reponses-final.ipynb

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   "cell_type": "markdown",
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   "source": [
    "## Instructions {-}\n",
    "Ce sujet est constitué de deux parties : la partie 1 correspond au sujet donné l'an dernier, dont la correction vous est donnée, la partie 2 constitue la partie qui sera évaluée et se place dans la continuité de la partie 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enoncé du problème (Partie 1)\n",
    "\n",
    "L'objectif de ce projet est d'estimer la longueur de câble sous-marin nécessaire pour relier deux côtes $A$ et $B$  en utilisant des simulations conditionnelles.\n",
    "\n",
    "\n",
    "Le câble reposera sur le fond marin dont la profondeur est inconnue.\n",
    "Le segment $[AB]$ est discrétisé par une séquence de (N+1) points. On pose $x_0=A$ et pour $i=1,\\dots,N$, $$x_i=x_0+i\\Delta$$ où $$\\Delta = \\frac{AB}{N}$$ de telle sorte que $x_N=B$.\n",
    "On note $z(x)$ la profondeur du fond marin au point $x$ de telle sorte \n",
    "qu'on pourra estimer la longueur totale de câble nécessaire par la somme \n",
    "des longueurs sur les segments de la discrétisation :\n",
    "\n",
    "$$l=\\sum_{i=1}^N\\sqrt{\\Delta^2+(z(x_i)-z(x_{i-1}))^2}.$$\n",
    "\n",
    "Enfin, notons que l'on dispose d'un ensemble de $n$ observations de la \n",
    "profondeur que l'on supposera situées sur des points de discrétisation $z(x_{j_1}),\\dots,z(x_{j_n})$.\n",
    "\n",
    "\n",
    "On adopte un modèle probabiliste pour la profondeur. On suppose que le vecteur des \n",
    "profondeurs sur les points de discrétisation \n",
    "$\\mathbf{z}=(z(x_0),\\dots,z(x_N))$ est la réalisation\n",
    "d'un vecteur aléatoire gaussien $\\mathbf{Z}=(Z(x_0),\\dots,Z(x_N))$ \n",
    "dont le vecteur d'espérance ne contient qu'une seule valeur $\\mu$ \n",
    "répétée $N+1$ fois et dont la matrice de covariance $\\Sigma$ a pour termes $\\sigma_{ij}$\n",
    "définis par $\\sigma_{ij}=C(|x_i-x_j|)$ où $C$ est une\n",
    "fonction décroissante, traduisant le fait que deux points \n",
    "géographiquement proches ont tendance à avoir des profondeurs plus similaires que deux points éloignés.\n",
    "\n",
    "On supposera que la matrice de covariance ainsi \n",
    "générée est définie-positive (en fait, $C$ sera choisie parmi les fonctions qui, \n",
    "appliquées aux termes d'une matrice de distance, produisent des matrices définie-positives). \n",
    "\n",
    "Si on note $L$ la variable aléatoire donnant la longueur de cable nécessaire : \n",
    "$$L=\\sum_{i=1}^N\\sqrt{\\Delta^2+(Z(x_i)-Z(x_{i-1}))^2},$$\n",
    "un bon estimateur de $L$ est fourni par l'espérance conditionnelle \n",
    "\n",
    "$$L^\\star=E[L|Z(x_{j_1})=z(x_{j_1}),\\dots,Z(x_{j_n})=z(x_{j_n})].$$\n",
    "                                                                              \n",
    "Cependant, cette quantité est difficilement accessible par le calcul. \n",
    "On va donc avoir recours à des\n",
    "simulations conditionnelles. C'est-à-dire que l'on va simuler \n",
    "un nombre $K$ de réalités (disons des réalisations du modèle \n",
    "probabiliste choisi), et sur chacune d'entre elle, \n",
    "la quantité de câble nécessaire sera évaluée. \n",
    "On disposera ainsi d'un échantillon $l_{(1)},\\dots,l_{(K)}$ de \n",
    "longueures simulées. Puis on approchera l'espérance conditionnelle  par \n",
    "$$L^\\star=\\frac1{K}\\sum_{k=1}^K l_{(k)}.$$\n",
    "\n",
    "L'objectif de ce projet est donc d'écrire un code permettant \n",
    "d'effectuer cette simulation conditionnelle, puis de l'appliquer \n",
    "au jeu de données fourni et d'en déduire une estimation de la longueur de câble nécessaire."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions théoriques\n",
    "\n",
    "1. Quel théorème du cours nous autorise-t-il à estimer l'espérance conditionnelle par la moyenne empirique de simulations conditionnelles ?\n",
    "\n",
    "*la loi forte des grands nombres, cf [Proba IV p.16](https://boisgera.github.io/CDIS/output/Probabilit%C3%A9%20IV.pdf), en vérifiant que $L$ est bien intégrable*\n",
    "\n",
    "2. Rappeler la loi conditionnelle du vecteur des composantes de $\\mathbf{Z}$ correspondant aux points de discrétisation\n",
    "sans observation, connaissant les valeurs prises par les composantes aux sites d'observation.\n",
    "\n",
    "*cf. [Proba III p.18](https://boisgera.github.io/CDIS/output/Probabilit%C3%A9%20III.pdf),*\n",
    "\n",
    "3. Si $\\mathbf{Y}=(Y_1,\\dots,Y_p)$ est un vecteur de composantes gaussiennes indépendantes, toutes d'espérance nulle et de variance 1, \n",
    "quelle est la loi du vecteur $\\mathbf{Z}=m+R\\mathbf{Y}$ où $R$ est une matrice $p\\times p$ et $m$ est un vecteur de taille $p$ ?\n",
    "\n",
    "*cf. [Proba V p.12](https://cloud.mines-paristech.fr/index.php/s/GLDwtTAMOJCYk3i/download)*\n",
    "\n",
    "4. En déduire un algorithme de simulation conditionnelle.\n",
    "\n",
    "*Appliquer l'algorithme de la q.3 à la loi conditionnelle (on calculera en particulier l'espérance conditionnelle de $\\mathbf{Z}$ sachant les données et la décomposition de Cholesky de la matrice de covariance conditionnelle sachant les données).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Données du problème\n",
    "Conventionnellement, $A$ est l'origine, $B=500$, $N=100$.\n",
    "\n",
    "Les données $$\\begin{array}{c|r}i & z(x_i)\\\\\n",
    "\\hline\n",
    "0 & 0\\\\\n",
    "20 & -4\\\\\n",
    "40 & -12.8\\\\\n",
    "60 & -1\\\\\n",
    "80 & -6.5\\\\\n",
    "100 & 0\\end{array}$$\n",
    "\n",
    "L'espérance de chaque composante du vecteur aléatoire $\\mathbf{Z}$ est donnée par $\\mu=-5.$\n",
    "\n",
    "La fonction $C$ est définie par $$C(h)=\\sigma^2 e^{-|h|/a},$$\n",
    "\n",
    "où $|h|$ correspond à la distance entre deux points, $a=50$ et $\\sigma^2=12$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implémentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Préambule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Chargement de dépendances\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Discrétisation\n",
    "A=0\n",
    "B=500\n",
    "N=101 #Nombre de points de discrétisation\n",
    "Delta = (B-A)/(N-1)\n",
    "discretization_indexes = np.arange(N)\n",
    "discretization = discretization_indexes*Delta\n",
    "#Paramètres du modèle\n",
    "\n",
    "mu=-5\n",
    "a = 50\n",
    "sigma2 = 12\n",
    "\n",
    "#Données\n",
    "\n",
    "observation_indexes = [0,20,40,60,80,100]\n",
    "depth = np.array([0,-4,-12.8,-1,-6.5,0])\n",
    "\n",
    "#Indices des composantes correspondant aux observations et aux componsantes non observées\n",
    "\n",
    "unknown_indexes=list(set(discretization_indexes)-set(observation_indexes))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "1. Ecrire une fonction qui prend en argument la distance entre les points, le paramètre $a$, et le paramètre $\\sigma^2$, et qui retourne la covariance entre deux points.\n",
    "On pourra fournir une matrice de distance à cette fonction. Dans ce cas, la fonction renverra la matrice de covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Fonction C\n",
    "\n",
    "def Covexp(dist,rangeval,sigmaval):\n",
    "    return sigmaval * np.exp(-dist/rangeval)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Calculer la matrice de distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "distmat = abs(np.subtract.outer(discretization,discretization))\n",
    "# matrice symétrique de distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Calculer la matrice de covariance du vecteur $\\mathbf{Z}=(Z(x_0),\\dots,Z(x_N))$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sigma = Covexp(distmat, a, sigma2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Extraire les 3 matrices de covariance suivantes :\n",
    "\n",
    " * entre les observations\n",
    "\n",
    " * entre les observations et les inconnues\n",
    "\n",
    " * entre les inconnues\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "SigmaObs = Sigma[observation_indexes,:][:,observation_indexes]\n",
    "SigmaObsUnknown = Sigma[observation_indexes,:][:,unknown_indexes]\n",
    "SigmaUnknown = Sigma[unknown_indexes,:][:,unknown_indexes]\n",
    "# division par blocs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. Calculer l'espérance conditionnelle des composantes non observées connaissant les observations et la représenter avec les données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "invSigma = np.linalg.inv(SigmaObs) \n",
    "Ec= mu+np.matmul(np.transpose(SigmaObsUnknown),np.matmul(invSigma,depth-mu))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "allval1 = np.zeros(N)\n",
    "allval1[unknown_indexes]=Ec\n",
    "allval1[observation_indexes]=depth\n",
    "plt.plot(discretization,allval1)\n",
    "plt.plot(discretization[observation_indexes], depth, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. Calculer la matrice de variance conditionnelle et tracer sa diagonale (variance conditionnelle) en fonction de la position. Commenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "SigmaCond = SigmaUnknown - np.matmul(np.transpose(SigmaObsUnknown),np.matmul(np.linalg.inv(SigmaObs),SigmaObsUnknown))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "allval2 = np.zeros(N)\n",
    "allval2[unknown_indexes]=np.diag(SigmaCond)\n",
    "plt.plot(discretization,allval2)\n",
    "plt.plot(discretization[observation_indexes], np.zeros(np.shape(observation_indexes)[0]), 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*On voit ici que la variance est nulle aux points de données (puisque la valeur est fixée) puis qu'elle augmente lorsqu'on s'éloigne des données*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. Effectuer une simulation conditionnelle. Sur un même graphique, tracer la simulation ainsi que les données et l'espérance conditionnelle. Commenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "Cholesky = np.linalg.cholesky(SigmaCond)  # matrice de Cholesky from matrice de covariance\n",
    "x = np.random.normal(0,1,np.shape(unknown_indexes)[0])  # vecteur gaussien Y\n",
    "simu = Ec + np.matmul(Cholesky,x)  # vecteur d'espérance Ec et de matrice de covariance C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "allval3 = np.zeros(N)\n",
    "allval3[unknown_indexes]=simu\n",
    "allval3[observation_indexes]=depth\n",
    "plt.plot(discretization,allval3)\n",
    "plt.plot(discretization,allval1)\n",
    "plt.plot(discretization[observation_indexes], depth, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*l'espérance conditionnelle est lisse car c'est la fonction des données qui minimise la variance ; la simulation conditionnelle reproduit les fluctuations du modèle et donc l'aspect du fond marin*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8. Ecrire une fonction qui calcule la longueur du câble en fonction du vecteur des profondeurs et du pas de discrétisation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def length(z,delta):\n",
    "    return sum(np.sqrt(Delta**2+(z[1:N]-z[0:-1])**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9. Utiliser cette fonction pour calculer la longueur du câble à partir de 100 simulations. Comparer l'espérance conditionnelle (estimée) de la longueur avec la longueur de l'espérance conditionnelle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "K=100000\n",
    "result = np.zeros(K)\n",
    "for i in range(K):\n",
    "    x=np.random.normal(0,1,np.shape(unknown_indexes)[0])\n",
    "    allval3[unknown_indexes]=Ec + np.matmul(Cholesky,x)\n",
    "    result[i]=length(allval3,Delta)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "522.4425566200596"
      ]
     },
     "metadata": {},
     "execution_count": 92
    }
   ],
   "source": [
    "sum(result)/K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "501.6468416918411"
      ]
     },
     "metadata": {},
     "execution_count": 93
    }
   ],
   "source": [
    "length(allval1,Delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*On donne ici directement les résultats pour 100000 simulations (comparer la vitesse d'éxécution avec votre code pour voir l'intérêt de la vectorisation).*\n",
    "\n",
    "*On voit ici que la longueur donnée par l'espérance conditionnelle est bien moindre que la longueur d'une simulation conditionnelle. Ceci est dû au fait que la simulation conditionnelle va reproduire les fluctuations attendues, au contraire de l'espérance conditionnelle qui minimise la variance.*\n",
    "\n",
    "*NB : On remarquera que c'est le seul endroit où on a utilisé une boucle dans cette correction. On aurait pu s'en passer en utilisant notamment les outils de la librairie Pandas mais le code est plus lisible ainsi.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10. Représenter la suite $M_n$ des moyennes des longueurs de câbles en fonction du nombre de simulations. Commenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
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104.769636 158.126957 \nL 104.870077 158.1637 \nL 105.019217 158.291052 \nL 105.165313 158.223361 \nL 105.086177 158.365064 \nL 105.1714 158.22728 \nL 105.26271 158.263332 \nL 105.207924 158.212644 \nL 105.280972 158.213793 \nL 105.305321 158.20544 \nL 105.357064 158.273005 \nL 105.384457 158.248325 \nL 105.518378 158.219051 \nL 105.564033 158.13552 \nL 105.634037 158.197096 \nL 105.664474 158.169184 \nL 105.84405 158.316271 \nL 105.8684 158.263709 \nL 105.944491 158.373676 \nL 105.947535 158.372167 \nL 106.057107 158.445317 \nL 106.069282 158.41384 \nL 106.169723 158.341134 \nL 106.102762 158.4443 \nL 106.227552 158.385719 \nL 106.32495 158.49342 \nL 106.385823 158.460081 \nL 106.498439 158.339253 \nL 106.519744 158.376104 \nL 106.623229 158.348714 \nL 106.626273 158.34383 \nL 106.671928 158.28725 \nL 106.738888 158.330268 \nL 106.805849 158.280978 \nL 106.7815 158.355588 \nL 106.851504 158.356889 \nL 107.219788 158.268252 \nL 107.225875 158.288006 \nL 107.265443 158.299344 \nL 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158.363956 \nL 110.056485 158.495446 \nL 110.15997 158.393289 \nL 110.275629 158.439175 \nL 110.217799 158.372552 \nL 110.281716 158.436773 \nL 110.561734 158.523395 \nL 110.604345 158.464134 \nL 110.665218 158.541576 \nL 110.671306 158.538205 \nL 110.926974 158.497946 \nL 111.237428 158.352077 \nL 111.249602 158.378015 \nL 111.383524 158.47139 \nL 111.389611 158.459212 \nL 111.407873 158.507522 \nL 111.480921 158.517502 \nL 111.575275 158.551281 \nL 111.496139 158.509444 \nL 111.593537 158.515588 \nL 112.38489 158.499144 \nL 112.488375 158.509967 \nL 112.424458 158.460685 \nL 112.497506 158.496826 \nL 112.543161 158.491732 \nL 112.585772 158.567378 \nL 112.588816 158.568188 \nL 112.692301 158.597341 \nL 112.710563 158.583241 \nL 112.783611 158.584506 \nL 112.804916 158.636485 \nL 112.947969 158.68761 \nL 112.9571 158.667934 \nL 113.039279 158.624782 \nL 113.011886 158.688502 \nL 113.078846 158.65067 \nL 113.197549 158.682845 \nL 113.087977 158.641484 \nL 113.20668 158.671451 \nL 113.234073 158.684646 \nL 113.331471 158.614357 \nL 113.474523 158.723982 \nL 113.550615 158.791986 \nL 113.593226 158.750231 \nL 113.711929 158.720016 \nL 113.718016 158.735103 \nL 113.891505 158.738546 \nL 113.727147 158.717772 \nL 113.894549 158.73444 \nL 113.991946 158.613609 \nL 114.016296 158.668423 \nL 114.168479 158.71705 \nL 114.189785 158.679408 \nL 114.265876 158.765782 \nL 114.275007 158.748307 \nL 114.436322 158.710665 \nL 114.445453 158.725627 \nL 115.233762 158.695625 \nL 115.322029 158.748397 \nL 115.346378 158.703318 \nL 115.623352 158.671932 \nL 115.739011 158.603065 \nL 115.742055 158.614059 \nL 115.839452 158.585287 \nL 115.869889 158.601384 \nL 115.930762 158.604366 \nL 115.949024 158.569633 \nL 115.979461 158.588779 \nL 116.089033 158.631547 \nL 116.000766 158.557693 \nL 116.1286 158.569511 \nL 116.274696 158.414998 \nL 116.27774 158.422773 \nL 116.594281 158.270834 \nL 116.627762 158.297299 \nL 116.658198 158.239237 \nL 116.70081 158.250292 \nL 116.852993 158.142839 \nL 116.706897 158.254352 \nL 116.85908 158.153549 \nL 116.977783 158.229479 \nL 116.989958 158.215092 \nL 117.187796 158.125727 \nL 116.996045 158.22494 \nL 117.193884 158.139913 \nL 117.321718 158.240061 \nL 117.446508 158.277143 \nL 117.528687 158.259206 \nL 117.483032 158.298579 \nL 117.55608 158.283509 \nL 117.686958 158.32371 \nL 117.690001 158.321741 \nL 118.231774 158.29923 \nL 118.383957 158.159124 \nL 118.399176 158.150946 \nL 118.520922 158.202114 \nL 118.660931 158.114043 \nL 119.193573 158.152179 \nL 119.205748 158.163127 \nL 119.287927 158.083934 \nL 119.29097 158.092164 \nL 119.415761 158.081451 \nL 119.300101 158.102118 \nL 119.418804 158.086747 \nL 119.726215 158.203619 \nL 119.851005 158.251001 \nL 119.914922 158.252978 \nL 119.939271 158.324311 \nL 120.012319 158.332008 \nL 119.945359 158.314381 \nL 120.051887 158.291585 \nL 120.164503 158.235621 \nL 120.173634 158.24032 \nL 120.977162 158.140282 \nL 121.022817 158.067057 \nL 121.092821 158.108225 \nL 121.196306 158.020168 \nL 121.251092 158.089807 \nL 121.257179 158.106488 \nL 121.278485 158.065483 \nL 121.354576 158.056197 \nL 121.461105 158.068186 \nL 121.369795 158.07508 \nL 121.467192 158.074284 \nL 121.582851 158.112726 \nL 121.476323 158.066208 \nL 121.601113 158.091917 \nL 121.686336 158.086621 \nL 121.607201 158.096347 \nL 121.707642 158.114563 \nL 121.820257 158.181785 \nL 121.84765 158.142227 \nL 121.850694 158.126871 \nL 121.902436 158.191492 \nL 121.957222 158.15127 \nL 121.984615 158.138411 \nL 122.042445 158.205049 \nL 122.057663 158.191819 \nL 122.203759 158.194551 \nL 122.209847 158.183342 \nL 122.282895 158.144824 \nL 122.331593 158.168026 \nL 122.428991 158.239436 \nL 122.456384 158.212508 \nL 122.568999 158.233664 \nL 122.51117 158.183579 \nL 122.584218 158.225013 \nL 122.687702 158.250379 \nL 122.69379 158.256808 \nL 122.797274 158.285701 \nL 122.824667 158.257159 \nL 122.922065 158.282305 \nL 122.85206 158.297692 \nL 122.931196 158.298594 \nL 123.208169 158.247919 \nL 123.311654 158.277653 \nL 123.24165 158.225837 \nL 123.326872 158.262679 \nL 123.402964 158.246796 \nL 123.436444 158.278899 \nL 123.54906 158.289494 \nL 123.570366 158.251664 \nL 123.774291 158.179935 \nL 124.023872 158.286659 \nL 124.03909 158.254219 \nL 124.066483 158.234822 \nL 124.136488 158.309998 \nL 124.160837 158.337522 \nL 124.233885 158.273942 \nL 124.367806 158.189618 \nL 124.434767 158.217293 \nL 124.376937 158.179846 \nL 124.480422 158.171299 \nL 124.535208 158.113447 \nL 124.596081 158.160676 \nL 124.73609 158.191666 \nL 124.739134 158.186157 \nL 124.748265 158.161109 \nL 124.796963 158.2218 \nL 124.845662 158.207569 \nL 127.374949 157.951076 \nL 127.460172 157.836993 \nL 127.508871 157.878178 \nL 127.557569 157.849716 \nL 127.642792 157.91092 \nL 127.764539 157.914957 \nL 127.676272 157.945002 \nL 127.767582 157.917808 \nL 127.858892 157.909793 \nL 127.880198 157.874309 \nL 128.111517 157.952605 \nL 128.385447 157.996476 \nL 128.491975 157.997687 \nL 128.498062 158.007621 \nL 129.587695 158.071376 \nL 129.675961 158.025769 \nL 129.715529 158.040135 \nL 129.922498 158.066276 \nL 130.007721 158.020701 \nL 130.047289 158.039956 \nL 130.169035 158.082666 \nL 130.302957 158.140804 \nL 130.439922 158.118578 \nL 130.57993 158.174273 \nL 130.680371 158.142172 \nL 130.613411 158.199646 \nL 130.701677 158.172294 \nL 130.829511 158.233464 \nL 130.707764 158.16226 \nL 130.844729 158.214601 \nL 130.987782 158.192335 \nL 130.856904 158.224348 \nL 130.993869 158.203235 \nL 131.130834 158.262648 \nL 131.380415 158.224878 \nL 131.465637 158.272431 \nL 131.392589 158.205678 \nL 131.502161 158.219335 \nL 131.660432 158.180177 \nL 131.663476 158.184172 \nL 131.776091 158.231435 \nL 131.785222 158.221942 \nL 131.82479 158.203154 \nL 131.876532 158.282357 \nL 132.09872 158.360123 \nL 132.183943 158.385129 \nL 132.217423 158.369985 \nL 132.351344 158.257679 \nL 132.488309 158.260296 \nL 132.491353 158.267441 \nL 132.740934 158.239597 \nL 133.051388 158.340589 \nL 132.774414 158.191175 \nL 133.054431 158.336051 \nL 133.127479 158.326877 \nL 133.06965 158.345183 \nL 133.167047 158.350387 \nL 133.230964 158.371662 \nL 133.276619 158.336459 \nL 133.395322 158.306861 \nL 133.404453 158.31108 \nL 133.538374 158.319719 \nL 134.274942 158.306325 \nL 134.551916 158.176881 \nL 134.661488 158.232368 \nL 134.567134 158.15952 \nL 134.676706 158.21043 \nL 134.807584 158.25074 \nL 134.813671 158.247128 \nL 134.901937 158.222505 \nL 134.932374 158.245401 \nL 135.075426 158.195285 \nL 135.197173 158.180056 \nL 135.325007 158.210185 \nL 135.449797 158.255847 \nL 135.458928 158.251227 \nL 135.614155 158.258862 \nL 135.617199 158.252034 \nL 135.696334 158.223144 \nL 135.735902 158.25295 \nL 135.84243 158.26359 \nL 135.848518 158.249564 \nL 135.939828 158.253447 \nL 135.961133 158.277761 \nL 136.067662 158.301658 \nL 136.076793 158.320579 \nL 136.454207 158.356417 \nL 136.508993 158.364119 \nL 136.554648 158.314061 \nL 136.575954 158.326127 \nL 136.685526 158.284378 \nL 136.807273 158.288011 \nL 136.706832 158.239099 \nL 136.810316 158.282204 \nL 137.282085 158.280974 \nL 137.412962 158.294922 \nL 137.41905 158.28953 \nL 137.552971 158.221435 \nL 137.702111 158.247289 \nL 137.912124 158.276501 \nL 137.918211 158.26607 \nL 137.939517 158.291559 \nL 138.088656 158.243776 \nL 138.204316 158.243645 \nL 138.359543 158.290302 \nL 138.234752 158.219639 \nL 138.362586 158.28614 \nL 138.603036 158.311343 \nL 138.718695 158.347648 \nL 138.73087 158.340275 \nL 138.752176 158.372537 \nL 138.864791 158.307662 \nL 139.577009 158.34361 \nL 139.689625 158.344917 \nL 139.640926 158.309201 \nL 139.692669 158.343853 \nL 139.79311 158.309686 \nL 139.82659 158.332226 \nL 140.076171 158.267641 \nL 140.091389 158.280466 \nL 140.240529 158.214142 \nL 140.566201 158.280192 \nL 140.633162 158.249194 \nL 140.684904 158.297418 \nL 140.782301 158.27471 \nL 140.724472 158.266354 \nL 140.791432 158.262528 \nL 140.907092 158.251642 \nL 140.812738 158.287399 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158.512484 \nL 149.849385 158.450209 \nL 149.852429 158.454524 \nL 150.035049 158.515419 \nL 151.861249 158.452788 \nL 151.967777 158.461176 \nL 151.885598 158.430547 \nL 151.982995 158.444954 \nL 152.022563 158.436167 \nL 152.059087 158.47949 \nL 152.089524 158.478402 \nL 152.208227 158.476657 \nL 152.214314 158.464156 \nL 152.308668 158.498281 \nL 152.317799 158.505238 \nL 152.436502 158.530652 \nL 152.445633 158.514717 \nL 152.570423 158.501909 \nL 152.573467 158.508108 \nL 153.909636 158.48103 \nL 154.03747 158.457698 \nL 154.143999 158.460428 \nL 154.150086 158.450135 \nL 154.168348 158.429392 \nL 154.302269 158.462931 \nL 154.484889 158.456157 \nL 154.490977 158.473307 \nL 154.606636 158.495783 \nL 154.624898 158.478233 \nL 154.7923 158.48544 \nL 154.795343 158.493223 \nL 155.127103 158.505961 \nL 155.309723 158.467562 \nL 156.040203 158.52692 \nL 156.171081 158.535452 \nL 156.04629 158.534818 \nL 156.180212 158.547167 \nL 156.256303 158.514278 \nL 156.295871 158.543585 \nL 156.420661 158.559778 \nL 156.423705 158.555554 \nL 156.524146 158.549222 \nL 156.533277 158.563178 \nL 156.68546 158.634913 \nL 156.703722 158.650346 \nL 156.813294 158.642387 \nL 156.953303 158.6714 \nL 156.956347 158.66441 \nL 157.221146 158.675727 \nL 157.352024 158.630105 \nL 157.47377 158.626384 \nL 157.604648 158.609823 \nL 157.607692 158.614168 \nL 157.616823 158.601246 \nL 157.744657 158.600579 \nL 157.765962 158.59786 \nL 157.823792 158.672903 \nL 157.83901 158.647785 \nL 157.957713 158.680323 \nL 157.963801 158.667261 \nL 158.082504 158.655716 \nL 158.085547 158.646362 \nL 158.274255 158.628071 \nL 158.399045 158.633229 \nL 158.517748 158.652794 \nL 158.529923 158.635273 \nL 158.636451 158.639449 \nL 158.645582 158.651347 \nL 159.659123 158.604227 \nL 159.774782 158.612081 \nL 159.78087 158.607459 \nL 159.875223 158.569439 \nL 159.899573 158.609799 \nL 159.993926 158.625567 \nL 160.006101 158.633857 \nL 160.112629 158.606966 \nL 160.070018 158.584647 \nL 160.118717 158.601467 \nL 160.757887 158.617385 \nL 160.903983 158.599938 \nL 161.040948 158.573323 \nL 161.159651 158.607781 \nL 161.168782 158.597552 \nL 161.342271 158.611128 \nL 161.473148 158.622367 \nL 161.479236 158.614338 \nL 161.485323 158.608241 \nL 161.658812 158.654139 \nL 161.783602 158.647601 \nL 161.798821 158.663144 \nL 161.923611 158.639146 \nL 162.401467 158.596166 \nL 162.538432 158.631343 \nL 162.544519 158.62461 \nL 162.581043 158.646879 \nL 162.654091 158.638101 \nL 162.839755 158.627279 \nL 162.842798 158.617185 \nL 162.934108 158.585377 \nL 162.964545 158.600824 \nL 163.512405 158.515724 \nL 163.606759 158.513795 \nL 163.625021 158.522546 \nL 163.783291 158.575753 \nL 163.786335 158.569505 \nL 163.935475 158.535908 \nL 164.063309 158.547813 \nL 164.200274 158.466196 \nL 164.206361 158.469717 \nL 164.477247 158.405963 \nL 164.574645 158.336546 \nL 164.608125 158.351712 \nL 164.732916 158.338314 \nL 164.739003 158.347485 \nL 164.930754 158.358793 \nL 165.064675 158.354819 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "indice_simu = 1+np.arange(K)\n",
    "plt.plot(indice_simu,np.cumsum(result)/indice_simu)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Comme attendu d'après la LFGN, on observe une stabilisation de la valeur moyenne. Les variations sont imperceptibles après quelques dizaines de milliers de simulations*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11. Représenter l'histogramme des longueurs de câbles générées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.hist(result,50,density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*L'histogramme ressemble à une densité gaussienne, avec néanmoins une légère dissymétrie (plus de valeurs fortes).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12. Donner un intervalle de confiance à 95% de la longueur du câble par 2 méthodes différentes. Commenter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*1ère méthode : par approximation gaussienne. L'histogramme précédent suggère qu'une loi gaussienne peut bien représenter la loi conditionnelle de la longueur du cable. On obtient un intervalle de confiance en calculant la moyenne (milieu de l'intervalle) et l'écart type de l'échantillon de longueurs de câble puis en appliquant la formule du cours.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[516.7769552776747, 528.1081579624445]"
      ]
     },
     "metadata": {},
     "execution_count": 96
    }
   ],
   "source": [
    "Ln = sum(result)/K\n",
    "sigman = np.std(result)\n",
    "[Ln - sigman*1.96,Ln + sigman*1.96]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*2e méthode : on extrait les quantiles à 2.5% et 97.5% de l'échantillon, c'est-à-dire les valeurs $x_\\alpha$ pour $\\alpha \\in \\{0.025 ; 0.975\\}$telles que* $$\\mathbb{P}(L<x_\\alpha) \\approx \\frac{1}{n}\\sum_{i=1}^N 1_{\\{L_i<x_\\alpha\\}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([517.13520198, 528.46683498])"
      ]
     },
     "metadata": {},
     "execution_count": 97
    }
   ],
   "source": [
    "np.quantile(result,[0.025,0.975])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*ATTENTION : ici l'utilisation du TCL tel qu'exposé au début du chapitre 5 fournissait un intervalle de confiance de l'**espérance de la longueur de câble** et non de la **longueur de câble** (erreur fréquente).*\n",
    "\n",
    "*On voit par ailleurs que la 2e méthode est plus précise car elle est basée directement sur la loi empirique de l'échantillon*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "13. Donner une estimation de la probabilité que la longueur du câble dépasse 525 m."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.18421"
      ]
     },
     "metadata": {},
     "execution_count": 98
    }
   ],
   "source": [
    "np.mean(result>525)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "14. Reprendre les questions précédentes avec 1000, 10000 puis 100000 simulations. Commenter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*cf. le commentaire de la question 10. On observe une stabilisation progressive des estimateurs des différentes quantités calculées : moyennes, quantiles, probabilité de dépassement de seuil.*"
   ]
  },
  {
   "source": [
    "<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enoncé 2021 (Partie 2)\n",
    "\n",
    "Nous nous plaçons dans le même cadre que ci-dessus. Nous tenons pour acquis les résultats précédents et allons maintenant approfondir l'analyse."
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.1\n",
    "### Valeurs positives\n",
    "\n",
    "1. A la question 7 de la partie 1, on peut s'apercevoir que certains profils de profondeur présentent des valeurs positives, ce qui n'a pas de sens si on considère qu'il n'y a pas de partie émergée entre les deux côtes. Proposer et implémenter un algorithme de type rejet qui ne génèrera que des valeurs négatives. Représenter un profil de profondeur généré."
   ]
  },
  {
   "source": [
    "## Réponse 2021.1\n",
    "\n",
    "Rejet : on re-simule jusqu'à ce que toutes les valeurs générées soient négatives."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def calc_simu(Cholesky, Ec):\n",
    "\n",
    "    while True:\n",
    "        x = np.random.normal(0, 1, np.shape(unknown_indexes)[0])  # vecteur gaussien Y, centré réduit\n",
    "        simu = Ec + np.matmul(Cholesky, x)  # vecteur d'espérance Ec et de matrice de covariance C\n",
    "\n",
    "        if np.all(simu < 0):  # condition d'arrêt\n",
    "            break\n",
    "    \n",
    "    return simu\n",
    "\n",
    "invSigma = np.linalg.inv(SigmaObs) \n",
    "Ec = mu + np.matmul(np.transpose(SigmaObsUnknown), np.matmul(invSigma, depth-mu))\n",
    "Cholesky = np.linalg.cholesky(SigmaCond)  # matrice de Cholesky from matrice de covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 1080x720 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "allval3 = np.zeros(N)\n",
    "allval3[unknown_indexes] = calc_simu(Cholesky, Ec)\n",
    "allval3[observation_indexes] = depth\n",
    "\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.plot(discretization, allval3)\n",
    "plt.plot(discretization, allval1)\n",
    "plt.plot(discretization[observation_indexes], depth, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.2\n",
    "2. L'emploi de cet algorithme a-t-il un impact sur la valeur moyenne de la longueur de câble ? Sur l'histogramme des longueurs de câble ? Sur l'intervalle de confiance obtenu par la méthode des quantiles ? Sur la probabilité de dépassement du seuil de 525 m? Donner une estimation du taux de rejet de l'algorithme. Considérer 10000 simulations."
   ]
  },
  {
   "source": [
    "## Réponse 2021.2"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "### Longueur moyenne\n",
    "\n",
    "La longueur moyenne (en mètres) est légèrement plus faible : 521.769 < 522.446."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Mean length: 521.7569951861256 m\n"
     ]
    }
   ],
   "source": [
    "# Calcul de la longueur moyenne (temps d'exécution: ~10s)\n",
    "\n",
    "K = 10000\n",
    "result2 = np.zeros(K)\n",
    "for i in range(K):\n",
    "    allval3[unknown_indexes] = calc_simu(Cholesky, Ec)\n",
    "    result2[i] = length(allval3, Delta)\n",
    "\n",
    "mean_length_2 = sum(result2) / K\n",
    "print(f'Mean length: {mean_length_2} m')\n",
    "\n",
    "# >>> Mean length: 521.8063514233934 m"
   ]
  },
  {
   "source": [
    "### Histogramme\n",
    "\n",
    "ancien en bleu, nouveau en rouge\n",
    "\n",
    "L'histogramme est pratiquement inchangé, mais on peut émettre l'hypothèse qu'il est légèrement décalé vers la gauche, au vu de la légère diminution de la valeur moyenne."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# Histogramme\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.hist(result, 50, density=True, histtype = 'step', color='blue')\n",
    "plt.hist(result2, 50, density=True, histtype = 'step', color='red')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Intervalle de confiance par les quantiles\n",
    "\n",
    "L'intervalle de confiance par les quantiles est très légèrement décalé vers la gauche (valeurs plus faibles) :\n",
    "\n",
    "```[516.70371097, 527.6874126]  < [516.757978619577, 528.1332425640344]```\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[516.61324203 527.52373328]\n"
     ]
    }
   ],
   "source": [
    "# Intervalle de confiance par les quantiles\n",
    "\n",
    "print(\n",
    "    np.quantile(result2, [0.025, 0.975])\n",
    ")\n",
    "\n",
    "# >>> [516.70371097, 527.6874126] "
   ]
  },
  {
   "source": [
    "### Probabilité de dépassement du seuil de 525m\n",
    "\n",
    "La probabilité de dépassement du seuil de 525m est plus faible : 0.1297 < 0.18537"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.1257\n"
     ]
    }
   ],
   "source": [
    "# Probabilité de dépassement du seuil de 525m\n",
    "\n",
    "print(\n",
    "    np.mean(result2 > 525)\n",
    ")\n",
    "\n",
    "# >>> 0.1297"
   ]
  },
  {
   "source": [
    "### Estimation du taux de rejets"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Taux de rejets : 0.8681208135796713\n"
     ]
    }
   ],
   "source": [
    "# Estimation du taux de rejets\n",
    "\n",
    "K = 10000\n",
    "rejets = np.zeros(K)\n",
    "\n",
    "for i in range(K):\n",
    "    nb_rejets = 0\n",
    "\n",
    "    while True:\n",
    "        x = np.random.normal(0,1,np.shape(unknown_indexes)[0])  # vecteur gaussien Y\n",
    "        simu = Ec + np.matmul(Cholesky,x)  # vecteur d'espérance Ec et de matrice de covariance C\n",
    "\n",
    "        if np.all(simu < 0):  # condition d'arrêt\n",
    "            break\n",
    "        \n",
    "        nb_rejets += 1\n",
    "    \n",
    "    rejets[i] = nb_rejets / (nb_rejets + 1)  # save number of rejets\n",
    "\n",
    "mean_rejets = sum(rejets) / K\n",
    "print(f'Taux de rejets : {mean_rejets}')\n",
    "\n",
    "# >>> Taux de rejets : 0.8701530475481956"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.3\n",
    "### Approche Bayésienne\n",
    "\n",
    "Dans la première partie, on a considéré que l'ensemble des paramètres du modèle était parfaitement connu. Toutes choses égales par ailleurs, on va maintenant considérer que la moyenne $\\mu$ est issue d'une estimation entâchée d'une incertitude. Plus précisément, on va modéliser cette incertitude en considérant que $\\mu \\sim \\mathcal{N}(-5,4)$.\n",
    "\n",
    "On va également décomposer le vecteur $\\mathbf{Z}$ en $\\mathbf{Z} = (\\mathbf{Z}_{\\text{OBS}},\\mathbf{Z}_{\\text{UNK}})$. On notera $C_{\\text{OBS}}$ et $C_{\\text{UNK}}$ les matrices de covariance respectives de $\\mathbf{Z}_{\\text{OBS}}$ et $\\mathbf{Z}_{\\text{UNK}}$ ainsi que $C_{\\text{OBS},\\text{UNK}}$ la matrice des covariances entre ces deux vecteurs.\n",
    "\n",
    "3. Montrer que $\\mu | \\mathbf{Z}_{\\text{OBS}}= \\mathbf{z}_{\\text{OBS}} \\sim \\mathcal{N}(\\widehat{\\mu},\\widehat{\\sigma}^2)$ avec\n",
    "$$\\widehat{\\sigma}^2 = (\\mathbf{1}^t C_{\\text{OBS}}^{-1} \\mathbf{1} + \\frac1{4})^{-1},$$ \n",
    "où $\\mathbf{1}$ est un vecteur de longueur 6 (soit la longueur du vecteur $\\mathbf{Z}_{\\text{OBS}}$) ne contenant que des 1 et \n",
    "$$\\widehat{\\mu} = \\widehat{\\sigma}^2 (\\mathbf{1}^t C_{\\text{OBS}}^{-1} \\mathbf{z}_{\\text{OBS}} - \\frac{5}{4} )$$\n",
    "Indication : écrire la densité jointe du vecteur $(\\mathbf{Z}_{\\text{OBS}},\\mu)$, calculer $-2 \\ln$ de cette densité puis identifier la forme quadratique faisant intervenir $\\mu$."
   ]
  },
  {
   "source": [
    "## Réponse 2021.3\n",
    "\n",
    "$$\n",
    "f_{Z_\\mathrm{OBS}, \\mu} (z_\\mathrm{OBS}, \\mu^*) = f_{Z_\\mathrm{OBS} | \\mu} (z_\\mathrm{OBS}, \\mu^*) \\times f_{\\mu} (\\mu^*)\n",
    "$$\n",
    "\n",
    "$\\mu \\sim \\mathcal{N}(5, 2^2)$ donc $f_{\\mu} (\\mu^*) = \\frac{1}{2^{3/2} π^{1/2}} \\exp \\left( - \\frac{(\\mu^* + 5)^2}{2^3} \\right)$\n",
    "<br>\n",
    "$Z_{\\mathrm{OBS} | \\mu} \\sim \\mathcal{N}(\\mu \\cdot \\mathbf{1}, C)$\n",
    "donc\n",
    "$f_{Z_\\mathrm{OBS} | \\mu} (z_\\mathrm{OBS}, \\mu^*) = \\frac{1}{(2π)^3 \\sqrt{\\det(C_\\mathrm{OBS})}} \\exp \\left( - \\frac{1}{2} {}^t (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1}) \\times C_\\mathrm{OBS}^{-1} \\times (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1}) \\right)$\n",
    "\n",
    "<br><br>\n",
    "D'où\n",
    "$$\n",
    "f_{Z_\\mathrm{OBS}, \\mu} (z_\\mathrm{OBS}, \\mu^*) =\n",
    "\\frac{1}{2^{3/2} π^{1/2}} \\exp \\left( - \\frac{(\\mu^* + 5)^2}{2^3} \\right)\n",
    "\\times\n",
    "\\frac{1}{(2π)^3 \\sqrt{\\det(C_\\mathrm{OBS})}} \\exp \\left( - \\frac{1}{2} {}^t (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1}) \\times C_\\mathrm{OBS}^{-1} \\times (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1}) \\right)\n",
    "$$\n",
    "\n",
    "donc\n",
    "\n",
    "$$\n",
    "-2 \\ln( f_{Z_\\mathrm{OBS}, \\mu} (z_\\mathrm{OBS}, \\mu^*) )\n",
    "=\n",
    "2 \\ln \\left( π^{1/2} 2^{3/2} \\right)  {1 \\over 4} (\\mu^* + 5)^2\n",
    "+ 2 \\ln \\left( (2π)^3 \\sqrt{\\det(C_\\mathrm{OBS})} \\right) + {}^t (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1}) \\times C_\\mathrm{OBS}^{-1} \\times (z_\\mathrm{OBS} - \\mu^* \\cdot \\mathbf{1})\n",
    "$$\n",
    "$$\n",
    "=\n",
    "\\ln \\left( 2^9 π^5 \\det(C_\\mathrm{OBS}) \\right) + \\left( {1 \\over 4} {\\mu^*}^2 + {5 \\over 2} \\mu^* + {25 \\over 4} \\right)\n",
    "+ \\left( {}^t z_\\mathrm{OBS} C_\\mathrm{OBS} z_\\mathrm{OBS} - 2 \\mu^* \\cdot {}^t \\mathbf{1} C_\\mathrm{OBS}^{-1} z_\\mathrm{OBS} + {\\mu^*}^2 \\cdot {}^t \\mathbf{1} C_\\mathrm{OBS}^{-1} \\mathbf{1} \\right)\n",
    "$$\n",
    "(en développant le produit matriciel par symétrie de $C_\\mathrm{OBS}^{-1}$)\n",
    "\n",
    "Puis on développe en identifiant $\\hat{\\sigma}$ et $\\hat{\\mu}$, et on identifie le résultat comme la composée de $-2 \\ln (\\cdot)$ et de la densité de la nouvelle loi normale."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.4\n",
    "4. Montrer que si $X$, $Y$ et $Z$ sont trois vecteurs aléatoires à densité, alors $f_{X,Y|Z = z}(x,y) = f_{X|Y=y,Z=z}(x)f_{Y|Z=Z}(y)$"
   ]
  },
  {
   "source": [
    "## Réponse 2021.4\n",
    "\n",
    "Décomposition du produit :\n",
    "$$\n",
    "f_{X,Y|Z}(x, y, z) = \\frac{f_{X, Y, Z}(x, y, z)}{f_{Z}(z)}\n",
    "=\n",
    "\\underbrace{ \\frac{f_{X, Y, Z}(x, y, z)}{f_{Y, Z}(y, z)} }_{= f_{X|Y, Z}(x, y, z)}\n",
    "\\times\n",
    "\\underbrace{ \\frac{f_{Y, Z}(y, z)}{f_{Z}(z)} }_{= f_{Y|Z}(y, z)}\n",
    "$$\n",
    "D'où la conclusion."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.5\n",
    "5. En déduire que la densité de $(\\mathbf{Z}_{\\text{UNK}},\\mu) | \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}$ s'écrit comme le produit de $f_{\\mu | \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}}$ et de $f_{\\mathbf{Z}_{\\text{UNK}}| \\mu = \\mu^\\star, \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}}$ que l'on exprimera.\n",
    "\n",
    "    Indication : $f_{\\mathbf{Z}_{\\text{UNK}}| \\mu = \\mu^\\star, \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}}$ est identique à la densité $f_{\\mathbf{Z}_{\\text{UNK}}| \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}}$ utilisée dans la partie 1 avec $\\mu = \\mu^\\star$"
   ]
  },
  {
   "source": [
    "## Réponse 2021.5\n",
    "\n",
    "On notera ${}^t A$ la transposée de la matrice $A$.\n",
    "\n",
    "<br><br>\n",
    "\n",
    "En appliquant le résultat précédent :\n",
    "$$\n",
    "f_{Z_\\mathrm{UNK}, \\mu | Z_\\mathrm{OBS}} (z_\\mathrm{UNK}, \\mu^*, z_\\mathrm{OBS})\n",
    "=\n",
    "f_{\\mu | Z_\\mathrm{OBS}} (\\mu^*, z_\\mathrm{OBS})\n",
    "\\times\n",
    "f_{Z_\\mathrm{UNK} | \\mu, Z_\\mathrm{OBS}} (z_\\mathrm{UNK}, \\mu^*, z_\\mathrm{OBS})\n",
    "$$\n",
    "\n",
    "<br><br>\n",
    "On décompose par blocs la matrice de covariance (modulo une permutation des lignes/colonnes) en:\n",
    "$\n",
    "C =\n",
    "\\begin{pmatrix}\n",
    "C_\\mathrm{OBS} && C_\\mathrm{OBS, UNK} \\\\\n",
    "C_\\mathrm{UNK, OBS} && C_\\mathrm{UNK}\n",
    "\\end{pmatrix}\n",
    "$\n",
    "avec $C_\\mathrm{UNK, OBS} = {}^t C_\\mathrm{OBS, UNK}$ par symétrie.\n",
    "\n",
    "Complément de Schur de $C_\\mathrm{UNK}$ : $\\mathrm{CS}_\\mathrm{UNK} = C_\\mathrm{UNK} - C_\\mathrm{UNK, OBS} \\times C_\\mathrm{OBS} ^{-1} \\times C_\\mathrm{OBS, UNK}$\n",
    "\n",
    "\n",
    "<br><br><br>\n",
    "On utilise la fonction calculée dans la première partie (cf. Proba III pg. 18) :\n",
    "\n",
    "$$\n",
    "f_{Z_\\mathrm{UNK} | \\mu, Z_\\mathrm{OBS}} (z_\\mathrm{UNK}, \\mu^*, z_\\mathrm{OBS})\n",
    "=\n",
    "\\frac{1}{(2π)^{k/2} \\sqrt{\\det(\\mathrm{CS}_\\mathrm{UNK})}}\n",
    "\\times\n",
    "\\exp \\left(\n",
    "-{1 \\over 2}\n",
    "\\ \n",
    "{}^t(y - \\varphi(z))\n",
    "\\times\n",
    "\\mathrm{CS}_\\mathrm{UNK} ^{-1}\n",
    "\\times\n",
    "(y - \\varphi(z))\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "$k = N - n$ étant le nombre de unknown\n",
    "\n",
    "\n",
    "<br><br>\n",
    "Alors :\n",
    "\n",
    "$$\n",
    "f_{Z_\\mathrm{UNK}, \\mu | Z_\\mathrm{OBS}} (z_\\mathrm{UNK}, \\mu^*, z_\\mathrm{OBS})\n",
    "=\n",
    "f_{\\mu | Z_\\mathrm{OBS}} (\\mu^*, z_\\mathrm{OBS})\n",
    "\\times\n",
    "\\frac{1}{(2π)^{(N-n)/2} \\sqrt{\\det(\\mathrm{CS}_\\mathrm{UNK})}}\n",
    "\\times\n",
    "\\exp \\left(\n",
    "-{1 \\over 2}\n",
    "\\ \n",
    "{}^t(z_\\mathrm{UNK} - \\psi(z_\\mathrm{OBS}))\n",
    "\\times\n",
    "\\mathrm{CS}_\\mathrm{UNK} ^{-1}\n",
    "\\times\n",
    "(z_\\mathrm{UNK} - \\psi(z_\\mathrm{OBS}))\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "ie\n",
    "\n",
    "$$\n",
    "f_{Z_\\mathrm{UNK}, \\mu | Z_\\mathrm{OBS}} (z_\\mathrm{UNK}, \\mu^*, z_\\mathrm{OBS})\n",
    "\n",
    "=\n",
    "\\frac{1}{\\widehat{\\sigma}\\sqrt{2\\pi}}\\exp\\left(-\\frac{(\\mu^\\star - \\widehat{\\mu})^2}{2\\widehat{\\sigma}^2}\\right)\n",
    "\\frac{1}{(2π)^{(N-n)/2} \\sqrt{\\det(\\mathrm{CS}_\\mathrm{UNK})}}\n",
    "\\times\n",
    "\\exp \\left(\n",
    "-{1 \\over 2}\n",
    "\\ \n",
    "{}^t(z_\\mathrm{UNK} - \\psi(z_\\mathrm{OBS}))\n",
    "\\times\n",
    "\\mathrm{CS}_\\mathrm{UNK} ^{-1}\n",
    "\\times\n",
    "(z_\\mathrm{UNK} - \\psi(z_\\mathrm{OBS}))\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "\n",
    "<!-- avec $\\psi(z_\\mathrm{OBS}) = m_\\mathrm{UNK} + C_\\mathrm{UNK, OBS} \\times C_\\mathrm{OBS}^{-1} \\times (z_\\mathrm{OBS} - m_\\mathrm{OBS})$\n",
    ", et $m_\\mathrm{UNK} = m_\\mathrm{OBS} = \\mu^*$ ???\n",
    "\n",
    "Ce qui donne :\n",
    "$\\psi(z_\\mathrm{OBS}) = \\mu^* + C_\\mathrm{UNK, OBS} \\times C_\\mathrm{OBS}^{-1} \\times (z_\\mathrm{OBS} - \\mu^*)$ -->"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.6\n",
    "\n",
    "### Simulation\n",
    "\n",
    "On va maintenant chercher à simuler les valeurs de $\\mathbf{Z}_{\\text{UNK}}$ en tenant compte de l'incertitude sur $\\mu$.\n",
    "\n",
    "En première approche, on pourrait chercher à obtenir la densité de $\\mathbf{Z}_{\\text{UNK}} | \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}$ en calculant \n",
    "$$\\int_\\mathbb{R} f_{(\\mathbf{Z}_{\\text{UNK}},\\mu) | \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}}(\\mathbf{z}_{\\text{UNK}},\\mu^\\star) d\\mu^\\star$$\n",
    "mais ce calcul a peu de chances d'aboutir.\n",
    "\n",
    "On va plutôt procéder par simulations en cascade, c'est-à-dire que pour chaque simulation de $\\mathbf{Z}_{\\text{UNK}}$, on va d'abord générer une valeur $\\mu^\\star$ de $\\mu$ selon $f_{\\mu | \\mathbf{Z}_{\\text{OBS}}= \\mathbf{z}_{\\text{OBS}}}$ puis on simulera $\\mathbf{Z}_{\\text{UNK}}$ selon $f_{\\mathbf{Z}_{\\text{UNK}}| \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}},\\mu = \\mu^\\star}$.\n",
    "\n",
    "\n",
    "6. Calculer $\\widehat{\\mu}$ et $\\widehat{\\sigma}^2$. "
   ]
  },
  {
   "source": [
    "## Réponse 2021.6"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "12 [-3.37613193 -4.48778451 -3.61663871 ... -3.21446112 -6.67596333\n -5.6489161 ]\n1.5368909974762894 -4.291350330933773\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "distanceMatrixObserved = abs(np.subtract.outer(discretization,discretization))\n",
    "covarianceMatrixObserved = Covexp( distanceMatrixObserved, a, sigma2 )\n",
    "\n",
    "distanceMatrixUnknown = abs(np.subtract.outer(discretization,discretization))\n",
    "covarianceMatrixUnknown = Covexp( distanceMatrixUnknown, a, sigma2 )\n",
    "\"\"\"\n",
    "\n",
    "\"\"\"\n",
    "SigmaObs\n",
    "SigmaUnknown\n",
    "\"\"\"\n",
    "\n",
    "# Retrieve depth array\n",
    "zOBS = depth\n",
    "\n",
    "\n",
    "# NEW SIGMA\n",
    "_1C1_ = np.matmul (\n",
    "    np.matmul(\n",
    "        np.ones(6).T,\n",
    "        np.linalg.inv(SigmaObs)\n",
    "    ),\n",
    "    np.ones(6)\n",
    ")\n",
    "newSigma2 = 1 / (_1C1_ + 1/4)  # np.linalg.inv(_1C1_ + 1/4)\n",
    "\n",
    "# NEW MU\n",
    "_1Cz_ = np.matmul (\n",
    "    np.matmul (\n",
    "        np.ones(6).T,\n",
    "        np.linalg.inv(SigmaObs)\n",
    "    ),\n",
    "    zOBS\n",
    ")\n",
    "newMu = newSigma2 * (_1Cz_ - 5/4)\n",
    "\n",
    "print(sigma2, mu)\n",
    "print(newSigma2, newMu)"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.7\n",
    "7. Calculer la probabilité de $\\{\\mu| \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}} > 0\\}$. Proposer et implémenter un algorithme de simulation de $\\mu| \\mathbf{Z}_{\\text{OBS}} = \\mathbf{z}_{\\text{OBS}}, \\mu <0$."
   ]
  },
  {
   "source": [
    "## Réponse 2021.7\n",
    "<!--\n",
    "La question est incompréhensible. Je calculerai ici la probabilité $\\mathbb{P} (\\mu _{\\mid Z_\\mathrm{OBS} = z_\\mathrm{OBS}} > 0)$.\n",
    "On a $\\mu | \\mathbf{Z}_{\\text{OBS}}= \\mathbf{z}_{\\text{OBS}} \\sim \\mathcal{N}(\\widehat{\\mu},\\widehat{\\sigma}^2)$.\n",
    "Donc\n",
    "$$\n",
    "f_{\\mu_{|Z_\\mathrm{OBS} = z_\\mathrm{OBS}}}\n",
    "=\n",
    "\\frac{1}{\\hat{\\sigma} \\sqrt{2π}}\n",
    "\\exp \\left(\n",
    "- {1 \\over 2}\n",
    "\\left(\n",
    "\\frac {\\mu - \\hat{\\mu}} {\\hat{\\sigma}}\n",
    "\\right)\n",
    "^2\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "Donc cette probabilité est :\n",
    "$$\n",
    "\\mathbb{P} (\\mu _{\\mid Z_\\mathrm{OBS} = z_\\mathrm{OBS}} > 0)\n",
    "=\n",
    "\\int_{0}^{+∞} {\n",
    "\\frac{1}{\\hat{\\sigma} \\sqrt{2π}}\n",
    "\\exp \\left(\n",
    "- {1 \\over 2}\n",
    "\\left(\n",
    "\\frac {\\mu - \\hat{\\mu}} {\\hat{\\sigma}}\n",
    "\\right)\n",
    "^2\n",
    "\\right)\n",
    "\\,\n",
    "\\mathrm{d}\\mu\n",
    "}\n",
    "$$\n",
    "\n",
    "<br><br><br><br>\n",
    "<br><br><br><br>\n",
    "<br><br><br><br>\n",
    "Else:\n",
    "\n",
    "$$\n",
    "f_{Z_\\mathrm{OBS} | \\mu} (z_\\mathrm{OBS}, \\mu^*)\n",
    "=\n",
    "f_{\\mu | Z_\\mathrm{OBS}} (\\mu^*, z_\\mathrm{OBS})\n",
    "\\times\n",
    "\\frac{ f_{Z_\\mathrm{OBS}} (z_\\mathrm{OBS}) }{ f_{\\mu} (\\mu^*) }\n",
    "$$\n",
    "\n",
    "Donc\n",
    "$$\n",
    "\\mathbb{P} (Z_\\mathrm{OBS} = z_\\mathrm{OBS} > 0)\n",
    "$$\n",
    "\n",
    "idfk\n",
    "\n",
    "\n",
    "<br><br><br><br>\n",
    "<br><br><br><br>\n",
    "<br><br><br><br>\n",
    "\n",
    "\n",
    "\n",
    "On cherche à simuler $\\mu _{| Z_\\mathrm{OBS} = z_\\mathrm{OBS}, \\mu < 0}$\n",
    "-->\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Probabilité : 0.000268522638816604\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats as sps\n",
    "\n",
    "proba = 1 - sps.norm.cdf(0, newMu, newSigma2**0.5)\n",
    "\n",
    "print(f'Probabilité : {proba}')\n",
    "\n",
    "# >>> Probabilité : 0.000268522638816604"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# Algorithme de simulation de mu\n",
    "newK = 10000\n",
    "\n",
    "while True:\n",
    "    mu = np.random.normal(newMu, newSigma2**0.5, newK)\n",
    "    \n",
    "    if np.all(mu < 0):  # condition d'arrêt\n",
    "        break\n",
    "\n",
    "\n",
    "# Représentation de l'histogramme des valeurs de mu\n",
    "\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.hist(mu, 50, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.8\n",
    "8. Générer un couple $\\mathbf{Z}_{\\text{UNK}}, \\mu| \\mathbf{Z}_{\\text{OBS}}, \\mu <0$ et représenter le profil de profondeur obtenu. On prendra soin de ne générer que des valeurs négatives de $\\mathbf{Z}_{\\text{UNK}}$ en utilisant l'algorithme de la section précédente."
   ]
  },
  {
   "source": [
    "## Réponse 2021.8\n",
    "\n",
    "Génération d'un profil de profondeur :"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def calc_mu():\n",
    "    while True:\n",
    "        mu = np.random.normal(newMu, newSigma2**0.5)\n",
    "        if np.all(mu < 0):  # condition d'arrêt\n",
    "            break\n",
    "    return mu\n",
    "\n",
    "\n",
    "# Mu\n",
    "theMu = calc_mu()\n",
    "\n",
    "theEc = theMu + np.matmul(np.transpose(SigmaObsUnknown), np.matmul(invSigma, depth-theMu))\n",
    "theCholesky = np.linalg.cholesky(SigmaCond)  # matrice de Cholesky from matrice de covariance\n",
    "\n",
    "# Calcul de simu\n",
    "theSimu = calc_simu(theCholesky, theEc)\n",
    "\n",
    "# Plot\n",
    "allval4 = np.zeros(N)\n",
    "allval4[unknown_indexes] = theSimu\n",
    "allval4[observation_indexes] = depth\n",
    "\n",
    "plt.figure(figsize=(15, 10))\n",
    "plt.plot(discretization, allval4)\n",
    "plt.plot(discretization, allval1)\n",
    "plt.plot(discretization[observation_indexes], depth, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.9\n",
    "9. Générer 10000 profils de profondeur et calculer les longueurs de câble associées. Comparer la valeur moyenne de la longueur de câble, dont on visualisera la convergence, l'histogramme des longueurs de câble, l'intervalle de confiance obtenu par la méthode des quantiles, la probabilité de dépassement du seuil de 525 m avec les résultats obtenus précédemment. Commenter."
   ]
  },
  {
   "source": [
    "## Réponse 2021.9\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "### Longueur moyenne"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Mean length: 521.6840177625238 m\n"
     ]
    }
   ],
   "source": [
    "# Calcul de la longueur moyenne (temps d'exécution: ~10s)\n",
    "\n",
    "allval5 = np.zeros(N)\n",
    "allval5[observation_indexes] = depth\n",
    "\n",
    "K = 10000\n",
    "result3 = np.zeros(K)\n",
    "for i in range(K):\n",
    "    allval5[unknown_indexes] = calc_simu(theCholesky, theEc)\n",
    "    result3[i] = length(allval5, Delta)\n",
    "\n",
    "mean_length_3 = sum(result3) / K\n",
    "print(f'Mean length: {mean_length_3} m')\n",
    "\n",
    "# >>> Mean length: 522.0400770010056 m"
   ]
  },
  {
   "source": [
    "### Convergence (écart à la valeur moyenne)\n",
    "\n",
    "approche précédente en bleu; nouvelle méthode en rouge\n",
    "\n",
    "La nouvelle méthode converge plus rapidement."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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116.083354 \nL 256.214841 117.201349 \nL 256.290947 116.251564 \nL 256.367053 117.030388 \nL 256.443159 115.916655 \nL 256.747584 118.324632 \nL 256.975902 116.125174 \nL 257.052008 117.002329 \nL 257.128114 115.482746 \nL 257.20422 115.733384 \nL 257.280327 115.65991 \nL 257.508645 116.720209 \nL 257.584751 117.426484 \nL 257.660857 116.69606 \nL 257.736963 116.83317 \nL 257.965282 119.592382 \nL 258.041388 119.762401 \nL 258.117494 118.294549 \nL 258.1936 118.475463 \nL 258.269706 118.913396 \nL 258.421919 117.489907 \nL 258.498025 117.78581 \nL 258.574131 117.146384 \nL 258.726343 117.511724 \nL 258.802449 117.104997 \nL 258.878555 117.964863 \nL 258.954661 117.745417 \nL 259.030768 117.593385 \nL 259.106874 116.888093 \nL 259.18298 117.051266 \nL 259.259086 116.600293 \nL 259.335192 116.7009 \nL 259.487404 118.269867 \nL 259.56351 118.077065 \nL 259.639617 118.191446 \nL 259.715723 118.037987 \nL 259.791829 117.361394 \nL 259.867935 117.906674 \nL 260.020147 117.219879 \nL 260.096253 118.073869 \nL 260.17236 117.912647 \nL 260.400678 119.5726 \nL 260.476784 119.135702 \nL 260.55289 120.272716 \nL 260.628996 119.657825 \nL 260.933421 121.399615 \nL 261.009527 120.121293 \nL 261.085633 120.303135 \nL 261.237845 121.61055 \nL 261.390058 120.506307 \nL 261.466164 121.161369 \nL 261.54227 120.101435 \nL 261.618376 120.21811 \nL 261.694482 120.462084 \nL 261.846694 119.302454 \nL 261.998907 120.143306 \nL 262.151119 119.916623 \nL 262.53165 122.121138 \nL 262.683862 121.599805 \nL 262.836074 123.601636 \nL 262.988286 122.433569 \nL 263.064392 123.197899 \nL 263.140499 122.775119 \nL 263.368817 124.237702 \nL 263.444923 122.902804 \nL 263.521029 123.129859 \nL 263.749348 124.739781 \nL 263.825454 125.081196 \nL 263.977666 123.604528 \nL 264.053772 123.749135 \nL 264.205984 123.041216 \nL 264.358197 122.743842 \nL 264.510409 123.194182 \nL 264.586515 122.742089 \nL 264.662621 122.833324 \nL 264.89094 123.604469 \nL 265.043152 123.905523 \nL 265.119258 124.644893 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126.721226 \nL 271.283855 125.911003 \nL 271.359961 125.924199 \nL 271.436067 125.883714 \nL 271.512173 126.310742 \nL 271.664385 125.604037 \nL 271.816597 126.391435 \nL 271.892704 126.070095 \nL 272.197128 124.442432 \nL 272.273234 124.577044 \nL 272.34934 124.946684 \nL 272.425446 125.963768 \nL 272.501553 125.586839 \nL 272.577659 125.158125 \nL 272.805977 125.950011 \nL 272.882083 125.79123 \nL 273.034296 126.661608 \nL 273.110402 125.307272 \nL 273.186508 125.349293 \nL 273.262614 125.95628 \nL 273.567038 124.850972 \nL 273.643145 125.246714 \nL 273.795357 124.667203 \nL 273.947569 126.172599 \nL 274.175887 124.473078 \nL 274.3281 123.127787 \nL 274.404206 124.039453 \nL 274.480312 123.766424 \nL 274.556418 123.635866 \nL 274.784737 125.657199 \nL 274.860843 125.64936 \nL 274.936949 125.404264 \nL 275.013055 125.863794 \nL 275.165267 124.241623 \nL 275.241373 125.061206 \nL 275.317479 124.904676 \nL 275.393586 123.225748 \nL 275.469692 123.577447 \nL 275.69801 124.973957 \nL 275.850222 125.887142 \nL 275.926328 125.814383 \nL 276.078541 125.660403 \nL 276.154647 125.414298 \nL 276.230753 125.472442 \nL 276.306859 126.119093 \nL 276.382965 125.932092 \nL 276.611284 125.006868 \nL 276.763496 125.758506 \nL 276.915708 125.1228 \nL 276.991814 125.740309 \nL 277.220133 123.979488 \nL 277.296239 124.08499 \nL 277.448451 124.277157 \nL 277.524557 124.210825 \nL 277.600663 125.221401 \nL 277.676769 125.04614 \nL 277.752876 125.128349 \nL 277.905088 124.710515 \nL 278.0573 125.904622 \nL 278.209512 125.622876 \nL 278.285619 125.795312 \nL 278.513937 127.652909 \nL 278.590043 127.167099 \nL 278.818361 128.76318 \nL 278.894468 129.828118 \nL 278.970574 129.658956 \nL 279.04668 129.401641 \nL 279.274998 130.943729 \nL 279.351104 131.351637 \nL 279.579423 130.577745 \nL 279.655529 130.814428 \nL 279.731635 130.472478 \nL 279.883847 132.118962 \nL 280.340484 130.137143 \nL 280.41659 130.115361 \nL 280.568802 130.301543 \nL 280.721015 131.4772 \nL 280.873227 130.440351 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132.771416 \nL 286.961717 131.769996 \nL 287.037824 132.303065 \nL 287.11393 131.015726 \nL 287.342248 133.923768 \nL 287.418354 133.817979 \nL 287.49446 133.378446 \nL 287.646673 134.208109 \nL 287.798885 133.431459 \nL 288.027203 134.533671 \nL 288.103309 135.053511 \nL 288.179415 134.575608 \nL 288.255522 134.769077 \nL 288.331628 134.528875 \nL 288.48384 133.291364 \nL 288.636052 134.268913 \nL 288.712158 134.194619 \nL 288.864371 134.099907 \nL 289.092689 133.46864 \nL 289.168795 133.896376 \nL 289.244901 133.869238 \nL 289.549326 133.043049 \nL 289.777644 134.008127 \nL 289.85375 133.713563 \nL 289.929856 134.558907 \nL 290.005963 134.177139 \nL 290.082069 133.260199 \nL 290.158175 133.529104 \nL 290.234281 133.725396 \nL 290.386493 132.843994 \nL 290.462599 133.024243 \nL 290.538705 132.646589 \nL 290.767024 134.581968 \nL 290.84313 134.822577 \nL 290.919236 134.504329 \nL 290.995342 134.730522 \nL 291.223661 135.810838 \nL 291.299767 135.83098 \nL 291.375873 135.174165 \nL 291.451979 135.518352 \nL 291.528085 134.433441 \nL 291.604191 134.614157 \nL 291.756404 133.828777 \nL 291.984722 135.587977 \nL 292.060828 135.493044 \nL 292.136934 135.616891 \nL 292.21304 135.500478 \nL 292.365253 135.952007 \nL 292.517465 135.235501 \nL 292.745783 136.02537 \nL 292.897996 135.275985 \nL 293.20242 136.890381 \nL 293.278526 136.753287 \nL 293.659057 139.265694 \nL 293.735163 139.631205 \nL 293.963481 138.383955 \nL 294.344012 140.564341 \nL 294.420118 139.246586 \nL 294.496224 139.70789 \nL 294.800649 141.658655 \nL 294.876755 141.542184 \nL 294.952861 141.846286 \nL 295.028967 141.189285 \nL 295.333392 142.302619 \nL 295.409498 142.128263 \nL 295.637816 143.448002 \nL 295.790028 140.886712 \nL 295.866135 141.198901 \nL 295.942241 141.435883 \nL 296.094453 141.161989 \nL 296.246665 142.177934 \nL 296.398878 141.360847 \nL 296.474984 141.589922 \nL 296.627196 140.650615 \nL 296.703302 140.719554 \nL 296.779408 141.076263 \nL 297.083833 143.973054 \nL 297.159939 144.528177 \nL 297.236045 144.173864 \nL 297.312151 145.122329 \nL 297.388257 144.529386 \nL 297.540469 145.704459 \nL 297.692682 144.538962 \nL 297.768788 144.792431 \nL 297.844894 145.519943 \nL 297.921 145.066894 \nL 297.997106 145.91766 \nL 298.073212 145.894221 \nL 298.149319 146.161806 \nL 298.377637 144.912629 \nL 298.453743 145.02074 \nL 298.529849 144.874083 \nL 298.682061 145.788029 \nL 298.834274 147.819293 \nL 299.214804 146.383144 \nL 299.443123 147.780877 \nL 299.595335 146.713907 \nL 299.671441 147.435905 \nL 299.747547 147.205174 \nL 299.823653 147.568873 \nL 299.89976 147.481734 \nL 299.975866 147.225503 \nL 300.051972 147.295602 \nL 300.128078 147.258675 \nL 300.28029 146.263679 \nL 300.432502 147.722063 \nL 300.508609 146.990798 \nL 300.660821 148.367234 \nL 300.736927 148.279096 \nL 301.041351 149.03461 \nL 301.26967 147.657971 \nL 301.345776 147.80532 \nL 301.497988 149.390778 \nL 301.650201 147.972673 \nL 301.726307 149.035474 \nL 301.802413 148.982008 \nL 302.030731 148.609396 \nL 302.106837 147.915699 \nL 302.25905 149.096898 \nL 302.487368 147.933478 \nL 302.715686 147.663669 \nL 302.791792 147.72883 \nL 302.867899 147.638974 \nL 303.020111 147.271567 \nL 303.096217 147.201239 \nL 303.172323 148.283537 \nL 303.400642 146.547973 \nL 303.552854 147.333882 \nL 303.705066 147.010527 \nL 303.781172 147.227804 \nL 303.857278 146.802357 \nL 304.085597 147.500865 \nL 304.237809 146.473738 \nL 304.313915 147.038038 \nL 304.390021 146.823456 \nL 304.466127 147.164631 \nL 304.61834 146.571935 \nL 304.770552 147.078276 \nL 304.922764 146.250802 \nL 304.99887 146.254654 \nL 305.074976 146.135157 \nL 305.151083 146.652698 \nL 305.227189 146.590248 \nL 305.303295 146.530517 \nL 305.379401 146.808571 \nL 305.455507 146.762258 \nL 305.531613 146.112478 \nL 305.759932 147.701487 \nL 306.064356 150.037847 \nL 306.368781 148.976973 \nL 306.444887 149.637349 \nL 306.520993 148.930189 \nL 306.597099 149.154218 \nL 306.673205 148.817952 \nL 306.749311 149.108243 \nL 306.825417 148.097569 \nL 306.901524 148.449504 \nL 306.97763 148.582746 \nL 307.053736 147.852682 \nL 307.129842 148.192555 \nL 307.205948 148.432756 \nL 307.282054 148.345423 \nL 307.35816 148.067585 \nL 307.510373 148.339454 \nL 307.738691 150.237621 \nL 308.043115 152.328096 \nL 308.195328 151.543991 \nL 308.271434 151.762782 \nL 308.728071 149.444011 \nL 308.804177 149.432163 \nL 308.956389 149.150458 \nL 309.032495 149.165938 \nL 309.260814 150.923408 \nL 309.413026 151.137135 \nL 309.641344 152.369336 \nL 309.71745 152.224276 \nL 309.869663 152.807077 \nL 310.097981 151.319385 \nL 310.174087 151.693226 \nL 310.250193 151.370254 \nL 310.402406 151.915785 \nL 310.554618 151.710648 \nL 310.630724 152.464101 \nL 310.70683 151.444889 \nL 310.782936 152.082072 \nL 310.859042 151.487752 \nL 310.935148 151.621391 \nL 311.011255 151.890229 \nL 311.163467 151.357275 \nL 311.239573 151.636164 \nL 311.848422 149.932037 \nL 311.924528 150.370652 \nL 312.000634 149.539473 \nL 312.305059 152.432182 \nL 312.457271 152.850844 \nL 312.533377 152.574141 \nL 312.685589 153.443822 \nL 312.837802 152.387673 \nL 312.990014 154.163301 \nL 313.06612 153.862958 \nL 313.142226 153.851529 \nL 313.370545 152.630406 \nL 313.446651 152.740554 \nL 313.522757 152.000573 \nL 313.598863 152.08701 \nL 313.674969 152.413067 \nL 313.751075 152.267943 \nL 313.827181 152.364425 \nL 314.0555 151.514899 \nL 314.207712 151.89044 \nL 314.283818 152.2463 \nL 314.512137 150.524104 \nL 314.664349 151.275484 \nL 314.740455 151.101819 \nL 314.892667 151.393437 \nL 314.968773 151.084013 \nL 315.120986 151.488063 \nL 315.197092 151.178306 \nL 315.273198 151.266005 \nL 315.577622 150.424586 \nL 315.653729 149.578678 \nL 315.805941 150.586106 \nL 316.110365 149.762495 \nL 316.262578 150.789491 \nL 316.41479 150.171964 \nL 316.490896 150.301253 \nL 316.643108 151.552033 \nL 316.719214 151.153169 \nL 316.871427 150.742597 \nL 317.023639 149.32409 \nL 317.099745 149.465384 \nL 317.175851 150.030039 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154.138582 \nL 322.655492 154.434988 \nL 322.731599 154.200341 \nL 322.883811 153.5271 \nL 322.959917 153.512455 \nL 323.036023 153.619073 \nL 323.188235 154.320111 \nL 323.264342 154.399072 \nL 323.340448 153.741289 \nL 323.416554 154.410782 \nL 323.49266 154.26085 \nL 323.644872 153.828781 \nL 324.405933 157.375522 \nL 324.48204 157.021191 \nL 324.634252 158.038879 \nL 324.710358 157.965225 \nL 324.786464 157.609776 \nL 324.86257 157.901977 \nL 325.090889 159.069894 \nL 325.166995 159.127234 \nL 325.243101 159.57888 \nL 325.623632 157.914339 \nL 325.699738 158.399356 \nL 325.775844 158.352085 \nL 325.85195 158.448492 \nL 326.004162 159.376853 \nL 326.080268 158.772726 \nL 326.156374 159.120134 \nL 326.232481 158.772332 \nL 326.308587 159.662684 \nL 326.384693 158.924033 \nL 326.460799 159.069421 \nL 326.613011 158.725272 \nL 326.689117 158.780496 \nL 326.765224 159.199405 \nL 326.917436 158.472158 \nL 326.993542 158.699879 \nL 327.069648 158.968583 \nL 327.297966 158.393725 \nL 327.374073 158.414189 \nL 327.450179 158.003135 \nL 327.526285 158.154242 \nL 327.602391 158.28525 \nL 327.678497 158.057659 \nL 327.906815 158.979906 \nL 327.982922 159.244129 \nL 328.059028 159.02442 \nL 328.287346 160.428083 \nL 328.363452 160.443594 \nL 328.591771 159.370519 \nL 328.743983 159.543756 \nL 328.896195 158.626009 \nL 328.972301 158.886513 \nL 329.124514 160.430881 \nL 329.20062 160.34712 \nL 329.276726 160.615712 \nL 329.428938 162.010453 \nL 329.58115 162.049576 \nL 329.657256 161.700438 \nL 329.733363 162.247194 \nL 329.809469 162.064129 \nL 329.961681 162.908533 \nL 330.037787 162.772548 \nL 330.113893 162.862618 \nL 330.189999 162.14742 \nL 330.266106 162.455544 \nL 330.342212 162.216028 \nL 330.57053 163.755696 \nL 330.646636 163.424747 \nL 330.722742 163.975545 \nL 330.798848 163.833198 \nL 330.874955 163.728989 \nL 331.331591 165.268912 \nL 331.407697 164.770315 \nL 331.483804 165.990655 \nL 331.55991 165.865793 \nL 331.636016 166.163198 \nL 331.712122 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336.65902 167.778479 \nL 336.811233 168.761708 \nL 337.039551 167.626967 \nL 337.191763 168.022916 \nL 337.343976 168.197041 \nL 337.6484 167.167575 \nL 337.800612 168.263177 \nL 337.876719 167.658314 \nL 337.952825 168.756979 \nL 338.028931 168.123706 \nL 338.105037 168.145792 \nL 338.333355 170.086527 \nL 338.409461 170.055813 \nL 338.63778 171.519053 \nL 338.713886 171.725868 \nL 338.789992 171.244922 \nL 339.094417 173.089072 \nL 339.322735 174.216628 \nL 339.474947 173.583071 \nL 339.62716 173.584647 \nL 339.703266 173.802352 \nL 340.083796 172.46519 \nL 340.236009 172.920761 \nL 340.388221 172.689703 \nL 340.464327 172.874797 \nL 340.692645 174.128588 \nL 340.920964 172.645826 \nL 340.99707 172.943745 \nL 341.073176 172.879369 \nL 341.149282 172.68822 \nL 341.301494 173.800177 \nL 341.529813 171.198202 \nL 341.758131 172.037304 \nL 341.910343 171.435783 \nL 342.138662 169.331071 \nL 342.214768 169.389408 \nL 342.290874 169.152803 \nL 342.36698 169.543149 \nL 342.443086 168.304181 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169.105512 \nL 348.836001 168.485222 \nL 348.912107 169.12098 \nL 348.988214 168.827092 \nL 349.06432 169.45387 \nL 349.140426 169.360179 \nL 349.216532 169.217001 \nL 349.292638 168.832021 \nL 349.368744 169.377277 \nL 349.44485 168.927256 \nL 349.520956 169.578834 \nL 349.673169 168.758513 \nL 349.749275 168.788295 \nL 349.825381 168.667783 \nL 349.977593 168.269242 \nL 350.129806 168.821997 \nL 350.282018 169.908519 \nL 350.358124 169.742817 \nL 350.43423 170.215403 \nL 350.510336 169.606845 \nL 350.586442 169.828431 \nL 350.662548 169.501472 \nL 350.738655 169.623088 \nL 350.966973 170.74713 \nL 351.043079 170.13531 \nL 351.119185 170.269099 \nL 351.195291 170.714076 \nL 351.271397 170.487587 \nL 351.347504 170.681807 \nL 351.575822 169.117673 \nL 351.651928 169.43698 \nL 351.880247 169.112701 \nL 352.108565 170.65586 \nL 352.184671 170.502368 \nL 352.260777 169.937879 \nL 352.336883 170.30601 \nL 352.489096 169.610693 \nL 352.565202 169.886377 \nL 352.641308 170.6556 \nL 352.869626 169.682482 \nL 352.945732 169.750726 \nL 353.021838 170.364047 \nL 353.097945 169.957972 \nL 353.326263 170.528391 \nL 353.402369 170.248101 \nL 353.554581 171.036303 \nL 353.706794 170.903252 \nL 353.7829 170.8173 \nL 353.935112 172.260179 \nL 354.011218 172.028522 \nL 354.087324 172.659279 \nL 354.16343 172.509732 \nL 354.239537 172.552674 \nL 354.315643 172.207373 \nL 354.391749 172.400559 \nL 354.467855 172.329007 \nL 354.620067 172.049312 \nL 354.696173 172.424888 \nL 355.076704 170.825439 \nL 355.228916 171.752242 \nL 355.305022 171.605206 \nL 355.533341 170.204371 \nL 355.609447 170.220651 \nL 355.837765 170.984099 \nL 355.913871 170.851474 \nL 356.066084 170.712514 \nL 356.218296 170.361001 \nL 356.370508 170.667991 \nL 356.446614 170.261936 \nL 356.52272 170.327099 \nL 356.598827 170.575913 \nL 356.751039 170.096107 \nL 356.827145 170.223108 \nL 357.055463 169.336307 \nL 357.13157 168.28363 \nL 357.359888 169.793265 \nL 357.435994 170.22585 \nL 357.5121 169.728072 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162.625513 \nL 362.306786 163.235106 \nL 362.382893 163.085313 \nL 362.535105 163.489305 \nL 362.611211 163.616157 \nL 362.687317 163.980174 \nL 362.839529 163.17943 \nL 362.915635 163.214781 \nL 363.22006 164.542031 \nL 363.448378 165.493052 \nL 363.524484 165.417454 \nL 363.600591 164.775455 \nL 363.676697 165.515367 \nL 363.752803 164.799829 \nL 363.828909 165.73871 \nL 363.905015 165.641911 \nL 363.981121 165.502573 \nL 364.057227 165.695724 \nL 364.20944 164.845459 \nL 364.285546 165.471789 \nL 364.437758 165.133128 \nL 364.742183 166.804864 \nL 364.818289 165.945924 \nL 364.894395 166.379696 \nL 365.122713 165.277757 \nL 365.198819 165.750393 \nL 365.274925 165.551683 \nL 365.655456 164.618059 \nL 365.731562 164.805563 \nL 365.807668 164.154603 \nL 365.883775 164.341025 \nL 365.959881 164.39816 \nL 366.035987 164.060301 \nL 366.112093 164.76454 \nL 366.188199 163.826943 \nL 366.264305 164.515155 \nL 366.340411 164.166401 \nL 366.416517 163.273699 \nL 366.492624 163.506596 \nL 366.644836 163.06694 \nL 367.101473 164.985002 \nL 367.177579 165.092703 \nL 367.253685 165.842872 \nL 367.329791 165.828864 \nL 367.405897 165.109869 \nL 367.482003 165.154525 \nL 367.710322 166.353245 \nL 367.862534 165.715892 \nL 367.93864 166.556019 \nL 368.014746 165.99741 \nL 368.243065 166.664012 \nL 368.471383 166.138027 \nL 368.547489 166.359124 \nL 368.623595 165.956536 \nL 368.851914 167.050065 \nL 368.92802 166.27868 \nL 369.156338 167.519529 \nL 369.30855 166.620526 \nL 369.384657 166.748286 \nL 369.460763 166.817346 \nL 369.536869 166.693016 \nL 370.145718 170.005055 \nL 370.374036 168.536448 \nL 370.526248 168.740842 \nL 370.602355 168.83453 \nL 370.678461 168.650913 \nL 370.906779 169.337516 \nL 371.135098 170.990559 \nL 371.211204 170.638033 \nL 371.28731 170.775332 \nL 371.515628 169.773498 \nL 371.66784 169.505437 \nL 371.896159 171.163434 \nL 371.972265 170.922622 \nL 372.276689 172.130972 \nL 372.352796 172.200491 \nL 372.428902 171.664612 \nL 372.505008 171.862484 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178.700214 \nL 378.517392 179.036008 \nL 378.745711 180.408893 \nL 378.897923 180.855525 \nL 378.974029 180.721619 \nL 379.050135 180.771398 \nL 379.126241 181.226641 \nL 379.35456 180.181749 \nL 379.582878 181.112103 \nL 379.658984 181.032499 \nL 379.73509 181.122303 \nL 379.811196 181.495839 \nL 380.115621 180.764903 \nL 380.191727 181.012992 \nL 380.343939 180.633964 \nL 380.496152 181.69998 \nL 380.572258 181.37652 \nL 380.648364 181.582497 \nL 380.72447 181.288749 \nL 380.952788 182.037271 \nL 381.028894 182.918739 \nL 381.105001 182.75943 \nL 381.409425 184.27397 \nL 381.485531 184.215359 \nL 381.561637 183.729537 \nL 381.637743 183.779699 \nL 381.71385 183.737832 \nL 382.170486 185.458531 \nL 382.322699 186.435693 \nL 382.398805 186.360595 \nL 382.627123 185.403193 \nL 382.779335 184.385419 \nL 382.855442 184.74353 \nL 382.931548 184.584822 \nL 383.08376 184.78066 \nL 383.159866 184.449575 \nL 383.312078 185.358974 \nL 383.388184 184.722107 \nL 383.616503 185.263512 \nL 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400.055427 192.225798 \nL 400.207639 193.335121 \nL 400.359852 193.023086 \nL 400.740382 193.634056 \nL 400.816488 193.740045 \nL 400.968701 194.272951 \nL 401.044807 193.383031 \nL 401.120913 193.513137 \nL 401.349231 192.95461 \nL 401.501443 193.845983 \nL 401.57755 193.819215 \nL 401.729762 193.534852 \nL 401.881974 193.686704 \nL 401.95808 193.281556 \nL 402.186399 193.78196 \nL 402.262505 193.74944 \nL 402.338611 192.840897 \nL 402.414717 192.958859 \nL 402.643035 193.960721 \nL 402.94746 195.451157 \nL 403.023566 195.339122 \nL 403.099672 195.349469 \nL 403.175778 195.871211 \nL 403.327991 195.116871 \nL 403.480203 195.544261 \nL 403.556309 195.477892 \nL 403.632415 195.633744 \nL 403.860734 194.2525 \nL 403.93684 193.107072 \nL 404.012946 193.203432 \nL 404.241264 192.084884 \nL 404.31737 192.20331 \nL 404.469583 192.820066 \nL 404.774007 191.890946 \nL 404.850113 192.011506 \nL 404.926219 191.88953 \nL 405.154538 190.862131 \nL 405.30675 191.489869 \nL 405.382856 191.048494 \nL 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508.202238 229.015096 \nL 508.278344 229.233351 \nL 508.582769 228.310139 \nL 508.811087 228.754 \nL 508.9633 227.879879 \nL 509.191618 227.764697 \nL 509.34383 227.349258 \nL 509.496042 227.50221 \nL 509.648255 226.939583 \nL 509.724361 227.024167 \nL 509.876573 227.458294 \nL 509.952679 227.836182 \nL 510.028785 227.733371 \nL 510.180998 228.012305 \nL 510.257104 227.941085 \nL 510.409316 227.620688 \nL 510.637634 226.348437 \nL 510.713741 226.510209 \nL 510.789847 226.214033 \nL 511.018165 226.739843 \nL 511.246483 226.607426 \nL 511.32259 226.61622 \nL 511.474802 226.886506 \nL 511.627014 226.639037 \nL 511.855332 227.534525 \nL 511.931439 227.145223 \nL 512.007545 227.241135 \nL 512.083651 227.139223 \nL 512.311969 226.401759 \nL 512.464182 226.388303 \nL 512.6925 225.740397 \nL 512.768606 225.763417 \nL 513.073031 226.523518 \nL 513.301349 226.22252 \nL 513.377455 226.211399 \nL 513.453561 226.32097 \nL 513.529667 226.123423 \nL 513.757986 226.950162 \nL 513.834092 227.025089 \nL 514.06241 227.835549 \nL 514.214622 228.261335 \nL 514.442941 227.564728 \nL 514.519047 228.023094 \nL 514.595153 227.870201 \nL 514.823472 227.967433 \nL 514.975684 227.506909 \nL 515.127896 228.408838 \nL 515.280108 228.219758 \nL 515.508427 228.3542 \nL 515.584533 228.550163 \nL 515.888957 227.841421 \nL 515.965063 227.948373 \nL 516.117276 227.65679 \nL 516.269488 228.22852 \nL 516.345594 228.113447 \nL 516.4217 227.745605 \nL 516.497806 227.797298 \nL 516.650019 228.039751 \nL 516.802231 227.860916 \nL 516.878337 228.183017 \nL 516.954443 228.141851 \nL 517.030549 228.260146 \nL 517.182762 227.439325 \nL 517.258868 227.702058 \nL 517.334974 227.605799 \nL 517.41108 227.496069 \nL 517.487186 227.877593 \nL 517.563292 227.748652 \nL 517.715504 227.26926 \nL 517.867717 227.383609 \nL 518.019929 227.431715 \nL 518.096035 227.76387 \nL 518.172141 227.694007 \nL 518.248247 227.643327 \nL 518.324354 228.012022 \nL 518.40046 227.823295 \nL 518.552672 228.23761 \nL 518.78099 227.73351 \nL 518.857096 227.943657 \nL 519.313733 226.78466 \nL 519.542052 227.382711 \nL 519.618158 227.172581 \nL 519.694264 227.28465 \nL 519.998688 227.607208 \nL 520.074795 227.506462 \nL 520.303113 227.423586 \nL 520.455325 227.000289 \nL 520.531431 227.124004 \nL 520.683644 227.622397 \nL 520.75975 226.534393 \nL 520.835856 226.762529 \nL 520.911962 227.183434 \nL 520.988068 226.900084 \nL 521.14028 227.25686 \nL 521.292493 226.62757 \nL 521.444705 226.856714 \nL 521.673023 228.039683 \nL 521.901342 227.771371 \nL 522.053554 228.505491 \nL 522.12966 228.156062 \nL 522.205766 228.198622 \nL 522.281872 228.099588 \nL 522.357978 228.345473 \nL 522.434085 228.303808 \nL 522.738509 226.93957 \nL 522.814615 227.196155 \nL 522.890721 226.778114 \nL 522.966827 226.811296 \nL 523.042934 227.386891 \nL 523.11904 227.058021 \nL 523.195146 227.502903 \nL 523.271252 227.283201 \nL 523.347358 226.643703 \nL 523.423464 226.883485 \nL 523.49957 226.846929 \nL 523.575677 226.488694 \nL 523.803995 227.217257 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232.711513 \nL 529.359742 232.20822 \nL 529.435849 232.465622 \nL 529.511955 232.346217 \nL 529.816379 232.883823 \nL 529.968591 232.727274 \nL 530.273016 232.80402 \nL 530.349122 232.359389 \nL 530.425228 232.721731 \nL 530.501334 232.587135 \nL 530.653547 232.422709 \nL 530.881865 232.957312 \nL 530.957971 232.883802 \nL 531.18629 232.361745 \nL 531.414608 232.466834 \nL 531.719032 234.053627 \nL 531.871245 233.569371 \nL 531.947351 233.813342 \nL 532.099563 233.515686 \nL 532.251775 233.924252 \nL 532.327882 233.776541 \nL 532.480094 233.286367 \nL 532.5562 233.699655 \nL 532.632306 233.614794 \nL 532.708412 233.510096 \nL 532.860624 233.848345 \nL 532.936731 233.445363 \nL 533.012837 233.78497 \nL 533.088943 233.745201 \nL 533.165049 233.385565 \nL 533.317261 233.6394 \nL 533.393367 233.42936 \nL 533.469473 233.630712 \nL 533.621686 233.373831 \nL 533.697792 233.440507 \nL 533.773898 233.876889 \nL 534.078323 232.880727 \nL 534.154429 233.015986 \nL 534.382747 234.018079 \nL 534.458853 234.133729 \nL 534.687172 233.449787 \nL 534.763278 233.343925 \nL 535.143808 234.357488 \nL 535.296021 234.295044 \nL 535.524339 234.622567 \nL 535.752657 234.176993 \nL 535.90487 233.752316 \nL 536.2854 234.053624 \nL 536.361506 233.842334 \nL 536.513719 234.136737 \nL 536.742037 235.570909 \nL 537.046462 235.572596 \nL 537.122568 235.759805 \nL 537.27478 235.33657 \nL 537.655311 234.713944 \nL 537.731417 234.649247 \nL 537.807523 235.138392 \nL 537.959735 234.559863 \nL 538.035841 234.561556 \nL 538.111947 234.384992 \nL 538.188054 234.773453 \nL 538.26416 234.339699 \nL 538.340266 234.550827 \nL 538.492478 233.790148 \nL 538.720796 234.349661 \nL 538.796903 234.103567 \nL 538.873009 234.329483 \nL 538.949115 234.241199 \nL 539.025221 234.207021 \nL 539.405752 234.84792 \nL 539.63407 234.369229 \nL 539.710176 233.945668 \nL 539.786282 234.059942 \nL 540.014601 234.878566 \nL 540.090707 234.736928 \nL 540.242919 234.787904 \nL 540.62345 233.44889 \nL 540.699556 233.707847 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551.126096 229.534285 \nL 551.202202 229.376685 \nL 551.43052 230.352404 \nL 551.506626 230.282239 \nL 551.658839 230.980051 \nL 551.734945 230.830114 \nL 551.811051 230.568347 \nL 552.267688 231.790828 \nL 552.4199 231.380952 \nL 552.496006 231.646207 \nL 552.572112 231.425874 \nL 552.648218 231.557301 \nL 552.952643 230.058922 \nL 553.028749 230.212667 \nL 553.104855 229.602909 \nL 553.180961 229.767948 \nL 553.40928 230.599008 \nL 553.485386 230.584747 \nL 553.561492 230.936785 \nL 553.78981 230.369498 \nL 553.865916 230.548338 \nL 553.942023 230.514543 \nL 554.018129 230.540517 \nL 554.170341 230.050737 \nL 554.322553 230.406743 \nL 554.398659 230.369441 \nL 554.626978 231.304543 \nL 554.77919 231.681629 \nL 554.855296 231.502058 \nL 554.931402 231.585327 \nL 555.159721 231.695089 \nL 555.235827 232.006609 \nL 555.311933 231.603217 \nL 555.540251 232.325895 \nL 555.616357 231.934502 \nL 555.692464 231.961949 \nL 555.76857 232.060289 \nL 555.844676 231.868936 \nL 555.920782 232.283823 \nL 555.996888 232.166869 \nL 556.072994 231.702894 \nL 556.1491 231.811306 \nL 556.453525 232.43772 \nL 556.529631 232.960218 \nL 556.605737 232.892619 \nL 556.834055 232.669134 \nL 556.986268 232.640243 \nL 557.366798 233.58386 \nL 557.519011 233.608296 \nL 557.595117 232.778375 \nL 557.671223 232.972553 \nL 557.747329 232.838829 \nL 557.823435 232.965613 \nL 557.899541 232.853043 \nL 558.12786 233.473653 \nL 558.584496 234.446646 \nL 558.812815 233.8833 \nL 558.888921 233.889562 \nL 558.965027 234.167642 \nL 559.041133 234.073365 \nL 559.117239 234.088902 \nL 559.421664 235.351346 \nL 559.49777 235.299091 \nL 559.649982 235.490941 \nL 559.726088 235.395056 \nL 559.802195 235.386825 \nL 559.878301 234.916847 \nL 559.954407 235.034243 \nL 560.106619 234.728938 \nL 560.182725 234.712293 \nL 560.334937 234.987811 \nL 560.48715 234.732709 \nL 560.563256 234.676648 \nL 560.791574 233.987594 \nL 560.86768 234.09918 \nL 560.943787 234.206853 \nL 561.019893 234.088473 \nL 561.095999 234.172526 \nL 561.248211 234.086277 \nL 561.476529 234.973155 \nL 561.552636 234.609735 \nL 561.628742 234.660171 \nL 561.704848 235.186496 \nL 561.780954 235.055039 \nL 561.85706 235.067814 \nL 561.933166 234.542335 \nL 562.009272 234.718989 \nL 562.085378 234.701853 \nL 562.161485 234.50233 \nL 562.237591 234.630066 \nL 562.313697 234.474556 \nL 562.389803 234.614377 \nL 562.618121 235.738105 \nL 562.694228 235.718687 \nL 562.770334 235.428151 \nL 562.922546 235.703988 \nL 562.998652 235.672368 \nL 563.150864 236.343933 \nL 563.22697 236.180577 \nL 563.303077 236.12419 \nL 563.379183 235.786216 \nL 563.455289 235.936657 \nL 563.531395 235.973647 \nL 563.683607 235.828869 \nL 563.759713 234.942293 \nL 563.835819 235.023925 \nL 564.064138 235.484878 \nL 564.140244 235.444247 \nL 564.21635 234.843269 \nL 564.292456 235.078193 \nL 564.368562 235.037565 \nL 564.596881 235.422054 \nL 564.672987 235.362687 \nL 564.749093 235.561225 \nL 564.825199 235.338871 \nL 564.901305 235.382343 \nL 564.977411 235.37214 \nL 565.281836 236.736865 \nL 565.357942 236.640877 \nL 565.434048 236.762021 \nL 565.662367 236.380024 \nL 565.738473 236.664434 \nL 565.966791 236.140197 \nL 566.271216 236.689496 \nL 566.423428 236.558367 \nL 566.499534 236.674721 \nL 566.57564 236.494506 \nL 566.803959 237.130242 \nL 566.880065 237.086443 \nL 567.032277 236.6902 \nL 567.108383 236.695924 \nL 567.260595 236.929776 \nL 567.336701 236.705838 \nL 567.412808 236.861701 \nL 567.488914 236.740397 \nL 567.56502 237.011104 \nL 567.717232 236.468558 \nL 567.869444 236.753615 \nL 568.021657 236.72718 \nL 568.173869 236.363785 \nL 568.249975 236.498109 \nL 568.326081 236.389926 \nL 568.402187 236.593005 \nL 568.630506 236.140638 \nL 568.782718 235.977597 \nL 568.858824 236.078547 \nL 569.087142 235.081568 \nL 569.239355 235.097288 \nL 569.695991 236.573916 \nL 569.772098 236.525509 \nL 569.848204 236.121063 \nL 569.92431 236.383424 \nL 570.152628 235.516497 \nL 570.228734 235.604557 \nL 570.304841 235.682219 \nL 570.380947 235.366528 \nL 570.533159 235.791714 \nL 570.837583 235.880776 \nL 571.218114 234.848127 \nL 571.29422 234.742378 \nL 571.446432 235.06853 \nL 571.522539 235.533835 \nL 571.598645 235.508871 \nL 572.207494 236.649342 \nL 572.2836 236.657266 \nL 572.359706 236.794943 \nL 572.435812 236.248889 \nL 572.511918 236.326955 \nL 572.664131 236.671334 \nL 572.740237 236.507422 \nL 572.816343 236.591754 \nL 573.120767 236.99763 \nL 573.196873 236.789854 \nL 573.349086 237.156813 \nL 573.425192 237.121455 \nL 573.729616 235.930021 \nL 573.805723 235.861221 \nL 573.881829 236.243682 \nL 573.957935 236.090562 \nL 574.186253 235.236173 \nL 574.338465 235.213047 \nL 574.414572 235.66786 \nL 574.490678 235.437207 \nL 574.566784 235.573677 \nL 574.871208 234.68904 \nL 574.947314 234.830724 \nL 575.175633 234.258798 \nL 575.251739 234.354151 \nL 575.403951 234.623353 \nL 575.480057 234.641905 \nL 575.556164 234.495998 \nL 575.63227 234.757465 \nL 575.936694 234.153237 \nL 576.0128 233.785072 \nL 576.088906 234.078697 \nL 576.241119 233.646251 \nL 576.545543 234.418283 \nL 576.773862 234.790466 \nL 576.849968 234.66582 \nL 577.230498 236.027054 \nL 577.306605 235.792936 \nL 577.382711 235.857764 \nL 577.534923 235.644281 \nL 577.687135 236.217316 \nL 577.763241 235.869629 \nL 577.839347 235.988226 \nL 578.067666 236.841589 \nL 578.143772 236.60112 \nL 578.448196 235.777958 \nL 578.524303 235.778382 \nL 578.980939 236.542985 \nL 579.133152 236.300867 \nL 579.285364 236.487008 \nL 579.589788 235.503833 \nL 579.665895 235.540202 \nL 579.894213 236.387597 \nL 579.970319 236.400411 \nL 580.198637 235.319279 \nL 580.274744 235.48952 \nL 580.35085 235.287811 \nL 580.807487 236.173378 \nL 580.883593 236.359306 \nL 580.959699 236.315198 \nL 581.111911 235.789107 \nL 581.188017 235.540125 \nL 581.340229 235.77654 \nL 581.568548 235.908453 \nL 581.72076 236.61063 \nL 581.872972 236.147911 \nL 581.949078 236.143708 \nL 582.025185 236.427169 \nL 582.101291 236.358587 \nL 582.634034 237.201719 \nL 582.71014 237.021028 \nL 582.938458 237.311719 \nL 583.014564 237.042315 \nL 583.09067 237.113584 \nL 583.166777 236.990202 \nL 583.242883 237.256403 \nL 583.395095 237.026351 \nL 583.547307 237.612529 \nL 584.003944 238.07597 \nL 584.232262 237.548485 \nL 584.384475 237.943121 \nL 584.536687 237.530164 \nL 584.765005 237.14522 \nL 584.841111 236.766819 \nL 585.06943 237.264807 \nL 585.145536 237.271086 \nL 585.297748 237.082075 \nL 585.44996 237.011543 \nL 585.602173 236.648634 \nL 585.678279 236.846808 \nL 585.754385 236.719679 \nL 585.982703 237.54346 \nL 586.05881 237.43805 \nL 586.211022 236.832851 \nL 586.287128 236.936183 \nL 586.363234 236.720108 \nL 586.43934 236.153384 \nL 586.667659 237.008233 \nL 586.819871 237.057102 \nL 586.972083 236.523041 \nL 587.124295 236.779818 \nL 587.276508 236.68457 \nL 587.504826 237.464362 \nL 587.961463 238.505072 \nL 588.037569 238.452007 \nL 588.113675 238.57381 \nL 588.189781 238.406994 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239.331323 \nL 593.821635 239.355804 \nL 593.897741 239.771811 \nL 594.049953 239.087904 \nL 594.126059 239.616675 \nL 594.202165 239.577609 \nL 594.354378 239.738677 \nL 594.50659 240.238686 \nL 594.582696 240.1772 \nL 594.734908 240.406104 \nL 594.811015 240.85124 \nL 594.887121 240.760295 \nL 595.039333 240.569209 \nL 595.419864 241.295286 \nL 595.49597 241.194253 \nL 595.572076 241.080358 \nL 595.648182 241.20651 \nL 595.800394 240.931644 \nL 595.952606 241.103778 \nL 596.104819 240.725373 \nL 596.180925 240.86662 \nL 596.257031 240.574794 \nL 596.485349 241.104641 \nL 596.637562 241.194146 \nL 596.713668 241.184837 \nL 596.86588 240.951066 \nL 597.018092 241.233508 \nL 597.170305 241.21982 \nL 597.322517 241.557041 \nL 597.398623 241.568555 \nL 597.550835 241.243366 \nL 597.626941 241.287091 \nL 597.703047 241.333166 \nL 597.779154 240.990016 \nL 598.007472 241.819907 \nL 598.616321 242.508679 \nL 598.768533 242.532653 \nL 598.996852 241.828979 \nL 599.301276 241.208208 \nL 599.377382 241.612906 \nL 599.605701 241.007618 \nL 599.757913 240.501577 \nL 600.59508 242.390355 \nL 600.747293 242.186881 \nL 601.051717 242.871146 \nL 601.127823 242.792274 \nL 601.203929 242.881225 \nL 601.280036 243.279138 \nL 601.356142 243.226098 \nL 601.432248 243.162942 \nL 601.660566 243.809596 \nL 601.812778 244.242559 \nL 601.888885 243.917343 \nL 602.041097 244.264687 \nL 602.193309 243.680448 \nL 602.345521 244.280444 \nL 602.878264 245.233205 \nL 603.106583 244.823135 \nL 603.182689 245.079404 \nL 603.334901 244.619612 \nL 603.411007 245.010591 \nL 603.563219 244.581284 \nL 603.715432 244.732531 \nL 603.791538 244.671813 \nL 603.94375 244.781481 \nL 604.019856 244.574042 \nL 604.095962 244.661772 \nL 604.248175 244.578185 \nL 604.324281 244.772276 \nL 604.552599 244.354703 \nL 604.628705 243.827518 \nL 604.704811 243.853804 \nL 604.857024 244.047006 \nL 604.93313 243.70937 \nL 605.161448 244.191934 \nL 605.389767 243.904602 \nL 605.541979 243.695205 \nL 605.618085 243.908714 \nL 605.92251 243.162394 \nL 605.998616 243.330333 \nL 606.074722 243.637012 \nL 606.150828 243.334758 \nL 606.226934 243.470399 \nL 606.455252 243.17512 \nL 606.531359 243.3023 \nL 606.683571 243.201452 \nL 606.759677 243.33638 \nL 606.911889 242.815012 \nL 607.140208 243.288868 \nL 607.29242 243.103484 \nL 607.368526 243.339954 \nL 607.444632 243.136013 \nL 607.520738 243.349001 \nL 607.825163 242.686021 \nL 607.901269 242.293161 \nL 608.053481 242.702932 \nL 608.205693 242.597505 \nL 608.2818 242.726434 \nL 608.357906 242.556939 \nL 608.586224 243.034205 \nL 608.814542 242.422088 \nL 609.042861 242.441964 \nL 609.118967 242.480724 \nL 609.195073 242.17062 \nL 609.271179 242.596537 \nL 609.423392 242.052168 \nL 609.803922 242.428525 \nL 610.032241 242.533644 \nL 610.184453 242.491875 \nL 610.336665 242.897012 \nL 610.412771 242.859214 \nL 610.488877 242.633417 \nL 610.64109 242.803229 \nL 610.793302 242.613439 \nL 610.945514 242.613104 \nL 611.02162 242.492162 \nL 611.097726 242.079998 \nL 611.173833 242.201723 \nL 611.326045 242.067753 \nL 611.402151 242.390196 \nL 611.630469 242.046007 \nL 611.706575 242.009977 \nL 612.239318 242.819555 \nL 612.315424 242.707117 \nL 612.391531 242.795649 \nL 612.543743 242.29471 \nL 613.457016 242.565295 \nL 613.609229 242.280691 \nL 613.837547 242.976089 \nL 613.913653 242.991476 \nL 614.065865 242.424927 \nL 614.218078 242.698515 \nL 614.294184 242.562782 \nL 614.37029 242.771636 \nL 614.446396 242.600681 \nL 614.598608 242.908924 \nL 614.750821 243.353456 \nL 614.903033 243.722893 \nL 615.055245 243.326114 \nL 615.131351 243.499698 \nL 615.207457 243.959694 \nL 615.587988 242.797489 \nL 615.664094 242.853673 \nL 615.7402 242.507019 \nL 615.816306 242.709481 \nL 615.892413 242.456073 \nL 616.120731 243.016719 \nL 616.272943 242.808037 \nL 616.653474 243.80347 \nL 616.72958 243.343942 \nL 616.805686 243.37362 \nL 616.881792 243.339083 \nL 616.957898 243.132375 \nL 617.110111 243.528751 \nL 617.186217 243.48168 \nL 617.338429 243.255644 \nL 617.414535 243.290096 \nL 617.490641 243.007201 \nL 617.642854 242.137331 \nL 617.71896 242.551922 \nL 617.795066 242.485909 \nL 617.871172 242.566013 \nL 617.947278 242.245237 \nL 618.023384 242.300978 \nL 618.09949 242.110901 \nL 618.175597 242.429721 \nL 618.251703 242.404789 \nL 618.480021 242.634581 \nL 618.632233 242.550507 \nL 618.708339 242.47166 \nL 618.784446 242.548721 \nL 618.936658 242.422216 \nL 619.08887 242.864668 \nL 619.164976 242.575345 \nL 619.241082 242.621271 \nL 619.317188 242.474802 \nL 619.469401 242.671336 \nL 619.545507 242.513671 \nL 619.697719 242.721895 \nL 619.849931 242.389163 \nL 619.926038 242.530866 \nL 620.154356 242.151027 \nL 620.306568 241.904136 \nL 620.382674 242.231051 \nL 620.45878 241.889453 \nL 620.534887 241.980484 \nL 620.839311 242.561492 \nL 620.915417 242.165928 \nL 620.991523 242.182549 \nL 621.143736 241.853443 \nL 621.372054 242.192722 \nL 621.44816 242.210764 \nL 621.524266 242.360264 \nL 621.752585 241.485059 \nL 621.828691 241.616602 \nL 621.904797 241.490992 \nL 622.057009 242.08179 \nL 622.133115 241.986111 \nL 622.209221 242.027862 \nL 622.285328 241.855696 \nL 622.513646 242.720058 \nL 622.665858 242.37664 \nL 623.046389 242.666089 \nL 623.122495 242.476805 \nL 623.274707 242.928842 \nL 623.350813 242.852466 \nL 623.42692 242.937178 \nL 623.503026 242.523805 \nL 623.579132 242.664531 \nL 623.731344 242.924408 \nL 623.80745 242.998496 \nL 623.959662 243.497459 \nL 624.035769 243.294135 \nL 624.264087 243.856163 \nL 624.416299 244.502769 \nL 624.568511 244.352959 \nL 624.720724 244.838066 \nL 624.79683 244.696286 \nL 625.025148 245.1427 \nL 625.177361 244.587766 \nL 625.481785 245.21985 \nL 625.557891 244.851044 \nL 625.633997 244.95125 \nL 625.710103 244.938581 \nL 625.78621 244.645297 \nL 625.862316 244.791239 \nL 626.014528 245.044471 \nL 626.16674 245.049698 \nL 626.242846 244.893349 \nL 626.547271 245.300582 \nL 626.699483 245.429824 \nL 626.851695 245.740726 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243.274833 \nL 632.940186 243.233649 \nL 633.092398 243.494149 \nL 633.320716 242.709452 \nL 633.625141 243.64554 \nL 633.701247 243.496034 \nL 633.777353 243.774363 \nL 633.853459 243.438287 \nL 633.929565 243.668071 \nL 634.081778 243.020969 \nL 634.157884 243.044009 \nL 634.462308 242.70128 \nL 634.614521 242.81014 \nL 634.690627 242.57607 \nL 634.766733 242.654518 \nL 634.995051 242.038987 \nL 635.147264 241.578144 \nL 635.375582 241.169762 \nL 635.527794 240.929349 \nL 635.680006 241.072717 \nL 635.756113 240.829587 \nL 635.832219 240.931702 \nL 635.984431 240.740685 \nL 636.136643 240.188354 \nL 636.212749 240.287859 \nL 636.288856 240.600779 \nL 636.364962 240.499111 \nL 636.441068 240.338325 \nL 636.517174 240.461232 \nL 636.59328 240.146956 \nL 636.745492 240.655855 \nL 636.821598 240.4041 \nL 636.897705 239.586874 \nL 636.973811 239.602555 \nL 637.049917 239.939024 \nL 637.126023 239.893429 \nL 637.202129 239.692737 \nL 637.278235 239.760783 \nL 637.430447 239.659808 \nL 637.734872 240.376081 \nL 637.96319 240.539717 \nL 638.115403 240.498184 \nL 638.267615 240.689339 \nL 638.343721 240.627574 \nL 638.419827 240.524316 \nL 638.572039 240.868016 \nL 638.648146 240.865605 \nL 638.724252 240.638734 \nL 638.95257 241.072542 \nL 639.028676 241.156682 \nL 639.256995 241.832318 \nL 639.333101 241.886945 \nL 639.561419 242.432117 \nL 639.713631 242.339732 \nL 639.865844 242.580716 \nL 640.018056 243.200453 \nL 640.094162 243.109863 \nL 640.170268 243.159468 \nL 640.474693 243.766328 \nL 640.550799 243.780099 \nL 640.931329 244.987062 \nL 641.007436 244.937914 \nL 641.083542 244.950483 \nL 641.31186 245.535113 \nL 641.387966 245.465165 \nL 641.464072 245.577472 \nL 641.540179 245.390837 \nL 641.616285 245.428819 \nL 641.692391 245.366425 \nL 642.072921 246.314509 \nL 642.149028 246.098499 \nL 642.225134 245.980389 \nL 642.30124 246.344683 \nL 642.377346 246.053473 \nL 642.453452 246.161799 \nL 642.68177 246.512583 \nL 642.833983 246.591838 \nL 643.214513 247.314177 \nL 643.29062 247.228919 \nL 643.518938 246.616521 \nL 644.127787 247.391942 \nL 644.203893 247.03212 \nL 644.279999 247.103033 \nL 644.508318 246.466117 \nL 644.584424 246.673252 \nL 644.736636 246.284334 \nL 644.888848 246.393973 \nL 644.964954 246.21548 \nL 645.041061 246.346568 \nL 645.117167 246.092532 \nL 645.193273 246.2537 \nL 645.345485 246.040025 \nL 645.573803 246.920633 \nL 645.64991 246.808875 \nL 645.726016 246.284361 \nL 645.802122 246.390872 \nL 645.954334 245.922668 \nL 646.487077 246.955593 \nL 646.563183 246.880317 \nL 646.639289 246.464952 \nL 646.715395 246.548957 \nL 646.867608 246.028448 \nL 646.943714 246.210402 \nL 647.172032 245.884836 \nL 647.248138 246.070404 \nL 647.400351 245.665465 \nL 647.476457 245.736699 \nL 647.552563 245.623376 \nL 648.085306 246.454781 \nL 648.161412 246.868959 \nL 648.237518 246.633325 \nL 648.313624 246.901166 \nL 648.465836 246.572736 \nL 648.618049 246.811919 \nL 648.998579 245.756968 \nL 649.303004 246.622378 \nL 649.455216 246.497465 \nL 649.531322 246.570928 \nL 649.607428 246.229377 \nL 649.683534 246.533798 \nL 649.835747 246.241246 \nL 649.911853 246.334037 \nL 649.987959 246.156519 \nL 650.140171 245.596609 \nL 650.292384 245.527672 \nL 650.444596 245.83265 \nL 650.520702 246.021913 \nL 650.596808 245.950956 \nL 650.672914 245.911636 \nL 650.825126 246.20407 \nL 650.901233 246.171599 \nL 651.129551 245.599622 \nL 651.205657 245.835956 \nL 651.281763 245.571983 \nL 651.357869 245.614837 \nL 651.510082 245.738634 \nL 651.586188 245.312017 \nL 651.662294 245.357782 \nL 651.7384 245.33916 \nL 651.966718 244.93614 \nL 652.042825 244.496834 \nL 652.118931 244.609715 \nL 652.195037 244.371001 \nL 652.271143 244.544036 \nL 652.347249 244.424547 \nL 652.423355 244.075588 \nL 652.499461 244.096402 \nL 652.575567 244.090418 \nL 652.879992 244.946268 \nL 652.956098 244.738363 \nL 653.260523 245.425141 \nL 653.336629 245.069492 \nL 653.412735 245.205979 \nL 653.488841 245.555338 \nL 653.564947 245.424092 \nL 653.641053 245.472326 \nL 653.717159 245.051462 \nL 653.793265 245.124045 \nL 653.945478 245.189088 \nL 654.021584 245.246587 \nL 654.09769 245.51702 \nL 654.249902 245.277085 \nL 654.478221 245.428235 \nL 654.934857 246.540111 \nL 655.239282 246.229079 \nL 655.315388 246.394098 \nL 655.391494 246.312748 \nL 655.543706 246.040221 \nL 655.619813 246.067799 \nL 655.695919 245.79936 \nL 655.772025 246.116727 \nL 655.848131 246.081851 \nL 656.000343 245.540723 \nL 656.076449 245.613533 \nL 656.152556 245.434373 \nL 656.228662 245.672341 \nL 656.380874 245.432321 \nL 656.913617 246.350466 \nL 656.989723 246.375198 \nL 657.065829 246.267859 \nL 657.141935 246.448827 \nL 657.294147 246.098477 \nL 657.370254 246.150903 \nL 657.598572 246.513808 \nL 657.674678 246.465755 \nL 657.82689 246.740081 \nL 657.902997 246.595626 \nL 658.131315 247.298904 \nL 658.207421 247.015985 \nL 658.283527 246.957343 \nL 658.511846 246.253905 \nL 658.664058 246.252762 \nL 658.968482 245.385538 \nL 659.120695 245.617461 \nL 659.272907 245.51558 \nL 659.577331 245.703107 \nL 659.729544 245.387339 \nL 659.80565 245.590577 \nL 659.881756 245.468407 \nL 659.957862 245.527778 \nL 660.033968 245.618906 \nL 660.110074 245.412522 \nL 660.262287 245.811247 \nL 660.414499 245.718826 \nL 660.566711 245.519807 \nL 660.642817 245.53188 \nL 660.871136 245.908646 \nL 661.17556 245.931597 \nL 661.327772 245.60351 \nL 661.479985 245.993808 \nL 661.556091 245.924425 \nL 661.708303 245.713591 \nL 661.936621 246.057969 \nL 662.012728 245.787029 \nL 662.088834 245.87396 \nL 662.16494 246.284592 \nL 662.317152 245.923995 \nL 662.393258 246.044909 \nL 662.54547 245.894421 \nL 662.773789 246.24105 \nL 662.849895 246.161047 \nL 663.002107 246.030809 \nL 663.078213 246.502124 \nL 663.15432 246.470026 \nL 663.306532 246.792218 \nL 663.382638 246.610375 \nL 663.53485 247.173001 \nL 663.610956 247.077166 \nL 663.763169 246.862743 \nL 663.839275 246.829209 \nL 663.991487 247.399645 \nL 664.067593 247.207384 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246.923248 \nL 669.318916 246.474381 \nL 669.395022 246.516168 \nL 669.547234 246.730079 \nL 669.623341 246.261654 \nL 669.699447 246.596462 \nL 669.775553 246.47739 \nL 669.927765 246.391864 \nL 670.079977 246.940679 \nL 670.156084 246.5899 \nL 670.23219 246.6579 \nL 670.308296 246.569991 \nL 670.384402 246.019723 \nL 670.460508 246.229382 \nL 670.688826 246.998885 \nL 670.917145 246.68209 \nL 671.297675 247.864525 \nL 671.373782 247.520575 \nL 671.449888 247.549158 \nL 671.525994 247.581447 \nL 671.6021 247.386449 \nL 671.754312 247.733942 \nL 671.982631 247.063236 \nL 672.058737 246.991938 \nL 672.134843 247.302196 \nL 672.210949 247.241476 \nL 672.439267 247.055297 \nL 672.515374 247.088114 \nL 672.59148 246.762508 \nL 672.667586 246.7932 \nL 672.743692 246.911243 \nL 672.97201 247.553091 \nL 673.048116 247.557512 \nL 673.352541 246.944341 \nL 673.428647 246.794896 \nL 673.656966 246.958727 \nL 673.809178 246.716601 \nL 673.96139 246.883645 \nL 674.037496 246.875931 \nL 674.494133 247.676849 \nL 674.570239 247.61935 \nL 674.646345 248.024638 \nL 674.722451 247.949283 \nL 674.798557 247.989685 \nL 674.874664 248.275146 \nL 674.95077 247.822608 \nL 675.102982 248.186358 \nL 675.407407 247.936421 \nL 675.483513 248.257631 \nL 675.559619 248.01533 \nL 675.635725 248.107384 \nL 675.787937 247.793866 \nL 675.940149 248.157061 \nL 676.016256 248.111047 \nL 676.168468 248.182955 \nL 676.396786 248.75022 \nL 676.472892 248.681283 \nL 676.625105 248.209517 \nL 676.701211 248.493517 \nL 676.853423 248.12511 \nL 677.157848 247.814859 \nL 677.31006 248.132778 \nL 677.386166 247.716616 \nL 677.538378 248.073738 \nL 677.614484 248.145002 \nL 677.766697 248.528801 \nL 677.995015 248.827935 \nL 678.223333 248.272277 \nL 678.299439 248.13896 \nL 678.67997 249.071927 \nL 678.756076 249.134853 \nL 678.908289 248.71839 \nL 678.984395 249.013513 \nL 679.060501 248.625046 \nL 679.136607 248.685632 \nL 679.441031 248.570419 \nL 679.517138 248.687815 \nL 679.593244 248.547447 \nL 679.66935 248.622501 \nL 679.821562 248.912766 \nL 679.897668 249.151225 \nL 679.973774 248.792443 \nL 680.04988 249.17021 \nL 680.278199 248.203057 \nL 680.354305 248.421868 \nL 680.430411 248.38466 \nL 680.65873 248.223205 \nL 680.887048 248.144113 \nL 680.963154 248.389079 \nL 681.115366 248.156629 \nL 681.267579 248.378907 \nL 681.419791 248.108753 \nL 681.572003 248.374013 \nL 681.648109 248.24131 \nL 681.724215 247.808624 \nL 681.800321 248.069929 \nL 681.952534 247.823078 \nL 682.02864 247.974453 \nL 682.104746 247.914199 \nL 682.256958 247.859227 \nL 682.333064 248.073575 \nL 682.40917 248.030382 \nL 682.485277 247.938563 \nL 682.637489 248.105397 \nL 682.941913 247.258279 \nL 683.094126 247.674446 \nL 683.170232 247.534833 \nL 683.322444 247.737705 \nL 683.474656 248.020439 \nL 683.550762 248.063023 \nL 683.779081 248.807075 \nL 683.855187 248.9288 \nL 683.931293 248.772364 \nL 684.083505 249.37009 \nL 684.311824 249.670445 \nL 684.38793 249.57163 \nL 684.464036 249.468745 \nL 684.540142 249.531753 \nL 684.616248 249.546744 \nL 684.692354 249.869906 \nL 684.768461 249.745547 \nL 684.844567 249.953717 \nL 684.920673 249.74104 \nL 685.072885 250.127116 \nL 685.301203 249.894356 \nL 685.37731 250.185599 \nL 685.605628 249.601847 \nL 685.833946 250.181172 \nL 685.986159 250.022006 \nL 686.062265 249.811265 \nL 686.138371 249.873168 \nL 686.442795 250.02915 \nL 686.518902 249.883292 \nL 686.671114 250.261573 \nL 686.74722 249.912364 \nL 686.823326 250.054727 \nL 686.899432 250.114598 \nL 686.975538 250.337043 \nL 687.051644 249.833159 \nL 687.127751 249.929043 \nL 687.203857 249.862382 \nL 687.432175 250.107437 \nL 687.584387 250.303631 \nL 687.660493 250.179566 \nL 687.812706 249.853298 \nL 688.041024 250.394659 \nL 688.11713 250.082627 \nL 688.421555 250.833255 \nL 688.573767 250.304892 \nL 688.649873 250.39307 \nL 688.725979 250.802571 \nL 688.802085 250.663681 \nL 688.878192 250.650223 \nL 689.10651 251.2082 \nL 689.182616 250.965455 \nL 689.258722 251.255193 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250.017698 \nL 695.042788 250.269388 \nL 695.118894 250.204466 \nL 695.423319 249.820532 \nL 695.499425 250.157598 \nL 695.727743 249.172819 \nL 696.032168 249.542282 \nL 696.18438 249.531287 \nL 696.260486 249.864293 \nL 696.336592 249.771807 \nL 696.412698 249.505356 \nL 696.488805 249.582053 \nL 696.793229 250.248093 \nL 696.869335 250.268066 \nL 696.945441 250.437443 \nL 697.021548 250.347687 \nL 697.249866 249.907349 \nL 697.402078 250.108168 \nL 697.55429 250.018198 \nL 697.630397 250.073473 \nL 697.782609 249.730152 \nL 697.934821 250.074639 \nL 698.010927 249.950482 \nL 698.163139 250.208186 \nL 698.239246 250.080721 \nL 698.315352 250.312112 \nL 698.391458 250.111096 \nL 698.619776 250.49003 \nL 698.771989 249.716459 \nL 699.000307 250.44266 \nL 699.304731 250.949867 \nL 699.53305 251.655192 \nL 699.609156 251.622971 \nL 699.685262 251.597736 \nL 699.761368 251.755679 \nL 700.294111 250.668617 \nL 700.446323 250.974524 \nL 700.598536 250.876524 \nL 700.750748 251.242693 \nL 701.055172 250.57719 \nL 701.131279 250.803717 \nL 701.207385 250.49622 \nL 701.283491 250.68803 \nL 701.359597 250.630027 \nL 701.435703 250.328971 \nL 701.511809 250.620737 \nL 701.587915 250.479786 \nL 701.664021 250.530326 \nL 701.816234 250.332304 \nL 701.89234 250.475473 \nL 701.968446 250.392042 \nL 702.120658 249.897278 \nL 702.348977 250.191947 \nL 702.501189 250.04752 \nL 702.653401 250.345018 \nL 702.729507 250.066405 \nL 702.957826 251.013027 \nL 703.033932 250.800187 \nL 703.566675 250.234781 \nL 703.642781 250.157857 \nL 703.871099 250.893404 \nL 703.947205 250.716398 \nL 704.175524 249.865134 \nL 704.479948 249.922854 \nL 704.632161 249.820095 \nL 704.708267 250.112345 \nL 704.860479 249.406812 \nL 704.936585 249.526777 \nL 705.012691 249.136433 \nL 705.088797 249.330063 \nL 705.469328 248.670365 \nL 705.773753 249.239914 \nL 705.849859 249.269473 \nL 706.002071 249.498819 \nL 706.078177 249.310684 \nL 706.154283 249.637377 \nL 706.230389 249.489775 \nL 706.534814 250.026003 \nL 706.915344 249.253201 \nL 707.143663 249.724056 \nL 707.371981 249.149875 \nL 707.448087 249.338544 \nL 707.524194 249.581479 \nL 707.752512 248.913192 \nL 707.98083 249.42087 \nL 708.056936 249.283814 \nL 708.133043 249.095391 \nL 708.209149 249.220134 \nL 708.361361 249.039735 \nL 708.817998 249.196401 \nL 708.97021 249.560419 \nL 709.046316 249.397925 \nL 709.122422 249.343116 \nL 709.350741 249.993824 \nL 709.426847 250.004533 \nL 709.502953 250.278521 \nL 709.579059 250.20214 \nL 709.655165 250.202479 \nL 709.807377 249.648023 \nL 709.883484 249.677033 \nL 710.035696 250.102201 \nL 710.187908 250.649501 \nL 710.264014 250.362037 \nL 710.644545 251.131889 \nL 710.872863 251.097147 \nL 711.025075 251.152842 \nL 711.177288 251.711754 \nL 711.3295 251.545924 \nL 711.405606 251.557008 \nL 711.481712 251.27927 \nL 711.633925 251.788951 \nL 711.710031 251.981692 \nL 711.938349 251.191206 \nL 712.242774 251.251358 \nL 712.394986 250.844676 \nL 712.471092 251.035942 \nL 712.775516 250.119295 \nL 712.851623 250.191476 \nL 713.232153 249.623751 \nL 713.384366 250.061068 \nL 713.612684 250.315493 \nL 713.68879 250.644623 \nL 713.764896 250.528062 \nL 713.841002 250.213373 \nL 714.069321 250.933836 \nL 714.145427 250.3622 \nL 714.221533 250.640401 \nL 714.297639 250.429869 \nL 714.449851 250.874271 \nL 714.525957 250.759159 \nL 714.67817 250.985977 \nL 714.906488 250.662716 \nL 715.0587 250.918442 \nL 715.287019 250.27633 \nL 715.363125 250.447432 \nL 715.439231 250.30395 \nL 715.515337 250.568917 \nL 715.591443 250.466812 \nL 715.667549 250.079998 \nL 715.743656 250.233956 \nL 715.971974 250.781066 \nL 716.124186 250.259224 \nL 716.200292 250.389338 \nL 716.504717 250.919958 \nL 716.656929 251.058526 \nL 716.733035 250.859652 \nL 716.809141 250.893383 \nL 716.961354 251.406723 \nL 717.03746 251.226668 \nL 717.113566 251.329617 \nL 717.265778 251.383366 \nL 717.341884 251.713199 \nL 717.41799 251.595479 \nL 717.494097 251.702146 \nL 717.646309 251.363767 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\nL 722.821526 249.56679 \nL 722.897632 249.788128 \nL 722.973738 249.740062 \nL 723.049844 249.726565 \nL 723.202056 249.903189 \nL 723.278162 249.674568 \nL 723.354269 249.78817 \nL 723.582587 249.728669 \nL 723.810905 248.81873 \nL 723.887012 249.204762 \nL 724.191436 248.237195 \nL 724.267542 248.359202 \nL 724.343648 248.581757 \nL 724.419754 248.397377 \nL 724.648073 248.923519 \nL 724.876391 248.330076 \nL 725.028603 247.803317 \nL 725.10471 247.935211 \nL 725.180816 248.221098 \nL 725.256922 248.188783 \nL 725.409134 247.952877 \nL 725.48524 248.116418 \nL 725.941877 247.300319 \nL 726.017983 247.601887 \nL 726.094089 247.553752 \nL 726.170195 247.316729 \nL 726.246302 247.405402 \nL 726.322408 247.406481 \nL 726.47462 247.269617 \nL 726.779044 247.560382 \nL 727.007363 248.205707 \nL 727.159575 247.312274 \nL 727.235681 247.375173 \nL 727.540106 247.136181 \nL 727.616212 247.312634 \nL 727.692318 246.95298 \nL 727.768424 247.0926 \nL 727.996743 247.31692 \nL 728.072849 247.533315 \nL 728.377273 246.719837 \nL 728.453379 247.015639 \nL 728.529485 246.974645 \nL 728.605592 247.134813 \nL 728.757804 246.855296 \nL 728.83391 246.947808 \nL 728.910016 246.517397 \nL 728.986122 246.532083 \nL 729.214441 246.136761 \nL 729.366653 245.708761 \nL 729.594971 245.494898 \nL 729.671077 245.56739 \nL 729.747184 245.436172 \nL 730.051608 246.227324 \nL 730.127714 246.450856 \nL 730.279926 246.1867 \nL 730.356033 246.354168 \nL 730.660457 245.83252 \nL 730.964882 246.164303 \nL 731.040988 246.179678 \nL 731.269306 246.612598 \nL 731.421518 246.60826 \nL 731.497625 246.896909 \nL 731.573731 246.843332 \nL 731.725943 246.155896 \nL 731.802049 246.468121 \nL 731.878155 246.425949 \nL 732.106474 245.968191 \nL 732.334792 246.37817 \nL 732.56311 245.76951 \nL 732.639217 245.887754 \nL 732.715323 246.081591 \nL 733.019747 245.713065 \nL 733.095853 245.66045 \nL 733.171959 245.783143 \nL 733.248066 246.164781 \nL 733.324172 246.077232 \nL 733.628596 247.008164 \nL 733.780808 247.504076 \nL 733.856915 247.408987 \nL 733.933021 247.477597 \nL 734.009127 247.484566 \nL 734.085233 247.617149 \nL 734.237445 247.501771 \nL 734.313551 247.718772 \nL 734.389658 247.673609 \nL 734.694082 248.070313 \nL 734.770188 247.832822 \nL 734.846294 247.897024 \nL 734.998507 248.000671 \nL 735.150719 248.015684 \nL 735.835674 248.760861 \nL 735.987886 248.658113 \nL 736.292311 249.269169 \nL 736.444523 249.347975 \nL 736.596735 249.517232 \nL 736.825054 249.171913 \nL 736.90116 249.15663 \nL 737.129478 249.616388 \nL 737.205584 249.380356 \nL 737.510009 249.978547 \nL 737.586115 249.806461 \nL 737.662221 249.972741 \nL 737.738327 249.876826 \nL 737.890539 249.920864 \nL 738.042752 249.505529 \nL 738.118858 249.713734 \nL 738.347176 249.294138 \nL 738.499389 249.392154 \nL 738.575495 249.077681 \nL 738.651601 249.276771 \nL 738.803813 249.058957 \nL 738.956025 249.408952 \nL 739.412662 248.503077 \nL 739.488768 248.660342 \nL 739.564874 248.543798 \nL 739.717087 248.888976 \nL 740.021511 248.480657 \nL 740.097617 248.538482 \nL 740.325936 249.069772 \nL 740.478148 249.123105 \nL 740.554254 249.032313 \nL 740.858679 249.342847 \nL 741.163103 249.433943 \nL 741.391421 248.866835 \nL 741.61974 249.249819 \nL 741.695846 249.260255 \nL 742.000271 250.160949 \nL 742.076377 250.122202 \nL 742.228589 249.846509 \nL 742.304695 249.836073 \nL 742.380801 249.962583 \nL 742.456907 249.898941 \nL 742.685226 249.837331 \nL 742.837438 249.87839 \nL 743.065756 250.188964 \nL 743.141862 250.131671 \nL 743.294075 249.61602 \nL 743.370181 249.438775 \nL 743.598499 249.996667 \nL 743.674605 249.852179 \nL 744.055136 250.331655 \nL 744.207348 249.890413 \nL 744.283454 250.058326 \nL 744.435667 249.527315 \nL 744.663985 249.80402 \nL 744.892303 249.478639 \nL 744.96841 249.45002 \nL 745.044516 249.567751 \nL 745.120622 249.307416 \nL 745.34894 249.72314 \nL 745.425046 249.694817 \nL 745.501153 249.820248 \nL 745.577259 249.669409 \nL 745.653365 249.976542 \nL 745.729471 249.845971 \nL 745.881683 249.571449 \nL 746.033895 249.500678 \nL 746.262214 249.659494 \nL 746.33832 249.383041 \nL 746.414426 249.660919 \nL 746.490532 249.447829 \nL 746.718851 249.957941 \nL 746.794957 249.528253 \nL 746.871063 249.627404 \nL 747.099381 250.295366 \nL 747.403806 249.878736 \nL 747.556018 250.211323 \nL 747.70823 250.009418 \nL 747.784336 250.093579 \nL 748.164867 250.852003 \nL 748.240973 250.758374 \nL 748.317079 250.629162 \nL 748.393185 250.767824 \nL 748.469292 250.550337 \nL 748.545398 249.93823 \nL 748.621504 250.020505 \nL 748.69761 250.086654 \nL 748.925928 249.930502 \nL 749.230353 249.855299 \nL 749.382565 250.411472 \nL 749.458671 250.321195 \nL 749.610884 250.246155 \nL 749.839202 250.796452 \nL 749.991414 250.833905 \nL 750.295839 251.115351 \nL 750.524157 251.131881 \nL 750.600263 251.189301 \nL 750.676369 251.396716 \nL 750.752476 251.305471 \nL 750.828582 251.353464 \nL 751.0569 250.811122 \nL 751.133006 251.035028 \nL 751.209112 250.921003 \nL 751.361325 251.054543 \nL 751.665749 250.706413 \nL 751.741855 250.807217 \nL 751.894067 250.663879 \nL 752.122386 251.15444 \nL 752.274598 251.286373 \nL 752.42681 251.160328 \nL 752.579023 251.563436 \nL 752.655129 251.557043 \nL 752.807341 251.908051 \nL 752.883447 251.741253 \nL 752.959553 251.811701 \nL 753.187872 252.248076 \nL 753.263978 252.135525 \nL 753.340084 252.487387 \nL 753.41619 252.330077 \nL 753.492296 252.444603 \nL 753.644508 252.132608 \nL 753.796721 252.507085 \nL 754.025039 252.059511 \nL 754.101145 252.330447 \nL 754.557782 251.186353 \nL 754.7861 251.694443 \nL 755.090525 251.492578 \nL 755.242737 251.208542 \nL 755.471056 251.536968 \nL 755.623268 251.86114 \nL 755.851586 251.343788 \nL 755.927692 251.318974 \nL 756.003799 251.109131 \nL 756.079905 251.22329 \nL 756.156011 251.196522 \nL 756.308223 251.463245 \nL 756.536541 251.275924 \nL 756.612648 251.485634 \nL 756.688754 251.215877 \nL 756.76486 251.254832 \nL 756.840966 251.1682 \nL 756.993178 251.631806 \nL 757.069284 251.569557 \nL 757.221497 251.384055 \nL 757.449815 250.961729 \nL 757.525921 250.984371 \nL 757.602027 250.836353 \nL 757.678133 250.976664 \nL 757.830346 250.777114 \nL 757.906452 251.039727 \nL 757.982558 250.908827 \nL 758.058664 250.879762 \nL 758.210876 251.204541 \nL 758.515301 250.672015 \nL 758.743619 250.622912 \nL 758.895831 250.570376 \nL 759.048044 249.993335 \nL 759.12415 250.063713 \nL 759.276362 250.347369 \nL 759.428574 249.909657 \nL 759.504681 250.002688 \nL 759.580787 250.339024 \nL 759.732999 250.043757 \nL 759.809105 250.104432 \nL 760.037423 249.569769 \nL 760.341848 249.345803 \nL 760.49406 249.633441 \nL 760.570166 249.583089 \nL 760.646272 249.822549 \nL 760.722379 249.776974 \nL 760.950697 249.809919 \nL 761.179015 250.16959 \nL 761.787864 249.347232 \nL 761.863971 249.35632 \nL 762.092289 249.091587 \nL 762.168395 249.098546 \nL 763.386093 251.184554 \nL 763.462199 250.978193 \nL 763.538305 250.438683 \nL 763.690518 250.869984 \nL 763.918836 250.253687 \nL 763.994942 250.302278 \nL 764.147154 249.918088 \nL 764.299367 249.956792 \nL 764.451579 249.502412 \nL 764.527685 249.661129 \nL 764.603791 249.515391 \nL 764.679897 249.856927 \nL 764.756004 249.769114 \nL 764.83211 249.910068 \nL 764.984322 249.543917 \nL 765.364853 250.317247 \nL 765.440959 250.265219 \nL 765.593171 250.598254 \nL 765.669277 250.527533 \nL 765.745383 250.465822 \nL 765.973702 250.760013 \nL 766.049808 250.811475 \nL 766.125914 250.726397 \nL 766.20202 250.383653 \nL 766.278126 250.573161 \nL 766.354232 250.047085 \nL 766.430338 250.120593 \nL 766.506444 250.137613 \nL 766.734763 249.776769 \nL 766.810869 249.646379 \nL 766.886975 249.745959 \nL 766.963081 250.071282 \nL 767.039187 250.004984 \nL 767.1914 249.971489 \nL 767.267506 249.581259 \nL 767.343612 249.626074 \nL 767.648036 250.104139 \nL 767.724143 250.088427 \nL 767.800249 250.24307 \nL 767.876355 250.186019 \nL 768.028567 250.15833 \nL 768.256885 249.975823 \nL 768.332992 249.966472 \nL 768.485204 249.535458 \nL 768.713522 249.623164 \nL 768.789628 249.504084 \nL 768.865735 249.692627 \nL 768.941841 249.605684 \nL 769.246265 249.589863 \nL 769.398477 249.516741 \nL 769.702902 250.173758 \nL 769.779008 250.040615 \nL 769.93122 250.432778 \nL 770.007326 250.382772 \nL 770.083433 250.369839 \nL 770.235645 249.738052 \nL 770.311751 249.823835 \nL 770.387857 250.069817 \nL 770.463963 249.810197 \nL 770.540069 249.92013 \nL 770.692282 250.100422 \nL 770.768388 249.82377 \nL 770.844494 249.950504 \nL 770.9206 249.865393 \nL 770.996706 250.00874 \nL 771.225025 249.457669 \nL 771.377237 249.324593 \nL 771.90998 249.995334 \nL 772.062192 249.341159 \nL 772.138298 249.375088 \nL 772.214404 249.25385 \nL 772.29051 249.472031 \nL 772.366617 249.000927 \nL 772.442723 249.083313 \nL 772.518829 249.016607 \nL 772.594935 248.791412 \nL 772.747147 249.115695 \nL 773.432102 249.573764 \nL 773.508208 249.398877 \nL 773.888739 250.225888 \nL 774.117058 249.851369 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246.879114 \nL 780.509972 247.372088 \nL 780.586079 247.289857 \nL 780.662185 247.152244 \nL 780.814397 247.361744 \nL 780.890503 247.393563 \nL 780.966609 247.184259 \nL 781.042715 247.468295 \nL 781.118822 247.39728 \nL 781.194928 247.284052 \nL 781.271034 247.406869 \nL 781.423246 247.124928 \nL 781.499352 247.179045 \nL 781.727671 247.543087 \nL 782.260413 246.048184 \nL 782.412626 246.307913 \nL 782.640944 246.118907 \nL 782.869263 246.341081 \nL 783.021475 246.024824 \nL 783.097581 246.256054 \nL 783.173687 246.198444 \nL 783.478112 246.305477 \nL 783.630324 246.114091 \nL 783.782536 246.370599 \nL 783.934748 245.941949 \nL 784.086961 246.2754 \nL 784.315279 245.893142 \nL 784.543597 246.038805 \nL 784.619704 245.802316 \nL 784.69581 245.886946 \nL 784.771916 246.116203 \nL 784.848022 245.972716 \nL 784.924128 246.187269 \nL 785.07634 246.044913 \nL 785.228553 246.524577 \nL 785.304659 246.475999 \nL 785.609083 246.197383 \nL 785.837402 246.167102 \nL 785.913508 246.244007 \nL 786.141826 245.863498 \nL 786.217932 245.547704 \nL 786.294038 245.647611 \nL 786.370145 245.51109 \nL 786.446251 245.63785 \nL 786.522357 245.584935 \nL 786.750675 245.278815 \nL 786.826781 245.39365 \nL 787.0551 244.860493 \nL 787.283418 245.666376 \nL 787.511736 246.384584 \nL 787.587843 246.226662 \nL 787.663949 246.468919 \nL 787.740055 246.377682 \nL 787.816161 246.526281 \nL 788.044479 245.912656 \nL 788.272798 246.268347 \nL 788.42501 246.1213 \nL 788.501116 246.154068 \nL 788.805541 245.902268 \nL 788.881647 246.184928 \nL 789.109965 245.570829 \nL 789.186071 245.611896 \nL 789.262177 245.733646 \nL 789.41439 245.33906 \nL 789.490496 245.308849 \nL 789.642708 244.763755 \nL 789.79492 245.013232 \nL 790.023239 245.710328 \nL 790.099345 245.742292 \nL 790.403769 246.314282 \nL 790.555982 246.137351 \nL 790.708194 246.576218 \nL 790.7843 246.493861 \nL 790.860406 246.621804 \nL 791.012618 246.442726 \nL 791.164831 246.785003 \nL 791.240937 246.691745 \nL 791.393149 247.043784 \nL 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173.03084 112.872236 \nL 173.183053 111.596602 \nL 173.259159 113.036423 \nL 173.335265 112.668227 \nL 173.411371 112.438172 \nL 173.563583 115.473966 \nL 173.639689 114.230517 \nL 173.791902 115.86372 \nL 173.868008 115.14175 \nL 174.096326 118.900569 \nL 174.248538 116.058523 \nL 174.476857 117.541343 \nL 174.552963 117.657861 \nL 174.629069 115.972658 \nL 174.705175 116.150735 \nL 174.781281 115.536262 \nL 174.933494 116.989479 \nL 175.0096 116.108335 \nL 175.237918 109.353491 \nL 175.314024 109.886632 \nL 175.466236 111.745164 \nL 175.542343 110.518435 \nL 175.618449 110.705226 \nL 175.770661 114.164254 \nL 175.922873 114.003131 \nL 176.151192 111.481713 \nL 176.455616 106.556397 \nL 176.531722 106.42624 \nL 176.607828 106.747689 \nL 176.836147 109.116714 \nL 176.988359 108.346592 \nL 177.292784 113.505665 \nL 177.444996 112.926154 \nL 177.74942 111.475248 \nL 177.825526 112.051095 \nL 177.901633 111.999038 \nL 177.977739 112.070099 \nL 178.053845 112.34024 \nL 178.282163 110.170446 \nL 178.358269 110.296892 \nL 178.434376 111.075736 \nL 178.510482 110.993113 \nL 178.662694 111.104709 \nL 178.7388 111.055122 \nL 179.043225 105.327383 \nL 179.119331 105.719311 \nL 179.195437 103.399334 \nL 179.271543 104.096759 \nL 179.423755 107.607568 \nL 179.499861 106.696935 \nL 179.575967 107.012277 \nL 179.72818 108.694318 \nL 179.880392 106.821431 \nL 180.032604 108.066598 \nL 180.10871 107.638405 \nL 180.337029 110.411631 \nL 180.413135 110.212356 \nL 180.793666 104.167466 \nL 180.945878 107.068624 \nL 181.021984 106.659773 \nL 181.09809 105.913156 \nL 181.174196 106.276605 \nL 181.250302 105.880443 \nL 181.478621 106.474551 \nL 181.630833 107.741792 \nL 181.706939 107.06832 \nL 181.859151 109.44602 \nL 181.935258 109.652385 \nL 182.08747 111.93376 \nL 182.163576 111.83204 \nL 182.696319 104.490087 \nL 182.848531 105.7764 \nL 182.924637 105.135409 \nL 183.152956 107.193401 \nL 183.381274 104.095089 \nL 183.45738 105.412109 \nL 183.685699 101.118443 \nL 183.837911 102.049536 \nL 183.914017 101.184324 \nL 184.370654 105.653753 \nL 184.44676 105.914915 \nL 184.522866 105.412906 \nL 184.675078 107.90636 \nL 184.82729 105.320847 \nL 184.903397 105.842661 \nL 185.283927 99.719793 \nL 185.43614 101.564494 \nL 185.588352 98.233865 \nL 185.664458 95.77617 \nL 185.740564 96.699362 \nL 185.81667 96.833613 \nL 185.892776 98.550767 \nL 185.968882 98.449114 \nL 186.044989 98.877693 \nL 186.121095 101.343035 \nL 186.197201 101.031978 \nL 186.273307 100.675562 \nL 186.349413 101.846096 \nL 186.501625 100.345974 \nL 186.729944 103.738682 \nL 186.882156 102.474313 \nL 186.958262 102.989979 \nL 187.110474 101.206357 \nL 187.262687 101.317616 \nL 187.338793 103.35003 \nL 187.414899 103.074358 \nL 187.491005 102.28461 \nL 187.567111 103.875056 \nL 187.643217 102.958192 \nL 187.79543 106.25464 \nL 187.871536 104.885639 \nL 187.947642 105.70982 \nL 188.023748 105.398681 \nL 188.099854 104.656326 \nL 188.252066 106.909982 \nL 188.328172 107.215094 \nL 188.404279 108.827406 \nL 188.632597 103.544942 \nL 188.860915 107.236316 \nL 189.013128 108.880327 \nL 189.089234 109.81895 \nL 189.16534 108.996336 \nL 189.241446 109.373239 \nL 189.469764 112.644986 \nL 189.545871 111.894067 \nL 189.850295 114.837016 \nL 189.926401 116.457044 \nL 190.306932 111.297086 \nL 190.383038 111.974899 \nL 190.459144 112.131691 \nL 190.53525 111.979353 \nL 190.611356 114.695144 \nL 190.687463 113.557744 \nL 190.763569 114.071322 \nL 190.915781 112.178716 \nL 190.991887 113.735144 \nL 191.067993 113.1475 \nL 191.220205 111.572829 \nL 191.296312 110.424996 \nL 191.372418 113.013561 \nL 191.52463 111.254458 \nL 191.600736 110.761601 \nL 191.676842 110.894164 \nL 191.905161 112.473049 \nL 192.133479 110.655875 \nL 192.209585 112.192755 \nL 192.437904 108.924159 \nL 192.51401 109.005779 \nL 192.590116 109.854346 \nL 192.742328 107.974193 \nL 192.818434 109.043618 \nL 192.89454 108.910528 \nL 193.046753 108.687547 \nL 193.198965 111.110814 \nL 193.275071 110.894866 \nL 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199.135243 134.434467 \nL 199.211349 135.550756 \nL 199.287455 134.205684 \nL 199.363561 134.435481 \nL 199.667986 137.131765 \nL 199.744092 135.961544 \nL 200.276835 139.249559 \nL 200.352941 138.898612 \nL 200.429047 140.921049 \nL 200.505153 140.78449 \nL 200.581259 140.505084 \nL 200.657366 141.457215 \nL 200.733472 139.907409 \nL 200.885684 142.736194 \nL 200.96179 140.580087 \nL 201.037896 140.894381 \nL 201.266215 137.498444 \nL 201.418427 134.301124 \nL 201.494533 135.240289 \nL 201.570639 135.03145 \nL 201.646745 133.055362 \nL 201.722851 133.722795 \nL 201.875064 132.082385 \nL 202.027276 134.889235 \nL 202.179488 132.543588 \nL 202.255594 132.825836 \nL 202.407807 132.107902 \nL 202.636125 135.136825 \nL 202.864443 131.911183 \nL 203.092762 133.190926 \nL 203.168868 131.999486 \nL 203.244974 132.842097 \nL 203.32108 132.722292 \nL 203.397186 133.101251 \nL 203.625505 136.067975 \nL 203.701611 135.239925 \nL 203.929929 137.907033 \nL 204.158248 135.90763 \nL 204.386566 134.791374 \nL 204.614884 136.054924 \nL 204.69099 135.804501 \nL 204.767097 136.675918 \nL 204.843203 136.30942 \nL 204.919309 136.310836 \nL 205.071521 136.900926 \nL 205.147627 136.62644 \nL 205.604264 142.167547 \nL 205.756476 140.840688 \nL 205.984795 142.073398 \nL 206.060901 140.73373 \nL 206.213113 142.222556 \nL 206.289219 142.211874 \nL 206.365325 142.522157 \nL 206.517538 143.816208 \nL 206.66975 141.453581 \nL 206.745856 141.777897 \nL 206.821962 141.255601 \nL 207.050281 142.171458 \nL 207.202493 140.363585 \nL 207.278599 142.172013 \nL 207.354705 141.428611 \nL 207.430811 142.827048 \nL 207.583023 141.893565 \nL 207.65913 141.529605 \nL 207.811342 143.225566 \nL 207.963554 140.419826 \nL 208.03966 141.067696 \nL 208.115766 141.413733 \nL 208.191872 141.183479 \nL 208.267979 141.899068 \nL 208.420191 140.726657 \nL 208.572403 141.700521 \nL 208.648509 140.956689 \nL 208.724615 140.987921 \nL 208.800722 140.889459 \nL 209.181252 144.216069 \nL 209.333464 145.480606 \nL 209.561783 144.067315 \nL 209.637889 143.297257 \nL 209.790101 144.454233 \nL 209.866207 144.42106 \nL 209.942313 143.914952 \nL 210.01842 145.371283 \nL 210.094526 144.942595 \nL 210.170632 145.395823 \nL 210.246738 144.296311 \nL 210.322844 144.418759 \nL 210.39895 144.713866 \nL 210.551163 143.510472 \nL 210.703375 145.40073 \nL 210.779481 143.983402 \nL 211.007799 147.415904 \nL 211.160012 146.234119 \nL 211.236118 146.277517 \nL 211.38833 145.732158 \nL 211.540542 146.763188 \nL 211.616648 146.148899 \nL 211.692754 146.480104 \nL 211.844967 143.898195 \nL 211.921073 143.150876 \nL 212.073285 143.922121 \nL 212.149391 143.732159 \nL 212.37771 145.872275 \nL 212.453816 146.348488 \nL 212.529922 146.117908 \nL 212.606028 146.763215 \nL 212.682134 146.355476 \nL 212.75824 146.413829 \nL 212.910453 148.192113 \nL 212.986559 148.423243 \nL 213.062665 148.239154 \nL 213.138771 148.299576 \nL 213.214877 146.881349 \nL 213.290983 148.994251 \nL 213.367089 148.924945 \nL 213.519302 150.699197 \nL 213.671514 149.156845 \nL 213.823726 150.439524 \nL 213.899832 151.056805 \nL 213.975938 150.780005 \nL 214.204257 149.117739 \nL 214.280363 149.529344 \nL 214.356469 149.18769 \nL 214.508681 151.14783 \nL 214.660894 149.084725 \nL 214.813106 150.473015 \nL 214.889212 150.19352 \nL 214.965318 150.086786 \nL 215.041424 150.358541 \nL 215.11753 149.621907 \nL 215.193636 149.744887 \nL 215.269743 149.8061 \nL 215.421955 153.250682 \nL 215.498061 152.741687 \nL 215.726379 152.964292 \nL 215.802486 152.516657 \nL 215.878592 153.019563 \nL 216.10691 156.192144 \nL 216.183016 156.532075 \nL 216.335228 158.747219 \nL 216.411335 158.941462 \nL 216.715759 153.972358 \nL 216.867971 154.655981 \nL 217.020184 153.475253 \nL 217.09629 153.910987 \nL 217.248502 155.663776 \nL 217.324608 154.284961 \nL 217.400714 154.778249 \nL 217.47682 153.665276 \nL 217.629033 155.896101 \nL 217.705139 155.827827 \nL 217.781245 155.532478 \nL 217.857351 156.073049 \nL 217.933457 155.74163 \nL 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232.469728 176.011363 \nL 232.545834 176.224389 \nL 232.62194 176.93722 \nL 232.698046 176.837264 \nL 232.850259 175.284723 \nL 233.002471 177.109222 \nL 233.078577 176.81211 \nL 233.230789 178.029674 \nL 233.383002 177.848665 \nL 233.61132 178.566798 \nL 233.687426 178.317492 \nL 233.763532 177.528528 \nL 233.839638 178.169194 \nL 233.915745 177.206597 \nL 233.991851 177.333717 \nL 234.372381 180.158958 \nL 234.524594 179.282402 \nL 234.6007 180.477271 \nL 234.676806 180.118627 \nL 234.829018 180.891063 \nL 234.98123 180.302696 \nL 235.285655 183.161714 \nL 235.361761 183.780446 \nL 235.437867 182.570076 \nL 235.513973 183.081112 \nL 235.666186 183.563296 \nL 235.742292 183.007071 \nL 235.818398 183.190605 \nL 235.894504 184.804657 \nL 235.97061 184.329154 \nL 236.122822 184.856182 \nL 236.275035 184.71841 \nL 236.427247 185.643925 \nL 236.579459 185.230368 \nL 236.731671 186.76536 \nL 236.807777 186.210775 \nL 236.95999 184.362066 \nL 237.264414 187.001871 \nL 237.34052 186.64995 \nL 237.416627 186.990986 \nL 237.568839 185.914066 \nL 237.721051 186.961442 \nL 237.797157 185.49632 \nL 237.873263 185.554394 \nL 237.949369 185.93957 \nL 238.025476 187.131616 \nL 238.101582 186.701745 \nL 238.177688 186.410447 \nL 238.253794 186.487174 \nL 238.3299 186.615304 \nL 238.482112 185.972657 \nL 238.634325 184.84182 \nL 238.710431 186.476116 \nL 238.786537 186.074588 \nL 238.862643 186.001215 \nL 239.090961 185.372209 \nL 239.31928 182.951992 \nL 239.623704 184.58827 \nL 239.775917 185.996693 \nL 239.852023 185.181227 \nL 239.928129 185.430374 \nL 240.004235 186.649999 \nL 240.080341 186.166589 \nL 240.232553 184.414121 \nL 240.460872 182.273731 \nL 240.765296 186.119307 \nL 240.917509 184.181252 \nL 240.993615 184.993443 \nL 241.069721 184.939205 \nL 241.298039 186.06933 \nL 241.526358 184.984638 \nL 241.602464 186.048245 \nL 241.754676 185.118756 \nL 241.830782 185.340703 \nL 241.982994 187.71912 \nL 242.0591 187.133148 \nL 242.135207 187.296795 \nL 242.211313 188.049101 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196.45828 \nL 247.38653 196.617579 \nL 247.462636 196.466232 \nL 247.843166 199.827359 \nL 247.919273 199.971668 \nL 247.995379 201.125194 \nL 248.071485 200.91272 \nL 248.223697 201.952449 \nL 248.375909 201.359641 \nL 248.604228 204.084731 \nL 248.75644 204.59629 \nL 248.832546 203.987054 \nL 248.908652 204.059126 \nL 248.984758 204.925586 \nL 249.060864 204.889522 \nL 249.136971 204.930159 \nL 249.213077 205.609274 \nL 249.289183 205.363883 \nL 249.365289 203.724628 \nL 249.441395 203.921721 \nL 249.593607 204.876865 \nL 249.74582 206.179978 \nL 249.898032 205.52803 \nL 250.202456 208.524777 \nL 250.278563 208.257606 \nL 250.354669 208.57349 \nL 250.430775 207.673707 \nL 250.506881 207.905197 \nL 250.735199 209.285504 \nL 250.963518 207.674688 \nL 251.039624 207.611049 \nL 251.344048 205.677833 \nL 251.420155 206.61256 \nL 251.648473 203.692428 \nL 251.724579 203.975377 \nL 251.876791 205.381607 \nL 252.029004 203.499902 \nL 252.257322 201.905047 \nL 252.333428 202.580137 \nL 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200.388782 \nL 271.359961 200.219091 \nL 271.436067 200.417209 \nL 271.512173 201.008468 \nL 271.588279 200.847004 \nL 271.664385 200.69439 \nL 271.740491 201.267868 \nL 271.96881 198.618445 \nL 272.044916 199.349714 \nL 272.121022 199.077851 \nL 272.197128 199.521799 \nL 272.273234 199.311144 \nL 272.425446 198.815112 \nL 272.653765 200.165911 \nL 272.729871 199.757267 \nL 272.805977 199.755448 \nL 272.958189 200.583971 \nL 273.034296 200.396889 \nL 273.110402 200.425289 \nL 273.33872 201.526027 \nL 273.414826 199.621069 \nL 273.490932 199.723447 \nL 273.643145 200.946202 \nL 273.871463 199.098834 \nL 273.947569 199.329786 \nL 274.099781 200.143794 \nL 274.175887 200.065104 \nL 274.3281 200.701951 \nL 274.404206 199.506878 \nL 274.480312 200.123984 \nL 274.556418 199.203655 \nL 274.632524 199.62321 \nL 274.70863 199.349092 \nL 274.784737 200.069579 \nL 274.860843 200.02067 \nL 275.013055 199.950764 \nL 275.317479 201.500667 \nL 275.393586 200.823589 \nL 275.621904 203.98926 \nL 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280.340484 210.986145 \nL 280.644909 209.196656 \nL 280.797121 209.871118 \nL 280.949333 208.915861 \nL 281.025439 209.300041 \nL 281.101545 208.995736 \nL 281.177651 209.709851 \nL 281.253758 208.889471 \nL 281.329864 209.120306 \nL 281.40597 210.006052 \nL 281.482076 209.173502 \nL 281.558182 210.15875 \nL 281.634288 210.110262 \nL 281.710394 210.016591 \nL 281.786501 210.716291 \nL 281.862607 210.543119 \nL 281.938713 210.534076 \nL 282.090925 209.131887 \nL 282.243137 209.696998 \nL 282.319243 209.324995 \nL 282.39535 209.959742 \nL 282.471456 209.319247 \nL 282.547562 209.642471 \nL 282.623668 208.564895 \nL 282.699774 208.976945 \nL 282.77588 210.024661 \nL 282.851986 209.965069 \nL 282.928092 209.930979 \nL 283.156411 211.189593 \nL 283.232517 210.429374 \nL 283.460835 213.424347 \nL 283.536942 213.352342 \nL 283.613048 213.170874 \nL 283.76526 213.959582 \nL 283.841366 213.126784 \nL 283.917472 214.27448 \nL 283.993578 214.180414 \nL 284.069684 213.668423 \nL 284.221897 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221.882791 \nL 321.209476 221.659355 \nL 321.285582 222.096896 \nL 321.437794 221.31685 \nL 321.513901 221.209822 \nL 321.666113 221.570874 \nL 321.742219 221.493222 \nL 321.894431 220.552109 \nL 321.970537 220.733373 \nL 322.046643 220.108523 \nL 322.12275 220.126164 \nL 322.50328 222.818331 \nL 322.655492 221.912139 \nL 322.731599 222.134858 \nL 322.959917 223.101386 \nL 323.036023 222.918411 \nL 323.112129 223.139152 \nL 323.188235 222.942187 \nL 323.264342 223.014374 \nL 323.568766 222.712641 \nL 323.644872 223.293195 \nL 323.797084 222.481005 \nL 323.873191 222.449012 \nL 323.949297 221.763921 \nL 324.025403 221.894637 \nL 324.177615 222.447956 \nL 324.253721 222.938217 \nL 324.48204 222.451704 \nL 324.558146 221.589282 \nL 324.710358 222.217031 \nL 324.786464 222.071088 \nL 324.938676 221.460225 \nL 325.014783 221.42468 \nL 325.090889 221.724774 \nL 325.243101 221.476031 \nL 325.395313 221.650369 \nL 325.547525 220.918617 \nL 325.623632 221.382369 \nL 325.699738 220.853382 \nL 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330.342212 221.187018 \nL 330.418318 221.541924 \nL 330.57053 220.076084 \nL 330.646636 219.998036 \nL 330.798848 220.419574 \nL 330.874955 220.33124 \nL 331.027167 221.061027 \nL 331.103273 220.339884 \nL 331.179379 221.333078 \nL 331.255485 220.981144 \nL 331.55991 220.26894 \nL 331.636016 220.738988 \nL 331.864334 219.185044 \nL 332.016547 221.257799 \nL 332.092653 221.106267 \nL 332.168759 221.249425 \nL 332.473183 222.895975 \nL 332.701502 221.954559 \nL 332.777608 221.854515 \nL 332.853714 221.268738 \nL 332.92982 221.688822 \nL 333.005926 221.615903 \nL 333.082032 221.504586 \nL 333.234245 220.258754 \nL 333.310351 220.777994 \nL 333.386457 220.542653 \nL 333.614775 219.914711 \nL 333.843094 220.845755 \nL 333.9192 220.656987 \nL 333.995306 220.408192 \nL 334.071412 220.67203 \nL 334.147518 220.407923 \nL 334.528049 222.621137 \nL 334.604155 221.829923 \nL 334.680261 222.026954 \nL 334.908579 220.198516 \nL 334.984686 220.440035 \nL 335.213004 221.128471 \nL 335.897959 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340.159902 210.942126 \nL 340.236009 211.53299 \nL 340.312115 211.462889 \nL 340.388221 211.065894 \nL 340.464327 211.465892 \nL 340.540433 211.124963 \nL 340.616539 211.291721 \nL 340.692645 211.689442 \nL 340.768752 211.512084 \nL 340.844858 211.416072 \nL 340.920964 211.536914 \nL 340.99707 212.364566 \nL 341.073176 212.157152 \nL 341.301494 211.005587 \nL 341.453707 210.393934 \nL 341.529813 210.68896 \nL 341.605919 210.035213 \nL 341.682025 210.18404 \nL 341.758131 210.284343 \nL 341.910343 211.242217 \nL 342.062556 210.515211 \nL 342.290874 211.529309 \nL 342.595299 211.042347 \nL 342.823617 212.052456 \nL 343.051935 210.988097 \nL 343.204148 210.250295 \nL 343.508572 211.747398 \nL 343.889103 210.162552 \nL 344.041315 210.548835 \nL 344.193527 210.340648 \nL 344.269634 210.437181 \nL 344.34574 210.283416 \nL 344.421846 210.84284 \nL 344.497952 210.543036 \nL 344.574058 210.620813 \nL 344.650164 210.90913 \nL 344.72627 210.359965 \nL 344.802376 210.495679 \nL 344.878483 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359.49086 222.095313 \nL 359.566966 222.601014 \nL 359.643072 222.561673 \nL 359.719178 222.135011 \nL 359.947496 222.877837 \nL 360.099709 221.955265 \nL 360.175815 221.860014 \nL 360.251921 221.176648 \nL 360.328027 221.251226 \nL 360.404133 221.176022 \nL 360.556345 221.970641 \nL 360.632452 221.944208 \nL 360.86077 220.549157 \nL 361.012982 220.675198 \nL 361.089088 220.97318 \nL 361.165194 220.911551 \nL 361.241301 220.527651 \nL 361.317407 221.101551 \nL 361.393513 220.921423 \nL 361.545725 220.645447 \nL 361.621831 221.343583 \nL 361.697937 221.126441 \nL 361.85015 220.731047 \nL 362.002362 220.176829 \nL 362.23068 221.05741 \nL 362.382893 220.954406 \nL 362.535105 220.170404 \nL 362.611211 220.220615 \nL 362.687317 220.533181 \nL 362.839529 220.289476 \nL 362.915635 221.314979 \nL 362.991742 221.261165 \nL 363.22006 222.421424 \nL 363.296166 222.460744 \nL 363.372272 222.199727 \nL 363.448378 222.307768 \nL 363.905015 222.279265 \nL 364.057227 222.277783 \nL 364.133334 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369.612975 225.496917 \nL 369.689081 225.269571 \nL 369.765187 225.763319 \nL 369.841293 225.574217 \nL 369.917399 225.94241 \nL 369.993506 225.834238 \nL 370.221824 226.335838 \nL 370.374036 226.392443 \nL 370.450142 226.085735 \nL 370.678461 226.678278 \nL 370.982885 228.065542 \nL 371.058991 228.221204 \nL 371.135098 228.874581 \nL 371.211204 228.761344 \nL 371.28731 228.841132 \nL 371.515628 229.340738 \nL 371.66784 227.744188 \nL 371.743947 228.699587 \nL 371.820053 228.547568 \nL 371.896159 228.333578 \nL 372.048371 228.902685 \nL 372.200583 228.474055 \nL 372.276689 228.473802 \nL 372.352796 228.723472 \nL 372.428902 228.647853 \nL 372.505008 228.063192 \nL 372.581114 228.134293 \nL 372.65722 228.426281 \nL 372.961645 227.282554 \nL 373.037751 227.327715 \nL 373.189963 227.551903 \nL 373.418281 226.841216 \nL 373.494388 227.016761 \nL 373.722706 228.419826 \nL 373.798812 227.810425 \nL 373.874918 228.041667 \nL 373.951024 228.556224 \nL 374.179343 227.650022 \nL 374.255449 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226.27069 \nL 394.195255 225.483407 \nL 394.423573 226.411112 \nL 394.575786 226.303427 \nL 394.727998 226.448451 \nL 394.804104 226.765902 \nL 394.956316 225.921264 \nL 395.032422 226.189206 \nL 395.108529 227.00857 \nL 395.184635 226.904737 \nL 395.260741 226.806917 \nL 395.336847 226.459621 \nL 395.489059 227.019895 \nL 395.641271 226.05644 \nL 395.717378 226.366817 \nL 395.793484 225.979979 \nL 395.945696 226.569115 \nL 396.250121 225.693938 \nL 396.326227 225.795716 \nL 396.402333 225.843795 \nL 396.478439 225.133945 \nL 396.630651 225.794636 \nL 396.706757 225.46374 \nL 396.782863 225.566994 \nL 396.85897 225.560572 \nL 397.163394 226.552143 \nL 397.2395 226.491956 \nL 397.391712 226.893092 \nL 397.467819 226.791618 \nL 397.620031 226.196186 \nL 397.696137 226.298595 \nL 397.772243 226.825538 \nL 397.848349 226.449563 \nL 397.924455 226.783707 \nL 398.000562 227.677312 \nL 398.076668 227.5924 \nL 398.22888 228.232075 \nL 398.381092 227.273266 \nL 398.457198 227.331748 \nL 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461.396968 238.916062 \nL 461.473074 239.230977 \nL 461.625286 238.646174 \nL 461.701393 238.666263 \nL 461.777499 238.710375 \nL 461.929711 239.658458 \nL 462.005817 239.544419 \nL 462.081923 238.879507 \nL 462.158029 239.024042 \nL 462.234135 239.194349 \nL 462.310242 239.12137 \nL 462.462454 238.784103 \nL 462.53856 238.983836 \nL 462.614666 238.612951 \nL 462.766878 239.044401 \nL 462.842985 238.803921 \nL 462.919091 238.946325 \nL 463.299621 237.59003 \nL 463.375727 237.808465 \nL 463.451834 237.510104 \nL 463.604046 238.222623 \nL 463.90847 237.57239 \nL 464.136789 238.429483 \nL 464.365107 237.829515 \nL 464.441213 237.48683 \nL 464.593426 238.186325 \nL 464.669532 238.325656 \nL 464.89785 239.713942 \nL 464.973956 239.748827 \nL 465.050062 239.656263 \nL 465.430593 240.527209 \nL 465.506699 239.992562 \nL 465.582805 240.207795 \nL 465.735017 240.495201 \nL 465.811124 240.132579 \nL 466.115548 240.931801 \nL 466.191654 240.228022 \nL 466.419973 241.119703 \nL 466.572185 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242.393522 \nL 546.179197 242.743366 \nL 546.255303 242.724213 \nL 546.483622 243.10128 \nL 546.559728 242.972172 \nL 546.71194 243.239297 \nL 547.016365 242.788761 \nL 547.168577 242.511424 \nL 547.244683 242.333131 \nL 547.396895 241.840811 \nL 547.549108 241.659753 \nL 547.625214 241.943937 \nL 547.929638 241.271618 \nL 548.005744 241.027203 \nL 548.08185 241.330029 \nL 548.310169 240.189245 \nL 548.386275 240.588755 \nL 548.462381 240.50157 \nL 548.614593 240.889527 \nL 548.766806 240.440592 \nL 548.919018 240.61505 \nL 548.995124 240.075852 \nL 549.07123 240.12416 \nL 549.147336 240.331829 \nL 549.223442 240.17639 \nL 549.299549 240.25233 \nL 549.451761 240.208045 \nL 549.680079 239.49945 \nL 549.832291 239.426972 \nL 549.908398 239.253076 \nL 550.06061 239.814274 \nL 550.136716 239.729636 \nL 550.212822 239.201355 \nL 550.288928 239.427327 \nL 550.365034 239.437311 \nL 550.441141 239.112713 \nL 550.669459 239.637088 \nL 550.745565 239.354928 \nL 550.897777 240.026504 \nL 550.973883 239.934075 \nL 551.202202 239.58718 \nL 551.354414 239.257074 \nL 551.43052 239.173611 \nL 551.811051 240.601327 \nL 551.887157 240.836706 \nL 551.963263 240.578915 \nL 552.039369 240.829857 \nL 552.115475 240.428853 \nL 552.191582 240.527607 \nL 552.267688 240.590776 \nL 552.496006 241.082033 \nL 552.572112 241.15923 \nL 552.800431 242.033686 \nL 552.876537 242.032533 \nL 552.952643 241.863018 \nL 553.104855 242.209917 \nL 553.180961 241.657414 \nL 553.257067 241.801305 \nL 553.333173 241.733446 \nL 553.40928 241.836926 \nL 553.485386 241.549681 \nL 553.637598 241.867778 \nL 553.78981 241.34016 \nL 553.865916 241.228428 \nL 554.094235 241.481703 \nL 554.170341 241.43159 \nL 554.322553 242.01093 \nL 554.550872 242.484165 \nL 554.703084 242.824306 \nL 555.083614 241.380881 \nL 555.235827 241.090679 \nL 555.388039 241.52009 \nL 555.464145 241.342546 \nL 555.692464 241.743008 \nL 555.76857 241.496418 \nL 555.844676 241.785108 \nL 555.996888 241.507199 \nL 556.1491 241.837235 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243.726295 \nL 561.780954 243.663399 \nL 561.85706 243.783326 \nL 562.009272 244.555644 \nL 562.085378 244.329926 \nL 562.237591 244.837245 \nL 562.313697 244.918443 \nL 562.542015 245.736747 \nL 562.618121 245.878201 \nL 562.84644 245.47278 \nL 563.074758 245.478994 \nL 563.150864 245.138094 \nL 563.22697 245.338485 \nL 563.303077 245.231068 \nL 563.455289 244.662862 \nL 563.531395 244.787144 \nL 563.759713 244.870097 \nL 564.21635 244.26214 \nL 564.292456 244.453669 \nL 564.368562 244.323257 \nL 564.444669 244.507497 \nL 564.596881 244.086667 \nL 564.672987 244.463486 \nL 564.977411 243.441946 \nL 565.053518 243.487138 \nL 565.281836 243.86194 \nL 565.357942 243.778747 \nL 565.434048 243.862234 \nL 565.510154 243.496186 \nL 565.738473 244.257176 \nL 565.966791 243.70197 \nL 566.042897 244.306431 \nL 566.119003 244.142866 \nL 566.19511 243.877233 \nL 566.423428 244.704202 \nL 566.499534 244.348654 \nL 566.57564 244.454634 \nL 566.956171 245.464821 \nL 567.032277 245.320812 \nL 567.108383 245.375245 \nL 567.184489 245.28516 \nL 567.260595 244.923385 \nL 567.336701 245.017665 \nL 567.488914 245.468788 \nL 567.56502 245.409358 \nL 567.717232 245.167508 \nL 567.793338 244.901053 \nL 567.869444 244.986398 \nL 567.945551 245.000093 \nL 568.097763 244.313308 \nL 568.173869 244.573275 \nL 568.249975 244.126232 \nL 568.326081 244.266625 \nL 568.706612 243.445302 \nL 568.93493 244.094613 \nL 569.087142 244.102156 \nL 569.163249 243.941807 \nL 569.239355 243.986147 \nL 569.315461 244.06864 \nL 569.619885 243.375375 \nL 569.695991 243.646705 \nL 569.772098 243.50808 \nL 570.228734 243.647174 \nL 570.304841 243.418408 \nL 570.380947 243.647717 \nL 570.533159 243.213012 \nL 570.609265 243.25267 \nL 570.989796 242.521053 \nL 571.065902 242.830128 \nL 571.218114 241.902254 \nL 571.522539 242.722594 \nL 571.674751 242.275655 \nL 571.750857 242.145985 \nL 571.979175 242.599373 \nL 572.207494 241.64274 \nL 572.2836 242.140464 \nL 572.359706 241.904305 \nL 572.740237 242.438934 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239.931186 \nL 579.057046 240.826451 \nL 579.133152 240.391101 \nL 579.36147 241.195909 \nL 579.513682 240.790696 \nL 579.742001 241.236963 \nL 579.818107 241.115415 \nL 579.894213 241.252028 \nL 580.046425 241.739855 \nL 580.122531 241.94409 \nL 580.198637 241.837211 \nL 580.274744 241.961838 \nL 580.426956 242.354434 \nL 580.503062 242.474379 \nL 580.579168 242.279212 \nL 580.655274 242.57685 \nL 580.73138 242.497331 \nL 580.807487 242.670019 \nL 581.264123 241.883022 \nL 581.340229 242.022435 \nL 581.492442 241.410435 \nL 581.72076 242.110272 \nL 581.872972 241.931404 \nL 581.949078 242.243877 \nL 582.025185 242.098891 \nL 582.177397 242.029438 \nL 582.253503 242.038212 \nL 582.481821 241.776395 \nL 582.938458 242.52595 \nL 583.09067 242.305758 \nL 583.166777 242.332146 \nL 583.242883 242.944939 \nL 583.318989 242.679102 \nL 583.395095 242.640518 \nL 583.623413 243.041432 \nL 583.699519 243.073794 \nL 584.003944 243.531702 \nL 584.08005 243.323965 \nL 584.156156 243.836412 \nL 584.232262 243.611684 \nL 584.308369 243.125283 \nL 584.460581 243.749655 \nL 584.536687 243.487299 \nL 584.612793 243.61996 \nL 584.688899 243.849506 \nL 584.765005 243.692137 \nL 584.841111 243.75535 \nL 584.917218 243.797946 \nL 584.993324 244.136752 \nL 585.06943 243.954826 \nL 585.221642 243.375096 \nL 585.297748 243.600557 \nL 585.373854 243.523203 \nL 585.526067 243.557816 \nL 585.678279 243.140923 \nL 585.830491 243.258681 \nL 585.906597 243.184423 \nL 586.211022 244.376677 \nL 586.287128 244.567921 \nL 586.363234 244.533374 \nL 586.667659 244.088484 \nL 586.819871 244.524489 \nL 586.895977 244.471025 \nL 586.972083 244.216893 \nL 587.048189 244.2609 \nL 587.124295 244.427465 \nL 587.200401 244.140857 \nL 587.352614 244.410253 \nL 587.42872 243.989625 \nL 587.504826 244.43694 \nL 587.580932 244.230492 \nL 587.885357 245.02357 \nL 587.961463 245.10793 \nL 588.037569 245.608986 \nL 588.113675 245.549339 \nL 588.189781 245.214131 \nL 588.265887 245.327275 \nL 588.341993 245.65043 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245.260138 \nL 594.126059 245.499405 \nL 594.202165 245.533934 \nL 594.278272 245.421789 \nL 594.430484 244.583026 \nL 594.50659 244.90309 \nL 594.582696 244.876335 \nL 594.887121 245.151178 \nL 595.267651 244.818132 \nL 595.343757 244.969883 \nL 595.49597 244.401524 \nL 595.572076 244.820555 \nL 595.800394 244.253066 \nL 596.028713 245.000469 \nL 596.104819 244.344259 \nL 596.180925 244.912261 \nL 596.257031 244.795359 \nL 596.333137 244.624155 \nL 596.409243 244.730361 \nL 596.485349 244.625122 \nL 596.561456 244.879361 \nL 596.713668 244.369467 \nL 596.789774 244.738462 \nL 596.86588 244.635958 \nL 597.170305 243.896048 \nL 597.550835 244.62641 \nL 597.703047 243.970722 \nL 597.779154 243.441613 \nL 597.85526 243.475639 \nL 598.388003 243.88643 \nL 598.464109 243.987476 \nL 598.616321 243.522715 \nL 598.692427 243.799588 \nL 598.768533 243.670453 \nL 598.920746 243.569578 \nL 599.149064 243.921634 \nL 599.22517 243.310085 \nL 599.301276 243.551167 \nL 599.377382 243.637259 \nL 599.453488 243.938524 \nL 599.529595 243.771647 \nL 599.605701 243.95872 \nL 599.681807 243.912875 \nL 599.910125 243.97883 \nL 600.062337 244.135814 \nL 600.138444 244.022109 \nL 600.518974 244.551609 \nL 600.59508 244.118277 \nL 600.671187 244.2625 \nL 600.747293 244.394393 \nL 600.975611 243.686923 \nL 601.051717 244.265728 \nL 601.203929 243.8213 \nL 601.280036 243.98486 \nL 601.432248 243.403195 \nL 601.508354 243.827138 \nL 601.58446 243.45863 \nL 601.660566 243.509444 \nL 601.736672 243.625971 \nL 602.649946 241.415831 \nL 602.726052 241.699684 \nL 602.802158 241.453164 \nL 603.030477 242.079511 \nL 603.106583 242.125703 \nL 603.411007 243.199134 \nL 603.487113 242.918892 \nL 603.639326 243.005786 \nL 603.715432 243.296031 \nL 604.019856 242.503292 \nL 604.248175 243.179085 \nL 604.324281 242.7492 \nL 604.400387 242.894503 \nL 604.476493 242.735933 \nL 604.628705 243.056441 \nL 604.704811 242.969808 \nL 604.93313 243.566199 \nL 605.009236 243.287496 \nL 605.085342 243.554741 \nL 605.161448 243.529309 \nL 605.237554 243.336963 \nL 605.31366 243.395006 \nL 605.465873 243.956844 \nL 605.541979 244.042454 \nL 605.694191 243.694769 \nL 605.770297 243.807393 \nL 605.92251 244.305147 \nL 605.998616 244.030436 \nL 606.226934 244.358608 \nL 606.30304 244.154511 \nL 606.379146 244.469328 \nL 606.455252 244.342772 \nL 606.531359 244.481353 \nL 606.683571 244.086485 \nL 606.911889 244.598749 \nL 606.987995 244.549481 \nL 607.064101 244.80295 \nL 607.140208 244.644597 \nL 607.216314 244.923063 \nL 607.596844 243.903685 \nL 607.672951 244.376791 \nL 607.749057 244.352082 \nL 607.901269 244.191717 \nL 608.053481 244.464995 \nL 608.2818 245.041055 \nL 608.434012 244.753948 \nL 608.66233 245.729793 \nL 608.890649 245.011803 \nL 609.042861 245.044269 \nL 609.118967 244.621696 \nL 609.195073 244.816991 \nL 609.347285 244.383611 \nL 609.727816 245.645209 \nL 609.880028 245.465117 \nL 610.032241 245.66309 \nL 610.336665 245.114644 \nL 610.412771 245.426011 \nL 610.488877 245.378585 \nL 610.793302 245.796621 \nL 611.097726 244.34545 \nL 611.326045 244.096228 \nL 611.630469 244.660499 \nL 611.782682 244.354613 \nL 611.858788 244.140489 \nL 612.087106 244.950971 \nL 612.239318 245.141831 \nL 612.467637 244.180834 \nL 612.543743 244.150278 \nL 612.619849 243.963798 \nL 612.772061 243.283988 \nL 612.848167 243.114777 \nL 612.924274 243.399697 \nL 613.00038 243.264468 \nL 613.152592 243.441912 \nL 613.228698 243.412761 \nL 613.457016 242.861932 \nL 613.533123 242.808156 \nL 613.761441 243.31462 \nL 613.913653 243.078573 \nL 614.141972 242.860021 \nL 614.294184 242.094285 \nL 614.37029 242.263161 \nL 614.446396 241.959283 \nL 614.522502 242.001172 \nL 614.674715 242.101556 \nL 614.750821 241.845896 \nL 614.826927 241.8967 \nL 614.903033 242.047863 \nL 614.979139 241.968193 \nL 615.055245 242.09987 \nL 615.131351 241.8607 \nL 615.207457 241.907771 \nL 615.283564 241.763421 \nL 615.7402 243.240804 \nL 615.968519 243.828865 \nL 616.120731 243.474201 \nL 616.196837 243.262191 \nL 616.425156 243.542518 \nL 616.577368 243.183947 \nL 616.72958 243.59946 \nL 616.881792 243.530726 \nL 616.957898 243.472169 \nL 617.110111 244.305264 \nL 617.186217 244.270033 \nL 617.490641 244.711761 \nL 617.71896 244.477936 \nL 617.871172 244.093632 \nL 618.09949 243.815923 \nL 618.175597 243.932342 \nL 618.327809 244.270694 \nL 618.403915 244.417921 \nL 618.556127 245.08404 \nL 618.632233 244.970124 \nL 618.784446 245.206597 \nL 618.936658 245.204535 \nL 619.241082 245.893513 \nL 619.545507 245.19683 \nL 619.621613 245.709405 \nL 619.697719 245.589176 \nL 619.773825 245.672668 \nL 619.849931 245.510003 \nL 620.154356 246.78911 \nL 620.230462 246.620061 \nL 620.382674 246.40681 \nL 620.45878 246.374167 \nL 620.610993 245.87395 \nL 620.915417 247.232482 \nL 621.143736 246.675341 \nL 621.600372 247.799345 \nL 621.752585 247.396315 \nL 621.904797 247.84103 \nL 621.980903 247.671789 \nL 622.057009 247.75432 \nL 622.209221 248.430149 \nL 622.285328 248.153746 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247.888796 \nL 627.384438 247.496941 \nL 627.460544 247.572196 \nL 627.612757 247.745033 \nL 628.297712 246.894954 \nL 628.373818 246.843137 \nL 628.449924 246.502748 \nL 628.602136 246.782842 \nL 628.906561 246.185877 \nL 629.134879 246.608364 \nL 629.287092 246.270025 \nL 629.51541 247.00577 \nL 629.667622 247.039278 \nL 629.819834 247.429146 \nL 629.972047 246.960346 \nL 630.200365 247.798976 \nL 630.352577 247.89167 \nL 630.428683 247.69855 \nL 630.50479 247.798166 \nL 630.580896 247.845288 \nL 630.733108 248.369384 \nL 630.88532 248.732771 \nL 631.113639 249.284127 \nL 631.189745 249.425409 \nL 631.570275 248.338589 \nL 631.646382 248.483224 \nL 631.798594 249.053476 \nL 631.8747 249.04345 \nL 631.950806 249.383167 \nL 632.026912 249.303726 \nL 632.179124 248.736239 \nL 632.331337 249.075774 \nL 632.407443 249.106556 \nL 632.711867 248.329035 \nL 633.168504 249.269154 \nL 633.320716 249.469256 \nL 633.625141 248.815401 \nL 633.777353 249.346141 \nL 633.853459 249.218028 \nL 633.929565 249.16782 \nL 634.081778 248.307114 \nL 634.157884 248.37981 \nL 634.23399 248.410857 \nL 634.614521 249.641214 \nL 634.690627 249.177514 \nL 634.766733 249.580367 \nL 634.918945 249.117854 \nL 634.995051 249.425609 \nL 635.071157 249.320699 \nL 635.147264 249.287381 \nL 635.22337 249.406195 \nL 635.299476 248.976224 \nL 635.375582 249.15398 \nL 635.451688 249.216695 \nL 635.6039 249.925054 \nL 635.756113 249.217348 \nL 635.832219 249.240056 \nL 636.060537 249.942443 \nL 636.212749 249.625445 \nL 636.288856 249.62383 \nL 636.364962 249.485576 \nL 636.441068 249.959413 \nL 636.517174 249.84418 \nL 636.669386 249.810784 \nL 636.745492 250.113852 \nL 636.821598 250.087669 \nL 636.897705 250.233103 \nL 636.973811 250.072381 \nL 637.049917 250.122353 \nL 637.126023 250.588957 \nL 637.202129 250.428528 \nL 637.278235 250.416665 \nL 637.430447 250.676589 \nL 637.506554 250.225214 \nL 637.58266 250.330428 \nL 637.658766 250.492228 \nL 637.734872 250.363078 \nL 637.887084 249.802517 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249.426719 \nL 644.051681 249.26711 \nL 644.203893 249.503524 \nL 644.279999 249.252393 \nL 644.356105 249.297725 \nL 644.432211 249.143188 \nL 644.508318 249.205885 \nL 644.964954 250.223472 \nL 645.041061 250.174681 \nL 645.193273 249.858932 \nL 645.573803 248.804488 \nL 645.802122 249.448096 \nL 646.03044 249.99792 \nL 646.182652 249.466089 \nL 646.410971 249.657583 \nL 646.563183 249.632947 \nL 646.639289 249.613783 \nL 646.715395 249.930883 \nL 646.791502 249.878316 \nL 646.867608 249.979564 \nL 646.943714 249.909227 \nL 647.324244 250.367946 \nL 647.400351 250.024844 \nL 647.628669 250.736945 \nL 647.704775 250.617512 \nL 647.780881 250.696102 \nL 647.856987 250.871521 \nL 648.0092 250.661945 \nL 648.085306 250.858916 \nL 648.161412 250.768161 \nL 648.38973 250.729718 \nL 648.694155 251.942777 \nL 648.770261 251.797105 \nL 648.922473 251.942464 \nL 648.998579 251.708247 \nL 649.074685 251.964725 \nL 649.303004 251.567565 \nL 649.455216 251.939787 \nL 649.683534 251.724523 \nL 649.759641 251.840174 \nL 649.835747 251.727735 \nL 649.987959 251.208927 \nL 650.140171 251.878817 \nL 650.216277 251.898698 \nL 650.444596 251.046332 \nL 650.520702 251.343456 \nL 650.74902 250.773827 \nL 650.977339 251.212615 \nL 651.129551 250.468174 \nL 651.205657 250.471961 \nL 651.281763 250.170349 \nL 651.433975 250.42246 \nL 651.510082 250.180707 \nL 651.586188 250.287308 \nL 651.7384 249.743481 \nL 651.814506 249.953113 \nL 651.890612 249.986245 \nL 652.042825 249.691214 \nL 652.271143 249.952523 \nL 652.423355 249.060624 \nL 652.651674 249.515927 \nL 652.72778 249.63123 \nL 652.956098 249.317124 \nL 653.336629 250.287781 \nL 653.412735 250.157539 \nL 653.488841 250.189031 \nL 653.641053 250.087031 \nL 653.717159 250.09652 \nL 653.793265 250.329897 \nL 653.869372 250.160655 \nL 654.021584 250.479622 \nL 654.173796 250.290938 \nL 654.249902 250.571297 \nL 654.326008 250.115856 \nL 654.402115 250.410042 \nL 654.554327 249.991057 \nL 654.782645 250.627432 \nL 654.858751 250.191259 \nL 655.010964 250.802743 \nL 655.08707 250.782649 \nL 655.239282 250.582718 \nL 655.391494 250.875213 \nL 655.4676 250.583877 \nL 655.695919 251.388139 \nL 655.772025 251.338168 \nL 656.152556 251.127524 \nL 656.380874 250.833609 \nL 656.45698 250.763686 \nL 656.533086 250.907228 \nL 656.609192 250.8444 \nL 656.685298 250.789699 \nL 656.761405 251.013997 \nL 657.141935 250.247487 \nL 657.294147 250.671719 \nL 657.370254 250.702285 \nL 657.44636 250.418231 \nL 657.522466 250.49233 \nL 657.598572 250.497917 \nL 657.750784 250.309531 \nL 657.902997 250.70454 \nL 657.979103 250.483454 \nL 658.055209 250.630129 \nL 658.131315 250.534834 \nL 658.359633 250.991581 \nL 658.435739 250.89118 \nL 658.511846 251.172812 \nL 658.587952 251.035443 \nL 658.664058 251.149398 \nL 658.740164 251.088501 \nL 658.81627 250.963474 \nL 658.892376 251.03245 \nL 659.044588 251.377732 \nL 659.120695 250.812784 \nL 659.196801 250.932079 \nL 659.653438 251.857152 \nL 659.957862 251.556401 \nL 660.18618 250.5379 \nL 660.262287 250.562646 \nL 660.338393 250.757818 \nL 660.566711 249.898625 \nL 660.642817 250.382134 \nL 660.718923 250.313377 \nL 660.871136 250.171713 \nL 660.947242 250.240657 \nL 661.023348 250.14285 \nL 661.17556 250.670949 \nL 661.327772 250.891356 \nL 661.403879 250.696147 \nL 661.556091 251.170425 \nL 661.632197 250.934465 \nL 661.784409 251.368603 \nL 661.860515 251.176865 \nL 662.088834 251.621123 \nL 662.241046 251.236043 \nL 662.317152 251.431984 \nL 662.54547 251.214321 \nL 662.621577 251.348842 \nL 662.697683 251.234532 \nL 662.926001 250.677695 \nL 663.002107 250.652747 \nL 663.078213 250.422589 \nL 663.15432 250.68107 \nL 663.230426 250.62631 \nL 663.382638 251.057597 \nL 663.458744 250.903649 \nL 663.610956 250.914977 \nL 663.763169 251.532828 \nL 663.839275 251.511223 \nL 664.067593 251.361181 \nL 664.143699 251.04818 \nL 664.219805 251.272831 \nL 664.295911 251.063739 \nL 664.448124 251.334747 \nL 664.52423 250.940763 \nL 664.600336 251.045189 \nL 664.676442 250.913574 \nL 664.828654 251.242194 \nL 664.980867 251.082207 \nL 665.133079 251.261633 \nL 665.285291 251.136522 \nL 665.437503 251.395974 \nL 665.741928 250.947455 \nL 665.818034 251.003735 \nL 666.198565 251.018835 \nL 666.274671 250.959898 \nL 666.350777 251.042095 \nL 666.502989 251.32634 \nL 666.579095 251.437142 \nL 666.655202 251.233108 \nL 666.731308 251.345314 \nL 666.88352 251.285056 \nL 667.035732 250.805942 \nL 667.111838 250.962332 \nL 667.492369 250.586731 \nL 667.720687 249.770445 \nL 667.8729 249.90285 \nL 668.025112 250.563189 \nL 668.101218 250.479539 \nL 668.177324 250.58077 \nL 668.329536 250.536921 \nL 668.405643 250.657827 \nL 668.481749 250.175001 \nL 668.557855 250.397128 \nL 668.710067 250.493737 \nL 668.862279 250.690037 \nL 668.938385 250.428344 \nL 669.014492 250.607132 \nL 669.166704 250.343776 \nL 669.318916 250.462385 \nL 669.395022 250.246266 \nL 669.699447 251.29268 \nL 669.775553 250.971337 \nL 669.851659 251.031854 \nL 670.308296 251.428494 \nL 670.688826 250.809895 \nL 670.841039 251.10541 \nL 670.917145 250.839834 \nL 671.069357 251.335865 \nL 671.221569 250.822259 \nL 671.297675 250.799486 \nL 671.6021 249.702956 \nL 671.754312 250.157049 \nL 671.830418 249.903154 \nL 671.982631 250.388521 \nL 672.058737 250.183821 \nL 672.287055 250.30421 \nL 672.363161 250.330246 \nL 672.743692 249.403993 \nL 672.895904 249.721849 \nL 672.97201 249.475929 \nL 673.276435 249.99708 \nL 673.352541 249.942493 \nL 673.580859 250.667848 \nL 673.656966 250.550659 \nL 673.733072 250.831776 \nL 673.96139 250.16559 \nL 674.113602 250.51762 \nL 674.265815 250.355753 \nL 674.418027 250.32359 \nL 674.646345 249.621423 \nL 674.95077 250.415305 \nL 675.179088 249.980525 \nL 675.3313 249.85175 \nL 675.483513 249.653326 \nL 675.635725 250.017987 \nL 675.787937 249.712792 \nL 675.864043 249.935223 \nL 675.940149 249.904524 \nL 676.092362 249.627246 \nL 676.244574 249.336002 \nL 676.472892 249.758623 \nL 676.548998 249.71747 \nL 676.625105 249.682917 \nL 676.777317 249.211648 \nL 676.853423 249.288017 \nL 676.929529 249.567083 \nL 677.081741 249.316537 \nL 677.157848 249.225881 \nL 677.31006 248.385406 \nL 677.386166 248.556724 \nL 677.538378 248.208598 \nL 677.766697 247.573872 \nL 677.842803 247.579872 \nL 677.918909 247.799573 \nL 677.995015 247.769148 \nL 678.299439 247.809426 \nL 678.603864 247.80943 \nL 678.67997 247.64496 \nL 678.756076 247.948334 \nL 678.908289 247.43261 \nL 679.136607 247.917316 \nL 679.212713 247.902627 \nL 679.517138 248.658597 \nL 679.66935 248.339024 \nL 679.973774 248.47255 \nL 680.202093 249.277381 \nL 680.278199 249.209758 \nL 680.734836 249.790935 \nL 680.810942 249.924106 \nL 680.887048 249.582174 \nL 680.963154 249.862878 \nL 681.03926 249.808861 \nL 681.267579 249.957701 \nL 681.419791 249.897594 \nL 681.495897 250.029051 \nL 681.572003 249.883271 \nL 681.800321 250.314445 \nL 681.876428 250.422081 \nL 681.952534 250.336715 \nL 682.104746 250.544996 \nL 682.333064 250.005326 \nL 682.561383 250.077602 \nL 682.713595 249.76671 \nL 682.789701 249.797584 \nL 682.941913 249.409458 \nL 683.094126 249.610798 \nL 683.170232 249.514016 \nL 683.39855 249.795734 \nL 683.474656 249.570413 \nL 683.550762 249.656589 \nL 683.779081 249.674015 \nL 683.855187 249.893216 \nL 683.931293 249.713271 \nL 684.083505 249.85194 \nL 684.159611 249.881152 \nL 684.235718 249.388466 \nL 684.311824 249.418015 \nL 684.38793 249.643354 \nL 684.540142 248.995146 \nL 684.616248 249.180871 \nL 684.692354 249.075197 \nL 684.768461 248.811695 \nL 684.920673 249.013022 \nL 685.072885 248.688062 \nL 685.37731 249.00416 \nL 685.529522 248.634259 \nL 685.605628 248.877076 \nL 685.681734 248.624268 \nL 685.75784 248.770006 \nL 685.833946 248.70752 \nL 685.910052 248.753459 \nL 686.062265 248.170559 \nL 686.138371 248.254508 \nL 686.442795 249.074942 \nL 686.671114 249.004258 \nL 686.823326 249.427933 \nL 686.899432 248.935609 \nL 687.051644 249.358646 \nL 687.279963 249.052505 \nL 687.584387 249.751375 \nL 687.660493 249.046608 \nL 687.7366 249.268596 \nL 687.812706 249.367599 \nL 687.888812 249.301889 \nL 688.11713 249.654314 \nL 688.345449 250.216097 \nL 688.421555 250.489097 \nL 688.497661 250.276817 \nL 688.573767 250.33244 \nL 688.649873 250.247382 \nL 688.802085 250.755119 \nL 688.878192 250.95613 \nL 689.10651 250.453273 \nL 689.563147 251.325749 \nL 689.715359 251.278255 \nL 689.943677 252.038807 \nL 690.019784 251.816402 \nL 690.09589 251.902796 \nL 690.171996 251.906129 \nL 690.324208 251.54056 \nL 690.47642 251.608854 \nL 691.085269 253.042093 \nL 691.161375 252.926623 \nL 691.541906 253.519682 \nL 691.618012 253.46239 \nL 691.694118 253.435118 \nL 691.770225 253.575754 \nL 691.922437 253.214055 \nL 691.998543 253.212418 \nL 692.150755 253.529393 \nL 692.302967 253.548686 \nL 692.379074 253.608237 \nL 692.45518 253.444559 \nL 692.531286 253.676806 \nL 692.607392 253.622779 \nL 692.83571 253.257112 \nL 692.987923 253.747009 \nL 693.064029 253.577311 \nL 693.140135 253.621695 \nL 693.292347 252.938172 \nL 693.520666 253.010483 \nL 693.748984 252.421946 \nL 693.901196 252.718762 \nL 693.977302 252.783254 \nL 694.053408 252.518194 \nL 694.129515 252.550246 \nL 694.205621 252.632364 \nL 694.433939 252.388433 \nL 694.510045 252.419359 \nL 694.586151 252.185257 \nL 694.662257 252.480215 \nL 694.738364 252.34503 \nL 695.195 252.801475 \nL 695.271107 252.671277 \nL 695.347213 252.760488 \nL 695.423319 252.803514 \nL 695.575531 253.073362 \nL 695.651637 252.567186 \nL 695.727743 252.864208 \nL 695.803849 252.753809 \nL 695.879956 252.567687 \nL 695.956062 252.610345 \nL 696.108274 252.629697 \nL 696.260486 253.004875 \nL 696.336592 252.991745 \nL 696.488805 253.073627 \nL 696.564911 252.521224 \nL 696.641017 252.601142 \nL 696.793229 252.497646 \nL 696.869335 252.336085 \nL 696.945441 252.433862 \nL 697.249866 253.214738 \nL 697.325972 253.049718 \nL 697.402078 253.095851 \nL 697.55429 253.087061 \nL 697.630397 252.809803 \nL 697.706503 253.061191 \nL 697.782609 253.033561 \nL 697.858715 252.593188 \nL 697.934821 252.650417 \nL 698.087033 252.917482 \nL 698.239246 252.619919 \nL 698.391458 253.063754 \nL 698.467564 253.008353 \nL 698.695882 253.369823 \nL 698.771989 253.06532 \nL 698.848095 253.412554 \nL 699.076413 252.874607 \nL 699.304731 252.870379 \nL 699.837474 253.393215 \nL 699.989687 253.27358 \nL 700.218005 253.641649 \nL 700.294111 253.650791 \nL 700.52243 252.985451 \nL 700.674642 252.875008 \nL 700.826854 252.986308 \nL 700.979066 252.699522 \nL 701.055172 253.077612 \nL 701.131279 252.783392 \nL 701.283491 253.018949 \nL 701.359597 253.091341 \nL 701.435703 253.379024 \nL 701.511809 253.334036 \nL 701.664021 253.546473 \nL 701.740128 253.491658 \nL 702.044552 254.176371 \nL 702.120658 253.963507 \nL 702.501189 255.091606 \nL 702.805613 255.076432 \nL 702.957826 255.002239 \nL 703.338356 256.378719 \nL 703.414462 256.562531 \nL 703.642781 255.954548 \nL 703.718887 255.997285 \nL 703.871099 255.527749 \nL 703.947205 255.610622 \nL 704.023312 255.418972 \nL 704.099418 255.507726 \nL 704.25163 255.360266 \nL 704.556054 254.411312 \nL 704.632161 254.498571 \nL 704.860479 255.038484 \nL 704.936585 254.678135 \nL 705.012691 254.856139 \nL 705.545434 253.923966 \nL 705.62154 254.005676 \nL 706.306495 254.807445 \nL 706.382602 254.995274 \nL 706.458708 254.897658 \nL 706.61092 254.602494 \nL 706.687026 254.659016 \nL 707.067557 254.896679 \nL 707.295875 254.151998 \nL 707.371981 254.303617 \nL 707.6003 254.548731 \nL 707.752512 254.603537 \nL 707.904724 254.793412 \nL 708.056936 254.464098 \nL 708.361361 254.671812 \nL 708.513573 254.339022 \nL 708.665785 254.264578 \nL 708.894104 254.160209 \nL 708.97021 254.369677 \nL 709.046316 254.228436 \nL 709.274635 254.636785 \nL 709.426847 254.515259 \nL 709.579059 254.854665 \nL 709.731271 254.567209 \nL 709.883484 254.917043 \nL 710.111802 254.525857 \nL 710.34012 253.93876 \nL 710.644545 254.848449 \nL 710.720651 254.448238 \nL 710.796757 254.564449 \nL 711.025075 254.329129 \nL 711.177288 254.362855 \nL 711.557818 253.323471 \nL 711.633925 253.356584 \nL 711.786137 253.69353 \nL 712.166667 252.936066 \nL 712.394986 252.778424 \nL 712.547198 252.958434 \nL 712.69941 252.638042 \nL 712.775516 252.720686 \nL 712.851623 252.560182 \nL 713.003835 252.937523 \nL 713.232153 252.126617 \nL 713.308259 252.181276 \nL 713.68879 251.393915 \nL 713.764896 251.538791 \nL 713.841002 251.167181 \nL 713.917108 251.344882 \nL 713.993215 251.436294 \nL 714.221533 251.148543 \nL 714.373745 250.754971 \nL 714.67817 250.83814 \nL 714.830382 250.628276 \nL 714.906488 250.584672 \nL 715.0587 251.089007 \nL 715.134807 251.04242 \nL 715.210913 250.933782 \nL 715.287019 251.113428 \nL 715.591443 250.590013 \nL 715.743656 250.855011 \nL 715.895868 251.097353 \nL 716.124186 251.098929 \nL 716.200292 251.266127 \nL 716.428611 250.752111 \nL 716.580823 250.747973 \nL 716.809141 251.223592 \nL 717.03746 251.167471 \nL 717.113566 250.844537 \nL 717.189672 251.042985 \nL 717.341884 250.73719 \nL 717.41799 250.80121 \nL 717.722415 251.34602 \nL 717.874627 251.704934 \nL 717.950733 251.145313 \nL 718.026839 251.295538 \nL 718.102946 251.09248 \nL 718.179052 251.140035 \nL 718.255158 251.34763 \nL 718.331264 251.217177 \nL 718.483476 251.836437 \nL 718.635689 251.452015 \nL 718.787901 251.460164 \nL 718.940113 251.144586 \nL 719.168431 250.903331 \nL 719.244538 250.943897 \nL 719.39675 250.658331 \nL 719.472856 250.7447 \nL 719.625068 250.541455 \nL 719.701174 250.706861 \nL 719.929493 249.929213 \nL 720.005599 250.01 \nL 720.157811 250.832387 \nL 720.233917 250.741512 \nL 720.38613 250.515064 \nL 720.462236 250.539491 \nL 720.538342 250.852397 \nL 720.76666 250.179079 \nL 720.918872 250.495552 \nL 720.994979 250.423811 \nL 721.071085 250.585776 \nL 721.451615 249.954785 \nL 721.603828 249.915808 \nL 721.679934 249.816373 \nL 722.060464 250.823854 \nL 722.136571 251.041934 \nL 722.212677 251.009118 \nL 722.364889 250.76971 \nL 722.440995 250.747588 \nL 722.669313 251.227068 \nL 722.74542 250.975708 \nL 722.973738 251.480467 \nL 723.12595 251.286158 \nL 723.963118 253.149625 \nL 724.039224 253.055806 \nL 724.343648 253.30336 \nL 724.419754 253.29489 \nL 724.495861 253.059797 \nL 724.571967 253.23349 \nL 724.648073 253.101533 \nL 724.724179 253.270199 \nL 724.800285 252.973209 \nL 724.876391 253.096197 \nL 724.952497 253.131803 \nL 725.10471 253.009788 \nL 725.409134 253.568512 \nL 725.561346 253.390277 \nL 725.713559 253.76756 \nL 725.865771 252.980345 \nL 725.941877 252.741674 \nL 726.170195 253.174014 \nL 726.246302 253.052235 \nL 726.550726 253.456426 \nL 726.626832 253.173738 \nL 726.702938 253.302411 \nL 726.855151 253.532119 \nL 727.083469 253.771907 \nL 727.159575 253.742881 \nL 727.311787 253.354815 \nL 727.387894 253.52731 \nL 727.540106 253.156824 \nL 727.692318 253.463777 \nL 727.920636 252.834419 \nL 727.996743 253.011787 \nL 728.377273 253.135256 \nL 728.529485 252.765789 \nL 728.681698 252.9935 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253.834998 \nL 733.704702 253.57157 \nL 733.933021 254.010972 \nL 734.009127 254.022848 \nL 734.313551 253.681712 \nL 734.465764 253.686973 \nL 734.54187 253.468038 \nL 734.617976 253.501987 \nL 734.770188 253.542888 \nL 734.9224 253.156356 \nL 734.998507 253.285683 \nL 735.150719 252.347827 \nL 735.226825 252.525112 \nL 735.455143 253.154318 \nL 735.531249 252.806103 \nL 735.607356 252.830062 \nL 735.759568 252.788701 \nL 735.987886 253.352995 \nL 736.216205 252.896567 \nL 736.368417 253.09733 \nL 736.520629 252.988713 \nL 736.596735 252.822908 \nL 736.672841 252.904825 \nL 736.90116 252.854042 \nL 736.977266 252.967127 \nL 737.28169 253.874276 \nL 737.357797 253.882577 \nL 737.510009 253.572863 \nL 738.042752 254.391747 \nL 738.27107 254.315595 \nL 738.347176 254.468501 \nL 738.423282 254.389595 \nL 738.499389 254.255572 \nL 738.575495 254.581766 \nL 738.651601 254.467968 \nL 738.879919 254.21789 \nL 739.032131 254.342697 \nL 739.564874 253.820333 \nL 740.097617 254.041606 \nL 740.63036 253.164105 \nL 741.61974 254.709755 \nL 741.695846 254.421274 \nL 741.771952 254.441624 \nL 741.848058 254.452911 \nL 742.000271 254.205979 \nL 742.076377 254.21041 \nL 742.380801 254.747626 \nL 742.533013 254.776563 \nL 742.60912 254.936321 \nL 742.685226 254.850851 \nL 742.837438 254.72804 \nL 742.98965 254.967961 \nL 743.065756 254.650852 \nL 743.141862 254.744051 \nL 743.217969 254.837761 \nL 743.294075 254.772281 \nL 743.370181 254.589129 \nL 743.446287 254.642926 \nL 743.598499 254.620068 \nL 743.674605 254.647188 \nL 743.750712 254.294348 \nL 743.826818 254.375023 \nL 744.359561 254.935701 \nL 744.435667 254.88913 \nL 744.587879 255.272419 \nL 744.663985 255.054974 \nL 744.740091 255.121377 \nL 744.816197 255.218696 \nL 744.892303 255.139423 \nL 745.196728 254.764182 \nL 745.272834 254.928515 \nL 745.501153 254.839554 \nL 745.653365 254.502806 \nL 745.805577 254.772037 \nL 745.957789 254.406916 \nL 746.186108 254.804692 \nL 746.262214 254.854881 \nL 746.490532 254.256772 \nL 746.642744 254.243806 \nL 746.718851 254.066001 \nL 746.947169 254.244972 \nL 747.023275 254.271418 \nL 747.099381 254.443314 \nL 747.175487 254.3724 \nL 747.479912 254.4836 \nL 747.70823 253.610437 \nL 747.784336 253.703886 \nL 747.860443 253.908955 \nL 747.936549 253.518243 \nL 748.012655 253.701008 \nL 748.164867 253.609296 \nL 748.240973 253.554215 \nL 748.317079 253.305482 \nL 748.393185 253.401964 \nL 748.469292 253.454893 \nL 748.621504 253.154136 \nL 748.773716 253.304817 \nL 749.078141 252.154756 \nL 749.230353 252.465361 \nL 749.306459 252.406037 \nL 749.534777 251.960516 \nL 749.68699 251.958888 \nL 749.763096 252.158086 \nL 750.06752 251.582977 \nL 750.143626 251.303189 \nL 750.600263 252.080002 \nL 750.752476 251.872651 \nL 750.980794 251.921175 \nL 751.361325 252.446054 \nL 751.437431 251.985803 \nL 751.513537 252.077794 \nL 751.894067 252.967664 \nL 751.970174 252.876877 \nL 752.198492 252.442477 \nL 752.274598 252.526672 \nL 752.42681 252.856411 \nL 752.502917 252.852576 \nL 752.655129 252.594277 \nL 752.731235 252.993175 \nL 752.807341 252.846228 \nL 752.883447 252.735667 \nL 753.035659 253.195971 \nL 753.111766 253.074882 \nL 753.187872 253.250207 \nL 753.263978 253.198845 \nL 753.340084 253.316989 \nL 753.568402 253.081061 \nL 753.796721 253.268984 \nL 753.948933 253.504453 \nL 754.025039 253.250712 \nL 754.101145 253.323892 \nL 754.253358 253.271885 \nL 754.329464 253.422716 \nL 754.40557 253.333332 \nL 754.7861 253.834969 \nL 755.014419 254.244091 \nL 755.166631 254.085627 \nL 755.242737 254.377723 \nL 755.318843 254.068878 \nL 755.394949 254.090395 \nL 755.471056 254.137685 \nL 755.623268 253.635998 \nL 755.927692 254.18903 \nL 756.536541 253.627733 \nL 756.612648 253.556385 \nL 757.069284 254.059753 \nL 757.14539 254.003524 \nL 757.221497 254.103356 \nL 757.373709 253.868521 \nL 757.525921 253.942001 \nL 757.602027 253.51757 \nL 757.678133 253.656845 \nL 757.906452 253.895981 \nL 758.13477 253.826796 \nL 758.210876 253.626069 \nL 758.286982 253.752065 \nL 758.439195 253.409846 \nL 758.515301 253.403517 \nL 758.743619 252.651456 \nL 758.819725 252.500632 \nL 758.895831 252.6941 \nL 758.971938 252.621867 \nL 759.12415 252.41389 \nL 759.200256 252.400086 \nL 759.352468 252.621013 \nL 759.504681 252.336746 \nL 759.656893 252.225492 \nL 759.732999 252.179418 \nL 759.809105 252.336147 \nL 759.885211 252.28752 \nL 759.961317 252.370919 \nL 760.037423 252.657341 \nL 760.11353 252.569525 \nL 760.189636 252.194809 \nL 760.265742 252.366125 \nL 760.417954 251.507737 \nL 760.570166 251.564593 \nL 760.722379 251.67731 \nL 760.798485 251.565813 \nL 760.950697 251.761817 \nL 761.179015 251.348172 \nL 761.255122 251.490626 \nL 761.331228 251.434723 \nL 761.48344 251.559955 \nL 761.635652 251.071772 \nL 762.016183 251.70159 \nL 762.320607 252.225215 \nL 762.396713 252.056382 \nL 762.47282 252.107181 \nL 762.548926 252.288524 \nL 762.625032 252.195054 \nL 762.777244 252.202558 \nL 763.157775 251.962453 \nL 763.309987 252.269028 \nL 763.538305 251.941046 \nL 763.614412 251.96943 \nL 763.690518 251.818511 \nL 763.766624 252.048017 \nL 763.994942 251.51191 \nL 764.147154 251.114084 \nL 764.451579 251.620997 \nL 764.527685 251.61334 \nL 764.603791 251.981662 \nL 764.679897 251.89332 \nL 764.756004 251.81112 \nL 764.83211 251.507687 \nL 764.908216 251.72962 \nL 764.984322 251.621455 \nL 765.136534 251.479335 \nL 765.364853 252.266995 \nL 765.440959 252.274435 \nL 765.517065 252.077851 \nL 765.593171 252.170022 \nL 765.821489 251.729883 \nL 765.897595 251.890937 \nL 765.973702 251.821895 \nL 766.049808 251.704917 \nL 766.125914 251.90995 \nL 766.20202 251.856931 \nL 766.506444 251.956438 \nL 766.658657 251.912721 \nL 766.810869 251.69726 \nL 767.115294 252.496379 \nL 767.267506 252.49477 \nL 767.419718 252.735931 \nL 767.800249 252.402385 \nL 767.952461 252.595658 \nL 768.028567 252.44971 \nL 768.180779 252.624107 \nL 768.256885 252.268962 \nL 768.332992 252.359947 \nL 768.409098 252.369591 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252.98892 \nL 774.117058 252.630084 \nL 774.193164 252.691485 \nL 774.26927 252.609327 \nL 774.421482 252.974854 \nL 774.573694 252.666419 \nL 774.6498 252.767767 \nL 774.802013 252.615483 \nL 774.878119 252.637263 \nL 775.182543 253.589552 \nL 775.334756 253.68309 \nL 775.486968 253.714978 \nL 775.563074 253.696298 \nL 775.63918 253.966774 \nL 775.715286 253.768455 \nL 775.791392 253.913967 \nL 775.867499 253.755125 \nL 775.943605 253.89482 \nL 776.019711 253.823798 \nL 776.095817 253.542953 \nL 776.476348 254.246827 \nL 776.704666 254.071378 \nL 776.780772 253.969315 \nL 776.856878 254.088062 \nL 777.00909 253.998487 \nL 777.085197 254.008628 \nL 777.161303 254.30545 \nL 777.237409 254.169864 \nL 777.465727 253.89216 \nL 777.694046 254.143839 \nL 777.846258 254.343647 \nL 777.922364 254.596147 \nL 778.150682 253.606687 \nL 778.226789 253.654768 \nL 778.455107 254.208512 \nL 778.607319 254.375364 \nL 778.835638 254.094154 \nL 778.911744 253.95111 \nL 778.98785 254.073428 \nL 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+AAAACBdBDuH58Ufprbds1I7qEjt3nz7Vd40scC5YHzCg7P4zzsheXQAAABA+ghzCU1Agde9uKaW6ph6oX9+WEydWz/mz6NVXbXn33UHZunXB+uLF2a0PAAAAwkOQQ26oVUu69lqbATuT1qyxZWxkkAg76aTE7fvuk+rVC7b/8Y/s1gcAAADhIcghd6xcKa1dK73zTubOGZt4XJK8z9x5Q1Cn1GQhseC2zz62ZBo+AACAmoMgh9wxZowt778/sdx76bvvKhfEvJf220/66KOg7IILql7HkP34o41guXp1UPbDD7Z8441w6gQAAIDsI8ghd5x5pi133jmx/JlnpAMOkP773/TPNWlSkHBiBg6MfKtcQYH0r39JDRsmlu++ezj1AQAAQDgIcsgdPXvaskOHxPLnnrPl5Zenfu7ixdK4ccH22rXJj7vqqsiHuWSOOsrGdcnDlwYAAIAkCHLIHZtsYssVK4KyVaukL74ItlMllQMOkDp2tNa7yZOl998P9sW38D30kNS/f4YqnDuaN7cRLOO7XAIAACB/EeSQO2rXlpo0sUm8YwYNSjwm1czXEybYslcvqV07qW/fYF/jxlK/fsF2xCcHT2bzzW3JFAQAAAA1A0EOuaVFC2nRomB7+fLE/fPmBevpDoIyYoTUu3ewnQdTEZQWC3JDhoRbDwAAAGQHQQ65pWVLaeHCYPvvf0/cv+WWwfoLL1iXynRa2OInXMvDINe5sy0//zzcegAAACA7CHLILZtvblMGXHKJVFQUlA8fbsvYyJaSNGWKLV9+ufxzdusmOSftv79tL1hgy+Ji6cILrcUu4rbaSmrVygY8AQAAQP4jyCG3NG1qywEDpK+/Dsp32SVYnzDBWu1+/dW2UwW5KVNsQvBnn7XtWGve+PG2/OIL6YknbEz/PFC6VyoAAADyl/M5Ol55QUGBHx5rhUHN4Vzycu8T93XqJI0cWf65li8PRsKUpN9/t+EdJWnlSpswPDYJeY7+O6iMI46QPv1UWrZM2nTTsGsDAACAqnLOjfDeJ211oEUO0fHww8F6RSFOshEw422+uXTiicG+WIiT8iLITZxoy6ZNLbMCAAAgfxHkkFuOOqps2fnn2/Jvfyv/uUOHJk5dkKx1b6+9kj932bJ0apfT7rorWB8wILx6AAAAoPoR5JBbXn21bNkRR9iyVtzbdZttyh7XubM1R735ZupJv3/7LXn5rFmVq2cOih8HZuXK8OoBAACA6keQQ25p2jRx8JJFixITSnx5vPgWtRNPlC6+OPn5//3vxO2PPrLljBmVrmouWrdOatCArpUAAAD5rk7YFQDKOP10qU0baY89Uo/asWaNLfv3l/785/RH99hii2C9SRNp551tfc6cja9vDqlXz17S7NmJ5cXFQYPmTTfZGDDHH2/TFdSvbz9uAAAARActcshNBx2UPJx9+GHi9sUXJ+9mmUr8fXOLFwcDoqQzeEpENGsmvf++tMMO0i+/2I+odm2psFB6/XXpzjulPn2kjh2lP/1J2npra8lbsSLsmgMAACBdBDlEy9FHZ+Y8HTpY81UsyA0YkBcjV0o2PZ4kTZ1qU+g9+qhtT5qUOCBKvAYNLDe/9VY2aggAAICqIsghui64YOOet3SpNGKErderF5THT0AeYZdeGqy/+Waw3rdvxQ2PPXpUT50AAACQWQQ5RNfGjrHftKnUsGHZ8jwZ6rFXr2B9ypRgvXRrW6qBPT/9tOw9dgAAAMgtBDlEzyef2DQFdTI0Vs/YsbZcvjwz5wvZnnuWv//MM60X6cUXJ/Ym3WEHWx5xhN03BwAAgNzFqJWInm7dMnu+Zs1suWRJZs8bklq1LKB9/HHy+dVLt8R9+62NAVOnjrTvvkF5YWHmsjIAAAAyixY5YLPNbLl0aajVyLQjj5See85Grvz5ZyubMMF6lsY74ACbS32ffRLLL7ggc+O/TJpkYfGnnzJzPgAAgJqOIAc0aGDL668Ptx7V4JxzpF13lXbbzULZjjuWf/zs2dZrVbIRL2vVkgYNKv85U6fadAbPPJM6+P33v7Y8/vhKVR8AAAAp0HEKiFdUZJOu1VBbbSX17CmddlpQduqpQUD79Vfp1lulF1+UVq+WFi2SdtopOHb8eOmzz2wA0Fg+/vVXaehQW68oSAIAACA9tMgBktS1qy3nzg23Hjni4osTt4uLbXn66TapeJcu0nHHJYY4Sbr3Xmn4cGsFjNltNyuTpPnzq6/OAAAANQlBDpCks8+25aJF4dYjR/TvL/XubSFMkkaPtmX9+rYcMUL67rvUz588OQh/8caOlRYuzGxdAQAAaiKCHCBJ775ry2uuSZ5AaqAnn5ROPtnW//xnG6hk1Kj0nz9lSjCjw777Si+9ZOsV3XMHAACAihHkAEm68UZbfvaZ3SM3eXK49ckRV15pyzlzpL32KjuYydixdl+c98Hj9ttt3x132GiVknTttXbfnXPS449nr/4AAAD5iiAHSJZS4gc5+eCD8OqSQzbdtGxZ797Se+9JH34odeggtW+fuP8f/wjWY0GuXbtgfruffgrCHgAAADYOQQ6IKSoK1jdsCK8eOSbWvTLm0kttoJOjj05+fGy0yueeC0a/bNcu8ZhbbslsHQEAAGoaghyQzKxZYdcgZzz7bLA+fbq0556VP0fjxraMz8oPPVSVWgEAANRsBDkgmQcfDNb79LGbuzYmweSBxo3tfrf27aWtt07vOf36Beu77x6s14r7xIndfydJhYVVqyMAAEBNQ5ADYv7zH+nyy4PtdessYdx3n22PHi2tXRtO3UJ2443SuHGJQaw8F19s99LdcYc0cmTivqlTg/Xrr7eMXLeuTSIOAACA9Dhfehi6HFFQUOCHx2YRBrLpppukO++0JNKzp3TUUcG+334rOws2Ks255OVvvy2dcEJ26wIAAJCrnHMjvPcFyfbRIgeU1qWLLZ96ykb2iNe+fTA5Gjbat98mL+/e3Vr+AAAAUD6CHFDaVlsF6xMnlt3/t79lry556oADrOFzjz2kadMS93XsGEqVAAAAIoWulUBphYV201a8RYukFi2C7Rz9dxNVo0dLBx0krVhh20VF6d+PBwAAkK/oWglURp060scfJ25vvnl49akB9tjDeqyed55tDxsWbn0AAAByHUEOSOaII6RttrH1Jk1sdI5nn5UOP9zK1q0Lr255LBbkDjiARk8AAIDyEOSAVDbd1JZLl9ry3HOlU0+19XHjbIjF+fNDqVq+ir8/7rPPEicQBwAAQIAgB6RSkKQ7cvPmttxrL+nEE6Utt5SeeCKr1cpnrVoF60ccYb1an346vPoAAADkKoIckErv3mXLCgvLll14YfXXpQZZtixxu1+/cOoBAACQy+qEXQEgZx10UNmybt2SHzt+vPTLL3Zf3f77V2+98lysR2vMjjuGUw8AAIBcRoscUJ7PP5cmTw62W7aUbrut7HEdOkg9e0qdO2evbnnsl1+C9VdeYeATAACA0ghyQHkOPVTaYYfEsj59pH/9S1q/PnHy8BhSR5XtumviODK1akmzZoVXHwAAgFxDkAMqq3596aqrbNLw004ru3/ChOzXKQ9tsYV07LHB9t//Lr33nq17L02dKl1wgY0/s2pVOHUEAAAIi/M52npQUFDghw8fHnY1gPIVFkozZ5ZttcvRf1dRU1ws1a6dWDZ7ttSrV+Kc7XfdJfXtm926AQAAVDfn3AjvfZKh1AlyQGY0biytXh1s5+i/qyjy3rpWpmPdOqleveqtDwAAQLaUF+ToWglkwuLF0tq1wbZz0pQp4dUnjzgnPf64tNlmZfctWJC43atX0P1y+XJp5cpg35IlNojK0KHVV1cAAIBsoUUOyKROnaRRo4LtHP33FVUHHyx9/bWtFxdbyHMu8RjnpKKioBXPe+nbb6UDDwyOefxxm9Zg8GA73zfflD0PAABA2GiRA7Kl9CTiySYQx0b76isb2MT7IHj17y917Roc472NQxPz3HOJIU6yOdwPO0y6915roTvhhOqvOwAAQCbRIgdkUlGRVKdOsD1/vg2/iGpX1Ra1HP0oBAAANRgtckC21K5tieDii217r72kRYvCrVMNsfXW5e+fPVsaPVoaMSL5/nnzMl8nAACA6kKQA6pDjx62nDNHatlSGjs23PrUADNn2n1zzz0nffKJhbaYwkKbu3333e02xqFDpb/8RfrtN+nZZ+2Y1q2t6yYAAEAU1Kn4EACVdsQRFuAWLrTtXXaRDjjARt1AtXFOOuecYPvss23Qk9Jz0XXubA/JpiyIuf9+G1AFAAAg19EiB1SX+BE3JGsGck566KFQqlMTPf980OKWym67SXPnWu5esyY79QIAAKgqghxQXRo2TF5+5ZXZrQcqtOWWNrLlZ59Jy5aFXRsAAICKEeSA6pIqyCEntW5ty2bNpOuus8bTESNsIFIAAIBcQ5ADqkuzZraMH3Ujhtmnc8599wXr995ry4IC6fjjw6kPAABAeQhyQHV57jnp8suljh2lN96wsvhRN1atCqdeSKpxY2n//cuWf/hh9usCAABQEYIcUF22394GNqlTx6Yj8D5xGoKrr5bWrw+teihr8GDpyy+lIUOkG28MyouLw6sTAABAMkw/AGTTTjsF6489JrVrJ11zTXj1QYKmTYPpBw4+2KYBHDgwmOc9DMuXS2vXSltsEc71AQBAbqJFDsi25cuD9RUrwqsHylW7tnTFFcH29OnZr8OyZRYuW7WShg+3skWLbGCWmTOzXx8AAJA7CHJAtm2ySbA+cGB49UCFdttN2nZbW2/bNvvX//LLYH2ffWzZsqU0b570f/+X/foAAIDcQZADwhALcLNmhVsPVGjSpGC9a1fptdcq9/wffti4KQyeekrq3j2xLH6w0w8/5BZLAABqMoIcEIZevaSjj7bx7SUbTePbb6WlS0OtFsqqW1fad19bHzJEOu00C1R9+0pXXVX+c3/9VdpvPxvvpjL32A0eLF1wQbAdmw6htPr1pRdfTP+8AAAgf2QkyDnnjnbO/eacm+Scuy7J/qucc2Odcz875z5zzm2XiesCkTZ2rN34VFQk9esnHXigtNlmYdcKSTz3XNmye+6RHnzQRrdctCj5866L+zQcMya9a40fLx1zTLD9+efStddKO+wQlH37bbB+9tkWGAEAQM1S5SDnnKstqZ+kYyR1lHSGc65jqcNGSSrw3u8uaZCk+wTUdDNm2PLUUxNH1UDOad8+9b5//tPuW4tZt0565hkLXu+/H5S//roNUPLJJ8nniJekiRNt2sEY76VDD7X1yZOlRx+1QVcOOCAxzD31VGVfEQAAiDrnqzimtnOus6RbvfdHlWz3lSTv/d0pjt9L0iPe+y7lnbegoMAPjw3TBuSjgw+Wvv66bHlRkVSLXs+5ZuVKqbBQatYs8V61mNhH6YEHJoasVBo1kp5+WurZMyiLP++sWVKbNuWfY/lyG9VSsta/O+9MnHMeAABEm3NuhPe+INm+THxbbCMpfiDsWSVlqfSW9GEGrgtE2223JS+vXVtavTq7dUGFmjSxECdJb75p97316ydtvbWVrVtny9Ih7qWXbD740lavDu63W7tWuvzyYN8++1Qc4iRp002D9XvuYRBUAABqkqz+2d85d7akAkn3p9h/oXNuuHNu+MKFC7NZNSD7CpL+ccWcfHL26oFKO/FEC26XXBIMePLhh0GYi+nRQzrjDOmNN4KyPfcse76GDaWHHw62K9PTNv7cF14onX9++s8FAADRlYkgN1vSNnHbW5eUJXDOdZN0g6QTvPfrSu+XJO/94977Au99Qcv4m06AfLTJJtKGDcn3DR5sY91Xseszqk+s9+vRR9uyR4/E0SU/+ihxqoJly6Q1a6RRo6wlb6edyga2nXaynrVnnpl+PXr0sEFXYp59lsFPAACoCTJxj1wdSRMkdZUFuB8lnem9HxN3zF6yQU6O9t5PTOe83COHGiN2Y9Qrr0gffJA4ROLQoVLnzuHUC2nxvuwtjc8+K517bnrPj/36d9pJ+u23ja/HE09Yi5xk4S6+pQ4AAERTtd4j570vlHSppI8kjZP0mvd+jHPudufcCSWH3S+piaT/Oed+cs69U9XrAnnj4INt2bOnJYB4P/6Y/fqgUpxLHLVSkk46Kf3njx0rPfKITTtQFX/9a9CA++abqadEAAAA+aHKLXLVhRY51BgrVkgLFwYThZ15pvTyy8H+GTOkbbZJ/lzkhP/9z3J4gwZS794WzMISP/LlXntJhx1mUyQ0aBBenQAAwMYpr0WOIAfkGu+l4mIbFlGyb+bFxeHWCZExZIjdXhnvgQekq68Opz4AAGDjVff0AwAyyTmbguAvf7Ft76Xvvw+3ToiMww+XzjsvsWx2meGnAABA1BHkgFzVv3+wzoAnqISBA+3WyxdekHbdtWqDqAAAgNxEkANyVf36iZOGFxWFVxdESq1a0pdfSmedJdWrZ4OhMvgJAAD5hSAH5LKbbw7WY10tgUq45BJbnnaatHZtuHUBAACZQ5ADcl1stuf4+eWANJ1+ui2HDJEaNpSmTw+3PgAAIDMIckCuu+KK5OXr1kkvvRRMHgYk0bix3ScXs9NO4dUFAABkDkEOiIImTWz5zDO2HDbMJgY76yzp449Dqxai4ZdfpClTbH39+nDrAgAAMoMgB0RBrZJ/qr16STNnWoCL+eqrcOqESNl+e+taKdn9cj/9JI0YIY0fL226qXT88dKSJaFWEQAAVAITggNRsGiR1LJl6v3ffSftv3/26oNI+uIL6bDDyj/m//5PuuEGaZttslIlAABQDiYEB6KuRYvy93fubBOJz5mTnfogkg49VOrYsfxjHntM2nbbrFQHAABUAUEOiIqZMys+5sUXq78eiLSLLrLlDz9IgwdbQ+877yTOdCFJd98trVmT/foBAID00LUSiJJjj5U+/NDWx4612Z7btUs8Jkf/TSM3FBVJv/+euqfu669Lp5xi63vsIT3+uLTjjtZSd8kldj8dAADIjvK6VhLkgKhzLnH7iy+kQw4JpSqIvmXLpGbNUu/P0f8yAADIS9wjB+SzGTOku+4KtseNC68uiLymTS2s9e2bfP/48VLPntK8edmtFwAASESQA6Jum23sW/fatdY6xzdsZED37snLO3SQ/vc/qXVraeTIxH3XXGNvQeaqAwCg+hHkgHxRv741pdx2G/3fUGX77SdNmyaNHm1vp3Xryh4TH/aGDpX+9S9bv+yyrFQRAIAajSAH5KPmzcOuAfLAdttJu+9u6/XqSQ8/bGVffGFls2ZZC1y9elKXLsHzPv2UvyUAAFDdCHJAPlqyRCouDrsWyDOXXWatdIccYiNYxmzYEKz36ydNmSLVqmVhrqgo69UEAKBGIMgB+WTJkmD99tvDqwfyXr9+0iabJJZdc4105pnB9nHHMbk4AADVhSAH5JNmzezmJsnulQOq0fLliV0oW7Wyt+A779j2hx9Kc+ZIZ51lXTD/8Q8rnzpV+u23rFcXAIC8QpAD8s3QocH6mDHVc43Jk6XFi6vn3Iicjz6Sdt45GOQkdl9dzEsv2fKBB6T586XOne34rl0tDAIAgMojyAH5plbcP+spUxL3/fOf0pVXVu38M2ZI7dpJbdtKhYVVOxfywpFH2vSF9evb9nbb2d8TrroqOKZePVtuuaWFOUkaMsTmrTvoIOnAA63VbrPNslt3AACiiiAH5KNDD7XlzJlB2Zo10o03Sg89JA0bVvlzfvutfdPebjvbXrlSqltX6tPHymmhQ5zOnW06Au+TT18QC3aS9M039vaSpKVL7e308stZqyoAAJFEkAPy0WefWciKb5GbMSNY/+mnyp/zwAOTl993ny1btKj8OVGjDBxoy9atpVWrgnvpkjnzTOm665hcHACAVAhyQD6qVcvGhI/N0CzZpF8xEyZUz3VXrqye8yIv9OplrXNz5kh16kjHH2/bxcXBVAXxUyDee6/dfwcAAMoiyAH5bs4cWz71VFBW2a6V8ROFSdJ33yU/jqEIsRGcs2WtWtKiRTbaZcwJJ4RTJwAAch1BDshXsZEmYiNLxN909O23NjpFus45J1j3Xtp/f1uuXy9NnCi9957tW7u2anUGJB1+eOJ2/BQHAADAEOSAfNWjhy07dUqchuD66xP3p+PVV21Zem66unVtBMvY/XEHHii9/vrG1RcoUa+ehbcnnrDtxx+3AVInTCDUAQAQQ5AD8tWOOwbrsW/EknTLLbb87TfptNMqPs/EicH6TTclP2aXXYL1AQPSryNQjp49bXnRRVKjRlL79tb9cuxYAh0AAAQ5IF+1ahWs/+c/tmzaNHHc99deq/g8kyfbcs89g5uZSmvSJOjC2bZtZWsKJLXppjZpuJR4m+YuuyTOUQcAQE1EkAPy2bx5idtDhtgyvoXuuOOSP/fKK21W50cese34wVKS2WKL4LjSk4YBGyl+4NV4Dz2UOBArAAA1jfM52j+loKDADx8+POxqANEX34oW/+89vrywUKpdO9geP17q0CHxPKWPSaZrVwuLEyYkdu1ctCj9eeYWLbIx6FO1/kXdrbdKDRrYJGlIy9Ch9tbdYw9r/I1/a8yeLW21VXh1AwCgOjnnRnjvC5Lto0UOqClKh7D4+9pi3SLPPNPuoVuxouLnJ3PzzbbcaSebjNw5e7Rsmd69cyNG2LEvvljxsVF1221S3742eRrScsABUpcuFuIk+/HFtGkTvM3+9rdw6gcAQBgIckC+i/U/Kx2khg4NRq484ww77uWXpdtvl55/fuOu1alTsP6nPyXuu+SS1M/r18++iReU/MHpnHOk6dOj10Vz5UprHho0SNprL3tNffoEoe3774NjN9ssnDrmgX/+U7rssrLl/fvbfXWDBmW/TgAAZBtdK4GabPHi8rs8Nm0qLVtmwwamOxpleV0iU33elPeco46SBg9O79phWbHCEkQq111nATl+oBnJEsfJJ1dv3fLYuHFSx47J9/32mzUMAwAQZXStBJBc8+ap99WqZfe61aol/eMf6Z9z9erE7bffDtbXrJFWrbL12ITipcPdAQckbn/0UeLgLLmovBAnSaNGJYa42FCM/ftXX51qgA4d7NbNDRvsbfTYY8G+9u3DqxcAANlAkAOQXHGxjURZVCTtsEP6z2vY0L5V/+tf0rRp0gknBIHl//7PbnR69FH7Fl6/vgVFSere3a757bdlz/nOO1V+OdVi1aqyrYktW0oHHyydcoo1C0kWRmNGjZI+/dRu7mrZMnt1zVO1a0t16tj6hReWHc8nNvMGAAD5hiAH1HR77hmsd+8uHX98Zs571VXSdtvZeiywxO69u/jiIOTE3H13EIouvNCWDRrYfHhNm2amTpl2333B+sUXW/PQ7NnSl19K//uf9e2LH5njb38Lft677Sa9+mrZFkxU2bPPButXXCF9/nloVQEAoNoQ5ICabuRICx7FxdJbb1lXyK+/lsaOzdw1KroPrHHjxOkOHn1U+uknCzkdOtgImLlmyRK7702SunWTHnzQmofq1k087uqrg/XYnHxSMGH7SSdVbz1roHPPTRzw5PDDbUBW56yBuDxFRdLEiTaN4m+/BT2BK1JUFL2xeQAA0UaQA2o656wrYKw1zDnpwAPLziNX1WuUvs+tc2fphx+sC+aiRWWP32MPW9apI333nXTBBVWrw/LlmQ2n99xjywYNpE8+sW6iyTRvLt17r72GeLHWvKlTUw8Cg4128smJP9aXX7blu+/aGD+p1KljDakPPSTtvLN01lnlX8d7qXVre16DBswqAQDIHkatBJA9t95qXQorM1LjZ59Zi5eUfuDZZx+7R61Pn6DsxBOttfH++6Vrrkn/+qnEgu/atalDXLrnkCwB5Osk6CH65hvpoIMSy1q0kBYuTO9YyRqtd901sbF17NjEqRjjFRamN+0iAAAVKW/USoIcgNwXCzgbNgQjW6SyYUPiCJGxz7g995RGj7b1u+6ylrLYvXgb409/spbEZcs2/hzxdZKsda5t240/H8rlfTC2jlT27RR7mx14oE2tWHqC8X//26YCfO21sueuV88GYY0pKkq8VnlmzbLbSDf27wEAgPzF9AMAou3JJ21Zt67097/byJeTJ0vXXmszQzsXdL2MTYAeM2GCLXfeOSi7/nobQbOoKP06DBokjRlj6xs2SPPnS+edt3GvJ+bHHxO3t98+d0fozAPOJQ6K2qePNHy4/WpvuSUo//prm79+4sTE5191VdkQV7u2NfSuWyf9/HNieTrj2EybJm2zjfU0ztG/qwIAchQtcgBy35Ahwdxr5fngA2sWOfHExPKpU63PXOmQJ1kzS4MGNupkvIkTbcbpTp3sm3a85s3tRqtXX5V69qzUS0kqvktlkyYWEhs1suXLL1uC+Pln69+HKps7V9pqq+T7nngi8XbM33+3YFf6LdWrl/TUU2V7w65ZY7+6mIr+i/3Pf2xkzZjp06Vtt63oFQAAagq6VgKIthUrKp50u7T335eOOy6x7MAD7UaoZLyXXn/d7q1L1+zZqRNBZRQXp3dT1dixNoLnwIHWjFTZe+pWrbLrNGiwcfXMI6l+dOX9l/jUU9abdocdpFNPTX3c779b1pekBQtSTxdYuhdwfHlFPYgBADUDXSsBRNsmm1T+OV26lC3bemvruvjtt4nTAkj2zb4yIU7KTIiT7GYq74Nv/6l07Cj9+c/SG2/Yo7KaNLEJ29MdUz+PDR5sb4eY5csrbj3r3du6Y5YX4iRp882DQVr/+ldp5kxb994aV595xrbPPtuW++5ro2QWlPw3/dZbwbkeflg65hiblhAAgHgEOQDR8P33wfr779v9crNn231m/fuXPb5pU2np0sQ+cQ8+aBOeH3CA9MADiZN1l+eXX4Lg16SJLW+9dSNeRAUuv7xs2axZliBKGzeucueOD2933SWNGJE4Okc2rVwZ3rVLHHWUBSzv7bExfysoz+mn2/Ltt62rpHOW1x980LplNmwY3G/38cf2q//+e2t4HjzYynv3tvLBgzPTgxcAkF8IcgCiYb/9bFz34mLp2GMtCGy1lTVjHHhg4rGxaQeaNrWmjBtvtEC05ZaJx911V+KIFLvtZuf33gZTOekk6YUX7N6066+38y5YYPfs3Xxz5l/jTTfZt/vly20Cs08+kdq0saD6+efBcQ0aWPfKyjj44GD9rrvs51bRMInO2aO80Dh5cnDcttvaa5gzx0L2zjvbzy++qWvyZEtN229fufpHTJMm1vqWytq1tmza1B6S9Xo9/PDg3rvSv+LSY+MAAGo27pEDkB/mzLFvwhMnWrfKfJ6TrfRrGz9eat8+9fHe241d06aV3XfccdJ775UtnzUrcZCXpUttlM6BA63vYMxtt1XcOnnnnTZwy3//m1g+Z47Npp2niostk8+eHYxT8+abUo8etn7KKdLzzyfesvjf/9rArDEPPWR/t9hpJ9t+8UXpzDOzUn0AQA5gsBMAyCeXX243T8Vbvdr660nWWrliRXDP3c03S3fcYetffikdckjicxcutFmy4518cur78J5+2hJKt26pZ8VO18qVUuPGVTtHxMyfbzl5773L7lu3TjriCBspc/RoaffdrfzKKy3USdZY++STQQB87TXptNOst2ynThVf//TT7b6788+37eXLk3ctnTvXWhabNLGZN3bZJb//PgIAuYggBwD5ZPnyoD9ezOOPW5iLH8u+sNCWsSEQW7a0rqG//GLj5P/73zaFwtNPB9/qS4+f37hxeoOjxLqj/u9/diPYggVlj+nWTRowwLpgxrp1Hn649NlnwTnih3wsbeZMSy1XXpn+bNt5ZLvtpBkzEsteeSW4H0+yVsDSYeu336zhc906aYstyp73r3+V7r3X3i433GANsal6Dr/xRtCiCACofgQ5AMg3o0ZZd8kmTVKPVb/99taM0727bce32kllu0+Wtueedp1dd7UmmbfeKjuhmmRdJ2+4Ifk5pk+34RkffDAYllGycNikiTU5jR4dnOemm2x92TLrIvvrr7bdsqW1HMZbv94GvalBHntMuuii1Pt33NG6Yu6yi91TFxs9M5OShcWqmjLF3lrPPJNeqyIA1BRMPwAA+WavvaxVrrz556ZODULcJ58khjjJxt8vb8Kyp5+25a+/WmtZ9+6JzT+SdMstqUOcZM1IX3+dGOIka+m74gqb6Nw5G/0jFuIke22xECeVDXGSTcJWw8bl/7//s1a5K69MLI/dpjhxok0yfuGFqUPcscfaW2P58sQG3Hhnn22NvDHx+f2EEzay8iksXSr96U/WULz33vaWvOEGm09vzZrMXgsA8gktcgAQdQ8+aEMktmhhI2q2aiX99JONsR9TVJS8O+Lnn1v3xtIqanb55BMLabFRODbG999LnTvb+mabSUuWlH/8ySfbpO2lxd9nt3SpneuSS6R+/Ta+bhHhveXdXXe1e+tivVRjTj3Vfu2vvmrbEydK7dolHrN+vf0qDjqo7K/8998tULVqZY2rbdta+XPPSeecU/X6p5oUPd4xx0gffFD1awFAFNG1EgDyXWFh2da1LbYIWrLK+6wfPdqGVjz2WBsxY889y2/py6RDD7UBWGJ+/NFu2urQwUbIbNBAWrTIpmC47jr71u+9tfLFD9oSK4ufZuGoo2wStmHD7PWdeGIQZmfNkj780I7ZdttsvNJqFwtFnTpZni99G2Um/O9/wZx2XbtKn35atfPdcUdwP9769daDdtmyssd99ZXNMsJgKwBqGoIcACB3depk9+JJ5QfO0ubPD+YG7NHDxvYv7Z57LABKwT1/3btL77wTHFMDR86sihNOkN59N9i++mori8/Q5Zk2rew0goWFwd8O1q1LnJIhXg28LRJADcc9cgCA3DVypPTyy9K331buea1a2cRqUmKI++ILG0hFCkKcZN1N+/ZNDHGSdOmlla1xjfb224mh7V//ssbRLbawFrNdd00+0Onzz9uvrHSIu+mmxAbg+vVtasSdd7bgFpuCQbIWx3PPrfprKC62cwNAlNEiBwCIrjlzpDZtbL1JE7tJbN99rWUv/p7ALbeU5s0Lti+5xCY4328/254ypWzCQLkeftimNCxPfINoKvGtcaksWyY1axZsH3CADdayZo3V49hjy3++90G3zMmTg/sE16xJ3foHALmAFjkAQH7aaqtgUvJFiyzESfat/dVXpfbtrQtm6QnYLr7Yjo3dZ7fDDjZsonP2mDCheuv9yy/BCCQR9fe/W0DasCH1MalCXGwgVO/Tux2zaVO7Tp8+tj10qJ1j8mTpuOOCX9tPPwXPeestq2PXrjYO0MqVtj9+sJf/+z9bDhpkI30mGxwVAHIVLXIAgGhbtMgGL9lzz4qPnTVL+uabYBqF0k09MQUFNvDK++9b377y5turrMsvt2YkSTr+eOvq6b30yCP2eOklG4c/otavtx/bSScFZZ0723zwt99e9fM/+aSNh5PK1Vfb7Bxnn51Y7lx6t2BecYUNBCtJc+da19Hrr5c233yjqwwAG43BTgAASGXlSmmTTcqWT5liLXWSBcBYF86iIhshs3lzabfdKn+90kMv3n233bsXr39/azWMsEGDpE03lY48MvPnnjQp+NVszACrxcXSCy+Uf79drVp2XMzatdYCOGaMDfR6552Vvy4AVBZdKwEASKVJE5tETbJv7rEJzmNJQbLJ06+91m6q2mMP6bDDrKVu5Mj0r3P//UGIa9fOpleQyoY4ye7hi7hTTqmeECfZj69WrSBsbdggjRuXeEyvXjbzxPLlNlJmzNKl9ms45xybPuHRR6Xhw6UVK6THHguOiw9xknXP3GUXm37hn/+0aQ0LC6vn9QFAOmiRAwBg1Sr7xt+6tbR6dfrTEfz739KVV1Z83Ntv2zx2McOG2T16XbrYDV+SNHasDbjSsKFt77KL9NBDdpNXTZlA7dprLfDefLM9sjWfYZwNG2w2i/fftxa4Bg2Cxthkbr/dRt7MdStW2NsoNqArgGigRQ4AgPI0bmwhTpIaNQqacN55x0bCLD3Z+nnn2fKqq+ymrNdesyao556TFiwoe/7LLkvc3mcfW37xhS1vuskmQW/QwK4nWR++I46wut12m30Lf/vtqr7S3DR9ur2++++37dtvl/r1q77reW9DX8ZGSRkw4I9ddetK771nh+ywg42nE5sZ47jjrGdt/Bz2N99sY9csWRKUTZ1a/iAw2fbZZ9bNdZNNbKaPHP0bPoBKokUOAIB0jB5tE4offLB9w2/b1gJIKt26SR9/bGHwxBNtErVhw6Tff7fROMpzyCHSV1+l3v/kk9Z3sFaE/x47c6alpNq1U7c4XnONTR53//3SG29YuHvxRRt5ZPlySyfpKC62x223Sf/5jzVPlfb66/Y7igW8ClxySUL++8N//mPj2Zx9ts2dp+ees0nomzZNr67l+OILuy2zefP0nzNhgg3eGu/66617KIDcV16LnLz3OfnYe++9PQAAOauoyPtWrWKj6Cd/HHZYsP7WW5U7/5o13vfsmfrc9et7/+671fPaqtNrr1ndY6/j0EOD9R9/tGN22638n+sxx9jyxRcrvt5jj6U+T6rrPPBA2i8nvvqlH9Oe+TzYWLz4j+d89pn3Bx3kvXPeX3ih7f7rX73v1/X1P46fP2t9yvN+8EH6P+7jjrPn1K3r/fvvB+eYNy/9cwAIj6ThPkVeokUOAICquPRSu6mqXTsb2rBHj7Ijb0hV7882fbp06KGJI3dINqJm8+a5P7P1smU2+skPPyTfP3lyMMBM6Qndy7N8ufUZnDnT+jQefLCVjx5tXVFvuSX5815+OZiG4i9/kZ5+uuwxu+9urZ+xrrApeG8Dn9x0yjhNf+cnrWrQQh+sPUyFqptw3Og/9dCek99Ieo5h2lf76seEsm01XTO1bdLjL7/cbqFM5rLLbCaLmJNPtlFEJWnIELvtcpNN7EcHILfRIgcAQDYVFXn/etC64pcty+z53367bDPNihWZvUamzJzp/UUXla1vly7B+pNPJn9uUZH3Dz7o/axZtr1hg/cdOyae5/DDvf/ii8Sym24qe7133/X+pZe8Ly5Ofq0rr/R++nTvn346eTPYwoXejx3rfdeu3i9aZM8pLraWth49ym9BTPLopaf87Yd+5vepM9IX1q77R/ldui7huBfdmV7yfsgQ+1HG/9jmz7cqrF/v/aRJ3q9c6f3IkWUvN3Nm4kvdf38rHzUqvV/h4MHeb7+9XQ9AdqmcFrnQA1uqB0EOABBpa9d637u392PGVM/5P/qo7Df2+JCyYUOwvm6dJYFsW726bB3/8hdLBIWFVTt3cXF6oemqqyp/7hdfrPi8ycJ0kkdzLfSS9z31SsXHv/++v/FG7x86aFBiuXPe//77H9W7886KT/Wvf3nfsqX3n3xS9uXNnRsct2ZN2f0rV9pyzRrvJ05MPO9f/+r9hAnev/qqHTNihPd//rP3L7zg/ZIllf9R56viYvsZxX6WxcWJ/yTzwZo19p7o1cv+kNC0qffvvRd2rfIPQQ4AgHz05ZcWVGLfsg85xFqd4r95e+9969bB9mOPWQisbuPHJ9ajQwdrmUzVIrYx7r03MbCtXJn4s6iqlSu9fyWNABZ73H+/tSIWF3s/ZIhfv7boj12HHup98foNib+L+Ee3bok/m1WrrDUy/phff/Xe22H1tNa30tySXcW+vy7yd6uPl7z/z38qfmnxt28uWpT+S0zncdFFFlomT/Z+u+28P+UU+9K/ww52b+Datf6P15GvHnkk+c+mqCjsmm28r75K7/c/dqy1Eq9e7f0zzyQ/xjnvb745eC8gNYIcAAD57IUXUn+r+uab5OXljXaxbl3VWswWLEi8Vqa7lsasXu39bbd5//PPidcePTqz1/n5Z++7d7fXsu++ia9t0qTKn6+42Fr9/vtfSzkTJ6Y+9vvvE6+3fLk1fZVsf3frYP/7sWf9sT2886VpVWHt2sqFs3XrvL/vvswGPsn7c8+Nq9T8+dbfc+HCP4oGD7a/V0TBSy9ZT9/yXu+AAWHXMj3r19vbtLjY+w8/zPzvPfb405/sZxLX4Owfv2+Jb6bf//ijwDHHeD97tv1xYM0aey8WFdlj/frwfkbZQpADACDf3X9/xd+Y4rcPPTT5eeK7DB57rPczZtg3J+8t3MXud4vdJxYT64N3ySWJ19mYoJPLCgvtnrxsGjWqct+O77zT+zfftFFAR45MedriYu+vuCJ4WufO3u+8s/e33mrbvXuX7Q44a5b3c+bYrYGSdaeLb1mLvzW0Mo9tNS2hYAvNS9i/YF6R94MGZbTvXlV798b89FPy13TvvfZ3lB49rAtqrLx37yCAFBXZP7lcuv9w6VKr51ZblX1Nl19uf0tYscJaXL237ruxLqQnnFD2OddcY915BwzwfupU70/rMtOffvK6kv3FJQ879r0bhv7xxMv1oL9Zt/r7dXXCMcker78e1k+r+hHkAADId0VFQViLhaz4bzqxb9tFRUFZr17B+vnn27f0VN+UatcuWzZ3bnD9zTdP3Lf99vnddy7b1q0r+/O/+eZgfckSm+Ii1e/v3XctPSxbZqOfTJtm5y0q8oUnnOiL69f3vnlz60pa+vc2bZqNspLm/Z6rVnn/8cfBaVautEBYVOT9uHHeN2ni/bi73/RjB0/3jbXCb60ZSetcV+v8zhrr/6Iny+4fOjTptYuLvf/3vy3Hlic24Evz5sEpX3gh6PpYVBSEk2SGDPH+6qu9v+OOxGo1buz9aadZC1JppWfC+MtfErf/9CcLRyNGeN+/v7WAXnRR5Vud5s+3zPvii94//LD9TF55xQLY6tUW1D780LpALl4ctCJeeWXqj4CjjrLfabJ7KtPyww+p35uSP1Mv+K/VpdxjSof7ZGFu4MDEsqeesn8aRUXW3fUf//C+T58qvI4QEOQAAKiJCgu9Lyiwb4TxTj653C9MvkWL8vfHP374wUadbNAgsby6ulPWZLEbzbp0CUYpLR26/vzn9H93l19uAT7ZvlWr7Hzvvlt231NPWSvhIYdYi9/UqVZ+112WBMaPD+qzcmXwfjrhBGuhLadOtbXBj1P7tOp//YljvJTQE7NMz1fJ+7vvDqpY0WOPPexH2q6dbXfvusJvpsX+0Uft/L/84v2oPYOf2cH64o/nxrJxRY46Kv1fUenH8uUWilP9jeTiizf+3PGPU0+1ZefOVfx7TLqDEsU9fnhkmPePPppyf592g3yfPt4vHT7Rf33jYD/oiq8rPG0drffN9Ls/Qy/6j9UtYedMtfEnaZD/6KGxVXih1YcgBwAAEu2zT+pvPbE/V8+aZd/kzjgj2Pfaa94PH578ef/9b7ivCdZyN3++NUHMmmVNEOl8ge7QoWzZZZdlJhWk+5gxw15DUZENuRm372ft6iXvt9A8P0tBn7999b2XrLXo5Zcrd7kLLrDlOedYy1Xp/fO0RVon6tfgqkq1mhUXB7Nc9Oxp9ysuX263S5Z3qXaa4A/UV17yfuut7W8lf/2r93vtlXicU5E/XS/51bUa++012R+uT31/XeTbaop3Kko4to5s4vnbbw/KTjghqGelB2d54QXv69TxfrPNyr6AE0+0e1jHj/e+b1/748/ChdaFu+SYDXMWJD/vNtsknuu11xK25+5xlD9fA30drfcnnuj9sGHe76Txfg+NqtSb4tenf6jkC65+BDkAAFC+2JeZfv3SO379evs2Gf9FaOnS6q0jNt7kyXZD3JQpFrj//vfg9xZ/31l819vYY8stbd/06dZ3cGNCWsOGidsrV3q/997ef/BB6n5uM2cGcwiWKCz0fvq04oRWu04a7iXvu+tNv1b1/Mo3P/arBzzjN4z5zd974/KSw+weq759ve/UyUZgLC3+XrdLlSTZlXoUnnt+sJ3u3AszZljfyXIUFyfev/fee97f3C5xSowj9JFPdt/YgUpjaMk2bYLBe+Ifkyf74nkbMTXIqFHWSnzDDamveccdlTtnMkOGWPKt6PXtt1/5zZ716nl/0kn+tRt+8sfqPT92p+DGvuLC3BtWtLwg52x/7ikoKPDDhw8PuxoAANQMRUXSsmXS5ptX7nkPPiidfrrUunX11AvV5/vvpVGjpIsvTiwvLJTq1rX1Xr2kgQMT969eLTVsKDknrVolPfSQdNpp0oYN0sKF0hZb2KNBA2nBAmm77ezY4mJp6VKpWTOpVq2q1//446X33qvcc1atkho1Srl78sRiLdr1UO23/msrmDVLatNGEyZId+3/ju7p+Jy2/GCgtOmmtv/zz6XDD09+siOPlD76KNhesEBq1SrYvuEG6c47pXXrpH79pLPOStwf89VX0iGHJL3EUHXWk6d9qk47rlD3glna5sSCYGfLlvb7qKwLLpDuu09q0sSe36ZN4v769a3OqVx8se3v3t1+3+ecY7//THn0UbtGjx7SoEHS0KHSGWfY7yqZli2l+fOlOXPKvpYIcM6N8N4XJN1HkAMAAEAkXXqphaCYhg2lNWtSH1+/vrR2rfT669ITT0innCKNHy99/bUFrWnTgmNvvlm67baK69C1qzRkyEa/hASDB0u//SadeqoFuOuuC+p0ww3SHXdIPXtagEnl6KOl22+X9tnH2pkkC1LeW9jp21d68UXp7LOl+++3sDl5sp17Y51zjvT889Izz0jnnbfx56mKJUvs5/L119Lw4dK330qbbRZOXTKIIAcAAID847303HPSP/9pQad0iJg/31qap0+3FjJJat/ewlJ5Zs+Wttoq/XqsXy/16WPPmT1bOv98aa+9yh530EHSu+/a9ffbLyiPBa1UunaVPv00sWzGDGvtjHfAARZgNtbUqdIOOySWnX229PTTdr2777bX2KWL1KGDtXDuvPPGXw8VIsgBAACgZps0Sdpxx2C7Uydp7lwLJp07S488ItWuLY0ZY2GvqoqLLax16WKB67LLpDp1gv1r1kivvWbdAmvXlm65xQJpvHPPla65Rtptt9TXWL/eurFm2vjxdt62bTN/bqSNIAcAAADccot1O7zjDunGG8OuDVCh8oJcnWSFAAAAQN656SbphBOkvfcOuyZAlWVgyCAAAAAgAurUIcQhbxDkAAAAACBiCHIAAAAAEDEEOQAAAACIGIIcAAAAAEQMQQ4AAAAAIoYgBwAAAAARQ5ADAAAAgIghyAEAAABAxBDkAAAAACBiCHIAAAAAEDEEOQAAAACIGIIcAAAAAEQMQQ4AAAAAIoYgBwAAAAARQ5ADAAAAgIghyAEAAABAxGQkyDnnjnbO/eacm+Scuy7J/vrOuVdL9g9zzrXNxHUBAAAAoCaqcpBzztWW1E/SMZI6SjrDOdex1GG9JS3x3reT9KCke6t6XQAAAACoqTLRIrevpEne+yne+/WSXpHUvdQx3SU9W7I+SFJX55zLwLUBAAAAoMbJRJBrI2lm3PaskrKkx3jvCyUtk9Q8A9cGAAAAgBonpwY7cc5d6Jwb7pwbvnDhwrCrAwAAAAA5KRNBbrakbeK2ty4pS3qMc66OpKaSFpc+kff+ce99gfe+oGXLlhmoGgAAAADkn0wEuR8l7eic2945V0/S6ZLeKXXMO5LOK1k/RdIQ773PwLUBAAAAoMapU9UTeO8LnXOXSvpIUm1JA733Y5xzt0sa7r1/R9JTkp53zk2S9Lss7AEAAAAANkKVg5wkee8/kPRBqbKb49bXSjo1E9cCAAAAgJoupwY7AQAAAABUjCAHAAAAABFDkAMAAACAiCHIAQAAAEDEEOQAAAAAIGIIcgAAAAAQMQQ5AAAAAIgYghwAAAAARAxBDgAAAAAihiAHAAAAABFDkAMAAACAiCHIAQAAAEDEEOQAAAAAIGIIcgAAAAAQMQQ5AAAAAIgYghwAAAAARAxBDgAAAAAihiAHAAAAABFDkAMAAACAiCHIAQAAAEDEEOQAAAAAIGIIcgAAAAAQMQQ5AAAAAIgYghwAAAAARAxBDgAAAAAihiAHAAAAABFDkAMAAACAiCHIAQAAAEDEEOQAAAAAIGIIcgAAAAAQMQQ5AAAAAIgYghwAAAAARAxBDgAAAAAihiAHAAAAABFDkAMAAACAiCHIAQAAAED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fMgAAAAAAUUHXSgAAAACIGIIcAAAAAEQMQQ4AAAAAIoYgBwAAAAARQ5ADAAAAgIghyAEAAABAxBDkAAAAACBiCHIAAAAAEDH/D3LwnJU0EpTxAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "i2 = list(range(result2.shape[0]))\n",
    "i3 = list(range(result3.shape[0]))\n",
    "plt.plot(i2, np.cumsum(result2) / i2 - mean_length_2, color='blue')\n",
    "plt.plot(i3, np.cumsum(result3) / i3 - mean_length_3, color='red')\n",
    "plt.ylim(-0.5, 0.5)\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Histogramme\n",
    "\n",
    "approche précédente en bleu; nouvelle méthode en rouge\n",
    "\n",
    "L'histogramme est imperceptiblement décalé vers la droite…"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 1080x720 with 1 Axes>",
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/QXc/1t1b3b11/vz5xX8KAACADTBPgHsyyd1VdVdVvSjJA0kuHjjnYpI3zF7fn+T93d3ZGzb5Z5Okqr4syTck+aVVFA4AALBpbhrgZs+0PZTkiSQfTfLu7r5UVY9U1Wtnp70tyUur6nKS705ybamBR5N8eVVdyl4Q/Nfd/eFV/xAAAACboPYaZafH1tZWb29vr7sM4IiqkqU+Xpa+EMY1923vzwfARqiqp7r7BY+eJcc/iQkAAAArIsABAAAMQoADAAAYhAAHAAAwCAEOAABgEAIcAKzZZLI3weTNtuSF+6bTtZYOwAk7t+4CAGDT7ezMeeIhqwhcC3YAbAYdOAAAgEEIcAAAAIMQ4AAAAAYhwAEAAAxCgAMAABiEAAcAozhkvYHOHOsPWGsA4MywjAAAjOKQ9QbqkKUFDj0JgDNBBw4AAGAQAhwAAMAgBDgAAIBBCHAAAACDEOAAAAAGIcABAAAMQoADAAAYhAAHAAAwCAEOAABgEAIcAADAIAQ4AACAQQhwAAAAgxDgAAAABiHAAQAADEKAAwAAGIQABwAAMAgBDgAAYBACHAAAwCAEOAAAgEEIcABw1k0mSdXi23S67soBOODcugsAAI7Zzs5y11WttAwAjk4HDgAAYBACHAAAwCAEOAAAgEEIcAAAAIMQ4AAAAAYhwAEAAAxCgAMAABiEAAcAADAIAQ4AAGAQAhywetNpOpXUEttksu7qAQBOrXPrLgA4g3Z3U+l0r7sQAICzRQcOAABgEAIcAADAIAQ44Lqm0+UeY0s8ygYAcBw8Awdc1+5ulnuOrZKdnVVXAwCADhwAAMAgBDgAAIBBCHAAAACDEOAAAAAGIcABAAAMQoADgIFNJsst9zGdrrtyAJZhGQEAGNiyS3ZcW7MRgLHowAEAAAxCgAOu62OZLjc2azJZd+kAAGeSIZTAdU2zm3SvuwwAAGZ04AAAAAYhwAEAAAxirgBXVfdW1dNVdbmqHj7k+K1V9a7Z8Q9U1XTfsT9RVT9bVZeq6her6nevsH4AAICNcdMAV1W3JHk0yWuSXEjy+qq6cOC0NyX5VHe/PMlbk7xldu25JP82yZu7+xVJviXJb62segAAgA0yTwfuniSXu/uZ7v5ckseT3HfgnPuSvH32+j1JXlVVleTVST7c3b+QJN39ie7+7dWUDgAAsFnmCXC3JXl23/srs32HntPdV5N8OslLk3xVkq6qJ6rqg1X1vUcvGQAAYDMd9zIC55J8U5KvS/LZJD9TVU9198/sP6mqHkzyYJLceeedx1wSAADAmObpwD2X5I5972+f7Tv0nNlzby9O8onsdev+a3d/vLs/m+R9Sb724Dfo7se6e6u7t86fP7/4TwEAALAB5glwTya5u6ruqqoXJXkgycUD51xM8obZ6/uTvL+7O8kTSb66qn7PLNj9mSQfWU3pAAAAm+WmQyi7+2pVPZS9MHZLkh/r7ktV9UiS7e6+mORtSd5RVZeTfDJ7IS/d/amq+pHshcBO8r7u/vFj+lkAAADOtNprlJ0eW1tbvb29ve4ygCSpSk7ZZwSwGnP98fYZALAWs3lDtg47NtdC3gAAAKyfAAcAADAIAQ4AAGAQAhwAAMAgBDgAAIBBCHAAAACDEOAAAAAGIcABAAAMQoCDDTCd7q3Hu+gGAMDpcm7dBQDHb3c36V7iQiEOAOBU0YEDAAAYhAAHAAAwCAEOAABgEAIcAADAIAQ4AACAQQhwAAAAgxDgAAAABiHAAQAADEKAAwAAGIQABwAAMAgBDgAAYBACHAAAwCAEOAAAgEEIcAAAAIMQ4ACAw00mSdXi23S67soBzqxz6y4AADildnaWu65qpWUA8AU6cAAAAIMQ4AAAAAYhwAEAAAxCgAMAABiEAAcAADAIAQ4AAGAQAhwAAMAgBDgAAIBBCHAAAACDEOAAYANNJknVctt0uu7qATbXuXUXAACcvJ2d5a+tWlkZACxIBw4AAGAQAhwAAMAgBDgAAIBBCHAAAACDEOBgA3ws0+WmmptM1l06AAD7mIUSNsA0u0n3ussAAOCIdOAAAAAGIcABAAAMQoADAAAYhAAHAAAwCAEOAABgEAIcAADAIAQ4AGAhk8mNl5BMrn9sOl1r6QDDsw4cALCQnZ2bnFDXX3ryWsADYDk6cAAAAIMQ4AAAAAYhwAEAAAxCgAMAABiEAAcAADAIAQ4AAGAQAhwAAMAgBDgAAIBBCHAAAACDEOAAAAAGIcABAAAMYq4AV1X3VtXTVXW5qh4+5PitVfWu2fEPVNX0wPE7q+ozVfU9K6obAABg49w0wFXVLUkeTfKaJBeSvL6qLhw47U1JPtXdL0/y1iRvOXD8R5L8xNHLBQAA2FzzdODuSXK5u5/p7s8leTzJfQfOuS/J22ev35PkVVVVSVJVfzHJx5JcWknFAAAAG2qeAHdbkmf3vb8y23foOd19Ncmnk7y0qr48yd9L8vePXioAAMBmO+5JTH4oyVu7+zM3OqmqHqyq7arafv7554+5JAAAgDGdm+Oc55Lcse/97bN9h51zparOJXlxkk8k+fok91fVP0zykiSfr6r/193/cv/F3f1YkseSZGtrq5f4OQCA02IySfaepHiBTpLDD33h2p2dYygK4GyYJ8A9meTuqrore0HtgSTffuCci0nekORnk9yf5P3d3Um++doJVfVDST5zMLwBAGfMDQJYVdI3+qva6wQ/APbcNMB199WqeijJE0luSfJj3X2pqh5Jst3dF5O8Lck7qupykk9mL+QBAACwQtU3/Guwk7e1tdXb29vrLgPOlpv+lTfAyZirA+fzCthwVfVUd28dduy4JzEBAABgRQQ4AACAQQhwMIjpdG9k0TIbAABnwzyzUAKnwO7uER4LEeIAAM4EHTgAAIBBCHAAAACDEOAAAAAGIcABAAAMQoADAAAYhAAHAAAwCAEORrLsYnCTyborBwBgBawDByM50mJwAACMTgcOAABgEAIcAADAIAQ4AACAQQhwAAAAgxDgAAAABiHAAQAADEKAAwAAGIQABwCcHpNJUrX4Np2uu3KAE2EhbwDg9NjZWe66qpWWAXBa6cABAAAMQoADAAAYhAAHAAAwCAEOAABgEAIcAADAIAQ4AACAQQhwAAAAgxDgAIATY51ugKOxkDcAcGKs0w1wNDpwAAAAgxDgAAAABiHAAQAADEKAAwAAGIQABwAAMAgBDgAAYBACHAAAwCAEOAAAgEEIcAAAAIMQ4AAAAAYhwAEAAAxCgAMAABiEAAcAADAIAQ4AAGAQAhwAAMAgBDg4QdNpUrXcNpmsu3oAANbt3LoLgE2yu5t0H+EL1MpKAQBgQDpwAAAAgxDgAIDxTSbLjU+fTtddOcBCDKEEAMa3s7PcdWVsOjAWHTgA4NRbtsGmyQacNTpwAMCpt2yDLdFkA84WHTgAAIBBCHAAAACDEOAAAAAGIcABAAAMQoCDkzadLj+V2mSy7uoBAFgjs1DCSdvdTbrXXQUAAAPSgQMAABiEAAcAADAIAQ4AAGAQAhwsYdl5SMxBAgDAUcwV4Krq3qp6uqouV9XDhxy/tareNTv+gaqazvZ/a1U9VVW/OPvnn11x/bAW1+YhWXTb2Vl35QAAjOymAa6qbknyaJLXJLmQ5PVVdeHAaW9K8qnufnmStyZ5y2z/x5P8he7+6iRvSPKOVRUOAACwaebpwN2T5HJ3P9Pdn0vyeJL7DpxzX5K3z16/J8mrqqq6++e7+3/P9l9K8qVVdesqCgcAANg08wS425I8u+/9ldm+Q8/p7qtJPp3kpQfO+ctJPtjdv7lcqQAAKzaZLPdQc9XeA9EAJ+xEFvKuqldkb1jlq69z/MEkDybJnXfeeRIlAQAb4lpGO9zODa+74bPL1/+iAMdmng7cc0nu2Pf+9tm+Q8+pqnNJXpzkE7P3tyd5b5Lv7O5fPuwbdPdj3b3V3Vvnz59f7CcAALiBnZ3lJp7a3V135QAvNE+AezLJ3VV1V1W9KMkDSS4eOOdi9iYpSZL7k7y/u7uqXpLkx5M83N3/bUU1AwAAbKSbBrjZM20PJXkiyUeTvLu7L1XVI1X12tlpb0vy0qq6nOS7k1xbauChJC9P8gNV9aHZ9gdW/lMAAABsgOruddfwRba2tnp7e3vdZcANVe0Nrzn5iwE4KTf9uPZ5DhyTqnqqu7cOOzbXQt4AAACsnwAHAAAwCAEOAABgEAIcAADAIAQ4WNZ0uvcA+6LbZLLuygEAGNS5dRcAw9rdNfsYAAAnSgcOAABgEAIcAADAIAQ4AACAQQhwAAAAgxDgAAAABiHAAQAADEKAAwBYxmSy3Hqg0+m6KwcGZh04AIBl7Owsd13VSssANosOHADAIZZtsGmyAcdJBw4A4BDLNtgSTTbg+OjAAQAADEKAAwAAGIQABwAAMAgBDqbThZ9O79Te0+0AAHCCTGICu7tJ90KXVCW9czzlAADA9ejAAQAADEKAAwAAGIQABwAAMAgBDgAAYBACHAAAwCAEOAAAgEEIcGysa8u/JQsvA2cJOACWN5ks/h+eqr3/cAEbzzpwbKzfWf6tFl4GDgCWt7Oz3HXX/tYR2Gg6cAAAK7Zsk02jDbgZHTgAgBVbtsmWaLQBN6YDBwAAMAgBjuFNp8lOTRceo9IxIwkAAzH5CRBDKDkDdneTaXbNRALA2WbyEyA6cAAAAMMQ4AAAThEjJYEbMYQSAOAUMVISuBEdOACAs8yidHCm6MABAJxlFqWDM0UHDgAAYBACHAAAwCAEOAAAgEEIcJwK0+nyz1dPJuuuHgDWz1wlsBlMYsKpsLubdB/hC3jGGoANZ64S2Aw6cAAAAIMQ4AAAAAYhwAEAAAxCgAMA4HDLzoxiVhQ4NiYxAQDgcMvOjGJWFDg2OnAAAACDEOAAAAAGIcBxuiy7orfVvAEA2ACegeN0OfKK3gAAcHbpwAEAAAxCgGNllh39aAQkAKyX1QJgHIZQsjJGPwLAmFa+WsC1RLioyWT5YmBDCHAAACzl+jltZ65rX5DVrB8HN2UIJQAAS9nZ2Rt9s8yWvHBI5k6WHMtpPCcbRAeOG5tO98ZGzqGT5Kh/ceZhOADYCIePlDx05wtUHfLYhu4dG0KA48YWeLDt0A9TAABgZQyhBAAAGIQAtwnM7w8AnHVLroWwU1OP2DGUuQJcVd1bVU9X1eWqeviQ47dW1btmxz9QVdN9x75vtv/pqvq2FdbOvK4Ng5xzm046ldm2uyPrAQCnyqFZbXfnC7+/XGebTg75vSe7c/2KNOeUAC9wlL9HFxo5zE2fgauqW5I8muRbk1xJ8mRVXezuj+w77U1JPtXdL6+qB5K8JclfraoLSR5I8ookX5nkp6vqq7r7t1f9g7A61nMDAE6zlS4VN+eadctO1raz+CVfsLvc93wB6+udKfN04O5Jcrm7n+nuzyV5PMl9B865L8nbZ6/fk+RVVVWz/Y93929298eSXJ59PQAAWL8510L4ohFKC2yHdf3m3SrLX7uS9uGClu026jQuZp4Ad1uSZ/e9vzLbd+g53X01yaeTvHTOa4ewrvb3Ub7vtS3x2BsAwFEsu+bdqWh8Lfl84KK/xC741M5q8+UGpcdTsYxAVT2Y5MHZ289U1dPrrGfVdnfn6swfm9r3v/NYd70HvCzJx9ddBMy4HzlN3I+cJu7HY7LW38mW+KVw2XpX/HPOfz+esl9897luS2WeAPdckjv2vb99tu+wc65U1bkkL07yiTmvTXc/luSxOWphw1TVdndvrbsOSNyPnC7uR04T9yOnyVm/H+cZQvlkkrur6q6qelH2JiW5eOCci0neMHt9f5L3d3fP9j8wm6XyriR3J/nvqykdAABgs9y0A9fdV6vqoSRPJLklyY9196WqeiTJdndfTPK2JO+oqstJPpm9kJfZee9O8pEkV5N8lxkoAQAAllNtvnhOsap6cDbEFtbO/chp4n7kNHE/cpqc9ftRgAMAABjEPM/AAQAAcAoIcKxdVe1U1S9W1Yeqanu273VVdamqPl9VW/vOnVbVb8zO/VBV/av1Vc5ZdJ378R9V1S9V1Yer6r1V9ZJ9539fVV2uqqer6tvWVjhnziL3os9GTsJ17skfnt2PH6qqn6yqr5ztr6r657PPxw9X1deut3rOkgXvxW+pqk/v+3z8gfVWf3SGULJ2VbWTZKu7P75v3x9L8vkkP5rke7r72h/OaZL/1N1/fA2lsgGucz++Onuz616tqrckSXf/vaq6kOTfJ7knyVcm+ekkX2WyJlZhwXtxGp+NHLPr3JNf0d2/Pnv9d5Jc6O43V9WfS/K3k/y5JF+f5J9199evoWzOoAXvxW/J3u+Sf34dtR4HHThOpe7+aHefqQXdGVd3/2R3X529/bnsrWmZJPcleby7f7O7P5bkcvbCHByLG9yLsBbXfmGe+bIk1zoD9yX5N73n55K8pKr+8IkXyMa4wb145ghwnAad5Cer6qmqenCO8++qqp+vqv9SVd983MWxcW52P/71JD8xe31bkmf3Hbsy2wersMi9mPhs5Pgdek9W1T+oqmeTfEeSa8PTfD5ynBa5F5PkG6vqF6rqJ6rqFSdd7KoJcJwG39TdX5vkNUm+q6peeYNzfzXJnd39p5J8d5J3VtVXnESRbIzr3o9V9f3ZW9Py362rODbKIveiz0ZOwqH3ZHd/f3ffkb378aF1FsjGWORe/GCSSXf/yST/Isl/XEO9KyXAsXbd/dzsn7+W5L25wRC02VC1T8xeP5Xkl5N81UnUyWa43v1YVW9M8ueTfEd/4eHh55Lcse/y22f74MgWuRd9NnIS5vjv9b9L8pdnr30+cmwWuRe7+9e7+zOz1+9L8iVV9bITLHflBDjWqqq+rKp+77XXSV6d5H/c4PzzVXXL7PUfSXJ3kmdOolbOvuvdj1V1b5LvTfLa7v7svksuJnmgqm6tqruydz/+95Oum7Nn0XvRZyPH7Qb35N37TrsvyS/NXl9M8p2z2Si/Icmnu/tXT7RozqRF78Wq+kNVVbPX92Qv/3ziZKterXPrLoCN9weTvHf25+pcknd293+uqr+UvTb3+SQ/XlUf6u5vS/LKJI9U1W9lb5bKN3f3J9dUO2fP9e7Hy0luTfJTs2M/191v7u5LVfXuJB/J3nC27zIDJSuy0L0Yn40cv+vdk/+hqv5o9u673SRvnp3/vuzNQHk5yWeT/LWTL5kzatF78f4kf7Oqrib5jSQP7BtJMyTLCAAAAAzCEEoAAIBBCHAAAACDEOAAAAAGIcABAAAMQoADAAAYhAAHAAAwCAEOAABgEAIcAADAIP4/6tSRd/Ao6icAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.hist(result2, 50, density=True, histtype = 'step', color='blue')\n",
    "plt.hist(result3, 50, density=True, histtype = 'step', color='red')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Intervalle de confiance par les quantiles\n",
    "\n",
    "Intervalle très légèrement décalé vers la droite (longueurs plus importantes) :\n",
    "\n",
    "```[516.75747378 527.97941006] > [516.70371097, 527.6874126]```"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[516.75747378 527.97941006]\n"
     ]
    }
   ],
   "source": [
    "# Intervalle de confiance par les quantiles\n",
    "\n",
    "print(\n",
    "    np.quantile(result3, [0.025, 0.975])\n",
    ")\n",
    "\n",
    "# >>> [516.75747378 527.97941006]"
   ]
  },
  {
   "source": [
    "### Probabilité de dépassement du seuil de 525m\n",
    "\n",
    "La probabilité de dépassement du seuil de 525m est plus grande que précédemment (0.1546 > 0.1297)"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.1546\n"
     ]
    }
   ],
   "source": [
    "# Probabilité de dépassement du seuil de 525m\n",
    "\n",
    "print(\n",
    "    np.mean(result3 > 525)\n",
    ")\n",
    "\n",
    "# >>> 0.1546"
   ]
  },
  {
   "source": [
    "<br><br>"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2021.10\n",
    "10. Qu'adviendrait-il selon vous si on rendait également aléatoires les autres paramètres du modèle $\\sigma^2$ et $a$ ?"
   ]
  },
  {
   "source": [
    "## Réponse 2021.10\n",
    "\n",
    "La covariance aurait une dépendance aléatoire, donc il pourrait y avoir de très grandes pentes."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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