Lectures/Lecture9/3dasm_Lecture9.ipynb

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    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "## Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 9\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor"
   ]
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    "**What:** A lecture of the \"3dasm\" course\n",
    "\n",
    "**Where:** This notebook comes from this [repository](https://github.com/bessagroup/3dasm_course)\n",
    "\n",
    "**Reference for entire course:** Murphy, Kevin P. *Probabilistic machine learning: an introduction*. MIT press, 2022. Available online [here](https://probml.github.io/pml-book/book1.html)\n",
    "\n",
    "**How:** We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.\n",
    "* If working offline: Go through this notebook and read the book.\n",
    "* If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.\n",
    "* If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book."
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    "**Optional reference (the \"bible\" by the \"bishop\"... pun intended 😆) :** Bishop, Christopher M. *Pattern recognition and machine learning*. Springer Verlag, 2006.\n",
    "\n",
    "**References/resources to create this notebook:**\n",
    "* [Car figure](https://korkortonline.se/en/theory/reaction-braking-stopping/)\n",
    "\n",
    "Apologies in advance if I missed some reference used in this notebook. Please contact me if that is the case, and I will gladly include it here."
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    "## **OPTION 1**. Run this notebook **locally in your computer**:\n",
    "1. Confirm that you have the '3dasm' mamba (or conda) environment (see Lecture 1).\n",
    "2. Go to the 3dasm_course folder in your computer and pull the last updates of the [repository](https://github.com/bessagroup/3dasm_course):\n",
    "```\n",
    "git pull\n",
    "```\n",
    "    - Note: if you can't pull the repo due to conflicts (and you can't handle these conflicts), use this command (with **caution**!) and your repo becomes the same as the one online:\n",
    "        ```\n",
    "        git reset --hard origin/main\n",
    "        ```\n",
    "3. Open command window and load jupyter notebook (it will open in your internet browser):\n",
    "```\n",
    "jupyter notebook\n",
    "```\n",
    "5. Open notebook of this Lecture and choose the '3dasm' kernel."
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    "## **OPTION 2**. Use **Google's Colab** (no installation required, but times out if idle):\n",
    "\n",
    "1. go to https://colab.research.google.com\n",
    "2. login\n",
    "3. File > Open notebook\n",
    "4. click on Github (no need to login or authorize anything)\n",
    "5. paste the git link: https://github.com/bessagroup/3dasm_course\n",
    "6. click search and then click on the notebook for this Lecture."
   ]
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    "# Basic plotting tools needed in Python.\n",
    "\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "from IPython.display import display, Math # to print with Latex math\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
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    "## Outline for today\n",
    "\n",
    "* Linear models for regression: one-dimensional examples\n",
    "    - A practical session on how to train linear regression models (no theory!)\n",
    "\n",
    "**Reading material**: This notebook + Chapter 11"
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   "source": [
    "## Today's lecture is going to be more practical\n",
    "\n",
    "Since we covered the fundamentals of Bayesian and non-Bayesian machine learning..."
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    "* Today we will focus on how to train **linear regression models** using [scikit-learn](https://scikit-learn.org)"
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    "* Soon we will derive the models that we are going to cover today..."
   ]
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   "source": [
    "As we learned in Lecture 2, let's load the pandas dataframe that is in the \"../data\" folder:"
   ]
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     "text": [
      "            x           y\n",
      "0    9.516939   29.749036\n",
      "1   72.398757  642.132203\n",
      "2   17.950326   36.648484\n",
      "3    9.440853   18.604106\n",
      "4   78.791008  769.656168\n",
      "5   16.961121   57.971010\n",
      "6   65.410368  559.093313\n",
      "7   58.671099  463.686613\n",
      "8   21.550603   92.242676\n",
      "9   36.866913  197.688573\n",
      "10  15.728748   56.885233\n",
      "11  58.511494  388.753795\n",
      "12  57.419190  399.807488\n",
      "13  38.459157  213.181519\n",
      "14   8.841742   20.387384\n",
      "15  60.733051  516.341724\n",
      "16  49.256663  307.931956\n",
      "17  35.895121  181.123049\n",
      "18  79.195652  750.178284\n",
      "19  69.156669  553.153541\n",
      "20  77.634896  746.031880\n",
      "21   9.254011   20.810698\n",
      "22  15.451468   39.872527\n",
      "23  14.438247   42.118771\n",
      "24  13.410999   44.775122\n",
      "25  53.747057  375.013937\n",
      "26  10.283719   19.438868\n",
      "27  82.005477  742.336845\n",
      "28  81.805562  706.620282\n",
      "29  51.837742  345.212876\n",
      "30  20.283785   65.303165\n",
      "31  28.359647  155.185137\n",
      "32  74.993715  676.628982\n",
      "33  21.827564   81.150935\n",
      "34  70.519111  700.520033\n",
      "35  74.208532  622.453560\n",
      "36  14.518958   40.927570\n",
      "37  13.357644   39.770922\n",
      "38  75.346253  707.973754\n",
      "39  44.923956  251.300805\n",
      "40  26.801159  124.098654\n",
      "41  29.906265  118.100900\n",
      "42  40.226356  215.082100\n",
      "43  66.282662  537.845048\n",
      "44  47.342777  308.558833\n",
      "45   3.087674    5.947997\n",
      "46  21.254611  101.295276\n",
      "47  46.939484  345.778352\n",
      "48  38.875692  219.095582\n",
      "49  76.705452  742.720134\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "# read csv data provided by someone else (this time I also specify that the first column provides the indices)\n",
    "car_prob_df = pd.read_csv(\"../data/data_for_car_prob.csv\", index_col=0)\n",
    "print(car_prob_df)"
   ]
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    "As before, we can separate the data into inputs (features) $x$ and outputs $y$ (targets)"
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      "Data_x is:\n",
      " [ 9.51693942 72.39875748 17.95032583  9.44085299 78.79100778 16.96112056\n",
      " 65.4103675  58.67109927 21.55060313 36.86691294 15.72874781 58.51149357\n",
      " 57.41918959 38.45915667  8.84174221 60.73305107 49.25666345 35.89512052\n",
      " 79.19565172 69.15666925 77.63489641  9.25401128 15.45146824 14.43824684\n",
      " 13.41099874 53.74705712 10.28371886 82.00547705 81.80556249 51.8377421\n",
      " 20.28378484 28.35964692 74.99371524 21.82756352 70.51911096 74.20853195\n",
      " 14.51895792 13.35764354 75.34625316 44.92395642 26.80115926 29.90626522\n",
      " 40.22635624 66.28266205 47.34277718  3.08767411 21.25461134 46.93948443\n",
      " 38.87569199 76.70545196]\n",
      "\n",
      "Data_y is:\n",
      " [ 29.74903647 642.13220315  36.64848446  18.60410602 769.65616843\n",
      "  57.97101034 559.09331318 463.68661322  92.24267632 197.68857288\n",
      "  56.88523327 388.75379474 399.80748803 213.18151905  20.38738432\n",
      " 516.34172363 307.93195589 181.12304936 750.17828361 553.15354059\n",
      " 746.03187971  20.81069833  39.87252654  42.11877078  44.77512244\n",
      " 375.01393668  19.43886782 742.33684483 706.62028237 345.21287569\n",
      "  65.30316533 155.18513747 676.62898211  81.15093549 700.52003305\n",
      " 622.45356019  40.92757044  39.77092163 707.97375405 251.30080489\n",
      " 124.09865438 118.10089977 215.08209978 537.84504756 308.55883254\n",
      "   5.94799685 101.29527607 345.77835213 219.09558165 742.72013356]\n"
     ]
    }
   ],
   "source": [
    "Data_x = car_prob_df['x'].values # select the input VALUES from your dataframe into Data_x\n",
    "Data_y = car_prob_df['y'].values # select the output VALUES from your dataframe inta Data_y\n",
    "print(\"Data_x is:\\n\",Data_x)\n",
    "print(\"\\nData_y is:\\n\",Data_y)"
   ]
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    "And we can plot the data:"
   ]
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 293,
       "width": 399
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_car_data, ax_car_data = plt.subplots() # create a plot\n",
    "ax_car_data.plot(Data_x, Data_y, 'b.')\n",
    "ax_car_data.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_car_data.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_car_data.set_title(\"Car stopping distance problem\", fontsize=20); # create title with font size 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Supervised learning: regression models\n",
    "\n",
    "As we have been discussing, when we do regression via supervised learning we want to:\n",
    "\n",
    "* create a machine learning model\n",
    "* train it on known data (known inputs $x$ and outputs $y$)\n",
    "* predict for new (unseen) data points, i.e. predict $y^*$ for a new value of $x^*$.\n",
    "\n",
    "Today we will talk about the simplest models: **linear regression**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear regression models\n",
    "\n",
    "Linear regression models encompass a class of machine learning methods that is larger than you might think..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As we will see, despite being called \"linear\" these models can do more than fitting a simple \"line\" to our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For now, let's consider 1d datasets, i.e. where we have one input $x$ and one output $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simplest 1d linear regression model: fitting a line to your data\n",
    "\n",
    "1. Observation distribution:\n",
    "\n",
    "Usually, assumed as a Gaussian distribution,\n",
    "\n",
    "$$\n",
    "p(y|x, \\mathbf{z}) = \\mathcal{N}(y| \\mu_{y|z} = \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma_{y|z}^2 = \\sigma^2)\n",
    "$$\n",
    "\n",
    "where $\\mathbf{z} = (\\mathbf{w}, \\sigma)$ are all the hidden rv's of the model, i.e. the model parameters.\n",
    "* the vector $\\mathbf{w} = [w_0, w_1]^T$ includes the **bias** term $w_0$ and the **weight** $w_1$.\n",
    "* the vector $\\boldsymbol{\\phi}(x) = [1, x]^T$ includes the **basis functions**.\n",
    "\n",
    "2. A chosen Prior distribution on each hidden rv of $\\mathbf{z}$:\n",
    "\n",
    "Usually, the prior on $w_0$ and $\\sigma$ is the Uniform distribution.\n",
    "\n",
    "However, the prior on the weight $w_1$ is often chosen as something else (but it can also be Uniform)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Does this model remind you of something we did?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Car stopping distance problem when we knew one of the rv's and fixed $x$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that,\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "p(y|x, \\mathbf{z}) &= \\mathcal{N}(y| \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma^2) \\\\\n",
    "&= \\mathcal{N}(y| w_0 + w_1 x, \\sigma^2) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we previously called $w_0 \\equiv b$, $w_1 \\equiv z$ and $\\sigma^2 \\equiv \\sigma_{y|z}^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Therefore, the only difference is that we now start to consider more than one rv, so we group them into vector $\\mathbf{z} = (\\mathbf{w}, \\sigma)$.\n",
    "\n",
    "About notation:\n",
    "\n",
    "* We can also write $\\mathbf{z}^T = [\\mathbf{w}^T, \\sigma]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 1d linear regression models with different basis functions: fitting a polynomial to your data\n",
    "\n",
    "However, we know that usually a straight line does not provide a good fit to most data sets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A very important realization:\n",
    "\n",
    "* The basis functions vector $\\boldsymbol{\\phi}(x)$ does not need to be a *linear transformation*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* It could be a polynomial or any other **nonlinear** transformation of the feature (input) $x$.\n",
    "\n",
    "As long as the parameters of the basis functions vector $\\boldsymbol{\\phi}(x)$ are **fixed**, the model remains **linear in the parameters**, even if is not linear in the input (feature). That's why we still call this a **linear model**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here's how our **linear** regression model looks like for a polynomial basis functions vector $\\boldsymbol{\\phi}(x)$.\n",
    "\n",
    "1. Observation distribution:\n",
    "\n",
    "$$\n",
    "p(y|x, \\mathbf{z}) = \\mathcal{N}(y| \\mu_{y|z} = \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma_{y|z}^2 = \\sigma^2)\n",
    "$$\n",
    "\n",
    "where $\\mathbf{z} = (\\mathbf{w}, \\sigma)$ are all the hidden rv's of the model, i.e. the model parameters.\n",
    "* the vector $\\mathbf{w} = [w_0, w_1, w_2 ..., w_d]^T$ includes the **bias** term $w_0$ and the remaining **weights** $w_i$ with $i=1,..., d$.\n",
    "* the vector $\\boldsymbol{\\phi}(x) = [1, x, x^2, ..., x^d]^T$ includes the **basis functions**, which now correspond to a polynomial of degree $d$.\n",
    "\n",
    "2. A chosen Prior distribution for each hidden rv of $\\mathbf{z}$, as mentioned previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear regression models from a Bayesian perspective\n",
    "\n",
    "The choice of likelihood and prior determines what is the linear regression model that you are choosing!\n",
    "\n",
    "| Likelihood | Prior (on the weights)    | Posterior      | Name of the model | Book section  |\n",
    "|---        |---         |---             |---              |---            |\n",
    "| Gaussian  | Uniform    | Point estimate | Least Squares regression  | 11.2.2  |\n",
    "| Gaussian  | Gaussian    | Point estimate | Ridge regression   | 11.3  |\n",
    "| Gaussian  | Laplace    | Point estimate | Lasso regression  | 11.4  |\n",
    "| Student-$t$  | Uniform    | Point estimate | Robust regression   | 11.6.1  |\n",
    "| Laplace  | Uniform    | Point estimate | Robust regression   | 11.6.2  |\n",
    "| Gaussian  | Gaussian    | Gaussian | Bayesian linear regression   | 11.7 |\n",
    "\n",
    "We will derive some of these models soon but not today. Today, we focus on the practical aspects!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Training (fitting) a linear model with Scikit-learn\n",
    "\n",
    "Let's see how to use [scikit-learn](https://scikit-learn.org) to train linear regression models.\n",
    "\n",
    "* [scikit-learn](https://scikit-learn.org) is a well-documented and user-friendly library that is great for introducing machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* You should really read the documentation.\n",
    "    - It includes many useful examples.\n",
    "    - It provides a short introduction to common machine learning algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example 1: training a linear model for the car stopping distance problem\n",
    "\n",
    "<img src=\"../figures/reaction-braking-stopping.svg\" title=\"Car stopping distance\" width=\"50%\" align=\"right\">\n",
    "\n",
    "Let's start by importing from scikit-learn the simplest linear regression model:\n",
    "\n",
    "* Least Squares Regression (i.e. model with Gaussian likelihood, Uniform prior and Point estimate posterior).\n",
    "\n",
    "And let's consider the simplest basis function:\n",
    "\n",
    "* A line (polynomial of degree 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression # For Least Squares Regression\n",
    "from sklearn.preprocessing import PolynomialFeatures # For Polynomial basis functions\n",
    "from sklearn.pipeline import make_pipeline # to link different objects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's define the model (Least Squares Regression + polynomial of degree 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# We start by defining the model (polynomial basis + Least Squares Regression)\n",
    "degree = 1 # degree of polynomial we want to fit\n",
    "poly_model = make_pipeline(PolynomialFeatures(degree),LinearRegression())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Then we train the model for our data (input Data_x and output Data_y that were loaded with pandas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Uncomment line below (this is just for students to understand: don't panic when encountering an error!)\n",
    "#poly_model.fit(Data_x,Data_y) # but it gives an ERROR!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This gives an error! Fortunately, scikit-learn tells us what happened..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Scikit-learn expects the inputs to be formatted as a 2D array (matrix), instead of a 1D array (vector).\n",
    "\n",
    "This happens because usually we fit machine learning models for multidimensional inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Reshape the input vector into a 2D array:\n",
    "Data_X = np.reshape(Data_x, (-1, 1)) # we use capital letters for matrices and lower case for vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.51693942]\n",
      " [72.39875748]\n",
      " [17.95032583]\n",
      " [ 9.44085299]\n",
      " [78.79100778]\n",
      " [16.96112056]\n",
      " [65.4103675 ]\n",
      " [58.67109927]\n",
      " [21.55060313]\n",
      " [36.86691294]\n",
      " [15.72874781]\n",
      " [58.51149357]\n",
      " [57.41918959]\n",
      " [38.45915667]\n",
      " [ 8.84174221]\n",
      " [60.73305107]\n",
      " [49.25666345]\n",
      " [35.89512052]\n",
      " [79.19565172]\n",
      " [69.15666925]\n",
      " [77.63489641]\n",
      " [ 9.25401128]\n",
      " [15.45146824]\n",
      " [14.43824684]\n",
      " [13.41099874]\n",
      " [53.74705712]\n",
      " [10.28371886]\n",
      " [82.00547705]\n",
      " [81.80556249]\n",
      " [51.8377421 ]\n",
      " [20.28378484]\n",
      " [28.35964692]\n",
      " [74.99371524]\n",
      " [21.82756352]\n",
      " [70.51911096]\n",
      " [74.20853195]\n",
      " [14.51895792]\n",
      " [13.35764354]\n",
      " [75.34625316]\n",
      " [44.92395642]\n",
      " [26.80115926]\n",
      " [29.90626522]\n",
      " [40.22635624]\n",
      " [66.28266205]\n",
      " [47.34277718]\n",
      " [ 3.08767411]\n",
      " [21.25461134]\n",
      " [46.93948443]\n",
      " [38.87569199]\n",
      " [76.70545196]]\n"
     ]
    }
   ],
   "source": [
    "print(Data_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "After reshaping the input as a 2D array, we see that we can fit the model!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;, PolynomialFeatures(degree=1)),\n",
       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PolynomialFeatures</label><div class=\"sk-toggleable__content\"><pre>PolynomialFeatures(degree=1)</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=1)),\n",
       "                ('linearregression', LinearRegression())])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_model.fit(Data_X,Data_y) # now we were able to train (fit) our linear model to the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "That's it! Here's your first ML model: fitting a straight line 😆"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now that we have a model, we can predict the output $y^*$ for any new input point $x^*$.\n",
    "\n",
    "In particular, we can predict the output for each of the input points $x$ that we used for training the model (i.e. at Data_X)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "y_pred = poly_model.predict(Data_X) # In scikit-learn, predicting from a model is a one-liner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Done! These are the predictions for all your training points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But we can also predict the output $y^*$ for other points.\n",
    "\n",
    "This enables us to visualize the model by predicting the output for a uniformly spaced set of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Now create linearly spaced points for plotting our linear model\n",
    "x_plot = np.linspace(0, 90, 200) # 200 points uniformly spaced\n",
    "y_plot = poly_model.predict(np.reshape(x_plot, (-1, 1))) # prediction of those points (note the reshape again)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Finally, we can just plot the data, the predictions for each input training point, and the linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# The usual plotting style for this model and the data.\n",
    "fig_poly, ax_poly = plt.subplots() # create a plot\n",
    "ax_poly.plot(Data_x, Data_y, 'b.', markersize=12,label=\"Data\") # Markers locating data points)\n",
    "ax_poly.plot(Data_x, y_pred, 'm*', markersize=12,label=\"Predictions\") # Markers locating prediction points)\n",
    "legend_str = \"Linear regression with Polynomial of degree \" + str(degree)\n",
    "ax_poly.plot(x_plot, y_plot, 'm-', linewidth=2,label=legend_str) # polynomial interpolation plotted\n",
    "ax_poly.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_poly.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_poly.set_title(\"Car stopping distance problem\", fontsize=20) # create title with font size 20\n",
    "ax_poly.legend(loc='upper left', fontsize=15) # replot legend\n",
    "fig_poly.set_size_inches(7.5, 6) # scale figure to be taller\n",
    "plt.close(fig_poly) # do not plot the figure now. We will show it in a later cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1zvay3m8YrSNseiul4vwsl6iFJDAWInQkuzyv8sC4guZjBB825wW4flX9KHfHr/511eAmh/8tlA/KPHkBo3bVno91Wgx/rNB+9OPSWh/B+IFuE43R/NVf//Az3URc9iWAbQRihvavb/5inM/jc90lsk6143g8TgAf+1mWV/1MV1Gux9Df9+JfGDWaVSnROn3Xmeprl+eBXOdOYdTCemW9QTPf4aUGSilPYx7cgnPf+A+11tsCKJMnt+Pc9/U5X0Gxjdb6W4ymqDbDglAeTwoxut94ZS276+cgkGvNW9qPcTOswdMIh5eyMWra/fF3l+eB9DOeYb1x45XWejPGmBY2TYBBAWzHE8f+zXsxumH56x2H/5Mwphjzx3St9SHfyVjs8nyJ1npTgOuFYXQ/EGcpCYyFCF1+/TipKkqpWKVUQ6VUC6VUS9sDo2bA8Q5sxwCyPQn4uuNfGccxBmWxGaeUau0pcXWwHrPGDi8tswajPllr8x3vZifhPLiKNzP8TAdGn1tHF/i53nGMJm4+aWNeTceBqJoopZp7Sl8J830nAW3MnbvL4SVPN1E6cXogLzBaPPg1CJrWej3gV41eBTm+T4G8F7n4eZwC9KfD/5H4H6jXCGWIU0o1drzGWT+zES7JA7nOrfLWYsHFdpfnns5D16DmE7epAjfY4f8sjHEHAuF4Pb+w8sXxaF4Ax3QeRl9fG3+vZ+Bcm+tNH5xbAc3Rfs5fbg1atzq8dI51EC9/VMd13S2lVCpGNwObudabO/5ag/PNUX/PlwV+ptvt8nyh21Tl7XJ5Hio31EUNkFGphQgdrs196lTnxpVS52IMJtQf446pv1/UrjXd3mz2tzaiIrTWWik1g9NNXxsCm5VSkzF+UKy2BkTVqZfL818CXH8NcLlLfls9pHW0zncSu00Y/Zlt3wmuZfZkQ4A/jNbh3KyxF8EPHAOpRXNslZHoIU03l+cbAysOG3FuYhwUSqlkjL6BNhV5L0YEs0wYTSVf4/TosX9VSg3EqGH/Vmt9NMjbC5hS6kKMwbzOB7pgDHbnj0CucxU9B8HzeehYY52ltfbnGuCVtfWJY7C0G2juf6MUwKjJtWmhlAoL8Dz0l9/XM611qVJqM/AX60utlFLJ3prUWu3XWp/wczPBuK53tv4fhjGqtT83jQO5rrum9fe67olrIHukAl0MTmKMxg3GKN/+cL155Emuy/M/3abyvZ6nz6A4C0hgLETocP3STqqOjSqlmgL/puI/kgP5Esms4DYC8TxGINnC+jweo2/uA0CeUmo1sBJjUJM1uuqnZnC9+7wzwPVdv9z9vZvtevfcI611sVLqAKenImngLX1FtmHlemfe3+0EIpAuCI61F641hDb1XJ4fCKw4Aaf3V0OX55V9LypNa31QKfV3jKbaNn2sD5RS2zE+e8sxmjlW1bEpxzp1y/9xOlgKVCDXuYqeg+DmPFRKReB8HvobKPiSjNHH1aYvRvPYilLWPLN8JayAipzfju91A8p/x7oK5PupJq7rBQHeXNqLMRq0rXVoZa+3TV2e/wvnz3qg/B3Lwt/Pk+tN74qu5+m7QJwFpCm1EKHjsMvzDm5TBZH1bu8KKldzFMh1xO8BcCpKa52JUQvirqloAsYIyS9gNBnMUEp9rJRq7yZtsCS5PHe9O+2L65e7vzVXldlOUjVsI5DtBCLYtVWuLTf8bc5pE+gx8ldSJbdTJWMYaK1fA+7E6IvtqiPG4D1TgP1KqbVKqTuCNCiQR0qpnhgBeUWDYgjsOhfsc9A1gMiponyDId53kgqpjmtNIN9PrvlVx3U9oG1YW2c5rpMUyPpuBPt88fdcqejnqSpaLohaTgJjIULHGpfnlW325I//crpmFYwv0Q+AkRhNSOtjjPIcprVWtgfGfMYhS2t9RGs9FCNA/hBjSg53kjB+xG9VSj1XPaULuO94QO0aK6Ei2wnVfQkm1xYFgdYmVNcAVCHzXlhHoG2NMT/4EjwP9NUHo6/sr0qpKrkRqJSKBKbhHHgcw5hT9iqM5tR1MeZ5VS7XuVAVrO4oVVEzVlXHLWTObw+qo3wVed+DeRyCfb6E8mdMnKWkKbUQoWMNzv08WyqlWmitqyQIVUr1x3lAlz+AS/wcGMrf/sc1Smu9BusNB6VUM4w+UgOAS3Hu32QCXlBKlWit/xnkYuS4PA+077hrE05fzQEd1wukaaDjdnL8XKey++LvdmqS6/EOpK9pRdL7K8fleWXfi6CyThnzPvC+dXTq3hjjFwzCmJfY8YZBV2CRUqp7INPH+el6nAcMWgpcZR2AzKMABkOqDq6170lVlO8UrfXYIOUdbKF2rXHNrzqu6wFtw9qH3PE8zglkfTdcz5dB/sx8IMSZRGqMhQgR1nkJV7m8fFsVbtJ1ao1x/gTFSqloqqn/czBprQ9orb/UWt+ntW6DUVv1rUuyZ5VSrn1KK8s1OG0b4Pquzbz9DXbb+E5isAYuzRxeOhbsbVi57ru/26lJroODdQlw/UDT+8v12FX2vagyWutirfVKrfWrWuvLMPpTPoDzD+1U4PEq2Lzjda4MGOMrKLbyNG1StbOOgu54rAIZIdubLJznum0XpHyrQqhda2riuh7rZTovd1rh/Du/sscgw+V5KJ8vQlSIBMZChJb/uDy/swonm3f8Is/XWq/0c70+1IJrh3UqnRE4TwURCwzxtEoFN7XB5Xmg8z6f7yM/T/oEsI3uOLcg8ncbvazz/PrLtUz+bqcmrcP5vR/o74rWWsfuwS4QgHX03HSHlyr7XlQbrXWe1vo9jM+f47G9wtMqldic43Vum9ba31HQXT93NW21w//1rYOJVYp1hP71Di/1VkqF6oi8fp+v1sHKHOcl3+vHiNSBCuZ1vQxjZgB/BPK5Dfb11rW7l6fvSiHOWGf8j1shapnZOI8Kmgq8UtlMPczl69gsK5ABhW6qZHFChnVakf+5vNzSQ3LHOSojPaRxt410wLEmPk0p5TqisFvW2utLHF7Kwf+pYK73Mx3AKJfnq92mKq8+5edXdcu6L44/pA4HEKTUGOsP6s0OL/ULYLC2G4Do4JfKzilYwv/3IhHnabNqhNb6Z2CPw0stPSR1nR/W788fzte5QAYvCrXrnOsc1XcGKd+fHP6PxJiyLxQNDaB5+1Ccmyr7ez0LxDqcRzO+2tqf3Sel1Dk4tyT5I4A5mqvjuu6W1no7cNDhpWFKqfqe0gtxJpLAWIgQorW2AI+5vPyAUurmiuaplHoE+MjNohyH/xsopZL8yKsDcGtFyxKiXH8se5q+yXEU0fpKKVMA2/jC4X8T8LSf6z2L84AnXwQwD3R/pVSar0RKqcY4/8guAr7ycxsAf/cz3VM478vnAWyjpn3i8L8C3lY+Jnu1zjP8QpWWqvwx9Pe9eIKqDdgD4fj58+ezB4E1c85x+L+tP7Xq1rmXL/GVrppNxXnO4HFBGrBsEs4B3nMhGuzEAI/6SmT9XLp+DoJ+rbF2ffra4aW6GIPN+eMll+efBbDp65VSPpswK6W6AVc6vHSE8jdXKuL/HP6PByYGIU8hQoYExkKEGK31HIyRoW3CgKlKqb8GEowppdorpeYCb+J+oL3fHf43AQ/5yC8FmInxAyUkKaU6KKVGBhi0utYMuc4v6e71CIyBhPz1Ps59+e5XSnlqNgqAdfkDDi+VUb6pvS+TvNVOW5scTsF5gJYvrc10/ZWmlPqrtwRKqYtxPr/MuL9ZE6qm4jyd2lDgP56mGbIGFj9Q9f1U5+Fc4+rPe5EGeE1TUUqpsUqpFr5T2tN3wbnJq6fP3h6c5/sdHECxHK9zKYDXm4xKqbYYgUpIjZhrnYZuksNLscAc6zz0Piml4pRS5abH0VrvBSY7vNQY+CbQ4FgpNaCKp70DeNI6aKQ3z+PchHgP7qfuC4Z3XZ6/pJTy2tRZKXUvxmjoNqdwfl99iQQ+89bFSilVB6MllOP34P9Zm85X1rs4z1N9p1LK3xu9tvLFKqVCtWWCOMtJYCxEaHoU+NnhuQJeA35TSt3saYAopVSEUupipdQnwBacv4Bdzca5797zSqknrAMxOeYZppS6EqN/0TkYNYpVPh9xBTUGZgC7lFIvK6V6egqSlVKNlFIf4dw0LQPnpoWOlrs8n2Kdg7W7UqqVUqqlw8OpNk5rvQfnJvEmYKZS6m9KKacbDUqpaKXU4xg3IRzL/rrW2t9m1GDUlLUGViilyjWxtdY2LQQudlnnqQC3AfAvpdRb1h9kjtuIVErdD8zFubb4da31rgC2U6OszRzvdXn5Poxphu5XSvW23oj6i1LqBYzm7udj1IB+U4XlKqN8LZWn9yLC+qP8W4wRoXOqoEhjMT57c5VSN3m5ToUppYYDP+L8O8RtzZnWuhhY6/DSQKXUJ0qpIUqpdi6fPdebEbNcnn+olLrN9bpgPT63Ysx33BQI9ujYwfAUzjcPOgHrlVJ3K6Vi3a2glOqqlHoZY4o9TwNEPQZsd3h+AbBZKTXORwDWXin1uFJqA8a88O667ARLDkYrhx+UUndZb+o5liVZKfU+RmDs6H7r5yTotNbLce6KEwcstH4vuJYvUSn1L8rf3Hw8gBuRpzBuEPUFlimlergmUEr1xfiu6ubw8h6M3w+VZh247mac5wh+WSm1wHpzxO0NJaVUlFJqsFLq3xgDGr4ZjPIIEXRaa3nIQx4h+MD4krUFr64PC0a/xx8xmol9izGISq6H9D942MZUN2lPYNR2fQZ8Dxx1WX4/xqA/tudLfeyH47qTq/iYpbnZn1MYfavmYvyImQX8aj2GjunKgBFe8lYYNxvcHV/XR5qb9cMxAlHXtHkYA4B9YX0/3b2Hy4BIH/s+2WWdW1ye7wLmYNw42ODhnLrWxzZauqzzT4xpvmzPi4DF1n2ZZz2XXLezBoj2sZ0JLuu0DEZaN+sudVgv3Y/0T/j5/tseD7gpX4sqOO/fcbNt1/ciy+WcG+eSfmwAnyu3aV2Op+2xx3pef4lxrVqAMTqua7q1QLiXMozy85iXux5hfH5c0x3BuGnxubV82Q7LLBgDgfl17aL852JCAO/dWJd1y107XNJ3Bg55eL9/xvh8T8O4wed6nLt7ybcdztd126MUoz/tHIzr51xgBUag6pr2siCe067H5V7reWt7fhzje+oL63lX7KY8b/uxHcd9Lnfu+LF+IsZ3seu2Hcu3GKMZvGuaaYFeozC61zjm8TvGd9pXuP9+KgD6+dhGwOev9f0wu9leFrAImG7d9x+sZSx1SXfUS94TXNK2rIrPksN6aS7rub2+yePseMg8xkKEKG30YbpGKXUXRj8ex9qXMIw7wt3crevgFMadYk93i8dh3OW/0OG1ZIymou48q7V+z1qjeaaIxfcIswXA3VrruZ4SaK21UmoUxs2C5oEWQmttttaSTcF5UJR4nGttXc0GbtJae+p/6Wl7/1NKNQf+YX2pDZ6nPCkB7tJaB9K3GIwf48MwfoS3xaiJ9DYA1BpgqNa6KMDthASt9b+UUpnAG3ifn/gUxvGcppR61WVZVbS2eBijieU4h9c8vRengGtwbppclVpZH94sBa7RXpp6aq2nK6XOAx6pQBmut27DcZqjRrgfBbsU41rwrYfKrxqltd5qPQ5zMOaGtokisO4drvnuVEr1xrgheqnDonDrdnq7XfE0M1XbkmgbcC3G9TAO4/vQ0/cUwIdU7FwJiNY6Vxl90mfj/HnzVb738NF9yYN/YLRouNv6vKv14U4exs1O12kgK01r/YFSaifG+eLYXacu/nV1yA52mYQIBmlKLUSI01p/DLQAHsQILHw1CyvFmA/5PqCp1voFrXWBh7wLML7MX6T8ADc2FoyazkFa6394SBMqVmNMATMJ59G9PcnGGEyko9ba5wAtWus/MJqT3w98h3EHPx/jLrNP2pjPdTTGiMCrvKxnq0G7Qmt9bUUDSa31yxg/zjz9MNIYQW1PrfXUCm5jH8aP5rfx/GPnGPAk8BetdU5FthMqtNafYgRYT2A0u83AuLFwCOM4PwG00VpPs66S5JKFp89ZZcqktdb3Ypz7nprbl2LUKvXUWi8Mdhms7gL+hhGEFnpPChjXs5uBwdqP6XS01o9iTIvzHkYtZhaeB+xyXC8Do/npv72UqwQj2OyjtZ7sR9lrjNb6IMb+3MTp1h+elGBcv2/AaN3hLd/j2phneghGv1zX0cBdFWO8138FmmmtV/hT/orSWi8AemGcx55u7GwDrtRa36u19uu6HIRy5WAcsxuB37wktWDUpl6otX5AV6CJt/Wzfg/G58bTtkoxapG7VOFnHa31Txg31h/FuSm+JxkYLTSuxvdNfSFqhKqm64YQIkisfQd7Ynwh1cfou5mH0Wx1N7CxIoGUta9rP4x+a3Ws+R0GftFaHw1O6auXtb9hZ4waq7oYtSoFGM3c/gB+11pXV82Zu/I1wKjlaYQRQJ3EaLq+MtBjrpSaDIyxPddaK5fl7YAeGLUNCuO9Xa61PhTANlrifMPhBa31BIflUcAAjBs5KRiBy07rdhwHHztrKKWWYRwTgBNaa7f9boO8ze4Y8yc3wrg2HMQ4p6qt36y1j2VnjJYEqRgtIzTGOZ6OcZ2q9uuKMqb8+Yu1XPEY14JDwCp/gvNQpIwB9vph1NzVwwiGT2D0R/7V2vqoIvlGY7S2aWnNNxrjRuAxjEBoW1W1/lBKjQU+dXhpkNZ6qcPy+hgtnZpiDB54FGNfHadWqxHWljrnY7wfCZz+Lv052OeYUupcjKmfUjEC4oPAEq11ltcVq4BSqgnGjasGGN+3ZRhdg/Zj3LDYW103K4SoKAmMhRCiFvAVGAdpGy3xEhgLZ9abTccwAjCARVrri2qwSEKcEXwFxkIIURWkKbUQQghRNW7gdFAMziMrCyGEECKESGAshBBCBJm1qefLLi9/URNlEUIIIYRvEhgLIYQQflBKfaqU8jaCuC1dG2AJRh9fm2XWwduEEEIIEYJkuiYhhBDCP32AsdZpSmYBvwD7MAYkqgO0xxgFfDTGoHg2hThPpSSEEEKIECOBsRBCCBGYdsBTfqYtAm7WWvsznYkQQgghaog0pRZCCCH8E+gUKOuBNK317KoojBBCCCGCR2qMhRBCCP+kYczTeZH1b1ugMRAHmDHmKz0ErAB+0Fr/VDPFFEIIIUSgZB5jIYQQQgghhBBnNWlKLYQQQgghhBDirCZNqWsJpdReIBFIr+GiCCGEEEIIIURNaAnkaq1bBbqiBMa1R2JMTEzdTp061a3pggghhBBCCCFEddu2bRuFhYUVWlcC49ojvVOnTnU3bNhQ0+UQQgghhBBCiGrXq1cvNm7cmF6RdaWPsRBCCCGEEEKIs5oExkIIIYQQQgghzmoSGAshhBBCCCGEOKtJYCyEEEIIIYQQ4qwmgbEQQgghhBBCiLOaBMZCCCGEEEIIIc5qEhgLIYQQQgghhDirSWAshBBCCCGEEOKsJoGxEEIIIYQQQoizmgTGQgghhBBCCCHOahIYCyGEEEIIIYQ4q0lgLIQQQgghhBDirBZe0wUQoUNrTUFBAbm5ueTn52OxWNBa13SxhBBCCCGEEGcIpRQmk4n4+HgSExOJjY1FKVXTxfJJAmMBQFlZGYcOHSI/P7+miyKEEEIIIYQ4Q2mtMZvN5OTkkJOTQ3x8PKmpqYSFhXZjZQmMBVpre1BsMplITk4mISGByMjIkD+BhRBCCCGEEKGjrKyMkpIS8vLyyM7OJj8/n0OHDtG0adOQrjmWwFhQUFBgD4qbN29OdHR0TRdJCCGEEEIIcQYKCwsjOjqa6OhoEhIS2L9/P/n5+RQUFBAXF1fTxfNIqgMFubm5ACQnJ0tQLIQQQgghhAiK6OhokpKSgNMxR6iSwFjY+xUnJCTUcEmEEEIIIYQQtUliYiJAyI9lJIGxwGKxABAZGVnDJRFCCCGEEELUJrYYwxZzhCoJjIV9SiYZaEsIIYQQQggRTLYBt0J9GliJhIQQQgghhBBCVIlQHonakQTGVkqpYUqpBUqpg0qpQqXUHqXUTKXUBR7S91NK/aCUOqGUKlBK/aaUelgpZfKyjTFKqbVKqXyl1Eml1FKl1PCq2yshhBBCCCGEEL5IYAwopV4FvgN6AvOBd4CNwFXASqXUzS7prwKWAwOAOcB7QCTwFvClh228DkwGGgMfA58B5wDfKqUeCPpOCSGEEEIIIYTwy1k/j7FSqhHwVyAD6Ka1PuawbBCwGHgRI5BFKZWIEdhagDSt9Xrr689a016nlBqttf7SIZ9+wGPAbqCP1jrb+vprwAbgdaXUd1rr9CreXSGEEEIIIYQQLqTGGFpgHIdfHINiAK31EiAPSHF4+Trr8y9tQbE1bRHwd+vTe122Mc7692VbUGxdJx2jtjkKuK3SeyKEEEIIIYQQImASGMNOoAToq5Sq77hAKTUASAB+cnh5sPXvfDd5LQcKgH5KqSg/15nnkkYIIYQQQgghQpLWmuKDxZhzzTVdlKA665tSa61PKKX+BrwJbFVKzQWygDbAlcBC4B6HVTpY/+5wk5dZKbUX6AK0BrYppeKAVCBfa33ETRF2Wv+2D8LuiFrA08h9kZGRJCYmUqdOHVq0aEHPnj0577zzGDZsGDExMdVaxsmTJ5Oeng7AhAkTqnXbQgghhBCiZpSVllG0pwhLngV1XBHbOZawyNpR13rWB8YAWuu3lVLpwH+BuxwW7QImuzSxrmP9e9JDdrbXkyqY3iul1AYPizr6s744c5WUlHD8+HGOHz/O7t27Wbx4MQBJSUmMGTOGF154gTp16vjIJTgmT57MsmXLAAmMhRBCCCHOBpZ8C4V7CtElxnzE2qwp3F1IbIdYVNiZMSWTNxIYA0qpJ4BXgHeB/wBHMQLNicDnSqnuWusn/M3O+jfQGaxDe8ZrUSPmzJlj/19rzcmTJ8nOzmbTpk0sX76c9PR0cnJyeOedd/jqq6+YNm0a/fv3r8ESCyGEEEKI2kRrTWlmKcUHistFLLpEU1ZShina44y1Z4yzPjBWSqUBrwJztNaPOizaqJS6GqPJ9GNKqQ+11ns4XcPrqWou0fr3pMtfT+l91Sg70Vr3cve6tSa5pz95iDPHiBEjPC7TWjNv3jwefvhhdu7cycGDBxk2bBirVq2iS5cu1VdIIYQQQghRK2mLpmh/Eeas8v2JTQkmoltHExZRO5pS1469qJzh1r9LXBdorQuAtRjHqYf15T+tf8v1CVZKhQOtADOwx5rHKeAQEK+Uauxm++2sf8v1WRbCG6UUl19+OevXr7fXEufm5jJy5EjKyspquHRCCCGEEOJMVlZURsH2ArdBcUTDCGLax9SaoBgkMAZjqiRwnpLJke31Euvfxda/l7lJOwCIBVZprYsdXve2zlCXNMKNLVvg3XfhH/8w/m7ZUtMlCh2JiYnMmDGDpKQkALZt28b06dPdpi0sLGTOnDncf//9nHfeedSrV4+IiAjq1KlDly5duPfee9m8ebPHbaWlpaGUsvcvBiNAd3249js2m838+OOPPPbYY/Tv358GDRoQGRlJQkIC7du3Z+zYsSxfvrzSx0IIIYQQQlReaU4pp7adoqzQpbIlDKJbRxPdLNrjgLFnKgmM4Wfr37uVUqmOC5RSQ4ELgSJglfXlWcBxYLRSqrdD2mjgH9anH7hs40Pr32eUUskO67QE7geKgU8rvSe10KJFMHAgdO0K48fDs88af7t2NV5ftKimSxgaGjduzN13321//t///tdtus6dO3PNNdfw/vvvs3btWk6cOIHZbCY3N5etW7fy4Ycf0r17d55++umglu/iiy/msssu480332TlypVkZmZSWlpKfn4+O3fuZMqUKQwcOJCxY8dSUlLiO0MhhBBCCBF0WmuKDxVTtKsILM7LwqLDiO0US0TdiJopXBU76/sYYwS6PwEXYUyvNAdj8K1OGM2sFfCk1joLQGudq5S6y7reUqXUl8AJjKmdOlhfd6qu01qvUkq9CTwK/KaUmgVEAqOAusCDWuv0qt7RM82kSXD33eCpVfDy5XDJJfDxx3D77dVbtlB044038q9//QuAVatWUVpaSkSE84WrsLCQunXrcvHFF9OjRw9SU1OJiIjg0KFDbNy4kRkzZlBaWsrEiRNp0KABDz/8sNP6//jHPzh+/Dh///vf2WKttnccIMymY0fnQdILCwuJj49nyJAh9OrVi5YtWxIdHc2RI0fYsmULn3/+OadOnWLKlCkkJSXx9ttvB+/ACCGEEEIIn8pKyyjaW4Ql11JuWXhyONEto1Gm2lVL7EhpLYMhK6UiMGpuRwOdMZpDn8DoX/yu1nqBm3UuBJ4BLgCiMaZ2+q81ffmzyVhnDPCAdRtlwEbgNa31d0HYhw09e/bsuWGDp9mcPNu2bRsAnTp1qmwxgmbRIiPo9aerbFgYLFgAQ4ZUfbmqg2OzlEA+nxaLhTp16nDq1CkANm3axLnnnuuUZv78+Vx00UWEh7u/J7Zv3z4uu+wytm/fTkJCAocOHSIhIaFcurS0NHtzan/KuGjRIvr16+dxvuWsrCxGjBjBihUrCAsLY9euXbRq1cpnvkIIIYQQovIspywU7j49FZOjqGZRRDSIqFTT6eqKN3r16sXGjRs3ehqw2BtpSg1orUu11m9rrc/XWidqrcO11g201sPdBcXWdVZqrS/XWidrrWO01udord/yFBRb15mite6jtY7TWidorQcGIyiujV580b+gGIx0L71UteU5E5hMJpo2bWp/npmZWS7NZZdd5jEoBmjRogXvv/8+AHl5eXz99ddBKduQIUM8BsUA9erVY8qUKQCUlZXx+eefB2W7QgghhBDCM601JZklFGwvKBcUqwhFTIcYIhtG1rr+xO5IYCxCzpYtRjPpQCxbJgNyASQn27uwk5WVVaE8+vXrZ///l19+qXSZ/NW6dWsaNWpU7dsVQgghhDgb6TJN0b4iiveVn5/YFG8itlMs4QlnT8/bs2dPxRmjogNqLVoEZ/v0vY7TNHm6s3fs2DGmTp3KggUL2Lp1K9nZ2RQUFLhNe/DgwaCVLTc3l88//5wffviB33//nePHj9ubfVfldoUQQgghhLOy4jIKdxdSVlC+iWZEwwiiUqNQYbW/ltiRBMYi5OTmVu96tUlOTo79/7p165ZbPn36dO655x5OnjzpV365QTqoS5Ys4cYbb+To0aPVul0hhBBCCOHMfNJM4Z7CcqNOEwbRLaNr7ajTvkhgLEJOYmL1rldbWCwWp5rWlBTnqbmXL1/OjTfeaK9V7tmzJxdddBFt2rShTp06REVF2dNeffXV9jwra+fOnQwbNozCwkIAOnTowNChQ2nXrh1169YlOjranvbuu+8mMzMzKNsVQgghhBCnaa0pOVJCyeHyU2OqaEVMmxhMMaYaKFlokMBYhJyKji5dW0alrqjff//d3iQ6Li6Ozp07Oy2fMGGCPSj+6KOPuOuuu9zm46l5c0VNnDjRHhQ/88wzvPTSSx6beXsqkxBCCCGEo8JCo7WgxQImk1FB4mWcz7Nemdk6FdNJN1MxJYUT3ap2T8XkDwmMRcjp0gUGDAhsAK6BA6V/8RdffGH/v1+/fk5zGJeUlPDzzz8D0Lt3b68B6L59+4Jarp9++gmABg0a8OKLL3oMivPy8jhx4kRQty2EEEKI2iU3Fw4fhvz88svi46FJE2lF6MrbVEyRTSPPmlGnfZFRqUVIeu45Y35if4SFwbPPVm15Qt2RI0f4+OOP7c/vuOMOp+VZWVmYzWYA2rRp4zWvH3/80ef2whzeHF/zGGdkZADQqlUrp/Vc/fTTT06DhwkhhBBCOMrMhB073AfFYLy+YwccP1695QplJcc9TMUUbkzFFNUoSoJiKwmMRUgaMgQ++sh3cBwWBh9/fHY3o87Ly+P666+3D7zVqVMnRo4c6ZQmNjbW/v/u3bu95vXWW2/53GZ8fLz9f19Nr23b3rNnj8cg2mKx8Morr/jcrhBCCCHOTrm54G+jtvR0GZRVl2mK0osoTi8/FVNYXBixnc+uqZj8IYGxCFl33AELFhjNpN0ZONBYfvvt1VuuUKG1Zt68efTu3ZsVK1YAkJiYyMyZM8vVzNapU4d27doBsH79eubMmVMuv/z8fEaOHMmBAwd8brtVq1b2/zdu3Og1bZ8+fQDIzMzk7bffLre8tLSUu+66i/Xr1/vcrhBCCCHOTocPB5b+yJGqKceZoKy4jILtBZQeLy23LKJBBLEdYgmLlDDQldwmECFtyBDjsWWLMU9xbq7Rb2TIkLOjT/HcuXPt/2ut7f1wN23axPLly9m7d699edOmTZk2bRpdPByYBx98kIceegiA6667jptuuon+/fuTkJDAH3/8weTJkzl8+DC33norU6dO9VquIUOG8O677wJGs+1HHnmEFi1aYDIZIxm2bduWtm3b2re7cOFCAB599FGWLl3KpZdeSr169di5cydTp05l586dDBo0iJ07d8ocxkIIIYRwUljoufm0J3l5xnpn24Bc5pNmCvcWgtllQRhEt4gmot7ZORWTP5Sv/oHizKCU2tCzZ8+eGzZsCHjdbdu2AUYTXFHzAu3nkZSUxK233soLL7xAUlKSx3Raa2655RY+//xzj2muuuoqpk2bZm/+PHDgQJYuXVouncViIS0tzV5T7er5559nwoQJ9udPP/00EydO9LjdCy+8kDlz5tCnTx/27dtHixYtSE9P95heCCGEEGePjAzwo0FbOc2aQcOGwS9PKPI6FVOUdSqm2Jqbiqm64o1evXqxcePGjVrrXoGuKzXGQpwhIiIiSExMJDExkZYtW9KzZ0/OO+88hg8fTowft0OVUnz22WcMGzaMjz/+mF9//ZWCggIaNGhA9+7dueWWW7j++uv9KovJZGLhwoW88847fP3112zfvp3c3FyP8w+/8sorDBgwgP/85z/88ssvnDx5kvr169OpUyduuOEGxo4dS3i4XI6EEEIIUZ6HnxdVtt6ZxttUTKYkEzEtY1DhMsCWL1JjXEtIjbEQQgghhKiNpMbYM0uBdSqmYjdTMaVGEtkoNKZikhpjIYQQQgghhKiEis5LXNvnMy49XkrRvqJyo06rcEV062jCEyXUC4QcLSGEEEIIIUTIiomB+PjABuBKSKi9A2/pMk3xgWJKM8uPOh0WF0ZMmxgZdboC5IgJIYQQQgghQlqTJoGlb9y4aspR08pKyij4s8BtUByRIlMxVYYcNSGEEEIIIURIS0yEFi38S9uyZe1sRm3ONVOwtYCyU2XOCxREt4wmukU0Kqzm+xOfqaQptRBCCCGEECLkpaRAVBQcOWLMU+wqMhKSkiAurtqLVqW01pQcLaHkUGhOxVRbSGAshBBCCCGEOCMkJhqPwkI4dgxOnoQSa7xYUmK8duyY0Se5SZMzv+ZYmzWF6YVYctxMxVTHRHSraMLCpRFwMEhgLIQQQgghhAgJhYWQm2vMQWwyGYGtu0G08vMhM9NzPvn5sGOH0ay6fv0qK26V8joVU5NIIhuHxlRMtYUExkIIIYQQQogalZsLhw+7H3natfY3Nxf27fMv3/R0o4n1mVZzXJplnYrJpTsx4RDTKobwOhLGBZvUuwshhBBCCCFqTGamUbvraTomW+3v8ePG88OHA8v/yJHKla866TJN0f4iivaWD4rDYsOI6xQnQXEVkaMqhBBCCCGEqBauTaXDwgKr/dU6sPmMwRioq7Cw4vMa+9u8u7LKSsoo3F1YftRpjKmYoppFyajTVUgCYyGEEEIIIUSV8tZUOhBHj1Z8+4EGs4E0764sc56Zot1FaLNLf2IFUS2iiKwfGZwNCY8kMBZCCCGEEEJUmcxM/2uFfSkurth6lvKDOnvlq8zBGtxLa01JRgklB91MxRRpnYopTqZiqg4SGAshhBBCCCGqRCADZVUlUwCxZXUN7qUtmqK9RZhzzOWWyVRM1U8CYyGEEEIIIUSVCHSgrKoSSOBakcG9Ag2MLYXWqZiKZCqmUCGBsRBCCCGEECLoCgsr36fYnaiowJpUJyT437+4ImUOdHCv0hOlFKW7mYrJBDGtZSqmmiJ180IIIYQQQoigy82tmnwbNQosfePG/qetaJn9WU+XaYoOFFG0x8NUTJ1lKqaaJEdeCCGEEEIIEXSBDnjlj4QESEkx/venH3DLloE1c65omX2tV1ZSRtGeIiz55ROG1w8nunm0TMVUwyQwFkIIIYQQQgRdIANe+ctW+5uSYjSpPnLEaMrsKiHBSBto39+KltnbeuY8M0V7itClbqZiah5FRP0I6U8cAiQwFkIIIYQQQgRdsOb4tXGt/U1MNB6FhUZTZovFCFATEwOfs9gxz2Ctp7Wm9FgpxQfKd4iWqZhCjwTGQgghhBBCiKCLiYH4+MoPwOWr9jcmpuKBsLu8ypdZk4AxpVIe4YBz7a67wb20RVOUXoQ5281UTInWqZgiZLinUCLvhjgj6DJNxrQMMqZloMvKD2svzjyTJ09GKYVSismTJ7tNY1uelpZWrWXzZOnSpfYyTZgwoaaLI4QQQoS8Jk0CS9+iBTRrZqzXrBl06QIdOgS/9tmb02XWJFBKfUpoQhFNKCKW8n2EXQf3shRaKNhW4DYojmwcSUy7GAmKQ5DUGIszQs7SHLbduA2AyEaRJA9KruESVR1vfUzi4+Np2LAhPXv25JprruHaa68lIiKiGktXu+Tk5PD2228D0L17d0aMGFGj5RFCCCFqm8REI9j1d6Cs+vWrvEg+2cqcuc9CE4qcl1FKgUMI5dq8uzS7lKK97qdiim4VTUSS/G4LVRIYizPC0clHnf6vzYGxN/n5+eTn57N7925mzpzJOeecw6xZs2jfvn1NF+2MlJOTwwsvvADAmDFjJDAWQgghqkBVDZRVlVJSICq7FFymYUrAzDE0cQnKqcxaa4oPFlOaUVour7CYMGLaxBAWLbXEoUwCYxHyzLlmMmdl2p9nzsqk3X/aEZ5Q+0/fOXPmOD3Pzs5m1apVfP755xQWFvL7779z8cUX8+uvv1K3bt0aKmXV0Tq0ms2npaWFXJmEEEKIM0FVDJRVlbRFo/LLN4UOAzo0KSWuSaT9tbJS61RMeW6mYqpnnYrJJKNOh7raH1mIM17mrEzKCk+3RykrKCNzViaNbwtgtvYzlLsazNtuu42HH36YtLQ0jh8/zv79+3n11Vd59dVXq7+AQgghhBABCOZAWVWpNLu0fHNoK5VrBmtgbM43U7Tbw1RMzaKISJGpmM4UUp8vQp5jM2pvr51NunTpwiuvvGJ/PmvWrBosjRBCCCFE7WI+Xr622MaSb8FSZKEko4TCPwvLBcUqUhHbIZbIBpESFJ9BJDAWIa1gVwEnfz5Z7vWTy09SuLuwBkoUOoYNG2b/f8+ePRQUFNifjx071j56cnp6OgCzZ8/myiuvpHnz5kRGer5Qr169mnvvvZfOnTuTlJREdHQ0zZs3Z9SoUXz//fd+l++7777jiiuuoFGjRkRHR9OyZUtuuukmVq9e7XcegYxKvWPHDp544gn69OlDSkoKERER1KlTh549e3L//fezaNEiezPo9PR0lFK0atXKvv6UKVPs23N82I4fBDYqdUFBAW+99RaDBg2iUaNGREVF0aBBA/r378/EiRM5ebL8ee1owoQJ9m0tXboUgDVr1nDTTTfRokULe37Dhw9n/vz5Po9PTk4Or776KgMHDqRBgwZERkaSmJhI69at6devH08++SRLly6VpuJCCCHOepYiC5b88s2iHRXtLjLmJ3b52jQlmIjtFIspXuYnPtNIU2oR0jKmZnhcdnTqUVq90Mrj8touJSXF6XlOTg6xsbHl0hUXF3PNNdeU66/s6tSpU9x55518+eWX5ZYdOHCAAwcOMGPGDIYNG8a0adNISEhwm4/FYuGOO+5gypQpTq/v27ePffv28eWXXzJx4kQaNGjgaxf9Yjabefzxx/n3v/+NxeL8JZabm8uvv/7Kr7/+yvvvv8/SpUsZOHBgULbrzZo1a7j22ms5fPiw0+uZmZlkZmaycuVK3njjDb744gsuueQSv/J85ZVXePbZZykrO92uKzMzk++//57vv/+e5557zj6QmKt169YxfPhwjh075vR6aWkpeXl57N27l9WrV/Pqq6+SnZ1NUlJSYDsshBBCnIEshRYKthT4TuiGYzc/pzzzLJzafIrYLrGYYiQ4PpNIYCxq1Kmtp1jXZV2F1t334j72veh57P8+W/sQ1ymuokULeZmZmU7PEz0M5fjII48wb9482rRpwy233EKHDh0oKChg2bJl9jTFxcVcdNFFrFmzBoDmzZtzww030KVLF6Kioti1axdTp07lzz//5Pvvv2fEiBEsXLiQsLDyjU4eeughe1AcGRnJmDFj6N+/P2FhYaxdu5ZJkybxt7/9LSgjQGutufbaa/nmm28AMJlMjBgxgkGDBtGgQQMKCgrYtm0bP/74I5s2bbLXhjZo0IA5c+Zw7Ngx7rnnHgAGDRrEQw89VG4bgQbwmzZtYvDgwRQWGi0aevTowY033kjz5s05evQoM2bMYOXKlWRlZTF8+HAWLFjgs0b8o48+Ytq0aaSmpjJ27Fi6dOlCSUkJ8+fPZ/r06WitefHFFxk4cCCDBw92WregoICrr77aHhQPGDCA4cOH07x5c8LCwjh+/Dh//PEHixYt4s8//wxoX4UQQogzUWUCYn+ZT5olMD7DSGAsalTWD1lVl/f3WbU6MHZs1tyyZUvi4+Pdpps3bx4jR47ks88+IzLy9AiKt99+u/3/J5980h4Ujxs3jnfeeccpLcDjjz/OnXfeydSpU1m8eDEfffQR48aNc0rz888/88EHHwCQlJTETz/9RK9evezLb775Zu6//37S0tKYO3duxXbcwWuvvWYPips3b853333HOeecUy7dP//5TzZs2EB96+SIsbGxjBgxwqmZdPPmzSsdrJeVlXHzzTfbg+Lx48fz5ptvOt1AeOihh3jppZd47rnnKC0t5dZbb2XHjh1ER0d7zHfatGlcfPHFzJkzh7i40+f0mDFj6Nu3L48++igAr7/+ernA+IcffuDQoUMA3Hvvvbz//vset/PLL78QcyaMiCKEEEJUgvmk5/7DwRCREkFkSqTvhCKkSB9jUaNS70ulyb1Ngp5vk/uakHpfatDzDRXbt2/nmWeesT+/7rrrPKZt2rQpn376ablA1+bIkSP2YGnIkCF88MEHbtNGRETwySef0Lp1awDefPPNcmneeOMNe63s22+/7RQU23To0IFPPvnEy975Jz8/3z4Sd2RkpMeg2KZXr160aNGi0tv15rvvvmPLli0AnH/++bz11ltua9WfffZZex/xAwcO8Nlnn3nNt169ekyfPt0pKLYZP348zZs3B2Dx4sWYzc5f9rt27bL/f9ddd3ndznnnnUdUVJTXNEIIIcSZLjIlkoiUiOBnrCC6dTTRLWR6pjORBMaiRpliTbR/vz1dv+5KRP3KX6Ai6kfQ9euutH+vPabYM7/5yty5c50ekydP5u6776ZXr172ptRNmjThiSee8JjH7bff7jagspkxYwYlJSUAPPbYY17LExERwahRowDYuXOnU41rcXEx8+bNA4zmxzfffLPHfIYNG0anTp28bsuXefPmceLECQBuvPFGr0FxdZk9e7b9/8cff9zrSJRPPvmk2/XcufXWW0lOTna7LCwszN5vuri4mN27dzstd+x3bgvahRBCiGAqLISMDDh82PhbGOLjoyqTIrpFNNFto1HhwQlgw2LDiDsnjoi6VRBwi2ohTalFSKh/ZX0Sfktg+5jtZC/MrlAeyZck03FyR6Ia154ar6uvvtrr8k6dOjFz5sxyA3E5+stf/uI1j59//tn+/7Fjx3w2cc7OPv3+bNu2jZYtWwKwefNme4CdlpaGyeT9xsSQIUPYtm2b1zTerFixwv7/lVdeWeF8gmnt2rWAMZr2xRdf7DVtv379iI+PJz8/n19++cVr2vPPP9/r8tTU060jHN8fgIsuugilFFprxo0bx+7du7nxxhtp166d1zyFEEIIX3JzjWA4P7/8svh4aNIEPAyBEhIikiIwdTZRlF6EJdf7KNTeRDaJJLKxTM10ppPAWISMqMZRdJvfjYNvH2TPU3vQJf5NG6MiFa3/2Zqm45uiwmr3BSkuLo4GDRrQo0cPrr76akaOHOmz6atj0OSOY63v2LFjAyqPYxDmOAJz27Ztfa7rTxpvDh48aP+/srXPwXLkyBEAGjVq5HHUbpuwsDDatGnD5s2bOXHiBCUlJR6bu9v6RnvieA4UFRU5LevcuTNPPvkkEydO5NSpU0yYMIEJEybQrFkz+vXrx4ABAxg2bFiVNzMXQghRu2Rmwj7PY6CSnw87dkDLluDja6xGhUWGEdMuhtKMUooPlZ9+yZfoVtFE1JNa4tpAmlKLkKLCFM0ebUbHTzv6vU7HTzvS7JFmtTIo1lo7PfLz89mzZw9fffUVN998s1/9QX0NpuRrPl1vbDXEYPT5tXE3bZQrb827/ZGbm2v/39PAY9UtLy8P8H/fHMttW9cdd/2UA/HKK68we/ZszjvvPPtrBw4cYPr06dx///20atWKyy+/nB07dlRqO0IIIc4Oubneg2JH6elG+lCmlCKyUSRRqYG3OrQUVLymWYQWCYxFSMpb5zlIKJd2vf9pRXm24Cw8PJzS0tJywbi3h2MNs2OQV1DgewqEU6dOVarcjtNT5btrw1UDbLXE/u6bY7l91TBX1tVXX82aNWs4dOgQX375JQ899BDdunUDjBsw8+bNo2/fvpVq3i6EEOLs4NBIzC/WBlUhrTSnlKJDxQGvZ8422wceFWc2CYxFyNFlmsxZmb4TWmXOykSXyQWpomxNrc1mc6VqDJs0OT26uONIyJ74k8abpk2b2v8PlWCucePGABw9etRrDTAYwahtoKx69ep5bEYdbE2aNGHUqFG88847bN68mR07dnDRRRcBRuuBZ599tlrKIYQQwj+hNrBVYaH7PsXe5OXVfLk90VpTfKiYol1FqAr8nNQlGsspqTWuDSQwFiEnd00uxQf9v2NXfKCY3F9CvI1OCLONaAwwZ86cCudz7rnn2oO7ZcuWYbF4/5JYvHhxhbcFzoOK2eYyDpRjE+Vg3O3t27evPa9FixZ5Tbtq1Sp7jbFtvZrQrl07Zs2aZR8szXFQMyGEEDUnNxe2b4ctW+DAASMwPnDAeL59e801T67odquyvFprSrNKKc0qDej7vKy0jMKdhZQcKfGd2AtzdtXOiyyqhwTGIuRkzvS/trgy6wjD6NGj7QHtW2+9xdGjRyuUT1RUFJdffjkAGRkZfPHFFx7Tzps3j61bt1ZoOzZDhw6lbt26AHzxxRf8/vvvAefh2Py7sk27Aa699lr7/6+//rrXL2fbHMyu69WEOnXq2KeDcp0HWQghRPXLzDQGrvJUM2sb2Or48eotF4CP+95BX8+vvPMsFO0tomhvEZY8/zZkOWWhYFuB36NRewu3pTl17SCBsQgp3ppRN7m3CU3GNXG7TJpTV1yzZs148MEHAcjKyuLSSy/12szZVhv68ssvl1vmOA/y+PHj2bRpU7k0O3fu5I477qh0uePi4uxzAZeUlHDFFVd4DY43bdrEPpeRQurWrUudOnXsyyv7pTZs2DC6dOkCwMqVK3n88ccpKysrl+6VV17h22+/BYzjf9NNN1Vqu968++67fPXVV5SWlnpMM3PmTI5bf12de+65VVYWIYQQvoX6wFY+ZmMM+nr+KM0qdfu/O1prSjJLKNhe4NcMKGVAPibcDfFqW1uaU9cOMl2TCCnumlFH1I+gw6QO1L/SGOu/7mV12X7HdsxZp2u2bM2p61xQp1rLW1tMnDiRTZs2sWjRIn777Tc6d+7MVVddxYABA2jUqBGlpaVkZGSwefNmFi5cyOHDhxkyZAjPPPOMUz79+/fnvvvu4/333yc7O5vzzz+fMWPG0L9/f8LCwli7di2TJk3i1KlTjBgxwuecyb789a9/ZcWKFXzzzTfs27fPPo1VWloaDRo0oLCwkD///JMFCxawfv16lixZUm5aosGDBzNnzhx2797NqFGjuOaaa0hKSrIvHzhwoM+RvW3CwsL43//+x4UXXkhhYSFvvPEGS5Ys4aabbqJp06ZkZGQwY8YMe3PliIgIpk6dSnR0dKWOgzcbN25k/PjxJCcnc8kll9CrVy9SU1MJCwvj6NGjLFiwgB9//BEwRuV86qmnqqwsQgghfKvIwFbVOVdwRbcV7DJqrTGfMKPLtFNTZnO2Gd1co0zlQ1ldpinaV+T0G9KbIsI4RAxmwoinlEYUYcIIiJX14bjd8HgJrc5k8u6JkOLaJDr5kmQ6Tu5IVOPTw+fXv6o+ffr2YfuY7WQvzHZaVwLjiomIiOCHH37gscce44MPPqC0tJRZs2Yxa9Ysj+t4mh/53XffJT8/n6lTp1JcXMxHH33ERx99ZF8eFhbGv/71L1JSUiodGCulmDVrFg8//DAffvghFovFa7ndTXv03HPPMX/+fAoLC5k5cyYzZ850Wr53715atmzpd5l69OjBokWLuPbaazly5AgbN25k48aN5dLVrVuXL774grS0NL/zrgjbPmdnZzN9+nSmT5/uNl1cXBwffPCBfSAuIYQQ1a8yA1v5eQ+30mJiID4+sHImJAS/fLbm0+WUQWl2KZH1nQe1LCsuo3B3IWUF5VtyhcWGOb2ugSwiySISW/ibTwTpmGhEEXGUrx32twm3CF3SlFqElJxlOQCoSEWbN9vQbV43p6DYJqpxFN3md6PNG21QkcYFK2dpTjWWtPaJjIzk3//+N9u3b+fJJ5/kvPPOIyUlhfDwcGJjY+1z3b7yyiv89ttvTJkyxW0+JpOJKVOm8O233zJs2DBSUlKIioqiefPm3HDDDaxYsYLHH388aOWOiIjgvffeY/PmzYwfP55zzjmHpKQkTCYTSUlJ9OrViwcffJDly5czYMCAcut3796dDRs2cOedd9KhQwe/5mD25YILLmDnzp28+eabDBw4kJSUFCIiIqhXrx4XXHABL7/8Mrt37+bSSy+t9LZ8+fDDD1m6dCnPPfccgwYNIjU1laioKMLDw6lfvz79+/fnhRdeYMeOHdxyyy1VXh4hhBCeheLAVu40cd+zzSPrpA1B5a3JtPm4c42w+aSZU1tPlQ+KwyC69elWWxooJIx9xJJFFLg0oDYTxkFiOEaUvRm1ilaE1wsnpm013ZkQVUZJR/HaQSm1oWfPnj03bNgQ8Lq2qW46deoU7GIFrPhwMXue3kPTh5uS0N2/eV3zNuVx8O2DtH6lNVFNAp+YXQghhBAiFBw+HHhTajAC1UCD1crKzPSvL3TLllC/fnC3rS2a/M35RgdgD+K6xqGiFCWHS9yOOq2iFTFtYjDFmCgrKaP4UDGl8ZHs2OdfZ+goLLRILCG+ZRRhkVLX6Et1xRu9evVi48aNG7XWvQJdV5pSi5AS1SSKTpMD+8AkdE8IeB0hhBBCiFATigNbeZKSAlFRRh/nvLzyyxMSjJriquj/XJpd6jUoBig5XkJZQZnbUafDk8OJbhlt74ccFhlGTKsYYoAW+BfwN25pIrG+1BLXJhIYCyGEEEIIEQJCZWCrQLabmGj0cc7NNaZkMpmM14LRp9hSaKFgS0GF1i096qWpdbaZsiZlmGLK31GoyYBf1CwJjIUQQgghhAgBoTKwVaBiYqqmDOaT/o0eXdG83QXGUPUBvwhNEhgLIYQQQggRIpo0gR07/E9fFQNb1STbNEwAkSmR6GJNaab3uYkDFZESQWRKpM90VRXwi9AkgbEQQgghhBAhIjERWrTwf2Cr2taktzSrlOL04qrJ3ATRraKJSIqomvzFGU0CYyGEEEIIIULI2dzPtfRYcGuHHUU2iJSgWHgkgbEQQgghhBAh5mzs56otmrIiH8NNV1BESgSRjXw3nxZnLwmMhRBCCCGECFGh2s+1KgJ2f6ZhClgYRLeW5tPCNwmMhRBCCCGEEH7JzYXDh92PnB0fbwweVtEm3ubjbkahNgHlpyL2W0S9CAmKhV/CaroAQgghhBBCiNCXmWmMmO1pOqn8fGP58eOB520psmDJdxMBWzCaQKvA8wRjWiatdcVWFmcVCYyFEEIIIYQQXuXm+jdSNkB6upHeHa01pVmllGaVOgWs5iwvcxYrMMW7n3PYF12isZyqRJWzOGtIU2ohhBBCCCGEV4cPB5b+yBHnJtWWQgsFWwqcE+31L6+SIyWBbdyFOdtMeLyEPcI7qTEWQgghhBBCeFRY6Ln5tCd5ecZ6NuaTXmqEq5g5W5pTC98kMBZCCCGEEEJ45KlZdCDrRaZEEl6/ZmptpTm18IcExkIIIYQQQgiPLBWMKR3XUyZV4X7CFaEinUfrMmfXXI21ODNIYCyEEEIIIYTwyFTBeNZ1PbfTMVVCREoEESmep2KKbHp6NGtLntQYC++kF7oQQgghhBDCo4rOS+w0+Jan6ZgqwgTRraLt8xOb6pgoSi8Ch7hbl2hM8SZiO8VSklFCVGpUcLYtai2pMRZCCCGEEEJ4FBMD8fGBrZOQYKxn43U6pgCYEk3EdYmzB8UAEUkRxHWOw5ToXEVtzjZjijUR0yqGsEgJe4R3UmMshBBCCCGE8KpJE9ixw9NSTTIlNMBhWqU8yFsf3DKYEkzEtItBKVVuWVhkGDHtYijNKKX4UDFoaT4tAiO3ToQQQgghhBBeJSZCixbul8VicQ6Kq0hZcZnX5UopIhtFEtsplvB64cS0jfGaXghHEhgLUctMnjwZpRRKKSZPnlzTxREiJLRs2RKlFC1btqzpopyRbNeUtLS0oOR3tr8fZ/v+14Rgn8OepKen27c1duzYKt1WoNasWcMNN9xAixYtiI6Otpfz4Ycf9juPlBRo395oJu0okVK36bte2ZXEPol0vbJrJUp+mr/TLknzaVER0pRaiBDj2DxIJqMXQpwJ5s6dy6ZNmwB4+OGHSUpKqtHyuEpPT6dVq1ZulymlSEhIoEmTJvTu3ZvRo0dz+eWXu22qKcSZatq0adx8882UlXmvcfVHYqLxKCzQnMowoy2aqJNmsP1kUYAJp4GwgsmcbSY8XkKYYMnNzWXjxo1s2LCB9evXs2HDBnbt2mX/Dbp3796z5iaenFVCCCGEqJS5c+cyZcoUAMaOHRtygbE3Wmtyc3PJzc1l+/btfPbZZwwcOJAvv/ySRo0a1XTxhKi04uJixo8fT1lZGeHh4YwbN46+ffuSYK32bdOmTYXyjTBbiMoqKr9AQ1TjKMwnKx4Zq0iFKcHkdsAuc7YZ3VTLzasgOHnyJMnJyVIRYyWBsRC1zNixY0Ou+ZYQNS09Pb2mi3BGq00/mlJSUvjoo4/sz7XWHD9+nMWLFzNr1izMZjPLli3j8ssv55dffiEiwvMcqeLMUZvO4UCtW7eOzMxMAO644w7+/e9/ByXf0iz3zafBCF5jOsSgTIEHr+H1w4luYTT1Lk0udTsNk+WURWqNg0Br7fTZUErRpk0bsrKyyM7OrsGS1Qw5o4QQQghx1oiNjWXEiBHlXr/rrrsYN24cl112GUVFRfz666988skn3HvvvdVfSCGC6MCBA/b/e/ToEZQ8tUVjzvZcI2zJt6CLtdGkOgBRzaOIbBBpfx6RFIGpszFHsSX3dN9iaU4dHOHh4YwePZpevXrRq1cvevbsSZ06dUhLS2PZsmU1XbxqJz3ShRBCCCGAgQMH8uijj9qfz5o1qwZLI0RwFBcX2/+PiooKSp6l2aXgo7tySWYJujSwmnp3o07bpmGKahpl9F9GpmEKlvj4eKZNm8Zf//pXBg0aRJ06dWq6SDVKAmMhahl/RqV2HZ2zoKCA119/nd69e5OcnExcXBxdunThqaee8rspTVlZGTNmzGDUqFG0atWK2NhYEhIS6NixI/feey+///67zzz279/Pf/7zH0aOHEmHDh2Ij48nMjKSBg0akJaWxquvvsrJkye95uFuRNBDhw7xzDPP0K1bN5KTk1FKMWHCBL/2Kxj55ufn8/bbb3PxxRfTpEkToqKiqFu3Ln369OG5556zN3HzJSMjgyeeeILOnTsTFxdH3bp16du3L2+88QYFBQWA79Fux44da98PW/Pi2bNnc+WVV9K8eXMiIyM99ttavXo19957L507dyYpKYno6GiaN2/OqFGj+P77732W32Kx8L///Y8rrriCZs2aER0dTUxMDM2aNaNnz57cfffdzJ49274vrg4fPsxzzz3HBRdcQN26dYmIiCA5OZl27doxcOBAXnjhBdatW+d23UBGAV6wYAG33HILrVu3djqPx40bx4YNG7yu6+48OX78OBMmTOCcc84hISGBhIQEevbsycSJEz3uqz9KSkqIi4tDKcXw4cM9pjv33HPtZbrzzjvdptFak5KSglKKCy64oNxyTyP62s4nW/9igFatWtnT+zs6r9ls5qOPPqJ///7Ur1+fmJgY2rVrxwMPPMDBgwe9rhtsw4YNs//v6br1yy+/cPfdd9OhQwcSEhKIi4ujTZs2jBkzhsWLF1d429u2bbMfs6uuusqvdd544w37Oh9++KHTsrS0NPsym+nTp3PxxRfTqFEjoqKiaNGiBbfddhvbt2/3a3tms5lPPvmEyy+/3H49q1evHr179+bvf/87R44c8bq+u++o9evXM2bMGFq1akVMTAwtWrTghhtu4I8//nBa12Kx8MUXXzB48GAaN25MdHQ07du358knnyQ3N9frdv0ZlXr79u289tprXHnllfbPf1RUFI0bN+ayyy7j/fffp6jITZ/aKrZt2zbGjx9P165dqVOnjv0YXX/99cyZM8fjerbr3m233WZ/7bbbbnP6bPq6JloKLeStzyv3KE4vJisniwn/mUCf6/vQ6C+NaD6kOQNvHci7/3uXgqICSjNKTw/I5c9+7t7GX5/+K927d6du3bpERUWRmprKlVdeyRdffEF4g3C/pmFasmQJI0eOJDU1lejoaJo1a8bVV1/NggULAFi6dKl9/z39FnA9X7Kzs5k4cSJ9+vShfv36Hq9rJSUlTJo0iSuvvNL+PZeUlES3bt147LHHAurWs2XLFh599FG3x+Pzzz8PykBqwoWtbbk8zuwHsKFnz566IrZu3aq3bt1aoXVF8GF8jWjj4xm4Tz/91L7+p59+6nUbAwcO1Lt379adO3d22q7jo0WLFnrv3r1et7lr1y7dvXt3j3kAOiwsTD/77LMe81iyZIlWSnnNA9ApKSn6559/9pjP3r177WnHjBmj58+fr5OTk8vl8/zzz/txNCuf7w8//KAbNGjgdZ8SEhL0119/7XX7ixcvdrs92+Occ87R+/fv1y1atLC/b+6MGTPGvs727dv11Vdf7TY/R/n5+Xr06NE+35thw4bp3Nxct9vNzMzUffr08ZkHoOfMmVNu/e+++07Hx8f7XLdOnTput+/ruGitdV5enr7iiiu85q+U0g899JC2WCxu83A9T9atW6dTU1M95te9e3edlZXlsUy+DBkyRAM6MTFRm83mcsuPHz/u9Llq3bq123x+++03e5qnnnqq3HLHa4Yjx/PJ22PMmDFO6zm+H5mZmfrCCy/0uG5ycrJev359hY+R1s7vi7dzQGutd+zYYU8bERHhtKy0tFTfddddPvd35MiRuqCgwOM2vJ2PAwYM0IA2mUz60KFDPvetU6dOGtCxsbH65MmTTssGDhxoL1NhYaEeMWKExzJHRUXpH374weu2/vzzT92hQwev+x4XF6enTJniMQ/X76h///vfOjw83GOZ5s+fr7XWOjc3Vw8dOtTjdjt27KiPHTvmcbuezmGbKVOm+HUut2nTxutvJtdrQGU999xz2mQyeS3TwIED9fHjx8utazvPvD18fR4K0wt17rrcco+Fkxbqekn1PObbqXUn/cc3f+jmjZtrQDdv3NxtPrnrcvWJ1Sf0uFHjdFhYmNey9u3bVx85csRreR9++GGveYwfP14vWbLE/tzTbwHHY7thwwbdrFkzn9e1devW6VatWnndfmRkpP7www+97kNpaal+6KGHgnI8Ksrx2uHrN6C/qive6NmzpwY26ArEU9I4X4izWG5uLsOGDWP79u1ceeWVDB06lLp167Jnzx4++OAD9u/fz759+7j11ltZvny52zx2797N+eefz/HjxwE477zzuOqqq2jVqhUWi4WNGzcyefJkTpw4wUsvvURYWJjbO7RFRUVorenSpQuDBg2iU6dO1KtXj6KiIg4cOMDcuXPZsGEDmZmZDB8+nE2bNvm8071r1y6uv/568vPzGTVqFEOGDCExMZG9e/eSmppa4ePmb75fffUVo0aNwmKxYDKZGD58OEOGDKFRo0bk5eWxZMkSpk+fTl5eHldffTULFy5k8ODB5ba3detWhg8fbq9d7NGjBzfffDNNmzYlIyOD6dOns3LlSkaNGoXZ7P8ooI888gjz5s2jTZs23HLLLXTo0IGCggKnfkXFxcVcdNFFrFmzBoDmzZtzww030KVLF6Kioti1axdTp07lzz//5Pvvv2fEiBEsXLiQsDDnBkl33XWXvTa3bdu23HDDDbRv356YmBhyc3P5888/Wb58Ob/88ku5ch46dIjRo0eTn58PGDV6ttr3srIyjh07xubNm1m4cKHPFgWeWCwWhg4dyooVKwBISkri9ttvp2fPnpjNZlasWMHUqVMpKSnh3XffpbCw0GkAJ3cOHDjAsGHDOHHiBDfddBODBg0iPj6erVu38t5775GVlcWmTZt4+OGHmTp1aoXKPWjQIBYtWkRubi4bNmygb9++TsuXLVtmu3kKwJ49e9i/fz/Nmzd3SrdkyRKnPP310EMPMWLECN599117Hv/3f/9HgwYNnNK5bs/GbDZz7bXXsnLlSgYNGsSIESNo3Lgxhw4d4pNPPmHLli1kZ2czevRotmzZQmRkpNt8gsmxBUdiYqLTsltvvZVp06YBEB0dzZgxY+jXrx8mk4n169czadIk8vLymDlzJidPnmT+/PkBj5w7btw4li9fjsVi4dNPP+WZZ57xmHbFihVs27YNgFGjRpUrr6Pbb7+duXPn0qtXL0aPHk3z5s05fvw4n3/+OatWraK4uJibb76ZP//8k/r165db/+DBg/Tv399+fNq2bcvYsWNp27Yt2dnZfPPNN8ybN49Tp04xduxYTCYTN910k9d9/e6775g9ezYpKSnceeeddO3alcLCQmbPns33339PcXExo0aNYu/evYwZM4Z58+Zx4YUXMnLkSBo3bsy+fft477332LdvH9u3b+eRRx7hs88+8+cwl1NQUIBSil69ejFgwAA6dOhAcnIyubm57Nu3j+nTp7Njxw52797N0KFD2bRpU5WPvv7UU0/xz3/+EwCTycTo0aMZPHgwMTEx/P777/z3v/8lIyODZcuWMXjwYNasWUNMzOma1I8++oiCggIWL15sH3DrwQcfdPqeiY2N9VoGbdHlXttzcA/XPnQtuaeMWvoubbtww+U3kNowlaPHjzJrwSw2bNnAmKfGUGr2PEAXgNaaMU+N4dul3wJQP7k+14+4nj4D+hAXF2c/9uvXr2ft2rUMGTKEdevWuS33Cy+8wNtvv+10vIYMGUJ0dDR//PEHkyZN4p133uHw4cNey+QoKyuLq666ioMHD3L55ZczbNgw6tevz6FDh5w+26tXr+aiiy6yf08PGTKEoUOH0qxZM4qKili9ejVTp06loKCAcePGERUV5bbGWWvt1BIgJSWFG264gR49egR8PEQFVCSalkfoPZAa41oDh7uBFRFIjTHWu5fffvttuTTHjx93uvP5yy+/lEtjsVhsd+a0yWTS//3vf91uLyMjw16jHBYWpv/4449yadLT0/Vvv/3mdd+++OIL+x3UsWPHuk3jeLce0PHx8XrZsmVe8/VHoPnu379fJyYmakA3bNhQr1271m26tWvX6jp16mhAN23aVJeUlJRL079/f/t277vvPre1lc8//7xftQCuNXwjR47UxcXFHvfD8e77uHHj3KYtKSnRt956qz3dBx984LQ8IyPD/r717t1b5+fne9xeenq6Tk9Pd3rttddes+f96quvely3rKxML1++3O0yXzXG//znP+3b6NChg9uauo0bN+q6deva07n73LieJ0lJSXrNmjXl0u3Zs0cnJSXZPzv+1Ay6s2LFCvu2/vnPf5Zb/sADD2hAn3vuuTo2NlYDevLkyeXS2VoORERE6FOnTpVbbtuGp9o2x/PKn9oF15osdzUohYWF+rzzzrOnmT59us98PQmkxvjpp5+2p01LS7O//uWXX9pfb9iwod6yZUu5ddPT052um//5z3/cbsPb+VhcXKxTUlI0oFu1aqXLyso8ltXxc7dq1apyyx1rfQD9zDPPlMvPYrE41SR7+oxddtll9jTXXXedLioqKpfm008/tX/WExIS9OHDh92mcSxT37599YkTJ8qlc6yZ79Wrlwb0xIkTy6XLyMjQjRs3tn+W3G1Ta9/n8B9//KH37NnjdpnWxnFyvBZNmDDBbbpg1RivWrXK3tojLi7O7fdNVlaW7t27t317f/3rX93m9X//d/qYv/32p9pLYwattdbmArPH2t3cdbk6rU+aPb+br7hZn1h9wmn5ybUn9QM3PuD0PrvWGBemF+rC9EL9z0dPX3uHpw3XB5cc1Hmb88qdp46fy7/97W/lyrxt2zYdERGhAR0TE6MXL17s9nj16NHDqVy+aoxt59WMGTM8Hq/c3Fx7jXJcXJzHlhc7d+7UzZs3t6fLzMwsl+btt9+2b3fEiBHlWoH4ezwq62ytMa7xgE4eEhgLZ9UdGL/44ose8/r444+9pvvqq6/8ykdrowmerTnYXXfdFdA+ObL9EIyJiXEbRLoGJu+8806Ft1WZfB988EF7Wk/Bms2kSZPsaT///HOnZevWrbMv69Kli9vmsjaOX2T+BMZNmzb1GqQePnxYR0ZGakAPGTLE6z6UlJTo1q1ba0C3a9fOadnq1avt23zzzTe95uPOPffcY1/f3Q9of/gKRBo2bKgBHR4e7vUGzcyZM+1lufDCC8stdz1Ppk6d6jGvZ555xq903pSUlOi4uDgN6EsvvbTc8i5dumhAP/HEE/qiiy5y+2O9rKzMHvC72yetT18zqiIwvv322z2mW7hwoV/pfPE3MP755591TEyM28DW8Qe1tybHv/zyiz2gadGihdvPrK8bNY8//rh9WwsXLnSbJicnx36zo0uXLm7TOF4TBg8e7LHMO3fu9Jpu8+bN9uUtW7b02kz8/vvvdwrEXTl+R0VGRpa7EWZz8OBBp24AQ4cO9bjNl19+2ednydc57C9bU/c2bdq4XR6swNixm8v777/vMV16err9PIiLi9PZ2dn2ZSdPar1tm9bPPXf6mD/33Kd63TrjdQ8xly46UuQxKF75+Up7Xm2bt9XHVx13m+7k2pO6V5de5QPjDbm6JNv47i4sLNQNUoyuRu1btnfKqzSvtFy5/vKXv2gwuo4UFhY6LXM879zdJLT5888/7QG0v4HxI4884jE/rbV+4403/L6WL1q0yJ725ZdfdlpWWFho73rVsWNHrzettfZ+PCrrbA2MpSm1CMhStbSmi1Cj0nRaTRchqEwmEw888IDH5Y7NrbZu3Vpu+f/+9z8AIiMjefDBB71uq3379vTt25fVq1fbB8CoiH79+jF16lQKCwv57bff6NWrl8e0sbGx3HHHHRXeVkXz1Vrz+eefA9C3b1/+8pe/eM1v1KhR3HPPPZjNZhYsWMCNN95oX/b111/b/3/ggQcwmTzPfTF+/PiAple4/fbbiYuL87h8xowZlJSUAPDYY495zSsiIoJRo0YxceJEdu7cSXp6ur2pu2MTry1btvhdPhvX9fv37x9wHt6sWrWKjIwMAIYOHco555zjMe11111H27Zt2bVrFytXruTYsWPlmg3bpKSkOL2XrgYPHszLL78MuP98+SMiIoJ+/fqxcOFCVqxYQWlpqX3e3czMTHu+ttFGf/rpJ6dm0wC//fYbJ06csKerbuPHj/e4bMCAAYSHh2M2myt8jFwVFBQwd+5c+3OtNVlZWSxZsoQZM2bYuyN07drVPlhZeno6v/76KwDnnHMOQ4cO9Zh/3759GTx4MIsWLWLfvn1um7j7cs899/D666+jtebjjz/moosuKpfm888/tzfbvPvuu33m6e04t23blmbNmnHgwAG3x3n27Nn2/x988EGn5rqunnjiCd5//3201syePZt//OMfHtNeccUVtGjRwu2y1NRUWrZsyd69ewG4//77PebjeE0I1nniSb9+/Vi+fDm7d+/m+PHjbpudV1ZxcTE//PADAPXq1fP6fWMbqGzSpEmcOnWKBQsWcP3115OZCfv2ed5Gfj7s2AEtW4LrLkSmRKKLNaWZ5ZtBf7PkG/v/94y6h8gI990blFI8eNODjH167OnXIhWx7WMJiza62vz4448cyzwGwH1j7nPKy910TDfffDM///wzubm5rFmzxmkgNdt3ZVRUFOPGjfO43+3bt2fo0KF88803HtO48vX7xvZbqHHjxj67DwwePJgmTZpw+PBhFixYwNNPP21f9uOPP3LsmHE8HnroIZ9dR7wdD1ExEhgLcRZr3749ycnJHpc79pd1Nzr1zz//DECDBg1YunSpz+3Zgrp9+/ZRWFjo9sfVL7/8wmeffcaaNWvYs2cPeXl5lJa676N08OBBr4GxrU9OsPnKd8uWLfZAo27duk4/wj2Jj48nJyfH3l/QZv369fb/fQUtgX4p+grYbe8vwLFjx3zuh+M5sm3bNntg3KVLF/sPgUmTJqG15q677qJv377l+iK7c/HFF/PWW28BcM011/DUU08xcuRImjZt6nNdf6xdu9b+/yWXXOJXeXbt2gUY5+sVV1zhNl3v3r293sjw9fny16BBg1i4cCGnTp1i3bp19OvXDzBGXtVaEx4eTv/+/e3TcOzfv589e/bQunVrwLl/cXX/sIqNjfV6IyIyMpL69etz9OjRSh0jR5mZmVx99dVe01xwwQXMnDnTPrVNoOfIJZdcwqJFiwDjHAk0MG7Tpg1Dhgzhp59+Yu7cuW4DsE8++QQw+jrffPPNPvM8//zzvS5PTU3lwIEDbo9zIPvfvHlzOnbsyLZt29i+fTu5ubke+z6fd955XvNq2LChPTD2dgwbNmxo/7+y58lPP/3El19+ybp169i/fz95eXlYLO6nBjp06FCVBMabN2+2T7GUlpbmM0C65JJLmDRpEmCcb5dddr3XoNhRejpERoLjW6RMioiGEW4D441bN9r/T+uT5jXvgX0Gnn4SBnHnxDn1y3X8jimOLWb+7/MxnzCDBhWliG4W7ZTfoUOH7P9v27bNfr3KyMiwj17fo0cPn1MOpaWl+R0Yp6am0qpVK4/LT548yW+//QYYgbE/+cbHxwOU+753PB75+fk+v3M9HQ9RcRIYC3EW8/WF7jjfoesUFfn5+WRlZQFGgOrrh6ar7Oxsp8C4pKSEO++8037n1R++pueozABblcnXcTqG+fPnM3/+fL/zdv1R5zhIiC2Q8SQ5OZmkpCRycnL82lYg++Fruh1XjvthMpn4v//7P6699lpKSkr473//y3//+1+SkpK44IIL6N+/P5deeqnHmxxDhw7lxhtv5IsvviAzM5NHH32URx99lHbt2tGvXz8GDBjA8OHDPdbc+uI4vUz79u19pndM421qmsp8vgLh+GNo8eLF9sDYFvD26dOH+Ph4+9/8/HwWL15sP59sN7UiIyPt61aXevXq+RycynacqmqaHKUU8fHxNGrUiN69ezNq1CiuuOIKp5s2VXWOeDNu3Dh++uknSkpKmDp1qtP8yhs2bLDXYF977bXUrVvXZ37+no+Oc97aOO5Du3btfG6rffv2bNu2Da01R48e9RgY16tXz68y+UobjM/SyZMnuf766wNq0eTrO6iiKnu+BTC2lHUd58AYwJzlfiDHo5lH7f+3auo5YASol1SPpIQkcvJyUOGq3Gfd8Tvmb3/7W0BldvyOCeR70t80Nr6+Jw8cOGCfNmnjxo0B/RZy/b53PB5PPPGE3/m4y0tUjATGQpzF/Kmt86Sio//a2Jro2tx///32oDgqKorLL7+cPn36kJqaSlxcnL3mzXF0TU938W28NferDF/5VubYuB6XU6dOARAeHm5vIutNXFyc34Fxde7H8OHDWbt2LRMmTOD777+ntLSUnJwc5s2bx7x583jmmWfo2rUrr732Gpdddlm5/D777DMGDx7MW2+9ZW+OvXPnTnbu3MmUKVMwmUxcf/31vPHGGzRu3Digsubl5dn/96eFge1uv+u6rirz+QqEY8C7ZMkS/v73vwOnA2NbSwNbzfH8+fNZsmQJd955J2VlZfYR588///wq+8x4Ul3HyFGLFi0CmksUqu4c8eaqq66icePGHDlyhE8++cQpMP7444/t/991111+5VeZY23bh/DwcKcg1JOq+IxU9bly3XXX8dNPPwGQkJDAFVdcQffu3WncuDGxsbH27X/55ZdMnz4d8P0dVFGVOd9ycvKwDuDvVSQWWmGdRz0P8tZ7T2+TX2hkHm4K99iM2lFsTCw5eTlulwXrO8b2PQm+R9kG/46pTVV+T7q2hgvmd66oGAmMRUBqWx9bUXGOX8RpaWnl+i0GIj093d4MrGnTpixbtszjHV3HpkOhyvHYTJgwgeeff77Cedm+wM1ms1P/UU8cfyBUlm0/wsPDKSwsJDy8cl8Z5557LnPmzCEvL4+VK1eyatUqli9fzqpVqygtLeWPP/7g8ssv53//+1+5flpKKe644w7uuOMO9uzZw4oVK1i1ahWLFy9m586dWCwWpk2bxooVK1i3bp1T00pfEhIS7P/7c/zyHX51Oq5bU8LDw7nwwgv58ccf7dPuZGdns337dsC5CX5aWpo9MAajyaatpqEm+hefKWriHAkPD+f222/n5ZdfZtu2baxYsYL+/ftTUFBgnzKqffv2DBw40EdOlWfbB7PZTElJic+mvaH2GfFl+fLl9qD43HPPZeHChaSkpLhNu3LlyiovT2XOt+ho/453HP5P7ecoPsb4XjBbzJSUlvgMjgsKrcG3dpOXw3dlenq6x/7mvjgGurZ+995UxfckGC2rPv3006DkVZnjISqu+m/VCiFqhTp16tgv4lu3brWNjl4hixcvtq//5JNPem3mtM/fjlM1yLHpVUUGm3LUpEkT+/979uzxmjY7O9vv2mJ/2PbDbDazY8eOoOWbkJDAZZddxosvvsjSpUs5cuQIjzzyCGAMhPToo496rYlp3bo1t956Kx9++CE7duxgw4YN9OjRAzCatb322msBlcexhnnnzp0+0zumcXx/apItqC0qKmLNmjX2wDcyMpILL7ywXLojR47w559/1mj/4jNJTZ0jd999t72m0tanePr06fYmvP7WFldWRfdfKUWjRo2qrFzBYguKAV5++WWPQTFUz3dQZc63Bg38O99yiCQH362QXDVKOf1+7j2412varJwse22xLiv/GyFY35WBfE/6m8Zfwfy+D2ZeomIkMBZCVNiAAQMAY2CmVatWVTgf24jAYAw6482PP/5Y4e1Ulx49etj71C1YsKBSd6d79+5t/99Xrbw/A6AFwrEmas6cOUHN21G9evV488037ft67Ngxv34M2vTs2dOpb/qKFSsC2r7joD4LFy70md4xTaCDKlUVx6B2yZIl9nPFtXl0r1697OfmkiVL7OdMdHS0z8GZvHFs5lqZm2ShKtBzxLGfamXOkebNm9u7FsycOZOTJ0/am1FHREQwZsyYCucdiED2/8CBA/bWCh07dvTYvziU+PsdVFJSEvTrrDvnnnuuvcn60qVLPQ5AaeN4vvXs6d/5plFkEM0hojHjvZ+/o15dTo8FsWyd91kQnJaXlb82BOs7pmHDhvbBGH/99VefTZKD+R7Wr1+fzp07A0bf/wMHDlQ4r+r6zhWeSWAshKgwxx9lTz/9dIX7Wzn2Cdq9e7fHdF9//bV99MdQZjKZ7E2BT548ySuvvFLhvK666ir7/++9957XY/zOO+9UeDvujB492t5k8q233uLo0aM+1qgc2yjWgH3KnOpYt1+/fvZare+//97rdC+zZ8+2B+39+/ev8IBfwda7d29780vHgNe1ebTJZLKPRv7TTz/Z+xdfcMEFREc7jwAbCMcmgMFsphgqWrZsSc+ePQGj+bm3AZrWr1/P4sWLAaM/s7eR8/1hm3qmoKCAZ555htWrVwMwYsQIrzWbwXTNNdfY///3v//tdYCr1157zT4Y0bXXXlvlZQsGf7+DPvjgAzIzM6u8PFFRUQwbNgyA48ePM3nyZI9pDxw4YG9aHxcXxxVXuBs1XHv4H/KJYB+xqDjPI+g7uiLt9Cj8H838iFKz+6Bda817095z2qzllPP31+WXX24fFG7q1KmVqiW1fVcWFxfz4Ycfeky3Y8cO5s2bV+HtuGP7LVRWVsZTTz1V4XyCeTxExUhgLISosOuuu44+ffoARh+tm266yetAK0VFRUyZMoUvv/zS6XVbHgCvv/6629EVf/nlF26//fYglbzqPf300yQlJQEwceJEXn/9dfuPRXcyMzP5xz/+US7w7927t32Ozj/++IOHHnrIbT4TJkwIaA5jfzRr1sw+f2NWVhaXXnqpfZoid7TWLFq0yD43r82PP/7IO++84/Uu/q5du+w1UfHx8U61Ni+++CILFy70evzef/99+//nnnuu9x1zERkZaW/KbTabGTlypNuRhH/77Tfuuece+/Mnn3wyoO1UJZPJZD9PVq1aZQ/e3fUbtr329ddf29+TyjajdpzOZOPGjV5SnrkcR80dO3asvVbU0f79+xk9erT9XH388ce9Ttnlj8svv5xmzZoBxs0xm+pqRg3QrVs3+9zNe/bs4bbbbnM72M///vc/exkTEhK47777qq2MleH4HfTiiy+6HZn722+/rdbP/OOPP25vifHYY4+57ducnZ3NddddZ78Zde+999K4cRIO96kAiKTM7f82MQlhxHWMIappFL4qj89pfw6D+hrXkB3pO3j0n+W7vmitee7fz7Hu93VOr5uznW9axsXF2cfgKCkp4fLLL3eaotCddevWuR2x+YEHHrCPwfHCCy+4bWF14sQJbrjhBp818IG6//777f2BP//8cx555BGvg2Hl5uby7rvvOjXhh+AeD1ExMviWECHMNrqsLz179nS6o19dwsLC+Oqrr7jgggs4dOgQ06dPZ8GCBYwaNYpevXqRlJREQUEBBw4cYMOGDSxcuJD8/Hxeeuklp3wuuOACevXqxYYNG0hPT6djx46MGzeODh06UFhYyOLFi5k+fTpaa/u0PaGuadOmfPnll1x55ZWUlJTw+OOP89FHH3HttdfSqVMnYmNjyc3NZefOnaxZs4aff/4Zi8XiNkD5v//7P/r06UNBQQHvv/8+q1ev5uabb6Zp06ZkZGQwffp0Vq5cyQUXXMD+/fs5dOhQ0EZwnThxIps2bWLRokX89ttvdO7cmauuuooBAwbQqFEjSktLycjIYPPmzSxcuJDDhw8zZMgQnnnmGXseR44c4eGHH+aJJ55g0KBBnHfeebRu3ZrY2FiOHz/OunXrmDFjhv3H3cMPP+zU/Hfx4sU8//zzNGrUiEsvvZTu3bvTqFEjysrKOHz4MN988419/seoqCin0Xv99dhjj/Htt9+yYsUKtm7dSpcuXbj99tvp2bMnZrOZlStXMmXKFPsP5rvuusteoxMqBg0axLx58+w15p6aR9sCY8ea9coOvDVkyBD7/0888QSZmZl06NDBPmBbamqq1/mKzwTXX389c+fOZdq0aRw5coSePXsyduxYLrjgAkwmE+vXr2fSpEn2/r+XXHJJUAJDk8nEnXfe6TSIX6tWrbjooosqnXcgPvroI3r27ElmZiZffvklGzduZMyYMbRt25acnBy++eYbvv/+e3v6Dz74IOAR4mvK1VdfTWpqKocOHWLt2rV07tyZO+64g9atW5OTk8MPP/zAt99+S2xsLNdccw2zZ8+u8jKdf/75/O1vf2PixInk5eUxcOBAbrjhBgYPHkxMTAx//PEHn3zyib0ZeLdu3XjxxRcBaNIEHIeFiMHi9n+bxo2N/uCRjSLRZZqSw95HOH7zyTcZeMtAck/lMuXrKWz8cyOjLx1NasNUMrIymPnjTNb/sZ7eXXtz+PhhDh81plOy5JXf9gMPPMC6deuYOnUq+/fvp2/fvlx22WUMGTKEpk2borXm+PHj/P777yxatIjdu3fTpk0b/vWvfznl07FjR5555hkmTJhAYWEhF198sf14RUdH88cffzBp0iQyMjIYOXIkM2fOBIIz2nlcXBxz585l4MCB5Obm8vbbbzNjxgyuv/56unXrRmJiInl5eezdu5e1a9eyZMkSiouL3U5PGazjEYjZs2eXu6Fpmz8c4I033ig3N/Q//vGPCm8vpGmt5VELHsCGnj176orYunWr3rp1a4XWFcGH0c4poMeYMWPs63/66af21z/99FOv2xg4cKDf5fGW9vDhw3rIkCF+ldVkMumPP/64XB47d+7UzZo187heVFSUnjRpks/927t3r9vjUlkVzXf16tW6devWfh2b+Ph4/dtvv7nNZ/HixTopKcnjul27dtX79+/XqampGtDdunVzm8+YMWPs6+zdu9evfSguLtYPPPCANplMfu3Hrbfe6rT+lClT/FpPKaXHjx+vLRaL0/qDBg3ya/369evrH3/80e0+tGjRQgO6RYsWHvczLy9PDx8+3GcZH3jggXJltAnkPAn2ubp27Vqnsg4ePNhtOovFopOTk+3pYmJidHFxsde8/bkO3HDDDX5do7T27/2oSFpPHI91ZfIpLS3Vd955p89z8brrrtMFBQUe8wl0nw4dOqTDw8Pt+b/88st+rTdw4ED7OsFI++eff+oOHTp43ffY2Fg9ZcoUj3n48x0VaPn9+Sz5OodXr17t9LlwfSQlJenvv/9eP//88/bXlixZUqGyBOLZZ5/1ee0dOHCgPn78uNN6x45pvW6d1hvWlen3nvvAnva95z7QG9aV6XXrjOWZmUb6srIyXZxRrHPX5fr1WPjJQl0/ub7HMnVq3Ulv+XaLbtHcONebpzbXlmL3182ysjL90ksv6aioKL+u9d6uQ+PHj/e67vjx4/XChQvtz9988023+fizLVfbt2/XPXr08GsfoqKi9Lx586r8ePjD8XeBv4+KqK54o2fPnhrYoCsQT0mNsRCi0ho3bsxPP/3EsmXL7FPmHDp0iLy8POLi4mjatCnnnHMOaWlp9rk5XbVt25Zff/2VN954g7lz57J3717Cw8NJTU3l4osv5t5776Vz585e+1qFovPPP58///yT6dOn880337Bu3ToyMzMpKioiMTGR1q1b06NHDy666CKGDRvmcX7FQYMGsX37dl5//XW+/fZb9u/fT1RUFG3btmX06NHce++9xMTEcOLECQDq1q0btH2IjIzk3//+N+PHj2fSpEksWbKEPXv2kJ2dTWRkJA0bNqRTp07079+f4cOHl6sZvOWWW+jevTuLFi1i2bJlbNmyhSNHjlBUVER8fDytWrWif//+3H777fbRpR199913/PzzzyxatIjVq1eza9cusrKyUEpRt25dunTpwtChQ7njjjvszdcrIj4+nm+//ZYff/yRqVOnsnLlSjIyMjCZTKSmppKWlsbdd99d6T6jVaVnz54kJibaayw91QKHhYUxYMAAvv76a8DoY+1r+h1//O9//2PAgAFMnz6dP/74g5ycnID7e4e68PBwPv74Y+644w4++eQTli1bxpEjRygrK6NRo0ZceOGF3HbbbQwePDio223SpAmdOnXi999/Jzw8nNtuuy2o+furffv2/P7770yZMoVZs2axefNmsrKy7J/jyy67jPvvvz9kRmsPxPnnn8/mzZv517/+xbx58zhw4AAxMTE0a9aMYcOGcd9999G8eXPWrl1breV68cUXGT16NB9++CGLFi3iwIEDlJSUkJKSwnnnnceNN97otsVYSgpERcHJ/aVO/SbDgHhK0QmRNG4MiYmgLZqifUWYT/j/eT3v3PNYN2cdH877kK+//pp9+/YRFRVFq9RWXDPkGu4aeRex0bH20ahVuCIs0n3trFKKv//97/bP1aJFi/jzzz85ceIEYWFh1K9fn44dO3LBBRdw+eWXex0o8O233+aqq67ivffeY9WqVWRlZZGSkkKfPn0YN24cl156qX0eagjud2WHDh3YsGED3377LbNnz2b16tUcPXqUU6dOkZCQQIsWLTj33HMZPHgwV155JcnJyVV+PERglDZqG8UZTim1oWfPnj03bNgQ8Lrbtm0DoFOnTsEulhCiGv3+++9069YNgIceeijog3EJIWrGzp07ad++PWAMMjR37tyaLZA4YxRsL8CS79yEWcWaiO9sDDhmKbJQtLuIskLPYzh4E9MxhvD40/VsWmtKM0opPlQMGsJiw4jr7P6Gb0157LHHePPNNwFjTAR3N2RF8FVXvNGrVy82bty4UWsd8F1sqTEWQoha4j//+Y/9/8r2GRVChA7HUXYdB4ATwhtLkaVcUAygCyyUFZUZQfHeItx0Oz6dltPjcTn+b2PONjsFxra+yqZEEyUZJUSlRlV2N4Lq5MmT9r699evXP+PHPhDBJaNSCyHEGeDnn3/2Oirze++9x0cffQQYAx0NHz68uoomhKhChw8ftn+227VrZ5/XWAhfzFmem0YXphdStMt7UAxGIJxDBDlEuB2wuiTLjLvWp6ZYEzGtYjw2n64KR48eZYfjqGMucnJyGDlypH3Krdtvv90+QKAQIDXGQghxRrjtttsoKipi6NCh9OjRg5SUFEpLS9m9ezdz5szh119/taf98MMP5cteiDPYsmXLKCgoYP/+/bz55pvk5+cD8Pzzz6OUj/l0xFnDUmihYEtBhdYty/fddNqMIoMo8jGmQTqFiUYUYeJ07bEyayynLE61xjVl165dDBgwgPPOO4/BgwfTvn174uLiOHnyJBs3bmTatGn26SBbt27t98wf4uxR82exEEIIvxw6dIhPPvnE4/KYmBg+/vhjqS0W4gw3ZswY9u3b5/TaVVddxU033VRDJRKhyHyy6ga3K0ZxkFjMDo1L84kg3RocxzlUNRdlmokPgcAYjD7Oa9asYc2aNR7TnHPOOXz77bckJCRUY8nEmSA0zmIhhBBezZgxg++++84+KmlWVhYFBQUkJyfTvn17LrroIu69914aNmxY00UVQgRJdHQ0bdq0YcyYMTz00EM1XRwRYiJTItHFmtLM0qDmW0AYB4lFu2k8bSaMg8SQTCkpFKNwPz9xTejduzezZ89m/vz5/PLLL2RmZpKVlUVYWBgpKSn07t2ba665htGjR2MymWq6uCIEyajUtYSMSi2EEEIIcfYpzSmlOL0Yba7cb3oNZBJFNv5N3xaFhWRKCG8URaOmMmyR8O5MGJVazmIhhBBCCCFClNaa0qxSSrNK3Q50FZEUQWznWEyJFa8FNSWaKGoS53dQDFCMiaPEoCIknBC1gzSlFkIIIYQQIkRZ8qzTKgExETGEJ5b/+R4WGUZMuxinOYT9oiCqaRQRDSJQRQoOB16+xMTA1xEiFMktHiGEEEIIIUJUaVap2/9dKaWIaBhBeB3/672iW0YT2TASpRQxMRAfH1jZEhIgJiawdYQIVRIYCyGEEEIIEYK0RWPOPj36tDnbjLa4rw4uM5dRuLMQc47/o1VbCpwHzmrSJLDyNW4cWHohQpkExkIIIYQQQoSg0uxScJxyuMz6mgvLKQsFWwuw5AY2QrQ52+zUbzkxEVq08G/dli2lGbXwz5ky2LP0MRYopdBaU1ZWRliY3CsRQgghhAgF5uPla3/Nx81E1j89SFZJZgnF+wPoV+xAl2gspyyEO8xDnJICUVFw5Ajk5ZVfJyHBqCmWoFj4yxYYK1V+CrBQIoGxwGQyYTabKSkpITo6uqaLI4QQQghx1rMUWbDkl68BtuRbKCsqQ0UqivYXuQ2eA2HONjsFxmAEvYmJUFgIublgsYDJZLwmfYpFoEpKSgBCfv5oqR50oJT6i1LqK6XUEaVUsfXvAqXU5W7S9lNK/aCUOqGUKlBK/aaUelgp5fEdV0qNUUqtVUrlK6VOKqWWKqWGV+1e+RZvHWkhz91tQSGEEEIIUe3MWZ4D3pJjJRRsL/A7KI5IiSAiJcL9dlyaUzuKiYGGDY2+xw0bSlAsKiY3Nxc4HXOEKqkxtlJK/R14CTgOfAccAeoDPYA04AeHtFcBXwFFwHTgBHAF8BZwITDSTf6vA48BB4GPgUhgNPCtUupBrfV/qmjXfEpMTCQnJ4fs7GwSEhKk1lgIIYQQoopZCi0UbCmo0LqlxzyPTu1IhSuiWkYRkWQExaY6JorSi8AhnnbXnFqIYCkqKiInJwcwYo5QJp8AQCk1EiMo/gm4Rmud57I8wuH/RIzA1gKkaa3XW19/FlgMXKeUGq21/tJhnX4YQfFuoI/WOtv6+mvABuB1pdR3Wuv0qttLz2JjY4mPjyc/P5/9+/eTlJREYmIikZHG8P2h3h9ACCGEEOJMobXGfMKM+WTlmkD7Yko0Ed0ymrDI0w1EI5IiMHU2gmPHgbrcNacWoiK01mitKSkpITc3l5ycHCwWC/Hx8cTGxtZ08bw66z8BSqkw4FWgALjRNSgG0Fo73pa7DkgBptqCYmuaImut8yLgXuBLh3XGWf++bAuKreukK6XeA54FbgOeD85eBUYpRWpqKocOHSI/P5+srCyysrJqoihCCCGEELWatmjKioyhplW4QpuDP2KvilSEWcKMKhlP5YjUlJWWgQaVqQjLlx6WomrEx8eTmpoa8pVtZ31gDPQDWgGzgGyl1DCgK0Yz6bVa69Uu6Qdb/853k9dyjAC7n1IqSmtd7Mc68zAC48HUUGAMEBYWRtOmTSkoKCA3N5f8/HwsFssZM7y6EEIIIcSZoHh/MaVZRp1LRL0IwpPDKUovqnSArMIVYTFhRDWLIizCd5CrIhSUGs2yI5tG+kwvhL+UUphMJuLj40lMTCQ2Njbkg2KQwBigj/VvBrAROMdxoVJqOXCd1jrT+lIH698drhlprc1Kqb1AF6A1sE0pFQekAvla6yNutr/T+re9P4VVSm3wsKijP+v7yJu4uDji4uIqm5UQQgghhHBhzjWzqtcqygqNGuOw2DD6He2HpaWF7WO2k70w20cO7iVfkkzHyR2JahwVzOIKcVaRNhPQwPp3HBADXAQkYNQa/wgMAGY6pK9j/XvSQ36215MqmF4IIYQQQtRCmbMy7UExQFlBGZmzMolqHEW3+d1o80YbVKT/NWsqUtHmzTZ0m9dNgmIhKklqjME2vZLCqBnebH2+RSl1NUbN8ECl1AVumlW7Y7uaBdoexq/0Wutebjdq1CT3DHCbQgghhBCimhydfNTta41va4wKUzR7tBkqXLFr/C6/8uv4aUca3tgw2MUU4qwkNcZga7OyxyEoBkBrXYhRawzQ1/rXVsNbB/cSXdL5Su+rRlkIIYQQQpzhCnYVcPLn8j/3Ti4/SeHuQgBOLDzBnr/t8TvPvPXlxowVQlSQBMbwp/VvjofltsDZNqW5LX25PsFKqXCMgbzMwB4ArfUp4BAQr5Rq7Cb/dta/5fosCyGEEEKI2iFjaobHZUemHGHfK/v47dLf7CNW+yNzVia6TAZKFSIYpCm1MZK0GWinlIrUWpe4LO9q/Ztu/bsYuAm4DJjmknYAEAssdxiR2rbOLdZ1PnVZZ6hDGiGEEEIIcQY6tfUU67qsq9C6+1/aX6H1ig8Uk/tLLnUu8NQwUQjhr7O+xlhrfRyYjtGk+TnHZUqpi4FLMZo526ZamgUcB0YrpXo7pI0G/mF9+oHLZj60/n1GKZXssE5L4H6gmPIBsxBCCCGEOENk/ZBVI9vNnJnpO5EQwqezPjC2ehTYhRG4LldKva6Umokxx7AFuEtrnQOgtc4F7sIYtGupUuoTpdS/gE3ABRiB83THzLXWq4A3gTbAb0qpt5RS7wHrgbrAX7XW6VW+l0IIIYQQokqk3pdKk3ubVEneje9qTJNx7vOW5tRCBIcExoDW+hhwHvAW0Ax4CBgMfA/8RWs90yX9XGAgRjPsa4EHgVKMAHu01rrc1Ulr/RgwFjgK3A3cCmwBrtBa/6cq9ksIIYQQQlQPU6yJ9u+3p+vXXYmoHxGcPBNNdP26Kx0+6kD7D9rTdW5Xwus594S0NacWQlSOchPDiTOQUmpDz549e27YsKGmiyKEEEIIcVYrPlLM9jHbyV6Y7TuxB3UG1qHztM7l5id2l3fTR5rS9s22Fd6WELVFr1692Lhx40ZPU9x6IzXGQgghhBBCBFFU4yi6ze9GmzfaoCJVYCuboM0bbei+uHu5oNhT3jlLc4JQaiHObjIqtRBCCCGEEEGmwhTNHm1GRMMItt+83a916vylDm3fbUtC9wS/8k4anMTBtw/S+pXWwSiyEGc1CYyFEEIIIYSoAuaTZtKfT/c7fULvBJ9BsVP67gl0mtypAiUTQriSptRCCCGEEEIEWf4f+Wzos4Gi3UV+ryMjTAtRcyQwFkIIIYQQIogypmWw8byNFO4sDGg9GWFaiJojgbEQQgghhBBBUFZSxs7xO9l24zbKCsoqlEfmzMwgl0oI4Q8JjIUQQgghhLDSZZqMaRlkTMsIqFlz8eFiNg3axKF3D/lM2+TeJjQZ18TtMmlOLUTNkMG3hBBCCCGEsMpZmsO2G7cBENkokuRByb7XWZbDllFbKM0o9Zouon4EHSZ1oP6V9QGoe1ldtt+xHXOW2Z7G1py6zgV1KrEXQohASY2xEEIIIYQQVkcnH3X7vztaaw68cYBNQzaVC4pNCSan58mXJNP7t972oBig/lX16fN7H5Ivdg6+pTm1ENVPAmMhhBBCCCEAc66ZzFmng9LMWZmY88zu0+aZ2Xr9Vnb/dTdYnJclX5pMdMtoAFSkos2bbeg2rxtRjaPK5RPVOIpu87vR5o02qEgFGLXWQojqJU2phRBCCCHEWWXLFli0CHJzITERhgyBLl2MQLis8PSgWWUFZWTOyqTxbY2d1j+17RRbrtlCwfaCcnm3eK4FLZ9rSUlGCXue3kPTh5v6nJtYhSmaPdqMpMFJHHz7IK1faR2cHRVC+E0CYyGEEEIIcVZYtAhefBGWLy+/bMAAmJB9FOXy+tHJR50C42MzjrH99u2UnXIedTo8KZxOn3Wi3rB6AEQ1iaLT5E4BlS+he0LA6wghgkMCYyGEEEIIUetNmgR33w1lZaDQDOIYAEtogEaxa3kBipNocAqOTy4/SeHuQqKaR7Hnb3s4+NbBcnnHd4+ny1ddiGkdUz07I4QIOgmMhRBCCCFErbZo0emgGKA7OTyLMfL0CSLZRDKXkgFQrsYY4ND7h8hbl8fJn0+WW9ZwTEPaf9AeU4zJzZpCiDOFBMZCCCGEEKJWe/FFaFZ2ismsK7fsLTb7XP/gm+VriW0ypmTQ/G/NiesU51dZPPVvFkLULAmMhRBCCCFErbVli9Gn+HqyqmwbWd9n+QyMffVvfu45I0gWQtQMma5JCCGEEELUWosWGX+/JpWvaRL0/Jvc14TU+1K9ppk0CS65xH1QDMbrl1wC//1v0IsnhPCTBMZCCCGEEKLWys01/hZj4m3as5fYoOQbUT+Crl93pf177THFeu5f7Nq/2ZOyMrjrrtOBvBCieklgLIQQQgghaq3ExNP/N6GAVhSgK5ln8iXJ9P6tN/WvrO8z7Ysv+g6KbcrK4KWXKlk4IUSFSGAshBBCCCFqLcd+u95GnvaHilS0ebMN3eZ1I6pxlM/0tv7NgVi2zFhPCFG9ZPAtIYQQQghRK5zaeop1XcqPPL0kSPl3/LQjDW9s6Hf6ijaLXrRIRqoWorpJjbEQQgghhKgVsn6oupGnAfLW5wWU3ta/OVAVXU8IUXESGAshhBBCiFoh9b5Umtwb/JGnbTJnZaLL/O+h7Ni/ORAVXU8IUXESGAshhBBCiFrBFGui/fvt6fp1VyLqRwQ9/+IDxeT+4n91bkXnJZb5jIWofhIYCyGEEEKIWqX+lfXp/Vtvki9OrlQ+7uqGM2dm+r1+ly4wYEBg2xw4UPoXC1ETJDAWQgghhBC1TlTjKLrN70abN9qgIgMbh/p3EvmGxm5Hrw60OfVzz0GYn7+4w8Lg2Wf9zloIEUQSGAshhBBCiFpJhSmajm9K3cvq+r3OdJryED15iw78na6ctE7iYguFK9Kc+qOPfAfHYWHw8cfSjFqImiKBsRBCCCGEqJVKMkvYfOlmsr7xf7Rqxx/HK6nP7fRhHclOtceBNKcGuOMOWLDAaCbtzsCBxvLbbw8oWyFEEMk8xkIIIYQQotbJXZvLlmu3UHywOKD1BpDJB7RBW0PhE0TxN7pxHQe5iz1EoMlZmhNweYYMMR5bthjzFOfmGqNPDxkifYqFCAUSGAshhBBCiFpDa83h/zvMrod2oUv97wts05BiOpHLVuqczhPFTJqxkSSu4yA3vtG6wuXr0kUCYSFCkTSlFkIIIYQQtYKlwML2sdvZee9Ov4Nid6nScN9UejcJvEonlv4eVYlSCiFCkQTGQgghhBDijFe4u5CN/TaSMTXDr/RN7m3CkT5N3I48PYBMlNuQ2ZDr/9hbQogzhATGQgghhBDijHb8u+Os77WeU5tPOb0eFlP+p25E/Qi6ft2V9u+3J/Pm9m5HnrY1p/YkMTFoRRdChAgJjIUQQgghxBlJWzR7n93LH1f8geWkxWlZbMdYUkamOL2WfEkyvX/rTf0r6wPGwFeeRp721Jzatp4QonaRwFj8f3v3Hp91fd////FOSKIgh2AECeCB1AAmRsvB1naDWirrDtWth9m5tV2hOnVbD25r14O01a7rtupcD9pqUebanzppV79r1dqlRXrYLIKKhoMCnpDTJZgEAwTC9f79cV2BHK6E5Mp15fi43265Xbk+n8/7/XkHL4En79fn/ZYkSRpyjuw9wvrfW8+LX3qx07nT3ncac34zh6anUzPIoThQcXMFNQ/VUDLl+PPBVVWwYMHxladvpYIj6Xh8PvUZ77twoYtnScORq1JLkiRpSGl8PL0V00sdtmIqhIp/rmDaJ6YRQuC8H53Hts9sY9rHpzH2grEZ+1q2DBYvhmSy/crT36HzytMFBXD99fn4iSQNNGeMJUmSNGTs+M4OnnjrE51CcdHkIi742QVMv246IaRmfUvKS5i9YnaXoRhSZdG3354KvXB85em9tF95uqAA7rjDMmppuDIYS5IkadA7evAom5Zu4tkrnyUebr9i9Li3jmPeunlMWDAhq76XLoVHHkmVSWeycGHq/JIlWXUvaQiwlFqSJEk5VVcHtbWpbY3GjUvNsvbludyDzx+k7j11vP7E653OTf3YVCr+pYKCor7N9yxalPrK9dglDQ0GY0mSJOVEbS3ccAOsXt353IIFqed5e1uKvPehvWz80420vNbS7njB6AJmLp/J5PdP7sOIO6uqMghLI5Gl1JIkSeqz5ctTi1hlCsWQOr54Mdx5Z8/6i8nIC198gad//+lOofjkypOZ+5u5OQ/FkkYuZ4wlSZLUJ7W1cNVVkEx2f10yCVdeCWee2f3M8ZF9R9j4gY3se3Bfp3Nlf1TGrBWzGDXOv8ZKyh1njCVJktQnN9xw4lDcKpmEG2/s+vz+J/azdu7azqG4AGb88wyqvl9lKJaUc/6uIkmSpKzV1XUunw5ELmYPAD9nEpHQ7vyjj6badXyWd+ddO3nu2udIHmqfsotOK+Lc+86l9OLSnI9fksBgLEmSpD6ore187ALquZ6NAOyjmCfpHGhra48H46OHjrLlY1vYefvOTteNe/M4zr3/XE6adlJOxy1JbRmMJUmSlLXGxs7H3smudt9nCsat7Q69eIi699ax//H9na6Z+ldTqbipgoJin/6TlF/+LiNJkqSsjRvX/v1oWlhA4tj7BSQ4mRY6GjcO9j2yj8fnPt4pFBecXMDs787mnK+fYyiW1C/8nUaSJElZ67i69EISnMTxZ4RPJsnCNkEZUs8gv3nLi6x/53pa9nbYiukNJzPn/+Yw+U/diklS/zEYS5IkKWtVVbBgwfH3v9OmjLpV29LqMRzhtlOf4cDXn4fY/rpTLzuVOWvmcErNKfkariRlZDCWJElSnyxbBgUFUM4BzqehXd6NwPk0UM5BKnidb7OWmXv3tu+gAM7+8tlU/6CaoglF/Tl0SQJcfEuSJEl9tGgR3H47/PojuwHabc7U+v3VbGE+r7UrswYoKiti9j2zmfiOif0zWEnKwGAsSZKkHmna0MSaqjUZz1Wkv7ry2+zNePzIq0dYf8l65m+Yz5jZY/o+SEnKgqXUkiRJ6pG9D2YOtznp+8f561uSTsRgLEmSpB6Zeu1Uyq8pz3m/5deWM/XaqTnvV5J6ymAsSZKkHikcXUjlrZVUP1BNUVnfF8kqKiui+oFqKr9ZSeHowhyMUJKyYzCWJElSr5RdWsa89fMovaQ06z5KF5cyb/08yi4ty+HIJCk7BmNJkiQdE5OR3ffsZvc9u4nJ2OV1JVNKqHm4hoqbKgjFocvrOgrFgYqbK6h5qIaSKSW5GLIk9ZmrUkuSJImYjOy5bw9NdU289A8vAVB8ejGlF3c9KxwKAtOvm87BrQfZceuOHt1n1l2zmHzF5JyMWZJyxRljSZIkUb+qno1XbDwWigF2rdjVbZvk4STPffS5HodigP2P7896jJKULwZjSZIkZQzBiZUJWva3ZLy++ZVmnnzbk7zy9Vd6dZ/EykS3JdqSNBAMxpIkSSNcS2MLiZWJTseTB5IZj7+26jUen/M4jf/b2Ot7Nb/cTONjvW8nSflkMJYkSRrhEisTJA8mM55rO5McY+Slr77EU+94iiN7jmR/v/s7h21JGkgGY0mSpBGuu2eJG1Y3cHDrQVr2t1D3vjq2/d02OHriPsuvKaf86vKM5yynljTYuCq1JEnSCHZgywEaftHQ7TUv3fQS9T+r5+Dmg+1PBKBDvi0qK2Lm8pnH9iee+M6JbFq6iZa9x59Vbi2nHn/R+Fz8CJLUZwZjSZKkEaBpQxNrqtZk1XbnbTszn+gQiksXlzJrxax2+xOXXVbG/Avns+lDm3jtp68dO564P2EwljRoWEotSZI0jDVtaGJVWJV1KO6RQqi4uYKah2raheJWJVNKqHm4hoqbKgjFAUhtDyVJg4UzxpIkScPY3gf35rX/k2eezKy7Zp1w9jcUBKZfN50Jb5/A9lu2M+PLM/I6LknqDWeMJUmShrGp107l5MqTc95vwUkFnPuf5/KmTW/qVUn02AvGMnvFbErKO88sS9JAccZYkiRpGIstkeaXm3Pa55gLxlDzYOayaUkaigzGkiRJw1h3exT3WoAzP38mZ11/FqEg5KZPSRoEDMaSJEnDWKY9ik+acRLN25uJh3u3l/Csu2dx+p+dnquhSdKg4TPGkiRJw1RXexQf2naIGV/p/eJXr697PRfDkqRBx2AsSZI0TO2+e3eX5176l5d63V9iZYKY7N0ssyQNBZZSS5IkDVFNG5qy3p/4yM4jvW7T/HIzjY819moVakkaCpwxliRJGqLyvUdxJmtvSvT7PSUp3wzGkiRJQ9TUa6dSfk15zvvtrlh6/48sp5Y0/BiMJUmShqjC0YVU3lpJ9QPVFJUV9bm/CGzmFDJtxNQahcc3N/PUPY19vpckDSYGY0mSpCGu7NIy5q2fR+klpVn30UQhH2EuVzOPz1FNQ3opmtZA3DYsP/cdy6klDS8GY0mSpGGgZEoJNQ/XUHFTBaE405xvZhF4jFIu5a1sYywAv6KMJcxnDaXtAvHR9OvJm+tzNWxJGhQMxpIkScNEKAhM/ehUJv7OxB63+Q5n8fecT7LDXwv3UcKnqOFWKjiSjsfbOZmHmcxL15yX03FL0kBzuyZJkqRh4vCew2z4kw3U/6y+x20m0NLluUjgfqazjgm8l+18hxnspYRn3p2DwUrSIOKMsSRJ0jDQ+Fgja+eu7VUoBrikJEHodh1q2MpY/onZ7KWEhQuhqqoPA5WkQchgLEmSNITFGHnltld44refoHl7c6/bT2hupir0bJXpggK4/vpe30KSBj2DsSRJ0hB19MBRNn1oE89d+xzxSPZ7C9/4jgQFJ/hbYUEB3HEHLFqU9W0kadAyGEuSJA1BB7ceZN1F69j9H7t7dH35NeWUX12e8dzkTQkeeTiycGHmtgsXwiOPwJIl2Y5WkgY3F9+SJEkaYl7971fZ+IGNHG042u54wckFJA8m2x0rKiti5vKZlF1aBsDEd05k09JNtOw9vuhW88vNzDulkVWrxlNXB7W10NgI48alZoh9pljScGcwliRJGiLi0cjzn3+el/7hpU7nRs8ezdj5Y9l99/EZ5NLFpcxaMYuSKSXHjpVdVsb8C+ez6UObeO2nrx07nrg/wfiLxlNVZRCWNPJYSi1JkjQEHH71MOt/d33GUHzaH5/GnN/MoenpJgBCcaDi5gpqHqppF4pblUwpoebhGipuqiAUp/Yorl9Vn9fxS9Jg5oyxJEnSINe4ppG699bR/FKHVacLoeJfKpj28WmEEDjvR+ex7TPbmPbxaYy9YGy3fYaCwPTrpjPh7RPYfst2Znx5Rh5/Akka3AzGkiRJ/SAmI3vu2wPApMsnEQrCidvEyM7v7OS5v3qOeLj9qtPFpxdz7n+ey4TfnnDsWEl5CbNXzO7VuMZeMLbXbSRpuDEYS5Ik9YP6VfVsvGIjkAq1pReXdnv90YNHee4vn2PXXbs6nRv/W+M59z/PzVgmLUnqPZ8xliRJ6ge7VuzK+H0mB58/yBNvfSJjKJ72iWmc/7PzDcWSlEMGY0mSpDxraWwhsTJx7H1iZYKW/S0Zr9374F7Wzl3L60+83u54wZgCzr33XN5w8xsoKPKvcJKUS/6uKkmSlGeJlYl2+wsnDyTbBWVIPYP8/Bee5+k/eJqW19qH5pNnnszcx+Yy6fJJ/TJeSRppDMaSJEl5lql0uu2xI/uO8PTvP82LX3wR2q+xRdm7y5j7m7mMqRqT72FK0ojl4luSJEl5dGDLARp+0dDpeMPqBg5uPUhLQwt176nj0AuH2l9QADO+MoPpfzudEE68grUkKXsGY0mSpDzafffuLs9t+cQW9j2yj9jcfpq4aFIR59577glXrpYk5YbBWJIkqQ+aNjSxpmpNVm33/vfejMeP7DnCU29/ivkb5jNmtiXUkpRvPmMsSZLUB3sfzBxuc9L3j/PXtyTpOIOxJElSH0y9dirl15TnvN/ya8uZeu3UnPcrSerMYCxJktQHhaMLqby1kuoHqikqK+pzf0VlRVQ/UE3lNyspHF2YgxFKkk7EYCxJktQDMRnZfc9udt+zm5iMnc6XXVrGvPXzKL0k+wWzSheXMm/9PMouLevLUCVJvWQwliRJ6oH6VfVsvGIjG6/YSP2j9RmvKZlSQs3DNVTcVEEo7vkWS6E4UHFzBTUP1VAypSRHI5Yk9ZTBWJIkqQd2rdiV8fuOQkFg+nXTOX3J6T3ue9Zds5j+iemEAvcrlqSBYDCWJEk6gZbGFhIrE8feJ1YmaNnfkvHaZHOSZ695lp3f2tnj/vc/vr/PY5QkZc9gLEmSdAKJlQmSB5PH3icPJNsF5VaHXj7EEwueYMe3dvS6/0zPLUuS+ofBWJIk6QQylU53PLbvf/axds5a9v+m97O/zS830/hYY9bjkyT1jcFYkiSpGwe2HKDhFw2djjesbuDg1oPEZOTFf3yR9b+zniOvHsn6Pon7O89AS5L6h8FYkiSpG7vv3t3luR237+CZdz/D8595HpJdXnZM+TXllF9dnvGc5dSSNHBGDfQAJEmSBlLThibWVK3Jqu3L//xyj64rKiti5vKZx/YnnvjOiWxauomWvccX8Gotpx5/0fisxiJJyp4zxpIkaUTb++DevPZfuriUeevnHQvFAGWXlTH/6fmUXlLa7lrLqSVpYOR9xjiEcBpwITAXOAc4EygDxgBFwAFgP/Ay8CKwHngceCrG2IOiJEmSpOxNvXYqh7YdYsdtvVtJ+oQK4Owvn80Zf3dGxv2JS6aUUPNwDdtv2c62T28jHo7Ur6rP7RgkST2Sl2AcQrgA+GPgd4GaTJdkONbxusYQQi3w38D3Y4yv53SQkiRJQOHoQipvrWTiOyeyeenmPi2gBTBq4ijGnD+GN9z8BsZeMLbba0NBYPp105nw9glsv2U7M748o0/37kpdHdTWQmMjjBsHixZBVVVebiVJQ1LOSqlDCKeEED4WQngGWAt8CjifVAjuGIRjhq9jXaW/xgN/BNwJ7A4hfC+EcFGuxtudEMIHQggx/fWRLq55SwjhwRDCvhDCgRDC+hDCx0MIhd30+6EQwm9CCK+HEBpCCKtCCH+Qv59EkiT1VNmlZcxbP69TeXNvlC4uZf4z83njz954wlDc1tgLxjJ7xWxKykuyvncmtbWwcCFUV8PHPgbXX596ra5OHa+tzentJGnI6nMwDiGcFkL4KrAduBmYTeYZ4dbAG4FGYDfwCrAPOETmAN3qZOD9wC9DCI+FEN7V13F3JYQwHfg60OUMdQjhMmA1sAD4L+CbQDHwr8C9XbT5KrACmALcAXwXOA/47xDCX+XuJ5AkSdlqLW+uuKmCUNzVX0s6C8WBipsrqHmohpIpuQ232Vq+HBYvhtWrM59fvTp1/s47+3dckjQYZV1KHUI4BfgM8NfAaI6H3tY/RSKp54V/mX59htQzxLsyPTscQhgHlAMzSQXGecBvA63/bNva7zzghyGEx4G/jzH+PNufIcMYAnAXsBf4AfC3XYzzDuAo8LYY4+Pp49cDPwPeG0J4f4zx3jZt3gL8DbAVmB9jfC19/F9Iza5/NYTwoxjjC7n6WSRJUnZay5sLxxXy7JXP9qjNrLtmMfmKyXkeWc/V1sJVV0HyBKu1JJNw5ZVw5pmp8mpJGqmymjEOIfw58CypcukxHA+tB4HvA38KlMUY3xhj/OsY4x0xxv+NMe7oakGtGGNjjHFTjPGBGOOXYox/GGM8ldSiXTcCda23T3/NA/4nhHB/CGFaNj9HBh8F3g58GGjq4pr3AqcB97aG4vT4DwGfS7+9pkObq9Ov/9AaitNtXiA121ySvqckSRoEmuqa2PbJbT2+fv/j+/M4mt674YYTh+JWySTceGN+xyNJg122pdR3ApM5HoifIBUGp8QY3xdjvCfGWJ+D8RFjfCLG+PkY43mkVre+nVSZc2tAfjewpK/3CSHMBr4C/FuMsYuiIyAVnAEeznBuNalVtt8SQmhbR9Vdm4c6XCNJkgbQnvv2sPZNa2l5reXEF6clViaIyXjiC/tBXV3X5dNdefTRVDtJGqn68oxxAB4B3hFjnBtj/HaMMa//XBpjfDzGeDVwBrAMSND1c8k9FkIYBfwH8BKp8vDuzEy/dqqtijG2AM+TKlGfke57DDAVeD3GuDNDf8+lXyt7ONa1mb6AWT1pL0nScBeTkd337Gb3Pbt7FVaTR5Js+cQWNrx/A8mm3u0Y2fxyM42PNfZ2qHmR7YJaLsQlaSTL9hnjXwGfjjH+MpeD6an0bPSXQgj/Suo54L7+SbQMeCPwWzHGgye4dnz6taGL863HJ2R5vSRJ6oP6VfVsvGIjAMWnF1N68YlXmW7e2cyGP95Awy+7+uP6xBL3Jxh/0fgTX5hnjVn+rSjbdpI0HGQVjGOMv53rgWQjxtgEfLEvfYQQLiQ1S3xTjPF/czCstouP9UaPro8xzs1409Ss8Zxe3lOSpGFn14pd7b4/UTCuX11P3R/XcWT3ifcvLr+mHCLs+NaOTucSKxNUfLWCUNDnYrY+GTcuu3ZNTfC1r7nXsaSRKetVqYeDNiXUzwLX97BZ6z8ld/VPwuM6XHei6080oyxJknqopbGFxMrEsfeJlQnO+cY5jBrb+a88MUa2/+t2tn5ya2qviW4UlRUxc/lMyi4tA2DiOyeyaekmWvYefw65tZx6oGeNs11d+itf6XxswQJYtswVqyUNf33ex3iIO4XUs72zgUMhhNj6BXw+fc0d6WO3pN9vTr92eiY4HbTPBlqAbXBsVvsV4JQQwpQMYzgn/dqz/SAkSVKXEisTJA8efz44eSDZLii3atnfwobLN7D1bzqH4pIz2u9DXLq4lHnr5x0LxQBll5Ux/+n5lF7SfjY6cX/ne/W3qqpUoM0F9zqWNFKM9GDcDCzv4uuJ9DW/TL9vLbP+Wfr1nRn6W0BqT+dfxxib2xzvrs3vdrhGkiRlqW0ZdVfHmjY2se5N6zKG2DM/dyajJqZml0NxoOLmCmoeqqFkSkmna0umlFDzcA0VN1UQilPl0/Wr6nPwU/TdsmVQkKO/5bXudeziXJKGsxDj4NhaYLAJIXyB1KzxlTHG77Q5Pg7YSqpk+q2texmHEE4iFW4vAv4kxnhvmzZvIbVg2VZgfutexiGEs4C1pPaCnpXe1zjb8a6dM2fOnLVr12bbhSRJQ9qBLQf4zTm/yXjuTVvexMkVJ7Nn5R42f3gzR19vP01cOL6Q2f8xm7J3ldG8o5ltn9nGtI9PY+wFY3t07/1P7mf7LduZ8eUZlJR3DtEDYflyuOqqnu9nfCILF8KqVbnpS5LyYe7cuaxbt25dV+sydWdEP2OcjRhjYwjhSmAlsCqEcC+wD7iU1FZOK4H7OrT5dQjhZuA6YH0IYSVQDFwOTAT+ui+hWJIkwe67d3d5bueKnSQPJtl+0/ZO58acP4bq71dzcsXJAJSUlzB7xexe3XvsBWN73Sbfli6Fs86CG29M7VPcV617Hbsgl6ThqF+DcQjhZOA84DRSM65Fve0jxnh3rseVxRh+GEJYCHwWeA9wErCFVPD9WswwDR9j/JsQwnrgr4CrgCSwDviXGOOP+m3wkiQNUU0bmlhTtSarti996aWu+32qieThHE2rDjKLFqW+6upSpdCtK07v3Jl5sa0Tqa01GEsanvIejNMLUn0E+BAwj74/19wvwTjG+AXgC92c/xXwe73s89+Bf+/TwCRJGqH2Prg3f33/eC9jZo/JW/8DraqqfaD90pey68e9jiUNV3kNxiGEGlJlxa0rOGe7sV9Mt/WBaEmSRqip107l0LZD7Lit8x7CfVF+bTlTr52a0z4z6ThrO5D7BGe713G27SRpsMtbMA4hzAR+Dkyg76E220AtSZKGicLRhVTeWsnEd05k89LNHHn1SJ/667g3cb7U1sINN6S2PupooPYJzvZ+7mcsabjK54zxbUApxwNxBB4htXLzFqCR1H6/kiRJPVZ2aRlj149l04c28dpPX8uqj9LFpcxaMSvjNky5dKKVoVv3Cb7jDliyJK9Daad1r+NMYb0rCxf6fLGk4SsvwTiE8AbgbRwvgd4G/FGM8el83E+SJA0fMRnZc98eACZdPolQ0LlwrHUP4e23bGfbp7cRD/esMC0UB2Z8ZQbTPjYtY7+5VFvbs+2SWvcJPvPM/p2RXbYsFcp7sp1TQQFcf33+xyRJAyVHW7938lvp10Bq9WVDsSRJ6pH6VfVsvGIjG6/YSP2j9V1eFwoC06+bzszvzOxx37PumsX0T0zPeyiGVPl0T/cQTiZT2yr1p0WL4PbbU6G3OwUFqRlty6glDWf5CsaT068ReNxQLEmSemrXil0Zv8/k8J7DPP+Z53vc9/7H92c9rt6oq+tdmTIc3ye4Py1dCo88kiqTzmThwtT5/izzlqSBkK9njNuuhrE1T/eQJEnDRGv5dPJgkj337zl2PLEywTnfOIdRYzv/laXh/xqoe28dh1853OP7JFYmqPhqRb+UUWfbrr+f4+1qr+OBXDVbkvpbvoJx23+6Hb6bAkqSpJxoLZ/uKHkgSWJlgikfnnLsWIyRHbftYMvHtxCP9G7Ti+aXm2l8rJHxF43v85i7k+1+vwO5T3DHvY4laSTJVyn1ao6vOH1enu4hSZKGie5KptueO3rgKJs+uInn/vK5XofiVon7E1m16w33CZakoSUvwTjGuBdYSWrxrbNCCL+dj/tIkqShr6WxhcTKrsNqw+oGDm49yIEtB1h30Tp2f3f3Cfssv6ac8qvLM55LrEwQk9mF6p5yn2BJGlryNWMM8ElgX/r7W0MI+a1ZkiRJQ1JiZYLkwe6Xb9722W2snbeWpvVN3V5XVFZE9QPVVN5aSeVtlVT/sJpRp7Z/cqy1nDqfWvcJ7g33CZakgZOvZ4yJMW4PIfwh8GPgXODREMIHXKFakqSRqWlDE2uq1mTVNnHficufSxeXMmvFLEqmlBw7VnZZGfMvnM+mD23itZ++dry/+xN5f87YfYIlaejIWzAGiDH+MoTwZuBeoAZ4IoTwc+CnwGaggdQ+x73ps5ebH0iSpMFg74N789b3qe86leofVmdcbbpkSgk1D9ew/ZbtbPv0NuLhSP2q+ryNpVXrPsFXXdV9OHafYEkaeHkNxgAxxo0hhM8CdwMTgLenv7Lqjn4YsyRJyr2p107l0LZD7LhtR077Pe2PT2PWXbO63YIpFASmXzedCW+fwPZbtjPjyzNyOoauLF0KZ50FN96Y2qe4o4ULUzPFhmJJGlh5DZkhhNOB7wFvSx9qXekiv5sHSpKkQaEv5dMnMmrCKGb9+yzKLi3rcZuxF4xl9orZeRlPV9wnWJIGv7wF4xDCacAvgbNJBWFDsSRJI0w+y6en/vXUXoXigeY+wZI0eOVzxvhrwAxSgTiSCsSbgJ8BW4FGju91LEmShqF8lU+XX1POGX9/Rk77lCSNXHkJxiGE6cD7OB6I9wIfiDE+nI/7SZKkwalwdCGVt1Yy8Z0T2bx0M0dePdK3/sYWMvu7s4fUTLEkafDL1z7GC9N9t5ZQv8dQLEnSyFV2aRnz1s+j9JLSPvUz6f2TDMWSpJzLVyn11PRrBJ5xiyVJkoavmIzsuW8PAJMun9Tl6tBtt03a+vdbIYvJ430P7yMmY7crUOeLi2dJ0vCVr2Dc1Ob7jXm6hyRJGgTqV9Wz8YrUH/fFpxdTenHXs8KhIDBh4QSKxhdlVVbd/HIzjY81Mv6i8VmPt7dqa+GGG2B1hn/mX7AAli1zuyVJGuryVUq9vc337jssSdIwtmvFrozfZ7Jz+U7WvXVdn541TtyfyLptby1fDosXZw7FkDq+eDHceWe/DUmSlAf5Csb/BxxNfz8rT/eQJEkDrKWxhcTK40E1sTJBy/7Om04cPXSUTR/ZxOaPbCY2x07neyOxMkFM9q2PnqithauugmSy++uSSbjyytT1kqShKS/BOMa4C3iI1OJbs0MI5+XjPpIkaWAlViZIHjyeHJMHku2CMsDBFw7yxG89wa7l3c8m91RrOXW+3XDDiUNxq2QSbrwxv+ORJOVPvmaMAT4HNKe/vy2EUJzHe0mSpAGQqXS67bG9D+9l7dy1vL729R73mWkueBcl7d7nu5y6rq7r8umuPPpoqp0kaejJWzCOMa4H/ozUmpMXAQ+GEE7P1/0kSVL/OrDlAA2/aOh0vGF1AweeO8ALN77A07/3NC372pdWxy5WlH6Ach6gnExnA7DjshmE4tTZ+lX1fRx997Iti7acWpKGprwtjBVCOANYAywBvgFcDGwJIdwHPAJsAhqAHhYppcQYX8rxUCVJUhZ23727y3NP//7THHzuYKfj4xeMp2F1KkxHUoF3P6P4CrP4Nan9idcwkb9jE+NpOXbNZJp5atJ43vXYHLbfsp0ZX56R+x+ojcYsK7WzbSdJGlj5XDH6BdpXQwVgNPDn6a9sRFzlWpKkftG0oYk1VWuyapspFAPHQjGk/mKwhlK+wiz2tSmV/hVlbGQ+f88m5vPasePlzyUYe8EbmL1idlZj6o1x4/q3nSRpYOXzGeNWrRVRkeNBOfThS5Ik9YO9D+7NW99HgW9SwaeoaReKW+2jhE9Rw61UcCT9x/+U3fV5G09H2e5L7H7GkjQ05TsYhzavhltJkoaQqddOpfya8pz3e/LMk7nz/DeykunEbv5aEAncz3SuYQ5PTp7M/P/pv00uqqpgwYLetVm4MNVOkjT05LMs+Yt57FuSJOVZ4ehCKm+tZOI7J7J56WaOvHqkT/0VlRUxc/lMyi4tY0kt3Lu4Z9shPV8wlvO+N5uS3Gf0bi1bBot7OMaCArj++vyPSZKUH3kLxjFGg7EkScNA2aVljF0/lk0f2sRrP33txA0yKF1cyqwVsyiZkiqbXrQIbr8drrqq++BZUAB33DEwJcpDYYySpNzoj2eMJUnSEFcypYSah2uouKkCinreLhQHKm6uoOahmmOhuNXSpfDII6kS5EwWLkydX7KkDwPvo6EwRklS37nCsyRJ6pFQEDh9yens/t5uXl/3eo/azLprFpOvmNzl+UWLUl91dak9gBsbUys7L1o0eJ7XHQpjlCT1jcFYkiT1yOvrX+eZdz/Doa2Hetxm/+P7uw3GraqqBn/IHApjlCRlx1JqSZJ0Qru+u4t1b17Xq1AMkFiZICbjiS+UJGkAGYwlSVKXkoeTPPtXz7LpA5tIHuzB8swdNL/cTONjjXkYmSRJuZNVMA4h/FUIYVCUYYcQzg0hLB7ocUiSNNwc2n6IJxc+yY5v7uhTP4n7EzkakSRJ+ZHtjPHXgE0hhA+GEApzOaCeCiGcE0K4C3gKePNAjEGSpOHqtZ+/xto5a2n8v57N9pZfU0751Zk3GracWpI02PWllPps4C5gWwjhuhDCxByNqVshhAUhhJXABuCDWA4uSVLOxBh56Z9f4ql3PMWRxJF254rLiztdX1RWRPUD1VTeWknlbZVU/7CaUae2LyqznFqSNNhlGyp/AoT01zTgX4BXQgj3hhAuCyGclKsBAoQQZoYQPhNC2Az8HPgjoDB9/3rgsVzeT5KkkailsYW699Sx7VPboMPjxBN/byJll5a1O1a6uJR56+e1O152WRnzn55P6SWl7a61nFqSNJhlFYxjjL8L/CGwleMBuQR4H/AD4NUQwo9DCJ8MIbw1hDCup32HlDeEEN4fQrg1hLCJ1OzwjcA5be53FPg2UBlj/Ek2P4ckSUppqmti7fy1vPpfr7Y/EeCsL57Fef993rFZ31AcqLi5gpqHaiiZUtKpr5IpJdQ8XEPFTRWE4gBA/ar6fP8IkiRlLesFtGKM/y+E8GNgCfBZ4AxSgRVgNPDO9BcAIYRXgBeBHcBrwCGgBTgJGAOcDkwFKtLHjjVtvWX6NQncC3wxxvhctuOXJEkpu+/ZzeaPbCZ5oP008ajSUcz+3mxO/d1TATjvR+ex7TPbmPbxaYy9YGy3fYaCwPTrpjPh7RPYfst2Znx5Rt7GL0lSX/VpZekY41HgjvQiWO8HPgrM63BZa7CdRir4did0eN92pY7XST3T/LUY47bsRixJklolDyfZ+ndbeeVrr3Q6d8qcU6haWcXJZ5987FhJeQmzV8zu1T3GXjC2123q6qC2FhobYdw4WLQIqqr6r70kaeTJyZZLMcYW4LvAd0MI5wMfAN5Lahb52GU96Yr24fgw8DPge8APY4wHcjFeSZJGuuYdzdT9cR2Nv+q8KNbpS07nnG+eQ+FJ/bvxRG0t3HADrF7d+dyCBbBsWSrk5qu9JGnkyvlexDHGp0htofS3IYRZwCXAhcAcUmXSnZe0PG4P8DTwOPAL4OcxxoO5HqMkSSNZ/aP11F1ex5Hd7VedDiWBc75xDuUfybztUj4tXw5XXQXJZObzq1fD4sVwxx2wZEnu20uSRracB+O2YoybgE1tj4UQpgCnkXoOeRRwANgPbDcES5KUPzFGtt+8na2f2ppawrKNkjNKqPp+FePm9Xi9zJypre0+1LZKJuHKK+HMM9vP/Pa1vSRJeQ3GmcQYdwI7+/u+kiSNZC37W9i8ZDOJlZ23TSpdXMrs782muKy7oq78ueGGE4faVskk3Hhj+2Db1/aSJGW7j7EkSRoimjY2se7CdRlD8ZnXn0nNgzUDForr6jI/E9ydRx9NtctFe0mSwGAsSdKwtuf+Pay7cB0HNrVfv3LUhFFU/3c1Z99wNqGw46YQ/ae2tm/t+tpekiQYgFJqSZLUOzEZ2XPfHgAmXT6JUHDiIJs8kmTb329j+83bO50bc/4Yqr9fzckVJ2do2b8aOy+K3at2fW0vSRIYjCVJGvTqV9Wz8YqNABSfXkzpxaXdXt+8q5kNl2+gYXVDp3OTPzSZylsrKRzdv1sxdWVclmt9tbbra3tJksBSakmSBr1dK3Zl/D6T+l/Ws3bO2k6hOBQFKr9Vyay7Zg2aUAzZL4LV2q6v7SVJAoOxJEmDWktjS7tFsxIrE7Tsb+l0XYyR7f+2nacuforDOw+3O1cyrYQ3/uKNlP9FOSEM3PPEmVRVwYIFvWuzcGGqXS7aS5IEBmNJkga1xMoEyYPH9yJKHkh2Wl265fUWNl6xkS0f30Jsie3OTVg0gbnr5jLuTYO3dnjZMijo4d9ICgrg+utz216SJIOxJEmDWKbS6bbHDmw+wLo3rWPPvXs6XXfGp8/g/J+cT/FpA7MVU08tWgS3337icFtQAHfc0bkMuq/tJUkyGEuSNEgd2HKAhl90XkCrYXUDB7ceJPGDBGvnr+XAhvZbMRWOK6T6h9XM+PKMAd2KqTeWLoVHHkmVOWeycGHq/JIl+WkvSRrZXJVakqRBavfdu7s8t/GDG2n8dec9h8acN4aq71cx+pzR+RxaXixalPqqq0vtM9zYmFo9etGinj0T3Nf2kqSRy2AsSdIAadrQxJqqNVm1zRSKAZqebuI3lb9h/ob5jJk9pi/DGzBVVX0Lsn1tL0kaeQzGkiT1s5iM7LlvD3t/tDdv99j7471DNhhLktTfDMaSJPWz+lX1bLxiIwCnXnoqe/9fbgNy+bXlTL12ak77lCRpOHPxLUmS+lnbVaVHTRhF9QPVFJUV9bnforIiqh+opvKblRSOLuxzf5IkjRQGY0mS+kFMRnbfs5sdy3e024c4sTLBhIsnMG/9PEovKc26/9LFpcxbP4+yS8tyMVxJkkaUvAXjEMJb89W3JElDTWv59LMfeZbkweSx48kDSRIrE5RMKaHm4RoqbqogFPd8i6VQHKi4uYKah2oomVKSj6FLkjTs5XPG+BchhLoQwnUhBP/5WpI0orUtn+7qXCgITPvYNCa+c2KP+5111yymf2I6oWBo7FcsSdJglO9S6lnAvwDbQwj3hRAW5/l+kiQNOi2NLe3KpztqWN3Awa0HOZw4zPp3ru/VYlz7H9+fiyFKkjSi9dczxsXAe4GHQgjPhxA+F0JwuUxJ0oiQWJloVz6dyYv/+CJr567ltf95rdd9x2Tsy/AkSRrx8rld0y3AnwFty6gDcCbwReDzIYRHgNuBH8UYj+ZxLJIk5V3ThibWVK3Jqu2u5V2XWnen+eVmGh9rZPxF47NqL0mS8jhjHGO8DpgKvB/4KdD6z9mtr4XAO4EfkCq1/scQwhvyNR5JkvJt74O53Y+4pxL3d12mLUmSTiyvpdQxxiMxxv+MMf4OMAP4ErCd1MxxqwBMBj4JbA4h/DyEcEUIwaU1JUlDytRrp1J+TXle+j79I6dTfnXmvi2nliSpb/JZSt1OjPElYFkI4fPA7wBXAn8AFHF8FjkAC9JfXw8hfBdYHmNc31/jlCSpN/pSPt0ThWMLmf3d2cf2J574zolsWrqJlr0tx66xnFqSpL7pr8W3jokpD8cY3wNMAz4FPEvnWeRS4K+AJ0IIvwkhXBlCOKW/xytJUnfyWT590oyTuHDzhcdCMUDZZWXMf3o+pZeUtrvWcmpJkrLX78G4rRhjIsb4LzHG2aRmie8GDra5JKS/5gHfAnaGEL4TQrio/0crSRLEZGT3PbvZfc9uYjLmrXx67FvGMu+peZRM6fxkUcmUEmoerqHipgpCcerfletX1ed8DJIkjRQDGozbijH+Msb458AU4Fpgbeup9GsAxgAfBn4ZQngmhHBtCGFsvw9WkjRi1a+qZ+MVG9l4xUbqH62ncHQhlbdWUv1ANUVlRX2/wSio+NcK5v5qLqNO6fqJp1AQmH7ddOY8NofJH5rMeT86r+/3liRphBo0wbhVjHE/qZnj24CXSQXi2OaL9LFzga8DL4YQrg8hnDQAw5UkjTC7VuzK+H3ZpWXMWz+vU4lzb01ZMoXpH5/e4+vHXjCW2StmU1LumpWSJGVrUAXjEMKFIYTbgZ3AHaSeQW4bhlu/SB8PwATgC8D6EEJ1f45XkjSytDS2kFh5/FnexMoELfuPL4LVtsSZLCeP9z20zxWmJUnqZwMejEMIE0MIHwshrAf+F1gKjKV9ED5Eahb5rUA1cDPwarqL1oD8BqA2hDC5f38CSdJIkViZIHkweex98kCyXVCGVIlz2bvLOGlqdoVMrStMS5Kk/jNgwTiE8I4Qwr3AK6SCbjXtV6YGqAM+BpTHGP88xvi/McYNMca/JTWb/JF0+1ZlwN/mf/SSpJGobel0V8f2PryXtXPXcuiFQ1nfxxWmJUnqX/0ajEMIU9PPA28DfgK8D2h9KKq1bqwZ+A/gt2KM58UYvx5jbOjYV4zxSIzxTqCGVICGVLD+/bz+EJKkYa3jqtOtDmw5QMMvOv1xRMPqBg5uPUhMRl644QWe/r2nadnX0um63kisTFhOLUlSP+p6ucscCSEUApeRmt29hFQYb/ucMOn3G4DbgbtjjPU97T/GWB9CuBG4N33orL6PWpI0UrWuOg1QfHoxpRenFtPafffuLtu88u1XOFB3gH0P7svJGFrLqcdfND4n/UmSpO7lLRiHEGaSCsMfAE5rPczx1aUDqdnhlcC3Y4y/6sPt1rf53mU5JUm91rShiTVVa9ode+rtT/Wo7fZ/2d7n+5ecUULzS83H3ifuTwyZYFxXB7W10NgI48bBokVQVTXQo5IkqefyOWO8keMBGNrPDm8kNTv8772ZHe7GwRz0IUkawfY+uDfv95hy9RQCgR3f2tHpXExGZnx1Bs9/5nni4Uj9qvq8j6evamvhhhtg9erO5xYsgGXLUiFZkqTBrj+eMW777PD3gAUxxqoY47/lKBQDtAAvAS+mXyVJ6pWp105lwtsm5KXvwvGFVD9QzczbZlJ5WyXVP6xm1Knt/2368PbDjH/LeOY8NofJH5rMeT86Ly9jyZXly2Hx4syhGFLHFy+GO+/s33FJkpSNfAfjAGwGrgOmxhg/EGP8Za5vEmN8JcZ4Vozx7Bjj2bnuX5I0/BWOLiQezf2CV6WLS7lw44WUXVp27FjZZWXMf3o+pZeUtrs2cX+CsReMZfaK2ZSUD94ng2pr4aqrIJns/rpkEq68MnW9JEmDWT6D8f8HLIwxnhtjvCXG+Foe7yVJUp90tep0tkJRoOLmCmoeqqFkSueQWzKlhJqHa6i4qYJQnHrqaCiUT0OqfPpEobhVMgk33pjf8UiS1Fd5e8Y4xvhn+epbkqRc627V6Z4KxYEzPn0Gh54/xLRPTGPsBWO7v74gMP266Ux4+wS237KdGV+e0ecx5FtdXdfl01159NFUOxfkkiQNVnnfrkmSpMEg06rTuTbrrllMvmJyr9u1lk8PBdmWRdfWGowlSYNXfyy+JUnSgOuPVaf3P74/7/cYaI2N/dtOkqT+YDCWJI0IU6+dSvk15Xm9R2JlgpjM/QJeg8m4cf3bTpKk/mAwliSNCIWjC6m8tZLqB6opKivKyz2aX26m8bHhPTWa7b7E7mcsSRrMDMaSpBGl7NIy5q2f12mrpFxJ3J/IS7+DRVUVLFjQuzYLF/p8sSRpcDMYS5JGnExbJfXGlKunUH515rLskVBOvWwZFPTwbxAFBXD99fkdjyRJfWUwliSNSK1bJc28c2aP2xSeUkj1A9XMvG0mlbdVUv3Dakad2n6Dh5FSTn377ScOxwUFcMcdllFLkgY/g7EkacRqaWjhhc+/0OPrJ10xibJLy469L7usjPlPz+9Ulj3cy6kBli6FRx5JlUlnsnBh6vySJf07LkmSsuE+xpKkEen1Z16n7t11HNp6qMdt9j20j5iMhILj5detZdnbb9nOtk9vIx6O1K+qz8OIB59Fi1JfdXWpfYobG1OrTy9a5DPFkqShxWAsSRpxdt+zm80f2UzyQLJX7VrLpMdfNL7d8day7Alvn8D2W7Yz48szcjncQa+qyiAsSRraLKWWJI0YycNJnvvoc2y8YmOvQ3Gr7sqkx14wltkrZlNSXpLtECVJ0gAwGEuSRoTmHc08efGTvPL1V054bfk15SN61WlJkkYaS6klScNe/aP11F1ex5HdR7q9rqisiJnLZx5bYGviOyeyaekmWva2HLumq3JqSZI0dDljLEkatmKMvHzTyzy56MlOobhwbGG796WLS5m3fp6rTkuSNAI5YyxJGpZa9reweclmEis7h9jS3ynl8I7DND3dRCgOzPjKDKZ9bFq71aZb5WPVaVdxliRpcDEYS5KGnaaNTdS9u44Dmw50OnfmsjM5a9lZHN59mG2f2ca0j09j7AVju+0vV6tO19bCDTfA6tWdzy1YAMuWpUKyJEnqXwZjSdKwsuc/97BpySaSTe1XnR41YRSzvzubU3//VABKykuYvWJ2r/puXXU6G8uXw1VXQbKLxbBXr4bFi+GOO2DJkqxuIUmSsmQwliQNC8kjSbZ9ahvb/3V7p3Njzh9D9Q+qOXnGyQMwstRMcXehuFUyCVdeCWee2X7m2NJrSZLyy2AsSRrymnc2s+HyDTT8oqHTuckfmkzlbZUUnlyYoWX/uOGGE4fiVskk3HhjKvxaei1JUv9wVWpJ0pBW/8t61s5Z2ykUh+JA5bcqmXXXrAENxcuXZw623Xn00VQgXry467atpdd33tn3MUqSNNI5YyxJGpJijGz/t+1s+7ttxJbY7lzJ9BKqVlYx7sJxAzS6lOXLU6XR2fjCFyDG7q/pqvRakiT1jjPGkqQhp+X1Fjb8yQa2fmJrp1Bc+o5S5q6bO+ChuPW54hOF2670tF1r6bUkScqewViSNKQ0bWpi3ZvWkbiv8/7EZ3zmDGoerqG4rHgARtZeb54r7qtHH00t0CVJkrJjKbUkachIfD/Bpj/fxNHXj7Y7XjiukNn/MZuyS8sGaGTt1dX1/rnivqqtdaVqSZKyZTCWJA16yZYkz3/6eV7+6sudzo05bwxVP6hi9BtGD8DIMqut7f97Njb2/z0lSRouDMaSpEHt8O7DbHj/BupX1Xc6N/nPJlP57UoKRw/cqtOZ9CWkhpDdc8njBvaRakmShjSfMZYkDVoNv27g8TmPdwrFoShwzjfOYdbdswZdKIbsQ2oI8MUvZtfWVaklScreiA/GIYRTQwgfCSH8VwhhSwjhYAihIYTwyxDC0hBCxl+jEMJbQggPhhD2hRAOhBDWhxA+HkLo8m9oIYQPhRB+E0J4PX2PVSGEP8jfTydJQ1OMke3f2M6TC5/k8I7D7c4VTy3mgtUXMPUvpxJCGKARdi/bkHrHHXD99bBgQe/aLVzo88WSJPWFpdTwPuA2YCfwc+AlYDLwbuA7wO+GEN4X4/HCthDCZcD3gUPAfcA+4F3AvwJvTffZTgjhq8DfANuBO4Bi4P3Af4cQ/jrG+I18/YCSNJQcbTrK5qs2s+f/29Pp3ISLJ3DuvedSPGngVp2uq0s9Q9zYmJoZXrSocyitqkqF294swLVwISxdmvp+2TJYvLhnq1oXFKTCtCRJyl6I2W6wOEyEEN4OjAF+HGNMtjl+OvAbYDrw3hjj99PHxwFbgPHAW2OMj6ePnwT8DLgI+JMY471t+noL8CtgKzA/xvha+vhZwNr0/WfFGF/ow8+xds6cOXPWrl2bbReSNOAOPHeAunfX0fRMU6dz0z81nbO/dDYFowam2Km2NrUFU6awu2BBKsy2nSmure1duH3kkfbtly9P7YPcXfuCgtQs85IlPf85JEkarubOncu6devWxRjn9rbtiC+ljjH+LMb4321Dcfr4LuBb6bdva3PqvcBpwL2toTh9/SHgc+m313S4zdXp139oDcXpNi8A3wRKgA/37SeRpKEt8cMEa+et7RSKC8cWUvWDKiq+UjFgoXj58lTI7WoGePXq1Pk77zx+bNEiuP32VHjtTmu47Vh+vXRpKiwvXJi53cKFqfOGYkmS+s5S6u4dSb+2tDn29vTrwxmuXw0cAN4SQiiJMTb3oM1DwPXpaz7ft+FK0tCTbEnywvUv8NJXXup0bnTVaKp/UM3oyoHbiqm29sQzt5A6f+WVcOaZx0Pu0qVw1llw443w6KOd2yxcmCqD7uqZ5EWLUl89Kd+WJEnZMxh3IYQwCvhg+m3bQDsz/fpsxzYxxpYQwvNAFTAD2BhCGANMBV6PMe7McKvn0q+VORm4JA2QmIzsuS/1XPCkyycRCk68MNbhxGE2/MkG6mvrO52b9CeTqLy9klGnDOwfVTfc0LNyaEhdd+ON7YNuLsJtVZVBWJKkfDIYd+0rQDXwYIzxJ22Oj0+/NnTRrvX4hCyv71YIoauHiGf1pL0k5Uv9qno2XrERgOLTiym9uLTb6xsfa6TuvXU0b29udzyMClTcVMHUvx74Vafr6nq3gBakZobr6jIvyGW4lSRpcBrxzxhnEkL4KKkVpDcBH+ht8/Rrb1c1G9mroEka8nat2JXx+45ijLzyrVd44ref6BSKi6cUc8GqC5j20WkDHoohNcPbn+0kSdLAcMa4gxDCXwL/BmwAFsUY93W4pHWGdzyZjetw3YmuP9GMcjtdrbCWnkme05M+JCnXWhpbSKxMHHufWJngnG+cw6ix7f+YOXrgKM9e8yy7797dqY/xC8Zz7n3nUnJ6Sd7H21ONjf3bTpIkDQxnjNsIIXwc+AbwDHBxemXqjjanXzs9E5x+LvlsUot1bQOIMTYBrwCnhBCmZOjvnPRrp2eWJWmoSKxMkDx4/EHc5IFku6AMcHDrQdZdtC5jKJ72N9M4/3/OH1ShGFLPAvdnO0mSNDAMxmkhhE8B/wo8SSoU7+ni0p+lX9+Z4dwCYDTw6zYrUp+oze92uEaShpxMpdNtj736o1d5fO7jNK3vsBXTKYWc+5/n8oavvoGCosH3R1JXq0Xnq50kSRoYg+9vIQMghHA9qcW21pIqn361m8tXAq8C7w8hzGvTx0nAl9Jvb+vQpnU/5M+GEErbtDkL+EugGbirLz+DJA2UA1sO0PCLzk+DNKxu4MCzB3j++ud55l3PcLThaLvzo2eNZs5v5jDpfZP6a6i9VlUFCxb0rs3ChS6yJUnSUDPinzEOIXwIuAE4CvwC+GiGBV9eiDGuAIgxNoYQriQVkFeFEO4F9gGXktrKaSVwX9vGMcZfhxBuBq4D1ocQVgLFwOXAROCvY4wv5OUHlKQ8y1Qa3Wr9767n0LZDnY6f9r7TmLl8ZqdnkAeDjtsqffCD8Mtf9mzLpoKC1L7EkiRpaBl8fyPpf2enXwuBj3dxzaPAitY3McYfhhAWAp8F3gOcBGwhFXy/FmPstMJ0jPFvQgjrgb8CrgKSwDrgX2KMP8rJTyJJedC0oYk1VWuyapspFAMk7k+QuD/B/A3zGTN7TF+GlzO1tak9izNtz1RZCc89B51/dz+uoADuuMMyakmShqIRH4xjjF8AvpBFu18Bv9fLNv8O/Htv7yVJA2nvg3vz1/eP9w6KYLx8OVx1Vdezws8+CyGkAvKzGZZKXLgwNVNsKJYkaWga8cFYktReTEb23Jdaf3DS5ZOYeu1UDm07xI7bduT0PuXXljP12qk57TMbtbXdh+JWMcKWLfCd70BT0/FS60WLfKZYkqShzmAsSWqnflU9G6/YCEDx6cWUXlxK5a2VTHznRDYv3cyRV4/0qf+isiJmLp9J2aVluRhun91wQ8+eH4bUdf/xH7BqVV6HJEmS+pmrUkuS2mm7zVLb78suLWPe+nmUXlKaqVmPlC4uZd76eYMmFNfVZX6muDuPPppqJ0mShg+DsSTpmJbGFhIrE8feJ1YmaNnfcux9yZQSah6uoeKmCijqeb+hOFBxcwU1D9VQMqUkl0Puk9ra/m0nSZIGJ4OxJOmYxMoEyYPH64qTB5LtgjJAKAic/uenM+bcni+aNeuuWUz/xHRCQaft8AZUY2P/tpMkSYOTwViSdEzb0umuju1ft5+1c9fS9FRTj/vd//j+Po8tH8aN6992kiRpcDIYS5IAOLDlAA2/aOh0vGF1Awe3HgRg5107WfeWdRx6IfP+xF1JrEwQk91sAjxAst1eyW2ZJEkaXgzGkiQAdt+9u8tzO+/cyearNrN5yWZic+8DbvPLzTQ+Nvjqj6uqYMGC3rVZuNDtmSRJGm7crkmSRoimDU2sqVqTVduXvvxSn++fuD/B+IvG97mfXFu2DBYv7tmWTQUFcP31+R+TJEnqX84YS9IIsffBvXm/R/k15ZRfXZ7x3GAup7799lTo7U5BAdxxh2XUkiQNRwZjSRrGYjKy+57d7L5nN+VXl1N+TebQ2lejTh1F9QPVVN5aSeVtlVT/sJpRp7YvShqs5dQAS5fCI4+kyqQzWbgwdX7Jkv4dlyRJ6h+WUkvSMFa/qp6NV2wE4PyfnU/lrZVMfOdENi/dzJFXj+TkHqWLS5m1Yla7/YnLLitj/oXz2fShTbz209eOHR+s5dSQmgletAjq6lL7FDc2plafXrTIZ4olSRruDMaSNIy13Wpp14pdlF5cStmlZYxdP7ZTaO2tUBSY8U8zmPaxaRn3Jy6ZUkLNwzVsv2U72z69jXg4Ur+qPuv79ZeqKoOwJEkjjaXUkjRMtTS2kFiZOPY+sTJBy/4W4HhorbipglDcOdR2JRQHzvz8mUz+4GTm/GYO0z8xPWMoPnZ9QWD6ddOZ89gcJn9oMuf96LzsfyBJkqQ8ccZYkoapxMoEyYPHl1pOHkiSWJlgyoenAMdD66hTR7H5zzf3qM9Zd81i8hWTez2WsReMZfaK2b1uJ0mS1B+cMZakYaptGXVXxw69fIhtn9rW4z7/d8X+Po9LkiRpsDEYS9IwdGDLARp+0dDpeMPqBg5uPQjAa7WvsXbOWo7s7vkiXM0/TVD708G35ZIkSVJfWEotScPQ7rt3d3lu57/vpHB0Ic9/9nlIdnlZRpNp5jufbGTRE4NzZWlJkqRsGIwlaQhq2tDEmqo1WbV96caXuj0fgZDh+1bjn0xQVzfelZslSdKwYSm1JA1Bex/cm7e+A/AA5TxAeadQDLAAy6klSdLw4oyxJA1BU6+dyqFth9hx246c9ttMAf/ILB5lEgBrmMjfsYnxtBybPZ5MM7s2NAKWU0uSpOHBGWNJGoIKRxdSeWsl1Q9UU1RWlJM+n2MMV/CmY6EY4FeUsYT5rKG03exx+XOJzh1IkiQNUQZjSRrCyi4tY976eZReUpp1H0ngLs7kL5jHPko6nd9HCZ+ihlup4Eg6Hk/ZXZ/1/SRJkgYbg7EkDXElU0qoebiGipsqCMWZngrOLBQFTpl3Ct9+4xzu5mxixieKUyKB+5nONczhycmTmf8/5+Vi6JIkSYOCwViShoFQEJh+3XRm3jmzx21mrZjFvDXzuOpfxlHQwz8Nni8Yy3nfm01JeeeZZUmSpKHKYCxJw0RLYwsvfuHFHl+///H9ACxaBLffzgnDcUEB3HFH6npJkqThxGAsScNAU10Tay9cy8EtB3vcJrEyQUymtl1auhQeeQQWLsx87cKFqfNLluRitJIkSYOL2zVJ0hC35749bFq6iWRTslftml9upvGxRsZflNp2adGi1FddHdTWQmMjjBuXOlZVlY+RS5IkDQ4GY0kaopJHkmz75Da237I96z4S9yeOBeNWVVUGYUmSNLJYSi1JQ1DzzmaeevtTPQrF5deUU351ecZzbcupJUmSRipnjCVpiKn/RT0b/ngDh3cd7va6orIiZi6fSdmlZQBMfOdENi3dRMvelmPXdCynliRJGomcMZakISLGyMv/+jJPXvxkp1BcOLaw3fvSxaXMWz/vWCgGKLusjPlPz6f0ktJ21ybuT+Rv0JIkSUOAwViShoCW/S1seP8Gtl63FY62P1d6SSknnXUSAKE4UHFzBTUP1VAypfNewyVTSqh5uIaKmyoIxQGA+lX1+R6+JEnSoGYptSQNck2bmqh7dx0HNh7odO6Mz57B2V88m8O7D7PtM9uY9vFpjL1g7LHzmVeYDky/bjoT3j6B7bdsZ8aXZ/TnjyNJkjToGIwlaRBLfD/Bpj/fxNHX208TF44vZPZ/zKbsXalS6ZLyEmavmH3sfG0t3HADrF7duc8FC2DZMli0aGy7NpIkSSOVpdSSNAglW5Js/but1L23rlMoHlMzhrmPzz0WijtavhwWL84ciiF1fPFiuPPOXI9akiRpaHLGWJIGmcO7D1N3eR0NjzZ0Ojf5zyZT+e1KCkcXZmiZmim+6ipIJru/RzIJV14JZ56ZKq+WJEkayQzGkjSINPy6gbr31XF4R/tVp0NR4A23vIHya8oJIXTZ/oYbThyKWyWTcOONuQvGmZ9nzk3fkiRJ+WQwlqRBIMbIK994ha3XbSW2xHbniqcWU7WyivFv7n6v4bq6rsunu/Loo6l2fQmwPXueOfv+JUmS8s1njCVpgB1tOsrGP93Ilo9u6RSKJ7x9AvPWzTthKIZUQM1Gtu3A55klSdLwYDCWpAF04NkDrHvzOvbcs6fTuTP+/gxqflJD8aTiHvXV2JjdGLJt19vnmfsSwCVJkvLJYCxJAyTxXwnWzl9L0zNN7Y4Xjiuk6r+qmPGPMygY1fPfpseNy24c2bbL5nlmSZKkwchgLEn9LNmSZOvfb6Xu3XUcbWy/FdPoqtHMXTOX0/7wtF73m+1zvNm068vzzJIkSYONwViSshCTkd337Gb3PbuJyXjiBmmH9xxm/e+s5+V/ernTuUl/Mom5j81ldOXorMZUVZVa7Ko3Fi7MbuGtgXieWZIkKV9clVqSslC/qp6NV2wEoPj0YkovLj1hm4b/a6DuvXUcfqXDVkyjAhU3VzD1r6Z2uxVTTyxbllrsqiclzgUFcP312d2nv59nliRJyidnjCWpF1pnil/4/AvHju1asav7NjHyyq2v8OSCJzuF4uLyYi5YdQHT/npan0MxpMqib789FXq7U1AAd9yRffl1fz/PLEmSlE8GY0nqhdaZ4oZfNhw7lliZoGV/S8brjx44yqYPbeK5v3yOeKR9yfX4heOZu3Yu49964q2YemPpUnjkkVSZdCYLF6bOL1mS/T3683lmSZKkfLOUWpJOICYje+5Lbae098G9nc4nDyRJrEww5cNT2h0/sOUAde+po2l9U6c20/92Omf/49m9WnW6NxYtSn3V1aWe621sTM3WLlqU3TPFHbU+z9ybBbiyfZ5ZkiQp3wzGknQCT66op2Fp6nniZGHIWGqza8WudsH41f9+lY0f2MjRhvarTheeUsjMu2Yy6b2T8jnkY6qq8hdG++t5ZkmSpHyzlFqSulBbm5rlvH/p8WeIC45mXoG6YXUDB7ceJB6NbPvcNp659JlOoXj07NHMWTOn30JxvvXX88ySJEn5ZjCWpAyWL0/Nhj6+uoUFJHrU5pVvvcL6313PS//wUqdzp73vNOY8Nocxs8bkeqgDqj+eZ5YkSco3S6klqY2mDU2sqVpDBdDbLXe3f3V7l+cS9yc464tnMWr28PttN9/PM0uSJOXb8PsbmiT1QabFtXLW94/3Mmb28JoxbiufzzNLkiTlk8FY0ogXk5GXb3qZbZ/clrd7lF9bztRrp+atf0mSJGXPYCxpxKtfVZ/XUDz5zydT+c3KvPUvSZKkvjEYSxqxWp8nzqfJHzIUS5IkDXYGY0kjVj6fJw7FgXPvO5fT/vC0vN1DkiRJueF2TZJGrKnXTmXC2ybkvN9RE0cxf8N8Q7EkSdIQYTCWNGIVji4kHo0573fyByczumJ0zvuVJElSfhiMJY1YB7YcoOEXDTnvd+e9rxKTuQ/ckiRJyg+DsaQRa/fdu/PSb3JXM42PNealb0mSJOWei29JGrb6Y9XpriTuTzD+ovEDcm9JkiT1jjPGkoatfK46fSKJlQnLqSVJkoYIg7GkYWvqtVMpv6a8X+/ZGoWbX7acWpIkaagwGEsatgpHF1J5ayXVD1RTVFbUL/cMbb5P3J/ol3tKkiSpbwzGkoa9skvLmLd+HqWXlPa5r66Ko9seb0nH4/pV9X2+nyRJkvLPYCxpRCiZUkLNwzVU3FRBKA4nbtDBXkbxEyaTqWUzod3xn3EaDzOZ4pvOy3q8kiRJ6j8GY0kjRigITL9uOpW3V/aq3d43nc77eCtfYTafo5qG9IL+rbPEJUS+z1SOpOPxWRzgn5jNqqdLcjl8SZIk5YnBWNKIcuilQ2z71LYeX3/qu09l4x/MIqZD768oYwnzWUNpu1niJIFrmMPDTOYzpGaKG117S5IkaUgwGEsacmIysvue3ey+Z3evtkTa9z/7WDt3LUd2H+lxm9fXvM64U9rfYx8lfIoabqXi2Czx+dSzlbH8E7PZS2qmeNy4Ht9GkiRJA2jUQA9AknqrflU9G6/YCEDx6cWUXtz9oloxGXnpKy/x/PXPQ7J392p+uZkFpzUC49v3SeB+prOOCbyX7XyHGZ3aLlrUu3tJkiRpYDhjLGnI2bViV8bvMzlSf4Rn/ugZnv9sz0JxpvnnU9YmWLAg8/UdZ4lbLVwIVVUnvp8kSZIGnsFY0pDS0thCYuXx/YETKxO07G/JeO3r619n3fx17P1/e0/Y7wOU8wDlGVedTqxMsOxzkYIe/o5ZUADXX9+zayVJkjTwDMaShpTEygTJg8enfpMHku2Ccqtd393Fujev4+CWgxn7aZ0ZrqeIz1LNLVRyC5UZV51ufrmZeac0cvvtnDAcFxTAHXdYRi1JkjSUGIwlDSmZSqfbHkseTvLsXz3Lpg9sahegAYomFx37PgBrKGUp8/g1ZceOd7XqdOL+BEuXwiOPpMqkM1m4MHV+yZKsfjRJkiQNEBffkjToxGRkz317AJh0+SRCQSqiHthygIZfNHS6vmF1Awe3HiSUBDa8bwON/9d5n6QpV06h8TeNHNl9hJYQ+HacwfeZdmwbprZaV51+L9u5km0UEalfVQ+kZoIXLYK6OqitTW3JNG5c6pjPFEuSJA1NBmNJ/aanYfLJFfU0LE2tOv2jXxfz5qtLqaqC3Xfv7rLvF774Avse3seRRPutmEJJoPLWSqYsmULzjmbWXbuNjzwwja2M7XasHVedvuKm9qtOV1UZhCVJkoYLg7GkvKuthRtugNWrO59bsACWLUuF5No7myhcuqbd+YpvPEXiG7DqBPfY/R+ZQ3NsjmxeuplxF41jzOwxrHn7bLY+0POxt646Xf401Fzc83aSJEkaOnzGWFJeLV8OixdnDsWQOr54MXz4w3DHR068enS29v441Xdj5yrrHsm2nSRJkgY/Z4wl5U1tLVx1FSRPsH9wMgkrVkAJU3kT+3gj9TkdR/m15Uy9diqQKuHORrbtJEmSNPgZjCXlzQ03nDgUt9VMIQXHNknqu6KyImYun0nZpcdXnc52GyW3X5IkSRq+LKWWlBd1dV2XT3elnAOcT0NOonHp4lLmrZ/XLhRDasGsBQt619fChS60JUmSNJwZjCXlRW1t79v8DqkFtDpvoNRzoThQcXMFNQ/VUDKlJOM1y5ZBQQ9/9ysogOuv78OAJEmSNOhZSi0pLzItVnUWr3MXj+f1vrPumsXkKyZ3e82iRXD77Sd+/rmgAO64wzJqSZKk4c5gLKlLPd13OJNMi1X9Ea/kdoAZ7H98/wmDMcDSpXDWWXDjjfDoo53PL1yYmik2FEuSJA1/BmNJnfR03+HutJ4PRC5mDwCjacnxSDtLrExQ8dUKQsGJC7IXLUp99eUfACRJkjT0GYwltbN8efclxq37Dt9xByxZ0nWobF3kav/qeq5nIwCH2zw9HEk9S9z6mivNLzfT+Fgj4y8a3+M2reOVJEnSyGQwlnRMb/Yd/shH4JZb4OmnO59vnVVetgxq37Hr2PHiNutNB+B5RnM2B3Iz+DYS9yd6FYwlSZI0srkqtaRjerPvcIyZQzGkZpXf8Q647i9aWECiyz4aKeJWKjiSxZzxlKunUH51ecZziZUJYjJ3+yFLkiRpeDMYSwKy23f4RKZuTXASmZN2BM6ngSMXllH412/ocZ+FpxQy7uvV/GT2TP5zaiUvfKSaMKF98UtrObUkSZLUE5ZSSwKy23f4RH6HXV2ea50j/uvSFxh1Z6KL+NzZY6dM4u/+uqzNkTImMp9/mrCJN9S/duyo5dSSJEnqKYOxJCDzvsM9EYi8j5e5hm1ZtS/4ye4eh2KA6bv2EYjENuXX+yjhqvoa3he2c3XhNkJLpH5VfVbjkSRJ0shjKbUkAJqasmv3Rl7LOhRnYzLNzKZzio8E/jNO5y+OziG5eDLn/ei8fhuTJEmShjZnjCVl5UyaWMGaAbn320iwgcxl0s/FsdzQPJtVmdflkiRJkjoxGEuDVFf7A+fLmDG9u/5N7M3PQNImvnMiJ511Eju+taPTuQUkuI2KduXUbT36aOrXz72JJUmS1BMGY2mQqa1NbZuUaYXo1v2BFy3K/X3Hjevd9Q8wlbfwKudnKGvukwI459ZzmPoXUwH4dctESr+zifG0EEkt2tVaTt3VrDGkfh0NxpIkSeoJnzGWBpHly2Hx4q63TVq9OnX+zjtzf+/ehu1mCpnIkZyOoXhqMW9+6c3HQjHA9jPLWMJ81lDabn74bd3sjwzZLyYmSZKkkcdgLA0StbVw1VWQPMESzckkXHll7rdXqqpKzUj3VDkHmM7BnN3/1HefykUvXcRJU09qd3zcuNSq05+ihlup4Eg6Hp9Pfbf99XYGXJIkSSOXwVgaJG644cShuFUyCTfemPsxLFsGBT38XeE9bM/pvU8+82RCQednhltnsiOB+5nONczhYSbzGbpfdTof5eaSJEkannzGWBoE6uq6Lp/uSj4WmFq0CG6/PTVzPT3Zv6tOJ1YmqPhqRadw3DqT3frrs5Wx/BOzu+1r4UKfL5YkSVLPOWMsDbC6utRMbTY++Un42tdSfeTK0qXwyCNw5bSdueu0B5pfbqbxscwPBvdmJrugAK6/PocDkyRJ0rBnMJYGSG1tamazuhp+8IPs+njwQfjYx1J9LFyYu+eOFy2CP72m/wtKEvdnXlCrdSb7ROG4oADuuMMyakmSJPWOwVgaACdafTobuV6x+rT3nZabjnohsTJBTMaM51pnshcuzNx24cLU+SVL8jhASZIkDUs+Yyz1s56uPp2N1hWrzzyz77OmL3/55dwMqhday6nHX5R5f+JFi1JfdXWpX8fGxtTq04sW+UyxJEmSsmcwlvpZb1afzkbritV9DcaJH3S/T3CvFEPZpWW8uvLVTqfCSYF46PgsceL+RJfBuFVVlUFYkiRJuWMptdSPsll9OhutK1Zna1/tPo42Hs18svOOSt0ae+FYFjQtoPr+aqp/WM2oU9v/e1w8FJn611MJxamO61fVZzFiSZIkKXsGY6kf5WpxrHzf68UvvtjluVDU82R8yvxTmPvYXApGpX6rKbusjPlPz6f0ktL2fY4KzHlsDpM/NJnzftT9/sSSJElSrllKLfWjxsy7EfX7vV79f6/yzGXPZNVvPJx5caxMDm46SEzGdnsTl0wpoebhGrbfsp1tn95GPBypX1XPG25+A7NXdL8/sSRJkpQPzhhL/WjcuMFxrx237+iXMRzdf5SG/23odDwUBKZfN91ZYkmSJA0KzhhryBtKKxT35/663d1r1opZPPm2JzlQdyDv43jl668w4a0TMp4be8FYZ4klSZI04AzGGrJqa1MrPGdazGrBAli2rH+DaE9UVaXGlu8FuBYu7P4fB4rLirnwmQvZ9tltvPSPL0HPq6N7bd+D+zqVU0uSJEmDiaXUGpKWL4fFi7sOmKtXp87feWf/jqsnli2Dgjz+n1dQANdf37NrZ/zDDOaum8uoiX37N7Ky95ZRfnV5xnNdlVNLkiRJg4XBWENObS1cddWJ9wJOJuHKK/t3JeieWLQIbr89P+G4oADuuKN3M+VjLxjLW3a/hVMvPbX3NyyCc79/LtX3V1N5WyXVP6ymsLSw02WvfP2V3vctSZIk9RODcT8KIUwLIdwZQtgRQmgOIbwQQrglhFB64tZqdcMNJw7FrZJJuPHG/I4nG0uXwiOPpEqec2XhwlSfS5b0vm3BqALOve9cRs8e3eM2xdOKuejFi5j07knHjpVdVsaFdRcy4R0T2l1b//P63g9KkiRJ6ic+Y9xPQggVwK+BScADwCbgQuBjwDtDCG+NMe4dwCEOCXV1vX8+99FHU+0G24JcixalvjouHlZfD3ffDVu3dm6zcGGqTPr003O74NjBFw5S9546Dmzs+WJcRacVUTKlpNPxkiklnP+T89l+y3a2fmortEDRpKLsBydJkiTlmcG4/9xKKhR/NMb49daDIYSbgU8A/wBcPUBjGzKyLYuurR18wbhVVVXnsS1bduLVtnP18+x9eC8b/3QjLftaetWuaX0TyZYkBaM6F560bsc04e0T2H7LdmZ8eUZuBitJkiTlgcG4H4QQZgCLgReAb3Y4/XngKuADIYS/iTE29fPwhpTGxv5tN5AyBeZcisnIi196kRe+8EJ2q1IfhV137qL8qsyLboHbMUmSJGlo8Bnj/vH29OsjMcZ2T8fGGPcDvwJGA2/u74ENNePG9W+74erIa0d4+l1P88LnX+jTVk07vr0jZ2OSJEmSBorBuH/MTL8+28X559Kvlf0wliEt232JB9t+xgNp/xP7WTt3Lfse3Nej60dXjWb0uZkX5Xr9qddJtvRwJTRJkiRpkDIY94/x6deuNnNtPT7hRB2FENZm+gJm5WCcg15VFSxY0Ls2CxcO3ueLsxWTkd337Gb3PbuJyZ5P+e5csZMn3vIEh54/1O544djOWywR4IzPnMGFz1zIhXUXcsanz4DQ4Zp0ObUkSZI0lBmMB4fWuNGHotaRY9mynu8BXFCQWsV5uKlfVc/GKzay8YqN1D9af8Lrk81JNv/FZjZ/eDPJQ+1neMe+aSwlZ7RfXXrUqaOYu24uM/7h+KJZM748g7nr5jJqYvulCSynliRJ0lBnMO4frTPC47s4P67DdV2KMc7N9EVq+6cRYdEiuP32E4fjggK4447hWUa9a8WujN9ncuilQzzx20+w8/adnc6VX1vOGx99I4e2HZ9BPvWyU3nLrrcw9oKxna4fe8FY3rL7LZx66anHjvVmiydJkiRpMDIY94/N6deuniE+J/3a1TPI6mDpUnjkkVSZdCYLF6bOL1nSv+PqDy2NLSRWJo69T6xM0LI/81ZL+366j8fnPM7+NfvbHS84uYBZd8+i8puVFJQU8MZfvpGTKk5i9r2zOe+H52XcgulY21EFnPfAecy+dzYnVZzEG3/5xtz8YJIkSdIAcbum/vHz9OviEEJB25WpQwhjgbcCB4H/G4jBDVWLFqW+TrTf73CTWJkgefB4OXTyQJLEygRTPjzl2LGYjLz0lZd4/nPPdyrQP6niJKq/X80p559y7NjYOWN585beLYo++fLJTL58cnY/hCRJkjSIGIz7QYxxawjhEVJ7Gf8l8PU2p78IjAG+7R7G2cn3fr8DJSYje+7bA8CkyycRClKPomcqnd61YtexYHyk/gibPriJvf+9t9N1p77rVGbdPYuiCUV5HLkkSZI0tBiM+8+1wK+Br4UQFgEbgTcBF5Mqof7sAI5Ng9BrP3uNjVdsBKBoUhETF03kwJYDNPyi86PoDasbOLj1IEebjvLMu5/h0Nb2q04T4Owbz+aMT59xLGBLkiRJSvEZ434SY9wKzANWkArEfwNUAF8DLooxdp7e04jUuhXT1k9sPXbs5X9+GYDdd+/ust2Wv93Cujev6xSKR506ipqHazjzs2caiiVJkqQMnDHuRzHGl4EPD/Q4NHg1bWhiTdWaTsdfe+Q1VoVV3bbd+8PM/7bSsreF9b+znvkb5jNm9phcDFOSJEkaVpwxlgaRvQ/mr3Bg748tSpAkSZIyMRhLA6y1dHr3PbuZdMUkKMz9PcqvLWfqtVNz37EkSZI0DFhKLQ2w+lX1xxbZmvZ30+Bo7vouKiti5vKZlF1alrtOJUmSpGHGYCwNsLbbL+3+964X1+qt0sWlzFoxi5IpJTnrU5IkSRqODMZSP+tqgS2AI3uO9Ln/UByY8ZUZTPvYNFehliRJknrAYCz1s5137cxr/7PumsXkKybn9R6SJEnScGIwlvpJdzPFubT/8f0GY0mSJKkXXJVa6if53IqprcTKBDEZ++VekiRJ0nBgMJb6ydRrp1J+TXne79P8cjONjzXm/T6SJEnScGEptZQn/VU6nUni/gTjLxo/IPeWJEmShhpnjKU8yXfp9CnzTmHKX0zJeM5yakmSJKnnDMZSnuSzdHrM+WOYt2YeM781k+ofVjPq1PbFH5ZTS5IkST1nMJbypHB0IZW3VlL9QDVFZUU57fvQ1kPHZoTLLitj/tPzKb2ktN01ifsTOb2nJEmSNFwZjKU8K7u0jHnr53UKrn1x9PWjNPxvw7H3JVNKqHm4hoqbKgjFAYD6VfU5u58kSZI0nBmMpX6QKbj21Stff6Xd+1AQmH7ddOY8NofJH5rMeT86Lyf3kSRJkoY7V6WW+klrcG1paOHFG17sc3/7fryPmIyEgvZBe+wFY5m9Ynaf+5ckSZJGCmeMpX4SY2T7v23nxS/1PRRD53JqSZIkSdkxGEv9oOX1Fjb8yQa2fHwLJHPXb8dyakmSJEm9Zym1lGcHNh/gmXc/w4ENB7JqXzi+kKMNRzOeq/9ZfR9GJkmSJAmcMZbyKvH9BGvnr806FANM+uNJnVe0Tv+fWzy5uA+jkyRJkgQGYykvki1Jtn5yK3XvrePo/syzvW0VnVbEqe85NeO5fQ/v47wHz2u3ovXJlScz+UOTqflJTU7HLUmSJI1EllJLOXZ492E2vH9Dj/YRDiWBGV+ZwfSPTwfg1QdeZdPSTbTsbTl2TfPLzexfs5/p101nwtsnsP2W7cz48gxKykvy9SNIkiRJI4ozxlIONfxvA4/PebxTKA6jAhMuntDuWOniUt78/JuPhWKAssvKmP/0/E6l04n7E8DxrZgMxZIkSVLuGIylHIgxsv0b23ly4ZMc3nG43bni8mIuWH0BLfWpWeBQHKi4uYKah2oomdI54JZMKaHm4Zp2pdM9mX2WJEmSlB1LqaU+Otp0lM1/sZk939vT6dyEt03g3HvPpXhyMef96Dy2fWYb0z4+jbEXjO22z1AQOpVOS5IkScoPg7HUBweeO0Ddu+toeqap07npfzeds798NgWjUoUZJeUlzF4xu1f9t5ZOS5IkScofg7GUpVcfeJWNH9zI0cb2q04Xji1k1l2zOO09pw3QyCRJkiT1hsFY6qV4NPL89c/z0j++1Onc6HNHU/2DakbPHD0AI5MkSZKUDYOx1AuHE4fZ8CcbqK+t73TutMtPY+Z3ZjLqFP+3kiRJkoYS/wYv9VDjbxqpe08dzdub2x0PowIVX61g6kenEkIYoNFJkiRJypbBWDqBGCM7vr2DLR/dQjwS250rPr2Yc+8/lwm/NWFgBidJkiSpzwzGUjeOHjjKs9c8y+67d3c6N/63x3Pufedm3ItYkiRJ0tBhMJa6cHDrQZ55zzM0PdV5K6Zp101jxldmUFBUMAAjkyRJkpRLBmMpg1d/9Cob/2wjRxvab8VUMKaAWXfOYtIfTxqgkUmSJEnKNYOx1EY8GnnhCy/w4pde7HRu9KzRVP2gijGzxwzAyCRJkiTli8FYSjuy9wgbrtjAa4+81uncae89jZl3zmTUWP+XkSRJkoYb/5YvAY2Pp7dieqn9VkwUQsU/VzDtE9PcikmSJEkapgzGGvF2fGcHz/3lc8TD7bdiKppcRNV9VUxYOGFgBiZJkiSpXxiMNWIdPXiU5/7qOXbduavTuXFvGUfV/VWUlLsVkyRJkjTcGYw15MVkZM99ewCYdPkkQsGJS54PPn+QuvfU8foTr3c6N/WjU6n4lwoKit2KSZIkSRoJDMYa8upX1bPxio0AFJ9eTOnFpd1ev/ehvWz80420vNbS7njB6AJmfmcmk/9kct7GKkmSJGnwcUpMQ96uFbsyft9RTEZe+OILPP37T3cKxSefczJzHptjKJYkSZJGIIOxhrSWxhYSKxPH3idWJmjZ39LpuiP7jvD0HzzNC194AdqvsUXZH5Uxd81cTqk+Jc+jlSRJkjQYGYw1pCVWJkgeTB57nzyQbBeUAfY/sZ+1c9ey76F97RsXwIx/mkHV96sYNd6nCiRJkqSRymCsIS1T6XTbYzvv2skTb3mCQy8candN0WlFnP/T8znjk2e4P7EkSZI0wjlNpiHrwJYDNPyiodPxhtUNNG1oYvu/bWfn7Ts7nR/7prFUrazipGkn9ccwJUmSJA1yBmMNWbvv3t3luacueYrDOw53Ol5+bTlvuPkNFJRYLCFJkiQpxWCsQatpQxNrqtZk1TZTKAbYcesOdty6g/kb5jNm9pi+DE+SJEnSMOG0mQatvQ/uzV/fP85f35IkSZKGFoOxBq2p106l/JrynPdbfm05U6+dmvN+JUmSJA1NBmMNWoWjC6m8tZLqB6opKivqc39FZUVUP1BN5TcrKRxdmIMRSpIkSRoODMYa9MouLWPe+nmUXlKadR+li0uZt34eZZeW5XBkkiRJkoYDg7GGhJIpJdQ8XEPFTRXQi8njUByouLmCmodqKJlSkr8BSpIkSRqyDMYaMkJB4LT3ncZJZ/R8/+FZd81i+iemEwpCHkcmSZIkaSgzGGvIeK32NdbOWcuhrYd63Gb/4/vzOCJJkiRJw4HBWINejJEXv/IiTy1+iiOvHulV28TKBDEZ8zQySZIkScOBwViDWktDC3XvruP5Tz8Pyd63b365mcbHGnM/MEmSJEnDhsFYg9brT7/O2vlrefWHr/apn8T9iRyNSJIkSdJwZDDWoLT7/9vNujev4+BzB9uf6GINrfJryim/ujzjOcupJUmSJHXHYKxBJXk4yXMffY6Nf7qR5IH2tdMnzzwZOuTborIiqh+opvLWSipvq6T6h9WMOnVUu2ssp5YkSZLUHYOxBo3mV5p58m1P8srXX+l07vSlpzPxkontjpUuLmXe+nmUXVp27FjZZWXMf3o+pZeUtrvWcmpJkiRJXTEYa1B4bdVrPD7ncRr/t/3MbigJVN5RyazvzKLhVw2pY8WBipsrqHmohpIpJZ36KplSQs3DNVTcVEEoTtVe16+qz/vPIEmSJGloGnXiS6T8iTHy8k0vs+3vt8HR9udKziyh+vvVjJ07FoDzfnQe2z6zjWkfn8bYC8Z2228oCEy/bjoT3j6B7bdsZ8aXZ+TrR5AkSZI0xBmMNWBaGlvYtGQTr36/86rTpb9TyrnfO5eiU4uOHSspL2H2itm9usfYC8b2uo0kSZKkkcVgrAHRtKGJZ979DAc3H+x07sxlZ3LWsrMIhV0sQS1JkiRJOWQwVr/bc98eNi3dRLKp/arToyaMYvZ3Z3Pq7586QCOTJEmSNBIZjNVvkkeSbPvkNrbfsr3TuTHnj6H6B9WcPOPkARiZJEmSpJHMYKx+0byzmQ1/vIGGXzZ0Ojf5Q5OpvK2SwpMLB2BkkiRJkkY6g7Hyrv4X9Wz44w0c3nW43fFQHDjna+cw5aophODzxJIkSZIGhsFYeRNjZPu/bWfr327tvBXT9BKqVlYx7sJxAzM4SZIkSUozGCsvWl5vYfNHNpO4L9HpXOk7Spl9z2yKy4oHYGSSJEmS1J7BWDmXbEny5G8/yetPvt7p3BmfOYOzbzjbrZgkSZIkDRoFAz0ADT8FowqYcuWUdscKxxVS/UA1M/5hhqFYkiRJ0qBiMFZelF9TzuQ/mwzAmPPGMHftXMouLRvgUUmSJElSZ5ZSKy9CCFR+u5KSM0s48zNnUjjarZgkSZIkDU4GY+VN4ehCZnxpxkAPQ5IkSZK6ZSm1JEmSJGlEMxhLkiRJkkY0g7EkSZIkaUQzGEuSJEmSRjSDsSRJkiRpRDMYS5IkSZJGNIOxJEmSJGlEMxhLkiRJkkY0g7EkSZIkaUQzGEuSJEmSRjSDsSRJkiRpRDMYS5IkSZJGNIOxJEmSJGlEMxhLkiRJkkY0g7EkSZIkaUQzGEuSJEmSRjSDsSRJkiRpRDMYS5IkSZJGNIOxJEmSJGlEMxhLkiRJkkY0g7EkSZIkaUQzGEuSJEmSRjSDsSRJkiRpRDMYS5IkSZJGNIOxJEmSJGlECzHGgR6DciCEsPfkk0+eOHv27IEeiiRJkiT1u40bN3Lw4MF9McZTe9vWYDxMhBCeB8YBLwzwUDqalX7dNKCjkLrmZ1SDnZ9RDXZ+RjXY+RkdOc4CGmOMZ/e2ocFYeRVCWAsQY5w70GORMvEzqsHOz6gGOz+jGuz8jKonfMZYkiRJkjSiGYwlSZIkSSOawViSJEmSNKIZjCVJkiRJI5rBWJIkSZI0orkqtSRJkiRpRHPGWJIkSZI0ohmMJUmSJEkjmsFYkiRJkjSiGYwlSZIkSSOawViSJEmSNKIZjCVJkiRJI5rBWJIkSZI0ohmMlRchhGkhhDtDCDtCCM0hhBdCCLeEEEoHemwaGUIIp4YQPhJC+K8QwpYQwsEQQkMI4ZchhKUhhIy//4UQ3hJCeDCEsC+EcCCEsD6E8PEQQmF//wwaeUIIHwghxPTXR7q4xs+o+l0I4bdDCN8PIexM/7m+M4TwSAjh9zJc62dU/SqE8Pvpz+P29J/320II94cQLuriej+j6iTEGAd6DBpmQggVwK+BScADwCbgQuBiYDPw1hjj3oEboUaCEMLVwG3ATuDnwEvAZODdwHjg+8D7YpvfBEMIl6WPHwLuA/YB7wJmAitjjO/rz59BI0sIYTrwNFAInAJcGWP8Todr/Iyq34UQPgfcCLwK/IjU76tlwBuBn8cYP9nmWj+j6lchhH8CPgnsBX5I6nP6BuBSYBTwwRjjd9tc72dUGRmMlXMhhJ8Ai4GPxhi/3ub4zcAngG/HGK8eqPFpZAghvB0YA/w4xphsc/x04DfAdOC9Mcbvp4+PA7aQCs1vjTE+nj5+EvAz4CLgT2KM9/brD6IRIYQQgJ8CZwM/AP6WDsHYz6gGQgjhfcB/Av8DvDvGuL/D+aIY45H0935G1a/Sf6a/AiSAmhjjnjbnLib1uXs+xjgjfczPqLpkKbVyKoQwg1QofgH4ZofTnweagA+EEMb089A0wsQYfxZj/O+2oTh9fBfwrfTbt7U59V7gNODe1j8o09cfAj6XfntN/kasEe6jwNuBD5P6fTITP6PqV+lHTv4JOABc0TEUA7SG4jQ/o+pvZ5LKM4+1DcUAMcafA/tJfSZb+RlVlwzGyrW3p18fyRBI9gO/AkYDb+7vgUlttP5FrqXNsdbP7sMZrl9N6i+GbwkhlORzYBp5Qgizga8A/xZjXN3NpX5G1d/eQqqK4UHgtfRznJ8KIXysi2c3/Yyqvz0HHAYuDCGUtT0RQlgAjCVV7dDKz6i6ZDBWrs1Mvz7bxfnn0q+V/TAWqZMQwijgg+m3bf9g7PKzG2NsAZ4n9azSjLwOUCNK+vP4H6Segf/MCS73M6r+Nj/9uhtYR+r54q8AtwC/DiE8GkJoOxvnZ1T9Ksa4D/gUqTVENoQQbg8h/GMI4T+BR0g9ovIXbZr4GVWXRg30ADTsjE+/NnRxvvX4hPwPRcroK0A18GCM8SdtjvvZ1UBYRmoBo9+KMR48wbV+RtXfJqVfryYVGN4BPEaqfPUm4HeA+zn+WIqfUfW7GOMtIYQXgDuBK9uc2gKs6FBi7WdUXXLGWP0tpF9d9U39LoTwUeBvSK2U/oHeNk+/+tlVToQQLiQ1S3xTjPF/c9Fl+tXPqHKldeuaQGqxwtoY4+sxxjrgj4DtwMKutsTJwM+oci6E8ElgJbACqCC18OZcYBvwvRDCP/emu/Srn9ERyGCsXGv9l7bxXZwf1+E6qV+EEP4S+DdgA3BxuvyqLT+76jdtSqifBa7vYTM/o+pvr6Vft8UYn2p7Il3h0Fp1c2H61c+o+lUI4W2kFoj7fzHG62KM22KMB2KM60j9480rwN+kF4cFP6PqhsFYubY5/drVM8TnpF+7egZZyrkQwseBbwDPkArFuzJc1uVnNx1izia1WNe2PA1TI8sppD5rs4FDIYTY+kVqBX+AO9LHbkm/9zOq/tb6mavv4nxrcD65w/V+RtVf/iD9+vOOJ2KMB0htz1hA6pEV8DOqbhiMlWutvzEtTm/zcEwIYSzwVuAg8H/9PTCNTCGETwH/CjxJKhTv6eLSn6Vf35nh3AJSq6n/OsbYnPNBaiRqBpZ38fVE+ppfpt+3lln7GVV/W00qJJwTQijOcL46/fpC+tXPqPpb6+rRp3VxvvX44fSrn1F1yWCsnIoxbiW1CuBZwF92OP1FUs993B1j7GqfTilnQgjXk1psay2wKMb4ajeXrwReBd4fQpjXpo+TgC+l396Wr7FqZIkxHowxfiTTF/D/0pf9e/rYfen3fkbVr9K/Z95Hqux0WdtzIYRLSC2+1cDxFf79jKq//SL9elUIYWrbEyGE3yU1IXMI+HX6sJ9RdSnE6LPlyq0QQgWp34AmAQ8AG4E3AReTKqF+S4xx78CNUCNBCOFDpBbiOAp8nczPC70QY1zRps0fkvpD8xBwL7APuJTU9g4rgT+O/qapPAshfIFUOfWVMcbvdDj3h/gZVT8KIUwCfgW8gVQI+Q2pVan/iNQCRVfEd3iWAAAADUhJREFUGO9vc/0f4mdU/SRdnfgTUium7wf+C9hF6jGVPyC1mNbHY4z/1qbNH+JnVBkYjJUXIYTpwA2kSlVOBXYCPwS+mGHRIynn2oSL7jwaY3xbh3ZvBT4LXAScRGq7hzuBr8UYj+Z+pFJ73QXj9Hk/o+pXIYSJwOdIheGppALIL4F/jDF2ejTKz6j6UwihiFSV4vuBc0mVQ+8j9Y84X4sxPpKhjZ9RdWIwliRJkiSNaD5jLEmSJEka0QzGkiRJkqQRzWAsSZIkSRrRDMaSJEmSpBHNYCxJkiRJGtEMxpIkSZKkEc1gLEmSJEka0QzGkiRJkqQRzWAsSZIkSRrRDMaSJEmSpBHNYCxJkiRJGtEMxpIkjQAhhIdCCDH99dGBHs9QFkK4ss2v5aMDPR5JUt8ZjCVJGuZCCJcC70y/fQH41sCNJvdCCAvbBNWjIYRJeb7lncDm9PcLQgiX5/l+kqQ8MxhLkjSMhRBGATe3OXRDjPHwQI0nTy5t8/1vYox78nmzGONR4IttDv1zCKEkn/eUJOWXwViSpOHtw0BF+vvtwHcHcCz58q423/+/frrnf5KafQc4A7iyn+4rScoDg7EkScNUCKEI+FybQ1+LMR4ZqPHkQwhhFnBOm0P/3R/3Tc8a/2ubQ58JIZzUH/eWJOWewViSpOHrclKzmQCHgbsGcCz50raM+vkY4zP9eO+7gUPp76cAf9KP95Yk5ZDBWJKk4etjbb5/IMb46oCNJH8GoowagBhjPfD9Noc+1sWlkqRBzmAsSdIwFEK4AJjX5tA9AzSUvAkhnApc1OZQv5RRd3Bvm+/PDyFcOABjkCT10aiBHoAkScqLP2vz/UHgJ7noNIQwBXgzMA0YA7wCPBpjfOkE7cqABcDZQBGwG/hljPG5Pgzn94HC9PcNwOoTNQghlANzgDOBcenDB4CdwDbg6Rhjcy/G8FNgPzA2/f7PgN/0or0kaRAwGEuSlIUQQgHwP8DFbQ5/Nsb45R62vwd4f5tD34wx/lUOh/i+Nt8/GmM80MNxfQH4fJtDZ8cYXwgh1ABfAn6P42G0VTKEcD/w0Y5bJYUQpgP/lB5Pp793hBBWAdfEGDf1ZHwdtH2++OHuFhYLIfwh8EnazzBncjiE8H/AvTHG2040gBhjcwihFvjD9KH3hRA+FmOMJ2orSRo8LKWWJCkLMcYk8KdAos3hG0IIv3WitiGEj9A+FD8F/E2uxhZCmM3xRbcAHu1jf+8hNQv6LjqHYkj9feJy4P/SM7Kt7X4LeJLUolRd/WP824Bfp0u/ezOmYmBxm0MZny8OIRSGEFYA/8WJQzFAMamZ7X/sxXDa/vqeDlzQi7aSpEHAGWNJkrIUY9wZQvgA8BAQSIXG/y+EcEGMcV+mNiGEKuDf2hx6HfjjXpbvnsglHd7/qg99vRW4k1RgBNgIbAJagNlAdZtrzwa+B1ycDucPcrzE+AXgaaCJ1L7K80j9mgGUAveFEM6LMR7u4bgubtN3C6n/Bpl8EfhQh2NNwBOkyqcPp/spB84FRvfw/m39ssP7S9L9S5KGCIOxJEl9EGP8SQjhn4FPpQ9NB1bQvswXgBDCycB9tA9ffxljfDbHw+q4ANTTfejrG6RC8f+RKnl+su3JEMLbgJXAqelDbwshvItU2fVYUkH62hjjqg7tzic1i3t2+lAl8BHg1h6Oq+2v7y9jjK91vCCEMBH4uzaHXgeuA/49UwAPIRSSmlV+N/BHPRwHQB2Q5Hgl3pt60VaSNAhYSi1JUt99Dvh1m/fvCiF8IsN1XwOq2rz/9xjj3XkYz5w237+S3lYoWxOAVcDFHUMxQDrwfqDD4buBGuAZ4K0dQ3G63VOknstNtjnccWa3O3/Q5vuutmm6hOMz3ZAK9nd0NSsdYzwaY/xljPE6UrPhPRJjPAhsbXNobk/bSpIGB4OxJEl9FGNsIfXMcNvy6a+EEI5tlxRCeD+pGdFWm4G/zPVYQgiBVKlyqxf72OVB4M9ijIe6uiDG+BCp8upWE4AIfCDTTG6bdutJrercal4IYcyJBpR+HrntM9RdbdN0Rof3/3WivtuMrcuftwttf53PCCGU9LK9JGkAGYwlScqBGOPLwIfbHCom9dzsuBBCBXB7m3OHgMtjjE15GMoU2s+S7uhjf/fFGF/pwXU/6/D+55lmmE/QrgA4rwdt2pZRb4wxbulBG4DTenhdNtr+GgVSJfWSpCHCYCxJUo7EGP8f7RfWmkFq4ar7OL5QFMB16VLifOgY/rqcse2hR3p43dYO73+a8arOOobanoTXd7X5vqsyakjNyrf1lfRzxPlQ3+F9WZ7uI0nKA4OxJEm59Ung8Tbv30P7Z06/35P9cfug46rKvS0J7qin+ws3dnjfMZT2tN247i5ObwfV9tezqzJqgFrg1TbvLweeCSF8PIRwVg/H11MHO7w/YUm4JGnwMBhLkpRD6YWdLqdz4IPUlkUfyXA8lzruONHSx/4aenhdx/tk267oBNe/i+PbPCWA/+3qwnSp+l+Set651SzgX4HnQwjPhxD+I4RwVQihsofj7Upvfw5J0iBiMJYkKcdijNvIvO3Q0j6uEN0TBzq8P6mP/SVPfElO251I2zLqH8cYu71PjPE/gcuA7RlOnwX8GfBtYHMIoS6EcF0IIZu9jE/u8L7jfwdJ0iBmMJYkKcdCCOeQecXp3mxHlK39Hd4Pm5LedGBd1OZQd2XUx8QY/xs4h9Sv/4Ok9jPO5FzgJmBTCOGiXg6vY5ju+N9BkjSIGYwlScqh9DY999J+sa1WHwwhfDDPQ+g4M3p6nu/Xny7h+Ax4Mz1fGIwY46EY490xxt8HSoH5wMeBH9I5KE8HHg4hzOzF2KZ0eP9yL9pKkgaYwViSpNz6F2BOm/e1tF+Y6Zs5eJ61SzHGA8CeNoem5uteA6DtNk0/jzF2NfPbrRhjS4zx8Rjjv8UY/4jUCtIfoH2YHQfc0Ituy9t83xRjfLXLKyVJg47BWJKkHAkhXAb8dZtD24B3Ax9rc+wUUvsbl+RxKE+3+b4ij1sU9ZsQQgB+v82h7rZp6pUYY3OM8bvAO2j/bPDv9eLXru0/djzd5VWSpEHJYCxJUg6EEKaT2rO41RHg/THGxhjjHcB/tjl3AfDVPA6n7XZRJwEVebxXf3kTMLnN+x49X9wbMcZnab/K9SnAqSdql/5vP6HNoce7uFSSNEgZjCVJ6qMQwijgHmBim8N/H2Nc0+b9lcDzbd7/VQjhD/M0pF90eD8vT/fpT23LqJ+IMWZaZToXOm6zdbgHbTr++q7O0VgkSf3EYCxJUt/dALy1zfsfk9or95gYYyPwflIzya3uTM825trPSS1O1WpBHu7R39pu09SjMuoQwntDCOf29AYhhMm0X/V6dw+311rY5vujwP/09J6SpMHBYCxJUh+EEN4BfKrNoVeAP48xxo7Xxhh/A3ymzaFS4J5cPwOcXoDrZ20OvT2X/fe3EMLZQHWbQz0to/4D4JkQwv+EEK4MIXRcObrtPX6L1K/ZuDaHv9fD+7T99f1VjPG1HraTJA0SowZ6AJIkDVXpGcbvcvwfmo8Cf3qCFYlvAi4Gfi/9/q3AF4HP5Xh43wN+N/39OSGE2THGjTm+R39pW0b9SoxxbS/aBlKzwIsAQgg7gI3APlJl0hOBGjqv3v0iPViVOoQwAzivzaGehmlJ0iBiMJYkKQvpVZL/g/YLQt0QY3y0u3YxxhhC+HPgSY5v8fPpEMLPY4y1ORziD4H9HN9P+T3Al3LYf39qW0bd10W3ymm/tVImTwN/EGNs6EF/727z/SHg/mwHJkkaOJZSS5KUnU8Dl7R5v4oeBs8YYwL4MyCZPlQAfDeEMClXg4sxNgF3tTn0oXSYH1JCCONp/4x0b4LxZ0ltn/UwnRfVyuTp9PVzYowv9fAef97m++9aRi1JQ1PI8AiUJEkaBkIIFcCzHP+H8ItjjKsGbkS9F0K4HLg3/bYJKIsxHsqinwJgFnAOMJ3jM+n7gZeBJ2OML/ayzzfTfnunmhijexhL0hBkKbUkScNUjHFrCOFe4Ir0oY+SmtkeSto+X/zTbEIxQIwxCWxIf+XKR9t8/4ChWJKGLmeMJUkaxkIIlaTCYCGp0u1zY4ybB3ZUPZPeH3oPqdW7AZbEGO/qpkm/CSGcCWwhNckQgTfGGJ8a2FFJkrLljLEkScNYjPHZEMJ3gL8gVVL9GeBDAzuqHpsIfK3N+x7tX9xP/p7jf4/6nqFYkoY2Z4wlSRrmQghlpJ41LiU1a3x+jPGZgR3V0BVCeAOpLZ9GAa8DM2OMOwZ2VJKkvnDGWJKkYS7G+GoI4U+BN6UPTQMMxtk7E/iH9PfrDMWSNPQ5YyxJkiRJGtHcx1iSJEmSNKIZjCVJkiRJI5rBWJIkSZI0ohmMJUmSJEkjmsFYkiRJkjSiGYwlSZIkSSOawViSJEmSNKIZjCVJkiRJI5rBWJIkSZI0ohmMJUmSJEkjmsFYkiRJkjSiGYwlSZIkSSOawViSJEmSNKIZjCVJkiRJI5rBWJIkSZI0ohmMJUmSJEkj2v8P3hfUiHt6dEEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 540x432 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 402,
       "width": 483
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_poly # just call the figure that we created in the previous cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can see all the things that we have done in a single plot!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## In-class Exercise\n",
    "\n",
    "1. Put it all together and create a linear model using a polynomial of degree 2 for the same data.\n",
    "\n",
    "\n",
    "2. Compare your plot with the one obtained for the straight line (polynomial of degree 1).\n",
    "\n",
    "\n",
    "3. Play a bit with your code by changing the degree of the polynomial. What happens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Write your code for In-class Exercise:\n",
    "\n",
    "# until here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Go back to the previous cell and try to keep increasing the polynomial degree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* You see the prediction getting worse!\n",
    "\n",
    "This is called **overfitting**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Overfitting is a natural consequence of having a model that is more complex than it should be!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- As we know, the mean of the data that originates from the car stopping distance problem is generated with a quadratic model: $y = z_1 x + z_2 x^2$\n",
    "    * Therefore, we don't need additional complexity to describe the *mean* of the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Also, the fit is better **within the domain** that we used for training ($x\\in [3, 83]$) than away from it.\n",
    "\n",
    "In other words, we **interpolate** better than we **extrapolate**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Nevertheless, overfitting is also an issue when we are interpolating...\n",
    "    - See this by making the degree very high, e.g. 30, and plot for $x\\in [5, 80]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It might be surprising, but this is an important issue in ML.\n",
    "\n",
    "It is very common to use models that are complicated (have many parameters) and that perform poorly even when interpolating, but especially when extrapolating!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "## Solution for In-class Exercise\n",
    "\n",
    "```python\n",
    "degree = 2\n",
    "poly_model = make_pipeline(PolynomialFeatures(degree),LinearRegression()) # model\n",
    "poly_model.fit(np.reshape(Data_x, (-1, 1)),Data_y) # training (fitting)\n",
    "y_pred = poly_model.predict(Data_X) # predict y for Data_x\n",
    "x_plot = np.linspace(0, 90, 200) # 200 points uniformly spaced\n",
    "y_plot = poly_model.predict(np.reshape(x_plot, (-1, 1))) # prediction for those points\n",
    "fig_poly, ax_poly = plt.subplots() # create a plot\n",
    "ax_poly.plot(Data_x, Data_y, 'b.', markersize=12,label=\"Data\") # Markers locating data points)\n",
    "ax_poly.plot(Data_x, y_pred, 'm*', markersize=12,label=\"Predictions\") # Markers locating prediction points)\n",
    "legend_str = \"Linear regression with Polynomial of degree \" + str(degree)\n",
    "ax_poly.plot(x_plot, y_plot, 'm-', linewidth=2,label=legend_str) # polynomial interpolation plotted\n",
    "ax_poly.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_poly.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_poly.set_title(\"Car stopping distance problem\", fontsize=20) # create title with font size 20\n",
    "ax_poly.legend(loc='upper left') # replot legend\n",
    "```"
   ]
  }
 ],
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