Thupelo "Metheo ea ho sebetsa ka katleho le mahlale a Wolfram": lihora tse fetang 13 tsa lipuo tsa video, khopolo le mesebetsi

Thupelo "Metheo ea ho sebetsa ka katleho le mahlale a Wolfram": lihora tse fetang 13 tsa lipuo tsa video, khopolo le mesebetsi

Litokomane tsohle tsa thupelo li ka kopitsoa mona.

Ke rutile thuto ena lilemong tse 'maloa tse fetileng ho bamameli ba bangata. E na le lintlha tse ngata mabapi le hore na sistimi e sebetsa joang Mathematica, Leru la Wolfram le puo Puo ea Wolfram.

Leha ho le joalo, ha e le hantle, nako ha e eme 'me lintho tse ngata tse ncha li hlahile morao tjena: ho tloha matleng a tsoetseng pele ho sebetsa le marang-rang a neural ho mefuta eohle ts'ebetso ea webo; jwale ho jwalo Enjene ea Wolfram, eo u ka e kenyang ho seva sa hau le ho e fumana joaloka Python; o ka haha ​​mefuta eohle pono ea libaka kapa lik'hemik'hale; ho na le tse kholo likotlolo mefuta eohle ea data, ho kenyeletsoa ho ithuta ka mochini; o ka hokela mefuta eohle ea database; rarolla mathata a rarahaneng a lipalo, joalo-joalo.

Ho thata ho thathamisa bokhoni bohle ba mahlale a Wolfram lirapeng tse 'maloa kapa metsotso e seng mekae.

Sena sohle se ile sa nkhothalletsa hore ke nke thupelo e ncha, eo ke leng ho eona hona joale ngodiso e ntse e tswelapele.

Ke na le ts'epo ea hore hang ha u se u fumane bokhoni ba Puo ea Wolfram, u tla qala ho e sebelisa khafetsa, ho rarolla mathata a hau kapele le ka mokhoa o atlehileng libakeng tse fapaneng: ho tloha ho mahlale ho isa ho boqapi ba boits'oaro kapa ho pasa marang-rang, ho tloha ho neural network ts'ebetso ea lipapiso, ho tloha ponong ea limolek'hule ho isa ho litšebelisano tse matla tsa kaho.

1 | Kakaretso ea Wolfram Mathematica le Wolfram Cloud


Likahare tsa thutoWolfram Mathematica ke eng?
- 'Mōpi - Stephen Wolfram
—— Lingoliloeng tse ling tsa morao-rao tsa Stephen Wolfram tse fetoletsoeng ka Serussia
- Lenane la mesebetsi le matšoao a hahelletsoeng
—— Palo ea mesebetsi e hahelletsoeng ho latela mofuta
—— Sebaka sa hard disk
- Ho feta ka Mathematica ka kakaretso
- Lihlahisoa tsohle tsa Wolfram Research
Likarolo tse Ncha le tse ntlafalitsoeng
- Khoutu ea ho fumana manane ana
E ncha ka pele
Puo e ncha ea jiometri
- Lintho tsa motheo tsa geometri
- Mesebetsi ea lipalo tsa geometri
—— Tekanyo ea sebaka
—— Bohole ho ya sebakeng
—— Ho sebetsa le libaka
- Mesebetsi ea ho hlalosa libaka
- Ho sebetsa ka meshes
- Khokahano e felletseng le mesebetsi e meng
Tharollo ea tlhahlobo le lipalo tsa li-equations tse fapaneng
- WhenEvent bakeng sa mesebetsi ea tlhahlobo
- Tharollo ea tlhahlobo ea DE ka ho lieha
- Mokhoa oa ho qetela oa element
Ho Ithuta ka Mechini
- Tšoaroa
- Pherekano
— Mohlala
“Puo Sehlopha"- puo e ncha ea ho sebetsa le li-database + Palo e kholo ea li-database tse ncha
Puo e ncha ea ho sebetsa ka litaba tsa sebaka
Litaba tse ling ke life?
- Katoloso ya puo ya motheo
- Association - lihlopha tse hlophisitsoeng
- Dataset - sebopeho sa database se hahelletsoeng
- PlotTheme
- Lipalo tse amanang le nako
- Tlhahlobo ea lits'ebetso tse sa reroang
- Letoto la nako
- Ho ikopanya le Wolfram Cloud
- Ho kopanya le lisebelisoa
- Litempele tsa litokomane tse tsoetseng pele, HTML
Wolfram Programming Cloud

2.1 | Kenyelletso ea puo, likarolo tsa eona. Mathata a mantlha ho basebelisi ba li-novice. Ho sebetsa le sebopeho sa Mathematica le bokhoni ba eona - sebopeho sa ho bolela esale pele, foromo ea mahala ea ho kenya, jj.


Likahare tsa thutoPuo ea Wolfram
Melao-motheo ea Puo ea Wolfram
Ke eng eo u lokelang ho e hopola ha u sebetsa le Wolfram Language?
Ho qala ho Mathematica
Litsela tsa bohlokoa tsa li-keyboard
— Shift+Enter kapa Kenya ka letlapa la dinomoro
— Ctrl+Shift+Enter
- F1
- F2
Ho fumana lintlha ka matšoao
—? - tshebetso Tlhaloso
- ?? - tshebetso Information
- Tobetsa ho F1
- Interdictive interface
Ho sebetsana le li-palettes
—Mothusi oa Motheo oa Lipalo
- Mothusi oa Phaposi ea ho Ithuta
—Mothusi oa ho Ngola
- Merero ea lintlha tsa Chate
—Merero ea Mebala
— Litlhaku Tse Khethehileng
- Ho sebetsa ka li-graph le litšoantšo
—— Lisebelisoa tsa ho Rata
——Fumana Likhokahano
—— Ts'ebetso ea mantlha ea litšoantšo
- Ho sebetsa ka li-graph
Puo le Sistimi ea Wolfram | Setsi sa Litokomane
Predictive Interface
- Ho phethela litaelo tse kentsoeng ho ipapisitse le maemo
—— Ho sebetsa ka mesebetsi e hahelletsoeng ka hare le lipaterone tsa syntax
—— Ho sebetsa ka mefuta-futa ea basebelisi
- Sehokelo se baloang - phanele ea ho fana ka maikutlo a liketso tse ling
Ho kopanya le Wolfram|Alpha
- Wolfram | Sebaka sa marang-rang sa Alpha
- Khokahano lipakeng tsa Wolfram|Alpha le Mathematica
—— Ho fumana liemeli tse koetsoeng tsa likaroloana tsa decimal
—— Litaba tsa khatello ea mali
—— Tharollo ea mohato ka mohato ea equation ea matrix ho sebelisa mokhoa oa Gaussian

2.2 | Ho hlakisa mesebetsi, ho sebetsa ka manane, mantsoe a template le mekhatlo


Likahare tsa thutoManane
- Lenane {...} le tshebetso List[…] - Pontšo ea manane a “tlhaho”
- Mekhoa ea ho etsa manane
- Indexing ea likarolo le litšobotsi tse ling tsa linomoro tsa lenane. Mesebetsi Length и botebo
- Ho khetha likarolo tse lulang libakeng tse itseng lenaneng u sebelisa tšebetso karolo([…]])
- Ho fetola mabitso a lintho tsa lethathamo
— Ho hlahisa lenane ka ho sebedisa tshebetso Lethathamo
— Ho hlahisa lenane la dinomoro ka ho sebedisa tshebetso Range
Mekhatlo
- Ho theha kopano le ho sebetsa le eona
- Dataset - sebopeho sa database ka Puo ea Wolfram
Template Expressions
- Kenyelletso ea litempele
- Litempele tsa mantlha tsa lintho: Ha e na letho (_), BlankSequence (__), BlankNullSequence (___)
- U ka etsa'ng ka li-template? Mosebetsi Litaba
- Ho khetha mofuta oa polelo ho template
- Ho beha lithibelo ho litempele ka ho sebelisa lits'ebetso boemo (/;), MohlalaTest (?), Ntle le moo, hammoho le tšebeliso ea mesebetsi ea teko
- Thepa ea litempele ka monyetla oa khetho e 'ngoe e sebelisang ts'ebetso mekhoa e meng (|)
Mesebetsi
- Ts'ebeliso ea mosebetsi o chechisitsoeng morao SetDelayed (:=)
- Ho sebelisa mosebetsi o phethahetseng Ipehele (=)
- Ho beha ts'ebetso e hopolang litekanyetso tseo e seng e li fumane le ts'ebetso e etsahalang khafetsa
- Litšobotsi tsa ts'ebetso le mesebetsi litšobotsi, SetAttributes, ClearAttributes, sireletsa, Se sireletse ho sebetsa le bona
Mesebetsi e hloekileng
- Ts'ebeliso ea ts'ebetso mosebetsi (&)
- Ho sebelisoa mesebetsi e hloekileng hokae?

2.3 | Ho etsa lipono


Likahare tsa thutoPuo ea litšoantšo ea tšoantšetso
- Litšoantšo tsa khale
—— One-dimensional
—— Bobedi-dimensional
—— Likarolo tse tharo
—— Thuso
- Mosebetsi grafiken
—— Syntax
——— Mohlala o bonolo ka ho fetisisa
——— Layer
——— Rearrangements lera
——— Litšobotsi tse akaretsang le tse khethehileng tsa masela
—— Dikgetho tsa tshebetso grafiken
--- AspectRatio
--- Lilepe
--- AxesLabel
--- AxesOrigin
--- AxesStyle
--- Malepa
--- TicksStyle
--- Background
--- ContentSelectable
--- CoordinatesToolOptions
--- Epilogue
--- Boithuto
--- foreimi
--- FrameLabel
--- RotateLabel
--- FrameStyle
--- FrameTicks
--- FrameTicksStyle
--- GridLines
--- GridLinesStyle
--- ImageSize
--- PlotLabel
--- LabelStyle
--- PlotRange
--- PlotRangeClipping
--- PlotRangePadding
—— Di-setting tsa setaele
——— Mebala (mebala e reheletsoeng + mebala e tsoang libakeng tsa mebala, e re RGBColor), ponaletso (Opacity)
——— Botenya ba mela: Thick, Bohlanya, botenya, Botenya bo Feletseng
——— Saese ya matheba: PointSize, AbsolutePointSize
——— Setaele sa mela e qetellang le lintlha tse robehileng: CapForm, JoinForm
——— Mosebetsi setaele ho lokisa ponahalo ya mongolo
——— Mesebetsi FaceForm и EdgeForm ho laola ponahalo ya sebaka le meedi ya sona
—— Mohlala
——— Tharollo e ka bang teng
——— Tharollo e nepahetse
——— Ke hobane’ng ha tharollo e tobileng e le molemo haholo?
- Mosebetsi Litšoantšo tsa 3D
—— Syntax
——— Mohlala o bonolo ka ho fetisisa
——— Litšobotsi tse akaretsang le tse ikhethileng tsa lintho tsa litšoantšo
—— Dikgetho tsa tshebetso Litšoantšo tsa 3D
--- AxesEdge
--- koa ya dibokose tsa
--- BoxRatios
--- BoxStyle
--- ClipPlanes
--- ClipPlanesStyle
--- FaceGrids
--- Setaele sa FaceGrids
--- Leseli
--- SphericalRegion
--- ViewPoint, ViewVector, ViewVertical
—— Mohlala: karolo e tšekaletseng ea k’hube
——— Ho tloha ho ntho e emeng ya mahlakore a mararo ho ya ho e sebetsanang
Mesebetsi e hahelletsoeng ka har'a ho etsa lipono
Mesebetsi ea mantlha ea 2D
- plot
- ContourPlot
- SebakaPlot
- ParametricPlot
- PolarPlot
- ListPlot
Mesebetsi ea mantlha ea 3D
- Plot3D
- ContourPlot3D
- SebakaPlot3D
- ParametricPlot3D
- ListPlot3D
Khokahano ea mesebetsi bakeng sa ho aha lipono le mesebetsi ea mantlha grafiken и Litšoantšo tsa 3D
— 2D
— 3D

2.4 | Ho theha lintho tse sebelisanang, ho sebetsa ka li-control, ho theha li-interface tsa basebelisi


Likahare tsa thutoPuo e matla ea tšoantšetso
- Mosebetsi phedisano
—— Mehlala e bonolo
——— Ho fetola paramethara
——— Pontšo ea kaho ea tharollo
— Litaolo
- sekwahelo
——— Mohlala o bonolo ka ho fetisisa
- Slider2D
——— Mohlala o bonolo ka ho fetisisa
- IntervalSlider
——— Mohlala o bonolo ka ho fetisisa
- Sebaka sa ho hlahloba
——— Mohlala o bonolo ka ho fetisisa
- CheckboxBar
- Setter
- SetterBar
- RadioButton - mofuta o khethehileng Setter
- RadioButtonBar - mofuta o khethehileng SetterBar
- Toggler
- ToggleBar
- E hlahisa
- ColorSlider
——— Mohlala o bonolo ka ho fetisisa
- PopupMenu
——— Mohlala o bonolo ka ho fetisisa
- InputField
——— Mohlala o bonolo ka ho fetisisa
—— Lintho tse ling...
Mosebetsi Ho laola
— Syntax
- Syntax e nolofalitsoeng ea litsamaiso
—— {x, a, b}
—— {x, a, b, dx}
—— {{x, x0}, a, b}, {{x, x0}, a, b, dx}
—— {{x, x0, label}, a, b}, {{x, x0, label}, a, b, dx}
—— {{x, qalong, label}, ….}
—— {x, mmala}
—— {x, {val1, val2, …}}
—— {x, {val1-lbl1, val2->lbl2, ...}}
—— {x, {xmin, ymin}, {xmax, ymax}}
—— {x, {Nnete, Maaka}}
—— {x} le {{x, x0}}
—— {x, Locator}
—— {x, {xmin, ymin}, {xmax, ymax}, Locator}
—— {{x, {{x1, y1}, {x2, y2}, ...}}, Locator} kapa
{{x, {{x1, y1}, {x2, y2}, …}}, {xmin, ymin}, {xmax, ymax}, Locator}
—— {{x, …}, …, Sebaka sa libaka, LocatorAutoCreate->Nnete}
—— {{x, …}, …, mofuta}
— Dikgetho Ho laola
- Ketso e Tsoelang Pele
- LocalizeVariables
- Ho qala
- SaveDefinitions
- SynchronousInitialization
- SynchronousUpdating
- TrackedSymbols
- Moqapi oa li-manipulators
- Ho theha li-manipulator tse hokahantsoeng le ho hokahanya libaka tsa sebaka le mothinya o sebelisa khetho TrackingFunction

2.5 | Kenya, romela kantle, ts'ebetso ea data, lifaele, litšoantšo, molumo, maqephe a webo. Ho sebetsa le API ea lisebelisoa tsa marang-rang ho sebelisa mohlala oa VKontakte API, hammoho le ho sebetsa ka mekhoa e hahiloeng ea ho sebetsa le API ea Facebook, Twitter, Instagram, joalo-joalo.


Likahare tsa thutoHo sebetsa ka lifaele le mabitso a tsona
- Patlo ea faele le mesebetsi e amanang le eona
- $InstallationDirectory, $BaseDirectory
- NotebookDirectory
- FileExistsQ
- FileNames
- Ho theha mabitso a lifaele
- DirectoryName
- FileNameJoin
- FileNameSplit
- FileNameTake
- FileBaseName
- FileExtension
Mesebetsi Kenya и Export
- Lifomate tsa ho kenya le ho romela kantle
- Kenya
—— Mehlala
- Export
—— Mehlala
Ts'ebetso ea data
- Kenya le ho lokisa data ho tsoa ho TXT
- Kenya le ho lokisa data ho tsoa ho MS Excel
Ho sebetsa ka litšoantšo
- U ka etsa'ng?
- Ho sebetsana le pokello ea litšoantšo
Ho sebetsa ka molumo
— Mohlala
Ho kenya le ho lokisa data ho tsoa maqepheng a tepo
- Ho kenya tlhahisoleseling ho tsoa webosaeteng ea Banka e Bohareng ea Rephabliki ea Russia
-- Tharollo
—— Kakaretso
- Ho kenya tlhahisoleseling ho tsoa webosaeteng ea Yandex.Dictionaries
Ho sebetsa le API
- VKontakte API
-- Mehato ea pele
—— AccessToken
—— Mohlala oa ho sebetsa le VKontakte API
- API e hahiloeng ka har'a Facebook, Twitter, Instagram

2.6 | Sebetsa ka li-database tse hahelletsoeng ka har'a Wolfram, ho kopanngoa le Wolfram | Alpha


Likahare tsa thutoTs'ehetso ea yuniti ka bophara
- Tšebeliso ea pele
- Mohlala oa tšebeliso lipalong
—— Ho rarolla litsamaiso tsa lipalo ka bongata bo nang le litekanyo:
—- Dimensional Analysis (Pi-theorem):
ho sebedisa mohlala wa bothata ba ho se tsitse ha matla a kgohedi a seaplane
——— Khouto ya mothusi
--- Tharollo
--- Liqeto
Embedded Databases
- Likarolo tsohle tsa ho sebetsa le li-database tse hlophisitsoeng tsa Wolfram Research
— Mehlala
—— Ho theha 'mapa oa lefatše o nang le mebala ho latela boemo ba GDP
—— Tafole ea nako le nako ea likarolo tsa lik'hemik'hale tse reheletsoeng ka mor'a. D. I. Mendeleev
- Ke boloka joang marang-rang a hlophisitsoeng a Wolfram Research bakeng sa phihlello hanghang?
—— Qeto ea Leonid Shifrin...
--- Khoutu
——— Mohlala oa mosebetsi
Setheo sa Puo
— (Ctrl + =) - ho fumana mojule bakeng sa ho fetolela kopo ea mahala sebakeng sa hau ho sebopeho sa Puo ea Wolfram
- Sehlopha
- EntityValue
- EntityClass
- EntityProperties, EntityProperty
- Phapang Sehlopha ka ponahalo
Toloko Mofetoleli
- Lenane la mefuta ea litlhaloso
- Mosebetsi Mofetoleli
- Mosebetsi Tlhaloso ea Semantic
- Mosebetsi SemanticImport
Ho kopanya le Wolfram|Alpha
— Kenyo ya mahala ya foromo (= qalong ya sele input)
—— Mehlala
- Kenyelletso ea mofuta oa mahala (Ctrl + = kae kapa kae ka har'a Input cell
—— Mohlala
- Sephetho se felletseng sa Wolfram|Potso ea Alpha (== qalong ea sele ea Input)
—— Mehlala e meng ea ho sebelisa Wolfram|Alpha
--- Lipalo
——— Fisiks
——— Khemistri
——— Khopolo ea monyetla, lipalo-palo le tlhahlobo ea lintlha
——— Boemo ba leholimo le litaba tse amanang le tsona
——— Marang-rang le litsamaiso tsa khomphutha
--- Mmino
——— Lijo, phepo e nepahetseng, bophelo bo botle
- Mosebetsi WolframAlpha
—— Mohlala 1: Litšoantšo tsa Euler-Venn le li-circuits tsa logic bakeng sa mesebetsi ea algebra ea Boolean ka mefuta e meraro.
—— Mohlala 2: Ho fumana mebala e haufi le e fanoeng

3 | Ho sebetsa le Wolfram Cloud: ho theha li-API tse tobileng, liforomo tsa ho kenya, CloudCDF, joalo-joalo.


Likahare tsa thutoWolfram Cloud ke eng?
- Wolfram Cloud e kenyelletsa eng?
- U ka etsa'ng ka Wolfram Cloud?
Wolfram Programming Cloud
- Mefuta ea Akhaonto ea Cloud ea Wolfram Programming CloudWolfram Programming Cloud Account
- Likoloto tsa maru
Mesebetsi ea Cloud ho Mathematica le Wolfram Desktop
- Mesebetsi ea mosebetsi o tobileng le leru, hammoho le tse ka sebetsang ka lintho tsa maru.
- Ts'ebetso ea tlhaiso-leseling ea leru
- CloudAccountData - lintlha tse mabapi le ak'haonte ea hau ea Cloud
- CloudConnect, CloudDisconnect — ho hokela kapa ho kgaola hotswa ho Leru
- CloudObjects - lintho tsa hau tsa maru
- $CloudCreditsAvailable - palo ea likalimo tsa maru tse fumanehang
Cloud interface, mehato ea pele
- Fensetere e kholo
- Fesetere ea lintlha tsa akhaonto ea hau
- Fesetere e nang le tlhaiso-leseling mabapi le ts'ebeliso ea lintho tsa hau tsa Cloud le Cloud Credits
- Fesetere e ncha ea tokomane
Mosebetsi FormFunction
- Morero le syntax
— Mohlala o bonolo ka ho fetisisa
- CloudDeploy
- Mefuta e fapaneng
- Ho sebetsana le maemo a fapaneng
—— “Mofetoleli” paramethara
—— “Default” parameter
—— “Input” parameter
—— “Label” parameter
—— “Thuso” paramethara
—— “Tlhahiso” paramethara
- Ho iketsetsa ponahalo ea foromo
- Ponahalo Melao
——FormTheme
- Mefuta e ka bang teng ea sephetho
- Ho kenya mongolo oa Serussia
—— Mohlala
— Mehlala
—— Ho theha sesebelisoa ho rarolla equation
—— Ho theha sesebelisoa sa ho sebetsa litšoantšo
—— Ho theha ts'ebeliso ea libaka tse nang le masimo a bohlale
Mosebetsi APIFunction
— Mehlala
—— Ho theha sesebelisoa ho rarolla equation
—— Ho theha ts'ebeliso ea libaka tse nang le masimo a bohlale

4 | Theknoloji ea CDF - ho kenella hanghang ha lintho tse sebetsanang le litaba tse entsoeng ho Mathematica maqepheng a webo, lintlha tse poteletseng. Sebelisa lintho tse sebetsang tse seng li entsoe ho tsoa webosaeteng ea Wolfram Demonstrations Project mererong ea hau 'me u e fetole. Mehlala ea sebele le lits'ebetso tsa khoebo


Likahare tsa thutoCDF - Computable Document Format - Computable Document Format
- Theknoloji ea CDF
- Papiso e khutšoane le mefuta e meng
- Mehato ea ho theha CDF
—— Mehato e bontšitsoeng
— Mehlala ea sebele
- Morero oa lipontšo tsa Wolfram
Ho theha CDF e thehiloeng ho Manipulate
- Mohato oa 1. Ho theha kopo
— Mohato 2. E boloke ka sebopeho sa CDF
— Mohato 3. Ho kenya leqephe la webe
Ho theha CDF ho latela DynamicModule
- Mohato oa 1. Ho theha kopo
— Mohato 2. E boloke ho CDF
— Mohato 3. Ho kenya leqephe la webe
- Mohlala o mong oa CDF e rarahaneng
Ho theha maqephe a tepo a seng a entsoe a ipapisitse le CDF
— Mohlala
EnterpriseCDF
- Phapano lipakeng tsa CDF le EnterpriseCDF
- Papiso ea mantlha ea CDF le EnterpriseCDF
- Papiso e qaqileng ea CDF, EnterpriseCDF, Wolfram Player Pro le Mathematica
CloudCDF
- CloudCDF ke eng?
— Mohlala oa ho theha CloudCDF
—— Mohlala 1
—— Mohlala 2

5 | Sebetsa ka Puo ea Wolfram le Mathematica, e kentsoe pele ebile e lokolohile ho Raspberry Pi (e nang le sistimi e sebetsang ea Raspbian)


Likahare tsa thutoRaspberry Pi, motsoalle oa pele
- Ke eng?
- Nka e reka hokae?
- Ho kenya OS hokae le joang, ka tšehetso ea puo ea Wolfram
Puo ea Raspberry Pi le Wolfram
- Leqephe la morero
- Leqephe la litokomane
- Raspberry Pi e shebahala joang kamora ho kenya
- Mohopolo oa ho hlophisa ka Puo ea Wolfram ho Raspberry Pi
Raspberry Pi Performance
— Ho bala khoutu e itseng
- Benchmark e hahelletsoeng kahare ea Wolfram
- Papiso le ts'ebetso ea Python ho Raspberry Pi
Mohlala oa roboto ea poso e sebetsang ho Raspberry Pi
Mehlala ea ho sebetsa le Raspberry Pi
- Ho theha tracker ea GPS
—— U tla e hloka
—— Sheba ka mora kopano
—— Lenaneo la Mathematica ho Raspberry Pi
— Ho nka foto
—— U tla e hloka
—— Sheba ka mora kopano
—— Lenaneo la Mathematica ho Raspberry Pi
- Sebelisa GPIO
—— U tla e hloka
—— Sheba ka mora kopano
—— Lenaneo la Mathematica ho Raspberry Pi
— Mehlala e meng
Nka fumana leseli le le leng ka Puo ea Wolfram le kopanyo ea Raspberry Pi?

Ke kopa tšoarelo bakeng sa boleng ba molumo, livideong tse ling ha e ntle kamoo nka ratang kateng.

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