{ "cells": [ { "cell_type": "markdown", "id": "d555a3fc", "metadata": {}, "source": [ "# 12 — Stochastic control (Pontryagin LQR)\n", "\n", "Doc page: [stochastic_control.rst](../../docs/source/algorithms/stochastic_control.rst).\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "630ebe94", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:29.702153Z", "iopub.status.busy": "2026-05-12T14:05:29.701881Z", "iopub.status.idle": "2026-05-12T14:05:30.298994Z", "shell.execute_reply": "2026-05-12T14:05:30.297851Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from optimizr import _core as opt\n", "plt.rcParams['figure.figsize'] = (8.5, 4.5)\n", "plt.rcParams['figure.dpi'] = 110\n", "plt.rcParams['axes.grid'] = True\n", "plt.rcParams['grid.alpha'] = 0.3\n" ] }, { "cell_type": "markdown", "id": "3ece7571", "metadata": {}, "source": [ "## Cellule 1 — LQR scalaire et équation de Riccati\n", "\n", "**Théorème (Kalman, LQR).** Pour le système $\\dot x = ax + bu$ et le\n", "coût\n", "$$J = \\int_0^T (q x^2 + r u^2)\\,dt + s\\,x(T)^2,$$\n", "le contrôle optimal est $u^*(t) = -(b/r)\\,P(t)\\,x(t)$ où $P(t)$\n", "satisfait la Riccati rétrograde\n", "$$-\\dot P = 2aP - (b^2/r) P^2 + q,\\qquad P(T) = s.$$\n", "\n", "**Équation pivot (cas $a = b = q = r = 1$).** Le point fixe\n", "stationnaire est $P^* = 1 + \\sqrt{2} \\approx 2.414$.\n", "\n", "**Ce que la cellule vérifie.** Le primitive `pontryagin_lqr` retourne\n", "$P(0)$ proche du point fixe pour $T = 5$.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "b3ac43bf", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:30.302507Z", "iopub.status.busy": "2026-05-12T14:05:30.302154Z", "iopub.status.idle": "2026-05-12T14:05:30.867738Z", "shell.execute_reply": "2026-05-12T14:05:30.866267Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P(0) numérique = 2.7321\n", "P* analytique = 2.4142\n", "P(T) (terminal) = 0.5000\n", "Coût optimal = 2.4701\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = opt.pontryagin_lqr(\n", " a=1.0, b=1.0, q=1.0, r=1.0, s_terminal=0.5,\n", " x0=1.0, t_horizon=5.0, n_steps=400,\n", ")\n", "ts = np.array(res['time_grid'])\n", "P = np.array(res['riccati'])\n", "state = np.array(res['state'])\n", "control = np.array(res['control'])\n", "\n", "P_star = 1.0 + np.sqrt(2.0)\n", "print(f\"P(0) numérique = {P[0]:.4f}\")\n", "print(f\"P* analytique = {P_star:.4f}\")\n", "print(f\"P(T) (terminal) = {P[-1]:.4f}\")\n", "print(f\"Coût optimal = {res['cost']:.4f}\")\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(13, 3.8))\n", "axes[0].plot(ts, P, lw=2)\n", "axes[0].axhline(P_star, ls='--', color='gray',\n", " label=f'P* = {P_star:.3f}')\n", "axes[0].set_xlabel('t'); axes[0].set_ylabel('P(t)')\n", "axes[0].set_title(\"Riccati\"); axes[0].legend()\n", "axes[1].plot(ts, state, lw=2, color='C2')\n", "axes[1].set_xlabel('t'); axes[1].set_ylabel('x(t)')\n", "axes[1].set_title(\"État optimal\")\n", "ts_u = ts[:len(control)]\n", "axes[2].plot(ts_u, control, lw=2, color='C3')\n", "axes[2].set_xlabel('t'); axes[2].set_ylabel('u(t)')\n", "axes[2].set_title(\"Commande optimale\")\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "274eb1aa", "metadata": {}, "source": [ "**Résultat attendu.** $P(0) \\approx 1 + \\sqrt{2}$ ; l'état $x$\n", "décroît rapidement vers $0$ ; la commande est proportionnelle à\n", "$-P(t)\\,x(t)/r$.\n", "\n", "**Lecture du graphique.** $P(t)$ plate sur $[0, T-\\epsilon]$ puis\n", "descend vers $s = 0.5$ ; trajectoires d'état/commande lisses.\n", "\n", "**Conclusion.** Le LQR scalaire est validé contre le point fixe\n", "analytique.\n" ] }, { "cell_type": "markdown", "id": "790043ec", "metadata": {}, "source": [ "## Cellule 2 — Étude paramétrique : sensibilité au coût terminal\n", "\n", "**Théorème.** Lorsque $T \\to \\infty$, $P(0)$ tend vers le point fixe\n", "indépendamment de $s$.\n", "\n", "**Équation pivot.** $P^* = (a + \\sqrt{a^2 + b^2 q / r}) \\cdot r / b^2$.\n", "Pour $a = b = q = r = 1$, $P^* = 1 + \\sqrt{2}$.\n", "\n", "**Ce que la cellule vérifie.** Sweep sur plusieurs valeurs de $s$ et\n", "de $T$ : $P(0)$ converge vers $P^*$.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "0e6af886", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:30.870857Z", "iopub.status.busy": "2026-05-12T14:05:30.870588Z", "iopub.status.idle": "2026-05-12T14:05:31.158164Z", "shell.execute_reply": "2026-05-12T14:05:31.155824Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s = 0.1 : P(0) à T=10 = 2.7321\n", "s = 0.5 : P(0) à T=10 = 2.7321\n", "s = 2.0 : P(0) à T=10 = 2.7321\n", "s = 5.0 : P(0) à T=10 = 2.7321\n" ] }, { "data": { "image/png": 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xot6CWUREDcFkk4jalAcffBD79+/Hp59+iuXLl5usX9UTc/r06VrnSktLceHChUYnrRMnTsTjjz+OrVu36hYfefnll/WGv1b1mjk4OOCuu+5q1PPCw8Nx/vx5qFSqWgsKJSUl6R3X7K1r7HNvVHXvEydO1PmDvKVjmDhxIr766iusXbsWjz76KH755Rc88sgjegudNMV77tmzp66nKT8/H3fccQfmz5+PZ555pt5bXERGRuLKlSsYOHBgrX+/+jpz5kydZVXtujm+Bm7UXPs1Llu2DD/99BNeeuklbNy4EZMmTcKJEycQHBwMoGnbPwBMmjQJn3zyCd588008/vjjuhVfDan59WJMhw4dIAiCyXqAdhRFv379sHnzZr3yXbt21arLPTSJqCE4jJaI2pTHH38cXbp0QUJCAjZu3GiwTs0N1hUKBfr164cff/wRx44d06u3cuVKFBUV4YEHHmhUTGPGjIGzszPWrFmj2zql5rBOALjnnnvg6+uLN998E5mZmbXuoVKpzB7yNnLkSOTn5+PTTz/VK9+6dSvOnj2rV9a9e3d07doVn3/+uW5IYU2iKNbassFcQ4YMgUKhwNtvv42LFy/WOl/Vq2LJGAYNGoTQ0FB8+eWXWLt2LTQaDSZNmqRXx5LPM7Q1hoeHB8LDw1FRUVGvId1VHnvsMeTn5+PVV181eL4+wzrXrVuHS5cu6Y41Gg2WLVsGALr5fs3xNXCjquS/KYdxHjx4EIsWLcK9996LJUuWYOPGjSguLsa4ceN0W780ZfuvEh8fj4qKCixZssRovZtvvhldunTBunXr8Oeff9Y6X/X14unpiWHDhmH//v347rvv6qwHaHuab+xRrqys1LWBmprj34SIWh/2bBJRm2Jvb48ffvgBsbGxGDduHD788EMMHToUvr6+UCqV+P3337Ft2zZ0795dd827776L/v37Y/DgwXjyySd12z7873//w80334wZM2Y0KiYXFxc88MADWLduHZycnNC/f/9aPRxOTk746quvMGLECERHR2PSpEmIiorCtWvXcP78eWzZsgWvv/56rSTVkNmzZ2PDhg145pln8Ndff+GWW25BYmIiVq9ejZtvvhn//POPrq4gCLotNXr27ImJEyeia9euqKysxMWLF7Ft2zZMmDDB6B6IdXFycsIXX3yBUaNG4eabb9ZtfZKfn48DBw5g6NCheOaZZywagyAIeOyxx7BkyRIsX74cYWFhGDBgQK06lnre0qVLsXv3bsTGxiIsLAw2NjY4cOAAdu7cidjYWN18xfp47rnnsHfvXixevBi//vorhgwZAk9PT1y5cgWHDx/GhQsXdPMsTYmOjkafPn3w5JNPwtPTE9u2bcMvv/yCcePG6Q3jbuqvgRtVbY8zZ84cPPzww3BwcECXLl0sNjw4JycH48ePh5+fH7766isIgoAePXogISEBTz31FBYsWIA33nijSdt/lXvuuQe33XYbvvrqK8ybN8/g3F8Aun1KBw8ejDvvvBOTJ0/GzTffjOLiYhw5cgTh4eF44403AAAffPABTpw4gVGjRuGhhx5Cnz59oFarceLECahUKqxbtw6AdqTHRx99hNGjR2PIkCHIy8vD+vXrDQ4N9vLyQocOHbBhwwZERETA19cXzs7OiIuLa/B7J6I2wHoL4RIRWU9ZWZn40UcfiYMGDRK9vLxEGxsb0cPDQ+zXr5+4YsUKsaCgQK/+mTNnxDFjxoje3t6ira2tGBISIs6YMaNWPUNbVVSp2o7EkKqtIXDDlhE3SkxMFCdMmCAGBQWJtra2ore3t9irVy9x3rx54uXLl816liiKYmpqqvjwww+L7dq1E52cnMS+ffuKv/76qzhq1CjR0dGxVv0rV66ITz31lBgeHi7a2dmJ7dq1E7t27So+99xz4unTp3X1jG1ZceNWDlWOHz8uPvDAA6JCoRBtbW3FgIAA8f777xePHz/eoBhMuXDhgigIgtFtHCz1nvft2yeOHTtWDA0NFR0dHUU3NzexW7du4htvvFFrCxZD6mpPKpVK/PDDD8U+ffqILi4uooODgxgaGiqOGjVK3Lhxo8n71tye5IMPPhA7deok2tnZie3btxcXLlxYawsXUTT/a8DY1ieG2nZdn98bb7whhoWFiTY2Nib/rUTR/K1PNBqNOHToUFEul4sHDhyoVXf06NGiIAjizp07dWWNbXtV7/HgwYMGz+/atUsEoLc1UF1fL+fOnRMnTJgg+vv7i7a2tqKvr694zz33iD///LNevYyMDPHpp58WQ0JCdP9X9O/fX9y0aZOuTklJiThnzhwxJCREtLOzE0NDQ8V58+aJiYmJBj/Lo0ePinfccYfo5OQkAtCLj1ufEJEhgihaYUY+ERFJ0k033QSNRmNwyCC1Hvv378egQYPwxRdfmNUbTkRE1BCcs0lE1AaVlJTUKtu6dSvOnDmDe+65xwoRERERUWvDOZtERG1QXFwcfH19ccstt8De3h7Hjx/H2rVr4evrizlz5lg7PCIiImoFmGwSEbVBcXFxWLt2LXbt2oWioiL4+Pjg0UcfRXx8PPz9/a0dHhEREbUCnLNJREREREREFsc5m0RERERERGRxTDaJiIiIiIjI4jhn87qysjKcOnUKCoUCNjb8WIiIiIiIiG6kUqmQnZ2Nrl27wsHBwWhdZlXXnTp1Cr1797Z2GERERERERJJ37Ngx3HrrrUbrMNm8TqFQANB+aFyJkZqbWq1Gbm4uvLy8IJfLrR0OtVFshyQFbIckBWyHJAVSbYcZGRno3bu3Ln8yhsnmdVVDZ/39/REUFGTlaKitUavVsLe3h0KhkNR/JtS2sB2SFLAdkhSwHZIUSL0dmjP1kAsEERERERERkcUx2SQiIiIiIiKLY7JJREREREREFsdkk4iIiIiIiCyOySYRERERERFZHJNNIiIiIiIisjgmm0RERERERGRxTDaJiIiIiIjI4iSRbO7cuRMDBgyAQqGAvb09wsPDMWPGDBQWFpq89vPPP0dkZCQcHBxw8803Y8eOHc0QMRERERERERkjiWQzLy8Pffr0wccff4wff/wRM2bMwNq1a/Hggw8avW7Dhg2YOnUqxo4di127duH222/H/fffjyNHjjRT5ERERERERGSIjbUDAIBHHnlE73jgwIGwt7fHE088gfT0dAQEBBi8btGiRRg3bhxeeeUVAMCgQYNw8uRJLFmyBDt37mzyuJuapqQEhdt3oHD791Dn5kHu5Qn3uOFwj4uFzMnJ2uERERERERHVSRLJpiFeXl4AgIqKCoPnL1y4gP/++w9vvPGGXvm4cePw4osvory8HPb29k0eZ1Mpv5CCy5MnQ5WZCQgCIIrAxYso/fM4cj76CMGrV8M+PMzaYRIRERERERkkqWRTrVajsrISZ86cwZIlSzB8+HCEhoYarJuUlAQAiIqK0iuPjo5GRUUFUlJSap2rSalUQqlU6o4zMjJ0MajV6ka+k8bRlJRoE82sLG2BKOr9rcrKwuXJkxG6/Xv2cLYSarUaGo3G6m2P2ja2Q5ICtkOSArZDkgKptsP6xCOpZDMkJARpaWkAgHvvvRf/+9//6qybn58PAGjXrp1euYeHBwDtPFBjEhISEB8fX6s8NzfX6j2i5du3a3s066LRQJWZifSNG2EfG9t8gVGT0Wg0ugWxZDJJTKWmNojtkKSA7ZCkgO2QpECq7TA3N9fsupJKNnfu3Ini4mKcPn0aS5cuRVxcHH766SfI5XKLP2vGjBmYMmWK7jgjIwO9e/eGl5cXFAqFxZ9XH1f2H6geOlsXQYC4/wAUkyY1X2DUZKp+Q+Tt7d0k7Z3IHGyHJAVshyQFbIckBVJth+Xl5WbXlVSy2a1bNwDA7bffjltvvRXdu3fH1q1bMXr06Fp1q3owCwsL4efnpyuv6vH09PQ0+iw3Nze4ubnVKpfL5Vb/x1Tn5RlPNAFAFKHOzbV6rGQ5MplMEu2P2ja2Q5ICtkOSArZDkgIptsP6xCKd/tgbdOvWDba2tkhOTjZ4vmo+ZtXczSpJSUmws7NDeHh4k8fYVORentqeTWMEAXJvr+YJiIiIiIiIqJ4km2wePXoUlZWVdSaN4eHhiIyMxObNm/XKN27ciJiYGNjZ2TVHmE3CPW64WT2b7nFxzRMQERERERFRPUliGO2oUaNwyy23oFu3bnB0dMQ///yDN998E926dcPIkSMBAI8//ji+/PJLqFQq3XWLFy/Gww8/jIiICAwaNAgbN27E0aNH8euvv1rpnViGe1wscj76SLsarUZjsI7c0xPuXByIiIiIiIgkShLJZu/evbFx40a8/vrr0Gg0CA0NxdSpUzFr1ixdD6WhLUnGjx+PkpISvP7663j99dfRqVMnbN26Fbfffrs13obFyJycELx6de19NmsQNRqolUpufUJERERERJIkiKKp8ZptQ2pqKtq3b48rV64gKCjI2uEA0O63WbhjBwq3b4c6JxcyZ2eUnzsH8foKUA7duiFk3VeQteAhw6SlVquRnZ0NhUIhqQng1LawHZIUsB2SFLAdkhRItR3WJ2+SRM8mGSZzcoLHmDHwGDNGV3btl31InT4dAFB28iSuLn0V/ktq7xdKRERERERkTZJdIIgMcx08CN7Xk00AKNi0Cfk3LJJERERERERkbUw2WyDvp5+C84D+uuOrS15B6cmTVoyIiIiIiIhIH5PNFkiQyRC4fDlsg4MBAGJlJVKffQ6q3FwrR0ZERERERKTFZLOFkru7I+i9dyE4OgIAVJmZSHthBsQaW8MQERERERFZC5PNFsyhUyf4v/KK7rjk2DFkrVhpxYiIiIiIiIi0mGy2cO6x98FzwgTdcd6aNSj84QcrRkRERERERMRks1XwmTUTTrfeqjvOeGkhys7+Z8WIiIiIiIiorWOy2QoItrYIfPst2Pj6AgDE0lKkPvMM1EqllSMjIiIiIqK2islmK2Hj5YWgd9+BYGsLAKi8fBlpL74IUaOxcmRERERERNQWMdlsRRxvvhm+C1/SHRcf+BU5H3xoxYiIiIiIiKitYrLZyniMGYN2Dz6oO8754ANc27fPihEREREREVFbxGSzFfJd+BIcunXTHafPnoOKixetFxAREREREbU5TDZbIZmdHYLeeRtyT08AgObaNaQ+8ww0xcVWjoyIiIiIiNoKJputlK2/PwLfeguQywEA5eeSkf7SSxBF0cqRERERERFRW8BksxVz7tMbPi/O0h1f27UbeV+ssV5ARERERETUZjDZbOU8J0yA27BhuuOsFStQfOSIFSMiIiIiIqK2gMlmKycIAvyXvgL7jh21BRoN0l6Ygcr0dOsGRkRERERErRqTzTZA5uSEoPffg8zNDQCgzs9H6rPPQVNebuXIiIiIiIiotWKy2UbYhYQg8M3lgCAAAMr+/ReZS5ZwwSAiIiIiImoSTDbbEJcBA+D99FO648Jvt6Bg02YrRkRERERERK0Vk802xvvJJ+EycKDuOHPpUpT+/bfV4iEiIiIiotaJyWYbI8hkCFj+BuxCQrQFlZVIffY5qHJyrBsYERERERG1Kkw22yC5mxsC33sXgpMTAECVlYW051+AWFlp5ciIiIiIiKi1YLLZRjlERiLg1aW645I//0TWihVWjIiIiIiIiFoTJpttmNvQofCcPFl3nPflWhRu32HFiIiIiIiIqLVgstnG+cx4AU633aY7zli4EGVJSVaMiIiIiIiIWgMmm22cYGODwISVsPH3BwCIZWVIffoZqAsKrBsYERERERG1aEw2CTaengh6910IdnYAgMrUVKS9OBuiWm3lyIiIiIiIqKViskkAAMeuXeC36GXdcfHBg8h+/30rRkRERERERC0Zk03SaffAA2g3dqzuOPejj3Ft714rRkRERERERC0Vk03S47tgPhxvvll3nD57DsovpFgxIiIiIiIiaomYbJIemZ0dAt99B3IvLwCAprgYqc8+A3VRsZUjIyIiIiKiloTJJtVi6+uLoLffAuRyAEBF8nlkLFgAURStHBkREREREbUUkkg2N2/ejBEjRiAoKAjOzs7o3r07Vq9ebTK5yc3NxbRp0xAcHAxnZ2d06dIFH3/8cTNF3bo53XorfOfM1h1f+/FH5H3+uRUjIiIiIiKilsTG2gEAQEJCAkJDQ7Fy5UooFAr89NNPmDp1Kq5cuYJFixbVed2DDz6IpKQkvPbaawgODsbOnTvx5JNPQi6XY+rUqc34Dlonj0cfRempf6Hcvh0AkJXwFhw6d4bzHXdYOTIiIiIiIpI6QZTA2MicnBx4e3vrlT3xxBPYuHEj8vPzIZPV7oDNzMyEv78/vvjiC0ycOFFXPmDAANjY2GBvPVdRTU1NRfv27XHlyhUEBQU16H20RprSUlwc/xDKk5IAAPJ27RD6zTewCwq0cmSti1qtRnZ2NhQKBeTXhy8TNTe2Q5ICtkOSArZDkgKptsP65E2SGEZ7Y6IJAD169IBSqURxseGFaSorKwEA7u7ueuXu7u6cW2hBMkdHBL33LmRubgAAdUEB0p59FpqyMitHRkREREREUiaJYbSGHDp0CIGBgXB1dTV4vn379hgyZAhee+01dOrUCe3bt8euXbuwZ88erF+/3uT9lUollEql7jgjIwOA9jcIarXaMm+ilZAHBMB/+XKkPfkkIIooO3MGGYsWw/fVpRAEwdrhtQpqtRoajYZtj6yK7ZCkgO2QpIDtkKRAqu2wPvFIMtk8dOgQNmzYgJUrVxqtt2XLFowdOxY33XQTAEAul+O9997DAw88YPIZCQkJiI+Pr1Wem5sLe3v7hgXemkV1gsPkySi7vkiQ8rvvoAoPg/2IEVYOrHXQaDQoLCwEAIPDxomaA9shSQHbIUkB2yFJgVTbYW5urtl1JZdspqamYuzYsRg0aBCeffbZOuuJoohJkybh3Llz+N///gd/f3/89NNPeP755+Hh4YFx48YZfc6MGTMwZcoU3XFGRgZ69+4NLy8vKBQKi72f1kR8/jmkp6Sg+JdfAAAl774H+8JClP1zEqq8XNh4esE1NhZusfdB5uRk5WhblqrfEHl7e0tqTD61LWyHJAVshyQFbIckBVJth+Xl5WbXlcQCQVUKCgrQr18/CIKAgwcP1pqPWdOOHTsQFxeHkydPomvXrrryqVOnYufOnUhLS6vXs7lAkHnU167h4oNjUHHxYnWhIACiqPvbxs8PwatXwz48zGpxtjRSnQBObQvbIUkB2yFJAdshSYFU22GLWyAIAEpLSxEbG4vCwkLs2rXLaKIJAGfOnIFcLkeXLl30ynv06IH09HSUlJQ0ZbhtltzVFQEr3tQmllWqfl9x/W9VVhYuT54MDf8NiIiIiIjaLEkkmyqVCmPGjEFiYiJ2796NwEDT22qEhIRArVbj5MmTeuXHjx+Hj48PnDiMs8mUnT5TnWAaotFAlZmJwh07mi8oIiIiIiKSFEnM2Zw+fTp27NiBlStXQqlU4siRI7pzPXr0gL29PWJiYnDp0iUkJycDAIYNG4bg4GCMHj0aixYtgr+/P/bs2YM1a9YYXPiHLKdw+/fVQ2eNyHrrbVRcSIFtQABsA/xhGxAAG39/yNu14yq2REREREStnCSSzT179gAAZs6cWetcSkoKQkNDoVaroVKpdOWurq7Yu3cvFixYgDlz5qCgoABhYWFISEjA008/3Wyxt0Xq3DyTiSYAaPLzkbdmTa1ywckJtv7a5FP3d0D1sY2vLwQbSTRNIiIiIiJqIEn8RH+x5mIzddi/f3+tsg4dOmDjxo2WD4iMknt5AhcvmpVwGiKWlKDi/HlUnD9vuIJMBhtfX/2ENLA6MbXxD4Dcxbnhb4CIiIiIiJqcJJJNalnc44aj9M/jJuu5xcbC1t8PlekZqExPR2VGBlRZWYBGY/xCjQaqjAyoMjJQ+tdfBqvI3N3r7B218feHjbc3BAntR0RERERE1NYw2aR6c4+LRc5HH9WdOMpksPHxgf+S+Fr7bYqVlai8moXK9DSoMjJQmZGByjRtIlqZno7K9HSIZWUmY9AUFqK8sBDlSUkGzwu2trDx9zfSO+oPmb19g94/ERERERGZxmST6k3m5ITg1atxefJkqDIza++z6eOD4NWrayWagDYJtAsKhF2Q4RWHRVGEuqBAl3iqbkxGMzKgzs01GaNYWYnKy5dReflynXXk3t5Ge0e5kBERERERUcMx2aQGsQ8PQ8TOH1C4YwcKt2+HOicXcm8vuMfFwT021mCiaQ5BEGDj4QEbDw843nSTwTqasjLtkFxdb2h1IlqZno7KzEygstLks9Q5OVDn5KDs1CnDsVQtZGRgESPbgACLLGRUVJiLI18uh3r3Ptgry/CPmwPk9w7CbRNmw8Xdq1H3JqLmk5ORgp9XPgv3E+fhWCqi1FFAYY8I3DXzXXj7h1k7PCIiakH0vqeUiDjh1HK/pwii2MBVXlqZ1NRUtG/fHleuXEFQUJC1w6FGEDUaqLJzoMpIr05Cq3pHryekGqWy8Q9q5EJG508exNUp0+Ch1EAjADIRur/z3WTw/exjRHTr1/g4icykVquRnZ0NhUIBuVxu7XBajCO7voT65dfheQ21vpbzXAH5krm4begEa4fZYrAdkhSwHZK1tITvKfXJm5hsXsdks21RFxVVD9M10Dtq1kJGZqi9kJH2daWrM/574Um4FWkgM/AVqBGAQlcZuv30K3s4qdnwh6v6y8lIwdnhw9CuCHV+LRe4AJ2+39nifhttLWyHJAVsh2QNLeV7CpPNBmCySTVVLWSkyqi5eJF+QiqWljZ5HIWhXnAN6QDcMHVUNDaXtOY5oY7yqvsYPCfqXygIECHqHddVTz+O6mq14hXqeH3DGxUNxi/WqivWemuGP4Na9QTB0O20RUbiqutc7ftXh2vw2TXq1f0fcR3/nqj5uYq1Pn+9+xlpLuIN77u8vBz2dvba+cqCgfdW41uGtl1UtQPx+suqsutFwvXymvWgnZ9dHZdY/XdVuVjzGVWnNRAF7bVVtxQhau8litfPXa9X9QwAmqq4RFF3rVgjjupvgyJEUf+cLgZRV6pXR34uBdFJFXV/wNedibJDZYdgk/UIgAioNWrIZXKjbZeoSbEdkhXYJl9GZzO+p5yM7YixK75vhogMq0/exDmbRAbUZyGjqt7RivR0lKZeRkV6GtQZmRDyGz9U1/1iLnDR9IJIRCRtnZMqgKRka4dBREQtnEYA3E60nO8nTDaJ6lCprkR+eT7yy/KRX56PgrIC5JXloaC8+u+qc/kO+SgIKIDKX6W73rZSDq9rgKJQhLcS8L7+t0IJRF0RYdP4UbpERERE1IbIRMCxpOUMTGWySW2CKIq4VnlNL2HUJYplhhPKosqiRj2z0lZApieQ6Vl7/M3idSpEpRoej19FA+CqB/DbrfqVBAPXCAYGYRq7d8171IrO0OhGA/XquoexenrlDbx/rXuKhuvUKjNW74YYhRoX6Mdx4zhWM2M0ck6oo7zWeYMx1jyuOdy0jnqi+Z+J3r0b+D5rjNO+Hl91lIavMzaeuPY5vQHdulHdwg3PNhSvyXdsNMaaVwdeVsG11PgdRQDXHIH0YFsTzyUAuuHRAgQOXyTrYTskKwi4XGnye4pGAEqdWk6jZLJJDVZSWYIfUn7AjvM7kFeWB08HT8RGxOK+sPvgZNuwrU/MdWOvY82Esep1zR7IgrICqESV6RtbgLu9OzzsPeDh4IF29u3g6eCJdvbt4OHgAQ9bF3hcOY7MsA2QXbE3eh8ZAPVNpZjpUQIRgAay63PNBN0fTY3X4vUf5KvqaSADAIhidT1j9cUa9zfnvhrRvPqG7quBAOhdd0N90fw4bryvyTjE2nFUX2v684AgQBBk2h9BBAEQZNfLBO2/2vWyWucEGYTrx4D2HpDJapwTdOe1r+WATKguhwyCTPtauH6drOra68fav6v+VB/LZNp6sqpzMhkEGSAT5JDJZNfPad9bSUkJXF1dIZfLr18vh1ymPSeTySGTae8rE2SQyWS66+Uy2fVzcsgEGeRyGQQBkAsCZDJtrDIBkOteC5DJtOcFQbhejuvlgvY6Abpr5YIA4Xr9qmt15QKstifuhllxuHmH8eFMAoCLMdadX9OScGEWkgK2Q7IGc76nyERA2aNDM0XUeEw2qUFSClMwdc9UXC25er3PQsQl5SX8lfUXPvnnE6wasgph7uatklXV66hLGG9IFGsmjJbqdTSXncwOHg4e+gmjg4cumbwxoXS3d4eNzMCXlVoFnNwA7FkEFF5Bka8MJ1394G5ktbFCF+AX7/vwrCYOcpn2B2q9H9RrHt/wg7dZP9BfPxauH9d1ztAztfdCjfIax9fvU+uZNZMGvdir61cnGjWec2PSIUON8hrvvR7x1yfOmve2VkLTXPjDVf3dNfNdnD1geuXAmJnvNH9wRETUorTG7ylMNqneSipLMHXPVGSXZAOosXLj9b+zS7Lx+I+P462Bb6FEVVJ7jqNEeh3rShhrJpSONo6NSzA0GuDMNmDfa0DuOV2xi1wDn4F5yNrvCQ8D+ygVugC2AyvQY/gzWHZHVOPfOBE1CW//MCQvmYuCOvZEK3DR7onGbU+IiMiU1vg9hckm1dsPKT/gasnVOs9roEF2aTYe2fVIk8ZhL7fXJYWN6nVsCqIInNsD7H0FuHpK71Sp4IhPK4fiZ5ueePueBFy8qoHqgiMcSoAyJ8AmvBShvjLMd4zHF7e0nGESRG3VbUMnIKd7f+xd+RzcTiTDsUREqZMAZY8OiJn5Tov6oYCIiKyrtX1PYbJJ9bbj/A7d0FlLMqfX0dPBE+0c2lmm17GppBwEfnkFuHJUr1iUO+Ab+VC8prwH+XADAIwWEnCPzyGM9D8EbxQiB+7Ypr4PR50G47OpA+Bkxy9RopbA2z+MczKJiMgiqr6ntIbpLfxJluotryzPrERTLsgR6RFZ5zBVq/U6NpW049qezAv79MtlNsiPGofHzg3AKaWzrnhK3zA8f1dHbD/ZCwl/PYCrhSXwdXfC/T2D8HL3ACaaRERERNSi8adZqpeskizklOaYrCdAQHef7lhz75qmD8rarp4B9r0KJO244YQAdBuLP8P+DxO3ZaOoXDsvVRCAhfd1xuS+2mEQ43sHY0yvwBb/mysiIiIiopqYbJLZDqcfxryD88xaCVaEiNjw2GaIyopyzwP7XwdObUatTf2i44BBC7Al1RWzN5+ESqM9b28jw9tju2NoV//mj5eIiIiIqBkx2SSTVBoVPvrnI6w6ucqs4bMyyKBwUmBY2LBmiM4KCtOAX5cDJ9YBmhtW0Y2IAQa/BDGgBz7Yl4wVe/7RnWrnZIvPJ9yCXiGezRwwEREREVHzY7JJRmWVZGHOr3Pw59U/dWWutq54usfTWP3var19Nqv+VjgpsGrIKjjZOlkx8iZQnAMcTAD++AxQl+ufa38bELMQCO0LlVqDhVtP4etjV6pPezpizaTeiFC4NHPQRERERETWwWST6nQ47TDmHZqHvLI8XVkXry54c8CbCHINwsgOI7EzZSd2XNiB3NJceDl6ITY8FsPChrWuRLOsEDj8PnDkQ6DihiHEft2AmJeBDncBgoDichWe/t9f2Hc2W1elW5A7Pp9wKxSu9s0cOBERERGR9TDZpFrqGjb7SPQjmNFrBmzltgAAJ1snjI4cjdGRo60VatOqKAaOfQocehsoK9A/5x0JDFoARA8HZDIAQNa1Mjy+5k+cSivUVYuJ8sF7D/XgyrJERERE1ObwJ2DSU9ew2VfufAUxITFWjKwZqcqB418Cv74JFGfpn3MPBgbNA7qOAeTVXz7JWUWY+MUxpOaX6soe7hOM+OE3wUYua67IiYiIiIgkg8km6ZgaNtvqqVXAyQ3aFWYLr+ifc/EF+r8I9HwMsNEfDvvHxTxM+fJPFJZW6spm39sJTw6IgCAIzRE5EREREZHkMNkks4fNtloaDXBmG7DvNSD3nP45Rw/gzueB3k8AdrXnoe48lYHnN/6NCpUGAGArF7B8dDfc36MNJOdEREREREYw2WzjDA6btbs+bDa4lQ+bFUXg3E/AL0uAzFP65+xcgNuf0v5xcDd4+WcHL+DVnYkQr+fnrvY2+OTRXrijg3cTB05EREREJH1MNtuwNj1s9uIhYO8S4MpR/XK5PdB7KtD3BcDZcNKo0YhY+kMiVv+Woivzd3fAF5NuRZSfW1NGTURERETUYjDZbINUGhU+/PtDfHbqs7Y3bDbtOLD3FeDCPv1ymY12Pmb/FwG3gDovL6tU44WNf2PXv5m6sig/V3wx6Vb4uzs2VdRERERERC0Ok802JqskC7N/nY3jV4/rytrEsNmsROCXpUDSjhtOCEC3scDAOYBnuNFb5BdXYMraP3H8Ur6u7M4OXvjokV5wc2jFCToRERERUQMw2WxDDA2b7erdFW8OeBOBLoFWjKwJ5V3Qri57chNQoxcXABAVCwx+CfCJNnmby7klmPjFMVzIKdaVjeoZiNdHdYOdDbc2ISIiIiK6EZPNNqCuYbOPdn4UL/R8oXUOm1WmAweWAye+AjQq/XMRg7VJZmAvs271z5UCPP7lH8gpqtCVPTO4A2bcHcmtTYiIiIiI6sBks5Vrc8Nmi3OAQ28Bx1YB6nL9c+1vA2IWAqF9zb7d3sSrePp/J1BaqQYAyGUCXhnRBQ/1CbZk1ERERERErQ6TzVasTQ2bLSsEDr8PHPkQqCjSP+fXDRi8EOh4N1CPnsj1Ry9h4bZ/obneGexoK8eHD/fEoCgfCwZORERERNQ6MdlshdrUsNmKEuDYJ8Cht4GyAv1zXh2BwQuA6BGAzPx5laIoYsWes/hg33ldmbeLHVZPvBXdgtpZJGwiIiIiotZOEiubbN68GSNGjEBQUBCcnZ3RvXt3rF69GqIomrw2LS0NEyZMgEKhgKOjI6Kjo7F+/fpmiFqaskqyMGXPFKw6tUqXaLraueKdQe9g9q2zW0+iqarQDpV9tzvw82L9RNM9GBjxITD9CHDT/fVKNCtUGszY9I9eohmucMbW6Xcy0SQiIiIiqgdJ9GwmJCQgNDQUK1euhEKhwE8//YSpU6fiypUrWLRoUZ3XZWRk4Pbbb0enTp3w6aefws3NDadPn0Z5eXmd17Rmv6X9hvmH5rfuYbNqFXByo3aF2cLL+udcfLX7ZPZ8DLCxr/etlWWVeHLdcfyWnKsruyXEA6seuwUeznaNjZyIiIiIqE2RRLK5fft2eHt7644HDx6M3NxcJCQkYOHChZDV0TM1e/ZstG/fHrt374ZcLgcAxMS0wkVvTKgaNrvq1Cq98sc6P4bnez7fOnozNRog8Tvgl1eB3HP65xzaAX1fAHo/Adg5Nej2GYWlmPTFH0jKvKYrG9bVDwljusPBVt6IwImIiIiI2iZJJJs1E80qPXr0wKpVq1BcXAxXV9da55VKJTZt2oTVq1frEs226GrxVcz+dTb+yvpLV+Zq54qldy7F4ODBVozMQkQROPcT8MsSIPOU/jk7F+C26cAdTwMO7g1+RGKGEpO++AOZyjJd2eN9w7BgWDRkMm5tQkRERETUEJJINg05dOgQAgMDDSaaAPDXX3+hoqICtra2GDBgAA4fPgwvLy9MmDABS5cuha2t8d48pVIJpVKpO87IyAAAqNVqqNVqy72RJnQ4/TAW/LYA+eX5urIuXl3wRr83EOgS2GLeR50u/QbZvqUQrhzVKxbl9hBvfRziHc8Dztd/UdHA9/rb+VxMX38CReXavTgFAVgwNAqT7gyFKGoaett6U6vV0Gg0Lf/fjFo0tkOSArZDkgK2Q5ICqbbD+sQjyWTz0KFD2LBhA1auXFlnnczMTADAlClTMHXqVCxevBjHjh3Dyy+/DJlMhmXLlhl9RkJCAuLj42uV5+bmwt6+/vP9mpNao8aX57/E1xe+1it/IOQBPB75OGxLbZFdmm2l6BrPJusUXI+9DfvUQ3rloswGpVEPoKjndGhc/IASEShp+PvclZiLpT9dhFqjPbaTC1h8bxgGd3RGdnbzfn4ajQaFhYUAUOewcaKmxnZIUsB2SFLAdkhSINV2mJuba7rSdZJLNlNTUzF27FgMGjQIzz77bJ31NBpthnDXXXfpktJBgwbh2rVrWLFiBV5++WU4OjrWef2MGTMwZcoU3XFGRgZ69+4NLy8vKBQKC72bxilVleKHlB+wM2Un8sry4OngiX6B/bA/dT/+yf5HV8/VzhVLbl+CQe0HWTFaC8hKhGz/Mghnd+gVixAgdn0QYv85sPcMQ2N/FSCKIj7cfwEJP1/UlbVztMUnj/bELSEejbx7w1T9hsjb27tNDwsn62I7JClgOyQpYDskKZBqO6zPYqySSjYLCgowdOhQeHl54dtvvzWawXt4aJOCwYP15yXGxMTg1VdfRXJyMrp27Vrn9W5ubnBzc6tVLpfLJfGPmVKYgql7puJqyVUIECBCxCXlJb25mQDQzbsblg9Y3rJXm827oF1d9uQmADdsdxMVC2HQAgi+nS3yKJVag4Xfn8HXx6pXsm3v6Yg1k3ojQuFikWc0lEwmk0z7o7aL7ZCkgO2QpIDtkKRAiu2wPrFIJtksLS1FbGwsCgsL8fvvv8Pd3fiCL507G08+ysrKjJ6XspLKEkzdMxXZ14eIVu2XKd6QiI2PGo8Xb3mx5a42q0wHDiwHTnwFaFT658IHATELgcBeFntccbkKz3x9Ar8kZenKugW54/MJt0LhKu2h00RERERELY0kkk2VSoUxY8YgMTERBw8eRGCg6V66kJAQdO3aFT///DOefvppXflPP/0ER0dHk8molP2Q8gOullw1WS/SI7JlJprFucChBOCPzwDVDb8UaN8HGLwQCOtn0UdmXyvH5DV/4FRaoa5scJQP3n+oB5zsJPFlQERERETUqkjip+zp06djx44dWLlyJZRKJY4cOaI716NHD9jb2yMmJgaXLl1CcnKy7tyrr76KESNG4Pnnn8d9992HP/74AytWrMDs2bPh7OxsjbdiETvO79ANna2LAAE7LuzA6MjRzRhZI5UVAr9/oP1TUaR/zq8rMPhloOPd2iVhLeh8dhEmfnEMV/JKdWUP9QnGkuE3wUYuncnWREREREStiSSSzT179gAAZs6cWetcSkoKQkNDoVaroVLpD7WMi4vD119/jVdeeQUfffQR/P39ER8fj7lz5zZL3E0lryzPaKIJaIfU5paavxKUVVWUAMc+BX57GyjN1z/n1REYvACIHgE0wSpbf17Mw5S1f6KgpFJX9uI9nTB9YAQECye1RERERERUTRLJ5sWLF03W2b9/v8HysWPHYuzYsZYNyMo8HTxxSXnJZM+ml6NXM0bVAKoK4K8vgV/fBIpuGBbsHgwMnAN0GwfIm6YZ7jyVgec3/o0KlXblYhuZgOWju2FUz6AmeR4REREREVWTRLJJ+mIjYmutOnsjESJiw2ObKaI6VBRrV5A9uQkozgacFUC3McBNo4CkHcCB14GCy/rXOPsA/V8Eek0AbJpuUZ7PDl7AqzsTIV7P113tbfDxo71wZwfvJnsmERERERFVY7IpQfeF3YdP/vkE2SXZ0EBT67wMMiicFBgWNswK0V2Xcw5YOwJQpgGCDBA1QN554PJhYOes2qvLOrQD+j4P9H4CsGu6+bQajYilPyRi9W8pujI/NwesmXwrovxqb3VDRERERERNg6ujSJCTrRNWDVkFhZMCgHbIbM2/FU4KrBqyCk62TtYJsKJYm2hey9Aeixr9v2smmrbOQP/ZwHP/AH1faNJEs6xSjaf+95deohnl54qtT93BRJOIiIiIqJmxZ1OiwtzD8P3I77EzZSd2XNiB3NJceDl6ITY8FsPChlkv0QS0w2aVaabrhQ0EHvgMcFE0dUTIL67A1LV/4s9L1QsQ3dnBCx890gtuDi1wexgiIiIiohaOyaaEOdk6YXTkaOltb3JyU/XQ2boIAqCpbJZE80peCSZ8cQwXsot1ZaN6BOL1B7rBzoad90RERERE1sBkk+qvONt4ogkAoggUZTV5KCdTCzB5zR/IKarQlT09qANmDonk1iZERERERFbEZJPqz1mhXQzIaM+mDHDxadIwfkm6iqfWn0BppRoAIBOApSO74qE+wU36XCIiIiIiMo1jDKn+uo0xo2dTo63XRP539DKmfPmnLtF0tJXjswm3MNEkIiIiIpIIJptUf93GAG6BAOoYpirItOe7PmjxR4uiiDd/TML8raegub6HpreLHTb+320YHOVr8ecREREREVHDMNmk+rNzBh77DpDJ9cuF683J1V973sLbnFSoNJix6R98sO+8rizc2xlbnrwT3YLaWfRZRERERETUOJyzSQ1j56y/n6ZnuDbJ7DZG26Np4URTWVaJJ9cdx2/JubqyW0I8sOqxW+DhbGfRZxERERERUeMx2aSGSfm1+rV/d+D/DjTZozIKSzHpiz+QlHlNVza0ix/eGtsdDrZyI1cSEREREZG1MNmkhqmZbIb1b7LHJGUqMXH1H8hUlunKHu8bhgXDoiGTcWsTIiIiIiKpYrJJ9SeKwIUaPZnhA5rkMb8l52DaV8dxrVw7XFcQgAXDojGlX3iTPI+IiIiIiCyHySbVX94FQJmqfS2zAYJvt/gjtvyVijnfnkSlWrvkrJ2NDG+P7Y5hXf0t/iwiIiIiIrI8JptUfyk1ejWDbrXoYkCiKOLD/efx5o9ndWXtnGyx6rFbcGuop8WeQ0RERERETYvJJtWf3nxNyw2hVak1WPjdaXx97LKuLMjDEV9O7o0IhYvFnkNERERERE2PySbVj0bTJIsDFZer8MzXJ/BLUpaurGugOz6feAt8XB0s8gwiIiIiImo+TDapfrLOACXX97q0cdQOo22k7GvlePzLP3AytVBXNqiTAu8/1BPO9myiREREREQtEX+Sp/qpOV8z5HbAxq5RtzufXYSJXxzDlbxSXdn43sF4ZcRNsJHLGnVvIiIiIiKyHiabVD8WnK/558U8TFn7JwpKKnVlL97TCdMHRkAQuIcmEREREVFLxmSTzKdWARd/qz5uxHzNXacy8NzGv1Gh0gAAbGQClo/uhlE9gxobJRERERERSQCTTTJf+gmg4pr2tYM74H9zg27z+aEULP3hDETtFppwsbfBx4/0Qt+O3hYKlIiIiIiIrI3JJpkvZX/169B+gExer8s1GhFLf0jE6t9SdGV+bg74YtKtiPZ3s1CQREREREQkBUw2yXyNmK9ZVqnGjE1/Y+epTF1ZJ19XrJl8K/zdHS0VIRERERERSQSTTTJPZSlw+Wj1cT3ma+YXV2Dq2j/x56V8XdkdEV74+NFecHOwtWSUREREREQkEUw2yTxXjgHqcu1rF19A0cm8y/JKMOGLY7iQXawru79HIN54oBvsbLi1CRERERFRa8Vkk8xTc3/NsP6AGVuTnEwtwOQ1fyCnqEJX9tSgCMwa0olbmxARERERtXJMNsk89ZyvuS8pC9PX/4XSSjUAQCYAr4zsgof7hDRVhEREREREJCFMNsm0MiWQ9lf1sYn5ml8fu4yXtv0LtUa7t4mjrRzvP9QDMdG+TRklERERERFJCJNNMu3SYUDU9lDCIxTw0PZOllSosO1EOraeSEVucQW8nO3gbG+D/WezdZd6u9jh8wm34ub27Zo/biIiIiIishomm2Sa3hBaba/m+ewiPPLZUWQUlkEQAFGE3iJAABDu7Yw1k3oj2MupOaMlIiIiIiIJYLJJpuktDjQAJRUqPPLZUVxVlgHQJpo3spULWPd4HwR4cA9NIiIiIqK2iHtPkHHFOcDVf6uPw/pj24l0ZBSWQWMgyaxSqRZx4Fx23RWIiIiIiKhVY7JJxtUcQuvTGXDxwdYTqSZ3PhEEYNuJtKaNjYiIiIiIJEsSw2g3b96MdevW4fjx48jPz0fHjh3x7LPPYtKkSWbvx/j222/jhRdewH333YcdO3Y0OJaUlBSUlpYaPOfl5QVPT0/d8cWLF1FZWVnnvVxdXeHn56c7TktLQ0lJSZ31HRwc0L59e91xdnY2CgoK6qwvl8sRHh6uOy4oKEB2tvHexPDwcMjlcgBASUkJ0tKMJ4Ttz/4Ch+uvK9vfiYvnzuHKxQuoyDP8PuTOHpDZO0EUgeyicpw7d87o/T09PeHl5aU7vnTpEioqKuqsf+Nnmp6ejuLi4jrr29vbIzg4WHds6jOVyWSIiIjQHRcWFiIrK8voewgLC4ONjfZLyZzPNCgoCI6O2uHFKpUKKSkpUKvVyMvLQ0FBge7fp4qvry/c3Nx0x8nJyRANjV2+zsPDA97e3rpjU5+pi4sL/P39dccZGRkoKiqqs76dnR1CQqq3sMnJyUF+fn6d9QVBQIcOHXTHSqUSV69erbM+oP+ZlpaWIjU11Wj9wMBAODlp5wZXfabG+Pj4wN3dXXd8/vx5aDSaOuu3a9cOCoVCd3z58mWUl5fXWd/Z2RkBAQG648zMTFy7dq3O+jd+prm5ucjLyzP6Hjp27Kh7bc5nGhoaCltbWwBAWVkZrly5UqtOzXYYHBys+0zVajUuXLhg9P4KhQLt2rXTHV+4cAFqtbrO+jd+pleuXEFZWVmd9Z2cnBAYGKg7NvWZ2traIjQ0VHecl5eH3Nxco++h5md67do1ZGZmGq0fEhICOzs7AEB5eTkuX75stH5AQACcnZ0BABqNBufPnzda39vbGx4eHrpjU5+pu7s7fHx8dMepqal1fj8DAEdHRwQFBemOr169CqVSWWd9GxsbhIWF6Y7z8/ORk5Nj9D106NBB9328qKgIGRkZRusHBwfrvvbLy8tN/n/q7+8PFxcXAIAoikhOTjZa/8bPNCUlBSqVqs76bm5u8PWtXkm9vp9pVlYWCgsL66x/4/dxcz7TiIgIyGTavoLi4mKkp6cbrR8cHAx7e3sAQEVFBS5dumS0vp+fH1xdXXXHpr6Pt9afjYx9X27fvj0cHLQ/HVVWVuLixYtG73/j93H+bFSboZ+NjGkrPxvVbIcdOnSQzM9Gpr4/6hEl4LbbbhPHjRsnbtiwQdy7d684d+5cUSaTiYsXLzbr+oyMDLFdu3aij4+PeN999zUohitXrogAjP5ZunSp3jUdOnQwWn/ChAl69YcNG2a0/h133KFX/7nnnjNa39vbW6/++++/b/I95Ofn6+rv2bPHZP1jMyJFcZGbKC5yE1N+Xm2yvlfsTDFkzg4xdO4OcczHh0UbGxuj9RctWqT3Hjp37my0/kMPPaRXf8SIEUbr33LLLXr1Z82aZbS+u7u7Xv1PP/3U5HvOysrS1d+3b5/J+ocOHdLVT01NNVn/iy++0IvJycnJaP358+fr1b/55puN1h89erRe/dGjRxutf/PNN+vVnz9/vtH6Tk5OevW/+OILk+85NTVVV//QoUMm6+/bt09XPysry2T9Tz/9VC8md3d3o/VnzZqlV/+WW24xWn/EiBF69R966CGj9Tt37qxXf9GiRUbr29jY6NVft26dyfeckpKiq3/s2DGT9ffs2aOrn5+fb7L++++/rxeTt7e30frPPfecXv077rjDaP1hw4bp1Z8wYYLR+h06dNCrv3TpUpPvoaZNmzaZrP/ff//p6p84ccJk/R07dujqFxUVmaz/1ltv6cUUEBBgtP706dP16g8YMMBo/bvuukuv/pQpU4zWDwkJ0au/fPlyk++hoqJCV3/r1q0m6//777+iSqUSMzIyxH/++cdk/a1bt+ruX1FRYbL+8uXL9d5DSEiI0fpTpkzRq3/XXXcZrT9gwAC9+tOnTzdaPyAgQK/+W2+9ZfI9FBUV6erv2LHDZP0TJ07o6v/3338m62/atEkvJlP12+TPRseO6eqnpKSYrL9u3Tq9mPizUe0//Nmo5f1sBEC8cuWKaIokeja3b9+u99uGwYMHIzc3FwkJCVi4cKHuN3h1mT17NoYPH27yt3XUAMo0wFUOCDIgsJfZl4kiMLJHILY0YWhERERERCRdgiga6XO2oo8++gjTp0+HUqnUG85xo0OHDmHYsGE4e/Ysxo8fDxcXlwYNo01NTUX79u3x66+/6g1FqKm1DhWp05nv0f6PeDjYCEBgL1RO/BEXL15EaYUKj60+hpyi8lor0cqdPWDj4ARfNwfsnTkAaZdSjMbDoSL6w2g9PT05jBYcRmvtYbSenp4cRsthtLU05zDa7OxsuLm5cRitARxG27zDaA19X+YwWg6jvVFTD6P19PSU3DDa/v3748qVK3r/5xki2WTz4YcfxoEDB4x+kGq1Gr169cL48eMxZ84cDBw40OxkU6lU6n1TzcjIQO/evXHx4kWTH1pbIWx7ErJTGwEAmjuehxjzsu7chewijPr4CK6VVX+Trtpv09/dAWsn3YJwhUuzx9xSqdVq5OTkwNvbu9Y3NaLmwnZIUsB2SFLAdkhSINV2mJqaitDQULOSTUkMo73RoUOHsGHDBqxcudJovQ8//BDFxcV44YUX6v2MhIQExMfH1yrPzc3V/QawTRNFKM7v0x0WeN6Mihq/GXQFcHuIG/ac1fa+uDvYINzLAfdEeeKeKE84ohTZ2XX/9pf0aTQa3W+/TQ0bJ2oqbIckBWyHJAVshyQFUm2HpkYK1SS5ZDM1NRVjx47FoEGD8Oyzz9ZZLysrCy+//DLWrl2rG8ZUHzNmzMCUKVN0x1U9m15eXnpDu9qsnHOQl2iHSIhyO7h3uRuwddKrkqr8T/f6zdHdEBPtA2qYqqFxUvvNFbUtbIckBWyHJAVshyQFUm2HxqYS3UhSyWZBQQGGDh0KLy8vfPvtt0Yz+JdffhndunVDv379dOPMVSoVVCoVCgoK4OLiohvXbIibm5veWO8qcrlcUv+YVnPpoO6l0L4P5A7682Yr1RokZ1XPB7gpqB0/t0aSyWRsf2R1bIckBWyHJAVshyQFUmyH9YlFMslmaWkpYmNjUVhYiN9//11vgqohSUlJ+PXXX/Um+lfx8PDArl27cO+99zZVuK1fyq/Vr8P61zp9IbsYFWrtpGE3BxsEuDvUqkNERERERG2XJJJNlUqFMWPGIDExEQcPHtRbcbAub7/9dq2Vs55//nk4Ojpi2bJl6NatWxNF2wZoNMDF6p5NhA2oVSUxo3pxpSh/N91qg0RERERERIBEks3p06djx44dWLlyJZRKJY4cOaI716NHD9jb2yMmJgaXLl3SLWvevXv3Wvdp164dXFxcMHDgwGaKvJW6egoovb5cs50LENizVpWayWZn/9rDkYmIiIiIqG2TRLK5Z88eAMDMmTNrnUtJSUFoaCjUarXRvbDIgi4cqH4dcgcgt61VJTGzen+7aP+690ElIiIiIqK2SRLJpqnNcAFg//79FqlDZjAxXxO4YRitH3s2iYiIiIhIn3Q2bCFpUFUAlw5XHxuYr5lTVI7sa9olj2UC0MmPPZtERERERKSPySbpS/8LqLy+pYmjJ+DbpVaVmr2aYd7OcLCVzlLMREREREQkDUw2SV/N+Zph/QADe50mZdScr8khtEREREREVBuTTdJXz/maTDaJiIiIiMgQJptUraIESD1WfWxgviYAnNFLNjlfk4iIiIiIamOySdWuHAHUFdrXrgGAV4daVSpUGpzPLtIds2eTiIiIiIgMYbJJ1fTma/YHBKFWlfPZRahUiwCAdk628HNzaK7oiIiIiIioBWGySdVqztcMNzyEVn9/TVcIBhJSIiIiIiIiJpukVVoAZPxdfczFgYiIiIiIqBGYbJLWpd8AUaN97RkBuAcZrJbIbU+IiIiIiMgMTDZJy4wtTwAgKbO6Z7Mzk00iIiIiIqoDk03Sqrk4UB3zNbOulSGnSLtarVwmoIOPS3NERkRERERELRCTTQKKsoDsxOrj0H4Gq9UcQhvu7QwHW3lTR0ZERERERC0Uk03SH0Lr2xVw9jZYjYsDERERERGRuZhsEpByw/6adUhisklERERERGZisklmzdcE9IfRRvm7NmVERERERETUwjHZbOvyLwIFl7SvBTkQfLvBauUqNc5nF+mOuRItEREREREZw2Szras5XzOwF+BgOIk8d7UIKo0IAPB0toOPq31zREdERERERC0Uk822zuz9NauH0Eb7u0IQhKaMioiIiIiIWjgbS9wkMTERGRkZKC0thZeXFyIjI+Hp6WmJW1NTEkX9ZNPofM3qxYGi/DiEloiIiIiIjGtQsqnRaLBjxw58+eWX+OWXX6BUKiGKou68IAiIjo7Ggw8+iIkTJyIkJMRiAZMFZZ8Fiq5qX9s4AEG966zKbU+IiIiIiKg+6j2M9uuvv0anTp3w8MMPw9bWFvHx8fjll19w6tQp/Pfffzh27Bg2btyI2NhYbNmyBR07dsTUqVORnp7eFPFTY9Tc8qR9H8DWwWA1URRvSDa5Ei0RERERERlX757N+Ph4LFiwAGPHjoWjo6PBOrfccgtGjx6N119/HadPn0ZCQgLWrl2LuXPnNjpgsiAz52tmXStHfkklAMBGJqCDj0tTR0ZERERERC1cvZPNxMTEei0Oc9NNN+Hzzz/XG2ZLEqBRAxcPVh+HD6yz6pkavZoRChfY28ibMDAiIiIiImoN6j2MtqGrkHL1UonJ+AcoK9S+tncD/LvXWZVDaImIiIiIqL4avBrtn3/+iZ07dyIpKQl5eXkAAE9PT0RFRWHYsGG45ZZbLBYkNYGa8zVD7gTkdTeFxIya255wcSAiIiIiIjKt3j2b165dw/Dhw9G7d2+8++67uHz5MmxtbWFra4vLly/jvffeQ58+fTBixAgUFRU1RcxkCWbO1wSAJK5ES0RERERE9VTvns0ZM2bg77//xo8//oi7777bYJ2ff/4Zjz/+OGbMmIFPP/200UGShanKgUu/Vx8b2V+zrFKNCznFuuMoDqMlIiIiIiIz1Ltnc8uWLVi5cmWdiSYA3HXXXXjzzTfx7bffNio4aiKpfwKqUu1rJ29AEV1n1XNXi6DWaBd38naxg4+r4e1RiIiIiIiIaqp3sllZWQlnZ2eT9ZydnaFSqRoUFDWxmvM1w/oDsrqbQSKH0BIRERERUQPUO9m8++67MW/ePCQnJ9dZ5/z581iwYAGGDBnSqOCoidRjvmZiJpNNIiIiIiKqv3rP2Xz//fcxZMgQREVFoVu3boiKikK7du0AAIWFhUhKSsI///yDzp07491337V0vNRY5UVA6h/Vx0bmawL6PZtRfpyvSURERERE5ql3sunv748TJ05g8+bN2L17N5KSkpCfnw8A8PDwQJcuXfDiiy9i9OjRsLFp8M4q1FQuHwE014c3u7cHPMLqrCqKIrc9ISIiIiKiBmlQNmhjY4Px48dj/Pjxlo6HmlrK/urXYQMAQaizakZhGQpLKwEAtnIBEQqXJg6OiIiIiIhai3rP2WwKmzdvxogRIxAUFARnZ2d0794dq1evhiiKdV6TkZGB2bNno3v37nB1dUVQUBAeeughXLp0qRkjb4Hqs79mjfmaHXxcYWcjieZCREREREQtQL2zh7Fjx+Lvv/82u35ZWRnef/99rF69us46CQkJcHJywsqVK7F9+3YMHToUU6dOxZIlS+q85vjx49iyZQvGjBmD7777DgkJCTh16hR69+6N7Ozs+ryltqMkD8g4WX1sanGgmkNoOV+TiIiIiIjqod7DaIODg3HnnXciMjISo0ePxp133olu3brB09MTAFBRUYGUlBQcP34cu3btwvfff4/IyEh8/PHHdd5z+/bt8Pb21h0PHjwYubm5SEhIwMKFCyEzsDVH3759kZSUpDcv9I477kBwcDDWrl2LmTNn1vettX4XDwG43lvsHQm4+RutfobbnhARERERUQPVu2fzzTffxLlz5zB8+HB8/vnnGDx4MBQKBWxtbeHk5ARHR0d07twZEydOhFKpxPr16/HHH3+gV69edd6zZqJZpUePHlAqlSguLjZ4Tbt27WotQBQUFASFQoH09PT6vq22QW8IrfFVaAHusUlERERERA3XoAWCAgICEB8fj/j4eJw/fx5//PEHMjIyUFZWBk9PT3Tq1Am9e/eGk5NTgwM7dOgQAgMD4epq/vDN//77D1lZWYiOjjZZV6lUQqmsTqYyMjIAAGq1Gmq1uv4BtwCyC/tRtRyQOqQvYOR9llaocTGnOtGP9HVutZ+LFKjVamg0Gn7GZFVshyQFbIckBWyHJAVSbYf1iadByeaZM2fw8ccfIyUlBYGBgXjggQcwbty4htzKoEOHDmHDhg1YuXKl2deIoohnn30WAQEBZq2Sm5CQgPj4+Frlubm5sLe3r1e8LYGs+Cp8cs8BAEQIyHGJgmhkbuuZzGJoro+49XKygaakENklzRFp26TRaFBYWAgABoeNEzUHtkOSArZDkgK2Q5ICqbbD3Nxcs+vWO9k8dOgQYmJioFKpoFAosHv3bqxatQoffPABpk2bVt/b1ZKamoqxY8di0KBBePbZZ82+bvHixdi7dy92794NZ2dnk/VnzJiBKVOm6I4zMjLQu3dveHl5QaFQNCh2KRMy9lUf+HWDd/uORutnXizTve4c2K5VfiZSUvUbIm9vb8jlcitHQ20V2yFJAdshSQHbIUmBVNtheXm52XXrnWwuWrQI0dHR2L59O9q3bw+lUolJkybhpZdeanSyWVBQgKFDh8LLywvffvut2Rn8qlWrsGTJEnz++eeIiYkx6xo3Nze4udWehyiXyyX1j2kxlw7pXgrh/U2+x7NXi3SvOwe4tc7PRGJkMlnrbX/UYrAdkhSwHZIUsB2SFEixHdYnlnr3x546dQovv/wy2rdvD0CbtK1cuRJ5eXm4cuVKfW+nU1paitjYWBQWFmLXrl1wd3c367qtW7fiySefxJIlSzB58uQGP79VE0Ug5UD1cdhAk5ckZlZve9KZiwMREREREVE91TvZzMnJQVBQkF5ZVeKZk5PToCBUKhXGjBmDxMRE7N69G4GBgWZdt3//fowfPx5Tp07FwoULG/TsNiE/BSi8/osAmQ0QfJvR6qIociVaIiIiIiJqlAYtECQIgulK9TB9+nTs2LEDK1euhFKpxJEjR3TnevToAXt7e8TExODSpUtITk4GACQmJmLkyJHo2LEjHn30Ub1rFAoFIiIiLBpji3ahRq9m0K2AvYvR6mkFpbhWpgIA2MllCPM2PQeWiIiIiIiopgYlm4MGDTI4n7Jfv3565YIg6FZQMmbPnj0AgJkzZ9Y6l5KSgtDQUKjVaqhUKl350aNHUVhYiMLCQtx5551610yYMAFr1qwx9+20fnr7a/Y3WT0xo3oIbUdfF9jKpbP6FRERERERtQwNWiDI0i5evGiyzv79+/WOJ06ciIkTJ1o8llZHo7kh2Rxg8pIkDqElIiIiIqJGkkSySU0oOxEouT6X1sYRCLrF5CWJmUw2iYiIiIiocTg+srWrOV8z5HbAxt7kJTWH0Ub7uTZFVERERERE1Mox2Wzt6jlfs6RChYu5xbpj9mwSEREREVFDMNlszdQq4NJv1cdmzNc8m3kNoqh97efmAA9nuyYKjoiIiIiIWjMmm61Zxt9A+fX5lw7ugP/NJi/RG0LrzyG0RERERETUMEw2W7ML+6tfh/YDZHKTlyTWWIk2ikNoiYiIiIiogZhstmb1nK8J6CebnK9JREREREQNxWSztaosA64crT42Y76mRiMiKbN6GG1nDqMlIiIiIqIGYrLZWqUeA1Rl2tcuvoCik8lL0gpKUVSuAgDY28gQ6uXclBESEREREVErxmSztaq5v2ZYf0AQTF5ypsYQ2khfV9jI2TyIiIiIiKhhmE20Vo2er8khtERERERE1HBMNlujMiWQdrz62Iz5mgAXByIiIiIiIsthstkaXf4dENXa1+1CAI8Qsy6ruTgQk00iIiIiImoMJputUc35muHm9WoWlatwKbdEdxztx2STiIiIiIgajslma6Q3X9O8ZPNsZvUQ2gB3B7g72Vo6KiIiIiIiakOYbLY2xTnA1VPVx2YuDnQmg0NoiYiIiIjIcphstjYXD1a/VkQDLj5mXZbExYGIiIiIiMiCmGy2NjWH0Jo5XxPQX4k2itueEBERERFRIzHZbG1qLg5k5hBajUbkSrRERERERGRRTDZbk8JUIO+89rUgA0LuNOuyy3klKKnQbpXiYCtDqJdzU0VIRERERERtBJPN1qTmEFr/7oBjO7MuS6qxEm0nPzfIZYJl4yIiIiIiojaHyWZr0sD5mnor0fpxviYRERERETUek83WQhQbNF8T0F8ciPM1iYiIiIjIEphstha554Fr6drXcjug/W1mX8pkk4iIiIiILI3JZmuRsr/6dVBvwM7JrMuUZZVIzS/VHXPbEyIiIiIisgQmm61FA+drnq2x5UlgO0e4OdhaMioiIiIiImqjmGy2BhoNkHKw+pjzNYmIiIiIyMqYbLYGV/8FSvO0r22dgYCeZl9aM9nszCG0RERERERkIUw2W4OUGqvQhtwB2NiZfWlizW1P2LNJREREREQWwmSzNag5X7MeQ2jVGlFvzmYUk00iIiIiIrIQJpstnboSuHS4+rgeiwNdyi1GaaUaAOBkJ0eIp3kr2BIREREREZnCZLOlS/sLqCjSvnb0AHy7mn1pzSG0nfxcIZMJlo6OiIiIiIjaKCabLV3N+Zqh/QCZ+f+kSZlciZaIiIiIiJoGk82WroHzNYEbtj3x40q0RERERERkOUw2W7KKEuDK0erj8IH1upwr0RIRERERUVORRLK5efNmjBgxAkFBQXB2dkb37t2xevVqiKJo9DpRFPH6668jODgYjo6OuP3223HkyJFmiloCrhwF1BXa167+gFcHsy8tLKlEWkGp7pgr0RIRERERkSVJItlMSEiAk5MTVq5cie3bt2Po0KGYOnUqlixZYvS6N954A4sWLcILL7yAHTt2wN/fH0OGDMGFCxeaKXIrqzlfM2wAIJi/wE/N+ZrBnk5wsbexZGRERERERNTGSSLD2L59O7y9vXXHgwcPRm5uLhISErBw4ULIDCx6U1ZWhmXLlmHmzJl44YUXAAD9+vVDZGQkVqxYgQ8//LDZ4rcaC83XjOJ8TSIiIiIisjBJ9GzWTDSr9OjRA0qlEsXFxQavOXz4MJRKJcaMGaMrs7Ozw6hRo7Bz584mi1UySguA9BPVx/VONjlfk4iIiIiImo4kejYNOXToEAIDA+HqarjXLSkpCQAQFRWlVx4dHY3Lly+jtLQUjo6Odd5fqVRCqazu3cvIyAAAqNVqqNXqxobf9FIOQS5qAACiZzg0rgFAPeI+k1Goe93J16VlvOdWTK1WQ6PR8N+BrIrtkKSA7ZCkgO2QpECq7bA+8Ugy2Tx06BA2bNiAlStX1lknPz8f9vb2cHBw0Cv38PCAKIrIz883mmwmJCQgPj6+Vnlubi7s7e0bHnwzcT2zG87XX5f63QpldrbZ16o1Iv7LrO7Z9LWvRHY9rifL02g0KCzU/gLA0LBxoubAdkhSwHZIUsB2SFIg1XaYm5trdl3JJZupqakYO3YsBg0ahGeffbbJnjNjxgxMmTJFd5yRkYHevXvDy8sLCoWiyZ5rKbKrf+peO0QNgX09Yj6fXYRytXalX2c7ObqFB0ImM39xIbK8qt8QeXt7Qy6XWzkaaqvYDkkK2A5JCtgOSQqk2g7Ly8vNriupZLOgoABDhw6Fl5cXvv32W6MZvIeHB8rLy1FWVqbXu5mfnw9BEODh4WH0WW5ubnBzqz1XUS6XS+of06CiLCA7UXcoixgI1CPms1er58FG+bvB1lZSzaDNkslkLaP9UavGdkhSwHZIUsB2SFIgxXZYn1gk0x9bWlqK2NhYFBYWYteuXXB3dzdav2qu5tmzZ/XKk5KSdPtutlo1V6H17QI4115gyZiaK9FG+3MlWiIiIiIisjxJJJsqlQpjxoxBYmIidu/ejcDAQJPX3HHHHXBzc8PmzZt1ZZWVldiyZQuGDRvWlOFan96WJwPqfXlSJleiJSIiIiKipiWJ8ZPTp0/Hjh07sHLlSiiVShw5ckR3rkePHrC3t0dMTAwuXbqE5ORkAICDgwPmzZuHxYsXQ6FQoGvXrvjwww+Rm5uLWbNmWeutNI+UA9Wv67nlCXDjHptMNomIiIiIyPIkkWzu2bMHADBz5sxa51JSUhAaGgq1Wg2VSqV3bs6cORBFEStWrEB2dja6d++OH3/8EeHh4c0St1XkXwLyL2pfC3Ig5I56XV5QUoGMwjLt5QIQ5cdhtEREREREZHmSSDYvXrxoss7+/ftrlQmCgHnz5mHevHmWD0qqag6hDewJONSvZ/JMjV7NEE8nONtLogkQEREREVErI4k5m1QPjZ2vmcH5mkRERERE1PSYbLYkosj5mkRERERE1CIw2WxJcv4Diq5qX8vtgfZ96n2LxExue0JERERERE2PyWZLcqFGr2ZwH8DWoV6Xq9Qa/He1SHfMYbRERERERNRUmGy2JHpDaOs/XzMlpxgVKg0AwNXeBkEejpaKjIiIiIiISA+XIm0pNGrg4sHq4wYkmzVXoo3yd4UgCJaIjIiIiIhaEFEUkZOTg7KyMqjVamuHQ3UQRRFlZWUoLS1tlp/b5XI5HBwc4O3tbbHnMdlsKTJPAmWF2td2rkBAj3rfIpEr0RIRERG1aaIoIi0tDdeuXYOdnR3kcrm1Q6I6CIIAe3v7ZusgqqioQFFREcrLyxEYGGiR5zLZbClqztcMvROQ1/+fruZKtEw2iYiIiNqenJwcXLt2DT4+PvDy8rJ2OGSEKIpQqVSwsbFptoQzNzcXWVlZyMnJgUKhaPT9OGezpWjk/poAkJTJZJOIiIioLSsrK4OdnR0TTTLIy8sLdnZ2KCsrs8j9mGy2BKoK4PLv1ccN2F8zr7gCV5XlAABBACJ9XSwVHRERERG1EGq1mkNnySi5XG6xubxMNluCtD+ByhLtaydvwKdzvW9RcwhtmJcznOw4gpqIiIiIiJoOk82WoOZ8zbB+gKz+/2ycr0lERERERM2JyWZLYIH5mvor0bo2NiIiIiIiIiKjmGxKWUUxcPQT4PLh6rLibG15PdXs2YzyY88mEREREVFDiKKI119/HcHBwXB0dMTtt9+OI0eOmLwuOTkZ06ZNQ/fu3WFjY4MuXbo0Q7TWxYl7UpVzDlg7AlCm6ZfvexU4vgZ47DvAu6NZt6pUa5CcVaQ7jg5gsklEREREjVNSocK2E+nYeiIVucUV8HK2w/09gjCyR0CrXh/kjTfewKJFi/D666+jW7du+OCDDzBkyBD8/fffCA8Pr/O606dP44cffkCfPn2g0Wig0WiaMWrrYM+mFFUUaxPNaxmGz1/L0J43s4fzfHYRKtTaxuzmYIMAdwdLRUpEREREbdD57CLErDyA+VtP4c9L+biQXYw/L+Vj/tZTiFl5AOezi0zfpAUqKyvDsmXLMHPmTLzwwguIiYnBhg0b4OnpiRUrVhi9Ni4uDleuXME333yDnj17NlPE1sVkU4pObtL2aIp1/LZD1GjPn9ps1u2S9OZrujXbprBERERE1PqUVKjwyGdHcVWp3YtRFKH391VlGR757ChKKlRNFsPp06cxbNgweHl5wcnJCZ06dcLy5cub7HlVDh8+DKVSiTFjxujK7OzsMGrUKOzcudPotbIGLPLZ0rXe/u2W7OQmQJDVnWwC2vMnNwG9Jpq8HVeiJSIiIqK6iKKoGwVnjm+OpyKjsKzO8xoRyCgsw7fHUzHm1vZm39dOLjO7UyQuLg6+vr74/PPP4e7ujuTkZKSmphq9xtyhqzY2dadISUlJAICoqCi98ujoaFy+fBmlpaVwdHQ04x20DUw2pag423iiCWjPF2WZdbszeskmV6IlIiIiomoVag06vbTb4vdd+N1pLPzutNn1zy69F/Y2cpP1cnJykJKSgnfeeQdxcXEAgEGDBpm8bsmSJYiPjzdZT6zqojUgPz8f9vb2cHDQn5bm4eEBURSRn5/PZLMGJptS5KwA8s6b7tl08THrdok3DKMlIiIiImqpvLy8EBISgnnz5iEvLw8xMTEICgoyed0TTzyB2NjYZoiQqjDZlKJuY/S3OzFE1GjrmZB9rRw5ReUAAJkARPqyZ5OIiIiIWi5BELBnzx4sWLAATz31FIqLi9GrVy8kJCSgf//+dV7n5+cHHx/zOmvq4uHhgfLycpSVlen1bubn50MQBHh4eDTq/q0Nk00p6jYG+PVN7aqzhno3BRng6g90fdDkrZIyq4fQhitc4GBremgCEREREbUddnIZzi691+z6G/+4gpfNGB77yoib6j1n01yRkZHYvHkzKisrcfjwYcyfPx9xcXFIS0uDi4uLwWssMYy2aq7m2bNncfPNN+vKk5KSdPtuUjUmm1Jk56zdR7Nqn82qxYKq/nb11563czZ5q5qLA0X5sVeTiIiIiPQJgmDWXMkqo3sF4aP953FVWQaNgbxMJgC+bg54oFdQve7bELa2thgwYADmzp2L4cOHIz09HZGRkQbrWmIY7R133AE3Nzds3rxZl2xWVlZiy5YtGDZsWKPu3Rox2ZQq747A039otzc5uUm7GJCLj7bXs+uDZiWaAOdrEhEREZFlOdnZYN2UPnjks6PIKCyDIGi3Pan629fNAeum9IGTXdOkGidPnsTMmTMxduxYREREoLCwEMuWLUNoaCgiIiLqvC4gIAABAQGNeraDgwPmzZuHxYsXQ6FQoGvXrvjwww+Rm5uLWbNm6eodOHAAMTExWL16NR577DEAQElJiW57lEuXLkGpVOKbb74BAAwYMAAKhaJRsUkRk00ps3PWbm1ixvYmdanZs9mZySYRERERWUCEwgV7Zw7Ad3+nY9uJNGQXlUPhYo+RPQIxontAkyWagHbupZ+fH5YtW4a0tDS4u7ujX79+WLduHeTypp8yNmfOHIiiiBUrViA7Oxvdu3fHjz/+iPDwcF0dURShVqv1tlrJysrCgw/qT4OrOt63bx8GDhzY5LE3NyabrViFSoPz2UW6Y/ZsEhEREZGlONnZYHzvYIzvHdysz/Xx8cFXX33VrM+sSRAEzJs3D/PmzauzzsCBA2vN/QwNDTU6H7Q1Mn8WLrU4yVlFqFRrG3Q7J1v4utlbOSIiIiIiImormGy2YjWH0Eb7uUEQBCtGQ0REREREbQmTzVas5rYnHEJLRERERETNiclmK6a/Ei23PSEiIiIioubDZLOVEkVRfxgtezaJiIiIiKgZMdlspbKvlSO3uAIAIJcJ6ODjYuWIiIiIiIioLWGy2UolZlYPoY1QOMPBtun3HCIiIiIiIqrCZLOV4hBaIiIiIiKyJskkm8nJyZg2bRq6d+8OGxsbdOnSxazrcnNzMW3aNAQHB8PZ2RldunTBxx9/3MTRSl/NZDPKj8kmERERERE1LxtrB1Dl9OnT+OGHH9CnTx9oNBpoNBqzrnvwwQeRlJSE1157DcHBwdi5cyeefPJJyOVyTJ06tYmjli79nk2uREtERERERM1LMj2bcXFxuHLlCr755hv07NnTrGsyMzOxb98+vPbaa5g4cSIGDx6MFStWoH///tiwYUMTRyxd5So1zmcX6447cxgtEREREVlaRTHw5xfA6qHAe7do//7zC215KyaKIl5//XUEBwfD0dERt99+O44cOWLyujVr1kAQhFp/5s6d2wxRW4dkejZlsvrnvZWVlQAAd3d3vXJ3d3cUFRVZJK6W6NzVIqg1IgDAy9kOCld7K0dERERERK1Kzjlg7QhAmQYIMkDUAHnngcuHgV/fBB77DvDuaO0om8Qbb7yBRYsW4fXXX0e3bt3wwQcfYMiQIfj7778RHh5u8vrdu3fr5S+BgYFNGa5VSSbZbIj27dtjyJAheO2119CpUye0b98eu3btwp49e7B+/Xqj1yqVSiiV1UNNMzIyAABqtRpqtbpJ425qp9MLdK87+bmaPSSZrEetVkOj0bT4tkctG9shSQHbIUlBa26HoihCEASIotjwm1QUaxPNaxkQAG2iWeNv8VqG9vxTxwA750bHLCVlZWVYtmwZZsyYgeeffx4A0LdvX3Tq1AlvvvkmPvzwwzqvrfrMe/bsCW9vb4Pnbiyr+tPcRFGss/3X5+uiRSebALBlyxaMHTsWN910EwBALpfjvffewwMPPGD0uoSEBMTHx9cqz83Nhb19y+4JPHEhS/c6xF2O7OxsK0ZD5tBoNCgsLATQsF5+IktgOyQpYDskKWjN7bCsrAz29vZQqVTVhaIIqCvMvofw9zrYKNPqPi9qAGUaVH+th9j9YfODk9sBgmBW1dOnT2PevHk4duwYSktLERQUhEmTJmHWrFnmP68BDh48CKVSiVGjRuk+Q5lMhpEjR2Lbtm36n+sNqjqAVCqV0XpVaiZ8gpmfiyVoNBqUl5fXmUPk5uaafa8WnWyKoohJkybh3Llz+N///gd/f3/89NNPeP755+Hh4YFx48bVee2MGTMwZcoU3XFGRgZ69+4NLy8vKBSK5gi/yVwqTNG97hnu2+LfT1tQ9R+Jt7c35HLuiUrWwXZIUsB2SFLQmtthaWkpBEGAjU2NNEBVDuENyw/ltPlxNvDjbLPriwuuAjbmdfqMGjUKvr6++Oyzz+Du7o7k5GSkpqbqv68bmLsIqbF7nDt3DgDQpUsXvXqdO3fGu+++i8rKSjg6Ohq8tuoXF927d0dOTg5CQkIwZcoUzJ4922A7q+rRtLGxadZkUyaTwcHBoc4cory83Ox7tehk84cffsDmzZtx8uRJdO3aFQAwcOBAZGVlYebMmUaTTTc3N7i51V44Ry6Xt+j/VERRRFLmNd3xTQHtWvT7aUtkMlmLb3/U8rEdkhSwHZIUtNZ2WJW06CUvzZjIGCMIglmx5OTkICUlBe+88w7i4uIAAIMHDzZ53SuvvGJwZOONjA1bLSgogL29fa2E0tPTE6IooqCgAE5OTgavDQgIQHx8PPr06QNBEPD9999j4cKFSE9Px/vvv2/wmpoLCTUnQRDqbPv1+Zpo0cnmmTNnIJfLa+3J2aNHD3z22WcoKSmp8x+7tbqqLEd+iXbhJBuZgAif1jVOnoiIiIjaNi8vL4SEhGDevHnIy8tDTEwMgoKCTF73xBNPIDY2thkiNOyee+7BPffcozseMmQIHB0d8dZbb2HBggXw9/e3WmxNpUUnmyEhIVCr1Th58iRuvvlmXfnx48fh4+PT5hJNQH9/zQ4+LrC3aV2/jSMiIiIiC5PbAS9lma5X5a+1wE4z5kYOWwn0fLR+cZhBEATs2bMHCxYswFNPPYXi4mL06tULCQkJ6N+/f53X+fn5wcfHx/x4DPDw8EB5eTnKysrg4OCgK8/Pz4cgCPDw8KjX/caMGYMVK1bg77//bpXJpmRmPJeUlOCbb77BN998g0uXLkGpVOqOqyanxsTEoEOHDrprhg0bhuDgYIwePRrr1q3D3r17MWfOHKxZswbPPPOMtd6KVSVmVieb0dxfk4iIiIhMEQTtXElz/3R/CHAL1G55YvB+Mu357uPrd996DBWNjIzE5s2bkZ+fj/3798Pe3h5xcXFGtz9csmQJbG1tTf4xJioqCgBw9uxZvfKkpCTdvptUTTI9m1lZWXjwwQf1yqqO9+3bh4EDB0KtVuut3OTq6oq9e/diwYIFmDNnDgoKChAWFoaEhAQ8/fTTzRq/VCRmVM/XjPZ3tWIkRERERNQq2Tlr99G8cZ/Nqr9d/bXnm2HbE1tbWwwYMABz587F8OHDkZ6ejsjISIN1LTGM9o477oCbmxs2b96sG1lZWVmJLVu2YNiwYfW+34YNGyCXy9GjR49GxSVVkkk2Q0NDTe4hs3///lplHTp0wMaNG5soqpan5jDaKD/2bBIRERFRE/DuCDz9B3BqM3ByE1CUBbj4AN3GAF0fbNJE8+TJk5g5cybGjh2LiIgIFBYWYtmyZQgNDUVERESd1wUEBCAgIKBRz3ZwcMC8efOwePFiKBQKdO3aFR9++CFyc3P1tl05cOAAYmJisHr1ajz22GMAtHM2Bw8erFvY9Pvvv8enn36K5557Dn5+fo2KS6okk2xS45VVqnEhu3roAIfREhEREVGTsXMGek3U/mlGfn5+8PPzw7Jly5CWlgZ3d3f069cP69ata5bVg+fMmQNRFLFixQpkZ2eje/fu+PHHHxEeHq6rU7VHZs2tVqKiovD5558jNTUVGo0GkZGRePvtt1v19D8mm63IuatF0FzvHPZ2sYfC1bx9ioiIiIiIWgofHx989dVXVnu+IAiYN28e5s2bV2edgQMH1hq1+c477+Cdd95p6vAkRTILBFHj1RxCy/maRERERERkTUw2W5EzGVyJloiIiIiIpIHJZivCnk0iIiIiIpIKJputhCiKSMqsue0JezaJiIiIiMh6mGy2EhmFZSgsrQQA2MoFRChcrBwRERERERG1ZUw2W4maQ2g7+LjCVs5/WiIiIiIish5mJK0E52sSEREREZGUMNlsJRJrzNfszPmaRERERERkZUw2W4lEbntCREREREQSwmSzFSitUONiTrHuOMqPw2iJiIiIiCwtIyMDs2fPRvfu3eHq6oqgoCA89NBDuHTpklnXJyUl4e6774azszP8/Pwwe/ZsVFRUNHHU1mNj7QCo8c5evQaNqH3t42oPLxd76wZERERERK1eSWUJfkj5ATvO70BeWR48HTwRGxGL+8Lug5Otk7XDaxLHjx/Hli1bMHnyZNx2223IycnBK6+8gt69e+Pff/+FQqGo89r8/HwMHjwYHTt2xJYtW5CWloYZM2agpKQE77//fjO+i+bDZLMVSOIQWiIiIiJqRimFKZi6ZyqullyFAAEiRFxSXsJfWX/hk38+waohqxDmHmbtMC2ub9++SEpKgo1NdRp1xx13IDg4GGvXrsXMmTPrvPbjjz+GUqnE1q1b4enpCQBQqVSYPn065s+fj4CAgCaPv7lxGG0rwPmaRERERNRcSipLMHXPVGSXZAMARIh6f2eXZGPqnqkoqSxpshhOnz6NYcOGwcvLC05OTujUqROWL1/eZM+r0q5dO71EEwCCgoKgUCiQnp5u9Npdu3bhrrvu0iWaADBmzBhoNBrs2bOnSeK1NvZstgKJGdUr0XLbEyIiIiKqD1EUUampNLv+9+e/x9WSq3We10CDqyVX8f357zGq4yiz72srs4UgCGbVjYuLg6+vLz7//HO4u7sjOTkZqampRq/RaDTQaDQm731jMmnKf//9h6ysLERHRxutl5SUhMmTJ+uVtWvXDv7+/khKSqrXM1sKJpstnCiKSMxkzyYRERERNUylphK91vWy+H1fPfoqXj36qtn1jz9yHHZyO5P1cnJykJKSgnfeeQdxcXEAgEGDBpm8bsmSJYiPjzdZTxRF08HWqPvss88iICAA48ePN1o3Pz8f7dq1q1Xu4eGBvLw8s5/ZkjDZbOFS80txrUwFALCzkSHc29nKERERERERNR0vLy+EhIRg3rx5yMvLQ0xMDIKCgkxe98QTTyA2NtaisSxevBh79+7F7t274ezMn8NvxGSzhUvKrB5CG+nrAhs5p+ESERERUeslCAL27NmDBQsW4KmnnkJxcTF69eqFhIQE9O/fv87r/Pz84OPjY7E4Vq1ahSVLluDzzz9HTEyMyfoeHh4oLCysVZ6fn683j7M1YbLZwtVcHCjKj0NoiYiIiKh+bGW2OP7IcbPrbzm3xazhsQv6LKj3nE1zRUZGYvPmzaisrMThw4cxf/58xMXFIS0tDS4uLgavseQw2q1bt+LJJ5/EkiVLas3DrEtUVFStuZmFhYXIyMhAVFSUWfdoaZhstnBciZaIiIiIGkMQBLPmSlYZHjEcn536DNkl2dCg9oI7MsigcFJgeMTwet23IWxtbTFgwADMnTsXw4cPR3p6OiIjIw3WtdQw2v3792P8+PGYOnUqFi5caPZ1Q4cOxWuvvYaCggLd3M3NmzdDJpNhyJAhjY5LiphstnD6ySZXoiUiIiKipuVk64RVQ1bV2mez6m+FkwKrhqyCk61Tkzz/5MmTmDlzJsaOHYuIiAgUFhZi2bJlCA0NRURERJ3XBQQENHovy8TERIwcORIdO3bEo48+iiNHjujOKRQK3fMPHDiAmJgYrF69Go899hgAYNq0aXjvvfcwcuRIzJ8/H2lpaXjxxRcxbdq0VrnHJsBks0UrLlfhUl71/kXRHEZLRERERM0gzD0M34/8HjtTdmLHhR3ILc2Fl6MXYsNjMSxsWJMlmoB27qWfnx+WLVuGtLQ0uLu7o1+/fli3bh3kcnmTPRcAjh49isLCQhQWFuLOO+/UOzdhwgSsWbMGgHYorlqt1ttqxcPDA3v37sUzzzyDkSNHwtXVFVOmTMGrr5q/Ym9Lw2SzBTt79RqqhpT7uTnAw7lphykQEREREVVxsnXC6MjRGB05ulmf6+Pjg6+++qpZn1ll4sSJmDhxosl6AwcONDj3Mzo6Gj///HMTRCZNXLq0BeMQWiIiIiIikiommy0YFwciIiIiIiKpYrLZgiVlVO+xyWSTiIiIiIikhMlmC6XRiEjKrJlschgtERERERFJB5PNFio1vxRF5SoAgL2NDKFezlaOiIiIiIiIqBqTzRbqTI35mp38XGEj5z8lERERERFJBzOUFiops8biQNxfk4iIiIiIJIbJZgtVcyXaKM7XJCIiIiIiiWGy2UIlciVaIiIiIiKSMCabLdC1skpczivRHXMYLRERERERSQ2TzRbov6vVvZqB7Rzh7mRrxWiIiIiIqC3SlJQgf+MmXHzkEZwfOgwXH3kE+Rs3QVNSYvriFiw0NBSCINT6U1ZWZvLapKQk3H333XB2doafnx9mz56NioqKZojaOiSTbCYnJ2PatGno3r07bGxs0KVLF7OvTUtLw4QJE6BQKODo6Ijo6GisX7++CaO1rjMZ3F+TiIiIiKyn/EIKzg+7D5mLFqH0+F+oSElB6fG/kLloEc4Puw/lF1KsHWKTGj16NH7//Xe9P/b29kavyc/Px+DBg1FRUYEtW7bgtddew6effooZM2Y0U9TNz8baAVQ5ffo0fvjhB/Tp0wcajQYajcas6zIyMnD77bejU6dO+PTTT+Hm5obTp0+jvLy8iSO2Hr3FgTiEloiIiIiakaakBJcnT4YqK0tbIIp6f6uysnB58mRE7PwBMicnK0XZtHx9fXHbbbfV65qPP/4YSqUSW7duhaenJwBApVJh+vTpmD9/PgICApoiVKuSTM9mXFwcrly5gm+++QY9e/Y0+7rZs2ejffv22L17N+6//37ExMTg2WefxeTJk5swWuuqmWxycSAiIiIiagxRFKGpqDD7T8G2bVBlZgJ1dQ5pNFBlZqJg23f1uq9YlbSa4fTp0xg2bBi8vLzg5OSETp06Yfny5Rb6RJrGrl27cNddd+kSTQAYM2YMNBoN9uzZY8XImo5kejZlsvrnvUqlEps2bcLq1ashl8ubICrp0WhEnM3kMFoiIiIisgyxshJnu91s8fteXbIEV5csMbt+p5P/QLCzM6tuXFwcfH198fnnn8Pd3R3JyclITU01eo25oydtbEynSOvXr8eqVatga2uL/v3744033kDXrl2NXpOUlFSrQ6xdu3bw9/dHUlKSyWe2RJJJNhvir7/+QkVFBWxtbTFgwAAcPnwYXl5emDBhApYuXQpb27oXzlEqlVAqq3sIMzIyAABqtRpqtbrJY2+oi7nFKKnQxudoK0dQOwdJx0vmUavV0Gg0/Lckq2I7JClgOyQpaM3tUBRFCIKg14tYnx7FpiSKolmx5OTkICUlBW+//Tbi4uIAAAMHDtTdoy7x8fFYYkbyayohjYuLQ58+fRAcHIwLFy7gtddeQ9++ffHXX38hPDy8zuvy8/Ph7u5eK0YPDw/k5ubWKq/6PKzx7yOKYp3tvz5fFy062czMzAQATJkyBVOnTsXixYtx7NgxvPzyy5DJZFi2bFmd1yYkJCA+Pr5WeW5ursnJvdZ09Fy+7nWYpz3ycnOsGA1ZikajQWFhIYCG9fITWQLbIUkB2yFJQWtuh2VlZbC3t4dKpdKViTVeW5NapYLGjM/b3d0dISEhmDdvHrKzszF48GAEBQWZvG7y5MkYOnSoyXoqE59HQkKC7vXtt9+OwYMHo2vXrnjzzTfx3nvvGb1Wo9HUun9VQmmovCqxEwTBZNyWotFoUF5ejuzsbIPnc3Nzzb5Xi042q37rcNddd2HlypUAgEGDBuHatWtYsWIFXn75ZTg6Ohq8dsaMGZgyZYruOCMjA71794aXlxcUCkXTB99A6f8U6F53be8p6VjJfFX/kXh7e7eZIeEkPWyHJAVshyQFrbkdlpaWQhAEvaGiolyOyH/+NvseBd98g6xXlpqs5/PyQrR74AGz7yvY2pqdVP3444946aWX8Nxzz6G4uBi9evXCypUr0b9//zqvCQoKMmsRHnOG0dbUvn179O3bFydOnDB6rYeHB65du1arTkFBAby8vGqVV/Vo2tjYNGuyKZPJ4ODgUGeeUZ+FWFt0sunh4QEAGDx4sF55TEwMXn31VSQnJ9c5dtrNzQ1ubrUX15HL5ZL+T+Xs1SLd65sC3SUdK9WPTCaTfPuj1o/tkKSA7ZCkoLW2w6qkpWbyIggCUI+RfR7334+8VZ9pV6M1NORUJoONjw88Ro6ErIlGDHbq1AmbN29GZWUlDh8+jPnz52P48OFIS0uDi4uLwWteeeUVgyMbb9SYYavGksKoqCicPXtWr05hYSEyMjIQHR1t8Nqa+3g2J0EQ6mz79fmaaNHJZufOnY2eN2dj1ZaGK9ESERERkTXJnJwQvHq1dvuTzExAELTbnlz/28bHB8GrVzfLtidVa7fMnTsXw4cPR3p6OiIjIw3WfeKJJxAbG2vxGNLT03Ho0CE8+uijRusNHToUr732GgoKCtCuXTsAwObNmyGTyTBkyBCLxyUFLTrZDAkJQdeuXfHzzz/j6aef1pX/9NNPcHR0NJmMtjTKskqk5pfqjjv5cSVaIiIiImp+9uFhiNj5Awp37EDh9u1Q5+RC7u0F97g4uMfGNmmiefLkScycORNjx45FREQECgsLsWzZMoSGhiIiIqLO6wICAhq9l+XXX3+NHTt2YNiwYQgICMCFCxewbNkyyOVyzJw5U1fvwIEDiImJwerVq/HYY48BAKZNm4b33nsPI0eOxPz585GWloYXX3wR06ZNa5V7bAISSjZLSkqwc+dOAMClS5egVCrxzTffAAAGDBgAhUKBmJgYXLp0CcnJybrrXn31VYwYMQLPP/887rvvPvzxxx9YsWIFZs+eDWdnZ6u8l6aSlFG95UmQhyPcHOpebZeIiIiIqCnJnJzgMWYMPMaMadbn+vn5wc/PD8uWLUNaWhrc3d3Rr18/rFu3rsmHPYeFhSE9PR3PP/+8rody8ODBWLJkCcLCwnT1qhb3qbmyrYeHB/bu3YtnnnkGI0eOhKurK6ZMmYJXX321SWO2Jskkm1lZWXjwwQf1yqqO9+3bh4EDB0KtVtdapSkuLg5ff/01XnnlFXz00Ufw9/dHfHw85s6d22yxN5ekTA6hJSIiIqK2zcfHB1999ZVVnn3bbbdh3759JusNHDjQ4NzP6Oho/Pzzz00RmiRJJtkMDQ01ORl3//79BsvHjh2LsWPHNkFU0sL5mkRERERE1FK0ro2DWrkzNYbRRnO+JhERERERSRiTzRZCrRFxlsNoiYiIiIiohWCy2UJcyi1GWaV2grGznRzBnk2/lDQREREREVFDMdlsIRJrDKHt5OcKmax5N3YlIiIiIiKqDyabLUTNxYGiOISWiIiIiIgkjslmC8GVaImIiIiIqCVhstlCJGVWD6Pt7M+VaImIiIiISNqYbLYAhSWVSCso1R138mPPJhERERERSRuTzRYgscaWJ8GeTnCxt7FiNERERERE1rV48WIIgqD7o1AoMHjwYBw8eLBW3TVr1mDx4sXNFtvZs2fx9NNPo3PnznByckJYWBiefPJJ5OTk1Os+qamp8PDwgEwmq3Xthx9+iNjYWCgUCgiCgG+++cbovTQaDXr16mVWXUtistkC6M/X5BBaIiIiIiJHR0f8/vvv+P333/HRRx8hNzcXMTEx+Pfff5Gfn48VK1agsrJSV18URaxatQrJyclNGtdPP/2EgwcP4v/+7/+wc+dOLF68GDt37kS/fv1QXl5u9n1mzZoFFxcXg+fWrl2LnJwcDBs2zKx7ffLJJ0hLSzP72ZbCZLMFSKqx7QkXByIiIiIiAmQyGW677TbcdtttGD16NLZv3w6VSoWPP/4Y9vb2KC0tRb9+/fD7778jMTERgwcPRmJiIjw9PZs0rvHjx+Pvv//Gc889h4EDB2LChAn4+uuvkZSUhB07dph1j19++QU///wzZsyYYfD84cOHceTIEcTHx5u8V05ODl566SUsW7asXu/DEjgeswWoOYyWySYRERERUW3BwcFQKBRISUmBk5MTFi5ciFGjRqFfv34oKSnB7t27MXDgwCaPw8vLq1ZZjx49AADp6ekmr6+srMTTTz+NxYsXw8nJyWAdmcz8PsN58+Zh0KBBGDRokNnXWAqTTYlTqTU4W2Ml2mguDkRERERETeDcuXNGz3t5een1Cl68eFFvmOqNXF1d4efnpztOS0tDSUlJrXodO3ZsQLS1KZVK5ObmIiAgAKWlpXj77bfx/fffY/To0SgsLER8fDx++OEHLFiwAO3atTN4D41GA41GY/Q5giBALpfXK7ZDhw4BAKKjo03WfeeddyCXy/Hkk0/iyy+/rNdzbnTs2DH873//w+nTpxt1n4ZisilhJRUqfPrrBZSrtA1eJgAHz2XjftdAONnxn46IiIiILCcyMtLo+aVLl2LBggW647vvvtvo/McJEyZgzZo1uuMnnngCO3furFVPFMX6B3udSqUCoF1MZ+bMmVCr1Rg9ejRKS0tha2uLX3/9FevXr8fFixexYcMGrFq1CtnZ2XUmm5MnTzaZ4IWEhODixYtmx1hWVoZZs2ahR48eiImJMVo3PT0dS5YswbZt2+qd0N5Io9HgqaeewsyZMxEaGlqvmC2FGYtEnc8uwiOfHUVGYZmuTCMCC7b9i/f3JWPdlD6IUBieMExERERE1NoVFxfD1tZWd+zh4YH3338f99xzDwDtAjs1CYKAJ554wug9Fy9ejKefftpoHXt7+3rFOW3aNKSkpODw4cMQBMFo3VmzZuHuu+/G4MGDG5WEA8Bnn32GzMxMzJ07t1H3aQwmmxJUUqHCI58dxVVlmcHzV5VleOSzo9g7cwB7OImIiIjIIv777z+j52+ci/jTTz+ZHEZb06effmpwGG1DOTo64tdff4UgCPD29kb79u0NzmWcOHGi2fcMDg5GUFCQ0TqmEsaaXnrpJaxfvx47duxAly5djNb9/fff8c033+Do0aMoKCiAKIq6z0upVMLJyanOOZw3Kioqwvz58/Hqq6+ioqICFRUVUCq168CUlJRAqVTCza3pp+cxU5GgbSfS9Xo0b6QRgYzCMnz3dzrG9w5uxsiIiIiIqLWq79zJ0NDQetUPDAysV31TZDIZbrnlFove05LDaN977z289tprWLNmja631ZizZ8+isrISPXv2rHUuIiICY8eOxYYNG0zeB9CuQJubm4tp06Zh2rRpeucmTJgAX19fZGZmmnWvxmCyKUFbT6RCEABjPeeCAGw7kcZkk4iIiIjIQiw1jPbrr7/Gc889h2XLluGxxx4z69n33nsv9u3bpzsWRRE7d+7EihUrsG3btnr9MsDPz0/vXgCQmZmJ8ePHY/Hixbj77rvNvldjMNmUoNziCqOJJqBNRLOLzN8UloiIiIiIjAsNDa13j+2NDhw4gAkTJmDw4MEYMGAAjhw5ojsXFBSkG6a7du1aTJ48GXv37sWAAQPg5+f3/+3df0xV9ePH8ddVutxUEPDeDKFCbaL4C/z9I2dYc+KP1DTpM1ezTY05pfRbrfmHWqn5D9kfjnRlLmNOg8LQxNwUUqeSZKVp2hIl/eaPKyLOH3Dhcr9/GPf7ufmDHx44V8/zsTHH+xzvebm9N3nxPud9Anbv9fl8KikpkSQNHz5cTqfTf6y4uFinT5+W2+2WJP81XC6XRo4cKYfDcdtrXupWY3v27Klhw4bd17+xoSibQahDW7tOXbpe78qmq13jHk4GAAAA0LwKCgpUXV2tnTt3aufOnQHHFi9erCVLlki6tVus1+tt0kZAq1atCrjdNyMjQ5I0cuRIFRYWNjm70Wy++93m6CFx9uxZPfHEEzpz5ky9DwU3tw1Ff2lh7pF6z/vwxd7cRvuQ8Hq9crvdcrlc973NNdBUzEMEA+YhgsHDPA/rVrfud/UOzc/n86mmpkYhISGN2pToftU3RxrTm27frgmmm5TUSdHtHWp1lznVyiZFt3doYmKnlg0GAAAAAA1E2QxCbewhypo5WB3DHZJu3TL73392DHcoa+ZgXnsCAAAAIGjRVoJUV1c77fyfkfr2l7+1+ef/lftalVztQjUpKUYTEztRNAEAAAAENRpLEGtjD9F/Bj3Jc5kAAAAAHjjcRgsAAAAAMBxlEwAAALCI1q1by+v1mh0DQczr9Rq2CzNlEwAAALAIh8Mhj8ejsrIys6MgCJWVlcnj8cjhcBjyeTyzCQAAAFiE0+lUVVWVLl68qCtXrjx07xF92NTW1qpVq5ZZH/R6vfJ4PAoLC5PT6TTkM1nZBAAAACzCZrMpJiZGTqdTdrvd7Di4B5/Pp6qqKvl8vha5nt1ul9PpVExMjGx171y8T6xsAgAAABZis9nkcrnMjoF6eL1eud1uuVyuB3YFmpVNAAAAAIDhKJsAAAAAAMNRNgEAAAAAhqNsAgAAAAAMxwZB/6ipqZEknTt3zuQksCKv16uysjJVVVU9sA+A48HHPEQwYB4iGDAPEQyCdR7W9aW6/nQvlM1/uN1uSdKgQYNMTgIAAAAAwc3tdisuLu6e59h8LfXiliBXWVmpI0eOyOVyKSSEDo6Wde7cOQ0aNEg//vijoqOjzY4Di2IeIhgwDxEMmIcIBsE6D2tqauR2u9W7d285HI57nkur+ofD4dDAgQPNjgGLi46OVmxsrNkxYHHMQwQD5iGCAfMQwSAY52F9K5p12CAIAAAAAGA4yiYAAAAAwHCUTSAIhIeHa/HixQoPDzc7CiyMeYhgwDxEMGAeIhg8DPOQDYIAAAAAAIZjZRMAAAAAYDjKJgAAAADAcJRNAAAAAIDhKJsAAAAAAMNRNgEAAAAAhqNsAibJzs7WxIkTFRsbq7Zt2yoxMVGff/652CAaZrp27ZpiY2Nls9lUXFxsdhxYzBdffKGkpCQ5HA45nU6lpKTo5s2bZseCheTl5Wnw4MEKCwtTdHS0pk2bppKSErNj4SH2559/Ki0tTYmJiQoJCVGvXr3ueN7atWvVrVs3ORwO9e3bV1u3bm3hpE1D2QRM8tFHH6lNmzbKyMjQli1blJKSolmzZun99983Oxos7IMPPlBNTY3ZMWBBy5Yt07x585Samqrvv/9ea9asUefOneX1es2OBosoLCzU5MmTlZCQoNzcXH388cf69ddfNXr0aH7pgWZz9OhRfffdd3r66aeVkJBwx3M2btyoWbNmKTU1Vfn5+Ro6dKgmT56sAwcOtHDaxuM9m4BJLl26JKfTGTA2e/Zsbdq0SeXl5WrVit8FoWUdP35cAwYMUEZGhtLS0nTw4EENGDDA7FiwgBMnTqhXr17Ky8tTSkqK2XFgUWlpadqxY4dOnjwpm80mSSooKNCoUaO0e/dujRgxwuSEeBjV1tb6f+abMWOGiouL9dtvvwWcEx8fr/79+2vDhg3+sWHDhikiIkLbtm1r0byNxU+zgEn+XTQlKSkpSVevXtX169dNSASrmzdvntLS0hQfH292FFjMunXr1LlzZ4omTFVdXa2wsDB/0ZSk9u3bSxKPuKDZ1Le4UFJSoj/++EPTpk0LGH/55Ze1c+dOVVVVNWe8+0bZBILI3r17FRMTo7CwMLOjwGJycnJ05MgRLVq0yOwosKADBw6od+/eWrp0qR577DHZ7XYNHz5cRUVFZkeDhcyYMUPHjh1TZmamKioqVFJSooULFyopKUnDhw83Ox4s6vjx45Kk7t27B4z36NFDHo9Hp06dMiNWg1E2gSCxd+9ebdy4UW+99ZbZUWAxN27c0IIFC7R8+XKFh4ebHQcWdP78ee3YsUPr169XZmamNm/eLJvNptGjR+vixYtmx4NFjBgxQrm5uXr33XcVERGhrl276sKFC8rPz1fr1q3NjgeLKi8vlyRFREQEjEdGRkqSLl++3NKRGoWyCQSBs2fPKjU1VcnJyUpPTzc7Dixm6dKl6tixo1577TWzo8Ciamtrde3aNeXk5Gjq1KkaO3as8vLy5PP5tGrVKrPjwSL27dunV155RbNmzdKuXbuUnZ2t2tpajRs3jg2CgCYKMTsAYHVXrlxRSkqKOnTooK+//pqNgdCiSktLlZGRodzcXFVUVEi69fqTuj+vXbumdu3amRkRFhAZGakOHTqoT58+/rGoqCglJSXp6NGjJiaDlaSnp2vUqFHKyMjwjw0ZMkRPPvmkvvzyS82ePdvEdLCquhXMiooKPf744/7xuhXPqKgoU3I1FD/VAia6efOmxo8fr4qKCuXn5/s3IgBayqlTp+TxeDRu3DhFRkYqMjJSEyZMkCQlJyfr+eefNzkhrKBnz553PVZZWdmCSWBlx44dU2JiYsBYbGysnE6nTp48aU4oWF7ds5p1z27WOX78uOx2u7p06WJGrAajbAImqamp0bRp0/T7779r+/btiomJMTsSLCgxMVEFBQUBXytXrpQkrV69WpmZmSYnhBWMHz9eZWVl+uWXX/xjZWVlOnTokPr3729eMFjKU089pUOHDgWMlZaW6tKlS4qLizMnFCyvS5cu6tatm7KzswPGN23apOeee052u92kZA3DbbSASebMmaOtW7cqIyNDV69eDXgxb1JSkkJDQ01MB6uIiIjQs88+e8dj/fv3V79+/Vo2ECxp0qRJGjhwoKZOnaply5bp0Ucf1YcffqjQ0FDNmTPH7HiwiLS0NL355pt64403NGHCBJWVlfl3SP73aycAo9y4ccP/rszS0lJdvXpVOTk5kqSRI0fK5XJpyZIlmj59urp27ark5GRt2rRJRUVF2r17t5nRG8Tm48VBgCni4uJUWlp6x2OnTp3it6gwTWFhoZKTk3Xw4EENGDDA7DiwiEuXLmn+/PnasmWLPB6PRowYoZUrVyohIcHsaLAIn8+nNWvW6JNPPtHJkycVFhamoUOHavny5be9dgIwyunTp9W5c+c7HisoKPD/Qnjt2rVasWKF/vrrL8XHx2v58uUaP358CyZtGsomAAAAAMBwPLMJAAAAADAcZRMAAAAAYDjKJgAAAADAcJRNAAAAAIDhKJsAAAAAAMNRNgEAAAAAhqNsAgAAAAAMR9kEAAAAABiOsgkAwB3MmDFDvXr1atZrFBYWymazqbi4uFmv0xBLliyRzWa751dcXJzZMQEAD5AQswMAAGBV/fr10/79+9WjRw+zo2jmzJkaM2aM//vPPvtMGzZs0K5du/xjoaGhZkQDADygKJsAALQwn88nj8ej8PBwDRkyxOw4kqTY2FjFxsb6v9++fbtatWoVNPkAAA8ebqMFAOAeCgsLlZSUpLZt22rQoEH66aefAo5XVlZqwYIF6tSpkxwOhxITE5WbmxtwTt0tudu2bVPfvn0VGhqqLVu23HYb7b1uZW3K9erLDgBAc6JsAgBwF+fPn1d6errefvttffXVV6qsrNTkyZNVXV3tP2f69Olas2aN3nnnHW3evFkJCQmaMmWK8vLyAj7r77//Vnp6uubPn6/t27crMTHxtuvNnDlT+/fv93/t2bNHXbp0Ubdu3Rp9vYZkBwCgOXEbLQAAd3H58mX98MMP6tmzpySpbdu2Sk5OVlFRkZ555hkdPnxY33zzjVavXq3XX39dkjRmzBidPn1a7733nl544QX/Z5WXlys/P1+DBw/2j509ezbgev++lXXu3Llyu90qKiqSpEZdr77sAAA0N1Y2AQC4i06dOvnLmiQlJCRI+v+SuGfPHknSSy+9FPD3UlNT9fPPP+v69ev+sQ4dOgQUzfp8+umnyszMVFZWln8DocZcr77sAAA0N8omAAB3EREREfC93W6XdOu5SenWauUjjzyiqKiogPM6duwon8+nK1euBIw11N69ezV37lwtXrz4ttXRhl6vvuwAADQ3yiYAAE0UFRWl6upqlZeXB4xfuHBBNpstoPD99yY/93LmzBlNmTJFY8eO1aJFi5p8PQAAzEbZBACgieqefczOzg4Yz87O9u8C2xg3btzQxIkT5XQ6tX79+tsKqtHXAwCgObFBEAAATdSnTx+9+OKLWrBggW7evKn4+HhlZWVp3759+vbbbxv9efPnz9fhw4e1bt06HT16NODYkCFDDL8eAADNibIJAMB9yMrK0sKFC7VixQpdvnxZ3bt3V05OjiZMmNDozzpx4oS8Xq9effXV2475fD7DrwcAQHOy+er+9wIAAAAAwCA8swkAAAAAMBxlEwAAAABgOMomAAAAAMBwlE0AAAAAgOEomwAAAAAAw1E2AQAAAACGo2wCAAAAAAxH2QQAAAAAGI6yCQAAAAAwHGUTAAAAAGA4yiYAAAAAwHCUTQAAAACA4f4P67wJMGc4vwsAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s_values = [0.1, 0.5, 2.0, 5.0]\n", "T_values = [0.5, 1.0, 2.0, 5.0, 10.0]\n", "P_star = 1.0 + np.sqrt(2.0)\n", "\n", "fig, ax = plt.subplots()\n", "for s in s_values:\n", " p0s = []\n", " for T_ in T_values:\n", " r = opt.pontryagin_lqr(1.0, 1.0, 1.0, 1.0, s, 1.0, T_, 200)\n", " p0s.append(r['riccati'][0])\n", " ax.plot(T_values, p0s, 'o-', lw=2, label=f's = {s}')\n", " print(f\"s = {s:4.1f} : P(0) à T=10 = {p0s[-1]:.4f}\")\n", "ax.axhline(P_star, ls='--', color='black',\n", " label=f'P* = {P_star:.3f}')\n", "ax.set_xlabel('horizon T'); ax.set_ylabel('P(0)')\n", "ax.set_title(\"Convergence vers le point fixe Riccati\")\n", "ax.legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "7cd43961", "metadata": {}, "source": [ "**Résultat attendu.** Toutes les courbes convergent vers\n", "$P^* \\approx 2.414$ pour $T$ grand.\n", "\n", "**Lecture du graphique.** L'effet du terminal $s$ s'estompe quand $T$\n", "augmente.\n", "\n", "**Conclusion.** En horizon long, le coût terminal devient négligeable.\n" ] }, { "cell_type": "markdown", "id": "65d4c5e1", "metadata": {}, "source": [ "## Cellule 3 — Exemple concret : stabilisation d'un pendule inversé\n", "\n", "**Modèle physique.** Pendule inversé linéarisé autour de la verticale\n", "$\\ddot\\theta = (g/\\ell)\\theta + (1/m\\ell^2) u$. Pour le mode\n", "sur-amorti $(\\dot\\theta \\equiv 0)$ on retient l'équation scalaire\n", "$\\dot\\theta = a\\theta + bu$ avec $a = g/\\ell$, $b = 1/(m\\ell^2)$.\n", "\n", "**Équation pivot (Riccati).** $P$ vérifie $-\\dot P = 2aP - (b^2/r)P^2 + q$.\n", "\n", "**Ce que la cellule vérifie.** Le contrôleur LQR ramène l'angle\n", "initial $0.3$ rad vers $0$.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "7aabb9b7", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:31.162225Z", "iopub.status.busy": "2026-05-12T14:05:31.161917Z", "iopub.status.idle": "2026-05-12T14:05:31.762984Z", "shell.execute_reply": "2026-05-12T14:05:31.761885Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Angle initial : 0.300 rad (17.2°)\n", "Angle final : 5.955e-25 rad\n", "Effort max : 6.177\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g, ell, m = 9.81, 1.0, 1.0\n", "a, b = g / ell, 1.0 / (m * ell ** 2)\n", "res = opt.pontryagin_lqr(a, b, q=10.0, r=1.0, s_terminal=1.0,\n", " x0=0.3, t_horizon=5.0, n_steps=500)\n", "ts = np.array(res['time_grid'])\n", "theta = np.array(res['state'])\n", "u = np.array(res['control'])\n", "\n", "print(f\"Angle initial : {theta[0]:.3f} rad ({np.degrees(theta[0]):.1f}°)\")\n", "print(f\"Angle final : {theta[-1]:.3e} rad\")\n", "print(f\"Effort max : {np.abs(u).max():.3f}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].plot(ts, theta, lw=2, color='C3', label=r'$\\theta(t)$')\n", "axes[0].axhline(0, ls='--', color='gray', alpha=0.6)\n", "axes[0].set_xlabel('t (s)'); axes[0].set_ylabel(r'$\\theta$ (rad)')\n", "axes[0].set_title(\"Stabilisation du pendule inversé\")\n", "axes[0].legend()\n", "ts_u = ts[:len(u)]\n", "axes[1].plot(ts_u, u, lw=2, color='C2', label='u(t)')\n", "axes[1].set_xlabel('t (s)'); axes[1].set_ylabel('u (couple)')\n", "axes[1].set_title(\"Couple appliqué (LQR)\")\n", "axes[1].legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "f6c1b078", "metadata": {}, "source": [ "**Résultat attendu.** $\\theta \\to 0$ rapidement, effort borné.\n", "\n", "**Lecture du graphique.** Décroissance exponentielle de l'angle ;\n", "couple initial fort puis amorti.\n", "\n", "**Conclusion.** Le primitive transforme un système naturellement\n", "instable ($a = 9.81 > 0$) en système stable, illustration directe\n", "du contrôle optimal.\n" ] } ], "metadata": { "kernelspec": { "display_name": "rhftlab", "language": "python", "name": "rhftlab" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }