{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Importance of Extended Least Squares\n", "\n", "Example created by Wilson Rocha Lacerda Junior\n", "\n", "> **Looking for more details on NARMAX models?**\n", "> For comprehensive information on models, methods, and a wide range of examples and benchmarks implemented in SysIdentPy, check out our book:\n", "> [*Nonlinear System Identification and Forecasting: Theory and Practice With SysIdentPy*](https://sysidentpy.org/book/0%20-%20Preface/)\n", ">\n", "> This book provides in-depth guidance to support your work with SysIdentPy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we import the NARMAX model, the metric for model evaluation and the methods to generate sample data for tests. Also, we import pandas for specific usage." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pip install sysidentpy" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "from sysidentpy.model_structure_selection import FROLS\n", "from sysidentpy.basis_function import Polynomial\n", "from sysidentpy.parameter_estimation import LeastSquares\n", "from sysidentpy.metrics import root_relative_squared_error\n", "from sysidentpy.utils.generate_data import get_siso_data\n", "from sysidentpy.utils.display_results import results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating 1 input 1 output sample data \n", "\n", "The data is generated by simulating the following model:\n", "$y_k = 0.2y_{k-1} + 0.1y_{k-1}x_{k-1} + 0.9x_{k-2} + e_{k}$\n", "\n", "If *colored_noise* is set to True:\n", "\n", "$e_{k} = 0.8\\nu_{k-1} + \\nu_{k}$\n", "\n", "where $x$ is a uniformly distributed random variable and $\\nu$ is a gaussian distributed variable with $\\mu=0$ and $\\sigma$ is defined by the user.\n", "\n", "In the next example we will generate a data with 3000 samples with white noise and selecting 90% of the data to train the model. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "x_train, x_valid, y_train, y_valid = get_siso_data(\n", " n=1000, colored_noise=True, sigma=0.2, train_percentage=90\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Build the model\n", "\n", "First we will train a model without the Extended Least Squares Algorithm for comparison purpose." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [], "source": [ "basis_function = Polynomial(degree=2)\n", "estimator = LeastSquares(unbiased=False)\n", "model = FROLS(\n", " order_selection=False,\n", " n_terms=3,\n", " ylag=2,\n", " xlag=2,\n", " info_criteria=\"aic\",\n", " estimator=estimator,\n", " basis_function=basis_function,\n", " err_tol=None,\n", ")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5499799245432233\n" ] } ], "source": [ "model.fit(X=x_train, y=y_train)\n", "yhat = model.predict(X=x_valid, y=y_valid)\n", "rrse = root_relative_squared_error(y_valid, yhat)\n", "print(rrse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly we have something wrong with the obtained model. See the *basic_steps* notebook to compare the results obtained using the same data but without colored noise. But let take a look in whats is wrong." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Regressors Parameters ERR\n", "0 x1(k-2) 8.9976E-01 7.41682256E-01\n", "1 y(k-1) 2.8734E-01 8.33321202E-02\n", "2 x1(k-1)y(k-1) 1.2348E-01 5.10334067E-03\n" ] } ], "source": [ "r = pd.DataFrame(\n", " results(\n", " model.final_model,\n", " model.theta,\n", " model.err,\n", " model.n_terms,\n", " err_precision=8,\n", " dtype=\"sci\",\n", " ),\n", " columns=[\"Regressors\", \"Parameters\", \"ERR\"],\n", ")\n", "print(r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Biased parameter estimation\n", "\n", "As we can observe above, the model structure is exact the same the one that generate the data. You can se that the ERR ordered the terms in the correct way. And this is an important note regarding the Error Reduction Ratio algorithm used here: __it is very robust to colored noise!!__ \n", "\n", "That is a great feature! However, although the structure is correct, the model *parameters* are not ok! Here we have a biased estimation! The real parameter for $y_{k-1}$ is $0.2$, not $0.3$.\n", "\n", "In this case, we are actually modeling using a NARX model, not a NARMAX. The MA part exists to allow a unbiased estimation of the parameters. To achieve a unbiased estimation of the parameters we have the Extend Least Squares algorithm. Remember, if the data have only white noise, NARX is fine. \n", "\n", "Before applying the Extended Least Squares Algorithm we will run several NARX models to check how different the estimated parameters are from the real ones." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "parameters = np.zeros([3, 50])\n", "\n", "for i in range(50):\n", " x_train, x_valid, y_train, y_valid = get_siso_data(\n", " n=3000, colored_noise=True, train_percentage=90\n", " )\n", "\n", " model.fit(X=x_train, y=y_train)\n", " parameters[:, i] = model.theta.flatten()\n", "\n", "# Set the theme for seaborn (optional)\n", "sns.set_theme()\n", "\n", "plt.figure(figsize=(14, 4))\n", "\n", "# Plot KDE for each parameter\n", "sns.kdeplot(parameters.T[:, 0], label=\"Parameter 1\")\n", "sns.kdeplot(parameters.T[:, 1], label=\"Parameter 2\")\n", "sns.kdeplot(parameters.T[:, 2], label=\"Parameter 3\")\n", "\n", "# Plot vertical lines where the real values must lie\n", "plt.axvline(x=0.1, color=\"k\", linestyle=\"--\", label=\"Real Value 0.1\")\n", "plt.axvline(x=0.2, color=\"k\", linestyle=\"--\", label=\"Real Value 0.2\")\n", "plt.axvline(x=0.9, color=\"k\", linestyle=\"--\", label=\"Real Value 0.9\")\n", "\n", "plt.xlabel(\"Parameter Value\")\n", "plt.ylabel(\"Density\")\n", "plt.title(\"Kernel Density Estimate of Parameters\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the Extended Least Squares algorithm\n", "\n", "As shown in figure above, we have a problem to estimate the parameter for $y_{k-1}$. Now we will use the Extended Least Squares Algorithm.\n", "\n", "In SysIdentPy, just set *extended_least_squares* to *True* and the algorithm will be applied." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABIwAAAGMCAYAAAC4bjkIAAAAP3RFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMS5wb3N0MSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8kixA/AAAACXBIWXMAAA9hAAAPYQGoP6dpAACm7klEQVR4nOzdeZyN9fvH8dfZZjeMXakslSUhWcueFJUKIUsp+5otUSj8SIiyRyRbWmQrUWkXyVLfFpJ9yW4Yw8ycOefcvz/OnGPOLIwxnJk57+fjMQ/n3Mu5P+fc7pm5r7mu62MyDMNAREREREREREQkidnfAxARERERERERkexFASMREREREREREfGhgJGIiIiIiIiIiPhQwEhERERERERERHwoYCQiIiIiIiIiIj4UMBIRERERERERER8KGImIiIiIiIiIiA8FjERERERERERExIcCRiIiIpIrGIbh7yGk4u8x+fv4gUyfvYiI5HQKGImIiGSRDh060KFDh1TLY2NjadWqFRUqVODrr7/2w8jSNmTIEBo2bJju+sOHD1OmTBmfrwoVKnDffffRo0cPtm3bdgNH62vq1KmUKVPG+3zr1q107dr1ml+3YcOGqd5z8q/+/ftn+LVSjsnzeX766afXPM6MmDFjBnPnzr0hxwKYP38+999/PxUrVmTGjBlpbpPWZ1qxYkUeeeQR5syZg8vlumHjvZ7+/fdfnn76aX8PQ0RE5JpY/T0AERGR3Cw2NpbOnTuzc+dOpk+fTr169fw9pKvWo0cP6tevD0BCQgLHjh1j4cKFtGvXjqlTp9KoUaMbPqannnqKOnXqeJ9//PHH7NmzJ0teu169evTs2TPNdVFRURl+nZRjKly4MB9++CG33nrrNY8xI95++2169+59Q44VGxvLG2+8Qf369Xn++ecpXrx4utu2bNmSp556yvs8Li6OL7/8kokTJxITE8PAgQNvxJCvq7Vr17J9+3Z/D0NEROSaKGAkIiJynXiCRTt27GDmzJncf//9/h5Sptx6661UrlzZZ1mTJk1o3749r7zyCjVr1iQiIuKGjqlo0aIULVr0urx2/vz5U73frBAUFHRdXjc7OHfuHC6Xi0aNGlGtWrXLblu0aNFUn0OtWrXYu3cvixcvpm/fvthstus4WhEREckIlaSJiIhcBxcuXKBLly78888/zJ49O81g0ccff8wjjzxChQoVqF+/PlOnTsXpdHrXDxkyhGeffZZXX32VKlWq0LRpU5xOJ2XKlGHx4sW88sorVK9enXvuuYcXXniBU6dO+bz+119/TfPmzbn77ru5//77+b//+z8uXryYJe8vKCiIPn36cPbsWb744gvv8rNnzzJixAjuu+8+7r77blq1asXGjRt99s3I+A8ePEj37t2pUaMGlSpVonXr1nz//ffe9clL0oYMGcLy5cs5cuSIt+SrRYsWtGnTJtW4O3bsyHPPPZcln8GGDRto1aoV99xzD9WqVaNHjx7ejKK0xpSyJO3TTz/l7rvvZsuWLbRo0YK7776bhx56iG+++Ya9e/fy7LPPUqlSJR588EE+//xzn2P/+uuvdOrUiWrVqlGhQgUaNmzI1KlTvSVdns9m2rRpPqV7u3btolu3blSpUoUqVarQq1cvDh06lKH32rZtW+69915q1KjBwIEDOXr0qPd9eEobX375ZZ/jXY0KFSpw4cIFzp07B8CZM2cYOXIkDRo0oEKFClSvXp1evXpx+PBh7z4dOnRg0KBB9O3bl8qVK3vP7eHDhxk8eDC1a9fmrrvuolatWgwePJjo6Gjvvg0bNmTatGmMHTuWGjVqcM899zBw4EAuXLjA7NmzqVu3Lvfeey99+vTx2Q8uf+1OnTqVadOmAe7zMHXqVABcLhezZ8/mwQcfpEKFCjz00EMsXLjQ53XTez+fffYZzZo1o2LFitSsWZNBgwZx/PjxTH3OIiIiGaWAkYiISBa7ePEiXbt25e+//2bOnDnUqFEj1TbvvPMOw4cPp1atWsyaNYt27doxZ84chg8f7rPdli1bOHr0KNOnT2fgwIFYLBYAJk+ejMvlYtKkSQwePJhvv/2WsWPHevdbvXo1vXr1olSpUkyfPp3evXuzatUqevbsmWXNeGvVqoXZbPb2MkpISODZZ59l/fr19O/fn2nTplG0aFE6d+6cKmh0ufG7XC66detGXFwc48ePZ8aMGeTLl48ePXpw4MCBVOPo2bMn9erVo1ChQnz44YfUr1+fli1bsn37dp/tjx49yi+//ELz5s0v+74Mw8DhcKT55XHo0CF69uxJhQoVmDlzJmPGjGHfvn107doVl8uV5pjS4nA4GDhwIG3atGHmzJmEhoYyaNAgunfvTv369Zk1axaFCxfmpZde4tixYwDs3LmTjh07ki9fPiZPnszMmTOpWrUq06ZN8wbvPvzwQ8Bd/uV5vG/fPtq0acPp06d54403GDNmDIcOHeLpp5/m9OnT6X4eK1as4Pnnn6dYsWJMmjSJoUOHsn37dlq3bs3p06epX7++N0DSo0cP7/Gu1r59+wgPD6dAgQIYhkG3bt3YsGEDgwYNYu7cufTu3ZuNGzfy6quv+uz3xRdfEB4ezsyZM+ncuTNxcXE888wz7Nmzh1dffZW5c+fyzDPP8PnnnzN58mSffefNm8fRo0eZPHkyPXr04LPPPqNFixb89NNPjB49mgEDBrB+/XqmTJni3edK1+5TTz1Fy5YtvefBU3732muvMWXKFJo1a8asWbN4+OGHGTt2LNOnT7/s+9m6dSuDBw+mcePGzJkzh6FDh7Jp06ZcUbonIiLZm0rSREREspAnWLR161bv85TOnz/PjBkzaN26NcOGDQOgdu3a5MuXj2HDhvHcc89xxx13AO6AwqhRo1KVX9155528/vrr3uf/+9//WLt2LeAOeEycOJE6deowceJE7zYlSpSgY8eOfP/99+kGMK6G1WolKiqKkydPArBy5Up27tzJRx99RKVKlQCoW7cuHTp0YOLEiSxbtixD4z99+jR79+71Bl0AKlasyLRp07Db7anGceutt5I/f36fkq9HH32UcePGsXLlSvr27esdX3h4OA8++OBl39eKFStYsWJFmus++eQT7r77bv73v/8RHx9Pt27dKFKkCOAutVq/fj0XL15Mc0xp/V9wuVx0797dG1SIiYmhf//+PPvss97skjx58tCiRQv+/PNPihYtys6dO7nvvvuYMGECZrP7b3/3338/33zzDb/88guPPPKI95jJy7+mTZtGaGgo8+fP95YQ1qpVi0aNGvHuu+/y0ksvpTm+iRMnUrt2bd58803vck/G29y5cxk8eDDlypXznosrld25XC5v8M0wDE6dOsXq1av55ptv6Ny5MyaTiePHjxMaGspLL71E1apVAahRowYHDx5MFZCy2WyMHDmSoKAgAHbs2EHRokV54403uOWWWwCoWbMmv//+O5s3b/bZNyIigsmTJ2O1WrnvvvtYvnw5x48f5+OPPyZPnjwA/Pjjj96gaEavXc/16vks9u3bx0cffcSAAQO8jdBr166NyWTinXfeoW3btt7+WCnfz+zZswkJCaFr167eZfny5eOPP/7AMAxMJtNlP28REZHMUsBIREQkC/3555/ky5ePxYsX8/LLLzNkyBBWrlxJoUKFvNts376d+Ph4GjZs6JO14inr2bBhgzdglC9fvjR79aS8KS9atChxcXEA7N27l2PHjtGtWzef169WrRoRERFs2LAhSwJGgM8N68aNGylUqBB33XWXz3EbNGjA+PHjOXfuHHnz5r3i+AsWLMjtt9/O8OHD+emnn6hduzZ169Zl6NChGR5Xnjx5aNy4MatWrfIGjJYvX07Tpk0JCQm57L4NGjSgV69eaa67/fbbAahUqRLBwcG0bNmShx9+mLp161KjRg0qVqyY4TF63HPPPd7HBQoU8L6+R758+QB3MAngiSee4IknniAhIYF9+/Zx4MABduzYgdPpJDExMd3jbNq0ierVqxMSEuI9PxEREVStWpWff/45zX327dvHyZMnU2Wz3Hrrrdxzzz2pAjAZMWPGjFSzqIWEhNC6dWv69OkDQJEiRViwYAGGYXD48GEOHDjA3r172bZtW6qgYalSpbyBFIBy5cqxZMkSXC4X+/fv58CBA+zevZu9e/f6/L8EdyDSar3063DBggUJCwvzBovA/fnv2rULuLprN7lNmzZhGEaa+82cOZOtW7d6m8enfD/VqlVj8uTJPProozz00EPUq1eP2rVr58gG+iIikrMoYCQiIpKF8ubNy/vvv0/ZsmUZP348bdu25aWXXmLu3LnewMrZs2cB0p0G/sSJE97H4eHhaW4TGhrq89xsNntLzTyvP3LkSEaOHHnZ178WcXFxnDt3zhvQOnv2LCdPnuSuu+5Kc/uTJ096A0aXG7/JZGLevHnMnDmTr776ihUrVmCz2WjUqBEjR470vsaVtGzZklWrVrFlyxYsFgv79+/njTfeuOJ++fLl4+67777sNsWLF2fRokXMnj2bTz75hAULFhAZGUnbtm3p16/fVWV9pNUwPOXnk1x8fDyjR49m5cqVOBwOihcvzj333IPVar1sueHZs2dZs2YNa9asSbUuf/786e4D7kBKSgULFuTvv/9O93jpadWqFa1atQLc5zo8PJzixYunanS9atUqJk2axNGjR8mXLx/lypVLM9iX1jXy3nvvMWvWLM6ePUvBggWpUKECoaGhnD9/3me7tD77sLCwdMd+NdduWvs98sgjaa5P3o8o5fu55557mD17NvPnz+e9995j9uzZFCxYkO7du9OhQ4d0xyoiInKtFDASERHJQmXKlKFs2bKAO0ukW7duTJ8+nXfffZcuXboAEBkZCcDEiRMpUaJEqtdI6+b8anhef/DgwVSvXj3V+owGXK5k8+bNOJ1O76xYefLkoUSJEj5lcMldbqr1lIoUKcJrr73Gq6++ys6dO1m7di1z5swhKioqVQ+b9FSvXp1bb72VtWvXYjabKVWqVJbOUpa8TG7r1q18+OGHzJo1i7Jly9KkSZMsO05KY8aMYd26dbz11lvcd9993gBHrVq1Lrtfnjx5uO+++9Js+p08yyY5T3ZTyobq4A4AesqorkbhwoWvGJDbsmULL730Eh06dKBTp07esr/x48d7yz3Ts3r1asaNG8eLL75I8+bNvcGwF154gT/++OOqx5tcZq9dz37vv/9+mgGum2666bLHrVOnDnXq1CEuLo5NmzaxYMEC/u///o9KlSplKqtNREQkI9T0WkRE5Drq2bMnd999N2+//Tb/+9//AHcgyWazcfz4ce6++27vl9VqZdKkST6zQGVGqVKlKFCgAIcPH/Z5/SJFivDmm29mKiskJYfDwYwZMyhYsKC3J1D16tU5evQoBQoU8Dnuhg0bePfdd70Nu69k+/bt3Hffffzvf//DZDJRrlw5+vfvz5133sl///2X5j6eXj7JmUwmmjdvztdff80333zDk08+mfk3nML8+fNp0KABdrudoKAgatWqxejRowG8Y0xrTFlh69at1KhRg0aNGnmDRX/++SdnzpzxzpKW1vGrV6/O7t27KVeunPfcVKhQgfnz5/PVV1+leaySJUtSqFAhPvvsM5/lhw4d4rfffqNKlSpZ/O7ctm/fjsvlok+fPt5gkdPp9JbOJX+fKW3dupXIyEg6d+7sDRZduHCBrVu3Xna/jMjotZvys/f0YYqOjvbZ78yZM7z99tveDKS0vPHGG7Ro0QLDMAgNDaVBgwbeflPpXQ8iIiJZQRlGIiIi15HVamXChAk8+eSTDBgwgBUrVhAVFUXnzp15++23iY2NpUaNGhw/fpy3334bk8nkzVDKLIvFQv/+/RkxYgQWi4UGDRoQExPDjBkzOH78eLolY+k5ePAgv/32GwCJiYkcPnyYpUuX8tdffzF9+nRv+VTz5s1ZtGgRzz33HN27d6dYsWL8/PPPzJkzh/bt26cqOUpP+fLlCQkJYfDgwfTp04eCBQvy888/s2PHDp555pk094mMjOTUqVN8//33lCtXjsKFC3vH5JnW/PHHH8/Q8c+cOeN9vylZLBbuvvtuatasycSJE+nVqxft27fHYrGwdOlSgoKCaNCgQZpjyioVK1bkiy++4IMPPqB06dLs3LmTmTNnYjKZvH2gPMfftm0bv/76K1WrVqVnz560adOGbt268fTTTxMcHMyHH37I119/7TMLWHJms5kBAwYwdOhQBg4cSLNmzYiOjmbatGnkzZs3zWylrHqPAKNGjaJFixacO3eOxYsXs3PnTsDdQDytcjLPvh988AHjxo2jQYMGnDhxgrlz53Lq1Klrzq7L6LXrySj67LPPqFSpEmXKlKFZs2YMHz6cI0eOUKFCBfbt28fkyZMpXrx4mtlKHjVr1uS9995jyJAhNGvWjMTERN59913y5ctHzZo1r+n9iIiIXI4CRiIiItdZyZIlGTx4MCNHjuTVV1/lzTffpF+/fhQqVIglS5bw7rvvkjdvXmrVqsWAAQN8Gu5m1lNPPUV4eDjvvvsuH374IWFhYVSpUoWJEyd6Z47KqJkzZzJz5kzAHQDLnz8/VatWZcSIET7Bp7CwMBYvXsybb77JhAkTOH/+PDfffDMDBw7k+eefz/DxgoODmTdvHm+++SZjxowhJiaGEiVKMGrUKJo3b57mPs2bN+f777+nV69e9O3b19tjpkiRIpQtW5aCBQt6M1Wu5Pvvv+f7779Pc12ePHnYsmULZcuWZdasWUyfPp0BAwbgdDqpUKEC8+bNo1SpUmmOqWnTphn+DC5nyJAhJCYm8tZbb2G32ylevDg9evRg9+7dfPPNNzidTiwWC927d2fGjBl06dKFNWvWULZsWRYvXszkyZMZPHgwhmFw5513Mn36dB544IF0j9e8eXPCw8N555136NWrFxEREdSpU4cBAwb4NHPPSjVq1GDEiBG89957rF27loIFC1KjRg2mTZtGr1692Lp1a7pNn5988kkOHz7MsmXLWLJkCUWKFKFevXq0bduW4cOHs2fPHkqXLp3psWXk2m3cuDErV65kyJAhtGzZktdee43XX3+dd955h6VLl3Ls2DEKFChA06ZN6dev32Wz7+rVq8fEiROZN28evXv3xmQyce+997JgwQJvyaCIiMj1YDIu1x1RREREJAc7fvw4DRo0YMqUKd5ZqERERETkyhQwEhERkVxnx44drF+/nnXr1uF0Ovnss8+uW08hERERkdxIvzmJiIhIrpOQkMB7772H0+lk0qRJChaJiIiIXCVlGImIiIiIiIiIiA/9uU1ERERERERERHwoYCQiIiIiIiIiIj4UMBIRERERERERER8KGImIiIiIiIiIiA+rvweQHRmGgculXuCSu5nNJv0/F8nBdA2L5Gy6hkVyNl3DklOZzSZMJlOGtlXAKA0ul8GZMxf8PQyR68ZqNRMVFU5MzEUcDpe/hyMiV0nXsEjOpmtYJGfTNSw5Wf784VgsGQsYqSRNfMTFxdG8+aM0b/4ocXFx/h6OXAdxcXE8/nhTGjRooHMsIiIiIiKSRPfDvpRhJCkY7N272/tYciODPXvc59gwdI5FRERERETcdD+cnDKMRERERERERETEhwJGIiIiIiIiIiLiQwEjERERERERERHxoYCRiIiIiIiIiIj4UMBIRERERERERER8aJY0ScFEsWI3eR9LbmTipptuxmw2YTLpHIuIiIiIiLjpfjg5k6F5tVNxOl2cOXPB38MQuW6sVjNRUeFER1/A4XD5ezgicpV0DYvkbLqGRXI2XcOSk+XPH47FkrFiM7+XpJ09e5YRI0ZQt25dqlSpwtNPP82WLVu865977jnKlCnj89WhQwfv+oSEBEaOHEmtWrW45557GDhwIGfOnPHHWxERERERERERyRX8XpI2YMAATp48yaRJkyhQoAALFy6kU6dOLF++nFKlSvHPP//w2muv0ahRI+8+NpvN+/i1115jy5YtTJ06laCgIF599VX69u3LokWL/PF2RERERERERERyPL9mGB04cIANGzbw2muvUbVqVUqWLMnw4cMpXLgwq1ev5vTp05w+fZpKlSpRqFAh71e+fPkAOH78OCtWrGDYsGFUrVqVihUrMmnSJH799Ve2b9/uz7eWY8XHx9O2bUvatm1JfHy8v4cj10F8fDytWzenadOmOsciIiIiIiJJ4uPjefrpFrofTuLXDKOoqChmz57N3Xff7V1mMrkb8cbExPDPP/9gMpkoWbJkmvtv3boVgJo1a3qXlSxZkiJFivDrr79yzz33XN83kAsZhou///7T+1hyH8Nw8ddf7nPscukci4iIiIiIAHy5+QA7dvwF6H4Y/BwwioyMpF69ej7L1q1bx4EDB3j55ZfZtWsXefLkYdSoUWzYsIGwsDAefvhhevbsSVBQEMePHycqKorg4GCf1yhcuDDHjh27prFZrX5v7+QXyZtfWSzmgP0ccjOdY5Gcz3MdZ7RhoYhkL7qGRXI2XcO517If9nof614pG/QwSm7btm0MHTqUxo0bU79+fV5++WUSEhKoWLEizz33HDt27GD8+PH8999/jB8/nri4OIKCglK9TnBwMAkJCZkeh9lsIioq/FreSo4VHHxp6sCoqHDCwsL8OBq5HpKf48jIUJ1jkRwsMjLU30MQkWuga1gkZ9M1nLvpfjgbBYy+/vprBg0aRJUqVZg4cSIAo0aN4qWXXiJv3rwA3HnnndhsNvr378/gwYMJCQnBbreneq2EhARCQzN/8bpcBjExFzO9f0528eKl9x0dfYGEBMOPo5HrIfk5jomJ0zkWyYEsFjORkaHExMThdCpdWiSn0TUskrPpGg4MufV+ODIyNMPZcdkiYLRo0SLGjBnDww8/zBtvvOHNGrJard5gkccdd9wBwLFjxyhatChnz57Fbrf7ZBqdOHGCIkWKXNOYHI7AvPCTf8NzOl0B+znkZjrHIrmHrmGRnE3XsEjOpms4d9P59fMsaQBLlixh9OjRtGvXjkmTJvkEfjp06MDQoUN9tv/jjz+w2WyUKFGCe++9F5fL5W1+DbBv3z6OHz9OtWrVbth7EBERERERERHJTfyaYbRv3z7Gjh3Lgw8+SLdu3Th16pR3XUhICA899BBjx46lYsWK1K5dmz/++IPx48fTqVMnIiIiiIiI4JFHHmHYsGGMHTuW0NBQXn31VapXr07lypX998ZyuKioKH8PQa6zqKgoTCbTlTcUEREREREJINbgCHSr5GYyDMNvRXmzZs1i8uTJaa578sknGTduHIsXL2bx4sUcOnSIQoUK0apVK7p27YrZ7E6OunjxImPHjmXdunUA1K1bl2HDhl1T0MPpdHHmzIVM7y+S3VmtZqKiwomOvhDwaZYiOZGuYZGcTdewSM6mazj3en7cNwDkiwhiUu/afh7N9ZE/f3iGexj5NWCUXSlgJLmdfsiJ5Gy6hkVyNl3DIjmbruHcyxMwigwP4q0+Chj5vYeRiIiIiIiIiIg/KZcmNQWMxEd8fDydOnWgU6cOxMfH+3s4ch3Ex8fTsWN7WrZsqXMsIiIiIiICuAwDl8POrvWT+e3z8bpXws9NryX7MQwXW7f+6n0suY9huNiyZTMALpfOsYiIiIiIiNNpYGAQe/JfQPfDoAwjEREREREREQlwDqdK0lJSwEhEREREREREAppD1RepKGAkIiIiIiIiIgHNqQyjVBQwEhEREREREZGA5nQqwyglBYxEREREREREJKA5XcowSkmzpEkqISGh/h6CXGehoTrHIiIiIiIiHp6AkdkS5OeRZB8KGImP0NAwNm3a7u9hyHUUGhrGr7/+TlRUONHRF3A4lHopIiIiIiKBzTAMLNZgKj/1FiaT+74p0KkkTUREREREREQCWvKKNMMAl6ESNQWMRERERERERCSguVL0MEr5PBApYCQ+EhIS6N27G717dyMhIcHfw5HrICEhgR49utChQwedYxEREREREdwZRS5nIru/n87u76dz8WK8v4fkd+phJD5cLic//fS997HkPi6Xkx9/dJ9jp9OJxWLz84hERERERET8y2UYGIaLmKN/AZDoSPTziPxPGUYiIiIiIiIiEtBStixyqCRNASMRERERERERCWwpexY5nQoYKWAkIiIiIiIiIgHNSJFi5FSGkQJGIiIiIiIiIhLYNEtaagoYiYiIiIiIiEhASxkfUkmaAkYiIiIiIiIiEuBSlqQpwwis/h6AZC+hoWH89ttOfw9DrqPQ0DD+/HMXUVHhREdfwOFw+XtIIiIiIiIifuUyDCzWYKq0mQGALTjEzyPyP2UYiYiIiIiIiEhAc6X4O7rLUIaRAkYiIiIiIiIiEtBSBojUw0gBI0khISGBQYNeYNCgF0hISPD3cOQ6SEhIYMCAvnTt2lXnWEREREREBHfPIpczkb0b5rB3wxzi4uP8PSS/U8BIfLhcTr7+eh1ff70Ol8vp7+HIdeByOfnyy7V8/vnnOJ06xyIiIiIiIgZgGC7OHtrO2UPbcTh0r6SAkYiIiIiIiIgEtJSzojnVw0gBIxEREREREREJbCl7GLnUw0gBIxEREREREREJbCkzjFI+D0QKGImIiIiIiIhIQEs1S5oCRgoYiYiIiIiIiEhgS9mySAEjBYxEREREREREJMCl6mGkgBFWfw9AspeQkFA2btzmfSy5T0hIKJs3/0ZUVDjx8S6cauYmIiIiIiIBznAZmC1BVGo5GQCLLdjPI/I/BYzEh8lkIjQ0zN/DkOvIZDIRFhZGWFgYCQkXAAWMREREREQksLkM972SxeoOFOkuSSVpIiIiIiIiIhLgUpagOZ0uP40k+1DASHzY7XaGDx/C8OFDsNvt/h6OXAd2u51XXnmJfv366RyLiIiIiIgAhmHgciayf9MC9m9aQEJCgr+H5HcKGIkPp9PB6tUrWL16BU6nw9/DkevA6XSwcuVyPv74YxwOnWMRERERERGXAYbh4sz+TZzZv0n3SihgJCIiIiIiIiIBLuUsaapIU8BIRERERERERAJcqh5GLrW9VsBIRERERERERAJaygyjlAGkQKSAkYiIiIiIiIgEtBTxImUYoYCRiIiIiIiIiAQ4laSlpoCRiIiIiIiIiAQ0laSlZvX3ACR7CQkJ5ZtvfvY+ltwnJCSUH37YRL58YZhMwTid+kYoIiIiIiKBzWUYmC1B3P3EGwCYrUF+HpH/KWAkPkwmE/nz5/f3MOQ68pzjqKhwoqMvAAoYiYiIiIhIYDMM972SLSQPkDrjKBCpJE1EREREREREAlrKEjSVpCnDSFKw2+1MnDgOgEGDhhAUpDS83MZutzNu3DiCg2288MKLmM36NiAiIiIiIoHNZRi4nIkc3r4MgITyvf08Iv/ze4bR2bNnGTFiBHXr1qVKlSo8/fTTbNmyxbt+48aNNG/enEqVKvHwww/z+eef++yfkJDAyJEjqVWrFvfccw8DBw7kzJkzN/pt5BpOp4OPPlrCRx8twel0+Hs4ch04nQ6WLl3C+++/j8OhcywiIiIiImK4wDBcnNr9A6d2/4BT90r+DxgNGDCA7du3M2nSJJYtW0a5cuXo1KkTe/fuZc+ePXTr1o06derw6aef8tRTTzF48GA2btzo3f+1117jp59+YurUqbz//vvs3buXvn37+vEdiYiIiIiIiEhOkrJnkVMlaf4tSTtw4AAbNmxgyZIl3HvvvQAMHz6cH3/8kdWrV3P69GnKlClD//79AShdujR///037777LrVq1eL48eOsWLGCWbNmUbVqVQAmTZrEww8/zPbt27nnnnv89t5EREREREREJGcwFDBKxa8ZRlFRUcyePZu7777bu8xkMmEymYiJiWHLli3UqlXLZ5+aNWuydetWDMNg69at3mUeJUuWpEiRIvz666835k2IiIiIiIiISI6WMsNITa/9HDCKjIykXr16Po2V161bx4EDB6hTpw7Hjh2jaNGiPvsULlyYuLg4oqOjOX78OFFRUQQHB6fa5tixYzfkPYiIiIiIiIhIzuZy+T5XhlE2myVt27ZtDB06lMaNG1O/fn3i4+NTzdLleW6324mLi0tzFq/g4GASEhKuaSxWq9/bO/mFxWL2eRyon0NupnMskvN5ruPk17OI5By6hkVyNl3DuVPK8JDLMAL+XinbBIy+/vprBg0aRJUqVZg4cSLgDvzY7Xaf7TzPQ0NDCQkJSbUe3DOnhYaGZnosZrOJqKjwTO+fkwUHm7yPo6LCCQsL8+No5HpIfo4jI0N1jkVysMjIzP+sExH/0zUskrPpGs5dbDaLz3OzxRywcQGPbBEwWrRoEWPGjOHhhx/mjTfe8GYNFStWjBMnTvhse+LECcLCwsiTJw9Fixbl7Nmz2O12n0yjEydOUKRIkUyPx+UyiIm5mOn9czKXy8W6dd8AEBfnJCHhgp9HJFnN5XLx9dffERERgt1u6ByL5EAWi5nIyFBiYuJwOl1X3kFEshVdwyI5m67h3Ck+IRGzxUbTzpM5cCwWp8tMdHTuu1eKjAzNcHac3wNGS5YsYfTo0XTo0IFXXnkFk+lS9kPVqlXZvHmzz/abNm2iSpUqmM1m7r33XlwuF1u3bvU2x963bx/Hjx+nWrVq1zQuhyNwL/wiRW4C3DWcrpSFnJIrFC16E1FR4URHXwjo/+siOZ3T6dI1LJKD6RoWydl0DecuLpeByWQmMqoIwbHBOF2BHRcAPze93rdvH2PHjuXBBx+kW7dunDp1ipMnT3Ly5EnOnz9Phw4d+N///sfEiRPZs2cP8+bNY+3atXTu3BmAIkWK8MgjjzBs2DB++eUX/ve//zFgwACqV69O5cqV/fnWRERERERERCSH8MyKZrOYfJ4HMr9mGK1bt47ExES++uorvvrqK591Tz75JOPGjWPGjBlMmDCB999/n+LFizNhwgRvNhHA6NGjGTt2LL179wagbt26DBs27Ia+j9wkMdHO1KlvAdCnTz9sttRNxSVnS0y089ZbbxMSYqNbt96YTH5PNBQREREREfErwwCX08G275Zw8mwctxZq5+8h+Z3JMAyFzVJwOl2cOZP7ahUzIi7uIrVqVQFg48ZthIaqIXJuk/wcb978G0FBIX4ekYhcLavVrLJSkRxM17BIzqZrOHeauux/bNlxhN8/6Q/AIz3mMKZbHT+PKuvlzx+e4R5GgT1HnIiIiIiIiIgEvJSpNCpJU8BIRERERERERAJcyuIrpwJGChiJiIiIiIiISGBLGR5ShpECRiIiIiIiIiIS4FwpMoxcLvWnUsBIRERERERERAJayh5GKklTwEhEREREREREAlzKEjSVpIHV3wOQ7CU4OIRPPlntfSy5T3BwCCtWfE5kZCghISEo01JERERERAKdYRiYLTZ6vjyTb7cfwTArXKJPQHyYzWZuv/0Ofw9DriPPOY6KCic6+oJqc0VEREREJOAZBphMZm4qXpLQvQYuw+TvIfmdStJEREREREREJKAZSU2MrBZ3mEQlacowkhQSE+28++47AHTu3A2bLcjPI5Kslpho5513ZhMaGkSHDs9jMunbgIiIiIiIBDYX4HI6WP/ZQv7be5qbKzTx95D8TneK4sPhcPDOO9MB6NixkwJGuZDD4WDmzGkAtGnzDEFB+jYgIiIiIiKBzTAMDMPJV6sXAlCk3IMYhoHJFLilaSpJExEREREREZGAZqRRgZbWskCigJGIiIiIiIiIBLS0ehY5A7yPkQJGIiIiIiIiIhLQ0somcgb4jNIKGImIiIiIiIhIQDPSiBgF+kxpChiJiIiIiIiISEBLKzakkjQRERERERERkQBmoAyjlDSftvgICgpm0aKPvY8l9wkKCuaDDz4hMjKU4ODggO/8LyIiIiIiYhhgNtv4v4lzWfL1LsxmW8BnGClgJD4sFgsVKtzt72HIdWSxWLj77opERYUTHX0BhyOwG7mJiIiIiIgYhoHJbOaOO8sT+Xsi9kRXwAeMVJImIiIiIiIiIgHNU35mMpmwmM0+ywKVMozER2KincWLFwLQrl0HbLYgP49Islpiop0FCxYRFhZEixZtMJn0bUBERERERAKbYYDL6WD1p4v4769j5C1ZF4cCRiKXOBwO3nprAgCtWz+tgFEu5HA4mDRpPADNmrUkKEjfBkREREREJLC5DAPDcLLwvWkAVCpxf8BnGKkkTUREREREREQCWlqTASlgJCIiIiIiIiISwAxSB4fU9FpEREREREREJICllWHkdAX2jNIKGImIiIiIiIhIQHOlETFSSZqIiIiIiIiISAAz0ggOqSRNRERERERERCSApRUbCvQMI82nLT6CgoKZM+d972PJfYKCgpk3byF58oQQHBycZq2uiIiIiIhIIDEMA7PZxriJ77Bm0wHOm204FDASucRisVCtWg1/D0OuI4vFQvXqNYiKCic6+gIOR2A3chMRERERETEMMJnNVLqnKtuORhB75FzAZxipJE1EREREREREApqBOzhkNpkwm02AStKUYSQ+EhMTWbbsIwBatGiFzWbz84gkqyUmJvLxxx8TFhZM06ZPYDJZ/D0kERERERERv3IZYLicrF7xIbt3nMCIqoLDFdjVGAoYiQ+HI5Fx40YD8PjjTypglAs5HImMGTMKgAcffISgIAWMREREREQksBmGgcvlYNqUNwCo1LJiwGcYqSRNRERERERERAJaWslETgWMREREREREREQCl5HG9NHKMBIRERERERERCWBpxIuUYeTvAYiIiIiIiIiI+FNaGUYKGImIiIiIiIiIBCjDMEgrNKSSNBERERERERGRAJVeWCjQM4ys/h6AZC82WxBTpszyPpbcx2YLYvr0d4iICCEoSOdYREREREQCm6cczWy2Mn7idDb88R8H46wKGPl7AJK9WK1W6tat7+9hyHVktVqpV68BUVHhREdfwOFIY/5IERERERGRAOFpX2QyW6hduw7HnXs5tP2IStL8PQAREREREREREX9JHhgymUyYzSZAJWnKMBIfiYmJrFmzGoCmTR/DZrP5eUSS1RITE/nss88JCwuiQYOHMJks/h6SiIiIiIiI33gyjAyXkzWfr+Cvf05iGLfjdAV2NYYCRuLD4Ujk1VdfBqBx44cVMMqFHI5Ehg0bAsDmzb8RFKSAkYiIiIiIBC5XUsTI5XIwetQwACq1nKySNH8PQERERERERETEX4x04kKBXpKmgJFIgDHS+24oIiIiIiISgAzSvkcK9ICRStJEAkjiPz8S++18fw9DREREREQk20jvb+oqSctG3nnnHTp06OCzbNiwYZQpU8bnq2HDht71LpeLKVOmUKdOHSpXrkyXLl04dOjQjR66SI4Qv2EROO3+HoaIiIiIiEi24UonYhToGUaZChgdP348q8fB4sWLeeutt1It/+eff+jevTs//fST9+uTTz7xrp8xYwZLlixh9OjRLF26FJfLRefOnbHbdVMskoojwd8jEBERERERyVaMdAJDyjDKhAYNGtC5c2fWrFlzzYGZ48eP0717dyZOnEiJEiV81hmGwe7du6lQoQKFChXyfuXPnx8Au93OvHnz6Nu3L/Xr16ds2bJMnjyZY8eO8eWXX17TuERyGyMx3t9DEBERERERyXY8cSGzyeSzXBlGmfD666/jcrkYNGgQtWvXZuTIkfzxxx+ZGsBff/2FzWZj1apVVKpUyWfdwYMHuXjxIqVKlUpz3507d3LhwgVq1arlXRYZGUn58uX59ddfMzWeQGezBTF+/FuMH/8WNluQv4cjWci4eBYAm8XMqIfLMGvWLIKCdI5FRERERCSweSYGslisjB//Fs90H47ZbA34gFGmml4//vjjPP744xw/fpzly5ezcuVKPvjgA26//XaaN29Os2bNKFiwYIZeq2HDhj49iZLbtWsXAAsXLuSHH37AbDZTt25d+vfvT548eTh27BgAxYoV89mvcOHC3nWZZbVmq/ZON4zVGkTTpk39PQy5DhyOOACsZhMNSkVRonEjYhPA6XT5eWQicrUsFrPPvyKSs+gaFsnZdA3nPmbvObXStGljQrYe5s8vdmIYRsDGBuAaZ0krUqQI3bt3p3v37vz111+MGzeOCRMmMGnSJG/ZWsqsoauxa9cuzGYzhQsXZtasWRw8eJDx48fz77//8v777xMX574BTpklERwczLlz5zJ9XLPZRFRUeKb3F8mOLp5xcj7Zc2f8eSLzFvbbeETk2kVGhvp7CCJyDXQNi+RsuoZzD7vhLkUzJcUC8uQJAdyBpECODVxTwAhgy5YtrFy5kq+++oqYmBjuv/9+6tevz3fffcfTTz/N4MGD6dixY6Zeu0ePHrRt25aoqCgA7rzzTgoVKkSrVq34448/CAlxn0S73e59DJCQkEBoaOYvXpfLICbmYqb3z8kcDgfr138FwAMPPIjVes3/RSSbsJ8+DYDDZfDj3jPk/+xz6jVpickUuBFzkZzKYjETGRlKTEycsgRFciBdwyI5m67h3Ofs2aT7f5eTpUs/YceBaAxXARISHERHX/Dv4LJYZGRohrPjMhUNOHDgACtXrmTVqlUcOXKEm2++mQ4dOtC8eXNveVj79u0ZNGgQM2fOzHTAyGw2e4NFHnfccQcAx44d8x7rxIkT3Hrrrd5tTpw4QZkyZTJ1TA+HIzAv/Li4eAYOfAGAjRu3ERoa5ucRSVZxXIwFINHpYsSX/8KXw9hc/1GCgkKusKeIZFdOpytgf16J5Aa6hkVyNl3DuUdi0nk0XA7v/XCllpNxBPg5zlTA6KGHHiI4OJhGjRoxevRon6bTyZUqVYr9+/dnenCDBw/mxIkTzJ8/37vM01z79ttv55ZbbiEiIoJffvnFGzCKiYnh77//pn379pk+rkhuZCTkrsi4iIiIiIhIVnAlNbc2pZglzaWm11dv+PDhNGvWjDx58lx2u549e9KzZ89MDQzcgamePXsybdo0mjVrxr59+xg1ahSPPvoopUuXBtyZTBMnTiR//vzcfPPNTJgwgaJFi9K4ceNMH1ckNzLsgVlmKSIiIiIicjlJk6Rh9o0X4VDA6OqtW7eOmjVrphkw2rlzJy+++CKrV6++5sE98MADvPXWW8yePZs5c+aQJ08eHnvsMfr16+fdpm/fvjgcDoYNG0Z8fDzVqlVj7ty52Gy2az6+SK6iDCMREREREZFUDEMZRmnJcMBoy5Yt3g9x8+bN/Prrr5w5cybVdt9++y2HDh3K1GDGjRuXalmTJk1o0qRJuvtYLBZefPFFXnzxxUwdUyRQGAnKMBIREREREUkpvQwjpwJGGfPxxx+zcuVKTCYTJpOJkSNHptrGE1B69NFHs26EIpIlDEeCv4cgIiIiIiKS7bjSyTByOhUwypBhw4bRokULDMPg2WefZcSIEdx+++0+25jNZiIjI70zmYlI9mEkxrsfWIP8OxAREREREZFsxJNhlCJe5A0kBaoMB4zy5MlD9erVAViwYAF33XUX4eHh121g4h9Wq42RI8d6H0sukpRhFBQWydCGpQgvU1O9vkREREREJOAZuANDZquVkSPHcvzMRTYetaokLaMbrlixgnr16hEVFcV///3Hf//9d9ntn3jiiWsdm/iBzWbj8ceb+3sYch0Yie6AkS0iH03LFibffZUx2Ww4HC4/j0xERERERMR/XEm3RFaLlccfb86eI+fYtHArLldg3ytlOGA0ZMgQPvroI6KiohgyZMhltzWZTAoYiWQ3SQEjU4h7dkNXYjwWf45HREREREQkG0g5S5o5qfu1MowyaP369RQqVMj7WHInh8PBzz//BMB999XGas3wfxHJ5jxNr522cH7eH02o5W/q3uMAzP4dmIiIiIiIiB95WxUZLn744TtOno3DcKkkLcPRgJtvvjnNxx4Oh4PY2Fjy5cuXJQMT/0hMtNO3b3cANm7cpoBRLmEYhjfDyGEJ5qU1/wD/sLnDEIKCQvw7OBERERERET/yNLc2XA7v/XCllpNxBXjAKFOpBQ6Hg2nTprF69WoAfvnlF+6//35q1arFs88+y7lz57J0kCJyjZx2SGrkZgpRs3oRERERERGPlCVpHk6nAkZXbcqUKcycOZOYmBgA/u///o98+fIxdOhQDh48yJtvvpmlgxSRa+NpeA1gsoX5cSQiIiIiIiLZi6ckLUW8KOBL0jIVMPr8888ZMGAA7dq1Y8+ePfz777/06NGDZ555hv79+/PNN99k9ThF5Fp4AkbWILDa/DsWERERERGRbMSTYWROmWGkgNHVO3HiBJUqVQLgu+++w2w2U7duXQCKFi3K+fPns26EInLNPA2vTdZgTGb1pRIREREREfFwpZth5Lrxg8lGMhUwKly4MIcPHwbgm2++oVy5cuTPnx+A7du3U7Ro0awboYhcu8R497+2ELAow0hERERERMQjvR5GhnGpIXYgylTA6NFHH+X111+nU6dObN26lRYtWgAwZswYpk6dymOPPZalgxSRa2M47IA7wwhLpi57ERERERGRXMmTYWQ2pbEugMvSMlWb0q9fP8LCwvj1118ZOHAgbdu2BeCPP/7g+eefp0ePHlk6SLlxrFYbQ4YM9z6W3MHwZhgFExQUSv86JbBEFsRm0zkWEREREZHA5skwslisDBkyHIfTxfoD7nCJ02lgtfhzdP6TqYCRyWSiW7dudOvWzWf50qVLs2RQ4j82m402bdr5exiS1ZICRiZbMNbgEJrfXRRboVuw2Ww4HIFdlysiIiIiIoHNU3Vmsbrvhx1OF99M+A7w9DEKzIhRprvfnj9/nk2bNnHx4kVvNC65J5544lrGJSJZyLckLemydzr8OCIREREREZHs4dIsae7nlmS1aQ6VpF2dH3/8kb59+xIXF5fmepPJpIBRDuV0Otm2bQsAVapUxWIJzEhqrpPoniUNazAuw8T2I+ewRENtpxNIo1BXREREREQkQHhiQoZh8OuvvwBgMgwMkwmnUwGjq/Lmm29SqlQphg4dSpEiRTCb1UQ3t7DbE+jS5VkANm7cRmhomJ9HJFnBcCYCYLLasDsN+q7cAcDm/gkEBYX4c2giIiIiIiJ+5ckwMpx2unTpBEDVNm9jYEsqSQtMmQoY7dmzhxkzZlC1atWsHo+IXA9JASMsNlDWmIiIiIiIiJcrKWBkMl2qvrCYTLgMcAZwSVqmUoNuuukmYmNjs3osInK9JAsYmcyaGU1ERERERMTD05Y5Wesibx8jlwJGV6dbt25Mnz6dw4cPZ/V4ROQ6MJIaXJss1ktNr0VERERERMRbkuaTYZQUMFIPo6u0evVqjh8/zoMPPkj+/PkJCfHtgWIymfj666+zZIAikgV8StIuXfaGEbj1uCIiIiIiInApw8iUPMPIYobEwC5Jy1TAqGjRohQtWjSrxyIi14nhU5KW7LJ3OfwzIBERERERkWwirR5GZrMJMHCo6fXVef3117N6HCJyPfmUpCVreu10+mlAIiIiIiIi2cOlDKOUJWmGStIya8+ePWzYsIETJ07QoUMHDh06RNmyZYmIiMiq8ckNZrVa6dfvRe9jySWSZRhZg0LoUetWAKymy+wjIiIiIiISADw9jCzJ7od3JdiABJWkXS2Xy8WIESNYtmwZhmFgMplo0qQJM2bM4ODBgyxatEglazmUzRZEx46d/D0MyWKekjSTxYYtKJi2994CLic2i4nATbAUkevN5XLhdKr0VbKWxWLFbM7UvC0iIiJp8pSk2aw27/3wiLmbcQeMAveOKVMBoxkzZrB69Wr+7//+j/r163P//fcD8OKLL9KrVy8mT57MG2+8kaUDFZFrkLzptedfl/NSbyMRkSxkGAYxMWeIi4v191AklwoNjSAyMr9P6YCIiEhmpd302v3EpQyjq7Ns2TL69u1LixYtcCbrgVKuXDn69u3LxIkTs2yAcmM5nU527PgbgHLlymNJ3u9GcqzkTa+dTic7T1zAsMdR1Z6AOdy/YxOR3McTLIqIiCIoKFg39ZJlDMPAbk8gNjYagLx5C/h5RCIikht4StIwXPz55x8AWHAvUw+jq3Tq1CnKlSuX5roiRYoQExNzTYMS/7HbE2jf/ikANm7cRmhomJ9HJFkiWdNruz2BLh/8CsDGznGE+nNcIpLruFxOb7AoIiLS38ORXCgoKBiA2Nho8uSJUnmaiIhcM08SkcuZSPv2bQBo2XcuQED3MMrUT9jbbruN77//Ps11mzdv5rbbbrumQYlIFktZkuZdrlnSRCRreTKPPTf1IteD5/+XemSJiEhW8GQY+cySZnGHSxzqYXR1nn32WUaMGEFiYiINGjTAZDJx4MABfvnlF+bNm8eQIUOyepwicg0Mb4ZRioCRS79oi8j1oTI0uZ70/0tERLJSWj2MzGb3E5WkXaWnnnqKM2fOMHPmTJYsWQLAgAEDsNlsdO7cmaeffjpLByki1yidDCPDUMBIREREREQCmyfDyJw8w8gTMArgkrRMBYwAunTpwmOPPcbmzZuxWq3kyZOHSpUqkS9fviwcnohkiXRL0hQwEhFJT8uWj3Hs2FHvc5PJRGhoGHfeWYbOnbtTuXIVP44ucxwOB8uWfUjr1u2u2zEOHz5Ex45Ps3DhRxQrdtN1O46IiEhWcV0mw0izpF2Fzz77jKVLl/L777/jcLhvNkNCQqhSpQpPP/00jRo1yvJBisi18cySZrL4XvKGSz2MREQup02b9jz9dHvAna4eE3OWd96ZzsCBfVi8eBlFixb18wivzldfrWXq1MnXLWC0f/8+XnyxH/Hx8dfl9UVERK6HNDOMknoYKcMoA5xOJwMHDmTt2rUUKVKERx55hIIFC2IYBseOHWPz5s306dOHxx9/nHHjxl3PMYvI1Uo3wyjxxo9FRCQHCQ0NpUCBgt7nBQsW5MUXX+aJJ5rwww/f0qpVzirD904bfB0sXPgeCxbM49ZbS3D06JHrdhwREZGs5kqj6bXV28NITa+vaMmSJXz55Ze88sortG/fPlWzQafTydKlSxk7dixVq1alZcuWWT5Yuf6sVivduvXyPpaczzBc4MkkstqwWqx0algZV8zJzNekiogEMIvFAkBQkDsIf+zYMWbOfJutW7dw/nwM+fMX4MEHH6Z7996YzWbWrFnN++/PpVat2nzxxWqqVKnK66+/yQ8/fMfChe+xb98eXC4XJUqUolu3XtSoUQuA3r27Uq7cXZw+fYoff/yOsLAwnnuuC6VK3c6kSeM5dOgAd9xRhldeeY1bbrkVgJMnTzBt2mR++WUjZrOFu++uSO/e/bnllltZs2Y1Y8eOBKB27apMmTKLKlWqsmHDj8yd+w779++jUKFCNGr0EM8+24mgoCDvts8914U1a1bjcCQybdoc7/GS++GH73j55VfJmzcffft2v85nQUREJOt4/p5isVi898OWpPthZRhlwIoVK2jTpg0dOnRIc73FYqFdu3bs3r2b5cuXK2CUQ9lsQfTo0cffw5CslKxPkclsxWYLonPj6jgO/g+rRbPMiMiNYRgG9kT//IUuyGbOslm1Tp48wZQpkwgNDaVmzdoADBkygAIFCjJ58nTCwsLYsOEHpkyZRIUKFalbtz4AR44c5tSpk8ybt5iEhAR27tzBsGGD6d27H7Vr1+PChVhmzZrO6NEjWL58DTabOxj18ccf0LVrLzp16sYHHyxk8uQJlChRkhdeGERYWBjDhw9h1qypjBkzgbi4OPr06UaZMmWZOnU2FouZpUsX07VrRxYsWMoDDzxIbGwsU6a8ycqVa4mMzMumTT8zYsQQ+vQZQLVqNThy5DCTJ4/n4MEDjB59KWN8+fKPmThxCg6HM81gEcCcOe8DsG3bliz5rEVERG4UTwau1RZE56T74flf7ADAoYDRle3bt48+fa4cSKhTpw6fffbZNQ1KRLJQ8rIzq/sGxNvLSE2vReQGMAyD1xdtY/eRc345/u3F8zK0XZVMBY0WLnyPpUsXAe5sarvdTokSJRk1ahxFixYlISGehx5qSsOGjShSxN3PqFWrtixa9D579+72BowAOnbszM03Fwfg33//oX//wTz55KU/sD31VBsGDerLmTOnva91xx1laNvW/ce65s1bsWLFMlq0aE2VKlUBaNCgET/++B0A69evIzb2PMOHj/ZmCQ8ZMpzt27eyatVyOnXqRkREBIC3zG7Bgnk0a9acJ55oAcDNNxfnxRdfpm/f7hw9+p+3afVDDzWlbNnyV/35iYiI5ASeDCNzsl8VLOakHkYqSbuyuLg48ubNe8XtoqKiuHDhwjUNSvzH5XKxd+8eAEqVKo056SKRnMvwBoxMYLK4z/GJczjOXKSsw47Fr6MTkYCRQxMan3iiBS1btgHAbDYTGZnXG3QBCA4OoUWLVnz33Xr+/vtPDh8+xJ49uzlz5jROp+/EArfccov38R13lCFPnrwsWjSfAwf2c/jwIXbv3gW4fxZ7FC9+aZ/Q0FAAb9DJffxgEhPd3+f/+ecfYmJiaNKkgc9x7XY7Bw7sT/P97dq1kx07/uKzz1Z4l3n+yrp//z5vwKh48bSzikRERHIDTw8jDIPdu/8FwIx7mUrSMsAwDG/N/uWYzebr2lBRrq+EhHhatnwMgI0btxEaGubnEck1S9bw2mQyER8fR9sJiwH4sVEcQX4cmogEBpPJxNB2VXJkSVqePJE+QZuU4uLi6NWrC3Z7Ag0aNKJJk8coX/4uevXqkmrb4OAQ7+Pt27cycGAfatW6n4oVK9O48cPEx8czdOggn33S6ieY3nsxDBe33nob48ZNSrXOE2xKyeUyaNv2GZo0eTTVuuTNvoODg9PcX0REJDfwxIQcTjstWz4JwICxH7vXKWAkIrmVN8PIaktjpUrSROTGMJlMBAflvpzGzZs3smvXTlatWkf+/AUAiIk5x5kzpy+739Kli7jnnqqMGTPBu+yTT5YCmZ/JrGTJ0qxd+zkREXnIly8fAA6Hg9dee5kGDR7kgQceTBVsKlWqNAcPHvAJim3btoWPP17KoEFD0g00iYiI5Caen73mZD8nLUn9XpVhlEGvvfaaTxp2WmJjY69pQCKSxZL6FJnMqS93I0W5hIiIXJ1ChQoDsG7dFzRo8ADHjx/nnXem4XA4sNvt6e5XuHBRfvzxO37//TcKFy7Mtm1bePfdWQDeErOr9dBDTVm8+H2GDRtMjx59iYiI4L335rBp08907twDuJRptHPnDkqWLEm7ds8wYsRQ3ntvDg880JgTJ44zbtxobrrpZp8MIxERkdzM87caU7Ia+ks9jBQwuqJq1aoBV/6rV3h4OFWrVr22UYlI1rlchpGaXouIXJPy5SvQp09/PvxwCXPmzKRQoUI88EBjChcuws6df6e7X+fO3Thz5hQvvdQPgBIlSjF06AhGjRrOjh1/cdttJa56LBEREUybNpvp099i4MDeOJ0uypQpy+TJ0ylRoiQAVapUo3z5CvTo8TzDh4+mYcNGjBwJCxfOY8GCeURGRnL//XXp0aNvZj4OERGRHMkT50ieiGs1ezKMArfptclQw6FUnE4XZ84EZuPuuLiL1KpVBVAPo9zCcfQf4la/jjlfMcJbve5zjr+f+gp563Tw8whF5GpZrWaiosKJjr6Aw5G9folJTLRz+vRRChQohs2mLmlyfeT0/2fZ+RoWkSvTNZz7fPTNbtZuPkjDSoWZONQ9g+mrb61g9ab/qF2xGM83LefnEWad/PnDsVgyNrmVpsASHzF2lRTmOt6m12kkFKokTUREREREApwrjQwjiyfDKIBL0hQwEi+X4WLGb3P9PQzJao5Ls6SlZLhUkiYiIiIiIoHN28MoWcTIrJK07BUweuedd+jQwbc8ZseOHbRv357KlSvTsGFDFixY4LPe5XIxZcoU6tSpQ+XKlenSpQuHDh26kcPONQ6dP8KJhNPcVL80tza8E3MG09QkezNc7oCRKSlgZLVaad+kPm0qF8NK4EbLRURERERE4FKGkdVq4ZlnnueZZ57HZnPfPwXyLGnZJiKwePFi3nrrLZ9l0dHRPPfcc9x6660sW7aMXr16MXHiRJYtW+bdZsaMGSxZsoTRo0ezdOlSXC4XnTt3vuzMJJK2vecOYLaaKdnsLm55tCyn7Wf9PSTJCikyjGy2IPq1e5Je992GzRy43/xERERERETgUtNrqy2IAQMGM2DAYIKD3T3yXAoY+c/x48fp3r07EydOpESJEj7rPvroI2w2G6NGjaJ06dK0aNGCjh07Mnv2bADsdjvz5s2jb9++1K9fn7JlyzJ58mSOHTvGl19+6Yd3k7Mdjv3P5/nB84f9NBLJSobTN8MI8PYzMjRLmoiIiIiIBDhPSZo5eQ8jk6ckTQEjv/nrr7+w2WysWrWKSpUq+azbsmUL1atXx2q91Ky3Zs2a7N+/n1OnTrFz504uXLhArVq1vOsjIyMpX748v/766w17D7nF6bgzGC4D46yD+DMXOX7hpL+HJFnBExRKChK5XC6OnjrL0Zh4XJ7sIxERERERkQDlKUnDMDhy5DBHjhzGZHIvC+QMozSmTbqxGjZsSMOGDdNcd+zYMe68806fZYULFwbg6NGjHDt2DIBixYql2sazLrOsVr/H0m640/FncCU62TRqDQA15lUNyM8ht3EY7oCR2RqE1Wrm4sV4HuvzCgDfjq5CpM6xSI7jmQo1o1Oi3kgul+nKG4lkEYvFlCN/V8nO17CIXJmu4VzMcPDII48AMG3+OgBcRmDGByAbBIwuJz4+nqCgIJ9lwcHBACQkJBAXFweQ5jbnzp3L9HHNZhNRUeGZ3j8ncricRMf7fmZn7NEB9znkRtFBJuKA4LBQoqLCCQ6+dDNnNbl0jkVysMjIUH8PIZX4eAunTplz7I285Awulwmz2UzevGGEhIT4eziZlh2vYRHJOF3DuYfVZgEgNOxSG488ke6fL6YAjA94ZOuAUUhISKrm1QkJCQCEhV36BcFut/v8spCQkEBoaOYvXpfLICbmYqb3z4mi489hYGA2Xfrl/vj5k0RHX/DjqCQrxMW6z6HdCdHRF7h48dL/7US7XedYJAeyWMxERoYSExOH05m9pnq12xNwuVw4nQYOR/Yam+QeTqeBy+Xi3LmLxMU5/T2cq5adr2ERuTJdw7lPfLy7VYc94VLLjoQ4dyzCbnfkqnumyMjQDGfHZeuAUdGiRTlx4oTPMs/zIkWK4HA4vMtuvfVWn23KlClzTccOtF9yz8bFABBhuxQ5jXPEcyEhnmBLUHq7SQ7gTHR/o3OZrDgcLp8faobTGXD/10VyE6fTle2uYaczcOv85cbL6YHJ7HgNi0jG6RrOPby/vyT7NcbT1siRw3/WXItsHTCqVq0aS5cuxel0YrG4U8Q2bdpEyZIlKVCgAHny5CEiIoJffvnFGzCKiYnh77//pn379v4ceo5z3h4LQESQb6rd2YRzFAkr5I8hSVZJanrtM0tainUiIpJay5aPcezYUe9zk8lEaGgYd95Zhs6du1O5chU/ji5zHA4Hy5Z9SOvW7bL8tT//fBUffriY//47QsGChXjkkcdp27aD93c4ERGR7MrT9NpsutS+w2z2zJIWmMEiyAazpF1OixYtiI2N5ZVXXmH37t18+umnzJ8/n27dugHu3kXt27dn4sSJrF+/np07d9K/f3+KFi1K48aN/Tz6nMUbMLJF+Cw/l5D5XlCSTTiT0irTCBgZLgWMREQup02b9qxcuZaVK9eyfPkXzJo1l/DwcAYO7HPNE2z4w1dfrWXq1MlZ/rpffvkFEyaMpUWL1rz//lK6dOnJokXvsWDBvCw/loiISFbzTIRmMl8KGFmSHmuWtGyqQIECvPvuu4wZM4Ynn3ySQoUKMXjwYJ588knvNn379sXhcDBs2DDi4+OpVq0ac+fOxWZLI5tC0nU+0R0wymNLmWEU44/hSBYylGEkIpJpoaGhFChQ0Pu8YMGCvPjiyzzxRBN++OFbWrV62o+ju3qGcX1+6V2+/BOaNHmUxx9vDsDNNxfn0KEDrFq1nOee63JdjikiIpJVDJcnw+jSMos3w0gBo2xh3LhxqZZVrFiRDz/8MN19LBYLL774Ii+++OL1HFqu58kwigyNpFWrtuw88y8mi4lzChjlfN4MI/flbrFYadXsURL3/orFyHmNQkVE/M1TYhUU5A7EHzt2jJkz32br1i2cPx9D/vwFePDBh+nevTdms5k1a1bz/vtzqVWrNl98sZoqVary+utv8sMP37Fw4Xvs27cHl8tFiRKl6NatFzVq1AKgd++ulCt3F6dPn+LHH78jLCyM557rQqlStzNp0ngOHTrAHXeU4ZVXXuOWW9yl+SdPnmDatMn88stGzGYLd99dkd69+3PLLbeyZs1qxo4dCUDt2lWZMmUWVapUZcOGH5k79x32799HoUKFaNToIZ59tpN3Ftratavy3HNdWLNmNQ5HItOmzfEez6NHjz7kyxfls8xkMnH+/PnrdRpERESyjKckzWq10qpVWwBsNvf9kwJGEvA8AaOosHy8/PIIVuxew1cHv+OsStJyvhQlaUFBQbw8oB/nPxqGyRy43/xE5MYyDAMc9itveD1YgzAl60lwLU6ePMGUKZMIDQ2lZs3aAAwZMoACBQoyefJ0wsLC2LDhB6ZMmUSFChWpW7c+AEeOHObUqZPMm7eYhIQEdu7cwbBhg+ndux+1a9fjwoVYZs2azujRI1i+fI03U/rjjz+ga9dedOrUjQ8+WMjkyRMoUaIkL7wwiLCwMIYPH8KsWVMZM2YCcXFx9OnTjTJlyjJ16mwsFjNLly6ma9eOLFiwlAceeJDY2FimTHmTlSvXEhmZl02bfmbEiCH06TOAatVqcOTIYSZPHs/BgwcYPfrSH/KWL/+YiROn4HA4UwWLACpWrOzzPDY2lhUrlnmDXyIiItmZp+wsKCiYl18eAcDe/2J81gUiBYwEgHhHPAChtlAA8gXnBVSSlhsYSQGj5CVpJnNSA1KVpInIDWAYBhdXjcF1fLdfjm8pcgehzV7OVNBo4cL3WLp0EQBOpxO73U6JEiUZNWocRYsWJSEhnoceakrDho0oUqQoAK1atWXRovfZu3e3N2AE0LFjZ26+uTgA//77D/37D+bJJ1t61z/1VBsGDerLmTOnva91xx1laNu2AwDNm7dixYpltGjRmipVqgLQoEEjfvzxOwDWr19HbOx5hg8fjdXq/hVvyJDhbN++lVWrltOpUzciIty9Cj1ldgsWzKNZs+Y88UQLwF1K9uKLL9O3b3eOHv2PYsVuAuChh5pStmz5DH1mFy9eZMiQASQkJNCr1wsZ/qxFRET8xdvDSCVpPhQwEgDinAkABJuDOHPmDMQZGIbBebtSyXO8FBlGhmEQHXOe83GJ5LMqYCQiN4aJrMnwudGeeKIFLVu2AcBsNhMZmdcbdAEIDg6hRYtWfPfdev7++08OHz7Enj27OXPmNE6nb9nvLbfc4n18xx1lyJMnL4sWzefAgf0cPnyI3bt3AeBKNhtL8eKX9gkNdf9RxxN0ch8/mMRE9/f5f/75h5iYGJo0aeBzXLvdzoED+9N8f7t27WTHjr/47LMV3mWePkf79+/zBoyKF0+dVZSW06dPMXhwf/777wiTJ0/z7i8iIpKdeUrSTOC+HwZMJvf9kwJGEvASHO6AkckBDZvcB0DN15t6S9Uk50qZYRQfH0eDR5sB8GW3WkT6bWQiEihMJhOhzV7OkSVpefJE+gRtUoqLi6NXry7Y7Qk0aNCIJk0eo3z5u+jVK3Wj5+DgEO/j7du3MnBgH2rVup+KFSvTuPHDxMfHM3ToIN+hW1P/qpbeezEMF7feehvjxk1Ktc4TbErJ5TJo2/YZmjR5NNW65M2+g4OD09w/uQMH9jNgQG8Mw2D69DmUKlX6ivuIiIhkB56yM0diAg0bNgTg09U/+awLRAoYCQDxTndJWojF9xdCz+xpkoN5ys4saVzuLgeGYWRZbw8RkfSYTCawXTnokNNs3ryRXbt2smrVOvLnLwBATMw5zpw5fdn9li5dxD33VGXMmAneZZ98shTI/ExmJUuWZu3az4mIyEO+fPkAcDgcvPbayzRo8CAPPPBgqu/3pUqV5uDBAz5BsW3btvDxx0sZNGhIuoGmlP777wh9+3YjT55I3nxzqrekTkREJCfw/Ow1J/s5qZI0MPt7AJI9xCdlGAVbg3yWxzniSXSpbClHS1GSlopmShMRybRChQoDsG7dFxw7dpTff/+NIUMG4nA4sNvTz6gqXLgoe/b8y++//8bRo//x+eerePfdWQDeErOr9dBDTYmMzMuwYYP5668/OXBgP//3f6+yadPPlC59O3Ap02jnzh0kJMTTrt0zfPfdet57bw4HDx5gy5bNjB07kgsXYn0yjK5k7NiR2O2JvPrqGKxWK6dPn/J+iYiIZHeeLCKz+VLAyOQNGLnS3CcQKMNIAEjw9DCyXEqXt5jcjZFj7bFEheTzx7AkCxhJGUamtDKMAJxOMOtbgYhIZpQvX4E+ffrz4YdLmDNnJoUKFeKBBxpTuHARdu78O939Onfuxpkzp3jppX4AlChRiqFDRzBq1HB27PiL224rcdVjiYiIYNq02Uyf/hYDB/bG6XRRpkxZJk+eTokSJQGoUqUa5ctXoEeP5xk+fDQNGzZi5EhYuHAeCxbMIzIykvvvr0uPHn0zfNxTp07y22/bAHjuubap1v/005arfi8iIiI3kickZE6j6bVK0iSguQwX8UkBoxDrpXKBiKBwYrnIeQWMcrYrZRg5E3NlmYiIyLX65JPVGdqudet2tG7dLt31TZs+RtOmj/ksy5s3n085msf69Q29j6dNm+2zrlixm1IFXzp16kanTt28z2+66eY0X9cjMjKS2bPn+yxr2LARDRs2SnefKwV8ChYspKCQiIjkaIYrrZI0978qSZOAZndeSplP3sMojy0cgBjNlJajeZpeY007YGSo5FBERERERAKYd5a0ZClGnvI0w7i0PtAoYCTe7CKzyYwtWWlSRJB72uDziRf8Mi7JIp5Z0szpZBi51MNIREREREQCl6dNkW+GkTnZ+sAMGKkkTbwNr0MswVitNh577AkAIkMi4QKcV4ZRzpYiw8hisfL4409i37XRXZfrVIaRiIiIiIgELk8GkdVm8d4PB9ku/cHd6TKwWvwxMv9SwEiId8YDEGwJJigoiNGjxwGwfPfncBrO22P9OTy5BobL6c6hBExJPYyCgoIYM+YNzr3XC1fceZWkiYiIiIhIQPMEjIKCgr33w4mOS7OjOZ0GpFOwkZupJE28GUah1hCf5Xk8JWkKGOVczmRTM6eYJc07a5oyjEREREREJIC50mx6felxoPYwUoaReHsYBVuCMQyD+Pg4ACKs7qbXChjlXEbygFFSDyPDMLh48SLxTrAahnoYiYiIiIhIQPO0KDJhEBd3EYCQkFBMgEHgzpSmDCMhwdPDyBpMfHwctWpVoVatKgS53AGG84kKGOVYnuwhkwVTUtO2+Pg4qlevTMM3vyDe4fINKomIiIiIiAQYIymDKDExwXs/HB8f550pzel0XW73XEsBIyEuqYdRiCXYZ7lK0nKBFA2v06QMIxERERERCWBplaTBpbK0QJ0lTQEjSZZh5NvDKCLIXZIWm3gBlxGYEdWczpM95Gl4nSb1MBIRERERkQDmyTAym1MEjCxJGUYB2sNIASPx9jBKlWFkcweMXIaLi4lxN3xckgU8GUaW9NuVaZY0EREREREJZJ4EopQZRp7nTmdgBozU9Fq8s6QFW30DRhazhXBrGBccF4mxn/dmHEkO4vAEjC5XkqaAkYhIWlq2fIxjx456n5tMJkJDw7jzzjJ07tydypWr+HF0meNwOFi27ENat26X5a/9ySdL+eSTDzlx4jg33VScp59uzyOPNMvy44iIiGQ1T8lZiniRStL8PQDxv/h0ehgBRCT1MYpNvHBDxyRZw5M9ZLpMhpFK0kRE0temTXtWrlzLypVrWb78C2bNmkt4eDgDB/bh2LFj/h7eVfvqq7VMnTo5y1935cpPmTlzKs8/341Fiz6mVaunGT9+DD/++F2WH0tERCSruYx0ehhZ3CETzZImASv5LGkpRdjCALiQePGGjkmySIYyjNT0WkQkPaGhoRQoUJACBQpSsGBBSpW6nRdffJmEhAR++OFbfw/vqhnXqQfDhQuxdO/eh8aNH+amm26mWbMnKVWqNJs3/3JdjiciIpKV0mt67S1JC9CAkUrShDhvD6MQzGYLjRo9BIDZbCHcdqnxteQ8hjN1wMhsttC48cM4j+/GbDJhKMNIRG4AwzCwuxL9cuwgsw1Tyhzza2CxWNyvG+T+3nrs2DFmznybrVu3cP58DPnzF+DBBx+me/femM1m1qxZzfvvz6VWrdp88cVqqlSpyuuvv8kPP3zHwoXvsW/fHlwuFyVKlKJbt17UqFELgN69u1Ku3F2cPn2KH3/8jrCwMJ57rgulSt3OpEnjOXToAHfcUYZXXnmNW265FYCTJ08wbdpkfvllI2azhbvvrkjv3v255ZZbWbNmNWPHjgSgdu2qTJkyiypVqrJhw4/MnfsO+/fvo1ChQjRq9BDPPtuJoKAg77bPPdeFNWtW43AkMm3aHO/xPNq2fcb72OFw8P3333DgwH6ee65rln3uIiIi14snHmS1+d4PB3pJmgJG4pNhFBwczMSJb3vXXcowUsAoR0pjlrTg4GAmTZqC/dtZXNjxs3oYich1ZxgGk7bNYO+5A345fqm8JRhQpUeWBI1OnjzBlCmTCA0NpWbN2gAMGTKAAgUKMnnydMLCwtiw4QemTJlEhQoVqVu3PgBHjhzm1KmTzJu3mISEBHbu3MGwYYPp3bsftWvX48KFWGbNms7o0SNYvnwNNpv7+/bHH39A16696NSpGx98sJDJkydQokRJXnhhEGFhYQwfPoRZs6YyZswE4uLi6NOnG2XKlGXq1NlYLGaWLl1M164dWbBgKQ888CCxsbFMmfImK1euJTIyL5s2/cyIEUPo02cA1arV4MiRw0yePJ6DBw8wevQ47/tevvxjJk6cgsPhTBUsSu7337fTp083XC4XjzzSjDp16l3zZy4iInK9eUrSUt4Pe2dJcwXmrOEKGMllexh5MoxUkpZDpZFh5OHta6QMIxG5IbIuw+dGWrjwPZYuXQSA0+nEbrdTokRJRo0aR9GiRUlIiOehh5rSsGEjihQpCkCrVm1ZtOh99u7d7Q0YAXTs2Jmbby4OwL///kP//oN58smW3vVPPdWGQYP6cubMae9r3XFHGdq27QBA8+atWLFiGS1atKZKlaoANGjQyNsnaP36dcTGnmf48NFYre7v8UOGDGf79q2sWrWcTp26ERHh7k1YoEBBABYsmEezZs154okWANx8c3FefPFl+vbtztGj/1Gs2E0APPRQU8qWLX/Fz+vWW29j7txF/PPP37z99iTy5s1Hz559r+ozFxERudGMdHoYmc0qSZMAl94saQDhSRlGKknLmTzlZqbLBIwMZRiJyHVmMpkYUKVHjixJe+KJFrRs2QYAs9lMZGReb9AFIDg4hBYtWvHdd+v5++8/OXz4EHv27ObMmdM4nb494m655Rbv4zvuKEOePHlZtGg+Bw7s5/DhQ+zevQsAV7K/YhYvfmmf0NBQAG/QyX38YBIT3Z/rP//8Q0xMDE2aNPA5rt1u58CB/Wm+v127drJjx1989tkK7zLPL8379+/zBoyKF08/qyi5qKj8REXl54477iQ6Opr33ptDly49vBlTIiIi2ZHnR2+qptcmlaRJgLuUYRRCXNxFatVyTxO8ceM2IpRhlLN5M4wuXerJz/GXXaoRpAwjEbkBTCYTwZYgfw/jquXJE+kTtEkpLi6OXr26YLcn0KBBI5o0eYzy5e+iV68uqbYNDg7xPt6+fSsDB/ahVq37qVixMo0bP0x8fDxDhw7y2ceTKZRcesEvw3Bx6623MW7cpFTrPMGmlFwug7Ztn6FJk0dTrfNkIbnHnvqPSslt2vQzRYoUpWTJUt5lpUvfgd1u59y5cxQsWPAye4uIiPiX548lCQlxVK5cGXDfD18qSVPASAKQy3CR4LQDSbOkpZgwSxlGOVtaTa9T0SxpIiKZtnnzRnbt2smqVevIn78AADEx5zhz5vRl91u6dBH33FOVMWMmeJd98slSIPMzmZUsWZq1az8nIiIP+fLlA9wNqF977WUaNHiQBx54MFWwqVSp0hw8eMAnKLZt2xY+/ngpgwYNSTfQlNKcOTMpXvwWRo4c6132999/kjdvXvLnz5+p9yMiInKjXJolzXd5oJekmf09APEvT7AI3BlGKUUEKcMoR/OWpKUfGzYc9nTXiYjI5RUqVBiAdeu+4Nixo/z++28MGTIQh8OB3Z7+99fChYuyZ8+//P77bxw9+h+ff76Kd9+dBeAtMbtaDz3UlMjIvAwbNpi//vqTAwf283//9yqbNv1M6dK3A5cyjXbu3EFCQjzt2j3Dd9+t57335nDw4AG2bNnM2LEjuXAh1ifD6Eratu3AN998xbJlH3L48CFWrVrOkiULef75rpjN+nVTRESyL8Mw8ISDTGaVpCWnDKMAl+B09y8ym8zYzFac+P6SGm7VLGk5WkYyjJJ6WImIyNUrX74Cffr058MPlzBnzkwKFSrEAw80pnDhIuzc+Xe6+3Xu3I0zZ07x0kv9AChRohRDh45g1Kjh7NjxF7fdVuKqxxIREcG0abOZPv0tBg7sjdPpokyZskyePJ0SJUoCUKVKNcqXr0CPHs8zfPhoGjZsxMiRsHDhPBYsmEdkZCT331+XHj2urlH1Aw80xuFwsGjRfKZPf5siRYrSv/+LPPbYE1f9PkRERG4kV7LM3lQ9jCzuP3oEaoaRAkYBztPwOsQSnGZPhPCkDKM4RzxOlxOL2XJDxyfXxlOSllbTa+82ChiJiKTpk09WZ2i71q3b0bp1u3TXN236GE2bPuazLG/efD7laB7r1zf0Pp42bbbPumLFbuKnn7b4LOvUqRudOnXzPr/pppvTfF2PyMhIZs+e77OsYcNGNGzYKN19Uh4zPQ891JSHHmqaoW1FRESyi+TZQxZzerOkuQhEyhEOcJ6G18GWtJtZhllDMSVNhXzBobK0HCcjGUaJChiJiIiIiEhgcjjTDxhZ1MNIApknwyjUmrp/EbhL1cJs7n4HsXaVpeU4GQgYKcNIREREREQClU9JWjoBI/UwkoAUn9TDyJNhZDZbqF27nvcxQIQtnAuJF9X4Ogcy0mh6bTZbqFOnHmb7ecwmE4YyjEREREREJEA5k2UY2axWn/vhQJ8lTQGjAJfg6WFkdQeMgoODmTbtHZ9twm1qfJ1jpZFhFBwczMyZcwiO3s2xD0ap6bWIiIiIiAQsTzDIbDIREhLicz+skjQJaHFJPYxC0ulhBBBucze+jlXAKMe5XNNrc5C7DFEZRiIiIiIiEqg8Da0tltSTQAV6SZoCRgHOk2EUbL1cwMidYXQxMe6GjEmyUFJJGpbUyYQmW9I5V4aRiIiIiIgEKE8wKGX/ouTLlGEkAcnTwyjU4s42iYu7SM2a91Cz5j3Exbl7FoVb3QGjWIcyjHKcNErS4uIuUq1aJe66/wHiEp3KMBIRERERkYDlCQZZTKZU98OBXpKmHkYBLj6NDKP4eN9MImUY5VzekjSrb0laXFyyc+mwYxgGJlPqiLqIiIiIiEhu5g0YJZWkJb8ftpjdOTYqSZOAFJ+BHkZh3qbXmiUtx/FkGJlT9zC6xACn/YYMR0REREREJDtRSVr6lGEU4FLOkpaWcAWMcixPhhHWdAJGSVlFhj0O02X+D4iIBKLevbvy22/bfJbZbDaiovJTu3ZdevZ8gZCQkCw7XsuWj9GkyaN06tTNZ7lhGLRu/QR33HEnY8ZMSHPffv16YjKZmDx5+mWPMWbMaxw9+h/Tps3OsnGnZdmyj1i6dDGnT5+ibNly9Os3iDvvLJuhfcePH0NiYiKvvPLadR2jiIgIXAoGWdMIGF0qSXPd0DFlF8owCnBxST2MQizp/8Lr6WF0waGAUY6T1PTaZE47NmwKyQOAcfHcDRuSiEhO0rDhg6xcudb7tXDhR7Rv35FVq5YzbdpbN2QMJpOJpk0fY+PGDcTGxqZaf+LEcbZt28Kjjz5xQ8ZzJV988RkzZrxNly7dmTt3IcWK3UT//r04e/bsZfdzuVy88850Vq1afmMGKiIiwqWAUVoZRpolTQLa1WQYXVSGUc5zhQwjc2heAIw4BYxERNISHBxMgQIFvV/Fi99C8+ZP0bhxE9av//KGjaNp08dwOBx8993XqdatW/cFefLkoW7d+jdsPJezYME8WrRoTePGTShZshRDh44gODiE1avTDwTt37+PXr06s3r1CooUKXoDRysiIoHO6XRnD3n6FSUX6CVpChgFuIz0MEpekmYYgXmh5FTeptfp9DAyhUW6t1OGkYjIVQkKCsZqvZS9mZiYyIwZU3jiiSY8+GAdunbtyObNm3z2Wb16Bc8+24aGDe+nUaPa9OzZmZ07/87Q8QoXLkK1ajX58su1qdatW/c5jRs3xWaz8fvv2+nbtzuNG9ejQYNatGvXknXr1qT5mkeP/kft2lXZtm3LZZd9/vkq2rVrScOG99OuXUs++ugDXOmk5kdHn+HQoYNUrVrdu8xqtVK5chV++217uu9v27Yt3HZbSRYu/JBixW664uchIiKSVTzZQ5bLlqQF5n2wehgFuJSzpJlMZu69t5r3MVwKGDkNJwlO+2WzkSSbSSPDyGQyU7VqdWw2C5Ywd4aRSwEjEbkB4uLSz1Q1my0EBwdnaFuTyezTO+hqtr1WDoeDzZs3sW7dGh5/vLl3+Zgxr3HgwD5GjBhNoUKF2bDhBwYP7sfYsRO5777afP/9t0yePJ6XXhpGpUr3cOrUKd56awLjxv0f8+cvydCxH3mkGa+99jInT56gUKHCAOzY8Rf79+9j1KjXOXnyBAMG9KZFi9YMHvwKiYmJLF78PuPGjaZatRrkz1/gqt/vypWf8s470xkwYDDlyt3Fv//+w+TJ4zl16gQ9e76QavsTJ04A7gBXcgULFuTff/9J9zjNmz911WMTERHJCs5kAaOU98OBXpKmgFGAu5Rh5P5lOiQkhLlzF/psYzPbsJqtOFwOLiReVMAohzAMl7eHEZZLAaOQkBDmz19EVFQ4/331AfH7fsF1cq+fRikigaRWrSrprqtdux7Tpr3jfd6gwf0+09omd++91Xx+VjVt+gDR0dFpblu+fAWWLPkkkyOGL7/8gu++W+99npCQQJEixWjbtgMdOjwHwOHDh/j663W8995i7rijDABt2rRn9+5/WbJkAffdV5u8efMyZMhwGjduAkDRosV49NFmTJo0PsNjqVOnHnny5OGrr9bRtm0HwN0vqFy5uyhV6naOHDlMp07dePrpDpiSJjXo0OE51q79nEOHDmYqYPT++3Pp2LETjRo9BMDNNxfnwoULvPnmG3Tq1N0nyAcQH+/+vcJm881sDQoKxm7XjJwiIpL9JO9hlPJ+ONBL0hQwCmAuw0VC0nTqlwsCmUwmwq1hnLPHcNFxkQJE3aghyrXwBIsAkyXtkjTbLXcRv/kTHPu34Tj8J9biFW7U6EREcoTatevSo0dfDMNgx46/ePvtiVStWp0OHZ7zlqTt2uXOnOnZs7PPvg6Hg4gI9+QClStXYf/+fcyf/y4HDuzn8OGD7NmzO93SrrTYbDYaN27KV199Qdu2HUhMTGT9+i/p2rUX4A7mNG3ajI8/Xsrevbs5fPgQu3f/C4DT6bzq9x4dHc2JE8eZNWs6c+bM9C53uVzY7QkcPfofJUqU9NnHE0BKTEz0WW63JxASEnrVYxAREbnenJctSXNX3TidChhJgPEEi+Dys6SBuyztnD2GC2p8nXM4k/2ynk7Ta2uR0ljvrINj148k/v2tAkYicl1t3Lgt3XVms8Xn+bffbkh3W0/JtMeaNevT2TL1tlcrLCyc4sVvAeCWW26lYMFC9OvXE4vFwqBBQ4CkjE5g+vQ5hIWF++xvTvpF88sv1zJmzKs0btyEChUq8vjjzdm7dw+TJr1xVeN59NHH+fjjD9i3by8HDx7AbrfTqFFjAPbt20vPnp0pU6Ys1arVoF69BuTLF0WXLs9m+PWTB5Y876tv3/5UrVoj1bZpNacuUsRdinbq1EmfYNKpU6coVKhQhschIiJyo2Skh5ErQHv55oiA0fHjx6lbt26q5a+//jrNmzdnx44djBkzhj///JP8+fPTsWNHnnnmGT+MNGdJcLr7F5lNZmxJ067HxV2kadMHAPcv4KGh7v5FyRtfS87gaXiNyQSmSzdinnNsMplYu/YbbHfeh2PXjzhPH/TTSEUkUHh+pvhz22tVpUpV2rRpx5IlC6lduy41a95HyZKlATh9+hR33lnWu+0770zHYrHQuXN3Fi+ez2OPPcGgQUO963/88XsADMPwlpBdSenSt1O2bHm++eYrDhzYT4MGjQgPjwBg5cpl5M+fn7femuHd/qeffkj3tTxlYxcvXvAuO3To0s+CqKj85MsXxX//HfEGzQDWr/+SH374lldeGZnqNaOi8nPrrbexfftWb+Nrh8PBb79t48kn1adIRESyH0dStq/ZbEp1P6yStBxg586dBAcH8/XXX/v8QpUnTx6io6N57rnnaNiwISNHjuS3335j5MiRhIeH06JFCz+OOvuLd1yaIS3555pWH4gwBYxyHkdSwMhiS3Ujkvwcm6NuBsA4fwrDYcdkDbphQxQRyYk6derODz98z8SJr7NgwYeUKlWa++6rw4QJrzNgwEuULFmK775bz6JF83n55VcBdxPoP/74nX/+2UlERAQ//fQ9n376EQB2uz1VL6DLefTRZnz00QecPHmSiROneJcXLlyEEyeOs3HjBkqWLMU//+zgrbcmeo+RUoECBSlW7CY++ugDbrnlNs6dO8ucOTO9PzNMJhPt2j3LnDkzKFKkKDVr3s/u3f8yceI46tSpR1BQ2j8v2rRpz9tvT6R48VsoW7Y8ixbNx25P4LHHnvBuc/r0KUJDwwgLu3HBPhERkbR4M4ws7qzg5PdK3lnSnBkvIc9Nri1P+wbZtWsXJUqUoHDhwhQqVMj7FRISwkcffYTNZmPUqFGULl2aFi1a0LFjR2bPnu3vYWd78UkZRsGWK/+SGm51/0J30aGAUU7hzTBKp3+RhykkD1isgIERF3P9ByYiksMFBwfz0kuvcPz4MWbPdmfzjBr1OvXrN2TChLF06NCKL774nCFDhtOkyaMA9O8/mKio/PTu3ZWuXZ/l559/Ytgwd4bOzp1/X9XxGzV6mOPHj1GoUCEqVarsXd6yZRsaNnyQ0aNH0KFDa95/fy5du/akWLGb0jyGyWRi2LBRxMbG0rHj04wfP5bu3Xt7y+gAnn66Pb1792fZso9o164lb789kWbNnvTJlEqpWbMn6dSpO3PmzKRz5w4cO3aUyZOnky9fPu82jz/+MB98sDDd1xAREblRHM4MlKQpwyj7+ueffyhdunSa67Zs2UL16tW9jScBatasyTvvvMOpU6coWLDgjRpmjhOXlGEUar3ydMMqScuBkgJG6TW89jCZTJhC82LEnsaIOwd5dM2IiABMm5b+H5/uuedefvzxV+/zkJAQ+vYdSN++A9Pc/qabbvYpFfN44IHG3seffLI6Q+OKiIhg/frUPZ6CgoIYOnQEQ1PEcjxBK4BXXnnNZ12lSpWZN2+Rz7Lvv//F53nz5k9d9bT3bdt28M7klpafftqS7rrLfe4iIiJZLdHhzh6yWVPn03hL0tTDKPvatWsXUVFRtGvXjn379nHbbbfRo0cP6taty7Fjx7jzzjt9ti9cuDAAR48ezXTAyJrGf5bcxu5yZxiF2kK879eThud57FmeJ9jdxDPOGRcQn03u4J4lzWQN8jlnaZ1jc1henLGnMSXE6PyK5ACe6zj59ZxduFwZ68UjkhUsFlOO/LmVna9hEbkyXcO5i6ehdbDNkupeyWZz94J1uQIjRpBStg8YORwO9u7dy+23386QIUOIiIjg888/p2vXrrz33nvEx8enqqH39AFISEjI1DHNZhNRUeFX3jCHM0e7L4zI0Ajv+w0OvvSLflRUuLe3QKEz+QBIICEgPpvcIO6chfOAJTjY55wlP8eRkaGEhYWRkDc/F0/sJZR4InV+RXKMyMjsN015fLyFU6fMOfZGXnIGl8uE2Wwmb94wQkKunCmdXWXHa1hEMk7XcO5gtbnDIuFhQT73TVFR4eSNdPcANFsCI0aQUrYPGFmtVn755RcsFov3F4IKFSrw77//MnfuXEJCQlI1cvQEijLbSNHlMoiJyf2lV6fOnQPAatiIjnbPkHLx4qX3HR19gYQEd1DJlOj+r3Lu4nnvtpK9JZ49D4ALi885S36OY2LiSEgwcFjd3/xiT5/CqfMrku1ZLGYiI0OJiYnLdk0Y7fYEXC4XTqeBw5G9xia5h9Np4HK5OHfuInFxTn8P56pl52tYRK5M13DuEnPe3arF5XT53DdFR18g7qI71pCQ4Mg198GRkaEZzo7L9gEjgPDw1JG8O+64g59++omiRYty4sQJn3We50WKFMn0MQPhl9wL9jjA3fTa835dLihfvoL3sWd5iNkdrIu1XwiIzyY3cHgCqWabzzlzueCuuypgtVowDPc5Nmzuv44443V+RXISp9OV7a5ZpzMwa/zFP3J6YDI7XsMiknG6hnMHe6L7Dw8WsynV/TBJv9Y4cvjPm8zK9gGjf//9l9atWzNz5kxq1KjhXf7nn39y++23U65cOZYuXYrT6cRicdcXbtq0iZIlS1KgQAF/DTtHiPc0vbZcSuUOCQlhyZJPUm0bbnMH7dT0OgfxzJJm9W16HRISwocffkpUVDjR0e4AkSkoKRvPrvMrIiIiIiKBI3nT65T3wxaLO6soUGdJy/bNBUqXLk2pUqUYNWoUW7ZsYc+ePbz++uv89ttv9OjRgxYtWhAbG8srr7zC7t27+fTTT5k/fz7dunXz99CzvauZJS0sKQPloiMOI0A7xOc4jqQMoyvMkgZgCnKfXyMp60xERERERCQQOJLKCm1plGl5Z0kL0IBRts8wMpvNzJo1izfffJN+/foRExND+fLlee+997yzo7377ruMGTOGJ598kkKFCjF48GCefPJJP488+4tzZjxgFG51Z6C4DBfxznhCrWrwlt0ZSRlGpgwFjNznVwEjEREREREJJMkzjFKymDwBo8ArR4McEDACKFiwIK+//nq66ytWrMiHH354A0eUO3hK0kKSBYzi4uJo3vwRAD799HNCQ92BIZvFRpDZht2VyIXEiwoY5QSekrQUAaO4uDhatHgUs9nE8uWfY7MFXwoYJagkTUREREREAkdiUoaR1WJOdT/syTAK1JK0HBEwkusj7ZI0g6NH//M+Ti7MFoY94RwXEi9SMFT9obK79DOMDP7774j7kae8MKkkTT2MREREREQkkPhmGPneD1ssgV2Slu17GMn14216ncFsoXCbOwtFja9ziHQyjNJiClZJmoiIiIiIBB5PhlGaJWnqYSSB6mqaXsOlPkYXFTDKEQxH2rOkpeVS02udWxERj969u/Lbb9t8ltlsNqKi8lO7dl169nyBkJCM/QzNiJYtH6NJk0fp1Ml34g7DMGjd+gnuuONOxoyZkOa+/fr1xGQyMXny9MseY8yY1zh69D+mTZudZeNOy7JlH7F06WJOnz5F2bLl6NdvEHfeWTbd7Y8fP8aMGVPYvn0rdrud8uUr0Lt3P0qVKn1dxykiImJPTD9gZDYFdkmaMowClGEY3qbXIZYMBoySMoxiHQoq5AiZaHqNMxHD6bieoxIRyVEaNnyQlSvXer8WLvyI9u07smrVcqZNe+uGjMFkMtG06WNs3LiB2NjYVOtPnDjOtm1bePTRJ27IeK7kiy8+Y8aMt+nSpTtz5y6kWLGb6N+/F2fPnk1ze7vdzosvvsDp06cYP34yM2a8S1hYKC+80IPo6OgbO3gREQk48Qnu+5/Q4NT5NJakmdMCNcNIAaMAZXcl4nC5LwxPIOhKwmzKMMpRrqIkDdulskQjUWVpIiIewcHBFChQ0PtVvPgtNG/+FI0bN2H9+i9v2DiaNn0Mh8PBd999nWrdunVfkCdPHurWrX/DxnM5CxbMo0WL1jRu3ISSJUsxdOgIgoNDWL16eZrb//77dvbu3cOrr/4fZcuWp1Sp0gwfPpq4uIts2PDDDR69iIgEmni7E4DQoDQCRgFekqaAUYCKtV8AwGq2EmwJytA+6mGUs3ibXmekJM1sBmuw+4n6GImIXFFQUDBW66VfLBMTE5kxYwpPPNGEBx+sQ9euHdm8eZPPPqtXr+DZZ9vQsOH9NGpUm549O7Nz598ZOl7hwkWoVq0mX365NtW6des+p3HjpthsNn7/fTt9+3anceN6NGhQi3btWrJu3Zo0X/Po0f+oXbsq27Ztueyyzz9fRbt2LWnY8H7atWvJRx99gCud6YWjo89w6NBBqlat7l1mtVqpXLkKv/22Pc19SpUqzYQJb1OoUGHvMovFAsD58+cv86mIiIhcuzi7O5EiJMiSal2gz5KmgFGAupDoDhhF2MIxJdVlupkoVep2SpW6HTD57HMpYKSAQo6QboaRidKlb+fOO+/0OfeX+hjp/IrI9REXdzHdr4SEhAxvGx8fn+ltr5XD4eDnn39i3bo1PPRQU+/yMWNe49dfNzFixGjmzVtMw4aNGDy4Hz///BMA33//LZMnj6dt22dYsuQT3nprJna7nXHj/i/Dx37kkWb89ts2Tp484V22Y8df7N+/j8cee5yTJ08wYEBvypYtz7x5i5g3bzHlyt3FuHGjOXPmdKbe78qVnzJ9+ts891wXFi78kC5derB48XxmzZqa5vYnTrjHVrhwEZ/lBQsW5MSJY2nuU6BAQWrVut9n2ccfLyUhIYHq1WtmatwiIiIZFZfgzjAKCbaQ8n7YGuAZRmp6HaBikwJGKcvRQkND+fTTz9Lcx9P0+oLjwvUdnGQJb9PrFAGj0NBQVq5cQ1RUONHRF3AkTSNpsoVgAEZi1t5ciYh41KpVJd11tWvXY9q0d7zPGzS4n/j4tAPY995bjblzF3qfN236QLq9bsqXr8CSJZ9kcsTw5Zdf8N13673PExISKFKkGG3bdqBDh+cAOHz4EF9/vY733lvMHXeUAaBNm/bs3v0vS5Ys4L77apM3b16GDBlO48ZNAChatBiPPtqMSZPGZ3gsderUI0+ePHz11Tratu0AuPsFlSt3F6VK3c6RI4fp1KkbTz/dwfsHgQ4dnmPt2s85dOgg+fMXuOr3//77c+nYsRONGj0EwM03F+fChQu8+eYbdOrUneDgYJ/tPQE6m833Z09QUDB2uz1Dx/z++2+ZNWsqrVq1pXTp2696zCIiIhnlcLpwJM2SFhpsJTTE5nM/nOB0/0HLmU5mbW6ngFGAik2WYZRRl3oYKQMlR7iKptcAJGUYqSRNROSS2rXr0qNHXwzDYMeOv3j77YlUrVqdDh2e85ak7dr1DwA9e3b22dfhcBARkQeAypWrsH//PubPf5cDB/Zz+PBB9uzZnW5pV1psNhuNGzflq6++oG3bDiQmJrJ+/Zd07doLcAdzmjZtxscfL2Xv3t0cPnyI3bv/BcDpdF71e4+OjubEiePMmjWdOXNmepe7XC7s9gSOHv2PEiVK+uzjCSAlJib6LLfbEwgJCeVKVqz4hMmTJ9C4cRN69XrhqscsIiJyNTz9i+DyJWmGAS7D8M6aFigUMApQmQkYXSpJU4ZRjnA1Ta+5NFOaml6LyPWyceO2dNeZzb6/pH377YZ0tzWZfCvq16xZn86Wqbe9WmFh4RQvfgsAt9xyKwULFqJfv55YLBYGDRoCgGG4gz7Tp88hLMz356rZ7D7+l1+uZcyYV2ncuAkVKlTk8cebs3fvHiZNeuOqxvPoo4/z8ccfsG/fXg4ePIDdbqdRo8YA7Nu3l549O1OmTFmqVatBvXoNyJcvii5dns3w6ycPLHneV9++/alatUaqbYsUKZrGMncp2qlTJ32CSadOnaJQoUKXPfaMGVNYsmQBrVu3o3fvfilK5kVERLJeXNIMaUFWMxZz6t8ZPCVp4O5jZLYE1s8mBYwC1IWkptcRQb6/2MbFxdGu3VMALF78MaGhl/4aGK4MoxzFSCfDKC4ujvbtn8JiMbN48cfYbO6/BptsIe79lGEkItdJaGjGZuW8ntteqypVqtKmTTuWLFlI7dp1qVnzPkqWLA3A6dOnuPPOst5t33lnOhaLhc6du7N48Xwee+wJBg0a6l3/44/fA2AYRoaDI6VL307ZsuX55puvOHBgPw0aNCI8PAKAlSuXkT9/ft56a4Z3+59+Sn+WMU/Z2MWLl/4QdOjQQe/jqKj85MsXxX//HfEGzQDWr/+SH374lldeGZnqNaOi8nPrrbexfftWb+Nrh8PBb79t48knn0p3LJ5gUa9e/Xj66fZX+hhERESyhCfDyJNdlPJ+2JzsXsrpMrCmTkLK1dT0OkCdT4wFIDxVhpHB3r272bt3N+Db2MsbMHLE4TICs4YzR3EkNZC1ppwFz2DPnt3s2rULw0h2jtX0WkQkQzp16k7x4rcyceLrXLx4kVKlSnPffXWYMOF1fvrpB44cOczixe+zaNF8br65OOBuAv3HH7/zzz87OXLkMB9+uJhPP/0IIMO9fTwefbQZ69d/ycaNG3jkkce9ywsXLsKJE8fZuHEDx44d5fvvv+HNN8ele4wCBQpSrNhNfPTRBxw4sJ///e835syZ6Q1emUwm2rV7lk8++ZBlyz7kyJHDfP/9t0ycOI7g4BCCgtKeZbVNm/YsXbqIL774jH379vL666Ow2xN47LEnvNucPn2Kixfds65u27aFJUsW0LJlGxo3fpjTp095vzzbiIiIXA+eDKOQIE8uje/9sCVFhlGgUcAoQJ1NiAEgX3BkhvcJsyYFFDCIc6gxcnZnONw3ByZb8BW2dDOph5GISIYEBwfz0kuvcPz4MWbPdmfzjBr1OvXrN2TChLF06NCKL774nCFDhtOkyaMA9O8/mKio/PTu3ZWuXZ/l559/Ytgwd4bOzp1/X9XxGzV6mOPHj1GoUCEqVarsXd6yZRsaNnyQ0aNH0KFDa95/fy5du/akWLGb0jyGyWRi2LBRxMbG0rHj04wfP5bu3Xt7y+gAnn66Pb1792fZso9o164lb789kWbNnvTJlEqpWbMn6dSpO3PmzKRz5w4cO3aUyZOnky9fPu82jz/+MB984G5c/tVX6wD45JOlPP74wz5fnm1ERESuB2+GUXDaqUPJy9QCcaY0k+GTYiAATqeLM2dyd5+eMb9M4r8Lx+hVqRPlC5TxLo+Lu+idxWbjxm2p0vwHfj+ceGcCr9Z8kcJhl+9FIP4Vu6APRvx5wlqOxpL/UilB8nO8efNvBAW5S9ESfl2GfftqbHc9QMj9HfwyZhHJGKvVnGqmw+wiMdHO6dNHKVCgGDZb2hkoItcqp/8/y87XsIhcma7h3GPzjuPMWvkXd96SjyHtqqS6Hw4JCaXTG98CMLlPbfKG57yfOSnlzx+OxZKx3CFlGAWoswnnAMgXnPeq9gvzNr5WFkp2580wsl5dhpFhV/aYiIiIiIjkfil7GKVkMpm8ZWkqSZOAkOC0c9HhDvhEhVxdwEgzpeUMhmFAUsCIDAaMsCWVpCkYKCIiIiIiAeBKASPAGzByugIvm0wBowB0Nv4sACGWYEKtoZffOIVw66XG15KNOe14mpabUjW9TptJTa9FRERERCSAxNs9Ta/TDxiZvQGjwMswsl55E8ltTsSdAqBAaP401pooVuwm7+OULmUYadaS7MxTjgakkWFk4qabbsZsNvlM46yAkYiIiIiIBJJLGUae0Ejq++FALklTwCgAHbtwAoCiYYVTrQsNDeWLL75Jd9+IoAgAYuznr8/gJGskJrj/tVgxmX0TCUNDQ/nyy29TN+rzBIxUkiYiIiIiIgEgZUlaWvfD3pI0Z+AFjFSSFoCOXUwKGIWnDhhdSVRSk+zopLI2yZ6Mq+1fBJg8PYyUYSQiIiIiIgHgUkla+rk0Vqs7bJLoVA8jCQDHPRlG4UWuel9vwCjhbFYOSbKaw51hlNEZ0gBMQSGAZkkTEREREZHAkJCBptdBVvc6e6LzhowpO1HAKMAYhnEpwyiNkrT4+Hjatm1J27YtiY9PHTjIF5IPgOj4c9d1nHJtjERPwCh1w+v4+Hhat25O06ZNfc6xN8PIacdwOW7IOEVERERERPwlZUlaWvfDQbakDCNH4GUYqYdRgImxnyfOEY8JE4XCCqZabxgu/v77T+/jlKKC8wFwNuEcLsOF2aSYY7bkKUmzpc4wMgwXf/3lPseu5FNDJmUYAWCPh5CI6zlCERERERERv0pZkpbW/bAnwyghMfACRrrbDzCehteFQgtgM199vDBfcCQmTDgNJ7GJF7J6eJJFjMyUpJmtYHFnJGmmNBERERERye1SZhilxZNhZHcEXkmaMowCjKccrUgmGl4DWMwWIoPycM4eQ3T8WSKD8mTl8CSreJtepy5JuxxTUAhGnF0zpYmIAL17d+W337b5LLPZbERF5ad27br07PkCISEh6ex99Vq2fIwmTR6lU6duPssNw6B16ye44447GTNmQpr79uvXE5PJxOTJ0y97jDFjXuPo0f+YNm12lo07LcuWfcTSpYs5ffoUZcuWo1+/Qdx5Z9l0tz99+hRTpkxi69bNmExmGjZsRPfufQgNDb2u4xQRkcDmDRgFX7mHUSCWpCnDKMB4MozS6l+UUVGePkYJ6mOUXWUmwwiAoDD3/sowEhEBoGHDB1m5cq33a+HCj2jfviOrVi1n2rS3bsgYTCYTTZs+xsaNG4iNjU21/sSJ42zbtoVHH33ihoznSr744jNmzHibLl26M3fuQooVu4n+/Xtx9uzZNLd3OBz079+Lffv2MGbMRCZOnMKuXTsZMmTgjR24iIgEnIzMkubJMEpQ02vJ7bwNrzOZYQSQPylgdDruTFYMSa6HpKbXV59hlPSXXGUYiYgAEBwcTIECBb1fxYvfQvPmT9G4cRPWr//yho2jadPHcDgcfPfd16nWrVv3BXny5KFu3fo3bDyXs2DBPFq0aE3jxk0oWbIUQ4eOIDg4hNWrl6e5/c8//8TevXsYNWoclSpVpkyZsowc+Trbtv3K9u1bb/DoRUQkUBiGkbGSNGUYSaA4fuE4cG0Bo0Kh7mbZJ+JOZcmYJOsZie6O/t4AUAaZbO7SCsOeeoY8EZFrFRd3Md2vhISEDG+bchbPq9k2qwQFBWO1XvprZGJiIjNmTOGJJ5rw4IN16Nq1I5s3b/LZZ/XqFTz7bBsaNryfRo1q07NnZ3bu/DtDxytcuAjVqtXkyy/Xplq3bt3nNG7cFJvNxu+/b6dv3+40blyPBg1q0a5dS9atW5Pmax49+h+1a1dl27Ytl132+eeraNeuJQ0b3k+7di356KMPfCdNSCY6+gyHDh2katXq3mVWq5XKlavw22/b09zn8OGD5MuXjxIlSvq837x586UqCRQREckq9kQXhuF+nKEeRgGYYaQeRgEkzhHHOft5AIpcpiQtKirqsq/jmV3t1MXTWTc4yVKG/SKQfsAoKioKk8mUarlne5Wkicj1UKtWlXTX1a5dj2nT3vE+b9DgfuLj0/5edO+91Zg7d6H3edOmDxAdHZ3mtuXLV2DJkk8yOeLUHA4HmzdvYt26NTz+eHPv8jFjXuPAgX2MGDGaQoUKs2HDDwwe3I+xYydy3321+f77b5k8eTwvvTSMSpXu4dSpU7z11gTGjfs/5s9fkqFjP/JIM1577WVOnjxBoULun+M7dvzF/v37GDXqdU6ePMGAAb1p0aI1gwe/QmJiIosX/397dx4dVZX1ffxbqVQqlZkwJZCADHaAIINNgiAo2shry+QD2A8KUZBBQQ0gCPSSB2VQkSQGFRFFRJtRBRoaEKEdoBWRQbtpaMEWiYGEIRAykHmoev8oUlCSQAoykt9nLdaCW+fe2jeVQ1K79tnnQ+bNm0NERFcCA+u7fL8bN67nnXfe4tlnp9K2bTg///wT8fHzOXcuhfHjJ1wxPiXFXsncqFFjp+MNGjTg559/KvU5GjRoyIULF8jJycbLyxuAnJxsLlzIJC1N1cwiIlI5SpajGQAP06WE0W/fD5dUGBXUwV3SlDCqQ0r6FwWY/bG4l96k02Lx4quvdl/1Oo1UYVTjORI+pSSMLBYvvv56D/XqeZOWlk3R5aWVJi1JExG53PbtW9mx4wvHv/Pz82ncOJhHHokiKmokAElJJ/j8820sW7aSW28NA2Do0OEcPfozq1b9he7de+Dv78/06f9Hnz5/BCAoKJh+/Qbw2mvzyx1Lz5534+vry9//vo1HHokC7P2C2rYNp2XL1iQnJzFq1BM8/HCU40OBqKiRfPbZFk6cOH5dCaMPP1zKiBGj6N37/wHQtGkI2dnZxMW9yqhRT2I2O/fKK6noMplMTsc9PMwUFBSU+hx33NEdX19fXnllDs8992eMRiOxsfMAKCwscjlmERGR8ihZjubhYcTt4s/N0t4Pa5c0qRNKEkaNvRre0HUaetl/4UzLS6ewuBCT0XSNM6TKXUwYGUwuLknzKFmSpoSRiFS83bvLXl7k5uZcCv7VV7vKHGswOK+o//TTL8oYeeVYV/XocRfjxkVjs9k4fPg/vP56LF26RBIVNdKxJO2//7VXzowfP9rp3KKiInx87LuJdup0O7/+msAHH7xHYuKvJCUd55dfjpa5tKs0JpOJPn0e4O9/38ojj0RRWFjIF19sZ+zYpwB7MueBBwbwySdrOHbsKElJJzh69GcAiotd/yU3LS2NlJQzLF78FkuWvO04brVaKSjI59Spk07LyABHAqmwsNDpeEFBPp6epf9M8vPzZ96815g790X69u2N2Wxm8OD/JSysLT4+Pi7HLSIiUh7l6V8EYHIvWZKmCiO5iVVEw2sAX5MPnkYzecX5pOadJ8i78bVPkiplu1gh5HoPIy1JE5HKY7F4VftYV3l5eRMSEgpAaGgzGjRoyMSJ4zEajUyZMh0Am83+C+Rbby1xLKkq4eZm/yVz+/bPeOmlF+jT54+0b9+BgQMHcezYL7z22qsuxdOv30A++WQ1CQnHOH48kYKCAnr37gNAQsIxxo8fTVhYGyIiunL33fcQEFCPMWMeK/f1L08sldxXdPQkunTpesXYxo2DSjlm/53g3LmzTsmkc+fO0bBh2R9YtW/fgTVr1pOWdh4vLy/MZk/69buPBx7oV+7YRUREXFGeHdLg0nK1ulhhpKbXdUhJhVHQVfoX5eXlMWpUFKNGRZXZKNRgMDj6GKXkaFlaTVSS8CktYZSXl8eIEcMZMmTIla+xh/1Nl01L0kRESnX77V0YOnQYGzas5bvvvgWgRYtWAKSmniMkJNTxZ8uWv/Hpp5sAWLnyA/r3f5Dnn3+RwYP/RKdOt5OcnATYd2kpr1atWtOmTTu+/PLvfPHFdu65pzfe3vYqnI0b1xEYGMiCBYsYNuwxunXrQWpq2f0GS5aN5eRkO46dOHHc8fd69QIJCKjHyZPJTvf100+HWbJkUalx16sXSLNmzZ12NysqKuJf//qBjh1L72GVlHSCceMeJy0tjXr1AjGbPTlw4J9kZmaUmqgSERGpCKVVGJX2fth8MWFUMr4uUcKoDilPhZHNZuX77/fx/ff7HJ8slqahxb4sTX2MaqZLPYyu/NTdZrOyf/9edu/efcVSiJIlaWiXNBGRMo0a9SQhIc2IjX2FnJwcWrZsRffuPYmJeYVvvvkHyclJrFz5IStWfEDTpiGAvQn0wYMH+OmnIyQnJ/HRRytZv/5jgDJ7+5SlX78BfPHFdnbv3kXfvgMdxxs1akxKyhl2797F6dOn2LnzS+Li5pX5HPXrNyA4uAkff7yaxMRf+fe//8WSJW87+h8ZDAaGDXuMtWs/Yt26j0hOTmLnzq+IjZ2H2eyJh4dHqfENHTqcNWtWsHXrZhISjvHKK7MpKMinf/8HHWNSU8+Rk2PfoCEoKJhz51JZsGA+J04c54cf9jNr1gz69h3oqO4SERGpaLkXK4wslyWMSns/7GW2VyDl5te9vnpKGNURhcWFpObadxpp7HXjS8gcja9VYVQzXaXC6Gou7ZKWU+EhiYjcLMxmM9OmPc+ZM6d5991FAMye/Qq9et1LTMzLREX9ia1btzB9+v/xxz/al1RNmjSVevUCefrpsYwd+xjffvsNM2bMAuDIkR9dev7eve/nzJnTNGzYkI4dOzmODxkylHvvvY85c2YSFfW/fPjhUsaOHU9wcJNSn8NgMDBjxmyysrIYMeJh5s9/mSeffNqxjA7g4YeH8/TTk1i37mOGDRvC66/HMmDA/zBlyp/LjG/AgP9h1KgnWbLkbUaPjuL06VPEx79FQECAY8zAgfezerV9pzt3d3diYhaQnp7B448PY+7cF7j//r5MnjzNpa+LiIiIKy5VGF19SZqXp/3xnDqYMDLYXKmDriOKi62cP5997YG1SHLWKV7eG4/F3UJMzxdL3VIdIDc3x7Ht8e7dP5TZF2Lv6R/48Mc1tPK/hWd/P77S4pbrc2HpWCguwHtoDG5+zj0jLn+N9+79Fx4el3bMKzpxkNytcbgFhuI9ZE6Vxiwi5efu7lb6Toc1QGFhAampp6hfPxiTqfQKFJEbVdu/z2ryHBaRa9Mcvjl8tuc4H391lG7hjRnTPxwo/f3wr6czmf3Bfur5mol76s7qDLlCBAZ6YzSWr3ZIFUZ1xOnsM4C9f1FZySJXBHvbG12eyj7jUu8FqXy24kIoti89MJhdawRrsPjZr5GbUeFxiYiIiIiI1BTlbXptMdfdCiMljOoIR8PrG9whrUSQV0MMGMgpyiWz4EKFXFMqhi334uthMJbaw+hqDF7+9mvkXcDmwlbPIiIiIiIitUlu/sUlaWbjVceV9DDKLyimuI69R1LCqI4oT8NrV5iMJhp62Rtfn7pYvSQ1gy3PnjAyePq4XE1m8PQFDGCzOa4jIiIiIiJys8lzNL0uX4URXEoy1RVKGNURjgojr2snjDw9LXh6XrtZ8uXL0qTmcCSMLL5ljrFYLFgsV77GBjcjBk/79sy23MzKCVBERERERKSa5TqaXjtXGP32/bC70Q0Pkz11UteWpV09lSY3hWJrMSm59t3MrlVhZLF48d13/yzXdYO9G3Pg7CFOZZ++4Ril4pQkeuzVQleyWLzYt+9AmY36DBZ/+5K03AxA2xmLiIiIiMjNx1FhdFkFUVnvh73M7hQUFpCbV7cSRqowqgPO5qZSZC3Cw81EoGe9CrtusHdjQBVGNU1JD6OyEkbXYvAqaXytCiMRuX7aEEEqk76/RETkRuXll15hVBpvTxMAWXmFlRpTTaOEUR1w8mIFULBPEG6GinvJL08YWW11q/lXTVaeJWlXY/CyJxWtWakVFpOI1B1Go/2XroKC/GqORG5mJd9fRqOK5UVE5PrkXlxe5mm+9s8SP28PADKzCio1pppGP2XrgOSsUwA0vdhz6Gry8/OZPDkagLi4NzCbzWWODfJqhMnNRG5RHmdzztG4ghpqy40pSfQYvANLfTw/P59nnonGZDISE/M6RqPJ6XE3P/vraMtMqdxAReSm5OZmxGLxISsrDQAPD7PLDfhFymKz2SgoyCcrKw2LxQc3N332KSIi1+dCrr1ayNdy6f1QWe+H/X3sCaP07Lr1gZgSRnXAySx7hVETn+BrjrVai/nmm52Ov1+N0c1IM98QfslIICHzuBJGNYTtgr1flZtvw1Ift1qL+fpr+2tcXFxcSsLIfp5VCSMRuU5+fvaEdUnSSKSiWSw+ju8zERERV1ltNrJyLiaMvDwuHS/j/XCAtz1xlKEKI7mZ2Gw2jmX8CkCob9MKv34L/2b2hFFGIncEd6nw64vrrFklCaMG13V+SYWRNfNshcUkInWLwWDA378+vr71KC6uW80hpfIZje6qLBIRkRuSk1eE9WI/PB+L6RqjL1UYZWQrYVTrWK1WFi5cyCeffMKFCxeIiIhg5syZhIZqh6czOWfJKszG5OZOc7+K/3q09G8OwE9pR7HZbFp2UM1sBbnYsu2f6JckflzlFmCvRLNln8eadwG362yeLSLi5uaGm5vHtQeKiIiIVKELOfbEj8VsxOR+7Q8hHAmjrLq1JO2m+Hhm0aJFrFq1ijlz5rBmzRqsViujR4+moKBuZf9K82PqEQBa+DXH5Fbx+cGwerfibjByNjeVMzlawlTdilOPA/b+RQZPn+u6hsHsjcHf3u/KmnKswmITERERERGpCVIz8wAI9PUs1/iScecy8iotppqo1ieMCgoKeP/994mOjqZXr160adOG+Ph4Tp8+zfbt26s7vGpls9nYc/oHADo1uq1SnsPT3UxY4K0A7Dq5t1KeQ8qv+PR/ATA2aH5D1zE2agVAUfKPNxyTiIiIiIhITXI2LReAhgGWco1v0sAbsCeMSnZXqwtqfcLoyJEjZGdn061bN8cxPz8/2rVrx759+6oxsupls9nYdXIPSVknMbm5c3ujDpX2XHeHdAfg6+Tv+DXzeKU9j1ydzVpE0c+7ATA263hD13JvcTsARUd3YyvIueHYREREREREaoqE0xcACG7gVa7xPhYT9Xztja+PncqstLhqGoPNdrHTUy21fft2nnnmGQ4cOICn56VysgkTJpCXl8c777zj8jVtNhtWa+39slhtVjLyMym2WQHwMlnwci9f5tRms5GcnARA06Yh5e5JlJl/gQKrvcu8xd0Tb1P5Jp5UEJsNa046FBeBwYCbT30o47Ur72tszUoFqxXc3HDz8odKWNIoItfHYLD3B7JardTun+IidZPmsEjtpjlcu1ltNs5n5GED/H3MeFzWw+hq75Uu5BSQV1CMyd2NAB9zVYddYdzcDOV+n1/r3wHm5tpLyTw8nJtqms1mMjIyruuaBoMBo7H2Nm824kYD9+vfarZ5c9eXM9Xz8r/u55OKYfSrX+6x5XmNjf4NbyQcEakC2ilKpHbTHBap3TSHaycj0Li+d5mPl/VeKaCc/Y5uJrX+O7ykqui3Da7z8/OxWMpXVSMiIiIiIiIiIpfU+oRRcLB9C/CUFOcdulJSUmjcuHF1hCQiIiIiIiIiUqvV+oRRmzZt8PHxYc+ePY5jmZmZ/Pjjj0RERFRjZCIiIiIiIiIitVOt72Hk4eHB8OHDiY2NJTAwkKZNmxITE0NQUBB9+vSp7vBERERERERERGqdWp8wAoiOjqaoqIgZM2aQl5dHREQES5cuxWQyVXdoIiIiIiIiIiK1jsFm00aAIiIiIiIiIiJySa3vYSQiIiIiIiIiIhVLCSMREREREREREXGihJGIiIiIiIiIiDhRwkhERERERERERJwoYSQiIiIiIiIiIk6UMBIRERERERERESdKGImIiIiIiIiIiBMljERuQlarlTfeeIOePXvSqVMnxowZw4kTJ8oc//PPPzN27Fi6du1Kt27diI6O5uTJk1UYsYhcztU5fLm//e1vhIWFkZSUVMlRikhZXJ3DhYWFxMXFOcYPHz6cw4cPV2HEInI5V+dwamoqkydP5o477qBr165MmjSJM2fOVGHEIpVDCSORm9CiRYtYtWoVc+bMYc2aNVitVkaPHk1BQcEVY9PS0hg5ciSenp4sX76cJUuWcP78eUaPHk1+fn41RC8irszhyyUnJzN79uwqilJEyuLqHH7xxRdZv349L7/8MuvWrSMwMJAxY8Zw4cKFKo5cRMD1OTxx4kROnjzJsmXLWLZsGSdPnuSpp56q4qhFKp4SRiI3mYKCAt5//32io6Pp1asXbdq0IT4+ntOnT7N9+/Yrxn/++efk5OQwf/58fve739G+fXtiYmL45Zdf+OGHH6rhDkTqNlfncAmr1cpzzz1HeHh4FUYrIr/l6hw+ceIE69at46WXXqJnz560atWKuXPn4uHhwaFDh6rhDkTqNlfncGZmJnv37mXMmDG0bduWdu3aMXbsWA4ePEh6enrV34BIBVLCSOQmc+TIEbKzs+nWrZvjmJ+fH+3atWPfvn1XjO/WrRuLFi3C09PTcczNzf5fQ2ZmZuUHLCJOXJ3DJRYvXkxhYSFPPPFEVYQpImVwdQ7v2rULX19f7rrrLqfxX375pdM1RKRquDqHPT098fb2ZsOGDWRlZZGVlcXGjRtp0aIFfn5+VRm6SIVzr+4ARKRinT59GoDg4GCn440aNXI8drmQkBBCQkKcjr377rt4enoSERFReYGKSKlcncMA//73v3n//fdZu3ateiaIVDNX53BCQgKhoaFs376dd999lzNnztCuXTumT59Oq1atqiRmEbnE1Tns4eHBvHnzmDlzJl26dMFgMNCoUSNWrFjh+BBWpLbSd7DITSY3Nxew//C6nNlsLldPouXLl7NixQqmTJlCYGBgpcQoImVzdQ7n5OQwZcoUpkyZwi233FIVIYrIVbg6h7OyskhMTGTRokU8++yzvP3227i7u/PII4+QmppaJTGLyCWuzmGbzcbhw4fp3LkzK1eu5MMPP6RJkyaMHz+erKysKolZpLIoYSRykylZWvbbpnz5+flYLJYyz7PZbCxYsIC5c+cybtw4oqKiKjVOESmdq3N47ty5tGjRgqFDh1ZJfCJyda7OYXd3d7KysoiPj6dHjx506NCB+Ph4AP76179WfsAi4sTVObx161ZWrFhBTEwMv//974mMjGTx4sUkJyezdu3aKolZpLIoYSRykykpn01JSXE6npKSQuPGjUs9p7CwkOeee47Fixfz5z//mYkTJ1Z2mCJSBlfn8Lp16/j222/p3LkznTt3ZsyYMQD069ePxYsXV37AIuLE1TkcFBSEu7u70/IzT09PQkNDSUpKqtxgReQKrs7h/fv306JFC3x8fBzH/P39adGiBYmJiZUbrEglU8JI5CbTpk0bfHx82LNnj+NYZmYmP/74Y5k9iaZOncpnn31GXFwcI0aMqKJIRaQ0rs7h7du3s3nzZjZs2MCGDRuYO3cuYO9Fpqojkarn6hyOiIigqKiIgwcPOo7l5eVx4sQJmjdvXiUxi8glrs7hoKAgEhMTnZar5eTkkJSUpKXiUuup6bXITcbDw4Phw4cTGxtLYGAgTZs2JSYmhqCgIPr06UNxcTHnz5/H19cXT09P1q9fz6effsrUqVOJjIzk7NmzjmuVjBGRquPqHP7tG8qShpxNmjQhICCgGu5ApG5zdQ536dKF7t27M23aNGbPnk1AQABvvPEGRqORgQMHVvftiNQ5rs7hBx98kKVLlzJx4kQmTJgAwIIFCzCbzQwaNKia70bkxqjCSOQmFB0dzZAhQ5gxYwYPP/wwRqORpUuXYjKZOHXqFD169ODTTz8FYPPmzQDMnz+fHj16OP0pGSMiVcuVOSwiNY+rc/jNN98kMjKSp59+miFDhpCVlcVf/vIXbT4hUk1cmcONGjVi1apV2Gw2HnvsMUaOHInJZGLVqlX4+vpW852I3BiDzWazVXcQIiIiIiIiIiJSc6jCSEREREREREREnChhJCIiIiIiIiIiTpQwEhERERERERERJ0oYiYiIiIiIiIiIEyWMRERERERERETEiRJGIiIiIiIiIiLiRAkjERERkWpks9mqOwQRERGRKyhhJCIiIjVKVFQUYWFhTn/at29Pr169mDVrFhkZGdUdYoXIzMxk6tSp7N+/v8KvferUKdq2bcusWbPKHHPo0CHCwsJYu3btNa+3Z88ewsLC2LNnT0WGKSIiIjWYe3UHICIiIvJb7dq144UXXnD8u7CwkP/85z+89tprHD58mNWrV2MwGKoxwht3+PBhNm7cyODBgyv82sHBwXTv3p2tW7fy/PPP4+5+5a98GzZswNvbmwceeKDCn19ERERqPyWMREREpMbx8fGhU6dOTsciIiLIzs7mjTfe4MCBA1c8Ls4GDx7MN998wzfffEOvXr2cHissLGTz5s088MADeHl5VU+AIiIiUqNpSZqIiIjUGu3btwfg5MmTABQXF/Puu+/Sr18/OnToQKdOnRg6dCjfffed45w333yT++67j4ULFxIZGUmPHj3IyMggLy+PuLg4+vTpQ/v27bn99tsZOXIkhw8fdpw7ffp0Ro0axUcffUTv3r3p0KEDQ4cOJSEhga+++or+/fvTsWNHHnroIafzAPbv38/w4cPp2LEjkZGRTJs2jfPnzwP2JV6PPvooAI8++ihRUVGO8z7//HMGDRrEbbfdxp133sncuXPJycm55v38Vu/evQkICGDTpk1XPLZz507S0tIYMmQIAPv27WPUqFFERETQvn177r33Xt58802sVmupr8P06dO59957nY4lJSURFhbG+vXrHcfS09OZOXMm3bt357bbbuNPf/oTu3fvLvWaIiIiUrOowkhERERqjYSEBABCQ0MBiI2NZfXq1UyePJmwsDDOnDnDW2+9xYQJE9ixYwcWiwWwJ5h27txJfHw86enp+Pv7Ex0dzf79+3n22Wdp1qwZiYmJvP7660yePJktW7Y4lrz985//JCUlhenTp5Ofn8+LL77I2LFjMRgMREdHY7FYeOGFF5gyZQpbtmwB7AmYkSNHcscdd7BgwQIyMjJ4/fXXefTRR1m7di3h4eHMnDmT2bNnM3PmTLp27QrApk2bmDJlCv3792fixIkkJycTHx/P0aNHWbZsmSOm0u7ntzw8POjfvz9r164lOzsbb29vx2MbNmzg1ltvpVOnThw5coQRI0Zw//33Ex8fj81mY9OmTSxcuJCWLVvSt2/f63qt8vPzeeyxxzh37hyTJk2iUaNGrFu3jtGjR/Pee+/RrVu367quiIiIVA0ljERERKTGsdlsFBUVOf6dkZHB3r17efvtt+ncubOj0iglJYVJkyY5VeiYzWaeeeYZfvrpJ8eytaKiIqZNm0aXLl0AKCgoIDs7mxkzZjh6+ERGRpKVlcW8efM4d+4cDRs2BCA7O5sFCxbQqlUrAPbu3cuaNWv44IMPHEmPxMREXn31VTIzM/Hz8yMuLo4WLVrwzjvvYDQaAejYsSN9+/Zl3bp1DBs2jNatWwPQunVrWrdujc1mIzY2lp49exIbG+u4n1tuuYURI0awc+dOx9Ky395PWYYMGcLy5cv5/PPPGThwIABpaWns2LGDKVOmAHDkyBG6d+9OTEwMbm724vM777yTL7/8kj179lx3wmjjxo0cOXKEjz/+mI4dOwJw1113ERUVRWxsLOvWrbuu64qIiEjVUMJIREREapx9+/YRHh7udMzNzY3u3bsze/ZsR6VNXFwcAOfPn+fYsWMkJiby1VdfAfak0OXatm3r+LuHhwdLly4F4MyZMyQkJPDrr7+Weq6/v78jWQTQoEEDAEcSBCAgIACw73xmMpk4cOAAo0aNckp8hYaG0qpVK3bt2sWwYcOuuOdjx45x+vRpnnjiCadkWUREBD4+PuzatcupF9Hl91OWNm3aEB4ezqZNmxwJo5IqqAEDBgDw4IMP8uCDD5Kfn09CQgKJiYkcPnyY4uJiCgsLr/kcZdm9ezcNGzYkPDzc6X7uuece5s+fT0ZGRqmVUSIiIlIzKGEkIiIiNU54eLhjS3iDwYDZbCY4OBgfHx+ncQcPHmTWrFkcPHgQi8VC69atadKkCWCvUrrc5UuyAL7++mtefvlljh07hre3N23atHE0gL783N8+Z4mymkVnZmZitVpZsmQJS5YsueJxs9lc6nnp6ekAzJo1y3Hvl0tJSbnq/ZRl8ODBvPzyy6SmplK/fn02bNjAH/7wBwIDAwHIy8tjzpw5bNy4kaKiIkJCQujcuTPu7u5XfA1dkZ6eztmzZ69I/JU4e/asEkYiIiI1mBJGIiIiUuN4e3tz2223XXVMVlYWo0ePJiwsjC1bttCyZUvc3NzYuXMn27Ztu+q5x48f56mnnqJ379688847hIaGYjAYWLlyJV9//fUNx24wGBgxYkSpy7lK+ir9lp+fHwBTp04lMjLyisevN7nSv39/Xn31VbZu3Uq3bt04ePAgEyZMcDz+0ksvsW3bNhYsWED37t0dibCr9RgyGAwUFxc7Hbu8MTeAr68vt9xyi9PyusuFhIRc1/2IiIhI1VDCSERERGqlY8eOkZ6ezqOPPuroBwTwj3/8A6DMHb4ADh06RH5+PmPHjqVZs2aO4yXJohuprPHx8aFdu3YcO3bMKemVl5dHdHQ0d999N61bt3b0NirRsmVL6tevT1JSEqNGjXIcT0lJYerUqQwdOtQp1vLy8/PjvvvuY9u2baSnp9OkSRPuvPNOx+Pff/89Xbt2pXfv3o5jhw4d4vz582V+Db29vUlLSyM/P99RMfX99987jYmMjGTHjh3Ur1/fUfUFsHjxYg4fPlxmIklERERqBiWMREREpFZq0aIFPj4+LF68GHd3d9zd3dm2bRtr164FIDc3t8xzw8PDcXd3JyYmhscff5yCggLWr1/Pjh07gCurZVz17LPPMnbsWCZPnsyAAQMoLi7m/fff58CBA4wfPx6wV+AA7NixA39/f9q0acOkSZOYOXMmRqORe+65h8zMTBYtWsSZM2fKXNpVHoMHD2b06NGcOnWKQYMGOZpbA3To0IGtW7eyevVqWrVqxZEjR3j77bcxGAxlfg3vueceli9fzvPPP8+QIUP473//y7Jly5ySYIMGDWLFihWMHDmSJ598kuDgYL799luWLFnC8OHDMZlM130/IiIiUvmUMBIREZFaydfXl0WLFjF//nwmTJiAt7c3bdu2ZcWKFYwZM4b9+/dz7733lnpu8+bNiYuLY+HChYwbNw5/f386derE8uXLiYqKYv/+/YSFhV13bD169GDp0qUsXLiQ6OhoTCYT4eHhLFu2zLFz26233kq/fv0cy+A2b97MQw89hLe3N++99x4fffQRXl5e3H777cTGxhIaGnrd8XTr1o2goCCSkpIYNGiQ02PTp0+nsLCQBQsWUFBQQEhICOPGjePo0aN8+eWXVyw9A/suatOmTWP58uVs27aN8PBwFi5cyNChQx1jvLy8WLlyJXFxccTExHDhwgWaNm3K5MmTefzxx6/7XkRERKRqGGw3UnMtIiIiIiIiIiI3HbdrDxERERERERERkbpECSMREREREREREXGihJGIiIiIiIiIiDhRwkhERERERERERJwoYSQiIiIiIiIiIk6UMBIRERERERERESdKGImIiIiIiIiIiBMljERERERERERExIkSRiIiIiIiIiIi4kQJIxERERERERERcaKEkYiIiIiIiIiIOFHCSEREREREREREnPx/gCjX8iUMbA8AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "basis_function = Polynomial(degree=2)\n", "estimator = LeastSquares(unbiased=True)\n", "parameters = np.zeros([3, 50])\n", "\n", "for i in range(50):\n", " x_train, x_valid, y_train, y_valid = get_siso_data(\n", " n=3000, colored_noise=True, train_percentage=90\n", " )\n", "\n", " model = FROLS(\n", " order_selection=False,\n", " n_terms=3,\n", " ylag=2,\n", " xlag=2,\n", " elag=2,\n", " info_criteria=\"aic\",\n", " estimator=estimator,\n", " basis_function=basis_function,\n", " )\n", "\n", " model.fit(X=x_train, y=y_train)\n", " parameters[:, i] = model.theta.flatten()\n", "\n", "\n", "plt.figure(figsize=(14, 4))\n", "\n", "# Plot KDE for each parameter\n", "sns.kdeplot(parameters.T[:, 0], label=\"Parameter 1\")\n", "sns.kdeplot(parameters.T[:, 1], label=\"Parameter 2\")\n", "sns.kdeplot(parameters.T[:, 2], label=\"Parameter 3\")\n", "\n", "# Plot vertical lines where the real values must lie\n", "plt.axvline(x=0.1, color=\"k\", linestyle=\"--\", label=\"Real Value 0.1\")\n", "plt.axvline(x=0.2, color=\"k\", linestyle=\"--\", label=\"Real Value 0.2\")\n", "plt.axvline(x=0.9, color=\"k\", linestyle=\"--\", label=\"Real Value 0.9\")\n", "\n", "plt.xlabel(\"Parameter Value\")\n", "plt.ylabel(\"Density\")\n", "plt.title(\"Kernel Density Estimate of Parameters\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great! Now we have an unbiased estimation of the parameters!\n", "\n", "## Note\n", "\n", "Note: The Extended Least Squares is an iterative algorithm. In SysIdentpy the default is 30 iterations (`uiter=30`) because it is known from literature that the algorithm converges quickly (about 10 or 20 iterations)." ] } ], "metadata": { "kernelspec": { "display_name": "sysidentpyv04", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 4 }