JP5618289B2 - Gelling agent and gel - Google Patents

Description

  The present invention relates to a gelling agent for gelling or thickening an organic compound and a gel using the gelling agent.

  Conventionally, in various industrial fields, a gelling agent is used for the purpose of solidifying a liquid substance, that is, for solidifying in a jelly form, or for the purpose of thickening. For example, it is used in fluidity control of adhesives, paints, printing inks, cosmetics, etc., imparting thixotropy, countermeasures for oil spills to the sea, disposal of cooking oil at home, etc., other food manufacturing industries, medical fields, etc. ing. These gelling agents include those that solidify moisture, such as collagen, gelatin, agar, agar (carrageenan), pectin, etc., and organic substances, especially hydrocarbons, alcohols, ketones, esters and other organic solvents. And a gelling agent that solidifies a solution mainly containing them.

  Among these, as the gelling agent for solidifying the organic solution, there are low molecular weight or high molecular weight organic compounds, and as the polymer gelling agent, there is an oil in the entangled molecule of the polymer polymer having lipophilicity. For example, polyvinyl alcohol / polyethylene / various elastomers, urea resins, polyolefin non-woven fabrics, and the like are known as those that retain a solid state but swell. Moreover, as a low molecular weight gelling agent, for example, a low molecular weight organic compound group having a hydrogen bonding functional group such as an amino group, an imide group or a urea group in the molecule is known.

  When these low molecular weight gelling agents are mixed in a solvent, heated and dissolved, and cooled, they form non-covalent bonds such as hydrogen bonds and associate to form a three-dimensional network structure in which solvent molecules And gels. However, when heated again, the non-covalent bonds break and the gel returns to a solution-like sol.

  The present inventors can gel various organic liquids by using a relatively small amount of the low molecular weight gelling agent as described above, and can maintain the gel state even at a relatively high temperature. Fluorine-containing gelling agents were provided as suitable gelling agents (Patent Documents 1 to 3).

  The general method of using these gelling agents is to add the gelling agent to the organic liquid to be gelled and heat it to form a sol of a uniform liquid mixture, which is poured into the intended container and allowed to cool or The gel was formed by cooling.

  However, when the organic liquid to be gelled or the substance dissolved in the liquid is altered by heat, the container used as a casting mold can sufficiently withstand the temperature of the organic liquid sol containing the gelling agent. In some cases, the conventional gelation method could not be used.

JP 2007-191661 A JP 2007-191627 A JP 2007-191626 A

  It is an object of the present invention to provide a gelling agent capable of causing a gel → sol transition at room temperature or lower.

  Of course, even when the gelling agent of the present invention is used, it is possible to transfer the gel to a sol by heating, and it is a gelling agent that can adopt a conventional method of use.

  The first aspect of the present invention is to provide a gelling agent comprising a compound represented by the following general formula (1).

（但し、ｎは２〜１８の整数）
本発明の別の態様は前記一般式（１）で表わされるゲル化剤と、室温下に液状の有機物質を含むゲルを提供する。

(Where n is an integer from 2 to 18)
Another aspect of the present invention provides a gel comprising a gelling agent represented by the general formula (1) and a liquid organic substance at room temperature.

Yet another aspect of the invention, after obtaining a homogeneous sol by irradiating ultraviolet rays at room temperature containing dispersed gelling agent to an organic material liquid represented by the general formula (1), by leaving Also provided is a method for producing a gel, characterized in that it is a gel.

  The gelling agent of the present invention can gel an extremely large number of organic substances that are liquid at room temperature (25 ° C.). In general, the gel using the gelling agent of the present invention can be converted into a sol by heating as in the case of a conventionally known low molecular weight gelling agent. Can be made into a sol without applying any heat. Then, it is gelled again by stopping and leaving the ultraviolet irradiation. By utilizing such a sol-gel transition function, it is possible to inject it into a mold as a sol without applying heat, and then to make it gel.

These are graphs showing the relationship between the sol-gel transition temperature and the gelling agent concentration in the gelling agent of the present invention. These are IR spectrum figures of an example in the gelatinizer of this invention. These are the NMR spectrum figures of the same compound as FIG. 2 in the gelatinizer of this invention. FIG. 4 is an IR spectrum diagram of another example of the gelling agent of the present invention. These are the NMR spectrum figures of the same compound as FIG. 4 in the gelatinizer of this invention.

  The greatest feature of the present invention is a gelling agent comprising a compound represented by the following general formula.

ここで、ｎは２〜１８の整数、好ましくは４〜１８の整数であり、ｎが１の場合は、ゲル化能がほとんど見られず、４以上で優れたゲル化能を示す。

Here, n is an integer of 2 to 18, preferably an integer of 4 to 18. When n is 1, almost no gelling ability is observed, and an excellent gelling ability is shown when 4 or more.

Further, the group represented by C _n H _{2n + 1} is an alkyl group which may have a branch. Generally, the longer the number of carbons, the higher the gelation ability, but if it is too long, depending on the type of organic liquid to be gelled In general, the number of carbon atoms is preferably 18 or less because they may not be dyed and may be difficult to synthesize.

  The aromatic group in the compound of the present invention may have a substituent such as an alkyl group or a halogen atom.

  The gelling agent of the present invention can gel a liquid organic substance at room temperature by using a relatively small amount, for example, about 2% by weight (when the total gel is 100%). In addition, the sol-gel transition temperature can generally be increased by increasing the amount of gelling agent used, and generally becomes substantially constant at 10% by weight or more.

  The gelling agent of the present invention can gel organic substances that are liquid at various room temperatures.

  Here, the organic substance includes not only a single organic compound and a mixture of organic compounds, but also a mixture of liquid organic compounds and the like at room temperature in which inorganic substances, ions, or organometallic compounds are dissolved or dispersed in the organic compounds. It is a generic name including.

  Representative examples of these organic substances include hexane, heptane, benzene, toluene, xylene, petroleum and other hydrocarbons, methanol, ethanol, isopropyl alcohol (2-propanol), octanol and other alcohols, ethyl ether, propyl Ethers such as ether, propylene oxide and tetrahydrofuran, ketones such as dimethyl ketone, diethyl ketone and methyl ethyl ketone, organic acids such as formic acid, acetic acid and phenol, amides such as dimethylacetanilide and dimethylformamide, propylene carbonate, methyl ethyl carbonate, etc. Carbonates, nitriles such as acetonidyl, lactones such as γ-butyrolactone, γ-valerolactone, imidazoles such as dialkylimidazolium and trialkylimidazolium Ums, ammoniums such as tetraalkylammonium, pyridiniums such as alkylpyridinium and dialkylpyridinium (these ionic organic liquids can contain various counter ions), soybean oil, olive oil, coconut oil, rapeseed oil, sesame oil Such as oils and fats, waste oils thereof, and those obtained by dissolving or dispersing solid substances or gases in liquid organic substances at room temperature.

  The gelling agent of the present invention may be added to a liquid-like material at room temperature in the same manner as a conventionally known low molecular weight gelling agent, heated to obtain a uniform sol, and then cooled to obtain a gel. In addition, the gel can be efficiently solated by ultraviolet rays (electromagnetic waves having a peak wavelength of 400 nm or less), particularly ultraviolet rays having a peak in UVA (400 to 315 nm).

  The reason for producing such a function is considered to be derived from the fact that the coumarin group and the aromatic group in the present invention are bonded via an azo group.

  That is, these compounds generally have a trans structure having a low energy level and are stabilized, but are activated by irradiating them with ultraviolet rays to form a cis structure. On the other hand, in order to gel organic substances that are liquid at room temperature, a certain degree of linear molecular length is required, and these are loosely bonded by hydrogen bonds, coordination bonds, and other intermolecular interactions. It is necessary to include a liquid organic substance between the molecules. In the gelling agent of the present invention, when a relatively long alkyl chain (at least 2 carbon atoms or more) is bonded to an aromatic group via an ether bond, and the azo group is a trans type It shows the length necessary for gelation almost linearly, but when it becomes cis-type by irradiation with ultraviolet rays, the molecule will be shrunk, and the liquid organic substance will be more solated with increased flexibility. It seems to be.

  Then, by stopping the ultraviolet irradiation and leaving it to stand or applying heat, the azo group returns to the stable trans form again. However, when heat is applied, the intermolecular interaction formed between the molecules in the trans form is also cut off, and the gelling agent is in the sol state while being in the trans form by exceeding the so-called sol-gel transition temperature. However, when this is cooled, it becomes a gel.

In the present invention, the gelling agent comprising the compound represented by the general formula (1) has the greatest feature and its production method is not limited in any way, but an example of synthesizing them is shown in the following scheme.

以上の如き方法により合成することができる。

It can be synthesized by the method as described above.

  The gelling agent of the present invention thus obtained can obtain a gel by mixing in a liquid organic substance usually at 2% by weight or more at room temperature. The method of gelation is achieved by means known in the art, for example, not only by mixing and stirring, but preferably by heating and cooling.

  Furthermore, once the gelled organic substance is irradiated with ultraviolet rays, it is made into a sol, which is injected into a container as a mold, and left to stand or heated to promote gelation to form a transformer, and then cooled. It can be made to gel again.

  Examples are shown below, but the gelling agent of the present invention or the gel using the gelling agent is not limited to these examples.

３００ｍＬのナスフラスコにＣｏｎｃ．ＨＮＯ_３３４．５ｍＬとＣｏｎｃ．Ｈ_２ＳＯ_４３４．５ｍＬの混合溶液を氷浴で冷却し、クマリン１５．０ｇを溶液の温度が２０℃を超えないように除々に加えた。全部加え終えたら氷浴を外し、室温で１時間攪拌した。反応物を水２００ｍＬに注ぎ、析出している固体を濾取し、トルエンで再結晶を行った。その結果、淡黄色の固体化合物（ａ）を得た。

目的物：１３．１ｇ
融点：１８８−１８９℃ ＜文献値 １９３−１９６℃＞
収率：６６％
ＩＲ（ＫＢｒ）
ν_Ｎ−Ｏ=１３５０，１５３０ｃｍ^−１
ν_Ｃ＝Ｏ=１７００ｃｍ<sup>−１

１</sup>Ｈ ＮＭＲ（ＤＭＳＯ−ｄ６）
δ=６．６９（１Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,７．６２（１Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,８．２３（１Ｈ,ｄ,Ｊ＝９．９Ｈｚ）,８．４１（１Ｈ,ｄｄ,Ｊ＝９．９，２．６Ｈｚ）,８．７３（１Ｈ,ｄ,Ｊ＝２．６Ｈｚ）ｐｐｍ

Conc. In a 300 mL eggplant flask. HNO ₃ 34.5 mL and Conc. A mixed solution of 34.5 mL of H ₂ SO ₄ was cooled in an ice bath, and 15.0 g of coumarin was gradually added so that the temperature of the solution did not exceed 20 ° C. When the addition was complete, the ice bath was removed and the mixture was stirred at room temperature for 1 hour. The reaction product was poured into 200 mL of water, and the precipitated solid was collected by filtration and recrystallized with toluene. As a result, a pale yellow solid compound (a) was obtained.

Target: 13.1 g
Melting point: 188-189 ° C <literature value 193-196 ° C>
Yield: 66%
IR (KBr)
ν _N-O = 1350, 1530 cm ^-1
ν _C═O = 1700 cm <sup>−1

1</sup> H NMR (DMSO-d6)
δ = 6.69 (1H, d, J = 8.9 Hz), 7.62 (1H, d, J = 8.9 Hz), 8.23 (1H, d, J = 9.9 Hz), 8.41 (1H, dd, J = 9.9, 2.6 Hz), 8.73 (1H, d, J = 2.6 Hz) ppm

３００ｍＬのナスフラスコに化合物（ａ）５．０２ｇをエタノール１００ｍＬ、トルエン１００ｍＬの混合溶液に溶かして水素添加を行った。反応後、Ｐｄ／Ｃを濾取し、ろ液をエバポレーターで濃縮し析出した固体をトルエンで再結晶を行った。その結果、黄色固体化合物（ｂ）を得た。

目的物：１．９７ｇ
融点：１６０−１６２℃ ＜文献値 １４５−１４７℃＞

収率：７８％

ＩＲ（ＫＢｒ）
ν_Ｃ＝Ｏ=１７００ｃｍ^−１
ν_Ｎ−Ｈ＝３３６０，３４７０ｃｍ<sup>−１

１</sup>Ｈ ＮＭＲ（ＤＭＳＯ）
δ＝５．２４（２Ｈ,ｓ）,６．３３（１Ｈ,ｄ,Ｊ＝９．６Ｈｚ）,６．７２（１Ｈ,ｄ,Ｊ＝２．６Ｈｚ）,６．８３（１Ｈ,ｄｄ,Ｊ＝８．６，２．６Ｈｚ）,７．０９（１Ｈ,ｄ,Ｊ＝８．６Ｈｚ）,７．８７（１Ｈ,ｄ,Ｊ＝９．６Ｈｚ）ｐｐｍ

In a 300 mL eggplant flask, 5.02 g of compound (a) was dissolved in a mixed solution of 100 mL of ethanol and 100 mL of toluene, and hydrogenated. After the reaction, Pd / C was collected by filtration, the filtrate was concentrated with an evaporator, and the precipitated solid was recrystallized with toluene. As a result, a yellow solid compound (b) was obtained.

Target product: 1.97 g
Melting point: 160-162 ° C <literature value 145-147 ° C>

Yield: 78%

IR (KBr)
ν _C═O = 1700 cm ⁻¹
ν _N−H = 3360, 3470 cm <sup>−1

1</sup> H NMR (DMSO)
δ = 5.24 (2H, s), 6.33 (1H, d, J = 9.6 Hz), 6.72 (1H, d, J = 2.6 Hz), 6.83 (1H, dd, J = 8.6, 2.6 Hz), 7.09 (1H, d, J = 8.6 Hz), 7.87 (1 H, d, J = 9.6 Hz) ppm

３００ｍＬのナスフラスコに５℃氷冷下で１２ＮＨＣｌ２．７ｍＬ、水１４．４ｍＬの水溶液を作り、それに化合物（ｂ）を１．９７ｇ加え、ＮａＮＯ_２１．１３ｇを加えて２０分間攪拌し、フェノール１．９３ｇ、ＮａＯＨ０．９６ｇ、水１４．７ｍＬの混合溶液を加え攪拌し、析出した固体をトルエンで再結晶を行い、化合物（ｃ）を得た。

目的物：２．６９ｇ
融点：２５０℃以上
収率：８４％

ＩＲ（ＫＢｒ）
ν_Ｃ＝Ｏ=１６８０ｃｍ^−１
ν_Ｏ−Ｈ＝３２００ｃｍ<sup>−１

１</sup>Ｈ ＮＭＲ（ＤＭＳＯ）
δ=４．２４（１Ｈ，ｓ）６．５５（１Ｈ,ｄ,Ｊ＝９．６Ｈｚ）,６．７７（２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,７．５１（１Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,７．７３（２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,８．０２（１Ｈ,ｄｄ,Ｊ＝８．９,２．３Ｈｚ）,８．１５（１Ｈ,ｄ,Ｊ＝２．３Ｈｚ）,８．２０（１Ｈ,ｄ,Ｊ＝９．６Ｈｚ）ｐｐｍ

An aqueous solution of 2.7 mL of 12N HCl and 14.4 mL of water was prepared in a 300 mL eggplant flask under ice-cooling at 5 ° C., 1.97 g of compound (b) was added thereto, 1.13 g of NaNO ₂ was added, and the mixture was stirred for 20 minutes. A mixed solution of .93 g, 0.96 g of NaOH and 14.7 mL of water was added and stirred, and the precipitated solid was recrystallized from toluene to obtain compound (c).

Target: 2.69g
Melting point: 250 ° C or higher Yield: 84%

IR (KBr)
ν _C═O = 1680 cm ⁻¹
ν _O—H = 3200 cm <sup>−1

1</sup> H NMR (DMSO)
δ = 4.24 (1H, s) 6.55 (1H, d, J = 9.6 Hz), 6.77 (2H, d, J = 8.9 Hz), 7.51 (1H, d, J = 8.9 Hz), 7.73 (2H, d, J = 8.9 Hz), 8.02 (1H, dd, J = 8.9, 2.3 Hz), 8.15 (1H, d, J = 2) .3 Hz), 8.20 (1H, d, J = 9.6 Hz) ppm

３００ｍＬのナスフラスコに化合物（ｃ）２．０３ｇを３−Ｐｅｎｔａｎｏｎｅ１５０ｍＬに溶解し、１−ブロモオクタン１．６６ｇ，炭酸カリウム１．０７ｇ加えて１５時間還流を行った。得られた固体をトルエンで再結晶を行った後、カラムクロマトグラフィーで精製した。充填剤としてシリカゲル、展開溶媒としてクロロホルムをそれぞれ使用した。その結果、本発明の化合物（I）１．４０ｇを得た。

目的物：１．４０ｇ
融点：１３６−１３８℃ （新規物質であり文献値なし）
収率：４４％

ＩＲ（ＫＢｒ）
ν_Ｃ＝Ｏ=１７２０ｃｍ^−１
ν_Ｃ−Ｈ＝３０７０ｃｍ^−１
赤外吸収スペクトル図を図２に示す。

^１Ｈ ＮＭＲ（CDCl₃）
δ＝０．８９（３Ｈ,ｔ,Ｊ＝６．６Ｈｚ）,１．２７−１．５８（１０Ｈ,ｍ）,１．８３（２Ｈ,ｑ,Ｊ＝６．６Ｈｚ），４．０５（２Ｈ,ｑ,Ｊ＝６．６Ｈｚ）,６．４９（１Ｈ,ｄ,Ｊ＝９．６Ｈｚ）,７．０１（２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,７．４３（１Ｈ,ｄ,Ｊ＝８．６Ｈｚ）,７．８１（１Ｈ,ｄ,Ｊ＝9.６Ｈｚ）,７．９１（２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,８．００（１Ｈ,ｄ,Ｊ＝２．３Ｈｚ）,８．１０（１Ｈ,ｄｄ,Ｊ＝８．９，２．３Ｈｚ）ｐｐｍ
ＮＭＲスペクトル図を図３に示す。

In a 300 mL eggplant flask, 2.03 g of compound (c) was dissolved in 150 mL of 3-Pentanone, and 1.66 g of 1-bromooctane and 1.07 g of potassium carbonate were added and refluxed for 15 hours. The obtained solid was recrystallized from toluene and purified by column chromatography. Silica gel was used as a filler and chloroform was used as a developing solvent. As a result, 1.40 g of the compound (I) of the present invention was obtained.

Target: 1.40 g
Melting point: 136-138 ° C (new substance, no literature value)
Yield: 44%

IR (KBr)
ν _C═O = 1720 cm ⁻¹
ν _C−H = 3070 cm ⁻¹
An infrared absorption spectrum is shown in FIG.

¹ H NMR (CDCl ₃ )
δ = 0.89 (3H, t, J = 6.6 Hz), 1.27-1.58 (10H, m), 1.83 (2H, q, J = 6.6 Hz), 4.05 (2H , q, J = 6.6 Hz), 6.49 (1H, d, J = 9.6 Hz), 7.01 (2H, d, J = 8.9 Hz), 7.43 (1H, d, J = 8.6 Hz), 7.81 (1H, d, J = 9.6 Hz), 7.91 (2H, d, J = 8.9 Hz), 8.00 (1H, d, J = 2.3 Hz), 8.10 (1H, dd, J = 8.9, 2.3 Hz) ppm
An NMR spectrum is shown in FIG.

３００ｍＬのナスフラスコに化合物（ｃ）３．００ｇを３−Ｐｅｎｔａｎｏｎｅ １５０ｍＬに溶解し、１−ブロモヘキサン１．９９ｇ、炭酸カリウム１．５７ｇ加えて１５時間還流を行った。得られた固体をトルエンで再結晶を行った後、カラムクロマトグラフィーで精製した。充填剤としてシリカゲル、展開溶媒としてクロロホルムをそれぞれ使用した。その結果、本発明の化合物（II）１．００ｇを得た。

目的物：１．００ｇ
融点：１４０−１４３℃ （新規化合物であり、文献値なし）
収率：４３％

ＩＲ（ＫＢｒ）
ν_Ｃ＝Ｏ＝１７３０ｃｍ^−１
ν_Ｎ−Ｈ＝２９４０ｃｍ^−１

赤外吸収スペクトル図を図４に示す。


^１Ｈ ＮＭＲ（ＣＤＣｌ_３）
δ＝０．９２（３Ｈ,ｔ,Ｊ＝６．９Ｈｚ）,１．３３−１．５７（６Ｈ,ｍ）,１．８３（２Ｈ，ｑｕｉｎ．，Ｊ＝６，６Ｈｚ），４．０３（２Ｈ,ｑ,Ｊ＝６．６Ｈｚ）,６．５２（１Ｈ,ｄ,Ｊ＝９．５Ｈｚ）,７．０２ （２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,７．４６（１Ｈ,ｄ,Ｊ＝８．６Ｈｚ）,７．８０（１Ｈ,ｄ,Ｊ＝９．５Ｈｚ）,７．９２（２Ｈ,ｄ,Ｊ＝８．９Ｈｚ）,８．００（１Ｈ,ｄ,Ｊ＝２．３Ｈｚ）,８．０９（１Ｈ,ｄｄ,Ｊ＝８．６、２．３Ｈｚ）ｐｐｍ

ＮＭＲスペクトル図を図５に示す。

In a 300 mL eggplant flask, 3.00 g of compound (c) was dissolved in 150 mL of 3-Pentanone, and 1.99 g of 1-bromohexane and 1.57 g of potassium carbonate were added and refluxed for 15 hours. The obtained solid was recrystallized from toluene and purified by column chromatography. Silica gel was used as a filler and chloroform was used as a developing solvent. As a result, 1.00 g of the compound (II) of the present invention was obtained.

Target: 1.00g
Melting point: 140-143 ° C (new compound, no literature value)
Yield: 43%

IR (KBr)
ν _C═O = 1730 cm ⁻¹
ν _N−H = 2940 cm ⁻¹

An infrared absorption spectrum is shown in FIG.


¹ H NMR (CDCl ₃ )
δ = 0.92 (3H, t, J = 6.9 Hz), 1.33-1.57 (6H, m), 1.83 (2H, quin., J = 6, 6 Hz), 4.03 ( 2H, q, J = 6.6 Hz), 6.52 (1H, d, J = 9.5 Hz), 7.02 (2H, d, J = 8.9 Hz), 7.46 (1H, d, J = 8.6 Hz), 7.80 (1H, d, J = 9.5 Hz), 7.92 (2H, d, J = 8.9 Hz), 8.00 (1H, d, J = 2.3 Hz) , 8.09 (1H, dd, J = 8.6, 2.3 Hz) ppm

An NMR spectrum is shown in FIG.

<Gelification test>
In a 10 mmφ sample tube, 0.0039 g of Compound (I) was heated and dissolved in 0.0695 g of GBL (γ-butyrolactone) to prepare a 5.3 wt% gel. This was irradiated with ultraviolet light of 18.4 W and 366 nm from a distance of 2 cm for 12 hours at room temperature. This gel partially transferred to the sol. When it was left at room temperature, it became a gel again. The gel was left at room temperature overnight, but did not become a sol as it was.

<Comparative example>
As a comparative example, 6- (4-methoxy-phenylazo) -chromen-2-one “English name; 6- (4-Methoxy-phenylazo) -chromen-2-one” (the following compound (III): CAS No. 372156 -87-1) was adjusted to 5 wt% with respect to ethanol, toluene, 1-octanol and PC (propylene carbonate) and dissolved by heating. However, none of ethanol, toluene and 1-octanol was dissolved. In GBL, it was dissolved by about 5.3% by weight but did not gel.

Claims (4)

A gelling agent comprising a compound represented by the following general formula (1) .

(Where n is an integer from 2 to 18) The gel of the organic substance which is a liquid at room temperature containing the gelling agent 2weight% or more represented by General formula (1) of the said Claim 1 . The gel according to claim 2, comprising 2 to 10% by weight of a gelling agent represented by the general formula (1) according to claim 1 and 98 to 90% by weight of an organic substance which is liquid at room temperature. A homogeneous sol is obtained by irradiating ultraviolet light onto a liquid organic substance at room temperature in which the gelling agent represented by the general formula (1) according to claim 1 is dispersed at room temperature, and the gel is left to stand. The method for producing a gel according to claim 2 or 3, wherein:

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