A control system project development model derived from System Dynamics

International Journal of Project Management 29 (2011) 696 – 705 www.elsevier.com/locate/ijproman

A control system project development model derived from System Dynamics A.S. White ⁎ School of Engineering and Information Sciences, Middlesex University, The Burroughs, Hendon, London NW4 4BT, United Kingdom Received 30 March 2010; received in revised form 18 June 2010; accepted 27 July 2010

Abstract This paper examines established Systems Dynamics (SD) models of projects in order to simplify them. These models are highly non-linear and contain large numbers of variables, with built in decisions using empirical data. A SIMULINK version of an SD model was created and conclusions are made with respect to the main controlling factors, compared to a NASA project. Stages in simplification are described leading to a control system model. This model is then used to develop criteria to judge stability, controllability and observability of projects with use for practical decisions by project managers. All the models and the NASA data are compared to allow the reader to judge the efficacy of the simulation. The developed model is then compared with another project solution. © 2010 Elsevier Ltd. and IPMA. All rights reserved. Keywords: Project development; Reduced model; Minimal project model; System dynamics; Control system analysis

1. Introduction Newspapers in the UK are continually reporting project failures from construction to military projects to IT. Software projects in particular have a poor success rate for reliability, meeting due dates and completing to budget (Smith, 2002; Yeo, 2002; RAE, 2004; Ahsan and Gunawan, 2010). Successful project management (Abdel-Hamid and Madnick, 1989) is related to technical production processes, time scheduling in a dynamic environment, individual differences in project managers, members and team processes. Capers Jones (1996) has estimated that such IT projects only have a success rate of 65%. The cost of such disasters such as the UK National Air Traffic System, UK Health Service IT systems and the London Ambulance Service computerisation is high in both human terms and money. Projects may be considered as a system in which demands are made (the requirements) and an internal project organisa-

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tion, which is controlled to produce the software goals, while being disturbed by the external environment. Significant progress has been made in the use of System Dynamics methods to describe the operation of software and other projects (Rodrigues and Bowers, 1996a,b). Lin and Levary (1989) describe computer aided software design using System Dynamics, expert systems and a Knowledge based management system used in the design of a space station. More recently Häberlein (2004) has discussed the common structures involved in SD models. Rodrigues and Bowers (1996a,b) have established the role of System Dynamics in project management and Madachy (2007) has recently produced a benchmark book explaining and detailing the used of SD methods in software projects. The models of operation of the software development process were described by the successful System Dynamics (SD) models of Abdel-Hamid and Madnick (TAH) (1991), which set up equations relating levels(states) such as the number of reworked errors and relates them to rates such as the error detection rate or the rework rate. The TAH model was validated against NASA data for a satellite project and the agreement is very good. The SD model structure is highly non-linear with a number of theoretical assumptions, for example about how the errors in the coding are

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A.S. White / International Journal of Project Management 29 (2011) 696–705

propagated. These structural assumptions do not allow for System Dynamics models to be used to develop any general rules to allow managers to make sound judgements based on good analysis. The comparison with models of inventory processes, which are related, is the rationale for this research programme. SD inventory models developed by Forrester (1961) were non-linear and contained a number of factors, such as employment rate, that made the problem too complex for simple rules to be developed. Disney and Towill at Cardiff (2002) and others devised linear control system models to enable operational rules to be investigated and optimal solutions to be found as well as stability margins to be obtained (White and Censlive, 2006). Simplification of the project development model is being tackled in the USA with control system models of software testing (Cangussu et al., 2002) and in the UK by linearising the SD model (White, 2007a). The whole purpose of this research is to develop simple control system models of the project development process, as in inventory analysis, and obtain rules for stability. This must include all the models of software development including the evolutionary project management methods of Gilb (2005) and iterative methods such as SCRUM and RAD. The advantages of such control analysis is to enable rules to be created for stability, controllability and observability to be used by project managers in the same way they can used scheduling and decision theory. They will also allow greater accuracy in prediction of projects at an early stage in the development process, in particular when to change the workforce for maximum efficiency. In order to succeed the project manager must have a mental model of how the system operates to achieve the system goals. It is also important to realise that no matter how successful we are at controlling the external disturbances, the goal of a successful project cannot be achieved if the internal processes are not stable. This is only possible if a good internal model is available and the best model basis extant is that of AbdelHamid. However to use this model requires a large amount of empirical data, most of which is not available ab initio. The purpose of this paper is to set out an analysis of the system dynamics model from a control engineering point of view illustrating how the initial state of the system is at best neutrally stable. It will show how the reduced system is also unstable. This is a consequence of major variables CUMSD and CRPRG increasing, of necessity, steadily with time.

2. System Dynamics models The model created by Tarek Abdel-Hamid (TAH) consists of four main subsystems (his terminology) (Fig. 1). The main functions set up in the model are an input block supplying information such as the size of the task, the estimate of the size etc. The blocks are Human Resource management, Production, Planning and control subsystems. Each of these has sub-subsystem blocks for example the production sub-system has the Manpower Allocation System (MAS), the Software Development System(SDS), the Software Testing System (STS) and the Quality Assurance System (QAS). Each sub-

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Fig. 1. Software development subsystems (from Abdel-Hamid).

subsystem has individual components with decisions built in as a representation of how management decisions were made.

2.1. Validation of the model Data from a NASA project with 24.4 K DSI was used by Abdel-Hamed with quite good information and a very good degree of agreement. The model has the flexibility to add in overtime at a particular stage of the project to see what effect this has on overall completion date and cost. The SIMULINK implementation of the SD model not gives only good agreement with the original Dynamo model but also agrees with the observed data despite using slightly different implementation of some decisions. This difference in these two sets of data is that the NASA data includes an amount of overtime, not available in detail. The NASA data lies between the simulated values of zero and full overtime. The major dominating eigenvalues depend on the hiring delay, the assimilation delay and the time of employment. This means that the whole trajectory of the project is dominated by the HR policies of the company. Non-linearity is apparent when convoluted decisions are incorporated in the model. This is quite typical of SD models in general. It is therefore difficult to predict stability in these models, even sensitivity simulation is difficult since small changes in parameters produce large variations in output behaviour and the following analysis is a first step in trying to achieve such insights. It is also the case that if the completion time predicted by the SD model is put back in as one of the initial trial values then the new completion time is not the same as originally predicted. This is also true of the other values that are initially guessed such as the size of the software. This is a result we might expect from such a nonlinear model. Although the model is validated using public data available, it is known that several larger projects have been validated using private company data by the System Dynamics software vendors. Although there are internal feedback loops the TAH system is not a closed loop control system since there is no target value to aim for and no error correction.

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Our future research is to compare the model predictions with developments of different software projects. The size of the project is not material in the model to its' operation except that since it is a nonlinear model the times and other results do not scale.

3. Improved reduced model The main disadvantage of using The TAH model is the amount of data incorporated into the model as empirical data and also the data to be inputted as constants to enable a system to be modelled for a particular project. What we were seeking here is a simplified model to enable predictions of to be made at the start of any project without assumptions about detailed performance to be known in advance. Ruiz et al. (2001) used a simplified TAH model but with half the complexity of the original. Initially a simple model (Ventana, 1999) (V5) which has only three states and less than twenty eight equations in the system model was used as the starting point for this work. The simple V5 model, in common use in System Dynamics texts, was chosen since it includes the effect of rework. Limitations of this simple SD model are that it has no effects of employees, no effects of staff hours, no error generation, no control function, no QA policy, no overtime, fatigue or effects of late discovery of extra work. White (2007b) has shown that despite these limitations the agreement with TAH is actually quite good for what is actually predicted.

The final SD model was based on the simple V5 project model but adding features from Richardson and Pugh (1981). This model was altered so that the tables were obtained as closely as possible from the TAH data set. This model has 6 states compared to Ruiz model with 16 and is shown in Fig. 2. Two versions with slightly different interpretation of the tables were included, rs4 and rs5. This model now shows a good match to the TAH data as indicated in Figs. 3–6. The major difference between these versions is the level of satisfactory code developed being raised from 85% to 87.5%. The level of rework now agrees more closely to the TAH plot of tasks discovered (tkdscv). The final scheduled completion date now agrees with the NASA data. The cumulative predictions of Staff days needed are slightly higher but are close at the end of the project. The FTE staff prediction is good until right at the end of the project. This model has no provision for overtime. The main TAH model includes most realistic parameters that affect project handling. The main quibble with it is the data used and the way decisions are mechanised. The final reduced order model, rsm5, was examined to see how well it reproduced the overall model predictions using the NASA data. It is clear that this simple model should only be able to give a general prediction of the main three states that are included. This model was altered one loop at a time until a better fit with the NASA data was obtained. The complexity of the TAH model representation can cause chaotic behaviour, although the causal relationships that are responsible are uncertain. Despite this very simplified description

Fig. 2. Model RS 5.

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Fig. 5. Rework comparison.

the results are impressive. Using the data from the NASA project the responses, where possible, are compared in Figs. 3–6. The comparison of the three model responses for the 400 task Initial Project Development (IPD) shows that the cumulative tasks developed (cmtkdv) are in surprisingly good agreement, certainly up to 250 days into the project. The simple project model disagrees early in the project, when recruitment is an issue but later is in good agreement. As shown in Fig. 5 after 250 days the TAH project model detects and adjusts for the increased workload discovered and goes on to complete more tasks. The tasks in the TAH model are more than in the simple model, not only because the model recognises the new tasks discovered in more detail but also the perceived values are not necessarily in line with true values due to the delays incorporated in the model. Around 250 days the perceived tasks are a peak compared to the simpler cases and this agrees with Fig. 3. The lower task remaining value in rsm5 is due to ideal productivity assumed in this model, which has a lag due to recruitment and this is even greater in the Abdel-Hamid model. At the end of the project the rate of change is nearly identical in all models. This is where no effect is felt from staffing changes. Fig. 4 shows how the number of tasks discovered, (tkdscv & URW), varies for the

three project models. The overall values are not hugely different, although the simple SD model is larger, with the peak values for the simpler models occurring before the middle of the project. The peak value for the TAH model occurs near the middle of the project. The problem of choosing the correct number of tasks at the beginning of the project is the key to making good predictions. In these examples shown in Figs. 3–6 we have an initial project size guess that is 35% less than the number of task eventually found to be needed. The key to getting this close agreement is to use values for error generation and productivity that are realistic. The interesting observation is that the cumulative number of tasks developed is nearly an s-shaped curve and fits a number of real processes observed by Sterman (2000). This would lead to the idea that a number of dominant processes in the project process obey quite simple rules and the complexity of the Abdel-Hamid model may not be necessary for good-enough prediction of project tasks completed. The staffing levels, the number of reworked tasks and other factors not shown here are not as easily predicted. Assuming the TAH model as a benchmark, the results given earlier for simple models do give a reasonable prediction to the cumulative number of tasks developed

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versus time, while not predicting the final number of tasks from an, initial, underestimate. They do not give a wholly accurate picture of the number of reworked tasks and not agreeing in shape the overall peak values. They are not greatly in error. The tasks remaining to be developed follow a similar curve but the values indicated by the Abdel-Hamid model are larger at each time interval and continue for longer. This relates to the error generation prediction mechanism and work rates required. It is the case that the data fixed in the TAH model has been adjusted to give the best fit after the project was completed. The basic structure of project models needs to incorporate the effects of rework but needs to add in the number of tasks to be reworked in the correct sense, unlike the two models shown here. The next feature that needs to be modified includes the generation of errors, which is done in these simple models by a mechanism that is too simple. This does not mean that we have to go to the level of detail in the TAH model as in that case over half of the variables are dummy quantities. Although it useful to have these expressed only a small number of these are essential to the manager's understanding of the management problem. For example there are nine equations that relate productivity in some fashion to similar variables in the TAH model. Feedback in the Abdel-Hamid model is complex, most of the sensory data is not real but perceived. Since it is very difficult to know whether any DSI is actually finished, there is going to be some uncertainty about when particular parts of the whole software are completed. However the feedback/feed forward paths number in the hundreds.

Fig. 7. Use of the simple model to control a real project.

The way these loops individually affect the response has yet to be tested. In effect the project models need to be tuned to give data to the manager that is useful but does not cause such complexity that the model becomes uncontrollable. This feedback that is most needed is what time the project can be deemed complete. This relies on two main pieces of data, one is the number of tasks to be completed and the second is what staff work output is needed to complete these extra tasks. Information such as fatigue does not have to be put into the model in as sophisticated a form as the Abdel-Hamid model. It would suffice to have the ability to input a maximum output or as a minimum.

4. Control System Analysis of the model The purpose of creating a control system model is to allow the panoply of modern control system analysis to be used to gain insight into the character of project development processes. Work by White has shown that the TAH model is initially neutrally stable and is unstable for the rest of the time, in the sense that several variables such as CUMSD are increasing without limit until the project is completed. Real projects do not continue forever. Many of the states in the TAH model are controllable and are controlled, workforce for example. If a control system model (Fig. 7) can be created that predicts the behaviour of the important states of the project, for example CUMSD ( an analogue for cost) , the workforce required and a small number of other important states then this model could be used as an analogue of the operation of estimators in hardware control loops. Many of the states that cannot be observed directly could be made visible by this means. This approach would allow the project manager to see what the result of their actions would give in the way the project was progressing. The control system model was obtained from the model rs5 by examining each loop and eliminating any non-linear components particularly multiplications and divisions common in SD models. These results for example in eliminating the dependence of the workforce estimation on the estimated time remaining, that is an important part in the TAH model. Over twenty different formulations were evaluated in the process, some giving good agreement to several states but poor for others. The best model obtained thus far is shown in Fig. 8. We can describe this model using state-space equations (D'azzo and Houpis, 1988). x ˙ = Ax + Bu y = Cx + Du x = 9*1; A = 9*9; B = 9*1; C = 1*9; D = 0 x are the states; y are the outputs; u are the inputs to the system; A, B, C, D are matrices describing the linear system.

ð1Þ

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Fig. 8. Control system model of project development.

Where 0

0 B0 B B0 B B0 B A=B B0 B0 B B0 B @0 0

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1 0 B 0 C C B B 0 C C B B scdn C C B C B B=B 0 C B 0 C C B B wfn C C B B wfpr C A @ Tr2 wfn

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0 0 0 0 0 a = tdrwm 0 1 = tms 0 0 0 0 0 0 0 0 0 0

1 fsat gprod ð1−fsat Þgprod = tdrwm 0 0 ð1−fsat Þgprod −1 = wfat 0 0

0 0 0 0 0 0 1 = wfat −1 = Tr2 0

1 0 C 0 C C 0 C C 0 C C 0 C C 0 C 1 = wfat C C A 0 1 = tdwfs

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C = ð1

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We can analyse this model using control system techniques. First we obtain the eigenvalues to see if the system is stable. 0

−1 = Tr2 1 = tdwfs 0 0 0 −q   0:5 tdrwm2 b + tdrwm−ðtdrwm4 b2 + 2tdrwm3 b + tdrwm2 −4tdrwm3 aÞ

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ð6Þ

The eigenvalues λ have two positive exponent solutions indicating that this system is unstable. This is necessary for the system is to produce a solution whereby the number of staff days has to increase, in the linear system without limit, while people are employed on the project, but in the non-linear system the limits will act to stop the project when the project tasks are completed. The parameters that have the major contribution to this behaviour are tdrwm and tdwfs. We can ascertain whether any particular mode of the system is controllable or observable by invoking the manipulation of the states of the system to give a modally separated set of states by diagonalising the state matrix A. We can devise (D'azzo and Houpis, 1988) a new set of states by transformation: x = Pz

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Λ is a diagonal matrix of eigenvalues and the states of z are controllable if B′ has no zero rows. The system is observable if CP has no zero columns.

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The matrix P can be obtained using MATLAB from the eigenvectors of the original system. This enables the matrix B′ to be calculated and this gives for the data used in the simulation: 1 1 C B 1 C B B −320000000 C C B C B −48 C B C B B′ = B −12 C B 319999998 C C B C B 1 C B A @ 1 0 0

ð11Þ

As it can be seen the last row is zero and hence the system is uncontrollable. We now need to examine which of these states is uncontrollable. The new modal states are: 1 64CUMSD−30CRPRG + NAS−10WFSa C B 16:32CUMSD−7:65CRPRG + SCD−2:51WFSa C B −3 −3 C B 0:026CUMSD−1:60e CRPRG−ð0:011 + 0:002iÞWF + ð−0:011 + 0:002iÞWFSb−5:70e WFSa C B B 0:1CUMSD + 0:0069CRPRG−1:0e−6 DURW + ð−0:006 + 0:009iÞWF−ð 0:006 + 0:009iÞWFSb + 6:3e−4 WFSa C C B C ð12Þ z=B 0:638CUMSD−0:206CRPRG + DURW + URW + WF + WFSb−6:3e−3 WFSa C B C B 1:25CUMSD−1:83CRPRG−ð0:375 + 0:927iÞWF + ð−0:375 + 0:927iÞWFSb−0:507WFSa C B C B CUMSD + CRPRG + WFSa C B A @ −2WFSa 1:47CUMSD 0

The result from this computation is that the state CUMSD is uncontrollable by itself, except in combination with other states. It is also possible to show that this model is stabilizable (Isidoro, 1996). This means that the divergence of the states can be curtailed by a suitable feedback gain. The last stage of this analysis is to determine whether the system is observable. In this case we determine C′ To find if there are any zero columns. 0

C = ð 83

−39

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This result demonstrates that it is possible to observe all of the states of the reduced control model although two of the states will be phase shifted. The problem of controlling the project cost CUMSD is due primarily to the inability to control the rework that is discovered. None of the models described in this paper has a comprehensive model of the testing process included. This work will be extended to include the Cangussi models of software testing. Nor have any SD models thus far demonstrated a controllable form of requirements capture. So what we have are only models of the overall development process minus the most important and difficult aspects, that of estimating the project size and how much remedial effort is required. However they do compare favourably to the COCOMO type results in the limited work we have done so far. This demonstrates the problem for the software project manager. They cannot at the beginning of the project observe how well the project is proceeding, in fact not before the first cycle of trainees reaches the production team. The fact that the project is therefore uncontrollable in the linear sense should not surprise us because if we cannot observe what is happening it cannot be controlled. It was usually stated that this problem was due to the lack of recognition of how much software had been written, but this problem starts before this and is due solely to the delays in the company in obtaining any information before a certain time delay has occurred. This means that setting the project on the right trajectory is exceptionally important as we have open loop control with no real feedback until the non-linear decisions start to provide the requisite feedback and control. To minimise the delays in reporting should be the prime directive of any project manager, in particular the first set of data is crucial to the onwards trajectory and the first corrections. It is similar to the launch of a vehicle into outer space. If we do not correct the initial direction there will not be enough fuel (staff effort) at the end to pull the project back on target. As can be seen from Figs. 3–6 the reduced order linear model does predict the experimental data quite well and does follow the simulation of the nonlinear model until the lack of progress right at the end of the project becomes so great that the project manager has to pull in extra staff to meet the deadline. The NASA project had a fixed deadline and this is not true of all projects hence there would be better agreement with the simpler models.

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The HR policies that are needed to be implemented to cater for these observations include a more rapid initial recruitment and a speeded up training programme. This will enable the whole project to be put on track more quickly and reduce the time to the first errors being detected and the subsequent rework being identified earlier and hence fixed earlier. This will reduce the overall ‘lost’ time in the project. The major lesson from the Abdel Hamid work is to reduce time constants for detecting all parametric values associated with development from training to error detection, to reacting to staff shortages. After the model was developed using the data from the TAH/NASA evaluation it was evaluated using the example in the TAH book of a 64 K DSI project with different parameters to the NASA project. These results are shown in Figs. 9–12. The agreement for CUMSD between the TAH simulation and the control model is within 12%. The agreement for schedule completion time is very good. While the agreement for Tasks developed and Full time equivalent staff are only moderate, but of a similar order of magnitude. The advantage of the control model is that it is pessimistic about costs and FTE staff. If it is to be used as an estimating tool then this would be beneficial.

5. Use by Project managers The control model described above requires certain information to enable a prediction of the project costs and staffing requirements to be made before starting the project. The initial estimate of the average number of staff required (wfpr) is determined from the estimate of the project size; the estimate of schedule date (scdn) is made using the average actual productivity (gprod) and the size of the project. The other factors that need to be known for an ab initio estimate to be made is the fraction that will be satisfactory (fsat) estimated from previous projects completed by the team or using industry standards and the initial workforce allocated to the project (wfn). The timing factors (tdwfs, tdrwm &wfat) in the model can be adjusted to represent the HR regime of the company and the likely response of the managers. This model will enable a prediction of completion date and overall cost to be made. These estimates will be within 20% of the real values on the basis of the experiments described here. Estimates of full time staff required while not as accurate are in reasonable agreement with the results from the TAH model as are the results of tasks developed. 6. Conclusions The SIMULINK model derived from Abdel-Hamid's Dynamo implemented System Dynamics model gives good agreement with the NASA data for a 24.4 K LOC project. The TAH model was shown by White to be neutrally stable at the origin t = 0, but unobservable and uncontrollable.

The major dominating eigenvalues depend on the hiring delay, the assimilation delay and the time of employment. This means that the whole trajectory of the project is dominated by the HR policies of the company. The reduced SD model gave a good prediction of the responses of cumulative staff days in the cost of the development, full time staff numbers but not as good for scheduled completion date and undiscovered rework, but still quite accurate. It under predicts due to not accounting for extra staff employed at the end of the project. The control system model responses are also quite good but do not estimate the total magnitude of rework and fail to predict exact values at the end of the project where the non-linear properties are used extensively. The thesis is that the control model illustrates the basic behaviour of projects in that they are uncontrollable in the control system sense, but are observable and so can be used as analogues of the required project progress to enable project managers to compare real project progress to that desired and execute the required control actions to achieve real project performance close to that predicted by the control project model. The control model can be used to predict the performance of the project using a minimum of information. Future research should allow a prediction based on the size of project, error rates, and staff levels to be developed in a graphical form for initial estimates of the control model parameters forming a family of models. The model would need to include a few extra states that may be necessary for specific projects.

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Fig. 11. Tasks discovered for example.

References List of symbols a Limit to rework A State matrix for control system b Delay to recognise rework B Control matrix B′ Modified control matrix C Output matrix C′ Modified output matrix CUMSD Cumulative staff days (cost) (state) CRPRG Cumulative real progress rate (state) cmtkdv Cumulative tasks developed (TAH model) DURW Desired rework (state) fsat Fraction satisfactory (measure of QA) gprod Gross average productivity IPD Initial Project Development (tasks) P Similarity transform matrix of eigenvectors q Delay in recognising effect of rework on schedule SCD Scheduled completion date (state) scdn Initial estimate of scheduled completion date tdrwm Detection time for undiscovered rework (based on past experience) tdwfs Adjustment time for workforce sought (based on HR policy and experience) tkdscv Tasks discovered in TAH model tms Adjustment of schedule due to undiscovered rework Tr2 Delay to recognise workforce needed URW Undetected rework (state) WF Workforce (state) wfat Workforce adjustment time wfn initial workforce available WFSa Workforce sought due to delayed limit (state) WFSb Workforce sought due to perceived workload (state) wfpr workforce perceived required base on perception of project size x States of the linear system y Outputs of the linear system z Modal states of the linear system

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