AMORPHOUS AND CRYSTALLINE FORMS OF SMILAGENIN AND ITS HYDRATES

Information

  • Patent Application
  • 20110144323
  • Publication Number
    20110144323
  • Date Filed
    February 22, 2011
    14 years ago
  • Date Published
    June 16, 2011
    13 years ago
Abstract
The invention provides smilagenin in novel amorphous, crystalline, hydrated and solvated forms, and the use thereof in manufacturing pharmaceutical or edible grade smilagenin and its derivatives.
Description
FIELD OF THE INVENTION

The present invention relates to novel amorphous and crystalline forms of smilagenin and its hydrates.


BACKGROUND TO THE INVENTION

It is well established that some organic compounds can crystallise in a number of different polymorphic forms or crystal habits, which may comprise the compound as such, solvates of the compound, hydrates of the compound, or combinations thereof. Alternatively, the compound, solvate or hydrate may precipitate as an amorphous solid.


The stability and bioavailability of the drug product may vary according to the polymorphic form present. The choice of crystal form is thus a critical aspect of drug development (Brittain, Pharm. Tech. pp. 50-52, 1994; Yu et al., Pharm. Sci. Technol. Today, 1, pp. 118 to 127, 1998; Byrn et al., Chem. Mater. 6, pp. 1148 to 1158, 1994; Byrn et al., Pharm. Res., 12, pp. 945 to 954, 1995; Henk et al., Pharm. Ind. 59, pp. 165 to 169, 1997).


Smilagenin is an A/B-cis steroidal sapogenin having the formula:




embedded image


Smilagenin and its derivatives have been identified as valuable therapeutic agents in human and veterinary medicine and in non-therapeutic human and non-human animal treatments. See, for example, U.S. Pat. No. 3,890,438 (use of smilagenin and certain 4-substituted phenoxyisobutyric acid compounds against high blood cholesterol levels); U.S. Pat. No. 4,680,289 (use of smilagenin against obesity and diabetes obesity syndromes); U.S. Pat. No. 6,258,386 (use of smilagenin against cognitive dysfunction and allied conditions); WO-A-01/23406, WO-A-01/23407, WO-A-01/23408, and WO-A-01/49703 (use of smilagenin derivatives against cognitive dysfunction and allied conditions); and WO-A-02/079221 and WO-A-03/082893 (use of smilagenin and derivatives thereof against non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment).


In a key article (Marker et al., J. Am. Chem. Soc. 65, pp. 1199 to 1209, 1943, at p. 1207), it was reported that smilagenin acetate shows polymorphic forms melting at 110, 130 and 152° C. The melting point of smilagenin from a number of sources was always in the range 183-185° C. However, the recrystallisation solvent was not stated and the article made no mention of polymorphic forms of smilagenin.


In J. Am. Chem. Soc. pp. 2525 to 2532, 1940, Marker et al. reported a melting point of 183-185° C. for smilagenin crystallised from alcohol.


In J. Am. Chem. Soc. 64, pp. 818 to 822, 1942, Marker et al. reported a melting point of 178-180° C. for smilagenin crystallised from acetone.


Askew et al. reported that fractional crystallisation of smilagenin from acetone gave long silky needles with a melting point of 183-184° C. It was further reported that smilagenin appeared to form a hydrate when crystallised from methanol (Askew et al., J. Chem. Soc. pp. 1399 to 1403, 1936). However, no evidence was provided to support this observation, and the reader was merely referred back to an earlier paper on a related compound (Power et al., J. Chem. Soc., 105, pp. 201 to 219, 1914).


Scheer et al. crystallised smilagenin from aqueous ethanol and observed a melting point of 187-188° C., but made no mention of the formation of a hydrate (Scheer et al., J. Am. Chem. Soc., 77, pp. 641 to 646, 1955).


In J. Am. Chem. Soc., 77, pp. 3086 to 3089, 1955, Wall et al. commented that the best samples of smilagenin from natural sources had a melting point of 188-189° C., whereas acetone or aqueous acetone failed to bring the melting point above 182-185° C. on samples generated by isomerization of sarsasapogenin. Again, no mention was made of hydrate formation. The infra-red (IR) spectra of the synthetic and natural materials were identical. However, the X-ray powder diffraction (XRPD) patterns were not. These differences were not attributed to polymorphism, and the XRPD patterns were not presented. The authors concluded that there was a pronounced effect of traces of sarsasapogenin on certain properties of smilagenin that depend on crystal structure.


Wall et al., (J. Biol. Chem., 198, pp. 533 to 543, 1952) reported the melting point of smilagenin to be 184° C. However, the recrystallisation solvent was not stated. The paper reported that the use of a Kofler microscopic melting point apparatus having polarizing disks allowed for the crystal form or habit to be observed. No mention was made of polymorphisin but the impact of impurities upon the melting point was noted. In J. Am. Chem. Soc., 77, pp. 1230 to 1237, 1954, Wall et al. reported the melting point of smilagenin to be 183° C.


Callow et al. (J. Am. Chem. Soc. 77, p. 1672, 1955) described the recrystallisation of smilagenin from acetone to yield crystals having melting point 157-160° C.


Parsons et al. (Henry Ford Hosp. Med. Bull., 12, pp. 87 to 120, 1964) described a specific crystalline form of smilagenin by XRPD. From the data presented it cannot be concluded that this form corresponds to any of the forms described herein.


In U.S. Pat. No. 3,169,959 (1965), a melting point of 178-180° C. was reported for smilagenin crystallised from heptane.


In Phytochemistry, 8, pp. 1523 to 1531, 1969, Blunden et al. reported a melting point of 181-182° C. for smilagenin crystallised from acetone.


In J. Nat. Prod., 44, pp. 441 to 447, 1981, Blunden et al. reported a melting point of 186° C. for smilagenin crystallised from acetone.


The use of crystalline intermediate complexes to assist the extraction of relatively pure smilagenin and other sapogenins from their plant sources has been proposed. Thus, for example, U.S. Pat. No. 5,017,562 described a crystalline saponin-containing complex, derived from the saponin-containing plants Agave, Yucca, Dioscorea, Quillaja, Medicago and Cyamopsis, which is substantially free of fats and non-saponin carbohydrates and which, on hydrolysis, can yield smilagenin and other sapogenins.


The prior art publications acknowledged above are incorporated herein by reference.


Depending on the administration route desired in the therapy, it may be desirable to improve or at least control the stability and water solubility of the smilagenin, to obtain a desired bioavailability profile. Furthermore, it can assist the manufacturing or purification process if the stability and water solubility of the smilagenin can be controlled.


In principle, the water solubility of polymorphic forms of an organic compound is not necessarily the same for all forms. Therefore, the use of specific crystalline forms or habits can offer useful control of the water solubility. In the case of sparingly water-soluble compounds such as smilagenin, even a slight adjustment to the water-solubility by means of an adjustment to the polymorphic form can offer useful processing or biological advantages.


We have examined commercially available smilagenin and have found that it occurs in a specific crystalline form, which we have characterised as form II.



FIG. 1 of the accompanying drawings shows an XRPD pattern obtained at λ=1.5406 Angstroms from a sample of commercially available smilagenin obtained from Research Plus, Inc. This is an example of form II crystalline smilagenin. The intensities of the XRPD pattern for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form II”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation. For present purposes, the approximately 20 strongest peaks may generally be considered characteristic of the crystalline form, subject however to standard practice in crystallography.


The present invention is based on our surprising finding that at least three further crystalline forms of smilagenin exist, two of which appear typically to be anhydrous and have been characterised as form I and form III. We have further found that form III can exist in at least one variant form in which the crystal structure is modified (“form IIIA”) and/or the hydration level is modified (smilagenin hemihydrate or smilagenin dihydrate). Furthermore, we have surprisingly found that smilagenin can form a crystalline monohydrate. We have characterised the typical crystalline form of this monohydrate as form V. Furthermore, we have surprisingly found that smilagenin can form a crystalline channel hydrate having variable smilagenin:water stoichiometry. We have characterised the typical crystalline form of this channel hydrate as form VI. It has also been found that smilagenin can be obtained in a non-crystalline form (the “amorphous form”). The prior art does not describe any amorphous form of smilagenin.


Furthermore, we have identified a crystalline solvate of smilagenin formed with iso-propyl alcohol. We have characterised the typical crystalline form of this iso-propyl alcohol solvate as form VII.


Surprisingly, we have found that form II of smilagenin can be converted to the monohydrate by a solvent mediated transformation in hexane or heptane. Further, we have found that the monohydrate may be obtained by other processes, including solvent mediated transformations in aqueous acetone, aqueous tetrahydrofuran and aqueous ethanol. The water content was determined by Karl Fischer analysis was found to be in the range about 3 to 6% w/w. Analysis by thermogravimetric analysis (TGA) confirms a water weight in the region of 4%.


Furthermore, we have found methods of controlling the transitions between not only the novel amorphous and crystalline forms but between them and the known form II, by controlling the organic solvent used for recrystallisation.


Surprisingly, and advantageously, we have found that precipitation or crystallisation of smilagenin from certain organic solvents does not result in organic solvates of smilagenin. However, the iso-propyl alcohol solvate (believed to be a hemi-solvate) can be obtained under certain circumstances, and is a newly recognised material.


These novel forms of smilagenin and associated methods therefore offer enhanced control of the preparation of pharmaceutical or edible grade smilagenin, and the possibility of preparing pharmaceutical or edible grade smilagenin with improved delivery and bioavailability characteristics.


BRIEF DESCRIPTION OF THE INVENTION

According to a first aspect of the present invention, there is provided smilagenin in any one or more of crystalline forms I, III, IIIA, V, VI and VII as defined herein.


According to an example of this first aspect of the present invention, there is provided smilagenin in any one or more of crystalline forms I, III, IIIA and V as defined herein.


According to a second aspect of the present invention, there is provided smilagenin hemihydrate, optionally in crystalline form.


According to a third aspect of the present invention, there is provided smilagenin monohydrate, optionally in crystalline form.


According to a fourth aspect of the present invention, there is provided smilagenin dihydrate, optionally in crystalline form.


According to a fifth aspect of the present invention, there is provided smilagenin channel hydrate, optionally in crystalline form.


According to a sixth aspect of the present invention, there is provided amorphous smilagenin.


According to a seventh aspect of the present invention, there is provided smilagenin iso-propyl alcohol solvate, optionally in crystalline form. This material may be prepared by precipitation from a solution of relatively impure smilagenin in iso-propyl alcohol that has been reduced in volume by azeotropic distillation.


According to an eighth aspect of the present invention, there is provided crystalline pharmaceutical or edible grade anhydrous unsolvated smilagenin, when obtained by crystallisation from a solution of substantially pure smilagenin iso-propyl alcohol (IPA) solvate in an anhydrous IPA-compatible organic solvent which does not form a solvate with smilagenin, such as acetone. The smilagenin may be in crystalline form I or III as defined herein.


The crystalline or amorphous material of the present invention may be present substantially free of other forms of smilagenin and/or substantially free of other steroidal sapogenins and/or steroidal saponins.


The crystalline or amorphous material of the present invention may preferably be present in at least about 50% by weight pure form, for example at least about 70% by weight pure form, for example at least about 80% by weight pure form, for example at least about 85% by weight pure form, for example at least about 90% by weight pure form, for example at least about 95% by weight pure form, for example at least about 97% by weight pure form, for example at least about 98% by weight pure form.


Any of the materials according to the present invention may if desired be present in admixture with one or more other materials according to the present invention, another form of smilagenin, any other biologically active material, any biologically inactive material, or any combination thereof. The said other form of smilagenin, when present, may be crystalline form II.


The novel forms of smilagenin provided by the present invention possess a number of advantages over the known form, particularly in terms of their stability and handling characteristics. These advantages are applicable to one or more of the manufacturing, purification, formulation and storage phases of the marketed smilagenin compositions and/or to the delivery of the smilagenin from the composition to the human or non-human animal patient for achieving the desired pharmacological effect.


The present invention also provides methods for preparing the materials of the present invention, preferably by precipitation of smilagenin from a solution of smilagenin in an appropriate organic solvent or solvent mixture or by other crystallisation of smilagenin in an appropriate organic solvent or solvent mixture, optionally in the presence of water, as well as medicaments, foodstuffs and beverages containing the said materials, methods of preparing the medicaments, foodstuffs and beverages, uses of the said materials in the preparation of the medicaments, foodstuffs and beverages, and uses of the medicaments, foodstuffs and beverages in human and veterinary medicine and in non-therapeutic human and non-human animal treatments.


The present invention further provides a process for obtaining pharmaceutical or edible grade smilagenin or a derivative thereof, wherein at least one step of the process includes preparing smilagenin in one or more of the forms according to the present invention. The smilagenin may be prepared in any suitable level of hydration and in any suitable physical form, for example as an isolated dry solid or in a liquid medium such as a crystal slurry.


The resultant pharmaceutical or edible grade smilagenin or derivative thereof may be subsequently formulated into a suitable medicament, foodstuff or beverage form.


The present invention further provides methods of adjusting the crystalline form of smilagenin between the forms I, II, III, IIIA, V, VI and VII (for example between the forms I, II, III, IIIA and V), methods of adjusting the form of smilagenin between its amorphous and crystalline forms, methods of adjusting the hydration level of smilagenin, methods of forming the iso-propyl alcohol solvate of smilagenin and methods of adjusting the form of smilagenin between two or more of the hydrated, solvated and unhydrated and unsolvated forms.


The terms “crystallise”, “recrystallise” and the like, used herein, refer to all methods suitable for forming a desired crystal form or habit or mixture or other combination thereof, and are not limiting. For example, crystal slurrying, crystal precipitation, and other solvent mediated crystal transformation, with or without seeding and/or nucleation, are all encompassed by the terms “crystallise”, “recrystallise” and the like as used herein.


The materials according to the present invention may therefore conveniently be present in substantially pure isolated form. The materials may suitably be prepared on a kilogram scale.


DETAILED DESCRIPTION OF THE INVENTION
Crystalline Form I

The term “crystalline form I” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 2 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form I”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.


The form I material can be prepared by recrystallisation of commercially available smilagenin from acetone. Alternatively, the form I material can be prepared by a solvent mediated transformation of form II or form III material in acetone, or more preferably in acetonitrile.


Karl Fischer analysis, differential scanning calorimetry and thermogravimetric analysis confirmed that the crystal form I that we have obtained is neither hydrated nor solvated.


Crystalline Form II

The term “crystalline form II” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 1 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form II”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.


The form II material was commercially available smilagenin obtained from Research Plus, Inc.


Differential scanning calorimetry (DSC), TGA, residual solvent and Karl Fischer analysis confirmed that the material was neither hydrated nor solvated.


Crystalline Form III

The term “crystalline form III” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 3 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form III”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.


The form III material may be prepared by solvent mediated transformation of commercially available smilagenin using methyl t-butyl ether, acetone, methyl iso-butyl ketone, ethyl acetate, iso-propyl acetate and toluene.


Solvent mediated transformations of commercially available smilagenin using butanone or from 50% aqueous ethanol yielded a mixture of crystal forms III and V.


These data show that crystal form II can be converted into form III by solvent mediated transformations using a range of solvents.


Karl Fischer analysis, differential scanning calorimetry and thermogravimetric analysis confirmed that the crystal form III that we have obtained is neither hydrated nor solvated.


Crystalline Form IIIA

The term “crystalline form IIIA” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 4 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The d-spacings may readily be calculated from the information in FIG. 4, using the Bragg equation.


The form IIIA material may be prepared by a solvent mediated transformation of commercially available smilagenin using dimethylformamide.


Crystalline Form V

The term “crystalline form V” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 5 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form V”. From this data, the d-spacings may readily be calculated using the Bragg equation.


The form V material may be prepared in relatively pure form by recrystallisation of commercially available smilagenin from ethanol, tetrahydrofuran, hexane or aqueous acetone. The acetone/water proportions in the aqueous acetone may vary widely, for example from about 0.5:1 (by volume) to about 25:1 (by volume), for example from about 1:1 (by volume) to about 20:1 (by volume), for example from about 2:1 (by volume) to about 19:1 (by volume),


A solvent mediated transformation of commercially available smilagenin in butanone or in 50% aqueous ethanol yielded a mixture of crystal forms III and V.


A solvent mediated transformation of commercially available smilagenin in dichloromethane yielded a mixture of crystal forms II and V.


Solvent mediated transformations in aqueous acetone, aqueous tetrahydrofuran or aqueous ethanol all yield crystal form V (monohydrate). In each case the proportions of water to solvent in the medium can vary widely. The purity of the resultant crystalline material appears to be higher when aqueous acetone is used, in comparison with the alternative media.


Karl Fischer analysis, DSC (FIG. 6) and TGA (FIG. 7) confirmed that the crystal form V that we have obtained is a monohydrate of smilagenin.


Crystalline Form VI

The term “crystalline form VI” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIGS. 8 and 15 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 2 to 28 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 2 to 28 degrees can be obtained from FIGS. 8 and 15. The 29 and d-spacings for the significant peaks, and the intensities of the significant peaks relative to the strongest peak, are given in Table B.


The form VI material may be prepared in relatively pure form by recrystallisation of commercially available smilagenin from methanol.


DSC (FIG. 9), TGA (FIG. 10) and vapour sorption (FIG. 11) analysis suggest that the crystal form VI that we have obtained is a channel hydrate of smilagenin exhibiting variable smilagenin:water stoichiometry and the potential to form channel solvates with solvents having appropriately sized molecules. As is well known, a channel hydrate is a hydrate in which the crystal lattice of the molecule forms a channel or cage enclosing a void which can wholly or partially accommodate water (or solvent) molecules. The stoichiometric (molar) ratio of smilagenin:water at any particular time will depend on such factors as the humidity of the surrounding atmosphere, as the water molecules are generally free to enter or leave the void.


Crystalline Form VII

The term “crystalline form VII” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIGS. 12 and 16 of the accompanying drawings (λ=1.5406 Angstroms).


The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 2 to 28 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.


The intensities of the XRPD peaks for this crystalline form in the 2-theta range 2 to 28 degrees can be obtained from FIGS. 12 and 16. The 20 and d-spacings for the significant peaks, and the intensities of the significant peaks relative to the strongest peak, are given in Table C.


The form VII material may be prepared in relatively pure form by crystallisation of smilagenin from iso-propyl alcohol (IPA). The material may subsequently be aged if desired (e.g. at ambient temperature and e.g. for a period of at least about 24 hours, for example at least about 48 hours). If desired, the form VII material may be subsequently recrystallised from acetone to afford anhydrous unsolvated smilagenin in substantially pure form. DSC (FIG. 13) and TGA (FIG. 14) indicate that the crystal form VII that we have obtained is a hemi-IPA solvate of smilagenin.


The form VII material is potentially important as an intermediate in the purification of smilagenin to produce pharmaceutical or edible grade smilagenin. Without wishing to be bound by theory, it is believed that a solution of relatively impure smilagenin in iso-propyl alcohol is especially convenient for being azeotropically distilled in order to efficiently remove water from the solution. The IPA solvate of smilagenin which is precipitated from the reduced solution after the said distillation can conveniently be recrystallised as pharmaceutical or edible grade anhydrous unsolvated smilagenin using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin.


Therefore, in one particular embodiment, the form VII material may be in substantially pure isolated, preferably dry, form and prepared by precipitation from a solution of relatively impure smilagenin in iso-propanol, which solution has preferably previously undergone distillation to reduce its volume and remove water or other impurities. Most preferably, the process by which the form VII material is made is conducted on an industrial scale (obtaining at least kilogram quantities of the form VII material). Preferably, anhydrous unsolvated smilagenin is subsequently recrystallised in pharmaceutical or edible grade from the said form VII material using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin. It is further preferred that at no stage in the preparation or purification of the smilagenin, including the stage of formation of any form VII material or other intermediate form of smilagenin, is it necessary (or done) to remove water from the smilagenin, or from any mixture containing it, using a solid hygroscopic material such as magnesium sulphate.


Examples 2, 6 and 7 of WO-A-2004/037845 describe certain laboratory scale batchwise procedures for purifying smilagenin via recrystallisation from iso-propyl alcohol (2-propanol). However, in none of these Examples is it stated that the precipitated material is an IPA solvate of smilagenin, let alone a hemi-IPA solvate. To the extent that it may be necessary in any jurisdiction to exclude the disclosures of those examples and subject-matter that is obvious therefrom from the scope of protection for the form VII material, processes for its preparation, and uses thereof, such disclosures—and especially the disclosures of the purification of the initial impure smilagenin using iso-propyl alcohol—are hereby disclaimed from the present application. In particular, in such jurisdictions the form VII material according to the present invention may comprise the form VIII material in substantially pure isolated form prepared on a kilogram scale. As mentioned above, this material is precipitated from the reduced IPA solution after azeotropic distillation and can conveniently be recrystallised as pharmaceutical or edible grade anhydrous unsolvated smilagenin (e.g. in form I or form III, e.g. in substantially pure isolated form prepared on a kilogram scale) using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin.


Amorphous Form

The amorphous form is non-crystalline. We have found that amorphous smilagenin appears to have potentially useful water-solubility and stability with respect to conversion to a crystal form. These characteristics offer improved manufacture, formulation, storage and bioavailability of smilagenin in comparison with the prior art crystalline form.


The amorphous smilagenin we have prepared has an XRPD pattern which shows no peaks that would be characteristic of any crystalline structure.


Derivatives

The term “derivatives” used herein refers particularly to the compounds defined and described in the prior art patent documents acknowledged above in relation to the known biological activities of smilagenin (U.S. Pat. No. 3,890,438; U.S. Pat. No. 4,680,289; U.S. Pat. No. 6,258,386; WO-A-01/23406; WO-A-01/23407; WO-A-01/23408; WO-A-01/49703; WO-A-02/079221; and WO-A-03/082893).


Such derivatives include pharmaceutically acceptable pro-drugs of smilagenin and pharmaceutically acceptable salts thereof.


Pro-drugs of smilagenin may especially include 3-position carboxylate esters such as the cathylate (ethoxycarbonyloxy), acetate, succinate, propionate, butyrate, valerate, isovalerate, caproate, isocaproate, diethylacetate, octanoate, decanoate, laurate, myristate, palmitate, stearate, benzoate, phenylacetate, phenylpropionate, cinnamate, p-nitrobenzoyloxy, 3,5-dinitrobenzoyloxy, p-chlorobenzoyloxy, 2,4-dichlorobenzoyloxy, p-bromobenzoyloxy, m-bromobenzoyloxy, p-methoxy-benzoyloxy, phthalyl, glycinate, alaninate, valinate, phenylalaninate, isoleucinate, methioninate, argininate, aspartate, cysteinate, glutaminate, histidinate, lysinate, prolinate, serinate, threoninate, tryptophanate, tyrosinate, fumarate and maleate esters.


“Pharmaceutically acceptable salts” means the relatively non-toxic, inorganic and organic acid addition salts, and base addition salts, of compounds of the present invention. These salts can be prepared in situ during the final isolation and purification of the compounds. In particular, acid addition salts can be prepared by separately reacting the purified compound in its free base form with a suitable organic or inorganic acid and isolating the salt thus formed. See, for example S. M. Berge et al., Pharmaceutical Salts, J. Pharm. Sci., 66: pp. 1-19 (1977) which is incorporated herein by reference. Base addition salts can also be prepared by separately reacting the purified compound in its acid form with a suitable organic or inorganic base and isolating the salt thus formed. Base addition salts include pharmaceutically acceptable metal and amine salts. Examples of suitable acid addition salts are those formed with acids selected from hydrochloric, sulphuric, phosphoric and nitric acids. Examples of suitable base addition salts are those formed with bases selected from sodium hydroxide, potassium hydroxide and ammonium hydroxide.


Medicaments, Foodstuffs, Food Supplements and Beverages

According to the invention, a composition may comprise a material as described above in admixture with one or more further component selected from: one or more other materials as described above, another form of smilagenin, any other biologically active material, and any biologically inactive material.


The composition may be prepared by a method comprising admixing a material as described above with one or more further component selected from: one or more other materials as described above, another form of smilagenin, any other biologically active material, and any biologically inactive material.


According to the invention, the material or the composition (e.g. the medicament, foodstuff, food supplement or beverage) may be used for the treatment of a condition selected from: high blood cholesterol levels, obesity and diabetes obesity syndromes, cognitive dysfunction and allied conditions, non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment.


Still further, the invention therefore provides a method of treatment of a human or non-human animal (e.g. a human) suffering from, or susceptible to, a condition selected from: high blood cholesterol levels, obesity and diabetes obesity syndromes, cognitive dysfunction and allied conditions, non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment, which comprises administering to the said human or non-human animal an effective amount of a material or composition as described above.


The active agent prepared according to the present invention may thus be formulated into any suitable composition form for administration to a human or non-human animal patient. The composition may consist of the active agent alone or may include the active agent and any suitable additional component, such as one or more pharmaceutically acceptable carriers, diluents, adjuvants, excipients, or vehicles, such as preserving agents, fillers, disintegrating agents, wetting agents, emulsifying agents, suspending agents, sweetening agents, flavoring agents, perfuming agents, antibacterial agents, antifungal agents, lubricating agents and dispensing agents, depending on the nature of the mode of administration and dosage forms.


The composition may, for example, be a pharmaceutical composition (medicament), a foodstuff, food supplement or beverage.


The terms “foodstuff”, “food supplement” and “beverage” used herein have the normal meanings for those terms, and are not restricted to pharmaceutical preparations. The appropriate pharmaceutical or edible grade of ingredients will be used, according to the desired composition form.


For further details of suitable composition forms and dosages, please refer to U.S. Pat. No. 3,890,438, U.S. Pat. No. 4,680,289; U.S. Pat. No. 6,258,386; WO-A-01/23406; WO-A-01/23407; WO-A-01/23408; WO-A-01/49703; WO-A-02/07922; and WO-A-03/082893.





BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:



FIG. 1 shows an XRPD pattern (λ=1.5406 Angstroms) obtained from a sample of commercially available smilagenin in crystalline form II (prior art);



FIG. 2 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form I;



FIG. 3 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form III;



FIG. 4 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form IIIA;



FIG. 5 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form V;



FIG. 6 shows a DSC trace of a sample of smilagenin in crystalline form V, shown to be a monohydrate;



FIG. 7 shows a TGA of a sample of smilagenin in crystalline form V, shown to be a monohydrate;



FIG. 8 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form VI (believed to be smilagenin channel hydrate);



FIG. 9 shows a DSC trace of a sample of smilagenin in crystalline form VI;



FIG. 10 shows a TGA of a sample of smilagenin in crystalline form VI;



FIG. 11 shows a vapour sorption graph of a sample of smilagenin in crystalline form VI;



FIG. 12 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin iso-propyl alcohol (IPA)-solvate in crystalline form VII;



FIG. 13 shows a DSC trace of a sample of smilagenin IPA-solvate in crystalline form VII;



FIG. 14 shows a TGA of a sample of smilagenin IPA-solvate in crystalline form VII, shown to be a hemi-TA-solvate;



FIG. 15 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form VI, with significant peaks marked by arrows; and



FIG. 16 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin IPA-solvate in crystalline form VII, with significant peaks are marked by arrows.





EXAMPLES AND DETAILED DESCRIPTION OF THE DRAWINGS

The following non-limiting Examples are provided as further illustration of the present invention, but without limitation, and are discussed with reference to the drawings.


Starting Materials

Samples of commercially available smilagenin were purchased from Research Plus Inc and Steraloids Inc.


The samples were analysed by XRPD and defined as form II by our nomenclature. A sample from Research Plus was examined by DSC and TGA and found to be anhydrous.


Example 1
Crystalline Form I

A. Crystallisation from Acetone


Smilagenin (10.0 g) was suspended in acetone (250 ml) and the mixture heated to reflux. The resultant solution was decanted from some undissolved solids and reheated to reflux to afford a clear solution. The solution was allowed to cool over about 3.5 hours to 29° C. and further cooled with an ice/water batch to 2° C. The resultant solid was harvested by filtration, washed with cold (5° C.) acetone (50 ml) and dried in a vacuum oven for 3 days to afford 7.4 g of pure smilagenin, which was characterised by XRPD as form I under our nomenclature.


B. Crystallisation from Acetonitrile


A suspension of smilagenin (1.05 g) in acetonitrile (10 ml) was stirred at ambient temperature overnight. The solid was harvested by filtration and dried in a vacuum oven at 80° C. to afford smilagenin form I (0.92 g, 88% yield).


Example 2
Crystalline Form II

Smilagenin was manufactured by stereospecific reduction of diosgenin according to the process described in PCT Patent Application No. PCT/GB2003/001780 (WO-A-2004/037845).


The smilagenin was subjected to XRPD and the pattern was found to be substantially similar to that shown in FIG. 1 of the drawings. On this basis, the material was characterised as form II under our nomenclature.


Examples 3 and 4
Crystalline Form III
Example 3

Smilagenin (10.0 g) was suspended in acetone (250 ml) and the mixture heated to reflux.


The resultant solution was cooled to 2° C. over about 15 minutes and the solid harvested by filtration, washed with cold (5° C.) acetone (250 ml) and dried in a vacuum oven for about 24 hours to afford 8.1 g of pure smilagenin, which was characterised by XRPD as form III under our nomenclature.


Example 4

Smilagenin (200 mg; form II) was suspended in tert-butyl methyl ether (4 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 40 mg, which was characterised as form III under our nomenclature by XRPD, DSC and TGA.


Examples 5 to 9
Crystalline Form V
Example 5

Water (200 ml) was added to a suspension of smilagenin (20 g) in acetone (200 ml) and the mixture stirred for about 2 hours. The solid was harvested by filtration, dried in a vacuum oven at 40° C. for about 24 hours to afford 20.5 g which was characterised by XRPD as form V under our nomenclature. The water content was determined as 4.4% by Karl Fischer analysis.


Example 6

Smilagenin (200 mg; form II) was suspended in hexane (10 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 80 mg which was characterised as form V under our nomenclature by XRPD, DSC and TGA.


Example 7

Smilagenin (500 mg; form II) was suspended in tetrahydrofuran (2 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 80 mg which was characterised as form V under our nomenclature by XRPD, DSC and TGA.


Examples 8 and 9

Smilagenin (Research Plus Inc.) was recrystallised using slurry crystallisation with butanone (Example 8) or 50% aqueous ethanol (Example 9) as the recrystallisation solvent. In each case the recrystallised material was subjected to XRPD and was characterised as a mixture of forms III and V under our nomenclature.


Example 10
Crystalline Form IIIA

Smilagenin (Research Plus Inc) was recrystallised using slurry crystallisation with dimethylformamide as the recrystallisation solvent.


The recrystallised material was subjected to XRPD and on this basis the material was characterised as crystalline form IIIA under our nomenclature.


Example 11
Crystalline Form VI (Smilagenin Channel Hydrate)

Smilagenin (260 mg) was weighed into a round bottomed flask and methanol (10 ml) was added. The contents were heated to 70° C. to affect complete dissolution, allowed to cool to room temperature and stirred at room temperature for 60 minutes. The solid was collected by filtration and air dried for about 2.5 hours.


The X-ray powder diffraction pattern is shown in FIG. 8, the differential scanning calorimetry trace is shown in FIG. 9 and the thermogravimetric analysis is shown in FIG. 10.


The DSC trace shows a weak broad endothermic transition up to 50° C., an exothermic transition at 120° C. followed by a final high energy melting transition at 188° C. TGA analysis confirms that the initial endotherm is associated with loss of water and that the transition at 121° C. is not associated with any solvent loss. Analysis of the sample by Karl Fischer titration confirmed that the solvent was water.


Vapour sorption studies (see FIG. 11) show that the sample is hygroscopic and adsorbs up to 9% water (about 2 mol. eq. water; i.e. a dihydrate) at high humidity and reversibly loses the water at low humidity. This suggests that this form is a channel hydrate of variable smilagenin:water stoichiometry, depending on the surrounding temperature and humidity.


Example 12
Crystalline Form VII (Smilagenin IPA-Solvate)

Smilagenin (150 mg) was added to iso-propyl alcohol (IPA) (5 ml) and the mixture heated to 70° C. to ensure dissolution. The clear solution was then allowed to cool to 40° C. over 2 hours, whereupon sudden precipitation occurred. The mixture was re-heated to 65° C. to dissolve the material and the solution re-cooled to 45° C., held at 45° C. for 15 minutes, cooled to 40° C., and held at 40° C. for 2 hours. The slurry was then cooled to room temperature and aged over a weekend at room temperature. After this time the solid was collected by filtration and air dried for about 3 hours.


The X-ray powder diffraction pattern is shown in FIG. 12, the differential scanning calorimetry trace is shown in FIG. 13 and the thermogravimetric analysis is shown in FIG. 14.


The DSC shows a broad endotherm between 40° C. and 140° C. that is consistent with loss of IPA from the sample. This is confirmed by TGA analysis which indicates 6.3% IPA present in the sample which is consistent with a hemi-IPA solvate of smilagenin. The IPA appears to be loosely bound in the crystal as it is lost from about 40° C. upwards in the DSC.


Example 13
Amorphous Smilagenin

Smilagenin (10 g) was heated to its melt using a temperature controlled heating mantle and held until a complete molten liquid was formed. The molten mass was poured into a Dewar containing approximately 150 ml of liquid nitrogen. The sample was decanted into a glass beaker and the liquid nitrogen allowed to evaporate. The sample was then transferred to a glass vial, flushed with dry nitrogen and then sealed. The sample was characterised as amorphous smilagenin on the basis of the XRPD pattern, which showed a lack of significant diffraction lines.









TABLE A







XRPD Intensities for Smilagenin Crystal Forms I,


II, III and V (λ = 1.5406 Angstroms)


at regularly spaced intervals in the 2-theta Range 5 to 50 degrees












λ = 1.5406 Å
Degrees (2θ)
Form I
Form II
Form III
Form V
















5
225
174
384
231



5.02
231
154
404
204



5.04
231
159
384
193



5.06
228
185
380
240



5.08
225
177
365
199



5.1
199
172
392
225



5.12
210
202
365
188



5.14
199
172
428
222



5.16
213
188
392
207



5.18
169
207
396
210



5.2
185
164
357
213



5.22
216
196
404
216



5.24
174
185
350
193



5.26
196
188
420
213



5.28
156
177
396
213



5.3
216
202
361
231



5.32
185
180
396
202



5.34
207
188
396
216



5.36
207
202
372
234



5.38
216
190
369
234



5.4
228
185
400
216



5.42
188
193
369
231



5.44
185
193
365
207



5.46
190
228
342
246



5.48
196
222
376
228



5.5
246
207
372
256



5.52
193
199
458
262



5.54
202
216
346
279



5.56
202
185
357
262



5.58
222
228
361
339



5.6
196
262
350
306



5.62
210
219
369
335



5.64
202
279
357
353



5.66
207
250
365
372



5.68
199
256
324
404



5.7
204
256
346
392



5.72
199
256
372
484



5.74
204
282
350
520



5.76
210
335
392
511



5.78
222
317
380
620



5.8
231
412
353
756



5.82
210
441
357
864



5.84
190
458
353
1116



5.86
253
471
342
1347



5.88
222
471
388
1529



5.9
193
372
342
1731



5.92
193
174
365
1576



5.94
196
177
384
918



5.96
210
172
396
424



5.98
199
146
380
231



6
202
161
365
243



6.02
193
146
369
185



6.04
213
185
400
177



6.06
196
149
392
174



6.08
216
139
424
159



6.1
216
149
428
159



6.12
272
169
449
154



6.14
240
128
462
174



6.16
219
237
467
180



6.18
210
151
506
182



6.2
250
164
502
154



6.22
289
156
529
154



6.24
262
149
552
154



6.26
246
137
543
154



6.28
272
154
424
156



6.3
269
128
380
177



6.32
272
174
342
185



6.34
259
164
313
164



6.36
310
117
369
146



6.38
313
137
324
128



6.4
331
159
320
161



6.42
384
137
339
146



6.44
365
137
350
156



6.46
384
144
299
135



6.48
437
151
339
151



6.5
467
151
335
146



6.52
543
137
317
139



6.54
590
137
328
166



6.56
600
144
361
146



6.58
751
142
372
159



6.6
864
142
335
142



6.62
986
156
328
154



6.64
1116
156
346
169



6.66
1274
151
335
177



6.68
1274
135
396
137



6.7
1190
146
388
159



6.72
1183
159
328
151



6.74
1325
182
376
159



6.76
1747
123
412
132



6.78
2070
132
380
151



6.8
2470
137
365
159



6.82
3226
137
380
149



6.84
3192
149
441
135



6.86
4122
144
424
130



6.88
6906
149
416
180



6.9
6939
161
449
144



6.92
4638
166
506
164



6.94
2162
151
520
159



6.96
718
139
515
161



6.98
342
161
576
169



7
310
135
566
151



7.02
272
132
640
151



7.04
259
146
671
123



7.06
250
154
745
139



7.08
276
146
801
132



7.1
256
128
858
139



7.12
237
114
847
144



7.14
269
128
1076
154



7.16
266
144
1082
159



7.18
259
137
1190
132



7.2
246
139
1267
146



7.22
234
149
1225
146



7.24
225
130
1043
156



7.26
213
137
740
144



7.28
185
128
534
154



7.3
174
142
400
139



7.32
164
146
369
164



7.34
180
114
380
172



7.36
166
151
313
169



7.38
164
128
342
146



7.4
172
142
286
123



7.42
169
135
313
139



7.44
146
154
299
154



7.46
169
142
289
139



7.48
164
144
296
149



7.5
164
117
306
159



7.52
151
128
286
156



7.54
166
142
299
169



7.56
154
154
303
144



7.58
144
130
299
119



7.6
128
156
292
144



7.62
154
156
289
154



7.64
164
117
286
139



7.66
146
144
269
144



7.68
137
121
256
144



7.7
159
169
286
161



7.72
149
144
269
142



7.74
161
164
266
166



7.76
132
125
266
139



7.78
151
112
282
130



7.8
161
130
289
149



7.82
156
128
269
151



7.84
142
161
299
139



7.86
166
128
272
149



7.88
135
139
276
146



7.9
139
142
269
142



7.92
128
144
266
159



7.94
132
130
256
172



7.96
210
144
276
161



7.98
128
146
279
151



8
146
128
292
146



8.02
146
130
253
137



8.04
151
137
299
159



8.06
259
119
256
161



8.08
125
121
276
154



8.1
142
123
276
156



8.12
128
135
292
142



8.14
149
139
289
137



8.16
177
123
253
137



8.18
135
139
299
137



8.2
130
121
272
144



8.22
121
137
262
172



8.24
100
106
262
139



8.26
213
119
266
132



8.28
144
110
276
139



8.3
130
117
279
128



8.32
135
112
269
137



8.34
139
130
266
135



8.36
177
130
216
137



8.38
128
130
296
144



8.4
139
132
279
123



8.42
125
92
282
125



8.44
125
112
272
154



8.46
114
121
256
135



8.48
303
130
262
137



8.5
114
117
289
142



8.52
119
128
256
139



8.54
149
110
282
125



8.56
132
121
289
188



8.58
119
132
279
142



8.6
110
128
243
121



8.62
106
98
272
137



8.64
110
130
289
159



8.66
125
117
313
128



8.68
125
117
299
114



8.7
114
104
303
313



8.72
135
128
317
132



8.74
121
125
303
135



8.76
112
128
306
121



8.78
112
130
313
112



8.8
130
106
320
135



8.82
119
142
350
151



8.84
119
125
320
137



8.86
114
144
259
142



8.88
117
142
286
146



8.9
130
156
303
130



8.92
139
137
269
164



8.94
137
149
262
144



8.96
110
182
262
164



8.98
142
144
292
154



9
119
151
282
137



9.02
135
154
269
166



9.04
130
159
262
207



9.06
130
161
286
169



9.08
149
188
279
199



9.1
137
188
303
202



9.12
144
199
313
210



9.14
130
210
306
225



9.16
130
210
292
222



9.18
144
216
286
219



9.2
149
253
303
250



9.22
142
222
313
225



9.24
149
276
313
276



9.26
164
310
328
269



9.28
193
335
310
303



9.3
182
369
357
342



9.32
182
392
392
361



9.34
188
441
380
433



9.36
228
511
400
388



9.38
213
543
408
449



9.4
246
529
462
502



9.42
250
625
428
557



9.44
213
635
506
625



9.46
210
600
480
600



9.48
199
562
562
605



9.5
219
372
557
586



9.52
210
250
635
471



9.54
202
172
595
384



9.56
207
125
620
222



9.58
180
108
493
169



9.6
182
125
454
128



9.62
130
100
376
146



9.64
149
94
282
135



9.66
137
121
299
130



9.68
121
112
259
128



9.7
135
104
282
98



9.72
119
100
286
119



9.74
125
108
228
117



9.76
123
92
272
119



9.78
123
96
292
137



9.8
108
108
250
98



9.82
110
102
276
106



9.84
119
83
286
108



9.86
125
79
276
98



9.88
123
137
292
106



9.9
112
98
256
108



9.92
114
102
262
106



9.94
121
88
272
106



9.96
123
86
262
112



9.98
119
98
279
123



10
119
106
282
94



10.02
96
98
250
98



10.04
130
108
286
117



10.06
144
112
266
102



10.08
125
108
269
108



10.1
146
108
289
83



10.12
125
102
256
125



10.14
146
114
292
106



10.16
132
121
289
104



10.18
142
108
286
114



10.2
156
94
282
125



10.22
164
130
269
123



10.24
169
104
256
98



10.26
154
102
286
114



10.28
182
100
286
110



10.3
172
102
292
125



10.32
161
90
286
94



10.34
172
79
269
102



10.36
204
313
276
102



10.38
219
164
266
94



10.4
240
96
289
96



10.42
225
92
306
100



10.44
188
90
292
110



10.46
219
81
306
119



10.48
234
86
262
106



10.5
266
79
292
98



10.52
279
100
272
106



10.54
320
88
317
108



10.56
346
108
262
96



10.58
353
100
303
106



10.6
428
76
303
112



10.62
590
108
324
112



10.64
812
102
372
119



10.66
888
100
303
100



10.68
745
96
286
100



10.7
681
92
289
110



10.72
671
100
292
98



10.74
818
108
299
117



10.76
1050
102
339
108



10.78
1116
112
353
125



10.8
1005
96
357
137



10.82
853
92
384
144



10.84
812
110
437
132



10.86
484
94
376
139



10.88
328
96
420
104



10.9
250
121
437
161



10.92
256
102
433
154



10.94
289
121
408
144



10.96
269
135
458
172



10.98
335
132
506
172



11
339
142
552
144



11.02
372
137
515
185



11.04
303
161
586
207



11.06
213
135
640
190



11.08
144
185
666
240



11.1
128
177
708
234



11.12
202
188
708
306



11.14
112
199
713
292



11.16
119
228
724
328



11.18
110
199
676
317



11.2
119
237
620
396



11.22
125
253
557
408



11.24
112
225
467
400



11.26
132
204
420
433



11.28
130
204
365
445



11.3
130
231
365
441



11.32
132
237
324
350



11.34
123
207
328
433



11.36
125
276
324
441



11.38
139
246
289
493



11.4
139
310
320
506



11.42
149
276
296
610



11.44
146
346
342
645



11.46
154
350
310
708



11.48
139
372
331
824



11.5
169
445
335
955



11.52
161
488
306
1089



11.54
207
524
335
1225



11.56
204
610
335
1414



11.58
207
702
313
1544



11.6
237
756
324
1840



11.62
225
847
310
2200



11.64
296
992
313
2694



11.66
328
1239
328
3434



11.68
335
1521
335
3844



11.7
250
1962
342
4173



11.72
256
2275
365
4651



11.74
188
1656
369
6147



11.76
161
870
420
7006



11.78
121
369
392
5227



11.8
149
193
384
2714



11.82
154
137
388
992



11.84
151
104
404
441



11.86
154
123
437
299



11.88
139
114
445
234



11.9
144
112
471
169



11.92
142
86
511
182



11.94
149
121
511
154



11.96
177
102
471
164



11.98
159
108
538
146



12
169
102
566
123



12.02
132
88
511
142



12.04
169
102
615
114



12.06
180
96
676
104



12.08
190
106
676
98



12.1
182
110
702
108



12.12
166
77
801
100



12.14
182
94
824
106



12.16
210
83
900
104



12.18
250
83
1018
104



12.2
231
79
1082
117



12.22
279
83
1204
100



12.24
269
92
1246
98



12.26
259
74
1362
92



12.28
324
77
1429
100



12.3
353
102
1560
98



12.32
376
98
1632
110



12.34
445
85
1714
108



12.36
428
92
1689
94



12.38
462
79
1722
108



12.4
420
98
1624
100



12.42
437
100
1592
108



12.44
497
92
1513
100



12.46
562
83
1296
104



12.48
676
90
1190
110



12.5
615
94
1096
90



12.52
635
110
1037
94



12.54
557
102
1024
102



12.56
497
102
986
123



12.58
488
117
980
128



12.6
493
98
924
119



12.62
497
108
936
106



12.64
400
108
1037
130



12.66
339
102
992
108



12.68
289
108
1050
144



12.7
262
92
1204
117



12.72
272
108
1260
256



12.74
303
102
1376
132



12.76
313
119
1513
121



12.78
328
132
1656
110



12.8
380
114
1747
98



12.82
353
135
1849
125



12.84
396
142
2153
121



12.86
388
117
2352
128



12.88
408
144
2570
121



12.9
562
128
2809
123



12.92
467
114
3025
128



12.94
529
146
3387
121



12.96
581
130
3516
114



12.98
534
154
3906
137



13
630
149
4238
135



13.02
581
142
4225
137



13.04
640
142
3881
151



13.06
610
166
3469
135



13.08
671
190
2894
132



13.1
660
146
2228
151



13.12
681
190
1927
172



13.14
718
199
1875
156



13.16
773
219
1823
164



13.18
894
213
1875
182



13.2
999
262
1998
222



13.22
1163
306
2237
262



13.24
1239
276
2343
228



13.26
1318
328
2530
228



13.28
1362
331
2725
228



13.3
1529
369
2841
240



13.32
1673
396
3069
262



13.34
1789
424
3329
279



13.36
1840
502
3457
282



13.38
2034
524
3672
292



13.4
2285
524
3697
350



13.42
2381
605
3528
376



13.44
2460
605
3493
396



13.46
2560
713
3505
380



13.48
2704
650
3341
424



13.5
2560
708
3341
462



13.52
2490
697
3457
467



13.54
2034
724
3446
529



13.56
1989
835
3318
548



13.58
2088
778
3181
581



13.6
2304
801
2884
590



13.62
2746
807
2520
655



13.64
3457
686
2247
610



13.66
3672
581
2162
576



13.68
3469
445
2125
497



13.7
3612
433
2247
416



13.72
3807
428
2294
392



13.74
4436
433
2372
320



13.76
5580
437
2470
324



13.78
7362
441
2621
317



13.8
10547
557
2756
331



13.82
10424
534
2798
361



13.84
7762
620
2841
380



13.86
4900
751
2809
357



13.88
2172
807
2714
458



13.9
1176
930
2601
511



13.92
778
1018
2314
562



13.94
650
1176
1945
610



13.96
718
1376
1665
729



13.98
702
1537
1296
734



14
745
1884
1176
900



14.02
724
2181
1037
949



14.04
740
2372
1011
1018



14.06
773
2673
1011
1163



14.08
894
3036
1043
1354



14.1
876
3411
1043
1490



14.12
936
3721
1211
1632



14.14
1024
4032
1218
1781



14.16
1082
4624
1318
2007



14.18
1076
4679
1421
2209



14.2
1170
5170
1490
2304



14.22
1163
5213
1764
2591



14.24
1142
5098
1772
2611



14.26
1050
4665
1892
2735



14.28
912
4199
2079
2735



14.3
724
3192
2266
2440



14.32
625
2098
2352
2061



14.34
497
1318
2500
1640



14.36
449
818
2746
1354



14.38
433
595
2884
1109



14.4
441
590
3025
818



14.42
484
600
3170
745



14.44
408
605
3283
778



14.46
480
702
3204
858



14.48
408
650
3047
930



14.5
404
740
2530
1109



14.52
445
734
2088
1102



14.54
376
784
1697
1183



14.56
339
876
1384
1310



14.58
396
924
1318
1399



14.6
372
906
1310
1490



14.62
328
858
1289
1482



14.64
328
681
1296
1296



14.66
250
471
1354
1089



14.68
286
331
1325
795



14.7
299
256
1436
571



14.72
310
279
1482
350



14.74
306
228
1600
256



14.76
292
243
1697
199



14.78
296
262
1731
188



14.8
331
272
1927
204



14.82
339
306
1989
222



14.84
369
317
2125
204



14.86
388
380
2352
240



14.88
449
412
2460
262



14.9
484
408
2601
262



14.92
571
420
2756
279



14.94
605
449
2970
262



14.96
713
449
3181
289



14.98
740
502
3283
328



15
900
511
3226
339



15.02
992
497
3260
342



15.04
1043
488
3329
320



15.06
1089
484
3552
353



15.08
1156
484
3493
365



15.1
1267
471
3624
372



15.12
1444
484
3931
380



15.14
1632
538
4147
408



15.16
1537
511
4083
392



15.18
1592
524
4382
433



15.2
1697
484
4436
369



15.22
1608
493
4382
404



15.24
1498
475
4122
342



15.26
1340
493
3931
350



15.28
1102
515
3457
420



15.3
918
600
2767
400



15.32
697
615
2362
437



15.34
660
724
1971
449



15.36
566
795
1731
506



15.38
600
882
1706
571



15.4
586
1063
1537
635



15.42
635
1183
1544
708



15.44
702
1362
1584
930



15.46
790
1467
1444
1018



15.48
807
1616
1399
1089



15.5
876
1884
1362
1211



15.52
882
2162
1369
1310



15.54
942
2266
1406
1391



15.56
1063
2460
1362
1616



15.58
1142
2735
1310
1858



15.6
1267
3025
1406
1936



15.62
1332
3125
1421
2190



15.64
1310
3238
1444
2352



15.66
1282
3295
1498
2470



15.68
1197
3249
1467
2570



15.7
1050
3114
1560
2540



15.72
1024
3058
1560
2550



15.74
1109
3014
1656
2652



15.76
1030
3114
1673
2809



15.78
1089
3047
1632
3102



15.8
1030
2894
1608
3283



15.82
1037
2520
1537
3014



15.84
961
1884
1436
2611



15.86
949
1225
1475
2116



15.88
973
734
1498
1537



15.9
942
400
1568
1063



15.92
894
259
1616
681



15.94
1030
219
1722
392



15.96
1050
199
1789
246



15.98
1096
161
1849
193



16
1037
185
1910
199



16.02
894
159
1962
169



16.04
692
164
2025
164



16.06
502
144
2007
196



16.08
416
130
1901
154



16.1
350
144
1849
174



16.12
310
137
1600
132



16.14
256
137
1544
151



16.16
269
121
1325
216



16.18
237
146
1197
130



16.2
269
151
1122
135



16.22
259
151
1136
149



16.24
256
161
1142
137



16.26
243
161
1260
144



16.28
303
151
1232
159



16.3
282
199
1414
161



16.32
313
188
1505
151



16.34
328
174
1592
177



16.36
320
234
1714
213



16.38
331
262
1875
202



16.4
361
299
1989
219



16.42
384
303
2200
210



16.44
361
292
2372
240



16.46
376
339
2725
266



16.48
420
342
2767
306



16.5
400
365
2992
313



16.52
449
396
3238
331



16.54
424
428
3422
342



16.56
471
428
3636
342



16.58
420
475
3697
365



16.6
424
428
3576
384



16.62
353
488
3295
412



16.64
339
529
2873
412



16.66
353
548
2673
408



16.68
339
543
2611
428



16.7
328
543
2652
437



16.72
313
557
2500
467



16.74
292
502
2500
441



16.76
317
449
2632
416



16.78
313
538
2683
380



16.8
296
529
2510
369



16.82
350
566
2530
396



16.84
350
605
2343
384



16.86
331
660
2070
404



16.88
369
671
1798
462



16.9
420
734
1459
538



16.92
420
762
1253
600



16.94
416
795
1129
590



16.96
454
882
1056
702



16.98
493
980
1030
729



17
538
1050
906
888



17.02
557
1274
949
955



17.04
548
1310
942
1056



17.06
571
1537
955
1197



17.08
620
1608
980
1303



17.1
630
1892
930
1459



17.12
671
2016
986
1568



17.14
801
2190
1050
1764



17.16
847
2480
1030
1971



17.18
900
2560
1043
2134



17.2
912
2673
1102
2381



17.22
967
2938
1102
2735



17.24
1030
2873
1129
2809



17.26
999
2894
1082
2916



17.28
1005
2591
1122
2809



17.3
1050
2088
1082
2470



17.32
942
1421
986
2285



17.34
955
858
1011
1927



17.36
949
534
1018
1429



17.38
1037
353
961
853



17.4
1218
269
924
590



17.42
1482
210
918
380



17.44
1781
185
999
250



17.46
1980
154
955
250



17.48
1962
169
1056
253



17.5
2043
169
1030
240



17.52
1989
169
1037
286



17.54
1866
174
1018
276



17.56
2162
219
1122
313



17.58
2218
219
1142
286



17.6
2088
240
1190
320



17.62
2275
190
1190
388



17.64
2694
174
1183
433



17.66
2611
144
1082
376



17.68
2430
154
1037
272



17.7
2323
123
999
253



17.72
2266
128
930
180



17.74
2266
128
942
119



17.76
2007
161
973
121



17.78
1927
117
918
149



17.8
1163
135
936
135



17.82
829
132
1018
149



17.84
506
139
1063
137



17.86
396
139
1136
154



17.88
376
180
1218
151



17.9
380
190
1332
137



17.92
493
185
1406
159



17.94
400
180
1444
190



17.96
376
182
1568
159



17.98
412
174
1640
204



18
412
164
1756
196



18.02
428
210
1866
180



18.04
433
286
2043
190



18.06
396
216
2034
216



18.08
353
196
2079
222



18.1
372
222
2052
213



18.12
320
182
1823
213



18.14
328
172
1640
202



18.16
246
154
1414
196



18.18
234
137
1156
149



18.2
246
132
936
177



18.22
222
151
801
146



18.24
237
130
740
159



18.26
216
121
630
164



18.28
253
144
625
164



18.3
262
154
640
182



18.32
213
180
655
161



18.34
225
166
671
199



18.36
228
188
692
207



18.38
225
185
692
225



18.4
272
185
745
246



18.42
256
253
745
276



18.44
269
250
778
269



18.46
250
282
745
320



18.48
269
331
829
324



18.5
317
372
876
388



18.52
282
392
900
408



18.54
339
480
924
420



18.56
369
502
961
515



18.58
369
562
924
581



18.6
404
615
1024
660



18.62
428
702
1037
713



18.64
441
724
1011
784



18.66
506
778
942
864



18.68
520
790
924
980



18.7
581
936
870
1156



18.72
620
980
795
1142



18.74
734
1005
724
1260



18.76
724
967
666
1176



18.78
692
992
605
1176



18.8
790
955
635
1136



18.82
864
864
576
1122



18.84
900
835
534
1063



18.86
900
818
529
961



18.88
900
692
538
870



18.9
847
543
543
762



18.92
858
376
511
620



18.94
853
289
529
497



18.96
864
369
534
369



18.98
900
166
557
231



19
864
130
586
196



19.02
912
112
586
144



19.04
1122
117
586
130



19.06
1282
90
595
132



19.08
1429
98
640
102



19.1
1436
104
640
112



19.12
1310
128
650
100



19.14
1218
98
671
130



19.16
1190
112
676
114



19.18
1296
85
686
106



19.2
1616
104
666
119



19.22
1475
112
655
114



19.24
1149
108
581
135



19.26
1043
128
543
117



19.28
773
130
576
114



19.3
562
142
543
110



19.32
488
128
557
117



19.34
458
121
590
106



19.36
380
142
600
132



19.38
380
166
615
128



19.4
384
174
566
144



19.42
408
151
686
130



19.44
424
169
713
146



19.46
441
199
778
154



19.48
441
188
773
164



19.5
506
180
745
154



19.52
484
180
801
174



19.54
534
185
773
144



19.56
671
202
762
149



19.58
625
196
740
161



19.6
552
213
692
169



19.62
686
234
713
210



19.64
751
196
660
185



19.66
762
210
630
199



19.68
864
219
620
199



19.7
1089
188
650
207



19.72
1163
202
666
213



19.74
1170
228
692
207



19.76
1414
253
620
262



19.78
1739
246
645
279



19.8
1632
246
625
253



19.82
1576
262
595
292



19.84
1475
272
625
306



19.86
1467
246
576
259



19.88
1498
225
534
276



19.9
1376
266
600
246



19.92
1096
256
543
207



19.94
692
292
645
190



19.96
524
259
650
219



19.98
441
372
660
240



20
292
400
610
246



20.02
266
404
718
262



20.04
256
471
708
253



20.06
313
515
734
331



20.08
339
562
767
380



20.1
306
571
790
392



20.12
320
671
847
420



20.14
328
702
858
441



20.16
350
829
829
515



20.18
353
853
888
467



20.2
331
930
829
576



20.22
372
900
751
543



20.24
369
1030
745
615



20.26
392
1018
676
681



20.28
424
1056
620
671



20.3
416
986
640
713



20.32
420
1005
586
702



20.34
408
818
610
692



20.36
416
686
640
615



20.38
384
488
655
511



20.4
372
353
600
471



20.42
380
296
713
339



20.44
388
222
645
279



20.46
357
190
630
231



20.48
376
154
620
180



20.5
372
161
600
164



20.52
365
156
600
154



20.54
384
172
552
144



20.56
484
182
586
166



20.58
433
210
493
151



20.6
441
185
538
156



20.62
471
199
529
193



20.64
458
231
488
185



20.66
548
246
488
190



20.68
650
289
543
202



20.7
697
276
475
210



20.72
812
306
475
246



20.74
980
353
506
279



20.76
1204
350
520
276



20.78
955
424
529
303



20.8
986
437
586
317



20.82
812
475
595
335



20.84
538
520
562
412



20.86
529
600
605
437



20.88
449
676
650
524



20.9
404
686
686
511



20.92
400
713
676
576



20.94
433
767
740
650



20.96
433
829
762
713



20.98
462
773
824
713



21
467
807
767
713



21.02
449
745
870
729



21.04
420
713
847
686



21.06
404
640
882
660



21.08
376
620
888
676



21.1
342
595
870
620



21.12
350
543
847
615



21.14
324
576
778
605



21.16
350
615
745
702



21.18
369
630
655
756



21.2
380
645
615
818



21.22
361
660
524
955



21.24
339
666
543
1011



21.26
296
581
515
1076



21.28
262
562
511
967



21.3
246
412
520
824



21.32
240
365
511
692



21.34
202
262
484
548



21.36
219
222
524
392



21.38
188
185
562
324



21.4
207
159
590
234



21.42
199
139
590
169



21.44
199
128
620
159



21.46
199
144
562
144



21.48
231
144
620
139



21.5
182
119
625
130



21.52
202
151
666
159



21.54
174
125
660
130



21.56
207
142
660
123



21.58
196
112
740
123



21.6
237
154
724
139



21.62
213
139
650
149



21.64
193
125
708
137



21.66
213
110
751
135



21.68
213
119
795
132



21.7
213
114
756
128



21.72
272
137
734
159



21.74
276
174
734
132



21.76
286
151
702
142



21.78
286
169
686
166



21.8
306
174
640
144



21.82
289
182
620
174



21.84
306
213
605
219



21.86
289
225
557
216



21.88
324
306
576
234



21.9
342
276
590
276



21.92
412
299
640
286



21.94
433
331
615
282



21.96
462
350
686
353



21.98
515
376
660
433



22
515
433
702
454



22.02
586
480
640
445



22.04
708
625
697
529



22.06
686
562
762
534



22.08
992
625
734
586



22.1
1170
630
713
671



22.12
1459
697
724
778



22.14
1303
767
708
870



22.16
999
795
692
864



22.18
812
858
708
912



22.2
645
900
671
1024



22.22
458
955
666
1050



22.24
313
900
734
1037



22.26
306
835
773
942



22.28
269
660
778
894



22.3
246
595
773
801



22.32
243
484
807
635



22.34
240
454
835
524



22.36
250
437
795
428



22.38
246
420
841
400



22.4
243
404
894
384



22.42
276
441
824
365



22.44
222
346
894
380



22.46
246
335
942
342



22.48
234
361
942
331



22.5
202
237
1076
350



22.52
222
210
1050
259



22.54
216
180
1018
250



22.56
210
161
1096
210



22.58
199
151
1018
185



22.6
182
121
986
196



22.62
151
112
980
159



22.64
164
125
882
161



22.66
177
110
807
166



22.68
193
144
734
159



22.7
196
146
630
159



22.72
188
123
557
174



22.74
188
125
605
146



22.76
246
121
515
172



22.78
193
159
497
154



22.8
256
174
493
149



22.82
243
146
529
190



22.84
246
164
484
174



22.86
250
174
488
182



22.88
262
188
467
193



22.9
279
164
454
190



22.92
282
185
454
253



22.94
299
210
445
237



22.96
303
204
437
256



22.98
317
199
412
276



23
306
216
424
310



23.02
384
269
467
303



23.04
365
246
416
331



23.06
342
289
471
388



23.08
361
282
445
428



23.1
292
313
458
502



23.12
313
384
484
543



23.14
243
365
538
520



23.16
210
376
562
562



23.18
180
384
524
615



23.2
196
342
557
595



23.22
240
306
586
600



23.24
199
346
630
620



23.26
199
317
605
630



23.28
202
296
635
605



23.3
216
289
681
600



23.32
240
286
635
640



23.34
210
339
645
676



23.36
207
350
666
734



23.38
225
396
708
824



23.4
222
388
697
847



23.42
237
416
650
961



23.44
243
543
635
1082



23.46
240
571
635
1267



23.48
286
745
620
1391



23.5
292
1109
615
1490



23.52
310
1354
552
1640



23.54
286
1069
529
1849



23.56
292
762
467
2209



23.58
313
681
445
2052



23.6
282
475
437
1225



23.62
286
299
428
1122



23.64
328
243
420
900



23.66
346
234
424
475



23.68
361
216
480
328



23.7
350
213
441
253



23.72
342
219
458
243



23.74
372
210
475
256



23.76
400
222
506
250



23.78
408
210
506
350



23.8
384
196
484
222



23.82
357
164
506
188



23.84
306
164
484
204



23.86
253
166
480
196



23.88
246
139
462
161



23.9
240
117
433
151



23.92
174
96
376
123



23.94
154
106
372
132



23.96
132
110
388
132



23.98
174
92
357
119



24
142
96
392
125



24.02
139
104
350
154



24.04
144
90
353
100



24.06
166
112
380
128



24.08
123
85
357
135



24.1
137
98
328
114



24.12
149
123
369
128



24.14
139
125
357
119



24.16
159
112
384
149



24.18
130
135
400
144



24.2
164
135
372
159



24.22
164
144
404
164



24.24
177
177
372
164



24.26
172
185
369
193



24.28
207
161
388
188



24.3
164
222
408
234



24.32
182
216
365
207



24.34
188
234
392
253



24.36
196
225
467
276



24.38
216
256
388
361



24.4
213
262
475
335



24.42
207
286
428
342



24.44
222
286
445
369



24.46
253
313
515
396



24.48
216
342
506
396



24.5
231
400
475
471



24.52
253
380
493
467



24.54
286
424
520
538



24.56
237
428
511
515



24.58
256
467
524
497



24.6
286
462
506
529



24.62
339
357
552
576



24.64
299
388
538
552



24.66
259
286
511
462



24.68
234
289
538
433



24.7
193
246
581
335



24.72
172
213
562
269



24.74
172
196
557
199



24.76
169
196
625
225



24.78
172
193
655
202



24.8
161
216
645
193



24.82
159
199
605
188



24.84
166
199
666
190



24.86
174
225
650
210



24.88
169
222
615
228



24.9
161
272
581
250



24.92
159
259
552
231



24.94
159
213
506
222



24.96
159
256
462
188



24.98
156
213
462
213



25
174
180
454
199



25.02
169
172
420
202



25.04
193
161
416
172



25.06
207
164
404
159



25.08
193
135
467
149



25.1
213
144
458
151



25.12
234
130
441
146



25.14
202
121
480
121



25.16
199
125
445
110



25.18
202
149
480
117



25.2
193
112
458
121



25.22
228
106
467
130



25.24
185
112
493
339



25.26
202
112
471
108



25.28
225
128
484
121



25.3
250
161
502
137



25.32
269
123
524
128



25.34
259
128
524
121



25.36
237
154
493
137



25.38
262
142
529
161



25.4
276
146
581
172



25.42
219
142
571
149



25.44
207
164
571
169



25.46
188
169
557
180



25.48
207
166
590
159



25.5
188
266
529
159



25.52
190
169
471
144



25.54
193
164
475
128



25.56
182
166
449
154



25.58
207
204
445
128



25.6
161
210
420
180



25.62
169
269
400
149



25.64
185
228
412
172



25.66
185
266
372
177



25.68
174
266
404
182



25.7
193
292
328
182



25.72
185
269
346
219



25.74
161
286
342
182



25.76
154
289
346
210



25.78
166
365
331
219



25.8
196
296
331
222



25.82
190
266
331
246



25.84
169
279
342
246



25.86
188
276
306
243



25.88
166
320
313
219



25.9
185
296
328
222



25.92
484
324
279
237



25.94
169
310
279
237



25.96
177
299
299
213



25.98
188
292
310
199



26
159
259
310
204



26.02
161
292
292
207



26.04
177
222
313
202



26.06
154
207
296
177



26.08
149
156
331
164



26.1
169
156
289
135



26.12
144
125
320
130



26.14
139
142
292
132



26.16
114
106
303
146



26.18
144
104
292
114



26.2
135
112
317
110



26.22
144
104
320
123



26.24
142
106
324
117



26.26
164
128
292
144



26.28
164
130
313
132



26.3
177
130
299
125



26.32
180
137
328
142



26.34
196
142
328
135



26.36
225
185
320
202



26.38
279
177
342
161



26.4
310
207
350
188



26.42
306
207
331
159



26.44
342
228
369
164



26.46
335
199
365
169



26.48
353
225
353
174



26.5
331
237
388
166



26.52
369
240
416
185



26.54
372
272
424
222



26.56
454
262
437
196



26.58
433
313
384
202



26.6
529
317
449
243



26.62
655
335
458
250



26.64
858
350
458
246



26.66
1109
320
454
256



26.68
1490
380
497
253



26.7
1347
331
454
234



26.72
1102
317
449
282



26.74
1063
335
458
269



26.76
1030
324
408
286



26.78
894
328
412
272



26.8
610
320
376
269



26.82
497
365
376
292



26.84
408
342
420
339



26.86
396
376
388
342



26.88
350
365
376
286



26.9
292
372
416
320



26.92
328
339
388
313



26.94
331
342
445
353



26.96
346
303
412
328



26.98
384
289
441
299



27
412
279
380
331



27.02
384
246
416
266



27.04
412
213
433
289



27.06
441
231
353
262



27.08
471
196
404
272



27.1
458
213
396
279



27.12
416
190
372
228



27.14
475
190
388
240



27.16
511
169
380
246



27.18
493
159
353
250



27.2
480
139
412
222



27.22
534
169
342
185



27.24
543
154
400
169



27.26
458
174
454
169



27.28
437
169
441
172



27.3
462
159
467
193



27.32
420
154
433
188



27.34
313
174
445
161



27.36
243
182
428
166



27.38
246
182
441
174



27.4
222
174
400
188



27.42
199
177
471
190



27.44
166
177
458
174



27.46
156
154
441
207



27.48
144
172
475
164



27.5
166
174
458
169



27.52
166
144
428
137



27.54
159
174
433
123



27.56
159
139
400
149



27.58
164
172
420
137



27.6
161
156
384
151



27.62
164
149
361
123



27.64
161
123
361
135



27.66
188
159
384
128



27.68
204
142
396
154



27.7
193
144
392
169



27.72
219
135
404
156



27.74
204
128
420
164



27.76
199
156
441
185



27.78
216
154
412
180



27.8
231
159
441
231



27.82
234
156
428
190



27.84
313
193
506
204



27.86
306
172
502
210



27.88
306
172
515
231



27.9
335
185
511
210



27.92
313
204
511
231



27.94
317
237
562
253



27.96
317
237
548
250



27.98
324
243
600
276



28
303
256
557
320



28.02
306
256
557
303



28.04
269
286
566
282



28.06
243
279
543
342



28.08
231
286
576
372



28.1
219
299
548
369



28.12
210
306
576
342



28.14
219
250
576
388



28.16
202
234
557
361



28.18
199
204
586
306



28.2
225
196
520
243



28.22
161
182
529
202



28.24
177
159
497
188



28.26
169
151
480
188



28.28
210
144
420
177



28.3
222
132
467
161



28.32
202
146
449
137



28.34
237
142
484
142



28.36
256
125
428
142



28.38
234
156
424
114



28.4
234
146
437
130



28.42
286
159
437
142



28.44
306
161
420
174



28.46
339
177
445
135



28.48
310
172
458
166



28.5
303
169
416
169



28.52
276
174
437
159



28.54
259
182
458
156



28.56
256
169
437
149



28.58
240
169
449
174



28.6
216
172
433
161



28.62
231
174
441
149



28.64
237
174
445
185



28.66
234
177
433
161



28.68
259
207
424
144



28.7
213
185
416
169



28.72
180
185
408
144



28.74
169
174
441
139



28.76
159
164
420
144



28.78
159
166
408
144



28.8
144
156
458
151



28.82
174
137
388
117



28.84
149
128
408
125



28.86
144
130
416
117



28.88
149
100
420
119



28.9
151
106
380
117



28.92
156
110
428
108



28.94
132
88
404
144



28.96
159
98
376
123



28.98
199
88
396
123



29
169
119
365
110



29.02
199
104
342
123



29.04
193
144
342
151



29.06
228
117
335
159



29.08
210
130
357
169



29.1
216
132
296
164



29.12
246
137
317
151



29.14
246
151
361
174



29.16
276
159
303
185



29.18
253
182
289
225



29.2
269
182
310
199



29.22
246
172
339
219



29.24
266
196
317
231



29.26
228
207
339
234



29.28
240
202
328
234



29.3
234
225
324
266



29.32
210
228
313
282



29.34
202
243
306
320



29.36
177
266
335
339



29.38
204
286
299
342



29.4
169
320
335
388



29.42
177
292
282
388



29.44
159
335
320
384



29.46
182
313
328
416



29.48
169
339
324
437



29.5
169
353
306
416



29.52
159
306
342
335



29.54
149
306
376
365



29.56
149
279
350
328



29.58
156
324
388
303



29.6
159
303
376
279



29.62
156
269
369
282



29.64
161
276
372
259



29.66
174
303
372
266



29.68
207
250
420
234



29.7
199
320
388
262



29.72
210
276
396
259



29.74
210
299
400
240



29.76
190
328
384
269



29.78
180
269
420
282



29.8
199
339
449
262



29.82
210
269
416
276



29.84
219
276
400
262



29.86
207
276
404
253



29.88
225
228
400
259



29.9
185
234
412
250



29.92
210
213
408
202



29.94
213
216
384
204



29.96
231
196
396
210



29.98
222
177
384
193



30
234
166
365
166



30.02
213
139
372
182



30.04
231
137
376
159



30.06
259
112
384
128



30.08
222
102
376
146



30.1
182
108
357
128



30.12
166
90
384
114



30.14
185
98
357
104



30.16
169
100
365
121



30.18
123
123
353
110



30.2
164
114
346
117



30.22
159
106
320
112



30.24
149
88
357
128



30.26
146
114
339
123



30.28
225
123
365
128



30.3
144
130
339
112



30.32
164
117
357
125



30.34
132
137
365
125



30.36
144
144
376
108



30.38
149
123
350
144



30.4
207
137
328
123



30.42
159
151
365
128



30.44
234
142
361
144



30.46
174
151
376
159



30.48
185
169
380
146



30.5
207
166
380
166



30.52
193
177
342
151



30.54
219
156
376
169



30.56
243
193
365
164



30.58
219
169
353
139



30.6
253
169
404
177



30.62
246
166
335
146



30.64
303
169
408
144



30.66
357
146
365
159



30.68
408
177
365
149



30.7
416
166
376
180



30.72
365
137
353
164



30.74
400
193
372
190



30.76
380
174
404
174



30.78
365
177
437
180



30.8
365
185
412
177



30.82
306
174
412
199



30.84
272
177
380
177



30.86
262
161
416
204



30.88
250
151
471
161



30.9
228
149
445
164



30.92
202
172
462
146



30.94
185
161
458
149



30.96
164
169
437
177



30.98
269
185
441
174



31
182
180
428
144



31.02
193
172
445
169



31.04
207
193
449
185



31.06
216
190
441
166



31.08
234
182
420
164



31.1
228
161
437
154



31.12
190
190
416
154



31.14
202
182
449
169



31.16
282
121
424
159



31.18
279
128
445
144



31.2
276
119
400
137



31.22
237
100
408
142



31.24
234
121
380
121



31.26
231
108
313
123



31.28
250
110
365
132



31.3
193
104
339
104



31.32
240
106
342
119



31.34
222
108
313
110



31.36
196
106
350
114



31.38
190
121
350
125



31.4
204
144
320
119



31.42
161
128
335
164



31.44
202
144
335
135



31.46
188
144
266
159



31.48
177
177
306
216



31.5
159
193
286
207



31.52
185
207
324
210



31.54
166
219
313
225



31.56
166
228
313
259



31.58
174
259
317
269



31.6
177
279
313
292



31.62
182
292
324
303



31.64
213
320
339
310



31.66
207
324
335
310



31.68
213
365
331
331



31.7
207
369
335
404



31.72
240
365
357
416



31.74
228
396
339
502



31.76
243
420
357
497



31.78
237
433
328
502



31.8
231
475
350
534



31.82
231
511
369
502



31.84
210
493
384
520



31.86
199
484
372
605



31.88
225
484
350
586



31.9
210
433
339
590



31.92
210
400
346
506



31.94
228
369
342
497



31.96
199
313
331
441



31.98
210
310
350
384



32
199
253
306
328



32.02
190
196
317
296



32.04
177
216
317
246



32.06
193
182
313
259



32.08
174
180
331
199



32.1
166
185
317
225



32.12
156
190
328
188



32.14
182
190
331
216



32.16
144
207
328
213



32.18
151
207
353
240



32.2
132
188
342
228



32.22
142
216
372
256



32.24
161
225
339
219



32.26
144
259
350
256



32.28
149
266
331
246



32.3
159
240
346
262



32.32
149
256
342
299



32.34
156
253
353
286



32.36
135
246
324
320



32.38
128
243
369
306



32.4
135
250
357
306



32.42
151
204
339
320



32.44
154
188
331
289



32.46
123
188
350
276



32.48
149
234
331
250



32.5
149
204
346
266



32.52
151
231
335
256



32.54
112
204
376
269



32.56
154
199
320
231



32.58
146
174
342
222



32.6
139
169
342
210



32.62
130
154
317
185



32.64
125
144
339
177



32.66
137
174
286
177



32.68
139
169
324
174



32.7
166
196
310
169



32.72
164
204
320
164



32.74
139
154
306
166



32.76
182
174
324
159



32.78
166
182
286
166



32.8
185
216
324
164



32.82
188
210
335
193



32.84
210
222
317
202



32.86
213
228
306
210



32.88
202
256
289
234



32.9
196
282
303
234



32.92
216
289
324
266



32.94
213
289
306
246



32.96
210
306
339
269



32.98
228
313
313
276



33
202
328
306
286



33.02
180
369
324
306



33.04
188
353
296
328



33.06
190
369
292
335



33.08
210
433
310
369



33.1
222
437
299
433



33.12
207
445
286
424



33.14
216
392
289
428



33.16
207
441
310
404



33.18
216
449
313
449



33.2
225
416
299
420



33.22
228
437
296
428



33.24
219
441
272
392



33.26
225
388
292
392



33.28
190
357
303
380



33.3
231
324
317
376



33.32
246
276
335
361



33.34
222
269
331
299



33.36
210
272
335
256



33.38
259
262
339
289



33.4
259
243
335
289



33.42
310
231
339
320



33.44
350
213
376
299



33.46
324
256
376
313



33.48
240
240
372
266



33.5
289
225
400
286



33.52
299
207
365
240



33.54
289
213
400
256



33.56
292
213
392
213



33.58
272
210
404
234



33.6
234
253
412
225



33.62
286
253
424
253



33.64
292
228
449
216



33.66
292
237
400
269



33.68
266
240
441
231



33.7
292
253
420
243



33.72
259
250
449
222



33.74
262
256
480
234



33.76
225
282
462
266



33.78
228
253
506
246



33.8
219
269
471
269



33.82
210
279
471
253



33.84
204
269
493
246



33.86
204
269
488
262



33.88
174
282
484
228



33.9
210
328
449
269



33.92
210
303
471
296



33.94
193
365
441
240



33.96
213
353
396
262



33.98
225
369
400
282



34
240
353
392
292



34.02
222
396
412
365



34.04
246
433
384
339



34.06
259
441
392
350



34.08
303
458
353
412



34.1
272
445
331
408



34.12
286
449
342
372



34.14
276
467
350
408



34.16
272
493
320
428



34.18
279
488
339
428



34.2
282
488
317
433



34.22
266
462
306
449



34.24
272
420
342
454



34.26
272
433
350
428



34.28
272
412
306
388



34.3
240
376
320
388



34.32
262
317
306
369



34.34
246
292
342
331



34.36
246
262
296
296



34.38
266
237
353
262



34.4
240
216
292
237



34.42
296
196
317
234



34.44
199
199
331
216



34.46
190
185
353
196



34.48
202
202
339
185



34.5
204
182
339
188



34.52
210
177
350
185



34.54
222
185
353
196



34.56
219
190
384
219



34.58
240
188
384
199



34.6
253
199
365
237



34.62
246
196
380
180



34.64
237
193
416
216



34.66
292
202
388
228



34.68
313
174
433
222



34.7
331
231
380
246



34.72
335
213
420
256



34.74
303
216
416
246



34.76
331
246
420
196



34.78
310
225
404
250



34.8
365
219
428
276



34.82
310
246
471
262



34.84
357
199
428
259



34.86
331
259
458
272



34.88
346
225
506
296



34.9
313
225
441
250



34.92
259
266
480
240



34.94
243
231
480
272



34.96
234
259
506
279



34.98
240
262
484
299



35
202
216
471
269



35.02
185
266
462
282



35.04
177
231
502
266



35.06
180
231
497
246



35.08
193
243
437
289



35.1
182
234
484
306



35.12
204
246
441
286



35.14
204
250
428
346



35.16
193
299
400
376



35.18
219
292
404
372



35.2
213
282
408
392



35.22
246
320
420
420



35.24
256
310
396
475



35.26
276
365
339
493



35.28
250
361
384
471



35.3
259
384
380
529



35.32
282
400
335
511



35.34
292
408
353
576



35.36
272
428
357
562



35.38
269
454
350
660



35.4
292
467
376
666



35.42
320
462
328
734



35.44
320
416
380
745



35.46
320
416
369
784



35.48
328
412
396
853



35.5
320
408
369
824



35.52
317
424
365
847



35.54
324
502
376
900



35.56
282
576
369
949



35.58
292
586
353
1030



35.6
286
529
365
1069



35.62
262
396
376
992



35.64
266
353
357
924



35.66
279
306
404
767



35.68
250
292
416
581



35.7
225
266
388
502



35.72
213
199
412
441



35.74
256
210
324
365



35.76
250
154
380
317



35.78
282
149
388
266



35.8
282
164
346
250



35.82
256
159
339
237



35.84
286
144
335
458



35.86
292
177
357
256



35.88
303
130
342
222



35.9
286
149
342
240



35.92
262
132
324
246



35.94
234
137
339
210



35.96
225
128
328
216



35.98
190
130
342
190



36
166
112
299
164



36.02
174
130
313
146



36.04
146
106
342
166



36.06
137
110
320
137



36.08
130
85
324
142



36.1
132
94
328
151



36.12
135
110
342
112



36.14
112
114
324
130



36.16
149
144
289
125



36.18
130
102
328
112



36.2
121
108
310
125



36.22
142
110
320
128



36.24
151
117
289
139



36.26
146
88
335
128



36.28
135
121
324
142



36.3
137
104
361
137



36.32
146
253
324
125



36.34
149
146
346
125



36.36
135
119
317
142



36.38
161
128
331
146



36.4
146
149
353
151



36.42
169
144
365
159



36.44
161
132
365
169



36.46
154
159
380
159



36.48
144
161
357
182



36.5
159
146
353
188



36.52
169
182
424
177



36.54
177
177
396
164



36.56
182
177
376
188



36.58
159
196
380
193



36.6
159
199
420
303



36.62
154
219
412
199



36.64
151
202
420
216



36.66
182
193
404
216



36.68
169
193
437
210



36.7
169
210
424
207



36.72
161
185
449
213



36.74
166
213
416
243



36.76
166
177
433
219



36.78
177
185
412
225



36.8
185
190
404
219



36.82
182
154
408
202



36.84
216
132
449
207



36.86
174
164
400
213



36.88
222
144
428
190



36.9
207
130
437
161



36.92
250
164
388
177



36.94
225
137
420
149



36.96
204
149
412
199



36.98
207
139
428
180



37
225
164
408
182



37.02
228
151
416
169



37.04
231
142
404
177



37.06
219
156
388
207



37.08
219
139
433
196



37.1
234
123
412
199



37.12
207
130
353
182



37.14
234
128
388
177



37.16
216
121
396
144



37.18
216
125
400
161



37.2
193
121
416
154



37.22
207
125
404
159



37.24
234
149
392
164



37.26
225
149
376
174



37.28
222
142
424
182



37.3
216
117
384
177



37.32
234
156
369
166



37.34
228
159
365
216



37.36
237
174
372
196



37.38
243
164
350
182



37.4
276
177
392
199



37.42
262
156
369
196



37.44
279
210
420
234



37.46
266
202
384
243



37.48
225
202
357
250



37.5
243
207
361
259



37.52
222
228
361
292



37.54
202
225
392
289



37.56
177
269
408
331



37.58
207
243
346
317



37.6
169
262
376
331



37.62
177
234
357
339



37.64
137
225
372
299



37.66
139
234
357
350



37.68
161
216
408
335



37.7
142
234
365
240



37.72
146
237
372
250



37.74
156
225
384
216



37.76
146
204
357
240



37.78
190
188
412
246



37.8
159
182
396
231



37.82
202
196
408
219



37.84
193
207
412
234



37.86
172
199
392
250



37.88
172
199
408
250



37.9
177
196
384
231



37.92
193
177
392
222



37.94
169
169
380
246



37.96
177
196
400
222



37.98
185
202
408
243



38
193
180
376
207



38.02
177
174
388
199



38.04
177
172
384
210



38.06
156
161
380
177



38.08
219
161
404
159



38.1
169
159
380
172



38.12
166
169
392
166



38.14
199
177
396
199



38.16
202
154
392
185



38.18
225
172
404
169



38.2
282
196
412
182



38.22
213
169
388
196



38.24
180
169
365
185



38.26
269
174
350
196



38.28
199
199
384
174



38.3
193
182
412
185



38.32
202
185
384
199



38.34
199
185
380
202



38.36
202
156
369
219



38.38
237
151
324
174



38.4
292
166
369
169



38.42
266
199
388
196



38.44
253
199
380
182



38.46
262
166
380
196



38.48
246
182
424
188



38.5
259
199
392
180



38.52
222
202
404
213



38.54
231
182
392
219



38.56
225
188
372
185



38.58
234
210
369
199



38.6
246
219
412
196



38.62
259
193
396
199



38.64
262
207
400
228



38.66
231
231
404
250



38.68
286
210
400
259



38.7
219
199
372
222



38.72
216
193
384
225



38.74
193
142
396
219



38.76
196
196
328
207



38.78
213
166
384
188



38.8
199
164
384
202



38.82
193
159
361
196



38.84
193
139
369
190



38.86
174
132
369
177



38.88
169
132
380
174



38.9
169
156
372
188



38.92
151
130
346
149



38.94
154
144
388
190



38.96
142
139
380
210



38.98
159
159
361
188



39
159
146
365
216



39.02
159
159
357
207



39.04
182
149
320
216



39.06
164
135
346
219



39.08
146
151
320
210



39.1
142
151
339
234



39.12
169
149
331
188



39.14
156
137
331
190



39.16
174
151
353
177



39.18
144
135
335
177



39.2
161
110
335
154



39.22
174
144
303
154



39.24
149
139
335
185



39.26
154
119
317
139



39.28
164
108
328
125



39.3
146
144
299
139



39.32
177
100
339
130



39.34
169
128
342
161



39.36
182
121
320
121



39.38
188
128
299
128



39.4
199
121
317
130



39.42
172
125
296
112



39.44
174
132
331
154



39.46
204
144
313
132



39.48
188
119
380
149



39.5
182
149
365
128



39.52
169
108
350
156



39.54
182
125
369
139



39.56
207
137
365
142



39.58
174
137
369
144



39.6
185
154
342
142



39.62
199
144
388
164



39.64
204
130
384
144



39.66
207
149
372
149



39.68
219
149
428
128



39.7
188
144
396
149



39.72
182
128
384
130



39.74
196
125
408
180



39.76
174
142
396
135



39.78
180
125
388
154



39.8
164
156
433
177



39.82
182
128
384
137



39.84
161
125
369
142



39.86
174
132
416
132



39.88
151
125
388
142



39.9
146
114
408
130



39.92
142
151
408
112



39.94
164
137
400
151



39.96
182
114
416
144



39.98
199
125
388
144



40
196
125
416
130



40.02
193
135
396
135



40.04
213
135
380
144



40.06
234
151
404
144



40.08
231
159
424
142



40.1
240
149
412
137



40.12
256
144
400
151



40.14
231
130
384
156



40.16
279
146
424
142



40.18
317
139
372
161



40.2
335
156
404
135



40.22
342
164
396
149



40.24
335
172
388
149



40.26
342
159
396
169



40.28
357
180
376
164



40.3
433
149
392
159



40.32
424
156
388
156



40.34
437
177
384
151



40.36
412
149
396
159



40.38
396
172
400
156



40.4
424
164
428
144



40.42
454
151
404
128



40.44
428
149
408
144



40.46
388
154
392
161



40.48
282
185
420
262



40.5
303
139
380
151



40.52
292
154
392
149



40.54
286
180
392
174



40.56
269
149
380
156



40.58
237
161
380
185



40.6
225
174
384
164



40.62
234
154
416
177



40.64
219
164
400
185



40.66
237
199
388
164



40.68
213
193
396
159



40.7
199
196
416
190



40.72
222
219
412
169



40.74
234
196
369
177



40.76
222
207
404
182



40.78
361
228
384
169



40.8
193
240
396
188



40.82
196
213
384
180



40.84
240
231
384
199



40.86
231
243
412
207



40.88
266
237
388
213



40.9
234
292
396
222



40.92
253
259
392
231



40.94
282
289
396
225



40.96
303
292
404
250



40.98
303
296
412
250



41
317
299
400
237



41.02
286
328
449
246



41.04
262
306
404
240



41.06
289
262
408
213



41.08
328
266
396
231



41.1
339
253
384
231



41.12
310
246
408
231



41.14
286
243
400
225



41.16
292
240
392
222



41.18
250
182
400
199



41.2
246
296
416
174



41.22
228
188
400
182



41.24
210
185
388
174



41.26
207
193
400
193



41.28
193
180
416
164



41.3
193
188
380
193



41.32
169
193
404
180



41.34
174
185
428
210



41.36
180
182
433
182



41.38
199
177
458
225



41.4
177
185
454
193



41.42
174
185
467
164



41.44
185
172
441
169



41.46
193
199
471
213



41.48
199
193
445
193



41.5
213
204
467
182



41.52
207
190
484
210



41.54
196
202
462
185



41.56
202
182
488
228



41.58
216
166
475
182



41.6
193
207
449
210



41.62
190
188
467
182



41.64
172
151
454
196



41.66
225
177
454
199



41.68
213
188
467
207



41.7
204
169
420
228



41.72
202
193
475
237



41.74
225
207
428
259



41.76
216
210
416
324



41.78
204
199
437
250



41.8
210
207
420
213



41.82
228
237
392
269



41.84
228
237
376
253



41.86
243
243
380
286



41.88
237
219
357
272



41.9
234
216
372
259



41.92
225
196
392
259



41.94
231
246
353
250



41.96
250
250
353
259



41.98
272
256
346
259



42
262
231
335
286



42.02
250
276
365
282



42.04
225
259
353
272



42.06
219
276
384
313



42.08
240
228
320
262



42.1
228
259
416
246



42.12
216
216
380
243



42.14
219
207
353
256



42.16
188
188
384
231



42.18
193
174
408
213



42.2
193
180
384
202



42.22
172
166
380
193



42.24
169
144
437
172



42.26
182
154
416
180



42.28
188
156
416
199



42.3
159
132
420
172



42.32
144
159
428
139



42.34
146
135
396
166



42.36
139
112
424
139



42.38
146
117
441
154



42.4
135
137
437
139



42.42
159
144
420
182



42.44
125
128
437
159



42.46
139
130
416
164



42.48
128
130
467
154



42.5
139
154
475
154



42.52
154
135
433
166



42.54
132
146
408
151



42.56
146
159
441
144



42.58
159
142
454
193



42.6
139
149
424
177



42.62
137
166
396
146



42.64
137
174
424
182



42.66
151
174
441
177



42.68
159
169
428
188



42.7
159
185
454
219



42.72
166
177
449
207



42.74
174
164
404
207



42.76
172
185
408
207



42.78
177
185
433
262



42.8
177
196
424
266



42.82
169
199
454
276



42.84
177
262
467
259



42.86
161
234
396
299



42.88
164
210
420
272



42.9
156
222
408
272



42.92
159
234
392
331



42.94
144
246
449
299



42.96
174
231
416
342



42.98
164
250
404
306



43
182
237
404
320



43.02
196
269
433
328



43.04
159
272
372
376



43.06
180
276
437
353



43.08
174
299
396
400



43.1
193
303
388
445



43.12
185
331
380
467



43.14
177
324
502
454



43.16
199
310
388
484



43.18
188
353
396
538



43.2
210
346
392
534



43.22
182
388
365
552



43.24
222
346
339
534



43.26
207
388
331
534



43.28
216
384
376
534



43.3
207
400
380
538



43.32
222
404
353
524



43.34
216
372
342
543



43.36
216
396
335
571



43.38
234
384
372
538



43.4
190
416
320
566



43.42
216
467
350
566



43.44
219
400
310
605



43.46
225
480
342
605



43.48
240
437
339
610



43.5
240
441
335
635



43.52
243
480
320
660



43.54
250
441
310
655



43.56
250
449
317
645



43.58
262
506
331
660



43.6
259
416
324
581



43.62
253
342
303
581



43.64
219
433
346
506



43.66
216
320
320
445



43.68
204
306
328
416



43.7
240
269
286
376



43.72
185
234
331
369



43.74
202
225
335
328



43.76
193
199
320
310



43.78
154
225
313
262



43.8
159
204
320
253



43.82
193
225
286
237



43.84
180
228
282
202



43.86
156
210
313
193



43.88
185
193
346
202



43.9
202
216
299
228



43.92
185
196
313
196



43.94
159
207
299
210



43.96
188
204
353
207



43.98
196
199
324
202



44
161
199
299
202



44.02
166
190
279
193



44.04
164
182
335
185



44.06
188
180
306
174



44.08
213
177
339
169



44.1
196
159
328
151



44.12
210
154
328
177



44.14
180
169
357
154



44.16
204
159
342
146



44.18
196
161
342
169



44.2
196
154
357
169



44.22
196
146
571
174



44.24
149
128
372
164



44.26
177
169
357
159



44.28
180
137
357
174



44.3
149
159
350
188



44.32
169
177
346
149



44.34
156
185
376
151



44.36
190
166
342
174



44.38
154
185
384
174



44.4
154
188
361
169



44.42
159
199
380
240



44.44
137
202
342
185



44.46
137
213
313
199



44.48
159
199
365
222



44.5
156
237
335
213



44.52
139
231
365
243



44.54
135
225
353
216



44.56
154
253
361
282



44.58
146
262
324
246



44.6
159
234
361
266



44.62
151
246
369
292



44.64
159
286
376
299



44.66
177
253
350
310



44.68
156
276
369
296



44.7
174
259
342
303



44.72
156
272
331
303



44.74
142
272
353
289



44.76
180
240
324
328



44.78
177
266
339
286



44.8
166
272
342
286



44.82
149
262
328
282



44.84
151
237
339
286



44.86
132
246
342
292



44.88
146
276
369
303



44.9
149
228
384
299



44.92
125
262
350
310



44.94
149
234
350
279



44.96
144
266
353
303



44.98
144
193
350
262



45
156
196
317
286



45.02
146
199
350
231



45.04
156
185
331
213



45.06
159
161
306
210



45.08
149
174
299
202



45.1
151
156
310
182



45.12
144
144
296
180



45.14
161
151
317
164



45.16
169
166
320
146



45.18
166
180
289
169



45.2
177
180
286
172



45.22
169
146
328
174



45.24
185
159
269
169



45.26
188
139
306
149



45.28
169
159
310
177



45.3
190
169
320
185



45.32
190
151
292
161



45.34
188
166
289
182



45.36
182
146
286
202



45.38
193
172
306
193



45.4
196
193
289
172



45.42
182
161
276
193



45.44
172
177
317
188



45.46
169
188
272
196



45.48
185
149
262
219



45.5
156
135
296
199



45.52
159
169
279
174



45.54
169
154
317
182



45.56
177
154
272
166



45.58
164
154
289
164



45.6
174
149
276
149



45.62
161
156
289
193



45.64
172
164
266
180



45.66
188
154
266
213



45.68
151
172
299
188



45.7
149
213
276
164



45.72
207
169
299
193



45.74
237
180
279
213



45.76
199
188
296
196



45.78
196
190
272
196



45.8
185
219
282
193



45.82
204
204
296
202



45.84
172
219
279
207



45.86
185
210
272
204



45.88
216
193
276
219



45.9
196
188
286
237



45.92
196
188
276
219



45.94
225
225
292
213



45.96
240
204
286
222



45.98
174
193
296
234



46
169
199
292
213



46.02
166
166
266
216



46.04
193
164
269
243



46.06
185
331
269
240



46.08
161
146
292
219



46.1
164
159
259
190



46.12
159
154
243
231



46.14
139
135
262
216



46.16
289
128
250
161



46.18
185
128
262
164



46.2
159
135
286
185



46.22
151
137
292
161



46.24
169
130
299
156



46.26
154
114
286
139



46.28
137
117
299
125



46.3
137
117
286
137



46.32
135
137
296
125



46.34
132
144
282
130



46.36
121
182
303
137



46.38
156
125
262
142



46.4
139
139
286
154



46.42
144
119
292
130



46.44
142
154
299
137



46.46
125
137
276
156



46.48
130
149
289
161



46.5
132
154
272
161



46.52
130
159
266
154



46.54
154
154
259
156



46.56
121
166
292
142



46.58
149
142
282
135



46.6
154
154
269
142



46.62
161
159
276
159



46.64
161
146
276
161



46.66
149
142
272
166



46.68
149
169
299
164



46.7
174
154
286
154



46.72
151
172
276
146



46.74
159
139
259
135



46.76
159
144
246
169



46.78
159
146
292
159



46.8
128
149
282
180



46.82
142
159
262
154



46.84
154
142
246
156



46.86
137
161
243
174



46.88
125
139
262
142



46.9
146
159
237
164



46.92
130
142
243
156



46.94
137
144
266
125



46.96
132
159
228
164



46.98
151
149
253
156



47
117
180
269
164



47.02
123
177
259
154



47.04
146
199
250
159



47.06
128
180
234
172



47.08
125
154
228
177



47.1
144
177
250
185



47.12
130
180
243
174



47.14
121
177
269
177



47.16
144
204
228
193



47.18
137
188
266
169



47.2
130
180
240
164



47.22
154
174
240
185



47.24
144
180
259
182



47.26
169
190
253
180



47.28
164
159
262
182



47.3
193
166
216
166



47.32
166
174
259
172



47.34
182
164
222
174



47.36
161
149
231
169



47.38
164
151
243
156



47.4
174
139
234
182



47.42
182
159
256
169



47.44
182
139
225
161



47.46
188
123
259
159



47.48
193
156
262
159



47.5
164
125
240
154



47.52
188
121
262
166



47.54
185
132
237
161



47.56
193
142
219
149



47.58
177
137
250
159



47.6
177
144
237
159



47.62
156
123
228
172



47.64
164
144
237
172



47.66
159
130
259
190



47.68
161
139
246
180



47.7
161
130
237
169



47.72
151
156
225
213



47.74
154
156
262
216



47.76
130
144
237
185



47.78
130
130
234
174



47.8
123
164
246
210



47.82
156
121
210
188



47.84
137
130
253
149



47.86
146
123
250
164



47.88
137
121
243
174



47.9
164
128
231
135



47.92
151
139
246
121



47.94
144
135
228
146



47.96
149
110
259
144



47.98
142
121
272
121



48
132
119
253
132



48.02
132
121
240
149



48.04
139
110
243
144



48.06
132
96
272
137



48.08
125
135
256
135



48.1
130
121
253
144



48.12
123
112
282
128



48.14
142
100
253
123



48.16
137
123
259
146



48.18
125
125
272
123



48.2
130
119
262
128



48.22
146
100
246
149



48.24
139
132
259
121



48.26
137
110
240
137



48.28
139
114
292
130



48.3
151
137
266
128



48.32
161
149
289
130



48.34
177
130
269
154



48.36
144
114
286
149



48.38
180
121
259
128



48.4
149
146
296
159



48.42
156
144
262
154



48.44
121
151
266
159



48.46
166
139
266
135



48.48
144
193
231
169



48.5
154
154
253
164



48.52
132
154
269
166



48.54
135
151
276
159



48.56
139
161
246
161



48.58
117
164
282
166



48.6
128
159
272
180



48.62
128
182
266
169



48.64
137
142
289
174



48.66
128
169
266
172



48.68
123
161
246
188



48.7
102
137
222
180



48.72
125
142
253
164



48.74
135
159
256
159



48.76
121
130
243
135



48.78
159
110
256
151



48.8
135
137
240
151



48.82
121
119
262
149



48.84
135
130
231
142



48.86
149
121
240
130



48.88
132
121
253
132



48.9
123
114
234
128



48.92
149
114
234
130



48.94
144
135
237
108



48.96
166
102
246
117



48.98
137
128
272
102



49
137
128
225
128



49.02
130
108
237
125



49.04
146
117
225
117



49.06
149
108
213
135



49.08
142
94
246
114



49.1
144
112
256
123



49.12
137
100
219
121



49.14
151
117
237
121



49.16
146
106
190
137



49.18
156
104
213
117



49.2
130
112
216
130



49.22
128
92
234
130



49.24
135
123
240
135



49.26
121
130
207
135



49.28
132
128
216
132



49.3
117
108
207
135



49.32
135
108
225
149



49.34
128
98
216
154



49.36
137
130
204
151



49.38
125
110
240
151



49.4
110
125
243
146



49.42
121
130
234
219



49.44
121
114
219
151



49.46
119
92
213
156



49.48
137
130
202
149



49.5
144
123
240
121



49.52
102
123
216
117



49.54
117
117
225
151



49.56
114
130
228
139



49.58
108
149
222
128



49.6
112
121
207
139



49.62
110
110
210
139



49.64
123
128
210
137



49.66
100
119
222
137



49.68
92
121
213
149



49.7
135
128
237
110



49.72
121
110
193
130



49.74
119
119
207
139



49.76
128
112
207
128



49.78
108
132
225
121



49.8
104
130
222
125



49.82
106
108
199
121



49.84
119
137
222
130



49.86
100
135
207
144



49.88
112
104
222
137



49.9
114
132
225
130



49.92
102
112
210
137



49.94
92
94
204
161



49.96
121
102
202
123



49.98
98
100
196
125



50
















TABLE B







2θ and d-spacing values of the significant


XRPD peaks shown by arrows in FIG. 15 for smilagenin


in form VI (smilagenin channel hydrate).









Angle (2θ)/°
d/Å
Relative intensity (%)












3.463
25.49368
3.0


3.930
22.46393
7.1


6.467
13.65546
15.6


7.000
12.61750
3.6


7.851
11.25135
11.3


8.667
10.19453
3.2


10.130
8.72471
8.3


11.213
7.88477
3.5


11.844
7.46603
4.2


12.421
7.11998
8.7


13.007
6.80100
12.1


13.642
6.48582
20.4


13.959
6.33900
42.5


14.236
6.21630
29.5


14.625
6.05196
28.8


15.059
5.87850
23.5


15.566
5.68787
15.5


16.550
5.35198
24.2


16.900
5.24192
48.0


17.221
5.14492
100.0


17.818
4.97399
26.7


18.377
4.82384
34.3


19.354
4.58246
18.7


19.752
4.49103
19.8


20.312
4.36847
26.0


21.837
4.06663
16.2


23.125
3.84295
19.7


23.630
3.76205
15.8


24.904
3.57235
11.7


25.868
3.44136
17.0


26.540
3.35581
13.2


27.100
3.28765
12.4





The relative intensity of each peak as a percentage of the intensity of the strongest peak is also shown. λ is 1.5406 Å and the 2θ range is 2.4° to 27.5°. The measurements were conducted at 25° C. (room temperature).













TABLE C







2θ and d-spacing values of the significant


XRPD peaks shown by arrows in FIG. 16 for smilagenin


in form VII (smilagenin IPA solvate).









Angle (2θ)/°
d/Å
Relative intensity (%)












6.459
13.67403
43.0


7.184
12.29531
18.4


10.215
8.65248
11.5


11.581
7.63461
25.4


12.639
6.99803
73.1


13.030
6.78879
100.0


13.658
6.47790
61.2


14.176
6.24260
93.2


15.150
5.84325
53.7


15.534
5.69963
82.5


16.378
5.40768
67.2


16.700
5.30424
56.8


17.276
5.12881
53.3


18.129
4.88935
51.4


18.820
4.71129
65.6


19.316
4.59146
60.0


20.334
4.36377
66.7


22.965
3.86941
44.9


23.523
3.77887
42.3


24.752
3.59400
37.5


25.448
3.49721
39.3





The relative intensity of each peak as a percentage of the intensity of the strongest peak is also shown. λ is 1.5406 Å and the 2θ range is 2.4° to 27.5°. The measurements were conducted at 25° C. (room temperature).






The foregoing broadly describes the present invention without limitation. Variations and modifications as will be readily apparent to those of ordinary skill in this art are intended to be covered by the present application and resultant patent(s).

Claims
  • 1-7. (canceled)
  • 8. Smilagenin channel hydrate.
  • 9. Smilagenin monohydrate.
  • 10. Smilagenin hydrate at a hydration stoichiometry other than 1:1.
  • 11-46. (canceled)
  • 47. A material according to claim 8, substantially free of another form of smilagenin.
  • 48. A material according to claim 8, substantially free of other steroidal sapogenins.
  • 49. A material according to claim 8, substantially free of other steroidal saponins.
  • 50. A material according to claim 9, substantially free of another form of smilagenin.
  • 51. A material according to claim 9, substantially free of other steroidal sapogenins.
  • 52. A material according to claim 9, substantially free of other steroidal saponins.
  • 53. A material according to claim 10, substantially free of another form of smilagenin.
  • 54. A material according to claim 10, substantially free of other steroidal sapogenins.
  • 55. A material according to claim 10, substantially free of other steroidal saponins.
  • 56. A material according to claim 8 in at least about 50% by weight pure form.
  • 57. A material according to claim 8 in at least about 90% by weight pure form.
  • 58. A material according to claim 8 in at least about 95% by weight pure form.
  • 59. A material according to claim 8 in substantially pure isolated form prepared on a kilogram scale.
  • 60. A material according to claim 9 in at least about 50% by weight pure form.
  • 61. A material according to claim 9 in at least about 90% by weight pure form.
  • 62. A material according to claim 9 in at least about 95% by weight pure form.
  • 63. A material according to claim 9 in substantially pure isolated form prepared on a kilogram scale.
  • 64. A material according to claim 10 in at least about 50% by weight pure form.
  • 65. A material according to claim 10 in at least about 90% by weight pure form.
  • 66. A material according to claim 10 in at least about 95% by weight pure form.
  • 67. A material according to claim 10 in substantially pure isolated form prepared on a kilogram scale.
Priority Claims (1)
Number Date Country Kind
0409567.5 Apr 2004 GB national
Divisions (1)
Number Date Country
Parent 11587738 Mar 2007 US
Child 13032548 US