Amine Fluoride Research Articles

Evaluation of antibacterial and antifungal properties of selected mouthwashes: in vitro studies

Abstract Introduction. Mouthwashes should include antimicrobial compounds to inhibit microorganism multiplication, thus the formation and development of dental plaque. Aim. The aim of the study was to evaluate the antibacterial and antifungal effectiveness of mouthwashes depending on their active ingredients. Material and methods. In the study, the effect of antibacterial and antifungal properties of mouthwashes on reference bacterial and yeast-like fungi strains was examined. The first type of the assessed mouthwashes contained only sodium fluoride or sodium fluoride and amine fluoride as active ingredients, while the second type contained sodium fluoride and cetylpyridinium chloride. In the study, a well diffusion method was used to test microorganisms constituting natural or pathogenic microflora of oral mucosa. The used reference microorganisms came from the ATCC: L. acidophilus ATCC 4356, Lactobacillus rhamnosus ATCC 53103, S. mutans ATCC 25175, and Candida yeasts: C. albicans ATCC 2091, C. albicans ATCC 10231, Candida parapsilosis ATCC 22019, Candida glabrata ATCC 90030, Candida krusei ATCC 14243. Results. The mouthwashes containing sodium fluoride and cetylpyridinium chloride showed an inhibitory effect against a greater number of reference strains used in the study than did mouthwashes that contained only sodium fluoride (or sodium fluoride and amine fluoride) as active ingredients. Against the four reference strains of Candida genus, the mouthwashes with an inorganic and organic fluoride compound showed no or minimum inhibitory effect or were much less effective than the mouthwashes that also contained cetylpyridinium chloride. Conclusion. Mouthwashes containing multiple ingredients with different antimicrobial mechanisms show synergistic action against the bacterial and fungal microflora responsible for the accumulation of dental plague.

The influence of biofilm maturation on fluoride's anticaries efficacy.

(1) To explore the influence of biofilm maturation and timing of exposure on fluoride anticaries efficacy and (2) to explore biofilm recovery post-treatment. Bovine enamel specimens were utilized in a pH cycling model (28 subgroups [n = 18]). Each subgroup received different treatments [exposure]: sodium fluoride [NaF]; stannous fluoride [SnF2]; amine fluoride [AmF]; and de-ionized water [DIW], at a specific period: early: days 1-4; middle: days 3-6; and late: days 7-10. During non-exposure periods, pH cycling included DIW instead of fluorides. Objective 1: part 1 (cycling for 4, 6, or 10days). Part 2 (cycling for 10days). Objective 2: early exposure: three sample collection time points (immediate, 3days, and 6days post-treatment); middle exposure: two sample collection time points (immediate, 4days post-treatment). The enamel and biofilm were analyzed ([surface microhardness; mineral loss; lesion depth]; [lactate dehydrogenase enzyme activity; exopolysaccharide amount; viability]). Data were analyzed using ANOVA (p = 0.05). Objective 1: Early exposure to fluorides produced protective effects against lesion progression in surface microhardness and mineral loss, but not for lesion depth. Objective 2: Early exposure slowed the demineralization process. SnF2 and AmF were superior to NaF in reducing LDH and EPS values, regardless of exposure time. They also prevented biofilm recovery. Earlier exposure to SnF2 and AmF may result in less tolerant biofilm. Early fluoride treatment may produce a protective effect against demineralization. SnF2 and AmF may be the choice to treat older biofilm and prevent biofilm recovery. The study provides an understanding of biofilm-fluoride interaction with mature biofilm (e.g., hard-to-reach areas, orthodontic patients) and fluoride's sustainable effect hours/days after brushing.

The Effectiveness Of Amine Fluoride Mouthwash In Preventing White Spot Lesions During Fixed Orthodontic Therapy: A Randomized Control Trial

The Effectiveness Of Amine Fluoride Mouthwash In Preventing White Spot Lesions During Fixed Orthodontic Therapy: A Randomized Control Trial

Efficacy of Experimental Mouth Rinses on Caries-Related Biofilms in vitro.

This study assessed the efficacy of tin and Polyethylenglycol (PEG-3) tallow aminopropylamine in different concentrations on Streptococcus mutans (S. mutans) biofilms to establish a new screening process for different antimicrobial agents and to gain more information on the antibacterial effects of these agents on cariogenic biofilms. Isothermal microcalorimetry (IMC) was used to determine differences in two growth parameters: lag time and growth rate; additionally, reduction in active biofilms was calculated. Experimental mouth rinses with 400 and 800 ppm tin derived from stannous fluoride (SnF2) revealed results (43.4 and 49.9% active biofilm reduction, respectively) similar to meridol mouth rinse (400 ppm tin combined with 1,567 ppm PEG-3 tallow aminopropylamine; 55.3% active biofilm reduction) (p > 0.05), while no growth of S. mutans biofilms was detected during 72 h for samples treated with an experimental rinse containing 1,600 ppm tin (100% active biofilm reduction). Only the highest concentration (12,536 ppm) of rinses containing PEG-3 tallow aminopropylamine derived from amine fluoride (AmF) revealed comparable results to meridol (57.5% reduction in active biofilm). Lower concentrations of PEG-3 tallow aminopropylamine showed reductions of 16.9% for 3,134 ppm and 33.5% for 6,268 ppm. Maximum growth rate was significantly lower for all the samples containing SnF2 than for the samples containing control biofilms (p < 0.05); no differences were found between the control and all the PEG-3 tallow aminopropylamine (p > 0.05). The growth parameters showed high reproducibility rates within the treated groups of biofilms and for the controls; thus, the screening method provided reliable results.

Evaluation of the efficacy of a dentifrice containing amine fluoride on gingival status - a clinical investigation

Evaluation of the efficacy of a dentifrice containing amine fluoride on gingival status - a clinical investigation

Knowledge, Attitudes, And Practices Of Pediatric Dentists Towards Silver Di Amine Fluoride

Silver diamine fluoride (SDF) is topically applied to treat tooth hypersensitivity (label indication). Considerable literature exists on the safety of SDF as used to treat cavitated lesions. While the evidence supporting the use of SDF is overwhelming, to the best of our knowledge, dentists&rsquo; usage is not commensurate. Learning experiences of the dentist, commercial availability, and type of clinical practice, are some of the factors that may have a bearing on the adoption of SDF in clinica

Combined effects of a topical fluoride treatment and 445 nm laser irradiation of enamel against a demineralization challenge: A light and electron microscopic ex vivo study.

This study investigated the caries-preventive effect of 445 nm laser radiation in combination with fluoride on the prevention of white spot lesions. Previously, several studies have indicated the ability of 488 nm argon ion laser irradiation to reduce early enamel demineralization. A diode laser (445 nm) could be an alternative technology for possible caries-preventive potential. Each sample of a group of seventeen caries-free bovine teeth was treated in four different ways on four different zones of the labial surface: control/no treatment (C), laser irradiation only (L) (0.3 W, 60 s and applied dose of 90 J/cm2), amine fluoride application only (10,000 ppm and pH 3.9) (F), and amine fluoride application followed by laser irradiation (FL). After treatment, the teeth were subjected to a demineralization solution (pH 4.3 for 48 h at 37 °C) to induce subsurface lesions. After sectioning, the teeth were examined by light microscopy. Three teeth were analyzed by scanning electron microscopy (SEM). The depths of the subsurface lesions in the C, L, F, and FL groups were 103.01 (± 13.04), 96.99 (± 14.51), 42.59 (± 17.13), and 24.35 (± 11.38) μm, respectively. The pairwise group comparison showed the following results: p < 0.001 for FL versus C, FL versus L, F versus C, and F versus L, p = 0.019 for FL versus F and p = 0.930 for L versus C. The SEM micrographs support the light-microscopic examination. The results of the current study have shown that using relatively low irradiation settings of 445 nm laser on fluoridated enamel may be effective for prevention of white spot lesions.

Comparison of Fluoride Ion Release from Fluoride Gel in Various Solvents.

ObjectiveThe aim of this study was to determine the concentration of fluoride ions present in various solvent solutions and compare it to the label amount of fluoride concentration.Material and methodsThe gel containing amine fluoride and sodium fluoride was compared to gel containing sodium fluoride only. The solvents used in this study were distilled water, redistilled water, tap water, 0.9% sodium chloride solution and the artificial saliva. The amount of fluoride ion (F-) was determined by the use of fluoride ion-selective electrode. The ANOVA and the Post hoc Tukey’s test were used. The significance level was α = 5%.ResultsThe differences between F- ion release in various solvents were statistically significant (p < 0.05). The F- ion concentrations measured in both gels’ redistilled water solutions were higher than the label concentration. There was a significant difference in fluoride ion release in sodium fluoride only gel solutions. Fluoride ion release was significantly different in combined fluoride gel solutions.ConclusionsAmine fluorides do not interact with other ions present in the solution, whereas F- ion release from sodium fluoride alters when other ions are dissolved in the same solution. Amine fluorides deliver F- ions for caries prevention more efficiently.

Comparative efficacy of a hydroxyapatite and a fluoride toothpaste for prevention and remineralization of dental caries in children

ObjectiveThis in situ study compared the effectiveness of two toothpastes containing hydroxyapatite or 500 ppm fluoride in promoting remineralization and inhibiting caries development.Materials and methodsTwo enamel blocks (human primary teeth), one sound and one with artificially-produced caries lesion, were exposed to toothpaste containing either 10% hydroxyapatite or 500 ppm F− (amine fluoride) via intra-oral appliance worn by 30 adults in two-arm double blind randomized crossover study lasting 14 days per arm (ClinicalTrials.gov: NCT03681340). Baseline and post-test mineral loss and lesion depth (LD) were quantified using microradiography. One-sided t-test of one group mean was used for intragroup comparison (baseline vs. post-test), while two-sided t-test of two independent means was used to compare the two toothpaste groups.ResultsPairwise comparison (baseline vs. test) indicated significant (p < 0.0001) remineralization and LD reduction by either toothpaste; however, when compared against each other, there was no statistically significant difference in remineralization or LD reduction between the two toothpastes. No demineralization could be observed in sound enamel blocks exposed to either toothpaste. While F− induced lesion surface lamination, HAP produced a more homogenous lesion remineralization.Conclusions10% hydroxyapatite achieved comparable efficacy with 500 ppm F− in remineralizing initial caries and preventing demineralization. Thus the HAP toothpaste is confirmed to be equal to the fluoride toothpaste in this study.

Effectiveness of antimicrobial gels on gingivitis during fixed orthodontic treatment: A systematic review and meta-analysis

The present study was aimed to assess the effectiveness of antimicrobial gels along with conventional tooth brushing to improve gingival health in patients undergoing fixed orthodontic treatment. All randomized and non-randomized clinical trials done on human subjects were explored in major health science databases (PubMed, CINAHL Plus, EBSCO Dent & Oral Sciences and Cochrane). An additional manual search was done on Google Scholar and on www.clinicaltrials.gov to identify any grey literature and unpublished data. Date of publication was not restricted during the data search. The assessment of risk of bias was done using the Cochrane Collaboration's Risk of Bias assessment tool. The meta-analysis was done using Review Manager Version 5.3.5 to analyse probing depth to be in two and four-week follow-up. This systematic review is reported according to the PRISMA statement and registered at PROSPERO (CRD42018084530). The electronic database search yielded 3733 records; hand search identified 14 articles meeting the selection criteria which were included in the qualitative data synthesis. Significant improvement in gingivitis has been reported using antioxidant-essential oil gel, cervitec gel (0.2% chlorhexidine), 2% chlorhexidine gel, amine fluoride gel, and 0.4% stannous fluoride gel with>98% availability of Sn+2 ions. Three articles with probing depth as comparable parameter were used for quantitative analysis. At the two and four-week follow-up, overall insignificant differences were observed in the antimicrobial gel group compared to the control group with regard to probing depth. The use of antioxidant-essential oil gel, amine fluoride gel, 0.4% stannous fluoride gel (98% availability of Sn+2) and 2% chlorhexidine gel resulted in significant improvement in gingivitis. However, probing depth in follow-up visits showed no significant difference between antimicrobial gel and control group.

Evaluation of free and total fluoride concentration in mouthwashes via measurement with ion-selective electrode

BackgroundThe aim of this study was to compare free fluoride concentration and total fluoride concentration in mouthwashes.MethodsFluorine-containing mouthwashes from various companies and manufacturers (Colgate Total Plax Classic Mint®, Colgate-Palmolive, New York, USA; Colgate Total Plax Gentle Mint®, Colgate-Palmolive, New York, USA; Colgate Total Plax Fresh Mint®, Colgate-Palmolive, New York, USA; Oral B Advantage®, Procter&Gamble, Cincinnati, USA; Reach Fresh Mint®, Johnson&Johnson, New Brunswick, USA; Foramen®, Laboratorios Foramen, Guarnizo, Spain; Lacalut Sensitive®, Dr. THEISS, Homburg, Germany; Sensodyne®, GlaxoSmithKline, London, UK; Vesna F®, Vita, Saint Petersburg, Russia; Lacalut Fresh®, Dr. THEISS, Homburg, Germany) were selected as study objects. Fluoride measurements were carried out using the fluoride selective electrode.ResultsFree fluoride:total fluoride ratio was more than 80% for six samples (Colgate Total Plax Gentle Mint® - 88%, Colgate Total Plax Fresh Mint® - 99%, Oral B Advantage® - 92%, Reach Fresh Mint® - 92 and 89% for the mouthwash of another batch, Lacalut Sensitive® - 94%) and less than 63% for three samples (Colgate Total Plax Classic Mint® - 56%, Foramen® - 62%, Vesna F® - 61%). Two samples had more than 70% and less than 80% of unbound fluoride, respectively (Sensodyne® - 77%, another batch of Oral B Advantage® mouthwash - 74%). Rinse containing sodium monofluorophosphate (Na2PO3F) (Vesna F®) had more than 50% of free fluoride, while the rinse containing amine fluoride (AmF) (Lacalut Sensitive®) had 94%. The difference in the free fluoride:total fluoride ratio can be explained by binding of fluoride ions by components contained in mouthwashes, such as coloring agents and polymeric compounds. The lowest concentration of free fluoride ions (0.000093 mol/L) was observed for aluminum fluoride (AlF3) rinse (Lacalut Fresh®), while the total fluoride amount was not determined due to possible generation of strong fluoride complexes. This implies that fluoride ions will not be uptaken by tooth tissue and may even be washed away from it, compromising the efficacy of mouthwashes.ConclusionsThe differences in free fluoride: total fluoride ratio between analyzed mouthwashes reveal a need to develop a method for evaluation of free fluorides in mouthwashes for proper updating of national and international guidelines.

Fluorides for preventing early tooth decay (demineralised lesions) during fixed brace treatment.

Fluorides for preventing early tooth decay (demineralised lesions) during fixed brace treatment.

Fluoride levels in supernatant and sedimentary saliva are probably lower when using a fluoride bioactive glass dentifrice than an amine fluoride dentifrice after 2 hours

Fluoride levels in supernatant and sedimentary saliva are probably lower when using a fluoride bioactive glass dentifrice than an amine fluoride dentifrice after 2 hours

Effectiveness of Theobromine on Enamel Remineralization: A Comparative In-vitro Study

BackgroundRemineralizing agents demonstrate potential to reverse early carious lesions. Theobromine containing dentifrices claim to remineralize enamel lesions effectively. The aim of this in-vitro study was to evaluate and compare the remineralization potential of dentifrices containing theobromine, 0.21% sodium fluoride (NaF) with functionalized tricalcium phosphate (f-TCP) and amine fluoride on artificial enamel caries.Materials and methodsSound extracted human premolars were demineralized to produce deep artificial carious lesions. The teeth were sectioned longitudinally and allocated to three treatment groups with nine specimens in each group: Group A (NaF + f-TCP), Group B (amine fluoride), and Group C (theobromine). The specimens were then subjected to pH cycling for seven days. Confocal laser scanning microscopy (CLSM) was utilized to record the patterns of demineralization and remineralization. One-way ANOVA and paired t-test were used to analyze changes in lesion depth. The level of significance was set at p<0.05.ResultsAll three dentifrices effectively remineralized artificial carious lesions (paired t-test, p<0.001). Of the groups, Group A (54.97%) reported the highest percentage change in lesion depth values followed closely by Group B (51.51%) and Group C (31.71%), respectively.ConclusionWithin this in-vitro study, theobromine containing dentifrice was effective in remineralizing lesions of enamel. However, theobromine demonstrated less remineralization potential in comparison to dentifrices containing NaF + f-(TCP) and amine fluoride.

Dentifrice Based on Fluoride-Hydrotalcite Compounds: Characterization and Release Capacity Evaluation by Novel In Vitro Methods.

Anti-caries activity of fluoride ions is due to the protection against demineralization and the enhancement of remineralization of tooth enamel. Dentifrices available on the market contain sodium fluoride, sodium monofluorophosphate, stannous fluoride, and amine fluoride as source of these ions. A new compound working both as fluoride ion source and as abrasive was projected. Hybrids based on F- ions intercalated between the lamellae of hydrotalcite-like compounds (HTlc-F), namely MgAl-HTlc-F and ZnAl-HTlc-F, were prepared and characterized. Then, three different percentages (2, 3, and 4%) of both HTlc-F compounds were assayed. After the rheological characterization, the dentifrices containing 3 and 4% of MgAl-HTlc-F and ZnAl-HTlc-F, respectively, resulted to be the most suitable ones. Two novel in vitro methods, "rotary toothbrush method" and "manual brushing method," were developed and used in order to study the F- ions release from the prepared dentifrices. The obtained results showed that the dentifrice containing ZnAl-HTlc-F (4%) was the most effective in releasing fluoride ions. The "rotary toothbrush method" resulted to be the most suitable as the simulation of the brushing movements is standardizable and reproducible.

Remineralization of Artificial Dentin Caries Using Dentin and Enamel Matrix Proteins.

To assess the remineralizing potential of dentin matrix proteins and enamel matrix derivatives (DMPs and EMDs) after application on artificially induced dentin lesions, given the hypothesis that these materials increase the mineral uptake, binding, and mineralization. Forty-eight caries-free human premolars were used. Teeth were cut, polished, and embedded, leaving an open window on the root surface, of which one-third was covered with a flowable composite to preserve the healthy untreated dentin. Then, samples were demineralized in Buskes solution for 33 days. A micro-CT scan prior to treatment was performed. Next, the samples were randomly allocated into four groups: (A) An untreated negative control (CON), (B) application of porcine dentin matrix proteins (DMP), (C) treatment with enamel matrix derivatives (EMD, Emdogain, Straumann), and (D) amine fluoride application (AMF, Elmex fluid, GABA). All samples were placed in artificial saliva for 21 days. A second micro-CT scan was performed, after which the change in gray scaling within a defined region of interest (0.25 mm3) was analyzed. ANCOVA was applied to discover statistical differences between the different treatments. Both, treatment with AMF; (P = 0.011 versus CON) as well as with DMP (P = 0.043 versus CON) yielded a statistically significant difference compared to the control treatment. EMD treatment was not found to differ (P > 0.05). Mainly the top layer of the defects showed clear signs of remineralization, which was also evident in CON. This study was able to visually confirm the remineralization potential of demineralized dentin especially after DMP application, which, however, did not outperform AMF. Based on this, additional studies combining proteins and fluorides are now warranted and ongoing.

Randomized investigation of the bioavailability of fluoride in saliva after administration of sodium fluoride, amine fluoride and fluoride containing bioactive glass dentifrices

ObjectivesBioactive glasses which degrade in aqueous solutions may release bioactive ions such as fluoride (F-) and support fluoride bioavailability in saliva. We investigated how these effects would be apparent in an in vivo experimental trial after toothbrushing in comparison with sodium fluoride and amine fluoride.Material and methodsIn this single-center, randomized, parallel in vivo trial with a three strata block design, where healthy subjects were randomly assigned into three groups. Each group brushed their teeth either with fluoridated bioactive glass containing dentifrice, with a sodium fluoride (NaF) containing dentifrice or with amine fluoride (AmF) containing toothpaste. Saliva was collected time intervals before, immediately after, 30, 60 and 120 min after toothbrushing. Fluoride concentration was determined in supernatant saliva and salivary sediment using a fluoride ion selective electrode. The data were evaluated statistically using non-parametric tests.ResultsThe increase of bioactive fluoride in supernatant saliva was higher after application of NaF or AmF compared to fluoridated bioactive glass. In salivary sediment bioavailability of fluoride lasted longer after application of fluoridated bioactive glass.ConclusionsToothbrushing with the fluoride containing bioactive glass dentifrices had positive effects on the fluoride bioavailability within two hours. Fluoride containing bioactive glass represent a new area for investigation in caries prophylaxis. The bioactive potential impact on the tooth remineralization should be examined further.Trial registrationDRKS00016038.

Clinical effect of stannous fluoride and amine fluoride containing oral hygiene products: A 4-year randomized controlled pilot study

This 4-year randomized controlled trial (RCT) aimed at investigating whether routine home use of both a SnCl2/AmF/NaF-containing mouth rinse and toothpaste has a preventive effect on oral health. Fifty-four test subjects were examined in biannual intervals. The primary endpoint “dental erosion” was determined by the Basic Erosive Wear Examination (BEWE). The secondary endpoints were “saliva pH”, “dentin hypersensitivity” generated by Visual Analogue Scale (VAS), and “discoloration” measured by the Lobene Stain Index (LSI). A mixed model for repeated measures (MMRM) was used to analyze the primary endpoint “dental erosion”. Primary analysis showed a significant intervention effect of the SnCl2/AmF/NaF-containing test product (p1 = 0.0242). This result was confirmed by two additional MMRM-based sensitivity analyses. Comparison of all models showed “dental erosion” values of the intervention group below values of the control group. Discoloration of the teeth was significantly higher in the intervention than in the control group at all time points. Saliva pH and dentin hypersensitivity were not significantly different between groups over four years. In summary, this RCT is the first to indicate a possible preventive effect of SnCl2/AmF/NaF-containing oral hygiene products on dental erosion over a follow-up period of four years.

Effect of toothpaste containing amine fluoride and stannous chloride on the reduction of dental plaque and gingival inflammation. A randomized controlled 12-week home-use study.

This single-centre, controlled, randomized, double-blinded clinical study in parallel groups was performed to assess the efficacy of an experimental toothpaste on plaque and gingivitis. In adult subjects with gingivitis, amine fluoride/stannous chloride toothpaste (test) and monofluorophosphate toothpaste (control) were applied twice daily by regular toothbrushing at home. Evaluations of plaque index (PI), gingival index (GI), modified sulcus bleeding index (mSBI) and safety took place at baseline and after 3 and 12weeks of study product use. After study completion, all subjects received a dental prophylaxis. A descriptive statistical analysis included means and standard deviations. Unpaired t tests compared index reductions between groups at a significance level of 0.05. Intention-to-treat analysis included 240 out of 241 subjects. Baseline mean PI was reduced by 0.87±0.35 in the test group and by 0.65±0.41 in the control group. Within-group differences and between-group differences in index reduction were statistically significant (P < 0.001). Mean GI and mSBI were reduced significantly over time (P<0.001) with no clinically meaningful differences between groups. Both toothpastes reduced plaque and gingivitis statistically significant and clinically meaningful over 12weeks. Compared to the control toothpaste, application of the amine fluoride/stannous chloride toothpaste led to a clinically meaningful and more pronounced plaque reduction.

The use of fluoride for the prevention of dental erosion and erosive tooth wear in children and adolescents.

Erosive tooth wear (ETW) has gained increasing clinical relevance. It is estimated that worldwide 30-50% of deciduous and 20-45% of permanent teeth are affected. One of the most important nutritional factors causing ETW is the overconsumption of soft drinks, but also patient-related factors like reflux or eating disorders can lead to erosive lesions. Whether acids lead to erosive demineralisation depends on their degree of saturation with respect to tooth mineral at their actual pH. Fluoride compounds like sodium or amine fluoride seem to be of limited efficacy against erosion, the main reason for this is the missing biofilm in the erosive process as well as the lower pH of the acids compared to bacterial acids. This means that to achieve some kind of preventive effect it would be necessary to use products with higher fluoride concentration, which is not an appropriate option for small children, and/or to increase the frequency of application. In addition, the fluoride compound plays a role as promising effects were found when fluoride is combined with titanium or stannous ions. TiF4 can cause acid-resistant surface coatings and when Sn2+/F- formulations are applied, Sn is not only found on the surface but is also incorporated into enamel and dentine. Both effects make the tooth surface more resistant against acid demineralisation. Different fluoride-containing vehicles have been tested to prevent erosion/ETW, such as toothpastes, rinses, gels and varnishes. Toothpastes offer some degree of protection, especially Sn2+-containing formulations, but effects of the active ingredients are sometimes counteracted by the presence of abrasives. Detecting associated factors and influencing them is the main instrument in arresting erosive tooth wear. Additionally, patients at risk for dental erosion should always use an additional fluoride source preferably containing Sn2+.