Influence of Substructure Design and Occlusal Reduction on the Stress Distribution in Metal Ceramic Complete Crowns: 3D Finite Element Analysis ´ Barreira Motta, DDS, MSc, PhD,1 Luiz Carlos Pereira, MSc, DSc,2 Fernando Pereira Duda, MSc, Andrea 1 DSc, & Kenneth J. Anusavice, PhD, DMD3 1

Department of Mechanical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil Department of Metallurgy and Materials Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil 3 Department of Restorative Dental Sciences, University of Florida College of Dentistry, Gainesville, FL 2

Keywords Finite element analysis; occlusal reduction; substructure; complete crown; stress distribution. Correspondence ´ Barreira Motta, Department of Andrea Mechanical Engineering, Federal University of ´ Rio de Janeiro, Cid. Universitaria-Centro de Tecnologia-Bloco G, sala G-202, Ilha do ˜ RJ, Rio de Janeiro 68503, Brazil. Fundao, E-mail: [email protected] Financial support from the Brazilian National Research Council (CNPq). This study was also supported, in part, by NIH/NIDCR Grant DE 06672. The authors deny any conflicts of interest. Accepted August 5, 2013 doi: 10.1111/jopr.12119

Abstract Purpose: Occlusal reduction is considered a fundamental step for providing adequate and uniform space for the ceramic prosthesis; however, a flat occlusal surface is usually found. The prosthesis design influences the resistance to deformation and the stress state within the ceramic. This finite element (FE) study analyzes the influence of changing the substructure design on the stress distribution of a metal-ceramic crown in a premolar tooth with three types of occlusal reduction. Materials and Methods: Each part of three-dimensional metal ceramic complete crown models was designed according to the space provided by different levels of occlusal reduction and the same external morphology of the tooth. Three models were designed: (1) correct occlusal reduction with a uniform thickness of the substructure (0.3 mm) and the veneering porcelain (1.5 mm); (2) flat occlusal reduction with different thicknesses of veneering porcelain to produce a uniform substructure; and (3) a flat occlusal reduction with different thicknesses of substructure for a uniform thickness of veneering porcelain. Results: Stress distributions were very similar in the three models. The highest tensile stresses were concentrated immediately below the midline fissure in both the veneering porcelain and the metal alloy substructure. Although models with flat occlusal reduction had lower stress values, this preparation results from a reduction that removes a greater amount of sound tissue, which may increase the probability of dental pulp injury. Conclusions: Occlusal reduction must be anatomic; however, when a flat occlusal reduction already exists, the substructure must reproduce the correct anatomic form to allow a uniform thickness of the veneering porcelain.

Tooth preparation is considered a fundamental step for the success of any tooth-borne fixed restoration.1-4 The amount of reduction reflects the choice of material for the planned restoration.5 Shillingburg et al6 proposed that metal ceramic crowns require 0.3 to 0.5 mm for metal areas of the alloy substructure and 0.7 to 1.2 mm for the veneering porcelain; however, Anusavice and Tsai7 and Anusavice and Hojjatie8 have shown that a metal thickness of 0.1 mm should be sufficient for anterior metal crowns. Deficiencies in the occlusal surface of the tooth preparation that have been caused by caries or previous restorations should be blocked out in the preparation or compensated for with extra thickness of the substructure in those areas to ensure a uniform

thickness of veneering porcelain.6 An excessively thick layer of veneering porcelain may result in a higher fracture incidence. Considering that any restoration has a risk of fracture, it is important to ensure that dental crowns have sufficient resistance to support occlusal loads and protect the tooth from fracture.9 Anusavice10 affirmed that metal-ceramic restorations based on a noble metal alloy substrate and a thermally compatible veneer ceramic can be considered the “gold-standard” because of their 97% success rate over 7 or more years of service. In addition, metal-ceramic restoration replacements that have exhibited porcelain fractures have totaled 3% of these restorations based on a 50-year review,11 8.7% after 18 years of full-crown use,12 and 5% to 10% over 10 years of service.13 Ceramic

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crowns used as a material of choice are expected to be as durable and clinically reliable as a metal-ceramic crown, particularly with regard to veneer chipping, core fracture, and marginal fit.14 Substructure design and stiffness influences the strength of metal-ceramic restorations.6 Most of the literature focuses on the ceramic thickness,15-17 the extension of the substructure in the cervical and buccal region of the restoration,18 and the analysis of different substructure materials.9,19-23 Other studies have focused only on analyses of ceramic crowns.24-27 Furthermore, most of the reported dental studies have been focused on analyses of anterior crowns and fixed partial dentures.8,28-32 Even though anterior and posterior teeth display similar mechanical and physical properties, their geometric and functional loading configurations must be distinguished.33 As tooth location proceeds anteriorly, the posterior segment of the occlusal table is gradually replaced by an incisal edge with a cutting function. This anatomic change completely alters the way occlusal loading is transferred to the tooth. Anusavice et al8,28 analyzed the stress distribution in anterior crowns with variable substructure configurations. A metal thickness of either 0.1 or 0.3 mm of Ni-Cr and Au-Pd alloy were investigated. They reported that the alloy type and substructure thickness have a negligibly small effect on the stress induced in porcelain. Proos et al26 examined the influence of ceramic substructure thickness on the maximum stresses that arise in a first premolar ceramic crown. They found that the peak tensile stresses in porcelain and in dentin decreased for an increase in core thickness. Rafferty et al27 evaluated by means of threedimensional (3D) finite element analyses (FEAs) the effects of different core thickness on the veneer layers of a ceramic crown’s maximum principal stress developed during simulated static loading of a molar tooth. No significant differences were observed for varying the thickness from 0.5 to 1 mm. Shirakura et al16 and Geminiani et al17 investigated the influence of incisal veneering porcelain thickness of metal ceramic systems on failure resistance after cyclic loading. Crowns with a porcelain incisal thickness of 2 mm showed greater fracture resistance than those with a 4 mm incisal thickness. Reports suggest that rational design of complex crown/tooth systems include various design parameters as well as their interactions.27 For manually produced restorations, the stress distribution is difficult to predict, as the substructure and the layer shapes and thicknesses of veneering porcelain are operator-dependent parameters; however, for computer-designed and computermanufactured prostheses, these parameters, as well as those of the preparation, are digitally controllable and more amenable to stress analysis and failure prediction.23 FEA is the optimal tool for the evaluation of stress states produced from external loading, and the resulting output can lead to reasonable predictions of the most likely fracture-initiation sites according to a specific restoration design and loading condition. Threedimensional FEA facilitates the investigation of complex structures, but requires more time for modeling, for refining mesh conditions, and for computing. Realistic models representing clinical details of complete crown tooth preparations are rare in the dental biomechanics field.24 Only in 3D models is it possible to study the influence of total volume and geometry of different types of crown designs and create more realistic situations when compared with two-dimensional (2D) FEA models. 2

Researchers must keep in mind that any study is a contribution, and that it is impossible to simulate all variables that exist in the oral cavity. Moreover, clinical studies are limited, as researchers cannot control all variables, and in most cases, they cannot confirm the true cause of failure. Sometimes it is difficult to obtain the correct dimension of occlusal reduction, and some specific methodologies have been described in the literature to create these space dimensions.5,34 However, in some cases a flat occlusal surface was prepared. Following Shillingburg et al’s recommendations,6 the prosthetic technician usually compensates for the flat occlusal reduction in the metal substructure; however, in some cases, dentists ask the technician to make the metal substructure without changes, with the ideal thickness and without any anatomic compensation to create a thick layer of veneering porcelain to obtain good esthetic results. Few FEA studies analyze the influence of the metal substructure design on stress distributions in metal-ceramic restorations. Using 2D FEA, Oyar et al35 reported that the maximum shear stress increased by approximately four times in the porcelain structure when a flat occlusal preparation was used. The authors concluded that less shear stress developed in the porcelain structure because of this design. The purpose of this study was to study the influence of changing the metal substructure configuration on the stress distribution within a metal-ceramic restoration on a premolar tooth with typical anatomic form as well as the design resulting from flatplane occlusal reduction. On the basis of these results, the stress state of each model submitted to simulated physiologic loading can be predicted. We hypothesize that the metal-ceramic restoration with an anatomically correct occlusal reduction and uniform thickness of the metal substructure and porcelain veneer will exhibit reduced values of tensile stress and that the stress will be more uniformly distributed within tooth structure.

Materials and methods A second premolar tooth was designed based on the dimensions and form of a natural tooth (approved by UFRJ Ethics Committee CEP/UFRJ, CAAE: 0713.0.000.197-05) using a 3DNURBS (nonuniform rational B-splines) modeling program R , version 3.0 Sr5b; Robert McNeel & Associates, (Rhinoceros Seattle, WA). This tooth was selected because it is located in the posterior region of the mouth, and it is typically treated with a metal-ceramic restoration.12 A tooth preparation was modeled by reducing the occlusal surface as follows: 1. Anatomic: Occlusal reduction of 2.0 mm following the anatomy of the cusps and ridges of the occlusal table (Fig 1). 2. Flat (nonanatomic): Flat reduction using the midline fissure as a reference to obtain a 2.0 mm reduction (Fig 2). The following parameters for the full crown preparation design were assumed: 1. Convergence of 12◦ between the buccal and lingual walls as well as between the mesial and distal walls.

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Figure 1 (A) Schematic illustration of the full crown preparation of a premolar tooth. (B) Photo of the natural tooth design.

1.5 mm thickness of feldspathic porcelain in all areas of the restoration (Fig 3C).

Figure 2 Flat occlusal reduction of a premolar tooth.

2. A 0.5-mm-deep reduction at the chamfer margin with an angle of 120◦ . 3. All angles were rounded. The metal-ceramic restorations were designed to occupy the space between the external surfaces of the original tooth and the prepared tooth design. The material references for properties and thickness used for the restoraR 99; Bego USA, tions were nickel-chromium alloy (Wiron Lincoln, RI), feldspathic porcelain (Vita Zahnfabrik, Bad S¨ackingen, Germany), and zinc-phosphate luting agent (SS White, Rio de Janeiro, Brazil). The luting agent was assigned a 100 μm thickness. The periodontal ligament, cortical bone, and cancellous bone were not included in the model.20,36-38 Three restoration models were created: 1. Anatomic design (AD): Uniform 0.3-mm-thick alloy with a 1.5 mm thickness of feldspathic porcelain (Fig 3A). 2. Flat occlusal reduction (Flat): Uniform 0.3-mm-thick alloy and variable thicknesses of feldspathic porcelain depending on the region (Fig 3B). 3. Flat occlusal reduction with alloy compensation (FlatC): Alloy with variable thicknesses to permit a uniform

R software, that is, each part Solids generated by Rhinoceros of metal-ceramic restoration (metal alloy substructure and veneering porcelain), luting agent, and dentin, were exported to the MSC.Patran software (MSC.Software Corporation, Santa Ana, CA) to generate a quadratic hexahedron mesh (C3D20). The total number of elements for the models ranged from ∼53,600 to 58,500 depending on the type of dental reduction and the restoration design. Each meshed part was individually exported for FEA using ABAQUS software (ABAQUS CAE 6.5 version; Hibbit Inc., Providence, RI). All structural components were assumed to be homogenous, isotropic, and free of defects, with a perfectly bonded interface between components. Their elastic properties (modulus of elasticity and Poisson’s ratios) are listed in Table 1.37,40 The encastre was positioned on the radicular region of the dentin 1.5 mm below the most cervical cement-tooth preparation boundary, which represents the usual location of the crestal bone (the highest position of compact bone), and constrained in all six degrees of freedom. Compressive loads of 100 N were applied within a 0.5 mm2 area, which is based on an average contact area as described by Okeson.41 Loads were applied simultaneously to both cusps to simulate physiologic loads during occlusion (Fig 4). The most relevant stress distribution criterion was based on the fracture prediction potential of the materials.31 The tensile strengths of dental ceramics are often an order of magnitude lower than their compressive strengths.9,27 Failure of the metal core is more likely associated with yielding, during which the ductile material (contrasted with ceramics) plastically deforms before ultimate failure occurs.19,21,22,31 Both yielding and ultimate failure are undesirable for the crown under typical masticatory loading. The material will fail when the equivalent von Mises stress exceeds the tensile strength of the material.21 Results from the 3D FEAs will be represented by figures that exhibit maximum tensile stress and the von Mises criterion effects.

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Figure 3 (A) Schematic cross-section of the anatomic design (AD) model. (B) Schematic cross-section of the flat occlusal reduction (Flat) model. (C) Schematic cross-section of the flat occlusal reduction with alloy compensation (Flat-C) model. Table 1 Mechanical properties of each structure

Mechanical properties Material

Elasticity modulus (E) (GPa)

Poisson’s ratio (ν)

18.6

0.31

2.1 × 10–3 68.9

0.45 0.28

Substructure (Ni-Cr)37,39,40

205

0.33

Zinc phosphate cement38-40

137

0.35

Dentin37,39,40

Pulp39,40 Veneering porcelain39,40

Results The Flat-C model exhibited lower maximum principal tensile stresses than the other two models, rejecting the null hypothesis that the AD model would exhibit less tensile stress. Maximum tensile stresses were 166 MPa for the Flat-C model, 365 MPa for the AD model, and 450 MPa for the Flat model. The maximum compressive stresses were 71 MPa, 129 MPa, and 82 MPa, respectively (Figs 5–7). All models revealed similar aspects: 1. The highest compressive stresses (negative values) were found in the region of the load application area. 2. The highest tensile stresses (positive values) were located at the midline fissure (mesiodistal groove). 3. Compressive stresses only resulted in the radicular region when loads were distributed on buccal and lingual cusps. 4. Tensile stress concentrations were located immediately below the midline fissure in both veneering porcelain and the metal alloy substructure. 5. High tensile stress was also located in the cervical region of the chamfer margin for both the dentin and luting agent. In the ceramic components of the models, tensile stresses were higher in the Flat model and lowest in the Flat-C model. In the luting agent region, the highest tensile stresses averaged 72 MPa, with values ranging from 20 MPa in the Flat-C 4

Failure strength (MPa) T: tension C: Compression YS: Yield strength 6025 48(T)8 165(C)8 – 34 to 69(T)8,19,20,25 340(C)8 700(T)28 690 (YS) 4.8 to 6.2(T)8 69 to 117(C)8

model, to 53 MPa in the Flat model, to 129 MPa in the AD model. The same behavior was found in dentin for these models. The models with flat occlusal reduction presented similar stress distributions and lower stresses when compared with the AD model; however, all models exhibited tensile stress in the cervical and distal regions. The metal alloy substructure was analyzed by the von Mises criterion. The AD model exhibited the highest stresses in several regions; however, all models exhibited stress concentrations mainly in the inner region of the substructure and in the distal side of the cervical region. In the AD and Flat-C models, significant stress concentrations resulted in the middle fissure, which was not found in the Flat model, probably because of the anatomy, since both cusps were lower than in the other two models (Figs 8–10).

Discussion This study investigated the effect of changing the metal substructure design on the stress distribution within a metalceramic restoration. The hypothesis that the MC restoration with anatomical occlusal reduction with uniform thickness of the metal substructure and the ceramic veneer (AD) would exhibit lower stress values and uniform stress distributions in all tooth structures was rejected. Results have shown that the model with the flat occlusal reduction and alloy compensation (Flat-C) exhibited the lowest levels of maximum tensile stress (166 MPa), followed by the AD model (365 MPa) and the Flat

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Figure 4 Boundary conditions applied in a 3D model—orange color. Arrows on the occlusal surface point to the region where the simulated physiologic loads were applied.

model (450 MPa) (Fig 5). Other studies also revealed that flat occlusal reductions yield more favorable stress distributions. Oyar et al35 found that a flat occlusal preparation design resulted in a more uniform stress distribution and less stress in porcelain. El-Ebrashi et al42 reported that the stress concentra-

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tion factor for a flat reduction of cusps was 40% less than that for anatomic reduction of the cusps because of the increase in the thickness of the restoration. In this study, the Flat-C model presented lower stress levels in the ceramic veneer (Fig 6). We suggest that this design is less likely to cause fracture of the ceramics than the other models. This is in agreement with Rosenstiel et al43 and Shillingburg et al6 who hypothesized that to prevent fracture, deficiencies in the occlusal surface of the tooth preparation could be compensated by an extra thickness of the substructure in those areas. It has been suggested that porcelain should be kept to a minimum thickness compatible with esthetic requirements and that relatively thin porcelain of uniform thickness supported by a rigid substructure is very “strong.”23 Proos et al26 also found that the tensile stresses in the substructure were significantly sensitive to a substructure thickness change. They reported that by increasing the substructure thickness by 100% (from 0.3 to 0.6 mm), the highest peak tensile stresses in the substructure, porcelain, and dentin decreased by 23%, 42%, and 3%, respectively. By increasing the substructure thickness another 50% (from 0.6 to 0.9 mm), the stresses decreased by another 15%, 49%, and 0%, respectively. Anusavice and Hojjatie8 found that the tensile stress in porcelain (at the porcelain margin) increased by 14% for a decrease in Ni-Cr core thickness from 0.3 to 0.1 mm. In

Figure 5 Stress distribution (MPa) in the model (A) with anatomic design (AD), (B) with flat occlusal reduction (Flat), and (C) with flat occlusal reduction with alloy compensation (Flat-C).

Figure 6 Stress distribution (MPa) in the veneering porcelain for the model (A) with anatomic design (AD), (B) with flat occlusal reduction (Flat), and (C) with flat occlusal reduction with alloy compensation (Flat-C).

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Figure 7 Stress distribution (MPa) in the luting agent for the model (A) with anatomic design (AD), (B) with flat occlusal reduction (Flat), and (C) with flat occlusal reduction with alloy compensation (Flat-C).

Figure 8 Von Mises stress (MPa) in the anatomic design (AD) model.

Figure 9 Von Mises stress (MPa) in the flat occlusal reduction with alloy compensation (Flat-C) model.

Figure 10 Von Mises stress (MPa) in the flat occlusal reduction (Flat) model.

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a laboratory study, using cyclic loading tests, Geminiani et al17 investigated the influence of incisal veneering porcelain thickness of metal ceramic systems on fracture resistance. Crowns with a porcelain incisal thickness of 2 mm showed a greater success rate for both metal-ceramic systems than for those with a 4 mm incisal thickness. Shirakura et al16 reported similar results. They concluded that metal-ceramic crowns with a 2 mm porcelain thickness showed a significantly greater fracture load than crowns with a 4 mm porcelain thickness (p = 0.004) after cyclic loading. One factor that may also contribute to porcelain fracture when there is an increase in the volume is that during the manufacturing of a crown, some voids and cracks are created in the bulk of the restorations during porcelain condensation and firing. When the volume of porcelain increases, the numbers of defects also increase, and the material’s fracture resistance decreases. Evans et al44 stated that small defects in a solid act as sharp notches. The stress at the tip of the notch can reach the fracture resistance of the material, and failure may occur, even when the solid is subjected to relatively low average stresses. Another finding of this study was that all models presented high tensile stress at the middle fissures in the ceramic (Fig 6). The Flat-C and AD models also exhibited increased stresses in the corresponding region at the interface between the ceramic and alloy substructure, but this was not found in the Flat model without a fissure. Similar results were reported in the middle fissure region by El-Ebrashi et al42 using photoelastic stress analyses and by Proos et al26 using 2D FE analyses. The deep middle fissure and their sharp tips act as stress concentrators that can initiate cracks. The authors agree with the suggestion of El-Ebrashi et al42 that a gradual and smooth middle fissure is recommended in crown design to ensure a more favorable stress distribution and minimize the risk for fractures in this region of the crown. Considering the cervical region, the two models with flat occlusal reduction exhibited a tendency to increase tensile stress, which varied from –5 to –10 MPa, with the greatest value in the buccal face region. In the AD model, the stress value was close to zero. These results are consistent with results from natural teeth studies associated with abfraction lesions.45-48 Oyar et al35 suggested that high cyclic stresses in restorations with a low modulus of elasticity could cause abfraction lesions at the crown margins adjacent to the dentin tissue. Restored teeth are also susceptible to abfraction lesions or crack formation in the cervical regions, as they are also submitted to the same loading conditions as natural teeth. The difference is that the visualization of the lesion is more difficult when a full crown is present, because the lesion is located below the gingival margin. The maximum von Mises stresses found in this study for the metal substructure were 325 MPa for the AD model (Fig 8), 213 MPa for the Flat-C model (Fig 9), and 299 MPa for the Flat model (Fig 10); however, the values were lower than the 690 MPa yield strength of Ni-Cr alloy. We can conclude that, at an applied normal load of 100 N, yielding of the metal does not occur. Although the prospect of this happening for the given load is small, it is important to keep in mind that such a phenomenon cannot be excluded for metal-ceramic crowns,

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and metal substructure may cause failure as a result of fatigue,19 especially when greater loads are applied. All three models presented the highest compressive stresses in the region of loading contact at the occlusal surface (Fig 6). This behavior is sustained by the Hertzian contact stress theory, which suggests that localized compression can cause conecracks clinically just below the contact surface or below this region, depending on the local stress distribution.49 Thompson et al50 and Wakabayashi and Anusavice51 stated that internal surface cracks probably are the most common cause of crown fractures. Rekow et al52 confirmed that stresses are usually high below the area of loading, and that the orientation of the applied load significantly alters the capacity of crowns to support these greater tensile stresses. In vitro studies are less time consuming and less costly than in vivo studies. Even though in vitro studies are limited because they do not completely mimic the clinical environment and distribution of load,17 such tests do provide criteria for further clinical evaluation. Mechanical simulation of restorative systems can be a useful tool for researchers attempting to develop restorative system designs, since it allows the simulation of the interplay between variables and their influence in the system’s biomechanics.24 Campos et al9 affirm that FEA can provide valuable insights for predicting the relative fracture risks of different materials and designs used in clinical practice because the predicted stress distribution patterns are not affected by microscopic defects. Besides, the extent and location of stress concentrations can be predicted. This is of particular importance when stress concentrations exist in areas where damage may have been introduced during fabrication and/or laboratory and clinical procedures.24 The decision as to whether to employ 2D or 3D FEA depends on many interrelated factors including the complexity of the geometry, the purpose of the analysis, and the accuracy required of the results.53 Three-dimensional FE models can capture the geometry of complex structures more fully, but sometimes the complexity of 3D FE models often makes it impossible to achieve the same mesh refinement and numerical accuracy as in 2D models.31,53 The advantages of employing 3D FEA must be weighed against the difficulties in modeling and preparing such models for mesh generation analyses.53 This FEA study provided some insights about tooth preparation. Low tensile stress in the veneering porcelain is obtained when this material is designed with minimum thickness and of a uniform layer thickness. For a flat occlusal reduction, the substructure must compensate with the correct form of occlusal morphology. Finally, the anatomy of the restoration must prevent acute angles in the occlusal grooves to minimize stress concentration.

Conclusions Within the limitations of this 3D FEA, it may be concluded that changes in the occlusal reduction and type of restoration design significantly influence the stress distribution in metalceramic crowns and the adjacent tooth structure. When there is a flat occlusal reduction, changes in the anatomy of metal substructure must be performed to reproduce occlusal planes

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and allow a uniform thickness of veneering porcelain. The resulting stresses will be reduced and distributed more uniformly with reduced stress concentrations. Although these models exhibit lower stresses overall, flat reduction represents the removal of more tooth structure with a higher risk for dental pulp injury. Therefore, occlusal preparation design must be anatomically prepared to minimize this risk. In addition, the middle fissure anatomy should be gradual and smooth for the metal substructure and the veneering ceramic to minimize stress concentrations in this area.

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Influence of substructure design and occlusal reduction on the stress distribution in metal ceramic complete crowns: 3D finite element analysis.

Occlusal reduction is considered a fundamental step for providing adequate and uniform space for the ceramic prosthesis; however, a flat occlusal surf...
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