TP1_Time_Series_Kervella_R.ipynb

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        "<a href=\"https://colab.research.google.com/github/SushiFou/Time-Series-Financial-Data/blob/main/TP1_Time_Series_Kervella_R.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "LHQEi30imTG9"
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      "source": [
        "# Time Series for Financial Data - TP n° 1 (ARMA Modeling)\n",
        "---\n",
        "\n",
        "Yann Kervella"
      ]
    },
    {
      "cell_type": "markdown",
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        "id": "NcprthVkmHcV"
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      "source": [
        "\n",
        "# Autocovariance function, spectral density and empirical estimation #\n",
        "\n",
        "Let $X_1,\\dots,X_N$ be observations of weakly stationary time series $(X_t)$ with mean $\\mu$ and autocovariance function $\\gamma$. \n",
        "\n",
        "The empirical mean and the empirical autocovariance function are defined by\n",
        "  \\begin{align*}\n",
        "    \\hat{\\mu}_N &= N^{-1} \\sum_{t=1}^N X_t \\\\\n",
        "    \\hat{\\gamma}_{N}(h)& = \n",
        "    \\begin{cases}\n",
        " \\displaystyle     N^{-1}\\sum_{t=\\max(1,1-h)}^{\\min(N,N-h)}(X_{t+h}-\\hat{\\mu}_N)\\overline{(X_{t}-\\hat{\\mu}_N)} & \\text{ if } h \\in \\{-N+1,\\cdots,N-1\\}\\\\\n",
        "0 & \\text{ otherwise } .\n",
        "    \\end{cases}\n",
        "  \\end{align*}\n",
        "Let us define the periodogram by\n",
        "$$\n",
        "I_N(\\lambda) = (2 \\pi N)^{-1} \\left\\vert  \\sum_{t=1}^N (X_t - \\hat{\\mu}_n) \\; \\mathrm{e}^{-\\mathrm{i} t \\lambda}\\right \\vert^2\\qquad\\lambda\\in\\mathbb{R} \\; .\n",
        "$$\n",
        "It is a $(2\\pi)$-periodic non-negative function.\n",
        "\n",
        "**1) Show that, for all lags $h\\in\\mathbb{Z}$,\n",
        "$$\n",
        "    \\hat{\\gamma}_{N}(h)= \\int_0^{2\\pi}  \\mathrm{e}^{\\mathrm{i} h \\lambda}\\;I_N(\\lambda) \\; \\mathrm{d}\\lambda\\;.\n",
        "$$\n",
        "What do you conclude about $\\hat{\\gamma}_{N}$ ?** [Hint: use the Herglotz theorem]\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xgI52MXcMs7E"
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      "source": [
        "> $ \\hat{\\gamma}_{N}(h)= \\int_0^{2\\pi}  \\mathrm{e}^{\\mathrm{i} h \\lambda}\\;I_N(\\lambda) \\; \\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= \\int_0^{2\\pi}  \\mathrm{e}^{\\mathrm{i} h \\lambda} (2 \\pi N)^{-1} \\left\\vert  \\sum_{t=1}^N (X_t - \\hat{\\mu}_n) \\; \\mathrm{e}^{-\\mathrm{i} t \\lambda}\\right \\vert^2 \\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi}  \\mathrm{e}^{\\mathrm{i} h \\lambda} \\sum_{t=1}^N (X_t - \\hat{\\mu}_n) \\mathrm{e}^{-\\mathrm{i} t \\lambda}\\sum_{t=1}^N \\overline{ (X_t - \\hat{\\mu}_n)\\mathrm{e}^{-\\mathrm{i} t \\lambda}} \\space \\mathrm{d} \\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi} \\sum_{t=1}^N (X_t - \\hat{\\mu}_n) \\mathrm{e}^{-\\mathrm{i}( t-h )\\lambda}\\sum_{t=1}^N \\overline{(X_t - \\hat{\\mu}_n)\\mathrm{e}^{-\\mathrm{i} t \\lambda}}\\space\\mathrm{d}\\lambda $\n",
        "\n",
        "> Let's note $k = t-h$ :\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi} \\sum_{t=1-h}^{N-h} (X_{k+h} - \\hat{\\mu}_n) \\mathrm{e}^{-\\mathrm{i}k\\lambda}\\sum_{t=1}^N \\overline{(X_t - \\hat{\\mu}_n)}\\mathrm{e}^{-\\mathrm{i} t \\lambda}\\space\\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi} \\sum_{t=1}^N \\sum_{t=1-h}^{N-h} (X_{k+h} - \\hat{\\mu}_n) \\overline{(X_t - \\hat{\\mu}_n)}\\mathrm{e}^{-\\mathrm{i}(k-t)\\lambda}\\space\\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi} \\sum_{t=max(1, 1-h)}^{min(N, N-h)}  (X_{k+h} - \\hat{\\mu}_n) \\overline{(X_t - \\hat{\\mu}_n)}\\space\\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= (2 \\pi N)^{-1} \\int_0^{2\\pi} \\sum_{t=max(1, 1-h)}^{min(N, N-h)}  (X_{k+h} - \\hat{\\mu}_n) \\overline{(X_t - \\hat{\\mu}_n)}\\space\\mathrm{d}\\lambda $\n",
        "\n",
        "> $ \\hat{\\gamma}_{N}(h)= N^{-1} \\int_0^{2\\pi} \\sum_{t=max(1, 1-h)}^{min(N, N-h)}  (X_{k+h} - \\hat{\\mu}_n) \\overline{(X_t - \\hat{\\mu}_n)} $"
      ]
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        "\n",
        "$I_N(\\lambda)$ is non-negative and defined on $[0,2\\pi]$.\n",
        "As $ \\hat{\\gamma}_{N}(h)= \\int_0^{2\\pi}  \\mathrm{e}^{\\mathrm{i} h \\lambda}\\;I_N(\\lambda) \\; \\mathrm{d}\\lambda $, we can conclude by Herglotz theorem\n",
        "that $\\hat{\\gamma}_{N}$ is Hermitian, symetric non-negative and definite ."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hxTVgtluFYAS"
      },
      "source": [
        "**2) Generate an i.i.d. $\\mathcal{N}(0,1)$ sequence of length $2^{8}$ and plot the empirical autocorrelation function $\\hat{\\gamma}_{N}(h)/\\hat{\\gamma}_{N}(0)$ using** \n",
        "*acf()*\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
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        "colab": {
          "base_uri": "https://localhost:8080/",
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        "id": "S---rBkaK8e2",
        "outputId": "e9410c85-8e5e-4cda-dc20-6a9aa19ea434"
      },
      "source": [
        "norm <- rnorm(2**8)\n",
        "length(norm)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
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              "[1] 256"
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            "text/latex": "256",
            "text/markdown": "256",
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        "id": "oiePy_v8FwlM",
        "outputId": "5511ea8a-b924-43f9-b685-947031a9c103"
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      "source": [
        "acf(norm)"
      ],
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      "outputs": [
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Hnu3Lm1tbV1S9nZ2T169CgpKSkpKcnM\nzIxxSACAGKVN2EVRlJOTU1paWlpaunXr1tWrVyc/eaJFixZFRUUeSwMASKewq5OXl1dcXBz3\nFAAAqSVtLp4AAKB+afmI3R6Vl5cPHTo0iqLZs2fv+70+++yz+fPn79ixo559Xn/99YMdbidr\n166NouiYY45pwGMCAEQhhV1VVdWLL764v/datWrVgAED6g+75BusbN++vUFeyTdq1Kgoih54\n4IGDPxQAwM7CCbuuXbsuX758f+/VqVOndevW1b/PpEmTrr766oZ6X5idr+cFAGhA4YRdXl5e\n9+7d454CACA2QV08sX79+rfffjvuKQAA4hFU2P3yl7/0NigAwGErqLADADicCTsAgECkzcUT\np5xyyufu89577zXCJAAAqSltwm7p0qVRFGVnZ9ezT/1vRwcAELa0eSp25MiRzZo1+/vf/751\n70aMGBH3mAAAsUmbsPvZz37WpUuXyy67bPv27XHPAgCQitIm7LKzsx999NHXX3/9xhtvjHsW\nAIBUlDavsYuiqFu3bh988EE9L6S78MILW7Vq1ZgjAQCkjnQKuyiKWrRoUc/qmWeeeeaZZzba\nMAAAKSVtnooFAKB+wg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIO\nACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDC\nDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQ\nwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAg\nEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4A\nIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIO\nACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBBZ\ncQ9wsLZv3/7Pf/5z69at3bt3z83NjXscAIDYpNMjdi+99NJZZ53VqVOnPn36LF68OIqiF154\n4dhjj+3evfspp5zSrl273/zmN3HPCAAQm7R5xK6srOz888/fsWNHixYtXnjhhfnz5//pT38a\nMGBAy5Ytr7jiiq1bt/7pT3+65pprjjvuuAsuuCDuYQEAYpA2j9jdcccdRx111LJlyzZu3PjB\nBx/07Nnz29/+dqdOnd58883f/va3Tz75ZHl5+bHHHnvXXXfFPSkAQDzSJuwWLVp0zTXXnHji\niVEUtW3b9he/+MW7775bWlrapEmT5A6tW7ceMmTIkiVLYh0TACA2aRN2Gzdu7NixY92X7du3\nj6Kobdu2O+9zzDHHVFZWNvZkAACpIW3Crk2bNuXl5XVf/vOf/4yi6O233955n/Ly8jZt2jT2\nZAAAqSFtwu6ss866++6758yZU1NTs3z58muvvbZbt2533nnne++9l9xhxYoV9957b+/eveOd\nEwAgLmlzVeyYMWNmzZp19tlnJ7888sgjX3755QsvvPCLX/ziaaedtnXr1ldffTWRSIwcOTLe\nOQEA4pI2j9h17dp10aJFl1122WmnnXbVVVctWrSoW7duf/jDH7p37z537tyysrKioqLp06f3\n7Nkz7kkBAOKRNo/YRVHUvXv3xx57bJctixcv3rRp05YtW3a5kAIA4HCTTmG3N/n5+fn5+XFP\nAQAQs7R5KhYAgPqF8IhdUnl5+dChQ6Momj179r7fa/Xq1eedd15NTU09+yTfGy+RSBzkhAAA\nh1Q4YVdVVfXiiy/u772OPvron/70p9u2batnn/nz5z/66KMZGRkHMR0AwCEXTth17dp1+fLl\n+3uvnJycK6+8sv59EonEo48+eqBzAQA0knDCLi8vr3v37nFPAQAQm/QLu0QiUVFRsXLlyqqq\nqiiKWrZsWVxcXFhYGPdcAAAxS6ew27Bhw7hx46ZMmbJu3bpdloqKioYMGTJixIgmTZrEMhsA\nQOzSJuzWrl3bq1evioqK4uLiPn36dOzYsVmzZlEUVVZWlpeXz5s3b/To0dOnT58zZ07r1q3j\nHhYAIAZpE3ajRo1as2bN1KlT+/fvv/tqbW3tpEmThg8fPnbs2AkTJjT+eAAAsUubNyieNWvW\noEGD9lh1URRlZmYOGzZswIABM2bMaOTBAABSRNqE3fr16zt37lz/Pt26dfvwww8bZx4AgFST\nNmFXUFCwbNmy+vdZunRpQUFB48wDAJBq0ibs+vbtO23atPHjx+/xUyI2b948ZsyYmTNnDhw4\nsPFnAwBIBWlz8cQtt9yyYMGCkSNH3nrrrT179iwsLMzPz08kEps2bVq1atWSJUuqq6t79+59\n8803xz0pAEA80ibsWrVqVVZWNnHixMmTJ8+dO7e2trZuKTs7u0ePHiUlJSUlJZmZmTEOCQAQ\no7QJuyiKcnJySktLS0tLt27dunr16uQnT7Ro0aKoqCgnJyfu6QAAYpZOYVcnLy+vuLg47ikA\nAFJL2lw8AQBA/YQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBA\nIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0A\nQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQd\nAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCE\nHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAg\nhB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBA\nIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCy4h7goNTW1r7xxhtV\nVVWFhYWFhYVxjwMAEKd0esRu0aJFw4cPr/vyd7/7Xfv27U888cRevXoVFRWddNJJ8+fPj3E8\nAIB4pc0jdnPnzj3//PNzcnLuvvvujIyMp556atCgQfn5+f3792/btu1bb7314osvnnfeeQsX\nLuzRo0fcwwIAxCBtwm7s2LGtWrVauHBhRkZGFEU//vGPO3bsWFZWdswxxyR3WLx48VlnnTV2\n7Njf//73sU4KABCPtHkq9q9//esVV1zRpUuXKIo2btxYUVHxox/9qK7qoig67bTTLr/88gUL\nFsQ3IwBAnNIm7Gpra5s0aZK8nZeXl5GR0aFDh1326dChw9atWxt9NACAlJA2YXfSSSc98cQT\n1dXVURTl5uZ+9atfLSsr23mHbdu2zZgx4/jjj49pQACAmKVN2P30pz996623evfu/cc//nHH\njh133333o48+Onny5Orq6u3bty9evLhPnz7Lli0bNmxY3JMCAMQjbS6e+MY3vnH//ff/8Ic/\nPP/885s0adKpU6ecnJwrr7yypKQkiqLa2tqMjIwf/ehH3//+9+OeFAAgHmkTdlEUDRky5OKL\nL54yZcrs2bP/8Y9/fPLJJ7m5ufn5+ccee2yvXr2uvPLKk08+Oe4ZAQBik05hF0XR0UcfPWLE\niBEjRsQ9CABAykmb19gBAFA/YQcAEIg0eyq2HuXl5UOHDo2iaPbs2ft+r61bt953331btmyp\nZ5/Fixcf7HAAAIdeOGFXVVX14osv7u+91q9f//jjj2/fvr2efT766KMoihKJxIEPBwBw6IUT\ndl27dl2+fPn+3qt9+/a7vNHx7iZNmnT11VcnP6MWACBlhRN2eXl53bt3j3sKAIDYpF/YJRKJ\nioqKlStXVlVVRVHUsmXL4uLiwsLCuOcCAIhZOoXdhg0bxo0bN2XKlHXr1u2yVFRUNGTIkBEj\nRjRp0iSW2QAAYpc2Ybd27dpevXpVVFQUFxf36dOnY8eOzZo1i6KosrKyvLx83rx5o0ePnj59\n+pw5c1q3bh33sAAAMUibsBs1atSaNWumTp3av3//3Vdra2snTZo0fPjwsWPHTpgwofHHAwCI\nXdq8QfGsWbMGDRq0x6qLoigzM3PYsGEDBgyYMWNGIw8GAJAi0ibs1q9f37lz5/r36dat24cf\nftg48wAApJq0CbuCgoJly5bVv8/SpUsLCgoaZx4AgFSTNmHXt2/fadOmjR8/ftu2bbuvbt68\necyYMTNnzhw4cGDjzwYAkArS5uKJW265ZcGCBSNHjrz11lt79uxZWFiYn5+fSCQ2bdq0atWq\nJUuWVFdX9+7d++abb457UgCAeKRN2LVq1aqsrGzixImTJ0+eO3dubW1t3VJ2dnaPHj1KSkpK\nSkoyMzNjHBIAIEZpE3ZRFOXk5JSWlpaWlm7dunX16tXJT55o0aJFUVFRTk5O3NMBAMQsncKu\nTl5eXnFxcdxTAACklrS5eAIAgPoJOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsA\ngEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7\nAIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAI\nOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQOw17O65\n556XX355l42vvfbae++9d4hHAgDgQOw17K699tqnnnpql41f+cpX7rjjjkM8EgAAB8JTsQAA\ngRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIHIqmftlVdeueWWW3bZuGTJkl027r4PAACNr76w\nW7x48eLFi3fZ+Oqrr7766qs7bxF2AACpYK9hN2XKlMacAwCAg7TXsLv88ssbcw4AAA7S51w8\nsW7durKyst23T5w48dNPPz00IwEAcCDqC7v58+cff/zxo0eP3mX73/72t+HDh3fv3n3lypWH\ncjYAAPbDXsNu7dq1l1566aZNm84+++xdlr70pS/9+te/Xrt27QUXXLB169ZDPCEAAPtkr2F3\n//33f/zxx/fee+8NN9ywy1JGRsa111575513vvXWW7/97W8P8YQAAOyTvYbdzJkzO3fuXFJS\nsrcdhg8f3qFDh0ceeeSQzAUAwH7aa9i9++67p5122hFH7HWHrKys008//fXXXz80gwEAsH/2\n2m2VlZVt2rSp/85t2rTZtm1bQ48EAMCB2GvYtWnT5t13363/zv/85z/btm3b0CMBAHAg9hp2\np5566osvvrh+/fq97fD2228vWLDg9NNPPzSDAQCwf/YadoMGDdq0adP3v//9HTt27L5aWVn5\n3e9+d8eOHVddddUhnA4AgH2217C79NJLzz333Keffvr0009/+umnq6qqkts/+uijBx988MQT\nT1yyZMkll1zyjW98o7FGBQCgPnv9rNiMjIxp06Z95zvfee655/r165eRkdGyZcva2tq6whs4\ncODDDz/cWHPWp7Ky8vbbb7/qqqu6du0a9ywAALGp7yPFWrVq9eyzzz777LOXXXZZp06dtm/f\nHkXR8ccfP3jw4Pnz5z/xxBNNmjRprDnrU1lZ+fOf//ztt9+OexAAgDjt9RG7OhdeeOGFF164\nt9U1a9Z06NChQUfasyFDhuxtqbq6Ooqiu++++5lnnomi6IEHHmiEeQAAUs3nh90e7dixY9as\nWffff//zzz+/x6srGtyDDz5Y/w5//OMfkzeEHQBweKrvqdg9Wrly5U033VRUVNS3b99Zs2ad\ncMIJh2Ks3ZWWlmZmZp500knPP//8hv8t+ekXTzzxRPLLxpkHACDV7GvY1dTUPPnkk//xH//R\npUuX22+/fd26dZdeeuncuXP/9re/HdL56vzqV7965ZVXoii68MILb7zxxoyMjGWQ/H4AACAA\nSURBVFb/X4sWLaIoatasWfLLxpkHACDVfH7YrVix4vrrr2/fvv23v/3t2bNnt2vXLoqiRx55\n5KmnnjrzzDMP/YT/csopp7z66qt33HHHI488csIJJ0yfPr0x/3QAgBS317DbsmXL5MmTe/fu\nfcIJJ/zqV7+qrq4eNGjQSy+9tGDBgiiK8vLyGnHIf8nKyvrJT36yfPnybt26/ed//uc3v/nN\n1atXxzIJAECq2evFE8ccc8zGjRszMjJ69+59xRVXDBw4sHnz5lEUpcK7inTu3Hn27NmPPPLI\n9ddff8IJJ1x//fVxTwQAEL+9PmK3cePGI4444pprrnnooYeGDBmSrLqUctVVV61YseIb3/jG\n2LFj454FACB+ew27ESNGHHnkkffcc09xcXGvXr0eeOCBysrKxpxsX7Rr1+7xxx9/9tlnr7/+\n+s6dO8c9DgBAnPYadr/85S/fe++9xx577Otf//qiRYu+//3vH3PMMYMGDZo3b15jzrcvLrzw\nwvHjx3fr1i3uQQAA4lTfVbE5OTmXXXbZnDlz3nzzzeuvv75p06a/+93vkp8A8cILL3z00UeN\nNSQAAJ9vn97H7otf/OL48ePXrFnz6KOPJt/i5IEHHigsLCwpKVm2bNkhnnBflZeXn3vuueee\ne+5+3WvlypU5OTkZ9br66qujKEokEodmcACAhpFxAL3y5ptv3nfffb/97W/Xr18fpUzxvPba\na1/5ylei/ZwnkUgsWrRoy5Yt9ezzhz/84a677qqqqsrPzz/YKaNo8ODBURQ9/PDDB38oAKDx\n1dTU5ObmLly48Iwzzoh7ll0dyGfFHn/88Xfeeeftt98+ffr0SZMmNfhMB6Zr167Lly/f33tl\nZGT06tWr/n3Ky8sPdCgAgMZzIGGXlJub+53vfOc73/lOA05zMPLy8rp37x73FAAAsTnwsItL\nIpGoqKhYuXJlVVVVFEUtW7YsLi4uLCyMey4AgJilU9ht2LBh3LhxU6ZMWbdu3S5LRUVFQ4YM\nGTFiRJMmTWKZDQAgdmkTdmvXru3Vq1dFRUVxcXGfPn06duzYrFmzKIoqKyvLy8vnzZs3evTo\n6dOnz5kzp3Xr1nEPCwAQg7QJu1GjRq1Zs2bq1Kn9+/fffbW2tnbSpEnDhw8fO3bshAkTGn88\nAIDY7dP72KWCWbNmDRo0aI9VF0VRZmbmsGHDBgwYMGPGjEYeDAAgRaRN2K1fv/5zPw22W7du\nH374YePMAwCQatIm7AoKCj73Uy6WLl1aUFDQOPMAAKSatAm7vn37Tps2bfz48du2bdt9dfPm\nzWPGjJk5c+bAgQMbfzYAgFSQNhdP3HLLLQsWLBg5cuStt97as2fPwsLC/Pz8RCKxadOmVatW\nLVmypLq6unfv3jfffHPckwIAxCNtwq5Vq1ZlZWUTJ06cPHny3Llza2tr65ays7N79OhRUlJS\nUlKSmZkZ45AAADFKm7CLoignJ6e0tLS0tHTr1q2rV69OfvJEixYtioqKcnJy4p4OACBm6RR2\ndfLy8oqLi+OeAgAgtaTNxRMAANRP2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEIqiw\n27BhwzvvvBP3FAAA8UinsPvb3/520UUXHXvssb179/7Nb35TW1u7yw4///nPO3XqFMtsAACx\ny4p7gH21cOHCc845Z9u2bU2bNn3//fdffvnlqVOnPv30061bt457NACAlJA2j9jdcccdn332\n2dNPP71p06aqqqpf/epXixYtOv/88zdv3hz3aAAAKSFtwu5vf/vbwIED+/btm5GRkZubW1pa\n+vzzzy9btmzAgAG7PycLAHAYSpuw++CDD4477ridt5x99tkPPPDAs88++6Mf/SiuqQAAUkfa\nvMbu6KOPfu2113bZOGjQoBUrVtxxxx0dOnQYOXJkLIMBAKSItAm7fv363X333ffcc8/QoUOz\ns7Prto8bN+7999//8Y9//P7773tOFgA4nKVN2I0ePfqZZ5659tprZ86c+ac//alue0ZGxsMP\nP9yyZcsJEybEOB4AQOzS5jV2bdq0+ctf/jJs2LDu3bvvspSRkXHXXXdNnz69c+fOscwGAJAK\n0uYRuyiKjjrqqIkTJ+5ttV+/fv369WvMeQAAUkraPGIHAED9hB0AQCDS6anY+pWXlw8dOjSK\notmzZ+/7vTZu3Dhq1Kht27bVs8+KFSsOdjgAgEMvnLCrqqp68cUX9/de27dv/+STT2pqaurZ\np7q6OoqiRCJx4MMBABx64YRd165dly9fvr/3Ouqoo373u9/Vv8+kSZP+8pe/ZGRkHOhoAACN\nIZywy8vL2/2dUAAADh/pF3aJRKKiomLlypVVVVVRFLVs2bK4uLiwsDDuuQAAYpZOYbdhw4Zx\n48ZNmTJl3bp1uywVFRUNGTJkxIgRTZo0iWU2AIDYpU3YrV27tlevXhUVFcXFxX369OnYsWOz\nZs2iKKqsrCwvL583b97o0aOnT58+Z86c1q1bxz0sAEAM0ibsRo0atWbNmqlTp/bv33/31dra\n2kmTJg0fPnzs2LE+NBYAODylzRsUz5o1a9CgQXusuiiKMjMzhw0bNmDAgBkzZjTyYAAAKSJt\nwm79+vWdO3euf59u3bp9+OGHjTMPAECqSZuwKygoWLZsWf37LF26tKCgoHHmAQBINWkTdn37\n9p02bdr48eP3+PFfmzdvHjNmzMyZMwcOHNj4swEApIK0uXjilltuWbBgwciRI2+99daePXsW\nFhbm5+cnEolNmzatWrVqyZIl1dXVvXv3vvnmm+OeFAAgHmkTdq1atSorK5s4ceLkyZPnzp1b\nW1tbt5Sdnd2jR4+SkpKSkpLMzMwYhwQAiFHahF0URTk5OaWlpaWlpVu3bl29enXykydatGhR\nVFSUk5MT93QAADFLp7Crk5eXV1xcHPcUAACpJW0ungAAoH7CDgAgEMIOACAQwg4AIBDCDgAg\nEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4A\nIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEFlxD5Auus2Zk9mkyf980bp1\n1KPH/9z+7LNowYJo+/Z/7Vr/6vr1x7Zp886B3deqVatWrVq1Gvvq/PkZUdQtSk0JPs9///d/\nR9GkKErU/a9Dh3+trlyZaNIkse+rzZp9ctVVVx3Yfa1atWrVqlWrqbH63wsXLkyknoxEIhF3\nW6a6SZMmXX311VVVVfn5+Qd/tMGDB0dR9PDDDx/8oQCAxldTU5Obm7tw4cIzzjgj7ll25TV2\nAACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQ\ndgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2cBh5\n5513SktL454CgENF2MFh5PXXX7///vvjngKAQ0XYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2KW9999/P5FIxD0FABA/YZf2vvSlL7300ktxTwEAxE/Ypb1t27Zt3bo17ikAgPgJO/6XDz74\n4Be/+EXcUwAAB0LY8b/85S9/ufXWW+OeAgA4EMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDC\nDgjW4sWLi4uL456CQ+Xjjz++9957454CUouwA4L18ccfr127Nu4pOFQWL148cuTIuKeA1CLs\nAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAApEV9wD7LZFIVFRUrFy5sqqqKoqili1bFhcX\nFxYWxj0XAEDM0insNmzYMG7cuClTpqxbt26XpaKioiFDhowYMaJJkyaxzAYAELu0Cbu1a9f2\n6tWroqKiuLi4T58+HTt2bNasWRRFlZWV5eXl8+bNGz169PTp0+fMmdO6deu4hwUAiEHahN2o\nUaPWrFkzderU/v37775aW1s7adKk4cOHjx07dsKECY0/HgBA7NLm4olZs2YNGjRoj1UXRVFm\nZuawYcMGDBgwY8aMRh4MACBFpE3YrV+/vnPnzvXv061btw8//LBx5gEASDVpE3YFBQXLli2r\nf5+lS5cWFBQ0zjwAAKkmbcKub9++06ZNGz9+/LZt23Zf3bx585gxY2bOnDlw4MDGnw0OW2Vl\nZWVlZQ14wMrKygY8GsRr5syZyXfmgkaTNhdP3HLLLQsWLBg5cuStt97as2fPwsLC/Pz8RCKx\nadOmVatWLVmypLq6unfv3jfffHPck8Jh5L777oui6Ktf/WpDHbC4uHjq1KlnnnlmQx0QYnT5\n5Zc/+eSTffr0iXsQDiNpE3atWrUqKyubOHHi5MmT586dW1tbW7eUnZ3do0ePkpKSkpKSzMzM\nGIcEDtLmzZs3bdoU9xTQMBKJRCKRiHsKDi9pE3ZRFOXk5JSWlpaWlm7dunX16tXJx7dbtGhR\nVFSUk5MT93QAADFLp7Crk5eXV1xcHPcUAACpJW0ungAAoH5p+YjdHpWXlw8dOjSKotmzZ+/X\nHd99990dO3bUs8PHH38cRdE777zTtGnTg5kwKfkM8sqVKw/+UEmJROKDDz5oqAN+8MEHiUSi\nAcfbsmVLFEUN+Bm+n376aatWrRrqaA1+wBT/fhv89+vv80Hy9/lgpP7vt2H/PkeH2e+3wQ/Y\ngN/v9u3bD/4gh0oiFEuXLj2A7+jtt9/OyMiI91cAAKSdhQsXHqKkORjhPGLXtWvX5cuX7++9\nOnfu/Omnn+58je3ulixZcsEFF3zwwQcNcolG8tHBrKwG+8lv27YtNze3oY7W4AccPnx4FEX3\n3HNPQx2wQ4cODz300HnnndcgR/vjH/9YUlKyZs2aBjlalPLfb9TQv19/nw+Sv88HKcV/vw07\n3uH2+03l77empuYLX/jCwR/nUAgn7PLy8rp3734Ad2zRokX9OzRv3jyKotatW7v29gAkf2it\nW7duqANmZGTk5+c31AHz8/MzMjIacLwU/345SCn++/X3+SA1+PfbsA63328qf781NTUHf5BD\nJP3CLpFIVFRUrFy5MvninpYtWxYXFxcWFsY9FwBAzNIp7DZs2DBu3LgpU6asW7dul6WioqIh\nQ4aMGDGiAV8ECrCLLl26xD0CQH3SJuzWrl3bq1evioqK4uLiPn36dOzYsVmzZlEUVVZWlpeX\nz5s3b/To0dOnT58zZ07KPooOpLubbrop7hEA6pM2YTdq1Kg1a9ZMnTq1f//+u6/W1tZOmjRp\n+PDhY8eOnTBhQuOPBwAQu7R5g+JZs2YNGjRoj1UXRVFmZuawYcMGDBgwY8aMRh4MACBFpE3Y\nrV+/vnPnzvXv061btw8//LBx5gEASDVpE3YFBQXLli2rf5+lS5cWFBQ0zjzQOIYOHXpg7+MD\nwGEobcKub9++06ZNGz9+/LZt23Zf3bx585gxY2bOnDlw4MDGn416tGzZsmXLlnFPkcbuvPPO\njh07xj0FAOkhbS6euOWWWxYsWDBy5Mhbb721Z8+ehYWF+fn5iURi06ZNq1atWrJkSXV1de/e\nvW+++ea4J+V/ufPOO+MeAQAOF2kTdq1atSorK5s4ceLkyZPnzp2784eAZWdn9+jRo6SkpKSk\nJDMzM8Yh2Z3fCJAuBg8eHPcIcLDSJuyiKMrJySktLS0tLd26devq1auTnzzRokWLoqIiH/YF\nwEH693//97hHgIOVTmFXJy8vr7i4OO4pAABSS9pcPAEAQP2EHQBAIIQdAEAghB0AQCDS8uIJ\nSFkDBgyIewQADl/CDhrShRdeGPcIABy+PBULABAIYQcAEAhhBwAQCGEHABAIYcdh7bTTTvvF\nL34R9xQA0DCEHYe1o446atiwYXFPAQANQ9gBAARC2AEABELYAQAEQtiRZr72ta917Ngx7ikA\nIBX5SDHSzPPPPx/3CAAh6NKlS9wj0PCEHUBsioqK2rVrF/cUHKZuuummuEeg4Qk7gNi88cYb\ncY8ABEXYAdBI2rVr16ZNm7in4DB1wgknxD1CYxB2ADSSlStXxj1CGjviiCOOOMIljwdu5MiR\ncY/QGPwVAYA0cOaZZ06bNi3uKUh1wg4A0kDTpk3PP//8uKcg1Qk7AKABtGzZsmXLlnFPcbjz\nGjsAoAFUVFTk5OTEPcXhziN2AIFo1apVq1at4p6Cw5eqSwXCDiAQvXr1euedd+KeAoiTsAMI\nR1aWF9jAYU3YAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEAKScjIyMjIyPuKdJP\nVtwDpIumGzZEOTn//4umUW7uv9aqq6Nt23ba1apVq1aDWK2tzcrM3JFqU1k9TFbPOOOMSZMm\npdpUdatR1DRKTQk+z8KFC6NoUhQl6v531FH/Wn377URmZsKqVatWw1vNy6u66qqrUm0qq1ZT\nY/W/Fy5cmEg9HrHbR7eXlQ3Ozs5OftGy5b8WOneO/vrXaPv2f22xatWq1TBWb7/9Zyk4lVWr\nsa8uXrz9lFNuj6LHo9STkUgk4p4h1S1atKhXr17btm3LqXsuFuAwMHjw4CiKHn744bgHgdRS\nU1OTm5u7cOHCM844I+5ZduXiCQCAQHgqFoA9y8zMjHsEYP8IOwD27Gc/+9nn7wSkEmEHwJ4d\nc8wxcY8A7B+vsQMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiE\nsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAI\nRFbcA6SBnJycKIpyc3PjHgQASBXJPEg1GYlEIu4Z0sCyZct27NjRIIe6+eabq6urv//97zfI\n0ThIr7322j333PPAAw/EPQj/Y8iQIcOHDz/ppJPiHoQoiqL7778/iiL/XqWI1157beLEiS+/\n/HLcgxBFUZSVlfXlL3857in2QNg1tsGDB0dR9PDDD8c9CFEURbNmzRo4cOCmTZviHoT/kZ+f\n/+STT1500UVxD0IU+fcqxfj3in3hNXYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYA\nAIEQdgAAgRB2AACB8FmxjS01P1rusJWTk+M3klL8RlKK30VKcXawL3ykWGPbsGFDFEWtW7eO\nexCiKIo+++yzd99999hjj417EP7HO++8U1RUdMQRnkxICf69Sin+vWJfCDsAgED4v8UAAIEQ\ndgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACB\nEHYAAIEQdgAAgRB2AACBEHaN59NPP/3hD3947LHH5uTkFBQUDBkyZO3atXEPdZh65JFHMvbk\ntttui3u0w8j27dtvuOGGzMzMU045ZfdV50sjq+fX4XxpZBs2bBgxYkTHjh1zc3M7derUt2/f\nV155ZecdnB3UIyvuAQ4XNTU155xzzl//+tdLL7305JNPLi8vnzx58ksvvfSXv/yldevWcU93\n2Pn000+jKLrsssuKiop23t6rV6+YJjrsrFix4vLLL3/rrbf2uOp8aWT1/zqcL43pk08+6dGj\nxzvvvHPRRRddeeWVK1eufPLJJ1944YUlS5Z86UtfipwdfK4EjeJXv/pVFEU///nP67Y8+eST\nURRdf/31MU512BozZkwURa+++mrcgxymNm7c2KRJk1NOOeWtt97Kzc3t0aPHLjs4XxrT5/46\nnC+N6Zprromi6O67767bMn369CiK+vTpk/zS2UH9PBXbSCZPnty8efPrrruubsuAAQO6dOky\nZcqURCIR42CHp+QjEK1atYp7kMPUjh07hg0btmjRoi5duuxxB+dLY/rcX4fzpTFlZ2efc845\nQ4cOrdtyySWXNGnS5PXXX09+6eygfsKuMWzdunX58uU9e/bMzc3defvXvva1devWVVRUxDXY\nYavuP1S1tbVr1qz5+OOP457o8HLkkUeOHz8+Ozt7j6vOl0ZW/68jcr40rv/6r/+aPXv2zr+O\nmpqaHTt2dOjQIXJ2sA+EXWNYvXp1bW1tYWHhLts7duwYRdHKlSvjGOqwtnHjxiiKJkyY0LZt\n28LCwrZt2x5//PGPPfZY3HMRRc6X1ON8idekSZO2b9/+7W9/O3J2sA9cPNEYqqqqoihq1qzZ\nLtvz8/PrVmlMyUcgHn/88R//+Mft27dfsWLFxIkTv/vd71ZVVe38DAixcL6kGudLjObNmzdy\n5Mivfe1rV199deTsYB8Iu8aTkZGxy5bk6yF2386hNmrUqOHDh19wwQV1/z5efvnlJ5988o03\n3jh48OCcnJx4xyNyvqQS50tcHn/88cGDB3fv3n3mzJlZWf/677Wzg3p4KrYxtGjRItrT/5eq\nrKyMoqh58+YxzHR4O/vssy+99NKd/1/vCSec0KdPn08++WTZsmUxDkbkfEk9zpfGl0gkxowZ\n853vfOess86aO3fukUcemdzu7OBzecSuMRQVFWVlZa1atWqX7eXl5VEUFRcXxzEUu2rXrl0U\nRZs2bYp7kMOd8yUtOF8OnUQiMWTIkIceeujaa6/9r//6r8zMzLolZwefyyN2jSEnJ6dHjx5L\nliyprq6u2/jZZ5/NmzevsLBwl/f85FDbtGnTvffe+/jjj++yPfluAsnXIBMj50tKcb40vtLS\n0oceeuj222//9a9/vXPVRc4O9oGwayTf+973qqurf/nLX9Ztue+++95///0hQ4bEONXhqWnT\npuPGjfvBD37wj3/8o27jzJkzX3755a985SvHHXdcjLOR5HxJHc6XRjZjxoy77rrruuuuu+GG\nG/a4g7OD+mV4P8PGUVtbe9ZZZy1YsOBb3/rWySefvGLFiieffLJ79+6vvPJK06ZN457usPP7\n3/++b9++TZs2/fa3v11QUPD3v//9mWeead68+Zw5c04++eS4pwvfvHnznnvuueTt8ePHt23b\n9sorr0x+OXLkyDZt2jhfGtPn/jqcL42pS5cu5eXl11577e5/1X/yk5+0bt3a2cHniO0zLw4/\nVVVVyc91zs7Obt++/TXXXLN+/fq4hzp8LVq06MILL2zVqlVWVlZBQcEVV1zx1ltvxT3U4eKO\nO+7Y279Idb8F50uj2Zdfh/Ol0dTz3+uKiorkPs4O6uEROwCAQHiNHQBAIIQdAEAghB0AQCCE\nHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAg\nhB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBA\nIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB3/r527B22qiwM4fGpfI5b4\nXTWmFEQcpKMGByk0IiIopDgIDtZVK0odFMXF70GL6KCLiIpGOjiJFkQHvyjSQqg6FCc/NkHE\nqtAGNegQLOHlxQ5K78vJ80zh3HPhf7cf9x4CAERC2AH1rlgsNjQ0HDlyJOlBAP6UsAMAiISw\nAwCIhLADmNzQ0NDmzZubm5tTqdTSpUu7urrevHlTu6G/v3/16tVNTU2ZTKanp2d8fLy1tXXl\nypUJzQvUqX+SHgDg/65UKnV0dMyfP7+npyeTybx69erChQv37t0bGRlZsGBBCOHx48ednZ0L\nFy48ePBgc3PzzZs3t27d+uXLl5aWlqRnB+qLsAOYxNDQUFtb25kzZ/L5fHWlpaVlz549fX19\nu3fvDiGcOHGiUqncvn07l8uFEHbs2LF+/fpPnz4lODNQn3yKBZhEd3d3qVSqVt23b9/K5XJb\nW1sIYeJr7JMnT1asWFGtuhBCY2PjgQMHkpkVqG/CDmBy169f7+jomDdvXiqVmjlz5rp160II\n379/DyGMjo6Wy+Xly5fX7l+zZk0ygwL1TdgBTOLQoUPbt28fGxs7e/bsw4cPnz59eunSpYmr\nHz58CCE0NTXV3jJr1qzGxsapHhSoe87YAfxOuVw+d+5ca2vrgwcP0ul0dbH2/Nz06dOr22rv\nGhsbq1QqUzknQPDGDuD33r17Nz4+nsvlJqouhPDo0aOJ35lMZtq0aW/fvq29a3BwcOpGBPhF\n2AH8zuLFixsaGmr/te7Zs2fXrl0Lv97SpVKpXC734sWLly9fVjdUKpVTp04lMSxQ73yKBQgh\nhLt3746Ojv5rsbOzc+3atZs2bbpz587OnTvz+fzIyMj58+dv3LhRKBT6+/v7+voKhcL+/fu3\nbNmycePGXbt2zZ49u1gsLlu2bMaMGYk8CFDPGn78+JH0DABJKhaLXV1d/3mpt7d3375979+/\n37t37/37979+/bpq1aqjR4+2t7cfO3ast7c3nU4PDw9nMpnLly+fPn369evXS5Ys2bZt2+HD\nh9PpdC6XGxgYmOLHAeqZsAP4+z5//jxnzpxCoXDr1q2kZwHqiDN2AH/qX7WT+QAAAOxJREFU\nypUr+Xy+VCpNrFy9ejWE0N7enthMQF3yxg7gTw0ODlb/vri7uzubzQ4PD1+8eDGbzT5//nzu\n3LlJTwfUEWEH8BcMDAycPHmyVCp9/Phx0aJFGzZsOH78eDabTXouoL4IOwCASDhjBwAQCWEH\nABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlh\nBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJ\nYQcAEAlhBwAQCWEHABCJnxI79Lo5ivzhAAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “Series  norm”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x8Gb1xVqF4TT"
      },
      "source": [
        "# Levinson-Durbin Algorithm #\n",
        "\n",
        "**3) Code the Levinson-Durbin algorithm into a R function taking**\n",
        "\n",
        "inputs: $\\gamma(0),\\dots,\\gamma(p)$ \n",
        "\n",
        "**and returning**\n",
        "\n",
        "outputs: $\\phi_{k,k}$ and $\\sigma_k^2$ for $k=1,\\dots,p$ and $\\phi_{k,p}$ for $k=1,\\dots,p$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LHpTsaajwPyy",
        "outputId": "0ccf0e90-c083-42ee-c987-84663d5feebe"
      },
      "source": [
        "gamma = acovf(X_t, fft=False)[:11]\n",
        "list(gamma)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.9327881917157219,\n",
              " 0.042324521616624526,\n",
              " -0.04917550251394579,\n",
              " -0.0848368596930547,\n",
              " -0.0006698169333025348,\n",
              " 0.0929848442942322,\n",
              " 0.01017976024267732,\n",
              " -0.033500353435843254,\n",
              " -0.03831809105497133,\n",
              " -0.05192550617660642,\n",
              " 0.06460773462816748]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 154
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tZHELNVA6Ulf",
        "outputId": "4d47714e-91b9-461d-e4f7-c27a96937716"
      },
      "source": [
        "gamma2 = acf(X_t, nlags=10, fft=False)\n",
        "list(gamma2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1.0,\n",
              " 0.04537420391093825,\n",
              " -0.05271883043833878,\n",
              " -0.09094975734738903,\n",
              " -0.0007180804165954422,\n",
              " 0.09968484284004575,\n",
              " 0.010913260194635612,\n",
              " -0.03591421260835694,\n",
              " -0.04107909104690855,\n",
              " -0.055666984892998435,\n",
              " 0.06926302798637639]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 155
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EIDz8bJyNbZr"
      },
      "source": [
        "def levinson_durbin_algo(gamma: np.ndarray, k: int=10):\n",
        "  \"\"\"\n",
        "  Levinson-Durbin Algorithm \n",
        "\n",
        "  Parameters\n",
        "  ---\n",
        "  gamma : auto-covariance process\n",
        "  k : nlags\n",
        "  \n",
        "  Returns\n",
        "  ---\n",
        "  phi \n",
        "  sigma\n",
        "  \"\"\"\n",
        "  #Initialization \n",
        "  kappa = np.zeros(k+1)\n",
        "  phi = np.zeros((k+1, k+1))\n",
        "  sigma_squared = np.zeros(k+1)\n",
        "  kappa[1] = gamma[1] / gamma[0]\n",
        "  sigma_squared[1] = gamma[0] * (1 - np.abs(kappa[1])**2)\n",
        "  phi[1, 1] = kappa[1]\n",
        "  for p in range(1, k):\n",
        "    kappa[p+1] = (gamma[p+1] - np.dot(phi[1:k+1, k], sigma_squared[1:k+1][::-1]))/sigma_squared[p]\n",
        "    sigma_squared[p+1] = sigma_squared[p]*(1 - np.abs(kappa[p+1])**2)\n",
        "    phi[p+1, p+1] = kappa[p+1]\n",
        "    for m in range(1, p+1):\n",
        "      phi[m, p+1] = phi[m, p] - (kappa[p+1] * np.conj(phi[p + 1 - m, p]))\n",
        "\n",
        "  #sigma_squared = sigma_squared[1:]\n",
        "  #phi = [line[1:] for line in phi[1:]]\n",
        "  phi_diag = np.diag(phi).copy()\n",
        "\n",
        "  return phi, sigma_squared, phi_diag"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zAvaC2MyGBgB"
      },
      "source": [
        "**4) Test your code on the previously generated white noise, first using the true auto-covariance and then the empirical one, for $p=10$.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kUtuobbr6siR"
      },
      "source": [
        "### True Auto-Covariance"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5shP7tAxXDQ4",
        "outputId": "c1e37a14-db6c-4b7a-a06b-2a4716282e2d"
      },
      "source": [
        "np.set_printoptions(edgeitems=10)\n",
        "np.core.arrayprint._line_width = 180\n",
        "phi_true, sigma_true, phi_diag_true = levinson_durbin_algo(X_t)\n",
        "print(np.around(phi_true, decimals=2))\n",
        "print(sigma_true)\n",
        "print(phi_diag_true)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
            " [ 0.    0.72  0.27 -2.96 -2.74 -2.74 -2.76 -2.76 -2.76 -2.75 -2.8 ]\n",
            " [ 0.    0.    0.62 -0.78 -0.81 -0.16 -0.2  -0.23 -0.21 -0.2  -0.34]\n",
            " [ 0.    0.    0.    5.17  5.05  4.94  5.35  5.31  5.33  5.24  5.24]\n",
            " [ 0.    0.    0.    0.   -0.04 -0.39 -0.41  0.15  0.14 -0.02  0.2 ]\n",
            " [ 0.    0.    0.    0.    0.   -0.13 -0.35 -0.37 -0.66 -0.63 -0.78]\n",
            " [ 0.    0.    0.    0.    0.    0.   -0.08 -0.37 -0.36  0.89  0.89]\n",
            " [ 0.    0.    0.    0.    0.    0.    0.   -0.1   0.05 -0.    1.26]\n",
            " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.05 -0.59 -0.64]\n",
            " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.   -0.23 -0.9 ]\n",
            " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.   -0.24]]\n",
            "[ 0.          0.37480292  0.22867926 -5.88953052 -5.87897385 -5.78216076 -5.74317338 -5.68145499 -5.66486017 -5.35362106 -5.0432725 ]\n",
            "[ 0.          0.72214837  0.62439411  5.17247971 -0.0423373  -0.12832648 -0.08211395 -0.1036648   0.05404513 -0.23439723 -0.24076927]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5fvBzzuQ6wtX"
      },
      "source": [
        "### Empirical (p=10)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WtMiLx7M60FX",
        "outputId": "847bc452-4465-4545-8b4a-22a282f01763"
      },
      "source": [
        "np.set_printoptions(edgeitems=10)\n",
        "np.core.arrayprint._line_width = 180\n",
        "phi_empirical, sigma_empirical, phi_diag_empirical = levinson_durbin_algo(gamma)\n",
        "print(np.around(phi_empirical, decimals=3))\n",
        "print(sigma_empirical)\n",
        "print(phi_diag_empirical)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.     0.   ]\n",
            " [ 0.     0.045  0.048  0.043  0.043  0.043  0.042  0.042  0.041  0.038  0.042]\n",
            " [ 0.     0.    -0.053 -0.048 -0.048 -0.039 -0.039 -0.036 -0.035 -0.037 -0.034]\n",
            " [ 0.     0.     0.    -0.091 -0.091 -0.086 -0.085 -0.086 -0.081 -0.081 -0.078]\n",
            " [ 0.     0.     0.     0.    -0.001 -0.005 -0.005 -0.008 -0.008 -0.003 -0.003]\n",
            " [ 0.     0.     0.     0.     0.     0.101  0.101  0.099  0.095  0.095  0.088]\n",
            " [ 0.     0.     0.     0.     0.     0.     0.011  0.013  0.011  0.007  0.007]\n",
            " [ 0.     0.     0.     0.     0.     0.     0.    -0.037 -0.035 -0.037 -0.031]\n",
            " [ 0.     0.     0.     0.     0.     0.     0.     0.    -0.042 -0.04  -0.037]\n",
            " [ 0.     0.     0.     0.     0.     0.     0.     0.     0.    -0.057 -0.06 ]\n",
            " [ 0.     0.     0.     0.     0.     0.     0.     0.     0.     0.     0.071]]\n",
            "[0.         0.93086775 0.92826993 0.92051648 0.92051599 0.91112324 0.9110095  0.9097776  0.90816371 0.9051948  0.90058346]\n",
            "[ 0.          0.0453742  -0.05282759 -0.09139245 -0.00072765  0.10101383  0.01117276 -0.03677278 -0.04211809 -0.05717637  0.0713744 ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k1QQTOq6GFb4"
      },
      "source": [
        "**5) What can we say about the sequence  $(\\sigma_k^2)_{k=1,\\dots,p}$ ? Compare the theoretical and empirical cases in the previous example.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yzA14phLA8kb",
        "outputId": "5d0c9d57-81b0-46ec-b302-192b4a2d50e0"
      },
      "source": [
        "sigma_empirical"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.        , 0.93086775, 0.92826993, 0.92051648, 0.92051599, 0.91112324, 0.9110095 , 0.9097776 , 0.90816371, 0.9051948 , 0.90058346])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 184
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hiIpagfm_rUo",
        "outputId": "d612b36f-fa66-4651-9acb-f1fd2f2f3892"
      },
      "source": [
        "sigma_empirical[1:].mean()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9146022462896933"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 185
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WBQhz0LtBA8n"
      },
      "source": [
        "The variance of the error is slowly decreasing with the number of lags but is very high. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NpGZ6EnOGJIs"
      },
      "source": [
        "**6) Load the time series in the file** https://perso.telecom-paristech.fr/roueff/edu/tsfd/data/test.Rdata\n",
        "\n",
        "\n",
        "```{r, eval = FALSE}\n",
        "load(url('https://m2:map658@perso.telecom-paristech.fr/roueff/edu/tsfd/data/test.Rdata'))\n",
        "```\n",
        "\n",
        "**Look at its (empirical) auto-correlations and partial auto-correlations up to lag 10. \n",
        "What order would you choose for an MA model? For an AR model ? In the latter case, use the Levinson-Durbin algorithm that you coded to estimate the parameters of the model. Compare with the built-in**  *arima()* "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "jkTalN11dkrU",
        "outputId": "164cf38d-e97b-487c-b42c-d43df05ab909"
      },
      "source": [
        "load(url('https://m2:map658@perso.telecom-paristech.fr/roueff/edu/tsfd/data/test.Rdata'))\n",
        "ls()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] \"data\" \"norm\" \"x\"   "
            ],
            "text/latex": "\\begin{enumerate*}\n\\item 'data'\n\\item 'norm'\n\\item 'x'\n\\end{enumerate*}\n",
            "text/markdown": "1. 'data'\n2. 'norm'\n3. 'x'\n\n\n",
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>'data'</li><li>'norm'</li><li>'x'</li></ol>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "UUyuv_TnHPVX",
        "outputId": "99adabed-71fe-4341-e6a9-b756e9107166"
      },
      "source": [
        "head(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] -1.6112849  0.4304038 -0.5113267  1.1574108  0.8872328  3.0726475"
            ],
            "text/latex": "\\begin{enumerate*}\n\\item -1.61128485280038\n\\item 0.43040379135137\n\\item -0.511326744764691\n\\item 1.15741075323375\n\\item 0.887232824780188\n\\item 3.07264747504032\n\\end{enumerate*}\n",
            "text/markdown": "1. -1.61128485280038\n2. 0.43040379135137\n3. -0.511326744764691\n4. 1.15741075323375\n5. 0.887232824780188\n6. 3.07264747504032\n\n\n",
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>-1.61128485280038</li><li>0.43040379135137</li><li>-0.511326744764691</li><li>1.15741075323375</li><li>0.887232824780188</li><li>3.07264747504032</li></ol>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kFJFybDfdvnP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "afc67965-7d41-4f61-ee97-8d3cbd2d147e"
      },
      "source": [
        "acf(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Hnz5m3evHlfO6xevXrRokVf/vKXD89gAAAcnH2G3cCBA8vKym644YbKysrPr5aU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\n4iefH7hX8BRGpAAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “Series  x”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TabquimfHWaa"
      },
      "source": [
        "for an MA model, I would choose as parameter 6"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "6WcAVVtDfLLH",
        "outputId": "7ae2a95b-4f40-42f2-ca40-248b7baba149"
      },
      "source": [
        "pacf(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RtvvPG8884rLCysnz8dAKDh23fYtWjRYv369VEUpaamNm/efMWKFVVLJ5544jvv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\nAAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “Series  x”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SO381MlegIGz"
      },
      "source": [
        "For the AR model, we would choose an order of 3."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lglyRZbZg9r8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "96b822b7-5106-4c13-ec51-121300c8f536"
      },
      "source": [
        "arima(x, order = c(3,0,0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "arima(x = x, order = c(3, 0, 0))\n",
              "\n",
              "Coefficients:\n",
              "         ar1     ar2      ar3  intercept\n",
              "      0.6127  0.3566  -0.2599     0.2164\n",
              "s.e.  0.0302  0.0340   0.0302     0.1082\n",
              "\n",
              "sigma^2 estimated as 1.014:  log likelihood = -1460.83,  aic = 2931.66"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "D1QwvNVWIeOd",
        "outputId": "64f06116-1d31-465b-a84e-f699b3c4c435"
      },
      "source": [
        "arima(x, order = c(0,0,6))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "arima(x = x, order = c(0, 0, 6))\n",
              "\n",
              "Coefficients:\n",
              "         ma1     ma2     ma3     ma4     ma5     ma6  intercept\n",
              "      0.6120  0.7288  0.4156  0.3435  0.1504  0.1019     0.2168\n",
              "s.e.  0.0312  0.0362  0.0413  0.0410  0.0356  0.0330     0.1053\n",
              "\n",
              "sigma^2 estimated as 1.014:  log likelihood = -1460.57,  aic = 2937.14"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WHUHrK7kGPeb"
      },
      "source": [
        "# S&P$500$ Data  and  MA Modeling #\n",
        "\n",
        "In this part we fit a MA model to the annual returns, computed every month. \n",
        "This model is then used for prediction. \n",
        "\n",
        "**7)  Load the time series from the file** https://perso.telecom-paristech.fr/roueff/edu/tsfd/data/spmonthly-1950-2015.Rdata\n",
        "\n",
        "```{r, eval = FALSE}\n",
        "load(url('https://m2:map658@perso.telecom-paristech.fr/roueff/edu/tsfd/data/spmonthly-1950-2015.Rdata'))\n",
        "```\n",
        "\n",
        "\n",
        "**Look at the downloaded SP500 time series using**\n",
        "\n",
        "```{r, eval = FALSE}\n",
        "plot(as.POSIXct(mdates),sptsm,type='l',xlab='Date',ylab='SP500')\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "Lw4h1wszb5-W",
        "outputId": "ac541781-f587-47ed-df93-dab8347edcb0"
      },
      "source": [
        "load(url('https://m2:map658@perso.telecom-paristech.fr/roueff/edu/tsfd/data/spmonthly-1950-2015.Rdata'))\n",
        "ls()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] \"data\"   \"mdates\" \"norm\"   \"sptsm\"  \"x\"     "
            ],
            "text/latex": "\\begin{enumerate*}\n\\item 'data'\n\\item 'mdates'\n\\item 'norm'\n\\item 'sptsm'\n\\item 'x'\n\\end{enumerate*}\n",
            "text/markdown": "1. 'data'\n2. 'mdates'\n3. 'norm'\n4. 'sptsm'\n5. 'x'\n\n\n",
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>'data'</li><li>'mdates'</li><li>'norm'</li><li>'sptsm'</li><li>'x'</li></ol>\n"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Z0E3VXBcBHy",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "96efd3cb-2c0f-4291-a1d8-9ae6ddf9fb78"
      },
      "source": [
        "plot(as.POSIXct(mdates),sptsm,type='l',xlab='Date',ylab='SP500')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/Jc/ZtrPm6Y+rWRBEZMx/Xy0K6LEruv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\n2cJz8dQJ3daC/mJrM7rUXoVw603tD1SteawFggSGOkJUt5qmS8a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Vbihjdeca3ZEkC0ECq7k51o+4aHQnkjQECazadjK6B0kdgpQy/Xgn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\nB9Jl5woUCv/qAAAAAElFTkSuQmCC",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oBKXhhG2GVDl"
      },
      "source": [
        "**8) What is the frequency of the corresponding time series ?  Let $P_t$,\n",
        "\t$t=1,2,\\dots$ denote the samples of this time series. Let\n",
        "\t$R_t=\\log(P_t/P_{t-1})$ be the associated log returns. Compute the\n",
        "\tautocorrelation function of the log returns and comment.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "MlztlqxkIDj6",
        "outputId": "8ba70ca9-c948-4707-acc8-3d6f6ae0372f"
      },
      "source": [
        "head(mdates)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] 1950-02-01 1950-03-01 1950-04-03 1950-05-01 1950-06-01 1950-07-03\n",
              "16446 Levels: 1950-01-03 1950-01-04 1950-01-05 1950-01-06 ... 2015-05-13"
            ],
            "text/latex": "\\begin{enumerate*}\n\\item 1950-02-01\n\\item 1950-03-01\n\\item 1950-04-03\n\\item 1950-05-01\n\\item 1950-06-01\n\\item 1950-07-03\n\\end{enumerate*}\n\n\\emph{Levels}: \\begin{enumerate*}\n\\item '1950-01-03'\n\\item '1950-01-04'\n\\item '1950-01-05'\n\\item '1950-01-06'\n\\item '1950-01-09'\n\\item '1950-01-10'\n\\item '1950-01-11'\n\\item '1950-01-12'\n\\item '1950-01-13'\n\\item '1950-01-16'\n\\item '1950-01-17'\n\\item '1950-01-18'\n\\item '1950-01-19'\n\\item '1950-01-20'\n\\item '1950-01-23'\n\\item '1950-01-24'\n\\item '1950-01-25'\n\\item '1950-01-26'\n\\item '1950-01-27'\n\\item '1950-01-30'\n\\item '1950-01-31'\n\\item '1950-02-01'\n\\item '1950-02-02'\n\\item '1950-02-03'\n\\item '1950-02-06'\n\\item '1950-02-07'\n\\item '1950-02-08'\n\\item '1950-02-09'\n\\item '1950-02-10'\n\\item '1950-02-14'\n\\item '1950-02-15'\n\\item '1950-02-16'\n\\item '1950-02-17'\n\\item '1950-02-20'\n\\item '1950-02-21'\n\\item '1950-02-23'\n\\item '1950-02-24'\n\\item '1950-02-27'\n\\item '1950-02-28'\n\\item '1950-03-01'\n\\item '1950-03-02'\n\\item '1950-03-03'\n\\item '1950-03-06'\n\\item '1950-03-07'\n\\item '1950-03-08'\n\\item '1950-03-09'\n\\item '1950-03-10'\n\\item '1950-03-13'\n\\item '1950-03-14'\n\\item '1950-03-15'\n\\item '1950-03-16'\n\\item '1950-03-17'\n\\item '1950-03-20'\n\\item '1950-03-21'\n\\item '1950-03-22'\n\\item '1950-03-23'\n\\item '1950-03-24'\n\\item '1950-03-27'\n\\item '1950-03-28'\n\\item '1950-03-29'\n\\item '1950-03-30'\n\\item '1950-03-31'\n\\item '1950-04-03'\n\\item '1950-04-04'\n\\item '1950-04-05'\n\\item '1950-04-06'\n\\item '1950-04-10'\n\\item '1950-04-11'\n\\item '1950-04-12'\n\\item '1950-04-13'\n\\item '1950-04-14'\n\\item '1950-04-17'\n\\item '1950-04-18'\n\\item '1950-04-19'\n\\item '1950-04-20'\n\\item '1950-04-21'\n\\item '1950-04-24'\n\\item '1950-04-25'\n\\item '1950-04-26'\n\\item '1950-04-27'\n\\item '1950-04-28'\n\\item '1950-05-01'\n\\item '1950-05-02'\n\\item '1950-05-03'\n\\item '1950-05-04'\n\\item '1950-05-05'\n\\item '1950-05-08'\n\\item '1950-05-09'\n\\item '1950-05-10'\n\\item '1950-05-11'\n\\item '1950-05-12'\n\\item '1950-05-15'\n\\item '1950-05-16'\n\\item '1950-05-17'\n\\item '1950-05-18'\n\\item '1950-05-19'\n\\item '1950-05-22'\n\\item '1950-05-23'\n\\item '1950-05-24'\n\\item '1950-05-25'\n\\item '1950-05-26'\n\\item '1950-05-29'\n\\item '1950-05-31'\n\\item '1950-06-01'\n\\item '1950-06-02'\n\\item '1950-06-05'\n\\item '1950-06-06'\n\\item '1950-06-07'\n\\item '1950-06-08'\n\\item '1950-06-09'\n\\item '1950-06-12'\n\\item '1950-06-13'\n\\item '1950-06-14'\n\\item '1950-06-15'\n\\item '1950-06-16'\n\\item '1950-06-19'\n\\item '1950-06-20'\n\\item '1950-06-21'\n\\item '1950-06-22'\n\\item '1950-06-23'\n\\item '1950-06-26'\n\\item '1950-06-27'\n\\item '1950-06-28'\n\\item '1950-06-29'\n\\item '1950-06-30'\n\\item '1950-07-03'\n\\item '1950-07-05'\n\\item '1950-07-06'\n\\item '1950-07-07'\n\\item '1950-07-10'\n\\item '1950-07-11'\n\\item '1950-07-12'\n\\item '1950-07-13'\n\\item '1950-07-14'\n\\item '1950-07-17'\n\\item '1950-07-18'\n\\item '1950-07-19'\n\\item '1950-07-20'\n\\item '1950-07-21'\n\\item '1950-07-24'\n\\item '1950-07-25'\n\\item '1950-07-26'\n\\item '1950-07-27'\n\\item '1950-07-28'\n\\item '1950-07-31'\n\\item '1950-08-01'\n\\item '1950-08-02'\n\\item '1950-08-03'\n\\item '1950-08-04'\n\\item '1950-08-07'\n\\item '1950-08-08'\n\\item '1950-08-09'\n\\item '1950-08-10'\n\\item '1950-08-11'\n\\item '1950-08-14'\n\\item '1950-08-15'\n\\item '1950-08-16'\n\\item '1950-08-17'\n\\item '1950-08-18'\n\\item '1950-08-21'\n\\item '1950-08-22'\n\\item '1950-08-23'\n\\item '1950-08-24'\n\\item '1950-08-25'\n\\item '1950-08-28'\n\\item '1950-08-29'\n\\item '1950-08-30'\n\\item '1950-08-31'\n\\item '1950-09-01'\n\\item '1950-09-05'\n\\item '1950-09-06'\n\\item '1950-09-07'\n\\item '1950-09-08'\n\\item '1950-09-11'\n\\item '1950-09-12'\n\\item '1950-09-13'\n\\item '1950-09-14'\n\\item '1950-09-15'\n\\item '1950-09-18'\n\\item '1950-09-19'\n\\item '1950-09-20'\n\\item '1950-09-21'\n\\item '1950-09-22'\n\\item '1950-09-25'\n\\item '1950-09-26'\n\\item '1950-09-27'\n\\item '1950-09-28'\n\\item '1950-09-29'\n\\item '1950-10-02'\n\\item '1950-10-03'\n\\item '1950-10-04'\n\\item '1950-10-05'\n\\item '1950-10-06'\n\\item '1950-10-09'\n\\item '1950-10-10'\n\\item '1950-10-11'\n\\item '1950-10-13'\n\\item '1950-10-16'\n\\item '1950-10-17'\n\\item '1950-10-18'\n\\item ⋯\n\\item '2014-07-29'\n\\item '2014-07-30'\n\\item '2014-07-31'\n\\item '2014-08-01'\n\\item '2014-08-04'\n\\item '2014-08-05'\n\\item '2014-08-06'\n\\item '2014-08-07'\n\\item '2014-08-08'\n\\item '2014-08-11'\n\\item '2014-08-12'\n\\item '2014-08-13'\n\\item '2014-08-14'\n\\item '2014-08-15'\n\\item '2014-08-18'\n\\item '2014-08-19'\n\\item '2014-08-20'\n\\item '2014-08-21'\n\\item '2014-08-22'\n\\item '2014-08-25'\n\\item '2014-08-26'\n\\item '2014-08-27'\n\\item '2014-08-28'\n\\item '2014-08-29'\n\\item '2014-09-02'\n\\item '2014-09-03'\n\\item '2014-09-04'\n\\item '2014-09-05'\n\\item '2014-09-08'\n\\item '2014-09-09'\n\\item '2014-09-10'\n\\item '2014-09-11'\n\\item '2014-09-12'\n\\item '2014-09-15'\n\\item '2014-09-16'\n\\item '2014-09-17'\n\\item '2014-09-18'\n\\item '2014-09-19'\n\\item '2014-09-22'\n\\item '2014-09-23'\n\\item '2014-09-24'\n\\item '2014-09-25'\n\\item '2014-09-26'\n\\item '2014-09-29'\n\\item '2014-09-30'\n\\item '2014-10-01'\n\\item '2014-10-02'\n\\item '2014-10-03'\n\\item '2014-10-06'\n\\item '2014-10-07'\n\\item '2014-10-08'\n\\item '2014-10-09'\n\\item '2014-10-10'\n\\item '2014-10-13'\n\\item '2014-10-14'\n\\item '2014-10-15'\n\\item '2014-10-16'\n\\item '2014-10-17'\n\\item '2014-10-20'\n\\item '2014-10-21'\n\\item '2014-10-22'\n\\item '2014-10-23'\n\\item '2014-10-24'\n\\item '2014-10-27'\n\\item '2014-10-28'\n\\item '2014-10-29'\n\\item '2014-10-30'\n\\item '2014-10-31'\n\\item '2014-11-03'\n\\item '2014-11-04'\n\\item '2014-11-05'\n\\item '2014-11-06'\n\\item '2014-11-07'\n\\item '2014-11-10'\n\\item '2014-11-11'\n\\item '2014-11-12'\n\\item '2014-11-13'\n\\item '2014-11-14'\n\\item '2014-11-17'\n\\item '2014-11-18'\n\\item '2014-11-19'\n\\item '2014-11-20'\n\\item '2014-11-21'\n\\item '2014-11-24'\n\\item '2014-11-25'\n\\item '2014-11-26'\n\\item '2014-11-28'\n\\item '2014-12-01'\n\\item '2014-12-02'\n\\item '2014-12-03'\n\\item '2014-12-04'\n\\item '2014-12-05'\n\\item '2014-12-08'\n\\item '2014-12-09'\n\\item '2014-12-10'\n\\item '2014-12-11'\n\\item '2014-12-12'\n\\item '2014-12-15'\n\\item '2014-12-16'\n\\item '2014-12-17'\n\\item '2014-12-18'\n\\item '2014-12-19'\n\\item '2014-12-22'\n\\item '2014-12-23'\n\\item '2014-12-24'\n\\item '2014-12-26'\n\\item '2014-12-29'\n\\item '2014-12-30'\n\\item '2014-12-31'\n\\item '2015-01-02'\n\\item '2015-01-05'\n\\item '2015-01-06'\n\\item '2015-01-07'\n\\item '2015-01-08'\n\\item '2015-01-09'\n\\item '2015-01-12'\n\\item '2015-01-13'\n\\item '2015-01-14'\n\\item '2015-01-15'\n\\item '2015-01-16'\n\\item '2015-01-20'\n\\item '2015-01-21'\n\\item '2015-01-22'\n\\item '2015-01-23'\n\\item '2015-01-26'\n\\item '2015-01-27'\n\\item '2015-01-28'\n\\item '2015-01-29'\n\\item '2015-01-30'\n\\item '2015-02-02'\n\\item '2015-02-03'\n\\item '2015-02-04'\n\\item '2015-02-05'\n\\item '2015-02-06'\n\\item '2015-02-09'\n\\item '2015-02-10'\n\\item '2015-02-11'\n\\item '2015-02-12'\n\\item '2015-02-13'\n\\item '2015-02-17'\n\\item '2015-02-18'\n\\item '2015-02-19'\n\\item '2015-02-20'\n\\item '2015-02-23'\n\\item '2015-02-24'\n\\item '2015-02-25'\n\\item '2015-02-26'\n\\item '2015-02-27'\n\\item '2015-03-02'\n\\item '2015-03-03'\n\\item '2015-03-04'\n\\item '2015-03-05'\n\\item '2015-03-06'\n\\item '2015-03-09'\n\\item '2015-03-10'\n\\item '2015-03-11'\n\\item '2015-03-12'\n\\item '2015-03-13'\n\\item '2015-03-16'\n\\item '2015-03-17'\n\\item '2015-03-18'\n\\item '2015-03-19'\n\\item '2015-03-20'\n\\item '2015-03-23'\n\\item '2015-03-24'\n\\item '2015-03-25'\n\\item '2015-03-26'\n\\item '2015-03-27'\n\\item '2015-03-30'\n\\item '2015-03-31'\n\\item '2015-04-01'\n\\item '2015-04-02'\n\\item '2015-04-06'\n\\item '2015-04-07'\n\\item '2015-04-08'\n\\item '2015-04-09'\n\\item '2015-04-10'\n\\item '2015-04-13'\n\\item '2015-04-14'\n\\item '2015-04-15'\n\\item '2015-04-16'\n\\item '2015-04-17'\n\\item '2015-04-20'\n\\item '2015-04-21'\n\\item '2015-04-22'\n\\item '2015-04-23'\n\\item '2015-04-24'\n\\item '2015-04-27'\n\\item '2015-04-28'\n\\item '2015-04-29'\n\\item '2015-04-30'\n\\item '2015-05-01'\n\\item '2015-05-04'\n\\item '2015-05-05'\n\\item '2015-05-06'\n\\item '2015-05-07'\n\\item '2015-05-08'\n\\item '2015-05-11'\n\\item '2015-05-12'\n\\item '2015-05-13'\n\\end{enumerate*}\n",
            "text/markdown": "1. 1950-02-01\n2. 1950-03-01\n3. 1950-04-03\n4. 1950-05-01\n5. 1950-06-01\n6. 1950-07-03\n\n\n\n**Levels**: 1. '1950-01-03'\n2. '1950-01-04'\n3. '1950-01-05'\n4. '1950-01-06'\n5. '1950-01-09'\n6. '1950-01-10'\n7. '1950-01-11'\n8. '1950-01-12'\n9. '1950-01-13'\n10. '1950-01-16'\n11. '1950-01-17'\n12. '1950-01-18'\n13. '1950-01-19'\n14. '1950-01-20'\n15. '1950-01-23'\n16. '1950-01-24'\n17. '1950-01-25'\n18. '1950-01-26'\n19. '1950-01-27'\n20. '1950-01-30'\n21. '1950-01-31'\n22. '1950-02-01'\n23. '1950-02-02'\n24. '1950-02-03'\n25. '1950-02-06'\n26. '1950-02-07'\n27. '1950-02-08'\n28. '1950-02-09'\n29. '1950-02-10'\n30. '1950-02-14'\n31. '1950-02-15'\n32. '1950-02-16'\n33. '1950-02-17'\n34. '1950-02-20'\n35. '1950-02-21'\n36. '1950-02-23'\n37. '1950-02-24'\n38. '1950-02-27'\n39. '1950-02-28'\n40. '1950-03-01'\n41. '1950-03-02'\n42. '1950-03-03'\n43. '1950-03-06'\n44. '1950-03-07'\n45. '1950-03-08'\n46. '1950-03-09'\n47. '1950-03-10'\n48. '1950-03-13'\n49. '1950-03-14'\n50. '1950-03-15'\n51. '1950-03-16'\n52. '1950-03-17'\n53. '1950-03-20'\n54. '1950-03-21'\n55. '1950-03-22'\n56. '1950-03-23'\n57. '1950-03-24'\n58. '1950-03-27'\n59. '1950-03-28'\n60. '1950-03-29'\n61. '1950-03-30'\n62. '1950-03-31'\n63. '1950-04-03'\n64. '1950-04-04'\n65. '1950-04-05'\n66. '1950-04-06'\n67. '1950-04-10'\n68. '1950-04-11'\n69. '1950-04-12'\n70. '1950-04-13'\n71. '1950-04-14'\n72. '1950-04-17'\n73. '1950-04-18'\n74. '1950-04-19'\n75. '1950-04-20'\n76. '1950-04-21'\n77. '1950-04-24'\n78. '1950-04-25'\n79. '1950-04-26'\n80. '1950-04-27'\n81. '1950-04-28'\n82. '1950-05-01'\n83. '1950-05-02'\n84. '1950-05-03'\n85. '1950-05-04'\n86. '1950-05-05'\n87. '1950-05-08'\n88. '1950-05-09'\n89. '1950-05-10'\n90. '1950-05-11'\n91. '1950-05-12'\n92. '1950-05-15'\n93. '1950-05-16'\n94. '1950-05-17'\n95. '1950-05-18'\n96. '1950-05-19'\n97. '1950-05-22'\n98. '1950-05-23'\n99. '1950-05-24'\n100. '1950-05-25'\n101. '1950-05-26'\n102. '1950-05-29'\n103. '1950-05-31'\n104. '1950-06-01'\n105. '1950-06-02'\n106. '1950-06-05'\n107. '1950-06-06'\n108. '1950-06-07'\n109. '1950-06-08'\n110. '1950-06-09'\n111. '1950-06-12'\n112. '1950-06-13'\n113. '1950-06-14'\n114. '1950-06-15'\n115. '1950-06-16'\n116. '1950-06-19'\n117. '1950-06-20'\n118. '1950-06-21'\n119. '1950-06-22'\n120. '1950-06-23'\n121. '1950-06-26'\n122. '1950-06-27'\n123. '1950-06-28'\n124. '1950-06-29'\n125. '1950-06-30'\n126. '1950-07-03'\n127. '1950-07-05'\n128. '1950-07-06'\n129. '1950-07-07'\n130. '1950-07-10'\n131. '1950-07-11'\n132. '1950-07-12'\n133. '1950-07-13'\n134. '1950-07-14'\n135. '1950-07-17'\n136. '1950-07-18'\n137. '1950-07-19'\n138. '1950-07-20'\n139. '1950-07-21'\n140. '1950-07-24'\n141. '1950-07-25'\n142. '1950-07-26'\n143. '1950-07-27'\n144. '1950-07-28'\n145. '1950-07-31'\n146. '1950-08-01'\n147. '1950-08-02'\n148. '1950-08-03'\n149. '1950-08-04'\n150. '1950-08-07'\n151. '1950-08-08'\n152. '1950-08-09'\n153. '1950-08-10'\n154. '1950-08-11'\n155. '1950-08-14'\n156. '1950-08-15'\n157. '1950-08-16'\n158. '1950-08-17'\n159. '1950-08-18'\n160. '1950-08-21'\n161. '1950-08-22'\n162. '1950-08-23'\n163. '1950-08-24'\n164. '1950-08-25'\n165. '1950-08-28'\n166. '1950-08-29'\n167. '1950-08-30'\n168. '1950-08-31'\n169. '1950-09-01'\n170. '1950-09-05'\n171. '1950-09-06'\n172. '1950-09-07'\n173. '1950-09-08'\n174. '1950-09-11'\n175. '1950-09-12'\n176. '1950-09-13'\n177. '1950-09-14'\n178. '1950-09-15'\n179. '1950-09-18'\n180. '1950-09-19'\n181. '1950-09-20'\n182. '1950-09-21'\n183. '1950-09-22'\n184. '1950-09-25'\n185. '1950-09-26'\n186. '1950-09-27'\n187. '1950-09-28'\n188. '1950-09-29'\n189. '1950-10-02'\n190. '1950-10-03'\n191. '1950-10-04'\n192. '1950-10-05'\n193. '1950-10-06'\n194. '1950-10-09'\n195. '1950-10-10'\n196. '1950-10-11'\n197. '1950-10-13'\n198. '1950-10-16'\n199. '1950-10-17'\n200. '1950-10-18'\n201. ⋯\n202. '2014-07-29'\n203. '2014-07-30'\n204. '2014-07-31'\n205. '2014-08-01'\n206. '2014-08-04'\n207. '2014-08-05'\n208. '2014-08-06'\n209. '2014-08-07'\n210. '2014-08-08'\n211. '2014-08-11'\n212. '2014-08-12'\n213. '2014-08-13'\n214. '2014-08-14'\n215. '2014-08-15'\n216. '2014-08-18'\n217. '2014-08-19'\n218. '2014-08-20'\n219. '2014-08-21'\n220. '2014-08-22'\n221. '2014-08-25'\n222. '2014-08-26'\n223. '2014-08-27'\n224. '2014-08-28'\n225. '2014-08-29'\n226. '2014-09-02'\n227. '2014-09-03'\n228. '2014-09-04'\n229. '2014-09-05'\n230. '2014-09-08'\n231. '2014-09-09'\n232. '2014-09-10'\n233. '2014-09-11'\n234. '2014-09-12'\n235. '2014-09-15'\n236. '2014-09-16'\n237. '2014-09-17'\n238. '2014-09-18'\n239. '2014-09-19'\n240. '2014-09-22'\n241. '2014-09-23'\n242. '2014-09-24'\n243. '2014-09-25'\n244. '2014-09-26'\n245. '2014-09-29'\n246. '2014-09-30'\n247. '2014-10-01'\n248. '2014-10-02'\n249. '2014-10-03'\n250. '2014-10-06'\n251. '2014-10-07'\n252. '2014-10-08'\n253. '2014-10-09'\n254. '2014-10-10'\n255. '2014-10-13'\n256. '2014-10-14'\n257. '2014-10-15'\n258. '2014-10-16'\n259. '2014-10-17'\n260. '2014-10-20'\n261. '2014-10-21'\n262. '2014-10-22'\n263. '2014-10-23'\n264. '2014-10-24'\n265. '2014-10-27'\n266. '2014-10-28'\n267. '2014-10-29'\n268. '2014-10-30'\n269. '2014-10-31'\n270. '2014-11-03'\n271. '2014-11-04'\n272. '2014-11-05'\n273. '2014-11-06'\n274. '2014-11-07'\n275. '2014-11-10'\n276. '2014-11-11'\n277. '2014-11-12'\n278. '2014-11-13'\n279. '2014-11-14'\n280. '2014-11-17'\n281. '2014-11-18'\n282. '2014-11-19'\n283. '2014-11-20'\n284. '2014-11-21'\n285. '2014-11-24'\n286. '2014-11-25'\n287. '2014-11-26'\n288. '2014-11-28'\n289. '2014-12-01'\n290. '2014-12-02'\n291. '2014-12-03'\n292. '2014-12-04'\n293. '2014-12-05'\n294. '2014-12-08'\n295. '2014-12-09'\n296. '2014-12-10'\n297. '2014-12-11'\n298. '2014-12-12'\n299. '2014-12-15'\n300. '2014-12-16'\n301. '2014-12-17'\n302. '2014-12-18'\n303. '2014-12-19'\n304. '2014-12-22'\n305. '2014-12-23'\n306. '2014-12-24'\n307. '2014-12-26'\n308. '2014-12-29'\n309. '2014-12-30'\n310. '2014-12-31'\n311. '2015-01-02'\n312. '2015-01-05'\n313. '2015-01-06'\n314. '2015-01-07'\n315. '2015-01-08'\n316. '2015-01-09'\n317. '2015-01-12'\n318. '2015-01-13'\n319. '2015-01-14'\n320. '2015-01-15'\n321. '2015-01-16'\n322. '2015-01-20'\n323. '2015-01-21'\n324. '2015-01-22'\n325. '2015-01-23'\n326. '2015-01-26'\n327. '2015-01-27'\n328. '2015-01-28'\n329. '2015-01-29'\n330. '2015-01-30'\n331. '2015-02-02'\n332. '2015-02-03'\n333. '2015-02-04'\n334. '2015-02-05'\n335. '2015-02-06'\n336. '2015-02-09'\n337. '2015-02-10'\n338. '2015-02-11'\n339. '2015-02-12'\n340. '2015-02-13'\n341. '2015-02-17'\n342. '2015-02-18'\n343. '2015-02-19'\n344. '2015-02-20'\n345. '2015-02-23'\n346. '2015-02-24'\n347. '2015-02-25'\n348. '2015-02-26'\n349. '2015-02-27'\n350. '2015-03-02'\n351. '2015-03-03'\n352. '2015-03-04'\n353. '2015-03-05'\n354. '2015-03-06'\n355. '2015-03-09'\n356. '2015-03-10'\n357. '2015-03-11'\n358. '2015-03-12'\n359. '2015-03-13'\n360. '2015-03-16'\n361. '2015-03-17'\n362. '2015-03-18'\n363. '2015-03-19'\n364. '2015-03-20'\n365. '2015-03-23'\n366. '2015-03-24'\n367. '2015-03-25'\n368. '2015-03-26'\n369. '2015-03-27'\n370. '2015-03-30'\n371. '2015-03-31'\n372. '2015-04-01'\n373. '2015-04-02'\n374. '2015-04-06'\n375. '2015-04-07'\n376. '2015-04-08'\n377. '2015-04-09'\n378. '2015-04-10'\n379. '2015-04-13'\n380. '2015-04-14'\n381. '2015-04-15'\n382. '2015-04-16'\n383. '2015-04-17'\n384. '2015-04-20'\n385. '2015-04-21'\n386. '2015-04-22'\n387. '2015-04-23'\n388. '2015-04-24'\n389. '2015-04-27'\n390. '2015-04-28'\n391. '2015-04-29'\n392. '2015-04-30'\n393. '2015-05-01'\n394. '2015-05-04'\n395. '2015-05-05'\n396. '2015-05-06'\n397. '2015-05-07'\n398. '2015-05-08'\n399. '2015-05-11'\n400. '2015-05-12'\n401. '2015-05-13'\n\n\n",
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>1950-02-01</li><li>1950-03-01</li><li>1950-04-03</li><li>1950-05-01</li><li>1950-06-01</li><li>1950-07-03</li></ol>\n",
              "\n",
              "<details>\n",
              "\t<summary style=display:list-item;cursor:pointer>\n",
              "\t\t<strong>Levels</strong>:\n",
              "\t</summary>\n",
              "\t<style>\n",
              "\t.list-inline {list-style: none; margin:0; padding: 0}\n",
              "\t.list-inline>li {display: inline-block}\n",
              "\t.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "\t</style>\n",
              "\t<ol class=list-inline><li>'1950-01-03'</li><li>'1950-01-04'</li><li>'1950-01-05'</li><li>'1950-01-06'</li><li>'1950-01-09'</li><li>'1950-01-10'</li><li>'1950-01-11'</li><li>'1950-01-12'</li><li>'1950-01-13'</li><li>'1950-01-16'</li><li>'1950-01-17'</li><li>'1950-01-18'</li><li>'1950-01-19'</li><li>'1950-01-20'</li><li>'1950-01-23'</li><li>'1950-01-24'</li><li>'1950-01-25'</li><li>'1950-01-26'</li><li>'1950-01-27'</li><li>'1950-01-30'</li><li>'1950-01-31'</li><li>'1950-02-01'</li><li>'1950-02-02'</li><li>'1950-02-03'</li><li>'1950-02-06'</li><li>'1950-02-07'</li><li>'1950-02-08'</li><li>'1950-02-09'</li><li>'1950-02-10'</li><li>'1950-02-14'</li><li>'1950-02-15'</li><li>'1950-02-16'</li><li>'1950-02-17'</li><li>'1950-02-20'</li><li>'1950-02-21'</li><li>'1950-02-23'</li><li>'1950-02-24'</li><li>'1950-02-27'</li><li>'1950-02-28'</li><li>'1950-03-01'</li><li>'1950-03-02'</li><li>'1950-03-03'</li><li>'1950-03-06'</li><li>'1950-03-07'</li><li>'1950-03-08'</li><li>'1950-03-09'</li><li>'1950-03-10'</li><li>'1950-03-13'</li><li>'1950-03-14'</li><li>'1950-03-15'</li><li>'1950-03-16'</li><li>'1950-03-17'</li><li>'1950-03-20'</li><li>'1950-03-21'</li><li>'1950-03-22'</li><li>'1950-03-23'</li><li>'1950-03-24'</li><li>'1950-03-27'</li><li>'1950-03-28'</li><li>'1950-03-29'</li><li>'1950-03-30'</li><li>'1950-03-31'</li><li>'1950-04-03'</li><li>'1950-04-04'</li><li>'1950-04-05'</li><li>'1950-04-06'</li><li>'1950-04-10'</li><li>'1950-04-11'</li><li>'1950-04-12'</li><li>'1950-04-13'</li><li>'1950-04-14'</li><li>'1950-04-17'</li><li>'1950-04-18'</li><li>'1950-04-19'</li><li>'1950-04-20'</li><li>'1950-04-21'</li><li>'1950-04-24'</li><li>'1950-04-25'</li><li>'1950-04-26'</li><li>'1950-04-27'</li><li>'1950-04-28'</li><li>'1950-05-01'</li><li>'1950-05-02'</li><li>'1950-05-03'</li><li>'1950-05-04'</li><li>'1950-05-05'</li><li>'1950-05-08'</li><li>'1950-05-09'</li><li>'1950-05-10'</li><li>'1950-05-11'</li><li>'1950-05-12'</li><li>'1950-05-15'</li><li>'1950-05-16'</li><li>'1950-05-17'</li><li>'1950-05-18'</li><li>'1950-05-19'</li><li>'1950-05-22'</li><li>'1950-05-23'</li><li>'1950-05-24'</li><li>'1950-05-25'</li><li>'1950-05-26'</li><li>'1950-05-29'</li><li>'1950-05-31'</li><li>'1950-06-01'</li><li>'1950-06-02'</li><li>'1950-06-05'</li><li>'1950-06-06'</li><li>'1950-06-07'</li><li>'1950-06-08'</li><li>'1950-06-09'</li><li>'1950-06-12'</li><li>'1950-06-13'</li><li>'1950-06-14'</li><li>'1950-06-15'</li><li>'1950-06-16'</li><li>'1950-06-19'</li><li>'1950-06-20'</li><li>'1950-06-21'</li><li>'1950-06-22'</li><li>'1950-06-23'</li><li>'1950-06-26'</li><li>'1950-06-27'</li><li>'1950-06-28'</li><li>'1950-06-29'</li><li>'1950-06-30'</li><li>'1950-07-03'</li><li>'1950-07-05'</li><li>'1950-07-06'</li><li>'1950-07-07'</li><li>'1950-07-10'</li><li>'1950-07-11'</li><li>'1950-07-12'</li><li>'1950-07-13'</li><li>'1950-07-14'</li><li>'1950-07-17'</li><li>'1950-07-18'</li><li>'1950-07-19'</li><li>'1950-07-20'</li><li>'1950-07-21'</li><li>'1950-07-24'</li><li>'1950-07-25'</li><li>'1950-07-26'</li><li>'1950-07-27'</li><li>'1950-07-28'</li><li>'1950-07-31'</li><li>'1950-08-01'</li><li>'1950-08-02'</li><li>'1950-08-03'</li><li>'1950-08-04'</li><li>'1950-08-07'</li><li>'1950-08-08'</li><li>'1950-08-09'</li><li>'1950-08-10'</li><li>'1950-08-11'</li><li>'1950-08-14'</li><li>'1950-08-15'</li><li>'1950-08-16'</li><li>'1950-08-17'</li><li>'1950-08-18'</li><li>'1950-08-21'</li><li>'1950-08-22'</li><li>'1950-08-23'</li><li>'1950-08-24'</li><li>'1950-08-25'</li><li>'1950-08-28'</li><li>'1950-08-29'</li><li>'1950-08-30'</li><li>'1950-08-31'</li><li>'1950-09-01'</li><li>'1950-09-05'</li><li>'1950-09-06'</li><li>'1950-09-07'</li><li>'1950-09-08'</li><li>'1950-09-11'</li><li>'1950-09-12'</li><li>'1950-09-13'</li><li>'1950-09-14'</li><li>'1950-09-15'</li><li>'1950-09-18'</li><li>'1950-09-19'</li><li>'1950-09-20'</li><li>'1950-09-21'</li><li>'1950-09-22'</li><li>'1950-09-25'</li><li>'1950-09-26'</li><li>'1950-09-27'</li><li>'1950-09-28'</li><li>'1950-09-29'</li><li>'1950-10-02'</li><li>'1950-10-03'</li><li>'1950-10-04'</li><li>'1950-10-05'</li><li>'1950-10-06'</li><li>'1950-10-09'</li><li>'1950-10-10'</li><li>'1950-10-11'</li><li>'1950-10-13'</li><li>'1950-10-16'</li><li>'1950-10-17'</li><li>'1950-10-18'</li><li>⋯</li><li>'2014-07-29'</li><li>'2014-07-30'</li><li>'2014-07-31'</li><li>'2014-08-01'</li><li>'2014-08-04'</li><li>'2014-08-05'</li><li>'2014-08-06'</li><li>'2014-08-07'</li><li>'2014-08-08'</li><li>'2014-08-11'</li><li>'2014-08-12'</li><li>'2014-08-13'</li><li>'2014-08-14'</li><li>'2014-08-15'</li><li>'2014-08-18'</li><li>'2014-08-19'</li><li>'2014-08-20'</li><li>'2014-08-21'</li><li>'2014-08-22'</li><li>'2014-08-25'</li><li>'2014-08-26'</li><li>'2014-08-27'</li><li>'2014-08-28'</li><li>'2014-08-29'</li><li>'2014-09-02'</li><li>'2014-09-03'</li><li>'2014-09-04'</li><li>'2014-09-05'</li><li>'2014-09-08'</li><li>'2014-09-09'</li><li>'2014-09-10'</li><li>'2014-09-11'</li><li>'2014-09-12'</li><li>'2014-09-15'</li><li>'2014-09-16'</li><li>'2014-09-17'</li><li>'2014-09-18'</li><li>'2014-09-19'</li><li>'2014-09-22'</li><li>'2014-09-23'</li><li>'2014-09-24'</li><li>'2014-09-25'</li><li>'2014-09-26'</li><li>'2014-09-29'</li><li>'2014-09-30'</li><li>'2014-10-01'</li><li>'2014-10-02'</li><li>'2014-10-03'</li><li>'2014-10-06'</li><li>'2014-10-07'</li><li>'2014-10-08'</li><li>'2014-10-09'</li><li>'2014-10-10'</li><li>'2014-10-13'</li><li>'2014-10-14'</li><li>'2014-10-15'</li><li>'2014-10-16'</li><li>'2014-10-17'</li><li>'2014-10-20'</li><li>'2014-10-21'</li><li>'2014-10-22'</li><li>'2014-10-23'</li><li>'2014-10-24'</li><li>'2014-10-27'</li><li>'2014-10-28'</li><li>'2014-10-29'</li><li>'2014-10-30'</li><li>'2014-10-31'</li><li>'2014-11-03'</li><li>'2014-11-04'</li><li>'2014-11-05'</li><li>'2014-11-06'</li><li>'2014-11-07'</li><li>'2014-11-10'</li><li>'2014-11-11'</li><li>'2014-11-12'</li><li>'2014-11-13'</li><li>'2014-11-14'</li><li>'2014-11-17'</li><li>'2014-11-18'</li><li>'2014-11-19'</li><li>'2014-11-20'</li><li>'2014-11-21'</li><li>'2014-11-24'</li><li>'2014-11-25'</li><li>'2014-11-26'</li><li>'2014-11-28'</li><li>'2014-12-01'</li><li>'2014-12-02'</li><li>'2014-12-03'</li><li>'2014-12-04'</li><li>'2014-12-05'</li><li>'2014-12-08'</li><li>'2014-12-09'</li><li>'2014-12-10'</li><li>'2014-12-11'</li><li>'2014-12-12'</li><li>'2014-12-15'</li><li>'2014-12-16'</li><li>'2014-12-17'</li><li>'2014-12-18'</li><li>'2014-12-19'</li><li>'2014-12-22'</li><li>'2014-12-23'</li><li>'2014-12-24'</li><li>'2014-12-26'</li><li>'2014-12-29'</li><li>'2014-12-30'</li><li>'2014-12-31'</li><li>'2015-01-02'</li><li>'2015-01-05'</li><li>'2015-01-06'</li><li>'2015-01-07'</li><li>'2015-01-08'</li><li>'2015-01-09'</li><li>'2015-01-12'</li><li>'2015-01-13'</li><li>'2015-01-14'</li><li>'2015-01-15'</li><li>'2015-01-16'</li><li>'2015-01-20'</li><li>'2015-01-21'</li><li>'2015-01-22'</li><li>'2015-01-23'</li><li>'2015-01-26'</li><li>'2015-01-27'</li><li>'2015-01-28'</li><li>'2015-01-29'</li><li>'2015-01-30'</li><li>'2015-02-02'</li><li>'2015-02-03'</li><li>'2015-02-04'</li><li>'2015-02-05'</li><li>'2015-02-06'</li><li>'2015-02-09'</li><li>'2015-02-10'</li><li>'2015-02-11'</li><li>'2015-02-12'</li><li>'2015-02-13'</li><li>'2015-02-17'</li><li>'2015-02-18'</li><li>'2015-02-19'</li><li>'2015-02-20'</li><li>'2015-02-23'</li><li>'2015-02-24'</li><li>'2015-02-25'</li><li>'2015-02-26'</li><li>'2015-02-27'</li><li>'2015-03-02'</li><li>'2015-03-03'</li><li>'2015-03-04'</li><li>'2015-03-05'</li><li>'2015-03-06'</li><li>'2015-03-09'</li><li>'2015-03-10'</li><li>'2015-03-11'</li><li>'2015-03-12'</li><li>'2015-03-13'</li><li>'2015-03-16'</li><li>'2015-03-17'</li><li>'2015-03-18'</li><li>'2015-03-19'</li><li>'2015-03-20'</li><li>'2015-03-23'</li><li>'2015-03-24'</li><li>'2015-03-25'</li><li>'2015-03-26'</li><li>'2015-03-27'</li><li>'2015-03-30'</li><li>'2015-03-31'</li><li>'2015-04-01'</li><li>'2015-04-02'</li><li>'2015-04-06'</li><li>'2015-04-07'</li><li>'2015-04-08'</li><li>'2015-04-09'</li><li>'2015-04-10'</li><li>'2015-04-13'</li><li>'2015-04-14'</li><li>'2015-04-15'</li><li>'2015-04-16'</li><li>'2015-04-17'</li><li>'2015-04-20'</li><li>'2015-04-21'</li><li>'2015-04-22'</li><li>'2015-04-23'</li><li>'2015-04-24'</li><li>'2015-04-27'</li><li>'2015-04-28'</li><li>'2015-04-29'</li><li>'2015-04-30'</li><li>'2015-05-01'</li><li>'2015-05-04'</li><li>'2015-05-05'</li><li>'2015-05-06'</li><li>'2015-05-07'</li><li>'2015-05-08'</li><li>'2015-05-11'</li><li>'2015-05-12'</li><li>'2015-05-13'</li></ol>\n",
              "</details>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DYjagxicj2UF"
      },
      "source": [
        "The frequency of this time serie is a monthly basis, the week-ends the market is closed so sometimes the datetime is not always the first day of the month. \n",
        "We probably have the monthly average of the S&P500's daily settled price."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UI9lnEl4k3QE"
      },
      "source": [
        "log_returns <- numeric(784)\n",
        "for (t in 2:784){\n",
        "  log_returns[t] <- log(sptsm[t]/sptsm[t-1])\n",
        "}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dgv7S8IQmyW9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "eb5c8f81-25dc-480f-da5f-b7a50e6f389f"
      },
      "source": [
        "acf(log_returns)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MIOACAQwg4AIBDCDgAgEMIOACAQTeMe\nID0sX768qqoq7ikAgEahadOmX/nKV+KeYi+E3f698sorp556atxTAACNyLJly0455ZS4p9id\nsNu/HTt2RFG0ffv27OzsuGcBAGK2Y8eOnJycZB40Nt5jBwAQCGEHABAIYQcAEAhhBwAQCGEH\nABAIYQcAEAhhBwAQiPQ7j10ikSgtLV21alV5eXkURa1atSoqKiooKIh7LgCAmKVT2G3atGn8\n+PFTp07dsGHDbkuFhYVDhw4dNWpUs2bNYpkNACB2aRN269at6927d2lpaVFRUd++fTt27Nii\nRYsoisrKykpKSubPnz927NgZM2a88MILbdq0iXtYAIAYpE3YjRkzZs2aNdOmTRs4cOCeq9XV\n1ZMmTRoxYsS4ceMmTJjQ8OMBAMQubT48MXv27MGDB++16qIoyszMHD58+KBBg2bOnNnAgwEA\nNBJpE3YbN27s0qVLzft069Zt/fr1DTMPAEBjkzZhl5+fv3z58pr3ef311/Pz8xtmHgCAxiZt\nwq5fv37Tp0+/++67t2/fvufq1q1bb7755lmzZl100UUNPxsAQGOQkUgk4p7hgHz22Wff+MY3\nXnvttSOOOKJXr14FBQV5eXmJRGLLli3vv//+0qVLKyoq+vTp8+yzz+bl5dXvL7148eLevXtv\n3749Ozu7fo8MAKSdHTt25OTkLFq06Iwzzoh7lt2lzadiW7duvWTJkokTJ06ZMmXevHnV1dWp\npaysrJ49exYXFxcXF2dmZsY4JABAjNIm7KIoys7OHjly5MiRIysrK1evXp385omWLVsWFhZ6\nLg0AIJ3CLiU3N7eoqCjuKQAAGpe0+fAEAAA1S8tn7PaqpKRk2LBhURTNmTPnwK/1+eefL1iw\noKqqqoZ93nzzzboOt4t169ZFUXTMMcfU4zEBAKKQwq68vHzu3LkHe633339/0KBBNYdd8gQr\nO3furJd38o0ZMyaKogcffLDuhwIA2FU4YXf88cevWLHiYK/VuXPnDRs21LzPpEmTrrnmmvo6\nL8yun+cFAKhH4YRdbm5u9+7d454CACA2QX14YuPGje+++27cUwAAxCOosLvrrrucBgUAOGwF\nFXYAAIczYQcAEIi0+fDEKaecst991q5d2wCTAAA0TmkTdq+//noURVlZWTXsU/Pp6AAAwpY2\nL8WOHj26RYsW//jHPyr3bdSoUXGPCQAQm7QJu9tuu61r164XX3zxzp07454FAKAxSpuwy8rK\neuSRR958880bb7wx7lkAABqjtHmPXRRF3bp1++ijj2p4I93555/funXrhhwJAKDxSKewi6Ko\nZcuWNayeddZZZ511VoMNAwDQqKTNS7EAANRM2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEomncA9TVzp07//Wvf1VWVnbv3j0n\nJyfucQAAYpNOz9j97W9/O+ecczp37ty3b9+XX345iqLnn3++U6dO3bt3P+WUU4466qj77rsv\n7hkBAGKTNs/YLVmy5LzzzquqqmrZsuXzzz+/YMGCv/71r4MGDWrVqtXll19eWVn517/+9Yc/\n/OGXvvSlb33rW3EPCwAQg7R5xu7OO+/8whe+sHz58s2bN3/00Ue9evX6wQ9+0Llz57fffvuP\nf/zjE088UVJS0qlTp9/85jdxTwoAEI+0CbvFixf/8Ic/POmkk6Ioateu3S9/+csPPvhg5MiR\nzZo1S+7Qpk2boUOHLl26NNYxAQBikzZht3nz5o4dO6Z+bN++fRRF7dq123WfY445pqysrKEn\nAwBoHNIm7Nq2bVtSUpL68V//+lcURe++++6u+5SUlLRt27ahJwMAaBzSJuzOOeece++994UX\nXtixY8eKFSuuvfbabt263XPPPWvXrk3usHLlyvvvv79Pnz7xzgkAEJe0+VTszTffPHv27HPP\nPTf545FHHvniiy+ef/75xx577GmnnVZZWbls2bJEIjF69Oh45wQAiEvaPGN3/PHHL168+OKL\nLz7ttNOuvPLKxYsXd+vW7U9/+lP37t3nzZu3ZMmSwsLCGTNm9OrVK+5JAQDikTbP2EVR1L17\n90cffXS3LS+//PKWLVu2bdu22wcpAAAON+kUdvuSl5eXl5cX9xQAADFLm5diAQCoWQjP2CWV\nlJQMGzYsiqI5c+Yc1BWXL19eVVVVww4ffPBBnSYDAGgQ4YRdeXn53LlzD/ZaJSUlPXv2rK6u\nPhQjAQA0pHBeij3++ONXrFixYsWKg7pWly5dqqqqEjX6/e9/f4hmBgCoR+E8Y5ebm9u9e/e4\npwAAiE36hV0ikSgtLV21alV5eXkURa1atSoqKiooKIh7LgCAmKVT2G3atGn8+PFTp07dsGHD\nbkuFhYVDhw4dNWpUs2bNYpkNACB2aRN269at6927d2lpaVFRUd++fTt27NiiRYsoisrKykpK\nSubPnz927NgZM2a88MILbdq0iXtYAIAYpE3YjRkzZs2aNdOmTRs4cOCeq9XV1ZMmTRoxYsS4\nceMmTJjQ8OMBAMQubT4VO3v27MGDB++16qIoyszMHD58+KBBg2bOnNnAgwEANBJpE3YbN27s\n0qVLzft069Zt/fr1DTMPAEBjkzZhl5+fv3z58pr3ef311/Pz8xtmHgCAxiZtwq5fv37Tp0+/\n++67t2/fvufq1q1bb7755lmzZl100UUNPxsAQGOQNh+euOWWWxYuXDh69Ohbb721V69eBQUF\neXl5iURiy5Yt77///tKlSysqKvr06XPTTTfFPSkAQDzSJuxat269ZMmSiRMnTpkyZd68ebt+\nu2tWVlbPnj2Li4uLi4szMzNjHBIAIEZpE3ZRFGVnZ48cOXLkyJGVlZWrV69OfvNEy5YtCwsL\ns7Oz454OACBm6RR2Kbm5uUVFRXFPAQDQuKTNhycAAKiZsAMACISwAwAIhLADAAiEsAMACISw\nAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiE\nsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAI\nhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMA\nCISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLAD\nAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISw\nAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiE\nsAMACISwAwAIhLADAAiEsAMACISwAwAIhLADAAiEsAMACETTuAeok+rq6n/+85/l5eUFBQUF\nBQVxjwMAEKd0esZu8eLFI0aMSP34X//1X+3btz/ppJN69+5dWFjYo0ePBQsWxDgeAEC80uYZ\nu3nz5p133nnZ2dn33ntvRkbGk08+OXjw4Ly8vIEDB7Zr1+6dd96ZO3fuf/7nfy5atKhnz55x\nDwsAEIO0Cbtx48a1bt160aJFGRkZURT99Kc/7dix45IlS4455pjkDi+//PI555wzbty4Z555\nJtZJAQDikTYvxb722muXX355165doyjavHlzaWnpj3/841TVRVF02mmnXXbZZQsXLoxvRgCA\nOKVN2FVXVzdr1ix5OTc3NyMjo0OHDrvt06FDh8rKygYfDQCgUUibsOvRo8fjjz9eUVERRVFO\nTs7Xvva1JUuW7LrD9u3bZ86cedxxx8U0IABAzNIm7H72s5+98847ffr0+ctf/lJVVXXvvfc+\n8sgjU6ZMqaio2Llz58svv9y3b9/ly5cPHz487kkBAOKRNh+euPDCCx944IEf/ehH5513XrNm\nzTp37pydnX3FFVcUFxdHUVRdXZ2RkfHjH//4qquuintSAIB4pE3YRVE0dOjQb3/721OnTp0z\nZ85bb7316aef5uTk5OXlderUqXfv3ldcccXJJ58c94wAALFJp7CLoujoo48eNWrUqFGj4h4E\nAKDRSZv32AEAUDNhBwAQiDR7KbYGJSUlw4YNi6Jozpw5B3XF1atX79y5s4YdPvnkkzpNBgDQ\nIMIJu/Ly8rlz5x7stUpKSoqKihKJxKEYCQCgIYUTdscff/yKFSsO9lpdunRZu3bttm3batjn\nscceu+mmm+owGgBAQwgn7HJzc7t3716LK+76hbN79YUvfKFWEwEANKj0C7tEIlFaWrpq1ary\n8vIoilq1alVUVFRQUBD3XAAAMUunsNu0adP48eOnTp26YcOG3ZYKCwuHDh06atSoZs2axTIb\nAEDs0ibs1q1b17t379LS0qKior59+3bs2LFFixZRFJWVlZWUlMyfP3/s2LEzZsx44YUX2rRp\nE/ewAAAxSJuwGzNmzJo1a6ZNmzZw4MA9V6urqydNmjRixIhx48ZNmDCh4ccDAIhd2pygePbs\n2YMHD95r1UVRlJmZOXz48EGDBs2cObOBBwMAaCTSJuw2btzYpUuXmvfp1q3b+vXrG2YeAIDG\nJm3CLj8/f/ny5TXv8/rrr+fn5zfMPAAAjU3ahF2/fv2mT59+9913b9++fc/VrVu33nzzzbNm\nzbrooosafjYAgMYgbT48ccsttyxcuHD06NG33nprr169CgoK8vLyEonEli1b3n///aVLl1ZU\nVPTp08dXRAAAh620CbvWrVsvWbJk4sSJU6ZMmTdvXnV1dWopKyurZ8+excXFxcXFmZmZMQ4J\nABCjtAm7KIqys7NHjhw5cuTIysrK1atXJ795omXLloWFhdnZ2XFPBwAQs3QKu5Tc3NyioqK4\npwAAaFzS5sMTAADUTNgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARin2H3\nu9/97sUXX9xt4xtvvLF27dpDPBIAALWxz7C79tprn3zyyd02fvWrX73zzjsP8UgAANSGl2IB\nAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAAC0bSGtZdeeumWW27ZbePSpUt327jnPgAANLya\nwu7ll19++eWXd9u4bNmyZcuW7bpF2AEANAb7DLupU6c25BwAANTRPsPusssua8g5AACoo/18\neGLDhg1LlizZc/vEiRM/++yzQzMSAAC1UVPYLViw4Ljjjhs7duxu2//+97+PGDGie/fuq1at\nOpSzAQBwEPYZduvWrRswYMCWLVvOPffc3ZZOPPHE3/72t+vWrfvWt75VWVl5iCcEAOCA7DPs\nHnjggU8++eT++++/4YYbdlvKyMi49tpr77nnnnfeeeePf/zjIZ4QAIADss+wmzVrVpcuXYqL\ni/e1w4gRIzp06PDwww8fkrkAADhI+wy7Dz744LTTTmvSZJ87NG3a9PTTT3/zzWOV04kAACAA\nSURBVDcPzWAAABycfXZbWVlZ27Zta75y27Ztt2/fXt8jAQBQG/sMu7Zt237wwQc1X/lf//pX\nu3bt6nskAABqY59hd+qpp86dO3fjxo372uHdd99duHDh6aeffmgGAwDg4Owz7AYPHrxly5ar\nrrqqqqpqz9WysrJLL720qqrqyiuvPITTAQBwwPYZdgMGDPjmN7/51FNPnX766U899VR5eXly\n+8cff/zQQw+ddNJJS5cu/d73vnfhhRc21KgAANRkn98Vm5GRMX369EsuueS5557r379/RkZG\nq1atqqurU4V30UUXTZ48uaHmBABgP2r6SrHWrVs/++yzzz777MUXX9y5c+edO3dGUXTccccN\nGTJkwYIFjz/+eLNmzRpqTgAA9mOfz9ilnH/++eeff/6+VtesWdOhQ4d6HQkAgNqo6Rm7GlRV\nVc2aNevCCy/s1KlTvc4DAEAt7f8Zu92sWrXqoYcemjx58rp166IoOvHEEw/BVAAAHLQDDbsd\nO3Y89dRTDz744Ny5cxOJRGZm5oABA6699tqzzjrrkM4HAMAB2n/YrVy58sEHH5wyZconn3wS\nRdHRRx+9fv36hx9++LLLLjv04wEAcKD2GXbbtm2bPn36Aw888OKLL0ZR1Lx588GDBw8ZMqRD\nhw7HHntsbm5uAw4JAMD+7TPsjjnmmM2bN2dkZPTp0+fyyy+/6KKLjjjiiCiK3n333QYcDwCA\nA7XPsNu8eXOTJk2GDx9+3XXXde3atSFnAgCgFvZ5upNRo0YdeeSRv/vd74qKinr37v3ggw+W\nlZU15GQAAByUfYbdXXfdtXbt2kcfffTss89evHjxVVdddcwxxwwePHj+/PkNOR8AAAeophMU\nZ2dnX3zxxS+88MLbb7/9k5/8pHnz5v/1X/81dOjQKIqef/75jz/+uKGGBABg/w7omyeOPfbY\nu+++e82aNY888kjyxHUPPvhgQUFBcXHx8uXLD/GEAAAckIP4SrGcnJxLLrlk3rx5b7311o9/\n/OO8vLzJkyf36NHj0A13gMrKyn72s5+99dZbcQ8CABCn2nxX7HHHHXfPPfesXbv2kUce+frX\nv17vMx2ssrKyX/ziF87DAgAc5g76u2JTkk/gXXLJJfU4TQ2S7+3bq4qKiiiK7r333qeffjqK\nogcffLBhRgIAaFRqH3YN7KGHHqp5h7/85S/JC8IOADg81eal2FiMHDkyMzOzR48ef/7znzf9\n/7355ptRFD3++OPJH+OeFAAgHmkTdr/61a9eeumlKIrOP//8G2+8MSMjo/X/aNmyZRRFLVq0\nSP4Y96QAAPFIm7CLouiUU05ZtmzZnXfe+fDDD3/5y1+eMWNG3BMBADQi6RR2URQ1bdr0+uuv\nX7FiRbdu3b7//e9/5zvfWb16ddxDAQA0CmkWdkldunSZM2fO5MmTFy1a9OUvf9mnJQAAojQN\nu6Qrr7xy5cqVF1544bhx4+KeBQAgfmlzupO9Ouqoox577LHLL7987ty5Xbp0iXscAIA4pXfY\nJZ1//vnnn39+3FMAAMQshLCro/Ly8qqqqhp2SH6zBQBAIxdO2JWUlAwbNiyKojlz5hzUtYqK\nihKJxH73PJB9AABiFE7YlZeXz50792Cv1aVLlxUrVlRWVtawz8yZM++4446MjIw6TAcAcMiF\nE3bHH3/8ihUranHFE044oeYdXnnllVpNBADQoMIJu9zc3O7du8c9BQBAbNIv7BKJRGlp6apV\nq8rLy6MoatWqVVFRUUFBQdxzAQDELJ3CbtOmTePHj586deqGDRt2WyosLBw6dOioUaOaNWsW\ny2wAALFLm7Bbt25d7969S0tLi4qK+vbt27FjxxYtWkRRVFZWVlJSMn/+/LFjx86YMeOFF15o\n06ZN3MMCAMQgbcJuzJgxa9asmTZt2sCBA/dcra6unjRp0ogRI8aNGzdhwoSGHw8AIHZp812x\ns2fPHjx48F6rLoqizMzM4cOHDxo0aObMmQ08GABAI5E2Ybdx48b9fhtst27d1q9f3zDzAAA0\nNmkTdvn5+cuXL695n9dffz0/P79h5gEAaGzSJuz69es3ffr0u+++e/v27Xuubt269eabb541\na9ZFF13U8LMBADQGafPhiVtuuWXhwoWjR4++9dZbe/XqVVBQkJeXl0gktmzZ8v777y9durSi\noqJPnz433XRT3JMCAMQjbcKudevWS5YsmThx4pQpU+bNm1ddXZ1aysrK6tmzZ3FxcXFxcWZm\nZoxDAgDEKG3CLoqi7OzskSNHjhw5srKycvXq1clvnmjZsmVhYWF2dnbc0wEAxCydwi4lNze3\nqKgo7ikAABqXtPnwBAAANRN2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYA\nAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2\nAACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQ\ndgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACB\nEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAA\ngRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYA\nAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2\nAACBEHYAAIEQdgAAgRB2AACBCCrsNm3a9N5778U9BQBAPNIp7P7+979fcMEFnTp16tOnz333\n3VddXb3bDr/4xS86d+4cy2wAALFrGvcAB2rRokXf+MY3tm/f3rx58w8//PDFF1+cNm3aU089\n1aZNm7hHAwBoFNLmGbs777zz888/f+qpp7Zs2VJeXv6rX/1q8eLF55133tatW+MeDQCgUUib\nsPv73/9+0UUX9evXLyMjIycnZ+TIkX/+85+XL18+aNCgPV+TBQA4DKVN2H300Udf+tKXdt1y\n7rnnPvjgg88+++yPf/zjuKYCAGg80uY9dkcfffQbb7yx28bBgwevXLnyzjvv7NChw+jRo2MZ\nDACgkUibsOvfv/+99977u9/9btiwYVlZWant48eP//DDD3/6059++OGHXpMFAA5naRN2Y8eO\nffrpp6+99tpZs2b99a9/TW3PyMiYPHlyq1atJkyYEON4AACxS5v32LVt2/bVV18dPnx49+7d\nd1vKyMj4zW9+M2PGjC5dusQyGwBAY5A2z9hFUfSFL3xh4sSJ+1rt379///79G3IeAIBGJW2e\nsQMAoGbCDgAgEOn0UmzNSkpKhg0bFkXRnDlzDvxaq1at6tat244dO/a7ZyKRqP1wAACHXjhh\nV15ePnfu3IO9VufOnefOnVtZWVnDPn/6059+85vfZGRk1GE6AIBDLpywO/7441esWHGw18rI\nyDjzzDNr3qekpKS2QwEANJxwwi43N3fPM6EAABw+0i/sEolEaWnpqlWrysvLoyhq1apVUVFR\nQUFB3HMBAMQsncJu06ZN48ePnzp16oYNG3ZbKiwsHDp06KhRo5o1axbLbAAAsUubsFu3bl3v\n3r1LS0uLior69u3bsWPHFi1aRFFUVlZWUlIyf/78sWPHzpgx44UXXmjTpk3cwwIAxCBtwm7M\nmDFr1qyZNm3awIED91ytrq6eNGnSiBEjxo0b50tjAYDDU9qcoHj27NmDBw/ea9VFUZSZmTl8\n+PBBgwbNnDmzgQcDAGgk0ibsNm7c2KVLl5r36dat2/r16xtmHgCAxiZtwi4/P3/58uU17/P6\n66/n5+c3zDwAAI1N2oRdv379pk+ffvfdd2/fvn3P1a1bt958882zZs266KKLGn42AIDGIG0+\nPHHLLbcsXLhw9OjRt956a69evQoKCvLy8hKJxJYtW95///2lS5dWVFT06dPnpptuintSAIB4\npE3YtW7desmSJRMnTpwyZcq8efOqq6tTS1lZWT179iwuLi4uLs7MzIxxSACAGKVN2EVRlJ2d\nPXLkyJEjR1ZWVq5evTr5zRMtW7YsLCzMzs6OezoAgJilU9il5ObmFhUVxT0FAEDjkjYfngAA\noGbCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIO\nACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDC\nDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQ\nwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAg\nEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMKOECQSibKysrinAICYCTtC8Oyzz371\nq1+NewoAiFnTuAdIF80/+yxj585//9CsWZSb+79rW7ZEqaX9rlZXZ2Vm7qzdda3ua3XLli1b\ntkSbNjWuqaxatWrVaqirUdQ8apwS7M/vf//7KJoURYnU/9q2TXz++b9X33030aRJ4sBXc3LK\nr7xySO2ua3Vfq7/5zZ+iqLqxTWXVqlWrVsNd/f2iRYsSjY9n7A7QHQsWXNa8+b/zvE2bKCPj\n3wtdukRvvBHt2PG/u9a8euedt0ZRonbXtbqv1aOP3tK27Teef/6FRjWVVatWrVoNcnXZsp09\ne94RRY9FjU9GIpGIe4bGbtKkSddcc015eXleXl7djzZkyJAoiiZPnlz3Q5HyxBNPXHfddR99\n9FHcgwAQvh07duTk5CxatOiMM86Ie5bd+fAEAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBA\nIIRdWpo8efKyZcvingIAaFyEXVp66KGH/vKXv8Q9BQDQuAg7Yvbhhx+eeeaZO3f9Tj4AoFaE\nHTH76KOPFi1atG3btrgHAYC0J+yAxm7hwoV9+vSJewqANCDsgMbuww8/fOedd+KeAiANCDsA\ngEAIO2qvqqrqwgsvXL9+fdyDAABRJOyoi4qKitmzZ69duzbuQQCAKBJ2AADBEHYAAIEQdgAA\ngRB2AACBEHYAAIEQdgAAgWga9wAHLZFIlJaWrlq1qry8PIqiVq1aFRUVFRQUxD0XAEDM0ins\nNm3aNH78+KlTp27YsGG3pcLCwqFDh44aNapZs2axzAYAELu0Cbt169b17t27tLS0qKiob9++\nHTt2bNGiRRRFZWVlJSUl8+fPHzt27IwZM1544YU2bdrEPSzwb5WVlX/84x+HDRsW9yAAh4W0\nCbsxY8asWbNm2rRpAwcO3HO1urp60qRJI0aMGDdu3IQJExp+PGCvVq5cec0111xyySVHHHFE\n3LMAhC9tPjwxe/bswYMH77XqoijKzMwcPnz4oEGDZs6c2cCDATVIJBKp/wfgUEubsNu4cWOX\nLl1q3qdbt26+kB4AOGylTdjl5+cvX7685n1ef/31/Pz8hpkHAGgYDz74YP/+/eOeIj2kTdj1\n69dv+vTpd9999/bt2/dc3bp168033zxr1qyLLrqo4WcDSDvV1dVDhgzZuHFj3IPA/q1fv37P\nE2KwV2nz4Ylbbrll4cKFo0ePvvXWW3v16lVQUJCXl5dIJLZs2fL+++8vXbq0oqKiT58+N910\nU9yTAqSBrVu3Pvzww9dee23btm3jngWoN2kTdq1bt16yZMnEiROnTJkyb9686urq1FJWVlbP\nnj2Li4uLi4szMzNjHBJgvxYtWlRQUFBYWBj3IECA0ibsoijKzs4eOXLkyJEjKysrV69enfzm\niZYtWxYWFmZnZ8c9HcAB+dnPfta3b98bbrihLgd56qmnvv71r3uyDdhN2rzHble5ublFRUUn\nn3zyySef3LVrV1VHYJ588skVK1bEPQWHSiKR+Pzzz+t4kOHDh8+dO7de5gFCkpZhB2GbMGHC\nf//3f8c9BY1aIpFwdkBgTxnB/NVQUlKS/NqiOXPmHPi13nvvvdNPP33Hjh017LN9+/aKiorW\nrVtnZGTUdcooqqioiKKoefPmdTlIeXl5VlZWbm5uHQ/SrFmzpk1r/3J8IpH47LPPWrZsWZe3\nNlZXV5eVldXx5t2xY8e2bdtatWpV6yMkD7Jz587kV9XVWmVlZRRFdb9rGsP9G0VRWVlZXl5e\nkya1/xeg+3dP9XL/bt68uVmzZnV5vaJe/vx+/vnnW7ZsadmyZa2PEEVRVVXVtm3b6vjdJI3n\n/t26dWtWVlYdX0pqJH9+G8/9W1lZuXPnzrofJKrz/ZuyadOmRYsWnXHGGfVytHqUTu+xq1l5\neXktXpgoKCj4wx/+sNdTqKS89dZbY8eOve++++r4Zyzpk08+iaLoC1/4Ql0Osnbt2latWuXl\n5dXlIFddddWQIUPq+KD817/+VVRUVJf/ZicSiXfeeefYY4+tyxg7duxYu3Zt586d63KQmTNn\nvv7667fddltdDnLfffdFUTR8+PC6HKSR3L/btm274oorbrzxxrrcsO7fPdXL/VtaWtq+ffs6\n1kPd//yWlpZef/31EyZMaNasWa0Psnjx4smTJ0+aNKnWR4ga0/07ZsyYr371q3U86Voj+fPb\neO7fLVu2bN68uX379nU5SL3cv0lVVVWXXHJJ3Y9zSCRCsW3bthUrVqxYsaLej7xo0aIoirZv\n317vR47X0Ucf/fjjj8c9RSNy++239+7du44HufLKK6+88sp6maeO6n7/bt68OYqiV199tb5G\nildg928j8eqrr0ZRtHnz5roc5PHHHz/66KPrOEnjuX979+59++231/Egdf/zu2XLliiK3njj\njbocpPHcv/WiHv/8Jp8PWrRoUb0crX6F84xdbm5u9+7d454CAOLXokWLRYsWnXjiiXEPQkNL\nv7BLJBKlpaWrVq1Knu6kVatWRUVFBQUFcc8FAI1II3z7V7xycnLiHqEhpFPYbdq0afz48VOn\nTt3ze0UKCwuHDh06atSourwPAAAI1S9/+cu4R2gIaRN269at6927d2lpaVFRUd++fTt27Jj8\n9FNZWVlJScn8+fPHjh07Y8aMF154oU2bNnEPy+HrMPkXIUDaqePHe9NF2oTdmDFj1qxZM23a\ntIEDB+65Wl1dPWnSpBEjRowbN27ChAkNPx4k3XXXXXGPAMDhK21OUDx79uzBgwfvteqiKMrM\nzBw+fPigQYNmzpzZwIPBro444og6nmmp8WjevPm3v/3tDh06xD0IjVdeXl5ubq6v/wlVp06d\nhg4dWsezA7Zt27aOZ/jioKRN2G3cuLFLly4179OtW7f169c3zDzQyDVt2rSOZ15s2rTpM888\nc9RRR9XXSITn2GOP/fjjj+vrjK80NkceeeQDDzxQl1NYR1H0zW9+8x//+Ed9jcR+pc1Lsfn5\n+cuXL695n9dffz0/P79h5oFG7q9//et+/y10WDnnnHO8AfdQqOOZltmrTp06ffGLX4x7CtJS\n2oRdv379fvvb35566qnXXnvtnu9P37p16y9/+ctZs2Zdf/31sYwHjU23bt3iHqFxOeOMM5z9\ngXTx0ksvxT0C6Sptwu6WW25ZuHDh6NGjb7311l69ehUUFOTl5SUSiS1btrz//vtLly6tqKjo\n06fPTTfdFPekAByEE0444fvf/37cU0Ag0ibsWrduvWTJkokTJ06ZMmXevHnV1dWppaysrJ49\nexYXFxcXF9fxrQAANLDu3bv/7ne/i3uKepOZmem/RMQobcIuiqLs7OyRI0eOHDmysrJy9erV\nyW+eaNmyZWFhoc9kAdAY3Hfffd4eR4zSKexScnNzi4qK4p4CAHZ3wgknxD0Ch7W0Od0JAAA1\nE3YApL3s7OysrKy4p4D4CTsA0t4Pf/jDRx99NO4pIH5p+R47ANhV8+bNmzdvHvcUED/P2AEA\nBELYAQAEQtgdvjIyMjIyMuKeAgCoN95jd/j67W9/e84558Q9BQBQb4Td4WvgwIFxjwAA1Ccv\nxQIABELYAQAEQtgBAARC2AEABELYAQAEwqdiASCKoujaa6+NewSoK2EHAFEURSeffHLcI0Bd\neSkW/s33cACQ7jxjB/82cOBA/14HIK0JO/i3oqKioqKiuKcAgNrzUiwAQCCEHQBAILwUe4B+\n/rWvZaXeW9+uXfTss1Hyx7Vro+9/P9q58393tWrVaqirH3304//4j18nLzeeqaxatdrAqwMG\nZEXRjVGjJOwO0KsDBnyemZmZ/OGLX4xSkde2bfSDH0SVlf+7q1WrVkNd/dOfXo6iRGObyqpV\nqw28OmjQ5y+//GoUXRA1PhmJRCLuGRq7xYsX9+7de/v27dnZ2XHPAsRpyJAhURRNnjw57kGA\nOO3YsSMnJ2fRokVnnHFG3LPsznvsAAACIewAAAIh7AAAAuHDEwAHKvUJKoDGSdgBHKjbbrst\n7hEAaiLsAA7UMcccE/cIADXxHjsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAI\nOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQAg7AIBA\nCDsAgEAIOwCAQDSNe4A0kJ2dHUVRTk5O3IMAAI1FMg8am4xEIhH3DGlg+fLlVVVV9XKom266\nqaKi4qqrrqqXo5H00ksvTZ06deLEiXEPEpRt27ZdffXVt912W6dOneKeJSi33XbbV77yle98\n5ztxDxKUZ555Zvny5WPGjIl7kKC89957Y8aMmT9/fosWLeKepdFp2rTpV77ylbin2Ath19CG\nDBkSRdHkyZPjHiQoTzzxxHXXXffRRx/FPUhQysrKWrVq9eqrr5588slxzxKUM8888/zzz//5\nz38e9yBBGT9+/HPPPffiiy/GPUhQXnvttZ49e27evLlly5Zxz8KB8h47AIBACDsAgEAIOwCA\nQAg7AIBACDsAgEAIOwCAQAg7AIBACDsAgEAIOwCAQPiu2IbWOL9aLt1lZ2e7Yetd06ZNmzRp\n4oatdx6uh4Jb9VDIzs5u0qRJ06ZSIZ34SrGGtmnTpiiK2rRpE/cgQamqqlq7dm3Hjh3jHiQ0\nq1at+tKXvhT3FKH56KOPWrZs2bx587gHCUpFRUVZWdkXv/jFuAcJjb8E0o6wAwAIhPfYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYNZzPPvvsRz/6UadOnbKzs/Pz84cOHbpu3bq4h0pvDz/8cMbe\n3H777XGPln527tx5ww03ZGZmnnLKKXuuevTWTg23qkdv7WzatGnUqFEdO3bMycnp3Llzv379\nXnrppV138FithZpvVY/V9NI07gEOFzt27PjGN77x2muvDRgw4OSTTy4pKZkyZcrf/va3V199\ntU2bNnFPl64+++yzKIouvvjiwsLCXbf37t07ponS1cqVKy+77LJ33nlnr6sevbVT863q0VsL\nn376ac+ePd97770LLrjgiiuuWLVq1RNPPPH8888vXbr0xBNPjDxWa2W/t6rHappJ0CB+9atf\nRVH0i1/8IrXliSeeiKLoJz/5SYxTpbubb745iqJly5bFPUh627x5c7NmzU455ZR33nknJyen\nZ8+eu+3g0VsL+71VPXpr4Yc//GEURffee29qy4wZM6Io6tu3b/JHj9Va2O+t6rGaXrwU20Cm\nTJlyxBFHXHfddaktgwYN6tq169SpUxOJRIyDpbXkvyNbt24d9yDpraqqavjw4YsXL+7atete\nd/DorYX93qoevbWQlZX1jW98Y9iwYakt3/ve95o1a/bmm28mf/RYrYX93qoeq+lF2DWEysrK\nFStW9OrVKycnZ9ftZ5555oYNG0pLS+MaLN2l/rqprq5es2bNJ598EvdEaenII4+8++67s7Ky\n9rrq0Vs7Nd+qkUdvrfz617+eM2fOrrfqjh07qqqqOnToEHms1lbNt2rksZpuhF1DWL16dXV1\ndUFBwW7bO3bsGEXRqlWr4hgqBJs3b46iaMKECe3atSsoKGjXrt1xxx336KOPxj1XUDx6DxGP\n3noxadKknTt3/uAHP4g8VuvPrrdq5LGabnx4oiGUl5dHUdSiRYvdtufl5aVWqYXkvyMfe+yx\nn/70p+3bt1+5cuXEiRMvvfTS8vLyXV9WoC48eg8Rj966mz9//ujRo88888xrrrkm8litJ7vd\nqpHHaroRdg0nIyNjty3J93zsuZ0DNGbMmBEjRnzrW99K/VV+2WWXnXzyyTfeeOOQIUOys7Pj\nHS8kHr31zqO3jh577LEhQ4Z079591qxZTZv+73/LPFbrYq+3qsdqevFSbENo2bJltLd/L5aV\nlUVRdMQRR8QwUxDOPffcAQMG7PoP9C9/+ct9+/b99NNPly9fHuNgIfHoPUQ8emstkUjcfPPN\nl1zy/7V3J6FVnW0Ax980MWKIddb0hkgRBRE3xtCFCCaIiBWSdlGQD4eN4BiioChu1DpRBxRR\nBCmpaCRIN2qVii40ilMgOCAqiNNOEHEkBus1XVwagq2Jxn45zXt/v1U89wSeHB70z7k3x/9V\nVFScOXNm4MCBmeN29XN86KoGu9rTuGPXHYYPH56Xl/fw4cP3jt+9ezeEMGrUqCSGitbQoUND\nCK9evUp6kEjY3u5kezvV2to6d+7c2tra6urq7du35+bmtr1kV7usg6v6IXb1P8sdu+6Qn58/\nfvz4xsbG5ubmtoPv3r1raGgoKSl575GPfKRXr17t2bOnvr7+veOZX9HPfFyaz2d7/x9sb5ct\nXbq0trZ248aNO3fufK8/7GqXdXBV7WrPk9QD9LLN3r17Qwhr1qxpO7JnL7QzcAAABbRJREFU\nz54Qwtq1axOcqkdLp9PFxcWFhYW3bt1qO3j48OEQwrhx4xIcrEf7x0fp2t7P9Peranu7JvPg\n3Jqamg+dYFe7oOOrald7nJxWz2zsFul0uqKi4ty5c1VVVaWlpbdu3Tp06NDYsWMvXbpUUFCQ\n9HQ91dGjR7/77ruCgoIZM2akUqkbN24cPny4b9++p0+fLi0tTXq6HqOhoeH333/PfL1169Yh\nQ4bMmTMn88fly5cPGjTI9nZBp1fV9nbByJEj7969W11d/ffFW7FixYABA+xqF3R6Ve1qD5N0\nWWaRly9fZv6X5V69ehUXFy9atOjJkydJD9XjXbhwYdq0af3798/Ly0ulUrNnz75z507SQ/Uw\nmzZt+tDfD20X0/Z+qo+5qrb3U3Xwb9n9+/cz59jVT/UxV9Wu9iDu2AEARMIvTwAARELYAQBE\nQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEA\nRELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgB\nAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AEARELYAQBEQtgBAERC2AHZrq6u\nLicnZ82aNUkPAvC5hB0AQCSEHQBAJIQdQOcaGxu///77wYMH5+fnf/3117NmzXrw4EH7E44f\nP/7NN98UFBQUFRXV1NS8fv26pKSktLQ0oXmBLJWX9AAA/3VNTU2TJk0aOHBgTU1NUVHRvXv3\ndu/effLkyZs3bw4aNCiEcPbs2aqqqiFDhqxcuXLw4MG//vrrjBkzXr58WVxcnPTsQHYRdgCd\naGxsHDNmzLZt28rLyzNHiouLq6ur6+vrFy9eHEJYv359Op3+7bffysrKQgjz5s2bMmXK8+fP\nE5wZyE7eigXoxIIFC5qamjJV98cff7S0tIwZMyaE0PZu7Llz50aPHp2puhBCbm7uihUrkpkV\nyG7CDqBzBw4cmDRp0oABA/Lz8/v06TN58uQQwtu3b0MIz549a2lpGTlyZPvzJ0yYkMygQHYT\ndgCdWLVq1ezZs5ubm7dv337mzJmLFy/+/PPPba8+efIkhFBQUND+W/r27Zubm9vdgwJZz2fs\nADrS0tKyY8eOkpKS06dPFxYWZg62//xcr169Mqe1/67m5uZ0Ot2dcwIEd+wAOvbo0aPXr1+X\nlZW1VV0IoaGhoe3roqKiL7744uHDh+2/6/Lly903IsBfhB1AR4YNG5aTk9P+qXVXr17dv39/\n+OsuXX5+fllZ2fXr12/fvp05IZ1O//TTT0kMC2Q7b8UChBDCiRMnnj179t7BqqqqioqK6dOn\nHzt2bP78+eXl5Tdv3ty1a9fBgwcrKyuPHz9eX19fWVm5fPnyH3744dtvv124cOGXX35ZV1c3\nYsSI3r17J/KDANksp7W1NekZAJJUV1c3a9asf3xpy5Yty5Yte/z48ZIlS06dOvXmzZvx48ev\nXbt24sSJP/7445YtWwoLC69cuVJUVFRbW7t58+b79+9/9dVXM2fOXL16dWFhYVlZ2fnz57v5\nxwGymbAD+Pe9ePGiX79+lZWVR44cSXoWIIv4jB3A5/rll1/Ky8ubmprajuzbty+EMHHixMRm\nArKSO3YAn+vy5cuZxxcvWLAglUpduXJl7969qVTq2rVr/fv3T3o6IIsIO4B/wfnz5zds2NDU\n1PT06dOhQ4dOnTp13bp1qVQq6bmA7CLsAAAi4TN2AACREHYAAJEQdgAAkRB2AACREHYAAJEQ\ndgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACR\nEHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJH4E3C0\ndpJwLnH5AAAAAElFTkSuQmCC",
            "text/plain": [
              "Plot with title “Series  log_returns”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0mZ1VFkynZg1"
      },
      "source": [
        "As we can see on the graph above, the Q value of the autocorrelation function is equal to 0 for the log return of the time serie data. An MA model can't be performing well considering the log returns, the time serie isn't stationnary."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f9fFwHbWGbQJ"
      },
      "source": [
        "---\n",
        "Next, we consider the time series $S_t$ of annual returns, defined by\n",
        "$$\n",
        "S_t=(P_t-P_{t-12})/P_{t-12} \\;.\n",
        "$$\n",
        "We propose to model this time series using a MA($q$) model of the form\n",
        "$$\n",
        " S_t=\\sum_{k=1}^q \\theta_k \\epsilon_{t-k} + \\epsilon_t\\;,\n",
        "$$\n",
        "where $(\\epsilon_t)$ is the innovation process of $(S_t)$. \n",
        "**9) Justify that $S_t$ can be roughly approximated as\n",
        "$$\n",
        "S_t\\approx\\sum_{k=0}^{11} R_{t-k} \\;.\n",
        "$$\n",
        "Which order $q$ does this suggest for modeling the time series $(S_t)$ using a MA$(q)$ ?**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jFQDNWSO8CA1"
      },
      "source": [
        "\n",
        ">$  \\sum_{k=0}^{11} R_{t-k} = \\sum_{k=0}^{11} log(P_{t-k}) - log(P_{t-k-1}) $\n",
        "\n",
        "> $\\sum_{k=0}^{11} R_{t-k} = log(P_{t}) - log(P_{t-12})$\n",
        "\n",
        "> $\\sum_{k=0}^{11} R_{t-k} = log(P_{t}/P_{t-12} +1 - 1) $ \n",
        "\n",
        "since $ log(1+x) \\approx x $\n",
        "\n",
        "> $\\sum_{k=0}^{11} R_{t-k} \\approx  P_{t}/P_{t-12} - 1$\n",
        "\n",
        "> $\\sum_{k=0}^{11} R_{t-k} \\approx  \\frac {P_{t} - P_{t-12}}{P_{t-12} } \\approx S_t$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OOdusUBurUIf"
      },
      "source": [
        "It suggests that we need to chose q = 11 for the MA(q). \n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BcT813PjJGIF"
      },
      "source": [
        "annual_returns <- numeric(784)\n",
        "for (i in 12:784 ){\n",
        "  annual_returns[i] <- 0\n",
        "  for (j in 0:11) {\n",
        "    annual_returns[i] <- annual_returns[i] + log_returns[i-j]\n",
        "  }\n",
        "}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "sbu3-IwzJSdf",
        "outputId": "d7099a73-ab1c-45b1-be86-c77f65e65efc"
      },
      "source": [
        "pacf(annual_returns)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CAQih0AQCAUOwCAQCh2AACBUOwAAAKh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\nxQ4AAEAIih0AAIAQFDsAAAAh/gdZ3WqroFdyUQAAAABJRU5ErkJggg==",
            "text/plain": [
              "Plot with title “Series  annual_returns”"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F6pUFfpEGegs"
      },
      "source": [
        "**10) Use ***arima()***to estimate the MA coefficients and the innovation variance $\\sigma^2$ of a MA($q$) model with $q$ chosen according to the previous question.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "iRgisw_dr5D9",
        "outputId": "4d12e2d3-35ae-4797-9920-8a197cb8671a"
      },
      "source": [
        "arima(annual_returns, order = c(0,0,11))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "arima(x = annual_returns, order = c(0, 0, 11))\n",
              "\n",
              "Coefficients:\n",
              "         ma1     ma2     ma3     ma4     ma5     ma6     ma7     ma8     ma9\n",
              "      0.9942  0.9909  0.9936  1.0065  1.0179  1.0179  1.0066  0.9936  0.9909\n",
              "s.e.  0.0127  0.0155  0.0187  0.0205  0.0208  0.0213  0.0217  0.0200  0.0188\n",
              "        ma10    ma11  intercept\n",
              "      0.9942  0.9999     0.0725\n",
              "s.e.  0.0168  0.0140     0.0177\n",
              "\n",
              "sigma^2 estimated as 0.001719:  log likelihood = 1358.66,  aic = -2691.32"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s1ODxRdXGhaZ"
      },
      "source": [
        "**11)  Use** *predict()* **to test the quality of the 1 ahead prediction of the model for the last 200 observations of $S_t$. Compare with a fitted MA(1) model.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0i5iWqZRLu-x"
      },
      "source": [
        "pred <- c(1:200)*0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gn3kfkAPJmW_"
      },
      "source": [
        "f <- list()\n",
        "for (i in 1:12) { \n",
        "  demfit <- arima(Dem2,order=c(0,0,1))\n",
        "  f[[i]] <- forecast(demfit, 1)  #start filling the f list with values\n",
        "  Dem2[length(Dem2)+1] <- f$mean[1]\n",
        "} \n",
        "f <- unlist(f)\n",
        "accuracy(f,Test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "wwAJgkClMbTb",
        "outputId": "fe53bb2f-ca99-4346-ae1d-f388eb687fb0"
      },
      "source": [
        "typeof(annual_returns)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1] \"double\""
            ],
            "text/latex": "'double'",
            "text/markdown": "'double'",
            "text/html": [
              "'double'"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 186
        },
        "id": "Z5nzYxHcJ2aU",
        "outputId": "e761854e-f9a8-433e-96c7-37bf82c66c0d"
      },
      "source": [
        "plot(c(annual_returns),type=\"l\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ERROR",
          "evalue": "ignored",
          "traceback": [
            "Error in xy.coords(x, y, xlabel, ylabel, log): 'x' is a list, but does not have components 'x' and 'y'\nTraceback:\n",
            "1. plot(c(annual_returns, pred), type = \"l\")",
            "2. plot.default(c(annual_returns, pred), type = \"l\")",
            "3. xy.coords(x, y, xlabel, ylabel, log)",
            "4. stop(\"'x' is a list, but does not have components 'x' and 'y'\")"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "aWSXi9HkKKoV",
        "outputId": "545c468c-fe81-42aa-8c09-458762ca5e9d"
      },
      "source": [
        "myfit <- arima(s,order=c(0,0,1))\n",
        "subfit <- arima(s[1:(length(s)-200)],order=c(0,0,1),fixed=myfit$coef)\n",
        "pred2 <-predict(subfit,n.ahead=200)\n",
        "plot(c(s,pred$pred),type=\"l\")\n",
        "lines(c(s,pred2$pred),type=\"l\", col='green')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2XtDEeSrWNgXMWOwY5yjMEu/7TQpz12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\nhf04bIbFoiv2O7I7Yal3ppeo2ImIGC0nTyRfeyoc38vL8XXsLI2KHbzO3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7SmLNWsYqdMn6JiB29xTbATkWOPPfadd9659dZbFy1a1K9f\nv8WLFzvdIiDXEl2xxf5ip9sC5J8Wkyd0i65YeI2bgp2I+Hy+a665Zu3atX379j3rrLPOOOOM\nTZs2Od0oIHc00SQgYklADzjdFiD/mM0WKKYrFh7ksmBn69Wr19KlSx966KGVK1f269eP2RLw\nDiVKlIjR9jsBL7KaL1CsmX7ld7A5QO65MtjZJk6c+PHHH59++ulz5851ui1Ajmj2z6zZ1vsA\nT2qxQDEVO3iQuwcfdOrU6fHHH7/ggguWLVvWq1cvp5sDZJ0SJUKwAw6g1QLFTJ6A1xTCFT96\n9OjRo0c73QogF6jYAelYzcfY6RZdsfAaF3fFAh5kBztlKacbAuQjZankip3oQsUOXlM4wW7D\nhg0jR44cOXKk0w0BskhXuggVO+AALGbFwusK50+Z2traZcuWOd0KILvoigXSaLFAsaVbAY2F\ngeAthRPs+vTps3btWqdbAWQXkyeAdJpvKUZXLDyocK74UCjUv39/p1sBZBdj7IB0TGlWsWNW\nLLzHfVe8ZVk1NTWfffZZbW2tiLRr1666urqqquq7fdqXX3551llnRaPRNO/Zvn27/e9+t38C\nyKB4VywXI5BKi3XsxCfMioXXuCnY7dq165ZbbnnkkUe2bdvW4qVu3bpNmTJl9uzZRUXfbmf0\nDh06nHvuuY2NjWne89Zbb33xxRdKUSOB8xhjB6TDOnbwPNdc8Vu2bBk2bFhNTU11dfWYMWO6\nd+9eUlIiInv37t2wYcPy5cvnzJmzePHiV155pbKy8uA/NhQKXXnllenfc//99z/77LOH1Hog\nQ5gVC6SRomKnUbGDt7gm2N1www2bN29+6qmnxo8f3/pVwzDuv//+yy+/fO7cufPnz89984Dc\nsCdPMMYOSK35GDvRhVmx8BrXrGP3wgsvnH/++SlTnYjouj516tSzzz77mWeeyXHDgFyiKxZI\no2XFTmNWLDzHNcFu586dbe4G27dv361bt+amPYAj7K5YKnZAaklj7CJGRBQVO3iOa4Jd165d\n16xZk/49q1ev7tq1a27aAziCih2QRvICxREjIsIYO3iOa4LduHHjnn766Xnz5oXD4dav1tfX\n33jjjc8999yECRNy3zYgZxhjB6STtKVYU6xJhK5YeI5rrvibbrppxYoVV1111c033zxkyJCq\nqqrS0lLLsurq6jZu3Pg89olhAAAcO0lEQVT22283NDSMGDHiF7/4hdMtBbKIWbFAGskVu6gZ\nFZGgHnS0RUCuuSbYVVRUrFq1auHChQ8//PCrr75qGPtXKvL7/YMHD540adKkSZN0nf2eUcjs\nHc2p2AEpKWv/5Am7Kzb+txDgGa4JdiISCARmzJgxY8aMpqamTZs22TtPlJeXd+vWLRBgeCw8\nQVNsKQYcmLV/uZP6aL2IFPuKHW0QkGtuCnYJoVCourra6VYADmDyBJBG8nIntZFaESn1lzra\nIiDXXDN5IqV58+YNHz7c6VYAucPkCSANZanEcicNsQahYgfvcXewW79+/cqVK51uBZA7rGMH\npJM0K9YOdmWBMkcbBOSau4Md4DXMigXSSJ4VWxetE5ESf4mjLQJyjWAHuIk9xo6KHZBS8hg7\nu2JHsIPXEOwAN6ErFkgjuWLXYDSISHmw3NEWAbnm7mB32223bdq0yelWALnD5AkgnaQxdo1G\noxgS0FkMC97iyuVOEioqKioqKpxuBZA7VOyANJIXKK6P1UtEpMjZFgG55u6KHeA1BDsgDSX7\nu2KbzCYV4ScFnkOwA9yEYAekkVyxazKbVJSfFHgOwQ5wE2bFAukkbSnWaDZSsYMHEewAN2Gv\nWCANZSlL7a/YaTHucfAcLnrATeiKBdJo1hVrEezgRVz0gJsQ7IA0kidPhK2wFuUeB8/hogfc\nhGAHpJFcsYtIhIodPIiLHnATFigG0mi23InV5DPcvVYr8B0Q7AA3oWIHpNGiYqcburPtAXKP\nYAe4CcEOSCO5YhdVUYIdPIhgB7gJwQ5IQ1n2aAURkYhE6IqFBxHsADexg53GTy6QSnLFLqIi\nPpNgB8/h9gC4CQsUA2kkj7GLqqjf9DvbHiD3CHaAm8S7YoVgB6TQbIydFqViBw8i2AFuwhg7\nII3kMXYxLRawAo42B3AAwQ5wE4IdkEaLip3foisWnkOwA9yEyRNAGsraH+wMzfALwQ6ew+0B\ncBMmTwBpqKQBqIbPoCsWHkSwA9yEih2QRvKsWEOnYgcv4vYAuIlf84vIvjsXgGZ00Q1l2I8N\nzQgIFTt4DsEOcBO7K1YXNkoCUvCZvpgWsx+bPjOogs62B8g9gh3gJsyKBdIIWIGoFrUfE+zg\nTQQ7wE3sih1j7ICUghKM6VTs4GncHgA3oWIHpBGwAgQ7eBzBDnATn+YTKnbAAQQlaPjikycs\nvxXSQs62B8g9bg+Am7DcCZBGSIWSg11AMSsWnsPtAXATu2JHVyyQUotgR8UOHkSwA9yEyRNA\nGiEVMv3xLcUsn1WkFznbHiD3uD0AbkJXLJBGcrCTgBDs4EHcHgA3iXfFCl2xQApFWlGsc6zs\nw7KIERGdYAcvItgBbmJX7Nh5AkipWC8Wn9QdVVcXqRMh2MGLCHaAm9hj7Jg8AaRUpBWJiBRJ\nbaRWCHbwJIId4CasYwekUeIrERFR8mXdlyJS5CPYwXO4PQBuwuQJII1ivdh+8FX9VyJS7Ct2\ntDmAA7g9AG5CxQ5II16xE9nSuEUIdvAkbg+AmzArFkgjEey2hreKSIm/xNHmAA4g2AFuwgLF\nQBql/lL7wfbodiHYwZO4PQBuQlcskEYi2O2I7RCCHTyJ2wPgJkyeANJIBLtd1i4h2MGTuD0A\nbkLFDkijLFBmP9ij9ohIaaDU0eYADuD2ALiJHezsuh2AFhLBrlavFSP+8wJ4CsEOcBMmTwBp\nlAfL7Qf1vnqJONsWwBncHgA3CegBIdgBBxDyhcQQEWkMNqoYqwLBi7g9AG5CxQ5Ib/iK4f5N\n/nBRWEUJdvAibg+Am2hKE4tgBxzQihNXlO4ojZZEVYRgBy/i9gC4jRmv2wFIKRANxEpiyiDY\nwYu4PQBuY1KxA9LxG36r2CLYwZu4PQBuQ7AD0tItXYKiTIIdvIjbA+A2FuvYAeloliZKqNjB\nmwh2gNtQsQPS0ixNhIodPIrbA+A2zIoF0tItXYSKHTyK2wPgMspSdMUCaeiiy766HeA1XPeA\n29AVC6RFxQ5exu0BcBuTyRNAOlTs4GVc94DbMMYOSCtesWPyBDyJ2wPgMoyxA9KLV+xMbnDw\nIq57wGVUVAW1oNOtAPKXXbGjKxbe5HO6AQC+nYd3PXza905zuhVA/vKJT+iKhVcR7ACXOa/P\neU43AchrdlesXbcDvIZKNQCgoDDGDl7GdQ8AKCh2Vyxj7OBNXPcAgILiUz6hKxZeRbADABQU\nKnbwMq57AEBBYecJeBnXPQCgoPiVX+iKhVcR7AAABYWKHbyM6x4AUFCo2MHLCHYAgIISnxUr\nBDt4EcEOAFBQqNjBywh2AICCQsUOXkawAwAUlHjFjmAHTyLYAQAKCjtPwMsIdgCAgkLFDl5G\nsAMAFBS/RrCDdxHsAAAFxa7Y2TvGAl5DsAMAFBQqdvAyd/9BYxjGRx99VFtbW1VVVVVV5XRz\nAADOC2gB2Ve3A7zGTRW7N9544/LLL088/dOf/nTEEUcMGDBg2LBh3bp1Gzhw4GuvveZg8wAA\n+YB17OBlrqnYvfrqq6eeemogEFiwYIFS6s9//vP5559fWlo6fvz4jh07rlu3btmyZaNGjVq5\ncuXgwYOdbiwAwDF2xY4xdvAm11z3c+fOraioWLlypVJKRK6++uru3buvWrWqS5cu9hveeuut\nk046ae7cuf/7v//raEsBAE6yx9jZdTvAa1zTFfuPf/zjggsu6N27t4js2bOnpqZm5syZiVQn\nIscdd9zPfvazFStWONdGAIDz7IodXbHwJtcEO8MwioqK7MehUEgpdeSRR7Z4z5FHHtnU1JTz\npgEA8ohdsWPyBLzJNcFu4MCBTzzxRENDg4gEg8Ef/OAHq1atSn5DOBx+5plnjjnmGIcaCADI\nC0E9KHTFwqtcE+yuvfbadevWjRgx4q9//WssFluwYMGjjz768MMPNzQ0RKPRt956a8yYMWvW\nrJk6darTLQUAOImKHbzMNX/QnH766f/93//985///NRTTy0qKurZs2cgELjwwgsnTZokIoZh\nKKVmzpx58cUXO91SAICT4rNiqdjBk9x03U+ZMuVHP/rRI488snTp0k8++eSbb74JBoOlpaU9\nevQYNmzYhRdeOGjQIKfbCABwWEBngWJ4l5uCnYh07tx59uzZs2fPdrohAIA8xRg7eJlrxtgB\nAHAwGGMHLyPYAQAKil2xs+Md4DWFE+w2bNgwcuTIkSNHOt0QAICT7DF2dMXCmwrnuq+trV22\nbJnTrQAAOMyu2NlzYwGvKZxg16dPn7Vr1zrdCgCAw6jYwcsK57oPhUL9+/f/tl8VDocfe+yx\naDSa5j3sPwsALkLFDl7mvmBnWVZNTc1nn31WW1srIu3atauurq6qqvpun7Z9+/Y777yzsbEx\nzXvq6+tFxO9nHC4AuECxv1hMKdKLnG4I4AA3Bbtdu3bdcsstjzzyyLZt21q81K1btylTpsye\nPbuo6Nv9JB955JEffvhh+ve88cYbw4YNU0p9u+YCAJwQ8oUe++Sx8f3GO90QwAGuCXZbtmwZ\nNmxYTU1NdXX1mDFjunfvXlJSIiJ79+7dsGHD8uXL58yZs3jx4ldeeaWystLpxgIAnHRun3Od\nbgLgDNcEuxtuuGHz5s1PPfXU+PEp/ggzDOP++++//PLL586dO3/+/Nw3DwAAwHGuWcfuhRde\nOP/881OmOhHRdX3q1Klnn332M888k+OGAQAA5AnXBLudO3f26tUr/Xv69u27devW3LQHAAAg\n37gm2HXt2nXNmjXp37N69equXbvmpj0AAAD5xjXBbty4cU8//fS8efPC4XDrV+vr62+88cbn\nnntuwoQJuW8bAABAPlCWZTndhoOye/fuU0455R//+EdZWdmQIUOqqqpKS0sty6qrq9u4cePb\nb7/d0NAwYsSIF198sbS0NLP/tL3cSTgcDgRY7hIAAK+LRCLBYHDlypVDhw51ui0tuWZWbEVF\nxapVqxYuXPjwww+/+uqrhmEkXvL7/YMHD540adKkSZN0XXewkQAAAA5yTbATkUAgMGPGjBkz\nZjQ1NW3atMneeaK8vLxbt27U0gAAANwU7BJCoVB1dbXTrQAAAMgvrpk8kdK8efOGDx/udCsA\nAADygruD3fr161euXOl0KwAAAPKCu4MdAAAAEgh2AAAABYJgBwAAUCDcHexuu+22TZs2Od0K\nAACAvODK5U4SKioqKioqnG4FAABAXnB3xQ4AAAAJBDsAAIACQbADAAAoEAQ7AACAAuHuyRO5\nEQgERCQYDDrdEAAAkC/seJBvlGVZTrfBBdasWROLxQ79c954441Zs2Y9+OCDh/5R+M4aGhou\nueSSW265pVu3bk63xdOuvvrq0aNHn3TSSU43xNPuu+8+n883ZcoUpxviaX/729/+/ve/33rr\nrU43xNNqamrmzJmzYsWKoqKig3m/z+f73ve+l+1WfQcEu5x6+eWXf/zjHzc1NTndEE/bvXt3\nZWXl6tWrBw4c6HRbPK1Pnz4zZsy45JJLnG6Ip11wwQWBQOCBBx5wuiGeds8999x///1r1651\nuiGe9s477wwZMqSurq6kpMTpthwSxtgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEAABQI\ngh0AAECBINgBAAAUCIIdAABAgSDYAQAAFAiCXU4FAoH83FrOU/x+v1KKE+E4fhzyAWchH3AW\n8kEgENA0zefzOd2QQ8WWYjllWdbnn3/es2dPpxvidZ999tlRRx3ldCu8bvPmzZ06deJ+5qxv\nvvlG07SKigqnG+Jp4XB4x44dRxxxhNMN8brCuDUQ7AAAAAoEXbEAAAAFgmAHAABQIAh2AAAA\nBYJgBwAAUCAIdgAAAAWCYAcAAFAgCHYAAAAFgmAHAABQIAh2AAAABYJgBwAAUCAIdgAAAAWC\nYAcAAFAgCHYAAAAFgmAHAABQIAh2AAAABYJglyO7d+/++c9/3qNHj0Ag0LVr1ylTpmzZssXp\nRhWaXbt2zZ49u3v37sFgsGfPnuPGjXvzzTeT39DmWeA0ZdbMmTOVUlOmTEk+yFnIjSVLlpxw\nwgllZWUVFRUnn3zyq6++mvwqZyE3Pvnkk/PPP79Lly5+v79jx44/+clP3n777eQ3cCKyIRqN\nXnfddbquH3vssa1fPfTveb6fFAvZFw6HBw0aJCI//elPb7nllkmTJvn9/p49e37zzTdON61w\n7Ny5s0ePHiIyduzYG2644d///d99Pl8oFPrggw/sN7R5FjhNmfXOO+/oui4ikydPThzkLOTG\ngw8+KCK9evX6xS9+MXv27I4dOwYCgZUrV9qvchZy48MPPywrK2vfvv2cOXMefvjhX/7yl4cf\nfrjP51u2bJn9Bk5ENnz00UeDBg0qKyvTNG3w4MEtXj3073n+nxSCXS7cddddInL77bcnjjz5\n5JMiMmvWLAdbVWCmTZsmIgsWLEgcWbx4sYiMGTPGftrmWeA0ZVA0Gh04cOD3vve9FsGOs5AD\nW7duLS0t/dd//de6ujr7yLp160pLS6dOnWo/5SzkxnnnnScif//73xNH1qxZIyInnnii/ZQT\nkXF79uwpKio69thj161bFwwGWwe7Q/+e5/9JIdjlwsCBA8vKypqampIP9u7du1OnTqZpOtWq\nAvPzn//8lFNOiUQiiSOmaRYVFXXv3t1+2uZZ4DRl0G233aaUWrJkSYtgx1nIgTvuuENEXnrp\npeSDyd89zkJuHHfccSKS/EvJsqzy8vIePXrYjzkRGbdz585Zs2bZ3/OUwe7Qv+f5f1IYY5d1\nTU1Na9euHTJkSDAYTD4+fPjwbdu21dTUONWwAvPb3/526dKlfr8/cSQSicRisSOPPFIO4ixw\nmjJow4YNc+fOvfTSS48//vjk45yF3Fi6dGlRUdHJJ58sIuFweO/evSKilLJf5SzkTJ8+fUTk\n//7v/xJHduzYUVdX17dvX+FEZEf79u3nzZuXfCNIdujfc1ecFIJd1m3atMkwjKqqqhbHu3fv\nLiKfffaZE43yhPvvvz8ajZ5zzjlyEGeB05RBl1xySUVFxa233triOGchNz755JOePXt++OGH\nw4cPLyoqateuXe/evRctWmS/ylnImWuuuaaysvJnP/vZ66+//vXXX69evfqcc84JhUI33nij\ncCKccOjfc1ecFIJd1tXW1opISUlJi+OlpaWJV5Fxy5cvv+qqq4YPH37ppZfKQZwFTlOmLFq0\naNmyZQsWLGjXrl2LlzgLufHNN9/U19ePHTv2+OOPf/rpp+++++5oNHrRRRc99thjwlnIob59\n+65atSoajY4YMaJLly6DBg1at27d0qVL7S5aTkTuHfr33BUnxed0A7wi0Q+SYFlWyuM4dI8/\n/vhFF13Uv3//5557zufbf5G3eRY4TYdo27Zts2bNOv3003/6058e6D2chWyLRCIbN2784x//\neMEFF9hHxo8ff/TRR8+aNWvChAn2Ec5CDnz88cdjx46NxWJ33nnn0UcfvW3btrvuumv06NF/\n/vOfR44cab+HE5F7h/49z/OTQrDLuvLyckkV5O2BL2VlZQ60qXBZlnXTTTfdfPPNp5122lNP\nPZX49rZ5FjhNGTF9+vRIJLJw4cKUr3IWcqO0tDQWi5111lmJI126dBk9evTTTz/90UcfcRZy\nZtKkSVu3bv3000+POOII+8g555xz9NFHT5w4saamhhORe4f+PXfFSaErNuu6devm8/k2btzY\n4viGDRtEpLq62olGFSbLsqZMmXLzzTdfccUVf/nLX5J/xto8C5ymQ7dkyZInnnhixowZmqZt\n3rx58+bNX331lYg0NDRs3rx57969nIXcsBd0bDF+vGPHjiJSW1vLWciNurq6t95667jjjkuk\nOhEpLi4+5ZRTvvzyy08//ZQTkXuH/j13x0lxYiqu5xx33HHFxcX19fWJI4ZhdO3ataqqysFW\nFZ7p06eLyK9//euUr7Z5FjhNh2jWrFlpftVcc801FmchJy6//HIRefPNN5MPjho1SkS++OIL\ni7OQE9u2bRORH/zgBy2On3322SLy7rvvWpyILEu53Mmhf8/z/6RQscuFyZMnNzQ02ItL2X7/\n+99/9dVXLbZawqF45pln7r777unTp1933XUp39DmWeA0HaLJkyc/39wTTzwhIqNGjXr++ecn\nTpwonIWcmDhxolLq+uuvD4fD9pF333136dKlAwYMsGfzcRZyoGPHjj179nz33Xc//fTTxMHd\nu3cvXbq0vLy8f//+wolwwqF/z/P/pCjLspxuQ+EzDOOkk05asWLFj3/840GDBn388cdPPvlk\n//7933zzzeLiYqdbVyB69+69YcOGK664ovW31F50oM2zwGnKuN27d1dWVk6ePPmBBx6wj3AW\ncmPGjBnz588fOHDgT37yk82bN//pT38yDOPll18+8cQThbOQK88+++xZZ51VWVl56aWX9urV\na8uWLQ888EBNTc3ChQunTp0qnIgsWL58ub0uuojMmzevY8eOF154of30qquu6tChw6F/z11w\nUpwuGXpFbW2tvT+93+8/4ogjpk2btnPnTqcbVVDSXOQ1NTX2e9o8C5ymzNq1a5c033nC4izk\nhGma99133/e+971QKNSuXbsxY8a8/fbbyW/gLOTGG2+8MW7cuI4dO/p8vsrKypEjR77wwgvJ\nb+BEZFbr5TMT1q1bZ7/n0L/neX5SqNgBAAAUCMbYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECB\nINgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECBINgBAAAUCIIdAABAgSDY\nAQAAFAiCHQAAQIEg2AEAABQIgh0AAECBINgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEA\nABQIgh0AAECBINgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECBINgBAAAU\nCIIdAABAgSDYAQAAFAiCHQAAQIEg2AHAt+Pz+Y4//ninWwEAKRDsAHjFJ598opQ67bTTnG4I\nAGQLwQ4AAKBAEOwAAAAKBMEOgHedd955Sqm6urprrrmmR48ewWCwqqrqt7/9rWVZife8+OKL\ngwcPLioq6tSp05QpU3bv3t3iQ7Zu3Tpt2rTu3bsHAoGOHTuOGzfunXfesV9aunSppmnnnXde\n8vvHjBmj6/rrr7+e7f8dAA8i2AHwrkAgICJnnXXW3r17n3jiiVdeeaVfv34zZ85ctGiR/YbX\nX3/9jDPO+Prrr+fMmfPrX/86HA6fccYZmrb/N+f27duPO+64Rx999Nxzz33wwQdnzpz53nvv\njRgxYvny5SIycuTISy655PHHH1+6dKn9/sWLFy9ZsmT69OnDhw/P9f8WgBdYAOANH3/8sYic\neuqpiSOTJ08WkXPPPTdxZMOGDSJy+umn20/tmRZvv/124g1Tp04VkeOOO85+etlll/l8vnfe\neSfxhi+++KKsrOzYY4+1n9bW1vbo0aO6urqpqamurq6qquroo49uaGjI3n8TgJf5HE2VAOC8\nCy+8MPH4qKOOKi4u3rx5s4iYprl8+fJevXp9//vfT7zh4osvvvfee+3HlmU9/fTTAwYMOPLI\nI7/++mv7oN/vHzp06Msvv1xXV1daWlpaWvrggw+ecsopt956a319/Zdffvn6668XFRXl8P8H\nwEMIdgC8rlu3bslP/X5/NBoVkS1btjQ2Nh511FHJr/bp0yfxeNu2bTt27NixY0eXLl1af+wX\nX3zRr18/ETnppJMuu+yy2267zTTNWbNm/eAHP8jKfwMACHYA4Pf7Ux5vaGgQkVAolHwwFAop\npezHtbW1IjJw4MBbb7219Zd37do18Xjy5Ml2ne+CCy7IUKsBIAWCHQCkZneYNjU1JR+sq6uz\n9s2ZLSsrsx+kX/TYNM3LL7+8c+fOsVhs6tSpy5cvT0RDAMgsZsUCQGqHH354IBCoqalJPvjB\nBx8kHnfu3Pmwww775JNPWqyBsn379uSnd91116pVq+6+++558+atWLHid7/7XVabDcDLCHYA\nkJrP5xs6dOj69esT69KJyMKFC5PfM378+KampjvuuCNxZPv27QMGDPjRj35kP/3000/nzJkz\nZsyYCRMmTJw48aSTTrr++uvXrVuXm/8CAK+hKxYADujqq69evnz56aefPmnSpA4dOixfvryh\noaFdu3aJN9x0000vvPDCr3/96y1btpxwwglfffXVfffdt3PnziuvvFJETNOcOHGipmmJibT3\n3XffgAEDLrrootdeey15PTwAyAh+rQDAAY0ePfrxxx/v3LnzXXfd9Zvf/KZTp06LFy8uLy+P\nRCL2Gzp16vTWW29ddtllS5cunTJlym9+85uBAwe+/vrrP/zhD0Xkt7/97apVq375y192797d\nfv/RRx/9n//5nytXrpw/f75j/ysAhUtZSTvnAAAAwL2o2AEAABQIgh0AAECBINgBAAAUCIId\nAABAgSDYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECBINgBAAAUCIIdAABAgSDYAQAAFAiCHQAA\nQIEg2AEAABQIgh0AAECBINgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECB\nINgBAAAUCIIdAABAgSDYAQAAFAiCHQAAQIEg2AEAABQIgh0AAECBINgBAAAUCIIdAABAgSDY\nAQAAFAiCHQAAQIH4/+e9uCi+BkNbAAAAAElFTkSuQmCC",
            "text/plain": [
              "plot without title"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KuA7gJtnte8C"
      },
      "source": [
        "\n",
        "## Some hints ##\n",
        "\n",
        "The object argument in *predict()* is the output of a *fit()*. Hence a new fit\n",
        "is necessary each time the learning data set changes. However, to avoid\n",
        "reprocessing the estimation of parameters (which can be numerically costly) one\n",
        "can use *fixed* parameters. Here is an exemple, where an ARMA(0,4) is fitted\n",
        "on the overall time series *r* (of length $\\gg 10$) and used to predict the last sample from the\n",
        "previous ones:\n",
        "\n",
        "```{r ,eval = FALSE}\n",
        "myfit <- arima(r,order=c(0,0,4))\n",
        "subfit <- arima(r[1:(length(r))-10)],order=c(0,0,4),fixed=myfit$coef)\n",
        "predict(subfit,n.ahead=10)\n",
        "```\n",
        "\n",
        "One can use *forecast()* from the forecast package instead of predict, which works similarly but with added features.\n",
        "Continuing on the previous example:\n",
        "\n",
        "```{r ,eval = FALSE}\n",
        "plot(forecast(subfit,h=10))\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gvxU8gtpGnGr"
      },
      "source": [
        "\n",
        "# VIX data and AR modeling #\n",
        "\n",
        "In this part we work on the VIX volatility index. \n",
        "We study the AR$(p)$ modeling of this series, denoted by $Y_t$, namely, up to a demeaning constant,\n",
        "$$\n",
        " Y_t=\\sum_{k=1}^p \\phi_k Y_{t-k} + \\epsilon_t\n",
        "$$\n",
        "where $\\epsilon_t$ are the innovations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HRvKaAjmGqAu"
      },
      "source": [
        "**12)  Load the time series from the file** \n",
        "\n",
        "https://perso.telecom-paristech.fr/roueff/edu/tsfd/data/vix-2011-2014.Rdata\n",
        "\n",
        "**The data starts in January, 3 2011 and ends in January, 3 2014, with a\n",
        "   sample every working day. Compare the trajectory to that of the SP500 index.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5YI0ASNBljx4",
        "outputId": "fad9f64a-4ad3-47f0-f9d7-4bf003d08a37"
      },
      "source": [
        "!curl 'https://m2:map658@perso.telecom-paristech.fr/roueff/edu/tsfd/data/vix-2011-2014.Rdata' --output data_3.RData"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
            "                                 Dload  Upload   Total   Spent    Left  Speed\n",
            "100  2206  100  2206    0     0   1821      0  0:00:01  0:00:01 --:--:--  1821\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "luMFhk1Vl0RN"
      },
      "source": [
        "data_3 = pyreadr.read_r('data_3.RData')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8pJRUb4noUOo",
        "outputId": "83ada702-f60e-4354-b7a2-68a3aa548923"
      },
      "source": [
        "print(data_3.keys())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "odict_keys(['vix'])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1qkFjif_tcck"
      },
      "source": [
        "from pandas.tseries.holiday import USFederalHolidayCalendar\n",
        "from pandas.tseries.offsets import CustomBusinessDay\n",
        "usb = CustomBusinessDay(calendar = USFederalHolidayCalendar())\n",
        "nbr_working_day = pd.date_range('1/3/2011', '1/6/2014', freq=usb)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MvkUf0U8nQiP",
        "outputId": "b71d3016-d89d-4010-8bbe-815e132c1b7b"
      },
      "source": [
        "nbr_vix = len(data_3[\"vix\"])\n",
        "print(f'There is {len(nbr_working_day)} working day between start=1/3/2011, end=1/3/2014')\n",
        "print(f'There is {nbr_vix} data in our dataset')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "There is 756 working day between start=1/3/2011, end=1/3/2014\n",
            "There is 756 data in our dataset\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hEd93EC_PANG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0929f32c-bed5-4204-9a95-49fc1e011cf2"
      },
      "source": [
        "df_3.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(756, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 122
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ySEKIorpPB-k",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6e5654c8-edb6-4699-a8c7-935160b2b368"
      },
      "source": [
        "df_2.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(784, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mht2hr1cmoHE"
      },
      "source": [
        "df_3 = data_3[\"vix\"]\n",
        "df_3.set_index(nbr_working_day,inplace=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e9NxhiFpxqZM"
      },
      "source": [
        "df_3_m = df_3.resample('MS').mean()\n",
        "df_2 = df_2.resample('MS').mean()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_oVZSlTJyHwU"
      },
      "source": [
        "df_4 = df_3_m.merge(df_2, how='left', left_index=True, right_index=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 194
        },
        "id": "xiPxk2tUytje",
        "outputId": "e140e7e7-14c1-4830-d822-c87f4ed9a8e8"
      },
      "source": [
        "df_4.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>vix</th>\n",
              "      <th>sptsm</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2011-01-01</th>\n",
              "      <td>17.245500</td>\n",
              "      <td>1257.62000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-02-01</th>\n",
              "      <td>17.733684</td>\n",
              "      <td>1289.14001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-03-01</th>\n",
              "      <td>20.650435</td>\n",
              "      <td>1328.64001</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-04-01</th>\n",
              "      <td>16.296667</td>\n",
              "      <td>1329.47998</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2011-05-01</th>\n",
              "      <td>17.152857</td>\n",
              "      <td>1365.20996</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                  vix       sptsm\n",
              "2011-01-01  17.245500  1257.62000\n",
              "2011-02-01  17.733684  1289.14001\n",
              "2011-03-01  20.650435  1328.64001\n",
              "2011-04-01  16.296667  1329.47998\n",
              "2011-05-01  17.152857  1365.20996"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "8zKeeUnTziJF",
        "outputId": "1d436b9f-d17c-4bf2-e643-faac21ab3081"
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(20, 10))\n",
        "ax.plot(df_4['vix'], label = 'vix', color=\"red\")\n",
        "ax2=ax.twinx()\n",
        "ax2.plot(df_4['sptsm'], label = 'sptsm', color=\"blue\")\n",
        "ax.set_ylabel(\"vix\",color=\"red\",fontsize=14)\n",
        "ax2.set_ylabel(\"sptsm\",color=\"blue\",fontsize=14)\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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k1bR77kmrwQYMgNNPz51GjaCSS6sWBa4OIXQkFXA3xhj/EUJ4MITQCwjASNIpkpIayYQJMHEi9O6dO0nrdOkCP/95muA5c2Z1b+WUJEmSqtTLL6e5YCuvDNdeCx075k6kRlCxIizG+ALQ9C33N6pUBklVqlhM1x/+MG+Othg4EP72N3jySVhnndxpJEmSpJry8cew9dbQrVs6h2q++XInUqNwGYOk/GqxCPv5z6FTJ0+PlCRJktpo6lTYbjsYOzZNG1liidyJ1EgswiTlVyika61sjQRYcME0K8w5YZIkSVKrxQi/+Q08+ihceSWstVbuRGo0FmGS8qvFFWGQJnq+8gq88UbuJJIkSVJN+MMfUgF24omw886506gRWYRJyq9YhBCgV6/cSdpmwIB0dXukJEmS9L2GD4ejjkoD8gcNyp1GjcoiTFJ+xSL06JFmbtWSH/8YVlnFIkySJEn6HiNHwi67wOqrw1VXefC68vF/epLyKxRqaz7Y7AYOhMceS8feSJIkSfqGQiFtplhooTRit1u33InUyCzCJOVXLNbefLBZBgyAmTPhzjtzJ5EkSZKqzpdfwjbbwCefpI0Uiy6aO5EanUWYpPxquQhbbTX40Y88PVKSJEn6mhjh17+GJ5+Ea6+FpqbciSSLMEnVoJa3RoaQVoXdcw9Mnpw7jSRJklQ17r0XrrsOBg9Oq8KkamARJimvCRNg0qTaXREGaU7YxInw4IO5k0iSJElVYebMdEJk377pKlULizBJeRWL6VrLRdiGG8J883l6pCRJktTi2mvh+edhyBDo2jV3GukrFmGS8ppVhNXq1khIf7NvvnkqwmbOzJ1GkiRJymryZDj++DRO9xe/yJ1G+m8WYZLyKhTStZZXhEHaHvnBB/DMM7mTSJIkSVldcAG88w4MHQodbB1UZfyfpKS86mFrJMAWW0DHjp4eKUmSpIb22Wdw2mlpw8TPfpY7jfRNFmGS8ioW08mLvXrlTtI+Cy8M667rnDBJkiQ1tNNPh88/T6vBpGpkESYpr0IBevaETp1yJ2m/AQPgxRdhzJjcSSRJkqSKe+cdOO882H13WGWV3Gmkb2cRJimvYrH2t0XOMmBAuroqTJIkSQ3oxBPT9ZRT8uaQvotFmKS86qkIW2opWHFF54RJkiSp4Tz/PPzlL/B//wdLLJE7jTRnFmGS8ioUoHfv3ClKZ+BAePTRNCVUkiRJahBHHw0LLgjHHJM7ifTdLMIk5VVPK8IgbY+cMQPuvDN3EkmSJKkiHnwQ7r4bjj0WFloodxrpu1mEScpnwgSYNKm+irA11kgr3JwTJkmSpAYwcyYceWTaDnnQQbnTSN+vDo5pk1SzisV0racirEMH2HpruOEGmDIFunbNnUiSJEkqm7/9DZ55Js0Hm2ee3Gmk7+eKMEn5FArpWk8zwiDNCRs/Hh55JHcSSZIkqWymTIHjjoNVV4Vdd82dRmodizBJ+dTjijCAjTaCeef19EhJkiTVtYsvhjFjYOjQtDFCqgX+T1VSPvVahHXrBpttluaExZg7jSRJklRyX3wBp5wCG28Mm26aO43UehZhkvIpFCAE6NUrd5LSGzAA3nsPnnsudxJJkiSp5IYOhU8+SdcQcqeRWs8iTFI+xSL07Amd6vDcji23TOvDPT1SkiRJdWbsWDj3XNhlF2huzp1GahuLMEn5FIv1ty1yll69oH9/54RJkiSp7gwaBDNmwKmn5k4itZ1FmKR8isX6OzFydgMHwsiR8M47uZNIkiRJJTFqFFx5JRx4IPTtmzuN1HYWYZLyKRTqd0UYpDlh4PZISZIk1Y2jj4b554fjjsudRJo7FmGS8qnnrZEAyy4Lyy1nESZJkqS68Oij8I9/pDKsR4/caaS5YxEmKY8JE2DSpPouwiCtCnv44XS+tCRJklSjYoQjj4Q+feCQQ3KnkeaeRZikPAqFdK3nGWGQ5oRNmwZ33507iSRJkjTXbrkFnnwSTjkFunXLnUaaexZhkvIoFtO13leErbVWOkHS0yMlSZJUo6ZNg2OOgZVWgj32yJ1Gap9OuQNIalCNUoR17Ahbb50+Qps2DTp3zp1IkiRJapNLLoHRo9N8sI4dc6eR2scVYZLyaJStkZDmhH3xRZouKkmSJNWQ8eNh8GBYf33YYovcaaT2swiTlEexCCFAz565k5TfJpvAPPN4eqQkSZJqzh/+AB99BL//ffrxXap1FmGS8igWUwnWqQF2aM87byrDhg2DyZNzp5EkSZJa5YMPUhG2446w5pq500ilYREmKY9isf7ng83uF7+At99Og/N33BGuuw4+/zx3KkmSJGmOBg+GqVNhyJDcSaTSaYClGJKqUqHQGPPBZtllF+jRA267La0Mu+mmtBpugw1gm23SHLHFF8+dUpIkSQLgtdfgsstg//1h6aVzp5FKJ8QYc2dos+7du8eJEyfmjiGpPZZcEvr3h2uuyZ2k8mbOhCefTIXY3/+efsoAWG21VIoNHJjOpnYIgyRJkjLZdlu4//50WuQii+ROo0oJIUyKMXbPnaOc3BopqfJibLytkbPr0AHWWQfOOANefRVeeSX9unNnOOEEWGWV9LHb4YfDP/8JM2bkTixJkqQG8vjjaSPDkUdagqn+uCJMUuWNHw8LLJCOnvnd73KnqS4ffAC3355Wij3wQBrK0LMnbL11Wi22ySbQrVvulJIkSapTMcJPfwpjxsAbb0D3ul4bpK9zRZgklUOxmK6NuiLsuyy6KOy7L9x5J3z8Mdx4I2y6Kdx6a9oy2aMH/O//wtVXwyef5E4rSZKkOjNsGPzrX3DSSZZgqk+uCJNUeY8/nj5muvtu2Gyz3Glqw9Sp8OijaaXYsGHw3ntpi+W66341V6xv39wpJUmSVMOmT/9qVO2LL6azndRYXBEmSeXgirC269IFNt4YLrgA3nkHnn4ajj0WPv0UfvvbdPjAqqvCoEHw3HNpTbskSZLUBpdfns5xOuMMSzB9uxDCFSGED0MIL812728hhJEtX/8JIYyc7XvHhBBGhxBeCyFsNtv9zVvujQ4hHF3RP4MrwiRV3IUXwoEHpnlYvXvnTlP73nwzrRIbNgweeyydSrnEEmmV2P77w/LL504oSZKkKjdxYjqvaaml0nlNHmDemL5vRVgIYT1gAvCXGONK3/L9s4AvYownhxBWAK4H1gR+BNwPLNvy0NeBTYD3gBHAzjHGl0v6h5kDV4RJqrxiMf3N2rNn7iT1Yaml4LDD4JFHoFCAK66Apia49NI0T0ySJEn6HmefnX6U/P3vLcE0ZzHGR4FPv+17IYQA7EgqvwAGAjfEGKfEGMcAo0ml2JrA6BjjWzHGqcANLY+tCIswSZVXLKYSzPXWpderF+y1V5olNmhQWtv++ee5U0mSJKmKffhhKsC23Rb698+dRjVsXaAYY3yj5fd9gHdn+/57LffmdL8iLMIkVV6h4JbISmhqSteRI7/7cZIkSWpoJ58MX34Jp52WO4mqQKcQwtOzfe3bhufuzFerwaqWyzEkVV6x6KD8SphVhD37LGywQdYokiRJqk5vvAF//jPssw/85Ce506gKTI8xrt7WJ4UQOgHbAqvNdnsssPhsv1+s5R7fcb/sXBEmqfIswipjkUWgT590iqQkSZL0LY47Drp2TVM1pHbYGHg1xvjebPeGAzuFELqGEPoCywBPkYbjLxNC6BtC6ALs1PLYirAIk1RZMbo1spKamtKKMEmSJOlrnnwSbroJjjjCH8/VOiGE64F/Az8JIbwXQti75Vs78bVtkTHGUcCNwMvA3cCBMcYZMcbpwEHAPcArwI0tj63MnyHGWKn3Kpnu3bvHiRMn5o4haW6MHw8LLJCmcf7ud7nT1L9Bg+DUU9P/u887b+40kiRJqhIxpukZr74Ko0fD/PPnTqRqEEKYFGPsnjtHObkiTFJlFYvp6tbIymhqgpkz4cUXcyeRJElSFbnjDnj00fS5qSWYGolFmKTKsgirrNkH5kuSJGmOJk1K87Leeit3kvKbMQOOPhqWWSYNyZcaiUWYpMoqFNLVIQSVscQSsPDCDsyXJEn6HuedB6edBgMHQr1P4rn6ahg1Ck4/HTp3zp1GqiyLMEmV5YqwygohrQqzCJMkSZqjzz9PI2xXWCEVRPvtl2Zo1aNJk+CEE2DttWHbbXOnkSrPIkxSZRWLqZzp2TN3ksbR1AQvvADTpuVOIkmSVJXOOgs++wyuvRYGD07Xiy7Knao8/vhHeP/9VPyFkDuNVHmdcgeQ1GAKBejVCzr5n5+KaW6GqVPhlVdglVVyp5EkSaoqH34I55wDO+4I/fqlH5eefBIOPTT9GLX22rkTls7HH8MZZ8DWW8O66+ZOI+XhijBJlVUsui2y0mYNzHd7pCRJ0jeccQZ8+WVaCQbQoQP89a/Qpw/ssAN89FHefKV03HEwYUL6M0uNyiJMUmVZhFXeMsvAvPN6cqQkSdLXvPceXHgh7LEHLLfcV/cXWghuuSWVYDvvnE5ZrHXnnw+XXAKHHZZmoUmNyiJMUmUVChZhldaxY1rn74owSZKk/3LqqTBzJgwa9M3vNTenkuyBB+DEEyufrZRuvz1t9Rw40NVgkkWYpMqJMa0I6907d5LG09QEI0emn/QkSZLEm2/C5ZfDvvvCj3/87Y/51a/g17+G006D4cMrGq9knnkGdtopFXvXXps+I5UamUWYpMqZMCENYHBFWOU1NcH48eknPkmSJHHSSdC5c5qb9V3OPz+VSHvsUXs/Sr3zDmy1VTqr6vbboXv33Imk/CzCJFVOsZiuFmGV19ycrm6PlCRJ4qWX0uqogw+GRRf97sfOMw/cfHMaor/ddjBpUmUyttcXX8CWW6bPoe+4w00Z0iwWYZIqp1BIV/8WrrwVV0wfeTowX5IkiRNPhPnnhyOPbN3j+/ZNxdkLL8ABB6SJH9Vs2jTYfnt49dU09H/FFXMnkqqHRZikynFFWD5duqSfgFwRJkmSGtyIEXDbbXD44dCjR+uf9/OfwwknwNVXw6WXli9fe8UI++8P99+fTon82c9yJ5Kqi0WYpMqxCMuruTkVYdX+EaYkSVIZHX98KsAOPbTtzz3xRNhss7SlcsSI0mcrhTPOSIcAHH887LVX7jRS9bEIk1Q5hQKEAD175k7SmJqa4KOPYOzY3EkkSZKyeOQRuPdeOOYYWGCBtj+/Y8e0RbJ377T18OOPS5+xPa6/Ho49FnbZBU4+OXcaqTpZhEmqnGIxHVnTqVPuJI2pqSld3R4pSZIaUIzphMgf/SjN+ZpbPXqk4fmFAuy6K8yYUbqM7fHYY/DLX8K668IVV6TPnyV9k0WYpMopFt0WmdOqq6afiCzCJElSA7r7bnj88TTnq1u39r3WGmvA+een1WXVsPLqjTdg4ED48Y/T/LOuXXMnkqqXRZikyrEIy2u++WDZZT05UpIkNZyZM9NqsL594Ve/Ks1r7rNPWoF18slw552lec258fHHsMUW0KFDytGWAwCkRmQRJqlyCoU0UEH5zBqYL0mS1EBuvTX9CHTSSekw7VIIAf70p7TofrfdYMyY0rxuW0yenFaCvfsuDBsGSy1V+QxSrbEIk1QZMboirBo0NcE778Ann+ROIkmSVBEzZqTtkMsvn2Z6ldK888Itt6QVZ9tvn4qpSpk5M61I+9e/4K9/hf79K/feUi2zCJNUGRMmwJdfWoTl5sB8SZLUYK65Bl59FU45JZ36WGpLLZWKqGefhYMOKv3rz8nxx8Pf/gZDh8IOO1TufaVaZxEmqTIKhXR1a2ReFmGSJKmBTJ2atkOuthpsu2353mfrreHYY+Hyy9NXuV16KZx+Ouy7L/zud+V/P6meWIRJqoxiMV1dEZZXjx6wxBIWYZIkqSFcfjn85z9w6qlpplc5nXwybLwxHHhgec8muvde2H9/2HzzNKOs3H8uqd5YhEmqDIuw6tHU5MmRkiSp7k2alLZD/vSnsNlm5X+/jh3huuugVy/Ybjv49NPSv8eLL6ZZZCuumLZFdupU+veQ6p1FmKTKmLU10iIsv+ZmeP31NLdNkiSpTl14IXzwAZx2WuVWTfXqBTffDGPHwu67p4H2pfL++7DFFjD//HDHHbDAAqV7bamRWIRJqoxiETp0SD8dKK+mpnSK59GO9hAAACAASURBVAsv5E4iSZJUFuPGpRlam20G665b2fdeay0491y4804YMqQ0rzlhAmy1FXz+eSrBFlusNK8rNSKLMEmVUSxCz57lOapHbTNrYL7bIyVJUp0655y0NbFURVRb7b8/7LYbDBoE99zTvteaMQN23hmefz5th+zXrzQZpUZlESapMopFt0VWiz590so8B+ZLkqQ69MkncNZZ6ZTI1VbLkyEEuPjiNMtrl13g7bfn7nVihEMOgX/8Ay64IG2NlNQ+FmGSKqNQgN69c6cQpJ/MHJgvSZLq1NChaSvhySfnzdG9O9x6K0yfDjvsAFOmtP01zj03nQx5xBFplZmk9rMIk1QZrgirLk1NMGoUTJ2aO4kkSVLJvP9+Wjm1225pNVZuyywDV18NI0aklV1tcdttcPjh6QTKoUPLk09qRBZhksovRouwatPcDNOmpTJMkiSpTgwZkn7EOemk3Em+ss02cOSR8Oc/p1KsNZ56CnbdFdZcE/7613TmlKTS8P+cJJXf+PHw5ZcWYdXEgfmSJKnO/Oc/cOml8Otfw5JL5k7z34YMgQ03hN/8Jg29/y5jxsDWW6epIsOHQ7dulckoNQqLMEnlVyymqzPCqsdSS8H88zswX5Ik1Y3Bg9MB5ccfnzvJN3XqBNdfDwsvnLY6fv75tz/us89gyy3TqrY774RFFqlsTqkRWIRJKr9ZRZgrwqpHhw7p7G2LMEmSVAdeeQX+8hc44IB0QHY1+uEP4aab0gmSe+wBM2f+9/enTk0l2ejRaT7YcsvlySnVO4swSeVnEVadmppg5EiYMSN3EkmSpHYZNAjmnReOPjp3ku/Wvz+cdRbcfvt/D8CPEfbdFx56CK64AtZfP19Gqd5ZhEkqv0IhXd0aWV2ammDSJHjjjdxJJEmS5tpzz6WVVr/9LfTqlTvN9zv4YNhpp7SF84EH0r1TTkmD9AcPTideSiofizBJ5Vcspq14PXvmTqLZNTenq9sjJUlSDTv+eFhoITj88NxJWieENNR/ueVSIXbmmWlF2557wgkn5E4n1T+LMEnlVyymEqxjx9xJNLvll4euXT05UpIk1azHH09D5Y86Cn7wg9xpWm+++eCWW2DyZDjyyHSi5CWXpJJMUnlVrAgLIcwTQngqhPB8CGFUCGFwy/2+IYQnQwijQwh/CyF0qVQmSRVSKLgtshp17gwrr+yKMEmSVJNihOOOS2NoDzood5q2W245+NvfYPvt4dZboYv/EpYqopIrwqYAG8UYVwX6AZuHENYGhgLnxBiXBj4D9q5gJkmVUCw6KL9aNTWlIizG3EkkSZLa5P774ZFH0tbI7t1zp5k7W2yR5pstuGDuJFLjqFgRFpMJLb/t3PIVgY2Am1vuXw1sU6lMkirEIqx6NTXBp5/CO+/kTiJJkqpYjHDOOfCrX8Gbb+ZOk/IceywssQTss0/uNJJqSUVnhIUQOoYQRgIfAvcBbwKfxxintzzkPaBPJTNJKrMY09ZIi7Dq5MB8SZL0Pb78EnbfHQ47DP7ylzRm9JBD4KOP8mUaNgyefhpOOimNPJWk1qpoERZjnBFj7AcsBqwJLNfa54YQ9g0hPB1CeHr69Onf/wRJ1WH8+DQF1Blh1WnlldOJnhZhkiTpW7z/Pqy/Plx7LZx6alpEvtdecMEFsPTScPrpMGlSZTPNmJG2Q/7kJ6mgk6S2yHJqZIzxc+AhYB1gwRBCp5ZvLQaMncNzLokxrh5jXL1Tp07f9hBJ1ahYTFdXhFWneedNk1o9OVKSJH3NiBGwxhrw8svw97+nwfQ/+hH8+c/w0kvppMNjj4Vll4UrrkgFVSXccAOMGgWDB4P/NJTUVpU8NbJXCGHBll93AzYBXiEVYtu3PGxPYFilMkmqAIuw6tfc7IowSZL0X667DtZdN51k+O9/w8CB//395ZdP5dijj8Jii8Hee0O/fnDnneU9g2faNBg0CFZdFXbYoXzvI6l+VXJF2KLAQyGEF4ARwH0xxn8ARwGHhRBGAz2AyyuYSVK5FQrp6tbI6tXUBGPHwocf5k4iSZIymzkTjjkGdt0V1loLnnoqTVKYk3XXTUXZTTelaRhbbgkbbZTmd5XDlVemYf2nnpqmO0hSW1Xy1MgXYoxNMcZVYowrxRhPbrn/VoxxzRjj0jHGHWKMUyqVSVIFuCKs+jU1paurwiRJamjjxsE228AZZ8B++8F990GvXt//vBBg++3TdsXzz0/XNdaAnXeGt94qXb7Jk+Hkk2GddVLhJklzww5dUnkVi+njup49cyfRnFiESZLU8N56C/r3T1sbL7gALroobYtsiy5d4KCDYPToNMx+2LA0ivTQQ+Hjj9uf8aKL0iL2IUNS+SZJc8MiTFJ5FQqpBOvYMXcSzcmCC0Lfvg7MlySpQT30UFrB9f77cM89cOCB7SuaFlgATjklFWJ77plWiS21VFpp9uWXc/eaEyakEyp/9rM0pF+S5pZFmKTyKhadD1YLmppcESZJUgO66CLYdNM0xWLEiFQ0lcqPfgSXXgovvgjrr59mjy27LFx1VdtPmPzjH+Gjj9JqMElqD4swSeVVLDofrBY0N6ePbceNy51EkiRVwLRpsP/+cMABsNlm8MQTadVWOaywAgwfDg8/DIsuCnvtlT6Du+uu1p0w+dlncOaZMGBAGuAvSe1hESapvCzCasOsOWEjR+bNIUmSyu7jj9MqsIsvhiOPTLO8Flig/O+7/vrw5JNw440waRJssQVsvDE888x3P+/MM9NndaecUv6MkuqfRZik8okxzQhza2T1c2C+JEkN4aWXYM014d//hr/+FYYOrewo1xBghx3g5ZfhvPPghRdg9dVh111hzJhvPr5QSNsid9oJVlmlcjkl1S+LMEnlM358OufaFWHVb9FFU2FpESZJUt0aPhzWWSf9ePbII7DbbvmydOkCBx+cJjMceyzcdls6YfKww+CTT7563Omnw5QpMHhwvqyS6otFmKTyKRbT1SKsNjQ1eXKkJEl1KMZUKG2zTSqbRoyonllbP/hBGoD/xhuw++5p9ddSS8Hvfw+vv562b+61FyyzTO6kkuqFRZik8ikU0tUirDY0NaV9CpMn504iSZJK5Msv07bDY49N2wsffRT69Mmd6pv69IHLLoPnn4ef/hSOOgpWXDF974QT8maTVF8swiSVz6wVYc4Iqw3Nzeks85deyp1EkiSVwNixsN56cMMNcNppcO210K1b7lTfbaWV4B//gIcegv/5Hxg0CJZYIncqSfWkU+4AkuqYWyNry6yB+c8+m6bWSpKkmvXUU2kr5Pjx8Pe/w4ABuRO1zQYbwMMP504hqR65IkxS+RQK0KED9OyZO4lao2/fNKjDgfmSJNW0a69NK8HmmSedDllrJZgklZNFmKTyKRahV6/KnsmtuReCA/MlSaphM2bA0Uen0yDXWSetCltppdypJNWTEMIVIYQPQwgvfe3+wSGEV0MIo0IIv5/t/jEhhNEhhNdCCJvNdn/zlnujQwhHV/LPYBEmqXyKRbdF1pqmJnjhBZg+PXcSSZLUBuPGpa2QQ4fCb34D997ronxJZXEVsPnsN0IIGwIDgVVjjCsCf2i5vwKwE7Biy3MuDCF0DCF0BP4E/BxYAdi55bEVYREmqXwswmpPc3M6NfK113InkSRJrfTmm2kF2F13wYUXwkUXQefOuVNJqkcxxkeBT792e3/gjBjjlJbHfNhyfyBwQ4xxSoxxDDAaWLPla3SM8a0Y41TghpbHVoRFmKTyKRQ8MbLWzD4wX5IkVb0HH4Q110w/dt13H+y/f+5EkhrQssC6IYQnQwiPhBDWaLnfB3h3tse913JvTvcrwiJMUnnE6IqwWvSTn6TJug7MlySp6l14IWy6afrc8amnYMMNcyeSVAc6hRCenu1r39Y8B1gYWBv4HXBjCCGUNWU7dModQFKdGj8+bbGzCKstnTrBqqtahEmSVMU+/xwOOACuvx623hquuQYWWCB3Kkl1YnqMcfU2Puc94NYYYwSeCiHMBHoCY4HFZ3vcYi33+I77ZeeKMEnlUSikq0VY7WlqSkVYjLmTSJKkr3nkkfSZ1Y03wimnwG23WYJJyu7vwIYAIYRlgS7Ax8BwYKcQQtcQQl9gGeApYASwTAihbwihC2mg/vBKhbUIk1QexWK6OiOs9jQ1wRdfwJgxuZNIkqQWU6fCMcek7Y9du8K//gXHHw8dO+ZOJqmRhBCuB/4N/CSE8F4IYW/gCmDJEMJLpMH3e8ZkFHAj8DJwN3BgjHFGjHE6cBBwD/AKcGPLYyvCrZGSymNWEeaKsNrT3Jyuzz0HSy6ZN4skSeLVV2HXXdNZNvvsA2efDfPNlzuVpEYUY9x5Dt/abQ6PHwIM+Zb7dwJ3ljBaq7kiTFJ5uDWydq20Uvp42ZMjJUnKKka46KL0GdXbb6dtkJdcYgkmSe3hijBJ5VEsQocO0LNn7iRqq3nmgRVWcGC+JEkZFYuw995wxx2w2WZw5ZWw6KK5U0lS7XNFmKTyKBahVy8HV9Sq5maLMEmSMrnjDlhlFbj/fvjjH+HOOy3BJKlULMIklUex6LbIWtbUlLa3fvBB7iSSJDWMSZPggANgq63SeUNPPw3/939pkb0kqTT8T6qk8igULMJqWVNTuroqTJKkinj2WVhttTQT7PDD4amn0thOSVJpWYRJKo9iMX2UqdrUr1+6WoRJklRWM2bA0KGw9towfnzaDvmHP0DXrrmTSVJ9cli+pNKL0a2RtW6BBWDppT05UpKkMnrnHdhjD3jkEdh+e/jzn2HhhXOnkqT65oowSaU3bhxMnmwRVuuamlwRJklSmVx/fRqI/8wz6UTIG2+0BJOkSrAIk1R6xWK6ujWytjU3w5gx8NlnuZNIklQ3vvgCdtsNdtkFVlgBRo6EX/4SQsidTJIag0WYpNKbVYS5Iqy2zRqYP3Jk3hySJNWJf/4TVl0VbrgBTjoJHn0UlloqdypJaiwWYZJKzyKsPnhypCRJJTF1Khx3HGywAXTqBI89BoMGpV9LkirL//RKKr1CIV0twmrbIotAnz4OzJckqR1eew123TXNAvvVr+Dcc2H++XOnkqTG5YowSaVXLEKHDtCzZ+4kai8H5kuSNFdiTKdAzhq5ecstcPnllmCSlJtFmKTSKxahVy/o2DF3ErVXczO8+ipMmpQ7iSRJNeOjj2DgQPjNb6B/f3jhBdh229ypJElgESapHAoFt0XWi6YmmDkz/QQvSZK+1113wcorwz33wDnnpGufPrlTSZJmsQiTVHrFIvTunTuFSsGB+ZIktcrMmXDIIbDFFmlh/IgRcOihaVqEJKl6+J9lSaVXLLoirF4ssQQsvLBFmCRJ32PIEDjvPDjooFSCrbJK7kSSpG/jqZGSSitGt0bWkxDSqjBPjpQkaY4eeAAGDUqnQ553XvrrU5JUnVwRJqm0xo2DKVPcGllPmprgxRdh2rTcSSRJqjrvvw+77ALLLQcXX2wJJknVziJMUmkVi+nqirD60dwMU6fCK6/kTiJJUlWZPh122gkmTICbb4b55sudSJL0fSzCJJWWRVj9mTUw3+2RkiT9l+OOg3/+Ey65BFZYIXcaSVJrWIRJKq1CIV0twurHMsvAvPM6MF+SpNkMHw6//z3st1+aDSZJqg0WYZJKa9aKMGeE1Y+OHaFfP4swSZJajBkDe+6Zpgece27uNJKktrAIk1RaxSJ06AA9euROolJqakpF2MyZuZNIkpTVlCmw447poOybboJ55smdSJLUFhZhkkqrUIBevdIqItWPpqY0CfjNN3MnkSQpq8MOg6efhquugiWXzJ1GktRWFmGSSqtYdFtkPWpuTlcH5kuSGtgNN8CFF8Lhh8M22+ROI0maGxZhkkqrWHRQfj1acUXo3Nk5YZKkhvXaa7DPPtC/P5x+eu40kqS5ZREmqbQswupTly6pDLMIkyQ1oEmTYPvt0zywv/0tfTYkSapNFmGSSifGNCPMIqw+NTenrZEx5k4iSVLFxAgHHACjRsG118Jii+VOJElqD4swSaUzblw6SskZYfWpqQk+/hjGjs2dRJKkirniCrj6ajjhBNh009xpJEntZREmqXSKxXR1RVh9ampKV7dHSpIaxPPPw0EHwcYbw4kn5k4jSSoFizBJpVMopKtFWH1adVUIwZMjJUkN4Ysv0lywhRdOWyI7dsydSJJUCp1yB5BUR2atCHNrZH2abz5YdllXhEmS6l6MsPfeMGYMPPwwLLJI7kSSpFJxRZik0nFrZP1rbrYIkyTVvfPOg1tugdNPh5/+NHcaSVIpWYRJKp1CATp0gB49cidRuTQ1wTvvwCef5E4iSVJZPPEEHHEEDBiQrpKk+mIRJql0isW0d8AhGvXLgfmSpDr2ySew446w2GJw1VVpNKYkqb5YhEkqnWLRbZH1ziJMklSnZs6E3XdPP87cfDMstFDuRJKkcnBYvqTSsQirfz16wBJLeHKkJKnunH463HUXXHghrLZa7jSSpHJxRZik0ikULMIaQVOTK8IkSXXloYfgxBNh553hN7/JnUaSVE4WYZJKI8a0Iqx379xJVG7NzfD66zBhQu4kkiS12wcfpAJs2WXhkkucCyZJ9c4iTFJpjBsHU6a4IqwRNDWl4vP553MnkSSpXaZPTyXYuHFw000w33y5E0mSys0iTFJpFArpahFW/xyYL0mqEyeeCI88AhdfDCutlDuNJKkSLMIklUaxmK5ujax/ffpAr14OzJck1bQ77kgD8n/9a9hjj9xpJEmVYhEmqTRmFWGuCKt/ITgwX5JU095+G3bfHfr1g/POy51GklRJFmGSSsMirLE0NcGoUWkunCRJNWTqVNhxR5gxI80F69YtdyJJUiVZhEkqjUIBOnSAHj1yJ1ElNDfDtGmpDJMkqYYccQQ89RRceSUsvXTuNJKkSrMIk1QaxSIssgh07Jg7iSrBgfmSpBp0001w/vlw6KGw7ba500iScrAIk1QaxaLbIhvJUkvB/PNbhEmSasbrr8Pee8Paa8PQobnTSJJysQiTVBqFgkVYI+nQIU0Y9uRISVINmDQJtt8eunSBG29MV0lSY7IIk1QaxSL07p07hSqpqQmefz5NG5YkqYoddBC89BJccw0svnjuNJKknCzCJLVfjG6NbERNTekj9jfeyJ1EkqQ5uvLK9HXccbD55rnTSJJyswiT1H5ffAFTpliENZrm5nR1e6QkqUq98AIccABstBGcdFLuNJKkamARJqn9isV0tQhrLMsvD127OjBfklSVxo1Lc8EWXBCuu86DrSVJSafcASTVgVlFmDPCGkvnzrDyyhZhkqSqEiM89BAMGgRvvgkPPuhndZJUL0KgCdgQWISvLe6KkSNb8xoWYZLazxVhjaupCW6+Of2rI4TcaSRJDWzKFLj+ejj33HSWS69ecNllsP76uZNJkkohBI4EzgDeBopAnO3b8Vuf9C0swiS1X6GQrhZhjaepCS69FN55B/7f/8udRpLUgD76CC6+GP70p/TZ3IorpgJs111hnnlyp5MkldBvgf1j5M/teRGLMEntVyymwRs9euROokqbfWC+RZgkqYJGjUqrv665BiZPTidCHnYYbLyxi5QlqU51AB4oxYtIUvsUi2n/gVNoG8/KK0OHDs4JkyRVRIxwzz2p9FpppVSC7bEHvPwy3HUXbLKJJZgk1bGLgL3a+yKuCJPUfoWC2yIb1bzzwnLLWYRJksrqyy9T6XXuuan06t0bTj0V9tsPevbMnU6SVCGDgTtD4DngJWDa7N+MkV+15kUswiS1X7HoiZGNrLk5HcklSVKJFQpp9tfFF8PHH0O/fnD11fCLX0DXrrnTSZIqbAiwKfAssBBtGJA/O7dGSmq/YtEVYY2sqQnefx8+/DB3EklSnRg5EvbcE5ZYAoYMgf794aGH0kjKPfawBJOkXEIIV4QQPgwhvDTbvZNCCGNDCCNbvraY7XvHhBBGhxBeCyFsNtv9zVvujQ4hHN3Ktz8A2CVG1oiRrWJk69m/WvtnsAiT1D4xWoQ1uqamdHV7pCSpHWbOhNtvh402Sn+13HJL2vr42mswbBhssIHzvySpClwFbP4t98+JMfZr+boTIISwArATsGLLcy4MIXQMIXQE/gT8HFgB2Lnlsd/nS6Dd/+iwCJPUPl98AVOmWIQ1sllF2LPP5s0hSapJEyem7Y/LLQcDBsAbb8DQofDuu3D++bDMMrkTSpJmiTE+CnzayocPBG6IMU6JMY4BRgNrtnyNjjG+FWOcCtzQ8tjvcw5waAi062MRZ4RJap9iMV2dEda4FlwQ+vZ1RZgkqU3eew8uuAAuuQQ++wzWXBOuvx622w46d86dTpLURgeFEPYAngYOjzF+BvQBnpjtMe+13AN492v312rFe6wLrAdsGQIv881h+QNaE7T1K8JCOJ8QvrkbP4RFCOGOVr+OpPoyqwhzRVhja2qyCJMktcrrr8Muu6TPUM48E372M3j8cXjiCdhpJ0swScqsUwjh6dm+9m3Fcy4ClgL6AR8AZ5Up28fArcCDQAH45GtfrdKWFWGbAxsQws7EmIaihbAVcDnwchteR1I9KRTS1SKssTU3w623pq2yP/hB7jSSpCo1eTJsvnk6AfLgg9NX3765U0mSZjM9xrh6W54QYyzO+nUI4VLgHy2/HQssPttDF2u5x3fc/473Ya+25JqTtswI6weMAEYQwmGEcBFwC3AusFEpwkiqQW6NFHw1J+z55/PmkCRVtXPOgTFj0mcnZ59tCSZJ9SCEsOhsv/1fYNaJksOBnUIIXUMIfYFlgKdI3dIyIYS+IYQupIH6w7//fegQwlc9Vgj0DoFfh0D/tuRt/YqwGCcCvyKE94A/ANOBTYjxkba8oaQ6UyxCx47Qo0fuJMpp9pMj11svbxZJUlV6/30YMgQGDoSNN86dRpI0N0II1wMbAD1D6ocGARuEEPoBEfgPsB9AjHFUCOFG0i7C6cCBMcYZLa9zEHAP0BG4IsY4qhVvfwdwN/DHEJiPNI+sOzBfCOwdI39p1Z8hxtjKPy4QwuHAqcD1wBpAF2BXYny69S/Sft27d48TJ06s5FtKmpNf/xruuAM++CB3EuXWpw/8z//AjTfmTiJJqkK//GUahj9qFCy9dO40kqRvE0KYFGPsnjvHtwmBj4CNYuTFENgDOBpYFdgVOCxGVmnN67RlWP59wFHATsT4K2B14F7gMUI4ro35JdWLYtH5YEq22gruvDMNgJEkaTZPPQVXXw2//a0lmCRprs0HfN7y602B22JkGml4/lKtfZG2zAiLwKrEOCz9Lk4hxoNJ+z8PasPrSKonxaLzwZRstx1MnAj33ps7iSSpisQIhxySPjc7zo/PJUlz7x3gf0KgO7AZcF/L/YWBSa19kdYXYTFuSozf3PsU413Ayt/39BDC4iGEh0IIL4cQRoUQDmm5f1IIYWwIYWTL1xatziQpP1eEaZYNNoAFF0wTkCVJanHddfDEE3D66TD//LnTSJJq2NnAX4H3SKdMPtpyfz3gxda+SOuH5X+XGD9uxaOmA4fHGJ8NIcwPPBPSdkuAc2KMfyhJFkmVEyMUChZhSrp0gQEDYPhwmDYNOnfOnUiSlNnEiXDUUbDaarDnnrnTSJJq2f/H3p3H2Vi/fxx/3fYShRJCWnwraVeytCkqSZjiK5UklYoUhTbttFrqm6WSpawhQhQilazZKnt2cyL7WGfm8/vjGj8qzJmZc859lvfz8ZjHGWfOuc81Y+bM3Ne5Fufo7XnMAcoC3zpHesaHVgIvBHuc41eEed5OPO/UjPd3Zfz76G+ZBuw2OefmZby/C/gdOCPYQEUkCu3YAQcOqDVSDmvQALZtg+++8zsSERGJAm++CRs2QPfukCsrQ1lERET+IWNA/mLnGOUcu4/40LdkYUZYZhVhrYBdGe+HbA6Y53nlgMuAmUA14HHP8+7DVl+2dc5tC9VjiUgYBQJ2qYowOaRWLShY0Noja9XyOxoREfHR6tXw9tvQuLEtFRYREcmhT4EJwJ//uL5QxscGBHOQ478u41x/nNuf8a/6wG5gcMb1f38Lkud5JwEjgDbOuZ1ATyxzdymwCXj3GPd7yPO8OZ7nzUlNTQ324UQknJKT7VKJMDnkhBPgtttg1ChIS/M7GhER8dEzz4DnWVWYiIhICHjYIsd/KgvsCPYgWSlQ3gP0BwJ43sd43nVZuC8AnuflxZJgnzvnRgI45wLOuTTnXDrwEXDV0e7rnOvjnKvknKuUJ09oRpuJSA6pIkyOpkED+PNP+OknvyMRERGfTJsGw4fbfLAyZfyORkREYpnnscjzWIglwaZ5HguPePsVmA5MCvZ4wWeUnLsbzyuIVYbdDXyL520CBgOf4dzi4wfuecAnwO/OufeOuL6kO7yNsj5w3OOISBQ5lAjTjDA5Uu3akD8/jBgB11zjdzQiIhJhaWnQpo0lwJ5+2u9oREQkDnyRcVkRGAd/mw92AFiNFV0FJWulVc6lAJ8Bn+F5pwGNgEeAdkEcqxpwL7DI87z5Gdc9CzT2PO9SLLO3Gng4SzGJiH+SkyF3bihWzO9IJJoUKmTzwUaOhK5drS9GREQSRt++MH8+DBkCJ57odzQiIhLrnONlAM9jNTDUOfbl5HjZ6zH0vAJADeBm4D/Auszu4pz7Aevn/Kfx2YpBRPwXCMBpp2kNlPxbUhJ89RXMmQNXXul3NCIiEiE7dsBzz0H16tCwod/RiIhIPHGO/gCeRw2gQsbVvznHlKwcJ/hEmLU21gSaAPWANGA4cCPOTc/Kg4pInAgE1BYpR3f77ZAnj1WFKREmIpIwXn0VtmyBCRNUECwiIqHleZyFtUBeDGzMuLqU57EISHKOVcEcJytlHJuAL4GTgPuBEjj3sJJgIgksENCgfDm6okXhhhtsTpg72mIXERGJN0uXQvfu8MADcPnlfkcjIiJx6BNgF3C2c5R1jrLA2cB24ONgD5KVRNgLufGYxgAAIABJREFUQCmcS8K5UTh3IEvhikj8SU5WIkyOrUEDWL4cfv3V70hERCQC2raFE06A11/3OxIREYlTVYDWzrH20BUZ7z+Z8bGgBJ8Ic+4jnNuelQhFJI45p9ZIOb569awvZkTQC1xERCRGTZgA48bBCy/oNTIREQmbtcAJR7m+AEHMrj9EE65FJHt27IADB/TXrhxbiRJQrZoSYSIice7gQXjySTj3XGjd2u9oREQkjrUFengeV3seuT2PXJ7H1UC3jI8FJXtbI0VEkpPtUokwOZ6kJDs7Wr4cypf3OxoREQmDDz+EJUtgzBjIn9/vaEREJI4NBvIDPwLpGdflwpY5fn7kkhbnKHysgygRJiLZEwjYpRJhcjwNGlgibORIaN/e72hERCTEtmyBl16CWrWgTh2/oxERkTj3eCgOokSYiGTPoUSYZoTJ8ZQtC5UqKREmIhKnXnwRdu2Crl1tLKSIiEgYzQbSnGMpgOdRE2gK/Aa86RxpwRxEM8JEJHtUESbBSkqCWbNgXdDzK0VEJAYsXAi9e8Ojj0KFCn5HIyIiCaAvcBmA51EG+BIoCjwKvBbsQZQIE5HsSU6G3LmhWDG/I5Fo16CBXY4a5W8cIiISMs5BmzZwyinWGikiIhIB5wPzMt6/E5jlHLWBe4HGwR5EiTARyZ5AAIoXh1x6GpFM/Oc/ULGitkeKiMSRL7+E776DV16BokX9jkZERBJEbuBAxvs3AuMz3l8JBN2qpDNYEcmeQEBtkRK8Bg1g+vTDLbUiIhKz9u2Dtm3hwgvh4Yf9jkZERBLIYqCl53ENlgibkHH9GcCWYA+iRJiIZE9yshJhErykJOujGT3a70hERCSHunaFP/6A7t0hj1ZviYhI5LQHWgBTgcHOsSjj+rrArGAP4jnnQh9amBUsWNClpKT4HYZIYitbFm64Afr39zsSiQXOQfnycM45MHGi39GIiEg2bdxoHe81a2r0o4hIPPI8b49zrqDfcRyL55EbKOwc2464rhywxzn+DOYYqggTkaxzzlrcSpTwOxKJFZ5nVWFTpsC2bZnfXkREotKzz8LBg/DOO35HIiIiicg50o5MgmVctzrYJBgoESYi2bF9Oxw4oNZIyZoGDSA1Fb76yu9IREQkG2bNskLwJ5+0Al8REZFYpESYiGTdoYHnSoRJVlx5JZQuDSNH+h2JiIhkkXPwxBNWDP7cc35HIyIikn1KhIlI1h1KhKk1UrIiVy6rCps4EXbv9jsaERHJgkGD4Oef4Y03oFAhv6MRERHJPiXCRCTrVBEm2dWgAezbB19/7XckIiISpN274Zln4IoroGlTv6MRERHJGSXCRCTrkpPtUokwyarq1eG002DECL8jERGRIL35pm2L7NHDintFRERimX6ViUjWBQKQOzcUK+Z3JBJrcueGevVg3DirDBMRkai2erVtiGzcGKpW9TsaERGRnFMiTESyLhCA4sX1srBkT1KS9dl8+63fkYiISCaeeQY8z6rCRERE4oHOYkUk65KT1RYp2XfDDXDyydoeKSIS5aZNg+HDoUMHKFPG72hERERCQ4kwEcm6QECJMMm+fPmgbl0YPRoOHvQ7GhEROYq0NGjTBsqWhXbt/I5GREQkdJQIE5GsCwSgRAm/o5BY1qABbNsGU6f6HYmIxAjnoGtXuPNOWLPG72jiX9++MH8+vPUWnHii39GIiIiEjhJhIpI1zqkiTHLu5pvtzErtkSIShIMHoUULeOop+PJLuOgi6NfPfiVJ6O3YAc89Z4t+Gzb0OxoREZHQUiJMRLJm+3Y4cECJMMmZE06A2rVh1CjrvxEROYbt2+HWW+GTT+D552HZMrjsMmjWzHZvbN7sd4Tx59VXYcsW6N7dBuWLiIjEEyXCRCRrAgG7VGuk5FRSkn0/zZjhdyQiEqX++AOqVoXvv7cKsFdfhbPPhilT4O23Ydw4qFgRxo71O9L4sXSpJcAeeAAuv9zvaEREREJPiTARyZpDiTBVhElO3XabDc4fMcLvSEQkCs2YAZUr26Lib76Bpk0Pfyx3bhvgPmcOlCwJt99urZO7dvkXb7xo29aKdl9/3e9IREREwkOJMBHJmuRku1QiTHKqUCGoVcvmhGnQj4gcYdgwuOEGKFzYEmLXX3/02110EcycCe3bW+vkJZfADz9ENNS4MmGCVdm9+KJ+zYuISPxSIkxEskYVYRJKSUmwdi3Mnet3JCISBZyDN96ARo2gUiX4+Wc477zj3yd/fujSxdonPQ+uvdYSY/v3RybmeHHwIDz5JJQvD61b+x2NiIhI+CgRJiJZEwhYT0qxYn5HIvHg9tvt+0nbI0US3oED0Ly5bSu8+26YPBlOPTX4+1evDvPnw4MPwltvwVVXwaJF4Ys33nz4ISxZAu++a13rIiIi8UqJMBHJmuRkKF4ccunpQ0KgWDHrfxoxQu2RIgls2za45Rb49FPo1Ak++8wqvbKqUCHo0we++spet6lUyYbqaznt8W3ZAi+9ZN3qder4HY2IiEh46UxWRLImEFBbpIRWgwawbBn8+qvfkYiID1auhCpVbLbXgAGWkPG8nB2zTh2rBrvtNnjmGcu3//FHSMKNSy++aIsGunbN+ddeREQk2ikRJiJZEwhAiRJ+RyHxpF49O/NSe6RIwvnxR7j6ati8GSZNgnvvDd2xTzvNik379bOWyYsvhr59VXx6yIEDtoigc2fo3RsefRQqVPA7KhERkfDzXAz+NVCwYEGXkpLidxgiialsWahRw84sREKlenUrR1iwwO9IRCRCBg+GZs3s18q4cTakPVzWrIH774epU6FuXfjoI+vyTyS7dlnia/p0e5s5E/bts49deaVtjCxa1N8YRUTEf57n7XHOFfQ7jnBSRZiIBM85tUZKeCQlwcKFsGKF35GISJg5B6+9ZgPxK1e25Ew4k2AAZ55pw/ffew8mToSKFWH06PA+pt8CAauIa9PGZqWdcgrcfLNVgKWkQMuW9vFAAGbNUhJMREQShyrCRCR427bZX8rvvgtPPeV3NBJPVq+Gs86CN9+0gT4iEpf274eHHrJZYPfcAx9/nL2h+Dnx66/22PPnW0Vat25QuHBkYwg152DVqsPVXj/8YKMXAU44wdpPq1eHa66x9wsV8jdeERGJXolQEaZEmIgEb8kSuOAC+PxzeylfJJQqVYI8eeDnn/2ORETCYOtWqF8fvv8eXn4ZXnjBv8HsBw5YDF26WGtm//5w7bX+xJIdaWm2DODIxNemTfaxIkUOJ72uuQYuvxzy5fM3XhERiR2JkAjL43cAIhJDkpPtUq2REg5JSfDss7B+PZQu7Xc0IhJCK1ZA7do2qysaXkvJlw9ef922St53H1x/PbRtay2bka5QC8a+fTB79uHE108/wc6d9rEyZWwr5qHE1wUXQC4NPxERETkmJcJEJHiBgF0qESbh0KCBJcJGjYJWrfyORkRCZPr0w8thp0yBatX8juiwqlWtRbJdO3jnHRsY/9lncMkl/sa1fbsluw5Ve82aZVVsABdeCI0bH058lS3rb6wiIiKxRq2RIhK8Hj3giSdsz/2pp/odjcSjihXte2vqVL8jEZEQ+OwzaN4cypWzzZDnnut3RMc2frzF+tdf8Mor8PTTkDt36B8nLc1+jW7YABs32tuh9zdsgLVr4fffbe5XnjxwxRWHk17VqkGxYqGPSURE5BC1RoqIHCkQsLMCrZaScGnQwPqV/vwTihf3OxoRySbnbAbXyy9b2+GIEdH/q6N2bZu71bIldOwIY8faUP+zzw7u/s5ZJdc/k1v/THQlJ1sy7Ei5clmx9RlnWLKwUSNLfFWuDCeeGPrPVUREJJGpIkxEgte8OXz9tf01LxIOCxbApZdCnz7QooXf0YhINuzfDw8+aNVgTZvaj3MsDWt3zuaYPf44pKZC167QpIkNo/9nUuufia69e/99vKJFoVQpezvjjL9fHnq/eHGr/hIREfFbIlSEKREmIsGrU8f+0p83z+9IJF45Z+UQ5cvbsB4RiSlbtthmyB9+sOLOjh392wyZU+vWwf3321yzoznhhH8ntv6Z4CpZ0m4nIiISKxIhEabXnkQkeIGABuVLeHmebY/s2tV6jE45xe+IRCRIy5ZZe+H69TBkiLX3xbIyZeDbb2HgQHsN6J9VXSefHLtJPhERkUSmRJiIBC852dZViYRTgwbw9tvw1Vdw771+R5NQZs2y2UVXXqk2LcmaadOsEix3bqugqlrV74hCI1cua+8UERGR+JHL7wBEJEY4ZwPMVREm4XbVVVZyMXKk35EklN69bTB31ao206huXejeHX791X78RY5lwACoWdN+PcycGT9JMBEREYlPSoSJSHC2b4cDB6BECb8jkXiXK5dVhU2YALt3+x1NQujbFx55xNrahg2Du++G33+HNm2gYkVrA7vnHujXz+YmiQDs2AEPPWQVU9dcAzNmBL9hUURERMQvSoSJSHCSk+1SFWESCQ0awL59GpgfAZ99Zhv+ataEESPgrrugVy9Yvhz++AM+/hhuuAG++QaaNYOyZeG88+Cxx6xob9s2vz8D8cO4cdYp/8kn0K6dLRTWSD8REZH453leX8/z/vQ8b/FRPtbW8zzned6pGf/2PM/r4XneCs/zFnqed/kRt23qed7yjLeIDiLQ1kgRCc7UqXY2PGkS3Hij39FIvEtLs3VrN94Igwf7HU3cGjYMGjeG666DsWPhxBOPfdv0dFi8GCZPtqeBadMgJcUK+K64wv6rbroJqlWDAgUi9zlIZG3dapWCAwdaIqxvX+tmFhERkfiQ2dZIz/OuBXYDA5xzFY+4vgzwMXA+cIVzbovnebWBVkBtoDLQ3TlX2fO8osAcoBLggLkZ94nIS6yqCBOR4AQCdqnWSImE3LnhjjssO7Nvn9/RxKVRo6wFsmpV20twvCQYWMLr4ovhySetGmjrVpg+HV54AfLnh3fesURYkSJ22aULzJljOU2JDyNHQoUKlpt+4QWYO1dJMBERkUTjnPse2HqUD3UFnsESW4fcgSXMnHPuZ+AUz/NKAjcD3zrntmYkv74Fbglz6P9PiTARCc6hRJhaIyVSkpJsRtikSX5HEnfGjoVGjWw75PjxUPCYr/kdW758UL06vPSSJcS2brUEWcuWtlejY0c7/qmn2n/lhx/CsmUavB+LAgFo2ND+H0uVgtmz4ZVXLAEqIiIi4nneHcAG59yCf3zoDODICbPrM6471vURoeXoIhKc5GSr0ila1O9IJFHUqAEnn2yDq+rU8TuauDFxoiU0Lr7Y5joVKhSa4xYqZMP2a9e2fwcCMGWKtVJ+++3hJaBlyhxuo7zxRhWZRjPnrPqrdWvYtQtefx2efhry5vU7MhEREQmjPJ7nzTni332cc32OdWPP804EngVqhT2yEFEiTESCEwhA8eLWHyUSCfnywe23w5gxcPCgzr5DYMoUqFcPLrjAht+Hc7j56afb/LHGjS2hsnLl4fliY8bYBso8eSwxV6NG+OKQ7Nmwwar7vvoKKle2WWAVKvgdlYiIiERAqnOuUhZufw5wFrDA8zyA0sA8z/OuAjYAZY64bemM6zYA1//j+qnZDzlrdEYrIsEJBFS6IZHXoIH13E2b5nckMW/6dMsrnnOOJaMiWdzpeXDuufDwwzB8OGzebPOlSpWCTp0iF4dkzjlLel14oX2fvPsu/PijkmAiIiJydM65Rc654s65cs65clib4+XOuWRgDHBfxvbIq4EdzrlNwESglud5RTzPK4JVk02MVMxKhIlIcJKTNR9MIu/mm22K+6G+OsmWGTOsZbFsWavKOvVUf+PJlQsuvxzatYMffrA38d/q1fYj17w5XHopLFwITz1lXfEiIiIiAJ7nDQZmAOd5nrfe87zmx7n5eGAVsAL4CHgUwDm3FXgVmJ3x9krGdRHhuRicWluwYEGXkpLidxgiieXQYJ9+/fyORBLNnXdaScqGDWrNzYbZs20eV/HiVlhXqpTfER22Zw+ceaa13o0d63c0iSs9HXr2hPbtrXrvrbesek8/biIiIonH87w9zrlsrFKKHfoTR0Qy55xaI8U/SUlWkThjht+RxJxffoFataBYMZsPFk1JMLBivyeesG2TCxf6HU1iWr4crr8eHn8cqlWDxYttNpiSYCIiIhKv9GeOiGRu2zYbVq7WSPHDbbfZ4PwRI/yOJKYsWgQ1a9o2xylTrKgzGj32GJx0EnTp4nckiSUtzeZ/XXyxJSH79oUJE6xCT0RERCSeKREmIpkLBOxSiTDxQ+HCltEZOdKqEyVTv/9uncz588N330G5cn5HdGxFilgF0tChsGqV39Ekht9+s+qvdu3sR+u336BZM2uLFBEREYl3SoSJSOaUCBO/JSXBmjUwb57fkUS9ZcugRg1rbZsyxbZERrs2bSBPHnj7bb8jiW8HD8Lrr8Nll8GKFTBoEIweHX0tsyIiIiLhpESYiGTuUCJMM8LEL3Xr2uo6bY88rlWrLAmWmmrbIc87z++IglOqFNx/P3z6qY2Dk9CbPx+uugqefx7q17cqsMaNVQUmIiIiiUeJMBHJ3KEzU1WEiV+KFbOJ3iNGqD3yGNassSTY3r0waRJceKHfEWXNM89YxVLXrn5HEl/274cXXoArr4RNmyyXPGSIbREVERERSURKhIlI5gIBq8YpWtTvSCSRNWgAS5daKYv8zfr1lgTbvh2+/RYuucTviLLunHOgYUPo2dM+D8m5mTPh8svhtdegSRP70alf3++oRERERPylRJiIZC4QsGqwXHrKEB/Vr299XGqP/JtNm2ww/ubNMHGiJT5iVfv2sGsXfPih35HEtj174OmnoWpV2LkTxo+Hfv30WoaIiIgIKBEmIsFITlZbpPivZEmoUsXaIwWAP/+0JNiGDfD111C5st8R5cyll8Ktt0K3bpbMkaybOtUqAt95B1q0gF9/ta+piIiIiBglwkQkc4cqwkT8lpQECxbAypV+R+K7v/6Cm26C1ath3DioVs3viEKjY0erbuvb1+9IYseePfb1uvJKuOEGSE+3jaG9ekHhwn5HJyIiIhJdlAgTkcwFAtoYKdHh0ICjBG+P3LYNataEZctgzBi47jq/Iwqd6tWtpe+dd2x4fkgsXw5vv23ZwssuswnycWDJEmjTBs44A5o3t4TY++/DwoWWEBMRERGRf1MiTESOzzlVhEn0OOssG4KVwImwHTvg5put5W3UKKsKiyeeZ1Vha9bYdsNscQ7mzIHnn4eKFeE//7G1lJs3w/z58NVXIY05kg4cgGHDLNF1wQU2T+3WW+H772HxYnj8cShY0O8oRURERKKXEmEicnzbtllZhhJhEi2SkuDnn21VYoLZtQtq14ZffoHhw+N39tNtt8FFF0GXLtbmF5SDB2HyZGjVCsqWtT7BLl2geHHo3t16SH//HUqXhk8/DWf4YbFmjeX1ypaFRo3s0+nc2X4MBg2Ca66xJKKIiIiIHJ8SYSJyfIGAXSoRJtGiQQO7/PJLf+OIsJQUqFMHZs60Sqm6df2OKHw8Dzp0gN9+y6R4KyXFyuLuu8+eo266CT75BCpVsjWJgYANy2rdGs48E3LnhqZNYcIE2LgxUp9OtqWl2cbH22+Hs8+2xNdVV9l1K1fa16h4cb+jFBEREYktnnPO7xiyrGDBgi4lJcXvMEQSw9Sp1oMzeTLUqOF3NCLmwgstA/Ddd35HEhF791oy5Lvv4LPPoHFjvyMKv9RU62gsXhxmzDii2mnLFhg71hJg33wD+/ZB0aL2BapXD2rVghNPPPaBV6yA8uWtWqx9+4h8Lln15582/L53b6v8Ov10ePBBeOghqwgTERERCRfP8/Y45+J60EIevwMQkSiXnGyXqgiTaNKgAbzxhs18Ou00v6MJq/377dOdMsWKnBIhCQaQJw88/TQ8+ihMG5rM9YGhlvyaPt36JcuUscxQvXrWF5gnyD9pzj3Xbt+3r80Ni5J+QufsU+vZE0aMsE7PG26At96CO+6AfPn8jlBEREQkPqg1UkSOT62REo2SkiwZMnq035GE1YEDcNdd1sn30UfWAZgQnIOFC2m28XVOz7OFzo0X2HrEv/6C556DuXNtaFb37pYtCjYJdkizZrZyc8aM8MSfBTt2wAcf2Ey0666z/+tHH7VxZlOm2P+/kmAiIiIioaOKMBE5vkDATjKLFvU7EpHDLrnENkiOGGE9Y3Ho4EGr/vrqK9sM2Ly53xGFWVoa/PSTzX778ktYtYoCnseTZYvSYU1L5o5ayxX1yoTmse66y4bqf/opVK0ammNm0bx5Vv01aBDs2WOz/fv2tUH4x+vsFBEREZGcUUWYSBY5Z4Oq5871O5IISU62IT259HQhUcTzrCps8mTYvt3vaMLi0Udh5Ejo1g1atvQ7mjDZt8/mfT34IJQsCddea+VR558PffrApk08sqAlhQvDm4NClAQDOOkkaNjQnswjOHN0715rb61cGa64Aj7/3JKdc+bArFlWqKYkmIiIiEh46cxWJAtSU20kTePGtpTs1lvhhx/8jirMAgG1RUp0uusuK5v64AO/Iwm5wYPh44+hY0d44gm/owmTlSuhdGkbcj98uG18HDrUhuGPGwctWsDpp3PyyfDYY/DFF9bNGDLNmsHu3VZVGGZLl8KTT0KpUvawu3ZBjx62uPLjjy0pJiIiIiKRoa2RIkFKSbGWlXHj7OS0cGF47z2b1X3ddTa25qabombucuhUqmTDyL/+2u9IRP6tYUMYMwYWLrQVg3Fg1Sq47DJbjPn991kffxUzHnvMskCjRtmT53EGYQUCUK4cNGlidwkJ5+x7pnTpsG0f/eEH6NTJZn3lzWtLD1q2tMK3uPtdISIiInEhEbZGqiJMJAh//mnzmL/+Gnr1smV1HTrYWvtu3WD5cqhVC66+2s7JYzC/fGyBAJQo4XcUIkfXvTsUKGClmunpfkeTYwcPwt13W5Jk0KA4ToL99ZfN57rnHqhdO9Np8KefDg88AAMGwPr1IYrB86w8a+pUyz6G2NKlVjW8bBm8/jqsW2edmNddpySYiIiIiJ+UCBPJxMqVUK0aLF5shQsPP3z4YyeeaG1Lq1ZB795WHXbHHTbHe+hQm/0c05xTa6REt5Il4e23Ydo0S6zEuE6dYOZM2xBZrpzf0YRR7942MOvJJ4O+y9NPW66za9cQxnHffTb/sF+/EB7Uht/feaflaGfMgGef1dOoiIiISLRQIkzkOGbPhipVYNs2m8ldt+7Rb5c/vxWkLFtmFQsHD8J//wsVKtj51cGDEQ07dLZts+B1BifRrHlz6zVr186WO8SoyZOhSxebG3/XXX5HE0b798P771sZbcWKQd+tXDmbz9i7txWUhUTp0lCzJvTvH7KKQues/fHXX62qr3TpkBxWREREREJEiTAJvX37YNEiv6PIsfHj4frrbbnYTz9ZQiwzefLAvffaCdDw4VYx1qwZlC8PPXvalyamBAJ2qdZIiWa5ctmGwb17Y3ay/ObN9txx3nnWbh3Xhg61hOVTT2X5ru3b27zGkO5HeOABWLvWBnmFwCef2AsiL71kOTYRERERiS5KhEnoPf+8TXresMHvSLKtb1+r/jr/fEuCZXUGd65c1hYzbx6MHWvdW48+CmefDe++a4vKYsKh6hpVhEm0O+88e+4ZNsx+6GKIc5aL+esvmyFVMJ5HkzpnW0YqVLCKsCyqWNGWTPboEcLn0bp1oUgRe+LPoV9+gccfh5tvtm9HEREREYk+SoRJaO3aZcNt0tJsoFaMcQ5eecU6rW680WYo56QYyvPgttssmTZ5MlxwgXVvlStnw5O3bw9V5GFyqCJMiTCJBc88Y6sWW7a056IY8cEHlrt75x2bLxjXvvsOFiywarBsTozv2BG2bg3h9sgCBWxDwahROXpS3r7dXgA57TT47DN7QUREREREoo/+TJPQ6tcPdu6EokVhxAi/o8mS1FQbhN+pk81PHjsWChUKzbE9D2rUsGTYTz/Zdsnnn4czz7TLLVtC8zghp9ZIiSX58lkifsOGmCnHWbDAkuN16lglUdx77z0oXhyaNMn2IapUsc2L774LBw6EKK5mzax3fciQbN3dObj/fuuwHD4cTj01RHGJiIiISMgpESahk5YG3bvbWcpjj8H339vgmxiQkgL169s59LPPWj4vb97wPFaVKpZkmzfPOoPeeMMSYk89BRs3hucxsy0QsMFnRYr4HYlIcKpUsT7k99+39YtRLCXFlmoUK2YLL7NZIBU7fv8dxo2z3w8FCuToUB07wvr1VnkVEpdfDhdfnO3No+++C6NH2+XVV4coJhEREREJCyXCJHTGjYOVK6FNG0hKsg1cX37pd1SZ2rzZ2iDHj4cPP7SWxUickF52mVUO/Pqrfbl69ICzzrKurtWrw//4QUlOtuoN9fhILHnjDShVClq0iOqVrW3awNKllsxJiAqibt1sxW7Lljk+VK1a9hz65pv2GkyOeZ5Vhc2aZU/KWTB9OnToYJs+W7UKQSwiIiIiElY6u5XQ6dYNypSBBg3slfVzzon69siVK6FqVWtPGjEiJOdnWXbBBbZhbNkya6355BM491x7f+nSyMfzN4GA5oNJ7Clc2LLaixbB22/7Hc1RDRtmM646drS26bi3ebM90d13nw3RyiHPs+TTsmUhfL2lSROrgM1CVVggAI0a2SKUjz9OgKo+ERERkTigRJiExoIFNgS5VSs7kfA8K3OaPBm2bfM7uqOaM8eSYFu3Wpj16vkbz9lnQ+/esGqVzQoaNsySZI0a2ZfXF4GA5oNJbKpb1yaXv/KKZUuiyOrV8NBDULkyvPSS39FESK9eNoOrTZuQHTIpCcqXh86dbUZXjp12mq2kHDgwqErCtDRo3NiG5I8YYflXEREREYl+SoRJaHTvDieeCA8+ePi6pCSbQD9mjH9xHcOECXD99XDCCTa8vmpVvyM6rHRpK65bvRrat4evv4ZLL7Xz+iVLIhxkspurAAAgAElEQVRMcrIqwiR29ehhs6gefjhEmZKcS021BYXOweDB4ZtFGFX27bPVmLfeChUqhOywuXPbotC5c2HSpBAd9IEH4M8/7Yk3E5062es/PXvCRReF6PFFREREJOyUCJOc+/NP+Pxz6+U7cqj6lVdaq2SUtUf262cb2sqXhxkz4Lzz/I7o6IoXt0qHNWvg5Zdt98DFF9syvL17IxCAc/Z/q0SYxKqSJeGtt2Dq1GwPQQ+1l1+2551evWwmYEIYPNieS556KuSHvvdeGwfXpUuIDnjLLVYF27fvcW82bpzNk3zwQWjaNESPLSIiIiIRoUSY5FyvXrbDvnXrv1/veTYv7JtvYNcuf2I7gnPw2ms2D7lGDZg2zc6To12RIvDii1YN1qiRnXxdeKGdiIXVtm3WHqTWSIllDz4I11wD7dpZq6+Ppk61n99mzaylLiE4B++9Z1n8G28M+eHz57f82pQpNuc+x/LksezauHGWvDuKNWvsJpdeakWHIiIiIhJbIpYI8zyvjOd533me95vneb96nvdExvVFPc/71vO85RmXRTI7lkSR/fttKHXt2kcvrUpKstuEPWtzfKmpNgj/hRfgnntg7NjYm+dSooSNrpkyxU7+6tSxPOO6dWF6wORku1RFmMSyXLmgTx9ISYEnnvAtjC1bbBZ7+fIJljyZNAkWL7ZsVZgmyT/0kL1g0LlziA7YrJn90vjss399aP9+2w6Zng5ffGHt9SIiIiISWyJZEZYKtHXOVQCuBh7zPK8C0AGY7JwrD0zO+LfEiqFDrcriWAOQq1a1DI6P7ZF79lg+rndv2zI2YADky+dbODl2ww02PP+NN2zW2QUX2GK8IGY7Z82h6hklwiTWnX++9RQPHepLUt45aN7ckmFDhsBJJ0U8BP+8+679Dvjvf8P2EIUK2YKRL7+E334LwQEvuACuvtraI/8xW65tW5g921rszzknBI8lIiIiIhEXsUSYc26Tc25exvu7gN+BM4A7gP4ZN+sP+Ly7T4LmnE11r1ABbrrp6LfJnRvq14fx4y0jFWFbtlg3zldf2azmzp3jY719vnzQsaOd9NWoYQOjL7sMpk8P4YMoESbxpH176ylu2TLirdoffmg7Q958035OE8bixTBxomWp8ucP60O1bm37Wt56K0QHbNYMfv3V1gtnGDwY/vc/67L1e8uwiIiIiGSfLzPCPM8rB1wGzAROd85tyvhQMqCz7lgxfTr88otVgx0vu5SUZEmwiRMjFxuwapUVpM2fbwVpjz0W0YePiHLl7AT7yy/t3P7aa21nwebNITj4oUSYZoRJPMiXDz76CNavt+qwCFm40KqIatf2tTPTH926We/gww+H/aFOPRVatLC9LWvXhuCAjRpZ7BlLFn7/3Y5fvbpV44qIiIhI7Ip4IszzvJOAEUAb59zOIz/mnHPAUXfce573kOd5czzPm5OamhqBSCVT3bpBsWI2dOt4rrvObhfB9si5c6FKFasImzTJitLi2R13WHVYhw52InjeeTYWKT09BwdNTrbB0UU0tk/iRJUqVhH2/vshmqx+fHv2WEdgkSKWT4mHatSgBQI2Y6tpU8tSRUDbtnb5zjshONjJJ9uLOIMHs3vzXpKSoGBB667NmzcExxcRERER30Q0EeZ5Xl4sCfa5c25kxtUBz/NKZny8JHDUNU3OuT7OuUrOuUp58uSJTMBybKtWWRnSww9nPi04Tx7L1Hz1lU0aDrOJEy33VqAA/PgjVKsW9oeMCgULWuvnggW2oO3hh60i7pdfsnnAQACKF7dh4yLxonNnKFXKtkmGfLDe3z31lG17HTjQfpQSSs+e9nx/rPmRYVCmjL0u8/HHIaqKbdYMt307j9QPsHQpDBpk3zoiIiIiEtsiuTXSAz4BfnfOvXfEh8YATTPebwqMjlRMkgMffGDzvx59NLjbJyXBzp1WnhVG/fvbNsVzz4UZM2zmcaKpUAG++86WAqxaBZUq2bnozp2Z3/dvAgG1RUr8KVzYBj0tWhSi0qGjGzHCFnQ888yxRyjGrb17bTBanTpH3yYcRu3bw759IdrMef319C76LJ//WI5XXrF5kyIiIiIS+zznjtqJGPoH8rzqwHRgEXCoYetZbE7YMKAssAZo6JzberxjFSxY0KWkpIQxWjmunTuhdGm4/XbrwwvG/v1WEpGUZJu4Qsw5K/R47jk7WRk50s53E922bfY16dXLclpdu0LDhkG2aF1xhQ3KHz8+7HGKRNydd8LYsZYQK18+pIdeuxYuuQT+8x/44YcEbKX7+GMbqDVliq25jbCkJHvoNWty9ntgzhyodnUqN6Z9w9g/KpKrXNnQBSkiIiISpTzP2+OcK+h3HOEUsURYKCkR5rMePWzq88yZcNVV//pwerot29q71zqPDhywy4Od3+HgnAUc7PMpB12ew9f/4+1o12d22x07bC5YkyaWZ8uXz4evSxSbPdtGI82da9Up//ufnaQfV+nSULPm/w+LFokrmzZZyejll8PkySEb4JWaarmfBQusLfmcc0Jy2NiRng4VK1pv+ty5vgxGmz3bfjW99RY8/XT2jrF1q31ruIOpzNt4OsVeaQMvvBDaQEVERESikBJhUUqJMB+lpVkGpUQJG8D1D6mp0LgxfPFFzh7G8yyZlTfvv9+OdX3NmtCxo0ZaHUtamo3tee45ax1q396+Xkcd8eYc5M9vQ466dIl4rCIR0aePDdPr2xeaNQvJIV96CV5+2ebEN2kSkkPGlq+/thWZAwdmvkgljG66yV6Q+eMPy8llRXq6jbWcONEq+q7qeCOsXg3Ll+sXjIiIiMQ9JcKilBJhPho9GurVg2HD4K67/vah9HR44AGb0/Xcc7ag7W/JqrR95LulBnnr3kreV144bnIrd26fPr8EkJxs29UGDYKzz7Zxb7fe+o8bbd1qmz67do3osGuRiEpPh+uvh8WL4fffrRU4B77/3qrB7rnHngcTUs2atsL2jz98Lc2dPNmSYb17w0MPZe2+XbrYiwQffACPPYZlNe+9F6ZOtU0sIiIiInFMibAopUSYj264wSawr1xp2yAzOAetWlnL3csvw4svHuP+DRva2eKGDcp2+WzKFNt1sHSpzdTp1s26IQE7kb3wQsuWNW7sa5wiYbVkiQ30atAABg/O9mG2brXDFCgA8+ZBoUIhjDFWLFxoX4TOnaFDB19DcQ4qV7b/lyVL/vbr6rimTrU5kw0b2tOf5wF79kDJklC/PvTrF8aoRURERPyXCIkw1fhL8ObPt7OEVq3+dVbx7LOWBGvbNpMxKklJto3wp5/CGqpkrkYNm2P0+uswbhycfz68+67NXCMQsBvlsEJGJOqdf76VsA4Zku3FEM7Bgw/aj82QIQmaBAOrID3xxKyXYIWB51kubuXK4Fv1N22C//7Xuv/79DlivNmJJ9oHhg+HXbvCFrOIiIiIRIYSYRK87t2hYEFo3vxvV7/xhrWSPPwwvP12JrORa9e22VMjRoQ3VglK/vyWxPztN+sQa9fOlkX++H2a3aBECV/jE4mIDh2gQgXbKLF7d5bv3rs3jBplhVBXXBGG+GLBpk22RbhZMyha1O9oAOviP/98+/2UWfF7aqrlunbtssTZv5KZzZpZZdiwYWGLV0REREQiQ4kwCU4gYH0i998PRYr8/9U9elgxRZMm8OGHQSwIK1QIbr7ZEmHp6WENWYJ31lnw1Vd2Mr99O1R/6SYe5CO2F1AiTBJAvnzw0Uewbh08/3yW7rp4MTz5pD2tPflkmOKLBR9+aNmkKJopmCuXLQVZsAAmTDj+bZ9/3rr2+/SxrvB/qVzZsmraoisiIiIS85QIk+D06gUHDkDr1v9/Vd++8MQT9qp7v35ZWKaVlATr19uOe/FfSgr88ANet67UG3Y3v+e9mGd4k37cz0XXFeGbb/wOUCQCqla1irAePWDWrKDusnevVREVLmzD8RN2oeCePbaS9o474Nxz/Y7mb+6+G8qUsWq9YxkzBt58Ex555DibPj3PtsH8+KMNVhQRERGRmJWof7ZLVuzfb6/233abDU/BukNatIBatWwmTrCDiAG4/Xa7g9ojI+/AAZg71xKbzZvDxRfbWfw118BTT8H06RS85FzefD2NGf2XU6iQx8032wmiRuNI3HvjDRuK3qJFxrC842vbFn79FQYMSPBxegMGwF9/2XNIlMmXz/6fpk+3HNY/rVoFTZtaS2vXrpkc7N57bcmLBuaLiIiIxDRtjZTM9e9vLZHffgs33cTYsbY86+qrYeJEmyOcZbfcAsuXw4oVQfRTSrakpVnlwuzZh98WLLDEJkCxYnDllYffKlWyJMAR9u2z5QfvvgtnnmldQddfH/lPRSRivvzSnuAy2Xw4apQtmmzXzmYjJqz0dLjgAkuoz5oVlc/nKSn2/HX11TB27OHr9+2DatUsGTZvnrWIZ+r22+3Ga9dq87GIiIjEpUTYGqlEmByfc3D55VYdsWgRU77zqF0bKlaEyZPh5JOzedyPPrLNYr/8ApdeGtKQE5JzsHr135Nec+ceHvx90klW8nBk4qtcuaBPWn/80XKhK1ZYd2znztlMgIrEgqQk2yC5aNFRW/3WrYNLLoGzz7YFuPny+RBjtBg71pJDgwZB48Z+R3NMr74KL75orwVcfLFd98gjtuhgzBj7FIIycuTh749bbw1bvCIiIiJ+USIsSikRFkHTplkJ0EcfMePCB6lZ0/In06ZZQVG2bd5sGwmffdbOUCRrkpP/nvSaPdtak8DOyi+99O9Jr/POy3H1QkoKdOwI778P5ctbd1DVqjn/VESizsaNtkXyiitg0qS/JYzT0qBGDSsKmjfPfhYSWo0aVt27ahXkzet3NMe0bRuULQt169pyy4ED4b77rOjvePPD/uXAATjjDPu9OHx4uMIVERER8Y0SYVFKibAIql8fpk9n/tj1XH9LAU47zTZr/aODLntq1LCEzm+/heBgcW7PHpvT9tNPlvRav96uz5XLVpwdmfS66KKwlqh89x00a2ZVMW3bwiuvQIECYXs4EX/07m0lQ3372jd8hk6d7Ht+wAAbGZXQfvnFKobfegueftrvaDLVrp3NAfvyS1tycOWVlufM0oxLsPWgH35oCdMcvSIkIiIiEn2UCItSSoRFyKpVcO65LHnoPa4d2YYCBWzg8Jlnhuj4//sfPP64TZuuUCFEB41TzZvbCfm55/496XXZZVAw8s9Ru3bZSWWfPvZf17+/jRgTiRvp6XDddfb8tGQJFC/O11/bzpD77tO8dMC+ECNHWmL+lFP8jiZTGzfaHLCDB225wS+/WGFyli1caL2xPXpAq1Yhj1NERETET4mQCNPWSDm299/nj1zncNPoVuTKZa+chywJBlZtBtoemZkvvrAkWMeO1oI0aJBVJFSv7ksSDKBQISuYmTABduywIdQvvGBdQyJxIVcuy/SmpECbNqxeDffcYwWXH37od3BRYMMGGDzYkvQxkAQDKFXKivs8z7YdZysJBjZk7IorbHuIiIiIiMQcVYTJ0e3cycZSlbjGm862vKczbZqdAIZctWp2ojl/fhgOHgfWrbOTrvLlbWJ9FM7g2b4d2rSxqrBLLjl8KRIXXn6ZfS91pvq5AVZsPpk5c446Pz/xdOxoLZHLl9vWgBhx4IAtfMzx/+GhimYtfBEREZE4o4owSVib3x/CTSlf8mf6qUyYEKYkGNj2rQULYOXKMD1ADEtLsyFEBw9aFVgUJsHAikH69YPRo23k25VXwmuvQWqq35GJhECHDjxxygDmrjiZ/r32KgkGto22Vy+r6o2hJBjY+MSQ/B82bmwHU1WYiIiISMxRIkz+Zftfadz8SlX+yHUOY8fn5qqrwvhgDRrYpdoj/+2tt2w95/vvx0QJSt26Nk4pKcnaJKtU0R4EiX39Buenz/aGdKAzd8x81u9wokP//lYK+tRTfkfin6JFoV49W0G5f7/f0YiIiIhEjOd5fT3P+9PzvMVHXPeq53kLPc+b73neN57nlcq43vM8r4fneSsyPn75Efdp6nne8oy3phH9HNQaKUdKSYFalf5i9pJCjH52Fre+Xj38D1qpEuTODTNnhv+xYsXs2VC1qlVcDB1qQ21iyPDh0LKlFY689pqNNMud2++oRLJmwQKbf1elCnzzn8fJ81FP+PlnK3tMVGlpcP75ti1xxoyYe24KqYkT4ZZb7Anvzjv9jkZEREQkJDJrjfQ871pgNzDAOVcx47rCzrmdGe+3Bio45x7xPK820AqoDVQGujvnKnueVxSYA1QCHDAXuMI5ty2cn9shqgiT/7dvH9xxB/y85BQGn9qaW1++OjIPnJQEs2bZPCyx7NHdd0PJkjaRPgZPNO+6y6rDbr0Vnn4arr3WRgmJxIrt2+2pqWhRmwmf583Xbbp6ixbWrpyoxo6FFSusGiwGn5tC6qaboHRptUeKiIhIQnHOfQ9s/cd1O4/4Z0EsuQVwB5Ywc865n4FTPM8rCdwMfOuc25qR/PoWuCX80RslwgSw87qGDWHyZOjLAyR1KA958kTmwZOS7HLkyMg8XrRr3dpmpg0cCEWK+B1Ntp1+uv2XDhxoLZKXXGJdnunpfkcmcnzp6dC0KaxZY8U+p58OnHwyfPCBlYm9957fIfrnvfegbNnDbe2JLHduuO8+W5+7caPf0YiIiIj4yvO81z3PWwc0AV7MuPoM4MiKl/UZ1x3r+ohQIkxIS7O/5b/6Cv5XeQBNC46A5s0jF8B//mPT+DUnzM66P/3UNrJdd53f0eSY58E998DixXD99Zbju+kmWL3a78hEju2tt2DMGHj3XetQ/n/169vbSy/Z6sFEM2cOfP89PPFE5F4oiXb332+Z04ED/Y5EREREJFTyeJ4354i3h4K5k3PuOedcGeBz4PHwhpgzSoQlOOfgkUdgyBDo8twuHv2lBTRrZqsAIykpCX74wdYOJqq1a+Ghh+Cqq+xEO46ccQaMGwcff2zn0hddBH362PefSDSZMgWeew4aNYJWrY5yg27d7LJ9+4jGFRW6doVCheDBB/2OJHqULw/XXAN9++oJTUREROJFqnOu0hFvfbJ4/8+BjLYvNgBljvhY6YzrjnV9RCgRlsCcszEvH39sJ37t87wLBw5Y2U6kJSVZQKNGRf6xo0FaGtx7L6Sm2hayvHn9jijkPM8KDRctgsqV4eGHbYbY+vV+RyZiNmyA//4XzjvPnhePOgKrbFkbfDdkCPz0U8Rj9M26dba4o0ULKFzY72iiS7NmsGyZLQ8QERERSUCe55U/4p93AEsy3h8D3JexPfJqYIdzbhMwEajleV4Rz/OKALUyrosIJcISWKdOVtzQujW8+tw+6NkT6tSxV7gj7cILrUUyUdsj33zTWo7efx/OPdfvaMLqzDPhm2/gf/+D6dOhYkXo31/FFOKvAwdsycPevTbb7qSTjnPj9u2hVClo0yZxht69/779kPrxQkm0u+suKFhQQ/NFREQkIXieNxiYAZzned56z/OaA108z1vsed5CLKn1RMbNxwOrgBXAR8CjAM65rcCrwOyMt1cyrovM5+Bi8OyzYMGCLiUlxe8wYtrbb8Mzz8ADD8BHH0GuAf3sVe1Jk+DGG/0J6tlnbThPIADFivkTgx9mzYJq1Wz49JAhCbWJbeVK+7abPh1uv92+F08/3e+oJBE98QT06GFFTw0bBnGHgQNtuGL//nYZz3btgjJl4Oab7Qsk//bAAzbjMTnZkmIiIiIiMcrzvD3Oubj+g0YVYQmoZ09LgjVqZHOacnnOSsMqVoQaNfwLLCnJWgRHj/YvhkjbvRuaNIGSJaFXr4RKggGccw58950tovv2W6hXT5VhEnlDhlgSrE2bIJNgYD+3V11liy127w5rfL779FPYscN66eXomjWz74NErWoWERERiSFKhCWYgQPh0UetA3LgQNv+zrRpsGCBnQX6mYi5/HIoVy6xTiRat4ZVq+Czz6BIEb+j8UXu3PDkk5ag/flnS0qIRMpvv9ns92rVrCA1aLly2QsIGzdm8Y4xJi3NPs+qVW24nxxd9erW1q72SBEREZGop0RYgnDOCo7uv9+KvoYPP2Iee7ducOqpcPfdfoZoSbgGDaw0aMcOf2OJhOHD7aSpY0e49lq/o/HdfffBZZfZ+KW9e/2ORhLBrl1WiFqwoHX8ZXlHRZUq0Lix9ZqvWROWGH03ejT88YeqwTLjefYLdupUe3FDRERERKKWEmEJYPduuOceaNkSata085oCBTI+uHIljBkDjzwCJ5zga5yAnZUePAhjx/odSXitXQsPPWQVFp06+R1NVMiVy1ok162Drl39jkbinXO2xXTZMkuCnXFGNg/UpYslQTp0CGl8UeO99+Css6xvWY6vaVP7XujXz+9IREREROQ4lAiLc7/+Cldeae1mr74K48f/Yxva++9DnjyWJYsGV19t29i++MLvSMInLQ3uvRdSU+Hzz7NRhhK/rr/ezrc7d7aZ0yLh0r27FWV27mzfd9lWtiw8/bQ9yf70U6jCiw4zZ8KPP1rbfO7cfkcT/UqXhlq1bIFComwTFREREYlBSoTFsYEDbZbz1q3Wbfj881Z18/927oS+fW1qfqlSvsX5N7lyWXvkhAnxO4D6zTfh++/hgw9sWrz8zdtvw/798MILfkci8eqHHyx3Va+eXebYM8/Yc+gTT8RXAuS99+Dkk20QvASnWTOr+J0yxe9IREREROQYlAiLQ3v3QosWNnOpUiWYP/8YyyD79rUhOW3aRDzG40pKgn374Ouv/Y4k9GbNslbIRo3sP0j+5dxzoVUr+OQT2+EgEkqBgG2GLFfOOthCsh+kYEFrkZwzxxZfxIPVq60y96GHoFAhv6OJHXfcAaecoqH5IiIiIlHMc875HUOWFSxY0KWkpPgdRlRavhzuussSCB07wiuvWOfjv6SlQfnyNhhn+vSIx3lcaWlQsqRl7+JpheCuXTYN/uBB+w865RS/I4pa27bZt+cll8CkSf4uM5X4kZpqcxJnzrQNpRdfHMKDp6fb8Pz162Hp0n/0oMegtm2tf/SPP6BMGb+jiS2PP26Z/E2b9DwvIiIiMcfzvD3OuYJ+xxFOqgiLI198AVdcYV0ZY8fCG28cIwkGNiD/jz+irxoMbBZNvXowbpxVhsWL1q3ta/7ZZzo5ykSRIvDSS9ZdFO97EyRynnvOlvr17h3iJBhYW3e3brBxo7U/x7KdO+Gjj6x0TkmwrGvWzH53xdMLOSIiIiJxRBVhceDAAZtz06OHLSEcOhTOPDOTO113HaxZAytWHCdb5qOJE+GWW2zFZd26fkeTc8OGWTvk88/b1gLJ1MGDlqxIT4dFiyBfPr8jklg2apSNH3zkEejZM4wP1KQJjBwJS5YE8UQcpbp2haeegtmzrb9essY5K2c94QQrPxQRERGJIaoIk6i3Zg1cc40lwZ54wmawZ3ruNW+e3bB16+hMggHccINVTY0Y4XckObd2rc3ZqVwZXnzR72hiRt688M47sGwZ9OrldzQSy5Yvh/vvtw263bqF+cG6dLFe3g4dwvxAYZKaai2R11yjJFh2eZ5Vhc2aZaubRURERCSqKBEWw8aNs5FTv/8Ow4fbCV5QVTPdu9v8mubNwx5jtuXLZ5VgY8ZYyVusSkuDe+6xy88/t+yOBK12bZvp9NJLtv1UJKtSUmz/Rt681j6eP3+YH7BMGSvRHTIEfvwxzA8WBqNG2Sssbdv6HUlsu+cee6FJQ/NFREREoo4SYTEoNdUG4depA2XLWoHXnXcGeefkZBg82F6tPvnksMaZY0lJsH17bK+h79LFlhH8739wzjl+RxNzPA/efRd27LDFDyJZ4Zy1Qi5ebHnosmUj9MDPPGOLSNq0sd7eWHHwILz1lq1urVPH72hi22mnwe23w8CB9nUVERERkaihRFiM2bgRbrzR8istWsCMGXbOErSePS2T1qpV2GIMmVq1rHItVtsjZ86ETp3gv/+Fe+/1O5qYddFF8OCDlktctszvaCSW9O5tuyleegluvjmCD1ywoD1Jz5ljiZBYkJpq883mzLEvWO7cfkcU+5o1gz//hK+/9jsSERERETmChuXHkMmT4e67Yfdum5mU5dzKvn1WEnH11dZyGAsaN4ZJk2wNfbTOMzuaXbvg0kutJXL+fG2JzKFAAMqXt9Fxo0f7HY3EglmzbMzVjTfa5tFckX7ZJz0dqlSBdessg3vSSREOIAvS0uC++2DQIBvMp7bI0EhNtVbZiy6yBTCe53dEIiIiIpnSsHyJCunptmiwZk0oVsxO8LKUBFu+3A5w2WWwebNN1Y8VSUmwZYu1F8aSVq1g9WorR1ESLMdOPx2efdbyt7HcKSuRsWWLtYuXLGk/ghFPgoE9aPfulsR/800fAghSerqVXA4aBG+8oSRYKOXJA+3bw7ffwief+B2NiIiIiGRQRViU27zZZu5+8411rfTqFWRhwdq1MGyYzQObN8+uu/ZaeOABe+U/Vl6ZTkmxWSsPPAAffOB3NMEZOtTaIV94QYOtQmjfPjj/fMsrzp2rzi05urQ0W7IwdSr89BNccYXPATVpAiNHwpIlQaz0jbBDQ9T69LF2yE6d/I4o/qSnW5v/jBlWHVy+vN8RiYiIiBxXIlSEKREWxX78ERo1suqGHj1sJthx81eBgK1FGzz48LaySpWsvbBhQyhdOiJxh1yDBvDzz7B+vU+lHVmwZg1ccglccIFVscVSO2cMOJRj/Pjj6F56Kv7p1Mnyz3362HOm79atg/POsy24Q4b4Hc1hzkHr1vYCQ8eO8PrrsfMCSaxZvx4uvtiSYD/8oO3BIiIiEtUSIREW5VmFxOScbcq77jrIn9+qGh566BjnKNu3Q9++9opzqVLw+ON23WuvWUvk7Nnw1FOxmwQDa4/ctMmSYdEsLc16VtPTbUWdkmAh17AhVK0Kzz9vY9hEjjR+vCXB7r/fuv2iQpkytkVy6NDDL1D4zRTuY90AACAASURBVDlo186SYG3bKgkWbqVL2+aGWbNsTIGIiIiI+EoVYVFm2zZbNDV6NNSvD59+Cief/I8bpaTYsKQhQ2DCBDhwAM4+2yq//vtfqFjRl9jDZscOa49s1coyhNHqtdesHXLAAG2JDKOZM23fw3PP2ZdcBOCPP6wNsmxZ60I74QS/IzpCSopVhZUoYckQPytbnbOBe1262HNq9+5KgkXK/ffbFtHvv4dq1fyORkREROSoEqEiTImwKDJ3Ltx1l3XSvP22zbT///OT/fst6TV4MHz1FezZYxVgjRpZAqxSpfg+mbntNvj1VzvbjcbP8+efoXp1K1n6/PPojDGOHBq7tHSpJT4kse3bZ3mFlSvtefScc/yO6Cg++8wS5P36QdOm/sXx0kvw8svw8MPQs6eeqyJp507bJuwcLFgAhQv7HZGIiIjIvyRCIkytkVHAOfjwQ2v5OnjQXixu0wa8tFSbkt+sma3Nq1cPJk2yYffTplnG7L334Mor4/9kJinJ5m/Nnet3JP+2c6dlZkqX1ollhHTubJcdO/obh0SH1q1tJ8iAAVGaBAO4+26oXNm+aXfv9ieGN96wJFizZvZLR89VkVW4sCVE1661ajyRo5k0yVoC5s/3OxIREZG4pUSYz3btsvOjxx6DG2+EX+amUyV1ul1RqhTcfLOVvtSrB19/bbOyeva0DZDRPjg+lO64w9YEjhjhdyT/1qoVrF5tlWD/6mOVcChb1kYbDRpkrZKSuD79FD76yPJLdev6Hc1x5MoF3brZc3iXLpF//HfesX7iJk3sC5ZIvz+iyaEhhwMG2GZnkUPmzoWaNe3tyy/9eZ4QERFJEGqN9NGiRdYKuXy549VHNtChQHdyDRtiG6ZOOAFuv91mft16KxQo4He4/qtZ06rCli6NnkqGIUOsNfXFF63SQiJm925bwnbWWTaDPFq+JST8AgHrFB8/3s4Xr7kGJk60XHnUa9LEEvpLl8KZZ0bmMXv0sF77u+6y7LEWefjr4EH7pl261P4QiOVlNpJzK1ZYcnToUChWzGaN/v67Zfk3bYKiRf2OUEREEkwitEYqEeaTZcvg0kvSKZw7hcEnt+SGjZ/bSvVbbrHkV926cNJJfocZXXr1gpYtYeFCuOgiv6OxpNwll0CFCtbPqpPLiOvbF5o3t3xko0Z+RyPhkpZmC3DHj7e3Qx3SJUpAnTrWKnvqqf7GGLR162xwft269o0bboeeN+vVswqkvHnD/5iSuRUrbF5Y5crw7beq0EtEgYCtue3TB/LlszLndu2shfaXX+Dyy22z62OP+R2pyN/9/LMN5WzSxO9IRCRMlAiLUvGQCHN/rObtsz/kPu8zStSoYFVF9evrlb/jSU62dtEXX7SBz35KTYUbbrCBxwsWWFmSRFxamu2J2LYNlixR4WQ82bLFqrzGj7fLv/6yXEGVKlYkW7u25aFjMn9waGD99Om2ZCNcDmWKb7vNWuzz5QvfY0nWffIJPPigbcdp187vaCRSdu60VuX33rNFSC1a2N81JUr8/XaXXmovsM2Z40+cIkfjHFx2mS2wWrPG/i4XkbijRFiUiodEGGAzpW688d9//MixXXutZT0WLfI3jldegU6dYOBAuOcef2NJcFOm2I9R587/196dx9lU/38Af30sydZiCWUKZVeW4qtSZMsalULLT4NK0aIIqVSokFJaCKWsKRJKsqckkiUGYxAz1mxhMMzM5/fH685jxjLMcu495977ej4e9zHcufecz8xn5sw57/P+vN9A795uj0ayKjmZBe9Tsr6WL+f5dtGiDHw1bQo0bhwi9wri45kVVrw4v1B/RPPGj2djlUaNgO+/V5TYi6xlI5hZs/hzUK2a2yMSf0pIAEaOBPr3Z6T/wQeBAQO4xv98PviAnZO8kgUvAjAwW7Mm/92vn/s3pkXELxQI86iQCYRJ5qWcGG7cyAvJQNuzB3jhBWDSJHY5mDAh8GOQc7RqBSxcCGzezAarEhwOHWJj3B9/ZM2vfftY661WrdSsr5tvDtKsr4uZMIFB9LFjgQ4dnN3211/z+FSvHoMsefM6u31xzoEDDHJccQXX/GquQk9yMmvzvfoqG+vUrw8MGsR05gvZv5/ZNt26MXtMxAuefJI3gWvWZJ2X7duVbSwSghQI8ygFwsJYbCxbBg4cCLz8cuD2m5wMjB4N9OoFHD/OfffuDeTJE7gxSLqio4HKlYGOHXnDXWjVKmDePKBECeCaa3hNdfXVQMGC7ozHWq4kTsn6+v13/moVKsTyiE2bslFu0aLujC+gkpPZQXDHDv4AO1UT8rvvWBT/ttvYaTh/SJ/DhIa5c5nu2K0bMHy426MRp1jLdd29e/PAV706O0E2apTx7i5t2rAGaVycgg3ivmPHeEJx//3MaGzeXEVaRUKUAmEepUBYmPvf/1ijK6Vitr+tW8c7YEuXMsNixAh3stHkgrp3Z3O81au1iiTFLbec/9ekQIHUoFjaR9pgWYkSziSn/Pcfg3E//si4zO7dfP7mm5nx1bQpM8CCouOj05YtY9Gzvn25RCq7Zs0C7ruPEz9njnsRT8m87t2BYcP4i9K0qdujkexavpw3zhYtAsqU4c27Bx/MfHrrDz+wI8i0aawjK+KmL77gHcclS3izpWxZnjj88ovbIxMRhykQ5lEKhIW5wYN5grl1q3+L1J84wYvTwYOByy8Hhg5lzZ2M3smVgDp4ELjhBgZYfv5Z07R5M1CuHH+E27QBdu0687Fz55n/T0g4dxtXXnnxgFnx4mc2IrSWNXRTsr5++41x68svZ7ZX06bM/lJpRJ9HHgG+/RbYtAm47rqsb2fOHHaivOkmRh4vv9y5MYr/nTzJpUb//ssamGGRFhmCNm1iYHvqVM7ha68BTzyR9WyuxERmwd9yCzBjhrNjFcms225jTYOoKJ5kDR3KRh9r1vBvj4iEDAXCPEqBsDC3ZQsjHu++y3bj/jB3LtClC4NtHTpwX0WK+Gdf4pgPPwSee46JMc2buz0ad735JmvYxsYycHUh1vLc9uxg2dlBs9272anzbFddlRoUW7+e+wTY1TEl6+vWW9kATc4SG8sM05YtWdsrK+bPZ9ZIhQr8d0h0FAhDa9cyGNakCTB9uqL5wWTXLnaCHTOGqbQ9erCeqBNZmb16MeAQF6c7COKe9euBKlXOPPc+eJAnGP/3f6pLIRJiFAjzKAXCBNWr82Rz6VJnt7tvH5eoTJzIlO+RI4G77nJ2H+I3p0/zPC1HDl5Tps1UCifWApUqMUC1eLFz201OZsJKegGzXbuY1JQS/LpYAE58Xn+dF9FLlgB16mTuvb/8wm92mTLsGKGAfXB7/30GUEaOZCaReNt//zFr/P33mb3VpQvwyis8+Dpl40agYkVgyBAG2ETc0L078PHHvDOWNmO1UyfWCdu5k00/RCQkKBDmUQqECQYMYAemuDhnrraTk4HPPwdeeonFQPv04ePSS7O/bQmomTO5Qmz4cNaeDkdr1gDVqgGffsrrMvG448eZFVasGGsLZbSO0NKlLLIeEcFaRGqZGvySk7mGeOlSdrsoV87tEcn5nDzJoMBbbzEr5qGHgP79GZD2h9tuY9Bt3TplCkrgJSQw7btBA2DKlDM/99dfrEnx/vvs6i4iISEcAmGh2JRewsH99/Pjd99lf1tRUSyC//jjrLK+di2zMxQEC0otWvBcrV8/LvcLR5Mmsfh8mzZuj0QyJF8+dpNbuRL46quMvWfFCmaClSjB5ZAKgoWGHDmAL7/k35+HH2aaq3hHUhLnp1w5ZmfVrMlAwIQJ/guCAUBkJM9Vli/33z5E0jN9OgO+nTuf+7kaNVj74JNPGMgXEQkSCoRJcKpYkY+pU7O+jZMnmVVWrRprH3z+ObMqKlRwbJgSeCn1Ww8dcqYRX7CxlqsUGjXSKrmg0r49O+L26cOs1AtZtYqZYIULAwsW8E69hI6rrwZGjQL+/JPLZsV91rL4ZLVqwGOPMfA8fz7w008s1eBvbduyHMQXX/h/XyJnGzWKdQ8aNjz/57t2ZYeeefMCOy4RkWxQIEyC1/33sz7Ovn2Zf+/8+cz+GjAAaNeONTgiI7XkIERUrcqyFcOH89wsnCxbBmzfzriKBJEcOYBhw4A9e4C3307/dX//zYuRyy5jECwiInBjlMC57z6gY0f+LCxZ4vZowtfhw6zXVrs2G1qcPMmlYcuXA/XrB24cl13Gc57Jk9nRWiRQtm7lOXOnTukv22/ThnXxPvoosGMTEckGBcIkeN1/P9Owp0/P+Hv+/ZfdbVLuas2bx6VIalUfcvr3B/LkYcOtcDJpEr/u1q3dHolkWu3aXA43dCjwzz/nfj4qiut+L72UQbBSpQI9QgmkYcO43O7RR1kfSgIjMRGYPZs3yYoXZ6HF+HgWXYyKAh54wJ2bZpGR/DlwoiSESEaNGcMAWGRk+q/Jk4flRWbNOv/fLhERD1IgTIJX1aq8SMjI8khrufSxQgXeUX31VWZWNGjg/3GKK4oX5yqz777jitdwkJTEZIXmzZlAIEHo7bd50XF2BDc6msernDkZBLv+enfGJ4FTsCAwfjybwoRr549AWr+eDXOuvZatb+fO5cX9n3/yfKFLF3dbEderx+C3lkdKoCQm8uetaVOgZMkLv/bJJ/m3a8SIwIxNRCSbFAiT4GUMs8IWLLhwVfSNG3kC2akTUKkSsHo18OabKoYfBrp35zXNCy8wSBTqFi0C9u7VssigFhHBINiUKalL4rZs4TKspCQuUSlf3t0xSuDUrs0bN+PH8yaOOOvAAS7nuuUWoEoVdr6rWROYNg3YvZvr62++2RtlE3LkYH2y+fO5/l3E32bP5u/B+Yrkny0iAmjVChg9mkuIRUQ8ToEwCW5t2vCO1YwZ537u5Em2DrzpJt7NHT0aWLyYwTAJC3nzshnfqlXAuHFuj8b/Jk0CChRgRpgEsZ49eff9+eeBbdsYBDtxgku5dfwKP337sitbly7Ajh1ujyb4nT7Nc4b77mPX1WeeYZB52DBg507g+++Be+8FLrnE7ZGeq0MHZrh/+aXbI5FwMGoU0+szelLRtSuDy19/7d9xiYg4wFhr3R5DpuXPn9/Gx8e7PQzxAmvZyaZatTODYQsX8qIhOpo1d957j4U8JexYC9x2G2+gR0czUBSKTp1iI7MWLcIj6BfyJkwAHnmEa1xz5GAWSI0abo9K3LJ1K8sB3HwzfxZy5nR7RMFn9Wpg7Fhg4kTWC73qKv6OdejAG2bBokEDBshjYtIvXi6SXTt3MqX+pZcu3MAlLWuBypV5orV8uX/HJyJ+ZYw5bq3N7/Y4/El/QSW4GcO7uj//DBw9Cuzfz6UDKcuIfv6ZS0oUBAtbxjAOuns3MGSI26Pxnzlz2OBMyyJDxEMPMQvIWk6ugmDhrUwZLtNbvBh49123RxM89u7lH4CqVYHq1Vnwvm5dYOZM1l4bOjS4gmAAi5Zv28au2SL+MnYsG1J16pTx9xjDrLAVKxQIExHPU0aYBL8lS4A772Q3yB9+YFelXr24nCRvXrdHJx7Rvj1XvERHX7zmazB66CHGS/bscbeeszjoyBHg+HEuTRGxFnjwQR7Ili1TcDQ9CQkMdH35JWscJSUBtWox86tdO6BQIbdHmD3Hj3NJZ+vWWiIp/pGcDNxwA5szLFiQufceOQJccw1vUuvnUyRohUNGmAJhEvySkvhHd+9e4PbbgZEjmZotksb27awx/sADobd0MD4+dZXPyJFuj0ZE/ObAAWYwXXYZsHIlkC+f2yPyBmuZhfLllyyWeOgQcPXVwKOPMgBWsaLbI3TWk08y2333brUIFufNnw80bMgl+g89lPn3d+vG+mJxcUDRos6PT0T8LhwCYVoaKcEvZ06mcI8bx6UCCoLJeVx3HbtHjh/P66VQMmsWkwS0LFIkxBUuzGDPxo1sqhDudu5kR5RKlYD//Q/4/HOgaVOmx+7Ywc+FWhAM4PLI48fZXVbEaaNGAVdeyayurHj6aRYuHTPG2XGJiDhIGWEiEjaOHmW2f9myXFFrjNsjckbr1gzu7dihGtoiYeHFF1n7atas8GsTe/IkMG0aA4Lz5nEZV506zPx64AHg8svdHqH/WcvgX6FCwG+/uT0aCSX793OVRZcuwAcfZH079esDW7aw0YdOTESCjjLCRERCSMGCwIABvG6YOtXt0Tjj8GGWwWnbVueaImHjrbe4RLJjR2DfPrdHExjJyVyqVb48u0Fv2sRaoJs3885G587hEQQDeBcnMhJYupTfBxGnjB/PbK7OnbO3nW7deHdu1ixnxiUi4jBlhIlIWElKYo3po0eBqCjg0kvdHlH2fPEFr4X/+IP1oEUkTKxfD9x8M2v5zJwZOimu57NwIdCjB/DXXzyAv/UW0KgRkCOM7+fu3g1ERHCJ7Ntvuz0aCQXWAlWq8K7hsmXZ21ZiIlC6NJcm//yzM+MTkYBRRpiISIjJmRMYOpTd5z/80O3RZN+kScD11wM1a7o9EhEJqMqVgcGD2S15xAi3R+MfUVFAy5ZcZrV/P2uBrlgB3H13eAfBAHaObNoU+Oor3uERya5ly/g7l91sMADIlYtNHebOVdaiiHhSmJ9FiEg4atgQaNGCyySDeVXRvn1s7tSuXWgng4hIOrp1Y1DoxRdZQD9U7NnDGkU33sgmOO+8w6/vkUcUAEsrMhLYtUsZN+KMUaOAAgV4UuGExx8HcucGPvnEme2JiDhIZxMiEpbefReIj2e96WD1zTcsm+PUOauIBJkcObg+Ol8+1s06dcrtEWVPfDzQvz+7mowZw0Dfli1Ar15A3rxuj857WrQAihRht0yR7DhyBPj6a55QFCjgzDaLFWMDi7FjgWPHnNmmiIhDFAgTkbBUvjzQpg1XFB096vZosmbSJJbzqFLF7ZGIiGtKlABGj2b9rH793B5N1iQlMZhTrhzw2mtAkyZcovXBBwz0yPldcgkDoDNmAAcOuD0aCWaTJwPHjzuzLDKtbt0YZJswwdntiohkkwJhIhK2evQA/vuPqwGCzY4d7H7Zvr3bIxER17VuzQvYQYOAxYvdHk3mzJkDVK8OdOoEXHst8OuvwLffAmXLuj2y4BAZyUzAiRPdHokEs1GjuBTZ6a47tWvz9/ujj1iMX0TEIxQIE5GwVbMmULcuMGwYcPq026PJnK+/5se2bd0dh4h4xPvvs3PGo48CcXFuj+bi1qwBGjdm9ld8PDBlCrB0KXD77W6PLLhUrcpAwxdfuD0SCVarVwN//slgutMFR40BunYF1q0DlixxdtsiItmgQJiIhLWePYHY2NTAUrCYNIk3bq+/3u2RiIgnFCjA5Ue7dwMREVwz/eyzwPffA4cPuz26VHFxzGKqXh1YuZJ3IjZsYC0hdf3Imo4dgVWrGNAQyazRo4E8ediMwh/atweuvBL4+GP/bF9EJAuMDcI01fz589v4+Hi3hyEiISA5masBcuXiNUQwXIdt2gRUqMAEkOefd3s0IuIpUVHAzJnAggXMwDhxgkX1a9QAGjQA6tdn1lX+/IEd19GjXLr53nusCfbss8DLL/MCWbLn4EHWiuvShXXVRDLqxAn+7DRv7t86Xj168Gdz+3bg6qv9tx8RcYQx5ri1NsAnCoGljDARCWs5cvD8bO1aYO5ct0eTMZMnM2D34INuj0REPKdSJXZZnDMHOHSINcNefZVdF997D7j7bgaf6tYF3niDwTJ/dptMTAQ+/ZSdIAcOZD2zTZuAIUMUBHNKoUJAq1YMZAR751AJrKlTWSzV6SL5Z3vqKQbAP/vMv/sREckgZYSJSNhLSABKlwYqV/Z+MMxaoGJF3sBduNDt0YhIUImPZzH6BQv4WLmSB5V8+YA77mC2WP36XLaYM2f29mUtM9N69QI2bmTgbcgQFmcU582eDTRrxkYD99/v9mgkWNStC+zaBURH+z8lvnlzdrfdvp0dT0XEs5QRJiISBvLkAZ57Dpg3j2VWvGz1aiZTqFukiGRa/vzMCBs0CFixAjhwAPjuO3ZsjItj0KpmTaBIEeDee4Hhw4H16zPf7W3FCqBePWYpWcs6ZQsXKgjmT40bc8mZiuZLRkVHA7/8wt//QNSF6NoV2LOHxxxxj7XMGNbdVAlzyggTEQFrSUdEAPfc498yGdnVqxdXN+3ZAxQu7PZoRCSk7NnDi6MFC4D584Ft2/h8sWKp2WL16wNlypz//f/8A/TtC0ycCBQtyqWXnTsDuXMH7EsIay+/zCBnXBzThkUu5KWXeEIRGxuYn5fkZKBsWeCaaxiAk8BbsgTo0wf47TfeGNm8WccKOS9lhImIhIkrrgCeeILdI7dvd3s055eczPpgjRsrCCYiflC8ONNNR40Ctm7lY8wYFtlfuBB4/HG2qi1dmlkkEyZwWdXhw7yoLl+e2R59+wIxMawLpCBY4Dz2GP9QjBvn9kjE606dAr78EmjZMnCBkBw5gKefZjBm7drA7FNozRouTb3zTt7gePtt/gz06+f2yCRIGWM+N8bsM8asS/PcEGPMRmPMWmPMd8aYK9J8ro8xJsYYs8kYc3ea55v4nosxxvQO6NegjDAREYqNZaJDt27syOg1v/0G1KnDaxx/dTkXETkva1nrKyVbbNEiFuMHgEsvZbHFDh2A/v2BkiVdHWpYq1MH2L8f2LAhONogizumTWMtuVmzGCAJlIMHmRH2f/8HjBwZuP2Gq5gY4LXXgEmT2Jykd2+e5ObLB3TvDnz4IYNkVaq4PVLxmItlhBlj7gRwDMBX1toqvucaA1hgrU00xgwCAGttL2NMJQCTANQCcDWAeQDK+TYVDaARgDgAKwC0t9ZG+enLOvNrUCBMRCTVo48yoSE21nsNzZ55Bhg9Gti3DyhY0O3RiEhYS0riBdSCBcCWLUCXLkDVqm6PSsaM4XLUpUuBW291ezTiVU2bAn//zRT47DbGyKxOnZjevnMn0/HFebt28abE6NFsTPD880DPnmd+vw8cYDffW28FfvzRvbGKJ2VkaaQxphSAWSmBsLM+dy+ANtbah40xfQDAWvu273NzALzue+nr1tq7fc+f8Tp/09JIEZE0evRgYzWv3ahMTASmTAFatFAQTEQ8IGdOoEYNHjQ//VRBMK948EFme6hovqRnxw4WS+/YMfBBMIBF848f59JMcdahQ8z6uuEGBsGefJI3KgYOPDfoWLgw8Mor7Dg7b54745VQ1hHAbN+/rwEQm+Zzcb7n0ns+IBQIExFJo2pV1uD64AOu9PGKhQuZCaZukSIikq6CBYEHHmDGzfHjbo9GvOjzz/mxY0d39l+jBrOQPv6YNe0k+44fB955h/U9Bg/mstdNm4CPPmLtx/R06waUKsUbGklJARuuBIVcxpg/0zyeyOgbjTF9ASQC8HD7MQXCRETO0bMnm6d5qXvk5Mm8vmna1O2RiIiIp0VGAkePsg6USFpJSQyENWrEAIhbunZlx0JlImXPqVPAJ5+wiUmfPsAdd3DJ+rhx6Xf3TStPHhbOX7MGGD/e/+OVYJJorb0lzeOzjLzJGPMYgBYAHrapNbh2AohI87KSvufSez4gAhYIS6ezwOvGmJ3GmNW+R7NAjUdEJD0NGgDVqgHvvuuNm5UJCcDUqcC99wJ587o9GhER8bQ77+RFcErmj0iKuXNZBLVzZ3fH0aYNcNVVzFiSzEtOBiZOBCpWZFCxbFng11+BGTOAG2/M3LbatgVq1WK3X2WRSjYYY5oAeAnAPdbatD9MMwC0M8bkMcaUBlAWwHKwOH5ZY0xpY8wlANr5XhsQgcwIGwugyXmef99aW833UKU+EXGdMcwK27DBG/VDf/oJ+O8/LYsUEZEMMAZ47DGuqd+2ze3RiJeMGgUUKQK0auXuOPLkAR5/nF0r//nH3bEEE2uBH34AqlcHHn4YuOwynqguXgzcfnvWtmkM7/zu3AkMG+bseCVkGWMmAfgdQHljTJwxphOAjwAUBDDXl+Q0AgCstesBTAEQBeAnAF2ttUnW2kQA3QDMAbABwBTfawPzNQSya+TZnQWMMa8DOGatfTcz21HXSBHxt9OnWWu0VCmeX7ipfXvexN29G8id292xiIhIENixg3/AXnsNeP11t0cjXrB3L1CyJPDccwx8uC02FihdmvWp3nnH7dF436+/shD+b79xKeSAAWyOkcOhvJZ77+VS1ZgYoFgxZ7YpQSsjXSODnRdqhHUzxqz1LZ280u3BiIgADDh17w788guwfLl744iPZ6b7Aw8oCCYiIhl07bVAw4bA2LHeWOMv7vvqK7ag7tTJ7ZFQRAQz00aPBk6edHs03rVmDdC8Oet/bd0KjBjBJQvt2jkXBAOAQYM4D2+84dw2RTzM7UDYpwCuB1ANwG4AQ9N7oTHmiZSuBYmJiYEan4iEsc6d2W16yBD3xjBjBks2aFmkiIhkSmQksH07sGiR2yMRt1nLgFOdOqwr5RVduwIHDgBff+32SLxnyxYuf6xWDfj9dwaqYmKAJ5/0z53RcuWALl2Azz4DNm50fvsiHuNqIMxau9e3PjQZwCgAtS7w2s9SuhbkypUrcIMUkbBVoADw1FNsvLVliztjmDwZuOYanruKiIhkWOvWwOWXA1984fZIxG1LlgDR0e4XyT/bXXcxMPfxx26PxDt27waefhqoUAGYPh14+WVmgr30EpAvn3/3/dprQP78QK9e/t2PiAe4GggzxpRI8997AaxL77UiIm545hkgVy7gvfcCv+9Dh4DZs9nQx8nsdxERCQN58zKd+Ntv2XFFwteoUSys/sADbo/kTMYwK2zFCnfrUHjBoUNAnz6s/zVqFDO/tmwBBg7k8oRAKFqUY5gxQ5mkEvICdmmVTmeBwcaYv40xawHcBaB7oMYjIpIRJUoAjzzCG+r79wd239OmsWi/lkWKiEiWREay7o+WnoWvQ4cYDH34Yf9nFGXFo48yBT8cs8Li44GZM7n8oEwZLn+8/35g0ybgo4+ABsaKYQAAGxJJREFU4sUDP6bnnmP9th49VF9QQlpAu0Y6RV0jRSSQNmwAKlVi461+/QK330aN2FU8Opo3TUVERDLFWqBKFWYD/f6726MRN3z8MdCtG7ByJVCjhtujOb9u3VjDLDaWWUmhLCYG+PFHPhYtAhISGAhs1gzo2xe46Sa3RwiMH88A5fjxDKBK2AmHrpEKhImIZEDLlsCyZaw7HIgbqnv2sDbYyy8D/fv7f38iIhKihg5ldkdUlLcKpYv/WQtUrw7kzMlAmFdFRQGVKwNvvw307u32aJyVkMAW5D/8wODX5s18vkIFBr+aNWMh2Dx53B1nWsnJQM2aXAqxaRNw6aVuj0gCLBwCYao6IyKSAT178nzgyy8Ds79vvuF5iJZFiohItjzyCAMhY8e6PRIJtJUrgTVrvFck/2yVKrFw/ogRQFKS26PJvthYYORIoFUroHBhoHFj/v+GG4Dhw1n7a8MGBqkbNPBWEAxgYdp33wV27AA+/NDt0Yj4hTLCREQywFqgdm12+d60idcU/nT77cCxYzx/FRERyZZWrViMPDaWHWAkPDz5JDBuHDsRXn6526O5sGnTWB/r+++Be+5xezSZc/o0lx6nLHn8+28+f911QPPmfNSr580abRfSsiWz2bZsAYoUcXs0EkDKCBMREQCs0dWzJ88Fpk/37762bweWLgXatfPvfkREJExERnLN/U8/uT0SCZRjx4CJE4EHH/R+EAxg8KtkSRaJDwZ793KZQNu2rGtWty4zvIoUYTZVVBSwbRtrtDVrFnxBMAAYPJgF/d980+2RiDhOGWEiIhmUlASUL89znN9/918B+0GDWCJj61agdGn/7ENERMLI6dMsPHnHHcDUqW6PRgLhiy+Ajh2BJUtYgyoYDBgAvPoqU+/LlXN7NGdKTgZWrEjN+vrzTz5fokRqra+GDdmYIpQ89RQbGURFAWXLuj0aCZBwyAhTIExEJBM++QTo2pWZ4nfc4Z99VKsG5M2rBl8iIuKgF19kfaJdu7TMKRzcdhtw6BADGMHSenrvXiAiAnj6aWDYMLdHAxw8CPz8MwNfP/0E/Psv62fVrp0a/KpWLXi+v1mxdy9rmzVurCB6GAmHQJiWRoqIZMJjj/H6YcgQ/2x/wwbWBdOySBERcVRkJDPDJkxweyTib+vX825a587BFaQpVgx44AFmsx07Fvj9WwusWsXulXfcwSWP7dszENa4MZea7tsH/PYb0LcvO3IG0/c3K4oVA3r1Yg23X391ezQijlFGmIhIJr3+OvDGG/7pRN+vH1cGxMUx215ERMQxNWsCp04Bq1eH/gV8OOvenbWpdu5kMCeYLF3KjkEjRrDYv78dOADMncuMrzlzWEsPAGrUYJH7Zs34e+PvLkledvw4l0VGRPi3Noh4RjhkhCkQJiKSSf/+C1x7LfDwwyyb4BRrWYMsIgKYP9+57YqIiABIXd+/ciUv9CX0JCQAV18NNGgATJni9mgyz1rg5puBxESmyDsddElKYn2vn37iY/ly1v8qVIhZX02aAHffDRQv7ux+g11Kzbmvv2YDBglp4RAI09JIEZFMKlqUK0zGjUu9ceiEVauAzZu1LFJERPykfXsgTx5e1Epomj6dta06d3Z7JFljDIO1f//NQv9O2LsX+Oor4KGHuNSvdm2m9lsLvPYasGwZlzxOmgR06KAg2Pn83/8BN93Ebk4JCW6PRiTblBEmIpIFMTFsaNSnDzBwoDPb7NkT+OADBtcKFXJmmyIiImdo354FwHftYlBMQkvDhjxJ2bqVhd2D0fHjQMmSQKNGzEDKrMRELuFLyfr66y8+X6wYs72aNuW2Cxd2dtyhbu5cZs0NHQq88ILboxE/CoeMMAXCRESyqE0bYMECYMcOoECB7G0rORm47jo2H5o505nxiYiInOPnnxkMmDKFhckldGzdClx/PfDmm8Crr7o9muzp0YN3B7dv51LPi4mLSw18zZsH/Pcf63rddhsDX02aAFWrBm9w0CuaNmUG3ZYt3r5rm5ysuc6GcAiE6adDRCSLevZkZ/IxY7K/raVLeQ6nZZEiIuJXDRow20bLI0PP55/z4j8y0u2RZN9TT7Ge12efnf/zCQksqNqzJ3DjjSyw+vjjwB9/MMA7dSoL4f/yC9P3q1dXYMQJgwcDR444txzCH0aM4B3qYsXYeKFDB6B/fy59XbGCJ+8S9pQRJiKSDXfeyYywmBggV66sb6drV16T7NuX/ewyERGRC3rlFeDtt/kH7Jpr3B6NOCExkanl1asDs2a5PRpnNG/OZY3btwOXXAJs2wbMns2srwULgPh4Pn/HHalZX5Uqqauhv3XuzJprGzcCZcq4PZpUiYnAiy8CH34I1K/PscXE8BEXd+ZrCxUCbrgh9XH99an/Llo07H+GwiEjTIEwEZFsmDkTuOceYOJEll3JisREZv3fdVfWSmGIiIhkSkwMULYs8NZbzJYRZ1gLrF7NTJSMLOdzUsoJyXffAa1bB3bf/vLjjwyG3XMPgy7R0Xy+TJnUwFe9erqDGGi7dvH40aKFd05cjxzhsorZs4HnnwfefZdLY1OcOMGlwymBsbSPHTu4lDJFwYJnBsnSPkqUCIsgmQJhHqVAmIh4RXIyULkykDcvu9Fn5W9jSrmWadOAe+91fowiIiLnuPNOdmfZtCksLuz8buNG4Lnn+EcdYKCgbt3UR0SEf/d/zz1c9rVjB5A7t3/3FSjJyUCVKsA///BuYZMmfNxwg35m3fb66+y8+fvv7MLppm3bgJYteSz7+GPgiScy9/6EBP6MnR0g27KF205MTH1tvnxnZo+lfZQsGTLLbxUI8ygFwkTES0aPZlmKefNYeiWzIiMZBNu7F7j0UufHJyIico6xY/kH6NdfWUfH35KSgNhYXqxGR/OisXXr4A9oHDnC+kPDhgH58wN9+/JiePFiYMkS4PBhvq5MGQbE6tXjx+uuc24MO3cC114LvPQSl7yGkhMn+DOiEyRvOXaMwd7rr+fPuVu/x0uX8jhy+jTw7bdZOxG/kMTE1Boo5wuUnTqV+tp8+fj7HgKBaAXCPEqBMBHxkpMngVKl2PHxp58y/95ixYD77lPdYhERCaBjx4DixbmcaPRo57Z74EBqsCvtx5gYZl6kdfvtwPDhrGsVbKwFxo9n8GnPHqBjRwahrroq9TVJScDatQyKLVrEwu0phbpLlUrNFqtXj//PajDhrbcYgNu8mZkpIoEwahSzr6ZO5YlsoE2YwN+7a69lXbzy5QO7/6QkBqFTAmP//svfwxCgQJhHKRAmIl6Tcg66Zg1w000Zf9/06VwO+dNPXB4pIiISMB07At98w0BO/kxc85w4wQu/s4Nd0dHAwYOpr8uVixkj5csD5crxUb48M0l+/JH1yfbvZ/HtgQNZpDoY/PUX8MwzzEapWRP46COgVq2Lvy85GVi3jkGxxYv5OHCAn4uISM0Wq1ePGWQZCYwlJzP4VaoUC8iLBEpiIu8CJyQA69ezcUEgJCcD/foBAwbwd+Xbb4HChQOz7zChQJhHKRAmIl5z6BDPYe+7j410MqptW2DhQtYdzU7XSRERkUxbsoS1wsaOBTp0OPNzZy9lTPkYHc2lQmmvIa6+OjXYlTboVbr0hf+4HT7MOkMffcRA3BtvAE8/7d2lRQcO8K7XZ58BRYoA77wDPPZY1usCJScDUVGpGWOLFzOrBGA3z7RLKcuWPX9gbP58oGFDZsc89FAWvzCRLJo9G2jWDPjgA+DZZ/2/v+PHeaz69lugUyfgk08CF4ALIwqEeZQCYSLiRc8/zxqdW7dmrCbusWNcQREZyfeJiIgElLUMWBUqBDz11IWXMhYseG6wKyW7K7td+6Ki+Ed07lygUiVeVDdsmL1tOikpCRg5EnjlFdYE69aNxcKvuMLZ/VjLovspQbFFi1hAFGC3urRLKcuXZ2CsXTsW6N+1S3W0JPCsBRo1YrfUmBjnfyfS2rULaNWK3amGDAFeeCH4awx6lAJhHqVAmIh40fbtXAGS0rX5YiZOBB5+mDfk69Tx//hERETO8fbbwMsv898pSxnPDnaVK8eClv686LQWmDED6N6dndruvRcYOpRZZW5asoTLINesYefCDz9kJ8NAsJaBybQZY7t28XPFijGb7/vvgS5dGDwUccPq1UCNGkDPnsCgQf7Zx6pV7Ax5+DBPoO+5xz/7EQAKhHmWAmEi4lUPPcR6nbGxwOWXX/i1LVvy3GH79pDptiwiIsEmIYGdI6+99uJLGQPh5EngvfdYMywpicXoe/XKXA0zJ+zcyX1PnMg076FDgTZt3M1AsZad6s7OGFu9mpl0Im557DFg8mRmNJYq5ey2p0/nnePChYGZM4GqVZ3dvpxDgTCPUiBMRLxq1SreFBs0iOfP6Tl4kM26nnuO2d0iIiKSRlwcA2ATJwIlSzLV+sEH/R+ISkgAhg0D+vdnMfCePYHevQMfiMsIazleLYkUt8XFcZn0ffexXp0TrAUGD2ZTjZo1mf1YvLgz25YLCodAmHIQREQcVL060KABVyicOpX+66ZNA06fBtq3D9zYREREgkbJkrygXrKE3STbtWNtrDVr/LfP2bOBG29k4KtBA9Yu69/fm0EwgEFBBcHEC0qWZM2uiROBP//M/vZOnWJX2969GQBftEhBMHGUAmEiIg7r2ZMlPCZOTP81kybxxln16oEbl4iISNCpUwdYsYLF6tevZ9r100+zg6NTtmxhzaFmzRhcmj2b2Sdlyji3D5FQ16sXg9Y9epzZVTaz9u9nAf6xY4F+/XjSnDevY8MUARQIExFxXOPGwE03cRXH+c4Ddu8GFi5kNpia3YiIiFxEzpzAE08AmzezY+Nnn/Fu0scfc/liVsXHsxNk5cr8wzxoEPD330CTJs6NXSRcXHYZ8MYbrF83c2bWtrFhA/C//wF//ME7yq+/rpNl8QsFwkREHGYMb4atX8+bymf75hsGyNq1C/zYREREgtaVV7L2wOrVTKnu1o0ZYosWZW471gJTpgAVK7Iof5s2wKZNLO55ySV+GbpIWOjcmZ1mX3qJNUAyY+5c4NZbgWPH+Dut+iHiRwqEiYj4Qbt2LJdwvkL4kyax4U3FioEfl4iISNCrUgWYNw+YOhU4ehS46y7WEdq+/eLvXbeO9b/atmUXuiVLgPHjgauv9v+4RUJd7twscL9pEzB6dMbf9+mnQNOm7F67fDlQu7b/xigCBcJERPwid27g+ed5QyttzdBt24Bly3STS0REJFuMYYe6qCjgzTeBWbOAChW4NOvEiXNff/gwWzVXq8aC+598wj/QdeoEfuwioaxlS6BuXdb3OnLkwq9NTASefZZ1/5o2BX77DbjuusCMU8KaAmEiIn7y+OMsl5A2K2zyZH5s29adMYmIiISUvHmBV18FNm4EWrViTaGKFYFvv+USyORkYMwYoFw5YPhw/nGOjgaeeoq1x0TEWcawUO6//7LuXnr++49Bs+HDgRdfBKZPBwoWDNw4JawZm52ODi7Jnz+/jY+Pd3sYIiIX1asXzwViYoDSpbkkMn9+YOlSt0cmIiISghYvZobJ2rVcMnnsGLtO3n47L7jVrlkkMB5+GJg2jU0uSpY883PbtgEtWjAo/cknDFCLZxhjjltr87s9Dn9SRpiIiB899xxvOL//PldvrF2rZZEiIiJ+U7cusHIlL67XrAHi4oBx41gLTEEwkcAZOJBZma+8cubzv/4K1KrFNuo//6wgmLhCGWEiIn4WGcnmVI89BowYAezcCRQv7vaoREREQlxK17rcud0dh0i46tWLNUJWrmQgetw4dpa87jrW9StXzu0RynmEQ0aYAmEiIn62fj0bXAFsVDVvnrvjERERERHxu8OHgRtuYG2QW29llthdd7GGX6FCbo9O0hEOgTAtjRQR8bPKldkIB9CySBEREREJE1dcAbz2GrBgAYNgjz8OzJmjIJi4LpfbAxARCQcDBrBDdJs2bo9ERERERCRAunRhXbA6dYBnnmFXSRGXaWmkiIiIiIiIiIhoaaSIiIiIiIiIiEioUCBMRERERERERETCggJhIiIiIiIiIiISFhQIExERERERERGRsKBAmIiIiIiIiIiIhAUFwkREREREREREJCwoECYiIiIiIiIiImFBgTAREREREREREQkLCoSJiIiIiIiIiEhYUCBMRERERERERETCggJhIiIiIiIiIiISFhQIExERERERERGRsKBAmIiIiIiIiIiIhAUFwkREREREREREJCwoECYiIiIiIiIiImFBgTAREREREREREQkLCoSJiIiIiIiIiMhFGWM+N8bsM8asS/PcA8aY9caYZGPMLWe9vo8xJsYYs8kYc3ea55v4nosxxvQO5NegQJiIiIiIiIiIiGTEWABNznpuHYD7APyS9kljTCUA7QBU9r3nE2NMTmNMTgAfA2gKoBKA9r7XBkSuQO1IRERERERERESCl7X2F2NMqbOe2wAAxpizX94KwGRrbQKAbcaYGAC1fJ+LsdZu9b1vsu+1Uf4beSplhImIiIiIiIiIiNOuARCb5v9xvufSez4glBEmIiIiIiIiIiIAkMsY82ea/39mrf3MtdH4gQJhIiIiIiIiIiICAInW2lsu/rIM2QkgIs3/S/qewwWe9zstjRQREREREREREafNANDOGJPHGFMaQFkAywGsAFDWGFPaGHMJWFB/RqAGFZQZYcePH7fGmBNuj8MhuQAkuj0IyRLNXWjQPAY/zWFw0/wFP81h8NMcBi/NXWjQPAa/UJrDvBf6pDFmEoB6AIoYY+IA9ANwEMBwAEUB/GCMWW2tvdtau94YMwUsgp8IoKu1Nsm3nW4A5gDICeBza+16f31B53wN1tpA7UvOwxjzp4NphxJAmrvQoHkMfprD4Kb5C36aw+CnOQxemrvQoHkMfprD4KKlkSIiIiIiIiIiEhYUCBMRERERERERkbCgQJj7QqoNaZjR3IUGzWPw0xwGN81f8NMcBj/NYfDS3IUGzWPw0xwGEdUIExERERERERGRsKCMMBERERERERERCQsKhGWSMSbCGLPQGBNljFlvjHnO93whY8xcY8xm38crfc9XMMb8boxJMMb0OGtbnxtj9hlj1l1kn02MMZuMMTHGmN5pnu/me84aY4r44+sNJR6bu7HGmG3GmNW+RzV/fM2hyGPzWN8Y85cxZp0x5ktjTC5/fM2hxKn5S2876exTx1CHeGz+dBzNIo/No46jWeDgHF5qjFlujFnj284bF9hnB992NxtjOqR5fqAxJtYYc8yfX3Oo8NjcLfL9XqYcR6/y59ceSjw2j22NMWt97x/kz687lDg1h2m2l9MYs8oYM+sC+9Rx1CustXpk4gGgBIAavn8XBBANoBKAwQB6+57vDWCQ799XAagJYCCAHmdt604ANQCsu8D+cgLYAqAMgEsArAFQyfe56gBKAfgHQBG3vzdef3hs7sYCaOP29yQYH16ZR/BGQiyAcr7XvQmgk9vfH68/nJq/9LaT0fnzfU7H0OCePx1Hg3wedRz1xBwaAAV8/84N4A8Atc+zv0IAtvo+Xun795W+z9X2jeeY29+XYHh4bO4WAbjF7e9JMD68Mo8ACgPYAaCo73VfAmjg9vcnGB5OzWGa7b0AYCKAWensT8dRDz2UEZZJ1trd1tq/fP8+CmADgGsAtAIPPPB9bO17zT5r7QoAp8+zrV8AHLzILmsBiLHWbrXWngIw2bcvWGtXWWv/yfYXFSa8NHeSdR6ax8IATllro32vmwvg/ux8beHAqfm7wHbOpmOog7w0f5J1HppHHUezyME5tNbalAyE3L7H+QoI3w1grrX2oLX2EDhXTXzbWGat3e3k1xfKvDR3knUemscyADZba//1vW4edBzNECevKYwxJQE0BzD6ArvUcdRDFAjLBmNMKTCj4A8AxdL88O4BUMyh3VwD3i1NEYfzn2RKJnhk7gb60pjfN8bkcWifYcXledwPIJcx5hbf820ARDi0z7Dg1PydtZ2z6RjqJx6ZPx1Hs8nledRx1AHZnUPfcp7VAPaBF2k6lgaIR+buC9+yyFeNMSbzX4W4PI8xAMobY0oZLi1vDR1HM82Bv4XDALwEIPkCr9Fx1EMUCMsiY0wBAFMBPG+tPZL2c9Zai/NH8sUDPDJ3fQBUANNrCwHoFYB9hhS359G3j3YA3jfGLAdwFECSP/cZSpyavwttR/zHI/On42g2uT2POo5mnxNzaK1NstZWA1ASQC1jTBW/DFbO4JG5e9haeyOAO3yPRzP5/rDn9jz6MoueAvA1gCVguQcdRzMhu3NojGkBYJ+1dqX/RilOUyAsC4wxucFflgnW2mm+p/caY0r4Pl8CjOhnZdsRaQpWdgGwE2dG9Uv6npMs8Mrc+VJxrbU2AcAX4LIRySAPzePv1to7rLW1APwC1haQi3Bq/s63HR1D/c8r86fjaPZ4aB51HM0ip/8WWmsPA1gIoIkx5n9p5vAe6FjqKK/MnbU25eNRsLaRjqOZ4KF5nGmt/Z+19lYAm6DjaIY5NIe3A7jHGPMPuPS/vjFmvI6j3qZAWCb5UobHANhgrX0vzadmAEjp/NABwPdZ2b61NtZaW833GAFgBYCyxpjSxphLwDunM7L+FYQvL81dmoOrAVOYL9i1UFJ5bB6v8n3MA2ajjMjKPsOJU/OX3nZ0DPUvL82fjqNZ57F51HE0Cxycw6LGmCt8/84LoBGAjdbaP9LM4QwAcwA0NsZcadhBrbHvOckkr8ydMSaX8XVM9gUDWkDH0Qzzyjz63pdyHL0SwNO4cJ0q8XFqDq21fay1Ja21pcC/bwustY/oOOpx1gMV+4PpAaAOmB65FsBq36MZWPB1PoDNYJHCQr7XFwfX/x4BcNj378t8n5sEYDdYcC8O6XRK8m0/Guy41DfN88/63pcIYBeA0W5/f7z88NjcLQDwN3jCMR6+bjF6BN08DgELa24C06ld//54/eHU/KW3nUzOn46hwT1/Oo6GxjzqOOruHN4EYJVvO+sAvHaBfXYE6xHFAIhM8/xg3/aSfR9fd/v74+WHV+YOQH4AK33vXw/gAwA53f7+BMvDK/Poe34SgCjfo53b35tgeTg1h2dtsx7S6Rp5kTnUcTTAD+P7xouIiIiIiIiIiIQ0LY0UEREREREREZGwoECYiIiIiIiIiIiEBQXCREREREREREQkLCgQJiIiIiIiIiIiYUGBMBERERERERERCQsKhImIiIiIiIiISFhQIExERERERERERMKCAmEiIiIiIiIiIhIW/h99UARl9EIPkgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1440x720 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 106
        },
        "id": "0-JYZjMn0y0n",
        "outputId": "f39ceb09-c6b3-4652-c05d-b9f24aed82cc"
      },
      "source": [
        "df_4[['vix','sptsm']].corr()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>vix</th>\n",
              "      <th>sptsm</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>vix</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.653989</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sptsm</th>\n",
              "      <td>-0.653989</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            vix     sptsm\n",
              "vix    1.000000 -0.653989\n",
              "sptsm -0.653989  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tGOmnjRpPjlu"
      },
      "source": [
        "In comparison to the S&P 500 index, the vix index is has a very important decreasing trend between 2011 and 2014, while S&P index has been growing since 2011. The two trajectories are opposite according to the graph."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pB4QnHYRGuSq"
      },
      "source": [
        "**13) Compute the empirical partial autocorrelation fuction. Which order $p$ does it suggest for AR($p$) modelling of this data ?**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "OrFVjc6VzVF_",
        "outputId": "c86deb41-c25b-4866-b79a-56ea73be3a48"
      },
      "source": [
        "plot_pacf(df_3['vix'], lags=30)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQtrTIZ8GKFc"
      },
      "source": [
        "With the previous pacf on the vix data we can choose p=2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B4vhUePnGxwd"
      },
      "source": [
        "**14) Fit the corresponding model.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0KLzfnef7Egl"
      },
      "source": [
        "model_ar = ARIMA(df_3['vix'], order=(2,0,0))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t4hbXQek7OrL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 342
        },
        "outputId": "bd14c913-cf06-4544-bd3b-c163ebaaa1ef"
      },
      "source": [
        "res_ar = model_ar.fit()\n",
        "res_ar.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>vix</td>       <th>  No. Observations:  </th>    <td>756</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 0)</td>    <th>  Log Likelihood     </th> <td>-1406.896</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.553</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Thu, 25 Mar 2021</td> <th>  AIC                </th> <td>2821.792</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>20:35:14</td>     <th>  BIC                </th> <td>2840.304</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-03-2011</td>    <th>  HQIC               </th> <td>2828.922</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 01-06-2014</td>   <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td>   18.5552</td> <td>    1.973</td> <td>    9.403</td> <td> 0.000</td> <td>   14.687</td> <td>   22.423</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.vix</th> <td>    0.8743</td> <td>    0.036</td> <td>   24.184</td> <td> 0.000</td> <td>    0.803</td> <td>    0.945</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.vix</th> <td>    0.0984</td> <td>    0.036</td> <td>    2.722</td> <td> 0.007</td> <td>    0.028</td> <td>    0.169</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0254</td> <td>          +0.0000j</td> <td>           1.0254</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -9.9082</td> <td>          +0.0000j</td> <td>           9.9082</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    vix   No. Observations:                  756\n",
              "Model:                     ARMA(2, 0)   Log Likelihood               -1406.896\n",
              "Method:                       css-mle   S.D. of innovations              1.553\n",
              "Date:                Thu, 25 Mar 2021   AIC                           2821.792\n",
              "Time:                        20:35:14   BIC                           2840.304\n",
              "Sample:                    01-03-2011   HQIC                          2828.922\n",
              "                         - 01-06-2014                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         18.5552      1.973      9.403      0.000      14.687      22.423\n",
              "ar.L1.vix      0.8743      0.036     24.184      0.000       0.803       0.945\n",
              "ar.L2.vix      0.0984      0.036      2.722      0.007       0.028       0.169\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0254           +0.0000j            1.0254            0.0000\n",
              "AR.2           -9.9082           +0.0000j            9.9082            0.5000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jOke1-LLG0Z-"
      },
      "source": [
        "**15) Test the quality of the 1 ahead prediction of the model for the last 200 observations of $Y_t$. Compare with a fitted AR(1) model.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cz9-uqs37ezK"
      },
      "source": [
        "model_ar_2 = ARIMA(df_3['vix'][:-200], order=(2,0,0))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vvHxq6kSe9Tt"
      },
      "source": [
        "model_ar_3 = ARIMA(df_3['vix'][:-200], order=(1,0,0))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YjdGT6l17e62",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 342
        },
        "outputId": "80e08544-b8ff-43cc-e3b2-1d113230383b"
      },
      "source": [
        "res_ar_2 = model_ar_2.fit()\n",
        "res_ar_2.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>vix</td>       <th>  No. Observations:  </th>    <td>556</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 0)</td>    <th>  Log Likelihood     </th> <td>-1097.996</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.739</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Thu, 25 Mar 2021</td> <th>  AIC                </th> <td>2203.991</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>20:35:15</td>     <th>  BIC                </th> <td>2221.274</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-03-2011</td>    <th>  HQIC               </th> <td>2210.742</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 03-20-2013</td>   <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td>   19.8349</td> <td>    2.310</td> <td>    8.586</td> <td> 0.000</td> <td>   15.307</td> <td>   24.363</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.vix</th> <td>    0.8659</td> <td>    0.042</td> <td>   20.562</td> <td> 0.000</td> <td>    0.783</td> <td>    0.948</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.vix</th> <td>    0.1040</td> <td>    0.042</td> <td>    2.466</td> <td> 0.014</td> <td>    0.021</td> <td>    0.187</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0280</td> <td>          +0.0000j</td> <td>           1.0280</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>          -9.3575</td> <td>          +0.0000j</td> <td>           9.3575</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    vix   No. Observations:                  556\n",
              "Model:                     ARMA(2, 0)   Log Likelihood               -1097.996\n",
              "Method:                       css-mle   S.D. of innovations              1.739\n",
              "Date:                Thu, 25 Mar 2021   AIC                           2203.991\n",
              "Time:                        20:35:15   BIC                           2221.274\n",
              "Sample:                    01-03-2011   HQIC                          2210.742\n",
              "                         - 03-20-2013                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         19.8349      2.310      8.586      0.000      15.307      24.363\n",
              "ar.L1.vix      0.8659      0.042     20.562      0.000       0.783       0.948\n",
              "ar.L2.vix      0.1040      0.042      2.466      0.014       0.021       0.187\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0280           +0.0000j            1.0280            0.0000\n",
              "AR.2           -9.3575           +0.0000j            9.3575            0.5000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RxUwd-j8fDuw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "fb965f45-8230-481b-b39c-40c8fbf3e46a"
      },
      "source": [
        "res_ar_3 = model_ar_3.fit()\n",
        "res_ar_3.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>vix</td>       <th>  No. Observations:  </th>    <td>556</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 0)</td>    <th>  Log Likelihood     </th> <td>-1101.019</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.749</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Thu, 25 Mar 2021</td> <th>  AIC                </th> <td>2208.038</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>20:35:15</td>     <th>  BIC                </th> <td>2221.001</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-03-2011</td>    <th>  HQIC               </th> <td>2213.102</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 03-20-2013</td>   <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td>   19.9336</td> <td>    2.110</td> <td>    9.448</td> <td> 0.000</td> <td>   15.798</td> <td>   24.069</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.vix</th> <td>    0.9665</td> <td>    0.011</td> <td>   91.820</td> <td> 0.000</td> <td>    0.946</td> <td>    0.987</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0347</td> <td>          +0.0000j</td> <td>           1.0347</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    vix   No. Observations:                  556\n",
              "Model:                     ARMA(1, 0)   Log Likelihood               -1101.019\n",
              "Method:                       css-mle   S.D. of innovations              1.749\n",
              "Date:                Thu, 25 Mar 2021   AIC                           2208.038\n",
              "Time:                        20:35:15   BIC                           2221.001\n",
              "Sample:                    01-03-2011   HQIC                          2213.102\n",
              "                         - 03-20-2013                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         19.9336      2.110      9.448      0.000      15.798      24.069\n",
              "ar.L1.vix      0.9665      0.011     91.820      0.000       0.946       0.987\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0347           +0.0000j            1.0347            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z6k7f8S1emxm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "13ca01c9-52c8-458f-dd6f-9fef2098d24e"
      },
      "source": [
        "df_3['vix'][-200:]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2013-03-21    13.07\n",
              "2013-03-22    13.34\n",
              "2013-03-25    12.85\n",
              "2013-03-26    12.95\n",
              "2013-03-27    13.72\n",
              "              ...  \n",
              "2013-12-30    12.21\n",
              "2013-12-31    12.87\n",
              "2014-01-02    13.43\n",
              "2014-01-03    14.32\n",
              "2014-01-06    14.06\n",
              "Freq: C, Name: vix, Length: 200, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rMKCXmfZex8H"
      },
      "source": [
        "predictions = res_ar_2.predict(start=datetime(2013,3,21), end=datetime(2014,1,6))\n",
        "predictions_2 = res_ar_3.predict(start=datetime(2013,3,21), end=datetime(2014,1,6))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qz-eswRaIKbn",
        "outputId": "08fc8559-f37a-4473-96d0-9b45a9deecd5"
      },
      "source": [
        "res_ar_2.forecast(steps=10)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([13.36506473, 13.54090424, 13.71240086, 13.87917798, 14.04141705,\n",
              "        14.19923605, 14.35275599, 14.50209391, 14.64736374, 14.78867629]),\n",
              " array([1.73917711, 2.30056466, 2.73809628, 3.09469626, 3.39793733,\n",
              "        3.66182205, 3.89509888, 4.10364643, 4.29166503, 4.46229054]),\n",
              " array([[ 9.95634022, 16.77378923],\n",
              "        [ 9.03188036, 18.04992812],\n",
              "        [ 8.34583075, 19.07897096],\n",
              "        [ 7.81368477, 19.94467119],\n",
              "        [ 7.38158227, 20.70125184],\n",
              "        [ 7.02219672, 21.37627539],\n",
              "        [ 6.71850246, 21.98700952],\n",
              "        [ 6.4590947 , 22.54509312],\n",
              "        [ 6.23585484, 23.05887264],\n",
              "        [ 6.04274755, 23.53460503]]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4Cvn4RGPeZbP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "outputId": "7fe76782-5d1b-4a78-e042-e25ce4ea19f9"
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(20, 10))\n",
        "ax.plot(df_3['vix'], label = 'true date')\n",
        "ax.plot(res_ar_2.fittedvalues, label = 'AR(2,0,0) fitted data')\n",
        "ax.plot(res_ar_3.fittedvalues, label = 'AR(1,0,0) fitted data')\n",
        "ax.plot(predictions, label = 'AR(8,0,0)')\n",
        "ax.plot(predictions_2, label = 'AR(1,0,0)')\n",
        "#ax.plot(predictions_3, label = 'MA(0,0,11) on all observations')\n",
        "ax.legend()\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tx_AbNYfrBBW"
      },
      "source": [
        "# VIX data and ARMA modeling #\n",
        "We now consider an ARMA$(p,q)$ model, namely, up to a demeaning constant,\n",
        "$$\n",
        "  Y_t-\\sum_{k=1}^p \\phi_k Y_{t-k}=\\sum_{k=1}^q \\theta_k \\epsilon_{t-k} + \\epsilon_t\n",
        "$$\n",
        "where $\\epsilon_t$ are the innovations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LZSXJa2SG3bR"
      },
      "source": [
        "**16) The AIC criterion is defined by, up to some normalizing constant: \n",
        "$$\n",
        "\\mathrm{AIC}(p,q) \\sim \\log( \\hat{\\sigma}(p,q) ) +2(p+q)/T \\;, \n",
        "$$ \n",
        "where $T$ is the\n",
        "length of the time series, and $\\hat{\\sigma}(p,q)$ is the innovation variance\n",
        "of the fitted ARMA$(p,q)$ model. This criterion is an output of** *arima()*\n",
        "**command. Determine $(p,q)\\in\\{0,1,\\dots,5\\}^2$ that minimizes the AIC\n",
        "criterion.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ED32FesaJz0k"
      },
      "source": [
        "def best_params():\n",
        "  p_values = [1, 2, 3, 4, 5]\n",
        "  q_values = [1, 2, 3, 4, 5]\n",
        "  aic = 999999\n",
        "  min_p = 1\n",
        "  min_q = 1\n",
        "  for p in tqdm.tqdm(p_values):\n",
        "    for q in q_values:\n",
        "      try:\n",
        "        model = ARIMA(df_3['vix'], order=(p, 0, q))\n",
        "        res = model.fit()\n",
        "        aic_candidate =  res.aic\n",
        "        if aic_candidate < aic:\n",
        "          min_p = p\n",
        "          min_q = q\n",
        "          aic = aic_candidate\n",
        "      except:\n",
        "        continue\n",
        "  print(f'Minimum AIC : {aic}, order = ({min_p}, 0, {min_q})')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vFtaNLHzKLix",
        "outputId": "913d9cd6-8132-485e-ce5f-6d8b5e4ce898"
      },
      "source": [
        "best_params()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 5/5 [00:11<00:00,  2.26s/it]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Minimum AIC : 2802.2456749514386, order = (1, 0, 4)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "peRagwS-G56G"
      },
      "source": [
        "**17)  Test the quality of the 1 ahead prediction of the model for the last 200 observations of $Y_t$. Compare with the previous AR model.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rlLspJcbK22G"
      },
      "source": [
        "best_model = ARIMA(df_3['vix'][:-200], order=(1,0,4))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "v_-cPhJdLQb_",
        "outputId": "232b1890-adfb-4e84-a2ea-2231e83e7648"
      },
      "source": [
        "res_best = best_model.fit()\n",
        "res_best.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>vix</td>       <th>  No. Observations:  </th>    <td>556</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 4)</td>    <th>  Log Likelihood     </th> <td>-1088.015</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>1.708</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Thu, 25 Mar 2021</td> <th>  AIC                </th> <td>2190.030</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>20:58:45</td>     <th>  BIC                </th> <td>2220.275</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-03-2011</td>    <th>  HQIC               </th> <td>2201.843</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 03-20-2013</td>   <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td>   19.2390</td> <td>    3.178</td> <td>    6.054</td> <td> 0.000</td> <td>   13.011</td> <td>   25.468</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.vix</th> <td>    0.9879</td> <td>    0.007</td> <td>  149.710</td> <td> 0.000</td> <td>    0.975</td> <td>    1.001</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.vix</th> <td>   -0.1423</td> <td>    0.043</td> <td>   -3.325</td> <td> 0.001</td> <td>   -0.226</td> <td>   -0.058</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.vix</th> <td>   -0.0127</td> <td>    0.043</td> <td>   -0.299</td> <td> 0.765</td> <td>   -0.096</td> <td>    0.071</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L3.vix</th> <td>   -0.1325</td> <td>    0.042</td> <td>   -3.166</td> <td> 0.002</td> <td>   -0.214</td> <td>   -0.050</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L4.vix</th> <td>   -0.1167</td> <td>    0.040</td> <td>   -2.915</td> <td> 0.004</td> <td>   -0.195</td> <td>   -0.038</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0123</td> <td>          +0.0000j</td> <td>           1.0123</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.3837</td> <td>          -0.0000j</td> <td>           1.3837</td> <td>          -0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>          -0.1719</td> <td>          -1.6786j</td> <td>           1.6874</td> <td>          -0.2662</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.3</th> <td>          -0.1719</td> <td>          +1.6786j</td> <td>           1.6874</td> <td>           0.2662</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.4</th> <td>          -2.1755</td> <td>          -0.0000j</td> <td>           2.1755</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    vix   No. Observations:                  556\n",
              "Model:                     ARMA(1, 4)   Log Likelihood               -1088.015\n",
              "Method:                       css-mle   S.D. of innovations              1.708\n",
              "Date:                Thu, 25 Mar 2021   AIC                           2190.030\n",
              "Time:                        20:58:45   BIC                           2220.275\n",
              "Sample:                    01-03-2011   HQIC                          2201.843\n",
              "                         - 03-20-2013                                         \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         19.2390      3.178      6.054      0.000      13.011      25.468\n",
              "ar.L1.vix      0.9879      0.007    149.710      0.000       0.975       1.001\n",
              "ma.L1.vix     -0.1423      0.043     -3.325      0.001      -0.226      -0.058\n",
              "ma.L2.vix     -0.0127      0.043     -0.299      0.765      -0.096       0.071\n",
              "ma.L3.vix     -0.1325      0.042     -3.166      0.002      -0.214      -0.050\n",
              "ma.L4.vix     -0.1167      0.040     -2.915      0.004      -0.195      -0.038\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0123           +0.0000j            1.0123            0.0000\n",
              "MA.1            1.3837           -0.0000j            1.3837           -0.0000\n",
              "MA.2           -0.1719           -1.6786j            1.6874           -0.2662\n",
              "MA.3           -0.1719           +1.6786j            1.6874            0.2662\n",
              "MA.4           -2.1755           -0.0000j            2.1755           -0.5000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ALZ4EuiWLfll"
      },
      "source": [
        "predictions_best = res_best.predict(start=datetime(2013,3,21), end=datetime(2014,1,6))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "UI8D6C7DLsO0",
        "outputId": "f570a57b-b73c-4387-e7a7-48954c1f7689"
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(20, 10))\n",
        "ax.plot(df_3['vix'][-400:], label = 'true date')\n",
        "ax.plot(res_best.fittedvalues[-400:], label = 'ARMA(1,4) fitted data')\n",
        "ax.plot(res_ar_3.fittedvalues[-400:], label = 'AR(1) fitted data')\n",
        "ax.plot(predictions_best, label = 'ARMA(14)')\n",
        "ax.plot(predictions_2, label = 'AR(2)')\n",
        "#ax.plot(predictions_3, label = 'MA(0,0,11) on all observations')\n",
        "ax.legend()\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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+DIDna6qXiIiIiIiIlMeFF15YlueMHz++01EzKU0VP2Xw4p4Xufzxy0l76cHeStkk0m0AeFYVPyIiIiIiIiLDlYKfMvjTwT/xcuPLNKeaB3srZZMf567gR0RERERERGTYUvBTBr71AUhkEoO8k/JR8CMiIiIiIiIy/Cn4KQOfERj8eNnvklFzZxEREREREZFhS8FPGeQrfryRFPwkAVX8iIiIiIiIjFSPPvooxhh27NiRv9bQ0EBFRQV1dXWccsopXHXVVaTT7f1s//CHP/C5z30OgB07dnDWWWcRjUZZsWJFfk0qlWLBggVkMqWHBd1zzz1Mnz6dK664grVr17J8+fL8fl555ZX8uvvvv5+33367T9+poaGBmTNn9rju6quvZs2aNd2uOZLPH4oU/JTBiDzq5aUA8ILvJiIiIiIiIiNLfX0955xzDvX19UXXTzrpJLZs2cK2bdvYvXs3Dz30UP6973znO9xwww0AHHPMMdxzzz388z//c9H9kUiE888/nwcffLDk5/7oRz/iqaeeYvXq1SxevJhbbrkFKE/wU06D/fnlouCnDHJVMSOq4sfPJrqq+BERERERERl5Wltb2bhxI6tWreKBBx4oucZ1XebNm8dbb70FQEtLC1u3bmX27NkATJgwgTPOOINwONzp3iVLlrB69epO16+77jr+/Oc/c9FFF3H33Xdz//3386UvfYnnn3+etWvXcuONN1JXV8edd97Jpk2buOKKK6irqyMej7N582bOPfdcTj/9dC688EL27NkDwObNm5k9ezazZ8/mhz/8YcnvYq3lS1/6Eh/84Af52Mc+xr59+/Lv3XbbbZxxxhnMnDmTa6+9Fmsta9as6fT5pdYNB6HB3sBIkPtjj6iKHz9bkqeKHxERERERkYFz5+/uZMfBHT0v7INpx0zj5nk3d7vmscceY+HChUydOpXa2lo2b97M6aefXrQmkUjw4osvsnLlSgA2bdrUq2NUADNnzuSll17qdP3HP/4xTz75JOvXr2fcuHHcf//9AMyfP5/FixfziU98gssuuwyAJ554ghUrVjB37lzS6TT/8A//wGOPPcb48eN58MEH+drXvsZPf/pT/u7v/o4f/OAHLFiwgBtvvLHkfh555BH+9Kc/8corr7B3715OOeUUPvvZzwLwpS99iW984xsAXHnllTz++ONcdtll/OAHP8h/flfrLr744l79PgaTKn7KwEscAkZYxY9V8CMiIiIiIjJS1dfXs2zZMgCWLVtWdNxr586d1NXVceyxxzJx4kRmzZoFwJ49exg/fnyvnu+6LpFIhJaWlrLs909/+hMvv/wyF1xwAXV1ddx+++3s3r2bpqYmmpqaWLBgAZANZEp55plnuPzyy3Fdl/e973189KMfzb+3fv16PvShD3Hqqaeybt06tm/fXvIZvV031Kjipwzs/lcBSLQ1DvJOyidO9ohXRsGPiIiIiIjIgOmpMmcgHDx4kHXr1rFt2zaMMXiehzGGu+66C2jv8XPgwAHOPvts1q5dy+LFi6moqCCR6H3BQzKZJBaLlWXP1lpmzJjBCy+8UHS9qampX89NJBJ84QtfYNOmTRx//PHceuutJb9jb9cNRar4KYNcH5xk8tAg76Q80n6aXO91VfyIiIiIiIiMLGvWrOHKK6/kjTfeoKGhgV27djFlyhSeffbZonXjxo1j+fLl3HHHHQBMnz6d119/vVef0djYyLhx40r2/+lKVVVVUYVQ4c8f/OAH2b9/fz74SafTbN++nZqaGmpqati4cSNAyb5CAAsWLODBBx/E8zz27NnD+vXrAfLhzbhx42htbS2a9FX4+d2tG+oU/JSBDcKReKp1kHdSHvFMPP/aQ8GPiIiIiIjISFJfX8/SpUuLrl166aWdpntBtklzW1sbzz77LNOmTaO5uTkfhrzzzjtMmjSJ7373u9x+++1MmjSJQ4eyBRHr169n0aJFfdrXsmXLuOuuuzjttNPYuXMnV199Nddddx11dXV4nseaNWu4+eabmT17NnV1dTz//PMA/OxnP+OLX/widXV1XTZcXrp0KSeffHJ+RP1ZZ50FQE1NDZ///OeZOXMmF154IWeccUb+nsLPj0ajXa4b6szR7EI9d+5cu2nTpqP2eUfLikeX8fPm7fz95MV86dxvD/Z2+m3v4b18bM3HAJhjRvHzq14c5B2JiIiIiIiMHK+++irTp08f7G0ckbvvvpuqqiquueaabtd98pOfZPny5UydOvUo7ey9o9S/H2PMZmvt3FLrVfFTBrnjUMn04UHeSXkUVvz4OuolIiIiIiIigeuvv55oNNrtmlQqxZIlSxT6DBEKfsogf9RrBAY/HkevIkxERERERESGtlgs1uXkrJxIJMJVV111lHYkPdFUrzLIVfwkCgKT4SwX/IStJaPgR0RERERERGTYUsVPGeQqfpKZ4THKrSet6WyT6irfV3NnERERERERkWFMwU8Z5Ct+vJER/DQnmgCo9Twd9RIREREREREZxhT8lIElF/wkB3kn5dEcbwSC4OcoTn0TERERERERkfJS8FMGuXAk4aUGeSfl0RQ/gLGWsZ5PZrA3IyIiIiIiIgPi0UcfxRjDjh07AGhoaKCiooK6ujpOOeUUrrrqKtLpNAAbNmzAGMN9992Xv3/Lli0YY1ixYkX+WiaTYfz48dxyyy2dPu+yyy7jz3/+MwBf+9rXOP7446msrCy5t//8z//EGMOmTZsA2LZtG1dffXVZvvd7jYKfMsiNPE/46UHeSXk0xRsZ4/uErcXXUS8REREREZERqb6+nnPOOYf6+vr8tZNOOoktW7awbds2du/ezUMPPZR/b+bMmUU/19fXM3v27KJnPvXUU0ydOpWHH34YW3CCZPv27Xiex/vf/34ALr74Yn73u9+V3FdLSwsrV67kQx/6UP7aqaeeyu7du3nzzTf796XfgxT8lEE++LEjoz6mOfkuNb5PCDTVS0REREREZARqbW1l48aNrFq1igceeKDT+67rMm/ePN566638tRNPPJFEIsHevXux1vLkk09y0UUXFd1XX1/Pl7/8ZU444QReeOGF/PXVq1dzySWX5H8+88wzmThxYsm9ff3rX+fmm28mFosVXb/44otL7lW6p3HuZZCrikn4IyP4aUo2U+35OE4Yb7A3IyIiIiIiMoK9853vkHx1R1mfGZ0+jeP+7//tds1jjz3GwoULmTp1KrW1tWzevJna2tr8+4lEghdffJGVK1cW3XfZZZfx8MMPc9pppzFnzhyi0WjRPU8//TQ/+clPaGpqor6+nvnz5wPw3HPPcfnll/e499///vfs2rWLRYsWcddddxW9N3fuXJYvX85NN93U43OknSp+yiA3zj0xQmKS5tQhanwf141oqpeIiIiIiMgIVF9fz7JlywBYtmxZ/rjXzp07qaur49hjj2XixInMmjWr6L5Pf/rTPPzww9TX13cKch5//HHOO+88KioquPTSS3n00UfxvOz/T96zZw/jx4/vdk++7/OVr3yFf/3Xfy35/oQJE3j77beP6Pu+l6nipwxy4UhyhEzAakq1cLLnEYpE8RgZk8pERERERESGop4qcwbCwYMHWbduHdu2bcMYg+d5GGP44he/mO/xc+DAAc4++2zWrl3L4sWL2/d73HGEw2GeeuopVq5cyfPPP59/r76+no0bNzJ58mQAGhsbWbduHRdccAEVFRUkEolu99XS0sLLL7/MRz7yEQDeeecdFi9ezNq1a5k7dy6JRIKKioqy/z5GOlX8lEGu4idubFHzquGqKXOYat/HjVRpqpeIiIiIiMgIs2bNGq688kreeOMNGhoa2LVrF1OmTGHXrl35NePGjWP58uXccccdne6/7bbbuPPOO3FdN3/t0KFDPPvss7z55ps0NDTQ0NDAD3/4w3wl0fTp03n99de73Vd1dTUHDhzI33/mmWfmQx+A1157jZkzZ5bjV/CeouCnDLyCsCflD++R7ikvRdxPU+P5uJFKPDPYOxIREREREZFyqq+vZ+nSpUXXLr300k4hz5IlS2hra+PZZ58tuj5//nyWLFlSdO2RRx7hox/9aFHPn0suuYRf//rXJJNJFi1axIYNG/Lv3XTTTUyaNIm2tjYmTZrErbfe2uO+169fz6JFi3r5LSXHHM0Klblz59pNmzYdtc87Wv5h9blsyBwEYOOyjVRHqwd5R0duX9s+zn/4fL5+KMk7E2fys9bX+MPVLw/2tkREREREREaMV199lenTpw/2No6qeDzOeeedx3PPPVdUKdRbyWSSc889l40bNxIKvbe71pT692OM2WytnVtqvSp+yiA3zh0gnokP4k76rynZBEB1pBrXuGSMGRHH10RERERERGTwVFRU8K1vfatoPHxfvPnmmyxfvvw9H/ocCf3GysAvmHyVzHTfrGqoa042A1ATG4vjZFNY3/q4pu+JrIiIiIiIiEjOhRdeeMT3nnzyyZx88sll3M17hyp+ysAvqIhJJJoGcSf9l6v4qRk1gZDJ5oKerxbPIiIiIiIiIsORgp8yKKz4iQ/34CfYf3XlcbhBxU/G00h3ERERERERkeFIwU8ZFPbASSaHd/DTfPgdAGrGHI/rBBU/GQU/IiIiIiIiIsORgp8y8LBU+NkGz4nEoUHeTf80te4h5vvExvwVoSD48RX8iIiIiIiIiAxLCn7KwMdSEVT9JNItg7yb/mlq20e170PlBNygx4+OeomIiIiIiIw8jz76KMYYduzYAUBDQwMVFRXU1dVxyimncNVVV5FOp/Pr//CHP/C5z30OgNWrVzNr1ixOPfVU5s+fzx//+EcAUqkUCxYsIJNRr9ihQsFPGfjWZ1Su4ic5vIOf5vi71Hg+VB7bftTLSw3yrkRERERERKTc6uvrOeecc6ivr89fO+mkk9iyZQvbtm1j9+7dPPTQQ/n3vvOd73DDDTcAMGXKFP7nf/6Hbdu28fWvf51rr70WgEgkwvnnn8+DDz54dL+MdEnBTxn4wKigzU8iNbyDn6ZUMzV+NvgJ5YMfVfyIiIiIiIiMJK2trWzcuJFVq1bxwAMPdHrfdV3mzZvHW2+9BUBLSwtbt25l9uzZAMyfP5+xY8cCcOaZZ7J79+78vUuWLGH16tVH4VtIb4QGewMjgY9lVJChJdJtg7yb/mlKH2aqD8SqcRwd9RIRERERERlIzz70Ggd2tZb1meOOr+TDn57a7ZrHHnuMhQsXMnXqVGpra9m8eTO1tbX59xOJBC+++CIrV64EYNOmTcycObPks1atWsVFF12U/3nmzJm89NJLZfgmUg6q+CkD31pGBf1wEunDg7yb/mn2E9S4MTAG1wkDmuolIiIiIiIy0tTX17Ns2TIAli1blj/utXPnTurq6jj22GOZOHEis2bNAmDPnj2MHz++03PWr1/PqlWruPPOO/PXXNclEonQ0jK8T8SMFKr4KQMfS8QJEbIpEpn4gH/eln1b+EvzX1h68tKyPte3Ps02Q3V4FEDBUa90d7eJiIiIiIjIEeqpMmcgHDx4kHXr1rFt2zaMMXiehzGGL37xi/kePwcOHODss89m7dq1LF68mIqKChKJRNFztm7dyjXXXMMTTzxRVC0EkEwmicViR/NrSRdU8VMGPhbHCRG19qgEP2teref7v/9e2Z/bkmrBB6oj1QC4blDx4yv4ERERERERGSnWrFnDlVdeyRtvvEFDQwO7du1iypQp7Nq1K79m3LhxLF++nDvuuAOA6dOn8/rrr+fff/PNN/nkJz/Jf/zHfzB1anF41djYyLhx4wiHw0fnC0m3FPyUgQ84xhCzkMgkelzfX4k9W8i0HezbTb/8a1j37W6XNCebAaiJZRt05Y96qcePiIiIiIjIiFFfX8/SpcUnSC699NJ8yJOzZMkS2traePbZZ5k2bRrNzc3541u33XYbjY2NfOELX6Curo65c+fm71u/fj2LFi0a+C8ivaKjXmXgY3FwiAHJoxCSJDNtpLF9u+mdbZDqvv9Qc9sBAGpGZc9thnIVPxrnLiIiIiIiMmKsX7++07UbbrghP6o9xxjDH//4x/zPn/3sZ3nwwQe55ppruO+++7jvvvtKPv+Xv/wly5cvL++m5Yip4qcMfGuzFT84JPyBD0kSfoZMX29KxwdWuJkAACAASURBVKF5V7dLmg69CUB15USgveInox4/IiIiIiIi73nXX3890Wi02zWpVIolS5Z0Ov4lg0cVP2XgA4Zs8BM/Cv1wkjZD2vTtnlQ6jkm2EPZ9cErnfU2HssFQTdUkABxHFT8iIiIiIiKSFYvFuPLKK7tdE4lEuOqqq47SjqQ3VPFTBj7gGoeYcUkeheAnYT08Y/B9r3c3WMs146u4c2wltO7tcllz6zsA1NRMBgqOeqm5s4iIiIiISFlZ28f2HSIc2b8bBT9lkO3xY4g5IRK9DWP6IWl9ADKZXvYTyiRoCIf5bUUMmnd3uaypbR/GWqpqTgTAdSLZ24/C8TUREREREZH3ilgsRmNjo8If6RNrLY2NjcRisT7dp6NeZZCf6uWE2ecfhebOBMFP+jCRyKge1/upwzQ7Du+6Loca/8SY488oua4pcZAxvo9bFfT4CWUrfnyvzx2FREREREREpAuTJk1i9+7d7N+/f7C3IsNMLBZj0qRJfbpHwU8Z5KZ6RZ0IiaAapy3dhuu4RN3uG18diUQw0Sudifdq/eF4I77JNgXavn8rZ3Wxrjl5iBprIJTdcyio+FGPHxERERERkfIJh8NMmTJlsLch7xE66lUGuYqfCjeSD2X+z//8H27/7e0D8nnJXPCTauvV+tyYdoCXm17vcl1TppVq054FukFolVGPHxEREREREZFhSRU/ZZANfhzCboyEyYYy7xx+Z8DOayaCiV6ZXlb8NMcLgp/4O12v8xKML6hQct2g4sfXUS8RERERERGR4UgVP2XgQ/aoVyhGwhjwPdJ+mowtf2Di+R6Z4NhWOt3Lip94IwATMx4ve61drmvyM9SERud/dp1Q8Jmq+BEREREREREZjhT8lIGHzTZ3DlWQNgYv2ULKS5EZgEqZZCaRf50peN2dQ8l3AZhPjH2OZV/bvs6LrKXJWKojY/KX3FDuqJcqfkRERERERESGIwU/ZWDJHvWqCGUnbCUTTaS8FN4AjHZPJg/lX2cyvaz4STQDcM6o4wF4ec9Lndak2hqJO4aa2DH5a7keP56nih8RERERERGR4UjBTxnkevxEw9ngJx5vJOWn8OxABD/N+dfpTO9GxzensvfMm3AarrW8/PaLndY0vbsTgJrRE/LXQkHw4w/AkTURERERERERGXgKfsrAN+BgiEUqgWzFT8bPDMgRqURRxU8vmzunWqjwfcZMmMkHUmlebtzeaU1TUwMA1aOPy1/LNXfWUS8RERERERGR4UnBTxnkKn5ywU8i0Zzt8TMAlTLJVHvwk+5lj5/mdCvVvg/jpjIzmWJ7yxudJo41t+wCoGbMpPw1TfUSERERERERGd4U/JRBe/CTbYx8OPkunvUGqOKnJf8609ujXpk2qj0fxp7IzHSGQ36SXUHQk9PUmh3zXlN9Yv6aG44BCn5EREREREREhisFP2WQD36iVQC0JLJTtAqbO8d7eSyrJ8lU+zj2tNfLqV6ZtmzFT3g0MyNjAdh2YFvRmqbD2Ulf1WOOz1/L9fhR8CMiIiIiIiIyPCn46SdrLb4xQfCTrfg5lGgC2nvjbNm3hfn189l7eG+/Py+Rbg9+el3x4yWotoAb4qTK44lZw8sHXi5ekzgIQE1sbP6ak+vxMwBNqkVERERERERk4Cn46SdLtleOYxxiQWhyKOjDk+vx807bO2T8DPva9vX785Lpw/nXGS/Vq3ua/RRjbPZPHa4+nmkZv1Pw05RsJmYhForlr4WcMKCKHxEREREREZHhSsFPP+VGtju0Bz8tqWwfntxRL9/3AUh6vavQ6U4i1ZZ/ne7F86y1HPJTjDFu9kL18cyMt7Lj4I6iHkRNfpLq3JqA62R/Hoix9CIiIiIiIiIy8Hod/BhjXGPMH4wxjwc/TzHGvGiMed0Y86AxJjJw2xy6ctOxXMchFq0GoCWoyslV/OSCk3IEP8lMe/DTm4qfjM2QwjLKhLIXqifxgWSKhJdgb1v70bNmP0WNCRfd6xgHY21RryIRERERERERGT76UvHzZeDVgp/vBO621n4AeBf4XDk3Nlz4QShijEssXAFkmylDQcWPLV/FT7KgSXS6F8FPLpgKuUGoUz2JSHAt7aXz61qsR5XTObtzAc9Pd7ouIiIiIiIiIkNfr4IfY8wkYBFwX/CzAT4KrAmW/BxYMhAbHOr84LiUgyEaTMFqCcKZ3FGqcgY/iYLgJ+P3/LxctZEJ+vVQcwLhDu8BJPGIOmE6CqEePyIiIiIiIiLDVW8rfr4H3ER2cjlALdBkrc0lAruBvyrz3oYFP6iGcRw33xi5JQhkBuaoV/sI97TXcyCTC53cXMXPmL8iFFT8FPb4SVhLrGTFjyGt4EdERERERERkWOox+DHGfALYZ63dfCQfYIy51hizyRizaf/+/UfyiCEtVw3jGAfHOEQtHPJTwXvBUa93/wJAsrX/U70SBeFRb3r85IIfJ1fNExlFKJIdO58PfnyPpLH5iqVCYdseYImIiIiIiIjI8NKbip+zgcXGmAbgAbJHvFYCNcbkOgYzCXir1M3W2nuttXOttXPHjx9fhi0PLbYg+AGIYjhks1VAlmxjZK+tEYDE4b2lH9IHSS9J1A969PSi904++HHbq3lCo2uL708dJmlM0Sj3nAiGpCp+RERERERERIalHoMfa+1XrbWTrLWTgWXAOmvtFcB64LJg2d8Cjw3YLocwL2iQ7ASj0GPGpaWgd45nvXxVUCqY9tUfSS9Fpe198JMfN18Q/LijswFcvuIndZiEMURLBD9Ro+BHREREREREZLjqy1Svjm4GvmKMeZ1sz59V5dnS8JKr+HGDip+YcTiEzb+f8TP5I1+JdFvnB/RRwk9RgcGxtqhHT1faK37aGzeHKo8DCpo25yt+RnW6P4pDymqcu4iIiIiIiMhwFOp5STtr7QZgQ/D6z8C88m9pePGC/jcmX/ETImPae+9kbCY/+SuVjnd+QB8l/TQxDCFsH496tffvCVceC+9CJtEEgE22kHQcYuESwY9xSfoKfkRERERERESGo/5U/Ahgg1DEdYLgp8NIdM/38uFQIlOOip80URxCmD5V/Lihgh4/sWoAMslmAJJBABQtGfw4JFXxIyIiIiIiIjIsKfjpp1yPH2MM0Dn4yfgZfD8bvqQKRrEfqaSfIWocwvRu2pafyVYfOQWj2kNOtvonNxUsmcgGQLFIZaf7I8Ylid/fbYuIiIiIiIjIIFDw00++zfX4yZ6ai3UYie5ZL99guXAU+5FKWo+YcQlhSPeiEsfzc82n2//UbigbTuWCn3jyXQCiJYKfmAmTsgp+RERERERERIYjBT/9lDvqZXLNnTsEP2k/3d7jpwzBT8L6RE2IMIZML3rv5MfNB0fRoETFT/IQANFIVaf7I45LoqBZtYiIiIiIiIgMHwp++qm9oibo8ePGOrxfWPGTor+S+MSc0BFU/BQEP6Hi4CeRbMnuPVrd6f6oCZMyCn5EREREREREhiMFP/3UPs49CH7CFUXve9bDDwKaZC+mcPUkgU/UCRMyDpleBD9+0IPILaj4CbvZfj/5ip9UNviJRsd0uj/qhul/nZKIiIiIiIiIDAYFP/3k5Y56BcFKNFQc/GT8TH5NshfNmHPSXppDqUOdriexRJ0wYRwyvei9kwudTEHFj+t2OOqVbgVKN3eOOmGSptfbFhEREREREZEhRMFPP/mdKn5GF72fsZn8Ua9kL8av59z38n1c/vjlna4ngZgbIWQc0r0Jfrzi/QGEcsFPUIGUSGXHzEdDMTqKOBGSGPDV4FlERERERERkuFHw00+54Mc42V9lRcfgx8/gBwFNshdHs3J2t+zmQPxA0TVrLQmTDWPCprcVPyWaO4eKg59kJhv8dOxPBBB1I6Qcg83owJeIiIiIiIjIcKPgp59yR6lcJzvOveNIdM/32o960fuqmdZUa75SKCfjpbHGEAvFCBmXdC+mbeV6/JRu7hxU/KSD4KdExU+uCiiVbun13kVERERERERkaFDw00+5ih8nN869w0j0oubOfRiL3ppuzQdGOYlcE2Y3mq346UWQVHKqV1DZk/GDHj+ZeP65HUWDRtC5yV8iIiIiIiIiMnwo+Omn9uAnW/FT0WEketpP4+WOevXhuS0tb+N1aAadTDQBEAtVEDIhMrYXFT9+cUUSQCio4vGC/j8JL7uz0ke9goqfVGsfdi8iIiIiIiIiQ4GCn36yQTVProdONNqh4scr6PFjgF6ENQAt8QNYyN8LkAimfEVDFYSdXh71srkeRO0VP8YN41pLxgZHvbxE8NwSFT/BlLJk+nCv9i0iIiIiIiIiQ4eCn37Kj3PPTfWKjAEgFAQ8mUwcLziSlTEGL9W7AKU1OKJVeNwrmcwGP7HQKMImRKYXwU+uqqew4gc3TMhaMsF7yeDIV8mjXiFV/IiIiIiIiIgMVwp++qnTOPcgKBkV/OxlEkVVO8n4wR6faa2lNagkyhQc90oE4Us0MoqQEyJt6HHMurXFPYiyP4QJkT2GBpDw0kQwxWsCkaDiJ6HgR0RERERERGTYUfDTT7nGzbmjVLngpyI0CoCMl8z3+AFIxt/t8ZkJL0HGBM8vrPjJH/UaTcgJkcFAEN50xcv1ICqs+HFCwVGvoOm0nyFqQqVuJxrOBj+pYOS7iIiIiIiIiAwfCn76qb15coeKn2AaViYdLw5+ggbN3WktqK7JZFL514lk9nosMppwruIn033LaJvbX2Gw44YIEYRC1pK0aWIFU78KRUOjs/tOK/gRERERERERGW4U/PSTb4uneuUmY1U42X45npcsPuqV7Dn4aUm3j073gsbL0N5gORqpJOSEyRgDXk8VP9n3TcejXtaS8TOQSZAwhqgTLnl/NDwq+GwFPyIiIiIiIiLDjYKffspV/OSOUuUqfmK5ip9MoqjiJ5Fs7vGZrQXHwTyvvaInF77EIlWEnTBpDHjdV/zkQifXLW7uHLZB/6DUYZLGEHNLBz+RSFDxk4n3uG8RERERERERGVoU/PRTe/DT4ahX0BTZ85L4tAc/qWQLPWlp3ZN/7RUc5UoEfXaikaqg4gfwUh1vL72/wqNeTpgQlozvQao1qPiJlLw/FlbwIyIiIiIiIjJcKfjpp1xz505HvYL/zWRSeLZ97Hoi1Yvgp21//rVXcJQrX/ETrSLkhkkbA5megp9cc+eCHj6Og2vJNnfOVfwEgVVH0VzFTzpR8n0RERERERERGboU/PRTPvhxs8FK2AnjGIdRwTSsTIceP72p+GktCn7aA5dEUHUTjVYTdiNkjMH20NzZsyWmegEhOgQ/bungJxKpAiDpKfgRERERERERGW4U/PRTx6NUxhjmTJjDjOqTAPC8FB6WiqDoJ5FuLfmcQq3xg/nXmYKjXMlMNnyJRasJObkeQt03Xe7YgygnhAmCn+CoV1cVP+FKAFI99BISERERERERkaFHwU8/5St+Co5S/Wzhz7j0hI8D7RU/FcGvOtWL6Vgtifbmzn5B8JPwEjjWEopUEQ6aR6cz3VfidJw6lhOCoMfPYRKOIRr0JOooGlXFj4iIiIiIiMhwpeCnn9qDn+JgxQ3GoGe8dLbiJ/hVJ4KR7N1pTRWOcy/o8eMliVqLCYXzFTrpHoIk389N9Sqe2hXCZKeNpQ6TMIZYsN+OQuHRuNaS7KGJtIiIiIiIiIgMPQp++qnk1CzADVdgrMXzU/jWUmGyv+reTMcqDH4yhePcvRSx4MhYLqiJp7oPkrqu+Mke9bLJFpodh+rYMaUf4IaIKPgRERERERERGZYU/PRTVxU/hGK4ZHv0eFhGkQt+ej4y1VLQt8crOuqVIhq8joWywU9PFURebqqX6xZdDxmHDD6Hk00kHYfa0cd2+YyYhaSv4EdERERERERkuFHw00+5iV2O2yH4cSOErcXzM9ngx2SDl970ymkpqAryC496+WliwZ8sFs6OWU9kug9+bLA/1+l81CttfRqDRtK1o4/r8hmR4LNFREREREREZHhR8NNPfq6ixhRX1BRW/PjWEjUOjoVkD+PXAVr9FBVBb55MQeCS8NNEMQBURILgJ9390bFcxY8pOdXLpzGZbSR9TMW4Lp8RtYakp+BHREREREREZLhR8NNP+YqfDhU1uBFC1pIJKn5cHKLG9KpXTotNU+1nm/l4hT1+bIaoKa74aeupuXNwFM3t2HzaOHhYDqaaAaitqO3yGRFjSAW9gkRERERERERk+FDw009eVz1+HAeXbMWNj8U1DlHcXh2ZarU+1cGfJlexA0HwQ7ayKBbOjllPeN1X/OSmenWq+DFBxU+6FYDaWNfBTwxD0lfwIyIiIiIiIjLcKPjpJ+t3EfwALiao+AHHOERMz8GPtZZWY6kx2QqiwnHuCd8j6gTBT+6oVw/Noruq+AnjksHSmD6MsTA2NrbLZ0RwSAbPEREREREREZHhQ8FPP3n5o16dg58w4NlsxY9jHGJOiGQPR6biqcN4xlATimWfXxAUJfGJBWPZK6JjAEj00Cw6P27e7dDc2ThkrKXRT1CDQ6jE/nOiRsGPiIiIiIiIyHCk4KefclOzOjV3Jlvxkw4qflzjEHFC2QAlOH5VSuvhdwCoCVUCHca54xMNegnFItmjXvFeVvw4pjj4cY2Trfjxkxxjug59AKJOSD1+RERERERERIYhBT/9lA9WOo5zJzs5y/O9goqfCAljINN1X56WlrcAGBNU9BT1+MESywc/2WAo0UOz6HwPok4VP8FRL5uh1ol0+4yoEyFhuw6rRERERERERGRoUvDTT11O9SLo8WMLKn7cMCljINna5fNaDu8FoCZ2DNDxqBdE3WxIEw2OgiW87sfD5/bXscdPPvjBo9aJdfuMqBMhpeBHREREREREZNhR8NNPfjc9fkLGwbNe0NzZJebGSBoDqa6Dn9a2/QDUVIwHIFNQ8ZMw2RAGss2iY74l4Xdf8dPV/kKOSwY4aKA2NKrbZ0RCUZIo+BEREREREREZbrpv7iI96nKcO7kGyj5+8DriRoPg53CXz2ttOwBA9ehjs88PKn483yNtDDE3ml8bA+I9HfXqsrmzS8pAyhiOCVd2+4yYGyVlul0iIiIiIiIiIkOQKn76yeaPUnXuk+Mah4xfUPETquix4qclcRCA6qr3AeAHFT+pdDYsyh3xAohZSNiexsPnmjt3POrV/qcfGxnT7TMioVjQm6j7kElEREREREREhhYFP/2UG+dunM5TvUI4ePj4JujxE6og6fRQ8ZNoBqCm+gQAMl42+EkG12MFwU8FhoTf/bQtz/oYazFux6Ne7T/X9BD8REOjSBuDnzzU7ToRERERERERGVoU/PRTvuLHLVXx45KxfnvFT3hUzxU/qUM41lI5ahwAXjBGPRGELlG3oOKnF8GPbz1cgA7j5kMFP1cHjaS7Eg1newCl4ge7XSciIiIiIiIiQ4uCn35qr/jp/KsMOQ5e0OPHdVyikdHZ4Ke7qV7pw1RaCAcBT67HTzKZrfjJhTAAFTgkgqNcXfGtjwHoUJFUVPEzqrbbZ0TDo7N7iL/b7ToRERERERERGVoU/PSTb31ca0u+FzIhMtbDMwbHuETDo3tu7pxpowoHN5Rt4pxrzpxItQAQC1Xk18aMQ9z2VPET7K9DxY9bFPyM7/YZkUgQ/CSaul0nIiIiIiIiIkOLgp9+stajq4FXrhPKT/VyjEs0UkXGGDLd9Mpp9RJUmhBuKFfxE/T4CYKfaBDCAMRwSfQwZt23fvaP3KHiJ+y0T/mqGT2x22dEg6lfyaQqfkRERERERESGEwU//eRZ2+UvMeSEyAC+MdmjXrleOcmWLp/X4qeodCK4QTCT6/GTDI6HxUIFwY/pzVEvL7s/UxxPhQqmfIVjNd0+IxrNNn/ONZgWERERERERkeFBwU8/Wevjlj7pheuESQWBi2Ncom72+FYi1U3Fj/WocmP5o1iZ3FGvdDb4iUYq82srnBAJuvjwgGd9nBJLQoVTvqJV3T4jH/x0E1iJiIiIiIiIyNCj4KefvFzz5BLCbiTb04fshK9c8JPqZqpXKz6V4Qock/3T+EFFTzLdBkCsIPiJmTDx3h716iAUVBRV+H4vgp/q7L41zl1ERERERERkWFHw008WH7eL96JulLgTBD+OSzSUq/jponImHafFQFW4CmMMIWvzPX4S6WxD6GhBSBNzQiR62F9XwU+uomi0b3sOfoKjYMluAisRERERERERGXoU/PRTdxU/UTdKPFfx44TyFT/JLqZ62bZ3aXUcKiPZIMYBMvmKnzgAseDYFUDMCZM2kPG7nuzldxFM5Sp+Kq3t1Pi50/fITfVK66iXiIiIiIiIyHCi4KeffNt1xU8kFMPP9/gpCH6CY1sdtbXuwTeGqqDCxrXtR70SXvaeaKQ6v77CiWTfy3Rd9+NbWzKYCgf3Vvbin0DEza5NpkrvW0RERERERESGJgU//eR3U/ETCUayQ3DUKxf8ZOIl17e07gGgMnYMACHA87M9fJLpbLgTjRVU/ASBTMLrOvjxugimTNDcebTpvtoHKNi3gh8RERERERGR4UTBTz/51ifURfQTDVXkXzuFR726CH5aD+8DoGrUOABcTPtRryDciUXbR6/HgqqdeBfPg+zUsVJ/5LjNBkqVJtzlvfnvka9U6vpzRERERERERGToUfDTT2mb6fqoV3hU/rXrhIgFFUBdBj9t2eCnctR4IPvH8fJHvZKErcUJGkQDxHLj4bs56uXh45QIpg6TfW6l04fgxwv2nU7AcyvhrpPhD6t7vF9EREREREREBkdosDcw3Hl+NxU/4dH5144JtffK8ZIl17fEGwGoHH0ckP3j+EFlTtJLErUWTPtnVfQi+PGtxbWdr0+KZauKPhQa2+W9+e+RG0OfjsMfH4B1t0Pzruybe1/u8X4RERERERERGRyq+OmnjPVwuwh+IgXBj+uEiLlBxY+fBt/rtL418S4AVaMnZO/BkAmCn4SXItohwAkHFUSpbo56+dYWZkV5Z4x5P/+16y0uHnVCl/fmv0cusGrdA4/8PYyqhb/9NVS9D5Ka9CUiIiIiIiIyVKnip5+8bnr8FAY/juO2ByjGQOowFDRqBmhJHgKgKhjZ7mLyR72SfppYh88JB89Ld9N7JzvOvcT+3DDHZzyIVnb39QAIOSFCOCRHj4fz74YZnwTHyd6bau3xfhEREREREREZHKr46acMPqFSJTVANNIeqhRV/OSCnw5aUtngpzKcvc81Bi931MtPE+0Q4ETcXMVP52fleF00dybX2yda1eW9RZ8VipGsWwanXpYNfQAilar4ERERERERERnCFPz0U8b6hLr4NUYi7aGK64TbmyR3Efy0pg/jWqgIpoG5GDyCo15+mqgp/pxI0Og5ne66x4/FlmzujNu34CfqRkl5qQ4XKyGpih8RERERERGRoUrBTz9lrI/bZcVPwVEvN0TICeFgSDim5BGplkycSuNggudlj3plG/skbYZYh/lhuR4/6W56/Hi2i+DHCU75Rcd0fq/UdwlFOzeRjlTpqJeIiIiIiIjIEKbgp5+yPX5KD3SPBsEMZI96GWOIOmFSpnTw0+onqTTt49VDBUe9EtYjaoo/JxJUBvXU3Lnk7nIVP5Gee/xAVxU/VTrqJSIiIiIiIjKEKfjppwyWkCn9awy77SGOE/TUiboREl0d9fLTVAUNmwEcnPxUr6T1iTnFvbjbp3p1M84dP19BVKSvPX7cSOcx9EehuXM8E+f1d18f0M8QERERERERGakU/PSTh99l8BN1ovnXbhDaRJxI6Yof36MFj0q3ov0eY/AJjnrhEzUdg5/s2nS3wY8tPdXruFPhtCvhxPldf7kCMTdG0u8Q/ByF5s43P3MzS9cuJd5NVZOIiIiIiIiIlKbgp58y1uJ2Ffy47cFPruInFoplK346NkVONNNqHKoKRsCHcPCC4CeBJeqEi26JhEcBPVT8WIspFfxERsElP4BRx3T95QqXuxGSmRIVP14KMqnSN5XB7/f9HqBzfyERERERERER6ZGCn37KHvUq3eMnUnBsyw2OfUVC0dJTveLv0uI6VIXbe+44xrQf9cIS6xD8hIOQqLuKH6+rip8+Kt3jJ2gMPYDHvcLBd0776QH7DBEREREREZGRSsFPP3n0teJnVBfBTxOtxqEyWp2/5JrCip9sf6BCkaAxc9rrvuLH6WLqWF+U7PGTaww9gMe9wl4GgFQ3I+tFREREREREpLQegx9jTMwY8ztjzB+NMduNMd8Krt9vjPmLMWZL8F/dwG936MlA7yp+cs2dQzGSjtupSsZva6TVMVTGavLXQjj4WKy1JA3ECoIkACcyipC1PTR37mKcex/F3Fjp5s4wsMFPWyMAqfiBAfsMERERERERkZGqNxU/SeCj1trZQB2w0BhzZvDejdbauuC/LQO2yyEsgyXUYdpWTvFRr+zrqBslVSL4aWvbjzWGqlh7zx3XcchYSyaTxDemqIIIgFAFYWtJdwxkCviUp+KntqKWXS27+H9b/x8ZP1uFk6/4GcijXkFolRzg6WEiIiIiIiIiI1GPwY/Nyv2/7nDwnx3QXQ0jGejyqFfICZGrBXKCcCjqRkk4bqejXq2H9wJQOWpc/pqDgwckk81AtjF08QdECVtLqrvgx5anx891s67jYyd+jHv+cA9X/teV7Gza2T4KvmOj6jIKB/9Ek6mBnR4mIiIiIiIiMhL1qsePMcY1xmwB9gFPWWtfDN76tjFmqzHmbmNMtJtHjFgedFnxAxAJop9cc+dsxU/nHj8tbfsBqBw9IX8tZFw8LPFEE5DtD1QkXEHEQqqbqVrlOupVE6thxbkruOvcu9jduptP/fpTrNr9GzIAAxjKRIwqfkRERERERESOVK+CH2utZ62tAyYB84wxM4GvAtOAM4BjgJtL3WuMudYYs8kYs2n//v1l2vYQ4XtkDLim6+AnGlQD5Zo7R90oCQN0GI3eGj8IwJjo2Pw117h4QPPhd4L3VSkUJgAAIABJREFUqoofHooSxpL2uw5+PCjLUa+chZMX8sglj3DupHP53mu/5MExlQNa8RPKVfwMYB8hERERERERkZGqT1O9rLVNwHpgobV2T3AMLAn8DJjXxT33WmvnWmvnjh8/vv87Hkq8NB6GsFO6uTNAJAiFinr8YCATL1rXElT1VEbax7m7TnaqV3NQDVQdPaboHkIVRKztdtS5xeKWeXjbuIpxfPcj36UqXMnuUGhgmzsHjbOTaVX8iIiIiIiIiPRVb6Z6jTfG1ASvK4ALgB3GmInBNQMsAV4eyI0OSV4qW/ETVPOUEgmOeDm54CcUJWFsp4qfllS2j09R8BNU/DQFE61qKmqLH+6GCFtIeR0qfl5ZC6s+DtbiAaaMFT85xhhGhytpdZyBbe4cVEwl04d7WCkiIiIiIiIiHXV9RqndRODnxhiXbFD0kLX2cWPMOmPMeMAAW4DrBnCfQ5OfIWNMtz1+ohW1kD6EG/r/2bvzIEnzu77z799z5V1n39doLvWMZgQjzVgnrJE4bJAthDFgBMaWl8XW2gtr8IYdjoWAhV0M9hrb6wCMAwMCtBICIcAgAcshiUHMjHpG0pw9mqvPqj7qyjufJ5/n2T+eJ7Mrq7Kqss7Mqv68IhRdnU8+T/2yuyaI/vA9khFIGTtDixhWrGCv+lWwoeTeaueyjU1oYKmRrDSfWDb/p8PFEHS2bHW89lm49BgEDSJ2ZrhzP0WvSM3eq4ofBT8iIiIiIiIim7Vh8BPH8ZeAN/V5/d27cqL9JAySrV7rDXdON3FZaeVKxs4QAu2g0fOHX2nXwF7Z6tVb8TOeX90q52Hw4xXBT2Um+dWvERFj1tg6tl0Ft0DVcXe34sdyIIJW0Nj4zSIiIiIiIiLSY3cSgdtE1G4SG4OzTqtXxk4qfey0cqXz+9bKip+wiYMha99a2e4Ym9AYlpqLOHFMPneIlTxj4a+s+Kkkw6AJakSAvQutXgBFt0jNsvek4sdX8CMiIiIiIiKyaQp+tqGdhjfrtnp1gh9rRfATLpvxE8dUQ5+i5fbM47GMTRtY8peYCCPMyq1eJDNw2nHY+2In+PHrRDFYu/TXXHAL6Yyf+q48H2792TbbCn5ERERERERENkvBzzZ0gx977YofN73WqfjJpq1fPcFPUKdiYopWpude23KIjGHRrzIRheAVVj3fw8ZfHvxE0a1Wr6BOaOJum9lOK3pFqoZV84p2ktWp+Al373uIiIiIiIiIHFQKfrahE/yst9WrU+HTCV+8dLtXa/kK9sYCVcui5OR77nU6M37COmNRDG5u1fNda0XwU5+DTuuXn7R6WbvU6lVwC9T6DKreSRERAM2wtcE7RURERERERGQlBT+b1SzDn/w4XHqcMA0jnDTM6acT9HSCn84Mn1bkQxwnb2osUrEMJbc3+LGdHG1jWGo3mIgN9AlwXGMTxNGtFyoz/Hkux/ceO0LcqiYzfnbpr7noFqmZmGgX27Ci9M/Ibyv4EREREREREdksBT+bNN+Y4+0XP8JvPPPLy2b8DD7cuVvxYwx0woxWmYplUXR7Z/hYbp4QWIp8Jkz/OUKe5eAT33qhMsPjuQyP5bL4foUIdnWrF0A92M2Kn+SztSJ/176HiIiIiIiIyEGl4GeTCsVjVC2LcmuJsL1xxc/KVq9uxY8xt1qk/BpVy6K4Yniz4xWTGT8mZtz0D5dcy11V8bNgJyFTs7VECNi7NePHTVbPV3dx/k6UfrZhBT+XKpeI43jjN4qIiIiIiIiMIAU/m5Rxc3hxTMWvEKSBh71O8ONavcOdeyt+0sCkVUlm/HhjPffaXhKsBMYwbvcOfu7wLIdgeQdYZZYFK/lrbfkVYti14c6FdNh0bRdDmU6rV2vlyvodUgtqfMvvfAtfvPHFVdeuVq/yno+/h8/NfG5XvreIiIiIiIjIblPwswWl2FAJaoRhEng41iYqfpzVFT9Rq0rNGIqZiZ577WUVQBNppdBKnuWuavWad9JwqVUmZPeCn27FT7R783c6w513K/i5Wr3KS4svce7auVXXrtevExMzV7+5K99bREREREREZLcp+NmCEhaVsEE7bfVar+KnO+PH6q34aRoD6WycWnOe2BhK2cmee23nVtgz4axe5Q5Jm1mw/IXyDAtOMg+o6VeJ2f1Wr1oUbPBOOD9/nn/6J/+U5iY3gHUrfuLdCX6qQRWAa7Vrq67VF14BwJ9dXQ0kIiIiIiIish/0nxgs6ypZLpXQ7271cp21g5+vOvlVzDXn8NKqoM6MH39ZxU+1uZA8N3+o595OexjAcbe3DazDszwiY2hHbRzLIa5cZSHd+u4HNUKz+8OdqwMEP+euneMzlz/DS4sv8eChBwf+Hp3hzv7yOUY7qFq7AcDszedXXWtUkzCo1Zjfle8tIiIiIiIistsU/GxByfKohFXaYRJ42GvM3wF44+E38sbDb+z+vqfiJ60YKreWAChmxnvujdPQ43V+wP0Th/s+30u/t99u4XgOjeo1WrkkXGoGtWSd+25X/BggbIO99o9TLagB8Fr5tU0FP53Bys3dCn6WLgBwrXxh1bVaaxEAP9i9dfUiIiIiIiIiu0mtXltQsnOU45B2uPFWr5V6K36SQKHhVwDIu/me93bakD64uITJ9q/46VQbBUENwoD55q3qlFbQIAKsZZVDO6kz3LlqWd3PspbOZ7lYvrip7xGmM358dif4qTTmAJgNyquu1VvJa61QwY+IiIiIiIjsTwp+tqDk5qmYuDvceb2Kn5U6M3+a1q2Kn1ZaDZNZ8Zzvvv+7+beZu/nGWh28/jN+vDRICloVqF7rbvQCaAR1YmN2b6uX0wl+bn2WtdTSAcmvLb22qe8RpXOrW+zOSvVaM6nqmYvbBGFvy1rdT8Kq1gafTURERERERGRUKfjZgpJbpGIs2mlg4zj9N27141gOFibZ6pW2ELX85DnZFZu7xjPj/M2x12MA0tXuK3WCHz+oJqvc7WXBT7sO7F7Fj23Z5CyXmmXdWk2/huqNZIbOxfkXNvU94s5WLwPEOx/+VNJ2LoBr1Zmea7W0Ssnf5EBqERERERERkVGh4GcLxjJj+JahnlaxbKbVyxhDxs6k69yTSpJmGtB4/Z6Tn05+XaPix3GSKqGgVYXKDHP2rZCnkbZfWcYMfL7NKloZqsbqbihbS2dezoXqle7cnkGEaaVPa9kw7J1UbVW6X8/eeKbnWj0N9lqhKn5ERERERERkf1LwswWlzAQAC+l8mM1U/ABkbK8nyGilv2b7PSc/ld5U6vssz01WePlBLVnlvrziJ0yeu1utXgAFJ5u2em0Q/KRtU9XI75lDtJFOSLS8Qmondap6AK5df7rnWic4CyJ/x7+viIiIiIiIyF5Q8LMFpVxShbOQVrHYmw5+Mn2Dn5UzfoANK348JxkInbR6zbBgu91r9bRSxd6lVi+AnJ2lOUirV7uBlw7sudBng9ZaOiOd28YQtlYPYN6uSrvOyaANwOzCSz3Xap2/n3DjdfUiIiIiIiIio0jBzxYUc4cAWEy3cTn25oOf5vLgJx0SvXLGDwBjJ5Nf84f6PstNQ6fAr0NllvlMgelsEhY10ufu1owfgKzt9XyWvsKAWtzm9UFyngubGPAcLRvq3GrufPBTC5scxaIUxVyrXO65Vo/S4duRgh8RERERERHZnxT8bMFY4SgAC+mab2dZlc0gJrKTLNq35uI004Ah4/Sp+Dn9FvjAp5Jf+/DcpBIoCOpQucqCl+FI/ggWUDdJaLKbwY+3onpplfIMXHiUqmV4vTeFE8dcuP7FgZ8fLZsH1Gotbfe4q1TCFgXjcNS4zDbneq7V0+DMj9s7/n1FRERERERE9oKCny0oFdPgJw1sHMvZ1P2Hcoe5aTurKn76tnoZA3e8Pfm1D89NW73a9XSrl81kdpKMcain91jWblb8ZNP5O2sEPx96L3zom6kZw/j0WU4FbS7OPT/w83sqfoL6do+7SjUOKFoex9wS19q1nmu1OKn0aUUKfkRERERERGR/UvCzBaXiCQAW0izG3mSwcjh/mBuOnWz1avs0iXGxtjSE2U2DnyBoJDN+DExmJ8kah4aVPG83hztnnOz6FT+LFwmAlmWRP/IG7miHXKheGfj5y4Mff0UwsxNqcUjJznA0f4RZK4bGQvdaIw6T75v+KiIiIiIiIrLfKPjZglJuEqC7Qcsxm634OcSSZSWbuPwqvjFkN1k11OGm27785gI0l5iPA6ayU3iWQyOt+NlsMLUZWSe3fvBz7CuopwFUsXSCM944F9sVojjq//4Vlr+r6e988FMhpujkOTZ2B/O2jX/9VjVSPT2jP+BZRUREREREREaNgp8tyNpZnBgW00Bl0xU/ucMA3Awq0KrQNIaMtbk5QR1u8RgAwfzLNI2hEbeZyk6RtVzqVhL8mF2s+PHc3PrDncMW1TveDkDBLfK60mmaxFyvXRvo+TExdmele3tn17m3whaBgaJT4Oj0WQCuzTzZvV5LY6cWCn5ERERERERkf1LwswXGGMaMTSWt+HE3GdoczifBz42gCn6NlmXIWN6WzpLNjAPQnPsyC2llzWRmkoyTpZEGPvYmK5I29f2dPC1r7Rk/fxTX+JCdBDZFr8iZQw8CcGH2yb7vXymMIU8SYDWDna34qbYq3XMdO/QGAGZvPgdAHMfU01Y+f1m7mYiIiIiIiMh+ouBni0rLVq/bm9yadShdB3+znbR6tYwha28t+MmnM37qjXnm0yBqMjtJNjfVbfXaza1eGbewbsXPD+V8PhzeBKDgFnjdqXcAcOHq4wM9PyImHyefoxHsbMVPtXEDgGJmnKOlZG7TtetPQxzTbDeI0z+/lgFCDXgWERERERGR/UfBzxaV3GL3681u9eq0et0IG+BXk1YvJ7vBXf0V0nXuNcuwYCcBz1R2ioybp+4klUi7udUr4+ZpG0M4QChTcAscOfNOMlHEhbSyZiMRMfm0cqkV7nDwU03azYqZcY7lk5a52aXX4NVPU2vMA2DiGN8Y2OFqIxEREREREZG9oOBni4rZie7Xm53xM5WdworhRtSCVjLcue8q9wE4lkPG2NSNxbyXA5KKH8/2aNhJIGXV57b07EFk08CqNUAwUnSLWNkxzsQ2Fwfc7BUBeZI/3+ZmZvz85X+Gn/+qNS9frlzmZ5/9peRcuSnybp6SV+Jafhz+9Cdo1JMqpTGsZHi1v/Or5EVERERERER2m4KfLSqlc3pg81u9bMtmytjcjPxlFT+5LZ+lYGWSip9cMu9nMjtJ1s7SSGfT2Ece2PKzN+KlLWprDV4+0r61Cr1TnXSHN8Fr7fJAz4+BfFpR1VhrgHQfn3vlk/wn/+qa13/isZ/gibln+Kp6g7OTrwfgTOkMf1Ys8cq1p6i98HsATBonCX4CBT8iIiIiIiKy/yj42aKx/BEA7DjGpLNgNuOwcbkRB9AsJzN+0lBkK/JunpplMZ8t4lgOJbdExs7QjpPQxRy6e8vP3kjWXr/ipxTd2ohVTNvjzpROc9mCdvX6hs8PicmnwVozHDz4+VjzEr9WykG8ejDzF17+FI9eeZR/slTl567dYGziTgB++G0/TNvJ8N0nT/Bnz3wIgEk7S9sYonQQtIiIiIiIiMh+ouBni0qZMQCcPsHCIA7ZOW7ShlY5qfjxth78FLwSNWNYcD0mM5MYY7otWAA5e+vVRBvJOEmLWrNfNU4U4i/LxDqDqF936AHaxjBz4dMbPj+p+Emqippha7BDtVucJyAwBkL/1uuvPQq//u383B/9MybDkL83/Sb4nt+BY8mmsQcOPcCH3/NhjuYO87Ol5M9vPA3k/NZgFUoiIiIiIiIio0TBzxaVvBIAtru1UKVo56gRQXOJlmVtq9UrnxmnbjssOC6T2UmAnplBp0unt/zsjXQrfvq1erVbyWBk4FTxFFY6pPnMybcDcOHKxpu9IsCzHOw4prk8xFlH7fpzXHLspFJneYvWR7+bL1x/ir/M5/jAV3wf+e/8CNz1NT33niie4Fe/+bd5Zzs567HMdPL5WksDfW8RERERERGRUaLgZ4s6wY+zxaHMeSdHHaCxkAQ/W3wOQN4rUDtylvnC1Krgx2A4VTq15WdvpPN9+lbjtJsExvB3x9/AJ973ie7Ldxx9IwAXFr+84fNDwMKQjeOBK36+fPnR7ir2wE9b0No+NOb52RN3MpWd4ju+8vvWvL+YHec/v+Mn+M1ri9w7fT+gih8RERERERHZnxT8bFE3+NnkKveOvFugbhlYukRrG1u9AApOgRoxC36ZqcwUcCuQOVY41h3AvBs638fvN38nrfjJ2pmezzednaYQw8Xm/IbPj4mxjEU2hmYYDHSm8ze+2P3a99PZPPWbPJXx+Fxzhg888IFu29lanPv/Nmf/xWt4peMAtDTjR0RERERERPYhBT9bNOYlM35ss7lV7h35TImGMcSLF2lBz0yezSq4BepBnYXmQrfip/O8Y4VjW37uILozfmafhk//dO/FsIWPwV0RahljOGxc5tsbr4CP4FbwEw0W/Lyw9Gr3627FT+0GPz8xzpRT4NvPfvtAz8GyyXjJQGo/qA52j4iIiIiIiMgIUfCzRduu+PHGiI2hVr5K27C9ih+3wJK/RDWoMpXtrfg5mj+65ecOojvjxxj4s/8TWrcCkjho4lumb8XRhJ1lIdq4dSsJfgw5DM14sODnxdZc9+tOYBNXb3Aum+Gbjr19w2qf5bxO8ONvHFKJiIiIiIiIjBoFP1vUWU2+9YqfcQAWTLLuvBOgbOlZbp5WOv+mU/HT+f2RdO38bunO+OmstK/MdK+10xXvXp9qpgmnwELc7rtufbkk+LHJYGhG7Q3PE4ZtXiRgPN0iH6TDnWuVq7Qsi6ObnHeUSbe3tXy1eomIiIiIiMj+o+Bni7Zd8ZOdAGDBTv4KOi1TW1Fwb62C71T8XK9fB3Y/+Om0lLXe9sHkhfKV7rVOlYzXJ9Sa9MZYtAxsMDsnMulwZyya8cbBz8VrX6BpGR60k7+fwE+Cn7nyJQCmSyc3fMZynpNUB/n1m5u6T0RERERERGQUKPjZos6Mny0HP7kkoFmw0uBnm8OdOzoVPw9MPwDAI8ce2fJzB9Fp42rlkiCL8tXuNT+t+HH7hFqT2WkWbJu4en3d50eAMRZZY9GMww3Pc/7yowA8WLqj5wxztaQSaXpsc6vtu5+vdmNT94mIiIiIiIiMAgU/W5RzctjG3nLwk8tNAzBvJ61i21rnvmxmTSf4ee/d7+VPv+1PuwHQbunO+HHTqp7lFT/d4KdPxU/hMIEx1MuX131+BNjGImcsGoMEPze+iBPH3H/kIQCCdrJtbC6tgJrOHdrwGct1/l5aqvgRERERERGRfUjBzxYZYyh5pa3P+EmDn8W01Ws7M356Wr3Sde7GGA7nD2/5mYPqzvghhNzUioqfpM3Kc3Kr7ptIt40tLL227vNjkq1eGRyacbThec6XL3BnEJKf6FT8pK1ezQXgVivcoLrr6puLm7pPREREREREZBQo+NmGklfaxlavZDj0gpVW/OzAjB/b2Iylw4j3im0lVU+tdgvGTkL51nDnYJ3gZzIdsrxQubLqWlccExqTtHpZNi0GCH78ee6zct1tXEG7AcBcUMZwqyJqUJ1WL9+vQHvjLWQiIiIiIiIio0TBzzZsq+InHRrcHe68zXXuAOOZcSyz93+lWTubbBEbO9Hb6pW2WXlun+AnrchZqM2u/eAoJKbT6uXQZP0NYPPNea7T5mz+GG7a/uanwc98u86EcTYd1HVbvYzp2VgmIiIiIiIish9srVxFAPj6O74eg9nSvbk0DFnYwRk/m21j2ime7VELaswXDzF15Vz39W6r17JWtI7JXNKGtlhfZ2hyHKXDnQ1Zy6ERrR/8nL/xNABnJ16P5yXfM0irdOaiFtNWaeDP1NGt+DEmqWaafN2mnyEiIiIiIiIyLAp+tuF73/i9W763W/Gzg1u9NtvGtFOydpbffum3+VPL4zP1m1hBE9xst+LHXTZ8umOis84+nb3TTxy1iYzBwsa1PNoGgijAtdzkDa/9BTz3u/BNPw3Ai1f+CoCzx97MfBo2BWET/DpzBqbd4qY/W3erl6GnmklERERERERkP1Cr15BknSwGmEsrfnJ95uAMqtPqNZkZTvDTmU+0FPksWVa3JcoPkzarfhU/RbeIE8OiX17zuXHUBsCyLHJp2NNaPmfnhd+Hx/8LRMm2r/M3n+ZIu83ksYe6M378dgvqN5mzLaYyE5v/bHaGnJPjy57XM7haREREREREZD9Q8DMklrHIYTPjJMHPoU2uGV+u0+o1zIqfjgXb6gYknTarfsGPMYYJ47DQrq/53LAT/BiLbFp50wybt97QSKuFgiRgeqF8gbN+ANP3dFfIB2ELajeYs22m001qm2EZi2+991v5VCHP5cWXN32/iIiIiIiIyDAp+BmivOUQGcOYN9YNb7aiE0686/S7dvB0gysvq9qZs+1bwU+49nBngEk7x0K49qasOAoAsLDIdtbGt/sHP37o82qwxFmTBS/fbQfzwxaN8gx1y2K6cHRLn+8fPvAPsTB8ePHZLd0vIiIiIiIiMiya8TNEucwENK5xrHBs28/60Xf86PYPtEVXqrdm3yxYFlSS4MdPK35c2+1736RbYNHcgHQm0EpR2sJlWfYGwU+Nl1s3aRNzNp/8WXaHMoc+L849B8DpyXu29PmOFo5yOjbMRs2N3ywiIiIiIiIyQlTxM0T5dMDx8cLxIZ9k58xnCt2KHz/0AfAsr+97J7wxFiwb6jf7Xo+Wt3pZ67d6nZ8/D8DZybMA3YqfIPJ5YuF5AP7aqb++1Y+Fg0U7jrZ8v4iIiIiIiMgwKPgZok57105U/AzTPRO3Kmnm82Pd7Vd+lAY/dv/gZzI7xaJtQfV63+tRp9XLWGTT4dfNdJ4PAI3F5Negzvlr58hFEWeOfEXP9wyigMeqF7jXbzM1dmqLnxAcDO043PL9IiIiIiIiIsOgVq8h6qx03+/Bz69/068TRAHv+e33MA/LZvxsUPGTP8KSZRFWr2P3uR6FnYofuztAut5a5InZJ/iTC/8fRS/ge+uGbNDg/M1nudcPsA/fl95j4cRQC32eCuf4tsgBY7b8GR2jih8RERERERHZfxT8DFGn4me/t3p1PsdUdor5sAI3V7R6rVXxUzxGZAzl8kX67SOL4mWtXun3+Oef/Vf4kY9nefgTJZ7Iuvxyq8b5ykW+wffh0Ou797vA02GVFhGP2MVtfUbXWLQjBT8iIiIiIiKyvyj4GaJc2r603yt+OiYzkyw0q1CZhTDAT2f0rDncuZS0Xi2UL/cPfqJbFT8nM1Pc3/I5c/fX8HV3v4f/oXgXP/frX88vT4xxtXaVctTivsiC0q0/SxfDNZJ2sSPZza9yX84xNi3a23qGiIiIiIiIyF5T8DNEnVav/V7x0zGdm+blpdeAGKrX8KMAE4Nj+v+YTRST9eqLtWt9r3eDH8um6JX4jauz8B3/EsZPwcyXmA6TmTsXajMAnCgc62nnco3FYhyCgcK2gx+Lmlq9REREREREZJ/RcOchKnklHMvhcP7wsI+yI6ayUyyEyQp3yjMEUYCHwawxW2cyk9T5LDRu9L3eWedujAVOss6dtH2MxgLZOE7ub80DkBs703O/h0XNJO8pFrb3Z+wamzbxtp4hIiIiIiIistdU8TNE77///bzl+Fu6q8f3u8nsJIvtOm3AKV/Bj0M8a+2BypPZJPhZbC70vd6p+LGNDZ12sfbq4GexPgdAbuJ1Pfd7xqKT1RSL26uqchT8iIiIiIiIyD6k4GeIDuUOcSh3aNjH2DFT2SliYhYti0Plq/hRG9deu6hsIjMBwIJf7ns9Xtbqhd2p+EkripqL3eBnvnwJgNzknT33u2nwY+KYXHF7c5RcY9OOFfyIiIiIiIjI/qJWL9kxnQqehUweOhU/Zu0fsayTJWdsFpoLcOmJVdfDNPjpafVaVvGTT7dszbcWAciNney53zXJkvhiFGOKR7b+wQDHcghU8SMiIiIiIiL7jIIf2THT6QDl+eJhKF/FD328NHxZy2TuEIvZInz426Hd6rkWx31avZbP+Elb5BbbdQByhd5wx0uHShfiCKbv3voHI2n1CtbuWhMREREREREZSQp+ZMd0hzUXJuH68wSRj+dk171nIjfNwuQZaMxDq9JzrTPjx/Rr9WoskHWLAMynK9uzK9q5XCut+ImBFfN/NsuxHM34ERERERERkX1HwY/smKncFABz2SLceB7fGFwnt+49k9lJFsNm8ps06OkI061elrHB8ZIX6/PwmX8Lz/4O2XRT16JlY+KYTOFoz/1eWhFUcHJgbe9HPQl+AM35ERERERERkX1Ew51lx4x741jGYsFLqnx8A65XXPeeycwkr60R/MTxsuCnU/Hz8f8J4ghe/43k3v5P4DP/Cwu2RTYG42Z67nfTVq+iW9ruR8O1XNrGJGe0D8YWNhERERERETn4VPEjO8a2bCYyE8zbSeDiGwvPWz90uXP8Tq4GS8za9qrgJwqXbfUqHYfsBNz7N+D7/hze/xFyxx4EYNGy6FdX5IVJC1g+O7GtzwXgWC6BMbdmDImIiIiIiIjsAxsGP8aYrDHmcWPMF40xzxpjfix9/U5jzGPGmJeMMR81xni7f1wZdVPZKeZN0g4VOBk8J7Pu+7/hjm8gBv6okIe0tasj6lb8WFCYhn91Ad7/ETjxJgCydlJZFBtDjtVDpN2gAUAxd2hbnwnAsd2k1WvFAGoRERERERGRUTZIxU8LeHccx18JPAT8TWPM24CfAn4mjuN7gAXgf9y9Y8p+MZmdZCFOKm18J4NnrZ8Hvm78ddyfO8YfFvKQVuh0ROlWL8v070jMLAuVclaf4CcNiApT29voBcmMn9gYwnZz288SERERERER2SsbBj9xopr+1k3/FwPvBn4zff1XgPftygllX5nKTjGfrlf3bQcorqmkAAAgAElEQVR3gHk475p8A1/KZqj65Z7Xe1q9+nAtF4dkx3rOWv19vHS9ezE7PvgHWIObBljttIpIREREREREZD8YaMaPMcY2xnwBuA78MfAysBjHcWcoy2Xg5O4cUfaTqewU834ZHvoufDeHZ2/cATiRDl9utXtDlWj5cOc15NIf4Zy1uqXMTcOgorv+gOlBuOnnaLcV/IiIiIiIiMj+MVDwE8dxGMfxQ8Ap4C3AfYN+A2PM9xljPm+M+fyNGze2eEzZLyazk5T9MsF7/yO1uD1Q6GJbSStXp8Knoxv8WGsvn8ul17JOdtW1TuhUcAuDHX4dTvqsIKhv+1kiIiIiIiIie2VTW73iOF4E/gx4OzBhTHf4yingyhr3/EIcx4/EcfzI4cOHt3VYGX3T2WkAFpoLVPwKY97Yhvd0gp9wxcasKFq/1Qsgm/4I5pzVe712suLHUcWPiIiIiIiI7EODbPU6bIyZSL/OAV8PPE8SAP3d9G3/APid3Tqk7B+T2UkArlSvEMYhpQ3WuQPY6Ryg9qrgJwLAmLV/TLPp7J1cn3CnM19oZyp+klaytoY7i4iIiIiIyD6ydg/NLceBXzHG2CRB0W/EcfzfjTHPAR8xxvwE8BTwi7t4TtknprJTALy29BrApip+omhF8JOOkLLXafXK2i4EkPVWBz+djWLFPtc2y0lDpEDBj4iIiIiIiOwjGwY/cRx/CXhTn9dfIZn3I9LVqfi5UL4AMFjFj7VWxU8y48esO+MnqcTJZVZ/n06r105U/Lh2MkNIW71ERERERERkP9nUjB+RjXRm/Gwq+EmracIo6Hm9M9zZNutU/KSzfXJp4LTczg53Tlu9wta2nyUiIiIiIiKyVxT8yI4qeSUc4/Ba+TUAxjKDtHolwU8U9gY/cZzM+FlvuHNu8o7k19LJVde++tRX84EHPsDxwvGBzr4ex02CH7V6iYiIiIiIyH4yyIwfkYFZxmIiO8HF8kUAxtwBgp/OcOcVFT9hutVrvVavbFrN02+r18niSX7wkR8c7OAbcDqtXqGCHxEREREREdk/VPEjO24qO4WfDmoerOInacmKov4VP/Z669zTQCbrZLd01kE5Tmerl7/BO0VERERERERGh4If2XGTy+btDDJfp9PqFYbtntc7M37MOjN+OpU+/Sp+dpKbPn/QGT/NoME//s338C9+7/2cv/Hsbh5NREREREREZE0KfmTHdVa6F9wCzjptWh3dVq8VW706rV7rzfjpVPrsfvDTafUaLPj5wjMf5i9rF/nD+af5rc/877t5NBEREREREZE1acaP7LhO8DPmbdzmBWDbnVav3oqfW8OdN6742f1Wr+T5QXuw4Ofci5/AimMyMfhBbTePJiIiIiIiIrImVfzIjusEP4Oscgdw0uBn5XDnTquXte469ySQyTv5TZ9zM5xuq9cAM36CJk8uvcRZu8hUbPBXBFoiIiIiIiIie0XBj+y4zVb8WJ0ZPysCkihKgx97neBnr4Y7u0nwE6wIp/oJzv8+X3QtHj72CC4KfkRERERERGR4FPzIjusMd95sxc/KVq9ogFavtx1/G++7532cKZ3ZylEHtpkZP89+6VdpWRaP3PvNZIyhpeBHREREREREhkTBj+y46ew0MHjwY3dbvfpv9bLM2sOdjxeP8+Pv/HHcdED0bukMqV7ZjrZKfZ5z158C4E3HHsbDIogV/IiIiIiIiMhwKPiRHdep+Bm41cvOABCunPHTafUaYDPYbnPSOUNBuEHw89wnOJdxuatwgqnsFJ6xaaUBloiIiIiIiMheU/AjO6474yczWPDjOGmr14qAZJBWr70yaMVP+KWP8lQux8Mn3wmAZ2z89HOIiIiIiIiI7DUFP7LjSl6JH3vHj/G+u9830PvtdLjzmq1e1u62cQ2iG/ysV/Gz8Bovzp6jauDhow8DkLFsAgU/IiIiIiIiMiTDL6WQA+nv3Pt3Bn6vZSUzfFZt9UoDEzMCFT9uJ5xab17PM7/Fk9mkba0T/LjGoYWCHxERERERERmO4f+LWm57nfk5Udw/+LFHKfhZb0PX7DOcG5vmZPEExwrHAPAsF594L44oIiIiIiIisopavWTo7LTipx31n/EzChU/nVavYJ0ZP/HiBc65plvtA5BR8CMiIiIiIiJDpOBHhs4yyY/h6lavzoyf4f+YGmOw49Xh1HKvVS4zT8Sbj7y5+5pru/h7cUARERERERGRPob/L2q57XVavcIVoUrcafUy9p6fqR+HdWb8BA3OxVWAFRU/Hr4BYlX9iIiIiIiIyN5T8CND12n1Clescw87rV7G7PmZ+nExBPEaFT+LF3nW8xi3c9wxdkf3Zc/28I2B9WYDiYiIiIiIiOwSBT8ydJ2KnpXBT5z+fmQqfoxZu9Vr8SIzjsOp/NGeoMqzM7SNIfRre3RKERERERERkVsU/MjQdSt+Vg13TtqjDKNR8eNgEbTKMPfy6ouLF5h1bI6XTvW87NnJene/VdmLI4qIiIiIiIj0UPAjQ7dWxU+n1asz/HnYnOw4bYBf+ka49mzPtXjhAjOOw7Gx1/W87jlp8OMr+BEREREREZG9Nxr/opbb2tqtXiM23NnJ0b7n3WBs+KVvgktPdK+VF1+lblkcLx7vuSfj5AAI1OolIiIiIiIiQ6DgR4bOGIMV36rw6YhGbLizYzm0vTz8o09BbhI+9M0w/yoAM+XLAKuCH9fOAtAKVPEjIiIiIiIie0/Bj4wEm9UVPxGj1erl2i7tqA2Td8C3/TIENbj6FAAzzTkAjhdWVPy4eQB8VfyIiIiIiIjIEIzGv6jltpcEPysqfqLRCn4c4xBEQfKbsZPJr/U5iGNmgjIAxwrHeu7x3KTVyw8U/IiIiIiIiMjeG41/Ucttz8asDn6IsdLNXqPAtdKKH0havQBqN6GxwKwFnrGZyk713OM5qvgRERERERGR4VHwIyOhb/ATR1gjssod0hk/neDHdpLwpz4HlRlmHJtj3viq6iSv0+rVru/1cUVEREREREQU/MhosE2/4c7tkfoB7Ql+APLTUL8JlVmuOzaHs9Or7vHcAgCtQMGPiIiIiIiI7L1R+ne13MaSip8V69zb/kj9gPa0egHkD6UVP7OULYuJ3OrgJ+MlwU/QbuzVMUVERERERES6Runf1XIb69fqFUY+ZsRavS5XL/N7L/8e9aCeVPzUklavJctivHBk1T2uVwSgpeBHREREREREhsAZ9gFEIA1+6B3kHIUBtjM6wc/77nkfLy2+xL/+i39NzsnxDdY4/7IxR6l6jbJtM96n1SuTBj9+u7nXxxURERERERFR8COjwTarW72i0Mc4o1OU9nV3fB3vPvNunrr+FB89/1F+59VP8u6oyjuWLtMyhrHM2Kp7PK8EQKDgR0RERERERIZAwY+MBBuLkHbPa1EYYJnskE7Un2UsHj76MEdyR/jkq5+kYmKWFl6CAoxnxle9vzvcud3a66OKiIiIiIiIaMaPjIak4qd3xk8cBdhmNH9Ei2kLV9UyLC28CsC41yf4cTIA+KGCHxEREREREdl7o/mvarntJBU/y2b8RCFh1MaM6I9oJ/ipWBZLdnLGvhU/tgeAHyn4ERERERERkb03mv+qltuObVYMd/arxMZgjWjFj2u55CyPimVRttYJfqw0+An9PT2fiIiIiIiICCj4kRHhGIt2vCz4aVWJYGSDH4CiW6RqWSx1gp8+rV7GGNwY/CjY6+OJiIiIiIiIKPiR0WBhEa2o+AkBy7KHdqaNlDLjSavXvV8L9K/4AcgArVDBj4iIiIiIiOw9BT8yEmyzYsZPq0o0wq1eAMVMicrd72Lp1MM4lkPOyfV9n4chUMWPiIiIiIiIDMHo/qtabiuOsXqXufsVqsZQcPLDOtKGSm6JalBjyV9i3BvHGNP3fR4WLQU/IiIiIiIiMgQKfmQkWMYiWjHjZ8m2mFyjfWoUlLwS1aDKUmtpzTYvAM9Y+HG4hycTERERERERSSj4kZFgG3vVVq8Fy2Y8MzG8Q22g6BUp+2XKfnnD4CeI2mteFxEREREREdktCn5kJDjGom0MRFHyQqvCom0xmZ0e7sHWUXJLVP0q5Va570avDs84tFTxIyIiIiIiIkOg4EdGgmUsIoC0MiZslSlbFuP5Q0M913qKXhE/8rlWv8ZYZmzN92UU/IiIiIiIiMiQKPiRkeAYm9DQDX4qjQUiY5jMHx7uwdZR8koAzDfnOVU6teb7spZLk2ivjiUiIiIiIiLSpeBHRoJt2bQx3eBnobUAwER2cpjHWlfRLXa/vnfi3jXfl7U9msvnF4lIV8MP+fd//CJLdW2+ExERERHZDQp+ZCRYxiZaVvGz1FoCYGKEhzt3Kn4A7p64e8335ewMTQOE+oetyEof+txr/Kc/+TKffGZm2EcRERERETmQFPzISHCMTbi84ieoADCZGd2Kn07w41kep0un13xfzs7QMAaWLsP5T+3V8URGXt1v8wufeQWAF2YrQz6NiIiIiMjBpOBHRoJtbNrLKn4WgyrAumvSh63T6nXXxF04lrPm+7JOloax4PH/Cv/vd8DSlb06oshI+/BjF5mr+UzkXT5//VHmm/PDPpKIiIiIyIGj4EdGgmXZPVu9Ftt1ACZHeMZPp+Lnnol71n1f1snRtAyU08Dn8uO7fTSRkdfwQ37+06/wjrunedf9BS64/w+/+tyvDvtYIiIiIiIHjoIfGQmOcQhN2up15UkWKldxscg7+WEfbU0TmQlcy+UN029Y931ZJ0dgDO3qbPLCpSf24HQio+3Dj1/kZrXFD3ztvUxOJJU+T19/fsinEhERERE5eBT8yEhItnqRDED+g/+NpUyBiewkxphhH21NeTfPx/72x/iOs9+x7vtybgGApxqz/Nj0JJEqfuQ21wxCfv7TL/O2u6Z4613T2NkkFD2/cH7IJxMREREROXgU/MhISLZ6GXjqV+HK51k4ej8TualhH2tDd0/cjWd7676nE/z8ITV+c6zE7PWnod3ai+OJjKSPPH6RG5UWP/C1rwegHidtkIv+TRabi8M8moiIiIjIgaPgR0aCYzmEAJ/7WTj1FhYz+ZFe5b4Z2XQW0A0TA3DRimH26WEeSWSoXpit8NY7p3j73dMAXKq+ghUl1X0vLrw4zKOJiIiIiBw4Cn5kJNiWQ9sYiCPib/xpLlQucrJ4ctjH2hGd4OembQNwyXXgktq95Pb1b771K/iVf/QWAOI45qXFF/maRg1Qu5eIiIiIyE5T8CMjwbKcZKvXw/+A6xMnmG/Oc9/UfcM+1o7IZlYEP4UpbfaS217WTf57uNG4QSWo8dZGk/HI8PLiy0M+mYiIiIjIwaLgR0aCM3aK0Bjid/9I9//jf1CCn1xmDFgW/BQn4fLnh3kkkZFxoXwBgNcFbSbDNhW/MuQTiYiIiIgcLAp+ZCTYXjIAOcyN88L8CwCcnTw7zCPtmGxmHADfSmaYXHJsWLoE5ZlhHktkJMzUkv8OTrTb5KM2zVZ5yCcSERERETlYFPzISLCtpBomiiNemH+B06XTFL3ikE+1M3IrhlRfbFeJQe1eIsDV6lUAClGObBzTbMwP+UQiIiIiIgeLgh8ZCbZJgp921OaF+RcOTJsXQDatZgIwQCNsMedm4fITwzuUyIiYKV9iOgw5l/lqslFMs7U07COJiIiIiBwoCn5kJHSCn7Jf5lLl0sEKfpxs9+s7Msn66svH7oNLCn5Eri6+zImgzfPZN+PENo2gOuwjiYiIiIgcKAp+ZCR0Wr2em3sOODiDnQFyTq779f2lMwBcnL4Drj4FbX9YxxIZCTO1WY6FIfO5M1i4tKL2sI8kIiIiInKgbBj8GGNOG2P+zBjznDHmWWPMD6Sv/6gx5oox5gvp/75p948rB1Wn4ueZm88AByv4ydiZ7tevH7sTy1hcyo9D2IJrTw/xZCLDFcURM/4CJ9ptKrmT2JFNMw6HfSwRERERkQPFGeA9beCH4jh+0hhTAs4ZY/44vfYzcRz/u907ntwullf8TGWnOJw7POQT7RzHcnBjCAxM5Y9wLH+Mi3ay4YtLT8DJh4d7QJEhmW/O48cRx60cVzNFTGzTiFXxIyIiIiKykzas+InjeCaO4yfTryvA88DJ3T6Y3F4ck2SQz809x31T92GMGfKJdlaO5PMUclOcHjvN5eYcZMdh/mW48Dl49hNDPqHI3puppqvc80fJujbEDs1k552IiIiIiOyQTc34Mca8DngT8Fj60j8zxnzJGPPfjDGTO3w2uY1YJvlRXGgtcHbq7JBPs/Oy6ecr5Q9xunSaS5VLUDwGlRlufvanufAnPzzkE4rsvau1ZJX7ibEz5FwbQofAQBip3UtEREREZKcMHPwYY4rAbwH/axzHZeDngLuBh4AZ4P9e477vM8Z83hjz+Rs3buzAkeUg6rR6Adw/df8QT7I7ciSfr5A7zJnSGRZaC1RKR6ByjX/XusAP5dTeIrefmfJFAI5P3UfWtYgiF4BW2BrmsUREREREDpSBgh9jjEsS+vx6HMcfB4jj+Focx2EcxxHwX4G39Ls3juNfiOP4kTiOHzl8+ODMbZGd1Wn1Ag5oxU8S/JQyY5wunQbgUn4MqrPMRA3mLSBoDPGEInvv6vyLFKOIscNnyTo2cRr8NNr6b0FEREREZKcMstXLAL8IPB/H8b9f9vrxZW/7FuCZnT+e3C46rV45J8cdpTuGfJqdl3WyABS9Yjf4uehloXyVBWJqlgX1+WEeUWTPzSxd4Hi7DVN3kvNs4sgDoBk2h3wyEREREZGDY5CKn3cCfx9494rV7T9tjHnaGPMl4F3AP9/Ng8rB1mn1unfy3p62r4MiO3UPAEX3VvBz2bEgajNvW9Qti6imVkjZn+pBnZ96/Kc2XalztX6NE+0QJu8k49q0owwAzVZ1N44pIiIiInJb2nCdexzHfwH0W7H0Bzt/HLlddVq9DuJ8H4CcV8AyFjknhzGG6ew0l2KfNrBkJ0FXvXKVIg8N96AiW3Du2jl+7flf412n38Vbjvft+u1rJijz5tiC/BQ5t04Up8FPc2G3jioiIiIictvZ1FYvkd3SafU6iPN9AHJ2joJb6K6pP106zcV2lUX71n+CterssI4nsi21dg0AP/IHvqfqV6nEbY5nkoWQWddaVvGztPOHFBERERG5TSn4kZFwsniSnJPjkaOPDPsou+LOiTu5d+Le7u/PjJ3hUmue+WVtbbXatWEcTWTb6kEdgCAMBr6nu8o9fwyAnGsTRDkAmq3yDp9QREREROT2tWGrl8heuGviLh57/2PdipiD5oNf+UE++JUf7P7+VOkUv9ucY9ZZFvzUbw7jaCLbVgs2X/EzU74EwPHxOwHIujZBnAxBV8WPiIiIiMjOUcWPjIyDGvr00xnw/HS+1H2t1lDwI/tTrZFspPNblYHvuXrzOQBOHLoPSIKfVpQHoOEP/hwREREREVmfgh+RIThTOgPAF/OF7mu15uKwjiOyLfX5lwEI5r488D0zC1/GjWOmjzwIJDN+OsFP09dWLxERERGRnaLgR2QIOhU/X8i43ddqam+RfaqWVugEYWvge66WL3O83caauhtIZvy0oiQIVfAjIiIiIrJzFPyIDMFEZoJjhWM0wha2Seb81NTeIvtUd8ZPuznwPTPNmxwPYyglw52zrk0jToOfdFh0P7/06Kv8/V98bBunFRERERG5vSj4ERkCYwx/666/BYBnewDU1vnHrsgoq7WTn91NBT9BhRN2HtLZXjnXphHlMXFMs732fwtfuLTIUxfVFikiIiIiMigFPyJD8t673wtAo93AxlALGxDHQz6VyObV2w0A/AFbvfzQ5wZtjmenuq9lXZs6ObJxTDN9Xj/lRkDDfpHv+eT34IeDbxETEREREbldKfgRGZI7x+/kjYfeyAce/AB5y6UG4NeGfSyRTaulgU8wYBAzW7kKwPHCie5rGceigZcGP2tXDpWbbabzT/PU9ae4sPjqNk4tIiIiInJ7UPAjMkQffs+H+cGHf5CCnaFmGWiVh30kkU2rRUngM+hw56s3nwXgxORd3dcsy+A5DpkYGuE6wU8j4E77NQAuznx+iycWEREREbl9KPgRGQFFO0vNsqCp4Ef2n3rUBsCPgoHeP3MjCX6OH36g5/WcZ5OJobVO5VC5GWDZSSvYhRtPb+W4IiIiIiK3FQU/IiMg7+STip+mVrrL/lMlCX4GbfWaWXwZE8ccO/pQz+tZxyYTG5rrBT+NNrGdVARdXHpliycWEREREbl9KPgRGQEFt0DdWGr1kn0niiPqJEPJB634uVq9wuEwwl3W6gWQcS3c2KIZ93+O345oBCFtK7l+sT67jZOLiIiIiNweFPyIjIBiZoyqZaniR/adxrINXIMGP3OtRQ5jg+30vJ5xkuCnkbaOrVRpJs/37eT6hUBBqYiIiIjIRhT8iIyAvDem4c6yL9WCW5vogjUCm5XKYYNxy1v1uudYONj4cdj3vqVGEvw0rAiA64Q9wZOIiIiIiKym4EdkBBSy40mrlyp+ZJ/ZSvCzFLUZt7OrXs84NlZs01oj+Ck321hE1CzDZJi859LCS1s4tYiIiIjI7UPBj8gIKGQmqFmGuLG54Odq9Sqfn9VKaxmeun8r+PEHDX4IGXMKq173bAsrtvDTmUErlRsBE5SpWobXh0lwdGnm3BZOLSIiIiJy+1DwIzICxjPjRMZQac5v6r7/cO4/8P1/+v3EcfIP5WfnnqU94D++RXZCLf2ZNXG8ZovWclEcUTYw4ZVWXfMcCxM7awc/zYBp+zqxMZxwTgFw4eaz2zi9iIiIiMjBp+BHZARMZicBWNxE8BPHMeeunaMSVCj7ZWaqM3znf/9Ofu25X9utY4qsUqvfBGA8iggGCH4q9ZtExjCeGV91LeNYmNimtWbFT5txZw4A493DVBhycVEr3UVERERE1qPgR2QETGQmAFhoDd7qdbV2leuN68nX1aucv/ksMTG/e/43duWMIv10Kn4mwoiAiI9/+eOcnz+/5vvLSxcBGM9NrbrmORbEDmvtBis3A0rWAgBN5wSnI8PFxrXtfQARERERkQNOwY/ICJjMpBU//uBbvZ689mT366uLr/LSpc8C8OXqJV5c5x/eIjup1kyCmIkowo8jfvKxn+RjL35szfcvVa4AMJ47vOqa51jEkU3L0G1f7PjJP3iejz5xiaKzCEAjPsQddpELQXWnPoqIiIiIyIGk4EdkBHRavebb9YHveeqVPyITJWutr8w+ycs3n2E8DHHimN9//Ge2dI4fefRH+A1VDMkmvFa+SC6KOB4ZGkQ0wyYVv7Lm+xerVwEYLx5ddS3j2ESxS2QM7bDVc+2/fOYVXp2fw80kVXGNaIIz+cNcN1rpLiIiIiKyHgU/IiOgO+NnM8HP7OM80grIRxFX517g5eoVHmjDOyKXP5h5lMgf/Fkdn73yWf7iyl9s+j65fT1fucDr/YCM7bFAEkSuF/ws1ZL2xPHiiVXXMo5FFDoABK3Vzyjc+R/548MXkuvtHGfG7gTg0s0XtvchREREREQOMAU/IiMg7+RxsViI/IHev1S+wktRnTdPnuVEBFcql3g1rHF39jDvecN3MWvBuc/8H5s+R6vdYq45t+n75PYUxREv1K5wn+/jOjkaJnl93eCnkfx8jY+dWnXNcyzaURL8tFqr2x4tb6H7tR9kOXP4AQAuzjyx5c8gIiIiInLQKfgRGQHGGCbtDIu0IW3fWs8XnvwFAN50/7dz0i3xeDBP08A9k/fwNQ//z+Qw/P6Lvw21zYU4jbDBXEPBjwzmcuUytcjnDS0fz8t3X183+ElnAo2NnVl1LeNYtCMXAH/ZMzrzfibapvtao2Vz5vhfA+Dizee38SlERERERA42BT8iI2LCzrFgWdCn0oHGInzhw5D+A/jJVz6FE8OD938rxwrHqaf/Hn7g5DvIu3m+7sRX80dZB//P/6+Bv38YhbSjNnO12VWDdUX6eX4+CVzuswt4Xqn7+rrBj79EMYpwMsVV1zzbIow8AHz/1tDmIEyDn2XvbfgRpSMPJCvdy69u52OIiIiIiBxoCn5ERsSkW2TRtvsHP899Aj7xQbj2DFx/nqeCed6QO0rOzXP8zFcD8P0Tb+LsV3w3AO95w/up2BafffWTA3//VjpMtxmH1Dcxa0huXy/Mv4ATwz1T9+NaXvf1SrBO8BNUGY9N32ueYxHGyXNay8KjIEyq4NrEvMUq8hbvx6n7IbhZzkQ2F+rXd+LjiIiIiIgcSM6wDyAiicnsFM/bFsy/ChMr2mAa6WyTK0/Suv4cz2QyfNeZrwHg7z30j3nw1Dt56/G3dt/+1uNvZcp4/L5T5WsH/P7NsNn9eq4xR8EtbOPTyO3g+bnnuTsI8M68Ebf+cvf1RrtBEAa4trvqnqV2g/E1/k9P0urVqfipdV/vBD8BMcesHGTv5ov+LABn3BJ/FdZWP0xERERERABV/IiMjInJu5JWr4ufW32xmayw5tJjPPv8bxIYw5tOvgOAglvoCX0AHMvhnbkTfNG1BpoZBNAKbgU/N+s3tvYh5LYRxzHP33yG+1otOPoAnp3pub5W1c9S1GK8TyAE4Dk27Th5zvJWL79T8WNiXNulkHGotUIAzuSPct1ENAJVqYmIiIiI9KPgR2RETBaOUrZt2hdWr1OPG4tUjIEvfZQnTbL566EjD637vHG3SN2yIBisGqLZWup+Pbf02uAHl9vSjcYN5v0l7vf9JPixesOcteb8LEYBE3au77Wk4icJfj7+5EvJi36diV95F19lPU0AeJZLzrVpBCFhFHPHeLLS/eL1p3fmg4mIiIiIHDAKfkRGxEQmGV27dOUctHvXun+6dpF3nznJTRPxVHGcO8fuZCo7te7zil6RmjFEzaV139fRWh78LLyyydPL7eaF+RcAuN8P4fB9uHa253p1WcXOcgsmZtIt9b3mORZBWvHzwsxNgjAinn2Gj/kXudM9T3e/j+YAACAASURBVGDAtT0KGRuAmt/m9OEHAbg0e25HPpeIiIiIyEGj4EdkRBzOHwZgljbMfKHn2iV/kaZl8azn8VQ2w5uPvnnD5xW8ErExNOo3B/r+zdZi9+u5yqVNnFxuR8/PPY8BzpbuACeD5/S2epVr11bd4/s1KpZhKjPZ95lJ8JMESLZpsVDzuXz5Uf7N9BTXS1cJjMGzM9x/fAyAv3p5jjtOvAWAC1rpLiIiIiLSl4IfkRHx4HRSufCljAcXHu25Vk23bH3yjoeoRD5vOvKmDZ9XyIwn99YGm9fTbN5qzblZmx3oHvn/2Xvz8Liys9z3t/ZQs6qk0mxbst3ddrvbPTlDDxAydCchIYxhDBD6gXDOYbpAOHDIzbnkwuFwmOGQcCEQhhCSJyGQcJI0CemkM5B00unu9OhZHmXZsqQaVPOe1/1j7ypJlmxLljXYXr/ncVdp19prr1KXqvZ+6/3e78blcOkwoz6kB8PXrWksdPzUCkcW7VOeDduu96R6l5wzbmjYQST8aA4zdZsTU8+G8wsLTwhMPcYDN/XSkzL5txcnyfTtocf3maievmrPTaFQKBQKhUKhuJ5Qwo9CsUkYSg8xkBrg2VwfnP7agscaUcetR91QxHnJwOUdP5modKzRWp7wM799dtEqLWsfxY3LoeIB9rQaMLgXoOP4iQUSgFr5+KJ9SpHw05saXHLOmKHhyDD/RxcOhbrDidlwHl0P/wZMPY6ha7zhjiE+f3AKKxAMSZ3ztnrNKhQKhUKhUCgUS6GEH4VikyCE4J7+e3g+HoPxJyDwO4/V/TDzxw1c+pJ9bOvadtn50skwA6jeWt4FsRV1YerzfIoXCeZVKAAqdoWzjUn2OC50HD+hYDPkewDUimMwOw7NEvguAOVqWELY07V1yXnjhoYdCT+acClULU5YoXApNRuAWOQsetOdW2g4Pl8+OsOQnuS8p1q6KxQKhUKhUCgUS2Fs9AIUCsUc+wb28ejpR5nyGgxO7YfhuwGoSxfQO2OEEJedK5PqC/e1yss6tu2EF85bAknRty4zWnEjc6QUlnHdHnX0AohFwk9/IJiQUD3/LPzvO+d2imUo7nk1APns6JLzxg0dO0iQIhR+rOIpTkRfTwSaC2gYkfBz/0158ukY//bCJMPxbp6yzl3156lQKFbG7376EDN1mz/5oUt3nVQoFAqFQrG+KMePQrGJaLdofy4emyv3ci3qyM6Y5ZR5AaSjsOimvbyuXlbU9n2rkaEofKSUl9lDcaNyqBQGKe8RSchuASBmpgDIaCZdsS5qu14H3/0eeMPvwavfCU6d8rmnAejpuWnJeWOGhh919RKaizlzgJNm2Cbe0bxoTCgwGbrGt+8d4vOHphhI9FPXBLVlutsUCsXa8NVjBQ6eq3KgcIAfeeRHaHmtjV6SQqFQKBQKlPCjUGwqbs3fSkJP8Fyufy7g2a7S0DR2x/u4f/h+Hhp9aFlzZVIDANTt5ZVt2ZHwsy3ZjyUEzVZx5U9AcUNwuHSYAamR798LkfusXeqV1hN0xXMUkln2j76ET/Vv4z25FO8a3sZB4WJISfYipYoxXQMZGlGF8AiqL1LTw48pRwui48yFSH/nXcM0HZ/AjzrizexfmyesUCiWxZlSE8cP+ObUNzlQPEChtbyukgqFQqFQKNYWVeqlUGwiTM1kb99enpdHQsePlGBVqGuCHYk+/vT171v2XJlE2NWr4VaXNd6Ovpndkt0OM2cozhwkvf2VK38Siuuew8VD3GZZsP2OzjYzcvykzTTZeJbPj3+ez49/HgBd6PgJDSFT9AUgdH3JeeOmBmjoUiKEh2UfgXT4WFPTFhwH4L6deXrTMU5X8mDA+ZlD7BpVr1mFYiOoNF2qlkcuZVKwQsEnkMEGr0qhUCgUCgUo4Ueh2HTsG9jH+6eepdUqkSwcBbtGXdNIx7pWNE8qukCuu8sLvW25LYSUDPfdBjNfpVg6yqgSfhQXYPs2J6snedBqdfJ9AGJmqNBkYl38ykt/hf2F/ezI7WBndicjXSP84IdfyXG/Ts8ljKaxyN0TkyCFTyuYBDSyUqemhc6imDEn/Bi6xrffMcSTL+RgB0zOLu4kplAo1ocz5SYAricpRo5RX/qX2kWhUCgUCsU6oYQfhWKTcU//PXgEHIjHeNnpx6F7lIbQyMSzK5rH1EziEhrLzFiwfYu4lPT174VDUCifvJLlK65zjs0ew5cBt84Ldoa5jJ9UPMd9w/dx3/B9C/bb17WD47P7yWuxi84dMyJXjwRD2JSMBmnRw6CMU9DCznbzHT8A33nnMB//xlYSUnK+NnFVnqNCoVg546VI+PEDilYo/ASBcvwoFAqFQrEZUBk/CsUm4+7+sJPXc129cPpryNYsdU2QjneveK40grq3vA5dlmcRl9DbfzsAxdrZFR9Pcf1ztHQUgN2OB/23dbab6bCLXCa3dMeufYNhKHmPkVrycQi7egEYUpDVa5yMmexIDWJgUItKvWKx9IJ97t2ZRxpp+n3J+dbMFT4rhUKxWs5Ewo/jB5SioHXl+FEoFAqFYnOghB+FYpPRnehmZ24nz2V74dTjtJozSCHIJHpWPFdG6NR9m6OTT112rO07xIHuVD9CSorN6StYveJ652j5KEkEI7lRiM2JOL257dzTfzd33v6DS+63b8drAchfomTR1MNyLkOCEC4nTYORrlswhIHXDpE2Fwo/hq4RN8JysJK7vCBzhUJx9Wk7fjxfUoxE2CBQwo9CoVAoFJsBJfwoFJuQe/rv4TlhI2vnqJ9/AYB0qnfF86SFyWe0Ft//6E+xf+zTlxxrBw5JBIZm0INO0S5f0dqvNpZn4fjORi9DEXGkfIRdnkQfvGPB9rge5x+/44PcPXDPkvttG7ibH9F7eWjnGy46txCCuKGhBxolXWPaMOjt2oOO2RljXuD4ATB1DV1qeCpIVqHYMM6Uw7Ji1/c6jp+gNrmRS1IoFAqFQhGhhB+FYhNyz8A9VHyLU6ZB/fhjAHQl8iueJ6PNXTBXK5fO7LECh3j0ltCrxSm69RUfby14+5fezru+9q6NXoYCkFJytHSEXc06XCD8XA6hafz3H/8SL3/5L1xyXMzQ0KXgSCzMAsrq29DmCz9mZtE+hi7QEEr4USg2kIm240c08Qj/Fn0l2isUCoVCsSlQ4c4KxSbknsg18VxXDzc3ysAQ6djiC97LkdZiEDntXauy9KBGAf7lJ7G9GokoR6XX7KJgVSAIQNs4fTiQAc9OP8ue/J4NW4MCmm6Tx8Yfo2SVqDhV9tn2gmDnq0ncCN07pajle4ItCOYCoU0zsWgfQ9PQUI4fhWKjCALJRLmFrgmkXp+33d3AVSkUCoVCoWijhB+FYhOyI7uDXDzHc30DDMbrQJPMEk6Hy5G2Gx1fXz2y3l+Ic+Bf+Zvy88ykk3Tr4TF6Ez2caZyD+hRkh6/0aayac/VzNNwGrq8uHjaSR08/ym88/hsAfEt6O991cnwNhR8dTYYvWi0QBE4eIWIgw8djS3QFM3WBLgUuKk9EodgIpmoWjh+wozfFmdac8OMH3gauSqFQKBQKRRtV6qVQbEI0oXF3/908l8rQeP1vAZA2F2ebXA6ra7Bzv3ER4eeJsU/wlz05xmIx4iLUgnvTg5R0DSob2x57rDwGgFNXOREbScUO3WI/Uq3xu+fPocW6oHv7mhwrZmgIGbp9TDdHqeHBfMePbi7ax9A1BBqelGuyJoVCcWnGi2GZ1839GYShHD8KhUKhUGw2lPCjUGxS7um/hxOVE5xrTgGQuYJSrzOxuQvmul2Bx/4HfPq/wbMfhMkXwK5zoHSoMyahhcJPX3aElqbRLB1b5bNYHWOzofBjtzZH0PSNStMNL+reUSyTLxwP3T5Rl62rTUzXEJHjR/pbKdRt5DzhZynHj6EJNKnhoYQfhWIjaAc739SfRujVznZPuTUVCoVCodgUqFIvhWKT0s75efzs4wBXVOp1V/9dHC0fBaDRKnDwG+8m70uG/Mh+L3QODMyFRieii+re3A4ACqUxRq/0CVwFjhYOAOCgsls2knqzQDII0DODYfnfGpV5AcRNjSIDQJ2ENkqh7iC1uVwfU1vs+DEjx4+rhB+FYkMYLzURAnb0pUkZpc47dqBKvRQKhUKh2BQox49CsUm5o+8OdKHz9cmvA1dW6vWOe9/Bp7/v03RJQbUxxU8MD/Id20f4/df8LIXv/jPkAz/P/nSuMz4eOX56syMAFKvjV+GZXDljxdCN5KgSng2lUTxKOpDw/X8L/bfBrtet2bFiukZd9AHQExuhWLfxiXceX7rUSyCU40eh2DAmSk2GswnSMYOkUexsVxk/CoVCoVBsDpTwo1BsUpJGstPNKhfPYWgrN+jF9Tgj2RHSwuAcHramMZoa5MOn/53vOPQX/E42TlE65I0UAMK1AOhN9gJQrJ27Ss9m5di+zenmeQAcdUG/oTTcOpkgCJ0+P/8E3PrGNTtWzNAwIlfPcDJ0/PhyzvGzZLizFmX8qNeJQrEhjJeajORTmLqGaVQRkVivMn4UCoVCodgcKOFHodjE/Pq9v86vvuxX+cAbPrCqeTKayYQRCkf/5Y638X++5//w6pFX89EjHwXgjUMPADDlhaGcfcnQcVFszazquKvhxOwJfCRDnocj1AX9RlL3mqRlAPGuNT/Wtp4kuUQSgWC0awczdRt3nvCzlAAaOn50lLdAodgYzpRD4cfQBRgNev2w2Es5fhQKhUKh2ByojB+FYhOzb2Af+wb2rXqetJ7gcNRppbtrhB25HfzBK/+An77zp3l26lnuzIzwoYnHOGeE3ZS6490IoBB1c9oI2sHOd9gOX0wlN2wdCmh4FmkpYIkyq6vN73zfnewv/CQvFO7BKXbheAF1JwZxMBGIJUKlDV1Dujru2uRNKxSKS2C5PlNVm9F8ipiu4ekWw75PwdBVxo9CEeEHkkcPnOfb9w6haerDSqFQrD/K8aNQ3ACkjSS2Fv6555NzYc67e3bzw3t+mJ1Dobj0vXe9DQhdFT1agqJ0wK6t/4KBo6WjxKTkFsfFFwI/8DdkHQpoBA5poa/LsUxdY9/gXTy892F6M2FZV7kVvnZNlj5ZNjURlXopFIr1ZiLq6DWST2JogpbhMuCH79fK8aNQhHzjZJGf/dAzPHmqtNFLUSgUNyjK8aNQ3ACkYxkIz83pjncvejxpJHn+J55HE3NacD7WRVEvQX16XUp8LmSseJCbHbfTYt7xbZJaat3XoQiFn4xY/4+LvkwY6jzbhFg3mGLp7yoMXeBJHU8I8D3Q1UebQrFenCk3ARjpSVG1q/gC+iKdPpBKsFcoAKqtUAQ9GwmlCoVCsd4ox49CcQOQiWU797sTi4UfYIHoA9AX76Go69AsLjl+rRkrH2WX4xDv2gqA4zQ2ZB0KaEif1BKhymtNW/jx/FDIiRlLl/wZuoYMoowf31mn1SkUCoAzpVD4Gc2naAazAOT1sAulcvwoFCEtN/xbOF+1NnglCoXiRkUJPwrFDUA6EntSwiSuxy8zOqQ32UtB16FRWMulLUnZKjPjVNjtuMS6RwFwnOq6r+NGo+bUeNtn38bp6unONikldemTWebr5mrS1xWJTUEo/JixpZ1npiaQ6Egh8F31bapCsZ6cKTWJGxr9XXGaXljGkjN6AFTGj0IR0XLCwPPzFSX8KBSKjUEJPwrFDUA6PQhAzzznz+XoTQ1S0rUNcfyMlcNg513EMDPh2h27vqo5606dd37lnUzWJ1e9vuuV47PHefL8kzw/83xnmxM4eALSRuISe64N+VQMIQAZOX70pV1Hhq4RBGEGkesp4UehWE/ardyFEDSbZwBIxwYAJfwoFG2ajnL8KBSKjUUJPwrFDUAmEn66M0PL3qe3aystTaNZP3/5wU4TrmL4cruj1+7cTcSj8h57lY6fg8WDfOrEp/iBT/3Aqtd3vVKNfsc1Zy7Qu+GGJXZpY/3zlQxdoycVQ0bCz1Kt3MPtgkCGwo/nNhc9/tkD53nqyx/g7BN/vnaLVShuUM6UWoz0hO/TjUboFkwmtgHgq4wfhQKAlhP+LUwp4UehUGwQSvhRKG4A0rEwb6En0bPsfQa6whP3ydrE5Qf/xX3wxF9c0dqW4mjpCD1+QG//XmKR08RdZcaPG7hAKG48Ofnkqtd4PdIWfurOnLuqEf3eM2ZmQ9bUl4l1HD+mtnQ7eUMXBFE5mLeE4+c3P3mAf9n/m/zCi+8BKddusRfh3GyL//cT+/nksU91XocKxfWAlJIzpSaj+VAYrrUm0aVES4Qlusrxo1CEtNxQ+JlUpV4KhWKDUMKPQnED0L5o74kvX/gZzYYn7meal3H8+C5jjUmq0weveH0XMlY8yG7HQQzuJRY5TRx3daVelj93svX0+BdXNdf1StWOhJ95v+tGdD8d2yjhJ44MLlPqpWl4bcePt/Ck2vZ8zlctSrrGcdOkcHY/H3ziNM9OPUsgg7VdfMQXDk/zj88+zn9//J08ce6JdTmmQrEeVFouNdtjJBJ+KtYMPX5AIzYMgH8VnaAKxbVMM3L8FOo2rr8+nz0KhUIxHyX8KBQ3AGkzdPxcrKPXUmzPbgdg3Lp0xo9sVXh4eJD318eufIHzCGTAscpJdjkODNxGLBZeUNirdPzY80J/p898fVVzXa9UnAqwsNSrbpUBSMeXnw91NenLxEGGTp+LOX5MXeC3HT/uQuHnbLmFlNASGlII/vrfPsi7PvMoP/HvP8HXzn1tbRcfUbVchAi7jbVL5xSK64Gzs+H76tbusNRrxi7S6we0jDyg2rkrFG3apV5SwnTN3uDVKBSKG5HLCj9CiBEhxBeFEAeFEAeEEL8Ubc8LIT4nhBiLbpdvJVAoFOtKW/hZieMnF8+RRWPcvXS2TqsxRU3XKHirc+S0mahN0AocdjluKPwY4dqdVV4w24WjAHT7PtORwHG98PGxj/OhQx9a9TxLOn6aYVe3TGz5ouHVJBR+Lh/u7F0k3Hk8ajVdFeEcjdZ+tFgoZk421ifou9ryQITf8LZU+LTiOqJYDwXN/q44ru/yvFviFkvDif5mleNHoQhpunN/C6qz143F148XOVlQX/ooNp7lOH484L9KKW8H7gd+XghxO/AO4DEp5S7gsehnhUKxCWmXeq3E8QMwqiUZD6ILVacJ/uK8hmp08Vz1r+wbLCnlgpKbdkev3Xoa0n3EYm3hZ3Fo70qwovyaUddj+iqJVJuFR048wr8c/ZdVz7Nkxo8VtmdOrfC1c7XozcQ6pV4XdfxoAq/t+LngdXimHL5+7ejTztbPIYzweZZapbVY8iKqlgsiPOmfX3KoUFzrFBvh31tvJs7zM89jETDUzOFHQqxy/CgUIS3Hx9QFoAKebzTe/k/P8ZdfOrbRy1AoLi/8SCknpZTPRPdrwCFgK/A9wD9Ew/4B+N61WqRCoVgdo9lRXrXtVdw7dO+K9hsxs4xHTgX++lXw5d9bNKbSmAagJq8stPaef7yHX/rCL3V+Plo+ipBwc343ALEoW8bxVin8RI6hbRhMB9eXzdr2bMpRSdZqqEZz1OYJIvXofibZu+r5r4T+eY6fi4c7a/iyHe688IT6TKlJzBBY0add0WyQNGbC+7Mn12jVC6m05oQf5fhRXE+0HT/5dIwnJv4DTUrs5i04UeaWcvwoFCEt1+uEoKuA5xuLUtPpZDwpFBvJijJ+hBA7gH3AN4BBKWXbJ38eGLyqK1MoFFeNpJHkzx/6805uz3IZTfQxqQvcZhkKR2F8cTBttRleRFev8JvdQAZ8aeJLnZ/HykcZ9X2SA3cA84Qfd3UnSlbkGBqJdVMWEsd3VjXfZsLyLWbt2VWHFVfr4Vt6vTnd2dawZwHIpPpWNfeV0tcVA3QEGqZ+8a5efpQDdGGp15lSk13dGi0RftN6PGYwEDsDQKl8fO0WPo9qyyUlQuHRasysyzEVivWgUHcwdUE2YfCNM//BXtthzN/dceAFUnX1UiggDHceziWJG5py/NxAWK6P4wXYngr0Vmw8xnIHCiEywMeAX5ZSVkV0Eg0gpZRCiCV75Aoh/jPwnwFGR0dXt1qFQrGubE8PE1ReZGL8K+wEmD60aEylFealVAXgWmAmruhYgQzQhMZY8RC7bBv69wAQi3UBq3f82F4LQ0q2pIegVWOmfp6tuevjPclqFvGlT82pkYvnrnieqh1mH9XniScNu4qQkuQGOX76MnEAdGFeotRL6wg/nrdQ0BsvNbk55zOuaaR8QVnXyccjx4+1XqVeHoNagSnAmj21LsdUKNaDYt2mNx2n4TZ4sXqCn7Is/kncwq2R8OOvU+c8hWKz03J8+jJxhnMJ5fi5gZhthm74C4UfGUgCKZG+JAgkUjJ3P1h8K4MoGqH9syTaPnc/kBICwnnnj5HR/u37MpyL6FZKLrg/N+bCx+bvRzgUJEA0tv382vPQfry9Pdof5v9n7jgssZ8EyQX7tY/PEvvNG3Ph4yz4eW5eTRc89PDtK/lfe02yLOFHCGESij4fklJ+PNo8JYQYllJOCiGGgeml9pVS/jXw1wAve9nLlhSHFArF5mQkOwrn4My5b4TCT7MA9RnI9HfGdMqDNA1aZTCHlz3//DKAs/Wz9CX7ON04xxsdFwbCN+BYvC38rK48y/YsElIy0L0TWmNMl45cP8JPYwoMg5JVWpXwU4nK4WrzSuGeqRxju+shElc+72poCz+GiF0i3HnO8eP5i0u9XrPHARsGrRQn0w1K8VAcKrnrk/VUa7nERHjy11pldzqFYj2xPZ+PffMsP/zyEXRN8PjZx8nEMtzdfzcApYZDbybG01NP4yO5X2T4az2PE4RfDgaBcvwoFAAt1ycV0xnMJphSws+a4XsBnuPjuQG+G4Q/t++7AZ43tz3wAnxP4nvBvH8y2h495gcEboDvy84+gR9t92U4ProftMf4siOyuG7AL1oJjKfrvPeZL3XEnBsOAR3LiBDhfdHeLhaOEReMad8IQcd3cuF+4oK5F8y3cL/wRizYTzdujEbnlxV+RGjt+VvgkJTyT+Y99EngYeD3ottPrMkKFQrFhjGcuwmA84VDnDV0cn5AZvogZF7VGVOJXCI1XcNvFtGzyxd+5gfdjpXGqKarSCS7HQcG2o6fsI24s8pQXMuziAeSgfytMPkoU6VjsPN1q5pzs2BHn1zlxjQ7cztXvP8Tk0/woYMfohr9jlvSxws8ZpozPFU/zc81GhDPXNU1L5fhXIL/68Fb6Or/BR7YdueSYwxdw2dxuHOl6VK1PIZSLbAh3hqE9InO46VgfU6+q5bLgBkKP6dLJd7z9N9y79Y7uG/4vnU5vkJxpXztWJF3/uuLjOZTvGJXH7/35O8xlB7ifa9/HwCFhkNvJs4Tk18gIeHu/rsxZwWu1NCkVI4fhSKi6YTCz1AuwTPjq8/ku1aRgcRrizNOeOu0fKymi91wsRoenuPjznvcc3xcO8CxPJyWh+cGc+KMO0+8cYOrIqpomkAzNXRdoBsauqGhGfPu6yL6p2HGw1tNF+j63H2hCTRNMF23eWL/efqycb7vJVvRtPCx9uNCY979pW7pjBdi4T5CLLyvaUTb5j3W+ZnFt6Itfiz988L7F4yBOfGlI+DQUVI6j8+rEFJsPMtx/Hwr8FbgRSHEc9G2dxIKPh8VQrwNOA380NosUaFQbBR9w/swpORcaYwfHx7itc0m/33mMNw0T/hxap379do5ckN3LHv++UG3R09+jvKWlwGwK9YLkcMkZoZhiM4Vdg1rY/s2CSSD/aGTaLp6alXzbSY6wk/hMGxZuZjwrsff1Wltnvd9SrpOw23wbyf/DYDvrDcgcl6tN0II/uvrbwVuvegYUxN4HcfPXKnXmXJYHtgTD2/r7iAD3lGmDYNMEDCrgRu4Fy0huxpIKam0XIZiofPhfK3KM4f+lvPWa5Two9j0tANJj0zVeMWuPgqtwoLHi3Wbm/vSfOPs19hntYjf9FLMExq2L9BQXb0UijaW45MwdbJJk6mqjZTymr4oDgKJa/s4LY9WzaExa9OoOLRqDq7l49pz/6yGS6vm0Kq5WE13QenPpTBMDSOmY8TC23jKIJY0SGUXizHtf2ZCx4zp6Gb4s2Fq4X1z/rh5+5nzbwW6riG0q/f/5XMHp/jiiTPc1p/kD998y1WbV6G4Ei4r/Egpv8o8d9YFPHR1l6NQKDYTenYrg77kABYFI8nzyRRMH1wwpjKvNXq1fp6VFAS1nLncnqMTj3NC+PRJwWjvns72mBGW+qy21MsKHOJSkM3vIhZIpuuTl99pAyhbZQ4UD/CKra9Y1ngpJZYWWlRLpbErOuZNuZs6ws8216Ok69ScGo8cf4R9sV5G/AmIBLjNiKFreEFYBjbf8TNeCl9fGTMsr9LNHrY7kmkDbrUdvplMMNsq058eWLO1WW6A60u0qKsXmosTNLFXKWQqFOuB7YWv26Pna7S8FnW3jhu4nYvWYt0hmWxwrHyS72pZsGUfpi5wfNClyvhRKCD8nG5GpV59mTiOF1BuuuTTS5cvbwRSSqy6S6NiYzc87KYXunCaHo2yTa1kUStZNCs2TiTsXAzd1DDjeudfPGXQM5xmy+4YyYyJGZ8Tc4yYRixukMiYJNIm8ZSBGdfRjasrwGwUlVY740eJ4IqNZ9nhzgqF4gZECIb1BM9EH75jho4zfZD5pyrVee2zq82pFU3fskO7cyII+HpQQjv3OK9pNBG7buuM0YSGISVOcGXt4ttYvkNcaIh0PwO+z/QF31xvFt5/4P38/f6/5/G3PE5X7PIuGyeYc7iUq6ev6Jh986zRWzyPF4jz1PmnOF45zm80gG33ziug3nyY+pzjx53v+ImEn4QWCj892T6GGiak4DbH5ZvJBMXKyTUVfqpW+LrVCB0/juYgCbA8lfGg2Pw4USDpkalax+1j+zZlu0xCy9JyfRraYQDuj4SfmPECrh+gIZXjR6EAHD/ADySpmMFQtukMAQAAIABJREFUNmyAMVlpravwYzVcSpMNGrN26MSxQidOZaZFZbrJ7HQLp7V0JpcR1+nKJ+jKx+nbliGWNIgldGLJUKRJZWOkcnHSuTjJrImu3xh5KcuhI/y4SgRXbDxK+FEoFJdkS6KXp+3QDeIJGCuPsVfKjhBQCWyEBCnmWrsvF8sK84EetiR/ldLAqfKKZqMT7NwmBtirbL9uBy4JNNA0BtCZdiqrmm+tOFA4gEQyXh1nb9/ey46fLyCU6+ev6Jitiac6nwZbvPDE7yNHPoIpdL69cBp+6PeuaN71wtA0PNqOnzmB8Ey5SXfKxPdDV9qW3iEGCxmM7hq30AN4lIpjV1Qet1yq0UmfEOHvtWGEt0r4UVwLtDvRjE3VKDTnxPLJ+iRZLbyALfj7yaGzJ70FUnlMXeD6ATrK8aNQQNjRCyBphhk/AFNVi71brl7TBMfyKEzUaVYc7KaL3fJoVhxKkw1KZ+s0KovPoYSArt4EuYEUu+/N0j2QIpOPE0+Fzpvwn0ksoV/TZWkbSaUZ/t5VO3fFZkAJPwqF4pIMZbaBPYkgLMs+IFz2Vs9BbisA1cBhSDOYxKO2wvbYragj2H25XTxeP8TBeJwHWhYM3LZgXFwK3GB1wo8lPVJCB2BQT7LfX117+LVASsnBUlhKd6p6apnCz1xOUvkK25M342nwZwHYGu8BAg4WD/KQb5DL3wK733hF864Xhi5wZQwTcBeUerUY6UnRsqsA/MC9d7DTuouHj32UJwffAOynWDm1pmtrO36EFgo+NSM8+Wv5rYvuo1BsFtrlCQ3H52jhbGf7ZGMSV9sKSE43n+dex0fb8lIATF2LHD8QBOpiR6FouZHwE5sTflba0l1Kid0M83SshofVcKkVW0yfrjF9ukb5fGNRdo5uauSH02y7LU9+S5reLRkyPfGOUyeW0NGUO2dNUaVeis2EEn4UCsUlGe7dDcWnuNnIMo3HwXgdpg/NCT/4bNO6mAxqVK3ZFc1tRRfkyf7b+Y1Tj3MkkyenxaF/z4JxJgJ7lW2BbemTj4SfgViWaXd604UrTtQmqEVh2ePV8WXtYztzGUtl78rErBaSUdflZZbNvv77wDoAwHcWJuG1fwja5j4xDEu9QuFnvuNnotTktuEsTSd8nQ1k8/Rt2QlHA+rJu0Dup1Q7e5FZrw7tkz4RlXr50ctNOX4U1wLzyxOOTJ3s3J+snEaYdyLMErPODPdXS3D7S4C28CMjx4+62FEo2iHpqZhOfyaOJliypbuUYWByqxaGIZcmG5wbm2X6VJVaycJzFgupyWyMwe1d3PLSAQZGu+jqTXRCkM24cupsNHPCjxLBFRuPEn4UCsUl2TL0Ejj6IXZmttEXS3KoUQ4Dnne9FoAKknuNDE85NarRBfZyaUXjk323cnOgc3tpCm79DjCTC8bFhFh1xo8tfRJaOG9/ohfbm6bqVMnFr57VerUcKIWCiy50Ti2z65hlzbWFLYsra2PaDBx2uB6/VShRvOslcPIA2UDySi0Hd23+ho2GpuG3u3pFr5MgkEyUW7xu7yCtepjxkzJSkN0CQCF5B7GGpNicXtO1VaPMBNNYeNKnhB/FtcD8i5VzxVNoUhKXksnSUbSkhRYLy79ucVzYsg+AWNvxo4OPuthRKOaXehm6Rn9XnPNVK+z6ON3izKES4wdLnDtaxrEWiqXJLpPBnTlGb+8lk4+T7Ip1gpAz3XFSuZgSdzYxbeHH8YJN92Wj4sZDCT8KheKSDOXD9pM7Rr4Fy7f56NTT+NOH0AEv8KhrguFYDt2epDbPfbIc2iU4yWQP9O2C8y+Gws8FxNFxV/nNsSUD4nooDgymh6B+iOnySXJD96xq3qvJ/pn9mJrJXf13Ld/xY4cOoXwgKWkCAh80fUXHbUmPVKwL3vLndGX6ME58gG+v14nd/8sQdVXbzBiaABk+Zy8qCZyqWTh+wGg+RStq6540krD3zbzzk0cwzR3kpaB4heVxy6Vd6mUaC0U5JfworgVszydp6uSSJsX6OfJBQDYImKyeRtgt9FiYlbbF82H4biAqvfQDdF2ocGeFgrDUKxGAfbLOc5PjvLJpkH5mlg8+93WqhfCzINuXYNfLB8n2J0lF4k6uP0n3YEqJBdcwbeEHQiE9Ya7s/EyhuJoo4UehUFySka4RHhx5kAdHH+LY7DFsIRgv7GcnUGsWAcjGusgKg+pKhR8ndGIkEt3Qfxuc3w+737BoXExo2P4qS72QJLRQ+BnIbocpmC4dYdcmEX4mahP889F/5oH0CMOnnuTT2dyyvh1ql8sNoHNak+BZEEuv6NhN6ZPSU3DrG4hVJ3nv+Wn2kICX/eQVP5/1xNA1ZEf4CU+yxouh2DPSk+JAlIOUNJKg6XzOfA2vDSS9IkbJra3p2trhzoa+UPhRGT+KawHHC4ibGruHuph2i/Tjk/d9JptT0LLoytTwgb6enZDIAmGpV8Px0VDhzoobm2bV4eTzMxz46ll+vppg/JFxxoFRDVo65G/r4Z7XjjJye57ugdRGL1exBswq4UexiVDCj0KhuCSmZvJnD/4ZQEeEGKueZmcQUInyUXLxHrr0OFW/BPM6fl2OlhsKRclEHr71F+GmV0Gmf/EahI4jLyj1cprwkR+Fkft4ZPud/NFTf8RjP/gY+kXcLpaQxPXQvTLQczMA0+Xjy1rnevBbX/8tNKHx/zTg880qtaRO2S6TT+QvuZ8dlcvltBi29JFOC7FS4YeAlB61lU33cZ9MwL3/CRKbpwzuUhi6ACLhJxIIz5RDYWU0n+Ip3yKuic5rI6Zr2F5A3khRsMtLznm1qFoeCVNDaAudD5Z76Tymptuk4TboTy3+e1Ao1gvbC4gbGrcOZjg9UWNn4DMYCA45FYJWi0SiSsaXGFGwM0QZP17Y1StQwo/iBqFaaHHqxSK1YotayaZWbDEzXkNKMHMmT8Y9fu7H7uQld/Tzvx49zMefO8eLP3fXRi9bscZUWy5ChKfGYcCzudFLUtzAKOFHoVAsm5tzN6MhGNPh9bOn5oSfZC/9ZhfntBLY1WULBu2L33giB92jMHTnkuPimoEzPyvC9+BffgpOfBE0gz+Z+RxFq8j4zIvsHFzs4JFSYgHxqGxpoDcMj56qTyz3qa8p35j8Bk9MPsGvv+xXGf7EO9muh+LF6erpBcLPV059js8ef4T/+dCfdba1w51zepLAt/DcGiZ9yz62lJImkNTDTiPoJvziM5C8tOC0mTA1DWQYQN1x/JSaCAFbupO0fJvUvIDquKHheAH5eDdH7cIVlcctl2rLJZswEWLhBbArfbzAw9AWfwz/+RfG+PDkz1D1pnnx4RfXZF0KxXIIhR+d3YNdfGrSoteD4WQfJVnHm61gDk0z3LI7+T4AMSMs9TIR+PLKcscUimsBz/U5+VyBg4+fY+Jw+CWCbmp05RNkeuK89I07uPklA/zHdJmvfPQFfvumHPGUyVB3iprl0bA90nF1KXa9IqWk0nLpy8SZqdkLwvIVio1AvdsoFIplkzASjKYGONpowPRhqo1Q+Ml2bWFv1w4+0pzErZzFXKbw0/KaJIMALZa55LiYZlJpZ0VICZ/+VTj6GTDT4LbY2b+TmdYMhz/wRnb+9BPQs33B/q7vIIUgEYkbsZ7tdPs+M42pFf4G1oa/eO4vGEwN8oOZ3eDU2W6Eb82nq6fZNzB3QfXxJ/6Qz9uT/Epjmnx6AIBWlPHTbabBL9Oyqiv6Psn2bQIBKSMxtzG9fOFoM2Docxk/rgxFs4lSk+FsgpgIaDq10FUWEYuEn95cH6XGSWR1EtG9bU3WVmm5ZJMmksVZJ7ZvLxJ+Wo7PH33uAF17wtBpFQap2EhszyduaOwaTNMyPHqcBMPpYbDGmG5O0y+KYb5P3y2dfdrt3BMox4/i+kEGktnpJpWZFpXpFqXJBsefmcZuenTlE9z7XTvZfe8Q2b7Eovfs1tmwLD4ZCz+nhnLhl1DnqxY391/6/Edx7fKZ/edxfcn2fCoUflRnL8UGo4QfhUKxInblb+dwZQKmD1KRUZlRboQ77dv5wMwTjE09w+2Dty9rrpbXIiklXE74MZI4gY/ntvjC53+N+5/9INlv/WWY2g+tMlszYWv5Q7EYb6xMLBJ+rKhFerwtbphJBgKYXuMyn+XywswLvPX2txI/8SUAtvTuwZBVTldPA/CRwx+hP9nPc61J0ODE2SfI7/5uAOzINZWL5cCawLIrZFdw7FaUf5Myrt18AVMXgIaQ4Aah8DNeajKST0HpOC0kKXPuNRY3olKvzBbcgqBWOkZ2jYSfquWSTRhIsfiEr+W1SJsLy/K+fHQGI32083PTay4ao1CsF7YbZvz057xQIJYphnM7wRrDMCapyxrDngeZwc4+7XbuGkJl/CiueXw34OhT53n20XHK5+dKdGMJndG9vdz+rVvYtqcHoV1coC/Ww6YDuWTUYCIbnotMVZTwc73yxcPT/OKHn+Wl23t46wPbefp0OSr1Uig2DiX8KBSKFbGr7zY+f+aLNKf2U8mE7dFz3Tu5Q4/D4b9jf+FFlif7gOXZJKQEI3bJcTEzhSMEjz35v/nV6S+T2b6Dt+R7eWvRpMdt4Ufix+G4Ca3FXZrsVijwJM05cWNAxJha42Df5eD6Lp70yJx5Ep7/DIw+gDl6P1tP/ROnZ08C8Dvf+J1wcFStdGLqWV4WCT+WFwZkdyd6oAp2FPa8XJpRqVjyGhZ+jKiMyyTsNAdwptzk23b1w9R+mkKQjM/JYR3HT3YUgFLpCNmbXr3s4332wHn+YeznePPuN/MDt//4JcdWWx69mdiSzoelOns9euA8yeyznZ9LVkkJP9coxXqLv9//p7x25xu5Z3Df5XfYhNheQEzXaPizAGh+huG+PTD1KN2pw9SRbFlS+AnQhCBQ7dwV1yhOy2P/V87ywmNnaFQcerdmeNWP3krftgy5/iSJjLlsN+apYoOhbKIT7DucC8+dzldVd8frka8dL/AzH/wme4a7+PuffDnPjofvn8rxo9holPCjUChWxO7u3UgBx0qHqOqhs6araxvdiV56fJ8XZ4/xQ8ucqxXYJOXlT5xisTSOEByaeBxDSh7Ycj/v2/8+PojGbyOxy6FAcjgWQzYKXDijZYcfuvF54sagkeZQsPHCT9OLWo2PPxm2sv/+v4WxR9k+9kFOl48il8jIOFk60rnfdvx0J3oBaDkrFH6sUBRLXcZ1tZkJw53DeGdP+liuz1TVZjSfgqkDtDSN1AWlXpYbkI9Cvouzp9ixzGOdLjb4Lx98nK49Y6Se+5vLCz+Wy039aUrNyws/Ukq+cGSa3NaDBH5ATdcot0qMdI0sc3WKzcLnD07x85/5bWJ9X+arxx/hY2/5ykWD5zczYamXTqFVAMCyuxgcugexX6IlQ0fisB9AqrezT6zdzh1Uxo/imqF8vsHJ5wuUJhuUzjUoTzbw3IBte3p48OHbGLktf8Vlt6eLTbb3zp1/DEWOn8mKEn6uNw6cq/DT//A0o/kUH/ip+8gmTOJG+OWUyvhRbDRK+FEoFCtid89uAMYak1S7smQCiWHEQDe5w/F5ojFOzanRFeu67Fwt3yaxSKZZzFBmK1PGMzzTmOAm3+NPHvpzjlVP8TOP/AifNJpoUSlXWdeZrp1h8IL92y6Y+DznxEC8m5JVwQ1cTG3juiy0S62SngV3/RDEUrBlH6Ouy1ONSarzhJy0hBHP50SUrQRgR+JBLh12f7IiB89yaUYOqWtZ+DH18KTKkAIv8JmIOnqN5JNw6CBNM0lu3v/7mK6FTpxsKKiUamcXT3oRzlcsuowwf+cFp3jZ10873LnQDNCkJBACISVSCCx/4Un/eKmJ74xTMQLeULf490yKcvUMDNy97PWtNRW7wsfHPs7Dex9GE9rld7gBmW06vP1fvkRs+5fZ5TiMUePRQx/mjXsvLRJuRhwvIJ02KNTCIPxiM0vQfQv9vk8hGYpBO4yuBeHoxrxSL+X4UWx2aiWLpx45yeGvTyIlpHMx8lvS7H3lVnbfO8jA9pUUTy/N6WKTh/YMdH5OxnSyCYMp5fi57vjEc+fwfMmHfvo+8unQzd4RflSp17oQOA5+uUzQaBA0WwTNBrLVImi1op+b+KUSQauFdBykE5ZiDv/2/9jgla89SvhRKBQrYmvXVpKayZihUa2fJxdZlxGCn/ST/KfA4h1feQfvfs27L/sNdytwSYrLfwt+75Zv4X2nHuFZ3ee7PQN0g1t6bmGrnsaiju47nbGTtXOLhB/LqgCQmNfmvD81gLTHKdanGMquTb7LcmgLP4lAwvZXhBu7R9lBjJb0OFQ6BMADrRYP7Ppejp7+Ek+7lc7+ltfClJJU1PbbdhorOn7TioSf+LXRun0pDG2h42eiHLqgRnpCx0+p12TPvOcXMzRsz6c3GboUis3lh3zP1G26zfPMAi0BR04+xh03v2HJsVJKqpZHNmngEZAKoK5D3g8oGnrn/32b/Wer3J18nOeBuLUHMuOUqmeW/4tYYz7x3Fn+v6c+wmTs/Xzb1m/jlp5bLr/TDchXjxVoygIp4O2lWf4k381fPvMeXn/bW64510+7nXuhcgqAqtvP0+d9+jyYTkhuJcGW1ML3DlPXcPwAXXX1UmxCrLobhjRPN5k6XePgV88hpeSuB0fY9/pR0lHw8tWibnsU6jajvQvLqYdzSeX4uQ4pNRx6MzEGsnMNM+JG+L6vSr2Wh19v4BcLoXDTaBA0mwSNBn6lgjczgzdTwCsW5x5rNQmaTWQjunXdZR1HJBKIWAwRi6Elk2v8rDYHSvhRKBQrQhMat2RGGWvUSPgtsvHuzmMvT23hHUGN35n4D9797Lt5+0vffsm5LOmRX4bwc8/IKzGlxBWCW8254yU1kxoSI3DJBpKqJjolCQuOE7lm4vNcSINdW6H8NFPFw5tC+El2bYVMKN4gBKO5ncAkz06FeS8/mb2DBx76I973kTfxiD1Ow22QNtPYfpiTlEj0RPOtVPgJy+CuaeGn7fhB4EmfSiv80O81LJrVM8zkRxiN8nwgPAlzvIDueDeCMEdnuUxXbdJGkdno52eOfuKiwk/D8fEDSTZhEhCQCAR1HYSXBsPCsheWGr54tkJ/6hCalExa3wqMU16BG2mt+eRz5zhZKpAYYoETTbGQUsNB6OHfYZ/v8zPdd/OrzUP8+4vv5013v22DV7cy2u3cC7WzpIKAUtDHr3z0Oe7IxYCA13na3PtWRLvUS2X8KDYLtZLF1//1OOMHithNr7NdaILdLx/k3u/eSbZ3bS78xovhFxE7ehdmtXWnzM5nleL6Ybbp0J1amFsZN9uOnxvr/VB6Hn6tRlCt4ldrBLUqXrGINzWFVygSNOqhoFOvEzRCF443PU3QuMR5rBDovb0Yvb1omQx6dzfmli1oySRaKoWWSqKl0+g9ebRMZm5bMonojEmhZ7MI48aTQW68Z6xQKFbN7v47eKx8lO2uR1afd7KU28YPv/BPHB3dzd/t/zt2Y/Kml/7CRedpBT4J7fJvQ4lEjrsdn6fjBntSw3Pb9ThTAmKBy1apUUVSWKJTlx2VPyXmCT8DuZ0ATJePwc7XXnYNa0VH+BlYGIm9Y3AfTE3yzclvANDbHz5+V8+tcH6cL538LG/a/WYs3yIuIR6FF1srdvyE7qFU4toVfsxOxk8o/DSd0E7dVR1jIvpgH+2aE37a4c6GZtAtTErO8rOeZuo2CSNszdvtBzwz8zw/cZGx1eikPps08ZCkAgFIdD8FWFjWwtfq/rMVUokyw0GWgjdEPAgoN6eXvba1RErJN8fLiFT4DXVtBb+zG41i3UEY4XuOH3Tzuje8h10feTXvff4v+fY7H8ZYxnveZsF2w3buheYUfb5PQfQwVbV5qD8PFHhdvQGjCz2Wpq4hZfj3GCjDj2IDCQLJi1+c4IlPnkAGkt33DpIfTpMbSNE9kCTbm0Q317Zk9XQx/EzefoHjpythcG5WOX6uN8pNl57UwvLvuYyfa7fUS0qJPzuLe+4c7rlz+MViKOrUGwS1Gn6thjc9jV8u41erBNUqQbN50flEKoWeTofiTDqNlk4Tv/VW0t/2CszBQfTeXvT2Y6lUeJvNYuTzN6Rgc7VQvzmFQrFidvXexsd0nQC4f342zGt/E9G7i/977LOccCu864X3cruZZ+ddP7rkPC18kiKx5GMX8q0keE663BplDAEk9BiWEBC4jGBwBJfCEp262rk38fg84ac3nGe6cnpZx18rWtHa2qVabQZH7ic++QgvFF4AoDe/C4CX73wDo2c+zUdeeF8k/DjEmetaZV9QPnT544e/r/nhx9ca7a5eutTwZEDDDr/RTc8e5nkz/JibH5AcM8JSFIC8kaIoK+C2wLz8N74zNRvdrGBKybfF+nncmUG6FsJc/DquWpHwkzDxRUDS1wAf3UsBJSxrtjNWSsnRszOktuncTC/7/W56goBSq3hFv5OrzYlCg9mmSzwTXqgox8/SBDKg1HBIJltIYMrdwt7MAD+35dW8vfBVPvPMe/mul11cDN9s2F5AzNCYtEr0+T5W7zZukml+escruPuFv+OmhgWZgQX7mNFFjobAV44fxQZRmKjzxQ8eZvpUldG9vbzqLbvJ9q1/OcepyPFzofCTiRvUbW+pXRTXMOWmw21DC3OhNlupV9Bq4ddqYb6NZRHYNkGjEYo6E2dxz57FKxUJqjX8WjW8rVaR1hJCpa6HzptMBmNgAHN0hERXFj2bRct2oXdFt9kcerYLPZ/HGBhEz6hupRuBEn4UCsWK2dUdihBVXScXm/cBl90Cr/o1zFf9Gr9x8gt873/8Evunn2EnSws/FgFJ/dKt3Nv8RHwrD058ndzemzrbknoCS2gQeKS0NHkBBX+x8GG74TduiXlr7cnfiiEl0/Vzyzr+WtGKLv7ntxsH0La8hBHP45imoUlJd9+ecPstr+WHv5TiDxsTHC4ewg5cEggSibAEruVd/BuWJY/fFn6S167w03b8aAhc3yFVDruexYqHGE+GwuS2rrlyvpiudU7A8vFuSvoUVM5C30Uya0onwn+3vJaZmg1Ggz7f56U3vZpPnfwYp458gp13/PCi3aqt8KQ+Fzl+8r7OrvgbMaqznMtN0LLnspqmazaaNU3R0HkJvZT8ONsDSdmpLJp3I/jm6cidpCvhZz6nCg2GuxPEDZ0/fvqP+afDH+bXZh/ks7EmehBwwt/KvqbLgw/+Lrd+6Ft474G/440v+ZlrxvXTKfVqVtnlS3754deQiJn0VzLc9Pi7w0GZxY4fiIQfuTkudBTXP1bD5dzYLOdPVKJ/VRJpg9e97XZ2vWzwijtyXY7f//fDzNRs/ugHlw7hPzvbpDtl0pVY6ALpSpjULFXqdb1Rbjh0X+j4WadSL+n7uJPncc+M45VK+JUKQaWCXwlLrNwzZ3AmJvALiyMROgiBMTCA0deHlu0i3n8zWlcGvSuLOTyEMTyMuWUrRn8/elcGkUyu2d+W4upzbZx5KBSKTcWunl2d+9mLCAbdfbcCUJ/nariQFpDUlxekGMsMcZPrQfdcyU7CSGJpAiEDEppJn65TDBaXOjXqYXhvMru1s02k+xjwfaaXyARaTzrCz4Vd0LpH2R5oHAN6/AA9Hwlemsb3vOQXeM+Lf8xHnvxjrMAlgTZX6uWtzDredKMyuGTPqp7HRiKEQNcEOjqe1+KHnn0rv6+/D336EGcyfXTHTXLzMozi5pzw05vs45B+DKoTSws/vkfzwz9CuXyMrW9+PzO1HgyzRbcn2HfbD8DJj/HssUeWFH4qnVIvAx9JTzLO2176K7xn/18BYM0rl5qqWnQbUzSAlNGH60OPMCm7K+vStlY8Ewk/uhYKq9e78DNZn+S9L7yX/mQ/P3XHT5EyU4vGlBsOr/vTL3Nzf4Z3v2Uf7z/wfgCSrX+kp/tbMHyfY3IrE+Um+W3d/OzoG/nlyUf5t2/8Kd/zwK+t8zO6MhwvIG5qFLwmD2hxRnojh2d6HyTz0CpBeqHjJzZPiHVQtV6KtefYN6f50ocOYzc9NF3QP9rFvteNsu91oyQya9u18/kzs0zX7Is+XrM8sonFa8gkQsePlFJdOF8nBIGk0nLpuTDj5yp09ZKehzsxgX3yJO74eJiZE4UeezMzOOPjuOPjSwYbi1QKo7sbc2SEzKtfRWzbCHp3NyIeR4vHwttkMhR1tm5Fiy3vC1nFtYcSfhQKxYrpSfTQb3Yx49bIpQaWHJNJ9QHQiFqp47sgAzBCoSeQAZYIXTvLov2tcm7OuZE0klhCoMmAmB6j1zQpaDPgWjCv9GayNo4uJf3dO+fm0zQGpMG0c3Fhaj2wot9P8kLhRQi2J/qAWfKBXFBOkdv3Vt70zT/l01NPsl2YpIRO0ggvTG1/pcJPg0QQoF/D4c4QdvZqxAZxUzmM6Se5JVaEqQOM77iZ0a6F4d1xPcz4kVKSzwxT0nSoTCwY85WxGTxfsnfyY/wRBT4zspWXf/W/Uan9AekBhz5XZzR/Oz1S45uF/bx5iTV1Mn4SJh6Qi8fpSpg0/PDieb7wU6jbZMwZAFKxIQB69ASng4tfUKwnz4yX2daTRNOnKAO1C35f1xOPHZrif37lbyjEPw6E73c/dtuPLRpXabm4vuTIVI3ves9XGd47QtE5w990Z0mIabJ+wMlgiLPlFndt6+bBV/82t/3jZ/mrIx/iTff+Moa+thekqyUIZNidS3ep4dNnzivr1XS45bXw4kcXl3q1HT9CI1BdvRRriOf6PP7Px9j/H2cZ2JHlW958M4M7sxjm+nXPa7k+zUuUbDVsj0x88eVWJm7g+hLbC0is43oVa0fVcgkk9KQXCicxvZ3xs7TjR0qJXyhgHz+Offx4KOzU6gT1MPzYnZzEOXMGLhB1RDIMMjZ6eojftJOu17wac3SU2Oh2jP4+9FwuDDFWQo4iQgk/CoXiitjVt5eZ/5+99w6Pq7zT/j+nTp/0QbUAAAAgAElEQVTRqNrqcjfGNsbGQKimhCSUhITQ0klC2qYn+ybZ3Xc3+6ZsdjebBr8sZFMgJLBpQAKBAAZTjDE2uFvuVrX6jDS9nPL748yMJEuyJVmS2/lcl69L1pzyTNGZ89zP/b2/Ha8RKF866uOqqCKbJvG8Y+H3H4ZoB3xsLQgCB/oPAOCRx1lzXzofVO9wx4/iRhME4qKIU1IpdQQ4KEnWKrRSWdiuLdnDbEkZUV5RLjnZp0+sNGqqSeZKeVyOkY6buqK50P8GJaIKQ1cEJYXbFt3OH5seYQ8Z3iI4kUUZyTRJ6hMTChLZBG7TtF7b0xhFEjEFFc1tCWCXSLshE6UVjfOOEn7U3OpbVjcp8dcQlUTS/S3kvWfdkRQf+PnreEnwe/d3eaY2gMdwsckBJdl9RGUdZ0olmtJY4a1hS/8BiHSAf/aw8xQyflwKWUxkQcKpiMTwIJlmIXsKrOygfGi022k504pkDyH95Gf8DCSz7OuK8cGL63ix0/p8RU6R0Onp4LnGLrqiR5BUkXr/XB4/8Piowk8qt3r7rzctYe2ebt5MdiGKJgdVFY8xQF1G5zVzFm1hyyUlqG7eX3Mt/9DxHAebXmDh3LfO6POaKPkcLF2wBMrSo69Ri2+EnX+A4oZhv5aHlXrZwo/N9DDQk+Dp+3fS2xrjvGtruehdc5Ck6Q1qHo1kRidxjNDeaGp04cfnlAuP28LPmUE4YX3nDw13NjMZMs3NXNWxnYa/bKTtz/1kWlsLbcjNZAojlQJtSLe5XNepfOixOqcB39VXozY0oDbUo9bXW4KOZH9ubCaGLfzY2NhMivnBhbza8Rp+Z9GojwuCgAeBWDaO1vo64p4nEAE6t5Monc/fv/hVinWd6wMLx3fC894PC98B6mAgnDNXfqELAg7JRamzhF5Jwoz3gm82jx54FBmJdi1OtXPWiEOWKz7Waz0TfepTSiJtTf5HOH6AulnnW8KPMlKUWXzxF1m+7zdsUyUcoowgCDhMSE1Q+InrSVyGWXBina5IooBgSmiS9bV2pbmZDNCRjXLTkFbuMCj8ZHSD4pxjLdx/iPwn5HCvVS740KINrOs30QUo6j6PeMUG/EoLhyWQNRehRIbzqy/j+XgzPXsep2z1J4edJ5/x43PKaJgoooxLkYibHpymSTI7WJbYE02jyDkR0FMPRAkoAZJGHykthVMepzNuGtjSYpV5rVlYzvPdGQAiqZHd884UuiJp5qh7yWoZLhUbeCj0DPvC+1gQXMAzTc/weufr/ONF/0gqt3pbFXRxz/vO4eKHM1wVT7LW4yYumhSbAkpgNi/u6+Hjl1ulmrXly6HjObrD+1nIqS385Fens1ify1JX6fANzrkJvrh7hOA5NHPLTvixmUr0rEHHwX5aG8PsfLENQRR4x6eX0bCs9Pg7TxOJjE4iPbbwE89olPtGXr/zwk8srVHmO72/f89mTF0n09xMeu9eoq9v5V82bGL+5gT7M0n0WAwz19nqq4AhiKTr61Dr661uVk4ngsuJ6HIjl5TgmDcXde5c5PJyu/zPZlqwhR8bG5tJsaDY6orlV/1jbuNFIq6l+MQLn2NHXQ339oS54NWf8F2ji0PxJu7r7qX03Oox9x+GJI8oKXANEUQcsoOApwJNEAiHD/Gz1qd4qPEhgqofZJGrPbOPPiIlziDxeM9JnVgnszFUw0Ryjnwd6+ouhz0/o2S0jluqm9urrmRbz8s4RWt1yYlAWp9YWOThTD9VBsMdRach1mRT4o3e7XyhvJx/795JuyJjYg5r5Q5DOmxkdYpzr21fpL0g/DSHEsymj8Wtv+FLdVU0uJfRF1sEFRsQ3S3WRpqPcDzD+XPfDnsf4s2DT3Hd0cJPKotHlVAkkawAiijjVCSiuJhtmKSGdGDriaaR1BiCaeJ1VwON+B0lkD5EON7F7EDddLxs4+LN5jCiAKsbitHWW2LWmdzOvSuSQnCmKdd1bmrdyiMBmT8f+DOZnut5eeC3tGXe4DPnfaYg/Dhlie6k5YBaEFd53m1iCgLFqp/bVtfyX8/uo6k3Tn2ph/Jcd77uyKlfKpfPo8galuus1Fc1ciP/yOtqvqxBQEC3M35spoBUPMuLD++laVsvWtZAFAWqFwW54s6FJ6VT11ASGZ2MbpDVjUKZ41BiKY2G0tFKvZTC4zanNlpfH6ndjaQaG0nt3k22vR0jEkGPWt2u8m4dWRSp8JQhLF+MZ1YJkseL6Peh1tbykXV9nHPhUr5168qT/GxszmZs4cfGxmZSrKlZw0eWfITl5aN3sgBwiwrxbJrXRR1Egc9WlPLJ5qd5rCTI3WIxF7/jn2DJzZMeg3NIeZJDcVFasggOwufX/wNbVZEFwQXsC+8DSaI6ODK4t8RZAnHoi3VSVVQ/6XGcCMlsHJdpwNHhzkBJ+TJucVZz1aL3jrrvWy//F37wuzWUOK19XQikjPELP0ktyT4tykf0mbfHTzWyKNI5kEX2wlqPk6Ro0lpUDZjDWrnDcMdPiasEgL6Bw2CaIAi0hhL8vfI71rlUeswsN1fdzD2bMzhMk6jH6gInpIsJJ7JcWbsYFyJvhhu5zjBAHHwtI8ksfpd1c68Bck74SaPgNI8SfmJpUJIETXAoVj2+x1EGQKj/0EkVft5oCbN4th+PQyYtWmJAJDsyRP1MoTuaJuDNUJbSWdy3mcvn38LjB/5C2/YFeOcdBhm2dm9FyC4BwKFIdOdK36RMMRXZKJ2qSbGrjGsvqOFHa/fz8KYWvv72xZSVWA7H7njH6CfPfQZPBfIB6Hq2HYBSf82xNi8w2NVLxLCFH5sTZKAnwV9+so1oKMWSS6uoPaeYygVFqM5TYwqTzFiT/kRGJ+AaRfhJ62Nm/ABE03Znr5ONaRhkmptJ7dxFaudOskfa0Qci6JEIWl8ves9gExClqsoquaqpKbQpVxsacC5ayF8HHHzpsUbWfeVKKkuHtyvv3v089dilWTYnl1PjqmljY3Pa4VN9fGnVl465jVdUiekxJEniKk89LyTb+X5JkJWly/jU2x+AE2xpPLQTlkP2UBq0yim2qiJfDvVzceVCbgnvA6BqlCyiYncZ9FmT/pMn/CRwmeawErY8gijyz7c9Nea+qrec37/t17i8llfFIYgkJyD8NPY1omGyVBzZseh0Q5YEMAcnzGFRpCUwC/SOkcJPbmKa0YyC4yeUiUB/CwTr6Onu5MvSy9xVtYJKxcE1DVfwfdZTrZt0Oy2xJp2uJhzPoIgKy9yVbEkfgkTvMFfaQDKL36lgmAaaIKCICi5FAgQcCKS0wbK8nmgah5ymDLkgTHnclpsi3N8EJ0n30XSDrS39vGdlNVk9i5ab10QnGCJ+uqDpBr2xNIgZSjUTA4GbDCfPZ0JIvp0ghwDY0r2FBsVykjkVkbZ4JwAprZTSdJZONUmxdxYVfidXLyrnD5vb+PK1C1HdJRTrxshugk2vwLp/g87t8IWdMIoDcKbJCz+ZTCeiaVJcNGdc+ynyUMePjc3k6W6O8MQ92zANeOcXVlA5b/TS8pOFaZqFfJ9ERiPgGhnYboU7j5zwD834sZl+TF0nffAgqR07yB7pQI9E0Af60bq6Se3ejRG1XKyCw4FSU40UKEKZPRvn4sU4FizAuXgxzsWLkAJjN8IIvXwIYERXL7A6e013O3cbm+NhCz82NjbThlt20S6Y6ILA8sA8Fiy4gUf3P8r3rvyvEUHLk8HpGCL8KG7mFs1lfnA+dy18HzfsfAp9/b146qqJiyI1JeeM2L/Ea02sQ5HWEx7LZEnmM3YckwtXLq48v/CzE4m0Of6byB092wBYWr5iUuc+lehPZBFLOgf/L4m0uLx40p6CuJOn4PjRDKr8OcePJELbJgjWkexr5YCisCnTxxfO/QK1Qeu9CWZFumWYpWns0eezImHl3awILuT+eCuJ0EHcQ4SfSCqL3yWjGXkbuIwiCYgCOExhWBB3TzRNsChLhegsCFMOl1VaE462T+lrNRH2dkWJZ3RW1gWJZq0bY9k0iXBmrlL3xjKYQpqUYKCafvYos1h9YBOGx0Ow6jlSWE6WX+76JfBLRPWLOBWJroFmAGRHPa50CnxJigP1ANxxYS3P7O7imd2d3LCsknJTpDsX6v7Ahu/Qs/dJbjyyl4WaCYYG8Z5TRPjJTWizPQR1A2mUsq7RGMz4sR0/NpOnZVcfT92/E5dH4cbPLSc4a+TiyMkmrRnk88sTmZEyp6YbJLM6nmOEO9ulXlOHaZpkW1vRurrQ+vvRw2Gybe0kt28ntWMHRnzQqSr6fEiBAHJJCf4brsd17rk4zz0Xx9y5CPLk7k/7E1lEYfC9HYpDlsbs6mVjM1PYwo+Njc204ZXdHMl9gQZ8lXxo+Se5e9ndiMLUlBa5hrQgdygegs4gf7rJasHMgncjzVnDufsfYGOyg+pRyhRKck6QvpM4sU5qaavUSznxm1qnIJEyxn8Tua1tPVVZjdKGK0/43CebWFrDp/QX/t8vSrSKUOurHRGSmBd+0pqBW/HhkpyEFCdmy0aEpbeQHejgkaAXVZR59/x343HIFLkVvFkHuNLM10xeUipp7IgAsLBkCUb7Wg53bWFJ7cWF80SSGrMDTrRc7pIiqgiCgEuRUE2JmJEpbNsbyyCW6CyRPThy41NdlqMkFB8UtGaaN5utEOfza4PEMpZLZbam0aoIaIY2JQLuqURXJIWYC9kOiF6e1lfxpdAv8fNOYoEtAFwbi/I3r/X3Kit9lvATPkiRruMsmYvckcQfbKWhwiqDvXx+GVVFLn67sYUbllVSJjro1hP84Nl9PNb2MCERHqiazXxnOe9p38Od6RinQrFXfnU6roUp1XXwjgzIH43hGT82NuPHNE16W2MceKObrc+2EKz0cOPfLcdTdGqGHyeHiD2jBTzHc48fq9QrdoxW8DYj0UIh9L4+9GgUIxpFj8bQOjtIbNlKcssW9FBo+A6yjHPBAgLvvAnX8uU4ly1DramZtLhzLMKJDEVuFVEceQV3KGJBTLexOVmcWXdsNjY2pxRe1Usm9wUYKLJqVaZK9AFwDhF+nEdn5AgCrHgfVzkFwvv/OGoIdXEuN6Uv3jVlY5ooST2NC3FYNsxkcQoSMXP8Xb229+3i/HQahogVpzOpjptRijYhudo4ohbRqidYGFwyYjvHEOEHoNhVwoN6ite6n+VXqSxKuou/eD28rfIygk6r21plwIWS9QJp5jlKqLigjgc3NPOFaxYwf/Zq2A77QnsYerZIKsuiWT6yWaurh5IP4VYk5msqfzISHIkdoUgtJ5bOoIhQ5igqZKQIzhpk0yR8dFnQDPJGc5hyn4PqoIvdIcvxU6nptCoKsUyMojG6+p2udEfTCLIl6BUpRfwysYIvOX/JZ31evgs4Dfh8eIABXLzmFWmQWnDKIl2xdio0nco5izl0pIKXikSkXLt2SRS4Y3UN//nMPg73xilXPOzKhvjR2v2ULjS5QanivPPv4nc7fsG/lRRzTaydCsbOTpsp8qvTET1Cma6Dp2xc+xU+v4Lt+LEZH7pmsOmJw+zb1EW0L4UgQMPyMq760GIcrpM7Vfn4g5upLXbzTzeMdA0PbeOeyIwUcPKizqjCT6HU68x0T04FpmmSbWsjsWkzic3Wv2xLy6jbqnV1eC+/HNeKFai1NUhFRda/4mJEx8wIh/2JLEXukeV+YJd62Zwa2MKPjY3NtOEeIrYUBRqm/PiuIcdX1dFLpe5cfCd3Lr5z1Mccvtl4DYO+1MmbWCeNDEXC1AT+OUWF3nE2UO6Kd9GlxViGE4L1U3L+k8mVC8t4ef9FJCLn4Vv4zzxd+yHa47/jWv/bR2ybd/wkMzpP7+ygPWY5vvaJOrtb9uNRekiIIhdWXVrYpyrowuwoAvqYXzSPC6+cy8Ovt/Dj5/fzH+85F6dhsj/SPOw8+XDnbC7EWZasG8Jij8qi7CIEtvLIGz/hlnP/CZcUQhMESp3FhfFlBZUiwyR8Elunv9ESZmVdEEEQiCWtcczKrVpGM5EzTvjpiqQKwk+Zq5wjlLKDudya3smfKhfi7mpku3EZrV2rwfswDjGOU5HoTvZRoetcd8lq1lzhRVJuG3bcW1fV8IPn9vPw6y1UOIKE9BCSkCQtCmRiTm5bdBuBWA9f3XUf8eTJe7+Hkl+d7jcSLBYUq7PiOCgIP+bZ7fhJaSmaI80sLF54sodySqNrBk/fv5Om7b3UnVvCqnfU07CsFJdvZE7KyWBba/+YE/bkELFntFKveF74GaP0R5VForbjB1PXSe1uJLHxNRJbtqJ1d6OHQmjhcKEduhQI4Fq1iuBtt6HMnoXo8yF6vUg+H1JJCXIweJKfheX4GS3fB8ClSPTFM6M+ZmMzU9jCj42NzbThHeLICbhLp/z4TmWwjevQvJ9x4y6mRNfpS/Uff9tpImlkqZwi4cchKqTGucK+o2c7AMtKlpwyXYROhF99ZDVvNId5z0/XYxoSA0YTmqmNCHaGQcfP3b/eTCKjo5ZcR1nwTSJKD3v2PIpTtibeJUPaV1cVuWg9VE2Jto/zay6j3Ofk/RfW8Yv1h/nMmnnMMUT2p3oK2xuGSTSt4XfKaHnHj2StOtaVePh97x1clX6DPxx+khWzPkWls5FuoKF4wZCuYzpBJELZ2LS8ZscilArxrsdupludz7IaK8Q9FrM6UbmzTgAi0Xbw18742KaT7kgKRbHe/9n+agCi9W9HbrqHe69/GvNX15NYcgvJLdb1RhaTVqlXNsISZERXAOcoxy33O7lmcTl/eKONr51XComDFDmayADpjDVRcOeul4n0qSL8GIBJyMxQKo+/FDWf8SMgjlOGPvPQDZN/efWbPHn4CV687cUROWM2FoZh8uwvdtG0vZfLb1/A0iurT/aQhqEbJn3xDIkxxJmhYk98FMdPPrh5tIwfAJ9DPqsyfsxMhtTefWg9PeihPrTeXpI7dpJ4/fVCuLLa0IBSWYnaUI8cLEatr8O9ahXq3LkIU+CMnk7CiSxVRaN9A4DXqdDUl5jhEdnYDMcWfmxsbKYNT65VNoDfMfVhpS55UPhxTMZ5ICmUGAKhXGjtySBp6riEqbkUuyR1bOEn1gOHXoCl7wVBYHvbKyimyaL6q6bk3KcCQbcCCJi6m57MfoBRhZ+qIjduVeL82iAfvLiOF/bWsHb3BVDzLTq6NqDIltAydLK2aJaPF4y38JyzF2XxuwH4xBVz+c3GFn68dj/zZQ/r9cHgyGhawzSxHD9ZS1jMO37qS9w8dEDka6vex7NN/8uj675JraePbmDh/Bvoyg7pOiY5CA9p+z4TtPQl+NxjfyUsh1CDG/lT11e4rPfficatluVmtgiI0tffBFVnRplgnq5ImiJXBM0wmF9dz3/WLmdl9Xz46T1UbPkt6Dr7ixqI5+Z7ipRCMzOEzCwVo5STDuXOC+v4264uEmnrWlXuOEAbEEtZEwVX7hqWyJy869FQMpoBUgJNgDJ17E42R5N3/IBw1go/H3tgExszm5Cc0JPosYWfUTANk3UP7eHgmz285T3zTjnRBywHh26Yo7p5YLjwc0zHzxjCj9cpn9FdvUzTJHP4MPFX1hNfv574pk0FB08epaYG/9vehvvCC/FcuBq5bHwlpSeL+148yObmMD/74KoRj/UnMiypHP17wOeU7bI+m5OOLfzY2NhMGx7X4M1uwDH+icN4ccqDKyuOSQpLJaLCQe3krcIkTR2X5Dr+huPAKaqM1WTbfOKLZPf8BTUdgQs+xrbOTSxOZ1DrL5uSc58K5C3Wpu4hqlmByLW+kY6UWQEnu755XSH0eWf7AD1xD9WIhDLNVDisz1XJEOHyvatquHrxe1B8g2WDZT4HH7y4jvtfPsTXlhTTq8cIpUIUO4uJJK0bPL9zsNRLkazx1ZW4SWUNqpZ+gQUHf88hcQPzvB7KDCgpO4dwtzXxT2sGQdnD7nTflL5Ox+Pxre3s7GzDVQ1az02YdRv5wF8/wCJvzgGVrCag7+Rfd/yUB+uuoNJbOaPjm0764ml8cpqkaSJ6SrjlnNxktHwJbHsEAKF4DnGzG4dpIktpuhOWIFbhLh/rsABcNq+U6qCLxk4n+MDtsEoMIxk3sbSGOycOJNKRaXp2EyOtGYiSJYIO/Vs4HoPt3EXO3CntsXlhbw+uOuu6HsmcGu/nqYRpmqz/wwEaX+1g1fX1rLj21HQOdkeszLxkdnThZ3i488hP+/GEH59TPmPCnbMdHcRefInktm1oPT1ovb1oXV3oYcvBqNbVUfSud+G+8EKUytnIxcVIJSWIztEdMqcqO9oHWNvYRSKj4VaHv69WqdfoGT8+p0zkDBb5bE4PbOHHxsZm2vB6rImQR5ALwbZTiUMaDOxzOCaXNVIsOnl9AoHIU00KA5c4NcGDDslBShDANIeXb3Xu5I/tz/Ov9TUs3vqf3FO7mt3xdm7RgfKRgZWnK36XgiCAqbsBcEpOytyjrx4O7fRV4nVgmgJzHOW0p5qp0pKAqxDsDFZAb5lv5Pt09+Vz+PVrzSQifvBAU/gAxbNXE8mt7FkZP5YcJw8p9QJo7k/jSF3DPs8zdBkJVqlWOaQqWaV/Wd0kqPoJZ3pGvqfTiCyJCLIlPi30XMYDN/093974bZ46/BQAh9Ln8PPO57m1SuZP+//E3634uxkZ10yQzOqoYhLDNME9ROw45yZY910AxJI5JIkQNExEKU13zBIZK7zHdiyIosDtF9TwxAse8IGoWt1n0rqXlr4E7pxQfrIdP4ZpICCQ1vRCh7NSz/g6esFgqReIGKd/FemkMXVL+DmZGV2nIj0tUba/0MqeDZ0su6qa1TdMff7fVNETs+4N4uMo9UqMIg5Fj+f4OU1LvYxEAq27m+yRI8Q3bCD24kuk9+0DQCorRZldiVJZiWvZMpxLluC55C2o1aeeo2syZDQDw4TdRyKsqh9c3ExldVJZg6IxMn78ToWMZpDWdBzy1JT329hMFFv4sbGxmTbcudKFommyuYuCiNOElADOSYbMliheBowkWSM7LeLUsTBMg5QALmlqhB+X7CAjCuiZOJJjSNj1G7/k9/4AAcXLbiHOr978CSkMlvkapqSb2KmCJAoEXAop3RJWqn3V4+oiV+yxbtQqfIt5MXmExZk4AUEZ1+ehxOvgjtW1HNpcBA3Q0r2D82evJpK0bub9LhktJ/wMdfwA/OylQ7zaehnVC59nQNRYVLwIGAyfzmgGQWcx0cRhsok+FM/U52SNRm8sjSqHEU34R+NhAgcz/PsF3+AqTaRt229IrLqC9NbHmGWYNB8VaH26k84ayHIKx9HCz+IbLeHHWYQrUAIIuEwTxCxdob0AVATnHff451T6eUCbDUBKsdw0Sd1PSyjBigZLaExkT24OxFde/Aou2cVcPoZf6iMLBH3jd3UNtnMXz+pwZ3LCT19qZh17pyKGYbLrpXZ2vXKEvrYYoiyw/JoaLnn3vGEi/KlGTzTn+Bmj1GuoE2jUdu7HFX4U2sIJ0prOE9s6uHlF1aitwE822SNHiD7/ArHn15LcvgMjNiR3TpZxr1xJ+Ve/ivfKK1DnzDml39MTJR/0vb1tYJjwE05Ywc1jhTv7Cl3cNBxeW/ixOTnYwo+Njc204VUs8cE/gTKBieJEJIWBqo4/fHQoxaofUj0MpAcodU3/xDqRTdAabaUh0IBmWDeFLmWKSr1ymUfp9ADuIcLP4fABdqsyX176Me5/4wf8sXsTAMuqL5mS855KBN0qR3KOn9HyfUajxGvdqGVYREJ8gd2qSrHsHvc5l1UHeGh9PZL5Mq09OwEYGFrqFcmXelmW9qoiF7IosHZPN/PKg9y0+A5+tufXLJx7HTBU+NEpdpdDCMLhg5TPoPATVLpRdY3ze5+A3z0GgsTb3CUQj3DoonN55I2LqE89R3N4/4yMaaZIawaKkkY9WvgpPwdK5oGzqGDvdxgCppilK2StdFeUHd89F3SrhMxiSg2DkGICAgk9QEsoziULLIdkIhs/9kGmCdM0+ben9rCxbz2znEXMLvkwXjlEGPD7x/e3BEMzfnLhzoZxRgnM40GVRUzD+nsPpUIneTQnn1f/eIBta1spr/Nx+e0LmH9BBU7PzC60TIa88JPI6pimOULQOF5Xr9hxwp39LpnIkSzP7u7iy7/fRoXfyaXzB6/zv9vcys9eOsQzX7x8RsQUM5Mh09aG1tVFtquLbEsL0XXrSO9uBKzg5cBNNyLPmo1cXoZSXo5z6VIk3ySaa5ymZHLCz472gWG/D8et7/ziMT7XeeEnksxS6p2Z9vI2NkdjCz82NjbThkexxJjpyPfJ4xJE+jGG5f1MBK+zCFIQzURnRPi5d+u9PLj7QWRRpiHX4t41AZHhWLhyndP2NK/j/KXvK/z+6XQHogzXz3snGzffyytolGg6lXPeOiXnPZUociu0J63Xc7R8n9Eo8Vg3YZ29luNil0NlhTL+G9naYje7zbnUaDqt/QcACqVeAZdCV1+u1Cv3GZUlkeqgi6a+BP/nbYu4YM5y4uhcUn8tMET40Q0qvZY7JNx/mPLqC8c9phOhJ5rG44oT0A3Eu54CQ4eDz8PBtVAyF7fHx1+Ni3i79jTboi2jTohOV9KajkrGEn5cQ9oDCwK89wHAxK1aq7WqIaCJGl0DLXgMA2/p8dt2B90qOhJ+HTqV3GumlNMSShTC6pMzHOadZ3NzmPvW78C3IIEUTzLgzuJVBizhJ1A/7uMUhB9TQBcEMDQQT43W3DNFwKUQyQXt9yXPbsfP7leOsG1tK8uuquayWxec7OFMiLzwoxsmGd0YUaKTF3u8DpnEKF29YhkNVRYL1/SjqQy46Iqmaeq1xN43msPDhJ8tLWH2d8dGPfdUYWQyxNevJ/r034g+/3yhuxYAgoDrvPMo/8qX8V51NY45p25Z3kyR0ccQfnKOn7FKvXwOSxAaK8z7wQ1NvNkc5oe3r5iikdrYjMQWfmxsbKaNvPBTNBPjrn4AACAASURBVMn8nfHgREIws6iTnFj4cmVo0Xg3BKb/pqY70U2Js4R3znsnu3p3MVvTWOQaf37Gsbhm2Uf41YFH+cyW7/OnhquYnRMNDusJqlUXZe4yzndX80q6iaVZDaHq/Ck576lE0K1iRq3PXe04W43nS712NbugDgxBoGQC5Yl1JR7iuKg0ZFoTXfD011H1twAifqdCm54v9Rpc5VtZV0xNsZtrFpcjCAJfv/DrhcfyGSkZzSBYZj2HUKRl3OM5UXpjacxAjNK0Dv4qCFRB3cVw1T8A4E5laTPLmG06iBtZ+lJ9MyKazgRpzcBLFgciSEet3M46FwAFS5xTTRFN1OhOdFGh6RA4vismmPuseXTROhBQWjSLllASWZRRTUjoY0W0T4yt3VuJZCJcXn35uLa/78VDONUOAMKCSTiRxKEkcBoGDm/FuM+b//yaecePefYVfAVcChHBet5ns/DTeXiAFx/ZS83iIJfcMv9kD2fCdEcH/xYT6ZHZLHnhp9ijEh+jq9dYZV4A1UEXumGyudnKgXqjZXgeVMdAKnecqcmF0UIh0vv2k+3sQOvsJL3/ALF16zDicUS/H9/VV+O+6EIro6eiHLmiAtE1NY7kM4W84+dgT4zYkPd3vKVeT+3s5LMPb+EPn7qYct/gguX/fXwXgC382EwrtvBjY2MzbeRLvabT8eNUvTgy2Uk7Dnwea0ITi7TDDDQnikXamKVpfNHZABfeAhvOhUX1U3Ls0uL53GMUc7MZ4ZUjr/DeBe8F0yRiZAhIlpCxonwFtDax3FEO8pm3Cl/kVjCHZPyMh6DbCoWOJhSK9CJ0qZ/ikvGvTAfdCl6HTIAi9moheO3/o7qyH7gBr1MeDHeWB4Wf/3zvslxe88jPbT4jJaObFActMTIc7Rj3eE6U3lgGd1GSUl0H78hOVW7FmoD4pdlAHy2RljNH+Mka6IKO4zjZUB5VQjIk0pJOV7qfckEe19+T3ykjiQIOXQY0VNOkrrSIXbnVYzcCCf3Ew+Z1w+Q7G79DV6KLdbeuO+718UB3jOcau6gr2k++MKk30YMsp/AbxnD303EQBAFZFLDCnQVMPYswReWspws+p4yQy385W0u9EpEMT9+3E0/AwVs/eu4pmV1zPPKOH7DKvY7+K0hmdZyKiNchDyv7yhNLaXgcYws21UHLnbq5yRJ8trSEMQyz8Fp1FoQfrbBAMVH0aJTos88RefJJ4hs2WKWXOaSyUnxvfxv+667Dc+GFCOqpd0+QzOhEUlkq/KdG96+MZuBSJJJZnd1HIqxusO6twgnL5Tt2Vy/r9y/t66EllODnrxzm629fPDODtrHJcXYVXdvY2MwoHsWDKIjDuiNNNa6iOlTVe/wNx8Drs1pUR6PtUzWkAq3RVq75/TW0DHFrxAaa8Ua74Pcfgh9aDgImmU80GnPr1hDUdbZ3vmn9IjXAgAj+nPvqvIZr+Hj/ADdVXzFl5zyVKHKp6Ik5rKm+huVly8e1jyyJFLmsmzK/bDlsSjzjdzgIgkBtsRuMWUQkkXuKAvSnmvHlJvmabq0EKrJr2D5jTYQEQUCVRMvxE6gDIJxrGT7dZHWDUDxFTMhQKqgjXS9Yr5dDFlEVS5RqHjg8I2ObCdKajo6Og2OvrrtVGcmQSQsmnXqCCnl81yBBEAi6FWTdEgG9pvXZaQsn0Q0TNyIJ48SFn3ff9zcaQ42EUiHaom3H3f5/Xj6EQxaZUzL4OUunmjHFpCX8OCcm3iuSiGlat5iGnp3Y4M8ABIC84+csDHfWdYOn799BOp7l7Z9citN76uf5jEZPLE3+Mn20sPPk9g6aeuO4FAmPQyI+SrhzLK3jdYz93KuDrtx2GrIoEE1pHOgZDE4uOH5GEZVGQwuHSbzxBgN/eYLe++6n7bOfY/8ll9LxjW+QaW6m5O6PU/vLXzD36adYuHULC15+mcpvfQvvZZedkqIPwH/8bS9v/cFLhfLp0dB0Y8zHppqMbnBejeVi397WX/h9f/w4pV45x8+hXuv9/c1rLYUsQBubmcIWfmxsbKYNRVL40ZofceuCW6ftHC7ZhVOa/EqQr8iaWEdjU++o2HjgSboSXRxue7Xwu5iewat44KPPwpp/gEU3QMPUiTDCvKs5N51hR8dr1i/iPUREEX/OdSXXXMjn6m6k/Py7puycpxLVQRcusZj/vOL7hVLD8ZBfTa12W2JG8QQ70dUWu+lJWaLRfcEAf5M78OdW+LI5B4c8gRwqVbaEn4CjCME0CQ1tCR3rgdD0iC2heAZBSqALJiXHyDnyOGRS8mJk06Sle9u0jOVkkNYMsoKBQzy2IdrjkBANhbho0otOhXP8AfZBtwq5AHIfInXFbjTDpGMgiVuQSBonNhnoHEixq//1wv+39mw95vbd0RR/erOdW1ZWk5W7UA0rm0bPtKCJGfymCNLEDOKKJEBe+DnB53M6ohnmoPBzlpV6xcIp1v6qkY4DA6z5wCLKak7f4N+eaJqqnDgzVNgZSGb5zG/f5JndXbhVGZcqj2jn3twXZ2trP6XesQWVyiIXeTPeVYssd+Uf37CE2mRGLwgDo4lKeYx0msjTT9P6iU+y/9LLaH7f+zny1a/S84MfkNy+naLbbqP+fx9h7rPPUP6FL+C5+GLU+npE56nhoDkem5tDDCSz/Hbj6OXO//XsPi767tpCCdZ0k9EMKotczPI72Tkk5yecyOJRpTHznPL3A6msgd8pE0tr/HpDE2AtuOQxctdfG5vpwC71srGxmVaurLlyWo/vlJ045Ml3SPAF5wIQS/RM1ZAKNLa+DEAyPDhJj5saHskJNautf1NNwxUskwO8kuwllhrAG+u2hJ+860p2wLvunfrzniK876JarllcMebN11iUeB0c7ImzuHQBO+JQMoGJPFgt2n++bymu4DMAGCTx51xEWj7jRx5/uYsiCWR0HUmUKEIknBkSJPm3b0B3I3zqlQmNcTz0RNMIsrUiWXqMbC63KtEiN1CV0Wju2zvl4zhZpDUDDQOHcOzbI5cqQ1alP5dnU5HL0xoPQbeKHvcAPXhF2XKLAS19CdyCfMKOn5f391Dh2Yyi6aRFga2dm7lx7o1jbv/Aq01kDYOPXzaHu/8ywPJ0mk0uJ6bRSUbM4DcmfquoyoOOH93Icnr6PSZPRjNAtibrCS1BUksWwrvPVHpao2x9roUDm7oxTZNV76hnweqpya87GcTTGtGUxnk1RbSGksO6drX0JQo/u1QJjyrR0T8Yyt4TTXPnzzaiGwbfeMfY5TyqLDLL76RjIMWFc0rwuxR+sf4wt68enk+XbwtvmiZ6KES2rY1MWxuJTZuI/PUpjEgEuaKCkrvuwr36ApTKSpTZsxHdU9M44mSR0Qz2dFhh0//z8iGWVQd4y9zBsuJnd3fx47VWZ8muSIqa4ul/vmnNQJVFllYH2D5E+OlPZMZ0+wB4nYPX0RW1QQQBfrG+iY9eOqeQDwSWo8gp2u3ebaYHW/ixsbE5rblxzo20xyZfpuX2zkI0TaLJqc9haIw0AZDMDFq3Y+j4pnMCIIosO/cOzH0PsHPzT1ldNN8Sflxl03fOUwiHLFFbMvGbv5Kc4+fahkvYE/8bS0qXTGj/yiIXWraM2P5vcP78/yYkHqHEYa3itefcZF6Hf9zHU2WRrGat/AUFlbA2ONGgvxkiU1+aCFawsyBHACg9xmfGo8o0UU1tVqclfmRaxjLTaLqBbphkBQNVOLZU4VElSA/e5FdMoOtV0KPQM2A58LyiWvi8toQSuESFhJk41u7H5eX9vSjuZlalUkRFka2dr4+5bTyt8dBrLbxtySwcjgE6RJ1LE162OLPo9JIUNAKTCM5XJBHTKnjC0DPH2frMQzNMyoQQ+UKQULSDquCckzqm6WTvxk6e++VuZIfEuVdWsfyqGvylp7fQlS+zmlfu5eX9vSSzg+VWzaF44WeXIuFW5YIwlMrqfPzBzYTiGX73iYtZPPvY1/3qoIuOgRRVRS5uXD6bp3Z08O0nd3PXpQ1gmiwJNeG471WauppJN+7BiA+eW3A68V1zDYGb34XnoosQpDNLMNjfHSWjG3zi8jk8trWdO3+2kUc//RZW1AZp6o3zpd9txeeUiaa0GRN+MpqOQxZZVhXg2d1dRFNZfE6FcCJDcIxW7gCSKOBRJeIZnQq/g1tW1nDrfRv4300tLK0eXGRJawZO5cx6H21OHWzhx8bG5rTm6rqrT2h/QRTxIBBN9x9/4wmQNbLs1SIgQCJrCT+maRLDxDNF7dvH4twVH4N9D7Bj18MsWfJhDEEg4Dl9V15ngjKfA1USWVndwG/qfjPh/a9aVM5rh/p4aie4CNAld3Ge0I8e6+aPna9ygSlRWjG+zCHIlXrl7N9B2UkoM0SYjHVBqt8K6RSntmK7J5pGcrYC0HCMrmguVWIgK3Ku7GVzNnJKtnQPp8Js6d7CVbVXjWv7dK5UIIOJUzy28ONWZZLGYKlERfHxW7nnCbpVmjXLgeeVnMwOuJBFgeZQApek0s/ku2CZpskrB3oQqnV0Lchqo4sfxtrY3bebc0rOGbH90zs7GUhm+dhlc1i35wEAIpEVlAU2YAgR4oKOX5p4BpmV8WNNXvSzMONH0w2cwqADJNS+8YwVfn75t/30P9ZC3bwirv/0MhxjhNuebnQMWO/f3DIrv2touVXzEMdPTzTNeTVFJDIahmHy5d9vY1tbP//9/pUsrT5+NlZ10M2mpjDVQRfBSB//d1aEl558iZZ1ae7bsZnaWDeG6oAl5xB45ztRGxpQqqtQqqpQa2rO6K5b+VKq21fX8uk181j5/57lmd1dLJrl55MPvYEoCHz/vcv52IOb6YqceDbaeMjoluPn3Nx7u+tIhIvmlBBOZMfs6JXH51SIZ3Rm+Z2sbihmVV2Qn718mL9/2+D3R1rT4azzSNrMFHbGj42NzVmPH4nYEFfOVHC4bx+Z3Dw4lbVuEhNaAlMQ8J5AGPV48DuLqHeWsV2PEdliTeb8E2jHfDby8cvmcN8HV6JIk/tarCl289P3r6SqyIVgFNMlyTTIfbz8549yRBK4feVnJ5STkg93BihW/IQxQNfANNmcCfG022mJP1NMx0AKh7eRJek0xYGxhR+PQyKR0an1VJLEoCc59aWSJ8qjBx7l8y98ns5457i2Lwg/AqjSsW/gPQ4JY6jwMwFRL+hRielWuYJXdiGJAtVBFy2hBG7JQZLxZTzEMjES2eHuoEhKI5wcICMKCOIs3hYT8QsyP9nyk8I292y5h7UtawHLZSQIsKw6wItNf6M+k+XV1BWU6JBR4iRF8MuTEX4ETPPsdfxkdRMEA8G03stYKnycPU5PTMNk35+bMICL7lh4xog+AB39luMnL/wkxyj16oykqAq6CCey3P3rzTy5vYOvvW0R1y0Z32JLrV/hirYtuL7yaQ5cfQ3LfvzP/N32R1m08Rmiqpv/WnErW378CPUP/5ZZ//efKP7A+/GtWYNzwYIzWvQB2NE+gM8hU1fsJuBSWFUfZN3eHv7xsZ3s7Yryw9vPY2WdJaJ3RlIzMqaMZuCQRZZWWcLPjrYBsrpBU1+cWcfpPJYPeC7PbffpNXNp70/ys5cPFbZJZ2cuqNrm7MMWfmxsbM56vJKDqH5i5RVH09j8fOHnZK5MJ5botc43je3t8yyrupjtbg8DuY4+fufYeS02lnCzZuHI1uUTpcLvIJwqJSMKXNL/EI8MNFIuuVmz7EMTOo4iiQUhIugsIiyJkOiFdJRfeR38IFgEyamfTK4/1AKudi5NpOAYYqFblYmnNeqKrbb3zX17pnwse0N7ebPrzUnt+/TODp5pPAjArt5d49rHWmk1yArgOE55k1uV0Qxr0qWaJkXF88Y9tqBbIaRZr61PtcpAaks8tIYSuCUXCUGwRL7j8IV1X+Bbr31r2O96Y2n8chcAxc4yDusN3JUWeaX9Fd7oeoNoOs7/7Pgf/rT/TwB0R9OUeFTSeoKN8TauwE2HUErAUAg5rIlUQJm4UK1IIkY+4+csdPxkdQNTMCjKtc5OpCMneUTTw7bnW6nWJZ53ZTE9Z1Z5ypGBJIIAc8os4TORGV7qtWyIm+fDb6lnaVWA5xq7uf2CGu6+/NjuLiOVIrV3L90//CFv/39387XNv8Hs7aH8K1+m7qFf0/E/f+DmG7/DP179OZ6tW030LHWA7OuMsWi2r9AB84oF5TR2RPjjm2189qr5rFlYTpFbQZVFumdA+NF0A8O0FmZKvQ4qA052tA/wyoFe+hPZ44p9+dy/fGv6NQvLWTTLx872wetDeoZCqm3OTuxSLxsbm7Mer+wimugH04QpKldp7NyMyzAwgaSW5I4n7qDBbd0UeI8RmjtVLCtdxp8P/pk9uRatAXX6xSYbmBVwsq65GMkN7endrC8q49NLPohynNKho3HIYqHTR9BVyoAookc7uPflI/RJIv2SOOXCTyKjsa13E0qlyaXJ5DGFH4+ac/zMXgVdz9Fy5HUuqLl8Ssfz/c3f53DkMM/e8uyE931yRyetfYfABzt7d4yrJDSdNQqdmI4XGO9RJbKGVbJZbooIEyi5C7pVknoQL+CttgLea4tdbGvt57IaFwlRgGwcpLH/Zl/c10NTfwuZo9w0PdE0fqWbfqDMX8nGJolPHfkTv1l4Lv/x+g9obLwIo0LncOebue1TlPmcvNr8HJoAayrfwiNdDgJZJ3GXVerin4RQbQk/lhBgmGef8KMZJqZgENANwpJELHPmCT/9XQk2PH6IA7LOLkUnkR5fy/FTGcMwCyJDR3+KUq+DQG6yPrRrV2soyeqGYlbWBVlaFcCpSPz8Q6t4amcnd15YO6Ls1chkiDz5VyJ/+TPpQ4fROnMuREHAe+WVBO+8A88llxSuI2tMk6sPJogkNTY3hwrhzmcbHZEkK2uDhf+vWVTG957ew2XzS/n81fMBEASBCr9jRhw/+fLrfPOIpdUBdrQPIEsCfqfMZQtKj7V7wfGTdwYJgsCn18zjcw9vGTyHLfzYTCO28GNjY3PW41N8dAgd1kTaPbE23mOxe+AQi7IGzbJIUkuxP9lCVy6E2uMKHmfvE2dp2VIAXimtBpL4JxAsbDN5KvxOUpliPMA9xcXIgsQtC2+d8HHy7dwBgp7ZmIJAf/gQew600zdLIiGKZGLdTDx2d2xeO9SHULSeEhycm9GhdMGY27odMomMxuyai1G2mDT3jM9VM17uf+kgjb0H6M/20JPoocw9sXDySDJLMe1EgJ0dm8a1T1ozQLBECod0bMu+2yGT1i0nQIU4sXKLoFvF1N2c47+ci2quAKCu2MNAMosiOkkKAkY6iugcXXAxTZOPP7gZ7/wQ3qPKB3uiaTxyD/1AfWkDf68v53PqWu5OwrfT28BnZUW1Z2Nk9Azd0TTlPgfr9v6BgK6z/JzbKT9g4osXgT8n/Dgnfr1SJAEjV+p1Vjp+NAPEQcdPPBMdvoGehUQf+E7P7DXDMFn7QCOmAM+4MiBA7DQXJ3703H4e3dLGrz96ITXFbo4MJKkMOHHIIoIAiVzGT1rTOTKQpKbYzZeuHbxGlvudfOgt9cOOqYVChB95hPDDD6P39KI2NOC58EKUulrU2jrcK85DqaoaMRZBEPjp+1dimCarvvUc8czp/dpOBsMw6RpIMysweH1dNMvP/R9YyUVzS5DEQXFtlt9J1wwIP/kyrILwUxXgb7u66IqkuGHZbBzysV1vPmfe8TO4sPCOc2fxg1IPh3ut0G7LeWpjMz3Ywo+Njc1Zj88RYL8oQrRjSoQf3dDZk+3nZjVItxEhqqdI62l6dCt80DfBSexkmB+cj0Ny8JooQRb8qi38zASz/E5MzZqwH1Ikrqu7ZsKiBVg3lqncTWY+aycU2o+SitGXa/XaHzvCiRenDfL7nS8gu5u4O5JCXnQ9+I7v+JGCDVRrBs3RlikcCdyzrhGzzsoN2t67natrJxbiHkllMSVrIrArvHdc4dNpTUcQLZFClY8j/KgSKcMqgaqYoCMm6FEBkQ/O/UdWVlht4PPdaEzDiSkIpJL9uAPVo+4fz+hktAxZ0gzEhndU64mmcchW9tPC2sUMMMDrDZ/hPXu+xferFpFyW8HdhgAtPTvpjqSZX+7m5dAuLk/ryLUXsaBiB8ldDYDVjc7vKpnQ8wPL8aMb1uTIOBuFH8PAFEx8upXxk8jGhz3eu+HHHN54Dxd88QCchq2bt61tpfPQAL1LvMTbrec2NPz4dGRfV5SmvgR3/Ow1/vcTF9MxkGJemRdBEHArUqFrV1s4iWlC3VEdpEzDIL13L+lDh8gcbiJ94ACx55/HzGTwXH4Zxf/2ITxvecu4Q/DzeXOeXFnt2UYokSGjG8wODL8Wv3WUcqpyv5PdR6bfVTfS8WO5t12KxGevmn/c/X1OGUkUKPEOCj+yJPLI3Rfx2qE+Pv/IVrvUy2ZasTN+bGxsznq8ziKiogDx3ik5XnP/QZICLA7MxYVIr54c9rhnBoQfRVQ4p+QcormOYoEZyBWysUq9TM0LuXyT2xbeNqnjDA13Dua6AfV07cJHL5ncSmc41yZ+KhhIZnm592G8hov3hLrhgo8dc/t8+2LDhDrJTUvacpIksgm+9/r3iB7tcJgA4XiGmD4YyLyze9uEjzGQzKLlRJyokaZlHMJUWjNwCFYel0M+tovHo0okdB8AFe6JBacvrw7wxWsWcMXCwetAbW4SmdGtSU4i2Tfm/v2JDIJkXVMi5vDJdk8sjawMoBomtbPmE3Qr3DNwMXvNBr4csUoDz0tZAvShQ8/RE0sjOA/Tb2pcGTwHJJlV9cXs1wYnMQHPxIPhVXlQ+NGNs0/40XQTUzCRDQnZNIkNCeHe0r2FNQd/xV2lXrQpbiow3YQ74zx93w5e/eMB6peVcthjFpwXp7vjJ5LKMsvvZCCZ5fb7N9AeTjK7yPp7dDvkQjv3fLBzXUlOrM1m6X/sMQ7ddBOHb343R778FXrvvZfUjh0Ebr6ZOU8+Qe399+O95JJJdT70OKwW4GcbnQOWcF9xnMBkGHT8mOb4gvEnS/47Wc2JchfUB7l+2Wx++ZELxtVK/vqls/nkFXOGuZXAeo7VQes7xxZ+bKYTW/ixsbE56/E5ioiJImZ6YpPVrngX39343RE5G41NVrDz4sqLcAkivcbwx70z1Fp9WekywBKBnMcpXbGZGqybVBHZLGJe0TxWVaya1HGUocKP03Kh9YYO4pYHxcmBxNR10vreC08guA7xiayAo2QhNBw7r8fjsFwKyaxOrbuCVrIYhs5fGx/hocaH+On6b056LE19cUTVep4ew2DHkdcKj/1h3x/G1aUrktRISzrzM9bf3s7enYXHHjvwGD9+88cj9klnDZx54Uc59k28W5XpNqy/41n1Vxx3PEORJZHPXzMfr2PQdF2bm0SmslbxXvIYXaAGklkkyRIMMgKktMESh55oGlFNUKbriJ5S5lf42HB4gH8XP8p7o13c1R/lg73W5OhA+yZ0wySZXotimlyy8N0AXFBfzG6zDr9uTTZ9kxB+hoY7G8bpLQhMFNM00QwTQzARTBG3YRLXkpimyYHuKP/04vcL22ZOk9DnVDzLC79u5OFvbqRld4gLbmjgrR9dQjiRLYiWidO8HCma0phf4eWhj15IfzxLMqtTmSszcqtSwdHU3Gc5nGrcAqEHH+TAW6+j42tfRxAlZn/7WzQ8/jgLt7zJvLXPMfub/4Jj7twTGpfHcXY6fjpyws/Rjp/RqPA7SGR0otP8OuVFmbzjx63K3Hvn+SyrHl9u4yXzSvnqdYtGfSxfJmZn/NhMJ7bwY2Njc9bjcwYxBIFEMjSh/Z5ueprf7vktb3YP7zzU2PE6qmEyp+EqnIJEz1Hhpl7f7BMe83jI5/z4Vf+kVhptJk4+tHGxchffufQ7k37d1SHhzvWBevyCwjqtB6c8KAiEUxP7vI5GIqPxL3/exaOHH8JpermjY4/l9jnOuN2qJVrEMxp1RXNJCwKbGjfwyiYr66e18VGIjq+N+tE09cWRVasz1dXxBDv7D6AbOqFUiG9u+Cbvevxdx9zfNE0iySxJ0eD8VBqHYbBzSHewJw4+wZ8P/nnEfmlNxyFaTprjCT8eh4SpFfH+uf+HGxZNPMPpaLwOmRKPykAm5/hJjO0+HEhkCUiDj0dS/YWfe6JpNDlJKQKIEgsrLFfSrTe/B2n5HXwxHCaaWkC5IdIUaQLgQPJNLkil8Sy8HoD55V5iuPleu86nw/0U+2sm/HwUSThrHT/ZXHmXIZgIiHhMaOrv54JvP8c1/7WOpmhjYdvMaeL4eenhvezZ0MnSNdV84FsXs/qGBhSHRF88U3AqnO7iRCyt4XPKLK8p4sGPrqa+xM35dYOlPM6OVnr/+7+Zdc93uXfdDwhfu4au73wXpaqSmvv+m4bHH6PoPe/BuXABonPqFlo8qlzIFzqbyIc1j0/4sbaZ7s5eeVHGIU/99Dl/TDvjx2Y6sYUfGxubsx6vy3JURJMTK/XaG9oLDHcTADQOHGSBpqOULsQlKMSF4fZjj2dmhJ+848cu85o5ZgWcSKLAqvKLWFyyeNLHcSoSvbE0HQNJHJKDd5acxwtuBw5nW2GbgXT/MY5wfDY1hXjHj17mVxv2o3oPc4sjiEP2wPLjl6flHT+JtE5txXIA/velJ2jttsSoTlmGN389qXEd7k3gdhyhQtNYnUoTN7M09h3g357ZCEA8G6c12jrm/mnNIKNrxCUBt1zEokyWXbmA539+fCd7u/cTGcVRk9YM1ILw4znmGAMuy5lzbe31U5afVVvipjtp5QYlEt1jbtefzOIf4vyKRNsLP/dE0yTFDKWClSFx16UN/Psty7hhWSVc802yntms08+jUgxwyIghqV0cMeNcqZYX8s3yXY36M3V8qj+CMIkwekUS0c2zM+NHywU6a5iIpoDLhP5MikWz/Hzpeh+ClGFZ0hJJ0hN0mZ4M2vaE2L+5m5VvpdPwYQAAIABJREFUr+OyWxfg8g1GyofjmUKJS+w0FyeiqWzBhbeiNsi6r65hZV0x6YMH+fDzP+fD93+Nnh/+6P9n77zD5Crr9v85ZXrb3neTbNqmd0IHKVKlSlGKDRCsP7Gg74u+tldUFAWxgL6ISlUQEBAUkBISQnrvyWZ7L9PbKb8/zszsbrK72d3sZpPlfK6Li83MOWeemTkzc577ub/3l6wDO4l7ssi+/nomPfE4kx97DPdZZ43Z4orLJp3wZXSDEU2o/T6/Zn8U+ZA8nIFICz/N/vioj683h2b8jCbpY6YDpE0O5z+7Wvj63zab4thRYAo/JiYmH3g8DqMFZzA2+ET6ub3PUROoyfx7V9cuoK/wo+s6OxNdzLL4QBRxHNLG26HpSPLwWnuPlCJXEXmOPDPY+Rhit0g8fstyPn36lKM6zsdOKkfX4bIHV7K5rptrq65HEQT+4ev52e46ihydvS1BrnvoPRRN57vXeNBIsrztAMy4AAboJtWbPo6fstOM28SDWFLZM82yDA3rRzS2g+1hZGsbk5MKc63GZ/PpzSt4dvOOzDZP7Hh8wP0D0SQO0fgsK65pzI0n2BmqRdEUXtraQEDtJKolSB4iSMQVFatgrBgfSfhZPiWHP9y8lEXlQ7P4D4WKHCc1QUP4CQ4m/ESSOKWe7yq/vye/qD0Uxy8p5KUyiqbkubh2acqx4ykk+aWt/EM7lUJxEnstEhW+NwA4e/L5fR7j5S+dztRFHwLJBs7hhztbJRHlA+74UQUdQZewayKKqHDbmZUUFRjv6ykxo1wokTy+hR9N1Vjx17148+wsvmBSn/tiSZVwQqXEZ0cUJoDjJ6Zkui7puk5s924a7ryTA5d+hKrqLby95EKmr1rJt6/7Ia/c9E0Kv/VNnIsXj/m4XKkOihOV/35uK7f+ad1htzf5YxR67Yfl4fRH2mk71p29ejJ+Rj+QPV3qZWb8DMzTa+v42/p6vv63LeM9lBMWU/gxMTH5wONJOX5CgzgouqKdfGfVd3h21Y8ASKgJqrurAdjavjWzXb2/hqCgM8trBPLapb4Ntz2jOvLBEQSBW+fdypXTrzyGj2pycmUuWc6ja7S+ZFIOz37uVGyyyLUPvcf24AyqEgqNFhl0AYcu0K2Ej3ygAdjdEkTT4eGblhKV9iAgsLi7GWZcOKT9XSnhJ5JQKcydgU3XSQpNyCnhpFsS0RrWwwjCNg92hNGlEAWKSv70q/GoGtvrVyBajDyU+arAS7v/ephwk8YfTZItG/lHmlTAHFs+MV1lZ/teOuOtaKl5hD/u77NfPKn1CD9W96BjFEWB82YXjuoq/6QcJ43dxuO2hAfOb+qOJrBLPWMPpDp7qZpORyRESIRCS//indNmoTTLQVKZiyYIBHO2MDOeoHj21X22m1PiY9ZlX4Xb3wXb4K9Ff1h6CT8ftIyfdImm4fgRsWoCSVEl22llc9tm7IKHaUnj3E3ER/4ZPhbsXNVEZ2OYU66chmztO9ntihj5WTkum5FDcwKLE4qqMbt2Gyf//XccvO569ixdRvXlVxB6621yb72VRz5/H88vvQIxK5vazshhHb3GEqdVPuHdVIOxtzXE3tbDBdBmf6xP2/PByDh+AjHCcQVVG5uQ54Qydo6fdKlXwnSzDMi2hgCCAP/Y3DjmZX0TFVP4MTEx+cDjTK3uRwZxUGyvXwFAd7fh+NnfvR9FV1ioQGukldau/QDsrDGCnWcXLwPAIfW9cHEpx/bi+OOzPs5V0686po9pMjrMKPTwwudPY16pj88/tZ125WwANNWFDwvd6sht7Z1hY9KW77GxrnkdVdYsvBow7bwh7e9MlXqF4wqiIFIu2OjSuxDEnjE1xjvAXz/QIfpF13Wq28MgJXHqGu1TrmBuIk57Yg8FWcaxP9PeSree5J29h+f0gNGdJ0syumIlyWFuqhRtZd0GREtPiVfgkFbosaSKLBoXk1brsZRoDcqynahJD4Ku0xofIL9J1ymrfRFnr6ynQCrsuiuSQE8JXhXOggEfZ1FFFhuaZyHrOnERzsYJhXMP31C2Qv6MET0XWRJI6sY5on7QSr3Sjh9AECQkVSQuamQ5LWxu20yZWIotJYjGk8ev8JOIKrz/jwMUT/MxdfHhnSg7Qmnhx4r7BA4gjqxdS80NN/L91f9H4ab3EKxWfJdfTtF3v8vUN16n4M6vYM/LoTOSoC0UJ65omY5exwKXVZrQjp+WQIz2UOKwUONmf4xi3+DdFdM4rBJeu0yTP8pZ977F71ccGIuhkkgF3o+J8GNJZ/yYjp/+6AwnaOiOMqvIcLBHPoCd7kYDU/gxMTH5wONIlUVEDr0Ib98HK+4DXWd7w3sAdKes+bs6jTKvq7qMCeauHX8DYGfjamRdZ9oUYwLt6NVNqzSp4HHmjd0TMZlw5LptPHbLclxWido2IzNIV9y4sNKlj3xCnZ60OW06m9s2szQShvKTwDW0sh5navU/ffFVYcuhSUwi9hJ+HvV5qTvw2rDGFVc0gjGFpKgiaBbarGXM0hz4rSGmlcbwqCJLoiJ5isqLm3/f7zECUQWPZAgnUT2HSRVn4dY0tjeswmrpKaEKdNf02S+uaFhE43Wx24698FPoswMSObpIa6L/bk+R+vd5Nvob4q46rKlV7UAqCHpjbTcuq5F9NNk7qd/9AZZOyqbOLzElbriVPjTtsiOGeQ8XiyQSVg3RWzsBcmxGE8Pxo6EJICEhazIJUUcXQ9QEapgq5GBNCT+J5PEb7rz+1RqiwSSnXzO9X2dbj+PH2qfr1fGKrijED1QTeucdOh9/nJZ7fkzNjTdRc9PNJOvreWDB1ez69V+Z9Jc/U/Sdb5N9/XXI2Ua+VZHPQXsozv424/2qyB28FHQ0MUq9VLQxcrGMJ4qq0R4yfjN6l2npuk5zIEbREIKd0xR67aw72EV7KM5/dg5cKns0jGW4c7pFvCn89M+2BsPlunSy8ZmMmc6oEWEKPyYmJh94nKkOPtFDL8LfexDe+B5EOtjWYeSLdKvGxcnuzl04dJ2lvukAdESMLkR7u/cxWVGxFcwGekQlWde5ovJSzp73iTF/PiYTC7tFYnllLmp0EoJuRVfcWEUvfkGD9Y+O6JhdkQQ+h4VdXduJq3GWdTTA3KuPvGOKdKlXepW/1J5DsyxmHDM2ycbTXg+/3/fssMZlCEkKqqCjqk780SRZwiQ0AfaH1lGixPlr8ixOEX1siDag91NK5o8mcaZKoQJqLmL5cubEExzwb8dr7XH5BIJ93UhxRUMU0o6fY5+Llc6pyMVCixrpd5v9+15lg93OTpuVAkVH0HUCqW6Ej66qptRjBD1XFA6cPbJ0slHaWhHMZVY8yayTvjCaTwMwVsSDmvF81BOkZflokVQ1EIxJiYiEpMnERJ39AaPj3SzdmRF+4sn+3+fxJtAeZfMbdcxcXkTBpP4/C2nXYNrxc7wGEOu6jv/ll9l/wYUcuPhi6m77LC0/+CFdTz+N6vdT8PWvoT/2DK9MOQWPu3+hochrR9dh/UHDaVdxDEu9MkH6yYk30e0IJ0jrWb2Fn0BMIZJQh9TRK02Rz86uZkNk3lTXTWwMXq9D27mPJrIkIomCGVw8AFtTws/iipTwY4Zgjwh5vAdgYmJiMt44ZeMiLpKM9r2j+h3j/8FmdkSMCWO3Zlzs7m7ZyPR4guz518CehwhEjQvCzkSAQskBonGx5rAYwo9L07h91o1QvGCsn47JBOS0aXn8Z1crU6Rr2BMUiORUo+it8M+vQ8EcKF82rON1hBPkuKysbV6LACxOKMMSfg51/PhsWcREEUGMkqfofHr2o7yy9QZqYsPrlBeOKyAZK8BxzUV3NEltcBY4a/An/MxXFVZo85irx+kS99IYqKPUV9HnGIFYEqtkiA2dyVzIncYcVWCd2oHb5kLUdTRBwB9qQtf1jJshrqhYRMNFZbMde+EnnWfh0+206v7D7m/sjrJi69uQiu9xqBJuWcOf8LO7OcjKfR2cPacTNaHgSAnP/VFV5MFllVjZcSuvXzYJ0X14Gc/RYpEEgqodCdAGcC9NVBRNzwg/kiAjKiJRATa3bUYWZOYqeqbUK3EcCD+/fnMfXeEEd19qnDO6rvPec/sRBDj5isoB9+st/ByvAcSR9etp+clPiW3Zgq2qiuL//SHWKVOwlJUh5+dnPvv7qw3xNB3ufChFPuOz+X51J6IApVlDK0EaDVy2HpE93XVsotBb7Gny9/zdnPp7OI6fAk/PtglVY2NtN6dMHX4w/WD0hDuPjW/CJouHlbyZGGxv9DMp10mBx/gsxiegEHosMB0/JiYmH3jSjp+I0kv48ddDp5Hb096xm1Ytjqzr+NHQdZ3d/v1UJRK4Zl+FrOt0p4Jiu7QkWVLPRaEjJSq5NR1cA+dumJgMxunTjBLBBd5LydKXomtuOiWZ97KL8P/tJgi2DOt4XSnhZ13zOmYqOr7K88A19DJEt11GEHomf26b0d0qaolj1QS+/WwNhbqb+gGcKwMRTiiZnCBFc7C5rps3umZRmjQmlQWqilI4n1jEKGXaXvvWYcfwR5JYJcO9F4g5QBSZ652CKkDI1UBlKlh3RcdWTn7iZP647Y9oukY8qSFLxvOxOUavW9dQ8TksWGURl+6iRdAPC8b+86qDJJWeNvZW1YpbFwkkQzy66iA2WSQmdTIpqUD25AEfR5ZEzpiez/TKqfhmnD4mz8UiicQ1YxKtHlrqFWyB9x8aUfD3iUBvx48kWhA0K7ogsLppNTNzZpKXaEdOze0SSnSQIx0bVuxt4+09RjZUoD3KSw9uZt/6VhZdMAl39sAT765wAlEwzluX7fgIINZVlfj+/fhfepn6L36RmhtuRGlupvhHP2LKs8+QdfXVOBcvxlJQ0Kd8LRQ3vhPc9v6FlSKv8Zu+vqaLkizHmDg+BiIt9vijEy8rqyUQ7/V3bxHI+FykXZBDIS3OuW3Gb9P71R2jNMoe0u3cx6LUCwwnkVnq1T+7moPMKvJmspBi5us0Ikzhx8TE5AOPXbIjAFGtV1hu9QraJZFXXE6auvYBMCWZxC8KNHQfIKglmOkoRPCV4NUF/Knsn25BI1vusYE7UiGxbk0b1sTaxKQ3MwrdXDCnkDOm55PltCIr5UTVGLd54PRcCxc/ewHrGlYP6VidsU7qk+/icwpsbt3A0nAQFlw3rPHYZInJuS72tBjnvddhrKz6JQ2PZExUvEIurSJEh5HxEo6rGeFH0xy8tKWJWr2AOapxuVIgu5lUXsHO9inIus62pjWHHSMQS+KSu5F1CESNyd3ckpMBUEWV6/yGKPR26CARJcJ96+/jc69/Dn+iEynl+LHajtzSfrQRBIEirx1Z9RCQRGKRnomLomocWP8aXZaeybWo2nAj409GeW5jPVcsLKE26Wey6DCCmQfh/o8t5JFPDs8lNhwskgi68dofJvxsegxe+QYEm8fs8ceTpKojpIQfWZARdOO92NGxgwV58yhtX8k+zXCpxY8D4SccV4nEFDa+VsuT33+fxn1+Tr92Oksvnjzofh3hBFlOK5IojHu4c/zAAeo+93l2L13GgUsupfFrXyO8chX5X/4SU//1KllXXYkwSAvuYMwYu2cg4SflPIkm1WMa7AwwJc/IE9rfevzmQY2U3mJP81E6ftKdvWYVe5hV5GVN9QAB+UdBPDl2pV5gCEpxs4QJoE8ZdyypcrA9zIxCd0/be9PxMyJM4cfExOQDjyAIOJCIqImeG6vf4Q+5+XyjII/ajt0ATNGtqILA+v3/BKCq9DQAfIj4lQhJNUlIAF+vjkB2q3HR5hIkkPq3kZuYHAlBEHjopqWcP7uQbKcFObKMd69/l4fPf5gvl5xLAwqrNj48pGPdu/Zeulx/ImxdQUxLslSVYMZFwx7TzEIPu1OZCh6nUS7UKku4ZSuiAA6pFID6pvVDPmY4rmAVUyHroht/NMn0Ag/zU2HF+b4K5pT42BorZkYiwY6uPYcdIxiO4reGceoWAlEFXdeJu5dxRTDElzoSnBOUcWo6EV0hy5bFt0/+Nuta1vFW8Ou0ObqQdR3Zcmwnd2kKvTZUxRCdWjuN7x1CrbQ+cTu/Vb7DQYsNIVaAQ5epT0zDJjjoUEJcbPsj3qK3CKIy2X5kgdkmS9gtA0+EjxajFCLVzj1xyIS1I9VxJ9rFRERJhTuD4fjRUyHXOjoLdQv2RCevJk8FIK6Mf0viUFxhbofOqmf3UTYzm4//z3IWnFOOKA4e+N0VMVyDQCrc+dgLP2ooRMtP7+XAZZcTWbuWrKuvpviee5jy/HPMWP0eeXfcgeg4cllW4AjCT7bTkpnsV+Qcu2BngGkFbgQB9rRMPOGnNRBDFIzMpKbeIlAghiD0Ld86EmnhZ2q+m+WVOWyo7Rr1sqm042fshB/JzPgB1h3s5OR73mBDrfEbcaAtjKbD9EJP5nfLdPyMDFP4MTExMQGcokxES1mpdR2q32GV28j52Nu+FYBKTzkA7+9/GUHXmTbbyETJEq341Rjdqe462daeMhFHKiTWLQ6+Am9iMlQqcpxsquvmsVVtnFJyCrec/0s8mk4g2nbEfSMJhXirIZbUJl8EYMmUC8Ay9AvsNFXFHqo7wkQTKh53IQBRUcQpWozwZ2kqAHUtG4d8zEhCwSUamTCiZAio58wqYGmpUZI0KW8e80p9hHBSpcpsj7Wi6X0vAOtCf+Jdp51l8nz80STn3vc2lz4X5bttXdwaaMavu3CqxqS2JBzi2hfv5smag3iVbmrtIaw6o97laqgUeO1EY0Z4ZUtXtVES9cBiCvc/w1Pixexzl5CIF3Nlya9p7r6KkK2KnTYrr5Xv5Kn9f6BcUTk5u2pcxt4biySgp0q9wolDHD+dKeEn1n2MR3VsSKo6CIaQYJGsaFrPZ2tB3RYSVh9vq0uMbY8D4UcLK8wOC1SdUsTFn5uPJ2do3wUdoQQ5TuN3zW2TCR/DjB9dVfG/8AL7L7qIzkcewXfF5Ux99RWK7v5vsq68AntVFYJ16L+5obTwY+t/cSbtxoNjG+wM4LTKVOQ4M+7KiURLIE6e20ZploOWQxw/eW7bsASWPsLPlBxiSY0t9aP7HXNMMn5UU9DY3RKkJRDnlj+t42B7mL2txrk/o9CTKbMbi/DuDwKm8GNiYmICOEQLEV01RJ/OAzSFm6jWjZKTvQlj1aGy5CQA3g/XMUnVcZafAoBPsuPXknSnugRlOXJ6jpsqGXHJw59Ym5j0xzcvquJDM/O591+76Upl7HgRCRw6we6Hz/5lPaEGIycmpHczI54ga9HNIxpHVZEXXYc9LUE87pLM7Q7JhsMqEZUMAaKu83BXzkCE4ioOKS38GALquVWFzFlwMy+FLCyb/wlmFnmQRYEyLZsQKgcDB/sco1nfwKJYjIsmfxYBKPbZ+daVJxG5+AF0QWS1NgubZqwaVsRCMP3DTD/t6yyOuwEYOx/MkSny2mkNG8+7afUD8Mo3SJYu46Lkvexd9C1CWidaMpsKXyleu4uDB08j3noh3/JcworGDv5Z18C0wkXj+AwMZElES+QjAPuUAYSf6EQVfjQEwZi8yZIVVTMcJ/m2bIr3vE5rxSWEdcM1ElfHX/iZ1aUjAPMvnNRv2/aBaA3GyU8FrbpsMrGklnI7jT66rhN86y1a7vkxB2+8kd3LTqLxrm9iKSpm8l+fpuSHP0TOHV6QbziucNH9K1i1r51gLIksCtgtA0+L0mVHx7rUC2B6gYfdE1H4CcYo9Nop8tn7hDs3+WPD6ugFRmj9hXOKOHdWASdNMc6F90e53CuhaIiC8f02FljNUi+gp1uoomp84o9rWH2gA1kUmJLnyjh+zCykkXHEM1cQhEcEQWgVBGFbr9u+KwhCgyAIm1L/XTy2wzQxMTEZW5yilagAJCNQ/Q7vOXouOvZZLFh1neKU0NMqiVTZC0A0vkK9spNuQaM7aLRSznb0dMlxpLoDeeRjaw83mbhkOa184tTJAOxoMkQSjyAR7J0XomnQsf+wfVfsbadT7ClnWKZboeLkEY1jVrHhyNnVHMDj7Akud0p2XDaZLr0Er6ZRF6wd0vEiyQh/qf42kq0JAJstB5/DwuKKLPCVMenzGxAKZ2G3SEwv9GBJGjkp21o2ZY7x1JpaFC1Cvipywekns+sHF/H4LSdzw/JJeJbfTOgbzXxH+WTG8dMVL+fVqXfD2XcRlQxXUfAIJS5jSaHXRnu0mHxF4edyiO2n3MaT03/OHrWID82xoeoqV8ydxyXzignHFYKBQsrES7juinvIuvVtWHwzVF06buNPY5VF0K2UYmNf7+y0RBhCqWyfiVrqpWmIgiHIWiQrimoIPwtEJ4ISpaPyCtANZ0lcjQ94nGNBoCvGrJjIVquK5B56KbKm6TR0RSnLSXWtTHeeSoz+Knyitpa6W26l/vY76HrqKVBUsq66itJf/pLJTz+FY/78ER13a4OfnU0BXtvZQjCm4LHLgwpf4+X4AZhZ5OZge3hClQGpmk5NR4RCr41Cr53WYCyT69Lsjw0r2BnAbpH43U1LqMx3k+OyMqPQPfrCj6qNabC3zQx3BgwHniDAHz91Es3+GE+uqWNyngurLGbCnc2Mn5ExlLP3UeDCfm7/ha7rC1P//XN0h2ViYmJybHFKdiKiCPGQUeblzcZtMRwAjRaZbGSyfJMz288sXJj5O8vqxS9AVyDl+HEVZe5z2I3Ve9c4tIc2mbjMLjbOpx2NhvDjlWwEek+w370PHlwK7fv67Dc134Um9mRZLS07fcRlTeXZTpxWiZ1NQdy9cq0csgOHRSKSVCnHQl10aC3d93Xv40B4HVF3DQAXLZrDL65b0O/qaonPTq0yH6emsTXV2UtRNX7w0g40KYnXlQuCcNhFuttuRRBExFTuSqv9dP7rua20BmO0C+eO5GUYVQq9dpq1An5lnYvdkcun29/hoW2/omDak/x405cBuGr+fLKcVm4/ayrXLCnj6dtOQRIFyJsOl/0KvMXj/CyMcwOgQvCwV+x1gd5Z3fP3BC71sqSEH6tkRdEM0X9h60HInkyieCnoUmrbxECHOSas+3cNIrDGpgwro6c1GCehapn32WU1ns9o5vzoySTtD/+eAx+5jOimTRTefTcz161l8lNPUnT3f+O98AIEceST8G0N/sz/Q3FlwI5eadIOlIpxcPzMKPSgaDrV7eFj/thjxY9f2Ul1e5gPzy4i12UlqeoEU+dPcyA2rGDn/lg+JZf1BztH1YWWULQxK/MCM+MnTTCu4LbJLJmUza8+tghRgJlFxjWGXTYdP0fDEc9eXdffAUY/Gt3ExMTkOMIpO4gKAsQDqNXvsNpm5ZyKc5AxJsU5FhdZrsLM9jOnXpD522fLIiqKtHYbDossT8/Ey5HqduQehy5BJhOXXLeNIq+d7Y3G5MUrOQnoqUlXpJPEyvs5IIuw8x999nPbLSQkhUXRJN9IeDnr1LtGPAZRFJhR6GFXcwBZtCOmVmsdFkMQiiRUKixeaofQ0j2haLyxyxCpElZDzFo4ZRrnVBX2u73LJrNWm8PceIJtbVsA2NsaIpxQiYrgsfTvsBMEAa/Dwi5lBgC3nXsh4bjCXc9sIaFkD+8FGANKshyoSOyb90v+cvmzFDhK8Vv/g8PZQVVOFV9Y+AWWFBj5MF8+bzr3XrMgU25zPDGj0BDN83UftbJIPJk6B9JlXjChS71kwRBhrbIdJZnLD9o6uLqjGeZfh1WWABGLrhMfR+EnFk6yZ2UTuywqfkknNAzRpr7LeD/Lsg9x/Byl8KPrOvHqarqff57qq66m7b77cJ95JpX/fJmcG29AsIxeg4TtKdF8e2MAfzQ5YL5Pmo8vr+DHV83Daz/2TRpmFBqT3okS8PzE+7X8fkU1nzhlEtcuK8+EhHeGEkQSCv5o8qiFn5Om5BBOqGxLvc+jQVzRUp/fscFmEUc9kPpEJBQzhB+AD88p4rFblvONC2YCRn6cKJgZPyNlcHl7cL4gCMLNwDrgq7quT0zPromJyQcCh+ygRRSgfi07lQB+nJxWchqra96gVQmT48jFY/Ug6EaX4qrCJZl9s1LizkG/sZqdlQqBBvBlV+IQZEoqP3xsn5DJhGdOiTczefFaXQTiraDrNK2+ny/mOtlj9fG3Xc8x84w7M/sEoklkn4oQd3H2ta9hyT661etZxR5e3dZMPKnj0ATCEjgtLpw2mUA0SVluEf9WOkkmI1gG6ZT1/KYGXnz3TSgBVdSQdB2rc+DuVC6bTFPCwTmyjz8nOkioCTbXdQMqcQFcg5RW+hwWmjUPVuDUSVV86yI/331xB5IoMHvGp7j2pPwB9x1rFldkM73Azf1v7KUsewFFwW+xa28zz/3XBZnJ0YlArttGntuKI5GDahWobttKVcnyHuFHtk/cUi9VxyIoJAG7xU5Mt3NFKOXUmH8dtqSx5mrRIZ5uKDAObHmzHjWh8b7HEGsiwwhnru8yykrLUt8f6Ul6fVeU6YWeAfcbiMTBg7T+/OdE1qxF9RtitlxcTNlvfo3nnHOGfbyhsL3RjywKRBIqW+q7mZrvHnT7SbkuJuWOT8l2Zb4LSRTY0xyEBeMyhFHj3b3tfPuFbZw9M59vXzobgBy38d3WEU6gpRYQhpvxcyjLK42sxTXVHSwszzrC1kMjoWiZcOGxwCpN/FKv+17bw9rqTp64dfmApZWheI/wA3Dq1J5rAUEQsMmSKfyMkJGevb8FpgILgSbg5wNtKAjCbYIgrBMEYV1b25E7jpiYmJiMB06Li6ggwq6XWZXK9zm55GRyHcYPTrZ3EpIo4bN6yLFlkefo+SHypiaoNdFWXJqG1Z3f67hOXr32DS6add0xfDYmHwRml3jZ3xYillTxWn0ERAE9HuKx5vc4YLUiCxLPR2vBX5/Zxx9NEpF0nKI90wXlaKgq8tIVSVLdHsamGZcUDosHp0UiklAoz6pEFQSaG3u1dO+uA63vRdvG2m6cUo+Ox3LGAAAgAElEQVQDxKnpCI6BL9bdNolQXGFe3lwUYFfbVjbXd+NxGpPX3qVnh+JzWEgG5/CRKdeQbcvm5lMmc+aMfFRNp0w+i5tm3zSCV2J0kESBr354Jgfawlz921W8trOVm0+ZekKJPmmmF3hIho3J1+62rZCMwZa/gq8CPEUTuNSrx/FT4PNQnJ8KHS5dCrlTM6UiVgQS4yT8JGIKW/5TR/Z0H+2SMdEOxYc+kTrU8VOVKsNIZ44NFV1V6Xj0UQ5cfgXh99fg+fD5FP3g+0x54QWmvf7aUYs+uq5z7792sa+1bzByNKGyrzXEubOMbLL2UIJzqgr6O8RxgU2WmJLnOuEDnus6I9zx+HqmF7j51ccWZcp4c9OOn3CC5lTIc5HXcVSPVeCxU5nn4v0Do1e0klDHVvixWaQJLfzous7fN9Tz3oEOttT7B9zuSKWXdsvEF8jGihGdvbqut+i6ruq6rgG/B04aZNuHdV1fquv60vz88VtFMzExMRkMh9VNRBQM4cebxaycWeTYc8j1Gu6dbJ/x/1xnAbNy5/RZqchyGaVdNUqILFUDe98Ja449B0kcz15BJhOROSVeNB12NQfx2rNRBIFIoIGacCf5qsjZRct52e0imSr30nWdQDRBWIRZBQWjElKZnvBtqO3GqhoXak6bp6fUK28OALUtG9F0jS1rfo3+y7mw7dk+x9lc141V7rkQdOk6yAOLHekuQrMnnw/A1v2vsLnOz6JiPTWGgTO1fA4LUmIyPzj92wiCgCgK3PvR+WQ7LceFwHLBnEL+98q5/OaGxay/+7zMqviJxoxCN21dPgoUhRdrXoPXvgOt2+GSnxvfkROk1EvVVF7Y9wK7O3ej6zpJVUdOZfzkutz85rYLQBBh4ccBY3IHYNXHT/jZvqKReEQhZ0nPAsZwyrTqu6Lke2yZDjseu4VJuc5M5thQSBw8SM1NN9P645/gOuUUKl98keIf/IDsa67BPnMGgnT0v5ldkSS/fnM/V/x6VZ/bdzYH0HS4YmEpTqvEvFIfnzl9ylE/3lgyo9DN3hNc+PnX9maCMYXf3rgET6+SuWxnWviJZ7p7Ha3jBwzXz5rqzmG52QYjoahjH+48gZ0sNR2RjFvwmfX1A24XjPV1/ByK6fgZOSMq9RIEoVjX9abUP68Etg22vYmJicnxjtPmJSIIhAXYLAt8ouRUgIyzJ8durFx//7Tv47b2tYT7PEYr6yZRZ64CSEdTRWtiMjTmlBi5Udsb/XhS5YZ/fPM9OtQoVtXOJTM/zmvN7/H2rmc47+TPEUmoCIRQBQGfdXQyp6qKDIFlQ20XsiYDCRw2H06bRDShUl6yDDZCXccukvte5os7f8c3vB5uat7KY3ICt9XNBRUfYXdLkCWFPfkVriOsS6UvCp0V55O//n/Z0vg+u1sWc/qyOBsD4LYP7BYq8TmYVuAxApFTFHrt/OsrZ+K0jv9nVxAEblg+abyHcdRML/SwI+HkxkCQ++Qd7Gh4g9nL74AZH4bVv5kwjp/NbZu5e+XdAFR4KiiSl4GtAwDZYgd3AXxhHeRUAmQcPxYE4trohSEPlXhUYdPrtZTOzEbL7RE6h5PxU9cVybh90swu9h7R8aN0dBDduJHI2nV0PfUUgs1GyU9+jPeyy4bVSn6opMWsQ5/b9lSw84LyLP7ymeWU5zjGrEX3aDGj0MMr25qJJlQc1hNzIWl7Y4BCr40peX1L5nJ7lXqlKr2OOuMH4OrFZTy5po5HVx3kc2dPO+rjJZSx7+qVGMUw6uONFXuNyp9FFVm8sKmBb186u9/XMxxXKMka+P03HT8jZyjt3J8E3gNmCoJQLwjCZ4CfCoKwVRCELcCHgK+M8ThNTExMxhSHM4+4KLJ6xtko6JyaEn5y7caEOi38zM+fT6Wvss++Pl9Ppk+WMP4TR5MPBmXZDjx2mR2NAbyp4PG6lmrCkoak2Cl3LCRftBvlXuF2ArEkPtHosOVNnc9Hi89podhnZ2NNF6JmhAw7bD6cVplwQiE/ZwZ2TacuUEtbw2oA7s/2oQSaeGznY/xi/S/Y3NCBqukg9bSjdwmDT2zSYbIR0cM8wc7WUB2qplPuMY7hSn1u++O/LpnFnz697LDbCzz2QVcZTYbHjEIPflx8NBDCpWk8WlgB53+PhJpgq9UyYTJ+QklDsLx59s2UecpY1/U8wYKVAFik1OQld2qme166HbEFkYR+bFetW2sC/PV/1xANJjnp0il9BJHIMB0/ZYfkg80u9nKwI9yvgBR6dyX7L7mUvaedTv0XvkjXE0/gPussKl98Ed/ll4+J6AN9BZ/ero/tjQGyU99dSyZlU+A5epFhrJlZ6EHXYV/riRvwvLXBz7zSwxcdnFYZu0WkK1XqleW0ZNxkR8PSyTmcU1XA797aPyxhcyAS6th29bLKIvHkxBU0VuxtpzzHwR1nTSUQU9hQ2/9vwKEZP4diOn5GzlC6en1M1/ViXdctuq6X6br+f7qu36Tr+jxd1+frun5ZL/ePiYmJyQmJM9V16z/lc3DIDhYWGO3a046fbNvAHX+y3CUIqVWqAmH8S0VMPhgIgsDsYiPg2es2yg0tiRo6JQFUF83+JB+pOI93HXbat/3N6FwjG3kHXufAwshwqSry0OiPoavG5MnpzMVplYglNTQEypCpjrSyat8eAOKiyGv+3bSEW+iMdfLi7ncA0OWedvSOIwiovbsIzfNNo05UsYl+8hxG9oh7kOfnc1hOiIneiU5lvgu/7sKj63w0FOPfFpXGWAeP7XyMG+O76JgAjp/1NV18/6XNAFxWeSkPZZ/M2ZFY5n5ZPvw8S08c5WMo/Oi6zpY363n23vVoqs6VX11MyfQsQrGeyXA4MbSxKKpGQ1eU8kMdPyVedB12N/e4frR4nJZ77qHullsAKPjaV5n0xOPMWLeWsgfux1I4trk6vSf7m+t6Skm3NfqZW+obM8FpLEiHZu9qHr0uVceScFxhf1uIuf0IPwC5Lhsd4QRN/hhFo5A/l+a6ZeUEYsqAgllNR5jLH3yXxu5ov/f3Jp4ca8fPxM742dcWYn5pFqdMzUUWBd7e03/2r9HVa+DueXaLSGwCC2RjyfHtazQxMTE5RjhTHYder3mdpYVLsUqGgJMp9XIM7JBwWpw8UHYxP25t5yvdJ+5qnMmJx5wSH7uaA7g9pQA4tTr8koSi+GjojnLFgltRBYGX9jyDP5LEJRsrbF7n6E24qoqNcq86xXC+OXzlOFOlCNGkSrnFQ70apiXcilPTEIE3o60oqfbzq1v/TWmWg4TUM0lzSYO3KHfbjOOH4gpzy88AYEnOBgTNmNy5R/H5mYyMXJeVhC2HBmcVN558FwIif9nxF95teBcNqFPDZOo6xpBn9zzLnW/deeQNR8D6mk4Odqa6UD1zG7z0/8hXegRMi+XwgNpMqZcuHTPhZ/ULB1jx9B7KZ+Vw3X+fRPFUY/KdLoUShaGXetV3RVE0/bByndklxvdAOucntnsPB6+5ls4//ZnsG25gyrPPkHvLLTgXL0a0Df75Hi16C1tpd0FC0djdHMyUyp4oTM51UuKz85u39g8rj+l4YWdTAF2HuQO87jkuqxHuHIiOSr5PmrSI1BqI9Xv/D1/eyeZ6P+8MIEL0JqEem1IvTRv778XxoC0YJ99jw2O3sGRSNm/vPvw11zSdUGLwcGcjBNt0/IwEU/gxMTExAZyyIfxElAhLerVqP7PsTL629GvMzZ076P5nL7+TS8IRsoLNYzpOE5PezCnxEktq+OOp3Cm5FYC4mkNDV5QpWZUssGTzfKyBUKALu5hq/57KpRoN0gHPcc2Y+DllJ45UVk4koVDuLKJJAk0Oka8IFEkuNjqMy4/SpEKHupZ5ZQ4iokpOarXzyMKPsRoYjqvMqboKgCL3bkJxY3LncheO2vMzGRmCIFCe7+ObuQ9QtOw2LpxyIX/d/QzrmzcC0CgJkBh7oXxl40peq3mN9mj7qB9b0yE3VT4pdTfBVX9As/eUAsvy4cKPKApYJRERkfgxEL7ikSRb/lPH9KUFXHLHfOzunpX0UFzBJou4bfKQS72q243W9JX5fYWfIq+dfJtA+3traP3lLzl4zTUoHR2UP/Q7ir59N6L92LvseotZe1LByHtagiRVnbmlAwfAH4/IksjPrl3AwY4w339xx3gPZ9hsTeUqzSs7gvDjj1HkO7qOXr1Jd69sDcb7vT/tOhlKblJHKEGOc+xc3eky0ImY8xNLqgRjCvke47f9rJn57GgK0BrsK8hFkiq63rO40x822XT8jBRT+DExMTEBHL0u0Gfn9nTRcVqcfGLOJ47clctTCBfcAzf+fayGaGJyGOlV9voO4+c8ZDVKnQRLSabl8hVTLmG/1ULrgSexSYbw43OXjtoY0gHP6VIvh+zAlXb8JFS81jJioki7PYZTkfHp2TTLhjD0qXASVVTI9q4jKEJOIlUuJjv7eaQeXL0cP4qUT0kCglID4VjK8ZMqfTMZX6bkuTJCwRkFHyWhxdAwJuMNsjzmnb0CsSRNoRYANrVuGvXjx5Iq2aIhNj6eeyfMvwa70CMoWPop9QIjy0NGIs7YT152rmpCSWgsumASgti3tCkYV/DYZdw2ecjt3A+k3s8peT1NDqKbN1P7yU/xyDN3ceHD/0PH7x7CdcYZVP7jBdxnnTXgsdYe7OSi+1cQHWKZ2XBJCz9FXjudYaPTWtqRdKI5fgBOnZrH586eytPr6nh5SxMH2kL86J87jYy045ytDX7yPbaMEHMouS4rzf4Y7aHEqJZ65bmtCEL/wk91e5hEarEhcoRzUNd1w7HiHTu3ml02ftcmYn5NW+r1Tws/Z043On2v2NNXkE+79AYv9ZrYJXFjiSn8mJiYmNBT6gUwK2fWyA5yyudg2rmjNCITkyMzrcCNVRbZ32JcKB60GIKKwzmZhlRmwYWLbseu67zV9QqyZEzavL0CyY+WynwXFklAjUzj7LJzKHQWZkq9wnGVYKIMgBZZxKLYUBM9LaRLF9xLoaLQ0vFnwqKIFDeyeVxWz6CP6e6V8bO5vhtvLIu9UoxgrBNB13G4zFKv44HJuS4auqO0BmLc84IfJTQdXbPgkeyG8DPGOT9feWoTezoaANjYurHPfQ9ufJA/bvvjUR0/rmhYJUNQ2NSoo2k6VrGno5xs6V/AtMkioi6RZGwn7Lqms/Wteoqn+cgvP/wzFY4ruGwyLps85PKh6vYQPoeFbKcFXdfpePRRDt5wI4maGqpPu5AfnfppKleupPzXDyLnDp4l9u7ednY2BWgZoAznaElPIiflOmkPGe/TtkY/bpvMpJzBxeXjlf933gwWlmfxzb9v4Zyfv83D7xygpiM83sM6ItsbAswtGdhlleOyZsSZ0Sz1kiWRXJeVtuDh59gvX9+T+ftI578/miShauS7x074SS9oDDVv60SiLdRX+Jld7CXPbTss5ycUTwIMXuo1wdvejyWm8GNiYmJCX4dB1iCtoE1MjicsksjMQg+7mkI4RDvVVmOVrMRXTEOXIfy47T5ucVSySg5S621G1nUcg2RWjWQM0wo8aPEi7v/QL7FIlkypVzSpsKW9x10kqW4au42VPo8K78VnURAoZ61oXJQnE/lMlsqZP+e6QR8zE+6cUNhc5ycSraRDktjXvQ+XDuKRHHomx4TKfBe6Djc/soZmf4wbpt5FpOY2Ci35NFokCI9++VVv9rUFSOiGuNTb8dMebecPW//AAxseoCZQM+Ljx5IqFtGYqLRGrexsDiAJPWKHxeLqdz+rLCIiEx9j4ad+VxeB9hjzzirr934jRDUl/CSGXuo1Jc+FFghQ/4Uv0vrjnxgdul54HuX2L7OiYDa1ysCr9b2p6zRciaPRcak/0setyHHSkZp4bmvwM7vEiyieOMHOvbFIIg9cv6hPPFZa1DpeiSZU9rYG++3olSbL2XPOTC3o/3MzUvI9dloDfR0/L2xq4IVNjXzp3OmAsUgxGGnHSsEoupEOxZkukT4BM5yORPr1Twtnoihw5vQ8Vuxt6+NYSzsPPYN09bJbjr6r10Nv72drvf/IG04wTOHHxMTEhCOXlpiYHK/MKfGyvdGPXcoiJBo/61Oyi2gOxDI29s8s+jyLYzHabQkKkUe9m82sIg8Oi5SZTKVLvdpDCVbXuJFSsxSrmENbxBCCbEkHr+9opV36ROY4ESWba6f9lnNnXDno46UdP6GU40e1nQbAGlHFxYk5oZuIpAOAdzUH+d5lc7l20Wy0WDluqcBw/AQax+yxdV2nNdwFgopX09nRsYOoYoihL+x7AVVXkXSNX224f8SPEUtqSFISi64T0+2s2teBIPY42vrr6gVpx49MXAC0sVu53r6iAbvbQuXC/H7vT7dNdtmkoTt+WkOcEq6j+qqrCb39NgXfvIuyB3+F5PP1BDw3Da3zVG1K+BmrsOJQXMFllcj32OgMJ0iqGjuaAgMGDJ8oVOQ6efDjizh7pvG+pkWt45UdTQE0nQE7egGZXJ/bzqxkyaTRW5gAKPDYaPTHuOEPq3ltRwuN3VHufn4biyqy+NI507DJIpEBhE9V03l1WxN1qdLpAo/p+BkJacdP79fvrJn5dEWSbGvoEWAypV6DOH7sFvGoSr3CcYV7XtnFDX9Yze7m4IiPcyJiCj8mJiYmgEUyVpuqcqrGeSQmJsNjdomXrkiSPHFp5rZ5JfloOlz24Lu8uq0JccrZPNgS5rn6Jv585s9GfQy3nlnJ9y+fk/l3Oijzrd2tJFSBIt34t8tWhJowJistiSnsbgmypGwe090VADSq5RnRaDBssogkCoRiClvqu5ldvASLDkFJxIXp9jleqMx3Y5NFPnZSOR9fXkFpljG5E4USGmUZzV/f7366rvNm7ZvE1ZFPaENxhbhu5O+cEw6j6Arb2rehqBoPrn2CRbEElwYCrKr5D/oIQ5bjioooJrBrOgV52azc345KT7D4QKVeVlkEXSYpCKCMTZlT2B+nenM7VacUI1n6v9zPCD9WeVDHgxaJ0P3MM9Te+TXuffq/uOyR76HrGpMf+wu5n/xkRkiemu/GKomZHJ0jkZ5MD9VtNFzCcaM7UK7bhqLpbKrrJpbUmDNIydGJwtkzC/jpR+cD0D6A8FPfFeG6h94b8P5jxfbGwYOdAS5bUMILnz+N/7p4hKX2g1DgsbGrOcDKfR3c88pOvva3zaiazi+vW4gsiQM63rojCW5/bD23P7aB+9/YB/SUKo0Frgns+GkLxhEFyO1VKnf6tDwEgT7lXplSr0EcPzb56Bw/6c9DIKZw8yPvZ/IQPwiYwo+JiYkJUOGp4PYFt/Orc3413kMxMRkW6UlMe+NJmdsunFvE/dcvJKFo3P7YBi75zRoes1zLSul6CirPG/UxzCr2cs3Sntyg9AXsv7e3YLeITLIY+SJez2T0ZDZoVpSUALSgLItLZ14NwEmVM1heOXguCBgdo1xWiT0tQdpDCRaV5zLLmg2AWxxamYnJ2OO2yay460P87xXzAKNEL8tpQVHyUQSBtu4D/e63rX0rX3rzSzy147ERP3ZLII5gMQSI88PGhf3G1o38e2ctitTKGZEIk0UHQVT8I8waiic1BFHBpussqSxlTXUnAXrOX0Huf5JokyUELMQFAZSxmZTvXNWEpunMOX3gDn5pYcQ9SKlXoraWg9ddT9Pd3ya8ejWb86fR+tk7qXz+eRwLF/bZ1iKJzChyD8nxE0uqtKTKP4YaLD1cgqkMozy30Ykp3bJ7MOfJiUSO0wgubhug1OvN3W28X93J+pquYzyyvmxvCJDjsg4a2myVRRaUj02ZfYHXlimNO9AWZtX+Dr5z6Wwm5RqORKdVItLrHIwlVR5+Zz9n/vRN3tjZglUW2VJvfEeMreOnx8k60WgLxslx2ZB6lVjmum3MK/VlPpff/cd2bn9sAzC48HO0jp90aeS3LqoimlC5+f/WHPeuudHCFH5MTExMMCaSn1/4eYpcReM9FBOTYVFV5EUWBWpbrVjDZ3PjrBsRBIHLF5by76+cyX3XLiChqPzEfz5rKz59TMaUDnfuCCc4uTKXcqfxuSrKrwJEFkh3k+gwuv0srMjiY1Uf4/unfp9HPn5FxhVyJNw2mfcPdAKwoDyLeXlzAXCJY9du12T4FHjsffJUSrMcRCKpbnTB2n73eW/LnwB4Y8eTI37cu1begb3gZQBmJJJMVXQ2tmzkqQ1bAChTFMKWBQDUdYysPXZcUUEwhJ+TpxcSSaisbOzlHpL6PxetsoimySQEAZLRET32YOiazo53GymdmUVW4cBlzKGUMOIcoNQrtGIF1R+9BqW1lfKHH6L6d3/lp0tvIP+665C8/btmZhd72dEYOKKLqvcq+5iVesUUPDaZvJTL4O09bdhkkan5o5shM17Ikki20zrgpDXtvBrv8OeOcIJCr33US4yHSoHHEJxKfHZmF3v5yIISrlvWs1BhdLUzzsFV+9o59+dv86N/7mLxpGz++eUzOGlyDroODos0qCBxtKR/N4/UYexEpC0Y79ctddaMfDbUdrGjMcBfVvfkrXkGDXeWUDQdZYRt79OOn9Om5fHIJ5fR0B3lU4+unZCC26GYwo+JiYmJickJjMsmc9E8o315Tuyj3HXSXZn7ZEnkqsVlvPHVs9nx/Qt44PpFx2RMjl7lWmdOz2fOzMtxilamlxnOj8VFs3FbvDitEtMLPDhkB1dOv3JYEwOXTSYYV7BKIlVFXuZOMjrqueWhCUcm40NZtoMuv+G4qI209r2zegXK3+/g3QOvAbAp2kJ7ZPgB0DElxp7AJkRbG4KuYy86hYWRMJta1vN+/W4AJAqoi0w2xtG6ZUTPJZbU0EUFOwInTzXKFnb7e11aD+j4EdF1C4ogoCZHf1Jet7OTYEeMOWeUDrpdMCWMFHjsdEeT+CNGmYWu67Q//HvqbvssluJiJj/7DO4zz6S6wxBrJucNLCbNLvbSEU5kwnDTxzuUdL4PjJ3wk+5alpty/Gyp9zOr2IssTZzpT57bSnsojqbp/PrNfby+oyVzX9p5dbBjfEtZIgkFt238SnDTLp1lU3L4xxdO44HrF/b5rXFapYzY8tN/7UbXdR6/ZTmPfuokqoq8VBUZjtV8j21MxaveTQsmGm3BWL/Cz5kzjLL0zz2+vk86n+sIjh+A2AhdP2nhJ89tY+nkHH5742LKs53IJ2jg+3CYON98JiYmJiYmH1A+c/oUAPa2hgbcxmmVj1knm3R3EjACHC+b9XFeveZ15hbnIwowtcBNWbaD+WW+Ptbv4ZC+MJxd4sUqi8wrNjKOXIVzj/4JmIwZpVlOWjocyAjUJHuVBB1cCY9fQ2Lrk2yzaCxV7egCvLX1T8N+jPpgT3ZQjqpRN/1TLE4kCalRBGfK3eOYz8GAUQZV17mnv8MckVhSRRcUbAhkOa3MLfGh9760FvufvFhlEVU3xIjEGLS0376i0Qh1XtB/qDNAUtWIKxoum8xJUwxHw5oddQT/8x/qP/8F2u67D+9FFzL5ySewlhldwQ60hSn22ft8vg9ldio4eXtKdHh3bzvzv/vvw3I0anuJEWPZ1cttk8l19Uw4J0K+T2/y3DbaQwn++/mt3Puv3dzy53U8+J+9KKrGrtR7UNsRYW9LkEAsOS5jDMeVQc+ZsSbdiWvp5BxkSTxMvOmd8dPkj3LatDxOm9YT0l5VbJwzY1nmBb0cP2NU+jietAXjmY5evVlUnsWUPBcHOyLcsLyC396wmEvnF2MZRJy1ycbrNNKW7u1Bo9Qrx2V8B59TVcivb1iM3TLx8wHH71NoYmJiYmJiMiosLM/io0vKWDIpe7yHAoAkCthkkTy3jco8F4IgkG3PJtsO//p/Z1KZ72ZagRvHUVxopS33C1KBoRWeCkpcJZTmmgHtxzNl2Q6iSaiUPdSKYYgFoG0XPHEtZJXzRc+lJHkGm/02yqK/4I0DL/PR5V8d8vGjCZWbHnkOUvO2AlWl3jGTRfkLQa/B7tuKVdOQ8pawqz6fQkWhboCSsyMRVzRssopTMCYpp07LZWuDn/NDsMahwQDuAJss0q67AUgEGnEkImBxDLj9cAh0RKne0s7Cc8sHDHWGHpeN2yYzs2479777G0r+UUO9piI4nRR8/WvkfPrTfSbJ1e2hTKe2gagqNtwROxoDfGhmAa/vbCEYV3huQwNfTLXOBtjS4MdllVB1fUy7erltMtlOC4IA+hE6S52I5Llt/Gt7M+truvjkqZPpjiT42b/3sPpAZ+r8FNnVHOQjD77Lp06bwl0XHvvvx3BCpTR7/CbVC8p83HVhFVcs7D/vymmVaA3EUVSNtmCcYl/fLKJZqXO6wDvWws/ROX6SqsY/tzZx0dxiI0D+OEHXddpC/Zd6yZLIm187u89taQfzQIyG48fnsBxXr9Gx4oP3jE1MTExMTCYgP7tmAR87qWK8h5GhNMvBhXOLDltdnV7oQRIF5pT4qMx3j/j46da36UBQQRB49rJn+cy8z4x80CZjzqRco0yo0JLHQYsMu/8Jj30UXPkcuPJB1mgvokYqWHugnHMs+bwfbyMU79tyV9EGnhgdaA8haXsB+EpnF1f6Y7QqbsTiC8lTVFQxTqmiYC1fQjduylSdumjbgMcbjFhSRRFUbIJxLp421VCbPtPt5d2WgQOOrbJEUDPO/Xh3DfxyLrz9kxGNoTddzWGev28jkkVkzpmDl3mlXTaT3n6J5jvuoEQJ8eb886h49FFmrH6P3M985rDPbnV7+IjCj9duYVKuk011hpPp/Wojh+u5TQ2Zkq+WQIyXNjdx5eLSVL7K2DgcQqnw6nQWDnDCt3I/lFy3NRN0e9Mpk/jFdQv56vkzeHefUSJ51ox82kNxYkmN6rbxyfqJjLPjR5ZE7jh7Kh57/8H/LquR8dMWiqPpUHiI8DOtwI1FEigcJJx6NJBEAYel/7ytofCzf+/my09t4tXtzYNut6a6k9bA2HQT7A9/NKXSC2oAACAASURBVElS1UfNMZV25ozU8dMRjmcC3z9omMKPiYmJiYmJyajz3OdPG9PVZbfNuIjv3QnGbXVjMbt6HdekO+m4xWLqZBntuc+C3cf2y+/j5ne+jqZJzJY/R0dIZW7O6SQFeHzDAzy+83HueucuLvn7JSx5bAlrm9f2e/zajghOaxNZqspN/ihzg1l0RZM8GZzPwpiR7VCm6mRXzAEESnQbtclgv8c6EnFFQ0HDnhJ+lk3OwSqJhCQfSAOfh1ZJJKAa5SOJ5s3okQ70lfdDqHXAfXqj6zrrW9b3yc5pPuDn7/duQEmoXHnnInz5Du7866Y+rZJ7EwzHuGPz3yn5y29wf+hDbPnur/nZ5POJzV2IaD18UtQVTtAVSR5R+AE4e0Y+7+xpo8kfZVdzgMm5Tg60hbno/hV89LeruPEP76NoGredMdUosxkDx4+u64RiSsYZmOuyIosCM4pGLjYfj6SDq/Pc1oy78ovnTud3Ny7mYydVcN6swsy2Dd2jHyQ+FMIJFZf1+C2jcdlkIgmFZr8hhhzafcwmS/zhE8u45YzKYzAWiXA/4c7bGvz89NVdA4amb6zt4qG3D2T+Hghd1/n0o2v5n39sH50BD4F03ld/jp+RYEs5dWLJETp+gonM5+aDhin8mJiYmJiYmIw6Y22lLvbZyffYmJI7MTr0fFAoz3EgCqAziZgo0mq1s/Li7/GJd79JJC4Srbmd/7nodGRRYL9yHrmKyoN7nuLHa37Muup/Mb2zHpeq8tymh/s9fk1nBCydlCcV/lj6Pe4Xb6Y1GOeJ7XHKtRwASm3ZVOQb5RvFuo8OFJ7d8+ywn4vh+NGwCYa44LBKfKgqn27PDMieMuB+NotIXDXEla6mjZxbXsLTdhFW3Dekx32j9g0++eoneW7fcwD/v707j4+rrvc//vrOZCYzk33f0zRN04UuaSldKEsLBQvIjoAbiIKC8kOuV7h4uT+vG16v/hRUUK/KRUVBQRDLquyUrdAVCqVbuqRJ0+zNvszM+f0xS7M3TZNmkryfj8c8mp45c86Z+WTm5Hzm8/182ft+DU/cvYloTxSX334y6VPiae7w8vjG8h7NfkN8zc34vvGvXLTnTVovvZrcn/2UxbMCFUKhCp3eSmsC1SKFQ5gR6/y5WXR4/fzoH9uxLPi/H5/NVYvyyE1y44yyEeuK4uazppOf4iHGOTqJnw6vH6/fCvcCy0xwMSsrPtwfZKII9U05pSC5R4XW6jlZ/Ndlc5mWfiReFWOU+Gnt9A7arHeseYLJlnDiJ6FvZc+ZxWlDnnHyuI7FGUVrP++HNVsq+MUru9mwr2dSp6wu0L9p7c5AhdesrHi2lA3cN6yxzUtzh5cXP6qi6QT1fBrxxE+w4qexvYuKhjbeP3CYhtbOIT++prlj0iZ+IvddKCIiIjKAm88q4tpTC05Yw2oZGdFRdrIT3TR0BqZT/lbJp3njrW/j68ggqvoG7li1kLm5CSwpTObvpR3cm5BB5aFtzLXHkRGXCwm5fLN+A/+sXEeHt53oqJ4XaftqW2mPbiGz00HuqZfzp+c+YsP7B6lv7WLm7BXQ/By5cfnEuxwkeRyUdE1luaniO29/h0RXImflncXXn7mGWUkzuP7U/xj0ubR3+egyFtHdqsx+8emTsbFw0H49TrsNb3ugj8V9tiaqo9z8PTWTq9ffD6feDAm5g+63JTgT2JsVb3LJtEt55U/bSUz3cPGtJbjjAgmlQ8GhHFVNR4Z0dB4op/m1V6l/6CFspXv5WckVXH/jLRi7nXm5CXicdt7cXcP5/fTY2BNM/ExNPXrFzKKCZFJjo3l8YzkxTjvLi1I5u1vlSXfdp9IeSaFthqaFvuuSufiOMsX8eJQajPcpBcn93l+cEce0tBiyE92s3VlDW6evx6yL3TV3eGnr9PW4QN+wr44ZmfHDnsa8w+ujy2dFdOInxhlFp9cfrojqXfFzQo8lOqrfip9Q0u7R9QdYFIy11+fn2gfeAQKz6eUmuTmtKIXfv7WPTq+/3y9eDgU/Dzq9fv75wSEuP3nwz5re3txVQ1pcNNMz4ob8mKoRTvyEegNe/eu3w8sWFyTzyI3LhvT46uYOTtdQLxEREZHxweWwj9gfknJiFaTEUNeQjM3YeKP6eeyd07h55k9467ZL+eIZ0wBYNSuDnVXNfK/ruzyb+wTur3wIX3wZrnqQ1Sd9ihZj8fq6e/pse29dAw12H0WeVM6fm0Wix0l9axfpcdGcs+Jm7qxv5uPFVwCQn+xhq7+Yn1RWMscWw+2v3s7/bLqPf9Zs5pWdTwDwXvV7XPLEJdS09Z1WvsPrpxMLV7fEj91mMDbboImfaIeNzrZUCnHyhidQRbCVTiptBl770aCvnd9v0dEV2Pb+xv2Ub6+npaGDRecXhJM+0D3x00HDY4+z+4KPs3vVKg5957tYXV0c/Pfv82zB0nBixGG3sXhqMm/tru13v3tqmomyGXKTjl71YLcZbl45jXNmZ/DwF5cOOltOYGjLKCR+2gPbjAn2lslP8QxpmNp4My83keVFKayek9nv/XEuBy/+6wouXxi4wO9vuFdjexddPj+fvX8di7//Ap+9fx1rtlTw6PoyLv/lW/zmtdIhHcvandV84ldv0t6t90pohipPBA/1Ch3b7upmnHZbeLansRDjtNPaz/shVI301HsV4fuf2FxBaXULpdUtbNhXz4yMOErykuj0+vmosv8eY6HPBZsJVBEdq1v+vIkf/WP7MT1mpCt+FuQn8i+rirntYzP4wWVzuXJRLu/srRtSRVuH10dTu3fSVvwo8SMiIiIiJ8yUFA/lNVHcMPVeWnb/Cw+s/i1fPnNOj6qAUG+SjWVNPLG1jgt//jpbyw8DsHjZbTgsiy0Vb/fZ9r76MiwDOXGBiqIkTyApc+nCHBwpU7j6yx+QOPfK4HHE8PvmJbhP+1fuK91GrmXnvvf/J7AdfztYFq/ufobdh3fzt+2P9tiPZVl0eP10GIto+7FdRETbbXR4/ZzpCDzHGd5AJcrLM1fApj9C3cAX2mu2VPDtpzYEjrFxH9vXVeJ0R1EwL6XHelWNHWBZLHv1MQ7eeSe7mv0k3347hc88w7TnnqNmRglAj9d8WWEKu6tb+m38uqemhfxkz6DTLHf3ueVT+c01i5iXmzjoeoEePyPf3DlU8RPJlSYjITU2mj9dv5TsowxDygkm7Honfrw+P8t/8BLT73yWTfsb+Pi8bEqrW7jl4U3c9tf3gMAU50OxdmcN7+6t5/luwwtDSb2YMWzufDShaqbdVS1kJET3aWp+InkGaHZ+8HA7mfEuWjp9vLu3nk6vn3te2EF8MHF78HA70zPiWJAfeL998+8f8PL2qj49gUIJpPPmZvH6rhpqmzuGfGyHW7uoae5kx6Fj64lW3dxBdJSNuBF6L0ZH2fnqqul8ZWURVy/O58YzA18WPLd18KbWALXNgSFhqZP0SyMlfkRERETkhJmaGkNDaxdPb4SC+EJK8pL6rJOX7OGuS+fw5y8t5S9fXEpHl5/Lfvkmf1q3D7vdSY5l40Cv2bg6vX587bsAyEkOTB0ems3pE6EhDU5PuBpn2bQUKps62HHSrSSuuJP/2beLmR1dzGvvoMFmaKjdybay1wB47MM/4reONBMNzaTUacBlP7YKgfxgX6rUxkCVxhWdCRTEF/Ci2wU2B7zygwEfu+1gI9lWWeAYOroo3VRFztxkGnoNl6qsb+Grmx/lwi3P8u7s07hpyY08kLWM6MKpGGNoaj8ynXvIqcFZyd4q7Vv1U1p99Bm9hmO0hnptrwxcnE7EKp/hCCWGyut7JnFqWzrDvwvLi1L42dUlrL19JX+6fgk3njmNzHgXhxqHlhwIbfuJTeXhZa3BYUue6Aiu+Am+B0prmsmKH/0+PoOJcdp79PipPNxOTXMHhxrbWT0nE7vNsH5vHY+sL+NAfRvfv2xuuLiwOCOW7EQ3P7hsLoca27nugXc576dr+We3Wb5Cw65uOL0Qn9/imfcP9tj/26W11AyQDNpTGxjuua+ulbZ+hqMNpLopMJX7aCXUCtNimZkZ1+e59GfbwUAl1JRkz6gcS6RT4kdERERETpiCYOJj28FGLlmQM+AFwaeXTGFhfhKLCpJ5+pbTWFqYwp1/28pX/7yZXHsMB7w9v3kub2gj2bkfgJyM+QB8fF4WXzqjkKL0vj0pVs5IB+Clj6p4Kf2z/NH/WR6tOMgVbYHje2vLc7zfXEGyz0d5VyPrDqwNP7ajyw/48BlzzBU/K2ekYQxsL0vgmbIK5lhTODv/bNbXvMfh+VfC1sfA3/+F1YGGNpy2VgB89i7mnb2FB2rr+Mxv1+H3B77d93d2UnTvd1m97x0eKl7F92ZeSpTDwa9f282GfYHmzaEqm+6zLc3OjifeFdVnuJffb7G3dnQSPyM1q9f2yib21R6ZrnxzWQMxTjtF6RNrFq/hyoiLxm4zfYbDhIb+/OTK+dx/7SkYY7DZDMuLUrnjvJnMz0sYclPoA/WB38tXd1SHK0nGQ+VV6D1Q09zZZyr3E34s0VHhZFmH18dlv3iDz//uXbx+i2lpMczOiueNXTX8/KWdnDwliQvmZlEc/GwrDvbduXpxPq/etpIff2I+Xr/FTX/aGE54HGpsJ8HtYH5uAtPTY3sM9+rw+vjs/ev49QBD+/bUNANgWYFhcUNV3dQxYlO5D2T1nEw27K8fMGkV8sr2ajxOOycX9P2yYTJQ4kdERERETpjTi1O58/xZ/PCKeVx/+sCzX3WXEhvN7z53CrecPZ01WyqIJ5Ey48PyHUmQvLOnFo+jkijLIi37FADOnpXBN86f1e82MxNczM6K55ev7OLzv1vPCwmX8wXXT3gq5lYAXi59lQabj2s67CT4fDz2zt3hx7Z7fRhb4CIjOurYqgRSYqM5OT+JQ1YSeV4vlSaDs/PPxmf5eM3lAL8XWvqfhr28vg2b7cjFzYdpdt6tbeKjyiZe2HYIy+fj4B13kPPheu6ddykPzl5Np9/iyyunkZXg5uuPvkdbp4/mji7cDjtR3YZu2W2GxVNTeLNX4qeysZ32Lj9ThzCj17EKXeiGklbDdcMf1nPeT9eGhxltLmtgXm4idjV/ByDKbiMz3tVnqFeomqcoPbbfXkw5iR7KG9oGnEa8uwP1bSzIT8Trt3g6WH3RGk4wRm7ix9Pt2KaPcaIwxnmk59Uj6w9Qcbid9w4EhrhmJrhZVJDExv0NHGrs4OvnzsAYQ0leIjYD09KOHLszysblJ+fy1xuXkeB28B9PbMWyLCoPt5MRH6i+uWh+Nu/urQ//TuyvbaXLZ1E6QFKntPpIYvVYhnuFKn5G0zmzM7CsQBJ/IJZl8cqOKk6dljLhZvcbKiV+REREROSEiY6yc8MZhVy5KK/HRdfR2GyGL51RGNiGSafZZuNw3Y7w/Y9vLMflbiDD5ycqPntI21w9J5PGdi+fXz6VJ76yHM+UhWyvzybKgg/YDcD03HO40J7Ei027qGsMDGPp6PLjMq3B53PsVQLnzM7goBXoy7PHl8ZJqSeR7knnxbbgMJnG8n4fdyCY+HH7/eS1XsL2lwwubwfJMU6efOg59nziShqfeZbnll/B88Wnhx83JzuBH31iHntqWvjv5z6iucPXbxXGqdNS2F/XGq7egO4zeo3GUK/ABdjxNHhu7/Kxv64Vr8/iiw+u596XdrLtYCPz8wbvLzTZFKbF8FFlzwv2UMVPxgAzWWUnumjt9NHQ2v/U399/ZhsvfXSItk4ftS2drJqVwczMOP4WHO4VimskN3fuPtzxzOK0MTySwLCz1g4fHV4fv3x5V4+ZubISXCyaEpjRa3lRCsumBT4/vrKyiHs/tbDf2doSPU7+9dxiNuyr5509dRxq6gjH+qKSwGfkU8Gqn721gfd86P3eW2lNCzmJbhx2w45DQ6/4qWpqH/XEz+yseLITXLzQrb9Ub3tqWiiraxvzGI8lJX5EREREZFyIiY4iOcaJ158DwIGDgUbH5Q1trNtTR5ezlWyba9BZtbq7acU0Xr1tBd+8cDYuh52pKR4q6jtJMFHsd/owlkVi8lKuOOVreI3hybXfAgIVP67gkCtX1LH3i/jkknwuPW81v07+Os/4FmMzNlbmreSNwztpMwYa+/araO/yUdPcgc3WicdvUblzJlc8/Ft++uYvuXf343z5sf+m9VA12T/+fzw2fQWzsuLDjy1IjeHUaal87tQCfvfmXtaV1oZn9OoudDH5dmldeFnpKCZ+QsmnUNPZ3vx+iyc2ldPY3jfxYFkW7+6tC1cifPeSkzh/Thb/75878PotSpT46WFBfhLbKxt7DK2ramzHZiBlgJmscgdoCg2B1/+BN/awZnMF5Q2B90JOoptLF+SwaX8De2tawjNQRfJQr+79h+bmJIzhkQQqfjp9fh5et5+Kw+38xwVHqhUzE1ycVpTKqdNS+PduVYz5KR7On5s14DYvXZBDbHQUj244wKHD7eHEz5SUGObnJYaHe+0Nvs/L6trw9VOBt6e6heKMWApTY4dc8dPp9VPf2kVa7OgOoTPGsGp2Bmt31vSYVa67V3cEqijPLE4f1WOJZEr8iIiIiMi4kZfsobp9CgAHaj4E4O+bAxUGtaaTbOfQL/gddhtTUo4kNApSY/BbkBUzB4Db6xqods1l2uzLKcHFXyvfxGpv4ondf8Y79bcARDuOPfET73Jw/RnT2JN7MWXBa6iz88+m3d/Jm24XNPadajnUa8Xj8uO2LBbOK+be0z5HVkstyRvf5Ml5q7nrqm8Tf/75VDV1Mi94EWszganrAW4+qwgIJHNi+7kYn5ERh9th54OKw+Flu6uaiXHayRygKuR4hI7hnLtf476Xd/W5/4Vth7j1L5v528a+FVA/e3EXn/jVW/z8pZ0AzMyM5+efXMAtZxWRn+xh8dTkET/e8WxBfiJ+i/DQIQgM9UqNje4x5K+7nMTA782B+r6Jn6YOL10+i4qG9vD9uUluLirJxhj426by8AxVMZHc3LlbpYxtjIcGhiogf/bSLkryEvns0imkxDhx2m2kxDhJ8Dh46IalnJQ99ASVxxnFBXOzeOb9g1Q1tfd4H180P5sPKhrZVdUcbt7c6fP36etkWRZ7alqYmhrLsmkpvLajml1VR6/6efr9wOdYduLo905aNSuDti4fb+yq6ff+V7ZXU5gaQ37K5GzsDEr8iIiIiMg4kpfkZtfhwCxdt5U9yeefu46Htj7Osjw/1TbIiR3aMK/+FASrWjxt15G9+2p2115CRVfgQuHyWZ9kb5SNDWu/x1uHXgJ7YGrgaOfwLyTS41zUtnTQ5fOzKHMR8c54XoqJgaa+iZ9Q1YUn2sJlwfcvm8vP7/kyRU8/ybR//oOMW7/KWxWtPLu1kk6fn8K0GGKcdnKS3OEhI6mx0aTGBqo7+rsYt9kMxRmxfHTwyDf6pTUtFKbFjsqsPN17v9z38i6qmo5U/liWxS9fDQy3691M9p09ddz9QmCYX6ivT0FqDDab4WvnzuC121eSPEAVy2S1IFgBtXF/fXjZoab2AYd5wZFp4Ptr8FwXnBq7vKGtW+LHQ1aCm2WFKTyxuTxcXRTJPX5SY6NZXJDMA9edMtaHEk6E1rV08tVV0zHGsKQwmfwUz3G9/z67bAo+v4XfOlLFBYHm98bAmi0V7K1pwWEP7KP3cK/qpg7aunwUpHq4+awi3E47337yg0F7P/3zg0q+/uh7LC1M5sL5w/9MHqolhcnERkfxwra+w73au3y8XVrLGZN4mBco8SMiIiIi40hesoeyhiMXQZUH3uJw3IPs8dyBZQzZSUXD3vbUYPXPix+0sc9ayO/851Ed7INy7oIbicXGQ6Vr2Nv4YfgxLsfwG8JmxLuwLKhp7sBhc3Bm7pm86vHgP9y3wiV0ce23efEYG+nxLuJdDjy5OTgyM7nqlDzS4qK59S+bAZiXm0BGgoupqT2Pb0ZmYPaf2GhHv8c0MzOe7Yeawhd1u6uamTYKjZ0B4t2BYzhrZjpdPj93Px+o3mls7+Ibj7/Ppv0NGNM38bN2ZzU2A8sKU/D6LZJjnCS4+38+EpDocVKYFsOm/Q3hZYcaO8iIH7j/SpLHgdth77fip641kPipbGxnf10rDrsJz9506YIc9tW2hqsv3P00jo4UDruNR25cFp7lbyyFhp3Nz01gRTBJ8Z2L53D/tYuOa7tzchJ4+xtn89D1S7hkQU54eUa8i6VTU3gymPgJVcntre2Z+CkLxj8vyUNqbDRfO6eYtTtrwknX3tburObmhzYxNyeB3157Sr+Nw0dadJSdM4vTeGFbVZ9m8W+X1tLh9bNihhI/IiIiIiLjQn6yB6/f4qfLfsHjs7/Mbf4LOL98Bks9+STYnMyd9YlhbzupW5XIWTPTSYlxUh2cItjj8HBBzgqed0XhxR9eL9p5PImfwIVyaHalJVlLOGyD3U37+qxbXt+G3WbopAu36Xsh5XLY+eLphXR6/dy8soiTpyTzg8vm8Y3zZvZYLzTtc+wAw29mZMZR19JJdXMHbZ0+yhvaeswYNJJOKUji4RuW8ttrFvGZpVP4y7v72XGoiV+8vJtH1pdx7bIpXDA3i91VPS9EN5c1MCMzPvwNfsEkHr5xLBbkJbG5rD6c1KtqHLzixxjD7Ox43iqt7XNfqOLH57d4Y1cN+cme8FCp1XMycdptrN1Zg8dpH/MhVONFKBa3nlMcrvBJjY3uMRx1uJJinJxalNonCXNxSTZ7alqoONzOKQXJeJz2PhU/oWbvoWqhzyydQnFGLN99+sNwT51P/eZtzvjhy3zpwfXc8If1TEuP5ffXLe53SOloWTU7neqmDj6oaOyxfOO+emwGlkxNOWHHEomU+BERERGRcSMvKXCRX3ooh5jpn+P26vOoy72De656ltc/u4HCtJOOa/u3rprOTSumcc9VC0iLc1HddGT69CnJVwFgug1xcDnj+2xjqEIXeqHZlUrSSwDY3NZ3WuLyhjYy4120+724Tf8XU58/bSoP37CUfzmnGIDFU5N7NHmGQB8fgNh+mjsDzAxWBG2vbKK0JlBpM22Uprk2xrBsWgo2m+GWs6YTEx3F95/ZxjPvH+S06Wl8++I5zMqKp7KxnebgsCG/32JLWQMleYksKkgCoGAELowng4VTEqlp7qSsro1Or5/als5BEz8QGA607WAju6p6NvSta+kM//xBRSPzc4/01opzOZidHfi9O5aZ+ya7RVOSWHv7yhNafXT5yblcs2xKcP/JTE+PZUtZQ491yupCiZ/AZ6/DbuNbF55EWV0bv3mtlH21Lby5u5Z4dxTbK5uYnRXPg19YTILnxFbhLQ4mdroPZ4RAtWRmvKvfmc8mEyV+RERERGTcyEsOfOv8vae38bF7XqO6qYNLuw1fOF63rirm31bPxBllIy0umqpg4uedPXXc9bfD+Nry8LbnhdePdsYNe1/pwYqfqmDiJz8un2Sbk81WC/Tqn1Fe30ZOkps2y4fb1v8Fld0WSKTYB6mwKA4mdgaaaWlGt8TP7uCMWYWjNNSru6QYJzevLOKV7dXsr2vlgrmZAOFhZnuCx7KntoXGdi8leQnMzUkgJcZJSb5m8BqKBXmBRNmmsvpwP6XBhnoBXDA31Aem50xzoaFeIfNyezYcDs2q5nbqcnOojDHkJZ/Y6jWH3cZ3Lp7DzrvO47TpqXxsTiYb9zeEkz0QSJykxkb3SJycWpTK+XMzue+VXTyyvgyAn129gFduW8njX15OauzoTuHen+wEF2lx0Wzulbg60NAW7lc1memdKCIiIiLjRnaim1lZ8ayckUZ7l484VxRnzRydb8jT46Kpbupga/lhvvC7d8lOcHPjzLtoK7sWRzAx44oefuInNSaalBgnf91Yjs9vYYxhvjubLU47tPe8eClvaCM30U0bPty24TcuLs6IwxllIz2u/0qPlNhochLdPLaxnE376zHmxFXUXHtqATmJbuw2w7mzQ4mfQLXR2l3VPPv+wfDsXyV5Sbgcdl7/t7P4zJIpJ+T4xrvijFg8Tjsb99VTVhfo25KdOPgFcXq8i8UFybzQq59LXUsnUd0SjPPzeibfQomggw3tSORzBGd2u3BeoBHzk+8daTBfVt/aoyl0SGha+fte3k1OopupqWNbeWeMoSQvsU/FUkVDGzlH+T2fDJT4EREREZFxw2G38exXT+eB6xZz/7WncPeVJaPWPDQtmPi59n/fIc4VxYPXL2FF0VQsXxzTmgMJCYd7+H0jbDbDNy+czZayBu5/vRSAkqQZ7HM4qKvcAu/8Bg6X0+Xzc/BwsOIHC5d9+N+mx0ZH8cwtp/OpxfkDrvOti05i28FGHnhjL6f10xdktLgcdn72yRL+69K54X5LU1JiiLIZfvjcdm7600b+tqmchfmJFAWHn7nVQ2bIouw25ucmsqmsIdzAdygX64unJrP9UBNtnb7wstrmTtLjokn0OIiymT5DCucFh355/QPP/CSRJy/Zw8L8RNZs7pb4qWvrtxIpN8nDTWcGmumfUZw6KjP/HauSvERKa1o43NoFBHpQVR5uP2qCczLQoEsRERERGZdGe3re9Ljo8IXrH69fQk6im8Tg7FEbym/nD5/uJDNt1nHt46L52Tz13kF+/M8drJqVwcysxXDgH+ze/ndi3/5fHIcPUHnyv+G3ICfRTVuFhTtq8L4sR1N0lJ4958zO4N9Wz6ShrZN/WVV8XPs6VidPSebkKcnh/zujbPzyMydzuK2L4oxYitJj1TfmOCzIT+TXr5Wy7WAjzigb2QlHvyCen5uIz2/xfvnh8MxP9a2dJMc6SSFwsd87OVg4xtUfMnwXl+Twn2s+YHtlE0XpsVQ0tPHxeVn9rvulMwvZW9vCJwdJJJ9IC4KVZ+v21HLuSZkcamzH67c01AslfkRERERE+lWSF6gsueeqEgqDQ45CvXH8VjTLT7r0uPdhjOGuS+Zwzt2vuusLxgAADe1JREFUcftf3+OeTy4BYOvel7g1P4c7Kl4nbdotAGQmOPAagztq9C9ibloxbdT3MVTnzM4Y60OYMBbmJ+H1Wzzz/kEKUjxDqpYK9VDaXFYfTvzUtnSSHBPNraum9xjyFWKzGW772IyjNo+WyHP+3Cy+/eQHrNlSzqeWTMHrt8KNnXtzOezcfVXJCT7CgS3ITyIn0c2dT2xlVlZ8uHG+hnppqJeIiIiISL8W5CfxwtfOZE5OQr/3j9TQhvR4F/954WzW76vnH+97cVvwlK2dRrudDa0HKA82Wk2ODUwj747S9OUyPKEkTk1z55B7sqTGRpOb5O7RNLeupYNkj4OF+UnhYV29fWVlEVecnHv8By0nVFpcNMuLUlmzpYLN+wMxn5E5OjP7jTS3087vrjuFji4fn3vgnfDU7v31KJpslPgRERERETkG583JHPFtXroghxUz0rj7hV0U2NzsiA70uNlps2g8tAeARGcgAeRyKPEjw5MaG01+sF9LwTEMxyrJS2Ttjhruf30Ph9u6qG/pIjnmxM/cJCfGRfOzKatr476XdxEXHcX8AZJ7kWh6Rhy/uWYRZXVt3PX0NuDoTcwnAyV+RERERESOwb2fWsj2760e0W0aY/jYSZk0d3jJcx7pXbTb6cBWuYm0uGj8XYcBcDvHx7fvEpkWBqt+jqUPz/85azrTM2L57lMfsvT7L9Lc4SUldvizy0lk+9icTJxRNj482MipRSlE2cdX2mBJYQo/vnI+nT4/SR6H+oKhHj8iIiIiIsfEbjPYbSM/01XoQtzyZgD7icJGiw3s9e+Sk7iI9rZ6ADzO4U8hL7IgP4knNldQkDL0xM+MzDge//JytpYf5g9v7eXZrZXMzo4/6uNkfIp3OThrRjrPfVDJ6dNHt4n+aLlwfjatnV6qmzrG+lAighI/IiIiIiIRINRAektNASS9S6FzDjs63yOr62UWJl9BW0fgAsbt1AW3DN/FJdnUtnSycErSMT92Tk4CP7xiPj+8Yv4oHJlEkk8tyef1XTWsnJk+1ocybFedEhmzjUWC8VWzJSIiIiIyQaXGOolzRVFaXYyvLY9ELgdgm8PFDVXfp621FgBXtBI/MnyJHidfO6cYxzgbviMn1hnFabz/rXM1I9YEoXe7iIiIiEgEMMZQmBaL5Yujde9XOFSTRm5sPvcnJvAh+2nb/CAAbtf4abQqIuPXSM1cKGNPiR8RERERkQgxLdjnxxllY1dVMzfP/i86OtO5NSONX/nrAHC7jn2IjoiITF5K/IiIiIiIRIjCtEDi55xZGbR3+dlb6aF1701cmHc5HwWneHe7k8fyEEVEZJxR4kdEREREJEKsmJHO4oJkrjolD4BXtlcBUfz78v/gFwtu4zp3AWlpJ43tQYqIyLiiWb1ERERERCLEnJwEHrlxGY3tXdgMbNhXT4LbQWx0FKfPu4bT510z1ocoIiLjjCp+REREREQiTLzLweo5mfgtyE3SrDoiIjJ8SvyIiIiIiESgL5w2FUDTKYuIyHHRUC8RERERkQi0MD+JTy7OZ2mhmjmLiMjwKfEjIiIiIhKBjDH812Vzx/owRERknNNQLxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCUqJHxERERERERGRCeqoiR9jzP8aY6qMMVu7LUs2xjxvjNkZ/DdpdA9TRERERERERESO1VAqfn4HrO617A7gRcuypgMvBv8vIiIiIiIiIiIR5KiJH8uyXgPqei2+GPh98OffA5eM8HGJiIiIiIiIiMhxGm6PnwzLsg4Gf64EMkboeEREREREREREZIQcd3Nny7IswBrofmPMF40x640x66urq493dyIiIiIiIiIiMkTDTfwcMsZkAQT/rRpoRcuyfm1Z1iLLshalpaUNc3ciIiIiIiIiInKshpv4WQNcG/z5WuDvI3M4IiIiIiIiIiIyUkxgpNYgKxjzMLACSAUOAf8JPAE8AuQD+4ArLcvq3QC6v21VB9eXyJUK1Iz1QciQKFaRTzEaHxSn8UOxGh8Up8inGEU+xWj8UKzGh8kQpymWZfU7zOqoiR+ZXIwx6y3LWjTWxyFHp1hFPsVofFCcxg/FanxQnCKfYhT5FKPxQ7EaHyZ7nI67ubOIiIiIiIiIiEQmJX5ERERERERERCYoJX6kt1+P9QHIkClWkU8xGh8Up/FDsRofFKfIpxhFPsVo/FCsxodJHSf1+BERERERERERmaBU8SMiIiIiIiIiMkEp8TPOGWPyjDEvG2M+NMZ8YIz5anB5sjHmeWPMzuC/ScHlM40xbxljOowxX++1rf81xlQZY7YeZZ/9rjfQPiVgpGI10HYG2OdqY8x2Y8wuY8wd3ZbfHFxmGWNSR/N5jyeRFKNu9//MGNM8Gs93vIqkOBlj1hpjNgdvFcaYJ0bzuY8nYxQnnZ+GYQRj5TLGvGOM2RLczrcH2ee1we3uNMZc2235XcaYMn3u9RRJMep2/5re77XJLFJiZIyJ63Ze2myMqTHG3DPaz388GaNYPWeMaTDGPNVr+VRjzDoT+PviL8YY52g97/FmpOLUbXt2Y8ym3jHotc7EPTdZlqXbOL4BWcDC4M9xwA5gNvBD4I7g8juA/w7+nA6cAtwFfL3Xts4AFgJbj7LPftcbaJ+6jWysBtpOP/uzA7uBQsAJbAmtBywACoC9QOpYvzaRcoukGAXvXwQ8CDSP9WsTSbdIi1O39R4Drhnr1ydSbic6TsH7dX4a21gZIDb4swNYByztZ3/JQGnw36Tgz0nB+5YGj0efexEao+D9lwEP9X6vTeZbpMWo23obgDPG+vWJpNuJjlXw/rOBC4Gnei1/BLg6+POvgJvG+vWJlNtIxanb9r4W/Nx6aoD9Tehzkyp+xjnLsg5alrUx+HMTsA3IAS4Gfh9c7ffAJcF1qizLehfo6mdbrwF1Q9jnQOv1u08JGKlYDbKd3hYDuyzLKrUsqxP4c3BfWJa1ybKsvSP7DMe/SIqRMcYO/Ai4fUSf5AQQSXEKMcbEA2cBqvgJGoM46fw0TCMYK8uyrNC3oY7grb9mkh8Dnrcsq86yrHrgeWB1cBtvW5Z1cCSf30QQSTEyxsQSuID63sg9w/EvkmIUYowpJnAxvPb4n+HEMQaxwrKsF4Gm7suMMYbA3w5/7b1PGdnrXGNMLnAB8NtBdjmhz01K/EwgxpgCApUc64CMbr+clUDGCTiEsdjnuDRSseq1nd5ygLJu/z/AABdL0lcExOhmYM14P8mMtgiIU8glwIuWZTUOdZ+TyQmK02B0fhqi441VsJR+M1BF4A9onZ9GWATE6LvAj4HW4Rz/ZBABMQq5GviLZVmazWcAJyhWA0kBGizL8gb/r8/CAYzA3xH3EPgy1T/IOhP63KTEzwQR/PblMeDW3hcewQ/7E/qBPxb7HC9GKlaDbUeOz1jHyBiTDXwC+PmQD3oSGus49fJJ4OFhPnZCi7A46fw0iJGIlWVZPsuySoBcYLExZs6oHOwkNdYxMsaUANMsy/rbsR355DHWMerlanRuGlCExUoGcLxxMsZ8HKiyLGvD6B1l5FPiZwIwxjgIvBn+ZFnW48HFh4wxWcH7swhkoYez7bxuzeFuPMrqI7LPiWykYtXfdvqJVTmQ1+1hucFlMogIidECoAjYZYzZC3iMMbtG5AlOEBESp9A2UgkMB3v6+J/ZxHKC4zQYnZ+OYqT/lrAsqwF4GVhtjFnSLVYXofPTsERIjJYBi4LnpteBYmPMK8f3zCaOCIlR6FjmA1GT/WJ3ICc4VgOpBRKNMVHB/+uzsJcRitNy4KLg59afgbOMMX+cbOcmJX7GOWOMAe4HtlmW9ZNud60BQp3IrwX+PpztW5ZVZllWSfD2q6OsPiL7nKhGKlYDbaefWL0LTDeB2QKcBL71WTNyz2jiiZQYWZb1tGVZmZZlFViWVQC0WpZVNFLPc7yLlDh129QVBBoFth/vc5tIxiBOg9H5aRAjGKs0Y0xi8Gc3cA7wkWVZ67rFag3wD+BcY0ySCczGcm5wmQwgUmJkWdYvLcvKDp6bTgN2WJa1YuSe6fgVKTHqtilVog5gDGLVr2C1yssE/o4Y0j4nk5GKk2VZ37AsKzf4uXU18JJlWZ+ZdOcmKwI6TOs2/BuBk64FvAdsDt7OJzBm9EVgJ/ACkBxcP5PAeMVGoCH4c3zwvoeBgwQaYh0AvjDAPvtdb6B96jaysRpoOwPs83wCHfB3A3d2W35LcHteoAL47Vi/PpFwi6QY9Vpn3M4gMBniBLwCrB7r1yXSbmMUJ52fxjZW84BNwe1sBb45yD4/D+wK3q7rtvyHwe35g/9+a6xfn0i4RVKMut1fgGb1itgYEZiRaOZYvy6ReBujWK0FqoG24OM/FlxeCLwTjOGjQPRYvz6RchupOPXa5goGmNUreP+EPTeZ4BMREREREREREZEJRkO9REREREREREQmKCV+REREREREREQmKCV+REREREREREQmKCV+REREREREREQmKCV+REREREREREQmKCV+REREREREREQmKCV+REREREREREQmKCV+REREREREREQmqP8PdsrD7gT6XzIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2oR43ROBG-U7"
      },
      "source": [
        "## Tiebraker open question ##\n",
        "\n",
        "**18) Use your favorite machine learning approach to build a predictor\n",
        "of $Y_{t}$ given its past, without using the last 200 observations,\n",
        "kept aside as a test dataset. Compare the obtained predictor with the\n",
        "ARMA predictor on the test dataset.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qDxLwyq9CXQb"
      },
      "source": [
        "import numpy\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas\n",
        "import math\n",
        "from keras.models import Sequential\n",
        "from keras.layers import Dense\n",
        "from keras.layers import LSTM\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "from sklearn.metrics import mean_squared_error"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}