08-Chaine_de_Markov.ipynb 305 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chaine de Markov"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 15,
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   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "np.set_printoptions(precision=3,suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attention, lorsqu'on part d'une matrice symétrique (ou hermitienne), pour obtenir la diagonalisation dans une base othornormale il faut utiliser `np.linalg.eigh` (h-comme hermitienne). Vérifiez-le!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Définition intuitive d'une chaine de Markov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "***NB:*** Le mot \"chaine de Markov\" (tout court) est pour nous synonime de \"chaine de Markov homogène en temps\". \n",
    "\n",
    "On considère un ensemble dénombrable $E$ : l'ensemble des \"états\". Par exemple   $E=\\{0,1,2,3,4,5\\}$.      On considère aussi que les éléments de $E$ sont des sommets d'un graphe, dont les flèches sont pondérées.  \n",
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    "\n",
    "![graph_ponder](./img/graph_ponder.png)\n",
    "\n",
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    "Une chaine de Markov $t\\to X_t$  est un processus aléatoire qui se ballade en suivant le graphe. Au temps $t=0$ elle se trouve en une sommet $X_0$ donné.  Si au temps $t$ elle se trouve en $X_t$, elle tire une des flèches partant de $X_t$,  avec une probabilité proportionnelle aux pondérations, et elle suit cette flèche pour arriver à un nouvel état $X_{t+1}$\n",
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    "\n",
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    "Notations:\n",
    "\n",
    "* Le poids mis sur la fléche allant de $x$ à $y$ est noté $P(x,y)$. \n",
    "* Quand il n'y a pas de flèche entre $x$ et $y$, on note $P(x,y)=0$.  \n",
    "* La matrice $\\big ( P(x,y) \\big)_{x,y \\in E}$ est appelée matrice de transition.\n",
    "\n",
    "\n",
    "***Remarques:*** Ici, les étiquettes que l'on a mises sur les états n'ont aucune importance. On aurait pu tout aussi bien prendre $E=\\{A,B,C,E,D,F\\}$. Dans les exemples suivants, le fait que les indexes soient des entiers aura son importance.   "
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   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 21,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.    0.    0.    1.    0.    0.   ]\n",
      " [1.    0.    0.    0.    0.    0.   ]\n",
      " [0.    1.    0.    0.    0.    0.   ]\n",
      " [0.    0.6   0.    0.    0.4   0.   ]\n",
      " [0.    0.244 0.024 0.    0.    0.732]\n",
      " [0.    0.    1.    0.    0.    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "def premier_chaine():\n",
    "    P=np.zeros([6,6])\n",
    "    P[0,3]=4\n",
    "    P[1,0]=2.1\n",
    "    P[2,1]=2.5\n",
    "    P[3,1]=3\n",
    "    P[3,4]=2\n",
    "    P[4,1]=2\n",
    "    P[4,2]=0.2\n",
    "    P[4,5]=6\n",
    "    P[5,2]=7.3\n",
    "    sumLine=np.sum(P,axis=1)\n",
    "    \"\"\" P[i,j]=P[i,j]/sumLine[i] \"\"\"\n",
    "    P/=np.expand_dims(sumLine,axis=1)\n",
    "    return P\n",
    "\n",
    "print(premier_chaine())"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 22,
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   "metadata": {},
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   "outputs": [
    {
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     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 1440x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    }
   ],
   "source": [
    "def markov_from_P(t_max,P,x0):\n",
    "    X=np.zeros(t_max,dtype=np.int)\n",
    "    X[0]=x0\n",
    "    for t in range(t_max-1):\n",
    "        X[t+1]=np.random.choice(a=range(len(P)),p=P[X[t],:])\n",
    "    return X\n",
    "\n",
    "\n",
    "t_max=300\n",
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    "P=premier_chaine()\n",
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    "X=markov_from_P(t_max,P,3)\n",
    "plt.figure(figsize=(20,3))\n",
    "plt.plot(range(t_max),X);\n",
    "plt.grid()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemples: Marches aléatoires\n",
    "\n",
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    "Les marches aléatoire sont des chaines de Markov (homogène en temps) qui possèdent en plus une certaine homogénéité en espace.  Donnons des exemples :\n",
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    "\n",
    "\n",
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    "* La marche aléatoire simple sur $E=\\mathbb Z$: elle monte de 1 ou descend de 1 avec proba $\\frac 12$.   \n",
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    "\n",
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    "* Les marches aléatoires non-simples: elles montent et descendent selon une loi donnée (pas forcément portée par {-1,+1}). Par exemple les sauts possibles sont {+1,+2,-1} avec proba {1/3,1/3,1/3}; quelle sera d'après vous la destination d'une telle marche aléatoire?\n",
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    "\n",
    "\n",
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    "* La marche aléatoire simple absorbée sur $E=\\{0,1,...,n-1\\}$. Elle monte ou descend avec proba $\\frac 12$. Une fois arrivée en $0$ ou en $n-1$, elle reste dans ces états. \n",
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    "\n",
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    "*  La marche aléatoire simple réfléchie sur $E=\\{0,1,...,n-1\\}$. Elle monte ou descend avec proba $\\frac 12$. Une fois arrivée en $0$ elle monte en 1,  une fois arrivée en $n-1$ elle descend en $n-2$.  \n",
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    "\n",
    "\n",
    "\n",
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    "***A vous:*** Simulez ces marches aléatoires. Pour les marches sur $E=\\{0,1,...,n-1\\}$, utilisez la technique précédente qui utilise `np.random.choice`. Pour les marches sur $\\mathbb Z$, inventez une technique.  \n",
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    "\n",
    "\n",
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    "***Généralisation:*** On peut aussi imaginez des marches aléatoire sur $\\mathbb R$ (par exemple avec des sauts gaussiens). Mais cela sort du cadre classique. \n"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Définition formelle d'une chaine de Markov\n",
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    "\n",
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    "***Définition:*** Une chaine de Markov générale sur $E$ est une fonction  aléatoire (=un processus) $t \\to X_t$ qui prend en $t=0$ une valeur $X_0$ donnée (possiblement aléatoire) et qui ensuite est régie par l'équation:\n",
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    "\n",
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    "$$\n",
    "X_{t+1} = f_{t+1} (X_t, U_{t+1})   \n",
    "$$\n",
    "avec \n",
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    "\n",
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    "* f_{t+1} fonction à valeur dans $E$\n",
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    "* U_{t+1} v.a indépendante de tous les tirages aléatoires précédents, à savoir $X_0, U_1,U_2,...,U_t$. \n",
    "\n",
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    "Si de plus, les $f_t$ ne dépendent pas du temps $t$, on parle d'une chaine de Markov homogène dans le temps. Pour le commun des mortels, le terme \"chaines de Markov\" sous-entend  \"homogène dans le temps\". \n",
    "\n",
    "La matrice de transition est définie par \n",
    "$$\n",
    "P_{t+1}(x,y) = \\mathbf P[X_{t+1} = y / X_t = x] \n",
    "$$\n",
    "et dans le cas homogène en temps: $\\forall t: P_t= P_0$. \n",
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    "\n",
    "\n",
    "\n",
    "\n",
    "### Propriété fondamentale\n",
    "\n",
    "\n",
    "***Théorème:***  Considérons $t\\to X_t$ une chaine de Markov générale.  La loi  de $X_{t+1}$ est indépendante de $X_{0},...,X_{t-1}$ sachant $X_t$:\n",
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    "\n",
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    "$$\n",
    "\\mathbf P[X_{t+1} = x_{t+1} /X_t = x_t ,  X_{t-1}=x_{t-1} ,..., X_{0}=x_0  ] =    \\mathbf P[X_{t+1} = x_{t+1} /X_t = x_t   ]  \n",
    "$$\n",
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    "\n",
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    "Si de plus elle est homogène alors\n",
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    "\n",
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    "$$\n",
    "\\mathbf P[X_{t+1} = y /X_t = x   ] = \\mathbf P[X_{1} = y /X_0 = x   ] \n",
    "$$\n",
    "\n",
    "\n",
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    "Ce théorème admet une réciproque: si un processus $(X_t)$ satisfait la première équation alors c'est une chaine de Markov générale. Si en plus elle satistait la seconde équation, c'est une chaine de Markov homogène en temps. \n",
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    "\n",
    "\n",
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    "Attention: classiquement, on utilise la propriété d'indépendance conditionnelle pour définir une chaine de Markov. La définition que j'ai choisi est plus proche de la pratique: les chaines de Markov étant toujours construites à l'aide d'une équation $X_{t+1} = f_{t+1} (X_t, U_{t+1}) $ plus ou moins cachée. Par exemple, dans le programme précédent:\n",
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    "\n",
    "    X[t+1]=np.random.choice(a=range(6),p=P[X[t],:])\n",
    "          = fonction(X[t], rand() )\n",
    "          \n",
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    "où la fonction `rand()` symbolise l'appel du générateur aléatoire de notre ordinateur. Chaque appel donnant un réel aléatoire uniforme sur `[0,1]` indépendant de tous les tirages précédents. \n",
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    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Mesure invariante"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "On appelle mesure invariante un vecteur (ligne) $\\pi$ sur $E$ vérifiant $\\pi P=\\pi$:\n",
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    "$$\n",
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    "\\forall y\\in E :  \\sum_x \\pi(x) P(x,y) = \\pi(y)\n",
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    "$$\n",
    "Si de plus $\\pi$ vérifie $\\sum_{x\\in E} \\pi(x)=1$ alors on parle de probabilité invariante.\n",
    "\n",
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    "***Théorème:*** Il existe toujours une mesure invariante. \n",
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    "\n",
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    "***Corrolaire:*** Quand $E$ est fini, il existe toujours une probabilité invariante: il suffit de renormaliser une mesure invariante $\\pi$, en la divisant par sa masse totale $\\sum_x \\pi(x)$. \n",
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    "\n",
    "***A vous:***\n",
    "\n",
    "* Reconsidérons la marche aléatoire simple sur $\\mathbb Z$. Donnez une mesure invariante (essayez de résoudre le système avec un $\\pi$ très très simple). Peut-on la renormaliser pour en faire une proba invariante?  Qu'en est-il de la marche aléatoire non-simple?\n",
    "\n",
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    "* Plaçons nous dans le cas $E$ fini.  Trouvez l'argument d'algèbre linéaire qui permet d'établir  l'existence d'une mesure invariante. Aide: il y a un vecteur propre à droite très facile à trouver pour $P$..."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 29,
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   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "val_pr\n",
      " [ 1.    -0.461 -0.461 -0.706  0.313  0.313]\n",
      "vec_pr\n",
      " [[ 0.25   0.26   0.26  -0.403 -0.171 -0.171]\n",
      " [ 0.25   0.278  0.278  0.284  0.139  0.139]\n",
      " [ 0.076 -0.184 -0.184 -0.464  0.527  0.527]\n",
      " [ 0.25  -0.564 -0.564  0.57  -0.544 -0.544]\n",
      " [ 0.1    0.113  0.113 -0.323 -0.151 -0.151]\n",
      " [ 0.073  0.097  0.097  0.335  0.199  0.199]]\n"
     ]
    },
    {
     "data": {
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qNjH4b+jBqrpxzGMtS5K3d28cIMnbgauAFfOOOKN/Ct1XRP/k6yeeBu6uqsPjnWp5kvwN8M/ALyWZS3LzuGdapsuA32Fw9fh49/Pb4x5qmd4DPJTkSQYXHg9U1ap4m+Mq8gvAt5I8weC7xO6rqr8f80y9+ZZNSWqIV/qS1BCjL0kNMfqS1BCjL0kNMfqS1BCjL0kNMfqS1BCjL0kN+V8zQ/rYGs9zXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" calculons l'unique probabilité invariante de notre chaine de Markov\"\"\"\n",
    "def mesure_invariante(P):\n",
    "    val_pr,vec_pr=np.linalg.eig(P.T)\n",
    "    val_pr=np.real(val_pr)\n",
    "    vec_pr=np.real(vec_pr)\n",
    "    pi=vec_pr[:,0]\n",
    "    pi/=np.sum(pi)\n",
    "    print(\"val_pr\\n\",val_pr)\n",
    "    print(\"vec_pr\\n\",vec_pr)\n",
    "    return pi\n",
    "\n",
    "P=premier_chaine()\n",
    "pi=mesure_invariante(P)\n",
    "plt.bar(range(6),pi);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***A vous:*** Pourquoi transpose-t-on la matrice dans `np.linalg.eig(P.T)`?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Théorème ergodique\n",
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    "\n",
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    "***NB:*** A partir de maintenant, nous supposons que l'espace d'état $E$ est fini. Dans une dernière partie, nous verrons les difficultés qui se rajoutent dans le cas infini. Notamment on introduira la dichotomie transient/récurrent.\n",
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    "\n",
    "\n",
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    "\n",
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    "On dit qu'un graphe est ***irréductible*** lorsque l'on peut toujours aller d'un état à l'autre en suivant les flèches. On dit qu'une chaine de Markov est irréductible quand son graphe l'est. \n",
    "\n",
    "\n",
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    "***Théorème:*** Lorsqu'une chaine de Markov finie est irréductible, il n'y a qu'une seule mesure invariante, à une constante multiplicative près. Donc il y a une unique probabilité invariante. \n",
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    "\n",
    "***A vous:*** Comment traduiriez-vous ce théorème en terme d'algèbre linéaire?"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notons maintenant $X^x_t$ la chaine de Markov qui part du point $x$. Notons:\n",
    "\n",
    "$$\n",
    "  \\Gamma_{T}^x(y) =\\frac 1 T  \\sum_{t=0}^{T-1}  1_{\\{X^x_t = y  \\}}\n",
    "$$\n",
    "C'est le temps moyen passé dans l'état $y$ en partant de $x$.  \n",
    "\n",
    "\n",
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    "***Théorème (ergodique):*** Quand $T$ tend vers l'infini: \n",
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    "\n",
    "* $\\Gamma_{T}^x$ converge vers une probabilité invariante. \n",
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    "* Quand la chaine est irréductible, il converge donc vers l'unique probabilité invariante, et par conséquent, la limite ne dépend pas du point de départ $x$.\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 30,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "[0.251 0.251 0.075 0.252 0.099 0.072]\n"
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     ]
    },
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_max=5000\n",
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    "P=premier_chaine()\n",
    "X=markov_from_P(t_max,P,3)\n",
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    "Gamma=np.zeros(6)\n",
    "for i in range(6):\n",
    "    Gamma[i]=np.mean(X==i)\n",
    "print(Gamma)\n",
    "plt.bar(range(6),pi)\n",
    "plt.plot(range(6),Gamma,\"o\",c=\"red\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***A vous:*** modifiez ce programme pour mettre en évidence la convergence: vous pouvez effectuer des moyennes à différents temps, et les afficher comme des petits points qui se rapprochent des points rouges ci-dessus. Attention il y a une erreur à ne pas faire (la même erreur que l'on fait souvent quand on veut illustrer la loi forte des grands nombres)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Marche aléatoire absorbée: un exemple réductible\n",
    "\n",
    "\n",
    "***Définition:*** Un état absorbant est un état duquel la chaine ne peut pas sortir. Par exemple, la marche aléatoire absorbée admet deux points absorbant: $0$ et $n-1$. \n",
    "\n",
    "***Exo:*** Considérons la marche absorbée. \n",
    "\n",
    "*   Montrez mathématiquement qu'il n'y a pas unicité de la probabilité invariante. \n",
    "*   Notons $\\Gamma_\\infty^x =\\lim_T\\Gamma_T^x$. Quelle est son interprétation probabiliste. Intuitez qu'elle dépend de $x$. Est-ce en constradiction avec le théorème ergodique?\n",
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    "*   A l'aide de simulations, tracez les courbes $x \\to  \\Gamma_\\infty^x (0)$ et $x \\to  \\Gamma_\\infty^x (n-1)$. Est-ce en accord avec votre intuition.  Aide: vous devez simuler la marche aléatoire jusqu'à ce qu'elle touche $0$ ou $n-1$. Il faut donc utiliser une boucle `while` (ou un `for...break`). Il ne faut donc par recopier le programme ci-dessous!"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 31,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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uuLm54e3tTYcOHThx4gSXLl2qglchVEb64sWUREfjOmsmRjVqVHc4gnDfREVFcebMGbp06YKHh0d1hyMIwn0kkkCC8ISJi19BXt5p/PymYWZWvoKUXq9n+fxRFBcX0n/EZxgZG5e1FWmKGHdwHCdSTlQ4X2xuLJ/t+4ykgqR7iuObk99wOfcy0ztNx86svFaKXpYZdzGRjanZFY7Jyk1n2M51nL580mD70KZDqe3Yjfcj4zmfW7HI7py9S+lh0QZ1r2ngWE/ZaG6rjN7JugJ5iUrix/TaCmjOjaDHJIjaAmd/rxh8bhJsGw2120HHj8u395oKNespD/Pq3AqHrTu4jslmbZD7fwm2bspGaycY+BWknlNG/AxZqSSiADzbQaeRSu2gCzsrnC866SIzL8bRw8aYV1wdDNpCroYw8dBE1NrKF5cW7pPIzXD2N+g6GtxbGTT9dv63ijVvatSGfvMg7rDh1MBrcktyGbN/DGfTz95TGP/E/8PUkKlo9dqKjQe/hEOLKm7XaWDTiFtOh0wvSmf0/tFEZ1csqn4i5QSrI1fzot+LdHTrCICRyoiZnWeilbVMOjwJvWyY4JJlmRlHZ5BXmseszrMwMVKmfDZ1asq7Td5l0+VN7Infc0+v+UE6EX2CiUsnEpMaU6Ht9OnTXLx4kV69elGrllIfxszMjMDAQHJycvjrr7/u6Vr5+fls27YNd3d3OnfuXLa9R48eODk5sWnTJoqLK19QW5Zl0r76iqxff63QpleruTp2LIUhIfcU45OoKDSUrP/7gRovvIB1167VHY4g3BO9Xs+WLVuIiIio0HZ9JKOLiwtdRd8WhMeOSAIJwhMkPz+CmJjF1Ko1ABfngQZta/74Ai5nEOqbSYq54TSMhaEL2XZlG2MOjCFHnVO2XaPXMO7gOP6K+4uJhyZWeMi7nRMpJ/g58mde8HuBTu6dDNpWJqTzY1IGI8/HE11YnsCQ9XrGhuxlk5kf70enU1hUXgNIKxuRaT+UAvOWvBx2FP0NoymOXAlhsdyKSIc+vIubYSA+XeGZRTBoCdRuY9jWYQR4doDtnyujca7T65WiznqtMspDVV5QG1NLCFwJeVeV6T03iIg9y2itLys9nudnh5vqw/gPhKdnKgmgWv6Gbd3Hg3MTZSRTYWb5a9Zq+PhsFBbaQhZFTEe64d5nFGcw9sBYNl/ezDenvkF4gArSlBFkrs2g6+cGTafSTjHn+By+C/+OHTE7DI9r9tK1qYHTlamBN5h9bDY7Yncw5sAYCjWFlQojMT+R8QfHsz56PavCVxk2XvwL9kxTilZH3zSV6MAXSn2iDUMNVq6TZZnJIZPZFbuLMQfGUKorr0NTUFrApEOT8LT1ZFSrUQanq21TmzFtxnAs+Ri/nf/NoG1bzDZ2x+1mRIsR+Dn4GbS93/R9/B38mX5kOpnFmTxsikqK+HP9n5ikmbDyt5UG7znZ2dns2LEDLy8v2rVrZ3Ccp6cnnTp1IiwsjIsXL1bqWtdHFWk0mrJRRdeZmJgQGBhIYWEh27dXoo7ZNXnbtpO5fAWpM2dRdNIwqZ6+aBG5mzaTNPpztJkP371/WOgKCrk6bjwmHh44j/n87gcIwkPm8OHDhIWFsXHjRjJv+LcuyzJbtmyhpKSEIUOGYHzDl4KCIDweRBJIEJ4QOl0JEZGjMTFxoIGfYd2a6Nhwrm7eR4GzMekNzRl/aHzZCJKDiQf5/eLv9PbqTU5JDjOOzigr9LoqfBURmRH08+lHWGoYqyPvXty2UFNI0OEgPGw8+LTVpwZt5wuLmROTTDd7GyyNVIyIikOjV6618eRfbDGvz+CSC8SZOjHtUPlD9JwrycSV6Glmls1VyYtxZ5XRA6WaEt66kISEDmddLH8XubI58aZvvFq/DS1eqRioykiZpqPXGk7TCf0eruyDp2coU8hu5tFKqelz+helxg9QUlrMiKgE7HUFdLQxY+rlZGKKbpoO0vEjaBRQ8XzGpkqyqTjbYHraN4c2ccrci7nqEJxjdilFpFE+vE0LmUaxtpgetXuwOnL1LUdwCVVAlmHzx1BSoCQDjcqLmRdpiph4aCKuVq40dWzKzKMzSS28YdTajVMDNwwtW7luZ+xOtsdsp493H5ILk1lwYsFdw9DLeiYdnoRKUtHFvQsrzqwgIvNavy/Kgs0jlGLmTv7KqJ+iayt4JYXBgQVKwXIw6Pd/Rv/JoaRD9PPpx6WcSyw5vaTsevNPzCelKIVZnWdhaWJZIZ5nfZ+ls3tnFoUtIiZXGTWTUpjC7KOzaVGrBW80rLgCoYmRCbM6z7qn4tIP0le/f4WF2gKtsxazbDO+2/kdoHyzvnHjRgACAgJQqSp+zHrqqaeoVasWmzdvpqio6K7XOnnyJNHR0fTq1QtHR8cK7W5ubnTr1o3w8PBbfqN/M01qKinTp2PerCkmbm5cHTcefaGSXCw8eoysn37Gpncv9AUFJE+e8tDd+4dF2vz5aJKScJs7B5WVVXWHIwj3JCUlhb1791KvXj2MjIwIDg4uS2afOXOGCxcu0LNnz7KRjIIgPF5EEkgQnhBXYhZRWHgRf/85mJjYl23X6bSsXTQZZHjx02nM6DyDmNwYvj75NbkluUwJmUK9GvWY02UOHzb/kL/i/mJHzI6yVYAG1BnAvC7z6FG7B4tPLuZS9p1rUyw4oawCNLvzbIMHxlK9no8i47E2MmJJQ0/m1a/NmfxiFselkpyRwLhsa1qrY/m21xDe11/iZxM/9pzdz6HsfFYmpvO2uyPb2nfFQZ/I6kxrQjPjGbrnO3LMfXlLFcHGdl0w1hfyyflE8jSVnCLl4AN9ZkHMfmXJ9oxL5UWdW799++O6jlFq+2z5BArSWXBwC1Hm7ix0gW+b1MVUJfFRVBy6yj5cuTRWag9FbYbwPzh75TQLdd4Ellxg8MBxykiif2ZAaiQbL21kX+I+RrYcyZwuc/C09WTSoUkUlBZU7lrCv3f6F7i4QykEXauBQdPC0IUk5icyq/MsZneZjUavYUrITQ/Y16cGppyFAwtIL0pn5tGZNHFswtwuc3m78dusj17P/oT9dwxjdeRqwlLDGNd2HHO6zMHBwoEJBycoid1tnypJnyErlD9FGbB9tLKq3YZhYOOijEjrNxdiD8Kx5STkJbDgxAI6uHZgbpe5PFf/OX489yMnU0+yN34vwZeCeafxOzRzanbLeCRJYnrH6ZgZmzHx0EQ0eg1Bh4PQylpmdZqF0Y2j6W7ga+/Lxy0+5p+Ef9hyZcu9/Syq0O7Tuym5XAIeMG3YNErsSkg4kUBEfATHjh0jLi6Ovn37Ym9vf8vjjY2NCQwMpKioiK1bt94xyZKVlcWuXbvw8fGhbdu2t92vc+fOuLu7s3XrVvLzb19QW5ZlkidMRNZocJ83D7e5c9AkJJC6YAG6/HyuThiPqbc3bvPn4/TpKAr27CE3eGPlb84TomD/fnJ+/52a77yNZatWdz9AEB4iWq2WDRs2YGlpyZAhQ+jfvz+JiYkcPnyYnJycspGM7du3r+5QBUGoIkZTp059YBdbuXLl1KFDhz6w61Wl2NhYvL29qzsMQbitG/tods4Jzp+fiLvbS3h6GiYvvvtxMpy5inNAV3p2fpbaNrXJKcnh1/O/EpoSSkJ+Akt7LcXFyoWmTk05mnyUTZc3EXI1BGMjY5b0WIK5sTltXdoSfCmYY8nHCKgXcMsHu/0J+1kYtpC3G79NgK/hqJcvYlLYlJ7D0oaeNLO1ws/KnJjiEn68msHhhMukq6z4rYkXNe2caO/uw47os2wqNOKvXA21TE1Z1dgHMyMj2tqZszalgM1X44g0qU/t4rP82vMtHMytUGmusq/QnmMpYbzk2aBCfLfk2lwZIXHyJyUZpCmC1zYoNYVuR2WkTCU7toJjyfF8ZteXVzQX+aDTM9gYG+Fubsp3iRlYqFS0q2FduTg82sKVfajP/MFLxp1RyXpWd2yPhbmVMq3t1BqSYvbwUfpBWtRqwcT2EzE1MqWRYyNWR60msziTpzyfqty1HqDH5r00Ow7Wvqz8nAZ8qYzsueZQ0iHmn5jPm43e5Nn6z1LDrAY2pjb8cv4XHC0caeTYqPw8Tn6QHY984js+L7lMXFEqy3ovo6ZFTVrWasm+hH1sj9nO4HqDsTCuWHD6UvYlPt//OV09ujKy5UjMjc3xreHL6qjVlKSG0+nUeqXeVaMAJeEjqeDYCqVvp4bD86uVKYkuTSD5DLqwH/hYfYEcTSHLey/HxtSGti5t2RGzgz3xe/g7/m88bTyZ22XubZM5AFYmVrhZu7Emag1Hko8QlhrG+Lbj6eje8Y63tYljE46nHGfTpU0M8BmAjanNvf9s7oPr/TS7MJvVa1ajM9Ix+t3RWJpZ4u3tzamTpzhz/gwJ0Qn4+vrSu3dvg6L7N7OxsUGlUnH8+HEcHR1xdnausI9er+e3336jsLCQV199FQuL2xcYV6lUeHl5cfz4cdLS0mjSpMktr5/z229kr16D84TxWHfpgombG/qiIrJXr6Ho+HFKr1yh9vJlmHp4YNG0KUXHT5C7YQN2zwzAyPYO73lPEG12NvHvvYepuztuXy5EMrp9v3+QHpv3UqHK/fPPP0RFRfHcc8/h4uJCrVq1SE9PJzQ0lNjYWIqKinjttdewtKw4svO/Ev1UeBQ8yv102rRpyVOnTl15t/3ESCBBeAzIssycY3Mq1v4A8ovTOXjyLTB2pF49wzo1pyMPk7v7FEWelrz2fHlNg1GtRuFt683ZjLN80PwD/GsqdWqMVcbM6jwLrV5LbF4sMzrOKCvqXNOiJpPbTyYqK4oVZ1dUiCM76zJT/vmE+lZuDG8+3KDtZF4hi+NTed7Fnn5O5aurzPJ1x4lSzpq6MdkihTpuvgCYm1mypIE7mca2JJdo+MbfE0sj5e2sTU1PXnXIpcDYDSNdIWvbdEZ17UP6SL+ONDSK5XhJbX6+YlgHA+BoTgEvn7lMWommfKMkweAl/OL2DCPsB6Ptv7C8qPO1ez8pOpGvYm9a/aiWP4U9pvCx47N4lGYyrUvfsqbAWjUY6FSD+TEpRBRULOa6JzOP185eIVdzQ0FflREELmeux8tcNHdnkZsR9rZOSpuVI/pnFjFJTkfSlTKj0wxUknI/mjk14x2/lwm+FMy+44srXOuxVVoIv72iFGm+X44sVaZ73byCl16vTJ1ChoClyopf1+SW5DLlsDKabkSLEWXbX/B7gQ6uHfgi9Avi8+INz9dvLusdXTmYeZZRzT6kjp0y7dDUyJTZnWeTW5prMC3zOo1ew4RDE7A2tWZKhyllSYCO7h15wWcgq1OPcKJ2c+j4SflBnUaBe2tIPAFth0Lda4lCSYJBi/nJ3p5T2ecZ32YMLlYuAFiaWDKz00xqxtXENcWV2V1mlxV1vpO+3n3p79wf23Bbutl143/1/2fQfunSJX755ReDAsfXi0vrZT1Bh4Mq1B3Ty3qmhkxlTeSau17/fvh67deYlZrRs39Palgp71X1XOvh28EXsyIzZCOZQYMG3TEBdF3Hjh2xd7bnj01/cDnlcoX2I0eOEB8fT79+/ahxw6pTsiyTOm8+6d8sMdjf0dGRnt26ER0dTcjqilNzS+PiSJ2/AKuOHbF/6aWy7U6ffIyZbz2Kz5yh5rChWDRTRnRJKhWuc+Zw0duL3xd+iV6nq9xNesylzpiBLicXt/nzUIkls4VHTHx8PIcPH6Zly5bUr18fUEZrDhgwAAsLC5KTk+nTp89tRzIKgvB4EEkgQXgMbLy0kV/P/8rXJ7/myNUjBm2bjr+GhVzMd6laMkrKpwmoS4vZ/M08tMYyb342x6B2hYWxBYu6L2J4s+G83dhw5JCXrRcLuy1kaoepFb7F7+nVk0F1B7EqfBXh6eFl22W9nhnb3iRX1jI7PgZTdXkcRTo9H0fF42JqwkxfwyVIa+TF8cPp0UzM+Zs3OwwyaGvi05xlxhF8GzWTlgmGK2fNyzxKv6T/Y6FtIvVq+Rq0rWvbC1N9NpOuZJNaXB5HrkbLB5Fx/JOVz+gLCQYP2OewZZzPh/zp/DTf2HY2ON9vKVmsSsxgbkwK+7LyDNqm1RxIvIUbi+s7Y21ZvgKaJEnMre+BvYkRH0XGUXJDUiG1RMOIyDi1ONBfAAAgAElEQVR2Z+Yx6ZLhimshUi1WuA/hdZN0ejQxLC69Rp9NqIU549LTcMs2PO6DuAj8SkqZErGSrKwnZCnp3ZPh/FYlOZMTf/f97ybuCOyaoIwIO3FTsvXYcog7BH3ngr2XQdOsY7PIUmcxu/NszIzMyrZLksT0TtMxVhkz8dBEdPryB+wETR4L7CxoV6zmpQTDItF+Dn6MaD6C3XG72R5jWAh45dmVRGVFMbn9ZGpa1CxvkGU+jY2ktlZPkI0xBbobpkMaGcNz/6cUse5lWCvsoiaHJbYW9C4s4plEwziMU43xzfOlQXYDSL/r3QNAp9NRJ74OzsXO1E+sj1ZbnuQsKChgw4YNREdHVyhwXFZcOuUYa8+vNWhbe34t66PXsyB0AafTTlcukH8p+EgwJIJZXTN6N+9t0PZ6z9dR11VzwPEAVzVXK3W+Yl0x/9j+g16nZ9VvqwyKS6empvLPP//QoEEDmjUznGaXt3UbWT/8QMa335K/b59Bm/f+A9RKTWXvxYukRZX/zGSdjqtjxyGZmOA6e5ZBkkplZob714txHD4cpw8+MDhfqqznZJMmRNvasG9pxZXrnjS527aRt30HTiNGYO7vf/cDBOEhUlJSQnBwMHZ2dvTp08egzcrKipdeeolevXrRsmXLaopQEIQHRSSBBOERl1SQxLwT82jl3AofOx+CDgeRV6okI/ad/wZXXTRxRn5cKVUZLNO8csUErLL01H/hGWq71K1w3nr29fig+QcYqyquCtHFowvP1n/2lvGMazsOJ0snJhyaQLFW+UZ/+4Gp7NbnMMKiDn4FWbBtVFmB49lXrnKpqISv/T2xNb5hWL1eB8Hv01wdy0c9XkK6RYHVgZ1fIdA0F7Z9BnnJysaE46gOf8UPNjpebPdqhWOczK2ZVdeeUpU9L50oX356YnQSaaUaXnZ14K/MPNamKMVyS/R6RkTFY29qQh9HWxbGphCerxRzTVCXEhSdRHs7K3wtzRh1PoGca6N39mTm8XNyFu/XrkWHOk0rxFHT1JiFfrWJLFTzRYwyikiWZT67kECxXs//XOz5IyWb7enKamwFWh2fnI/Hy8KMKe17GJzrcs5lvj75NU+5d2GwygGCh0HptYKz4X9iErmJ2TXbky/BjG1vIt88kuVxc2mPkqhp8j9ANizs/W+UFMDG96GGJ9R5SkkwZVxLpqWdV1bZqt8PWhj2t50xO9kRs8NgNN2NXKxcmNhuIqfTT/NjxI8A6PQ6Jh2ahEplwgyPfqiOr1AKkd/gzUZv0typObOOzSKlUOk74enhfHf2OwbVHURPr56GFwr9Pyyv7GWW70skqzNYEHpTcWl7L2WKmGn50H+NTsOEgxOwNavBpFrdkA4sgCRl9Fxubi7bt2+ndu3a91TgOCQkhOSrybRq1YqsjCz27t0LGK5E06xZs1sWOB7iO4SuHl1ZFLaIK7lXALiSe4VFYYvo6NYRVytXJhyaQJHm7nH8G7nqXI7vOU6xeTEjnx9ZoV2lUjHmf2PQ2Cn3TaPT3OIshhaELiBWF4uxnzFmOWas3K6M3tZqtQQHB2NmZsbAgQMNEjaalBRSZszAolkzzPz8SJ4UhDY7G4DCI0fIWbOGnlbWSLLM+h9/RKdR4sj8/v8oPn0al6AgTFxcKsRiVscHp48/QrphZEtpaSnBwcHY2tnhXlLC4bQ0kk5WHEH5pFAKaiv3vuY7d6gJJwgPqd27d5OdnU1gYCBmZmYV2j08POjcuXOlRjIKgvBou2sSSJKk2pIk7ZUkKVKSpAhJkj65tn2qJElJkiSdvvanf9WHKwjCjfSynkmHJgEoBWc7zyajOIO5x+ZSqEsjJ3ExmTpzXum0jtGtR5ct0xwStouSwxdR+9XguWeG3+Uq98bG1IaZnWYSmxfL1ye/JiXlNLNiNtBcNuHNZ/+Ep8ZD5CYI/5ODWfmsSszgXQ9HOtvfVOvj8NeQeBz6LwQ791tfzMgYAleARq0soV5SoCRAbD2gz5zbxviaT0vamiUQqfPm6wshbE3L4c/UbEZ6OfOFX2061rAmKDqJuOIS5sekcL5QzZcNPPmqgSc1TYwZERVPkU7PJ1HxyMBif0+WNPQivVTDxOgksjVaPj0fj5+VOWN9XG8bR29HO15xdeDb+DSO5xTwa3IWf2fmMamuGwv9atPU2oLPLySSXqphyqUkEtWlLG7gidUNyTKNXsP4g+OxMrFiSqcZSAHfQtZl+HuKslT9ts/Aow31A75nRM02/K3PZev+yffyI320FGcrK145+sGgb6DvHKXA8fGKUxQr7a9JSs2fwOXKinHGZko/0xQrf5taKSt73fDBOb0onZnHZtLUsWmF0XQ36u/Tn95evVlyegkXsi6wOnI1J9NOMq7tOFyfngs1fWHjh6DOLTvGSGVUNi1z8uHJFGmKmHBoAk6WToxrO87wApmXlfjr9qB510m80/gdNkRvYF/Cvju+5GVnlnEh+wJTO07FYcCXSv2g4GHoS4vYuHEjer2ewMDAsgLH27Ztu+P5kpOT2bt3L40aNeKZZ56hdevWhISEEBsby+nTp8tWohk0aBBubm4VChxLksTUDlMxNzZn4sGJqLVqJhycgLmxOTM7zWRmp5kk5ifyZdiXd4zj3zoYeRATrQkBgQFYmt26ToaDuQNTO0zlQvYFlp1Zdsfz7UvYx4boDbzd+G2Cng9CbacmMSyRc3HnOHDgACkpKQwaNAirG1adurGos9u8ubjNm4suN5eUqdPQ5eVxdfwETH188J0xnafq1CXVwoJ/vl2K+vx50r/5Bps+fbB9ZkClX/Pu3bvJysoiICCA/73/PsY6HRt+W4dWXcnC+o8RWZZJnhSEXFqK27y5SGLJbOERc+nSJUJDQ+nYsSNeXl53P0AQhMdaZUYCaYHPZFluCLQHPpQkqeG1tkWyLDe/9mf77U8hCEJVWBO5htDUUMa2GYu7tTuNHRsztOlQtlzZQox6FhaSngb+87EwseF/9f9HJ/dOLD6+iL+XLabEHIaOuvty0/9GO9d2vOL/Cr9E/cIHu95BC8zqsRgjY1OlHolHW3J3TeaTyBjqWZoxoY6b4QlSzsHe2dBwMDR57s4Xc6wHvafDpd3w/dOQFQOBy+5cuBlY07YPFrpUFiRo+fxCPE1tLBjp5YJKkvja3xMJeO1sDEvj03jNrSa9atpib2LMogaeXChUMyDsIiE5BczwdcfTwoxmNpaM8nJhfWo2Q05dIlOj5Rt/T8yN7vw2O62eO+7mpnwYFc/kS0l0rmHN2+6OmKpULG7oSYFOx/OnL/NLchYfetai7U2FpL87+x1RWVFM6TBFmQLk0xXaD4fjK2HNs6ArVRJlRsa80W8FLWQT5sRuJCXl1J3v66Nq+xgoTFNWvjKxgBavQf2+ymid9Av3fr7o3RD2A3T8CLw6gq0rPPMlJIXCdz0h+bSyopdNeWFfWZaZEjKFEm0JMzvPvOVouuskSSKofRB2pnZ8tv8zFp9aTI/aPRhUd5AyMidwBeQnww7D5I6nrSejW4/mSPIRXt3xqlKjq9MMw8LJeh1s/EBZqn7QEpAkPmj2AX72fkwJmUKWOuuWMZ1OO833574nsF4g3Wt3B4saMHgJZFzkxK+ziYmJoU+fPjg4OODq6kr37t2JiIggPDz8lue7PrLF0tKSAQMGIEkSvXv3xt7enuDgYIOVaIyMjAgMDESj0bB582aDaZlOlk4EtQ/iXOY5Xt7+MhGZEQS1D8LJ0onWLq15veHrrLuwjsNJhyvxg628Nf+swTrPmhoNa9DBr8Md933K8ykC6wXy/bnvbzs9LUudxZSQKfjZ+zG82XCMVEa8+9K7yJLMr2t/5eDBgzRv3pwGDQyL12evXUthSAjOYz7H1Nsb8wYNcProI/J37SLu1dfQpqfjNm8uKgsL2r/1Jl4lJRzJzODcuPEY2dnhMnVKpb/hv3TpEidOnKB9+/b4+PhQw8uL3o2bkGlpwa7FT1BtsWty1v1O4cGD1Pp8NKaPaLFQ4clVVFTEpk2bcHJy4qmnHr4FIgRBePDumgSSZTlZluWT1/47H4gCbvO1vCBUndLSTMLCXiQtbVd1h/KvHNk9lp0buqAuzr37ztdotQWcOvU6V5P/rNB2fQpQ99rdCahXvtLWe03fY6C9Lf4WBeSZtaeph/LN7/VlmptfsMMqX6LlGy/jZH/DKBW9Dv58G/bN/fcv8gaftPwEG9vehNb6jA/d+uLpea2WjpExBC5nkuc7pJZqWdygvKiz8qJLlNEVFvYwYJHB6IrbavMu1OkOaRHQ4UPw7ny3I7A1MWexf220KktytRqW+HtholKuVdvclJm+7lwsUuNpbsrUuuVJqh41bQl0NCGqUE07G3jJxaGs7WMvZ+qaaYkqVPO+uw1Nbe6+soa1sRGL/T1JVJeiAr7y90R17TU3sLJgvI8rUYVq/K3M+dzHcBrHuYxzrDy7suIUoJ6TwbE+pEUqCbKaynQ/I2NTZvX8Bi0QtGsYep2Wh1JJAfwcAGE/VWzLiIZVvSD+aMW2iGAI/x26jgG3Fso2SYKBi8HEUulXlZimU6YoSxlVVKshPDWxfHvjZ7la90VWpTUm2fcVJVl5g/XR6zmYdJBRrUbhY+dz18vYm9szreM04vLisDG1YXKHyeUP6x6toMtncOZXiDJcJv1/9f9HJ7dORGdH84r/K7R3vWk535DFkHDMYDSdiZEJszrPIr80nxlHKhaXzinM4aeff6Kpuilj2owpb6jbg4wmw9gdK1PP3YFWNyyL3alTJzw8PNi2bRt5eYZ1sQD27t1LWloagwYNKlttxszMjMDAwLL9AwICyuqSOTk50atXL6Kjozl1yjBZ2ce7D/19+hOdHU1/n/708S6va/FRy4+oa1eXyYcnk1tS+fdZjV7DJ/98wg/nfqjQdiX1ClGHoigwL2DEkBG3OLqiMW3G4GLpwsRDEytMT9Pr9ewZ+RLPbs5kZqeZZQW167nUo37H+piqTVFZqOjbt6/BcbHnjpAwdxbaNk2o8eKLZdtrvvM2Fi1aUHLxIo7DhmHRVJl6qlKpGDJ8OCY6HYc8Pak1bSrGlSz0WlxczKZNm5RC0z3L31dav/wS9bRaQgsKuHLgQIXj8nbsUJJR16an3Sh98Tckjf68WqeiyrLM9u3b2bp1a4V+fyelcXGkzptXoaD23Rw5coS1a9ca1L4CpQ8EBwfz999/VzimuLiYH3/8kbNnz1b6OoJwN9u3b6ewsJAhQ4ZgYnL3Iv6CIDz+pHv5RShJkjdwAGgMfAq8CeQBoSijhSr85pckaSgwFMDZ2bnVb7/99l9jfigUFBRgbV3JpZ2F/0yWZfTyUuAkYIFKmo4kOdztsIdGUVYYprZLkVRQcNUfO4/RlTpOr/8JmQOACSppMpKkJCN0so6FKQvJ1mYz3m08tkblo15MSq5QKs2kuESmZawP5xsHlSVS8pPiubj5d2Q/N1r3eNngWrXjN1D3ivLQfabpVLIdWvyn15xdnMEoEw/URuZ0lUsYripf8ee4bMKXWDEq7icCTUy46l4+m9Tnys94xa8nvPEkMh3bVPp6piXZOKfuJcl9AHqjinPdb+e7wnBCC44w1LoVrazKH2xlGXZjij9aakvlDy46WceC1G+INm2Aa0k4k5w/wlxlDkCuNpfpacvJMW9CK20CHzgNrfQ37yGyCfbo8ZcMV+DRy7ATM1qiweWGOEr1pcxLnodG1jDObRyWKsOEk0VREg5ZJ0lyf6ZCIu1c4kpW6MJ5V+VPs9r3dzrgvbrVe6nvxWW4X92JXjImrNWXFForQ9clvY4Wp8Zimx9NsXktQlt/jc5Yed2mJdm0OfERxRYunGoxF/mm0TeO6SE0jphHjPdLxHm/SGX4R36BU/oRTrZcQIFNnbLtOp2OsNATFBWrsbK0oGWr1hhdW4EuQ5PBnOQ5+Jj5MLzW8LJV2irjaMFRXExc8DbzNtgu6TW0PDkWs5IMTrRZjMa0fKWofF0+xwqO0dWmK6aq8nouVgWxtAr7jAzHdkQ2/LxCH/g792825Wzi9Zqv08a6/N/Z9rPbscyyBAlat2pd9rPR6/WcPnWS0vxM3jHdyvm288ruPSjfNIeGhlKjRg2D5clzcnI4ffo0rq6u+Pn5VXjNaWlpmJiYVFiJRpZlzpw5Q35+Pq1btzZYHr1IX0RIfggdbTpW6PcJJQl8kfIFLS1b8obTG3e839dty9nGztydSEh84vwJdc3rlr3m7WHbMS8yx6uBF77Ovnc5U7lodTSLUxfTxboLz9d8vmz71f1rabFWSaDkvvkG6vbliTu9Xs/66PWEq8IZ5jUMd1MlcafTlqKZO5aaGWpmDHXggwaTsFCV3w9VdjbmJ0Ip6tkDblquPCsykrNpaXh5eeHjc/eEJEBkZCTp6em0bNkSGxvDabravDzCQkIw1ulo3qMHRtd+LqqMDGrOmImqpAR161bkvvtu2TGm585hv+RbAPKfe46iXjfVrHpAUlNTibpWLNvPzw9X19tP1S2j12P/xUKMk5PJnByEvpKJtNzc3LIEpqenJ3XqlL9/JCYmcumSUlOscePGODo6lrVFRUWRmpqKSqWidevW97REt/hcKtxKWloakZGR+Pj4PBTTwEQ/FR4Fj3I/feqpp8JkWW59t/0qPalZkiRrYD0wUpblPEmSlgEzAPna3wuBCoUPZFleCawEaN26tdy9e/fKXvKhtm/fPh6X1/IoSE7eQGTUSTw8XiM5eT12thtp3vxHpHt4wKoupep8/tn1MTq1KVKpN1auUbjWSMav+Z2/UczI2MuZswdwc32e9IzdmJv/TutWf6BSmbD09FIS4hNY1H0Rvbx6lR0j6/Wc2TmSUhNokNkCl8w9uNglQsvXKCkq4qfPf8Le1Y3XJizGxNy8/GKpEXBwLfj1h8zLNItZCf1ClNE4/4JOp2XwX1sxk7U872jOzxnwViM/+jnVIL1Uw4fHL9DUzIRRRgmYxh6mft9hymiV+GOwPxhavk6TQZ/f/UIVBFKxxPWdddZ35o2dR9mQu4HXnnqNWpa1ytpuNWh62ellJMVf5kPfrvx4LoGj5keZ2nEqsiwzfM9wVPoM3vNw4JeoHWS5Z922gPbNut+hrcctts07Po80bRrfPf1dxREgZV7hVo+t3fRdiVjdgTXaSAZ7S3h7d7vFXg9GhffS6L9h305o8SqqCztpk7gK3t0Dxqawfz7kR0PHj7E4soQuhduVaUqyDGtfBDSYvP4r3Zzq3+JK3cEoFp9zf+DTeyi432X1k/A/Ie0g9AiidVfDX207d+6kqFhNp06dOHz4MDqdjp49e6LT63h719uYGZux5JklZUuqV1b3O/WCxh6wohudMn+HF38xSOoMZKDhvtoS+G4iWDpQ683V1LKqyc266LsQvyue4OxgXnvqNVysXNh8bDOWWZYYexhjlm1GQkIC7733HsbGxhw4cIC8/AKee6o9TvuW41SwDQK+NTino6Mj27dvx8bGhtatW1NSUsLy5cuxt7fnzTffvGUh0jtp0aIFy5YtIyUlhTfeeMNgBcP+3L4MYdGZIpacXsIL3i/Q17vvbfcDZTTd7u276ePdh3MZ5/iz8E/W91yPpYklK7atwLrQGudWzvja+N7T7/zudCf7RDarI1fzavtX6ejekauXz2Kz4SAJPtbUt6+P6s/11Hn9dUzcykcatujYgsBNgWxQb2Btz7WYGpmyY/p7eCeqOTX8KeKtQzhkeohZnWcZXjAw8DaBdEe1cSNnzpyhd+/eeHh43Hq/ayIiIkhLS6N79+63fb0uwJ8nT5IbGsqQoCBkvZ74N95EbWyM3bNDyP51LXVeegm7AQPQZmcTEzQZI19fTNzckDZvptmbb2BWr16l7+X9kJeXx9KlS/Hw8MDIyIjY2Fj69etHjRo17nhcxnffkX7lCm4L5tNo4MA77ntdaWkpy5cvx87Ojtq1axMREUHv3r2pXbs2GRkZHDp0iLp161JYWEhMTAz9+vXDysqKyMhI9u3bR+vWrQkPDyc5OZm33nrLoN/fifhcKtwsPz+fpUuX4u7uzquvvlr2ZUV1Ev1UeBQ8Cf20Ur9ZJEkyQUkA/SLL8gYAWZZTZVnWybKsB74D2lZdmMKTTK2+yoWL06hh14b6vkHUqzeerOzDJCb9Ut2hVcqhXcMwsSmktvPndO3zC9pCC2ISZlKYl3bbYzSabKLOj8fayg8/v6k08JtJfn44sXHLy6YADawz0CABBJB09GMyzfPxtexDvNcI8OoMO8dDdhx7f1pJQWYmfYd/apgA0pYq02TM7ZRCukNWKDVVdoz916956aFNhJp7M9e+gJmN6tPU2oLR1wocf34hgQKdjsUNPTEdvFipVxL8vlL4NngY2HlAn9n/+tr3ylhlzOzOs9HoNUwOmXzHaQIRGRGsPLuSZ+o8w6etPuWtxm+xPno9BxIPsD56PYeSDjGq1SjGtBlDW5e2zD8xn8T8xPse87HkY6yJWsPLDV6+QwLo9iSViml9V2EKTNw7Eq3mISn0WpQFm0eAUwNlCtOgxZByFg4sgKunYP88ZcWvp2dAp5FwajVc2KH8fXEn9JoKt0wAXdNvPljVUvqbpvj2++UllxXUppPhSlAxMTEcPXqUtm3b0rt3b1q1akVISAhxcXH8HPkzJ9NOMr7d+HtOAN1VLX9lmt+FbXBm7Z333TcXUs8p/55vkQCCa8WlO81CK2sJOhxEak4qR3YfQW2mZuSrIxk4cCCpqans37+f5ORk9u3bR6NGjWjcbTB0/hROr4HzhqUA27RpQ506ddi1axeZmZn89ddfZGdnExAQcM8JIIAaNWrQr18/4uLiOHr0FtP/buOdJu/QxLEJM4/OJL3o9uvXq7Vqxh8cj5OlE5M7TGZW51kkFSTxRegXnIs7R0JoAmo7NcMGDLvn2AE+bvExdezqEBQSRE5xNmc/HYZKL+O3cAlu8+Yi6/VcnTjRYIrU9amBF7MvsuzMMqKO7cDjt0NcaeXKiyOW8G6Td9l8eTN74vfc4cqG+vbti62tLcHBwZSWlt52v/z8fLZu3YqbmxtdunS57X6NBw2ikSRxVqcjatt2sn7+maITJ3CeMAHnCROwaNaMlOkz0KSmkTpjBtqcHNzmz8N11kxUVlZcHTsOWXMP0zL/I1mW2bRpEzqdjsDAQAICApBluazA+e2oL1wgY/H1gtrPVPp61wtqBwYG8swzz5Tde7VaTXBwMMbGxgwePJjAwEDUajVbtmwhPz+fLVu24OrqSr9+/RgwYAAJCQmEhITcj1sgPIFkWWbz5s1oNBoCAwMfigSQIAgPj8qsDiYB3wNRsix/ecP2G8fRBgLn7n94wpNOlvVERo0F9DRsOB9JMsLd7SVqOnTl0qW5FBXFVHeId3Th9Fr01seQc5vRsM3bmFs5UNd7OsYWakL2vHvLY2RZ5vyFyWg0OTRsuBCVyoxatfri4jyY2NglLAoZiaOFI+PaGRaKLbp6gOjC7TiorXHv8C1IKghYCsClFcOJ2Pc3bQP+h1t9w2Kj7J8HKeFK3RQrR6WWStfP4ew6iNh4z685IvYs87WeDCy5SEDLpw0KHA88Gc3OjDzG+bjSwMoCbN2Uh/3E47CiG2THQsByMLO563XuJy9bLz5t9SmHkw7zx8U/brmPWqtmwqEJOFg4ML7deAA+bP4hvva+BB0OYv6J+bRzbceLDV5EJamY0WkGkiQx8dBEdHrdLc/5b+SX5hN0OAhvW29Gtqq4VHVl1XJuQlCd5zir0vLDjqH3Lb7/ZPvnUJiuFEM2MYcGA6DZy3BwIax7HaycoP+1Yubdx4FzY2VVuJ3jwbsLtL3Lw7pFDWX0SsYF2DPj1vvIspKI0paUFdS+Tq1Ws3HjRhwcHOjVS0nAPv3009jb2/PH+j9YGraUXp69eKZO5R8Y70n74Upid8dYyIm/9T7xx+DwV9DydfC78yiY2ra1Gd16NEeTjzLjxxmYaE0YMHgA1ubWNGjQgObNm3Po0CHWrVtXVtQZgG5jwaUJbPkYCjPKzidJEoMHD0alUrFmzRrCwsL+80o0zZo1w8/Pjz179pCWdvvE+Y2MVcbM6jyLEm0JU0Km3Dax+/XJr8sKatua2tLKuRVvNnqTPy78wQ/rfkCWZN596d1Kj8S4mbmxObM7zyazOJNvJw/E60IOme8+g1fDdpjWro3z2LEUHTlK9i+/GhzXrXY3hvgO4efT33N1zFgKLVV0WPgDKpWKYU2H4e/gz/Qj08kszqxcHObmDB48mMzMzFvWoQHl986WLVsq/cA4cORIbIqL2XrgAFcXf4N1jx7YDQlEMjZWElwlJcS99hp523fg9OFwzP39MXZ0xGXaVNQREWQs/w+r9d2j0NBQLl++zNNPP03NmjWxt7enT58+xMbGcvz48Vseoy8t5eqYsaj+Q0Ftb29vzM3NCQgIICsrixUrVpCUlFSWGHJ2dqZHjx6cP3+e//u//6O0tLTs3jdp0gR/f3/27t1LSkrK/bwdwhPi5MmTREdH07t3b4Mph4IgCFC5kUCdgNeAHjctBz9fkqRwSZLOosyaGFWVgQqPttLSDI4fH8TVq7/f03GJiavJzg7Bt95ELCw8AeVBo4H/HEr1MtuOPItGaziKobA4n+kjh7Doq4/uW/y3I8syO779km2LF1R40CjMSyMmYSbaQgs6P72qbLtv0yEYFXVEZRdB+NGlFc55JuRL0tK24+r0NjY2/mXb69efQolOoodZLNPbjsXWtLwOkE5TzKHDH6DTqfBv8yP/z955BkRxrX/42cbSexeQJsUGKIq9G8WOxhiN6TE3uan3mqKxxtg1PUZNTGIs0ZhErLEFGxaKioI0kSIovbcFtv0/rCysCwajKf4vz8c5e2bOnJ2dnfPO7/29gsZFi1VHagct4li8HDs7M/o+eocXSk4snPkIAmeCX7P0ioGzNcGgA/+BqgL9EwOODfUAACAASURBVD88F7Y/BncYC9c3yHg1OQcrZTUr+w7VjsPPxIg5Hk5kyRroY2HCi652TZ26PQqdJ0FZ5m1T5/4tTfWfzjTfafR16svaC2vJrtRfYH8W9xkZFRnaBSOAgciA5QOWU9lQiVggZmn/pVoPGGdTZ+b0nsOlwktsS96mt7+rxVeZuGciFwsu3tM4V8WsorC2kOUDlmMkNvr9Dndh9ODFhIqs+bL0Esmpe9vcT61Ws+DsAt469RYq9QMyer26G67+rAkwOAc2bQ9dCWZOUJGtSf1qTFEUSzVBGln57YDnemjLYt1rGPSaBVHrIDNSr/nK3i9Yf92RykGLtYbajRw+fJjKykrCwsIwMND470ilUsZPGE9VZRVBZUEs6LugzQvGe0Yo1ASx1CrY82+4U8VQX33ParqpPlMZJh2GbbktZn5mDOzcpABpVJCUl5czceLEJn8SsQGEfaVR7+1/QxM4u42FhQVjx46lrKwMe3v7+65EIxAIGD9+PFKplN27d+uZ7CoUCrZu3crRo0d1tntYePBmzzeJvBXJL2m/6O23NTXdK0Gv0LehL2a1Zvj088Hb8f7SlrrYduFN28cYe6iErM5WDHttlbbN8rGpmAwaSOHatdRnZOj0ezv4bZ6NMsK5QA5z/o21oyaQJhFJWD5gOdUN1bx//v02Gxx7enoSEhJCTEwMGXccCyAuLo5r164xYsQI7OzsWtiDLoYWFkwcNYpaqZS4HkE4LXlfe90buLtj//ZbyLOzMQzojk0zfyDzRx7BYuIEijdsQNZCNbnY2Fg2btxIba2uoXZjkOrHH3+8q3rnThoVaV5eXgQHN1kk9OjRA08bG479+iu5cfqVEou/WEd9aipOHyzRMdRWqVT89NNP7NmzR2/uWzPU9vDwoE+fPpSVldG1a1e6du2qbevbty9ubm6UlZUxYsQI7O016cgCgYBx48ZhaGhIeHi43nWvVCrZvn07hw8fbvNcANy4cYMvvviCmzf1FaoXLlxg48aN1NTU6GxXq9UcOHCAnTt33tPct/PnIpfL2bx5MydOnNBrKy0t5fDhw3h6etKrV9u9Fdtpp53/HdpSHeyMWq0WqNXq7s3LwavV6ifVanW329snqNXqvL9iwO08fKjVapJT5lFVnUjqtcXU1KS3qV9NTTrX01dhYzMEZ+dpOm2n8+LZXqzGWlDBngsv67RtWPcuJnkNqM5n8utx/cX3gyTh+BGSTh8n5ewprhw7pNN2LuIFxEZ1eLkvwdBE18S6/6gNyCvNyC35jIqSLO32kvwkCis3UpNvxJWfClE1U5DEJexiU7EQR4ka22sf6ezv3K6piGzqyI50IutaU3UetVrNsahC6tUGjLE4h6i02dw31GgWjOYuMHqF7omJJJoFtrxW87a/+cNu0j6I+hLSjsCZj3W6rYncT7JhBz50FGBjobuQeNHVjg99Xfmqizui5otkgQDGfwrjPoZhC/Tm+K9CIBCwpP8SxAIx88/O11HvxObHsjVpK4/7Pk4/5346/fys/Vg3bB3rR67XSwGa6DWRoa5D+fTSp1wvu67dLlPImBs5l4yKDOadmUd1Q3WbxhiRHcHe9L2adBe7bvdxtk3MG/c9Vip479xC6uvaVlFpz/U97Lm+hyNZR9iR8jupSW2hKh8O/hc69NSkGjXH0AJm/gJTvwdv3fRHHLvCE7s07ZaubT/eyPfB2ksTSKlr+r2UZFzmwOV8CrBj3w0TnUVeSkoKly9fZsCAAbi66h7rQNkBrllcw7ncmeLsYv5UrNw1v9esSIj5Srft2MJ7VtNVV1fjdMMJQ2tDXpuiGzg3NDRk5syZTJ06lU6d7nCXcugMw+ZDygGNarAZ3bp1IywsjOnTpz+QSjSmpqaMHz+e/Px8Tt9Rler06dOkp6dz7tw5UlNTddqm+00nxCmENbFryKnK0W6vaqhi/tn5LarpyorKcClwwdLNkieHPXnfY1crFAzafBmRoRG9PtmsoyoSCAQ4LV2K0NCQ3DlzUTdb6AuvXmN4ZBVVoX3o8+grOvv0tvLm9R6vcyLnBPvS97V5LCNGjMDGxoY9e/YgkzWlQ5aVlXH48GHc3d3p3bvtmf3ew4bR270jGS4uXC/Wve6tpk/HadlSXD77DIFY137SYd48xHZ25L7zLqq6ppc4BQUFHD58mLy8PL0KXgkJCVy8eJHk5OQ2pwYqlUrCw8MRiURMnDhRJzirLC0l4JfdiORyftmxE0WzcdReiqNk0yYsHp2C2R1BzNjYWBITE7l8+TKXL1/WabtbBabhw4czbtw4xt2RViYUCpk6dSrjx48nJCREp83ExIQJEyZQUFDAyZMnddoiIyNJS0sjKipKa3b9ezSmoxUXF+ulBhYUFHDo0KEW5/7q1atcuHCBlJQUzp8/36ZjtfPnExERQVZWFqdOndIJ7KpUKvbs2YNQKNQqM9tpp5127qT9ztDOn05+/m6Ki3+jo9uLiETGJCbNRqW6ux+ASqUgKflthEIj/P1W6Dy8FcuK+SDqAxqMA8ilAxY1p4nPOQBAxLndqGNvUO9vTY05XNqyg8LS3D/lvMoL8jn5/SbcugbQsXsQp7Z9Q1m+5lgJURsQWiQikvWnU/fJen0NpCaaVC8DBVGnnkelUqFSqYg99yICoRpr6YvcSknh4gFNOlZV5S3mX/6UhloRjg2u5AhTKUvSLACzY76jzj4FRa4FhoJeRHyznupSTZpAcuQJrseep/+UqdhaiHRLZP+2GErTNSljhuZ6Y8TOV+Oxcu0wxN0OplUXwoE3wSkAuoTBqZWQq3kQjkmNZp3Am5kNqYzsPkRvdyKBgCecbbCXtrAoNLKE4Oc0KUB/I44mjrzX5z3iCuP4PklTKa26oZr5Z+bT0bwj/+nZsuCxX4d+BNgF6G0XCAQs6rsIMwMz3jvzHvLbc//JxU/Iqszi9aDXyavJY82FNb87thJZCUvOL8Hf2p+Xur90H2epi4WlO+93mcV1oYp1B5753c/fqr7FqthVBDsEM6DDAD6++DEZFfrKgjajVmtSuuQyvfQrLfZ+0GVSy/29hoHrPVrSGZhojlV5E45oUvtUCjl7dm5BiIqBvQO5np7OxYsalVZNTQ379+/H0dGRwYN1TbSvFF3hm6vf4B3sjb29Pfv27dNTMTxwgp4En9Hw2yIouqbZdv03uPDNPanpGtUVCrmC56c/j2ELvz87Ozu6dOnS8g76vgpufTVpfBVNygKBQEBAQIBexa/7wd/fn4CAACIjI7Uqhps3bxIZGUm3bt1wcHBg3759OioGoUDI0v5LEQlEzD/TFNhdFbOKotoiPTWdQqEgPDwcI0MjZk2b9UAWTyWbNlEfn4Db+x9g66bvVyWxt8dx8SLq4uMp+fprAFQ1NeTOmYukQwd6fvBFi/ud6T+Tng49WRmzkrzqtr2Dk0gkhIWFUVVVpVWQNC4YBQIBkyZNuudzHvnUUzg4OLB//36duRcIhVhOmYLEwUGvj8jcHOfly2jIzKTwI80Ljca5NzQ0pG/fviQlJXH1qsZloKKigoMHD+Lq6npPqYHnzp3j5s2bjBkzBnPzpv84tVpN3sJFSEtKGGpnR4mxEUc/+0wzH7W15M6dg8TJCYc5uinXRUVFHDt2DG9vb9zd3Tl06BBlZZqiuImJiSQkJDBo0CCcmxl9NyKRSAgODsbQUP83ZmZmRs+ePVuce19fX4KCgjh79iw5OZpA5q1btzh9+jRdunTB0dGR/fv3U139+y8Sjhw5QkVFBcOGDdNJDWyce6lUSr9+/UhOTibhtkqrsrKSgwcP4uLigp+fH8ePH6egoAV1cDt/KY3edEFBQdrAbt3tQOb58+fJzs5mzJgxWFhY/M0jbaeddv6ptAeB2vlT0Zg6L8HSsjdeXm/h6/uB1uD4bty4sYHKyiv4+S5BKm2q1qRWq1l8bjEyhYzlA5YT2msLMrWIlJR3yS/J5Nymb5CZwCuzP2HES68hrYOvP/4jVabujkql5PCXHyEUiRj18puMeukNRGIxh9Z9RHlxJrklnyCvNGPAqPWt7sPNZziGitGILbOIi1xFzPH5SCzzMBM+Sv/Jr+Hdqy9nf9xKUXYWqw48RYEQloXMx2/wTxg1iEjKXo2sJJWknNWo6oX0Gfwto/89G4VcztGNn9FQVUnEtxvo4NeZnpNnapQ2eZfh9FpIP65REfR5BTxaNwCl9780XiuH52gUBvte16SchH0FYz/SeLSE/4uayiJezyzHtaGYxQPv7kPyT2esx1hGdhzJF3FfkFqayurY1eTX5rNswDKMJW0v19uIjZENC/ssJLk0mY3xG4nKi+KHlB+Y6T+TWd1n8WyXZ9mdtpuTOSdb3YdareaDqA+obqhm+YDlSET3r65ozsCQN5gqdWZzdRqXrmxp9XMqtYr5Z+YDsHTAUpb0W4Kh2JD5Z+ajUCla7Xc3nPKOQdpRGPE+2La9BPd949pLozqK0xgcn9v5ITkN5owJ9mDo6Alag+PS0lL2799PXV0dYWFhiJupGmQKGfPOzMPR2JF3Q94lLCyM2tpavTfpDxyBQOPhJTGG8Bc1vjx7bxtq34OarjEFaPjw4W1KAdJDKNKk4amULaenPWBCQ0MxMzMjPDyc2tpawsPDMTMzY+zYsYSFhSGTyTh48KDO3DuaODI3ZC6XCi+xNWmrVk33QrcX9NR0J0+epKCggAkTJmBiYnLf461LSqLoi3WYjwnFotFPqQXMQ0MxHzuWonVfIktMpGDNGuQ5OTivXIHItOVxiIQilvZfikqtYsHZBW1Oy3RxcWHQoEFcuXKFpKQkoqKiuHHjRpsqZbWEWCxm8uTJ1NXV3dN1b9KvH1ZPPEHZlq3UREVz6tQp8vPzGT9+PCNGjMDFxYWDBw9SUVHB3r17UalUhIWFaVMDw8PDUSpb91rLz8/nxIkTdO7cmW7ddL/nij17qY6IwO4//6Hvf/+Ll0JBbHU1GadPU7h2LfLsHJxWLEfUrDywUqlkz549SCQSJk6cyMSJEwHYu3cvlZWVbTLU/qOMGjUKCwsLnevexMSEcePGMXnyZOrr63937lNTU4mLi6N///4MGjRIJzXw9OnTOnPv6urKr7/+qp37RkPt8ePHt5qe1s5fR3NvutDQUJ3AbkFBAcePH8ff35/u3bv/3UNtp512/sGIFi9e/Jcd7Kuvvlr84ov/EAPS+yQrKwt3d/e/exj/CNRqdYseGGq1ioSr/6a+voCgwM1IJJaYmnRCVnuDW7e2Y2MzBKlU/y1hZdVVkpJm4+AwFk+P13Xa9qSFszlpM28Fv8Vg18EYSy0paBBgWHOG81H7UaWY0ueVWfh5BeHq7M3FvAsI43K5JS2li++9qQXUKlWr3h4X9odz9cQxRs56FdfOXZEaG2NmY0fcob1UCb7HwLIG/06fY23ve+ek6JR2dvEcwbX4HdQRRYM6EUWVI4PGbEMoFOLWNYCrJ38jMeoIP9hn8YJlFyYMWoxQYoK52pbs6ghysnYiMlPgKJ+EW6+nMDIzR2piQtyh/ZSlp4JSyZR5H2BkZq5ZIJZmQezXGtWAhStM/U6T+tUaAoEmCHThW9TxPyHIi9NUZvIbAxIjjUIj6kvmV5hz2qwrm13FeDn9taV/HzQCgYDejr3Zc30PhzIPcbHwIi90e4GJ3hP/8D49LT25VX2LH1N/5MytMziaOPLh4A8RC8X0cOjByZyTHMo8xETviS36/OzP2M+mhE38p+d/GObWUsH4+6eX+ygOXd1CRN45wjpNxsDAVO8z25K38dO1n1jQZwG9nXpjIjHB2dSZbcnbkAglBDsGt7Dnu1CaidXhVxC694Mxa3V+G38Jbn3h2mHyLx/hl0J3/MxqGfbUuwiFQtzd3blw4QIJCQnk5uYyYsQI/P39dbqviV3DmVtn+HTYp3hYeGBmZoZAICAmJgZbW1scWlBBPDCkpmDtAVHrNeXsa4rgiZ/A8u4lwBspKytj586duLq6Mnbs2D/uY2RkpalAFr0BjG3BpWfLn7vj3ve721tALBbj4OBAVFQU8fHxlJeXM23aNOzs7DA1NUUkEhEdHY2NjY3O3PtY+ZBWlsaua7s4l3sODwsPlg9YjkjYZH6cnZ3Nvn37CAoKon9/fSVVa//5rf3/qerryXnxXwgEAlw2rEdodHf/LpOQ3lTs2UvlwYPURsdg/fxzWE2detc+5lJzrA2t2Z6yHUupJd3tWl703TlGNzc30tLSiI+P5/r16/j6+jJ8+PA/fA00zn1MTAzW1tY4OrZcGe/OcRj37kXVkSNknD/HCbmcwMBABgwYgFAopGPHjsTGxhIfH09BQQFjxozBy8sLAwMDrK2tiYqKQiAQ4OHhoXcchULBtm0a9eqMGTO0/l0A8txcbv773xh1764xfBYK8erShbhz50hLScFxz15sn34aq2mP6ewzMjKS+Ph4Jk2ahKurK0ZGRpiamhIdHc3Vq1epr69n5syZmJrq3zfvF7FYjKOjI+fPn9e57u3t7TExMUEikRAdHY2RkZGO31AjNTU1bNu2DWtra6ZMmaKd36SkJBISEkhPTycgIICBAwciEAhwd3cnJiaG+Ph48vPzCQ0NxdvbGwMDA2xsbLTpeC3N/f8qrd0H7tb2R/oAHDx4kBs3bjBjxgysra0xNzdHpVIRHR1NamoqIpGIJ554Que6/yfRvn5q52HgYb5O33///bzFixd/9Xufa1cCtXNflFdc5OzZ/hSXnNRru3lzC2Vl5+nUaR5GRk0eGj4+izAwsCUx6S2USl1TZ6WynqSkt5BIrPH1WazTlp0Si+2T85l13Y0Z/jO02wf7vUpBbUe83MswHWrO0L5NaSMv/ms5ln1KMVZ9QWZOy1VAWqK6Ko9Hvw/io1/0U7mK445z9odv8fZ1o/OgpgW5X//B+I92wtSlBEPFaNx8hut2jFgC6/tpjGxvIxIZEBj0OQKBCrUKevX7SisJNza3oM+0yciKahh+zYqXxnyr7WfhMwObGj8wUqG6ZUu3cWu1bYEjx+DWLRB5TTVDnnoBS4dmD+Shq8DMUVOKO2yDJpDze1i6kvPIh/T2/4jvus6GkGYeTN4jiAhZwBa7kbykSqOv372XK/8n0limuVBWiJ+1Hy8HvPz7nX6HOb3nYGdsR3l9OcsHLMdQrEkLaDSXrmio4IOoD/Te5uZV57EiegU97Hsw03/mfY+jNYxN7VnW821yhWrWHnharz29PJ1PLn7CEJchTPJu+o2Ndh9NqHsoG65sIKkkqe0HvK0eUQuEMPHLtpk6P2jEBigmrCe8rh+GggbGPfWm1szcwsKC/sP7U1VVhZGdEX379tXpei73HDtSdjDTfya9HJuMN/v3769VMVRWVvKn0nkidHsMqnL1DbXvgkqlIjw8HOAPpQDp0eNp8B6p8SQqTtNvPzQHvhqs8SFrjqIBNo+D8Jd0fcfuQqPBcVVVFSEhIXh6emrb+vXrp6NiaEQgELCg7wLMDMyoldfqqenqysv5af16TNVqRo0a1ebTroqI4PqQocgS9IujFn32GfVpaTgt/UDHWLg1RJaWOC1biqKwEGknb+xef/13+wBM7jSZQS6DWk3LXB27mmkHplErb0pRFIlEhIWF0dDQgFQqZdy4cfdtZt7a3APacuzfffedjoJEaGSE3bKlnPX2xkSlYvToJhWpjY0Nw3r2pKqqio6mmnSpRhpTA0+fPt2iwfGJEycoLCzUU3SpVSpy35sHKhVOK1cguF0BzdTBgbF9+lJpYkLSwAHYvfmGzv5yc3M5deqUnqlzYGAgPj4+VFVVtdlQ+4/i7u5O3759qaqqolevXnh5NZnW9+nTRxvYKy8v1+nXaOosk8l0lIwGBgZa5aKZmRmhoaHaPtbW1jzyyCNUVVXpGWo3Vg2MjIzUpqf9rxMbG8unn36qTQ1szr59+/j222/1lFNyuZxNmzZx4MABvT6lpaV88skn2nTk5qSkpBAXF6fnTTdo0CAcHR2pqqpi/PjxD0TJ2E477fz/pl0J9Ad5mCOEDwqFoobLV56hrj6XsrJzODlOQSTSBBVqatJJuPoq1taD6OQ9V+cBUyQyxMTEh5yb36JS1WNj0ySfTk9fTXHxb3Tr+jmmpk2lzJVKBTHPTsEprx6v69VYPPIIYmuN2bKsqpKYDScw61iCq7sCZ+epCIWaNyC1NcnUqr5DLFWSnvwbfp3bVu536e4wzqqqudxQSoBchVsHjYpIWVfD7sVvoFIqmewQhUHAoxrjWqC+Pp+C2jVIcKPfsO8RNnvLTMbJ2+WUi6C6APybzCHNEnZB1Bns8hpwtvXSmOOieWBddXYWxbUKOuZY4NkjBDMbTZlPeV0dh786TX2pkEdm/oDEqMnvQCAQ4BkUTEldA4OnTNN9uJcYQqdRGiVPR91FbWuo1GqeK5CSqJRyxsSXUHtLbA00C6gyuYLpxRa4UMeG/oMQP+A0pb8Tdwt3uth04anOT2EubcEz6R6RiqQMdhnMUNeh9HDoodNma2SLWCjmh5QfcDN3w8dK4x2iUqv478n/UlBbwIaRG7A0vPd0jXvByTEA2fXf+EF2g671cjq6aIJ6cpWcVyJeoV5Zz/qR6zGR6D5g9nbqzd70vZy5dYawTmGIhS34+tzJuS8gbgupvv/GLrgVv5+/gOPRCSRnF/PomKE4+TQFUVRqFUsTl5LYkMhl48sM9hiMjZENABX1Fbz020vYG9trFV2NNFcx5Ofn07179z+vWhhoPJEcu0LPZ9scSDt//jyXLl1i3LhxD+ZtvkAAHoPg0ma4cRYCn2gaS8qvcGSO5r5XVwE+zYIsJ1dA/E4ouKoxvHZsm9m5u7s79vb29O7dW6eUuUAg0M59Xl6eztwbiY0Y2GEgo9xH0cVW1+MofOVKbopE9D9+AgdvL6QtzMmd//mKoiJyXpiFsqSE2osXsZwyRWuAXHvhAvkLF2H52GPYPPtMm84JwKBjR4y6dcP6mWcQtzE1SyAQEOIUwi9pv3Ah/wKTvCdpKxSeyjnFypiVFMuKqayvZLBrk5+ViYkJ7u7uBAcHY21t3dru20yjgiQ2Npbc3FyduY+Pj+fkyZNUVFSgVqt1AncRly+TWVxMvxMncfD0RHq7Ta1QoFiwEJNrqXS6dAnrUY8gajYn7u7uxMfHc+3aNYKCgrTXQaOiq0ePHvTrp2viX7Z1G+U7duCwcAGmdwR17f18KU9L46pajbuXl9bPSi6Xs337dgQCATNmzNAxfBYIBHh7e+Pk5ERgYOCf+zu/fc52dnaEhIS0et3fec9JSEggMjKS4cOH07lzZ539mZub4+bmRkhIiI5nEoCzszP29vb069dPT1Hi7u5OQkICqampOnP/v0hhYSE//vgjMpmMgoICvbk/fvw4lZWVKJVKncDdsWPHSE5OJjc3F3t7e20AUaVSsWPHDgoLC8nIyKBz587aqow1NTVs374da2trJk+erPMsKxQK8fHxwd3dHT8/P/7JtK+f2nkYeJiv03YlUDt/OtfTVyKT5eDjsxi5vILU1IWo1WqNqXPSW4hExnqmzo3Y2AykQ4eZZOd8S1lZNABlZTFk53xLhw4zsLHRNV/9bfUbuKVXUfTMaETGJuS+Owe1XI5area3TV8iK5Ph12kF9fW5pF3XVLpSKutITHoLqdSekrKuWDtUsHv/C3pjuZMT59cS3lDAU8aeeCoFLEzYQEWFpmT4+U/+Q1G1mJFj+mIsksNejQ+GWq0mOXkOarWCniEbEYmaPTTJyjV+GTadoN9rcGWHpsIWQH4CnFiOl9cQ3Dv2gaMLoERTwWv/yXlEqCsJHuCFmY0th7/8CPlt479T27+jvKCQgZM/wthKP/3DyMwcKy/flh9Kbb3Bc7D+9lbYdLOIc+U1zPN0wkQs4rWkbBpue3+8d+0mJXIlXwR1w9Dg/sqV/xMZ7DoYB5MHl9LT0bwjIU4hLbY92+VZAu0CWR61nPyafAB2pOwgOj+ad3q9g6vZPVS/ug9eHbcZb5WQRYlfU16WCcDX8V+TVJLEgr4LsDWy1etjIbVgSf8lpFek8/mlz3//IAVJcPwD8BtHgcP9lRC/H7Kzszl79ixBQUH49tatPLYzZSfR+dE8OuBRpMZS3otsMvZeGbOSElkJKwas0Cq6mmNjY8PIkSNJT0/nwoULf+5JSE2h65SWDbVboLCwkIiICHx9fQkMbJtyqE2YOWp8wm5dbKoaWFOsCX47dNP4i8Vu0qSiAuTEQuSHEDAd3PrBoXegvG3KAolEQrdu3VqsPGZjY8MjjzxCRkYGsbGxOm3eVt56AdiEPXtJBLoLhbja2JC3YCGK0tK7Hr/RWFhVW4vD/Pk0ZGRQ9LHmnJXVt02dXVxwePedNp1Pc0wHD0bi5HRPfWyNbFnQZwFXS66yKWETAGV1ZSw6twgfKx9m+M1g17VdRN6M1OnXsWPHB5qyaG1tzahRo8jMzNTOfUVFBb/++iuurq4EBgZy5swZrYIkPT2dmJgYQnr1ws329tyXaIoalGz6hrorV+g5fQaGarXmP7+ZB5CRkRGTJk2ipKSEiIgIAOrr6wkPD8fS0lJP0VWfkUHhhx9iOngwlo8+2uL4xzz9NNbW1jomu8ePH6eoqIiJEydqF+PNaUzB+isqMInF4lave2tra7y8vMjMzCQmRqN6bm6ofWdArBFPT09sbGz0tgsEArp06dLiORsaGjJp0iRKS0u15tL/iygUCnbv3o1UKmX48OFkZWURHa15nm1uqN1o7H3jxg2gydQ5ODgYZ2dn9u/fT1VVFaAxM8/JyWHkyJGIxWKt91Wjoquuro7JkyfreNM1Ym5ujq+vr972dtppp52WaFcC/UEe5gjhg6C45CRpactwc3sBD/dXEAjE3Lz1PcbGHhQX/0Z+wV46d16LhYV+xaRGrKxCKCg8SFHRURzsx3Al/kUkEku6df1Sq+QBSLsYgfT9dWR3s2PYxzswcOtI2ZYtIUyLGgAAIABJREFUIBSSragj6ped9J82k64DJ6NU1nLz5hbMzQPIzd1JSclxunVbR1DAf4i/sBlz03RkSl/sbVv2rSktvc7LZ+fgphax9tFfCTRzZfutE+SmH6FLpQVH9p6ii4cpvf+7TuN/Eb0BjKy5JUjl5q0t+Pgs0lE2AZpqWjnRMGOXJnUj7Sgk7NIs3HY9DWoVPPEz+DwCFzdD9jnyHPx47dIauiJl0dQ9OHh04uLBPdTLahEKhZzY/BU9x04iYERoi+cBD+YaTa2p48XELIZbm7PCxwVPYylf39SUAi5uULA2q4C3PRyZ6PDgqgD9ryIUCAl2CGZn6k6SS5LpYtOF2adm079Df2YHz/7T3zI3IhJLCTTuwPZbEdxKP0IH597MOzOPcZ7jeLF76/dvN3M3SmQl7EjZQbBjMB1MO7T8QUUD/PCopkrdzF/Iyi36W+6lDQ0NbNu2DQMDAx5//HGdh+rMikxmn5xNH+c+LOizAHdzd7Ylb0OlVlHZUMnncZ/zcsDLjPEc0+r+nZ2dycnJIS4urtXF1F+NQqFg+/btKJVKZs6ciVQqfbAHsPeH4utwYZOmetmxhVCQqLm/dZ2iKSefGA5dJ8POGZoqbdN3aNRMF76B3EvQ/fH79oZydnbm5s2bXLp06a5zX11QwA+//IyJXM7MuXMxDelN2dZtNGRlYhYaqvOba34/rdi9m9JvvsXhnbexfupJlGXllG3dhnFwL0o3b6Y2KgrXL9dh0LHjfZ3HveBl6cWNyhvsSt3FQJeBfHLpE1LKUlg/Yj2hnqFE3IjgSNYRJnlPajFw+aBwcnLi1q1bXLp0ic6dO7N//34qKip48skn8ff31ypI/P392bFjB2ZmZjw2bRqmwcG35z4LAw8Pbr3zDuajR+EwZw4SJ0fKtm5FYGiIcbO0MCsrK2QyGdHR0bi5uREdHU1GRgaPP/44trZNwWq1QkHOSy+jrq3FbdPXiFpJlRGJRDg7OxMVFUVNTQ2GhoYcOHCA4OBgvXTQfyLFxcUYGBhw6dIl/P39OXDggHbuH/T9x8rKirq6OqKjo3F1dX0garKHjZMnT5KYmMjkyZPp0aMHeXl5XLx4EX9/fw4ePEh5eTlPPvkknTt3JjExkZSUFDp37syOHTswNTVl2rRpeHh4EB0dTVFREfb29vzyyy/4+fkxevRorKysiI6ORiQSUVFRQWRkZIvedA8b/+vrp3YeDh7m67StSqD2INAf5GG+OO4Xubycy5efxdDQma5dPkMoFGNhEURp2Vly836mrOwcDg7j8PR49a77EQolmJt3IzvnO/LyfqahoYiA7l9hbOyu/UxDfS3xzzyOSK6k6/c7MbWwQertRUN2Nnk/7eLUrXTsPbwY9dIbmpK0Fr0oKj5GXt5uysujcOnwJK6uT2lSs6Q+VJYdJC/7BJ18n9dN10KTfrVg1yRSBXWsH7gae/vO2Nv6o846y4/VNzAMT8ZYCJOWbkBsZKYpk54bR23S98RLL2Bl3Q+fTvN1F+vJ+zVeQIPfgYBpmmo6bn0g+itNVaKKbHj0W3DqDlIzsHBFFb2e/+ZHUCASsmHEBiyt3LGwd6C+ppq4w/vJjLuAuZ0D49+cg7CZDFupViMA7fHv9xqVq9TMTMigTqViR4AXJmIRnUwMuVFXz+bcYk6VVdHZxIhP/NwQ/tWGvv9PsZBaYG5gzg8pP3A46zBioZgNIzZgYvDX5vfb2voiyo5ie20mv2UcxNzQis+Hf45U1CxooFJpApiCpjfgvRx7cSjzEMdzjhPWKQwDUQvGlCdXaAIBUzaBc+Dfdi89fPgw6enpTJ8+XWfBqFApeO34a9Qoatg4YiMmBiZ4WHiQX5PPjtQdnM09i7elN0sHaEqPt0ZjesyFCxfIyclpNV1EqVS2qiK4W9sfofmipUOHVoJ094v7QLi8Ay5vh7wrMHwhdJ6gUSq5BGsC53HbNT5Gj28HO1+NuXSzoDou92gwfgeNhsEXL14kOzubgICAFudx14qVFInFTAsdg623N2JbWwQGEsq2bcfAzRXDZmkVjddpw81bGmPhoCAcFy1EIBBoDI4PH6Zi715kFy9qTJ1bUZv8mfR27M2+9H3sTd9LUkkSrwW9xiPujyAWiulu153tydu5VX2Lke4jW+yvUCm0qWR/lMbr/uLFi8TFxVFUVKQ1dW40OI6KiuLy5cvU1tbyxBNPYGlpidjGBoFUStnWbVQdOYLQxBjXDRsQGhkh9fGh/vp1yn78EbNhQxE3+702GhxfuXKF7Oxs+vbtq+NhA1C4/kuq9h/AeeVKjALuXjHJwsIChUJBTEwMqampmJmZMW3atBaVF/80bty4wdChQ7l06ZJ27htNne8XtVqNSo3Of33Hjh1JTk4mMSmJoMDAFhVKf+X97W486HHcvHmTPXv26BlqX7p0icuXL1NYWMjo0aPp1KkTYrEYJycnzp8/z+XLl6mpqWH69OlYW1tjYmKCgYEBMTExJCYmIpFItKbO9vb2FBcXc+HCBTIyMujQoQPjx4//y14I/Vn8L6+f2nl4eJiv0/Z0sHb+NFJTFyGXl9Kl84eIbi8KBQIRnf3XoFYrMZDY6Jk6t4aFRQ+cBaHIFeU4MQpLS92Ht51vPk2yhSPVL8/ArkPTg4zDvHkkeDihkNUy6oVXtcEQkUiKn/sSFPUVGNSY4uXVVB7ev9NwKqt6YmFbw88/6Jcx/23zvxjnVMYCVS98vJsUNi+M/ZpXVUK8J2fTe8YIpNa3pfoCAarxH5PkY4xQIcffZ5nun3N1Eex/UxMsGtSsTL29v2ZhJCuFHk+Bb7OxdJ3CDp/+REvFvOPyCK6uTW8fB8x4GmtnFxpktYx5dTbiZnn6dUoVYy5e46mETFQPqDT1Jzfyia+SsdrHFTuDpoe7pd4dcDSQIFep+byzG2Lhw/1A8k/jMd/H6O/cn/L6chb0WYCd8Z9nNno3ng39iu4qCeVKGUuC3sDcoJlnhEoJ28Lgu1CNsuc2xhJjlg9cTm51Lmti1+jvtDEFKPAJ8Gu9ZPafzfXr14mNjaVv3756f/LfJHxDQnEC8/vM15n7d3q9g6OxI/WKelYMWIFE+Pv+VxYWFowdO5acnBzOnTun156YmMjq1avJyNA39I2IiODjjz/WM9n9o9y8eZPIyEgCAgL+3DfJxtYwcZ3m/ubaR5MC24hzEAx6R9PW598aH6FGejyl8Sv7bREUXbvvYZibmzN27Fhu3rzZ4txf2L6d6xIxvUxN8Rg4QLvd+tlnMerRg/yly5Dn5en0UatU5M2dCwIBziuWa03EhUZGOK9aibKyEmmnTm02dX7QWEgt+KD/B5TXlxNoF8izXZ7VtnW26cxLAS9xKOsQhzMP6/XdkriFIbuGkF6eft/jMDc3Z9y4cchkMry9vXVMnT08POjTpw8ymYxBgwbpBCOtn3kao+CeKMvLcV66VGuoLRAIcFy8CJGFBbnvzkHV0HTPMTAwYOLIkdTV1mKlVjNsmG71xMSz+yhct47ywd0xH9020+8hQ4bg4OCgNVN+4Iq5PxEzMzPt3N9p6vxHUanUPP/9BSZ/eZZ6RVNKnkQiYWToeCorK1m+cYdev9zcXNasWdNiSuzly5dZvXr1X2IunZWVxerVq7l6Vd/APTo6mrVr11JQUNDm/TU0NBAeHo6ZmZmOmbmZmRnjx49HJpPh6elJr15NBQM6duxIv379kMlkeqbOISEhdOzYEZlMpmfqPGbMGIyNjVGpVA/GxL+ddtpp5zbtSqA/yMMcIbwfCgoOkJn1GZ4eb+DgME6nTSKxxNZmMB06zMDQsG0+A4qyMsr/9RHixDqkByuxnBSmLaV7ZtdXpF28ilIkRCgxp8vgYQhuv6VMiDzO1fiL+N8qxqFBgenAphSs0mXrYHcqxseUGDn7Yujjc/tgDfhGfsqlBiXWDqWU5YGzm8afJTV6NzUGW1FJZBgbVGFrMwEDY02p19S47YiNjyEyUJEhukFX9+e0wZ4bedvJqzmPf2oFlgozcL9dWlitht2zoCgFZu4Gszvmo0MwuPSCXs/rlGjPqMxkdupm+lv6Mnv0V3cYaovx7t2HTr374eStm/e9LCOXA0UVZMjqsZaI6WFucl/X6OXKWl5PyWaKgxVvuuuW+zUUCRlta0GYgxX+pv//fID+bgQCAYNdBxPiFMIQ1yF/2ziEIjHDHHoxMGozfcoLoftjTWk6Zz/TpC5W3gIEOot5JxMn6pR1/JDyA11suuBu4a5paKiFbZNvpwD9ALdTUv7qe6lMJmPbtm2Ym5szdepUHVPT5JJk5kbOZZT7KF4O1K0IZyAyYLjbcEI9QvG1brvvgr29PUVFRcTGxuLr66stIV1ZWcn27dupr68nMzOToKAgrdogMzOTffv20dDQQFFR0X2bSzemvonFYqZPn97iG/sHio0ndBwAfV7WfN/Nce2juff1fFajjGxEIACPgXDpe8g6A4Ez77tiXOOb9NjYWHx8fDAzMwOgNDOTXYcPY1nfwONz5iBspvIQCIUY9+pF2Y4d1CVexWLCBAQCAVlZWZifOkX5rl04Ll6MSYiut5fE0RGTvv2wenImYguL+xr3/eBq7kovx1484f8ExhLdFKBA+0DO5Z5jf8Z+xnmO0xq8p5am8tbpt5ApZMQXxzPJe9JdVW5twd7eHldXV/r06aN3vbm7u2u9UpovagVCIWbDhmEyYCCmA/rr9BEaGWHg4UHZ91tAocSkX9MLkurlK7CMjMQ74SrmPp2Q3jbgra0uJ+25p1CgZO6EaoZ1GoWl9PcNt4VCIX5+fvj5+dHxL0zpu18a76V3m/s/wuZzWWw+l0VBZT1ypYqBnZqC4x8czSQ1vwrnhpvcqpPQ3dsNaDLUrqys1DM4LisrY8eOHTQ0NHDjxo0/1Vy6rq6OrVu3UlNTQ0ZGBt26dcPQUPPfU1BQwK5du2hoaODmzZsEBga2Kchy9OhR0tLSmDZtGvb29jptdnZ2v3vd9+jRQ/e6Fwjw8/PDy8uLTp066fSRSCT4+fnRvXt3vWM9rPyvrp/aebh4mK/TdiVQOw+c+voCUlIXYW4eQMeOL7X4GTOzLhgbt+2hSa1Wk7/4fVRllXg+sxZ1eRX5ixajVqupKM7nys5fkCiV9J36OLmpSVw8sAeAsvxcTm79ho7dgwh8ZCyl32+hJkpjxlcVEUFFeDhOI/+FacdA8j/4AHnjG55TKxEVJhLsPAOlXMit/PXU1pQgr5ORd+NL1AIVJgVTUBqVceXofwGoLs8lJ38V8ioTKo2H4SQo4uCVOZpjVSWRkfkp9vZjcHCcAKdWQW6c5liXf4DUgxrFj30LlRqEQug0UqdEu0KlYF7kPAzFhiwe8YX2LbPO/Frb4uyj+xY/qryaDTlFPOVswzBrM5am55JeW9em76AlZEoVryXfwN5AwrJOLaeMdDSS0t3s7/c4+f+KmYEZfZ3/fg8KK+ce9Bq8ENIj4MK3mo0FiXBiGfiP1/i3RH4IN3VL2b4S+AqdrDqx6Nwiyupul839bRGUpsOkL7UV9f4Ofv31V2pqapg8ebLOQ3q9sp73zryHlaEV8/rMa7Gvs6mzXmWp30MgEDB27FiMjIwIDw9HoVCgVqvZt28fCoWCsLAwqqqqOHToEKBZtOzZs0dbpvlBmEtHRERQUlLCpEmTMDL6iwK3HgM1qqA7EYk1/mfiFlIFzRxh3Mcab6AzH933EBrn3tjYWDv3KpWK8I0bUYhETJn+OGJDfX8cAzc3HN55h9rzUZT9oFE4iHLzKProY0yHDcNicliLxzPuEYTkH7BQ6+XYCytDfZ82sVDMsgHLqFPUsejcItRqNQ3KBt478x4WBhYs7LuQpJIkNsVveiDj8PLy0i64dcYhFuPj49Piwl9kaYlJn5bN882GDsXi0SmUfPMNtZcuAVD5669U/vorftOmYeXpSf6ixVpz6eMLXsChsIGad55FYSpl3pl5KFSKFvetdywzs4cqAHQnrc39vXK9sJqVh1IY5mfP9N6ufHU6g9gsjXH6wfg89l7OZcCAgdSIzLgadYKsfI1n4IkTJ7SG2s0NjlUqFXv2aJ7lGs2ljx07dt/jbI0jR45QWVlJWFgYSqWSffv2oVarUSgUhIeHI5VKGT9+PPn5+Zw+ffp395eRkUF0dDS9e/fWqXLXHC8vrxbvsyKRqNXr3sjIqNX9WVtb43SPZvHttNNOO79HexConTahVqtJTpmLSlVHZ/+1CNtSAvp3qDxwkKojR7B77TUsxo/H7o3XqTp2jMr9+/nlrRepk0jwHT2EvlOeoFPvfpz9cSuFWRkcXvcxIpGYUS+9gcPbb2HQsSO5783V+AQtXITU3x+7117FedVK1PX15M2bjzo7WlOxJnAmHsPm0VATjKl1A3t+Gs+JbS+itM1Emd2bPtNXY1w4lDqHaBJ/Xc+5488jMmzA13sZE3qvJ19liahkN+mFZ0hMmo1EYomf7xIEY9aCiR2EvwTFaXDo3dtvwv/d5vnYlLCJqyVX7ykFqFqh5PXkbNwMDVjk5cxHfm5IhUJeS85G+QezwlZk5JFWW88nfm5YSP75Pgjt/MkEPw+eQ+HofChKhd3/0gRxxn0Coas0C/fwf2mUPrcxEBmwYsAKKhoq+CDqA9TXj0PMVxDysm4K0F9MYmIiCQkJDBo0CGdnZ522L+K+4Hr5dZb0X4KF9MEGqUxMTJgwYQIFBQWcPHmSixcvcv36dUaOHKn1lLhy5QrJycnaRcukSZPo27cvXl5eHD16lJLbC9t7pS2Lln8UXcKg21TdoPp9YGxszIQJEygsLOTEiROc3bSJHEND+tvb4xwU1Go/y2mPYTJwIIVr11KflobF5u8QmpjgtOT9h9qTw8PCg//0/A9nbp3h57Sf+fLyl1wru8b7/d5nqs9UxnqOZWP8RhKLE//uobaIxijaidw5c2m4cYP895dg2L07tv9+GedVK1FVV5O3cBEXD2/F41Ai6cM68chj7zAvZB5Xiq6wOXHz330KDw0KpYrZuy5jZCBi5eRuzBvbGRcrI2bvukJWcQ3z9yQQ4GLBGyN9mTZ1CmK1kvVbdpGVlcW5c+cIDg4mKCiIcePGcevWLc6ePUt0dDQ3btwgNDSUwMBA+vTpQ2xsLNevX3/g409NTSUuLo7+/fsTEBCgE1Q/ffo0+fn5TJgwgZ49exIQEEBkZORd09MaA/Q2NjaMGDGi1c+100477TwMtAeBHmJkCtkD3Z9K1YCqlbdkmkpbp/D2egcTE92FhLy+ddVJa23y/HzyP/gAo6AgbJ5/DmjyYriychllMhWWRkIemTUHgUDAiFmvIDUx5cfF75J7LZnhz72EmY0tQmNjnFetRJFfQGbYZFSVlTivWonAwAADd3fs336LmjNnKF/6Api7wGhN+fgJj/1A0U0z7F0KEHeMRVToxdCnvwagx4SPEFc5USD+ApHlNSR1Q/DoMh6RUMzAoE2ogbSE56ipuYa/3wokEiuNsenEdVCUgmrjKECtUTw0U/Oo1WpUDco7pwKAxJJENl7ZyBiPMYxy1/UtqFVqStC3xOLrueTUNfC5vxsmYhGOUgkrfVy4VFnLPlr2MVCp1ciUqhbbzpRV8dXNIp7tYMtga7MWP9PO/xhCoebaFkrg6+FQkADjPwMTWzCy1LSVpEHE+zrdfK19eSXwFY7dOMavh18DWx8YsUjnM43KjJaor6xste1uNDTzC2lOVVUVBw4cwNnZmYEDdSv4Xci/wPeJ3/OYz2MM6DCgxf73i6+vLz169ODs2bMcOXIEDw8PrWfEoEGDcHJyIjw8XLtocXNzQyAQMHHiREQikfZNeku0ds4ymewfsWhRq1So6lr+L1DV1+uU/gZgzBowsUO1618gb6WfrPX/vzvbfHx86NmzJ2fPnuVkdjZOMhlD/n33AL1AIMBp6VIEUilZj09Hkp2D45L3dUyJH1am+00nxCmENbFr+C7xO6Z0msJg18EAzO09FxsjG+aemUud4o8rSh8Udz7niExNcVqxHHlODhmTp6Cqr8d55UoEYrHGj+nNN6mOiED47gpKbMQMWfEdAKEeoYxyH8W6y+tIKU35O07loePLk+lcuVnBskndsDc3xFQq5sOpgeSU1TLu8zPUNij58LFAJCIhwX7uWPv0xKi2kC3btmNlZcXIkRoD8q5du9K1a1dOnjzJb7/9hq+vL4GBgQAMHz4cW1tb9uzdS21tbYvjaO3+djdqamrYt28fDg4ODBkyBIDg4GC8vLw4cuQIkZGRBAYG4nfb/D00NBQzMzPCw8NbPd6hQ4eoqqoiLCwMA4MWlIzttPMXIWtlLaFWq1tta6edO2kPAj2kXCy4yIAdA9ievP2B7E+prCP2QhiX4qbrBYJqa2+Qdn05Vlb9cHF5Uqct/WIM6557nKTTx/X2ef7nHXw56wkKs3RNT9VqNXnvzUMtl+O8cgWC29JYgUiE0bzZxDtaYSiXM2XtRm0fY3MLRr74Gg0yGZ1C+uE3YIi2zSgwEJtZs1DV1GD35htNHkCA1fTpmPjYUnC2gYbei8Gwydx20ICNiOotECgldOj4MuLbqSFSEzNczd5ELZQjKnOkz4jPtH3cbIIwqRiDRKBEktcVW9uhTSfmPZxq56XkVn1NfY+PwUpXSl720zXyV8eirKzX2V6vrGde5DysDa15L+Q9nbYbsnp6nEvkvbRbevN7rLiCbXklvOJmT29LU+32SQ5WTLK35GcMSajSfahSq9U8k5DJoJgUyuW633OlQskbydl4GkmZ79UuPW6nGRYdNAvzhiqNV4tfs9LoXkOh9780lZ0yTup0e6bLMwQIzVhmDPmhy3XTHxUKvvnmG+Li4lAodK/F4pQUPlq5kp/eX3JPw4yMjGT16tXcuqX7e2lMv5LL5YSFhenI8WvkNcw/Ox8XMxdmB8++p+PdK6NGjcLCwgKhUKhj8ikWi7XpCs0XLdAGg+MLF1i1ahXp6fqGvocPH/7bFy1qtZpbb7xJeugYFGVlOm2qmhoyJ4WR/fwLuoEgIyvqeywgbVMFhW9O09tn5eHDXOsdQuVhfYPjwg8/JG3AQOrvmI+Rw4djKpcjVKuZ8vzzOpUVW0PiYI/jwgWoamqQhYRgPrLlqloPG0KBkKX9NdXtnEyceLtXU+GCRnPpzIpMPr306d84SkgsTmTQzkFsStBNTzPp3ZuSif1Q19RQ/UIYUk8PbZv1009R6GOLQYMaiw8WYGphA2iCevND5mMptWRu5FwalPceWPhfIuFmBZ9FpDEx0Jmx3ZueB3p7WDNroCfV9QreHe2Ht33Ts8frj4+hxsAKpVxO/+GhOobajQbHjelXjWo6iUTC4EfGUVlVzbIWzKUzMzNZtWoVMTExbR67Wq3mwIED1NXVERYWpvVaawyqi8VizM3NdUydDQ0Ntelpv/32m94+k5OTuXLlCgMHDsTFxaXNY2mnnQfN5rOZBCw5SkxmqV7bf3ddYdCaExRW/v0B/Hb++bQHgR5CauQ1zDszjwZVAx9d+OiBVPNIz1hLdXUKFRWXuHFjvXa7Wq0kKfmd29W/VmmNmQFqKys4uvEzlAoFEd9uoLKoUNuWl5bK+Z93oKiv59AXH6KQy7VtZTt2UHPuHA7vvI3BHTn33+z6GJlERMArz2FpqxuI8A4OYcayDwl9dbaeHN/u9dfo+MN2rJ99Vme7IOMETn5XEUik5H7xi85CQ7grB/eYRVh91xmzE8nNzlmN5Kfj2OwcjEfcfKp+OKNtU5RV4nFmGG7R83G/8gppERHaNnlhLeXZQYABpVfcUdU1LWxr44uovVSIqlpO2S9pOsqezy99TnpFul4ailKt5o3kbMoVSr67VUxESaW2rVSuYHZqDv4mhrztoWvcDLDCxwVz1LyWnE1dM9XPltwSjpZUklPXwLw7AksL026RVy/XqIr+JJPGdh5iuj8Gzx+DcS14tYxYDDbesOcVqGuqZiVO+ZVlN1JRiCUsyvhZ57o/ceIEeXl5VFVV6XgxqJRKfv7uO+oNDEgWwOWffmrT8HJzczlx4oTW60He7J4TFxdHWloaI0aMwM5ON9VyTewacqtzWTZgmZ6R7oNGKpXy3HPPMWvWLCzuMA+2t7fnxRdf5KmnntIrR921a1e6dOnCiRMnyM/P124vKSnhyJEjKJVK9u7di6yZAuafsmip2L2bqmPHUOTlkf/+Ep1roGD1GhoyM6mNiqL0+y3a7Wq5nNx1e1AphJREpFKz7xttm7ywUOMdJ5eTv2gx8sKm/52amBhKNn2DqqaG3HfnoG52DdTs/JFhB39lRrdu2DZ7UfB7WIwdi/vOHVTOfOKPTsE/EkcTR3aO28mW0C1ag+hG+jn343Hfx9mWvI2YvLYvvh8kdYo6jRpJWce6uHUkljSlp+VU5vBWlyvMf1LEu3Ynqahvuuecyo3k7XFlRC97lIBhj+ns09LQkvf7vc/18ut8cfmLv+xcHjbq5Er+u+syNqYGLJnQVa/9nVG+/PJyX57t766zXSQS8tKzTxFBN9acLUGlavqtGxsb88ILL/DCCy9ozfFB87y15kwhV+ROSCpy2HrobNM4bqdfKZVKjh49SlFRUZvGHx8fT3JyMkOHDsXRUff5yNzcnFmzZvH888/reSZ5enoSEhJCTEyMTlC9urqa/fv34+joyKBBf186czvtpBVUsfxQCg0KFbN/ukx1fdM6Y9+VXMLjblFUVc+c3QmtZhC0004j7UGgh5DGRcvHQz7GRGLC3Mi5yFXy3+/YCqVl58nJ+Q6XDk/i4DCBzKwvqKzSlNLMzv6GiooL+HRaiKFhk4eGWq3mt6/XUV9TzcS3F6BWqzm8/hPUKhXy+joOrfsIUxsbxrz+NsU5Nzi3axsADVlZFK5Zi8mAAVg+/rjOOH45uBFpShmSft4MGK7/9hfAydsXiYF+mpNAJMK4Rw9dM2VZGex9FYlbJxwXLkQWF0fJtxpz2+rIeORidpbrAAAgAElEQVSltkhqa3Hs1p2yLVupiYoCoGJ3ONUnTuDSpy/C6mpkiVCXfhOAgjUHERpYYeRkh1ohR7CngPrqatRKFaW7UhEaiLCZ6Y+yvJ7yAxoFlLKygfI915G4mmEx1pO61DJqYjQLudj8WLYkbWGa7zT6d9CthvJVThFRFTWs9nHBz8SQ//4fe+cdFsW1/vHP7C679N6lCYpiA7uxG3uNGMu96dckmsSYxBKNvYIttkRT/KUY062xRmPvvYAoRQQE6b0ssHV+f6wCK6Co6DW5fJ7HR50z58yZwzDnzHve9/tGJZKjMYjKTo2+Ta5Gx5om3iiqEJC2M5ExhmKilKUsjTdcK75YxdzYFLrZWTHJx4Ut6bnszMgDYG9mPr+l5TDe24XWNhaV2qujDgQBPNuBrIowQ7k5BH8NhSnwp0E4naIM2PUR3k7NmNR2CqdSTrExeiMAt27d4uTJk7Ru3RoXFxeOHz/O7duG37Eja9eSZmZGD2dn7EpK2HvpEgXJlT3hKqLRaNi2bRsWFhYMHz6crKwsDt4x0Obm5rJ37158fHxo166dUb1jt4+x5cYW/tPsP7R0rl4fpjaxtrbGsZqQIhcXF6P0wHepKHC8detWtFotOp2Obdu2IZVKGTVqFIWFhey94xnzrHy0qG/fJj0kFPO2bXH66CMK9+6lYPceQx+PHSPv99+xHz0ay149yVy1CtWNGwBkfb2O0ogI3BbOxcRaIHXBp+iyUgxepLNmoVep8PjiC/SlpaTOMsw/uqIiUqdNx8TTE7fFiyiNiCBrnSE5RmlMDJkrV+LUqRM+o6qeW+6HWVAQPOmMav8FvK29cTavWsh6QusJeFt7M/PkTIrURU+5Z7D60mri8+NZ1m0Z9qb2zDg+A5VOhU6vY+bJmUikJox79TNyVLmEng0FIKc0hzmn5uDp2ohXXphVZbtdPboy3H846yPWcyn90tO8pb8Ny/+K5kZGEcuGB2JjXvm5l0kltPa2r1Iby8/Njg8Gt+NsfA7fnYw3KrO1tcXe3lgs/ueziRyLyWRw354oZdZcP1suLr13714KCgoYNWoUJiYmZQah+5Gfn8+ePXvw9PSkY8eOVZ7j4OCAtbV1lWW9evXCwcGhzKguiiI7d+5EpVIxbNiwSgb6Oup4Wmh0eiZsvIKlQsZXr7Tidm4JIbuvA5BeUMqsPyJo6WXLjAEBHIrK4Pfz1etb1VEH1MAIJAiCpyAIhwVBuC4IwjVBED68c9xeEIT9giDcuPN35VQUddQ6FT9aenn3Ys5zc4jMieT/wv/vkdrTaguJvD4FMzMfGjSYQiP/uchNHLh+fTIFBeHcjFuJk1MfXF2Ns6FEnjjCjXOn6DjyFRq0aU+P198m6Vo4l/fu5PgvP5Cbmky/dycQ0KkbzXv25fzOrdy+Fk7KJ9MQTExwC1lotIC4nR5P9O/bUdoJvPPOoscaozL2TIGidAj+CuvgF7Hq04fMzz6n+HIYOVtiQavEZWJvnCdNRO7jQ8q06ZRGRZEeGop5u3Y4jH4DhzeCQJCSufYEuZuOIuo9kJql4fHGILL9MzC18OTqwm8oPJyE5nYRtsENMGvmiFU3D4ovpFNyPZvcLTGIGj32I/2x7OSOooEt+bvjKEjPYdbJWXhYeTCx9USjrkcpS1gUl0p/RxtedXfg8wAvsjVapsXc5o+MPHZm5vFxfVea3idFe0tBy2vuDnyZlMHJ3EI+iEzERAIrG3vykbcrgVZmTI1JIrKohEnRSTS1NGWSj0u17dVRx33xaANdJkHYLxC5E3Z8AKoiCP6akY3/TUf3jiy/uJzYrFj++OMP7Ozs6NOnDw0bNizTYkg4d46TmZl4lqro8s47BAcHo5bJ2Lp27X31gQ4dOlSWiaZZs2a0bduWM2fOEBcXx7Zt2xAEwSj8CiC3NJfZJ2fT0K4h44LGPY0ReizuFTg+deoUt2/fZuDAgQQEBNC1a1fCwsK4fv36M/HRIur1pE6bDoKA26JFOLz9FmZBQaTNn09pdDSpM2YaNFw+/AC3efOQWFqSPHUqxZcuk/Xll1gPHozt8FG4z5uBpkgkfcKr5G3ahPLoMZwnTcLq+R44T56M8ugx8jZtIn3xYjSpqbgvXozt0KFYDx5M1pdfUXz5MimffILEyupvL+r8NDE3MSekcwjpxeksOb/kqV77XOo5for8iX83/jf9fPoxv9N8bubf5PNLn7Ph+gYuZVxiWvtpPO/1PGMDx7Infg97E/ay4PQCCtQFhHYORS6tPvxxcpvJuFu6M+PEDIo1VevQ/K9yJi6bb07E80oHL7r61yxBxb2MaO1BrwBnlu6L5kZ6YbXnJWQpCdkdSZeGjozu7Mu/hr+IVNTx5Q8biYyM5MqVK3Tu3JmAgIAycekTJ05U255er2f79u3o9XqCg4NrlO79XkxMTIwyNoaFhREdHU3Pnj3/MSna6/h78vmhWCKSCwgNbk6/Zm6M6erLr+eSOBiZzpTN4ai0OlaMDOLNzvV5zteBBbuuk5RT936ro3pq8obUApNEUWwCdADGCYLQBPgEOCiKYkPg4J3/11ELlKVUvoe80jzmnJpj9NHS07sng30H8+3l/yMspepdrXxVPnqx6g+omBsLKVWl0bTJp0il5piY2BAQsBil8gYXL41CJrOicSNjg01OWjIHv/0C90ZNaDPYYBxq1qM3vq3acvTn77m8dyet+g/Bq1kLALq/+iY2Ts7sWrqAwvAwXGfPxsSl3Nig1+v5fsVUZBqBQeOnYKqohZCMa3/A1Y3QbQrUa4UgCLjOnYPUxoa00C1ITJ2w7GiFiZsjEjMz3JcuQZuRQcJIwy6xW2gogkSCeVBDFN7FCPJ6FJ3ToS/NxGXyEABavfMfckrCcNEHkX/wFuZBTpg3NyyarHt5Y+JqQfYvkZRG52LTzwcTJ3MEiYDdcH+QCMT8cJL0ojRCO4cahaGo9XrGX0/ESiZlaSMPBEGguZU5k31c2Z6Rx0dRibSxNuc9zwcvSOb4ueNlKuel8DjOFyhZ1NADd1M5JhKBzwO8Kdbp6XcxhkKtjjUB3sgfYdFURx1ldJ0Cri1g85sQ86dBCNq5MYIgMK/jPGQSGWt/X0tubi5Dhw5FoVAgk8kYOnQo2dnZbNi1C5lOx4vvjEUikeDVoQPt7exIkMs5t2FDlZdMSEjg9OnTtGnThgYNGgDQu3dv7O3t+fnnn0lMTKR///7Y2tqW1RFFkWUHZpOvzmdR50VGH4yiKFbSrnlW8Pf3LxOXPnz4ME2bNqVZM0O4xl1x6S1btjwTHy05GzZQfP48LtOnI/eohyCV4r54EaJGQ8KIkWjz8nBfugSJQoHMwQHXeXNRXY8k8Y03kDk64jpzBgDm/V/BoVcT8s+nkL5gAebPdcDu5ZcAsHv5Jcyf60D6whDyN2/B4a23MG9l8OhynTkDmYMDia+/gep6JK7z5iJzcPivjcffkUCnQN5s9iZ/xP7BocTKun+PQ3XrnCJ1ETNPzsTb2psJrScA0KleJ0Y1GsWG6xv47PJn9PLqxSDfQQC81fwtmjs2Z8bxGRxIPMD7Qe/TyL7Rfa9tYWJBSOcQkouS+fTCp7V6X4+CKIrkKKvWKNLo9OSXPLqn98NQWKph8qYwvOzNmT4g4JHbEQSBRcNaYKmQMXFjGJoqElHo9CKTNoUhkwosHd4CiUSgdWNvHBu1wawkg42bNuPq6kq3bgbB8rvvuqNHj5KSklLldY+fMhj++/btW8nj6GHw8PCga9euhIeHs3PnTry9venQocMjt1dH7VJYqkGl/d8SPw5LymPt4ViGtaxHv2aGEMeJvf1p5GLFuz9f4mhMJtMHBFDf0QKJRODTkYFIBIFJG8PQ6R8uLEz7FN85dfx3eeAXnyiKqaIoXrrz70IgEqgHvAD8cOe0H4ChT6qT/0v8eP1Huv3ejcOJh42Oi6LIgjMLyFPlVdrlmtxyIoNPubF9zmyKivON6iUWJNJ3S1+mHptaKT40M3M/qamb8fEei41NeSiEg0NX6tV7Gb1eTUDjEOTy8oWzVqNm4/jRaJVK2g4djERyR9RZEGg/fAQSlQqFTkv7F8tj8eVm5gR064iypJgLgd5YD6wgKgv8vHk55gnFWPUMpFVT46w9j0RhOuyaAO4tDZ4Jd5DZ2+M0YT4mvj0RJLexG14eJmHWogWOY8cgqtW4TJ+G3KNeWZnjuEGI6mQQJNi/2ABpBe8br6lD0anz0ZXmYfJ8+TgJMgl2oxqBCIoGtlg8Vx5KJ7NVkNZJg2uOLSEmUwlyDjLq/sqEdK4WlbCskQdO8nJX7Pe9XGhlbY4Egc8CvJFJHryjbSGT8nmAFxq9yEAnG4a5lDvs+VuYMsPXHZVeZEp9VwLu41VURx01QiaHYYYQHLw7G1LC38HVwpVxHuOwybTB0t8S7wp6YL6+vrQwNUMvkdC7aTNsfXzKynqNH49zSQkHb9wg+540wnc1I+56Fd1FLpcTHByMXq+nUaNGBAYGGtU79n0Ir04+wPzMLpU+GDMWL+FG126UhIc/7mg8Efr27YutrS3m5uYMHDiwzEAvlUoJDjYY5b28vP6rHy2q2FgyV6zEskcPbIaVe5HKfXxwmfIxolqN07j3MA0o/9C07t0bm6FDEdVq3EJCkFbQTHJc8gMKRykCGtxnflwW9itIJLiHhiIoFCgaNcLx/XKPLqmNDW6hIYhqNTYvvPCPEXV+2rwb+C6N7Box7/Q8ckorC5E+CptiNtH1967sidtTqWzJ+SWkF6cT0jkEM1n5nDSx9UQ8rTyxllsz67lZZc+9TCIjpHMIEkFCkFMQbzR9o0Z9aO3SmjeavsGmmE0cv328Vu7rUVmyN5p2IQe4eMt4fPV6kde/O0fP5UfJKlJVU7v2WLgrkpS8ElaMDMRc/ngehE5WCkKGNuNqcj5rDlVO/77uWBwXb+Uy/4WmuNmU/5zHj+qPUm6PVqfnuZ79jTwZBwwYgIWFRSXNN4ArNxLZv/8AGgtnWrdu/Vh9B+jcuQulJtaodCJdew94JK+iOmqf/GIN/VYd51/rzqCtJsvtP41SjY4JG6/gbKVgzpCmZccVMikrRgUiiiKdGzjySvvyNVU9WzNmD27CuYQcvjsRX1WzVaLXi4z+4QI9Pj1SJy79P4DwMMJRgiD4AMeAZkCiKIq2d44LQO7d/99TZwwwBsDFxaX1b7/99vi9fgYoKioyErerDVLVqSxNXYoOHZYSS6a5T8NKakjTfUF5gR+yfmCw7WD62PQxqpd04hAZVw1eQAUNrenRawwAelHPqvRVJKgSEBF53fF12li0AUAUC9CLswFbJMJMBMF4whdFHZCOILgbHY/ZuJbC7BKaJGWidhCxnrC4bEGe9dVs6kfkIBNFrvVoiPvwjwDQqIuRLPyEdFNrUu1sMenVhhYNuwOQnptI3ObfKLGR0u3FD5FKHzN0QRRpFhGCXW4YF1uvoNjCs6xI0ILXSQnodCR20iMq7hE/1uuRpqWhc3Mz6J9UQChRI88sROVVeSc55/IxmqzfRVgrG1xen2FUZqIErSmIFS5VpCsiNDmUqbf/Q8vCRtzuqEd9Jxv7DVHKHCzpjIb3hMpunKUiFCDBWXjw5FfxGU0RJTijR3aP3UgU4TYSPNDfe8t11PHImJakopbbo5eW6wdpNBrOnz9PkVDEXte9TKw3EQ+5B0VFRdhmZ2O7dCnZHZ5DfPWVSu2pkpM5FxmJfXEJTQYOKMsoGBUVRVpaGi1btqwktAxQXFyMqamp0QK+KOsWrgsXY1YKyOXkzJyB7o7HjElUFParViMKAjpnZ7JnTIdnMBWwWq1GFEWj7Dt3KSkpQS6XG2VAe6rodNgvWYI0J5fs2bPQ36u9IYpIU1LQubtXes+i0yHNzETnWlns3iIzmhbnZ1Lg1ZprTaca1ZXk5CCamSGaVTZkS9PS0Dk5wWOOx5OY8/8upKhTWJa6jCZmTXjL6a3HCqnL1GSyOHUxGlGDqcSU6W7TsZUZlo5Xi6+yLnMdfa37MshuUKW6Sp0SrajFRlb5dz1Lk4WV1AqFpArNsmrQiBqWpS5DqVcy3W06FtKnr4cXnaNj8TnDx5aTucD8jmaY3pmo9yVo+DVKjQAEOUv5oKXivmP/OM/olQwtqy6pGORrwnD/2nvnrQtXcSZVy8wOpvjaGH4Hkwr1zD1VQktnKeOCKt9TZpGGJWcKcLAyZ2o7UyQVPdFzcggPD8fDw6PM81Or07PnxEUU+lL+UDXjP4FWtHN7vLXkXwkaNkWVoEBLAydzPmx1/7Gvo+Y8znP6dXgpZ1J0iMCwhiYM8Xv25ufa5udIFftvafm4jSlNHSvPY+lKPXamAnKp8fMpiiKfXVZxNVPHvI5m1LN6sCHzwC0NP0Ua3jnNnaRM+B9+7v/Oc36PHj0uiqLY5kHn1fgtKQiCJbAF+EgUxYKKD4UoiqIgCFVak0RRXAesA2jTpo1YMfXt35kjR45Qm/ei0Wl4ec/LWJtas6TrEt478B4HJQdZ2W0lGcUZzNgxg0CnQOb3m49MUv5jS4wI4+LVS7TsN5gLaRewvpKKunc6fbqN4tur3xKfGM+CTgvYHLOZrflbebX7qzibO3M14j2yslS0a/s1lpb3d52+S9iRHSgzlVigRTK0Pf7f7Sfl2l/0HL+YEz9/StMrmcS/2Bb97VSaH4pG8u8CmnYawu6P/4VvhgbZnGBiDx9GeuIcAcPextHWhZBJI5GL8NLkBTT2DXpwJx7EpQ2QfR76LaZdB+N09rlbb6AsTcNpbCvq+1ReRD4y3buzK/4KLf6KpOjFm7Qd9Ga1p4qiyKSjkygRSmj8Wmdk6/Pxi5PjPC6IEgFmnI/GTa/nm3YtsJY93kdLbT+jddTxOGzevBmtVsvrr73OqbOn2Fq6ld96/sapg0dw+30jekcnOq9YbuQBUhGzL7/kUHo6QlQU3ceNIzo6miNHjtC5c2d69epVoz7o9Xr+GtYZmQ7MvliCZupCPP/YjvePG9AXFxM3bz4SHx+cp3zM7ffG0fjCBVynT6/NYfjHk/nZ52QlJlFv9Wqa9u3z4Ao1pju4FeN0YC7dHTIN2eqeIv/r79PSiFJWXlxJkVcRg/0GP1IbOr2ON/a+gUKm4MseX/L+offZK+7ly25fkqvKZc72OTS2b8yiAYswkT4dIW6PbA9e2v0SR2VHWdpt6VO55l2KVFpmrT6Gp705c4c04c0fLnCiyJGFQ5tzI72QLQdO0CvAmXb17QndE0W2dUOGt64+09+jPqM5SjWTVx6jsasVy0d3QvGYa4+KtGyvod+qY/wcK2X3B10QBFi85iR2Fgq+frsLDpbVGO1ck/h4czhxMm/e6uJrVCSXy7lw4QK9evXCx8eHpeu3YS0q8WrbA/9bMn65oeSNgR1wtjatuu0HEJthGPsujd3o6OfAwt2RZFo1YGQbzwdXruOBPOpzuudqKqdTLvFRr4bEZSrZcTWV0f3a06xeLa7nnzFOxWaxf+9Z3ujow7gKXkA1pXlbFX1XHuOXeBO2vdcJuax6Q1BcZhGbDx6nm78T3fydmL/rOmkWfvy7ndfj3MLflv+FOb9G/o2CIJhgMAD9LIri1juH0wVBcLtT7gZkVFe/jgfzdfjXROZEMrvDbDq4dWB8y/EcTDzIzridzDk1B41eQ0jnECMDkKpYyd4vVmHnVo8uL73OOx8so9gKzn2/gXMJp1h7ZS29vXvzgt8LhHQOQavXMvvUbFLTtpGZ+Rd+vhNqbABSlSg59fkaJKJI75lz6TVpBbf8bbD7v+2EH9mMfPl3pNQzpdfsr+j06XcUWkrInDaL8zu/wWdnGDe7+tLt35Po895HyFUC36z4mG83zMciVY3roC61YwDKTYC908CnC7Qba1RUEpWD8lwall09UNSmAegOPUK/Jd3JBM38leRlVZ/JaHf8bvbf2m/QLfAIwC64IZpUJQUHEwm5mcLNEhWrA7we2wBURx3PElevXiUiIoLu3bvTyKcR8zrO40buDdZeWYvl9h2o4+JwCw2p1gAE0HnsWOqVlnI8NZWbZ8+yY8cOXFxcHmqSPrh6Ct5RuWSOHojv80NwnTWTkkuXyPn+e9JDF6FNT8d9yWKsnn8eu1deMcoaWMeDKbl6layvv8bmhSFY16oB6A4dPwDP9rB7MuTfP2NcHbXL601ep6VzS0LPhpKmTHukNtZfW8+VzCtMaz+Ndm7tmNR6EidTTrIxeiPzT8+nUF1IaOfQp2YAAghwCODdoHf5M+FP/oz/86ldFyBk93Vu5xrCr55v7MKbnerz05lEDkWlM3FjGJYKGYuGteDNzr60q2/PvB3XuJ1bu0KvoigyY9tV8kvUrBwVVKsGIAAbMxOWDQ/kZqaSpXujWX3gBlFphSwe1rx6AxAwvLUHvZu4sHRfNDH3iEv36dMHOzs7/vjjDw5fuEZRfDgqK3dGD+rGipGBlKh1TN0S/kgpsjU6PRM3hmEul7L4xeaM7lSf9vXtmb+zTmT3v0lGYSkztl2lhYcN43o0YP4LTXGwlDPh9yuUav6Z+kAFdzS6fB0tmNqv8SO14WipICS4OddSClhz6Ea152nvPPcKmZSlw1vwRkcfOvoZxKUTs+ue+38qNckOJgDfApGiKK6oULQDeP3Ov18Httd+9/45aPXaahdOVzOv8s3VbxjiN4Se3j0BeK3Ja7RybsXsk7M5mXKSia0n4m3tbVTv8Pp1FOVm0//9iZgoTLG2sKX72HdRlMD6z2dgLbdmZoeZCIKAt7U3k1pP4nr6Ca5FzcTGpg1eXtV7rNzL75Nep1gmx6tVAH6BHZFKZbRYuQ5RAMm7s1CoRLw/XYFcYY6dkyeyGR/ikqHGbMpycu2kdFv6PQAdgnph2qUxprEF5O+7iNLLjNf+NfURR7UCej388R4gwNAvoEL4h06pIXdLDDIXc2x6e1ffxkOQWKIyWmBYWNrhEDIPq0Id2+ZNqrJOmjKN0LOhRroFZk0dMG/twp/hiXybnMVbHo50trMyqqfNUyE+w7HPoiiizand2GFdgQpR8+ze8/8qubm5VWbpEkWR3GrElAsKCti9ezf16tWjU6dOAHTz7MaLDV/k3O5vsTh4ELuXXsLyTll1SCQShr39NlK9np/27KGkpITg4GAjzQidTktSzMUq6ydcO43Td7tJCLCj54eGHX/rwYOx6tOHjJWryN+2DYexYzC7ox9UMWugrrD6DDe1iSYjA31p1b9L6tvJiPfJkPbfRl9aSsqUqcicnHCZMePBFR4FiRSCvwK9FraPM8SzVuqIDvKqSY2rKgJlVtVlhWmgKam9vv7DkEqkhHQKQScaUrRXl2yiOqJzoss2pu6KOo9sNJKO7h1ZdG4RBxMPMr7leBraNXwS3b8vo5uNpoVjCxaeWUhG8dPZzzwUlc6v55IY29WPNj4GEePJfRvR0NmStzdc5GpyPiFDm+FkpUAqEVg+IhC9KPLxpnD0Dyn0ej+2X0nhz4g0JvZuRIBb1WnTH5fODR15/TlvvjsZz1dHbzKyjQe9mtw/E6lBXLo5VgoZEzdeMRKXvqv5lp+fz5Fdm1ELJox/3eAZ6OdkybT+jTkcnclv1aTIzlGqKSytWvh27eFYwm/nExLcHGcrU4PI7gjDnDB5U1itjn0dNUMURaZtuUqxWseKkYGYSCXYmstZOjyQGxlFLP8rulavdzu3+Jn4Oc/feZ20glKWjwzETF5unL3fmlvU6tEVGOuH9WvmyrBW9Vh75CZXkvKqrPfVUUPZwqHNcLE2PPfLRgQiFQQmb3p4cek6/h7UxBOoE/Aq8LwgCFfu/BkALAZ6C4JwA+h15/91VIEoikw5NoX+W/sTmR1pVFaiLWH6iek4mTvxSbvyBGtSiZSFnRaikCro6N6RUY1GGdW7cf40144epP3QEbg1KPfm6dJ2ICYdG+B324KPrF/G3rQ8Q8II/+G862aORqfCzmsCglCzHZ8zPy0mK6sEK30xwdOWlx1392tBwaiWSEVIG1ifBi17lJW1e2EMN3v6IwDmcz/ByrY8S83YN+dRZKNGI9Pz+pgJtSO4d+YLuHUS+i8BW2PXxbztseiLtdiPaoRwH1fImrIvK592ZyIJjUs1Ot68azCrJ3/AtGGf8OmWH4zKRFFk9snZaPVaQjqHIJWUj726hwuzmplgX6xkkrOdUT11ShFpy86T80vUI+1qPQ2KTqaQtvQ8RedSH3xyDdBml5D26UWyvo9ArJt4nhliYmJYvXo1Bw4cqFR29OhRVq9eTUREhNFxURTZsWMHWq2W4OBgI52aSQHv8v4eyLCXYvnhezXqg4OfH70aN0YUBNqbW+B6j3bMnxNGUjTkFc5tX2d0XKtRc2PSeLRSgaAV68reOYIg4DpvLlJ7O0ybNMHp3XIha4mZGe5LFqNNTyc9dFGN+vc4qG8nEzdgIIlvvYWoM97ZLDp2jJu9epGx5OmGqzwMGStWoI6Pxz00BOm9OkC1ib0v9FkAcYfh/DeVy7ePg9WBkHTe+LhWBd/1hS+eq2wIykuCNe1gw1CDEamOKvG09uTjth9zNvUsv0b9WuN6ap2a6SemG21MAWVZAy1MLGjl3IrXmrz2pLp+X+6KS6t1amafmv3E59pcpZqpW67S2NWKCb3LjV6mJlJWjgpCIsCwlvXo39ytrMzT3pxZg5pwOi6bH04n1Eo/UvNLmLU9gtbedozp6vvgCo/BJ/0D8HWywN3WjFmDmtSozl0vhojkAj6/R1zay8sLiWtjBETadO2Nu2O5JOlrzxm8GBZW4cWQV6ym/+pjBH9xqpIHSfjtPNYciuWFIHcG3DP2swc34Wx8Dt+fSnjIO6/jcdl04TYHozKY2q8xDZzLN0m7+TvxcnsvvjkRz9m47Fq51umb2XRZepiZ2yMefPITZN+1NDZfvM24Hg1o6WX8XVDw1y3Slp6n5JrxPCbqRbLWXyNt2QU0WcYbGnMGN8XFSsHEjdDckSgAACAASURBVFcoURs/9xHJ+aw6cINBLdwYHFiuA1vP1oy5Q5pyLiGHb0/E1fId1vEsUJPsYCdEURREUWwhimLQnT97RFHMFkWxpyiKDUVR7CWKYu2kjfgHcjcECBGmn5iOSldupV19aTUJBQks6LQAK7mxB4intSe7h+1mzfNrjIS5ivPz2L9uDc4+fnR48V+Vrvf+e8uw8/IiZesRivPLrb7JyT/hIuSwt8iKOefXoKvBYrcwO4WLWw8h0+kY5BcBVzeVF+Yl0oNj2AzLoa/VeUi/blS3/2dbsNu9kVZ9jYVe5WfWMMntAm80uIL32eVV7+Y+DBmRcHA+NBoIQS8ZFRWHZVASnoV1L2/k7o8v8JWl1jIpKgmZAGsTMziXV1RWdjFfyR7f55DqtKyT1ycyoXx34vfo3zmdeprJbSbjZW1spBp7IZwihYJuUec5/GO5Q52o1ZO7MRpEKLmWTfHlZy/iUpOuJH9vPEgE8nfFoc1+vJ10US+SsykGUatHFZdP0cmqU8HW8XQpLi5mx44dSCQSTp06RUJCQllZcnIyR48eRSKRsHv3bgoreM1cvHiR2NhYevfujaOjo1Gbhcs+w65Az2cDYeX1L2rcl3avvca/CgrwXL+e0uvl75zzu77D769ItBLQhqwmN7N8F3j/onF4JCgpGv9v3Oo3M2pPZmeH744deP/8E8I9ItBmgYE4jB1D/rZtFFZh/KotRL2e1GnT0JeWUnLhIjnry43Iurw8UmfMBJmMnB9+QHn23BPrx6OiPHOG3A0/Yvfyy1h07PjkL9hmNPj1hL9mQfbN8uPXd0DYrwbR6G1jQV3hA/BwKKRHQEkO7PywfN7R62H7e6BRQtIZOPXZk+//35jhDYfTuV5nVl1cRXx+zbLOfBn2JTG5McztONdoYwoMWQN3DN3Buj7rjDZHnjY+Nj5MbDORk8kn2Xxj8xO7jiiKzPwjgrxiNctHBlYKv2pWz4bjU55n2YjASnVHtfXk+cbOLP4zitiMokrlD9uPKZvD0elFVowMRFqDbKOPg5lcyvZxndj9QResTGse7lfmxXA41siL4Vx8Dt8lWKBq3J/hz7c1qnPXi0FShRfDrO3XyCpSE5tRxKf7ytdopRodEzeG4WApZ/4Q4zkCYERrD3oFOLNkbxQ30p+OZ2gdkJRTzLyd13jO14E3OvpUKp8+IAAve3MmbQqjSKV9rGsV3gm/kgoCv5xN5HD0f2fNnVWkYvrWqzR1t2b888aekapbBRQeSQKJQO7WWHRF6rIy5ZlUVLF5iDqR3I3RRpuoNmYmLBsRSFymkiV7o8qOl2p0TNoYhr2FnAUvVH7uh7WqR58mLny6L4botLrn/p9GXc7DJ0zFEKBVPVYRmxfL2strATiTeoafI3/m5YCX6eBWdTpfRzNHo/h4URT5a90a1CXF9H9/IlJZ5clUZiJnyPgpqIuV/LVuDaIoolTGEXtzKQ4O3ejbfCFhmWF8f+37B/Z/84evUWoip2FrL9wbBpVrMZSFX4H7uD1gamNYdGvLX0hSqQx33+bGDSZfgmPLsGzxIu7950HsAbi4/oH9qBatGraOAYUVDF5tlDFGl68i94+byL2ssOpavZhiTRFFkSnRSRRodfzRsiEepnI+iEpEqdWh1OkYH5mIm8KEtdZKShSmTDx0Fp1Ox62CWyy/sJxO7p0Y4T/CqM2vLkVwVmFFsKCin5kb4VkxRB67AkDB/lto0opxeCUAuY81eTtuos178mlia4qo05OzMQaJQorze4EgEQwGnMfw3ik6kYw6oQC7FxtiGmBP/r54NOnKWux1HQ+LKIrs2rWL4uJi3njjjTItBpVKhUajYdu2bVhZWTF69Gg0Gg07duxAFEVycnLYt28fvr6+tG1rvEgvPHSI/K1bcXx7DB5NerIxZuNDpWluMGsWMjtbUqZ+gl6tJi8rGc38FWQ4maBdNRPrQj0nPx4NQNTZvXj8doK4Vq50/U/VYUoyOzskVWSWAnB6910UTQJInT0HbXbt7DbeS+6PP1J8/jxu8+Zi1bsXmatWURoTA0Da/AVoc3Px3vADJt5epE6bhq7o8T4AaxNdYSEp06cj9/HBeXLVobC1jiDAC2tApjDMOzotFGXAro/ALRBe3gQ5N+HAHMP5iWfg5Gpo9Ro8PwuidkH474ayc+sg/hgMXAEBQwzGorT/7i7ws8xd7x25VM6MEzPQ6u//4XUl4wrfRXxHcINgunt2r/IcBzMHFNKaZ/V6UoxqNIoObh1Ydn4ZSQXVhBQ+JjvCUth9NZWPevnT1L1qDTRXG9MqjTKCILD4xeaYy6WVQqQelp/O3OL4jSymDwjA2+HpZEWzMjXBxuzh9Z7u9WIoUmmZtOkKnnYWzAyuOh18VV4MO8JS2BmWwoReDXm1gzffnozn9E3DO33ZvmhiM4pYNjwQG/PKfTSEp7XAUiFj4sawxxr7OmqGXi8yaVMYgiCwbEQLJFX8TlgoZCwfEUhKXgkLd12vopWas2DXdVLzS/jxzfb4u1gydXM4ecXqB1esRURRZNrWqxSWalkxMshIyFmv1pG7MRqprQKnsS3Ql2rJ3RqLKIpoMovJ/zMe00Z22I/wR51YSOGx20Ztd2rgyBsdfVh/KoGTsQYvopX7Y4hOL2TJ8BbYWVTOtCYIAqHDmmNlKmPC71dQa+ue+38S0rlz5z61i61bt27umDFjntr1niQJCQn4+Pjc9xxRFJl0ZBIpyhS+7v01gc6BZJZk8mvUrzR1bMrc03NxNHNkefflmEhqNjFeP3aI89s30/WlN2jQ9rlqzzO3sUUql3Nl706snZxILQhFq1XSMmg9jR2DiM2LZWPMRnp49sDRzLHKNo6smUpcXA42khJGrd4M3h0N7vepYYbd1IvfGxbOjfqBg58hJAugfteqO6UpgZ+Gg8QEXvoNvDpC0lm49CM0CwYzu6rr3Y8ji+HaVhi2Duq1LDssiiLZv0ShyynF8c3mSC0fX2hyc3ounyVmMM3XjaEudjSzMmNdUia5Wh0nc4s4lFPI983r06eBP0nHdrK/fmuKzuxiS8b3FKoL+arXV1jKy72REnLzeDs2DSdNKRu7t8W/hT8Rp68QGRdNE3s/inbfwqKtK1bdPFDUt0F5JhVNchHmQc41StlYk2f0cSg4mEhJWCZ2Ixth2tAOqZUc5akUJAopCu+HDwfRpCnJ/iUK0yYO2PT1wdTPluLzaaji8rFo44LwhHcq66iaiIgIjh07Ro8ePWjRogXu7u6cOXMGpVJJYmIiMTExjBw5Eh8fH+RyOefOncPKyoojR45QXFzMq6++ilkFA4s2J4ekt8cg9/am3rKlyDIVxBLLvoR9DG0wFFPZgzO6SMzMUPj5kfPDBtBoOP3zSlzi8jBfuZDA50dyIe0Cvn9Fcs0sl8LlnyOKIoHrf8fC2v6Bbd+LIJVi3qoVuT/9hCo+Duv+/Ws1ZaoqNpbkjyZg2bUrzpMnY9GhA3lbt6I8fRqJuRlZX3yJ0wfjsRk8GNNmzcjZsAFtVhZWPXvWWh8eh7S58yi5eBHPr75E7vH4xvYao7ACG084+6XBGHThO8iMhle2gmdbKC2As1+BS3PYPRFMreBfv4BPZ4g7Cld+Bfcg2PG+wauoz0LD3HX5J0OoWctXoEIihif9Pv07YWFiQT3LevwU+RMmEhPauFadibZYU8w7B97BXGbOZ89/hlz6bKdzFgSBdq7t2BS9iSuZVxjiNwSJUHt7pWn5pYxef54m7tYsebHqj9oHYaGQ4WlnzvcnE5BJJHTwdSgrq+kzGp+lZOxPF+nYwJHZg5o88ymgTU2kNHaz5tsT8ShVWg5HZ3DqZjbfvN4GH8fqDVgBblZEpRXwy9kkgrxs+XhTOAFu1iwd3oKODRzYHZ7K3og0vO3NmbfzOq928OY/nepX256FQoaXvTnfnUxAIgg85+dQ7bl1VE9Nn9NvT8Tz67kkQoKb8Zxf1d8pAO62ZpRq9aw/lUALDxvqOz681//+6+ks/jOK93r4MaqtFy297Pj+ZAJJuSVGoYFPmi2Xkvnq6E2m9m9E36bG4e55O+NQxebh+GoTFPVtEEwkKE+lILNVkP/XLUSVDsfRzZF7W6HNKEZ5NhXTAHukVuXv3fb1HfgzIpU/r6bi42jBnJ3XeKm9F291rj4c1Fwuo76jBd+dTACg431+Fv8k/s5z/rx581Lnzp277kHn1XkCPUGqCgH6uM3H1LOsx/sH3yezOJPQzqGYyco/kPSiyLWikipj0tMz0ti0ZRP1Gjel1cAXjMoSC1NJLDTWZGk98AXqNW7K1QvzKSgIo3Gj+SgUBgPCrA6zsJHbMO3ENNS6ypbu7FvXiTh0BYVWy4vLvjQcdPAzLJTjDsO+GeDf37BQBmg8EIJehuPLK2sx3OXgAsiKNuzgmtkZxJtfWGtYaG979+G1GG5fNFwv8N8QYJyyVnk2DVVMLjYD6mPiWPUO/8OQXKpmesxt2tlY8K6XQd/oOVtL3vF0YkNKNt8lZzHGw6lM1Hnpq2/SOCmaH+2acyshhRntZ+BiUS6EqNfrefPMVdRSKWub+mBmYoLc3JShg1+gWFSze9MOpLYKbAYZFiQyBzNsBvpSGJvFra1nH7r/mnRllULLoiiiTil6aA0EdVIhhYcTMW/pjHlzw4Rg3soZ06YO5O9LQJNWtfeOJk1Zpci1qNWT83s0EjMZdsENEAQBqZUc2+CGaJKLKDj0ZHZl6zCE4FX3DORlZrJ75048PDzKRJ29vLzo1KkTly5d4syZM7Rr1w4/Pz8A2rVrR/369dm1axdJSUkMGDAAmwoZv0RRJG3OHPQFBbgvWYIgl2MimBDaJZTc0lxCzoRU2UelRkliQaLRMctu3bAdMYLsb77F73QiicPa0qxrMAC9Zn1BiocZTst+wTVNBZ+8h4Nb9Yv7B6Fo2BCnjz6i6MBB8rc/fA6E0pgYRE1lIVJRoyFl6idILCxwWzAfQRCQ2dvjNn8eqshIUqZ+gmlgCxzeegsA85YtcXj7bfK3bKXw0OFHvp970er0RKYWPHS9wgMHDILaY94uE9R+qjQfDk2D4dBCiN4DPWeD850sKj1ng6M//P6KIXPk0K8MhiOJFIK/NIhL/xgMJuYw5HODd5GFIwz+zBA2duQpyRzqdX9Lz6N+9fvR36c/X4V9xfXsqnfgV1xcQVJhEgs7LzTaAHmWcbVwZVr7aVzOuMwP1394cIV7iM0oqjJbkSiKTNkSjkYnsmJkEDLpoy+/B7Zw44Ugdz4/dIOrt/OrPCcmvbDKXXtDFqArhixAL7Z4Jg1AxZpiEvITjI5V9GL49VwSY7r40tbn/kZ9QRAIDTZ4Mbz23TlUWoOwsEwqwVwuY/nIIFLzixi7cRc+DuZMG/DgDEz9m7sxrGU91hyOJawakd3Y3Ngq19X3o1Sje2phZjq9yPWUglrVvrqZWVRJa+ZxiEkvZOm+aHo3cWF46wdvLnzUqyGNXa2YsvkqOcqHG/vsIhXTthoMhB/29AcMYZkf9mzIzrAUdoRVLUtwK1tJQTUC41FpBWirWOvq7zP2yXklzNtxjXY+9rx5j1GmNCYX5ZlULDvVQ+Fr0L+y7FwPuY81uVtvoEkqxHZoA6TWcgRBwHZoAyRmMkNYWIX3gJlcyoqRQaQXqnhrwwU87cyZMSDggWPUp6krw1t7sPZwLJcSq04CciO9EJW2TlPv70SdEegJUV0IkLmJuUEYWJAytsVYmjsZh0stjkul5/lofk0zlljS6XSMOBnGuhfexus/7yOpEDufWZJDvwtR9LsQTWZJeT2JREqHXs1wCkylONYGJ4e+ZWV2pnZlaZq/uFJZj2Pb1PdRyWQ06xmEnWeFNPJtRkPDPncWy8bhV/RbBNb14I93jLUYAOKPw5m10PYtaFBhB9vGAwYsu6PF8Pl9x9QIdbEhDMDKDfoZL9a1WSXk745D0dAWiw6Pb8HXiyIfRSWiAz4L8EJa4Z6n1nejiYUpjSxMmeZbfi0TmQmfNHBGK5OhcvqY3p69jdr89FwY10yteNVER0evemXHvVs2pKXehlhpGkn2cUgU5TvRpkH27JGd4cerf5F0/EKN+6+Kzyd91SWyf6ssLl10IoWMzy5TePR2NbUrI2p05GyMRmopx3aIX9lxQRCwCzZMPDm/G088ACXXs0lfdYncbbH3NknBwUQ0qUrsghsitSzftTBv7oh5S2cKDyeiTqqLR34SFBxMJOOzyyjPGmcv1Ov1bFq+HE1xMf2bNDESde7evTuurq44OjrSq1evsuMSiYR+zVsgV6vxKSykedOmxtfasYPC/Qdw+vADTBv5lx1v4tCEdwLf4c+EP9kbv9eojlavZez+sQRvDyYuz1icUPrhW6TbS7ntaUav2V+VHZcrzPFetgK1Cdzs5keH4eMefYDuYP/6a5i1aU36whA0KTXXqio6doz4IS+QOnNWpbKsr76m9No1XOfORVZBM8mqZ09shr9oEKdetBihQgY0p3HvoWjcmNRZs9Dm1I4UX8ieSPqvPl7tYrcqtNnZpM6egyIgAKf3aibs/UQYuAKs3Q1ePB0q9MPEDIK/BqkJdPoAfCpkn7P3NcxXggCDVoJVhUxFjQcYNjdOroKkp6C/9Ncs+KoThG968LnPGDM6zMDO1I4ZJ2YYaR0CnEo+xe/Rv/Nqk1dp69q2mhaeTQb5DqK3d2/WXF5DTG5MjeuFJeXRd9Uxxv54sdJc+/PZRI7FZDJ9QGPq38d7pabMH9LMkCJ7Y+UU2SduZNFn5TEmbwqrVO/rY3FcTsxjwdBmuNo82OvyaaMX9Yw7OI7gHcFE5xhnfZrarzENnS0JcLNmQm//alowxsFSwaJhzRGAGQMC8HUqN0a29rYjqOUhzOuv4pXnizCXy6pvqAJzhjTF+U542r1jfzb1LME7gplxouYZEkVR5MPfLtNn1bFaEzi+H8v2RTPgs+Nsvljzdd/9uHo7n74rj/H2hgu1klVLc8dQaamQGX52NTBUKmQGUfX8EjUz/7haYwOXKIpM33aVghItK0cFGoVfvdvdj0BPW2b9EUF6gXE2rvgsJf1WHefl/ztbKTRwb0Qa/VYdZ9b2a5Wu9+lfhrHfdMF47PV6kY83haEXRT4dYazRpS/WkLM5BpmzOTZ9fcqOCxIB+xH+CAop5kFOmLdwKiuTWphg92JDNGnFFBy4ZXStIE9bxj/fAKkgsHxkIBaKmj33swc3wc3GjMkbwyoZ/M7EZdNn1TE++u3KM5vEpo7K1BmBngBavZbpJ6ZjIjVhXsd5lV5grVxacWTUEd4Netfo+Pl8JWsSMzCTCMy+kUxiSfmiasHBo8TYumAiSJieoaS0wkvno8tHyMeKfCz56PKRsuOakgISUxdBsYSbJ1w4FTrf6Hp30zR/f+17LmdcLju+J3QM+aI59goV3cctMb45QYB//wbjLxkvnMGgCzT0C8iOhQNzy4+XFhj0g+x9obdxHwBoMdLgyXM4BNIrvzSr5OA8yL4BQ9eCWXlWiLvCwkgl2A33r5Vdru+TszieW8S8Bu74mBnrFphKJexp7c/e1v6YVdjZ02q1xF2JpMvNCBId3Zi+sdx74FpGFp8XaqlfWsjCTsbx7EXHT+C3eR32efkcjA8nr4IA71+ffUaWzPBM7Nh3EG3Jg/WB9CotOZtiEGQSSu8Rl9akK8nfF49gIqFg/y3UqTXT3snfm4A2swS7Ef5IzIwnD6mlHLvghmhSlRQcKvfc0BWpyd16A8FEQvGFdEquly90VIkGoTvz1i6YNa3sXm07xA+ppZycjdGIVeyw1vHo3PXoEkwk5O+OQ1sho8Txr9eRbGpK0LVrlC5YaJS6XCaT8eabbzJmzBjkFcSURbUa5fz5DPprP+127yF3w49lZZrUVNIWhmDWqhX2//lPpb682fxNmjs2Z+FZ4zTN66+tJywzDIkgYfqJ6Wj0hp03URRZGP4p09+UU//nX5ArzI3aa9CyO/UPH2DAlzsef6AwhIW5L1oEej0p02fUKF27NjeX1BkzEUxNyd++nYL9+8vKSq5GkPXVV9i8MATrvn0q1XVbsIAGRw6j8DX2YBLkctyXLEFfUEDanLmPveA6FZvF9ycTMDWRVLnYrQpRFEmbOxd9YSHuSxZXEtR+qpjbw7iz8Mo2g3dpReq1gskx0Gte5XqtX4cpcdB0aOWyvovA2uOOuPQT1CSLP2bYHJGZwZ5JUPD3EsK3Udgwr+M8YvNiWXN5TdnxfFU+s07NwtfGlw9affBf7OGjIQgCMzvMxFpuzfTj09Hoqt7tr0ipRseEjVcwkQocjcnkl3Pl819ClpKQ3ZF0aejIKx28a6WPNuYmLBseWEngOL9Ew8ebwzA1kbAjLIVd4eXP1LWUfFYdiGFgCzeGVMgC9Czx0/WfuJB+AZkgY/qJ6UYeNWZyKTvHd2bbex0xNam5iHifpq5cntWHV5/zMTp+JOkIN0oOopCa8mPsp+SU1syobmNmwtLhLbiZqWTp3vKxL1QXMvPkTEylpuxN2Muf8X/WqL2tl5LZdy0dhUzC5M2PL3B8P84n5PD1sZuYmkiYv/M6t3OLH1zpPtx97mVSgROxWfx09taDKz2Azw/FEpFcQGhwcxwta64Vdtc4uOdqWo03NLZdNoz9xD7+NHY1ljGQSSWsGBmISqtj6pbwsrlWq9MzaeMVRESuJuez9nD5xmZWkYoZ265iaiLh13PG4tIXb+Xw1dE7Y7/rOkk55WP/w+kETt3MZuagJng5GK9lcnfcRF+kwX6kP4KJ8RwnczDDbWo77EY24l7MAhywaOtK4dHbqBKMPQY/6uXPxZm9H+hNVxFrUxOWjWhBXJaxuPRdQW2FTMKfEWlsv/L3msf+l6kzAj0B1l9bT3hmODPbzzQKAaqIjcJYEFCp1TE+8hb1TOXsaW3Y4fgwKhG9KHI+PoFvBCua5aXxbQtfopSlLIk3hH79eOMQB1W+jLa9zX9skzmo8uXHG4cAuL7tDTSOKhrZfIizzoLzVy+Sdua00XU/bvsxbhZuzDgxg2JNMSnXThN7MRFTjZqRq3+kSiRSMK1G86V+V2j/Lpz7Gm7eCVfYNw0Kbht2ZeVV7IAJAgxaZTAibTUWl66SuCMGrYd2Y8G3u1FR4bHbqG8VYPeCHzKbxxeajC0uZeHNFJ63t+IVt6rjv02lEiMDEMDhw4fJyMhgTo+ONM5M5heX+pw4fwmtTsfbFyNBEFjXshGyCt4VhixAMzBr4Mewf41CI5Wy9euv0ev1xB8/wfnCQvw0Wno7NyRTVsK+5d8+sP/5u+PR5ZbiOLqZQVx6+020eaUVRJ1lOL8fZHAbrcJ7515Kb+ZRdDIFi+fcMG1YtYaTWVMHzFu7UHg4CVWiwe01b1ss+hItTmNbYOJmQe7WG+iK1HeE7mKQ2iiwHVx1TLLETIbdCH+0mSXk70144D3XUTP06jseXVYKnN8PAqmkTNg77epVjiXfxr2klB6TJ6OOjydjxQqj+iYmJkYGIIDMtV+gioqi/tIlWPfuRebKlYZQKL2elOnTEXU63BcvQpBWXsDfTdNcqi1lzqk5iKJIVE4Ua6+spZ9PP0K7hHIt+xrfhBvSgm+/uZ3DSYcZ2+FDGjhX7cZv61ivLB18bSD39MR52icUnzlD7k8/P/D89AUL0Obl4f3jBkybNCFtzly02dnoS0tJmToVmZMTLjOq3jEWBKHaVOumjfxx+vADCvfvp2Dnzke+n4I7izdfJwu2vdcJtVbPlM3hDzQs5W/fbvDo+ugjTP1rtiP/RFFYgbSa3UwzO2OP1XvLqsLU2hAylhMP+2fXTh/v5e7miEMDeOsA6DSG9PZ/s13ULh5dGOE/gh+u/cCFNIOH6qJzi8gpySG0S+gzIfj8KNib2jO341yic6P5MuzLB56/ZG8UcZlKvnmtLV0aOrJwVyQJWUp0epGJdz6Slw6v3fCrrv5OvNLBy0jgeN6Oa2QUqvjl7Q4Eetoy848IMgpKUWl1TPw9DFtzOQuryAL0LHAz7yarL62mh2cPPu32KTG5MZXG3tRE+lAGoLvcK/acU5rDnFNzaGTXiB/6r6dQXciC0wtqbFTv0tCJ15/z5ruT8Zy6aRDZXXxuMZnFmfxfn/+jhVMLFp4x3tCoiuS8EubeCQHaMLo9ybklhOx+PIHj6lCqtEzaGIannTnbx3VGL4p8vCn8sbx3Pr0jqP31q23o3siJ0D2RxGU+euKCK0l5rD0cy7BW9ejXzPXBFe5hbFc/WnvbMeuPCNLy77+hkZJXwpwd12jjbcfbXapef/o5WfJJv8Ycic7k13MGWYKvj8VxKTGPpcMDCW5Zj88PxRJ+O69c1FmlZfM7HWnkYsXUzeHkKtUoVVombgzD3daM7eM6AzB5Uxh6vUhsRhGL/4yiRyMn/tXW0+j6xeGZlFzJxLqnF3IPq0r9A8MauTrNTJtB9ZHaKsjZFINeZbyJWpUA+oPo6OfIfzoZwjJP3DA89wt2XSclr4Sf3mxPG287Zm2PIDX/8TIF1/F0qBOGfkSqE4yKyoli6vGp9PbuzXtB79V4wp91I5ljuUWsb16fltYWOMllfHM7C1NBIDQsCpVUxub2zWjtZE+GWsN3yVnUl6uYFV+EtySLb9v2p6tzA3bfvsLufHM6p/xJjmIrdqn+NB7yGV6BLQk/8Ce3zpyixZBhSO6EF8ilchrZN+Kn6z+Rr8onZdG3lApyOgT3oH77fo82OD6dIHIHXP8DzB0M2VY6T4CWL1dfR25uWAyf/QJEPfh2q/q80nz48UWwdIaRGwyu/ndQpyrJ+S0Ks2aOWPf2fuzFllYv8mp4PIU6Pb8G+mElq9nC49atW+zYsYPWrVvTsWNHOilk/JxdxOHsAuIzMjkqs2C8BbzYuIFRvdQZMymJiMBr3dfYt2yJNiKCqxoNXL/OkfPnEUSR1z78EN8eHf6fvfOMj6Jc+/A120vqpvdGAoFAhoO7tQAAIABJREFU6FVQAalSFRB7Rw82UI9KERAUsOsRFWyIgErvKFWQUEJNSCW99952N1veDwsJSzYQih49r//fjy8z88zODpuZ57nv/33d5Ow7Tby5Er8GEZpQ25nF4uhMFKfqsb/DF3Uvz2a4dG4thnItDbGlaKa0Rx7shMRNaWnHbjKjaGd7YWTSGij9Ng6xnQyXB8MRrsI0kIc4Un+uBG1iOYJERO3hPBxHBKLq4oYswIHao/kYSxvQ59Sgu1CBy0MdkbqrWj2fxEWJsa6RuqMFyIIckWj+ejb2v5uqdmagTa7A5aFw5P4OSJzk1EblYxab+Hnzt+hEIh5+4gmcunbFWFVNxQ8/oOrZs1X4b/3ZsxTMnoPjxAm4Pvkkqr59qdy4kbrjxzE3aKn86Wc858zBboB1C/HLn6XOCmfUUjVrk9biKHfkP2ctJaLLhiyjk2sncmpy+Cn5J0KcQlh4fCGRbpHM7Tf3T+VaKDp2RBsXR+X69dgPH4bE2fbfS9XOnZQu+xy3F1/EcdSoZrh0ejra+DjqfjuEzycfowgNtTn+WlJGRlJ3/DhVm7fgOOZuxPa2J4hX06xNcZzOruDbR3vR2ccRR6WE745m4u4gp4uvk80xjfn55D77LxRdOuO1YD7CLQyy/aXk5G8J1EQvB9/eZFaLbi0kcsdMyD4K96+zAKqVzpbkhp2bxcH0N1Ivz17sztjNgZwDqKVqVsSu4JmuzzAqaNR/+9JuSoGOgRTWFfJj8o/08+qHp9r2ovRoailzt8bzaP9AHu4fSL8QF9acyOZ0VgWltTo2nsnj3Xu6XFfWva3qG+zCjouAYxkG1sZW8sLgUCZ296V3kIZVxzJJLKwhpaiWXxOKWHZ/d8K9r79xwx+tRlMj/9r3L/RGPV8M/YJwl3CK64v5Menq9/5GZDabmX1ktiXIdNcXhGvCkYqlrE1ai5+9H+01LV0VttQ32IXd5wvYHVeIu+cFPo/5D093eZqx7cbS06MnPyX/RFJFEqODRtt8R5lMZp5dfZrCKi2rHu9DR28HGhpvDnB8Nc3fHk9UWilfP9KTLr5OuNnJ+e5oJo5KKd38r78xy7G0MuZsjWsCavcLceHH6ByiM8q5t4dvq+Dz1tZP2kYjD38bjUIi4qtHet1QsE8kCPQJ0rDqWBbx+VVM6ObT+r1fc5r8Si2rnuhtszPWJXXxdeJUVjnrTuUQ4qZm3rZ4Rnb2YuZdYfQLcWHTmTwOJBUjEon4+vcM3hjZgRERXnQPcGLl0Uyyy+s5mVnOkdRSvnqoJ5F+Trjay1l5NBOlTMxnB1Op1xtZ9Xhv7BTNaxpjtZ6ylfFIPFRoJrW/oeYogkSEzNuO2qg8TPWNKMNvHmbeN9gCl951vgCNWsaHe1N49o4QJvX0o0+whh+OZxGXV834rrbv/d9F/4Ch/9F1SaerZ8X3L+IsdWROnzlWP/7qwgySfmnJ3gHYlBbP9/llTPNzo5+T5aF/n6eG4a4OvJ1RSI6jK6/ZQbC7pd5zXog3AQoZ0y9UoEXOsk6hyMRS5BIZyzqFokXOLJ0EcZWEiLGrAHBsF8qgIaOoEEz89ubrVp/fy7MXD3d8mKrV26kRqXB1NNDnwddu/EZIlTDhS/TVpWRvnm/pznLHG1aHGGv0LeHBHUZB1wfhyEetshiyN8xFX10CE1ZYAkeXzqc3EL8mCkEhxml8uzY/eHK1etLqbWcLPssu4mxNPUvCfPGUty1irtPp2LJlC87OzgwbZinxCG0XzIy6EgqcXPjBrKCjtobXene1Gle9axfVO3fiNv1fKDp2BODO6dPxbGjgUEkJVUolo/v2w87D4iwb98QUlGYJ249Foatsycox1jXiHidC6qnGYaglSCRxUeJ4dzC6tCpqDuSg6u6OMsLCIVGGu6Dq6WHTNnpJldvTMVbpcJ4chkh29ZezSHHRvVPaQOXmVGQBDtgNtAQPZF5qHIcF0BBfRt2xAuwGeKMIsV5wahMTMVRYw+ccRwYhcVVSsf4CJu312aXr6+vJvw6Oy99FZpMZXXolZhuZPJPOgC7bNuxXm1pB7dF87Pp7NwX9lJFuKDu7ErX/d0qUSoaEhuLSzhKodJ85A1lgIPlvzMJY0/L3ZqqvJ//115F6euLxhuVvXaLR4LXwLXQJiRQvXYp60ECcJk9qMfZKTe0wlT5efVgSvYTUylQW9F+Ak8Ly+3ijzxu4KF2Y+dtMSznYbYusuvc01OuJOWabc2Cs0be55PFqEgQBz4VvIVIoyH/tdcyGlr/FxqIiCt9aiDIyEpcnLK3q5aGhuM2YQe3+/VSs+gHnBx7AbsCAFmPbfB1iMd5LFmM2GimYbbs8zVhVRUOc7RLbX+IK2Xgml+l3hNDVz3J/H+wbYOViuFLmy0rhvBfbdnT9T2nIXHBtD1ufQ9JoI7ttbITMKNvunYZKyDtj+7xJO+HcarhtJvhe7KzV83FLl7I9c6Es7dZ9hz9BKqmKdwa+Q35tPm8efZMIlwie7Pzkf/uybon+3evfeKo8efng61RpW/4Gmtx0rmpeG2FxJHo5Klk4LoLTWRW8v+cCozp7Mq7rH1N+pZJJ+HByJAVVDXwTp6ezjyPPDbY8t0Pc7HhjZDi/JZew/HA6U3v7c2cH9z/kOm5WK2JXkFieyLx+83BRWhaql5zqs47Mor6xZdmSzqjjdFFL/hJAhbaCpPKkFtsBdqTvYF/2Pp7r9hxhzhYn4yMdH6GbezcWn1hMYV2hzXFXSikT88HkSApqS5gf9RbhmnCmdZkGQIBDADN6zCAqL4r1F2zzvmyVAM2468YBx9XaxlZh1RtiYvnxzBkroPaknr4M6eDO0l+SSC228V43mVh97iA1upaujkslQAGaZqC2h4OCReMjOJdTyZeHrv8ZdslN996kSByVN97RN9BVzazR4fyeUsrqE9k2j/nw0GGOZmYwe3Q4AS5XZ3SJRALv3Wvh9Dyz+oyVm85RaSmRSiupY+6WOPoEaXj8Yoe5Tt6OvDQ0jB2xBaw5kc1TA4Ppc7Gb36QevgwN92Dj7gtk5lbz9vjOuDs0JzfNZjMVm1Iw6U1oJrdHEN94MEUe7IjdbT7UnShEe8E21FmfU2NzXt00xzQ2/40ppBa4dHGNjpnrYgj3cuCloZa/owAXNbNHh1+1NPBCUQ3FbSg7/0d/vP4JAt1C7Zv9GE8tz2Zp3oCmRQuAsVHPkX3jyJN9QOzmd6zGZJfnMyurCG9zLk85NL/kBEHgBSEFZ3MZtxmO8nT/5hasaomYuW6pyMw6ZrgV0cW12Y7fxTWMpzI2cU7oSaLseWQOzaCwrs8+R4DKgZiMC2Tt/dXqOh6iO35FLqgatUz5eN1N3wuzd3c2uz3Pt9xHQuQckDRH2U16IyXLYyledo7Gkite7CNaZzEk7l3Ft6kaNrlMx3xFpvSXlVvYWnuUC51qEKvb9vKobDQw5kwKo06nUKCzftmer6nn/cxCxrs7Md6j7RmSPXv2UFFRwfjx45HLm23wL068m975Gai19SzTKK1KVBqLiylc8BaKLl1weeqppu0isZh7H3sMuV5PZ5GIiHFjm/Y5BPlyV3AnKsU6dn78ndU1mM1mKrekIm4E58lhCJeB7tS9PFF0dEHsosBpTIjVOKe7g1u1jTbEl1F/ugj7O/yQ+7cti6gIccLudl8EpcRSy3xZFsNuoC/yYEeknmocRwRajdMmJpIxeQrZjz2OWd/8/yKSiXGeHIaxSkfldmtA8NVkNBpZvXo1X331FXl5eW0e93dQ9b4sSlacp+Y36+5pZrOZstWJlHwe0+Klb9IaqFifgsRVicNl914QBGr8KjktySDI4ESv+x9s2idSKvF+dymG4mKK3rZ+hgEUv/8+jVnZeC1ejNiuOXtpP2QITpMnI3ZzxWvhojYFZ0WCiEUDFqFRaLiv/X0M8h3UtM9B5sCiAYuQi+XM6jMLHzsfq7G/f3oal60Z/L7NGihqbjRS8lUsxcvO0lh084Egqbs7ngvmoz1/ntIV1skWs9lMwZy5mPV6Cy/nMqiz5pGHUffvjzy0He6vvHzT1yHz98fj3/+m7ugxKn780fo6DAZypj1D5uTJNJw7Z7XvErcgwseB5wY3O5EEwVKyIhELvLI+BuMVwcWKNWupP34cj9dfQ+ZnbVv/n5RUCROXQ10xoSk2kmp75sLKURB9xT6TEdZOhq+HQPYV3RzrSmH7i+DZGW6/LNkiCJbOmWIpbH7m+rtl/pfVzb0bT3d5GjupHW8PfBup6MYXcX8l2cnsGKR5nqKGfB7a3LI0cMG2BIpqdHw4pSvKy5Ij47p6M66rN96OChaNbxvc9kbVI0DD84NDUUrgw8mRSC9z6T7UN4A727sR7GZZnP0VFVcax1exXzE2ZCxDApobh6ilahYOWEhuTS4fnv6wxbhFxxfx6C+Psi3NmvvWaGzkqT1PMXXn1BaBoMK6QhafWEw392480vGRpu1ikZi3B7yNwWxgbtRcTOZrM9/AAtntEPErOlM9d3vNRHqZO31K+yn08+rH+6feb9HdsrUSILnEssCuatAzd0tcm8vTTCYzT31/ivGfR3H8Crh0VkUxC04/i33wFzx0W/N8VhAEFt/TGZVMzMx1MS0Ax6/t/YqlMS8wdaN1EhcsJUAFVQ18MDnSCqg9JtKbMZHefLwvhbg82wlFW7rEpnu0fyAD2t18C/IH+/gzKMyNd3YmknFFQuNwRgIrM2fg0u4bJnR3a+UM1vJ2sgR25RIR797Txco5NDDUjSdvC8JJJeX9SZFWDqhpg4LpHaShk7cDMy+DmQuCwNv9gvkKNd8pHRnVyRodUn+yCG1SOY4jA6/qkm+rHIcFInFXUb7hAqZ6a8aZNq2S4mXnKFuV0CKhWPt7HiUrzlO9J9Nqe6SfEzOGhqKWiflwsjVQ+/7e/tweZrs0MKO0jnGfRTFlxXHq9X8c++oftU3/lIPdoK60iZ3b+yMun6yjUSlFdeYCdkOGIHG1RHwPf3sfooBsjDoR1aZY3J3uRm5neRA/HLWVTMGHV4yLqc/dRbuQBxAEAZ22mriTUxkq7KKv9HcEBJyd+wLQ0JBDcdKTTHXM5d4ur1pNLmrWfITPkh9J7BrGVudOjFfpcbJrtiAH9O5H3K5tZJw5SeeRYxDL5ZiMRra9+Ax1IjH3/usZnDpYu1RuROfPn+f30wnI5XJScorp2rVrEz/kUhmKIBWhz6xG1cOjOUAgkVsmx8eXWUq/wiwdzWqLslizaTciAYrqRTg7O+PpabEHp0Un8cvpA8jEUjKLc2jfvj12dte20b6cnMOZasvLIa5Gyz0ezgiCgNZo4v7YdETA6i7BLXg/rSklJYVff/2V/v3706NHjxb77/X3YvCM6SiPHMbpnnsQJBLMZjN5L7+MPisb/6++QuJibdVUubrSp29fOt91V4vzeXXtQNH+s8QLlbgVN+AeYVnMNcSUUHMgh7IwMz6DrHkdgiCg7OKKXR8vRHLrLL7FNqqmNiofU4MBZQfL78ZYq6d0ZTwSFyWaKddnSVWEOmM/wMeq49el61B1c0fdyxPhMsuvSa8n56mnMTc0YMjPx2wyo+7Xt2m/xFGO2Wim7mg+Ui+7Nr0cf//9d86fP49cLictLY3u3btbdbr6u0qXXU3FhgsIMjG61EoUHTSIHSz3ue5EAXVHCxDkYnQXKlD38Gi6zxWbUtBnV+P6aIRVWZ2+vp7VXy3HjMAIYx+kZgmKds3BbKmHBxgNVPywGkWHDsiDLTX0tUeiKHr7HTSPPILzfVNaXKfdHXegeeABJI6OLfaBbcutncyO+8Pv5w6/O1osnvzs/Xik0yN0crXuPHZk+wVCU2qow4wypw5juDN2DpZAbNXuTEtpolSMLqMadU+PG7JWXy55u3boM7Oo+PEn7AbdjtTdkmGv/HkdFatW4THrDewGDrQaIwgCDmPG4DxpEiLFrSlpVHTqRENsLJXrN2A/fHhTeVrZV19TtWULIrWauqijON0zEUEqxWw289LP57hQXMv3j/e2yj4C2CukeDsq+TYqE5VMTM+LWWNdejp5L76I+rYBeLz22t/a5n1dsvcCM9jFrwa38OYW9OmHLDBnuQOk7oOO4y3lzwBRn8C5NRZWUdp+S7cxicziGNr0NBQnwIObwOGKEhe5PTj6wYkvQKKAgH5/7ne9SfX26s1DHR/CTdm2hdXfQZmldbz2Uy5isZZK6UHE+kB6+ljetb/GF/Lur8k8f2c7JnS3LpMVBIERnTx5sG8A9oo/PiDWL8SFMHMevTtblzIJgsDYSG+m9vFvc/erP1Nag5Zpe6chl8j5dPCnLRhSPnY+1DXWsSZpDZFukfg7+ANwIPsAH5/5GDupHUfyjjAqaBT2MktJ7LJzy9iTtQeVRMWJghNMDJ2IWCTGZDYx87eZFNQVsHzocqtkLVhYnY5yR9YmrUWj0NDZ1bp7ry1tS9vGlozVOGsncCTGg3t6+DbdZ0EQ6OXZi/XJ6zlXco6xIWMRCSIMRhNPfH+SOhslQABu9nIkYoGVRzMJdlO3ABbb0jdHMvgxOgd7uYTDKSVM6umL/CLCYOKGF6kjE6kEMqrTGBU0qun5rZZLCNCo+DYqE4lIRN+LTpXj2cl8GDsLwSylypyCWetHb1/Lb2tfQhGLdyc1lQBdqf4hLmw4ncvhC6VM6umL5Io59JXv/GptIw9/E42bvZzPH+hhFcS8UQmCQL9gF9aeyOJUZjn39vBDJAhoG/VM2fo0RqEWo6iK+sZ6BvoOvPYJgQ5eDjw1MJhQj5al14PC3Hi0fyAuV4CsRSKBid19mdLLr+n/A8DcaKJ2dSKCwYxaawJBaHLEG8q1lK1KQB7ogNPYtlc2XE2CWEDm70BtVD6GCh2qzpZA2yXMA2ZLZ2WRUtKU6G0srKPsxyTLHDO9Cnk7JyROzfOF3kEuPHFbEF6OSuvPEgT6XywNPJlZzr3dLaWBBqOJp1adorxOT3GNjhqt4S/rTIR/ysH+URtVW1VKzbx3qHCWELhpAyIHB/Jffx2zXk9W1AYaA86iy3bAj+eRqA1Ebb8fgI+OreOEOIKJQhwdlQNRKFI5dtzSjSvq12nI7OsI1szEy3M8mVmfU10di9lsJCHhVUCga8fFCJeVQhjy0il4fzlKjYhlg3oiMpt58WwsRmNzRlHt7c3gCVOpEcG+Wa8CcOK1JyiUyOnl54rXkAk3fT+qqqrYuXMnfn5+PP744+j1erZt24bZbEab0lyG4jyxnaU70WFrFwNBA6HvdDj5NaTux2wysf2H/6BDwuOTR+Pv78/u3bupqqpCW9PA1t3bsBMpmfb00yiVSjZv3ozBRonG5dpeXMnGogpeCvBkXjsffquo4ft8S/bk3YxCkuu0fNjBH2dp2yZN9fX1bN26FXd3d+68806bx0idnAhZMA99ejolH30MQOX69dQdOoz7K6+06AJ0STJ161bVMc89hL1Jxu74s9QWlGKs0lGxJQ1ZgAOVQbYzSIIgWLmDLpc82MliGz1egPZChcWSehHqrJnSvtVxV9OV3QyatotaXkfpf/6DLiUFnw/ex3HiRMq++qqFi8FhiL8VXPpqys/P59ChQ0RERDB58mTKysrYt2/fdX+Hv5qagNr2cjxe7I5ILb3YPc1EY2kDVTszkIc54/ZkZ4y1+ibnVENcKfVnirG/ww+Zn/VEZvfHn1ChVDKiWySann7UHMpBl2VdTub6zDMoOnak4M15GMrKMFZVUTB7NrKQENxmvGTzWgVBQCS/fjisXCxvdfJz5UKhKL8aTVQhmTIQPxyOFEj4JhaTyYQuvZLaqDzUfb3QTAqjMa+W6gM5Ns97vfKcOweJRkP+669h0unQZ2VRtHQp6v79cZ461eYYQSS6pd20BEHAa9EiBLmcgtffwGwwoE1MpOSzz7AfMQLfZcvQZ2VR/IElk77xTB57E4r49/D2hNmYzILFxTCqsycf7rlAYkE1ZoOB/NdeR6RQ4LVw4f+fANAlDZxJtX072DEDaoosCYpLUOdphyyOoc3TwGiAwjg48DaEj4WpP0JFZjNcOvZnSNoBg+eCR0fbnxVxD3SaYGHpFZ7/077irdLfFQRtS5egzlKxwMapbyE2eLIs7h1yKssordUxa1NLN93lEgThhrgmNypZKyUjIpFgtQD9K+mTM5+QWZ3JwgELcZDZDnY83/15QhxDeDPqTap0VZQ1lLHg2AI6aDqwdvRaTGZTk3snpiSGb+K+YXy78SwdtJTUylSWnVsGwM/JP3O84Div9noVPwfbTsZJYZMY4DOAD099SGZV5lWvPb82nyXRS+jh0YMV42ZQozUwe7N1e3JPtSez+s7ibPFZvk/4HoDPf0sjJreqRQnQ5Zo2KITu/k5tAhynFNXw7q/JDA33YOXjvcivbGDRjkQAFv22lhLTCXo73cfLPWfye97vbErZZDV+ZGevi4DjFGJzK9EbDLyw73UEs4jlg39AYvDiy4QlZFeWUFar4/VNsVYlQFfKSSVj6b1dSC6q4aO9F6567dC6m+5m5emoYOH4CM5kV7L8sKU87V87P0AnzmBK0EweDH+QtUlrOV5wvM3nvNrfc2v7xCKhRWCrak8mhuJ6XB4IR9XNnZqD2ehzaiwdjtclgwDOk8JuOll1uWQ+djgM8achpoT62BKgGfPg+kQEig4aqn7JpLG4HrPBRPnPyYiUEjxe7I7YWWGzSqC173ypNPBsdiXLD1vmn5eA2u9M7MwTtwWx6lgWv6eU3LLv94+uX/84gW5Ql0cI97w0Be/EUsTvziKw553IAgOo+H4VBn09sXyKIDHTq+t3BPSdSNrenUja5RJ/Kou3pL3wNReweuB4Av0HkZS8C6PxEOUFdWjF26E6kj5Dl+Ls1I/Cws2Ulh3EYKihoHAj4R0W4ezcp+l6zCYTBY/fjbawAf9PluDS5TY8SmP52hyAfe4JegU024DdukRSun8vyaUFSJLjOZ6chrtRz6gvf75pxoPJZGL9+vVUVVXx0EMP4ebmhlQqJTo6GkeVPZKdpYgdZGgeCEfmY09jcT11xwutXAwABPSHxO0Qv4WYAj1RuXBXmB3hg+8jICCAkydPkp+fT+aJZHLqipg0bDy+4UG4urpy/PhxTCYTwcG2af/FukYePJ9OmFrBp+EBdHdQcaa6njX55XjIJbydXsDD3i5M82t7hHrLli0UFBTwwAMP4NiK4wEs5RvG8goqVq9G6uVF0eIlqHr2wHPO7BtaWEntVDiV13O2OIvy6GS8CpwwlmtxezyC7JK8G4piy4McLeVfsSUIIoG6qHwcRwQ18YP+KNWfPk3BnLk4TZqEy2OPoerTh6rt26k9cLDJxQCW4JE80AKXNpQ2oOziavPeNTY2smbNGkQiEffffz8eHh7U19cTHR2Nv78/zq0Aff8OuhzqLPOxR+Khou5IPuZGE3VH8zE1GHF7PMLilDJD7dF8RGopVbsykLgpLTXml00uUvbtZ29aGh3MZoZOn4482JH6mBIaEspQ9/RsCtYJYrEV4Lju2HEaYmLw+/JLZD43xry42WyLyWQi+pPTuDaacXi4IyHhbpwtqqZ9npZzhTWoThQhUklxeagjMi87DGVa6o7nowjTIL7JDoIihQJ5u1Aqvv8ec0M9FWvWYqysxP+br28I1HyjEtupkXp7UbHqB0CgbPlywIzf8i9RtGuHqaaGih9WUxfakWn7Cunm78TbVylREQSBfiGurDuVy+8pJdx1Zhe1O3bgvXQJqsjIP+17/WUkEhNTocInbyeUJELmEcg5AfevB49OFoj0iS8As4VpZzbBA+striFdjQUube8Nv7wBPj1gzMcgtBJQFwRLl81zayD1gMVFJPrrOTj+P+jLQ2lsOJ3Hu/d2YUCIB16K9uzP38j+lGTOJPq26qb7b+nvlrk+UXCCRScWcX+H+5nawXbQHCydI7u4dWFN4hry6vI4mHOQlIoUvhj6Be2c2qFRaFiTtAaZSMbnMZ+jkqj4dPCnhDqHNsGlPdWevHvyXfp69+XVnq9e9dnX27M3Gy5s4EzRGca1G2fFnbskk9nEjN9mUFRfxPK7lhPi4o5cKmLl0Sz8NSo6XgbfDnUKJbUylXXJ6/CV9WTBlmzGRHrzwpDWmwKIBIHeQS78cA3AcaPRxOMrT6EzmFj5WG/audujNVjg0gpFLd+lzkFu9mPjvR/T1T2Ss0Vn2Zy6mRFBI6y6FF8CHB9MLuFI8UayGg8ywf9FHu42FB9lB/blb2DvhURikwNILKhm5WO98XRs/Xcf5KqmuEbH98cy6R/iio9zs1vk8t/p1dx0t0LtPexJLa5lzYkskOWxreB93EW9+WbcbHp69GRv1l72ZO5hfOj4Py2ArUuvpHJLKuq+XtgP8EEe4kT92WK0SeWYtUbqzxTjPDEURbDt5gw3I1mAA9qUChrOFiMoJNQcyMH+Tj/UPTws13GyEF16FYYKHdq4MjRTOiAPcLDApY9cH1y6vafl3q8+noWXo4K3dyUyMsKLGXeF0SfYhV/iC9kZW8CkHn5/arC8rfq7PU8v1z9OoD9JB79/D5cTOWSO6ky3YZbuV/ZDhuA4cSKxjfuRu2txqhiJa1hvAG5/YB3aUjnLXDqhR857QX4opQrEYgm9ey3DbBZRrf8KQ52S24ZZWiFLpQ50DH+X+vp00jM+ws31Ljw9J1pdR/bH71KQqcBtfG8UAy3smMm9RjFCm8KSRh+Ssq3hoMMXf4DaBL+fj0Uwmxn1+hxEtyA7ferUKdLT0xk+fDgajaWMoG/fvgQEBLD711+orKlCM7l9E1jYaVw7UIk5s+YQBu1ldaoX4dKVNfXsjislQF5N38kzANBoNIwYMYKMjAziylLo7tmR0P4WSFv79u3p1q0bUVFRZGe3BMKZTCaeOZNIncHEf8IDkIoEBEHgww5+yASYkZSDv0LGvJC2L2jPnz9PfHw8d9xxB15eXtc83v2Vl5EFBFA3O+3uAAAgAElEQVQwe44F7vrOOzfVYafjvcOJFFxIEleRkpqC42gLQPly1UZFtQAttyZBKkIzOQxTbSNVO9KRBTpgN9Dn2gOvIbPZTO2hQxhrW8I1TXV15L/+BlIfH9xfs3AyxHZ2eL+z2OJieP8Dq+OlnmochwWijS+jaleMzc/bu3k3JSUljBs3DpXKUjY2dOhQXFxc2LJlC1rt3xNMd7mbrgnq3F6Duo8ntUfy0GfX4Dw+pCnAYX+nHxJvNee3n0Cr1bZwdGkrKti6dy8qvY6xL1rcPCKFBM2kMIzlWqp2Z1h9vjw0FLeXXqJ2/36qt2/H9dlnUXa++ZbDJp2RhsQymwyEgqoGojPKbY47tD6R9nUmMiOcCW5vCVTeMaUTF5QCIfGVGCp11s+csSGI7GXk/BCPtqGlk8zUYKAhubzNLAa7gbfhNPU+yr9fRcPZs3i+ORep563rZGNLqcU1JORbu7QcR4/GYdRISj//HF1KCl4LFzaVhrnNmIEsOJii2XNQ6upacAtM9fXUHDxoBZfWqGUsvaczjUmJlH3+BQ6jR+MwwrpjZHx+FanFttsBH0kppaxWd6u+Mjnl9ZzNbtsz7I9QvdoPhs6HC79AzI8w8GXwvVj2GzERIu6Fw+9BURyM/RTUF4Pmg+eCWwfY/oKF8zP+cxBdY8Kr0sDYz6A43uIIsqXC81CSbHvf/6gaS+rR59n+vekyqjBU3brfW0J+NR/tvcDozl6MjbTMB8Z17EMPh0kUmY5yIGcfrw5r3U13pQwmA7/l/IbOeOuu8a8us9nM4dzDNqHONfoa5kTNIdAhkJd62HaRXq6OLh2ZFjmN3Rm72Z+9n+e7Pd8EdZ4YOpFBvoP49OynZFVnsei2RdjJLEiAV3u9iredN28efROZWMaC/guumXBzV7kzp+8cYktj+S7uO5vHrE1cS3RhNK/1fg1fe0vw4onbgukdqGH+tnjyK5thyoIgMKfvHOxlDsw5OhuNnYi3xl77nRl0EXB8JCuR9w8dsHnMZwdSOZ9XxdvjI3Czt7zzXxoaSntPOz6JeRuzYOCjO5egkMoQCSIWDliISBAx58gcjJdxxy4BjtOrUjlRuQYNPZh/58MAjAnvRW+n+ygxn2Bv9q/MvKs94V7Wrq3ogmhKG0qtts0eFY6fs4qX15+jVtfSnX/JTdfJu3U3nS3pc2swlLatBbkgCCwcH4GjSuDLhEUIJju+vdvyTFVIFLxz2zuUNpSyNHppmz//knSZVRgqr28eadIaKF9/AbFGgeMoi/tfpJTgfG8YhpIGqvdmoejogqr7H1MmJYgFy/xeb6JycypSLzUOQywllmJ7GU4T2tGYW0vtoVxUPTxQdrIEfORBjtgNtMClG5Jtz8VsaeG4CNxUMrZsSMBVKWPh+Igmh+SHkyMpqdUxf7vt5hWZpXXE5toGnf+jW6N/gkA3oYK0BM5v28+xUG+6P7fQal9Jn3AkvbNR5vWk27j3mrbL7JzYZ5zNOaEHI3L20y+gmb/j5hZGYXwfGhtlVBTdh0LdzPKxU/cmP7s7Wq2a+or7rV5ilWfP8EtCBGe6z0T+0mdN2wWRiPf6DsTO2MDz8eno9c2TD7mzhmG3hSA1GBkYEYymVyst2a9DpaWl7Nmzh3bt2lkxcUQiESM73g5GM1Gu6Uh8msubxGop50NL+aX+JLtXbrE6n8mrK1ucn8SMiPFTH0Mkaa6b7tqhM8EiT9xEjox8dLzVuOHDh+Po6MjmzZvR6awnXEujz3FUa2JkVQGhquaov5dcxn21xcgb9TzZWIm6jdbp6upqdu7cia+vLwPa2OlHpFLhvXQJYkdHPOfNQ9qGwNG1NGrmYzgb5PwuPo/Rz3rxWrNvHzlPPEne8y/Y7CBkSzJfexyHByKyk6K5RZbUqk2byZn2DPmv/rvFArvo3fdozM3Fe8lixHbNvw913z5oHnmYirVrqT0SZTVG3l6KsTKdmoPFaC9YB/xSjsYRHX+GTrJAQgKbHWEymYwJEyZQU1PD7t27b/o7/dkyNRio2HABiZs11BnAcVQwUk+V5cUd2czkEMQi0qQx/CqL4aD5CGI36wDhtk8+oVYhZ8ztt6NyaX7mXFkaeLk0jzyMeuBAVD174jrt1rg7KzalUPZ9AnXHC6y2axuNPPRNNPetOMaZK4IA2WkV+J4tI0UpcMd9zYwgsURE+8c6U4qJ3Q4CkstK30RKCQeCVMirG/lthXWpodlspmxtImXfxdMQ03absserryJv3x7HceNwuPvu6/na162SGh2Tlx9n8vJj5FZYL67yH32efLULhyIGIx3QzDkQKRScuv8F1HVVfFxyAD+NNUur4M155D77LyrWWsOl7wx2YmHCBsplagoffc5qX055PZO/PMaU5ccovSLYczCpmAe/OcFTq061gEvfiGq0jdy34jhTlh8nubBlF5s/Tb2nQdgI8O8Hg1613jfqPdAEW45pP7J5u1QBE74EpebiMbbLflsobBh0f8TCF8o6Zr2vIgu+HQnfjYTa4pv7Tn8TGWv1lCyPpWR5LIYy6wWgLruakhWxlH5zHnPjzQO1dQYjM9edw0nVvGi5pC/GvIrCFIidz1bG9mi72++b89/w/IHnee/ke9c++H9E65LXMX3/dOZGzW3xzl8SvYSS+hLeue0dlBJlK2ew1pOdn6SXZy/6e/fn4Y4PN20XBIEF/Rfgpfbiqc5P0cuzV9M+tVTNO7e9g6PckXn95uGuatviemTQSEYEjuDzc5+TWJZotS+9Mp2Pz3zM7b63M6FdM0JBLBJ4f1IkRrOZVzfEYLrs2adRaOgkfQKDJI+Bvc/iqGobJ+ruSAecgr/m+4xXicqyhlzH5FTy2cFUJnbzYWTn5nmkXCJmdP8sJHYXGO71JAODmktPvey8eKPPG5wpPsMPCT9Yna9vsBM+oZsRmZV8e/cSqwYmn49+GaUpCDvvrYzvac3cPJZ/jCf2PMH0/dNpNDUnc9VyS+e63IoG3t6ZYDXGbDbzxqbz1OgMfDSlqxVY+GpqLKm3NJZZEdsCcNyaNGoZt/U6hVhRxDMdXydQ0/wb6OzWmae6PMW2tG3sy2o7KkCfW0PJivOUfh2HSd/2Z07ljnSMVySm4CI/83ZfxM5ynCfeGg5Qa5K6qXAaE4xILWmRFFR1dkPd2xOJuxKnMdbVFI53BSLxUFGxIaXN995ZLWNFkBdLUbE80BPNZUDtLr5OPD+4HZvP5rHrvPW8r6q+kSkrjjF5+THSSmwH/v/RzeufINBNaPvsmRjEYsRyBQe/XYHpInuntqyUSj5HrLfHJ/kxUr6MbRpzNCmH9W7t8S0rJmzXUX5965PmfRv2UnK8lDMHJpOcayQppjkD//N320nL7MTpE5PYe+AoVZWWPwqT0ciej09gEsQgV3Hwp3Srl62bsyfvuTVyXuHHR0cu66BQGEdw9Vqm36Oh+7zmwNGNymg0smXLFiQSCWPHjrV6gBlr9Jj2FDHArjO51YWcONHcLSUrK4sTiadRSuScLogn9XhzRDg6OprMCiMjxkzAOdAa0Fe5PZ07tZ148vEnkSqtHUwKhYLx48dTUVHB3r17m7afLyzm81oTftXleJw9TkxMs4PkwoULCNFHePbcbxT8to/Cwmu3CDWbzWzbtg2DwcD48eOvCzas7NqV0KNRON49us1jria5gx3jR92OTjCwZdkyTBeDPYayMgrenIdYo6H+1CnKv1/V5nPa3+6L16w+SFzaNkG7mvS5eRS98w5ijYbagwep2rS5aV/t4cNU/vwzmscfQ9WzZ4uxl1wMBbNnY6yydJswm80UznsT7blVgIiSL45hMlj+/hqq6ti2dycOgpKe1YFU77MOEPn6+jJw4EBiYmJITEy88uP+0qrcnoaxRt9iAgEgkotxf6G7JWh32d9faVISv+WmItfryZEZOPr11037zm/ZSgIQKZXSYeRIrlRrHSUEsRi/FcvxX/V9U5nezag+ppiGmJKmkrXGy7J87/2aTGpxLU4qGS+vi2nqKGEwmMhcFYcRCHusM+IrJpE+/o5kTArmnaoqVhxu7iZ3NruCebE57JAYiCjQcfpwcxvTuhMF6FIqEamlVGxJw9hGZ4FIpSJo00a8liz+QydvlolzLLU6A2azmVfWNy806nQGXv4lk3+PncuSdqOsWAypxbW8mWTi+IBxOEftp/qX5u6Q1bt3U71jB2KNhuL330eX3vzeKfn4E5yLc1k96CFm/pJB3cVsrtFk5uV1MZaOcjoDb2xq5mBU1On598ZYXNQyKxbDzeit7ZZONEqZmBk/n0NvaFsw+5ZLJIKpP8Gju6w6XgIW985zp2DUuy3HeXeDV1Oh2wPX93nD37aUmm15BnQXJ8Imk4VHhNmybdsLtlvU/w/pcjYdApSvv9DUxeYSH02kkmAobqDqV9ttia9HH+1NIamwhqX3dLZatACopHJ+Gv8JEkkjC48vaJNjMKEsgS9jvkSj0PBz8s9E5UVdc8zfXVnVWXxw+gM0Cg17svawO6M56bI/ez/b0rbxROcn6Ox2bfjyJUlEEr4e9jVfDv0S8RVuOlelK7sn7uaF7i+0GNfdozuHJh9iWOCw6/oOs/vMxlnhzKwjs5ocXI2mRmYdmYVSomR+//ktnvf+Lirm3t2RqNQyVh3LbNp+PL2M3Sc1+EvvYF/+T5wrtk5A2JLZbGbRiUUgqkNAzEv7X0PXaHkPaxuNzFh3Dnd7OfPGWjdJyK7OZnXKZ/T16sd7w59pcd4xwWMY4j+ET89+SkpFStP2L2K+oNKYxYdD3ibExdrNqpDK+GnCJ0glJhYcn9f0u6/WVzM3ai4ahYaEsgS+iv3KalzPQA1PDwrmx+gcDiQVNW2/xKa7Hjed2WimfN0FEAuYahup2Na2d8vpotMcKFjPvaGTmN53TIv9T3d5mnBNOG8de6uFm8nmdTQaKV+XjEghxlDa0MIt3ZoaEsuoP1WE/e1+yANa8q8cRwbh+WqvFo1U/gjZ9fHCa3ZfpJ4tmaPOE0PxeKkHIoV1GbKlSqA9prpGKra27d7rMqtwjitHpJaiia9Al2HdMW76ne3o4uvI7M3nKa5pdlW9uS2Oslo9MrGImetiMBj/S+/8/3FdMwgkCMK3giAUC4IQd9m2+YIg5AmCcO7iv1F/7GX+9ZS24ztqzBJc3e0Y/syLFKQkc3LbRgBOb5uJwb4Ide2T1GrccCxrIGdfNrpGA88npSMym/kiogNysSuJSUfIOXGO8oJSjm/8GqnCg8f+NR0RUjZv3oSuQU9sdDJpBbG4qwMZN3oSRrSs/XoDAKfmfkKJsj093BLof28YOQnlxB+2boM9qttQJuuT+ZRgzqSeBoPOArFUOiMe94mFQXCTioqKIjc3l9GjR+Pg0PxwM5vNVGxKwaQz0v+hoYSFhbFv3z6Ki4vR6XRs2bIFJycnnnn2WRxEKrb+uoOG6jpKSkrYt28fYWFhdOtu3WmrPraEhnMlOA4JQO5r++URGBhIv379OHXqFKmpqRiMRp4+mwxmM9/17UxgQAC7d++msrKS+vp6tm3bhru7O/965hlUKhWbNm26Jlz69OnTpKamMmzYMFxdr5+Xc7P8pSsV0L8/vR0dyZDJOPnDajCbKXhzHqbaWgK+X4ndkCGUfPQRupSUa5/s0jXeAgeQ2WSi4A1Li9HAn39C1asXRe+8gz43D2NlJQWz51hKjF5oOXkDi4vBe+lSDKWlFC56G2gGartNfwx5UAOC3JuSz3YAsGPlJmpNDYwbNRbHnt42AceDBg3C09OT7du3U2ujPO2vqKtBnS/pyv8vk9HIhu++wywIPP7AA3g2NPBbdjbFiYnUFhWx68RxHBsaGD1jhu3zXVYaeOWESxCEmypjvCSxFgvM3M8e9+e7gkRExbpkzEYzx9LK+OZIBg/3C+Cz+7uRUVrHkt2WbOjBH84TrIOi3m74+NvmcI3v7svICE8+3JtMYkE1DXojL6+LwcNezoQZvSkQmxHvzqKqssEymduZgTzUCbdnuoDRRPnGlDaXhQli8R8OTF5/Opd9icX8e3h75o3pxPH0cr47mgnA27sSyamo54uHezG1tz8rfk8nOqOcRqOJmevOoZKJGfPeGygiIiicPx9DSQmNxcUUzl+AoksXgjZuQCSXW5oaGAzURUdTvnIlTlPv47GXppJdXs/i3Zag6bdHMojOLGfemI68Oqw9exOK2HgmD7PZzJwtcVTW61n1RG9Gd/bio70XWpSuXY/2xBey/nQuz94Rwnv3diGhoJpP97f9GXbLJQiWYJAtXa3M61olYLYkt7e4iCqyYM8cy7YTX0DWERixBIbOgwu7Lfyg/2HVny1GG1+G47BAnMaGoM+spvaIZZ5TtTsDQ2kDmvvDUff1ovZIHtq0Gy8hOJVZzorDadzXy4/BHTxsHhPiHMxL3V/iUO4hNqdutnnMJemMOmb9PguNQsP6MeutAMf/qzKajMw+MhuJSMKPo38k0i2SRScWUVRXRFlDGW8de4twTTjPdGkZoLiWRIKo1efslYGhtu5rTU4KJxb0X2CBS5+1wKW/Pv818WXxzO07F1el7Xnffb38uLO9G4t3J5FWUkutzsAr62Pw16j4btxCPFWezDoyy2aZ3OXanbGbPVl7mN5tOpMCX0QrTmf6Tgvgf+kvSaSX1PHevZE4KpsTMUaTkTlRc5AIEhYOeMsmz0gQBN7s9yb2MntmHZlFo7GRc8XnmoDaQwMG27yeYKcgZvacSVReFOsvrAdgyYkllDaU8tngzxgTPIYVsSuIK42zGjfzrjDae9jz2sbzVNTpKWswsWBbPL2DNDx+WxudkUDNbzk05tTgPDHUAjg+1ww4bk11jXXMPjIbHzsfXu31is1jpCIpiwcupq6xjgXHrh3Yrfo1C0NxA5qpHbAb4E3dsZZu6StlrGukYmMKUk81DkP9Wz3uVoKgr6WrfVZr+2Q+djgMvQiXvoZb2qQzUr7uAmJnxRVw6ea1lVQs4sPJkdTrjbyx0ZJM2hGbz9Zz+bwwJJR3JnYmJqeSL367+WTSP2qpa4KhFyxYUAF8C0yYP3/+5xe33QEcNpvND8+fP//L+fPnt2lG9r8Chk6PPUbc1l0oTAYe+vJHPINDKc/LIWbvLozVuTT6b0GS05f+DyzGuYsrJb/nYUqvYk5lJqdcnHisXsdDAyJwd/Um8eRhUqPPk3zqHLq6Aka/OJfATkEIegWpuXFkJZZwJuYkAmKemv4oASHe5CSXkVN+gdqEUpLSvHHVpTH0k+l4BDlSmF5FQlQB7Xq4o1A3vxgGePqwMTOdfeU13Je+GmnyDrj3G/C6echnQUEBmzZtomPHji06Y9WfLqL2cB6OI4NQdXIlMDCQM2fOkJmZSVFRERkZGUydOhUPL0/clM6cuhBDRXIR51LPo9frefDBB5Ff1lnIWK2nbGU8Ek81mnuvXqYUEBBAUlIS8fHxbNYJHJba8ZJaxIQOIQQGBjbBpTMyMpqgzq6urk1waaPRSEhIiM1zl5WV8fPPPxMYGMiIESP+Mt1ygnr2JPHXPSRUVhCYkoJ0927cX34Z+6FDUPftQ+XGjdQfP47TxIm3PAjVmsq//57KdevwnD8fdd++qHr3pvLHH9GeP0/9yZM0xMfjv2L5VcvipB7uYDJRsXo1IqWKko8+QtmzB55z5qDqFUb17mMYa51JLUjhSEEsvXwi6DP2dmvAcS9PhIsdGkQiEf7+/pw4cYLS0lIiIiL+Mv+HtmSs0VO6Mg6Ju6oF1PlqOrhsGfGNjdzp60vHkSMJ9PPjVEwMmWfOkH7yJCUSCVNGjcK1XbtWzyG+2Ga97mg+EncVUo/Wu9Vdr8xmM9qtOcgaBFwfj0DqokTiLKc2Kh89Zh7fn4SrnZwvHuxOsJsd1Q0GVh7NxEsPEWfKSLEXc8dTXa8OOA52Yf3pXH5PKSW1uJbDKaUsf6gH4b5OlDtIcEqoICahFMeUKkwNRlyfiECqUSJSSqg7mo/YXoaslWDzn6ncinqeWnW6CercyceB+Pwq1kZno5SKWXYwjWmDgrmvtz/9gl3YHlPArwmFlNTo2HW+kI8md6VrgAuqHj0sYO/UVGoOHECfmYX/118j8/dD6utDxapVmPV6yr5cjtjJCb//fIqfuyN1OgMrj2ZhJ5fw3p5kBndw57URHejq78zx9DI2nMpFJBL4LiqTl4e1Z3QXb/pdbBX8+8WWxZLrDBqW1ep4bOVJAlzUfDylG2Ge9uRVNLDqWCYDw9xatKb9I/Vfg0Q6+YG+zgKXljvAvgUQOgzuegt8ekJmFJxdY+kqprz1INH/tgyVOspWxiPzs8d5YihSbzWNhXXUnShAkIupOZCD3W0+2PX1Qh7sSENsCQ1xZah7elx3N8s6nYFHvovGTi5hxcM9r1qiEuEawZmiM2xO2czIoJE4yG13tvr49McczD3IB3d8QLhLOJ3dOrMmcQ35dfncFXDXdV3ftfRXAZl+G/ctW9O28lb/t+jh0YMeHj34OflnksuTicqLIrUylS+Hfombyu3aJ/svK8AhgNKGUtYmrcVeZs9nZz9jZPBIpkVOa3XMpRbZP53M4URGOXG5VURnlPPNIz0JdXOmg6YDqxNWU62vZpDvIJvnKKorYvqB6YRrwpnffz63B3Zhw/nTXGjYS01ZGF/9Vsoj/QJ4pH+g1biV8SvZnLqZ+f3n08Ojh81zAyglSgIcAliduJoGQwPfxX+HUqLkP4P/g0zcuhOlk0snzhWfY3PqZqQiKSsTVjItchp3h9xNL69ebE/bzuG8w0xoNwHJRaC9RCSie4ATK49mklVWz/7UKir18MMTfXBStc31os+rpfznZJRd3HAcGmAFOFZ180Aktz2fXRy9mOiCaP4z+D/4O7QefNEoNCglStYmrcXbzpsOmg42j9OmVVK5NRV1Py/s+/tYnjlxpTScL0XdwwPBBuDYbDZTsS6ZxoI6XB+PQHKTDSn+25L5O6BLqaD+bDGqbu6I5LYbF1RuT0OXVonrwx2ReqqR+VyES9cZrODSGrUclUzCyqOZSMUC7++5QHtPB96/twsdvBxIL6lj9fEsBndw/1Mh/H+V5+mN6JaBoc1m82Gg7RSo/3Hl5+fy1oVTaP296ffcv5ArLQuiIU88i8xFw0HPLEz1HnQbZYnWS9UyHCaGEm/XwA5XB8LKy1kwytLVK+j23oQG9UVnLKKmJJ6gHncT1tti6xw0vBce9kHklCfRKNQxfPBIHJ0sdbhTHhuLHAdOFyRjFrQMe7EPootZ6MEPh4PYyIav92AwNNepOtg587GvglS5F6+WOFg6jrRvWf7Rmn6JK6SgqiWIrbqmge9W/oRSqWL0aOvSJkO5lsrt6ciCHLEbYAEL29vbM2bMGBKqatiWnkP//v0JCAgAoF2fjvTwjiChIo38/Hzuvvtu7C/rsGM2m6nYeAGT3oRmchjCZe1Q64xGNhSWo7uMeSOVSpkwYQI5ZhE/meVEaGt4pbcl6OXs7Mzw4cPJyMggISGBO++8swnqHBYWRvfu3Tl69GircOktW7YgEokYN26cVd30f1timYx7HnwAkyCQUFGBomcPNI9YauclLi54LphPcW4OZz/91Ob4hJ07yT15ssV2k8nEydWrqcpp2Vrb1NBA1bZtmHQtS2d0qamUfPgRdnfeieNES+28zNcHj9mzqI+OpnrXbtyem46iYyvtki+T6zPTUHTqRPF774FI1ATUFolEuE2/Ha25nn3pp3EROTDsYQsc3QpwvMvasuvu7s7gwYNJTk7m9METtj6ShvhSDJUtv5fZYKLubHGLdpl/hC5302kmh7V5YZN/9ixRxcX4abUMePJJAFw7dODOoGCKlErSpFJ62dsTdNtt1zyX/R1+SP3sqdySirG6JUz5RlUXXYi6VMBxZBBSNwunRhXpjrKLK/UHc1BX6vhgciQqmWWS8e8R7QlzVeN2OJ96Abo+GXnNvz8XOzmLJ3YhqbCGNSeyebR/IP3bWTK4nXv5kBSopmN5YxNQ+9IETd3XC3moE1U709sMofyjZDJZSr+AJqizIAgsntgFO7mERTsTCfOwY8ZdFlCqWi7hg8mRNJZriTuczfiu3k3MCHlICO4vz6T2t9+oO3QY95dfRh5sycY6jByJw6hRlH39DY0FBXgvWYLoIlT95WHtCXW3Y9HOROzlEhZPtHQXE4sEPpgUiclsZsnuJLr5OzFtkIUlcAkunVRYw8f7bOeKjqeXkVjQ0ilkNpuZtfk81Q0GPpoS2bQgf3NMR7wclby8LoaG62Ax/K1152xwC4dfZ4HczgKevuRIGv+55Zit0y2lYleo8UIS2oP7bZ5Wl16FPv86nZCNWoj5GRqv72+isbCuVYeO9kIFjSUtXRFGg4kL353HbDI3sekEQcB5QjtECglVO9KRuCtxHG6ZQ4hkYpwnt8dYpaNyR3qL811L7+xKJLu8ng8mRWLXysLmkkSCiEUDFlkgu1FzMJlb3vtThadYlbCKyWGTGeBjYQZ2cunE05FPsytjF79m/tpiDMDerL0U17dkPemMOranbafB8N99Hl1NyeXJLDu3jLsC7mJUkKVIIMAhgJk9ZhKVH8WBnAM83+152jm3nnj4q+mVnq/gY+fD0pNL0Sg1vNH7jWuOcb/YIjsmp5L1p3OZdnsIPQIszL1enr14qONDrZYGms1m5h2dh8Fk4O3b3kYikiASifjm7sUIJhXfpy4myFXG6yPDrcYllyfz2dnPuCvgLu4OvjabbrD/YMaFjGNVwioLUHtAM1C7NV2CS0sECR+c/oBwTThPd7Ek9x1kDiwcsJCMqgw+OfOJ1bj/Y++8A6Oq8rf/udNnMikz6b0QkhBCEkLoRbAgCtIEdBXFsip2Xdeua2/rz8W+rhVFRUGaYAeRDqGFEEhIQhJCei/Ty73vHwNJxgSICK7u6/Nf5sy599yTM+ee8z3P93kGRvhz1/lJfLW/hoJmkRt+ZQ0AACAASURBVEenpPbQpjsRJKfoSb/yUWKY5jmYFeQCxtkegeOW5b0zdrflbaRk736uSbuGrNAsrzJbSQvOOrPXZ3NT55Idms3zOc9TbarucT1zRwdVi/chN6rxv8jzzhSUcoyXJeM2OWhd3fucY831BKb9LohFFX7mDtH+WxDkAoY5SUhOkZYTsKWth5ox76hFPzYSdbyHqa2O80c/NgpzTi3WQu+wwrWj4hgRb2DP96Wo7SIvzc5AcezQ9slpAzH6qPjbklxsvWi+1bbZ+Da/psfnf+LUEPpCdRcEIQ5YI0lS2rG/HweuAdqBXcA9kiT1yoUTBOFG4EaA0NDQIZ999tkZaPZ/DwfyNvNi2rnEuCp5RAhApeyKYv+no5z1+kwuqt7LvMguiqNDFPm7WYlJpeLV2nb0sV0MHaW5nv2LvsYlwtBJmVgTuoSipf2FbKtqxtjuIGXaSOjGiOGLT/gpMIogt8jA88Z3noRLkkTuzgO0WRoJ8YkndWhsZxW3281Ltc3siejPXW1HGBFwYivz7thZ6+KNXDuxfjIeHaFB0Y2F8NP6YhCqkJypTLigm+CeBBE7ZWjaoGK0iKvbXG+SBO52aTHJFTwptdO/W+BcdIkUbt6HQdITObo/YrdDAr+jAiEHZDQMEGmL9R63b0tafkTNFGzMFbrySl0S3O9Q0yzIeZE2glRdfS9JEgUFBbhcLtLS0rw2ky6Xi127dgGQnZ2NQtG1IKyoqKC0tJSUlBTCzrIL0OmiftMmDrrdJIeHE56c3Pm50+lk94YN2GUysiMi8UnpKrMUl7DzaAUqp5PsYcNQdrNQb9y0iXy3m8CODtIuvtiLReT7ySfoNm3GfP55mGbN6mqE243xhX8ib26m6R+PInZLE0SS8Fv4IbKOdlpvvRX6yEqS19RgeP0NOqZPwz60S/xRkiSKN+ZQK9oYZxPgIu/TtcBCAUO5jOohbizdDh8VJon9Obk0CyaGDx6KIqDrlMGnDsL3yrH7ShwdKXqFzI1FAsZSGe0RIvXpZ1ePw7dSIDRfRmOySGt83+4lOp3kffcdFpWKoVlZKLulK0qiyOGvv8YuSQy46CJkir7ZTytNEL1VhjUQarJE+JXEKYUFYrbIMPu6qBsu87regWoXo/OUiEponyB59b1sPyRUydmS4CQ0qe8B2MUFdopbRe4fpkHdLYDsckm410OFJBI6ToafpqtMboOYzTIceqga/uuf+XTxXbmTxYUOrktTMS7KW4Npb72Ljw86uCNLTaxf1+9IcEPABoFAh4zSDDdid6KdKOL/n7dBEGi78Qav9CbBbMbw0r+wZ2djvtj7oKC8zc1re+3MTVUxOMR73GytdrGi2ME92RrCfLz/L+/n29lU6eKh4Rr6G7raeLRD5ImtVrRKeGa0Dj91VwdvqXLyzn4Hc5KUXJzgfVpc0OTmhZ02zotRcFXqb3OqajKZ0OtPvkE6m9B3lJKW/xzF/f9KU9Bwr7KwmrWkHHqNkn7XUxk9tfNzhc1CwgY7omSkJbWMppi4zjJVh+f3LCqgYoyIu4/dmFj8DlFVa6iKuIjipL6l88jtEL1FhtwJR0eJOLoR6zQtELlDhksDR0eLiN2Gd81ekbF1Sj72sTF8jMKL8aerh+CDMmoHi9h/tpQ5Pj9XZ7mx9NFkJ6/Bxb9225kUp+TylL5rcuww7eDjpo+ZYZjBuX5daTQ20cZz1c8hE2Q8EP4Aalk3RrPk5l+1/6LJ1cSD4Q/ir+h6gN3m3SxsXEiMKoa/hf0NudD1e1nWvIyfOn5ijH4MlwVe1qMt/+0x6pSc/F/N/9Hh7uChiIfQy7vaIkkSHzR+gFNyckPwDb2mKf2eUWorZWHjQq4IvIIUbe8skd7w4QE7VSaRe4dqUHZbOzslJ/+s+SdW0cpD4Q+hk3ctkjd3bObz5s+ZbZzNOF/vtczq2n18b3+XbPV5zAub7nW9433/YMSD+Mr7xl61ilZeqX2FQbpBTA7ou0blHvMeVrWsYn7IfMJV3izupc1L2dixkdtDbydJk9T5uVuUeHmPHbXg4tYsnz6zr0+0fgPwLxcILpRRP1CkvZspis1qIXKLhK/Lh6MjXLgDut5X6jaI2i7DrfLsT7rvM5pcTTxX/RwxqhhuC73Na5x27ColvbEfn6duZFhMl/ECgLFYwHhYRk2mG3O3bcHvZQ1xNuB/RCC4oGffyxyetZ1bCZUjRaRuy3vBDVHbPO+Cn/e9UCrRr0hBjU7EPFby6qsTzc8uUeKp7TaOtIvckqlmWFjf1rN9wX97Pv01mDBhwm5JknqKrP4MpxsECgUaAQl4CgiXJOm6U10nOztbOr6x/iPj758u4OPwCcxu2MRrc24HYMHn7/FCyBCCnO00KfS8omllzijPgmD+j9tYKWh58HAzs6u1hN49BLmvyiPmuGgGzkM5HF7jh9qgIu67HAS1Bnd7O6VTpyGKImJDA4a/XE7YP/4BgG3zGspu/DtlY7PICU9i+vTpZGZ6gke5ubmsXLkSlVyLw2Xj8plXkZLhOZX96quv2Lp7DyuGnotTJmfzqDRCfU8+wOs7bFy4YCMapZyaNhu3n5vIPRM9gYMVq3PYt+trFLYwDG1JRE6JYfoUz+lOx+Yq2taUYri0Pz5DvQMl8w+Us6ahFYNCQYBSzvfZyWjlXROtvaqDhjf3oU0NxHhFCoIg4GqyUvfKXlTReoKuH+SVDvN9YxtX7y8jUq2k2u5k+eBERh5jTb1QWsOCI3W8NzCOySG9U+UlSer1ZVReXs7ChQvJzs5myjHHn9raWt555x2SkpKYM2fO7zaFSJIkXn31VUwmE/Pnzycw0EO9XLZsGQcOHEBltaISRW59+GHUfn44zGbefPJJbDIZDqWSWJeLq55+GplMRn1BAW9/8gkqlwuLRsNo/wAuuNtj6WrasIGjN81HER6Oq7aWmIUL8Rk+DICG116n8Y03iHzlFfwu7F2Q8UR9f6pn+3mdvLw8li9fzlCbnYQ1a4j7/DO0A7vEEiWnSN1rexFtLsLuykKmUyKJEg1v7aOpvpHl0jZCNEauv+9mZHIZbpODugV7EBQC7jYHvuOj8J/kCezaj7TT8NY+5H5q3G12AucOQJv2yzWh+gJXi426l/egjNATfMOgPqeBff3Pf5JjsTClfxLZV17R63dEUfzFLLaOLVW0rS7FMLM/PsNOPwAqiRIN/8nDWWembLiDMReN7yxrMtm58OWNTFBquLMF9OdEEXDs1M1e0U7Dv/ehywrBODv5BFc/yX1PMN4O1bRzyetbmJASzFtzh3h9x5JbT/Nnh/CbFIff+Ohf/rC/EsV1HUx+bTPj+gfxztXZvba/t+dqXVOKaXMVcn8Vkgihd2Uh9/EOggN9vt6vKTPZXUx6eSNymcDXd4zFR63A4RKZ9sYW6tptmOwuzkkK5u2rPH1f3WrlwgUbSQ7z5fObRiLvZdw/ufog728pY9H1wxjb/+ynlfz000+MHz/+rN/npJCk3jX8JAkW/wUO/wg3bYQQzya1+aUPsTTEIpN1IAguQu+fgMwvAMklUv9GLu52O6JdRNM/gMCrU089F5f+BB9NA78oaK+Eucsg8fxTNFmi6eMCbIXNyDQK5L4qQm7LRFDIEB1u6l/Zg+hwI5qd6DJDMM7x/K5LDzUifnCQgwqJO1wmnpo2kKtGxvW4dq/j9/jzdTg84/4UQqutFgcTF2wkQKfky9vGoOklpeNkz3fn+jvZUrWFz6d83slweXzr46woWcHCSQsZHDK4R73StlLmrJ7D8PDhvH7u6wiCQJ25jplfzkSn1FFrruXWzFuZn+EJtOXU5HD999cT5hNGrbmWN897k7FR3hvR//YYXbB7Ae/nv8/r577OOdG9O86ezjv/94LTbfuJ6h1oOsDcr+YyMW4iL4zzWJRXtFcwa/UsMoMz+c8F/+m13mNbHmPl4ZVeY+uVPa/w7v53ee3c1xgfPf6/+lxWl5U5q+dgd9tZNnUZvipvRv+GDRv6PE7tpW00vJOHz7AwDDN62shLokTje/txHDUReudgFIFaJEli/SufE18XilynROWjIfT2wQhKOZLTTd2rexGtLkSLC+2gIAL/4h3UW1G8gn9s/Qf3Db2Pq1KvAiBnw09EfCNnddgm/m34jIWTFnqxiyS3SP2b+3C32Dr3eJIk0fh+Po7ydkLvzEIR9NulL/8WkMRjz1dx7PmOmcg0LS7Eur+RkFszUUX23GM6qk3Uv5Hb6x5PplXgbrPjPzke37FRXvUeXrGfT3Mq+OyGEQxP8Oxp/vVDEa+uKybcX4PN6ea7u8adsZSx//Z8+msgCEKfgkCnFYqXJKlOkiS3JEki8A4w7HSu80fFs5feQrr9ACuDhvP5l5+Tm7eHfwcnEuuuZGVKNBG2el5odVLb0sTXxaWsQsNIRwe3TB3hcbI4Tl3c+S6Urkc5/Skibr0cW62TpkevB6DumWdxNTQQ8/prGOfNo+XTxZg2bUa0dFB9/wPI1XD+w08QExPTKXDc2trKN998Q0xMDDfeeOMxcekV2K0OSkpK2LlzJ+OGD+Nf/SMwKVXcuHXvSZ9TkiQeWr4fs8PNouuHMWtIFG+sL2FPRQt1DW3k5fyIIGq45o7LaFNDyddHqKo14awz0/ZtGZoUI7psb2HFlXUtrKxv5Z64MF5PjaXYYue5Um8anzrS1yM8tr8R674GJFGieWkRCGD4mV15k8PFPYeOMsBHw9qhycRqVdxRUIHJ5WZPm5lXK+qYHWY4YQAIet8EgUdcetSoUezatYvi4mJcLhcrVqxAo9EwZcqU3/VCRhAEkpOTkcvlrFixAlEUyc/PZ//+/YwbN46po0fTrtWy+uWXAfhqwcu0arVMHj6c4f4Bx8SlFyG63SxbuBAkieuuuYZYu51tzU0czcnB1dJC9SMeUeeEFctRxkRT8+CDuE0mrPv30/jWW/hPm3rCANDxdp7Os3VHW1sbX3/9NdHR0Uy8714UBgM1DzzglZ7Wm8Bxx8ZKHBUdxE5L59z0MVTZG9i05IcuJxqbi6Br0/AZGkbHhkrs5W3HnGgOIfdXE3LHYJSRelpWlOA2nbkUqeOQRImWpUUg0ZkK0ReUbdrMTpOJRJfrhAEg4LTSGPUjI1D386d1TWkPm+ZfAtOmKhxH2gmYloir27pIkiQeXpFPu9XF9fMy8BkWhmlj974vQu6vJuCS3rW6ToUTjbfkcD/+fmES3x2oY/keb2F9bUYw2kFBtP9wBEeNudf6ZwseUed96NUKnpuZflLto+6wHW7FtKUKnxHhBM4biGhx0rqqpEedvl7v15bp1Qpemp1BRbOFZ7/2iEu/sq6Igpp2Xrg0nfsu9IhLf7G7ElH02Cu7JYmX5mT0GgACT2pgv2Af7l2aR5u1b3a1f3icqO8FwZMiptZ7TB/cTqzff4elIQHf+KMEXmLE7TbS9t4qANrXVeCsMWOYmYT/pDhsBc1YdtX1fu3jsLZ6XMkC+8P8TRCUDKtuA+vJBVEte46JOl8Yh2FWf5y1ZtrXehy82r4uw9VsI/AvKfiOj8aypx5rfiNOh5vqTwpwAMNuGcy4pGCe+bqAskbv398Jx69ChmFOMqLVReuKklMKvf5j1QGazQ7+NSfzFwWAjrfhsZGPoVfpO0V2NxzdwLLiZVw78NpeA0AACf4J3D3kbjZWbmR58fLOFCCn6OTdie9ycfzF/GfffzjQdIAORwePbHmEOL84vrjkC/r59+OxrY/9rsSl99bvZeGBhVza/9ITBoDg9N75vxecbttPVK97auC35d/iFt08tPkhFDIFT45+8oT17ht2H+E+4Ty8+WEsTgu59bm8n/8+MxJn/OIA0Mnad7r1tAotz4x5hjpLHS/kvHDa9xLtLpq/KEJu1OB/cUKv3xFkAobZSV6ugdvWriWpNpLS9BZCLhvo5RrY9m05rgYrxsuSPeLSvQgcT0+czvio8by8+2UOtx6mqakenx+sVOka+MsNNxOpj+ShzQ9hdnbNR4JchvGyZM865ViKlHm7x23Uf3LC/1wACI71/awkkAk0L/H0/XGnV7/zY3oNAAGoIvQn3OMF35yOZoCRtu/Ke6TrPXTxAGKMOu5Zug+T3UXu0VbeWF/CzKxIFl0/HIvDzQPdnEr/xKlxSmFogCeeeCIAuOK4MLQgCOGPP/646VjZtYDq8ccf/+JU1/lfEYaWKxQIO/exRa8nV+4ip62Wo4pQnrG1MXroSAwNFSwlkMKC7SwyKVGKIitGZ+Jn8EFQyj0Cq8p2VOuvhfhzYNLzqLMn4Nj4GS2bDkN7LS1LVhB083z8p05FN3QoHWt/oOObb3DuXI25sInIB29AN3YKsbGx7Nq1i+rqag4dOkR7eztz584lMNiIzKGhuDKfI4V17Du4C39/f2bNmkVycCCHy8pZq/DBr7WRIeG986WX7qrkPxtLeejiAZw/IJQR/QJZlVvNuoJ6mrZsQhJayBg6keHZiWjCtVTvbGBXXj0pFR3gFAm6Ls1LMKzW7mRuXikDfLS8nBJDgk5Ns9PFu1WNjAjwIUbbRZdWxfhhL2nBvLse0eLEmteIYWZ/NAldwRxJkrijsIIDJhufZvQjRqsmXa/lncoGquxO3q9qRCOT8eGgeDTy06Mex8TEUFhYSH5+Pm1tbRQVFTFr1qxO/aDfMyorK0lPT2fHjh3Y7XY2bdpESEgI06dPJzQlhcaNG8kXRSw5Oeyx2UgVBM6dP5/4odkUfv89B1taaN6+g8NyGefFxpEycSIJycnsycmh5MABIn9Yi6OwkJi3/4MqOhpNWhrNH32Es6aGlk8XI6hURP/7TWTqs5euIUkSS5YsobW1lblz56IPDESd2I/mDz3itvrRozu/213gWJKg48cKtGlB+F0QS2RKLOU5ReyvOURMWwDS3lb8L4pHOzAIdT9/LLkNWAuacdVZsJe2eYTuQn1Qx/lh2lqNq96KNj3ojC5wTVuqMe+oxTA9EU1i3wRf7R0dLHr3XQRR4uo770R1hqmsgiCg7uePeXsNjooOdFmhv/iZnbVmmhYXok0NxG9iLEeOHOkU31uZW8Ub6w9z76RkJqWFo04I8Ah7H2jCVW/BXtJK4FWpKEP6piXwS5AZbWD74Sa+2F3JtMGR+Gk8rBnPMwdg2VWHvbjVIzj7Gzl4vPZjMV/uq+ZfczLIiO7bGBBtLhrfz0fuoyTwqlRPiqMMzFtrUARre7WE/S0QZdBhcbhZuLUcAYHX15cwOzuK+ef0IzM6gO2lTSzdXUm73cmKvdU8MTXtpAwfhVzG4JgA3t9STm2bjQvTzm5q7u9eJFLlA4Y42PFv3O1WGjdHoFA2Y7x9Jor4BMSijZirE6DpMB3bTeiGhOI3PhpVlC+OsjbMu+rQZQQj056ATr/mLji6A65YAoH9ICobdrwFbUchdWqvVVytNpo+POgRdZ7RH2WIDnebA9M2j96GaWOVR9R5eDjqWD9sh1qw5NaTW9hAQrOTmtFhpGZHMDIhkE93VLCzvJlZWVHI+vD7k/uqEBQCpq01KIK0J9TiWL2vmpfXFnP3+UlckhHRp67+OXRKHTG+MXxc4BH7fW//e0T7RvPCuBdO6kqVFpTG3rq9rChZgdlpZtXhVdw/9H7GRI5hWNgwvjz8JZuqNlHQXEBuQy6vn/c6sX6xpAen80nBJ1SZq7zEpf9bY9TitDB/7Xz0Sj2vnPvKSYWF/4Q3MkMy2VK1hTWla2i2NfP9ke95ctSTPTRsukMlV5FiTGHRwUXUW+r5uOBjfBQ+vHruq7+bvg/1CcXpdvJp4aekGFOI9++SyOjrOG39spuw8EmCKDKNArmfCvPWaszmDmRbO6jRNzHqhmmoQ3xwm5yYj805HRsqO0WdTyQuLQgCw8KHsaJ4BTk1OUT9qCbEFIBqbiyR4TGkBqay6OAiWu2tXkE3uY8SQeXZ4yFKdKyrQJ0YQMCUhD908PNkkGkUyP3VmLdUI9ndtK8/iircB8MpjHtOtsfzrLdqsR9u81pvqRQyBkX68/6WMmpabXy4rRyNQsY784YSEaBFr/aIS4f7a0iL7Jvcycnwu3/nnwRnTBhaEITFwDYgWRCESkEQrgf+KQjCfkEQ8oAJQO/+wv/DiAqPZm5tHkcUsezUDOCy5r3MnOzJz50z6lymt+znJ+NAmtU6no0OJETvWYDoR0egivej9bs6XEIUTHu983Qv7JWPUWih8aNlaAYMIGi+hwYsU6uJeP4FXE2NtG46TMCwSHyvvAcAo9HYKXBcVlbGhRdeiNHoEZ8be+FQwnwTONpUhNlkZsaMGSiVno3NS2OGEG4z81yDmfKaph7Pl1dQxbrl6xkR58+1x9wH/DRKXpydjrG+BpEqVKp4ZlziIYENzQxDmWFgqFnEWWUmYEZ/T8rbMUiSxN8KK7CLIq+lxnTqCj3SL4IErZo7Cyro6CZk7REeSwa3iGlTFZqBgeiyvINVK+pbWdPQxn3xYQzUe14QwwL03BoTwhd1LRy22nk5JQZ/5enniCqVSmbOnInZYmHnzp0MHjyY5GTvNJTKQy0cLfxttNMLatpZk9dTsO5EGDRoEKmpqWzfvh2n08mMGTOQH9PfueSuu/CzWsmxWNDb7Ey9804A5EolM+fORRQE9rmcxNjtjLzuWgD8o6OZlJlJi1bLjppqgm+9Fc0AjzihbvBgAm+4gfYvV+MoLSXi2WeQ+/XumHKmsHPnTkpLS5k4cWJnypt+3DgCLruMpg8+oOj7DV7f9x0fjSJKT8e6CtAoCJieiCAIyGQyZs6bjUKQ8/WeH1HE6tGP8YiZy9QKjLOTaWhuZP/ePPSjI1EfC0YqQ33wvzAO28EmWpfnnLHnctZbaPu2vFc23cnw9cuv0KbVMnnkSPShfa/3S6AI0PSwae4rJJdI8+eHkGkVBMxI9FoYVbda+ceqA2THGrhhrOfUT6aWY5yThLvFhmVXHfrREWj6nR0HJLlM4P+OCRzf98U+RLHrNEnuo8RwqYfFsG/xwV7rf5tfy/7KnifzoijxyY4j1LbZepS1tlhZ98l+LL0wyfIqW3ntxxJmDI7sFHU+DntZ2wktaVvXlOJus2OYk4xM5fmt+46LRhXjS8vKw7jbewqd/1b42wVJJIXqWbC2iHB/LY9O8QjCy471vSRJ/GdDKeOTg/nLsFOn3qVHBXDbhESW763im/09hSFFUeLTHRW9mhr80WErasFe+rPxljoNadDltOboESUdxstTEDQearz/NbNQKGto36tE7qck4BLPb6zzJB2R5vc3ILl6EdsuWA37FsO4v0PUMcehiMEw7j7YvxQO9LRJl0SJli+KezAZ/afEI/iraV9bgTxYi/+FcZ52KDxsTbfNTWKFhYMBCsZc4tETCfPX8NT0NPZWtPKfjb2Lr67eV82h2g6vz/Rjo1DG+lK/rIiGqp7i43XtNh5dlU9GdAA3jz89duFxnBd7HlP7TWVx4WLaHG08O+bZU27Ij4vsygQZ7+W/x8jwkVyW7NH68Vf789TopyhtK+Wr0q/466C/kh6cDkBqYCrzM+bzTdk3fFv27a9q95nAS7teorKjkqdHP42P8o8vfPtbQilT8szYZ7C5bCw6uIiJsRM7BbVPhuywbOYNnMeqw6s8fT/m1KLOvzVuzriZFGMKT2x7giZrz31Gg6WBJYeW4BZ7zjnFO/dhzqnFd1wU6jjvDf2GoxvY17DP6zNdVgiagYGI21tQiDKirhzcud/xvzgehVFD+9oKFEHaLlFnuYCxU+C4yItBEqQN4tGRjxJapiepPoqyzFaSkj0SA1mhWVyTdg1fFH3BpspNXu3Qj/Ls8TrWH0WSg/HS/v+zAaDj0GUGo00L9KwHXSKGnxn39IaT7fHkvioMM/rjrDLR/qO3GU12nJGbzulH8946ZA1WXpydgb/W83+eNzKOkQmBPLXmIEebexoNnAy7j7Tw4neFOFw9Bf7/l9EXd7C/SJIULkmSUpKkKEmS3pMk6SpJkgZJkpQuSdJUSZL+v5TlfuyK25jQvp102z5uGXyeV9nNqdlEttQzpXwD54d05cMKMgFj3EaQ3DRrX0DSdy3u5eFxRDx0O2p/JxHToxBUXQsIMTYSdYYLWZBI3o0ved3LLyqJUjGIUjEIv6gkr7Irr78UtRiAwZ1EkLEriKJTqfinTYtDruC6bXm43V2TsMvpZsWnSwhXlzKJBq9TtwF+SjI0ZQhuH267Y47Xva65uB9JGhnlDjc1ft6Bl49rmvixuYNH+kWQqOvK19TJZbw2IIYau5NHi703lMogLQHTE1FG6jH8fMNoc/BgUSXZfjpuifEODv09PozxBl/uiQtlrPHXWzv7BwZTpEigTtRDVIZXWWudha9e38dXr+fRfJZTRVotDua9n8Ntn+5lY1HDqSvgOdGYPHkyERERXHzxxQQHd52sq/38mD55MgFWK9MmXoCmmxB02KBBnN+vH4EWKzNvvtkrdWjwnDkkyxUUpKZinXSh1/2Cb70FnzFjCLrlFnxGjfqVT3xyNDU18cMPP9CvXz+ys71TX/OmzKNWa6TuoYdpb+7aKAlygeURSkpw85EBZLquceofZmTSyPNpkLVTENfkdYrh9LHxjWw761X5VNjzvO4lN7TiairGtLUNW0H5r34uyX3MCUMlw/ALFhCF33zDPpeTgUDatN5P5s8UdFkhaFIDPZTd2r6P+640lP5eOh2dKUBizxQgdZw/fhfGoU7wx39S3Jl8jB6ICdTx6JRUtpQ08dG2cq+yjkgfvpO7MBxoJm9HpVfZjtImbv5kN9d8kEOjyTvI8v6WMh5ekc/Nn+zG5fZeYOS8tZfk/a1sejfX63Ob083dn+cSrFfz+NSBXmWuJiuNH+TT+OGBHn1vPdiEZVcdvuOjUcd2BWA7F1wukeYvenfz+C2gUcpZcFkmKWG+LLgsE19Nl0ZRtFHHc5emMzDCjxcuPXHq289x27mJDIr056EV+6nv8A605/WMmwAAIABJREFUfbC1nIdW7Gf+x3t69P0fGc5aM40fHqBxYX6PtExL1ANYxdH4p7WiHNj1vhJ0Ooyz+6MUyjGGrkSm6Zr7FH4KAgJW4mjUYVq81PtmpgZYfReEZ8C4e73Lxv7NEwxa8zfoqPUqMm+rxl7Siv+U+E6tCPAE1T8JklGCm89C5QjKrneL26jhQ52bIpnI0Bu837VTMyKYnB7Oy2uLOFDtHfxaX1jP7Yv3Mu/9HK/UQEEmsCpChdMlkv9uHu5uC3xJkrh/WR42p5t/zelyovk1eGDYA2QEZ3D/0PtJNvZNsyxcH87jox4nxZjSIwVoVOQobky/kdGRo5mf7i3Cff2g6xkUNIindzzdq5PYb4XNVZtZUrSEq1OvJjvslBIUf6IXJPgn8PDwh0kLTOOREY/0fe4bfBvDw4dza+atDA0beuoKvzGUciXPjnmWDkcHT21/yuu94xbd/H3D33lq+1N8cOADr3rNTQ3YV1VRpq6iIM17XtnfsJ8719/JzWtvps7clcIqCAIb0w9SpDlCxWgLsXFd7nMylRzDZckow3QYL+s6HAFQBuvwvyge26EWzDu97zXBfxx3NcylMqCRcZde4lV2W+ZtJAYk8tjWx2i1dbkeCjKB79L3cFh9lE/7/YDg523k8L8IQRA8e7UoPQHTEjudXk+Fk+3xtGlB6LJC6FhfgeOod3D/lvhgnkbHv1V+jAjvChDKZAL/NycDmSBwzxLPerIvsDhc3LMkl5V7q7H3dgjyP4w+pYOdKfyvpINBF01scuxAWr7eQFlZGYMHD0Yul2O1Wlmy+DPSW2p4pO45igvziBh1uadiTR6yL69DHhGLuToBmUbutVhXpQ7DEFaK4uCHEDcWAmIA2Pv2TQzU7uapgQ/yfomGmVmR+KgVuNwif/1wF0V2P+pkgeSUNTN7SBddWq1RkRCZzKF1HTgsLuIGeQRs7WVt6L6spF3RzvrwIFwF5YxN8py8LnhlOXbnUeSijhZTFSGGaILDPOyid1//GIurlTkzLyMqtiv4IjndNH9wADewscXBrtx6Rp8bg0wmUG61c21+OSMCfHimf1SPF1yERoVTkni3qpE0vZZEn64gkSpCj354uNekLUkSNx44QoXNwWcZ/QhUeQecFILArDAjow2/PgAE8NSag3xVascZEMu3BxuYOdjT96Jb5Ks383DYXMgVMqqLWkgZFd4nqvrp4L4v8sirbCPSoOW7/DpmD4k+qX7B8TGqUqkYMmRIrylshthYRlxwAYEJPfOtowcPZvgFF6Dx70mr7D98GPvz8zlUXNw57gEEuRz/qVPxGT68R50zCbfbzeLFi7HZbFx11VVoNF1jptFk59qP91IfEc95+T+yd18pyTM9rhe7jzRz95f57AtSsba2jYgAb9poeGIUTU1N7MrdQ//+/fH19YyhJc8/T4NcQG+3U1RTRWZaGiq9HtFup/Kmm3A1HEIRPhzLrhJ8zx+AcBp6O8fR8WMF1twGDHOSUUf3bQxbmpr4+NNP0bhczL33XhSaMyOMdyIcTwuz7KrDfrgVnyGnTpGyV7TT8kURuuxQ/M7pYnmUl5ezsUbgo21HTpgCpI7z99zjDGzUToWBEX7sr2rj05wKLkoLx+jjEXi847NcVjW3MxEVrkMt+A0NQ6VWYLK7uPr9HHzVSlqsTkrqTVySHo4gCBTXdXDrp3uJNeooqOlArZQzLN4zl2768hBJJSZq5BIJHW6KFBAR52E5Pft1IT8W1vPvuVkkhXYT1RQlmhYdRDQ7kanlXulpbpODxg8OoAjUYrwsucf/Q65TItMqMG+tRu6nQhV1ZubHX4oQXw1zR8QSaehJ708O8+XK4bGntOfuDrlMYFi8gYVbj3j6PiMCQRAoqe/g1k/2EGvUUVjbgUohY1h84Gm3+/dCDZdcIo0fHABRAgmvtExXq52mj4tQRfliuGZ8j3etPDQcvep7FLn/8mj7hHqYWGxZgLJgAU7lIMw1MWgjLciDQzyC08tvgIZCmLscfH/GLpTJIWYk5LwN9QUwaBYIAs56C02fFKLpH4D/ZO9UiK/yanhiQwl5QSq+LW9mcIyBuEAPe+Sf3x3ineI6ZlyTwYCfpT8KgsCohECW7q5kY1Ejc4ZGoZDJaDE7mPdBDka9irp2u1dqYF5lK7ev3I9Sp+Q8i8Duhg4S0j3PsDjnKO9tLuPRKalMSOmjhdgpoJarmdl/JmlBab+oXmJAInOS5/TK5BgePpwpCVN6pJXJBBlZoVksLlxMUUsRk+Mne6XW/hZos7dx8w83E+YTxovjX0QhO3POPP+/YUDgAGYlzUKr6Lt2jEKmYGq/qb/r4FugNhC1XM0nhZ8Q5RtFsjGZ8vJyNlk2sax4GXF+cayrWMeE6AkEaYMQRZFt76wmtMPAa8lLWVG3mhmJM1DL1dhcNuavnY9SpsTmtlHYXMiUBI8+Z0V7BXdsvpPGFDu3T7qnx9yn8FejHxGB3L+nPIEyUo/jSDuWnbXo0oM7jUOaPylAaHeRdMtYFHrvenKZnMyQTD4u+JgqUxUT4zzal4XNhfx9x33kx1Sw0bYNX6UvGSEZPe75vwaZSo5+WDiqiF/GRuttj3cc6oQALHvrsRU2o8v2rP9Em4uWDw4i0yqQ29y4m2xoB3VJMfhplIT4afhgazm+agVDYg09rvtzPLn6IJtKGnn76mz6BXe1//fyzj8dnLF0sD9xcmi1WqZPn05jYyPr1q0D4JtvvqGjo4PLLr+C/fE3MKRjPbu+egdcdo9oo86I7ur5JxS/YuLTYIiFlfPB3kHeT8sY3rSSnLDLueO6a7A43Dy4zCN+9eZPh9lX2cYz0wfx9PQ09lW28eZPh70uF5lkIPO8aPI3VlFxoMkjtra0CLlBwwtzziG2vY23VErySqrYsKWQjrYDCO4gbr3tRuQoWbnSIy79w6rNNFkrSY4eTGqmN3X6uNhayF9S0I4IJqBD5INF+3FLEncUVKAQ4OWUGGQnOOH4W1woaXot9xw6SoPj5CKfH1Y38VNLB48lRpCgO7v2wBuLGvho2xGuGx3Pe9cMxeZ0c/+yPCRJYs93FdSVtXPOX5I554pk6o90sPubI2elHav3VfPlvmruOK8/b14xhEaTnce+zD8r9+oLNBoN06ZNo7m5mbVr1/7m99+6dSuVlZVMnjwZv24pZ5Ik8eDy/XTYXTxw72UcPnc6/Xf9yJaPV2K2u/jbkn1EBGhZedtoRiYE8uTqnrTRiy++GB8fH1asWIHT6WTXJ59QolAwVK/n0ilTsCmVrHjtNQAaXnkVe3EJ4Y/di6afHUEdQcNrq0/7uRyVHbT/WIEuMxjdoL47jq165RUsKjVTJ05EE3B20qV+DrlehWFmIs5qM+0/Vpz0u16izlO8A461ZpHnvinocwrQ2YYgCDw/cxBalZx7lu7D5RZZsusoPxbWc+fFKQhT4ggRYct7HvbOM18dpKrVyiuXZ3LvRI/A8bI9VTjdIncvyUWvVvD5TSM7WQwHq9uprWonaGsdZSoYcP9wquUSiu+O0NpiZevhRt7fUsbVI2N7BMRMm6pwlLcTMLUfhpn9cdaYaV9XgSRJtK4sQbS6MMxJRlD0/mr3GR6Oun8AbWtKcTX+76RIJYb4ct+FyawtqGfprspOQW2dSs5nN41gSno4L68tJr/q9yOke7rozqbrTMvcVHUs/aoIROnkQvKj74bIbPjqHmivgdr9sP45hLQZGOZPRybYaF6cj+SwQ+6ncOgrOO8fnY5jPRCcDOc/DsXfwZ6PkNxSNyZjktdmrL7dxiMr95Me5c/q28eQFKrnvi/20WZxsqO0iXc2lXLl8BjGJ/celDH4qHjh0kEcquvgXz8UAfDoqnxaLA7emjukMzXw2/waLzbd7X8bSZGPQOz+FkoPNVLRZOHprw4yOjGQq0bE/or/xn8X8f7x3D3kbjZXbWZZ8bLf/P7P7HiGZlszz459FrX87K7F/sQfF1elXkVWSBbP7XiOGlMNNY4aXtnzCudGn8tHF32Ev8qfhzY/hMPtYNvaH0iujaI0o4U7J91Lg6WB53OeBzwOaOXt5Twz9hnuGXIPW6u3dqaTPbz5YRTCyQW1TwQvgeNj4tLm7TUeJuPkBC8mY3ekGFO4JeMWvi3/lm/KvsHhdvDgpgcJUAew6KJFjI8ezyt7XuFw6+Fe6/+Jk0OmVWCYlYSrwUr7t+WARyfK3WEn8MoB+J0f2yku3R2XZkUyMTWUF7871CNF+OfYWNTAou2ePd6IhNM/JPqj4k8m0Gmie4TQaDRiNpvJycnBbreze/duzjnnHNLT0wkbOJbibauJrVyF1FSGsnw9zFqIED7ohOJXKFQeivW2N3E0laPY9TYNsiASb11KSIAevVrBB1vLabc5eWdjKZdkRHDHef1JCvWltMHMx9uPMCE5hNBuNnkR/QMozW2kZFcdUW12nOVtBM1LRR3iQ7ZMweI2MxurapFv/AkEkSvmzSUqOgi5U0vx0XyK8yopLM9DK/Pjr7dfiazbibztcCutKw93iq1lpAezdvNROGzim3BY3W7i/5KjGRFw4gixXBAY6u/De5WNlFrsTA0J6HUiL7XYuS6/nLEGPU8lRp7VXNs2i5N57+cQ5q/hjSuyCPHVHBMeO0KQS6B8TQWJQ0IYNiUBY4QPbfUW8jdUEZsWiE/AmVsQ1bfbuO7DnSSH+fF/s9IJD9AiSbBwazlJob70D+39RP9sR7ENBgNWq5WcnByio6M7tajONmpra1m2bBmpqamMH+992v3F7kre2lDKA5NSmDgwjNgJozi4dA2qDWt5W5vC1iozb1/lifaP7BfIJ9sr2FPRysysqM4ApVKpJCQkhO3bt9PW0EBOfj4BdgeXP/AAgQkJWHftYr/bjXLLFvjoIwIuv4zAefPQDkmk/dvtuE0GFEYHqohfZhsvOd00fpCPIJMRNG8gQh9danKXLmVLYyNZag2j5l39i+75a6EM0eFqtmHeVoM6yYCil1M28OjU2Itaeog6u9widy0/hEOS89F1w9Brfh/UaR+1gmiDjve3lNFodvD2hlKGxhl5cmoaEbEBbC+oZ2CNnWW1Lby+t5L55/RjztDoLoHjXZVUt9r4sbCeBZdlkhEd0Mli2FTUQNL2eoxOiYB5AwmN8KXFX4nfwWb2Hmjg0YNVBOnV/HtuFspu86yXoPaFcZ6+b7Vj3laNZHNj2VWH/6Q4dGknHnfHRa7NO2pwHOlAN+SXC3v/XnG877/YXUlNm421BfUsmJNJZrSBkQmBLNtTyYaiBmZnR59W6s/v4VTQfuQYm+6YqLMyzAdXrRnTjhokiwvrvgYCpvZD0/8kp58yGcSOhpx3oDYP9n0GSHDlUmSGEBSuUkyHA6HkBzQH/gFRQ2HKghM7kwFEDIEjWyH3Ezo6zsea34FhdhLqGO8A/R2f5VLaYOaj64YR5q9lcIyBD7aUU9Zo5uMdRwjQqXhr7hBUJwhiAsQH6alrt/HhtiOYbC4+23mUeyYmMzk9guw4Az8damBlbjVljWa2lDTx77lZJIf5oU0MwJxTS93BRp6pqKPJ4uSj64bjp/19zDmni7SgNPbW72V58XIGaweT2i/1N7nvt2Xf8ua+N7k582Yuir/oN7nnn/hjQibIyA7L5rNDn3Gw6SBbmrcgKATePP9NjFoj8f7xLCpYhKW5g8E/RVDj28ToG6YT7huOS3TxaeGnWJwWFhUs4soBV3J5yuUMDBxIXkMey0uW02BtYF3FOp4Y/cRJBbVP2sbj4tJbqhHNTkwbK/sk6pwRnMG2mm18efhLKjsq2Vq9lRfPeZFkYzLDwjzi0jtqdjC9/3Tkwi9zHvwToAjUIlpcmLZWI9rdmHfU4jshGp+sUC9xaZ/BIZ0pzoIgMLJfIEt2HWXL4UZmD4nu1WX053u8n68Lfg/v/NPFn0yg3xgXXHABRqORbdu2ER4ezrhx4wBQKFXoLn8XpeRCe2AxUtY1kOShDcp9VQRM7138ipgRMPpOVAXLMUhtuKa9hUbroUzPGxnHqH6BfLClnEC9iiendlGPn5w2kP46Fes+yMVq6WLUKJRyLrg2FV+rC/veei+xtcFJUdxos1PmH0BebAgx/UaQlOihU4+ZmE24Xz/qOsoAkTmXz0LRTWhZtLloWVrkJbYmk8m48rbB1AbIea+1jYsC/ZgVempK3gC9lvsTwvm6sY0v6nqKnrpEiTsKjqCSCfwrJfqsb14e+zKfRpOdBd1sY68eGceYBCNla46g9FEw7i9def9jL0tC46tk6eu5mMxnxjL8uG6B1eGtW3DLhH5kRPnzcC86GL8lzj//fIKCgli1ahVW69lnFrhcLpYvX45Op2Py5MleY6CyxcKTqw8yLN7IdWM8Y1Gj0xL+/PP42C0kfPImfx0d1xntjwzQ8tjUgeSUN/P+5jKv+yQmJpKdnU1eYSEuuZxL/3J5Z4rVxDvvJMhqZYPJhDMhgdB7PToZMpmMkNvPAdFJ08f5iLaeAryWPXtoXd5TRBWg/t/rcdVbMcxOQqbr2pi4nU5+WPAytXl5Peq0V1fz7Z49GKxWLr77rl/SlWcMAVP7ga+KsoX5vQoc24pbMG+rQT8msoeo81sbDlPaJvL09DSvoPXvAZPTw5mWGcGnOyqQCQIvzs7oTPUcd30mVXKJzPw2skJ8ufuC/oAnNeml2RlEiSDm1DJzcASTjqWmGHxU/PPSdJLrbCRZJCoGGYhP8ozFtOwIDsXrGdTqon+rk5fmZKDrluZ6IkHtgCkJyP3VmDZXoYr1Qz826pTPpfBXEzAtEceRdkybKk/5/T8KjotLA3y6o8JLUNvgo+KFWekU1ZlYcIxB8nuEJEmYtlXjqDb1KPOw6Q552HTHRZ0FgYAZici0Ckxbq9EkG/AZ1geXtKBEmPgUHP4R6g/A1NdB5wniaydNQhdUSsfRZByuOJj+pidwdLwdVhft6ysQu60vkMlg+r+xueNp39yCJj0IXbo3i+3znR423f2TUkg8ppOYFunPnef155v8WqparLw0OwOfPqQCPjw5lSiDlnc3lzE4JoCbxnn6QymXseCyDEx2F1/srmReNzZdWKQfjaNCiXdA8hELT0wdSERA1wl/Z99X9ez7k8HVaqf9p6NIvQiK2ivaMefU9lLrzEEmyHh69NMoBAWLmhb1KrK7s3Yna0rXnLF7NlgaeHrH0wwKGsRfB/31jF33T/zvIto3mvuG3seO2h0cdRzlsZGPEaj1vP/OiT6HSxMvJWVrIApRTvQVWSgUnnngpvSbGGAcwIcHPyTOL447szwGJoIg8MSoJ1DIFHx+6HMuiL2AyfGTf1UbdYND0A4MxLy9BhQyjLNOrcmokCl4dsyzOEUnK0pWMCtpFuOiPPu/IG0Qj418jILmAt7OO+V+/E+cAH6T4lAEaTFtqkIZqcfvXI9MSndx6eYvfibsrVfzzIxBHKhu5/Ufi3u9bm97vP/f8CcT6DTx8wihXC4nKiqKxsZGpk+fjr6bNbO/MZTtzTqO1NSzI/0J0mK6FkfKUB2uJhvm7dVokoxe+apft8dTfnAnlf3nMmTilZ2fC4LAiH6B5Fe28fjUgV5MELVcxvA9LWS0uNlV0kji8MjOMo1Chn5XLR1OEduQUAK7aUIITbC/tpr8iBgeHJpKsH/X4ihlYH/ydxUzOG0YQ8cO8uqHlhUlOMrbCLxmIEpjVx2dr5IHacftEpmUb2XM0L5Zrw7x07GlxcRnNc1cGmrAT9H1w3y9op7Pa1tYkBLDMP+z64Lw9f4aXvqhiDvPS2JqZlfbBUHA55AJW7mZ3CgFl5wT18kgkSlk/GffUUJrnewobmTUmFNvyE6Fz3Ye5d3NZTw6eQDnpnTpMchlAkPjjHy4tZziOhNTj+lgdMdvEcWWy+VERkayfft22tvbGXDMKexsYd26dRQWFjJr1izCwro2O6IoMf/jPdS221h0/XACdF2iw8GxEeTXmkjb8R3jzh2CLqUrcDcg3JeCmnY+3VHBhWlhBHbL+zbk5nJ0Xx4jEvsxcGqX0LJMLicqOJjdRUXYhmSRMXJkZ98rAnxx1ZfjbvHHsmc3vmO7RH2ddXUcmXsVHV9/jTY9HVVsVxpC6+pt2A7KcFZswv/igV6uautefZUtbW2U7NlD1qhRyI8JxouiyGfPP0+zQsFfpk7FEN9lwfpbQpIJvJRbwchmN7uKGkkc0TXniBanx67cX0XgFSlemj75VW3c9XkuQ0PlPDx98H+j6afEqIQg8ipb+fvEZLK65ZYrlXI6AlX45bcwMcpA0JCusegrlzFyZxOj7TLGZ4TjE9+lORWNjIHbGziqlzN2fpZXyk5MejAl26q5SKYi+by4TrtagPYfjmDd34jx8hRUkd3mbYUMVZQeV6MV45wk5D59YzUow3S46syYdtSiSQ30cnL8I8NfqyQuyIdWq4MXZ2d4Lezig3yo77Dz4bZyRvUL6lWT6GT4LeZTy556WpeXYCtsxic7zEs02cOma+3BppOp5B5GUKsN45xkL8HnkyJ8MLRVQdIkyL7Wq0g9IAbLjlJs6on4TBjk9btt/qII85ZqXM3eWgxWUcfhH6PQSWbKjRuIyhzXWedos4UbP9pFdqyRp6aleb2rhsQaONxgZvaQ6D5btKsUMjKiAihrNPF/szO95m2jj5owPw1Ot8jzM9O92HSxyUHsy63lXKvA4HPjUPh11bPkNtC6rNjT90NC+8TElNwSTQvzseyuBxE0iV1BbrfJQcNbeVjzGlCG+Xj9z8409Co9wbpglpUtQ6fUMTikaz6tMlVxzbfX8E3ZN2SHZhPpG3mSK50akiRx78Z7OdJ+hLcueKtzI/8n/sSpMMA4gAZrA5HOSOaP8BY6Tz8aR3C+mtoxTgYO6xK5lsvkZIVmUdRSxGMjHyNC3zVH6FV6EvwTaLI18cyYZ9Aqf9mc/nMc1zp0Vprwvyi+z7p5AeoAwvXhWF1Wnhj1hJcrYEJAAlWmKj4r/IwxkWMI0Z0Z/bH/nyDIZahifHHWWzDO6o+827wt1ymR6RSYt9Yg91V6/c8SQ/QcbbayaPsRxvUPIrzbvvZEe7zu+JMJ9Cd+ESIjI7nuuuu8HJiOY/SMW3gn7iWe+K6CI03eGkABU/sh91XRvOQQktNzilPfbuOh1UW8HvYUY694oOe9ArQsmT+SUf28qf+mzVVo66w06uQMqLKyZ7NHq+O4ZoRclCgP0LBhSTHmNg9TwWR2sHVxCRN3SOhEgdv3l+Nwdp0m6f10/O3hW5g0c5zXvawHm7DsPuZEE+NtBf5SeR3VCokJRTY0ua1s29U3Azm5IPDqgBjcwF2FFYjHIrsHTFZeLKvlkuAAZoScXc2T+g4bD6/w6BbcMsFb+6i6uJWSTTVoU/z5trmN9zZ32dW+v6WM75raKDfI0JRZ+H79r9MHqmiy8NQaj27B1SPjepQnhui5f1IK6wrrWbLraM8L/EaIjIxk3Lhx5OXlcfBg7/bZZwJHjhxhy5YtZGVlkZTk7YK3cGs520qb+MclqUQbey62z338b2gzM2l69hmcdd6OEs/OHISvRsHdn+d22kM6Kitpfv4FLrLbGXXzzT2uF5GZycTJkymtq2PPnj1eZYFXnQ9iJa7WYDp+8ujGSJJEzSOPItntqOLiqHn4EdytHkcJZ1Mb7T82INqacBSvoebBB5FETzsqduSwrbkZg9VKq1bLVwte7rxPzkcfUa5SMdxgIGbEiNPp0jOCj7aV81F1C+t0MLDWzu4NXeO+dXUpbpMD45xkr02VzenmniX7MPqouCr196sl4a9T8ukNI3pYtAMMyAzHcEEsykOtWPK6ctLbvy1H0+5EGe6Dfd1RnPUezSlJlGheWoRSJWf4bUO8UmoBVCoFmTdnohIlWpZ3OXjZK9rp+OkouiGhaFN7brjUcf6EzM84oW5Bbzju5iHTKmj5/FCvLIY/Ki4eFM4nfx3RaRvbHQ9fPIBog457luZisrv+C607MVytNlq/PIwiVIe7w0Hrl106EraiY2y60RE92HQAmiQDITdleC2OTwmZDKa/Aec+3LPIYMQwbxSudgVtx7QYACx5DVj3NaAM9+mhxbDhvVwCRD212u8YXLqA8oM7AXCLEvcs2YcgCLw4O72HcYJCLuONK7O4YVxPc4KTYUisgaXzRxEf1NOSfHZ2NAuvHYa2F7HRUTdnodCraFlShOT0jHtXq53WVSWevjc5vfr+ZOjYWImjogNluA8dG45iP+KxoZckiZblJYh2F4pgLS0rSnD3wpI8k7gk4RLStem8tvc1ils8J9+iJPLI5kcAiNJH8ciWRzA5fhnT6edYVryMTVWbuHvI3cT7/3cOHv7EHxOCIPDYyMeYavB2L3U1WrF+W4U6ycDwyRf0qNcvoB8fXvQhA4MG9iibEDOB9y58D4Pm1NkGfYFcryL4/7F3noFRVekffu70mWSSmfTee0JC76I0sdFEQNfe/e+ua9td+9p11bWtu+q6q2JXQKkKKk3pPYEQ0ntvkzIzmT7/DwMJwwQIEKSY5wtkbu6dc2/uPfec97zv73dXZq/v2uNxVdxV/Gfqf/CSevZHD498mABlAI9ufBST7exl7p/PyCLUBN2ThTTY8/p2ax1+V+ahdfjUjDSC1XIeWphDl+XQ/Po4c7zfGgNBoF8JkUjglWsyEYs8reuOFL9qX11+zBKgE2FtMND+YzmKNH8SHxhGowj4vpzOdhNdOU107W/GZ0o0Y29Px2ZxsP7TfJxOJ++9vQe1FYZcHssLfv4cUAr845fe0+cOY9db0H1bhDTUC5/JUW7bdrcbeLuigWtD/Hj+uizMItjwyUEMXccXfD5MtFLOMwlhbNTp+bCmGbPDwR/zKtBKxfw9ydNdrD9xOp08+s1+jIeu/ZGriBaTjbUf5+Hjr+CGuzOZlh7MP34opKC+k6KGTl75oYApqUE88dgYOqWQvbiElrZTK5GyO5w8tCig375xAAAgAElEQVQbsSDw6jVZx3Qcu2VszDEFjn9NJkyYQGhoKCtXrkSvP71BZm+YzWaWLl2KRqNh2jR3W/riRj0vr85nUkoQ84b3LiwsSCSE/f0lnFYrdY897pE2+uLVPWmjToeDukceBZGIsJdePKbT14gRI4iNjWX16tW0tra6bQt+8FKw6tEtLcPeaaTt64UYNm4k6C9/Jvz117DpdNQ/+xwADa9+jyDzRXNVJMGPPIRx505aP/kEW1cXS779BpnNxi333kuqE3KsFgp++IGW4mLWFhUR1NXFlHvvPZ1Le1qUNOl5aVU+E5MDmfugS+BYvNolcGzc34RxbyM+k6I8VtTe+KmQgoZOXr4mE2/Z+atJo74kEmmkmralxdg7LJiK29BvqcV7bBgBt2UgkolcwX27wzVhrOhAMzPhmNpJ0mAvfKfFYjrYinF3g7ug9vSTmySfCJewdyLWegMda44v7H2h4CWX8Nq8LKp1Xbzw3ZkLWJ8sLlHnInA6CbgpDfXEKIx7G+nKbcZhtKJbXIgkUInvZTG/WpsUiVq8xoSi31yLqbgNe4eFtqXFSCPVBP1hMLIoNbqlJdjbzezZVElaTRcHgmVE3/M4ekGF7Zu7sZhNfLipjB3lrTw1PY0I7ZnLhukrYi8p2msSsTUYaf+pwk1QO+CmNHwmRWLMbsK4v+m4x7HU6ulYU4EyM4DAuzMRa+S0LizAYbZj3NOIKa8F30tj8L8hFYfZhu7bYrf3Tn8jCALX+l+LWqbmsU2PYbVb+SzvM3Y17OLhEQ/z9wl/p8HYwMs7Xz7l76jqrOKVna8wKnQU16Vc14+tH+C3itPhEpJHLMJvzonLr85HfGQ+PDfuOco7ynlrz1tnuzkXHIJwSNhbfGi8dcT82kch5dW5WZQ2G3h5df5x53i/RQbKwU6RU0kTUyukhPoq+GhzOSqZmOExPUK6En8ldoMVw5Y6NptN/HtvtUcJ0PFw2hw0LzgANicBt6UjV8tpUonxy9dx8EAjqlwdsjAvtHOSUPrIkCnF7FtfTWllO9bCTozRSm6+eRBpYb7kH2zkC4mFCQ4J4X6eUVen00nrwkKs9QYCb8twW3002O1cl1OKSiLi40Fx+KvltIidmA+0s72khTFj+1YilemtZG+Hkc/rWijtsrBRp+e9tGgy1Gd2ELlwVxXvbyzj8StSmZzqfu1/+aqQ6gIdV/4+E02wF2Pj/Vm0u4pNRc38lNeA2eZgwa0j8VPLsWuktGY3s/1AE+MviTrGtx2b/20s5eud1bx09SBGHUex/rAA2ufbKtlT1cacoT1Bsl8zlVEkEhEVFcX27dtpamoiIyOjX1/mq1evprS0lOuuuw5//57rYbU7uP3jnXRZ7Hx820i85ccuhxFrNIh81Og++wxJgD/KQT2ljUemjU7ctwbHiqWEPPMMXkekJR+NIAjExMSwe/duqqurycrK6j5nsbcKR1cjtgYV+g0b0X32Bl4jRhD8+GNIg4IQRCJ0n36Gtc6B05mM2LuegFunIk9NxZSXR9vChWxpqKdcLufKzExixowhYXAW2Rt+prC8nJLduzGIxdxw/fWoQz2zVH4NbHYHt3+8C4PFxie3jUSjltN2SOA4P7cJrwOtSIJVHk5FO8paeXTJfn43Koo7xsed1ym3gkhAHuuDfksd1lo9xp0NiNUy/K5PRaySIvZTYNhci11nRr+1FmW6Pz6XRh/32ZBFqjGXtmPc3YCt0YilrMOjBKi/kAb2iEvLE7VI+lHQ/lwlXKOky2pnwZYKsiI0vWaS9MaZvE8NW2oxbKtDM9Ml6iyP8cFUoMOY3Yil1oC1Vk/ArRlItL+ubpY8zteV8bO/GXNFO7YWE4G3ZyBWy5DF+mLYWouxsgP9rgb0Agy7fzi+fn4cNAeSXvk5a/IbeSLbj0mpQTx8Wco5M8GTBiixd1owbK3F3mbGdKClW1BbFu2DqVBH195GVEOD3coyD+O0OWj5yOXOGXBLBmKVFFmYF/rNtdiau9BvqUUWpUY7OxGxWoYgEWHYUovET3HSFsonQ11lHRdnXsxnBz+jWl/NFwe/4KKIi3hg2AOEeIVgtVv5Iv8LUv1STzqLx+6wc9/6+9CZdLw/9X3Usr6VygwwwNEc2Zd2/lyNcXcjftckduuUXohEqiNpN7fzef7nDAseRoT69OUiBuhBpJAg0cjRb65FkIrc7qUoPxVtRisLtpRT325ixb66Xud4R3M+j00HysHOUWYNDufyjBBe/7GQg3Udbtt8L4/FqZUTsqmeSTF+HiVA5ooOOtZV9rqa1LGuEmutAe3sBMTernrUrDER5EepiNfZsNvsLutgsWsQNujiCEKSNLTs19EphXvuHdZ9rFfGJ+FvhfsKqzGaPLN3ftpZxf/0HfheGoM0xH0A/XxJHaVdZt5KiUJ9SM9nxmXx6CMUyIr1rNvYtxVnQRB4IyUKpUjEtw06bgj1Z2qA+wtiTV4Dn2/vP0v2wlIdP35ZwPgoP24ZG+O2rXx/M3mbahkyNYrQQ3X//t5yXpw9iLy6DvbXtPPCrAwC1a5J1MVjI7AnqfGuM7NkpWdWVafJyt9X5VOt88zeKajv5B8/FDItPZirh564fj9co+Rv09PYUdbKh5vLPLbbHU5e/6nwjNsjBwUFMWXKFAoLC8nOzvbYbrVaWbNmDU1Nniusde1dvLTqIO29ZIut3ryXXbt2MWbMGKKj3e1831lfwr7qdl6YPYgg9YknSNrrrsNr7FgaXnkVS3m527anZqQxxNYKH7yLcuIkfGfNdNu+paSZ938pcXv+NBoNl19+OZWVlSxY8qP7d80ejyCpAXECYv8kQl98oTuryP+OO2D4aLbaZejNNYQ85EqPFgSB0OeepSk0lByxmCS7nSHz5gGg0GqZMWUyermcOqWSCeERBGdkcLZ4d0MJOVVtPD8rg6BDos7phwSOE9pt2Mx2VxnYESsterONhxZlE6lV8fgVZ1Y/6tdCGqhCc3kM5qI27J1m/OYnIzpUhqIaFIhqcCDGvY0uUedZCSecCAsiAb+5rnLHrn3NvQpq9yeHxaV1CwtwWDxFZS9EHpyaRHKwmr9+sw9dLyL++6vbeXNNIQ7HmcvcOIy10UjbqnKXqPMIl7aUIBbhNy8Ju8mOKa8F9UTPbLpToc1o4aVVB2no8CxJKG7s5NUf8jHbeu4BkUyMdl4S9g4z5qI2NJfHIA10BSOlAUp8r4zFXtaBvwOkM+LwOqTNM3Tajez0vYzJTZ8xRl7KS1cPOmcCQIfxvSIOsVaBcXcD8qQeQW3XtU/GYXGg+6ao9/HWTxVY641o5/TocMnjNHiPD6drfzM4wW9ucnfw23t8OLIYH9qWl2DTeV57a6OR9h/Key3LNBXq6Nxc0+s56LfV0pXvnoU6KWoSsxJm8V3pd3hJvXhqzFPd1/7/sv6PZG0yT299mlZTq8fxLDX67uyoo/k071P2NO7h0VGPEuLVB/HxAQbAZR7TvqoMW5unUYalVk/HTxUoBwWgzPKU0bjQuH/Y/cT4xPDk5ifptBzfunyAk0eZFYhyUAAdP1V4mCs8fFkKcYFefL2rijFx/h5zvN8qA0GgXxlBEHh+VgY+SikPLszp1iABcEpEvKmw4o/As96+biVAdoOVlk/z6PixAsN2d7cJS1WnSzNiaBDKo+yBL74ti+0KJ6+JLXQqe1a0BJHAjkAokdoZd0Myau8eITM/HwWvhQdTqhR45qiysMpGPf/X3sKbKQrWJLuvTP/c2slHNc3cHRHIOK37gPXuPw3DIBHY+XUxuva+1cQGy6W8nRbNFQG+PJ3gLtxV3KjnD1/s4fElufxcePy07b5gtzlY9E4OQ41i5om93K69SW9l/af5+IV5MeqokoxL00O4b3Iif5yY4KEbcvfvh9Iuh5LvK6mpd++QnluZx3s/l3D/V9lupYEWm4MHvs7GRynhxdl9HzhfMyyCqWnBvPJDAYUN7i+X//xSwj/XFnHPZ7vPuA7GqFGjiI6OZtWqVeh07g5v69evZ9OmTSxatAirtSfY43A4uf+rbP7zcylPLz/gtk99SzsbflqFzqGkVuVeu7uvuo231xUxa3AYV/Si2dIbgiC4gjFSKbWPPIrT3jPhUYucPHVgIQaxnC8vut7t2te3m7jn0928+H0+y7Jr3Y5p8Aqnwq6hbN92tue5B+GC/3wlODpRjfs/xJqeZ9MpErEzfRT7FfVsj29DUPZkYOgVKn4YOQ6RxUbT0Olux0uaOpUJAQGkA+PvPntZlbk17by1togZWWFclen+bE68NZPtSnhTYqZN6b6K/sJ3eVTrunh9Xt9cgM4XvMaE4TUqBM30eGSR7n2fZkY8ilQ//K5N7g7QnwiJnwK/uUkoBwXgOy36xDucBiKFBL95SdhaTbR/7xlEvhCRS8S8Pj+LNqOFJ5bmuk3027us3PXpLt5cU9RrUL0/cdpdOlEimQjtnCS3PkenEvOG2MxqLPzo2z8BlCeXHeA/P5fy4MJstwCXyWrnns/28O/1Jby1xv2dL4/yQTMjHq9RIXiNcX/Wt6lFfIuFPQlqska7r2wn3/oO7ZIA3vX6LwGycy+4KJKL8b8uBUWKn4cLkDRIhe9lMZjyWzHuanDbz1zeTucv1XiNDEGZ4ue2zffSGJSZAWjnJiHx61mU6A7sOkG3qNAtyOK0Omj57CCd66vo+Ml9UcvWaqLls4O0ryilK7fZbVtXfittS0to/fwg1qN0MB4e8TCTIifx0kUvEaDsee9IxVJevOhFOi2dPLv1Wbf73mGy0fJpHp1rKz1cA4t0Rfxz7z+ZHDWZ6XHu76QBBjgebctL6Py5mtav893ve5sD3cICRKq+LY5cCCglSl4Y/4KrLHPHqZdlDtA73VqHKgm6he5ah0qZmH9eO4RJKUG9atP9VhkIAp0F/L3l/P3qQRys6+CttT12tR9sKuWbujbqU7WQ20LXAddL/7Cos6PLhjTCm/bvSrvFrxwWO60LCxCr5S6r5qNQKKSk3T2Y720mnli6v/ul/8OBer4+UEf49CguGuWZbTJ1UBi/M0v5RGJm/QGXqLPd7uDencU4gDSFnEeLaqg3uybzbVYb9+dXkqiS80ic54Rc4yNnxPwEvGxO3n97j8f2YzHF34cPB8XifYRLmNXu4MGF2ahkYuIDvfjr4hzajX3TGzoW//0wB43egTRYQdXeZkr3ugJLTqeTDV8UYDJYmXJrGmKp5yPzwNQk/jwt2eNzpULCpbelIXXAx//cg+OQ2O9PeQ0s3FXNiBgtuyp0/Hdjj7j0P9cWkVfXwYuzB7k5npwIQRB46epBqOUSHlyYjdXu+q682g7e+KmQoVEaatu6eH7lmdXBEIlEzJo1C4Bly5Z1n3NFRQVbtmwhMjKSxsZG1q9f373Ph5vL2F7WyogYLUv21rBqf4+I+FsLFiJzWmnwy+TlH4soaXIF00xWOw8uzCHAW84zM04uG0YaEkLIk0/SlZ1Nywcfdn/e/N57SEqKyL329/xnn47NxT3P31+/2YfV7iQt1Icnl+VS1+56/jpMVv6yeB/V6lRsgoTF33xDl7nnXpRo1AT+YTxOs0Dbyp6/866Vmyk11xPuG0xZcz27d+/u3vbGgm+QiO0UhY7lnzubyalqc2v/pHvvZe7TTyM6hlbRmcZktfPA19n4e8t4dqanUKNMJiHznsGstFt4bElPn7M+v5Evd1Rx94R4t1LYCwFBJKCdnYj3GE+XCZFKSsDN6SgSTk64UpkRgP/1qX1yKTpd5HEavMeFY9hWh6lQd+IdLgDSw3y5f0oS3+2vY3lOT2D3mRUHaOw0MzhS02tQvT/p3FCFtaoTzawExD49AcLDugXfOSwsDZfxzHcHT1vzbXlOLStyahkRo2VzcQufbusJOLz6QwHFjXqGR2t57+cSdle4Z4l4jwlDOzvRrayz1WDhkSW5fB8i5YpbMj2+z0fjj//1/0PVWQZrnj6ttp8pZJFqAm5J71VQ23tsGPI4X9pWlGJrdS1cOcx2WhcVItYq8L3Ss5xKkIrw/10qqkEBHtsk/ko0V8VhLm1Hv7Xnfmv/sRxboxFZtA+dv1RjLndl7LqE5AtAcLn56ZYUYe90Za3ZDVZ03xQiCVKCROSa8Nh7JtjeMm/emvQW48LHebQjSZvEH4f8kbWVa91s49tWlGJvNyOLUtP+YwWWOpeBidVu5bFNj6GWqfnbmL/9JibrA/QPXbnNGPc0IovxwVLWgf6IjLaONZ7ZdL8FMgMzuWPQHSwrWcbayrVnuzkXHGIvKdo5SVjrjXSscQ+qZ4T78uEtI84JbbpzhYEg0FliSlow84ZH8O6GEnZX6LpLgC5NC2bE79KQhnmh+9blKNEt6jw1Gv8b09zErzpWl2Nr6kI7N+mY1rCpoT48MDWJ7/fXszynlma9mce+3U96mA/3Tko8ZhufvTiJCDM8WFVPu97Mf7aUsl0Fj6t8+G9WLGaHgwfzXeVpTxTV0Gix8nZqNMpjCG1NuigKS4I33tUmlq/qm/tGbxxZAvTm/CG06C38bXnuKR9vz/5GzHtaafeTcNuTowiMUrPhi3yMHRaKdjVQsqeREVfFEhh58un4w7NCkGZp8W218eWifFr0Zh79dh+poT58fsdot9LAPZU63tlQzDXDIrg0/eTTrQO85bwwexC5NR28va4Yq8PJgwuz0ahk/O/mEdx9cTxf7axi7cGGEx/sNNBqtVx22WWUl5ezfft2zGYzS5YsQavVcsMNNzBs2DC2bNlCRUWFm6D2F3eOJjPCl8eW7Kex08SC7zYi76zBOzaTf942EYVUzIMLc7DZHfzj0KTllWsy8VWd/ADC56orUU+bRtPbb2PKz6dr3z6a//M+vjNncsOfbyYu0Is/L8qhvcvK59sr+aWwiceuTOWd64diszv56+J9OJ1Onl2RR32HiVeuHUnW2El42fW8/slSt++SR/ugvjgS464GuvJaaKlq4qc9PxMq9ee2e+8iLi6OH374gdbWVpb+sgehuQSCEnn7rmkEqeU8sDAbk/XcWUl//adCihr1vHJNFhpV75kticFq/jotmZ/yGli8uxqdwcJfv9lHSoiaB6Yeu88Z4OzhOy0GSZCK1sWFOE4zqH6+cPeEOIZEafjbsgPUt5tYnVvHt3tq+MPEBP5383DUcnfXwP7EUqOnY20lyqxAVJnupRALd1WxNr+Rhy9L4d3rh+F0OvnzopxTLk9r6DDx5NJcBkdq+PLO0VySHMhLqw5S0qRna0kLH24u46Yx0Xx06whCfZU8uDAHo+XYWaNOp5PHl+ynvcvCG/MHI5ccI1AZdzGMugd2/AdKN5xS288WgkhAOzcJBGhd5BpvtX9fir3VhN/cJESnkMmoGhGMIsWP9lXlWBuNroDQphq8RocScFu6S1x6USEOsx395hosZR1opsfjd10KDrMd3ZLinkVBow2/a1PQzorHUtlJ5y99dwi9Oe1mhgQN4aXtL1FvqHdzevW/Kc3NNfDdnHfJb83nqTFP4ae4sIL3A5w57J0WdEuKkIZ7E3jnIBRp/rT/UI61wYBC59IC8hrhmU33W+CezHtI9Uvl2a3P0tLVcrabc8GhTPHDa0QInT/3BNUH6J0BYehTpD8Eo0bH+bMsu5Y1BxtYl9+I1e5gwW0j8VJKkUf7oN9Si7VGj2FHA7Jwb7RzEhEre8SvbI1GjLsb8B4b1usK9JEMjdKyubiZxbur2VvZRlmzgY9vG0mwz7F1VGRSMRkOMR8ZO8kpbuFrzIw1iXhxYjL+MilqiZgPapopNJhZ2tjGQzEhXB1y/NXurCHB/LK+El1+G/EjgvH26lt5xGH2V7fz4MJsZmSFce/kxO72L9hSTmKQmqTgkwvUmC02Pn1lJ4IDrv/LcDS+CkLjNexbX01jRQcHN9cREOHNpBtT3FZBT4bBQ4JZu6ECc3EnX9Q3U9Rq5OPbRhDso2BMnEtcemNRM6v216OUSfjvzcOPPag+AQlB3lS2Gvl0WwXVnQ72N5j41++GkBbmy4gYLWvyGlieU8c1wyJ6tc/tL0JCQqirq2P37t3U19dTU1PTLeocExPDgQMHOHjwIO/nOTHZYMGtI1ErpIyI0bJgSwV5lQ1YCzZikqh5/P9uxEclI1yj5KPN5RQ16lm0u5obR0dz67hTs6gVBAHV6FG0f7sEw6bNdP7wI4JcTuQ7/0amUpIVqeGjzeUcrOvgyx1VjIn356npaWi9ZGhUUhZsKae4Uc+y7Fr+OCmBq4dGkBEfyU/ZpTgai7Grg4gL65nYyWN8MB1sxZDdyIr9a9Dburjxhhvw9vchJiaGXbt2UVZeQe6+fVhEch75/a34qOSkhPjwwaYyDBYblyQH9def55TZXtrCY0v2c/2oKG4bf/xrPzhSw7bSFhbtrianup3ixs7uSeaRnM/iexcSglhAFqlGv9kllnt0afGFiEgkMCrWn0+2VpBdpWPhrmrig7x4fd5g1Aop0f5efLS5HAEIFev77T51Wh00f5gLIoHAW9Ldsr2qWo3c+ckuhkf78dzMDDQqGYHechZsKcdHKWVo1MlllDmdTv7wxV4qWg18cttI/L3ljIn358sdVWwvbWFpdi1+XjLevWEY3nIp6WE+fLi5jI4uG5NSeu9zlmXX8q/1xfx5WvKJS3Gjx0HecshbCoOvB+mvK259OoiUEsRqGYYth8ZbexrxnhCO98hTE+MXBAF5nAbjznrMJe0YcxoRqaT435iGSC5BFuaNfnMN1noDhh31KFL88b0sBrG3DEEq6m5H1/5mfC6NRpUZiDTEC2ujEcP2evSBDiKTY058XoKI4cHD+argK8rqihm+PgKJv9KlZ6aQIAlQot9cS4O+gUern2VG/AxuH3T7KZ3zAL89nE4nrV8XYm00usxj1HLk8b6u+764DVmlFZm3Av+b0hAkv71cBLFIzJCgIXxx8AvKO8qZFjNtIMOun5HH+2LMbqLrYCtew0NO6T47n8emA8LQ5wFqhZTX5mVR0Wokr66Dl64eRMChEiBpiBe+02IwF7eB3eHmsHNY/KprfzOSQCU+fbCNFYsEXpubhdXuZFNxM3+elkRyyIkDJmOTg7jLoeAXlROFA94andBdhnJreAATtN6saGojS63kvugTO5mplFIm3pKK3AEfHqMs7N/ri/luX53H5yarnQcWZnuUAP3+kniyInx5Yul+GnsRvFy3sZLXXt6GuZeVzffe3YuvCWKmRRIR6roefmFejJ4VR3W+DrvNwZRb0hCdho2gVCJi9j2ZiAD/PD0PTE0kJcQHcJUGvnR1Jvn1nZQ2G3h1biY+itNLjX1qejrBajm7G+xcOyKy22FOLhHzxvzBtHdZ3EoDT5eati5X9s4R114QBGbMmIFYIqWwsJAxY8Z2izrL5XJmzZpFW1sbqsYDboLaCUGuDBJZ9V5ETge/mz8HmdS14jo9K4zpWWGsyq0n2k/Fo1eknFa7JVotoc89i7mwEEtZGWEvvoDYx/V3GRyp4Q8TE1hf0IRULPDKNZndL+nrR0UxISmQ7/bXeWTTPXDLXMyCnB+/W0GH4YjrIRGhnZfMfnM51ZYmJmaMJfBQ2aSvry9XXHEFdbU1yJwWrpw+E7XKNVEanxjAzWOi+WhzOVtK3DUhzgROp5PXfyzoNVvMJeqcQ5Sfisf6IOosEgn8Y24WTqeTXwqbuH9KEulhF677x4WALELdY5G9z1NrzW6woltS1F2OfCSWOgO6pcU4zJ5Za115LS7B2V76nM5fqjFmN/bPCZwAY3Yjnb+4653EBnjx2OXJpJUayOxy8vq8wd22sZdlhDBnaAT/3lBCaVv/ZeMdLgHym5OI6IhMRofDyUOLchAEwU23YO7wCKakBvHy6nyKTrI87csdVfxc2MRjV6QSF+hypgr2UfD8rAxyqtupa+/itXmDUclc/ezoOH9uGxfLp9sqetXbq2vv4m/LchkWreXuCZ4l6B7IVDD7P9BZD6sfOam2nwuohgWhSPN3jbeCVfhOjTmt44l9ZGhmJWCt0WNvM7uyig4tyMjjfPG+KBzTwVZEcgnaq3u0UrzHhSOLdbm1yaLUqCdEdh9TM9OlgxG8T9SruLQxp4mODe6ZQpE+kfxl+F8Yl5OCzWjBb35y90RJmeaPfGgAih0mxjqG8vDIh/t8fqaSNtq+K+1VXNqwo96tFG6A8xdrw6H+3uQ5rjbubsSU14LvtBikwS7zGLG3DO3sRKy1BqRGl3D6qWTTXSgkaBO4d8i9rK1cy4rSFR7bOywdPLf1OUrbSj22lbaV8tzW5+iwdHhs21Szibf2vNXru/bzg5+zpGhJ/5zAOY5ILsFvbjL2VhPt33tewwFcDGQCnSL9FSGM0KrQKKUMj9Fy3Sh3AVBZpBqH0Yr3+AjksT2TJ0EQkMdrcHSY8b0qDommbytrGpWMhCAv/L1kPDA1GVEfI89jIrRUF7Vyf1ggQ2J77LkFQWCcxptGi5UXkiIIkPUteBERqmZXhQ5FmZFSk5mMtJ4V5xU5tTyxNJc1BxuYlh7ipovz91X5rDnYyDvXD3ULYIlEAiNi/Ph4SzmFDXpmZIV1D5zqGgz88K99KHU2dlboGDWqJ2Nq47YaGtbUoA+Rc9c9Q9zaGBzjg8loI2tSJGGJp+/ME+ivokJvRlZqYFxaECFH/D3jA72RikVMSQ1mxuATu4GdCIVUzOAoLdW1dbz6u1HIjoiAB6rlSMQCC7ZUEBfo1R2MOlUcDid3frKL1bn1FDXqmTm459obrPD65iaMVgeymMGMie/JjKnohG92lZMqaeTiIclutu/2xhIaivcTM3gsV4wb6vZ9Y+P9qW838cRVaYT3Q12vPDYWQSZHfcnF+F51ldu24TFamvUW/jgpgUHhPfeAIAiMjfenqdPMU9PTuwNYACqFHLNUTVNJLlsK65g4Mqt7W05dPWty1yF2aPAaM47UIwIiuxsdrNpfS1xyOtdPG+3WjrQSeJQAACAASURBVNFx/qzaX8eq3HrmDo845SyxvvDVzipe/D6ftQcbmJ4Z5lZq97dluWwrbeF/Nw0npo+22r5KKUnBanyVEv58aXKvYnzn82rLhYibRfaQHotsp9OJblEhxj2NmCs78BoW0r0w4bDYaf5gP+ZCHY4uK8rUnufZ1txF8//2Yy5uQ6J1t8juOtCC7psiug62okj1Q6w+uczQk8FSq6d5wQHMhTqkod5Ig3r6j/gGM6l57VwskhE9NsItMDMm3p+le2rYVW/m+jFx3QGiU8Vc2k7b0mK8RoWgHu8upvzBpjK+3FHFC7MzGBPf814UBIHR8f58vbOKraWtzB0egbgPmakVLQbu/nQ3o2L9eWp6uttqc3KIGofTFVyfdlT58ahYP1YfqOe7fbXMGxaJQtpzD/z+8z1U67r45LaR+PU1k9cnDJx22P4eBKVDoKeG3rmKa7zli73DgnZ6PGLfvmv1HYvDE2NlZgCqDPdSQHmML/ZOCz5To5CF9Dwr3e3QW9HOjHfTURHJxEiCVFh2NOG0O1Ek9mSLWesNNH+Ui7moDUmwF9Lgnvs+piKAwL1SPglaSfTINLSKnv3e0X1IcJkXU83jCRwb5+byeCzsnRaa/7sPc3G7h02zubydls8OYsrXIYvxQeKnPM6RBjiXcdocNH2Qi7lAh73TijL9iP5eZ6LlkzxkUT5ojxJ8lgapQBCokeuImHj+9AFnikEBg9hRv4Nlxcu4MvZK1LKeec2zW5/l2+Jv2dO4h9kJsxGLXH2wxW7hrjV3sbFmI81dzUyOmty9T52+jjt+vINtddvwU/iREdCzWL65ZjOPbHyEn6t/ZmzY2N+Ew59Eq8BhtmPYUocsygeJ/8n1Oefz2HQgE+g84pZxsfyxF20eQSSgnZnQq8ig2EuK37UpbgPqvnBZRijPzMzo0wDyMHKZhH9dnsG0TM+SszCFjHfTY4hXnVyK9513ZtGmEqhZW0N5latms6HDxJPLcskI98H7KIHjbaUtfLC5jBtHRzMhydNKMiHIm0cuT2FdfiNf73SteDkcDj56ezdyB7SpRZDXzpadrlUovcHC5s8L6BLD7X8a5nE8QSQwYX4SCcP6rwRn3vwUotL92LakBF29wW3bHyYmnLC85mQYFq3lrkw53r2stNw9IZ5h0VqeXNojcHyqfLi5jB1lrVycFMiGgia+3NGz2vjkslxKTCqIHs6/NpSxr9olcOwSdc6mRhGPf0Agy5cvx2h0iZ62trby448/EBcXxy0zJ3t8n0Yl481rh5AR3n8ZJQF33YnfzTd7fC4Vi3jp6kFM7KUMK9hHwVvXDiEhyPP5u2rcYAhKRGguYdkvewGwWG18uXAxVkFETuAgnlpxkNo217Vv7DTxxNJcbMHpPHjdNI/jKWViXpuXRV17F8+uOHPC3pUtRp5fmcfQKA0iQeDPi3K6nevW5Tfw1c4q7r745EWdp6YF8/ysQUhOc/I8wK+Dm0X2tz0W2Ye16eRJWqzVejqPyCw4rE0nT9Ji2F5PV4FLWNjpcNK6sADEImSRatpW9Fhk2/UWdN8WIQ31QqSS0Pp1Qa9ZDP2B0+ag9WuXE400xAvdt0XY9S6RXZvORPuKUmSRaiRScbfe3mF8FFJenZtFvcHJy6vzT6sdDrON1kUFiP0U+F7h7jRZeEgfbWpaMNcMi/DYN0it4MXZg9hf086/1hWf8LvsDicPLcxBLHJlMvYWgH1wahLXj/J0n1NIxbwxb7CH3t5n2yrYWNTM41em9jkQ3M2Ev0BoFqy8H/S/TuZXfyH2luF/bQrSkJM85+PgMyUa79GeYypBKsLvmqReheQlWgX+16X0OplRpvjRHuFAf6S49OH7XilBGuZF2xHi0rY2M23LSxAilawK3sLjmx7H5nBldWyt3conJZ+xb3Qdkg5nn1wDnU4nuiWuTEB5nK/LpvmQuHS3oLZGjiRAiW5RIY6uM+tUOsCZo/2nCmwNRuRJWoy7G+g64NK1cTpcCwU4cateOBKfyVG0R/dPFvr5jlgk5vnxz+NwOnhy85M4nK7335qKNSwvWc648HEU6gp5J/ud7n3eyX6HIl0R48LHsbxkOWsrXOLSRx5jSNAQXtv1GhUdLmHkdnM7f9v8N+J84whWBfP4psfpsp3e2P98wffS357W4clwwlG5IAgfCoLQKAhC7hGf+QmC8JMgCEWH/j25IvUBfvPIZBJm3pWJ2Amf/ysbu93Bw9/sw2S189a1Q3jxCIHjTpOVPy/KOWEJ0M1jYhgb789zK/OoajXy9TcF+DbbEGdquPPhkZjF8POn+egNFt57ew9qK2ReHUfgr7QiJQgCk25MRSwVsWbBQRz2MzPhORFHlgYeFjg+FQq7RZ2D+eiWEYxPCOD57/KoaDGwPKeWlfvquH9KEu/eMIxAbzkPfO0SOH5ldQElTQZenjeYa+ZcjdFo5LvvvsPhcLB06VJEIhEzZ848a+5X/cFDt8zBKFKxZd0qGnSdvPHZCrxsHSSPuJjXrx+F3eG69g6Hk8e+3Y/BYueN+VnHzDIYEqXl95cksHh3NT8cqO/39todLuFZkSDw9u+G8tSMdHaUt/LBplJaDRb+ung/KSFq7p8yIOr8W0AapML38h6LbFu7Gd3SEmTRPgTcko5ycCAdayuxVHdiKtah31KL99gwAm5MQxKsQre4CIfRSucv1VgqO9HOdInbHmmRrVviKiXwm5+Mdk4StgYj7UdZZPcXhyct2jlJ+F2bjMNkc4nsHjlpuS4F7czDIrvuJWPjEgKYGi1hwZbybtfAU2rHyrKeEiB5T0afxebgga+z8ZZLeOnqQcfUh7h8UCizh4Tzr/XF3UH1Y/HfjaXsqtDx7Mx0wjQn/44bFOHLvZMSWZZdy3f76ihrNvDC9weZkBTI9aOiTvp4iKWusjCzHlbcD/1UjjxAD80pTsRaBa0LXeLSHWsrsdYZ0F6diN+1KTgsdldg1+FEt7gQnE6Cr03niTFPsL95Px/mfkiHpYMnNz9JrG8s1027tc+ugUeWAPldn+omLt0jqJ2M3/xk7J0W2lacujnIAGcPc3k7+l+q8RoZQsBNaUhDe4Lq+i21mEvb0UyPQ+J3/mh/nU0i1ZH8dcRf2V6/nS/zv6S5q5lntz5Lql8qb096mzmJc/jowEdkN2azt3EvHx34iDmJc3h74tsuceltLnHpL/O/ZHv9dv464q+8OuFVpGIpj216DJvDxovbX6TV1MqLF73I8+Oep6Kjgjd2v3G2T/1XQZCK8JufjENvRbdsoM85mhOWgz3zzDM64ENg9tNPP/3Ooc+eAfKcTuf8Z555JhyY+vTTT6850ZcNlIMNcCRBASpymzqRlhhYlFfH9zWtPHlVGhNTgtwEjrOr2jhY18H/bh5BtP+xV+IOp8x/vq2SPYUtaHa1oVeJ+NMjo/HxltEmha7cNn7eVoO6wYIxWsnNNw36Fc8YZAoJan8F+9ZVI5YIhCWeufjp8e5RjapH4DjAW0ZW5MmVvFlsDm5dsBOLzcGCW0firZAwOs6fz7dXsq20hSV7a0gL8+HlOZmoZBKSQ9R8sKmcnOo2lmXXctOYaG4ZG4tarUYQBHbs2EFNTQ1lZWXMmDGjWz/ofEUulSDzCaAyP4eN2QU4myuw+ITz0M2z0ahkaFUyPtpSTnZVG+sLmnj08hSmpB0/PXd4jB9rDzayPLuWOcMiujU8+oP/bSzlq51VvHT1IEbF+ZMaquZgXQdfbK9iT6WuW0g+xLf/A6YDfem5iSxCjaWsHcOuBizlHTg6zC6RTy8pijhfDHsaMRW00rWvBbGPzDXxk4mRRfmg31yLpbIT455GlBkB+EyNRqySIvaWot9Si6WqE3N+K76Xx6JMD0AaoMTeYcGwtRZ5gqbPJc59wVzeTtu3RXiNDEF9UYSbyK6lqhNzcRvaWQkoEjRIQlTYGo0Yttd5lKfJO6rI65Sxan8dc0dEnnRZZld+K+3fl6G+JAKv4e7P+ltrClm5r4435g8mM+L4ffGYeH++3VPDuvxG5o+I7DXDLr++gz99mc2l6cE8dGnyKYuODovW8nNhE0v21rC1pIVOk41PbhuF+lR167wCQaqEHe+BJgpCPa3lBzh1yivLSRqb4XIWq+rEuLcR1fBgfC6OROwlRZCJe+77ojY0M+JRJGpJ0CZQ1l7GwoKF7G/aT3FbMe9Mfocw7zDksT50HWjGuK8Zr2HBbiLmhzm6BEgkFyMJdIlLW6r1dO1r7hbUFvvKcdqdGLbUIQ3xcivLHODcxmG20fzhAURKiUvMXCZGHuMysbFUdmDc04giSYvvFbHH7XMG3vnupPqlcqDlAIsLF5PdlE11ZzXvTXmPQFUgI0JG8H3Z96yrWse6ynV4S715a9JbKCSKbnHp7Kbs7syhh4Y/hLfMm1CvUD4/+Dm5zbmsq1rHPYPv4YrYKwhXh9Np6eSL/C8YHDSYSHXkiRt4niP2cb3HDVtqkQSq+pzReT7fp/1WDuZ0On8BWo/6eCbw8aH/fwzMOukWDjAAcOtNg2jzERFebmJyhJYbR/dM/p+ans4gqRyfnA7uGRfLsOgTB0zCNUr+Nj2NqOIuRE6YdXcm0kOaOFdeGochUoGmw06nFO6517MM7NcgcXgwicOD2LmynKZKT5HPhvIOfvzgACbDmU1dPCxw/OL3+ZQ1Gzy2bytt4cGF2b1aBf9rXREHajt4cfagbk2cMI2SZ2akk1PdjsXm4PV5g7snKBclBnLTmGg2FjUTG+DFI5f3ZHSNGzeO8PBwiouLSU1NJTPzwpgYXDwkGWVUBipzKxZByn23zOvedt3ISC5JDuTnwiZGxfpxWx9czmQSEW/MH0ynycbjSzyFvZ1OJy98l8e3e6qPcYTeKajv5B8/FDItPZirh7o0qQRB4MWrB6FWSNhW2soDU5NIDT09/agBzi8EkYB2nssi21LRge+VsUgCXEFAkUqK3zVJ2Bq7sHea8ZuX3C1uKwv3xmdyFObSdkRKCZojdCFUw10W2eZCly6I9/geDTTfK+Pcshj6itPppG1VGYZdnmLmDrOd1oWFiLUKfK/sKb/yHh+OLMYHc6EORYofquEu8XxBENDMSnBlMSwsdCtPk4sFXp83mIZOM88s9yzLtNkc/PDGDjZ/V+SxraXJQMVnedj9FfhMcQ9wZ1e18e8NJVw9NJzLMk6s0+CrlPLq3ExKmgy8srrAY7srqygHH6WU52dlnJbrjFQs4vV5WXRZ7Oyrbue5WRmE+J5mgG707yF6PKx6GNoqT+9YA3ggj/XF+6IIzMVtiH3laK464r4fG4Y8zhdzoQ55khavkT332+OjHker0LK9fjt3Zd5FekA6AIJU7CoP1VtpW+65kn6sEiBlqj+q4cGYC3Uegto+k6KQhnujW1LcXZY5wLlP+3dl2HUm/Ob1ZDJKQ7zwvTQGS1kHIpkI7ZzEAaerk0QQBJ4e8zQKiYLdDbv509A/kaBNAMBL6sXz456nurOa6s5qnh/3PF5SVxAjQZvAn4b+id0Nu1FIFDw95unua3957OVMi5nG5trNZPhncMegO7q/776h9xHrG8uTm5/sVVz6QkR9SSTSSDVty4qxdwz0OYcR+lIKIghCDLDS6XRmHPq5zel0ag79XwB0h3/uZd+7gLsAgoODh3311Vf90/KzjF6vx9v75PR4BuidZp2Dmp+cKDUCiVOE7kGEzeSk4HsHWAQ0iRA+rG/lQS1FDup3gzXJweCh7tkSXSYH2zbaiU0TExN+9sqNbGYnJauciOUQd6mASOw6Z7vVSclqJ1YD+EZDxJhTb2Nf7lGdycHjm7oI8xbx6EhFt1ZUp8XJ45u66LA4mRwl4ca0HjHM0jY7z283MTpUwl2Z7iKZTqeT5SVWItUihga7X3uzzcnCQgsXR0iI8nFfTezq6qKqqoqYmBhksjMnDvtrY7HZ+XFPMTFhQWREuAcx20wOlpVYuSpOir+y73/nVWVWvi6wcOcgGePCe1bkN1RZWXDAgliAp8cqiVSf+Jg2h5PntploNTl4YbwKH5n74K2g1c7eRjvzkqV9FpI/WQb60nMbVRModAKtiU446hbwrRBwiKEz4qhxhAP8CwUMwU5MR8XuxWbwKxbQxTmxHZVYpmiF8B0iOiKdNKX3rVxIXS0QnCvCKTipGuPAckSsMvCAgE+VQM1IB6ajpKwkXaAtFWhNcGI/SutX1Qhhe8ToYh20JLvacfg+/bbIwvISK/cOkTPsiD6ufreD8U1STDjJHW5DE+B6/pwOJ4afId0s5hGFkdsukiM/1N+b7U6e2tKFxQ7PjVPiJe37M/Zpnpm1lTYeHqEg1b+nP11caGFlqZX7hsoZEtQ/2YK76m3UGhxMj5P2ywRP0dXA8F1/olOdQE7WcyCcv6W/5xKH71HB7nr+OsOcmI+Sz+u+7+Od2I+K55WaSsk2ZjNTOxOx4P6O1hYL+BeLqBtsx3BErNK3XCAwX0RDhsOjHxBsrnZ0RDqxHGVGK+uEiK0ijAFQP8Th0bcMcG6haoKw3e59YjdO19/ZGOCky7/3/Y9k4J3fOwVdBeSb8pmumY7oqD5xc+dmnDgZrx7v9rnD6WBF2wpSFCkkK93Ftg12AyvbVjLJZxKBUnct1UpzJa/Vv8Ywr2HcFHDTmTmhcwypHiK3iOjyh7qhJ+5zzuf7dOLEibudTufwE/3eaQeBDv2sczqdJ0zTGD58uHPXrl0n/L7zgQ0bNnDJJZec7WZcMBRsr2fNR3mMmR3P0GnROJ1OVr+fS/n+ZqLT/SnLaWbG/YOJTDm+KG1bg5GvX9hBWIKGq+7NOqdXJCpyW1j5rxwGT41i3BxX1H/D5/kc2FRL/JBASvY0Me3OjFMWp+7rPbosu4b7vsrmL9OS+cPEBJxOJ3/4Yg8/5TUwMTmIH/Ma+Oz2UYxPDKDLYufKtzfSZbGz+v4J+CpPz85+gJPH7nBy3fvbOFjXweoHJhCuUVLZYuSyt34hI9yX0iYDAd4ylv1x3AlLVl77sYC31xXz/o3DuDT97LhFDPSlAxxJ2/dl6H+pxv/WdJTJx+/vba0mGt7cgzTMC1uLyWWT/cchCFIRXQWttHx0AO8JEWiuOHnR/dbFhRh3NxB4dybyGN/u+9Ric3D1u5upazPxwwMTCPCWU5jbiOSzfCpUIkKMDpplAqOfGItUJuaXpQXEbWtkfbCUJxtauGVsDE/PcGVZPL38AAu2lPP5HaMYl+BpAHE8jBYbV/5zExabg9X3X4RaIWV3hY65723hmmERvHJN1okPcjbZ8wksvxcu+zuM/r+z3ZoLgjPZlzrtDhrfzcHeaiL4/mGIfWRYG400/HMvigQN/jennfR4q/OXatq/L0N7TRJeh7LxBjj3sBusNLy5x9W/3jsEQXJ6QduBd/65wTvZ7/Buzru8fsnrTI2eerab86ug31xD24pSNFcn4D0y9Li/ez7fp4Ig9CkIdKpPcoMgCKGHvigUOL+sHgY450gaGUz80EC2Ly+luVpP4Y4GSvc2MWp6HFNvT0cTrGLdxwcxH8dRwmF3sPbjPMQSERNvTD2nA0AA0Rn+pF8URvaaSmqLdFTktnBgYy1DpkQx9fZ0gqLV/PxFAYZ28xltx4ysMK7MDOXNNYXk1XawPKeW7/fX88DUJP553RDiA734y+Ic2rusvLw6n9ImA69ekzUQADpLiEUC/5ibhd3p5C+LcrDZHTy0KBuxSODN+YN5ec4g8us7eWuNZ1nKkeyp1PHv9cVcMyzirAWABhjgaHynRneLS9uPUxLrdDhpXVQIAi5x6WsSD4lLl2M3WNEtLjpUhnJq+mKaq+IQa+S0LnIvT5NJRLw+bzCdZhuPfrsfs8lG89cFGIFBdw+maUwwsRZY/+l+aqvaCdzWQKkcrrt3JLeOi2HBlnI2FTWzubiZBVvKuWVszEkHgABUMomba6DRYuOhhdmE+ip58qq0UzrnX5UhN0LSZbDmaWjyLGsb4NzCwzXQ7qB1YcFplQB5jw9HFuvj5ho4wLlH27JiHEYrfvOTTzsANMC5w52Zd5Lmn8azW5+luevUDQ/OJ7zGhCFP0NC+shRby2/DIe14nOrTvBw47Kl8M7Csf5ozwG8VQRC4+HfJyL2k/PjBAX75qpDQeF8GT41CKhMz5ZY0DO0WNn1deMxj7P2pkvrSDiZcl4S3Vn7M3zuXGDsnAR9/BWsWHGTdpwfxC/Ni5IxYxGIRU25Nw2qxs/6z/FN28OoLgiDw/MwMNCoZf/pqL08uzWVYtJa7J8SjkIp5fd5gGjvN3PrRju5Jy/jEk5+0DNB/RPmrePKqNLaUtHDt+9vYWa7jmRkuF6DJqcHMHx7Jez+XsLviaDk3F10WOw8tzCHU16WhNcAA5wqC9NBk02ClbdmxrdD1m2uxlB1yotEqUCb74TUqBP3GGlo+PtAzaZGe2jBHpJDgNzcJe6uJ9lXuFtlJwWr+Oi2Zn/Ia+OyNbURZoeOSMAKCvRk/PZE8XzGJRR2Uvb8PCRB1QxoSiYiHL0vpDqr/ZVEOcQFePHzZsR0vT8TQQ66Bi3ZXc+MHO6hoNfLavKxTF27+NREEmP5PkKpgyd1gH7DvPdeRBqnwvczlGtj0/n6s1Xo0sxPdBNRPBkEk4Dc32c01cIBzC2NOI137mvGZEoUs7PwsjRmgd6QiKS+Nfwmj1cgzW545o/OMcwVBJKC9JglEAq0DfU6fLOK/BLYCyYIgVAuCcDvwd2CqIAhFwJRDPw8wwGmh9JYx6YYUdHUGHA4nk29JRXRIoyY41odhl0WTv62e0r1NHvs2V3eyY0UZCcOCSDyP0oplCgmTb0mjs9WESW9lyq1pSA65b2hDvBgzK56K/S0c3Fx3Rtuh9ZLxypxMihv1WO1OXpub1a0PlBWp4Y8TE9hT2Xbak5YB+o9rR7jEpXdV6LgsPYTZQ3pEdp+4KpUwjZIHF+ZgMHtmz/191UHKmg28ek0mPufDhHGA3xSycG98pkTRta8ZY45norG1wUD7D2UoUv1QDevp732vcIlLWyo78Zl8+pMWeZwG7/Eui2zVUa+d28bFMjdUy5R2Bwf8pYy9zFXSKxKJGH5HFp0CRFuhMsuPmESXUMaRQfX6DhOvzctCKTs5l7Gj+dPkRNJCfdhdoeO2cbGMjuuDKMe5gjoYpr8JtXth42ue242t8MW1ULbRc1tdDnw+d0Bc+lfmsLi0paID1eBAVINOb0FI4qdAMz0Oc2k7+i21Htvt7WaaP8rFUuVpojHA6eO0O2j9Kh/DHk9hfXuHGd3SEmRRatQTLnwXqd8icZo47ht6HxuqN7C0eOnZbs6vgkQjRzM9Hkt5B/qNNWe7OWeVE6oGOp3O646xaXI/t2WAAYjJDGDCtUn4BCjxDXS3Dh1+RQwVuS1s+CKfkHhfVIds/+xWB2s+ykPhJeXi607dDvdsEZagYfLNqUikYgIj3dUTMydGULaviU2LiohI0eIT0P8W3YeZmBLEc7MyiNAoiQlwt1D84ySXVtCVmWGnPWkZoH8QBIFXr8nig01l3DUhzu2+Vyuk/GNuFtf9dxsvrTrI87MGdW/bVNTMx1sruHVcDGNPoQxlgAF+DdQXR2I62IpuaQnyWF/EPq7sTlcZSiEiuRjt1e5lKCK5GP8b0+jKbUZ9cf9MWnwvjcFUoCMo14DjSisi1aGgqc3BfWYJBrmT0Xe66+/4BXpRc3U8efuamDLfPdMuK1LDG/MH43Q6GRJ1YsfLEyGTiPj39UNZvLuKeyclnvbxfnXSZkLmfPjlVUi8FMKHuj53OmHlA1C4yhUk+v1WUB3SiLJ2weLboaUIlv4ebloOooEylV8DQSTgNz8Z/dbafnvGVMOD6TrQQvvqchRJ2m7beKfTSeviQsxFbVibuwj+09BuV6oB+oeOdVUYs5sw5jYjC/dGGuwa+7mufRHYHGjnJSOIz69x9QB954a0G1hftZ6Xd77MyNCRhHuHn3in8xzV0CC68lpo/7EcRbK2z7bxFxoDb80BzjkGXRJBdIbnaqZYImLyLalYuuxs+LynRGrHylJaagxMvDEFhff5mdWQMjq0VwFoQSQw+eY0BAHWLMjDcYZTF28cHc3EFM92SMUiHrw0meQQdS97DXC2CFTLeeTyFPy8PNPxR8f5c8f4WD7bVsnPha40hvYuK39ZnEN84EBG1wDnNoL4kEW9zUHr4qLu/r5jXRXWGj3aY5ShyEK98J0a3W+TFkEqwm9+MmIL6I6wyO5YXQ6tZqJvSsdX4xmcHzQinEtvH4yol+DEjKwwZg7uv4F2bIAXf5mWgkJ6nk6QL38FvIJgyT2uAA9A7jeQtxQGXw/GZvj+zz2/v+YZVwBo6E1QvhG2v3d22v0bRewrx/eyWETK/nGfEwQB7ZxERDIRrQsLcNodABi212EuakM1PNhVlvl9ab983wAuLFWddK6vRJHmj0gupnVhYc+131GPuVCH7xWxSM/g4uMAZx+RIOL58c8D8MSmJ3A4HWe5RWceQRDQzk5ApJTQ+nUBTtuFf869MRAEGuC8wj/Mm1Ez4yjLaaZgWz21xW3s+bGStPFhxJxmWvK5itpPwfh5SdQVt5OztupsN2eA84iHLk3m/9u77/Coy2yB4993WjLplUAKLY0kNCHShVBUrIAiiA1d7+oWdb27d3etF13FbXebZb0Xd+27IhYQ7BSjVKW3QBIgIdSE9N5m3vvHDEhIKIFJJpM5n+fhSebX5gweXmfe+b3nJPYI4Ffvb6eitomnl+6mqKqBP88a6rkfGIXXMEf6EXxNPxpyyqj57vipDy1+l/XAOrDzxntLTACl8Zq6bSeo3XGC+twyqtcdJWBsNL7xIee/gDg3awhMfwmKs2HlM1B5FD75OcSNhBtfgIxHHJNCO9+HA1/Dty/DiPsdNYWSr3UUly7a6+5XIS6BMdBCyIwEmg5XU/XVIZqK66j4JA+fpFBCb04k4IpYar49Tl1223Xuj/Wo4gAAIABJREFURPvoJhuli7IxBvoQdksSIdMTaTpSTeWqQzQX11Hx8QF8EkPwH3nuDkqie4gJiOHXl/+aTYWbeDvrbXeH0ymMARZCZyTSdKyGypXeuaxYJoGExxkyOY7oxBC+eTeHFa9lERTuy9iZCe4Oq0MNGN2TfkMi2PDRfkqOVrs7HOEhTtYgKalu5NZXNvDh1iP8dGICQ+Lkg6vwDP6jep3q5lGycK/jw+KN8Z0eR1l/jTkukPIl+yh7PwdTpJXgqX07PY5uK34SXP5D2PASvD3TUSh6+stgMMLY/4SYdPjkF47lX+EJMOUpZ3Hpv4FPgBSX7gb8BkXiNzSSylUFlLyZBUYDYc7OY6d3DbTXyn/nS1XxeT7NJ+oIvSURg9WE36AI/C7rQdVXBRS/lQVGRwFdZZBlYN5iesJ0MmIz+NuWv7G/fP/5T+gGrGnh+A2PoirzEA0Fle4Op9PJJJDwOAaDYvLcFNBQVVrP5LmpWHxdc1tyV6WUIuP2AfhYTax4LQtbJ9y6uH9LEUv+soX6Nto0b/wkj+Wv7W5XZf2aigYW/2kL+Ttbt6I8fqCCD/+4mfLC2lb79qw7xrLnt9F0Wpvmk9a8l8vX72R7RVeDizUoNpiHJiey51glA2OCeHBS954wFd3LqW4eRoWtpJ7QmUkuW4bSLgYIm5WEvdGOraqRsFnJKLmbzrWufBrC4qFoN1z1DIQ7J/uMJpjxf9DcAFXHYMYCsDhrBgb0gOv/Cse2wTf/477YhUuE3BiPMcBCc1EtodPjMQY7aoGd3jWw7CPv+IDaUer3l1O99igBY6LxTfi+LlnIjfEYAy00F9YSOi0BU7BndNkVrqGUYt6Yefib/XlszWM02b1jsjXkhv4Yg30oW5SDvbH154zuTCaBhEcKirBy7U8Gc9UP0ohO9I67GvyCLGTcNoDiQ9Vs+jS/Q5+rsqSOVW/u4Uh2Od+8k91iX8HuEr5blkfOt4Xs+OrwBV1Pa03m23s5mlvOytf3UFPRcGpfY30zy1/dzbH9FSx/LQu77fsJrtKjNXz972wKskpZ92HLdtG5GwvZvvIQu74+QvaG45fwaru/n2TE8+g1A3j59uGYjTLsC89iCvEhYm4aobOS8E289GLKF8sc6UfEXamE35aCJU7qo7mcxR/mvANTfwfp97bcF5EAc/4NM1+F2OEt96XeCINvdRSXPrKl8+IVLmfwMxM+N42Q6fFYh0S22Heqa+D2E9Rub90lVpyfvb6ZsvdyMEVYCTrjTkaD1eT4u58Wj3VoZNsXEN1ahDWCJ0c/SVZJFq/seMXd4XQKg6+J0FuS8E1y33sLd5FPA8JjxSaHkni557SDd4X+l0UyYFRPNn9+kON5FR3yHNquWfXmHrSGtPEx5G4qIneTo31ofU0Tq97cQ2gvf/oMDGf94v2UHqs57zX3rDtG/s4SBmXE0tRgI/Pt7wt7r31/H5Ul9QyZEkdRfiVbvjgIgM1mZ8XrWZh9jAwY3ZNdXx+hYHcJADXlDXz9TjZR/YLolRDM6ndzqCqt75C/j+7AZDRw/4R44sL8zn+wEF2QT79g/Ie5f7z3TQrt1HpEXicyGUb92LHU60zxkyBtetvnXfN7COzpWBZ2sri08EiWmAACRkW32ek1cEIclrhAyj/ah62yoY2zxbmULzuArbKBsNnJGNro9GqJDiBgdNt/98I7XNnnSq7vfz0LdixgV/Eud4fTKXzjQwi5Mb7NfxPdmUwCCeFhxs1Owj/YwsrX99DUAbcu7sg8zJHscsbdksj42YlE9Qvi63eyqSlv4JuFOdRVNTHl7hQm3ZWC2dfIytezsNnOvjytsriONYtyiUkO4YpZiYyeEU/+zhLnxFAxWWuOctmVvRk3M5HE9B5s/DifEwVVbP7U8TPj9mQm3JZMaE8/Vr25xzER9dZebE12ptydyuS5qdg1rHxjT7uWpwkhhOgmrCEw7SUozoGVv3F3NKKDnOwaqJvslH2QK0vB26Fudwm1mwsJzIiTOxnFOT068lHCreE8uvpR6pvlC9buSiaBhPAwPlYTk+amUF5Yy4bFrl0bX3a8hvWL99NnUDgpY3thMBqYPDcFW6OdxX/eQu7GQtKv60uPPkHO5WnJFB2sYvNnB9u8nrZrVr6xBxRMuisFZVAMnhhLTFIIaxblsuqtvYRF+zPyhv4AjJ+TjG+gmc8X7GTTZwdJGhlF/LAemMxGptyTSl1VE+//fhMFu0sYfVMCIVF+BEdaGTczgSPZZezIvLDlaUIIIbqZ+ImOrmEb/g5537g7GtFBzJF+BF/bj/psR9dAcX626kbKPszFHO1P0KTe7g5HdHFBliCeGfsM+ZX5/G3L39wdjuggMgkkhAeKGxDG4Imx7PjqMIf2tq9l6oYl+1n2/LZWxaVtNjsrXsvCZDEw8Y4Bp24HDu3pz+ibEqgoqqNHn0CGTe1z6pz4YT1IGhnFpk/zKTrYurL+9lWHOJpbzhWzkggKtwKOQq+T5qaAgoaaJqbck4rR7BiKfP3NTLorhcrievyCLIyfnXTqWj36BJF+XV8qiuqIHRDKoAkxp/aljos+tTyt7Pj5l6cJIYTohqY85egetuQnUO993V68hf9IZ9fATw7QXCLL/85Fa03Z4n3YG5oJm52MMslHP3F+Y6LHMGfAHN7e8zbfHfuu1f7P8j7jlmW3UFhT6IbohCvISCCEhxo1I56QKD9WvbGHhgtsmXpwVwmbPz9IQVZpq+LSWz4/SNHBKjJuG4D/GV0hBk2IYeIdA5h6/yCMZxQWHj87Cb8gCytey6L5tOVpJUer2bDkAP2GRDBgdM8W5wSFW7nhwaFc+5PBRJ5xW3KftHCu+o80bnhwCD5+5hb7hk3tw4TbkrnyB2ktWpcqpZh45wBMFgMrziguLYQQwktY/BydxCqPwOePujsa0UFOdQ00KErfy5Gl4OdQu6WI+t0lBF/VF3OUv7vDER7kP4f/J32C+vDE2ieoaqw6tf1w1WGeWvcUe0v3Mm/dPFmW6aFkEkgID2W2GJlydyo1FY2sXpR73uMdtXQcRZ2TRkSx+bN8jh9wFJcuOljJpk/ySbw8ioThPVqdqwyK1HHRBIb5ttrn42dm8l0plB2vZcOSAwDYmh13FVmsRjJuH9BmkcFe8cH0SQtvM9bE9CjCYwJabTcaDQwcH4NfkKXVPv9gHzJuG+BYnvZ528vThBBCdHOx6XDFL2Db27D3E3dHIzqIKcSHkGkJNOZXUr36iLvD6ZKay+spX7ofS98gAsbFnP8EIU5jNVmZP24+hbWF/P673wNg13aeWPsESinuHXgva4+u5b2c99wcqbgYMgkkhAeL6hfE8Kl9yN5wnANbz90y9Zt3sqmvauLKe1IZPycZ/1AfVr7hKLS84rUsrIFmxt+adM5rnE1cahiDMmLZvuoQh7PL2PRpPsWHqsm4bUCbEzYdJWF4DxIvj2LTJ20vTxNCCOEFxv8Keg6GpQ9BtbQT7678hkZiHRhOxZf5NMlS8Ba0XVP2Xg5oCLslqcXd00JcqCGRQ7h34L18tP8jVhWs4q2st9hcuJlHRjzCQ8MeYnSv0fzPpv+hoLLA3aGKdpJJICE8XPq1fYnsHUjmv/dSW9nY5jG5mwrJ3VTE5dc7jvWxmpg8N5XywlreffY7yo7XMmluCr7+5jbPvxCjb3IsT1v+z91s/vwgA0b1pP9lkRd9vYs1/tYkrIHmVsvThBBCeAmTxbEsrKESPn4YZLlCt6SUImR6AgaridJ3s9HN7V8Kfq6lLJ68zKVm/VEa9lcQcn1/TM6ajEJcjB8P+TEDwgbw1LqneH7L80yMm8i0+GkYlIHfjP0NJmXi8TWPY7PLe25PIpNAQng4o8nA5LtTaKyzkfmvva3etNSUN/D1O9n06BvEsKu/L+ocmxzK4EmxVJc1MHB8DL1T216adaHMFiOT56ZQV9WIf7CFcbMv7q6iS3WyuHTZ8Vo2LD3glhiEEEK4WVQqTHoS9n4MO951dzSigxgDLITelEjTsRoqV7bvboSazYUc/8NGmotbF5cuX7afE3/fjt0Dv0xqKqql/LN8fAeE4Xd5lLvDER7ObDTz3LjnqG6qxt/sz7zR806Veejp35PHRj3GthPbeH336+4NVLSLTAIJ0Q2ERwcwanp/8rYXs3f99y1TtdasemsvtkY7U+5OwXBGUefRM+KZck8qY2cmuCSOnv2DueHBodz4s6H4WE0uuebF6J0WzsDxMWxfeYgjOWVui0MIIYQbjf4p9B4Dn/4SKg67OxrRQayp4filR1GVeYiGggtbCt5cXEf5kn3YyhpaFZeu211C9dqjNB6qovKL/A6KumNom6Z0UTYGi4HQmxLbrMkoRHslhiay4MoFvHLVK4RbW35pfF2/67iyz5W8uO1Fskuz3RShaC+ZBBKimxgyKY7oxBDWLMqh0tkyNWvNUQp2lzD6pnhCe7buCmEyG0ke2ROTxeiyOOJSw9p8rs425uYEgiKsrHxjD411ze4ORwghRGczGGH630HbHW3j7dI5srsKub4/xmAfyhblnPfuHW3XlL6XA0ZF0NS+NB6spOobxyShrbqRsg9zMffyx39kT6rXHqV+X3lnvASXqMo8RNPhakKmJ2DsxJqMovtL75lOclhyq+1KKZ4Y9QTBlmAeW/MYjba2S1OIruWSJoGUUvlKqZ1KqW1KqU2uCkoI0X7KoJg8NwWtYdWbe2io0qx5fx+xA0IZNCHW3eF1OrOPo3tadWk9a94/f/c0IYQQ3VBYP7j6Ocj7Gja+4u5oRAcx+JoIm5VEc0kdFZ/lnfPYqm8O03iwktBpCQROiMU6KILK5QdpPFZD2eJ92OubCZudTPB1/TFFWCl7Lwd7fdf/MqnxSDWVKwuwDo3Eb3Dn12QU3ivMN4ynxjxFTlkOL29/2d3hiAvgijuBJmqth2qt011wLSHEJQiKsDJuViJHssvJW6ExGBST7krx2q4QveKDueyqPuxZe4y8HcXuDkcIIYQ7DLsLEq+G5fOg+CxfCkhRU4/n0z+EgLEx1Kw/Rn1u20vBG4/VULn8INZBEViHRrYoLl38jx3U7y4h+Oq+mHv6Y7AYCZudjK2qgfKl+zv51bSPbrJT+m42hgAzoTfGuzsc4YUy4jK4KfEmXt31KtuKtrV5jM1uO2vBdVcXltZaY9dy9+fZyHIwIbqZlDG96DsoHFsDjJ+dSGCYr7tDcqsR1/cjPCaAr97eS1213KIqhBBeRym48Xkw+8Li+8F2xl0dNcXw/FD44nH3xCdcJvjqPph6OO/eqW1qsU832yl7NxuD1UTI9IRT9XKM/mZCb07EXtOMpW8QAeNiTp1jiQskMCOO2i1F1O3uul8mVXyZT3NRLWEzkzD4XXynVyEuxS/Tf0kv/148vuZxaptqW+yrbapl9sez+fXqX7eaCMqvyGfSe5N4Y/cbLonDru08sOoB5n42lyZb0/lP8ELqUtofKqXygDJAA/+ntV7QxjH3AfcBREVFDV+4cOFFP19XUl1dTUBAgLvDEKJNtiZN6aE6IvpZpSggUF+uOfClJjAaYscq+TvpQmQsFZ5A8rR7iCxaS1rWH8jrezsH+85ybNSatN2/I7J4AwDbB8+jLGyYG6O8OJKj3/OpgNgNBqp6aYoGf/85JyxHEXbAwNFhNmp7tD7PWgINgWA/s5SO3XE9Uz0cGmvH5tOx8beXbynEfGegMk5zIq1rt7WXPO3+cutzeaHwBcYFjGNW+KxT2xeVLmJ11WoA7gi/g5EBIwGwaRt/Pf5X8hvzMWLkv3r9F7GWSytjkVmZyQdlHwBwddDVXB96fbvO9+Q8nThx4uYLWaF1qe17xmmtjyilegDLlVJ7tdbfnH6Ac2JoAUB6errOyMi4xKfsGjIzM+kur0V0T5KjLW2xHmT94v1E+6WQPLKnu8MRTpKnwhNInnYXGfBBHv12v0u/q+6D6KGwfSEUb4CJj8OuDxiStwCuWQ/WUHcH2y6Soy1V+h9ErSig78QB+A2KpOFgJSe+2I5fehQjZia1+3pNaTUUvrCVlMIIwu9M6TJfJtkbmin86xYIV6T8cBhpLmz00REkT7u/DDIo31jOm1lvcvuo2xkbM5Z1R9exevlqbk+5nb2le1lSuoS7Mu6iV0AvXtnxCvkF+Tw28jEW7FjAh/UfsnDyQizGiytsfqDiAB8v+5gJsRMI8Qlh2YFl3DnuToZEDrnga3hDnl7ScjCt9RHnzyJgMTDCFUEJIYSrDb2yNz37B/PNwhyqy+rdHY4QQgh3uPaP4B/pWBZWst/RPr73aLjiFzDj/6DmhGOb8GiBE+MwxwZQvngfzSV1lC7KxhjiQ8j1/S/qeuYof4Kv6kt9Vgm1W4pcHO3Fq/g4D1t5A2GzkjF08Qkg4T0eGvYQ8cHx/Pfa/+Zw1WGeXPsk/YP78/Cwh3l27LPYtZ0n1z7JnpI9/H3735nadypzBszh6TFPk1uWy0vbXrqo522yN/HY6sewmqw8NeYpHhnxCFF+UTy+5nHqmutc/Co920VPAiml/JVSgSd/B64CdrkqMCGEcCWDQTH57hTsNjur3txz1sJ0QgghujFrKEx7EU7shQUZjoLQ0192tJOPHgoTfg0734NdH7Z9vq2pdU0h0eUoo4GwWcnYG+0UPr8VW2k9YbckYfC9+EUQAeNisPQLonzpfprLO+fLJG3X6Oa2i9vW7SmhZuNxAifE4tMnqFPiEeJC+Bh9mH/FfErrS7ll2S2U1JXw3Ljn8DX5EhsYy68u/xXfHv+WH3zxA0J9Qnl8pKMe2/jY8dyceDOv7XqNrUVb2/28/9j5D3aX7ObJUU8SYY0gwBLAs2Of5WDlQf6y+S+ufpke7VLuBIoC1iiltgPfAZ9orT93TVhCCOF6IT38GDszkUN7ytj19RF3hyOEEMIdEqZA+r3QUAlTn3O0kT9p3M8hZjh88nOoOt7yvKZ6+MdkeP1ax2SQ6NLMPfwIntoX3WAjYFwMPv1DLul6yqAIuyUZNJS9l4O2d+yXSdquKX51F4UvbMXe2LJzkq2mibIPcjH39CdoSp8OjUOIi5EWnsb9Q+6nuqma+wffT1pE2ql9NyXexPjY8VQ3VfP0mKcJ8f3+3+YvL/8l0QHRbRaXPpfdxbtZsH0B1/W/jqv6XnVq+4heI7gj5Q7e2fsO646uc82L6wYuehJIa31Aaz3E+SdNaz3flYEJIURHSLsimt6pYaz7YB/lhRf+PxchhBDdyNTfwT2fw7C5LbcbTY5lYU11sPQhOP2u0a/mw7HtcOhbWP3nzo1XXJSAMdFE3j+Y4Kl9XXI9U5gvIdf3p2F/BdXrj7rkmmdTveYIDfvKaS6speKzvFPbtdaUL9mHva6Z0NnJKJM0exZd0w8H/ZDXp77OfYPva7FdKcUfx/+Rf137L66IvaLFPn+zP8+OfZbDVYf506Y/XdDz1DfX89iaxwizhvHoiEdb7f/ZsJ/RL7gfT659ksrGyot/Qd2IjBpCCK+ilGLinSkYzQZWvJ6F3db2bdZCCCG6MZMF+ox2tI8/U0QiTHkacr+ALW86th1cD+tegOF3w6BZ8M0f4Gj7lyuIzqUMCp9+wSij6z7y+F0ehe+AMCo+y6epqGO+TGo6XkPFF/n4poUTMDaamvXHqM8tA6Bu+wnqdhYTdGUfLL38O+T5hXAFo8HI8KjhGA2t61X5mf0YHDm4zfPSe6YzN20ui3IWsfrw6vM+zwtbX+BAxQGeGfsMwT7Brfb7mnz57bjfUlJXwu++/V37X0g3JJNAQgivExDqw/g5SRTmVbJ1eYG7wxFCCNHVjLgP+o2HLx6D47schaRD+8BV8+HaP4B/D/jwfscdQ8KrKKUIvTkRg8VA6aJstM21y8J0s53Sd7MxWE2EzkggeGpfTJFWyt7Loel4DWVL9mPpE0Tg+Etroy1EV/bAZQ+QEJLAvHXzqGioOOtxG49v5K2st5idPJsx0WPOelxaRBr3Db6PZQeWsfzg8o4I2aPIJJAQwislpkeRMLwH3y3L48ShqjaPqa9pOuua//oaqQchhBDdlsEA0/4OyuCoA1ReANP/F3wCvi8uXZwNq551d6TCDYyBFkKmJ9B0uJqqzENtHqNtduwN7S8iXrmqgKZjNYTOSMQYYEGZjYTNSsZW3Ujhi9vAZifsliSUoWu0qReiI/gYfZg/bj5l9WXM/7btqjPVjdU8seYJ4gLj+Pnwn5/3mj8c/ENSw1P5zfrfUFxX7OqQPYpMAgkhvJJSiglzkvH1N7PitSxsTS2XhZUX1vLm4+tY9eaeVuce2HaCV/9rNTszD3dWuEIIITpbSBxc8wdorocxDzqWj52UMBku/w9Y/xLknX+5guh+/AZHYh0aSeXKAhoPt/wySds1J/6xi8I/b8Zee+FfGjUUVFL11SH8hkdhTQs/td0SF0jgxN7QbCf4un6YIqwuex1CdFWp4an8aMiP+CzvMz7Pa91/6g8b/8Dx2uPMHzcfP7Pfea9nNpj57bjfUttUy9PrnvbqTsEyCSSE8Fq+AWYm3jmA0qM1fLvswKntdpudlW9k0dRgY++G4+zfUnRqX21lI5n/2osGKS4thBDd3ZBb4UdrYcpTrfdd+RtHZ7ElP4F6KTbqjUJvjMcQYKZ0UQ76tC+TqlcfoTGvAltlI2Uf7b+ga9kbbZQtysEY7EPIDf1b7Q+a3JsePxuG/8heLotfiK7u3kH3MihiEM9++ywnak+c2p55KJPF+xZz78B7Gdpj6AVfr39If3427GdkHs5kyb4lHRGyR5BJICGEV+s7KILUcdFsXV7A0X3lAGxdXsDxA5VMnptCZO9AMv+VTW1lI1prMv+1l8Y6Gzc+NFSKSwshRHenFPQcCG0UNsXi7+gkVnnYUTtIeB2Dn5mwmUk0F9VS8WU+4Czq/GU+1rRwgqb0oW77CWq3nzj3hYCKz/JoLq4j9JYkDL6mVvuVQWHp5Y9qq5i5EN2UyWBi/rj5NDQ3MG/dPLTWlNaXMm/dPJJDk/nxkB+3+5p3pN5BelQ6v9/4e45UH+mAqLs+mQQSQni9sTMTCAr3ZeXrWRzdV853y/JIGN6D5JE9mXJPKk0NNr56ey971x8jb3sxo6b3Jy4ljAm3JVOYV8mWL6S4tBBCeKW4ETD2Ydj6FmR/5u5ohBv4JoXiP6oX1WuOUJ9bdqqoc8iMBAIz4jDHBVL+0T5slY1nvUZ9bhk1648RMDYa3/iQToxeiK6vX3A/Hh7+MKuPrOb93Pd5Zv0zVDVWMX/cfMxGc7uvZ1AGnh3nqOf2xJonsGvv+zJXJoGEEF7P4mti8txUKkvq+ejPW/H1NzNhTjJKKcJ6+TNqen/ydxST+XY20YkhDJkUBziKSyem92Djx3mcKGi7uLQQQohuLuNRiBoESx+EGu8uNuqtgq/thzHMl+LXdjuKOt/kLOpsVITNSkI32Sn7IKfNGiT2umbK3s/BFGkleGrfzg9eCA8wZ8AcRvYayXMbnmNFwQoeuOwBksOSL/p6MQEx/PryX7OpcBNvZ73twkg9g0wCCSEEEJ0YwmVTemO3aybeOQDfgO+/WRgyKY6YpBCMFgOT56a06Mgxfk4yvoFmVryeRXOTzR2hCyGEcCeTBWb8L9RXwMcPgxcXG/VWBoujgxdo/NKjsKZ+X9TZHOlH8NS+1GeXUbPxeKtzy5fux1bVSNisZJS5jWWHQgjH3Ttjn8VqsjKsxzDmps695GtOT5hORmwGL257kbL6MhdE6TlaLzgVQggvNfqmeAZmxBAU3rLrhjIobnhwKPW1TfgH+7TY5+tvZtKdKXz84na+W5rHmJsTOjNkIYQQXUHPgTDxcVgxD3YsgiGz3R2R6GQ+fYLo+asRGIMsrfb5j46mbk8pFR8fwDc+BJPzfUbtzmJqtxYROLk3lrjAzg5ZCI/S078nS2csJdASiLGtOm3tpJRi3ph5FFQWEOob6oIIPYfcCSSEEE5KqVYTQCcZzYZWE0An9RkYTtoV0WxdUcDR3PKODFEIIURXNeZBiBsFn/4SKryz2Ki3M4X4tLhb+CRlUITOTAKDovS9HLRdY6tqpHxxLuaYAIKcy8yFEOcWYY3Ax9j2+/GLvd6wqGEuu56nkEkgIYRwgTE3O4tLv5FFY32zu8MRQgjR2QxGmPEy2Jvho5+A3fuKjYqzM4X4EHJjPI35lVSvPkLZh7nYG22EzU5GGeUjmRCi88iII4QQLmDxNTHlbkdx6bXv73N3OEIIIdwhrD9c/SwcyIRN/3R3NKKL8busB75p4VR8nkf9nlKCr+6HuYefu8MSQngZmQQSQggX6ZUQwrCrepO15ij5O6VDjBBCeKXh90DCFPjySSiWLwXE95RShM5IwBBgxic+mICx0e4OSQjhhWQSSAghXGjE9f0Jj/Hnq7f2Ul/d5O5whBBCdDal4MYXweQDS34ENlkiLL5nDLDQ8xfpRPxgYJv1g4QQoqNd0iSQUmqqUipbKbVPKfWIq4ISQghPZTQbmHx3KvU1TWT+OxstrYKFEML7BPWC6/4EhzfC2r+6OxrRxRh8TVIHSAjhNhc9+iiljMBLwDVAKjBHKZXqqsCEEMJTRcYFMuKGfuzfUkTupkJ3hyOEEMIdBs2EtJsg87dwbLu7oxFCCCEAMF3CuSOAfVrrAwBKqYXANCDLFYEJIYQnu+zK3uTvKOabd3KwNdkxyC3fbSrP02T7HnN3GEKck+SpuGhRj8POZvjny5A0tcOexn70CNlF5R12fSFcQfJUdEkGRfLMae6OolOpi12qoJSaCUzVWv+H8/GdwEit9QNnHHcfcB9AVFTU8IULF15axF1EdXU1AQEB7g5DiLOSHHW/hirNgS81dikNJIQQQgghRJdjoImUW31OPfbkz1ATJ07crLVOP99xl3In0AXRWi8AFgCkp6frjIyMjn7KTpGZmUl3eS2ie5Ic7RoapzRTV93o7jC6rG83fMvIUSPdHYYlUeIvAAAGc0lEQVQQ5yR5Ki5ZbRk0VnfY5bdt387QIUM67PpCuILkqeiqghOTT/3uDZ+hLmUS6AgQd9rjWOc2IYQQTharCYu1w+fbPZYlUBEc6efuMIQ4J8lTcek6Nn/0kWMtPsQI0RVJngrRNVxKWfqNQKJSqp9SygLcCix1TVhCCCGEEEIIIYQQwpUu+utprXWzUuoB4AvACLyqtd7tssiEEEIIIYQQQgghhMtc0hoFrfWnwKcuikUIIYQQQgghhBBCdJBLWQ4mhBBCCCGEEEIIITyETAIJIYQQQgghhBBCeAGlte68J1PqBHCw056wY0UAxe4OQohzkBwVnkDyVHgCyVPR1UmOCk8geSo8gSfnaR+tdeT5DurUSaDuRCm1SWud7u44hDgbyVHhCSRPhSeQPBVdneSo8ASSp8ITeEOeynIwIYQQQgghhBBCCC8gk0BCCCGEEEIIIYQQXkAmgS7eAncHIMR5SI4KTyB5KjyB5Kno6iRHhSeQPBWeoNvnqdQEEkIIIYQQQgghhPACcieQEEIIIYQQQgghhBeQSSAhhBBCCCGEEEIILyCTQO2klJqqlMpWSu1TSj3i7niEOEkpla+U2qmU2qaU2uTcFqaUWq6UynX+DHV3nMK7KKVeVUoVKaV2nbatzbxUDs87x9cdSqlh7otceIuz5OhTSqkjzvF0m1Lq2tP2PerM0Wyl1NXuiVp4G6VUnFLqK6VUllJqt1LqZ87tMp6KLuEcOSrjqegylFK+SqnvlFLbnXn6tHN7P6XUt858fFcpZXFu93E+3ufc39ed8buKTAK1g1LKCLwEXAOkAnOUUqnujUqIFiZqrYdqrdOdjx8BVmqtE4GVzsdCdKbXgalnbDtbXl4DJDr/3Ae83EkxCu/2Oq1zFOAvzvF0qNb6UwDn//NvBdKc5/zd+d5AiI7WDPxCa50KjAJ+6sxHGU9FV3G2HAUZT0XX0QBM0loPAYYCU5VSo4Df48jTBKAMuNd5/L1AmXP7X5zHeTyZBGqfEcA+rfUBrXUjsBCY5uaYhDiXacAbzt/fAKa7MRbhhbTW3wClZ2w+W15OA97UDhuAEKVUr86JVHirs+To2UwDFmqtG7TWecA+HO8NhOhQWutjWustzt+rgD1ADDKeii7iHDl6NjKeik7nHBOrnQ/Nzj8amAS879x+5lh6cox9H5islFKdFG6HkUmg9okBDp32+DDnHtyE6Ewa+FIptVkpdZ9zW5TW+pjz9+NAlHtCE6KFs+WljLGiK3nAuYzm1dOW0kqOCrdzLke4DPgWGU9FF3RGjoKMp6ILUUoZlVLbgCJgObAfKNdaNzsPOT0XT+Wpc38FEN65EbueTAIJ0X2M01oPw3EL+E+VUuNP36m11jgmioToMiQvRRf1MhCP41bxY8Cf3BuOEA5KqQDgA+BhrXXl6ftkPBVdQRs5KuOp6FK01jat9VAgFsfdZwPcHFKnk0mg9jkCxJ32ONa5TQi301ofcf4sAhbjGNQKT97+7fxZ5L4IhTjlbHkpY6zoErTWhc43iXbgFb5foiA5KtxGKWXG8eH6X1rrD52bZTwVXUZbOSrjqeiqtNblwFfAaBxLZk3OXafn4qk8de4PBko6OVSXk0mg9tkIJDqrh1twFDNb6uaYhEAp5a+UCjz5O3AVsAtHfs51HjYX+Mg9EQrRwtnycilwl7OrzSig4rRlDkJ0mjNqp8zAMZ6CI0dvdXYL6Yej6O53nR2f8D7OGhT/BPZorf982i4ZT0WXcLYclfFUdCVKqUilVIjzdytwJY76VV8BM52HnTmWnhxjZwKrnHddejTT+Q8RJ2mtm5VSDwBfAEbgVa31bjeHJQQ4agAsdtYpMwH/1lp/rpTaCCxSSt0LHARmuTFG4YWUUu8AGUCEUuowMA/4HW3n5afAtTiKQ9YC93R6wMLrnCVHM5RSQ3EsrckH7gfQWu9WSi0CsnB0wvmp1trmjriF1xkL3AnsdNayAHgMGU9F13G2HJ0j46noQnoBbzg70RmARVrrj5VSWcBCpdSzwFYcE5o4f76llNqHo4nEre4I2tVUN5jIEkIIIYQQQgghhBDnIcvBhBBCCCGEEEIIIbyATAIJIYQQQgghhBBCeAGZBBJCCCGEEEIIIYTwAjIJJIQQQgghhBBCCOEFZBJICCGEEEIIIYQQwgvIJJAQQgghhBBCCCGEF5BJICGEEEIIIYQQQggv8P8U94lAar/7pgAAAABJRU5ErkJggg==\n",
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      "text/plain": [
       "<Figure size 1440x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def marche_absorb(n):\n",
    "    P=np.zeros([n,n])\n",
    "    for i in range(1,n-1): \n",
    "        P[i,i+1]=0.5\n",
    "        P[i,i-1]=0.5\n",
    "    P[0,0]=1\n",
    "    P[-1,-1]=1\n",
    "    return P\n",
    "\n",
    "\n",
    "t_max=300\n",
    "nb_essaies=10\n",
    "plt.figure(figsize=(20,3))\n",
    "plt.grid()\n",
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    "n=31\n",
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    "P=marche_absorb(n)\n",
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    "for i in range(nb_essaies):\n",
    "    X=markov_from_P(t_max,P,n//2)\n",
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    "    plt.plot(range(t_max),X)\n",
    "    \n",
    "\n"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "Faites tourner ce programme en variant les points de départ. Que constatez-vous?"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calcul exacte de la probabilité d'absorbtion\n",
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    "\n",
    "Considérons la probabilité que la chaine soit absorbée en 0:\n",
    "$$\n",
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    "\\gamma_0(x) = \\mathbf P_x[X_\\infty=0] = \\Gamma_\\infty^x(0)\n",
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    "$$\n",
    "\n",
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    "***Lemme:*** Le vecteur (colonne) $\\gamma_0$ vérifie $P\\gamma_0=\\gamma_0$. \n",
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    "\n",
    "En effet\n",
    "$$\n",
    "\\begin{aligned}\n",
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    "P\\gamma_0(x)& = \\sum_y P(x,y) \\gamma_0(y) =   \\sum_y P(x,y) \\mathbf P_y[\\lim_n X_n = 0   ]    \\\\\n",
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    "&= \\dots\n",
    "\\end{aligned}\n",
    "$$\n",
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    "Completez, en n'oubliant pas de justifier les interversions entre limite et espérance. \n",
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    "\n",
    "\n",
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    "Ainsi $\\gamma_0$ vérifie les trois propriétés suivantes:\n",
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    "\n",
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    "* C'est un vecteur propre à droite de $P$ associé à la valeur propre 1. \n",
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    "* $\\gamma_0(0)=1$.\n",
    "* $\\gamma_0(n-1)=0$. \n",
    "\n",
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    "***A vous:*** Vous avez tous les ingrédients pour calculer ce $\\gamma_0$ explicitement.  Observez le programme ci-dessus. \n",
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    "\n",
    "\n",
    "***Vocabulaire:*** Dans la théorie des chaines de Markov:\n",
    "\n",
    "* Les vecteurs lignes sont assimilés à des mesures sur $E$; Par exemple, si $\\mu_t$ est la loi de $X_t$ alors qui est: \n",
    "$$\n",
    "\\mu_t P = \\sum_x  \\mu_t(x) P(x,\\cdot)\n",
    "$$\n",
    "\n",
    "* Les vecteur colonnes sont assimilités a des fonctions. Par exemple, considérons $f$ un vecteur colonne sur $E$. On peut calculer ceci:\n",
    "\n",
    "$$\n",
    "Pf(x) = \\sum_y P (x,y) f(y) = \\mathbf E_x[f(X_1)]\n",
    "$$\n",
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    "\n",
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    "En particulier les vecteurs vérifiant $P\\gamma = \\gamma$ sont appelées des \"fonctions invariantes\". \n",
    "\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 32,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "val_pr\n",
      " [-0.707  0.     0.707  1.     1.   ]\n",
      "vec_pr\n",
      " [[ 0.     0.     0.     0.73   0.   ]\n",
      " [ 0.5    0.707 -0.5    0.548  0.183]\n",
      " [-0.707 -0.    -0.707  0.365  0.365]\n",
      " [ 0.5   -0.707 -0.5    0.183  0.548]\n",
      " [ 0.     0.     0.     0.     0.73 ]]\n",
      "f: [0.    0.183 0.365 0.548 0.73 ]\n",
      "g: [0.73  0.548 0.365 0.183 0.   ]\n",
      "M\n",
      " [[0.   0.73]\n",
      " [0.73 0.  ]]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=5\n",
    "P=marche_absorb(n)\n",
    "\n",
    "val_pr,vec_pr=np.linalg.eig(P)\n",
    "val_pr=np.real(val_pr)\n",
    "vec_pr=np.real(vec_pr)\n",
    "\n",
    "\"\"\" on voit qu'il y a 2 vecteurs propres associés à la valeur propre 1. \n",
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    "Attention, ils sont situés à la fin de la matrice!\n",
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    "On les notes f et g\"\"\"\n",
    "print(\"val_pr\\n\",val_pr)\n",
    "print(\"vec_pr\\n\",vec_pr)\n",
    "f=vec_pr[:,-1]\n",
    "g=vec_pr[:,-2]\n",
    "print(\"f:\",f)\n",
    "print(\"g:\",g)\n",
    "\n",
    "M=np.array([[f[0],g[0]],[f[n-1],g[n-1]]])\n",
    "print(\"M\\n\",M)\n",
    "ab=np.linalg.inv(M) @ [1,0]\n",
    "gamma=ab[0]*f+ab[1]*g\n",
    "\n",
    "plt.plot(range(n),gamma,\".\")\n",
    "plt.title(\"proba de finir en 0 en fonction du point de départ\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "Remarquons que la technique que nous avons utilisée marcherait pour n'importe quelle chaine de markov avec 2 points absorbants. N'hésitez pas à en inventez une.\n",
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    "\n",
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    "***Exo:*** Le programme précédent n'est pas très robuste car les vecteurs propres  proposés par `np.linalg.eig` sont classés dans un ordre que nous ne maitrisons pas. Modifiez ce programme pour qu'il fonctionne quelle que soit la matrice `P` en entrée. Aide: repérer les indices où les valeurs propres valent 1 à l'aide de la syntaxe `==1`\n",
    "\n",
    "***Exo (difficile):***  Pour $x,y \\in \\{0,...,n-2\\}$ on a:\n",
    "$$\n",
    "\\mathbf P_x[X_1=y / X_\\infty=0] = \\frac{ \\mathbf P_x[X_1=y , X_\\infty=0]}{\\mathbf P_x[X_\\infty=0]}\n",
    "= \\frac{ \\mathbf P_x[X_1=y , X_\\infty \\circ \\theta_1 =0]}{\\gamma_0(x)}\n",
    "= \\frac{ \\mathbf P_x[X_1=y ] \\mathbf P_y[X_\\infty=0]}{\\gamma_0(x)}\n",
    "=\\frac{\\gamma_0(y)}{\\gamma_0(x)} P(x,y)\n",
    "$$\n",
    "Essayez d'itérer cette argument pour vérifier que:\n",
    "$$\n",
    "\\mathbf P_x[X_1=y,X_2=z / X_\\infty=0] =\\frac{\\gamma_0(z)}{\\gamma_0(x)} P(x,y)P(y,z)  = \\frac{\\gamma_0(y)}{\\gamma_0(x)} P(x,y)\\frac{\\gamma_0(z)}{\\gamma_0(y)} P(y,z)\n",
    "$$\n",
    "ainsi on voit que le processus $X$ conditionné à finir sa vie en $0$ est une chaine de Markov sur $\\{0,...,n-2\\}$ ayant comme matrice de transition $(x,y) \\to \\frac{\\gamma_0(y)}{\\gamma_0(x)} P(x,y)$. \n",
    "\n",
    "Imaginez un procéder de simulation pour vérifier cela. Aide: il y a deux étapes:\n",
    "\n",
    "* Comment simuler un processus conditionnée à finir en 1 point donné.\n",
    "* Comment estimer le noyaux de transition d'une chaine de Markov à partir de simulations.\n",
    "\n",
    "\n",
    "\n"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence en loi\n",
    "\n",
    "\n",
    "### apériodique\n",
    "\n",
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    "***Définition:*** Considérons un graphe irréductible orienté. Il est périodique, de période $n>1$, lorsque tous les boucles qu'on peut faire en suivant les arrête ont une longueur multiple de $n$. \n",
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    "\n",
    "Remarques:\n",
    "\n",
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    "* Grâce à l'irréductibilité, il suffit de tester les boucles issues d'un état donné. \n",
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    "\n",
    "* Pour montrez qu'un graphe est apériodique, il suffit de trouver un état $x_0$ est de trouver deux boucles issues de $x_0$ dont le pcgd des longueurs est 1. \n",
    "\n",
    "\n",
    "*** Théorème (convergence en loi):*** Considérons une chaine de Markov irréductible apériodique. Alors $(X_t)$ converge en loi vers  l'unique probabilité invariante. \n",
    "\n",
    "\n",
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    "Il y a une histoire de point fixe derrière ce théorème: Notons $\\mu_t$ la loi de $X_t$. On a $\\mu_{t+1}= \\mu_t P$. Donc si $\\mu_t$ converge, il converge nécessairement vers un $\\pi$ vérifiant $\\pi=\\pi P$. \n",
    "\n",
    "\n",
    "***A vous:*** Vérifiez que cette convergence en loi équivaut au fait que toutes les lignes de $P^t$ convergent vers $\\pi$ quand $t\\to \\infty$ (j'insiste sur \"toutes\" les lignes!)\n",
    "\n",
    "***A vous bis:*** Construisez une chaine de Markov très élémentaire de période 2. Constatez que la convergence en loi ne peut pas fonctionner dans ce cas.\n",
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    "\n"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 37,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "val_pr\n",
      " [ 1.    -0.461 -0.461 -0.706  0.313  0.313]\n",
      "vec_pr\n",
      " [[ 0.25   0.26   0.26  -0.403 -0.171 -0.171]\n",
      " [ 0.25   0.278  0.278  0.284  0.139  0.139]\n",
      " [ 0.076 -0.184 -0.184 -0.464  0.527  0.527]\n",
      " [ 0.25  -0.564 -0.564  0.57  -0.544 -0.544]\n",
      " [ 0.1    0.113  0.113 -0.323 -0.151 -0.151]\n",
      " [ 0.073  0.097  0.097  0.335  0.199  0.199]]\n"
     ]
    },
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=premier_chaine()\n",
    "\n",
    "pi=mesure_invariante(P)\n",
    "P_infty=np.linalg.matrix_power(P,50)\n",
    "\n",
    "plt.bar(range(6),pi);\n",
    "plt.plot(P_infty[0,:],\"o\",c=\"red\")\n",
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    "plt.plot(P_infty[1,:],\"o\",c=\"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "Avec $t=50$ cela n'a pas encore bien convergé. Essayez avec $t=51$, observez les points rouges et noirs sur la première bare. Comment expliquez-vous cela? (aide: observez le graphe de la chaine)"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Cas infini\n",
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    "\n",
    "\n",
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    "### Récurrence/transience\n",
    "\n",
    "***Définition*** On dit qu'un état est récurrent quand la chaine passe un nombre infini de fois dessus. Sinon l'état est dit transient. Quand une chaine est irréductible, les états sont: ou bien tous récurrents, ou bien tous transients. \n",
    "\n",
    "\n",
    "### Classification des chaines de Markov\n",
    "\n",
    "Notons $dimInv$ la dimension de l'espace vectoriel des mesures invariantes. \n",
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    "\n",
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    "Dans le cas fini nous avions à nous poser les questions dans cet ordre: \n",
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    "\n",
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    "* Réductible $\\Rightarrow dimInv\\geq 1$\n",
    "* Irréductible $\\Rightarrow dimInv= 1$, une proba inv, théo ergodique\n",
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    "    * pédiodique\n",
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    "    * apériodique $\\Rightarrow$ convergence en loi \n",
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    "    \n",
    "    \n",
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    "    \n",
    "Dans le cas infini c'est plus complexe:\n",
    "\n",
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    "* Réductible $\\Rightarrow dimInv\\geq 1$\n",
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    "* Irréductible\n",
    "\n",
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    "    * Transient $\\Rightarrow dimInv\\geq 1$, pas de proba inv\n",
    "    * Récurrent $\\Rightarrow dimInv =  1$ \n",
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    "        \n",
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    "        * Récurrent nul $\\Rightarrow$ pas de proba inv\n",
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    "       \n",
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    "        * Récurrent positif $\\Rightarrow$ une proba inv, théo ergodique\n",
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    "            * pédiodique\n",
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    "            * apériodique $\\Rightarrow$ convergence en loi \n",
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    "        \n",
    "            \n",
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    "Le théorème ergodique marche encore dans le cas récurrent-nul. Mais il s'exprime comme ceci:\n",
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    "\n",
    "$$\n",
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    "\\lim_{T\\to \\infty} \\frac{ \\sum_{t<T}  1_{X_t = x} }{  \\sum_{t<T}  1_{X_t = y}  }  = \\frac{\\pi(x)}{\\pi(y)}\n",
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    "$$\n",
    "\n",
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    "Moralement: Dans le cas récurrent nul, la chaine visite si peu souvent les états que $ T \\to \\sum_{t<T}  1_{X_t = y}$ est négligeable devant $T\\to T$. Mais quand quand on fait le rapport de deux négligeables ... \n",
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    "\n",
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    "\n",
    "***Exo:*** Retrouver le théorème ergodique classique à partir de cette version générale. Aide: vous avez uniquement à utiliser le fait que, dans le cas récurrent positif, $\\pi$ est de masse fini.  \n",
    "\n",
    "\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 34,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "np.random.seed(1234)\n",
    "\n",
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    "nbEssaies=10\n",
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    "for i in range(nbEssaies): \n",
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    "    Xt=3\n",
    "    X=[Xt]\n",
    "    while Xt!=0:\n",
    "        Xt+=np.random.choice(a=[-1,1])\n",
    "        X.append(Xt)\n",
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    "    plt.plot(X)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour quelle raison ce programme est-il risqué pour votre ordinateur? (Notamment si vous comptiez regarder votre série préférée ce soir). Quel est le lien avec la nulle-récurrence? Pour éviter tout problème, j'ai gelé la `seed` du générateur aléatoire. "
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Cas transient\n",
    "\n",
    "\n",
    "Considérons $t \\to X_t$ une chaine de Markov sur $\\mathbb Z$. Notons $\\mathbf P_x[X \\in \\cdot]$ sa loi quand elle  démarre en $x$. Supposons que son graphe ait cette allure là:   \n",
    "\n",
    "![./img/marcheTransiente.png](./img/marcheTransiente.png)\n",
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    "\n",
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    "\n",
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    "***Exo1:*** Mettez des poids sur les flèches ci-dessus de telle manière que:\n",
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    "\n",
    "$$\n",
    "\\mathbf P_0[\\lim_t X_t = +\\infty] =\\mathbf P_0[\\lim_t X_t = -\\infty] = \\frac 12\n",
    "$$\n",
    "\n",
    "Considérons les fonctions:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\gamma_+(x) &= P_x[\\lim_t X_t = +\\infty]\\\\\n",
    "\\gamma_-(x) &= P_x[\\lim_t X_t = -\\infty]\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
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    "Vérifiez que ces fonctions vérifient $P\\gamma_\\pm=\\gamma_\\pm$ (on a déjà fait cet exo, essayez de le refaire de mémoire). Donnez un argument simple qui indique que ces deux fonctions ne sont pas proportionnelles. On voit ainsi que dimInv est au moins égal à 2. En fait on peut montrer qu'il est exactement égal à 2.  On est en dans situation exactement similaire au cas d'une chaine de Markov finie avec 2 points absorbants, sauf que maintenant, les points absorbants sont... \n",
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    "\n",
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    "En vous inspirant d'un exercice précédent: Comment interpréter une chaine de markov dont la matrice de transition est $(x,y)\\to \\frac {\\gamma_+(y)}{\\gamma_+(y)} P(x,y)$?\n",
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    "\n",
    "\n",
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    "\n",
    "***Exo2:*** Supposons maintenant que $P(x,x+1) = \\frac 3 4$ et $P(x,x-1)=\\frac 1 4$. Ainsi on a:\n",
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    "\n",
    "$$\n",
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    "\\mathbf P_x[\\lim_t X_t = +\\infty] = 1\n",
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    "$$\n",
    "\n",
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    "Donc $\\gamma_+(x) = 1$ et $\\gamma_-(x)=0$, on n'a donc trouver qu'une seule fonction invariante par cette méthode, et c'est la fonction 1 qu'on connaissait bien.   En fait, dans ce cas, toutes les fonctions invariantes bornées sont constantes (cela vous rappelle peut-être un théorème d'analyse complexe!). On est dans une situation simitaire au cas d'une chaine de Markov finie avec 1 point absorbant: $+\\infty$. \n",
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    "\n",
    "\n",
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    "Cependant: En essayant de résoudre le $P\\gamma=\\gamma$ on tombe sur l'équation de récurrence:\n",
    "$$\n",
    "\\frac 34 \\gamma(x+1) - \\gamma(x) + \\frac 14 \\gamma(x-1) \n",
    "$$\n",
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    "\n",
    "\n",
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    "Dont les solutions sont:\n",
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    "\n",
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    "$$\n",
    "x \\to \\lambda  + \\mu 3^{-x} \n",
    "$$\n",
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    "\n",
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    "Ainsi on trouve une seconde fonction invariante positive: $x \\to 3^{-x}$\n",
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    "\n",
    "\n",
    "\n",
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    "Si vous avez mis des poids très très simples, vous devriez trouver une seconde fonction invariante non bornée, de la forme $x \\to e^{kx}$ (essayez de résoudre $P\\gamma=\\gamma$). Cette seconde fonction \"correspond\" au point $-\\infty$. \n",
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    "\n",
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    "On montre que: à chaque direction de fuite possible dans le graphe, correspond une fonction invariante. Si cette direction est 'probable' la fonction est bornée. L'ensemble des directions de fuite est appelé la frontière de Martin.  \n",
    "* Exemple simple: si le graphe est constitué des 3 copies de $\\mathbb N$ recolées en $0$, il y aura 3 fonctions invariantes linéairement indépendantes. \n",
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    "\n",
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    "* Exemple plus complexe:  La marche aléatoire simple dans $\\mathbb Z^3$ est transiente. Sa frontière de martin est une sorte de sphère de dimension 2 à l'infini. Ainsi l'ensemble des solutions de  $P\\gamma=\\gamma$ est de dimension infinie. Et bien sur il en est de même pour les solutions de $\\pi P =\\pi$.\n",
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    "\n",
    "\n",
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    "Retenez surtout que dans le cas où $E$ est infini, il peut y avoir moulte fonctions/mesures invariantes. "
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