case-ordered because they are ordered, T-
equal and there is an event, e.g. e3, that occurs between them in the same case but is
T-unequal to them. The T-case-ordered relation lTforms a strict partial order over E
for each CaseID. This can be sketched briefly. T-case-ordered is an irreflexive relation
because elTeimplies elehence timestamp(e)<timestamp(e) which is not possible.
From the definition of T-case-ordered, it can be proved that T-case-ordered is a transitive
relation by case distinction with four cases.
Given two case-related events and a schema T, if there exists no T-case-ordered
relation between the two events, it means that they are T-equal and non-separable in
time from each other by another case-related T-unequal event. In this situation, we say
that they are T-equivalent, i.e. e1∼Te2iffe1
.
=e2∧ ¬(e1lTe2)∧ ¬(e2lTe1).
4 H. Nguyen et al.
The T-equivalent relation ∼Ton the event set Ec={e∈L|CaseID(e)=c}of a
caseid cforms an equivalence relation, where the corresponding quotient set of Ecis
Ec\∼T. Two T-equivalent events are in the same equivalence class of Ec\∼T. We refer to
an equivalence class in Ec\∼Tas a fragment. Visually, a fragment is a row of events as
shown in Fig. 1, e.g. in Fig. 1a, {e1,e2}is a fragment in case c1.
Based on the notion of fragments, we now define process abstraction.
Definition 2 (Process Abstraction) Let L be a log, T ⊂S a schema, and CIDLthe set
of CaseIDs in L. An abstraction over T from L is defined as AL
T=S
c∈CIDL
Ec\∼T.
Let AL
Tbe an abstraction over schema Tfrom log L. From the definition, AL
Tis a
set of fragments where each fragment is a set of T-equivalent events. There is a follows
relation between fragments F1,F2∈ AL
T, i.e. F1F2iff∃e1∈F1∃e2∈F2[e1lTe2],
and a directly-follows relation between fragments F1,F2∈ AL
T, i.e. F1→F2iffF1
F2∧@F3∈ AL
T[F1F3∧F3F2].
3.2 Perspective Graphs
From a process abstraction as shown in Fig. 1, one can look at different relations be-
tween event attributes. For example, one can look at the co-occurrence of two attributes
in the same fragment, e.g. two resources working in the same department or location.
Alternatively, one can look at an inter-fragment relation where an attribute occurs in one
fragment and the other attribute occurs in a directly following fragment, e.g. the flow
from an activity performed in one department to another activity performed in the next
department. More generally, instead of focusing on one attribute, one may focus on a
number of attributes depending on the type of analysis, e.g. it may be a pair (resource,
activity) representing a task assignment.
In order to represent different types of relation between event attributes, we propose
two types of graphs, intra-fragment and inter-fragment, defined as follows.
Let AL
Tbe an abstraction over schema Tfrom log L. Let V⊆S, then πV(e) denotes
a projection on event eof attributes in Vwhich is defined as {(v,v(e)) |v∈V}1.
Definition 3 (Intra-Fragment Graph) Let AL
Tbe an abstraction over schema T from
log L and let U,V⊆S . An Intra-Fragment Graph IAGU,V
T(L)is a node and arc weighted
undirected graph G =(N,E,WN,WE), defined by:
–N={πU(e)|e∈L}∪{πV(e)|e∈L},
–E={{πU(e), πV(e0)} | e∈L∧e0∈L∧e∼Te0∧πU(e)6=πV(e0)},
–WN(n)=|{e∈L|πU(e)=n∨πV(e)=n}| for all n ∈N,
–WE({n1,n2})=|{e∈L|πU(e)=n1∧πV(e)=n2}| +|{{e1,e2} | e1∈L∧e2∈
L∧πU(e1)=n1∧πV(e2)=n2∧e1∼Te2∧e16=e2}| for all {n1,n2} ∈ E.
Intra-Fragment Graphs represent a co-occurrence relation between event attributes
as they co-occur in the same fragment. For example, it can be a task assignment relation
when a resource and an activity co-occur in an event, or a co-location relation when two
resources co-occur in the same location.
Let AL
Tbe an abstraction over schema Tfrom log L. Let φ, ϕ:AL
T→ E such that
for all F∈ AL
T,φ(F)∈ E and ϕ(F)∈ E.φand ϕare two choice functions on AL
T, i.e.
choice functions can be used to extract events with certain properties from fragments.
We will not specify their semantics. Just as an example, φcould be chosen such that
it returns the latest event in a fragment, and ϕcould be chosen such that it returns the
earliest event in a fragment.
Given two choice functions φand ϕ, two events are in an inter-fragment directly-
follows relation, denoted e1→Te2, iff∃F1,F2∈ AL
T|F1→F2∧e1=φ(F1)∧
e2=ϕ(F2). The set of all inter-fragment directly-follows event pairs in log Lis
E→T={(e1,e2)∈ E × E | e1→Te2}.
1(v,v(e)) is abbreviated to v(e) when it is clear from the context for the purpose of readability
Multi-Perspective Comparison of Business Process Variants 5
Definition 4 (Inter-Fragment Graph) Let AL
Tbe an abstraction over schema T from
log L and let U,V⊆S . An Inter-Fragment Graph IEGU,V
T(L)is a node and arc weighted
directed graph G =(N,E,WN,WE), defined by:
–N={πU(e)|e0∈ E ∧ (e,e0)∈ E→T}∪{πV(e0)|e∈ E ∧ (e,e0)∈ E→T},
–E={(πU(e), πV(e0)) |(e,e0)∈ E→T},
–WN(n)=|{(e,e0)∈ E→T|πU(e)=n}| +|{(e,e0)∈ E→T|πV(e0)=n}|, for all n ∈N,
–Let (n1,n2)∈E and En1,n2
→Tbe the set of all inter-fragment directly-follows event
pairs corresponding to (n1,n2), i.e. En1,n2
→T={(e1,e2)∈ E→T|πU(e1)=n1∧πV(e2)=
n2}.
WE((n1,n2)) =
|En1,n2
→T|if frequency −based
P(e1,e2)∈En1,n2
→Ttimestamp(e2)−timestamp(e1)
|En1,n2
→T|if time −based .
Inter-Fragment Graphs represent a flow relation between event attributes. For ex-
ample, it can be a hand-over from a resource in one department to another resource in
a directly following department, or a flow from an activity executed in one location to
another activity executed in a directly following location.
3.3 Comparing Perspective Graphs and Visualizing Differences
In comparing two perspective graphs, common nodes and edges on the two graphs are
compared in terms of their weights. Note that the weights defined in Section 3.2 are
computed for the whole log. Instead of comparing graphs based on these weights, this
paper looks for statistically significant differences by comparing sample populations of
weights obtained from log observations.
Different techniques can be used to make observations of logs. Case-wise observa-
tions are made on cases in the log, i.e. weights of nodes and edges are computed from
events in each case. Differences determined by the tests can be understood as differences
between the two variants synthesized from all cases. Time-wise observation allows one
to see differences between logs over time. This technique uses a sliding time window
starting from the earliest event in each log. Observations are made on each window, i.e.
weights of nodes and edges are computed from events occurring within each window.
17
0 0.6 0.7 0.8
-0.6 -0.7 -0.8 1
-1
P(XA < XB) P(XA > XB) Common nodes/edges with differences
Common nodes/edges with no differences
Only occur in variant A Only occur in variant B
Uncommon nodes/edges
Fig. 2. Color scheme
The result of graph comparison
is a differential graph containing
common nodes and edges and also
uncommon nodes and edges that
appear in one graph only. If nodes
and edges are common with a sta-
tistically significant difference, their
weight is the effect size of the differ-
ence. This paper chooses common language effect size [11] due to its interpret-ability.
For example, an effect size of 80% indicates that given any random observations of the
two variants, variant A has 80% chance of having a higher mean weight than variant B.
If nodes or edges are common without a statistically significant difference, their weight
is simply zero. Lastly, if they are uncommon, their weight is the relative weight among
all uncommon nodes or edges in the graph. Differential graphs are visualised in the
form of matrices (nodes are row and column headers while edges are cells). Matrices
can be symmetric (for undirected graphs) as shown in Fig. 5 or asymmetric (for directed
graphs) as shown in Fig. 4. Nodes and edges are color coded based on their weight and
the color scheme shown in Fig. 2.
4 Evaluation
We implemented our approach as a ProM plugin named Multi-Perspective Process
Comparator (MPC).2The plugin allows one to import two event logs in MXML or
2Executable and source code are available from http://apromore.org/platform/tools
6 H. Nguyen et al.
XES format as input, mine different perspective graphs and compare them to identify
statistically significant differences. Using this implementation, we evaluated our ap-
proach on two real-life datasets and compared the results with the ProcessComparator
(or PC) plugin in ProM [4].
We looked at the public real-life event logs available in the 4TU Data Center3and
selected two representative datasets, namely BPIC13 and BPIC15. These two datasets
come with business questions that entail variants comparison, which have been posed by
the process stakeholders of these datasets, as part of public contests on process mining.
Due to space limits, we only report the result of our technique on the BPIC13 log
focusing on aspects our technique can improve over the baseline. Detailed evaluation is
documented in a technical report [12].
BPIC134records cases of an IT incident handling process at Volvo Belgium. An
IT ticket is raised for each incident to be investigated by various IT support teams.
Teams are organized into technology-wide functions (org:role attribute), organization
lines (organization involved attribute), and countries (resource country attribute). For
our evaluation, we selected the following question from the description accompanying
this dataset: “Where do the two IT organisations (A2 and C) differ?” where A2 and C
are the main organization lines responsible for most of the IT tickets.
For each dataset and business question above, we compared process variants using
three sub-questions. With reference to Fig. 1, these questions are focused on two levels
of granularity, event and fragment, and time-wise differences.
Q1. What are the differences at the event level?
At the event level, we can look into either inter-event or intra-event relations where
each event is a fragment. Regarding the former, both PC and MPC can provide the same
insight. Specifically in the case of MPC, we can use the event ID attribute to create a
process abstraction, then create an inter-fragment graph using the pair of event name
and status attributes as nodes.
29
Fig. 3. Resource Country and Activity Status
However, regarding the
intra-event relations, PC cannot
provide a solution while MPC
can investigate these relations
through intra-fragment graphs.
For example, on the event-based
abstraction, we can use the coun-
try attribute as a node and the
activity status attribute as another
node. The matrix in Fig. 3 reveals
that the teams in Brazil, India
and the USA in the organization
C choose the “Wait User” sta-
tus for IT tickets more frequently than in the organization A2. This is an operational
concern since IT staffcan choose this status as an excuse to delay incident investigation.
Q2. What are the differences at the fragment level?
In the BPIC13 dataset, we can create fragments using the country attribute to look into
how process activities are related between IT teams from different countries. In this as-
pect, PC aggregates the activity flow between fragments. For example, PC shows a flow
from [Sweden] to [Poland] through the Accepted activity meaning that this activity is
performed by Sweden and then work is transferred to Poland. It may however consist of
two possible flows: either Accepted by Sweden followed by activity Queued performed
by Poland, or Accepted by Sweden followed by Completed performed by Poland.
3https://data.4tu.nl/repository/collection:event_logs_real
4doi:10.4121/uuid:500573e6-accc- 4b0c-9576-aa5468b10cee
Multi-Perspective Comparison of Business Process Variants 7
25
BPIC13, Inter-Fragment, EventName + Status
Node1 = status + country + event name
Node2 = status + country + event name
Fig. 4. Impact, Country, and Event Name
Similarly to PC, MPC can
look into the same flow by first
using the country attribute to
create the process abstraction,
then choosing the pair of coun-
try and event name attributes as
node and the country attribute as
another node to create an inter-
fragment graph. However, be-
yond that, MPC can elaborate
the activity flow between coun-
tries by using other event at-
tributes. Fig. 4 shows an ex-
ample where we chose impact,
country and event name to repre-
sent a node. From this figure, we
can see that the process activ-
ity flow from Sweden to Poland
through the “Accepted” activity
is actually the control flow from
“Medium Sweden Accepted” to “Medium Poland Accepted” (i.e. from “Accepted” to
“Accepted” activities for medium impact cases only).
26
BPIC13, Intra-Fragment, Impact, Impact + Status
Fig. 5. Medium Impact and Activity Status
Further, MPC can look into the dif-
ferences between A2 and C within each
fragment through intra-fragment graphs,
while this is not possible with PC. For ex-
ample, we use the impact attribute to create
a process abstraction, and the pair of impact
and activity status attributes as the node. The
result is shown in Fig. 5 for medium impact
incidents. Remarkably, we can see that for
medium-impact incidents, most of activity
statuses in A2 have approximately 60-70%
chance of occurring more frequently than
in C. There are no significant differences
between the two organization lines in high-
impact incidents.
Q3. What are the time-wise differences as compared to case-wise differences?
So far, the evaluation only finds case-wise differences, i.e. differences synthesized from
cases in A2 and C. Time-wise observations, however, are not available in PC.
27
BPIC13, Inter-Fragment, Impact, Impact + Status
Fig. 6. Event Name and Activity Status
For MPC, we use time-wise observations
with a sliding window set to three days as
most of events in a case occur within a day.
We use the event ID to create a process ab-
straction, and the pair of event name and ac-
tivity status as node. In this case, the node
(edge) weight captures their relative occur-
rence frequency in each window. The result is
shown in Fig. 6. We can see that there are two
remarkable differences between A2 and C
over time in the node “Accepted Wait-User”
and the edge “Accepted In Progress” →“Ac-
cepted Wait-User”. The difference magnitude
is approximately 56%, i.e. there is a 56% probability that “Accepted Wait-User” in A2
has lower frequency than in C. In MPC, clicking on the edge “Accepted In Progress”
8 H. Nguyen et al.
→“Accepted Wait-User” views detailed time series which shows that this difference
mostly occurred between 21 Jan and 10 Mar 2012.
5 Conclusion
This paper contributes the notions of perspective graph and differential graph. A per-
spective graph is an abstraction of an event log in which nodes represent entities refer-
enced by an event attribute or combination of attributes, and links refer to co-occurrence
or directly-follows relations. Perspective graphs generalize directly-follows graphs and
hand-offgraphs, commonly supported by process mining tools. Differential perspective
graphs allow us to compare two event logs (abstracted via perspective graphs) and to
identify their statistically significant differences.
The example-based evaluation of differential perspective graphs on real-life logs
shows that we can identify differences that are beyond the scope of the existing Pro-
cessComparator approach, and that the matrix-based representation of differential per-
spective graphs provides a more compact representation for displaying such differences,
compared to node-link (graphical) representations used in process mining tools.
While the examples highlighted the possible advantages of the proposed approach,
these need to be confirmed via a usability evaluation with end users, which is left as
future work. Another future work avenue is to extend the approach in order to identify
differences between variants that can be causally related to performance, e.g. structural
or behavioral differences that can explain differences in cycle time between variants.
Acknowledgements. This research is partly funded by the Australian Research Council
(DP150103356) and the Estonian Research Council (grant IUT20-55).
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