The history, importance and anatomy of the specimen that validated the giant Purussaurus brasiliensis Barbosa- Rodrigues 1892 (Crocodylia: Caimaninae)

The Solimões Formation is a southwest geological unit of the Brazilian Amazon, being well-known for the Cenozoic giant eusuchian fossils. Among the eight species of Crocodylia described for this formation, the alligatoroid Purussaurus brasiliensis is the best known worldwide due to its enormous size. The holotype was described in 1892 by Barbosa-Rodrigues, composed by a right hemimandible. Later, two other species were assigned to the genus, but the loss of the type specimen brought a series of doubts and discussions about genus and species validity. Here, we provide a historical reconstruction of the genus Purussaurus, especially with a new description of the specimen DGM 527-R, which was fi rst described by L. I. Price. We also provide a review of Purussaurus brasiliensis as a valid species, highlighting the importance of the paleontologist Diogenes de Almeida Campos to the preservation, study availability and divulgation of the specimen. From the six mandibular features discussed, at least two are putative synapomorphies for the genus: the false ziphodont teeth and the thinning of the medial surface of the mandible posterior to the fourteen alveoli, while the lateral surface become laterally expanded from ninth alveoli to behind. The review of the other species of the genus was aggravated due to little sampling of photos and low quality of those contributions. Finally, the curatorial efforts initiated by Price and kept for decades by Campos turned possible the revision of DGM 527-R, an important specimen for understanding the paleobiology and evolution of the genus, and, consequently P. brasiliensis. Such importance was recognized here scientifi cally and by Campos when considered this specimen as the center-piece of the exhibition in honor of the centenary anniversary of Price.


INTRODUCTION
The specimens of Purussaurus are known from the Miocene of South America, having been recovered from four different countries: Brazil (Solimões Formation, P. brasiliensis; Barbosa-Rodrigues 1892, Price 1967, Bocquentin-Villanueva et al. 1989, Souza et al. 2016, Colombia (Honda Barbosa-Rodrigues, 1892 was erected, based on a right hemimandible that preserves the first nine alveoli. After its description, two other species were assigned to the genus: P. neivensis (Mook 1941a) and P. mirandai Aguilera, Riff & Bocquentin-Villanueva, 2006(Aguilera et al. 2006. For a complete history of the genus as well as their relationship with Dinosuchus terror (Gervais 1876) and Brachygnatosuchus brasiliensis (Mook 1921a) see Aguilera et al. (2006).
Unfortunately, some years after the description of Purussaurus brasiliensis, the Museu Botânico do Amazonas (Manaus, Amazonas, Brazil) was closed in 1890, and the type specimen was never recovered, currently being considered lost (see Price, 1967 for a detailed history of the whereabouts of the holotype). Due to the fragmentary status of the holotype and the fact that it was missing, the validity of P. brasiliensis was debated (Patterson 1936(Patterson , 1943. However, both the genus and the type species of P. brasiliensis are considered as valid and their diagnoses were properly established (Price 1967, Bocquentin-Villanueva et al. 1989, Aguilera et al. 2006. Despite recent attempts to improve our understanding on Purussaurus species (e.g., Blanco et al. 2015, Aureliano et al. 2015, Scheyer & Delfino, 2016, Scheyer et al. 2019, most of its anatomy is still unclear. A significant number of fossils are attributed to the three species of Purussaurus, mainly based on their size and overall shape (e.g., Price 1967, Bocquentin-Villanueva et al. 1989, Scheyer et al. 2013, Salas-Gismond et al. 2015, Souza et al. 2016, Scheyer & Delfino 2016, Solórzano et al. 2018. However, few works adequately describe and compare their anatomy (e.g., Aguilera et al. 2006, Souza-Filho et al. 2019. Also, a new species, Acresuchus pachytemporalis Souza-Filho et al., 2019, from Solimões Formation was recently described and inferred to be the sister species of Purussaurus. Nevertheless, further studies should better address the anatomy and evolution of this clade (Souza-Filho et al. 2019). Some recent and preliminary efforts compared the type specimens of Purussaurus and probably related species, providing some hypotheses regarding the validity of a few species (G. M. Cidade & A. Hsiou unpublished data).
The present contribution presents a historical reconstruction of the importance of L.I. Price's work in the corroboration of Purussaurus brasiliensis as a valid species and exalts the importance of Diogenes de Almeida Campos in the preservation, study availability, and divulgation of the specimen that will be here redescribed.
Herein we redescribe the specimen collected and described by Price (1967) and figure it for the first time in the literature. We also include comments on the mandibular characters of Purussaurus, aiming to provide a solid anatomical base for future studies with those species.
ANATOMICAL ABBREVIATIONS: 1 st , first dentary alveolus; 4 th , fourth dentary alveolus; 13 th , thirteenth dentary alveolus; an, angular; d, dentary; mg, Meckelian groove; san, surangular; sp, splenial. The transport of the material was made via airplane to Rio de Janeiro (Campos, personal communication). The fossil comprises a mandible of 1,75m maximum length. However, during transportation and packaging into the collection, the material broke into at least three portions: 1) the anterior portion; 2) the posterior portion of the left hemimandible; 3) the posterior of the right hemimandible. The anterior portion (1) includes the fused mandibular symphysis of the hemimandibles, with 14 alveoli in the left and right side, and half of the 15 th alveolus in the former. The left hemimandible (2) includes the remaining alveoli (total of 21) and the mandibular fenestra extension until the retroarticular process. The right hemimandible (3) includes the remaining alveoli and the anterior parts of the mandibular fenestra. From those, only the (1) and (3) portions were recovered until the finalization of the present work.
The species assumes a dubious status due to the fragmentary state and loss of the holotype (e.g., Patterson 1936). The specimen DGM 527-R described by Price (1967) and its reassessment were the keystones for a clear understanding of Purussaurus brasiliensis.
A new exposition in the Museu de Ciências da Terra was inaugurated in 2005, in honor of the memory of L. I. Price's centenary (25 years after his death in 1980), named "Llewellyn Ivor Price + 100, um Paleontólogo". L. I. Price was the advisor of Diogenes de Almeida Campos and enabled him to study paleontology and develop fieldworks, including activities in the state of Acre. Diogenes was responsible for the organization of this exposition and decided to put DGM 527-R in the central portion of the exhibition due its grandiosity, beauty and importance, and to honor the efforts to collect and bring this enormous and historical specimen to the MCT collections ( Figure 2).

GEOLOGICAL BACKGROUND Solimões Formation
The Solimões Formation crops out in Amazonas and Acre states (Brazil), yielding a high diversity of fossils (Riff et al. 2010), including plants, invertebrate and vertebrate remains (Latrubesse et al. 2010). This formation is characterized by several facies of conglomerates, sandstones and mudstones with fining upward vertical profiles, showing high lateral heterogeneities (Caputo et al. 1971, Brazil 1976

Studied Locality
The outcrop where DGM 527-R was collected is named as Petrópolis (Locality 43 in the original contribution, but Locality 18 in RADAMBRASIL vol. 13;Price et al. 1977), a 'Terra Firme' region in the left side of the upstream Juruá River, State of Acre, between Porto Walter and the debouching of Igarapé Ouro Preto (Price 1967).
As the Petrópolis locality was in a riverbank, this area described by Price (1967) was lost due to the natural erosion that occurs in this kind of outcrop. Therefore, we provide the main geological and stratigraphic information of that site based on Price (1967).
Petrópolis locality was a terrace outcrop located four meters above the water level during the 1962 dry season of Juruá River. Two layers are described: the first is thin, friable clays, predominantly reddish-pink colors arranged in bands, indicating poor lodging; the second one, which contains the fossil remains, is characterized by clayey sandstone, fine, limestone, light gray (Price 1967). The mandible was found with only the symphyseal portion nested within the rock matrix. Also, other fossil remains were recovered from the same level such as smaller crocodylians (Crocodylia), deers (Cervidae), gastropods and bivalves, which attribute a Pliocene-Pleistocene age for this level (Price 1967). The recovered fossils lack signals of transportation and were found in situ (Price 1967). Based on the outcropping region and the recovered fossils of this rock, they indicate a deposition during the Upper Miocene-Pliocene of the Solimões Formation. However, it is important to note that the surrounding outcrops present different ages such as Eocene (Bond et al. 2015) and Pleistocene (Latrubesse & Rancy 2000).

Studied specimens and species
The specimen in focus here is the mandible of Purussaurus brasiliensis (DGM 527-R). As already mentioned, the specimen was almost complete, but the posterior portions of the mandible is lost. The specimens of P. brasiliensis UFAC 1118 and the holotype, which was based on descriptions and original drawings presented by Barbosa-Rodrigues (1892), are included in the comparisons (Figure 1a-c). The holotypes and referred specimens of P. neivensis and P. mirandai are also compared as well as mandibular remains referred to Purussaurus sp. (Table I).
As Purussaurus is well known to belong to the Caimaninae, the comparisons were predominantly based on species within this clade and other closely related forms within Alligatoroidea. Therefore, all extant Caimaninae species were included in this study (Table II; see Souza 2018 for developmental categories of the specimens). Regarding the fossil specimens, all those with mandibular remains were included for comparisons (Table III).

Specimen information acquisition
The historical information about the analyzed specimen was based on literature (e.g., Price 1967, Price et al. 1977, the register book of the collection, and personal communication provided by Diogenes de Almeida Campos.

DESCRIPTION
Unfortunately, Price (1967) did not entirely illustrate DGM 527-R (Figure 1d) and, as portions of the specimen are missing, we based its general description on the textual information provided by him. The specimen DGM 527-R consists of an entire left hemimandible articulated at the symphysis with the right hemimandible, which preserves only its anterior half. Based on the recovered portions of DGM 527-R (Figure 3, 4) the following bones are preserved: dentary, splenial, surangular and angular. The dentition is not complete, including only a few preserved teeth, but the dental formula can be reconstructed by the number of alveoli on both sides of the mandible. From the left hemimandible, the following bones are damaged: the central portion of the surangular, over the mandibular fenestra; the anterior facet for the Meckel cartilage; the medial border of glenoid surface and medial border of retroarticular process.
The dentaries of both hemimandibles join medially, creating the mandibular symphysis that extends along five alveoli, reaching the anterior half of the fifth (Figure 1d,3a). The dorsal surface of the symphysis is dorsoventrally inclined. The anterior half of this surface, with the alveolar region, is taller than the posterior half, which corresponds to the posterior margin of symphysis (Figure 3b, c, 4a, d). In the posterior surface of the mandibular symphysis, in the most ventral portion, there is the Meckelian groove, visible as a large lateromedially expanded and dorsoventrally compressed foramen ( Figure  3c). In dorsal view, the dentary contacts the splenial, and medially by the surangular (Figure  1d, 3a, b). At the medial surface, the dentary contacts posteriorly and it is covered by the splenial (Figure 3a, 4b). In the lateral surface, the dentary contacts the angular ventrally at the anterior margin of the mandibular fenestrae at the mid-portion. The surangular contacts it dorsally (Figure 3a, b). There are 21 preserved alveoli in DGM 527-R (only 14 on the left side in the preserved region), all of them are dorsally  directed (Figure 1d, 3a, 4d). The largest alveoli are the first and fourth with similar sizes, followed by the second and third (Figure 1d, 3a, 4d). The fifth and thirteenth alveoli have similar sizes, but the thirteen is slightly larger than the fifth. Despite their size, they are smaller than the second/ third. The sixth alveolus is the smallest with the seventh until twelfth growing continuously and progressively (Figure 3a). From the fourteenth to the twenty-second, the alveoli reduce in size continuously (Figure 3a). In lateral view, the region of the first alveoli is the tallest, followed by a concavity, along the second and third alveoli, being limited by the fourth alveolus that has almost the same height as the first ( Figure  3b, c, 4a). In the region of the fifth to the eleventh alveoli there is another concavity in lateral view, while from the twelfth alveolus to the posterior region of the dorsal margin of mandible, they are inclined dorsally and become continuously tall (Figure 3a, b). In dorsal view, the second alveolus is posterolaterally displaced to the first. The mid-section of the second alveolus is aligned with the posterior margin of the first. The third alveolus is located posterolaterally in relation to the lateral margin of the second alveolus, while the fourth and the fifth follow anteroposteriorly the third. Such conformation shows a convex lateral margin of the anterior mandible ( Figure  3a, 4c, d). A consequence of the different size of the alveoli, the lateral expansion of the dentary at the level of the fifth alveolus is followed by a posterior concavity, which ends at the level of the eleventh and twelfth alveoli (Figure 3a). The internal surface of the dentary is reduced from the region of the thirteenth and fourteenth alveoli, with a lateromedial thin splenial close to the medial margin of those and posterior alveoli ( Figure 4a). Insofar, the posterior region of the lateral margin of the twelfth alveolus is not equivalent with the external limit of the dentary. The dentary region is convexly projected, being thicker than the medial part ( Figure 3a). The dorsal surface of the dentary, near the medial margin of the alveoli, presents a continuous line of small, rounded, deep and well-delimited foramina, known as dental foramina that suggests neural and/or blood systems passage (Figure 3a). The ventral surface of the dentary also presents well-delimited rounded pits, those being mainly concentrated in the anterior part, and becoming sparse and spaced posteriorly until the disappearance after the level of the thirteenth alveolus (Figure 3b, 4a, c, d).
The splenial has the anterior half preserved in the medial surface of the left hemimandible, while the right hemimandible is mostly complete, missing only some portions of the posterior region (Figure 4b). Due to the fragmentary state of the splenial at the posterior region of the right hemimandible, we could not recognize the contacts with the coronoid (Figure 4b). In this fossil, the anteroventral surface of the foramen intermandibularis caudalis seems to be preserved (Figure 3b, 4b). The anterior end of the splenial, from both hemimandibles, does not reach the mandibular symphysis and it is bisected by the Meckelian groove (Figure 3c, 4b).
Only the anterior process of the surangular is preserved (Figure 3a, b). In lateral view, this process surpasses the anterior margin of the mandibular fenestra, reaching the level of the posterior margin of the twentysecond mandibular alveoli (Figure 3b). Despite unpreserved, the surangular does not exhibit contact to the anterior half of the mandibular fenestra ( Figure 3b). In dorsal view, this process borders the lateral margin of the alveoli, reaching the posterior margin of the twentieth pair of alveoli ( Figure 3a). This dorsal anterior process is bifid as consequence of a posterior process of dentary that contacts itmedially (Figure 1d,3a).
The angular surpasses the anterior margin of the mandibular fenestra, but prior to the end of the surangular lateral anterior process, this bone becomes restricted to the ventral margin of the mandible, reaching the level of the nineteenth alveoli (Figure 3b). The angular does not compose the anterior half of the mandibular fenestra (Figure 3b).
The presence and morphology of the coronoid cannot be provided, due to the fragmentary medial surface of the right hemimandible ( Figure 4b).
Only the anterior half of the mandibular fenestra is preserved in the right hemimandible (Figure 3b). The posterior portion of the dentary exclusively composes this structure ( Figure  3b). The overall shape of the anterior portion indicates a long and tall mandibular fenestra, being slightly inclined dorsoventrally (Figure 3b).
The foramen intermandibularis caudalis has the anteroventral margin preserved in the medial surface of the right hemimandible (Figure 4b). No further information can be given due the fragmentary state of this portion. Some in situ teeth are partially preserved in the specimen DGM 527-R (Figure 1d, 3, 4). The right hemimandible has the second and fourth alveoli with preserved teeth; the second is fully erupted and exhibits a broken apical portion of the crown (Figure 5b); the fourth has only the tooth apex exposed, with the missing enamel (Figure 3a, 5b). In the left hemimandible, the second, third and fifth alveoli are preserved in situ (Figure 3a, 5b), being the second (Figure 5a) and the fifth fully erupted with the crown apex broken. The third has only the apex exposed with the enamel preserved. Those teeth are subcircular in cross-section with smooth enamel presenting longitudinal and transverse striae along the crown, while the anterior and posterior carinae are relatively coarse with crenulations forming perpendicular denticles (Figure 5c).

DISCUSSION Comparison
The three specimens (the holotype, DGM 527-R and UFAC 1118) present the first four dentary alveoli proportionally larger than in Purussaurus mirandai. Furthermore, UFAC 1118 has the 13 th alveolus larger than the posterior one to the fourth alveolus. Therefore, those specimens are recognized as P. brasiliensis.
The species Purussaurus brasiliensis is mainly known for three mandibular elements, which are: the holotype (Figure 1a-c), the specimen DGM 527-R (informally known as the neotype; Figure 1d, 3, 4), and the UFAC 1118 (associated with the most complete skull, UFAC 1403, of P. brasiliensis; Bocquentin-Villanueva et al. 1989, Aureliano et al. 2015. The preserved portions of the holotype and the specimen UFAC 1118 share the same descriptions as here proposed for DGM 527-R. The specimen UFAC 1118 differs by not presenting the splenial suture visible, and the Meckelian fossa and canals enclosed, whereas the holotype is neither fully prepared nor described, which enable a proper verification of this feature. Another difference is the total number of alveoli in dentary, which is 21 for DGM 527-R; 20 for UFAC 1118 and unknown for the holotype. Those differences related to UFAC 1118 could be both related to the preservation type of the specimen, which presents the external surface modified by the fossilization process, or due to ontogenetic differences. All specimens attributed to Purussaurus (Table II) present the following features: 1) false ziphodont teeth (as proposed by Aguilera et al. 2006, Aureliano et al. 2015, Souza et al. 2016; 2) two well-marked dorsal concavities in the lateral view of the mandible, one between the first and fourth alveoli and the other between the fourth to eleventh alveoli, with the dorsal margin inclined dorsally from the region behind the eleventh alveolus; 3) in dorsal view of the lateral margin between the fourth and twelfth alveoli presenting a well-marked dorsal concavity in the lateral view of the mandible; 4) thin medial surface of the mandible from the fourteenth alveolus towards the posterior, while the lateral surface becomes laterally expanded from the ninth alveoli to the posterior ones; 5) the mandibular symphysis extending to the mid portion of the fifth alveolus; and 6) the anterior margin of the mandible markedly convex due to the anterior position of the second alveoli and the lateral position of the third and fourth alveoli. The main differences between the specimens of the Purussaurus species are related to the number of dentary alveoli, with DGM 527-R (P. brasiliensis) presenting 21, similar to P. mirandai and differing from the most complete mandible of P. neivensis (MUSM 1392) that has 19-20 and UFAC 1118 (P. brasiliensis) which has 20.
The specimens of Purussaurus can be considered as presenting some heterodonty in their dentition as observed in other crocodylians (D'Ampore et al. 2019) with tall, slight compressed labio-lingually and sharp teeth in the anterior alveoli, while the posterior ones are rounded and blunted (Langston 1965, Aguilera et al. 2006, Aureliano et al. 2015, Souza et al. 2016). The false ziphodont condition (sensu Prasad & de Broin 2002) is proposed for Purussaurus teeth (Aguilera et al. 2008, Aureliano et al. 2015, Souza et al. 2016. This condition seems to be, at least among eusuchians, exclusive to this genus, being observed in the remaining eusuchian species the conidont ( The specimens of Purussaurus present two well-marked dorsal concavities in the lateral view of the mandible, being the first one between the first and fourth alveoli, and the second one between the fourth to eleventh alveoli. In the former, the dorsal margin is dorsally inclined from the region behind the eleventh alveoli. This condition is similar to the one observed in the specimens of Acresuchus pachytemporalis, Bottosaurus harlani, Caiman latirostris, Krabisuchus siamogallicus, Melanosuchus niger and Necrosuchus ionensis. The specimens of Mourasuchus present this surface straight, while the remaining specimens of Caimaninae have a well-marked convexity at the level of the ninth to thirteenth alveoli, posteriorly followed by a concavity. A condition only observed among the studied specimens of Purussaurus was the relative thinning of the medial surface of the mandible posterior to the fourteenth alveoli pair, while the lateral surface becomes laterally expanded, starting at the ninth alveoli pair, and extending posteriorly. Those medial and lateral variations are here initially considered as biologically dependent (see Fitzhugh 2006) and, more specifically, dependent of the position of the toothline relative to the mandible long axis (i.e. closer to the medial surface than to the lateral one in dorsal view). Therefore, are treated together aiming for a unique explanation for this whole condition. The remaining specimens, Acresuchus

MANDIBULAR CHARACTERS OF PURUSSAURUS: POTENTIAL SYNAPOMORPHIES AND AUTAPOMORPHIES
As only Purussaurus brasiliensis specimens are considered in this work and as the specimens attributed to the remaining Purussaurus species miss all views figured and some mandibular features are not described, the content here proposed must be verified and reviewed by future works, in which authors could personally study the remaining specimens. Therefore, these commentaries are an important guideline for future contributions to the understanding of Purussaurus paleobiology and evolution.
In a preliminary work, G. M. Cidade & A. Hsiou (unpublished data) revisited the types of Purussaurus species aiming to review their diagnoses. They concluded that the size variations in the first four mandibular alveoli are enough to distinguish such specimens in different species. The present contribution considers this differentiation method with caution due to such size variations that are directly related to the specimen's size. Tounderstand their phylogenetic signal and potential taxonomic value, the allometric and the ontogenetic development of such features should be at first understood (further discussion of feature variation among crocodylian species in Brochu & Sumrall, 2020). Therefore, we do not consider such results as applicable, for now, waiting for the conclusion of their work.
From the six mandibular features discussed here, some interesting implications could be inferred. There are at least two potential synapomorphies for Purussaurus that must have their homologues (sensu Owen, 1847; Fitzhugh 2006) tested and latter included in future phylogenetic inferences (sensu Souza 2017). These characters are the false ziphodont teeth and the thinning of the medial surface of the mandible posterior to the fourteenth alveoli, while the lateral surface becomes laterally expanded from the ninth alveoli and extending posteriorly. The features related to the mandibular symphysis reaching the mid portion of the fifth alveoli could be potentially considered as an interesting condition; however, variations in the mandibular symphysis length are quite common among crocodylians and should be treated with caution. The other three characters, two related to the dorsal concavities in the lateral view of the mandible and the latter with the anterior mandibular margin morphology, are features directed related with alimentary habits and their homologues must be tested prior to the inclusion in new phylogenetic inferences aiming to verify if those similarities reflect convergent feeding habits (becoming analogues) or related to ontogenetic development.
This contribution does not find any new autapomorphic mandibular feature for the Purussaurus species. In the literature, only P. neivensis presents an autapomorphic mandibular feature that was described by Langston (1965), which is the development of a well-marked ridge in the lateral surface of the angular. It is important to note that the absence of mandibular autapomorphies is not definitive, as this we could not handle first-hand the specimens of P. neivensis nor P. mirandai, being strongly limited and biased by poor preservation of many specimens and, often, poor description of the data. The review of such species, considering what was here discussed, is strongly recommended for future works.

CONCLUSIONS
The extensive field works made by L. I. Price and D. A. Campos in the Solimões Formation enabled the finding of important materials, including the specimen informally regarded as the neotype of Purussaurus brasiliensis. The curatorial efforts initiated by Price and kept by Campos made possible the revision of DGM 527-R, an important specimen for the understanding of the paleobiology and evolution of P. brasiliensis and the genus as a whole. Such importance was recognized here scientifically by Campos when he considered this specimen as the centerpiece of the exhibition in honor of the one hundred anniversary of Price.
Regarding the scientific novelty here produced, we have identified six new mandibular characters that should be considered in future contributions about caimanine evolution. Also, from such characters, at least two indicate synapomorphies for Purussaurus. The only species of the genus that have had a mandibular autapomorphy recognized here is Purussaurus neivensis, which further anatomical and homologue studies should properly address the autapomorphies of such key species to the genus. The reduced resources for the development of this project hampers us from analyzing first-hand the non-Brazilian specimens, and the culture of not completely illustrating and describing the mandibular materials created a strong bias and limitation to this work. Therefore, as made here, future studies should provide better illustrations and descriptions of described materials to enable scientific progress.

Acknowledgments
We thank curator Rafael Costa (MCT/DNPM) for allowing access to the specimen described here and for his help during its examination. In addition, our acknowledgments to Diogenes de Almeida Campos, honored in this special volume, due to his valuable contributions about the specimen studied here, as well as his fieldwork notes. We also thank the editors for inviting us to participate in this special volume. We posthumously thank the academic and personal efforts made by L.W. Price, who greatly improved (and still promotes nowadays) Brazilian paleontology. Christopher Brochu, Aline Ghilardi and Torsten Scheyer are thanked for comments and useful suggestions on the manuscript. Thanks to Victoria Barros for the English review. The paper was improved by photos of non-Brazilian Purussaurus specimens provided by Douglas Riff (UFU) and Giovanne Cidade (UFSCAR). LGS thanks the paleo and geohistory exhibition at Museu da Amazônia (PRONAC 183808) the post-doctoral scholarship granted by Fundação de Amparo à Pesquisa do Estado do Amazonas (FAPEAM 062.00166/2020). RVP thanks FAPESP for a scholarship (#2019/10231-6). ASB is grateful for his Doctorate scholarship from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES -PROANTAR fellowship # 88887.336584/2019-00).