{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read())" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last Updated On: 2020-02-24 10:31:59.155920\n" ] } ], "source": [ "from datetime import datetime\n", "print('Last Updated On: ', datetime.now())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_TP1 EDO : calcul approché VS formel." ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul approché avec la fonction `odeint` du module `SciPy`\n", "--- " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'ECUE M62 n'est qu'une introduction aux méthodes numériques d'approximation d'EDO en utilisant Python comme langage commun de programmation. \n", "Nous allons étudier, programmer et tester plusieurs méthodes numériques.\n", "\n", "Cependant toutes ces méthodes (et bien plus) se trouvent déjà dans le module `SciPy`. \n", "Bien sûr vous devez toujours faire un peu de programmation avec Python pour les utiliser et une compréhension des fondements de la méthode numérique que vous utilisez est toujours indispensables. \n", "\n", "Voyons sur trois exemples comment utiliser la fonction `odeint` du module `SciPy` pour approcher la solution d'abord d'une EDO ensuite d'un système d'EDO (ce qui inclut les équations différentielles d'ordre 2 ou plus)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Principe d'utilisation de `odeint`\n", "\n", "Le principe d’utilisation de `odeint` (pour intégrer numériquement des équations différentielles) est le suivant: pour avoir une estimation numérique de la solution du problème de \n", " $$\\begin{cases}\n", " \\mathbf{y}'(t)=\\boldsymbol{\\varphi}(t,\\mathbf{y}(t)),\\\\\n", " \\mathbf{y}(t_0)=\\mathbf{y}_0\n", " \\end{cases}$$\n", "avec $\\mathbf{y}(t)=(y_1(t),y_2(t),\\dots,y_n(t))$ le vecteur des fonctions recherchées, dépendant de la variable $t$ et $\\boldsymbol{\\varphi}=(\\varphi_1,\\varphi_2,\\dots,\\varphi_n)$ une fonction de forme quelconque, on donne comme argument la fonction $\\boldsymbol{\\varphi}$ (qui doit avoir deux paramètres, même dans le cas autonome, avec $t$ comme deuxième paramètre), la condition initiale $\\mathbf{y}_0$ et le domaine de temps qui nous intéresse (qui commence à $t_0$). Elle retourne un tableau `Numpy` (même si $t$ était une liste). \n", "\n", "Notons que la résolution de $y''(t)=F(t,y(t),y'(t))$ passera par celle du système différentiel\n", "$$\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=F(t,y_1(t),y_2(t))\n", "\\end{cases}$$\n", "avec \n", "$y(t)=y_1(t)$, \n", "$y'(t)=y_1'(t)=y_2(t)$ \n", "et \n", "$\\varphi_1(t,y_1(t),y_2(t))=y_2(t)$, \n", "$\\varphi_2(t,y_1(t),y_2(t))=F(t,y_1(t),y_2(t))$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 1\n", "\n", "En guise d’exemple, considérons le problème de Cauchy $y(0)=1$ et une équation logistique simple de la forme\n", "$$\n", "y'(t)=\\frac{3}{2} y(t) \\left( 1-\\frac{y(t)}{6} \\right). \n", "$$\n", "On crée alors la fonction $\\varphi$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# def phi(y,t):\n", "# return 1.5*y*(1-y/6)\n", "# ou \n", "phi = lambda y,t : 1.5*y*(1-y/6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction `odeint` peut être appelée avec au minimum trois arguments: \n", "- la fonction $\\varphi$, \n", "- la valeur $y(t_0)$, \n", "- le vecteur $t$ (qui commence à $t_0$) où la fonction $y$ sera évaluée.\n", "\n", "Elle renvoi un vecteur `sol` contenant l'évaluation de la solution en les points du vecteur $t$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "y0 = 1\n", "tt = linspace(t0,5,201)\n", "sol = odeint(phi,y0,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution peut alors être tracée simplement " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol)\n", "xlabel('t')\n", "ylabel('y')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NB: le nombre de points en lesquels les résultats sont évalués n’est pas (du moins directement) relié à la précision des calculs internes (ne pas imaginer que cela fixe le pas de la méthode, en particulier)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Champ de vecteurs\n", "\n", "Bien qu'il soit trés rare que l'on puisse résoudre explicitement une équation différentielle donnée, on peut souvent avoir une idée de l’allure des graphes des solutions en observant le champs de vecteurs associé. \n", "En effet le graphe d'une solution de l'équation $y'(t)=\\varphi(t,y(t))$ est par définition tangent à son vecteur vitesse $(1,y'(t))$ et donc au vecteur $(1, \\varphi(t,y(t))$. \n", "La connaissance de la fonction $\\varphi$ en chaque point $(t,y)$ permet donc de représenter facilement ces vecteurs tangents même si l'on ne connait pas les solutions. \n", "Et si l'on en trace un grand nombre, uniformément répartis dans le plan $(t, y)$, on obtient une représentation\n", "du champ de vecteurs associé à l'équation différentielle qui permet souvent de deviner les graphes des solutions puisqu'il s'agit des courbes qui sont tangentes en tous leurs points aux vecteurs de ce champs de vecteurs. \n", "Il est alors intéressant d'y superposer la solution numérique obtenue avec `odeint`.\n", "\n", "La fonction `quiver` du module `matplotlib` permet de tracer un champ de vecteurs.\n", "Utilisons-la pour obtenir celui associé à notre équation différentielle.\n", "La courbe rouge est la solution déterminée par `odeint`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "\n", "# quiverplot\n", "# define a grid and compute direction at each point\n", "g1 = linspace(0,5,21)\n", "g2 = linspace(0,8,21)\n", "T,Y = meshgrid(g1,g2) # create a grid\n", "DT, DY = 1, phi(Y,T) # compute growth rate on the grid\n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M==0 ] = 1 # avoid zero division errors \n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "\n", "plot(tt,sol,'r')\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "title('Champ des pentes');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’un système d'équations différentielles d'ordre 1\n", "\n", "Considérons deux espèces: une proie (des lièvres par exemple) et un prédateur (des lynx par exemple). \n", "Ces deux populations sont représentées par $y_1(t)$ et $y_2(t)$ des fonctions continues du temps $t$. \n", "Si on suppose qu’il n’y a aucune autre intervention extérieur, une modélisation possible pour ce genre de système a été proposée indépendamment par Alfred James Lotka en 1925 et Vito Volterra en 1926:\n", "$$\n", "\\begin{cases}\n", "y_1'(t) = y_1(t)(a-by_2(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_1(y_1(t),y_2(t),t)] \\quad\\text{équation équation des proies}\\\\\n", "y_2'(t) =-y_2(t)(c-dy_1(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_2(y_1(t),y_2(t),t)] \\quad\\text{équation équation des prédateurs}\n", "\\end{cases}\n", "$$\n", "soit encore en notation matricielle\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(y_1(t),y_2(t),t)\\\\\n", " \\varphi_2(y_1(t),y_2(t),t)\n", " \\end{pmatrix}.\n", "$$\n", "\n", "On suppose qu’à ce jour il y a $y_1(0)=2$ unités de proies (une unités = $1000$ animaux) et $y_2(0)=1$ unités de prédateurs et on se demande comment vont évoluer les populations de ces deux espèces. \n", "Pour les simulations on prendra $a=2$, $b=1$, $c=1$ et $d=0.3$. \n", "\n", "Soit $\\mathbf{y}(t)\\stackrel{\\text{déf}}{=}(y_1(t),y_2(t))$ le vecteur des deux fonctions inconnues. \n", "On commence par créer la fonction vectorielle \n", "$$\n", "\\boldsymbol{\\varphi}(\\mathbf{y},t)=(\\varphi_1(\\mathbf{y},t),\\varphi_2(\\mathbf{y},t))\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# yy est une liste a deux composantes\n", "pphi = lambda yy,t : [ yy[0]*(2-yy[1]) , -yy[1]*(1-0.3*yy[0]) ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En faisant varier le temps sur l'intervalle $[0;20]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$ on écrit" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "yy0 = [2,1]\n", "tt = linspace(t0,20,201)\n", "sol = odeint(pphi,yy0,tt)\n", "sol_1 = sol[:,0] # [y_1(t) for t in tt]\n", "sol_2 = sol[:,1] # [y_2(t) for t in tt]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_1$ et $y_2$ en fonction du temps $t$ peut être obtenu par " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol_1,tt,sol_2)\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "legend([r\"$y_1(t)$ proies\",\"$y_2(t)$ prédateurs\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_2$ en fonction de $y_1$ peut être obtenu par" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmYAAAGvCAYAAADxIxlrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzsnXd4FNX7xc/upiekkISQ0DsovUkv0qUJioAUBWmCIkhXiHQjBKkKhKJU6b0GSOg1dBKkh5IESO9ls3N+f8QdsxAgZO8gfH/zeZ59lGRzz87dmbln7n3v+2pIQkVFRUVFRUVF5b9H+19/ABUVFRUVFRUVlSxUY6aioqKioqKi8pagGjMVFRUVFRUVlbcE1ZipqKioqKioqLwlqMZMRUVFRUVFReUtQTVmKioqKioqKipvCaoxU1FRUVFRUVF5S1CNmYqKioqKiorKW4JqzFRUVFRUVFRU3hIs/usPkFfc3NxYvHhxRTWSk5Nhb2+vqMb/Amo/5Q61n3KP2le5Q+2n3KH2U+5Q+yn35KWvzp8/H0XS/VXve2eNWfHixREUFKSoxuHDh9GkSRNFNf4XUPspd6j9lHvUvsodaj/lDrWfcofaT7knL32l0Wju5+Z96lKmioqKioqKispbgmrMVFRUVFRUVFTeElRjpqKioqLyxsjIyFBcIzo6GgaDQVENg8GAW7duKaoBABcvXkR6erqiGuHh4QgODlZUgyR27twJvV6vqM6JEycQGhqqqIbSqMZMRUVF5S3n9u3bePz4saIaGRkZmDp1Ku7fz1UYTJ5ZuXIlfvrpJ8TFxSmq07hxY2zYsAGSJCnSvk6nw4IFC9C7d2/cuXNHEQ0A0Gq1qFChApYvX47MzExFNDw9PTFw4ECEhobi7t27imhoNBpERETg/fffx7p16xT7XsqVK4fatWvj22+/xZMnTxTRUBrVmKmoqKiYwbJly7BhwwbFBk0A8PLyQtOmTTF48GDcu3dPEQ0rKyuUKFECpUuXRv/+/RUboHv37o2//voLxYsXx8SJExUxaK6urvj000/RtWtXVK1aFXFxcSApXGf8+PHYvn07ypcvj4EDB+Lhw4fCNapUqYImTZrgq6++UszUaDQa/PLLL4iOjka5cuUwePBghIeHC9UAgL59+8LCwgLdu3dH9erVsXv3buHfi5ubG0aMGIEFCxagVKlSGD9+vOIPAcIh+U6+atSoQaUJDAxUXON/AbWfcofaT7lHRF+lpqZy9OjR9Pf3p8FgMP9DvYCYmBgWLFiQRYsW5cyZMxkbG6uIzo4dOwiAOp2OPXr04NWrV4WfU5IksX79+rLOF198wRs3bgjVIP89FgB0cnLixIkTGRcXJ1QjPT2dZcuWJQD6+vqyevXq3LVrFyVJEqozY8YM+VisrKw4dOhQRkRECNV49OgRbW1tZZ3KlStzx44dwo9l2bJlsoaNjQ1HjRrFqKgooRo7d+6UNQCwfv36PHr0qFCNlJQUFilSRNZwcXHhL7/8wuTkZGEaebn2AAQxF/7mPzdYeX2pxuztQe2n3KH2078kJia+dFAR1VfHjh2jVqtl8eLFOXnyZD58+FBIu8+yefNmeRBwcHDg0KFDeefOHeE6HTp0MBnUlixZwpMnTwrVuHDhAjUajayh1WrZt29fpqSkCNOQJIktWrQwOZbixYszJCREmAb5rwH09fWVB+jly5cL1UhNTWWJEiXk47C3t+fgwYOF9hdJTpgwwaS/OnXqxGvXrgnV2LdvHy0sLGSNGjVqcP369UI1JElikyZNZA1XV1dOmzaNiYmJQnVWrFhh0l/9+/cX2l9KGjN1KVNFReWNExsbi4YNG2Lo0KHw9/dXLLi5QYMGGDduHEJDQ+Ht7Y1ixYqhXbt22LZtm9Ag5M6dO6NTp04AgKSkJMybNw8NGzbEqVOnhGkAwNy5c2Frayv/W5IkWFtbC9WoVq0aBgwYIP+7QIECmDx5somuuWg0GsyePRs6nU7+2YwZM1ChQgVhGgDQrl07NGvWTP533bp10b17d6EaNjY28PHxkf+t0+nw+eefC+0vABg9ejQ8PDzkf3t6egrvL2trawwePFj+d0xMDGrXri1UQ6PRwNfX10TDw8MDDg4OQnV69uyJKlWqQKPRAABCQ0NRokQJoRqKkRv39ja+1Bmztwe1n3KH2k+mnDlzhjY2NvIsw8cff8wlS5YwLCxMaF9lZGSwVq1aJk/P3333nfDlprCwMDo5OckaI0aMUGQJddq0afJS46+//sqdO3cK14iMjKSLiwtLly5NAKxXrx5jYmKE63zzzTesUKECS5YsSZ1Ox7Vr1wrXuHz5MmfNmsVvvvmGAPjhhx8Kn52RJIl169blmDFj6O7uTnt7e0Wudz8/P3bo0IFdu3YlAPbr10/oORYYGMjIyEh6eXlx3bp1tLKyYtGiRRWZ/e3RowcXLlzIqlWrEgAXLlwoXMPf35+ffPIJJ06cKH/3SUlJQtpWlzJVY/ZWo/ZT7nhX+ulVy4wi2bBhg4lhAsCOHTvy4MGDQnVu3LhBOzs7k2Wg+Ph4oRpk1sBpY2PDNm3aEAC7dOkifEkrLS2NFSpU4PHjxzlv3jzqdDouXbpUqAZJLliwgIcPH+avv/5KAKxUqRLDw8OFakRHR3PhwoV89OgRK1SoQI1Gw8WLFwvVILOWmkly6tSpstEUHdN25swZxsTEMCQkhJ6enrSxseG+ffuEamRmZvL06dPU6/Xs1asXAbB3797MzMwU0r7xHnXx4kWS5J49e2htbc1ChQrx5s2bQjSMhIaGMjExkdHR0axRowYBcP78+UI1SMqfe8qUKQTAxo0bCzHmqjFTjdlbjdpPueNd6acDBw6wSJEiLF++PJs3b84vv/yS48eP56JFi7h7927hhsY4WOKfeKbx48czICBAqAZJLl68mOXKleN3331HACxbtiyDg4OFakiSxMmTJ1Ov13PIkCEEwDp16vDJkydCdW7dukUya0agSpUqBMCpU6cKNdR6vZ56vZ4k+ccff1Cr1bJkyZLCZ0+MnzkyMpLVq1eXY8JEkv3aMxrNGjVqCA9sN3Lr1i0WKVKEVlZW3L59uyIamZmZ7Nu3LwGwW7duzMjIMLvNnO5RBw4coK2tLT09PYXHABqJjY1l7dq1CYC//vqrIhok6ePjQwBs0KABExISzGpLNWaqMXurUfspd7xL/XTjxg15R1v217hx44Qvz0mSxJ49e9LKyooffvghAXDBggU8deqUcJ2NGzeSJNeuXUs7Ozva29srEtxs/O+cOXOo0WhYvHhx4SaQzDqn4uLi5H4bPHiwsNmTZ9m6dSutrKzo6enJq1evKqIRFxcn7wr19vYWZjSfvfYWLVpEjUbDihUrCl/SNnLv3j2WLFmSFhYW3LBhgyIaBoOBX3/9NQGwc+fOTE9PN6u9F92jAgMDaW9vzwIFCij63detW5cA+MsvvyiiQVLeCFK3bl2zZk1VY6Yas7catZ9yh5L9JEkSw8LChLYZExPDli1bmhizSpUqcfHixcLiNIykpaXxiy++oCRJ9PPz4+zZs6nRaDh8+HChW9yzc+XKFTmG6vvvv5dnh0Szfft22tnZ0cnJSfgSrfGcSktL42effUYA/OSTT5iamipUx0hAQAAdHBzo4uIi3DgbSUpKks+7YcOGCTFnOV17K1eupFarZdmyZfngwQOzNXLi0aNHLFu2LLVaLVetWqWIhiRJ8ixwu3btzPruX3aPOnbsGB0cHOjq6spLly7lWeNlJCQksGHDhvIMsFLMmTOHAFi7du08p7dRjZlqzN5q1H7KHSL7KSYmhvv27ePEiRPZunVr5s+fn7NnzxbWvhG9Xs+hQ4cSAJs1a0YvLy8CoLOzM7///nvevn1bqJYRf39/tmvXjgBYsmRJRZY2yayndGMKisaNG/Px48eK6Jw/f55eXl60sLAQGg+W/ZwyGAzyd9WoUSPF8qmdO3eOrq6utLOzo7+/vyIaaWlp7NSpEwHwq6++MnsW8EXX3saNG2lhYcFixYopEuBOkhEREXz//fep0Wi4ZMkSRTQkSeKYMWMIgC1btsxzXOOr7lGnTp2io6MjXVxcGBQUlCeNV5GUlMSmTZsSACdOnKiIBpkVQ2lc0o6Ojn7tv1eNmWrMzELpQG5jP72JgPE3oaHX64XqGNvKfj5JkvTau9zS09P5yy+/sFy5ciazWFobB1rkL8x2XXpw0OAh9Pb25rx587hmzRru37/fZMYp05C341q8eDF///13ZmRkcMOGDfJTrUajYdu2bYVfK4GBgZQkiWvWrKGrqysBcMCAAcJ305FZhmbatGnUaDT08vISnhfMyMOHD+V4sLFjxwpZEn623yVJkuNoKlasyEePHpmtkRMhISEsXLgwLS0tFVumyx7g/tlnn5m1TPey83PXrl20traml5cXr1+/nmeNlxEZGclq1arJy/RKIEkSvb29CYBNmzbN06x2bq7jc+fO0dnZmU5OTjx9+nQePumrSU5OlvPcjR8/XrH7/qJFiwiA1apVe+14QyWNmcVr59f4f8KMGTNQpEgRkJTzoIjm/Pnz+OGHH7B+/Xo4OzsropGQkIDPPvsMY8aMQdOmTRXRAICpU6ciPDwcv/32m2L9tXfvXvzwww84cOAA3NzcFNEICAjAd999hwkTJuCzzz4zqy2DwYB58+ahZs2aaNiwIUhi79692LlzJ3btP4jiletg9pw5AAASiIhPw72oZIRGJeNOVDKuhcXDIPGZVt8HPp6FYjnoXf3nhXQAYf+8oAcCAnP8fHZWOlQq5IQSbvYo7GKLQi62KOxiB1d7K2j/+Q6NX2XrT3rCVifB0tISXbp0QZcuXXD58mUsWLAAa9asQY0aNdCkSROz+utZNBoNPv/8czRv3hxDhw5FYGCgSd4rUWi1Wvzwww+oWbMmevXqhaSkJOEaAFC4cGEcO3YM3bt3R3h4uCLXiUajwZgxY1CwYEFMmjRJsXqEFSpUwIkTJ9CyZUukpqYqomFhYYE///wTDg4OePDggSIaANC2bVvs3r0bffv2VayslpubGw4dOoQ2bdogJSVFEQ2NRoNJkybBysoKu3fvVuy7r1mzJgICAtCpUyfFCpLb2dlhx44d6NSpk2LnFwAMHDgQFhYWmDt3rmL9lRc0WSbu3aNmzZoMCgpSpG0/Pz8MHDgQixYtQp8+fWBlZSVc49y5c2jRogW0Wi0OHz6MypUrC9eIjIxE69atceHCBcyaNQvff/+9cI2MjAysXbsWffr0wYcffojdu3fDxsZGqEZmZiYmTJgAHx8fFCpUCLt370aVKlWEaoSGhmLkyJHYvHkznJ2dMXfuXPTu3TvP7f3999/o27cvTp06jTGTfXDyViTsS1ZDcKI1tJZi++e/oHzBfKhW1BlVizijWD4NXO2t4FnAFXaWOmi15huOw4cPP2f0YmNj4eLiYnbbLyM5ORn29vaKamRmZkKSJCH3lZz6yUhaWprwa/FZ0tPThSe4fRaS0Ov1ZvXXy/rJSEZGhiL3+jetYY5ObvrJXI3XQa/Xw8LCQrGHfSN5OZbX6SsjGo3mPMmar3qfOmP2DOvXr8egQYNQrVo1lC5dWpET78yZM2jZsiUsLCxw8OBBRUzZw4cP0aJFC9y8eROLFy82yeQtipiYGHTu3Bnt27dH3759sXDhQuH9FRYWhu7du+PYsWNo3bo1Vq1aJWS2bOfOnWjfvj1SUlLg4+ODmTNnIj09HQMHDsSUKVPg7u6eq3YMEnEtLB7Hb0fh1J1onLkXDb3hn4edRj+iWCNgXTIALwBpgNYyb583n40FSrk7oEA+azjYWCCftQXsrS3k/4+JfAqScHYrgOQMA1IzDEjOyERKugEpegOS0vSIiE/Do9hUJKWbPyvw9+NE/P04EX+dfXHR5sqFndDyPQ9UL+aCSoWckM8mjwf/D0qbMgCKmzIgayboTaC0KQOguCkDsmaC3oSZ+V/ReFM6b0LD0tK8e0ZueVPfS25RjVk29u3bh169eqFMmTLYt28fQkJChGucOnUKrVq1gpWVFQ4ePIiqVasK17hx4wZatGiBx48fY926dWYvyeXEnTt38NFHH+HmzZsYNGgQvv/+eyFPNXq9Xr4Y/f390bNnT0RHR2P69OkYM2YMtFrzq4j5+flh2rRpSE5OxqhRo/Do0SM0bNgQ8+bNe+H3kZyeiZtPEvEkIR1BoTFYH/QQiWl5MziWOg2aV/BAk3LuKOuRDyXdHOBoa+5TYXEz/vZ5JIlISNMjOjkD96OTceZeDM7cjcGlh3G5buPKo3hceRSf4+/qlnRFgzJuKORsCzcHa1Qs5Ahnu7fr5qiioqLyX6Aas384fvw4OnfujIIFC+LAgQMoUKCAcGN28uRJtG7dGtbW1jh06JAiM2UXLlxAq1atkJKSgp07d6JVq1ZC2s2+nHDixAl07NgRSUlJWL9+PQoUKCDElBkMBvTr1w/Lly/HpEmTMHXqVBQsWBCBgYFo1KiRgKP4d0aUJLp3747ChQvL5vXZY4hLycCaMw8wc/+N19Yprr8Pz8wncJbiYQED2rdvDysrK+FxWEqh1WrgbGcFZzsrlHJ3wIflPV74Xr1BwuP4NIREJODC/VjsuByOiPi0l7Z/6m40Tt2Nfu7nFQs5okuNInBMe3viPVRUcsIYkyTiYfFlpKSkwM7OTlGNhIQExWeLSeLp06cm9T6V4NGjRyhUqJDiy59K8v/amBnXlS9duoR27drBwcEBBw8eRNGiRYVpxMfHw8nJCcePH0ebNm1ga2uLgIAAVKxYUZhGUFAQatasiSNHjqB9+/bQ6XQ4ePAg6tatK0zjzz//hJeXF2JiYvDll1/CyckJgYGBqFu3Lg4fPixEw8fHBytXrsSdO3dw4sQJtGjRAqtXr0aBAgWEtL9nzx707NkTxrhKe3t77Nq1C1WqVEFYXCrO3ovGudBYrD2Tu0Djsh4O6FDFC+2reKGY66tvaqL66W3DUqdFkfx2KJLfDq3eL4hxH5kWVpYk4lFsKo7cikTg308R8PfTF7Z1LSwB18KCAQDDD+8GAOi0GnxSvRDql86aYSvqaocC+d79OL3XIftMspIaFy9eFF60+lm2bt2KsmXL4v3331dM4/bt21i9ejW+++47xZbANRoNvvvuOzRv3hzt27dXzAjs2bMHgYGB+PHHH+Hl5aWIhlarRatWrfDNN98otuHNWLg+IyMD48aNy3W4yOsSGRmJLl26YOrUqSYF7N8pcrN18218mZsuIzU1lf379+eNGzfo7u5OR0dHXrhwweQ95qYACAsLY9euXXnkyBE5a/K1a9fMavNZIiIiWKBAAa5bt47W1tYsWLAgr1y5IlzDxcWF7733HgGwfPnyJjl/RKRKOHbsGHU6nUmGeZEZzI8cOSIXzAZAS0tL1m3QiJ+OX8RiY3a98tVh/jEevfmU8al5L3vyv5J+RSQJqRkMCo3huC1XcvU9ZH95b7vKQ9cfMylNmcSwueXs2bNMS0tTVOPmzZvs1q0bz549a/Jz0efU8OHD2bRpUwYEBCiWouDhw4d0cHBg165dhd8Ps9OnTx86OTlx0qRJwhP7Gjl37hwBsFatWty3b58ifWYwGFirVi3a2Nhw5MiRjIyMFK5BZqXE8fX1Za1atejv76/IsURFRdHJyYkODg709vYWXq/UiDHNSrNmzXjmzBlFNNQ8ZgoYs99++41arZaFCxemra0tjx079tx7zL3p9e/fn1ZWVrSzs6OHh4ciJVm+/PJL2WyUKFFCkSSJXbp0kTWKFCnCp0+fmvze3H6Kjo5mkSJFTHJzFS1alJcvXzarXSNBQUH08vJikzYd2dd7LtvO3PvKQX/a7hA+jhebPV01Zrln274Arjh5j+3mHcu1Ueu97AxP3I6k4Z9cbWlpaTx37pziue9OnjxJLy8vTpo0SXhNzOz8+OOPBMAPP/xQHjhFn1NxcXH08PAgANavX18xs2EsKK3RaBQzaOHh4bS3tycAzp49m9OnT1ckD57RBOCfGoyHDx8WrnHs2DFZI1++fIqYGr1eLyddBcAmTZrwxIkTQjVI8pdffpE18ufPzxkzZuQ5Ie6LuH//Pq2trWWdTp06CR9/VWMm2JilpaWxcOHC8pfWs2dPhoeHP/c+c256ISEh1Gq1ssb3338v/Enn1KlTJmamQYMG3Lt3r1CNbdu2PVcvccCAASYFc83pJ0mS+PHHH8tt16xZk/PnzxfWVwaDxDWBl9nA59ArZ1/CYsXeHJ5FNWa5J6e+StNn0j/4MdvMOZprs9Zh7G8sX68lfXx/VdQ0GUviWFtbs0+fPoqUrElJSWGJEiXka6V69ercsmWL8NqYf/zxh8n1Xrt2be7YsUOoQUtJSWGxYsVkDaNBu3nzpjANkpw6dapcFB0A3dzc+McffwjVePDgAW1tbU36rEuXLsJLiXXu3NlEo0iRIsJXR7Zv326iodPpOH/+fKEaqampLFq0qIlOx44dzS4q/izGSgjZJy6enXE2B9WYCTZmxmy/xlepUqW4c+fO595nzkBqLPNifLVq1eq5pVJzMBgMrFmzpty+g4MDx40b99xsljnExcXJJXhsbGw4cODAHDNjm9NPCxYsoJeXF8eMGSP0iSYhNYPfrr3wwgG7woS93H8tQp5deROoxuxfbt26xaVLl74wM31u+yo5Xc9dl8NZe9qBXBm194Yu44AFuxgQEsF0vbhi7ImJiSxevLjJNd+0aVPhMw67d+820Zg9ezbnzp0r1DQZDAbWqVNH1nBzc+PixYuFG40NGzaYHMtvv/0mfEk4JSWFRYsWlY1Z165dTR4qRTFhwgT5OAoWLKhIaa9bt27RwsJC1lm3bp1wjcDAQDZr1kzW6NChgyL9tWrVKlnD1dVVkdWk2NhYuWoIIL4wumrMBBqz9PR02a3b29vTx8fnhTeDvA6kR48elU+GDz74QJE6f0uXLiUAOjk50dvbO0+1vl7F119/zYIFC3Lq1KkvncHKaz/p9XoeOXJEyBO/JEm88zSRPnuvv3BQbj7rMB9EK1MQOzeoxsyUkSNHEsgqjD569GgGBgbKg4A5ffUgOpkTd1zLlVFrOjOQ2y+FMSXd/HPQ39/fxGiMHj1akUEt+8zJ77//rshMYFBQEDUajawzbdo04UuakiSxUaNGdHBwoE6nY8mSJXn37l2hGiS5bt06+vr6skyZMgTAmTNnCtdITExkwYIF+cEHH8glfpSIBfvuu+9Yvnx5Fi9enJaWlty8ebPQ9gMDA3nx4kVqtVp269aNAPjJJ5+YVQ4rJwwGA6tXr85u3brR3t6e7u7uwmf/yKxi5dWqVZNLyE2fPl1Y26oxE2jMlixZQgDs1asXw8LCXvrevHS8JEmsU6cOK1SowC1btigSnxEbG8ty5cpxypQpihUqfvz4MVeuXJmrJ9j/0nCExabwx60vDhzvsvAknySIjRXLK6oxM8VgMPCTTz4xMTP58uVjly5deODAAWE6yel6Dp2zLldGrdviUzx9J4r6zLzNpvXp00c+DltbW27atEnYcRh58OAB7e3tOWjQIPr6+rJUqVJCi8kb6d+/P+fMmSMXlB4+fLiQ+p7ZuXjxIgcMGMBt27bRysqKhQoVYkhIiFANSZK4fPlyxsfHs0GDBgTAn376Sfi9edmyZQwJCaGfnx81Gg3ff/99RkRECNWIjo7mokWL+ODBA5YuXZo6nY5//fWXsPaN96gFCxZQkiR5ib59+/bCZzMDAgJ47949Hj9+nPny5aOrqysvXrwoVCM9PZ2bNm1iUlISmzRpQgCcNGmSkLZVYybImGVkZPCzzz7LdZHivHT82bNnuXz5cur1yu0Uu3v3LuPj4xVr/3X5LwxHRFwqG88IyHFwrTppP+9Fvn4BX6V5V4zZnj17OGnSJPr5+XHnzp08f/48w8PDhccykVnFimvXrm1izjZv3iy8ryRJYrdu3WhjY8NiJUvRrmw9lhq9/ZVGbcia89x28RHvR+VupjUmJoa1atXi33//zdKlS8tP6UqYgMzMTG7dupXW1tZ0d3fnuXPnhGpERkby8ePHTE1NleNAe/fuLXwWMCYmhiR58OBB2tvb083NjefPnxeqYVy1SEpKkotjjxw5UvgSsLG9VatWUavVsmzZsnz48KEwDZKyRlhYGMuXL0+tVssVK1YIafvZ606SJI4aNYoA2Lp1a+FB+kZOnTpFR0dHuri4MCgoSBGN5ORkNm/enAA4YcIEs7971ZgJMmZpaWmv9cT3rgyk/zVvqp9SMzK5KejhCwfRgyGPFd+BZw7vyvlkMBhMYmaML61Wy3r16jEqKkqo3uPHj+X4LAsLC1pbW/Ovv/4SvnwSGxvLbt26MTo6mh999BEBsHHjxnwYFs71Zx+wxpRXx6n9FniL4XEvH5yMsyRRUVFs1KgRAfDLL78Ufjxk1jl17Ngxuri40N7eXvjmHyN6vZ59+/aVZ0+UGqBPnjxJZ2dnOjo65rhTPq9kv/ZSU1PlGOBBgwYJnwU0snHjRlpYWLBEiRKKLNGS5JMnT1ipUiVqNBr6+fmZ3V5O9yhJkuQdwc2bNxcea2jk3LlzdHZ2ppOTE0+fPq2IRkpKClu1akUgKyWTOeOFaswEGbPX5V0ZSP9rlO6nqMQ0Dl59PseB8qs/zzE5/b/NY5Vb3rXzaePGjbSzszMxZ6NGjRJuzEgyODiY7u7uvHbtGuvVq0dfX19WrFhR+A3aaCgMBgOnTp1KjUZDT09PHj16VH5PYpqeS47eeaVJG7bu4itTqqSnp/OLL76QTaDovjOeU8HBwSxSpAgtLCz4559/CtUwkn32pGHDhorloLp06RILFChAW1tb7tu3T0ibz157GRkZcgxVr169FFvh2LFjB62srFi4cGHeuHFDEY2oqChWr16dAMzeQfmye9TkyZMJZKXRUCLtCEleuHCBrq6uzJcvnyKpOsgsY258MBs1alSezZlqzFRj9lajVD/pMw0cvCZnQ7b3qtjYjTeB6H4yGAy8du0aly5dyq+++oqTJ08W2j5JXr58WZ7NsrKyklNCfPHFFzx9+rTQGUpjfInBYOCGDRuYL18+ajQafvvtt8K30hs5cOAA3dzcqNPp6Ovrm+PxPIxJ5vD1F19q0uoEgSLFAAAgAElEQVRMP8i9VyOYmEOyW0mSOH36dAJgmTJlhA7Q2c+pR48esVKlSootnxox5qGqWrWqIrsPSfLGjRssUqQILS0thcTp5XTtZWZmyrOAn376qSIzmmTWphBbW1sWLFhQsYS6sbGxckiAr69vntt51T3q559/JpCV406pcJrLly/Tzc2NDg4OPHLkiCIaaWlp8qzpsGHD8nStqMZMNWZvNaL76Ul8KnsuPZ3jABgR93YE8ucFc/tJr9dzz5499Pb2ZosWLejo6GgymzVz5kzu37+fQUFBvHfvHhMSEoQMzpGRkWzatCknT57Mffv2sUOHDnKOvurVq3PJkiVMShIb0xcYGMiHDx+yY8eOcs6mXbt2CdUw8vDhQ9atW5cA2Llz55cOOJkGif7Bj1n2xz2vzIsX8PcTk00EGzdupI2NDV1cXIRdM8+2Exsby8aNGxMABw8erEhcIJm1K1yr1bJ06dK8d++eIhr3799nmTJlqNVqzZ4FfFF/GwwGfvvttwTAjz76SLEl2sOHD9PBwYFubm5C0yZlJz4+nvXr15d30eaF3JyXs2bNkjMOKLX57Nq1a/Tw8KCdnR0PHTqkiEZ6ejo7depEAPzmm29e+16pGrP/wJidPHlSsYHASFxcHOfNm6doXJQkSVywYIFiT7Zk1gl64sQJs59sQ6OS2PCX5wP6uy4+yZT0TD5+/Jg//vijYoMNmTWwjRgxQliC0PPnz8uxMoGBgUxMTOS2bdvYv39/jhgx4rXbCwkJ4ahRo+Ts7K96WVlZCRk4MzIyTJIz3r9/n+PHj5c/R//+/c3WyI7xpidJEjdt2sSCBQvS3t5esXI06enpHDp0KAFw7ty5uf67R7EpHLQq6KUmbezmK7zzNGvp5+zZsyxYsCCrV68uJLYpp8EhNTWVXbp0oYWFhfANAdnZvHkzraysOHz4cMU0Hj9+zMqVK7No0aJmmf+XDaKSJHHs2LEEoOg9/+TJk3RycmK3bt0U00hMTGTTpk3p4uKSpx2huTUb8+fPJwAuX778tTVyy/Xr1+np6ckmTZooNkZmZGSwS5cutLW15d9///1af6saszdszK5du0YXFxfOmzdPsentuLg4OedN9vgWkRgMBg4bNowAOGTIEEU0yKwbtLW1NQsXLszU1Nef0TIYJI7ccOm5AW3w6vPM/CcB7MGDB+nh4UGNRqNIyRO9Xs+FCxfSzc1NDgw1h5SUFI4ZM4Y6nY6rV6/m7Nmz6efnJy8HajQatm/fPs/tZ2RkcPv27ezYsSN1Oh0tLCy4Y8cObty4kYsWLeK0adP4/fff84svvlBsGZDMMjTr168XnoPo2ZteTEyMYvUOs3Po0KE8G6bUjEz+Hnj7pSZt9MbLvHbzLkNDQ4V83pfNBCkVQJ2d8+fPK5KrLTsxMTG8deuWWW3kZhBV0sQauXbtmmKzckZSUlLynLD1dcyG6J2zOXH79m3FZuWM6PX6PD2Iq8bsDRqze/fu0cvLiw4ODty9e7ciGtlN2bx58xTR0Ov1ch3NTp065ckwvQpJkjhp0iT6+vqyfPnyr51LSZIk/nH8bo4B/Rn/LAFlZmbS29ubGo2GHh4ewgbn7Fuy/f39WbFiRQJguXLluGvXLrOe0I4cOSIns8z+mjNnDj///HOuWbNG6MxPREQEZ86c+UaMy5viXQ8jyMg0cM+V8FduHshtGo4X8a7305tC7afcofZT7lHSmFlARebp06do2bIloqKisGfPHuh0OuEa8fHxaNWqFc6cOYP58+fjm2++Ea6RlpaG7t27Y9u2bejTpw/8/PxgYSH2q05PT0e/fv2wevVqLF68GCdPnoSLi0uu/tYgEevOPcCPW6+Z/Pw9T0ds/roubK2yPmtYWBh69OiBI0eOoHnz5li9ejU8PDzM/uynT59Gu3btcPLkSYwcORI7d+6Ei4sL5s6di6+//hqWlpZ5ajchIQFjxozBokWLTH5erFgxrF27FhkZGfjuu+/M/vzPUrBgQYwcOVJ4uyp5x1KnRZtKngj1aQtJIg7ffIq+fwaZvGfrxTBsvRgGAGj1vgc+qV4YdUu5Ip9N3s4/FRWV/w1UY/YPCQkJaNOmDW7fvo0NGzagWbNmOHz4sFCNuLg4tGrVCmfPnlXMlCUmJqJjx44IDAzEiBEjMHPmTGg0GiFtk4RGo0FUVBQ6deqE48eP46uvvkKZMmVybcqeJKThg+mHnvv5hQktkN/eCpMmTcKECRPg7++PXr16ISYmBlOnTsXYsWOFGOVLly6hTZs2iIuLw/vvvw+SGDp0KH766Sfkz58/z+1GRERg7NixuH//Pho2bAhJkiBJEgwGAyRJQnh4ONzc3Mz+/CrvHlqtBh+W90CoT1uQxOGbkej75zmQ/75nf/AT7A9+AgDoXK0Q+jYogYqFnP6jT6yiIh7+c8KLGo9ehCRJ0Gq1imoozf9rY2Y0Gmlpafj4449x4cIFLFq0CJ9++qkwDYPBAJ1OZ2LKFixYgCFDhgjTCAsLQ6FChRAVFYU2bdogKCgI06dPx9ixY4VdBJcuXcKdO3dQsWJFtG3bFnfu3MGMGTMwcuRIHDlyJFdtrD3zAD9svWrys91DG+B9r6wBaM+ePZg4cSLu3buHFStWwMvLC4GBgWjUqJGQY7h+/TpatmyJuLg4AFk3iMDAQDRo0MDstj09PbFixYqXvke00Vd599BoNGhargDu/dwWABD491P0+fOcyXu2XAzDln9m0ny7VEG7yp6wsRQ/e/8smZmZ0Gg0iqwUZOfmzZsoU6aMogN0aGgoEhISULlyZcU0JEnCn3/+iU8//RSOjo6K6ezcuRP29vb48MMPFdOIiIiAn5+fkHvhy5gyZQqaNm2Khg0bKqbh7++PixcvYujQobC3t1dMR0nebVtpJrNmzYLBYECPHj0QGBiIKVOmYODAgcLalyQJw4YNQ1xcHFq2bKmIKTMYDOjUqRMuXbqEhg0b4vz581i4cCHGjRsn7MaXmZmJr776CnPmzEGdOnUQHh6OzZs3Y9SoUbnSiExMR/Gxu01M2fi2FRDq01Y2ZY8ePULv3r0BACtWrEDr1q1x6dIlYabs7t27aN68OSIjI+Wf2dvbY9myZUhNTRWiofL/E0mS8vy3TcsXQKhPW9z7+SMs6lnjud+P3HgZ5SfsQ52p+/Hn5t3yrIMS6HQ6DBo0CCtWrIBer1dM59GjR6hRowa2b9+u2PEULVoU/fv3x2effYbg4GBFNLRaLXQ6HUqUKIEZM2YgOTlZEZ3GjRuje/fuaNasGU6dOqWIhqenJ2JiYnD16lVMnz4dSUlJwjU0Gg06dOiAxo0bo02bNrhw4YJwDQBo2bIltmzZglKlSmHBggXIyMhQREdRchOI9ja+zA3+v3fvHnU6nVw7a+jQoc8FfJsbCLlu3ToCYOXKlQmAv/32m1nt5YSfn5+c9NPCwoLr1q0TrjFjxgw5gN3FxcUkbQL54n5KTtez/4pzJgHPlSfuf65AtF6vZ8OGDU0C5StXrpzrmqav4uHDhyxevDhLlSrF3r17c/Hixbx27ZpipVhehBpYm3tE9NWbKs+1bNkyjh8/nmFhYULayzRIXH069IWbBjr/vIlxSVk7+0SfU5cvX6ZWq2Xx4sW5aNEi4YWrjXTu3FlOUrt161ZFvqvjx4/LO6CXL1/O69evC9cwGAxy1n0PDw/OmTNHkY1WCxculO+Nbdu2VSQXWmRkJGfPnk0ALFCggGLHYqyEAYBdunRR5Hs5fPiwrFG8eHGuWLFCeJoldVemAsZs0KBB8hdXq1atHE9Ac2566enpLFWqlKzRu3dv4SdGTEyMnN4B/5RJEZV/y8itW7doY2NjYpo6d+5sklPo2X6SJIl/nbn/3IBy83HOaRvGjx8vt+3k5MT+/fvz6NGjwozTlStX8pTTRzSqMcs9IvoqIyODw4YN47JlyxRNGaLX61mjRg1aWFiwW7duPHXqlDCjkabP5KQdwS/OkbZ8P+NSxKarMCZcBUAvLy/OmTNHeH3Eu3fv0traWtapUqUKt2zZIvxhqWvXrnI2fK1Wy549e/LmzZtCNbKbAAAsVKgQFy5cKDTVkl6v53vvvWei8+mnnwov82ScTDC+ihQpwpUrVwrVePjwocmYotVq2bdvX+GVBNq3b29yLO+99x7PnDkjrH3VmAk2Zo8ePZLzSRmfqIYPH/6ccTJncFiwYIHJSeHs7Cy8hp0xIabxVa9ePe7bt0/YoCBJEps0aSK3X7VqVa5YseK5p+js/ZSRaWDjGQHPpQV4EQcOHKC1tTU7dOjAjRs3KvKE9ragGrN/SUxMfOl5Kqqvbt68SXt7e9rZ2bFXr15m5Sl7GVeuXKGlpaXJw96qVauEDs5PE9JYa+xfLzRpq0+H8mmC+TNcsbGxdHd3N7m3fPzxx8LNrbEwtvHVqVMn4fnwQkNDaW1tTV9fX+KfeqUHDhwQqkFSziBvnG3atWuX8Pxue/bseS79juicaAEBAXIJNiCrYH10dLRQDZL84YcfZI38+fMrMmsWEhJCnU4n6/z+++9CZ2ZVYybYmA0fPtzkBvoiF53XwSEhIYEFChQgANrY2HD06NGMiYnJ8+fNiatXr8onXePGjXno0CHhywF+fn7UaDTs2LEjDx8+/ML2jf10NzLpucHiZQOFwWDgpk2bFMvm/rahGrN/efr0KRs1asTevXtz9erVz1WmENlXK1asMBnQihYtygkTJvD+/fvCNEhy4sSJJjp169YVngw5NTWVZcqUoZVn2ZfW7Vx1KpSpGXmfoV++fLlJ+EL2vH+iSEpKYqFChWQdpYqJ//jjj/T19aVGo6Grq6six3Lz5k1aWlrS1taWADh8+HDh92NJktiiRQvmy5ePOp2OpUqVEn4OBwYG8q+//pJnSzUaDZcsWSJUg8wqH+Xu7s6SJUsSAD/88EPhZd1IcuDAgXR3d2f+/Pnp6OgoLDyGfMeNGQAbAGcBXAYQDGBSDu/5EkAkgEv/vPq9qt28GrOnT5/S1taWrq6uXLJkyUufnvM6OPz000/UarXs168fHz58mKc2XoYkSWzatCmbNWumSBZ8MuvC8fb2zlXS2EMBAfxhy5XnMpyrmKIaM1Nu3bplshRftWpVjh49mgcPHmRAQIAwHUmS2KNHDxPT5O3tLXwgSE9Pl4uIG42ZEqXQDhw4IA+cM2b6ssW3Pi80aVN3BTMm6fVn7QwGAz/44AO2b9+ezs7OzJcvn9DvxMiaNWvYuHFjuZj4xx9/LHzWPDExkfPnz2dAQACdnZ3p6OjI48ePC9Ugsx74t27dyo8//pgAOGjQIOGzs5cvX+bgwYO5ZcsWWlpaslixYrxz546w9gMDAylJEjt27MgnT56watWqisVH//bbbzx69CgnT55MAGzUqBETExOFakRERHDcuHG8dOmSXBjdWCLPXN51Y6YB4PDP/1sCOAOgzjPv+RLAgtdpN6/GbPz48Rw8eHCupmfz0vGPHz9mr169GBISkodPlzvu37/PEydOKNb+6/AgOvm5weBupPgnn/8F3hVj9uTJkze2pHzq1Cl5lsH4+vLLL4UvN8XHx5vEfJYoUUKRmZOgoCBaWVlxypQp1Gg0LFq0qPDlOZLs0aMHHzx4IM9stWvXjo8iY9l81uEcDVqNKf689eT1Br2goCCeOHGCV65coaenJ62srLh582ahxyFJEo8cOUJJkuSVjGbNmgkfoPft20eSvHTpEt3d3WlnZyf8HIuJiWFaWhozMjLYrVs3AuAXX3whPLbYWKJo9+7dtLa2ZqFChYTFmhnvUcaYwpiYGNaqVYsAOHv2bCEaRjIyMuS+8fHxIQDWr19feKyZcUn56tWrLFCgAO3t7YVMaLzTxsxEDLADcAHAB8/8/I0Zs9cpG5SXjle6btzbxMUHsSY3/6a+gW9sJ9y7yLtizC5dusQSJUrQ0dGRpUuXZv369dmpUycOGjSI3t7ewmeBtm7dSo1GI5um5s2bywOpSM6ePUsPDw9u2rSJjo6OtLKy4sKFC4Wfs+vXrydJ7tq1iw4ODnRwcODOnTuFahiNS2BgIEePHk0ArF27Np88eUKSDPj7yQtn0RYevi3XoM0t9+7dY+nSpanVaunn5yf0WIxIkiTPntSpU0dobFP2a+/69essVKgQraysuGPHDmEa2cnMzGSfPn0IgF27dlVsXDhw4ABtbW3p4eHBa9eumd1eTveouLg41qtXjwDo4+NjtsaLmDVrFgHwgw8+UKw+ZkhICAsWLEhbW1uzS9i988YMgO6fJcokAL/k8PsvAUQAuAJgE4Air2pTySLmRt6VgfS/YO7BmyY3e/9g8Us2/2u8S+dTdHQ0W7VqZTKTBYATJ05URG/+/PkEwAEDBtDCwoKzZs3i1KlThQbPk+TRo0dJZi2jGpdpPv/8c+EzNEauXLnCYsWKUaPRcNasWcJNoPGcmj9/PjUaDUuVKmVS8Ds5Xc/Bq8/naNDq/XyI5+/H5PozPXnyhNWqVSMATp8+XbGHsLlz5xIAK1WqJGw39bPX3t27d1miRAnFUgyRWcvBgwcPJgB26NBBsdQjR44coYODA93c3Hjx4os3WuWGF92jEhIS2KhRIwLg5MmTzdJ4Gcb7QI0aNRTZdECSf//9N728vGhjY8P9+/fnuR0ljZkm671vBo1G4wxgK4BvSV7L9nNXAEkk0zUazSAAn5F8Ls2xRqMZAGAAAHh4eNRYt26dop83KSkJDg4Oimq8a6QbiIEHUkx+NrMO4e6s9tOrUOp8MhgMSE5ORmZmplllpXIiPDwcERER8r81Gg2cnZ3h5uYmPNt5WFgYvLy8kJ6ejqSkJNy/fx82NjYoVqyYIv1GEg8fPkRkZCRsbGxQqlQp2NjYCNfJzMzE7du3kZycDDc3NxQtWlRY8ufs51RcXBzu3r0LnU6HMmXKwM7OzuS9wVEGzAxKy7Gdj0pYokEhC3g5vDznuCRJuH37NhITE+Hh4YHChQsLOY5niY6ORmhoKKytrVG2bFlYWVmZ1V5O155er8fNmzeRlpaG4sWLw9XV1SyNF/Ho0SM8efIEjo6OKFWqlCLlgpKTk3Hr1i0AQNmyZZ/77nPLy+5R2b97T09PeHl55fnzvoyoqCjcv38ftra2KFu2rPA6z0BWreebN29Cr9ejdOnSebqX5eV+3rRp0/Mka77yjblxbyJfAH4CMPIlv9cBiH9VO+qM2Zvn1pNEkyfu+j6HSKr9lFtE9JPBYGBwcDCXLl3Kvn37skKFCvJsluj4HyObN2+mg4MD27Zty88//1xONVO8eHFOmzaN4eHhQnSyz8AEBgZy8eLFdHZ2JgD269dPsSfoVatW0c7Ojra2tlyxYoUiGqmpqfIGhCZNmgg7lmfPqePHj9PFxYV2dnbctWtXjn+TlPbiWbRWs4/w6qO4Vx6LMcC9V69eii3Tbd68mVZWVixcuLDZ6RRedO1lD3CfO3euWRovQpIkent7y9+9Ujn1goKC6OLiYtbmhlfdo1JSUti6dWsC4KhRoxSbNV22bBk1Gg0rVqwoL8+L5u7duyxWrFiel7Tf6aVMAO4AnP/5f1sAxwC0e+Y9ntn+vxOA069qV2ljFhUVZfYa9KuQJIl///23ohokGRwcbHYAanBYvMkNfNmxu/LvAgMDGRsb+1rxe3lBkiRhO2peRkBAgLAUHklJSXLSX+OFnJCQwG3btnHjxo2v1VZmZiYXLlzI0qVLP7fEaHzZ2NiwUKFCrFSpEps0acLOnTsLWQ4KDg7mjBkzSGZlCJ81axbLlStHANTpdJw0aZLZGtkx9lVERAS7d+8u54eKiooSqmMkODhYNrlK7EAjs87fqVOnEgCrV68uZMdeToPD9evXWaxYMep0uueqdDz7eV4WixYU+uIUP3q9nl999RUB8LvvvjP7OF6Ev78/7ezs6OnpadYu2pcNojExMaxTpw4BcNu2bXnWeBU///wzAfCTTz5RTMO4ucHBwSFP131uzEZaWpqcvHXRokV5+JS5Y8WKFdRqtaxXr55iBjA0NFRe0n5d8/+uG7PKAC4iK37sGgDvf34+GUCHf/7/Z2Sl0rgMIBBA+Ve1q6QxS05OZt26dfnbb78pFhcgSRLHjh1LKysrnjp1ShENkty7dy9tbW05atSoPLfhH/zY5IYdEm66a2bfvn0sX748S5UqpdhuvqdPn7Jt27bUaDSKbHUnswJD27VrRwAcMWKE2e3t3buXxYoV4/r163nx4kX+9ddfbNy4MS0sLIh/MlHnBaNB7dOnD+3t7Yl/kiQPHjyYPXv25EcffcQPPviAZcqUYf78+YU9cT57czTuqOvRo4fw2bpnb3r79+/nDz/8IFTjWRITEzls2DDFzJ+RjRs3CtsM8KLBITw8nJMmTcr1gBaZmMamvoE5GrQN5x7k+DeSJPHnn39WJCVQdk6cOGF2HNirBtGEhAROmjRJ8c1bixYtUvxhPDg4OM8bNHJrNtLT0zl58mThFSGeZd26dS99uBDBgwcP8rTj9J02Zkq9lDJmer1efhow7q4SjSRJcubjtm3bKmb+1q1bR0tLSxYpUiTP26mn7jItB/Ns+Zdjx45xzpw5tLa25tq1a0V87OcIDAykl5cXAXD06NFCbp7h4eFyYPmTJ0/49ddfU6fT0cLCgt9++61ZM2ZPnjzh559/Ls9iOTg4EMgqC+Ph4cHevXtz7dq1QmblEhMT+ccff7BRo0bcsmWL2e29LajL47lDdD9lGiQuOnw7R4P2/fpLTEwTnwD2TaCeT7lD7afcoxqzN2TMJEliv3795PVzJU5SSZLk2pAfffSRYqZs8eLF1Gg0LF++PB88yPmJ92XoMw1s8Mshkxvzs8XHV61aRSsrK86ZM0eRvGp6vZ7e3t7UaDR0d3cXlkLhyZMnrFChAh88eMDp06czX758cnJLc/IBSZLE5cuX08XFxWR50d3dnT///DP37NmjaOF00eVZ/kvUASJ3KNlPQaExORq0Sj/t49l70e9Uahz1fModaj/lHiWNmfjtDu8wEydOxNKlS9GzZ0/4+Pjg6NGjimhMnToVrVu3xubNm2FtbS1cw8fHB+PGjUONGjWwd+9euLu7v9bfk8R73vuRYZAAAJY6DW5N+0j+vSRJ+OmnnzB16lS89957qFChAurVqyfks2/duhVNmjRBUlISevTogWPHjqFZs2ZYtWoVPD09zW4/OjoazZs3x/Xr11G9enVERUWhZs2a8PX1RePGjfPcbmRkJIYNG4b9+/dDkiTY2dlBr9dDr9cjMjISRYoUga2trSI7sozY2toq1rbK/z9qFHNBqE9bxCRnoMuik7gTmQwASEjLRJdFpwAAo1uXQ/daReFib96uSRUVlX9RbpR4x1i8eDEmT56Mli1bYtmyZYoMoJMmTZI1tm7dKmxrfnJysuy0x4wZg3HjxqFx48YICAjIkykrMW6PbMrqlMyPW9M+QkJCArZs2YLU1FR0794dU6dORcuWLXHy5Emzt7IbuXv3Lvr06YOZM2eiatWqOHnyJKZPnw5/f38hpiw2NhYtWrTA1atXAWRty/bz88OZM2fMMmUA4O7ujjVr1iAqKgpxcXFITk5GRkYGSCIzMxNdunQx+/OrqPwX5Le3wqERTXB7Whv0rlvM5Hcz9t1AtSkHMMv/BpLSM3PVniRJSnxME+Lj4xXXkSQJd+7cUVQDAC5duoTU1FRFNZ48eYLz588rqkESW7duVfxYTpw4gWvXrr36jW8x/6+NWUBAAJKSkrBt2zYMHjwYNWrUwKZNm4QZDQBYuHAhJEnC5MmTMXHiRLRo0QLbtm0Tmi9p/PjxCAkJwYABAzBjxgy0b98ee/fuzVNulhLj9sj//2W94lg3oC4AYOzYsViwYAGaNm2KDRs2YPDgwdi9ezecnJyEHEN6ejo+++wzxMfH4+eff4aDgwOOHj2KcePGCTHJ8fHxaNWqFS5evGjy83Xr1iExMdHs9l+GTqcTek6p/P8jKioKer1eUQ2DwYClS5ciLi4ux99b6LSY3LEi7v38EWZ3rWLyu/kBt1Hxp/2YsisEaXrDS3X++usvzJw5E8nJycI++7OQRIsWLbB582bFDJpWq8XixYvRs2dPOYeYEtjY2KB8+fL4/fffkZGRoYhGgQIFMHbsWNy5cwfBwcGKaGg0GqSnp6NMmTLw8/NT7HyuXLkyWrZsid69e+Pu3buKaChObtY738aXuTFmkiSxbt26HDBgAG1sbFiqVKnnSs2Yu94eHh5OW1tbdunSRS41IzoOKDg4mDqdTg6O79mzZ56C4zMNkkkcydJs6TAOHz4sx0tptVrOnTv3uZxT5jJkyBCTuKwGDRrw9OnTZrdLZu24qlevHm1sbFi/fn2OHDmSmzZtUnw32bOo8Ru5513qq4CAAMXPpbi4ONapU4dz5swxqVIgup9WrFhBR0dHjhs3jk+fPn3l+58ty2Z8DVlznhmZOcdTpqens1y5cnRzc6OPj49iVRcWLlxIAKxSpQq3bt2qSExcbGwsXV1dqdPp2KdPH969e/fVf5QHvvnmGwJgsWLFuHz5cur14jdhXLx4kb6+vtRoNOzZs6ci6Y8kSWLt2rUJgKVKleKaNWsUibv9/fffCYCWlpYcPHiwsFyL2VGD/xUwZkeOHJFNgJOTk0kZEyPm3vQGDRoka9SqVUv41mJJktisWTNZo1y5cnmqY5iQmmFyU9128ZH8u5SUFJO8WTqdjt26dTO5aZvbT+vXrzcxZXXq1OH8+fOFpXk4f/48z507J7y8z+vyLpmN/xoRfaXX6xkQEKDIIJad+/fv08XFhV26dJELciuB8TpxcXHhjz/+yMePHws/pyRJYv369QmAtra2HDZsGB89evTKv7sflZyjQev023HGJj9/3e3du1e+3l1dXTl9+nThiVf1ej0rVqwo74iuVq0at2/fLvz7WbBggXwsFhYWHDhwYJ42XL2MyMhIOjk5yTply5blXy+dxP8AACAASURBVH/9JdzU/PHHH88dS26+/9fh6NGjJvf7SpUqCf9eMjIy5DyLxnN5zJgxjIl5cW6+10U1ZgoYszZt2picHPXq1XvuCdGcm97Nmzep0+lMNEaMGCH0QtqyZYtJ+/ny5aO3t/drDURxyaambN8106SExgLJAGhvb88hQ4Y8t3PR3H7Kly8fy5Urx8mTJyuepPa/RDVmuUdUXy1cuJAeHh4cPnw4L168qJhpWrx4sXydVKlShUuWLFHkQSz7fcva2porVqwwaydxTly6dIlarVbWsbKy4sCBAxkX9/KKACQZnZTOhr8EPGfQakw58FxFAWNaIuPL09OTQUFBQo/l4MGDsjEz3sPmzZsnVEOv15tU4LC1tWW/fv2EzwTOnDnTpL86depkdm3MZ/H396etra2sUb16da5bt074dWOsHAGAzs7OnDVrFuPj41/9h6/Btm3bTPpr8ODBQnPIqcZMsDG7ePGiyVPBmDFjcswqbc7g0LVrV5Mb9b59+4Se3CkpKSxevLg84+ft7f3aZV70mQaTm+eBZwqRnzt3jlqtlsWKFaOvry9jY2NzbCev/SRJEleuXMmgoKB3aut9XlGN2b88evSIixYt4o0bN3L87kX1lSRJcigBAFasWJEzZsxgWFiYkPaz6zRv3txkIHBxceH27duF6ty9e9dk4FywYAFXrVol/Pr59ttvZQ1HR0eeP3/+tf4+JT2Tny06meMs2ubzD5makclbt27J5b0AcMmSJUKPwUjHjh1lY9akSRNFlk737NljYszMKY79ItLS0liiRAlZ5/PPPxc+GxwYGMgJEybIGgULFmRwcLBQDZK8ceMGLSwsqNFoCIA+Pj7CNSRJYsOGDeUJklq1aqkzZkq/zDFm3bp1IwA2btz4pSddXgeHoKAgAmDRokW5cuVKRdbQJ0+eTGdnZ06aNOmFhulVZL9Z+j9jyjIyMjhkyBBu2rTplRe/ajhyh9pPpsyaNYsAWLhwYX7xxRdcuXKlbJhE9lVcXJzJgAZk1fk0lsoSxb179+RkwgDYv39/RR44fHx8ZI1ff/1VWH6/7MTGxrJAgQIsUKCAvKKQl/qe+kwDv14d9EKDNnrMGHp6erJMmTLUarVcvny58GO5desWZ82axa+//poAWLdu3TzfM1+EJEls2bIlhw0bxsKFC9PKykq4KSezlrNbtGgh59v85JNPhIZoBAYGMiEhgUWLFuX27dtpb29Pd3d3Xr58WZiGkSFDhnDhwoVs1KgRAXDy5MnCNc6cOcOOHTvyt99+k2cARVX2UI2ZQGN269Ytenp65uopM6+DQ7du3Thz5kzFyhPFx8dz9uzZeZ76NTwT6L/nyvOBka9jJlXDkTvUfnqeESNGmBgmAKxWrZpws3H27FlaWlrKGkOHDlWk/I4x4NwYl9mvXz/hsY0ZGRmsWLEif//9d86bN486nU4RQ/Pnn39y+fLlnD17NgHw/fffz/MmB4NB4g9bruS8UWDibD5+/JhVqlSRzaZoNm3aRJLysVStWjVXmxteh2vXrvHBgwe8e/euXH/R3FJSzyJJEk+fPk2DwSBvCGjfvr2wscZ4j7p69SrJrHJYjo6OzJ8//2vPmr6Kp0+fMjY2lklJSXKs9Pjx44U/zISGhpL8N9ygSpUqQr571ZgJNGanTp3K9dNSXjo+PT1d6HSpaJ7dfbkxyPzdZKrhyB3vSj8dO3aMQ4cO5eTJk/n7779zw4YNPHToEC9fvsywsDChRsNgMJiUrwLAadOmKdJXv/76KwHIg0CdOnXkm7YoJEnixx9/zMTERPbs2ZMA2KhRIyHlt7Jz5swZpqen09/fn5UrVyYATpw4UeigZjAY5ID81atX08LCgkWLFn3tYs/ZkSSJv+y9nqNBu3w3XN54MGHCBKHHkv18Wrp0qVwVRXRgu5GHDx+ybNmy1Gq1/PPPPxXRkCSJo0aNIgC2bNlSSExjTtfd2bNn6ezsTGdnZ2E75Z8lJSWFrVq1IgCOGTNGsdCW5cuXU6PRsGLFinnaKJcd1ZgJNGavw7sykL4O2QsV/x4oJtD+f7GflOBd6qdVq1aZxDJlj5eMiIh4dQOvQXp6uhyfZVwK9PPzEx7Ubiy5JkkSfX19aWFhQRcXF+7YsUOojjEljrHIt0ajYYkSJeRZCJEEBgYyPj5e7r++ffsqVoh7z549tLOzo6urK8+cOWNWW5Ikcf6hm8+Zs/e997L5Rx0IgN9++62wMJBnr71169bRwsKCJUqU4J07d4RoPMvjx49ZqVIlAuDChQsV0ZAkid7e3sLi5150j7pw4QJdXV2ZL18+Hjt2zCyNF5Gamsp27doRAIcPH66YOVu5ciW1Wi3Lly9vVhoN1ZipxkwIM/f9Ld8AR20UF1/zv9ZPSqFkP2VmZgo3MpcvXzZJlQKAH374Ibdu3Sp88I+Pj2e1atV4/vx5jh49mrNmzaKVlRUnTJggNPdf9njJU6dOsWjRogTA77//XrF0Ktu2baO9vT0dHBy4c+dOoW0bz6n09HT27t2bANiqVSvhqSeMnDp1ivnz56e9vb2QAHdJkrj4yPNF08uMWEeNpTV79eolJMA9p2tvx44dtLa2ppeXF0NCQszWyImoqCjWrFmTADhr1ixFNEhy+vTpcvxcbnbPvoiX3aOuXLnCAgUK0N7eXrF7WXp6Ojt16kQAHDJkiGK1hdeuXUudTseyZcvmedZUNWaqMTObQ9cfyze9ZrMOC237f6mflER0QPv+/fs5ceJEtmzZko6Ojhw7dqyw9rPrGLe2FyxYUJ5F8/Dw4KhRo8xa1nqWiIgI+Yl/7969clBwyZIluWfPHmE62YmOjpbTNnzwwQfClzaNXL58mcWKFaNGo+GMGTOEzQZkP6ckSZJ31FWrVk2RpJokGRISwsKFC9PS0pJr164V0qYkSfQ7cuc5g+bZZz7bdfrU7BiqF117Bw8epJ2dHd3c3HjhwgWzNF5EXFycvEQ7ZcoUxWaCjEv1NWvWzNNGDfLV96iQkBB6enrS1taW/v7+edJ4FRkZGfJO6gEDBihmzjZs2EALCwuWKlWK9+/ff+2/V43Zf2DMJEl6I4YjMzNTcY0rD6JNbnaiCQwMpCRJbySBq+jKCTkRHx8vdBu6MZYh+/mUkJCQY1Ljl2EwGLh8+XJWqlRJ3mae/dWgQQN269aNX3/9NX/88UfOmjWLf/zxh9n5gSRJ4i+//PJ/7F13VBTXF75badIEaSoWFLEQezeIGjW2WBMTC/YWYwtqsMfeQCxRiaKxxN6VIqhgwYJdAXsBQUABBSlL2/l+f5CdsIC6sm8sv+x3zp5DvXfmzpv3vnffLejbty9SU1Ph4+ODxo0b83pbtmyJQ4cOaaWjKFRjatu2bXxmYO/evbXyBrwNHMdhxYoVkEqlMDMzEyTLEQBevHjBL9CDBg1isuCUNEdt3LgREokElSpVwoMHD7TWURKePXsGJycnEBHWrVvHVPa60OIeNMexG/AkofSxu++ay8+fPw9TU1OYmppqfUT7NmRkZKBt27YgIsyYMUMQHcC/Fe+/+uqrUmUfarLmPXjwABUqVICenh4CAwNLcZXvR15eHh97OmTIEMHI7MGDByGTyVC5cuUPLgqsI2afgJh5eHhg69atglYNP3nyJJydnQVt53LzfrTaBCfEAA8JCcHw4cPRq1cvwXY3HMdhzZo1sLW1ZV5VW4WcnBysXr0a5cqVw59//qm1vMTERPTr1w8LFy5Efn4+/P39MX/+fLi4uEAqlcLFxaVUcqOiojBlyhTY2NioETN7e3sYGxsXI2ysApyL7ipv376NiRMnwsLCAkuXLmWiQ4XCk96rV6/w888/o1GjRoJuZC5duoTq1avjypUrgunIzs7G4MGDMXXqVCby3rY4BAQEoEmTJoImIiUnJ6NVq1aCEFmO49RCL1SfHmvDcD/xw49p37eIXr9+HY0bNxZsbgEKNpXdunXD33//LZgOANi0aRN69uxZqnADTcnGkydP0KRJE0FqnKmQn5+PQYMGwdvbWzAdQMGR9jfffFNiLdN3QUfMPjIx8/Hx4QseCkXMTp8+DQMDA9jZ2QlW7f7RY/Wjgew89otaSkoKn4Y8YMAAQbxmSUlJ/HFTgwYNmATr5uXl8XE4HMdhz549cHBwABGhZs2aWi02SqUSf/75J8zMzPiAeXNzc77Ipa2tLdzc3LROpc/Ly4Ofnx/69OkDmUyGkJAQAAVHAS9fvsS9e/dw4cIFwYLBVcjOzv7gSe19KGnS+xgeWaHbNwEF402ooPbCEGqTVBhCF4bmOA4eB24VI2idV53FxcfJGuvXZBH9GEWuP1Yh7dLq+RCy8V+3l5DETEw6qCEgIIB+/vlnatCgAVWtWpWkUilzHWFhYdSlSxcyNTWl0NBQcnBwYK4jKiqK2m24y39/waMt6UklTHU8ePCAmjVrRunp6bRgwQLatm0byeVypjpCQkKobt26dOzYMXJ3d6eLFy9S1apVtZKZn59PAwcOpLt379Lp06epadOm1LdvX8rKyqKNGzfS7du3qWPHjqWSHRERQV9//TWNGjWKUlNTiYjo7t271LRpU6pYsSJFRETQ8+fPaevWrdS3b1+t7kMqlVKXLl1o3759lJCQQGZmZkREJJPJqFy5clSjRg1q3rw5yWQyrfS8D3p6emRkZCSoDiJiPrZKghDve1GIRCISi4Wfej+GDpFIJLj8xb2+okcLO5FrjXL8z6Pi39CPGy5R59Vh9OhlBjNdQuNj6PhYev5fdHxMPZpC+FnoC8K1a9fohx9+oIoVK5K/vz/du3ePuY5Lly5Rp06dyNDQkEJCQsjR0ZG5jitXrlD3OVtI/lVnIiLyGdCQ7MwMmOoIDQ2l3r17k0KhoKpVq1LPnj2ZyH38+DHl5+dT1apVac6cObRkyRIqV64cHT9+vNRkqTCUSiUNGjSIdu/eTZGRkRQZGUnGxsa0YMECmjhxYqkJRmZmJs2bN49WrFhB+fn5xX4/depUEolEVKdOHW1voURYWFiQhYWFILJ10OFTQyoR05YhTSgnX0kdvc9SdEoWERHdTXhD36w4Q/2a2tPsrrVIX8Z286mDDp8COo/ZP4iJiaGuXbuSVCqlgIAAsrGxYa7j6tWr1LFjR9LT06OQkBCqWbMmM9lKpZKICghTB7fxPClr62RF39bR/l4A0MmTJ4mIaNOmTdShQwfS09Ojs2fPkrm5udbyiYgUCgX16dOH9u7dS19//TUtXryYOnbsqJUHqzCUSiUNGTKEdu7cSUREkZGRNHr0aHr8+DHNmDFDK6+PXC4nDw8PiouLo5iYGHrw4AFFRkbStWvX6PTp02Rqaqr19eugw38delIJnZ7ShiJ+76D2853hz8hp1nHadzX2o10LAOI4TnA9CoVCcB3p6emUl5cnuJ74+HjBdURHR/Pr4ZeK/zQxUygUdPfuXXr9+jV16tSJUlJS6PDhw1SrVi1mOi5fvkzJycl048YNat++PUkkEjp58iRTz0lAQAAFBQXR0aNHqXPPH8i0+0z+d5sHN2aiY8+ePfTbb7/R1KlTafjw4VS7dm26fPkyNW7MRj4R0YQJE+jmzZs0e/Zsun79Onl5eZG/vz9ZW1trLVupVNLQoUNp+/btaj+/evVqiR6uD4VMJiNzc3OytrYme3t7ql69OtWuXZsaNGhAzZs3pwYNGmitQwcdhATHcRQXFye4ntDQUHr27JlWMoz1ZRS9pAtd8Gir9vMp+29TZQ9/Onn9IS1dupTS09O10vM+TJ8+nY4ePVoQsC0QTp8+TaNGjaLYWOFIp0wmoy5dutCrV68EJZu+vr40cuRIQe8lLy+PGjZsSAcPHhT0uQgKTQLRPscPi+D/P//8EwMGDICrqyuIqFi2DItyGW3btsW4ceNQtmxZmJqa4urVq1rLLIycnBw4OjqiXr16BSnyhQJk85VsAidfvnwJS0tLPsuvW7duahWmWdhp69atapmETZs2ZVb0UalUYvDgwXwtru7du2PBggUIDg7+qO2zdPXeNMeXZKuPUcIlJiYGCxYsKNbaibWdfv31VwwaNIhpfbqieP78OcqWLYsRI0bgyZMnTGTein1dYpsnC/vqWLRoEU6dOsVET1FERERALBajUaNGCAgIECRYneM4tGnTBnK5HOPHj2feeUOFXbt2wdPTE3Xq1MGhQ4cEuZc3b97A2toaenp6mDRpEvN+pSqo+og2atQIwcHBgtyLLitTAGKmVCrh6Oio1p+vKLSd9E6ePMnLNzY2FqTP2PLly3kdtj2m8hPS0yR2WXI//fSTGmkaPXo0nj59yv9eWztFRESotf8pW7YsRo4cibNnz2p34f/g1q1bOHjwIGJjYz9alk9J+JLIxqcGC1t9rGd99OhR9O3bF2fPnhVU58SJE2FgYICff/6Zr4HHeky9fv0aVlZWEIlE6N27N/ONpApLliwBEUEikWDIkCEfXNPvbfC/HV+MnNkN98E8rz+wePFirVsWlYTRo0fzc1fz5s1x4sQJ5uPg+vXrfO1CAwMDTJkyhXn/VY7jsH79ev5eGjdujKCgIOb3osrip39asM2cOVPj/tWa4uXLlzAxMeH1tGnTBhcvXmSqQ0fMBCBmR44cUSMbTk5OOHPmjNrfaDPpcRyHJk2a8PLFYjF69OjBdAAmJCTwdauk5nb8RLTgyC1mOo4ePapmpyZNmmDHjh1qpQu0sdObN29Qo0YNGBkZoX///vDz8/soZRE+BXTETHOwsJVSqcS0adOwbNkyQWsFAv9uXpydneHj4yMIAUhPT0fFihVBRBCJROjVqxf8/NgXjC7qve7YsSOzTZIK2dnZau2+xGIxBg4cyKStGMdxWH2yeB/Ocr1mwrJSDfzxxx9MyUZREkBE6NKlC/NiyEOGDFHTYWVlxbwgrp+fn5oOiUSCJUuWMLVXXl4eatWqVcxerMnZ4sWL1XRUr14dYWFhzOTriJkAxKxVq1b8A3NwcMCJEyeK/Y02i8OhQ4d4+VKpFOPGjWO+w1Edz5FYKkhl/9evX8POzg4SiQQ//vjjW3cc2thp586d2L17N/M6WJ8jdMTsXygUindO9qxslZSUhAoVKkAkEqFNmzbw9fVlvgAABcVWra2t+XfexMQE48ePx71795jqKbpR8vT0hLu7O9OaZRzHqc2PBgYGcHd3L1Ul+XehKAmYNm1aqVsJlYTcfCXcNl0qRtCm7r2O9Gy29eoKn1yYmZkxO6ItjOfPn8PQ0JDX4+Pjw1xHaGgoevfureZpEuKo3t/fX/DTpKysLH4jQ0SYPHkyU4KpI2aMidnFixd5wjR9+vS3DrzSLg75+fn8jqB3796CtEUJDw8HEcGldWu1SUfJKK4MKOh+MG3atPd6G3SEQzPo7PQv0tLS0LlzZ/zwww9Yt24d7ty5ozZpsrRVWFgYJBIJP0Hr6emhd+/ezL0NRb3w7dq1w7Vr15jqAKC2cK5du5YpmVHh1q1bajZbuHChIMe0nTt3hkQigVQqFayF1L7DxWPPKv3mhzP32cU3ZWdnw8HBAQ0aNIBYLEaNGjWYddwojLlz56Jy5cqoVasWRCIRNm3axFR+aGgoHj58CJlMBjc3NxAR2rZty3zjzHEc2rVrh59++gkWFhYwNjbGuXPnmOoACry/derUwXfffQciwoQJEwTpU6spdMTsHejTpw9atGiBiIiId/5daReHbdu2oVmzZkzdpoWhVCoxffp0nD59GvOPRfETzd0E7XoiFgbHcRo3DtYRDs2gs5M6Xrx4oRbnaW1tjb59+2L9+vUICgpiqmvp0qVqpGn8+PGCdERQLWZEBHNzc5w8eZK5jufPn8PExARff/01PD094eTkJIiHZuLEiRg1ahTatGkDIsK4ceOYdxO4f/8+OnfuDH9/f+jr68PKygo3btxgqgMoaFN07UFcMXLWcH4wUrPYjIMDBw7g9OnT2L17N6RSKapUqcL8uWRkZGDVqlV4+fIl6tatCyLCH3/8wUy+ao5SeePmz58PIsLXX3/Nd0phhRs3biAqKgq3b99GuXLlYGRkxHyOVCqVOHLkCHJyctCrVy8QEX7++WfB+tS+Dzpi9hYkJSVhw4YNGj2Y0g6Sq1evChoErJL98k02P8EM+euyYPreBx3h0Axfip3i4+Px/Pnzj5JtGB0dDTs7OzXS1K9fP+aERqlUokuXLnw8k56eHvNYI6Cgr6ednR127twJW1tbSCQSrF69mrmetWvX4v79+zh48CDkcjmsrKxw+TLbOSAtLQ03btyAQqFAnz59QETo27cvsrOzmeqJj48HAJw9exYmJiYwNTVl7j1RtSvLzs5G64GTihE0r2A2sW2qdeXo0aOQy+WoUKECk7i5onqAgnZ4jRs35o+0WaCkOWrZsmUgIjRr1kyQMACgoP+vjY0NDAwMSgwrYoHc3Fx8//33ICKMGDFCa3KmI2aMPWaa4nNfSIWIKysNPnc7fS74Uuz0/PlzfP311/yxn42NDWrWrIkWLVqgW7duzEspREZGwtzcnCdmdnZ2OHjwIHMyk5ycjIoVK+L8+fNo0KABiAg9evRgfhQYFhYGjuPw/PlzfuEcPnw406QWpVIJjuMQGhqKs2fPwtzcHIaGhjhy5AgzHYWRn5+PMWPGgIjwzTffMPeeqHD9+nWUK1cOBgYGCAgIYCa38LuXm5uLfv37w6LLr8UI2uWn7MZCcHAwDAwMYG1tjdu3bzOTWxipqalo0aIFiAjz58/XWt7b5qhVq1aBiNCwYUNBjs6BAu9p+fLloaenh8DAQEF05OXloV+/fiAiDBkyBPn5pe8frSNmOmJWDFP3/dvY91XGp81i/Jzt9DnhS7JTXl4ePDw81DxZKm8Wa48JAFy4cAEGBgYYO3Ys7O3t4enpCVdX1/eGG3wobt0qyFjOzs7GxIkTQUSwt7cXLOwgKysLAwYMABGhVatWePHiBVP5qjF19+5dVKlSBWKxmOnRVmFwHIe5c+fyCzTre1Hh/v37sLe3h1Qqxa5du5jILPruKZVKjB49GiK5YYnxZ7GvMpnoPXv2LIyNjVG2bFlcuXKFicyiSE9P54+bZ8yYodWG5l1zlI+PD4gIX331lWD1xx49egR7e3vI5XIcPXpUEB35+fkYNGgQiAgDBgxAXl7pEkF0xExHzNTwLCWTn0A8g9hmfZUGn6udPjewthPHcbhz5w58fX0xZMgQuLm5Mfcy+fn5qXmziArqzP3yyy/Mj+wDAgJw5coVZGZmYseOHZDL5ZBIJJg4cSLz0gMqHD16FGXLloVEIsHChQu12kG/DRzHYenSpRCJRLC3t2caQ1V4TCUmJvIeOtaZmoXh4+MDsViMatWq4fHjx4LoiI2NhZOTE0QiEdavX6+1vJLePY7jMHXqVBARWnTrX4ycjdp2FUnp2m9CLl++DHNzc5iYmAi6Afj2229BRPj1119L/V6+b47666+/IBKJUKtWLcEK3T59+hRVqlSBVCrF/v37BdGhVCoxbNgwEBF+/PHHUpEzHTHTETMeHMd9NkeYKnyOdvqcoHrpi9rpQydPjuMQFhaGRYsWoWvXrihbtqwaYRoxYgR27tyJwMBAXLp0Cffv38fLly+1XqCjo6PRpEkTNGvWDJs3b4aLiwuvs3bt2li+fDkfJ8QKquwwVVyYtbU1tm7dKgjZiI2N5Y9u27VrJ9iC4+fnB2NjYxgaGmLfvn1MZBYdUxkZGejWrRuICH369BEsTvDAgQOQy+WwsbERJFgfKIgHbtiwIYgIixYtEsQTxHEcFi5cyMdQzT98sxhB8wy6p3V5jVu3bsHKygqGhoaCJIQABV7g7t27g4gwZsyYUr0rmszlO3bsgEQigaOjoyCZpwDw7NkzVKtWDRKJBLt37xZEh8prqqqe8KHJQDpi9gmIWVBQEA4fPiyojsTERHh4eHwQW59XKAtTk8lCqVTCw8NDkDR0FUJDQ3HgwAGsXbtWMB1AQYeA/v37C3KUpsKdO3fQq1evYsWGSwOO47B161ZMnDgRQIGdwsPDsXDhQrRt2xb9+vX7YJlxcXFYsmQJnJycih0zvu1TuEtDaZGTk6N2RPb48WPMmTMHlStX5jP2WKLwpHfs2DFUrVoVZcuWFayFVl5eHubMmQORSITNmzcLogMoGF/VqlWDi4uLYJlh+fn5GDt2LAwNDQWLbVLpNjExwZw5cwTTkZaWBldXV9SuXVurkg3vW0RXrVoFuVyOU6dOITMnD5U9ih9vXo3WbuzdvXsX5cuXx8iRI7WS8y7k5ubihx9+gL29famOmjUlG/v27YNcLseePXs+WIemeP78OWrUqIHvvvtOsGQ6juMwbtw4WFhY4NGjRx/0vzpi9pGJWVRUFExMTLB69WqNS0Z8KFJSUuDs7AyxWKxxVW1Fbv6/1f39ot7797m5uXyg46+//qrtJZcIjuOwa9cuEBEcHR0FsRfHcVizZg309fVhYGCACxcuMJFbmODFxMRg6NChEIvFkEgk8PLy0kp2ZGQk71lq164dunfvDm9vb54sWVlZYcyYMaWWz3EcwsPDMWbMGJiZmYGI4Ovri5CQEBw4cAC+vr5Yvnw5pk+fLmjxXqVSidOnTzNrqaNC0UlPoVAIUhOsKCIiIgRv5ZSSksIsRuddnqAPXWhKg6dPnwpuL4VCgcTERK1kaLKIxsTEqH1/Oza1GDn7bf8t5OaXnlA/f/681DFNmiIvLw/Pnz8v1f9+CNl49uxZqXR8CF6+fCnYGqwCx3Gl6gyiI2YfkZi9fPkSVapUgZGREdOsoMJITU1Fo0aNQETYsmWLxv/3IUeYCoWCL6o3cuRIQWJnsrOzMWjQIHh6esLFxYV5ZXCg4Hl07doVRIT69eszywjctGkTtm3bhqSkJPz666/Q09MDEeGHH37QKr09IyMDv/32G6RSqZrXqkyZMti4cSO8vb1x+/ZtpouZQqHAnj17sH37dmYyPzV0x+OaQWcnzVBaXiCz6gAAIABJREFUOymVHGYdjihG0KKes6sZ+TlBN540h46YfSRilp2djVatWkEkEuHw4cOCDNL09HQ+vXndunUa/19Aoea8Canv3kGkp6ejbdu2ICJMmTJFkB1tUlISH5ezZcsWZqUAcnJycP36dQAFx8k2NjZ8Ow1WR5gbN24s6Jrg4sL3Gu3QoYNWDZs5jsOhQ4dgb29f7ChRKpXi8uXLuknvA6CzlWbQ2UkzaGunlIycYuSs97rzTDutfA7QjSfNISQxk5IORFRAUEeOHElhYWG0bNky6t69O50+fZqpDoVCQd27d6cLFy6Ql5cXjRkzRqP/U3KgMTuuExGRfVlDsjHVL/Y3AEgkEtGrV6+oc+fOFB4eTgsWLKDp06eTSCRicv03btyg+vXr0927d6lr16709OlTWrp0KVWqVInkcjkTHe7u7qSnp0fbt28nb29vsrW1peDgYGrfvj0T+X/++SeNHj2aiIjOnj1LTZo0ocWLF1Pbtm21kpudnU3W1tb0119/kUKhKPa5d+8eVaxYkcUt6KCDDh8ZZY3kFL2kCx27FU/jdt0gIqKrMa+p6vQA8hnQgL6tY/uJr/DLgGqdEhJKpZIkEomgOgSHJuztc/yw8pip4gpUneiHDh3Ke5hY7B7y8vJw+/Zt5OTkoHPnzqUqBNhzbRi/SyvJ+/Xq1Sts2LABCQkJcHZ2BhFh1apVWl97YURHR8PW1hYBAQEwNTWFoaEhDh06BIDdLmvHjh1qnqbvvvuOaeP3tWvXFvNmtWrVCtHR0cx0vAu63ajm0NlKM3yJdmL5Tr8NL168UEt4Ymmn3HwlOqw4U8yDFpPMpvZZUZw8eRLBwcGCxvKlpKRg9uzZglXdV2Hx4sUICAgQ9F7Onj0LDw8PwRKFVNAdZQpEzNLT0+Hs7Iw9e/aAiNC6dWu1IzkWL/PmzZvx008/8X26PDw8PmhQZmTn8S/+0ZslB3ROnDgRtWvXRvXq1SEWi/HXX39pfd2FwXEcOnTowJOZ8uXL88eNABs7RUZGwtDQkNdRpUoVpsHLq1ev5tvx1K5dG25ubli1ahXCwsIEDY4vjC9xEf1U0NlKHS9fviyxNAFLO3EchwULFuDMmTOCL5zt27dnkvn8NnAcB1dXV7i5ueHhw4eCjKebz14XI2czDt1GmoJtD1aFQoFKlSrBxcVF40Sx0mDWrFlYsWIFZs2aJVjrJVWD9FatWgl2LxzH4ZtvvoGpqSkWLlyI9PR0QfToiJlAxEzlQRGJRHBwcCgWvK7ty5yTk8OXE6B/Gid/6IT3voD/O3fuqAWas6qUXRibN29W8zK5ubmpeZm0tVNaWppaM2siQsuWLeHj48OkpMCTJ0+wZs0anD9//qORsJKgIxua40uy1ZkzZ3Dp0iVByYxSqYSrqysGDhyImzdv8j9nbadbt25BIpGgRYsWOHbsmGD39NNPP/Gb4ZMnTwqi59q1axCJRJBIJPjrr7+YZw4DBc+l5rBlxQjazvAYpvekynynf+Jhw8PDmclWIT09nW+9ZG5ujkWLFgkyX6o6bhAROnbsqFVs79tw48YNiEQiPgN+1apVzMss6YiZAMRMqVSiRo0a/ACpVKkS5s2bp0YEtJ30VC0sSjsILz9N4V/0xLSSA/5V1Z5Vn6pVqzLtZRgfH8+XYyAimJiYYNKkSWoVv7WxE8dxfIPkhg0bYvny5cXS1v9f8CWRjU8NFrZS9ZIUuhl7RkYGHBwcUL9+fWzcuFEw8h8VFQWZTAb6p19lYGCgIGOq8MLp7OyMnTt3Mi/xEBcXByMjI15P8+bNERgYyJygqaq7e3p6QiKRYPDgwcwJ2rVr1yA1sSpGzob+Fc7Me8ZxHJo1a6Y213fr1o15nbp9+/ap6bCyssLatWuZPpfk5GS1NYX+KfDKOqtf1XZJ9bG3t8fp06eZydcRMwGIWWBgoNpDGzx4cLEzaW0mPYVCgQoVKvDyq1WrhkOHDn3QAH+ft8zf35+Xb2xsjJkzZzJtMMtxHHr06AEiQvXq1bFmzZoSmxdrY6egoCAsWLBAkN3s5wYdMdMcrGwVGBgIU1NTDBw4EAEBAR9c3VtThIWF8Tt0U1NTjBs3Dnfu3GGuZ/bs2Wrz1tq1a7Fp0yam95WWlgZbW1s1PY0bN2beEUEV16v61K1bl/k7kpiYCGNjY3h6eoKIUKdOHfz999/MCeCQIUNARDBzcStG0CLi2LQTu3Dhgpq9Zs+ejbQ0tmU7QkND+ThlIoKrq6sgMYGq50H/lBIq7AVmhdjYWOjr6/N6li9fzvS564iZAMRM5WmqWLHiWzvZazNJqGKazMzMsGLFig8uJ7Hn8jP+xc4roaBhTk4OHB0dUaZMGcyYMUOQGmJ79+5Fhw4d4O/v/84jRR3h0Aw6O/2LtLQ0bNq0CZGRkSWOLZa2mjVrFj85W1hYYPTo0Thz5gzz9k5TpkxRWzglEskHlcTRBAqFQs3Tv3r1aly4cIE50Sh8dCaTyXD+/Hmm8oGC8kTVq1fn9fz000/Myu4UxvLly3kiYGpqKsi9xMfHw8jICHK5HGI9o2LkbF3oIybP6Mcff4Senh709fVhZ2fH9HQEKHjvgoKC+FhiIsKSJUuY6gAKnn3lypVRrVo1/rSEpVNBhenTp8PMzAwVKlSAnp4e/P39mcnWETPGxOzevXsQiUQYM2bMO3ccpV0cMjMzUbFiRfzyyy+l3m0UbqRbEjZs2CAYIVNB05YeOsKhGXR2UsfevXshFothYWGB7t27w9PTE+Hh4cjNzWVqq/z8fLRr106NNFWqVOmtG7LSQqFQoHbt2ryO1q1bM/doAAUxbfRPfTxPT09MmDCBeQFpjuPQrl071K5dG2ZmZihTpowgGXv+/v6ws7PDyJEjQUTo1KkTMjPZZjfm5ORgzZo1OHDgACwtLWFoaIjg4GCmOgBg4cKFWL9+PQYOHAgigsvIucUImrZHm0+fPsVPP/2EU6dOwdDQEFZWVkyPM1Xv3ffff4+kpCS0bt0aRITff/+dOfnfvXs3jh07xof81K1bl7l3Li0tDVOnTsWTJ09QqVIlyGQyHDlyhIlsHTFjTMxWrlyp0VlzaReHa9euaXWMMfdo1DuPMAEI2i/yQ6EjHJpBZ6fiUBX7LfwpW7Ysjh07xlTPixcvYGdnx+to1aqVILGMV69ehVQq5Ysv16xZU5A+tSNGjMDWrVvh6+sLIkL37t2Zx7bdu3cP69evR0REBMqXLw+ZTCZIctHBgwfBcRymTZvGJ/6wzgpUdXFR9auUy+V8uR9WyMrKQnJyslpz7K49+xQjZwG347XSowq5OXfuHIyNjVG2bFlmAfSqOUpFjjMzM9G+fXsQEaZNm8aUnHEcxx/Bb968GSKRCLVr19a6/VZRqOIjo6OjUbVqVUilUuzfv19ruTpixpiYabq7/BQLqVLJ8S/w5rAnH11/aaAjHJrhS7HT/fv3MXLkSIwbNw4zZszA0qVL4ePjg507d8LPz495D8bC8SZEhF69euHkyZNMdQAFcWASiQS9e/eGRCKBmZkZ9u3bx1zP77//jtjYWGzfvh16enowMzPD8ePHmep4/fo1UlJSEBoaCnd3dxARGjVqxDwOTHXcGxMTAycnJxARvL29meooDNVY+Oqrr5jeS+F37+nTp3BwcIBEIsG2bduY6SgMjuPw66+/gojQvn17+ITcUyNnDtP8kZ2nvZfz8uXLMDc3h4mJCZMj2pLmKIVCwdfgnDRpkmCZutu3b4dYLIaTk1Ope32+D7GxsahevTokEgl2796tlSwdMWNMzDTFp1hICxcu/FLwpRCOT40vyU5Xr16Fg4NDMW9W/fr1mTXgLoyZM2eCiFCuXDkQEVauXIlNmzYxjwPz8vJCXFwcLl68iCpVqoCIMGLECKbepsIZjFeuXEGFChUgFouxbNky5ouaakytXbsWYrEYlSpVQlRUFFMdKiQnJ6N58+YgIkydOlWwBXrz5s0Qi8VwcHDAkydsNqdF3734+HjUqVOHT6AQAhzH8ckaX3/9NWITk4t5z4IitSefN2/ehKWlJYyMjLSeY972/zk5OejZsyeICGPGjGH+Xqqwe/duSCQSVKtWTbAm6c+fP4eTkxPEYrFW/YV1xOw/QszSFLn8C3v6PvvFTyh8SYTjU0IoO6WlpSEoKAhLlixhGjydlpaGvn37qhEzc3NzjB49GufPn2d+rPHLL79gw4YNOHbsGNasWcMHBbMM1uY4jr/u1NRU9OvXD0QEJycn3Lhxg5mewkhISOD74/br149p+Y7CY+rYsWMwMjKCqakpTp06xUxHYWRmZqJr164gKqhnKFSW68GDByGXy2Fra4uIiAit5ZX07iUnJ6Nx48YgIixatEhrHW/DsmXL+MzWlJQU/BHyUI2cNVpwAi/faBeaEhUVBRsbG+jr62vlnX3XHJWbm8vPB8OGDWMe16jCwYMHIZPJUKVKFTx9+lQQHYmJiahVqxZEIlGpC7LriNl/hJi9rzzG5wodMdMMrOz07Nkz7Nq1C2PHjkW9evUgFotBRBg3bhwyMzOZE6YNGzZAX18f5ubmcHV15Ula1apVMXv2bGYxVEqlkq9uHxISgqVLl6JMmTI8oYmNjWWipzA4jsPWrVtRpkwZyOVyeHt7C+IJys7OxogRI0BEaNCgATNvQNExde3aNdja2kImk2Hr1q1MdBRFXl4ehg4dCiLCt99+K1hl9VOnTqFMmTIwNzfHxYsXtZL1tnfvzZs3fID7b7/9JpgXUFXM3NnZGYmJiXjxRlHMe7btYjTytWiK/uDBA1SsWBFyubzUAe7vm6Py8/Ph5uYGIsKAAQOY17dT4dixY5DL5bC3t2ceOqHCy5cv8dVXX0EkEmHDhg0f/P86YvYJiFlcXJwgmTuFoVQqERYWBgDIzsvnX9BbsWwDX0+fPg2FouQCtSwQGhqKZ8+eCVLBuTAUCgV27twpqI68vDxs2rSJWf/MmJgYTJs2DUCBnfLz83H16lUsX74ca9as+WB5J06c4APL3/aRy+WwsrKCo6MjmjZtyiRe4/bt22jevDl/T4sXL0atWrV4nR4eHlrrKAzVpJeQkIDBgweDqKC4sVD97x4+fIhGjRrxJSiEAMdxWLduHaRSKb766ismx0ElLQ7Pnj3jj+muXLmitY6SwHEcZsyYASLC2LFjBdEBFMRQWVhYwMrKSqtszXctollZWejSpQuICAcPHiy1jvdhy5YtEIvF6N69O/8z97031chZ/XnBWtU9e/r0KapWrQoDA4NSBdFrQjaUSiWGDx8u6DEwABw/fhz6+vpo1qyZYIQ5OTkZ9evXh0gk+uDSIzpi9pGJmUKhQOPGjbF69WrBqoZzHIexY8dCJBIhJCREMG/Zjh07IJFIBJ08/f39YWNjgwoVKghGACMiIvjCh6yqNxdeGJVKJXbu3MnXVXJ3d9dKdnZ2NhYtWgRDQ0O4urrC29sbvr6+ahWvGzRoUGr5jx8/xpw5c/g4KVUdqAkTJmDQoEH47rvv4OLiAmdnZ2YlVTIyMtQmSI7jcP36dUyaNIl5cHvRSe/y5ctYuXIlUx1FkZOTg6VLlwretuvMmTPMjmfftjikpqbC19eXiY53Yfv27YI3i75z547WySDvW0RzcnLg6+sraFstADhy5EixjdLTpIxi3rN5x6KQk1c64h4XF1fqrGZNyYZSqcTmzZsF85ipEBISIkhWc2G8evUKe/fu/eD/0xGzj0jMOI7jd+h79uwRRAfwb7Dz999/j/SsHP6FvJ9YvLJ+abFx40aIRCLUqlUL8fHapWi/DXv37oWXlxfMzc0REhLCXD7HcVi9ejX09PRgYGAAHx8fJpPn3bt3sWjRInAch8OHD/Okz9bWFmvXrtUqVisoKKhY708iwooVK9C5c2csX74cV69eZRKjoVQqcebMGQwdOlRrMvk5QXc8rhl0dtIMn7udlEoOrZepb9BbLwtBcvrHLYv0udvpc8IXTcyISJ+ILhPRLSKKIqK5JfyNHhHtIaJHRBRORJXfJ1coYqYKOh40aJBgg9TLywtEBb0zc3JyBPGWqZrRCpVFx3EcFixYACLCmjVrcP/+fWayVVllCQkJfIeGBg0aMKtyHRERASsrK7Rs2RJNmjThK8IvX75cq+OSmJgY9O7du8TjxS1btgg+6Qm9e/2Y0C0QmkFnJ83wpdjpzP2XxbxndxPYFyl+G74UO30OEJKYSUl45BBRWwAZIpFIRkRhIpEoEMClQn8zjIheA6gmEol+JKKlRNT3I1ybGs6cOUOTJk2iRo0akY+PD126dOn9//SB2Lx5M7m7u1OLFi3owIEDJJL8+wj8x7diomPx4sU0ffp0atasGQUGBpKZmRkTuU+fPiV7e3vKz8+n4cOH099//02urq5Us2ZNcnR0ZKLDz8+PVq9eTePGjaOhQ4dSSkoKeXh40Ny5c0kul2st/8aNG9S+fXtKSUmhly9fkomJCc2dO5cmTpxIJiYmpZabn59P4eHh1KZNG2rSpAllZmbyn6ysLIqKiqJKlSppff3vglT6MV5nHXTQQSi4OJaju/O+pZqzj/M/+3blOZrXvTa5Na/86S5Mh48LTdgbqw8RGRLRdSJqWuTnQUTU/J+vpUSUTESid8li5TF79eoVOI5DTEwMypUrBysrKz5jitXuQVWLZ//+/RCLxfjqq6/4uIy2nqFMvGXbt28Hx3GYPn06iAqaz5bUcLy0UCqVcHV1RXBwMFq2bAkiwtChQ5GTk8PMTo8ePYKZmRmkUimICvqYstzBhYeHq8V4ERGaNm3KLND/fdDtRjWHzlaaQWenkpGdna0W8iCUnYQqhAoAXkHqRWmbLToJpRZZm+9CWloaLl68KPh4Onr0KNN1qSRcvXpV6yxeTSCkx0xU8LfCQiQSSYjoGhFVI6K1AH4r8vtIIvoWQNw/3z/+h7wlF/m7kUQ0kojI2tq64e7du7W+tvj4eDIyMqL4+HhSKBTk6OhIZcqUISKijIwM/uvSguM4unv3LlWoUIEeP35McrmcnJycSCqVEgAaEpRFREQeTfTJqaykVDqysrLo3r17ZGlpSUlJSWRqakoODg4kEom0uvbCSE5OppiYGBKJRASAKlSoQNbW1kTEzk737t0jhUJBREQikYicnJzI0NBQ62snIsrMzKQHDx4Qx3EkFovJ0NCQDA0NycDAgMqUKUP6+vpM9LwLLOz0X4HOVpqBtZ0yMzPJyMiImbySkJGRQbm5uVS2bFnBdHAcR9HR0WRpaUkmJiaCjafExETKzs4mW1tb0tPTYy4/IYOjaWEKtZ8tbGlA5Y3FzHU9efKETExMyMjIiAwMDJjLJyJKT0+nJ0+ekK2tLZUrV47pGqUCAIqKiiIDAwOys7MT7F5KM6batGlzDUCj9/6hJuyN1YeIzIgolIjqFPl5FBFVKPT9YyKyeJcsFh6z3Nxc2NjYQE9PD0SEP/74Q+33LHYPquKCIpEI5cuXVyuYN2n3Da29ZRzH8R4sIkKPHj2Y99F89uwZjI2NeR0tWrRQqy2jrZ04juNr46g+lpaWGDt2LJPd1atXr7BgwQLs2bMH9+/fF6xq9fug825oji/JVkLV8SqM1NRU/PLLL8U8AazttHPnTjg6OsLX11ewfrz5+fmoX78+HBwc4Ovry7QocmHs3LkTRIRmzZrhyJEjgmRcZmVlwd7eHhKJBMOGDROkIKpSyeErj31q3rMFxyK1qnlWEp48ecLHP/fp00erfs/vgqq9U4UKFbBhwwZBihTv37+fX3f79+8vSC20Lzr4v5hCojlENLnIzz7JUabq4RERJBIJ+vfvrxZgru2kl5mZybeYoX/6v23cuJGvPq56yXaGl76Z8t69e4tVZmfZ/43jOP5FUn1atWqFAwcO8BOdtnZav3496J/m1cOHD0dwcPD/VSC7Cl8S2fjU+JJsFRERgbZt22Lbtm2C1gvctWsXiAjNmzfHvn37kJeXx9xOHMehXbt2ICLY2dnB09NTkKOnsLAwfj6xt7fH2rVrmduu8KbV09MTTZs2RWBgIHOCtnv3bv5epFIpRo0ahZiY0s/pJSEjIwPlW/YqlhhwP6H0Nc9Kwvbt2/l7EYvFcHNzw+PHj5nqiIyM5ItiExEcHBywY8cOphtmjuP4bhuq5zJ69Gi+gDULfNHEjIjKEZHZP18bENE5Iupa5G/GEpHPP1//SER73yeXBTFr3769GqHZtWuX2u+1nfRUuw/VZ9CgQXzZij2Xn2ntLVMoFKhcubJavFRwcDDTiUf1ospkMgwcOLDEIrLa2On+/fsYNWoUAgMDBWvv8rngSyIbnxqsbLV+/XrMmTNHsN2/CsuXL+c3F5MmTcK9e/eY6+A4ji+ESkSoXLky9uzZg7Q0tll79+7dg0wmU5sbZ82ahaSkJKZ6Bg4cqDY/2tnZwc+PbR3Hq1evQiQS8c3RiQiTJ08WlASIRCJ06dIFL168YKYD+KdArZFZMXL2R8hD5OWzuZ+TJ0/CwsKCv5caNWpgw4YNzE8ZRo4cyeswMDDA4sWLmY+v8+fPq42vIUOGIDIykpn8L52YfUVEN4joNhFFEtHsf34+j4i+++drfSLaRwXlMi4TUdX3ydWWmD18+JB/YB07diwxiFObxSErKwvW1tYgIjRq1KjYEYTqpRq1rfTV8hcvXgyign6C/v7+zHeCiYmJqFmzJmbPno2EhLc329URDs2gs9O/UCqV7xyvrGyVk5PDN952dnbG/PnzmZZ2USE/Px8uLi5qC4Grqyt2797N9L2MiYnh21SpPEFubm7MC2GrqvqriMaqVauYe87i4+PVQiTc3d0FOW4cNmwYT8zq1auH16/ZdlYBCgogq+5DJpPhwIEDzHUolUo0aNAARCJY91uiRs76/nkBmTnanzKEhoZi9erV/L2Ympri0qVLDK5eHQkJCTAyMoJIJAIRYdKkSYI8+z59+kAkEkEikcDR0VHnMRP6oy0xmzJlCgwNDbF+/fq3DghtFoeVK1fCysoKmzdvLrbbeJaSyb9QpR2MCQkJaNWqFQ4fPixYtero6GiNjhd0hEMz6Oz0L3Jzc/Hzzz+jT58+8Pb2Rnh4uJrHlKWt4uLiYGVlpUaa6tWrh7///puZDqAgRqcwaXJ2dma6Q1dBVWuRiODt7c2sE0ZhZGVloUqVKnyGdPPmzZl1kCgMFWGqXr06RCIR1q1bx1xHYmIivL290bNnT/7Zs/ZmAYCbmxt++OEHVKtWDRKJBNu3b2eu4/Tp03BycoKHhwcMqjUp5j3TtiBtaGgocnNz4ejoiP3798PCwgJlypTB2bNnGd3Bv5g3bx4WL16MHj16gKigtRdrz9zDhw/Rtm1b7N27F1KpFA4ODsyOmXXEjDExy87ORrdu3d7b6qG0i0NeXh48PT2Rmlry+T+LgrLJycmfLIi9KHSEQzPo7KSO7OxsdOjQQe1Iw8XFBR4eHqVuKfM2hIaGQiKR8Lpat24tSDzYpk2beC8TUUEPURYdHgojPz8fzZs3R5cuXbBq1SrIZDKmcaUq+Pn5wc3NDStWrAARwcnJiXlpmZycHLi5uSEpKYnvVTpv3jzmm829e/ciMzMTmzZtglgsRo0aNZg1klchLi4OFy9eRHx8PGrXrg2RSAQfHx+mOgDg7Nmz4DgOc+fOhdjQtBg5e5JU+pZiqjnq1q1bAP4txm1oaKh1W6yiyMjIwPPnz5Gbm4sffvgBRIQRI0YwX9dUz/ngwYOQyWSoXLkykyQNHTFjTMwyMjI0Ci4XYiFNz87jX6A0xf9HTJWOcGiGL8VOKSkpuHfvHuLi4pCamipoIkZmZmaxI8AmTZogODiYuS5VhrQqfqpXr17MvUAcx6Fbt27YuHEjOnXqxIdKsO4nGRkZieDgYAQFBaF27dogIsyZM4c5oVEFfu/atQsymQy2trb8os0KquzPN2/eoG3btiAiTJgwgekCXfjd27t3L2QyGezt7QXrw5icnIyGDRuCiODl5SWIDkA1pkWo+stfauQsMKJ0LfhKmqPu3r0LOzs76OnpISAgQMsrLhl5eXno378/H4vNejOjwrFjxyCXy1GxYkWtMzV1xIwxMdMUQiyk7VecFqRZ+afEl0I4PjW+FDtlZ2fD3d1djSzp6enBwsIC9vb2zONn3rx5w7fGUmWDbd26lXkrMY7j0KtXL2zZsgW//PILH3DO2hOQmJiIhIQE5Ofn8wWfHRwcEBERwVQPUDCmUlNT+USmAQMGCFbm4uTJkzA2NoaJiYlgYzk7Oxu9evXi74VVQlDR6w0ICICBgQGsra1x+/ZtJjqKIjU1lc8KnTt3rmAhJ6qj7ZrdRqqRs0m7b3ywzrc910ePHsHe3h5yuRyHDx9mcNXFkZ+fz/ep7tevn2AbwsDAQOjp6cHOzk6reFMdMfs/Imaql+bMffb9Kz8VvhTC8akhpJ04jsODBw+YemYCAwOLxWY5Ojri3LlzzI8bXr16hbp166Jr167o2bMnPD09YWJigmXLljElGmlpaYiNjQUA+Pv78/c3efJkwQjN/v37YWRkBCMjI+zfv5+pbNWYys3NxfDhw0FE+PrrrwWJBwOAGzduwMbGBnK5HHv37hVER35+PoYNGwYiQpcuXbTqX6tCSe/e2bNnYWxsDHNzc8EqxWdkZOCbb77hx5hQ5MzX1xcikQhOTVyLHW2mZmpObt81R0VHR6Nq1aqQSqWCPXulUolRo0aBiPD9998Llql/4sQJGBgYwMbGptQZ2zpi9n9CzM4/Svq/85YBOmKmKVjaKTc3F+Hh4fDy8kKvXr1gZWWF2rVrM99lJiQkqMWBqT729vaYOnUqbt68yWyxefHiBbZs2QKg4Mihfv36ICJUrVoV+/fvF2RRe/HiBV+Col69eoKV1YiIiICDgwOICNOnT2d2VFN4THEch6VLl/LB9A8fPmSioyiePHnCB+uvXr1aEB0cx+G3334D/VM3UdtMyre9e1evXoWFhQWMjIzQc/8FAAAgAElEQVRw6tQprXS8DQqFAt26dQMRYfTo0YLFBu/YsQMSiQQOjjWKkbOwh5qVonjfHBUXFwdHR0eIxWJBkhuAgmc/btw4EBG6d+8u2IYpNDQURkZGKFeuXKm82Tpi9gmImRDFG1Uvybcr/81wEbIgpQpCVyYPDQ1Ffn4+83pKJeFdZTtYITo6mskuHSiYZHbt2oXU1FR+PHEch6ioqFLt0m/evIlOnTrBwMCgGFkqX7482rVrh969e2PYsGFwd3fH/PnztfaiKZVKLF++HFKpFBEREVi2bBnq1avH661VqxbzSVo1pjZv3gwbGxsQEVxcXAQpdcBxHNauXQt9fX3o6+sLUuoAKPAKfvvttyAidOvWjQnRLGmO2rt3L3/0LMTxKQAkJSWhadOmICIsXLhQEB3Av3GBdevW1eqdfNdcHhUVxcdQhYSElFrHu5Cbm4u+ffuCiDBq1ChBdAAF3lmZTIZKlSph4IYwNXL2+9FIKHLfvSHQZM1LSEjgkxv27NnD6MrVwXEcH07RvXt3wTyN586dQ5kyZWBhYfHBGxkdMfsExMzd3R2+vr7MFmhFbj7/gqhaafj5+aFChQrMg2kL48mTJ6hcuTJWrVolmI5Tp06hS5cucHFxEay9ikKhwKRJk2BoaCiYVyMuLg5jxoyBTCbD8uXLtZZ369YttG7dmg+Y3rNnD3r37s13g2jatGmp5L5+/Rp//vmnWisuFTGrUqUKzM3N1Sprq4oaa4srV66o1fu7c+cOZs2ahWrVqmHNmjVMdKhQeNJLT0/HjBkz8O233wo2QQMFC3SrVq0ECwgHCo7ppk2bxiwg/G2Lw8WLF9GjRw9BN34ZGRn44YcfcPnyZcF0AAWZrjNnztRKxvsW0SdPnqBnz57MkzQKIz8/H6NHj0ZQUJBgOoCCI/pffvkFHMfh8I04NXLWeMEJPEt5+5qmKdlISkpCr169mNYFKwqO4zBz5sxihd9Z48KFCxg0aNAHH5vqiNlHJmZHjhwBEfHtk1ig7twgtWPM8PBwGBoaolKlSiUWt2WBhw8fomLFipDL5cwraqsQGxuLtWvXgojw22+/CeKmj4iIgLOzM+9pYBEUnpubi1mzZgEo2AFOmDCB75natWtX3Lhxo9SyX716hV9++UWNHKmKgRoaGuKbb77B/PnzERYWpvV9PHz4ELNnz0blypUxcOBA/uccx+HNmzd49uyZYBlOhXWxjgUpadITkpR9TB0soQsj0Az/ZTs9epmucUmN/7KdPhQ6YvYRiVl0dDTMzc1hb2/PNFtL9UJci3mF+/fvw9LSEmXLllXrzckS9+7dg52dHfT19XH8+HFBdFy9ehW2trbw8vLCxo0bmcl98uQJgIIjtJUrV0JPTw8GBgbw8fFhsnCqYj7s7OwwefJk/liwY8eOCA8PL7VcpVKJjRs3wtLSstgx46BBg+Dn5yeYR1GpVOLSpUtfHLF4G3QLhGbQ2Ukz/NftlKbILUbOHr4o3snhv26nD4GQxExKOvDIzc2lvn37Unp6OgUEBFB2djYTuecfJfNf28lzqIXrt5SRkUGnTp0iJycnJjoK486dO9SuXTtKS0sjPz8/ateuHRO5ACg+Pp7Kly9Phw8fpv79+5NMJqPq1atTt27dmOh49eoVtW/fnoKDg2n06NF04sQJatSoEf39999Uo0YNreVnZmZSz5496cSJE0RE5OnpSW3btqV58+ZRy5YttZJ99OhRun37NnXt2pUyMjIoPT2d/8TExJC+vj7J5XKt76EkiMViatq0qSCyddBBhy8bJvoyeryoMzVffIpepucQEdE3K87SwZ9bUAN78098dToUhY6YUcFibWRkRNOmTaPw8HDy8vKiZs2a0enTp5nI7+8bTkRE5U31qEuXLhQTE0OHDh2iFi1aMJFPRHT58mWyt7enpKQkateuHWVlZVFgYCC1bt2amY6tW7fS48ePyczMjKZMmUKVK1cmf39/evHiBRP5HMdR//796fHjx+Ts7EwKhYKmT59Ov//+O8lkMq3lv3nzhrp06UJhYWH8z+zs7GjNmjVUq1YtreX36NGDevTo8dbfsxpPOuigw38HeXl5TOY/iVhEl2d8Q78fjaItF6KJiKjXugvk9X1d6lqnnNbyNUFiYiLZ2NgIqiMuLo7KlStHenp6guoREuJPfQGfGllZWTRkyBA6cuQIrVixgrp160aTJk1iJp/jwH9teGYFXb9+ndavX0/fffcdMx0AyN3dnRYsWEBt2rSh7OxsCgoKYkrKXrx4Qb/++it5eXnR5MmTqXnz5hQeHk41a9ZkpmPevHl0/PhxIip4LkuWLKGFCxcymZRevXpF7dq140mZjY0NdezYkfr3708PHjwoONfXQYf/OJRKpeA6Hj9+TGlpaYLqUCgUtGnTJlIoFILqWbduHfn7+ws6f0RFRdGIESMoJiaGibzfv6tNK/vW479333eL5gU8oIFubpSSkkL5+flM9JQEf39/6tevHz18+FAwHfr6+tS0aVPasmWLoPciJP7zxOzw4cO0b98+6t+/P9nb29OWLVtIJBIxk+++9zr/9cmgQJo9ezaNHDmSmXwioiNHjlBYWBitXbuW8vLyKDg4WOtjuaIYN24cvX79mhQKBRkaGtLChQvJ0tKSmXx/f3+aO3cu/71IJCI/Pz+KiIjQWrZSqaS//vqLfvzxRzpx4gS9ePGCEhIS6Pjx47Rs2TLq0aMH02eugw6skZubS+fPnxd8A/Hnn3/SokWLKDU1VTAdlpaW1LRpU5o1axalpKQIosPAwIDi4+PJwcGBVq9eLZjdevbsSX379qVmzZpRUFCQIHrq1atHOTk5VL16dRo7diw9f/5ca5k96pcnv3Gt+O93hD+j6NqD6eHTGKpVqxbt2rWLOI7TWk9RDBo0iG7fvk01a9akESNGUGxsLHMdlpaW1K9fPxoyZAg5OzvT/v37v7yNtyaBaJ/jh1Xwf+HimU5OTliwYAGfxcYiEFIVaGnc8DtIpVJMnDiR7z/HArm5uXB0dOTvQSaToV+/fkxrlx0+fFgtkN3MzAxTp07lm7Rra6dHjx7BzMwMRISWLVti1apVgqZhfyroAms1x5dkq8ePH+PgwYOCVSlXYfr06ahXrx62bt3KJ5GwtpNCoYCDgwOMjY0xZcoUwTLGt2zZAiKCkZERpkyZIkh9wqysLFSqVAlEhFWrVmHlypXIyspirmfhwoX83NiiRQucPHmSeRJObGwsn6Skp6eHSZMm4cWLF1rLTU7PLpYUILMssJmzszMOHz7M/F78/f15e8nlckycOJHJvRSGQqGAvb09r6dhw4Y4fvw403vRZWUKRMzi4uLUShq0atWK70QPaD/ppWUq+MFORLC0tMSWLVuYDo4//viDv359fX1MnjyZaTuW169fw87Ojq8m/scffxQjfdrYKSsrC2PGjIG3tzffKuf/FV8S2fjUYGWriIgIvHlTPPuMJTiOQ9++fWFjY4Pp06fzWcWsoVAoUKNGDRARbGxsMH/+fJw4cYK5nuPHj6stnMOHD9eqp2BJUCqVaN68udrcNX78eOZzwL59+/hSNSq7eXt7M82OLkwAVZ/WrVsjOjqamQ4AmD17tpoOIyMjJn0rc/OVxciZkfM3vJ6xY8cy7SjCcRzatWundi9NmjRh/uy3b9+upqNChQpM+3zqiJlAxExVVVokEmHmzJnFBp+2i4PzzKP8QB85ciRSUlK0klcUaWlpKFeuHKRSKUaNGiWIl2nkyJFo27Ytjh079tYaZdrY6f+lvIMm0BEzzcHKVk+ePEH58uXRo0cP/P3334J1p0hJSUH58uX5RaBDhw7Yv38/cy/a2bNn1RYbLy8vDB8+HElJmrXc0RTff/+9mp7q1atrVduvJFy7dg0ikUiNzLBuKM9xHFxdXXliVqVKFeb3AQB79uzh70MikQjS3ik9PR22tra8nsmTJzOTzXEc6hWqtVnpNz+YtR6MWrVrC1J098aNG/yzl0ql8Pf3Z65DqVSiQYMGvL369+/PlGDqiJkAxIzjONSuXRs2NjZvfYm0JRyqAf6X39n3/0MpMHPmTPTv31+wnnhZWVkadSXQEQ7NoLPTv+A4Dv7+/oiKiiqR8LO0VVBQEO8Zl8vl6NatG7Zt28YfxbNCcHBwsfp1Q4cOZV67bsyYMWrETIhxFRcXhzJlyvB65s6dK8gmavTo0bwOOzs7QVpI3bp1C56enjAxMQERYfz48cwLYXMch5YtW8Le3h5yuRwVK1Zk7mUEgM2bN0Mul/PtsJYsWcJUfu8VgWrkzKTZ96hfvz7TUxgVBg0ahE6dOqFSpUqQyWRMvVkqhISEoFy5chgxYgSICH379mW2WdIRMwGI2fXr19GxY8d3nm1rM+EdO3lW0IblHMcJRsg+FDrCoRl0dlJHREQELC0tYWJigvbt22PWrFnw9/dHcnIyc1stXry42DHQwoULmS/Q48eP53WUK1dOq4LFb0NaWhoqVKgAY2NjeHp6olatWnj69ClzPd7e3rC3t+ePnUaPHs28i0RycjLs7Oxw5MgRlClTBubm5rhw4QJTHQCwdetWnDt3Dr169QIRYfDgwUy9J0BBy7IVK1bg+PHjMDAwgLW1NW7fvs1UR35+PmbMmIE3b97AxcUFRITZs2czI82hoaFYf/qRGjkzbtAVderUQWJiIhMdKsTGxuLUqVOIjo5G1apVIZVKsW/fPqY6AODQoUNQKpX4+eefQUTo3bs3k82SjpgJQMyio6PfOylrszgUHtj/79ARDs2gs1Nx3Lx5E+bm5sU8TTt27GDqoeE4jl+UiQgWFhY4ePAgM/kqZGVloWbNmmjatCnMzMwgl8vh6+vLXM+xY8fg7u6OAwcOQCaTwcrKCpcuXWKqIy8vD+vXr0dOTg5++ukn0D8NpVkH0N+8eRMAcPnyZVhYWMDQ0BCBgYFMdZw8eRJKpRJ5eXkYPHgwiAi9evVCdnY2Uz2qBf/MmTMwNjZG2bJlceXKFaY6VOtWZmYm2rdvDyLClClTmLwvqjkqOCpRnZzV64QaNWoIlpQVGxsLR0dHSCQS7NixQxAdHMdhwoQJICJ89913Wj97HTETgJhpAhbE7H6isIHHnwN0hEMzfCl2ysrKwowZMzBgwACMHDkSEyZMgIeHB+bNm4fly5dj9+7dTEnT1atXYWpqypMmGxsbQXq7vnnzBk5OTmjRogWfsTVkyBDmyQHXrl3D1q1b8ejRI77H66hRo5iTgMTERISGhuLMmTMoW7Ys9PX1sXfvXqY6VFAqlXB3d+czD4U42gKAu3fvomLFipBKpdi5cyczuYXfPaVSyXs2O3TogIyMkvtGaovLly/D3NwcxsbGOHfunCA6VO3lVEH62nqAC9spIi5V/VizQRc4ODggJiZGy6suGfHx8ahVqxbEYjG2bNkiiA6O4zBlyhQQETp37gyFQlFqWTpi9oURs8IpyP8FfCmE41PjY9iJFWHKzMzEqFGjinmyDA0NBQmevnTpEoyNjVGmTBkYGRnB09MT33//PR49esRUz927d+Hj44PU1FQMGDCADwhn0VC+MFQLZEZGBn788UcQEZo1a8a8/IRqTD148ADVq1cHEWHRokWCJdWsWLGCLy3EOutQhWfPnsHJyQkikQhr1qxhIrPou8dxHJ/l2LJlS7x+/ZqJnqK4desWrKysYGBggODgYEF05OTk8Mkaw4YN0+q4uaidnqVkqpEz8+bfo1KlSkxLPhXGixcv4OzsDJFIxLT/cmFwHIfp06fzxLy0HmAdMfvCiNl/6RgT0BEzTSGEnV69eoVjx47ht99+Q8uWLXHmzBmm8g8fPgwLCws1cmZvb4/Jkyfj8uXLTAlAWFgY2rRpg/j4eGzZsgVisRgymQyTJk1imtFc+Jr37NkDc3NziMVizJgxQ5BaZBzHwcvLCxKJBNbW1ky9J4XHVEpKClq3bs17AlknHaiwe/duyOVy2Nra8seQrJGUlITGjRuDiDBnzhytx9nb3j0vLy8QEerVq8e8lpYK9+/fR4UKFSCXywUJcAcKjp0HDhwIIkK/fv1KHT9Xkp1SMnLU1jTL9qNQvnx5QZIbgIK4w/r164OIsHbtWkF0cByHOXPmgIjQtm3bUnlNdcTsCyVmd+KFSc3/3PD/Rsw4jmNKOFJTUxEVFVXMTqXZqSUlJeHvv//G6NGjUadOHTXCZGVlhdWrV2Pr1q04fPgwTp8+jRs3bmi9QD9//pyPZenfv79aCnrVqlXh4eGByMhIrXSooIphCQ0NRUREBDp16gSigqLGnp6ezI8DVTq/+aagblPDhg1x9+5d5jqAggwxS0tLSKVS/PHHH0xjglTIycmBm5sbiAiurq7MS/SoEBISAhMTExgbGwtSGgIoOHpWPRdtj+neNUf5+vpCLBajRo0aanUsWeLp06dwcHCARCJhekRbGEqlEiNHjuTj50rz3r/NTpk5eWrkzOb7ObC2tmH23hfFq1eveGLu7e0tiA4AWLBgAYgILi4uHxzSICQx+8+3ZHob/P39KTk5uYC9fgBeZ+byX9e0NXnn38bHx9OIESMoPT29VNeoCfLz82nEiBF05coVwXQQEfn4+NCsWbME1RESEkKtW7cWzF4AyM/Pjxo3bkxHjx7VWh7HcbRp0yaqXr06JSUlUU5ODm3cuJHc3NyocuXK1KdPnw+WaW5uTtbW1pSZmUlPnjxR+93Lly9p/PjxNGjQIOrRowe5urpS/fr1KTExUav7sLOzo+PHj5OXlxd17tyZrl27Rg8ePKD58+eToaEhLVmyhHbs2KGVDhXKly/Pf12nTh0KCAig4OBgsre3p5UrVwrSJqZ8+fIUFBRE3t7eFBkZSQ8ePGCug4ioTZs2dO3aNapbty6FhIQIokMul9OWLVtowYIFFBUVRa9fvxZET5s2bejcuXNUpkwZunPnjiA6jI2Nyc/Pj/r06UO3b9+m3Nzc9/9TKTBs2DDavXs3JSUlaf2uvA2VK1ems2fPUo0aNSgyMlIQHWKxmHx8fGj8+PH08OFDyszMZCbbUC6lBws68d/rVW1M8v+xd91RUV1fd8/Qq9IEVBQLERF7iRp7i12jsfcSG5bEij3YRdGooGKsiCVqLICCKCU2LDGKYEEUEEGpgvQy8873B5n3Y5QyMPdZ8s1ea9Zihpmz39x57979zjn3nMFr8fIV+5ZKQNE8d+XKFbRv3x5hYWEVXocVxfLly7F582a8fv1a8P6tFYIi6u1LfAjpMUtKSuK9DxVV0Z2cAxUKY2ZnZ1OrVq1ITU2NgoODlTncUiGRSPjdVEuWLBGEQyqVkqenJ+9tEKLlSV5eHi1cuJD3Ct2/f5+JXX9/f3rw4AFfU0t2h1a1alU6dOiQUrZv3rxJLVu25D1LRkZGfJFLDQ0Nat++Pa1bt04pjszMTDpy5Ah1796dRCIRNWvWjMLCwujGjRvk4+NDx44do927dzP9TUrKX3n8+DHzqt0f3o1KJBLm+WYlQagWRMWRm5vLrGVaWXftQnnLikOo3KzikEgkSm/QUMS7IVTx4eLIyMgQvKg2x3GVHq/yxkki5eQ8Z3UcfSg+jf2cL0NWVhbzEi0loTLjpQplfkJhVnxbvZeXV4U/LzthA56WXvNFKpXyyZqurq7KHG6pkEgkfM7BjBkzBJkM8vLyaOTIkbR161bq378/s8VGKpXyC/2TJ0+oWbNmBID69evHLA/k/PnzpKmpSU5OTnyxxipVqpCTk5NShUfj4uJozJgxHyXN169fn44fP05BQUGCiNfY2FjauHEjJSUlMbf9OfBfC48LBdU4KQbVOCkGRcZJ+oE4q73Eh+6/Yt8d4EuHkMJM/VN76L50HDt2DGfPnoWDgwMMDAwq9Fkq5m7tZmte6vucnJxw+vRpODg4wMHBodLHWho4jsO0adNw9OhRTJ06FW5ubhCJRExsv3nzBtWrV8e7d+8wePBgXL9+HX369MG5c+egrs7mdFqzZg2qVq0KTU1NLFiwAADg5uaGmTNnMvkex48fx/jx4yGVSrF69WoYGhpi9erV+Pnnn1G1atVK23369ClWr16N+Ph42NvbIyMjg38kJSXByMgIXbp0Ufr4S4KVlRUcHR0Fsa2CCiqoIINYLEL0xr6os/QS/9qQ3bewbXhTDGlR8zMe2X8Iiqi3L/HB0mMmSyh+/fo1ValShWxsbCgrK6vCinjDxSelhjFlveyOHz9OAKhnz57MK09funSJOI7jyxxMmDCBaWXz7Oxsatq0KUVERPDNlDdv3sz0bvTixYsEgG8H06xZM3r8+DEz++7u7nL9+QDQwYMHmdkvCRzHUVZWlmBJ0v9FqDwcikE1TopBNU6KoSLjxHEcWTvKe87O/VN2AdpP0RuZdTeP0qBK/hcYnp6euHz5MiZPnozMzEx4eHhAT0+vwnbcrxUlY0/+ro7c61KpFIMGDcKNGzcwadIk2Nra4tSpU8w8TAAQEhKCSZMmYc6cOXB3d8eYMWNw4MABiMXsfuK1a9ciNDQUzZs3R3R0NE6ePInFixczsx8dHY2xY8cCALKysmBnZ4dr167Bzs6OiX0XFxdMnz4dRASRSIR69erhhx9+wKtXr/Du3TsmHCVBJBJBT0+P6W+hggpfK4TYwFESR3x8vOA8t2/fFnTzFgDExMTA29tbLiLDGhzHYevWrSgsLFT4MyKRCFEb+kJPU41/7ec/HiL0dXqpnzl58iROnDgh6DkQFxcHBwcHxMXFCcYhNFQrBYCzZ89i+PDhuHLlChwdHdG2bdsK2yh+0azo11Duf97e3rh16xa6d+8OPT09eHt7KxUyK4l72bJlSExMhJubG4YPH47Dhw9DTU2t/A8riEePHmHr1q0AgJycHIwYMQK9e/dmZj83NxdDhw6V20WWnJyMvXv3MpmQAgMDERsbi99//x137txBZmYmXrx4gbNnz+LXX3+FsbGx0hwqqCAkhFyYZbh9+zZiYmIE5UhOTsa0adME250IFO1Q3LZtG6ZPn45Xr14JxlO1alV88803cHZ2ZroLsjisra3h6uqKdu3a4erVq4KcB2KxGNbW1ggLC8P8+fORnJys0OdEIhEer+mNqroa/GuD3G4iKSOvxPcPHDgQCxYsQPPmzQUTm7Vq1YKGhgbq16+PBQsWICUlhTmH4FDErfYlPliFMtPT00lTU5MPa3Xq1IlP+q+Iq/Lmi+RSw5hdu3bl7derV482bNjANIzp7+8vF5qztLSkkydPMrMvkUj4BHnZo3PnznT16lUiUj5MwHEcTZo0ie9h+NNPP9HVq1eZh3o/N1ThFMXxNY1Vfn7+JwmfbNiwgXbv3i1XDJP1OKWmppKlpSWNHTuWeQPu4nB2diYA9MMPPzDbZf0hUlNTydjYmDQ0NOjIkSOCdSqQtXeqVq0abdu2TZDNPY8ePSKxWMzPvUK0eOI4jvbu3UsASE9Pj1asWFGhXbfN1/jLhTVzC0reTbl//35+HWnXrp0g13pKSgrf5s3AwIB+/fVX5q3XVLsyBRRmspwv2WP16tX8JFuRgZedjHWXXpR7PTQ09CNBExkZyeTYiYouplatWvH2bW1t6cKFC0xj+a6urgSAxGIxjRgxgu7evSv3f2UvrDNnztDkyZPJz89PkMrrXwq+JrHxufE1jVVhYSGNGjWK1qxZI1iTZ6KixaZatWpkZGRES5YsodevXwsyTocOHeLnk/79+wsiAvLz8/k8Vfy74zokJIQ5j5ubGwGgrVu3koaGBk2bNo25QEtNTSUjIyO5G+OdO3cq1YexJMiKx8oe33///UdzsbLw8fGR4zAyMqINGzYoLDabOl2WE2f5hR/fsEgkko+KY/fs2ZOePXvG9Lts3rxZjsPU1JSOHj3KzL5KmAkozH788Uc+2fzcuXNy/6uMMEt4L38xTp06lbe/e/du5nfWf/75J3+3tmfPHuZepri4OLK0tKS5c+dSVFRUie9RdnH4VMmanxtfk9j43GA1VlFRUeTo6EghISGCnmcvXrwgPT09EovFNGDAAPLy8hLE4/vHH3/wC42amhodPHiQ7ty5w5SD4zjq2LGj3KL23XffMd+8cvny5Y/KyqxcuZLpTWVhYSHZ29vzNQS1tLRowoQJSpXEKQk7duyQ+x7Tpk1j3kEiISGB3xQFgPr06cPc2xgUFEQjRozgOWrUqFGh1mscx1GjVX5y4iwz7+PrwNfXV268jh8/zvz6zMnJISsrK55j4sSJTK9JlTATSJjl5OSQnp4e1a9fv8Sdf4oOfG6BpMQwZkpKCmlra1PPnj0FcaNLJBJq2bIlrVixgrmbVob79++XW6hSJTgUg2qcFAfLsZItmjVr1qS5c+fSX3/9JUjRyt9//11usalRowatXLmSaQ9GjuNo0KBBPMfWrVvpu+++o7CwMGYcRETh4eGkrq7O80ydOlWQOWbw4ME8x7ffflupnoXl4erVq3LC7MKFC8w5CgoK5DyAffv2FSSkuX79ev57GBgYMPdmBgUFUVRUFGlqapKxsTEBoOnTp1dINHEcR/WWXpQTZ4kZuR+9p0ePHmRubk4aGhpUu3btUm/8lYGHhwcBoIYNGxIA2rt3LzPbKmEmkDC7cOEC9e7dm969K7k4nqIDP9Pz7xKF2d69e+nAgQOCbRGOj48XNHSiKFSCQzGoxkkeN27coBEjRpCzszMFBwfLFShmOVYcx/HFlmUPc3NzmjVrVqnXfmV5iosmsVhMhw4dYi4C4+LiyNDQkBdms2bNEsQ7t3jxYj5HR1tb+6OIAgtERUWRtrY29erVi885EqJjwf79+2natGlUt25dUlNTo2PHjjHn8PHxoQEDBtDSpUsJAHXt2pVZ0W0ZcnJyqHnz5vTgwQOqVq0a6erq8rm+LCC77hYuXEg3b96kkSNHEgCaNGlShc7jDzsE1F7iQ1HJ8qL7wYMHtGbNGrp48SJpaWmRlZUV0zQfoqJozNSpUyk1NZXvxMKqqA6/RjAAACAASURBVLtKmAkkzO7du1fmyabowMtOPJfL8jFyIRouf4lQCQ7FoBqnj+Hp6cnXlROLxWRvb0+TJ0+m06dPMxVNsgWteBjw8uXLzOzLkJSURObm5vx3aty4sSCtpNzd3almzZp04MABAkC9e/dm3lIoKyuL2rZtS8+fP6e6deuSWCymPXv2MOUgItq4cSNlZWXR9u3bCQDZ29szb411+fJlevLkCcXHx5OdnR2JRCLm34XjON5zKfNstWvXjnnbKtnYPH36lKpXr05aWlp06dIlJrZlc9T79+9JKpWSRCKh8ePHEwAaM2ZMhW4ACiTSj8TZw1j5sZB5FS9fvkza2tpUvXp15rlmsrzltLQ0atOmDQGg3377TWm7KmEmkDArDxUVZlKp8MXzvkSoBIdi+JrG6dmzZ/T06VOKjo6mN2/e0Lt37ygnJ0eQPK0jR458VPT3jz/+YO5pjomJIRMTE57LwsKC2YJWHD4+PtStWzfav38/aWpqUtWqVenixYvlf7ACkEqldPDgQQoKCqLly5fzgoZ1yoSsxVdCQgLvcVi+fDnT36a4LQ8PD1JTUyNra2um3pPi115ycjL/XTZt2sSM40PIhGbz5s35AuOs8eLFC6pVqxZpaGjQ2bNnlbZX0hwl8zoBoGHDhlVog1bxNJ/SwpoyBAQEkK6uLpmbmzMtKl4c6enp1K5dO97brAxUwuwLFmbJmXkKNS3/L+NrEhyfE1/TOD1+/JjvUfrho3nz5szDTQcPHpQTZ7t27aJTp04xF2cBAQHUtGlT8vPzI0tLSwKKesmyzm16+PAhERHdvXuXatasSSKRiNasWcNc2MrOqcOHD5OGhgaZm5sz3wwgQ2ZmJn3//fcEgCZPnizYDmovLy/S1tYmc3NzevDgARObH15779+/p06dOhEAWrp0qWDpJvv27SORSER2dnb05s0bQThevXpF9erVIzU1NTpx4oRStkqbo6RSKTk4OBAAGjRoUIWiQRm5BXLCrM9v10p1Yvz111+kp6dHZmZmgpVrycjIoA4dOhAA2rhxY6XtqITZFyzM2qy/ohJmX5Hg+JwQcpxev35NJ06coJ07dzKzmZ+fT4sXL/7ImzV+/HgKCQlhvpjJ6hstX76cT9j/9ttv6a+//mLK888//xBRUZmD4cOHEwCysbGh27dvM+WRITExka9lOGDAAKY7AoufU8HBwWRkZETa2tp0+vRpZhzFUVBQwIe2+vbtK0iyPlHRAm1oaEiGhoZMfv+Srr3s7Gzq06cPASAHBwfBdu16enqSmpoa1atXT7BaavHx8WRra0tisZgOHz5caTtlzVEcx9H8+fP5374i5UDeZeXLibM13qV7xG7evEkGBgZkYmLCX6uskZmZSZ07dyYAtHbt2krZUAmzL1iYyU40n1Bh7oa+BqiEWfmIi4tjNk4cx9GTJ0/I3d2dxo4dS9bW1rxo2r17N717945pwnlQUBC/7VxHR4fnsrKyovnz5zMVae7u7hQXF0cBAQG0Zs0avjzAwIED6cmTJ0w4ioPjODp27BhVqVKF1NTUaOXKlYJ4ggoLC2nhwoW8CGS1i/LDcyoiIoLq16/Ph+mE8ARxHMcnuLdu3ZoPd7KGLMFdW1ubL/pdWZR27eXn59OwYcMIAI0bN06wotZnz54lDQ0NsrKyoufPnwvCkZiYSE2aNFFq92F5c1Tx375Hjx6UnZ2tsO24tBw5ceYbVvqaefv2bapSpQpVrVqV7t27pzBHRZCVlUXdunUjoKh+aUWvFZUw+wzCLCYmRqHkYNlJVpkJUCKRkI+P8J42b29v5nV7iiMoKIiePHkieJPutLQ02rJli6CNcNPS0mjVqlUUHh7OxF5GRgYtXbqUunbtSkFBQRQXF0cnT54kBwcHWrFiRYXtSaVSOnToEDVu3LjEMGPxh76+PtWoUYNiY2OV/h5paWk0evRoGjhwIL18+ZI2bdrE5+kAoHnz5inNURyySS8hIYFmzZpF6urqpKenJ9h5HBsbS927d2e6a6sknDx5knR1dalZs2ZMzuOSFoeUlBTq2LEjiUQi+vvvv5XmKA27du0ikUjE/LcvjsjISLK2tiZLS8sKiYAPUdYiKpFIaMqUKQSAzp8/X2mO8uDr60va2to0ZMgQwThkuw/19fUpISGhwp9XRGxwHEe//vprpQRg6Os0OXH25E3pG1b+/vtvMjIyovbt2ws25+fk5FCvXr1IQ0OjwnXnVMLsEwszjuOob9++tG3btjJzaRLe5yoVxpSd3H/++WdlD7VcnDt3jsRiMY0fP14wDh8fHzI2NiZzc3OlJs+ycPPmTapduzYBYOZ5KiwspN27dxNRUVKok5MT38Zj2bJlStmWSqV05MgRPo+pZs2atGvXLjnh1Lt3b6U4Hj58SPPnzycLCwve5qJFi2jx4sU0ffp0GjlyJPXp04fprrCbN2/KPZeJtBs3bjDjICrZEyREiYPikEql5OHhIXj3ibCwMGbCv7RrIS8vj/mGg5Jw5coVQep1FUd8fLzSuWaKeIL8/PyU4lAEISEhgt4kExXNZZUNy1dkbvX396+UYPIJfSMnzqKTSw+Hh4aGVkpgVgS5ubl07dq1Cn9OJcw+sTC7cOECASi3fUP7jQGVFmb+/v4kEomoW7dughS7JCrKOdHS0qJ69eoJdnL7+fnRtm3byMTEhGmOjqzEgEQioXXr1pGamhoZGRkx2XlEVBTCGDp0KNnb29P69ev5liqtWrWiixcvKnWHdvv2bX5bdvHHnj17aNGiReTl5cU0eb6wsJB8fX1p9OjRgpQz+BxQhccVg2qcFINqnBTDpxonF/8IOXEWmci23tungEqYfUJhlp2dTbVr1yYLC4tyC/fJTqrTf7+uEEdcXByZmZmRpaWlYILp4cOHZGhoSBYWFvTy5UumtmUJrMePHyd1dXXauXMn0/yftLQ0qlevHj179oy6dOlCAKhjx45MQnJERe5rWdJv8Z2GXl5eSgmygoIC2rRpE9WoUYP09PQ+EmZ//PEHk+MvC0KJ/E8N1UKqGFTjpBhU46QYPuU4jfn9tpw4e/ZWmO41QkFIYaYOFQAA+fn50NLSwqZNm/Dq1St4enpCTU1Noc8ObVFDofclJibC2NgYI0eORGpqKoKCgmBubq7MYcshKSkJkZGRsLS0xPfffw8A8PPzQ926dZlxXL58GSdOnECLFi0wb948NGzYELa2tmjYsCET+0SESZMm4eXLl2jWrBkKCgrg5OSE5cuXK/x7lIXMzEwMHDgQwcHB/Gs2Njbw9/eHqampUrY1NDSwZMkSLFmyBAAgkUiQkZGBjIwMvH//HnFxcSAiiEQipXjKAosxUkEFFVQQGkentEGdpZf45312XIPvvE5oYGHwGY/qy4D4cx/Al4LZs2fjwYMH2Lx5Mzp16oTRo0eX+f6cAgn/tyIL7aNHjzB//nwsX74cN27cwPr169GpUyelj7s4tm/fjvXr16NXr15IT0+Ht7c3mjZtysx+fn4+5syZg+PHj2PevHlo27Ytrl+/Dg0NDWYc27dvx/nz5wEAeXl5WLZsGVauXMlEcKSlpaFnz568KNPU1ESzZs3Qrl07BAYGKm3/Q6irq8PY2BjW1tZo2rQp9PT0BBVlKqigwqdFXl6e4Bz5+flISkoSnOfBgweCc4SHhyM2NhZA0br5dE1v/n8cAQ7H/0GhlFOKIzs7G3/++Sc4Tjk7nxMqYQagoKAAJ06cQIcOHSCVSuHm5lbuArrqwuMKcRw5cgQnTpzAli1b0L9/fyxevFiZQ/4IaWlpcHNzg6+vL16+fIljx44xF34uLi6IjIxEYWEhAGD48OFQV2fndL116xbvbQKKLtwbN27g/v37StvOz8+Hi4sLunXrhhMnTuDx48fIysrCgwcPcOTIEQwfPlxpDhVU+NqRn59flOMiIIgIfn5+kEgk5b9ZCZw8eRLnz58X9Pu8ffsWw4YNw8OHDwXj0NLSwrx587By5Uqkp6cLxhMdHY2nT5/Cz89PsDGrU6cOOnfujPnz5yMlJQU6mmq45diN//+LpCzsuxalFIeenh6CgoLQqlUrXL58WfDzWQiohBmAe/fuITs7Gzk5OQCAMWPG4MmTJ2V+5sz9OADAkOblhzELCwvh6enJnyBPnjzBrl27lDxqeezatQuZmZn883nz5jGdLGJjY7Fu3Tr+uaGhIZKTk5Gfn8/EfnJyMoYPHw6JRIKWLVvCxcUFr1+/5i8wZaGlpYV169Zhw4YNGDlyJOzs7Jh6+lRQQWg8e/YMCQkJgnIUFhZi2LBhOH/+vGAeB5FIhKioKNjZ2cHDw0Mwgda3b19Mnz4dLVu2xPv37wVZoOvUqQNra2s0b94cI0aMwLNnz5hzAMDKlSuxYcMG1K1bF5s3b+bXKpb44YcfIBaL0adPH3Tp0gW3bt1izqGnp4elS5di+/btqFu3LtasWQMDNQmOTf2Wf8+WyxGISclWimfVqlWIjIxE79690b17d9y5c0fZQ/+0UCQR7Ut8sEz+X7t2LZ+gXaVKFb7SdFnJfbKExdyC8pOtvby85JLAlyxZwnRLfkZGBhkbG/P2hw0bxixRXoahQ4cSADIxMaG1a9fKlWBQNmFUIpHQnDlz6Ndff6WIiAglj/TLhSoBWXF8bWMVFBREr169EpQjIyODbGxsaNKkSXy7GiHG6fTp0wSA7Ozs6OjRo4IUXS0sLOSLodarV48OHjwoSJmS33//ne+L2Lp1a/L19WVeEystLY1MTEwIAF+aiPWGKyKiadOm8XO8hYUFubq6Un5+PlMOHx8fubWqf//+FBoaypSjsLCQbG1teQ4zMzPasWMHOV0Ik9sMoOzv5OTkJPddhgwZUuFaZWVBtStTYGEma5diaWkpdxKWNvAcx1WoTMaQIUP4i8nf35/FIcvB2dmZAJCtrS1duXKFuX1/f3+ytLQkFxcXysz8eFuzsouDVCoVtGjsl4KvTWx8TrDskvD27VsmtsrC69evycTEhPr160deXl6C7Y69ePEiv9D06tWLLly4wPza4TiOevXqxfNYW1vT7t27K9SCRxEEBwfLLZx16tSh/fv3MxVoEomEmjZtSlu3buV52rVrx6zzggw7d+6U+y6ampp0/Phxphxv376V2+2toaFBc+fOZSqcg4KC+JtwAKSurk4//vgj8z6f58+f/6im47Vr18h2hS+/tn63SbmC5ZmZmWRubs5z2Nvbk4eHB7PrRUhh9v8+lJmXl4dbt27BxsYGt27dQpMmTcr9zLXIFIXtp6SkwNvbG3369EFoaCh69uypzOF+hNzcXOzbtw/Ozs4IDQ1Fjx49mNoHinb6RUVFYf78+dDX12duXywWq5LiVRAEIpEIFy5cQJs2bbBlyxZERSmXv1IaatasiV27duHixYsYOHAgrK2t4eTkhLi4OKY8ffv2xahRowAA/v7+iIyMROPGjXHs2DFmoTqRSARXV1doamoCAGJiYvDzzz9j+fLlTMOOnTt3xrBhw/jnKSkpEIvFzNIjgKK5a/v27XKvzZw5E40aNWLGAQAzZszAN998wz+fOHEiRo4cyZTDwsJCLge3du3aWLRoEdM8XwDYuHEjb1MqlaJPnz6wtLRkyjFw4EB06NCBf15QUICWLVsi7Nde/GtxabnY7Ff50LC+vj5+/fVXAEXn9KtXr1C/fv2vY61RRL0p8wBgBSAIwFMAjwHMK+E9XQC8B/Dw38eq8uyy8pgFBgZSq1atSuz3VpoiLu5uLQ979+6lbdu2CdYg9/nz5/T6dcXqqLGGyhOkGFTjJI+CggK6f/9+ieEYlmPFcRxNnjyZv3Nu0aIFbdiwQZCehSNGjPjIc8K6Y0FiYiKfurB161bq2rWrIP0qV6xYwX+PWrVq0bNnz5hzxMTEkI6ODqmpqREAmjFjhiDexv3795OZmRnp6uqSmZmZ0p0ESsKFCxdITU2Nb+01f/585t7MrKwssrS0JAcHB1JXV6e6desybYwuu+5mz55N06ZNo2bNmhEAcnd3Z8Yhw61bt6h169Z8KlGXLl0oKyuLYlOz5dbYk3crnyJQUFBADRs2pCtXrpCpqSnp6+sz61LyVYcyAVgCaPHv3wYAngOw++A9XQD4VMQuK2EWHBxMGRklF7YrT5gFR5Q/GbJsh/OlQiU4FINqnD7G4cOHSUdHh9q2bUtz586lY8eOUWRkJPOxys3NpdatW8uJJh0dHTp58iRTntTUVKpevTrPMXDgQMrLy2PKQUR06NAhAkDbtm0jAOTk5MRcBMiKbU+aNIl0dXXJxMSE7ty5w5SDqKg1nYuLC40aNYoA0MiRI5nnm/n5+dGSJUvoxo0bZGhoSFWrVqWQkBCmHBzH0bp16ygvL48GDRpEAGjWrFnMb8rPnDlD+fn5dOHCBdLQ0KDatWszy2mTXXdJSUkUHh5Oqamp1KJFCwJAbm5uTDiKQyaQN2zYQACoU6dOlJmZSX/cjZUTZ96h8ZXmkN2AhYWFkZmZGenr69P169eVPvavWph9RAhcANDzg9c+mzArC+UJs/8PeVGKQCU4FINqnErGgQMHPuqS8Ntvv1W4QXJ5iI2NJTMzM56jc+fOguSfXb58mW/vBYC+/fZb5l5tjuOoe/fudOnSJerWrRsBoAkTJjBPBvfy8qKEhAQKCQkhY2Nj0tXVJV9fX6YcOTk59ObNG5JIJDRjxgwCQH379mXadzcoKIjPkbt//z6ZmJiQvr4+82tStiYUFBTw3tPJkycLmnOopaVFNWvWZOIBLmk83r17x9/U7NixQ2mO0rB582YCQB06dKCMjAzqt/OanDi7/TJFaY7w8HCqVq0a6enpVao/ZnH8Z4QZAGsAsQAMP3i9C4BUAKEAfAE0Ks/W5xJmBRKpUo3L/4tQCQ7F8DWNU3Z2Ni1btozGjBlDU6ZMIQcHB1qwYAEtX76c1q5dS56enkz53N3d5YSZq6urIKIpMDCQ1NTUqHXr1iQSicjU1JTOnTvHnGf27NmUkpJCO3bsIDU1NapWrZrSC8GHePPmDQUFBVF+fj5NnDiRDwe9e/eOKY8MT548ISsrK1JXVycPDw9BODiOo6VLl/Jt2Fg1/P7w2gsPDycLCwvS1tZmLjRlkEgkNH78eAJAo0ePFmR3K1HR5ixtbW2ytLRUetdhaXNUeno6tW3blvfSCgXZJo327dvTu7R0OWHW+7drJJUq7wx5/PgxmZubk56eHl+BoTIQUpiJit4rPEQikT6AvwCsJ6KzH/zPEABHRFkikagvgB1EZFOCjWkApgGAubl5y5MnTwp6zFlZWR8luwe/LsThxwUAgMO99QTl/1pQ0jip8DE+xThJpVIUFhZCW1tbaVscxyEuLg7Jyclyr4vFYjRs2JAJR3EkJycjNjYWIpEINWrUwJs3b2BhYQFzc3OIxez2KSUmJkJPr+jajY6ORkFBAUxNTWFlZcWMh+h/rbeysrLw8uVLSKVSWFlZwczMjAmHzLbsnEpISEB8fDy0tbVhY2PDJ++zRGFhISIjI5Gbm4uaNWsybSlXHImJiYiLi4Ouri5sbGyUTnAv6drLz8/H8+fPUVhYiLp166Jq1apKcZSG2NhYJCcnw8jICHXq1BEk+TwzMxMvXryAWCxGgwYNKn1tljVHcRyHyMhIZGVlCfrbJyUl4fXr19DT04OpVX0svP6/zSDTmmihfXXlNzvk5eXh+fPnkEqlsLGxqdS8XJn5vGvXrveJqPzCnIqoN2UfADQAXAYwX8H3xwAwLes9n8tjJlPvNssvCc7/teBr8gR9TgQEKLf9+0NwHEfR0dHk4eFB06ZNo4YNG5JIJKLbt28z5fH29pYLAeLf2kMzZsyggIAApp6AXbt20eDBg8nb25u/Q7ewsCB3d3dmPBzH8Xlf6enpNG7cOL5cA6vE4A8RGxvLhzYnTpzIrPTEh9fe8ePHSVNTk8zMzJifBzK8e/eOOnToQABowYIFgm1s2rdvH4lEImrQoIHSdRlLm6NevXpF9evXJzU1NTp69KhSHKWB4ziaO3cuXxeMddkRGa5du0b6+vpkampKDx8+rJSN8ubyzMxM6tSpEwGg9evXV4pDEezYsYMAUJs2behg8DM5z5kitUMVwdOnT8nCwoJ0dXUpMDCwwp//qkOZAEQAPAD8VsZ7LADee9cGReFOUVl2hRZmhYWFZQqzEAbxbqKiXTZCIzU1VVD7QUFBlJeXR8nJyYLyEBHTAoGl4e+//2a6aSMrK4tWrFjBh38yMjLIz8+PfHwqFw7PyMigRYsWUY0aNT7KzdLQ0KD27dtTnz59aOTIkTR9+nQmv0tCQgL169ePANCkSZOoY8eOJBKJCABVq1aNXF1dleaQISwsjIKCgojjODpz5gzVr1+fAFDDhg2ZhbY+xKlTp8jIyIjEYrFgYbrc3Fw+5NixY0cmOaolzVHXr18nY2Nj0tbWpvv37yvNURJycnL4BPfFixcLwkFE9Mcff/AJ7srMlWUtom/evKFGjRqRSCSiixcvVpqjLHAcR4sXL+Y3NwiFW7dukaGhIRkbG1cqFUARsZGVlcXX/ty/f38ljlIxuLq68rmg1o7/E2Zb/NjtDn727BlZWlqSjo5OhdeWr12Ydfh30XiE/5XD6AtgBoAZ/75nNopKaYQCuA2gfXl2hRZmzs7OtHv37o9Obpb5ZXfv3iUTExO6fPkyE3slITk5maytrWnhwoWCcQQGBlLfvn2pUaNGpe5wVRZ5eXk0Y8YMUlNTo1u3bjGzm5aWxouKJ0+e8MUVly9frrRtjuPoxIkTVLNmTQJAe/bsoVatWpFYLCYA1Lx580rblkqlFBAQQBMnTiR9fX1emOnp6VGjRo2oZs2aZGBgQACY5WpxHEd79uzhyz/Ex8fTzp07qWPHjnTw4EEmHDIUn/QKCgrI1dWVJk+ezJTjQ8TFxdHw4cOZF9MsDo7jyM3NjVmOXmmLw/Pnz2n27NmCJZ0TFd28Lly4UJCyI8Xh6+tLe/bsUcpGeYtoSkoKzZkzh3JycpTiKQscx9GGDRvo77//FoyDqGhd2bx5c6U+q6jYyM7Opnnz5gledcDd3Z0CAgIor1Ai5zVLzWK3ySUiIoJWrlxZ4Rulr1qYCfUQUphlZWWRmZkZubm5ybnppdKKVfwvC/n5+WRvb0/6+vrM2yfJUFhYyO/YOn/+vCAceXl5fNsTR0dHpjtVZaGYmJgYPgw0YsSIErsPVAapqanUqlUr6tKlC02aNInEYjGpqanR1KlTlf5NHjx4QB07dpTzZm3dupW++eYbmjp1Knl4eFB0dDST75GVlUWenp70/fffk4GBgVzyt0QiYb57WKjQVXGowuOKQTVOikE1TorhSx6nm5HJFaohKjSEFGZsSwb/R7Bnzx4kJyfD0tJSLhn4wet0ZhwbN25EeHg4du/eDSsrK2Z2i2PhwoUIDAyEk5MTBg0axMxufn4+IiIi0KBBAwwZMgTdunWDo6MjNmzYwCyx9enTpxgwYAAOHz6McePGISMjAzt37sTs2bOZcKSmpqJHjx58o/fg4GAMHz4ca9asQYMGDSptNyMjA8uWLcOePXs+agItFotx/PhxtGzZUqlj/xB6enoYM2YMxowZgzdv3iAnJwdGRkYAiiqfswbLRHwVVFBBBUXQvr4pmtasgtC49wCA364+x889vinnU18nVMKsGPLz8yGRSODs7Ax7e3t+cZNh/qmHStl///49JBIJ3r59i/Xr16NTp06YPn26UjY/xK1bt6CpqYnHjx9jx44d+OGHH7BixQqmHHv27MHDhw+RnJyMS5cuYfTo0Zg/fz4zUZafn4/Ro0cjOTkZ/fr1Q/Xq1eHt7Y327dszsZ+cnIzu3bsjLCyMf61169ZwdXVVesecoaEhdu3ahc2bNyMjIwMZGRnIzMzk/3737p2yh18mqlevLqh9FVRQQYXPhXOzvkPdZZcAAL9djUSH+qZoZW38mY+KPVTC7F8UFhZi3LhxaNOmDZKTk+Hm5vbRe16l5gAApneqWykOf39/BAQE4MGDB1BTU8P+/fuZex/27NmDyMhIPHz4EPb29jhy5AhTjvfv32PdunVITU0FADg6OqJGjRpMt4AvX76c92QBwMiRI2Fvb8/EdmJiIrp3747Hjx8DAIyMjNCiRQu0aNEC4eHh6Nq1q9IcIpEIenp60NPTk+sxFxwcjC5duihtXwUVVFCBNVj2QS0NHMchJyen0mWDxGIRzs5qjyG7bwEAftwbgpuO3VCjqo7c+xISEmBhYaH08X4uqGIS/+LFixc4ffo0li5dijp16qBdu3YfhaJkmNP9oxJrCuHixYtwd3fH3bt3MW/ePNSrV0+ZQ/4IKSkpOHXqFO7cuYP8/Hz88ssvzIXf1q1beVEGFI0by6bDV65cgYuLC/+8WrVqEIvFSEpKUtp2Tk4OnJ2dMXjwYPz555+Ijo5Gamoqrl69CmdnZyaiTAUVVCgfBQUFgnNIpVI8evRIcJ4zZ84gISFBUI6AgAAcPnwYUqlUMI709HTExMTg+fPngnGIxWIsWrQI7u7ulRaCLWoZoUnNKvzzn478jZwCeVvBwcEYMWIEoqKilDrezwWVMPsX4eHhAIruGqKjozFo0CDZrtKPoK9VcUcjx3Hw9fXln2/evFlOgLDA4cOH5Sa8nTt34uXLl8zsJyQkYNu2bfzzJk2aYMqUKdDS0mJiPyUlBRMmTIBYLEb//v1x7tw5xMXFYcuWLahfv77S9nV1deHi4oJ169ZhyJAhsLa2FqTYowoqCIXS5iSWCA8P5+dDoZCTk4NRo0bh7t27gnHIohLDhw9nevP4IaytrWFjY4PVq1cjMzNTEI4uXbrA2dkZzZs3h6+vryDngampKbS0tGBnZwcHBwcmN8MlwcHBATNnzkSTJk3g7e1dqe9yano7/u8nbzOw6PQjOTvDhw/Hs2fPYGtri/nz5wueQsIciuwQ+BIfrHdlrlq1it89Z2trS0lJ1nTCYwAAIABJREFUSXK7LiRK7si8c+cOb19bW5v++OMPRkdeBKlUSvXq1SMAJBaLadmyZcz75s2cOZMAUO3ateno0aP87jwWO3k4jqNFixbRxo0bKT6+8g1rv2R8yTuevjR8jWP1KXrnXrhwgX777Te+ppcQ45Sfn08NGjSg4cOH0+PHj5nbl2Hnzp0EgAYNGkSPHj0ShCMxMZH09fVp69atNH36dMHmlmHDhsnV9GM99xIRnT17ll9DunXrJkjZjYCAADIxMSEAZGBgQOvWrWPas1QGWVFn/Fun7N69exW2EfgsUW6X5sm7r+T+7+3tzXNUrVqVtmzZwrS4r6pcxicQZkOGDOFFh6zhcPGBv/0yRSlhJhN+5ubmdOfOHRaHLAdZ4+RvvvmGQkJCmNt//vw5WVhY0Pbt2/mq6TKwWBykUul/vin81yg2Phe+xrH6/fffadOmTZSSwqb4dEmQSCTUvHlzMjU1pXXr1tHVq1cF4fHy8iIAJBKJaNSoUYIUds7PzycbGxueZ8yYMRQZGcmcZ82aNXwPRh0dHXJ0dGRefysiIoLU1NR4IVCvXj36448/mM5pHMdRmzZt5ErwjB49mqKiophxBAUFkYuLixxHjRo1mDsSoqKiSENDQ45n5syZVFBQUCE7xYVZly1BcuPNcRy1a9dOjqNZs2bMxLlKmH0CYWZjY0MWFhZyE0Pxge+6JUgpYdayZUtq3LgxvXr1qvw3VwJDhgyhuXPnCnJ3Q0QUEhJSatX1r3ER/RxQjZPiYD1Wp0+fpidPnjC1+SHy8vKoUaNGpK2tTVOnThXMCxQSEsIvNNu3b6elS5dSYmIiUw6O46hnz548j1gspjFjxlBERARTnuJeIACkrq5Ozs7OTAVNVlYW3+JH5gn6+eefKywCysO0adPkCj1v2LCBeTeUwMBAufHavHkz06b1QUFBlJubyxfFxr+dPoRYV2bNmsVz2NnZVao+5busfDlxdi9avstNcHAwz6GlpUX//PMPq8MXVJipcswA5ObmIi0tDf7+/qXmMkWlZAMARrWpVWH7b9++haWlJW7evIlatSr++fKQl5eHefPmYceOHdDV1WVuHwDatm2LKlWqlP9GFVT4AtGkSRN8++23aNmyJbZt24Y3b94w59DS0sLBgwdRUFCA/fv3o0mTJujWrRvOnz/PNGm7bdu2mDp1KoCiBPeNGzfCxsYG/v7+zDhEIhG2b9/Obx6S7abLyclhxgEAgwcPRocOHfjnPXr0wIIFC5jmfurp6cmVkdHV1cW0adOgoaHBjAMAVq9eDR0dHYjFYmRnZyMvLw+mpqZMObp27YqePXvC0NAQYrEYR44cQWFhIVMObW1trF69GiKRCPXq1YOHh4dcfjQrrFixAjo6Ovjuu+/w5MkTTJgwocLfxUhPE0Na1OCfjzsgn7PYuXNn9OrVC926dYOGhgb69OmDZ8+eMTl+QaGIevsSHyw9ZhERESU2/C2uiGWKPDkz76P3lYfk5GRBW6N8bqg8QYpBNU4fg+M42rdvH+3bt4+ePn3Ke0qEGKuTJ0/KeYB69OhBhw4dovfv3zPlWbRokZxXo1WrVsy/T3JyMhkbG/MhOkdHR6b2ZZB5NdTV1cnc3FwQL+Dt27cJAH333XcEgH766Sfm3SWCgoLom2++odWrV5Oenh6Zm5sLkj/n6OhIrq6u1KtXLwJAv/76K3OOe/fu0YIFC+jo0aMkEonI3t6ekpKSmNiWnaeFhYX0008/UXx8PNnY2JC6urog3WPWr19P2dnZfJP34cOHU2FhYYVscBwn5zULi5OP7Ny7d49u3LhB165dI11dXbK0tGTSRkwVyvwEocySUJIwU+FjqASHYlCNU8lIT0+n5s2bEwAyNTWlwYMH08mTJ+nu3bvMw02yDSyyR5MmTcjf358pR05ODn3zzTc8R/fu3ZmGm2Rwd3cnFxcXPo9mwYIFzAVNcnIyNWrUiIKDg8nAwICMjIwEyZF1dHSkwsJCGjNmDAGgiRMnMr2ZDQoKooCAACosLKRr166Rnp4eVatWjcLDw5lxEBX13k1NTaWcnBw+FOzk5MSUg4j4tJIjR46QSCSiJk2aMMlt/LBHLVFRD9l69eqRhoYGeXt7K81RHLIbMY7j+Gtz9OjRFf7tfULfyIkzibTkUHhgYCDp6OhQzZo16eXLl0odu0qYqYTZFw2V4FAMX9s4cRxHERERFBsbS+/evavwnWxFkJSURLa2tnJ9RcViMa1bt45pvlFubi4vAgFQ/fr1BdndduPGDdLQ0CBHR0d+Uw7rZt9SqZQ8PT0pJyeHBg4cSABo7NixzMWsrKfr3bt3ydjYmPT19Sk4OJgph0xQSiQSmjhxIr9AszrnPrz2rl+/Tvr6+mRmZkZhYWFMOD5ETk4O9ejRgwDQmjVrBOEgIjp48CCJRCJq1qwZpaamlv+BMlDaHPXq1SuytrYmTU1N8vX1VYqjNEilUpo6dSoBoAkTJlT4JqO4MHPxLz0X0t/fn7S0tKhWrVoUExNT6eP9IoQZgJ4AfgfQ7N/n0xT9rBCPTynMMnILVMKsDHxtguNz4Wscp+vXr5OVlZVcAq2pqSlZW1vTkCFDKCcnhxnX69evqXbt2rwws7CwoLNnzzLfrRsZGUkGBgbk4OBAhoaGpKGhQdu3b2fOc+TIESIqCqFqa2uTkZERBQYGMuUoHnqaMmUKAaDevXtXKpFaEYSFhZG5uTlpa2sLukDLEumHDRvGRGiWdO3duHGDF2dCbdTIzs6m7t27EwBau3atIBxERPv37ycA1KJFC6W8s2XNUdHR0VSrVi3S0tJi7mWWQSqV8sJ8ypQpFRJnzxMy5MTZnajSReqlS5dIU1OT6tSpw1dhqCi+FGF2DkBVAFsBdAOwW9HPCvH4lMJsT/ALlTArA1+j4PgcCAoKosLCQkF2OHEcR8+ePaMDBw7QpEmTaMSIEczCWqmpqTR48GC5ECAA2rJlC3MBEBkZSRYWFrRjxw6ysLDgQ4GsvRqnTp2i+Ph4evnyJbVu3ZoAUP/+/ZnvopPhzp07ZGFhQerq6rRv3z5mdotfexzH0fLlywkAtWnTRrDv8vz5c6pVqxZpaGjQmTNnBOHgOI5mz55NAGjw4MFK1wUrbY66efMmGRgYkKmpKYWGhirFURqys7OpW7duBIDWr18vCAdRUWhbltNY2XIg5c3lL1++pJo1a5K2tjYFBARUiqM8SCQSGjt2LAGgGTNmVOiGaaDrDX6tbrfhKqVnly7qvby8SF1dnerXr1+pEhpfijDbV+zvTQDuKfpZIR6fUpgVV+EqfIxPKcyEqnVWvDZbfn6+IDw+Pj7UrFkzSktLo8LCQnr79m2lbXEcR3fv3qUtW7bQoEGDyMzMTE40jR8/njw8PMjb25svRqoMOI4jNzc30tLSkuPR0dGhkSNHMg1tPXr0iA4dOkQZGRm0ZMkS0tTUJLFYTA4ODoJ4gvLz82nhwoV8zabr168z5yAiio2NpWbNmhEA+uWXX5gI55KuvV27dpFIJKIGDRooFaopC69evSIbGxsSi8W8Z5A1OI6jX375hQBQv379lCoOWtYcFRISQoaGhmRiYkIPHz6sNEdZyM7Opq5duxIA2rBhgyAcRES7d+/mhXlp5Y3KgiJzeWRkJFWvXp10dHSYh7RlKCwspJEjRxIAmjNnjsLzceL7XLn1et9fZeeR/fnnn6SmpkYNGjSo8Hz8pZTLuCj7g4gcAXhU4LNfHW7cuIG3b9/KtXJY2Osbphw5OTmYNGkS31BbKMyfPx9nzpwRlOPYsWOYOXMm863bRedyEe7cuYPWrVsjPj6eKYdEIsGoUaOQm5uLy5cvo0mTJjh+/Dgz+6mpqfjpp5/w7NkzPH/+HOPHj4eJiQnGjh1baZsikQg1atQAEeHFixdITk6W+7+HhwfGjx+PAQMGIC0tTdmvAJFIhFmzZuHu3buwtbXFwoULcerUKfTq1Qt//vknrl+/rjSHDI0bN0atWrVgYGCATZs24fHjxxgwYAACAgKYtf8qDk1NTWzZsgUXL16ERCIptUeusrCyssL169cxePBg5OTkCNYObPbs2Th58iREIhE0NTUF4ahVqxauXbuGJk2aCPKbAEXnnIuLCxwdHaGlpQU1NTVBeNq2bQt/f3++JZEQ0NXVhbe3N7p27QoDAwNBOABg5syZcHV1hZ6eHtTVK946UBHUr18fgYGBsLa2ho6OTvkfqATU1dVx9OhRDB06FFWrVlX4c9UMtTGg6f9Ko3iFll0WZ8iQITh+/DgMDQ2Zl09RCuUpNwBXATRVROV9yofQHrPRo0eTi4sLJSUl8eo7NYttmw3ZVnfWVZWL49KlS3yRQNaQ3cX4+PiQlpYWNWzYkHnpgWPHjlFUVBRdunSJdHV1ydjYuFLtO0oDx3F8bo4sF8TExISOHz/OxPbBgwfJ1NSUz5vCvwUuBwwYQHv37mXwDYp47t+/T3PnzuW5XF1d6fr16+Tl5cW8PUxWVhZdvHiRf56amqp00vGHKOlulHW19pLAMmeuNEilUmYJ+mXdtbPeBFAShNwQIgPHcUrv0FTEu/EpShp9qrJJleWpiBfoSx2v4jnhtZf4UIoCJa4qw/NZQ5kAWgAIBHAIgKUiRj/FQ0hh9v79e9LR0aH9+/cTkTA7MrOyssjMzIwaNWrEfIu7bOLPyMggKysrMjc3Z75dXyKR0LZt2+j169e0Y8cOMjY2Zt5OJT09nSwsLKhfv36kpqZGtWrVYt4aZsmSJXKhuVmzZjERGWFhYdShQwc52zJhNmTIEMEmtfz8fDp//jwdOHBAEPufCqq8RcWgGifFoBonxfBfGadJh+7y6/bK88LsuhVSmJXr6ySifwB0E4lEQwH4iUSiswCciSiXmdvuC0F+fj40NTVx+vRp5ObmwsTEhDlHTEwM9PT0cOTIESQnJ8PNzY2vrs0Kf//9N27cuIHo6Gi8fv0aZ86cgZGREVMOPz8/rFixAh4eHhg3bhzOnDlTateEymLVqlVISEjAxYsXUb9+fQQHB6NGjRrlf1BBbNmyBZs3b5Z7LTY2lkkoy9zcHB4eHsjNzUVeXh5yc3Px7t07+Pj4IDc3F0lJSbC0tFSa50Noampi0KBBzO2qoIIKKnwt2D2mBWxX+gEAPEJeYVV/O6irfT2NjhQKQouKkiEiAOwBsA7ATyKRaCkRHRXy4D417t27h8DAQFy9ehXGxsaoUqUKpByV/8EK4ObNmzh8+DBCQ0Nhb2+PoUOHMrUPAJcuXcKWLVuQm5uLIUOGCMLh6uqKnJwcPHz4EHPmzIGdnR1T+w8fPoSrqyv//MWLF1i3bh127drFJHfi4MGDWLx4MQCgbt266NKlCzp37ozOnTszaaNiZmYGMzMzudeCg4PRpUsXpW2roIIKKqhQOrQ11NC4hiHC4jMAAK5BL/BzD7Y54kKiXAkpEoluAIgHsB1ADQATAXQB0EYkEu0T8uA+NdLS0rB69Wpcv34d9erVQ2JiIiLiksv/YAUQFhaGq1evIjk5GaampnBxcWHaRw8oEmY5OTkgIoSGhmLDhg1ySfTK4vnz5/Dz8+Ofv3//Hl5eXsw4OI7DzJkzec/Vt99+i/Pnz8PNzY2JKAsNDcXdu3dx9OhRxMbG4uXLlzhw4ADGjx+P2rVrK21fBRVU+HLAcu4ri6P4RjGh8ODBA8E5AgMDkZ6eLihHSEgIbt68KSjHpj7/60v929VIxKay7fMqJBTx7c0AUIOIehLRSiLyIaIXRDQHQEeBj++TovjJeO/ePRAR/J4pv6OtOMLCwvi///77b3Tu3JnpbqPExETcu3ePf966dWvMnz+f6Q6w3bt383/36tULjRo1wk8//cSM49ChQ7h9+zZ69uyJwMBAhISEYNCgQcxCvk2bNsXevXsxduxYWFlZMbGpggr/NUgkEsE53r17h3/++UdQjoKCAsTHxyM1NVUwDpFIBEdHR3h6egoqBK9du4YhQ4bgzZuydxsqA2NjY9jZ2eHPP/8U7Lu0aNECw4YNw8yZM/H+/XtBOBrVrw11yf8yrpafD/skIp0Fyl3piCicSv82/Rgfz2dFcWHWo0cPWFpa4sCNaKYcMmGmra0Nb29vtGnThqn94p6sVatW4fjx49DW1mZmPysrC4cOHYKhoSH2798PPz8/plvy09LScPfuXdy7dw/+/v7o2rWrYGUFVFDha0ViYiJyc4VN801OTsaMGTMEFTTGxsaYP38+Fi1ahOzsbEE4tLS0IBaL0bBhQ5w8eVKwxXncuHEYN24c+vbti1evXgnCMXnyZAQEBMDOzg779u0TpLRLs2bN0LBhQ/z444/44YcfmJcnAop+k1mzZmHv3r1o2LAhzp49y5wDAFZ1Nef/vh6ZgksPhPldWEMpFwQRRbE6kC8BMmFmYWEBT09PAEB2QVGYcWCx2ijK2H/9+jXU1dVx5swZQfKNLl26BE1NTXh4eMDJyYm5qDl69CjatWuH8PBwTJkyhbn9KlWqwN3dHa1atWJqVwUVPhUSEhKQkyNs2ERPTw+dO3cWzNsAAJaWligoKICtrS08PDwEEzRz587F1q1b0bhxY/j7+wvCYWZmhoyMDIwaNQoDBw7E69evmXN06NABLVu2hJ+fHxo1aoSdO3cyT1MxMDDATz/9hPfv32P69Ono1q0bnj9/zpQDKKp9CQAXLlyAnZ0d9uzZw1wEzpw5Ezo6Onj79i2GDh2KH374AXFxcUw5xvXtIM+5ehvOnTvHlEMIfD3bFD4B0tLSIBaLcfLkSZibm8v9b1SbWqV8SnGEh4dDJBLB09MT/fqxdzZKJBLcv38fV69exbhx45jbB4rCgL6+voKFAFnvUFVBheL4FKEMfX19dOrUCR4eHoIVq9XX10e/fv3w4sULDBo0CNHRbD37MixcuBApKSmYMGECunfvLogIGDRoEOrWrYvo6Gh8//33GDduHFJSUphyqKur8wWdfXx8YGdnBzc3N6a/j0gkwi+//AIAyM7Oxrx589ChQwfmBcTnzJnDp7/89ddfaNKkCTZt2sT0u/Tp0we2trYAgIyMDMyaNQs//vgjUy+tiYkJJk6cyD8/f/48Ro8ezTRMKxKJMKjW/0Ly0uqNsXPnTty9e5cZhxBQrYLFkJ6ejrVr16Jz584f/a+VtfLlJsLDw/H7779jxIgRStsqCW/fvoWfnx86dhQu9a99+/aq0KIKXy3i4uIwe/ZsREZGCsahr6+PsWPHYsKECWjdujWCg4MF4ZkzZw7EYjG8vLxgZ2eHtWvXIi8vjymHnZ0d+vfvDwAICgpC48aN4eTkhPz8fGYcampq+Pnnn/nnnp6eaNiwIdNuEgDkOLKysuDp6QlfX1+mHMOGDUP16v+LrlhZWTFPpK9du7bcTvsuXbpg2rRpTG9qxWIxLzKBomr/Hh4ezCv9//LLL/x6oqOjgy1btsiNHwusndib/1vDqDo6durMPIWINVTCrBjatWsHR0fHEv+nwaAGSv/+/TFlyhSl7ZQGKysr5rXEVFDhUyE/P19wj5aVlRVMTExga2uL0aNHIzw8XBCeGTNmoGbNmvjnn3/QtWtXDBo0CBEREUw5jI2NUa1aNQBAXl4eVq1aBXt7e9y+fZspz6JFi/i/CwoKkJiYiGfPnjHlmDRpklzrne3btzO/wbS3t0evXr345zY2Nujbty9TDk1NTcyZMwdaWlqoUqUKbt68KchO7/nz50MsFqN9+/a4fPkyLl68WP6HKohx48bB1NQUM2bMwIsXLzBmzBjmoVkbGxsMHDgQq1evho6ODgYMGMDc+2uoqwV10f+8iS6nAnD48GGmHMyhSBXaL/EhROX/DxulBgUFqZqXK4D/SrVooaEap7KRmZlJgwcPJicnJ/Lz8xOMJycnh6ytrfmODIMHD2ba5ksGd3d3uc4Penp65O3tzZTjypUrco3lDxw4oHDDZ0XBcRy1adOGtLW1CQANHz6cebcSoqIuHB06dKDq1atTlSpV6PHjx8xsy649X19fmjBhAt+GzcnJiRmHDKmpqTRr1iy6evUqqaurU9OmTSkjI4M5j7OzM6Wnp5OdnR1paGjQX3/9pbTND+eo8+fPE8dxtHDhQgJA8+bNU5rjQzx48IDy8vLo2rVrpKmpSba2tsw71QQ9jpNr06Surk5XrlxRzubnbMn0pT6E7pVJpBJmikIlOBSDapzKR1hYGOno6NDWrVupdevWtH37dnrz5g1znvPnz8uJJtkizVLUFBQUUN26dXn7K1asYGZbhqCgIJo1axY1bNiQjIyMyNTUlCIiIpjznD59mpydnWnmzJkEgBYuXMicIy4ujgICAuiff/4hPT09sra2poSEBCa2Zdcex3EUHR1NBQUFfG9cT09PJhzFkZubS0RE+/fvJwDUt29f5n1FZedqdHQ0mZubk5GRET179kwpm6XNUVKplIYOHUoAaOfOnUpxlIXjx48TAOrSpQvl5ZXf47IiKC7MajTrTIaGhvTo0aNK21MJs88kzK4EBKqEmQJQCQ7F8DWPU25uLm3YsIG2bdtGFy5coLCwMMrOzhaE6/Dhw3xfUQAkFoupd+/eTAUax3HUp08fnqN9+/aCfB8PDw+qWbMmde7cmQDQtm3bmNoPCgqimJgY8vDwoJs3b5KOjg5ZW1tTfHw8Ux6JREJpaWlUWFhIAwYMIAC0a9cuphzF4ePjQ2KxmFq3bs3kdynp2ktLS6OGDRuSpqYmXbt2TWmO0uDo6EgAaPbs2YJx3Llzh3R0dKhevXqUnJxcaTtlzVHZ2dnUpk0bEovF5OXlVWmO8rB+/XoCQGPHjmV6ozRw13V+Pe/pfJn09fXJysqq0teKSph9JmH2x8UAlTBTAF+z4PgQrMNAxVF8nAoKCgTlIiIqLCyk0NBQev/+PRN7r169Int7ezkvk4WFBX333Xe0e/duJhwyHD58mOcQiUTMQ4BERJGRkaSpqUk9evQgANShQwfmIRSJREKHDh2izMxMat++PQEgNzc3ZvaLe4KIigSNmpoaNW7cmNLS0pjxFEdWVha1bt2aRCIRnTt3ThAOIiJXV1c+1CyRSJSyVdocFRUVRWZmZmRsbEzPnz9XiqM0SKVSGjZsGAGgHTt2CMJBRHTmzBkSiUT03Xff8R67iqK8uTwhIYGsra1JV1eX7t+/XymO8sBxHB9qXrVqFTO7zxMy5Lxmm45eIjU1NWrWrFmlQs0qYfaZhNmKI/4qYaYA/kvCbPv27VRQUCCIbdk4RUdH0/fff89UmHEcRzExMXTq1ClauHAhderUifT09Kh9+/ZM84HS09N5ISN71KxZk3m4MTAwkJo0aULq6uqko6NDOjo65O7uzlzMrl27lrKzs2nLli0EgBo3bszc2yRDeno6tW7dmgDQ/v37mdgs6dqTidqOHTtSTk4OE54PkZiYSHXr1iVtbW0KCQkRhIOI6JdffiEA9Msvvyhlp6w5KiQkhLS1tcnGxoZSUlKU4ikNOTk59O2335JIJBLU2yQ7j0eNGlWpa0WRufzx48dUpUoVsrS0pNjY2EocZfkoKCignj17EgA6fPgwM7vFhdn6i0/o999/JwDUu3fvCs/7KmH2GYRZUlIS9droI7gwCwwMFGzylOH27duCLTZERSdoXFycoALtr7/+IolEQrt376b8/HxBOMLCwkhDQ4OmTJnCNPFYhqCgIDpz5gxVqVKF9PX1md0NSqVS2rdvH9WuXfujvCkdHR2KiYlhwiNDfn4+TZw4UY5nypQpTDmCgoIoIiKCOnToQI8fP6bGjRuTgYEBcwFYfPE6fPgwqampkYuLC1OO4nj37h01a9aMmjZtyuQGoLRrbvPmzaSpqUnXr19XmqM0REREkImJCTk4OAjGIZFI6IcffqDatWtTampqpe2UNzedPn2a1NTU6MyZM5XmKA8yb9OQIUME4+A4jqZNm0ampqaVuu4VncMDAgJIQ0OD9u7dW2EORZGenk6NGzemTp06Mbu5HOkewq/pc47/Q0REy5YtIwMDAwoNDa2QLZUw+wzCbO/evfwP+M3yS4JwxMTEEABasGCBIPaJii7UBg0akI2NjSChs5iYGAoKCqJJkyYRAKWTT0tCeno6GRkZkYODAwFgHjYjKrpDa9myJS80xo8fz9R+Tk4OHTlyRE7M9OrViymHRCIhPz8/+vHHH0ldXZ0AUI8ePSgrK4spD1HReeXk5ERVqlQhf39/5gnnskkvLi6OiIpy3O7cucOUoyQ8fPhQ8BBzcnKyUnlAxVHa4sBxHEVGRjLhKAtRUVGC7NAsjuzsbKU3ASiyiEZFRSnFoQhiY2MF88jLUFBQUGlPVkXExqcYrzdv3jB1XDyMTePX9cFuN4io6FqpzHcRUpip6piVgpCQEP7vHnbmZbyz8vDy8gIADBgwgLltIkJ0dDSCgoIQERGByZMnC1IYdtmyZUhMTMThw4cxcuRINGjQgDnH6dOnkZaWBjc3NzRu3FiuWjQrODs74/79+/xzX19fnDhxgontJ0+eoE2b/2PvvKOiuro2/szA0IvSEVSssWEvWBDsXaxJrLFrRDQi0ZgYscdO4idix6BRI/aCFBsiqASNigpYsKCg9CplYPb3B+9MGELnHDTJ/a3FWjOXmf1cDrc895S9OyMhIUGxTVtbG+/evWNagkRFRQUDBgyAt7c33r59i02bNqFFixbQ1tZmpiFHJBJh+fLl8PDwQL9+/dC0aVPmGgBgYWEBoLC2bE0khWzTpg33BMpGRkYwMjLiqiESiWokp2GDBg24V+vQ0tL6WyUWHjRo0IC7Rt26dSGRSLhqSCQSbpVZilIT7WVubs40qW1rS33F6z9fFyb+FYlENfK3VAbVj70DnxoFBQVQUVEpTNI4YiwAwLYx24vo3bt3YWZmhjNnzsDAwADdu3dnGh8AkpKSMGjQIFhZWUFNTQ3Tpk1jrgEAoaGhaN++PYgI9vb2iIyMVJTyYIWnp6fidXi8h8LuAAAgAElEQVR4OCZNmoRDhw4xK87+8OFDrFy5EkBhxuthw4Zh3rx56NOnD5P4RARvb2/ExMQgLS0N2traipIqvDAxMYGLi0thtzhHxo0bxzW+gICAACuKP3QR0SdZyUboMSuGm5sbfvvtN6Us3Z0YlGMqyrNnz2Bra4vAwED06tULd+/eRVZWFlONuLg4REVFwc/PDwYGBli8eDFevXrFVCMpKQnPnj1TvF+1ahXzp+cnT54gJCQEQGFW7W3btsHb25uZKZNKpZgyZQp0dXWxePFiPH/+HKdPn0bfvn2ZnbAtW7ZEs2bNIJFIoKenx92UFeVTvOgICAgIfCxm92yoeH3nVcpH3JPSEYxZMVRUVBTFbuXUM9BiqiGTyRAdHY38/HycOHEC69atg5YWW424uDjF63fv3qFJkybMS4P88ccfiteWlpYIDAxkPqQlL53RrFkzhIaGwsnJianZCAgIgKOjI968eYMNGzbAysqKWWwBAQGBmoBlAfOy+PDhA3eNolM+eDDD9i9jtjXgCVetqiIYs2IYGhr+bZtElW0PR9GTyMDAADt37mTesxEbG6t4PXbsWHz//fdM4wPA7du3ART2ZAUGBjKf01JQUAAvLy/MmDEDYWFhaNOmDdP4ADB48GBMnTqVeXFeAQGB6sG6LmNJxMTEcNcICwtDSgrfnpk3b97g1KlTXDUAcLmPlKTBs72MddUVr0OeJyErN5+bVlURjFkxSjJmrClqzLZv3w4zMzPmGvIes9atW8PT05PLkFZoaCisrKzw2WefoWHDhuV/oZLcuXMHW7duxZ49e7hMYBcQEKgarKdFlIS7uzv3nqBff/0VwcHBXDXi4uLwzTffcNVQVVXF7Nmzufc2eXt749ixY1w1EhMTMWfOHO7zY+WcuRdb/odqGMGYFUNuzNTU1LhpyC82o0aNwpdffslFIy4uDoaGhjhz5gwXU0NESEpKwrVr17i1VadOnfD5559ziS0g8G8kLy9P0ZPNk3nz5iEnJ4erxrVr17Bz506uGjKZDNOmTUN2djY3DbFYDC8vL5w7d46bhoqKChISErgbGolEgjlz5iiNyLBGQ0MDx44dw6FDh7hpdNb5q0fu0K1XNWYCK4pgzIohN2ZOTk7cNGQyGYyMjODh4cFtcnZCQgKOHz/Obc5UVlYWvL29mc9bK4owcV3g30R0dDTevXvHVUNuNHJzc7nqPH78GGvWrOGqQURYsmQJ9965J0+ewNXVlVt8+YKo2bNncxuiU1UtTLBw8uRJZml+SkJNTQ0pKSmYNm0aNzMjX9jl6OiIly9fctForv/XMPnjuHQ8fJvORaeqCMasGAYGBjAwMMAPP/zATYOI4O7uDhMTE24aCxcuhL29Pbf4Ojo6NZIrR0CgJkhLS6sRDd49GkRUI6ZJJpNh/fr1uHfvHleNzMzMGhnW2rJlC7eeRvkDZlxcHBYsWMBFo+hKb0dHR249WvLRET8/P269mXJjlpGRgUmTJnGZa9iwtnIuuXsRT5lrVAfBmBWjVq1aWLVqFWrXZpsioyh9+/blPkRXE8k4BQT+Lfj5+cHX15erhlgsxpkzZ3D48GFuGvJpEjVhmgoKCjBt2jTk5/OZPC03Y76+vjh48CAXDTk8exqLphA6ePAglyFNeY8ZAKSmpmLGjBlczGzR5LguLi54+pS9oSmaCunGjRvYsGEDc41ausrTezasXc19aL4yCMasGCoqKpgzZw5XDaGnSUCg4rx9+5a7hoaGBqZMmYL4+HhuGvIbtJOTk1I6G5bIb8b5+fmYNm0apFIpFx25Afzzzz+xZcsWLhpFjcU333zDfRj48ePHWL16NfO4RadkmJiYYM2aNcyHNIv2mOnp6aFRo0a4e/cuUw2gsMdMPmd53bp1XIYaNTQ0UK9ePQDAsmXL0KdPH+Yms3h6qgN7dzGNX10EY1YCNZkAVEBAoGxOnDjBPRWAlpYW3r9/z3XujNyYpaSkYPbs2Vx0isb8888/sXnzZuYagPLKcldXVzx5wj4fVFGNvn37wtvbm7kGAEXuxUWLFqFv377MV4KKxWI4ODigfv36qFevHm7fvo1atWox1VBVVcXo0aMxb948pKenY9GiRejQoQNTDQAYMWIETp8+DaAwnUm/fv2Ya3Tv3h1//vknTExMcPXqVXTp0oX5fOMGDRrAQOuvXsa45HRmSctZIBizUiiQfVqrNAQEPkV4DWMVpU6dOpg0aRIePHjATUOex+7ChQvYsWMHF42iQ1rnzp3jMjxX1Jipq6tj27ZtiIiIYK4jEonQrFkziEQiXLp0iUvPXMOGDbF//34AgL29PZcFWba2trhz5w7MzMxw+/Zt2NvbM69e0qZNG3h7e8PBwQFhYWF4+/Ytc6OhqqqKo0ePKqbIyM0Ta5YuXYrevXvDzMwMJ06c4KIxdOhQGBgYYPTo0QgODubSY964cWMMsq6jeH/IP5S5RnUQjFkpZH6CSecEBD419u7dq1T8nQcWFhbIysrC8OHDuQ01Fh3acHFxwaNHj5hrFL3ha2trY/ny5cxvOkSERo0aoXv37lBVVcWLFy+4rMzet28f1q9fDyLC69ev0bJlS+Yabm5umDhxIvT19XH+/Hnm8QGgV69e0NHRwdChQxESEoKkpCTmGkZGRpBIJBg+fDgAcJljJhKJoKqqim7dusHY2JibMQMKj+ORI0ciJCSEa9oMuck8fvw4l/i2Tf6qgX03ln9Fg8ogGLNSyM7jn3VaQOCfTvv27WFra8ttmAkoNGZAYVLTMWPGIC8vj7lG0coPOTk5GD9+PPPJwGKxGC1btoS1tTVq1aqF6OhoGBsbM9XQ0NDAjRs3MHXqVGRlZeH69etcqloMGDAAffr0gZqaGnx8fJjHBwp7gSQSCQYMGICrV69yLQc0dOhQyGQyXLx4kZtGz549oa+vjzNnznDTUFFRwfDhwxEUFMQ12ezo0aMBgOsUA1tbW5iamnJLaFun1l/nhVTPAg+fRHPRqQqCMSuFrDyhx+xTQiaTISsri/uy+by8PGRmZnLVAArnZ6SmpnLVuH79OjZv3sw1FUTHjh2hr6+P7777jtvTs7m5OVRVVSEWi9GlSxcuea20tLQgFotRu3ZtNG3aFDt27GDee2JsbIzAwECMHz8eb9++RXh4OPPkzOrq6jAzM8PgwYMBgOtKUx0dHdjZ2cHf359rhv4hQ4YgJycH169f56bRt29fqKurczVmEokEgwcP5m4yR44cCZlMxvV/b2dnB0NDQ5w9e5abhoqKCkaNGoWbN2/i/fv3zOOb6SnPKdt16gpzjaoiGLNSuHYzrEZ02rRpA0dHR64ay5Ytw2effcYtu3VGRgb++OMPWFhYcOtCF4lEsLe3R8eOHeHs7MztZpCWlobWrVujb9++uHXrFvP4ci5evIg2bdpwfart1q0bdHR0uFaxEIvF8PT0xKVLl1CnTp3yv1AFJBIJfv31V9y5cwcbNmxAkyZNmGvo6Ojg0KFDuHz5MkJDQ9G9e3dFTx0ratWqBUNDQ0ydOhWRkZFcar/KMTc3x82bN7F+/XpuGgCwbds2PHr0iPm8rKI4ODjgwYMHGDBgADcNbW1tBAUFYd++fdw0AGDVqlWIjo7+26pAlvTp0wehoaGYMGECNw1VVVX4+vri5MmT3DQAYPHixXj+/DlMTU2ZxzbUUVd6/+Wo4cw1qopq+R/5b/I2MR0A39WZ8mSQ7du35xI/MTEREokEz549Q2xsLLdC3UlJSZg9ezbi4uLw66+/IjAwEG5ubkw1RCIR4uPj8fr1a9y9excFBQXo378/Uw2gcBjrxYsXeP36NdebzalTp7Bt2zbmQ1lFUVVV5Z76BQAGDhzIXWP8+PFc4xsYGGDcuHFcNeSYmppyudEUx8bGhrtGs2bNuGvo6+vD2tqau06nTp24azRu3Ji7hoaGRo38LR07duSuwatyDQCoiJUXYDQ10+emVVm495iJRKK6IpHoqkgkihCJRI9EItHfUh+LCtkmEomeiUSiByKRiI9TqQSpWfxqpwGFS9mTk5ORn58PIyMjSKVS5ivcCgoK0KJFC9y8eROamppYsGABgoKCmGoAhRcCeV6m06dPY+jQocw1AChuZrq6uli2bBkXDfm8IldXV25JeokIGzduhIODA5f4AgICAgKVw0iH38hCZamJocx8AIuIqDkAGwCOIpGoRbHPDALQ5H8/swB41MB+lcrq1avxPj5R8d7Pz4+5xo0bNxR5Zq5cuYI+ffowz59mamqqWDWVkJCAU6dOoWvXrkw1AOVMzR06dEDv3r2ZawB/GTMXFxduPU05OTno1q0bli5dyiU+UNj7J6/JKiAgICDw8fmUajNzN2ZEFEdEd//3OgNABIDikzccAHhRIbcA1BKJROa89600wsPDcfb8BcV7HnlUbGxsFJOY7969i4EDB3I5MNq1a6d4PXv2bKXSHawoaswWL17M7QA3NTWFiYkJnJ2ducQHCjNbHzx4kEs7CQgICAiwhdWCsA9lLPgjIm5VNEpCxHuVm5KYSGQF4DqAVkSUXmT7eQDriejG/95fBrCEiMKKfX8WCnvUYGpq2uHo0aNc9jMhIQHnIjNwPauwh2ZfPw3mvVlEhD///FNxULVu3VqpDhkrYmNjERcXB5FIhNatW3MxHBkZGXjy5AnU1dXRqlUr5vHlxMbGQiKRcJ2XxZPMzEzo6Oh87N34RyC0VcUQ2qli/FPaqaCggHvlmfz8fMhkshIXBbFsp+TkZBgYGDCJVRofPnyAVCqFvn7V5odN8c1SvP6+iwaa1v572xMRYmJiULduXaVOh6q0Va9eve4QUfmT84ioRn4A6AC4A2BUCb+7AKBHkfeXAXQoK16HDh2IF/fv3yeddoOp/pLzVH/JeW463bp1IwA0ePBgbhre3t4EgMaPH89N4+rVq9SwYUNyd3fnpkFEdOHCBcrNzeWqwZOrV69+7F34xyC0VcX4lNtJJpNx1/jw4QNFR0eX+7nqtFNBQQH99NNPVFBQUOUYFeHIkSO0detWrhpRUVHUvHlzysjIKPH3LI6n3Nxcmjx5Mjk5OVU7VlmcPHmStLS06NWrV1WOIb/H119ynvZcf/6338fGxlLnzp3pyy+//NvvqtJWAMKoAn6pRtJliEQiCYATAH4jopLW174BULSytyUAfimFy6FVq1bQlPCvlylfNTV9+nRuGvKhTN4pOWxtbTFlyhSuGoMHD+aa+kFA4L+AVCrlmncMKOwt4VFyqigpKSno378/19XTubm5GD9+PO7du8dNh4iwZcsWjBs3Dj179uSiAQAhISHo1q0bzMzMuPUepqSkYMCAAfDy8sKgQYO4aND/Fk+NHj0aDRs2VBQ8ry4pH5QTV//555/o3LkzQkNDMWzYMCYaFaUmVmWKAOwDEEFEW0v52FkAk/+3OtMGQBoRxfHet9IQi8Vo1qQhdx0bGxsYGxtzW8UIFBZr7dmzJ5dJ/0VZt24d19w8AgL/BQoK+FYcSU9Ph7OzM1cz8/LlS3Tv3p1rUeiYmBj06NED7969Q/369blopKWlYdCgQfj999/Rt29fLhoFBQVYuHAhXFxcYGhoqDQnmCUnTpxA7969kZSUxCXNEABER0eja9euuHbtGtTV1WFnZ8dcIy8vDzNnzsSSJUtARBgyZAiz2DYN/1qQdfr0afTo0QNv3ryBiopKjaQEKkpN9Jh1BzAJQG+RSHTvfz+DRSLRHJFIJE+y5AMgGsAzAHsAzK2B/SqT1i345+exsbHBpEmTuCcAdXd3577ihFdyUQGB/wJEhM2bNyM6ml9ZGLmZ4cm9e/fQtWtXREVFcVudHR4ejq5du+Lx48fo06cPF43Y2Fj07NkTV69eBQAuxiw7OxtffPEFfvnlFwCFiWF5GGY3NzeMHTsWubm5AMAlUe+tW7dgY2ODqKgoAIVF51k/qKekpGDgwIFKSYBZGrNOVgYgIqxfvx4jR45UVGfo3r0797lyxamJVZk3iEhERK2JqO3/fnyIaCcR7fzfZ4iIHImoERFZU7FJ/x+DHh34JzS0tLTEwoULuevwnJAvIPBvJyMjAyEhIdzi5+TkYPLkydi7dy+XqgZA4bCMjY0NwsPDuT39BwQEoGfPnnj37h3atWsHIyOj8r9USQIDA2Fra6tYKc/DMEVERKBr16548OABAKBRo0bME50mJyejX79+OHHihGJbv379mGoAgIeHB1xdXRWLzIyNjZlXnEhLS4Onp6fSwjIex1hkZKQixRRQWEmjOiNB+QXKw/kaEhVIpVLY2dmhe/fuiu01PYwJCCWZSqV7R37lUuSIRCJYWlpy1xEQEKgad+7cQfv27bkN08fGxsLOzg6HDh3CiBEjuGj4+PjA1tYWsbGxUFNTg729PXONgwcPYvDgwcjIyADAx2ScOXMG/fv3V9R+FYlE6NWrF1ONgoICnDlzBiYmJoptPMyfWCzG+vXroaurq9jGo82+/vprfPfddwAKa0/ymJOnr6+PZcuWISMjQzFywmN+WdeuXfHu3TvF6wEDBlQry0B6zt/TY8hHr0JCQtCvXz+YmJgIxuxTopa2evkfEhAQ+Gi8ePECe/fu5RJbJpNhy5Yt6Nq1K7S1tdG2bVvmGrdv30bHjh0RGhoKAFyMmYeHB4YNG4asrMK0AHZ2dtDW1maq8fr1awQFBSnF5WEyhg8fjiNHjijet2vXjnmiZhUVFSxYsADJyckwNjaGkZERl+HSWrVqISAgABkZGVi8eDFatGjBZa7cs2fPsGrVKnTt2hUeHh5c5pcREebOnYsPHz7g9OnTWLRoEZo2bcpc5+LFizh06BCmTZuGM2fOVLsWaGScImMX9DQKDV5OTg6mTZsGPT09eHp64vDhw1z+lvIQsmiWgkRF8KwCAp8i6enp+Omnn+Dm5obAwEDm8d+/f48pU6bA19cXALisNvby8sKsWbMU837MzMyYlwDLzc2FhYUFOnXqhNu3bwPgM8RUr149TJkyBXv27EHjxo3x5s0bpaEgVuTm5uK7776DoaEhNm/ejIiICOYaAPDTTz8hOjoav/76K8RiMfNeOQCIiorC+vXrYWdnh/Xr12PixInMNYgIc+bMQUFBAXbt2oWWLVsqDDpLvL29cf78eXzzzTfo1KkTOnTowHxOc0ZGBmbPng0zMzNs3rwZtWvXrnZPVvjbNMVrfa3CHKIrVqxAZGQk9u3bBwsLC1hYFM+FXzMIxqwUxJ9QeQYBgX8KRISoqCjcunULEyZMYJo0uaCgAJ6enli2bBnev3+PIUOGoEuXLsziA4C/vz8mT56M9+/fAygsBM+6gDoRoXXr1hg2bBiOHz8OAHBwcGA+xKSurg4rKyvcuXMHPXv2REREBBdjJpVKMWfOHOjp6eH69evw8vLisiJz06ZNePr0Kfbu3YspU6Yo/kcsefLkCTZs2AA7OztMmjSJy6IpuWEiIuzcuRMikYhLkfbffvsNly9fxnfffaeIX3TolAUpKSmYP38+6tevj9WrVwMAlwUMS5cuRUxMDE6cOIHatWsziXkvJlXxOjVLij/++AObNm3CgAEDMHXqVCYaVUUwZqUgURGMmYBARcjNzUVgYCAuXLiA8+fPIyYmBgEBAUxNWXBwMBwdHXH//n3FtpUrVzKLDxTeMFVVVdG+fXtcvHgRQOGqr6LzjVggEomgo6MDHx8ftG3bFnl5eVyGMQsKCjBjxgxIJBLs378fT58+RfPmzZnr/PLLLwgPD8f27dthbm6OxYsXM9d4/vw51q5di27duilumvLauayQD8nJZDLs2LGD20r2gwcP4tq1a1i2bBmaNeOz+j8pKQkLFy5Ew4YNsXz5ci4aAPDtt9/i/fv38PHx4ZYbLSgoCO7u7hg9ejRGjRrFLO7Fh+8Ur7s1MsC0adOgra2N3bt3f/S6mYIxK4WP/Y8RKJuYmBhYWFhwzcf08OFD7itafXx8MGDAAG5lWIgI8+bNQ15eHlq1aoVWrVqhc+fOTJ+cP3z4gHXr1imGFffv3888h1GHDh1ga2urMGYODg5KK7RYIF+MExQUhEaNGiEuLo7LMGZBQQGmTJkCqVQKLy8vJCUlcckz6O7ujj/++AMbNmxAo0aN0KhRI+Yar169gqurKzp27Ig5cwqzH7G+dsqP4fz8fHh4eHA7548cOaLoYWrRogUXjeTkZCxatAiNGjXC999/z0UDKDRMiYmJOHz4MDQ1NbloXLt2Dfv27cO4ceO4JZPNycnBjBkzUKtWLWzfvp2LBgDkP7mOhw8fYufOncwS1lYHwZiVQlxczeS33b59O+Lj47Fq1SpuGnfu3MH27duxYsUKbskYpVIpXF1dUadOHTRt2hTt2rXjUtMyMDAQ7u7uePHiBY4fP87l75HJZJgyZQqCg4Nx5swZbubs6tWr+OKLLzBy5Eh4enpyMWcikQhBQUEIDw9Hz549Ua9ePeYrDOXzPSIiIjBlyhQuwwAaGhqYOXMmXr16BR8fH+a9ZXLMzc0xatQoODs7w8/PD4MHD2auIRaLMXXqVIwZM4bLEJYce3t7TJ06lWtKHgMDA8yaNQsTJ07kWuNx2rRpsLOzQ+vWrblpdO7cGV999RV+/PFHbhpaWlpwdHREt27duBkmAPjiiy9gYmLCZRGGnKZNm2Ly5MnYtGkTNw2JRILZs2fDxMQEZmZmzOLK04fImT6kGySJszFr1ixmGtWiInWbPsUfnrUyiYhiYmK418okIho2bBgZGBhwrSvn5+dHAOjAgQMUEhLCPH5AQADdv3+fGjVqRCYmJqShoVGh+nWVZefOnWRjY0MACAD5+voy1yAi8vDwIB0dHQJA8+fPZxa3eG21gwcPkqWlpaKWqVQqZaZVlOPHj9Pdu3e5xC7K0aNHmdUTLKsO3a5du5holEdN1HqsLp9yrcxPCaGdKsZ/pZ2evs9Q3N+df79XpRj/+FqZ/0TMzc1rRKd169ZITk7Gq1ev4O/vzzx+aGgoZDIZRCIRNm3ahDFjxjDXEIvF+Pzzz/H8+XPEx8cjJycHOTk5zHXGjh2ryJMEgNuqrGnTpmHBggUQi8U4ePAgl78FACZOnIiYmBi8f/8ekyZNQmRkJBed0aNHcyv1UpQvvviC69CynJp6qhWmMwgI/Dv57fYrxeuvuvEZRaoOgjErgdjYWCUDsG3bNqVJxywgIixZsgRPnz4FUFj2wc/Pj6kGUDhBduTIkSAiPHr0COrq7POzicVi/Pbbb0rJ/uRpAFhiYGAAX19f1K1bWO+el5FRU1PDmjVrEBgYCH19faXs3DwwMTHBwIEDhQoNAgICAjWAZ/BLxesGRmzz+rFAMGYlIBaLlSYALliwgHlJDpFIhPbt2+PYsWMACs2g3HCwpH79+liyZInivZ6eHnMNoHBydtF5crx6mSwtLeHv7w9DQ0NuxkxOjx49cP/+feTl5XHVERAQEBD4OGipfXpT7QVjVgJmZmZKy3It69WHvr4+c52xY8eiZcuWive8VoMsXrxYEZt1HpviOvIiybyMGQA0a9YMPj4+ePPmDTcNOXp6eh89p42AgIAAT2ri4TMmJoa7RmRkJOLj48vej+QPiteqYhFUxJWbspCQkIDz589Xaf8qimDMSqHoSqZG7dhnsQYKe+ZcXV0V73kZMy0tLWzZsgUAvx4zoLCcycGDB6Grq8tlKLMonTt3xo4dO5CZmclVR0BA4J8FFVtxx4NXr15xv/aEh4fD29ubq8bDhw8xYcIEZGdnc9OIjo7G2LFjcfnyZW4aSUlJcHJywqxZs8rNBnD0j9eK17oaFe8ty83NxaZNm9C0aVPuNa4FY1YKbdr8VcRcpwnbUilFGT16tGLJPM/8KaNHj0avXr24GjMAsLKygru7O9ceMzn9+/fnltRQQECALe/evYNMJuMWXyqVYu/evYrkwDxITEyEs7MznJycuF173r59i+nTp8PGxoZ5ZQs5cXFxmDlzJtq0aYPWrVtzGRFKTU2Fi4sLmjdvjvDwcC5lp3Jzc7F161Y0btwY27dvh6ura7mLdtyvPle8bmJa/ggSEeHEiRNo0aIFFi9ejL59+3KpnVuUT29w9RMkVZvfqg2xWIwVK1Zg/PjxXPJ+yRGJRPjll1/g4eHBTUPOxIkTkZCQwF1HQECg+rx+/RoikYjLHFegcAhr/fr1UFNTg5ubG/P4MpkMR48ehaurK1RVVREeHs5cIysrCz///DM2btyI9PR03L17l7lGeno6NmzYADc3N2RnZ2PhwoXMH9azsrKwZcsWbNy4EVlZWTAzM8O8efOYakilUuzcuRMrV65EUlISgMIqHUUXh1UXIsKpU6ewePFiPH9eaLTs7e3Ru3fvMr+Xm1+g9H7JwM/K/PydO3fg7OyM69evAyi8j65YsaLqO15BBGNWBrXVRUjJJbzJYVdapiRGjBiB4cOHc1+eb21tjQULFnDVAAoPXtZlbAQE/mtIpVI8ffqUWxb6+/fvY9OmTXjy5AlCQkKYx3/16hV++ukn7N+/H9ra2ooV6KwgIpw9exY//vijwoydO3eOqQGQSqXYv38/VqxYgXfvCkv4jB8/nmn6mby8POzevRsrV65EYmIiAEBHRwdLly5lpgEAR48ehbOzs1Ly9B9++AHa2uxWJSYlJWH48OFKx5O1tTXGjh3LTAMorAPq4uKiVC919erV5d5Dt195pnjdzEwXHeoblPrZxMRE7Ny5E2FhYYpt48aNU5oXzgthKLMMulvUjG8Vi8VcniRL4rPPyn5CEBAQKB95IkgevHjxAt9//z0aN26M/Px8prGJCAEBAejfvz/atm2Lw4cPw93dnamZefnyJWbNmoUmTZpg165dkEqlWLVqFYyMjJhphIWFwcbGBiNGjFCYst69e2PIkCHMNIgIGzduxOLFixWmTCKRYM2aNcw0gMIhv9zcXKSnpyu2ubi4MB9BGTZsmFIlgPr162PmzJlMNQwNDXHgwAGlRWarV69mngUzyQ4AACAASURBVN/wyy+/VCw0A4ABAwYovS+N/ytizDwmll3SzcjICL1791bMv1NRUVGaE84TwZiVQdc6NdehaGFhUWNaAgIClUcmk+H27dv47rvvmJftkUqlOHnyJAYMGIBGjRrhp59+gqOjI7MSRDKZDIcPH0b79u3Rv39/BAQEAADmzZuHTp06MdEAgLS0NKxYsQJeXl6QSqUAgJYtW+Lrr79mpgEA7dq1w4QJExTvRSIRNm/ezHTUQSQS4euvv1aqMTp37lw0aNCAmQZQaAAiIyORl5cHNTU1GBkZwdnZmakGAPj6+uK3335D48aNIRKJ4Orqyjyv5evXr9G/f3/k5eVhyJAh6NSpE4YPH85UQ15r9sSJE5g3bx7MzMywevXqcr8Xn64877m8/GWnTp3CpEmT0KxZM2zcuBGTJ09G06ZNq7XvFUUYyiwDMy0h87eAwD8FIkJcXBx0dXWZpYWRSqW4fv06Tp48iTNnzuDt27ewtrZGSEgIMxMgH5aR98oAgK2tLRYtWsQkPlDYK1/c5NWpU4d574++vj4cHBxw5MgRxbZt27Yx7ZEDCodhV65cCV1dXaioqMDBwYF5dYukpCT07dsX9+7dww8//IBt27bhhx9+YKpBRJg7dy727t2LiRMnonPnzsjPz2ee1ujs2bP48ssv0bBhQwQGBmLFihWYNGkSU43Y2Fj06dMHb9++xcmTJ/HZZ5/hxYsXTM2yTCbDnDlz8Ntvv2HmzJnYtm0bhg0bVqGHi303Xihed21oWOZnL168iC+++AJWVla4dOkSdHR0kJycXO39rzAVqdv0Kf7wrpVJVFgLqybqZf7T+a/UV6suQjtVnPLaSiaT0bNnz8jb25uWLl1KAwcOJFNTU5o7dy6zep3nzp0jAwMDRW1WAGRgYEDPnz9nEl9OQUEBOTg4KDR0dHQqXGu2oseUTCajNWvWEABSU1MjAHTixIlq7HXJeHp6klgspkaNGtGMGTNo1KhRzDVu3bpF+vr6VKtWLbp9+zYtWLCAYmJiyvxOZc+9xMREatu2LQGgPXv2EBHR2bNnq7rLJSKTycjR0ZEA0Lhx4yg/P58SExMpOzubqY6Pjw+pqalRw4YNFe2Ul5dX4mereo16//49NW/enFRUVLgcV0SF7eXk5EQAaOLEiZSfn1/h7xYUyBT38vpLztNPPhGlfvbKlSukoaFB9erVo5cvX5b6OZ61Mj+6warqj2DMPh0Ew1Ex/u3tlJOTQxkZGZSamkpJSUn0/v17io2NpZiYGHr58iWlpKRUOFZZbXXu3DmqXbu2kmECQAsWLGBaeDwvL4/GjBmjiK+iokKXLl1iFp+IKCsriyZMmEAAyMTEhADQ/v37K/z9ihxTUqmUZs6cSQCoV69e5OfnR0OHDmVepP3nn38mAGRtbU1xcXEUHh5eYYNZUYKCgkhXV5cMDAzozp07REQVMjKVOfeKmrK9e/dWdVfLRCaT0YIFCwgAjR07lqRSKRedgIAAUldXL9dkyKnKNSopKYlat25NIpGIDh8+XIW9LB+ZTEaLFy8mADRmzJhKt9fliHdKxuxBTGqJnwsODiZtbW0yNzenp0+flhlTMGaCMfuk+TcbDpY3r5La6cWLFxQfH89MoyTevn1LK1asoCtXrlBWVhY3HX9/f1JXV/+bYQJAs2fPpvT09ArHKuuYiouLo549eyrF//bbb5n+rx49ekQdO3ZUMkxubm7M4hMV/u/lBmDGjBkUFRVFDg4Olfo7yjv3MjIyaPDgwQSAJkyYQDk5OZSfn19uD1NlkMlk5OrqSgCoa9eulJyczCx2Ua5cuUJaWlpkbGxMDx48qNR3K3qNSkhIoDZt2pBIJOJqypydnQkAjRo1qtTeq+py7do10tTUJAsLC3r27FmFvlPZa3lqaip16NCBAJCnp2fld7KCrFixggDQ0KFDKTc3t9LfL2rK3AKiSvxMWFgY6enpkbGxMT1+/LjcmIIx+wSM2bs0tt3L/yY+ljHjaTLksBwaK95OMpmMnjx5Qvr6+vTzzz9zu0DHxcWRra0tASCJREJdu3alxYsX0/nz5yvVi1UWL1++JDc3N7KyslIyTBYWFuTr61vpeCUdU8nJyfTdd9+RlpYWASBtbW0CQD/88AMzU5afn0+bN28mdXV10tDQIDc3N7p06RJ99dVXTI1fQEAAGRoakkQioV27dhFR4fGQlJRUqTjlGdj27dsTAFq6dCmz47goBQUFNH/+fAJA/fr1o8zMTOYaRER+fn6koaFB5ubmFbppFqci16iipmzfvn1V2MvyKdrz4+DgUCWTURFu3LhB2traZGZmRlFRJRuRkqjMtTw9PZ26du1KAMjDw6MKe1kxNmzYoDi+qjLM++RdupIxy8v/+3nw4MEDMjAwoFq1atG9e/cqFFcwZh/BmEmlUjp79qzin7nZL5KLzuvXr7k+aRAV3mx27dpVoa7sqiA/QO/evUvu7u5EVPgkxYPs7GyaNm0avXz5ksaNG1epXpjKsG7dOpo3bx4BIEdHRyY35eIncmhoKBkbGytMTIsWLcjf37/aOsUxNTUtsRdLIpHQqFGjqnSjK458qKzonKzJkydX2fiVdNHz8fEhAGRra0tBQUE0Y8YMWrlyZTX3XJmUlBSysLCgzp07U0RE4TyU1NRU5vN+pk+fTmZmZhQcHFytOGXdHPz9/UlNTY127txZLY2ySElJoWbNmtGoUaMoJyeHm46LiwtZWlrSkydPqvT9itxEg4ODSUdHh5spIyL68OEDderUqco9PxVl48aNZGxsTI8eParU9ypjNsLDw8nAwIB5T3JR8vPzqX///tSzZ88qP4gXNWVXIt+X+Jn9+/eTnp4e3b59u8JxBWP2EYxZamoqbdmyRemfyoPp06eTSCQqdzy7Ojx48IBEIhF9/vnnRFRoBlkiP0AHDx5MIpGIfHx8qH///sxvZkREgYGBJJFIqE6dOqSqqkrOzs7MNWQyGX3++edKJsbFxaXa5qz4iXzr1i1q3br13wyTg4NDhYceKsIvv/xCvXv3VsTv1q0b7dixgxITE5lpPHr0iIKCgujx48dkYmJCp0+frla8ki56MpmMbty4ofg/sDCUJfHkyRNuc37kZGdnU2xsbLXjlHdzYDlkWRrv37/n3l4ymYzevy/5ploRKnoTrY5GRUlNTeVqYuVUZYpEZc0G72kYRIXnSlUfwKOK9ZaVRUJCQqVi8zRmQh6zUtDX1y8sxn3nFFcdJycnEBHc3d3x6tUrREVFMdewtrbG9OnTcezYMWzfvp15UkE5np6eqFOnDkaNGgV/f3+cOsW+7WxtbbFixQrExsYiPz8fv/zyC/MSLEQEGxsbpSX+mzdvZp5c0MrKCqmpqQAATU1NmJmZoWnTpnj79i3mz5+P27dvM9GZN28eNDU1sWLFCjx79gzBwcH4+uuvYWhY9pLxytCiRQv06NEDOjo6ePToERwcHJjFliMSidC9e3fF8vvmzZsz1wCAJk2aME/vUBwNDQ2Ym5tz1QDAvdgyAJiYmHBvr5qqJlITGvr6+szzh5UEzxJ/NamhoaFR5fQh/d2uK15P6FJ2eSuWCZCri2DMyqBWrVqID/bmqtGmTRvY2dlh//79GDZsGB48eMBcIykpCV9++SVUVFTg5OSE69evIy8vj6lGQUEBdu/eDS0tLUUB87179zLVAIDg4GB4eXkp6To6OhZ2/zIiLy8PrVq1wo8//oiBAwcqCvyuXr0a69atY6ajpaWFP//8E3l5efjw4QPi4uIQFRWFP/74AxcuXGBawPjcuXNwdXVVSpbJg7p1635SFzgBAYH/Jpcj3iu979vc9CPtSeURjFkpeHl5IScnB7Ls9PI/XEVyc3Px+eefIzo6Gunp6QgPD0dMTAxznbS0NMyaNQsFBYUFXLOzs5kX4VVRUcGUKVOUCiFfuXJFUWCWFT169MCjR4/g7e2N9u3bAwCCgoJw8OBBZhoaGhro168fli9fjosXLyI5ORmPHj3C3r17ER0djYsXLzLR0dXVhYGBASQSvrVYxWIx9zqsAgICAp8K+QUyTP/1rxqXn3e0hP1n/Hv3WCEYs1Lo3bs3kpKSuGqoq6tj7dq1yMzMVGx7/fo1c52GDRsiKChIqfhqUFAQcx1LS0sEBARg8+bNUFNTAwDs37+fuY6KigrGjBmDsLAw+Pn5wc7ODt9++61iWJA1YrEYLVq0wPTp07F3714MGjSIi46AgICAQPVZcuKvkSdddVWsGWHN/OFU3tHBA8GYlYKlpaVS7w8AJGbmMtdp0qQJTp48qZijwcOYAYXlVwIDA9GxY0cAfIwZUGhiFi1ahNDQULRo0QKenp7MCzHLEYlE6N+/P65du4ZTp07hxo0bXHQEBAQEPhY1UQrozp07iI2N5aoRFBSEw4cPc9UIDg7GhBlzceLuW8W2a9/aQ02VndW5f/8+HBwcFMXNeSAYszIwNDTEkCFDFO9/8onkomNvbw8PDw8A4DKUKcfQ0BCXL1+GnZ0dbty4AZlMxk2rTZs2CAsLw5gxY+Dr68tNR063bt0wdOhQ7joCAgKfPm/evGE677Q4GRkZ+OWXX/D06VNuGpGRkZg6dSo8PT25aYSEhGDw4MFYsmQJt8UogYGB6N27N4YOHYo+ffpw0bh58yb69++PHj16INjor3v2lG5WMNRhs9Di0aNHGDt2LNq2bQuxWAwdHR0mcUtCMGblsGvXLuS/Kzz5Ttx9w01nxowZWLhwIbceMzl6enq4ePEiunfvjsePH3PV0tTUxLZt22BjY8NVR0BA4NNHJpPBz8+Pm5khIvj7+2PIkCE4evQol3mVcXFxWLp0KerVq4e7d++iSZMmzDXu3LmDMWPGoEWLFrh16xacnJyYxiciXL16Fb1790b37t0REBCAbdu2MW+va9euwd7eHvb29rh69SqWL18OU1O2E/BDQ0MxaNAgdOvWDQEBAWg9WrmtXAZ8Vm2NqKgojB8/HtbW1jh+/DgkEgk2bdpU7bhlIRizcrCwsMA33WpmldmmTZvQuXNnxapGXmhqauLkyZPQ1tbmqiNHWKUnIPDpIpVKcfHiRezZs4dLL1NsbCzWrl2LRo0aYfv27WjcuDHT+JmZmdixYwdatGiBAQMGICEhAd988w1TjcePH2PatGmwsrLC+vXroaKigi1btjCLT0S4cuUK+vXrh44dO+LEiROKNEry+bosNHx9fdGjRw/07t0bV69eBQDMnz8fLVq0YKIBABEREbCzs0OvXr0QGBgIAGjatClTg1lQUIBvvvkGXbp0UYzIiDX1kNZ4gOIzX3aqCx316qVxuXXrFvr06YMjR44ozg0nJyfmx3BxBGNWAZxnjK8RHRUVFfz222/c5mQVRSKRoEGDBtx1BAQEqs6zZ8+wfft2xMXFMY1LRLh58ybmzZsHCwsLfPXVVxgyZAizXpOCggJcvHgRI0eORL169bBs2TJkZmZi7969zDRevXoFZ2dnWFpawtHREZGRkZBIJNi/fz+zvGpEhBUrVqBly5bw9PRUpBnasmUL0wfO6OhoeHh44NKlS4pt48aNQ+/evZlpAIUpoKRSqeK9qakp8/yMzZo1w+zZs5W2ubm5MTOYQOG9cu3atbC2tlZsqzv/r/lrDYy04dy/abV1bGxsMHfuXMV7Q0ND/Pjjj9WOWx58swL+SxCLa86/6unp1ZiWgIBA1cnKysKbN2/w2WfVHy6Rk5eXh6CgIFy4cAEXLlzAkydPsHXrVmbzfyIjI3Ho0CEcPnwYL168AFC4iMbPzw916tRhoiGVSuHo6Ig9e/Yobd+7dy/ToSwDAwPUqlULaWlpim0//vgjWrVqxUxDJBLh22+/xYULFxAWVph+oXfv3pg8eTIzDQBo0KABLCwsFO91dXWZ9sgBhX9LVFQU7t69C4lEAqlUik2bNjG/59y/fx8LFy6EpqYmtLS00KVLFwwePJipRnp6OoYOHYrw8HDY2dnhscZfGQf0NFRxeGYXmOhqVEuDiODq6orVq1ejZ8+eePv2LZydnVGrVq3q7n7FxP+JPzVVxFyOvKRDyDN2ZWz+LXysIub/NIR2qjifWlvl5uZSWFgYeXh40LRp06hVq1Zkbm5ODx8+ZBL/5cuXNHr0aNLV1VUqzzV79uwyS4FVtp2ioqKof//+Shqurq7V2/kSePDgAZmbmys0pk+fzlwjIiKCGjdurNBo27Yt5eXllfjZqh5P7969o44dOxIAsrGxIXV19SrX6yyNnJwcRQm4UaNGkZ2dHf38889MNYiItmzZQgDI2tqagoODqXv37n87tqp73t24cYP09fVJT0+PgoKCaNGiRZUqol4REhMTFf+TjRs3UuDD10pll14nVa2mZlFkMhk5OzsTABowYABlZWXRgQMHlEqPCbUyPyFj1nDpBe66/zQ+tZvop4rQThWnom0lk8koMTGRHj58SJcuXaJDhw7R5s2bafPmzUzqEWZnZ9P48eNJXV1dycwYGxtTeHh4teMXZffu3Uoa/fr1K9VoyKnsMXXixAmqVauWQqNPnz6Un59fjb3+O0ePHiUtLS3S0dGhzp07U4MGDapc67A0/P39SV9fnzQ1Nen48ePUsWNHunv3bqmfr8q5FxERQVZWViQWi2n79u305s0bWr16dTX2+u+kpaUp6tjOnTuX8vPzydfXl2ntUZlMRkuXLlXUyU1OTiaiwoeB4lTnGuXn50daWlpkbGxMd+7cISKqcuHx0oiNjaWWLVuSSCQiDw8P+pCbr2TKnsdnVFujoKCA5syZQwBoxIgRpV5HBGP2CRizs/feci1m/k9GMBwV47/STqmpqZSVlVWtou/ltZVMJiNXV1eSSCR/KwLfpUsXevPmTZW1i+Pv76+kY2RkxNSU5ebm0sqVK0kikZBYLCYA1Lx5c0pJSSn3uxU9pj58+EBff/01AaD69evTpk2byNzcnN69e1fNvf8LqVRKLi4uBICaNm1Kjx49okOHDtGNGzeYaRARubu7k4qKCtWpU0dhAMoraF/Zcy8wMJBq165NmpqadObMGcV2liY2NjaW2rZtSwBozZo11TpfSiM/P59mzpxJAGjQoEHlGqWqXqO8vb1JIpGQpaUlRUZGVilGebx8+ZIaN25MKioqdPDgQZLJZEqm7MjtV9XWkEqlNGnSJAJAX375ZZkPRoIx+wSMWdGDQECZ/4rhqC4fu51ycnLo9OnTiidmXgQHB5OamhqpqqqSkZERNWrUiNq3b0+9evWir776qsQn9eKU11Z5eXnk7e2t1PsDgKZNm8akp4yIKDIykkaOHEkASENDQ2HKHjx4wCQ+EVFoaChZW1sTAOrRoweFhYWRkZERPX/+vELfr8gx9fjxY4XG2LFjKSUlhZKSkujatWvV3Pu/SEhIoD59+hAAGj58OKWmphIRWyMjlUpp3rx5BIA6dOhAb9++rfB3K3PuHTlyhNTU1MjExIRCQ0OrsKflExUVpeiN27t3LxeNnJwcGj16NAGgCRMmlNv7SlS1a9S+fftILBZTkyZNKnRuV4WoqCiqW7cuSSQSOnnyJBERjdoRrLgn99p8tdoaubm5NGbMGMV1pLxjVzBmn4AxI/prOLOggP2TzT+Zj204eJOZmckkTlntdP/+fVq7di2lpaUx0SqNCRMmkEgkovbt29OiRYvowoULzIaZ0tLS6OLFi/TDDz+QhYWFkmESiUQ0c+ZMev/+fYVildZWL1++pB9++IHMzMyUDJOqqipt376dSa9DbGwszZ49m1RUVEhFRYVmz55NMTExZGhoSPfv3692fKLCIR4XFxcSi8Wko6ND7u7uVFBQQESk6AWqCGUdUzKZjPbs2UOampqkqalJu3fv5tIrExYWRvXq1SORSESrVq1S/B0sSU1NpQEDBhAAGjNmTKWHyCpyjZLJZLR+/XoCQJ999hlFR0dXcW/LJjQ0lIyMjEhTU5POnj3LRSM9PV1hlJ2cnCr8P6nstXzr1q0EgNq0acO097UoDx48IFNTU9LU1CRfX18iItpz/blSb9mrxOoNmWZnZ9OQIUMq1V6CMftIxuzy5ctKT2Xyg2D7lafMNGQyWaUuxFXlzp073HpK5AdocnIyXbx4kYtGUTw8PCghIYGIiF68eMF8jgwR0cmTJ2nXrl2Unp5OFy5coK+//ppyc3OrFbP4ifzkyRP6/PPPadWqVXTs2DFSV1cnAwMDWrNmDVOD1r9/f2revDnVr1+f9PT0/jb0p6KiQra2thQUFFRljSVLliiG4QAo9WTZ2tqWOf+nJEq66Pn6+pJIJCIA1K5dO9q9ezc9ePCATExMKDAwsMr7XpSsrCwyNDQkADRy5EiKiIhQ/I5lT9n48eMJAA0cOJBevar6EExZN4czZ84QAGrVqhU9evSoyhplkZmZSUZGRqSvr0/nz/MbTZg6dSoBoGXLllXJ+FXkJnrp0iUCQD179qSkpKQq7GX55OTkUN26dcnAwIBCQkK4aBARLVq0iADQqlWrKmXGK2M27ty5o5i3VpFh96pQUFBA1tbWpKurS9evXyciosCoeCVTtvZC2cPYFeGnn34iALRkyZIKt5dgzD6CMcvOzqZt27bRyJEjFds+3xnCfDhzzZo1JBaL6ebNm8xiFic2Npa0tbXJ3t5eMczD8qlWfoBOmTKFRCIRubm5kUwmIz8/P+ZP6Pfu3SMAZGhoSAcOHKCff/6ZnJycmOv069ePAJC2trbitY2NTbXmLhU/kX19fUlLS+tvRgkA1a5dm1avXs3EoA0dOpRsbW1pwIAB1KlTJ6VeLHt7e9q1a5fC6FaVo0eP0qxZs+jgwYP08uVLOnToENWrV49+//33Kv1vSrroZWVl0Zw5cyg0NFQRMzY2ll6/fl2tfS/Orl27KDg4mGnM4jx+/Ji8vLyqfdyWdXMoKCigbdu20YcPH6qlUR4+Pj7MVyoWJz4+nry9vav8/Yr2mHl5eTEbCi+NkJCQcufEVZfMzEw6duxYpb9XWbPh7e3NbEShNB4/fkx//PEHERFFvUtXMmXTD4TSh9zqP5jn5eXR0aNHuZlYOYIxY8CBAwcIgGKib2pWLnNjFhMTQ3p6etSsWTPKzs6mZ8+eMYtdlLVr1xIAGj9+PCUnJ9O6deuYxZYfoPHx8WRjY0MAaN68edSxY0c6ePAgMx05AQEBimXy8vQCmzdvZqqRl5dHJ06coIEDByp6aQBUq3empBO5oKCAnj9/TkuWLCnRoBkbGysmurLgq6++oi5dupCbm1ul5uhUlrt371bLEPzbh8dZIbRTxRDaqWJ8yu30Pj1byZQtOX6f8j/itCKexkxIMFsGZmZmEIvFWLduHSZMmAB9fX3F74iISQZrS0tLuLm5Yfr06fj+++8REBCAy5cvw8TEpNqxi7J06VK8evUKu3fvxsOHDxETEwMnJyemhViNjY1x5coVTJ48Gdu3bwcALFy4EAMHDmSaJbtv374IDw/H0KFDcfnyZQCAi4sLLC0t8cUXXzDRkEgkGDVqFDIzM3Hp0iVFNYb4+Hj07t0bW7Zswfz586t9DIjFYlhaWiIxMREzZ85E/fr1lX7q1KnDLIs5AKxZswaWlpbM4pVGu3btuGsICAj8N0jPkaLz2suK9yPbWWD96NYfcY/4IhizMlBXV8f48eNx+PBh+Pj4YMOGDQAKb2p7gqIxq2cjJjqTJ0+Gp6cn3NzcAAAXLlzA1KlTmcSWQ0SYOXMmTp8+jQcPHgAA9u/fj/nz5zPViY2NVTJ7iYmJcHZ2hpeXF1Od8+fP4+HDh0rbJk+eDHNzc/Ts2ZOJhkwmQ8OGDXH06FHEx8cjISEB8fHxiI+Px6lTp5CVlYUlS5ZARUWlWjpqamrYu3cvk30uj5owZQICAgKsyMzNR+sV/or3rSz04PZF24+4R/wRjFkp5OfnIzo6Gr///jtkMhnS0tLw+PFj2LVph8AnCVjnE8nEmOXm5mL8+PG4ceOGYtvZs2eZG7PMzEx4enoiISFBsc3NzQ1z585l2iNjZWWFoUOHIioqCjdv3gQAHDx4EBMnTkT//v2Z6YwZMwajR49GeHg4/P39ERAQgOvXr8PBwQHBwcFMivKKxWL06NGDwd4KCAgICFSW7LwCtHL1U7xXEYtwam73j7hHNYNQxLwUVFVVYWVlhS5duii2RUREYNekDkx11NXVcezYMSxZskSxzd/fH9nZ2Ux19PT04O7ujpCQELRuXdgF/PLlSxw/fpypjoqKCkaPHo2QkBCEhIRg7NixEIvFmDNnDrKysphqiUQitG7dGi4uLvDz80NycjK8vb1x9erVGikELyAgIPBvoXAKFF9SUlKQm5tboc/mSAvQfLmv0ja/b3pColK2bYmLi8OjR4+qvI8VIS4uDklJSdzaTDBmZSAWi3Hu3DlFBfuIiAhoSP4atvqQx+bmr6KigvXr18PLywtqamr48OGDYu4Ua2xsbBAWFoaNGzdCU1MTmzZt4nZwde3aFceOHcOzZ8/g4OCAzZs3c9GRo6mpib59+8LR0ZFpL6CAgIBASbB+2CyOTCaDj48P4uPjuWmkpqZi48aNOHLkCDeNN2/eYNGiRXBycoK6unq5n8+RFqDZj3+ZMjUVMa4sskNjk9LnRL948QJz585F9+7dUbduXSb7XZzXr19j3rx5aNiwIdTV1ZnMMy8JwZiVQ61ateDn54cGDRrgzZs3SE9PV/xuhHswU61JkyYhMDAQpqamOHv2LNPYRZFIJPj222/x+PFjmJmZ4erVq9y0AKBBgwZwc3PDokWLauSpTEBA4L+LTCbDlStX8PTpU24aYWFhmDZtGnbv3s0lfkZGBv7v//4PzZo1w7Fjx5gvBgOAV69ewdnZGXXr1sXhw4cxduxY5hoRERGYOnUqGjZsiJ07d2Lt2rXlfic9R6pkyhqb6OC+a380NC7ZlD1+/BiTJ09GkyZN4OHhgTVr1kBPT4/Z3wAAz58/x4wZM9CoUSO4u7tj+wCHYAAAIABJREFU5MiRTBfOFUcwZhXA3Nwc/v7+MDU1RWRkJNzHtwcAPHmfyVzLxsYGf/zxB2JjYyGTyZjHL4qVlRXOnz+Pxo0bc9WRo6Ojw+0JQ0BAoPrwfHBKSUnBvn37sHbtWi7XtpiYGKxevRqNGzfG5s2bmV/XsrOzceDAAXTu3BmdOnXCw4cP4eTkxFQjOjoazs7OsLS0xPz585Geno6tW7cy1bhz5w7GjRuHRo0awc3NDVlZWdizZw8kEgkzjZs3b2LEiBFo0aIFDhw4AKlUihUrVqB+/fplfi8uLVtpor9tEyNccraDptrfF1iFhYVh1KhRaNmyJQ4ePIiCggLY29tj3LhxzP6O2NhYTJo0CU2bNsW+ffuQn58PbW1tbNq0iZlGSQjjPRWkcePG8PX1xatXrzB8eCfFdlZpM4pSt25d/P7778jJyYGWlhbT2MURiUSoV68eVw0BAYFPl5iYGFy4cAGXLl3C8uXLFXNQWZCVlYVz587hyJEjuHjxIgwNDfHnn39CLGbTJ5Cbm4uzZ89i37598Pf3BxHBxMQEnp6ezK7Lz549g4eHBzw9PZGSkgIA0NDQgJeXF7MpE7m5uXB0dMT+/fuVzPGOHTtgYGDARAMALl26hK+++gqxsbGKbfPnz0enTp3K+FblyMjIgL+/v9JITKtWrfDNN9+U+b1HsWkYsu2vRXB9m5ti71cdS/28rq6uUlupqqrC3d2d6f3Y3NwcEyZMUCwCBIDly5fDwsKCa48sd2MmEon2AxgKIJ6IWpXwe3sAZwC8+N+mk0S0ivd+VYW2bdvC2tpa6R+/xf8JXAZ8xlxLW1ubeUwBAYF/DomJiQgODkZQUBC0tLTg6upa7dQsQOFQX1hYGM6dO4fz58/j3r17AIDDhw8zM2U3b97Etm3bcPbsWXz48AFA4Vza33//HWZmZkw08vLy4OjoiH379ilt9/T0hKmpKRMNoNAAZGZmKkwZAKxbtw7NmjVjpqGuro7Vq1fjwoULePfuHYDCleejRo1ipgEAdnZ26NevH3799VcAhelzVq9ezVRDV1cXurq6StN+PDw8yuyRO3PvLRYcvad436OxEXaXs9AuNjYWly9fhqqqKvLz87Fw4UImq/GLa3z77beQSqUwNDSEoaFhuQaTBTXRY3YAwHYAZSWyCiKioTWwL9VGfmGc1r0B9ge/wParz7gYMwEBgU8TIsK7d+/w5MkTREVFoUePHkxuCNHR0bhx4waCgoJw48YNREZGAgC6d+8OPz8/JqYsIyMDY8eOhZ+fn9L25cuXMx0CatOmDTQ0NBSmDCg0M6xyDAKF+f+mTJmCM2fOIDExEUBh78/gwYOZaQCFE77Pnz+veG9ra4sFCxYw1Xj+/DmGDh2Kd+/eoUGDBkhNTcX//d//MdVIS0vDmDFjcOnSJUUv0I4dO6Crq8tMQyaTwcXFBW5ubujatSs6d+6MzMzMMtMOLT5+H8fC3ijef9mpLpYPawGxuPSer+PHj2PChAkwNDTElStXMHHiRCxfvpzZ3wEAT58+Rb9+/fDmzRt4eXnh5cuX6NKlC9TU1JjqlEhFygNU9weAFYCHpfzOHsD5ysasiZJMZZVcyC+QKUpDsK7T+E/jUy7j8SkhtFPF+ZTa6smTJ7Ry5UoaP348dezYUakQ/Lp165id//7+/lSvXj2lklzt27en1NTUUr9TlXY6efIkSSQShcbYsWOZ1s6VyWTk5uZGampqCo3hw4cz19i6dSupqKiQkZERderUiaytrSk7O7vEz1f1ePLy8iJ1dXWqXbs2+fj4kKmpKfOyedevXydDQ0NSV1enw4cP0+HDh+nXX39lqvH69WuytrYmALRy5UpF+xWnOuddTk4OffHFFwSARowYQR8+fKDw8HBKTEws8fP5BTJquPSCUpmlKxHvy9Vxd3cnkUhETZs2pRcvXhARUXR0dJX3uyTu3r1LxsbGpKGhQefPF5ZgLH4e/uNrZVbAmCUBuA/gIoCWFYn5sY0ZETGtbv9P5lO6iX7KCO1UcSrSVnl5efTtt9/SmDFjaNCgQdSzZ0/q0KEDNWvWjKysrOiXX35hYgby8/Np9uzZSoZJRUWFPD09qx1bTm5uLm3ZsoX09fUVGs2bN6f4+Pgyv1eZYyohIYHGjRtHAMjCwoK0tLSoY8eOlJWVVc29/4v379/T4MGDCQB16tSJzp49Sw0aNKDk5GRmGmlpaTRmzBgCQDY2NvT69WvavXu3oqZxSVT23JNKpbRo0SICQC1atKCnT58SESmKabPi119/JYlEQiYmJhQSEkJERFlZWUwf9u/evUvm5ub0/+ydd1wUx/vHP0dvKiIKIgqKihUTezQaS6zERGONLSYqsSR2o7HHrkGNLYIdK6KCimJFMYqiQUUFCyoiglJEej3uPr8/+HFfTtpxtxdNsu/Xa19wc7vPszs3O/PZZ2Zn9PT0yhR86tZRSUlJ7NSpEwFw/PjxzMsrfWHxd9e9tJt1kkkZOaUeI5fLOX/+fAJgy5Yty7w31OXSpUusUKECzc3NeeXKlVL3Ky+qCjMJ/4bpCyQSiT3yo2LFjTGrCEBOMl0ikfQGsJ5kvRLsuABwAQArK6sWnp6e2jtp5M+WX9orscef5sLnqRQAsLvnf3dMWFn5JJLPh5JPMplMkG6x0khJSUFsbCz09fUVm56enuJ/Q0PDUs9B1bxKSUnB06dPldIMDAxQu3ZtQfI6JycHsbGxSpNJ6ujooE6dOkpr52pCSkoKoqOjlV72kclkcHR0LPNNOVXzKSkpCVFRUcjLy4OlpSVsbW3x/Plz2NnZCfY2XmpqKiIjIyGVSmFtbQ0bGxsA+W8zCvUSU3Z2Np49e4bs7GxUq1YNtra2Kg32Ls+9J5PJEBERgdTUVJibm6N27dqCvaxQmFevXuH169cwNjZG3bp1tdJFlpqaimfPnkEikcDBwaHMbkt16iipVIonT54gKysLNWrUKHMM4b2EPKy99b9JZk30gE1dTaBTxu8YFRWFhIQEVKxYEQ4ODlr5TZKTkxEREQE9PT3Uq1cPxsbGJe6rTl517tz5FsmS32goQBX1pumGUiJmxewbCcCyrP0+hIiZXP6/7szcPOHC9P80xEiQapSVT7Gxsbx3757Wz8PZ2ZmtW7fmL7/8wgsXLpTY/aMuMTExPHHiBKtXr64UZQLASpUqccWKFUxPTy/VRml5FRUVxd9++43NmzcvYv/rr79mYmKixtdw584dDh48mDo6OgTAPn36cMCAAaxSpQqDgoI0tk+SYWFh7NGjBwGwatWq3Lp1K/Py8rh48WI+e/ZMJRtllanXr1+zf//+BEA7OzueO3dO8V1KSoomp68gJyeHM2bMIABaW1vz/Pnzgth9lwMHDtDExIQmJibcv39/uY5VtY4KCwtj3bp1CYDz588XtPu1gIyMDEXEr1evXoL9Du/i7u5OXV1d1qpVi6GhoSodU966PDQ0lLa2ttTT0+Pu3btL3Vcul3P07r+UomQjdtxgnqz06GBWVhb79u1LABw6dChzckqPrKnLjh07qKOjQwcHB5Xuv397V6Y1oIjctQYQVfC5tO3vEma5ubml7lNQwJr9elZtP2lpaWofqypv3rwpM7ysLgUFVCqVMioqSis+CnP79m2lClMblee9e/cYFham6FK4efOmxgL03ePj4uK4Y8cOXr58mTExMczJyaGFhQV79erFixcvCtad8dtvv3H27NmcPHkyXVxc2LFjRyUxY2RkxK5du3L58uW8deuWWj4OHjxIZ2dnWltbFxFLBT5+/vlnlUVTcXl9584ddujQQWHT1taWM2bM4A8//EBjY2Nu3bpV4zzLzs5WdMXp6upy+PDhii6ybdu28dGjRxrZL2DZsmXU1dWlvr4+Z8yYoTR+pTzlubQyGRgYSAsLCwLgxIkTmZqaqskpF0tmZiZbtGhBAHR2dtZa99KiRYsIgPXr11dZZBRGlXv35s2brFChAk1MTHj48GE1zrJscnNz2bp1awLgpEmTKJVKteLH1dVVMUbx1atXKh9XnjouLCyM5ubmNDU15ZkzZ0rdNz1bWqTrcoXfQ0rLCGjI5XJ26dKFADh16lSt1PUkuX37dgJgs2bN+Pr1a5WO+UcLMwAHAbwGIAUQDWA0gHEAxv3/9z8CCEP+GLMgAO1UsattYZaXl8edO3dy+PDhpe53PzpZUdDUwdfXl5aWlgwODlbreFVITU2lk5MT+/fvz8zMTMHtFxTQ5cuX08zMjNu2bVM0kAkJCYL6io6OpoGBARs3bkxPT0/m5eXR3d2dly9fFtRPv379CICOjo785ZdfuG/fPgLglClT1M7Dd29kPz8/JfFiYmJCQ0NDxeeWLVvSy8tLY0Fta2ur5KfwwG8A1NHRYZcuXejm5qZ2w7po0SJaWFiwW7dunD17Ng8fPsyff/6Zurq6dHFxYXR0dLnsFVfpRUVFsVq1apwwYQKvXLmiqKR37tzJBw+EG+fZt29fTpgwQfABxYU5dOgQ+/Tpw/DwcI3slNY4JCUlsWPHjgwICNDIR1lMmzaNGzZs0OpLUFevXuWQIUPUji6p0ohmZGSwX79+DAkJUcuHqqxevZqbN2/Wqo+wsDAOHTq03A/95REbubm5HDlyZJlt15/h8UqCrM4vp/joteoPCR4eHly1apVWy9eLFy84ZMgQJiUlqXzMP1qYaWv7OyJmu3fvJgD6+vqWul9BgQuOLP8A14KnDisrK0VDIHQELS8vj5MmTSIAtmvXjm/evGF4eLhiQKumFBTQ4OBgNm7cWBGij46OZvfu3VXullGFjIwMrlmzhtWqVVMMkHZ2dqaRkRFPnTolmJ87d+5w3rx5bNSoUZHoT4MGDdQaBPzujZyamsqrV69y9+7dnDdvnqJ7493NwcGBf/zxh9oh/Li4OL59+5ZZWVmUy+Vcs2YNJRIJP/vsM27evFnlJ8TSyM7OLlJx7tixg48fP1bLXkmVnraivoX5O96yFsqHOIxANcR8Ug0h80kul7Pv5qtKomzX1Yh/zSwGojB7T8LswoULrF69Om1sbJiUlER3d/di9/ts9UWNomaXL1+mgYEBHR0d+ezZMw4ZMkST0y6Wgga5oDtg2rRp7NatmyA3SeECmpWVxZ9//pkSiYTm5uY0MjJi48aNBe9GycjI4Nq1a2llZaUQMHp6evT09BTUD0k+ePCgyDQGurq6XLBgQZld3YUp60ZetmwZDQ0N2aRJE/bv359z5syhh4cHg4KCyvUkVxbe3t6MiYkRzJ42EBtS1RDzSTXEfFINofLp5duMIl2XCWnZgtj+UBCF2XsSZpcuXeLx48cJgK1bt6axsXGx3ViF5zRT9yUAT09PAmDlypUJgGFhYZqefrEcOnRIaX6h8g6iLY7iCuj58+epp6en8NOvXz/BxwekpaUp5s0p2CQSCbdu3Sqon4MHD7JTp0789NNP2aZNG7Zo0YJOTk5s2LAhhwwZwri4sufeIcu+kV++fPm3RIT+CYgNqWqI+aQaYj6phhD5NPvoXSVBNsbjr39NlKww2hRm4lqZpZCXl4eIiAhUq1YNN2/eBABcvHgRzs7OSvvpFpqhuN7c04hcqfx9WWRlZUEqlaJOnTqIiIgAALi6umLnzp0aXoEyOTk5ePjwIczMzPD27VsAwNSpU9GrVy9UrlxZMD8pKSlwdXVFXl6eIs3HxwdLlizBwoULBfOTlJSE3r17o1atWggNDUVoaChevnwJFxcXpKSkYMaMGYL4GTJkCIYMGSKIrdKwtbXVug8RERERbRCXmo02y/2V0v4Y1hy9m1Z/T2f0z0X4iUD+Rejp6SE3NxcJCQmKtMJLcxTmz5md1fZjZGQEY2NjZGdnK9L27duntNCsEBgaGuKbb77BwIEDYWhoCACIj4/H7NmzBfVTqVIlnDlzBuHh4Vi1ahU++eQTAMCiRYvg4+MjmJ+aNWti5MiRWL16Nfz8/BAVFYWkpCQEBgaiYsWKCA8PF8yXiIiIiEjxLDgeWkSUnfix/b9alJFUCj4IiSjMyuDnn3+Gj4+PYlHxkydP5vcBv0OtKv+bQHHigdvl8iGRSNC/f388fPgQkyZNgo6ODqRSKdavX6/ZyRdD/fr14ebmhhcvXmDevHmoXLkytm7dimvXrgnuq169evj5559x7do1vHr1Cm5ubjhw4IBWBZO5uTnatWsHFxcX1K9fX2t+RERERP5NREZGlvuYZwnpsJ99Cnuuv1CkjfvMAfcXdYeTrbnSvnl5eThy5IhSoENoMjIysHHjRnh7e2vNR0pKClatWoWoqCitTdQtCjMV+Oqrr3D16lXUrFkT0dHRuHv3brH7bRnWHABw6t5rtfxUrFgR69evx40bN9C8eXO4ubkhJSVF7fMuDSsrKyxZsgRRUVFYv349VqxYAalUqhVfAFC9enX88MMPOHz4MOrWras1PyIiIiJ/ByQRHBys1Xrz6dOnmDVrVoltjqZIpVIcOXIEn332Gc6dO6fycTI5MWx7ELquuaxI09eV4ObcrpjdqwEqGP1vNYnk5GS4urrCwcEBFy5cQNWqVQW9BgCIjY3FvHnzULNmTezcuRNffvml4D5ev36NWbNmoVatWvj1119RvXp1lVadUAdRmKnIRx99hJs3b6J169Yldmf2KhS2XXH6odq+WrZsiRs3bmDx4sU4ePCg2nZUwczMDJMmTYK3tzdyc3O16qsAbSylISIi8s+ApFbrmtevX2P9+vU4ffq0Vuy/evUKq1atQsOGDXH27FnBlrQqQCqV4ujRo+jWrRvq1auHrKwsNGvWTFAf8fHxWLZsGWrXro2BAwfCwMAAY8eOVenYK08S4DDHD4FPExVpO0e1xJNlvVGtgpEi7dmzZ5g0aRJsbW0xc+ZM5OXlYdWqVYJex8OHDzF27FjY2dlh2bJlSElJwdatW6GnJ9zw+fDwcIwdOxb29vZYvXo1UlNTsWDBAq0soaVAlTcEPsTtfS3JlJmZyXXr1pV4zM6rERpNnVGcvw8d8Y0n1RDzSXXEvFINofNJiOWsikMqlfLixYucMmUKBwwYIOjC6ST59u1bbtu2jV26dKGOjg579Oih9Ba4pvmUnZ3Nw4cPs3fv3oplujp16iToW9SRkZGcO3eu0uoZjo6OguZVaGgoR4wYofRmvpmZGZ8/f06yjAmLM3KKTIHRcfVFZuYo50F2djbHjBlDiUSi9Mb88ePHBbsOMn+CbnNzcyUfkyZNEtRHYmIiR44cqTQpd6NGjZiTk6PVtzLF0EU5MTY2xuTJk0v8/rv2tRX//+J9TxB/IiIi/21IIicnp+wdy0lcXBwOHTqEH374AY0aNUJgYKBgttPS0nDkyBGMGDEC1apVQ5cuXXDw4EGsXbtWkEXNSeLQoUP48ssvYWVlhbFjx+LixYuwsbHBvn37BIvMP3r0CI0aNcLAgQPh5+cHuVwOCwsL7N27V7AxRnK5HL6+vti5cydiY2MBALq6utizZ49gC8ADgIODA+zt7ZUilr/99hvs7e1LPIYkJuy/hY8Wn1dKXze4GS7P7AxjA+U8MDQ0xJIlS5QWMx80aJDg3YvdunXD119/rfhsa2uLpUuXCurDwsICHTt2hFwuV6Rt2bJFu9EyQJwuQx3K6lf+ffBHmHIoBAdvvsSKr53+prMSERH5NyCTyfD48WPcuXMHd+7cQUhICPT09LB//37F29TqIpfLcfz4cVy8eBEXL17EgwcPFN/t2LEDffr00fT0AeSLmd69e+P58+eKNAMDA/j4+KBmzZqC+JBIJGjcuDEeP36sGOelp6eHw4cPw9LSUhAfANCgQQNMnToVP/30kyJtx44dgk5vo6OjAxsbG6SlpSnS5s6di9atWwvmAwCCg4Ph5uYGfX19SKVSdOnSBS4uLiXuf/RWNKYfVh7fNs+5IUZ+Yg8DveKF7/Pnz+Hs7IzXr1/DwcEBb9++xYYNGwS9joyMDAwZMgQnT57EV199hePHj2PTpk2oUKGCYD5IYvHixVi0aBE++ugj1K1bFxUqVEDHjh0F81ESojDTAn0/roEph0IAAH02XoXvT5++5zMSERHRBLlcjvj4eERHRyMmJgbR0dGK/zt27IjRo0drPBD45s2bmDx5Mu7evYusrCxFetu2bXH69GmYm5uXcrRq6OjowMLCAl5eXoiPj1ekr1ixAt9//73G9guoU6cO+vfvD1dXV0Xa1q1bFVPnCEFmZiY2bNig9Jb3mjVr0LZtW8F8ZGdnY8qUKXB3d0eDBg0QHh4OFxcX9O3bVzAfcrkcCxYswLJly1CnTh0MHz4cf/31F+bNmyeYDwDYtWsXfvjhB5ibm+PixYuYOHEitm/fXmxkMexVCpw3XFVK697ICpuHNYe+bsmRyOvXr+Orr75CSkoK9u3bByMjI6Snp8PKykqw64iNjcUXX3yBW7duYdasWVi+fDmWLVuGr776SjAfeXl5GD9+PLZv347PP/8cR48exe3bt9GkSRPBfJSKKv2dH+L2vsaYqcr1Z28U/fBSNVcD+KcgjgdSDTGfVEfVvHr06BH//PNPBgQE8NKlS7x48SIvXLjA8+fP89y5c4IsPZWdnc2vvvqq2HVMly1bJtis5lKplMOGDVOy36FDh1KXMytvmXrx4gX79++v5GPy5MmCzsweEhLCZs2aEQCdnJwIgNOnTxfMfoGPhg0bEgC/+eYbzpgxgwMHDizxOtS59yIiIti8eXMC4JAhQ5iWlib4+LikpCT27t2bANijRw8mJibyzp07fPDggWA+8vLyOG3aNAJg06ZNFePJnj59WmRf79P+RcaR2c06ycT0stfp9fT0pKGhIatUqcIrV66QzB8jLWTZevDgAe3s7Kijo8MtW7Yo0oX0kZ6eTmdnZwLg8OHDS1yjWFyS6R8ozEgqFex/M6LgUI3/Uj5lZ2fT1dWVe/fu5eXLlxkZGUmpVKry8eURZgUL2hfejIyMuHbtWkEGZ8fGxnLhwoVKg5lNTU3p4+OjsW2SlMlkPHToEB0dHRXLigFgly5dmJ6eXuqxquZTTk4OV6xYQRMTE0okEo4fP55OTk4cOnSoYEul5ebmctGiRdTT06OJiQk3btzItLQ09u7dW7BB8nK5nOvXr6eBgQFNTU25e/duyuVyBgcHMyUlpcTjynvvnThxgubm5tTX1+fmzZsVDb+QL2OFhYWxXr16BMDZs2drZTm2lJQUhfD78ssvSxT5xQ3st5t1kqfuvSrTh1wu55IlSxQvKxQn+IQgICCA5ubmNDExoa+vr1Z8xMfHs1WrVgTAWbNmlXpviMLsHyrMEtKyFQX8SVyaMCf1AfJfEhyaoEo+JScna/08goKCOHz4cHp4eGh1MfPly5cXWfi9Vq1a7NChA/fv31/qU25ZeZWcnExPT08OHTqUFStWVPLTvn17hoeHa3Tucrmc165d49ChQxVvZFWtWpUAaGdnx7t372pkv8CHr6+vIrpkZWXFDRs2cO7cuezRo4dKIkCVMnXu3DmF6GvdujWDg4NJkps2bSoxGlBe7t69y48//pgA2LFjR6XGuSxxqSrx8fGKSEaLFi34+PFjlY9VtY6SSqWcNWsWAbBWrVq8ceOGmmdbOj4+PjQzM6OJiQkPHTqkFR/Pnj1jo0aNFMKvOJGRkSNlm2UXigiyfUGRzJaWLRRzcnL47bffEgA7d+7Mt2/fauNSuH//fhoYGNDKyop//fWXVnw8ffqUdevWpUQi4caNG8vcXxRm/1BhRn44UTNtLiJbOJ+EXqi8OIRqTEojLS2tSJ4FBQVplI/vlqesrCzGxMQo5dn69evZvXt3+vn5CZaXISEhDAwMpL+/P/38/Ojt7a30Sn6jRo04efJk+vr6ltptVhqPHj3irl27OG3aNHbv3p02NjbFdv316tWLQUFBZdor7t6Lj4/nhg0b+Pnnn1NPT48AqK+vz08//VSwKJlUKuXOnTsVXVi6urocOHAgL1++TB8fH3bo0IHx8fFq2y8gICCAbdu2JQBWrlyZK1euVAiYa9euMSsrSyU7pdVR0dHRHDhwIAGwSpUq3LZtm+D3p1Qq5eLFi6mvr09jY2Nu2LBBK3XA+fPnFWV25syZ5a4DVKnLX79+zc8++0xRTt+8eaPm2ZaMTCbj/PnzCYC1a9cWROAXR0BAAKtUqUIDAwPu2bOnyPdZuXlst6Jot+UCj3Mq13GJiYmK/Pruu++0Ui/L5XKuWLGCANiwYUNFN6zQ3Lx5k1WrVqWhoSGPHj2q0jGiMHtPwszb25vLli3TyIZcLlcU+tG7iyr9mJgYduvWjRERERr5KYvvv/+ev/76q1bC5QUF1M/Pj05OTrx48aLiu9zcXEFFYXZ2NmvWrMmRI0fy5s2bivTNmzcL2iCMGzeOVlZWisjSq1evOG7cOHbq1IkPHz5Uy+a7N3JAQAAB0MDAgA4ODuzSpQv79OmjNIfR5s2bmZamWbS1evXqxYqkd7dq1apx0qRJagmPgjEsAGhjY8Pu3btz6tSpivmSVBVkBRRX6QUHBxMALSwsOGLECB4+fJgpKSkMCgoSJEpG5jec9evXp5WVFefPn8/o6GjFd5GRkYI1PgsXLqSZmRkXLFigUZS0tMYhLCyMBgYGdHFx0YrIIPPHL7Vt25YdOnTgkydPtOKDJH///XdaW1vz3Llzah2vSiP69OlTWlhYcOnSpVp7wMzLy2Pv3r3ZrVs3rf0mJLlv3z5aWVnx2rVrSunZ0jy2Xna+iCD7/Xz+vVMesRETE8OaNWtyxYoVWnvwl8vlHDlyJD/77DOtRePI/LaratWqirFxqiAKs/cgzORyObdu3UoAGoea/e69UtwAyRm5St+dPn2aBgYGtLGx4f3790lScPGUmZnJTp06KboZXr58STJ/skEhKCige/fuZaVKlQiAffv25ZMnT3j79m3++uuvgvgh859q+/Xrp5jksVWrVvTw8GDdunXZr18/jUVMAdu2bWPnzp1uC2dOAAAgAElEQVSVJhYs6DIzMDDgggULVI5qFPDujfzkyRPOnz9fUfHY29srIkGFN3Nzc86cOZMvXrxQ61oOHDjA3bt309PTkz4+Pjx9+jTr1q2rEGPjx4/nxYsXNSp3Dx8+5OXLl5Uamzt37rB3795qdQcVV+nJ5XL++eefRcaqvXnzRtB75vHjx1qPyqampjIhIUFjO2U1Dtrsqi4gISFB65FyuVyu0eS3qjai2mz8C0hLSyvXeEt1KTzmLjMnj43mny4iyCYdvM2MnP+dS3nFhroR9vKQk5PD7Oxsrfspb9shCrP3FDG7cOEC69WrR2NjY966dYs3b95Uu6IrrUvT39+fZmZmrFy5Mq9fv86dO3fy9u3bmp6+Enl5eVyyZAl1dXVpYWHBY8eOsVOnTjxz5ozGtgsX0Pj4eE6YMIE6OjrU19dXjAlxdXXV2E9hXrx4wV9++YWWlpZKIsbJyYmRkZGC+UlPT6efnx8nTZqkEIMFW7169XjhwgWVbalyI48ePVoxALxevXr8+uuvuWDBAnp5eZVrTE1pPHv2jOPHj+elS5e0EkEtIDc3t+ydSkAct6gaYj6pxn81n96mFz+of4lvGONTi4qd/2o+qYMozN6TMLt06RIfPnzISpUq0dbWlt26dePChQvVsiXNkyluiiHu14t8f/PmTVapUoUmJiZs3Lgx27dvr5Xw8NWrV1mrVi3F+BlLS0tFBE1diiug9+/fZ7du3ZSETOHXm4UiMzNT8RZNwVa1alVevXpVUD9Tp05V2Dc0NGTFihVZtWpV2tractGiRSpFWMq6kVNTU+nh4cFbt279I5bi0iZiA6EaYj6pxn8tn6ISM4oVZIf+iip1+qb/Wj5pgjaFmbgkUxk0aNAA69evR3R0NM6fPw93d3e1FuDV09XB1hEtAADXIxIR+SZD6ftWrVrh7NmzyMvLQ1hYGAIDA7F//35BrqEw7du3x65du6Cvrw+ZTIY3b95g8ODBipmzhcLCwqLI4r4TJkzA3r17BfUTEBAAa2trNG/eHNWqVQMAJCQkoHPnzti5c6cgPsj8GaBzc3Mhl8uRnZ2NlJQUxMfH4+XLl1i4cKEgS3RUqFABI0eORPPmzcWluERERMpNUEQi7GefQofVl5TSvX74BJErnTGoZU3olTJBrMiHgfgLlcGlS5cwZcoUxefY2Fh4e3urZat74/+tHdbJNSA/ZPn/xMXF4aefflISfTNnzkRqaqpavkoiKSkJPj4+qFSpkiLt2rVrmDNnjqB+LC0tsXDhQqxduxb9+/eHtbU1SGLUqFE4evSoYH569eqFEydO4NatW4iLi0NOTg6eP3+OS5cuwczMDHFxcRr7kEgkMDMzg76+vsazu4uIiIgICUls+zMC9rNPYcjWIKXvTk/ugMiVzmhd2+I9nZ2IOojCrAw6d+6M0NBQODs7K9I2bdqktr3nK3or/q/9i5/ifysrK1y9ehXe3t74+OOPAeSLwMWLF6vtqzgqV66MjRs34tWrVzh9+jSGDx8OU1NTuLq64vjx44L5MTAwQOvWrTF16lQcOXIEr169wtOnT7Fr1y4EBATgyZMngvl616+9vT3at2+PQYMGCboUiIiIiMiHQk6eDCN23EDtX/ywzO+h0ne+P36KyJXOaFi94ns6u5IpHJDQFkI8kJcGSaSlpSE7O1sr9kVhpgI1atSAr68vdu3ahUqVKiEwMBB37txRy5ZEIsGNOV0Vn6f9/5qaQP46dv369cOtW7dw8uRJtGnTBuvXr8fDhw+LM6UR+vr66NmzJ/bu3Yv4+Hh4enrCx8cHr169EtwXkH/dDg4OGDlyJDZu3Ih69eppxY+IiIjIv43MzEzF/1GJmbCffQqO887gypM3ivRqFQxxbGJ7RK50RlPbSsWZKZGUlBT4+PgIdr7FcevWLUycOBEvX77Uin2ZTAYfHx907twZN27c0IqP7Oxs7Ny5E05OTkhNTYWRkZFW/IjCTEUkEglGjRqFsLAw9OrVC5s3b1bbllVFI8zs4QgA8L4Tg5vP3xbx5ezsjOvXr8PPzw9HjhzR6lOGiYkJBg8ejN27d6N69epa8yMiIiLyd6HtyExycjL279+P9PR0rdhPT0/H7t270b17d4SGhuLQX1Gwn30KHX9THj827jMHPFrSEzfnfo6Paqq+0D1JBAUF4fvvv0eNGjUEGSf7LtnZ2dizZw/atm2Lli1bok6dOqhVq5agPpKSkuDq6oq6devi66+/RvXq1fHll18K6iMhIQGLFy+GnZ0dRo8ejezsbNjY2AjqozB6WrP8L6VGjRo4deoUvLy8kJOTA0NDQ7XsTOxcF7+dfQwAGOR+HXcXdEclE+XB8hKJBN26dUO3bt3+lvBvgU8RERERbZGbm4vMzEyYm6suIlRFKpXi8uXLOHbsGFq2bIlRo0YJaj8jIwO+vr44ePAgzpw5g7Vr18LMzEww+3K5HJcvX4aHhweOHDmCTKkcTtP3YZB3AoAEpX33jW6DT+tZlttHUlIS9u3bh61btyI0NBQAMG7cODg7OyMgIECAqwCeP38ONzc37NixA4mJiQDyXzwrPF5bUx4+fIgNGzZgz549iohi1apVsWHDBsF8JCcnY+bMmdi7dy9ycnIU6Vu3btVqWykKMzWQSCQYPHiwxnYiVzrDfvYpAECzxefwbHlv6OoU/2OLgklERESb5Obm4tGjR2jSpAl0dITrTCGJsLAwnD9/HhcuXEB6ejpOnjwpmP3U1FScOXMGx44dg5+fH1JSUjBgwACMHDlSEPs5OTk4e/YsDh48iBMnTihEwDfffIMJEyYI4kMul2Pt2rXYtGkTXrx4AWOHVqj24yEAQLJceV//6Z/Boap6YjAkJARffPEFYmJiFGn16tWDq6ur2uf+Lrm5udizZw+2bt2K5ORkAPm9Mrt374aurq5gfkxNTZGenq7Uzbtp0yZYWpZfrJaEubk5xowZgwMHDijSxowZg86dOwsmYotDFGbvmecreiteAnCY44fIlc5lHCEiIvJfIzExEdnZ2ahRo4Yg9kji+fPnuHHjBm7evIkbN24gNDQUe/bsgZOTk8b2ExIS4OfnhwsXLuDChQuIjY0FANjb2+P69euoUKGCxj5IYuXKlVi0aJHS2+zNmjXD7t27BROX8fHx8Pb2hqenpyKtYcOGgkZNdHR00G/wMGyKsoadSeUi389zbohhbexgbKCZsGnWrBnGjh2LRYsWAQB0dXWxb98+mJqaamS3MAYGBqhfv77SwPhVq1ahbt26gvkAgOjoaJw9e1bxuV+/fhg4cKCgPl6+fAkXFxdFhNfIyAirV68W1EdxiMLsPSORSBD6aw80WZhfwOxnnxLFmYjIf5DMzEw8efIE4eHhRbb69esLEmUqEDPr1q1DQsL/usZ0dXVx6NAh9O3bV2MfAGBsbIw7d+5g3759irQqVargzJkzsLa2LuVI1ZFIJBgzZgz27t2reEGqatWqOH78uKBCQ1dXF9HR0YrPpqamOHr0qCBdmHI5seXyM8WwFhQSZfo6QOAvXVGtgjADzNPT0zF69Gh4eXmhTZs2uHnzJhYsWIDWrVsLYh/IH4A/d+5crFq1Co6OjmjVqhViYmIEiywWsG/fPowePRoVK1bEhQsXMHLkSGzevFnQnqXbt2/jiy++QEJCAnbu3ImXL1+icePGqFy5qHAWGlGYfQCYGerhr7mfo9WyCwBEcSYi8iFBEjt27MDjx4+RlJSEt2/fKv0dNmwYFi1apPZ40wKSkpIwbtw4BAUpz0XVp08feHp6wsTERCP7QL6YGTZsGP744w9Fmo6ODvbv34/+/ftrbL+AW7du4dy5c4rPRkZG8PX1haOjo2A+fHx8MG7cOMTHx8PKygpv376Ft7c37OzsBPNx4sQJfP/990hKSlIIju3bt6Nhw4Ya2b31Ign9t1wr9rvuFomoEH8PawTsXnzy5Am+/vprhIaGYsKECVi3bh0mTpwo6PyVKSkpGDZsGE6dOoXevXvjwIEDuH//PmxtbQWLXsrlcixYsADLli1Do0aN4Ovrizp16uD06dOCvrjm6+uLIUOGQF9fH2fPnkWXLl3w5s0bVKlSRTAfpaLK8gAf4vZ3Lcn0d/LwdUqpa2p+qIjLeKjGfy2fXrx4ofbiw6rm1ZMnT9iuXTu2b9+eXbp0Ya9evdi3b18OHjyYo0aN4vXrRZc/U4d79+7RxMREaekvMzMzenp6CmJfLpfz1KlTbNeunZKPsWPHlrrgdXnKVEpKCufOnUtjY2MCoL6+PnV0dLh//34BriCf+Ph4fvvttwTAypUrc86cOdTR0eGxY8cE85GYmMhhw4YRAGvVqsXz589z8eLF3LZtW4nHlPfey8zM5IQJEwiANWvW5J9//kmS3Lx5s9rn/To5i40XnCl2qSTb7zdy5xE/kuTLly9VWuJNVXx9fVmpUiUaGhpy165divTiypW6dVR4eDgbNGhAAJw1a5ZW1uDNyMjggAEDCIA9e/ZkcnKy4D5Icv369ZRIJLS3t+eDBw9K3E9cK/M/IsxI8trTN/84cfZfExzq8qHkU3Z2Nt3c3Pj48WOtrMdawLZt2yiRSGhnZ8euXbty3LhxdHV15bFjxxgaGlpq46NKXsnlct67d4+9evVSEjMA2LhxY165ckXjawgJCeGUKVNYtWpVJftNmjTho0ePNLYvlUq5f/9+Nm3alABYoUIFOjk5EQAXLVpU5u+jSj7l5uZy06ZNimv49NNPGRQUxPbt29PDw0PjayBJmUzGbdu2sXLlygTAESNGMC4ujklJSfzjjz8E8UHmiwxra2sC4JgxY5iSkkKSjIuLK/W48tx79+7dY+PGjQmAAwYM4Nu3b9U+38ycPA7ccq1YMWY36yT1Le3Yrl07RkVFqe2jJGQyGRcuXKgQsMHBwWUeo04ddfbsWZqbm9PIyEhQkV+Y6OhotmjRggA4efLkUh9W1EUqlfLHH38kALZt21bQMlWAKMwE4H01pFefJPyjxNmHIji0TVxcnEZCRpV8Cg8P57fffssbN26o7acs5HI5x4wZQwC0s7Pj2LFj6eXlxcTERI3sJicn8+bNm9y7dy/nzZvHgQMHUkdHp1jRtHfvXrUiQTExMfTw8ODw4cMVDXThzdjYmCtXrtQo4hAfH8/ff/+dH330kcJuu3btOGXKFALgt99+y4yMDLXtk/kRmc2bN7N27doEwGrVqnH58uVMSkri0qVLuXXrVpXslFam5HI5jx49ynr16hEAHR0deezYMUUZvnPnjkbXUMC9e/cUkT5HR0devHhRELuFSUpK4qhRowiANjY29PPzK9fxqgr9jRs30tDQkCYmJty+fbta93tunoxTD90pUYytPXKZdnZ2BMDp06czNze33D7KIikpiV988QUBsGvXroyPj1fpuPLU5XK5nGvWrKGOjg5r1KjBv/76S82zLZ3g4GDa2NhQV1eXW7Zs0YqP1NRUOjs7EwAHDhzIzMzMMo8Rhdl7EmZnzpzhqVOntOpDKpVy2bJlTEtLU0r/63mi0s2saWRj586dPHPmjEY2SqKggD58+JCTJ09mdHS00vdCRmXkcjmHDx9ONzc3pSdZf39/lW4mVVmzZg2HDh3KP/74g/fu3aNMJqOfnx8/+eQT3rx5Uy2b797It27dopOTE3v16sUxY8Zw4cKFdHd3Z7Vq1QiALVu25K5duzS+rmbNmtHCwoJmZmbU19cvImYKNolEwg4dOvDatWvl9jF9+vQi9kxNTWlmZqb43LZtWx4/fpwymaxMe8VVepcvX1bY0tfX52effcalS5fyypUr1NPTY+/evRkREVHucy9MXl4eraysCIC2tracM2cOHz9+TJI8d+6c2o31u4wfP54AWLt2bf7xxx9Kv3FqaqrKdkprHAICAhSib8uWLVqJMuTm5tLW1pZGRkZcsmSJ2l3XZTF16lSFKFYngqVKI3rjxg0C4Mcff1zuaGieTM5FJ0JLFGO/nghjfGo28/Ly6OjoSHNzc0G7d9+lIFL2888/l+t3L4/YePDgAfX09Ni2bVu+evVKjbMsG7lczjZt2tDc3Jznz5/Xig+S3LBhAwFw9uzZKtVPpCjM3pswc3Nzo76+Pk+cOKE1H97e3gTARo0aKVUGcrmcT+JSlW7urFz1+u1zc3MVT+ZDhgzh69evSeZHH4QYy1BQQFetWkUANDAw4Pjx4/nixQuS5OTJk5menq6xHzL/nC0tLRV++vXrR29vb86bN49Nmzblw4cPBfHz448/0tDQUCEEKlWqxI4dOyo+jxw5kjExMeWy+e6NfP36dbZq1Yo2NjbFRpYKNgsLC86cOVNt0fH999+zf//+HDp0KEeNGkUXFxd26tRJYd/Q0JB9+/blvn371B634ePjw8mTJ/OPP/6gv78/o6OjKZfL6ejoyO7du/PSpUvlEjTFVXoZGRmcOnUqT506pfQgExkZycOHDwv2ALBr1y6ePXu2yDgZIR8wHj58yP3792sslsqKmG3btq1cQk8dLl68yKdPn2rVR1JSEk+eVL/3QNVG9NixYyqLS2mejAuO3S9RjC33e8DUrKLRsJCQEI0fIMoiJyeHZ8+eLfdx5RUb/v7+WhPjBTx//lyQYQOlIZPJyi38RGH2noTZ2bNnWbt2bYU4k8vlahX2svDw8KCRkRErVKjAI0eOUCqVcuHChSTJxPQcpZv9WXxa6cZKIDExkWPHjlWIjD/++IMHDx7k8OHDNW5wChfQoKAgRUhYX1+fY8aMoY2NDdu1a6fRWI3C5Obm0tfXl4MGDVKIJ4lEQgA0MTERbNxMdnY2AwMDuWrVKvbp04fm5uZFIkLLli1jVlaWSvZKu5GlUimjo6Pp4+OjuJaCMUcdOnTgTz/9xN27dwsWFezTpw8HDBhAT09PrTXc6enpKo1rKY7/Sve4poj5pBpC5VO2NI8T9t8qUYwtOhFKaZ5qEZcPEbE8qY4ozN6TMLt06RJfvHihEGdLliyhjY2NxuNLiiMkJIR16tQhAA4aNIgSiYT+/v4kyRypTOnm33FF/aetq1evKga2VqpUiQA4Z84cjc69uAIaHBzMvn37KgmZpk2bCh7yTk5OVkTqCm+jRo0SLEpH5j+xF7x1VHirUKECO3bsyPv375dpQ5Ub2d3dnXPnzuXhw4f59OlTlcPq5UEul2ulDAuJ2ECohphPqqFJPr1Nz2GbZRdKFGN2s07y3kvtvCH4dyOWJ9XRpjAT5zErg1q1auHSpUvo3Lkz5s+fDwDYuHEjZs2aJaifZs2aITg4GCNGjICXlxcAYOTIkbh37x4sLCyUVghYfPIBNl96ilvzu5XbT/v27XH79m0lP8uXL0fNmjUxbtw4wa6nRYsWWL58OUJCQhAZGQkAuH//Pj799FOcP38ederUEcSPoaEhgoKCYGVlhZSUFMVs07t370ZQUBC8vLzQtGlTjf28ffsWW7Zsgbm5OSpVqgRzc3NUrFhR0CVGAMDFxUVQe8UhkUgEmRNLROTfyoNXqei94UqJ31cw0oPPhHaoW03zFQxERN5FFGZlIJPJ4Obmhrdv3yrSVq5cibFjx8LCwkJQXzdu3EBISIjic0xMDH744Qd4eXlBIpEgcqUzXPYE49yDOCRm5MJ+9imEL+0FA73yTd73559/4soV5Upn4sSJqFGjBvr06SPItRScv4uLC8LCwvDgwQM8fPgQERERaN++Pc6dOyeIYDIyMoK3t7fic25uLlJTU5GSkoLU1FRkZWWBpMYzQtepU0cwMSkiIvJhQRIbLz7F2vPhJe4zrE0tLOjTCIZ6wj6MiYi8iyjMykBXVxfz5s2DmZkZVq1ahbS0NCQnJ2PlypWCr5nVo0cPHD16FNu3b4enpyfS09Nx5MgReHh4YNSoUQCArSNb4sqTBIzYcRMAUH/eaez4tiW6NrRS2c/nn3+OmJgYhIaG4vz58zh37hwuX76MIUOG4NKlS4It0fH555/j888/V3yWyWSIjIzEgwcPcP36ddSvX1/j2dLfxcDAAJaWloIuZCsiIvLvIy41G21X+IMseZ8tw5qjZxNrQZf6EREpC2HWSfiXY2pqirlz5+LZs2eYPHky9PX1sXHjRqX104RAIpGgTZs22LZtG16/fo2dO3eiXbt2+Omnn/D06VPFfh3qVcWjJT0Vn0d7BMN+9qly+2ratCmmTZuGM2fOICkpCSdOnMCVK1eUFp8VEl1dXTg4OKBPnz5wcXERXJSJiIiIlARJuF9+BvvZp2A/+xTaLC9elJ34sT0ilvdG5Epn9GpaXRRlApOZmalV+xkZGbh2rfjlroQiMjISsbGxWrsWUZiVg6pVq+L333/H48eP0b9/fyxevFhrvszMzPDdd98hMDAQN2/eVOriBAAjfV1ErnRGM9tKijT72acQGpOilj8jIyN07doV06dPh5GRMIvmioiIiLxPnsanw372KYw6k4Hav/hhxelHRfaZ2NkB4Ut7IXKlMyJXOsPJ1hw6Oh+OGCOJ2NhYrdoPCQnBpk2btOYjKSkJmzdvRvfu3ZGcnKwVH/fu3cPEiRNhZ2enlTZMLpfj3Llz+Oqrr+Dg4AADAwOtjdUVuzLVoHbt2ti3bx/u3bsHqVQKfX19rfpr2LBhiYvmHv/xUzyKTUXP3/PHjH2x8SoA4PmK3uKTnoiIyH+KbKkMoz3+QuDTxFL38/3xUzQt9FCrDo8fP8bZs2cxYsQIVK5cWSNb70ISd+7cgZeXF06ePIn9+/fD2tpaUB8xMTE4cOAA9uzZg0ePHuHq1avIysoSzL5cLselS5ewY8cOeHt7IycnBz4+PrCxsRHMR1ZWFry8vODu7o7r168DAJYsWYLmzZsL5iMlJQUeHh7YvHkzwsPzxyB++eWXgo8xL4wozDTAycnpfZ8CAKCBdUVErnRGw/lnkCWVAQBq/+KHVf2bYnCrWu/57ERERET+R3p6OjIyMmBlpfq42JKQy/MH7a+7UPKgfQAY7GiAhcM6w8RA/SZPJpMhKCgIx48fx/HjxxEeHg4PDw/BRBlJ3L9/H4cOHYKXl5di+IqHhweaNWsmiI/09HR4e3tj79698Pf3z58zC4CrqyvatGmDgIAAjX3k5OTA1dUVO3bswPPnzxXpLi4u6Nu3r8b2Czh16hRGjBiBpKQkRVqbNm0we/ZswXy8ffsW33zzDc6dO6dIq1y5Mtzc3PD48WPB/LyLKMz+RTxc0hPP32Sgs2sAAGDW0fuYdfQ+bs/vBgtTg/d7ciIiIh808fHxePz4Mdq2bStYLwBJRERE4Pr167h27RquX78OQ0NDnD17Vm17R2/HYMbhu6XuV0n6FgGLB6Gyaf441oCAALVFWXh4OFauXImTJ08iISFBkT5jxgyMHDlSLZvvIpfLMWvWLLi6uiqljx8/XjAfABAdHQ0fHx9cuHBBkebs7IypU6cK5sPQ0BB9+vTB77//rkhzdHTE2rVrBfMBAL1798aAAQOwbds2AICxsTH27NkDPT3hZI2FhQV++OEHXL58GTk5OQCATZs2oXr16qIwE1Gd2pamiFzpjDk+93HgRhQAoPmS8wCAiOW9P6ixEyIiIqUjk8kQFxeHmJgYGBsbo0mTJhrbTEpKQlhYGEJDQxV/Q0NDkZaWBi8vL0FEWWRkJKZNm4bAwEDEx8cr0p2cnODn54dKlVTrRpTLiSO3o/HzkXtl7vt67wzkvg5Hr549cPz4ccHEZb169eDo6Ihdu3Yp0nr37o2VK1cKYh8AdHR0MHr0aBw+fBgvXrwAkB/9WbdunWA+AEBPTw9RUVGKz7a2tvDw8ICOjnDDzePi4jB58mS8efMGenp6kEgkOHDgAExNTQXzkZmZibFjx+LAgQOoU6cOIiIi8Ntvv6F+/fqC+SCJJUuWYOHChXBwcICZmRlq166Nb775RjAfJSEKs38py/s1xYIvGqHB/DOKtDpz/NC2jgU8XT55j2cmIvLPRS6XIycnB9nZ2Up/a9SoATMzM41sR0dHY/Xq1YiJiUFMTAyio6MRGxsLmUyGHj164ODBg4Jcg5eXFyZPnqyIAAD5LxudPn0anTt3FsSHvb092rdvDx8fH0VagwYNcP78+VLH5uTmybHp0lNs8H9Spg/v8e3w4MopTJs2TRHJatGihWDiEsj/vbds2YIlS5Yo0ho2bIgDBw4INrk0Sbi7u2PatGkgifr16+Pt27c4fPiwoG+ue3l5YcyYMcjJycHSpUuxcOFCHDx4EFWqVBHMR2BgIAYOHIjY2FgsXboUqampsLS0FHTMV2RkJPr164eQkBCMHTsWrq6uGD58OCZMmCCYj4yMDHz33Xc4fPgwunTpAi8vL3h6emLAgAF/y9htUZj9iyl4c/Pl20x0WH0JABAU8Rb2s09hSKuaWNn/wxgjJyKiLklJSTh37hwqVaqktJmbm8PExESwSnTdunWYNWsWpFKpUrqBgQFWrFiBKVOmaOzD1tYWFStWxMaNG5XSp02bhlWrVgnSRZORkYH09HSYmZkphJmFhQXOnDmDVq1aaWwfAKKiojBnzhzs379fkebg4AB/f39Uq1ZNad836TkYtu0GHsellWn3j2HN0bOxNXR0JAgPD8eE0QPh7++P2rVro1q1asjMzMSpU6c0FsgFREREYPTo0QgICECzZs2wdu1aDBgwACdOnFA54lcWCQkJGD16NHx9fdGsWTMcOHAAJ0+eRIsWLVCzZk1BfGRlZWHq1Klwd3eHg4MDvLy80Lx5c9jY2ODTTz8VxAdJbNiwATNmzEClSpVw9uxZdOvWDeHh4ahbt64gPgDg4sWLGDRoEFJTU+Hu7q5YKeXgwYOC3etRUVHo27cv7ty5g4kTJ2LdunXQ19fHhAkT/r4X6lRZt+lD3P6utTL/TfwZHl9kjbeJ+29pbPfflk/a4kPKp6dPn2q8eH1ZHD9+nIMHD+avv/5KLy8vhoaGMicnR6VjVc0ruVzOsWPHFlnDFABtbW154sQJDUNCjZsAACAASURBVK4gn/j4eLq7u7Ny5cpK9ps0acK7d+9qbF8qldLHx4eff/65kn0DAwPu3Lmz1GNVzaf09HSuXr2aVatWJQA2atSIFSpUoI2NDUNDQzW+BpJMTU3l3LlzaWRkRAD89ttvefDgQdaqVYuRkZGUy+X0vRtT6pqThbfzYbGUyZTLaFZWFhctWkQDAwPq6+tzzpw5zMjI4Lx58/jo0aMSz608955MJuOmTZtoampKPT09Lly4kDk5OZTL5bx69aq62VOE06dP08rKigA4ffp0ZmdnkyQzMzMF8/Ho0SM6OTkRAAcPHsyUlJRS91enjkpLS+PgwYMJgK1bt+aLFy/UPNuSkcvlXLNmDXV0dGhtbc3AwEDBfZBkYGAgq1WrRj09Pbq5uZW6r7iIuSjMBMXrr6gilWCLJefVbqj/rfn0Lrm5uRodr0o+ZWdn87fffuPr16818lUWM2bMYI0aNfjdd9/R09OTb968Ecy2VCplREQEz549SwsLCyWxoaury/r169PFxYVxcXEl2igtrzIzMxkQEMClS5eyZ8+erFixYhFBM3v2bKampqp9DfHx8XRzc2PXrl2pq6tLADQ0NFT4mDp1KrOystS2X+Bj+fLlrFWrFgHQzMyM48eP58CBA2llZaVS41NWmUpLS+PKlStpaWlJAGzcuDEPHTpEmUzGrl27MiIiQqNrIMm8vDxu3bpVITI6duzI4OBgxiRlsu3SsyqJsEFu15icUfr95e/vz/r16xMAO3TowLCwMMV3Uqm01GNVraMiIiLYuXNnAqCTkxNv376t0nHlISsri5MmTSIA2tjY8Pz584L7IMl9+/bR1NSUhoaGdHNzU6l+L29d/uDBAzZs2JAAOH78eIW4FJKMjAwOGzaMANi2bVvGxMQI7oMkd+7cSX19fVapUoUBAQFl7i8Ks/ckzPz9/fn8+XOt+wkMDNR69OKvv/7iq1evlNKOhxT/9JqcWT4BUlBAExISePz4cebl5Ql12sWya9cuhoaGKuVZaGioRg3xu5w+fZo7duzg3bt3FZV+REQEu3XrxuDgYLVsvnsjP3/+nLNnz+a6det44MAB+vv7MzQ0lN27d6eenh779+/Pc+fOUSaTaXQt06dP57fffsuhQ4dywIAB/PLLL9muXTslMSORSNiqVSvOnTuXV65cKXd53LVrF7t27cratWsrhExxW4MGDbh169YyowLFVXr37t3jJ598Qn19fYW9KlWq8KuvvqKpqSkBsF+/fnz69Gm5zr0wMpmMvXr1oo6ODgHQ3Nyco0aNop+fH0+fPs0aNWoI0pCuXr2aBgYGijzZuHGjIprh5ubGqKgoleyU1jgEBwezSpUqBMCmTZvy8OHDSmVJiPtFKpWyZcuWlOgZ0n7QHJWjYR7XnjMzR/V6YtmyZQRACwsL7tixo9z3hCqN6J07d2hqakpdXV3Onz9f5ehueZDJZGzdurWirAr5QFQYV1dXAmD9+vUZEhKi8nHlERuPHz+mmZkZjY2NuWfPHjXOsmzkcjk7depEABwzZoxWhB9Jbt26VREFV/VhRRRm70mY7dixg5aWloKGr9/F39+fAOjs7Mzo6GhFupBCLS8vj/Xq1aOJiQnnzp3L5ORkkvmRh7i4OIbFpJTYlaAKBQV0xYoVBEB7e3uuXr1aUemsWLGCL1++FORa4uLiKJFICIB169blzJkzGRgYyOPHj9Pe3l6w6F2/fv0Ujb+xsTE/+eQT/vjjjzQxMSEADho0iOHh4eWy+e65nT59ukQBU3irU6cOV6xYwdhY1X6Pd6lZsyYNDAxoZmZGCwsLWllZ0drauogw69ixI9evX6+yKCjMsmXLaGdnx86dO3P06NFcunQpDxw4wB49ehAAO3XqxJMnT6rcoBb3O7569Yr29vYcMWIE3d3d+eDBA8pkMiYmJtLJyYkXLlwo93kXx/Dhw/ndd9/Rz89PqXEODQ1lYmKiID6OHTvGr7/+mv7+/hrd66WV96ysLPbs2ZPe3t4ai/vCSPNk/P18uMoibIj7dSakadaghoSE8LvvvmN8fLxax6tSL+Tl5fG7777jrVuaD+8oje3bt3P79u1afRiPioriuHHjyi2+y1N/yuVyzpgxg/fu3Svn2ZWPEydOlNmtqCmJiYn88ccfy5VfojB7T8Ls5MmTtLS0pIGBAfft20eS9PPzE9RHZmYmp0+fTolEwkqVKnH37t2Uy+WcP3++xl0lhbl69So//fRTRZRh7dq1jIiIYOPGjRVdSglp2cVWrPXn+jFbWvLTbUEBTU5O5vr161mvXj0CoJGREUePHs2uXbvS2tqaQUFBGl+HXC7n7du3OX/+fDZt2lQhLMzMzBT/T5o0iRkZGRr5SUlJYUBAAF1dXfnNN98orqnwpqenx/Hjx6vc7fjujSyTyfjmzRuGhYXR39+fBw4c4Lp162hjY1Oka65169acMmWKWmH84hqA7du3U09Pj926daObm5vaoq80ZDIZp06dqlZDV55KLyMjo8yurH8r2h5GkCOVcc3ZRyqLMLtZJ/lneDylecIJQSH4rwy30BQxn1TnHy3MAOwEEA8gtITvJQA2AHgK4B6A5qrY/bvGmD179oyNGjUiAM6fP592dnY8deqU4L4CAwMV4yecnZ1Zo0YNjhw5UtCnKrlczhMnTrBx48YEoBh30qhRI6WGWS6Xc/j2oGIr3XXnHxexW5zgOHPmDL/44gtFdKtgjE6BwBWKp0+fcs2aNUXGMtWrV0/wAaKLFi0qIs4kEglr165NLy+vMn8rVW7ky5cv86OPPuKYMWPo7u7OW7duaaVL5fLly4JFf7SB2ECohpD59CYtmxP23yqXCPN/GKv1YRhCIJYn1RDzSXW0Kcz+jukydgPYBGBPCd/3AlDv/7c2ALb8/98Pgjp16uDatWsYNGiQYi6bH374AWFhYahYsaJgftq1a4eQkBAsWLAAa9asAUns2bMHTZo0wcyZMwXxIZFI0KdPH/Tu3Rvbt2/H+PHjAQAPHjxAly5dcPHiRVhZWUEikWDv6PyfoPA6nADw+4Un+P1C/hxDG7/5GH2aFV33TEdHBz169ED37t0xduxY7NixA0D+Uh3Dhw9HWFgYli5dKsikhg4ODtDX18fbt2+V0p88eYIOHTpgxowZ+PXXXzVe1DYzMxMVKlSAh4cHrKysYG1tDSsrK1haWgo603SHDh1w584dweyVRMeOHbXuQ+TDRC4nAsLj8f3u4HIdt/Gbj9G1YTWNljUSEREpG63fYST/lEgk9qXs8hWAPf+vJoMkEom5RCKpTvK1ts9NVWJiYpTWQ4uOjsasWbOwZcsWQf3I5XKQhK6uLvLy8gAAs2bNQsOGDfHFF18I5iczMxNHjx4tiFgCKCrOCihYh5MkXM89xuZLzxTf/XTwDn46mC8iVpu+xKBWyvPuhIeHw8rKCiNHjkR0dDSio6Px8uVLrFixAg8ePMDevXtRoUIFja/np59+wsSJEyGTyZCXlweZTKa0Fb5OdTExMcG0adM0tlMW4sLzIkLyKDYVo3cHIya5fItTe09oh+a1hF2YW0RERDUkQjRaZTrJF2YnSRZZT0QikZwEsJLk1f//7A9gFskij3MSicQFgAsAWFlZtfD09NTmaSsmYiSJpKQkxMXFITMzU/G9o6OjYJMZFpCdnY3k5GQkJycjIyMDQH4EqmHDhhpHfd5FKpUiMzMTGRkZyMjIQGZmJvT09ODo6FhqFEgqJ36/lY2wRHmx3ztW1sGs1kbQKUFkyGQy5ObmQkdHR9CZrT90CsqTSNmIeaUaBfn0PEWG9bdzkJxTvvq8iaUuRjQ0gJWpcEvyfIiI5Uk1xHxSHXXyqnPnzrdItixrvw9BmJ0CsOIdYfYzyVul2WzZsiWDg8sXii8vAQEB6NSpk+IzSVy/fh3r16/H0aNHUbt2bdy9excmJiZa8R8bG4uTJ0/ixIkTiIiIQEBAACwtLbXiC8i/vhcvXiA1NRVOTqqtCpCaLYXTonOl7uP1wydoXbvkZVj+K7xbnkRKRsyrouTJ5PC+HYOfj5a9buS71DA3xq7vWqG+leYR6n8iYnlSDTGfVEedvJJIJCoJsw9hsEA0gMJ9YLYAXr2ncykViUSCdu3aoV27dnj58iU2b96MDRs2YPbs2VrxZ21tjTFjxmDMmDHIzMxEYmKiVvwUIJFIYG9vX65jKhrpY3dPU3Tq1AkkMf3wXXjfjlHaZ5D7daXP13/pguqVjDU9XRGRfyXhcWn4xfs+br1IKvex1SsZwX1ECzSqXhF6uv/uKJjIPw+SSE1NFWxJq+KIjo5GaGgoevbsqRX7crkcFy5cQHx8vNYijB+CMDsB4EeJROKJ/EH/KR/S+LKSqFmzJlauXKm0ELA2MTEx0VpkTigkEgnWDvoIawd9BCC/gem+7s8i+32y4qLS53NTO/5nn+RF/nuQxLOEdCw5+RCXwxPUstHOoQr+r717D4u6yh84/j4gF8Vboqama1JipCao/dQ1fUzQQlIrb2kqrpX7mK6X2jJL2vCKd1NDt5VV0RUNuTy6mC0BahneM5SsDY2LeUEIEJGLMOf3B8hG3kbmSzPm5/U88wDDzPl8ODrz/cw553u+swd3ICP5sGEXHhe2SWtNZmZmlbW/RiorK2P//v0cPXoULy+vGolx8uRJtmzZwt69e4mIiDC8MCsoKCAyMpLQ0FAOHTrE4cOHDW0fIC0tjfXr17N+/XrS09PZsWNHjU371nhhppQKA/oAjZVSZ4G/AQ4AWuu1wC5gAOXbZVwF/lTTORnpflojdbfcH6xHapBf5c//OpjGe1Enb3jcr4u3AR2bsWy4J84O9jWeoxA1obCkjOjjPzEz8oRF7Xz4kie+HZrjWOvmo19nv5WTRaxBa01ycjL79u1j+PDhhi8xKSwsJD4+npiYGBISEti8ebOhhdm1a9fYs2cPERERREdHk5eXx/79+7l8+bJhMc6cOcPWrVsJCwvj5MmT2NvbEx8fT7NmzQxp32QysXfvXjZu3Mj27dsr12SHhobi7u5uSIzi4mKio6MJCQnh888/rzyR7K9//ashJ67dym9xVubIO/xeA5NqOg9hfS93a83L3VpX/rzpQBoB0TcWartOXGDXid1V7vvjI658NKozD7g41nieQtxJ7tUSNiWmsTT2vxa3NcvPg5e7taa24/3xQaSwsJD8/HyaNm1qaLvXrl3j+PHjJCYmkpiYSLdu3Zg6daphZzqnpqYSFxdHXFwc8fHxXLx4kfXr1xtWlGVkZBATE0NMTAxxcXEUFpafSRsREUGXLl0MiXHo0CGCg4PZsWMHOTn/myrfvHkznTt3Zs+ePRbHKCgowN/fn4iIiCr3z5s3z9BteiIjI5k8eTIXL16svG/s2LGMGTPGsBgFBQV8++23xMXFVRZlnp6ezJ07l8TExDs8u/psYSpT3KfGdG/NmO7/K9TO5lyl37J9FF4ru+GxX53OxmtO7A33z3j2MV7t1QYHWU8jDHK1pJSYpPMs3P09WVcsX6rQyMWRDwa1p+9jTanrZJtvucXFxWRkZJCenk7Pnj0NmQkwmUycOXOGEydOVN6SkpKoV68eu3btsrh9rTU7d+7kyy+/JDExkSNHjlBUVASU7zVpVFF24sQJRowYwalTp6rcP3/+fMaNG2dx+wClpaVs3LiR+fPnVxZkAAsWLODFF180JAZAx44dsbe3r1KUTZ8+nZdfftmwGC4uLsyaNYvdu3dXjmINHDjQsP04r+vWrRtubm6VhZm7uzsfffSRoTHs7Ow4fvw4JlP5DgTOzs5s2bKlxmfKbPNdQtyXWj5Qh1Nzqi7YTM0qwG/lFxSU3FisASzc/R0Ld393w/2tXeuwbLgnnf/QUPYGEwCUmTTJ5/L4xxc/svMb484valzXifcHPo73Y01xMaDwKisr4/Lly+Tl5ZGbm1v5tWnTpvTo0cPi9sPDwzl27BhpaWmkpqaSlpbG+fPnqV27tmEHnTNnztC/f39Onz5d5f4ePXoQExNTZV/I6lJK0aRJE0JDQ6uMmvj7+xMcHGzY6759+/b4+flVKcwmT55s6ElfSilq1656QpS/vz8zZswwLIbJZCI4OJjNmzdX3vf000+zaNEiw2JorfnnP//JlClTMJlMNGrUiPr167Nx40ZDNhS/bteuXYwdO5bc3FxefPFF/v3vf7Nt2zZD13wlJSUxZMgQUlJSeOONN0hISOC1117Dw8PDsBi3IoWZsGkPN3YheXbVYq24tIzghNN8GPfDLZ+Xln2VIWu+uuXve7i5Ms2nLU8+3Ag7Oync7lUlpSaOpuXwyZEMor7+6c5PqIbxPdvQxnSW/HNnqGVvh729Pfb29tjZ/e/7Pz7kaHFRduHCBfr378+JEzeuSxs1ahRr1661qP3rPD09mTx5MpmZmZX3tWjRgp07d9K5c2dDYjRs2BBvb+8qhZm3tzfR0dGGHTz/+9//snDhwipF2UsvvURISIhhRcA333zDxIkTSUxMpF69euTn5zN06FBWrFhhWOGXnJzM+PHjOXToEF26dOHq1as0btyYv//974bFSEtLw9/fn7179/Lkk0/yxhtvMGPGDLZt22bYlUtyc3OZMGEC4eHhtG/fnq1bt7J06VImT55sSCEO5SOLs2bNYuHChbRs2ZIdO3bQqlUrnn76aTw9PQ2JAeVTuxMmTMDe3p5PPvmEYcOGsXPnTkM3er8dKczEPceplj3T+7kzvV/VBZ5F18qISTrPm+Hf3LGNxDPZJH585+1HXuvVhoGdWuDRvL5Ml96lU6dOkZ6ezhNPPEGzZs1ue5DRWnMpv5iDP/5MTNJ5dicXwO6YGs2veQNnpvm0xdvjQR6o44j9bQr09PS6PDlhTJViBuChhx5i7dq1hqwz+vnnn/H09KxSmDk7O7Nq1SpeeeUViw/SRUVFbN26lRUrVlT5Ozw9Pdm5cyctW7a0qH2AnJwcli1bxocffkh+fj6urq5kZ2czaNAgtm3bZsgm2dnZ2cyePZvg4GC01rz++ut89tlnPPHEE4SGhmJvb/lavfz8fP72t7+xcuVKHBwcmDNnDj179iQwMJBNmzYZEqOkpISgoCDmzp2Lvb09ixYtYvr06cybN49JkyYZMnKptWbjxo1MmTKFq1ev8sEHH/Duu+9SVFSEu7s7TZo0sTgGwP79+xk1ahTp6em8/vrrLFmyhNq1a7N06VIaNTJmD8uzZ88ycuRIvvzyS3x9fQkNDaVx48ZorZk0yZhl6iUlJUyfPp3g4GA8PDyIiIioHCEbOHCgITHMIYWZ+N1wdrBnSJeWDOly4wFGa83Fy8WsjP+BLQfTzW7zH1/8yD+++PGu8qjrVIve7o156tEmdG7dkDaNXXCqZd4budaahIQEevfubeg1OH9t8eLFfPvttzz77LP4+Pjg6uparXbKTJrsK8WkXLrCibN5fJ2ey7H0HDLzf7E2K+GYQVmb58rJeK6ciGXgU14sCAzg0UcfrVY7hYWF7N27l127drFr164birKJEycSFBRk0TVzL126RFhYGKGhoRw9Wr6ntrOzc+WBMzw83OzNnm/l4sWLrFmzhjVr1pCZmUmzZs2YPXs277//PgMHDmTLli0Wj2Ll5uayfPlyVqxYweXLl+nRoweBgYGkpqaSkJDAxo0bcXBwsChGcXExq1evZu7cueTm5uLn58fixYvx8PBgwYIFvPnmmxbH0FoTHh7O9OnTOXfuHAMGDGDVqlW4ubmRnZ1NdHS0IcXl0aNHGT9+PElJSTz11FOEhIRUnkkYEBBgyIjfpUuX+POf/0xUVBSPPfYYmzZtomvX8r1NHRwcDBkdLSsrY968eQQGBtKwYUOioqJ4/vnnK39vVFG2e/duxowZQ05ODgsWLODtt9+u7COjRhXPnj3L0KFDOXjwIMOGDSMkJKRGz7y8HSnM7uDatWsWv9jvpKCgABcXlxqNkZubS4MGDWp0vVVRURFXr1417MV4K6dPn6ZNmzZV3rzS0tJo3LjxLftRKUWzBs7Mf6Ej81/oeNPHlJk053IL+dfBdNbuPX3Tx5jjSnFpxZmlF278pbmjQP/5rNrxzfM4PPg4CV8DXx+o4VjV59G8PsO6tMTH40Hsi/PYtjWMw4cPc+TIEVJSUm76nP79+7MgakO1Djxaa9auXUtMTAzx8fGVC7E7d+7MsGHDCA8Px93dnXXr1tGrV69q/13x8fGsWLGCTz/9lNLSUlq0aMHbb7/NmDFjmDNnDrVq1WLt2rUWHRgyMjJ4//332bJlCyUlJXh5ebFkyRKGDx9OaWkpOTk5LF682KLRH5PJxJw5c1i+fDl5eXl069aNwMBA+vfvj1KK1NRUxo8fb/EI06effsrkyZM5c+YMnTp1Yvv27Xh7e1f+fubMmRa1D+X99corrxAbG0urVq2Iiopi8ODBle+Z1f3w8ktaa959910WL16Ms7Mzq1evZuLEiVXey4woyj777DPGjh1LZmYmU6ZMISgo6IY1bJa6cOECI0aMYN++ffTp04dNmzYZMur6S1prAgICmDdvHi1atCAhIcGi192t7Nu3j6FDh5KTk8Py5csNPZu3OqQwu43MzEx69uzJli1bqv2p+04yMjLo1KkTEydO5J133ql8IzaZTIYulhw1ahQ//fQTb731FiNGjMDBwQGtNSkpKbRt29aQGFFRUYwbNw4/Pz/GjBnDgAEDcHJyYtWqVfTt25f27dtbHKO4uJiOHTvi4uKCt7c3Pj4+9OvXj8zMTHr37s2qVasYNGhQtdq2t1O0alSHd3wf4/tPFrJhwwbq169Phw4d6NixIx06dGDp0qWkp6czctQoZsx8j6YtH+ZIag6fnjzP7pMXKDXV/CXO7iWqKI/8lKMUnjmCR2Mnprw2lhHDh91xmuZmlztJTv6RN998E2dnZ7y8vPD19aVr1654eXnRq1cv3N3dCQoKom/fvtXPVynWrVtHSkoKfn5+DBgwgGeffZbmzZuzfv162rZtS0BAgMWjJklJScTFxfHSSy8xduxY+vbtW1m8TJs2je7du1t8YLC3tycsLAw/Pz+mTZtGr169Ktt0dHRk2bJlFrUP5UXEgQMHaNeuHYGBgTzzzDNV8r7bK4ncSk5ODoWFhYSEhODv72/IVOKvubi4kJyczIwZMwgICKiRD8tKKc6fP4+3tzcff/wxrVu3vvOTqsHe3h4nJydiY2Px8fGpkRh169YlKyuLefPmMWPGjBr5N1FKce3aNZ555hk2bdpk2NTrr9WpUwcXFxciIyN56qmnaiTG3fhNrpVZE36La2WGh4czevRoHBwcWLVqFePGjSMiIoLnnnvOsAuK//DDD0yYMIE9e/bQrFkz5s2bh7+/P3PmzMHf3582bdpYHENrTVBQEB9++CEXL16kVatWTJ8+nVdffZV27doRGRlJ9+7dq93+9YPowYMHWbZsGTt27KCoqIgHHniA4cOHk5uby44dO/joo48YN26cRQecK1eusGbNGmJjY/niiy8qT49v3bo1aWlpAAwePJiVK1fyhz/8odpx4uLi2LdvHydPnuTEiROkpKTw69eKnZ0dI0eOJCAggHbt2t2xzV8XG+fPnycuLo7s7GyysrLIysriUlYWh49+zdmLWdg51kE5OmPnXBfn+o15zLMr3r6DcajbkKJrZRSXmiguLaPoWvnXklITSinsVHmRaafKbzk/Z+Ngp3FxsKOekz2N6tRCX81lydz30YX5dH7icQYO8OX5gQNo96jbbdda3Upqaio5OTm0atUKV1fXyn/jgQMH0qBBA/7yl7/QrVs3s9u7WWFWVlZGcnIyjz/+eJVp3rNnz3LgwAGGDBliyKfctLQ0WrRoccNIeUlJCY6Oxuyjd+XKFbTWFk+V3Ol6fVlZWTV6fV2AvLw86tevX6MjDCaTicLCwmoXS+Ze1/Dq1as1foWVoqIinJycanxEpqio6K6PU3d7/UcjXxO3Ulpaip2dnaEDFTdzt7NjNXmtTLTW9+StS5cuuqYlJCTo48ePaw8PDw3oYcOGaR8fH/3qq68aGsdkMumoqCj9yCOPaEB7enpqLy8v3aZNG52RkWFYnMLCQv3xxx9rd3d3DeiGDRtqpZSuXbu2jo6Orna7CQkJVX7Ozc3VISEhuk+fPhqochs9erS+fPmyhX9JucLCQv3555/rGTNm6NatW1eJ4+LiopcsWaJLSkoMiVVQUKBDQ0Nv+HsA7erqqhctWnTHWL/up5vJz8/XLVu21G5ubnrUqFF65cqV+tChQ7q4uNiQv+O6sLAwvXbtWn3+/HlD2/0lk8mkMzMzq/Vcc/pKSD+ZS/rJPNJP5qtOXwFHtBn1jdULrOrefqvCTOvyg/LEiROrHIxDQkIMj1dUVKSXLFmi69evXxmnXbt2+uLFi4bGKS0t1ZGRkbpp06aVcezs7PTq1aur1d7t/oNu2LDhhkLG3d1dHz9+vJrZ3+i7777TjRo1qhLDzs5O16lTR/fp00d///33FscwmUx69uzZ+q233tKrV6/WO3fu1ElJSTovL8/sNsx5IWdnZ1e7mPk9kQOEeaSfzCP9ZB7pJ/PVZGEma8zM4OjoyJNPPklYWBi5ubkATJo0CS8vL0Mv+urk5ESnTp1o0KBB5TXLvv/+e/r160dCQoJhi+rt7OxITk6ucpaZyWRi8uTJZGRkMH/+fEOGjQsKCjh16hR/+tOfyMvLq9w08/Lly7zwwgsEBgYyevRoi4f0XV1dSUpKwtnZGScnJ5ydnQ0/o1EpRUBAgKFt3kxNnzghhBDCtklhZqZWrVoxZMgQIiMjycnJoaioiKFDh3LkyBHDNs8DcHNzY+7cuXz11Vfs37+f5ORkkpKS8PX1JTY21qJT869TSjFr1iymTp3K6dOnSUlJISUlhdOnT3Pw4EFmzpzJ3LlzLT4b1cXFhaCgIIvzvZOaXkMjhBBC/FakMDNDrVq18PHxwcfHh+DgYGJjY9m2vcXD8wAABjxJREFUbRvR0dH4+/sTHR1t2MJENzc33NzcGDt2LFC+zUViYiL79+9n+fLlvPfee4aNBtWrVw9PT09Dd0wWQgghRPVJYXaXHB0d8fPzw8/Pj8LCQnbv3k1SUlKNFTcNGzbE19cXX1/fGmlfCCGEELZDCjML1K5dmxdeeMHaaQghhBDid0Iu/ieEEEIIYSOkMBNCCCGEsBFSmAkhhBBC2AgpzIQQQgghbIQUZkIIIYQQNkIKMyGEEEIIGyGFmRBCCCGEjZDCTAghhBDCRkhhJoQQQghhI5TW2to5VItS6hKQVsNhGgNZNRzj90D6yTzST+aTvjKP9JN5pJ/MI/1kvur0VWutdZM7PeieLcx+C0qpI1rrrtbOw9ZJP5lH+sl80lfmkX4yj/STeaSfzFeTfSVTmUIIIYQQNkIKMyGEEEIIGyGF2e19bO0E7hHST+aRfjKf9JV5pJ/MI/1kHukn89VYX8kaMyGEEEIIGyEjZkIIIYQQNkIKs5tQSv1TKZWplDpp7VxsmVKqlVIqQSl1SimVrJSaau2cbJFSylkpdUgp9U1FPwVaOydbppSyV0p9rZT6t7VzsVVKqVSl1Aml1HGl1BFr52PLlFINlVLblVLfVbxX9bB2TrZGKdWu4v/S9dtlpdQ0a+dli5RS0yvex08qpcKUUs6Gx5CpzBsppXoDV4BQrXUHa+djq5RSzYHmWutjSql6wFHgea31t1ZOzaYopRTgorW+opRyAL4EpmqtD1g5NZuklHoD6ArU11o/Z+18bJFSKhXoqrWWPafuQCm1EfhCa71OKeUI1NFa51o7L1ullLIHfgK6aa1req/Qe4pS6iHK378f11oXKqU+AXZprTcYGUdGzG5Ca70P+Nnaedg6rfV5rfWxiu/zgVPAQ9bNyvboclcqfnSouMknoptQSrUE/IB11s5F3PuUUvWB3kAIgNa6RIqyO/IGTktRdku1gNpKqVpAHeCc0QGkMBOGUEo9DHgBB62biW2qmJ47DmQCsVpr6aebWwG8DZisnYiN08B/lFJHlVITrJ2MDXMDLgHrK6bH1ymlXKydlI17CQizdhK2SGv9E7AESAfOA3la6/8YHUcKM2ExpVRdIAKYprW+bO18bJHWukxr7Qm0BP5PKSVT5L+ilHoOyNRaH7V2LveAnlrrzoAvMKli+YW4US2gM7BGa+0FFADvWDcl21Ux1TsICLd2LrZIKfUAMBhoA7QAXJRSo42OI4WZsEjFmqkI4F9a60hr52PrKqZR9gDPWjkVW9QTGFSxfmor0Fcptdm6KdkmrfW5iq+ZQBTwf9bNyGadBc7+YoR6O+WFmrg5X+CY1vqitROxUT7Aj1rrS1rra0Ak8Eejg0hhJqqtYlF7CHBKa73M2vnYKqVUE6VUw4rva1P+4v7OulnZHq31TK11S631w5RPp8RrrQ3/NHqvU0q5VJxsQ8W0XH9AziC/Ca31BSBDKdWu4i5vQE5OurWRyDTm7aQD3ZVSdSqOf96Ur602lBRmN6GUCgMSgXZKqbNKqVesnZON6gmMoXxk4/pp1gOsnZQNag4kKKWSgMOUrzGTrSBEdT0IfKmU+gY4BMRorXdbOSdb9hfgXxWvP09gvpXzsUlKqTpAP8pHgcRNVIy8bgeOAScor6EMvwKAbJchhBBCCGEjZMRMCCGEEMJGSGEmhBBCCGEjpDATQgghhLARUpgJIYQQQtgIKcyEEEIIIWyEFGZCCCGEEDZCCjMhhBBCCBshhZkQ4r6llOqolNr/i587K6XirZmTEOL+JhvMCiHuW0opO+Ac8JDWukwplQC8qbU+ZuXUhBD3qVrWTkAIIaxFa21SSiUD7ZVSbYF0rfUxpZQb8B7QQGs91LpZCiHuJzKVKYS43x2g/LqvHwDvAmitz2it5Rq5QojfnIyYCSHudweADcBHWuufrJyLEOI+JyNmQoj73XdAMbDQ2okIIYQUZkKI+91UYKbWuuD6HUopV6XUWsBLKTXTeqkJIe43clamEOK+pJR6BIgB9st6MiGErZDCTAghhBDCRshUphBCCCGEjZDCTAghhBDCRkhhJoQQQghhI6QwE0IIIYSwEVKYCSGEEELYCCnMhBBCCCFshBRmQgghhBA2QgozIYQQQggb8f/SaKD59FPINgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "Y1,Y2 = meshgrid(linspace(min(sol_1),max(sol_1),21),linspace(min(sol_2),max(sol_2),21))\n", "V1,V2 = pphi([Y1,Y2],tt) \n", "r1=sqrt(1+V1**2)\n", "r2=sqrt(1+V2**2)\n", "quiver(Y1, Y2, V1/r1, V2/r2) \n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons la fonction\n", "$$\n", "E(t)=dy_1(t)+by_2(t)-c\\ln(y_1(t))-a\\ln(y_2(t))\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est une intégrale première du système, c’est-à-dire que si $(y_1, y_2)$ est une solution alors l’application $E$ est constante:\n", "\\begin{align}\n", "E'(t)\n", "&=dy_1'(t)+by_2'(t)-\\frac{c}{y_1(t)}y_1'(t)-\\frac{a}{y_2(t)}y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1'(t)+\\left(b-\\frac{a}{y_2(t)}\\right)y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1(t)(a-by_2(t))-\\left(b-\\frac{a}{y_2(t)}\\right)y_2(t)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(by_2(t)-a)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(a-by_2(t))(dy_1(t)- c)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.94227800416e-07\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = 0.3*yy0[0]+yy0[1]-log(yy0[0])-2*log(yy0[1])\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = 0.3*sol_1+sol_2-log(sol_1)-2*log(sol_2)\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 2\n", "\n", "Considérons l'EDO $y''(t)=-\\sin(y(t))$ qui décrit le mouvement d'un pendule non amorti, équivalente au système différentiel\n", "$$\n", "\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=-\\sin(y_1(t))\n", "\\end{cases}\n", "$$\n", "avec $y(0)=0$ et $y'(0)=1$. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pphi = lambda yy,t : [ yy[1], -sin(yy[0]) ]\n", "\n", "t0 = 0\n", "yy0 = [0,1]\n", "tt = linspace(t0,10,1001)\n", "sol = odeint(pphi,yy0,tt)\n", "\n", "figure(figsize=(18,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,sol[:,0],tt,sol[:,1])\n", "xlabel('t')\n", "ylabel('y')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "plot(sol[:,0],sol[:,1])\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$')\n", "grid()\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons l'énergie suivante (somme de l'énergie potentielle et de l'énergie cinétique):\n", "$$\n", "E(t)=-\\cos(y_1(t))+\\frac{1}{2}(y_2(t))^2\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est conservée au cours du temps:\n", "\\begin{align}\n", "E'(t)\n", "&=\\sin(y_1(t))y_1'(t)+y_2(t)y_2'(t)\n", "\\\\\n", "&=-y_2'(t)y_1'(t)+y_1'(t)y_2'(t)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.44859039897e-08\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAm0AAAG0CAYAAABg0hDEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3XecXVW5//HPmt77ZNImvUICAUIJNXRRipeiICICXuxef169oqhXxa7Xdr0WFBVsiKFIkxYYekuoKaT3Ppne2/79sc6ePsmUs8s55/t+vfLac87s2fuBMzPnmWet9SzjOA4iIiIiEm5JQQcgIiIiIoenpE1EREQkBihpExEREYkBStpEREREYoCSNhEREZEYoKRNREREJAbEbdJmjPm9MWa/MWZVFK51pjHmjV7/Wowx7x3m1y41xtT2+tqvRSGe040xrxljOowxl4/1eiIiIhJ+Jl77tBljTgcagDscx1kQxesWARuByY7jNA3j/KXA5x3HuTCKMUwD8oDPA/c7jrMsWtcWERGRcIrbSpvjOM8AVb2fM8bMNMY8YoxZaYx51hgzbxSXvhz413AStsMxxnzQGPNKpAL3G2NM8nC+znGcrY7jvAV0jTUGERERiQ1xm7QN4Vbg047jHIetUv1yFNe4EvjbCL9miTHmTWPMv4wxRwIYY+YD7wdOcRxnEdAJXD2KeERERCQBpAQdgF+MMTnAycA/jDHu0+mRz10KfHOQL9vlOM75va4xAVgIPNrrue8CFw3ytfc5jvMV4DVgquM4DcaYdwP3AbOBs4HjgFcj8WQC+yPXvAM4dpBr/tJxnNEkmiIiIhLj4nZOG3TP/XrQcZwFxpg8YJ3jOBPGcL3/AI50HOfGMVxjK7AYuAqY6DjOl8ZwrT9i//s0p01ERCTOJczwqOM4dcAWY8wVAMY6eoSXuYoRDo0aY8abSCnNGHMC9v/5QWA5cLkxZlzkc0XGmKkjjEdEREQSRNwmbcaYvwEvAnONMTuNMTdg54zdYIx5E1gNXDKC600DyoGnRxjK5cCqyD1/DlzpWGuArwCPGWPeAh4HhlUFNMYcb4zZCVwB/MYYs3qEMYmIiEiMievhUREREZF4EbeVNhEREZF4EnerR0tKSpxp06Z5fp/Gxkays7M9v48Mn16TcNLrEj56TcJJr0v4+PGarFy5stJxnNLhnBt3Sdu0adNYsWKF5/epqKhg6dKlnt9Hhk+vSTjpdQkfvSbhpNclfPx4TYwx24Z7roZHRURERGKAkjYRERGRGKCkTURERCQGKGkTERERiQFK2kRERERigJI2ERERkRigpE1EREQkBihpExEREYkBStpEREREYoCSNhEREZEYEGjSZox5lzFmnTFmozHmpkE+/zljzBpjzFvGmOXGmKlBxCkiIiIStMCSNmNMMvB/wAXAEcBVxpgj+p32OrDYcZyjgGXAD/yNUkRERCQcgqy0nQBsdBxns+M4bcCdwCW9T3Ac5ynHcZoiD18CJvsco4iIiEgoGMdxgrmxMZcD73Ic5yORx9cAJzqO86khzv8FsNdxnG8N8rkbgRsBysrKjrvzzju9CzyioaGBnJwcz+8jw6fXJJz0uoSPXpNw0usSPn68JmeeeeZKx3EWD+fcFE8jOTQzyHODZpDGmA8Ci4EzBvu84zi3ArcCLF682Fm6dGmUQhxaRUUFftwnNBr2Q3oupGYGHcmQEu41iRF6XcJHr0k46XUJn7C9JkEOj+4Eyns9ngzs7n+SMeYc4GbgYsdxWn2KTXpr2A8/XQg/PwZa6oKORkREJCEFmbS9Csw2xkw3xqQBVwL39z7BGHMM8BtswrY/gBgF4J0HoaMF6vfAituCjkZERCQhBZa0OY7TAXwKeBRYC9zlOM5qY8w3jTEXR077IZAD/MMY84Yx5v4hLide2v4S5E6EicfCmn8GHY2IiEhCCnJOG47jPAw83O+5r/X6+Bzfg5KBDm6E0jkw5WSo+A601EJGftBRiYiIJBTtiCCH5jhQuRGKZ8HkyOKWXa8FG5OIiEgCUtImh9Z4AFproXg2TDrWPrdrpf9xtLfA6vuUMIqISMIKdHhUYsDBjfZYPAsyC+3R78Spqwv+fjVsfMI+PuMmOPNL/sYgIiISMFXa5NAqN9hjySx7nHQc7Fphh0398vxPbMJ29tfg6Kvg6e/B5qf9u7+IiEgIKGmTQzu4EZLTIT/SUm/ScdCwD+oGtNTzxsbl8OS34chL4dTPwYU/hbzJ8PT3/bm/iIhISChpk0Or2gxF0yEp2T6eGJnXttvDIdLWBti3Bl77E9x1LYybDxf/HIyB1AxY8knY9jzseNW7GEREREJGc9rk0A5ugqKZPY/HL4SkFNj9Osy/aOD5O1fC6nsgswBmng0Tj7HJVkcbrHsY9q+1jXpdne1Qsw2qttgKXnuT/eeasAiu/KvdQst17Ieg4nvw8q+h/Pjo/zeLiIiEkJI2GVpXF1RvgVln9zyXmgHjjuhZjOA48MZfYOtzNiHb8wYkp0FnGzz5LSidbyt121+E5mr7NcnpPddLSob8yVA0A6acCKlZkFUEBVOhcDpMXNRT5XOl58AxV8Mrv4WG70LOOG//P4iIiISAkjYZWv1uWxUrmtH3+UnHwup77T6kD34WVt0NOeNtcnb+d+HYa2wFbc0/4a2/Q/VWmH0eLLwCZpwJyVH4tlt8Pbz0S3jtdjj9C2O/noiISMgpaZOhVW22x+KZfZ+ffT6s/CN8b4p9fM7X4ZTP2mHQ3hZfZ/95oWQ2zFgKL/3aVv7mvtub+4iIiISEFiLI0A5ussf+lbbZ58HUU6F0Lnzg73Dq/xuYsPnhnK8DDtz5AXjkJv/vLyIi4iNV2mRoVZvs/LO8yX2fT06B6x4KJqbeJh4Dn1sLj94ML/+avGOmAUsDDkpERMQbqrTJ0PatscOQSSH+NklJh3O/AZlFTN75QNDRiIiIeCbE78YSKMeBPW/alhthl5YNCy6jpPIVaKkNOhoRERFPKGmTwVVvhaZKmHB00JEMz9FXkuREVqyKiIjEISVtMjg3+Zl9TrBxDNek42jOKIM19wcdiYiIiCeUtMlADfvtjgNTTh64cjSsjKGy5ETY8jS01gcdjYiISNQpaZOB1j8CHc1wQWxtyl5ZcpLdiWHjE0GHIiIiEnVK2mSgrc9B7gS7z2gMqcubB1nF8M7DQYciIiISdUraZKCqLbbVRxANc8fASUqGORfA+ke1ilREROKOkjYZqGab3bA9Fi2+Dtrq4cdHwsrbg45GREQkapS0SV/tzdCwDwpjNGmbvBiuXgYTF8EDn4E3/hp0RCIiIlGhpE36qtlujwXTAg1jTGadDdfcZ/dH/ddNUL8v6IhERETGTEmb9FW9zR5jtdLmSk6Bi35qV8E+8d9BRyMiIjJmStqkr5pI0lYwJdg4oqFkNpz0cXjzTrsll4iISAxT0iZ9VW+FlAzIKQs6kug49XOQWQiPfcXupyoiIhKjlLSN1YF18LOj4dkfBx1JdNRss1W2GGv3MaTMAjjzy7DlGbh1Kbz4f9DWFHRUIiIiI6akbazeustWp17/c9CRREd1DLf7GMrxH4Hzv2MT0Ue/DL85HQ6sDzoqERGREVHSNlZ73rDHqk3QVBVsLNFQsz32FyH0Zwws+STcWAHX3AvN1XDbOXbnBxERkRihpG2s9q2GtBz7cd2uYGMZq5ZaaKmJv0pbbzPPghufgpzxcMcl8LerbC+3rq6gIxMRETkkJW1j0dUJDfth/FH2cdPBYOMZq4Mb7bFoerBxeK1gCtzwKCy+Hvavhfs+Dn99H3S0Bh2ZiIjIkJS0jUVTFTidMG5e5HGMJ2371tjjuCOCjcMPmYXw7h/CZ16HC34AGx+3yZtWmIqISEilBB1ATGvcb49uktMY60nbKkjNgsI4r7T1Zgyc+FFoa4Dl34RJx9n5byIiIiGjpG0sGiLbI5XMscdYrrR1dcI7D0P5iZCUgAXYUz8Hu16Dx74KrfWw4HIomRV0VCIiIt0S8N05ihoO2GPeJMgoiO2kbeNyqN0Ox3046EiCYQy891cwYylUfBd+eRKsvi/oqERERLopaRsLt9KWU2rnSDXHcMuPN/4C2eNg3nuCjiQ4GXlwzT3w/9bAxGPgn5+E2hhfESwiInFDSdtYNO6H5HRIz4P0HGhrDDqi0XEc27Ns1tmQnBp0NMHLnwSX/dYOGT/6paCjERERAZS0jU3DAcgZZ4fW0nJjN2mr2gxNlTBlSdCRhEfhNDjlP2DNP2HvqqCjERERUdI2Jo37IbvUfpyeYyewx6KDm+yxdF6wcYTNSR+zyfgzPww6EhERESVtY9IYqbQBpGXHbqWtdrs9FpQHG0fYZBbCiTeq2iYiIqGgpG0sGg5Adon9OC3H9vqKRbU7ISnVbu0kfS35FGQV2y2vnvupmu+KiEhglLSNltNlK23ZkUpbei60xmjSVrPDTr5PxP5sh5NVZFeUTjgKnvhvePV3QUckIiIJSu/So5Ta3mC3sOozPNoQm5WY2h2Qr6HRIU04Gj54j+3h9uS3YncYXEREYpqStlFKba+xH7gLEdJyAAfamwKLadRqdthN1GVoxsDSL0FLDay6O+hoREQkASlpG6W0tkjS1rvSBrFXhelog/o9qrQNR/mJdl9W7ZQgIiIBUNI2St1JmzunLbPQHhv2BxPQaNXtAhytHB0OY+CIi2HL09AUw7tfiIhITFLSNkppbdX2A7fSNvl4e9zydDABjVbtDntUpW14jrgEujpg/SNBRyIiIglGSdsopbcegNTsngpb4VQYvxCe/r7dEipW1ESSNlXahmfisZA7QUmbiIj4TknbKGW0VEL+ZDtk5nr/X+zChNsvgpW3x8ZK0todgIG8yUFHEhuMgdnnwcYn7XxAERERnyhpG6X01gM2aeutcCr8+1Mw7kh44DOw8g/BBDcSNTsgdzykpAUdSeyYewG01cO2GKqoiohIzFPSNkoZLYMkbQAZefDvT8K00+DRm+1uA2FWvQUKpgYdRWyZfgak58Mrv4uNaqqIiMQFJW2j0d5MWnvt0JP3U9Lgkl9ARwusCHG1zXFg/1oonRt0JLElLcvuSbruIXjylqCjERGRBBFo0maMeZcxZp0xZqMx5qZBPp9ujPl75PMvG2Om+R/lIGp32eOhJu8XToPJJ4R7UULjAWiugnHzg44k9px5Mxz1fnj+Z2r/MRwNB6CzI+goRERiWmBJmzEmGfg/4ALgCOAqY8wR/U67Aah2HGcW8BPg+/5GOYTuNhmHmbxfNKPn3DDaucIexy8MNo5YZAyc+DG1/zictkaOWP0D+NEs+NFsWHVP0BGJiMSslADvfQKw0XGczQDGmDuBS4A1vc65BPh65ONlwC+MMcZxApxI1N7M1nu/wTTgUw8d4EDKi0Oeenm94bKG3Xzw18/QaVJ9C3FYHIfP1vySo00WH3mki04z9H9HrKipaeZX63z873AcbjM5vPTY/fz25en+3TdGFHce4AtVX2dKx2YezL6U2W1rmb3sBr715H5Wpx8ddHgJzfefFRkWvS7hk9fVytKlQUfRI8ikbRLQuwy1EzhxqHMcx+kwxtQCxUBl75OMMTcCNwKUlZVRUVHhUciA4zC3eT9PJ53Ipvo0ukzNkKdu68glCYe06k3sSRrvXUyjMLtrE0tan+We5As4WBtjW28NobOzk5qaoV8PL6w305na/A41jr/3DTPjdLGkawWfabuNNNr4asrnWdl1HBnJLfyi48t8suq7fDTjh9Sb3KBDTVhB/KzI4el1CZ/MzE5vc4oRCjJpM4M817+CNpxzcBznVuBWgMWLFztLvU6LT3uDdc+9wL8Od59NGfCnX/PHq2bDtFO9jWmk3vgb3AeXfvwWLi2ZHXQ0UVFRUYHnr31/j70AL/2KR79wHiQl+3vvMKrfB3dcAgfWQtkCuOw2zluzl++4r8veWXDrUpbNWQ6X/ibQUBNZID8rclh6XcInbK9JkAsRdgK9Z/JPBnYPdY4xJgXIB4Kf9T3cnmbZJfbYWHno84JQvRUwUDAl6EhiW/Es6GoP99xFPz15i/3eeu+vIz0L5/X9/PiFcNp/wlt3wp1Xw963AwlTRCQWBZm0vQrMNsZMN8akAVcC9/c7537g2sjHlwNPBjqfbaSyIklbUxiTti12IUVKetCRxLbimfZ4cFOwcYRBZwe88xDMvwgWXTX0HzdnfBFO/gxsfRZ+fwFUbfE3ThGRGBVY0uY4TgfwKeBRYC1wl+M4q40x3zTGXBw57Tag2BizEfgcMKAtSKhlFdtj48Fg4xhM9VbblkTGpiiStFVtDjaOMNj7pm0hM+f8Q5+XlAzn3QIfew5w4In/9iU8EZFYF+ScNhzHeRh4uN9zX+v1cQtwhd9xRU1Kmu2cH8ZKW9WWw7+5yuHllEFSKtTtCjqS4G2LrHob7vzNgilwwr/Dcz+126kdqu+hiIhoRwTPZRdDU8gqbW2N0LhflbZoSEqye7fW7ws6kuBte8H2JswdwUrpY68FHFh1t2dhiYjECyVtXssqCd9ChOqt9lik3mJRkVMG9XuCjiJYXV2w/UWYcvLIvq5oOkxaDG8v8yYuEZE4oqTNa9kl4au0uUmbKm3RkTse6vcGHUWw9q+x89mmjjBpA1h4Bex72+6DKyIiQ1LS5rWs4vBW2gpVaYuK3AmqtG160h5nnjnyr11wKZhkeOuu6MYkIhJnlLR5za20halTSdUWu0AiszDoSOJD7nhoqYH25qAjCc7mp6B0HuRNHPnX5oyDmWfB2/+ww6wiIjIoJW1eyyqxzVdbaoOOpEf1ViiaZjc9l7HLnWCPiTpE2t5sFyHMPGv01zjmg7ZB8d3XQ3N19GITEYkjStq85u6KEKZ5bdVbNJ8tmtzVkomatL3zEHS0wJx3jf4aR1wCJ34c1twPf79GFTcRkUEoafOam7Q17A82DldXJ9Rs13y2aOqutCXgvLbODnjh5/aPgGmnjf46xsAF34P3/MjulLDhsaiFKCISL5S0eS0/0jA0LHtT1u2GzjZV2qIpUSttjgP3fhT2vAlnf832rBurY66BvEmw4vdjv5aISJxR0uY1d0P26m22wvX2smC3tXK3W1KPtujJLLS7IjSGpJrql12vwapldi/RBZdF55rJqXDkv9mFDS110bmmiEicUNLmtdRMyBkPFd+BXy6Bu2+AP77bDisFwe2FVTovmPvHI2MguxQaDwQdib+2R7atWnx9dK8770JbDd74eHSvKyIS45S0+aFkNjhdULbADiMdeCe4OTv7V0Nmke3iL9GTXQINCZa07VppK8kj2bZqOMpPsEnw2geie10RkRgX6IbxCePy38Pet2D6GXYe0LM/tlWEee/2P5Zdr8H4BWr3EW2JWGmr2gQlc6J/3aRkmH2+Tdo6OyBZv6ZERECVNn/kjINZ59j5OilpdpXd5gr/49jzFuxbZd8QJbpyxoVv5wsvOQ5UbfVuFfKc86C1Fna+4s31RURikJK2IEw92S4IqN/n730fuQkyCmDh5f7eNxFkl9iFCGHa+cJLTVU2qSqa4c31ZyyFpBRY/6g31xcRiUFK2oLgbqq94yX/7tnZDjtX2M7z0Z6DJHZ4tKMF2hqCjsQf1Vvs0atVyBn5MP10u7VVe4s39xARiTFK2oIw/ihIyYRtL/p3z/1robMVJh7j3z0TSfY4ewxLE2WvVUWSNi+bNJ/0CajbBb9a0tOqRkQkgSlpC0JKml0h9/ZdULvTn3tWrrfHsiP9uV+iyS61x0SZ1+ZW2gqneneP2efCNffavUiXXa+trUQk4SlpC8p534K2Jnj8a/7cr3qrPRZ4+CabyNztyhJlBWnVZsidaPsQemnmWXD+d2D367Bpubf3EhEJOSVtQZlwFBx3Lax90CZvXqvZbqtBaVne3ysR5USGRxNlV4SqzVA80597LbjM7jrx5p3+3E9EJKSUtAVpzvl2ntnW57y/V802Vdm8lOVW2hJkePTgJv+2QktJhyMvhXce1NZWIpLQlLQFqfwk29Zguw8LEqq39eyDKtGXkmZXPCbC8GhLLTRVQpFPlTaAo95vV+eu+5d/9xQRCRklbUFKy7IrSXe87O19ujrtggcvJ42LXUGaCKtH3ZWcXvVoG8zk4yF3Aqy93797ioiEjJK2oE05ye7h2Nnu3T3qdkNXu4ZHvZZdmhjDowc32aNfc9oAkpLsRvIbl0Nbo3/3FREJESVtQSs/wQ777H7Du3vUbLNHVdq85e6KEO/86NE2mCMuho5mm7iJiCQgJW1Bm3YapOXAQ5/zroJQHUnaVGnzVs64xJjTVrXJtvvweyXylJMhs8jukiAikoCUtAUtuwQu/wPsfQte+a0396jZBhjIL/fm+mJll9pGsF4OdYfBvtVQOtf/+yanwOLr7Ly2P11q/1+LiCQQJW1hMOc8W0V4/c/eXL96G+RNsiscxTvZCdD2o6MNDrxj+wwG4Yyb4KyvwpZn4L5PBhODn9pb7JzUjragIxGREFDSFhZH/hsc3NAzyTuaarZpPpsf3P1H43mIdP8a6Gyzq56DkJIGp38ezroZ1j0E214IJg6vdXXBS7+GH82GH8+H70+F+z8NjQeDjkxEAqSkLSxmn2uP6x+N7nUdB/atgZI50b2uDNS9/2gcJ21bnrHHqacEG8eJH4OMAu+mFASpdhf86b3wyBftQqX3/BgWXgFv/BV+d5bd3UREEpKStrAomm4Tq3UPR/e61VugtRYmLorudWWgREja1v0LSuZC3oRg40jNhEUfgLUPQEOM//9uroadK+Gdh+FfX4RfHA87V8BFP4Orl8HxN8DFP4frHoGmarjjvdBUFXTU3ttcAX+5Ajpag45EJDRSgg5Aejnq/fDkLfDkt+3wTzRsfd4eJx4TnevJ0HIiSVu8Ntjd8ARsfwHO/WbQkVjHfRhe+iW8+Tc45TP+3LN2l90RIj0XMvIgPQ+M6XtO40E7jLx/LdTvAaer1z8HcKC13lbMDm6Cup09X5ucBkdcAmd+eWDz4vLj4eq74PaL4M6r4UP32S2+4tXTP4Btz8Pby+CYq4OORiQUlLSFySmftZO8n/kBzDwTpp48tuu1NsCL/wfFs4Kbg5RI0vNsS4oD64KOxBvLv2G/lxZfH3QkVulcmHwCvPEXOPnTA5On0Wqqgsr1tmLadNAuLNm32u5cUrer77lJqXYBSlYJGKBuj93iq/vzKWCSwSTZ+EyS/ZeaabeVm3oylB1p/1uyx9ljes7QsU05Cd77K7j7Bvjnp+A9/2OTx3iUnmuPm55U0iYSoaQtTJJT4OL/hU1P2WRrrEnbqrvhwFp435+i94YmQzPGvmZbnrETyZPiaPZB3R7bluacr/e8mYbBMVfDA/8BO16BKSeO7hrbXrQ/K7U7bIVssDljuRPt9ctPsv342hoie7AetMldY6Wtok08xg4fj5sP446A3PHR/9lbeLmd9vDkt2D1vXD0lXDhTyA5Nbr3CZrbxHmPh43HRWKMkrawSc2EYz4IL/yvXeqfN3H019rxiq38zL8oevHJoc27EN55EF75DZz08aCjiZ59q+xxypJg4+hvwWWw/Ba490Y4+79hwaUj+/oNj8Nf329/7gqnwaTFsPgGW/3KGQdZxfZfaqYn4Y/aaZ+3jbnf+jus+L3dlzVaUyrCwt3J5eBG23g8LTvYeERCII5KAXHkuA8DDjz65cgcmFHatRImL1aVzU9HXwmTjrNDdvHEfQMtmBJsHP2l58Llv4fULFh23chWk+5cCXd9yCZon1sDH38ervgDnPpZu5p7wtGQPzl8CRvYn+kpJ9kK28Ir4IWfQ/3eoKOKno42u73fuCPt45odwcYjEhJK2sKoaDqc/TU79LHq7tFdo6vTbjc0bn50Y5NDMwbmXwx73479VY291eyw87dyxgcdyUAzzoCPPguzz4PHvmor1IdzYB389Qq74vfqZZCR732cXjnjJpvgvHln0JFET1uDPY6bZ49qcyICKGkLr1M+a98g1z8yuq+v2W6boBbPim5ccnjuSt29bwUbRzTVbLdVp7DO00tOgXf/EJxOeOo7Q5+37QV47Cvw27PtgoBr7oXcMv/i9ELJLDus+/ayoCOJHncfZvePTrfSK5LgQvobWDAGpp0KW58b3de7OysoafPf+IX2uOfNYOOIprrdNmkLs8JpdmXrG3+F2p0DP//OQ/CHC+Dl39ihxRsroHimz0F65Kj3wb63Yf87QUcSHW7SVjgdktNVaROJUNIWZhOOtn2eRrMxduV6e1TS5r+sItu+ocqDLcmC0rAXcmKgIrUksh/py7/u+/z+tXDPjbYK+l9b4IPLwp+EjsS8C+1x4xPBxhEtbtKWnmsrofHa+1BkhJS0hVnJbHus3Djyr61cb7f5cbv0i78Kp0F1nAzpOI5908wN4Xy2/gqm2Oa0K2+Hljr7XFMV/O0qu/rwyr8eug9arMqfZP9Ac7cZi3XunLa0bPsHUMO+YOMRCQklbWHm7hfqVs1GonKDbdSplaPBKJwaP0lbaz20N9kWGLHg5E9Ba50dBm2shD9fapvivv/PY2uhE3bTT7c7CHS2Bx3J4a1/zO6JPJT2JntMy7YVXlXaRAAlbeFWMNV2U6/eMvKvrVzfU6kT/xVMtdsTxcIb6OG4VY4wrhwdzKTjbG/Cp74FPznSJgfvu8Nuvh7Ppp9uK1S7Q96MtnaXXbn7q0P0/HOHR9Ny7PZwjUraREDNdcMtOcVWBkbao6i52v6Scyt14r/8SXavyYb99uNY5iZtsbTK8r2/spPYO9vh2GtsL7Z4N+10e9zytN2nNKx695NrrLTbgPXXf3i0sRI6O+zvRJEEpkpb2OWX2+11RsKdA6ekLTjupP14mIvjvsnGwkIEV3ounHcLXPC9xEjYALKLoWwhbK4IOpJD670364EhVrt2V9qyI/NyHWiu8jw0kbBT0hZ2BVNGvtzd3XJISVtw3KHEeEja3PlEsZS0JaqZZ8L2l3oWYYRRY6+m05UbBj/HTdpSs+xqbBjdKnqROKOkLewKym2PrM6O4X/NtuftG2zRDO/ikkNzhxLjYWuhhr2QnAaZhUFHIocz513Q1Q6bnwo6kqE19qq0NQ6xa0h7MySlQHJqz/edkjYRJW1kA6HQAAAgAElEQVShl19uu7zX7Rre+S11tlfTtNO0cjRI2ZGVlvFQaavfZ/8I0PdT+JWfaLfkWv9o0JEMrakSUjIhPb9vAtdbR4s9B3qStiYNj4ooaQs7d4Pu4c5ru/sj9i/SJZ/wLiY5vJQ02ydvqDelWBIrjXXFTtSfdxG8dVd49yJtqo40oC45dKUtNcN+3D08qqRNRElb2LlJ23BWkNbsgA2Pwqmfs20PJFhZRfHxRlO3O777m8Wbc79ht1K796PhbLbb3mTnqmWX9F2U0FtHC6REkrZDDY86Drz5d9j+sjexioSMkrawc7faGc5iBHcLm6Ov9C4eGb7Motgf0nEc21crL8bbliSS7BK47mHInQDP/CjoaAbqaLFVtKwSaDw49Dlu0paeZ/tVDvaztPZ+uPdG+P15Qy9qEIkjStrCLiXdrkSsHUbStvNVyCrWqtGwyCyM/cnTLTXQ3hj7veYSTWomHHutrbQ1DDEEGZT2ZjtfLbv4EMOjLT3Do8YM/bO07QV7TM2GJ2/xJl6REAkkaTPGFBljHjfGbIgcByxLM8YsMsa8aIxZbYx5yxjz/iBiDYWC8uFV2na+CpOP14TxsIiH4dHayAIYVdpiz7z3AE74NpF3K20ZBXa7sUHPae5ZiABD/yztWglTT4Hjb4C1D8bHam2RQwiq0nYTsNxxnNnA8sjj/pqADzmOcyTwLuCnxpgCH2MMj4Iph5/T1njQbl0V71v1xJLMIjvpOpa5q5bdYXqJHWUL7ErS7S8GHUlf7U2R1aN5NoHraBvknF6VNrA/S4NV2irXQ+k8WPQBu8p+3cPexS0SAkElbZcAt0c+vh14b/8THMdZ7zjOhsjHu4H9QKlvEYZJ0Qy7evRQ86N2vGSPU072JyY5vMxCaKuP7f1Ha3faoyptsScpybYA2fFK0JH05SZkGXn2cWv9wHP6V9oyCwf+AdRcAy21UDjNJm4FU2HdI56FLRIGQW3kVuY4zh4Ax3H2GGPGHepkY8wJQBqwaYjP3wjcCFBWVkZFRUV0ox1EQ0ODL/cByG6axPFdHRz83eWsWvBlnKSBL9vMjXcxyaTy7KYGnC3+xBU2fr4mwzFxVyVzgOeXP0R7WmwWiadvfoEpJPH0a++AGd1E77C9Lolkemse5ZXrefbJJ/r83gjyNTmxoZra5Fqqu3YxH3jpmcdpyRzf55zjaw/S2JHNmkiMc+taKazZw0u9Ys6p38xiYNXuBiqffppZ2QuZsOkxnl/+CF3JGcQi/ayET9heE8+SNmPME8D4QT518wivMwH4E3Ct4zhdg53jOM6twK0AixcvdpYuXTqyYEehoqICP+5jLYW8gxQ/eQtnJK2EpV8ceMqGb0L5Ys4461yfYgoff1+TYXi7EjbcyimL5sG4eUFHMzpVf4OaiSw98+xRXyJ0r0siKdwL25dxxsJyKJ3b/XSgr8mrkDl5GuNnHQ/vwEmL5sOEo/ue80Yy2RPKGefG2Po4HHypb8xr6mAlLDjl3TBxEZQ78KcHOX2yA3OXEov0sxI+YXtNPBsedRznHMdxFgzy75/Avkgy5iZl+we7hjEmD3gI+IrjOC95FWtMOP3zMP9iePEXA4cTarbDrtdgxpnBxCaDi4ftd2p3auVoLHMTtaE2Zg+Cu9tB+qGGR3u1/AD7s9TeZIdWXdVb7bFwmj1OWWL7v21c7kXUIqEQ1Jy2+4FrIx9fC/yz/wnGmDTgXuAOx3H+4WNs4XXyZ+xqq7eX9Ty3fy3ceTWYJFh0VXCxyUDx0Mm9ch2UzA46Chktt/3PgXXBxtGbu9tBeq59PNjm9u0ttm2Ja7A/gGq22YUWmZGpB6kZMO1U2KSkTeJXUEnb94BzjTEbgHMjjzHGLDbG/C5yzvuA04EPG2PeiPxbFEy4ITF5MZQthBW/t01PqzbD7RfbStu//aZn9wQJh8xI0harDXYbD9o+WqUxOrQrkJYN+VPCk7R1ddoN7VMybcIFh1iI0KvSNtgfQNXb7OKD3madY38vHhx0+rNIzAtkIYLjOAeBAZNkHMdZAXwk8vGfgT/7HFq4GQOLr4OHPger74Hlt0BXB9zwOJSqoW7odL/RxOjw6P419qikLbaVzg1P0tbebI+9K239e7V1dUJnW79K2yA/SzXb+szTA2Duu+FfX4RnfmgTuP1r7M4Qcy9Q2xqJC0GtHpXROup9sPwbsOx6O3/j2geUsIVVWg4kpcbu8Oj2lwCjfWxjXfFM26vNcYJvvN0RmZOWkml/fwG0NfY7pzVyTr85bdBTte7qspW2Oef3/dqCcjjiYnjzb/YfBnDg4S/ArLPhvG/H7qIgEZS0xZ70XLj+MdjwmO14Xjwz6IhkKMbY+TaxWmnbtBzKjuypGEpsyi+Htgb7fRj0a9m70uYmbe1Nfc/pTuwGGx6N/Cw17IXO1p5FCL39262w4HIonArjjrQVuTfvhBW3wR/fA594EXIO2WVKJLS092gsGjcPTvmMErZYkFFgm4DGmh2v2OrMUe8LOhIZK3eua+1hdlXxQ+9KW1KSPfZP2nondq7uhQiRSlv/laO9pWbYatuEoyE5xf6ePOtmuPZBm/Q9+z/R+q8R8Z2SNhEvZRbYTddjzVPftnOBFl8fdCQyVgXl9jic/Yu91p2QZfYc24aqtPWa05aaBcnpPcOj3Unb9OHfu+wIWHg5vPHXvq1DRGKIkjYRL8VqpW3vKph9Xs9kcYld7grLw+1f7Ac3IXOraGnZw6u0GWOrbe7waPVWwNih35E46v124cPGx0cauUgoKGkT8VIsVtpaaqGp0u55K7EvsxBSs8NVaXOraKlZg8xpa+17jiurqG/Slj8ZUtJGdv/pZ0BWcd9elyIxREmbiJdisdJWtcUelbTFB2PsvLYwzWnrrrRlDTI8OkilDWzbj95J22Dz2Q4nOcXuLLPhcQ2RSkxS0ibipcwCW7nqGnTb3HByKzJq1hw/Cspjp9LWPsicNrA/S+6ctoObRpe0Acy7ENobYcvTo/t6kQApaRPxUkYB4AxsIBpmjZGtgHPKgo1Doic/ZEmbW0VLzRqkT5ub2KX3fd4dHm3Yb4fvxx0xuhimn2Z7KK57eHRfLxIgJW0iXnL3RYyleW0NB+wxuyTYOCR68ifb78HWhmDj6OhXaUvL6knkXG6lLbV/pa3QtvzYt9o+Lhtl0paSDrPPhTX3D7y3SMgpaRPxUkYkaYuleW2NB+z8oeTUoCORaHFXWdbtCjaO9n5z2lIHWT3andgNMqetsw22vWAfly0cfRyLb7AJ4G3n9VxPJAYoaRPxktsUNJYqbY371TE+3rj7bga9GKF/pS01c+htrPpX2nLH2+OqZVA8G7KLRx/H9NPgop/bn8s73gu7Xx/9tUR8pKRNxEuZMVhpazgA2aVBRyHR1J20haHSZnrmqw06PDpEpa1ktj1WbYapJ489luOuhX+vsHPlHvgPuzerSMgpaRPxUkYMzmlrVNIWd3IngEmC2p3BxtHRbJMxd+P61Gz7XO/V1YPtPQpQMqfn4wWXRSee7GI46yuw503Y9GR0riniISVtIl6KxUpb4wENj8ab5BTInRh80tbe0rf/mjsE2nteW3szJKfZmHtLz4WJx8Ds82HaadGLaeEVkDMeXvh59K4p4hElbSJeSs2CpNTYqbS1t9j2JKq0xZ/8yeGY09a7/1patj32SdqaBs5nc33kSbj6LrvZfLSkpMNJH4PNFbbiJhJiStpEvGSMrbbFSqWtu0ebKm1xJwxJ24BKW1bk+f5JW9bgXx/NZK23466zvdue+6k31xeJEiVtIl7LiKH9RxvdHm2qtMWdwml20/jO9uBi6GjpV2mLJGdt/YZHh6q0eSWzAE64EVbfA787VxU3CS0lbSJei6VKW3djXVXa4k7xLHA6oXpbcDH0T8gGrbQ1D11p89KZN8M537DVyD9eaPc3FQkZJW0iXoulSlvDPnvM1RZWcad4lj1WbQouho6WYSRth5jT5qXkFDj1s3D9I/bxPTfG1p7BkhCUtIl4LaYqbZE5bRoejT8lswET7NBfe3PfVh5hGR7trXAaXPB92PEyvP2P4OIQGYSSNhGvxVSlba/dxaH/Zt0S+zILYPwC2PB4cI1kO/ovRHBXj/baFaGtsef5oBx1JUxYBMu/qf1JJVSUtIl4LbMAWmpjY6ilYR/kaGg0bh1xCex8hUm7Hgrm/u39Wn64FbUwVdrArlI9/9tQtxMe+jzU7ws2nljQ2aFdJXygpE3Ea5mF4HRBa23QkRxew34lbfHs1P+EmWcxbetfezZv91P/StugfdoCWojQ37RTYcmn4I0/w8+OgrUPBB1ROLXUwl+ugFuK4TsT4W8fgD1vBR1V3FLSJuI1Nwmq3xtsHMNRv1dJWzxLSoIlnyS1oxE2PuH//dub+lXaQrQQYTDnfxs+8TKULYC7P2L3PZUeTVVwxyV2C7Aln4JFH4DtL8KtS2Hl7UFHF5eUtIl4rWCKPdYE3Nj0cBwnUmlTu4+4Nn0pnUkZsOVp/+/dv7muuyih97yxMAyP9jZuHrz/T5CUAo98KehowqN+H9x+MexbDe//i01w3/M/8JnXYOaZ8MBn4OXfBB1l3FHSJuK1/Mn2GHQ3+sNprbfbDOWODzoS8VJyCrX5c2Hbi/7et6sLOlv7VtqSkmy1ra2x55yOkAyP9pY3Ec74L1j/CGx5JuhogtXVCe88BL89y1Yer7oT5r6r5/OZhfa5eRfCv/4LXr0tuFjjkJI2Ea/llNm/0msCbGo6HG67Dw2Pxr363Dmwf42/89o6IvfqXWkDW1VzK20dzT3Phc0JH4XcifDktxJrwn3Dflh9L9z3SfjlEvjeVLjzA7Zdy4cfhFlnD/ya5FS4/A8w+3x46HPwixPg0ZuDmUcZZ1KCDkAk7iUlw+QT4O274ayv2l9oYdQQmXOn4dG415Az1e6OcHADjF/oz03dpC2lX0KWmt0zp81N3tICbvkxmNQMWPpFeOA/4N6PwYwzYNppUFAedGRj194CTZV2qHPPm7D7DajeAo2VPfsRZ+TDlCUw9RS7SGPuBYduDZSSZoeVX/olbH0eXvwF1GyH991h92SWUVHSJuKHkz4Gd30Itr8E008LOprB1e2xx9wJwcYhnmvMnmo/2P+Of0mbm5ANWmlzk7amnufC6JgP2aTm9T/DW3cCBmYsheOuhZln2cTGb11d0Fxl2/W0NkBnmx2Gbq6B+j12cVH9XmhrgK4Ou/dse7PtHdlSa8/rbO11QWN3zyiZA5OOg9J5UH4CTDzW7hoxEinpcOr/s/+e+wk88XXY8BjMOT+a/wcSipI2ET/MPAuSUu2KvbAmbTVb7TE/DioHckjNmRMAAwc3+nfToSptaVk9fdraQzw8CnYO3oU/gQt+aLcDW30fvHYH/OPDYJJgwtGw8Ao4/iPeNKh2HNt65LU7bCWstR6aDtpkbCgpmXZbuvQ8W+VPSrX/z/Mm2h6SGfm2AXhmAZTOtw2Y03OjH/uST8GK38PzP1fSNgZK2kT8kJ4L4+bDvlVBRzK06q12PltayCaBS9Q5Sam2ourn4pghK21ZPZ9zFySEbSFCf8kpUDrXDpee9p+2zcXW52zri0e/DK/8Fs7+qh0+jdZ0g32r4V9fhK3P2q22JiyyCVd2if25zSmzv2eS0+y/zAK7qCg9LxzDkcmpcMw18NS37Ur6eBhWDoCSNhG/lMyBna8EHcXQqrfZNwNJDAXldo6RX4ac05Zl51NB+Cttg0lOsdXz6afBmV+y1fRHvwLLrrefn3chXPhTyBnhfr4tdXa16r5VsHeVTQgzC+DdP4Ljrhv5UGUYLLzcJm2rltkhUxmxGHzVRWJUyRxYdbcdCgpjNatyg+2vJIkhfzLsWunf/YZKyHqvHu0+J4Q/H8M16xyYvtRWxLY9Dy/8Av7wLrjuX4etupmudtjwhJ0vt/ZBu5o2KRWKptuK3pJPQlaRP/8dXiiaAZMWw5p/KmkbJSVtIn4pmg44ULsTSucEHU1fDQfs6tGyBUFHIn7JL4c199uJ7Ek+dH/qbvnRf05bdq85bSFfiDBcySn2D6CZZ9ok7o5L4J4b4YP3DPx/XbUZHv4C7FzB6S11QJcd9lx0FRx9lV0MkJQcyH+GJ+a8C576lv2dM9Lqo6hPm4hv3FWZ9buDjWMweyN7Bfq1klCCV1AOXe09rV685lbRUgab09Z/IUIMV9r6m3ISXPB92PyUbXvR2+p74TdnwM5XYcGlbJ9ymW1M+5/r7YKH8hPiK2EDmH2OPW5aHmwcMUpJm4hf8ibao9taI0w2LreTlycdG3Qk4pd8n7dXG6rSNmjLjzhK2gCOvdbObXvyFti5Ag5ugvs+YVedlsyBjz0HF/6ELTM+aPuf9V+sEU/GHw3ZpbDh8aAjiUkaHhXxi7s9VH3Ikra6PfDm32xbEi+W+ks4uav3ancAJ3p/v6EqbWmR5rqOEz/Do/0ZAxf9DH57JvwusoOASbbz1M64yTaiTRRJSXbIeP0jdkuseKskekxJm4hf0rIhPT98SduqZbY55znfCDoS8VN+76TNB4eqtIFN6uK10ga2NccNT8Cbf4W0HJj7bsifFHRUwZh1jv1DcddrUH580NHEFCVtIn7KKYXGA0FH0de2F+2qrnHzgo5E/JSeY7eQavDp+9FNyAbMaYtsWdXebBckmOTwbvU2VrllWjUJtqpvkmDj40raRkhz2kT8lFVsO5iHyd637Qo1STw5pT17S3rN3Sx8QNLmVtoaobUOMkLSDFa8k1VkW39oXtuIKWkT8VNmETRVBx1FD8exexZqv9HElD3Ovv5+6GiG5PSBLS/cnoXtzbahbHqeP/FIsGafC7tfh3qfvv/ihJI2ET+FrdLWUms3i84pCzoSCULOOB+HR1sGXxXpzl9r61Vpk/g3/yI7RPqXy6B2V9DRxAwlbSJ+yiqyk/4dJ+hILHd+XbT2R5TYku3j8GhH88AtrKAnaeuutOX7E48Ea9x8eN8dcHAz3P/poKOJGUraRPyUVWRX0bmTsoPmDo0paUtMOeOgqQo6O7y/1+Eqbe1NqrQlmvkXwhlfsI12968NOpqYoKRNxE+ZkX0Dm6qCjcPVEKmyZCtpS0jZpYDTs2G7l4aqtKX1Sto0py3xLPogYGDtA0FHEhOUtIn4KSMy9NNaF2wcLjdp05y2xORWWBt8GCIdstIWSeTaVGlLSDmlMPEY2PhE0JHEBCVtIn5ydxxorQ82DlfjftsXK7Mw6EgkCG6F1Y95bR0tQ8xpc/u0NdqfC1XaEs/Uk2H3G9DRFnQkoXfIpM0Y81+9Pr6i3+e+41VQInHLrbS1hKXSts9WW/q3YZDE0F1p82EFaXvz4NtTucOj9XvB6YTMAu9jkXCZvNiuYt/3dtCRhN7hflNf2evjL/X73LuiHItI/OuutIUlaTsQmdckCcl97f3o1dbRMkTSlmOrvZUbIjFpfmXCGX+UPWoxwmEdLmkzQ3w82GMROZywDY827NN8tkSWnmt3KPBjIUJ788DdEMDufpBZAJXr7eMc/RGRcAqmQlJqz/eADOlwSZszxMeDPRaRw3Hn64Sl0tZ4QO0+EpkxkFUCjX6sHh1iIQLYOZXuG7YqbYknOQWKZ0LlxqAjCb3DJW1HG2PqjDH1wFGRj93HC0d7U2NMkTHmcWPMhshxyFnQxpg8Y8wuY8wvRns/kdBIywZMOCptjmNXDSppS2zZPiVt7UO0/ADIKICuSK84DdcnpuJZcHBD0FGE3iGTNsdxkh3HyXMcJ9dxnJTIx+7j1DHc9yZgueM4s4HlkcdDuQV4egz3EgkPY2y1LQxJW3M1dLWrspHoskt7dsbw0uEqbQAYu9WbJJ6S2VC1xZ9GzzEsqCVjlwC3Rz6+HXjvYCcZY44DyoDHfIpLxHsZeeFYPdrdo01JW0LLLvF+P1zHOXSlzU3aCqfaoTJJPMWz7R+RNduCjiTUgvrpKHMcZw+A4zh7jDED3jWMMUnA/wDXAGcf6mLGmBuBGwHKysqoqKiIesD9NTQ0+HIfGb5YeU0WdyTRvGszqwOOtaD6LRYBb2zcTc1B72KJldclkfR+TWZUNTOpfh/PPvWUrQR7IKmzjdNx2LxjD9sH+V6YVdXIZOCgKebtBP5eSeSflbzaeo4F3qq4l6rixUGHA8Dcd/6Xoxq2U8EPgw6lm2dJmzHmCWD8IJ+6eZiX+ATwsOM4O8xhfpE4jnMrcCvA4sWLnaVLl44g0tGpqKjAj/vI8MXMa7JpPDkpacHH+nYlvAmLTj0fSud6dpuYeV0SSJ/XJOUN2HEfS08+HtJzvLlhczU8CzPmHMGMJUsHfn5yB/z5IYrnLkno75WE/lmpnwevf5GjyvPhhKVBR2PtuZWG+vZQvSaeJW2O45wz1OeMMfuMMRMiVbYJwGDtuJcApxljPgHkAGnGmAbHcQ41/00k/NLz/GmxcDjd+45q4ndCc1//xgPeJW3tLfY41Jy2WefAdY9A2RHe3F/CL3ucbftRtyvoSHp0tNCVNJbp+9EX1Jy2+4FrIx9fC/yz/wmO41ztOM4Ux3GmAZ8H7lDCJnEhPTccCxEa9tlfktrCKrG5SZuX89o6mu1xqDltAFOX9OwYIoknKQnyJkBtuJK2zuS0oKPoI6ik7XvAucaYDcC5kccYYxYbY34XUEwi/kjPDcdCBLdHm0fzmCRGZEdWa3q5grQ9krQNtiOCiCtvcggrbeFK2gJZiOA4zkEGWVzgOM4K4CODPP9H4I+eBybih4yQtPxw9x2VxNY9POrhkH1bkz2meTT8KvEhfxLsfDXoKHq0t9CVlBt0FH1ol2gRv6Xn2eGizvZg42jYrx5tYndEAGgcbGpxlLQ32qO7ObzIYPImQd1u6OoKOhIrhJU2JW0ifgvL/qOqtAnYRCo9r2dhihfaIklbqpI2OYS8SdDZFo6FWqCkTUTo2X+0pTa4GDra7Jt0/uTgYpDwyB0P9Xu8u3738Gi2d/eQ2Jc/yR5rdwYbh0urR0Wk+43LrT4EoX434ChpEyt3PNTv8+763cOjStrkEPIiSVtYFiO0t9CVlB50FH0oaRPxm9sLK8ikzf1L1v0lKYktd4I/lTYNj8qhuH9EhqXthyptItK9gq6tIbgY3F+KqrQJRCpte72bAN6mSpsMQ1YxpGRAXQiGRzvbwelUnzaRhBeGpK1qE5gkKJgSXAwSHoXTobPVu2Gp9kbbyDk5XFULCRljIG9iOCptHXYXDy1EEEl0YZjTVrkeCqZCSrjma0hASubYY+U6b67f1qQqmwxP3qRwzGlrV9ImItCr0hZk0rah541axP1e2L/Wm+u3NSppk+EpmAI1O4KOQpU2EYlwFyIE1aetrREOvKPNuaVHdgmULYRXb7PtYKKtvVGLEGR4CqbYRTFefB+OhJI2EQHsRFuTFFylbeer0NUBU08J5v4SPsbAOV+H6i3w+h3Rv76GR2W4CqYADtQGXG3rTtrCNQ9TSZuI34yxQ6RBJW2v/QlSs6H8xGDuL+E062xbbXvrH9G/druSNhkmd3FUzfZg49CcNhHplpYDbQEMj255FlYtgxM/ajeuF3EZA/MvhB0vQ1NVdK/d1qDhURmesCRtGh4VkW5p2cFU2jY+DslpcMZ/+X9vCb+pJwMO7FoZ3eu2NWmzeBme3IlgkpW0DUFJm0gQgkra9q6C0rmQmun/vSX8Jh5r51vueCW6121v6lk1LXIoySl2D9KQJG1qrisikJ4LrQE0192/BsYd6f99JTak50DRTPt9Ek1tWj0qI1AwNQRJWyughQgiApFKm89JW3uLXUpfPNPf+0psGTcPDkS5yW5bo4ZHZfiKZ8KBtd5tqzYc7c0A2jBeRAhmeNTdJD6/3N/7SmwpnQdVm7srDWPW1Wm3yErV6lEZpvKToKUW9r0dXAxq+SEi3dJy/K+0uX2PCpS0ySEUTgenM3pbCWmzeBmp6afbvWof/kJw1TYtRBCRbkH0aXOTtvzJ/t5XYoub1EdrK6HupE3DozJM+ZPgop/Z9jNr7g0mBiVtItItPZK0+flXZM0OuzIwb5J/95TY4yb17nD6WLU32aOGR2Ukjr7Ktv94e1kw929vAZOMk5QSzP2HoKRNJAhp2YDT84bmh9qdkDsBksM1R0NCJm8SYKK3jZC7x266Wn7ICCQlwbz3wOanobPD//t3tNgtB0NGSZtIENz5PX4Okdbu0CIEObyUdMgpi97waEutPWbkR+d6kjimnATtjdFvQTMcHS2QqqRNRADScu3Rz8UINds1n02Gp6A8ipW2OntU0iYjNXmxPUZ7h47hUKVNRLp1V9oGSdocJ/r36+ywqwG1clSGI39y9JI2t9KWrr1uZYTyp9i5kNHuGzgc7S226hwyStpEgjDU8Oj2l+AHM2DN/dG9X90u6Oqw7RxEDie/HGp3RWehjIZHZbSSkqBkNhx4x/97d7RASvi2+1PSJhKEdHd4tF/S9uz/QHMVPHpzdO9XvdUeC6dF97oSn/In24a4TQfHfq2WWsCo0iajUzoXKtf7f98OVdpExOVW2tyVdWA7x2970X5cux0Obore/ZS0yUhkl9pj4/6xX6ulziZsSXq7kVEonA51u6O3Q8dwdbRCqiptIgKDD49Wroe2ejj50/bxrteid7/qrZCUoh5tMjw54+yxIRpJWy1kqMomo1QwBXCi1zdwuNqbVWkTkYi0SM+q3knb3sg+ewuvsAlWNJe5V2+185SSw9UoUkIqO5K0NR4Y+7WaqzWfTUavcKo91mz3974drZrTJiIR3Ulbr+HRA+vAJEPpfCieBfvXRu9+1VuhSIsQZJhyIsOj0ai0NVVCdsnYryOJqWCKPfqetKnSJiKulDS7IXLvStuBd6Bohv1c8Syo3hKdezmOvVbB1OhcT+JfRgEkp0VnTltjJWQpaZNRyhlvjw37/L2v5rSJSB/pOQPntJXOtR/nl9s5HNHo2Va/1w5RjZs/9mtJYjDGLn1HlxcAABi+SURBVEZoiMLwaNNBVdpk9FLSILPI/6RNc9pEpI+0HGiNNNftaLOrRbuTtsm28W5z9djvs/ctexx/1NivJYkju3TslbaOVrsjgpI2GYucMvvHp580p01E+kjP7dnip2oTOJ1QOs8+dncuiMaKqZ0rwCTB+AVjv5YkjpxxY5/T1lhpjxoelbHILYvO/MqR0Jw2EekjsxCaa+zH7qKDkjn26LbmqNs99vtsWg6TFvc09BUZjuxxY1896g5puX3fREYjpwwafKy0dXbYHWQ0p01EumUW9gx/7lsdWTkaqbR1Nzcd45vm5qftZstzLxjbdSTx5JTa77+xbGXlrvhzVwCKjIZb9fViX+bBdEYa+arSJiLdMgt6JW2r7B57qRn2cTSStuYauPMDdvXV8TeMLVZJPNnjbLWhpWb011DSJtGQM95uK+VOJ/Fae4s9pmT4c78RUNImEpTelba9q6Cs15yztCy7UMGdEzQaq++1ixmu/Iuam8rIReMPh5pt9nsvsyA6MUliyimzx3qfVpB2KGkTkf4yC+1k17o9ULdz4EKB7JKxvWHuWmkngE86bmxxSmLKiULSVrne7h0pMha5kaTNr7YfStpEZIDMQnvc+pw9lvVP2sbYcuHAOjtHzpjRX0MS11grbZ3tduVy+QnRi0kSU05ASVuqkjYRcblvim/93bbk6F8Ryy4d/fCo40Dlup6+byIj5X5/jrbB7oo/QHsTTDs1ejFJYsqJ7IXrV9sPzWkTkQHcZrcbH4eJx0JWUd/PZ5eOvsrRsA9aantWo4qMVFYxYEb3PdjVCc/9GKaeAvMujHpokmDS8+3q+qaD/txPw6MiMkDBlJ5fCsd+aODn3UrbaFouHHjHHkvnjD4+SWxJyTZxG03StvsNqN8Di6+31xEZi6Qk+73YNIaFWSPR0WyPIUzaUoIOQCRhGQOX3WYb6B7zwYGfzy61uyQ0V0N28ciufWC9ParSJmMx2mrvwY32qK3TJFqyise2mn4kOiJ92lIzgGZ/7jlMStpEgjT/EENHvVfvjTRpq1xnhxTcCbwio5EzyqStajNgoHBq1EOSBJVdAk1V/tyrPbyVNg2PioRV9+q9UUy+rVxvm/Vq5aiMxWgrbdVbIH9yKDvKS4zKKvJxeNTdEUFJm4gMl7vJ9mgm31Zu6NnHVGS0RruCuWaHdkGQ6Moq8XEhgiptIjJS2ZGkbaRvmq31dhJ4yezoxySJJbvEbh3ktkAYroZ9GpqX6MoqtsOjXZ3e36vPnLZwUdImElZu892R/nVZucEeVWmTscqO9Mca6RBpwz7IHR/9eCRxZZcAjt1T2Wua0yYiI5acChkFStokOKPZFaG1we55q0qbRFNWZDGWH/PaOloBA8lp3t9rhJS0iYRZdsnIh0cPvGMbURZO8yQkSSDdSdsIvgfdrYaUtEk0uUmbH20/OpptlS2EC7kCSdqMMUXGmMeNMRsix8IhzptijHnMGLPWGLPGGDPN30hFAjaahpJ73oRxR0BK+P5KlBiTM4oVzG7SlqukTaIoewwLs0aqozW0K5+DqrTdBCx3HGc2sDzyeDB3AD90HGc+cALg08ZjIiGRNcLeRI4De96AiYu8i0kSx2iGR+v32mOO5rRJFPk5PNreDKmZ3t9nFIJK2i4Bbo98fDvw3v4nGGOOAFIcx3kcwHGcBsdxmvwLUSQEsopGNhxwYJ39S3Ty8d7FJIkjLRtSs0a2abyGR8UL3UlbYlfagtoRocxxnD0AjuPsMcaMG+ScOUCNMeYeYDrwBHCT4zgD1vsaY24EbgQoKyujoqLCs8BdDQ0NvtxHhi8eX5PpB5sob6zkmaee6jO/IqN5L+mtldTmHwGm52+vyTvuYxbw4oFMWkPy/yIeX5dYN5LX5ISUAho2vc6aYZ4/ffOrlJsUnnnlrVDOCQoz/awc2qnJmexd9yYbuyo8vc+Re3aQ1drFqxUVoXtNPEvajDFPAIPVx28e5iVSgNOAY4DtwN+BDwO39T/RcZxbgVsBFi9e7CxdunTkAY9QRUUFftxHhi8uX5O0VbD9bpYuORYy8u1zVVvgV1dBexOUzodTPwsLLoOOFnj7P2HiMSx51/uCjbuXuHxdYtyIXpOdR5LVsJdxwz2/+u9QM56lZ5452vASln5WDuPNMiYXZTLZ6/9Hu/4PUotYunRp6F4Tz5I2x3HOGepzxph9xpgJkSrbBAafq7YTeN1xnM2Rr7kPOIlBkjaRuNV7xZSbtD33E+jqgLO+AqvugXs/Cvd/GjrbAQeu/Ftg4UocKpoB21+y8yWHUzlr2As5gw2eiIzRaBZmjUZHS2jntAU1PHo/cC3wvcjxn4Oc8ypQaIwpdRznAHAWsMK/EEVCoHvFVBUUz4S2JpuoLXwfnP4FOO3zsOEx2PqcnYMx7TSYcUawMUt8KZoBbfVQuxMKyg9/fsN+bWEl3sgqsX8UeK29BdKyvL/PKAS1EOF7wLnGmA3AuZHHGGMWG2N+BxCZu/Z5YLkx5m3AAL8NKF6RYHRX2iLF6HcetG+gi66yj42BOefDebfYypsSNom2OefZ4+t/Ht759Xu1CEG8kVUMjX4sRGiBFFXaujmOcxA4e5DnVwAf6fX4ceAoH0MTCZf8SGWjdqc9vv4nW8WYcnJwMUliKZoB8y6EF/4Xjv0Q5E8a+tzOdjt8paRNvJAdGR4d7lD9aHW0hHb1qHZEEAmz7BLbmbt2h92easszcOy1kKQfXfHR+d8GpxMqvnvo8xoiFWE11hUvZJXYhKrd4+5fIZ7Tpt/8ImFmDORPhpod8MpvISnFVjtE/FQ4DY6+Et5eBi21Q5/X3aNNjXXFA35tZdWuSpuIjFZ+Oay5D1b8Ho66UivzJBjHXmv3ZHzrrqHPqd9jj6q0iRf82sqqozW0c9qUtImE3YJL7TE9F87572BjkcQ18Ri7p+3q+4Y+p263PeZN9icmSSx+7YrQ0RzaSltQLT9EZLgWXW23Epp+Rs8G3iJ+c1cqv/C/0FIHGXkDz6nbbYfws/V9Kh7wI2nr6oLONjuXOIRUaRMJu6RkWHi5EjYJ3qxzbWPnzRWDf75uN+RO1EIZ8YY7PNowWD/+KOloscdUJW0iIhLLyk+A9HzY+MTgn6/bBXkT/Y1JEkdGvv3+q93h3T3cpE2VNhERiWnJqTDlJLut1WDqdkPeBH9jksRSMAVqtnt3fSVtIiISN8qPh8p10Fzd93nHiSRth2i+KzJWStpERESGafIJ9rhzZd/nW2rsqjsNj4qXiqZD1WZoa/Tm+u2a0yYiIvFi0nFgkmDnK32f7273oaRNPDT33bYadqjWM2OhSpuIiMSN9BwYdyTseLnv8zWRyeHq0SZemnoyjF8Iz/zQtueItvZme0zNiv61o0BJm4iIjEz5CXZ4tKuz57mqTfZYNCOYmCQxGANLPgXVW2D369G/vruvqZI2ERGJC+UnQFs97F/b89zBTbYlQ1ZRcHFJYphzvh2i3/Bo9K/dnbRpGysREYkH5e5ihF7z2qo22SqbMcHEJIkjsxBK58POFdG/dvfwqJI2ERGJB4XT7VZV23vNa9u3xu5NKuKHycfBrpW21Uw0uZW2tOzoXjdKlLSJiMjIGAPlJ/YsRqj//+3da4xc5X3H8e9/d+2117u28W29vrTmYmE7hFuccA2xC0hpiwqpFKmt2qI0Fa3S0KSKVJHmRd+iJqqaqlElRNPSNsJKaSg0oU2Ji+UqpFGDgWBwCJeAsVnfMLZ3vb6s8dMXZ+wYPMa7M2fmnDP7/bx5ds48c+YvP/L65+c55zy74fCe7AJxqR0GP5g9ZmZ0d77nPe7yqCSp0yy/JrsYfHQPvLklO7b48mJr0tSxYGXW7vtpvuf17lFJUsdZcWPWvrwRXnkCemZmz3CT2mHhpVm798V8zzs+Bl092ZZtJdRTdAGSpAoauhIGlsCWf8xm3C78aGmfIq8ONDCU/Ufh7dfyPe/4GEwr5/Vs4EybJKkRXV1w7R/C9idhZBiu/UzRFWkqiYC5y/Pfh3R8rLTXs4EzbZKkRl33WegdgP5BuHh90dVoqmnF5vHjRwxtkqQO1NUNa3+v6Co0Vc1ZDju35HvO8SOlvQkBXB6VJElVNGcpHNkP40fzO+fxwzDd0CZJkpSf/sGsPbwnv3OWfHnU0CZJkqrnVGgbzTO0jbk8KkmSlKtZC7M2z10RnGmTJEnKWctm2nxOmyRJUn5Oz7TlHdqcaZMkScpPz3SYeYHLo5IkSaXXP5jf3aMnT8KJo96IIEmSlLv+Rfktj46PZa3PaZMkScrZrEX5LY+OH8laZ9okSZJy1j8Io3vzOdepmTavaZMkScrZrAUwfjjbfqpZp0ObM22SJEn5mrUga8f2N38uZ9okSZJapG9+1o7ta/5cx0aztneg+XO1iKFNkiRV0+nQ9lbz5zo2krWGNkmSpJydDm05LI8a2iRJklqkJTNts5s/V4sY2iRJUjXNmAPRlVNoO5S1zrRJkiTlrKs72380r5m27unQ09v8uVrE0CZJkqqrb0F+oa3Es2xgaJMkSVXWNz+/GxEMbZIkSS3SN8+ZNkmSpNLrm59PaDt6AGbMbf48LWRokyRJ1XUqtKXU3HnG9mc3NZSYoU2SJFVX33w4eQKOHmzuPEf2Z0utJWZokyRJ1ZXHA3ZTgiNvw0xDmyRJUmvksZXVsUPZbJ0zbZIkSS2Sx0zbqcDnTNvZImJeRDweES/V2rpX/kXEX0TE8xGxLSL+OiKi3bVKkqQSOzU71kxoO3IqtHkjQj33ABtTSiuBjbXX7xIR1wM3AJcDlwEfBj7WziIlSVLJzVqQtc2EtpHdWTsw2Hw9LVRUaLsdeKD28wPAHXX6JGAGMB3oBaYBu9tSnSRJqobp/dmeoc2EtkM7s3b20nxqapFIzT7XpJEvjTiQUpp7xuu3U0pnzUlGxFeA3wcC+JuU0pfOcb67gLsABgcHP7Rhw4bWFH6G0dFR+vv7W/49mjjHpJwcl/JxTMrJcWncdU9+iv3zrubFVXc39PkLX/0nlr/xMJtv+heI7tPH2zEm69evfyqltHYifXtaVUREfA9YXOetusGrzucvAVYDy2qHHo+Im1JKm9/bN6V0H3AfwNq1a9O6desaqnkyNm3aRDu+RxPnmJST41I+jkk5OS5N2LaEoTm9DDX657f/QTi4lHXrb37X4bKNSctCW0rplnO9FxG7I2IopTQcEUPAnjrdPgH8b0pptPaZ/wCuBc4KbZIkaQprdv/RA9thTrmXRqG4a9oeBe6s/Xwn8EidPtuBj0VET0RMI7sJYVub6pMkSVXRNx/G9jX22ZMnYfdWGPxAvjW1QFGh7V7g1oh4Cbi19pqIWBsR99f6PAS8AjwHPAs8m1L69yKKlSRJJdbMpvH7X80erjt0Rb41tUDLlkffT0rpLeDmOsd/RHbjASmld4A/aHNpkiSpavrmw5ED8M4J6J5ktNn8ZeiaBis+2pracuSOCJIkqdr65gMJjh6Y3OeGn4Ufb4AbPw/zLmxJaXkytEmSpGprdCurnU9l7dW/m289LWJokyRJ1dZoaNv7U5g2C2YvO3/fEjC0SZKkams0tO17ERashK5qxKFqVClJknQujYa2gzvgghW5l9MqhjZJklRtffOydrKhbWQXDNTbvKmcDG2SJKnaps2E3jlw6M2Jf+b44ez5bIY2SZKkNhr8AAz/eOL9R3Zl7cBQa+ppAUObJEmqvqErYNdzMH50Yv1PhzZn2iRJktpn9W1w4gh8/6sT6z8ynLXOtEmSJLXRihth1W3wg6/BsdHz93emTZIkqSDX3w3HDsIL/3b+viPDMK0Peme3vq6cGNokSVJnWH5N9ty1Fx49f99Tj/uIaHlZeTG0SZKkzhABl9wKr/0PnDj2/n1HdkF/dZZGwdAmSZI6ySW3wPgYbP/B+/cbGa7U9WxgaJMkSZ1kxY3QPR1e3njuPinVlkerc+coGNokSVIn6e2HxZfDzi3n7nNsBMYPO9MmSZJUqCVXwfAzcPJk/fdHd2etM22SJEkFWnIVHB+Ft16u//7pB+s60yZJklScJVdm7fAz9d+v4L6jYGiTJEmdZsGl0DMT3ny6/vunZ9oG21dTDgxtkiSps3T3wKLVsOeF+u+P7ILpA9A70N66mmRokyRJnWfRatizrf57I8OVm2UDQ5skSepEC1dld4mO7T/7vQruhgCGNkmS1IkWrcnavT85+72DO2Du8vbWkwNDmyRJ6jyLVmXte5dI3xmHQzth7i+0v6YmGdokSVLnmb0UemefPdN2cAekk4Y2SZKkUoiAhZeePdN2YHvWGtokSZJKYuEqQ5skSVLpLVoDY/vg8L6fHzvwOkRXtnxaMYY2SZLUmerdjHBgO8xeBt3TiqmpCYY2SZLUmRauztozQ9vbr1dyaRQMbZIkqVMNLIYZc2BvLbSlBPtehPkXFVtXgwxtkiSpM0Vk17XtqT32Y2QYjrwNgx8stq4GGdokSVLnWrgqm2lLCXZtzY4Nrim2pgYZ2iRJUudatDqbXRvZBdufhK4eGLqy6KoaYmiTJEmda/lHsvZnm+GVJ2Dph6C3v9iaGmRokyRJnWvxFTBrIXznCzD8DKy5o+iKGmZokyRJnaurC9Z9EY6PwAUr4MrfKrqihvUUXYAkSVJLffjTcNG67BEg02cVXU3DDG2SJKnzzb+46Aqa5vKoJElSBRjaJEmSKsDQJkmSVAGGNkmSpAowtEmSJFWAoU2SJKkCDG2SJEkVYGiTJEmqAEObJElSBRjaJEmSKsDQJkmSVAGFhLaI+GREPB8RJyNi7fv0+3hEvBgRL0fEPe2sUZIkqUyKmmnbCvw6sPlcHSKiG/ga8MvAGuA3I2JNe8qTJEkql54ivjSltA0gIt6v20eAl1NKr9b6bgBuB15oeYGSJEklU0hom6ClwBtnvN4BXFOvY0TcBdwFMDg4yKZNm1pe3OjoaFu+RxPnmJST41I+jkk5OS7lU7YxaVloi4jvAYvrvPWllNIjEzlFnWOpXseU0n3AfbXv3bt+/frXJ1xo4xYA+9rwPZo4x6ScHJfycUzKyXEpn3aMyS9OtGPLQltK6ZYmT7EDWH7G62XAmxP43oVNfu+ERMSPUkrnvIlC7eeYlJPjUj6OSTk5LuVTtjEp8yM//g9YGREXRsR04DeARwuuSZIkqRBFPfLjExGxA7gO+E5EfLd2fElEPAaQUjoBfBb4LrAN+GZK6fki6pUkSSpaUXePPgw8XOf4m8CvnPH6MeCxNpY2GfcVXYDO4piUk+NSPo5JOTku5VOqMYmU6l7bL0mSpBIp8zVtkiRJqjG0SZIkVYChbZLcD7V8ImJ5RDwREdtqe9p+ruialImI7oh4OiK+XXQtykTE3Ih4KCJ+Uvs7c13RNU11EfEntd9dWyPiwYiYUXRNU1FEfD0i9kTE1jOOzYuIxyPipVp7QZE1Gtomwf1QS+sE8IWU0mrgWuCPHJfS+BzZ3d8qj68C/5lSWgVcgeNTqIhYCvwxsDaldBnQTfaIK7XfPwAff8+xe4CNKaWVwMba68IY2ibn9H6oKaXjwKn9UFWglNJwSmlL7ecRsn+ElhZblSJiGfCrwP1F16JMRMwGbgL+DiCldDyldKDYqkT2JIeZEdED9DGBB8krfymlzcD+9xy+HXig9vMDwB1tLeo9DG2TU28/VMNBiUTECuAq4IfFViLgr4A/BU4WXYhOuwjYC/x9bdn6/oiYVXRRU1lKaSfwFWA7MAwcTCn9V7FV6QyDKaVhyCYIgEVFFmNom5wJ74eq9ouIfuBfgc+nlA4VXc9UFhG3AXtSSk8VXYvepQe4GvjblNJVwGEKXu6Z6mrXSN0OXAgsAWZFxG8XW5XKytA2OQ3th6rWi4hpZIHtGymlbxVdj7gB+LWIeI3sMoJfioh/LrYkkf0O25FSOjUT/RBZiFNxbgF+llLam1IaB74FXF9wTfq53RExBFBr9xRZjKFtctwPtYQiIsiu0dmWUvrLousRpJS+mFJallJaQfb35L9TSs4eFCyltAt4IyIurR26GXihwJKULYteGxF9td9lN+PNIWXyKHBn7ec7gUcKrKWYbayqKqV0IiJO7YfaDXzd/VBL4Qbgd4DnIuKZ2rE/q22DJund7ga+UfuP56vApwquZ0pLKf0wIh4CtpDdCf80Jds6aaqIiAeBdcCC2v7ofw7cC3wzIj5NFrA/WVyFbmMlSZJUCS6PSpIkVYChTZIkqQIMbZIkSRVgaJMkSaoAQ5skSVIFGNok6TwiYm5EfKboOiRNbYY2STq/uYChTVKhDG2SdH73AhdHxDMR8eWii5E0NflwXUk6j4hYAXw7pXRZwaVImsKcaZMkSaoAQ5skSVIFGNok6fxGgIGii5A0tRnaJOk8UkpvAd+PiK3eiCCpKN6IIEmSVAHOtEmSJFWAoU2SJKkCDG2SJEkVYGiTJEmqAEObJElSBRjaJEmSKsDQJkmSVAH/D2V9WFbV30KLAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = -cos(yy0[0])+yy0[1]**2/2\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = -cos(sol[:,0])+sol[:,1]**2/2\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid(); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul analytique avec le module `sympy`\n", "--- \n", "https://docs.sympy.org/latest/modules/solvers/ode.html" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’une équation différentielle d'ordre 1\n", "\n", "Considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "u'(x)=-3x^2u(x)+6x^2,\\\\\n", "u(0)=4.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{d}{d x} u{\\left (x \\right )} = - 3 x^{2} u{\\left (x \\right )} + 6 x^{2}$$" ], "text/plain": [ "d 2 2\n", "──(u(x)) = - 3⋅x ⋅u(x) + 6⋅x \n", "dx " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.Symbol('x')\n", "u = sym.Function('u')\n", "phi = 6*x**2-3*x**2*u(x)\n", "edo = sym.Eq( sym.diff(u(x),x) , phi )\n", "edo" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$u{\\left (x \\right )} = C_{1} e^{- x^{3}} + 2$$" ], "text/plain": [ " 3 \n", " -x \n", "u(x) = C₁⋅ℯ + 2" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solgen = sym.dsolve(edo,u(x))\n", "solgen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prise en compte des conditions initiales:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left \\{ C_{1} : 2\\right \\}$$" ], "text/plain": [ "{C₁: 2}" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0=0\n", "u0=4\n", "consts = sym.solve( sym.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n", "consts" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$u{\\left (x \\right )} = 2 + 2 e^{- x^{3}}$$" ], "text/plain": [ " 3\n", " -x \n", "u(x) = 2 + 2⋅ℯ " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solpar=solgen.subs(consts)\n", "solpar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On transforme le résultat en une fonction:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "func = sym.lambdify(x,solpar.rhs,'numpy')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import *\n", "figure(figsize=(10,7))\n", "xx=linspace(0,3,101)\n", "yy=func(xx)\n", "plot(xx,yy)\n", "xlabel('x')\n", "ylabel('u')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’un système d'équations différentielles d'ordre 1\n", "\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(t, y_1(t),y_2(t))\\\\\n", " \\varphi_2(t, y_1(t),y_2(t))\n", " \\end{pmatrix}\n", " =\n", " \\begin{pmatrix}\n", " y_1(t)-y_2(t)\\\\\n", " y_2(t)-y_1(t)\n", " \\end{pmatrix}.\n", "$$\n", "avec $t\\in[0;10]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{d}{d t} \\operatorname{y_{1}}{\\left (t \\right )} = \\operatorname{y_{1}}{\\left (t \\right )} - \\operatorname{y_{2}}{\\left (t \\right )}$$" ], "text/plain": [ "d \n", "──(y₁(t)) = y₁(t) - y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{d}{d t} \\operatorname{y_{2}}{\\left (t \\right )} = - \\operatorname{y_{1}}{\\left (t \\right )} + \\operatorname{y_{2}}{\\left (t \\right )}$$" ], "text/plain": [ "d \n", "──(y₂(t)) = -y₁(t) + y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\left [ \\operatorname{y_{1}}{\\left (t \\right )} = - C_{1} + C_{2} e^{2 t}, \\quad \\operatorname{y_{2}}{\\left (t \\right )} = - C_{1} - C_{2} e^{2 t}\\right ]$$" ], "text/plain": [ "⎡ 2⋅t 2⋅t⎤\n", "⎣y₁(t) = -C₁ + C₂⋅ℯ , y₂(t) = -C₁ - C₂⋅ℯ ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "\n", "y1 = sym.Function('y1')\n", "y2 = sym.Function('y2')\n", "\n", "phi1 = y1(t)-y2(t)\n", "phi2 = y2(t)-y1(t)\n", "\n", "edo1 = sym.Eq( sym.diff(y1(t),t) , phi1 )\n", "edo2 = sym.Eq( sym.diff(y2(t),t) , phi2 )\n", "display(edo1)\n", "display(edo2)\n", "\n", "solgen = sym.dsolve([edo1,edo2],[y1(t),y2(t)])\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left \\{ C_{1} : - \\frac{3}{2}, \\quad C_{2} : \\frac{1}{2}\\right \\}$$" ], "text/plain": [ "{C₁: -3/2, C₂: 1/2}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\operatorname{y_{1}}{\\left (t \\right )} = \\frac{e^{2 t}}{2} + \\frac{3}{2}$$" ], "text/plain": [ " 2⋅t \n", " ℯ 3\n", "y₁(t) = ──── + ─\n", " 2 2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\operatorname{y_{2}}{\\left (t \\right )} = - \\frac{e^{2 t}}{2} + \\frac{3}{2}$$" ], "text/plain": [ " 2⋅t \n", " ℯ 3\n", "y₂(t) = - ──── + ─\n", " 2 2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABDAAAAGvCAYAAACtnCUnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3Xl4VdW9//HPOudkTiCEDAwhMgXRADJERMGhigNqBYdacCi2KmDl2jq0atv7u7Wt1dte6wyoxTrUCWdUHMA6FaoSBpnnMYwhjEnIdM76/bFP4ABBAiTZZ3i/nmc/e++1z/DNvX3M4pu1P9tYawUAAAAAABDOPG4XAAAAAAAAcCQ0MAAAAAAAQNijgQEAAAAAAMIeDQwAAAAAABD2aGAAAAAAAICwRwMDAAAAAACEPRoYAAAAAAAg7NHAAAAAAAAAYY8GBgAAAAAACHs+twtoLpmZmbZjx45ulwEAQFiZNWvWNmttltt1xALmIgAA1K+h85GYaWB07NhRRUVFbpcBAEBYMcasdbuGWMFcBACA+jV0PsItJAAAAAAAIOzRwAAAAAAAAGGPBgYAAAAAAAh7MZOBUZ+amhoVFxersrLS7VKOWmJionJzcxUXF+d2KQAAAAAANLmYbmAUFxcrLS1NHTt2lDHG7XIazFqr0tJSFRcXq1OnTm6XAwAAAABAk4vpW0gqKyvVunXriGpeSJIxRq1bt47IlSMAAAAAAByLmG5gSIq45kWdSK0bAAAAAIBjEfMNDAAAAAAAEP5oYAAAAAAAgLBHAwMAAAAAAIQ9Ghgumz9/vgYOHLjvfPbs2Tr33HNdrAgAAAAAgPAT049RDXXfewu1aOPuRv3Mk9u10P/8sOB7X1NQUKCVK1fK7/fL6/Xqzjvv1EMPPdSodQAAAAAAEOloYLjM4/GooKBACxcu1PLly5WXl6e+fftq1apVuv/++7Vr1y698cYbbpcJAAAAAICraGAEHWmlRFMaMGCApk+frnHjxumjjz6SJHXu3FkTJ07UVVdd5VpdAAAAAACECzIwwsCAAQP0u9/9Tpdffrnat2/vdjkAgDBUVlXb6Lc64vgZYy4yxiw1xqwwxtzTnN+9a2+NlmzmfxMAgNjhegPDGNPBGPOZMWaxMWahMeYXwfEMY8xUY8zy4L5VcNwYYx4LThTmGWP6uvsTHL/u3bsrISFBd999t9ulAADC1Nuzi3XxY19p6eY9bpeCIGOMV9KTkoZIOlnSCGPMyc31/X94b5GuGDdDnyzc3FxfCQCAq1xvYEiqlXSntfYkSQMk3Rr85X+PpE+ttfmSPg2eS84kIT+4jZI0vvlLblyPPvqoHnjgAaWkpOwbKy0t1ZgxYzRnzhw98MADLlYHAHCbtVb//HqderZvqW45qW6Xg/36S1phrV1lra2W9Kqkoc315XdfdKLys1M1+p+zNO7zFbLWNtdXAwDgCtcbGNbaTdba2cHjPZIWS2ovZwLwfPBlz0saFjweKukF6/haUroxpm0zl90oVq5cqe7du2vv3r0aOXLkAddat26tCRMmaOXKlbr33ntdqhAAEA5mrtmhpVv26LoBeTLGuF0O9msvaX3IeXFwbB9jzChjTJExpqikpKRRvzy7RaJeG326ftirnf7y0VLdOek7Vdb4G/U7AAAIJ2EV4mmM6Sipj6RvJOVYazdJTpPDGJMdfNnhJgub6vm8UXJWaSgvL6/J6j5WXbp00ZIlS9wuAwAQ5v759VqlJfp02SnkJIWZ+rpJByyDsNY+LelpSSosLGz0JRKJcV49Ory38rNT9dDUZVpTWq6nri9UVlpCY38VAACuc30FRh1jTKqkNyX90lr7fYlUR5ws7Bu09mlrbaG1tjArK6sxygQAoFmV7KnShws26ap+uUqK97pdDg5ULKlDyHmupI3NXYQxRv91Xr7GX9tXizbt1tAn/k3gKwAgKoVFA8MYEyenefGStfat4PCWultDgvutwfGwmCwAANAcJhWtV43f6trTTnC7FBxqpqR8Y0wnY0y8pOGSJrtVzJCebfXGmDMUsNJVE2boY8I9AQBRxvUGhnFu5p0oabG19m8hlyZLqguGGCnp3ZDxnwSfRjJA0q66W00AAIgm/oDVy9+s0xldWqtrNuGd4cZaWytprKSP5WR4TbLWLnSzph7tW2ry2IHKz07VGMI9AQBRxvUGhqSBkq6XdK4xZm5wu1jSg5LON8Ysl3R+8FySpkhaJWmFpGck/dyFmgEAaHKfL92qDTv36roBrL4IV9baKdbabtbaLtba+92uR9of7nlpMNzzDsI9AQBRwvUQT2vtv1V/roUknVfP662kW5u0KAAAwsCLX69VdlqCzj85x+1SEGES47x6LBju+bepy7SWcE8AQBQIhxUYAADgIOtKK/TFshIN75+nOC+/rnH0jDG67bx8jQuGew57cjrhngCAiMaMCACAMPTSN2vlMUYj+nc48ouB73Fxz7Z6ffQZ8gcs4Z4AgIhGAwMAgDBTXlWrV75dp4sK2qhtyyS3y0EU6JlLuCcAIPLRwHDZ/PnzNXDgwH3ns2fP1rnnnutiRQAAt701u1i7K2v1s0Ed3S4FUaQu3POHwXDPOyd9p6pawj0BAJHD9RDPsPHhPdLm+Y37mW16SkMe/N6XFBQUaOXKlfL7/fJ6vbrzzjv10EMPNW4dAICIEQhY/WP6Gp2S21J981q5XQ6iTGKcV48O762uwXDPNYR7AgAiCCswXObxeFRQUKCFCxfqzTffVF5envr27at33nlHN998s4YOHapPPvnE7TIBAM3ki2UlWrWtXD8b1EnGHO4hXcCxI9wTABCpWIFR5wgrJZrSgAEDNH36dI0bN04fffSRJGnYsGEaNmyYduzYobvuuksXXHCBa/UBAJrPs9NXK6dFgob0aOt2KYhyF/dsq7yMZN30fJGumjBDj/y4ty4oaON2WQAAHBYrMMLAgAED9Lvf/U6XX3652rdvf8C1P/3pT7r11ltdqgwA0JyWbdmjr5Zv009O76h4H7+i0fR6tA+Ge+akaTThngCAMMfsKAx0795dCQkJuvvuu/eNWWt19913a8iQIerbt6+L1QEAmss/pq9Wgs+jEf3z3C4FMSS7RaJeGzVAl4aEe1bWEO4JAAg/3EISBh599FE98MADSklJ2Tf2+OOPa9q0adq1a5dWrFihMWPGuFghAKCpbS+v1luzN+iKvu2VkRLvdjmIMYlxXj02vLfyCfcEAIQxVmC4aOXKlerevbv27t2rkSNHHnDttttu06xZszRhwgSaFwAQA175dp2qagP62cBObpeCGFVfuOfiTYR7AgDCBw0MF3Xp0kVLlizRxIkT3S4FAOCiyhq//jF9jc7Mz1R+Tprb5SDGXdyzrV4ffYb8Aasrx8/Q1EVb3C4JAABJNDAAAHDdW7M3aFtZlcac3cXtUgBJUs/clnp37EDlZ6dq1ItFGv/5SsI9AQCuo4EBAICL/AGrp79cqZ7tW+qMLq3dLgfYJ6dFol4bfbou7dVO//vREt056TtV1RLuCQBwT8w3MCL1rwmRWjcA4ECfLNysNaUVGnN2Fxlj3C4HOEBduOcd53fTW3M26JpnvtG2siq3ywIAxKiYbmAkJiaqtLQ04poB1lqVlpYqMTHR7VIAAMfBWqsJX6xUx9bJuqhHG7fLAeoVGu65cOMuDX2CcE8AgDti+jGqubm5Ki4uVklJidulHLXExETl5ua6XQYA4Dj8Z1Wpvivepfsv7yGvh9UXCG8X92yrDq2SdfMLRbpy/Aw9OryPzj85x+2yAAAxJKYbGHFxcerUicfVAQDcMeGLVcpMTdCVfWlIIzLUhXuOeqFIo14s0q8v7K4xZ3fm9icAQLOI6VtIAABwy8KNu/TlshL9dGBHJcZ53S4HaLC6cM9LerZ1wj1f/06VNYR7AgCaXkyvwAAAwC1PfbFKqQk+XTfgBLdLAY5aYpxXj4/oo245afrb1GVaW1qhp67vp8zUBLdLAwBEMVZgAADQzFaVlOn9eRt17Wl5apkU53Y5wDEh3BMA0NxoYAAA0Mye/Gyl4n0e3XRmZ7dLAY7bxT3b6vXRZ8gfsLpy/Ax9snCz2yUBAKIUDQwAAJrR2tJyvTN3g6477QRlpbHcHtGhLtwzPztVo/85S+M/Xxlxj6kHAIQ/GhgAADSjJz9bIZ/HaNTZrL5AdDkk3HPSd6qqJdwTANB4CPEEAKCZrN9eobdmb9D1p5+g7LREt8sBGl1duGd+dpoenrZMa0rL9dT1haw2AgA0ClZgAADQTMZ9vkIej9GYs7u4XQrQZIwx+sXgfD15TV8t2rRbw54k3BMA0DhoYAAA0AyKd1TojVnFGn5qB+W0YPUFot8lvZxwz9pAQFeOn6Gpi7a4XRIAIMLRwAAAoBmM/3yljIxuOYfVF4gdPXNbavLYQcrPTtWoF4sI9wQAHBcaGAAANLHiHRV6vahYPyrMVduWSW6XAzSrQ8I9XyfcEwBwbAjxBACgiT06bblkpLHndnW7FMAVB4d7ri2t0FPX91NmKuGeAICGYwUGAABNaMXWMr05u1g/GXACqy8Q00LDPRdu3KWhTxDuCQA4OjQwAABoQg9PXaakOC/ZF0BQXbinP2AJ9wQAHBUaGAAANJEFG3bpg/mbdOOgTmrNUnlgn565LfXu2IGEewIAjgoNDAAAmsj/fbJULZPidNNZnd0uBcfAGPNXY8wSY8w8Y8zbxpj04HhHY8xeY8zc4DbB7VojEeGeAICjFRYNDGPMs8aYrcaYBSFjvzfGbAiZHFwccu1eY8wKY8xSY8yF7lQNAMDhfbt6uz5fWqJbzumiFolxbpeDYzNVUg9rbS9JyyTdG3JtpbW2d3Ab4055ka8u3PP2wd301uwNuvaZb7StrMrtsgAAYSosGhiSnpN0UT3jD4dMDqZIkjHmZEnDJRUE3zPOGONttkoBADgCa63++vESZaUlaOTpHd0uB8fIWvuJtbY2ePq1pFw364lWoeGeCwj3BAB8j7BoYFhrv5S0vYEvHyrpVWttlbV2taQVkvo3WXEAABylfy3Zqplrdui2c7sqKZ4ee5T4maQPQ847GWPmGGO+MMacebg3GWNGGWOKjDFFJSUlTV9lBLukV1tNGn26agMBXUW4JwCgHmHRwPgeY4P3nT5rjGkVHGsvaX3Ia4qDY4dg0gAAaG61/oD+PGWxOmemaHj/PLfLwREYY6YZYxbUsw0Nec1vJdVKeik4tElSnrW2j6Q7JL1sjGlR3+dba5+21hZaawuzsrKa+seJeL1y0/XurYPUJRjuOeELwj0BAPuFcwNjvKQuknrLmSg8FBw39by23t9sTBoAAM3t1ZnrtbKkXPcM6a44bzj/moUkWWsHW2t71LO9K0nGmJGSLpV0rQ3+Szq4CrQ0eDxL0kpJ3dz6GaJNm5aJem2UE+754IeEewIA9vO5XcDhWGv3rRs0xjwj6f3gabGkDiEvzZW0sRlLAwCgXnsqa/Tw1GXq3ylD55+c43Y5OE7GmIsk3S3pbGttRch4lqTt1lq/MaazpHxJq1wqMyolxTvhnvnZaXp42jKtLa3QU9f3UyaPIwaAmBa2fxoyxrQNOb1cUt0TSiZLGm6MSTDGdJIzafi2uesDAOBgE75YqdLyav3ukpNkTH0LBhFhnpCUJmnqQY9LPUvSPGPMd5LekDTGWtvQLC80UGi450LCPQEACpMVGMaYVySdIynTGFMs6X8knWOM6S3n9pA1kkZLkrV2oTFmkqRFcu5HvdVay7pCAICrNu7cq79/tVrDerdTr9x0t8tBI7DWdj3M+JuS3mzmcmLWJb3aKi8jWTe9MFNXjp+hR4f3YYUTAMSosFiBYa0dYa1ta62Ns9bmWmsnWmuvt9b2tNb2stZeZq3dFPL6+621Xay1J1prP/y+zwYAoDn838dLZSXddeGJbpcCRJ2euS01eewgdSXcEwBiWlg0MAAAiGTzi3fprTkbdOOgTsptlex2OUBUymnhhHteTLgnAMSssLiFBACASBUIWP2/yQuUmRqvW87p4nY5QFRLivfqiRF9lJ+dqkemLSfcEwBiDCswAAA4Dm/N2aA563bq7ou6q0VinNvlAFHPGKNfDu5GuCcAxCAaGAAAHKPdlTV68MMl6pOXriv75rpdDhBTLunVVpNGn67aQEBXjZ+haYu2uF0SAKCJ0cAAAOAYPTZtuUrLq/SHy3rI4+GxqUBz65WbrndvHaQu2am6mXBPAIh6NDAAADgGy7fs0XMz1mj4qR3UM7el2+UAMatNywPDPe96fR7hngAQpQjxBADgKFlr9fv3Fio53qu7LuCxqYDbDg33LNcEwj0BIOqwAgMAgKP04YLNmr6iVHdecKJa8w8kICyEhnsuINwTAKISDQwAAI7C7soa/X7yQp3ctoWuPS3P7XIAHCQ03PPK8TM0lXBPAIgaNDAAADgK//fxUm0rq9IDV/SUz8uvUSAc9cpN1+Sxg9Q1O1WjCPcEgKjBzAsAgAaavW6HXvx6rX5yeked0iHd7XIAfI+cFoR7AkC0IcQTAIAGqPEH9Ju35isnLVF3XtDN7XIANADhngAQXViBAQBAA0z892ot2bxH9w0tUFpinNvlAGigunDPJ67po/kbnHDPJZsJ9wSASEQDAwCAI1i/vUKPTFum80/O0YUFbdwuB8AxuLRXO70+JhjuOW6GphHuCQARhwYGAADfw1qr37w9X15jdN9lBW6XA+A49MpN17u3DlKX7FTd/GKRniLcEwAiCg0MAAC+xyvfrtdXy7fpnotPUrv0JLfLAXCc2rTcH+75wIdL9Ks3CPcEgEhBiCcAAIdRvKNC93+wSKd3bq1r++e5XQ6ARlJfuOf46wj3BIBwxwoMAADqYa3VvW/Nl5X0l6t6yeMxbpcEoBGFhnvOKybcEwAiAQ0MAADq8epM59aRey8+SR0ykt0uB0ATIdwTACIHDQwAAA6yYede3f/BYm4dAWLEweGeEwj3BICwRAMDAIAQgYDVr9/4TgFruXUEiCGh4Z4PfrhEd71OuCcAhBtCPAEACPHs9NWavqJU91/eg1tHgBhTF+7ZNStVj37qhHtOuJ5wTwAIF6zAAAAgaPGm3frLR0s1+KQcXcOtI0BMMsbo9vOdcM/5Gwj3BIBwQgMDAABJlTV+/fLVuWqZHKf/vbKnjOHWESCWXdqrnSaNPl01fsI9ASBc0MAAAEDS/360REu37NFfr+ql1iwXByDplA7pmjx2kDpnOeGeTxHuCQCuooEBAIh5Xy4r0T+mr9ENZ3TUOSdmu10OgDDSpmWiJo0+XRf3aKsHPlyiX71BuCcAuIUQTwBATCvZU6U7X/9O3XJSdc+Q7m6XAyAMJcV79fiIPuqavT/cc/x1hHsCQHNjBQYAIGb5A1a/fG2Odu+t0WMj+igxzut2SQDClMezP9xzXjHhngDgBhoYAICY9cS/Vmj6ilL9YWiBurdp4XY5ACIA4Z4A4B4aGACAmDRjxTY98ukyXdGnva4u7OB2OQAiCOGeAOAOGhgAgJizdU+lbnt1rjpnpuiPw3rwyFQAR41wTwBofoR4AgBiij9gdftrc1VWVaOXbjpNKQn8KgRwbOoL95xwXT8exQwATYQVGACAmPLXj5c6uReX9dCJbdLcLgdAhDsk3PPJ6Vq6eY/bZQFAVAqLBoYx5lljzFZjzIKQsQxjzFRjzPLgvlVw3BhjHjPGrDDGzDPG9HWvcgBAJHl/3kZN+GKlrj0tT1efSu4FjswY83tjzAZjzNzgdnHItXuD85GlxpgL3awT7qsL96yuDeiKcdP16WLCPQGgsYVFA0PSc5IuOmjsHkmfWmvzJX0aPJekIZLyg9soSeObqUYAQARbsnm3fvX6PPU7oZX+54cFbpeDyPKwtbZ3cJsiScaYkyUNl1QgZw4zzhjDc3hjXGi4500vFOnpLwn3BIDGFBYNDGvtl5K2HzQ8VNLzwePnJQ0LGX/BOr6WlG6Mads8lQIAItGuihqNfnGW0hJ9Gn9tX8X7wuLXHyLbUEmvWmurrLWrJa2Q1N/lmhAGQsM9/zxliX5NuCcANJpwnsHlWGs3SVJwnx0cby9pfcjrioNjAAAcwh+w+sVrc7Rx516Nv66vslskul0SIs/Y4G2rz9bd0qoGzkeMMaOMMUXGmKKSkpLmqBVhoC7c8xfn5ev1WcW67u/fqLSsyu2yACDihXMD43Dqe9ZdvWvzmDQAAB78cLE+X1qi319WoH4nZLhdDsKQMWaaMWZBPdtQObeqdpHUW9ImSQ/Vva2ejzpkPmKtfdpaW2itLczKymqynwHhpy7c8/ERhHsCQGMJ5wbGlrpbQ4L7rcHxYkmhyWu5kjbW9wFMGgAgtr3y7To989Vq3XBGR1172glul4MwZa0dbK3tUc/2rrV2i7XWb60NSHpG+28TafB8BLHth6cQ7gkAjSWcGxiTJY0MHo+U9G7I+E+CTyMZIGlX3a0mAADUmb5im/77nQU658Qs/e6Sk9wuBxHqoJytyyXVPTFtsqThxpgEY0wnOeHi3zZ3fYgMdeGenbJSCPcEgOPgc7sASTLGvCLpHEmZxphiSf8j6UFJk4wxN0paJ+lHwZdPkXSxnLCsCkk/bfaCAQBhbcXWMo355yx1yUrV4yP6yOcN5349wtxfjDG95dweskbSaEmy1i40xkyStEhSraRbrbUkNeKw2rRM1Oujz9Cdr8/Vn6cs0fItZfrT5T2U4OPhNQDQUGHRwLDWjjjMpfPqea2VdGvTVgQAiFTby6v1s+dmKsHn0cQbCpWWGOd2SYhg1trrv+fa/ZLub8ZyEOGS4r16YkRfPZK9XI99ulxrSss14bp+ap2a4HZpABAR+JMUACBqVFTX6mfPzdSW3ZV6+ieFym2V7HZJAHAAj8foDsI9AeCY0MAAAESFGn9At740W/OKd+qxEX3UN6/Vkd8EAC4h3BMAjh4NDABAxLPW6t635uuzpSX647AeurCgjdslAcAREe4JAEeHBgYAIOL93ydL9casYv3ivHwelwogotSFe17co63+PGWJfvXGPFXVkgcLAPUJixBPAACO1T+mr9aTn63UiP4d9MvB+W6XAwBHLSneq8dH9FGX7FQ99ulyrSXcEwDqxQoMAEDEem3mOt333iJdWJCjPw7tIWOM2yUBwDEh3BMAjowGBgAgIr07d4PueWu+zuqWpcdG9JHPy680AJGPcE8AODxmewCAiPPJws26Y9J3OrVjhp66rp8SfF63SwKARkO4JwDUjwYGACCifLmsRGNfnqMe7Vvq2RtOVVI8zQsA0acu3HNIjzb685Ql+jXhngBAAwMAEDk+X7pVN71QpM5ZKXr+p6cqNYEsagDRKyneqydG9NVt5+Xr9VnFuu7v36i0rMrtsgDANTQwAAAR4bMlWzXqhVnqmpWql28eoPTkeLdLAoAmR7gnAOxHAwMAEPamLdqi0S/OUrc2qXr55tOUkULzAkBsIdwTAGhgAADC3McLN+uWl2bppLZpeulGVl4AiF2EewKIdTQwAABh663Zxfr5S7NV0K6lXrjxNLVMjnO7JABwFeGeAGIZDQwAQFj6x/TVumPSdzqtU4b+edNpaplE8wIAJMI9AcQuGhgAgLBirdXDU5fpvvcW6cKCHD17A08bAYCD1YV7Pka4J4AYQgMDABA2/AGr+95bpEc/Xa6r+uXqyWv6KjHO63ZZABC2LjulnV4LCff81xLCPQFELxoYAICwUFnj160vzdZzM9bopkGd9Jcre8nn5dcUABxJ7w7penfsQHXKStGNzxfpmS9XEe4JICoxMwQAuK60rErXPPO1Pl60Wf996cn63aUny+MxbpcFABGjbcskTRp9uob0aKP7pywm3BNAVOKmYgCAq9ZsK9cN//hWm3ZVatw1fTWkZ1u3SwKAiJQc79MTI/rqkezleuzT5VpTWq4J1/VT69QEt0sDgEbBCgwAgGu+WVWqK8bP0K69NXr55tNoXgDAcSLcE0A0o4EBAHDFK9+u07V//0bpSXF66+cD1e+EDLdLAoCoQbgngGhEAwMA0Kxq/QH9fvJC3fvWfJ3RNVNv3zpQnTJT3C4LAKLOweGeT3+5knBPABGNBgYAoNnsKK/WDf+YqedmrNGNgzrp2ZGFapkU53ZZABC1QsM9/zxliX79xjxV1wbcLgsAjgkhngCAZjG/eJfG/HOWSvZU6S9X9tLVp3ZwuyQAiAkHh3uuLa3Q+Ov6Eu4JIOKwAgMA0KSstXrl23W6cvwMSdLrY06neQEAzSw03PO74p2EewKISDQwAABNprLGr1+/MU/3vjVfp3XO0Hv/NUindEh3uywAiFmh4Z5Xjp9BuCeAiEIDAwDQJJZt2aOhT0zX67OKddu5XfXcT/srIyXe7bIAIObVhXt2zEzWjc8X6ZkvVxHuCSAi0MAAADQqa61e/madLnvi3yotr9LzP+uvOy44UV6Pcbs0AEBQaLjn/VMWE+4JICIQ4gkAaDS79tboN2/N1wfzN+nM/Ew9dPUpyk5LdLssAEA99oV7Zi3TY/9aQbgngLDHCgwAQKP49/JtuuiRL/Xxws26Z0h3Pf/T/jQvACDMeTxGd1xwoh4d3ltzi3dq2DjCPQGELxoYAIDjsrfar99PXqjrJn6jpHiv3rzlDI05u4s83DICABFjaO/2mjT6dFXWEO4JIHzRwAAAHLM563bokse/0nMz1uinAztqym1n8pQRAIhQvTuka/LYgTqhtRPu+fevCPcEEF7IwAAAHLWK6lr97ZNlenb6arVpkaiXbzpNZ3TNdLssAMBxatsySa+POV13TvpOf/pgsZZt2aM/DeupeB9/9wTgvrBvYBhj1kjaI8kvqdZaW2iMyZD0mqSOktZIutpau8OtGgEglsxYsU33vDVf67ZX6NrT8nTPkO5KS4xzuyyg0RljXpN0YvA0XdJOa21vY0xHSYslLQ1e+9paO6b5KwSaRnK8T09e01ePTHPCPddsI9wTQHgI+wZG0A+stdtCzu+R9Km19kFjzD3B87vdKQ0AYsOO8mo98OFiTSoqVqfMFL06aoAGdG7tdllAk7HW/rju2BjzkKRdIZdXWmt7N39VQPOoC/fskp2qX70xT0OfnK6JI0/ViW3S3C4NQAyL1LW+RgL+AAAgAElEQVRgQyU9Hzx+XtIwF2sBgKgWCFi9NnOdzn3oc705e4NGn91ZH/7iTJoXiBnGGCPpakmvuF0L0Nzqwj2ragn3BOC+SGhgWEmfGGNmGWNGBcdyrLWbJCm4z3atOgCIYos27taPnvqP7n5zvrpmp2rKbWfq3iEnKTHO63ZpQHM6U9IWa+3ykLFOxpg5xpgvjDFnHu6NxphRxpgiY0xRSUlJ01cKNIGDwz2f+ZJwTwDuiIRbSAZaazcaY7IlTTXGLGnoG4MNj1GSlJeX11T1AUDU2V5erb9NXaqXv1mn9OR4/fWqXrqqX66cP0QD0cMYM01Sm3ou/dZa+27weIQOXH2xSVKetbbUGNNP0jvGmAJr7e6DP8Ra+7SkpyWpsLCQf/EhYoWGe94/ZbGWbyXcE0DzC/sGhrV2Y3C/1RjztqT+krYYY9paazcZY9pK2nqY9zJpAICjUOMP6MX/rNUj05apvNqv6wecoNvP76b05Hi3SwOahLV28PddN8b4JF0hqV/Ie6okVQWPZxljVkrqJqmoCUsFXEe4JwC3hXXL1BiTYoxJqzuWdIGkBZImSxoZfNlISe/W/wkAgIaw1uqThZt10SNf6g/vL9IpHdL14S/O1H1De9C8QKwbLGmJtba4bsAYk2WM8QaPO0vKl7TKpfqAZlUX7vno8N6aW7xTQ5+crqWb97hdFoAYEe4rMHIkvR1csuyT9LK19iNjzExJk4wxN0paJ+lHLtYIABFt1trtemDKEhWt3aHOWSmaOLJQ53bP5nYRwDFch4Z3niXpD8aYWjmPeR9jrd3e7JUBLhrau71OaJ2im18o0pXjZ+ixEb11bvcct8sCEOVMrATwFBYW2qIiVnYCQJ2lm/fooU+W6pNFW5SVlqDbB3fT1YW58nnDenEeGpkxZpa1ttDtOmIBcxFEo0279uqm54u0aNNu/fbik3TjoE40wAEctYbOR8J9BQYAoJGt2FqmRz9drvfnbVRKvE93XdBNPxvUScnx/EoAAByd0HDPP32wWMu2EO4JoOkwWwWAGLGqpExP/GuF3pm7QYlxXt1ydheNOqszGRcAgONCuCeA5kIDAwCi3KKNu/Xk5ys0Zf4mJfg8uunMzhp9VmcmlgCARlMX7tklO1W/emOehj45XRNHnqoT26S5XRqAKEIDAwCi1Ky1OzT+8xWatnirUhN8Gn1WF904qJOy0mhcAACaBuGeAJoSDQwAiCL+gNXURZv19JerNHvdTqUnx+n2wd10wxkd1TI5zu3yAAAxoHeHdE0eO1A3PV+kG58vItwTQKOhgQEAUaCsqlZvzirWs9NXa21phTpkJOm+ywr0o8JcwjkBAM2OcE8ATYFZLQBEsFUlZXrhP2v1xqxilVXVqneHdN1zUXddUNBGXg9/6QIAuKcu3PPhacv0+L9WaE1phSZc108ZKYRHAzg2NDAAIMLU+AP6dPFWvfztOn25rERxXqNLe7XTyDM6qneHdLfLAwBgH4/H6M4LTlTXfeGe/9bEkaeqWw7hngCOHg0MAIgQ67dX6LWZ6zWpaL227qlS25aJuuP8bhrRP49gTgBAWAsN97xiHOGeAI4NDQwACGN7q/36aOEmvV5UrBkrS+Ux0g9OzNaI/nk658Qs+bzcSwwAiAyEewI4XjQwACDMBAJWM9ds19tzNuj9eZtUVlWrDhlJun1wN11VmKv26UlulwgAwDEh3BPA8aCBAQBhYsnm3XpnzkZNnrtBG3dVKinOq4t7ttWPCnPVv2OGPIRyAgCiwCHhntsqNOF6wj0BHBkNDABw0fIte/TB/E36YN4mLd9aJq/H6Kz8TN09pLvOPzmHR6ACAKIS4Z4AjgUzYwBoRtZaLdq0Wx8v3KKPFmzSsi1lMkbq3zFDfxhaoEt6tlXrVAI5AQCxYWjv9srLSNaoF2fpinEz9PiIPvpB92y3ywIQpmhgAEATq/EHVLRmh6Yu2qJPFm1W8Y69MkY69YQM3XdZgYb0aKPsFolulwkAgCv65LXSu7fWhXvO1G8I9wRwGDQwAKAJ7Civ1hfLSvTpkq36YulW7a6sVbzXo4FdW2vsD7pq8Mk5ymSlBQAAkqR26Ul645bTdcdrTrjn8i1l+uOwHoR7AjgADQwAaAT+gNXc9Tv1xbISfbmsRN8V75S1UmZqvC4saKPzTsrWoPwspSbwn10AAOqTHO/TuGv3h3uuLi3XhOsI9wSwHzNpADgG1lqtLCnXjJXbNH3FNv1nZal2V9bKY6RTOqTrF+fl6+xuWTolN52nhwAA0ECEewL4PjQwAKABrLVaU1qhr1eV6ptVpfp61XZt3l0pSWqfnqQhPdrqzG6ZGtQ1U+nJ/KUIAIDjQbgngPrQwACAevgDVos37VbRmu2auXaHZq7erq17qiRJmakJOq1zhgZ2ydTArq2Vl5FM0BgAAI2McE8AB6OBAQCStpdXa+76HZqzbqdmr9uh79bvUllVrSSpbctEnda5tQZ0ztCAzq3VOTOFyRMAAM2AcE8AoWhgAIg55VW1WrBhl+Zv2KXvindpXvFOrS2tkCR5PUbd26RpWJ92OrVjhgo7Zqh9epLLFQMAELvqwj3/NnWZnviMcE8gltHAABDVtpdXa/Gm3Vq0cbcWbNylBRt2adW2clnrXG/XMlG9ctM1/NQ89c1LV8/clkqO5z+NAACEE4/H6K4LT1R+jhPuOezJ6Zo4slD5hHsCMYVZOoCoUF0b0MqSMi3bskdLNu/R4k27tXjTbm3ZXbXvNe1aJqqgfUtddkp79WjfQr1y05WVluBi1QAA4GjUhXve/IIT7vnYNX30gxMJ9wRiBQ0MABGlssav1dvKtWJrmZZvLdOKrXu0fEuZVm8rV23AWVbh8xh1zU7VGV0ydVLbNJ3UtoVOattCmak0KwAAiHR98lpp8thguOdzhHsCsYQGBoCw4w9Ybdy5V2tKy7VmW7lWbSvXqpJyrSwp04ade/fd/uExUl5Gsrpmp+qCghx1y0lT9zYt1CkzhXAvAACiGOGeQGyigQHAFeVVtSresVfrt1doXci2trRc63fsVXVtYN9rk+K86pyVor55rXRVv1x1zkpVfnaqOmWmKDHO6+JPAQAA3EK4JxB7aGAAaHTWWu2oqNHGnXv3bRvqth17Vbxjr0rLqw94T0q8V3mtU5SfnabBJ+WoY2aKOrZOUafMFOW0SGBZKAAAOAThnkBsoYEB4KhU1wZUUlalLbsrtXW3s9+8u1KbdwW33ZXauHOvqkJWUEhSgs+j9ulJat8qSRe0a6HcVsnqkJGsDq2S1CEjWa1T4mlSAACAY0K4JxAbaGAAUHVtQDsqqrWtrEqlZc7e2aq1bU+Vtu6pUsmeKpWUVWn7QSsnJCc0M6dFotq0TNTJbVvovO7ZapeepHbpiWrbMknt0pOUmUqDAgAANB3CPYHoRwMDiDLVtQHt2lujnRXV2rm3RjvKq7WzokY7Kqq1o8I5Ly2v1o6Kam0vr1ZpWZV2V9bW+1kJPo8yUxOU3SJBJ7ROVmHHVspKS1CbFonKaZGorLQE5bRIVOuUeHk8TA4AAIC76sI9b39trv70wWKt2FqmPwwl3BOIFjQwgDBTVetXWWWt9uzbarQ7uN9TWavdlTXavdfZ79rrbLv37j+uqPYf9rPjvEYZKfFqlRyv1qnxKmjXQq1T4tU6NUGtU+P3HWemJigzNV6pCT7+agEAACJKcrxP46/ttz/cc1u5xhPuCUQFGhjAMbLWqqo2oMoav/bW+FVR7VdFlV8V1bWqqAk5rvarvLpWFVXOvryqVuUhx3sqa4PHTuOi2h844nenJvjUItGnFklxapEUpw4ZyeqRFKeWSXFKT4pTenKc0pPj1TIpTq2S45WeHKdWKfFKiffSkAAAAFGPcE8gOtHAQMTzB6yqawOqrg2oyu/fd1ztD47VXav17zuvqnHOK+vZV9b4VRlsTFTW+FVVE9De4PG+fbVzHLANr9NjpJR4n1ISfEpO8Col3qfUBJ9yWyUrLdGnlASv0hLjlJrgc87jnX1aYpzSEn1qEdynJfrk87IMEkBsMsacL+lqSU9aa+caY0ZZa592uy4A4YlwTyC6RGwDwxhzkaRHJXkl/d1a+6DLJYUla638ASu/tQoEJH/wPLBvzNnX+q0C1qo2eK02EHzfQcfOeeCAcWcfUI0/eO4PqDbgfGZt8LwmZLzGHwhec95Td72mdv/16oOOa/zOa52904Sou3Y0TYTDMUZK9HmVGOdRYpxXCT5n72wetU6NV3K8d99YUt0W7+yT453j5HhfyLHTpEiO9yolwacEn4fVDwBw/H4u6aeSfmeMyZDU+3g/0BjzI0m/l3SSpP7W2qKQa/dKulGSX9Jt1tqPg+PMQ4AIQbgnED2O2MAwxkyTdKe19rtmqKdBjDFeSU9KOl9SsaSZxpjJ1tpFzfH9Xy4r0VuzixWwkpUUsFY22CCwss64dfYBu//c7juv/zWBwMHXnIaAtU7jIRD8jsC+a8EGRejrDmpM2Eb4x31j8XmMfF6jOI9HPq+Rz+tRnCe49xrFeT2K8zrX4rweJcV51SK42iDe51F88HU+r3O8fyx4HNwSQs+9HiXE1e2dxkTdeF1zIsHnVZzX8EsMACJDibV2p6S7jDEPSjq1ET5zgaQrJD0VOmiMOVnScEkFktpJmmaM6Ra87No8BMDRI9wTiA4NWYHxa0kPG2PWSvqNtXZTE9fUEP0lrbDWrpIkY8yrkoZKapaJQ/zSybp52QRJRlZG1nhkJVl5ZI3zH8G64/3XTfBa/eeSR9YYWeOVjJGV1xn3GMkEP9d4ZWUk45U8+8ec685enuCYxytjQo49XlmPTyZ43QTHnGs+yeuTx+OT8Trj+4/j5PF65fHGyeP1yXjj5PX55PH59o15fQnyBc+9cXHy+eIV5/PKG2wueD1GPg8NAgBAo/ig7sBae48x5r+O9wOttYsl1fd7aqikV621VZJWG2NWyJmDSC7OQwAcG8I9gch3xAaGtXa2pHONMVdK+sgY85akv1hr9zZ5dYfXXtL6kPNiSac115cPyG8r7ewg2YAk6+ytDW6B/du+a7VSwB88D47tOw+EvN/v7AP+/a/ZNx6Qs8SjbvPvf53CaJlFKE+c5PE5m9fnnHuDY964/eeHPY4PbvUc+xKCx8G9L+HQY1/Itu88MWQ8UfJ43f6/EgCgAUJWhL4bOm6tfbwJv7a9pK9DzouDY1ID5yHGmFGSRklSXl5eE5QI4GgQ7glEtgZlYBjnTxJLJY2X9CdJNxtj7rXWvtiUxX1fSfWMHfKv+CabNHS/2NnCxb6mR2jjo67JEdLsCNQe2Pioe8++awFnv288eBz6Xn/N/tf5a6RAjfMdgVrnuO66vyY4Vnvga/0hr6s791fvP67ZGzwPvsdfHdxqQs6rgo2bRuCJC2lqJEpxiZIvKbhPlOKSnM0X3MclO9f2HQe3+Lp9yv593RaX4qyMAQAcj+NaERpsgLSp59JvD26KhL6tnjErqb7/qNf714RgwOjTklRYWBimf3EAYg/hnkBkakgGxr8ldZa0UM5fIW6QtETSL4wxZ1prRzVphfUrltQh5DxX0saDXxQzkwZjnBUOkZvJevQCfqeZUVu1v8lRd3zAvsrZ11ZKtdXBfZVUu7ee8yqngVJbuX9ftjV4XiHVBMdryo++gXJAUyPN2SekSvGpwX2alHDw1kJKbHHgPiHN+f83AMSY410Raq0dfAxf+33zjSPOQwCEN8I9gcjTkH/xjpG00NpD4iD/yxizuAlqaoiZkvKNMZ0kbZATsHWNS7XADR6v5Amuimhu1joNkpoKp6FRXRE8rpCqy/fvDzguk6rKnPOqMql6j1SxXdq5zjmv2uO85ki3AxlPsKHRcv+WlC4lpofsWx24JWdISRlO04RfyAAimAsrQidLetkY8zc5IZ75kr6VszKDeQgQBQj3BCJLQzIwFnzP5UsasZYGs9bWGmPGSvpYzuPLnrXWLnSjFsQgY/bnaCS1arzPDQSc1R1Ve5ytcrdUFdwqd0uVuw48rtwlVe6Utq1w9nt3OitJDscb7zQyUjKdpkZy6+CW6YylZIXss5yfjYYHgDDRlCtCjTGXS3pcUpakD4wxc621F1prFxpjJskJ56yVdKu11h98D/MQIEoQ7glEDnPoworoVFhYaIuKio78QiCS1VQGmxk7nK1ie3BfKu3d7uwrgucV26Tybc7r6+OJcxoZqdlSas7+fVqb4NbW2afmOOGpACKSMWaWtbbQ7TqOxBjTQ/WvCJUxZrG19iQXyjoqzEWA8PfOnA369Zvz1KZFIuGeQDNq6HwkhkITgBgQlyjFBRsMDeWvcRod5SXBbZtUvtXJ/ygvkcq2SHs2SZu+c8YPyf8wTqOjRbsDt5YdpBbtpZbtpbR2ko+/YgA4duG4IhRA9BnWp73yWidrFOGeQFiigQHEOm+clJbjbEcS8DsNjrLN0p7NTmNj9yZpz0Znv2OttO4/zqqPAxhnxUZ6B6exkd5BSj9BanWCs0/PYxUHgGNmrV3ldg0Aokdfwj2BsEUDA0DDebz7mx1tTzn866rLpd0bpV3rpV0bpF3FzvHOddKGImnRO86jcusYj9QyV2rVScro5Oxbd5EyujjnboS1AgCAmEW4JxCeaGAAaHzxKVJmvrPVJ+B3Ghw71zqrNnaskXaslravlha/52R07GOc5kbrrs7ntQ5+blZ351YZ/hoCAACaAOGeQPihgQGg+Xm8wdtIOkgdBx16vXKXVLpS2r4quF8pbVsuzX3FeQRtnYQWUtaJzpZ9spR9krNPzaGxAQAAjpvHY3TXhSeqa3aqfv3mPA17cjrhnoCLaGAACD+JLaX2fZ0tlLVOqOi2ZVLJ0uC2RFr2sTTnn/tfl5Qh5RRIOT2kNj2lNj2cFRu+hOb9OQAAQFQg3BMIDzQwAEQOY/Y/xrXTWQdeK98mbV0kbV0sbVkobVkgzXpOqt3rXPfEOSs02p4S3Ho7zY24xGb/MQAAQOTpm9dK744dqJuD4Z6/veRk/WxgR8I9gWZEAwNAdEjJdJoaoY2NgN+5DWXzfGfb9J20dIo050Xnusfn3HLSvq/Uvp+Ue6qUeaLkIaALAAAcqn1IuOcf31+k5Vv2EO4JNCMaGACil8e7P0y0xxXOmLXS7g3SxjnShtnSxtnSwred1RqSk6tR18zIG+DsE1u49iMAAIDwQrgn4B4aGABiiwk+1aRlrnTSD52xQMAJCi2euX/76v8kG3Ae8ZrTQ8o7XTrhDCd0NCXT3Z8BAAC4inBPwB00MADA49m/UqP3Nc5Y1R6puEha97W07j/ObSffPuVcy+ruNDI6nSV1PFNKznCvdgAA4BrCPYHmZay1btfQLAoLC21RUZHbZQCIVP4aaeNcac1X0trp0tr/SDXlkowTCtr5HKnLD5yVGjztBBHEGDPLWlvodh2xgLkIEL027Nyrm54v0tLNuwn3BI5BQ+cjNDAA4Fj4a6QNs6RVX0irPpeKv5UCtVJcsrMqo+tgKX+wlNHZ7UqB70UDo/kwFwGiW3lVre6YNFcfL9yi4ad2INwTOAoNnY9wCwkAHAtvnBPymTdAOuduqarMWZ2x4lNpxTRp+cfSh3KeatLtQqnbRVKH0yQv/9kFACAapSQQ7gk0NWbSANAYElKlE4c4mySVrpSWT5WWfSR9PV6a8ZiUmO5c736p1OVcKT7Z3ZoBAECjItwTaFo0MACgKbTu4mwDxjiBoCv/JS2ZIi39UPruFcmXJHU9Tyq43FmhkcDEBgCAaEG4J9A0aGAAQFNLSJNOHups/honBHTx+9Li96Ql70u+RCn//GAzYwgrMwAAiAJ981rp3bEDddPzRbrxuZmEewKNgAYGADQnb5zzxJLO50hD/iKt/1pa+I606B2noRGf6txi0utqqdPZZGYAABDB2qcn6Y0xp+v21+bqj+8v0oqte3TfZYR7AseKmTEAuMXjkU44w9kuekBaO0OaP0la+K4071UpJdtpZPS+Vso52e1qAQDAMUhJ8GnCdf300NSlevKzlVpVUq4J1/VTK8I9gaNG6w8AwoHHK3U6U7rscelXy6Uf/1Pq0F/6ZoI0/nTp6XOkb5+R9u5wu1IAAHCUPB6jX13YXY/8uLfmrN+poU9O1/Ite9wuC4g4NDAAINz4EqSTfigNf0m6c6l00YOSv1aacpf0UHfp7Vuk9d9K1rpdKQAAOArD+rTXq6MGqKLaryvGzdBnS7e6XRIQUWhgAEA4S8mUBtwi3fJvadQX0ikjpMWTpYnnS+MHOqsyqsrcrhIAADRQXbhnbkaybnxupib+e7Usf5QAGoQGBgBEina9pR8+4qzK+OGjTsDnlLukv50kfXiPVLrS7QoBAEAD1IV7Dj4pR398f5F+8/Z8VdcG3C4LCHs0MAAg0iSkSv1ucFZk3DhVyr9AmvmM9Hhf6aWrpdVfcXsJAABhri7c89YfdNEr367X9RO/0Y7yarfLAsIaDQwAiFTGOEGfV02Ubl8onX2PtGGW9PylTujn/Dec7AwAABCW6sI9H/7xKZqzfqeGjZuuFVsJ9wQOhwYGAESDtDbSD+6Vbl8gXfqIVF0mvXmj9FgfJyejptLtCgEAwGFc3idXr9w8QOVVtbr8yRn6nHBPoF40MAAgmsQlSYU/lW6dKQ1/xWlsTLlLerSXNP0xAj8BAAhT/U5opXfHDlJuRrJ+9txMPUu4J3AIGhgAEI08Hqn7xdKNn0gj35OyuktT/1t6pKf074el6nK3KwQAAAcJDff8A+GewCFoYABANDNG6nSWNHKydOM0qX0/adrvpUd6STOekGr2ul0hAAAIQbgncHg0MAAgVnQ4VbruDefJJW16SJ/8Vnq0t1T0rOSvcbs6AAAQRLgnUD8aGAAQazr0l37yrnTDFCmjk/T+7dK4AdKiyTx+FQCAMEK4J3AgGhgAEKs6DpR++qET9mm80qTrpYnnS+u+cbsyAAAQRLgnsB8NDACIZcY4YZ+3zJAue1zaVSw9e4H05k3OMQAAcN2h4Z4LVOMn3BOxhwYGAEDy+qS+P5HGFkln/Upa/J70eKH0+YNSdYXb1QEAEPPqwj1/fk4XvfLtOsI9EZPCtoFhjPm9MWaDMWZucLs45Nq9xpgVxpilxpgL3awTAKJKQqp07u+kW7+Vul0off6ANO40aelHblcGNBljzI+MMQuNMQFjTGHI+PnGmFnGmPnB/bkh1z4PzkPq5inZ7lQPIJZ4PEa/vsgJ95y9jnBPxJ6wbWAEPWyt7R3cpkiSMeZkScMlFUi6SNI4Y4zXzSIBIOq0OkG6+nnphg+kuGTplR9Lr1wj7VzndmVAU1gg6QpJXx40vk3SD621PSWNlPTiQdevDZmnkKwHoNkQ7olYFe4NjPoMlfSqtbbKWrta0gpJ/V2uCQCiU8dB0uivpMH3Sas+k57oL01/VPLXul0Z0GistYuttUvrGZ9jrd0YPF0oKdEYk9C81QFA/Qj3RCwK9wbGWGPMPGPMs8aYVsGx9pLWh7ymODgGAGgKvnhp0C+d20q6nCtN/X/S38+TNs93uzKgOV0paY61tipk7B/B20f+2xhj6nuTMWaUMabIGFNUUlLSPJUCiBmEeyLWuNrAMMZMM8YsqGcbKmm8pC6SekvaJOmhurfV81H1thqZNABAI0rvIA1/SfrR89LuDdLT50j/+pNUW3XEtwJuO8Kc40jvLZD0v5JGhwxfG7y15Mzgdn1977XWPm2tLbTWFmZlZTXGjwIAByDcE7HE5+aXW2sHN+R1xphnJL0fPC2W1CHkcq6kjYe8yfn8pyU9LUmFhYWspwKA42WMVDBM6nSW9PFvpS//6jyx5PIJUrs+blcHHFZD5xwHM8bkSnpb0k+stStDPm9DcL/HGPOynNtZX2iMWgHgaNWFe+bnpOruN+dr2LjpmjiyUF2z09wuDWhUYXsLiTGmbcjp5XICtiRpsqThxpgEY0wnSfmSvm3u+gAgpiVnSJePl659U6rcLf19sPTFX8jGQFQxxqRL+kDSvdba6SHjPmNMZvA4TtKl2j9PAQDXHBzu+cUyVqEjuoRtA0PSX4KPLZsn6QeSbpcka+1CSZMkLZL0kaRbrbV+98oEgBiWP1j6+Qyp4HLps/ulZy+Qti3//+3deZhcdZ3v8fc3nRB2YiQgZgGCCAKDhDQRBgkKjBBk2MEAAkE0gHCVcVBhkGWcO3cuoqOjghiEICAEDEvCsHNR0EBIggRIwmIIIBGGZEDCkhCy/O4fVT1WOt2dTqe7fqeq3q/nqSfV55xOf89W9etvn/Op3FVJayUijoiI+cBewJ0RcW951lnAx4ALWn1cal/g3vIYZSbwZ+DKHLVLUmuV4Z6njJ/G+CmGe6p+RKMczM3NzWnGjBm5y5Ck+jXrVrjzG7DsfRh1Cex+UumWExVaRDyeUmrOXUcjcCwiqZreW7qcf7hpJvfNeZ3jRgzhu4ftTJ+mIv/9Wo2ss+MRj2BJUvfY5Ug441EYPALu+BpM/BK8vyh3VZIkNaTW4Z4nXTXNcE/VPBsYkqTus+lWcOJtsP+FMGcSXLEPzPcvzpIk5dAS7vnvx36Sx1/+C4dfPoW5C97JXZbUZTYwJEndq1cT7POPcMrdkBJcfSBM/VnpuSRJqrojdx/EjWMN91Tts4EhSeoZQz4Fp/8Otj8Q7jm3dEvJ0ndzVyVJUkMy3FP1wAaGJKnnbNAPvnA97H8RzLkdrtwPFj6fuypJkhrSwH4bMPH0vTjgE1vyz3fM4Z9um8WyFStzlyV1mg0MSVLP6tUL9vlGKRtj8Rtw5Wfh2TtzVyVJUkMy3FO1zAaGJKk6hn4GTnsYNv84TDgeHr7UXAxJkjJoO9zT2zxVfDYwJEnVs9lAOOUu+Jtj4MH/DbecCsuW5K5KkqSGtEq45+VTeNhwTxWcDQxJUnX12QCOvLKUizHrVrj6IHj7tdxVSZLUkIZv/SFuP3NvBsp+VbkAAB7sSURBVPbbgDGGe6rgbGBIkqovopSLcdyN8MZc+MUB8Pqc3FVJktSQBn1oQ24542/Z33BPFZwNDElSPjuMglPuhpXL4eoDYd5DuSuSJKkhbdS3Nz//4nDOMNxTBWYDQ5KU11a7wpcfgE0HwvVHwZMTclckSVJD6tUr+LbhniowGxiSpPz6DYYv3QND9oTbToPf/cBPKJEkKRPDPVVUNjAkScWwQT/44q2lTyj5f9+F+y+wiSFJUiatwz2vMdxTBWADQ5JUHL3XgyPGwR5fgUd+ApPPghXLc1clSVJDqgz3vPiOOZx/u+GeyssGhiSpWHr1goMvhZHfgieuh4ljYPnS3FVJktSQKsM9b3jMcE/lZQNDklQ8EbDf+XDgv8Ezd8CNo2HZktxVSZLUkAz3VFHYwJAkFddeX4XDLoMXfgM3fAE+WJy7IkmSGlYp3PNThnsqGxsYkqRiG/ZFOOIKeOl3cMOx8MF7uSuSJKlhDd+6v+GeysYGhiSp+D45uhTu+fIUuP5oWOplq5Ik5dIS7rnfjoZ7qrpsYEiSasOux8BRv4BXHoNfHe2VGJIkZbRR396MO9FwT1WXDQxJUu3Y5ai/NjEmHA/L3s9dkSRJDctwT1WbDQxJUm3Z5chSsOe838Kvx8CKZbkrkiSpoRnuqWqxgSFJqj27HQ+f/wE8fzfcOhZWrshdkSRJDc1wT1WDDQxJUm3a48vwd/8Cs2+FyV8DB0mSJGVluKd6mg0MSVLt2vtrsO+3Yeb18MDFuauRJKnhtYR7nr5vKdzz5Kun8dZiwz3VPWxgSJJq22fOg+YvwZQfwdQrclcjSVLD69UrOHfUjvzgmE8y46W/cPhlhnuqe9jAkCTVtgg4+Puw4yFwz7kw69bcFUmSJOCo4aVwz3cN91Q3sYEhSap9vZrgqKtgyF5w22nw4sO5K5IkSawa7nnKNdMN99Q6sYEhSaoPfdaH426A/tvBhBPg9Tm5K5IkSfw13POzO2xhuKfWiQ0MSVL92OBD8MVbYL2N4IYvwLsLclckSZIw3FPdwwaGJKm+bDYQjrsRFv83TDgeli3JXZEkScJwT607GxiSpPrz0WFw5DiYPx0mnQneaytJUmG0hHu+877hnlo7NjAkSfXpE38PB1wMs26B3/5b7mokSVKF4Vv3Z9JZpXDPMeOn8ctHXjLcU2uUtYEREcdExOyIWBkRza3mnRcRcyPiuYg4sGL6QeVpcyPi3OpXLUmqGXufDcO+CA9dAk9PzF2NCqq98UhEbBMRSyJiZvlxRcW84RHxdHk88uOIiDzVS1LtGvShDZl4xt+y345bctHk2XzHcE+tQe4rMGYBRwKrfN5dROwEjAZ2Bg4CLo+IpohoAi4DRgE7AceVl5UkaXUR8PkfwuA9YdJZ8F9P565IxdTmeKTshZTSbuXH6RXTfwaMBbYvPw7q+TIlqf5s3Lc3Py+He/7KcE+tQdYGRkrpmZTSc23MOgyYkFJamlJ6EZgLjCg/5qaU5qWUPgAmlJeVJKltvdeDY6+FDfqVPl518Zu5K1LBdDAeaVNEbAVsmlJ6NJWud74WOLzHCpSkOtdkuKc6KfcVGO0ZCLxS8fX88rT2pkuS1L5NtoRjr4N3XoNbToWVK3JXpNqxbUQ8EREPRcQ+5WkDKY1BWrQ7HomIsRExIyJmLFxoSJ0kdcRwT61JjzcwIuKBiJjVxqOjKyfauo80dTC9vZ/toEGSVDJ4Dzj4+/DCg/Dgv+SuRlXWxfHIa8CQlNIw4BvADRGxKWsxHkkpjUspNaeUmgcMGLDuKyJJda4y3POUa6Yb7qlV9O7pH5BSOqAL3zYfGFzx9SDg1fLz9qa39bPHAeMAmpubPeolqdENPxlefQJ+/8PSR63u5F2IjaIr45GU0lJgafn54xHxAvBxSuOUQRWLdjgekSStnZZwz7MnzOSiybN5/vV3uPjQnenTVNQbCFQtRT0CJgOjI6JvRGxLKRxrGjAd2D4ito2I9SgFfU7OWKckqdaMugQGNpdCPd+cl7saFVhEDCgHiBMRQymNR+allF4D3omIPcufPnISMCljqZJUdwz3VFtyf4zqERExH9gLuDMi7gVIKc0GbgbmAPcAZ6aUVqSUlgNnAfcCzwA3l5eVJKlzeveFY8aXPqHk12Ng+dLcFSmz9sYjwEjgqYh4EpgInJ5SakmBPQP4BaWg8ReAu6tctiTVPcM91Vo0yv1Ezc3NacaMGbnLkCQVxbN3wYTjYMRYOPjS3NVkExGPp5Sac9fRCByLSFLXPf7ym4y99nE+WLGSy47fnZEfN1eonnR2PFLUW0gkSepZOx4Me50F08bB7NtzVyNJkjpguKfABoYkqZHtf1EpD2Py/zIPQ5KkgmsJ9/zsDltw0eTZfOf2WSxbsTJ3WaoiGxiSpMbVe71yHkYvmHgqrFiWuyJJktSBlnDP0/YdarhnA7KBIUlqbP2GwN//B7z6B3joktzVSJKkNWjqFZw36hN833DPhmMDQ5KknQ+H3U6A3/0AXn40dzWSJKkTjh4+iBvHfop33l/OEZdP4eHnF+YuST3MBoYkSQCjLildjXHrWHh/Ue5qJElSJ7QO97xmyouGe9YxGxiSJAH03QSOvBLe/jPc9c3c1UiSpE6qDPe8+I45hnvWMRsYkiS1GDwCRn4TnroJnp6YuxpJktRJLeGep++7neGedcwGhiRJlUZ+EwbtAXf+I7zzX7mrkSRJndTUKzh31I6rhHu+sNBwz3piA0OSpEpNveHwn8Hy9+E//wG8j1aSpJpy9PBB3PCVUrjn4ZcZ7llPbGBIktTa5tvDft+B5+6Cp27OXY0kSVpLzdusGu75y0deMtyzDtjAkCSpLXt+FQaNgLu/5a0kkiTVoMpwz4smzzbcsw7YwJAkqS29muDwy72VRJKkGtYS7nnavkMN96wDNjAkSWpP5a0kT/86dzWSJKkLmnoF5436hOGedcAGhiRJHam8leRdQ8AkSapVrcM9f/dH39drjQ0MSZI60qsJDv0JLH0X7js/dzWSJGkdNG/Tn9vPLIV7jhlvuGetsYEhSdKabLEjfPpseOomeOE3uauRJEnrYHB/wz1rlQ0MSZI6Y59zoP92pUDPZUtyVyNJktaB4Z61yQaGJEmd0Wd9OOSH8JcX4eHv565GkiStI8M9a48NDEmSOmvovvDJ42DKj2DBM7mrkSRJ3cBwz9phA0OSpLXxuX+FvpvCHWfDSu+XlSSpHrQO97z20Zdyl6Q22MCQJGltbPRh+Ny/wCtT4akJuauRJEnd5K/hngO4cNJsvnP704Z7FowNDEmS1tYnj4dBe8D9F8H7i3JXI0mSukkp3LOZ0/YdyvVTDfcsGhsYkiStrV694OBL4b2F8NtLclcjSZK6keGexWUDQ5KkrvjoMNj9JJj2c1jwbO5qJElSNzPcs3hsYEiS1FX7XwTrbQx3fwtSyl2NJEnqZoZ7FosNDEmSumqjD8N+34EXH4JnJueuRpIk9QDDPYvDBoYkSeti+Cmw5S5w7/nwweLc1UiSpB7QOtxzzHjDPXOwgSFJ0rpo6g2jvgeLXoFHL8tdjSRJ6iEt4Z6XHr0r01/8C0dc/ojhnlVmA0OSpHW1zd6w4yHw+x/CO6/nrkaSJPWgY5oHc8NXPsXbS5ZxhOGeVWUDQ5Kk7vB334UVS+G3/yd3JZIkqYe1hHt+1HDPqrKBIUlSd/jwdrDHl+EP18KCZ3JXI0mSeljrcM8Lbp9luGcPs4EhSVJ32ffbsN4mcN8FuSuRJElVUBnued3UlxkzfhqLFi/LXVbdsoEhSVJ32bA/jDwH5t4PLzyYuxpJklQFleGe0158k8Mvn2K4Zw/J2sCIiGMiYnZErIyI5orp20TEkoiYWX5cUTFveEQ8HRFzI+LHERF5qpckqQ0jxkK/IaWrMFauyF2NOqGD8cgJFWORmeX5u5Xn/TYinquYt0W+NZAkFUEp3HNPFhnu2WNyX4ExCzgSeLiNeS+klHYrP06vmP4zYCywfflxUM+XKUlSJ/VZHw64GF6fBU/dlLsadU6b45GU0q9axiLAicBLKaWZFYucUDFWWVDFeiVJBbXHNv2ZdObebLWZ4Z49IWsDI6X0TErpuc4uHxFbAZumlB5NKSXgWuDwHitQkqSu2PlI2Go3+M2/wfKluavRGnRyPHIccGM16pEk1bbB/Tfklq8a7tkTcl+B0ZFtI+KJiHgoIvYpTxsIzK9YZn55WpsiYmxEzIiIGQsXevmOJKlKImD/C2DRn0qfSqJ68AVWb2CML98+ckF7t7Q6FpGkxmS4Z8/o8QZGRDwQEbPaeBzWwbe9BgxJKQ0DvgHcEBGbAm0NDlJ7/0lKaVxKqTml1DxgwIB1WxFJktbGdvvD1nvDQ9+DD97LXU3D6+J4pOV7PwUsTinNqph8Qkrpb4B9yo8T2/pexyKS1Lhah3secfkU5hnuuU56vIGRUjogpbRLG49JHXzP0pTSG+XnjwMvAB+ndMXFoIpFBwGv9mT9kiR1SQTsfyG8twCmjctdTcPrynikwmhaXX2RUvpz+d93gBuAEd1ftSSpHrSEe761ZBmHXzaF3//xv3OXVLMKeQtJRAyIiKby86GUwjrnpZReA96JiD3Ll2qeBHRm4CFJUvUN2RO2PxB+/yNY8lbuatQFEdELOAaYUDGtd0RsXn7eBziEUhCoJEltqgz3PHn8NK579KXcJdWk3B+jekREzAf2Au6MiHvLs0YCT0XEk8BE4PSU0pvleWcAvwDmUroy4+4qly1JUuft9x14/y149Ke5K1E7OhiPQGlMMj+lNK9iWl/g3oh4CpgJ/Bm4smoFS5JqUku452c+PoALJs3mwkmzWG6451qJ0od51L/m5uY0Y8aM3GVIkhrRr0+B5++Frz8JGxcrByEiHk8pNeeuoxE4FpEkAaxYmfjePc/y84fn8emPbc5lx+/OZhv2yV1WVp0djxTyFhJJkurKZ8+H5e/DlB/lrkSSJGXW1Cs47+BSuOdjL75huOdasIEhSVJP2/xjsOuxMP0qeHdB7mokSVIBGO659mxgSJJUDfucAyuWwiM/yV2JJEkqCMM9144NDEmSqmHzj8EuR8P0X8B7/oVFkiSVGO7ZeTYwJEmqlpHnwLIlfiKJJElaxcZ9ezPupGZOGzmUax99mTHjp7No8bLcZRWODQxJkqplwA6wy5Ew7UpY/Oaal5ckSQ3DcM81s4EhSVI1jfwmfPAuTL08dyWSJKmADPdsnw0MSZKqaYtPwE6HwWM/hyV/yV2NJEkqIMM922YDQ5Kkahv5LVj6Nky9InclkiSpoFqHe15w+yyWNXi4pw0MSZKq7SO7wA6fh8eugKXe2ypJktpWGe553dSXGTN+WkOHe9rAkCQph0+fDe+/BU9cl7sSSZJUYJXhntNefLOhwz1tYEiSlMPgETDkb+HRy2BF4/4lRZIkdY7hnjYwJEnK59Nnw6JXYNYtuSuRJEk1oNHDPW1gSJKUy/afgy12gin/ASnlrkaSJNWARg73tIEhSVIuEbD312HBHPjjfbmrkSRJNaJRwz1tYEiSlNMuR8Fmg+H3P8pdiSRJqiGNGO5pA0OSpJya+sBeZ8KfHoFXpuWuRpIk1ZhGCve0gSFJUm7DToT1+3kVhiRJ6pJGCfe0gSFJUm59N4YRX4Hn7oI35+WuRpIk1aDB/Tdk4hl71XW4pw0MSZKKoPlU6NUbHhuXuxJJklSjNlm/T12He9rAkCSpCDbdCnY5Ep64Dt5flLsaSZJUo+o53NMGhiRJRbHnGfDBu/DE9bkrkSRJNa4ewz1tYEiSVBQfHQZD9oLHroCVK3JXI0mSaly9hXvawJAkqUj2PAPe+lMp0FOSJGkdtQ73vHDSLJbXaLinDQxJkopkh8/DZkNg6s9yVyJJkupEZbjntY++zJjx02sy3NMGhiRJRdLUGz41Fl6eAq/OzF2NJEmqE5Xhno+9+EZNhnvawJAkqWiGnQh9NiplYUiSJHWjWg73tIEhSVLRbNAPhp0AT0+EdxfkrkaSJNWZWg33tIEhSVIR7fFlWLkMnrgudyWSJKkOtYR77ltD4Z42MCRJKqIBO8A2+8CMa/xIVUmS1CM2Wb8PV57UzNgaCfe0gSFJUlHtcSos+hPMfSB3JZIkqU419Qr+qUbCPW1gSJJUVDseAhtvCdN/kbsSSZJU51qHe06ZW7xwTxsYkiQVVVMf2P1k+OP98JeXclcjSZLqXGW450lXT+O6qS/nLmkVNjAkSSqy4WMgesGM8bkrkSRJDWCVcM/bZxUq3DNrAyMiLo2IZyPiqYi4LSL6Vcw7LyLmRsRzEXFgxfSDytPmRsS5eSqXJKlKNhsIO4wqfRrJ8qW5q6lLjkckSVpV63DPU64pRrhn7isw7gd2SSntCjwPnAcQETsBo4GdgYOAyyOiKSKagMuAUcBOwHHlZSVJql/NX4LFb8CcSbkrqVeORyRJaqUl3PN7R+/K1HnFCPfM2sBIKd2XUlpe/nIqMKj8/DBgQkppaUrpRWAuMKL8mJtSmpdS+gCYUF5WkqT6NfSz0H8oTL8qdyV1yfGIJEntO7ZA4Z65r8Co9CXg7vLzgcArFfPml6e1N71NETE2ImZExIyFCxd2c7mSJFVJr16lqzBemQqvz8ldTb3r1vGIYxFJUj2oDPf8yrUzePO9D7LU0bunf0BEPAB8pI1Z56eUJpWXOR9YDvyq5dvaWD7RdsMltfezU0rjgHEAzc3N7S4nSVLh7XYCfGRX2OITuSupSbnGI45FJEn1oiXc88lXFtF/o/Wy1NDjDYyU0gEdzY+Ik4FDgP1TSi1v7POBwRWLDQJeLT9vb7okSfVrw/4wdN/cVdQsxyOSJK27Tdbvw6e33zzbz8/9KSQHAd8GDk0pLa6YNRkYHRF9I2JbYHtgGjAd2D4ito2I9SgFa02udt2SJKl+OB6RJKk29PgVGGvwU6AvcH9EAExNKZ2eUpodETcDcyhdynlmSmkFQEScBdwLNAFXp5Rm5yldkiTVCccjkiTVgPjrVZL1rbm5Oc2YMSN3GZIkFUpEPJ5Sas5dRyNwLCJJUts6Ox4p0qeQSJIkSZIktckGhiRJkiRJKjwbGJIkSZIkqfBsYEiSJEmSpMKzgSFJkiRJkgrPBoYkSZIkSSo8GxiSJEmSJKnwbGBIkiRJkqTCs4EhSZIkSZIKzwaGJEmSJEkqPBsYkiRJkiSp8GxgSJIkSZKkwouUUu4aqiIiFgIvd+N/uTnw3934/9ULt8vq3Carc5uszm2yOrfJ6npim2ydUhrQzf+n2tBNY5F6Oy/qaX3qaV2gvtanntYF6mt96mldwPVZF50ajzRMA6O7RcSMlFJz7jqKxu2yOrfJ6twmq3ObrM5tsjq3iertGKin9amndYH6Wp96Wheor/Wpp3UB16cavIVEkiRJkiQVng0MSZIkSZJUeDYwum5c7gIKyu2yOrfJ6twmq3ObrM5tsjq3iertGKin9amndYH6Wp96Wheor/Wpp3UB16fHmYEhSZIkSZIKzyswJEmSJElS4dnAWIOIOCginouIuRFxbhvz+0bETeX5j0XENtWvsro6sU3GRMTCiJhZfnw5R53VFBFXR8SCiJjVzvyIiB+Xt9lTEbF7tWustk5sk89ExKKK4+TCatdYbRExOCJ+ExHPRMTsiPh6G8s01LHSyW3SUMdKRKwfEdMi4snyNvnnNpZpuPcerfn9t8jaO9cj4uKI+HPF+X1w7lo7KyJeioiny3XPKE/rHxH3R8Qfy/9+KHedaxIRO1Rs/5kR8XZEnF1L+6atMUd7+6Lo77PtrMulEfFsud7bIqJfefo2EbGkYh9dka/ytrWzPu0eWxFxXnnfPBcRB+apun3trM9NFevyUkTMLE8v9P7p4HW52OdOSslHOw+gCXgBGAqsBzwJ7NRqma8CV5SfjwZuyl13AbbJGOCnuWut8nYZCewOzGpn/sHA3UAAewKP5a65ANvkM8B/5q6zyttkK2D38vNNgOfbOH8a6ljp5DZpqGOlvO83Lj/vAzwG7NlqmYZ67/HRufffIj/aO9eBi4FzctfXxXV6Cdi81bTvAeeWn58LXJK7zrVcpybgv4Cta2nftDXmaG9fFP19tp11+RzQu/z8kop12aa9cVZRHu2sT5vHVvk14UmgL7Bt+TWvKfc6rGl9Ws3/AXBhLeyfDl6XC33ueAVGx0YAc1NK81JKHwATgMNaLXMY8Mvy84nA/hERVayx2jqzTRpOSulh4M0OFjkMuDaVTAX6RcRW1akuj05sk4aTUnotpfSH8vN3gGeAga0Wa6hjpZPbpKGU9/275S/7lB+tA6sa7b1HNf7+20DneuW5+Uvg8Iy1dMX+wAsppZdzF7I22hlztLcvCv0+29a6pJTuSyktL385FRhU9cK6aC3Hg4cBE1JKS1NKLwJzKb32FUZH61N+Hz4WuLGqRXVRB6/LhT53bGB0bCDwSsXX81n9zfZ/lim/sCwCPlyV6vLozDYBOKp8adHEiBhcndIKrbPbrdHsVb5M/u6I2Dl3MdVUvuR/GKW/rldq2GOlg20CDXasRERT+RLUBcD9KaV2j5MGee9RHb02tHGun1UeM1xdC7dcVEjAfRHxeESMLU/bMqX0GpR+OQC2yFZd14xm1V++anXfQPv7otbPpS9R+it4i20j4omIeCgi9slVVBe0dWzV+r7ZB3g9pfTHimk1sX9avS4X+tyxgdGxtv6a1fqvYJ1Zpp50Zn3vALZJKe0KPMBfO3iNrNGOk874A7B1SumTwE+A2zPXUzURsTFwC3B2Sunt1rPb+Ja6P1bWsE0a7lhJKa1IKe1G6a9sIyJil1aLNORx0uDqYp+3ca7/DNgO2A14jdLl17Vi75TS7sAo4MyIGJm7oHUREesBhwK/Lk+q5X3TkZo9lyLifGA58KvypNeAISmlYcA3gBsiYtNc9a2F9o6tmt03ZcexagOwJvbPGsZgqyzaxrSq7x8bGB2bD1RePTAIeLW9ZSKiN7AZ9X3Z/Bq3SUrpjZTS0vKXVwLDq1RbkXXmWGooKaW3Wy6TTyndBfSJiM0zl9XjIqIPpTeJX6WUbm1jkYY7Vta0TRr1WAFIKb0F/BY4qNWsRnvvUR28NrR1rqeUXi837FZSGjMU6nLxjqSUXi3/uwC4jVLtr7dcUl3+d0G+CtfaKOAPKaXXobb3TVl7+6Imz6WIOBk4BDghpVIgQflWizfKzx+nlBnx8XxVdk4Hx1ZN7hv4n/fiI4GbWqbVwv5pZwxW6HPHBkbHpgPbR8S25a70aGByq2UmAyeXnx8NPNjyolKn1rhNWt0LdSil+6ka3WTgpHJ6757AopZLsxpVRHyk5Z79iBhB6fXojbxV9azy+l4FPJNS+vd2FmuoY6Uz26TRjpWIGBB/TZjfADgAeLbVYo323qPOjUkKq71zvdWY4QigzU+uKpqI2CgiNml5TilkcRarnpsnA5PyVNglq/z1uFb3TYX29kXNvc9GxEHAt4FDU0qLK6YPiIim8vOhwPbAvDxVdl4Hx9ZkYHSUPmlrW0rrM63a9XXRAcCzKaX5LROKvn86GIMV+tzpXe0fWEtSSssj4izgXkqpzFenlGZHxHeBGSmlyZR2+nURMZfSX79G56u453Vym3wtIg6ldInbm5Q+laSuRcSNlD4pYfOImA9cRCl4j5TSFcBdlJJ75wKLgVPyVFo9ndgmRwNnRMRyYAkwugF+AdsbOBF4upxvAPBPwBBo2GOlM9uk0Y6VrYBflgc9vYCbU0r/2cjvPWr//TdzWWujvXP9uIjYjdJlyC8Bp+Upb61tCdxW7q32Bm5IKd0TEdOBmyPiVOBPwDEZa+y0iNgQ+DtW3f7fq5V9086Y4//S9r4o9PtsO+tyHqVP5ri/fMxNTSmdTukTMb5bfn9cAZyeUirU1XjtrM9n2jq2yr9T3AzMofR7xJkppRU56m5PW+uTUrqK1fNjoPj7p73X5UKfO1HfY0BJkiRJklQPvIVEkiRJkiQVng0MSZIkSZJUeDYwJEmSJElS4dnAkCRJkiRJhWcDQ5IkSZIkFZ4NDEmSJEmSVHg2MCRJkiRJUuHZwJBUVRExKCK+kLsOSZLUOCLibyJiSsXXu0fEgzlrkrT2bGBIqrb9gd1zFyFJkhrKbGC7iGgqf/0D4JyM9UjqAhsYkqomIj4N/DtwdETMjIhtc9ckSZLqX0ppJaUmxs4RcRTwp5TSHyJiaERcFRETM5coqRMipZS7BkkNJCLuAc5JKc3KXYskSWocEfGvwHzgq8BBKaU/V8ybmFI6Oltxkjqld+4CJDWcHYDnchchSZIazlTgGuCyyuaFpNrhLSSSqiYiPgwsSikty12LJElqOM8CS4FLchciqWtsYEiqpm2BV3MXIUmSGtLXgfNSSu+1TIiID0fEFcCwiDgvX2mSOsMMDElVExEbAw8CGwJjU0qPZC5JkiTVuYjYDrgTmJJSOjV3PZK6zgaGJEmSJEkqPG8hkSRJkiRJhWcDQ5IkSZIkFZ4NDEmSJEmSVHg2MCRJkiRJUuHZwJAkSZIkSYVnA0OSJEmSJBWeDQxJkiRJklR4NjAkSZIkSVLh/X+yZ0UGef8y3wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t0 =0\n", "y1_0=2\n", "y2_0=1\n", "consts = sym.solve( [sym.Eq( y1_0, solgen[0].rhs.subs(t,t0)) , \n", " sym.Eq( y2_0, solgen[1].rhs.subs(t,t0)) ] , dict=True)[0]\n", "display(consts)\n", "\n", "solpar_1=solgen[0].subs(consts)\n", "solpar_2=solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(18,7))\n", "\n", "tt=linspace(0,3,101)\n", "yy_1=func_1(tt)\n", "yy_2=func_2(tt)\n", "\n", "subplot(1,2,1)\n", "plot(tt,yy_1,tt,yy_2)\n", "legend([r'$y_1$',r'$y_2$'])\n", "xlabel(r'$t$')\n", "ylabel(r'$y$')\n", "\n", "subplot(1,2,2)\n", "plot(yy_1,yy_2)\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy)\n", ">Calculer la solution **exacte** du problème de Cauchy \n", "$$\\begin{cases}\n", "y'(t)=\\dfrac{3}{2} y(t) \\left( 1-\\dfrac{y(t)}{6} \\right),& t>0\\\\\n", "y(0)=1.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{d}{d t} y{\\left (t \\right )} = \\frac{3}{2} \\left(- \\frac{1}{6} y{\\left (t \\right )} + 1\\right) y{\\left (t \\right )}$$" ], "text/plain": [ " ⎛ y(t) ⎞ \n", " 3⋅⎜- ──── + 1⎟⋅y(t)\n", "d ⎝ 6 ⎠ \n", "──(y(t)) = ───────────────────\n", "dt 2 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\left [ y{\\left (t \\right )} = \\frac{6}{e^{C_{1}} - e^{3 t}} \\left(- e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right), \\quad y{\\left (t \\right )} = - \\frac{6 \\left(e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right)}{e^{C_{1}} - e^{3 t}}\\right ]$$" ], "text/plain": [ "⎡ ⎛ ___________⎞ ⎛ ___________⎞ ⎤\n", "⎢ ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟ ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟ ⎥\n", "⎢ 6⋅⎝- ℯ + ╲╱ ℯ ⎠ -6⋅⎝ℯ + ╲╱ ℯ ⎠ ⎥\n", "⎢y(t) = ───────────────────────────, y(t) = ───────────────────────────⎥\n", "⎢ C₁ 3⋅t C₁ 3⋅t ⎥\n", "⎣ ℯ - ℯ ℯ - ℯ ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "phi= sym.Rational(3,2)*y(t)*(1-y(t)/6)\n", "edo= sym.Eq( sym.diff(y(t),t) , phi )\n", "display(edo)\n", "solgen = sym.dsolve(edo,y(t))\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$y{\\left (t \\right )} = \\frac{6}{e^{C_{1}} - e^{3 t}} \\left(- e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right)$$" ], "text/plain": [ " ⎛ ___________⎞\n", " ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟\n", " 6⋅⎝- ℯ + ╲╱ ℯ ⎠\n", "y(t) = ───────────────────────────\n", " C₁ 3⋅t \n", " ℯ - ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solgen=solgen[0]\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left \\{ C_{1} : \\log{\\left (25 \\right )}\\right \\}$$" ], "text/plain": [ "{C₁: log(25)}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$y{\\left (t \\right )} = \\frac{6 \\left(- e^{3 t} + 5 \\sqrt{e^{3 t}}\\right)}{- e^{3 t} + 25}$$" ], "text/plain": [ " ⎛ ______⎞\n", " ⎜ 3⋅t ╱ 3⋅t ⎟\n", " 6⋅⎝- ℯ + 5⋅╲╱ ℯ ⎠\n", "y(t) = ────────────────────────\n", " 3⋅t \n", " - ℯ + 25 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t0=0\n", "y0=1\n", "consts = sym.solve( sym.Eq( y0, solgen.rhs.subs(t,t0)) , dict=True)[0]\n", "display(consts)\n", "solpar=solgen.subs(consts)\n", "display(solpar)\n", "\n", "func = sym.lambdify(t,solpar.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(10,7))\n", "tt=linspace(0,3,101)\n", "yy=func(tt)\n", "plot(tt,yy)\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy)\n", ">Calculer la solution **approchée** du problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\sin\\left(t y(t)\\right), & t>0\\\\\n", "y(0)=a\n", "\\end{cases}$$\n", "pour $a=-2,-1,-\\frac{1}{2},-\\frac{1}{10},0,\\frac{1}{10},\\frac{1}{2},1,2$ et afficher le champ de vecteurs." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint\n", "\n", "phi = lambda y,t : sin(t*y)\n", "tt = linspace(0,10,201)\n", "\n", "figure(figsize=(10,7))\n", "\n", "T,Y = meshgrid(linspace(0,10,31),linspace(-3,3,31))\n", "DT, DY = 1, phi(Y,T) \n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M == 0] = 1 # avoid zero division errors \n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "grid()\n", "\n", "for y0 in [-2, -1, -0.5, -0.1, 0, 0.1, 0.5, 1, 2]:\n", " sol=odeint(phi,y0,tt)\n", " plot(tt,sol,lw=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy - système)\n", "> 1. Calculer la solution générale **exacte** du système \n", "$$\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}'\n", "=\n", "\\begin{pmatrix}\n", "0&1\\\\\n", "-1&0\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}\n", "$$\n", ">1. Pour $x(0)=-1$ et $y(0)=1$, afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe.\n", ">2. Afficher ensuite $x\\mapsto y$.\n", ">1. Calculer analytiquement $E'(t)$ avec\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHQAAAArBAMAAABbbLE2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrvvmVREEIndzSJ2Zqtw62vAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACo0lEQVRIDZ1UPYgTQRT+skl2Nn93h61FgtrpmSBiI0K0Og69i6VYGNDGKotXKSGX4hrlijSCcCIriIU2i39goezBIRbB28JGRUitV0QhxkLQ92Y2MPnxYOcj+2be++bbzLx9bwDGgZNyMDIDIxWL7KGx1OkYS7NVQ+mLzWLNTGqfRtk1k66FWDZTYtXFPUPpCYhfZlLxG+m+oXSAOe+ymfYYPvXaZtJW9+BeXZPmQnb+v483TKd9tpO4IQNzMzmiREny36WdME/J34LwJsIjN0vvzPi4NfK1sVCl7fSBTS2mTz+ScwVwAj2o5vRGpDxgbZqSkS2yVH2iMs2/plCmDWTr0xxFch0yXH2Pdbr54dX7ADvAtfKRAE5V52gudgI8d/NV2Od+ngc2NFq0C/czHhYpRGdBwWPOeSJR5aldwS6sUKUCn5mO4LjO0PZxl1zupDTvTMdLysAhZGoqFbikcQJWidxT9PBZEn0yOtxkgD9I1lUqUMTfEWjlfAAplZ00JUXDTfxAsg6s00NSHcUF8mjDdh8u7A5T0Vl7PF9GviI33IAArnMoQtrdRd7lNDleeiFK04jk8TisnkzTHVzEWJoatTKotCnpqV6TTJtWj2EFjVB+sxURAEsa1+o2L4RyI7lFGrO8+zG0uqu+PMezrxR/OMZJhwuRcVMNY5Y/GhciQXTYJg5XeYjA5c+YKv85T2aey58Qlf98jdtohKNyMt10mdAKiLLUyqjpGq4svUirWj1aEcV4sLtneYhaXf0BbqvSY4KgLpgvyplh5QVTiHb5SJXejGX7h3JL2wPVRvuvm8Fe9a2h2SUuzvB1Qr/4SA35OuEbJTaSJe4h2UZxtett/qayjWJLa/iW9mUbxZVaQeGBA9lGcaVib/vtO8g2iin9B9t7pfBIEGuHAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\frac{d}{d t} x{\\left (t \\right )} = y{\\left (t \\right )}$$" ], "text/plain": [ "d \n", "──(x(t)) = y(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{d}{d t} y{\\left (t \\right )} = - x{\\left (t \\right )}$$" ], "text/plain": [ "d \n", "──(y(t)) = -x(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\left [ x{\\left (t \\right )} = C_{1} \\sin{\\left (t \\right )} + C_{2} \\cos{\\left (t \\right )}, \\quad y{\\left (t \\right )} = C_{1} \\cos{\\left (t \\right )} - C_{2} \\sin{\\left (t \\right )}\\right ]$$" ], "text/plain": [ "[x(t) = C₁⋅sin(t) + C₂⋅cos(t), y(t) = C₁⋅cos(t) - C₂⋅sin(t)]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "x = sym.Function('x')\n", "y = sym.Function('y')\n", "edo1 = sym.Eq( sym.diff(x(t),t) , y(t) )\n", "edo2 = sym.Eq( sym.diff(y(t),t) , -x(t) )\n", "display(edo1)\n", "display(edo2)\n", "solgen = sym.dsolve([edo1,edo2],[x(t),y(t)])\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left \\{ C_{1} : 1, \\quad C_{2} : -1\\right \\}$$" ], "text/plain": [ "{C₁: 1, C₂: -1}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$x{\\left (t \\right )} = \\sin{\\left (t \\right )} - \\cos{\\left (t \\right )}$$" ], "text/plain": [ "x(t) = sin(t) - cos(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$$y{\\left (t \\right )} = \\sin{\\left (t \\right )} + \\cos{\\left (t \\right )}$$" ], "text/plain": [ "y(t) = sin(t) + cos(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t_0=0\n", "x_0=-1\n", "y_0=1\n", "consts = sym.solve( [ sym.Eq( x_0, solgen[0].rhs.subs(t,t_0)) , sym.Eq( y_0, solgen[1].rhs.subs(t,t_0)) ] , dict=True)[0]\n", "display(consts)\n", "solpar_1=solgen[0].subs(consts)\n", "solpar_2=solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(17,7))\n", "tt=linspace(0,30,101)\n", "xx=func_1(tt)\n", "yy=func_2(tt)\n", "subplot(1,2,1)\n", "plot(tt,xx,tt,yy)\n", "legend([r'$x(t)$',r'$y(t)$'])\n", "subplot(1,2,2)\n", "plot(xx,yy)\n", "xlabel(r'$x$')\n", "ylabel(r'$y$')\n", "axis('equal');" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{1}{2} \\left(\\sin{\\left (t \\right )} - \\cos{\\left (t \\right )}\\right)^{2} + \\frac{1}{2} \\left(\\sin{\\left (t \\right )} + \\cos{\\left (t \\right )}\\right)^{2}$$" ], "text/plain": [ " 2 2\n", "(sin(t) - cos(t)) (sin(t) + cos(t)) \n", "────────────────── + ──────────────────\n", " 2 2 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiXZmMs1UEN0i77urRJlR0qN3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAUUlEQVQIHWNgYFQWYWBgCGOomMDAvICBMYCB+wAD23cG/gMMvN8Y6h8w8H5imC/AwAIkHzCwfISKAGXZvjFwb2Bg/g7VxdDGUOXAwFCodIQBAG3HFgUteuAKAAAAAElFTkSuQmCC\n", "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "E=(solpar_1.rhs)**2/2+(solpar_2.rhs)**2/2\n", "display(E)\n", "Ep=sym.diff(E,t).simplify()\n", "display(Ep)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système)\n", "> 1. Calculer la solution particulière **approchée** du système \n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t)+y^2(t)x(t)\\\\\n", "y'(t)= x(t)-x^2(t)y(t)\n", "\\end{cases}\n", "$$\n", "avec $x(0)=0$ et $y(0)=1$.\n", ">1. Afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe pour $t\\in[0,14]$. \n", "Afficher ensuite $x\\mapsto y$.\n", ">1. Afficher\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "Calculer analytiquement $E'(t)$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA+wAAAGtCAYAAACMQv5oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3Xd4HNXVwOHf7Kr3XizLKrZsucod29hGLrhgMIQSSkKAJBAIAQIJCTWm93wklIQSSiD0hO6GMZaNG+64yrYsyZLcVK3edne+P0YSxlVldmdGOu/z+Flpy8zZ9e5qztx7z1FUVUUIIYQQQgghhBDmYjM6ACGEEEIIIYQQQpxIEnYhhBBCCCGEEMKEJGEXQgghhBBCCCFMSBJ2IYQQQgghhBDChCRhF0IIIYQQQgghTEgSdiGEEEIIIYQQwoQkYRdCCCGEEEIIIUxIEnYhhBBCCCGEEMKEJGEXQgghhBBCCCFMyMvoADojKipKTU5O1mVbtbW1BAYG6rItM5LnZ23y/KxNnp+16f38Nm7cWKqqarRuGxSAvscE7tbdPzNGkdfVfeS1dQ95Xd3HKq9tR44JLJmwJycns2HDBl22lZWVRWZmpi7bMiN5ftYmz8/a5PlZm97PT1GU/bptTLTR85jA3br7Z8Yo8rq6j7y27iGvq/tY5bXtyDGBTIkXQgghhBBCCCFMSBJ2IYQQQgghhBDChCRhF0IIIYQQQgghTEgSdiGEEEIIIYQQwoQkYRdCCCGEEEIIIUxIEnYhhBBCCCGEEMKEJGEXQgghhBBCCCFMSBJ2IYQQQgghhBDChCRhF0IIIYQQQgghTEgSdiGEEEIIIYQQwoQkYRdCCCGEEEIIIUxIEnYhhBBCCCGEEMKEdEnYFUV5XVGUYkVRtp/idkVRlOcURclRFGWroigjj7ntGkVR9rb8u0aPeIQQQghhDDkmEEIIIfSj1wj7m8Cs09w+G0hr+XcD8E8ARVEigHnAWcBYYJ6iKOE6xSSEEEIIz3sTOSYQQgghdOGlx0ZUVV2hKEryae5yIfCWqqoqsFZRlDBFUeKBTGCJqqrlAIqiLEH7I/+eHnGdUUMlgTX54HKCze6RXQprUFWVg5UNhPp7E+Sry8fE2hxN0FgNdi/wCzU6GmEydU0OKuubiQvxQ1EUo8MRBrPsMYEQPZTLpVLd6KCyrpkGh5Mmh4tGh4tmp4uCKieVdc3YbGBTFOw2BUUBu6JgUxRsNvnOF8LdPJWJJACFx/xe1HLdqa73jH3fMGbDbbDtL5A8EWY+ChEpHtu9MJ/aRgfPfLWbr3Yc4cDRegASwvy5fEwiv5yY0rOSd1WFvV/B2n9C7jLtOsUO6XNg3G8habyx8QlDOV0qS/Kb+eMjX1Na0whon5VzB8Xy28y+xIT4GRyhMDFzHhMI0Q00NDvZUniUdXnl7DxYxe4j1eSV1nZpm39Z/dUpbwv19yY8wJvwQB8iAnwIC/AhIlD7PTxA+xcRqF2XEBaAv48MkAnRUZ7KPk52+k09zfUnbkBRbkCbOkdsbCxZWVldDsq7SSEg5UZiG/KIycmCnLPZNfA2yqLO6vK2zaKmpkaX18qs9Hx+JXUu/r6pgQM1KiNi7GQO9KHBobK3oon/W7KHV7P2cN0QX0bGei5pN+r/z7vpKOnZfyeyfBONPpEc7nMJTT4R+DWUELd3KV67viA7/VaOxE3t0n7k/WlNlY0qz25sIL/KxaBIG5m9vPG1Kewsb+I/a/L5YF0+l/X3YUqil6VH3Lvr/58JmPKYwBPkPeUePel1dakqBVUutpY62V3uZFe5C9dJPyUd422DEB8FXzt42RS8bNp14d5OUiJ8camgomqXqvbBdLigtlmlpqmRmtoGco5CdZNKTZNKk+vk+wnzVYgNUIgJsBEToBDbchkTYCPA27p/LzqqJ71nPa07vraeyjyKgMRjfu8NHGy5PvO467NOtgFVVV8BXgEYPXq0mpmZebK7dVhWVhgjMjOhIh8+vIah2x+HX3wGqefosn2jZWVloddrZUZ6Pb/i6gbO+/tKmhx2/v3LkUzuH/2j27cUHuX+T7fz3OZKfj+9D7dOTfPINDBD/v8ObIT3fgP1FTD7KXxH/5Iku/cPtzfVwvs/Y2D2cwxM6wujOl8XSt6f1tPocPKzV7/jcH0DN2X48qcrpv0oKc8rreXeT7bx1s4yGgNiefQnQ/CyW7MhSXf8/zMJ0x4TuJu8p9yju76uhysb+GB9If/bVERBeV27Hzc8MYxxqZEMTQhlQFwQSZGBeHfye7izr219k5OKuibKa5s4WtdMWW0jheV15JfVUVBWx+6yWr490Pijx0QE+pAUGUBaTBBDE0IZ2juM9Lhg/Ly736h8d33PmkF3fG09lbB/DvxOUZT30YrJVKqqekhRlMXAY8cUlZkB3O2hmH4sPBmuWwAvnwOf/AZuWg0BEYaEIjxLVVXu/t82qhua+fx3ExkQF3zCfYYnhvHRjeO555Nt/O3rvZTVNPHQhYMtPXp4UoXr4D+XgH84XL8U4oaeeB+fQLjyfXj/Kph/B/QeA7GDPB+r8DhVVZn32Q427K/g+StHEFyx54TPQEpUIO/8+iyeXbKH577JoaSmkX/8bGS3POASnWb+YwIhPKy20cFnWw7y1pp8sg9Xn/a+qdGBTEuPYXzfSEYlRRDq733a+xvB38eOv48/vcL8T3mfuiYH+8vqWv7Vkt9y+fWuYj7cUARoo/1pscEMTQhhaO8whiaEdtskXohT0SVhVxTlPbSz4lGKohShVXn1BlBV9SVgAXAekAPUAde13FauKMrDwPqWTT3UWmzGED6BcOlr8Oo0+PwWuPw/0N0SMnGCjzYUsTS7mPvPH3TSZL2Vn7edv16WQXSQLy+vyMXHy8Z9cwZ2n6S9aCO8/RMIioVrvoDQ0ywd9faDi1+FF0bBgj/CtfPls9IDfLu3lPfXF/LbzL5ckNGLrKw9J72foijcMWMAMSF+3Pfpdn7//hZe/NlI7FKcqEfoNscEQrjRtqJK/vb1HpZmF5/yPooC14xP5tJRvRkUH9LtCrwF+HgxMD6EgfEhP7q+tfDvtqJKth04yrYDVSck8f1jgxmbEsGEvpGclRppypMWQuhFryrxV57hdhW4+RS3vQ68rkccuojPgCn3wNIHYf8qrRid6LaqGpp5+MudnJUSwXUTks94f0VRuGt2Oo0OF6+tzCMm2JffnNPX/YG6W8V+eO9yCIjUku+Q+DM/JjASpj8AX9wGWz+AjCvcHaUwkKqq/PWr3SSE+XPb9LR2Pebn45JodLh4+Mud3P/Zdh69aEj3OcElTqlbHRMIoZNdh6p44Zsc5m87dMr7zB4Sxy/GJzMuNaJHf1cqikJCmD8JYf7MGhIHHJvEH2XbgUq+L6zk/fUFvLk6H5sCQxJCGd83kgl9oxiTHE6ATw8qEiy6PXk3n8y4m2DNi7Dyb5Kwd3PvfVdAdaOD+88f1O4z14qi8JfzB1Fc3cATi7JJiw1ianqsmyN1o4ZKePen4GyCaxe0L1lvNeIXsOltWDIPhlwCdjnD3V0t2XmE74sqeeqSYfh6tX8q4q8mplBS3chLy/cxIDaYa9pxYkwIIaxOVVW+2HqIu/+3ldom5wm3RwX58ocZ/Zmb0YvAntSBppN+nMRrxymNDiffF1ayel8pq/eV8frKPF5enou3XWF4YhgT+kYxfWAsQxJCevQJEGF98g1xMt7+MO5G+OYROLzt5Ot4heU1O128uTqf8amRDEnoWG9xm03hmcsy2F9Wx63vbeHz351NanSQmyJ1I1WFz34HpXvh6k8gun/HHm+zwTl/0hL+7C9h8E/cE6cwlMul8n9L9pAcGcDFIzveZetPMweQU1zNw1/uZGB8CGNTpD6IEKL7qW108Pw3Oby0fN8Jt9kUuHfOIK4a20dam+nE18vO2JQIxqZE8Pvp2pr4jfsrWL2vjNX7ynj+m738feleeoX6MWNwHDMGxTImJaLTBfiEMIok7Kcy5tfaCPuqv8Ml/zI6GuEG87ce4lBlA4/9pHMnZAJ8vHj1F6OZ89y3/O7dzXz82wnWK4Ly3cuw63OY8UjnOyP0mw5hfWD9a5Kwd1Nr88rIPlzNM5dldKriu82m8H+XD+fCF1bx23c2sej3k4gK8nVDpEII4Vn5pbXM+3wHy/eUnHDb0IRQHr5oCMMTwwyIrOcJ8PFiUlo0k9K0Tj/ltU0s3XWEr3Ye4b112vT5UH9vpqXHMGNwHJP7R8nUeWEJ8i49Ff9wGHUtrP0nzHwcgqLP+BBhLf9amUtaTBDn9O/8/22vMH/++tMMfvnmBh5fsIsHLxyiY4RudnALfHUfDJgD43/X+e3Y7DDqOq3uQ8luiB6gX4zCFD7ZdIAgXy/mDO3AconjhPh588+fj2TuC6u486Pvef3aMTJFUQhhSUfrmrj30+3M33rievQrxiRy58wBRMpJScNFBPpw2ehELhudSF2TgxV7Svlq52GW7irm480H8PWyMX1QLJeMTGBSWrSMvAvTkoT9dIZfBWte0EYgx/zK6GiEjnKKq9l+oIoHLmj/2vVTmZoey68npvCvlXlkpscwZUCMTlG6kaMRPr0JAqPgohe7XuF9xNWQ9bg2yn7eU/rEKEyhvsnJwu2HmTUkrsvTONPjQrhndjoPfLGTf6/O59qzU3SKUggh3KvR4eRvX+/ln1knTnefd8Egrhzbx3qz7HqQAB8vZg2JY9aQOJqdLtbnl7No+2G++P4g87ceIirIh7kZCVw8MoHBvWTNuzAXSdhPJ2YQRPWHHZ9Iwt7NLNx2GIDZXRgxPNadswawYm8J93y8jcW3TybEz+TF15Y/CcU74aqPtNkkXRUUDQMvgG0fwszHwC5fLd3Fkl1HqGl0dGrt+slcMyGZ5XtKeGxhNpP7R1uz9oMQosfYe6SaK15ZS1lt04+uvymzL7dP74+Pl4zKWo233caEvlFM6BvFfXMGkbW7mI83HeDttfm8viqPAbHBXDwygYtGJBAb4md0uEIg3zKnoyjamtz9q6D6iNHRCB0t2H6Y0Unhun0R+3rZefrSDI5UNfD4gl26bNNtDmyElc/CiJ9D/xn6bXfgBVBfAUXr9NumMNwnm4roFerHuJRIXbanKApPXjIMPy8bd328DZdL1WW7QgihF5dL5fmle0m+az7nPruiLVmfmh7Dxvumk//EHP48K12S9W7Ax8vGjMFxvHT1KNbdM52HLxpCgK+dxxdmM+GJb7jpPxtZva8UrRulEMaQYbAzGfwTbTRy1+cw9nqjoxE6yCutZdehKu4/f5Cu281IDOP6yam8vDyXOUN7MTEtStft66K5AT79LQTHayPheuo7DWzesHsBJE3Qd9vCEBW1TazYW8r1k1K7vHTkWDEhftw3ZxB/+t9W3l1XwM/HJem2bd24nARX7QUyjY5ECOEh+aW1XPPGOvaX1f3o+uevHMH5w+JlmnQ3Fx7ow9Xjkrh6XBK5JTV8sL6QDzYUsnD74baaR9dNTCEhzN/oUEUPI6cGzyRmIEQP1KbFi25h4XatSMysIXG6b/v26f1JjQ7kz//bSk2jQ/ftd1nW41CSDXOfA7+OtbI7I78QSJkM2Qu0dnHC8lbtK8XpUjl3UKzu275sdG/O7hfJEwuzOVRZr/v2u2zD64za9EcoXG90JEIIN1JVlf+s3U/yXfPJfCarLVkfmxzBpvvPJf+JOVyQ0UuS9R4mNTqIu88byNq7p/HUpcPw9bbxr5V5nP3ENyTfNf+kXQGEcBdJ2Ntj0FzYv1qb7issb9H2w2QkhrnlDKmft52nLx3Gwcp6nlyYrfv2u+TgZlj9HIz8hdaKzR0GzIbyfVpfd2F53+4pJcTPi4zeOp/cQZsa//hPhuFwubjvk+3mmm5YdRC+fpDy8OHQe7TR0Qgh3EBVVR6dv5OUuxdw36fb265/8pKh5D1+Hh/eOJ6IQB8DIxRm4Odt56ejE/nidxN54uIf2gBf8/o6ku+az1tr8g2LTfQckrC3R+oUQIX8lUZHIrqooraJrUWVTEt3XyX3UUkR/PLsFN5eu5+N+8vdtp8Ocblg/h8gIErrue4uA2Zrl7sXuG8fwiNUVWXF3hImpkV1qvd6e/SJDOCPMwawNLuYL07SHskwC/8Mrmb29L+x6x0UhBCmUtPo4Fdvrifl7gW8+m0eAJGBPiy/M5P8J+Zw+Zg+MpouTqAoCleM7UP+E3P48paJbdf/5bMdJN81n4e+2Ck1WYTbSMLeHgmjwDsA8lYYHYnoou/ytAR6Ql99Cmidyh3n9ic+1I+/fLYDpxm+wDe/pRWbm/GI/lPhjxXaG+KGwZ5F7tuH8Ih9JTUcqmxgUlq0W/dz3dkpZPQO5cHPd1BZ3+zWfbXLnsVazZJz/kSDvz5dJIQQxmtodnLlK2sZMm8xS7OLARidFM72B2ey8f5zSYoMNDhCYRVDEkLJf2IO390zjbiW4sWvr8oj9Z4F3P7BFnMc94luRRL29vDygT7jJWHvBtbmluHvbWdY7zC37ifQ14t75wxkx8Eq3l1X4NZ9nVFtGXz9ACSdDcN+6v79pWZC0QZoNuG6ZNFuy/eUAjDJzcUT7TaFR38ylPK6Jv729R637uuMHI2w6C6tnef4W4yNRQihC6dL5db3NpN+/yLW5JYBcNmo3ux5ZDb/vWkCQb5Sf1l0TmyIH2vvmcaOB2cyNiUCgE82H6DvPQv4w4ffy4i70I0k7O2Veo5WrEvau1na2twyRieHe6QVy5yh8UzoG8kzi3dTflz/Vo9a+gA0VMF5z3hmem/SBHA1ayP6wrK+3VtCanQgvcMD3L6vIQmhXDm2D2+t2c/uw9Vu398prXkRynNh9pPaiVohhGWpqspDX+yk7z0L+Pz7gwBckNGLPY/M5unLMqQlm9BNoK8XH/5mPLsfmcWUAdqstP9tKiL1ngU8/OVOc9VoEZYk31btlTJZu5RRdssqq2kk+3A141LdOx2+laIoPHThYGobHTy1yKACdIXrYdNbMO4miNW3jd0pJZ6lXe5f45n9Cd01OVyszS1jspunwx/rzhkDCPL14oHPdxhzcFN1EFY8A+nnQ9+pnt+/EEIXqqry4rIcUu5ewOurtDXq41Mj2f3ILJ6/coQk6sJtfL3svHHdWHY/MqttxP21lXlavYQVuQZHJ6xMvrXaK26YtvY3b7nRkYhOal2/7qmEHaBfTDC/nJjCBxsK2VJ41GP7BcDlhPl3aD3XM+/y3H4DIiBmEBSs9tw+ha52HqqiodnFWS0HHJ4QHujDH2f0Z01uGQu2HfbYftt8dT+4HDDzUc/vWwjRZaqq8s53+0m5ewFPL94NQFpMEDsenMl7N4zD18tucISip/D1svPhb8az48GZDIgNBuDRBbtIvms+y1rqJwjREZKwt5fNDsmTZITdwtbmlhHgY2eYG1pUnc6t09KIDvLlL59t9+x6pi3vwOGtWqE532DP7Re0mg+F68Bpwl704ow2F2gtLEf0Cffofq8c24f0uGAenb+TuiYPvnf2r4bt/4Wzb4PwZM/tVwihiz0VTlLuXsC9n2jt2cIDvNl433SW3HEOgbJGXRgk0NeLxbdPZsN909tmdlz35nqS75pPSZ3L4OiElUjC3hF9xsHR/VBTYnQkohO+yy1ndHIE3m5qUXUqQb5e3HPeQLYWVfLplgOe2WljDXzzCPQeC0Mu8cw+j5U0AZpq4Mg2z+9bdNnmgqPEh/oRF+rn0f162W08OHcwBysb+GfWPs/s1OWEBX+CkN4w8XbP7FMIoYvK+mb637eQx75raLtuxZ1T2PyXGUQG+RoYmRA/iAryZc8js1lw66S26+5cUc+sv62g0eE0MDJhFZKwd0TCKO3y4CZj4xAdVtPoYE9xNaM8PGLYam5GL4b1DuXpxbtpaPbAl/Oqv0PNEZj5mDF9pPuM1y5lHbslbS6sYKRBn5WzUiO5IKMXr6zI5eBRD3Qa2Py2dmJp5iPg4/4Ce0KIrnO6VO786HsyHvyKJoc2Uvnu9WeR/8Qc+kTK51iY06BeIeQ/MYenLh0GQPbhagbct4iXlnvoBLWwLEnYOyI+AxSbVL+2oB0HKlFVPD4dvpXNpnDveQM5VNnAayvz3LuzyiJY/bw2sp44xr37OpXQBAjrI+vYLaikupHC8npG9HFv68PT+dPMAagq/PUrN7d5a6yBZY9phRIHXeTefQkhdLFybyl971nARxuLAPhtZl/enBXIhL7ubUEphF5+OjqRN2YGMGdoPABPLMwm+a755JXWGhyZMCtJ2DvCJxCi0+GAjLBbzdaiSgCGGpSwgzZyOGNQLP9YlkNJdaP7drT0YVBdMG2e+/bRHr3HwoHNxsYgOuyH9evGJeyJEQFce3YyH28uYufBKvftaM0L2kyUcx82ZiaKEKLdmp0upv41i5+/9h0ACWH+7HxoJn+alW5wZEJ0nKIovPizkWy4b3rbdVOeyeLn//pO+reLE0jC3lEJI7URdumpaClbD1SSEOZPlMFr2u6anU6jw8XfvnbTyOGBTbD1fRj/WwhPcs8+2is+A6qKoLbU2DhEh2wuPIq3XWFwL+NObgHcnNmPED9vHl+4yz07qD4Cq56DgXOhz1nu2YcQQhfLdheTdu9Ccku0Ecj3rh/HqrumEuAjBeWEtUUF+ZL/xBz+dvlwAFbmlJJ6zwK+3Sv1ssQPJGHvqF4job5cKz4nLGNr0VHDpsMfKzU6iJ+PS+L99YXsPVKt78ZVFb66DwKiYOId+m67M3ppf3w4tMXYOESHbNpfwaBeofh5G9sCKTTAm1um9uPbvaUs3+OGA5esx8HZCNMf0H/bQghdNDlcjHtsKde9sR6AsckR7HvsPMb39Vx7ViE84aIRCeQ8OptB8SEAXP3aOiY8vpRmp1STF5Kwd1xr4TlZx24ZlXXN7C+rM3Q6/LFunZZGgI+dxxdm67vhvV/B/lVaz3W/EH233RlxWlEVDn1vbByi3ZwulW0HKhmRaNx0+GNdPT6JxAh/Hl+wC6eeUwRLdsOmt2D0ryCyr37bFULoZuG2Q/S/byGHq7QK8J/dfDYf3jgeu02Wr4juyctuY8Ftk/jktxMAOFjZQNq9C2W0XUjC3mGxg8HuK+vYLWTrgaMADEswRxISEejDzVP68U12MevyyvXZqMulrV0PT4FR1+qzza7yD9N6WkvCbhn5ZbXUNTkZ3MsEJ3wAXy87f5qZTvbhav63qUi/DS+Zp9UkOedP+m1TCKGL2kYHQ+ct5qZ3tOOsqekx5D1+HhkmOZEohLuN6BNO3uPnMaFlJsnVr61j5rMrZG17DyYJe0fZvSF+GByUYlpW0VZwLsEcI+wA14xPJibYl6cXZ6PqUQ9hx8daa6op92rvUbOIz5CE3UJ2HdIKvA2MN0fCDnD+sHgyEsN4dskefVoi7l8DexbCxN9DoFSVFsJMPtlcxOB5i6ludACw8LZJvH7tGBQpCil6GEVRePf6cXzcMtq++0g1qfcsYPuBSoMjE0aQhL0zeo3QkhCXrCuxgq1FR0mODCA0wDyJrL+PnVumpbE+v6Lr63OdzfDNIxA7RGvlZibxGVCRD/UVRkci2mHXoSq8bAppsUFGh9JGURT+NHMAhyobeG9dQdc2pqrwzcMQFAtn3aRPgEKILnO5VGb//Vtu/0A7wTtnWDy5j51nqpOHQhhhZJ9wch87jwGxwQCc//xK7vlkm8FRCU+ThL0zYgZBUw1UdvHgUXjEjoNVDDHR6Hqry0cnkhjhz9OLd3dtmtOmt6AiD6b9BWwm+0jHZ2iXh+WPixXsOlRN3+ggfL2MLTh3vLP7RTE+NZIXl+VQ1+To/IZyl2l1Hib9EXwC9AtQCNFpheV1pN6zoG2Gz5e3TOTFq0Zik7XqQgBgsyksvn0yL1+t1dF697sCku+aT01jF/4eCksx2dG9RcQO1i6P7DQ2DnFGNY0OiirqSY8LNjqUE/h42bjj3P7sOFjFwu2HO7eRpjpY/hQkjoO0GfoGqIf41krxMi3eCnYdqmJgvPk+KwB/nNmf0pom3lyd37kNqKpW5yE0EUZdo2tsQojOeWXFPiY9tQyAyEAfch6dbcoT7EKYwczBcWx94IdjvSHzFrNsd7GBEQlPkYS9M2IGapfFO4yNQ5zRnpbWaQPizDmtbm5GAv1jg/jrkt04OtO6Y90rUHMYps8DM67xC4yCkN5wUFq7md3RuiYOVTaYdgrqqKQIpgyI5uXluVTWN3d8A7sXwsFNWqE5L1/9AxRCtFuz08XoR5bw2AKtW8q8Cwax8f5z8bLLYakQpxPi503+E3O4fHQiANe9sZ5b3pO6Wt2dfDN2hm8whCXJCLsF7DnckrDHmnPU0G5T+MOMAeSW1PLxpgMde3BDFax8FvqdC0kT3BOgHuKGQLF8VsxupwkLzh3vDzMGUFnfzGvf5nbsgS4XLHsUIvpCxlXuCU4I0S7ltU2k3buQ0pomAFbcOYXrzk4xOCohrOXJS4fx0Y3jAfji+4Mk3zVfn8KswpQkYe+s2MFwREbYzS77cDUBPnZ6h/sbHcopzRgUS0ZiGH9fupcmRwdG2de9DA1HYeq97gtOD9HpULpXK44nTGvXIe3klpkT9iEJoZw3NI7XVuZRVtPY/gfu+BiObIcp94Ddy30BCiFOa1NBBSMfXgKAv7edPY/Mpk+k1JMQojPGJEew48GZbb+n37+obWap6F4kYe+smEFQlgOODhw0Co/bfbiatNhgUxevURSF26enceBofft7TTdUwZoXof8srWuBmcUMBFczlHdwVFR41K5DVUQF+RAdbO7p4nec25/6Zicvr2jn+8npgKzHte/swRe7NzghxCn969tcLv7HagB+Oro3ux6ehY+XHIYK0RWBvl7kPzGnrWf7jGdX8J+1+w2OSuhNvik7K3YQqE4o2W10JOI09hypJt2k0+GPdU7/aDJ6h/Lishya27OWfd0rWqu0c/7s/uC6KjpduyzeZWwc4rS0gnPmHV1v1S8mmAuHJ/D2mv3tG2Xf8bF2cjXzbvN1URCih7j85TU8Ml/7G/DCVSN46tIMgyMSont59/pxPHnJUADu+3Q7v3pzvcERCT3pcvSiKMosRVF2K4qSoyjKXSe5/VlFUba0/NujKMrRY269nFUfAAAgAElEQVRzHnPb53rE4xExLZXiZW2uaZVUN1JW20R/E1aIP56iKNw2PY2iino+OdNa9sZqWPMCpM2EhJGeCbArovoDCpRkGx2JOAWnS2VvcY0puymczM1T+tHgcPKvlXmnv6PLCSue0UbX08/3THAC6KHHBeIEDc1Oku+az3d55QBk/TGT84f1MjgqIbqny8f04avbJwOwNLuY5Lvmd61tsDCNLifsiqLYgReB2cAg4EpFUQYdex9VVW9XVXW4qqrDgeeBj4+5ub71NlVV53Y1Ho+J7At2H1nHbmKt63iskoRMGRDD0IRQXliWc/qK8a2j65kWGF0Hrd91eJKMsJtYYXkdTQ4XaTHW+Kz0iwliztB43lqdz9G6plPfcednULobJt8po+se1GOPC8SP5JbUkH7/orbfsx+eRXJUoIERCdH99Y8N/tG69tR7FnSus4owFT2OYMYCOaqq5qqq2gS8D1x4mvtfCbynw36NZfeG6AEywm5i2S0V4vtbYEo8aKPst05Lo6C8jk+3HDz5nRqrYfULWs/1hFGeDbArogfKCLuJ5RTXANA3JsjgSNrvd1P7Udvk5PVV+Se/g8ulja5H9YdBp/uTJNygZx4XiDaff3+QqX9dDsCopHDyHj8PP2+7wVEJ0TME+nqR9/h5hPp7A5Dx4FfkFEsxOivTI2FPAAqP+b2o5boTKIqSBKQA3xxztZ+iKBsURVmrKMpFOsTjOTGDZNTQxPYcriYy0PxFtI41fWAMg+JDeOGbvScfZV/3KtSXwzknzDA1t5h0bR2xVIo3pZwSLWHvF22dhD09LoSZg2N5Y1UeVQ0neV/tXgDFO2DSH8EmiYKH9dzjAsGLy3K4taUv9J9npfO/myagKOYt/CpEd6QoCt/Pm8GFw7UlKNP/bwVZu4sNjkp0lqKqXVvboCjKZcBMVVV/3fL71cBYVVVvOcl9/wz0PvY2RVF6qap6UFGUVLQ/2NNUVd13ksfeANwAEBsbO+r999/vUtytampqCArq3EFqn/0fkpr3Dt9OfB+nlznbhnXl+VnB6Z7fQ2vq8bXDn8ea8//mVDYecfD85kZuGObLsJCGtudnczYybu2vqQ7ux7Zh8wyOsmNiD2cxMPtZ1o15nrrAPm3X9+T3p5n8a1sjW0ucPDe1Y+2VjH5++ZVOHljTwMVp3szt6/PDDarKqI1/wMtRy7qx/0DtZMKu9/ObMmXKRlVVR+u2QZPyxHGBu44J3M3oz4y7vb69kRVFDgDuHO3H4CjPnCzr7q+rkeS1dQ9Pvq6L8pp5f7e2fOy6wT6ck+jtkf0axSrv2Y4cE+jRkLYISDzm997AKebzcgVw87FXqKp6sOUyV1GULGAEcELCrqrqK8ArAKNHj1YzMzO7GjcAWVlZdHpbOysh7x0mDYqHXsN1iUdvXXp+FnCq56eqKiVZX3Hh8F5kZg71fGBdMNmlsuTQtyw95GJcfOAPz++7V6C5isgLHyMzabyhMXbYoXDIfpaxycEwOLPt6p76/jSbv+9cxaDeNjIzO/a+MsPz+7ZiPd8UVPDQzycS5NvyJ23PV7B8H8x9gXNGTuv0ts3w/CzK7ccF7jomcLfu/J665J+r2VhUC8CS2yeT5sHlaN35dTWavLbu4cnXNTMTpu88wq/f2sAbO5oIiu3DH2YM8Mi+jdAd37N6TIlfD6QpipKiKIoP2h/fE6q6KooyAAgH1hxzXbiiKL4tP0cBZwPWWRQe1V+7LN1rbBziBKU1TVQ3OOhroSm+rWw2hZsy+7KvpJYtxU7tSmczrH4eEs8CqyXroH1WFBsUyzp2s1FVlZziGvpZaP36sW6ZlsbRuuYf+s6qKqx4CkL7QMYVxgbXc/Xc44IeyOF0MWTeYjburwBg3b3TPJqsCyHObPqgWD69+WwAnv/mh2Urwhq6nLCrquoAfgcsBnYBH6qqukNRlIcURTm2uuuVwPvqj+fgDwQ2KIryPbAMeEJVVev8YY5I1ZKQ0j1GRyKOk9uyJjfVggk7wJyh8fQO92dBXsva3B2fQGUBTLzd2MA6y9sfwpOhRGo+mE1JdSPVDQ5LrV8/1vDEMCb2i+L1lXk0OpywfxUUrYeJt2nFQYXH9ejjgh7G4XTR796F1DRq0+B3PDiTmGA/g6MSQpzM8MQwlt+ZCWiFIa98Za2xAYl202NKPKqqLgAWHHfdX477/YGTPG41YK35ysfy8oWwJCiTEXazyS3VpuWlWrSFjJfdxvWTUpn3+Q7W55UxZuWzWqX1tJlnfrBZRfWHshNWuwiDtVaI72eRlm4nc8PkVH7x+jo+23KQn+5+DgKiYPjPjA6rR+uxxwU9iMul0u/ehW2/Zz88SyrBC2FySZGBbLhvOqMf+Zo1uWXM/vu3LLxtktFhiTOQxrRdFdVfpsSb0L7iGny9bCSEWavg3LEuG92bIG9YvehdrX3gxN9bu5d0ZD8tYXedpse88Li2CvEWnRIPMCktioHxISxelgV7F8PYG7RZHUIIt1BVldR7fjgfs+eR2ZKsC2ERUUG+bHtgBgC7DlUx5ZksYwMSZ2Tho3+TiErT2lVJEmIquaW1pEQFYrNZt5VMgI8X05O8GX/obZqDEmDIJUaH1DWRfcFRD1UHjI5EHCOnuIYgXy9iQ6zT/vB4iqLwm8mpzKz8CKfdD8b82uiQhOi2VFUl5e4fkvW9j87Gx0sOJ4WwkmA/b3Y8qM3azCutZfzjSw2OSJyOfMN2VVQaOBqgsvDM9xUek1tSY8mCc8e7LCyHsbbdfBl4ifXX40amaZdlOcbGIX4kp7iGvtGBlu+TPCcFfuK1iiW+50JgpNHhCNEtHZ+s5zw6G2+7HEoKYUWBvl7semgWAIcqG5ggSbtpybdsV0mleNNpdDgprKgnNdqa69ePNeDQJ9TZQ/lL4QgOVdYbHU7XRPbTLiVhN5V9JTX0tfB0+Fbe61/BjotHK6aypfCo0eEI0e0cPw0+59HZeEmyLoSl+fvYyX5YS9oPVjYw9a9ZxgYkTkq+abuqddRQKsWbRkFZHU6Xav0R9rJ9RJatp3nUL6nDj9e+zTM6oq4JjgPvQCk8ZyJ1TQ6OVDVatjhjm8Zq2PAGzvQLOOqbwCsr5D0mhJ5UVaX/fQtpree/V5J1IboNP29720h7bkktP31pzRkeITxNvm27KjAK/MKkUryJ7CtpqRBv9RH2715GVeyETrqJOUPj+WB9IbUtrXMsSVG0dezyWTGN/NI6AJKtnrBv/Dc0VuI96TZ+Pi6JRdsPs7+s1uiohOgWXC6V9PsX0ezUsvU9j8g0eCG6G38fe1shunX55dz49kaDIxLHkm/crlIUbVp8iYywm0VuqVb1OsXKSUhDJWx5h+KYiRAcy7VnJ1Pd6ODjTUVGR9Y1rUUahSnktyS1yZEW/qw4HfDdS5A0ERJGcd2EZLxsNl5fafEZKUKYgKqqjHh4CY0OrbBu9sOzpMCcEN1UsJ83m+4/F4BFOw4z77PtBkckWsm3rh4i+0F5rtFRiBa5JbXEBPsS7GfhIm2b34GmGop6XwDAyD7hZCSG8cbqfFwu1eDguiCyHxwtAEej0ZEItMqwYPER9t0LtKKf424CICbEj/OHxfPfjUVUNzQbHJwQ1nblq2uprNc+Rzsfmimt24To5iICfVhz91QA/r1mP6+ukPzGDCRh10NEKlQfhKY6oyMRaEmIpUfXXU5txDBxHDXB/dquvm5CMrkltXybU2pgcF0U2Q9UF1TkGx2JAPJLa4kO9iXI18voUDpv3SsQmggDZrdddc2EZGqbnHy8SVoICtFZD32xk7W55QB8P28GAT4W/p4QQrRbfKg/i38/GYBHF+xi8Y7DBkckJGHXQ2SqdlkhUzDNoKC8jqTIAKPD6Lw9i+Dofhh344+uPm9oPNHBvry5ysLvs8i+2qV0VTCF/LJaUqw8Hf7ITsj/Fsb8Cmw/jPxlJIaRkRjGv9dYfEaKEAZ557v9vN7yt2bN3VMJ9bfwjDUhRIcNiAvmP786C4DfvL2R7QcqDY6oZ5OEXQ8RLQm7TIs3XH2Tk5LqRvpEWDhhX/tPCOkN6Rf86GofLxs/O6sPy3aXkFtSY1BwXSSt3Uwlr7SO5CgLf1bWvwpefjDymhNuunZCErkltay08owUIQyQtbuYez/R1q5+ectE4kP9DY5ICGGEiWlRPPaToQCc//xKiqsaDI6o55KEXQ/hKdqlJOyGK6zQliUkWjVhP7xdGzEcez3YT5x++LOzkvC2K7y1Zr8BwenALxQCY6RSvAlUNzRTWtNo3fXr9Ufh+/dhyKUQEHHCzecNjScqyIe31uR7PDQhrGpfSQ3XvrEegJevHsWQhFCDIxJCGOmqs/pw3dnJAIx9bCmNDqexAfVQkrDrwT8MAiIlYTeBgjItYbfsCPt3L4GXP4z8xUlvjg725YJhvfhoQ6F1C2pFpEKFRU84dCP7Wz4rlp0Sv+UdaK7TTm6dhK+XnSvH9mFpdnHb94IQ4tQamp1M++tyAO6cOYCZg+MMjkgIYQbzLhjMkIQQAAbct8jgaHomSdj1EtEXyvYZHUWPV1CuHZgnWTEJaaiEbf+FYZeddMSwVWtBrY82WLTFW3gylFt4HX43YekK8S4XrHsVEs+CXsNPebefnZWETVF4e22+52ITwqLS79cOxIcmhHLzlH5nuLcQoif58pZJbT/PfWGlgZH0TJKw6yUiVZIQEygoryPI14vwAAsWyNn6ITjqYdR1p71bRmIYwxPDeHddAapqwYJaESlQdUBauxksv9TCPdhzvtaKfI694bR3iwv1Y9bgOD5YX0hdk8NDwQlhPTe+vbHt589uPtvASIQQZrXnEa0by9aiSv7+tSxt9CRJ2PUSkQpVRdBcb3QkPVpheR2JEQEoimJ0KB2jqrDxTYgbBr1GnPHuV43tQ05xDRv2V7g/Nr2FJwOq1o9dGCavrJa4ED/8fSzYV3ndKxAUCwPnnvGu10xIpqrBwedbDnogMCGs5+NNRSxqadu0/cGZ2GwW+/sphPAIHy8bq+7SerQ/+/UeVu+Toq6eIgm7XlorxcvaXEMVlNfRJ8KCFW0PbIQj22H0ddCOkw3nZ8QT5OvFe+ssmPS2FWmUGSlGyi+ttWaF+KOF2gj7yF+Al88Z7z4mOZz+sUG8v77QA8EJYS25JTXc8eH3AMy/dSJBvtJrXQhxaglh/rxx3RgArnr1OypqmwyOqGeQhF0vkdLazWiqqrYk7BZMQja8Ad6BWsXrdgjw8WLu8F7M33qIyjqLFZ8LT9YuK/KNjKLHKyivs+Z0+C3vapcjrm7X3RVF4aejE9lSeJTsw1VuDEwIa2lodjK1pcjcg3MHM7iXVIQXQpzZlAExXDshGYARDy+x5vJMi5GEXS9tvdil8JxRSqobaXS4rJewN1TC9v/B0EvBL6TdD7tqbB8aHS4+3XLAjcG5QVAMeAdoa5CFIWobHZTWNFmv/aHLBZv/A6nnQHhSux928cjeeNsVPpBRdiEA7QR3a5G5McnhXNNy8C2EEO3xwNzB2FuWz8x9YZXB0XR/krDrxT9c+ycj7IZprRBvuSSkrdjctR162JCEUIYkhPCe1YrPKYo2yi4j7IYpqtBqbVju5FZeFlQWnLLt4alEBPowY3Acn2w+ID1khYC2XusAH/5mvIGRCCGsavfDswDYdqDSmks0LUQSdj1FpEprNwO1JuyWSkI6WGzueFeM6UP24Wq+L6rUPzZ3Ck+RNewGsuRnBWDTW9qJ0fTzO/zQy0cncrSuma92HHFDYEJYx4cbClm+pwTQisxZrkirEMIUvOw2lv7hHADu/ngbhS3HFkJ/krDrKTwFjkrROaMUlNehKJAQbqGicx0sNne8C4f3wt/bzvtWO7PZOsJupZkB3UihFWej1JZB9nwYdgV4+Xb44RP7RZEQ5i/T4kWPVlbTyJ/+uxWAL2+RInNCiK7pGx3EvAsGATDpqWXWmvFpIZKw6yk8Watg7JR+v0YoKK8jPsQPXy8Ltana+GaHis0dL9jPmwsy4vn8+4PUNFrofReRAo56fJos2JauGygoryPI14vwAG+jQ2m/rR+AswlGtq/Y3PFsNq343MqcUhkFED3WqEe+BuA3k1MZkiBF5oQQXXfd2SlEBWldWy54YaXB0XRPkrDrKTwZVKfWj114XGsPdstoroedn8GgCztUbO54V4ztQ12T01p9plsqxfs1yPRkI7R+ViwzFVZVYfPbkDAKYgd3ejOXje6NosBHG2SUXfQ8t3+wpe3nu88baGAkQoju5rt7pgOw/UAVX+04bHA03Y8k7HpqrVosvdgNYbmWbrsXQGMVZFzepc2MSAwjLSaITzZb6ERRSy92//pDBgfSMxVW1JFotaUjxTs7XGzueL3C/JmcFs1HG4twumTanug5NuSX88lmraPIzodmGhyNEKK7sdsUvrxlIgA3vL2RWivN+rQASdj1JP2lDdPQ7ORIVaO1EvbvP4DgXpA8qUubURSFi0YksD6/wjpTfcMSAQX/ehlh9zRVVa13cmvTW1orwMEXd3lTV4xJ5FBlAyv2lugQmBDm19Ds5NKX1gDw2jWjCfCRdetCCP0NSQjlslG9ARg8b7HB0XQvkrDrKSQBbF6SsBugqKKl6nWkRZKQmhLI+RqGXQa2rq+5v3B4LwA+s0pPdi9fCO2NX4NMm/K0kppGGppd1vmsOBphx6ddXjrSatrAWEL9vflss0U+K0J00UUvaj2SRyWFM21grMHRCCG6s6cvy2j7+aXl0jlLL5Kw68lmh9BESdgNYLke7Nv/p9U7GHaFLpvrHR7A2OQIPtl8wDoVOsOT8a+XhN3TCsu1HuyJ4Rb5rOxdAo2VMLRzhRmP5+Nl47yh8Xy18wh1TTJlT3Rv6/PLyT5cDcD7N4wzOBohRE+w7p5pADyxMJuymkaDo+keJGHXW3iytHYzQEGZxfpKb30f4oZC7CDdNnnRiAT2ldSy42CVbtt0K0nYDWG5lm7bPoKAKEjJ1G2TFw7vRV2Tk693Feu2TSHMRlVVLmuZCv/Or8/C2y6HfEII94sJ8eOOc/sDP3SmEF0j3956a+0vLTyqoLyeAB87kYE+RodyZiV74OBm3UbXW80ZGo+P3dZWWMj0wpPxaT4KTbVGR9KjtM5G6W2FonMNVbBnEQy5GOz6rbsdmxxBXIgfn1tlCYkQnfDrf28AICHMn7P7RRkcjRCiJ7l1Wlrbz6+uyDUwku5BEna9hSdBXRk0VhsdSY/SWkTLEm2qtr4Pik23Kb6tQgO8mZIezeffH8ThdOm6bbeI0CrFywkuzyosryM2xBc/767XTnC77PngaIChl+m6WZtNYe7wXmTtLqGitknXbQthBjnF1SzN1maQLPtjprHBCCF6pO9apsY/umAXlfXNBkdjbZKw662tUrxMi/cky/Rgd7lg64fQdyoEx+m++YuGJ1BS3cjqfWW6b1t30lXBEJaqEL/tIwjrA73H6L7puRm9cLhUFm6XZRmie1FVlen/twKA568cgY+XHOoJITwvNsSPGyanApDx4FcGR2Nt8i2uN0lCPM5SbaoKVkNloe7T4VtNSY8h2M+LT60w1belFzvlecbG0cNY5uRWTQnkZmmj626YOTO4Vwh9owOt01lBiHa6/7PtbT9fkNHLwEiEED3dPecNbPt5/tZDBkZibZKw6y0sSbuUhN1jSmuaqG92WiNh3/YReAdC+hy3bN7P286cofEs3n7Y/BWw/cNx2APls+JBTQ4Xh6oarFEhfuenWicFnafDt1IUhQuHJ7Auv5yDR+vdsg8hPO3A0Xr+s7YAgG0PzDA4GiGEgK/vmAzAze9uwuWySCcjk9ElYVcUZZaiKLsVRclRFOWuk9x+raIoJYqibGn59+tjbrtGUZS9Lf+u0SMeQ/mHg2+oVIr3oNYiWqZP2F1ObU1u/5ng475YLxqRQG2TkyU7j7htH7pQFOr946BCRtg95cDRelTVAp8V0E5uxQ6BmIFnvm8nzc3oharCl1sPum0fPZUcF3ieqqqc/cQ3ANw3ZyDBft4GRySEENAvJpjhiWEAXPPGOoOjsaYuJ+yKotiBF4HZwCDgSkVRTtar6gNVVYe3/PtXy2MjgHnAWcBYYJ6iKOFdjclQiqIVnpNRQ4+xTJuqgjVQWwKD5rp1N2OTI4gN8bXE1KN6/1iZEu9BBVb5rFTkQ+F3MOQSt+4mOSqQjMQwPtsiCbue5LjAGK+t/OG79NeTUg2MRAghfuy/N44H4Nu9pRyQWW0dpscI+1ggR1XVXFVVm4D3gQvb+diZwBJVVctVVa0AlgCzdIjJWJKwe9T+Mou0qdr5GXj5Qb9z3bobm01h9pB4svaUUNNo7mnxDX5xcLRAm30g3K7QKrNRtv9Pu3Rzwg5wYUYvdhysIqdYOnvoSI4LPMzhdPHI/F0ArLprqsHRCCHEj3nZbTz2k6EAbTOBRPvpkbAnAIXH/F7Uct3xLlEUZauiKP9VFCWxg4+1lvBkrUq8ywKttbqBgvI64kL8zN2myuWCXV9Av+ngG+T23Z03NJ4mh4tvWtr6mFW9fxy4mqFKCn95QmF5HT5eNmKCfY0O5fR2fga9x2onP91szrB4FAUWbJNq8TqS4wIP+2VLz/VxqREkhJn85LUQoke66qw+bT9bYRaomXjpsI2Tle89vqLAF8B7qqo2KopyI/BvYGo7H6vtRFFuAG4AiI2NJSsrq9MBH6umpka3bbXqVdJMf2cjq5d8QpNvpK7b7ih3PD8zqampYVtePSF2TP08QyqzGVl9iJ1KGsUdiLOz/38uVSXUV+Hf32wlpGJPhx/vKb6EArBl2accDR9mcDT6M9vnb+PuBiJ8VVasWK7L9tzx/Hwbihl/6Hv2pV5DoYdeu76hNj5am8Mw+49PHJnt/89C3H5c4K5jAndzx3vqaKOLFXu0KabX92uwzGuhJ/msuo+8tu7RU1/Xxyf6c/fKem5+dxMBZQEobugC0x1fWz0S9iIg8ZjfewM/WhCoquqxTaFfBZ485rGZxz0262Q7UVX1FeAVgNGjR6uZmZknu1uHZWVlode22ux1wN6XmJDeC5LG67vtDnLL8zORrKwsqpxOJqZFkZmZYXQ4p7Z4Cdi8GXTh7QzyC233w7ry/3dh1XY+WF/ImPETCfTV46Ouv7ULtcJ4w/uEwqhMY4NxA7N9/p7Z9i3pvX3JzByry/bc8vzWvgRA3zm30Teyr77bPoUcey6PzN9FytAxJEUGtl1vtv8/C3H7cYG7jgnczR3vqeS75gNw73kDmTa5Z65dl8+q+8hr6x49+XX9x85vKCyvZ3l1DA/MHaz79rvja6vHlPj1QJqiKCmKovgAVwCfH3sHRVHij/l1LrCr5efFwAxFUcJbisrMaLnO2qQXu8c0OVUOVzWYe02uqsLOz6HvFOhAst5Vs4fE0+hwsWy3eafFN/pGgc1LKsV7SEFZnbk/KwDZX0L0QPBQsg4wc3AcAAu3y7R4nchxgYes3lfa9vP1PTRZF0JYy+Lfa23e3lydT5NDlg+3R5cTdlVVHcDv0P6g7gI+VFV1h6IoDymK0loO+1ZFUXYoivI9cCtwbctjy4GH0f64rwcearnO2sISAUVau3lAab02U9LUScihLVBZAIPaW3NJH2NTIogM9OGrHeZt76ba7BCaqNV8EG5VWddMVYPD3D3Y68ph/2pIn+PR3SZGBDA0IZRFkrDrQo4LPOeqV78D4P0bxhkciRBCtE+AjxfnD9PO2V756lqDo7EGXebJqqq6AFhw3HV/Oebnu4G7T/HY14HX9YjDNLx8IaSXjLB7QEm9dmbO1G2qdn4Oih0GnOfR3dptCtMGxrBw22GaHC58vPSYUOMG4UlycssDCiss0NJtz2JQnR5P2AFmDYnj6cW7OXi0nl5StKvL5LjA/Y6dPTUu1dh6OUII0RHPXTGCL7ceYuP+CspqGokMMnkxXIOZ9Ai+GwhPloTdA0rqTD7CrqpaxeuUSRAQ4fHdnzsojupGB9/llZ35zkaRz4pHFFihpVv2lxDcC3qN8PiuZw3RpsUv3WXeGSlCHOu6N9YD8OUtEw2ORAghOsZmU/jzrHQApjyTZWwwFiAJu7tIEuIRJXUu/L3tRAX5GB3KyRXvhPJ9MHDume/rBpPSovD3tpt6WjxhSVBXBo3SB9udWhP2xAiTjh431UHOUm103Q1VY8+kb3QQqVGBLNll3poPQrRavOOH5RtDEjxXG0UIIfRyU6ZWq6aqwUFhyzGKODlJ2N0lLAmqD0Fzg9GRdGvF9Sp9ItzTFkIXu74EFEg/35Dd+3nbmdw/iiU7j6CqJ+2YaLy2Io0yLd6dCsvrCA/wJtjP2+hQTi53GTjqYaAxnxWA6YNiWbOvlOqGZsNiEKI9fvP2RgC+vmOywZEIIUTnPX2p1tJ30lPLDI7E3CRhd5fWJORogaFhdHcldS6Tr8ldBL1HQ3CsYSGcOyiOw1UNbC2qNCyG05KuCh5RUG7yCvHZ87UuCklnGxbCtPQYmp0q3+4tPfOdhTDIp5sPtP3cLybYwEiEEKJrLhv9QwdQGWU/NUnY3UWSELdTVZWSlhF2U6o+Agc3Qf9ZhoYxLT0GmwJLs0061bft5JaMsLtTYXkdvc36WXE6YPdC7bNiN24GwKikcMICvPl6p4mXkIge7/cfbAFg+Z2ZxgYihBA6+OtlGQBMflpG2U9FEnZ3CU/SLiUJcZuy2iYandDHrGty936lXRqcsIcH+jCiTzjLzJqw+4eDb4ic3HIjp0vlwNF6857cKlgD9eWGVIc/lpfdxtQBMXyzuxiHU3rDCvP5z1rtmMJuU0iKDDQ4GiGE6LpLRvUGtDrNRRUyyn4ykrC7S1AsePlJEuJGbVWvI02ahOxZBCG9IXaw0ZEwNT2GbQcqKa4yYU0FRdFqPsgadrc5XNVAs9PEs1F2LwC7L/SdZnQkTBsYy9G6ZjYVHDU6FCF+RFVV7vt0OyCj60KI7pKefq0AACAASURBVOWpS7S17FOfWW5wJOYkCbu7KIpUinezQjO3qWpugH3LoP9MQypeH2/KgBgAsvaUGBzJKYQnyWfFjQrKWirEh5vwswLabJSUSeAbZHQkTOofhd2mkLXbpDNSRI/15up8AIL9vOht1s+yEEJ0wk/HaGvZm5wuymoaDY7GfCRhdycZNXSr1iTElAcu+1dCc63h0+FbDYwPJj7Uz7zT4sOTteUjZq1kb3GFFSY+uVWeB2U50G+60ZEAEOLnzaikcLJ2m/TkluixHvxiJwCLfi+V4YUQ3c9ds7W+7Jf8c7XBkZiPJOzu1DrCLkmIWxSU1xHmq+DnbTc6lBPt/VpbEpEyyehIAFAUhcwBMXy7t5QmhwnX5oYng6MBaqTYlzsUltdhtynEh/kZHcqJcr7WLvuda2wcx8gcEM3OQ1VUNJjwsyJ6pFU5P3QuSAgzad0WIYTogt9MTgUgv6zOnMeqBpKE3Z3Ck6CpGuorjI6kWyooryMmwPjp5ie1b6nWnsrbPAdWUwZEU9PoYEN+udGhnEh6sbtVYXkd8aF+eNtN+JW/d4n2/x/Z1+hI2mT215aQbCt1GhyJEJqf/es7AD692bi2h0II4U6KovCTEQkA3Pnf7w2OxlxMePTWjbQlIXmGhtFdFZbXEe1vwrfw0QIo3QP9jC+gdayz+0XhbVdYYcYe02EtXRVkHbtbmLYHe3MD5K3QRtdNUOuh1cD4YGJDfNlaIgm7MF5eaW3bz8MTwwyMRAgh3OvJluJzn205aHAk5mLCbKcbaUtCZNRQb40OJ4eqGog24wh7zlLt0gQVr48V6OvFqKRwvt1rwrW5YX20S0nY3aKg3KQt3favAkc9pJlnOjxoZ/nP6R/NjjKntHcThrvg+ZXAD72KhRCiu/LxsrUdr/y7pdCmkITdvcJl1NBdDlTUo6oQ7W/ChH3fUq2dW/QAoyM5waS0aHYcrKLUbBU4vf0gOF4rPCd0Vd/kpLSmkUQzJuw5S8HuA8kTjY7kBJkDYqh3wK5D1UaHInqwhmYnNY0OAC4emWBwNEII4X4f3TgegHmf7zA4EvOQhN2dfIMhIFKSEDdo7cEeE2Cyt7CzGXKXQ7+pppri22pyWjTw4wJGpiFtEN2itUK8KRP23CzoMw58Ao2O5ART02N4bkoAQ3uHGh2K6MGeXJQNwOwhcSgm/JsihBB6iw35oUDuzoNVBkZiHibLdrohSULcorUHu+lG2Is2QGOV6abDtxrcK4TwAG9W7DFhwi5tEN2itf2h6abEVx+B4h2QOsXoSE7Kz9tOiK/Jvl9Ej/PGqnwAnrx0mLGBCCGEB712zWgALvrHKoMjMQdJ2N1NkhC3KCivw9fLRqjZDqhzs0CxQeo5RkdyUjabwsS0aL7dW4JqtnaD4clQdQAcJpuub3FtI+zh5ulYAGjF5gBSM42MQgjT2n6gsu3nED9vAyMRQgjPmjYwFoAmh4tmqSUjCbvbhSdDZSG4pNqwnlqrXptuimDecojPAP9woyM5pUlpURRXN7L7iMnW5oYnAypUFhkdSbdSUF5HoI+diEAfo0P5sdws8AvTPi9CiBNc+cpa4IeRJiGE6ElmD4kD4MmF2QZHYjxJ2N0tPAlcDm3kUOjGlFWvm2qhaD2kmHN0vdXEflEArM4pMziS47QVaZQ2iHoqLK8j0Wwnt1RVS9hTJoPNbnQ0QpiOw+miuqXYXOtIkxBC9CRPt3TG+NdKOS6UhN3d2nqx5xsZRbfy/+zdd5xkV3Xo+9+uqk7VuTpNz3Sanpw1UQmkkZCQhDA5OwgbDH42/tx3sUHw4IIvD7jYz77cB8Y8sMHogkGATBASymgklEYzGk3OnXPOuar2++NU9bRGEzpU1d6nan0/n/mcmu6qOquq+3Sddfbea2mtZ5MQqzS/6FycWXmT6UiuaHlBFtVFfl6osy1hr3G2soQkplr6J+w7VvrqYLhVpsMLcRn/9MRZwCl+KIQQqSgnwzd7+5xts0ITTBL2eJNe7DE3MD7D6FTQvhH2+mfAkwZV15uO5Kqury1if0MfobBF69hzloE3Qy5uxZDWenb5iFXqn3a2q+wsOCeEad/eVwfA199/jeFIhBDCnG99aAcAf/S9/YYjMUsS9njLrwDllSQkhqIt3axLQhqehco9kG5ZXJdw/aoiRiaDdrXL8HigoEraIMZQ7+g0EzMh+46Vxt9DXgUUrjQdiRDWOdVx4e9yfpYUmxNCpK67t5YD0DWc2gWJJWGPN28a5K+QJCSGmvrGAKgusigJGe+HjiPWr1+Pur62CIAX6ixr71ZYLRe3YuhCD3aLKsRrDY3PQ80bwKZ19UJY4sP//jIA3/jgdsORCCGEeatLcwD4xaHULUosCXsiSC/2mIr2YK8otChhb3oe0NavX48qzctkdWkOL9ZbuI5djpWYabFxNkrPGRjvdRJ2IcRraK1nR5L+IDKyJIQQqew7f7wTgE/+7IjhSMyRhD0RpBd7TDX3j1Oam0FWukXVpZteAF8mrNhpOpJ5u762iAMN/Xb1tyyohskhmBgwHUlSaO6z8OJW4++drSTsQrzO02e6AViWl2lXZwchhDBkVUnO7O2wTbWXEkgS9kQorIGxbqftl1gyK4toNT0PFbvBZ1mv6yu4flURY9MhjrUNmQ7lAqkUH1MtA87Frcw0my5uPQ95Ky78rIUQsz7+w1cA+PYf7TAciRBC2OPG1c5Szh+80Gg2EEMkYU+E6InpYLPRMJJFi2092CeHoPMYVN9oOpIF2bMyAMCBhn7Dkcwxe6xIwh4L1l3c0hoan5P160JcQjismQk5o0fbqwoNRyOEEPb4h/c4Pdm/9NBJw5GYIQl7Ikgv9piZDoZpH7Ksr3TLy6DDUH2D6UgWpDgng9ribA402pSwR9sgNhoNI1lY14O99yyM9bju4pYQifDgkXYA1i/LNRyJEELYZUXBheK5VrUkThBJ2BNBpvnGTNvgBFpbVkSr6Xnw+Jwp8S6zuybAgcYBe9YEZeZDVqEcKzEwHQzTYdvFrcbnnK2sXxfidT71gFNQ6R/fu81wJEIIYZ+960oA+N5z9YYjSTxJ2BPBXwRp2TJqGAOzPdhtaunW9AIs3+GK/usX270ywNDEDOe6R02HckGBtHaLhfbBCcK2XdxqfglyyiBQazoSIawTnQ6/eUW+4UiEEMI+X33nFmf729OGI0k8SdgTQSlnlF3W5S5Zs21tqqbHoe2Q66bDR+2pcdaxv2zVtPgaOVZiIHqsVBZa1IO95SWovFbWrwtxkVMdwwCkeeXYEEKIS1k+Z1q81pbMDE0QSdgTpVBau8VCS/84GT4PJTkZpkNxtB2E8IxrE/bKQBaluRmWFZ6rdgo0hi1qN+dCLQOWzUYZ7nB+rlXXmY5ECOt86TdOIaUvv2Oz4UiEEMJe68qcGh+Pneg0HEliScKeKIU1zjTfFLsiFGvNfeNUBvx4PJaMQrTsd7aVe8zGsUhKKXavDHDQthH20DSMdJiOxNWa+8dJ93ooy800HYqj5SVnWykJuxAXe7G+D4D37Kw0HIkQQtjry+90Lmr+3YOpVS1eEvZEKaiGmTEY7zMdiatZ16aq5WUoWe8USnOpPTUB2ocmaY2MyBonXRVioqV/nIrCLHsubjXvB18WlG81HYkQVhmfDs7e9tpyvAohhIV2R5Zydg5PGo4ksSRhTxRJQpZMa02LTQl7OAytB1xZHX6undXOxYZXmgYMRxJRIK3dYqGpb9ye6fDgjLCv2AneNNORCGGVb++rA+A9OysMRyKEEO7RNzplOoSEiUnCrpS6Uyl1Ril1Xin1mUt8/5NKqZNKqaNKqaeUUtVzvhdSSh2O/HswFvFYSfpLL9ng+AwjU0F72lT1nYeJAaeIloutX5ZLVpqXV5sHTYfiyK8E5ZHCc0ugtaa5b5yaomzToTimx6DjKFS5+1gR8yfnBfP3zd+dB+DTd6wzHIkQQtjv4zc5nWb+15PnDEeSOEtO2JVSXuBbwF3ARuCDSqmNF93tVWCX1nor8ADwD3O+N6G1viby721LjcdaMmq4ZNZViG992dm6dP16lM/rYWtFPq82WzLC7kuHvBVyrCxB/9g0I1NBe46VtldAh2T9eoqQ84L5C4cv1LUpzbOk3oQQQljsr25dDcAPX0qdgZ1YjLDvAc5rreu11tPA/cDb595Ba/201jq6QPYlIPXmfaX7IbtUkpAlsC5hb9kPmQVQtMZ0JEu2o7qQE+3DTM6ETIfiKKyRrgpL0NjnHCs1xRYdKwCV7l4+IuZNzgvm6fm6XgCqbVq+IoQQFsvLTL2ldb4YPMcKoGXO/1uBK817/AjwyJz/ZyqlDgJB4Gta619d6kFKqY8BHwMoKytj3759S4l51ujoaMye62q2e4sIN7zKkQTtDxL7+uLtmbppABqPH6TjtFOYx+Tr2316H5P+VRx79tm47SNRry9tKEgwrPnhQ/tYU+iN+/6iLvf61k2mE+g/zosu/9019fv5QrtTxKrz/An2dZ6K237m+/o2H3sMf9YKXt5/JG6xxEMy/f1MsLifF8TrnCDeLv6d+ur+CQDurgi55jXYSI7V+JH3Nj7kfV2aggzF4JTm33/9FCvzX3vemozvbSwS9kuVNL1k7zKl1B8Bu4Cb53y5SmvdrpSqBX6nlDqmta573RNq/V3guwC7du3Se/fuXXLgAPv27SNWz3VVA9uh4ZnE7Y8Ev744+23vEYpzerjjtltmv2bs9U0Mwr5msq/9E/beHL/9J+r1bRqZ4huvPglFK9kbWRuUCJd9feoAPP0Ue2+8FtKyEhZPrJn6/Xz1ibModY5333kzGb74XYCZ1+vTGg58FNbe5rq/Rcn09zPB4n5eEK9zgni7+Hfqw48+DMAn33crPq/UAV4sOVbjR97b+JD3dWk+42/mM784xrP9ufzp21+7NDUZ39tYfDq0AnMbh1YA7RffSSl1G/A54G1a69myflrr9si2HtgHbI9BTHYK1MJwG8xMmI7ElRr7xllpyxTftlecbZJM8S3JzaAykMWrLZasY492VRhsNhqGWzX3j7M8Pyuuyfq8DbXAWI9TIV6kCjkvmAetL1zDkGRdCCHm7107nFVUT5/pMRxJYsTiE+IAsEYptVIplQ58AHhNVVel1HbgOzgfyt1zvl6olMqI3C4GbgROxiAmOwVWOltZx74oTX1jVNtS9brtkLNdnjznkdsrCznUZEml+NmuCrKOfTEa+8bsWRPbetDZVuwyG4dIJDkvmIf9Df0ArCy25HNNCCFcIt2XWhc5l/xqtdZB4BPAY8Ap4Gda6xNKqS8ppaLVXf8fIAf4+UVtWjYAB5VSR4CncdaqJeUHM+CMsAP015uNw4XGp4N0DU/Zc2LTfgiK10JmvulIYmZHVQGdw5O0D1owAyQ6wj7QYDQMt2ruG7fo4tYr4M2A0k2mIxEJIucF8/PPkXZu/+VN7i9cKoQQiZYemZnUOjB+lXu6XyzWsKO1/i3w24u+9oU5t2+7zONeALbEIgZXiI6wS8K+YNEK8VaMGmrtJCG1t1z9vi6yrbIAgKOtQywvMLxuPLsE0nOgXxL2hRqenKFvbNqOYwWcEfbybU67PpEy5Lzg6p4771SIv2PTMsORCCGE+3z0jSv5l311/Pvzjfy3t17cOTS5pNZ8AtOyCiErIAn7IjT2jgFQY8Oo4XA7jHbBih2mI4mpDeV5+DyKo60WTItXyrnA1f+6+pPiKpqjLd1sSNhDM9BxWKbDC3EFWekW1JoQQgiX+fANNQB877nkH9yRhD3RArWSsC9CtK90lQ1JSHtk/XqSFdHKTPOyblkux9qGTIfiCKyCPknYF6opeqwELLi41X0SgpNJd6wIsVQT0yHTIQghhKuV5mWaDiFhJGFPNEnYF6Wpb4yi7HTyMtNMh+IUnPP4oGyz6UhibmtFPkdbh15TvdiYQC0MNkEoaDoSV2nsc2ajWDElPtpNQRJ2IV7jkeMdANy2odRwJEII4X7BUNh0CHElCXuiBWphqBWCU1e/r5jV2DtuRwICThJStgnSku/K3taKAoYmZmZrBhhVtArCQRiS1m4L0dw3TnFOBtkZMSlRsjTthyGz4EIRQSEEAP+x3/m79qFrqwxHIoQQ7rWzuhCA35/rNRxJfEnCnmiBWtBhaVe1QE19Y9TYUCE+HHaSkCQdMdyywql6f7TVgmnxgVXOtk9mpCxEY9+YHevXwVm/vvwapyaBEGLWK00DANy8VkbYhRBisd6/uxKA+w8k9+COJOyJJq3dFmxyJkT70KQdBef662BqCJYnV8G5qHXLckn3eewoPDd7rMg69oVo7h+3o9ZDcAq6TkL5NaYjEcJaXo9czBJCiMW6e0s5AI+d6DIcSXxJwp5okrAvmFUt3TqOONvlyZmEpHk9bCzPs2OEPac00tpNjpX5mpwJ0WHLxa3ukxCeSdpjRYjFGp6cMR2CEEIkBSuW/yWAJOyJ5g9ARr4kIQtgVUu3jiPgzYCS9aYjiZutFfkcbxsiHDZceE4p5wKXVIqfN6subrUfdrYywi7EazxyzCk4d9dm6b8uhBDi6iRhT7TZ/tKSsM9X02xfaUsS9rKN4LWgWn2cbFmRz9h0iPrIhRKjArUyJX4BosdKtRXHymHIzJeCc0Jc5DdHnIT9XTsqDEcihBDul5nmpLPdw5OGI4kfSdhNkNZuC9LYN0ahP418v+EkWWvoPArLtpqNI842LXcKz53sGDYcCU6l+IEmCMkU0vlo6ovORrFkhL18mxScE+Iiz513qhm/YXWx4UiEEML97t6yHIBHjncajiR+JGE3IVALg82ShMxTY9+YHSOGQy0wMQDlyZ2wry7NIc2rONFuwTr2wCrQIed4EVfV1DdOXqaPAn+62UCC084adpkOL8RlZaV7TYcghBCud/dWZ3nRw5HlRslIEnYTArWShCxAY++4HSOG0YJzSZ6EpPs8rC3L5WS7BSPsUqRxQRptaX/YfRJC01JwTgghhBBxdWNkttLLDf2GI4kfSdhNmE1CGszG4QJTwRDtQxN2jLB3HAXlgdKNpiOJu43leZxsH0Zrw4XniqK92GUd+3w0949TFbDg4lbnUWeb5Be3hFiosRnDf1OFECLJZPiSf7aSJOwmyKjhvLX0T6A11BRbkIR0HIHidZBuQSxxtml5Hn1j03QNT5kNJLsE0nPlWJmHmVCY1oEJO4ozdh53WvIVrjQdiRBWaRwKA7BnZcBwJEIIIdxCEnYTckohLVuSkHmItnSzYoS982jSr1+P2jhbeM7wOnaloEgqxc9H28AEobC2o6Vb13FnJopHPmKEmOvMQAiAPTWSsAshRKwFQ2HTIcSFnE2ZEO0vLQn7VTVGql6vNJ2wj3bDSIdT9ToFbCjPBeBEmyXr2GVK/FU19VvS0k1rZ4R92WazcQhhobORhH23jLALIUTMrF/mnLcebbOgYHIcSMJuivRin5cLVa8Nt3TrPOZsy1IjCcnNTKO6yG9Ha7fAKumqMA/WtHQbbIapoZQ5VoRYiLMDzujPjqoCw5EIIUTyuK62CICDjclZeE4SdlMCtTDQCOGQ6UisFq16rUz3cu464WxTKAnZtDyPEzZUii+S1m7z0dQ3Tlaal5LcDLOBdB13tstSY/mIEAsRjtScy800fBFaCCGSyLZKZynnkVYZYRexFKiF8AwMtZqOxGpNfePmp/iCk7DnlkN2kelIEmZjeR7N/eMMTxoe2Y4WaZRp8VfU0DtGdZHf/MWtzuOAgrLk76YghBBCCPO2Vjizlo60DBqOJD4kYTdFKsVf1XQwTOuAJT3Yu09A2SbTUSTUhvI8AM52jpgNJBBp7SaF566ovmeU2hIbLm4dc/6+pVsQixBCCCGSXrTWVevAhOFI4kMSdlMkYb+q1oFxwhrzbapCM9BzJuUS9nWRAh6nTSfs2cWQkSfHyhVMB8O0DExQW5xjOhQpOCfEZUwFZQmcEELEg8djeHZhnEnCbkpuOfiyJAm5gqY+p+q18R7sfechNA2lqZWwryjIIjfDxxnTCbtSTpFGmRJ/Wc3944TC2vwI+9QIDDRA2RazcQhhoehn2spimX0ihBBi/iRhN8XjcYpp9Z4zHYm1GiI92KsChk9uZgvOpVbCrpRi7bJc8wk7ONPiZUr8ZdX3jAJQW2J4hL3rpLOVEXYhXudcl3Ocri2zYCaMEEII15CE3aSi1dB71nQU1qrvHSU300dxTrrZQLqOg8cHxWvNxmHA2rJcTncOo7U2G0hRpLVbcNpsHJaKXtwyPnLXHbm4VSoF54S42PluJ2FfXSoJuxBCiPmThN2k4rUw2ATBKdORWKm+Z4xVJTnmq153nYDideAzfOHAgPXLchmeDNI5PGk2kEAt6LC0druM+p4xinPSyc8y3Cqq+xSk50BBldk4hLDQuW5nttKa0lzDkQghRPKJLmOfDhkeZIoDSdhNKl7jJCH9DaYjsVJdzyirTE/xBSdhT7Hp8FHWFJ6TSvFXVN87akfBue5TULrBqTsghHiNuh5nJoyMsAshROzVRGYZ9oxLwi5iqXiNs5Vp8a8zOhWka3jKfBGtiQEYbkvZhH19JGE3vo69aLWz7TtvNg5L1feMmZ8OD07CXrLedBRCWKl1wCk6V56faTgSIYRIPtHWbp3jYcORxJ4k7CbNJiFSeO5i0SJaxkfYu0872xRdk1vgT6csL8N8wp5dBFkBp72eeI2h8Rn6xqbNX9wa7YHx3pQ9VoS4mpHJIAA5mT7DkQghRPJZFrkYOjglI+wiljJynfZuvTJqeLG62YTdcBLSc8rZlqbuqOG6ZXnmp8QDlKyTrgqXUN9rSYX47kiF+NINZuMQwnIZPq/pEIQQIukEsp1aU6PTkrCLWCteI1PiL6G+ZwyvR1FVZLgHe/dpSMuGvAqzcRi0flkudd2jBEOGpxjJsXJJ9T2WVIjvic5GkYRdCCGEEIlV6HcS9hFJ2EXMFa1xpsSbbptlmbqeUSoLs8yPRPScdkZ2Pal7qKwty2U6FKapf9xsIMVrnSnX4/1m47BMfe+oc3ErYPri1knIKoScMrNxCCGEECLlzI6wzyRfTpW6WYgtitfC5BCM9ZiOxCp13WPm16+Dk7Cn+IjhmkhF43Ndo2YDKV7rbGWU/TXquseoCvhJ9xn+c959ylm/LhXihRBCCJFghdkywi7ipThSeE7W5s4KhTUNfWOsMt36ZrwfRrucEfYUFv05nO82vI5dEvZLOt8zar5NlNbO8pEUv7glhBBCCDMCs1PiDQcSB5Kwm1YUae0mleJntQ1MMB0MU2t8TW6kInlJaichORk+VhRkca7b8Ah7QRV4MyRhn2MmFKaxd2x2FoQxw+0wNSQt3YQQQghhRGF2GiBT4i9LKXWnUuqMUuq8Uuozl/h+hlLqp5Hv71dK1cz53mcjXz+jlLojFvG4Sn4l+LKkXdUcdZGq18ZH2KVC/KzVpTmcN52we7xOK0SZjTKrqW+MYFibH2Hvjh4rqX1xS1wg5wVCCCESKSfDaZkpCfslKKW8wLeAu4CNwAeVUhc34v0IMKC1Xg18Hfj7yGM3Ah8ANgF3Av8Seb7U4fFAyVpJ2OeoiySGxkfYu09Deo5zUSXFrYkk7KGw4T+CUin+NaIXUYwn7NGfiYywC+S8QAghROJFa/mYPlWNh1iMsO8Bzmut67XW08D9wNsvus/bgfsitx8A3qSUUpGv36+1ntJaNwDnI8+XEKNTQc4NhJgOGm5XVbJeEvY5znWNUpSdTlFOhtlAek4766aliBZrynKYCoZpG5gwG0jJOhhohJlJs3FYIpqwGy/Q2HsGsgKQXWw2DjEvSqknlVLb4rgL154XCCGEcCdfpKNTMjbeikXCvgJomfP/1sjXLnkfrXUQGAKK5vnYuPnd6W6+sn+S+l7DU31L1sFwK0wOm43DEue6R8yPGIJUiJ9jdWku4PxsjCpeCzoM/fVm47DEue5RVhRkkR2ZBmZMz9kLRQGFG3wa+LpS6t+VUuVxeH7XnhcIIYRwp3AkU0/CfJ1YnOVdavjx4vfqcveZz2OdJ1DqY8DHAMrKyti3b98CQry0geEQAA/ue5nOZeZOeIt6g2wBXnn8fkbyYnvSOzo6GpP3KlG01pxqH+f65b55xR2v1+ebGeUNo13UDftoMfj+2fLzG4usB3rsxSN4u9Jj9rwLfX05I8PsAk4880t6SrtjFke8xPvnd7h+gkC6MvY7En19N3Qcp7f4Ws5a8LsaS7Ycf7GmtT4E3KqUejfwqFLqF8A/aK1jNYUm7ucF8TgnSBQ3xeoWyXqs2kDe2/iQ9zX2JoPOR0VYJ9/f2Vhkqa3A3EW+FUD7Ze7TqpTyAflA/zwfC4DW+rvAdwF27dql9+7du+TAJ6ZDfPGFR8ksqWbv3jVLfr5F66uE419lZ2U2bN8b06fet28fsXivEqVzaJKJx55i7/Z17L2+5qr3j9vra3kZnodV193NqrVxeP55sunn96UDTxLKKWHv3tjNpF3w65u5Fg79DZtKPGDJ+3Il8fz5hcOarqce5batVezde/Hy4MTYt28fe3dvgX3DLN+yl+U37DUSR7zYdPzFWmT6+Rng28CXgT9XSn1Wa/3DGDx93M8L4nFOEHePPgyQtL9TJiXzsWqavLfxIe9r7A2Nz8CTj5PhTb6/s7GYEn8AWKOUWqmUSscpFvPgRfd5ELgncvs9wO+01jry9Q9EqsWuBNYAL8cgpnnJSvdSlKmo6zHdrqraaVfVc9psHBaITrleE5mCbUy0iFbRarNxWGRNaa75XuxpWVBYc6GCfwprG5xgciZsfvnIbMG5dWbjEPOmlHoOaMMp9rYC+DCwF9ijlPpuDHbh2vMCIYQQ7jQ2HQTA70u+2lNLHmHXWgeVUp8AHgO8wPe11ieUUl8CDmqtHwS+B/xQKXUe5wr6ByKPPaGU+hlwEggCf6W1Di01poUoz/GYT9i9Pqf6tRSe42yX87NYtKJDlQAAIABJREFUU2ZBEuJNdy6mCMCpRP7zgy1orVEmC/GVbLjQRiyFRQvOGe/B3hv5u1VscJaSWKi/AE5EEuS5/lopteSDy+3nBUIIIdxnZDKSsKcZDiQOYrJwW2v9W+C3F33tC3NuTwLvvcxjvwJ8JRZxLEZ5tuK59jHCYY3HYzIJWQetB83t3xLnu0cIZKdTbLpCfO85CKxyLqYIAFaV5jA2HaJzeJLy/CxzgZRugLOPQnAKfIZ/TwyypqVbz1nwZUF+ldk4xLxprY9f4dt3x2gfrj0vEEII4T7DkzMAZCXhCHsspsS7Wnm2h4kZJwkxqmQDDDbD9JjZOAw72zVqPgEBJ2GXEcPXWFWcDUB9j+Hf0dINoEPQd95sHIad7RqhOCeDAn/sigAuSu9ZKF4NnpT/OEkKWmtpwSCEEMJ1RiIJuz9NEvakU57tvAXGp8WXrAO0kyimKK0157pGzE/xDc3AQIMk7BepjfT6rjd+rKx3tik+Lf5M1wjrlxmu9QDOlPhiWb8uhBBCCHOGJ6Jr2A0HEgeSsOc4V2Hqui1JQlK48FzPyBTDk0HWlhlOQvobIByUvtIXKcvLIDvdS53pEfbiNaC8KX2shMOas10jxo8VT2gKBluk4JwQQgghjIpOiU/GonMpn7DnpytyM33mk5DASqfIWQqPGs4WnDM9wh6tei0j7K+hlGJlSTb1vYaPFV8GFK1K6WOluX+cyZmw8RF2/3gboOVYEUIIIYRRwxOyhj1pKaVYVZJjfkq8N82ZVtp1wmwcBp3tirR0Mz3CPtvSTZKQi9UW55ifEg/OjJQUTtjPRI6VtYYT9qyJSHtsOVaEEEIIYVD7kFOPLJAlCXtSsiJhByjbCN0nTUdhzOnOYYpz0inJNVz5u+885CyDzDyzcViotiQ70v/bcJel0g1OnYEZw8UiDTnTGUnYDbc/nE3YA7VG4xDCDdK8zkmk8b+fQgiRhJr7xgEokYQ9Oa0qzaZreGq2uqAxpRthuA0mBszGYcjpzhHWL7MgSe49K1N8L6O2JAetobHPhkrx4Qs9wFPMma4RqgJ+/OlmK6v4xzsgdzmk+43GIYQbrChw2mG2DU4YjkQIIZJPc7+TsJf6ky+9Tb5XtAi1xc4oVWPvuNlAyjY52xSc6huKFNFaZ7rqtdaRhF0Kzl1KbaS1W1236YR9o7NNwWMFnBF248cKkDXR5tQTEEJcVXWR8/ezwXTNHCGESELRhL0wQ0bYk1JNsTM61GB61DCasKfgOvamvjErimgx1guTQzLCfhm1JdFe7IaXkARWgTcDOo+ZjcOAqWCIht4x1pmu9QBkTXTIdHgh5mnjcmcG2amOYcORCCFE8krzmo4g9iRhB6oDThLSaLr6dW45ZBakZMIeXZNrfEp8f72zDcio4aX4032U52earxTv9TnT4lPwWKnrHiMU1sYLzjExSPrMsIywCzFPG8udz7eTkrALIUTceJSMsCelrHQv5fmZ5tflKuWMsqdg4blTnSN4FKwxXESL/jpnK6OGl1Vbkm1+hB2gbDN0HTcdRcJFuykYn40ye6xIwi7EfERH2CVhF0IIsRCSsEdUF/nNj7CDsza366SzljqFnOkcZmVxNpmm57H014PyQkGV2Tgstqokh/qeMbTp39Flm2GsB0a7zcaRYKc7R0jzKmoi62GN6YvMRpERdiHmJXrMNvUZrpcjhBDCVSRhj1hZnG3Hh2jZJpgegcFm05EklDUV4vvroaASfOmmI7FWTVE2I1NB+semzQYyW/MhtUbZT3YMs6Y0l3Sf4T/f/XVoFBSuNBuHEC7h9STfNE0hhLDBVDC522VKwh5RXZRN39g0w6Zbu81Wik+dafFjU0Ga+sbNT/EF6KuT6fBXES3S2Gj6AlfZZmfbmWIJe/vw7NRao/rqmMoogbRM05EIIYQQIoWd7nCWC24ot+D8KA4kYY+YnapmurVb6QZApVQSEl2Ta7xNldbQ3yBrcq+ienZap+ElJP6A0wM8hQrPdY9M0js6NVu8yqj+Osb95aajEEIIIUSKO9I6CMA1lQWGI4kPSdgjVkb6Sxtv7ZaR64zwdh4xG0cCnbLlqth4P0wNyQj7VVQUZqGUBSPs4KxjT6Ep8dFjxZYR9oms5aajEMKVjNcAEUKIJHK4JZqw5xuOJD4kYY+oCkSm+dpQeG7ZFug4ajqKhDnePkRepo+KwiyzgUiF+HnJ8HlZnp9Fs+mLW+AsIek5A0HD6+kT5GS7U116g+l6D+P9MDnIRJaMsAuxEAUZzjr2lv4Jw5EIIUTyOBJJ2LdWyAh7UrOmtRtA+VYYbIKJQdORJMSJ9mE2Lc9Hme6b2C9Vr+erpthvxwh72WYIz0DvWdORJMTJjmFWFGSR708zG0ifc3FLRtiFWJj1Aee068X6XsORCCFE8qjrcfK36IzpZCMJ+xzWtHZbts3Zdh4zG0cCBENhTncMs8mSKb4oj7R0m4fqomzza9gBlm11tp2pMSPlZPuQHdPhI7NRZA27EAuzpdhpXbrvTI/hSIQQIvkYbw8dJ5Kwz2FNa7fyaBKS/Al7fe8YU8Ewm1bYkITUQ34F+DJMR2K9miI/A+MzDI0b7qpQtArSsqEj+Ws+jE8Hqe8ds6PgXN95UB4mM8tMRyKEq2wr8QHw+Mkuw5EIIYRwC0nY57CmtVtOKeQsS4lRwxPtQwBsWm5BkYj+eqkQP0+zleL7DY+ye7yRmg/Jn7Cf6RxBa3sKzlFQhfYYnpovhMvkpDtLv0JhKTonhBCxMDGd3D3YQRL217CmtRukTOG5E23DZPg81Jpec6K1M81XCs7NS/RYsWIde/k251gJh01HElcnO5yCc1aMsPfXycUtIYQQQhi3v6EPgN01hYYjiR9J2OewprUbONPie07DzKTpSOLqePsQ68vz8HkN/ypODMCktHSbr2hXhSYbaj6Ub4OZsQtV/pPU8bZhO7opaA199VKcUYglklF2IYRYul8fbgfgD7YlbyFcSdjnsKu121bQIeg+aTqSuNFac7LdkoJzUiF+QbLSvSzLy7RnhB2Sflr8sbZBtlYUmO+mMNYD0yMywi7EIm2IzJI53DJgOBIhhHC/X77aBsBbt0rCnhKsa+0GSZ2EtA5MMDwZZLMN69f7pAf7QlUV+e2oFF+yDrwZ0HHYdCRxMxUMcaZzhM0rLDpW5OKWEItyxyanWOMjxzoNRyKEEMkjkJ1uOoS4kYT9Ita0ditcCZkF0P6q6Uji5nhbtOCcLSPsCgprTEfiGjVFlvRi96bBss3QnrwJ+5nOEWZCmq0VFiTs/ZKwC7EU79y+AoBfREaFhBBCiCuRhP0i1rR2UwqWb4f2Q6YjiZsjrUOkeRXry3NNh+IkIfmV0tJtAaqLsukdnWJsKmg6lAuF53Ryrgk92upc3Npiywi7xwf5VaYjEcKVol02+semDUcihBDuFh1kTebRdZCE/XVqbGntBk7C3n0KZiZMRxIXR1sH2VCeR4bPazqUSEu3laajcJXZrgo2XOAq3wZTQzDQYDqSuDjWOkSBP818wTlwLm4V1oDXZzoSIYQQQqSw/zzUCsB7dlYYjiS+JGG/SLVNrd1W7IBwEDqPm44k5sJhzbHWITum+IKTsMsU3wWpLopUirdhHfvy7c42SZeQHGsbYsuKfPMF58CpEC8F54SIia7h5O4EI4QQ8fTAK07C/q4dKwxHEl+SsF/EqtZuy3c42yScFl/fO8bIVJCtFQWmQ4HxfqetmxScW5Bowm7FOvbSjeDLhLbkO1YmZ0Kc7Rqx4+KW1s4Iu1zcEmJJPnxDDQD/sb/ZbCBCCOFiHUPORc91ZRYsr40jSdgvYlVrt7zlkF2alKOGR1sHAdhmQ8LeH5lGLQn7guRmplGck27HCLs3zZkW3/aK6Uhi7nTnCMGwtmP9+kgnzIzLsSLEEt0TSdjve6HRaBxCCJEMrJiBGEeSsF/EqtZuSjnT4pNw1PBo6xD+dC+rS3NMh3KhB7tM812w6qJsO44VgBU7nUrxIQuK4MVQ9OKWFS3dojUCpN6DEEsSnc03NGFBvRwhhHChtsHkrPF1KZKwX0JNUbYdI+zgrM3tPQtTI6YjiakjrYNsXp6P12PBFbH+OqSl2+JUF/ntKDoHTsIenICeU6YjianDzYOU5GawosCCgnMDTc62UBJ2IWJFJ2l3CyGEiKcfPO8MInz85uSf9ScJ+yXUFFuUhCzfAeik6jE9Ewpzsn3YjjW54Iyw562AtEzTkbhOdSCbjqFJJmdCpkNxZqNA0k2Lf7VlkGsqC+yY7jXQCCinBaIQYklqI6Psh5oHDUcihBDu86+/dxL2P7sx+QcRlpSwK6UCSqknlFLnItvCS9znGqXUi0qpE0qpo0qp98/53g+UUg1KqcORf9csJZ5Ysaq124qdzrbtoNk4YuhM5whTwTBbKy1Yvw5OX+mi5L86Fw81xU7Nh+Z+Cy5wFa6ErMKkStgHxqZp6B1je5Ulx8pAo3Nxy5fc/U7F4iXreUE8/PlNzufOt/fVGY5ECCHcqywv+QfcljrC/hngKa31GuCpyP8vNg78idZ6E3An8L+UUnPPPj+ltb4m8s+KYeRo4bkWG5KQ7CKnwFPLAdORxMyrzQMAXGNDwTmI9GCXhH0xom0QrVhCopRzgas1eRL2w5H169srX5fzmDHYJEtHxNUk5XlBPETbED15qstwJEII4S5WDKom0FIT9rcD90Vu3we84+I7aK3Paq3PRW63A91AyRL3G1eVNiXsABV7oPWA01IpCRxqHqQ4J4PKgAVrcieHYKJf1uQuUk2RRSPs4CTsPadgatR0JDHxavMgHoU9y0cGGiVhF1eTlOcF8ZDh85oOQQghXOk/XnJaYr5t23LDkSTGUhP2Mq11B0BkW3qlOyul9gDpwNz5X1+JTIn7ulIqY4nxxMSFhN2S6oOVu2Gs2xndSgKHmgfYUWXLmtxoEa0ao2G4VYE/nfysNIsqxe8CHU6aVoiHWwZZW5ZLdobPdCgwMwEjHVBYbToSYbekPC+Il0J/GgDH24YMRyKEEO7x94+eBuBv37zOcCSJcdWzQKXUk8CyS3zrcwvZkVKqHPghcI/WOhz58meBTpwP6+8C9wJfuszjPwZ8DKCsrIx9+/YtZPeXNTo6esnn8vvgxePnWBNujsl+liJnxMMu4OTj99FddvOCHnu512fK8JSmqW+ca4tnYhLXUl9fcc+LbAYO1vcy2rP0eGLNtp/fpQTSQ7x6rpV9+/oW/NhYvz7fzBRvAOqfvZ/mJvOF8Jby+sJac7B+nD3LfFb8DvjHWtkDnOwcpzsSjxt+P5ci2V/fYtlwXhCvc4J4u/h36p21iu8fh3t//AKf2m3BrDOXkmM1fuS9jQ95X2Oj/tjL1F/0taR8b7XWi/4HnAHKI7fLgTOXuV8ecAh47xWeay/w0Hz2u3PnTh0rTz/99CW/fvc3ntX3fH9/zPazJMEZrb9crvXDf7vgh17u9Zny+IlOXX3vQ/rlhr6YPN+SX9/z39D6i3laj/fHJJ5Ys+3ndyl//eND+savPbWox8bl9X1zt9Y/ek/sn3cRlvL6znWN6Op7H9I/PdAcu4CW4sxjzrHSfOHvoht+P5ci1q8POKiX8Jnrhn8mzgtieU4Qbxf/TgVDYV1970O6+t6HzASUJJL9b5FJ8t7Gh7yvi3e+2zk/qv3sw5f8vlve24WcEyx1SvyDwD2R2/cAv774DkqpdOCXwP/WWv/8ou+VR7YKZ53b8SXGEzOVhX571uV6fU7Lqlb3F5471DyAz6PYssKWNblNkJHvVBcXi1IV8NMxNMlMKHz1OydC1bXQ8jKELYlnkaLFGbfb0k1hoNHZFsiUeHFFSXteEA9ez4WlYeFwctSpEUKIePr7R5zp8J+/e4PhSBJnqQn714DblVLngNsj/0cptUsp9W+R+7wPuAn48CXatPyHUuoYcAwoBr68xHhipirgp3Vgwp4P0Ird0HnMWUfqYq80DbBpeR6ZaZYU2xlolDW5S1RV5CcU1rQPWvK7WXktTA5C71nTkSzJwcYBCvxprCrJMR2KY7AJfFmQc8UlyUIk7XlBvFy7MgDAr4+0GY5ECCHs9/hJp7PGH16bOufvS6pkpLXuA950ia8fBD4auf0j4EeXefytS9l/PFUE/EwHw3SPTLEs34L+fpV7IByEtkNQc6PpaBZlJhTmaOsgH9xTZTqUCwaboCQ1ClbES7QNYnP/+GybN6Mqr3O2LfuhdL3ZWJbgQFM/O6sK8XgsKM4IFyrE21AsUlgrmc8L4uWzb9nAO771PF95+BTv3F5hOhwhhLBWaM5AarpvqePO7pE6r3SBZnuxD1gyLb7yWmfb/KLZOJbgVMcwkzNhdlRZMv08HHamxMsU3yWZm7BboWgVZAWcafEu1Tc6RX3PGLtqAqZDuWCgSWajCBEH10SWvfSOThuORAgh7PbQ0XYAdlVbkkskiCTsl1FZ6FRrbe6zJAnxB6BkvasT9pcb+gHYbUsSMtoFoSlp6bZEZXmZpHs99iTsSjkXuFpeMh3Joh1sctav766x5ANJa+nBLkQCWHPOIYQQFvryw6cA+Mxd7p1BuRiSsF/GisIslLJohB2g6vpIMS3z7aoW40BjP1UBvx1LDOBCES1JQpbE61FUFGbRYkvCDk7hub7zMNZrOpJFeaVpgHSfhy0VlhRnHO+H6RE5VoSIk//21o0AfPHBpK6xJ4QQS9IzMgXAThlhFwAZPi/L8jLtGTUEqL4Bpoahy30f6FprDjQO2DO6Ds76dZAkJAYqAxZ1VQDn4hZA0wtm41ikA439bKvIJ8NnSXHGwUZnK8tHhIiLe653jq2nz/QYjkQIIex0qmN49rZKsXo6krBfQWXAT2u/JZWvYU4S4r5p8XU9o/SPTc9Ww7XCQCRhz680G0cSqAr47ZrKuXyHU9HchQn7xHSI421Dlq1fb3S2cnFLiLjweS+cjvWOThmMRAgh7PTpB44C8D/ft81wJIknCfsVWNWLHaCg0kkum92XhOyPrl+3KmFvhNzlkGbJFH0Xqwr4GZ4MMjQ+YzoUhy8dKndD03OmI1mwwy2DzIS0PevXYU4Pdos6PAiRZP7P29YA8MUHTxiORAgh7HOsbQiAd25fYTiSxJOE/QqqAn66RiaZnLFozXj1Dc4Iu7akP/w8vdzQT0luBjVFftOhXDAoVa9jpSryc23qHzMcyRzVN0LncZgYMB3Jguxv6EMp2Fll08WtJsgugQxLesILkYT+cu9qAB4+2mE4EiGEsEtdz+js7VSbDg+SsF9RZSALraFt0LJp8WPd0FdnOpJ501rzckM/e2oCdh1kUvU6Zqxr7QZOwo6GZndVi3+pvo9Ny/PI96eZDuUCOVaEiLu5PYUHxqTFmxBCRH3q50cA+L/fsdlwJGZIwn4Fs73YrUtCcNVU39aBCTqGJu2a4hucguF2KaIVI5U2JuwVu8CbDk3Pm45k3iZnQhxqHuT62iLTobzWQKMcK0IkwCducUbZP/8r9xWXFUKIeNBac6h5EIAP7E7NulOSsF9BpY0Je/EayFkGDc+ajmTeXqzvA+D6VcWGI5ljsAXQMmoYIzkZPoqy0+06VtKyYMVOaHRPwv5q8yDTwTDX2ZSwh4Iw1CrHihAJ8F8i69gfPibT4oUQAuDpM90A5Gb6SPOmZuqamq96nkpyMsjweWgZsGhKvFKw8iZo+L1r1rG/WNdHUXY6a8ssWv8abVMla9hjxrrWbuDMSOk4ApPDV7+vBV6s78OjLCvOONwKOiQJuxAJMPdktKHXopogQghhyJ/94CAAP/zItYYjMUcS9ivweBQVhVl2tasCJ2Ef64aeM6YjuSqtNc+f7+X6VUX2rV8HSUJiqMrGhH3lG51ks9kdrRBfqu9j84p88jItW78OcnFLiAT5p/c6LYs+ct8Bw5EIIYRZM6Hw7O1rKgsMRmKWJOxXURXw0zJgYRICrpgWX9czRvfIFDeutmg6PDhVr70ZzvICERNVAT/tg5Ov+eNqXOW1zs+5fp/pSK5qcibEYSvXrzc5W7m4JURCvGuH07KovkdG2IUQqe0fH3MGJ9+yJbXP1yVhvworp/kW1jj9kBueMR3JVb1Y1wvADatsS0IanffQI4dArFQV+QmFNR2Dk6ZDuSAtC6qug3r7j5VXmgaYDlm2fh2cY8Xjg7zU63sqhAlKKWpLsgF44JVWw9EIIYQ533m2HoCvvXur4UjMkmzlKqoCfkYmgwyNz5gO5bVW3gSNz0HYotHMS3ihro8VBVmzFfetIT3YYy76M7aqFztA7c3QfQJGe0xHckW/P9eLz6PsWr8OzrGSXwker+lIhEgZ379nNwB/G2llJIQQqWZuIWOrlgoaIAn7VVQUWtiuCmDlzTA5CJ1HTUdyWeGw5sX6PvvWr4P0lY4DK3uxA9TudbaWz0h57nwPO6oKycnwmQ7lteRYESLhaoqzZ28PTVg2YCCEEAnw8R++AsCXU7T3+lySsF/FbC9269ax3+xs635nNo4rONkxzOD4jH3T4ScGYXJI+krHWFleJulej30Je/k1kJlv9Tr2/rFpTrQP88Y1ltV6AEnYhTDkr25ZBcBf/+RVw5EIIURihcOakx1Oh58P7qkyHI15krBfRWUgC7Bw1DC3DMq2WJ2wP3PWmYL8BtuSkEEpohUP3khXBat6sYMzlbvmjVaPsD9/vhetLTxWpkZgvE+WjwhhwN/cvg6AZ8/avZxHCCFiLVq/Y1leJl6PZbN0DZCE/SpyM9Mo9KfZl4QArLoFml+CqVHTkVzSs2d72FCeR2lupulQXkvaVMWNlUUawZkWP9gMfXWmI7mk5871kpfpY2uFZS1LpEK8EMZ4PIrl+c7n588OtBiORgghEufT/+ks+f3Jx64zHIkdJGGfB2uTkFW3QngGmp43HcnrjE4FeaVpgJvWWjZiCJKExFFVwE9zn4XHyurbnO35p8zGcQlaa35/rocbVhXbdxV59uJWjckohEhZP/uL64ELJ69CCJHsznePzN5eOaeeRyqThH0eKgN+WgcmTIfxelXXgy/LyiTkxbo+gmHNzWtKTIfyegONkFngrGsWMVUV8DNsY1eFwEoIrILzT5qO5HXqe8doH5q0bzo8XFg+IvUehDAiWvgW4HTnsMFIhBAiMf7gm85A5L/84Q7DkdhDEvZ5qCz00zowTiisTYfyWmmZUHOjlevYf3+uh6w0LztrCk2H8nqDTTJiGCdVRZZWigdnlL3x9zBjUZ944JkzzvrUm2y9uJWRD1kWHsdCpIjv3bMLgLu/8ZzhSIQQIr5Gp4JMzIQAeMuWcsPR2EMS9nmoCviZCWm6hu060QecafF95y5M87bEs2d7uK42QIbPwt7NA42yfj1OrO3FDk7CPjMOzS+ajuQ1nj7TzaqS7NmLHVaJHiu2tWUUIoW8aUMZAKGwZnjSstlLQggRQ3/940MA/NF1Uhl+LknY58HaSvEAq293tuefMBvHHE19YzT2jXPTWgtHDMNhp/iYjLDHRaWtvdjBmY3izbBqWvz4dJD99f3csq7UdCiXNtAkF7eEsMBf7nVavN3z/ZcNRyKEEPExFQzxdGTW4efv3mg4GrtIwj4Ps73YbUxCitc4yefZx01HMuupU90A3LrewiRkpANC07ImN05yMnwUZafbeaykZ0P1DVYl7C+c72M6FOYWG4+VcFiWjwhhiU/d4bR4e7V5kGAobDgaIYSIvb/52REAbt9YRmaahTN0DZKEfR6WF2ThUZYm7ErBmjucHtPTdsQXneJbXWRhZUfpwR531nZVAFhzO/SctmYJydNnuslO97LLxloPo10QnJRjRQgLKKW4c9MyAP5r5KRWCCGSRSiseehoBwD//KHthqOxjyTs85Dm9VCen0WLjZXiAda+2Tmxbvy96UgYnQryUn3f7Jo760ibqrirsjlhX3unsz37mNk4cNq57TvTw42ri+2s9TBbIb7GaBhCCMc3IyexvznSTti2IrhCCLEE90ZaV75xjaXnRIZJwj5PlYEse5OQ6jdAWrYVSchz53qZCWm71+SiIL/SdCRJqyrgp31wkhkbp20WrYKiNXD2EdORcLZrlLbBCTunw4Nc3BLCMmleD29Y7bR//L9+ecxwNEIIERvhsOaBV1oB+LdIVwzxWpKwz1NVwG/nlHhw2rvV7oVzj4M2e9X9d6e7yM302TnFF5wkJG8F+NJNR5K0qor8hMKajkELuyoArLsTGp+DqRGjYTx5qgvA4otbjYCCArm4JYQtoiez9x9oQRv+vBdCiFj4woPHAdhTY2l3KQtIwj5PlYV+ukemmIz0BrTO2jtgqAW6jhsLIRzWPH2mh5vXlpDmtfRXS4poxZ3Vrd3AmRYfmoa63xkN44mTXWyryGdZfqbROC5roAnyloMvw3QkQoiIzDQv11QWAPDFB08YjkYIIZYmFNb86KVmAO77sz2Go7GXpVmVfaI9klsHLB1lX3cXoODUQ8ZCONI6SM/IFG/aYOmIIUibqgSosrm1G0DldZBZAGceNRZC9/Akh1sGuX2jpbUeINKDvcZ0FEKIi/z4z68F4H+/2CRr2YUQrvY/fnsKgK0V+WSly+j65UjCPk8VhZYnITmlTsuqUw8aC+GxE134PIpb11mahMxMwki7JCFxVpaXSbrXY++x4vU51eLPPQahoJEQnoy0PrzN5oR9sEnaHwphIX+6j+triwD45M8OG45GCCEWJxgK82/PNQDwo49eazgau0nCPk8XerFbWikeYMMfQPdJ6D1vZPePn+zkutoi8v1pRvZ/VUMtzlaSkLjyehQVhVn21nwAWP9WGO+D5heM7P6Jk51UBrJYV5ZrZP9XFZyC4XaZjSKEpX7wZ7sB+NXhdnuX6gkhxBV89benAVhTmkNepqW5gyUkYZ+n4px0stK89o4agpOwA5z+TcJ3fb57hPqeMe7YZPGIoVS9Thire7GDM8Luy4KTv074rsemgjyd03v8AAAgAElEQVRf18ftG5ahlEr4/udlsBnQULjSdCRCiEvI8Hl5784KAN73nRcNRyOEEAszFQzx/eed0fUH/uIGw9HYb0kJu1IqoJR6Qil1LrK9ZGlwpVRIKXU48u/BOV9fqZTaH3n8T5VS1pbuVkpRGbB81DC/ApbvgJOJnxb/2Amn4vXtG5clfN/zNpuwy6hhvFUF/DT3WXyspGfD2jfDqd9AOLGjU/vO9DAdDPNmmy9u9TsfonJxSyxUKp0XmPYP79kKwNHWIfpGpwxHI4QQ8/eH/7ofgLu3lNs7M9ciSx1h/wzwlNZ6DfBU5P+XMqG1viby721zvv73wNcjjx8APrLEeOKqstDyUUOAjW+D9kMw2JLQ3T5+opNtlQX2VrwGJ2H3ZUKOxYlSkqgu8jM8GWRofMZ0KJe38e0w2gUt+xO6298e76A4J53dNYGE7ndBohe3AjLCLhYspc4LTFJK8Zm71gNw/dfMdr0QQoj56h2d4mDTAADf/OB2w9G4w1IT9rcD90Vu3we8Y74PVM5c0FuBBxbzeBMqI73Yre59uiFy3nM6cdXi2wYnONI6ZPd0eLhQRMvWachJpNL2SvEAa97sXMA58auE7XJyJsTTp7t586ZleD0W/x4ONEKaH7JLTEci3CelzgtM+4ubVwEwHQxzvG3IcDRCCHF11371KQA+c9d6PDafC1lkqQl7mda6AyCyvVw/r0yl1EGl1EtKqeiHbxEwqLWOlmluBVYsMZ64qgr4GZsO0T82bTqUyytaBaWbnKm+CfLIsQ7AmdZitYFGmQ6fINb3YgfIyIXVtzmdFcLhhOzymbM9jE+HeMtmNxwrNXJxSyxGSp0X2CDau/it33zOcCRCCHFlrzT1E4q0o/z4TbWGo3EP39XuoJR6ErjUwuTPLWA/VVrrdqVULfA7pdQxYPgS97vs0LVS6mPAxwDKysrYt2/fAnZ/eaOjo/N+ruFu5xzil08+x+oCe3sF1mRtobrpp7zw+K8YnfbF7L26nJ+8OEF1noeGYwdoiOueXm/ePz+teUNPHZ3eKs7H+f2IpYX8ftpkIugcyvsOHien/+xl72f69ZWqNWwceYhDv/kOw/kbYv78F7++HxyZJCcNJluOsa/N3mR4V+txJjPLOH6Vn43pn1+8JfvrWywbzgvidU4Qb/H+nfrcD57g9prUWw8qx2r8yHsbH6n4vmqt+dPHnJmXn9yZwTPPPBOX/STle6u1XvQ/4AxQHrldDpyZx2N+ALwHUEAv4It8/Xrgsfnsd+fOnTpWnn766Xnf91zXsK6+9yH9q1dbY7b/uOg8rvUX87Q+8P0Fvb7FaB0Y19X3PqS/9fS5uO7ncub9+kZ7nffkhW/FNZ5Yi/fPL552fOlx/Zn/PHLF+xh/fRNDWn+pWOtHPhuXp5/7+iZngnrzFx7Vn/r54bjsK2bCYa2/vGxe74nxn1+cxfr1AQf1Ej5z3fDPxHlBLM8J4i1ex0zn0ISuvvchXX3vQ3o6GIrLPmyW7H+LTJL3Nj5S8X393C+P6up7H9LrP/9IXPfjlvd2IecES50S/yBwT+T2PcDreiQppQqVUhmR28XAjcDJSKBPRz6kL/t4m1QURqb52lz9GqB0IwRqnam+ceae6fCRsX8popUw1rd2A8jMg1Vvctq7xbk2xb4zPYxMBXmL7cfKWA/MjEuFeLFYKXVeYIuyvEz2rnNqTrzn/5M2b0IIu/SNTvGjl5oBePlzbzIcjfssNWH/GnC7UuoccHvk/yildiml/i1ynw3AQaXUEZwP4q9prU9Gvncv8Eml1HmctWvfW2I8cZWZ5mVZXqb9CbtSTvG5hmfxzVxqhmHsPHysg80r8qguyo7rfpZstk2VJOyJUuWGhB2cavHDrdB2KK67+fXhNoqy03nD6uK47mfJZtsf1piMQrhXSp0X2OT79+wG4EjLIPU9o4ajEUKIC3Z++UkA/vbNa8nNTL1lO0u1pIRda92ntX6T1npNZNsf+fpBrfVHI7df0Fpv0Vpvi2y/N+fx9VrrPVrr1Vrr92qtrW8kWlXkt7sXe9Tmd0M4SGn383HbRXPfOK82D3L3luVx20fMSA/2hKsK+GkfnGQmlJiCbou27i7wpMHJ+FWLH56c4clT3bx1azk+71Kvk8aZ9GAXS5CK5wW28HgU/+8HrgHg1n+Kz9pQIYRYqF8fbpu9/Ylb1xiMxL0sP3O0T1XAb3fl66hlW6BkA2Vd8fvQ/uWrbSgFb7/GDQl7A+SWQ1qW6UhSRlWRn1BY0zE4aTqUK8sqgFW3OO3d4lQt/tHjnUwHw7x9uwsKXg80AgoKqkxHIoRYoLdfc+FvzDeeOmcwEiGEgGAozH+5/zAAT/3NzYajcS9J2BeoOuCna3iKyZmQ6VCuTCnY9n7yh09dGDGLIa01vzrcxnUri1he4IIkuL9BpsMnWJUberFHbX4PDDVDy0txefoHD7dTXeRne2VBXJ4/pgYaIW85pGWajkQIsQivfP42AP7nE2cZHLe4Da0QIum969svAHB9bRGrSnIMR+NekrAvUFWRk4S4Ylr8lvc622M/j/lTH24ZpKF3jHe6YcQQnBF2KTiXUK7oxR614a2Qlg1HfhLzp+4enuSFul7evm05yg19zQcaZDq8EC5WlJPBX+5dBcA1X3rCcDRCiFR1on2Io61DAPzoo9cajsbdJGFfoNkkxPbCcwD5FQwUbIajP415BexfvtpGhs/DXVsu1YrXMjMTMNIhI+wJVpaXSbrX444R9vRsp/jciV85vy8x9OCRdsIad0yHB2eEXRJ2IVzt03eun719/8vNBiMRQqQirTV3f+M5AL79hzvwelwwYGExSdgXKFoNvckNSQjQVbYX+s5De+wqYM+EwvzmSDu3byxzR6XHgSZnKyPsCeX1KCoKs9wxGwVg2wdgahjO/DamT/vrw+1sWZHvjqlgsxe3akxHIoRYot9/+hYAPvOLY4xOBQ1HI4RIJZ/9xbHZ23fZ3s7WBSRhX6BCfxo5GT7XJCG9xdeDNwOO/ixmz/nMmR4GxmfcNR0eJAkxwBW92KNq3gh5FXDk/pg9ZcdomGNtQ+4ozAgwGBmJk9koQrheZcDPh651ikdu/uJjhqMRQqSKc10j3H+gBYDDX7jdcDTJQRL2BVJKOZXi+1ywLhcIpuXAujvh2AMQmonJc/7y1TYC2enctLYkJs8Xd9KD3ZiqgJ9mNywfAfB4YOv74PxTMNIVk6d8sSOIUvC2bS5J2KWlmxBJ5avv3DJ7+7vP1hmMRAiRCrTW3P71ZwH4+vu3UeBPNxxRcpCEfRGqi/yumRIPwNb3w3gv1O9b8lMNT87wxKku/mBrOWm295OOGmiAjDzwB0xHknKqi/wMTwYZGo/NxaK42/YB0CE4/sCSn0przUsdQW5YVURpnksqrg80OltJ2IVIGi999k0AfPW3p+katrzNphDC1T7wXafbTnFOBu/cXmE4muThkozLLlUBP639E4TDsS3kFjerb4esQqf43BI9cqyD6WCYd+5w0UHYH6l67YYK3Umm0k2t3QBK1sHy7TGpFn+gcYDucc07rnHJ0hFwEva0bMguNh2JECJGluVn8uk71wFw7VefMhyNECJZPXeul/0N/QC8+NlbDUeTXCRhX4SqIj/ToTCdbrlS7UuHTe+EUw/B5NCSnuoXh9pYWZzNtor8GAWXANLSzRhX9WKP2vZB6DwGnceX9DT3v9xMlg/u3uqiYivRCvFycUuIpPKXe1fP3v7Ej2NXhFYIIcCZgftH39sPwI8/eq17ZuG6hLybi+Cq1m5R2/8YghNLKj7X0DvG/oZ+3r1jhTv6SQOEQ04hLZnia0Slm3qxR21+N3h8cHTxxeeGJmZ4+FgH15X78Kf7YhhcnMnFLSGS1qkv3QnAQ0c7eKm+z3A0QohkobVm6989DsBtG0q5YbXM0os1SdgXoTrgtHZzS6V4wJnmu2wrvHLfonuy33+gGa9H8d5dlTEOLo6G2yE0LQXnDMnJ8FGUne6uYyW7GNa8GY78dNGFGn99uI2pYJibK1yUrGstPdiFSGJZ6V5+9JFrAWed6fi0tHoTQizd//GjC7N2/vVPdhmMJHlJwr4Iywsy8XqUu0YNlYKdH4auY4vqyT4dDPPAwVbetL6UMrcU0IILLd1k1NAYV7V2i9r5YRjrhtMPL/ihWmt+8nILm5bnUZPvjX1s8TLaBcFJSdiFSGJvWFPMWyPLdDZ+QVq9CSGW5tHjnTx6ohOA4//9DvfMwHUZSdgXwef1sKIgy11T4gG2vBfS/PDKDxb80CdOdtE3Nj3b09U1pKWbcVVuTNhX3wb5lfDKvy/4ocfbhjnVMcwHdrtoJgpIhXghUsQ/f2jH7O3/+tPDBiMRQrhZ98gkf/GjVwD45V/eQE6Gi2YVuowk7ItUXeR31zRfgMw82PwuOPafMDWyoIf+5OVmVhRk8cY1Lum9HjXQ4KxHznNRpe4kU13kp31wkplQ2HQo8+fxwo4/cVoh9i2sd/FPDjSTmebhbW6qDg/Sg12IFHL8v98BwC9fbePp092GoxFCuI3Wmj1fcbpOfOKW1WyvKjQcUXKThH2RKgMu68UetfNPYWYMjs2/z3RT3xjPne/lA7sr8XpcNtVloBEKqsArV/1MqQz4CYU1HYMu6aoQtf2PQXkXNCNlfDrIg4fbecuWcvKz0uIXWzwMNALKOV6EEEktJ8PHzz5+PQB/+oMD9IxMGY5ICOEmt/zjPgByM3z87R3rzAaTAiRhX6TqgJ/B8RmGJhZXlMqYFTuhdNOCkpD7D7S4r9hcVH+DTIc3zJWt3QDyymHdXXD4PyA4v5PZh452MDoV5IN7XJj0DjQ6M1F8GaYjEUIkwJ6VAT5+cy0Au7/yJKHw4grSCiFSy3eeqaMxsiz48BffbDia1CAJ+yJVFzlJiOumxUeLz3Uchvarr12bDob5+cEWbl1fyrJ8FxWbi5I2Vca5NmEH2PWnMN4Hp34zr7v/9EALq0qy2VXtwqlhAw0yHV6IFPPZuzZQludcpFv3+UcMRyOEsN2J9iH+xyOnAXj2U7e4b+atS0nCvkiVbuzFHrX1feDLhEP3XfWuT53qond0mg+5ccRwvB8mh2SE3bCyvEzSvR53dVWIqr0VCqrh4NWLz51sH+aVpgE+uKfKnVVSpaWbECnppc++CYBgWPM3PztiOBohhK2GJ2e4+xvPAfC1d22hKjJ4KeJPEvZFqi5yerG7MgnJKoBN74KjP3MS2iv48cvNLM/P5Ka1Lis2BxdaukkSYpTXo6gozHLfbBQAj8eZkdL0HPScveJd73uhkaw0L+/d6cKlI1MjTls3mY0iRMpRSnEkMq31Pw+18vODLYYjEkLYJhzWbP27x4H/v737jo+izB84/nnSKwkpBBIghd4JXZp0KQrqqXd2D7HxOz07YEHseLbT09M7G3IWPBVPpSNN6SAdAgSSQEIJIYEUSEKSfX5/zBIBKSm7Ozub7/v1ymuzs5NnvjOZ3Z3vPA36NI/kT1asyLMwSdhrKMTfh8hgP2smIQA97oJTRbDpiwuusudIIb+kHuWmnk2t2eTl9DRVkoSYzpJzsZ+WfIsx08BFpng7duIU/9t0gGu6xBEWZLHB5gDy0ozHyObmxiGEMEVYoC+z7u8LwGPfbGFL1nGTIxJCuJM2k+dV/v7ZnT1NjKRukoS9FppEBFmzSTxAXBdo0hPW/AtsFedd5ZMVGfj5eFlzAC2QaarcSNOIIPZb9b0S0gDajIaNn0Np0XlXmbEuk9JyG7dfluDa2Bwld4/xKAm7EHVW+7gwXru+EwCj31lBdoHFZvYQQjjFndPWUVpuTM2b9tJIa3b7szhJ2GshPtLCCTtAz3uMZuOpC3/30vGTp5i54QBXd44lMsSio0YfS4eQGPALNjuSOi8+MoiCknLyT1psVoXTeo2H0nzY/OXvXiqvsPGfVRn0bhZJq4ahro/NEXLtNewRSebGIYQw1XVdGzO2j9EqredLiygpO/8NfSFE3fDO4lQW7TwCwNYpw/CyYotbDyAJey0kRgVzML/Yul9obUZDaCysee93L81Yl0lxWQV/7mPh5uR5GVK77iaaWHmkeIAm3SGuG6x+D2y2s176KSWbg/kl3N47wZzYHCF3jzGlm58MICNEXTf5qrZ0aRoOQOun52GT6d6EqJNmbsjitQXG+D2LHrmc0AALdvnzEJKw10JSdAhaQ/pRCw48B+DtC93vhLSlcGRn5eLyChvTV2bQKymCNo3qmRdfbeXukSa+bsLSU7uddtl4yNsLqQvOWvzJigziwgMZ0ibGpMAcIHcPRDYzOwohhJuYOb5P5e9JT8wxMRIhhBkW7sjmYfusEZ/8uTvNokNMjqhuk4S9FpKijKbWlk3YAbr+Gbz9Yc37lYsW7DBqDC1du15SAEWHJWF3E5XTIFpxVoXT2ow2aqFX/7NyUcqhAtak53HbZfHWHJjxtLy98l4RQpwl/eWRlb/3mbrYxEiEEK60am8ud01fD8A/b+7CwFYNTI5ISMJeC4n2hD0t5/wDUVlCcCR0vB42z4DiYwB8siKdJhEeUGMIENXC3DgE4AGzKoDRIqXHXZC+DLK3AzB9VQYBvl78sbsFp3I77WSe8d6PkBp2IcRvlFLsemE4AAeOF/OH91aaHJEQwtm2ZB3nxg9WA/DqdR0Z2aGRyREJkIS9VoL9fWhYL4A0K9ewA/S8F8qLYcN0th3IZ13GMW6/LMHaNYaVo15Lwu4u4iODrN0aBaDL7eATCKvfI7eolJkbDnBNchzhQX5mR1ZzuXuNR6lhF0Kcw9/Hm+3PXgHAr/uOcd9nv5ockRDCWVKzCxn9zgoAplzVluu7WbgywsNIwl5LSdHBpOVYPAlp2AHi+8KafzNteSpBft7Wf5MeTQXlJXOwu5Fm0SHWf68ERUDnG2HLf/nvz5soLbdxZ1+Lj6wuU7oJIS4i2N+HDU8PBWDutsNM/HaLyREJIRxtf+5Jhr75MwAPD23JHVbuFuuBJGGvpcSoYNJyitDa4qOo9nkACrJg67fc0K0JYYEWHwny6G4Ijwcfi05J54GaNQjhSGEpBSUWndrttJ73QUUptnUfMbRtDM0bWHwgltw9oLyhfrzZkQgh3FREsB8rJw4CjFlknvl+m8kRCSEc5VB+Mf1fXQLAnX0TeWCwtE51N5Kw11JSdAgFJeXknThldii102IY2QFJ3OX1I+P6JpgdTe3l7pH+627m9Aijlq9lj25JZlRf/miby319PKBvV95eI1n3tvhNOiGEU8WGB/LL4wMB+HTVPp7631aTIxJC1FZOYSmXvWwMKnltlzievrKtyRGJ85GEvZY8YqR44HhxGW+cHEErr0waH11udji1Y7MZ/XKl/7pbaRZtvFf2HLHwII0Y0x6+XDCCKFVAl1wPmO5Ipj8UQlRRk4ggfn7MSNo/W72fSTOlebwQVpVbVEr3F38CYGCraN64obPJEYkLkYS9lpKiT48Ub+2EffqqfXx7qidlIXGw/O9mh1M7BVnGIHpRkoS4kyYRQfh6K/ZaeVYFYPbWQ8wpSORYVBdY8TZUWLiJf+XNLXmvCCGqpmlkUGVN+5drM3noq00mRySEqK7sghK6vmAk650ah/HJn3uYHJG4GEnYa6lxfXsSctS6SUjxqQqmrcygf+tYfPveD/tXQuZas8OquaOpxqPUsLsVX28v4iOD2WvhGnatNf9alkaz6GDChjwO+fth20yzw6q5/EwoOwnRrcyORAhhIU0iglg+wUjav9t4gDs+sfA1gxB1TMbRE/R8aREA/VtG8/1f+pockbgUSdhrydtLER8ZTLqFa9j/uz6TvBOnuPfyZtDlNgisb+1adpmD3W01iw62dA378j1H2XGogHv6N8Or5RXQoC0sf9OoqbainF3GY3Rrc+MQQlhO4/pBrH1yMABLd+Uw+PWl5gYkhLikbQfyGfDaUgCu79qY6WOlZt0KapWwK6UilFILlVKp9sf651lnoFJq0xk/JUqpq+2vTVNKpZ/xmiU7T1g5CSmrsPHvn9PoGl+f7gn1wS8YetwNu2b/djFvNUdTwS8UQmLMjkSco3mDEPblnqSswpoJ7vvL9tIg1J8xybHg5QV9H4KcFEidb3ZoNZOz03iMamluHMJjyHVB3dIgNIDNzwwDYG/OCZImzbb+rDlCeKgVe45y5T+McaruG9CMV6/vZHJEoqpqW8M+EViktW4BLLI/P4vWeonWurPWujMwCDgJLDhjlcdOv661tmRHqBYNQsnIPUlpeYXZoVTb7C2HOHC8mHsvb4ZSyljY4x7wCYQVb5kbXE3lphr910/vj3AbzaJDKLdp9uedNDuUavt1Xx4r9uQyrl8i/j7exsJ210J4U/jlDbDiRWrOLuPGVlCE2ZEIzyHXBXVMWKAvO58fDoBNQ+KkOZa9KSuEp/rPqgxu/nANAJNGtGbCcGlZZyW1TdjHAJ/af/8UuPoS618HzNVaW+9q/SJaNgylwqYtN1K8zab559I9tGgQwuDWDX57ITgSut4OW76CYxmmxVdjR3ZCdBuzoxDncXpqNyv2Y3970R4igv24pdcZ85V7+0DvByBrLexbaV5wNZWzU/qvC0eT64I6KMDXm70vjax83uLJueSftPCAnEJ4kAdnbOTp77cD8MYNnbjn8mYmRySqS9Wm6ZJS6rjWOvyM58e01r9r/nbG64uBN7TWs+zPpwGXAaXY78RrrUsv8Ld3A3cDxMTEdJ0xY0aN4z5TUVERISEhtSojs9DG0yuKubejP71ifRwSl6NcbP/WHi7nn5tKubeTP70anR23X2kuvVbfw+GGA9jd6i+uCLVGzt0/n7IC+q64lb1Jd5DZ9BoTI3MMR5yf7qS4XHPfTye5vqUvo5L8LLN/accreG51Cde19OXKJL+zXvOqKKXX6rsoCklgS6fnznrNrfdPa/ouv5HDDQexp8XdNSrCrffPARy9fwMHDvxVa93NYQW6IVddFzjrmsDZPP09A/DI0pPklhjXli/2DSQuxPnDJdWF42oWObbO4YrjqrXmL4tPcsJ+7+zZ3gHE1/N26jbdgVXO2WpdE2itL/oD/ARsO8/PGOD4Oeseu0g5jYAcwPecZQrwx7gTP/lS8Wit6dq1q3aUJUuW1LqMkrJynTRptn513s7aB+RgF9q/igqbHvbGMj3otSW6vMJ2/j+e/ajWz0ZonZfhvABr6Xf7l75c62fqab17oSnxOJojzk930+PFhfrhrzZpra2zf2M/Was7PTtfF5aUnX+FFW8b592+VWctduv9O55lxLz2gxoX4db75wCO3j9gva7Cd5y7/7jbdYEjrwmczdPfM6fd/8UGHT9hlo6fMEvP33bI6durK8fVDHJsncPZx/VEaVnlezB+wiydV1Tq1O25E6ucs9W5JrjkbU+t9RCtdfvz/HwPZCulGgHYH49cpKgbgO+01pVtpLTWpz/FS4FPAEsOVejv401iVDC7sgvNDqXK5m0/zK7sQh4Y3AJvrwv09e7zICgvWP6Ga4OrjSM7jMcG0iTeXbWMCWW3hd4r2w7ks2jnEe7sk0iI/wVa0HQbC8HRsPRl1wZXG6cHnJMR4kU1yXWBuJS3b0xmylVtAbj7P7/y6vydJkckRN2RcfQEbSf/Nhju3pdGUj/Y7yJ/Idxdbdsp/QDcbv/9duD7i6x7I/DlmQvO+FJXGP3cttUyHtO0jAkh1SJJiM2meXtRKknRwVzZMfbCK4bFQfKtsPFzOJ7pugBr40gK+IdBvYvslzBV64ZGwl5ukUGJ/rE4ldAAH27vk3DhlfyCoc9fIW0p7FvlqtBqR6Z0E84h1wUCgDv6JPLFXT0BeHfJXoa9uUxGkBfCyRbvzK6ctq1/y2gypo66cMWcsIzaJuxTgaFKqVRgqP05SqluSqkPT6+klEoAmgDLzvn7z5VSW4GtQBTwQi3jMU2LBqHsyztJ8Sn3Hyl+wY7D7DxcyAODLlK7flrfh4xHq9SyH0kxatdlhHi31bphPUrLbWTkuv8YUymHCpi/PZuxfRKpF+B78ZVP17Ivm+qa4GorZycERUJwlNmRCM8i1wWiUu9mUayeZMzVvju7iMRJcygskcHohHCGNxbuZuy09QA8PryVzLHuQWqVsGutc7XWg7XWLeyPefbl67XW485YL0NrHae1tp3z94O01h3sTelu0Vpbb+hou1YNQ9Eat5+P3WbTvLVoD0lRwVzVqQq10OFNIPkW2PAfyM9yfoC1obXRJF6aw7u11o1CAdh12P1bpPxjcSoh/j6M7ZN46ZX9go1uJFapZc/ZJbXrwuHkukCcq2FYAKkvjqh83mHKArZkHTcxIiE8i82mGfPOct5elArAp2N7MH5Ac5OjEo7k/KE764iWMcZohO7eN3dhSjYphwr4y6DmVW8i0+9h4/EXN69lLzwMJcehQVuzIxEX0bxBCN5eip2HC8wO5aK2HchnztbD/LlPAmFBl6hdP80qtexaG61RZEo3IYQL+Hp7kTF1FKPtFQWj31nBP+zJhRCi5vJOnCLpiTlszsoHYMmjA7i8ZbTJUQlHk4TdQeIjg/Hz9nLrgecqbJo3FuwmMSq48kuzSsKbQpdbYcN0956XXQacswR/H2+SooJJOeS+7xWA1xfsIizQl7v6J1X9j/yCrFHLfiwDSvOhYUezIxFC1CFv35jMP25MBuD1hbvp+vxCKmzSr12Imli4I5suzy+sfL7z+eEkRgWbGJFwFknYHcTX24uk6GB2u3Ez3x82H2BXdiEPD22Jj3c1//X9HwMvb1jqxjWHR1KMR0nY3V7rRvXcuoZ9fUYeS3blcO/lzS7dd/1c3cZCSAwses6oyXZHh7caj40kYRdCuNZVnWJZNWkQALknTtHsiTnsOSI9H4SoKq01d09fz13Tjf7q4/omkjF1FAG+nj/Hel0lCbsDtW4Yyo5D7pmEnCq38cbC3bRtVI9RHRpVv4B6sdDjbs5XNCAAACAASURBVNg847fE2N0cSYHgBjKIlgW0bhhK1rFiisvdL6HVWvO3+buICvHn9t7x1S/AL8i4wbV/JRF5GxwfoCMc3gLKW7qPCCFM0SgskPSXR9Is2qgNHPLGMt5ZLE3khbiU7IISEifNYcGObAC+va83T10p3+WeThJ2B2ofF0Z2QSlHCkvMDuV3vlq3n8y8Yh4b3gqvmk7v0Pch8A+FxW46aO/hzRDTzuwoRBW0bmgMPJdV6H5Tu/2SepS16XncP6g5QX4XmHf9UrrcDvUTSEr7D9jcbx85tAWiWoJvoNmRCCHqKKUUix4ZwN/+YLT0eW3BbhImzqakzP1n2xHCDO8v20vPlxZVPt86ZRhd4+ubGJFwFUnYHahDXBgA2w+4Vy37yVPlvL14Dz0SIhhQm4EogiKg9/2wcxZk/eq4AB2hrNioYY9NNjsSUQWt7Al7ppsl7FprXluwi7jwQP7Uo0nNC/Lxg4FPEXIiHbbPdFyAjnJ4qzSHF0K4hRu6N2HNE4Mrn7d+eh5Ldh0xMSIh3EthSRkJE2czde5OAB4Y3IL0l0cSWt0ue8KyJGF3oHb2hH3rgXyTIznbtJUZ5BSW8tjwVqjazk/e6z5j7ubFzzkmOEfJ3g62cknYLSIuPJDQAB+3S9jnb89mS1Y+fx3SAn+fWvYFa/8HioITjBYpFW407/CJo1B4UAacE0K4jZh6AWRMHcXQtjEA/PmTdQz/+8/YZEA6Ucd982sWHaYsqHy+atIgHh7asvbX88JSJGF3oBB/H5Kigt0qYT9Rpnl/6V4Gtoqme0JE7Qv0D4V+jxijYKctrX15jnJwo/EoCbslKKXoEBdGRr77JOzlFTZenb+TpOhgrk2Oq32BXl6kJd0Kx9KNGRbcxaHNxmPDDubGIYQQ5/jgtm58N743ADsPF5L0xBw27D9mclRCuF5JWQVtnp7Ho18b39m39oonY+ooGoVJV7a6SBJ2B2sfF8Y2N0rYZ6eVUVBSzqNXOHC+5W53Qr3GsHCy+/TPPbgJgqIgrLHZkYgq6tQknP2FNrfprzhjXSZ7c04wcXjr6s+icAF5EV2haW9Y9gqcOumQMmvt9AjxkrALIdxQctP6pL00snKsk2v/uZKr310hte2izpi//TCtn55Hsf36aPEjl/P81e1NjkqYSRJ2B+sQF8ah/BKOFpWaHQqZeSdZsK+Ma5LjaBcb5riCfQNg8NNGTd3W/zqu3No4uBFiO4M0EbKMTo3DqdC4xcwKRaXl/P2n3fRIjKhskukQSsGQZ6AoG1a967hya+PwFghrYoxJIYQQbsjLSzHvwf78584eAGzKPE7SE3NYslP6tgvPVVJWwYBXl3DPf4xxooa2jSH95ZEkRYeYHJkwmyTsDtbe3o/dHWrZ/zZ/Fwp4zJG166d1uAEadTbmmi4rdnz51XHqJOTIgHNWk9w0HIDNmcdNjgT+tWwvR4tO8eTINo7vF9a0F7S5Cpa/CYXZji27Jg5ukv7rQghL6Ncimr0vjaR9XD0A/jxtHa2fnsvJU+UmRyaEY325dj+tn55HRq7RGu9//9eHD27rJn3VBSAJu8O1s3+pmJ2wb9x/jB83H2R4gi+x4U7o7+LlBVe8CAUHzK85zN4G2iYJu8XE1Augvr9ik8kJ+6H8Yj74JY3RnWLp1CTcORsZ8ixUnILFzzun/Ko6cRTy9kKTHubGIYQQVeTtpZh1fz9m3d8XgJIyG20nz+ftRTJvu7C+A8eLSZg4m0kzje5qA1pFs/uFEXR21vWIsCRJ2B2sXoAvCZFBbMkyL2HXWvPC7BSiQvwZmeTEKR8S+kKrUUbNYZGJzdRODzjXqLN5MYgaSQr3Mr2G/fUFu7HZnNQS5bTIZtDzHtj42W99yM2QucZ4bNLTvBiEEKIG2seFkTF1FDf2aArAGwuNedu3ZJnfSkuI6iq3acZ9uo4+UxdXLvvl8YFM+3MP/HwkPRNnkzPCCbo0rc+G/cfQ2pwBUuZuO8yv+47xyLCWBPo4uSnN0OegvASWvOTc7VzMgQ0Q3ADqxZoXg6iRpDAvMnJPcvzkKVO2v+NgAd9uyOLPfRJoEhHk3I31fwwC68P8J8CkzwYy14C3n7RGEUJY1svXdmDD00Mrn49+ZwX3LjxBQYkbTZ8pxAVorfnXsr2MW3CSn1KMyq4Xrm5PxtRRzr8OEZYlCbsT9EiM4GjRKfbmnHD5tkvLK3h5bgqtYkK5oVsT528wqrkxavyGT+FIivO3dz77VkLTnjLgnAUlhRlznW82oUWK1prnZm0nLNCX8QObO3+DgeEw8AlI/xl2z3P+9s5n/xqjJYpvgDnbF0IIB4gI9iNj6iimjzW695RUQMcpC3joq02mVZYIcSk/7cgmcdIcXp67E4COjcNIeW44t/SKNzky4e4kYXeCHonG6Mtr0/Ncvu1PVmSQmVfME6Pa4O3logT28gnG/OxzJ7i85jCgOBvy90NCP5duVzhGQpgXShljLrjarC2HWJ2Wx6PDWhEW6MSuI2fqegdEtYQFT0G5i1sVlJca3UeaSnN4IYRn6N8ymoypoxiVaHyGf7fxAImT5vDJinSTIxPiNymHCkiYOJtx09cD4OuteHNAID/8pS+Bft4mRyesQBJ2J0iMCiY61J+16bku3e6h/GLeXpTK4NYNuLxltOs2HBwJA5+C9GWw43+u2y4Qlr/d+CW+j0u3Kxwj0EfRpmE91qS59ubWidJyXpqTQrvYepX9IV3C2xeGvQi5e2Dtv1y3XTCmYawolf7rQgiPc30rP3Y+P5wO9pl6nv1xBwkTZzN7yyGTIxN12ZGCEhInzWbEW79ULpv3YD9SXxxJ/QBJwUTV+ZgdgCdSStEjMYI16XlorV02JcMLs1OosGmmjG7nku2dpdtY2Dgd5j0BzYeCv2vmjAw/vs3oF9ygrUu2Jxyvb4sopq3IoPhUhcvuNL+7ZA+H8kt456Zk17VEOa3FUGg5HJZOhXbXQlica7a7f7XxaPGEvaysjKysLEpKSpy+rbCwMFJSqt/VJyAggMaNG+Pr66KWG0IIAny9+fH+vhwpKKHPK4spq9D83xcb+L8v4ItxPendPMrsEEUdUVRazg3vr2LHoYLKZR/f0Y1BrWNMjEpYmSTsTtIzMYLZWw6RdazYJYNILE89yuwth3hoSEtzBq3w9oGRr8PHw+DnV2Hosy7ZbPjxbZDQx5hmTlhS72aR/PvnNNbvy6NfC+e3DEnLKeKDX9L4Q5fGdI2PcPr2fkcpGPEKvNvTGIDuhk9ds93MNRCRBCENXLM9J8nKyiI0NJSEhASn3wwtLCwkNDS0Wn+jtSY3N5esrCwSExOdFJkQ4kIa1Asg9cWRpOUUMej1ZQDc9KExQ8aMu3vRKynSzPCEBys+VcFd09ezfM/RymVPjWrDuH5JJkYlPIFkOU5yuh/7Ghf0Yz9VbmPyD9uIjwzinstN/FBo2hM632zMy56z2/nbO55JYEm2Mb2csKweiRH4equzvuCcRWvNsz/uwN/HmwkjnDiN26XUT4B+jxpdSPYscv72Ksog/ReP6DpSUlJCZGSky1ouVZdSisjISJe0ABBCXFhSdAgZU0fxv//77XPvT/9eTcLE2fy0I9vEyISnKSwpY/Q7y2kzeV7ltcz1XRuz58URkqwLh5CE3UlaNgglLNCXNWnO78f+0fJ00nJOMGV0OwJ8TR68Ysiz4BsEcx9z/gB0+1YYjx6QhNRlQX4+JDetz8o9zn+vLNyRzbLdOTw4pAUNQk0eKb3PAxDRDOY8CmVOTu4y10JpPrS8wrnbcRF3TdZPc/f4hKhLOjcJJ2PqKGaO7125bNz09SRMnM1X6/abGJmwuuyCEi5/dQkdpixgi322mz92a0LqiyN49fpO+HhLmiUcQ84kJ/HyUvRtHsWSXTnYbM5LXA8eNwaaG9Y2hoGt3KCpa0g0DHoK0pbC9pnO3Vb6z5T5hEBMe+duRzhdn2ZRbDuY79T52AtKypj8/XZaxYRye+8Ep22nynz8YdRrkJcGK9927rZS54OXLyQNcO52hBDCTXVpWp+MqaOY/2D/ymUTvt1KwsTZPPfjDqdeqwnP8ktqDgkTZ9PzpUXsyz0JwD39k0h/eSSvXNcRX0nUhYPJGeVEw9rFcLSolI2Zx51SvtaaiTO3AvD0lW406Fq3sRCbDHMegxNOauZcUQ675pIX0VX6r3uAPs0j0RpW7XVeLfvLc1I4UljC39zpy7TZIGh3DfzyOuTudd52UhdCfG9j+kUhhKjDWjUMJWPqKFZOHFQ5pefHK9JJemIOI976hZzCUpMjFO6owqZ5cbYx+8CtH62tXP748FakvTSSSSPbSOsq4TRuctXqmQa0aoCPl2Khk/pKfb0+i5935zBxRGtzBpq7EG8fGPNPKCkwknZn2L8SivPIib7MOeULl+rUJJxQfx8W7TzilPJX7DnKl2szuatfEp2ahDtlGzV2xctGbfv/xoOtwvHlH8+EIzugxTDHl10HrVu3jo4dO1JSUsKJEydo164d27ZtMzssIUQ1xYYHsvmZYWx/9gr62keQTzlUQPcXfyJh4mwWpUg/d2FMmTzotaU0e2IOH/ySXrl85vjeZEwdxfgBzfFy9Wwzos6RUeKdKCzQl15JkSzYcZiJI1o7tOyDx4t5ftYOeiVFcGuveIeW7RAxbWHABFj8ArS7GtqOcWz5KT+CTyB5EcmOLVeYwtfbi2HtGjJ/+2FevKY9/j6OG4vh5KlyJs7cQmJUMA8Nbemwch2mXiMY8Sp8d7cxYGOfBxxbfuoC49EDE/Znf9zOjoMFl16xGtrG1uOZqy48NWb37t0ZPXo0Tz31FMXFxdxyyy20by/dcoSwqmB/Hz4b1xOtNR8tT+eF2cZUjnd+uh6AUR0a8bfrOhLsL5fMdYXWmnnbDnPf5xvOWt6/ZTTv3pRMaIBM2SlcSz59nGxYuxgmf7+dPUeKaN7AMXOTn24KX6E1f/tDJ/e9s9fnQdjxA8x+BOL7QrCDplKx2SBlFjQfjM3b5IHDhMNc1akR327IYtmuHIa1a+iwcl+dv4vMvGK+uruX+YMyXkjHGyDlB+MGV4th0MCBN/h2zYXweIhq4bgy67jJkyfTvXt3AgICePttJ48/IIRwCaUU4/olMa5fEjsOFnD1P1dwqtzG7K2HmL31EAB/+0NHru/WWJo+e6iDx4sZ//kGNp3TlfXZ0e247bJ4+b8L00jC7mRD2hgJ+4Idh2neoLlDyvzv+kx+3p3Dc2Pa0TTSjZrCn8vbF65+D/59Ocx9HK77yDHlHtwAhQehzRQ45pgihfn6NI8iItiPHzYfdFjCvj4jj2krM7i1Vzw93XnuXaXgyr/DP3vC/+6FOxca75/aKjgIexdB7weMbXiYi9WEO1NeXh5FRUWUlZVRUlJCcHCwKXEIIZyjbWw9dr8wgrIKGy/NSeGTFRkAPP7tFh7/dgtRIX58fEd3OjZ2sy5WotpOlJbzxsLdfLQ8/azloQE+fHlXL9rHhZkUmRC/kT7sThYbHkjnJuF8+2sW2gHTnGUdO8kLs1LolRTBLT3dsCn8uRq2h/6Pw7ZvYPt3jilz20zw8vGYKaqEwdfbixHtG7Io5QgnT5XXurz84jL+OmMTceGBTHBwlxSnCImGK9+Egxth+ZuOKXPTF6Bt0OU2x5QnALj77rt5/vnnufnmm5kwYYLZ4QghnMTX24tnrmpHxtRRLHtsAK0bGgN3Hi06xeh3VpAwcTaj31nO3pwikyMV1VFYUsYz328jYeJs2j0z/6xkfcpVbUl7aSRbp1whybpwG1LD7gK39Irn0a83s2JPLn1bRNW4nFPlNu7/ciMa3Lsp/Ln6PWxMK/XDA9CoM0Qk1rys0iLY+Bm0uQoC5c62pxndKZbP1+xn4Y5sxnSOq3E5Wmue/G4rhwtK+PreywixSt/DtmOgw/Ww7BVjBPnG3Wpels1mvFcS+kFkM8fFWMdNnz4dHx8fbrrpJioqKujduzeLFy9m0KBBZocmhHCi+Mhg5tmnhFu8M5ux04w+7luy8hn8+jIAEqOCefW6jnRLiDAtTnF+OYWlPPvjdmZtOfS718Z0juW5Me0rZw0Qwt1Y5CrW2q7s2IiX5qQwbWVGrRL2V+fvZOP+47x7Uxf3bgp/Lm9fuO5jeL8/fDMWxs4HH7+albXpCyjNh17/59gYhVvonhBBfGQQHy1PZ3Sn2Br3F/t8zX5mbTnE48Nb0aVpfQdH6WQjX4XMtfDf2+Gen2s+9sO+5XAsHQZMcmx8ddxtt93GbbcZLRa8vb1Zs2aNyREJIVxtUOsYMqaOQmvN179m8fg3WwBIP3qC695fBYCftxcvXNOe67o0tk4Fi4fZc6SIyd9vY+V5poy97bJ4HhnWSpJ0YQmSsLtAgK83N/Zowj+X7iUz72SNpmCbteUgH/ySzm2XxTOqYyMnROlk9RPg6nfhq1tg9sMw+h/V71Nrs8Ga9yCuGzTp7pQwhbm8vBT3Xd6MiTO38nPqUS5vGV3tMtZl5DHlh+0MaBXNvf0tWLMcWB9umA4fDYOZ4+Dmb8CrBoPlrfsQ/MOg7WjHxyiEEAKlFDd0a8IN3ZoA8NOObB77ZjPHTpZxqsLG499sqUzmh7SJ4eGhLWkbW8/MkD1aSVkFn67M4OW5O8/7+kNDWnLvgCSHzkQjhCtIwu4iN/eM5/1laXy0PJ0po6s3UNLG/cd45L+b6Z5QnydHtXFShC7Q5iro/xj8/Co0aAOXVbOWPHU+5KXBdU85Jz7hFq7t0pi3FqXy7uI91U7YDxwv5r7PfqVJRBBv/SnZurUasZ1h1Gvww/3GgI0jX6veDa7MdbDje+P95hvovDiFEEJUGtI2ho2TjSk0tx/M5/lZO1idlgfATynZ/HTG3O7Xdonjr4NbEB8pg1bWVEFJGf9dl8mHv6RzuKDkvOs8P6Ydf+rRFF9vGbZLWJck7C4SGx7IDd0a85/V+7iua+MqD2SRfvQEd03/lZh6Afzr1m7Wvys44AnI2QULnoLQRtD+2qr9XVkxzH/SmJ6qjdQYejI/Hy/u6Z/ElB93sHLvUXo3q1o3kqNFpdz64RpKy23MuK2r9Zu5dbkNjqbCyrchrAn0fbBqf6c1zH8CQmKMqRWFEEK4XLvYMGbcfRkApeUVfL0+i9cX7OLYyTIAZm44wMwNByrX79s8itt7JzCwVTQ+klz+jtaa7QcL+Gh5Ot9tPHDB9a7qFMujw1rKjRDhUSRhd6GJw9uwcEc2T3y3le/G98H7ErV/aTlF3PjBamxa8/Ed3YgIrmG/b3fi5QXXvA+f/QG+HWc09W075tJ/t+QlyNsLt33vmOmuhFv7U4+mfLg8nce/2cLsB/pdMvk+fvIUt320loP5xXx2Z0+aNwh1UaRONuRZKDgAPz1jzIzQ+y+X/ptt30LWWqPbiX+I82MUQghxUf4+3tzSK55behmz+5woLefTVRn8fWEqpypsACzfc5Tle46e9XcDW0VzU894Lm8ZjZ9P3Uri03KK+G6jcVPjwPHiC653bXIcd/RJoH1smHVb1QlxCbVK2JVS1wNTgDZAD631+gusNxx4C/AGPtRaT7UvTwRmABHABuBWrfWp2sTkzsKCfJl8VTse+HIjby9K5aGhLS+47sb9x7jnP79SYdN8eVcvz0lAAPyC4eavjaT9m7Ew4hXodueFm/zuWwmr3oGud0DSABcGKswS4OvNP25M5vr3V/H4N5t5/5auFxyALv3oCcZOW8eBY8V8cHs3zxqd18sLrn4fbOWw4EkoOW60UvG6wIXbwY3w44PQqBN0vtm1sQqBXBcIURXB/j6MH9Cc8QOaA1BWYWPutsN8tnofa9PzKtdbsiuHJbtyzvrbyGA/BrRqwOWtounXPIr6Fq7MKS2vYH3GMZbtzmHZrhx2ZRdedP2G9QK4q38Sf+zexDqzvwjhALU927cB1wL/utAKSilv4F1gKJAFrFNK/aC13gG8AryptZ6hlHofuBN4r5YxubWrOjZiyc4jvLUoldJyGxOGtzorESmrsPHpygxembeTmHoBfHxHd1rGeFCyfpp/qDGY1rd3wuxHIGs9DHsBgs9p/pwyy6iJD4+Hoc+ZE6swRXLT+kwY3poX56QwaeZWJl/VliC/3z6ybDbNtxuyeHFOCl5K8fldPenuScn6aT5+cN0n8ONfjfEf9q+Gq9+D8CZnr5e9Az67zhi07sYZNRuoTojak+sCIarJ19uL0Z1iGd0ptnJZSVkF87Yd5os1+1mb8VsSn3viFN9uyOLbDVm/K8ffx4vkpuEkN61P5ybhtIutR8N6AaY0sddaU1hazq7DhWzJymdr1nE2Zh5nX+7JKv19dKg/1ybHMbpzLK0b1rtkq1QhPFmtEnatdQpwqamXegB7tNZp9nVnAGOUUinAIOAm+3qfYtyV9+gvZqUUr13fiUA/b95ftpeVe49ybXIc9YP92Jd7ki/X7udQfglD2sTw+vWdCAvy4ObfAfXgxq+MOaeXvWIMkpV8i1E7qLxh91zY8QPEdTHWC6hav3/hOcb1SyTv5CneX7aXtRl5XNe1MUlRIaRmFzJv+2G2HywguWk4b/0x2VpTHVaXl7fRxL1JT5g3Ef7RFdpcCS2GAQrSl8HmGUayfut3UC/2kkUK4QxyXSCEYwT4enN1chxXJ8dVLtNak5lXzM+pOSzbncPPu3MoLbdVvl5abmN1Wl7lQHeX4u2liAz2IzLEn/BAX3y8FX7eXvh4K3y8jMejR0qZl7uFcpvmRGk5Rfaf/OIyDhwrPmv7NdE1vj6Xt4ymf8to2jQKtf5YTUI4gSvak8QBmWc8zwJ6ApHAca11+RnL46gDvL0UL17dnraN6vHZ6n1M+XFH5Ws9EiN46ZoODGgVXeM5qC3FywsGToL2f4BfXoP1HxvNf8EYNKvXfTDoafDz4GRMXJBSignDW9OveRSTf9jO3+btsi+HVjGh/P2PnRndKbZu9FtTCrrcCon9jS4iW782+qsD+ARAz3uhz18hNMbcOIW4NLkuEKIGlFI0jQzilsjf+sOfprXm2Mkyth7IZ9P+42zMPMauw4Ucyj//6OkAFTbNkcJSjhSWXnzDBzMv/voFeHsp2seF0TEujA6Nw+jYOIxm0SEyYrsQ1aS01hdfQamfgIbneelJrfX39nWWAo+er6+avT/bFVrrcfbnt2LcXX8OWKW1bm5f3gSYo7XucIE47gbuBoiJiek6Y8aMKu3gpRQVFRESYu7ATIdP2LBpCPNXBPs6NvFwh/2rDmUrI6DkKN4VxRSFJIC6+Ie61favumT/znaiTJN9wkZMsJfD3yvO4Mz/n7KVEVh8GK28OeUXRoWP60fENeP8DAsLo3nz5i7ZVkVFBd7eZ9f2PP/880RGRjJ+/HgAnnvuOaKjo7nvvvvOWm/Pnj3k5+eftWzgwIG/aq27OTdq53OH6wJnXRM4m6d/pptFjmv12bSm3AZFZZqCUs2JMqjQmgoNFTaMRw0nikvw9fPHS0GgjyLAGwJ8FEG+inB/RZDPJVvUiPOQc9Z5rHJsq3NNcMkadq31kFrGkwWc2dmyMXAQOAqEK6V87HfTTy+/UBz/Bv4N0K1bNz1gwIBahmVYunQpjirLHcn+WZvsn7XJ/jleSkoKoaH2cT3mToTDWx27gYYdYMRUAAoLC3/blt348eO59tprmTBhAjabjZkzZ7J27drfrRcQEEBycrJjY3MT7nBd4KxrAmfz9M8Es8hxdR45ts4hx9V5PPHYuqJNyjqghVIqUSnlB/wJ+EEbVftLgOvs690OfO+CeIQQQogaSUhIIDIyko0bN7JgwQKSk5OJjIw0OyyrkesCIYQQoopqO63bNcA/gGhgtlJqk9b6CqVULMY0LSO11uVKqb8A8zGmb/lYa73dXsQEYIZS6gVgI/BRbeIRQghRh9hrwl1t3LhxTJs2jcOHDzN27FhTYnBXcl0ghBBCOFZtR4n/DvjuPMsPAiPPeD4HmHOe9dIw+q0JIYQQlnDNNdcwefJkysrK+OKLL8wOx63IdYEQQgjhWK4YJV4IIYTwGH5+fgwcOJDw8PDfDUonhBBCCOFIkrALIYQQ1WCz2Vi9ejVff/212aEIIYQQwsPJRIhCCCFEFe3YsYPmzZszePBgWrRoYXY4QgghhPBwUsMuhBBCVFHbtm1JS0szOwwhhBBC1BFSwy6EEEIIIYQQQrghSdiFEEJYijFdt/ty9/iEEEIIYR2SsAshhLCMgIAAcnNz3TYp1lqTm5tLQECA2aEIIYQQwgNIH3YhhBCW0bhxY7KyssjJyXH6tkpKSmqUeAcEBNC4cWMnRCSEEEKIukYSdiGEEJbh6+tLYmKiS7a1dOlSkpOTXbItIYQQQojzkSbxQgghhBBCCCGEG5KEXQghhBBCCCGEcEOSsAshhBBCCCGEEG5IuetIuxejlMoB9jmouCjgqIPKckeyf9Ym+2dtsn/W5uj9i9daRzuwPIHDrwmczdPfM2aR4+o8cmydQ46r81jl2Fb5msCSCbsjKaXWa627mR2Hs8j+WZvsn7XJ/lmbp++fcD05p5xDjqvzyLF1DjmuzuOJx1aaxAshhBBCCCGEEG5IEnYhhBBCCCGEEMINScIO/zY7ACeT/bM22T9rk/2zNk/fP+F6ck45hxxX55Fj6xxyXJ3H445tne/DLoQQQgghhBBCuCOpYRdCCCGEEEIIIdxQnU7YlVLDlVK7lFJ7lFITzY7HkZRSTZRSS5RSKUqp7Uqpv5odkzMopbyVUhuVUrPMjsXRlFLhSqlvlFI77f/Hy8yOyZGUUg/Zz81tSqkvlVIBZsdUG0qpj5VSR5RS285YFqGUWqiUSrU/1jczxtq4wP69aj8/tyilvlNKhZsZY22cb//OeO1RpZRWSkWZEZuwLqXU9fbPOZtS6oKjFnvy9YgzVPWzVSlVoZTaZP/5wdVxWsmlzkGllL9S6iv762uUUgmuj9J6qnBc71BK5ZxxHQclbAAABsBJREFUno4zI06rudh3tv11pZR6237ctyilurg6Rkeqswm7UsobeBcYAbQFblRKtTU3KocqBx7RWrcBegH/52H7d9pfgRSzg3CSt4B5WuvWQCc8aD+VUnHAA0A3rXV7wBv4k7lR1do0YPg5yyYCi7TWLYBF9udWNY3f799CoL3WuiOwG5jk6qAcaBq/3z+UUk2AocB+VwckPMI24Frg5wutUAeuR5yhqp+txVrrzvaf0a4Lz1qqeA7eCRzTWjcH3gRecW2U1lON9/ZXZ5ynH7o0SOuaxnm+s88wAmhh/7kbeM8FMTlNnU3YgR7AHq11mtb6FDADGGNyTA6jtT6ktd5g/70QI9mLMzcqx1JKNQZGAR734aaUqgf0Bz4C0Fqf0lofNzcqh/MBApVSPkAQcNDkeGpFa/0zkHfO4jHAp/bfPwWudmlQDnS+/dNaL9Bal9ufrgYauzwwB7nA/w+MC9PHARnwRVSb1jpFa73rEqt59PWIk3jMZ6ubqMo5eOYx/wYYrJRSLozRiuS97SQX+c4+bQwwXRtWA+FKqUauic7x6nLCHgdknvE8Cw9LaE+zN1tKBtaYG4nD/R3jQtpmdiBOkATkAJ/Ym/x/qJQKNjsoR9FaHwBew6i1PATka60XmBuVU8RorQ+BcRMNaGByPM40FphrdhCOpJQaDRzQWm82Oxbh0erM9YgDVfWzNUAptV4ptVopJUn9hVXlHKxcx36jNh+IdEl01lXV9/Yf7M22v7G36hK151Gfq3U5YT/fXUGPq0FRSoUA3wIPaq0LzI7HUZRSVwJHtNa/mh2Lk/gAXYD3tNbJwAms3Zz6LPb+hmOARCAWCFZK3WJuVKKmlFJPYnTD+dzsWBxFKRUEPAlMNjsW4d6UUj/Zx+I496eqNWl14nqkuhxwXAGaaq27ATcBf1dKNXNSuFZXlXNQztPqq8ox+xFIsHct+4nfWjGI2vGo89XH7ABMlAWceRerMRZvknsupZQvRrL+udZ6ptnxOFgfYLRSaiQQANRTSn2mtfaUpC8LyNJan24V8Q0elLADQ4B0rXUOgFJqJtAb+MzUqBwvWynVSGt9yN4U64jZATmaUup24EpgsPaseUKbYdxQ2mxv9dkY2KCU6qG1PmxqZMKtaK2H1LIIj78eqYmLHVelVJU+W7XWB+2PaUqppRitDfc6I16Lq8o5eHqdLHtXtjAu3iRZVOG4aq1zz3j6ATI2gKN41OdqXa5hXwe0UEolKqX8MAa88pgRRO39ij4CUrTWb5gdj6NprSdprRtrrRMw/neLPShZx54QZCqlWtkXDQZ2mBiSo+0Heimlguzn6mA8aFC9M/wA3G7//XbgexNjcTil1HBgAjBaa33S7HgcSWu9VWvdQGudYP+cyQK6SLIunMCjr0ec5JKfrUqp+kopf/vvURg3+j3pe9SRqnIOnnnMr8O47vKkm7TOcMnjek6/6tF45rWQGX4AbrOPFt8Lo+vlIbODqqk6m7Db+9/8BZiP8eb4r9Z6u7lROVQf4FZg0BlTRYw0OyhRLfcDnyultgCdgZdMjsdh7C0HvgE2AFsxPov+bWpQtaSU+hJYBbRSSmUppe4EpgJDlVKpGCONTzUzxtq4wP69A4QCC+2fMe+bGmQtXGD/hKgVpdQ1Sqks4DJgtlJqvn15rFJqDtSJ6xFnOO9nq1Kqm1Lq9EC0bYD1SqnNwBJgqtZaEvbzuNA5qJR6zj6WBxiVQJFKqT3Aw3hWqz+nqOJxfUAZUz9uxpg95w5zorWW831nK6XuVUrda19lDpAG7MFouTDepFAdQsnNMSGEEEIIIYQQwv3U2Rp2IYQQQgghhBDCnUnCLoQQQgghhBBCuCFJ2IUQQgghhBBCCDckCbsQQgghhBBCCOGGJGEXQgghhBBCCCHckCTsQgghhBBCCCGEG5KEXQghhBBCCCGEcEOSsAshhBBCCCEqKaWWKKWG2n9/QSn1ttkxCVFX+ZgdgBBCCCGEEMKtPAM8p5RqACQDo02OR4g6S2mtzY5BCCGEEEII4UaUUsuAEGCA1rrQ7HiEqKukSbwQQgghhBCiklKqA9AIKJVkXQhzScIuhBBCCCGEAEAp1Qj4HBgDnFBKXWFySELUaZKwCyGEEEIIIVBKBQEzgUe01inA88AUU4MSoo6TPuxCCCGEEEIIIYQbkhp2IYQQQgghhBDCDUnCLoQQQgghhBBCuCFJ2IUQQgghhBBCCDckCbsQQgghhBBCCOGGJGEXQgghhBBCCCHckCTsQgghhBBCCCGEG5KEXQghhBBCCCGEcEOSsAshhBBCCCGEEG7o/wGchvy0JoefTQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint\n", "\n", "pphi = lambda yy,t : [ -yy[1]+(yy[1])**2*yy[0] , yy[0]-(yy[0])**2*yy[1] ]\n", "\n", "yy0 = [0,1]\n", "tt = linspace(0,14,201)\n", "sol = odeint(pphi,yy0,tt)\n", "solx,soly=sol[:,0],sol[:,1]\n", "\n", "figure(figsize=(17,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,solx,tt,soly)\n", "grid()\n", "legend([\"x\",\"y\"]);\n", "\n", "subplot(1,2,2) \n", "plot(solx,soly)\n", "grid()\n", "xlabel(r'$x$')\n", "ylabel(r'$y$')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "E'(t)=x'(t)x(t)+y'(t)y(t)=0.\n", "$$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.16411889473e-07\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA9MAAAGmCAYAAAB/fdceAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3Xd4XNWd//H3lWS5qLj3XrGNbWxserPpAUJCEtIT0pZNNr+EbDbJbsqmbcqWbDadhJBeIIRAEjqhmB4MphiDcTfItlwk2ZYsucjS/f1xNNgYF5W5M6OZ9+t59FyQZs792tcGfXTO+Z4ojmMkSZIkSVL7FWW7AEmSJEmSuhvDtCRJkiRJHWSYliRJkiSpgwzTkiRJkiR1kGFakiRJkqQOMkxLkiRJktRBiYXpKIp+HkXRliiKlqZhrAVRFD1zwMfuKIre2M73To2i6LEoivZEUfSprtYiSZIkSVKU1DnTURSdCewEfh3H8Yw0jjsAWAWMiuO46aCvrYvjeNxBnxsCjAXeCGyL4/hb6apFkiRJklSYEpuZjuP4QaDuwM9FUTQxiqI7oyhaHEXRQ1EUTe3E0G8B7jg4SB+hji1xHD8BNHfiXpIkSZIkvUam90xfA3wsjuO5wKeAH3VijLcD16W1KkmSJEmSOqAkUzeKoqgcOBX4YxRFqU/3bPvam4CvHuJtG+I4vuCAMYYDM4G7DvjcD4HT2v51RBRFz7T98x/jOP56Wn8RkiRJkiSRwTBNmAXfHsfx7IO/EMfxTcBN7RjjrcDNcRy/smQ7juOPpv65bc/0a8aXJEmSJCmdMrbMO47jemBtFEWXA0TBcR0c5h24xFuSJEmSlGVJdvO+DpgPDAI2A18C7gOuBoYDPYDr4zg+1PLuQ403DngEGB3HcethXnOobt7DgCeBSqCV0GF8elu4lyRJkiSpwxIL05IkSZIk5atMd/OWJEmSJKnbS6QB2aBBg+Jx48YlMXTaNTY2UlZWlu0ylAE+68Lhsy4cPuvC4bMuLD7vwuGzLhzd6VkvXry4Jo7jwUd7XSJhety4cTz55JNJDJ12CxcuZP78+dkuQxngsy4cPuvC4bMuHD7rwuLzLhw+68LRnZ51FEUvted1LvOWJEmSJKmDDNOSJEmSJHWQYVqSJEmSpA4yTEuSJEmS1EGGaUmSJEmSOsgwLUmSJElSBxmmJUmSJEnqIMO0JEmSJEkdZJiWJEmSJKmDDNOSJEmSJHWQYVqSJEmSpA4yTEuSJEmS1EGGaUmSJEmSOsgwLUmSJElSBxmmJUmSJHVO827Y05DtKqSsMExLkiRJ6pxbPwFXnwq7d2S7EinjDNOSJEmSOuflv8P2l+GOf812JVLGGaYlSZIkddyeBti2FipHwrPXwQt/yXZFUkYZpiVJkiR13OYXwvV1/wUj5sAtn4CGTdmtScogw7QkSZKkjtu0JFyHz4bLroHmJvjrxyCOs1uXlCGGaUmSJEkdt3kp9OoHfUfB4Clw7ldg5d2w+JfZrkzKCMO0JEmSpI7btBSGzYQoCv9+4pUw/iy46/PQWJvd2qQMMExLkiRJ6pjWFtj8PAydsf9zRUUw/7PQ3AhVf89ebVKGtCtMR1G0Loqi56IoeiaKoieTLkqSJElSDqtbA/t2hZnpAw0/DqJiWG9kUP4r6cBrF8RxXJNYJZIkSZK6h03PheuwGa/+fGkfGHosbDBMK/+5zFuSJElSx2xeCkUlMHjqa782ah5seDosBZfyWBS3o3V9FEVrgW1ADPwkjuNrDvGaK4ErAYYOHTr3+uuvT3Opydi5cyfl5eXZLkMZ4LMuHD7rwuGzLhw+68Li8859M5d8lZ57anjyhO+95mvDqu9l6vLvseiE79NUNuaI4/isC0d3etYLFixYHMfxvKO9rr3LvE+L43hjFEVDgL9FUfRiHMcPHviCtoB9DcC8efPi+fPnd7TmrFi4cCHdpVZ1jc+6cPisC4fPunD4rAuLz7sbWPwRmHjGoZ/T1uGw/HucOKII5hzi6wfwWReOfHzW7VrmHcfxxrbrFuBm4MQki5IkSZKUoxproWHjqzt5H2jgZOjZ1yZkyntHDdNRFJVFUVSR+mfgfGBp0oVJkiRJykGbD9N8LKWoCEbOsQmZ8l57ZqaHAg9HUfQssAi4LY7jO5MtS5IkSVJO2tQ2rzZ05uFfM3IebH4B9jZlpiYpC466ZzqO4zXAcRmoRZIkSVKu27wUyodB+eDDv2bUPIhboPoZGHtq5mqTMsijsSRJkiS136alh1/inTKyrRGy+6aVxwzTkiRJktpn317Y+iIMO8ISbwiz1v3GuG9aec0wLUmSJKl9apZDa/PhO3kfaOQ8WL84+ZqkLDFMS5IkSWqfVPOxo81MQ9g3Xb8eGjYlW5OUJYZpSZIkSe2z6Tko6QUDJh79te6bVp4zTEuSJElqn83PwZDpUHzUQ4Fg+CwoKnHftPKWYVqSJElS+7Snk3dKj95hb7Uz08pThmlJkiRJR7e7HnbVwcBJ7X/PqHmw8WlobUmuLilLDNOSJEmSjq6hOlwrRrT/PSPnwd6dsHV5MjVJWWSYliRJknR09RvDtbIDYXpUWxMy900rDxmmJUmSJB3dK2F6ePvfM2Ai9KyE6iXJ1CRlkWFakiRJ0tE1tIXpig6E6aKi0IRs03PJ1CRlkWFakiRJ0tHVV0PvAaFLd0cMmwmbl0JrazJ1SVlimJYkSZJ0dPUbO7ZfOmXYzNCEbNva9NckZZFhWpIkSdLRNWzs2BLvlGEzw3WT+6aVXwzTkiRJko6uvrpzM9ODp0JRifumlXcM05IkSZKObN9eaNzSuTDdoxcMOsYwrbxjmJYkSZJ0ZDs3hWtnlnlDWOptmFaeMUxLkiRJOrL66nCtHNm59w+bCQ3VsHNr+mqSsswwLUmSJOnI6jeEa2UnZ6aHzwrXzc5OK38YpiVJkiQdWUPbzHRnl3kPnRGuLvVWHjFMS5IkSTqy+o1Q0ht69+/c+/sMgL6jodrjsZQ/DNOSJEmSjqx+Y1jiHUWdH8MmZMozhmlJkiRJR9ZQDRWdOBbrQMNmQu1K2NuUnpqkLDNMS5IkSTqy+g2dO2P6QMNmQtwKW5alpyYpywzTkiRJkg4vjqFhU+c7eacMmxmum9w3rfxgmJYkSZJ0eE210LK368u8+42Fnn3dN628YZiWJEmSdHhdPWM6JYrampA5M638YJiWJEmSdHj1bWdMV47s+ljDZsLm56G1petjSVlmmJYkSZJ0eA0bw7WiizPTEMJ0cxPUren6WFKWlWS7AEmSJEk5rH4jREVQPrTrYx3YhGzQ5K6Ply9aW8IPGVqaw/70fXsgboHi0kN8GOFyhU9CkiRJ0uHVV4cgnY4QN3gqFPUITchmvLnr43UnLc2weSlULYINi8MPKRproHFraPJG3L5xoqL9wbpiGAyZBkOmh+uIOdBvTKK/DO1nmJYkSZJ0eA0b07PEG6CkNATq6mfTM16ua6yFpTfCC38NAXrfrvD5iuHQfxwMmgRjT4GywVBaDiU9obhHCMpRMbSmZqr3hmtLM7Ts2f+5HVWwaWkYnxiIYNolcPo/w8i5WfyFFwbDtCRJkqTDq98IAyelb7wxJ8Ez14UwmI9a9sGqe+CZ38HyO0IgHjoD5r4PRp8YPvqOSu899zZBzQpYdgs88dNwHX9mCNUTFoRO6ko7w7QkSZKkw6uvDsEsXSbMhyeuhfVPpG/MXLHlRfjTB8Ny7j6D4MQrYfY7YdiMZO9b2gdGzA4fp38CFv8SHvsh/OYyOPYyuOQ70LtfsjUUIMO0JEmSpEPbsxP27EjfMm+AcWeEfb9r7oei09M3bjbFcQiwd34WSsvgLT+HaZeGJduZ1rMCTv1YCPKP/QDu/wasfxLefC2MOTnz9eQxj8aSJEmSdGgNqTOmR6RvzN79wn7eNQvTN2Y2NdXBDe+BWz8RwupHHg3N1bIRpA9U0hPO+Bf4wN1QVAy/eB0s/M+wDF1pYZiWJEmSdGj1bWdMpzNMQ1jqvWExJc070ztuJm1aCnd9Hn54Ytgbfd5X4d03QUUajhBLp1Fz4R8fgpmXw8Jvwo9PhyV/NFSngWFakiRJ0qGlZqYr0h2mF0DcSr/tz6V33CQ174L1i+GR78HVp8OPT4PHfwyjToAP/g1OuwqKcjRe9aqEN10Db/11+PebPgQ/mBeWpu/bk9XSujP3TEuSJEk6tPoN4VqZxj3TEAJojzL6b8vhI7L27QldsVf+DTYtga3LIW4JXxs5Fy76Fhz7JigbmN06O2L6G2Dq62HFHfDgt+CWq+CB/4FzvwQz3pK7PwzIUYZpSZIkSYdWXw29+oamWulUUgrjTqP/+hwM09teCjO2T/0ammqgbEjokj31Yhg2C0bMgX6js11l5xUVhV/LMReFJnD3fBlu+ocwy37BN8PRZWoXw7QkSZKUSa2t3WcGsH5j+pd4p0xYQJ+Vd8P2l6HfmGTu0RHbX4a7PgfLbg3nMk+5EE74IEw4u/s8r46IIph4NoyfD0uuh3u/Cj8/PxylddG3oGxQtivMeXn4p0KSJEnKUS/eBv8zIZxH3B00bEz/Eu+UiQvCNdtdvVtbwpnMPzwJVt0LZ3wSrloC77gOJp2bn0H6QEVF4Szsjy2Gs/4NXrwdfnIWbHgq25XlvDz/kyFJkiTlkA1Pwa5tcOP7Q0OrXFdfnf5O3imDp7KntD+svj+Z8dujeglce06YkR53Onz0cTjni917GXdnlZbBgs/CB+8Ks9Y/vxCe/m22q8pphmlJkiQpU3ash5LesOWFEOCOprUlNIi67p2ZP8qopRl2bk5umXcUsa3/cbD2gbD0PZNaW+Ghb8M182HHBnjLL+CdN+TGcvNsGzEHrlwY9k7/5aNw6ydh396ujVm9hH7blqSjupximJYkSZIyZcf60Mzq1I/Dkz+HF/5y5Nf+6vVw/9dg+W1Q/Uzm6oQQpImTW+YNbOs/G5pqYXMGj8hqrIXfvxXu/QpMvxT+3yKY8aYwG6ugbBC8++a2P6c/g6tPgedvhjju+FjVS+DXlzJlxY/z7mxrw7QkSZKUKTtehr6j4ex/D8cr/eVjoXv0wZbdAlefBhufgQv/C4gyvxy6vu2M6cqRid1iW/9Z4R8y9Wt7+e/wkzPCbPjF/xtmpHv3z8y9u5viEjj/P+BdN0JRD/jj++CnCzq2x70tSFNazpJZXwxj5hHDtCRJkpQJrS2hO3bfUeFoqDf/DIjhTx+CFXfB49fAnZ+D37wJ/vBu6D8WPvwQnPxhGD4rHGOUSQ1tYbp8aGK32NtzIAyelpkmZE/9Bn5xERSXwofugRM+5Gx0e0w+Dz7yCLzxamisgV+/Aa49Dx74b6h64vCzzQcEaa64hd29h2W27gzIrx8NSJIkSblq52Zo3RfCNMCA8XDJ/8GfPhiWHUPYT91/HJz+SZj/2RC6ASYsCB2n9+yEnuWZqbepJlzLhyR7nwnzYfEvYE8D9KxI5h4r7oZbPh7udfkvw9nZar+i4tDx+9g3hWXfS/4A938D7v869KyEsafC4KkwcBIMnAhxa/iBUFuQZsB44BArMLo5w7QkSZKUCdurwvXAJlcz3wIDJoSQ3W9sCK6Hmi2dMB8e+Q689AhMuSAT1YZZSIA+CZ83PPNyePxqWPTTcCxVum18JixRHjYT3vqbzP0wIh/16AWnfDR8NNbCugfDqoKXHgvHirU2739t39EHBOn8ZJiWJEmSMmFHW5hOzUynjDz+6O8dcwqU9ArBJWNheiv07Lt/djwpo+bCpPPg0e/Dif+Q3tnp7S+HWf8+A0K3boN0+pQNhGMvCx8QtjHsqILaVaF53uTzkztWLUe4Z1qSJEnKhB3rw7UzDb169AqBOpNNyBprQlfnTJj/WdhVF2an02XXdvjd5dC8G971R6jIvz27OaWoOGxRmHQuzH1f3gdpMExLkiRJmbFjfdir26uyc++fuAC2LtvfZTtpjVszF6ZHzQ0zmY9+L+yd7qq9TWHPbu1qePtvYci0ro8pHcQwLUmSJGXCjiroO+borzucCQvCNROdryGc/1w2ODP3Ajjr32DXNlh0TdfG2dsE170N1j0cOlCPPzM99UkHMUxLkiRJmbBj/Wv3S3fE0BmhGVimjsjK5Mw0tM1OXxD2Tu+u79wYe5vgurfD2ofgsp/ArMvTW6N0AMO0JEmSlAk7qroWpouKYMJZYWY6jtNW1iG1toaZ6aQ7eR9s/r92fna6eRdc/w5Y+yBc9mM47m3pr086QLvDdBRFxVEUPR1F0a1JFiRJkiTlnd31sHsH9BvdtXEmLAjnVW95IT11Hc6ubeGs4Ewu8wYYORemXNjx2emaVfD7t8GaB8LS7uPenlyNUpuOzExfBSxLqhBJkiQpb6U6eXdlZhpCEzJIft9049ZwzeQy75Sz/jX84OEnZ8KLtx1+Fr5lH7zwV/j1G+AHc+GlR+GNP4LZ78hsvSpY7QrTURSNAi4Grk22HEmSJCkPvRKmuzgz3XcUDJyc/BFZTTXhmo0wPfJ4eM9NUFwK178Tfn0pbFoalp5vXQ5P/xZuuQq+MxNueE+YlT77C/DPz8Psd2a+XhWsKG7Hfosoim4EvglUAJ+K4/iSQ7zmSuBKgKFDh869/vrr01xqMnbu3El5uYe3FwKfdeHwWRcOn3Xh8FkXlnx83iM23MGUlT/m0VN+zt6eA7s01qSV1zC8+h4ePv13xEU90lThqw3e8gjHvvDfPDHvuzSWj0vkHnDkZx21tjC8+k7Gr72Okn2NtBT3pqSlEYB9xWVs7zed6uHnUTdgHnFRcWI1Kj2609/rBQsWLI7jeN7RXldytBdEUXQJsCWO48VRFM0/3OviOL4GuAZg3rx58fz5h31pTlm4cCHdpVZ1jc+6cPisC4fPunD4rAtLXj7vexbC6h6cet5loZFYVwxrhOtv46zxvWD8GWkp7zUWrYQX4ISzXgcVQ5O5B+151ufArs/Bo9+npKkWRp0Ao06gZOBkBhUVkYV5c3VSPv69PmqYBk4DLo2i6CKgF1AZRdFv4zh+d7KlSZIkSXlix3qoHNH1IA0w9rRwffnvyYXpxrZl3n26NoueFr37wzlfzHYV0msc9W9zHMefjeN4VBzH44C3A/cZpCVJkqQO2LG+6/ulU3r3g8HToOrx9Ix3KI1bQ4gtbs/cm1SYPGdakiRJStr2qq4fi3Wg0SfC+kWhKVcSmmoyfyyW1M10KEzHcbzwUM3HJEmSJB1Gyz5o2Nj1Y7EONPqkcHxU7cr0jXmgRsO0dDTOTEuSJElJaqiGuDXNYfrEcE1qqXdjTW7sl5ZymGFakiRJStKOqnBNZ5geOCnsaU4sTG91Zlo6CsO0JEmSlKQd68O175j0jRlFYal31aL0jZnSsg921RmmpaMwTEuSJElJemVmemR6xx19ItSsgKa69I67q228Mk9xlo7EMC1JkiQlacd66D0ASsvSO+7ok8J1/ZPpHbdxa7gapqUjMkxLkiRJSUr3sVgpI+ZAVJz+fdONNeHaxzAtHYlhWpIkSUrSjvXQN4EwXVoGw2YmEKZTM9PumZaOxDAtSZIkJSWOw57pdHbyPtDok2DD4tA0LF2aasPVMC0dkWFakiRJSsru7bB3Z4Jh+kRoboLNS9M3ZuNWiIrC0VuSDsswLUmSJCXllWOxEljmDQc0IXsifWM2boU+A6HIqCAdiX9DJEmSpKQkHab7joKK4endN91YY/MxqR0M05IkSVJSXgnTCS3zjqKw1DvdYdpjsaSjMkxLkiRJSdn+MhT3TLaZ1+iTwn3qq9MzXlONzcekdjBMS5IkSUnZsR76jkx2//Er+6YXpWe8xq3OTEvtYJiWJEmSkrJtHfQbk+w9hs0Ks99VaQjT+/bC7h3OTEvtYJiWJEmSkhDHULcaBkxM9j4lpTBkGmx5oetjpc6Y7jOw62NJec4wLUmSJCWhqS7M8g5MOEwDDJwEtau7Pk7j1nB1Zlo6KsO0JEmSlIS6tnCb9Mw0hMC+owr27enaOE014WqYlo7KMC1JkiQlITVTnImZ6QETIW4Ne7S7ojEVpm1AJh2NYVqSJElKQt1qiIqg39jk75UK7F1d6m2YltrNMC1JkiQloXZ16ORdUpr8vQZMCNe6robprVBUAr36db0mKc8ZpiVJkqQkZKKTd0qfAdC7fxpmprdCn0EQRempS8pjhmlJkiQp3eIYatdkZr90yoCJXZ+Zbqq1+ZjUToZpSZIkKd0at8LehszNTEMI7rVrujZG41Yo84xpqT0M05IkSVK6ZbKTd8qAiVC/Hpp3dX6MxhpnpqV2MkxLkiRJ6fbKGdMTMnfPVHCvW9v5MQzTUrsZpiVJKnRxDFuXw471sG9vtquR8kPt6tAVOxPHYqV0taN38+6wNL2Py7yl9ijJdgGSJCnLVtwF171t/7/37g/lw+CED8IJH7Krr9QZdatDkC7O4LfbXT1ruil1xrQz01J7GKYlSSp06x6Ckl5w4X+G5kM7N8Om5+D2T4WvXfp96NU321VK3UumO3lD+HvaZ1DnZ6Ybt4Zr2aD01STlMcO0JEmFrupxGDEH5r1//+daW+Gx78M9X4HqJfDWX8Hw47JXo9SdxHEItONOz/y9u9LRu7E2XJ2ZltrFPdOSJBWy5t1Q/SyMPvHVny8qgtOugvffDvv2wLXnwZIbslOj1N00VENzU+ZnpqFrZ007My11iGFakqRCVv0stOyFUSce+utjToYPPwTDZ8Edn4GW5szWJ3VH2TgWK2XghBDm9zZ2/L2pMN3HMC21h2FakqRCVvV4uB48M32gskFw2idg1zZY93Bm6pK6s1eOxcrSzDRAXSeWejfVQHFP6FmR3pqkPGWYliSpkK1fBP3HQ/mQI79u0jnQowyW/TUzdUndWe1qKC6FvqMyf++udPRu2BT+W2AHf6ldDNOSJBWqOIaqRUeelU7p0RsmnwfLboXWluRrk7qzujXhh1RFxZm/d1fOmq5ZCQMnpbceKY8ZpiVJKlTbXwrHYLUnTANMvxQat+xfGi7p0GpXZ2e/NIQl2uVDO97RO45DmB40JZm6pDxkmJYkqVBVPRGuh2s+drDJ54f9lC+41Fs6rNZW2LZ2/wxxNnSmo3fDJtjbAIMmJ1OTlIcM05IkFaqqx6G0HIZMb9/re1aEvdPLbgmzWJJeq34D7NudvZlpCB29O7pnumZFuDozLbWbYVqSpEK1fhGMPB6KS9r/nmmXQv162PBUcnVJ3Vk2O3mnDJgYtmTsrm//ewzTUocZpiVJKkR7dsKmpTD6pI6975gLoagEXvhzMnVJ3V02z5hOSd27I0u9a1ZAaQVUDEumJikPGaYlSSpEG5+CuKX9+6VTeveH8WeFI7Jc6i29Vt0aKOkFFSOyV8OAThyPVbMi7Jf2WCyp3QzTkiQVoqpF4TpqXsffO/1S2LYONj2X1pKkvFC7OjQfK8rit9mvHI/VgY7edvKWOswwLUlSIapaFL5x7jOg4++deglERWF2WtKr1a3ObidvgNI+YWa8vTPTexpC4zQ7eUsdYpiWJKnQxHFoPtbe86UPVjYIxp7mEVnSwVr2hVUb2dwvnTKwA8dj1a4K18HHJFePlIcM05IkFZraVbBrW8ebjx1o2uuhZjlsfzl9dUnd3dZl0LIXhs7IdiVhdrx2Vft6G9SsDFeXeUsdYpiWJKnQVD0erh1tPnagYbPCdevyrtcj5YtXehGckN06IBx7t2vb/iOvjmTrcoiKof/45OuS8ohhWpKkQvPSY9Crb9dmoVLvbc836lKhWP8ElA2G/uOyXUnoug+w5oGjv7ZmBQwYDyWlydYk5RnDtCRJhaSlGZbfDpPP71q34bKB0HuAYVo6UNWisOIjF46XGjAe+o2Bte0J03byljrDMC1JUiFZ+yDsqoNjL+v6WIOm7N9rKRW6xtrQ8Gt0DizxThl/Jqx7CFpbDv+aln2hbjt5Sx1mmJYkqZA8fzOUVsDEc7o+1qDJzkxLKeufCNeu9CJIt/HzYfcOqH728K/Z/lJomubMtNRhhmlJkgpFSzMsuwWmXgQ9enV9vEFToHErNNV1fSypu1u/CIpKYMScbFey3/gzw/VIS73t5C11mmFakqRCseYB2L09PUu8Yf8336kzaqVCVrUoHIlV2ifblexXMRQGTwvbOw4ntbpk4KTM1CTlEcO0JEmF4vmboWclTDw7PeOl9li61FuFrmUfbHgKRufQEu+U8WeGDv779hz66zUrQgfyPgMyW5eUBwzTkiQVgn174cVbYOrFUNIzPWP2GwvFpYZpacsL0NyYG+dLH2zCWbBv1/493QerWeESb6mTDNOSJBWCNQtDI6J0LfEGKC6BAROhxmXeKnDrF4VrLobpsadBVHTo86bjGLYuN0xLnXTUMB1FUa8oihZFUfRsFEXPR1H0lUwUJkmS0uj5m6FnX5iwIL3j2tFbgqonwlLp/uOyXclr9e4XmqIdat90U23oo2CYljqlPTPTe4Cz4zg+DpgNXBhF0cnJliVJktJm3x548TaYdgmUlKZ37EFTYNva0ClcKlTrF4UjsaIo25Uc2vgzYcOTsGfnqz+f+kGYYVrqlKOG6ThI/c3r0fYRJ1qVJElKn9X3w540L/FOGTQFWvdB3dr0jy11B401ULcGRufgEu+U8WeFv6cvPfrqz78SpidnviYpD5S050VRFBUDi4FJwA/jOH78EK+5ErgSYOjQoSxcuDCNZSZn586d3aZWdY3PunD4rAuHz7p9pi67moEl5TxaBfGGhWkdu6K+nrnA0oU3UTM4uYVrPuvC0p2e98CaJ5gJPF1Tyo4crbmoZS+nRz3Y8ODvWL1x/+qUiavuY0RRKQ89sxqi7PxArDs9a3VNPj7rdoXpOI5bgNlRFPUDbo6iaEYcx0sPes01wDUA8+bNi+fPn5/uWhOxcOFCukut6hqfdeHwWRcOn3U7xDH8/Qo49lLOOvu89I+/Zy489SlmDCuFM+anf/w2PuvC0q2e970PQlEJcy56f26dMX2wqpMZvXs1ow/8fd3wQxh8DPMXpOm4vE7oVs9aXZKPz7pdYToljuPtURQtBC4Elh7l5ZIkKdsat4YGQyNmJzN+zwqoGAE1K5MZX8p1VYtg6IzcDtIQlnrf/zW472ud56RWAAAgAElEQVSwcws0VMO6h2HKhdmuTOq22tPNe3DbjDRRFPUGzgVeTLowSZKUBrVtx1YNnJjcPezorULVsg82PAWjT8x2JUd3zIVABA9+C5bfAQ2bYNwZcMKHsl2Z1G21Z2Z6OPCrtn3TRcANcRzfmmxZkiQpLV4J05OSu8egKbDkhrCkPFe7GUtJ2PICNDeGTt65bthM+LeXoEcfKO6R7WqkvHDUMB3H8RJgTgZqkSRJ6Va7CopLoe/o5O4xaHLoFr5zC1QMTe4+Uq5Z91C4jjkpu3W0V6++2a5AyivtOWdakiR1V7WrYcAEKCpO7h6pY3Vc6q1Cs/wOGDId+o3JdiWSssAwLUlSPqtdlewSbwjLvMEwrcLSVBfObT7mddmuRFKWGKYlScpXrS1QtybZ5mMQunn3KLOjtwrLqnsgboFjLsp2JZKyxDAtSVK+2lEFLXuTn5kuKoJBk5yZVmFZfjuUD4URx2e7EklZYpiWJClfZaKTd8qgKc5Mq3Ds2wsr7wlnNBf57bRUqPzbL0lSvqpdHa4DJyd/r0FTYMfLsLcp+XtJ2fbSw7C3wSXeUoEzTEuSlK9qVkLPvlA2KPl7pTp6p2bDpXy2/A4o6Q0Tzsp2JZKyyDAtSVK+ql0Vmo9FUfL3sqO3CkUcw4u3w8SzoUfvbFcjKYsM05Ik5ava1ZnZLw3Qf3y4bluXmftJ2bLpOahf75FYkgzTkiTlpeZdoZt3psJ0aR/o1Q8aqjNzPylblt8BRDDlgmxXIinLDNOSJOWjurVAnPwZ0weqHAH1hmnlueW3w6gToHxItiuRlGWGaUmS8lEmj8VKqRgODRszdz8p03ZsgOpnYKpdvCUZpiVJyk+vhOlMzkwPd2Za+W3FneHqkViSMExLkpSfaldD+TDoWZG5e1YMh8Yt0LIvc/eEcLZ1pu+pwhPH8PRvw2qPVPd6SQXNMC1JUj6qXZXZJd4QwnTcGgJ1puxthB+dBD88ITSGiuPM3VuF5cXbYONTcPo/Z+a4OUk5zzAtSVI+Sp0xnUmVI8I1k0u9H/kebH85hPjr3g6/fRNseTFz91dhaG2B+74GAyfDrLdnuxpJOaIk2wVIkqQ027UNmmqyMzMNbU3I5iZ/v/qN8Mh3Yfob4c3XwhPXwv3fhKtPhTM/BQs+l3wN3VljDdSsgJqV4YcvtavDn53mpvCxtwla90FRCRQVh2txDygtg9Ly8NHzwGtFuPashN79oHf/cFxaxTDoMyDbv9quWfon2LoMLv8lFPvts6TA/xpIkpRvateEa6bDdKZnpu/9KsQtcN5XQsg7+SMw83K4/dPwwH/B5AtgVAZCfXfRVAfrHoI1D8DaB6F25f6vFZfCgAlQNhjKh0KP3iE0FxVDa2sI1XELtOwNS+v37ISmWtjTAHt3hn9v2XP4e4+YE5p2TbkQhs3sXsukW5rh/q/DsFkw7Q3ZrkZSDjFMS5KUb7JxLBZAn0FQ1CMzx2NteAqevQ5O+wT0H7f/82WD4NLvwZqFsPCb8O4bk68l19Wsgnu+FPb8EkOPMhh7Ksx5Nww9Nvw56TcmBOeuaGkO4XpPPezaHma5d22DutWw4i64/xshlPYdDRd8HaZ3k2D69G9g2zp45x+hyB2SkvYzTEuSlG9qV0FU9OqQmQlFRWFJb9Iz03EMd30+hPcz/uW1X+9ZAad9HO75MlQtgtEnJltPrmqqgwf+G574KZT0Co2zplwAI+eGmfx0K+4RlnP3GQD9D/ramZ+GnVtCqH7iWrjhvXDOF+H0T+b2LHXzrvB7OPpkmHxetquRlGMM05Ik5ZvaVdBvLJSUZv7eFcOTn5le9ld4+VG45P+gV+WhX3PCP8CjPwizoe/9c7L15Io4DvvINy+FDYvh8Z+EWeLj3wsLPg/lQ7JbX/kQOP49YSn+Xz4alunXrILXfzc7f1bb44lroaEa3vyz3A79krLCMC1JUr7JxrFYKZXDYfMLyY2/bw/87YswZDrMee/hX9ezHE67Cv727/DSYzD2lORqyqa6tbD8dlh5N1QvgV11+7828Rw4/z/CUu5c0qNXaBg3aHJYir/9JXjbb3OvSdnq+8Ks9MRzYNxp2a5GUg4yTEuSlE/iOHRlHpulb/4rhsOqe5Mbf9W9Yf/qO64/elflEz4Ej34fFn4DrrgluZoyrXY1PHt92AO95fnwuSHTYdolMHQmDJsRAnSvvtmt80iiCOb/GwyYCH/5J/jFRfC+26BsYLYrC3+HHvku3PsVGDwNXv+dbFckKUcZpiVJyicNm6C5MfNnTKdUDG/r7twQ9i6n28q7whFME885+mtL+8Dpn4C7PgfrHoZxp6e/nkxavxge/S688NcQRsecAhd8I3TJHjA+29V1zqzLoWIo/O5y+O1l8N6/hmO1smVvY1iC/vzNcOxl8IYfhq7mknQItiSUJCmfvNLJO0thOsnjseIYVtwNExe0f4/tvA+Eo57u/0Z4f3e0+n74xcVw7dmwemFoJPbJZfD+2+GUj3bfIJ0y/sywzHvzCyFU79mZnTp2boVrz4MX/gLnfgXe8guDtKQjMkxLkpRPtq0L1wETsnP/iuHhmkQTsk3PhXGnXND+9/ToHTp+v/RI2APbnezcAjd+AH7zRti2Fs7/OnzyeTj3S6Frej6ZfB685eehcdp1b6foSGdWJ+XOfwtnb7/rxrCiwYZjko7CMC1JUj7Ztg6iYqgclZ37JzkzvfKucJ3UwSOK5r4vdDe/+wvQ2pL2stKutRUW/wp+MA+W3QLzPwsffxpO/X/JLJ3PFdMvhTdeDeseZsbSb0JjTebuvfo+WHpj+MHLpHZsIZAkDNOSJOWXbWuh3+ijN+dKSpIz0yvuhhFzwh7bjijpCed9Fba8AE//Jv11pdOu7fCr18MtH4ehM+DDj4RGXSU9s11ZZhz3Nnj9d+m3fQn84AR45vfJL89v3g23/UtohnbaJ5K9l6S8YpiWJCmfbFsH/cdl7/6lfUIX6TTPTPfYWw/rn4DJHVjifaDpbwgNu+77GuyuT2ttadOyD258P1T9HV7/PbjiVhg8JdtVZd7cK1g89//C8W5//gj8+tLQwTwpD38b6tbAxf8bju2SpHYyTEuSlE+yHaYBKkZAQ3rD9IC6p4AYppzfuQGiCC74OjRuhYf/L621pc3f/j0sN774f2HuFVBUuN+mNZaPhQ/cBRd/GzY+Az86BZbckP4b1awMfx5mXh4a20lSBxTuf6UlSco3u+uhqRb6Z7m7c+VwqE/vMu8BdU9C2RAYPqfzg4ycC7PeBo/9ELa/nL7i0uGp38DffwQnfTjs8Vb4YcIJH4SPLoJRJ8BN/wB/vzp948cx3PrPUNI7HDEmSR1kmJYkKV9sfylc821mumVfmJmefH7XZ2vP+SJERXDPl9NSWlq89FgIdRMWhI7derXK4fDuP8G014eO2/d8JT37qJ/+Dax7KHRHLx/S9fEkFRzDtCRJ+SJ1LFbWw/Qw2Lk57AFOh6rH6bGvsfNLvA/UdxSc+jFY+ieoWtT18bpqexX84d3Qbwxc/ovsNY7LdT16weW/CrP2D38b/vqxrv35WnoT3PIJGHcGzH1/2sqUVFgM05Ik5YtcCdOVwyFuDfuT02HlXbRGJWHmNh1OuyrMnv/5n2BvY3rG7Kw7/hX27YZ3XA+9+2e3llxXVAyXfAfO/HSYVb7+HaH7eUct/RP86UMw+kR4x3UFvTddUtf4Xw9JkvJF3Vro1Q9698tuHRVtZ02n63isFXezo+906FWZnvF6lsNlP4baVSHMZsvah2D5bXDGJwuza3dnRBGc/YXQmGz1fXDNfNj8Qvvf/9yNbUH6JHjXjfl9brekxBmmJeWuPQ3Q2prtKqTuIxc6eUOYmYb0HI+1/WXYuozagfO6PtaBJpwVQuzTvwkzlZnW2gp3fx76joaT/ynz9+/uTvggvO82aG6Ca88Jy7YPp7U1HH319x+HJmZjToF3/TH8UEWSusCNOZJy06bn4Cdnhi6rg4+BIdNg8FSY8WboOzLb1Um5ads6GDYz21UcMDOdhjC98m4AagfOZVLXR3u1+Z+FtQ+GvbMj52b2BxFL/gDVz8KbroUevTN333wy5mT4xwfhhveG87lfvBXKBoctBnFrWD6/dXmYuW5uW84/7gx45x+gtCy7tUvKC4ZpSbnp+ZuBCOa8K3wztOpeeOZ3sGExvPVX2a5Oyj2tLWEWd9rrs11JCDRFJek5HmvdI1A5kl29E/ghWnEPePPP4Menw40fhA/cGT6XtL1NcO9XYcTx4QeE6ryKYXDFreGM7mevD5+LisJHUQkMmgzHvweGHgtDjoURs8Pea0lKA8O0pNz04u0w9lS46H/2f+6vH4OlN8O+vVBSmr3apFxUvxFam2FAls+YhtDQqXxYemamqxaF/a1R1PWxDqX/WHj9d+DGD8D93wjHJCXtsR+E/eRv+bnNr9KhpBRe91/hQ5IyyP+CS8o9dWtg6zI45qJXf37K62BvA7z8aHbqknJZrnTyTqkc3vWZ6R0boH596LqcpBlvhtnvgke+G1bCJKlhEzz8HZh2KYw9Jdl7SZISZZiWlHuW3xGuUw8K0xPOguKesOKuzNck5bpcC9MVw7s+M72+7RzopMM0wHlfhdJyuOtzyd1j3164/VPQshfO+0py95EkZYRhWlJ2XPcOuP0zh/7ai7eHvW0Hh4LSMhh/ZgjbcZx4iVK3sm0tRMVQOSrblQSVI7rezbvqCSjpBUMz0FStbBCc9RlYdQ+suDv94+/cCr++FJbdEo52GjAh/feQJGWUYVpSdrz0KDxx7f7ZtJSmurCM++BZ6ZRjLgyhoWZl4iVK3cq2ddBvNBTnSDuUimFhW8aehs6PUfV4aNKVqR4JJ14JAyeF2emW5vSNu/GZcB7yxmdCw7PTP5G+sSVJWWOYlpR5zbtg93aIW8LewQOtuCscaXLM6w793skXtL3uzmRrlLqbXDljOuWV47E2de79zbvD0VGZWOKdUlIK538daleGH/Z1VRzDkj/Czy8E4tAtfOZbuj6uJCknGKYlZV6qKVHZkHDc1YFNipbfFvZaDp9z6Pf2Gw1DZ7hvWjpYroXpyuHh2tkmZNXPhO7kmQzTAFMugAkLYOE3obG2c2O0tsKyW+Hac+CmD4XjmK5cGK6SpLxhmJaUeammRGd/IZyN++j3w78374ZV94VZ6SMdFzPlQnj5Mdi1Lflape5gdz001UL/HDgWK+WVmelO7puuejxcR2U4TEcRXPhN2LMzBOqO2LcXnv0DXH0K/OFd4Zlc8n/w3r9C+ZBk6pUkZY1hWlLmpZZ9jj4JZr0NnvxFaM6z9gFoboRjLj7y+6dcGJaIr7o3+Vql7mD7S+GaTzPTVYvCDwfKB6evpvYaMg3mfQCe/Bn86UOw7uEjNz3cugLu/gJ8exrcfCVERfCma+H/LQ7jZGrPtyQpo3KkS4mkgpL65rpyOJzxSXj2Ovj7D8NMc2k5jD/jyO8feTz0GRT2Tbv/UMq9Y7EgdN/v2bdzM9NxHML0xLPTX1d7nfulEIqfvR6e+2NoTHb8e6FyZGiqtndnuK59MKyUKSoJP+g7/gqYdO6RV9dIkvKCYVpS5jVUQ48y6FkJvfrCsW+ERddCj14w6Rwo6Xnk9xcVw+TzYfnt0LIvd7oXS9lStzZccylMQ/iBWWdmpretg8Ytmd8vfaCeFXDRf8O5X4YX/gKLfwl/++JrXzdwMpz7FZj9TpdyS1KB8TtQSZnXUB2+yY6i8O9nfAqevzkco3O0Jd4px1wIz/4+7Kscd1pytUrdwbZ10Ksf9O6X7Uperf/4zh1jt/6JcM1mmE4p7QOz3xE+tr0E+3aHFTQ9K8LVGWhJKlj+H0BS5tVXh47dKcNmwJTXhWWSk89r3xgTFkBRD4/IkiD3OnmnjJgDNSs6ftZ01eMhqA6ZnkxdndV/LAw+BvqOhF6VBmlJKnD+X0BS5jVsfHWYBrj0+3DFLdBnQPvG6FUZZqQ9IkvK3TA9ci4Qw8ZnOva+qsdh1LywpUOSpBxlmJaUWXEcunlXHhSmywfD2FM7Nta406FmOezekb76pO6mtQW2v5ybYXpE23nxGxa3/z17dsLm5zN/JJYkSR1kmJaUWU110LL3tTPTnTG87Rv16me7PpbUXdVvhNZmGJBDZ0ynlA0MIX/jU+1/z4bFELeGo/MkScphhmlJmdXQ1tk3HWF6xOxw7egSUimf5OKxWAcacTxs6ECYrloUrqPmJlOPJElpctQwHUXR6CiK7o+iaFkURc9HUXRVJgqTlKcaNoVr5Yiuj1U2CPqOhmrDtArYthw9Fitl5FzYUQU7t7Tv9esXweCp0Lt/snVJktRF7ZmZ3gf8SxzH04CTgY9GUZRj7TUldRupM2crhqVnvOHHOTOtwla3FqJiqByV7UoObeTx4dqe2enm3bDukY73T5AkKQuOGqbjOK6O4/iptn9uAJYBI5MuTFKeaqgO1/I0hekRs6FutU3IVLg2L4VBk6G4JNuVHNrw4yAqal8TsnUPQ3NjOCpPkqQcF8Vx3P4XR9E44EFgRhzH9Qd97UrgSoChQ4fOvf7669NXZYJ27txJeXl5tstQBvisc8OU5T9kUM3jPHrar9My3oDap5j13Fd45rj/YHv/WYDPupAU/LOOY0599ApqB85l+dTc3YU174mPs6fnQJ6b9aUjvm7yih8zbNN9PHLab2ktLn3V1wr+WRcYn3fh8FkXju70rBcsWLA4juN5R3tdu3+MHUVROfAn4BMHB2mAOI6vAa4BmDdvXjx//vz2V5tFCxcupLvUqq7xWeeIDT+CeGz6nkXjDHjuK8weApwWxvRZF46Cf9bbXoIHdjB87sUMP2F+tqs5vB1nUv7ircw/6yyIokO/Jo7hqY/C5HM485zzX/Plgn/WBcbnXTh81oUjH591u7p5R1HUgxCkfxfH8U3JliQprzVsTE8n7xSbkKmQpY6cGnF8dus4mpHHw65t+zuPH8rmpVC/HqZcmLGyJEnqivZ0846AnwHL4jj+dvIlScpr9dVQmcYwDTYhU+HasBiKS2HojGxXcmQj2465OtK+6eV3huuUC5KvR5KkNGjPzPRpwHuAs6Moeqbt46KE65KUj/bthaYaqEjDsVgHsgmZCtWGp2HYTCgpPfprs2nIdCjpBRufPvxrVtwRZtjT1elfkqSEtaeb98NxHEdxHM+K43h228ftmShOUp7Z2XbGdLq/WR4xJ1yrn03vuFIua20J4TQ165vLinvAsFmHn5lu2By+doxdvCVJ3Ue79kxLUlrUtx2LVZnmmenhbWHapd4qJDUrwjFSub5fOmXk8eEHXi37Xvu1lXeFq/ulJUndiGFaUuakzphOZwMygLKBNiFT4UnN8naHmWkIdTY3wdYXX/u15XdC5aiwZF2SpG7CMC0pc5IK02ATMhWeDYuhZyUMnJTtStonNYOe6kCe0rwb1twfGo8d7tgsSZJykGFaUubUb4TintBnQPrHHjHHJmQqLBueCs33irrJ/8oHTIBefV+7b3rtg2HG2v3SkqRuppv8H1hSXmjYFJqPJTH7NGJ2uNqETIWgeXc4l7m7LPGGEPpHzAk/BDjQijuhRxmMOyM7dUmS1Ekl2S5AUgFpqE5/87GUVzUhm5XMPaRcsXkptO7rPs3HUkbOhYe+DT8+AwZNhkFT4MXbYOIC6NEr29VJktQhhmlJmVO/EYYnFHQPbEI2yDCtPNfdmo+lnPChMKtesxzWPwlLbwJimP6GbFcmSVKHGaYlZUYch5npJI++STUhG/Te5O4h5YINT0H50ORWeiSlcgRc+I39/968K/x3of/47NUkSVInuWdaUmbsqQ9NhioT6OSd0taErHhfY3L3kHLBhsVhVrq7d7/u0Ts0Juvuvw5JUkEyTEvKjPoEj8VKGR6akJXvXJfcPaRs270Dald2v/3SkiTlGcO0pMxo2BiuSYbpIdMAKGt8Obl7SNm28elwHWmYliQpmwzTkjKjYVO4JrnMu3IE9KykT1NVcveQsi11tNSIOdmtQ5KkAmeYlpQZ9RmYmY4iGHwMZY2GaeWxDYvDPuM+A7JdiSRJBc0wLSkzGqqhV7/QcChJg49xmbfyV2srVC3qfkdiSZKUhwzTkjKjYVNmjvEZPJXS5u3QVJf8vaRM2/AkNG6ByRdkuxJJkgqeYVpSZtRvTHaJd8rg0ISMrS8mfy8p05b9FYp6wJTzs12JJEkFzzAtKTMaqjMUpo8JV8O08k0cw7JbYfyZ0KtvtquRJKngGaYlJa+1BXZuTraTd0rfUewr7gVblyd/LymTtrwA29bCtNdnuxJJkoRhWlIm7NwCcWtmZqajiKY+o2HLsuTvJWXSsluACKZenO1KJEkShmlJmbCj7aiqvqMycrvGstHOTCv/LLsVRp8E5UOyXYkkScIwLSkT6taGa//xGbldU58xsHMT7NqWkftJiatbC5ufc4m3JEk5xDAtKXnb1gIR9B+bkds1lo0O/5DJ2ektL8L2l0OTKCndXrw1XKddkt06JEnSK0qyXYCkAlC3FipHQknPjNyusWxM+IetL8KYk5O/4dqH4FdtIae0AoZMhSHTYfa7YMxJyd9f+W/ZrTBsJvQfl+1KJElSG2emJSVv21oYkJkl3gB7eg6CHmVhtjhpzbvglqtCyLn42zD7HVDSC57/M/zu8nC+ttQVDZuh6nGY6hJvSZJyiTPTkpJXtxamXJC5+0VFMHhKZs6afvB/oG41vOfPMHHB/s/XrYGrT4O/fgzedSNEUfK1KD8tvw2IXeItSVKOcWZaUrL27ITGLRmdmQZg8LTkw/SmpfDId+G4d746SAMMmADnfRVW3QNP/TrZOpTflt0a/jwNmZ7tSiRJ0gEM05KStW1duGaok/crBh8DDdWwa3sy47e2wC0fh1794IKvH/o18z4I48+Euz4fmpNJHbVrG6x9EKZe4uoGSZJyjGFaUrK2tR2LlemZ6SHTwjWpjt6LfgobFsOF/wl9Bhz6NUVFcOkPgBj+8lFobU2mFuWvx34Irc0w8/JsVyJJkg5imJaUrAyfMf2KwceEaxJLvXesh3u/CpPOhZlvOfJr+48NM9drH4Qnf5b+WpS/6qvh0R/AjDfD8FnZrkaSJB3EMC0pWdvWQu/+0LtfZu/bdwz06JPMzPRjP4KWvaF7d3uW3h5/RQjef/sibK9Kfz3KTwu/Aa374Ox/z3YlkiTpEAzTkpJVtzbzs9IQllgPmgJbl6V33JZ98NwNoTt5/7Hte08UwSX/B3EMd30uvfUoP21ZBk//Fk78h8xvkZAkSe3i0ViSkrVtLYycm517D54K6x5K75ir74PGrTD7nR17X78xcOa/wH1fg1X3wqRz0ltXvmjeDc1NsG8P7NsdrnELEIUjz6IISnpC2WAoLct2tcm558tQWgFnfjrblUiSpMMwTEtKTktzWNY84yj7ipMyZCosuR5274BefdMz5rO/h94DYNJ5HX/vqR+HZ34Pd3wGPvJoCIWFqLEGNj4DG58Oe9obNsHOzeFjT337x+nRh5OKy2HV2PCDk2GzYNgMGHps+p53Nqx9CFbcCed++fDN7SRJUtYZpiUlZ0dVmFXM1jLVwVPDdesKGH1C18fbtR1evB3mXgElpR1/f0lPeN3/wO/eHLo0n/HJrtfUXaxfDE/+HNY+EP5cpPQbC5UjQgCeeDaUD4HS8vB7VdIr/D5HxUAclsnHrWHGurEGGreyY81Sepe0wPLb4enf7B939Mkw931w7BuhR+9M/2o7r7UV/vbvUDkSTvpwtquRJElHYJiWlJxsdfJOObCjdzrC9At/hpY9cNw7Oj/G5HPDmcEP/k847qjf6K7Xlauad8HSP8ET14ZZ6NJymHwenHgljJgTOlR3cQb5xYULGTZ/fgjaDZtg03PhXs/dAH/+MNz5rzDr7SFYD52ell9WYpp3wYPfCvW/8eru9UMASZIKkGFaUnKydcZ0Sr9xYXYzXcdjPXMdDDomBMGuuPCb8IMTQzOyt/3m6K/vbuIYltwAd30WmmrDCoGLvgWz3ga9KpO5ZxRB5fDwMeV8OOsz8NIjsPiXsPgXsOgnMOrEttnqy6C0TzJ1dEZrS/j9uu9rUL8epr8h/F5JkqScZpiWlJy6tSHMlg/Lzv2LisKseGqGvCvq1kDV3+GcL7XvOKwjObAZ2bqHYdzpXa8vV+zYALf+M6y8C0adAJf/Kvz6uvp71lFRFO477nS48L/C3vnFv4S//BPc+VmYdXnYyz/6pPDnJFteegxu/zRsfg6Gz4bLrobxZ2avHkmS1G6GaUnJ2bYO+o/LblgZOBFqV3d9nGevB6L0zRie8jF49Psh4OVDmI7jsGf5rs+HxnMXfBNO+kcoKs52ZVA2EE75KJz8T/DyY+H3/OnfhuXn5cNg+qUw/Y0w5pTM/lmtr4bfXR7OYX/zz+DYN2X374okSeoQw7Sk5GTrjOkDDRgPq+4JjZ06G1RaW+HZ62DCWdB3ZHrq6tErzIw+87v0dhvPhjgOs6tP/BTGng6Xfi/8ECPXRBGMPTV8XPy/sOIueP5meOrXsOia8IOfeR+A2e8OATxpd30WWvbCe/+cm79fkiTpiPwRuKRkxHGYmc7WfumUARNC9+eG6s6PUfV32P4yHNfBs6WPZva7Qm3P35zecTNt4X+GIH3K/4MrbukewbBnBcx8C7z9d/DpVfCmn0LFCPjbF+Hb0+Cmf4QNTyV3/5X3hOd+5qe6x++XJEl6DcO0pGTs3ALNjTkwMz0hXOu6sNT7md9DjzKYdkl6akoZeXxozvXM79M7biY9/hN44D9hzrvh/K91z2XKPStg1lvhA3fARx6D498DL94GP10Av387VC9J7/2ad8Ht/wIDJ8NpV6V3bEmSlDHd8LseSd1Ctjt5p7wSptd07v27d4TjnWZcBqVl6asLwrLj2e+EqsehZmV6x86EJTfAHZ8JR31d8t3MNxlLwmLEuroAACAASURBVNDpYQn4J1+As78ALz8KPzkDbrgCtqSpK/yD3wqrNi75djhPW5IkdUuGaUnJyPYZ0ymVo6C4Z+fD9LN/gOYmmPfB9NaVMuttEBV1r9npnVvgyZ/Dnz8C484IzbOK86wFR69KOPPTcNUSOPMzYd/9j06C37457LVubencuFuXwyPfDWeV27VbkqRuLc+++5GUM7atDSGx35js1lFUFBpLdSZMx3EIjSPmhCXZSagYBpPODd3Cz/5CbnS/PtieBlj7IKx5IFy3LgufH3E8vP33oZlavurdD87+PJz04bAv/MlfwO/fCv3GwgkfhMnnh+Xa7flhwvYquOWqsMLhvP9IvnZJkpQow7SkZNStDbPCJaXZriQs9a7tRJh++bEQHC/9fvprOtDsd8If3wdrFsKkc5K9V3vVrApnRa+8G9Y9Aq3N0KNPOD7quP/f3n3HWV3d+R9/nRmQLl16kyIqoiCxQFQU7I2YmGhsWbMxm42mbHZTfqZtNmWzyS/7y8a2xl5iiZpoMIoGQY0VBBUEQYrK0BHpMDAz398fZ0YRB6bd7/3OzH09H495XObOne/3I4dB3vec8zmfi7OqvY5onOE/De26wvjvwnHfgvl/icdqPfnD+NGiDfQcAb0Oh27DoH2P+CZJh55QthPenAzzH4EVs+O1Jl0P7btn+98jSZIazDAtKR3vL4UuA7OuIupyYAyqSVK3fb0zboZWHWHEp1MrDYCDzoDWneJS7yzD9K7tscP0jJtg+Svxue7D4ZivxBnYfkc3jjdHslTcEkacFz/eWwwlM2Hla/Hj9fuhdFP139d7NEz8MRx8jt27JUlqJgzTktKxfikMPzPrKqIug6BsO2xeBfv3qt33bFkL8x6OS3lz3XhsTy1awWHnw+w7YfuGuLQ4n95/G17+Pcy+C3ZsiLOrp/48NhbrPCC/tTQlXQfHj8M/Fz+vqIDt6+MxbJtXw5ZVUL4rLuPv1C/bWiVJUs4ZpiXlXulm2LYu+07eVapmAtcvqX2YfvWuuLT5yH9Ir67dHfH5uCf3jYdgzOX5uefmVfD0f8Gs2+Pnw8+Kbx4MPK55dObOt6IiaNctfvQ8LOtqJElSygzTknKvsXTyrrL7WdMDx9X8+oqK2GhqwCfhgOHp1lal9yjocRg89z9wxEXpHpm0bX3sKP3S/8Y3DEZfGjtX7987vXtKkiQ1Mx6NJSn3GssZ01X27wtFLWvf0XvxVNjwDnwiTzPEEGeCT/5x/L176Yb07vP2c3DNmBimDz4brpwBZ/23QVqSJKmOnJlWtGkFvP13WPEqDD8DBn4y64rUlL23OD52HphpGR8obhH3/tY2TM+8Bdp1h+Fnp1vXnoZMhKGnwtO/iucQtz8gt9efdSdM/mYcl0sfdimyJElSAximC9nWdTDtZ/Hs2PWV4ScUwYvXwujL4OSf5L8RkpqH5a/EpdWtO2ZdyYe6DK5dmN6xERY+DmOvyqZz9ak/h+uOhqk/gXOvyc01K8rhbz+C538HB54I59/mz7YkSVIDucy7kD3+3ThT1W0onPIzuOJp+O6yGCJm3wnXHh3PU5XqIknicUF9P5F1JR9VddZ0kuz7dStfh6QCBh6fn7r21G0IHP1PsbP2ilcbfr0dm+Dez8cgfdQVcNEDBmlJkqQcMEwXqhWzYc4fYdzX4PP3wdgrofcR0Ko9nPJT+NJTcZnrfRfDn/4pHu8i1cam5fFIoMYYpndthS1r9v26la/Fx14j069pb074NrTtGt/wqin878uquXDjeHjrSTjj13DGr+KSd0mSJDWYYboQJQk8+UNo0wXGfb361/QeBVdMg+O/Da/dA/dfBmWl+a1TTVPJjPjY58hs69jTBx29a1jqvfI16NA79/uV66J1R5jwA3j3hXhUVn3MvhtumgA7t8IXJsNRX8ptjZIkSQXOMF2IFk2Fpc/ACd/Z957W4pZw0tVw+n/Bgkfhngth57b81ammqWQmtGgNPUZkXclHVXUWrzFMvxpXaWRt1CXxqKy//ltc8l1RXrvv27UdHrkKHv7nuDrgy8/AgLHp1ipJklSAagzTIYRbQghrQghz81GQUlZRHmelOw+EMbU89ufoL8M5v4PFT8Hd50Pp5lRLVBNXMgN6HZFN86596TQAilrsO0yXboF1b0Gvw/NX194UFcOnb4p1P/xVuOGTsPCJ6pd979oBbz4KD10Bvx4Gs+6A474Fl/wZOvTIf+2SJEkFoDab524DrgHuSLcU5cXr98GaN+Azt9Qt7Iy+FFq0gT99Ge78FFz6COzXNr061TSV7YxNsxrjkuLiFtCp/4ed66uzei6QNI4wDXDA8Ni/4I0/xe7efzgf+h0NHfvGPgYVZVC2A5a9DDu3QOtOcPA5MOoiZ6MlSZJSVmOYTpLkmRDCwPRLUep2bYenfgq9R8Mhn6r79488Pwbw+y+DR78Fk66DEHJfp5qu1XOgvLTxNR+r0uXAfc9Mf9B8rJGEaYg/YyPOg+FnwSu3wcyb47F2xS2hqGV8k+DQT8Ghk2DQCfF5SZIkpS4ktegUWxmmJydJstdNkCGEK4ArAHr06HHkvffem6MS07Vlyxbat2+fdRl50e/dhxi85HZePfynbOh8WL2vM3DpHxj4zn0sGPYVVvY+LYcVpquQxjorfUomM3TR73nhmJspbd0tszr2NtZD3rqRnqum8fdP/qHaN4IOevO3dH3vFZ4fe7tvFDUR/lwXDse6sDjehcOxLhxNaaxPPPHEV5IkGVPT63IWpnc3ZsyYZObMmbV5aeamT5/O+PHjsy4jP64bGxuOXf5Yw65TUR73Tr/9LFz+eOPr2rwXBTXWWXnwH+Ht5+Bb8zMtY69j/eL18bipf1sM7aoJ+9ePgw494eIHU69RueHPdeFwrAuL4104HOvC0ZTGOoRQqzBtN+9CsWVt3Cs9dGLDr1XVGKl9T7jvUtj6XsOvqeahZCb0rfHvnex0GRwf36tm3/SuHbBmfmyeJkmSJNXAMF0olj4dHweNz8312naBz90BW9fCg5fX/tgeNV9b18H7SxvvfmnY91nTq9+ApLxx7ZeWJElSo1Wbo7HuAV4ADgohlIQQvph+Wcq5pU9Dq465PT+39yg441ewZDq8fn/urqumqaRya0djnpnu1B9CUfVheuWr8dEwLUmSpFqoMUwnSXJhkiS9kiRpmSRJ3yRJbs5HYcqxJU/DwE/GJdq5NPpS6NgP5v8lt9dV01MyA0Jx414m3WK/+Oe12jD9WjxaqlP//NclSZKkJsdl3oXg/bdhwztw4Am5v3YIcNAZsPgp2Lkt99dX01EyA3qOaPznj3cdHPdG79l8ceVrcVbaLt6SJEmqBcN0IVhStV86hTANMPwMKNseA7UKU0U5LJ/VuPdLVxl2emzGt3DKh8+V7YQ183K7DUKSJEnNmmG6ECx9Onbe7n5QOtcfMC4eubXgr+lcX43f2gWwc3PTCNNj/gG6DoUnvg/lu+Jza9+E8p3ul5YkSVKtGaZz7e3n4PHvfXwJaVaSBJY+A4OOT2/5anFLGHYaLHgMysvSuYcat5IZ8bEphOnilnDKT+G9t2BGZQuIla/Fx8a831uSJEmNimE6l7ZvgAcuhxevg3ULs64mWjMvHl+Vxn7p3R10BmxfD8teSvc+apxKZkCbzh8ePdXYDTsVDhwP038B29bHTt77dYDOg7KuTJIkSU2EYTqXnvg+bF0Tf71oara1VEl7v3SVIROguBW8+Wi691Hj9M7z0PeoptO8KwQ49edQugme+VVl87GRUORfiZIkSaod/+WYK4ufgtl3wtivQbeDYNHfsq4oWvp0nC3s1C/d+7TqEGe/35zceJa4Kz/eWwzrF8OQiVlXUjc9DoVRl8DLN37YyVuSJEmqJcN0LpRugUe+Hpsajf9unKV95znYtT3busrL4h7utGelqww/Mx7BtWZefu6nxqGqK/awU7Ktoz5O+j60aFPZfMz90pIkSao9w3QuTP132LgMzr0GWraJYbpsRwzUWVoxK3ZYTnu/dJVhpwPBpd6F5q0pcTVG54FZV1J37Q+A4/81/rrvmGxrkSRJUpNimG6od56Py0SP/jL0PyY+N2ActGid/b7pqv3SA4/Pz/069IjdnA3ThaN0c1z90BRnpauM+zpcORO6Ds66EkmSJDUhhumGmnI1dOoPJ/3gw+datoEBY7MP00ufhp6HQbuu+bvn8DNjZ+SNJfm7p7KzZDpU7IKhp2ZdSf2FAN2GZl2FJEmSmhjDdENsWRuXUo++DFq1/+jXhkyEdQtgw7JsaivbGY+pytd+6SrDz4yPCx7L732VjYVToFXHD1dlSJIkSQXCMN0QSyuXUR944se/NnhCfFyc0ez02jdjU6U+o/N7325DoftwmHU7VFTk997KrySBt56EISdBccusq5EkSZLyyjDdEEumQeuO0LuaLsDdD4L9+2Z3RNaqOfGx58j833vcN+L95/05//dW/qx8DbasatpLvCVJkqR6MkzXV5LA4ukw6HgoKv7410OIM3ZLnobyXXkvj9Vz45E/XQ7M/71Hfha6HwzTfhaP51Lz9NYTQIChJ2ddiSRJkpR3hun6em8xbCqpfol3lSEToXQTlMzMX11VVs2BHodWH/TTVlQME34A7y2CV+/O//2VHwunQJ8joV23rCuRJEmS8s4wXV9LpsXHwfsI04NOgFCc/6XeSQKrXo+dvLNy0BnxmKzp/wm7tmdXh9KxdR0sfwWGucRbkiRJhckwXV9LpscjsToP2vtr2nSKgTLfTcg2lsCOjdBzRH7vu7sQYMKPYPMKmHFTdnUoHW89CSQwtAmfLy1JkiQ1QIusC2iSystg6bNw6KQYGvdlyIS4d3jLWmjfPT/1Zdl8bHeDjoPBJ8Gzv4HRl8ZmbY1dRTmsXwqblsPmVbB5JWxZDWU74tcqyiEpjysOWrb58GO/dtCmM7TpEh/bdvnw8xb7Zf1flXtvTYH2PaHX4VlXIkmSJGXCMF0fK2ZD6UY4cHzNrx0yMYbphY/FQJkPq+cCAQ44JD/325cJP4Qbx8Pz18BJV2ddzcft3AbLXoR3X4qPJTNh55aPvqZluxiYi1rE/eChOAbqXdtg1w4oq2EZ+37tKwN2V2jfI76p0u4A6NQPeo+Oe9ub0tFSZaWw6Ck45Jya30ySJEmSminDdH0smQ6EuCe6Jr1HQdehMPvu/IXpVa/HLt6t2ufnfvvSexQcMgleuAYOvwC6Ds66orinvGQmzL4T5j4EOzcDAXqMgJGfi021OvWDDr2gQ09o1WHf16uogF1bYfv78WPb+spfVz5uq/z11nVxpnvV67BlTQzkAMWt4gxv/6PhuH+N2wMasxeujW8mHXZ+1pVIkiRJmTFM18eSadBrJLTrWvNrQ4DRl8CTP4S1C6H7sPTrWzUHelVz9nVWTv1ZfAPioS/B5VPSn4UtL4Nt78HWtfGxdDOUbqZPySyY9jzMexjWvgkt28Khn4JDz4N+R0Hr/et3v6KiGLhbdYj76GujogI2vgvLZ8VGXstfgReui13iL/hD453x3VgCz/wKhp8FB9bizSRJkiSpmTJM11XpFlj2Mhz71dp/z8gL4G//Dq/eBSf/JL3aAHZsgvffhlEXp3ufuujYF87+Lfzxstjde8IPcnPdNfOhZAasX/Lhx8blcRa4GkMBFhGbwp39PzDivJpnndNSVASdB8aPEefF5164DqZ8D168rm5/vvJpytWQVMCpP8+6EkmSJClThum6eud5qNi17yOx9tShBww7DV69B076Qbozs6vfiI9ZNx/b06GTYNHF8Oz/jU3JBo5r2PVe/j089p24VLqoRQylXQ6MQbndAfHs43bd4z7l1vtDqw48N3MO4048FVq2zsl/Us4d8xV4++/w5I+g3zHQ98isK/qoxdNg3p/hxKuh84Csq5EkSZIyZZiuqyXToEXrGHbqYtTFsODReKTQ8DPSqQ126+Sd4RnTe3PaL+ObEQ9dAV95rn57gyvK4+zoS9fHNyhO+wV07A/FNf9R3rXfu403SENc2j3pWrjhePjjF+CfnomNyxqDsp3w2LfjUXBjv5Z1NZIkSVLmPGe6rpZMh/7H1j2UDT05zpjOviuVsj6wek48jqlDr3TvUx+t2sOnb4Itq2DyN2MjsLoo3Qz3XBiD9DFfjXuLuxxYqyDdZLTpDOffGs/nfvjKuv8epeWl62HdQjj9l437DQlJkiQpTwzTdbGxBNbMq92RWHsqbglHXAgLH4fNq3Nd2YdWzYmz0o21gVWfI+HE/wNvPBSPDKttWNy6Dm45DRb9Dc78DZz283hMVXPUd0zcW//mZHj6l9kH6o3LYfovYdjpMOzUbGuRJEmSGgnDdF3MugMIcf9vfRxxcdzj+/q9OS3rA+VlsSlXY1zivbtx34BRl8Su0I/+S1y6vS8VFfCnL8O6t+CiP8InvpifOrN0zD/HxnXTfwGPXBmXWWdh6zq469NAEpfUS5IkSQIM07VXvgteuR2GTIzNruqj+7C413r2XenMNr63CMp2NP4wXVQM5/wOPvlNmHkLPHA5lJXu/fUv/C7OSJ/2CxgyIX91ZikEmHQ9nPCd+OflrvPi+dX5tG093DEJ3l8KF94LXQbl9/6SJElSI2aYrq2Fj8e9vmMub9h1Rl0c956WzMhNXbtrzM3H9hQCTPwxnPKz2CH67vPjnug9LZsBU38CB5/T8N/7pqaoKC6JP+/3sOwluGkirFuUn3vv2BgD/LoFcMHdniktSZIk7cEwXVszb4H9+8DQUxp2nUMnQct28FoKS71Xz4Hi/aDbsNxfOy1jr4RJN8Qjoa49Jv6+VFTEr23fAA9eDvv3jjPZjXUfeNpGfhYumxwD7s0TYeXr6d6vdHNc2r1qLnz2zrgaQ5IkSdJHGKZrY/0SWPwUHPmFhneObtUB+h8D776Yk9I+YtUc6D483XOs03DEhfCFydCua9wbfeMJsWv6I1fBphXwmVvrd4xWc9L/aPjHJ+MbMXecAytfS+c+5bvg3otg+azYVfyg09K5jyRJktTEGaZrY+atEIpj06xc6DsG1s6H0i25uV6VVXOh58jcXjNfBoyFL02PS5q3vw93nAvzH4EJP4y/X4rHgH1hMuzXHm5PKVA/8X1Y+nRcCXDw2bm/viRJktRMGKZrUlYaG0ANPwP2z9HZzX3GQFIBK2bn5noQj9vaugZ6jsjdNfOtqCguab5yJpzyUxj7NTj2qqyraly6DIqBulWHGKhXvJq7a8++C166IZ7hPeqi3F1XkiRJaoYM0zWZ9whsX5/b5ldVM63LZ+bumk2p+VhNWraGsVfBKf8RA7Y+qvPAykC9f5zBX7uw4ddcNgMmfzOeoX7yTxp+PUmSJKmZM6nUZOYt0HkQDBqfu2u27RKX7JbkMEyvrgzTPZrwzLRqrypQF7WA+y+BnVvrf61NK+G+i2Ojt8/c2vC+AJIkSVIBMEzvy5r58O7zcVY61zOkfcbA8ldyd71Vc6Bjfxt1FZLOA+DTN8HaBXFWuT5nl+/aHoN06Wa44J74Ro8kSZKkGhmm92XOA7Hx2BGfz/21+46BzSth4/LcXG/VnOaxxFt1M/hEGP89eP0+eOW2un1vksDDX43bDc77X+hxSColSpIkSc2RYXpfFv0N+n4C2nXL/bX75HDf9M5t8N6ipt18TPV3/L/B4Anw2Hfq1pBs+i9g7oMw8cd27pYkSZLqyDC9N1vXxaOHhkxM5/o9R0DxfrnZN71mfuwO7sx0YSoqikeKtesG918KW9bW/D2v3w9P/xJGXQzjvpF+jZIkSVIzY6ehvVk8DUhgyEnpXL9Fq3gmdC72Ta9uRp28VT/tusL5t8Gtp8Ovh8IBB0O/o+NH71Fxf3XLNvG1774Yl3cPPA7O/G8IIdPSJUmSpKbIML03i6dCmy7Q64j07tF3DMy6A8rLGtZBedWceExSpwG5q01NT7+j4EtPwcIpMTDPfRBeufXDr3foFTvTr50PHfvBZ++AFvtlV68kSZLUhBmmq1NRAYumxuZORcXp3afPGHjphhhuGjKrvGpOPBLLGUb1Ojx+QPxzvHY+rJ4H7y+F99+G9Uuh61CYdL2duyVJkqQGMExXZ/Vc2LomNnVKU98j42PJzPqH6YoKWP0GHHFR7upS81BUBD0OjR+SJEmScsoGZNVZPDU+Dkk5THceBG27Nqyj9/tLYecWO3lLkiRJUh4ZpquzaGpcNt2hZ7r3CQH6HAklDWhCtsrmY5IkSZKUb4bpPZVuic2bBqfUxXtPfcbA2jdhx6b6ff/quRCKofvBua1LkiRJkrRXhuk9vf0sVOxKf4l3lb5HAgmsmF2/7181B7oNg5atc1qWJEmSJGnvDNN7WjQVWraF/sfm5359KpuQ1Xff9Kq5LvGWJEmSpDwzTO9p8VQYeBy0aJWf+7XpDF2H1G/f9Lb1sKnE5mOSJEmSlGeG6d2tXwrrl+RviXeVPmOgZAYkSd2+z+ZjkiRJkpQJw/Tuqo7ESvt86T31Pyaea71+Sd2+b/Xc+NjDMC1JkiRJ+WSYrlJRAXMfgk79oevg/N57wNj4+M7zdfu+VXOgfU9o3z33NUmSJEmS9sowXeXvv4F3noOxX4vnP+dTt2HQtmv9wrRLvCVJkiQp7wzTAIunwbSfwYjPwCf+Mf/3DyF2D3+3DmG6bCesXWCYliRJkqQM1CpMhxBOCyEsCCEsCiF8N+2i8qnVjnXw4Bfj7PDZv83/rHSVAePg/bdh4/LavX7tm/E8bDt5S5IkSVLe1RimQwjFwLXA6cAhwIUhhEPSLiwvynZyyLz/grJS+Oyd0Kp9drVU7Zt+94Xavb6q+VjPkenUI0mSJEnaq5DUcBxTCOFY4MdJkpxa+fn3AJIk+cXevmfMmDHJzJkzc1lnKl6+9osctfYBftPpal5qc1ymtYSknFtWn8/f25zEzR2vrPH1l228gQnbHuOyng+RhOI8VNj0bdiwgU6dOmVdhvLAsS4cjnXhcKwLi+NdOBzrwrF/xSZ+/5VTsy6jVkIIryRJMqam17WoxbX6AMt2+7wEOLqaG14BXAHQo0cPpk+fXrtKM9J6+0qOXPtn/lh0OlNKD4PSDVmXxBthKMO2v8qGpOZaDtvxMvOKhvL+xs15qKx5KC8vZ8OG7MdZ6XOsC4djXTgc68LieBcOx7pwtGlT3ugzYl3VJkxXt4n4Y9PZSZLcCNwIcWZ6/PjxDassH0YdxgHzVjHlpIlZVxI98wY89R9MuepoaNtl769buwCuXUG/0/+FKUednr/6mrjp06fTJP5cqsEc68LhWBcOx7qwON6Fw7EuHM1xrGvTgKwE6Lfb532BFemUk2c9R5AU1eb9hDwZMC4+1rRvev5f4uPwM9OtR5IkSZJUrdqE6RnA0BDCoBDCfsAFwCPpllWg+oyG4lY1nzc9/y/QZwzs3zs/dUmSJEmSPqLGMJ0kSRlwJTAFmA/cnyTJG2kXVpBatIK+Y/Ydpjcsg5WvwsFn5a8uSZIkSdJH1GqNc5IkfwX+mnItgnhE1rO/gdLN0KrDx7/+5uT4OPzs/NYlSZIkSfpAbZZ5K5/6HwtJOSx7ufqvz58M3Q+GbkPyW5ckSZIk6QOG6cam31EQiqtvQrZ1Hbz7PBzsrLQkSZIkZckw3di06gC9Rla/b3rBXyGpcL+0JEmSJGXMMN0YDRgHJTOhrPSjz8+fDJ36Q8+R2dQlSZIkSQIM043TgHFQXgqPfgt2bIrP7dgES6bFxmMhZFufJEmSJBW4WnXzVp4NOxXGXgUvXAtLpsPZv4UdG6B8p/ulJUmSJKkRMEw3RkXFcMpP4eBz4eF/hrvOg3YHQLvusUGZJEmSJClTLvNuzPp9Ar78LIz7BmxbB4dMikFbkiRJkpQpZ6Ybu5at4eR/h6O+BG27Zl2NJEmSJAnDdNPRsW/WFUiSJEmSKrnMW5IkSZKkOjJMS5IkSZJUR4ZpSZIkSZLqyDAtSZIkSVIdGaYlSZIkSaojw7QkSZIkSXVkmJYkSZIkqY4M05IkSZIk1ZFhWpIkSZKkOjJMS5IkSZJUR4ZpSZIkSZLqyDAtSZIkSVIdGaYlSZIkSaojw7QkSZIkSXVkmJYkSZIkqY5CkiS5v2gIa4F3cn7hdHQD1mVdhPLCsS4cjnXhcKwLh2NdWBzvwuFYF46mNNYDkiTpXtOLUgnTTUkIYWaSJGOyrkPpc6wLh2NdOBzrwuFYFxbHu3A41oWjOY61y7wlSZIkSaojw7QkSZIkSXVkmIYbsy5AeeNYFw7HunA41oXDsS4sjnfhcKwLR7Mb64LfMy1JkiRJUl05My1JkiRJUh0ZpiVJkiRJqqOCDdMhhNNCCAtCCItCCN/Nuh6lI4TQL4QwLYQwP4TwRgjh61nXpHSFEIpDCLNDCJOzrkXpCiF0CiE8EEJ4s/Jn/Nisa1I6QgjfrPw7fG4I4Z4QQuusa1JuhBBuCSGsCSHM3e25LiGEJ0MIb1U+ds6yRuXOXsb7V5V/j78eQvhTCKFTljUqN6ob692+9q8hhCSE0C2L2nKpIMN0CKEYuBY4HTgEuDCEcEi2VSklZcC3kiQ5GDgG+Kpj3ex9HZifdRHKi98CjydJMhw4HMe9WQoh9AG+BoxJkmQEUAxckG1VyqHbgNP2eO67wNQkSYYCUys/V/NwGx8f7yeBEUmSjAQWAt/Ld1FKxW18fKwJIfQDTgbezXdBaSjIMA0cBSxKkmRJkiQ7gXuBczOuSSlIkmRlkiSzKn+9mfiP7T7ZVqW0hBD6AmcCN2Vdi9IVQtgfOB64GSBJkp1JkmzItiqlqAXQJoTQAmgLrMi4HuVIkiTPAOv3ePpc4PbKX98OTMprUUpNdeOdJMkTSZKUVX76ItA374Up5/bysw3w38C3gWbRBbtQw3QfYNlun5dgwGr2QggDgVHAS9lWohT9P+Jf0BVZF6LUHQisBW6tXNZ/UwihXdZFKfeSJFkO/Jo4TelqTAAAAllJREFUi7ES2JgkyRPZVqWU9UiSZCXEN8WBAzKuR/lzOfBY1kUoHSGEc4DlSZK8lnUtuVKoYTpU81yzeHdE1QshtAceBL6RJMmmrOtR7oUQzgLWJEnySta1KC9aAKOB65MkGQVsxaWgzVLlftlzgUFAb6BdCOHibKuSlGshhKuJ2/PuzroW5V4IoS1wNfDDrGvJpUIN0yVAv90+74tLxpqtEEJLYpC+O0mSh7KuR6kZB5wTQnibuHXjpBDCXdmWpBSVACVJklStNHmAGK7V/EwEliZJsjZJkl3AQ8DYjGtSulaHEHoBVD6uybgepSyEcBlwFnBRkiROcDVPg4lvir5W+W+1vsCsEELPTKtqoEIN0zOAoSGEQSGE/YiNTB7JuCalIIQQiHsq5ydJ8pus61F6kiT5XpIkfZMkGUj8mX4qSRJnr5qpJElWActCCAdVPjUBmJdhSUrPu8AxIYS2lX+nT8Bmc83dI8Bllb++DHg4w1qUshDCacB3gHOSJNmWdT1KR5Ikc5IkOSBJkoGV/1YrAUZX/v+8ySrIMF3Z5OBKYArxf8j3J0nyRrZVKSXjgEuIs5SvVn6ckXVRknLiKuDuEMLrwBHAzzOuRymoXH3wADALmEP8t8uNmRalnAkh3AO8ABwUQigJIXwR+E/g5BDCW8Suv/+ZZY3Knb2M9zVAB+DJyn+n3ZBpkcqJvYx1sxNcSSFJkiRJUt0U5My0JEmSJEkNYZiWJEmSJKmODNOSJEmSJNWRYVqSJEmSpDoyTEuSJEmSVEeGaUmSJEmS6sgwLUmSJElSHf1/U55h2bOHYq4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(17,7))\n", "\n", "E0 = yy0[0]**2+yy0[1]**2\n", "EE = solx**2+soly**2\n", "print(max(abs(E0-EE)))\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "plot(tt,EE)\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système - stabilité)\n", "> Considérons le système \n", "$$\n", "\\begin{cases}\n", "x'(t)= x^2(t)+y^2(t)-25\\\\\n", "y'(t)= x(t)y(t)-12\n", "\\end{cases}\n", "$$\n", ">1. Afficher le champ des vecteurs et les solutions stationnaires.\n", ">1. Calculer les solutions particulières **approchées** pour des données initiales proches des points stationnaires." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les solutions stationnaires vérifient\n", "$$\n", "\\begin{cases}\n", "x^2+y^2=25\\\\\n", "xy=12\n", "\\end{cases}\n", "$$\n", "On résout $x^4-25x^2+12^2=0$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-4. -3. 4. 3.] [-3. -4. 3. 4.]\n" ] } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "\n", "# numpy calcule les racines d'un polynome\n", "x_sol=roots([1, 0, -25, 0, 12**2])\n", "y_sol=12/x_sol\n", "print(x_sol,y_sol)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAGfCAYAAAB2nSf9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3XlcVWXix/HPuVx2EAEBF0QQFXcFzSVTQa3MsrTMabN9mbLFtpmaampap6bJlmnfF8tsUstKyw0rM1fcRVxBAQVX9uVyz+8PrV9OhgtXzl2+79erlwmXc7883bhfnuec5ximaSIiIiIiDWOzOoCIiIiIN1CpEhEREXEBlSoRERERF1CpEhEREXEBlSoRERERF1CpEhEREXEBlSoRERERF1CpEhEREXEBlSoRERERF7Bb8aTNmjUzExMTrXhqy5WXlxMaGmp1DLel8amfxqd+Gp/6aXzqp/Gpny+Pz/Lly/eYphlzrMdZUqoSExNZtmyZFU9tuczMTNLT062O4bY0PvXT+NRP41M/jU/9ND718+XxMQwj93gep+U/ERERERdQqRIRERFxAZUqERERERdQqRIRERFxAZUqERERERdQqRIRERFxAZUqERERERdQqRIRERFxAZUqERERERdQqRIRERFxAZUqERERERdQqRIRERFxAZeUKsMwmhqG8V/DMLINw9hgGEZ/VxxXRERExFPYXXScF4BZpmmOMQwjAAhx0XFFREREPEKDZ6oMw2gCDALeBjBNs8Y0zQMNPa6IiBzJNE027ttIeW251VFE5ChcsfzXFigG3jUMI8swjLcMwwh1wXFFROQ31u9bz5gZY5iTO8fqKCJyFIZpmg07gGH0Bn4GBpimudgwjBeAEtM0H/qfx90I3AgQFxfXa/LkyQ16Xk9VVlZGWFiY1THclsanfhqf+nn7+JimySP5j9A8oDk3x958wl/v7ePTUBqf+vny+GRkZCw3TbP3sR7ninOqdgI7TdNcfPjv/wXu+98Hmab5BvAGQO/evc309HQXPLXnyczMxFe/9+Oh8amfxqd+vjA+Wcuy+HD9h6T2TyUiMOKEvtYXxqchND710/gcW4OX/0zT3AXsMAwj5fCHhgLrG3pcERH5veFJw3GYDi0BirghV+1TdRswyTCM1UBP4EkXHVdERH6jU1Qn2jRpwzfbvrE6ioj8D5eUKtM0V5qm2ds0ze6maY4yTXO/K44rIiJHMgyDEUkjWLprKbvLd1sdR0R+Qzuqi4h4mBFJIzAxmbV9ltVRROQ3VKpERDxMYkQi3Zp146utX1kdRUR+Q6VKRMQDndv2XLL3ZbNp/yaro4jIYSpVIiIe6Jykc7Abdr7c8qXVUUTkMJUqEREPFBUUxcD4gXy19SscTofVcUQElSoREY81qt0o9lTuYWH+QqujiAgqVSIiHmtg/ECigqKYtnma1VFEBJUqERGP5W/z5/zk81mwYwF7KvdYHUfE56lUiYh4sNHtR+MwHTphXcQNqFSJiHiwthFtSYtN4/Ocz3GaTqvjiPg0lSoREQ93ccrF5JXmsWTXEqujiPg0lSoREQ93ZpszaRrYlCkbp1gdRcSnqVSJiHi4QL9ARrUbxby8eRRVFFkdR8RnqVSJiHiBsR3G4jSdfJbzmdVRRHyWSpWIiBdo3aQ1A+MH8tnGz6itq7U6johPUqkSEfESl3W8jL1Ve5m1fZbVUUR8kkqViIiX6N+yP0kRSUzaMAnTNK2OI+JzVKpERLyEzbBxRacrWLd3HVlFWVbHEfE5KlUiIl5kZPJIIgIjeH/d+1ZHEfE5KlUiIl4k2B7M2A5jmb9jPtsPbrc6johPUakSEfEyl3W6DH+bP++v12yVSGNSqRIR8TLNgptxfrvz+WLzFxRXFFsdR8Rn2K0OICJyLFW1dZRVO6h2OKmurTv05//+u6OO9bscONbvJtDfRqDdj0C77ch/t9sIC7ITaPez+ls65a7tci1TN03lww0fclevu6yOI+ITVKpExDI1Did5+8opOFBFcWk1xWXVFJUc+rO4tIqi0mqKS6sprXIc/0FXLjvmQ5qG+BMTFkhMeCCx4Yf+/OWf2PAgWjYNpnVkMHY/z53Mb92kNWcnns2n2Z9yXdfriAiMsDqSiNdTqRKRU660qpYtxeVsLipjS3HZr3/m7a3A4TxyP6XQAL9fC07H5uEMbNeMmPBAmgT7H55tOnIGKujwnwF2G0uXLKV7ai+qHXW/zl5V1R76s7rWSVVtHSVVjkMF7nCJW563n6KSaqodziNyBPjZSGwWQrvYMJJjwn79s21MKCEBnvGj84ZuNzBz20w+2vAR43uOtzqOiNfzjJ8MIuIxSqtqWbnjACtyD7Aibz/Zu0rYXVL96+ftNoPEZqF0iA3nnK7NSY4Jo3VUyK8zR6GBJ/9jqSDcRrf4E5+RMU2TsupDZauotJod+yrYXFzGlqJyNhSWMmvtLn7b/Vo1DaZTi3DS2kSSlhBJj/imBAe435Ji+8j2DE0YyqT1kxjXeZzVcUS8nkqViJw00zTZuqecFbn7WZF3gBW5+8kpKsU0wTCgQ2w4A9o1O2K2JyEqBH83W1YzDIPwIH/Cg/xpGxNGv7bRR3y+2lFH7t6KQzNsRWVsKipjbf5B5mwoAsDPZtC5RRPSEpr+WrTiI4MxDMOKb+cIf+7xZ+bmzWXS+kl0opPVcUS8mkqViJyQopIqMjcWM39jET9v3cv+ikM37w0PspOaEMk53ZqTlhBJz4SmNAnytzitawTa/egQF06HuPAjPr6/vIasHftZnrufFbkH+Gz5Tt5flAtATHggpydHk5ESy+AOMUSGBlgRnY5RHRnSeggfrv+QB+MetCSDiK9QqRKRetU5TVbuOEDmxiLmZRexrqAEgBYRQQzrFEevNpH0ahNJckwYNpv1MzONKTI0gCEd4xjSMQ4AR52TjbtLWZF7qGj9sGkPX6wswGZAz9ZNGdIxlvSUWLq0bNKos1i39LyFMTPGMK9kHiMY0WjPK+JrVKpE5HdKq2qZl13E/OwiFuQUs7+iFj+bQa+ESP4yPIWMlFg6Ng93i+Utd2L3s9GlZQRdWkYwrn8iTqfJmvyDzMsuInNjEc9+l8Oz3+UQGx5IekrMryUryP/Uno+VEpXC8MThzMudx97KvUQHRx/7i0TkhKlUiQgAtXVOfthUzLSsAmav30VVrZPo0AAyOsaSkRLLoPYxRIR4x3JeY7HZDHq0bkqP1k2588wOFJdWsyDn0NLpzLW7mLJsJ2GBds7p2pzRaa3olxR9ymb7xvccz3fbv+ON1W9wf9/7T8lziPg6lSoRH2aah5b2pmflM2N1IfvKa4gM8efiXq25oGdL0hIifW5J71SKCQ9kTK94xvSKp7bOyZJt+5ielc/Mtbv4bPlOWkQEcX7PloxObUXH5k1c+tyJEYn0C+vHlJwpXNH5ClqHt3bp8UVEpUrEJ+3YV8HUFflMX5nPtj3lBNhtnNk5jtE9WzGoQwwBdve6Os8b+fvZGNCuGQPaNeOxUV2Zs2E301bk8/YP23h9wVY6Ng9ndGorRqW2Iq5JkEuec0TECFZUruClFS/xzOBnXHJMEfl/KlUiPsI0TX7aspd3F25jbvahrQD6JUVz8+Bkhndr7jVX6nmiIH8/zuvekvO6t2RvWTVfrylkWlY+T83M5l/fbmREtxZcMyCR1ITIBj1PhD2CK7tcyRur32Bc53F0i+nmou9AREClSsTrVdbUMS0rn/d+2kbO7jKiQwO4NaMdl/ZJoGXTYKvjyf+IDgvkyv6JXNk/kW17yvno51ymLN3Bl6sK6NG6KdcOSOScri1Oejbx2q7X8nnO5zyz9Bk+OOcDXWwg4kIqVSJequBAJR8symXy0jwOVNTSuUUT/jWmOyN7tDzlV5uJayQ1C+Wh8zpz55kd+Hz5Tt7/aTt3TF7JE+EbuKJfGy7rm0CzsMATOmaofyi3pd7GI4se4dvt3zI8afgpSi/ie1SqRLzMhsIS/jN/M7PW7sI0Tc7u0pyrT0+kT1KUZiU8VFignatOT2RcvzYs2FTMuwu389zsHP4zfzMX9GjJ+Ix2JDYLPe7jjWo3iskbJ/Pv5f9mcOvBBNs1YyniCipVIl4iZ3cpL8zZxNdrCgkPtHP9GUmM69+G+MgQq6OJi9hsBhkph7a42FxUyns/beezZTuZmpXPRWmtuG1Ie1pHHfu/t5/Nj/v63MfVs67mrTVvcVvqbY2QXsT7qVSJeLgtxWW8OHcTX64qIMTfj9uGtOP6M9pqTykv1y42nMdHdeP2Ie15JXMLHy/JY+qKfMae1ppbM9od83y5XnG9GJE0gvfWvseo5FG0bqItFkQaSqVKxEPl7i3nxbmbmZa1k0C7HzcNSubGQW2Jsugec2KN2CZBPHJ+F24a3JZX5m9h8tI8/rtsJ5f2ac0tGe3q3Y7h7t53s2DnAp5Y8gSvDn1Vy8MiDaRSJeJhikqq+Pd3Ofx3xU7sNoNrByTx5/TkEz5hWbxLi4hgHhvVlZsGt+Xl+ZuZtDiPyUt3cEW/Ntw+pP1RZy5jQ2K5teetPL30aWbnzuasxLMsSC7iPVSqRDxEjcPJN9tqGD8vk9o6k3H92nBzerLLNoYU7xAfGcJTF3bn5sHteHHeJt5duI1pWfnce3YKcab5u8df0vESvtzyJf9c8k/6texHkwDX7uQu4ku0bbKIB/g+p5jhL3zPlI219G0bzXd3DuKR87uoUMkfSogO4dmLe/DVbQNJjgnl/qlreGxRFVl5+494nN1m5+HTH2Zv1V6eX/68RWlFvINKlYgb27Gvgps+XMaV7yyhzmkyIS2Qd64+7YQunxff1rllE6bc1J8XLunJ/mqT0a/8xD2fraK4tPrXx3SJ7sK4TuP4LOczlu5aamFaEc+mUiXihqpq63h+Tg7DnlvA9zl7uPfsFL6dMIiesVqxlxNnGAYX9GzFUwODuWlwW75Ymc+QZzN5+8dt1NY5ARifOp7W4a15+KeHqaitsDixiGdSqRJxM4u27OXMiQt4fs4mhnWOY+7dgxmf0U67oEuDBdsN7j+nE7MmDKJnQlMe+2o9I1/6kbX5Bwm2B/OP0//BjtIdvJj1otVRRTySSpWIm6isqeMfM9Zx6Zs/42cYfHx9X16+LE335xOXS44J44Nr+/DaFb3YV17DqJcX8sKcTfSM6cVlHS9j0oZJLClcYnVMEY+jUiXiBlbk7efcF3/g3YXbuap/G765YyCnt2tmdSzxYoZhMLxrc767cxDndm/BxDk5XPjKT4xsfT1tmrThgYUPUFJTYnVMEY+iUiVioWpHHc/MymbMqz9R7XAy6fq+/OOCroQE6NwpaRxNQwJ44ZJUXrk8jfwDlVz4yjL6hI6nuKKYJxc/aXU8EY/isp/chmH4AcuAfNM0z3PVcUW81fqCEu6aspLsXaWM7R3Pg+d1pkmQbi0j1hjRrQWnJUbxwLQ1vDNvN4nJIzgwYzqrH1iAf/FB7C1aEHvnBCJGjrQ6qojbcuWvw3cAGwDtHCdSD9M0efOHrfzr2400DQng7at6M7RTnNWxRIgJD+T1cb2YlpXPdy+u4KZl4O84AICjoIDCh/4OoGIl8gdcsvxnGEY8cC7wliuOJ+KtSqpq+fNHy3nym2yGdYrjuwmDVKjErRiGwYVp8UzYPp8gx5E7sJtVVRRN1AahIn/EMI9y24ITPohh/Bd4CggH7jna8p9hGDcCNwLExcX1mjx5coOf1xOVlZURFhZmdQy35c3js7PUyUtZVRRXmvwpJYCz2thP+Aa23jw+rqDxqd+JjE/sn2/maK9OEyh67VWX5nIXev3Uz5fHJyMjY7lpmr2P9bgGL/8ZhnEeUGSa5nLDMNL/6HGmab4BvAHQu3dvMz39Dx/q1TIzM/HV7/14eOv4TM/K54m5awgLCmDyjWn0SYo6qeN46/i4isanficyPptatsRRUPC7j9fFxHntGOv1Uz+Nz7G5YvlvAHC+YRjbgcnAEMMwPnLBcUU8Xo3Dyd+/WMuET1fSLT6Cr28/46QLlUhjir1zAkbQkfeWrLLDxOReTJydg9PZ8FUOEW/T4Jkq0zTvB+4HODxTdY9pmlc09Lginq7wYCU3f7SClTsOcOOgttx7dgr+ftrFRDzDLyejF018HkdhIbbmsXzcv5K1HVcxb/5qVu44wPN/6klkaIDFSUXchzbDETkF1hUc5Jp3l1JRU8erl6dxTrcWVkcSOWERI0cecaXfZUVZzPn2WnqkfcWirIu58NWfeP+aPiREh1iYUsR9uPTXZtM0M7VHlfi673OKGfvaIuw2g6m3nK5CJV4jNTaVv/X9G1vLl3P+kBXsr6jhwlcXsmrHAaujibgFrUWIuNBny3Zw7XtLSYgOZdr4AXSIC7c6kohLXdzhYi7teCnf7pzCn8/bQ5C/H5e88TNzN+y2OpqI5VSqRFzANE1enLuJe/+7mn5to5lyUz/imgQd+wtFPNBfTvsLp7c8ndfX/osHxvjRLjaMGz5YxqTFuVZHE7GUSpVIA9XWObl/6hqem53DhWmteOfq0wjX7WbEi9ltdp4d/CyJEYk8uvg+Hh8bzeAOMTwwbS3/+jYbV+x/KOKJVKpEGqC82sENHyxj8tId3DakHf++uAcBdv1vJd4vPCCcV4a+Qog9hLu+v5XHLorn0j6teXn+Fu6esooah9PqiCKNTj/9RU5SWbWDq99dwg+b9vDUhd24+6yUE94hXcSTtQhrwSvDXqGitoJb593CX0ckcM9ZHZialc/4j1eoWInPUakSOQll1Q6ueXcJK/IO8OIlqVzaJ8HqSCKWSIlK4cUhL7KjdAfj547n2oGtePSCLsxev1vFSnyOSpXICfrfQnVud22ZIL7ttOan8czgZ1i3dx23z7+dP/VpoWIlPkmlSuQEqFCJHN3QhKE8NuAxFhcu5u7Mu7m0j2asxPeoVIkcJxUqkfqNTB7JQ/0eYsHOBdz7/b1c2lfFSnyLSpXIcVChEjk+Y1PGcl+f+5ibN5d7F9yrGSvxKSpVIsdQVVvHte8tVaESOU6Xd7r812J194K7uaRPy1+L1e2fZFHn1D5W4p1UqkTq4XSa3PnpSpZs28fEP/VUoRI5Tpd3upwH+j7A/B3zuX3+7Vx8WhwPndeZWet28eiMddogVLyS3eoAIu7s8a83MHPtLh48txPn92hpdRwRj3JJx0sI9Avk4Z8e5uY5N/PSkJfYdTCJN3/YRqvIYG4clGx1RBGXUqkS+QNv/bCVdxZu49oBSVw/sK3VcUQ80uj2owm2B3P/D/dz7bfX8sqQVyk4WMWT32TTPCJYv6yIV9Hyn8hRfL26kCe+2cA5XZvz4LmdrI4j4tGGJw3npaEvkVuSy5WzxjFheCR9kqK4Z8oqft661+p4Ii6jUiXyP5Zu38edU1bSKyGSiX/qic2mW8+INNQZrc7gzbPepKy2jOtnX80dIwJIiA7hxg+WkbO71Op4Ii6hUiXyG5uLyrj+/WXERwbz5pW9CfL3szqSiNfoEdODD8/5kBB7CHcsuIkbzi4j0N+Pq99Zwu6SKqvjiTSYSpXIYQcrarnmvSX4+9l4/5o+RIYGWB1JxOskRiQy6dxJpESl8Piy+xiVns3Byhquf38ZVbV1VscTaRCVKhEOb50wZSW7DlbxxpW9aB0VYnUkEa8VFRTF22e9zTmJ5zB58+v06fMdawr28I8Z66yOJtIgKlUiwMvzNzMvu4i/n9eZtIRIq+OIeL0gexBPD3qaW3veyrK9c0js+h6TV6xhyrIdVkcTOWkqVeLzvs8p5rk5OYzq2ZIr+rWxOo6IzzAMg5t63MQLGS9QZewiot3LzH71X6wflMGGTp3ZNGQoB2fMsDqmyHFTqRKfln+gkjsmZ9EhNpwnL+yGYehKP5HGNiRhCB+P+Jjztvhzy+LZGEW7wDRxFBRQ+NDfVazEY6hUic+qdtRxy0fLcdSZvHpFGiEB2gtXxCptm7blyh9tBDmO/LhZVUXRxOetCSVygvQuIj7rsa/Ws2rnQV67ohdtY8KsjiPi8+p27T7qxx2FhY2cROTkaKZKfNKXqwr46Oc8bhrUluFdm1sdR0QAe4uj37C8MjoMh9Nx1M+JuBOVKvE5u0uqeHDaGlITmnLv2SlWxxGRw2LvnIARFHTEx6rtNt44vYyrZl1FXkmeRclEjo9KlfgU0zT56+erqalz8u+Le2D30/8CIu4iYuRIWjz2KPaWLcEwcMbG8ULPP1GRdgfbDm5jzIwxfJr9KaZpWh1V5Kj0jiI+5dOlO8jcWMx9wzvqPCoRNxQxciTt582l04b1dPk+k45XjOX7lfHc2+VNUmNTeXzx49ww+wbyy/KtjiryOypV4jN27Kvgsa/W079tNFf2T7Q6jogchwnD2pMSF85TMwr55+kv8lC/h1hTvIbRX4zm4w0f4zSdVkcU+ZVKlfgEp9Pk3v+uwjAMnhnTHZtN+1GJeIJAux//HtuDfeU1PDJjPWNTxjLtgmmkxqby1JKnuHLmlWzev9nqmCKASpX4iPcXbefnrft46LxOuq+fiIfp2iqC24e254uVBXyzppCWYS15bdhrPHHGE+SW5HLxjIt5fvnzVDoqrY4qPk6lSrze1uIynp6VTUZKDGN7t7Y6joichJvTk+keH8GD09dSXFqNYRicn3w+X476khFtR/D22rcZNX0Uc/Pm6kR2sYxKlXg10zR5cPpaAvxs/POi7roNjYiH8vez8e+Le1BW5eCpbzb8+vHIoEieOOMJ3j37XUL8Q5gwfwI3z7mZrQe3WphWfJVKlXi1mWt38dOWvdxzdgpxTYKO/QUi4rbax4Vzw6Akpmblszx33xGf6928N1NGTuEvp/2F1cWrueiLi3h6ydMcrD5oUVrxRSpV4rUqa+p4/Kv1dGwezmV9EqyOIyIuMD6jHS0igvj7F+uocx65zOdv82dc53HMGD2DUe1HMWnDJM6ddi4frf+I2rpaixKLL1GpEq/1SuZmCg5W8Y/zu2iTTxEvERJg528jOrGuoIRPlhx9h/Xo4Gge7v8wn438jM5RnXl66dNc8MUFzNo2S1swyCmldxrxSnl7K3j9+61c0LMlfdtGWx1HRFzovO4t6Nc2ime/28j+8po/fFxKVAqvn/k6rw57lWB7MPd+fy+XfHUJP+z8QSezyymhUiVe6dGv1mO3Gdx/Tiero4iIixmGwT/O70pplYN/z954zMee0eoMppw3hSfPeJKSmhJumXsLV826iiWFSxopsfgKlSrxOvM3FjFnw25uH9qe5hE6OV3EG6U0D+fK/m2YtDiPtfnHPhndz+bHyOSRzBg1gwf7Pkh+aT7XfXcd18y6hiWFSzRzJS6hUiVepcbh5NEZ62nbLJRrByRZHUdETqEJwzoQFRLAI1+uO+5S5O/nz586/olvLvqG+/rcR25JLtd9dx1XzbqK9ZXrVa6kQVSqxKtMWbaDbXvKefC8TgTY9fIW8WYRwf7cc3YKy3L3M3dD0Ql9baBfIJd3upyZF83k/j73U1BWwNR9U3UiuzSI3nXEa1TV1vHy/M2kJTQlIyXW6jgi0gjG9IqnTXQIz83OOalZpkC/QC7rdBkzL5zJTbE34WfzOwUpxVeoVInXmLwkj8KDVdx9Vop2ThfxEf5+Nu4Y2p71hSV8u25XA47jT4x/jAuTiS9SqRKvUFVbx8uZW+iTFMXpydpCQcSXXNCzFW1jQpk4exNOp86JEuuoVIlX+OjnXIpLq7nrzA6apRLxMX42gwnDOrBxdynfrC20Oo74MJUq8XgVNQ5eW7CFAe2i6aeNPkV80nndWtAhLozn52z63e1rRBqLSpV4vA8W5bKnrIa7zuxgdRQRsYjNZnDnsA5sLipjxqoCq+OIj1KpEo9WVu3g9QVbGNwhhl5toqyOIyIWOrtLczq1aMLzc3Jw1GlrBGl8DS5VhmG0NgxjvmEYGwzDWGcYxh2uCCZyPKYs3cH+ilomDGtvdRQRsZjNZnDH0PZs31vBd+t3Wx1HfJArZqocwN2maXYC+gHjDcPo7ILjitTL6TR5f9F20hKakpoQaXUcEXEDZ3aOo3VUMO8u3GZ1FPFBDS5VpmkWmqa54vC/lwIbgFYNPa7IsczfWETu3gqu0e1oROQwP5vBVf0TWbp9/3HdE1DElVx6TpVhGIlAKrDYlccVOZp3F26neZMghndtbnUUEXEjF/duTUiAH+8u3G51FPExhqtuHmkYRhiwAHjCNM2pR/n8jcCNAHFxcb0mT57skuf1NGVlZYSFhVkdw20d7/jklzp5YGElF7X3Z2RyQCMkcw96/dRP41M/XxqfD9dXs2CHg3+nhxAReHx71/nS+JwMXx6fjIyM5aZp9j7W4+yueDLDMPyBz4FJRytUAKZpvgG8AdC7d28zPT3dFU/tcTIzM/HV7/14HO/4/G3aGgLtO3ngknSiQn2nVOn1Uz+NT/18aXxadylj7r8XsN0vnjvSj+9CFl8an5Oh8Tk2V1z9ZwBvAxtM03yu4ZFE6negooapK3YyqmcrnypUInL8kmPCGNwhho8W51Lj0PYK0jhccU7VAGAcMMQwjJWH/xnhguOKHNXkpTuoqnVyzRmJVkcRETd2zYBEikur+XqNNgOVxtHg5T/TNH8EdLM1aRSmaTJpcS792kbRsXkTq+OIiBsb1D6GtjGhfPRzHqNT462OIz5AO6qLR1meu58d+yoZ27u11VFExM3ZbAZjesWzPHc/eXsrrI4jPkClSjzKtKx8gv39OLuLtlEQkWO7oOehbROnr8y3OIn4ApUq8Rg1DidfrS7krC5xhAa65MJVEfFyrZoG0zcpiulZ+bhqCyGRP6JSJR5j/sYiDlbWMipVG/aLyPEbndqKrXvKWbVTO6zLqaVSJR5jelY+zcICGNiumdVRRMSDnNOtBQF2G9OztAQop5ZKlXiEg5W1zN1QxMgeLbH76WUrIscvItifYZ1imbGqgNo67Vklp47encQjzFxTSE2dk9Fa+hORkzCqZyv2ltfw46Y9VkcRL6ZSJR5hWlY+bWNC6dYqwuooIuKB0lNiaRrizzQtAcoppFIlbm9/eQ1Lt+/jvG4tOHRXJBGRExNgt3F25+bMzy7SEqCcMipV4va+31SM04QhneKsjiJ4ccW5AAAgAElEQVQiHiyjYyyl1Q6Wbd9vdRTxUipV4vbmZxcRHRpAdy39iUgDnNG+Gf5+Bpkbi6yOIl5KpUrcWp3TZEFOMYM7xGCzaelPRE5eWKCdPklRzFepklNEpUrc2sodB9hfUUtGx1iro4iIF8hIiSVndxk79+tegOJ6KlXi1uZnF2EzDt1tXkSkodJTDv2CNn9jscVJxBupVIlbm7+xiF5tIokI8bc6ioh4geSYUBKiQsjM1hKguJ5Klbit3SVVrCso0dKfiLiMYRhkpMSwcMseqmrrrI4jXkalStzWgpxD0/PpHVSqRMR1MjrGUlXrZPG2fVZHES+jUiVua9n2fUQE+9OxebjVUUTEi5yWGIXNgOXbVarEtVSqxG2tyDtAWkJTbaUgIi4VGminY/MmrMg7YHUU8TIqVeKWDlbUsrmojLSESKujiIgXSmvTlJU7DlDnNK2OIl5EpUrcUtaOQ7eRSGujUiUirpeWEElZtYNNRaVWRxEvolIlbmlF3gFsBvRo3dTqKCLihX6ZBV+RqyVAcR2VKnFLK3L3k9K8CWGBdqujiIgXahMdQnRoAMtzdXNlcR2VKnE7dU6TlTsOnaQuInIqGIZBakIkWXkqVeI6KlXidjYVlVJW7dBJ6iJySqW1acrWPeXsL6+xOop4CZUqcTurdhw6xyFVM1Uicgr98ovbqp06r0pcQ6VK3M6m3WUE2m20iQ61OoqIeLGUuEMbC28uKrM4iXgLlSpxO1uKy0hqFoqfNv0UkVMoMjSAqNAAthSrVIlrqFSJ29lcXEa72DCrY4iID2gXE6aZKnEZlSpxKzV1Jjv3V6pUiUijSI5VqRLXUakSt7Kr3IlpQnKMSpWInHrJMaHsr6hln64AFBdQqRK3Ulh+6D5cmqkSkcbwy88azVaJK6hUiVspKHNiGJDUTFf+icip98usuE5WF1dQqRK3UljupHVkCEH+flZHEREf0KppMEH+Ns1UiUuoVIlb2V1hapZKRBqNzWaQ1CyMbXvKrY4iXkClStzKgWqTFhFBVscQER/SvEkgRaVVVscQL6BSJW6jzmlSUm0SEx5odRQR8SEx4YEUl1ZbHUO8gEqVuI195TWYoFIlIo0qJjyQPWU1OE3T6iji4VSqxG38Mv0eq1IlIo0oNjyIOqdJWa3VScTTqVSJ2/hl+l0zVSLSmH75mXOwWjNV0jAqVeI2fi1VYTpRXUQaj0qVuIpKlbiN4rJDpapZeIDFSUTEl8SE/VKqnBYnEU+nUiVuo6ikmiA/CAmwWx1FRHyIZqrEVVSqxG3sLa+hSaBhdQwR8TGhgXaC/f0oqVGpkoZRqRK3UVVbR6CfSpWINL7gAD9qtPonDaRSJW6j2uHEX69IEbFAoN1GbZ3VKcTT6S1M3EZ1bZ1KlYhYItBuo9ap5T9pGL2Fiduodjjx1/KfiFgg0O5HrZb/pIFUqsRtaPlPRKwS6G9TqZIGc8lbmGEYww3D2GgYxmbDMO5zxTHF91Q7tPwnItY4dE6Vlv+kYRr8FmYYhh/wMnAO0Bm41DCMzg09rvie6lon/jYt/4lI49Pyn7iCK+YF+gCbTdPcappmDTAZuMAFxxUfc+icKqtTiIgvKjhQybaDalXSMK4oVa2AHb/5+87DHxM5ITWOOuyaqBIRC2zdU45W/6ShXHE/kKO9Df7upWkYxo3AjQBxcXFkZma64Kk9T1lZmc9+78fkdFBVY2p86qHXT/00PvXT+PyxyECD/dX6+VMfvX6OzRWlaifQ+jd/jwcK/vdBpmm+AbwB0Lt3bzM9Pd0FT+15MjMz8dXv/VjCf54HfrUan3ro9VM/jU/9ND5/rOuWxRQW79P41EOvn2NzxfLfUqC9YRhJhmEEAJcAX7rguOJjAu02ajT/LiIWOHShjNUpxNM1eKbKNE2HYRi3At8CfsA7pmmua3Ay8TkBdu0TIyLWOLSli07qlIZxxfIfpml+A3zjimOJ7wr096O20uoUIuKLqh1OQnX1sTSQJjvFbWjzPRGxiu7oIK6gl5C4jUAt/4mIRQ7d0F3Lf9IwKlXiNrSjsYhYRTNV4gp6CYnbCPLX1X8iYo3K2jrd0UEaTKVK3EZ0aAAlNSpVItK4KmocVNTUER6g5T9pGJUqcRuxTYKodEBVbZ3VUUTEh+wprQEgQqVKGkilStxGTFggAMWl1RYnERFfUlxWBUDTQJUqaRiVKnEbMeGHS1WZSpWINJ5ffpGLUKmSBlKpErfxS6kqKlGpEpHGU/RrqdJbojSMXkHiNmI1UyUiFigurcZmQHiA1UnE06lUiduICg3AQOdUiUjjKi6tJjosEJuh5T9pGJUqcRt2PxvhASpVItK4ikurf71QRqQhVKrErUQE2thdUmV1DBHxIbtLq4htolIlDadSJW4lLsRg255yq2OIiI8wTZNtxeUkRodaHUW8gEqVuJUWYTby9lVQ7dAGoCJy6u0qqaK8po7k2DCro4gXUKkSt9Iy1Ead0yR3b4XVUUTEB2wuKgOgXYxKlTScSpW4lRahh66++eUHnYjIqfRrqdJMlbiASpW4lRahh16SW1SqRKQRbCkuo0mQnWZh2qRKGk6lStxKoN2gVdNgNherVInIqbe5qIx2sWEY2qNKXEClStxOcmwYW1SqRKQRbCkuJ1nnU4mLqFSJ20mOCWVLUTlOp2l1FBHxYgcraykurdb5VOIyKlXidtrHhlNZW8fO/ZVWRxERL7Zpdymgk9TFdVSqxO10j48AIGvHfouTiIg3y8o7AED3+KYWJxFvoVIlbqdj83BCAvxYkatSJSKnzvLc/SREhRATrlvUiGuoVInbsfvZ6B4fwYrDv0WKiLiaaZqsyNtPWoJmqcR1VKrELaUlRLKhsITKGt2uRkRcL/9AJUWl1aS1ibQ6ingRlSpxS2kJkTicJqt3arZKRFzvl5nwtASVKnEdlSpxS7/89qglQBE5FVbk7ifY34+OzcOtjiJeRKVK3FJUaABJzUJZrpPVReQUWJG3nx6tI7D76W1QXEevJnFbqQlNycrbj2lqE1ARcZ2q2jrWF5Ro6U9cTqVK3FbvNlHsLa/RLWtExKVW5O7H4TTppZPUxcVUqsRtDerQDIDMjcUWJxERbzIvu4gAPxv92kZbHUW8jEqVuK34yBA6xIUxL7vI6igi4kXmbyyib9soQgPtVkcRL6NSJW4tIyWWpdv3UVpVa3UUEfECeXsr2FJcTkZKrNVRxAupVIlby+gYS22dycLNe62OIiJeYP7GQzPfQzqqVInrqVSJW+vVJpLwIDvztQQoIi4wf2MRSc1CSWwWanUU8UIqVeLW/P1sDGofw/yNRdpaQUQapLKmjkVb9pKeEmN1FPFSKlXi9tJTYigqrWZ9YYnVUUTEgy3auodqh1NLf3LKqFSJ20s/fEKplgBFpCHmZRcR7O9Hn6Qoq6OIl1KpErcXEx5IakJTvlpdaHUUEfFQjjons9buYnCHGALtflbHES+lUiUeYXRqK7J3lbJBS4AichJ+3LyHPWU1jEptZXUU8WIqVeIRzu3WArvNYPrKfKujiIgHmp6VT5MgOxkddZK6nDoqVeIRosMCGdwhhi+yCnA6dRWgiBy/8moH367bzbndW2rpT04plSrxGKNSW7GrpIqft2kjUBE5ft+t30VlbR2jtfQnp5hKlXiMMzvHERZoZ3qWlgBF5PhNyyqgVdNgereJtDqKeDmVKvEYQf5+nNO1OTPX7KKqts7qOCLiAYpKq/hxUzGjU1thsxlWxxEvp1IlHmV0aitKqx3M2bDb6igi4gG+XFmA04RRqS2tjiI+QKVKPErfttE0bxLEZ8t2Wh1FRNycaZr8d/lOurZqQrvYcKvjiA9QqRKP4mczuKRPaxbkFLO1uMzqOCLixhZv20f2rlIu79vG6ijiIxpUqgzD+JdhGNmGYaw2DGOaYRhNXRVM5I9c3rcNAX423v9pu9VRRMSNvbtwG01D/BnVU1f9SeNo6EzVbKCraZrdgRzg/oZHEqlfTHgg5/VowX+X76SkqtbqOCLihnbsq2D2+t1c2ieB4ADtTSWNo0GlyjTN70zTdBz+689AfMMjiRzbNacnUV5Tx5SlO6yOIiJu6MOfczEMg3H9tPQnjccwTdfsTm0YxgzgU9M0P/qDz98I3AgQFxfXa/LkyS55Xk9TVlZGWFiY1THc1omMzxM/V3Kg2uTpQcHYDN+4VFqvn/ppfOrnK+NT7TC5M7OCrs38uKVn0HF/na+Mz8ny5fHJyMhYbppm72M9zn6sBxiGMQdofpRPPWCa5heHH/MA4AAm/dFxTNN8A3gDoHfv3mZ6evqxntorZWZm4qvf+/E4kfEpjypk/McrqIvrzJDOcac2mJvQ66d+Gp/6+cr4fPhzLhWOtfxlVB96J0Yd99f5yvicLI3PsR2zVJmmOay+zxuGcRVwHjDUdNW0l8hxOLtLHC0ignh34TbO9JFSJSL1M02T9xZuo1urCHppB3VpZA29+m848FfgfNM0K1wTSeT42P1sjOvfhp+27GV9QYnVcUTEDXy/aQ9bisu5ZkAiho+cFiDuo6FX//0HCAdmG4ax0jCM11yQSeS4XdYngbBAOy/N22R1FBGxmGmavDAnh5YRQZzbvYXVccQHHXP5rz6mabZzVRCRk9E0JIBrz0jixbmbWFdwkC4tI6yOJCIWycwpZkXeAZ4c3Y1Au7ZRkManHdXF4113RhJNguxMnK3ZKhFfZZomE2fnEB8ZzJhe2t1HrKFSJR4vItifGwa2Zc6G3azaccDqOCJigTkbili98yC3D21PgF1vbWINvfLEK1w9IJGmIf5MnJNjdRQRaWROp8lzs3NIjA7hwlTdkkaso1IlXiE8yJ+bBiWTubGY5bn7rY4jIo3o23W72FBYwh3D2mP309uaWEevPnEfJYXQgK3OruzfhujQACbO1myViK9wOk0mzskhOSaU83tolkqspVIl7sFRDW8OITXrr5Dz7UmVq9BAOzenJ/Pj5j0s2rL3FIQUEXczY3UBObvLmDCsA3427Usl1lKpEjdhwKB7CKzeDx+PhTfSYePMEy5Xl/dtQ8uIIB79aj11Tm3wL+LNKmocPD0zm84tmnBuN+1LJdZTqRL3YA+A065jcd9X4fz/QNUB+OQSeDMDNs057nIVHODHA+d2ZkNhCR8vzj3FoUXESq/M30LBwSoevaALNs1SiRtQqRK3YtrskDYObl0G578E5Xth0kXw7gjI+/m4jjGiW3P6t43m2e9y2Fdec4oTi4gVtu8p543vtzI6tdUJ3TRZ5FRSqRL35OcPaVfCbcthxLOwbwu8czZ8cikUb6z3Sw3D4B8XdKGs2sG/vq3/sSLimR77aj3+fgb3n9PR6igiv1KpEvdmD4A+N8DtWTDkIdj+I7zSD2ZMgLKiP/yyDnHhXNU/kclL81iz82AjBhaRU21+dhFzs4u4Y1h7YpsEWR1H5FcqVeIZAkJh0D1w+0o47QbI+hBeTIMfJx66cvAoJpzZnujQAB7+ci1OnbQu4hWqHXX8Y8Y62saEcvXpSVbHETmCSpV4ltBoGPEM3LIYEs+AOY/Ay31h46zfPbRJkD9/Hd6RFXkHmJqV3/hZRcTl3vphG9v3VvDIyC66HY24Hb0ixTM1aweXTYYrpoJfAHzyJ5g0FvZtO+JhF6XFk5rQlH/O3MB+nbQu4tF27KvgP/M2c3aXOAZ1iLE6jsjvqFSJZ2s3FG5eCGc9DrkLD51v9f2/wHGoQNlsBo+P6sqBilr+/uU6i8OKyMlyOk3u+WwVfjaDv4/sYnUckaNSqRLP5+cPp98Gty6FDsNh3uPw2hm/bsHQpWUEdwxtz4xVBXy1usDisCJyMt77aTuLt+3j7yM706ppsNVxRI5KpUq8R5OWMPZ9uGwK1FYe2oLh63uguoyb05PpER/BQ9PXUlRaZXVSETkBW4rLeHpWNkM7xnJxr3ir44j8IZUq8T4dzoZbFkHfm2HpW/BKf+y53/PvsT0or6njb1PXYjbgxs0i0ngcdU7unrKK4AA/nrqwG4ahndPFfalUiXcKDINz/gnXfntor6sPLqDd0n/wt2EJzNmwm89X6GpAEU/w+vdbWbnjAI9d0FV7UonbU6kS75bQF276AfqNh6VvcdXqcVzasph/fLmOggOVVqcTkXpsKCzh+Tk5nNu9BSN7tLQ6jsgxqVSJ9wsIgeFPwlVfYjiqeXL/XVxvfs77j77CpowhbOjUmU1DhnJwxgyrk4rIYTUOJ3dNWUVEcACPXdDV6jgix8VudQCRRpM0CG5eiPH1XVz91ZfkL43EUXfoU46CAgof+jsAESNHWhhSRAAe/3o9GwpLeOvK3kSFBlgdR+S4aKZKfEtwU7jobYo2J2LUHfkps6qKoonPW5NLRH41PSufDxblcsPAJIZ1jrM6jshxU6kS32MYOPaWHPVTjsLCRg4jIr+VvauE+6aupk9SFH8d3tHqOCInRKVKfJK9RYujf7x5bCMnEZFflFTVcvNHKwgP8uc/l6Vi99NblHgWvWLFJ8XeOQEj6MjLsw0/k9jORbBrjUWpRHyXaZrc+9kq8vZV8PJlacSGa/sE8TwqVeKTIkaOpMVjj2Jv2RIMg/LIZnySOoyA1g54+yxYN93qiCI+5Y3vt/Ltut3cf05H+iRFWR1H5KSoVInPihg5kvbz5tJpw3p6/LiADWdczlnlj1IR1Qk+uwoWPAPaeV3klFu0ZS9Pz8pmRLfmXHdGktVxRE6aSpUI4O9n4z+XpVIV1IwRB/5KZeexMP8JmHojOKqtjifitbYWl3HLpOUkNQvlmTE9dBsa8WgqVSKHxTYJ4u2rerO7wuTiXeOoGfwArJkCH46Gyv1WxxPxOsWl1Vz17hJshsE7V59GWKC2ThTPplIl8hvd45vyyuVpbNhVxg3b0nGMfhN2LoV3hsPBnVbHE/EaFTUOrnt/KcWl1bx99Wm0iQ61OpJIg6lUifyPjI6xPD6qKwtyinlgU0fMKz6HkoJDJ7AXZVsdT8TjOeqc3PpxFmvzD/KfS9Po2bqp1ZFEXEKlSuQoLu2TwG1D2vHpsh28tLUFXPMNOB3w7nDYudzqeCIeyzRNHvpiHfOyi3j0gq7aMV28ikqVyB+468wOXJjWiudm5/DZzqZw7SwIbAIfnA/bf7Q6nohHeiVzC58syeOW9GSu6NfG6jgiLqVSJfIHDMPgnxd254x2zbh/6hoyi8Pg2m+hSSv4aAxsmWd1RBGP8vnynfzr242M6tmSe89OsTqOiMupVInUI8Bu49Ur0ugQF85NHy7nh912uPpriE6Gjy+BTXOsjijiEb5Ymc+9/13F6cnR2jpBvJZKlcgxhAf589H1fUlqFsr17y/jh0LgqhkQkwKTL4PNKlYi9fliZT53frqS0xKjeOuq3gTY9dYj3kmvbJHjEBUawMc39Pv/YpVfB1d+ATEdYPLlsHWB1RFF3NJvC9W715xGSID2ohLvpVIlcpyOWqzGfQFRbeGTSyDvZ6sjirgVFSrxNSpVIifgd8WqwAnjpkN4C5g0FgpXWx1RxC2oUIkvUqkSOUG/K1a7bIeWAgPD4aMLYd9WqyOKWEqFSnyVSpXISfhtsbru/WV8s8MO46aBs+7QvQLLiqyOKGKJD3/OVaESn6VSJXKSokID+OSGfnRrFcH4j1fw9kZ/uPyzQ4Xq47FQU251RJFG43SaPD0rm4emryUjJVaFSnySSpVIA0SGBjDp+r6c3bk5j321nsdWhuC86B0oXAX/vfbQzJWIl6txOLlrykpezdzCZX0TeH1cLxUq8UkqVSINFOTvx8uXp3H16Ym8/eM2blseR+3Zz0DOLPj2b1bHEzmlDlbWctU7S5i+soB7z07hiVFdsfvprUV8k36VEHEBP5vBwyM7Ex8ZzONfb6CotAsf9rqJoMWvQbMOcNp1VkcUcbmCA5Vc8+5SthSX8dzYHlyYFm91JBFLqVSJuIhhGFw/sC3NI4K469NVjCw7my8TNxM88y+HilXSQKsjirjMhsISrnl3KeXVDt6/tg8D2jWzOpKI5TRHK+Ji53VvyYfX9WF3mYPheVdSEZ4IU66E/blWRxNxiW/WFDLm1Z8AmPLn/ipUIoe5pFQZhnGPYRimYRj6P0sE6Ns2mmnjBxAQFsl5xTdTXVOD+ekVUFtpdTSRk1Zb5+Txr9Zzy6QVdGgezrTxp9OpRROrY4m4jQaXKsMwWgNnAnkNjyPiPZJjwpg+fgBduvXi5so/U/LzJjYN7M+GTp3ZNGQoB2fMsDqiyHErKqni8jcX89aP27j69EQ+vbE/LSKCrY4l4lZccU7VROAvwBcuOJaIVwkNtPPiJT35Kj+LHV9E41dXDYCjoIDCh/4OQMTIkVZGFDmmxVv3cusnWZRVOXjhkp5c0LOV1ZFE3FKDZqoMwzgfyDdNc5WL8oh4HcMw6PjNJPzqnEd83Kyqomji8xalEjk20zR58/utXPbWYsID7UwfP0CFSqQehmma9T/AMOYAzY/yqQeAvwFnmaZ50DCM7UBv0zT3/MFxbgRuBIiLi+s1efLkhuT2WGVlZYSFhVkdw2156/jE/vlmjKN83ASKXnv1uI/jrePjKhqf+p3I+JTVmLy3rpplu+voFefH9d0CCbYf7VXsPfT6qZ8vj09GRsZy0zR7H+txxyxVf/iFhtENmAtUHP5QPFAA9DFNc1d9X9u7d29z2bJlJ/W8ni4zM5P09HSrY7gtbx2fTUOG4igo+N3H94ZGETx1Br3aRB3Xcbx1fFxF41O/4x2f+dlF/PXz1ewrr+Evw1O4YWBbDMO7CxXo9XMsvjw+hmEcV6k66eU/0zTXmKYZa5pmommaicBOIO1YhUrEF8XeOQEjKOiIjxl+TrJTU7j4tUU8NXMDVbW6pY1Yq7Sqlvs+X8017y0lMiSA6eMHcOOgZJ8oVCKuoM0/RRrBLyejF018HkdhIfbmzYlNreC62DkUJ17O6wu2Mj+7iOfG9qRrqwiL04ov+mnLHu79bDWFByu5OT2ZCcPaE2j3szqWiEdxWak6PFslIn8gYuTII6/027sFXhvI/TUv0v/q1/nr1LWMenkhtw5px/iMdvjr/mnSCCpr6nh6Vjbv/bSdpGahfPbn0+nVJtLqWCIeST+1RawSnQxnPw5bM0kvmcF3EwYzskdLnp+zidGvLGRdwUGrE4qXW7JtHyNe/IH3ftrO1acn8s3tA1WoRBpApUrESr2ugeQhMPthIqp2MvFPPXntijQKD1Qx8qUfeWj6Wg5U1FidUrzM7pIqJkzOYuzri6hxOPn4+r48cn4XggO03CfSECpVIlYyDDj/JTBs8OVtYJoM79qCeXenc2X/RCYtziXj2Uw+XpxHnfPkrtQV+YXDafL6gi0MeTaTb9bu4rYh7Zh91yBO1737RFxCpUrEahHxh5YBt/8Ay9879KEQfx45vwtf3z6Q9nHh/G3aGka9vJDN+3WFoJycBTnFPLiwkqdmZtM/OZrZdw7i7rNSCAnQ9UoirqJSJeIO0q6CxIEw+2Eo/f9dSTq1aMKnN/bjhUt6UlRaxeOLq7h7yiqKSqssDCueZMe+Cm78YBlXvbME04R3rzmNt646jTbRoVZHE/E6KlUi7sAwYOQL4KiCmX/9n08ZXNCzFfPuTufcJH++XJXP0GcX8MKcTZRU1VoUWNzd3rJqnvxmA8OeW8CPm/fwl+EpPH5GMBkpsVZHE/FaKlUi7iI6GQbdC+unQ853v/t0aKCdi1MC+HbCIPonRzNxTg4Dn57Py/M3U17tsCCwuKP95TU8Myubgc/M560ftnJu9xbMvXswt6S3w9+mTTxFTiUtpou4kwF3wJopMPNeSBoI/sG/e0jbmDDeuLI3a3YeZOKcHP717Ube/nEbfx7clnH9EnUFl486WFnL2z9u450ft1Fe42Bk95bcMaw9yTG+ea82ESuoVIm4E3sAjHgWPjgfFr4I6X/9w4d2i4/gnatPIytvPxPnbOLJb7J54/tt3JKezGV9EwjyV7nyBaVVtby7cDtv/rCV0ioHI7o1546hHUhpHm51NBGfo1Il4m7aDoYuo+HH56DHJRDZpt6HpyZE8sG1fVi6fR8TZ+fw6Ffref37LVwzIIlLTmtN05CARgoujamopIqPFufxwaLtHKio5czOcdw5rAOdWzaxOpqIz1KpEnFHZz0OG2fBdw/Cnz48ri85LTGKj2/ox6Ite3lp3ib+OTOb5+fkMDo1nmsGJNIhTjMX3mDljgO8t3AbX68pxOE0GdoxjjuGtqdbvO4ZKWI1lSoRdxQRDwPvgvlPwPYfIfGM4/7S/snR9E+OZkNhCe//tJ2pK3byyZI8BrSL5prTkxjSMRabTlj2KLV1Tmau3cW7C7eRlXeAsEA7V/Rrw1X9E0lspq0RRNyFSpWIu+p/Kyx/H779G9yQCbYTu1i3U4sm/POi7vxleEc+WZLHh4tyuf6DZbSJDuHK/omM6RVPRLD/qckuLrGnrJrJS/L48OdcdpdUkxgdwsMjOzOmVzzhQfpvJ+JuVKpE3FVACAx7GKbecOiKwB6XnNRhokIDGJ/RjhsHtWXW4dmOx75az9OzshnWKZbRqfEM7hBDgF07rLiDypo6Zm/YzfSsfBbkFFPnNBnYvhlPXdiN9A6aZRRxZypVIu6s6xhY9DLMfQw6j2rQofz9bIzs0ZKRPVqyeucBpq7I58tVBXyzZhdNQ/w5r3sLRqe2Ii0hEsPQG3djqnOaLNqyl2lZ+cxaW0h5TR3NmwRx/cAkxqTF017nw4l4BJUqEXdms8FZj8H7I2HJ60APlxy2e3xTusc35YFzO/HDpmKmZRXw2bKdfPRzHglRIYzq2ZILUltpj6NTyDRN1heW8MXKAr5Ymc/ukmrCA+2c270Fo1Jb0TcpGj/NSol4FJUqEXeXNAjaDYMfnsPe62WXHtrfz8aQjnEM6RhHaVUt3647tOz00vzNvDhvM22bhZLRMZaMlFhOS8poKWsAAAzkSURBVIok0K69rxqisqaORVv3MC+7iPnZxeQfqMRuM0hPieHv58UztFOs9hcT8WAqVSKeYOjf4fVBxO/8AjjvlDxFeJA/Y3rFM6ZXPLsOVjFzbSHzNxbz4c+5vP3jNkID/BjQrtmvJat5RNApyeFt8vZWMH9jEfOyi1i0dS81Dichh8dyfEY7hv9fe3cfXFV953H8/SWBi8kND4HcBAwgCwoFqQoBa1m34EPHOq32wVo67taxTq2dbas7uzO7rTs7nTqdbrt9mOm0625t6ew67mqfsLRjrbaF2tZigZQKiJTgEuWhJmAIBEIeyHf/OFdM8N6TaA735J7zec1k7r2eX+79+p3fST75nQcubqC2WvcSE0kChSqRcjDjElj0bhp3r4cTn4fq6ef04xomT+S2lXO5beVcTvb281TLETbsbmPDc208/uxLQHB14V9dOJ2lc6aydPZU6moy57SmcnGos5utrR1sbe3gyT+1s7f9BABzp1dzy+WzuWphjhVza7XqJ5JAClUi5WL1p6l4dj089TW49rMl+9iqCZVcs6ieaxbV4+786aWuMysva3/7f/znk88DMLu2iqWzp5wJWQsbaqisSPYVhb39A+w82MnW1g7+8MJRml/o4FDnKQAyleNYMbeWWy6fw+qFOebqflIiiadQJVIu6hbQlruS+t/fD1d8ArJ1JS/BzFjQUMOChhrufNs8TvWdPhMqmluP8tTeIzyy7SAA542v4JJZk7l45mTm57LMy2WZX5dlahke6nJ3Dnf10tLWxd72Llrauth+oJPtBzrp7R8A4Pwp59F0QS1LZ09h2ZypvGnGJMYnPFSKyFAKVSJlZN8FN1Pf/utgtert98ZdDhPHV7BsTi3L5tQCQfg4cLSb5heO0tzaQfMLHTywqZWefPAAmFY9gXl1QciaV1fN/FyWxqlV1NVkmDSxMrbbObg7nd19tB3v4cWXT9LS1jUkRB071X9mbPWEChbOmMStV8xhWX5lLjdJ55iJpJ1ClUgZ6a5qhIvfB5u/BSvvhuppcZc0hJnROLWKxqlV3HDJTAAGBoKgNTig7G3v4rEdh+g42Tfk+zOV46iryQRf2cyZ57maidRMrCRTOY7M+IrgsXIcmcoKMuNffX60Z4AXXz5JT/8APf2ng8e+Qc/7B+js7qP9eM+gr1PBY1cPfad9SD3Tsxnm56q54dKZzKvLBitudVlmTJ6oe3mJyGsoVImUmyv/AbZ/D56+D67657irGda4ccas2ipm1VaxemFuyLYjXT3sbT/Boc7uoUGnq4fWIyfZ0trByyd6X98Hbtgw7BAzmFb9amibn6vJh7fg9cwp5zG/LsvkKv1TMCIycgpVIuUmtxDe9C74/TfhrZ+EiZPirugNm5bNMC0bftVg3+kBDnf1cKKnn1N9A8VXofpOs2fPHpYsWhi6mjVpYiW11RMSfxK9iJSeQpVIOfrLv4NdP4at34GVd8VdzTk1vmIcMyafN6KxG3v2sapp1jmuSESkMP2pJlKOzl8Gc98Gm+6D/td5eExERM4JhSqRcrXyk3D8UHB+lYiIxE6hSqRczbsacovhd98A9+HHi4jIOaVQJVKuzOCKv4W2nfD88Fe8iYjIuaVQJVLOltwE1bng3CoREYmVQpVIOavMwPLbYc/jcLgl7mpERFJNoUqk3DV9GMaNh833x12JiEiqKVSJlLtsDha/B/7wIPQcj7saEZHUUqgSSYIVH4He4/DMd+OuREQktRSqRJKgcTk0LIHN39btFUREYqJQJZIEZtB0e3B7hf2b465GRCSVFKpEkmLJTTAhC1u+E3clIiKppFAlkhSZGljyfti5DrqPxl2NiEjqKFSJJMnSD0F/N+z4ftyViIikjkKVSJLMvAzql0DzA3FXIiKSOgpVIkliBpfdAoe2wZ93xF2NiEiqKFSJJM2Sm4M7rG97MO5KRERSRaFKJGmqp8GC62D79+B0X9zViIikhkKVSBJd8kE40Q4tv4i7EhGR1FCoEkmi+ddC1TR45uG4KxERSQ2FKpEkqpwAi98Lux+FU8firkZEJBUUqkSS6s03Q/8p2PXjuCsREUkFhSqRpGpcDlPm6EagIiIlMupQZWafMLPdZrbTzL4YRVEiEgEzuPh98PyvoKs97mpERBJvVKHKzFYDNwJvdvfFwJciqUpEorHkJvDTsOtHcVciIpJ4o12p+hjwr+7eA+DubaMvSUQik1sE0y+CnY/EXYmISOKNNlRdBFxpZk+b2a/MbHkURYlIRMyCqwD3/QaO/znuakREEs3cPXyA2c+BhgKb7gE+B/wSuAtYDjwM/IUXeFMzuwO4A6C+vn7ZQw89NLrKy1RXVxfZbDbuMsYs9SfcG+lP5lQ7mZ4jHJt0EViyr03R/Amn/oRTf8KluT+rV6/e6u5Nw40bNlSFfrPZYwSH/zbmX+8F3uLuoWfFNjU1+ZYtW97w55azjRs3smrVqrjLGLPUn3DqTzj1J5z6E079CZfm/pjZiELVaP9sfQS4Kv+BFwETgMOjfE8RERGRslM5yu9fC6w1sx1AL3BroUN/IiIiIkk3qlDl7r3AX0dUi4iIiEjZSvZZqyIiIiIlolAlIiIiEgGFKhEREZEIKFSJiIiIREChSkRERCQCClUiIiIiEVCoEhEREYmAQpWIiIhIBBSqRERERCKgUCUiIiISAYUqERERkQgoVImIiIhEwNy99B9q1g60lvyDx4bpwOG4ixjD1J9w6k849Sec+hNO/QmX5v7Mcfe64QbFEqrSzMy2uHtT3HWMVepPOPUnnPoTTv0Jp/6EU3+Gp8N/IiIiIhFQqBIRERGJgEJV6X0z7gLGOPUnnPoTTv0Jp/6EU3/CqT/D0DlVIiIiIhHQSpWIiIhIBBSqzjEze9jMtuW/9pnZtiLj9pnZ9vy4LaWuMy5m9hkzOzCoR9cXGXedme02sxYz+6dS1xkXM/s3M3vOzJ4xs3VmNqXIuFTNn+Hmg5ll8vtei5k9bWYXlL7KeJjZLDPbYGa7zGynmd1VYMwqM+sctN/9Sxy1xmW4/cUCX8vPn2fMbGkcdcbBzBYMmhfbzOyYmd191phUz58wlXEXkHTu/oFXnpvZl4HOkOGr3T2N9wD5qrt/qdhGM6sAvgFcC+wHNpvZend/tlQFxugJ4FPu3m9mXwA+BfxjkbGpmD8jnA+3Ax3uPt/M1gBfAD7w2ndLpH7g79292cxqgK1m9kSB/eXX7v7OGOobK8L2l3cAF+a/Lgfuyz8mnrvvBi6FM/vaAWBdgaFpnz8FaaWqRMzMgJuB/427ljK0Amhx9+fdvRd4CLgx5ppKwt0fd/f+/MtNQGOc9YwRI5kPNwL/lX/+feDq/D6YeO5+yN2b88+PA7uA8+OtquzcCPy3BzYBU8xsRtxFxeBqYK+7p/Vm3a+bQlXpXAm85O57imx34HEz22pmd5SwrrHg4/kl9rVmNrXA9vOBFwe93k86f0l8GPhpkW1pmj8jmQ9nxuRDaScwrSTVjSH5w56XAU8X2HyFmf3RzH5qZotLWlj8httf9DMnsIbiCwFpnj9F6fBfBMzs50BDgU33uPuP8s8/SPgq1Up3P2hmOeAJM3vO3Z+MutY4hPWHYFn9XoIfcvcCXyYID0PeosD3Juay1ZHMHzO7h+CwzoNF3iax86eAkcyHRM+ZkTCzLPAD4G53P3bW5maCf3ajK38e4yMEh7rSYrj9RfPHbAJwA8EpB2dL+/wpSqEqAu5+Tdh2M6sE3gssC3mPg/nHNjNbR3CIIxG/FIfrzyvM7H7gJwU27QdmDXrdCByMoLQxYQTz51bgncDVXuQeKEmePwWMZD68MmZ/fv+bDLxcmvLiZ2bjCQLVg+7+w7O3Dw5Z7v6omf27mU1Pwzl5MKL9JdE/c0boHUCzu7909oa0z58wOvxXGtcAz7n7/kIbzaw6f0IpZlYNvB3YUcL6YnPWeQrvofD/92bgQjObm//raQ2wvhT1xc3MriM4Mf0Gdz9ZZEza5s9I5sN64Nb885uAXxYLpEmTP3fs28Aud/9KkTENr5xjZmYrCH4XHCldlfEZ4f6yHvhQ/irAtwCd7n6oxKXGrejRlTTPn+Fopao0XnNc2sxmAt9y9+uBemBdfo5WAv/j7o+VvMp4fNHMLiVYWt8HfBSG9id/5dvHgZ8BFcBad98ZV8El9nUgQ3CIAmCTu9+Z5vlTbD6Y2WeBLe6+niBUPGBmLQQrVGviq7jkVgJ/A2y3V2/h8mlgNoC7/wdB0PyYmfUD3cCatIROiuwvZnYnnOnPo8D1QAtwErgtplpjYWZVBFfXfnTQfxvcnzTPn1C6o7qIiIhIBHT4T0RERCQCClUiIiIiEVCoEhEREYmAQpWIiIhIBBSqRERERCKgUCUiIiISAYUqERERkQgoVImIiIhE4P8BHvxwV5kAigkAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "\n", "t=linspace(0,2*pi,101)\n", "plot(5*cos(t),5*sin(t))\n", "t=linspace(-5,-2,101)\n", "plot(t,12/t);\n", "t=linspace(2,5,101)\n", "plot(t,12/t)\n", "grid()\n", "plot(x_sol,y_sol,'o')\n", "axis('equal');" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": "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