Multi-objective optimization for parametric bamboo-metal
mixed scaffolding design in Hong Kong
Xi Wei 1*, Fan Xue 2
This is the authors’ version of the paper:
Wei, X. & Xue, F. (2025). Multi-objective optimization for parametric
bamboo-metal mixed scaffolding design in Hong Kong. Proceedings of the
29th International Symposium on Advancement of Construction Management
and Real Estate, Springer, in press.
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Abstract: Bamboo, as an outstanding decarbonization construction material, has historically been
the primary choice for scaffolding in Hong Kong. In contrast, globally adopted modern metal
scaffolding ensures top-tier safety and stability at construction sites, and this type of scaffolding is
utilized at some large-scale construction sites in Hong Kong. Apart from these two well-established
scaffolding methods, this paper proposes a parametric bamboo-metal mixed scaffolding system to
cater to the requirements of sites. The mixed system is parametrically generated by the multiobjective optimization, taking into account multiple site-specific objectives such as time efficiency,
load-bearing capacity, and cost-effectiveness. The proposed designs leverage the strengths of both
bamboo and metal scaffolding. In summary, the unique attributes of this innovative scaffolding
system are well-suited to the demands of small-scale construction sites and contribute to the global
decarbonization efforts within the construction industry.
Keywords: Bamboo-metal mixed scaffolding; multi-objective optimization; site-specific
scaffolding system; sustainable construction.

1 Introduction
Bamboo scaffolding is a type of scaffolding commonly found in Hong Kong and is also used in
southern China and various Southeast Asian cities (Fang et al. 2004). In Hong Kong, the use of
bamboo scaffolding is not only driven by considerations of cost and time, but also serves as a means
of inheriting traditional scaffolding techniques. Its existence is close to a thousand years (Huang
2021), and bamboo scaffolding-like structure is depicted in the renowned “Along the River During
1Xi Wei

Department of Real Estate and Construction, The University of Hong Kong, Hong Kong SAR, China
* Corresponding author, weixi77@hku.hk
2Fan Xue
Department of Real Estate and Construction, The University of Hong Kong, Hong Kong SAR, China
E-mail: xuef@hku.hk

the Qingming Festival” painted by Zhang Zeduan from the Northern Song Dynasty (Figure.1a)
(SCMP 2022). The craftmanship of constructing temporary bamboo structures is not only used for
scaffolding projects on construction sites but also finds application in temporary gatherings or stage
spaces during some important festivals in the Great Bay area (Figure.1b). The distinctive feature of
bamboo scaffolding lies in its utilization of natural bamboo as the primary material, combined with
bamboo or nylon strips for tying purposes.

Figure 1 Traditional bamboo temporary structure. (a) Bamboo scaffolding-like structure in “Along the River
During the Qingming Festival” (b) Temporary bamboo opera theatre

In Hong Kong, the primary sources of bamboo scaffolding materials are the Zhaoqing region in
Guangdong Province and certain areas of Guangxi Province. Among the more than 1,200 species
of bamboo worldwide, moso bamboo (Mao Jue) and penny bamboo (Kao Jue) are the principal
types used at construction sites.
Bamboo scaffolding significantly contributes to the global decarbonization of the construction
phase. Carbon emissions from the construction industry are one of the major causes of global
warming, and how to make the construction industry carry out sustainable development has always
been a concern for all walks of life. Scaffolding, as an important part of the building construction
project, has a budget of about 15% of the total project cost (Hou et al. 2017), and the implementation
of environmentally friendly scaffolding systems can notably decrease the overall carbon footprint
of a project. Therefore, the promotion and application of sustainable scaffolding types, such as
bamboo scaffolding, should be encouraged. (Laleicke et al. 2015).
In Hong Kong, bamboo scaffolding offers five key advantages over metal scaffolding as below:
1. Lower cost: The region surrounding Hong Kong is rich in bamboo resources, making it a more
cost-effective option. High-quality bamboo is approximately 5% of the price of metal tubing
(MBMSS 2009), presenting an attractive choice for various construction sites.
2. Lightweight: Bamboo has nearly half the weight of standard metal tubing of the same length,
making it a crucial option for specific building projects that require truss-out structures.
3. Faster assembly and disassembly: Due to the lightweight nature of bamboo and the extensive
professional training of workers, bamboo scaffolding can be erected up to six times faster and
dismantled up to 12 times faster than steel scaffolding.
4. Flexibility: Bamboo's flexibility allows for the size of members to be adjusted according to site
conditions, which is particularly advantageous in a high-density city like Hong Kong.

5. Lower carbon footprint: Bamboo's natural material properties result in a significantly reduced
carbon footprint compared to metal scaffolding, promoting the sustainable development of the
construction industry.
Overall, these benefits make bamboo scaffolding an appealing choice for construction projects in
Hong Kong and other regions with similar conditions.
During the 1990s, nearly all construction projects in Hong Kong utilized bamboo scaffolding, with
only 5% of projects employing metal scaffolding (Chang & Yu 2002). Construction projects under
the supervision of the Building Department even achieved a 100% bamboo scaffolding usage rate,
including many large-scale projects such as the Convention and Exhibition Center. However, this
trend is gradually shifting, as metal scaffolding now accounts for 30% to 40% of construction
projects in Hong Kong, particularly in prominent public projects like the M+ Museum, where metal
scaffolding has been used exclusively. Common metal scaffolding can be further categorized into
steel scaffolding and aluminum alloy scaffolding.
Bamboo scaffolding is gradually being supplanted due to several factors. The primary concern is
safety. According to Bambhava (2013), the most important factors that employers consider when
choosing the type of scaffolding are "safety" (32%) > "availability" (30%) > "cost" (25%) >
"erection and dismantling time (12%)". Safety is the primary consideration. However, bamboo's
characteristics, including uneven strength, susceptibility to moisture and damage, and inadequate
wind resistance, have resulted in safety incidents related to bamboo scaffolding. Another
significant factor contributing to the decline of bamboo scaffolding is the high demands it places
on construction workers. As per the Code of Practice for Bamboo Scaffolding Safety in Hong
Kong (HKLD 2001), qualified workers must undergo an extensive training period of up to three
years and secure a certificate of authorization before being permitted to erect and dismantle
bamboo scaffolding. As society accelerates, fewer young people are willing to invest several years
to acquire this skill. Table.1 and Figure.2 show the comparison of scaffolding made of bamboo,
steel and aluminum materials.
Table 1. Comparison of Bamboo, Steel and Aluminum alloy Scaffoldings
Material

Bamboo

Steel

Aluminum alloy

Cost

Lower

Higher (In Material)

Safety (Strength)

Lower

Higher (In Labor)
Higher
(In Weight Bearing)

Safety (Durability)
Availability
Erection and
Dismantling Time
Consumption
Flexibility
Weight
Sustainability
Maintenance

Higher

Lower
(susceptible to moisture,
rot, and insect attacks)
Lower
(Specific Regions)

Higher

Higher
(In Corrosion)

Higher
(Worldwide Spread)

Higher
(Worldwide Spread)

Lower

Higher

Higher

Higher

Lower

Higher

Lower
Higher
(Natural Material)
Higher

Higher

Lower

Lower

Lower

Lower

Lower

Figure 2 Comparison of Bamboo, Steel and Aluminum alloy Scaffoldings

Bamboo scaffolding and metal scaffolding have different suitable applications in construction
sites. For instance, small truss-out renovation projects greatly benefit from the lightweight and
quick-to-assemble bamboo scaffolding. In contrast, large-scale projects that prioritize safety and
have longer construction timelines are more suitable for metal scaffoldings. However, in highdensity cities like Hong Kong, construction projects of varying scales and requirements must often
choose between bamboo and metal scaffolding, leading to certain compromises on safety or cost.
This situation not only reduces project efficiency but also results in a waste of resources. A more
tailored approach to scaffolding selection, considering the specific needs and constraints of each
project, could help mitigate these issues and optimize overall construction efficiency and resource
utilization.
Therefore, this paper aims to propose a hybrid bamboo-metal mixed scaffolding system that
quantifies a project's scaffolding requirements in terms of strength, weight, cost, and time
consumption based on the actual circumstances of the project. This approach involves a multiobjective optimization of material combinations for scaffolding components, generating a sitespecific scaffolding combination scheme that leverages the respective advantages of both materials.
In this paper, a building façade renovation project in the Sham Shui Po area of Hong Kong was
selected as a case study to demonstrate the effectiveness of a bamboo-metal mixed scaffolding
solution.

2 Literature Review
2.1 Hybrid material scaffolding
In current literature, many of the researchers are conducting experiments and exploring alternative
materials for scaffolding due to the high carbon footprint of steel scaffolding during production,
transportation, and installation, as well as its larger self-weight. Examples of these alternative
materials include aluminum alloys (Chang et al. 2021), high-strength plastics, fiberglass resins
(Małek et al. 2022). These materials provide new options for construction scaffolding selection and
demonstrate superior characteristics compared to steel or bamboo in certain aspects. However, they

also introduce new limitations. At present, there is no single scaffolding material that consistently
outperforms others across most criteria. This highlights the need for continued research and
development in the field of scaffolding materials and the potential benefits of hybrid systems that
combine the advantages of multiple materials to optimize performance in various construction
settings.
The new material scaffolds mentioned above still adhere to a single-material system, and there is
limited research on mixed-material scaffolds in existing literature. So Yu Shing (2009) proposed a
Metal-Bamboo Matrix System Scaffold (MBMSS), where the primary load-bearing components of
the bamboo scaffolding system were replaced with steel pipes to enhance the overall structural
strength and consequently, safety. The remainder of the secondary structural and non-structural
components mainly used bamboo material to minimize cost and self-weight. However, this hybrid
material system is not site-specific. The ratio of bamboo to steel is fixed at around 6:4, and it simply
provides a third option between bamboo scaffolding and steel scaffolding for construction projects
in Hong Kong. It does not address the issue of wasted scaffolding resources due to differing
objectives at various types of construction sites. This paper aims to address this gap by proposing a
site-specific hybrid bamboo-metal mixed scaffolding system.

2.1 Optimization on scaffoldings
As a crucial component of the building construction process, scaffolding is produced, transported,
installed, used, maintained, and dismantled in a manner that considers all relevant aspects. Therefore,
the decision-making process for scaffolding use involves balancing multiple needs, some of which
may even conflict with each other. Consequently, scaffolding optimization is of immense
importance.
Jin (2023) developed an automated decision-making model to optimize scaffolding, selecting three
factors for consideration: accessibility, worker protection, and health risks in scaffolding
construction. These factors were chosen to optimize the scaffolding planning method, reduce
construction costs, and enhance the safety of the scaffolding system.
Similarly, Hou et al. (2017) formulated a multi-objective discrete firefly algorithm to optimize the
time and cost of the scaffolding construction process, generating a case-specific scaffolding
scheduling plan. Hou et al. (2014) developed a mathematical optimization algorithm framework to
digitize the scaffolding erection and dismantling process in virtual simulation scenarios, aiming to
reduce risk during the construction process.
Kim et al. (2016) developed an optimization engine based on Building Information Modeling (BIM)
to generate multiple alternative scaffolding plans. These plans were then simulated by a safety
simulation engine based on real-life construction site conditions to identify safety hazards.
These models and algorithms all underscore the complex interplay of factors involved in scaffolding
use and the need for robust optimization strategies. However, the main object to optimize in these
models is only the plan and frame of the scaffolding systems rather than including the material of
the scaffoldings.

3 Research Method

This paper presents a multi-objective optimization method for bamboo-metal mixed scaffolding
system based on site-specific situation and demand analysis, which is divided into four parts as
shown in the Figure.3. Analysis of the site situation to quantify the site-specific demands; 2.
Define the objective optimization functions according to the site demands; 3. Solving the MOO
formulation by the Wallacei X plugin on Grasshopper platform; 4. Pareto frontier and final
solution. This systematic approach allows for a comprehensive analysis of site-specific needs and
the optimization of the scaffolding system to meet these needs, balancing multiple objectives and
integrating the advantages of both bamboo and metal materials.

Figure 3 Research method

3.1 Site analysis
This paper selected a local renovation project in Hong Kong as the case study. The project
involves the lower part of Building No. 39 on Un Chau Street in the Sham Shui Po area. The
façade of the building measures approximately 7.8 meters in width and 6.9 meters in height. The
site is located on the side of the street and houses commercial stores with doors facing the street.
This case study provides a practical example for the application of the proposed bamboo-metal
mixed scaffolding system.
To minimize the impact on the normal activities of the stores at the site, one of the main
optimization objectives is to minimize the time consumption for the erection and dismantling of
the scaffolding system. Additionally, ensuring the safety of the system is another optimization
objective due to the site's location in an area with higher pedestrian traffic density compared to
regular residential areas. Finally, cost, as a fundamental optimization objective, is also considered.
For this site, the traditional bamboo scaffolding framework is shown in Figure 4. Define set 𝕏𝕏 =

{x1, x2, ..., xn}, n = | 𝕏𝕏 |, and xi is one of the bamboo elements within the scaffolding framework.

Figure 4 A bamboo scaffolding frame with the group of different parts

3.2 MOO formulation
The MOO formulation for bamboo-metal mixed scaffolding system consists of three objectives, as
shown in Eq. (1).
𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨𝐨 𝐹𝐹(𝑋𝑋) = 𝐦𝐦𝐦𝐦𝐦𝐦 𝐸𝐸𝐸𝐸𝐸𝐸(𝑋𝑋), −𝑆𝑆𝑆𝑆(𝑋𝑋), 𝑂𝑂𝑂𝑂(𝑋𝑋)

𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬𝐬 𝐭𝐭𝐭𝐭 𝑋𝑋 = �𝑥𝑥1 , 𝑥𝑥2 , … , 𝑥𝑥𝑦𝑦 �, 𝑥𝑥𝑖𝑖 ∈ 𝕏𝕏, and 1 ≤ 𝑖𝑖 ≤ 𝑦𝑦 ≤ 𝑛𝑛,

where X ⊆ 𝕏𝕏 is a collective metal element set; x ∈ 𝕏𝕏 represents a metal tube that replace the
bamboo element; EDT(X), SS(X), and OC(X) are the main objective functions regarding time
consumption, safety, and material cost, respectively; and y = | X | is the quantity of metal tubes
that been used as the replacement of bamboo elements.

(1)

For the erection and dismantling time, this paper took a simplified way to quantify and compare
the time consumption of each scaffolding element during the process of erection and dismantling.
Because of the characteristic of being modular, the time consumption can be calculated by the unit
time and the number of the element joints. The ratio of the erection and dismantling time between
bamboo and metal is around 1:6 and 1:12 respectively (SCMP 2022). Define the time
consumption of a bamboo-bamboo joint as a, and the number of bamboo-bamboo joint as b1,
define the time consumption of a metal-metal joint as c, and the number of metal-metal joint as b2.
To simplified the calculation, we set c = 9a, which is the average ratio of erection and dismantling
time consumption. For the bamboo-metal joint, the time consumption can be calculated by the
average of bamboo-bamboo and metal-metal scaffolding, which is 5a, and the number of bamboometal joint is b3. Thus, the first objective of time consumption can be defined as below:
𝑬𝑬𝑬𝑬𝑬𝑬(𝑿𝑿) = 𝑎𝑎 ∗ 𝑏𝑏1 + 9𝑎𝑎 ∗ 𝑏𝑏2 + 5𝑎𝑎 ∗ 𝑏𝑏3

(𝟐𝟐)

Regarding the safety issue of the scaffolding system, it is necessary to optimize the structural
strength of the overall system. The design strength of metal scaffolding is around 4 kPa and 1.45
kPa for bamboo scaffolding (MBMSS 2009), thus the strength ratio of the two material can be
inferred correspondingly. By simplifying the strength ratio of bamboo material and metal material

in the optimal state, set the structural strength of bamboo under the same function as k, and then
the structural strength of metal as 2.75k.
As shown in Figure.4, in the scaffolding framework, the bamboo elements in different positions
have different functional attributes and structural contribution degrees. The purple part is the main
support structure, the number of bamboo elements is t1, the number of metal elements is l1, and the
weight of the component attached to this part is 2; the cyan part is the regular support structure,
the number of bamboo elements is t2, the number of metal elements is l2, the weight of this part is
set to 1; the yellow part is brace, the number of bamboo elements is t3, the number of metal
elements is l3, the weight of this part is set to 1.5 since the scale of the structure of the wind
resistance requirements are smaller; The rest of the components are auxiliary connecting
components, the number of bamboo elements is t4, the number of metal elements is l4, and the
weight of this part is set to 0.5; the node part is not given weight in this paper due to the similarity
of the strapping technique and the metal coupler in terms of structural strength. In the context of
the selected site, ∑(t+l)=n. Therefore, the second objective relating to the structural strength is
defined as below:
𝑺𝑺𝑺𝑺(𝑿𝑿) = 𝑘𝑘 ∗ [2(𝑡𝑡1 + 3𝑙𝑙1 ) + (𝑡𝑡2 + 3𝑙𝑙2 ) + 1.5(𝑡𝑡3 + 3𝑙𝑙3 ) + 0.5(𝑡𝑡4 + 3𝑙𝑙4 )]

(𝟑𝟑)

𝑶𝑶𝑶𝑶(𝑿𝑿) = 𝑒𝑒 ∗ ∑𝑡𝑡 + 2e ∗ ∑𝑙𝑙

(𝟒𝟒)

For the cost aspect, the way to quantify the material cost is similar to the method of quantifying
the structural strength. Define the unit cost of each bamboo element in average as e, then the cost
of metal element in average is 2e. Therefore, the third objective regarding system overall cost is
defined as below:

In order to unify the optimization direction of the three objective functions, in this paper, the
second objective function SS(X) is inverted in the calculation to facilitate the simulation of multiobjective optimization in the later stage.

3.3 Solving the MOO formulation
This paper employs the Wallacei X plugin (ver.2.7) on Grasshopper to calculate and solve the
MOO formulation Eq.(1) using the NSGA-II algorithm. For each group of structural elements,
there are two parameters to control the number and position of which bamboo element is replaced
by metal element. By inputting the parameters into Wallacei X as gene pools, the three objective
functions defined in the previous section can be calculated using the built-in functions of
Grasshopper. The amount of the generation was set to 200, and the population size of each
generation was set to 100, thus 20,000 population size in total.

3.4 Pareto frontier and the final solution
After a calculation of 11 minutes and 22 seconds, the MOO formulation was solved within the
Wallacei X plugin. The number of unrepeated Pareto optimal solutions from the last generation of
simulations was 20, which forming the Pareto frontier of this MOO problem.

Figure 5 MOO problem solving interface

Figure 5 shows the Wallacei X interface solving the problem. The parallel coordinate plot depicts
the relationships among the three objectives. The first objective and the second objective show a
strong negative correlation, which means the functions EDT(X) and SS(X) show a positive
correlation, the more time spent on the erection and dismantling stage, the more structural strength
is within the system. Meanwhile, the second objective SS(X) and the third objective OC(X) show a
positive correlation, which means the more structural strength of a system, the more cost it will
take for the construction site.
After obtaining the Pareto Frontier, the determination of the final solution can be made by the site
decision-makers. A comprehensive analysis of the demands can be conducted to finalize the
choice, considering the weighted relationships among the various objectives. In the case of the
selected site discussed in this paper, a detailed demands analysis has not been performed.
Therefore, the final solution was chosen based on the average rankings of the three objectives
collectively. Figure 6 illustrates the final material placements for the scaffolding framework, with
the red components representing metal pipes and the green lines indicating bamboo tubes.

Figure 6 3D visualization of the final solution of the proposed bamboo-steel scaffolding system.

4 Discussion
4.1 Pros and cons
This paper presents a novel scaffolding system that employs multi-objective optimization to
facilitate the mixed use of bamboo and metal materials, tailored to various construction scenarios.
In a context where most scaffolding systems exclusively offer a binary choice between bamboo
and metal frameworks, this innovative design delivers customized bamboo-metal hybrid
scaffolding solutions for different construction sites, effectively addressing the diverse
requirements of distinct projects.
The primary contributions of this paper can be divided into two folds. First, by incorporating a
mixture of bamboo and metal materials, the significant drawbacks of both types of scaffolding can
be mitigated, enhancing the safety of pure bamboo scaffolding and avoiding the high cost and low
efficiency associated with pure metal scaffolding. Second, the ratio of different materials in the
new scaffolding system is determined through multi-objective optimization, which is tailored to
each specific construction site. This approach fully capitalizes on the advantages of both materials,
catering to the diverse demands of various construction projects in terms of time, cost, safety, and
durability. Consequently, this minimizes waste and reduces the carbon footprint of construction
projects.
This paper presents certain limitations as well. First, it solely considers bamboo and steel
scaffolding materials, overlooking the emergence of various other types of scaffolding materials in
the market, such as aluminum alloys, high-strength plastics, and fiberglass. Each of these
materials possesses unique properties that cater to diverse needs. Moreover, the chosen
scaffolding structure is based on the traditional bamboo scaffold framework, which is relatively
denser due to the disparities between bamboo and metal materials. However, after substituting
some components with metal materials, the overall scaffold frame still adheres to the bamboo
style, potentially resulting in excessive structural redundancy. Lastly, the calculation of the
strength and deformation of the bamboo-metal mixed scaffolding system is oversimplified by
equating the strengths of the two materials to a fixed ratio and adding them together. In reality, the
stress conditions of different materials in various positions may differ, necessitating a more
comprehensive mechanical simulation analysis for the evaluation of structural deformation.

4.2 Future work
To address the three primary limitations previously mentioned, the future work of this paper can
be segmented into the following three areas. First, a comprehensive review of existing scaffolding
materials, particularly newer ones, can be undertaken. This analysis would assess the feasibility of
integrating these materials further into the proposed bamboo-metal mixed scaffolding and
incorporating additional materials as design variables in future multi-objective optimization.
Second, future work should consider incorporating the number of components and the spacing
between them as part of the variables in the multi-objective optimization process. Additionally,
future research will involve evaluating and compiling the entire life cycle of the scaffolding
system, extending beyond the on-site phase to encompass the production and transportation of raw
materials, as well as storage and disposal after dismantling.

Lastly, during the formulation stage of defining structural deformation, mechanical simulation
plugins for Grasshopper platforms, such as Kangaroo and Karamba3D, can be employed to
perform mechanical simulations on mixed scaffolding systems with varying materials. This
approach would yield accurate component deformation variables, serving as the foundation for
multi-objective optimization. Multiple advanced technologies can be applied in the field of
scaffolding design and management such as Machine Learning (Liang & Xue 2023), Blockchain
(Zhao et al. 2023), CIM (Li et al. 2024), 4D Point Cloud (Liang et al. 2024), etc.

5 Conclusion
Bamboo scaffolding is a type of scaffolding with exceptional sustainability features and is
considered intangible cultural heritage in Hong Kong. It offers several unique advantages
compared to metal scaffolding. However, due to increasing safety requirements for construction
projects and the demand for standardization and durability in large-scale construction projects, the
prevalence of traditional bamboo scaffolding in the Hong Kong construction market is
diminishing. On the other hand, metal scaffolding also has notable limitations, with high costs and
low assembly and disassembly efficiency being its primary drawbacks. In most cases, construction
projects are forced to choose between bamboo scaffolding and metal scaffolding, leading to
compromises and concessions. This results in a waste of time and cost in many construction
projects, as well as a higher carbon footprint during the production, transportation, and assembly
processes.
This paper proposes a bamboo-metal mixed scaffolding system, which analyzes the specific
requirements of construction projects concerning various scaffolding characteristics, such as
safety, cost, erection and dismantling time, durability, flexibility, self-weight, and other factors. A
multi-objective optimization method is employed to optimize and select the materials of
components at different positions. On the one hand, it combines the advantages of both material
types while also preventing waste of time and costs. This paper selected a section of the facade of
No. 39 Un Chau Street, Sham Shui Po, Hong Kong, as a case study, analyzed the requirements,
formulated corresponding optimization objectives, and performed simulations. In future research,
the review and application of new materials, as well as the comprehensive mechanical simulation
analysis of the mixed scaffolding system, will be conducted to enhance the rigor and
comprehensiveness of the study.
The design of a mixed scaffolding system allows for customization of metal and bamboo
components based on the specific requirements of a construction project. The computational
results of the pilot project demonstrated that this approach is technologically feasible and holds
great significance for optimizing scaffoldings, balancing engineering efficiency, structural
strength, and project costs – at least for small-scale projects. Broader adoption of this mixed
scaffolding system in cities near bamboo habitats can contribute to the global decarbonization
efforts within the construction industry.

Acknowledgement

The study was supported by Hong Kong Research Grants Council (RGC) (No. C7080-22GF).

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