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14th MANCO analogue Programming Approach for Irrigation Scheduling A casing Study H. MD. AZAMATHULLA, Senior Lecturer, River Engineering and Urban Drainage research Centre (REDAC), Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Pulau Pinang, Malaysia email emailprotected usm. my, emailprotected com (author for correspondence) AMINUDDIN AB GHANI, Professor, REDAC, Universiti Sains Malaysia, email emailprotected usm. my NOR AZAZI ZAKARIA, Professor, REDAC, Universiti Sains Malaysia, email emailprotected usm. my CHANG CHUN KIAT, scholarship Officer, REDAC, Universiti Sains Malaysia, email emailprotected sm. my Abstract There is an increasing aw atomic number 18ness among irrigation planners and engineers to design and black market offshoot systems for maximum efficiency to maximize their benefits. Accordingly, signifi so-and-sot work has been do on seed functioning for known total irrigation consumement and on the optimum al fixing of water available to wreaks at the farm level. genuinely few studies be possessed of been conducted to derive optimum artificial lake operation policies incorpo lay out the root operation with the on-farm utilisation of water by the variant rambles.This extradite paper deals with the development of standard unidimensional Programming (LP) to be enforce to real snip seed operation in an existing Ch swooninger reservoir system in Madhya Pradesh, India. Keywords cut backping trope, water system resource instruction, Irrigation management, Optimization 1. Introduction In most develop countries, a huge sh atomic number 18 of the sterilizeed compute goes to creating facilities for irrigation. Construction of reservoirs requires re tout ensembley high investment and also throws socioeconomic and environmental issues. piddle in the reservoir has multiple claimants and subscribes to be optimally employ to generate maximum benefits by means of proper operation, which must remain order ed despite un reliable future inflows and motives. According to the World Commission on Dams, m both large transshipment center lying-ins worldwide atomic number 18 failing to put out the anticipated benefits (Labadie, 2004). Similarly, small storage count ons made for local beas in developing countries, like India, atomic number 18 also failing to meet expectations.The main cause identified at various levels of discussion, as reported by Labadie (2004), is lacking(predicate) run acrossation of the more mundane operation and maintenance issues once the project is completed. For existing reservoirs, optimum operation is critical, since all the expected benefits are establish on measurely water releases to meet the stipulated demand. palpable- prison term operation of a reservoir requires making relatively quick decisions regarding releases based on short-term schooling. Decisions are dependant on the storage in the reservoir and information available in the form of forec ast hydrologic and meteorological parameters.This is especially valuable during floods and power generation, where the system has to respond to changes very quickly and may need to adapt rapidly (Mohan et al. 1991). For reservoir systems operated for irrigation scheduling, real time operation is not very common because of longer decision steps. Traditionally, the reservoirs meant for irrigation purposes are operated on heuristics and certain rules derived from old experiences. This defies the concept of water-management much of the water is lost, which in turn leads to loss of revenue.In the earlyish 1960s, mathematical programming techniques became popular for reservoir planning and operation tending(p) literature is available. An excellent review of the topic is given(p) by Yeh (1985), followed by Labadie (2004) and Wurbs (1993). Along with simulation studies, Linear Programming (LP), Dynamic Programming (DP) and Non Linear Programming (NLP) are the most popular computer s imulationling techniques. A proportional study on the applicability and computational difficulties of these places is empowered by Mujumdar and Narulkar (1993).Mevery of the aforementioned techniques have been implemented in realistic scenarios, and many reservoir systems worldwide are operated based on the decision rules generated from these techniques. However, there exists a gap mingled with theory and practice, and full implementation has not been achieved yet (Labadie, 2004). 1 14 & 15 February 2009 Kuching, Sarawak The basic difficulty a reservoir manager faces is to tamp a real-time optimum decision regarding releases according to the future demand and inflow. This leads to the line of optimization of the random domain.Two progressiones of stochastic optimization are deft i) Explicit stochastic Optimization (ESO), which works on probabilistic descriptors of haphazard inputs directly and ii) Implicit stochastic Optimization (ISO), which is based on historical, gener ated or forecasted nourishs of the inputs through the use of Time Series Analysis or other Probabilistic go aboutes. The ESO approach has computational difficulties ISO methods are simple, notwithstanding require an additional forecasting feigning for real time operation. In the case of irrigation reservoirs, decision making at the reservoir level depends upon the water demand arising at the firmament level.In order to operate the reservoir in the trounce possible way, it breaks imperative to understand the processes occurring in the do work- stain-water-atmosphere system. This helps not only in the estimation of accurate demands, but also ensures optimum utilisation of water. If the processes at the field level are also layled properly and interconnected with the reservoir level sit around, the goal of water management can be achieved in the best possible way. Dudley et al. (1971) pioneered the integration of the systems in the determination of optimal irrigation clock under limited water supply using a Stochastic DP model.Dudley and his associates then improved the model (Dudley and Burt, 1973 Dudley, 1988 Dudley and Musgrave, 1993). Vedula and Mujumdar (1992, 1993) and Vedula and Nagesh Kumar (1996) have also contributed to this neighborhood. Their approach was to derive a steady estate reservoir operation insurance mend maximizing the annual vagabond yield. DP-SDP and LP-SDP were utilise in the modelling. However, for real-time reservoir operation, Vedula and Nagesh Kumar (1996) stressed the need to forecast inflows and rainfall in the topical season to implement the steady state operation insurance polity.As a result, the ESO model has to be supplemented with an ISO model to get a policy for the current check. As an extension to the work of Vedula and Mujumdar (1992), a significant contribution to the real-time reservoir approach was infixed by Mujumdar and Ramesh (1997). They addressed the issue of short term real-time reservoir ope ration by forecasting the inflow for the current designate, a form production state variable and a crap wet state variable. Their work was based on SDP, but had all the limitations of SDP regarding the bane of dimensionality.Against this background, a model for the derivation of real-time optimal operating policy for a reservoir under a multiple cut back scenario is proposed in the present study. The primary issue is that the reservoir gets inflows during the wet season (monsoon season) and is operated for irrigation in the dry season (non-monsoon season). The reservoir storage and the bemire wet level are considered to be the principal state variables, and the irrigation knowledges are the decision variables.An optimal allocation model is embedded in the integrated model to gauge the irrigation water depth supplied to contrasting decorates whenever a competition for water exists amongst various plays. The model also serves as an irrigation-scheduling model because it s pecifies the amount of irrigation for any given two weeks. The impact on crop yield due to water deficits and the ready of tarnish wet dynamics on crop water requirements are taken into account. Moreover, a group emersion model is pick out to consider the operations of varying line of descent depths on wet transfer.The only stochastic element in the season is the evapotranspiration. The handling of stochasticity has been accomplished through dependability based forecasting in an ISO model. The rest of the variables, such as soil moisture lieu and the reservoir storage military position, at the fount of any result are considered to be state variables. The basic saying is based on a LP model and is later transformed into a GA framework. 2. The modelling Formulation and Concept The real-time operation model proposed in the present study integrates the reservoir level and a field level decision ( body-build 3).It considers the soil-moisture status and the reservoir stor age as the state variables and the utilise irrigation depths as decision variables. The formulation is based on the conceptual model for soil moisture accounting and the reservoir storage doggedness congressships. A major emphasis is laid on maintaining soil moisture in a state such that the evapotranspiration from the crops takes place at a rate that achieves better results in the form of increased yields from the crops. To assess the measure of irrigation water application, the soil moisture status of the crop is an outstanding parameter.Whenever the soil moisture status approaches a critical limit, irrigation is applied. Thus, the soil moisture status is monitored either by physical measurement or through soil moisture models. Soil moisture models are more popular since they do not require a lot of instrumentation to be installed in the field. Soil moisture models can be formulated either by a physical approach (Fedders et al. , 1978) or a conceptual approach (Rao, 1987). Th e conceptual approach has been used by Rao et al. (1988), Rao et al. (1990) and 2 14th MANCO Hajilal et al. (1998) for the problem of irrigation scheduling.Vedula and Mujumdar (1992) utilised the conceptual model in their study. The same concept is adopted in the present study. Figure 3 Flow chart of real-time operation of reservoir 3 14 & 15 February 2009 Kuching, Sarawak 3. The Conceptual Model In the conceptual model for the Crop-Soil- piss-Atmosphere (CSWA) system, the basic assumption is that the soil acts as a reservoir, the main inputs to the reservoir are rainfall irrigation, and the main outputs are evapotranspiration, percolation and drainage. The extent of the reservoir is considered to be up to the effective settle down zone at the particular time.The soil water reservoir is governed by a continuity equation ? ik +1 ED ik +1 ? ? ik ED ik ? IRR ik + AET i k = RF k (1) The conceptual model declared by Eq. 1 is used to compute the irrigation to be applied for the LP model with area as a decision variable. The undermentioned parameters are important for the conceptual model. Figure 1 shows the sketch for the conceptual reservoir. In the scene of the conceptual model two parameters are important IRRk RFk AETk EDk ?k Figure 1 Conceptual model Variation of Evapotranspiration with the addressable Soil wet Evapotranspiration as a function of the available soil moisture is uttered as kAETi k = PETi k if aai ? Zww (2) or AETi k = k aai PETi k Zww where AETi k (3) is the substantial evapotranspiration that has occurred from crop i in two weeks k (mm), PETi k is the possible difference evapotranspiration in a particular geographical location (mm), Zww is the critical available moisture limit (mm/cm) = (Zf? Zw) d, Zf is the field capacity for the soil (mm/cm), Zw is the permanent wilting k point for the soil (mm/cm), d is the depletion reckon and assumed to be 0. 5 in the present study, and a ai is the average available soil moisture over a fortnight (m m/cm). The average available soil moisture over a fortnight is given by ik + aik +1 a= 2. 0 k ai where otherwise aik = ? ik ? Zw if aik Zww aik = Zww k +1 A similar expression can be used for ai . 4 14th MANCO radix regularize Depth exploitation The root depth selective information in relation to the time details are prepared according to the Linear Root Growth Model (adopted by Narulkar, 1995). The model assumes that maximum root depth is achieved at the start of the yield formation demo. It remains at the maximum depth until the maturity stage. A minimum depth of 15 cm is considered in the first fortnight to account for the conditions of bare soil and an area with sparse crops.The root depth model is shown in Figure 2. Life thwart of group Growth stages of group V F G Root Depth Max. Depth Figure 2 Root Depth emergence model relative Yield Ratio The yield of a crop is affected by water deficits and the rate of evapotranspiration. The rate of evapotranspiration tends to d ecrease depending on the available moisture content. There are many methods to model the phenomenon. However, the model used in the present study is the most commonly-adopted model. The relative yields are computed on the foothold of the expression given by Doorenbos and Kassam (1979) YaiAETi k ? k? = 1 ? Ky ? 1 ? ? PET k ? ? Ymi i? ? (4) Equation (4) gives a yield ratio for a single finish only. However, the aggregate effect of moisture deficits over all fortnights of crop growth is also evaluated. The final examination yield ratios computed for the crop during various time periods of a season is computed by a multiplicative model (Rao et al. , 1990). The determination of the yield ratio is very important since they reflect the operation policy for an irrigation system. The expression is given by ? AETi k Yai ncr ? = ? ?1 ? Ky k ? 1 ? ? PET k ? Ymi i =1 ? i ? (5)Water Requirements of the Crops The model derived for an optimal crop build uses predetermined irrigation demands . On the basis of this, the optimisation model selects an appropriate area for an private crop. The irrigation demands are determined using the conceptual model stated in Eq. 1. The irrigation requirements may be calculated by substituting a apprise of critical soil moisture content instead of soil moisture in either of the fortnights k and k+1 and replacing the value of actual evapotranspiration by potential evapotranspiration and rearranging the terms of Eq. ( ) IRRik = ? cr EDik +1 ? EDik + PETi k (6) 5 14 & 15 February 2009 Kuching, Sarawak where ? cr is the critical soil moisture content below which the actual evapotranspiration may fall below the potential rate. 4. Integrated LP Formulation In the objective function, the weighted sum of all the actual evapotranspiration set is maximised. The weights are assigned according to the yield response factors for exclusive crops in individual periods. The objective is to maximise the actual evpotranspiration rate to minimise the deficits in the yields.The available soil moisture in any time period in the objective function is indirectly maximised ncr np ? a k + aik +1 ? Ky k MaxZ = ? ? ? i ? 2. 0 ? Zww i =1 k =1 ? (7) subject to the following constraints 1. Soil moisture continuity ? aik + aik +1 ? PET = RF k ? 2. 0 ? Zww ? ? ik +1 EDik +1 ? ? ik EDik ? IRRik + ? (8) ? ik +1 ? aik +1 ? bik +1 = ZW (9) where with physical move ? ik +1 ? 4. 0 a 2. k +1 i (10) ? 0. 9 (11) germ continuity ncr A k S k +1 ? B k S k + ? i =1 S k +1 ? 31. 1 5. IRRik * AREAik = ? ID ? Ao RE k Eff (Maximum source talent M m3) (12) (13) Crop manikin ModelThe optimisation model presented above yields just about irrigation depth values that are based on forecasted values for the book of facts evapotranspiration. This reference evapotranspiration, in turn, is based on a dependability model. However, the actual evapotranspiration value differs from these values, and thus, out front going into the next fortnight, the soil moisture status must be updated with the applied irrigation and actual climatic factors. The formulation for crop simulation is as follows First compute the final soil moisture with the following relation ? ik = (? ik +1 EDik +1 + IRRik ?Fkcik APET k + ARF k ) / EDik If (14) ? ik +1 3. 1 ?k ? Fkcik +1 APET k +1 Fkcik +1 APET k +1 ZW + ARF k +1 ? ? i EDik + IRRik +1 ? + ? 2. 0 2. 0 ? EDik +1? ik +1 = ? k +1 k +1 Fkci APET EDik +1 2. 0 ( ) (15) or 6 14th MANCO ? ? ik = ? ik ? 1 ? EDik ? 1 ? ? Fkcik APET ? Fkcik APET Fkcik APET + Zw + ARF k + IRRik ? ? EDik ? 2 . 0 2 . 0 2 . 0 ? (16) or ? k ? 1 ? k ? 1 Fkcik APET ? Fkcik APET Fkcik APET ? k k ? ? = i ? EDi ? Zw? ? ? EDi ? ? + IRRi + ? ? 2. 0 2. 0 2. 0 ? ? ? ? k i (17) The computed soil moisture status of the crops is used in the next fortnight to compute the demand. . Stochastic Analysis of Evapotranspiration It was previously stated that the data regarding the climatic factors is uncertain in nature and the determination of these factors beforehand is impossible. However, there is a general course of action to assume the expected values for these factors and carry out the operation. The concept does not give a clear picture of the actual scenario and the appropriate weights for the individual growth stage of the crops are not assigned. The present study proposes a different method of forecasting the expected values for the climatic factors.The method of analysis starts with the computations of dependability values of reference evapotranspiration factors from the available data. The dependability of acknowledgment of any stochastic variable is outlined as the fortune of equalling or exceeding that variable with a particular value. Mathematically, P(x ? X ) (18) where P (. ) is the probability and x is the variable under consideration and X is a stipulated value of the variable. A traditional method of estimation of the dependability value is the use of standard frequency formulae (e. . Wiebulls formula or Hazens formula). In the present study, a detailed probability analysis for the data is performed. The data is fitted to a standard probability dispersion and the best fitting distribution is tested through the Kolmogorov Smirnov Test (Haan, 1977). Once the values corresponding to different dependabilities are evaluated, dependability values for reference evapotranspiration are assumed to be different in different growth stages. The analysis is performed on the basis of the yield response factor.A high yield response factor signifies great sensitivity towards the deficits, and thus, a higher level of dependability is assumed for the evapotranspiration data and a lower level of dependability is assumed for the rainfall data. This forget ensure a higher value of irrigation required for the crop in the sensitive period. As a result, the crop will be safeguarded against any poor moisture content conditions. 7. LP Model Formulation for Optimal Cropping variant At the start of each dry season , depending on the storage hatful in the reservoir, the crop linguistic rule must be determined.To evaluate the crop pattern, another LP model is used. In this model, irrigation depths are calculated from Eq. (6). The formulation is as follows The objective function is MaxZ = C1 X1+ C2 X2+ C3 X3 (19) which is subject to the following constraints 1. Total available area X1+X2+X3? A (20) where X1, X2, and X3 are the decision variables related to the area of individual cropsC1, C2, and C3 are the cost coefficient for each crop in Indian Rupees (1 US $ = 50 INR) and A is the maximum area available for irrigation. 2.Area of each individual crop 7 14 & 15 February 2009 Kuching, Sarawak The area under each crop is required to be constrained thus, there are lower and hurrying bounds on the area under each crop. The lower bounds indicate the minimum area that can be allocated to a crop, while the upper bound indicates the maximum. In the present study, the lower bounds were be for all th e crops except cash crops, while the upper bounds were defined considering the present cropping pattern. The constraints can be expressed as Li? Xi? Mi (21) here Li corresponds to the lower bound of the area for the ith crop and Mi corresponds to the upper bound on the area of the ith crop. 8. Model activity The developed models were applied to the Chiller reservoir system in Madhya Pradesh, India (Latitude 23o23 N and Longitude 76o18 E). In the central part of India, many reservoir projects have been constructed for irrigation, but no irrigation is available from these reservoirs during the monsoon period (from June to September). The area receives about 90 to 95 % of its rainfall during the Monsoon season. The rainfall then becomes runoff to the reservoirs.These reservoirs are designed to apprehend the runoff in the monsoon season, but there is no runoff during non-monsoon months. The present formulations are specially suited for these types of reservoirs. Non-monsoon rainfall i s rare and provides little runoff. A systematic data base was prepared for the various physical features of the reservoirs, including the meteorological and hydrological data such as evapotransiration, expatiate of crops in the command area, details of net returns from individual crops and soil properties collected from the College of Agriculture, Indore, India. . Results and Discussion Optimum Crop sit A separate computer program was run before the real time operation program to determine the optimum crop pattern for all possible storage values. The results of the optimum crop pattern are stated in turn off 1. The results indicate that from a storage level of 31. 10 M m3 to a storage level of 26. 06 M m3, the cropping pattern is same as the one that has been adopted in the project formulation. However, below a storage level of 26. 06 M m3, the crop pattern changes suddenly, and wheat (ordinary) is not recommended by the model.The area of wheat (hybrid) also gets reduce when the rainfall storage is below this level. However, the area for deoxyguanosine monophosphate is full, up to a storage level of 15. 83 M m3. The change in cropping pattern indicates that efficient water usage is maintained. Table 1 Optimum Cropping Pattern for distinct exist shop Values Area (ha) for different crops Live storage (M m3) Wheat (ordinary) Gram Wheat (hybrid) 4. 3230 342. 910 120. 00 8. 2379 427. 580 500. 00 12. 3246 15. 8632 20. 7581 26. 0986 28. 8610 30. 1250 31. 1000 300. 0 300. 0 300. 0 300. 0 1084. 015 1100. 000 1100. 00 1100. 000 1100. 000 1100. 000 1100. 000 500. 00 855. 00 1434. 00 1700. 00 1700. 00 1700. 00 1700. 00 Results from Real-Time Operation Model The real-time operation model gives an optimal operating policy for the available storage in the present fortnight considering the future. The model also yields the values of irrigation to be applied to individual crops in the fields. In the wake of deficient water supplies, the model distributes the available w ater over the time for different crops optimally. The sample results of the present model are stated in Table 2.The available moisture to the crops is not affected, and generally the soil remains at the upper limit of the available soil-moisture. This 8 14th MANCO is because the crop pattern is predicted according to the accessibility of the storage in the reservoir. The results are indicative of successful application of the real-time operation strategy proposed in the present work. Table 2 try out Results Showing the Soil Moisture, Available Soil Moisture, warehousing, and Irrigation to be applied for Different Crops for a Real-Time Reservoir Operation Model (LP) Live Storage in the Reservoir 31. 1 M m3 FORTNIGHTPARAMETER 1 2 3 4 5 6 7 8 9 10 11 Reservoir Storage (M m3 ) 29. 28 28. 17 26. 30 22. 22 Crop 1) Soil Moisture (mm/cm) 3. 76 3. 89 3. 84 3. 07 2) Available soil Moisture 0. 9 0. 9 0. 9 0. 87 (mm/cm) 3) utilize Irrigation (mm) 53. 62 90. 63 92. 87 36. 04 Crop 1) Soil Moi sture (mm/cm 3. 90 3. 07 3. 28 3. 15 2) Available soil Moisture 0. 9 0. 87 0. 9 0. 9 (mm/cm) 3) Applied Irrigation (mm) 68. 76 22. 27 60. 67 41. 59 Crop 1) Soil Moisture (mm/cm 4. 00 2) Available soil Moisture 0. 9 (mm/cm) 3) Applied Irrigation (mm) 94. 21 19. 68 14. 64 10. 87 Wheat (ordinary) 3. 54 3. 30 3. 22 0. 9 . 9 0. 9 5. 62 4. 24 3. 63 3. 60 3. 17 0. 9 4. 0 0. 9 -. 163. 9 8. 44 23. 02 GRAM 3. 28 3. 66 0. 9 0. 9 19. 94 102. 6 3. 23 0. 9 3. 47 0. 9 37. 64 53. 15 Wheat (hybrid) 3. 06 3. 48 3. 32 0. 86 0. 9 0. 9 0. 00 33. 17 3. 28 0. 9 3. 38 0. 9 3. 18 0. 9 3. 19 0. 9 37. 19 162. 9 0. 00 36. 09 0. 0 3. 4 0. 9 26. 96 127. 9 78. 89 congeneric Yield Ratios Relative yield ratios computed for different crops at different live storage values are shown in Table 3. The relative yield ratios for all the crops become one if live storage in the reservoir is equal to or greater than 28. 9 M m3. The GA model is found to be better for application in real world operation of the re servoir. Table 3 Relative Yield Ratio for Different Live Storage Values Computed With a Real-Time Reservoir Operation Model Relative yield ratio for Live different crops storage LP (M m3 ) Wheat Gram Wheat (hybrid) (ordinary) 4. 3230 0. 9677 1. 000 8. 2362 0. 9083 1. 000 12. 3246 0. 9576 1. 000 0. 989 1. 000 20. 7581 26. 0986 1. 000 0. 987 0. 987 0. 911 0. 952 28. 8610 1. 000 0. 987 1. 000 30. 1250 31. 1000 10. 15. 8632 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 ConclusionA real-time model using an integrated Linear Programming Model for a reservoir system meant for irrigation has been developed in the present study to obtain an optimal reservoir operating policy that incorporates field level decisions, while also deciding the appropriate time and amount of water to release from the reservoir. 9 14 & 15 February 2009 Kuching, Sarawak From the analysis, the following conclusions can be drawn The developed model can be successfully applied to irrigation supporting reservoir systems. Furthermore, the models ensure an optimum reservoir release over different time periods.In addition, they also ensure optimum allocation of the available water over the different crops in the fields. objet dart allocating the water to different crops in the fields, the model takes into account the critical growth stages of the crops and allocates sufficient water to each crop to safeguard it against any ill effects of water deficits. The optimum crop pattern model used in the study will only allow productive irrigation, so the amount of wasted water is reduced. Acknowledgements The authors would like to express sincere give thanks to Universiti Sains Malaysia for the financial support of this work.Nomenclature AETi k k Actual evapotranspiration in period k from crop i (mm) APET ARFk Ak and BK Ao d Actually occurring potential evapotranspiration in period k (mm) Actual rainfall value in the fortnight k Constants relating the storage to reservoir evaporation Area of open at dead st orage level Depletion factor EDik Effective root zone depth of a crop i in period k (cm) k +1 i ED Effective root zone depth of a crop i in period k+1 (cm) Eff Fkcik ID Overall efficiency Crop evapotranspiration coefficient industrial supply from the reservoir (mandatory release) IRRikIrrigation applied to crop i in stage k (mm) k Ky Yield response factors for a crop i in period k PETi k RE RF k Potential evapotranspiration in a particular geographical location (mm) appraise of evaporation in fortnight k k Sk Sk+1 Zf Zw Zww rainwater in period k (mm) Reservoir storage at the beginning of period k Reservoir storage at the end of period k Field capacity for the soil (mm/cm) Permanent wilting point for the soil (mm/cm) Critical available moisture limit (mm/cm) ? ik ? ik +1 concluding soil moisture in a particular time stage k for a particular crop i (mm/cm) Yai Ymi Actual crop yield Maximum crop yieldInitial soil moisture in the time stage k in for a crop i (mm/cm) 10 14th MANCO Ref erences 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 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