Quantum_Classifier-PCA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational circuits for a classification problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Author: Javier Marin 2020. Adapted from Slimane Thabet code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is an illustration on how variational quantum circuits can be used for solving machine learning problems. In this case, we will take the example of a binary classification problem. We will implement a method proposed by Maria Schuld and al. in [Circuit-centric quantum classifiers](https://arxiv.org/pdf/1804.00633.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is a variational circuit ?"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the general case, a variational method is the approximation of an intractable function $f$ (for example solution of a PDE or an optimization problem) by a function $v$, more easily computable. The goal is then to find $v$ that will minimize a specific cost $\\mathcal{L}(v)$. The cost function may be expensive to compute, which makes the problem difficult to solve. The idea of using Quantum Computing is to reduce the cost of estimation and in some cases gain an advantage on classical computers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our Machine Learning problem, let us suppose we observe $N$ samples of labeled data $(x_i, y_i)_{i \\in [1,N]}$ with $x_i \\in \\mathbb{R}^2$ and $y_i \\in \\{0,1\\}$. The goal of the task is to construct a predictor $f$ to estimate $y$ given a new value of $x$. The problem can be restricted to a set of parameterizable functions by a real vector $\\theta$. We will train a model with the training input by finding the parameters $\\theta$ that will minimize a loss $l$.\n",
    "\n",
    "$$\\arg\\min_{\\theta} \\frac{1}{N} \\sum_{i=1}^{N} l(f(x_i;\\theta), y_i)$$\n",
    "\n",
    "In our case, $f$ will return the probability of $x$ to be labelled $1$. It is then a number comprised between 0 and 1.\n",
    "The authors use the square loss $l(f(x),y) = (f(x)-y)^2$, another usual loss is the binary crossentropy loss $l(f(x),y) = - y log(f(x)) - (1-y)log(1-f(x))$. In both cases, the farther $f(x)$ is from $y$, the greater the loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The use of quantum computers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea of the proposed circuit is to compute $f(x;\\theta)$ with a quantum computer, and then to optimize the cost with a classical optimization algorithm, with the hope that it will be more efficient than a full classical algorithm.\n",
    "\n",
    "Quantum circuits are a very good framework to represent our problem, since the probability of a qubit to be in the state $|0\\rangle$ or in the state $|1\\rangle$ can be estimated by measurement. \n",
    "\n",
    "The circuit is composed of 3 steps and a postprocess step: \n",
    "\n",
    "- STEP 1. State preparation: encode the classical data $x$ into a quantum circuit buy creating an operator $\\phi(x)$ which will result in the state $\\phi(x) |0_p\\rangle$ with $p$ the number of qubits.\n",
    "- STEP 2.Model circuit: apply an operator $U(\\theta)$ to the feature state, with $\\theta$ the trainable parameters.\n",
    "- STEP 3. Measurement: measure the qubit $q_0$ to estimate $f(x;\\theta) = \\mathbb{P}(q_0=1)$"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### State preparation\n",
    "\n",
    "The classical data need to be converted into a quantum state. A quantum state is a unitary norm vector of complex numbers and can be written $|\\psi \\rangle = \\sum_{i=1}^{n} a_i |i\\rangle$ with $\\sum_{i=1}^{n} |a_i|^2=1$, and $n=2^p$. Vectors with a power of 2 number of features can be normalized and represented into a quantum state using amplitude encoding, which means that the data are directly associated with the amplitudes of the quantum state. For other number of features, a strategy is to pad with the required number of features to reach a power of 2. The padding features can be zero on non-zero. It can be shown that the encoding can be done linearly with reference to the size of the input vector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model circuit\n",
    "\n",
    "Given the quantum state $|\\phi(x) \\rangle$ which represents the vector $x$ in the quantum circuit, we create $U(\\theta)$ a unitary operator such that $U(\\theta)|\\phi(x) \\rangle$ is a quantum state we can measure. \n",
    "\n",
    "We decompose $U(\\theta) = U_1...U_L$ as a product of one or two qubits parametrized gates. In the following we will use a combination of C-NOT gates and general unitary gates whose general formulation is:\n",
    "$$U(\\theta, \\phi, \\lambda) = \\begin{bmatrix}\n",
    "  cos(\\frac{\\theta}{2}) & -e^{i\\lambda}sin(\\frac{\\theta}{2})\\\\ \n",
    "  e^{i\\phi}sin(\\frac{\\theta}{2}) & e^{i\\lambda+i\\phi}cos(\\frac{\\theta}{2})\n",
    "\\end{bmatrix} \n",
    "$$\n",
    "This parameterization  is chosen because it is the one used by the language Qiskit. The authors of the paper choose another equivalent simpler parameterization, which doesn't need to compute imaginary parts (cf Training section)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement\n",
    "\n",
    "The measurement of the 0 qubit of the quantum state $|U(\\theta)\\phi(x) \\rangle$ generated by the previous circuit gives $f(x;\\theta) = \\mathbb{P}(y|x=1;\\theta) = \\mathbb{P}(q_0=1|x;\\theta) = \\sum_{k=1}^{n} |(U(\\theta)\\phi(x))_k|^2$. For clarity, the explicit dependency of $\\theta$ will be removed and we will just note $U$ for $U(\\theta)$\n",
    "\n",
    "Let us denote $\\pi(x;\\theta) = \\mathbb{P}(q_0=1|x;\\theta)$. It can also be expressed by the expectancy of the operator $\\sigma_z$ applied to the first qubit. $$\\mathbb{E}(\\sigma_z) = \\langle \\phi(x)|U^\\dagger (\\sigma_z \\otimes \\mathbb{I} \\otimes ... \\otimes \\mathbb{I})U|\\phi(x) \\rangle$$ and $$\\pi(x;\\theta) = \\frac{-\\mathbb{E}(\\sigma_z)}{2}+\\frac{1}{2}$$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training\n",
    "\n",
    "The model is trained to minimize a loss function\n",
    "$$\\mathcal{L}(\\theta) = \\frac{1}{N} \\sum_{i=1}^{N} l(\\pi(x_i;\\theta), y_i)$$\n",
    "The parameters are updated via batch stochastic gradient descent. The difficulty is to be able to compute the gradient in an accurate way. Fortunately, as later explained it is possible to evaluate the gradient via quantum circuits.\n",
    "\n",
    "$$\\nabla_\\theta\\mathcal{L}(\\theta) = \\frac{1}{N} \\sum_{i=1}^{N} \\nabla_\\theta(l(\\pi(x_i;\\theta), y_i)) = \n",
    "\\frac{1}{N} \\sum_{i=1}^{N} \\nabla_\\theta\\pi(x_i;\\theta)\\partial_1l(\\pi(x_i;\\theta), y_i)$$ where $\\partial_1l$ is the partial derivative of $l$ with reference to the first variable.\n",
    "\n",
    "$$\\nabla_\\theta\\pi(x_i;\\theta) = \\frac{-\\nabla_\\theta\\mathbb{E}(\\sigma_z)}{2} = -\\frac{1}{2} \\nabla_\\theta\\langle \\phi(x)U | \\sigma_z |U\\phi(x) \\rangle$$ where $\\sigma_z \\otimes \\mathbb{I} \\otimes ... \\otimes \\mathbb{I}$ is abbreviated to $\\sigma_z$.\n",
    "\n",
    "Let us now consider $\\nu$ an element of the vector $\\theta$ and let us examine $\\partial_\\nu \\pi(x;\\theta)$\n",
    "\n",
    "$$\\partial_\\nu\\pi(x;\\theta) = -\\frac{1}{2} \\langle \\phi(x)\\partial_\\nu U| \\sigma_z |U\\phi(x) \\rangle -\\frac{1}{2} \\langle \\phi(x)U |\\sigma_z |\\partial_\\nu U\\phi(x) \\rangle $$ by the rules of derivation inside an expectation. \n",
    "\n",
    "$$\\partial_\\nu\\pi(x;\\theta) = -\\frac{1}{2} (\\langle \\phi(x)\\partial_\\nu U| \\sigma_z |U\\phi(x) \\rangle + \\langle \\phi(x)\\partial_\\nu U| \\sigma_z |U\\phi(x) \\rangle^*) = - Re\\{ \\langle \\phi(x)\\partial_\\nu U| \\sigma_z |U\\phi(x) \\rangle\\}$$\n",
    "\n",
    "Generally speaking, $\\partial_\\nu U$ is not a unitary operator, and therefore cannot be implemented in a quantum circuit. However, due to our circuit architecture, il will be possible.\n",
    "\n",
    "The derivative of $U$ w.r.t $\\nu$ involves only the derivative of the elementary gate to which $\\nu$ belongs, due to the factorization of the circuit. It means that $\\partial_\\nu U = U_1...\\partial_\\nu(U_i)...U_L$ where $U_i$ is the gate to which $\\nu$ belongs.\n",
    "\n",
    "For an elementary unitary gate as described above, we have the following identities:\n",
    "\n",
    "$$\\partial_\\theta U = \\frac{1}{2} U(\\theta + \\pi, \\phi, \\lambda)$$\n",
    "\n",
    "$$\\partial_\\phi U = \\frac{i}{2} (U(\\theta, \\phi, \\lambda) - U(\\theta, \\phi + \\pi, \\lambda))$$\n",
    "\n",
    "$$\\partial_\\lambda U = \\frac{i}{2} U(\\theta, \\phi, \\lambda) - U(\\theta, \\phi, \\lambda + \\pi))$$\n",
    "\n",
    "Therefore $\\partial_\\nu U$ can be computed as the form\n",
    "\n",
    "$$ \\sum_{k=1}^{K}a_k Re\\{ \\langle \\phi(x)U(\\theta^{[k]})| \\sigma_z |U(\\theta)\\phi(x) \\rangle\\}+ \\sum_{l=1}^{L}b_l Im\\{ \\langle \\phi(x)U(\\theta^{[l]})| \\sigma_z |U(\\theta)\\phi(x) \\rangle\\}$$ where $\\theta^{[k]}$ and $\\theta^{[l]}$ are the modified vector of parameters from the above identities. The imaginary part comes from the $i$ in the same identities for $\\phi$ and $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing and cleaning the data, state preparation\n",
    "\n",
    "We use as an example this dataset. This dataset is composed of several variables. We want to only needna 2 feature columns dataset, so we reduce dimensions with for example a PCA analysis. The data are then padded with constant values and renormalized to have a unitary vector. We use a special routine to encode the data in the quantum circuit. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Important: I suggest to use quantum algorithms in a separate environment dedicated only to quantum computing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MatplotlibDrawer needs pylatexenc. You need to install it:\n",
    "#pip install pylatexenc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from qiskit import *\n",
    "from qiskit.tools.jupyter import *\n",
    "import matplotlib.pyplot as plt\n",
    "import pylatexenc\n",
    "from scipy.optimize import minimize\n",
    "from sklearn.preprocessing import Normalizer, normalize, binarize, Binarizer\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler\n",
    "from sklearn.decomposition import PCA, KernelPCA, LatentDirichletAllocation\n",
    "import pandas as pd\n",
    "import gc as gc\n",
    "backend = BasicAer.get_backend('qasm_simulator') # for using a quantum simulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To run the experiment on a real quantum computer, you need to setup your account first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using other quantum processors from IBM\n",
    "#from qiskit import IBMQ\n",
    "#IBMQ.save_account('c42be77bc7bcc969263dd866c03b2a05fefd1d203ae6aedc6765543cae8ac3d862c8fcdff5aca2f486c0ba36f764393e76718d54bc679c1aeeec78ff32bab7dd')\n",
    "#provider = IBMQ.load_account()\n",
    "# You can check in IBM site the cues in different backend processors. \n",
    "# You can choose processors with lower cues to speed up your work. \n",
    "#backend = provider.backends.ibmq_london "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from qiskit.tools.monitor import job_monitor\n",
    "#shots = 1024        \n",
    "#max_credits = 3   \n",
    "#job_exp = execute(qc, backend=backend, shots=shots, max_credits=max_credits)\n",
    "#job_monitor(job_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "123"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gc.collect()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"General.csv\")\n",
    "data = data.drop(columns=['Unnamed: 0', \n",
    "                          'reconocimiento medico', 'seguro medico', 'revision medica', \n",
    "                          'cobertura medica' , 'fecha', 'BlobText_seguro'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Removing outliers for a better accuracy. As alterntive you can apply a \n",
    "# RobustScaler algortihm. \n",
    "Q1 = data.quantile(0.1)\n",
    "Q3 = data.quantile(0.9)\n",
    "IQR = Q3 - Q1\n",
    "data = data[~((data < (Q1 - 1.5 * IQR)) |(data > (Q3 + 1.5 * IQR))).any(axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1440x684 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using Random Forest to gain insights on Feature Importance\n",
    "data['Vader_gimnasio'] =(data['Vader_gimnasio'] > -0.050).astype(int)\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier\n",
    "clf = RandomForestClassifier()\n",
    "clf.fit(data.drop(columns='Vader_gimnasio'),data.Vader_gimnasio)\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "importance = clf.feature_importances_\n",
    "importance = pd.DataFrame(importance, index=data.drop(columns='Vader_gimnasio').columns, columns=[\"Importance\"])\n",
    "importance.sort_values(by='Importance', ascending=True).plot(kind='barh', figsize=(20,len(importance)/2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Importance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Vader_iecon</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_running</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_salud</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cierre</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_fitness</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_deporte</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_seguro</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>consumo electrico</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_salbe</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_salbien</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_recon1</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Situación económica de los hogares</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tendencia prevista ICC</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Afiliacion</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ICC</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IC comercio minorista</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>salud</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DG ECFIN Business and Consumer Survey</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vader_trabajo</th>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                       Importance\n",
       "Vader_iecon                                  True\n",
       "Vader_running                                True\n",
       "Vader_salud                                  True\n",
       "Cierre                                       True\n",
       "Vader_fitness                                True\n",
       "Vader_deporte                                True\n",
       "Vader_seguro                                False\n",
       "consumo electrico                           False\n",
       "Vader_salbe                                 False\n",
       "Vader_salbien                               False\n",
       "Vader_recon1                                False\n",
       "Situación económica de los hogares          False\n",
       "Tendencia prevista ICC                      False\n",
       "Afiliacion                                  False\n",
       "ICC                                         False\n",
       "IC comercio minorista                       False\n",
       "salud                                       False\n",
       "DG ECFIN Business and Consumer Survey       False\n",
       "Vader_trabajo                               False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importance.sort_values(by='Importance', ascending=False) > 0.07"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class_labels = ['Interés bajo', 'Interés alto']\n",
    "# We choose only the relevant features and remove the rest\n",
    "X = data.drop(columns=['Vader_gimnasio', 'salud', 'Vader_trabajo', 'Vader_salbe', 'Vader_salbien',\n",
    "                      'Afiliacion', 'consumo electrico', 'ICC', 'Tendencia prevista ICC', 'Vader_seguro',\n",
    "                       'Situación económica de los hogares', 'DG ECFIN Business and Consumer Survey', 'Vader_recon1'])\n",
    "Y = data.Vader_gimnasio\n",
    "Y = np.array(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#scale value from 0 to 1 (so we remove negative values)\n",
    "scaler = MinMaxScaler().fit(X)\n",
    "X = scaler.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_dim = 2\n",
    "# I use linear Kernel PCA to reduce the number of dimensions of the dataset to n_dim = 2\n",
    "pca = KernelPCA(n_components=n_dim).fit(X)\n",
    "X = pca.transform(X)\n",
    "scaler = MinMaxScaler().fit(X)\n",
    "X = scaler.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantum algorithms that are only polynomial in the number n of qubits can perform computations on $2n$ amplitudes. If these 2n amplitudes are used to encode the data, one can therefore process data inputs in polylogarithmic time.\n",
    "Given a unitary vector of dimension 4 ( $2^2$, as we use 2  qbits in this example ), we extract 5 angles with the function `get_angles`. These angles will serve as arguments to the encoding quantum circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_angles(x):\n",
    "\n",
    "    beta0 = 2 * np.arcsin(np.sqrt(x[1]) ** 2 / np.sqrt(x[0] ** 2 + x[1] ** 2 + 1e-12))\n",
    "    beta1 = 2 * np.arcsin(np.sqrt(x[3]) ** 2 / np.sqrt(x[2] ** 2 + x[3] ** 2 + 1e-12))\n",
    "    beta2 = 2 * np.arcsin(\n",
    "        np.sqrt(x[2] ** 2 + x[3] ** 2) / np.sqrt(x[0] ** 2 + x[1] ** 2 + x[2] ** 2 + x[3] ** 2)\n",
    "    )\n",
    "\n",
    "    return np.array([beta2, -beta1 / 2, beta1 / 2, -beta0 / 2, beta0 / 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First X sample (original)  : [0.23503585 0.65878131]\n",
      "First X sample (padded)    : [0.23503585 0.65878131 0.3        0.        ]\n",
      "First X sample (normalized): [0.30882101 0.86559352 0.39417945 0.        ]\n",
      "First features sample      : [ 0.81034968 -0.          0.         -1.22809981  1.22809981]\n"
     ]
    }
   ],
   "source": [
    "print(\"First X sample (original)  :\", X[0])\n",
    "\n",
    "# pad the vectors to size 2^2 with constant values\n",
    "padding = 0.3 * np.ones((len(X), 1))\n",
    "X_pad = np.c_[np.c_[X, padding], np.zeros((len(X), 1))]\n",
    "print(\"First X sample (padded)    :\", X_pad[0])\n",
    "\n",
    "# normalize each input\n",
    "normalization = np.sqrt(np.sum(X_pad ** 2, -1))\n",
    "X_norm = (X_pad.T / normalization).T\n",
    "print(\"First X sample (normalized):\", X_norm[0])\n",
    "\n",
    "# angles for state preparation are new features\n",
    "features = np.array([get_angles(x) for x in X_norm])\n",
    "print(\"First features sample      :\", features[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP 1. State preparation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 641.233x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def statepreparation(a, circuit, target):\n",
    "    \n",
    "    a = 2*a\n",
    "    circuit.ry(a[0], target[0])\n",
    "    \n",
    "    circuit.cx(target[0], target[1])\n",
    "    circuit.ry(a[1], target[1])\n",
    "    circuit.cx(target[0], target[1])\n",
    "    circuit.ry(a[2], target[1])\n",
    "\n",
    "    circuit.x(target[0])\n",
    "    circuit.cx(target[0], target[1])\n",
    "    circuit.ry(a[3], target[1])\n",
    "    circuit.cx(target[0], target[1])\n",
    "    circuit.ry(a[4], target[1])\n",
    "    circuit.x(target[0])\n",
    "    \n",
    "    return circuit\n",
    "\n",
    "x = X_norm[0]\n",
    "ang = get_angles(x)\n",
    "q       = QuantumRegister(2)\n",
    "c       = ClassicalRegister(1)\n",
    "circuit = QuantumCircuit(q,c)\n",
    "circuit = statepreparation(ang, circuit, [0,1])\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP 2. Model circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are intermediary functions that will help us to build our circuit. The ciruit is composed of several stacked blocks, which we can call layers, to make an analogy with neural networks. A layer is composed of a general parameterized unitary gate applied to both qubits, and "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u_gate(param, circuit, target):\n",
    "    '''Return the quantum circuit with u3 gate applied on qubit target with param as an iterable'''\n",
    "    circuit.u3(param[0],param[1],param[2],target)\n",
    "    return circuit\n",
    "\n",
    "def cu_gate(param, circuit, control, target):\n",
    "    '''Return the quantum circuit with cu3 gate applied on qubit target with param as an iterable wrt control'''\n",
    "    circuit.cu3(param[0],param[1],param[2], control, target)\n",
    "    return circuit\n",
    "\n",
    "def circuit_block(param, circuit, target, same_order_x=True):\n",
    "    '''Return the block applied on qubits target from the circuit circuit\n",
    "    - param : array parameters for the two u gate\n",
    "    - target : array of integer the numero of qubits for the u gates to be applied\n",
    "    - if same_order_x == True : cx(target[0], target[1])\n",
    "    else: cx(target[1], target[0])'''\n",
    "    circuit = u_gate(param[0], circuit, target[0])\n",
    "    circuit = u_gate(param[1], circuit, target[1])\n",
    "    if same_order_x:\n",
    "        circuit.cx(target[0], target[1])\n",
    "    else:\n",
    "        circuit.cx(target[1], target[0])\n",
    "    return circuit\n",
    "\n",
    "def c_circuit_block(param, circuit, control, target, same_order_x=True):\n",
    "    '''Return the controlled block applied on qubits target from the circuit circuit\n",
    "    - param : array parameters for the two u gate\n",
    "    - target : array of integer the numero of qubits for the u gates to be applied\n",
    "    - if same_order_x == True : cx(target[0], target[1])\n",
    "    else: cx(target[1], target[0])'''\n",
    "    circuit = cu_gate(param[0], circuit, control, target[0])\n",
    "    circuit = cu_gate(param[1], circuit, control, target[1])\n",
    "    if same_order_x:\n",
    "        circuit.ccx(control, target[0], target[1])\n",
    "    else:\n",
    "        circuit.ccx(control, target[1], target[0])\n",
    "    return circuit\n",
    "\n",
    "def create_circuit(param, circuit, target):\n",
    "    order = True\n",
    "    for i in range(param.shape[0]):\n",
    "        circuit = circuit_block(param[i], circuit, target, order)\n",
    "        order = not order\n",
    "    return circuit\n",
    "\n",
    "def create_c_circuit(param, circuit, control, target):\n",
    "    order = True\n",
    "    for i in range(param.shape[0]):\n",
    "        circuit = c_circuit_block(param[i], circuit, control, target, order)\n",
    "        order = not order \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final circuit including state preparation, model and measurement is implemented below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:3: DeprecationWarning: The QuantumCircuit.u3 method is deprecated as of 0.16.0. It will be removed no earlier than 3 months after the release date. You should use QuantumCircuit.u instead, which acts identically. Alternatively, you can decompose u3 in terms of QuantumCircuit.p and QuantumCircuit.sx: u3(ϴ,φ,λ) = p(φ+π) sx p(ϴ+π) sx p(λ) (2 pulses on hardware).\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1423.98x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([0.53896774, 0.79503606, 0.27826503, 0.0])\n",
    "ang = get_angles(x)\n",
    "\n",
    "params = np.array([[[np.pi/3,np.pi/3,np.pi/4],\n",
    "                    [np.pi/6,np.pi/4,np.pi/6]],\n",
    "                    [[np.pi/6,np.pi/4,np.pi/4],\n",
    "                    [np.pi/3,np.pi/7,np.pi/6]],\n",
    "                    [[np.pi/3,np.pi/3,np.pi/4],\n",
    "                    [np.pi/6,np.pi/4,np.pi/6]],\n",
    "                    [[np.pi/6,np.pi/4,np.pi/4],\n",
    "                    [np.pi/3,np.pi/7,np.pi/6]]])\n",
    "\n",
    "q       = QuantumRegister(2)\n",
    "c       = ClassicalRegister(1)\n",
    "circuit = QuantumCircuit(q,c)\n",
    "circuit = statepreparation(ang, circuit, [0,1])\n",
    "\n",
    "circuit = create_circuit(params, circuit, [0,1])\n",
    "\n",
    "circuit.measure(0,c)\n",
    "\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function executes the circuit and returns the result of measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.128"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def execute_circuit(params, angles=None, x=None, use_angles=True, bias=0, shots=1000):\n",
    "    if not use_angles:\n",
    "        angles = get_angles(x)\n",
    "    q       = QuantumRegister(2)\n",
    "    c       = ClassicalRegister(1)\n",
    "    circuit = QuantumCircuit(q,c)\n",
    "    circuit = statepreparation(angles, circuit, [0,1])\n",
    "\n",
    "    circuit = create_circuit(params, circuit, [0,1])\n",
    "    circuit.measure(0,c)\n",
    "    result = execute(circuit,backend,shots=shots).result()\n",
    "\n",
    "    counts = result.get_counts(circuit)\n",
    "    result=np.zeros(2)\n",
    "    for key in counts:\n",
    "        result[int(key,2)]=counts[key]\n",
    "    result/=shots\n",
    "    return result[1] + bias\n",
    "\n",
    "execute_circuit(params, ang, bias=0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost and accuracy functions\n",
    "\n",
    "We define now the cost function, square loss, binary crossentropy and accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(probas):\n",
    "    return (probas>=0.5)*1\n",
    "\n",
    "def binary_crossentropy(labels, predictions):\n",
    "    loss = 0\n",
    "    for l, p in zip(labels, predictions):\n",
    "        loss = loss - l * np.log(np.max([p,1e-8]))\n",
    "\n",
    "    loss = loss / len(labels)\n",
    "    return loss\n",
    "\n",
    "def square_loss(labels, predictions):\n",
    "    loss = 0\n",
    "    for l, p in zip(labels, predictions):\n",
    "        loss = loss + (l - p) ** 2\n",
    "\n",
    "    loss = loss / len(labels)\n",
    "    return loss \n",
    "\n",
    "def cost(params, features, labels):\n",
    "    predictions = [execute_circuit(params, angles=f) for f in features]\n",
    "    return binary_crossentropy(labels, predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(labels, predictions):\n",
    "\n",
    "    loss = 0\n",
    "    for l, p in zip(labels, predictions):\n",
    "        if abs(l - p) < 1e-5:\n",
    "            loss = loss + 1\n",
    "    loss = loss / len(labels)\n",
    "\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following routines will compute $Re\\{ \\langle \\phi(x)U(\\theta^{[k]})| \\sigma_z |U(\\theta)\\phi(x) \\rangle\\}$ and $Im\\{ \\langle \\phi(x)U(\\theta^{[l]})| \\sigma_z |U(\\theta)\\phi(x) \\rangle\\}$ for given parameters $\\theta^{[k]}$, $\\theta^{[l]}$ and $\\theta$.\n",
    "\n",
    "Let us assume we can prepare two unitary states $|A\\rangle$ and $|B\\rangle$ (result of an action of unitary operators $A$ and $B$ on $|0_p\\rangle$) conditioned to the state of an ancilla qubit $a$, that is the state \n",
    "$$ \\frac{|0\\rangle|A\\rangle + |1\\rangle|B\\rangle}{\\sqrt{2}}$$\n",
    "\n",
    "Applying a Hadamard to the ancilla leads to \n",
    "$$ \\frac{|0\\rangle(|A\\rangle+|B\\rangle) + |1\\rangle(|A\\rangle-|B\\rangle)}{2}$$\n",
    "\n",
    "$\\mathbb{P}(a=0) = (|A\\rangle+|B\\rangle)^\\dagger(|A\\rangle+|B\\rangle) = \\frac{1}{4}(2 + \\langle A|B\\rangle + \\langle B|A\\rangle) = \\frac{1}{2} + \\frac{1}{2}Re(\\langle A|B\\rangle)$. By measuring the ancilla, it is then possible to obtain $Re(\\langle A|B\\rangle)$.\n",
    "\n",
    "To compute $Im(\\langle A|B\\rangle)$, the procedure is very similar. We prepare the state \n",
    "$$ \\frac{|0\\rangle|A\\rangle + i|1\\rangle|B\\rangle}{\\sqrt{2}}$$\n",
    "This can be done by applying a $U(0,0,\\pi/2)$ gate to the ancilla. We then apply a Hadamard to the ancilla, and we have $\\mathbb{P}(a=0) = \\frac{1}{2} - \\frac{1}{2}Im(\\langle A|B\\rangle)$\n",
    "\n",
    "**How to prepare the initial conditioned state?**\n",
    "\n",
    "We start with $p$ qubits and an ancilla, and apply a Hadamard gate to the ancilla. It leads to the state\n",
    "$$\\frac{|0\\rangle|0_p\\rangle + |1\\rangle|0_p\\rangle}{\\sqrt{2}}$$\n",
    "\n",
    "We apply $B$ controlled by the ancilla to the $p$ qubits, which is\n",
    "$$\\frac{|0\\rangle|0_p\\rangle + |1\\rangle|B\\rangle}{\\sqrt{2}}$$\n",
    "\n",
    "We flip the ancilla\n",
    "$$\\frac{|1\\rangle|0_p\\rangle + |0\\rangle|B\\rangle}{\\sqrt{2}}$$\n",
    "\n",
    "We apply $A$ controlled by the ancilla to the $p$ qubits\n",
    "$$\\frac{|1\\rangle|A\\rangle + |0\\rangle|B\\rangle}{\\sqrt{2}}$$\n",
    "\n",
    "We flip again the ancilla\n",
    "$$\\frac{|0\\rangle|A\\rangle + |1\\rangle|B\\rangle}{\\sqrt{2}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def real(param1, param2, angles, shots=1000):\n",
    "    \"\"\"Returns Re{<circuit(param2)|sigma_z|circuit(param1)>}\"\"\"\n",
    "    q = QuantumRegister(3)\n",
    "    c = ClassicalRegister(1)\n",
    "    circuit = QuantumCircuit(q,c)\n",
    "    circuit.h(q[0])\n",
    "    circuit = statepreparation(angles, circuit, [1,2])\n",
    "    circuit = create_c_circuit(param1, circuit, 0, [1,2])\n",
    "    circuit.cz(q[0], q[1])\n",
    "    circuit.x(q[0])\n",
    "    circuit = create_c_circuit(param2, circuit, 0, [1,2])\n",
    "    circuit.x(q[0])\n",
    "    circuit.h(q[0])\n",
    "    circuit.measure(q[0],c)\n",
    "    result = execute(circuit,backend,shots=shots).result()\n",
    "    counts = result.get_counts(circuit)\n",
    "    result=np.zeros(2)\n",
    "    for key in counts:\n",
    "        result[int(key,2)]=counts[key]\n",
    "    result/=shots\n",
    "    return (2*result[0]-1)\n",
    "\n",
    "def imaginary(param1, param2, angles, shots=1000):\n",
    "    \"\"\"Returns Im{<circuit(param2)|sigma_z|circuit(param1)>}\"\"\"\n",
    "    q = QuantumRegister(3)\n",
    "    c = ClassicalRegister(1)\n",
    "    circuit = QuantumCircuit(q,c)\n",
    "    circuit.h(q[0])\n",
    "    circuit = statepreparation(angles, circuit, [1,2])\n",
    "    circuit = create_c_circuit(param1, circuit, 0, [1,2])\n",
    "    circuit.cz(q[0], q[1])\n",
    "    circuit.x(q[0])\n",
    "    circuit = create_c_circuit(param2, circuit, 0, [1,2])\n",
    "    circuit.x(q[0])\n",
    "    circuit.u1(np.pi/2, q[0])\n",
    "    circuit.h(q[0])\n",
    "    circuit.measure(q[0],c)\n",
    "    result = execute(circuit,backend,shots=shots).result()\n",
    "    counts = result.get_counts(circuit)\n",
    "    result=np.zeros(2)\n",
    "    for key in counts:\n",
    "        result[int(key,2)]=counts[key]\n",
    "    result/=shots\n",
    "    return -(2*result[0]-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradients(params, angles, label, bias=0):\n",
    "    grads = np.zeros_like(params)\n",
    "    imag = imaginary(params, params, angles)\n",
    "    for i in range(params.shape[0]):\n",
    "        for j in range(params.shape[1]):\n",
    "            params_bis = np.copy(params)\n",
    "            \n",
    "            params_bis[i,j,0]+=np.pi\n",
    "            grads[i,j,0] = -0.5 * real(params, params_bis, angles)\n",
    "            params_bis[i,j,0]-=np.pi\n",
    "            \n",
    "            params_bis[i,j,1]+=np.pi\n",
    "            grads[i,j,1] = 0.5 * (imaginary(params, params_bis, angles) - imag)\n",
    "            params_bis[i,j,1]-=np.pi\n",
    "            \n",
    "            params_bis[i,j,2]+=np.pi\n",
    "            grads[i,j,2] = 0.5 * (imaginary(params, params_bis, angles) - imag)\n",
    "            params_bis[i,j,2]-=np.pi\n",
    "    p = execute_circuit(params, angles, bias=bias) \n",
    "    grad_bias = (p - label) / (p * (1 - p))\n",
    "    grads *= grad_bias\n",
    "    return grads, grad_bias\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP 3. Measurement "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "num_data = len(Y)\n",
    "num_train = int(0.75 * num_data)\n",
    "index = np.random.permutation(range(num_data))\n",
    "feats_train = features[index[:num_train]]\n",
    "Y_train = Y[index[:num_train]]\n",
    "feats_val = features[index[num_train:]]\n",
    "Y_val = Y[index[num_train:]]\n",
    "\n",
    "# We need these later for plotting\n",
    "X_train = X[index[:num_train]]\n",
    "X_val = X[index[num_train:]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: DeprecationWarning: The QuantumCircuit.cu3 method is deprecated as of 0.16.0. It will be removed no earlier than 3 months after the release date. You should use the QuantumCircuit.cu method instead, where cu3(ϴ,φ,λ) = cu(ϴ,φ,λ,0).\n",
      "  \n",
      "/Applications/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:35: DeprecationWarning: The QuantumCircuit.u1 method is deprecated as of 0.16.0. It will be removed no earlier than 3 months after the release date. You should use the QuantumCircuit.p method instead, which acts identically.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter:     1 | Loss: 0.3100236 | Acc train: 0.6757576 | Acc validation: 0.6396396 \n",
      "Iter:     2 | Loss: 0.3080325 | Acc train: 0.6878788 | Acc validation: 0.6486486 \n",
      "Iter:     3 | Loss: 0.2932128 | Acc train: 0.7000000 | Acc validation: 0.6486486 \n",
      "Iter:     4 | Loss: 0.2921732 | Acc train: 0.7090909 | Acc validation: 0.6396396 \n",
      "Iter:     5 | Loss: 0.2835880 | Acc train: 0.7151515 | Acc validation: 0.6306306 \n",
      "Iter:     6 | Loss: 0.2752897 | Acc train: 0.7303030 | Acc validation: 0.6306306 \n",
      "Iter:     7 | Loss: 0.2720776 | Acc train: 0.7272727 | Acc validation: 0.6306306 \n",
      "Iter:     8 | Loss: 0.2694250 | Acc train: 0.7303030 | Acc validation: 0.6306306 \n",
      "Iter:     9 | Loss: 0.2722688 | Acc train: 0.7303030 | Acc validation: 0.6306306 \n",
      "Iter:    10 | Loss: 0.2658310 | Acc train: 0.7303030 | Acc validation: 0.6486486 \n",
      "Iter:    11 | Loss: 0.2646052 | Acc train: 0.7303030 | Acc validation: 0.6486486 \n",
      "Iter:    12 | Loss: 0.2546762 | Acc train: 0.7333333 | Acc validation: 0.6486486 \n",
      "Iter:    13 | Loss: 0.2515599 | Acc train: 0.7363636 | Acc validation: 0.6486486 \n",
      "Iter:    14 | Loss: 0.2461293 | Acc train: 0.7333333 | Acc validation: 0.6486486 \n",
      "Iter:    15 | Loss: 0.2458180 | Acc train: 0.7272727 | Acc validation: 0.6486486 \n"
     ]
    }
   ],
   "source": [
    "layers = 6\n",
    "params_init = np.random.randn(layers,2,3) * 0.01\n",
    "bias_init = 0.01\n",
    "batch_size = 5\n",
    "learning_rate = 0.01\n",
    "momentum = 0.9\n",
    "\n",
    "var = np.copy(params_init)\n",
    "bias = bias_init\n",
    "v = np.zeros_like(var)\n",
    "v_bias = 0\n",
    "\n",
    "for it in range(15):\n",
    "\n",
    "    # Update the weights by one optimizer step\n",
    "    batch_index = np.random.randint(0, num_train, (batch_size,))\n",
    "    feats_train_batch = feats_train[batch_index]\n",
    "    Y_train_batch = Y_train[batch_index]\n",
    "    grads = np.zeros_like(var)\n",
    "    grad_bias = 0\n",
    "    var_corrected = var + momentum * v\n",
    "    bias_corrected = bias + momentum * v_bias\n",
    "    for j in range(batch_size):\n",
    "        g, g_bias = gradients(var_corrected, feats_train_batch[j], Y_train_batch[j], bias)\n",
    "        grads += g / batch_size\n",
    "        grad_bias +=g_bias / batch_size\n",
    "    \n",
    "    v = momentum * v - learning_rate * grads\n",
    "    v_bias = momentum * v_bias - learning_rate * grad_bias\n",
    "    \n",
    "    var += v\n",
    "    bias += v_bias\n",
    "\n",
    "    # Compute predictions on train and validation set\n",
    "    probas_train = np.array([execute_circuit(var, angles=f, bias=bias) for f in feats_train])\n",
    "    probas_val = np.array([execute_circuit(var, angles=f, bias=bias) for f in feats_val])\n",
    "    predictions_train = predict(probas_train)\n",
    "    predictions_val = predict(probas_val)\n",
    "\n",
    "    # Compute accuracy on train and validation set\n",
    "    acc_train = accuracy(Y_train, predictions_train)\n",
    "    acc_val = accuracy(Y_val, predictions_val)\n",
    "\n",
    "    print(\n",
    "        \"Iter: {:5d} | Loss: {:0.7f} | Acc train: {:0.7f} | Acc validation: {:0.7f} \"\n",
    "        \"\".format(it + 1, cost(var, features, Y), acc_train, acc_val)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6243"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gc.collect()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Applications/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:25: UserWarning: No contour levels were found within the data range.\n"
     ]
    },
    {
     "data": {
      "image/png": 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TJk3C2toaHx+fMkVWhBCiNJVSetyFEMJoZs2aRWhoaKXzBlatWkXz5s0rDIkrXyGsocrOzmbChAm8/vrrdOvWzdzNMbkjR45w8OBBJk2aBMCyZcs4dOhQmaFWQgghhDA+GQInhImcPn2asLCwSr9vbW1Nr169TNgi09mzZw/9+vWjT58+TTL8AISGhvLPP/8wfPhwIiIi2Lt3r64stBBCCCFMR3qAhDCRm2++mTVr1sjaFEIIIYQQZmS0HqBDhw7pHZO8fft2Ro8ezdixY1m1apWxLi+Exfnnn38k/AghhBBCmJlRiiAsXbqUdevW6Sb4ligoKODtt99m9erVODo68sADD9C/f3+8vb2N0QwhhBBCCCGEKMMoASg4OJhFixbxwgsvlNl+7tw5goODUavVQPEib//88w9DhgypcI4DBw4Yo2lCCCGEEEI0eD169DB3EwwqNzeXjb//QcRdfeu03mBtGCUA3X333XrL5GZmZpZZu8TZ2ZnMzMxKz9NZSTZG80Qjl5ubW6N1agzGN6ROh1k5qw3bDlEvObm5OJryc9NIabPSK25Mulj7E9Xw58pcP0elX6eiKMULntbldYomzeT/XokyPvv8e4ZmZBLq5qLbdiEjk41uLjz+6AQztqx6R1QVF/9u6Jb9tIU2QV58sGwNzz96v1GvZdJ1gFxcXMjKytJ9nZWVVWExRyHMrg6BRsKMEMXK/yxos9Ib5c9U6fbl5OZiX5Sn/3VKKBLCYoX37826739mBBDs4kRMZjbrNJn0G3m3uZvW5OTm5tI+xJv3V/zJsw/0pqCgwKi9QCYNQC1btuTSpUukpaXh5OTEP//8w9SpU03ZBNEU1fLhy9IfvIRoSJrKz5O+16k3/EkgEsJidGodChNGs3HHH6RcTsbLz4d+I+8u3i5MatlPW0hMzST5Whb7jsXx9/E4o/YCmSQARUZGkp2dzdixY3nppZeYOnUqiqIwevRofH19TdEE0diVesiwVxRQqcp8u6k8hAkhLIfeUNRQe4kkyIlGqlPrUAk8ZlbS+7Py96MAbNt/jlcfusOovUAWuw7QgQMHZA6QKKuanpyShw2ZyyHqQj43oq7q89nRO2cKjDpvqi70Dm0sT0JRrckcIFFXR1Q+jaYIwqffrSUxNZMt+87qtt17RwdUKozWC2TSIXBCVKmGAUcIIRqLGg+dq8f5jKFR9W4JIcymfO9PCWP3AkkAEqYlIUcIIarUUP8elFAkhKitkrk/ufmFZbZnZOcZdS6QBCBhWDX4rWVD/cddCCFE7dS4KqCEIiGanMp6f0oYsxdIApConlRRE0IIYQC1GvInoUiIRq2y3p8SxuwFsjLo2UTD4htSsz8U/6NV0z9CCCFETVX670gl/x5ZmvgrV3nw9YVV7vPT9j8pKCyq1Xl/33+Y1dv31qdpBrH/+BmeX/RNjfb9Yt02jpy7ZOQWGeZaa3btY+GKSKBu74+on5Len10HL1a537b957ilQyAFBQUGvb70ADU2tfgHQsKKEEIIS2TMnqIfN+3k9U9WE5t0kSDfEGZPv48HhvSrUztr6ou1WxkR3hOwrvExA3p2MV6DjOSREQMb5LXq8v6I+qmu96eEsXqBJAA1RFWEHAk1QgghGiNDhKIfN+1k+rwVZOd+DYQTkxjF9HkPARgkBE2Zu4h2LQI4E5tIVk4u7z31EH8dO01KuobnP/6Gj555hA9WRHLg5Hm0ipYHBvZmeJ9bmDJ3ER6uLmRk5fDJ848yd9lPXEq8gqIozLh/KD07tOajVRvYd+w0iqIwpFd3JpZr7+Cn59ClVTCxSVdpFdScNx8ZR2ZOLi9/8j2ZObkUabXMuH8ot3Zswz0vzqdFcx/sbK1558nJunOcjklg/re/oKDg7uLM7Ecf0Ps6FUXhra9Xc+x8LF7ursQlp/Lxc4/wyc+bGdKrOylpGew6eIzc/AJS0jJ48O6+7Pj3KGdjL/Ps+JHceXNnhj0zl25tQrl4OZlmalcWPv0wObn5zPpiBZqsHNIysxjd/zbGDgxnxdYo1u35G5VKRfe2YTw7fiSvfvYDQ3p159aObXj98x+JTU5Bq9UyaUg/BvfqXqa9y3/bw+/7D1NYVISLowMf/O9h3fd+2flXmfdnwfdrOHj6PABDb+/BhMF31PtzIcqqbu5PecaYCyQByNJVEnYk6AghhGjqaltG/PVPVl8PP/2vb+lPdu7XvP7JIwbrBeoU1oIXJ97LR6s2sHHvvzwyYiBLft3Cgicnsyf6OPFXUvnujf+Sl1/AA6+/T9/unQAYdnsPBvTswsptUbi7FoePNE0WD81ZxJp3XmLdnv18PXMGPh5q1uzeV+G6SalpPHnf4wQ39+bZj75m+4EjRJ++SK/ObZkw+A6SUtOYPPsjNr7/Gtm5eTx2z120Dwksc443v1jJ7EcfoGVgc37Z+RfL1m+nV6c2Fa6148BR0jRZ/DjnGVIzMhn+7NwK+2Tl5PH5y0+wae+/fLdpJz+8+T/2Hz/L91t2cefNnYlLvsqXr/6H5s08mPjGhxw9F4OtjTVDet3EwJ5dSb6WzpQ5ixg7MJw1u/fx8qTRdG0dwsptURQW3Riu9tP2P3F3debt6RPIysllzKvvcmunNni4ugCg1WpJ12Sx9OUnsLKy4rH5n3L0XIzu+Hv73aZ7f3b9e4z4K6n88Ob/KCzSMnn2h9zSoTVtgv3r9mEQetW096eEMXqBJABZGj1/aUvYEUIIIWqmsn8ztVnpxCZdBMLLfSf8+nbDaB8SAEBzT3dS0jPKfO9M7GWOX4hlytxFABQWFXE55RoAIX4+un0OnDyvm99SpC0iTZPFgicn8eHK9aSkZxDetX2F6/p5eRDc3BuAbq1DuJiQzPmEJIb1Ll4s09fTHWdHB1I1WWWuV9r5hCTmfv1TcdsKtbTw89b7Gs8nJNG1dQgAnm4uhPr5Vtin3fX74OrkSKi/LyqVCjdnR/ILih963V2dad7Mo/heNXMnv6AAPy8Pvt+8i237D+Pi6KALOnMeHc/XG7azcEUkXVuHoCil2hKfpAtpzo4OhAU0JzYpRReArKyssLWx5oWPv8XJwZ6k1PQyAar86+reLgyVSoWtjTVdWoVwPj5RApAB1bb3p4She4EkAJmThB0hhBDCJKyc1QQFtCEmLoobPUAAUQT5tzJcJTqVSs8mK7SKQqi/Lz07tOaNR8ai1WpZ/NNGAn2aFe9jVXxcqJ8Pvp7uTBs5iNz8fD5fsxUnB3t++zuad56chKIojHpxPkNu646/t6fuGsmp6aSkZeDl7sbB0xeICO9JWmY2/548R/uQQJJS08jIysbdxan4fuhpZ4ifD/Men4CflwcHT53nSlpGhX0AWgf6ERm1n4lDID0rm4uJV/S85ornr+77X2/YTtfWIYwdGM7fx86w++BxAH7esZfXHx6DvZ0tj83/lOgzF3THhAX4cuDUOQb07EJWTi5nYi8T4N1M9/1TMQlsP3CE5bOfIScvn7GvvVsmQBW3pfj9CfP3Zc3ufUwa0o+CwiKiz1xgRJ+eVb4OUTu17f0pYeheIAlApiJhRwghhDCruTNn8PjTD5Od8xXFPUFRODk+zNzXn6/5mkVQ62DUo10Y0xcs4atXn2T/iTNMnv0R2bl59O3WHmdHhzL73j+gN298sYKH5iwiKyeXsQPDsbO1wc3ZifteWYCbsyO3d26Hn5dHmePsbK2Z9/XPJKZeo0urEPp170j3tqHM/PxHfvv7EHkFBcyaOhYb68on+r/28P288tn3aLXFCeHNaeO4ci29wn59b+rAnkMnmPDGB3ip3XCws63yvDXV76ZOzFn2Exv+OIDaxRlrayvyCwppHeTHuJnv4+nmgo+Hmi4tW7BmV/EwwPvv7MUbX6xk0psfkptfwBP33k0ztavunMG+Xjja2zP2tfews7HB211NclrZ11T2/TnLg7MWUlBYxN23daNDaFC9X5coVtfenxKG7AVSKUr5HGwZDhw4QGcl2dzNqBsJO2aVk5uLo4ND9TsKUYp8bkRdyWenYflx9Rpem7OI2PjTBAW0Ye7MGTxw36gaH6/NqhgIdGoZjHJzc3Ew0Gen3/SZ7PxkjkHOVZ3zCUmcuhTPkF7dSdNkMerF+fz24SzsbOX36qZyROVDjx49zN2MWvn0u7UkpmayZd/ZOp/j3js6oFJRaS/QoUOHePfdd/nuu++qPI98UutLihQIIYQQDcYD942qVeApr6o5RobqMbJ0zT3dWfhjJN9v2kWRouV/4yIk/Igq1bf3p0RVvUBLly5l3bp1ODo6Vnse+bTWhoQdIYQQQuhRq2BkhEBkqt4fACcHexY9+4jJricavsuXL7Pj3wu1nvtTXslcoLAWgQQFlR2eGBwczKJFi3jhhReqPY8EIH1knR0hhBBCGEBVc4vsFaW4aEIj6yESoryMjAyW/3aIqxk59T7Xit8PM7R3+woB6O677yYuLq5G55AAJL06QgghhDCR0s8XJfPHtIaqQCeEhVIUhbYdOpCdp78EeW14u9nX+xxNJwBJ0BFCCCGEBapRBToJRAI4cuYCa3acYdRjE8zdlAat8QUgCTpCCCGEaMD0PbNU6CWSQNTkHDlzgYXfX8TdNcLcTWnwrMzdgHrzDSn7h+K/OMr/EUIIIYQwtPjLiTzwyPQq91m1JpKCwtpN/t62cw8/rV2v+7rCM025Zx9j2X/8DM8v+qZG+36xbhtHzl0yansMda01u/axcEUkAD9t/5OCwvoNzTodk8A/J87VeP/nF31T68/Emh1ncHcdjIebrE1UmcDAQFatWlXtfg2rB0jW1xFCCCFEPRw+doI16/cTE3eN4EAPRg3vSZeO7Y16zaXf/MDIIXfX6qlrYL8+lX6v9LNPheFyZuwZemTEwAZ5rS/WbmVEeE+g7ou5btt/CC+1Gze3b1mj/RfMmFzra8RcziTQ17/Wx4mKLDsASeARQgghhIEcPnaChYv/xl09nED/IK6lxbJw8Xr+9x8MEoIemv40bVu34uz5C2RmZbPwrVns3X+AlNRUnnt9Nov+by4LP1nKP9GHUBSFB0aPImLwIB6a/jQe7u5kaDR8+t7bzFnwAZfi4tFqtTz12FRu6d6NDz/7gn0HDqLVahk6aACTxt0H3Hguunv0eDq3bUVsQiKtQoJ589n/kHnxJC9/8j2ZObkUabXMuH8ot3Zswz0vzqdFcx/sbK1558kbD+KnYxKY/+0vKCi4uzgz+9EH9L5ORVF46+vVHDsfi5e7K3HJqXz83CN88vNmhvTqTkpaBrsOHiM3v4CUtAwevLsvO/49ytnYyzw7fiR33tyZYc/MpVubUC5eTqaZ2pWFTz9MTm4+s75YgSYrh7TMLEb3v42xA8NZsTWKdXv+RqVS0b1tGM+OH8mrn/3AkF7dubVjG17//Edik1PQarVMGtKPwb26l2nv8t/28Pv+wxQWFeHi6MAH/3tY971fdv5FSrqG5z/+ho+eeYQF36/h4OnzAAy9vQcTBt9R7fuelJrG2t1/Y2tjQ/vQQF7//Efd/X3mgZHMXfYTeQUFpGdm89g9dzHg5i7c/d83WbfgFWZ/tQo7WxsSrqRyJS2DuY+Np0Oo/h6eYD8XrmUkSA+QAVh0AJKwI4QQQghDWbN+P+7q4Xi4hwBc/+9w1qzfYLBeoM4d2vHy/57kw8++YMPW7UybNJ7Pln3Hu7NfZ8/efcRfvswPn39MXl4+46Y+wR29ewEw7K4BDOzXhxW/rMXdXc2cV18gLT2dSU/8l3XLv2bdpt/45tMP8fFqxpoNmytcNzH5Cp9/sIAWQQE88+obbP9jH9HHT9Lr9l5MuDeCpBPRTJ79ERvff43s3Dweu+cu2ocEljnHm1+sZPajD9AysDm/7PyLZeu306tTmwrX2nHgKGmaLH6c8wypGZkMf3ZuhX2ycvL4/OUn2LT3X77btJMf3vwf+4+f5fstu7jz5s7EJV/ly1f/Q/NmHkx840OOnovB1saaIb1uYmDPriRfS2fKnEWMHRjOmt37eHnSaLq2DmHltigKi24MV/tp+5+4uzrz9vQJZOXkMubVd7m1Uxs8XF0A0Gq1pGuyWPryE1hZWfHY/E85ei5Gd/y9/W5jya9bWPDkZHb9e4z4K6n88Ob/KCzSMnn2h9zSoTVtgqvudfH1dGdk31vwUrvRuWWLMvd379FTTB7aj54dWhN9+gKLf97EgJu7lDne38uTWVPHsnr7XlZv38vrU/UHnFH9W7Pw+83AYECekevDogOQEEIIIYShxMRdI9C/7MOl2i2ImLhrBrtG+7atAWju40NKamqZ750+d55jJ0/z0PSnASgsLCQhMRGAkBZBun3+jT7CkWMnACgq0pKWns6C2TP54NOlpFxNJbzXrRWu6+frQ4ugAAC6de7EpaSrXIhPJGLYMAB823fD2dWNVAfP4uv5+VQ4x/mEJOZ+/dP1tmlp4eet9zWeT0iia+sQADzdXAj1862wT7uQ4ra4OjkS6u+LSqXCzdmR/ILieS/urs40b+ZRfK+auZNfUICflwffb97Ftv2HcXF00AWdOY+O5+sN21m4IpKurUNQlFJtiU/ShTRnRwfCApoTm5SiC0BWVlbY2ljzwsff4uRgT1JqepkAVf51dW8XhkqlwtbGmi6tQjgfn6gLQDGJV5j1xQoAIsJ7cm+/2/SeB27cX293Nz5f8xu/7NyHSoXea7drEaC7DyW9T/p0bh3K/ybAmh2RgFSBqw8JQEIIIYRoEoIDPbiWFqvrAQJIz4glONDDYNdQoaqwzcrKCq2iJbRFMLf06MabLz2HVqtl0dJlBPkXP1xbqYrrUoW1CKa5tzePPjSB3Nw8lnzzPU6OjmzZvosFs2eiKAojx09h6MD++Ps1110j+UoKV66m4t3Mk4OHjxIxZBBp6RkcOHSY9m1Hk5R8hYysbDybB4K1DVbNQ8DOrkw7Q/x8mPf4BPy8PDh46jxX0jL0vsbWgX5ERu1n4hBIz8rmYuKVivdBVfE+VPf9rzdsp2vrEMYODOfvY2fYffA4AD/v2MvrD4/B3s6Wx+Z/SvSZC7pjwgJ8OXDqHAN6diErJ5czsZcJ8G6m+/6pmAS2HzjC8tnPkJOXz9jX3i0ToIrbYoVWUQjz92XN7n1MGtKPgsIios9cYESfnrr9gpt7s+y1GZW+Hm2pE1tdf30f/7SJ0f1vo0+3Dvy6ax9rd/9d63tVWufWoXRuHcqRGh8h9JEAJIQQQogmYdTwnixcvB4YjtotiPSMWNLS1zNlwi1GvW73rp154pmXWLZ4Ifv/jWbi40+RnZ3DHb1vw9nZqcy+Y0ZFMOvtd5n8xH/JzMpm3OiR2NnZoXZz5d5Jj6B2deX2W2/Gr3nZXhc7O1veeu9DEpOS6dqpA/3Db6d7l87MnPcOv+3YTW5eHm+8+Cw2NtagssLKSY2VfdkA9NpzT/HKZ8vQarUAvPnck1xJSQUH5zL79b2pA3sOnWDCGx/gpXbDwc4WG+u6FxAo0e+mTsxZ9hMb/jiA2sUZa2sr8gsKaR3kx7iZ7+Pp5oKPh5ouLVuwZtc+AO6/sxdvfLGSSW9+SG5+AU/cezfN1K66cwb7euFob8/Y197DzsYGb3c1yWnpZa7bo10Y0xcs4atXn2T/ibM8OGshBYVF3H1bt0rn45TXMTSI95avI8y/7Pty161dmf/tL3yxbhu+nu6kabLqeZeEIagUpXwOtgwHDhyga6ifuZshGqCSlbWFqA353Ii6ks9Ow2KOKnCVMeRnp++we9m94ReDnKs8bVbZwHA+Jo5T5y4wpH8f0s4eY9SL8/ntw1nY2crv1U3liMqHHj16mLsZNRYdHc1rP0STnVe/cuMA3m72zBzXjU6dOtX5HPJJFUIIIUST0aVje7MFnoaqfFEq/xA7Pli2nO9/jqRIq+V/j03BLrBV2YNkoVZhwSQACSGEEEI0cMbq/dHHydGRj995q8p9tFUt0CrhSJiZBCAhhBBCCGFQlS1lUmHh1tIkGAkTkQAkhBBCCCFMokbBSIKQMDIJQEIIIYQQwqxKB6Myw+ckDAkjsDJ3A4QQQgghhChh5ay+EYh8QyofMidEHUkAEkIIIYSoo/jLiTzwyPQq91m1JpKCwsJanXfbzj38tHZ9fZpmEH//G81zM2fXaN+l3y7n8LETBrt2VUHoi3XbOHLuUo3O02/6zBpf8/lF39T6vRINjwQgIYQQQjQZK1b/Qreut2DvFUi3rrewYrXxq6ct/eYHtEXaWh0zsF8f7h853EgtMo5pk8YbpcR4SRCyclbrgtAj0x6hc8sWBr/WghmTsbWRGSKNnbzDQgghhGgSVqz+hdeffoEvc3IIB6Li4pn69AsAjLvv3nqf/6HpT9O2dSvOnr9AZlY2C9+axd79B0hJTeW512ez6P/msvCTpfwTfQhFUXhg9CgiBg/ioelP4+HuToZGw6fvvc2cBR9wKS4erVbLU49N5Zbu3fjwsy/Yd+AgWq2WoYMGMGncfWWufffo8XTu2J7YuARah4Uw+5XnyczK5qU33iIzO5uiwiJmPPYwt93cnZEPTiEkKAhbO1venX2jd+T02fPMW7gIFAW12o25r76g93UqisKcdz/g2InTeDXzJD7hMovfncfiL75myMA7SUlNZWfUn+Tl5XMl5SoTxo5mx+4/OHP+As/PeJw7+4bzw0+/sm3XHgoLC3F1duaD+bPZ8Nvv7PnzL3Jz84iNT+DhiQ9wz7DB/PjzGtZu3IKVlRXdu3TmuRmP8/Ks2Qzp14dbu3fh9TnziU1OQavVMmlIPwb36l6mvfkFhTy/6BsSr6bRJtiP16bcT1JqOnOX/UReQQHpmdk8ds9dDLi5C3f/903WLXiFlPQMZi1dQUFhESqVipcn3UvbFgH1/owIyyABSAghhBBNwvw58/kyJ4f+17/uD3yZk8OMOfMNEoAAOndox8v/e5IPP/uCDVu3M23SeD5b9h3vzn6dPXv3EX/5Mj98/jF5efmMm/oEd/TuBcCwuwYwsF8fVvyyFnd3NXNefYG09HQmPfFf1i3/mnWbfuObTz/Ex6sZazZsrnDdxOQrfP7BAloEBfDMq2/w++4oog8fo9ctPZg49j6Skq8w8fGn2Lz6B7Kzc3h8ykTat21d5hyz5r/LnFdfoFVoCD+v28BX36+g1y03V7jWjj1/kJ6ewcqvPiX1WhpDx0yosE92dg5LP1zAxq3b+XbFT/z4xSf8/W8036/6mX7ht5OekcGXH72LlZUV055+nqPHTwKgycpi6QcLuBQbx3+ee4V7hg3m1w2befWZp+jaqQMrfllLYWERKhs7VA7O/LR+C+6+frz95mtkXTzJmFff5dZObfBwddG1Ja+ggP+Ni8Df25NnP/qanf8ew8HelslD+9GzQ2uiT19g8c+bGHBzF90x7/2wjvF39eXOmztz8mIcry9dwcq5z9btQyEsjgQgIYQQQjQJJ+ITCC+3Lfz6dkMpCRXNfXxISU0t873T585z7ORpHpr+NACFhYUkJCYCENIiSLfPv9FHOHJ9Lk1RkZa09HQWzJ7JB58uJeVqKuG9bq1wXT9fH1oEFfdQdOvciYuXYjl/6RLD7x4IgK+PN87OTqSmpZW5XmnnL8Ywd8EHABQUFhISXHEfgHMXY+jaqSMAnh7uhLYIrrBPuzatAHB1cSEspAUqlQo3V1fy8vKxsrLC1saG51+fg5OjI0nJVygsKio+rnUr3f3Ly88H4K1XX2TZ8pW8v3gJXTt3REHRXedCQjK9evYEwDmkHWFhYcQmpZQJQH7NPPD39iy+N61DuHg5mT7d2vP5mt/4Zec+VCp019fdi4QkerRvWdymkEASr17Tey9EwyQBSAghhBBNQvsAf6Li4nU9QABR17cbigpVhW1WVlZoFS2hLYK5pUc33nzpObRaLYuWLiPIv/jaVqriadlhLYJp7u3Now9NIDc3jyXffI+ToyNbtu9iweyZKIrCyPFTGDqwP/5+zXXXSL6SwpWrqXg38+Tg4aNEDBlEWnoGBw4dpn3b1iQlXyFDk4m7m7rM9UoLCQ5i3usv49/cl38PHeHK1dQK+wC0DgslcvNvwH2kZ2i4GBNX8T6oKt6HEqfOnuP33VGs+PJTcnJzGfPQYyiKUulxq9etZ9YLz2Bvb8e0p58n+vBR3ffCQlpw4NBhBvbrQ1ZWNmcvxRLQoRt4uBfvkHSRpNQ0rlxLx9tDzcFTF7in3618/NMmRve/jT7dOvDrrn2s3f13mWuG+fvy78nz9O/RiZMX4/Byd6v09YiGRwKQEEIIIZqEl2a+xNTSc4CAqY6OzJ75klGv271rZ5545iWWLV7I/n+jmfj4U2Rn53BH79twdnYqs++YURHMevtdJj/xXzKzshk3eiR2dnao3Vy5d9IjqF1duf3Wm/Fr7lvmODs7W95670MSk5Lp2qkD/cNvp3uXzsyc9w6/7dhNbl4eb7z4LDY21pW28/UXnuaV2W9TpC0u2DDnledJTrlaYb87et/Gnr37eHDak3g188TRwR4b68rPW15wYACOjo6MmfIYtra2eHk140pKSqX7t24ZxtiHH8fDwx1fby+6dOzAr9eHAd4/ajiz3n6XCY/NIC8vjycenoR3YHFxhJLFVdVqN97+9heSUtPo1jqUPt06oMnOYf63v/DFum34erqTpskqc81nHxzBG1+s5OsN2yksKmL2tHE1fn3C8qmUkshtYQ4cOEDXUD9zN0M0QDm5uTg6OJi7GaKBkc+NqCv57DQsK1b/wvw58zkRn0D7AH9emvmSweb/1JYhPzt9h93L7g3Gr2gHxUPlTp45y9BBd5KWns6I8VPY9usK7OzsTHL92tJmpd/4opqFVQc8OYvfPpqFtZVlF0o+ovKhR48e5m5GjUVHR/PaD9Fk5xVVv3M1vN3smTmuG506darzOaQHSAghhBBNxrj77jVb4Gksmvt68/4nS/hu5WqKtFqemf6oxYYfQLeWUEmPEKA3CP3vg6/o0qqFxYcfUX8SgIQQQgghGjhT9f4AODk68vE7b5nseoZSIQiVC0ELn37Y9I0SZiERVwghhBBCNBklQahkUVXR9EgAEkIIIYQQTYqVs7psEBJNigQgIYQQQgjRJElvUNMkAUgIIYQQQjRZ0hvU9EgAEkIIIYSoo/jLiTzwyPQq91m1JpKCwsJanXfbzj38tHZ9fZpmEH//G81zM2fXaN+l3y7n8LETRm5R7a/Vd1jNqv5ZOat5fu67FHgG1DoI/XPiHKdiEmq8/9MLv6rV+YVhSRU4IYQQQjQZR44dJ2r9JlLi4vEKDCB8+BA6d+xg1Gsu/eYHRg65u1ZPXQP79TFeg4xk2qTxDf5a7709B6i8Ulxlft31F0N6dadtsH+N9v/gf1JxzpwkAAkhhBCiSThy7Dg7Fy9hhFpNsL8fMWnprFu8BP7zmEFC0EPTn6Zt61acPX+BzKxsFr41i737D5CSmspzr89m0f/NZeEnS/kn+hCKovDA6FFEDB7EQ9OfxsPdnQyNhk/fe5s5Cz7gUlw8Wq2Wpx6byi3du/HhZ1+w78BBtFotQwcNYNK4+8pc++7R4+ncsT2xcQm0Dgth9ivPk5mVzUtvvEVmdjZFhUXMeOxhbru5OyMfnEJIUBC2dra8O3um7hynz55n3sJFoCio1W7MffUFva9TURTmvPsBx06cxquZJ/EJl1n87jwWf/E1QwbeSUpqKjuj/iQvL58rKVeZMHY0O3b/wZnzF3h+xuPc2TecIfdP4KYunbgYE0szTw8+mPcmObm5vD5vAZrMLK6lpXPfyGGMu3ckP/68hrUbt2BlZUX3Lp15bsbjvDJnPkMG3sltPbsz8613iI1LoEhbxOQH7mfIwDvLtLegoIDnZs7mclIybVu1ZObzT5N0JYXZ7ywkPz+ftPQMnnh4EgPuCGfQPeNYv+JbUjJymDlnHgWFRahUKl4eN5S2LQL03o9jF2L54/BJTlyMo2VAcybP/ohQfx/CAny5t18vFny/Bq2ioMnO4eVJ99KtTSj9ps9k5ydzmDJ3Ee1aBHAmNpGsnFzee+oh/L096/lJFNWRACSEEEKIJiFq/SZGqNWEuhfP9wh1VzMC2Lh+k8F6gTp3aMfL/3uSDz/7gg1btzNt0ng+W/Yd785+nT179xF/+TI/fP4xeXn5jJv6BHf07gXAsLsGMLBfH1b8shZ3dzVzXn2BtPR0Jj3xX9Yt/5p1m37jm08/xMerGWs2bK5w3cTkK3z+wQJaBAXwzKtv8PvuKKIPH6PXLT2YOPY+kpKvMPHxp9i8+geys3N4fMpE2rdtXeYcs+a/y5xXX6BVaAg/r9vAV9+voNctN1e41o49f5CensHKrz4l9VoaQ8dMqLBPdnYOSz9cwMat2/l2xU/8+MUn/P1vNN+v+pk7+4YTl3CZrz5+Hz9fHx589EmOnjiFra0NQwbdyaB+fUm+ksLk6U8z7t6R/LphM68+8xRdO3VgxS9rKSws0l1n1a+RuKvVzJ/1CllZ2dz30KPcdnMPPK6/xwC5eXk8M/1R/P2a88yrb7Aj6k8c7R14aPwYbunejYOHj7L4i68ZcEe47pgFiz5lwrgx3Nk3nOOHDvL6+4tZOWuG3ve8Y2gQvbu0Y0iv7vh5eZCYmsaqt57D3dWZzXv/5bkHR9Im2J8Nfxxgza59dGsTWub4TmEteHHivXy0agMb9/7LIyMG6r2OMBwJQEIIIYRoElLi4gn29yuzLdjNlZS4eINdoyRUNPfxISU1tcz3Tp87z7GTp3lo+tMAFBYWkpCYCEBIiyDdPv9GH+HI9fktRUVa0tLTWTB7Jh98upSUq6mE97q1wnX9fH1oEVTcQ9GtcycuXorl/KVLDL+7+GHa18cbZ2cnUtPSylyvtPMXY5i74AMACgoLCQmuuA/AuYsxdO3UEQBPD3dCWwRX2Kddm1YAuLq4EBbSApVKhZurK3l5+QB4qNX4+fro2p6Xn4+frw/frVjNtp17cHZ2ovD6vKm3Xn2RZctX8v7iJXTt3BEFpVSbL9GrZw8AnJ2daBnagtj4+DIByM/XF3+/5mXuTd/bb+Wzr7/nl8iNqK6/F2XvxSV6dOsKQIeuN5F0JfXGvKCkiyz/bQ9b/44GYP70iWWO9XB1xt3VGQAfT3eWrPkNBztbsnLycHa0r3Cv2ocUv2/NPd1JSc+o8P2jZy4QteMPUi4n4+XnQ3j/3tDGp8J+ouYkAAkhhBCiSfAKDCAmLV3XAwQQk6HBK1D/0Ka6UKGqsM3KygqtoiW0RTC39OjGmy89h1arZdHSZQT5F88ZsVIV16UKaxFMc29vHn1oArm5eSz55nucHB3Zsn0XC2bPRFEURo6fwtCB/XUP9QDJV1K4cjUV72aeHDx8lIghg0hLz+DAocO0b9uapOQrZGgycXdTl7leaSHBQcx7/WX8m/vy76EjXLmaWmEfgNZhoURu/g24j/QMDRdj4ireB1XF+1DuRlWwbPlKunbuyLh7R7LvwEF2/7kPgNXr1jPrhWewt7dj2tPPE334qO6YsJAWHDh0mIH9+pCVlc2ZcxcI8CsbcpOSr3Al5SreXs349/ARRkcMZdHny7hv5DD69LqVX9dvqtCrVnLeO/v05sTpszRr5qGrFKf1DWH8xBDG33VjnpaVlQqtolR47fO//YX50ycQFtCcxas3kZCi555Wca+OnrnAzu9/ZoSrC8G+XsRkZLLu+5+5Y3bFECxqTgKQEEIIIZqE8OFDWLd4CSMo7vmJydCwLj2dfhPGGfW63bt25olnXmLZ4oXs/zeaiY8/RXZ2Dnf0vg1nZ6cy+44ZFcGst99l8hP/JTMrm3GjR2JnZ4fazZV7Jz2C2tWV22+9Gb/mvmWOs7Oz5a33PiQxKZmunTrQP/x2unfpzMx57/Dbjt3k5uXxxovPYmNjXWk7X3/haV6Z/TZFWi0Ac155nuSUqxX2u6P3bezZu48Hpz2JVzNPHB3ssbGu/Lw11S/8dua8s5D1W7bhrnbDxtqa/Px8WrcMY+zDj+Ph4Y6vtxddOnbg1+uB5f5Rw5n19rtMeGwGeXl5PPHwJJp5epQ5r7vajXnvLyLpyhW6de5In163kqHJZN77i/Bq9gPNfby5lp5e5pjnZzzBrLff5evlqygsLGTOKzfmQ1k5q28USQBIukjnli34YEUkgeXm7wzr3YOn3v+SZmpXfD3VXNNk1eqeRO34gxGuLoS6uQAQ6ubCCCC96sNENVSKoijV72Z6Bw4coGuoX/U7ClFOTm4ujg4O5m6GaGDkcyPqSj47DYs5qsBVxpCfnb7D7mX3hl8Mcq7qnL8Yw8kzZxk66E7S0tMZMX4K235dgZ2dnUmub0x3jrifrb+uwLqGgU6bVSqK1LBiXG3MffN9XvP1wtrqRo9dkVbLkSeeo0ePHga/nrFER0cz6aM/0eTUrhy8Pv4ejiyZ3otOnTrV+RzSAySEEEKIJqNzxw5mCzyNRXNfb97/ZAnfrVxNkVbLM9MfbRTh578vv07nju1rHH6AG8PiyvUIGYqXnw8xGZm6HiCAmMxsg53flG7p1Y3c+ucfPByqGV5ZAxKAhBBCCCEaOFP1/gA4OTry8Ttvmex6pvLh2zVb8FWfCkHIQCEovH9v1n3/c/GwTRcnYjKzWafJ5A6DnL3pkgAkhBBCCCGEAZQulADUOwh1ah0KE0azsVQVuH4j78Yi5680IBKAhBBCCCGEMCBDBqFOrUOLg1ApR+p8NgFQsQaiEEIIIYQQot5KghC+ITfmCAmzkwAkhBBCCCEapRWrf6Fb11uw9wqkW9dbWLHadHOlSlg5qyUIWRgZAieEEEIIIRqdFat/4fWnX+DLnBzCgai4eKY+Xbyez7j77jV5e4xdMU7UnAQgIYQQQgjR4JRe0ynfzg4bwCo/X7e+0/w58/kyJ4f+1/fvD3yZk8OMOfPNEoBKSBAyPwlAQgghhBCiQTly7Dg7Fy9hhFpNuo0NG//YS3sUbu11G3lp6axbvITjcfGElzsuHDgRn2COJldgrNLZonoyB0gIIYQQQjQoUes3MUKtJtRdzd6z5xjv6kJ/Vzfiz54j1F3NCLWa9q6uRJU/Dmgf4G+OJldKN0eoZH6QzBEyOukBEsLEruJcq/2bkWWkljQMNblfTf0eCSFEU5MSF0+wvx8AVzI0BLu6oAKyMzQABLu50qNTB6ZGH74xBwiY6ujI7Jkvma3dVZGhcaYjAUgII6rs4V1lY1fzcxRWv09DDAA1DYI1uVc1uUflNcR7JoQQophXYAAxaemEuqvxdnMlJjcXd1Q4ubkCEJOhoWef3tz10ARmzJnPifgE2gf4M3vmS2ad/1MTEoSMTwKQEAZgiKBTGUMFAFM88Nemd8sQ96Y+5yp/z7T2TmSjqvIYCU1CCGEZwocPYd3iJYwAerVqyfK9+4rnAHW6jQtp6axLT6ffhHF07tjB4gNPZSQIGY8EICFqyZhhp64M2Uui7yHfXMHGmMq3syA3BwcHxyqPkZ4mIYSwDJ07doD/PMbG9ZtIicskv3cvooHD+fl4uat14acx0K0hBGhLglBytnka00hIABKiEpYYdOqjJu1WCvMb3es2pNreg6rupz4SloQQouY6d+xgkSGndHnukpLchmrnjTAkAag+JAAJQeMLO3XV1F6vsdX2fta2h0kCkxBCWJbS5bmD/f2IuV6Sm/88ZpFhramSACSaFAk6wpLV5nNY094lCUlCCGE6pctzA8UluYGN6zdJALIgEoCERattyWiofjK7hB3RGNT0c1y+V0kCkRBCGE/p8twlgt1cSYmLN1OLhD4SgITB1CWsVKcuYaUmk9mFaCrK/wxJIBJCCOMpXZ67REyGBq/AADO2SpQnAUgAhgkv0rMihOUr/XOqbxidBCIhhKi70uW5g91cicnQ6EpyC8shAaiRkAAjhKit8j/zEoiEEKJ+ypbnLq4C15hKcjcWEoAaiOoCjoQXIUR9VReIJAwJIUT1LLU8t7hBApAFkZAjhLAkMn9ICCFEYyQByMSqCjkScIQQlkwCkRCNkzEX7hTCEkkAMgIJOUKIpsBSCyrUd06kBDnRlMjCnaIpMkoA0mq1vPHGG5w6dQo7Ozvmzp1LixYtdN9ft24dy5Ytw8rKitGjRzN+/HhjNMNoZKiaEEKUZeiCCvUNMfX5e7h0z5aEIdHYycKdoikySgDatm0b+fn5rFy5kujoaObPn8+nn36q+/4777zD+vXrcXJyYtiwYQwbNgy1Wl3FGU2npv/oSsgRQojK1SQQ1eZ4Uyp9bRnmJxo7WbhTNEVGCUAHDhygT58+AHTr1o2jR4+W+X7btm3RaDTY2NigKAoqlUrveXJycw3Snkx7zxrvW1BUVLMdC3Pq2BphbFqtQm6uvD+iduRzY2Es8O9YW2srruCk+9olLxUARas12L9XommxhM+Oe3Mfzl27RmipX0RfSE/HvbmP2dsmhLEYJQBlZmbi4uKi+9ra2prCwkJsbIov17p1a0aPHo2joyODBg3Czc1N73kcHRwqvUZtfpNoXYvfJFrb1nhXYaFyc3NwcHA0dzNEAyOfG1EbSmE+2Q7NANAqCt6qbDO3SDREObm5VT7rmEK/USPYtHgJI6xtdAt3bsrMot/kCWZvmxDGYpQA5OLiQlbWjWECWq1WF35OnjzJzp07+f3333FycuL5559n06ZNDBkypMJ5pJiAEEIIS1Tm36CCPFkvSTRYsnCnaIqMEoC6d+/Ojh07GDp0KNHR0bRp00b3PVdXVxwcHLC3t8fa2hpPT08yMjL0nkdCjhBCCEtXUKQt03so84ZEQ9OUFu5csfoX5s+Zz4n4BNoH+PPSzJcYd9+95m6WMDGjBKBBgwbxxx9/MG7cOBRFYd68eURGRpKdnc3YsWMZO3Ys48ePx9bWluDgYO655x5jNEMIIYQwuarKg0sYEsJ8Vqz+hdeffoEvc3IIB6Li4pn69AsAEoKaGJWiKIq5G6HPgQMHCGrdNH4bIQxL5nKIupDPjairmn52lMJ8QEKQuMES5gA1Jd263sKiuHj6l9q2A5gRGED0ob8Nei1jLy576MJlevToYbDzGVt0dDQf788mt7D6favj4aDisZ6udOrUqc7nsKp/M4QQQghRHZWNHSobO67iXO91joQQtXciPoHwctvCr283pJLFZYempfOavx9D09LZuXgJR44dN+h1RN1JABJCCCFMqGSInAQhIUyrfYA/UeW2RV3fbkilF5e1trIqXlxWrSZq/SaDXkfUnQQgIYQQwsRKeoOgdss6CCHq7qWZLzHV0ZEdQAHFw9+mOjry0syXDHqdlLh4gt1cy2yTxWUti1GKIAghhBCieiobuzKFEmR+kBDGU1LoYEapKnCzjVAFziswgJi0dELdbywuG5OhwSswwKDXEXUnPUBCCCGEGUlvkBCmM+6+e4k+9Dd5KXFEH/q71uFnxepf6Nb1Fuy9AunW9RZWrP6lwj7hw4ewLj2dC2npFGm1XEhLZ116OuHDK655KcxDeoCEEEIIC6ALQderJElvkBCWpaZltGVxWcsnAUgIIYSwIOWHxYGEIdF4GLs8tDHNnzOfL3NydGW0+wNf5uQwY878Cj1JTWlx2ZpK1uSRXVD/1XcKC60A12r3q4oEICGEEMLClF5MFW70ClVGApJoCErKQ49Qqwn29yMmLZ11i5fAfx5rEGHBVGW0G6u+3fwoUOo/+8bJSgvUb0EhCUBCCCGEhSsfiMqrLiCBhCRhfqXLQwPF5aGBjes3NYgA1D7An6hyC6kao4y2MD4pgiCEEEI0cCWFFCr7AzfWHarsjxDG1tDLQ5uqjLYwPukBEkIIIRq56nqQys850kd6kER9NfTy0KYqoy2MTwKQEEII0cTVJSBJIBK1FT58COsWL2EExT0/MRka1qWn02/COHM3rcbG3XevBJ5GQAKQEEIIIaqkLyBJuW5RW5ZQHrohV6EThiMBSAghhBC1Vn7dIpAwJKpnzvLQDb0KnTAcKYIghBBCiDrTV2hBCEtUugqdtZVVcRU6tZqo9ZvM3TRhYhKAhBBCCFFvEoSEpWvoVeiE4UgAEkIIIYTBSBASlsorMICYDE2ZbQ2pCp0wHAlAQgghhDC40usQyXpDwhKEDx/CuvR0LqSlU6TVciEtnXXp6YQPH2LupgkTkyIIQgghhDCqkh6h0uW0pWCCMDVLqEInLIMEICGEEEKYhAQhYW7mrEInLIcEICGEEEKYlAShpunwsROsWb+fmLhrBAd6MGp4T7p0bG/uZokmSOYACSGEEMIsZJ5Q03H42AkWLv6ba2nDCPR/mWtpw1i4+G8OHzth7qaJJkgCkBBCCCHMrnz1ONG4rFm/H3f1cDzcQ7CyssbDPQR39XDWrN9v7qaJJkgCkBBCCCEsRvkeIdE4xMRdQ+0WVGab2i2ImLhrZmqRaMokAAkhhBDC4kgQalyCAz1Iz4gtsy09I5bgQA8ztUg0ZRKAhBBCCGGxZFHVxmHU8J6kpa/nWtpFtNoirqVdJC19PaOG9zR300QTJFXghBBCCGHRpGpcw9elY3v+9x9Ys36DrgrclAm3SBU4YRYSgIQQQgjRIEgQati6dGwvgUdYBBkCJ4QQQogGpXzFOBkaJ4SoDQlAQgghhGiQJAgJIepChsA1IMePHmVD5J/ExaYQGOTFsIjb6dCpk7mbJYQQQpiVDI0TQtSG9AA1EMePHuWTRbtJSxuCf8CrpKUN4ZNFuzl+9Ki5myaEEEJYhJIeodLls6VXSAhRngSgBmJD5J+o3SNwdw/Fysoad/dQ1O4RbIj809xNE0IIISyODI8znxWrf6Fb11uw9wqkW9dbWLH6F3M3SYgyZAhcAxEXm4J/QHCZbW5uwcTFppipRZbvSFJmjfft7OtixJYIIYQwFxkeZ1orVv/C60+/wJc5OYQDUXHxTH36BQDG3XeveRsnxHUSgBqIwCAv0tJicHcP1W3LyIghMMjLjK0yjdoEGQCtosVKVYSNtcpo16iMBCkhhLBMJUEI4Grhje0ShuruyLHjRK3fREpcPF6BAYQPH8L8OfP5MieH/tf36Q98mZPDjDnzJQAJiyEBqIEYFnE7nyyKBCJwcwsmIyOG9LRIHpzY19xNq7G6hozaBBmA3NwC7BwcjHoNfQqLFIMFqYZCAp8QoiGSXqH6O3LsODsXL2GEWk2wvx8xaemsW7yE43HxhJfbNxw4EZ9gjmYKoZcEoAaiQ6dOTJ8BGyI36arAPTixb5kqcA3h4dsQQcNSNebXVhkZZiiEaMj0BSGQMFQTUes3MUKtJtRdDUCou5oRwBeurkRpNLoeIIAooH2AvzmaKYReEoAaiCNJmeAdwuCHQ3Tbiij7ANoUH8CFeRljmKEEJSGEqZUeHie9QjWTEhdPsL9fmW3Bbq706NSBqdGHb8wBAqY6OjJ75ktmaacQ+kgAshDVPRxKuBENXU0/wxKUhBDmJMPjasYrMICYtHRdDxBATIaGnn16c9dDE5gxZz4n4hNoH+DP7JkvyfwfYVEkAJmQhBwhqleTn4Oq5ltJMBJCGIIUTSimr9BB544dCB8+hHWLlzCC4p6fmAwN69LT6TdhHJ07dpDAIyyaBCADqyrkSMARwjCq+lmq6mdQwpEQoi6aaq9QZYUO+M9jdO7YAf7zGBtLhaOS8COEpZMAVEvSiyOEZavsZ1B6jYQQ9dXUglBlhQ42rt9E544ddH+EaGgsOgBZalUzCTlCNDzV9RqVrB9VmgQjIYQ+TWV4XGWFDlLi4s3UIiEMw6IDkAQNIYQp2Fir9K4fJcPphBDVacy9QpUVOvAKDDBjq4SoP4sOQEIIYU4ynE4IUVONMQhVVehAiIZMApAQQtSSBCMhRGUaUxCSQgfCkDLzishXtPU+j2Jd/3NIABJCCAOpbTCSUCRE49VYgpAUOhCG0r+1F1hZ1/s8qqICyLtar3NIABJCGMX5k8c4sXk9moR4XP0DaD94OGHtOpq7WWZRWTCS3iIhGj99BRMaYhASojGRACSEMLjzJ49xeuknRKjV+Pv5k5CRzsaln8C06U02BOmjLxjJMDohGq+SMFQShLT2TjiSbcYWCdE0SQASQhjcic3riVCrCVK7AxCkdmcoELl5vQSgasgwOiEaP12vUEFegx4eJ0RDJQFICGFwmoR4/P38y2zzd3VDkyBrR9SVDKMTovEpKNLi4ODY4OcJCdHQSAASQhicq38ACRnpuh4ggARNBq7+snaEodV0GJ0EIiEsV2MpmCBEQ2Fl7gYIIRqf9oOHszE9ndj0NIq0WmLT09iYnk77wcPN3bQmwcZaVeYPFPcUlf4jhLA8Khs73Z+rOOvCkBDCsKQHSIha+P7TRfz42WqyMrNwdnHmgcfvY8ITM8zdLIsT1q4jTJtOZOkqcGMelPk/ZlK+l6h8D5H0DglhecoXTADpFRLCUCQACVFD33+6iK/e34FW+ylwG1mZf/HV+68BSAjSI6xdRwk8Fqp0IJLhckJYNhkeJ4ThyRA4IWro+8Xfo9XeBuwAvgA80Grn8uNnq83cMiHqrrrhckIIy1AyNA6Q4XFC1JP0AAlRA+dOHic3JwB4FAgFYoB1QB+yMuU3caLxKD9cTnqHhLAs0iMkRP1JABKiGudOHuejN5cAg4ALgCvFIWgE8CnOLvJbONF4VTVcTsKQEOajW0sImSckRG1JABKiCudOHueL9zZz8Ywt9g7DycvNBA4ANwEKsIsHHr/PvI0UwkSkd0gIyyS9QkLUjgQgIarw7cffcXCvJ7m5ycCnqFT+KEoIsAobmzQ69wyWAgiiyZLeISEsiwQhIWpGApAQlTh38jh/7TxEfu4QVKrXULQFKFiD6nccHTLpc7cXY6dJ+KmP8yePcaJ0qezBw6VyXAMlvUNCWA4JQkJUTQKQEJXYvXkfBXluKMowVNyESnUFhQug+JJX8Ctjp31Ey3YdzN3MBuv8yWOcXvoJEWo1/n7+JGSks3HpJzBtuoSgRkBKbQthfjUJQkeOHSdq/SZS4uLxCgwgfPgQOneUf9tE4yYBSIhKHNp/CK3WGchBUTIAH8AWVAk4ODhK+KmnE5vXE6FWE6R2ByBI7c5QIHLzeglAjUx1C7GCBCIhjElfwYRmZHHk2HF2Ll7CCLWaYH8/YtLSWbd4CfznMQlBolGTACSEHudOHuf00QtAayAPOAXkAipQLhMY0tys7WsMNAnx+Pv5l9nm7+qGJiHeTC0SplI+EEHFIXMgoUgIY1DZ2Ol6hLau38ZotZpQdzUAoe5qRgAb12+SACQaNVkIVQg9vv7wa7IzbSn+HcGG6/8NAi5ga/cb4x8fYdb2NQau/gEkaDLKbEvQZODqH2CmFglzqm5BVlmUVQjDKVlUNTUuDi83zzLfC3ZzJSVOfhElGjfpARJCj/17DgD3Az2AtcCLQBFQQK/+rek3JMKczWsU2g8ezsalnzCU4p6fBE0GG9PTaT/mQXM3TVgA6SUSwviaBbcgLi2NFm6uADhRQEyGBq9A+UWUaNykB0gIPXJzEile6+c0xeFnG/AhYMXkpx4xZ9MajbB2HWkzbTqRbmrevZxApJuaNlIAQVRBeomEMKyeESOJTEvjUoaGIq2W42lZ/JSeRfjwIeZumhBGJT1AQujh6eVMasoe4A6Kh8BdBM7hpr4kxQ/q4NzJ46z5bg3Hoy+CyoqON4Ux8sHhtGzXUQKPqDPpJRKifjp06gwz/svGyLVcjY2lWVAQt02YiH/HTiBls0UjJgFICD2eeOUl/u+lNynMLwKcABU2dn8zY9YsczetwTl38jhL3/2V+EvuOLvMQ8Gdg3t3cyVxM488iwRKYVDVVZyTMCREWR06dS4OQqXI+kGisZMAJAxuy8lkAO5u52PmltTOuZPH2b15H0kJqfj6e/LQU48Qufwnki+fwsevLY88N4tBI+81dzMbnN2b95GW6o6z6wPY24cCoFL159pVFbs375MAJIxKFmgVomaOHz3C/lI9QT0jRtK+XVuu4iwhSDQ6EoBEpUqCTF242ttUe7wlBaRzJ4/zxXubuXb1JvLzunDxbAYezQ4yb+ln8oBeT0kJqRTkWePsGqzbZmfnRqbGjaSEVINfr3yQ7Tv4VnkPhU5VgUjCkGiqjh89wl+LPiTC3Z2ggABi09KIXPQhzPivLgSB9AaJxkMCUBNQ3yBjrGMtKSB9+/EyDu7NID8/GhUqrG39cXENZu0P63lmjjw814evvycXz2aTnx+j6wHKz8/Azj4DX3/Pao6unXMnj7Ny6V5c1BF4+wWhyYhl5dJIxk6ToXZCv5JAVHqonAQh0dTsj1xLhLs7Ie7uAIS4uxMBbIxcS4dOrwE3hsVJCBKNgQSgBqauYaY+QcZYLCUgnTt5nL92nCc/73ZUVpNRaEZB/g7SUnexb+dhg1yjKes7+FZOHf2V+Es/gjIWBXeyNbsJDI2m7+DBBr3W7s37cFFH4KoOAbj+3wh2b94gAUhUSYKQaMquxsYSFFC29HWQmxtXY2N1X5deQFVCkGjoLO+puAmpS5ixxCBjLHUNSIpWi8rKqsYBaffmfRTkB6KyGo+1VdvicygD0SoFpF37u3aNFhW0bNeBac9xvQrcK6Cy4qZeJVXgDBtKkhJS8fYLKrPN2TXIKEPtRONUPghJCBJNQbOgIGLT0nQ9QACxGRk0Cyr796nKxg6Aq4XXj5MgJBqopvM0bWQSZkyvsvuXm5OLg71djd+TP/efQKtoQWuPVpuBysoJsEMpskJRWTfYog6mVtXcm5btOvDsW8bvgfH190STEavrAQLI0sQafKidaPxKrzME0hskGreeESOJXPQhERT3/MRmZBCZlsZtEyfr3V96g0RDJ0/gVahNqJEwY3lq8p5cPn+K1NirqFReKMpVUGxRihJRWeVjZX0NrwBv3XnqM5eqNiwtaJ0/eYwTm9ejSYjH1T+A9oOHV1i7x1Lm3vQdfCsrl0YCETi7BpGliSUzPZJhY3qZrA2icbGxVsmwONHo6V0PaOLkCuWxS5PeINGQNdmn9po8zEqoafy2f78aTWo3FOU8sBKYAqhRlN04ue2g7wN36fY11efBkopDnD95jNNLPyFCrcbfz5+EjHQ2Lv0Epk0vE4IsZe5Ny3YdGDsNdm/eoOuJGjaml8z/EfUi84NEU6BvPaCakN4g0RA1uif8mv6WXsKNuHz+FOf+vYSN3WxsHa6So/kEbeEMVCoFK5t0Ip6aRpe+d5u8XVV9NjV5hSYNSCc2rydCrSZI7Q5AkNqdoUDk5vVlApAlzb1p2a6DBB5hFDI/SAj9pDdINDQNKgVIuBGG9NfazRTmF4LqA6ytw3B0nY6VVWvgIM7u75ol/FSnus92dQGptuFIkxCPv59/mW3+rm5oEuLLbJO5N6IpKT8/qLXa2pzN0fl51SrmzX6H+LiTBAS245XXX2D0mDHmbpZoQqQ3SDQURkkKWq2WN954g1OnTmFnZ8fcuXNp0aKF7vuHDx9m/vz5KIqCt7c3CxYswN7evsJ5yj/ISbARhnL5/CnOHUzHzmEaeTmBaPEgP3sHNvZxaAu30e62oOpPYoEMXVrc1T+AhIx0XQ8QQIImA1f/suVSZe6NaIpK5gedSivASlVk1h6hn1et4tmn3iQn50sgnLjYKJ59aiqAhCBhUtIbJBoCoySKbdu2kZ+fz8qVK4mOjmb+/Pl8+umnACiKwsyZM/noo49o0aIFP/30E/Hx8YSFhVU4jwQeYSzH9hzE0W04Nnad0KbEoS3KQFvUnMK8r3FtpuW2kVPN3USjqG1ASm17O1/88jWDruXg4+SCo30RG9PTaT/mwTL7ydwb0VTZWKvIzS3AytberMPi5s1+53r46X99S39ycr5k3uwnJQAJs5DeIGHJjJIwDhw4QJ8+fQDo1q0bR48e1X3vwoULuLu7880333D69GnuuOMOveEHissZi7pLvHCGk3sPkZ6cjtpHTbteXWke2trczTI6raKt9rNzNeEqPi06En8qBRfPAPJz0snPdQPlKv0njsTDr0WT/PzZlvs6oEVLkkZNZO3e38lPvoy1jz8ed44BbTNOH08st7cnfncN4YEwd92W3NyGcw+1Wm2Daq+wHFqtlsKCPAAOJWoBaOte/qfJuOLjTgLh5baGEx93ktzcHJO2RdScVqs0iffnirUTAC55siabsAxGCUCZmZm4uNz4LZi1tTWFhYXY2Nhw7do1Dh48yMyZM2nRogWPP/44nTp1olevikNlHBwdjNG8JuHy+VPsX3ccB5dReDYPJDcrjv3rNhA+xg6/sLbmbp5R5ebkVvvZaebfjBxNASGd/EiOSSTXNhfXZlkEtOpGj0HDTdTShqFFhy606NClxvvvuphR7T6WVuobisOag4P8nSNqr/xnp7BI4Ux6EWC6anEBge2Ii43iRg8QQBQBge1wcHA0SRtE7eXm5jSZ90cpzCfboZlZeoOOHDtO1PpNpMTF4xUYQPjwIXTuKCMUmjKjBCAXFxeysm58wLVaLTY2xZdyd3enRYsWtGrVCoA+ffpw9OhRvQFI1N2xPQdxcBmOo2vx3Kvi/w7j2J71jT4A1UTHPjcRtWoDDi7DCO3cntysOHIz/+bWEQPN3bQGryZDV2tS0MQSQ5IQNWGOstmvvP4Czz41VTcHCKJwdJzKK6/PMup1hagpc80NOnLsODsXL2GEWk2wvx8xaemsW7wE/vOYhKAmzMoYJ+3evTu7d+8GIDo6mjZt2ui+FxQURFZWFpcuXQLgn3/+oXXrxj8sy9TSktNwcA4ss83BOZC05DTzNMjC+IW1JXxMNxxd15OeMh9H1/WEj+km4dBEXO1tqvwDxSFp4adf8eBtXbizlQ8P3taFhZ9+xZaTySZblFaI+rCxVlWoGGcso8eM4b2PZhEY9CQqlQOBQU/y3kezZP6PsDi6IISzSa4XtX4TI9RqQt3VWFtZEequZoRaTdT6TSa5vrBMRukBGjRoEH/88Qfjxo1DURTmzZtHZGQk2dnZjB07lrfeeotnn30WRVG46aab6NevnzGa0aS5+7iTo4nT9QAB5GbF4e7jbr5GWRi/sLYSeEwg8fxJkvdsJS85AXsff3z6DKJ5WLsqj3G1t+HQ75EcWDSL7/Jyi3+ffeUykxbNwsHWmrDwIRVCkPQYCUtVPgQZqzdo9JgxEnhEg2DK3qCUuHiC/f3KbAt2cyUlLr6SI4SxFBUpKIpS7/NYFdX/HEYJQFZWVsyePbvMtpYtW+r+v1evXqxevdoYlxbXlQzxykpvQ0ZKDFnpsVhZJ9F/YvlJskIUzxk7tucgaclpuPu407HPTQYJh4nnT5K16itGuajx9WpOkiaDrau+InHMw9WGoD++fJ9v83JL1bSCb/NymfTl+3QdEFFhf329QpYeis6dPM7uzft0lfP6Dr5VKuc1YiVls001LE4IS2eKSnFegQHEpKUT6q7WbYvJ0OAVGFDFUcIY2vs4Y21d/+hRkJ/HtcT6FdQwyhA4YX5+YW1pe7s7SRe3kJnug5N6FM1DH+XUn2lcPn/K3M0TFuTy+VNErYomRzMctddL5GiGE7Uq2iCfk+Q9Wxnkosbf1Q1rKyv8Xd0Y5KImec/Wao9NuHJZT02r4u366BtKVzJcrvQfS3Hu5HFWLt2LJmMY3n6voMkYxsqlezl38ri5myaMyJTD4oRoCFQ2dqhs7LiKs1GGxYUPH8K69HQupKVTpNVyIS2ddenphA8fYvBriYZDFtppxJIvXCOs65NlhsHlaDykEIIow5gFM/KSE/D1al5mm6+zC3nJCdUe6+/tR1RyQrmaVsXba6p8QQZNXqHF9BTt3rwPF3UEruoQgOv/jWD35g3SC9QEmGpYnBANRUlvkKF17tgB/vMYG0tVges3YZwUQGjiJAA1YmnJaai9pBCCqJoxPyf2Pv4kaTLwd3XTbUvKysTex7/aY3tPfYZJ77/GtyVzgIBJ9g70nvpMndujr0JdSShStFpUVjc6xY0dipISUvH2Cyqzzdk1iKQEWSejKZFhcULcoLKx42qh4ecEde7YQQKPKEMCUCMmhRBETRjzc+LTZxBbV33FIIp7fpKyMtmamY7P0NHVHlsyz2fSl++TcOUy/t5+dIwYx5W4LFYv+Mxgc5VKQlFuTi4O9sUTc03RU+Tr74kmI1bXAwSQpYnF19/TYNcQDYM5ymYLYcmMOSdICJAA1KiVFEKAYTg4B15f62YDNw+9ydxNExbE0J+T8lXfrG7vz5oLZ29UgRs6utoCCCW6DojQBaGSuUoOLsNQewWSo4kjatUGwsdg8CGdVfUUlVfXUNR38K2sXBoJRODsGkSWJpbM9EiGjZE10ZoqCUJCmG+9ING0SABqxIrXuoFje9brqnvdPNQw1b1E42HIz4neqm9/7sC5BlXfqmPuxX0NHYpatuvA2Gmwe/MGXRW4YWN6yfwfoTcI1YaEJtEYlK4QBxKEhGFJAGrkZK0bURP6Pid1KY2dvGcro65XfQOKq74Ba/ZsrXcAssQ5bfUNRS3bdZDAIypVEoRqQ0KTaExKeoOMXSpbND0SgIRoRAy1ns+N4WbDazXcrD5V36rTUOa01TQUWfoaRaJhMlVoksAkTEl6g4ShSQASopGoa2jRp67DzepT9a06DXlOm75QZCnluIWobWgqCUwSgoQpSW+QMCQJQEI0EoacI1PX4Wb1qfpWncY2p82S1ygSoiqyhpEwJ+kNEoZQaQBKTU3l888/x97enoceeggPDw8APv74Y5588kmTNVAIUTOGnCNT1+FmzcPakTjmYdZcrwJXYGtHob0jjj9/Q7KPPz59BtVrLlBjntMmQ+dEQyNrGAlzkd4gUV+VBqAXXniBQYMGUVhYyIQJE/j8888JCAjg77//NmX7RBNw8Pf1bP3yc9KunMHduzWDpj7KTQOGm7tZDY4h58jUZ7hZ87B2xUHoekW4QS5qfN09iyvCrfqKRANUhDOkknlTVxOu0sy/mUHWFjIUGTonLF35inUSgoQpSclsUVeVBqD8/HzGjh0LQPv27Zk+fTrfffcdiqKYrHHCNAw1cb4uDv6+njXvL6Ig7ysgnLTkKNa8/zCAhKBaMuQcGUMMNzNmRThDKT1vys2rOTmaRKOtLWQoMnROWCLpDRLmVHpYnIQgUROVBqCioiJOnTpF27Zt6d69O4899hhPPPEE2dnZpmyfMDJDTpyvi61ffn49/PS/vqU/BXlfsfXLJyQA1ZKh58jUtzS2MSvCGUrpeVOFhYUmX1vIEGoydE7CkDCFhtYb9POqVcyb/Q7xcScJCGzHK6+/wOgxY8zdLFFH0hskaqPSAPTaa68xd+5cFi5ciJeXF0OHDqWgoIB58+aZsn3CyMy9uGTalTNAeLmt4de3i9oy5hyZ2oZlY1aEMxRLXFvIEMqHIplHJEypIRRJ+HnVKp596k1ycr4EwomLjeLZp6YCSAhq4KRIgqiJSgNQ+/bt+e6778psGzlyJBEREUZvlDAdcz8Aunu3Ji05ihs9QABRuHu3Nsn1LZGlzomqbViurCKcVZfuHP5mEXnJCdiXK4yQeP4kydcLKJT/njE0lLWF6qt0IJLeIWEqpYfFWVoImjf7nevh58bog5ycL5k3+0kJQI2AFEkQ1al1GWwrKytjtEOYibkfAAdNfZQ17z+smwMEUdjaP8ygqTNMcn1LY8lzomoblstXhLP38ceqS3cc/9xRXBjBqzlJmgzWfvUBfzVrhyZVQ2jiEe4LDSLUL9gkRRNKz5uysW9Ojia+wawtVFcShoQpWWpvUHzcSfSNPijeLhoL6Q0SlZF1gJo4Uy4uqW/+SMlD/dYvnyjV4zHD7A/75mLJc6LqEpZLKsKVvPcpP6xgoq2CWytHrK2scCvMp2NcNievFeFi15w+FJJ/IZEcp1T8PbxqXDTh8vlT/LV2M7EnYwErgtu34NYRA6sdDlh63lRJFbiGvLZQbVU1VE7CkDAkSyuSEBDYjrjYiqMPAgIto0CLKRw/epQNkX8SF5tCYJAXwyJup0OnTuZulsFJb5DQp9oA9MknnzB9+nTd1++99x7PPvusURslTMdUi0tWNX/kpgHDzf5wbykseU5UXcNy6ffeUTmBWutCzLGzBHeE5JhEfJw6Y1eogUINvi4BaPPdSI45jYuHV42KJlw+f4rfvtzC1YRm2DtNB0XN+egoMlJ2Mejh6ot5lMybys3JxcHRoba3pVEpHYhk3pAwNEsqkvDK6y/w7FNTdXOAIApHx6m88voss7XJlI4fPconi3ajdo/APyCYtLQYPlkUyfQZNMoQBA2rN+jIseNErd9ESlw8XoEBhA8fQueOHczdrEal0gD0008/sXr1as6dO8fu3buB4spwhYWFEoAaGVMsLmnOYgu//xNX5usBNwdWsqf5WfKcqLqG5dLvfaZLEOn5aXjYtSE55jS5WblobEBxLn5Pruan4W2nJjcrF6hZ0YRjew6SleaBvfM4bO1CAFCp7kCTVvy9ptKbY2hNcajcuZPH2b15H0kJqfj6e9J38K20bCcPHYZmCb1BJfN85s1+slQVuFlNZv7Phsg/UbtH4O4eCnD9vxFsiNzUaAMQNIzeoCPHjrNz8RJGqNUE+/sRk5bOusVL4D+PSQgyoEoD0MiRI+nVqxdLlizh8ccfB4rn/zRr1sxkjRPmVT441MeJ4wnYq91QaTJ02xTFjbzYBFQGvA6AVlGwUql0Xzd3u/Fb/cSM3Fq9LlOHJUuZE1VZueu6hOUyc4eChrPj+GL627nhnJlDlh1sy7oMrSYCsOP4YvrkafB1sSdBk8HWzHR8ho6u9vyFBXbYOwfpttnYuZGT5dbgq7lZiqYQhs6dPM7KpXtxUUfg7ReEJiOWlUsjGTsNCUFGYAm9QaPHjGkygae8uNgU/AOCy2xzcwsmLjbFTC0yLUsumR21fhMj1GpC3dUAhLqrGQFsXL9JApABVRqA7OzsCAwM5M033+To0aPk5eUBEBcXR8+ePU3WQGHYIFIbpYNDfSX7upOfnYSd042/cPOzE3D1dTfodQByc3NxcNB/ztpeq7b3vr6ByRLmROkbrrjuo8+4Gv8UmWkxta5MV3rukItnR1I6/IflZ3/ATpWHd6t2XLriiYetCw7OgcSF3Mvyi58R4GqDu6sbPkNHVzv/x93HneSLBRQWxOp6gArzM7Cxy2h01dwsQWOdN7R78z5c1BG4qkMArv83gt2bN0gAMiJLLZLQ2AUGeZGWFqPrAQLIyIghMMjLjK0yPUtcQDUlLp5gf78y24LdXEmJizdTixqnaucAPfXUU1y9ehU/v+I3Q6VSSQCqgrHCiqFDgqkFdevIiW0bgaHYOgZQkBNPfvZGWt7e0dxNq1Jt7ruhepfMPSeq/HDF9JQ8Yo77omjvA+bVujJd+blD1rYuFAQFcsuY4fiFtSX0/CndsDqvQHc6PvBMrXqZOva5ifjTW7iasAKUsaCoycuOwivwHzr2uaMut0DUQmOZN5SUkIq3X1CZbc6uQSQlpJqpRU2LJZfMboyGRdzOJ4sigQjc3ILJyIghPS2SByf2NXfTTM7SeoO8AgOISUvX9QABxGRo8AoMMGOrGp9qA1BKSgorVqwwRVsqMFfPR3009KBiLB6BLWk/EGKjI8lK1eDs6UrL2zviEdjS3E0zGEP3LplrrlL5ctfn/j2Aop0M/ADYUpPKdOXX82l3e2uSLuifO1TfOWh+YW25ayrXq8C9DFgR1q1mVeCEYTXkoXK+/p5oMmJ1PUAAWZpYfP09zdeoJkZ6g0ynQ6dOTJ8BGyI36arAPTixb6Oe/1MdSymSED58COsWL2EExT0/MRka1qWn02/COLO0p7GqNgCFhoaSlJSEr6+vKdpThoSJxsUjsGWjCjz1VdXnu6reJGMHo/LlrvOyr17/jnepvSqvTJd4/iRZq75iVKm1frb+uZ1ORlzPxy+sLff8r2LYMfXCquKGhhaG+g6+lZVLi38j7uwaRJYmlsz0SIaN6WXupjU5llAkoSno0KlTkw48+lhCkYTOHTvAfx5jY6kqcP0mjJP5PwZWbQD6999/6d+/Px4eHqiuTyyPiooyesOEaMqqCkeVBaOOnpkGedgvP2TNzkEhP/cL4MFSe1VemS55z1ZGuajxd3UDwN/Vrcbr+RiS3iB2fWHVknaWvlfufiEma1tT0xDCUMt2HRg7DXZv3qCrAjdsTK8q5/+UVI1LiL2Cf5C3VI0zIEsokiCaLnP3BnXu2EECj5FVG4C2bNliinbodXj9OoK6Na5hUkLUl75wdC3uLGdXfs+dji40c3Dm6rl4th/9mH1978fFr2Wteo3Kl7tudXMyp/7aQVHh3UABpSvT6ethyUtOwNereZlz1mQ9H0OrLIh9v+5HfHNzKgSjvBETaNGhi0nb2BRZchhq2a5DjQNM6apxXs390GRclqpxRiC9QcJcLKE3SBhPtQHozJkzzJo1C41GQ0REBK1bt6Z///7VHWYQ+dkRnNi2kfYDkRAkRBVyo3dxn9odXydXANwc7BhuZ8PqM3/RvG3HKucb6QtH5eflHPy9e4XKdH6hrfT2sOTYO5KUlakLHlC8nk+BrR3bvllRobS2sVQWxDL/2s6EzrdUCEar9/7e4ANQQxvyV1kYMncQqonSVeMKCwulapwRSW+QMCdLrBQn6q/aADR37lzefvttXnvtNe677z4eeeQRkwWg4pLJQ4mNjpQAJEQVlNREvDzKPjR6OTqjpCYCdRtSBzfCkb7KdIe/WaS/h6Uwn62Z6QyiOHAkZWWyNjGWs0p7PGxulNaOWrWB8DEYLQTZ+/iTpMmoEMS019tVmq+zC/mJDbvEaFVD/iw5BJUoCUMNJQhJ1TjTk0pxwlxKQpBoPKxqslOLFi1QqVR4enri7Oxs7DaVYesYQFaqxqTXFKKhUXk2JyWn7G+mUnKyUHk2r+SIG5q7Oej9A8XhqPSf0vKSE/QGCduCfJzHPMwaVzc+Sknk+8J8dl21IeXyLVw+ryEr/RqOri1wcBnGsT0Hq2zbwd/X8874EbwyqD3vjB/Bwd/X1+R2AODTZxBbM9NJ0GRQpNXqFlZ1ateNpKzMMvsmZWVi5+NXyZkahuQ9Wxl0PZBaW1kVB1IXNcl7tpq7abXiam+jC0NbTiZXKK1tKXz9PcnSxJbZJlXjjK98pTghTEVlY6ebEyQavmp7gNRqNStWrCAnJ4cNGzbg5uZW3SEGVZATj7Onq0mvWVvX4s4RG31MV95Z5i0JU3Podge/b/uRART3/KTkZPF7tgaH2+u+nlD5XqPylek0hS56h7rZ+/jTPKwdzcPa6RZVLci7grPbPRTmZRFz7DTBHcFZHUhaclql1z/4+3rWvL+IgryvgPBarz/UPKwdiWMeZk3pIWFDR9MG2LrqqzI9VFsz02l2Z0Rtbo/Fqcvcq8vnT3Fsz0GTDUusjcrWF7KUXqHSVePsHf3QpMdJ1TgTsfRy2cePHmVD5J+68tLDIm6XamuNiAyFaxyqDUDz5s3js88+w8PDg6NHj/LWW2+Zol0A5GfHWPximdfiznFi20nsnCJw8gggPzte5i0Jk/MIbMW1gQ+wOnoXSmoiKs/mONw+HI/AVga7RvlAlNkpnG93/8Sdjpriwgu5WZxw0uIzdLRun5JFVZ3dt1OQH4etfQjQhuSY0/iFZeHu417p9bZ++fn18FMy5Lb69YcqtPl6ECtPXzBq6FXgKhvyZ+/jr3f/knDq4GK6YYl1ZYnD40pXjSupAldd1ThhWJY4JO740aN8smg3avcI/AOCSUuL4ZNFkUyfgYSgRkDmAzUe1QYgFxcXpkyZQl5eHgDZ2dm4u7sbu10A2DlFWvximbHRx7Bzirg+X0nmLQnz8QhsBQYMPCUu/v0bZ9d9RnJqMj6ePrQa8Tght9xFq7YdueZsz8broSvL2QtVx3BcUl04llrcU1SyqKp30K3EHC/+bbmNbSCZaRfJzYzh5qE3VXrd4nWGwsttrXz9odrQF4xyc3LrfV5z8ukzSG/PVulAWlpJOC1Z76n4v8M4tme9xQWgEpYWhEqqxuXm5uLgIOvWmYOlhaANkX+ido/A3T0U4Pp/I9gQuUkCUCMhIahxqDYAvfHGG+zevRsfHx8URUGlUrFixQpTtI0uw0eY5Dr1kZWqwckjoMw2mbdUtQt/byV63fdkp57HyTOMbiMmEHrLIHM3q4yG0EZTuPj3b1xcPp8f8/MIB6JSk5i4fD4AIbfcVWXoSszI5VqhFckXTmLrGIS1dxdsczeSlRaDi3si4WMmVvmg7e7dmrTkKG70AEFV6w81BvUZklbZkL/KCiCUhNPSHJyrHpZoKSx9eJwwrdJD4swdguJiU/APCC6zzc0tmLjYFDO1SBiDFEVo+KoNQIcPH2bbtm1YWdWoXkKT4+zpSn52vK4HCBrGvCVzufD3VvYtX0ZR/jIgnOzUKPYtnwJgMQGjIbTRVE78soiH8/PYDZwA+gDf5efxwLrPCLnlriqPbe7mgP2tXTmxbQt2RUNRXFpTaOOMtXUKPn3v4niqM35hlR8/aOqjrHn/Yd0coNLrDzVGhhiSVtmQP33cfdzJ0cTpeoAAcrPiqhyWaIksrVdImI+Ntcrs84ICg7xIS4vR9QABZGTEEBjkZZb2CONR2dhxtdD0i6QKw6g2ALVo0YK8vDwcHR1N0Z4GJ6hbR05s2wgMxdYxgIKceIuft1SVa3FnyS09j6TbHQadRxK97vvrweLGvI6i/GVEr3vUYsKFKdrYEApnXIs7S0hGKo8BoUAMsI7iEJScWrPKXB6BLWk/EGKjIylI1eDh6UpQv+LXWr6oApRdk6hknk/59YdqOv+noTH1kLSOfW4iatUGYBgOzoHkZsWRm7mhymGJlkyCkADzD4kbFnE7nywqHu7r5hZMRkYM6WmRPDixr8nbIkxDhsI1TNUGoMuXL9O/f39atCj+R9mUQ+AagtIPeCUPs5Y+b6ky1+LO4rjtR4Y7ueLl4UNKtobft/3ItYEPGCwEZaeeR9+8juLtlsHYbWwohTNyo3dxt50j1vk5WFMcgkYAnwA+njV/sPQIbKn3dTV3cygTBBVnRzSX2+FaqltogJ71hxorUw9J8wtrS/gYOLZnvW7I3c1DLacKXF3pC0IgYagpMWcI6tCpE9NnwIbITboqcA9O7CvzfxopmQ/UcFUbgN577z1TtKNBq+wBr6Eome/inHqWiXZu2LW/CWunlvg6uTIAWB29y2CT6508w8hOrTivw8mzirFQJmbsNjaUwhlKaiJh7Xry69E/uEdbRDBQBGywsqLViMfrff7yQbAgJ54rezfiNdBedx+q6iFqbMwxJM0vrG21gceSS2VXpfQ8IekVanrMHYIk8DQdEoJqTiksQFG0BjlPfVUbgKytrZk3bx7nzp0jJCSEl19+ud4XFZaj9HwXL77BOb+I+CORAHgEtMTL0RklNdFg1+s2YgL7lk/Rza+BKKztptBtxBSDXaO+jN3GhlI4Q+XZnAIHDe6dw/n51D9k5WaRZ+eIY/tbqp3/UxM1CYLlS2835kBkiUPS6jsvKfH8SZJLF2XoM6jGc5Rqoqbnr8nwuN/Xrmb5u29x4XI8oX4BjH/uVQaMvM9gbRWmZ+7hcKLpkKIINeNJNjbUv6ZALoWk1fMc1Qag1157jQceeICePXvy999/8+qrr/LNN9/U87LCUuaAlJ7vksMu0rmGh3Ykiaci8QhoSUpOFirP5tWep6ZK5tBEr3u0VIW1KRYz/weM38aGUjhDt7iqhw8t+t+vW1y1+cAHDHL+ugTB0oGo/Byihh6GLHFIWsm8pKJCZy4cOUFuVi7Wtq3Zt24bo56uul2J50+SteorRrmo8fVqTpImg62rviJxzMMGCUF1OX9lQej3tav59tVnWJaTU/wrj4Q4prz6DICEoAZOQpAwFSmK0LBUG4Dy8vIYMGAAAAMHDmTZsmVGb1RjZ0lzQErPd7nCvezhXfrghjr3GknZGn7P1uBwu2HnYITeMsiiAo8+xmxjQymcYezFVesbBC0pDB36PZI/vnyfhCuX8ff2o/fUZ+g6IKLW56nJkDRDqOmwtrTkNKxtHIg9noiNXRscnNwoyLvG2QMruXz+VJVtTd6zlVEuat3CrP6ubgwC1uzZapAAVJ/zly+j/e3bs/kuJ6dU2RNYlpPDtHffkgDUCEgIEqYkQ+EahmoDUFFREadOnaJt27acOnUKlUplinY1apY0B6TsfJcuHOQ54ngPVztXQpxcDfrAK4o1pMIZ5df5uRZ3jsPr19Wr57Kk0qBr3BlSUv5A4/cILj531CsImjMMHfo9kj/ef41v83KLew+SE5j0/msAdQpBxlabYW3uPu6c2n8YG7s7sLFXF2+0ysDJrRPH9hysMgDlJSfg61W299jX2YW85ASDvA5Dnd/V3obLKYl6yp7Ahcvx9WukqNL5k8c4sXk9moR4XP0DaD94OGHtjPOLIAlBwhRkPlDDUaMhcK+88gpXrlzBx8eHOXPmmKJdjZolzQGpON/lKql2u2g9/ln8LLyXpiFriIUzDNFzWabSYEBL4uziWX95AafzN+IRFGqQIGjqMPTHl+/zbV5umd6Db/NymfTl+xYZgKort116Xo2TrR2alH24NuuMorhQWBBLYV4kQe0HkJa8rsrr2Pv4cyH+IlYpmeRm5eLg7IDWywX7gBCDvA57H3+SNBm6HiCApKxM7H38a30uf28/opITypU9gVC/gMoOEfV0/uQxTi/9hAi1Gn8/fxIy0tm49BOYNl1CkGjQJAQ1DNUGoA4dOrB06VJiYmIICQnB3d3dBM1q3CxpDkht57sYe50gYbkM0XOZG72L4U6u+DoVf9Zb+ARxn4s7q51c8Bs+wuBtNkUYSrhyWW/vQULyZYOc39CqKrddYV5NViZ59uc4nPshRYXNcHBuhn/L27GxdcbR1b3K66hCW/PD1j0MdGyPr7M/lzUJbEs+gU+4YX6x4tNnEFtXfcUgint+krIy2ZqZjs/Q0bU+V++pzzCpdC8eMMnegSnPvWqQtprSuZPH2b15H0kJqfj6e9J38K20bNfB3M2q4MTm9USo1QSp3QEIUrszFIjcvN5oAQiKQxAgIUgYlRRFsHzVBqAffviBb7/9ltatW3PmzBmmT5/OyJEjTdG2RsvS5oDUdL6LKdYJEmVZSrEMMEzPpZKaiJdHcfWtnIxUMhKvkJudS6pVPg7d+hn1tdlnxJe5l2suF39mrxw9iYeNFhdPF7r271nrOTiV9R64O7iVmSdj7IpoNVVVuW1982oeaNuaxAtncOn8eK2q0yVdSCOl/cv8evUAqqw4FNcgckNGoVw4RWcDrAnZPKwdiWMeZk3pezp0dJ3uaUlP3aRy87gK2/Zly8nkBlM6+9zJ46xcuhcXdQTefkFoMmJZuTSSsdOwuBCkSYjH369sb52/qxuaBNMMO7SxVnEkKRNAgpAwGukFslzVBqCffvqJdevWYW9vT05ODhMmTJAAVE8NaQ5IaeV/e2+MdYIsRcnaSDd6xSaYvHCDJRXLgPr3XF46sJO4U+fYl3MUbzsbrKydcHTricZWIRcVJ7adNNpr03cvU39fiaLk4Or9EKmKL0mX4jn96Sbuf6JmJZ5L9J76DA++8zI/FBXoeg8etHakWcfndfNkjF0RrTaqKrcd9/PXFebVhPoFE5B7inzX2lWnS0tOo5l/f1SBA3XbnLVFpCXvM9hraR7WzmD3r+uACL1DFisrnV26bHZIc38efP41sxdM2L15Hy7qCFzVIQDX/xvB7s0bLC4AufoHkJCRrusBAkjQZODqb7phhzIkThiTDIWzbNUGoGbNmmFtbQ2Ag4ODDIEzkIY4B6T0b+9LGHqdIEtQem0kCCc7NYp9y4vXADJlCLKkYhlQv57LSwd2cnDNKaysX2KPspbbMq6hJo34a9EccPemqNOz2Nk4616boXu+YqOPodX2JfnscbLTf0JFDlqlAAcXFc1aBGMHFNoEo7WLYP3KXwkb5Kw7trqhcl0HRPD3+m2MOXeUq9nxNHMOwLfba/iE3ENa8nzA+BXRaqOqcttXKplX496yPV0mj6vVdcyxsKsxlC+drbds9uV4iyibnZSQirdfUJltzq5BJCWkmqlFlWs/eDgbl37CUIp/HhI0GWxMT6f9mAdN2g4JQcKYJARZrmoDkKIojBo1iptuuonjx49TWFjIs88+C8B7771n9AYKy6HybE5KtkbXAwQYfJ0gS1B6baRi/SnKX0b0ukdNGoAsqVgG1K/n8vSu/djaP0tRUSB/59lwgS044kEOiVxJ60Kgxg53/+LXZoyer2tx8VyLj6UgNwUr68cBH/Kz/kZb8DU5GSdxdCsOIbaOARRcy9HNHarpvKHQbr3IafkWXUo97OdoLuke9o1dEa22Kiu3bch5NZa4sGt9uNrb6EJQfcpm17XyWU0WavX190STEavrAQLI0sTi6+9Zy1drfGHtOsK06USWvhdjHjTq/J/KSAgSxiTzgSxTtQHo8ccf1/1/RITlVTSqD3MMc/pj9z9GPX999e57c6Xf0y2MSXHPz6HkePZcPk+hlx+X139Z64IIljDMTJ/SayPdEH59u+nUZsiZqeYK1bXnMjs9Bwe39qRfPAsM4wptgRBgJjCdxFOROHvY4uzpWqbnKyfjJBmJ/5CbeY1/Vv3CzWPurdP187MzKcw7j5X1FKysQwCwtmmJotxORuI/ugBU/v7WtIhCdQ/7hqxYVl9VrVlkyHk1lriwa32V9AbVtWx2XSuf1XSh1r6Db2Xl0kggAmfXILI0sWSmRzJsTK86vFrjC2vX0SyBRx8JQcKYZJFUy1NtAPLz82PHjh3k5eXptk2bNs2ojTIFfcOc9n43hgM/fUFeVoLugTwh18Og1w31dq5+JzOqLqDle3ThcNwhtNeOE5h1jd7q5ngVOnPtzFl2HT9CdNv+2JXrtdAXqixlmJk+ZddGKhGFk2eYSdtR0yFnljZXSB8ntSP52SdQigoBNRAMbAdsgQAKc8+Tn51Ey9s7cnL7Xzh5BJCTcZKUC/uxthmGnXMgOZo1dZ4nZOtoj7boNNZWroCCok3HyiYObaELuZknUZQi8rNj0eZvqXRIX9VhqOqHfUP2rNRHTdYsMuS8GlMt7GpqdS2bXdfKZ8vffYtlNehxatmuA2Onwe7NG3RV4IaN6WVx838slYQgYWwyFM5yVBuApk+fzl133YWbm1t1uzYoFYc5JaIUOZGX9TU3AtFkmvXsT+eeBihZ1EBUG9C820CbNmTuW8vwvGy87Z0AaIYd6jxbVl07gUubNmUO0ReqYtd9RVH+15QfZrZv1UP1Dp2KVovKykrv96rq4SpRcW2kKKztptBtxJRqjzVkT0xNh5wZe66QIXrq2tzRk4NrloLqblCuApeBDYAT8BQ2DjtpP/BVPAJb4ux5jPzseDIS/8HaZhjWtiEUFaTj6NoCO6d2dXpdnkEhZKakkpcVhbbQEysbB5zUniicxcH5MtnXFmDn5khY3641Orf+MOSMqmM4902uOEzOkD0r9dHQ1iyyVPrKZk9xdGRSNWWz61r57MLl+Br3OLVs10ECTz1ICBLGIkPhLEuNeoBmzJhhirYYVHU9GRWHOb0FfE3pB3Kl6Bs0x6ZAEwpANWWlSaWZS9mg0szOEStNxcm2+kLVxew49A0zK8qOq3cvWW5uLg4ODnq/p+9zUT4U1XZtpBLG6ImpyZAzY84VMlRPXYse/QA4tP5zNEn/B4QCDwA+WNtN4ZZxU3Svs6TnKzfzGnbOgRQVpFNUcAaPIG9sHdV1el1B3Tpy9dJuFO1hbBzGgOJGQe4fuPkcoeuI4mF1VX1uqlLTYXKG7Fmpq0rXLLpimWsWWaryZbP9vJpz8+Snq53/U9fKZ6F+AUQlxMlCrSZSEoKEMAbpBbIM1Qag/v378+6779Kq1Y25HaNGjTJmm6pV03k0VT1IX3YNIk9TepjTCfQ9kOdpYuvSRJPTXIkj5XwsuZocHFwd8QoLwtXb8Kvel9C6enK1VA8QwNX8HLSuNZtsa1/h/gNEYe8aVNkhBqHvM6E/FNVsbaTSzFW1zZgL6xqyIIRSlI9TwUkyScLF6jga7VqcPFtVCJclPV//rPqFHM0aHF1b4BHkjaObJ/nZMXV6XR6BLek2Ek7v3knKhVdQqazwbeNPm77hBn1vKgtDhlp0tb4qG7rl7+1nriY1WKXLZufm5FJgZVPtmkF1rXw2/rlXmVJ6DhA163ES9SO9QMLQpBfIclQbgDZu3EhYWBjnzp0DQKVSGb1RJaoKOvXtJQjrdRentk9GW/gNxcEnlOJ/Vkz7QG4ImitxxEZfwcZ+JPYuzSnISyQ2egtB3TBeCArrzo7o3+hPcc/P1fwcduRlQ/vyIbKSwyvc/yisbCYT1muwcdpbhZqHoqqHz9WmJ8aQBSCMubCuoQpCXPz7Ny4un8+P+XnF77a2kIl29oSMeJAQPa/bI7AlN4+593qPWjtsHdXkZ8fU63V5BLbk1vF1Dzu1Hd5YOgzVpJKcKegbujXJ3oHeU58xW5ssTV0XrC0pkKBvzaASda18VtKzNK1UFbhJeqrACcORoXDCmKQXyPyqDUB2dna8+eabpmhLBcYsGNC87a0AnN87hTxNLNb2nmgLJqJov8PcD+S1lXI+Fhv7kdjaFz98F//3blLOrzVaAHLxDuJKt7tYdf5frDSpxT0/7cNx8a5ZYCx//+1dgwjrNVi33dzKf/YuXMmqNhTVtCfG0AUgjLmwrqEKQpxd9xk/5ueVmXvyXX4eD6z7jJBb7tJ7jCUtGFzf4Y21LattLOWHbpWvAtfUGWLB2tLlsisLQXWpfDZg5H0SeExMQpAwBukFsgzVBiB/f3+WLFlChw4ddL0/4eE1+y2/pWve9tYyD9yJp/ZZ7AN5VXI1Odi7lF1jxMauObmaHKNe18U7CGoYePQpf/8tmb4wXj4U5RVBxsXvCAyZWGVPjDHWGTLWwrr1KQhRWnJqst65J8mpyRX2NVVJ79ow1PDGms4XMqbSQ7dEWYZasLa6ECQaDpkPJIxFeoHMq9oAVFhYyMWLF7l48aJuW2MJQOU1pAfy0hxcHSnIS9T1AAEU5ifi4OpoxlY1fhVCkXdrTnKGxLglFGXnYe1kj1OgP8fPX6N3qWdbS1lnqCbqWhCiPB9PH6JSkyrMPfHxLPtwaKklvY1RaMLS5ws1RtUNbzPkgrUSgozv3Mnj7N68T1fyu+/gW41WAU96gYQhSS+Q+VUbgN5++21Onz7N2bNnCQ0NpX379qZol6gFr7AgYqO3AHdjY9ecwvxECvO24NfeOPOXTF1woSFp16Y1tGldZlv5niJrp0CKss2/zlBNhd6ivyDEtbiz5EbvQklNROXZvMqFcFuNeJyJy+fzXckcIGCinT2tRjxeZj9zFZKojjELTYBlzhdqCA7+vp6tX35O2pUzuHu3ZtDUR7lpwHC9+9ZkeJuhF6wtHYJA/7wgUTfnTh5n5dK9uKgj8PYLQpMRy8qlkYydhsFDkAyFE8YivUDmo3+xlFK+++47Zs6cycGDB5k5cyZffvmlKdolasHVO5Cgbt7Y2q8lL/MDbO3XEtTN2yihpKTgQkHeSOxdnqYgbySx0VfQXImr/uAmKtTbucyfNuF3o7KeDOwACoAdqKwn49Tm9hpXODS3a3Fncdz2I/dla3jCw4f7sjU4bvuRa3Fn9e4fcstdhIx/iQc8fbFHxQOevoSMfwm1f0sOr1/H3m9/4PD6dVyLi8fW0TglvesjqFtH8rM3kp8dc33R1OKCDEHdDL+KfXM3B10g+v2fON0fUdbB39ez5v1FpCV/Ckouacmfsub9RRz8fb3e/ZP3bGXQ9eFt1lZWxcPbXNQk79mq28enzyC2ZqaToMmgSKslQZNRvGBtn7ovzuxqb1OhQIKov92b9+GijsBVHYKVlTWu6hBc1BHs3rzPKNezsTZdASjRNKhs7MzdhCat2h6g9evX88MPP2BjY0NBQQHjxo1j6tSppmibqAVX70CT9MKYo+BCY1NVAYjKii2UV5MFXY0pN3oXw51c8XUq7gHxdXJlALA6ehdU0gsUcstdZQoe6BvulpnyPtZ2x3Hz6azbryY9LcaeN2SOggyGnC90+fwpju05SFpyGu4+7nTscxN+YW0N1lZz2Prl5xTkfUXpuXQFeV+x9csn9PYC1WR4mzEXrJUhcYaVlJCKt1/ZUQ7OrkEkJVRci85QbKxV0gskDE56gcyj2gCkKAo2NsW72draYmtra/RGCctlroILDUVNhwdWNt+sJpUPLSEkKamJeHmUfYjzcnRGSU2s8Tn0DXdT+40k/fIKHFzUNS7pXd28oZJwlHj6JFcvHUVbcA5wwdbZhZ73P17j+UzGKjRRE/WZL3T5/CmiVkXj4DIctVcgOZo4olZtIHwM9Q5BdS0ZbQhpV86gby5d8faKajq8zZgL1pozBJlyvowp+Pp7osmIxVUdotuWpYnF179ma9HVh4QgYSgyF8h8qg1APXr04KmnnqJHjx4cOHCAm266yRTtEhZKCi5UzlTrMVlCSFJ5NiclW6PrAQJIyclC5dm8iqPK0ldYwNWnL4X5G7FzqnlPS1XzhgBObDtJTkZXrpz1Ap4B/gHUFGTNZu93HwN1Kz9eHWP1SpUOQ2sid3Pl6Ely0zJp38Ffb8/OvrWbILYIbeG7ZDkHQtBwHFyGcWzP+joFoJLQk3z2OO6J8QwPbU2oX3CdSkbXh7t3a9KSK86lc/durXd/nz6D2LrqKwZR3POTlJVZPLxt6Gijt7U0c4QgU86XMZW+g29l5dJIIAJn1yCyNLFkpkcybEwvo15X5gMJY5BeINOrNgC9+OKL7Ny5k3PnznHvvffSr18/EzRLWCpTF1xoSCxpeKC+kFS+dyrPw6vakFRZQHLodge/b/uRART3/KTkZPF7tgaH2/VPQNenssICnkEhdBk+osy+VYWJqiq0nd4dRUZSOKmx14AuQFsgCNgEfI1SNI3odd8bPACZoprdtbhzXNl7ATune3D2CeD0uRiOH91IcN8kRkX0BYrDitvBndzt2ptmTv5czU9jx/HFXGn/BGnJabW+ZulCAv9kZjAAFfkXzpDj5IK/h1edSkbX1aCpj7Lm/YevD4MrLq1ha/8wg6bO0Lu/MYe31VZNFk01pNLzZYDr/41g9+YNDTYAtWzXgbHTYPfmDbperWFjepnk9UhpbGFI0gtkHlUGoJUrVzJ69Gj69euHi4sLZ87oH1ogmo7igguQcn6t7kHar71UgQPjDw8sXqfqt1Lzhu6qcdl2fb1T2ktb8PK4Vul7V74XqXQY8ghsxbWBD7C6dBW424dXWgVOn6BuHTmxbSMwtMrhbtWFicqClJVNIYknL2PnFI6ivQh0BU4DwcAVYBpwgWwjTBkwRTW78tfwcA8l3y6CK0d/5Xe/4oqCmq0/c7+bGx6KFVYqK7zt3OkPLD/3Ix63FIfG2swPKr1OTmZ2Jm1cXMjOz+dkzDlcPLzqXDK6Lkrm+Wz98olSVeBmVFoFDow7vK0uTNUbZI75MqbQsl0HswU4mQ8kDE16gUyr0gC0aNEizpw5w4gRI7CxsaF58+Z8/fXXXL16lSeffNKUbRQWxlQFFxoaYw4PTDy1j1PbN6Mt/AYIJ08TxantkwFqFILq0jtVuhepdBjq3ffm6z0yx8lKdcDZs3OdhnfVtLBAdWGisiBlbVeIvXMHIAOVtRNKkYriHqBdgDfFxbhDcfI0fHUnY6wbVNNrFFzLwT4jntjoYxRE/4Vi50hK/t94ed2CjZ0baq0Cmn/o2Gd4recHlS4k4ObsSkJ+HoF2dhRlFb+u+pSMroubBgyvMvA0BKYIQTWZL9PY5giZioQgYQjSC2R6lZbB3r17Nx9++CGOjsUPb4GBgSxcuJAdO3aYrHFC1ITmShwX9u3lxLbtXNi3l6yr8WZph1dYEIV5WyjIi0dRiijIi6cwbwteYfUfHnh+72/Xw09/wBboj7bwG87v/a3aYxNP7SPm373EH/qH2OjdZKYU35/a9E6VlPAG2L52HbuW/8HFM7fi5PE8+dkRnNh2kmtx52r9ujwCW9Jl+Ah6TXqQLsNH6A1RWamaKktjFwepdtg5RZJ9bQF2TpG0H9gObaED7oH9KCrcgJNHPnAMuAisBeyBh1BZp9NtxIRat7s6zp6uFOSU/Rwact2gqq5hZZPLiW0nyc+OwNpjCFmq1qiwIU3zFykpO0i3OkJAj7b4hbXl2J6DOLgMw9G1BSoraxxdW1yfH3RQ7zXtffxJysoEoH1QSzbm5XEyMxOcXAxSMrqpMnaZ7L6DbyUzPRJN+kW02iI06RfJTI+k7+DiX56UzBHSZAzD2+8VNBnDWLl0L+dOHjdKexqLktLYR5IyzdwS0Vhcpfo5vsIwKu0BcnJyQqUq+5tRW1tbnJ3lzRH1Y8iFVPUN7Uo4vBE7uziT91IZc3hgniYWfRWvirdX7kbP0VhgIkX51qRcWAOAvSu17p0K9XbmwvkU3NUjySz0ITYmCbChubfxFiutySKk+iq0OXseIz/bFa/QnmQkRqEUXSI77QooO4DV16vAPWmUAgg1Hd5njGtY29lg5zQUO6dgcpsPZc+Fz+ljH4K3YwK5vr7syMnkass7AUhLTkPtFYgm9ThXYveRm3UVBydPHFz0r+dUupBAiLsnV0Jas/DiGaxc1bi7upltTk1t1WYBVVMx5ryg6ubLNMY5QqYi84GEoUgvkGlVGoAcHByIjY0lKOjGb69jY2MrhCIhasPQldL0De0qKryblPPrzTJMz1jDA+1dg8jTVKx4Ze9ade/SjZ4jL2ADMAKUCFJjv8G75bU6Fa8omevkYW+t23Y5uQhtzgU0bv/Uu/z2xb9/4+y6z0hOTcbH0we/8HvIz659mCgJCHZOQ/Fp/QAegcXHtR84yujlrE2zbpCCn91xss9Gkq3Yo4R2pv3A/pzc/hcOrsU/Dw5u7YkNfZTViRsh/Si+bdvh0G8ULm6B/P5PHNcKrShM2EHSxYvY2Edg7xREbuZxcjJPcPn8qQrD4CoUEggMod0D0xpE6ClRsoBqSfGEtOQo1rz/MIDZQxAYb0hcVfNlGuscIVOR+UDCkGQukGlUGoCee+45pk+fTq9evQgKCiIhIYGoqCj+7//+z5TtE42MoSul6Ss8YG3n2+jWJQrrdRentk/WzQGCKKxsJhPWa3CVx93oOSpZv2sTkIS24HOCuk2v0T0v32OnssqhML/sXCdX26vYuhT3yJSeK1RbF//+jYvL5/Njfl7xq0xNYuLmZXgPnkJRYe3ChDkWLy1/fWNd61rcWRy3/chwJ1e8Ove4XoXvMjkoFXrMHNzak2/jjF0bB/zKVdfTdGrHsRUrQPUs3i4tKMzPAHJpHvogx/b8oXcekKUVEqit2i6gag6mLpVtzjV1GhMJQaK+pBfIdCoNQK1bt2b58uX8/vvvJCcn07FjR/7zn//g4iI/3KLuDF0pTV/hgaL8pEa3LlFJoYPze6eUqgI3uNoCCGV7jjpf/7MDe9dvahx+yvfY5WX9CiwH9XhdKfSc/2/v3uOjLu+8/7/mkDlmkkzOCQmHgBxEJFgqHkClgFoErLpFEcWqW9fe9/Z3791u9+6963a7Pbjudtfdve22bq1ajyhaDxysCIhKEEGUICJBIRwy5ExOk5nMKTO/P4aZzCSTZI7JJPk8Hw8flGHynW9ipPPO57reV+eLeI29+A7vDy5rHKxBbignNj/ORpcz5K0pPOdysq7qdZb/4rWorhFquBASWq+tydJTsXD+qB12GgtH9fusMpiC5zAVGUwsA16tfp/yyuuiXn530ayLqS96H2uXldbW3ah1GmbOnYIx20xH87YBz+/fGFc4zUzzqfbg74um5eA79RUdJ4/R1t2L1VhGyYyLhmyWG2mxHqA6WkYyBI3WmTrjiZwPJJJJpkCpN2QNtslk4lvf+tYI3YqYCJLdlDbYuUT588bfuUTFsxZFXXsdEOvkqH/VtqlgNlrT/wyf2GXfgtfzHBla/14nhbIHyEGpvgW1ZuCyxqHqtPtrbmuO8NbU/3iy9a/X7rGe5djO7Uk9qydVfG2N5JvD3xTn64342hpjnnyZyyZhtGcFJ0YtPR7q22qYOT0n7Hn9G+NaLbs5tGM7ky9eT27JPFotu1Hs+CduKc9G2aKgU1HCHqsTi24WVZuqB22WG2mxHqA6mkJDEES/LyjWRrfRPFNnPJH9QCIZZAo0MoY9CFWIZEr2QaqRigfyphdKTTd9YcbrOQeKW8HXidY0edDJUaSqbWf3/yRvai8ZBX3PU2uKcboymLbI/9PhU/v3oVQPvqxxqDrt/gpzC6lqa+r31tT/eLINrNcux6tOXZlDMilyi2m1W4MTIIDWHhuKXP90NZbld/3LFDS99eDZTnfuNHYdtLBsof+/JX9j3Cr0pikAdJ2vQ6v/CzpbHeRNUqE7/wnL9XNwn/kMk3kxJdpslro6eOX8J6gq7uDonq1pEYBiPUB1tAXKEaKdBgUa3TKzV1NQUo61q46Xn9jC7d9l2BAkgSdxsh9IJItMgVJLApAYUaloSutfPOBwOJJwp2Nb/zCD7xkKFT+k2KRF29HI6Y/fov7oJ2GHqoZXbeP/1XcT7ZZPMBX0NbD1n9jFsqwxEIYGmwrNWPMgd7/4CM8F9gABd2u0zFjzYDK+LGFG4qyeVNFVXsuunRtZhn/y498DZEV3Vex7WIabGO06aAH6GuMCHLbzaI1zcNj2AaCwWSgyltLcchBzURYAeRlZKGwWdMYyOpo7EvukkySeA1TTQeg0aAatg054pNEtPUgIEomQKVDqSQASMem/RKriyutjXpYlB6mmXniY+YwFfMAS3zLyWnbhU2Ww2XKKU77/BO4JHqrq9Zxj4N6IdXjd38XtvHzQiV08yxoHnwpd73/VkBa4GWseZOrl1yf4FRkomnrtdGUum0H78nW8Wv0+vrZGFLnF6K5ahblsRpzXG3xiVJylA6DWo6T5VA0zp/v3EumMeTisx9CZ/H/uM5bRZK1DZ9DgcXWh1mZz3t2Fz1iGw2YhpzAnrntLhbF2gGro3iuv0oH1vJ75c+6POOGRRrfR1/98IAlCIl4yBUodCUAiapGWSB1/9x6AmEOQSK3Qc4MKeI0lmDEzBa/7ddRNFhb7bqAOCy0hh6r6l8n13xvRiVrfENzvE2lil+iyxoFTody4Cg9i1X/pl8teh9e1Paln9aSSuWwGxBl44jFn0XyO7dzOlydBrSslK6+czub/pmjaenzeXhx5X2Nn8zvcMiUfV8txWlwl7KEXR8kyVN3bWLhywYjd63jSf+/VVwcfw959MbV5SuZnqwZMeKTRLX1IMYJIhEyBUksCkIhapCVSXs8z1O67VwJQmgltf9NzlmzKgDOoNdl4XJ1kMwc9Z0M+YjH4OlGqwwsTFMq78XndnD7wdHDiZyooo+n4RzTve43z1jbyTLlkzb0OrzexZY2hU6F4GuRi1X/plyZLT8U16dMC1245gSN0wlN5bdwTnmTo+3q9ha3NitWop/Qbk8lT7aWjeRv5ZTkULrmPqlNf0ZFxjLbuRn8LXNnxtGqBG2v6773yeDzojUs4X3eCk+Y8pucbwyY80uiWXiQECZGeJACJqIVOFfosvvC4SCeh7W89TKKTz8lV7PIvnbKcpMV1jB4uDfmIKtT6YnJKLqbt7F/i9bSizOjF64Fe5yuETvy66k/grdnLJo/LH5Osbaw/uBXzNzYwbdE3knL/kfYKDRaEQqusjbkmyiujP+sndOmXw+FAp9Ml4e4TF3bOj7mQVruVXTs30r583aiHoNCvbWOXf7+deS7BsgSuGfpsKhGb/nuvdMY83M5O3D1OAE622ijMaAlOeKTRLf3IkjgRL4Vaw3kPsgwuBSQAxaj6UPVo30JcKhdUJnyN8DNlAqrQmsZf5fRYF3puUIv1DB+qjawqmYohr5RWt5Mqy3ZafCsBN1AFynUYcq5Da1pP+QL/Mrb6z35Epq8FG8swMplufonX8wxdR1fwpq837KyeFzwu1u57jaJZVwx5X/0PVc2vGHpSNFwQ6l9l7bKf49jOt9K+yvr0gXc4McQ+p6HO+Rls2dtw10yFwP6gxi4Huw5aaDj0LvW7Xw0pF3hgTO21iVfjqa848fFROpo7cHafoe3YHpraWyktKOHq+3/A/GWr4752TmEOPVZLcAJUUL6IU5+9jNZ4MRkKH1brWb7s3sb//mHf38vS6JaeZBokJjqvvQuvUpHwdXweb8LXGJcBKJUhZWZ5fsqunUrxfk1Cg1OsZ8oExPqmVwwUz9cw9Nyg7pY6ttV+itLahrekgvZJs9Ae/QVO619cOO+nEq1pfbDIwGX9jELfSTbiufBv+gzreIAmfku3rzfiWT3nrUNvso50qGroeUFDGWx5XPuRg+h7v0ndZ5/gcexErTOTP/US6qoPp20AOn3gHU6/+AgbA013bU3c/eIjAMHA0v+cn45zJ7HWfMxJp52jH20bEG6iuWYqFWfpOHVgBzWvPYfX/QdgMR3NVbzx6H0A4zoENdQe56PXj2DMXoPDup/2/b/lhV6H/99Dcz0bHn0IIO4QNHfJAqo2bQNuQmcsQ51hJK+0jeyCfXS2HiCnMIcrV13GCfJJxXd8rGcKiaFJCBLxGDdlCC1ngWSclaUCXWlCV0hJAPJ6vfz0pz/l+PHjaDQafvGLXzBlypQBz/v7v/97srOz+eu//uuI14n3TftYDSmpFO/XJPzfgRZdxcU4zqzH62xCqS1CN+VSGu1aGiP8u6pcUJnQm17hl4yvYWZBORT0TeoygalfXxn8/bGd76LW9FVZuy2/5jU8YVOejdhZw49QKFRUhUyAwF9XnWcaepN1a20dau3g5wVFKzQMNTSfo7OlHrgVmIzHcZbG46/T66mh3DI34tK4RJbMJcOJzY+z0eUM+9o+53KybvPjwbASes5Px7mTdByp4gpvL3rgkgjhJpprplr15ucvhJ++u3A7n2LHk98bNACFtpvlFOZQNC0H36mvcDbXoy0spXDJCoorZo/I/cfr6J5DaDNXojdN4asdN7Op1xH27+FZp4MNTz4adwAqqZjF4rVwdM/W4Nfp+pU3RNxTFeuBqcOJ90whMbTQEHRRtmq0b0ekOSlDSI2UBKCdO3ficrl4+eWXqa6u5pFHHuG3v/1t2HNeeuklvvzyS77+9a8Peh0JMqNvwL+D8nz42vCbab+sa6X6UDU9Z07h9dyKUq0CWgAVXs9ldO59Df2U1qQszRvvkhUchtK/yrrT1RRxymOjmdK5S1lfs5cXAnuAgPVqDYVX3jrka8RyXlC03J1nga8D0y48Mg18C2mp/Q+O7Zw7YGncpHl1nDtii7hkTp8/aYhXSp7mtuaIX9vmtubg70PP+bHWfMwV3l4OAd8A5jEw3ERzzVSzt9USaY9gR/NXYQeqBvRvN2u17Eax459Yf3E500om02TtYsemp2hce1/CIaixtobmPTtSEqw6mjsw5vg/t/O2cxH/PZxrrmfnMy/FXQZRUjErqo8LPSsoGSFIzhRKncC+oOMdbpSKXpkGiWGNmylQmkhJAPrkk09YsmQJAJWVlXz++edhf37o0CEOHz7M7bffTm1t7aDXkQMtx67JBf6/zM+eVZCRNQmFou+nXD7fJNw9CiYXZPLpJ4eiut7Fc+dE/do+r3dcfe/YOrrRGPPxeDx9DyrzsXV0J+3zzCor5OzHr+LuuQpvbw6ZSjNV3rYBU55srZHJV95Ga8Fkvv3xZtq628nNNJP79TVkT6kc8n7U+gyc9nOotX1ja4+zHrU+I+7Pw+s6CRwEyoHJwFn/770OWtu+hrJbBTRSWlaK0nMDx3b/GzmlP0SpKaW314dS43+89uBm5lxfMiLfNwXmAqramwd8bQvMBcHX1+eX0XnNrbz0WRVnnHb09IUf6As3gedHc81U05un0dM+cI+g3jwNr8/Hjo/9ZSlLLikA4PDuj1HrV5Ghn0Sv14em5WOW6WdDcwO+Ii+FegPf6PXw+u4/kVMyNe77ajr1Jc7Xn2F1ZhaFOfk0d7SxY+MTOG+5h6JpM+P/hC/IzM2kx2pBoZxCnmESVXbLwOmoYRLWjht5f+NbXHGLi+JpFyX8uoPJAFwoefuLRq6ryInrGrXHj7F35yfs3lpFboGSydOvwpzvr4fX6kuor2sZV3/Hjiav14tao+VwYxezcjJG+3ZEGstQKelxyn93yZKSANTd3U1mZt9PM1QqFR6PB7VaTXNzM7/+9a/59a9/zZ/+9Kchr5MujUwifoYsPR5XG+qMkuBjHlcLhiw9Op2O2VOi+3dcc6wmqudVLqhMqzavZDDmZOJ2tqIOOWjU7WzCmJOZtM/TrdGiVLlQqr4AenFo5rHO8QEb8YVNeUqvXYdOp6PskiWUXbIkptconjmNuuqd+Hr7zgvy9e6keOa0iJ9HNIfuak2TcVqzgT/hnzAWANko1QXkmstRKFS029zUn2vG51Njb+6kZNbksECuMk3G3t6DUqmk8bMPUl4kcNHN3+PuFx/hucB+HeBujZaLbv5e2NdBVzEXKuZy/OB2LmlrCoYfLnxMYW5h8PnRXrO/eIsTIlV0L7j5bva/eC+9rqcJ7BFUae5lwc33UprtPxS3scvB3qOtAHS3dZOdPxWF0v/vQtVTT7FxEq6eM6jV/v9rKs3Kobe1EZ0+/u/zzo/f51vZuZSasgAo1+Ryo0rNGx+/z5SLLx3mo4c3f+nXeX/jW6jVayis/FvW7/9B3x4gYL1KT9GCv8eUMx21ag0nPt7K1IvnDXfZhOgAq9PD+6e7Yp4Enaz5gjee/ZTM7DXkF11Ft9VAzWfvM3eBityCS7B2WigtLxhXf8eOJofDgUatwtPr46tOmQSJwfk8Luy6PJkCJUlKAlBmZiY2W9+/IK/XG/w/tLfffpv29nYeeOABWlr8P0WqqKjg1luHXj4jUsfW3kS7pRWnzYXWqMFclo/RXJSUa5vL8mmo2QGsQJVRSK+7GY9rBwUVsS1vjGY5ZGDZndfrQzlEy8hYW3aX6EGj0WitrUOffSdZhZPobj2H7fx0mljCGv4LGx0YUZI9++phW96GYiooo7wSWmuHPy8o2kN3/cUc/3jhed8lUMyRO/liPC7/kj6z0f9TVbezGadezZkTh1Bq/FOoyVNKcfecw5hrou6TnZx75dGUFwkErrUuyuAxY82DA8LNeqUan3ken23dTHnl3JivCfEXJwxW0c3ydSy6816qNz+Ava0WrbEULx4+/MPPqN78PJVr7mLa5SsAfxBqam/Fd/rv0Xis+IxluJRammz1lJj63lg32brRFia20dXZXE9RfvjSyyJjJs7m+oSuG1BSMYsrbnFx4uOtOHs6yL1iJeuP7aGxrYU8QxlFCx6iqOLPANAZy+ho7kjK6w4n3uVwocvepl5k5PNP6kBxLWdO7CFDkylnCqVI6L4gkKpsMZDsBUqulASgyy67jN27d7Ny5Uqqq6uZObNvmcGGDRvYsGEDAK+99hq1tbXjMvykMlQkk629iYYaB2rNLWgMhXhczTTU7KBkdlNS7tdoLqJkdhPtlteDX4uCitR8LQIhaagJUCAk9ZfOoSiW4BCv0P057ZaT4PsWMJlu1MA/0M1u3GfuJZEFQ7E02UV76G5o3XffpOhGjLmTIobG6ZfN5PyZXajVN2B153H6q4N43dvJmpVD71tP8tIIFQlMvfz6qK8ZHm6ayNZkYZj+VxROvTdsD9PUy68nu3R6sOChq9nh/3cJEUsf4i1OGKqie9qq+5l2+QpOHdjB/hefptf1LLAYe1sV+1+8F4Bpl69A22VhbtdXfO28m2m5C+h0tvN61wm2e1rYMO0ier1emmzd7OjupHDlbfF8iYO0haU0WbuCEyBITrAKVTztogFTnZ3PvESPte8AUwCHzUJOYU7SXnc48YSgpvo2Ckr8P1wx5xdwydfg9FdnON/8Lguu8MiZQikU2BckLXFiKLIXKDlSEoBWrFjB3r17ueOOO/D5fDz88MNs2bIFu93O7bffnoqXTCupDhXJ1G5pRa25BbXGv0TN/+sK2i2vJ+1ejeaitPm8I02SxkIoMhWUpbQ1L7QEodfVSd9+moILz0jswNtYm+xiOXQ3tO471GCh0WC20Fr7JgZXDzpzXxB7b3tqigROHdhB9ebnsbfVYsitCJuERCsQmD7buhmXfTUaw2SAC7+upK56C8CAM5Gq3/wDCoWeXs+VtJxqotd5mi92PsncGy+Ouzihf0U3QL7eiK+tMfj76s3PX1gK1xevel1PU735AaZdvgJH9fv8WXE5WfluWs8dReFwcYtZzZaCqbwzaWpfWcHK2xIuKyhcsoIdm55iBf7JT7KC1XD611c7bBYc3dtYuHJBSl+3v1hDUFFpLtauumDxgTm/AHWGjQVXXMO9f3Vviu9WgFRli8HJFCh5UhKAlEolP/vZz8Iemz59YM3seJz8wMiEimRx2lxoDOH/p6jKKMRpmzj/gQ22vC7dQ9FQmo5/RPO+1zhvbSPPlEvhlbcOuXwtdJmdMsOE170Xgr1jkOiBt7E22YUfuvsZBbyGno9waUx0t9T5a70vGGyyNFhoHOzx3EwzVd3tAzawF+bG36bVNwnx74vpPwmJla3NisEc3laXoZ+Erc1KXfVRNIbwcOTszsNhK8fe1oTPezMwmV7XXo5svZ9cYxZVts4Bn29+Vi6fbd08aE14aEV3QGuPDZs6g4atT+Jra8TYdgI72f3ufvGFpri+EKVSKCnPyqXb6cHr85KXYefSe74f89dlKMUVs2lcex9vhLbAJSFYDSdSffXClfG1wA3n8K4tfPDf/0xjWwtmnYmSr63gG/d8J/hasYSga25cxMtPbAFWYzSVY7PWybK3USAhSAzlPMbhnySGNC4PQh1tYylUaI0aPK7mYFgD6HU3ozVqRvGu0kOkYDQWQlHT8Y9of/dZNgVqqq1trH/3WYBBQ1DoMjtTwVk6G34Dvv8LzAZ2R3Xg7VBircDuO3T3JyzgPZZgJ4cPURZN5kD1O7RUXk9mQXlSz5nK/foa1u/ZOKDe2znp62z9r8fptTtRGbRcffOKqM8NGm4SEitjrgmX/Vww5ADBPUyRwlGvx4PtvA98N9NXFX41Pu8yunmduzXasL1Fd6k1KPKvxmUfWBMe+JxDK7rz9UZae2y81nKOIgV8U60h31zIR5osdrt+zCH+FbgUf4j9N0waIw1bn8SmzqC1xxYMUZlaNU12K+c8mXRFqMxOVHHF7FE5Tyja+upEHN61hap/+zteCPx7dFhZ/9FbbOlQsPp/3RNzCJo++2Ju/y588Pa24OGnsuxtdASWxMm+IBFKpkDJIQEoBVIdKpK5vyhZJQUTRbShCEYnGFlbLNS/t5HXPK6wvR0veFys3ffakFOgwGRk2qIrLzSw/Ryn9YHgvppIy8yi1f+cIQCPqxGdSR/x+YHXan/vr1ni6qRAk4257CIy8ydhdNrZVPspFJQn9Yyk/BlfJyMjg7Uhk7Osudfh7ShBrb0BdX4xbR0W3n9xO1mzjqI1l3L1NQuHvOZgZ+MEJiGRRGpYM5fNAKC8ci7Hdr4FrCRDPwl3zzlc9reYfpX/0NfQcNRx7nW8jU+g8HVh5Fd08zCwHv/Sxrk4bU8w9Tt/H1acoCn/Oibz30RcYhcIQOayGbQvX8erIffoMBdyqzojGGimFpey7OwOLMynmyJmU8C1ijNcPHsBHruVP3W08JoPbi2YFAxRu+xW8pevwgkRzw0Ske198lGe67eX64VeB9+u3cvRPZeGBbBYQlAyAs/Jmi/44O39wSB1zY2LJEjFQaZBQiSfBKAUSGWoSPb+opEsKRiv0mVfUWAa0umyR9zbcd7axqn9+4YsHwgYbF9NPPfUWluHtaUVR9fjGHJvxJBzRVRNdsWzFpFV9wWVmWaUir5WvzyNHqW1DUj+4apFs64IC4mn9u9Drb0hGLDyzFNwO28io/1NMJey94ODwedGCkOG3ArsbQPPxjHkVkR8/cEa1tqXr8NcNgNz2XTmLIe66i3BJWrTr+pbohYIR/a2j3F//mPe8AamO2dZxwM00QIogEwMuRVkl06n8IrvYLxwrXbLOTL0/aZI7i6ch3dR33YkPJBdCGUA9c/+knxTDgAd507itnzFXwAGwE4TGTRRUj6bvAsf8838STzvcfOqwdQX9K5aFQx6jV0Odh20AEgQGkZ9S0PE/97bepoiNs6ZtP7/20/WYamDOVnzBS8/sY/M7NUUlJRj7arj5Se2cPt3kRAUBwlBIpRCLat0EiUBKAVSGSpSsb8onUoKxotEQlEsbWmhAtOQbM0fqXI1DtjbkanM5/zpRXQ176PiitiXiMUqdHlaZn4xSvUJ7G1v0Ot+m6zCkqia7LymXM477RRoDcHHzrt68JpygdgnS7EaKmDNKehbg32qxRYMQ6FBqHLNXRHPxqlcE3kz+VANa4HAYS6bHnEJXmg4avrwv3jNGz4V2IidNfyMbn6FSvNzZixeOaA0obv1UVSaL8gq9DeaObqOUXbiP/mGzsfsCIEsIHRfUNvxg9zm7fXfP/7TmdYDbzT3FVjk641o25spWXV/xK9DcZa/xTEQhMZKCGqoPc7RPYeCe37mLknNnp9QpQUlVDXXD/jvPVdfNGTjnEmrZnuNv/AiFUEotE4buPDraj54e5sEoDhJCBIieSQApUiqQsVY2l803rWePkLd4f247PVoDKWUz19E/tTBDziMJhR5ulsxOPLi2tMSeLOeUfaX3Hn6F7zo7TuMcR06erP+AZXiGno6VJw78jazv5HaN5X9l6cZzbPQGO4iQ/sm0xZFuaG64jJ2V7/DUvyTn/OuHnY77TDH/zPvVJ+RFG3AmnYhDPUPQoF9PoGzcfwtcPcOuv8nmoa1oQTC0edv/UvEqYCNdgy5j1C55l6szT1oDCvDlrtll9xMZ8NL6DKzydBPQlX3Ekt856koL0elUEYMZBC+L8jqsNELbMNfobHnwnNsjr7a1tYeG4rc8GAZSXGWbsxMgxpqj1O1qRpd5iqy88vosVqo2rSNxWtJaQi6+v4fcPe//V34OVEqHaaKq5m7ZOjGuXjPCopGaJ12gNFUTlN9W1JfZ6KRfUFCJIcEoDFGSgvSQ+vpI5w6sB9vr/+cE5e9ilMH/OdbDRWC+usfig5XnaLdswKlWgW0UFwS/Z6WwJt1Y/43sQG3Wn5Np6uRTEUBvdn/QIbB37qo0lyBtWljDJ9tfJKxPC2zoJyWyuvZVPspSmubf/IzZ3GwBS7VZyTFGrAiB6EVURceDNawFk1YCFWYW0hVW1OERrsilv/iGQD2PfvCgNIEU+E1eFxvoTH4l9hl9R7koosq0GflBp8TKZCZy2bwefFU9r3zMnrADmwAAv8l/B5QavT0+rzB/T66q1ZF9bmMlWnQ0T2H0GX2nfvj//Umju7ZmtIANH/ZagDWD2iBu2fA6w42oUpFCOpfpw1gs9ZRVJo7+AeJqMk0SIjESAAaY6S0ID3UHQ6En5CDOnufpe7whpgCUH+ZajWarCkoFCrOd9ppbGjE5wOfy0KnpnrIPUShb9YNedfjMV2K9di/4jH+GI2+7+MUdOLFG/y9v/DgnZCDRK+Pa/9Pd0sdhAQVpVKFx5X48rTMgnIoGHyik8ozkuINWP2D0HBlCQGRGtZiCQsBM9Y8yN0vPhI2Fbhbo2XGmgeDzxmsUS63fCqXrloDQMNWB912a1jhaqRAdurADj5/+0/0uv4I1PEcD7ASJ26gFXharaZszuV81N48YL9PJO2WkwMOby0um57W06CO5g6y88PvSWcsi7gPJ9nmL1sdDEKDGW5CNVgIirfIQOq0U09CkBDxkwA0xkhpQXpw2euJ1O7lfzx+oRO+vGz/vhePqwF1ThZ2whvn+oehSG/Wc8rU2Nt24fXkolBNwtd7Do/rj+RM8p/R0nh8P8fffRuv5xn8B40+y7Ed/0T956cxl02Oev9Rd0sdBdXvsFRrIC/TzHmnne22Fj7lBVwZV+OyNeLuaUShbGTKwikJfY1GWiIBKxCEIu0PiiRSw9pwYSGSqZdfDxDW8DZjzYPBx2HoRrmAaANZ/7rvJlSs4QfYaKYwt4iL+r32UNotJwfsTQpUcRdf2PuUjtOgnMIceqyW4AQIwGGzDLkPZyQNN6GKtBwukSIDqdMeGRKChIiPBKAxSEoLRp/GUIrLPrDdS2MoTei65rJ86g6/jNmpQue14VAa6db2Uj6/lDJz35Sv/96h6WX5YcUJZfNnYioow9pSTu1HNbh7XqTX3YtSpUKf08ykefMBqN33zoXwsxQ4AnSD7ymsLQfJLLgo+jN1aj9lqdYQLCso0Bq4IbuA+u6TnGnz4fVeS4ZuIdpMB+fP7MVgtqS8hCGdxBKE+jesxWvq5dcPGTqGa5QL3Es0gWxg3fd6ulkL6Fj+i9diuu9IB7r2r+IO3RuULiFo7pIFVG3aBtyEzliGw2bB0b2NhSuH3oczUqKZUPUPQYkWGSSrTlsMLXRfkIQgIaIjAUiIOJTPX8SpAxuCe4CgCqVqA+XzE6uOVuDja4pjXIEXk0+JFS8fKZS0UBL2vNC9Q7b2Jj579ziolqNQFeDraKGn69NgcKm4gn6tcrOD4cNpraPvjeseYA0wGa97d0xn6iitbeRlmsMey9PoUXSeJafsrrBlcG5nZlzn9IwH0wqMMS+LS5VTB3ZQvfn5kHKGuwZplxs+kMVa9z2UwIGu7edO0nj8MzyOdlTabHLLa7iUNcHnpVsIKqmYxeK1cHTP1uAem4UrU98CF61oJ1SBEARSZDAWSQgSIjoSgISIQ2CfT93hDVG3wEVDbTnG8swcCnL9+2TygUxXD69YjoE58kb4dksr5py+avTznSraOy+jc+9r6Ke0UrmgctCwoTWV47QG3ri2AJOBs6g0/iVy0ZYWeE25nG2oRdVkwePqRK3JpreoDDta1JrkndMzHoSGIOibBkXa92Iumz7kwajxOnVgB/tffDpYz21vq2L/i/dia2skz+OK+bVirfseijHXREvtPpq+bMLnvRmYTK9zL621/8WpAzvCCiXSMQQNFXgO79rC3icfpb6lgdKCEq6+/wfD7t2JR6Syg1gnVNtrmqXIYIyR5XBCRE8CkBBxyp86L+HA05/S1kmeISvssbwMHUpb56Af078aPS/bgM83BZddTS9wcM9O3OeteJ0eSqeWhe3rqbjyeo6/e8+FZXC5wF5QfBJ80xttaUGrMoPNllMs9t1ANnNocR2jyrKd9tL5GJNQhDDe9C9JuLjCzOE338fU7cXkseJs6OHwmVamXXGWoiNVgx6MGq/+e3ZgKb2u76De+u9cXTCFokwTLo+bvVG+VqS674sWfxNd81nqn/1lMEyBImLIO33gHU5c2K+Un5XLeVsBPu9/EwjkcAif98dUb35kQKNeoCUuXcsRAg7v2sLeRx/iWeeFevrmejY8+hBAUkPQ4GUHlSxeWxnVhCowBZIig7FHQpAQ0ZEANM7Y2xtRW46htHXiNWbjKZuDYZDJgUg/XmM25109FGj6AsJ5twOvMXvQjxmqGt2c2UuDRY9BvwZVViH1dWeoP70TbWkN6sx8Khf4l+zV7rsXp/UsSvViskvuxphXjNt5LuozdeqPfsIp339ShwU9Z+nhUlp8K1G3/QStKXXn9AwnnkNl4z2INp57o7aO1hYrO94+zRVKNStMs8jVldLmsfJuq4W67Qe5c8bMQQ9GjbSMLZrK7YF7do5QwD6u9k6j2HQdXncXyvqvuLpUz9Z+Z/6EhpXQcoVpl/fVfbdbTqDfuZFlIcHtT5t/x6e+2WQW3BtWbpBd/CEtbz/NxkBjXdd51nGeJn4P7AYK8J8oNBt72wODfk7pNg3qb++Tj/Ks0xF2OO2zTgcbnnw0LAA11tbQvGcHzuZ6tIWlFC5ZQXHF7KhfZ6iyg+X33BHTkrwT5HP7d6+UIoMxJhCChBCDkwA0jtjbGymp+ZDrNDryDFmcd/XwXs2HNMy+SkLQGOEpm8N7NR9yHf7Jz3m3g/dcDjwVlzHYSU9DVaO3W1pRa/qWxxXkVeBxrUbteT2kVU6LYf5qrlpQeeHN/34c1vcGVD4PVZft30t0Dy1khNyZG0/PX1BeWZCyc3pg8MBibbFQV90S06Gy8XxMvPcceJ28/GJcDT9lobcZlbcDZX42+RnZLMXHy80HyZ8XvkQpcA7PYMvYgGFD0MA9O3vQo8KsLEaBAlVGNnAR6vbj+NR9Z/6cPvAOp198pC+stDVx94uPAIQVLjiq32eVwRQW3L5udfAVXjKmhJcbnHlnJX90OcOCwUZgDdvppinkrncPu6conUNQfUtDxMNp61sagr9vrK3BtukpvpWZTVF+MU3WLnZseorGtfdFHYKSVccdmAJJkcHYpFYpZAokxBCUo30DE5mtvQnLkaOc/OgQliNHsbU3Df9BQ1BbjnGdRkeBRo9SoaBAo+c6jQ615ViS7likmsFcTMPsq3hFo+d39i5e0eiHDbD+anQdas3ruOyPoda8TslsHUZzEU6bC1VG+LkeqoxCnDYXM8vzg/+APwydtLTSqdEzZ/k3mLboyrDwc/zdt3FanwYcOK1Pc/zdt2k8vh/w7yXynzYTqgqtyR9Gpi26csA1kyEQJNzOm9Fm/hVu583UVbcEQ5FaewMZ2kkoFCoytJNQa2+gtbZu0OvF8zHx6P86RoWTXOUsvK4WOjutAOT4fGSoVbT22MI/9sI5POHL2DLwL2N7murNzw/7+pVr7kKluRf/hMUNfEYPvbhz+078UWZk0dRtDTvz58Tmx/mOy8n3AR3wfeA7LicnNj8edn1fWyP5emPYY5lu0HqsYY9l6CfR4eiKGAxsNIfc3+4Le4ruGvZz678kbjiNtTV89sxjfPyr/8tnzzxGY21NVB8Xq9KCkgj/hfgfD2jes4MVmdmUmrJQKZWUmrJYkZlN854dUb9OTmEODlv4555IHff2mua4Pk6khyNN3aN9C0KkJQlAo8TW3kRDjQOP6xY0hu/jcd1CQ40joRCktHWSl6ELe2y4/SMi/RjMxWjmLUV9xbfQzFsa1fTOaC6ibN5cpl+xgLJ5c4M16Vqjhl53+BuYwPK4UKFhaGZ5PtWHqoP/QP+6bP+bba/nGWr3vQP49xIp1fcQ+oZVqb6HiiujO/slXkMFFoe1J+YChng+Jh79X6c3s4x2bycKbzc+n4+OtnpaHUdRz5jLLruVJruVU52tbDn6ES99/iGOrjbsbSfwR4UXyGQqCpRk8p0Ljw9t2uUrWHTnvRhyHwB0qHXv4Z26lI+0ClrdnXh9Xprt59ir9l7Yu+PX3NbEi8BjgOPCry9eeDyUIrd4QHDrzgCn2hT2mLvnHDm6rIjBINeYHbw/Q+4DLLrz3qiW90H0ISg4cbF28f/lF/Mtaxe2TU+lJARdff8P2KDVhfwXAhu0Oq6+/wfB5zib6ykyhv/EvsiYibM5+vPF5i5ZgKN7Gz3WM/i8vfRYz+Do3sbcJbHXcZu0skhkLAutxxZChJO/3UZJ/6VJ/l9X0G55Pe4zfuLZPyLGt6GWxw0lMBUKnDfktJ4FPgc+wL8nYwn+g1P9k5HAUjj/XqLAErkbg4/HI5q9OA5rD9rMyIFFZ9Ljdg5ewND/+lllhcN+TLL0fx1n4Tep6voHrnF8hcFRTY9CzQfZRTQUfoOir83lDx+8Rv7xT1hqzOIbsxbSrc7ArTHxset7FLGRjdgvdK+dZR0KTh94Z9iDR8P37PgPH63tXU1T5yGU3V/hVHZReOM6SkL2/2QplTzp9YYtV3sSuEUZ/rO0SAeofmzSYfUpybSfDTt4dcr1d3L320/zXGBZHXC3Rsvsb/9V1IenRhLNcrjmPTv41oWJC+CfuABv7NkR076baAT2+WwYogVOW1hKk7UreD8ATbZutIXRny8WWsddf+IEDpsDfaaJo3t8tFpO4Tv1Vcz7i0IPRxVji+wHEiIyCUCjpH9zF/QtTYpXPPtHxPjmXx7XRLvldZw2F1qjhoKK/KhD9szyfGztTXSorsbXOx+4Gn8r138CfwR8fPiHnwf3AyUSeEJFuxenf5Dobj1HW90BvO6dqPUqDDndmArXDyhgiHT9+s/eonC6hvNntuO2zyTLdoSMnlOg7MKw8GtJ+bwC8ivKqavuK4dwdB3gpPMrrsELgM/n4WRXE4rOBr6onURFVh6rLrkquKfGCNxaMYeGmqd4Fl+//TM+1m1+PKbw0Hco6lFsGW6MM+cxo3LugHOBurzeiMvVurzefteLcIDqmgeYjyLiwaunc4tYF6FYIVHDhSBncz1F+eEBOtaJy2AiVVHPX7Z6yMa3wiUr2LHpKVZcuI8mWzc7ujspXHlbTK8dKDpob1BgLvLXXrdadqPY8U+sv7icaSWTo9pfFChk6G6w4Jkzgzk3rqJi9tyY7iUeJ2u+4IO39weLF665cZHsQ0qA7AcSYiAJQKNkqOaueAX3j4S2wFVcJgUIE4itvYl2S2sw7JjL/GEnlqli/ybB5h4NpoLb6Wo6CL5yoAvIBO4AHsZpreL4u/cAJC0A+Ze23RwMNoMdyhoaJBxdvZw/dRDwAH/C09NJl3MdGn0Hvdq8sAKGU/v3Dbh+r+cG7O1byZuSQd7Bx1jsVZKvM+DI1LD3zGFazEVkFvjb6xJtijMVlFFeSbAcwtv0Jq/hDTtGdKXXw9qj22DqQpqOfU6P3gxT+5aQTZ92MaqaAxEDSXNb7Ps2zGXTIx6EGqowt4iqtqZ+x536Hx94vcgHqEZ6jamXX5+UwBPJUDXZyZi4RDJ4FTVDtrAVV8ymce19vBHaArfytrimUf3b4HTnP2G5fg7K1kZUk5TDTrtCCxnM+cU0n2nk6BO/ge/+j5SGoJM1X/DyE/vIzF5NQUk51q46Xn5iC7d/FwlBCZIQJEQfCUCjJN6lScMxmIvDDsyUyc/EEdhXptbcgsZQiMfVTEPNDkpmN0UdgCI1CW5pPMmJom9jnlRIZ+PreD0O4DvAC4TvB7o3aQFoqKVtoUKDREPdPmAlsAG4cD6TdyPWlnu56jt/P+z1VZoirC2tZFjOstirpFBvxGDOIs+YxVKnnU21n0JB5OlRPE1xpoKy4PPfO/ZixCBz3trGvAIj3QVFtLd3ojxTz+Qp/jfnrT02FDojVQ5bhECSmuVKM9Y8yN0vPjJgudqMNQ+m5PWSKdI0KFkTl8ZTX3Hi46PBaU93+3l0mfdErKIeroa6uGJ2Upbf9W+DU9gsFBlLcdhOBx8batrVf3lgSWYWUzLcbHl7a0oD0Adv7ycze3Xw8FX/r6v54O1tEoASIOcDCRFOShBGyVDNXWLiSUYjoH9f2QrUmhIUChVqTQlqzQraLa1RXyNSk+BSrQ5jx9sYcgopmX0Z/i3c4N8LFODfDxRanJAInUmPx9UY9thge3ECLXNeTw3wMMHwE3Jf0Vzf0XkSR5cbdU8u+brFeHtn0dVox2nrIk+jR2ltA1LTFJdnyo1YBJBnyvX/puIyPlW5Oe+yc/r0OZrsVnbZreRcfxd3a7RhG+tTGUimXn49U+/8Metyi9CiYF1uEVPv/HHKpjfgP1OoYeuT1D/7Sxq2Pkm7ZfiSh8H0nwYVV8zGuPY+3jBl8f9aG3nDlIUxhspp8E97Pnr9CD3WVWTn/5ge6ypOfHIWjzu8kCaeKupE9G+D8xnLaLLVozP23ddQ065IhQw9ThXW+nOcrPmCp//jaR75m3/j6f94mpM1XyTtvpvq2zCaws8JM5rKaapvS9prTFRSiiBEH5kAjaJYlyaJ8SkZkxtIzr4ypa2TPENW2GMlOdlomj+jx9WAKqMQhcqFr/f3wPqQZ1WhMZQyszw/WJwAULmgMurXDtV/j0w0B6hqTeU4raFn2/jvS2sa+DGRrt/T8SbGvBvx2D6n3dNFnjoLmI69/TgetRrvhTAS7XQqFoVX3sr6d5/lBY8rOFlZr9ZQeOWtAGQWlNNSeT3baz9FaW2jrQVsZfNZeuPNnM4tTsn+mcGkcrlaf4EDVVeFHKi6a+dG2pev8y+xi0P/SVCiE5ejew6hzVwZNu0xZF1C/cnPmJXb11qXSBV1POYuWUDVpm2Afw+QI+9r7Gx+h/XTyun1eoeddvVfHqhRKTnT3YUnU5vSJWpFpblYu+qCEyAAm7WOotLchK8tpBRBiAAJQEKMsmQ1AiZjX1mkJkGrWkVGUQ5qjb9IIbuknY5zx8F3A/65QxVK1QbK5/uXv/VvkAuIJQz13yMTzQGqFVdez/F377lQ1+2PEf4q7hujur4m04oh5wpsmkLeb3yOawGzykBzj43DTh3M8S9SS7QpLtL+oaJZVwCwdt9rnLe2kWfKpfDKW4OPgz8EcWEPkgE41WJj7wcHufqakQskI61x21PccOwAza4ebDojubMWssxcyKvV70fcXxStZB6Y2tHcgTHHfw1r2xe01O2nx9aCreMJWksU5JUuxWGz4OjexsKVsVdRxyu0Da6juYP8shwKl9zHO6EtcEPsLwpdHkhLA5988jE7HR0c0UxlweW3UDJ5KpD8JWrX3LiIl5/YAqzGaCrHZq2ju3MLN629MuFriz6yFE5MdBKAhBhlyWoETMa+ssGaBJWzr6IsZG9Z6+kC6g5vwGWvR2MopXz+IvKnzgu7ViAIAXFNhUL3yEQj1iru/tf/au8ePK5GNMaLOFl8N43t76LuOYlHbySn8vpgAUI806mAofYPFc26IizwDGdagTEkBC2M+uNS4dSBHVRvfh57Wy2G3Aoq19wVrNge6s+GcvrAO/Qc2cN9Xi/TgLMOG68fqSLrkqvxOWzDfvxwkhWCcgpzsHZYcHQ7OfvFh6i1q9EZslCpt9N0ejsuxzZKZ8xg4coFw+7/SbaSilkDX/OagT8QiCRQyPDbZ/+LM/v2YfPeSgv/C1y/45N9J9AZJlExew6Q3CVq02dfzO3fhQ/e3hZsgbtp7ZWy/yeJZD+QEBKAxrXBGsFEeklWI2CildcQfZNg/tR5AwLPUCJNheJdHjeUeKu4rS0WXPYuuhr+iwzdLIx5V2AvWIXHuZ3yygIyQ4JSPNOpgGjb7aI1rcAIwN4PDgKMShA6dWAH+198ml7X08Bi7G1V7H/x3uCfD/Znw4WgE5sf526vFxWgAqYBt3h7eaLmYxTL1yXl3pMRguYuWcD7G9+irb4XteYOFD4zHveXTL1kMSr1AvSmrSy/5464rh2o0m448RUmm4XcTBU50+dEfX5PooorZvPsl2fo8G6mb2nppXh7L+HTDz8KBqBkLlGTCuyRIUvhxEQnAWicSta+EpF6yWwETMa+slQ2CYZOheJdHpdsgamMUrWBnEkmbK21dFj+iLncS3nl/IjBJNbpVEAq9g/B8NOgdstJ/xk/F87fKY9wxk+8qjc/fyHg9J1G1Ot6murND9DrcdLruh3/AbrHgCXBPxsuADW3NbMO2AysASYDvcB2Vw/Fldcm5d5h6JrsaJRUzOKKW1xs/s/n8PmuRJ/ZSulFxWSa8/F5zXEXHwSqtHt7ZzGt8XOWUEx2VwM63Wn2DnN+TzJ1tHwFYR2FS4Ad2LrP4vX2JnWJmlRgjyw5H0hMZBKAxqlk7Cvpfx6Mp2yOnCmUAsmY3IxFIzUVGk5gKqNQFaFWq9Flfg23s5gMbXxTmaEkun9oKKEhCPqmQe2WkxzbWYPGsBqDeRIu+zmO7XyLOcsjn8kTK3tbLUQo8ba3nQQWAH+Bf35zFn+cWXLhY4ZWmFtIZ1sT3wD+BLQA3cDprFzmJLD/ZzCJTIOKp13ExVddRo+1OFiGAIkVHwTO8emtfYml2hwKNDl4nFkoW79kRcXkQc/vSUSkw1tzCi6iozm0XGQecACNfjstDfqkLlGLpQJbJkXJIyFITERSgz1OOW0uVBnx7ysJnAfzbVcPDxiy+Larh5KaD7G3Nw7/wSJmRnMRZfPmMv2KBZTNmzvuw0+omeX5wX8CNdrJqNKOlsPag1qT/KlMJPkV5Xic23E7z+Hz9eJ2nsPj3E5+xfD7h6IxrcA4YFlcXfVRNIaVaAyTUShUaAyT0RhWUld9NCmvacitgAgl3mrdTFSaVRC2iG0NsPHCxwxtxpoHuVujpRX4LnANsFGjZc6t30/KfUfSfxoUi7lLFuDo3kaP9Qw+by891jM4urcxd0l8xQcdzR3ojGUobBbyMvxNbGpNFg6bY8jzew7t2sq/3LmGv10xh3+5cw2Hdm0d8JzDu7bwmzuX8tCK2fzmzqUc3rUlOHEKrfOu2lTN11etJkN7H4SUrWdof8GN//M+fvwvP+Tev7o3acEj2grswKTI2nUTBSV/i7XrJl5+Yl9S67gnCqnGFhOVBKBxSmvU0OsOPw0+ln0lkc6DuU6jQ205lorbFQLoC0PAiAWhWM4cSpR//1ABGdo3cXb/BxnaNymvLIh60mRtsXBq/z6O7XyXU/v3YW2J/EY9NATZ2qxk6CeF/XmGfhK2Nmtin8wFlWvuQqW5l9A3yCrNvZjLZlM8+xoUyjeBU/gXsPWiUL5F5Zq7hr3uaJw5BPGHIH/rWiV601Y6Wx9Bb9rK4rWVcRcfBM7x8RnLOO/uAsDj6kJn1NFk66bN1j0g6BzatZU3Hn2Mjubfgs9BR/NveePRx8JC0OFdW9j76EM821yPw+fj2eZ69j76EO8+8wd0mTehN01BoVShN01Bl3kTvW4T3/rB98kp/B4odOQUfo9v/eD7XHHjzWyvaR7s9uNSVJqLrd+5XZH2F4VOipRKFabsqWRmr+aDt/cn9X4mikAIEmIikSVw41Si+0oinQeTl6FDaetMwd0KEW4k9woFWt0UquWoVJNianWLR7z7h4ZqkIt0vUAI+vSIlZbzh5h6Ud/eIHfPOYy5prg/h7DXubCXp3rzAyFNb/dibe7BZdcxaV4ljce34HG0o9J4KZkzN6oWOBjZM4dCxbsvKGLrGpGXlg0XjALn+PTmfY3dp//IEqeVbF8DykkmXj5xlL019Xg8LwCL6Wiu4o1H70OtceF2Pk/ofiy38yl2PPk9FixbBcDeJx/lWacj5BnwrNPBn32yg8Lbfht2D4HDW5ffc0fw4/vbXtPMDbMLI/5ZrKKtwG6qb6OgRA5LTTZZCidSzXO+CXy9iV9HpYWSyIc4R0sC0DiV6L6SSOfBnHc78Bqzo74HaaETyRAIQ18cq2HfG6/jdXoonVpGfkV0zWvDCbS6NX75Bs5ud0ytbiMp3ga5i+ZN59hH2zn9FUyZsQB3zzlc9reYftXcpN3btMtXBENNoHChre40trb/JrvkDmYvXRN83TnLVyftdVMtGS1xgaVlusxVZOeX0WO1ULVpG4vXMmQI6jvH5xCnHFpabRZyM9XkTJrKzkNHLoSf8KDjdq4h0n4sf5GBX31LQ4RnQLvDisNmibiHqbG2huY9O/rOD7rQQmfSqrE6PXF9XSKJtgJbDktNPqnGFiPB3tCCqted8HXcWgOUDP+8oUgAGscSaQQb7DwYT8VlUbWCSQudSCZbexOaDj0G/Ro6fJnU17VQf3onl34j8vQjVqaCMjJM+eh0uiTcbWrE2yBnKihjzhXw1ZHXOfHxP6PvPkaHowv7iSJmrHkwbMLSbjmBo/p9fG2NKHKL0VVeizmGwoHQwgVz2STUmg/orH+SXpcBc9kkpl+VvPa5kZJoCAqUGQSChf/Xmzi6Z+uwU6DBJkovPf8bIgUdsOHfj7U05PEqcgouCv6utKCEqub6fs+A4twCHN3bgJvQGcuCh7dOvTQH26an+FZmNkX5xTRZu9gR0kJn0qqTOgWaPvviYfcUyWGpQohEyR4gEVHwPBiNnt/Zu3hFo6dh9lVRt8D5W+hWoNaUoFCoUGtKUGtW0G5pTfGdi/Eo9PspP8dEQV4FqJbz+d6PR/vWRkykvUpdjdU0nzzA7sce4MM//JzG45H3QJgKypg0SUtO+6f80dGFE9jY1sTpFx/h9IF3AH/40e/cyJ/ZrXzPXMif2a3od26k3XIi6nvsX7iQVbSUopk/wFw2iUtXrcFcNp12ywkatj5J/bO/pGHrkzFdf7QElsTFI1BmECqwtCxe/kAzsHjCkFUWobDgPlbc/0DwWWVXXMc6FCHPgA1aHdf8xf+JuIfJd+orVmRmU2rKQqVUUmrKYkVmNs17doS9erL3Aw1FgY/Jhho6DtzDiZ3fxON8gtu/K4elJoNMf8REIRMgMahEzoNx2lxoDPG30AkRKtL3U37uFFpbPFQfqh7Vc4RGSmCvEtyAWlNMV2M17ZZnwfdjYANOaxXH370HIOJhsM37XmNTrzts78dzLifrNj/O1Muvx1H9PqsMJooM/r1BRQYTy4BXq9+HKKdAtjYrBvPghQtnPtmN5u2NXO1RUpRpwuVxs3fnRtqXrwMUKTurKFnimQLlFObQY428tCxeK+5/gDcevQ+38yn8k58qMrT3cdP//CsAdjz5PTpaviKn4CJW3P/94P6dQ7u28sn2D3Hzf1nD89ioIxMlc2+4lfnL/EsT+0+cLH/8A0X54T/46t9CF1gKl8xJ0GBqa47y5RO/YUN2NqXLrqXe2sVbnfUokEM9hRDRkwAkUkJr1OBxNQfPIYLYWuiECDXY91NBYRZlF+qzYXQPVE01U0EZeVOaOHfk17hsbnqs9eBbB9x/4RlL8XqeoXbfvRED0HlrW8RFU81t/p/c+9oayTf3C5l6I7626KvvjbkmXPZzaAyTg48FChfaLSdp/tPbrGMOhaZJeN1dKOu/4upSPa9+8DoNrotTdlZRMgSWwsUqUGbQf2nZwpXx1WMDwUAzWNAZrLBgx5O/uxCaltLNLwGwspuaj77Hmv8v8mtpC0tpsnZRauorxWmydaMtDN+APFIh6NjbW1mdnU15dg4A5dk5rAS2vL2VitnJ29c20Xh6JUCKiUWWwImUMJfl43HtwONqwOfrxeNqwOPagbksuhY6MX61nj7CoTd/z/6NP+PQm7+n9fSRYT9muO+n0Ors8craYuH8GSWZBX9J4cx/Bu+NgAkI/fotxtmvRjggz5QbYdGU/8BRAEVuMa09trA/b+2xociN/vDj8sq5uOxv4bKfxefrxWU/i8v+FuWVc6mrPorWm0WBvhQFClQZ2agyLkLTbsN++mRKzypKluIs3ajXYwcsWLaKv3lxMw/vOMbfvLh50NATyl+GMHRJQn+FS1awo7uTemsXvV4v9dYudnR3UrhkYJOfSev/mWoql8NZ68+FhTGAUlMW1vpzKXvNiUKWv4mJRCZAIiUSbaET41Pr6SOcOrAfb++zwGJc9ipOHdgAQP7UeYN+XDTfTzPL8/myrnXcToP6t8CpNFPpdV0G7AECX7sqtKbI9d2FV97K+nef5QWP68KiKbhTlYF3pr8EQVd5Lbt2bmQZ/slPa4+NXXYruquGf2MdYC6bzpzlUFe9JbiULVB8UPPuR+gzL6LN3UV+hr9NUpmRRaPVil2tRZPCs4qSLdalcIOVGQxnsPa1eOUUXERH89AlCf0VV8ymce19vBF6HytvG/Q+kt0MN+D6pZOo7+oMToAA6q1dmEonDf5BQgjRjwQgkTKJtNCJ8anucCD89O1E8fY+S93hDUMGIIju+ykwCQoEofEUgvq3wJnLptNa+zHwFf7t7FUo1fdQceWNET++aNYVAKzd9xrnrW3kmXIpvPJW7Lnz2PvBQa6+ZiHty9fxamgL3FWrYmqBC9xXpGVrxlwTVvcc3mvcwnVArtpES089e9VefNPm4e6JvHQu3RRn6fjq+BfsfKYqeK7PjK/PZerFQ3//xqqxtmbI9rV4DLZ3aMX93x/y44orZsf0msluhgs158ZVvPXEb1iJf/Lj3wPUyZy165P+WhOFLH8TE5EEICHEiHHZ64m0BMf/ePKEToNSGYKsLRZaa+twWHvQmfRJO5soEp1Jj9vZGJwAZeZPotfdSGfTLrwuHVpTORVX3hhx/09A0awrgkEo1KkWWzAERVt4EKvyyrkc21lDbfFqmjoPoez+Cqeyi8Ib13FR0WSO7XwLWEmGflJKzipKlnbLSVr2naJefQMXTZtNj9XCR69vRqvTJLysLVTznh1860L7Gvjf7K8A3tizI+4ANNzeoWRKVQiqmD0Xvvs/2PL2Vqz15zCVTmLO2vWy/ydBsvxNTDQSgIQQI0ZjKMVlH7gER60twHLkaFIPze2/LyjZQcjaYqGuugW19ma0mcW4nY3UVW+nvDLy2USJhqX+LXAeVyMa42Euu/WuhEPXtAJjeAhKgb7lcUexZbgxzpzHjJCmt8GWzqUbf9X3alCVcrrRxrTSKXh6V3J0z9uUVMyiofY4R/ccCk6H5i5ZEFcwcjbXD9u+Fo8Fy1aFtcLtePJ3vPLIjy6EoQeSHoZSFYIk8AghEiEBSAgxYsrnL+LUgQ3BPUBQBYp16ExX4nH1HZpb99lmNPqT+Lz6hANRqqZB/ffk+H+9gdbaN8MCibXFwrkjR2m3dJGhm4UxbxluZ+aQYSkSU0EZ5ZXQWvtmMESVzEnexGmkQtBgoWaoP0sngapvjUJF94W9LjqD/1yfhtrjVG2qRpe5iuz8MnqsFqo2bWPx2oH10sOJtn0tXod2beWNRx8LLofraK7ijUfvAwZvkYvVSNZji/h4en0y/RETkrTACZFmbO1NWI4c5eRHh7AcOYqtvWm0bylp8qfOY9rli9AYNgA6NIYN5EyahTF3bfDQXG9vFg7rUuztFWgM38fjuoWGGkdCX4fQaVCymuIc1h7UmvCf0Ks1xTisPcHfB6ZE3S0rUGsfBd+dWJuO4fXYUWtvoLU2cmPbYEwFZUxbdCVzln+DaYuuTPpyu2kFRgD2fnAwpo9rt5zks62b2ffsC3y2dTPtlpNJva90Ysw14e7xN45latWcqu/CYfef63N0zyF0mTehN01BoVShN01Bl3kTR/ccivl1QtvXOtua2f/xx/z+wMfUtvXSUHs84c8jtBIbMoCluJ1PsePJ3yV87VAj0QwnhBCxkgAkRBqxtTfRUOO4MA1Jzpv/dJM/dR4Lbv5zFq37CQtu/nPUGWZUGX0/HXZ02VGpL8fn9aFQqFBrSlBrVtBuaU3odWeW5ye1Lltn0uNxhZ+R43E1ojPpg7/3T4luwOvNRaXORqmejFJ1E/b2zweEpXQRawhqt5zk2M4aXPbVGMw/wmVfzbGdNUkNQacPvMPOh27lxf+xmJ0P3crpA+8k7dqx6l/17e6p46zlNeYuWUBHcwc6Y3go1Rn906FYFVfMxrj2Pp73uPjJp1/xom8+nZW/QZXx51Rtqo46BDXUHmfnMy/x6q8eZ+czLwU/Lp5K7HhJCBJCpBsJQEKkkXZLK2rNiuA0JFlv/tOZ1qih1933xsjj7gVFJ6qMvgYwVUYhTpsrKa+XrBCUX1GOx7kdt/Oc/42w8xwe53byK/pqqANTIrUmA29vNwAK1SR6XZ0DwlI6iSUE+ffEpOYMn3bLCY7999/S9uzPubutiYP42NjWxOkXHxm1EOTfyzQbjWEL9vZfYc55i/Il0ympmEVOYQ4OW/g5QQ6bfzoUj+KK2djNc9At+j3myx/GlDcvpqlSYElej3UV2fk/pse6Khie/NXXA0+GGqoSOxGBECTShyx/ExOZBCAh0ojT5gqbhkBy3/yno/6HnCqV5+l1v44ua07wOb3uZrRGTdJeMzANSmRJnH9PTgEZ2jdxdv8HGdo3Ka8sCFuWFpgSGcxZeD0n8fZ24eutQ6FSDAhL6SbaEGRrs5KRgjN82i0n0O/cyA3HDrDZ6+V/4D/xKB94zuXkxObHE7p+Isxl07l01Rqu3LCeS1etYcrU6ew6aGHukgU4urfRYz2Dz9tLj/UMju5tzF2yIO7XSmSqNNSSvBX3P0CG9j5gN/4a9d0XKrEfiPtehxNohhNCiNEmP5IRIo1ojRo8rmbUmpLgY8l+859u+h9yajC7cNo1KFWL8Pl66XU343HtoKAiP+mvHVqQMHtO7NXCpoKyIffhBJrb1NobMBUZsLV+gNuxHXO5l0nz5qesMjtZoilGMOaacNmHP8On3XLS3wB3oeWtvHLoljdH9fusMphodvUwDVABa4A/Ad8FmtvS7430F21GFq+t5OiercEWuIUr42uBC8gpzKHHakFvmhJ8LNqpUkdzB9n5kcPT8nvuAOKrxD68awt7n3yU+pYGSgtKuPr+HzB/2eqoPycpRRh9cvaPmOgkAAmRRsxl+TTU7ABWoMooTOmb/3TS/5BTW3tfINIaNRRUJF6LPZhACPri6DGUSkVSm+JCm9t6XT3kTdWTXzEv7YNPqOFCkP98n6HP8AnsE9IYVmMwT8JlP8exnW8xZzmDhiBfWyNqezcaFJzFxzRgMtCCf+FWYW7kN9CnD7zDic2P09zWTGFuITPWPMjUy69P+OswnOIsHY1dDkoqZiX1PKC5SxZQtWkbcBM6YxkOmwVH9zYWrhx+qjRceAqtxI7W4V1b2PvoQzzrdPh7HJvrWf8v/5cDW3cyrfLKYWu/pRkufcjyNzGRSQASIo30n4ak+s1/uuofiABaTx+h7vB+XPZ6NIZSyucvIn/qvKS83szyfBwOB2dbupNelz3clGgkdbfUQe2nKK1teE25UHEZmQXDL8MLXQ7XPwT1ne8z+Bk+gbNzAlMi/68rqaveMmgA6uyx8cWRQ2RzNX/kI27DQy/QDdyt0TJjzYMDPub0gXc4/eIjbHQ5/W/O25q4+8VHAAYNQaGByZxlZuq0eWTrjShyi9FVXos5hoNhi7N07DpoYdnC5P37LqmYxeK1xDVVSiQ8DWbvk4/yrNMRPMlrKfBCr5vbvjxE1VeLePe5n5JpbuObDw4+TZIQJIQYbRKAxIjy/2S/NakHXo43kd78T3Stp49w6sD+4PlBLnsVpw5sAEhaCILUnRkUrXgDSrTXLqh+h6VaA3mZZs477eyufoeWyuujfo1pBcZBQ9BQy9kCZ+eEGmqfULvlJIe/OI3PV8wS1Hi5hv/iY3ZjpQYlC+78ccRAc2Lz42x0OcPenD/ncrJu8+MRnx8amLKBTV1tqD7bw7R5i3HrrOzauZH25etiCkEAuw5auDjXlpQDUYG4p0qJhKfB1Lc0ROiOgw5nEz7WAPPpbn+CP/7z43Q0NbD0zu9GvI6EoNEjy9+EkBIEMYImQsWzSI26w4Hw03dmibf3WeoO70/6ayWjICEegYCy1mnnLzLNrHXaKah+xx+KkqH2U5ZqDRRoDSgVCgq0BpZqDVD7aUyXCYSgWISenRMQaZ8Q9C2X63V/i0NsZCOX8gzdPMt6PuUT7Aw+zWlua4745nyw/UInNj/OcxcC00fAXwB/7vPS8eUnFBlMLDOYcFS/H9PnWpylw9pQO2j72kgrqZjF8nvu4M9+9CDL77kj4eV5pQUlEbrjwEgx4AKWAF/H6/09771wcMjPWZrhRo8sfxMTnQQgMWImYsWzSA6XvZ6+M0uOAL8B3sNld6UsQCfzzKCoxBBQmo5/xJE//A3vPfbnHPnD39B0/KMhL910/CM6P92O9fAumqp30N3qr2rO0+hRWttivtVYQ1D/s3Nc9rO47G9RXjl3wHMDtdpqXQWQSwv/yVleooV5QCeG3IpBX6cwtzDim/PB9guFBqYW/HuMJgO1Dhvvfvkp+786hPXwB7RbTkT9uQK0fF5Di/3apByImm6uvv8HbNDqQrrjYB0ZdPMgMAuwAkXA1bid84f9nKUZbmTJ9EcIPwlAYsRMxIpnkRwaQyn+t7JHgHeBbwJ3o1D9ecxTxNbTRzj05u/Zv/FnHHrz97SePjLoc0NDUKqDkNLaRp4m/FygSAGl6fhHtL/7LJusbTiBTdY22t99dtAQFHj+Go+Lu4HlLgee2kPYv9hL45mjOJTx/RQ+lhDU/+wcjWELc5bPjrhsLlCrXTzrUhTKN4FTwCTgM1Sae6lcc9egrzNjzYPcrdGGvTkfbL8QhAemAuAs8A7gUaq42e3kQVUGa9UZ6HdujCkEKWw9qHWlnKrvCj4W74Go6Wb+stVc/YNfsKGwFB0K/kyXzXn1aqASaAM2458CnUWjr4jqc5YQNLJk+iOE7AESI2giVjwny0TfO1U+fxGnDmzA23sH/oVKgGIzOSXzUWsuod3yelRfj6H2EmUWRz4AMhCCUr03yGvK5bzTToHWEHzsvKvHvxcoRPO+19jkcYVvQve4WLvvNYpmXTHguoHn5wPPA5cCq4GDtg4OqTWYbO10t9TFtddosD1BkQy3TyggUKttnuR/buPxLXgctah173H5Hfcy7fIVg35sYGncuihb4GaseZC7X3yE51xOrgD+G/gK+I65iBwUnPI4KamYxzJ1Bq9Wvw9R7gXyfw5NuFSldLcdhbqteDtqUOdYaaytoeHUCXY8+buQ+ukHYm5jG03zl60O1l431B5n17Mv80XVQ/h/MHEnkIlS9SaT55aTU9gR9XVlP5AQYqRIABIjZqJWPCcqsHdKrbkFjaEQj6uZhpodlMxumjAhKFB0cOrANry9BpTqbLKLyzDkFOLz9UY9RQzfSwR9e4k2MGeQABSQ8oKEisvYXf0OS/FPfs67etjttMOc8F0t561tEfe5nB9kKVvg+RnAS8Ax4DBwzOfl0kkzmanOYFPtpxBn2cJgIajdcgJH9fv42hpjalQLrdXOKZ2K0ZyBy97EnOV/F1WAmnr59VHXXvcPTOYsM1NUGbRq9bRlaFCXz0SflYvG58XX1hjVNUM/B7tjBtqmzaw06MhWdqHLN7Hl//2MLTX1eDwvAIvpaK7ijUfvAxgyBDXUHk9aqUKyHNq1NRjktIYC3K4P8XpcaPQVTJ5bjinni6gPgZVShNST5W9C9JEAJEaMVDzHx7936pbg5Mz/64qopx7jRf7UeTisSjyu2XFPEcP3EgUsvvD40OztjUztOIbS1smJM/vpzJvO15Ysj+EzGFpmQTktldezKbQFbs7iAZOZPFMuVda2YIQD/+LAvH6TokjP1wA/xr/U6xWNjiJjNl6fL659QKH6h6B2ywn0OzeyymAi31xIqz36RrWharVTccZP/8DUsPVJHHYrRYa+gobWHhuK3OKorxn4HM5s+m8WezspMeVTOLmETHM+Mz6swuxZQ0tICHc7n2LHk9+jeNpFA0IOwEdvvs3JQ53os1ZROv1SeqwOqjZtY/FaBoSg0FCSyunSoV1beePRx3A7nwIW47RXoVLfxcWLp6IzKskp7Ig5pAVCkBBCpJoEIDGipOI5dk6bC41B9k6Bf4p49vDL9DpL8Hq9KJVKVNoGJs8vjerjNYZSXPYq6Bcf/HuMBmdvb6Sk5kOu0+jIM2Rx3u3gzfpDfLKHpIeg4SYxhVfeyvp3n+UFj8t/1g2wXq2h8Mpbh31+LrAX+FihxFg2B+hbZpeMCu5ACHJUv88qgykYIooMJpZB1MvIIi2Xi+eMn3joKq9l186NLAPy9UZae2zsslvRXRVbiDCXTacnP5sFF11Ej8sLuKg9/Dk6hxc9x/HvZwtUuC+mo/lLqjZVo8tcRXZ+GT1WC+88+RQKhY7u9lz0pv+BwpdL3RdfMnlu8YVSha1hAaN/KIl2uhSPHU/+7sLr9AW5Xs/z1H/5Pf7mxc0JXVumQKmhVilkCiTEBVKCIESa0xo19LrDNwhP5L1TCoUeuASf71rgkgu/j075/EUoVRsgZJu8UrWB8vmLhvw4teUY12l0FGj0/oY2jZ6bc7LJPn9yRKuyAYpmXYH5GxtYa8pFC6w15WL+xoaI+3/6P///A36s1tBdNhtD3iRanHZ2O+3YzaUJV3AHDksF8LU1kq83hv15vt4Y0zIy8E+SGrY+Sf2zv+TcS//KP16orPYXofvP+Dmx+fGYrjkcc9kMepav41WDid+2N/OqwURPHGcBAShyi2ntseHsbufs0UY8zpl0qyrpYQ7+Mo9AAUcVWsMsdJk3hTXH2TrMWDsW4vF4UGsmo9Zmo9bMpPlsY8RShfBQ4v8q+adLv0voaxJJR8tXRJqm+h+Pn1Rjp96Rpu7RvgUhRp38TSNEmptoe6daTx+h7vB+XPZ6NIZSyucvCu4Bare0osu8BXVuYAlcKR5XbtTLAQPXqTu8YcD1HQ7HoB+ntHWSZ8gKeywvQ0ehu4tuGPGDU4tmXTFo4Bnu+d0tdWzrt8zOEFLBDfgruCGqvUHWFguttXU4rD30KFW8217PnNxiWhNcRtZ/Gd1eh41O+s9NBj/jJxHmshlRFx4MJTBNmt/Ugt4zF7Q+qvMMtLbkg28B8B7QSob2PkqmL0RnLAv7eI/bjY8s9Jl5uF11ZGimotZk4bA5cNgs5BTmhD0/VaEkIHQfklY/E6f9WeD+kGdUkVMw9F66aMkUKDVkCiSEnwQgIdLcRNo7NVRLW/7UeUlZDpg/dV4wCEXLa8zmvKuHgpCa6vNuB15jdlhV9kiGoHhFWmZnP7yTvExz2GPRnBFkbbFQV92CWnsz2sxiVK5GOo5v47MSH+Zea0LLyPovoyvTGVnosLGHvgA01Bk/6cBcNoP25et4/pnHyOjtxqgpgq/fxZzODE588jGunkfJKdSx4v7vc97STY/Vgt40Jfjx6owMfIouCsoXcfaLLcBq8GahymjH0X2AhSvDCwZyCi6io3ngEs9khJKG2uNhS/TKL76ak5/+Jz4vwAagigztfay4//sJv5bsBUq9I03dUoctJjQJQEKMARNl79RQLW35U+eNWpW6p2wO79V8yHX4Jz/n3Q7ecznwVFxG4JVnluePmRDUX7QV3P211tah1t5MhnYSABnaSeRk30R31yv03LyOV0Nb4K5aFdMyMl9bI/nmvnCTO2shBz7bwwmfFzf+8DPUGT/pwlw2A+38ZbR3rMSuL2dabhaZuZCdr0Vv6mD5PXcAgYCxDbgJnbEMh82CMacdheIg6oyZlM9ZROPJjditnzPja5NZtGb5gIKBFfc/wBuP3hfcA5TMUHJ0zyF0mauCAW3ynOsAqPviIZw9D1woXPh+UvcaBaZAJ2u+4IO399NU30ZRaS7X3LiI6bMvTtrrTDQyBRJCApAQYgQNtbwNhm9pC10O2OvppqfjUzyur8gq0mBrT10tuMFcTMPsq3jF4m+B8xqz8VRchsEcvqRrzIagKCu4+3NYe9Bmhn8N1JpierucfFHbwdWr7h/kI4en6LeMLmfSdFqcPWw/fRStw560FrhEtVtOUnvwMK6uHoy5Jsor5w4ocCivnEv3zu24e27A552Nw2bB0b0tbIJTUjGLxWvh6J6twRa461feAPgfczZ3MPPyHOYuuW/QZrVA+Njx5PdCWuCSE0o6mjvIzg9folc+awlZed/kz370ZsLX7y8wBTpZ8wUvP7GPzOzVFJSUY+2q4+UntnD7d5EQlCCZAomJTAKQEGJEDLe8DYZvaQssB2z66g9Ym/QoVRdTrC5A11KPtfVDHHNnkjdlbkru32AuhpDAM9TMaayFoGgruPvTmfS4nY3BCRCAx9VIfoE/tER7SGrEa0doY/s4K5eLf/Abrk7C/pxkaLec5NjOGpSaNRjMk3HZz3Fs51vMWU5YCArUYh/bv5mamheZc3EpC1cOrIguqZgVMdzEUiW9YNmqlNRe5xTmDFiiF2kfUrI9/cJuCrO/jSl7KsCFX1fzwdvbJAAlQKZAYqKTFjghxIgIX97mb6jyL2/bH3xONC1tRnMRGn02xrwruEzxCeuVLv5cM4U7Kabo6AHs7bE1jSWLrb0Jy5GjqM7V0XPmFAf37ByV+xhJ+RXleJzbcTvP4fP14naew+PcTn5FeVgrXDyS2caWKnXVR9EYVqIxlKNQqNAYJqMxrKSu+uiA55rLpnPVbbdy8bfXsvyeO0b9ENNYzV2yAEf3NnqsZ/B5e+mxnsHRvS3qg07jYdKq6WzuwGgKD+JGUzlN9YmdXSX8pBFOTFQyARJCjIhoDiEdqqUtlNPmIqfnC65VZZKn8k8b8jSFLHZ8yTuWY2GTmpFga2+iocaBWnMLGkMh2e5m2uu3cHDPThYm8ZygVOluqaOg+h2Wag3kZZo577Szu/odWiqvH3IKZCooo7wSWmvfxGHtQWfSUzKnHFNB31KpRKZAyWpjSxVbmxWDeRK9IT9Jz9BPwtZmHfLjdh20sGxh2ZDPSTeRluhFmmIlW3ZhDsfOHmfu1L5pj81aR1Hp0PvTxPBkCiQmMglAQogREe0hpNG0tGmNGjLOn8Gs6VuO4+u1ka/VobR1Jnyv9vZG1KH7fcrmDNjvE6rd0opac0uwnEGtKcGcs5rO8y+MjeVwCdRgmwrKwgJPqGkFRk612BIKQenMmGvCZT+HUtP3PezuOYcx1zToxxRn6WjsGrxyPZ0NtkQvlRZcdxm7X9qGtdOA0VSOzVpHd+cWblp75Yjex3gme4HERCRL4IQQIyLeQ0gjMZfl41B00uZuxocXb68Vb28tdoMarzE7ofu0tzdSUvMh33b18IAhi2+7eiip+XDIpXVOmwtVxsB67ky1/2dMI31YaqyU1jbyNOEHykZTgx2NRJfCpbPyyrm47G/hstfh8/Xisp/FZX+L8srh96HtOmgZgTsc+0oqZnH5rfNpdr9CS8PDmLK2cft3r5T9P0miVilG+xaEGBUyARJCjIhol7dFw2guwjF3Jh8cPcBix5fka3U4MtXsVSrwlM0ZsqBgOGrLMa7T6IJn/hRo9FwHvDLE0rqh6rnLyvP5sq41rSdB8dZgx2I8ToEC5Qa1Bzdjb/e3wE2/amALXH9jeQo0GmbMvpiiaTPlYNQUkimQmGgkAAkhRkw8h5AOJm/KXLqy8ngnhqVqQ7F3NNPaYsV4upYMXSaubC8avX96kZcx9NK60HpuVUYhve5mPK4dFFT4D0mdme4hKM4a7GiN56Vw5rLpzM2fhE6ni/ljx+JeoNEUOBdIJJfsBRITkQQgIcSIOn/6M9oP76LN3kmuIRvz/GXkTb00rmvFUk09FFt7Ey0nPGj1t+DR62hzNeNtbSIz34ZGb+S82zHk0rpAPXe75XWcNhdao4aCivywc4nSOQTFW4Mdi0AISsSpAzuo3vw89rZaDLkVVK65i2mXr0jSHY4smQLFJnAukEgdmQKJiUQCkBBjTKwb9NPJ+dOfYTuwhVd63f5z6u2drD+wBSDuEJQM7ZZW1BmrUWtK6M66lg9aN3ENRSg7z9KpUvKey4Gn4rIhA5bRXDTsQayJhCBri4XW2rpg21p+Rfmg5QPxyCwoH7bwIBninQKdOrCD/S8+Ta/raWAx9rYq9r94L8CYDUEgU6BYyRQoNWQKJEZCT91ZlC5nwtfxZGZDZWLXkAAkxBgS2KB/nUZHniGL864e3qv5kIbZV42JENR+eBev9LqDPXBLgRd63Xz78K5RDUBOmwulxv+mKkM/na/y19LQ9T7qni8wagrxVFyWtK9vPCHI2mKhrroFtfZmtJnFuJ2N1FVvp7ySpIageDQe30/tvndwWuvQmsqpuPJ6imdFLrZIZClc9ebnL4Sfvu+eXtfTVG9+YMwGIJkCxUamQKknUyCRSh2NXhSO3oSv48vxkpHgNaQFTogxJHSDvlKh8G/Q1+hQW46N9q1Fpc3eGeEkIP/jo0lr1OB1Nwd/n6Gfjs38TWxTr0Azb2nSw+XMcv/eoGjb4Vpr61BrbyBDOwmFQkWGdhJq7Q201tYl9b5i1Xh8P8fffRun9WnAgdP6NMfffZvG4/sH/Zh4W+HsbbVEOkfK/3jqtFtO8tnWzex79gU+27qZdsvJpL+GNMLFZntN8/BPEjGTRjgxkUgAEmIMUdo6ycsI32w93Ab9dJJryKaq32NVFx4fTeayfDzunXhcDfh8vXhcDXhcOzCX5afsNWMJQQ5rD2pNeAhTa4pxWHtScWtRq933Dl7PM/inMhnAUryeZ6jd986wH7v3g4MxvZYhtwIifPf4H0+NdstJju2swWVfjcH8I1z21RzbWZPUEFScFXt5wkRm0srClVRSqxQcaeoe7dsQIuUkAAkxhniN2Zx3hy+ZGW6DfrRs7U1Yjhzl5EeHsBw5iq29KeFr9meev4z1qoyQk4BgvSoD8/xlSX+tWBjNRRTMUKPWvI7L/hhqzeuUzNYNu6cnUdGGIJ1Jj8cVfg6Rx9WIzqQf5CNGhtNaR6SpjP/xwcUzBapccxcqzb2EniOl0txL5Zq7Yr5WtOqqj6IxrERjmIxCoUJjmIzGsJK66qNJfy2ZAgkhxMiRACTEGOIpm8N7Lgctrh68Ph8trh7/Bv2yOQld19beREONA4/rFjSG7+Nx3UJDjSPpIShv6qUYL1/Ntw3ZaIFvG7IxXr56VPf/BBhyCimbN5fpVyygbN7clIefgGhCUH5FOR7ndtzOc/h8vbid5/A4t5NfkfrSgqFoTeVEmsr4Hx/atAJjTFOgaZevYNGd92LIfQDQYch9gEV33pvS/T+2NisZ+klhj2XoJ2Frsyb1dWQKFBuTVi3L4FJIpkBiIpBZshBjiMFcTMPsq3gltAUuCRv02y2tqDW3BA/y9P+6gnbL60kPAnlTLx31wGNrb6Ld0hqsrDaX5aPSj94yvOGKEUwFZZRXQmvtm8EWuJI5yW2Bi0fFlddz/N17LiyDWwxUoVTfQ8WVN0Z9jVgKEaZdvmJECw+MuSZc9nNoDJODj7l7zmHMNaXk9aQRTgghRoYEICHGmGSdfRPKaXOhMYRXy6oyCnHaXEm4enoJTLvUmlvQGArxuJppqNlB7jQnuuLJw18gRaIJQakIPInUawfa3mr33RvSAnfjoC1w/SXjbKBUKq+cy7GdbwErydBPwt1zDpf9LaZfNTfpryWNcLEJTIGkEjs1AlMgaYQT45UEICEEWqMGj6s5OAEC6HU3ozUmI16ll8GmXV0Nr5A7igEI+kLQSElGvXbxrEVRB57BRDsFarecpK76KLY2K8ZcE+WVczGXTU/a8/szl01nznKoq94SvMb0q2K7hhBCiPQjAUgIgbksn4aaHcAKVBmF9Lqb8bh2UFCRuha00TLYtKvH6h6lOwo3szw/roNS4+Gv176ZDK1/n4v/1xtorX1zxJbXRTsFCjSyaQyrMZgn4bKf49jOt5iznIiBJPB8p1VLz6nnOeWop26niak33sncG++O+v7MZdNHLPAUZ+lkGZwQQoyAlJQgeL1efvKTn3D77bdz9913c+bMmbA/37p1K9/+9re54447+MlPfoLX603FbQghomQ0F1EyWzfiLWijQWvU0OsO30Dd625GY0j0WLWxJ13qtaMpRIi1ka2u+ihOqxrf8V/xR8c5nPh4zdVF09bfc/rA8DXdQgghxq+UTIB27tyJy+Xi5Zdfprq6mkceeYTf/va3ADgcDv7jP/6DLVu2oNfr+cEPfsDu3btZtmx0anCTvdwk0OgkxFhjNBeNy8DT32DTrtxp5tG+tTDDTYES2bsToDPpcTsbgxMgGN167aGWwtnarBjM0Tey2dqs9Jx6nj96e1h64bGlwAteD+s2P87Uy69P4p0nl0yBRDqQfUBiPEtJAPrkk09YsmQJAJWVlXz++efBP9NoNLz00kvo9f7/g/V4PGi12ojXcTgG3xB6uik5NaQXz02sPjjUF0ePUXOmJaaPmVqUmjahiczr9Q35vSMmNpU+m9xpTroaXqHH6kZjyCB3mhldVkHafN9MLsjkdJN10PuxnT9H/WftqLWrUOmKcNiaOH1wO6WXOjHmTYr4MZFklRVS/9lb9HpuQKUpotfVhMe5nbzphUn/WrScOMjZj9/F1W1Bk1nG5K9/g4IZfWGnxKSivtM96OtqsvT0WM+iMfRVbLvsdWiy9BE/RpOlp8NRH+GUImhua07q5+f1epN2vRwNtDl9OHrS43sxnflQps1/s/FK5vdOKijVGTgco3vgshCpkJIA1N3dTWZm308MVCoVHo8HtVqNUqkkP98/JXnuueew2+1cffXVEa9ztmXwHnqlUjEia+RjcdnXFsT8MdGcAh9KJkzDczgc6HRyroYYnK548oDCg3T7vlEqu6k5VhPx77kGSzNaY8jenYzJuNUr6bK8Sd6k6PardLfUobV8zuTeOqzt+2nTFGMqLCV/XvLrtRuP76d2z65gXbaru4raPfeQkZERVqCgsPbyyYHPI06BKhbO59jO7XjVfY1sXtd2Kq6ZH/HfW8XC+TS+Z6LK1RWcAIH/1KLC3MKk/rtO9veO0uVAp0+f78V05XZ60uq/2Xik2987/Xl6feh0o3vgshCpkJIAlJmZic3Wt6nV6/WiVqvDfv+rX/2KU6dO8dhjj6FQKCJeJ90CTirE+jkOFZgkHAkxfgzVCOew9qDNjH/vTndLHQXV77BUayAvv4zzrh52OztoqbiczBSUH9Tue+dC+OlbjOb1PEPtvnvDAtBQhQixNrKZy6Yz9cY7Wb/197zg9Vw4pQju1miZsebBpH5+ySZlCEIIkVopCUCXXXYZu3fvZuXKlVRXVzNz5sywP//JT36CRqPhN7/5DUplSnoYxq2hAlNoOJIwJMT4EGkvUMJ7d2o/ZanWQIHWAECB1sBSYFPtp1BQPvTHxsFprYMIi9H8j4cLFCJEmgLF2sg298a7MeYWsW7z4zS3NVOYW8iMNQ+m9f4fIYQQqZeSALRixQr27t3LHXfcgc/n4+GHH2bLli3Y7XYuueQSXn31VRYuXMg999wDwIYNG1ixYuRO9x6vQt8k9Z8USSASYuwZbAqUX1FOXfV24AbUmmI8rkY8zu2UzIkuvCitbeRlhpc+5Gn0KK1tybjtAbSmcpzWKui3GE1rGvx+oz0baDhTL79+zAYemQINzur0yCGoI0SKEMR4lJIApFQq+dnPfhb22PTpfT+1q6mpScXLihD9w1DomygJQ0KMLf2nQKaCMsorobX2zWALXMmc6PfueE25nHfagxMggPOuHrym3CTfuV/Flddz/N17gnuAoAql+h4qrrwx4vOjPRtoPCvO0tHYlb6b48XEoFYp8PT6Rvs2hEg6OQh1ApAwJMTYNdgUyFRQFn9ZQcVl7K5+h6X4Jz/+PUB2mNN/mVpyBPb51O67F6e1Dq2pnIorbwzb/xNJsqZAQgghRCgJQBOMhCEhRGZBOS2V17Op9lOU1jb/5GfOYjJTsP8noHjWomEDT6h82vnqyEn2nT6OMddEeeXghQfjmSyDE0KI5JMANIFJGBJibJhZnj/swaixyiwoT0nhQTJYWyzUVbfg7b2F1q4iMnQ+ju18iznLGVMhqN1ykrrqo8HWulhDnCyDE0KI1JAAJICB7XLSKCeESAVri4XW2rrg3qX8ioF7l1pr61BrbyZPO4l2mxuNoRRYSV31lmEDRLvlBI7q9/G1NaLILUZXeS3mshkp/IwGu4+THNtZg8awGoN5Ei77uTEZ4oQQYjySDuoonWqxTahNuZULKoP/fFnXGvaPEGLkBaZAY1lgsuN23ow2869wO2+mrroFa4sl7HkOaw9qjf+cI7Mxg7Nn6snQT8LWZh3y+u2WE+h3buTP7Fa+Zy7kz+xW9Ds30m45kbLPaTB11UfRGFaiMUxGoVChMUxGY1hJXfXRmK4TOBNIiNGiVik40jT4wfRCjEUTegIUS6AJbMTd+8HBAX82rcCYtHtKR7JUTgiRDIHJTuD8Iv+vN9Ba+2bYFCjSOUdnThxi6kWmIa/vqH6fVQYTRQb/84oMJpYBr1a/DyM8BbK1WTGYJ4U9Fk2IE0IIkXrjMgDFE2wSef5ECkUShoQYXcneCzSSHNYetJnFYY+pNcU4rD1hj/U/5yhT3UyHbTvllVcPeX1fWyP55vCzYfL1RnxtjTHdZzKW0RlzTbjs59AYJgcfc/ecw5g7dIgbjJQhCCFE8oyZAJTKUJOoiRqKJAwJMbIGq8QeKyJNdjyuRnQmfdjzIp1zlDUrny9q27l6iAygyC2m1W4NToAAWntsKHKLB/+gfgLL6FYZTOSbC2m1W9m1cyPty9fFFILKK+dybOdbwEoy9JNw95zDZX+L6VfNjfoaAYOVITTUHufonkN0NHeQU5jD3CULKKmYFfP1hRBioknrANQ/9Iyl8yAmWigaLAxJEBIi+cbqFKj/ZMfjasTj3E7JnIFtdJHOORruB2G6ymvZtXMjy/BPflp7bOyyW9FdtSrqe0zWMjpz2XTmLIcvP3iW5iP1+Hxe8qcVA7OjvsZQGmqPU7WpGl3mKrLzy+ixWqjatI3Fa5EQJIQQw0jrADSWAk80JkooCrwxkyAkRPKN5SlQpMlOyZyBLXCDmVZgHPJwVHPZDNqXr+PV0OVrV62KaXKTrGV0Ab2ufApnbAhOgRJpggtdBnd0zyF0mavQm6YAXPj1Jo7u2SoBSKTEkaZu5hVljvZtCJEUaR2AJoLxHIokCAmROmN1ChRpshOr4UJQIoUHyVhGF+Bvglsd3Afk/zW6Ou/++i+D62juIDs//OuoM5bR0dwR830KMRy1SoGn1zfatyFE0kgASkPRhiIYG8FIgpAQyTWWp0CJmlZgTOmRBMlYRheQyia4nMIceqyW4AQIwGGzkFOYk/C1hRBivJNzgMaIq69ZOOAf6DufaCycURQ4VwiYsG/ehEimsX4uUCIG+6FQosxlM+hZvo5XDSZ+297MqwYTPTEWIAQYc024e86FPZZIExwQPBNo7pIFOLq30WM9g8/bS4/1DI7ubcxdsiDuawshxEQhE6AxLHRStPeDg2EhKJ0nQ5ULKoPTIJkECREfmQKl7oc+iS6jC0hmExyEL4MrqZjF4rVwdM/WYAvcwpXSAieEENGQADRODBaG0jUIhS6LA1kSJ4QYfwJNcHXVW7C1WTHmmph+1dy4ChAiKamYJYFHjAhPr08KEMS4IgHogkhnLAynOEuXgjtJXCAMjYWpkEyDhEjMWC1DmCjMZdOTFniEEEIkx7gLQPEEmYBYTtneddAS8bXSKRSNlamQhCAh4jPelsFZWyy01tYFK7LzK6KvyBZCpIa0v4nxKK0DUDxhJpYQk4hIr5POoSjdp0ISgoSY2KwtFuqqW1Brb0abWYzb2Uhd9XbKK5EQJMQok+VvYrxJ6wA0UmEmWQa730BrT6jRCkXpPBWSECRE7GaW54+LZXCttXWotTeTofXXRvt/vYHW2jclAAkhhEiqtA5A48Vg06JIRjIYpeNUSEKQEBOTw9qDNjP8sFG1phiHtWeU7kikK6vTww2zC0f7NiYEKT8Q45UEoFGSTkvo0m0qJA1xQsRurE+BdCY9bmdjcAIE4HE1ojPpR/GuhBBCjEcSgNJIOoSidJoKyTRIiOiMhzKE/Ipy6qq3Azeg1hTjcTXicW6nZE75aN9a2tl10DLmloiLsUfKD8R4JgEozUW7ryjZgShdpkISgoSYGEwFZZRXQmvtm8EWuJI50gLXX+hhqEKkmix/E8n0xcl2em2JL2vWFMIlCV5DAtAwrE5P2O9N2vT4koUGo9ApUSomQ/3DUMBIhSEJQUJEZ6wvgzMVlEngEUIIkXLp8W4+BfoHl0SEbrbcXtMc9mfpEIgCYSjVQQgiL5EbiSAkIUiIoY2HZXBCiPQg5QdivBv9d+9DSCTEpKohpv91+wciGL1QNBpBCEZuKiTlCEIIIYQQIlFpHYDGQs1lpEA02svmRjIIwchPhWQaJMTgxvoyOCHE6JLyAzERpHUAGovSKRD13ycEIxOEoG8qlKogJCFIiIEm0jK4aQVG9n5wMOzvHSFEcsjyNzHeSQBKsUhTrNHYRxQ6FYKROVsoMBGSECSE6G6pg9pPUVrb8JpyoeIyMguk4loIIcTIkwA0CkZzH9FIBqHQEASpmQZJCBIi3Mzy/LRbBtfdUkdB9Tss1RrIyzRz3mlnd/U7tFReLyFogmioPc7RPYfoaO4gpzCHuUsWUFIxa7RvS/Qj5QdiopAAlAZGY9ncSAWh/vuDUhWCoK8cYXKB/OUtRFqp/ZSlWgMFWgMABVoDS4FNtZ+CBKBxr6H2OFWbqtFlriI7v4weq4WqTdtYvBYJQUKIUaEc7RsQA90wuzDsH/A34oX+kyzLFpaxbGEZjV2OlB6uFwhCgWlQKgSC0Okma8peQ4ixIvADgXSgtLaRp9GHPZan0aO0to3SHY1txVm6AYdhp7Ojew6hy7wJvWkKCqUKvWkKusybOLrn0Gjfmggh5QdiIpkwE6Bk/4etVimSer2hjMQ+ov4TIUj+VGiklsR9+skhWRInJrR0K0PwmnI577QHJ0AA5109/r1AYtzraO4gOz/8gFudsYyO5o7RuSExKFn+JiaKtA5AyQwtyf6P+khTd9jvRzIQwcDDWQNToWQGoVRUaI/EkriL586h5liNhCAh0kXFZeyufoel+Cc/51097HbaYc7i0b4zMQJyCnPosVrQm6YEH3PYLOQU5ozeTQkhJrS0DkDp/JOI/vc2moEoEIbGWhBK9b4gKUcQE126lCFkFpTTUnk9m0Jb4OYslgKECWLukgVUbdoG3ITOWIbDZsHRvY2FKxeM9q2JC6T8QEw0aR2AxpJ0CEQjEYTGWggC/5tACUFiokm3ZXCZBeVSeDBBlVTMYvFaOLpna7AFbuFKaYETQoweCUApEhqIjjR1hy3nS3UY6h+EktEgt2xh2ZgMQQEyCRJCiNFTUjFLAo8QIm1IC9wImFeUGfwH/KPmwD+pFNoglwyBaVCy2+JS3RCXDkuAhBBCiHQky9/ERCQBaISNdBgaayEoldJpOZAQQgghhBgdEoBG0UiFobEUgmQKJERyfFnXOq6/71N5ppgQQojxbUIEIJ/HldR/UiHVYWishCBI7VI4mQIJMX6MxOQ4HTV2OYJ/BwuRCDn8VExUaV2CkKywkUfy3lCfxxi8L4Vac2Cl8gAAEiRJREFUk7TrhhqsQCHR8oQbZhemfTHCSJQiSCGCEEII4Sf7f8RElNYBKJnBJVlC7+l8yDBlpMJQQLxhKLQhDpJbk53sEJQKgfOBhBBCCCHExDQhlsClSh62YCBK5fK4gNBlcokukUvFkrhkL4eTpXBCCCGEECLZJAAlQSAI5WFL+V6hgEj7hWKVziEo1dXYIK1wQgghJi6pvxYTmQSgJButqRDEt5lxLISgVAi0Y0kIEkIIIYSYWCQApUikIJTKMDSeQ5BUYwshhAgV2McqhBDxkACUYqHL4yC1U6HxGoJAlsIJIfrIGUATWzJaTCc6qb8WE924CkBeW+eI/BOvkZgKpVMIguScE5TK/UCyFE6MRxPh+3mingEkRLLI/h8xkaX1j1FiDhtNp1NyH2GKpgbvS2nMjusSYVXaKThXKPCXWqA2O5bK7NCa7GRUZCfrnCCpxhYiNrLEUwghhIgsrQPQiASaWAXuKQlBCPrCUGgQguSEoXlFmcGDVGM9NyhwaCokttwg2YelygGpQoiJLNnHDQghxEQ0rpbAjaim08F/krk8Ltl7hdJhSVzgsNRE/49blsIJIUTf36lCxEP2/wghASg5AmEIEg5CkPy9QukUghI1EtXYQgghxHgm+3/ERCcBKJlSFISSMRVKlxCUrFKEVFZjyxRICCGEEGL8kgCUCkleHgfJOWA1cGiqp9cXcxBKZkNcstawSzW2EEIIIYSIlQSgVEvhVCje5XHxToOSEYJkP5AQIhFyBpAQQohEpXULnKe1YbRvISJ1fknsH5Tk9jgY2CAXS3NcvA1xgXY4q9MTdztcsprhpBpbiIlJzgASQgiRiLQOQLZzTaN9CwMYJxUFg1lCQQjwFk0N/u9Eq7RHOgQBCdVkJ7MeW6qxhRDp7NSBHVRvfh57Wy2G3Aoq19zFtMtXjPZtiQnI0+uTAgQhkCVwMbOdawoGs4QnVP2WxyUidH9QLJJRjhCvZDTDSSucEOG+rGuV7900curADva/+DT2tt8BDuxtv2P/i09z6sCO0b41IYSYsCQAxSlpIQiSduBrIATFSn4aJIQQqVG9+Xl6XU8DS4EMYCm9rqep3vx8zNdq7HLIGUBCCBGBx+Nh5cqVLFiwgIULF/Lhhx8O+XwJQAlI9hK9RKdAQggh0ou9rRZY3O/RxRceF/FIRhvpRCQHoIrx7NFHH8XtdnPo0CH+5m/+hh/96EdDPj+t9wCNFZ7Whvj2A4VqOg0he4KEEEKEO9ViG3MFCIbcCuxtVfgnQAFVGHIrYrpOso4PGC8SXYI9UcmKDzFalEol7c2t2M7WJ3ytHNVMlMrwGc6+ffu49tprAVi7di3/8A//MOQ1JAAlyHauCeOkotG+DSGEEGmocs1d7H/x3gvL4BYDVag091K55t6YryXL34QQY1V+fj6T7/02nz/zZsLXmrzhNvLzwwuq7HY7OTk5YY85HA50ushFWxKAhBBinJCzq9JPoO2tevMDIS1w98bUAifTnz5Wp0emP0KMQYWFhRRcOgtDQS72lra4r5M1uYSsySUDApDBYKCzM3wryWDhB2QPUFLYzjUl7cyisbYP6IbZhbIeW4g0Ig1w6Wfa5Su45RfPsP43e7jlF8/EVYEt0x+RCKm/FqNNrVZzdvd+KlYuSeg601ddx6m3qwYsgbviiit47733ANi0aRPZ2UMfLyMToHSShH1Aedg47yGm84Cg70ygWM4DEkKIkXKqJb6WSzF+yA/bhBjbbnvor/h47764p0CB6c8N37ljwJ/98Ic/5P333+eyyy7D5/Px7//+70NeSwJQktjONWEkzsNRRVqqPlQ92rcghAgx1goQkkGqr8PJ8jchxq7QKVA8e4EC05+rly8d8GdqtZq33nor6mvJErg0NNaWwY1nM8vzh3+SEEKIlJLpT/xk+dv4E+uh9+nktof+KrgXKBaB6c+d//J3SbkPCUBJlvBeoCQdiiqEmFi+rGuV/T/jjJQfhJPpjxBjO/xA/HuBBtv7Ey8JQEmU7INRhRBCTOz9P7L8TQgREAg/eYztvxNjnQIle/oDEoBSIlmNcBOF/JRTCDGcibj/R/hJ9XX8ZPnb+DPWww/EPgVK9vQH0jwA2U+fDv4zViRrCjRR9gHJTzeFEGIgKT8QQoTyeVzjIvwERDsFSsX0B9I8ALXX99Je3wuEh6GxEIgSmgLJPiAhhBBCyg+EYPyFH4h+CpSK6Q+keQAKCAShQBiC9J4OjfZeoDxsY36TnBAielKAML7IsuBwsvwtPp5e32jfgkiC8Rh+AoabAqVq+gNjJACFCg1DY3U6JIQQIjqnWmwTcv+PLH+T6U8yyP6fsW28/zB7uClQqqY/MAYDUH/pOh2ynWtKeBncSO8DmleUKT8xEkIIkTZk+iMmqvHS+DacwaZAqZz+wDgIQKFkOiSSpfpQ9WjfghBiApLlbyIZ5IeZY9tECT8w+BQoldMfAHVKrpomQqdC5lIVwIAQZJg6NaX34GltQJ1fktLXEKkxszx/tG9BCDEByfI3qb5OBln+NjZNpPATcNtDf8XHe/dhKMjF3tIWnP7c8J07Uvaa4zoAhQoNQxA5ECU7DNnONWGcVJTQNby2TpTG7CTdkRBivBnPBQgT+QDUsaCh9jhH9xyio7mDnMIc5i5ZQEnFrNG+LSHGrIkYfiB8CvT5M28Gpz9XL1+autdMxUW9Xi8//elPOX78OBqNhl/84hdMmTIl+Ofvvvsu//Vf/4Varea2225j7dq1qbiNIY3kdCjuKVDTaShKzj2kmtXpwaSdMHlaCDFCJlIBwlg6+6eh9jhVm6rRZa4iO7+MHquFqk3bWLyWhEOQlB8kRpa/jU0TNfwEBKZAxQvnpnz6AynaA7Rz505cLhcvv/wyP/zhD3nkkUeCf+Z2u/mnf/onnnrqKZ577jlefvllWlpaUnEbUYu0dwiSU6Yw2pXYI0GWKQghxMRydM8hdJk3oTdNQaFUoTdNQZd5E0f3HErK9eX/VxIjy9/GlokefqBvCjTvvttSuvcnQOHz+ZL+o4J/+qd/4tJLL+Wmm24CYMmSJezZsweAmpoafvWrX/Hkk08C8PDDD7NgwQK++c1vhl3jk08+SfZtCSGEEEIIMS587WtfG+1bSCqPx0NTUxMlJSUpD0ApWbPU3d1NZmbfTx9UKhUejwe1Wk13dzcmkyn4Z0ajke7u7gHXGG//UoUQQgghhBCRqdVqJk2aNCKvlZJ4lZmZic3WN8bzer2o1eqIf2az2cICkRBCCCGEEEKkSkoC0GWXXcYHH3wAQHV1NTNnzgz+2fTp0zlz5gwdHR24XC4OHjzIggULUnEbQgghhBBCCBEmJXuAAi1wX375JT6fj4cffpgvvvgCu93O7bffHmyB8/l83Hbbbaxfvz7ZtyCEEEIIIYQQA6QkAEVrLNRli/Q03PfO1q1beeaZZ1CpVMycOZOf/vSnKd9QJ8aG4b53Av7+7/+e7Oxs/vqv/3oU7lKko+G+dz777DMeeeQRfD4fBQUF/OpXv0Kr1Y7iHYt0MNz3zebNm3n66adRKpXcdttt3HnnnaN4tyIdHT58mH/913/lueeeC3tc3icnwDeKtm/f7vs//+f/+Hw+n+/QoUO+Bx98MPhnLpfLt3z5cl9HR4fP6XT6br31Vl9zc/No3apIM0N97/T09PiWLVvms9vtPp/P5/vf//t/+3bu3Dkq9ynSz1DfOwEbN270rV271verX/1qpG9PpLGhvne8Xq9vzZo1vtOnT/t8Pp9v06ZNvpMnT47KfYr0MtzfOVdffbWvvb3d53Q6g+97hAj43e9+51u1apXv29/+dtjj8j45MaP6I/FPPvmEJUuWAFBZWcnnn38e/LOTJ08yefJksrOz0Wg0fO1rX+PgwYOjdasizQz1vaPRaHjppZfQ6/WAv1ZRfgorAob63gE4dOgQhw8f5vbbbx+N2xNpbKjvnVOnTpGTk8MzzzzDXXfdRUdHBxUVFaN1qyKNDPd3zqxZs7BarbhcLnw+HwqFYjRuU6SpyZMn89hjjw14XN4nJ2ZUA9BgddmBP4umLltMTEN97yiVSvLz8wF47rnnsNvtXH311aNynyL9DPW909zczK9//Wt+8pOfjNbtiTQ21PdOe3s7hw4d4s477+Tpp5/mo48+Yt++faN1qyKNDPV9A3DRRRdx2223cdNNN3HdddeRlZU1Grcp0tQNN9wQbFIOJe+TEzOqAUjqskW8hvreCfz+n//5n9m7dy+PPfaY/ERNBA31vfP222/T3t7OAw88wO9+9zu2bt3Ka6+9Nlq3KtLMUN87OTk5TJkyhRkzZpCRkcGSJUsG/KRfTExDfd/U1NTw3nvvsWvXLt59913a2tr405/+NFq3KsYQeZ+cmFENQFKXLeI11PcOwE9+8hOcTie/+c1vgkvhhIChv3c2bNjAa6+9xnPPPccDDzzAqlWruPXWW0frVkWaGep7p7y8HJvNxpkzZwA4ePAgF1100ajcp0gvQ33fmEwmdDodWq0WlUpFbm4uXV1do3WrYgyR98mJGThTG0ErVqxg79693HHHHcG67C1btgTrsn/84x9z//33B+uyi4qKRvN2RRoZ6nvnkksu4dVXX2XhwoXcc889gP+N7YoVK0b5rkU6GO7vHSEGM9z3zi9/+Ut++MMf4vP5WLBgAdddd91o37JIA8N939x+++3ceeedZGRkMHnyZG655ZbRvmWRxuR9cnKMag22EEIIIYQQQowkORhFCCGEEEIIMWFIABJCCCGEEEJMGBKAhBBCCCGEEBOGBCAhhBBCCCHEhCEBSAghhBBCCDFhSAASQogx5quvvuKBBx7g7rvv5rbbbuP//b//x1gq9HQ6nbzyyiuD/vnDDz/Mxo0bR/COhBBCTCQSgIQQYgzp6uriBz/4AX/7t3/Lc889x6ZNm/jyyy956aWXRvvWotbS0hIxALW1tfHnf/7nvPvuu6NwV0IIISaKUT0IVQghRGx27drFokWLmDp1KgAqlYp//ud/JiMjA4BHHnmETz75BIBVq1Zxzz338OMf/xi1Wk19fT0ul4uVK1eye/duGhoa+M1vfkNDQwOPP/44SqWSlpYWbr/9dtavX88XX3zBz3/+c1QqFVqtlp///Od4vV5++MMfUlxcTF1dHfPmzeMf//EfsVqt/N3f/R3t7e0APPTQQ8yaNYvrr7+eyy67jFOnTpGXl8djjz3G448/zokTJ/j1r3/NX/7lXwY/N5vNxve//30++OCDkf2iCiGEmFBkAiSEEGNIc3Mz5eXlYY8ZjUY0Gg27d+/GYrGwadMmXnzxRbZu3crx48cBmDRpEk899RQVFRVYLBaeeOIJrr/++uC0pampid/+9rds2rSJP/zhD5w/f56HHnqIn/zkJzz//POsW7eORx55BIDTp0/zy1/+kldeeYUPPviAlpYWHn/8ca644gqee+45fv7zn/PTn/4UgLq6Ov7X//pfvPzyy7S1tXHkyBEefPBBZsyYERZ+AMrLy5k/f36Kv4JCCCEmOpkACSHEGFJaWsoXX3wR9lhdXR2NjY2cPHmShQsXolAoyMjIYP78+Zw8eRKAiy++GICsrCwqKiqC/9vlcgGwYMECNBoNABdddBFnz56lubmZOXPmAPD1r3+df/u3fwNg8uTJZGZmAlBQUIDT6eTLL7/ko48+4k9/+hPgX6oHYDabKSkpAaCkpASn05maL4wQQggRJZkACSHEGLJ06VL27NnD2bNnAXC73TzyyCN8+eWXTJ8+Pbj8ze12c+jQIaZMmQKAQqEY8rrHjh2jt7eXnp4eTpw4wZQpUygsLKSmpgaAjz/+OLjsLtK1Kioq+M53vsNzzz3Hf/zHf7B69epBn6tUKvF6vfF9AYQQQogEyQRICCHGkMzMTB555BEeeughfD4fNpuNpUuXcuedd6JQKDhw4AC33347brebG2+8kblz50Z1XY/Hw3e/+106Ojr43ve+R25uLr/4xS/4+c9/js/nQ6VS8fDDDw/68Q8++CB/93d/x6ZNm+ju7h6wvC1UXl4ebrebX/3qV/zoRz+K+WsghBBCJELhG0vdqUIIIZJu//79vPTSS/z7v//7aN+KEEIIkXKyBE4IIYQQQggxYcgESAghhBBCCDFhyARICCGEEEIIMWFIABJCCCGEEEJMGBKAhBBCCCGEEBOGBCAhhBBCCCHEhCEBSAghhBBCCDFh/P8TOOwcZAJo9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "\n",
    "cm = plt.cm.RdBu\n",
    "\n",
    "# make data for decision regions\n",
    "xx, yy = np.meshgrid(np.linspace(0.0, 1, 20), np.linspace(0.0, 1, 20))\n",
    "X_grid = [np.array([x, y]) for x, y in zip(xx.flatten(), yy.flatten())]\n",
    "\n",
    "# preprocess grid points like data inputs above\n",
    "padding = 0.3 * np.ones((len(X_grid), 1))\n",
    "X_grid = np.c_[np.c_[X_grid, padding], np.zeros((len(X_grid), 1))]  # pad each input\n",
    "normalization = np.sqrt(np.sum(X_grid ** 2, -1))\n",
    "X_grid = (X_grid.T / normalization).T  # normalize each input\n",
    "features_grid = np.array(\n",
    "    [get_angles(x) for x in X_grid]\n",
    ")  \n",
    "\n",
    "\n",
    "# angles for state preparation are new features\n",
    "predictions_grid = [execute_circuit(var, angles=f, bias=bias, shots=10000) for f in features_grid]\n",
    "Z = np.reshape(predictions_grid, xx.shape)\n",
    "\n",
    "# plot decision regions\n",
    "cnt = plt.contourf(xx, yy, Z, levels=np.arange(0, 1.1, 0.1), cmap=cm, alpha=0.8, extend=\"both\")\n",
    "plt.contour(xx, yy, Z, levels=[0.0], colors=(\"black\",), linestyles=(\"--\",), linewidths=(0.8,))\n",
    "plt.colorbar(cnt, ticks=[0, 0, 1])\n",
    "\n",
    "# plot data\n",
    "\n",
    "ce = cost(var, features, Y)\n",
    "plt.title(\"$p$, probability the model guesses for the correct class = {:0.7f}\"\n",
    "         \"\".format(np.e**(-ce)))\n",
    "\n",
    "plt.scatter(\n",
    "    X_val[:, 0][Y_val == 1],\n",
    "    X_val[:, 1][Y_val == 1],\n",
    "    c=\"b\",\n",
    "    marker=\"o\",\n",
    "    edgecolors=\"k\",\n",
    "    label=\"Interés por el gimnasio alto\",\n",
    ")\n",
    "\n",
    "plt.scatter(\n",
    "    X_train[:, 0][Y_train == 1],\n",
    "    X_train[:, 1][Y_train == 1],\n",
    "    c=\"b\",\n",
    "    marker=\"o\",\n",
    "    edgecolors=\"k\",\n",
    "    alpha=0.5,\n",
    "    label=\"Interés por el gimnasio alto - train\",\n",
    ")\n",
    "\n",
    "\n",
    "plt.scatter(\n",
    "    X_val[:, 0][Y_val == 0],\n",
    "    X_val[:, 1][Y_val == 0],\n",
    "    c=\"r\",\n",
    "    marker=\"o\",\n",
    "    edgecolors=\"k\",\n",
    "    label=\"Interés por el gimansio bajo \",\n",
    ")\n",
    "\n",
    "plt.scatter(\n",
    "    X_train[:, 0][Y_train == 0],\n",
    "    X_train[:, 1][Y_train == 0],\n",
    "    c=\"r\",\n",
    "    marker=\"o\",\n",
    "    edgecolors=\"k\",\n",
    "    alpha=0.5,\n",
    "    label=\"Interés por el gimnasio bajo -train\",\n",
    ")\n",
    "\n",
    "plt.xlabel('Component 1')\n",
    "plt.ylabel('Component 2')\n",
    "plt.ylim(0,1)\n",
    "plt.xlim(0,1)\n",
    "plt.legend()\n",
    "plt.savefig('/Users/javiermarin/desktop/Grafica4-o.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-entropy loss and probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use binary cross-entropy loss as a $loss function$ for this two classes classification problem."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where 𝑦 is the binary class label, 1 if the correct class 0 otherwise, and 𝑝 is the probability of each class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,6))\n",
    "# Binnary cross-entropy loss\n",
    "def cross_entropy(p):\n",
    "    return -np.log(p)\n",
    "ps = np.linspace(0.005, 1, 100)\n",
    "ces = [cross_entropy(p) for p in ps]\n",
    "ce = cost(var, features, Y)\n",
    "\n",
    "\n",
    "plt.plot(ps, ces, lw=3)\n",
    "plt.title(\"$H$, Cross Entropy Loss = {:0.7f}\"\n",
    "         \"\".format(ce))\n",
    "plt.suptitle(\"$p$, Probability = {:0.7f}\"\n",
    "         \"\".format(np.e**(-ce)))\n",
    "plt.ylabel('$H$, Cross-Entropy Loss - binary')\n",
    "plt.xlabel('$p$, probability the model guesses for the correct class')\n",
    "plt.hlines((cost(var, features, Y)), 0, 1, colors='red', lw=2, linestyles='dotted')\n",
    "plt.vlines(np.e**(-ce), 0, 5, colors='red', lw=2, linestyles='dotted')\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,5)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}