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{"version":3,"file":"HPC102-mUJOkhH3.js","sources":["../../src/exercices/HP/HPC102.js"],"sourcesContent":["import { courbe, integrale } from '../../lib/2d/courbes.js'\nimport { repere } from '../../lib/2d/reperes.js'\nimport { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu } from '../../modules/outils.js'\nimport { aleaVariables } from '../../modules/outilsMathjs.js'\nimport { all, create, sqrt } from 'mathjs'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\n\n// const math = { simplify: simplify, parse: parse, derivative: derivative }\nexport const titre = 'Calculs de probabilité avec la loi normale'\nconst math = create(all)\n/**\n * Calculs de probas\n * @author Maxime Nguyen\n * Référence HPC102\n */\n\nexport const uuid = '89071'\nexport const ref = 'HPC102'\nexport default function CalculsLoiNormale () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.consigne = 'Calcul de probabilités pour une loi normale. Les évaluations numériques peuvent se faire à l\\'aide d\\'une table de valeur de la loi normale centrée réduite.'\n this.nbQuestions = 4\n this.nbCols = 1 // Nombre de colonnes pour la sortie LaTeX\n this.nbColsCorr = 1 // Nombre de colonnes dans la correction pour la sortie LaTeX\n this.sup = 1\n this.spacing = 1\n this.spacingCorr = 1.5\n this.nouvelleVersion = function () {\n this.sup = Number(this.sup)\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n this.liste_valeurs = [] // Les questions sont différentes du fait du nom de la fonction, donc on stocke les valeurs\n let listeTypeDeQuestionsDisponibles\n if (this.sup === 1) {\n listeTypeDeQuestionsDisponibles = ['N01']\n } else if (this.sup === 2) {\n listeTypeDeQuestionsDisponibles = ['Nmusigma', 'Nmusigmaintervallecentre']\n } else {\n listeTypeDeQuestionsDisponibles = ['N01']\n }\n const listeTypeDeQuestions = combinaisonListes(listeTypeDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, texte, texteCorr, variables, expression, gaussienne, r, C, I, graphique, resultat, resultatA, resultatB, bornea, oppbornea, borneb, oppborneb, mu, sigma, bornec, borned, calculstep, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n switch (listeTypeDeQuestions[i]) {\n case 'N01':\n variables = aleaVariables(\n {\n a: 'pickRandom([-1,1])*round(random(0.1,3),2)',\n b: 'pickRandom([-1,1])*round(random(0.1,3),2)',\n test: 'a<b'\n }\n )\n gaussienne = x => 1 / math.sqrt(2 * math.pi) * math.exp(-(x ** 2) / 2)\n r = repere({\n xMin: -4,\n xMax: 4,\n yMin: -1,\n yMax: 3,\n xUnite: 2,\n yUnite: 6,\n axesEpaisseur: 1,\n yThickDistance: 0.5\n })\n C = courbe(gaussienne, { repere: r, step: 0.1 })\n I = integrale(gaussienne, { repere: r, step: 0.1, a: variables.a, b: variables.b, hachures: 0 })\n graphique = mathalea2d({\n xmin: -9,\n xmax: 9,\n ymin: -0.8,\n ymax: 2.8,\n pixelsParCm: 30,\n scale: 0.75\n }, r, C, I)\n bornea = texNombre(variables.a)\n oppbornea = texNombre(-variables.a)\n borneb = texNombre(variables.b)\n oppborneb = texNombre(-variables.b)\n bornec = bornea\n borned = borneb\n resultat = 0.5 * math.erf(variables.b / sqrt(2)) - 0.5 * math.erf(variables.a / sqrt(2))\n expression = `$\\\\mathrm{P}(${bornea} < X < ${borneb})$`\n calculstep = []\n texte = 'Soit $X$ une variable aléatoire réelle suivant une loi normale $\\\\mathcal{N}(0,1)$. <br> Calculer à $10^{-2}$ près la probabilité : ' + expression\n texte += '<br>' + graphique\n texteCorr = 'On décompose pour exprimer la probabilité avec la fonction de répartition $t \\\\mapsto \\\\mathrm{P}(X \\\\leq t)$ en utilisant la tabulation de ses valeurs pour $t \\\\geq 0$ : <br>'\n calculstep.push(`\\\\mathrm{P}(${bornea} < X < ${borneb}) &= \\\\mathrm{P}(X < ${borneb}) - \\\\mathrm{P}(X \\\\leq ${bornea}) &&`)\n if (variables.b < 0) {\n resultatB = texNombre(0.5 + 0.5 * math.erf(-variables.b / sqrt(2)), 3)\n if (variables.a < 0) {\n resultatA = texNombre(0.5 + 0.5 * math.erf(-variables.a / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X > ${(oppborneb)}) - \\\\mathrm{P}(X \\\\geq ${oppbornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= 1 - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) - (1-\\\\mathrm{P}(X < ${oppbornea})) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &= \\\\mathrm{P}(X < ${oppbornea}) - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) &&`)\n calculstep.push(` &\\\\approx ${resultatA} - ${resultatB} &&`)\n } else {\n resultatA = texNombre(0.5 + 0.5 * math.erf(variables.a / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X > ${(oppborneb)}) - \\\\mathrm{P}(X \\\\leq ${bornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= 1 - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) - \\\\mathrm{P}(X \\\\leq ${bornea}) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &\\\\approx 1 - ${resultatB} - ${resultatA} &&`)\n }\n } else if (variables.a < 0) {\n resultatA = texNombre(0.5 + 0.5 * math.erf(-variables.a / sqrt(2)), 3)\n resultatB = texNombre(0.5 + 0.5 * math.erf(variables.b / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X < ${(borneb)}) - \\\\mathrm{P}(X > ${oppbornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= \\\\mathrm{P}(X < ${(borneb)}) - (1 - \\\\mathrm{P}(X \\\\leq ${oppbornea})) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &\\\\approx ${resultatB} - (1 - ${resultatA}) &&`)\n } else {\n resultatA = texNombre(0.5 + 0.5 * math.erf(variables.a / sqrt(2)), 3)\n resultatB = texNombre(0.5 + 0.5 * math.erf(variables.b / sqrt(2)), 3)\n calculstep.push(`&\\\\approx ${resultatB} - ${resultatA} &&`)\n }\n setReponse(this, i, resultat.toFixed(2))\n break\n case 'Nmusigma':\n variables = aleaVariables(\n {\n a: 'pickRandom([-1,1])*round(random(0.3,2.5),1)',\n b: 'pickRandom([-1,1])*round(random(0.3,2.5),1)',\n mu: 'randomInt(-30, 30)',\n sigma: 'round(random(1,4),0)',\n test: '(a-b)/sigma<-1'\n }\n )\n gaussienne = x => 1 / variables.sigma / math.sqrt(2 * math.pi) * math.exp(-((x - variables.mu) ** 2) / 2 / (variables.sigma ** 2))\n r = repere({\n axeYisVisible: false,\n xMin: -4 * variables.sigma + variables.mu,\n xMax: 4 * variables.sigma + variables.mu,\n yMin: -1,\n yMax: 3,\n xUnite: 2 / variables.sigma,\n yUnite: 6 * variables.sigma,\n axesEpaisseur: 1,\n xThickListe: [variables.a * variables.sigma + variables.mu, variables.mu, variables.b * variables.sigma + variables.mu],\n xLabelListe: [variables.a * variables.sigma + variables.mu, variables.mu, variables.b * variables.sigma + variables.mu],\n yThickDistance: 0.5,\n grilleXMin: variables.mu - 4 * variables.sigma,\n grilleXDistance: variables.sigma\n })\n C = courbe(gaussienne, { repere: r, step: 0.1 })\n I = integrale(gaussienne, {\n repere: r,\n step: 0.1,\n a: variables.a * variables.sigma + variables.mu,\n b: variables.b * variables.sigma + variables.mu,\n hachures: 0\n })\n graphique = mathalea2d({\n xmin: (-5 * variables.sigma + variables.mu) * r.xUnite,\n xmax: (5 * variables.sigma + variables.mu) * r.xUnite,\n ymin: -0.8,\n ymax: 2.8,\n pixelsParCm: 30,\n scale: 0.75\n }, r, C, I)\n bornec = texNombre(variables.a * variables.sigma + variables.mu)\n borned = texNombre(variables.b * variables.sigma + variables.mu)\n bornea = texNombre(variables.a)\n oppbornea = texNombre(-variables.a)\n borneb = texNombre(variables.b)\n oppborneb = texNombre(-variables.b)\n mu = texNombre(variables.mu)\n sigma = texNombre(variables.sigma)\n resultat = 0.5 * math.erf(variables.b / sqrt(2)) - 0.5 * math.erf(variables.a / sqrt(2))\n expression = `$\\\\mathrm{P}(${bornec} < X < ${borned})$`\n calculstep = []\n texte = `Soit $X$ une variable aléatoire réelle suivant une loi normale $\\\\mathcal{N}(\\\\mu=${mu},\\\\sigma=${sigma})$. <br> Calculer à $10^{-2}$ près la probabilité : ` + expression\n texte += '<br>' + graphique\n if (variables.mu < 0) {\n texteCorr = `On pose $Z = \\\\frac{X + ${texNombre(-variables.mu)}}{${sigma}}$ `\n calculstep.push(`\\\\mathrm{P}(${bornec} < X < ${borned}) &= \\\\mathrm{P}\\\\left(\\\\frac{${bornec} + ${texNombre(-variables.mu)}}{${sigma}} < \\\\frac{X + ${texNombre(-variables.mu)}}{${sigma}} < \\\\frac{${borned} + ${texNombre(-variables.mu)}}{${sigma}} \\\\right) &&`)\n } else {\n texteCorr = `On pose $Z = \\\\frac{X - ${mu}}{${sigma}}$ `\n calculstep.push(`\\\\mathrm{P}(${bornec} < X < ${borned}) &= \\\\mathrm{P}\\\\left(\\\\frac{${bornec} - ${mu}}{${sigma}} < \\\\frac{X - ${mu}}{${sigma}} < \\\\frac{${borned} - ${mu}}{${sigma}} \\\\right) &&`)\n }\n texteCorr += ' de telle sorte que $Z$ suive une loi $\\\\mathcal{N}(0,1)$. <br><br>'\n calculstep.push(`&= \\\\mathrm{P}\\\\left( ${bornea} < Z < ${borneb} \\\\right)`)\n calculstep.push(`&= \\\\mathrm{P}(X < ${borneb}) - \\\\mathrm{P}(X \\\\leq ${bornea}) &&`)\n if (variables.b < 0) {\n resultatB = texNombre(0.5 + 0.5 * math.erf(-variables.b / sqrt(2)), 3)\n if (variables.a < 0) {\n resultatA = texNombre(0.5 + 0.5 * math.erf(-variables.a / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X > ${(oppborneb)}) - \\\\mathrm{P}(X \\\\geq ${oppbornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= 1 - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) - (1-\\\\mathrm{P}(X < ${oppbornea})) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &= \\\\mathrm{P}(X < ${oppbornea}) - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) &&`)\n calculstep.push(` &\\\\approx ${resultatA} - ${resultatB} &&`)\n } else {\n resultatA = texNombre(0.5 + 0.5 * math.erf(variables.a / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X > ${(oppborneb)}) - \\\\mathrm{P}(X \\\\leq ${bornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= 1 - \\\\mathrm{P}(X \\\\leq ${(oppborneb)}) - \\\\mathrm{P}(X \\\\leq ${bornea}) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &\\\\approx 1 - ${resultatB} - ${resultatA} &&`)\n }\n } else if (variables.a < 0) {\n resultatA = texNombre(0.5 + 0.5 * math.erf(-variables.a / sqrt(2)), 3)\n resultatB = texNombre(0.5 + 0.5 * math.erf(variables.b / sqrt(2)), 3)\n calculstep.push(` &= \\\\mathrm{P}(X < ${(borneb)}) - \\\\mathrm{P}(X > ${oppbornea}) && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &= \\\\mathrm{P}(X < ${(borneb)}) - (1 - \\\\mathrm{P}(X \\\\leq ${oppbornea})) && (\\\\text{par passage au complémentaire})`)\n calculstep.push(` &\\\\approx ${resultatB} - (1 - ${resultatA}) &&`)\n } else {\n resultatA = texNombre(0.5 + 0.5 * math.erf(variables.a / sqrt(2)), 3)\n resultatB = texNombre(0.5 + 0.5 * math.erf(variables.b / sqrt(2)), 3)\n calculstep.push(`&\\\\approx ${resultatB} - ${resultatA} &&`)\n }\n setReponse(this, i, resultat.toFixed(2))\n break\n case 'Nmusigmaintervallecentre':\n variables = aleaVariables(\n {\n a: 'round(random(0.6,2.5),1)',\n mu: 'randomInt(-30, 30)',\n sigma: 'round(random(1,4),0)'\n }\n )\n gaussienne = x => 1 / variables.sigma / math.sqrt(2 * math.pi) * math.exp(-((x - variables.mu) ** 2) / 2 / (variables.sigma ** 2))\n r = repere({\n axeYisVisible: false,\n xMin: -4 * variables.sigma + variables.mu,\n xMax: 4 * variables.sigma + variables.mu,\n yMin: -1,\n yMax: 3,\n xUnite: 2 / variables.sigma,\n yUnite: 6 * variables.sigma,\n axesEpaisseur: 1,\n xThickListe: [-variables.a * variables.sigma + variables.mu, variables.mu, variables.a * variables.sigma + variables.mu],\n xLabelListe: [-variables.a * variables.sigma + variables.mu, variables.mu, variables.a * variables.sigma + variables.mu],\n yThickDistance: 0.5,\n grilleXMin: variables.mu - 4 * variables.sigma,\n grilleXDistance: variables.sigma\n })\n C = courbe(gaussienne, { repere: r, step: 0.1 })\n I = integrale(gaussienne, {\n repere: r,\n step: 0.1,\n a: -variables.a * variables.sigma + variables.mu,\n b: variables.a * variables.sigma + variables.mu,\n hachures: 0\n })\n graphique = mathalea2d({\n xmin: r.xUnite * (-5 * variables.sigma + variables.mu),\n xmax: (5 * variables.sigma + variables.mu) * r.xUnite,\n ymin: -0.8,\n ymax: 2.8,\n pixelsParCm: 30,\n scale: 0.75\n }, r, C, I)\n bornec = texNombre(-variables.a * variables.sigma + variables.mu)\n borned = texNombre(variables.a * variables.sigma + variables.mu)\n bornea = texNombre(-variables.a)\n borneb = texNombre(variables.a)\n mu = texNombre(variables.mu)\n sigma = texNombre(variables.sigma)\n resultat = 0.5 * math.erf(variables.a / sqrt(2)) - 0.5 * math.erf(-variables.a / sqrt(2))\n expression = `$\\\\mathrm{P}(${bornec} < X < ${borned})$`\n calculstep = []\n texte = `Soit $X$ une variable aléatoire réelle suivant une loi normale $\\\\mathcal{N}(\\\\mu=${mu},\\\\sigma=${sigma})$. <br> Calculer à $10^{-2}$ près la probabilité : ` + expression\n texte += '<br>' + graphique\n if (variables.mu < 0) {\n texteCorr = `On pose $Z = \\\\frac{X + ${texNombre(-variables.mu)}}{${sigma}}$ `\n calculstep.push(`\\\\mathrm{P}(${bornec} < X < ${borned}) &= \\\\mathrm{P}\\\\left(\\\\frac{${bornec} + ${texNombre(-variables.mu)}}{${sigma}} < \\\\frac{X + ${texNombre(-variables.mu)}}{${sigma}} < \\\\frac{${borned} + ${texNombre(-variables.mu)}}{${sigma}} \\\\right) &&`)\n } else {\n texteCorr = `On pose $Z = \\\\frac{X - ${mu}}{${sigma}}$ `\n calculstep.push(`\\\\mathrm{P}(${bornec} < X < ${borned}) &= \\\\mathrm{P}\\\\left(\\\\frac{${bornec} - ${mu}}{${sigma}} < \\\\frac{X - ${mu}}{${sigma}} < \\\\frac{${borned} - ${mu}}{${sigma}} \\\\right) &&`)\n }\n texteCorr += ' de telle sorte que $Z$ suive une loi $\\\\mathcal{N}(0,1)$. <br><br>'\n calculstep.push(`&= \\\\mathrm{P}\\\\left( ${bornea} < Z < ${borneb} \\\\right)`)\n calculstep.push(`&= \\\\mathrm{P}(X < ${borneb}) - \\\\mathrm{P}(X \\\\leq ${bornea}) &&`)\n resultatA = texNombre(0.5 + 0.5 * math.erf(variables.a / sqrt(2)), 3)\n calculstep.push(` &= 2\\\\times\\\\mathrm{P}(X < ${(borneb)}) - 1 && (\\\\text{par symétrie de la loi normale})`)\n calculstep.push(` &\\\\approx 2\\\\times ${resultatA} - 1 &&`)\n setReponse(this, i, resultat.toFixed(2))\n break\n }\n calculstep.push(`&\\\\approx ${texNombre(resultat, 2)} &&`)\n texteCorr += String.raw`\n $\\begin{aligned}\n ${calculstep.join('\\\\\\\\')}\n \\end{aligned}$ <br>`\n texteCorr += `La probabilité est : $\\\\mathrm{P}(${bornec} < X < ${borned}) \\\\approx ${texNombre(resultat, 2)}$` // ${resultat}$`\n\n // texte = texte.replaceAll('frac', 'dfrac')\n texteCorr = texteCorr.replaceAll('frac', 'dfrac')\n if (this.interactif) {\n texte += '<br><br>' + ajouteChampTexteMathLive(this, i, 'inline largeur25', { texteAvant: `La probabilité est : $\\\\mathrm{P}(${bornec} < X < ${borned}) \\\\approx $` })\n }\n if (this.liste_valeurs.indexOf(expression) === -1) {\n this.liste_valeurs.push(expression)\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireNumerique = ['Niveau de difficulté', 2, '1 : Loi normale centrée réduite \\n2 : Loi normale quelconque']\n}\n"],"names":["interactifReady","interactifType","titre","math","create","all","uuid","ref","CalculsLoiNormale","Exercice","listeTypeDeQuestionsDisponibles","listeTypeDeQuestions","combinaisonListes","i","texte","texteCorr","variables","expression","gaussienne","r","C","I","graphique","resultat","resultatA","resultatB","bornea","oppbornea","borneb","oppborneb","mu","sigma","bornec","borned","calculstep","cpt","aleaVariables","x","repere","courbe","integrale","mathalea2d","texNombre","sqrt","setReponse","ajouteChampTexteMathLive","listeQuestionsToContenu"],"mappings":"qRAYY,MAACA,EAAkB,GAClBC,EAAiB,WAGjBC,EAAQ,6CACfC,EAAOC,EAAOC,CAAG,EAOVC,EAAO,QACPC,EAAM,SACJ,SAASC,GAAqB,CAC3CC,EAAS,KAAK,IAAI,EAClB,KAAK,MAAQP,EACb,KAAK,SAAW,6JAChB,KAAK,YAAc,EACnB,KAAK,OAAS,EACd,KAAK,WAAa,EAClB,KAAK,IAAM,EACX,KAAK,QAAU,EACf,KAAK,YAAc,IACnB,KAAK,gBAAkB,UAAY,CACjC,KAAK,IAAM,OAAO,KAAK,GAAG,EAC1B,KAAK,eAAiB,CAAE,EACxB,KAAK,iBAAmB,CAAE,EAC1B,KAAK,cAAgB,CAAE,EACvB,IAAIQ,EACA,KAAK,MAAQ,EACfA,EAAkC,CAAC,KAAK,EAC/B,KAAK,MAAQ,EACtBA,EAAkC,CAAC,WAAY,0BAA0B,EAEzEA,EAAkC,CAAC,KAAK,EAE1C,MAAMC,EAAuBC,EAAkBF,EAAiC,KAAK,WAAW,EAChG,QAASG,EAAI,EAAGC,EAAOC,EAAWC,EAAWC,EAAYC,EAAYC,EAAGC,EAAGC,EAAGC,EAAWC,EAAUC,EAAWC,EAAWC,EAAQC,EAAWC,EAAQC,EAAWC,EAAIC,EAAOC,EAAQC,EAAQC,EAAYC,EAAM,EAAGtB,EAAI,KAAK,aAAesB,EAAM,IAAK,CAChP,OAAQxB,EAAqBE,CAAC,EAAC,CAC7B,IAAK,MACHG,EAAYoB,EACV,CACE,EAAG,4CACH,EAAG,4CACH,KAAM,KACP,CACF,EACDlB,EAAamB,GAAK,EAAIlC,EAAK,KAAK,EAAIA,EAAK,EAAE,EAAIA,EAAK,IAAI,EAAEkC,GAAK,GAAK,CAAC,EACrElB,EAAImB,EAAO,CACT,KAAM,GACN,KAAM,EACN,KAAM,GACN,KAAM,EACN,OAAQ,EACR,OAAQ,EACR,cAAe,EACf,eAAgB,EAC5B,CAAW,EACDlB,EAAImB,EAAOrB,EAAY,CAAE,OAAQC,EAAG,KAAM,GAAK,EAC/CE,EAAImB,EAAUtB,EAAY,CAAE,OAAQC,EAAG,KAAM,GAAK,EAAGH,EAAU,EAAG,EAAGA,EAAU,EAAG,SAAU,EAAG,EAC/FM,EAAYmB,EAAW,CACrB,KAAM,GACN,KAAM,EACN,KAAM,IACN,KAAM,IACN,YAAa,GACb,MAAO,GACnB,EAAatB,EAAGC,EAAGC,CAAC,EACVK,EAASgB,EAAU1B,EAAU,CAAC,EAC9BW,EAAYe,EAAU,CAAC1B,EAAU,CAAC,EAClCY,EAASc,EAAU1B,EAAU,CAAC,EAC9Ba,EAAYa,EAAU,CAAC1B,EAAU,CAAC,EAClCgB,EAASN,EACTO,EAASL,EACTL,EAAW,GAAMpB,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAI,GAAMxC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EACvF1B,EAAa,gBAAgBS,CAAM,UAAUE,CAAM,KACnDM,EAAa,CAAE,EACfpB,EAAQ,uIAAyIG,EACjJH,GAAS,OAASQ,EAClBP,EAAY,kLACZmB,EAAW,KAAK,eAAeR,CAAM,UAAUE,CAAM,yBAAyBA,CAAM,2BAA2BF,CAAM,MAAM,EACvHV,EAAU,EAAI,GAChBS,EAAYiB,EAAU,GAAM,GAAMvC,EAAK,IAAI,CAACa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACjE3B,EAAU,EAAI,GAChBQ,EAAYkB,EAAU,GAAM,GAAMvC,EAAK,IAAI,CAACa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACrET,EAAW,KAAK,wBAAyBL,CAAS,2BAA4BF,CAAS,+CAA+C,EACtIO,EAAW,KAAK,gCAAiCL,CAAS,0BAA2BF,CAAS,+CAA+C,EAC7IO,EAAW,KAAK,wBAAwBP,CAAS,2BAA4BE,CAAW,MAAK,EAC7FK,EAAW,KAAK,cAAcV,CAAS,MAAMC,CAAS,KAAK,IAE3DD,EAAYkB,EAAU,GAAM,GAAMvC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACpET,EAAW,KAAK,wBAAyBL,CAAS,2BAA4BH,CAAM,+CAA+C,EACnIQ,EAAW,KAAK,gCAAiCL,CAAS,2BAA4BH,CAAM,8CAA8C,EAC1IQ,EAAW,KAAK,kBAAkBT,CAAS,MAAMD,CAAS,KAAK,IAExDR,EAAU,EAAI,GACvBQ,EAAYkB,EAAU,GAAM,GAAMvC,EAAK,IAAI,CAACa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACrElB,EAAYiB,EAAU,GAAM,GAAMvC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACpET,EAAW,KAAK,wBAAyBN,CAAM,uBAAwBD,CAAS,+CAA+C,EAC/HO,EAAW,KAAK,wBAAyBN,CAAM,gCAAiCD,CAAS,+CAA+C,EACxIO,EAAW,KAAK,eAAeT,CAAS,WAAWD,CAAS,MAAM,IAElEA,EAAYkB,EAAU,GAAM,GAAMvC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACpElB,EAAYiB,EAAU,GAAM,GAAMvC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAG,CAAC,EACpET,EAAW,KAAK,cAAcT,CAAS,MAAMD,CAAS,KAAK,GAE7DoB,EAAW,KAAM/B,EAAGU,EAAS,QAAQ,CAAC,CAAC,EACvC,MACF,IAAK,WACHP,EAAYoB,EACV,CACE,EAAG,8CACH,EAAG,8CACH,GAAI,qBACJ,MAAO,uBACP,KAAM,gBACP,CACF,EACDlB,EAAamB,GAAK,EAAIrB,EAAU,MAAQb,EAAK,KAAK,EAAIA,EAAK,EAAE,EAAIA,EAAK,IAAI,GAAGkC,EAAIrB,EAAU,KAAO,GAAK,EAAKA,EAAU,OAAS,CAAE,EACjIG,EAAImB,EAAO,CACT,cAAe,GACf,KAAM,GAAKtB,EAAU,MAAQA,EAAU,GACvC,KAAM,EAAIA,EAAU,MAAQA,EAAU,GACtC,KAAM,GACN,KAAM,EACN,OAAQ,EAAIA,EAAU,MACtB,OAAQ,EAAIA,EAAU,MACtB,cAAe,EACf,YAAa,CAACA,EAAU,EAAIA,EAAU,MAAQA,EAAU,GAAIA,EAAU,GAAIA,EAAU,EAAIA,EAAU,MAAQA,EAAU,EAAE,EACtH,YAAa,CAACA,EAAU,EAAIA,EAAU,MAAQA,EAAU,GAAIA,EAAU,GAAIA,EAAU,EAAIA,EAAU,MAAQA,EAAU,EAAE,EACtH,eAAgB,GAChB,WAAYA,EAAU,GAAK,EAAIA,EAAU,MACzC,gBAAiBA,EAAU,KACvC,CAAW,EACDI,EAAImB,EAAOrB,EAAY,CAAE,OAAQC,EAAG,KAAM,GAAK,EAC/CE,EAAImB,EAAUtB,EAAY,CACxB,OAAQC,EACR,KAAM,GACN,EAAGH,EAAU,EAAIA,EAAU,MAAQA,EAAU,GAC7C,EAAGA,EAAU,EAAIA,EAAU,MAAQA,EAAU,GAC7C,SAAU,CACtB,CAAW,EACDM,EAAYmB,EAAW,CACrB,MAAO,GAAKzB,EAAU,MAAQA,EAAU,IAAMG,EAAE,OAChD,MAAO,EAAIH,EAAU,MAAQA,EAAU,IAAMG,EAAE,OAC/C,KAAM,IACN,KAAM,IACN,YAAa,GACb,MAAO,GACnB,EAAaA,EAAGC,EAAGC,CAAC,EACVW,EAASU,EAAU1B,EAAU,EAAIA,EAAU,MAAQA,EAAU,EAAE,EAC/DiB,EAASS,EAAU1B,EAAU,EAAIA,EAAU,MAAQA,EAAU,EAAE,EAC/DU,EAASgB,EAAU1B,EAAU,CAAC,EAC9BW,EAAYe,EAAU,CAAC1B,EAAU,CAAC,EAClCY,EAASc,EAAU1B,EAAU,CAAC,EAC9Ba,EAAYa,EAAU,CAAC1B,EAAU,CAAC,EAClCc,EAAKY,EAAU1B,EAAU,EAAE,EAC3Be,EAAQW,EAAU1B,EAAU,KAAK,EACjCO,EAAW,GAAMpB,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EAAI,GAAMxC,EAAK,IAAIa,EAAU,EAAI2B,EAAK,CAAC,CAAC,EACvF1B,EAAa,gBAAgBe,CAAM,UAAUC,CAAM,KACnDC,EAAa,CAAE,EACfpB,EA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