TP_Reseau_Notebook_7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Travaux pratiques sur les réseaux d'eau"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Données et fonctions du problème"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On charge dans l'environnement :\n",
    "1. les fonctions de Python qui seront utilisées,\n",
    "2. les données du problème,\n",
    "3. les fonctions utilitaires du problème."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import random\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Probleme_R import *\n",
    "from Structures_N import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Visualg import Visualg\n",
    "from Verification import Verification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  On charge les prototypes d'algorithmes d'optimisation :\n",
    "\n",
    "* **Gradient_F** : algorithme de gradient à pas fixe,\n",
    "* **Newton_F** : algorithme de Newton à pas fixe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " **Algorithm 9.2: Backtracking line search.**  \n",
    "given a descent direction $ \\Delta x$ for $f$ at $x \\in \\operatorname{dom}f$, $\\alpha \\in(0,0.5)$, $\\beta \\in (0,1)$, $t:=1$.  \n",
    "while $ f(x+t \\Delta x)>f(x)+\\alpha t \\nabla f(x)^{T} \\Delta x $:  \n",
    "  $ t:=\\beta t $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BacktrackingLineSearch(qc,critere,gradient,delta_x,\n",
    "                           alpha = 0.1, beta = 0.9):\n",
    "    step = 0.0006\n",
    "    qc_new = qc + step * delta_x\n",
    "    q = q0 + B.dot (qc_new)\n",
    "    critere_new = 1/3*q.dot(r*q*abs(q)) + pr.dot(Ar.dot(q))\n",
    "    while critere_new > critere + alpha * step * gradient.transpose()@delta_x:\n",
    "        step *= beta\n",
    "    return step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gradient_F(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "    \n",
    "    iter_max = 10000\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "\n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "\n",
    "        # Direction de descente\n",
    "        direction = -gradient\n",
    "        \n",
    "        # Backracking Line search for step size\n",
    "        #gradient_step = BacktrackingLineSearch(x,critere,gradient,direction)\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    ##### Resultats de l'optimisation\n",
    "\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "    \n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "\n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt, gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_F(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from numpy.linalg import solve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables    \n",
    "    \n",
    "    iter_max = 100\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient, hessien = Oracle(x)\n",
    "\n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Direction de descente\n",
    "        direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        critere_list.append(critere)\n",
    "   \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Résolution du problème primal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from HydrauliqueP import HydrauliqueP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.a On écrit les oracles pour le problème primal d'optimisation :\n",
    "\n",
    "* **OraclePG** : calcul de la fonction et du gradient,\n",
    "* **OraclePH** : calcul de la fonction du gradient et du Hessien."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ q=q^{(0)}+B q_{c} $  \n",
    "  \n",
    "$ z=r \\bullet q \\bullet|q| $\n",
    "  \n",
    "$ \\nabla F\\left(q_{C}\\right)=B^{\\top}(r \\bullet q \\bullet|q|)+B^{\\top} A_{r}^{\\top} p_{r} $  \n",
    "\n",
    "$ F\\left(q_{C}\\right) = \\frac{1}{3}\\langle q, r \\bullet q \\bullet|q|\\rangle+\\left\\langle p_{r}, A_{r} q\\right\\rangle $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePG(qc):\n",
    "    \n",
    "    gradient =B.transpose()@(r*(q0+B@qc)*abs(q0+B@qc))+B.transpose()@Ar.transpose()@pr\n",
    "    critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n",
    "    \n",
    "    return critere, gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\nabla^{2} F\\left(q_{c}\\right)=2B^{T} \\operatorname{diag}(\\mathrm{r} \\cdot|q| ) \\mathrm{B} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePH(qc):\n",
    "    q = q0 + B@qc \n",
    "    M =2 * np.diag(r * abs(q))\n",
    "    temp = B.T.dot(M)\n",
    "    hessien = temp.dot(B)\n",
    "    critere, gradient= OraclePG(qc)\n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On teste la validité des oracles en résolvant le problème :\n",
    "\n",
    "* **OraclePG** avec la méthode du gradient à pas fixe,\n",
    "* **OraclePH** avec la méthode de Newton à pas fixe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS FIXE\n",
      "\n",
      "Iteration : 4222\n",
      "Temps CPU : 0.484375\n",
      "Critere optimal : -3.734007048043507\n",
      "Norme du gradient : 9.988775146630822e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 9.988725708787172e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_GF, gsl_GF, cl_GF = Gradient_F(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg(gnl_GF, gsl_GF, cl_GF )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Input variables  \n",
    "  1. $ gradient \\ list$: array containing the norm of the gradient  of the criterion at each iteration of the optimization algorithm.  \n",
    "  2. $ step \\ list $: array containing the length of the gradient step at each iteration.\n",
    "  3. $ criterere \\ list$: array containing the value of the criterion "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE NEWTON A PAS FIXE\n",
      "\n",
      "Iteration : 6\n",
      "Temps CPU : 0.015625\n",
      "Critere optimal : -3.7340070480435745\n",
      "Norme du gradient : 6.147549404245316e-13\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 4.414801857421935e-13\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_NF, gsl_NF, cl_NF  = Newton_F(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAI4CAYAAAA/PH0eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdd5wV9b3G8c+z9N6WtvQmiLQY7CXGaEQBMc2ScmNi4jW5RnM1RXNTzE28MTfXFKO5iSbGtKvBkohoLClGUIyCoYMKCIJLR3qH7/1jBjwsu7C47M7s7vN+vfbFOTPnzO87cw7nOfOb35lRRGBmZpY3RVkXYGZmVh4HlJmZ5ZIDyszMcskBZWZmueSAMjOzXHJAmZlZLjmg7KiT9LSkT2VdR3kk3STpt+ntnpI2S2qQdV11jaSzJC07yss8Q9LLR3OZb6OGr0j6eZY11CcOqByStFjSSkktCqZ9StLTGZZV50TE6xHRMiL2VHVZeQ7luiIiJkXEwH330/8n51RXe+WFbET8V0T4da4hDqj8aghcW9WFKFEnX2dJDbOuoa6qy+8bqPvrV1f4Bcqv7wFfkNS2vJmSTpX0oqQN6b+nFsx7WtLNkp4FtgJ9JYWkz0p6VdImSd+S1E/SFEkbJY2X1LhgGWMkTZe0XtJzkoZVVKikcyXNT2u5HVDBvP1daun93mkt5YaLpOMl/TOt8X5Jv5f07XTeWZKWSfqypBXALyW1kzRR0mpJb6a3uxcsr4+kv6fLewoorqgWSW0k/ULScklvSPr2vu4/SZdLmizpf9J2XpN0fjrvZuAM4Pa0y/D2Ctbtfkkr0u30jKTjyrxmnyq4f7mkyYfY5qenr8t6SUslXV6wDr9Ot8cSSV/d90F8uNeigvfN5ZIWpdvvNUkfqaCeZpLuSbfNXOCEMvNLJD2Y1vWapGsK5p0oaWr6Plwp6fsVtLF/j0bSb4CewCPpNv9SOv3kgu0yQ9JZZbZx2fX7hKR56fotkvSv6WNbAH8CStLlb07Xoew2vFDSnLS9pyUdWzBvsaQvSJqZvua/l9Q0nVecvlfXS1onaZIcmAeLCP/l7A9YDJwDPAR8O532KeDp9HZ74E3gYyR7Wpel9zuk858GXgeOS+c3AgKYALROp+8A/gL0BdoAc4GPp88/HlgFnAQ0AD6e1tSknFqLgY3AB9N2/h3YDXwqnX8T8NuCx/dOa2lYzrIaA0tI9hwbAe8HdhZsg7PSZX8XaAI0AzoAHwCaA62A+4E/FixzCvD99PFnApv21VO2FuCPwM+AFkAn4AXgX9N5lwO7gE+n2+QzQCmggm3+qcO8rp9Ma2wC/BCYXjDvgOen7U2uYDk90/W4LN1OHYAR6bxfAw+n7fQGXgGuqMxrwcHvmzbpazswnd8VOK6Cmm4BJpG8N3sAs4Fl6bwiYBrw9fQ17gssAs4reI0+lt5uCZxcQRtn7Vtm4f+TgvvdgLXABWmb56b3Ox7i/8VooB/Jl6p3kQTX8eW1V3YbAscAW9J2GgFfAhYAjQvqewEoSbfLPOCqdN53gJ+mz2tE8gVHWX/25O3PiZ1vXwc+J6ljmemjgVcj4jcRsTsi7gXmA2MLHnNPRMxJ5+9Kp303IjZGxBySD5AnI2JRRGwg+bb4jvRxnwZ+FhH/iIg9EfErkkA7uZwaLwDmRsQDaTs/BFa8zfU9meSD47aI2BURD5H8By+0F/hGROyIiG0RsTYiHoyIrRGxCbiZ5IMGST1Jvsl/LX38M8Aj5TUsqTNwPvD5iNgSEauAHwCXFjxsSUTcFckxq1+RfGB3ruzKRcTdEbEpInaQfNANl9Smss8v8BHgzxFxb7qd1kbE9HRv7xLgxrSdxcCtJF9kKmv/+4bky8BeYIikZhGxPH3vlOdi4OaIWBcRS4HbCuadQBIS/xkROyNiEXAXb23bXUB/ScURsTkinj+Cegt9FHgsIh6LiL0R8RQwleQ9etD6pdvu0YhYGIm/A0+ShEVlXAI8GhFPpe/9/yH50nRqwWNui4jSiFhH8t4bUbDOXYFeaR2TIsInRi3DAZVjETEbmAjcUGZWCcmeRqElJN8g91laziJXFtzeVs79luntXsD1affDeknrSb4Vl5SzzJLCttL/ZOW1XRklwBtl/qOWXdbqiNi+746k5pJ+lnZnbQSeAdqmH9YlwJsRsaXg+WW32z69SL7JLi9Y55+R7Entsz94I2JrerMllSCpgaRbJC1M61yczio+xNMq0gNYWM70Yt7aC92n7PvicApfyy0kH8JXkWyXRyUNquB5B7wPytTQi6SrrPD99BXeCvcrSPZG5ivprh5zBPUW6gV8qEw7p5MEwUHrByDpfEnPp91s60nCrLKvyQH/DyNib7r8wu1d+GVtK2+9X75Hsrf1ZNq1WPb/uOGAqg2+QbJHU/imLyX5z1ioJ/BGwf2qfBtbSvJtuG3BX/N0T62s5SQfmEBy8LnwPkkXSPOC+10O0e5yoFu6jH16lHlM2fW6HhgInBQRrUm68SDpslkOtFPBaEiS7VSepSR7icUF69w6Io6r4PFlHW57fxgYR9J124ake21fnXBk22kpSbdUWWtIvpkXvjcK3xeVaeOA9YiIJyLiXJIP+fkkez7lOeB9wIHbeSnwWpn3U6uIuCBt49WIuIzky8B3gQfKvGYVKbvNlwK/KdNOi4i4pbznSGoCPEiy59M5ItoCj/HWa3K41/SA/4cF7/03KnzGvgUne7jXR0Rfkp6P6yS953DPq28cUDkXEQuA3wPXFEx+DDhG0oclNZR0CTCYZG/raLgLuErSSUq0kDRaUqtyHvsocJyk96cH26/hwA++6cCZSn5z1Aa48RDtTgH2AFen6zUOOPEwtbYi2ftbL6k9SaADEBFLSLp4vimpsaTTObAblILHLifp3rlVUmtJRUoGkbzrMO3vs5Lk2Mqh6txBckykOfBfZeZPB96f7hH2J9mrqMjvgHMkXZxupw6SRqRdj+OBmyW1ktQLuA7Yd1D/SF4LJHVOBwG0SGvfTPL6lGc8cKOSQSvdgc8VzHsB2KhkcEuzdG9yiKQT0nY+KqljugeyPn1OZYb+l93mvwXGSjovbaOpkoEV3St4fmOS44Grgd1KBr28t8zyOxyiG3Y8MFrSeyQ1IvmytAN47nCFKxmE1D8NtY0k61vlnzvUNQ6o2uE/SQ7cAxARa4ExJP8h1pIcnB0TEWuORmMRMZVkr+12ksEXC0gO2pf32DXAh0gOkq8FBgDPFsx/iiRgZ5IcKK8wRCNiJ8nAiCtIPqg+mj5+xyHK/SFJv/8a4Hng8TLzP0wy2GMdSXj9+hDL+heSD625JOv9AAd2Dx3Kj4APKhnFdls5839N0h30Rrr8ssdZfkAyIGQlyfGt31XUUES8TtIVdT3Jek0HhqezP0eyp7QImAz8H3B3+rxKvxaporSN0rSddwGfreCx30zX7zWSoP9NQb17SL4YjEjnrwF+TrInCTAKmCNpM8l2vLSwG/cQvgN8Ne3O+0J67GscSffhapI9qi9SwedceszyGpKgeZPkvTKhYP584F5gUdpGSZnnv0zyHv1xuk5jgbHp+/hwBgB/Jgn9KcBPIuLpSjyvXtk3AskslyT9A/hpRPwy61rMrGZ5D8pyRdK7JHVJu64+Dgzj4L0iM6sH/Et8y5uBJF0uLUlGqn0wPT5kZvWMu/jMzCyX3MVnZma5lOsuvuLi4ujdu3fWZZiZWTWaNm3amogoe8acfAdU7969mTp1atZlmJlZNZJU7hle3MVnZma55IAyM7NcckCZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHIp1z/Uraon56ygdP02Th9QTL+OLTnwQq1mZpZndTqgnpizkgdfWgZA59ZNOK1fMaf2L+a0/h3o2qZZxtWZmdmh5Pps5iNHjoyqnupo6bqtPLtgDZMXrGHKwrWs3ZJc7LJvxxac1q+Y0/oXc0rfDrRp3uholGxmZkdI0rSIGHnQ9LoeUIX27g3mr9jEcwuTwHrhtXVs3bmHIsHQbm04tX8xp/cv5p292tG0UYOj1q6ZmVXMAVWOnbv3MmPZeia/uobnFq7hn6+vZ/feoHHDIkb2asdp/ZM9rKHd2tCgyMevzMyqgwOqEjbv2M2Lr63b3yU4f8UmAFo1bcgpfTvsD6x+HVt4wIWZ2VFSUUDV6UESR6plk4a8e1An3j2oEwBrNu/guYVreS4NrCfnrgTSARf9i/cfw+rSpmmWZZuZ1UnegzoCr6/dyrML3xpwsS4dcNGvY4v9e1cn9+1Am2YecGFmVlnu4jvK9u4N5q3YyHML1u4fcLFtVzrgontbTuuXdAl6wIWZ2aE5oKrZzt17mb50PZMXrOG5BWv459L17NkbNGlYxMje7fZ3CQ7xgAszswM4oGrY5h27eeG1tUx+dS3PLXxrwEXrpg05pd9bAy76FnvAhZnVbx4kUcNaNmnI2YM6c/agzgCs3rSD5xau2d8l+MScZMBFl9ZN07BKQqtzaw+4MDMD70FlIiJ4fd3WtDsw2cN6c+suAPp3arn/+NXJ/TrQuqkHXJhZ3eYuvhzbuzeYu3xjeoaLtbxYMOBiWPe2yd5Vv2KO94ALM6uDHFC1yI7de/jn6+v3//5qxrIN+wdcnNC7/f4uweNKPODCzGo/B1Qttmn7Ll54bd3+LsGXVyYDLto0a5Se4SLpEuzjARdmVgt5kEQt1qppI95zbGfec2wy4GLVpu1MWbg2PYfgWh6fswKArm0KBlz0K6aTB1yYWS3mPahaLiJYsjYdcLEwCaz16YCLAZ1a7h/OflLf9h5wYWa55C6+emLfgIvJC9bw7II1vLh4Hdt37d0/4OL0/sW8e1BHju/Zzt2BZpYLmQeUpIuA0UAn4I6IePJwz3FAVd2O3Xt4acn6/dfAmpkOuOjerhkXDi9h3IhuDOzSKusyzaweq5aAknQ3MAZYFRFDCqaPAn4ENAB+HhG3FMxrB/xPRFxxuOU7oI6+jdt38dSclUyYUcrkBWvYszcY2LkVF44o4cLhJfRo3zzrEs2snqmugDoT2Az8el9ASWoAvAKcCywDXgQui4i56fxbgd9FxEuHW74Dqnqt2byDx2Yt5+HppUxb8iYA7+zVjnEjSrhgaFeKWzbJuEIzqw+qrYtPUm9gYkFAnQLcFBHnpfdvTB96S/r3VET8+RDLuxK4EqBnz57vXLJkSZXqs8pZum4rE2aU8vD0N3hl5WYaFInT+xczbkQJ7z2uCy2beMCnmVWPmgyoDwKjIuJT6f2PASeR7FV9nGSPanpE/PRwy/YeVDbmr9jIw9NLmTC9lDfWb6NJwyLOGdyZC4eXcNbAjjRp6LNZmNnRU5O/gypvaFhExG3AbdXQnh1lg7q0ZtCo1nzpvIG89PqbPDy9lIkzl/PozOW0btqQ84d0ZdyIEk7q28FnsjCzalMdAbUM6FFwvztQWg3tWDWTxDt7teedvdrztTGDeXbBGiZML2XizFJ+P3UpnVo1YezwEsaNKGFotzYetm5mR1V1BNSLwABJfYA3gEuBD1dDO1aDGjUo4qyBnThrYCe27dzDX+avZML0Un4zZQm/mPwafYpbcOHwEi4cUUK/ji2zLtfM6oCqjuK7FzgLKAZWAt+IiF9IugD4Ickw87sj4ua3s3wfg8q/DVt38ficZCTglEVriYAh3Vozbng3xg4voUsbn27JzA4t8x/qvh0OqNpl5cbtPDKjlAkzSpm5bAMSnNSnPeNGdOP8IV1o27xx1iWaWQ45oKxGLVq9mQkzkpGAi9ZsoVED8a5jOnHhiBLOObYTzRt72LqZJRxQlomIYE7pRh6e/gYTZpSycuMOmjduwHsHd2bciG6cPqCYRg2Ksi7TzDLkgLLM7dkbvPDaOibMeIPHZq1gw7ZdtGveiNHDujJuRDfe2bMdRR62blbvOKAsV3bs3sMzr6xhwoxSnpq7gu279tKtbTPGDk/OCXhs11Yetm5WTzigLLe27NjNU3NX8vD0N3jm1eQEtgM6tWTciBIuHN6Nnh18AluzuswBZbXC2s07eGz2CiZMf4MXFycnsH1Hz7aMG17C6GEldGzlE9ia1TUOKKt1lr25lUdmLGfCjFLmLd9IkeC0/sWMG9GN847rTCtfIdisTnBAWa32yspNTJheysMz3mDpum00bljEewZ1YtyIEs4a2ImmjXwCW7PaygFldUJE8M+l6/efE3DN5p20atKQUUO6MG5EN07p5xPYmtU2Diirc3bv2cuURWt5eHopj89eweYdu+nYqglj0mHrw7v7BLZmtYEDyuq07bv28Lf5q3h4eil/nb+KnXv20qtDc8alJ7Dt36lV1iWaWQUcUFZvbNi2iyfmrGDC9FKeW7iGvQGDu7Zm3IgSxg4voaRts6xLNLMCDiirl1Zt3M7EmclIwOlL1wNwYp/2jBtRwgVDutKuhU9ga5Y1B5TVe4vXbOGRGaX8cfobLFy9hYZF4l3HdExPYNuZFk18AluzLDigzFIRwdzlG5kwPbk0yPIN22naqIizB3VizLAS3j2wE80ae9i6WU1xQJmVY+/e4MXF63h01nIem7WCNZt30KxRA95zbBJWZw3s6N9YmVUzB5TZYezZG/zjtbVMnLmcx2evYN2WnbRo3IBzB3dm9LASzjymmCYNHVZmR5sDyuwI7PuN1aMzl/P4nBWs37qLVk0acu5xnRkzrCun9+9I44a+jpXZ0eCAMnubdu3Zy7ML1vDozOU8MWcFG7fvpnXThpx3XBfGDC/h1H4dfNFFsypwQJkdBTt372XygtVMnLGcp+auZNOO3bRr3ohRQ7owemgJJ/dtT0OHldkRcUCZHWXbd+1h0qtrmDizlD/PXcmWnXvo0KJxElbDunJSH58X0KwyHFBm1Wj7rj08/fIqJs5czl/mrWLbrj0Ut2zCBUO7MHpoV07o3d6XszergAPKrIZs27mHv85fxaOzkvMCbt+1l86tm3D+kK6MHd6Vd/Ro57AyK+CAMsvAlh27+cv8VUycUcrTr6xm5+69lLRpygVDuzJ6WFdG9GjrM65bveeAMsvYpu27+Mu8VUycWcozr6xh5569dGvbjDHDkrAa2s2XB7H6yQFlliMbtu3iqbkreXRmKZNeXcPuvUHP9s0ZPawro4d25biS1g4rqzccUGY5tX7rTp6cs5KJs5bz7II17Nkb9CluweihXRkzvCsDO7dyWFmd5oAyqwXWbdnJE3NWMHFmKVMWrmVvQL+OLRgzrIQxw7oyoLMvvGh1jwPKrJZZs3kHj89Owuofr60jAgZ2bpV0Aw7rSr+OLbMu0eyocECZ1WKrNm3nT7NW8OjM5by4JAmrY7u2TgZYDO1K7+IWWZdo9rY5oMzqiBUbtvPYrOU8Oms505a8CcCQbq0ZPTTpBuzRvnnGFZodGQeUWR30xvpt/GnWch6ZuZwZ6SXth3dvw5hhJVwwrCvd2jbLuEKzw3NAmdVxS9dt5bFZy5k4czmz3tgAwDt6tk3CamgXurZxWFk+OaDM6pEla7cwceZyHp25nLnLNwJwQu92jB7alQuGdqVT66YZV2j2FgeUWT21aPVmHp2ZHLOav2ITEpzYuz1jhnVl1JCudGzVJOsSrZ5zQJkZr67cxKNpN+CCVZspEpzctwNjhpUwakgX2rdonHWJVg85oMxsv4jglZWbeXRmKRNnLmfRmi00KBKn9uvAmGFdOe+4LrRt7rCymuGAMrNyRQTzlm9iYhpWr6/bSsMi8cnT+/DF8wb6cvZW7RxQZnZYEcGc0o38espixk9dxogebfnxZe/wb6usWlUUUP5qZGb7SWJItzb89weHc8eHj2fhqs2Mvm0Sj89ekXVpVg85oMysXKOHdeXRa86gd3ELrvrtNG6aMIcdu/dkXZbVIw4oM6tQzw7NeeCqU/nkaX2457nFfOB/n2Pxmi1Zl2X1hAPKzA6pccMivj52MHf9y0iWrtvGmB9P5pEZpVmXZfWAA8rMKuXcwZ157NozOKZzSz537z+58aFZbN/lLj+rPg4oM6u0bm2b8ft/PYWr3tWPe194nYvueJYFqzZnXZbVUQ4oMzsijRoUccP5g7jnEyewatMOLrx9Mg+9tCzrsqwOqrGAktRC0q8k3SXpIzXVrplVj7MGduKxa85gSLc2XDd+Bl+4fwZbd+7OuiyrQ6oUUJLulrRK0uwy00dJelnSAkk3pJPfDzwQEZ8GLqxKu2aWD13aNOX/PnUS17xnAA++tIwLb3+Wl1dsyrosqyOqugd1DzCqcIKkBsAdwPnAYOAySYOB7sDS9GE+smpWRzRsUMR15x7Db684ifVbd3Hh7ZO574XXyfNZaqx2qFJARcQzwLoyk08EFkTEoojYCdwHjAOWkYTUIduVdKWkqZKmrl69uirlmVkNOq1/MX+69gxO6N2eGx6axbX3TWfzDnf52dtXHceguvHWnhIkwdQNeAj4gKT/BR6p6MkRcWdEjIyIkR07dqyG8sysunRs1YRfffJEvvDeY5g4s5Qxt01idnp1X7MjVR0BpXKmRURsiYhPRMRnIuJ31dCumeVAgyJx9dkDuO/KU9i+ay/v/8lz/GbKYnf52RGrjoBaBvQouN8d8M/OzeqZE/u057Frz+DU/h342sNz+OzvXmLDtl1Zl2W1SHUE1IvAAEl9JDUGLgUmVEM7ZpZz7Vs05u6Pn8BXLhjEU3NXMvq2SUxfuj7rsqyWqOow83uBKcBAScskXRERu4GrgSeAecD4iJhT9VLNrDYqKhJXntmP8VedQgR86KfP8fNJi9zlZ4flCxaaWY3ZsHUXX3xgBk/OXck5x3biex8cTrsWvrR8fecLFppZ5to0b8TPPvZOvjF2MH9/ZTWjb5vE1MVlf6lilnBAmVmNksQnTuvDg585lYYNirjkzuf5ydML2Ls3v705lg0HlJllYlj3tky85nRGDenCfz/+Mpff8yJrNu/IuizLEQeUmWWmddNG3H7ZO7j5fUN4ftFaLvjRJKYsXJt1WZYTDigzy5QkPnJSL/742dNo2bQhH/n58/zwz6+wx11+9Z4DysxyYXBJax65+nQuGtGNH/75VT7683+wauP2rMuyDDmgzCw3WjRpyK0XD+e/PziMfy59k/N/NIlnXvFJo+srB5SZ5YokLh7Zg0euPp0OLRvz8V++wPeemM/uPXuzLs1qmAPKzHJpQOdWPPxvp3PJyB7c8beFXHbX8yzfsC3rsqwGOaDMLLeaNW7ALR8Yxo8uHcHc0o1c8KNJ/HX+yqzLshrigDKz3Bs3ohuPfO50urRpxifvmcrNj85l5253+dV1DigzqxX6dmzJHz57Kh87uRd3TXqNi382haXrtmZdllUjB5SZ1RpNGzXgWxcN4ScfOZ6FqzYz+rZJPD57edZlWTVxQJlZrXPB0K48es0Z9C5uwVW/fYlvPDybHbv3ZF2WHWUOKDOrlXp2aM4DV53KFaf34VdTlvCB/32OxWu2ZF2WHUUOKDOrtRo3LOJrYwZz17+MZOm6bYz58WQmzCjNuiw7ShxQZlbrnTu4M49dewbHdG7JNff+kxsfmsX2Xe7yq+0cUGZWJ3Rr24zf/+spfOasftz7wutcdMezLFi1OeuyrAocUGZWZzRqUMSXRw3ink+cwKpNOxj748k8OG1Z1mXZ2+SAMrM656yBnfjTtWcwrHsbrr9/BtePn8HWnbuzLsuOkAPKzOqkzq2b8rtPncQ17xnAQ/9cxtgfT2b+io1Zl2VHwAFlZnVWwwZFXHfuMfzuipPYuH03425/lvteeJ0IXwyxNnBAmVmdd2r/Yh675gxO6N2eGx6axbX3TWfT9l1Zl2WH4YAys3qhY6sm/PqTJ/KF9x7DxJmljP3xZGa/sSHrsuwQHFBmVm8UFYmrzx7AfVeewvZde3n/T57j11MWu8svpxxQZlbvnNinPY9dewan9e/A1x+ew2d++xIbtrnLL28cUGZWL7Vv0ZhffPwEvnLBIP48byWjb5vE9KXrsy7LCjigzKzeKioSV57Zj/FXnUIEfPB/n+Pnkxa5yy8nHFBmVu8d37Mdj11zBmcP6sS3H53Hp341lTe37My6rHrPAWVmBrRp3oiffeyd3DR2MJNeXcMFt01i6uJ1WZdVrzmgzMxSkrj8tD48+JlTadywiEvufJ47/raAvXvd5ZcFB5SZWRlDu7dh4udO5/whXfjeEy/z8V++wJrNO7Iuq95xQJmZlaNV00b8+LJ38F/vG8o/XlvH+T+axMsrNmVdVr3igDIzq4AkPnxSTx7+t9OICK6975/s2O0LIdYUB5SZ2WEc27U1t7x/GPNXbOKHf34163LqDQeUmVklnDO4M5eM7MHP/r6QaUs8uq8mOKDMzCrpq2OOpWubZlw3fgZbdvgCiNXNAWVmVkmtmjbi1ouH8/q6rXznT/OyLqfOc0CZmR2Bk/t24IrT+vDb51/n76+szrqcOs0BZWZ2hL5w3kAGdGrJlx6YwYatPgt6dXFAmZkdoaaNGvD9i0ewdvNOvj5hdtbl1FkOKDOzt2Fo9zZ87uwBPDy9lIkzS7Mup05yQJmZvU2ffXc/hndvw1f/OJtVG7dnXU6d44AyM3ubGjUo4taLR7Bt5x5ueGiWryN1lDmgzMyqoH+nlnx51CD+On8Vv39xadbl1CkOKDOzKrr81N6c0rcD35o4l9fXbs26nDqjRgNK0kWS7pL0sKT31mTbZmbVpahI/M/FwymS+ML9M9jj60cdFZUOKEl3S1olaXaZ6aMkvSxpgaQbDrWMiPhjRHwauBy45G1VbGaWQ93aNuMbFx7HC4vXcffk17Iup044kj2oe4BRhRMkNQDuAM4HBgOXSRosaaikiWX+OhU89avp88zM6owPHN+Ncwd35ntPvOxrRx0FlQ6oiHgGKHsK3xOBBRGxKCJ2AvcB4yJiVkSMKfO3SonvAn+KiJfKa0fSlZKmSpq6erVPI2JmtYckvvP+obRq2pDrxk9n5+69WZdUq1X1GFQ3oHDYyrJ0WkU+B5wDfFDSVeU9ICLujIiRETGyY8eOVSzPzKxmFbdsws3vG8qc0o38+K++dlRVNKzi81XOtAqPDkbEbcBtVWzTzCzXRg3pwgeO785Pnl7I2YM68Y6e7bIuqVaq6hm7dskAACAASURBVB7UMqBHwf3ugM/5YWb13jcuHEznVk24fvwMtu30ZeLfjqoG1IvAAEl9JDUGLgUmVL0sM7ParXXTRnzvQ8NZtGYL3318ftbl1EpHMsz8XmAKMFDSMklXRMRu4GrgCWAeMD4i5lRPqWZmtctp/Yu5/NTe3PPcYp5dsCbrcmod5fncUSNHjoypU6dmXYaZ2du2beceRv94Ett27uHxz59Jm2aNsi4pdyRNi4iRZaf7VEdmZtWoWePk2lGrNu3gm4+4g+lIOKDMzKrZiB5t+bez+vHQS2/w+OzlWZdTazigzMxqwNVnD2BIt9Z85Q+zWb1pR9bl1AoOKDOzGtC4YRHfv3gEm3fs5it/8LWjKsMBZWZWQ47p3IovvncgT81dyQPTlmVdTu45oMzMatAnT+/DiX3a881H5rLsTV876lAcUGZmNahBkbj1Q8OJCL5w/wz2+tpRFXJAmZnVsB7tm/P1sYN5ftE67nlucdbl5JYDyswsAxeP7MHZgzrx3cfns2CVrx1VHgeUmVkGJHHLB4bSvHEDrhs/g117fO2oshxQZmYZ6dSqKTe/bygzl23gjr8tyLqc3HFAmZll6IKhXbloRAm3/3UBM5etz7qcXHFAmZll7JsXDqG4ZROuGz+D7bt87ah9HFBmZhlr07wR//3BYSxYtZnvPfFy1uXkhgPKzCwHzjymIx87uRe/mPwaUxauzbqcXHBAmZnlxI0XDKJ3h+Z84f4ZbNq+K+tyMueAMjPLieaNG3LrxSNYvmEb35o4N+tyMueAMjPLkXf2asdV7+rH+KnLeGruyqzLyZQDyswsZz5/zjEc27U1Nz40k7Wb6++1oxxQZmY5k1w7ajgbt+3mP/4wu95eO8oBZWaWQ8d2bc117z2Gx+es4I/T38i6nEw4oMzMcurTZ/RlZK92fP3hOZSu35Z1OTXOAWVmllMNisStFw9nz97gSw/MrHfXjnJAmZnlWK8OLfiP0ccyecEafvuPJVmXU6McUGZmOffhE3vyrmM68l+PzWPR6s1Zl1NjHFBmZjknif/+4DCaNEyuHbW7nlw7ygFlZlYLdG7dlG9dNITpS9fz078vzLqcGuGAMjOrJS4cXsKYYV354Z9fZfYbG7Iup9o5oMzMapFvjRtC+xaNub4eXDvKAWVmVou0a9GY735gGC+v3MQPnnol63KqlQPKzKyWefegTlx2Yk/unLSIF15bl3U51cYBZWZWC3119LH0aNec6++fzuYdu7Mup1o4oMzMaqEWTRpy68XDWfbmNm5+dF7W5VQLB5SZWS11Qu/2XHlGX+594XX+Nn9V1uUcdQ4oM7Na7N/PPYaBnVvxpQdn8uaWnVmXc1Q5oMzMarGmjRrw/UuGs37rTr728OysyzmqHFBmZrXccSVt+Pw5xzBx5nImzCjNupyjxgFlZlYH/OuZfXlHz7Z87Y+zWbFhe9blHBUOKDOzOqBhgyJu/dBwduzew5cfnFknLhPvgDIzqyP6dmzJVy44lr+/spr/e+H1rMupMgeUmVkd8tGTenHGgGK+PXEei9dsybqcKnFAmZnVIUVFybWjGjYQ198/gz21+DLxDigzszqma5tm/Oe445i25E3ufGZR1uW8bQ4oM7M66KIR3Th/SBd+8NQrzFu+Mety3hYHlJlZHSSJb180hNbNGvHvv5/Ojt2179pRNRpQklpImiZpTE22a2ZWH3Vo2YRb3j+U+Ss28aM/v5p1OUesUgEl6W5JqyTNLjN9lKSXJS2QdEMlFvVlYPzbKdTMzI7cOYM7c/HI7vz07wuZtqR2XTuqsntQ9wCjCidIagDcAZwPDAYukzRY0lBJE8v8dZJ0DjAXWHkU6zczs8P42pjBdG3TjOvHz2Drztpz7ahKBVREPAOUjd4TgQURsSgidgL3AeMiYlZEjCnztwp4N3Ay8GHg05J8/MvMrAa0atqIWy8ezpJ1W/nOY/OzLqfSqhIS3YClBfeXpdPKFRH/ERGfB/4PuCsi9pb3OElXSpoqaerq1aurUJ6Zme1zct8OfPK0Pvzm+SX8/ZXa8dlalYBSOdMO+4uwiLgnIiYeYv6dETEyIkZ27NixCuWZmVmhL543kP6dWvKlB2awYeuurMs5rKoE1DKgR8H97kDdOc+7mVkd07RRA35w8QjWbt7JNybk/9pRVQmoF4EBkvpIagxcCkw4OmWZmVl1GNq9DZ87ewB/nF7KozOXZ13OIVV2mPm9wBRgoKRlkq6IiN3A1cATwDxgfETMqb5SzczsaPjsu/sxrHsbvvrHWazamN9rR1V2FN9lEdE1IhpFRPeI+EU6/bGIOCYi+kXEzdVbqpmZHQ2NGhTx/YuHs3XnHm54aFZurx3lod5mZvVQ/06t+PKoQfx1/irGT116+CdkwAFlZlZPXX5qb07p24H/fGQuS9dtzbqcgzigzMzqqaIi8b0PDUMS14/P37WjHFBmZvVY93bN+cbYwbyweB13T34t63IO4IAyM6vnPvjO7pw7uDPfe/JlXlm5Kety9nNAmZnVc5L4zvuH0qpJQ/7999PZubvcM9HVOAeUmZlR3LIJN79vKHNKN3L7X/Nx7SgHlJmZATBqSBfef3w37nh6IdOXrs+6HAeUmZm95Rtjj6NzqyZcN34623Zme5l4B5SZme3Xplkjvveh4SxavYXvPp7ttaMcUGZmdoDT+hdz+am9uee5xTy7YE1mdTigzMzsIF8eNYi+xS344v0z2Lg9m2tHOaDMzOwgzRo34PuXjGDlph18c8LcTGpwQJmZWblG9GjLv53VjwdfWsbjs1fUePsOKDMzq9DVZw/guJLW/McfZrFm844abdsBZWZmFWrcsIgfXDKCTTt2c2MNXzvKAWVmZod0TOdWfPG9A3lq7koefOmNGmvXAWVmZof1ydP7cGKf9nxzwhyWvVkz145yQJmZ2WE1KBK3fmg4eyP44v0z2VsD145yQJmZWaX0aN+cr40ZzJRFa7nnucXV3p4DyszMKu2SE3pw9qBOfPfx+SxYtbla23JAmZlZpUnilg8MpXnjBlw3fjq79lTftaMcUGZmdkQ6tWrKze8byqw3NjBl4dpqa6dhtS3ZzMzqrAuGduWpfz+T/p1aVVsb3oMyM7O3pTrDCRxQZmaWUw4oMzPLJQeUmZnlkgPKzMxyyQFlZma55IAyM7NcckCZmVkuOaDMzCyXVJNXRzxSklYDS6q4mGJgzVEopy7xNjmYt8nBvE0O5m1yoKO1PXpFRMeyE3MdUEeDpKkRMTLrOvLE2+Rg3iYH8zY5mLfJgap7e7iLz8zMcskBZWZmuVQfAurOrAvIIW+Tg3mbHMzb5GDeJgeq1u1R549BmZlZ7VQf9qDMzKwWckCZmVku1emAkjRK0suSFki6Iet6sibpbkmrJM3OupY8kNRD0t8kzZM0R9K1WdeUNUlNJb0gaUa6Tb6ZdU15IamBpH9Kmph1LXkgabGkWZKmS5paLW3U1WNQkhoArwDnAsuAF4HLImJupoVlSNKZwGbg1xExJOt6siapK9A1Il6S1AqYBlxUz98jAlpExGZJjYDJwLUR8XzGpWVO0nXASKB1RIzJup6sSVoMjIyIavvhcl3egzoRWBARiyJiJ3AfMC7jmjIVEc8A67KuIy8iYnlEvJTe3gTMA7plW1W2IrE5vdso/aub32KPgKTuwGjg51nXUp/U5YDqBiwtuL+Mev7hYxWT1Bt4B/CPbCvJXtqVNR1YBTwVEfV+mwA/BL4E7M26kBwJ4ElJ0yRdWR0N1OWAUjnT6v03QTuYpJbAg8DnI2Jj1vVkLSL2RMQIoDtwoqR63R0saQywKiKmZV1LzpwWEccD5wP/lh5COKrqckAtA3oU3O8OlGZUi+VUepzlQeB3EfFQ1vXkSUSsB54GRmVcStZOAy5Mj7ncB5wt6bfZlpS9iChN/10F/IHksMpRVZcD6kVggKQ+khoDlwITMq7JciQdEPALYF5EfD/revJAUkdJbdPbzYBzgPnZVpWtiLgxIrpHRG+Sz5G/RsRHMy4rU5JapAOLkNQCeC9w1EcH19mAiojdwNXAEyQHv8dHxJxsq8qWpHuBKcBAScskXZF1TRk7DfgYyTfi6enfBVkXlbGuwN8kzST5kvdURHhYtZXVGZgsaQbwAvBoRDx+tBups8PMzcysdquze1BmZla7OaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlksOKDMzyyUHlFWapLMkLcu6jvKUrU3SHElnZVhSnSUpJPU/ysvcLKnv0VzmEbZ/hqSXs2rfyueAqsUkLZa0Lf3PvVLSL9Orw9Z7EXFcRDxd1eVIuskXp6t+EdEyIhYBSLpH0rers72yIRsRkyJiYHW2aUfOAVX7jY2IlsDxwAnAVzOup8okNcy6hrqsrm/fur5+9YkDqo6IiDeAPwFDJLWTNFHSaklvpre773uspMslLZK0SdJrkj5S3jIlNUu/zb4paS5JABbOL5H0YNrOa5Kuqag+SR0kPSJpo6QXJX1b0uSC+SHp3yS9CryaTvuRpKXpc6ZJOuMIalss6Zz0dpGkGyQtlLRW0nhJ7dN5vdO2Py7pdUlrJP1HOm8U8BXgknQvdUYF67Zv2ZskzZX0voJ5B+yBFbRX7oeopB6SHkq36VpJtxesw1clLZG0StKvJbVJ5x3U9Vpm/W+S9ICk30raCFwu6URJU9Ntu1JShVcUlvRFScsllUr6ZJl5TST9T7rtVkr6qZIr8SKpOH3vrZe0TtIkSeV+5uzbo5F0JfAR4EvpNn8knV/he+0Q6zclbXu5pNuVXFkbSc+kT52RtnFJ2W0o6VhJT6fPnyPpwoJ590i6Q9Kj6Wv+D0n90nmS9IP0NdogaaakIRVtWzuMiPBfLf0DFgPnpLd7AHOAbwEdgA8AzYFWwP3AH9PHtQA2AgPT+12B4ypY/i3AJKB9uvzZwLJ0XhEwDfg60BjoCywCzqtgWfelf82BwcBSYHLB/ACeSttqlk77aLouDYHrgRVA08PVVs62+TzwPNAdaAL8DLg3ndc7bfsuoBkwHNgBHJvOvwn47WFehw8BJek2uQTYAnQt7/kF7TUsZzkNgBnAD9LXqSlwejrvk8CCdDu3BB4CfpPOO6tw3ctZ/5uAXcBFaY3NSK6s/LF0fkvg5ArWbRSwEhiS1vR/af390/k/BCakr0Mr4BHgO+m87wA/BRqlf2eQXiS1nHYKl3kP8O2CeYd8r1Wwfu8ETiZ57/Qmuar258trr+w2TGtdQPLlpDFwNrCJt/7P3AOsA05Ml/874L503nlprW0BAcfuey/47218xmVdgP+q8OIlH0KbgfXAEuAnpB/uZR43Angzvd0iffwHyntsmectAkYV3L+y4D/xScDrZR5/I/DLcpbTIP0AGVgw7dscHFBnH6aeN4Hhh6utYNvs+4CeB7ynYF7XtJ59H14BdC+Y/wJwaXr7Jg4TUOXUOR0YV97zOXRAnQKsrmDeX4DPFtwfWLAO+z9cK1j/m4Bnysx/BvgmUHyYdbkbuKXg/jFp/f3TD+AtQL8y6/Baevs/gYcpCIJDtHOogDrke6289Stn+Z8H/lBee+n9/duQJEhXAEUF8+8Fbiqo7+cF8y4A5qe3zwZeIQnHokPV5L/D/7mLr/a7KCLaRkSviPhsRGyT1FzSz9LuoI0kH0ZtJTWIiC0k3/KvApan3RSDKlh2Ccmezj5LCm73AkrSLpD1ktaTfOPsXM5yOpJ8kBYua2k5jztgmqTrJc1Lu0rWA22A4krUVlYv4A8Fdc4D9pSpdUXB7a0kexWVIulfJE0vWP6QgjqPRA9gSUTsLmdeCQeu4xKSbVre9i5P2e19BUnYzFfS5Tqmgucdajt3JNkjnlaw7o+n0wG+R7In8qSSLuUbKllrWZV5r5V97xyTdi+uSP8P/BeVf01KgKURsbdg2hKgW8H9ct8vEfFX4HbgDmClpDslta5ku1aGA6puup7kG/ZJEdEaODOdLoCIeCIiziXZk5hP0r1VnuUkH5r79Cy4vZTkm3Lbgr9WEXFBOctZDewm6WLbp0c5j4t9N5Qcb/oycDHQLiLaAhv2rcNhaitrKXB+mVqbRnLc7nDiUDMl9SLZflcDHdI6ZxfUuYXkQ3yfLoeps2cFx6dKST6o9+lJsk1Xlm1DUgPeColy1yMiXo2Iy4BOwHeBByS1KKfdQ23nNcA2ki7ifdu1TSSDdoiITRFxfUT0BcYC10l6TwXrXmGtVO69VvY5/0vy3h6Q/h/4Cm+9JodTCvQoc7ysJ1CZ9wsRcVtEvBM4juRLwBcr2a6V4YCqm1qRfHCsVzIY4Bv7ZkjqLOnC9MNoB0kX4Z4KljMeuFHJoIvuwOcK5r0AbJT0ZSUDFhpIGiLphLILiYg9JMdMbkr37gYB/1KJddhN2uUl6etA4TfRQ9VW1k+Bm9MwQVJHSeMO0/4+K4HeFR3cJ+kyjbROJH2CZA9qn+nAmZJ6KhnUcOMh2nqBJBBukdRCUlNJp6Xz7gX+XVIfJT8l+C/g9+ne1itAU0mjJTUiGcnZ5FArJemjkjqmewnr08nlvQ/Gkww6GCypOQXvpfS5dwE/kNQpXW43Seelt8ekAx9EctxzTwVtlLWS5DhT4Xap1HutQKu0zc3p++0zh2mj0D9IQv9Lkhop+T3dWJJjqIck6QRJJ6WvwxZgO5VbZyuHA6pu+iHJgeI1JIMDHi+YV0Syh1VKcqD3XcBnK1jON0m6Nl4DngR+s29GGjpjSY5vvZa29XOSbrjyXJ3OW5Eu516SgKzIEySjEl9Ja9jOgd04FdZWjh+RHMh/UtImkm1y0iEeX+j+9N+1kl4qOzMi5gK3kgw6WAkMBZ4tmP8U8HtgJsnB84kVNVSwTfsDrwPLSLpjITkW9BuS7trXSLbH59LnbSB5DX9O8i1/S/rcQxkFzJG0mWT7XBoR28up6U8k76e/knTX/bXMQ76cTn8+7Ur7M8neO8CA9P5mku3zk6jcb9N+AQxOu/P++DbeawBfAD5MMrjhLpLXoNBNwK/SNi4us847gQuB89O2fgL8S0TMr0TtrdP23iR5f64F/qcSz7NyKOKQPRhm1ULSd4EuEfHxrGsxs3zyHpTVCEmDJA1LfydyIslB+j9kXZeZ5Zd/cW01pRVJt14JsIqkW+zhTCsys1xzF5+ZmeWSu/jMzCyXct3FV1xcHL179866DDMzq0bTpk1bExFlf7uX74Dq3bs3U6dOzboMMzOrRpLKPROMu/jMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrlUYwElqa+kX0h6oKbaNDOz2qtKASXpbkmrJM0uM32UpJclLdh3Fc2IWBQRV1SlPTMzqz+qugd1D8l1ZfZLr+Z5B8m1VAYDl0kaXMV2zMysnqlSQEXEMyQXvSt0IrAg3WPaSXIVyspevRRJV0qaKmnq6tWrq1KemZnVYtVxDKobB175dBnQTVIHST8F3iGpwsteR8SdETEyIkZ27HjQqZnMzKyeqI5z8amcaRERa4GrqqE9MzOrg6pjD2oZ0KPgfnegtBraMTOzOqw6AupFYICkPpIaA5cCE6qhHTMzq8OqOsz8XmAKMFDSMklXRMRu4GrgCWAeMD4i5hzhcsdKunPDhg1VKc/MzGqxXF/yfeTIkeHrQZmZ1W2SpkXEyLLTfaojMzPLJQeUmZnlkgPKzMxyKZcB5UESZmaWy4CKiEci4so2bdpkXYqZmWUklwFlZmbmgDIzs1xyQJmZWS45oMzMLJccUGZmlku5DCgPMzczs1wGlIeZm5lZLgPKzMzMAWVmZrnkgDIzs1xyQJmZWS45oMzMLJdyGVAeZm5mZrkMKA8zNzOzXAaUmZmZA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlku5DCj/UNfMzHIZUP6hrpmZ5TKgzMzMHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS7lMqB8JgkzM8tlQPlMEmZmlsuAMjMzc0CZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlku5DCifzdzMzHIZUD6buZmZ5TKgzMzMHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlksOKDMzyyUHlJmZ5ZIDyszMcskBZWZmueSAMjOzXHJAmZlZLjmgzMwsl3IZUL7ku5mZ5TKgfMl3MzPLZUCZmZk5oMzMLJccUGZmlksOKDMzyyUHlJmZ5ZIDyszMcskBZWZmueSAMjOzXHJAmZlZLjmgzMwslxxQZmaWSw4oMzPLJQeUmZnlkgPKzMxyyQFlZma55IAyM7NcckCZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlksNa6ohSS2AnwA7gacj4nc11baZmdU+VdqDknS3pFWSZpeZPkrSy5IWSLohnfx+4IGI+DRwYVXaNTOzuq+qe1D3ALcDv943QVID4A7gXGAZ8KKkCUB3YFb6sD1VbLdSvvnIHOaWbqyJpszM6p3BJa35xtjjqm35VdqDiohngHVlJp8ILIiIRRGxE7gPGEcSVt0P166kKyVNlTR19erVVSnPzMxqseo4BtUNWFpwfxlwEnAbcLuk0cAjFT05Iu4E7gQYOXJkVKWQ6kx2MzOrXtURUCpnWkTEFuAT1dCemZnVQdUxzHwZ0KPgfnegtBraMTOzOqw6AupFYICkPpIaA5cCE6qhHTMzq8OqOsz8XmAKMFDSMklXRMRu4GrgCWAeMD4i5hzhcsdKunPDhg1VKc/MzGoxRVRpHEK1GjlyZEydOjXrMszMrBpJmhYRI8tO96mOzMwslxxQZmaWSw4oMzPLJQeUmZnlUi4DyqP4zMwslwEVEY9ExJVt2rTJuhQzM8tILgPKzMzMAWVmZrnkgDIzs1xyQJmZWS7lMqA8is/MzHIZUB7FZ2ZmuQwoMzMzB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1zKZUB5mLmZmeUyoDzM3MzMchlQZmZmDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS7lMqD8Q10zM8tlQPmHumZmlsuAMjMzc0CZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1zKZUD5VEdmZpbLgPKpjszMLJcBZWZm5oAyM7NcckCZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS7lMqB8slgzM8tlQPlksWZmlsuAMjMzc0CZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJccUGZmlksOKDMzyyUHlJmZ5ZIDyszMcskBZWZmueSAMjOzXMplQPmS72ZmlsuA8iXfzcwslwFlZmbmgDIzs1xyQJmZWS45oMzMLJccUGZmlksOKDMzyyUHlJmZ5ZIDyszMcskBZWZmueSAMjOzXHJAmZlZLjmgzMwslxxQZmaWSw4oMzPLJQeUmZnlkgPKzMxyyQFlZma55IAyM7NcckCZmVkuOaDMzCyXHFBmZpZLDigzM8slB5SZmeWSA8rMzHLJAWVmZrnkgDIzs1xyQJmZWS45oMzMLJdqLKAk9ZX0C0kP1FSbZmZWe1UqoCTdLWmVpNllpo+S9LKkBZJuONQyImJRRFxRlWLNzKz+aFjJx90D3A78et8ESQ2AO4BzgWXAi5ImAA2A75R5/icjYlWVqzUzs3qjUgEVEc9I6l1m8onAgohYBCDpPmBcRHwHGPN2C5J0JXAlQM+ePd/uYszMrJaryjGobsDSgvvL0mnlktRB0k+Bd0i6saLHRcSdETEyIkZ27NixCuWZmVltVtkuvvKonGlR0YMjYi1wVRXaMzOzeqQqe1DLgB4F97sDpVUrx8zMLFGVgHoRGCCpj6TGwKXAhKNTlpmZ1XeVHWZ+LzAFGChpmaQrImI3cDXwBDAPGB8Rc45GUZLGSrpzw4YNR2NxZmZWCymiwsNGmRs5cmRMnTo16zLMzKwaSZoWESPLTvepjszMLJccUGZmlksOKDMzy6VcBpQHSZiZWa4HSUhaDSyp4mKKgTVHoZy6xNvkYN4mB/M2OZi3yYGO1vboFREHnToo1wF1NEiaWt7okPrM2+Rg3iYH8zY5mLfJgap7e+Syi8/MzMwBZWZmuVQfAurOrAvIIW+Tg3mbHMzb5GDeJgeq1u1R549BmZlZ7VQf9qDMzKwWckCZmVku1emAkjRK0suSFki6Iet6sibpbkmrJM3OupY8kNRD0t8kzZM0R9K1WdeUNUlNJb0gaUa6Tb6ZdU3/397dvNgUx3Ecf3+aRmmQjTTNVWMhGws0zWbKQsjDhCXFStlQZKH8E/IHsBGRGkoUppCmPEwzBnlI0pRp1CwkZiV8LO5ZTB4W6k7f35z7fdXpnt/dnE+32/n+zvn+7j2lkNQh6amkG9FZSiBpUtILSROS5uVfvWvbg5LUAbwFttJ8uOIosN/2q9BggSRtAmaB87bXReeJJqkb6LY9LmkpMAbsbfPviIAu27OSOoER4JjtR8HRwkk6AfQBy2wPRueJJmkS6LM9bz9crvMVVD/wzvZ729+Ay8Ce4EyhbD8APkXnKIXtj7bHq/2vNJ9r1hObKpabZqthZ7XVcxb7HyQ1gF3A2egs7aTOBaoH+DBnPEWbn3zSv0nqBTYAj2OTxKtuZU0AM8Cw7bb/TIAzwEngZ3SQghi4I2lM0uH5OECdC5T+8l7bzwTTnyQtAYaAQyTqxAAAATZJREFU47a/ROeJZvuH7fVAA+iX1Na3gyUNAjO2x6KzFGbA9kZgB3CkaiG0VJ0L1BSwas64AUwHZUmFqvosQ8BF21ej85TE9mfgPrA9OEq0AWB31XO5DGyWdCE2Ujzb09XrDHCNZlulpepcoEaBNZJWS1oE7AOuB2dKBakWBJwDXts+HZ2nBJJWSFpe7S8GtgBvYlPFsn3KdsN2L83zyF3bB4JjhZLUVS0sQlIXsA1o+erg2hYo29+Bo8Btms3vK7ZfxqaKJekS8BBYK2lK0qHoTMEGgIM0Z8QT1bYzOlSwbuCepOc0J3nDtnNZdfrdSmBE0jPgCXDT9q1WH6S2y8xTSiktbLW9gkoppbSwZYFKKaVUpCxQKaWUipQFKqWUUpGyQKWUUipSFqiUUkpFygKVUkqpSL8AAA4e+R3F2wsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg(gnl_NF, gsl_NF, cl_NF )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.b On écrit l'algorithme de recherche linéaire (conditions de Wolfe)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Notation   \n",
    "$ x^{k}$  \n",
    "$g^{k}$ : $ \\nabla f(x) $  \n",
    "$ d^{k}$ : $ \\Delta x^{k} $  \n",
    "$ \\alpha^{(k)} $: $t^{k}$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- condition  \n",
    "$$ f\\left(x^{(k)}+\\alpha^{(k)} d^{(k)}\\right) \\leq f\\left(x^{(k)}\\right)+\\omega_{1} \\alpha^{(k)} g^{(k)^{\\top}} d^{(k)} $$  \n",
    "$ \\Leftrightarrow $  \n",
    "$$ f(x^{k}+t^{k} \\Delta x^{k})>f(x^{k})+ t^{k} \\nabla f(x^{k})^{T} \\Delta x^{k} $$  \n",
    "$$ \\left(\\nabla f\\left(x^{(k)}+\\alpha^{(k)} d^{(k)}\\right)\\right)^{\\top} d^{(k)} \\geq \\omega_{2} g^{(k)^{\\top}} d^{(k)} $$  \n",
    "where $ 0<\\omega_{1}<\\omega_{2}<1 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "cond1 = (1<3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Wolfe(alpha, x, D, Oracle):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy import inf\n",
    "    from numpy.linalg import norm\n",
    "\n",
    "    ##### Coefficients de la recherche lineaire\n",
    "    \n",
    "    omega_1 = 0.1\n",
    "    omega_2 = 0.9\n",
    "    \n",
    "    alpha_min = 0\n",
    "    alpha_max = inf\n",
    "    \n",
    "    ok = 0\n",
    "    dltx = 0.00000001\n",
    "\n",
    "    ##### Algorithme de Fletcher-Lemarechal\n",
    "    \n",
    "    # Appel de l'oracle au point initial\n",
    "    #print(Oracle)\n",
    "    res = Oracle(x)\n",
    "    critere = res[0]\n",
    "    gradient = res[1]\n",
    "    \n",
    "    # Initialisation de l'algorithme\n",
    "    alpha_n = alpha\n",
    "    xn = x\n",
    "    \n",
    "    # Boucle de calcul du pas\n",
    "    # xn represente le point pour la valeur courante du pas,\n",
    "    # xp represente le point pour la valeur precedente du pas.\n",
    "    while ok == 0:\n",
    "        \n",
    "        # Point precedent pour tester l'indistinguabilite\n",
    "        xp = xn\n",
    "        \n",
    "        # Point actuel\n",
    "        xn = x + alpha_n*D\n",
    "        #print(\"xn: \",xn)\n",
    "        \n",
    "        # Calculation of Wolfe conditions\n",
    "        \n",
    "        # f(x^k+t^k d^k) gradient_f(x^k+t^k d^k)\n",
    "        \n",
    "        res_n = Oracle(xn)\n",
    "        critere_n = res_n[0]\n",
    "        gradient_n = res_n[1]\n",
    "        \n",
    "        #print(\"critere_n\",critere_n)\n",
    "        #print(\"gradient_n\",gradient_n)\n",
    "        # condition 1\n",
    "        condition1 = (critere_n <= critere+omega_1*alpha_n*gradient.transpose()@D)\n",
    "        \n",
    "        # condition 2\n",
    "        #print(critere_n.transpose())\n",
    "        #print(D)\n",
    "        condition2 = (gradient_n.transpose()@D >= omega_2*gradient.transpose()@D)\n",
    "        \n",
    "        # ---> To be completed ...\n",
    "        # ---> To be completed ...\n",
    "        \n",
    "        # Test of Wolfe conditions\n",
    "        #\n",
    "        # - If both Wolfe conditions are true,\n",
    "        # set ok = 1: we then exit the while loop\n",
    "        if condition1 and condition2:\n",
    "            \n",
    "            ok = 1\n",
    "            \n",
    "        \n",
    "        # - Otherwise, modify the value of alphan and loop back\n",
    "        else:\n",
    "            if not condition1:\n",
    "                alpha_max = alpha_n\n",
    "                alpha_n = 1/2 * (alpha_min+alpha_max)\n",
    "            if not condition2:\n",
    "                alpha_min = alpha_n\n",
    "                if alpha_max == inf:\n",
    "                    alpha_n = 2*alpha_min\n",
    "                else:\n",
    "                    alpha_n = 1/2 * (alpha_min+alpha_max)\n",
    "        \n",
    "            \n",
    "            \n",
    "        # ---> To be completed ...\n",
    "        # ---> To be completed ...\n",
    "        \n",
    "        # Test d'indistinguabilite\n",
    "        if norm(xn - xp) < dltx:\n",
    "            ok = 2\n",
    "\n",
    "    return alpha_n, ok"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.c On écrit l'algorithme du gradient à pas variable et on le teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gradient_V(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 1000\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "\n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "\n",
    "        # Direction de descente\n",
    "        direction = -gradient\n",
    "        \n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        #print(\"gradient_n\",gradient_step)\n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    ##### Resultats de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS VARIABLE\n",
      "\n",
      "Iteration : 321\n",
      "Temps CPU : 0.59375\n",
      "Critere optimal : -3.7340070480435283\n",
      "Norme du gradient : 8.549729762255891e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAI4CAYAAAA/PH0eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdd5hkZZX48e+p3FVdndN0T84MQ3QYojBkUBCzgGLC5Ycu6q5hF11dw+qqq7suIoqoiKIrYiYpSBgGkDSEgRmGybGnZzrH6q74/v6491ZXd1d3V6fpdD7PM89U3XvrhqrqPv2+77nnFWMMSiml1FTjmuwTUEoppbLRAKWUUmpK0gCllFJqStIApZRSakrSAKWUUmpK0gCllFJqStIApcadiKwXkY9M9nlkIyJfFpFf2o/ni0iniLgn+7xmGhFZJyIHx3mfbxSRbeO5z1Gcw+dF5CeTeQ6ziQaoKUhE9orIEREJZSz7iIisn8TTmnGMMfuNMfnGmORY9zWVg/JMYYx5whizwnlu/5xcMFHHyxZkjTH/aYzRz/ko0QA1dXmAT451J2KZkZ+ziHgm+xxmqpn8vYGZf30zhX5AU9e3gc+ISFG2lSJyhog8LyJt9v9nZKxbLyJfF5GngAiwWESMiHxMRHaISIeI/IeILBGRp0WkXUTuFhFfxj4uE5GXRaRVRP4uIscPdqIicqGIvG6fy/cByViX7lKzny+0zyVrcBGRk0XkJfscfysivxGRr9nr1onIQRH5VxE5DPxMRIpF5D4RaRCRFvvx3Iz9LRKRx+39/Q0oG+xcRKRQRH4qInUiUisiX3O6/0TkgyLypIh8xz7OHhG51F73deCNwPftLsPvD3JtvxWRw/b7tEFEju33mX0k4/kHReTJId7zs+zPpVVEDojIBzOu4Rf2+7FPRL7g/CIe7rMY5HvzQRHZbb9/e0TkvYOcT56I3GG/N68Bp/RbXy0iv7fPa4+IfCJj3VoR2Wh/D4+IyP8Mcox0i0ZE7gTmA/fa7/m/2MtPy3hfNonIun7vcf/r+5CIbLWvb7eI/D972xDwF6Da3n+nfQ3938O3iMgW+3jrReSYjHV7ReQzIvKK/Zn/RkQC9roy+7vaKiLNIvKEaMAcyBij/6bYP2AvcAHwB+Br9rKPAOvtxyVAC3ANVkvrKvt5qb1+PbAfONZe7wUMcA9QYC+PAo8Ai4FC4DXgA/brTwbqgVMBN/AB+5z8Wc61DGgH3mkf55+BBPARe/2XgV9mbL/QPhdPln35gH1YLUcv8HYglvEerLP3/S3AD+QBpcA7gCAQBn4L/Cljn08D/2NvfzbQ4ZxP/3MB/gT8CAgBFcBzwP+z130QiAP/YL8nHwUOAZLxnn9kmM/1w/Y5+oH/BV7OWNfn9fbxnhxkP/Pt67jKfp9KgRPtdb8A/mwfZyGwHbg2l8+Cgd+bQvuzXWGvnwMcO8g5fRN4Auu7OQ/YDBy017mAF4B/tz/jxcBu4OKMz+ga+3E+cNogx1jn7DPz5yTjeQ3QBLzJPuaF9vPyIX4u3gwswfqj6hyswHVytuP1fw+B5UCXfRwv8C/ATsCXcX7PAdX2+7IVuN5e9w3gVvt1Xqw/cGSyf/dMtX8asae2fwc+LiLl/Za/GdhhjLnTGJMwxvwaeB24PGObO4wxW+z1cXvZt4wx7caYLVi/QB4yxuw2xrRh/bV4kr3dPwA/MsY8a4xJGmN+jhXQTstyjm8CXjPG/M4+zv8Ch0d5vadh/eL4njEmboz5A9YPeKYU8CVjTNQY022MaTLG/N4YEzHGdABfx/pFg4jMx/pL/ov29huAe7MdWEQqgUuBfzLGdBlj6oHvAldmbLbPGPNjY41Z/RzrF3ZlrhdnjLndGNNhjIli/aI7QUQKc319hvcCDxtjfm2/T03GmJft1t57gM/Zx9kL/DfWHzK5Sn9vsP4YSAGrRSTPGFNnf3eyeTfwdWNMszHmAPC9jHWnYAWJrxpjYsaY3cCP6X1v48BSESkzxnQaY54Zwflmeh/wgDHmAWNMyhjzN2Aj1nd0wPXZ7939xphdxvI48BBWsMjFe4D7jTF/s7/738H6o+mMjG2+Z4w5ZIxpxvrunZhxzXOABfZ5PGGM0cKo/WiAmsKMMZuB+4Ab+62qxmppZNqH9Rek40CWXR7JeNyd5Xm+/XgB8Gm7+6FVRFqx/iquzrLP6sxj2T9k2Y6di2qgtt8Pav99NRhjepwnIhIUkR/Z3VntwAagyP5lXQ20GGO6Ml7f/31zLMD6S7Yu45p/hNWScqQDrzEmYj/MJwci4haRb4rILvs899qryoZ42WDmAbuyLC+jtxXq6P+9GE7mZ9mF9Uv4eqz35X4RWTnI6/p8D/qdwwKsrrLM79Pn6Q3u12K1Rl4Xq7v6shGcb6YFwLv6HecsrEAw4PoARORSEXnG7mZrxQpmuX4mfX4OjTEpe/+Z73fmH2sRer8v38ZqbT1kdy32/xlXaICaDr6E1aLJ/NIfwvphzDQfqM14Ppa/xg5g/TVclPEvaLfU+qvD+oUJWIPPmc+xukCCGc+rhjhuHVBj78Mxr982/a/r08AK4FRjTAFWNx5YXTZ1QLFkZENivU/ZHMBqJZZlXHOBMebYQbbvb7j3+2rgCqyu20Ks7jXnPGFk79MBrG6p/hqx/jLP/G5kfi9yOUaf6zDGPGiMuRDrl/zrWC2fbPp8D+j7Ph8A9vT7PoWNMW+yj7HDGHMV1h8D3wJ+1+8zG0z/9/wAcGe/44SMMd/M9hoR8QO/x2r5VBpjioAH6P1MhvtM+/wcZnz3awd9hbNjq4X7aWPMYqyej0+JyPnDvW620QA1xRljdgK/AT6RsfgBYLmIXC0iHhF5D7AKq7U1Hn4MXC8ip4olJCJvFpFwlm3vB44Vkbfbg+2foO8vvpeBs8W656gQ+NwQx30aSAI32Nd1BbB2mHMNY7X+WkWkBCugA2CM2YfVxfMVEfGJyFn07QYlY9s6rO6d/xaRAhFxiZVEcs4wx3ccwRpbGeo8o1hjIkHgP/utfxl4u90iXIrVqhjMr4ALROTd9vtUKiIn2l2PdwNfF5GwiCwAPgU4g/oj+SwQkUo7CSBkn3sn1ueTzd3A58RKWpkLfDxj3XNAu1jJLXl2a3K1iJxiH+d9IlJut0Ba7dfkkvrf/z3/JXC5iFxsHyMgVmLF3EFe78MaD2wAEmIlvVzUb/+lQ3TD3g28WUTOFxEv1h9LUeDvw524WElIS+2g1o51vWO+3WGm0QA1PXwVa+AeAGNME3AZ1g9EE9bg7GXGmMbxOJgxZiNWq+37WMkXO7EG7bNt2wi8C2uQvAlYBjyVsf5vWAH2FayB8kGDqDEmhpUYcS3WL6r32dtHhzjd/8Xq928EngH+2m/91VjJHs1YwesXQ+zr/Vi/tF7Duu7f0bd7aCg3Ae8UK4vte1nW/wKrO6jW3n//cZbvYiWEHMEa3/rVYAcyxuzH6or6NNZ1vQycYK/+OFZLaTfwJPB/wO3263L+LGwu+xiH7OOcA3xskG2/Yl/fHqxAf2fG+Sax/jA40V7fCPwEqyUJcAmwRUQ6sd7HKzO7cYfwDeALdnfeZ+yxryuwug8bsFpUn2WQ33P2mOUnsAJNC9Z35Z6M9a8DvwZ228eo7vf6bVjf0Zvta7ocuNz+Hg9nGfAwVtB/GviBMWZ9Dq+bVZwMJKWmJBF5FrjVGPOzyT4XpdTRpS0oNaWIyDkiUmV3XX0AOJ6BrSKl1Cygd+KrqWYFVpdLPlam2jvt8SGl1CyjXXxKKaWmJO3iU0opNSVN6S6+srIys3Dhwsk+DaWUUhPohRdeaDTG9K+YM7UD1MKFC9m4ceNkn4ZSSqkJJCJZK7xoF59SSqkpSQOUUkqpKemoBSgROUZEbhWR34nIR4/WcZVSSk1PYwpQInK7iNSLyOZ+yy8RkW0istOp0muM2WqMuR6rLP+asRxXKaXUzDfWFtQdWHW00uxpDm7BmltnFXCViKyy170Fqz7YI2M8rlJKqRluTAHKngCuud/itcBOY02EFwPuwirgiDHmHmPMGVgTrimllFKDmog08xr6Tgp2EDhVRNZhVar2Y00XkZWIXAdcBzB//mBT9yillJrpJiJASZZlxi4lv364FxtjbgNuA1izZo3WYVJKqVlqIrL4DtJ3Zs25WPPJHHV/frmWu57bPxmHVkopNUYTEaCeB5aJyCIR8QFXkjEJ2NF076Y6bn9qz2QcWiml1BiNNc3811izQa4QkYMicq0xJgHcADwIbAXuNsZsGfupjtzSinz2NHaRSKYm4/BKKaXGYExjUMaYqwZZ/gBDJEIcLUsr8oknDfuaIywpz5/s01FKKTUCM7rU0dIKKyjtrO+c5DNRSik1UhqglFJKTUkzOkDl+z3MKQywSwOUUkpNOzM6QIHVitrZoAFKKaWmmxkfoJZXhtl+pINkSu/5VUqp6WTGB6iVVWF64in2NXVN9qkopZQagRkfoI6ZUwDA1rqOST4TpZRSIzHjA9TSinzcLuH1w+2TfSpKKaVGYMYHqIDXzZLyEFvrNEAppdR0MuMDFMDKqgLt4lNKqWlmVgSoxeUhDrV1E0toTT6llJouZkWAmlscxBioa+ue7FNRSimVo1kSoPIAONiiAUoppaaLWRagIpN8JkoppXI1KwJUVUEAt0u0BaWUUtPIrAhQHreLqoIAP3liDxd/dwM98eRkn5JSSqlhzIoABVY3X3c8ybYjHexr0q4+pZSa6mZNgMpsNR3SbD6llJryZk2AWruoJP34UKsGKKWUmupmTYD67MUr+fuN5+F2CXWtPZN9OkoppYYxawKUz+OiuiiPqoIAh1q7aeqM8sGfPceBZh2PUkqpqWjWBChHTVEeta3dfOeh7azf1sC9rxya7FNSSimVxawLUHOKAtS2dvP4tnoAUinDn1+upb5du/2UUmoqmXUBqrooj4Mt3RxqswLSa3XtfPKul7l744FJPjOllFKZPJN9Akdbeb4fsLr6/B4Xz+1pBqCxMzaZp6WUUqqfWdeCOndlBZccW8UfPnYG80qC6cDU1KUBSimlppJZ14JaVBbi1mveAFg1+hxNndHJOiWllFJZzLoWVKbKwt4A1awtKKWUmlJmdYDq04LqivHCvma9L0oppaaI2R2gCv3pxy1dMT7y843c9MiOSTwjpZRSjlkdoCrCVguqJOQjkTK0ROIcae/hh+t3cbMGKqWUmlSzOkAtKc/nlIXFXHFidXpZQ0eUezcd4i+bD0/imSmllJrVASrP5+a315/BuhUV6WWNnTGOtPfQ3hOfxDNTSik169LMsykN+dKPm7uipAyEk/rWKKXUZJrVLShHaX5vgEoZ6//OaIKU82QMookkf9/ZOOb9KKXUbKMBCitJAiDg7X07jIHD7T1jntzwr5sPc/VPnqVOZ/FVSqkR0QAF+D1uzlpaxttOmttn+X/c9xrv/tHTtEZiPPBq3aj23dZtjWW1dyfGfJ5KKTWbaICy/fIjp/IPb1zUZ9krB9uoa+vhdy8c5GO/epGWUVSbiMSSAHTHk+NynkopNVtogMpQFvb3eV7b2k0yZdhvV5cYTWafE6B6NEAppdSIaIDKEPZ78HkGviV7m6wA1dGTYE9j14j22R2zuva0BaWUUiNz1AKUiCwWkZ+KyO+O1jFHSkQoz/dTnVFEFmBfkxWU1m+r59zvrGfb4Y6c9+kEpqgGKKWUGpExBSgRuV1E6kVkc7/ll4jINhHZKSI3Ahhjdhtjrh3L8Y6GNx8/h3eumddnWW2LlYH3uh2YDo0gI0/HoJRSanTG2oK6A7gkc4GIuIFbgEuBVcBVIrJqjMc5aj7/pmP4p/OX4ZLeZQn7fqhaO+W8vTv3saju9BhUavxOUimlZoExBShjzAagud/itcBOu8UUA+4Crsh1nyJynYhsFJGNDQ0NYzm9UXO5hHDAO2D5Qbsl1d6TyPlGXqfl5AQqpZRSuZmIMaga4EDG84NAjYiUisitwEki8rnBXmyMuc0Ys8YYs6a8vHwCTi83hXkDA1RDhzXr7t7GLk766kOc8JWH2HSgdcj9pLP4EsMHqAdereNbf319FGerlFIzz0QEKMmyzBhjmowx1xtjlhhjvjEBxx1XBXlWLT7JcjVbDrURTxo6ogke3z50Ky/dxZdDC+qhLYe5+/kDw26nlFKzwUQEqINAZpbBXODQBBxnQhXmecnzuikN+Qesy0w1H26q+HQXXw5JEpFYMt3iUkqp2W4iAtTzwDIRWSQiPuBK4J4JOM6EKsv3U1OcR2HewKrmR9qtrj4RaIkME6BGkCQRiSXpjifHpUitUkpNd2NNM/818DSwQkQOisi1xpgEcAPwILAVuNsYs2Xsp3p03XjpSn743pMpCvoG3WZZRT7NXTH+7Y+vDto1FxnBjbrOtrmMVyml1Ew3pkmPjDFXDbL8AeCBsex7ss0pzIPC3mSJkM9NV0b3m9/jYm5xkMNtPTyxo5FfPbuft5xYTcDrZtvhDm59fBdd0cSISh0520ZiSYI+D5tr23jXrU/z2GfWUdXv5mGllJrpdFa+YRTZAWpucZBtR3orSJSGfJSEfPx9V+9cT1/802ZqW7v5+66mAfvJJUB1Oa0tO1DtauikO55kf3NEA5RSatbRWnzDKLAD1LySvD7LS/P9lIR8fcaWfvvCQfY0dvEvl6zg3950TJ/tcxmD6s5oQYE1aSJAxzhMP7+roVML1iqlphVtQQ3jmDlh5pXkUVlgtWDCfg8d0QQldgvK8ad/PJNlFfnked24XDIg/TyXMaiuqBOgrMAUifYNVKMVS6S47HtP8pmLV3DtWYuGf4FSSk0B2oIaxntOmc8T/3JeurLE3JIgYE0TX5KRQFFTlEfI78Fl10gqz++bnj5c6yWVMgOqTjhdfh09YwtQkViC7niSxs7omPajlFJHkwaoHIUDVmNzvt3VVxryUWy3oLxuoTTUN9uvPGNuKZcM34LKXN/Vr6tv7AFKyy0ppaYfDVA5cgLUvGKnBeVPd/FVFgTSLSdHSciH215WHPQNW0nCaS1Bbxef07XXGR3bGJQGKKXUdKRjUDmqCPsRgaUV+QB9xqCqC/MGbO92Wa2q+o4oxSFf1ooTxhie39vCn1+upTSjSzCdLBEdny6+9P40SUIpNY1ogMrRhauquPeGswj63IjAorJQegxqsBTw8rCf+o4oJUFfek4pYww76ju5/5U6/vhSbXo6eX/GTL6v2/dRdTpJEuMwBgW9s/sqpdR0oAEqR26XsLqmEICnbzyfqsIAqZQh5HOzsDSY9TUVYT9bgOKQl+54ku8/uoM/vlTLroYuROD0xaV88vxlPLz1CH/ZfDj9uv97bj+xRIpVcwoA6BhjFp/TctI6f0qp6UQD1Cg4LSaXS/jjP57JnCFaUEC6K/A7D21n7cISPnjmIi5eVUmFnbqeeQMwWGnh0DtB4ljvg+p/f9VoJZIpRCQ9tqaUUhNJA9QYLa8MD7quf4ACuOPDpxD09X3b+6ekO9rsmXvHeh/USMotDeW6O19gTmGAr7/tuDHtRymlcqEBagKdsrCE1TUN6Zt8S0K+AcEJoCw8eEFaGPsYlDP2lNmCuvmRHXRGE3yuX8WLoext7Eq37pRSaqJpmvkEWreigvs+/kZCdlBaWZW9tVWe39tFmO8fGMDG6z6ozAC1YUcD67cNPdlitv3kUhFDKaXGgwaoo6CuzRpLWllVkHV95k29pfkDW1NjTpJI3wfVu5+OnsSIx7YisYTeS6WUOmo0QB0FF6yqxO0S3nfa/KzryzKCUkm/ihR5XjexRIroGOaIclo9kXgSY6zJEK0ANbLA1x1PasFZpdRRo2NQR8HKqgJ2/eebBl1fHLSqTvjcrgFdfFWFAfY0dtHZk8Cf7875mB09cX717H7+8modIXufxkA0kSLgddPeE6cjmiCZMjll5cWTKeJJo6nqSqmjRgPUFOCyq04kU4Y8b98gVBH2WwEqmuhTbWIw9e09/Pzpvfzi6X3pFpJkxJ/uWBKf25VRRimRnpRxKOlCtiNoQe1vilAWzp4YopRSw9EuvimiPOwn6HcT9FkByunqc+65Gqo7zhjDxr3NfPzXL3HGNx/lB+t38cZlZfz+o6fb63u3rW3tprEzml6W6ziUM/Y0kgB1+fef5PYn9+S8vVJKZdI/baeIqoIAxkDQ7o5bVpHPs3uaqbJT1Bs6Bk6V0RqJcf+rdfzfs/vZcqidcMDDB85YyDWnLWBhWQiAoqCX1khvEHrrLU+xbkVF+vkdT+3lyZ2N/OulKzk3Y3l/TtdeLJHKqVswlkjR1h3Pet5KKZULDVBTxI2XrqQrluQvr9bhcQmLy60AddriUn77wkF+tGEX61aU09QV46mdjdy7qY7Ht9cTTxpWVIb5+ttW87aTarLeBJwZoBIpwysHW9PP79l0iPqOKNff+QKvfvlifJ7sjepIRgZgdzyZNR0+03hVr1BKzV4aoKaIZXZFitKQjzcsKObV2jbA6vr75PnL+NI9WzjtG49wpN1qkVQW+PngGQu54sQajq0uQCR7i6Ys38+O+k7yvO5091x9RqvGeRxNpGiNxNLll/rLTC/vjuUQoLT+n1JqjDRATTHzSoLMKwlywK5+HvJ7uPrU+XTHk2w/3MGSinzOWlrG6prCnLLvMsstObX9BtM8RIDKDDS5pJqnp63XCupKqVHSADVFnbm0lHNXlFNdFMDrdnH9OUtGtR8nQJXlDx6gllbks7O+k/1NEZ7e1cQ1py3A4+7b1ZcZoHJJlMhWvUIppUZCA9QUtbKqgJ99aO2Y9+MEqKFS1FdUhdlZ38lNj+xgy6F2BPjgmYvS63fWd9LU1dstmEs1Ce3iU0qNlQaoGc6plF4aGlhCScRKQV9ZGeZ+6tLjUfe+Usf7T1/I+u313LZhN8/sbqYsI8DlEnR6W1DaxaeUGh0NUDPcYC0oj0sozPPS1BVLJ2g4KeEv7GvhzG89Sl1bTzrNvbGztwXV0RMnmkji9wxe2aI7PYuvtqCUUqOjN+rOcL1JEn2rRYQDHsIB6++TmqK89OPqwgDvesNcTp5fzE1XnsgT/3ouJ88v6vPaf//zFq75yXNDHtdpQXVpgFJKjZK2oGa4ucVW8FlSnt9neTjgJRywglZ52E9JyEdHT4KVcwr49rtO6LNtZrV1gMPtPcMWr02XRtIApZQaJW1BzXDhgJeX//0izltZwf+8+wQe+uezCfnc6RaUiJXhVxzsW1opU/8ABdASiZNIDj55oROYYskU8SG2cxhj+MOLB3XMSimVpgFqFnC7BBHh7SfPZXllmPKwn3DAQ0HAS2nIh8ft6q39l+U+KGdCxf435+6o72TD9uyTHmYmUuSSVLGvKcKn7t7EA68ezvm6lFIzm3bxzUJvOaGagjwvc4uDHD+vECCnFlRJyJeugg7wsV+9yJ7GLh759DnpLkRjDPubI3RllkaKJdMV0x/acpj12xv48uXH9imr1G4XrW3pio3npSqlpjENULPQpy5aMWCZk0QxZ4gAle/34HO7iNlddnsauwC48+l9/Nubj+HBLYe55bFdbK1rp7Kgt1uwM5pgf1OE4pCXnzy5h+f2NJNMGr71zuP7bAPQ1j2yWX4Btta1s6IyjCuHyhpKqelDA5QCoHioLj47QAV9bgLe3gDl+NWz+7hn0yGau2LpbZ2agQDX/PRZ6tp6OG9lRbqb8DcbD/C1t63Ga1esiEStbsDW7pG1oA62RLj0pif48fvXcOGqyhG9Vik1tWmAUgCcsrCEk+cXMa8kOGCdE3TyfG7yfG7aM+ameuOyMhaWhuiMJnjLCdWcs7ycE77yEB0ZXYF1bT0A7G3q6jM5YkskRkXYCohOl2Bm5fVcNNtdgs1dOq2HUjONBigFWAHqDx87M+s6pwpF0Oe2p/PoDQYnzS/mUxcu77N9eYGfjoaB2Xjt3XEw4BJIGSu4pAOU3YLq38X34w27cbmEa89aNGB/0JuA0RMfPlNQKTW9aBafGlbA66Yg4CHo8xDwuvF5XOmgVVOULevPanE5N/+CdT9WSyROcyTGYjuhoqnTav20dcfpGmQM6p5Nh/jzy7WDnlt3OkDp/VZKzTQaoFROPnH+Mt56Ug15XheVBf50bb7qorwB2zpTdpRnlFc6rqaQZMrQGomz2J7tt6krxsa9zZz01YfYcsia/6p/F19nNJEOZNlERjEVvVJqetAApXLykTcu5pzl5cwpzGNpeX76vqmaLAEqXaA2v7dA7eqawvTjJRVWC6q5M8oL+1pIGdha1wFY09hn6uhJpMeZsnFu7NUuPqVmHg1QakT+653H872rTkoHn+wtKGcOqt4W1MqqcPrxwtIgLrHGoLYdsQLTwZYIAB3RBMmUSW/bGY3THU8OWmHCaTnlOoniw68dGXY7pdTUcNQClIgsFpGfisjvjtYx1fgL+T2EA16WV4ZZWpFPwDuwonmFnfVXFOxtQWWWSyoJ+SkO+mjqirHdDlBOUVljrGrpAPFkKt0yGqybz+niG642IMC9mw7xkV9spL69Z9htlVKTL6cAJSK3i0i9iGzut/wSEdkmIjtF5Mah9mGM2W2MuXYsJ6umjn88dyn3f+KsrOucYBTy9Qav4oxgVRT0UhLy0dARZceRzgGvd8ahOjPS2Qfr5nOSJHIpStvebe0vsxqGUmrqyjXN/A7g+8AvnAUi4gZuAS4EDgLPi8g9gBv4Rr/Xf9gYUz/ms1VThtsluF3Z54NyUseDGQGqJGPCxKI8K0C9dKCVaGLg2FFbd5x9TV105BKg4rmnmWtKulLTS04ByhizQUQW9lu8FthpjNkNICJ3AVcYY74BXDbaExKR64DrAObPnz/a3ahJ5HTx5Qc83HXdaVQX5hH0WenpsUSKwqCX0nwfz+5p7vO6cMBDR0+C1u44//CLjX2mCGkaJEClkyRy6OKLxHPfVik1+cYyBlUDHMh4ftBelpWIlIrIrcBJIvK5wbYzxtxmjFljjFlTXl4+htNTk6U45OMH7z2Zd5w8l9MWlzK/NIiIUGJ38xXmeSkNWUGsqiDAsdUFQG9G4L6mLuo7omw93J7eZ1Nn9koRkRHcB6X3TCk1vYylkkS2ypwmyzJrhTFNwPVjOJ6aRt503JwBy4pDPotBSK8AACAASURBVNp74vg9bprtdPIPnbmQp3c3AVaAev1wBy/tbwX63hM13BjUSLr4otrFp9S0MJYAdRCYl/F8LnBobKejZrKSkJe2iFWL771r53OwOcLVp87n9cNWJt+8kiDhgIdHXx84XNm/i6+jJ86WQ+0ja0HF9aZepaaTsQSo54FlIrIIqAWuBK4el7NSM9LahaXpBIozlpbx5xusLMCioBW08v0eTphbxJM7G/u8riLsT7egmjqj/Oypvfz86b109CQosMspjWcX300P76CtO86/X74q94tTSo27nAKUiPwaWAeUichB4EvGmJ+KyA3Ag1iZe7cbY7ZM2Jmqae+TFyzLurwozy5G63dzwrzCAQFqQWmQps4oj22r56O/fIFoIsXJ84t5YV9LurJ6bl18uW379O7GEVdVV0qNv1yz+K4aZPkDwAPjekZq1ikO9baglmZk7oGVzr6sMsy9mw7xhxdryfd7ue/jpxLyezj9G4+mt8slMy/XFlR3LJk1/V0pdXRpqSM16ZyKEyGfhxPnFQEw356XKt/v4Zg5BXT0JHhyRwMnzitkaUW4TxklyO1G3fR41TDBLBJLaqafUlOABig16YrtMaiQ301FQYBPnr+Mj61bAtgByq7j1xKJs7LKSkn3ul19bv6NJlIYM2gSKZD7Tb0aoJSaGnTCQjXpVlYVsLIqzKo5VsXzf75wOfUdVr28cMDD8oxCsyvn9D52kidErBp+0UQqa21AR3c6zXyYLr54UjP9lJoCtAWlJl152M9f/+ls5pf2TjdfEvQhYgWogoCXucXWTbxOC8p5HVilk2DwsaUX9rXw+PaGnFPSI7EEPfHhW2RKqYmlLSg1JXnc1qy9+X7rK7qyqoCGjigLM4KYE6CKQz5aIta0HEX2OmMMz+5p5uZHd/DUzib8Hlc68WGoLr5kyqTXD9ciA3jTTU9w1dp5XHP6wlFeqVJqMBqg1JR16qJSltqTG15/zmLOP6YCj7u30e8EqNKQj90NXfTEUyRThr9uPsxtG3ax6WAbZfk+Tl9cmq5WAUMnSWR27fXEk0MGKGMMWw+3sz1LRXal1NhpgFJT1i3vPTn9eM3CEtYsLOmz3rnp15nK47cbD3D/q3Xsa4qwoDTI1966mne+YS4PvXakb4Aaoosvc2LE4ZIprMQMrUyh1ETRAKWmLacF5WTz/WD9LlZWhfnhe0/momOrcLuscpEV4b4p6UMFnsx09eHHqnKfi0opNXIaoNS0VVNktaAqCwLpZf9yyQrOW1nZZ7vyfgFqqBZPJDNADXu/VGLY/SmlRk+z+NS0dfL8Yn72oVM4Z0XvtCyZWX6O/gFqqDTzzAA1XMvIWZ/ZLaiUGj8aoNS0JSKcu6Kiz8y9cwoDA7YL+z34PdZXvTDPO4IuvuFv6AXo1uk7lJoQ2sWnpr2ApzdAiQycpkxEKA/7OdjSTUnIN6DrrjOa4NfP7uf7j+1kXkleenkuJZEAurUFpdSE0AClpj2f3ToKeAfvEHACVHHQS21rNwANHVF+9tQe7nxmHx12VfS22t4q5j3DdfHFdQxKqYmkAUpNeyX2Db3/+fbjBt2mPL8342/7kU6++KfN/GbjAeLJFJeuruL/nb2Emx/dwcNbeydLzL0FpQFKqYmgAUpNewGvm81fuXjIbdJlkYI+OqMJ7nxmH28/uYaPn7eMRWUhe5u+41c5j0FpgFJqQmiAUrNCVUEAl1hVJxxfecuxhAPe9POB90vlmMUXT2KMyTr+pZQaPQ1QalZ472kLWF1TyOuHOwArUGUGJxjZ/VKZ63OppK6UGjlNM1ezQknIx7krK9KJFPNKggO2cVpQToHaobr44snUiO6ZGotUynDTwzto6oxO2DGUmoq0BaVmFa9dbHZBaZYAZVekCPrcJFKprDf07qzv4PuP7uSeTYfSY1dgtaaKJ+ic9zR18d2HtzOnMMC7T5k3QUdRaurRAKVmlfp2ayLEecWDt6CCPjexZCqjC8/wzO5mfvrkbh55vZ6Ax03KwK6GrvRr27rjVIT9faqtj5dINLep6pWaaTRAqVnFaSWtXVQyYF2ZnYqe5/PQE0/RGU3wx5cO8pMn9rDlUDslIR8fP28ZHzxjIeu+/RjtPb036F7z02e54JhK3vGGudS19XDZcXOIJcdnXMoJlJotqGYbDVBqVrl67XxOmFvEcXMLB6zzeVyUhHyEfG66Yy7+8GItf3ixlqUV+Xzz7cfx1pNq0gGnPOzvE6AaO2PsrO/kxxt2s+VQO23dcb73yA7u+/hZ/HD9Lv7lkhV892/bueHcZRQGvQOOPRQtSqtmKw1QalZxuSRrcHJUFgQI+T10Rq2gsLqmgHtvOGtACnlFONCniw+gJRJDxOru21XfSUNHlHs3HeKOv+9lSUU+P35iD8fPLeLyE6pHdM7d6Zp/GqDU7KJZfEpl+I8rjuUzF61It5SOqynMen9Terr5jNZQSyROc1eMzmiCBjvj7kBzBICDLdb/rZHYiM/JyRaMalFaNctoC0qpDM6svS12IFk1Z+D0HdCbUFES8tESser3tUZipIwBYH+TFZD2pwOUVf+vuSvef1fDiugYlJqltAWlVBb77ABzzCABymlBleb33tybMtBqB6u9TVb3X/8A1TKKFlS3jkGpWUoDlFJDWDlYC6rADlAZpZMyOdXRncBUa3fxNXeNvosvM0A9tOUwL+xrHvG+lJpONEAplcVZS8uA3qoS/ZXnW+nqJYMEKEc0YY0bNXZagWl0LSj7PqiMAPXNv7zOrY/vHvG+lJpOdAxKqSx+9qFTSCTNoOudFlRB3shSxsfSgsoMUJ3RBJ09OlGimtk0QCmVhdftYqh7bNNVJ0Z4I27LOHXxdUUTdOlMvmqG0y4+pUahKOjjK285lreeVDOi1zWPpovPmbnXDlSplCEST2oLSs142oJSapQ+cMZCAG5938nUFAV56w+eIpky+DwuYons9yz1xFN0x5Lk+YZueaVShodeO8yGHY002eNXTnX17ngSY0jfTKzUTKUBSqkxumT1HACK8rx0RhNUFgTY3xzBJVbqeX/X3bmRT1+0ghPnFQ1YF0ukuO+VQ9z6+C62H+kEwGXfJ+yMQTldexqg1EynXXxKjZPikI+SkI8iu7rEnMI8AJxCFFV2odondjTy3b9t7/PatkicH6zfyRv/61E+dfcmAD578QqgN8h1x5P85IndvLivBbDGppLZIqBSM4S2oJQaJ8VBL163i0I7s29BaZDa1m7mFAQ41NbDgtIgh+3pPjbsaOBAc4T6jh5+/2Itf3qplkgsyVlLy/jWO47nnOXldEQTfPvBben9R2JJvnb/Vk5fXJpe9sK+FoxdveLhrUf4tzevOopXrNTE0gCl1Di57uwlxBIp/rrlMODMOdXEvJJgOkA9u6eZoM9NTzzJ2d9+DGMg4HXx5uOqufasRayq7r0xOOz3EPC6Bszse6itO/34y/dsIZFKccaSMu74+14+e/FKfJ6J7xjZXNvGSwdauea0BRN+LDV7aYBSapxcuKoSgE0HW6ks8FNs38Q7r8QKTCfOK6amKMiVa+exq6GTp3c1saA0xCWrq7LeECwiVIQD6XJJjrrWnvTjPY1dhAOedOWKlkiMSrsrcSL9duMBfrPxgAYoNaE0QCk1zm44bynvPXU+979aB/TO3lsU9HL1qfMBa1qPM5aUDbuvirCf/c0RCgKe9PxTsWRvi8q5N6qjx6oB2NgZPSoBKhJL0hNPYYzJWu1dqfGgSRJKjbOCgJcFpSHOWlrGJcdWsawyP718pLIVpe2vO55Ml1ByUtJTKUNrJMZp//kIN/zfi+NeCd2psB4dJJ1eqfFw1AKUiBwjIreKyO9E5KNH67hKTZbj5xZx6zVvYM2CYs5eXs6x1dkLzw6lIsu8U9nU2kVpm7qiPLL1CIs//wCPb2/gcHsP971Sx+9fPDjyCxhCtvqASo23nAKUiNwuIvUisrnf8ktEZJuI7BSRG4fahzFmqzHmeuDdwJrRn7JS00tFQYBffHhtekxqpK8FKAkN3oIC0tmBTZ0xfvbUXgA27m1Jr6/viI742ENxpqHvn8Ch1HjKtQV1B3BJ5gIRcQO3AJcCq4CrRGSViBwnIvf1+1dhv+YtwJPAI+N2BUrNYOX5Q0/r4XBuh2rqiqWTKjIL07aNosTSUHQaenU05BSgjDEbgP6Tz6wFdhpjdhtjYsBdwBXGmFeNMZf1+1dv7+ceY8wZwHsHO5aIXCciG0VkY0NDw+iuSqkZotyuml6S3zdAhQYpldTUGU0HqH3N1qSJfo+L1u44tzy2kyd3NI7LeTmBabguvkQyRUpvJlajNJYxqBrgQMbzg/ayrERknYh8T0R+BDww2HbGmNuMMWuMMWvKy8vHcHpKTX/HVhewojLMSXZZJKfsUVHQh8898Md3a11H+rEzK/CC0iCtkTjffnAb7/vps+n1v3l+Px/71QvpANIZTXDnM/vS3XdDyVZhPZv33PYM//23bUNuo9RgxpJmni23dNA/lYwx64H1YzieUrNORTjAg/98NvvtYDO/JMjepgj5fg/d8eSA+aVerW1LP+7oSeBzu6gsCHCgpfdeqm2HO1hRFea//rqNpq4YN1fuZN2Kcg62dPPFP23mpod38Phn1xEaZLJGyD1JYm9jF3MKJz7tXc1MY2lBHQTmZTyfCxwa2+kopbIJ+Kwf1SXlVsp60O8m5Hfjdff+nei0qMIBT7rcUkGel6KgLx3gAD58x/Pc+cy+9L6++/B2rrjlKWpbrW0aO6M8t2fo6eSdFlR0mCQJ634pHadSozOWAPU8sExEFomID7gSuGd8Tksplakg4KUk5OP0JVYdvpDPQ77fm74JGCDkt8al3nHy3HRh2sI8D0V5XhJ2N966FeVEEyl+/8JBWiIxTllYzHkrKwDYVd+V3tdQM/+mUibdtTdUF5+znWb6qdHKNc3818DTwAoROSgi1xpjEsANwIPAVuBuY8yWiTtVpWavgNfNC1+4gPeeapUWCvndVBX4WVgWImx3xc0vDQFw1dr5FNr3TRXmedOtKYB/vWQlZy8vo6EjSnNXjGWVYa5aa1W32N3Ymd6uuSvGbRt2cbitt6ySoyfRG5SGah0522kLSo1WTmNQxpirBln+AEMkPCilxo+IkOdz4/e4CPk8/OfbjkFEuPzmJ+mIJvjy5VYl8xVVYYryegNUUcZNvuVhP+VhPw0dURKpFKX2FCEAuxu6qCnK40h7D6/UtnHvpkPc9fwBHv30uj7nkVmVYqjWUa6JFEoNRmvxKTXNnDC3iBVV4XT5o3DA+jGeU5hHlZ2QUJSlBeUSKA76KM/3p+v5FQd7A1RTV4zVNQXEkim2HW4HrKCVShlcLqGtO84vn9nX51yGCj4jrTZR19ZNZTiAy6W1/ZRFA5RS08zd15/e57lT488JVGCloUPfAFUS8uN2Sbo6BUBpfm+AAitgxROGnQ293X13PX+A7Uc6+O3GA3T1q+k3VPCJpAPU8GNQzV0xzv6vx7j5qpO5ZHXVsNur2UEDlFLTXDjgwe0Sghk37xb26eKzAlCZfbNveUbh2eKgj4KAB49LSKQMRUEf8WSK5JHeO0Y+/8dX8bqFy4+vZn9zhI37eksoDR2gEsNu42juihJPGo60DxzzUrOXBiilprmCPC/hgKfPtBd908ytx05ldOd/gJKQDxGhOOSjoSNKcdBLMmW1eDwu4enPnc+OIx0sqcinsiDAzY/syDlAjaSLL6LFZ1UWGqCUmubecmI1S8pDfZY5Qakgo4vPaTn1D1Bg1fpr6IhSFPSRtFPSK+yEisztMx9DbkkSPYnh543ShAqVjQYopaa5c1dUcO6Kij7LivIGjkGV2cGlIODB73ERTaTSAao46PzvxRgrQJVnmfiwf4AaKqA4c0YlU4Z40uDzDB6gtPisykYDlFIz0PHzCnnLCdWcsrCEgNfN59+0knOWW0FMRCgP+2nuihHwWuNWTjHaoqAXOz5RGR44xUdmgPJ5XMN08fXW9OtJJPF5Br/tMt3aGueJFdX0pgFKqRmoIODle1edlH5+3dlL+qzv3xIqCToByofYZTYrCoYOUCVB36ABqr6jh46ejAAVTw45o7CTUKEtKJVJA5RSs9CJ84r6ZMxldvW57LGiyvDALr7SjIkTi0O+AWNQmw60cvOjO3h4az3VGUVie2JDp5r3pEsnaVkk1UsDlFKz0JcuP7bP81K7i68k6MMtg7egfB4XxUEvrd1xivK89MSTpFKGx7bV8+MndvPM7mYK87z43C4OZZRJyiyPlE06SSKjiy+eTOESwa037s5aGqCUUlx+fDUA80rymJMKcO1ZizhvZWXWbcvy/UQTKYI+N8/tbeOi/93AzvpO5hQG+PybVnLV2vlccctT7G7oLT47XPp4tjTzj/x8I/NK8vjaW48b6+WpaUoDlFKK4pCP95++EACvW/jiZasG3TYzwaKjJ0Ek1sX/vudE3nz8HLz2lB8VYX+fANU9TPJDthl69zV1kTI6G+9spgFKKTUi80uCNHXG8HutYLSsIp+3ntR3Mu2KfuNXPYnh5o0amCTRFUumW1ZqdtIApZQakRsvXUlnNMEP1u8C4LiawgHbONl+ImBM7l18mQEqEk3QFR1++nk1c2mAUkqNSFHQR1HQR4s9qeHxcwcGqAo7QBXmeWmNxAcNUIlkij2NXb1lkez/UylDJJ7UtPNZTgOUUmpUdtRbFc9XZ2lBORmAJSFf1gAVS6T4/YsH+eH6XexvjlBml2FKj0UlkhiDdvHNcmOZ8l0pNYu96bg5ABwzp2DAOmcMyrkB2Llfqr0nzk+e2M05336Mz/3h1XQKeWNnFLACVGskRmskDljdfGr20haUUmpU/vmCZXxs3ZJ0uaRMzhhUsX0D8L6mCF++Z0t6Tqm1i0r41juO59jqAt7wtYfTr+uJp7jwuxu44BirLFMknkwXr9X7oWYfDVBKqVERkazBCXrHoJwW1O1P7cHrFi47vpoPn7mI4+xxq1TKpOeicjR0RHmtrgOwEiy++OfN7Gvq4qPnLOWPL9Xy3+8+YSIvS00h2sWnlBp3hXlegj43RSGrqgTAu9bM47vvOTEdnABcLkmPP2Wqa+1OP950oJWd9Z2s31bP7188qHNGzSIaoJRS405EuPPaU/nIWYuJJa3xp1VZxqqgtzvQn1HtvMEekwI40m4VnnWKz7Z1xyfqtNUUowFKKTUh3rCguE/182zJFNAboErt8SqAzAISjZ0xIrEkTXZau5NAoWY+DVBKqaNiZVU463Jnpt/ijACVzSG7228sLShjDJtr20b9enV0aYBSSh0VIX/2nKzMe6aGUmsHqNZIbNTn8PddTVx285O8frh91PtQR49m8SmlJtQVJ1YT8GTP9oPeLr7hApTTcmrNaEF19MQJB7zc/uQe6juiXLV2HgtKQ4Puw5kDq661h5VV2bsc1dShAUopNaFuuvKkIdc7XXzDBSjHkzsa+eH6XXRFE9R3RLn9g2v46n2vAZBMpfi3Nw9eid1JtGgZQytMHT3axaeUmlROCypbunk2f3vtCHsau8i3uwyf3d2cXlffER3sZYDV4gJo0USLaUEDlFJqUp04r4jPXLScC1dZEySG7cDj82T/9dQdTxL2e7jn42cBsP1IR3pdY+fQAardbkGNZRxLHT0aoJRSk8rjdnHDecvSaeaLK/KB3q6/bGqK8wj53AS8LrYfsYrWLiwN0pBzC2pggIonUxxp7+GpnY3srO8YsF4dfToGpZSaEvIDHkI+NyfNK2LTgVaKgl6OtPf0KYPkmFscREQoDfnT2X0rqsI8v7cl6753N3RS29qdbkG1dMUxxrC/OcKG7Q2cf0wln7r7ZZ6xuwtXzSnggU++cYKuVOVKA5RSakrwe9w89tl1xBIp7vj7XoI+N0Gfm/aeBG6XkEwZvG4hnjTMK8kDoCzflw5QyyvDPLjlCL9+bj8pY3jXG+axYXsDv35uP4+8Xg/ACfOKANjb1MXp33iUw05WX1sPO450ctriEvY3RTjYEpmEd0D1pwFKKTVlVIQD6ckLgz4PQZ+HzmiC8nw/h9t7qCnKY29ThLnFQQBK7W7AoqCXqkJrio/P/eFVAL74p82kjJWEsbA0yN6mCLvsOay2HLLug/rouiX8cP0u6juitERinLKwhDULSvjB+p2kUgaXVlCfVBqglFJTSsDrwud2EfJbLaiCPC9FQS+H23uYVxK0A5TVgnLGrUpCvj5ZgCfMLeSMpWWcPL+YdSvKeWFfC1fe9gyd/eaX+uAZC9mwvYHdDZ2kDBQHfYhAylj3W+Wa+p5NXVs3zV0xjq0eOKGjyo0GKKXUlCIilIf9FOb5CPrdJI2XcMD6VTW/xGo5OQGqJN8KIKUhX5+6f1+4bBWnLCxJP68ID0y4yPd7qAj7KQn5ePlAq7WffB8iVqupqTM66gD155dr+eRdLwOw8QsX5JxCr/rSLD6l1JTzo2vewCfPX0bQ56Ewz0tBwAvACXOLyPd70oGqLOQUmvX3yfrrX/cvM3jZ8YfF5SFErOk+nBt4S0I+yuyg5BSnBUimTLoKxWOv1/P9R3dQ39Ez6PlvrevNAnRep0ZOW1BKqSlndY3VLXbdGxeTSBn+urkOn8fFO98wl4tXVxG2A1ap3YIqye9tQc0vCabXO/L9HvK8brrjSaoL86ht7WZJuZXOntlKKg768NrzV+1vjtDcFWPj3hbufeUQjZ1Rbv/AKXzojucBK6njH85enPX8MwvatnTpTcGjpQFKKTVlXWDfvLuroZOlRzpxuYTCvN7g4yRJlIZ8BLxuwgEPx8wZWDXd6Tbc3xxhXokToEL2PnwZ+/PhcVkB6mv3vUZ7TwKf28XqmgIaOqL8fVdjetuhWkbtGQGqqWvoe7PU4LSLTyk15X1s3RLutStHZHKSJJz//+OK1dxw7rKs+3DGoRaVWYFpqX1DsNNNCFYLqjjoRcSqOnFcTSEvf+nCdD1BJ/sPhi6r1NYdZ2Gp1Q3Z0jX6qhXNXTEu+u7js/bGYW1BKaWmPBHBnSXje1FZiJPmF7HGToh460k1g+7D6QI8Z3kFaxeVcP4xVuvM6eKzKlNYVdeLgz6au2KcMK+QoM+D5FsHf63OClCr5hQM2YJq7Y6xoDTEPrubsL+GjiiNnVGWlOcPWtIJrBuMtx/p5MX9rSytyD6f1kx21FpQIrJORJ4QkVtFZN3ROq5SauYK+T388WNnpseshuK0oAryPLztpLnpsabMcSyH0yJbbaeI5/nchP0eWiNx8rxuFpWHsragUimDMYa27jjFQS9FeV6aIzEisQTP723mlsd20tgZ5bKbn+DSm57ga/e/NuQ5t9ulmYYr4TRT5dSCEpHbgcuAemPM6ozllwA3AW7gJ8aYbw6xGwN0AgHg4KjPWCmlRsFpQRX0S6AoDTnTffR29Tmtqsx7mMoL/HQ0JCgP+6kMB3is3apOkUimeOlAK4++Xs//PbufZRX5tEXiFOZ5KQn5eHZ3Myd+9W/EEikAXCIcabcCzq6GziHP2cku1AA1tDuA7wO/cBaIiBu4BbgQK+A8LyL3YAWrb/R7/YeBJ4wxj4tIJfA/wHvHdupKKZW7+aUhRAZO65FuQQV7A1dZvh+PS1helZ9eVp7vZ3dDlxWgCvxEYkne9oOn2HSglZQhXY5p474WRKAwz0tpyM9ze636ft9+5/F89nevsLWudxyrrm3oFHSndmDDMFXaB5NKGb74581ctXZ+Tq3Mkbhn0yF+9cw+fvahUwj6Jma0KKe9GmM2iMjCfovXAjuNMbsBROQu4ApjzDewWluDaQEGvWtNRK4DrgOYP39+LqenlFLDevNxc1hWkZ8uieQI+tz4Pa4+LajLT6hmUVkIf8ZMwBUF1uvK8/3paepf2t/KpauruOz4at64vIw/vVTLv/95C8ZAQZ6X4pAV9EI+N+84eS7/87ft6enmF5YGqWvtwRiTvjm4PycbcLQtqJZIjF89u5+qgsC4B6j9TV08u6c53VU6EcYS9mqAAxnPDwKnDraxiLwduBgowmqNZWWMuQ24DWDNmjUDyxgrpdQouF3CMXMGTvMuInz8vKWcOK84veyS1VVcsrqqz3bOjcBOF5/jMxevSN9TVV2Yl15udfFZr1leFcblsm4KdhItVtcUsrepjvbuBIXBvt2ODqeLr3GUAcop7dTRr8TTeOiKJfG6ZcoGqGwhf9CAYoz5A/CHMRxPKaUmxA3nZU9Nz+SMYZWHe1tQlQV+Fttp6wDVRb0Bqijoo8RuQTmVLcrDfpK11q/J42oKue+VOurau/sEqIaOKH96qZZXatvw2b/8D7f3cOVtT3P9OUtYt6Ii5+tyApwzD9Z46o4lJ6xrzzGWvR8E5mU8nwscGtvpKKXU1FTRJ0BZLagzl5T16Z6rKcreglpRaQeojPGv4+wut9uf3IPbJQR9Hl492Mbz+5ox9p/6zrQikViSZ3Y3s7KqYFQBqr17/FtQkViCoM89/IZjMJYA9TywTEQWAbXAlcDV43JWSik1xTitpvJ8P2G/h0+cv4yL7EoXjoI8a9LFrljSDlBWy2hFldW16LTC8v0eFtotr7s3HsTjsrrKFpeH+OT5y5hfEuRTd2/iYEt3n/3vaewa0Tk7Laf2CWhBdcWS5E2FACUivwbWAWUichD4kjHmpyJyA/AgVube7caYLRN2pkopNYlOXVTKZy9ewVnLrFbTpy5cPmAbEWFOUR476zspzPNy3opK/umCZaxZaI1vOQGqNL9v9fXvvOuEPjcZ19s3ARtjFbd1WlQjDVDpMaie8W9BdceShKZCF58x5qpBlj8APDCuZ6SUUlOQz+PiH89dOux21RkBKs/n5p8u6A1kTlAqy/f3SS44/5i+3Xal+X5c9rxUNUV5HGzpRgQOtkSIJVJDVp+obe3mtsd38dcth7nQbuF19MTpiSd56LUjrKgMs6JqdFUpWiMxfvj4Cj4vOAAAIABJREFULvxuF5FYYmq0oJRSSuWmpiiAz+Mi4B0YRMoyituCNQ7lcsmA6utuO+OvviPK6upC2rrjnLO8nPteqWNvUxfLKvIHpKZvOdTGHU/t5Y8v1ZI0BmPg6V1NgHU/1ftvf47n9jSzbkU5d3xo7YiuqSee5Od/38stj+2kvSdBUdDL/JLgmCZ0zIUGKKWUGkcfOnMRaxaUZL23Kd2Csv+/54Yz0913/VUWBKjviFJTnMcrX7qIlw+0ct8rdVz03Q2sqAxzzekLKA352FnfyV+3HGbLoXb8HhfvO20BV586n4u+u4H9zRHAKl774r4WAFojuY9HJVOGP71Uy//8bTu1rd2cu6KcoN/DX16toyuaYF5xcCRvzYhpgFJKqXG0vDLM8srsXWiZXXxgjVkNco9uOmswHPAgIukq7ADd8SRf+NPm9PPjagr5yluO5YoTqykK+jDG4Pe4iNrllZwyS2B10w3HGMODWw7z3w9tZ0d9J6trCvj2O4/njKVl/OjxXdz/Sh2NnTHt4lNKqZki3+/hpitP5NRFpcNu66SyO7UDi4I+3risjHUrKvjwmQs50NxNZzRBTVHegBt9nZmCa1v7ZgFWFwayVld3GGPYsKOR7zy4jVdr21hSHuKWq0/m0tVVuFxWJC2w5+Nq645P6TRzpZRSI3TFiYNPCZIpswXluPPa3mI980uH7l4ry/cNCFDHzCngkdfriSdTfZI0jDE8ubORmx/dyXN7mplbnGdlFp5YjadfpYjMYrvaglJKqVnIue+qfwJFrkrzB5Y8XVVtBaiWSIyKcIBEMsVftxzm1sd3sbm2ncoCP/9xxbG855T5g2YKFuT1ho0pkWaulFLq6HLq/WUGhJEos6u0F+Z5aeuO43YJy+yxsdfrOvjR47u5Z9MhGjqiLC4L8a13HMdbT6rpUyA3m8wWlHbxKaXULHTWsjJuvHQlaxaUjOr1TguquiiPtu445fn+dND659+8THtPnPNWVvCOk+dy/jGVuF2DZGv044xBgXbxKaXUrBTwurn+nCWjfr2TKVhdGGBrXTuVhYH0fUtNXTEuO34O37/65BHvN3NMbKK7+I7alO9KKaWOHqe15FRYryrwUxLsvbF2sFT44WQGqIluQWmAUkqpGciZyr6qMIAIVBUEKM6o/LCsIn+wlw7J73Gnq2ToGJRSSqkRKwv3Jkl84c2rOH1xKV63i3DAQ0dPIp0wMRoFAS898eiUng9KKaXUFLWoLMQVJ1Zz5tKyPlUoSkI+euJJFgxzH9VQCvK81HdEtQWllFJq5PweNzddedKA5cVBHwGPe0xTtRfY41AaoJRSSo2bT56/jNRgFWpz5KSaaxefUkqpcXPuytynjB+MU91ioltQmsWnlFJqRJwuvjyvBiillFJTyPLKMIvKQukK5xNFu/iUUkqNyPtPX8AHzlg44cfRFpRSSqkRyTZb8ETQAKWUUmpK0gCllFJqStIApZRSakrSAKWUUmpK0gCllFJqStIApZRSakrSAKWUUmpK0gCllFJqShIzxqq2E0lEGoB9Y9xNGdA4Dqcz1eh1TR8z8ZpAr2u6mcrXtcAYU95/4ZQOUONBRDYaY9ZM9nmMN72u6WMmXhPodU030/G6tItPKaXUlKQBSiml1JQ0GwLUbZN9AhNEr2v6mInXBHpd0820u64ZPwallFJqepoNLSillFLTkAYopZRSU9KMDVAicomIbBORnSJy42Sfz1iIyF4ReVVEXhaRjfayEhH5m4jssP8vnuzzHI6I3C4i9SKyOWPZoNchIp+zP79tInLx5Jz18Aa5ri+LSK39mb0sIm/KWDflr0tE5onIYyKyVUS2iMgn7eXT+vMa4rqm++cVEJHnRGSTfV1fsZdP688LY8yM+we4gV3AYsAHbAJWTfZ5jeF69gJl/Zb9F3Cj/fhG4FuTfZ45XMfZwMnA5uGuA1hlf25+YJH9ebon+xpGcF1fBj6TZdtpcV3AHOBk+3EY2G6f+7T+vIa4run+eQmQbz/2As8Cp033z2umtqDWAjuNMbuNMTHgLuCKST6n8XYF8HP78c+Bt07iueTEGLMBaO63eLDruAK4yxgTNcbsAXZifa5TziDXNZhpcV3GmDpjzIv24w5gK1DDNP+8hriuwUyX6zLGmE77qdf+Z5jmn9dMDVA1wIGM5wcZ+ks41RngIRF5QUSus5dVGmPqwPqhAyom7ezGZrDrmAmf4Q0i8ordBeh0rUy76xKRhcD/Z+/N4y85rvrQb93fb0aSbVkGbBPvMrYDOI7DIuwkrB8CwRAMJCQGvzjYYNAjLHksSSBscd4jLC8JEJ4BYxvbYMDYBm/yvsqyLFmbtS+jZbTMSLNrNo00M7/f7Xp/dFf3qVOnqk51375zZ6a/+ozu/fWtPnWquqrOWtVfi1orP2OeF2sXcJo/L2PMmjHmBgB7AXzCWnvaP68zVUAZ4drpnE//jdbarwPw3QB+2hjzLaeaoSXgdH+GfwLgeQC+BsAuAP+ruX5atcsY8wQAfwfg56y1R1JFhWunU7tO++dlrZ1ba78GwDMBvMQY86JE8dOiXWeqgNoJ4Fnk72cCeOgU8TIY1tqHms+9AN6L2hTfY4x5GgA0n3tPHYeDEGvHaf0MrbV7mgWjAvAmdO6T06ZdxpgtqBfxv7LWvqe5fNo/L6ldZ8LzcrDWHgJwKYCX4TR/XmeqgLoGwAuMMc81xmwF8MMAPnCKeeoFY8zjjTHnu+8A/jmAW1C359VNsVcDeP+p4XAwYu34AIAfNsacY4x5LoAXALj6FPDXC25RaPAvUT8z4DRplzHGAPgzALdba3+P/HRaP69Yu86A5/UUY8yTmu/nAfgOAHfgNH9epzxLY6x/AL4HdYbOPQB+9VTzM6AdX4E62+ZGALe6tgD4MgCfAnBX8/mlp5pXRVvegdp9soFag3ttqh0AfrV5ftsAfPep5r+wXW8HcDOAm1AvBk87ndoF4JtQu3xuAnBD8+97TvfnlWjX6f68Xgzg+ob/WwD8RnP9tH5e01FHEyZMmDBhJXGmuvgmTJgwYcJpjklATZgwYcKElcQkoCZMmDBhwkpiElATJkyYMGElMQmoCRMmTJiwkpgE1IQJEyZMWElMAmrChAkTJqwkJgE1YcKECRNWEpOAmjBhwoQJK4lJQE2YMGHChJXEJKAmTJgwYcJKYhJQEyZMmDBhJTEJqAlqGGO+zRiz81TzIYHzZoy51RjzbaeQpTMWxhhrjHn+gmk+Yoz5ikXSLKz/m40x205V/RNkTALqNIYx5j5jzGPN5N5jjHlr86bQsx7W2n9grb10KB1jzOuMMX+5AJYmJGCtfYK1djsAGGPeZoz5zTHr40LWWvs5a+1XjlnnhHJMAur0x8uttU8A8HUAvgHAr51ifgbDGLN+qnk4k3Gm9++Z3r6zCZOAOkNgrX0QwEcAvMgY8yXGmA8aY/YZYw4235/pyhpjXmOM2W6MOWqMudcY828lmsaY8xpt9qAx5jbUApD+/nRjzN819dxrjPkPMf6MMV9mjLnEGHPEGHONMeY3jTGXk9+tMeanjTF3oX65Gowx/9sYs6O55zpjzDcX8HafMeY7mu8zY8wvG2PuMcYcMMa8yxjzpc1vFzZ1v9oY84AxZr8x5leb314G4FcA/FBjpd4YaZujfdQYc5sx5l+S3zwLjNQnLqLGmGcZY97T9OkBY8zrSRt+zRhzvzFmrzHmL4wxFzS/Ba5X1v7XGWP+1hjzl8aYIwBeY4x5iTHm2qZv9xhjfi9gpqP1n4wxu4wxDxljfoz9do4x5n82fbfHGPMGU7/RFcaYJzdj75Ax5mFjzOeMMeKa4ywaY8zFAP4tgP/c9Pklze/RsZZo35VN3buMMa839du1YYy5rLn1xqaOH+J9aIz5amPMpc39txpjvo/89jZjzB8ZYz7UPPOrjDHPa34zxpjfb57RYWPMTcaYF8X6dkIGp/qNidO//v8A3AfgO5rvz0L9xt3/B/VbNH8QwOMAnA/g3QDe15R7PIAjAL6y+ftpAP5BhP7vAPgcgC9t6N8CYGfz2wzAdQB+A8BW1G/+3Q7guyK0/qb59zgALwSwA8Dl5HcL4BNNXec1117VtGUdwC8C2A3g3BxvQt/8HIAvAHgmgHMA/CmAdzS/XdjU/SYA5wH4RwBOAPjq5vfXAfjLzHP4NwCe3vTJDwE4huaNrPx+Ut+6QGcN9ZuTf795TucC+Kbmtx8DcHfTz08A8B4Ab29++zbadqH9r0P9tt8faHg8D8CVAP5d8/sTAPzjSNteBmAPgBc1PP11w//zm9//APUbaL8U9Vi7BMBvN7/9NoA3ANjS/PtmoH5JqlAPpfk2AL9JfkuOtUj7vh7AP0Y9di4EcDuAn5Pq433Y8Ho3auVkK4BvB3AU3Zx5G4CHAbykof9XAP6m+e27Gl6fBMAA+GqQt/NO/wrXuFPNwPRvwMOrF6FHABwCcD+AP0azuLNyXwPgYPP98U35H5TKsvu2A3gZ+ftiMolfCuABVv6/AHirQGetWUC+klz7TYQC6tsz/BwE8I9yvJG+cQv07QD+GfntaQ0/bvGyAJ5Jfr8awA8331+HjIAS+LwBwPdL9yMtoP4JgH2R3z4F4KfI319J2tAurpH2vw7AZez3ywD8NwBPzrTlLQB+h/z99xv+n98swMcAPI+14d7m+/8N4P0ggiBRT0pAJcea1D6B/s8BeK9UX/N324eoBeluADPy+zsAvI7w92by2/cAuKP5/u0A7kQtHGcpnqZ/+X+Ti+/0xw9Ya59krX2OtfanrLWPGWMeZ4z508YddAT1YvQkY8yatfYYai3/JwHsatwUXxWh/XTUlo7D/eT7cwA8vXGBHDLGHEKtcX65QOcpqBdSSmuHUM67Zoz5RWPM7Y2r5BCACwA8WcEbx3MAvJfweTuAOeN1N/n+KGqrQgVjzI8YY24g9F9E+CzBswDcb63dFH57Ovw23o+6T6X+lsD7+7Wohc0dpna5fm/kvlQ/PwW1RXwdaftHm+sA8D9QWyIfN7VL+ZeVvHJoxhofO3+/cS/ububAb0H/TJ4OYIe1tiLX7gfwDPK3OF6stZ8G8HoAfwRgjzHmjcaYJyrrncAwCagzE7+IWsN+qbX2iQC+pbluAMBa+zFr7XeitiTuQO3ekrAL9aLp8GzyfQdqTflJ5N/51trvEejsA7CJ2sXm8CyhnHVfTB1v+iUArwDwJdbaJwE47NqQ4Y1jB4DvZryea+u4XQ429aMx5jmo++9nAHxZw+cthM9jqBdxh7+X4fPZkfjUQ6gXaodno+7TPbwOY8waOiEhtsNae5e19pUAngrgdwH8rTHm8UK9qX7eD+Ax1C5i168X2DppB9bao9baX7TWfgWAlwP4BWPMP4u0PcordGON3/MnqMf2C5o58CvonkkODwF4FouXPRuAZrzAWvuH1tqvB/APUCsB/0lZ7wSGSUCdmTgf9cJxyNTJAP/V/WCM+XJjzPc1i9EJ1C7CeYTOuwD8F1MnXTwTwM+S364GcMQY80umTlhYM8a8yBjzDZyItXaOOmbyusa6+yoAP6JowyYal5cx5jcAUE00xRvHGwD890aYwBjzFGPM92fqd9gD4MJYcB+1y9Q2fMIY86OoLSiHGwB8izHm2aZOavgvibquRi0QfscY83hjzLnGmG9sfnsHgJ83xjzX1FsJfgvAOxtr604A5xpj/oUxZgvqTM5zUo0yxrzKGPOUxko41FyWxsG7UCcdvNAY8ziQsdTc+yYAv2+MeWpD9xnGmO9qvn9vk/hgUMc955E6OPagjjPRflGNNYLzmzofacbbv8/UQXEVaqH/n40xW0y9n+7lqGOoSRhjvsEY89LmORwDcBy6Nk8QMAmoMxN/gDpQvB91csBHyW8z1BbWQ6gDvd8K4KcidP4batfGvQA+DuDt7odG6LwcdXzr3qauN6N2w0n4mea33Q2dd6AWkDF8DHVW4p0ND8fhu3GivAn436gD+R83xhxF3ScvTZSneHfzecAY80X+o7X2NgD/C3XSwR4A/xDA58nvnwDwTgA3oQ6efzBWEenT5wN4AMBO1O5YoI4FvR21u/Ze1P3xs819h1E/wzej1vKPNfem8DIAtxpjHkHdPz9srT0u8PQR1OPp06jddZ9mRX6puf6FxpX2SdTWOwC8oPn7EdT988dWtzftzwC8sHHnva/HWAOA/wjg/0Cd3PAm1M+A4nUA/ryp4xWszScBfB+A727q+mMAP2KtvUPB+xOb+g6iHp8HAPxPxX0TBBhrkx6MCRNGgTHmdwH8PWvtq081LxMmTFhNTBbUhKXAGPNVxpgXN/tEXoI6SP/eU83XhAkTVhfTjusJy8L5qN16TwewF7Vb7P2nlKMJEyasNCYX34QJEyZMWElMLr4JEyZMmLCSWGkX35Of/GR74YUXnmo2JkyYMGHCiLjuuuv2W2v53r3VFlAXXnghrr322lPNxoQJEyZMGBHGGPEkmMnFN2HChAkTVhKTgJowYcKECSuJSUBNmDBhwoSVxCSgJkyYMGHCSmIlBZQx5uXGmDcePnz4VLMyYcKECRNOEVZSQFlrL7HWXnzBBamzICdMmDBhwpmMlRRQEyZMmDBhwiSgJkyYMGHCSmISUCPimvsexmveejXmVf68w7d+/l787kc1r5spw8nNCq9681W4aeehfOEEfv19t+Bvr8u9YqjGvLL40bdejau2HxhUZw4HHjmBH/yTK7D7cPAaowBX3LMfP/7n16DKPIvf+/g2vPlz27P0qsrix//8Glxxz341v31w6NGT+ME/uQIPHnps1HpK8K5rduB1H7g1W+7n33kDPnrLrmy5w49t4F//yRXY8fCji2BvwhmESUCNiOsfOIhLt+3DsZOb2bKfv3s/PnPH3oXzcPDRk7j87v24ceewhJNP3LYHX1AKnEdPbuIz2/bhhh3DhGIO2/cfw3X3H8S2PUezZa9/4BA+eftenJxXyXKf2bYPn7srL3ROzit88va9uP6BJbVx95FR6ynBFffsxydv35Mt99FbduOa+w5myz1w4FFce/9B3LZrddo4YTUwCagR4Q6K1xwYP9ah8i3dgRVYWDUJyz7HQte/+ZpcmVxRC6viu6TuISgZQ8uChXJMK8eM6/FVauOE1cBKCqgzJc3cBl/SZceYoO3kH0rHQrl0L29RbYWOqmzzmSltrVLgLW1RXb3FW62oKMeMLZkoE84qrKSAOlPSzLWLYl1Wq7uXoVqQsLDt/xRlW8Ex7oLThpMU1Wj7oRZQBfTyRQfB8VKtkISy0PGjt7Saz9Vp4oQVwUoKqDMFbhIrciRQWV25UtiWh4EuPmvVNJZmQUHfNm3ZSqkoLKpfc1iWICxBZZWuO2tV1mjJPJlwdmESUEuAzmU0TjxjUcKidtcoy7b3jC6hmnoURQsW+lXS+rWxs6WiwHW3SPfrhLMPk4AaEWUxknGn5+AYFEpiD8tZVEuSMbQCReviKxF4Q2CFb6ca+uQH7RhYQSE8YSUwCagR4VwWKheUcmEs58FN/mHEqwIXX9fuQVUq6ilw8Sn7QdtOLb2hWEX3V1Vp3da6viyZJxPOLkwCakR0Kd6KstD56/vysFwX33KSJPqk8efTzAvdUksyoVZp7bbKXip18U2YwDEJqBFRkuJdIgDKePB56U2nRxBqWS4+1WKpfBbadi6qX1elnhKUWPvaZApt2QlnF1ZSQJ0x+6AKNfxR9kEtaPLXOrOOSElsaAhK2qbdWKtt59LibCtpQSkFfVs6T6/+XKFGTlgJrKSAOnP2QeljJCUxnhIsKh5kbR170NW5nPiMLWibth+sXSy9oSiJsy0Lmi0Hbf8oxkzbRuX4mnD2YCUF1JmCEktCn/HUj4tFuPhW7iSJgrZpy2r37iwtzjYq9X7QWPtFm7Wt9zFhQotJQI0IrVupLjQ2DwPpFNBYWnympG1KbUGbJLEsP+YqxmfqsZB3lQJK92tbdoUaOWElMAmoEVFyXttoWXyLolOSI7Hs+IymLPtM0SxaVBV1D4Gjv2ouPk0/AmVZfKvTwgmrgklAjYiSc/DGOuqo8+8PI14pXV9AWWxoCEpiXa79qqOOlDFDSncsrKIFVSmEeEnsbFkxywmnHyYBNSI6zVCXFTaGS2xR2mmRi6+g3UPQz42UKae0FJel9a+idaFx8XmFlUUm+TSBYxJQI6LMxTfOBF1YwkKJi29JUe8yBcCV1dNNlikoOwRFccwlYfEuPpdQMWGCj0lAjYnCRXGMCdq6T4Zm8RXEyJb3Kgq9AqB1I2lPbXeuvVWyEpeJXB91yplCeXCfK9bGCacek4AaEaVnxY2pJQ8NlZTEyNr9X2PHZ5rPkmrysZOyhXLsRXVRCsYioXndRsk+sWW9umTC6YeVFFBn5UkSynJ9eRhKvOS0dcs+x0KJ+2t65fvioLH2+73teMIEHyspoM6YkySEb9GyI7n4FvbKd+gX4+Vv1NWU9e+JlrNat9Sy4iarF5+xFlmGOr1IHx9cKSk8YSWwkgLqTEHZG3XHPupoqAVVksW3HJdNl8aviBkpn4XWxbesV0Ss4qsoNGPVNscWlcQHV+mVIhNWA5OAGhFFLr7C2IeeB30iQZaG9qij/lUVYYzDYrVOvumw2FwZ/ZgpsbYmnF2YBNQSoJ2kY54kMYRy6SK57NToMhdfppxSUVhanG0FXXxQuEFLlbOG7IQJHiYBNSLKNPxx8rQWoYGXhgiWtaj2WgQVsZOyJAlF4QFYyX1QCpWrbMwsxxqdcPphElAjYhVe+b6IV5OXvvLBvTZh/PiMnq/T/ZXvq7R4L/6oI/+eCRMcJgE1IlbpsNiFuPjUdS45PrPAspoMNUpnWWvqSllQCuHc59lMmMAxCagRUTLxRkszX4CLqPToomXFFFr6JWnhORef0tXatXHcVq5ifEYjnEuVM23ZCWcXJgE1Ikq0bKssV4pFuIhKF+NlxWe6UxY0ZdGUzQT3oXVLLclKhHOVjVtPCVybk/1kgy9Zeqt0WsaE1cAkoEbEkFe+377rCP7dn12F4xvzgTw4+t213//EnXjL5fcOopEsX3AOGwAcevQkXvGnV2LX4ce867/zkTvw11c9kKqo5kvBWNuGzGvF1Vl8hX3SF1W7n6ir6FffezM+cOND41acgOaUiJKjjqR9UP/1/bfgvdfv7MmhjG27j+JVbx4+p3L42K278R/ffeNgOnuPHMcr3nAlDjxyotf9xzfmeNWbr8Idu48M5oXjU7fvwc+/84aF0+WYBNSIKHLPMBffjTsO4XN37cf+noOzI2u9TwD41B17cNld+8ppKAVOqQV1z75juPreh3HHrqPe9Y/fthuX3x3ns+wkibAfxHJWuQ+qYJ/PEEjUP3rLblx5z4FR602hzMWn7x9a9KO37sYVdy+2jTfuPITL796PvUeGzakcrtr+MD58867BdLbtOYqr73sYd+99pNf9e4+cwOV378dNOxd/ZNzV9z6MD900vI05TAJqRJTEf2z7P/I39It8mrBPpzRjsDxJwn2W3RGUz/BZJAiVZbWuVts1clRIWxX0YnkcaFxy/RJYrHdt4S1cVtwQizkVZmj8cczX3liM34/AigqoM+aw2BINn2nui4pxSC6W+mTyAs3WfSpvKeW9dQdV/Hp6ope81kPb3lIX39hT1NGn/FfWZl2VY0KT1FAyZiR6pWNUg2UdqbSoLSOl2zvC+306i0RV2aXERVdSQJ0ph8WWnRXnT5xFBY67IDvVTstolr6SuzhmFVnsc9ZMn3cOLeqV71K/jgEp3lNbF6fOgqoU5+y5uKDu3VqOntfKhUv/TmiO/8wWUYUNvpTzMeD2NG2M34/AigqoMwUlLii+D6pLsFg8D7bUgiq2FiIuuwhimmJtQSn4KrF4NC6+PLmlZSpK9eT6ZWy0C/2Clj7J2jqdLahF8T50DRjVglrSGJwE1Igoc/ExLbm9PtSC8nlx34vIFi7GpfGZ2GJf/x0nUrJQqllSumcKm9gbouW3IBdSX2iO8CpTHiQrcfE2YsfLyBbUwmNQfWnln1NflMTXh2ASUCOidXUp06A9DbJ1kQzjQdIaSzW84qOOCjW32MkEtaWXv68slTldWHvU0dD4gBYSfa0bcixYxfMtO4YqpFfyBmctFuWVyKGyixGBJan6qftHOaFmQTHyHCYBNSLK3irqL9LU3hnGhKPv11UysCQXTLJ8oe87Zo3YzEJc5GZTlrUCH6m6x8/ic5/+iDiFBpTKM1AyZqQkidyz74PScdy7Huv+DfR+FMZ+JT6AccbKsjwIk4AaEWWT1C87VHvq6IZDiVtrWRp9BY7yhngMSmdBlexbyrVCL7z1dQ+B1JdjvdxSC41iUPRshIW0dIxqUJK4MQSLsi4qRT+n72/aO4LJuCwPwiSgRkSJD5lP0oUNciHjyip5ouUpT9k6SwVaZCLmtsyWTGBN5lldp66dQxcPNQS31BiLdwk046GPckYLl45RDZZpQQGLWLyHKUGjWlBLGv+TgBoRJfuBuEYyPEDq7vfp17TLMnCK92QVTlCJR1efbhHUW1C5dltb5uJb2mvtmdP3VFpQmvFQomDJcdLF7/Va3jMrU9DidJrPnv0w5jmO2rMth2ISUCOijxbJBdPQSSotFFVm4Y8xV/zKd2UVsQUj996hRb/yvcTnv7xXvof1jPVySzUUmnk/74H1ri26lcsS6jGFq5jOQAtIM+b7YznjfxJQY2LAJF2UhmLZp6NZQrXUNVJs/UU1W+XLA/VVKBfVxdBbBCQr0dolVJyAxnIdopwBLlOxD3eK+kbuu8WdAqNXmCSM2U6ty3woJgE1Isrec8Nce+yzNw+SBVWVmf2lmlz5UUdy+ZwFVVKPau+Oo6vonKW9bkPo+1OfJJF3HRWNGcElZjP0+2BZgf1SF3eGzIA08/Hau6yTVCYBNSJKXn3Og+6LWgCjZn4B4dKBXuriiAnj3MniJTEFjbujKHZKDZoqAAAgAElEQVQwqvukgzQOLMYXjClorPuhr3y3I5iJQ11m6nqaz+GnwAyz00s9H0W0l9SXk4AaEaWHxdJ7HBalhYUaeDkNtceupwVVnGZewJambMl6MGzpKAePz5xSC0oRhCrxAFhhtbOZZ98HYx7949fjxv/AudvyO4yPMZMkJgvqNEavBY9p5kMfv2Q5lAagF7XxtrS8rRlN8MW/pMrmhWbp0VSU7ljgi9SYB4BqodGey97VFdKrrcQFW1BLCuwPFSwtnYH8FseCS2hPSRKnP7qJp3dBca1nqIayiBTeEldaXb5Mg0wfdZR3I2lq0bilStq5tFc3sIVgzONrtND0U5ny0NAjnTnGYaTLUioWZUGVhAgkjJlpuqy+nATUiGiDyQphwBfbEhdJkgf26b6XkC3lZVHltXyWZPot7HR09jkWuGBdVnp7CiWHxZack+iN0bTx3AvLsj41Y62ETl8y3VoyggW1pHE4CagRURRIZIvj4vzYIZ3Sc85KX29eGkCNHeuUy1Yr2weV78+Sdg49J00L7iZelu8/Bc3CWTpmgFArX3Tfdhtfx35mC7KgBtJZ1IHTIu0ljcOVFFBnzht1m88CDZ/Hn4c+fklYWFum+ZRaRMUvOIwsZjk+S96oq4qbFGj9y5IPPJ23JLYzFiSXXKyMTnloPpk7c9F9XKo4Da1nsGAY2A/d+jOQjxTtxZP2sJIC6sx5o65egwmPOmr+HjjKpbfOlu6jKU15L3VxpCwozWnmOhdfXmhWBSvY8t6oK3+eyhcWLjpGx8fXWPt3lv2KlEVZUH35HbO902GxZwC6Z6dxGfklF6XtSdqoLaRbYgl6dWrpR1TmHJ+adOeAp0TZTisseF4jCwoeN1lWcDoFjWbex3sQa+uiUDAdh9WzICVicD+MaTEuyYSaBNSIKBlgXMNflIYiLaRVVWZBlQvLMg0yNqFtNgal50sloAqEzvIEVP0ZO0z4VIC75FJlyujVGEs7X+YLC+vPU21B1Z9jKDPLymKdBNSIKHthIbyyi9L2eOyiJVlEt2xRLB20MfdbLgZVEoxWpaQXLCxSv46BmEV9ao+L1SxO+jETiz0tuoUawbqgmsj/B1AZ2A9j7lVaVl9OAmpEFMVIIpryotwE/H1CZTEon7dsnYXlu/0evN70Xhipbfmy8cIl+6pK6h6C8HSNZlws+FUUJdBo5iVjho+XsdyYy9L6F5UtODQbcMxMu8mCOgNQosEE8ZRFaSiCK6r0dQ3FMaVCzS2wGsnfy3zlO7dWkuRiTC8YfLFenhUQh8YzUOZ+9emNpfl3z3dkq3dBbtiS8ZjkYxgbMm1Wx1iYBNSI6BUjaf5enAUVrqRVoQVVLHBKBAfiWU9ZF1/rSlFo6YqoLt8rlqOorXsIuKW2rDhKCpqFs+zdWv7nWJr/suJ3C4tBDdzHVOrJKKO9nL6cBNSIKHFV8Em/KDeH9Gpyi7J37XRldTcVx2ciVl6ORtEr3wssKA3NZb/yPVASTqWAUozNEjYt+zaa5r8k63NRj4hblOX3F2jIpbSXNP4nATUiSjS2WOxpsJtA0KJy71mK81ZWt34flN92eq/uaCKNlp5vg/e6hyy98J4xEHsNy6k8SUITq+s19lkscrT3QY0cv+OZuH0xtB+GnuWXpL2kcTgJqBFRogFxF1+fo2JkHoTFxJZZZqXWXEzLf8fVD+B/fOwOgceweNnRRAqe2D3JQpl6Y3X/2eX34o8+czc+cvMu/Mp7b8aNOw7hx//8Gjx06DG88o1fwMPHTio4Tdcj9dUHbnwIr/vArd59B4+dxCvf+AXsOXJcpPv2K+/D733izvbv23cdwWveejVObM41TNUfqS4qUh7cLXwSdPd+6KZd+LX33Rzce3xjjh95y9W4a8/RgnpC/Nr7bsaHb96VvP/hYyfxw2+8EnsjfRrUI7TdWouf/qsv4sp7Dij4HaalCt24MCzLkJ8E1JjoMb64b3eothdz8fXRyrS3xFx8n922Dx+7dU+0vGRBpeMc+TJF9ITyJfQ+fccefPL2PbjingP40E278MUHDuKTt+/FVfcewJXbD+CefY/kGeU8scVOstw+f9d+fIgtrvfsewRXbj+A23cdEeleum0fPnFb9yyuf+AQLt22DwceyQtRV3Nyjxr71NALrcSuzOfv2Y8P37w7uHfPkeO47M59uGHHoWw9qdjQB2/ahSvu2Z+8/649R/GF7Q9jW0YYpjwOJ+cVPnTzLlx738NZfnlMrhTLeB/UlCRxGkObXMDf1USvDX78kcW/zyGe2rTZ2MSKHbEkCRqNdaSJU/FK0vTC+rN1s2fn+rbeZFxfn1chfS344i0Fp+sjofz7cgKZHyNVcnRTyWnmqjZztzbjyRWReCtxhafmo3t26fv9OqPlEjyVCB3N8VwqPkawc5aVrDMJqBGhzebhe5TotcGnmUvXbJkFVbI/iJYLsvIQmbRCeU2Mp2yyyzxRVEL9Wrrt/U3f1l+bSdxmY5U/y2BvUMsfFS5CX2diBBah0kLrSfPkaOT7Urfp2acnxYqsIITddW09Kddb7txHj68B5TTjuqPjf5Yjr0j0ptzSHFdCTQJqRGitIEmT7SbrUB78T0ezyO0YfMnVKbfbWou50CBJI9do4Ny6SPOkp6dBrF8r6xSAbkHdHCCgHFPBUUekiGSZdtabXGdl/d/cM4iV91nKL3xFz4bFnrgwrvmVre+2nSWWn/hbvu1aT4L7Vea3h0DNlpQxphtuUetTDpOAGhHahZ3+HFoFw0YAjwf12Z1e6m6MCYPY/ivJEtK4nLrfNNqo3w8S+InvpfScYKoqv63zxhQYIJ+icRp3TTrHsC4XocsskhIrTyXsi8ZX88nu9Z9HzGWmXyhzgiMfd9TVlXKBllmW5XPV58PR6XV7EtUAt3UJJgE1IvQuvnBhXNTg6rQ+/+8SssVHHUV851KshNKli31JkoQmkURTVrLgSug5C8pp+9yK6eXiq/h4CBe/lAUVW9z4PSXupG4MpYS9z28KfHxxYSzxy+8tOo8xMga1rvhcuVTb+7jt+gqB4v2IBVjW62YmATUmlJaHtzC21+KTqYiF9tPnpWxglfESE4LWyvWKFlSB9qg7SULmSeIjVy5Gz72p2DbXHV9zhbDN1xNXXKxFwHDOBcOtLj7u0jzlx0OfY774wl6xByJaUK6dGtdkQnDYCH2/jG5MJveAlQjuIa7hrqpxLKgBY7oEk4AaEZImmL2HPfihGkosPbkXT0pNLNbuysoxqIo3GjRwnuKrYBFULC7cXVdKz7mhXMDd/eRcfH2eJe+a7pPWm4hBKS2oNgalEVCqZ+PKqCSUR0+iH7WgGgt2rqgmt+lbG4OaZyz2lBLYJYAsRqlK3r8gJVcmXn9MFtRpDO0k9Z+xrzUNffx8svcRfKWCNuZa4Fp7eF9YaToG5fOXQsmiGvCSKdtd65IjKtstQpvMTVeCIHYoWCZSv+biF5Q/Wl7lLmX3iGUKNOxufPljP9gaIdAqi9PELRKdi09n0aTceCV7k0riVRIkZWZRGFswOUwCakRoB6OY7tv8PTzN3J/AnbWip8HjINk63QRli10slVeOQeXrLNq7E4mLSXw0N6jo8WfXxZ9IDGref6Hhj0tK8ZYW12yaufWTAkrijJpnU7QQs/HV0vX4S++h07nMGH3Gb46Euo8SQrOkn0uEvIQ+3hItNErKIjAJqBHRTbT0Q/QMBzaAhz7/2CAvIdutF7q7hPUFgGaRCWnk3DJiRYmyaYFHv2eemUDPHcLr/rVZfAOeZfCaDYFWZUNu23PYIhYRz6gssnjaMvHCVviWKxu8uJCVSadtZ6tJxsVi9L0yyueYsuz7uKX7ouvHxQuRMYUfxSSgRoR2/ZT2QS3Kx8t56OM2KNbkIhqk5IqqeQnpa1LIC+RTeZJETkkW6FWVv9AtYqNu+Nz8vx2v0qboVJ2hBdV/XKR+KxF4fEHlMTJxwW8++2QLerRtnoY6iy+RuFHCb1u2Z5ZDifAuRYnlOgSTgBoRWm3J0xTZgx/6/Pli2cdtUHIoa11nhI6NTVrrfVL+0ougLAhlnjT92f2ojUdIyQrukos9dRt1s2yGHAXaePgsXHq7xF+sHaEFVX/PJUnwpJBEyYDPeEn/2YgKSyUL4qKkg6Av/evZ5AfXR9oNvaIypqNB6fRdAlolagwBxT7HwiSgRoRWy7DeXhp/Yg/P4nN0fHp9NGXtPbH4R87F51sweT5TC0FYuOMhBsnFmKubW120jW4Rcp99XDY8Zigt3lboV81GXTH2qbQicmX7xFoCy5MJf1qW86DbvyU/B22ihTa1OtWXJfughidJ9B93p5I2xSSgRoT6sFjBcijJUNPxIn+q7lVOzKAuQauXJqZ48Cr7TPJVwpOCHv+upVdZ22r6QCigellQhDbli1tuYV/793FEs/hy7RaekVzO/9TQ7Noa3htT2IoEIeOtlIZWYKSEZlWgrMT41WKoBaaiPa58mgTUmNAOEOkhL0pDqdhst20mk55uyf4gIC5cLWKBbv8TpFzKdVOSYlwpZtTQfVAWvmXCXXx9gtWcbUmQdAtZXNEJ6MIXam35nPuKfE9at4qsSU6zKyr0LRNiYPeUWSQyr1nh3NLJlGvHf37splCWQi/dr6+rnHZ/pasEk4AaEdLCkSoHSJryYnjg6ckldEssi7qMrGnG9rLE3GVARktHvkwRPWHRz5XlQtUiXBiGTWZfuEmLX0rAR/dBVX1jUAFryXJFz4b1kz8v3CcfUwWCMCI4uPCP36/so4TAKxoLBX2Y4mMMK0ey5MfA0gSUMeYHjDFvMsa83xjzz5dV76mENtFBTPdVanU5xOiVaFUef0WVc16sOLkl14lqH1TBJNEciSM9h3jdvuBw99TutvpaYEH1mMx8705nWYa8SP0XP83cfxb6+IpuLJQk+fC4qyQwYvRKkg5iwkHruiuNVSW9BUX89lsEzhoLyhjzFmPMXmPMLez6y4wx24wxdxtjfjlFw1r7PmvtTwB4DYAf6s3x6YSIxhYUEzT3dmEa6EEONO+IqyRNg3wv0lR9RJMkUjRUbqQsSz0sqJyWHN7jYmztojn3P/ulmecXAmkhy7r4bMSlWsBjiTWdLMPKSsIoZuWUuPjaIoJlDyB7ika3tyw3n+OCrKSfB3tResz14ipGzuNbV5Z7G4DXA/gLd8EYswbgjwB8J4CdAK4xxnwAwBqA32b3/5i1dm/z/dea+854SIuYXI4uLL5mPlRD4ZqxlifGoPQ1Uac8QWmqsDGmo9ljgaVligSUst350z9Ceq5t7pKzUIZt1G2/eX971oVwQkLWxUcsvY66Pr7CeYiV0zQ5NjZlAerfW+bik2loMkYpf+oYlFCuJOuwJOMvdf+YRx2NQNqDSkBZay8zxlzILr8EwN3W2u0AYIz5GwDfb639bQDfy2mYekX6HQAfsdZ+MVaXMeZiABcDwLOf/WwNeysLfWYUvYddGzoC2OTjcQcqKGKQXC3JKtuy8nVrAVqtNKGlvVFBPUXaaL6sFJPJ0ZOy6bgbp9uom2VT4MnV5/Mo9pXC4ujuiQiADJOlLr6yZ+PotiOFlPHL8utlFglTnJTKizqLj9GVeNDNo/wcSN4/ohAZbN0pMSQG9QwAO8jfO5trMfwsgO8A8K+NMT8ZK2StfaO19iJr7UVPecpTBrB36mGDCZcu50oDw7Unn5p8QUtbWvg05cNgtG9RdHyEE1/T/nAZy5dNlilsJ6dbC6d4DGqYi88tVghoSbGGLjYj0+XuVu3C6bc3pTz4n0maTHD0saBym2xTNEo3KQ9JR++zP6yvEFhODGpcCaV18UmQVO8ot9baPwTwhwPqO+0wZB9U59IZNgD4IA83WuYtqFIOYu2ODWpJ0LTtTgmoXotgokyeTJJeEINawEZdnsnFBRWlWyJwrHX/aitaa+Wp90EpynRluSIT1hVz5fWyoNh1/T4o/zNbjyigmn5WvWRz2BrQPoMRZEjJ8x2CIRbUTgDPIn8/E8BDw9g5s6DWwqnQaD4XZUF1C5r/WUJb2l+TLi+XjblSpMVHs2h0v+WZ4v0gQVoQS+h1FlT9dyigsmyGPBHa/mfYV5S8JgZF79Uu0qISIZVTKBhdWf9TsnQkBYuWLdqfF7Xgc/fLCla8XH8a9P6+a0BJvKuctl/HWBgioK4B8AJjzHONMVsB/DCADyyGrTMD7aQq8OvzneZDH39K4Gl925KrJVlnVNuNTE5RcOXbz9uW5ElRVloQS+h1Maj64iLO4gtTsENh116jqecCfx7/TBhoN9Z6dSSKllg2XDjytlJ6cQsqW01LORh+ysVWa7GnypXwO3QfE/fGLBJjxrcotGnm7wBwJYCvNMbsNMa81lq7CeBnAHwMwO0A3mWtvXURTBljXm6MeePhw4cXQe6UQStkUhbU4lx84QKkJ22Fb4o6I9djyRPFMZGCPtItLvp2yi6+mpf4Rt3yZxk8v7YuotQIfZWrk//eWX0ZfkR3dLycarxEMhT9vpWFfJ+07TBVvf47fwhsWTlxS0XBmB0aQ1pUJrCEMKFlHGiz+F4Zuf5hAB9eKEc13UsAXHLRRRf9xKJpLxOdJlhwD1vch2oofGHzNe8ynii9FHKuPD7BpRciajKrpHhMDNLG2rBMSDtXtyfUGuG0yI26/Lm1feXxHS6IuQ2hHT1XXrfQa/uoyAXEFjtJwYluXShYxGPjRetKK3WDykkSzRwoEKh9MWaaebfxfeGkPUxHHY0IyyZerhwtq1lQVTywLyWLcEAD4eSWy8u8xyaMZb/ze2MTTOtyoXUoDDI1TV7OZcZxYTIkzZyPg7avCDHRfRuxOCivqc8oP5HvsXK68dJ8svEhpbRH9zANeFW9No5VGquSyGlpUH56W1BKwdsH3UEC42ISUCOidEAD4aI7OM08sQBpSXv3qLKP3H0ynWigmyZwKGIdRa98VyxCvrWRUyrk/rSWxqAq77OXBRWMh9AKkPsv3TcxF1+ORWmspsppmhzwINCPWS9lFlRIl9antR7VsSphDJVYNSUKmIQSD0NfjJ1mPgmoEdE+uhKtlC9EgwWUX4e0sGlp1PcrJpZwH/07jAGk60mlSmsR40kqo6EtuqEqC5dqDizqdRtM0Eh9JfYfknVyJYLzHOXH+zle1uevbEGXhGssnlsSZ4kpKVoLN+aiDss5uiIXHi1NfUOFwOl8ksRKCqhVSpK4/K79+IV33oDt+x7Bq99yNfYePY5Xvfkq7Dr8GADgP777Rnz2zn3ivdIiJpejWrj/4IcOzthJBADwd9ftxO985A4AwC0PHsZP/MW12BCi5NLC/dFbduE33n9LULYuI4lD6o6Rr8cSOGI9oD0BgNaZKipp7FF6EUFh0bUjFFDlzzJmUVtr8cbL7sGbP7ddXMi4ZfHz77wBn797v8C/3/eVtXj05CZ+5C1X4/4Dx0J+ENYh8i20IVdWUqb+7PJ78YbP3tO244YHDuEn335dIPTd76/7wK340E275Hqasgcf3cCr3nwV9hw57l2n4/L9NzyI3/zgbeL9Ls74f/3N9bjinv0I0fXljocfxb/7s6tw7MSmx6/j//Wfvgtvv/I+md/m8+Rmhde+7RrcsfsIfulvb8Jn7tgrluegsd3/9O4bcem2+r43f2473nTZdhWNGLTW5FCspICy1l5irb34ggsuONWs4AvbD+A91z+IG3Ycwmfv3IfP370fl9+9H7c8eAQA8N7rH8SV9xyI3K3TMjwtfEGCqaPtL16U7Ge27cOHbq63rl13/0F84rY9OPjoyZCGt/DV3y+/ez/ef4O87S3u4pOvS9q+LyxifeGETr6v+CIolwkVhVxZnjmXsqD6PNJw0e4W5k/ctgefuG2P2N9UGbDW4r3XP4gvbD8Q/M6Fp7XAjocfw2V37sONOwUFMfKMooz7t0SK+jzQmNAnWRuvvvcAPnrrbhx5bEO894M3PYTP3RVRGBtO7tr7CC6/ez9ue+iIWC8AfO6u/bjkJn98U77mlcX7b3gIV21/OKiHKi837TyMz921H/cfeLT+jQnWj966G5+8XRY4rr49R0/gU3fsxfUPHMJ7b3gwIhSl9nZ03nv9g7iyef4fv20PPn7bbhWNGJbhPgRWVECtErhZvzkPJ3bcz+/TiMG3HPwHrzmWP02bf5IFtbJhFpfgloi5jqIZYizRo60v4rJIxVV4/RJfqkwixbOQ3GbZsqxvrCVjhn32SXjhAXya3ltr8mEZel9lZfcdjwdSC7sbCyG/2n10JXvnAk8D4YkLfZcROWdjiSo/0VeMsNPIW8UhwjN3JtAFPzW3aWJLmITil+Hv5ZIqpC5PK/AVA1U6Kmu9PZaa15OkQPtiTAw56uisQDyeUA8Wm5gQQ/ZBLWqjblAX+b5ZVYGrREp/lfa+WCu/28krE6k7FoOKJXBk5m+ZBZUqUyKgBHoxZWZz7vdxCbrx4D6p4LEwQhn6nQqcudC/XPA5urQdPj95xYHSzZWjNLkl6DIiaeo+F5587FSpcdnU45JWQiHn8xxTpHJ9lOpL6b1sqXd2UX6dslEaO3YCdd4qo8B84MKyrI26k4DKwA2Gjcr/nFehK4dDWjhS5egf0qLdB6EG3tGbV91k5inRHkueAO3aH59Y4X2UB369JWPpNbqYpiewpou6JIN4YU1iRltWtFrqT67MLCQGxf6GbZ7VTF5gqaY+F54tdzW1Lj/bWdWishJ5RkE573uuL/17aEr9vNH823k47/gU+a9s1LLnz4ef2kLvk8a3JfdLQr8r1z0PXk4UqJn1g/KbmncpPuhnqo+0WNT6lMMkoDJwD3KzUT/cp+cKiTwkPgGidXgLi09z6PPnWimlt0kGqkYj5PSi2XWRTKW4QA/L+wuhWE3gvkyB94OEkjkr0bNsMVrM+6D8MUT7trIArMwLXRi7hVXin4+3nItP14hYPFEuywQFea5unlHhQD8DC8UmrIPmeugmDHmmLrH2WkX7yL/mVUPnCHMr8r5NzaPArcn4zsGV4vcvwsU3tmByWMkY1Cpl8aW04tSiDujcSoDsmmnvHTgQ+KZZTxhSC8q1M6ERUv5Sml+s4dEYlPDCPSkuF68m30cl75fivGjptX3DNHStoiLX09BsaXfXnZtZikFxVyAgK0JBNlzWOpC/h+UK+tLyT3+M0ja05xpWflnqMotbUP7z4EKOK0jha2G6z67/hPa0NMI1ggvDpAUV41cpXIL2CmOiL7pxOa6gWkkBtUpZfHxiUG0ka+YKE04sRid9W6//d19wy4lbUMEklTRC77tbDGvaUttiGT6x/SaS8KRF4hZUx0sOMbejzwctnyYq0YuNlSGHxQZHVZG63ELDA/A+f7IiFYwLcj1lHVCoYyHZjEi/HB+jLtYLAPMgftTcS4RMTmHk7+eKWaCBi4+MU8uSiygo3ZZvJgRpmZjF5+6V1h4N+P3UihtsQVXhsxoDKymgVgntosNcfM79AHTaHEenSaXrEI/1iVgbpQgtsu436ovm7inGYEAvlTotacI+D/51SRh7i2NmAqt6SFM2X2Wy7pS1Xf9e/izbO4SFzWVhSv3dWXO+tt7RlRdMZ5VRvj1+hLEg8q0sR3/v+rS7wXkqQktEFi5plxmjwYQMz4LkZDwrTdFHtFxLK+DXBvOhpQO/Di6cc+DjUUry6At390A5l8UUg8qAB2dpkDbnE5Y0Wwm+Fu5/DtdQ/MnHJ38bJ6m6axypGNncWszYSw9jg1fSVOl1f8OyXL9fj37h15T1XTxpmsGZidbvV+mzz2TmwttTMKyFsXELwH1KJzNwoSVZIJJmH7NyU+W0CSfcjQl0AspRaDMiI+456qIM6+loAmFscO49w3Be09RwHl+koPO+m19csHbXc2nx7vcN1vYcQgHn6NpeY9GjLczZMTBZUBmktOKcK0TSCFPlXGl6z+IGUljXvFLug0rQS2mQ4WGxfh925ZmWCd1CKLUpBq7BJsuki3kFcsKBfvY7i48LF7LwM+tCErDziLYfpm137UiNa38sxNtjI99TZaWtFc6Vzt2nc9anVADkYjo8liO5t6VEAk/oC/dI7WnXDyaEvaSOqEvS57dLjxeLh/ezuij/g/dBCXN2DEwCKgPLJgb1XyfdYqBadqYOMdAe/tYHPB5EFzG6eKVOTpb4jyU8eHVa+Tq/R5QdVFhkLFRND2nKahdfiR4tH4tBDZnMkiCcWz+BwBfw3X3dohj+3llo4biWx0I4VlP85spxmrxeN0a5NcGtUto/0ZgOoUk/JUVHFlpdHd13oTJCjyc6SMpL1uJja5A69sfaqRHiWnRzdlwJNQmoDNzE4DEo1T6oQk0HCBfroRoKN8Upuc25MotPEqARa8i/L8aLf10SXL5FEqFf0EmSIAnp6RZf+jt3TwHA3LmB2WevGJSVP4H6+dFYSSzGJAmccI9MRz89Fuj31LMXBnW0bFc3/QRcGyXrJ2xH7KxHhy6enBYa9ff6cy5c8xNP4vVQ9yqP2dJnlttPuMnHkVK4BPcTgTw0BqUNXwzFSgqoVUoz59oLzaTJBb+TWhaB5K+XYht94O6mk8vBuU/oqRC54234xJSPRpJ5j/WHtDBpzsXjbUtBskA4Kq/+DD12D9f6pc9+Maj4IuqSXKR4JbWQuAbt/c4WemnzNkUfCyo//v1yfIxSZTA8BaK7l1tXMZ5iVpgvjEJa1CJJzX06NuaRttF5FB8XPg99s/i4S5Py3xcxZXPRWEkBtZpp5v67fXLZTkCJi498DzSsHkyL9EJe6IBPWkSeZu7TS2nZMUsp3F8STnZPWMT6wLUtG+PTLaoQLMU4zfjfsSSJfjGoGIfNRmsbLnr0OxVgPG7jlSMLaco68JWIFN/hmMmVbccN+a1NM4e8SNMYWsryq8t2NOtyfv2pOKJ/LVz8/Xq6ey3rS+lZZC0oFoPSWj9B3I702eAsPuXcG4qVFFCrhJjWRTWf2OGN2ocoTfpYHBlQOL0AACAASURBVKcUfPKL1pAl+0wSAofSSwm0WLwnliwgNVEjVLR9FLPMUuVKrF66gAIJAZVmU+aJKTlcuNDFRlJ0vCw+ZjHQdviLb175oPeIfHsKhq7lMUFbx9nqv+Np5unEBYl+7Lin+je/PlrOE+JSHxF6vFyYlKLYqOsEDTuoWovgGVflNALeFpTElcMkoDJwD5WnmceypyhajTD7EP3Fzrt3oIbCefCC+e7YpopM1ozWTF1H9Wd8gvLf+L2cST+GQu8b1r/Swj2kHAddQIHERt0es5krOZ4FPK+8mJG3sJOFnCtZkqXqLarseB6JH/49KBf5LpYNeOh+25xXniUivU3AfaaULIo2jswUJlFwC8dDpY464ooVLxe6+uLju4shOe+NE3bJ5gW80Li5uz78qKO2kkF0cpgEVAYxbVhz1JE2kCi5sxZuQYmTsP6c29AN5PMXLjeptktjlx9fI9GPlY91QSrbTCrHv3NISQZamhqXSZ81oRsPIY9ucZNifpaVofdKliJ9ninrIKZEpMpprVHL/u74D9vPX0DptVM5H8Pjh3zhAsTjUrHxz5W5WDkpdsZhWdnyo47Y/eTv4aED3do2FJOAysANOPem2Q2axZc47oTem9MhvYW5C6w0vy1G02mFBuGlDThXafeIpDUnBVTCqqI8xWgG5TM++hw8BSBRTmsdSDRtxM3r31P+LMMNwd1v7nUpXIjRumgCjGRBcbq5hT6mRKTKZbP4EmN9s/ItqI05T5IQ2pmZj20spwr7NpaaTctVNrSIHAL3ZOXTC91tqTRz6/G7wSyhHPjrRRaZJCG5RcfAJKAy4AuxFGjMLdK5ZygeUbMgDaUVTNb/BHyNTGMR0e8p4SwtYimNWtbshcZE+Mr2rzL5wWtnIc2xgsXtc2v+pn3nsttkC7Qr0y26CMpx68HbXCqOhR59GS/m0Yy3Mf+W4rntzseLxYSDuSzMscBSY9ZcXWe8j/wxFLoCg43xVp91yNPFc4j3WfydWRpYoU/GwiSgMuCZMNrMN8mNEq8j/N4uvkNjUIGm2f1Gd+Wng76hcNG33f+k97blhfukOmMV5V188br9cmTxLbB66QKaQh8Lqr2HjQugy3CT3X/dAhiLgwDhQq9NAKi/6/pSO/5jY5QqUHyzKl34s0kShCYtJ70HTBJANDGg6yPeFloeQV9y+ikXX2ztUR911BSTXi8y5H1Q3hjoTUWHlRRQq7QPyj3HYKNuZGFw8DWpdB3SYbELt6CaT8mNRlORtS4+bun5dYbt8RcBTj9dJiqf2KcGqbJSO7V0dDGo8ofJn1sYhI8dddTdx5UJykXgchIEmsePcnEq6cvOne148u91/2gbnJVE+yclWCl9anXx+ng/57L4wiQJnxbvy/B5xud4wG/hYbGB+5YI90EWlFDHWFhJAbVS+6CY9kK1GLWLL1eJMOn54OyLlg//w4N7a6n7HrIXLnz8kFkKKeaTsmKkhQmesEprmNpjiTgfHH3eqOtojp0kIfUj0LjwhN/oAhi6tML+oAJAOxZS7fE3WqeRSqV3fPAjx6R089QGY5Gu4Kbm6eVSvI7Gn7NJEoJ7jfKYigfxMdXXgnKgcbVa6PdbXLTzaRFYSQG1SmjN7Ln/OScuBSnt09cy0nVI63JsspaiW+DCCedQ4q7kdLLlidbZXfPvkQSNJORi9WQXwIjgS5UroWkRvppBvqf8WXLhE1qfodVNy9UJBs13t0h6Z/Lxhb5go26iPdpyvKz0txSDklxlXHni4H0njzufrmdBkRdrxqw1ruTwNaKLY3Vl4md5+iiPQbF5xuN2Pd0zKWVz0ZgEVAaxQGOdodOUER50akFOleWTZrgF5ei6C0L9kXcGdTzF6eVcfJKrki98ti0b1lN/j0xgG5YVy5HvsXd38fq1mWfuPp2AypcJ72EChDFGF2+pz6S0cTEG1dJLu/i0C5LGRctpxttIFcVwTw/A4qjRGJR/ncffPB4ka5MoZzEXHx9Dsfifswqt1Vt8XdatWDy8n/3Nn39fNx+Ps42J6X1QGbiHseFSPYXU7LzVkYZUtlswhg0BnqYsWlA5rVlw8SWPeZKEoCCEu7/D2zRuhLavshp6uMgMKcd/1++DKn+WXAiHVkC4wNPvNrFI+nTDxTd/qkiCb2W2H6UZUzjq51K/c0zaoOvuSQnW+rr/N98HRb9L88GPQTU0uAXFnoGzAKSzA3MWH79c6uLj4427NFPKmhaTBXWKwYUQ9efzyR1DdgH1yvo0hz5+vvhLrHh7aZQuPh7X8OuUBBqlJ0/qWNwuHkTW9ZFWm/fqzExe7oIcLQbFWxcIdxvp4+53LnAkRcBfOOMLoWRtRBiPtyFCM3Z8TmXJuGPz0WtnYkxKkJNLfB78JIluYY/1ERd2gRJL6FPhKq0RoYApax/vdn6000IsqHHl0ySgcuhet2G9z6oKN0BSlFlQdGEOJ94QhBq4PBG0g59r8tmX2jELjt4b45GXj55mLtwnF5R5610OnFfdRB1mQcmLt7SA0nLewi0lBXD6VVdOHguyEhEv1cOCElxxjs/wqCM0n2kvgCvD6db12uBaztqMzhcmwOcsDED7ey7UGyEFIHxNSA5Be5lQXUQM6qzM4lsltL5vdpp5yZEwuXHga6XsnsHP39cOJXI5d2UlLIIpF1+yPcI9UgKHRyN2GG8i8UMqlytbEjfkLj7VPO3xLHn/hXEJuc/o5lyuTEhWkOjiE2NQtI4E3xHBKYELX2m+tJtVmeCggjUVF5X4leKjoYsvbIeftCHTdPXF4n/Ua0F/92n5f/NXjeTAS6XeIFyCZVpQUwwqA/cAgiy+nCvEo6Ff7Lonrlt8c+ALisSLf1xOpi3wy+VdfGE7wuyijj+RRmRll5IDUuUaYlHQn0qUCroQpfkof5Z8j1iKr1iyTSpJggutysrPrONHri8oF/kulm0LKB8ohHhKRrDSsh2NUGAHLj7Rgoq7+GLznltQ1MVX/y4wzJWRwtPMA2s70bYSlMyToZgEVAadBcU0uCoeKAW4iyoNb4K09eruzYHzIY3J3OTmizHlTzz9XPie0rpyFlRsHmndC9pn4ZPLKBWM5lgxqK6+PFc8LlZfCzPOZIuBlq+/a89ZTPHLv4tlA7d2nr6cdCALja4eRiPh8pSsDNGC4sqWQIuWk9yJEh1+P9BnH1QokCWhWQq6TWHs90GtpIAyxrwcwMuf//znL73u/+9Td+HJ55+DLWszPHDgWBBnor7v5Csqon8IZcnvl27bh9t3HYnGHEpBb/+1992Mk5shwWxGIqHytivuw3X3P5wOSJNLv/nB2/Ctf/+p+IYLv6S9VlmLq7YfwB988i68/bUvEdu40Cw++j2p9efrlGj+1odvxzOedF76BgAnNuf48T+/Fr/0sq/EC778/Gx5yse8svjpv/4iZsZEy35h+wH8xZX34e2vfamnQLQ0hEUycJXZXEYn5U3Xl3lh3/H3s++4HvEWdpAsv5xlENt/R8cafS064M8H6mWIucliFuZc8BJ4Aioz72gZ/UkS4d+S0CyFdrP2IrCSAspaewmASy666KKfWHbdH7p5F57xpPOwdX2GbbuP4vzztgAQYlDWii4TB2kzZAz098vv2g8AOG/rWk2n5yBq+SC3/911D+JJj9si1i9pk93v3feP3bIbOw8+Kk7utk4ygN93/UMAgK9/DhVQwC+860Y8eOgx7Dp8vF2/fLeez5/cuJA/sZhgMUiQLBANzfff8CBe+LQnZu4Adh0+jpt2HsZ3vvCpagHl2n7k+AY+dNMufPkTz4mWfdsV9wEA9h094T0f6dQFTp/GY6RTFHh5TodD2+f090dPzHHJjQ/hqefH2xjj2wrtTPHk30uuCYpoUGdFsgkZ0TAZKFQAHDbmVryv48X/u3wfVCjgpKObSuG7zMeVUCspoE4l5pVtjx/xjlgRsvgkLcuhrza+WVUwxnSxh4HPn06IzaryguoOc5I2Kw5+RiN3dh+dWJtVhc25v0+oqiy2rtf5ORvNC+lYNSq3XJeKn9PQ87Q4AyVKxbyy3mITA3/ppQauJD/ROl1PJVpE0gn0reuQKAmpce1nqSX4VgoyWrZTAvNtDDbqVmE7OaIxKGGuyino3W+xJCH+V3h0UvfrJmG0KItPuSgE+75sOA/7YJmnmU8CisEJp2pmvUEvvg8qZUV42nhuAe2+VxYwIHtbFujjrWy3E58i2xZGI7drn7sANis2MazFlrXakbMx70pHs/hiGrFQNlWuLhsvXKIY8j7ZVOx65KcgaMBdvZrFe2NeEWEUuqs8N09gXenHQnLTs7IcRdtGhYnAM/C8dmbGS0BDPPqpoSXEoKwlwp49D574kEpQocpGLo4N9H8fVMcPyxzsKV18T8O4EmpKM2dwh8C6QzPnTAPyjjpKaJqxYKmEcOOqPHn6gI/7GK/attRlSPwtI5yBevHmQnjLmmBBwS8To8evl7j4UoKHLjbZacfbqLBsXN9uaH00EPpSce/JeeUlnvBFUo5BdTxqx0KyL9lCnULMskmhO81caGfkfi5MJJcgj8nNhXmcej0NV6xSngbpnL8YLY9fpWDhxbgFdTrEoCYBxdC59/xUcvF9UFV8QvTVxh1cPYPfB8Xul118+iw+AJ6LLxdIB+rFm09cJ6BObHbCK2Z1Rs/i62wo8XeRllbrzzw0Tb9y8JO4NQj6UnHviY2qfT7WSptPCf1WyHe/qTM6U3wXaNmhQpNvI7d0aDsBeRHnV6TEhcDioUoLsYJiiSRcMU3R81x8wnjjgpu/1ykHScB5Are3iy9ex6IxCSgGt+GvDrqGk7XLpAknCYX/4MomKEA3JJbxzxEGWgUBVeDW4eU1rgnJxbe1FVBzEm+TNbNYF0j7p8RyyglVMvGCflVYNu07xXq4+FoainuPb3R96llECQuqW+ht2jpO8BYvl+a3jxCWY1Dkd4VlL415bvFEXXxMsEt1SCfDUx5pLFInUMsUnCBrsbJe8lZvC6pA+RiKSUAxdK49/1XTyX1QmThMfoIKQqPqJsMQxFJVKaoq/n4biYeSFxwCgoCqLLas1zGoExsViUHJRHKaXq6LtAF7r/oCqwwANjSxITeGeiRJOGgWp+OblbeA8oC+tJD7b4uN16Xuy4JxK+3XyaGzCuu/aTtjNGL10Kvc5SlllqbcidzC5POEJ9ek+I1ZUNokiZRiGatTA62bdxGYBBSDSx/vBJT8BHJHHUlugxjS42TYCNAMoHxbmCYmLHpe+YB+5bWRxqBqC8rdFy4GEj3OV65/tc+iLPPM/7vMgtLHoLSLEQW1oDxtX4y5uN/qT38shLS12rNkpcXLJn8WEaaZg42x/LgULSiW6SidZk6ttfAkCb/dqfgftRRz+wkp+ltQZbHBKN1EHYvGJKAYnIuDJkpIyB51xDSpXJ0xDHXxacYPTS1WuRosOShXqIAvDrUrw5+4TkAd3+iSJLxsKsG1EtbT8FcgTFJFfUGWpsl/L4lBlbn41EVbHN+YexZUuEhS+v7CWeXGtTJA7teR5rfPEOfWD1cmdck+rs1hGe4WBeAJfSmJIqSFoC9p6TkZ8CXv3qJ0U+Ak5zbvBtXAn5u9SKgxCSgGug+KurI4vAw/UVvTa+MpDN6oq5j+le3aIL9FVdDEKn/i+eX9v3l8wFq0Maha25f4jv1BL4daaaqcxFu8XFat8P7SuO26vXT9s/g0OEGFPlm4pX1Q4SnbdCxkFC9tX2b47TPGedp2ZX1lsiQrTrL2pKQGWlcsHsRp8dMfaN9v5NLMwyYQ2okfI/dT69j9PRSTi2/JmDeCx2XxRV185DeqUTmUWVDx35ZhQZXs6XLl3TXNxNokqeTuHrcPqtb2pYUiTo/zVda/8dJDnplqH1TBRtQhoG5TL9FHsKBaweSla6P9zuH3kbIvswpEOaSjjuZsjKV4qu9J9IcgpC3pl2iSBPuDx/Poo/f2QSkUPQqNcJH6fVMQuKXw+2vcsTwJKIbKuqQB651jFpTLaCN+IDH9EJNxEQXPKWjuzy1Ksqsg1DDbOhmNTZKE4epoXXybxM0RWdRi/WPbsuLPQTleB4efpKGnCehOh9goPI265ql8BFC3ae2yhlevtO9HcgnKY0EnxbmrK4U+bZSO5up7tl2qP+aR32IZvHzc8jgprWvTc/EF7Cb7RdNnUhFqvS8iSWJsrKSAMsa83BjzxsOHDy+9bn7UUewh0jfqur8ptK6Q3O9DXXyawURPOdZM7JKXNQLNPijmZlsnLr52MY244mJNkNLTJWiVBe17ozS/p1B01FGPaqjblMdmqsoyge33oXe4bCYemVas9NK+Txsl60dKCffv8f+e2/B6IFCEeEuVmC/cuuAWFCL8aiw+vy35TpPK5FLbNdCOgUVgJQWUtfYSa+3FF1xwwdLrnluWJBF5APOKbwyM08ynLCd+G/j8tS6+1EGbgYuPTjyBfriJlZ0kUVm4Vh/fqMhiKtOIWlDhnE+Wy5Ud4uIrwbwgfarPPpPjm3NI2j4Quq0ryz+t6I5q+dEqXgtS0GKQxutG1mUWKlr8ujuXshXSgnJT91FIp/4N3vcuVoX23r78UuhcfOG13OZgDaY081MIZx3kNsUFLj4++D2tNVPnQFM+Bc3doqZHaTAeqMWlT5LwJ7Grx49BwSuTa4O7nu8jeQEJ+dZPvCFPpWQfVB8l1xf6LHOLPDv3O//sUqzTYyHFmiQEYxiSJBGzoOQsPkYj4uLzhIxkQQlC34En2oT9K/OrSYv32qLQcUQLajPdRxpwK3FMTAKKgbr3gPi5aYGLL2HqZ7Xg5KKZvjULlYuPBoUFEuzv/Msa/b835mF6q6vnxGa3UTcmIKJHHQmLlFwuTysol3VL9X8wy0kz7xSI1ALcWqFk8dW6+FK8+eUyfZn8VYa0p8uL6bA6xddZiIpRPLYspeLzMlRwWKEvY/xq0uIpNNaPVGIj0UdaqN8OsABMAorAmfYuSQKILybBxOcCyqObqTfxmIdqKJq1MHvUEdc8M1q2tN+Ex4Hc3yc26EZdmUasCwS3frJcDn79mbIDHkvJRt0+S4C3t8yGWjsdq3zhzCVJaLVnX9insSgXXyorTqpDcmXawDrqfqMxqCrSD7GNupIw3MwddZTol95ZfF4fZUnIdDN1LBKTgCKgexachhJzx+Q2vZVoGVpNtA9U+6CqjItPyH6yZLKG5X2Ep5l3LtTj5Cy+2IIXm4ttHxcoAMm+LtAqhpxBVnTUUY9qjm/OPfen59KrZEXAdwnGlQ9tuxeloMWQc/El078ZDW4xeWNVtKDCe7oy5F5STtpzlUuSSMmgVcniG1k+TQKKgm5WdUruyZiLr0qfDCxlBsWgjYv0geZ2qlVrJkpugyFfDTaDuEd333F28nZbRlgYYtXkJqtW6/c14TSGWVD6m/tY0CfISRLWhguhnCTRLL6VHNDn5Wvayr4cMP6j9wjWz4bnMovzw2nENtcCPM1cLsPdepRW6oWFGxkXX2oUaoSLGIPKxL000M6nRWASUAR0p31uAFRs0Q0Xar2Wod3w2Aea+z1XRKGrIXccDoDmjbr+Pe6+4xtzb5NoR4PyF6lcZ0CpM8+KtP4lCag+1dRJEp3CESZJEPqCBZXccqAV4lb8Khft0UinI3ln25W6+AQrLHDxUUUJXXnPcmMCjkJKQpH41aTFe7xrXHzCtY3NyYI6bUH39uSCkC4dvf07mSSRRlIADBwB2n1QKRdfUpNTTKzNyj9JwnPxbcw7DTSqmcn18z08McRiBAESC02KZilGP+rISzMPs/akBZi6+lIuPopkDKpAQesjhuUkibyg8Gm43/xy0Sy+ipaJCTFOy+9LSts7LFZxxJjHu2JgSI8vlUiiBXdjjolJQBF0R/jHD4ntyrKBzQaYr42naaV+Hfn5AyhPkvDuVUys8IWFXT3HN+QJo5kEln1qsDALqqBOjiHvg9KAppkHLj4eYyHlAN/ikthUW6OegpYZ/30sKOee866VWQdymjmLEwlKC7dKufLVfidrRGcs0WeRy+LL856E5OLL7L3SoOTZDsUkoAhoHCZnQdFMNHePR0vwXadoRXka+PxVLj6yaJWmu2r2b0gvLHT1UG0/JtRj1dNFOAXtoloSgxoyL0sWhj6LNz3NHPDHppRRCfguKG2GZoq1kvHfR5PvEhy6a6nXV0h1SK/A4Acb+7HQ7lOXJBHuF6SKbO5cvDEsqNxeMQ0WdRC2BpOAIqBZPVkLKmHmA4tz8Q0dAToXH81gLGNBq/ltskns6uGbStsyHj2ZAW0gXuvi8wVZut+W5uLrQZ9mRtb1+QshX0RpPdYimTCj7aOSvuzTRinBIZW2LbEgvQLD2niSBB07sXgXj9HxI8G0afExnrvy8d8kfh3ovs6+Y7gkAWwoJgFFQLWcnHLBNa3UaebZlOUxLShFmezhr4l7xUEuXDvJgrOuHs+CEhbOVP3aLl50uRRPGizDxecvhP6BvMksPuriy4wFdV9m+O2zxslJB/LBw7xcigZ38fmuvO77PBLL4cKOv+LEs/gywiLVLaosPkGIeWfx9RzEsf4ZA5OAIqAv4dNk8aVcfEXvw0n+NmwEqF5slkmSSLrFlAKNa25dkkTlae9SndE2WPFrWEzplvKt3v5KRQ5DXvmuAXfx+cF4+egj6uKlsZaAH4XrNfgtJ+x7ufjqz5jLLPBoSDSExIVkkgThcyNSlytvjK8MSAk9ORdfqWudQyqRO71CA08x70VBj0lAEdDz9zRZfLRI7lTjFFLjpO9rmVs+FGXo24E1r3zn94blw3IbTLvt9kGR15N7u/DT9MLycR7pL8lyysWX0yzF2K98P0HSzIFwA6vfTp527sda0u850/VlyT41LTr3XLydXh3i6yzCsskMvch8lyyoNWM8d6qc1EHrCflLu/gUAkogsJFJbdfBHz9jYhJQBHTdyFtQXHPyf49ZAxLSr4AYBs34oa/PKHXxSRNLGvjUxVe7Puoym5VtJ42vmeUnkkaIufpU5SK0c3WXYuyz+E7OK68OnrnF3VaxBBZX3uMnokQEfNPvIwh7ceNrah+UUEt3ukN3Lb1Rl/apvCnYlZnNjKeIScIw9+qLlABRncUnFFnMSRLpOhaJSUAR8GynXFmNi29tZtQPcW1mgmvDT5KwIl2K3EkSKRqxjb28/Ek2MWg9j23M23ooDel7jC9N8sPazGRdgRp6jmiuX2ModfH1qeexk/OuPubWCV6qR+4LLIiIBZUb135fpqEZoxxSBl7qVRJiRptAg7+kVMriAxLZcM3X9ZkBbG4fVPrVF6l+07zLSRJwGwsQUCWu8KGYBBRByQOTfPkU7s+Z0bj4bFuWY6iGYiN0Kai7Utbk4jRiE4uX39jkgfruN2ddxZJOYv1H69FYRvWaES9I26nR+nvKpyIXn7W2Vz1O6Nf1+X2ZtqBYTCY4Mqj+nJn04kT7UuPiLm2jdNSR187A5S6M62gMKm9BxeJH7nLt4uvGkXyaeVohHvw+KOHaIlx8fK/XmFhJAbWsN+qe3Kzw7//yOty15yh+/X234NJte4vuj2XyAN3gMsZgz5Hj+LG3XYMjxzdEOu5WY8JZevDRk/jRt16NfUdPFPFGaUt0KWjCR0zgxGjEXvnOy/tp5vE0/te89Wp81+9fhs/eua+99pdfuB/f+Xufxa+/7xZWT8fXT//VF3HLg/J4of370KHH8Nq3XYNjJzbFco7eB254CP/zY9tEerxsKUr3QfWph1pQc+b68tx0VXg4auoIL3evMQbX3PcwfuFdN4gLKR0zf3LpPfjrqx6I8moRjpccxD1MSRdfnAbfIO7HoOD95hBzlbWekzXjCbuWJlVqM8IiGYNSufjCMr41nSURoUu+n40W1LLeqLvnyHF85JbduPb+g3jnNTu8RVGD5NlfzeeaMTj46AY+fcde3LXnqEiHluXYe/QEPrNtH255qJ+wrqwV6VJ4b8iNnAwRoxFLkuDlT2z6wjy2SF+6bR+27TmKO/c80l67cedh3LX3EXzkll0eT0BXz6fu2IsvbD8g0qxI2f2PnMSn7tiL7fuOhXyja+e2PUfxni/uFOk5mrl+jaHole+Qx0UOVCFIW1DS+6IS45pYCDsefgzv+eKD3mkgXbmuf27Ycch7dmHZ8jZmLajAxSePU54kEpwSEaEZ2xTMLajQxae3oJJZfJp9UMLtufP/NJjSzJcEN0A25xU2qspbRDVIBTmpr95BmsixshwniMumBFI8iGNeIZskEaMReyUDL8+z+PpMDtp/Up/Fnp/4LDbD/uR9dTwxHjT9GkOZBdU/1uXAtWa+wHgWlPU3a8fec+aPa3lses8mMvYdzYXHoHh1kS6XYnIxF59vQclz39GazQzkfVAxfuV5F0PvFxYu4qgj+n0SUOPBuehONmfFlQuoeJCzc/F112ITuRLKcsSEmwY55ZS6dWJJEjEaMc2Ul/c26jYWVKlhQPvP1arp384tlS7L2xmj5+rvaUAVppmX1SOV5ZY+P4GDW1BJF580rgVhX/G+FMpQmqV92b0SpLvmtTOwoCJ0cjG5iAUVS5KgFiZ1F4pJEgNcfKcySUJ7gssicFYLKKdNuIXoZKGASmlA7q+ZyVtQDrPELE0tlilU1ibpAv4kjWXlxWjEXBO8vJsYpklUmFuLc9bLht9mZVvff5dYktfk3RzKPQsr0Iu+i0rRrzGUZPEB6XHBQfvU3cZPsHZ/GuM/e2P8eCQQ9wxk+9Lqno1UVgN6mrnYTkWaeV3Op0GtHiB037lyMeWUZu9Sa4y+sFDil1t8uYVftw8qvLbo08xHNqDObgHVHljaTJ4TCS1PQiojRnbxxRZQG5Tl6CugNK6obJJEgoYYs0JY3vXV+szUi0JlsXWtfPg5t9tQF6psQfnZZJWNx4uGuPj4Cxxj0IwLDtqn6819wWnm5PfaxWe9v2MLdIynWF9qng0w1MUXbydFzoKiNOIbda1YZTDTXAAAIABJREFUF+0v970TUH79MX7DmJnML+U7B9mCGu7i4xb3mDirBZSLQblFr9iCimzWA4gvmmqREQEoaaUcqXhIChY6C8rxEIspxWjIZ/GFbXH7oNzEnVuLretrihb4cIuhW2ZVFpSyrNTO6DNT9GsKJRpwST20T92izwP6FREydBHlWr/Ep+wZyPdl2oIq70tqQcXayeuQ4GJQjkYYk/MX41xd7pvbJ8Zf/hiloUiLp9C4+EQLKhGW0ILeNcWgRoR7WH1dfLHzuAB/v4hDTIuUyob39regUnSB9CnQjr/oPqhIcDe2D2p9Nmu1dOqOkuhL11oBJfVvJkkiV9a5cFRxrUSfaKA5TSK2Py5VL+3T9Vn9nT/fzmKaNVls9O/0PhftuOZjJjV+pfGl2bsHOItEbieFNAZcOUrDuZ/berwUclJXxJ1In5kl99MTJSR+NesHhTbNPJiHVbyPtLCkjZMFNSJaC8oJqMKNARubcX+upLXHXIhSWUCXoZZDJVgzyVMeIi6+EgsqFYNqLajKj0FJLh7p2gnm4vP6N5OEkitbFzOsXEypGGZBaQSUZK0AaXeY1Kc8MO5ZTOTk/rWZCV8RH7FEsuPa8jJl8VfN6SeAb5Gkk5Zkus6i7CwobkF2ZauK1hVzA9aftSIWxnZj/MbWj5LsWQ4r3O+/8j1LQqYb6csxcHYLqDZJoqeLL7WPQXiIuRhJqEXqXCRphGnKfDHIHVop0ZDubUvbTAyqdfFRCyqkT685vz138WnSwqnbxUFeMGuNk3ISVyqGTdC5IlEithCkBOPW9XQMih5gut4IJD8GlXbxOeTGNd9qcGKzEt1WsThbTvjTdznJcSFukchKoDvJf70VUDwN3xc+YrzLa1dTD0+SIGU0MbOce1djuUhKVO4EdQ0ob5MFNSKcmX68TZLon2YeakA1ZqSHYxq+K8t302uDzClY6/PA6QL5l5hJNByiMStW3vXtWhuIL7OgHn/OOoCuH9pJQuqJCnFlWSu6+CL9nugTDTYUqeatZZ15fhRSn24yBYTGoCyLQVkbT60G5H6XhLg0ZqT5JdGjvMdAT4FQxXQidJ2AXiNCw7MgWV9Idfn95eqBd66fi0fpY2Yyvx1f4uWARmquD02SKDlntC/ObgHVaLFu4pQ+sLQPOdTYUll8fGHk9/beqItQCwu0qkxmT8qdFRVoERfferMo1mnmXUA/Z0E9oRFQJ1oLKiwTVwB0z6KyFqb5L1XO1X+qkiRS9dI+XW8XQt/1xbP2XP+sKxZ67biWxkysnNSmbGJP0yRq1fjt1NXjshodDf5GXc+CIuViyQatYDGylVRVMr+xtPjovFPFMDNzfWCSxGRBjQwegypFShuRFpeUi89AElDd99RGxxSkhSIInM7jEwVIL8YxF1+QxecsqDVTn2ZecRdfSJtecwLK9YO8UEbiRRVUZUssqKExqA2FChwXUPF7aJ+urbnF1Nf2Wy1/jWXxrSlcTy0PORdfyHesHKdX/x0U9UBPZoi106un7UtGp/JpVDa+IZeWi/VROy4ld6mzoAR++XBYRJKEc1lT5Oa6BjRJYrKgRkT7VtdC1167Wa/qNt1FXXwKIeNSclOB4kEuPjZIKV1jusweY1IWUUi73ugp1RmfGG3wmAkoypP76rv4assgcPGp+lcoK6ZG1wvlMrL4dEHubiGgSLm/tkpZfGSc0n0+XUal9cpvzCuycZXxJPW7Yk9ZqhynB6TbaIyfJCG2M5Lc4ejScjSzjsboaD31b/k+cl9dPM8pPUDn8qP8unpCV6rPL2274zOHyobtpXN96Os2JhffyHAmdqn7bEubJlq130MNKBxg8aOOGs2dXdfcm4N0lhv9e8ts1rortsxmomZWCTRcee3ZfX4WH4KTJGj5c7esBdeecO4WAKQfBB99yUZoOc28mbzUxZdQKoYkSejSzOvP1PPjkPp0XtlunJIFuM7i8/+Wyvs8SeNaskbD/okdiVTaRjruaJzF4zsTg6Ll3EkS/CSNLY0yJbUpVhfNcnTWmNf38Gm4emJp5rwfHC3dPigbtDc31zXwYpZn42nmy8ImO+pIi3Vi5rffA1Wz/tC7+EyQJLGILD7J3QZ0VsL6mmn7YX3NRE9JltxZ6427jkNyf50kWXzuOJlYFp8TUH4Myregilx84rOQU6ONUe5dq4bFoDTHHUkp3dLfFFIW32ZVteOULsCtli/EoNYFV1aMB/HgXYHPlBegpI3ra0Y8SYK3k4KPl7actW1KfCdUSD0shVzsIykGNevO4qN9WdkwBkXb0xGS+yH3XPw2h+1199VzvacFReJjPUmocXYLqDaLr8x95gbYxrzq0lMjQU6jEDIWFshaUH1PkpD9++7K+sy0GWUu7TigIQq5boHTlC+yoJrrngXVZvHFkyTiQlwSZvKiWmvSOsVA6hN3KfbpoDkwVmojIFsXroiYxTcnR/RwC8raQFun5WOup2xf2jArNe3i07dxfWY8F1+snVI9riw/2mhmuo2nncvT+Ce7R+qSsh5p39JynIarJyZQeT907Qu6JwC1oOiaJbWtBH7W52RBjYbuqKMy68RpqRvzLo4SfW+Ol46bSFk2mSy+nkkS1oYp37WVUNPeuj5rB+3W9dDVULMX0kiXD9OGT26SiSEmSaQtKJdm3m3UbRZK1r/yXhuIZcNyteVHH0P8FR5yn7jsrding86CCvkGZMG4Rp6nQ7coWWxZ61xDvgUF72+gFp65cZ3tS1jwoxZj5fq0kSZJ0Haur8kuMG5B0fa12ZvG74+t67MghVzso4gF5fqOlqM03N7ALWvhPIopJ46W9qgj3l5a5/AkicmCGhVtmnmxBdX5c2lwlaLVMhTaOJ0gFIuyoPjiSBMB1mczoslFJncV0nDlYxYUL08tKDcZzxHOjQO6yeQlSWyVLajUixFbfoSyUtyxso1l6bn4Eht1pUW04Tn26aA6ScJp0Qrrwl2T+nReVZ2Asr4GTI8+ovtzomNBOa6lMSOnmYf0cm10yR3uftrOmTGtlU4RWlCz9rqLAdevyOgsSjq+tX1UkWfWutO8BAzr8Qs0woLxG7eg5NigBCu0t41BrclzVwPPjdmLgh5nt4DqaUE5f+4G8UPHXCFU6KReqJdLkuhrQdUBYJ+yQZcIsL5mulMeIvG02Cu519dkDUp65TvN4qMWm0MuSWJ9zWDr+ixIM+f1SMqGVDaW8mwMP+oooVQkBNR65NNhsyDNPKW4ODj6sSw+GoPoYk7+cTzt4jePx1Yl17XU5xZaF5/8HFNtpLEhnhU3awRN1sVH2ucs55lhWY5r1JXoeBD6iMapms/ZzHgxJiCexbe+FrrKOb9tHxTFoGzQ3o0qbFspvFNcJhffeHAaTGkfO210c95ppsFp5s2nKssMXZCWQhOsz4FmOTkYYkFtWZu1E6lrSzhZxCw+wTUByFl8J8lJEm5i0ldD0OLnbpkF17aszXDu+qxbDCMTOPamXF5WLhdumE4dQCulALsrs+Y3/umgPUuN8w1E9ow5AbUWCv1N6uILYlBh/2xUVXIscJ5igofzHRNkpW2k7kpaz+a8ETSz1MZXeDTmTRbjbEYy71x23VpoQXULPekjUhW1eueETl0uHoOKnWbO+2FLxIUpoXbx+fctwoLq9hVCVFAXibNaQMXe9ZOD5/OOBpPrT42Lz1p5o+5C0swZD4C/GXV9ZshJ45G2CDRceXmjrg3KuwNp66zBcgtqbWZw7pa1rIsvlvzAy0aTJOBbsiUuPqpk5Fx8G6oFptzF51lQbkNo1SXz1KcZdIstfaOul52aGAsA66OIdR88m5TyUOTi66wfmiW3WVWdBZVJ26btc1mnxoBZlKEFRVPEpSSJtj1rnSLmJ0kg4Hc2Eyy+SD/EkkAkeBYUi3vF5q4GlLcpzXxE9H1AThvZmKc0Tee66K6lTiUI/HvwA6T0bbJFsHLyhaO9ZW3WLpaptkhZvzEtrHbv0Pq6ibE2MyRQa0gZIqDWwySJdS6gWveXX3dsTw4vGyvnAuVduYRSEfSrL/hTn3NFFl8VaWMsoxKIn8W37mnx3e80KWCNLGJRz4BkZUbcquGzSbn49G2k45TGoOqNukZe8FmSBKdhUAsKKrBpbCjZR6QuGlNzl31rzT+Lb2YM1kw8iy+W3aiyoIT2tq72tdmALL6ON8UwHoSzWkD1WvDRLayp/SKtL5pq7ZvxV4jXFlRai+zz0kJpTxJ1RW0hFs0W4iunoNlAFFti+6Aq61kS68QVuE5885Smb0GFw7IWULPkPihAn8ocTY2GP/nje9ekfjWtGypmQfFsqhQ0r2Hh19ZmpnXrdOfLAVvJ/iC678m5uGh5oBsLkouPj9X4SRL82SQOiy1o4xYS96VvuXVuV5f84dUTo+Gy+BpBMfcElB/rAvJ9JJ2yv8WLd/nPxSV1aFyp7u81QQCLIMJ7naxZQD0e+mbxUff6yB6+s1xA9XxA60QjcsFVTZDTWvmdU3XKcrewOAQCqoebzwp0qAW1TrTEdUEjjNHo7pUtqHbBNMab1GuzbmMwd+E5SGnm62uz2oLaZC4+RR9Ji4aUku4WDNr+pIuPx6AIz7E083Mi6dvRSoR6xMWbKQS83DqxiFzV7rBPaayuk5iVz1KYih9zl+qeTXkb11n8iJZtXXwRC6pbsP2xXlu/fkyOKlY0scRBSmmnfSuV46eydLEv2YKS5m7twgy6JwCtiyaB8LaVgp+GPyYmAdUD63xCSBpQu7/DH2CxNOhaK/Wvc62yz0sLnfCjMO3//LZI76lxNCQXX9SPbWlyAK9j5qWcO9C2ukWc1rk+Mzh3fa0NtHf7oBT96xaNTNk6W9Fvf3ofVLh4uCuxJAlnQRW9sFCoh2NGFqLOnSgce9RmrdVlLXHxeYtvdCyEB+pG95Spno38HFNt7GI6/ll87r7ZLFzAuaUWbtStF3B6mjndiM5jUB4Nukhb6/3Gy0n8piwoKXFqNtOdxUddfG6dojwt4jTzkeXTWS6glE5YHj/gG0y51g3ETyOOvubB+K95ABZjQVU25MGYcAMf/R7b08XpxDbqup35QGNBscwytzjHXHyOD/77OVu6NHNb1L9yWZ5VxuMNMXquLKfntHAgHnty+5Q07uXOjelflxIv1sm1deH3NWfpE5eWW+gkbT01Fgx763DMdTfk2Uht4/PPxdNoWdNYUNH9W4xGfXJENyec0HNl6IkVAV/CsUpte4S+dBafH591MTO//dyqdW1vXZGFaebUa2IaYdXXxcdPyxgTZ7WA0gSqgXBB8CyoWcTnHYmRiKm2VragNBlqKv6FWAkP5tPvUjytvsen404i4LCkztksdPFRC8qRpDw6gUar27I2wznra8Fp5mGmWFxLz2WV1YuHP/njaeZhpqLTwl3bpM8iCyrSxrZvDcL6iELgj1O0sQsnXJ1riWatOcTHQj1YPQsqcTI8RezNu6k21rzL889ZP3x8STEaPgY6Gp2C6BZcGm9q08wrePcBxPohdXWuxK5ubvG5+wAnUONp8dR16z5nMc8Fg7X+PKTCSh3HitB1vI1sQC1PQBljvtoY8wZjzN8aY/79supNQZPqCwjaMNu/k/IJq4L4kAUAF1ile6FimyAN4Yu2hfr2GaHaOmD0Y35st9ADvkbvtNQ2o6/RBt1vLV1XntCs08xn5IWFcttScY58WRvs7Ui9BVl6Xp0LaSZ+un1KqqOOIny7P+mmYkefLkTchToz3enl7t465iJZB7Gx0FiKmRPfpSQSMR3dpttIhXDbl3RPl9ROYR8Uz4jkcayZca+PoWn3oQW1zjJP+dynWXwONN5lWZtiLr6A31a46CwXnh3p1in33Y2FPqC0V8KCMsa8xRiz1xhzC7v+MmPMNmPM3caYX07RsNbebq39SQCvAHBRf5YXh7nWxbfmTwyeHj0TBkwlaFJAKr05fZIEUP5akM5N4F+nsRLaFpodReHScLnA3CKdwgx457CtGdO+oI1aGEC9mHLtGPBjIbQuKc08OO8tckq5VJY/i8pKSkH8NfKcniHti8WgztniFkaFi6+SxxC1ltoYQ9uPwJZWkRK0/YrGoLpFnpePjwV3LFd3bWNuxQVW82yqyLPxsxL9NtLsOWutxzfNxqPgiTJeJiC697HVMbmuD7okCZ8vQI4HdeW6BlF+uz1Xfvu0SR1aFx93Ebp1yn0fZEG1bTQY24TSWlBvA/AyesEYswbgjwB8N4AXAnilMeaFxph/aIz5IPv31Oae7wNwOYBPLawFA7ChdPG5AeY++wQ5Xep0bLOiJADc4HJJA6VHMsVSsY2hsZLwaBzJrSO7+OQDJ2sXUreouHfROM2ta1/owgD8Y2i6srM6zXwzl2YeP+ooeBYb3MVnPcuAprVLNKUAdrfwQPx0FlTJJvFYCrZbICn9GVEIYtltXVJA4+KrbFC+Gws+LzyGEu1L+P0T68tcKr1bkGkb6TjlMai6T/Jp25wGzcZ1484/8y/so5kgLGQXH493EUXGWUSZmNmWNfrM8xYU55e6Fdu4ec89THS8jG1BrWsKWWsvM8ZcyC6/BMDd1trtAGCM+RsA32+t/W0A3xuh8wEAHzDGfAjAX0tljDEXA7gYAJ797Gdr2FPh6nsfxt9dtxMXf+tX4BfedSO2zEybzpwDd5lsIaPPuXUuuekhXHPfw+31Bw8+BqCbeI/fuo7jGyfxi++6EY/b6td7556jeMr55wQWlLv3cVvXcGKzwq+/71b8v+duU7f5HJeuzSwxftSRg/v+439+bRsrWV8zuOXBI/hnX3VuwF99TJLFy/7gsvbaeVvXcHKz6jR66m+H8U6t5pPGgcYH2mtrdRbfwUdP4mV/cBmOHt8U2/anl23H331xp3dtx8OPemXds/gPf3M9zmv6yBiD23cdwYufeUF73xPOWce+R0547QPqNPhjJ+dyFl9zyWnQ/NM9kzd89h6869odSOHYSbmNXWaWCTT2NaIQSNlt77v+QWIRG+w6dBy/+O4bg/JuLPzvT92Jv7jyvvb6Pfse8Y5TesI5dV/+wB993ouz7Xj4Mbz4GU9qyz1+6zquu/9g0JdOsEljtOYbQZ863n7mHdc3JzowhdEYfHbbPq+uA8dOen3naPyPj23DjoOP4pue/2TMjMGn79iLG3YcasscO7np0aF1uX1v7/niTnz+7v0AgAcPPebxSuv61ffejAcPPea5gl3s65aHDnv1PHJi0+PXEzTG4MM378b1DxxCDHyrBq2zFor1s+TPQwPXRjr+xoJKQEXwDAB0hu0E8NJYYWPMtwH4VwDOAfDhWDlr7RsBvBEALrroooW1/7I79+Gd1+7A1z3nSbixGYBf9vitqnt5HOEcspF0bWZw8bc8F9fed7C9dsfuozh6wl9cXvzMC/Alj9+KR5qF1eHKew4QDU7WIl/w1PPx3Cc/HgcfPalu76HHNnD1vbXADCwodD5w2paXfsWXYmNeeccJfeK2PfU9xgQW3ne/6O/h0ZObrQb5yIlNXHHPAa/OtZlphZ0xvkCkm0qlPVFUq1yfGfyLFz8NOw8+hgcPPeZNEoef+rbn4e69j3g83vrQERw7OffKfu2zvwRPPHe9XQQA4NJt+9p2OvzLr30GHnj4US+V9tjJTXz+br+NDn5MSP584rnreO03PbcVmjHsOXIcd+wO2whQ6wKYwadPFQKaoWmMwf/5rV+BP/7MPXjkxCbOP2cd/+rrnoHrdxzE9n3HgvJPOf8cvPqfPAe7Dh9vr11938PYmFucu95ZDd/+VU/FsZPz9risjXmFzzR9SYXOq//phbjlwcN+G4+ewB27j4ptdIKJuqZcG//p874Me44cx+WNUPCyamcGr/nGC/HZhgegXoj3HT3h9d2FX/Y4/Juvfybefd3Otn9+9BsvxO9/8i7cf6B+Nt/74qfh2IlNPHjoMdzc8O6f1AH85Lc+r11PbthxqFWcKE8vfuYFeOTEBj526562bfU8mGNmgFe+5NmtogQAOw8+hp0HnaDzLb61mcGPf/Nz27kt4eCjJ3FNsx5R5XorcbW/4qJn9UoRv3Fn18aVsaAi4Ao1kPBIWmsvBXDpgPoGwS26hx7daK8dPbEZK+7BuZzc5+PIYJoZg4u/5Xm4+Fu68v/9Q7fhTZ+7F0CdoQMAF5y3Bb/3iq8JaH//6y/HjTsPJ/dBnbNlht/91y9W8epw887DePnrL/d4aOnOuiA3bcvTLzgPf/jKr/XKPu9XPox5ZT0N7P9v79qDLCvK++879965d5bdnYVdlh12kX3vsuwi4AZWXgK7Aq4xqyZUoUQlQjARUDExEo1RK6VViTH5IzGmNFqxqKixKopCTBE1RpMqDPJ+FCIgorzRlYUFdmZnpvPHOX36668f59yZO869s/2rmrozd/qc7q8f37u7NU5YNYJdW44q//7JM/tx7ie/Z9WZZbY2x61Wzkz5u31HyDSzDCe97HD841tegX+/6wlc8cXbHNr+5ILNTj98+Ov34As3PWKVPXxBC5+48OVWuR0f/w6efO6ANal3rF2KD752i1XuZ798EWd94rtO3YBmqIY272dG+NBv2u/04cZ7n8Q7rr3VWw8X/kq7W5hLVccrONNrZMA7z16P/7j7Sdz92D4QAaevX4Y9L1+Jv/32j53yzYzw0T1brXov/qcf5MKZjBt4/fKFuPysdWWZ/WMT2PrhG5127znxaLxr5wbrff/1o6fw9n++xUsjwVgLcvPzysOH8Z5dG0oB1bHWI3Dxqcfi4lOPLb/71HcfxCduvN/qu6Fmho+/cVspoDIC3vLK1fj2fU/jez/OhdvJLzsc52xejhvuehxXfvH2vI+G7LV/xTnry7+v+tLtuP7Ox52+HBlu4c9eu4UJqDzhZ99LOU27t41i97bRsvxXb3sU7/3KnVZ7Ne8hIlx25lpcduZahHDrI3vx25++yXqer70sI+w87ijsPO6o4DtCuPpf78DXbn+sfGc/74N6FMAx7O9VAB6fWXNmDzp+8+xLRkCN19z4KrXgBUP2gpDoCAEG2CY/R5u5mNx9UPrTpwvEwY8LcjfqGsulkhZt/cDVSGRMyqKbafT8dPKO0HaNhmfe47WgGAeL0ea039OmpuSG7J2cJF+/x+rmMbZMjB1PbKgDX7t5Pfmnm7HHT+5YMOTOw3IsMvtvt7ynTcUeLgKPcWSijO1u0/D2ZTNGI5VKm8/N1RHC1Ld3rqxHCGpdrtXIHAWJ9wdlbjuHPWvb0OPvSyK7DcTa77uyxddensVXBftOMN1W5vLvnp2wttkWZD8LqB8C2EBEa4hoCMBFAL7Rm2b1HjpAyy0oH3yuJuniGx4yhmfVBNP/b3mYoiyrJcB0mVrove4CN+2qSwuxZxqBxeKrM8vIOvy1LSwo2TbAv0Of/99XTwhtT1lflmBJJ/uOuyNj77OYHGkaMut/ZZma3MHH6Hk9ejzk/xoZGUvfK6Aa3r9l+fhcMJut5bxuNjJrU6lGt33J3XvSDZyRUBSY4uNXGG23sn4/4D7nm1vhPpL1hAWZ215tzdRrb7mNoAYvsAWcGQujKE5fQskLMfviqCMi+hKAmwBsIqJHiehSpdQEgCsB3AjgPgBfUUrd24tGEdHriOgz+/btqy5cE9rFt++leBzHl3btJklQGSj2CQ/pp+bPSpQLJDOLpMV8xfn/up9QbbEg+HvB4kl8wfktBsPQ9H99JxXkZd06G1zbJXfxcBeEhm8PToutZF89IXjb5HmoLRh3qJzvfXy8fALD+pyOBSXq0XIwt9jstvKN0e1mg+2ZQvkdYAQxp8fH2DjazBL2Zf7J9/isYrtcuC+pINLXp1lGFqPkFonXgmqGBaGhmZyyjVJAmXa2I31k9aVYV7bSiqiwiLW3noDyKDdkFEWf8lEXUoBP97zZuqgloJRSb1JKjSqlWkqpVUqpzxXff1MptVEptU4p9bFeNUopdb1S6vKRkZHqwjWhLah9L8UtKF9Wm4xBEVEphPwakDuJ5Y2qsizBuPh0vb2yoGT2YW5B5f8brnDrtJnrS8dYuFZm1em5bryRsb5i/QZIF59rQXEXH/9/6Kp4H3xt8lmzHZbIoeErN9TIWFaZ3a+AKzCmbUFFx4/KH57tBoisSYLV9/l7NZ2udVA1F7gFpa3bltcatedvuFyYRi6AXQvKZfjtGMP31ONalHbb9Xvl8zF3YtiCguNObHuulNHwCcFmwx7nGLz0ZraCMV1I6y7dB9Uj6CvTn33xoMUkJXgKrf5dxqC4P7euiy8Ug+oIAcDr9e0RqgufFjZkLf78u2FPW33vyTdn5syvQf7FwrV3bhlx37dMkihjNZYFlf/OXXwtKwZV38VXNx7IFYWyfZ5yROTcV6X7VZ9MbdclP6PNZe1xteBybhZzRWdBZmTHvrggk5c/SobMhX2li49ZX3oLgNfSKt/J+tIb9wvP0dxit4Vw2MVH9V1mYu5KweZ38dlCy6fMyGd9fdnhilpEWPjaK9dVDHKN6TboPpoOPwm9uy8sqPmAMRaDWjzcCpbzW1D2J/cp+zU2d4KFGBN3Tcg9GqHrwuvAdxlgy1r8rsCILRZjQdk70iWkxp5n8bn9pv/Hs890Pea2U/NeOwblMu+wheqW9VpQniSJqnf6+lU+K7P46vr/fYzSGr/CTdsofzf1cK3ZuHX8bef9M9wy8cjYvCYyG0tjCSdZRV/64mylBcUEr/QkSAuKz+MqC8rMMy00bMHW9qyHtlD2QnVxxTcWy6JptLfJlKAqyEQk0+6Zx6Dku/s5SWKgoLP49r10EMOthmUpcVhuiabN/JqWBhfOiPG5oEJCps2z5Miu1zC3OG0+cA24dJ80jRDQAtHHwH20UCHUGpk/NVxDuz84U7EWpvDxZx5GXu685zEoNl7d9a8b1I5p/ZaACnR8W2iiul+teEnD/1mXOfhuxi3HD8YK1qcScDeY7j+Cy5QknSELKjavlVLlpZO+hBNvX3pjWh4XH+sRm+DWAAAZpElEQVRLThuRYc5ciZF0+iw/qy+FolC6sEFOWVlGvz+09jk90sXH3523N+Li87TXl3gSgnV7ALMY+TqcLmSSU18kSfy6MZtJEvvHJtBpZdak4+AM2IkFMWZY+tkrLKjyvYFZwRMINHphQQFmYZSCj53nBdJ0VCVJ2G5B+/w3t07JnHgWn1Kuf1xaUBmZo3rCWXxunCDcv6Ysv8o7TKdrBQXLyn6F6RMenLY+pxGDkvVoyyIrmDbfRM3drLamLum0/+bvD7VTlx2fmPLejyTL2e5ST7mmO44t4cbUmYq5Amf6kDNqTqdPp/Buf8h0G6SF6ZZ1rTU3xibp8W1H4GMRchOG22vPo7qwt3uEhWJdSLpm+ySJvhRQs5kkAeQTIHTMEWeaOrDbErEo7vOuikGp8lyvuICamFTlu8oYlCc+0w1KTV+8VwubTFg0scVSuvgysvaSOHUKwc33QY1PTDkTXMZm+AWHk+IkCdkmq56K/gX8l8756DR1+pdHsF9Ja/5GIEjru66A8mnRQ0zB0GNRCipugTJrTWYn6vHWwt9mhqb+2Lwem5gqx8bvLnX70vc+n6Y/JNzQuTCyrVNfZlss6UDu3eHtibk8y+f5GkF4DxPvS5+Ljx89VtfFp9vLlZNuwOntSZKE2GN1SFpQswF+mGWn2fBORAClVpqRq7002SSJufj4IOrhq3LxjU1Mlu8qLbcutW7n3WJTphuDIpGOHl4s+f9kkoRHQDXtOvliHJuccpMkPJaGz8XHmZmVNcfcrj7wcQ7dC+XSWbQvNGaxfiWymKljfddUNjjzk/Vwhp156rMVKbutmk69SV0yUk2yd15rRWPSCKiqrQl14dAILYA5rXbbhqz1GHPxuQpNMIuPldWw47k8zmqXCwso/Z0Zv5AVlrfBFdzdzp/S1c5dfD1OM09JEj0EF1DtVuaY9qWrqGDADWYpyNPMqza9+dxKoYnFGYYuUe6r6cLv7APXRu32sxiUJ9vPR0su0IrnIkJBpuBGLSjiAX3z6T/N3N8HUhBIcOakX+e1FD2ZnT5XIBDuV558wueT/el9ZRTO+IHYeNjxSyKTfehTpPhY8L91GV/Ch4ZtjVa7S2dCo6ZLzxEi45YsPQ1M+EYVRo/LzPSHsDA9nhXbnRi2fuw9Za7ix7M/Y/GgpkcBs/aH1YCjKLI6656g432viMclC6pH4DejchffsPjUDFjHWwCz4MtP7jqJaJBA3K3Ey45NTJWTz2iRheU2QwvKdRMYN5TP/WG9QzN40szPuF18i8VxT4o4l5URldk+cl2e30CqETqJo3IjtIepxgL2B9kR6lUWlOxX3aehEx6A6blrfW4enxWl6+GKiJMkoZlUQadtMZDF9B26WdmoBeVJkuiWxjL2xPpTWts8wShqkXizasn+H7llfcgtqJCAYhaUR/Hjyp4uW3Wvk8uDosVLSDc0j5uPT/eeDbix0ZTF1wNMTSlLa8gFVFb+zj91kkQjM5ZCeQFcqeVzbcitj2sZsR33eb3axWcsKM0k5CVr3UIuJH6quL4qoG1NuLCw1RuJ9S24IYtQ1pnv+ueapUySML8DtouvFxYUZzixvTtcUdAIKQaSRr6Buwzoi3Z3u1GXIzh+FhMv6iO+UdfV9julIPbEoCjsvsrLup6BmLCXZ0t2TyPKvV5cIXLLunvT7Ha7iUD6XXIsQ7FpjZj3JHS2oM9a0/1cZc00BA/qNgvU3js2cwtKCt5DMkmi11l8UmPoNLNysPRA8gHVTFhqW1ZQtubO9fKitJCLr2k0KXOJIFnPTjfrhgfV+XsB4z6pSjPX/88vLSziAhl5GRhgMw0gz6riQrAttNmoiy9w1BEH3//jgy9hxW/1GkVBI5RmLvtVu6HseEnvLCg5fvpG2zyDD6XFr2njlnJbZItJV6ZMq5buSw7elxPlPqiwi68bWeyjEZBxNl02/+Tu5LawhDjs+9sMw+Y0SRdoCD63qUYwri3ifxn5LfbYs6HTW0JoN905qr+rqjMGK4MWfXLl+68bvc7ik7d9dlqNUnOSFpQOdOuFDxhGZcWgIhYU1zKmIkyR15u/F0U9mfXsdOIWgBsotY7KyfK28/1gMf/9wUlzC6veHOpDW9TZyOw4l9Qy/UkS7rtD/SfT1EPtB9hV1T7m29TapZkroSw+NwBtrErt5tOPOnvopmFBOeOXue49nwXFmak5V862EGxNnx/j47aDP6uVB+8G3C7228i+5IlIxl1qXJq8zVaSRDF+vhueOWQGaqmAFY+1PUkSHFypk2MZsr50sbZl8dW0oISVXnf6mP2Ipg09saBEPC+5+HoAedV0u2n2QXktqMxON5enmfPYjY9R83iJXi9Bd5HQSACg1bQXzXT3QbXFJG1x9wnsEwgAv9ZcZhkWQl67PkNN0pohZwT2XhvzoM+CamTk1cpDqIpBcQvBd223aXd9C0r2a94ndmyIBDOVmnAdmMOKi79LWsy+oEZmMjL1+5tWDMqOlcaO+SISe+UCdAOIniShy9XJ8JJ9yVP2jbC3hbDL8LkiVY/hm3fYz1VZUMSEoeyiUN8ad6Lb3qp4kLmsMWzZ+iAFP3dNTswg9Y7TeMhaUL2Gz4LqBCyo0r2XGebZbNjMxTqh2wO+uGNuJUDssdCui4aIQU3TxSfPC+Tum4zc98YSPvIkjnxhN7Jwm6RrQSZJyBMunGNssnpJIdLlEWL83L0T3QfV7CIGJZSTMqFGu/aIxaA8FmJd8FM8ANtiIMrjd/p3/VZ7o67R1PX/4/PWZWwclgUViUF1o6lLGuXJ8I2Mx9nsPrRiUGUCQJxhymO6pGs3ZEHZdfnjXe1A38r28oy6sS4tqLoKjjkfkq3DCuuwDuRaPiRjUL3GgQkpoDKWJGF/6swynk4t3TR8QVRNsKnI3hteL2AmvF6kVRmAVTAZdaL9QMFM7fJ+t45xRWiGEUuSkEcdydMqrPoy9z3cquqGtjqMP2ZB+ZhqyI051LAZVKOcM24MaiYuPtmX1nUbzFLT9QK6/3hsJpwUIZERWW5ECStJougm791aNd1XgBvM5xmR2ko0/Yrify7DL7MTxVqXCO2D8u0Ls9rJlIPSQhSWSHhvpd3e/ESVmi4+4Squq9/IDfM87jUTuFl8yYKaMaSLj6eZx7L4TIZZ4eLzbNStmmBl3CPQ07EY1EyTJOQkbTZ42q7LgL2BcR2bmZwqmWKWUXChDIm2831QElwYaWuRJ0l0Q1utPor0Z12GweueKNwzZdYnsRiUmDtmi0J1M8t6YjFEEp/apZrxjC/X9RVzYdkxqPBcAIwFFRX2NYLxDo3MUuHzlAthXeXQNNajcbnqtmrLK94/dayf0PmexjNixqLKJem6vrt08cnj0iLrsBvw8c4opZn3BNLF1+Zp5trVx9JNtYUgLQ/ufug04xNMw+wX8Xe1HYOy61MRJlAHMoPLJDjAOjeurN9rQenFOGkOi2XWZYieg4x5h1wL/HqKKSbQQskJMdrq9FGdwP5YhQbO69Y0mjnD9+8Y68r+rD+WkkZ+yoLO5JN70hpE1sG0HTEecQvKddFyeJMkIkcd1enLIUEjP45LK0TmxHbdTo/LrByTqiQJ4wUBeHJMvH94O+Uc1whZ3LK9ByenTFJHoLmucmIL5yrIA425a7JXINChGYPqdZq5FlCLOvl1Ap2mOUmiTJZgG/30GXFGQ0X5P/3Zrqlxl5ZEDQsKZOq3n52ugLI1WZ7gwDcia/jcZGXywMGpMiifZe6zTp0ThnkHzz0kc1oHmDCuZUEJoVenj3RwOJZmXi+wXzBg0a/5/UXGBcfrms7Bv+F9bGYM+d4r3Radkk/wMOBYHILcY7bs9riT2OviY3OmCvKsQBmDypMkYCWCmIQPlh1a04KSsUBp7YVOD+EnkWshWjddu1G214QFqqwZ51aALudPOVfKNlTv8eoWGeHQjEH1Os1cm+JLFuT3QFkuPmFBySQJXyyKqL4bo/KoI7Hxje+/0s9O08NnNP0J04YGkdlHU8fF5yRJ1EszNxZUOLuJJ0mUwoP8aeYS3J8P1Fu4sXhgVXqxr+5caJs5o/uHnyThHBbbxWDGY1Bm7xUfS34ALzGXnRamoVP8gcLFF8mg9PVxbKNuVXwWMLEdbwyK7JiesaDyT03bOHOZ1c2K0/3VrilMefp9WW/NdG3Z3lxAxeebvFctdgRV7Hm+rnzHec0IlNLMewJtQS0ZHgIgT5KwP/lGVHNatOsHrrsTvMoK4mnX2u1m4jLFs9OUUEOOsNAWECyXiUY0BlWcdGEEt7/ONmMaus6Q8OBJEryNdVx8bqZj5SO1DjitA84Y8zFzLe5QDGo6SRL6EXlUlc3Ai/qILHeQfma8zFKrF4Oqax14XXzNetYMYGjUCF1rb8egbItyfGKq/skMQsjVFWz8CKghMceDz4iUfV97q+pzDwmIPuY8r/sjP8289xYUMLuJEoeEgNLakbag2s3M2ajbbGTmFInMxFqIOIMwC0S6skKYrMjik/fa8PhOLOusDrzCgsAOG7XfS57ZYPYHTRapzWQJlmCdzMUXAk+S0LEDniYdpa2MA+i4UvVUjm2ajlkWTlnLgtJ9glLwx7L4ukszt7Xglic+o4UTT7fnwlBatLGTCHwCrQreCwvZnKmCnC9cYGmFzcT2dDsLhs/aWjttW8Sg6go2303bVc9IBaNs7+RUpbCQSQ7dXPnO6zZxUvcUkZlCO5Zn80TzQ0JA6TRzfdV7p9VgsadCQBWMkadRa2tBHsOSm/n571VaVNU+KA7tTiyZ2Eyz+DzCQgfVORPl9UtYLj4UFh6FNTmpucWEK98MXQpRqtdXmjZtHde5Cru0oCKWYh3IK1IyNme04O/FRl3JZDjTMvEZ26WYEduoi+4EDoFqz2uN2EbdOi4+aY1YJ8MTS0DJjFDRw8cVMJkMEkLoNPNKYaPjThNTTNDEOTOnxWrvxGSNGJQ9H7u5UTd/Xgqo7jbA10GyoHoE4+LTAsqcxacnSrORCyjt4jMuG7aZlDEInTJaNbF5dloVtAutTJIovp/2PihPPEgLXPIIAj/jNgyOC+2QEOF+dl+ci4Mz8onJaovLrifv/5fGJ2s/N1kmSbj/C52W7gNnwAQq90HxdujmyKB8d0kStpXYYoKnnCtkJ2U0MnujbjfxEspsq6QOYvG8bvZBHRRJCjrOpueIjpsCZj3wWGDXSRLFO+pmHJZxtckp1qfxZ6Sbjq+NWKwPYNZz0S9auNS1wM0JGTPzwsSgm5IsqBlC74MaGQ4nSTQy7eIzrqdGBsvFx83sur76UmuvwwB13WS7+KZ/1JGdCq+1fO3Pl6/1zX3dTxNTyglax+rkMasQdB/nbeyOVr2AX2RHMFXBnMDtTvtu7tyyGDAbM70fSbul8rpm4uKzmS7fI8STMfhYZmTHK7qJKU0nBuW/lqO+BSXnKPdSuD+2EsCz6aq2fchrREyaua0EhMAF91DdZ8ojn5T198HJqcr5NlQKKHtrRF1W4Lp26z3XDTQNahZz+Q4RATWJZkY4rK3TzBvlxNQMuJXlu+hNkoRtRQH+hV/lCom5lSQI2nrL/646Cb0KjotPuywBr3UTc/FpdJMkoTPNQuDMdJwJ0TrQ9WgLqps085l6Oni/5m5PnlFXcZp5F3XLGGKZPl6YUJJ56/p5ooFmrDFhwZMqus1Q87a75ikrvKwzR0mn7fuFMGCvwXLzdECdl1lx3br4+JjXtTJluW6sU1/8GOhegTvYpWeiG5SRiFm0oJqz9+rpg4heB+B169evn9F7PnTdPbjtZ7/Ck/sOiNMj3Os2Gg0Tf2pYwsloCtx1Iid8CPI8vxgyspMk5AbhbjE8JIQLd5mwBd9pZThQpEyH2p+3rzpJQl/8qJSytF4f8n6021g3WWFhoWxohlSVFQUwK6ZOwCoC7e5RUKZPmEWTKwB+AdUNo9AKFbekMzJ7gjIiTJHetEtOXUSmP2P1Luq0sPeFcUxOKSwY0nXWbqYDc75edVldH1fGGmSUKCqsUrC5pPt2QTG/p6aUs6lZYnGnhecPTGByymbY5jDdeDsPa+flJqcUO4sx/szCTu6xkcdM1bknS89veShv3ekj1/4sePhKOg45AaWUuh7A9du3b//9mbzniMOGMDrSwehIByesWoJXH3cUfrl/DEcuamNkQQuXnLYaO49bjnft3IDztqzAok4LG5YvxLMvjmNiSmF0pIMNyxfi7E3LsfeFMezachQuOW01jj96MdrNDO86dz1ef9JKb903XHUG/ueBX+CNJ6/E5/73YZy6ZmmwnX//5pPQzAhLFgzhhGOW4JVrl2J8YgqXnLYaIwta2HOiv44q7N42ijt/vg9Xnrsea49ciPO3rsDShW2sXroA+8cm8FLhHrvuitPxrXufCm5S/MDuzdixdikeemY/RoZbaGYZntx3wFv21LVLcflZa/H209fgujsewxnrlwEA/uHik8uJfMNVZ+D7DzwDALj61RsBAO+/YDNGF3dw+VlrAQAf/a3jcfzRi/HUc2Neq+Oa12xGp9XA+y/YjOWL2vjDs9cF++HrV5yOmx/ei90njOLamx7BCSv9++s+/oZtOHbpArw4PokXxyeC7zvpmCV4x6vW4q2vXI1v3vUETllzBI5fuRiLOy0MNTOcsX4pTli1BO1mhtPXL8OlZ6zB+cevwCWnrY7OA4n3npf3zXt2bsTUlMJZG5bhfedvxpkblmHNssNw5KI2FIC9+8exacWiMkt1x5qluOS01di0YhGGGhmuOGcdLnzFMeV7/+5NJ1lj/ZV37MANdz2Bhe0mfu/01Xjm+TFceuYab5s++9bteGFsAscuXYBbH/mVt8ziThNX79qI3dtW4Oaf7sWaZYcFabzy3PU4cHAS7z1vIxoZ4VWbjsQfnbcRp61bVtLUzDI8+dwBbD16xLLoL9x+DB565gVctXMDiAjvvyDvGx+uvfQUXHf7Y7hg6yjue+J5bB5dBCAX5u87fxPO2bS8LPv5S7bjVy8ctJ7/wO7jsGCoid3bRtFqEN559jpc9Bsvc+r54mWn4uFfvgAA+NSbT8K1P3gEm1fkdW1bOYI/eNU6/O6O/LmPvWEr1iz1981fvH4rRkeGcdmZa7H3xXGcs2k53r1zA87bclSwLzl+5xWr8MBT+3H1ro1YMTKMXcflz/31hS/H0sOGar0jhC9fvgMPPPU8jlzUxq7jls+K+1CDZvuwv5lg+/bt6pZbbpnrZiQkJCQkzCKI6Fal1Hb5/SERg0pISEhIGDwkAZWQkJCQ0JdIAiohISEhoS+RBFRCQkJCQl8iCaiEhISEhL5EElAJCQkJCX2JJKASEhISEvoSfSmgen2jbkJCQkLC4KEvBVSvb9RNSEhISBg89PVJEkT0DIBHZviaZQB+0YPm9BsSXYOD+UgTkOgaNPQzXccqpY6UX/a1gOoFiOgW3xEag45E1+BgPtIEJLoGDYNIV1+6+BISEhISEpKASkhISEjoSxwKAuozc92AWUKia3AwH2kCEl2DhoGja97HoBISEhISBhOHggWVkJCQkDCASAIqISEhIaEvMW8FFBFdQET3E9GDRHTNXLdnJiCinxLR3UR0BxHdUnx3BBF9i4geKD4Pn+t2VoGIPk9ETxPRPey7IB1E9KfF+N1PROfPTaurEaDrI0T0WDFmdxDRbva/vqeLiI4hou8S0X1EdC8Rvbv4fqDHK0LXoI9Xh4huJqI7C7o+Wnw/0OMFpdS8+wHQAPAQgLUAhgDcCWDLXLdrBvT8FMAy8d1fAbim+P0aAH851+2sQcdZAE4GcE8VHQC2FOPWBrCmGM/GXNPQBV0fAfDHnrIDQReAUQAnF78vAvDjou0DPV4RugZ9vAjAwuL3FoD/A7Bj0MdrvlpQpwB4UCn1E6XUOIAvA9gzx23qNfYA+ELx+xcAvH4O21ILSqnvA9grvg7RsQfAl5VSY0qphwE8iHxc+w4BukIYCLqUUk8opW4rfn8ewH0AVmLAxytCVwiDQpdSSu0v/mwVPwoDPl7zVUCtBPBz9vejiE/CfocC8J9EdCsRXV58d5RS6gkgX3QAls9Z62aGEB3zYQyvJKK7Chegdq0MHF1EtBrASci18nkzXoIuYMDHi4gaRHQHgKcBfEspNfDjNV8FFHm+G+R8+tOVUicDeA2AK4jorLlu0K8Bgz6GnwawDsCJAJ4A8Mni+4Gii4gWAvg3AO9RSj0XK+r5bpDoGvjxUkpNKqVOBLAKwClEtDVSfCDomq8C6lEAx7C/VwF4fI7aMmMopR4vPp8G8DXkpvhTRDQKAMXn03PXwhkhRMdAj6FS6qmCYUwB+CyM+2Rg6CKiFnIm/i9Kqa8WXw/8ePnomg/jpaGUehbAfwO4AAM+XvNVQP0QwAYiWkNEQwAuAvCNOW7TtEBEhxHRIv07gPMA3IOcnrcVxd4G4Otz08IZI0THNwBcRERtIloDYAOAm+egfdOCZgoF3oB8zIABoYuICMDnANynlPob9q+BHq8QXfNgvI4koiXF78MAdgH4EQZ8vOY8S2O2fgDsRp6h8xCAD851e2ZAx1rk2TZ3ArhX0wJgKYDvAHig+Dxirttag5YvIXefHESuwV0aowPAB4vxux/Aa+a6/V3SdS2AuwHchZwZjA4SXQDOQO7yuQvAHcXP7kEfrwhdgz5eJwC4vWj/PQD+vPh+oMcrHXWUkJCQkNCXmK8uvoSEhISEAUcSUAkJCQkJfYkkoBISEhIS+hJJQCUkJCQk9CWSgEpISEhI6EskAZWQkJCQ0JdIAiohISEhoS/x/4Tr/v/9kOTBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 7.939079135210747e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt,gnl_GV, gsl_GV, cl_GV = Gradient_V(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg(gnl_GV, gsl_GV, cl_GV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.d On écrit l'algorithme de gradient conjugué (Polak-Ribière) et on le teste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ d^{(k)}=\\left\\{\\begin{array}{ll}-g^{(1)} & \\text { si } k=1 \\\\ -g^{(k)}+\\beta^{(k)} d^{(k-1)} & \\text { sinon }\\end{array}\\right. $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\beta^{(k)}=\\frac{g^{(k)^{\\top}}\\left(g^{(k)}-g^{(k-1)}\\right)}{\\| g^{(k-1) \\|^{2}}} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1,2,3,4,5]\n",
    "a[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PolakRibiere(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 1000\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Formule de Polak-Ribi`ere for Direction de descente\n",
    "        if k == 0:\n",
    "            direction = -gradient\n",
    "        else:\n",
    "            #print(\"k:\", k)\n",
    "            #print(\"gradient_list: \",gradient_list)\n",
    "            #print(\"gradient_norm_list:\",gradient_norm_list)\n",
    "            beta = gradient.transpose()@(gradient - gradient_list[-1])/(gradient_norm_list[-1] * gradient_norm_list[-1])\n",
    "            direction = -gradient + beta*direction\n",
    "\n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        #gradient_step =  default_gradient_step\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 214\n",
      "Temps CPU : 0.40625\n",
      "Critere optimal : -3.7340070480435603\n",
      "Norme du gradient : 7.177834913244605e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 4.72677894158835e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiere(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg(gnl_GC, gsl_GC, cl_GC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.e On écrit l'algorithme de quasi-Newton (BFGS) et on le teste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ d^{(k)}=-W^{(k)} g^{(k)} $  \n",
    "$ \\delta_{x}^{(k)}=x^{(k)}-x^{(k-1)} $  \n",
    "$ \\delta_{g}^{(k)}=g^{(k)}-g^{(k-1)} $  \n",
    "$ W^{(k)}=\\left(I-\\frac{\\delta_{x}^{(k)} \\delta_{g}^{(k)} \\top}{\\delta_{g}^{(k)^{\\top}} \\delta_{x}^{(k)}}\\right) W^{(k-1)}\\left(I-\\frac{\\delta_{g}^{(k)} \\delta_{x}^{(k)} \\top}{\\delta_{g}^{(k)^{\\top}} \\delta_{x}^{(k)}}\\right)+\\frac{\\left.\\delta_{x}^{(k)} \\delta_{x}^{(k)}\\right)^{\\top}}{\\delta_{g}^{(k)} \\delta_{x}^{(k)}} $  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BFGS(Oracle, x0, alpha0):\n",
    "    import numpy as np\n",
    "    from numpy.linalg import solve\n",
    "    from numpy import dot\n",
    "    from numpy import eye\n",
    "    from numpy import outer\n",
    "    from numpy import vdot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 250\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    x_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    I = eye(len(x0))\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        res = Oracle(x)\n",
    "        critere = res[0]\n",
    "        gradient = res[1]\n",
    "        #hessien = res[2]\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "                # Valeur du critere et du gradient\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction_n = - solve(hessien, gradient)\n",
    "        #print(\"direction_n\",direction_n)\n",
    "        \n",
    "        # Formule de BFGS inverse for Direction de descente\n",
    "        #print(\"k:\",k)\n",
    "        if k == 0:\n",
    "            Wk = I \n",
    "            #print(\"Wk\",Wk)\n",
    "        else:\n",
    "            #print(\"gradient\",gradient)\n",
    "            #print(\"gradient_list[-1]\",gradient_list[-1])\n",
    "            delta_xk = np.array([list(x - x_list[-1])]).transpose()\n",
    "            delta_gk = np.array([list(gradient - gradient_list[-1])]).transpose()\n",
    "            \n",
    "            #print(\"delta_xk\",delta_xk)\n",
    "            #print(\"delta_gk\",delta_gk)\n",
    "            \n",
    "            #print(\"(delta_xk@delta_gk.transpose())\",(delta_xk@delta_gk.transpose()))\n",
    "            \n",
    "            A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
    "            #print(\"A:\",A)\n",
    "            #print(\"B:\",B)\n",
    "            #print(\"C:\",C)\n",
    "                        \n",
    "            Wk = A@Wk@B + C\n",
    "\n",
    "\n",
    "            #print(\"Wk\",Wk)\n",
    "            #print(\"Hessien\", hessien)\n",
    "        direction = -Wk@gradient\n",
    "        #print(\"direction\",direction)\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        \n",
    "        #gradient_step =  default_gradient_step\n",
    "\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x_list.append(x)\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 23\n",
      "Temps CPU : 0.03125\n",
      "Critere optimal : -3.734007048043571\n",
      "Norme du gradient : 2.220149804937683e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 1.525684885095302e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg(gnl_QN, gsl_QN, cl_QN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n"
     ]
    }
   ],
   "source": [
    "# experiment of comparison\n",
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT A PAS FIXE\n",
      "\n",
      "Iteration : 3957\n",
      "Temps CPU : 0.453125\n",
      "Critere optimal : -3.7340070480435\n",
      "Norme du gradient : 9.984468154399097e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 9.984420770159375e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_GF, gsl_GF, cl_GF = Gradient_F(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DE NEWTON A PAS FIXE\n",
      "\n",
      "Iteration : 5\n",
      "Temps CPU : 0.046875\n",
      "Critere optimal : -3.7340070480435763\n",
      "Norme du gradient : 2.3324847955473776e-11\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 9.71445146547012e-17\n",
      "Sur les pressions : 1.999262908003452e-11\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DE NEWTON A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_NF, gsl_NF, cl_NF  = Newton_F(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT A PAS VARIABLE\n",
      "\n",
      "Iteration : 259\n",
      "Temps CPU : 0.484375\n",
      "Critere optimal : -3.7340070480435035\n",
      "Norme du gradient : 9.980616892539242e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 9.598970013291463e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt,gnl_GV, gsl_GV, cl_GV = Gradient_V(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 189\n",
      "Temps CPU : 0.296875\n",
      "Critere optimal : -3.7340070480435656\n",
      "Norme du gradient : 9.772456840615705e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 5.908401026211152e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiere(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 20\n",
      "Temps CPU : 0.03125\n",
      "Critere optimal : -3.7340070480435728\n",
      "Norme du gradient : 8.550875761754614e-07\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.3877787807814457e-16\n",
      "Sur les pressions : 6.840609456659763e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Visualg2(gradient_lists, step_lists, criterere_lists): \n",
    "\n",
    "    import matplotlib.pyplot as plt \n",
    "    \n",
    "    plt.subplot (2, 1, 1) \n",
    "    plt.gca().set_title (\"Gradient norm during iterations\") \n",
    "    plt.gca().set_yscale ('log') \n",
    "    plt.plot(gradient_lists[0], label = \"Gradient norm_Algorithm1\")\n",
    "    plt.plot(gradient_lists[1], label = \"Gradient norm_Algorithm2\") \n",
    "    plt.plot(gradient_lists[2], label = \"Gradient norm_Algorithm3\") \n",
    "    \n",
    "    plt.subplot (2, 1, 2) \n",
    "    \n",
    "    plt.gca().set_title(\"Stepsize during iterations\") \n",
    "    plt.gca().set_yscale('log')\n",
    "    plt.plot(step_lists[0], label = \"Step length_Algorithm1\") \n",
    "    plt.plot(step_lists[1], label = \"Step length_Algorithm2\") \n",
    "    plt.plot(step_lists[2], label = \"Step length_Algorithm3\") \n",
    "    \n",
    "    plt.tight_layout (rect = (0, 0, 1, 2)) \n",
    "    plt.show ()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "gradient_lists = [gnl_GF,gnl_GV,gnl_GC]\n",
    "step_lists = [gsl_GF, gsl_GV, gsl_GC]\n",
    "criterere_lists = [cl_GF, cl_GV, cl_GC]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg2(gradient_lists, step_lists, criterere_lists)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.f On écrit l'algorithme de Newton à pas variable et on le teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_V(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from numpy.linalg import solve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables  \n",
    "    \n",
    "    iter_max = 100\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "           \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_V(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Résolution du problème dual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from HydrauliqueD import HydrauliqueD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.a On écrit les oracles pour le problème dual d'optimisation :\n",
    "\n",
    "* **OracleDG** : calcul de la fonction et du gradient,\n",
    "* **OracleDH** : calcul de la fonction du gradient et du Hessien."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDG(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDH(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.b On exécute tous les algorithmes d'optimisation déjà écrits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Gradient_V(OracleDG, x0, 5)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt = PolakRibiere(OracleDG, x0, 5)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt = BFGS(OracleDG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_V(OracleDH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Résolution de grands réseaux (facultatif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On charge dans l'environnement les données du problème\n",
    "\n",
    "Ces données correspondent à un réseau de taille paramétrable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Probleme_P import *\n",
    "from Structures_S import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.a On écrit des oracles primal et dual avec Hessien creux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePHS(qc):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDHS(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.b On écrit un algorithme de Newton exploitant le creux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_S(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from scipy.sparse.linalg import spsolve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables  \n",
    "    \n",
    "    iter_max = 100\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "           \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.c On résoud le problème dans le primal et dans le dual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL DE GRANDE TAILLE\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_S(OraclePHS, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL DE GRANDE TAILLE\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_S(OracleDHS, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}