Exercise 04—Binary Classification Using a Simple Linear Function.ipynb

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    "%config InlineBackend.figure_format = 'retina'\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=3)\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning Excercise 1"
   ]
  },
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   "source": [
    "## Binary Classification"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a data set below, containing 6 data points, each containing a 2-dimensional vector associated with a label. For example, a vector `[1.2, 0.7]` is associated with the label `+1`."
   ]
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   "source": [
    "| vector [x,y] \t| label \t|\n",
    "|--------------\t|-------\t|\n",
    "| [ 1.2, 0.7]  \t| +1    \t|\n",
    "| [-0.3, -0.5] \t| -1    \t|\n",
    "| [3.0, 0.1]   \t| +1    \t|\n",
    "| [-0.1, -1.0] \t| -1    \t|\n",
    "| [-1.0, 1.1]  \t| -1    \t|\n",
    "| [2.1, -3.0]  \t| +1    \t|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a better understanding of the data, we can plot these two-dimensional vectors on a cartesian plane:"
   ]
  },
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   "source": [
    "<img src=\"img/neural_networks_33.png\" alt=\"drawing\" width=\"500\"/>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Here, the location on the point in the plane is given by the pair of coordinates, and its colour is defined by the label. Red points have the label `+1`, and the blue points have the label `-1`.  When we give the computer a pair of (x,y) coordinates, we want the computer to tell us should whether the point should be marked `-1`—red or `+1`—blue, according to what it knows from the data.  What does learning means in this case? The computer needs to define the boundary between these two given classes."
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   "source": [
    "### Classification by using a simple linear function "
   ]
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   "source": [
    "First we will use a simple linear function to implement binary classification:"
   ]
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   "source": [
    "\\begin{align}\n",
    "F = f(\\mathbf{X},\\mathbf{Y})=A\\mathbf{X}+B\\mathbf{Y}+C\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, $\\mathbf{X}$ and $\\mathbf{Y}$ are the input vectors, and $A$, $B$ and $C$ are the parameters that we are trying to learn. This can be represented schematically:"
   ]
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  {
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   "source": [
    "<img src=\"img/neural_networks_16.png\" alt=\"drawing\" width=\"400\"/>"
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   "source": [
    "So, if our data point is $(\\mathbf{X},\\mathbf{Y})=$ `[1.2,0.7]`, and if the chosen parameters are $A=$ `1`, $B=$ `-2`, $C=$ `-3`, initialise the variables:"
   ]
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   "source": [
    "For the corresponding data point label, initialise the variable `label`:"
   ]
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   "source": [
    "Compute the output of the function $F = f(\\mathbf{X},\\mathbf{Y})$ and assign it to the variable `output`:"
   ]
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   "execution_count": null,
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   "cell_type": "markdown",
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   "source": [
    "<img src=\"img/neural_networks_17.png\" alt=\"drawing\" width=\"400\"/>"
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   "source": [
    "The prediction has to do with how do we interpret the output $F$ of the function $f(\\mathbf{X},\\mathbf{Y})$.<br>\n",
    "\n",
    "__We can define that in our algorithm, the parameters $A$, $B$, and $C$ must be tuned such that the function $f$ outputs a number greater than 0 when it encounters a data point associated with the label `+1`. In the same way, the function should output a number less (or equal to) than 0 when it encounters a data point associated with the label `-1`.__\n"
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   "source": [
    "| Neuron Output \t| Label | Action         |\n",
    "|--------------\t|---------- | ------         |\n",
    "| Output > +1  \t| +1    \t| do nothing     |\n",
    "| Output > -1 \t| -1    \t| minimise output|\n",
    "| Output < +1   \t| +1    \t| maximise output|\n",
    "| Output < -1 \t| -1    \t| do nothing     |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decide whether we should minimise or maximise the output of the function $F = f(\\mathbf{X},\\mathbf{Y})$ for the current data point?"
   ]
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  {
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   "cell_type": "markdown",
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   "source": [
    "Create a python function `decide(output, label)`, that prints whether we should minimise or maximise our function $F = f(\\mathbf{X},\\mathbf{Y})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "cell_type": "markdown",
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   "source": [
    "Test the function `decide` for the current output and label, and try some other values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "If the formulas for maximising and minimising functions are respectively:\n",
    "$$x_{new} = x_{old} + \\frac{dy}{dx}x_{old} \\cdot c$$\n",
    "and\n",
    "$$x_{new} = x_{old} - \\frac{dy}{dx}x_{old} \\cdot c$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How can we use a number-holding variable, for example `sign` to modify this function so that it can maximise and minimise according to its value:"
   ]
  },
  {
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   "cell_type": "markdown",
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   "source": [
    "Initialise the variable `sign` to zero, and write code that will set its value to `-1` or `1` according to the current values of the variables `output` and `label`"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "What is the value of `sign` for the output of our current data points and their label?"
   ]
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   "source": [
    "### Computing the gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_16.png\" alt=\"drawing\" width=\"400\"/>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "We have computed the partial derivatives in terms of parameters $A$, $B$, and $C$:"
   ]
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   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial F}{\\partial A} &=\\frac{\\partial F}{\\partial G}*\\frac{\\partial G}{\\partial A}; &\\frac{\\partial F}{\\partial B} &=\\frac{\\partial F}{\\partial G}*\\frac{\\partial G}{\\partial B}; &\\frac{\\partial F}{\\partial C} ;& \\\\\\\\\n",
    "\\frac{\\partial F}{\\partial A} &=1*X &\\frac{\\partial F}{\\partial B} &=1*Y &\\frac{\\partial F}{\\partial C} &=1 \\\\\\\\\n",
    "\\frac{\\partial F}{\\partial A} &=X &\\frac{\\partial F}{\\partial B} &=Y &\\frac{\\partial F}{\\partial C} &=1\n",
    "\\end{align*}"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Initialise the partial derivatives using the variables `dA`, `dB` and `dC`, and print their values:"
   ]
  },
  {
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   "cell_type": "markdown",
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   "source": [
    "Introduce the variable `step_size` to hold a very small number and minimise/maximise the value of `dA`, `dB` and `dC`:"
   ]
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   "source": [
    "Evaluate the  function $f(\\mathbf{X},\\mathbf{Y})$, with the updated parameters $A$, $B$, and $C$:"
   ]
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   "source": [
    "This result should be better then the original result `-3.2` !"
   ]
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   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1:\n",
    "Write a simple algorithm for binary classification by using the previously written code:"
   ]
  },
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   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple linear classification algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the previous steps are put together in an working algorithm. "
   ]
  },
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   "source": [
    "| vector [x,y] \t| label \t|\n",
    "|--------------\t|-------\t|\n",
    "| [ 0.0, 0.7]  \t| +1    \t|\n",
    "| [-0.3, -0.5] \t| -1    \t|\n",
    "| [3.0, 0.1]   \t| +1    \t|\n",
    "| [-0.1, -1.0] \t| -1    \t|\n",
    "| [-1.0, 1.1]  \t| -1    \t|\n",
    "| [2.1, -3.0]  \t| +1    \t|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can represent the data as a 2-dimensional numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array([[ 0.0, 0.7],\n",
    "                 [-0.3,-0.5],\n",
    "                 [ 3.0, 0.1],\n",
    "                 [-0.1,-1.0],\n",
    "                 [-1.0, 1.1],\n",
    "                 [ 2.1,-3.0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can represent the labels as a simple numpy array of numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = np.array([ 1,\n",
    "                   -1,\n",
    "                    1,\n",
    "                   -1,\n",
    "                   -1,\n",
    "                   +1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the data using the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code_folding": [
     0
    ]
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   "outputs": [],
   "source": [
    "def plot_data(data, labels):\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.scatter(data[:,0], data[:,1], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    nudge = 0.08\n",
    "    for i in range(data.shape[0]):\n",
    "        d = data[i]\n",
    "        ax.annotate(f'{i}',(d[0]+nudge,d[1]+nudge))\n",
    "    ax.set_aspect('equal', 'datalim')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(data,labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a function to evaluate the accuracy of the training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": [
     0,
     15,
     22
    ]
   },
   "outputs": [],
   "source": [
    "def eval_accuracy(data,labels, A,B,C):\n",
    "    num_correct = 0;\n",
    "    data_len = data.shape[0]\n",
    "    \n",
    "    for i in range(data_len):\n",
    "        X,Y = data[i]\n",
    "        current_label = labels[i]  \n",
    "        output = A*X + B*Y + C\n",
    "        predicted_label = 1 if output >= 1 else -1 if output <= -1 else 0\n",
    "        if (predicted_label == current_label):\n",
    "            num_correct += 1\n",
    "    return np.round(num_correct / data_len,3)\n",
    "\n",
    "def create_meshgrid(data):\n",
    "    h = 0.02\n",
    "    x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1\n",
    "    y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "    return (xx,yy,np.ones(xx.shape))\n",
    "\n",
    "def plot_learning_simple(grid,data,labels,A,B,C,iteration, accuracy):\n",
    "    xx,yy,Z = grid\n",
    "    \n",
    "    for i in range(xx.shape[0]): # row\n",
    "        for j in range(yy.shape[1]): #column\n",
    "            X, Y = xx[i][j],yy[i][j]\n",
    "            output = A*X + B*Y + C\n",
    "            output = 1 if output > 0 else -1\n",
    "            Z[i][j] = output\n",
    "\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.title(f'accuracy at the iteration {iteration}: {accuracy}')\n",
    "    ax.contourf(xx, yy, Z, cmap=plt.cm.binary, alpha=0.1, zorder=15)\n",
    "    ax.scatter(data[:, 0], data[:, 1], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    ax.set_aspect('equal')\n",
    "    nudge = 0.08\n",
    "    for i in range(data.shape[0]):\n",
    "        d = data[i]\n",
    "        ax.annotate(f'{i}',(d[0]+nudge,d[1]+nudge))\n",
    "    plt.xlim(xx.min(), xx.max())\n",
    "    plt.ylim(yy.min(), yy.max())\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the main algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_neural_network(data, labels, step_size, no_loops, iter_info):\n",
    "    #A, B, and C are parameters of the function F. Here, they are set to 1, -2, -1\n",
    "    A, B, C = 1, -2, -1\n",
    "    # this function is used for plotting, it can be ignored\n",
    "    grid = create_meshgrid(data)\n",
    "    \n",
    "    # the main training loop\n",
    "    for i in range(no_loops):\n",
    "        # we randomly select the data point, and store its info into: x,y,label\n",
    "        index = np.random.randint(data.shape[0])\n",
    "        X,Y = data[index]\n",
    "        label = labels[index]\n",
    "        # we calculate the output of the function\n",
    "        output = A*X + B*Y + C\n",
    "        # We need to define how to affect parameters.\n",
    "        # If the label is 1 but the output is smaller than 1, we want to push the score up.\n",
    "        # If the label is -1 but the output is larger than -1, we want to push the score down.\n",
    "        sign = 0.0\n",
    "        if (label == 1 and output <= 1):\n",
    "            sign = 1.0\n",
    "        if (label ==-1 and output > -1):\n",
    "            sign = -1.0\n",
    "         # partial derivative of dF/dA is X, dF/dB is Y, and of dF/dC is 1. \n",
    "        dA, dB, dC = X, Y, 1\n",
    "        # here we update the parameter values using partial derivatives\n",
    "        A = A + dA * sign * step_size\n",
    "        B = B + dB * sign * step_size\n",
    "        C = C + dC * sign * step_size;\n",
    "        \n",
    "        # after a number of iterations, show training accuracy and plot it\n",
    "        if (i%iter_info==0):\n",
    "            accuracy = eval_accuracy(data, labels, A,B,C)\n",
    "            plot_learning_simple(grid,data,labels,A,B,C,i,accuracy)\n",
    "    # the algorithm returns the learned parameters A, B, and C\n",
    "    return (A,B,C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/oWBC/55mNpTRxLsVnBVAkh4Mn5uFj3+Kgk8Bj1Hw/t81hP0P1a8VzIsbJekBMzsmrGmcmV0u6dJwva8757Ymbmw7T+n0uIfHjk7LtizJvh83s6+Y2WFRCxYLvNPMHpD0b+F61/bTxgW++G5kxmVkXRT8sYpvEtihnV3fa7Wzw/uyJNuO087O0dHlbQ18iqPLtPN0Ok7Bp6lSnuIoRZ3RqV22KWgQ2qr+G7ruVn/Cemcl1BR/aqCXJH1U/TTEHMpzitt2Ttx6ryuN7uJJ9vW5hNcp/pRTDQrCQqrX+OS47bYoaFTbKumXaTz+7LjXrVfBaGGrpD/FrXPhIF6TlO+bgk+KPaDdn2dnwn0/TvO1e1wpmtFK+kbcfjeGz6lVCadhUnCoPv5UTVsUzCXamlDbAQnbRffP6Ke+sQoOgUbrxp+qyyk4XVR/z+HOhNcreg7nDPI1GMwpjqrTeS/j1lmmFL8vBvG+TZO0Lq6OmHb9HfSDQbznKb8Xs/jY0WuZ7Hs8/nXeGn4Pxf8+cZJuFg1d8/LCiBjS4py7TNLFCv5Ib1HQAqVRwX9z79fOifLJtt3inDtPQbuF3yqYsDxBwS+NpyR9TcGnMhO3+66CuVA/VvALZ4yCj6+vlnSjgtMuJbpc0n8qOM1Kj4JfRP8n6WTn3LK0nnTy5/KAgiDyBwW/TMco+MNyXVjr+tRbD/k5Rds+L6kpvPkTN0C/swHquEnB+Q6j0bHRktZK+rqCXlcpWwg45x5TEEifUHDIo0rB5OzKVNsk2cdaBXNmahUEo8pwH0nn9w2Fc26Tc+4sBecH/ZWCsFemIKg0KzhkdI6C75dM+aaClgGrFYycHhBedjlU6Zx7WFK1gn9gVin4HpikINj/WdLVCk6B9VK6BbhgVOVUBadPWqed/4j8QdIHnXPfGmAXn1ZwOrMXFPwTFT2HQTUbdc41K+go/00FpzKKPCfpWwpO19WUbNtscs6tV9DAdomC7/XRCr7PV0j6kHNuoH5z+fjYVyj43fmMgn+OyxW83y8oGDE/xjn3WRemNuQX430BRhYzm64gvI1S8Ed6rd+KAABDxYgYMPJcrOBn94+EMAAY2QhiwAgSfgLt8+HN3c67CAAYWTg0CYwAZvYnBR2xKxXMOVqp4IMG/AADwAjGiBgwMkxT0MLgnwpOdbSQEAYAIx8jYgAAAJ4wIgYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACejPZdQC6YWYuCc2+1ei4FAAAUhhmSupxzBw5nJ0URxCSVz5gxY69Zs2bt5bsQAAAw8v3jH/9Qa2vrsPeTF0HMzKZIOkvS+yUdLqlK0lZJz0r6saQfO+d2DOMhWmfNmrVXbW3tsGsFAABYsGCBWjOQxPIiiEk6V9IPJL0maYWkNklTJS2UdLuk083sXDqJAwCAQpIvQaxJ0hmSfhc/8mVmX5VUJ+lsBaHsfj/lAQAAZF5efGrSOfeYc+63iYcfnXOvS7o1vDk/54UBAABkUV4EsQH0htfbvFYBAACQYflyaDIpMxst6fzw5oAz7c2sPsWi2RkrCgAAIEPyfUTsGkmHSXrIOfd/vosBAADIpLwdETOzz0m6XNJaSYsGs41z7qgU+6qXdGTmqgMAABi+vBwRM7PPSLpR0hpJJznnOjyXBAAAkHF5F8TM7FJJ/yvpOQUh7HXPJQEAAGRFXgUxM/uypBskNSoIYf/0XBIAAEDW5E0QM7P/UjA5v17SKc65Nz2XBAAAkFV5MVnfzC6Q9E1J2yX9UdLnzCxxtVbn3LIclwYAAJA1eRHEJB0YXpdIujTFOk9IWpaTagAAAHIgLw5NOucWO+dsgMt833UCAABkUl4EMQAAgGJEEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACeEMQAAAA8IYgBAAB4QhADAADwhCAGAADgCUEMAADAE4IYAACAJwQxAAAATwhiAAAAnhDEAAAAPCGIAQAAeEIQAwAA8IQgBgAA4AlBDAAAwBOCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACeEMQAAAA8IYgBAAB4QhADAADwhCAGAADgCUEMAADAE4IYAABAGmKxmKZPn56RfY3OyF4AAAAKWG9vrySpp6dHdXV1Wrt2bUb2SxADAADoR29vr1avXq3Ozk5JUnd3tzZu3JiRfRPEAAAAkojFYpKkpqYmtbW1qbq6WpJUUVGRsccgiAEAACRobm5WW1tb3yhYdXV1RgNYhCAGAAAgqb29XVIwEtbY2KiqqirNmTMnq49JEAMAAEWvvb1dK1euVFlZmSSpqqpKM2fOzPrjEsQAAEBRisVifaNgDQ0Nmjx5sg4//PCc1kAQAwAARScWi6m2tlZlZWUqLS31EsIkghgAACgSURsKSVq3bp3Kysp09NFHe62JIAYAAApW1IhVklauXKmuri5VVlZq2rRpOZkDNhCCGAAAKEiJjVi7uro0b948z1XtiiAGAAAKSnwj1paWFtXU1EhS1ltRDAVBDAAAFIzm5mY1NDRo9Ogg4tTU1GSlEWumEMQAAMCIFt+ItaGhIW/mfw3GKN8FAPfdd5+qqqpUVVWln//8577LAQCMIFEj1qefflpr164dUSFMYkQMnr366qu66qqrNGHCBG3atMl3OQCAESAfGrFmCiNi8MY5py984QuaPHmyFi1a5LscAEAe6+3tVW9vb18j1rVr16q1tXVEhzCJETF4dMcdd+jJJ5/UfffdpyeffNJ3OQCAPBW1oTCzvGnEmimMiMGLf/zjH1qyZIkuuugiHXPMMb7LAQDkoVgsplgsppUrV6qtrU1btmxRVVVVwYQwiRExeLBt2zZ97nOfU1VVlb7yla/4LgcAkIfq6+vV2dmpkpISdXV1qbq6Oq/bUAwVQQw5d8MNN+i5557Tgw8+qNLSUt/lAADyRDQBf/369bs0Yq2oqCjIECYRxJBjDQ0Nuvnmm/WpT31KRx11lO9yAAB5ImrEWlZWJin/G7FmCkEMORMdkpw5c6a+9KUv+S4HAODZSG7EmikEMeTM5s2btW7dOknSgQcemHSdK664QldccYU+8YlP6Bvf+EYuywMA5FDUiHXy5MmSVJQhTCKIIYfGjh2rD3/4w0mXPfvss3ruuef07ne/WwcddBCHLQGgABVSI9ZMIYghZ0pLS3XdddclXXb99dfrueee07nnnqt///d/z3FlAIBs6e3tlST19PSorq5O3d3dKi0tLdoRsEQEMQzLjh3SypXSCy9IPT3SpEnS/PnSAQf4rgwA4Ft8I9YNGzaou7u7oHqAZQJBDEOycaN0223Srbeampttl2VmTu97n/TZzzqddpqnAgEA3sRiMUlSU1OT2traVFlZqbKyMs2ZM8dzZfnHnHO+a8g6M6s/7bTTjqytrfVdSkF4+WXpAx8wPfecpVjDSQqWXX650zXXOI3iHA4AUBSam5vV1tamkpISdXR0FGwj1gULFmj16tWrnHPDmtTMiBjS8tZb0nveY2pqShXCpCiESU7XX28aPVpasqTwAz8AFKv4NhSNjY2qqqpSeXl5QTdizRSCGNJyxRUDhbB4Jsnp2mtN73uf0/HHZ7MyAIAPiY1Yq6qqmISfBoIYBu3NN6Vf/lKKP/Q4sGC9W24xHX88o2IAUAja29v75oHRhmJ4CGIYtDvvlLZsGWwAi+f0q19J7e3S1KkZLwsAkENRI9aysjKVlpYSwoaJIIZB++MfhxLCJMnU2yv99a9OZ5yR0ZIAADkQi8XU1NQkSVq3bp3KyspoQ5EhBDEMWlfX8Lbv7MxMHQCA7EtsxNrV1aXKykoasWYYQQyDFs7DHLIJEzJTBwAgu6JGrJ3hf9BdXV2aN2+e56oKE92dMGiHHTbULYNJ+ocemrFSAABZEIvFFIvFtHr1arW0tGjq1KmaOnUqISyL8mJEzMzOkXSipHdI+hdJe0i6yzn3Ua+FYRcXXeR03XVBS4rBf2pSkkwnnOA0e3aWCgMADFtzc7MaGxtVUlIiSaqpqaEHWA7kRRCTdJWCALZR0npJ/MnOQ9XV0qmnOj3ySDohLAhtn/40rSsAIN8ka8TK/K/cypcg9gUFAaxZwcjYCr/lIJWlS51OOEGKxQYTxoIQdtppTueck+3KAADpiG9DIdGI1Ze8CGLOub7gZTbUFgnIhSOOkB580Omss6SuroEOUwaHJO+5xykc6QYAeBSLxfpGwWjEmh+YrI+0zZ8vPfmk07/+a+qTee+9t9NVVznV1jqVl+e0PABAgt7eXsViMdXW1mrt2rVqbW0lhOWJvBgRw8hz6KHS/fc7vfyydOedTk1Npu5uadIk6aSTnM4+Wxo3zneVAFDcojYUZkYj1jxVUEHMzOpTLGLyf5ZMny5ddZUUtagAAPgXNWNduXJlXyNW5oDlp4IKYgAAFLv6+noasY4gBRXEnHNHJbs/HCk7MsflAACQE7FYTJLU1NSklpYW1dTUSJLmzJnjsywMQkEFMQAAik1zc7MaGho0enTwJ51GrCMLQQwAgBEmvhFrQ0MDJ+IewQhiAACMIImNWAlhI1teBDEz+1dJ/xrerAyvjzWzZeHXbzrnvpjzwgAAyAM0Yi1ceRHEFJzs+4KE+2aGF0l6SRJBDEjDa6+9pqVLl2rFihV6++23NXXqVC1YsECXXXaZ9txzT9/lARhA1IKip6dHtbW1KisrU2lpKSGswORFEHPOLZa02HMZQMFobW3VmWeeqTfffFPvfe97dfDBB6uhoUG33367VqxYoV//+teaPHmy7zIBpEAj1uKRF0EMQGZ99atf1Ztvvqlvfetb+vjHP953/+LFi3Xbbbfpmmuu0bXXXuuxQgDJRG0o6urqaMRaJDjXJFBgXnrpJT3xxBOaPn26Lrzwwl2WffGLX9T48eN1//33a/PmzX4KBJBUfX29nn76aa1atUpdXV2qrq7WzJkzCWEFjiAGFJgnn3xSknTCCSdoVMJZ2SdOnKijjz5a3d3dWrVqlY/yAMRpb29Xe3u76uvr1dLSorKyMlVUVKi6uppeYEWCIAYUmBdffFGSdNBBByVdfuCBB0qS1q1bl7OaAOyuublZK1eu1NNPP63XXnut7xBkRUUFIayIMEcMKDDRHJM99tgj6fLo/uhcdAByp729ve9nlDYUkAhiQNEyM98lAEUlvhErbSgQIYgBBSYa8Yr+604U3V9eXp6zmoBiFYvF1NTUJEm0oUBSBDGgwERzw6K5YolaWlokiU9iAVkS34i1rq5O3d3dmjJlCqciQlIEMaDAzJs3T5K0cuVK7dixY5dPTm7cuFFPP/20SktLdeSRR/oqEShYUSPWaA5md3c3I2DoF5+aBArMjBkzdOKJJ+rll1/WsmXLdll23XXXafPmzTrnnHM0fvx4PwUCBSgWiykWi2n16tVqa2vT1KlTNXXqVEIYBsSIGJDvtm6VHnhA9uijUkeHVFoqV10tXXihtP/+STdZsmSJzjzzTP3Xf/2X/vSnP2nWrFlatWqV/vznP2vmzJm68sorc/scgALW3NystrY2lZSUqKOjgx5gSAtBDMhXW7dK11wju/VWWXv7LotMkvvWt6QPfEDum9+UEj55NWPGDD388MN9J/1+9NFHNXXqVF100UW67LLLNGnSpBw+EaDwtIc/k7FYTI2NjaqqqlJ5eblmz57tuTKMNAQxIB9t3Cg76yzZY4+lXmfHDtlvfiM99pjc/fdLp566y+L99ttPN9xwQ5YLBYpPfBsKSZwLEsNCEAPyzY4dsg9/WPbYY3IKRr+Sie63jRulhQvlnnhCeuc7c1QkUFxisVjfKBiNWJFJBDEg3/z617KHHuo3hCWyTZukyy+X628EDcCQxGIx1dbW0ogVWUEQA/KM/eAHwXUa2zhJ9sQTcmvWSIcempW6gGJCI1bkCu0rgHzy4ouyRx+VS3OzvsOUt92W6YqAotHb26ve3l7FYjHV1dWpra1NW7du1bRp0whhyBpGxIB8smaNpPRGw3bx/PMZKwUoJomNWLu6uvqaIwPZRBAD8snmzX63B4pMdO7VpqYmtbS0qKamRpI0Z84cn2WhiBDEgHwy3BNxcyLHkhOUAAAgAElEQVRvYNCam5vV0NCg0aODP4U1NTU0YkXOEcSAfHL00XJjx0pbtw7p8KT7//6/jJcEFJL4RqwNDQ2ciBveEcSAfFJRIZ17ruyuu9LazEnSmDHSxz+elbKAQpDYiJUQhnxAEAPyjLvkEtldd6XXR0ySO+ccaerULFYGjDw0YkW+o30FkG/e/W65r30tCFeD3MQddJAcpzMCJO3ahqK2tlZr165Va2srIQx5iRExIA+5b3xD2rZNdu21wW2lHh1zNTVyy5dLe++ds/qAfBW1oTAzGrFiRGBEDMhHZnJLlmjH738vd8YZ0qjdf1TdzJna8Z3vyP35z9KMGbmvEcgjsVhMsVhMK1euVFtbm7Zs2aKqqipCGPIeI2JAPjvlFLlTTpHa2uRWrJA2bJDGjZNmzZJOOilpQAOKTX19vTo7O1VSUqKuri5VV1fThgIjBkEMGAn231+64ALfVQB5IxaLafPmzVq/fv0ujVgrKioIYRhRCGIAgBElasQataGgEStGMoIYACDv0YgVhYogBgDIazRiRSEjiAEA8g6NWFEsCGIAgLzQ29srSerp6VFdXZ26u7tVWlpKCENBI4gBALyLb8S6YcMGdXd30wMMRYEgBgDwJhaLSZKamprU1tamyspKlZWVac6cOZ4rA3KDIAYA8KK5uVltbW0qKSlRR0cHjVhRlAhiAICciW9D0djYqKqqKpWXl9OIFUWLIAYAyInERqxVVVW0oUDRI4gBALKmvb29bx4YbSiA3RHEAABZEd+IlTYUQHIEMQBAxsRiMTU1NUmS1q1bp7KyMtpQAP0giAEAhiWxEWtXV5cqKys5FREwCAQxAMCQRY1YOzs7JUldXV2aN2+e56qAkYMgBgBIW3wj1paWFtXU1EgSjViBNBHEAABpaW5uVmNjo0pKSiRJNTU19AADhoggBgAYULJGrMz/AoaPIAYA6Fd8GwqJRqxAJhHEAAC7icVifaNgNGIFsocgBgDYRSwWU21tLY1YgRwgiAEA+tpQSFJLSwuNWIEcIYgBQBGLmrGuXLmyrxErc8CA3CGIAUCRqq+vpxEr9Pbbb+vhhx/Wo48+qr///e96/fXXNXbsWM2ePVvnnXeezjvvPI0aNcp3mQWLIAYARYRGrEi0fPlyXXnlldpnn3103HHHqaqqSm+88YYefvhhffGLX9SKFSv0wx/+UGbmu9SCRBADgCLR3NyshoYGjR4d/OqnESskaebMmVq2bJlOOeWUXUa+rrzySr3//e/X7373Oz300EN6//vf77HKwkUQA4ACFt+ItaGhgRNxYzfHHXdc0vv32WcfLVq0SNdee63+8pe/EMSyhCAGAAUqsRErIQzpGjNmjCT1jaIi83hlAaCA0IgVmbJt2zbdd999kqT58+f7LaaAEcQAYISLWlD09PTQiBUZs2TJEq1du1Ynn3wyQSyLCGIAMIJFjVjNTOvWraMRKzLijjvu0A9/+EMdfPDBuvnmm32XU9AIYgAwAkVtKOrq6mjEioxatmyZrr76alVXV+vuu+/WpEmTfJdU0AhiADDCRI1YS0pK1NXVperqatpQICNuu+02LV68WLNnz9bdd9/N91UOEMQAYASIJuCvX79eLS0tqqqqUnl5uSoqKvhjiYz4/ve/ryVLlmjOnDn65S9/qb322st3SUWBIAYAeS5qxBq1oeAQJDLte9/7npYuXaojjjhCv/jFLzgcmUMEMQDIQ+3t7X3zwGhDgSHp7ZXMpAF6gN17771aunSpSkpKNHfuXN1xxx27rTN9+nR96EMfylalRY0gBgB5JmrEOnnyZEkihGHQRj/3nCbceadKly/XqPCE7tv33lvdZ52lzeefr+1JRlLb2tqC9bZv12233ZZ0v8ceeyxBLEvMOee7hqwzs/rTTjvtyNraWt+lAEBSUSPWzs5OrVu3jvCFtFhHhyZ/5jMa98QTu9zvJMWfqrv7rLO04brrpPAwN4ZuwYIFWr169Srn3FHD2Q8jYgDgSXwj1rq6OnV3d2vKlCmcighpsbfeUsVZZ2l0c/NuwSv+ayep7IEHVPLKK3rrF78gjOUJghgAeBDfiHXDhg3q7u6mESvS55wmf/KTGt3cLGnX4JXIFISxsXV12vPKK9V54425qBADGOW7AAAoJrFYTLFYTKtXr1ZbW5u2bNmiqVOnEsIwJGPq6jTuqac02ElGURgru+8+lbz8chYrw2AxIgYAOdLc3Ky2tjaVlJSoo6ODRqwYtgnLlknqfyQskUmScxr/058q9tWvZqEqpIMRMQDIovb2drW3t6u5uVmNjY0qKytTRUWF5s2bRwjD8GzZotKHHhr0aFii0gceyGg5GBpGxAAgS6I2FDRiRTaMevttWfiBj6Eo+ec/JeeCXmPwhiAGABkUtaGQaMSKLBtu+6kiaF81EhDEACBDYrGYamtrVVZWptLSUkIYsmrH5MlyJSXS9u1pzRHr237vvRkNywMEMQAYhlgspqamJknSunXrVFZWxicgkRulpep573tV9tBDQ9q8+4wzMlwQhiJvJuub2TQz+5GZvWpmW8ys1cy+Z2aTfdcGAPF6e3vV29urWCymuro6tbW1aevWrZo2bRohDDm1+YIL0t4mOiC5edGizBaDIcmLETEzO0jSnyXtI+nXktZKerekz0taYGbHOefe8lgiAEja2Yi1MzyPX1dXl+bNm+e5KhSrrccfr63vfKfGNjQMehuT1P2BDyQ97yRyL19GxG5REMI+55z7V+fclc65kyXdIOkQSd/2Wh2AohffiLWlpUVTp07V1KlTCWHwy0xv33GHtk2fPuCq0UjY1iOOUOd3v5vdujBo3oOYmc2U9B5JrZK+n7D465I2SVpkZhNyXBoASAoasdbW1uqRRx5RW1ubampqVFFRQR8w5IUdlZV66ze/0daj+j/3tEnqOfVUddx7r9zEibkpDgPKh0OTJ4fXv3fO7Yhf4JyLmdmTCoLaMZIezXVxAIpT1IIiFoupoaGBE3Ejr+2YOlVv/eY3GvvXv2r8smUqffjhvh5jO8rK1HPWWdp0/vnadsQRnitFonwIYoeE100plv9DQRCr1gBBzMzqUyyaPbTSABSjxEashDCMCGbaeswx2nrMMUFLi85OadQoufJyaZT3A2BIIR+C2J7hdWeK5dH9k3JQC4AiRSNWFJSSErm99vJdBQYhH4LYQKJucwO2AHbOJT1AHo6UHZnJogCMfL3hoZuenh4asQLwIh+CWDTitWeK5eUJ6wHAsEVtKMyMRqwAvMmHIPZCeF2dYvms8DrVHDIAGLRYLCZJqqurU1dXlyorKzkZNwBv8iGIrQiv32Nmo+I/OWlme0g6TlK3pKd8FAegcNTX16uzs1MlJSU0YgWQF7x/jMI596Kk30uaIekzCYu/IWmCpJ845zbluDQABSBqxFpfX9/XiLWiooIQBiAv5MOImCT9p4JTHN1kZqdI+rukuZJOUnBI8mseawMwQjU3N6uhoUGjR4/WmDFj+hqxAkC+yIsg5px70czeJembkhZIep+k1yTdJOkbzrkOn/UBGDloxApgJMmLICZJzrmXJX3Mdx0ARi4asQIYafImiAHAUNCIFcBIRhADMOLEN2Ktq6tTd3c3jVgBjEgEMQAjSnwj1g0bNqi7u5tGrABGLIIYgBEhasTa1NSktrY2VVZWqqysTHPmzPFcGQAMHUEMQN6Lb8Ta0dGh6upq2lAAKAgEMQB5KZqAv379erW0tKiqqkrl5eWqqKgghAEoGAQxAHknasQataHgXJAAChVBDEBeaG9v75sHRhsKAMWCIAbAu/hGrLShAFBMCGIAvIjFYmpqapIkrVu3TmVlZbShAFB0CGIAciaxEWtXV5cqKys5FRGAokUQA5ATUSPWzs5OSVJXV5fmzZvnuSoA8IsgBiCrEhuxVldXSxKNWAFABDEAWdTc3KzGxkaVlJRIEo1YASABQQxARkWNWGOxmBobG+kBBgD9IIgBObJ8+XI99dRTev7557VmzRpt3LhRCxcu1M033+y7tIyJb0Mh0YgVAAZCEANy5MYbb9SaNWs0YcIE7bvvvmpubvZdUkbEYrG+UTAasQJAeghiQI4sXrxY++23n2bMmKG//OUvOvfcc32XNGyxWEy1tbU0YgWAISKIATly3HHH+S4hI6I2FBKNWAFguAhiAAYlasa6cuVKGrECQIYQxAAMqL6+nkasAJAFBDEAScU3Ym1paVFNTY0kGrECQCYRxADsprm5WQ0NDRo9OvgVUVNTQyNWAMgCghgASbs2Ym1oaGD+FwDkAEEMwG6NWAlhAJAbBDGgSNGIFQD8I4gBRSRqQdHT00MjVgDIAwQxYIg2bZJWrJDefFMqKZGmTZNOOCH4Opna2lrV1tZKkt544w1J0t/+9jddeumlkqS99tpLV199ddbqjRqxmhmNWAEgTxDEgDQ1N0vf/77pzjulzk7bZdn++zt96lNOn/ykNGXKrts9//zzuvfee3e5r62tTW1tbZKCeVnZCGJRG4q6urq+RqycjBsA8oM553zXkHVmVn/aaacdGY1GAEN1//3SokWmLVus3/X2289p+XKnf/mXHBWWQtSItaSkRB0dHaqurqYNBQBkwIIFC7R69epVzrmjhrMfRsSAQfrNb6R/+zfTjh39hzBJevVV06mnSk8+6VRdnYPi4kQT8NevX6+WlhZVVVWpvLxcFRUVhDAAyDMEMWAQNmyQzj9/cCEs0tFhWrRIeuopJxv8ZsMSNWKN2lBwCBIA8htBDBiEn/xEisXSTVNOf/ubqa7Oae7crJQlKRgBi+aB0YgVAEYWghgwAOekW28dypBWsM0tt5jmzs3OXMyoEevkyZMl0YgVAEYaghgwgNdek154YejHFh9/PHO1SDRiBYBCQhADBrBhg9/tpV0bsdbV1am7u1tTpkxhBAwARjiCGDCAcN77kI0fP7zt4xuxbtiwQd3d3TRiBYACQRADBrDfftIee7ghTNYPHHLI0B43moDf1NSktrY2VVZWqqysTHPmzBnaDgEAeYcgBgxg3Dhp0SLplluGtv0nPpH+RP3m5ma1tbXRiBUAChxBDBiET3/a6ZZbTJJT9GnIwaiocDrnnMGtG03Aj8Viamxs7GvEOnv27PQLBgCMCAQxYBDmzJH+8z/TCWPBOkuXOpWWDrz/qA0FjVgBoLgQxIBBuuEGp44O6Ze/7C+ERSHN9J3v7ND556deM7ERK20oAKD4EMSAQRo9WvrpT52OOsrphhtMr76aLJCZjjjC6eqrnc46K/W+4kfASktLCWEAUKQIYkAaRo2SLrtM+uxnnX77W6cHHzS98YZUUiJNmyYtWuQ0b56SnlsyFoupqalJkrRu3TqVlZXRhgIAihxBDBiCMWOkhQulhQv7/0RkYiPWrq4uVVZW0ogVACCJIAZkTdSItbOzU5LU1dWlefPmea4KAJBPCGJAhsU3Ym1paVFNTY0k0YgVALAbghiQQc3NzWpoaNDo0cGPVk1NDY1YAQApEcSAYYpvxNrQ0MD8LwDAoBHEgGFIbMRKCAMApIMgBqQpFov1jYLRiBUAMBwEMWCQent71dPTo9raWhqxAgAygiAGDCBqQ2FmNGIFAGQUQQxIIWrGunLlyr5GrJyMGwCQSQQxIIn6+np1dnaqpKSERqwAgKwhiAGhVI1YZ8+e7bMsAEABI4gBohErAMAPghiKFo1YAQC+EcRQlGjECgDIBwQxFA0asQIA8g1BDAUtakHR09Ojuro6dXd3j/hGrN/+9rf1zDPPaN26dero6FBpaammTZumBQsW6GMf+5gmT57su0QAwCARxFCw4huxbtiwQd3d3QXRiPW2227TYYcdphNOOEEVFRXavHmzVq1apeuvv14/+9nPtHz5cu23336+ywQADAJBDAUnakNRV1fX14i1rKxMc+bM8VxZZrzwwgsaN27cbvdfe+21uummm3TzzTfrf/7nfzxUBgBIF0EMBSWxEWt1dXXBtaFIFsIk6YMf/KBuuukmtbS05LgiAMBQEcQw4kUT8NevX6+WlhZVVVWpvLxcFRUVBRfC+vOHP/xBkvoa0QIA8h9BDCNa1Ig1akNRTOeCvPXWW7Vp0ybFYjE988wzqqurU01NjS655BLfpQEABokghhGnvb29bx5YMbehuPXWW/XGG2/03T7ppJN0ww03aMqUKR6rAgCkY5TvAoB0RI1Y165dq9bW1qINYZLU2NioV155RY2Njbr99tv10ksv6T3veY+effZZ36UBAAaJETHkvVgspqamJknSunXrVFZWVhBtKDJl77331umnn67DDz9cxx9/vD7/+c/rscce810WAGAQCGLIS8kasU6ZMoVTEfVj2rRpqq6u1vPPP6+Ojg7ttddevksCAAyAIIa8EzVi7ezslKSCacSaC9EnSEtKSjxXAgAYDIIY8kY0Ab+pqUltbW2qrq6WpKJqQTGQ5uZmlZeXa5999tnl/h07dmjp0qV688039a53vUt77rmnpwoBAOkgiCEvNDc3q62tTSUlJero6CjIRqzJ9PZKv/99qVasGKcNG0xjxkgHHLBdH/rQZs2cuX239VesWKH//u//1ty5czVjxgxNnjxZb7zxhp566im99NJL2meffbR06VIPzwQAMBQEMXgTHUaLxWJqbGwsqh5g27ZJP/jBBP34xxP0+uu7H0a86aaJOvHELfryl2N6xzt6++4/4YQT9JGPfERPP/201qxZo66uLo0fP14zZ87U2WefrYsuukiTJk3K5VMBAAyD9yBmZmMk/aekd0h6p6RDJY2R9Enn3O0+a0P2RG0oirERa0+PdPHFk/XII6X9rOX0xBPj9Je/jNUPfvC2Tj99iyTpkEMO0ZIlS3JTKAAg67wHMUkTJH0v/Lpd0uuSpvsrB9kSi8X6RsGKtRGrc9Kll04KQ5iTZCnWDO7futX06U9P1j33vKW5c3tTrAsAGKnyoaHrZknvk7Sfc65S0o8814MsiMViqq2tLfpGrE8+OVa/+U2Z+g9hu+rtNV111Z5yLqulAQA88D4i5pzbKulh33Ug86I2FBKNWCN33jk+/GpwISzg9PzzY7Rq1RgddRSjYgBQSPJhRAwFpLe3t++ycuVKtbW1aevWrZo2bVrRh7A33hil2trokGQ6gtD205+OH2A9AMBI431ELJPMrD7Fotk5LaRIJTZi7erq0rx58zxXlT9efHG0tm9PZyRsV01NBfXjCgBQgQUx+BHfiLWlpUU1NTWSpDlz5vgsK+90dw89hEnS5s3D2x4AkH8yEsTMrFXSAWlscpdz7qOZeOx4zrmjkt0fjpQdmenHQ9CItaGhQaNHB99KNTU1RdGIdSj22GPHMLdntj4AFJpMjYi9KKknjfVfzdDjwoP4RqwNDQ2ciHuQDj10m/bYY4disaFNzTzmmK0ZrggA4FtGgphz7pRM7Af5L7ERKyFs8MaPdzr33G796EcT0tzSyUxatGhzVuoCAPjDHDEMiEasmXPBBZv14x+Pl3PpzPcynXJKj/bff/dzTwIARjbaVyCpqAUFjVgza9asbbr66lh4a3Bzvvbdd7uuvbYze0UBALzJixExM7tSO1tMvCO8/piZHR9+/SfOO5k7URsKM6MRaxZcfPEm9fZKS5aUh/ek7rJ/wAHb9LOfdWjffYc30R8AkJ/yIohJWiDpxIT75oWXCEEsy6I2FHV1derq6lJlZWVRnYw7V8ykSy7ZpLlzt+qOOybooYdKtW3brutMm7ZNixZt1qJFmzVpEp+WBIBClRdBzDk333cNxa6+vl6dnZ0qKSlRV1eXqquraUORZUcf3aujj96g9vZRevLJseroGKVx46T999+m44/fqpIS3xUCALItL4IY/Igm4K9fv36XRqwVFRWEsByaOnWHFi5Mp/sLAKBQEMSKVNSINWpDQSNWAAByjyBWRGjECgBAfiGIFYmoEevkyZMl0YgVAIB8QBArYDRiBQAgvxHECkxvb68kqaenR3V1deru7lZpaSkjYAAA5CGCWAGJb8S6YcMGdXd304gVAIA8RhArAFEj1qamJrW1tamyslJlZWWaM2eO58oAAEB/CGIjXHNzs9ra2lRSUqKOjg4asQIAMIIQxEag+DYUjY2NqqqqUnl5OY1YAQAYYQhiI0xiI1bOBQkAwMhFEBsB2tvb++aB0YYCAIDCQRDLc1Ej1rKyMpWWlhLCAAAoIASxPBSLxdTU1CRJWrduncrKymhDAQBAASKI5YnERqxdXV2qrKykESsAAAWMIJYHokasnZ2dkqSuri7NmzfPc1UAACDbCGIexTdibWlpUU1NjSTRiBUAgCJBEPOkublZjY2NKikpkSTV1NTQAwwAgCJDEMuhZI1Ymf8FAEDxIojlSHwbColGrAAAgCCWVbFYrG8UjEasAAAgEUEsS2KxmGpra2nECgAAUiKIZVDUhsLMaMQKAAAGRBDLgKgZ68qVK/sasTIHDAAADIQgNkz19fU0YgUAAENCEBsCGrECAIBMIIilqbm5WQ0NDRo9OnjpaMQKAACGiiA2CPGNWBsaGjgRNwAAyAiC2AASG7ESwgAAQKYQxJKgESsAAMgFglgoakHR09NDI1YAAJATBDHRiBUAAPhR1EEsakNRV1dHI1YAAJBzRRvEokasJSUl6urqUnV1NW0oAABAThVVEIsm4K9fv14tLS2qqqpSeXm5KioqCGEAACDniiaITZ8+fZc2FByCBAAAvhVNEOvs7OQTkAAAIK+M8l1ArrS2thLCAABAXimaIBb1CQMAAMgXRRPEAAAA8g1BDAAAwBOCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACeEMQAAAA8IYgBAAB4QhADAADwhCAGAADgCUEMAADAE4IYAACAJwQxAAAATwhiAAAAnhDEAAAAPCGIAQAAeEIQAwAA8IQgBgAA4AlBDAAAwBOCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPvAcxM5tlZl82s8fM7GUz22pm7Wb2azM7yXd9AAAA2TLadwGSviXpPElrJD0kqUPSIZLOkHSGmX3eOXeTx/oAAACyIh+CWK2ka51zDfF3mtmJkv4gaamZ3euce81LdQAAAFni/dCkc25ZYggL739C0uOSxkqal+u6AAAAss17EBtAb3i9zWsVAAAAWZAPhyaTMrMDJJ0iabOklYPcpj7FotmZqgsAACBT8jKImdk4SXdJGifpS865tz2XBAAAkHEZCWJm1irpgDQ2ucs599EU+yqR9FNJx0m6W9J1g92pc+6oFPusl3RkGvUBAABkXaZGxF6U1JPG+q8muzMMYT+TdK6keyR91Dnnhl8eAABA/slIEHPOnTLcfZjZaEk/VxDCfi7pfOfc9uHuFwAAIF/lxRwxMxurYATsTEk/kfQx59wOv1UBAABkl/f2FeHE/AcUhLA7RAgDAABFIh9GxG6V9D5Jb0p6RdLVZpa4zuPOucdzXBcAAEBW5UMQOzC8rpB0dT/rPZ79UgAAAHLHexBzzs33XQMAAIAP3ueIAQAAFCuCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACeEMQAAAA8IYgBAAB4QhADAADwhCAGAADgCUEMAADAE4IYAACAJwQxAAAATwhiAAAAnhDEAAAAPCGIAQAAeEIQAwAA8IQgBgAA4AlBDAAAwBOCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPCGIAAACeEMQAAAA8IYgBAAB4QhADAADwhCAGAADgCUEMAADAE4IYAACAJwQxAAAATwhiAAAAnhDEAAAAPCGIAQAAeEIQAwAA8IQgBgAA4AlBDAAAwBOCGAAAgCcEMQAAAE8IYgAAAJ4QxAAAADwhiAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnBDEAAABPRvsuAACA4Zg7d67Wr1+fdNnee++txsbGHFcEDB5BDAAw4pWXl+sTn/jEbvdPmDDBQzXA4BHEAAAjXnl5uS6//HLfZQBpY44YAACAJ4yIAQBGvK1bt+r+++/XK6+8ovHjx+vQQw/V3LlzVVJS4rs0oF8EMQDAiPfPf/5Tn/vc53a5b//999d3v/tdHXvssZ6qAgbGoUkAwIh23nnn6Z577lFjY6Oam5v12GOPadGiRXr55Zf10Y9+VGvWrPFdIpASQQwAMKJddtllOu6447T33nurrKxMhxxyiK655hpdfPHF6unp0fXXX++7RCAlghgAoCCdf/75kqSnnnrKcyVAagQxAEBBmjJliiRp8+bNnisBUiOIAQAKUn19vSTpgAMO8FwJkBpBDAAwYr3wwgvasGHDbvevX79eX/va1yRJCxcuzHVZwKDRvgIAMGItX75c//u//6vjjjtO06dP18SJE/XSSy/pkUce0ZYtW3TyySfrP/7jP3yXCaREEAMA5AfnNGbVKo3/6U815tlnZZs2yU2cqN53vEObzj9f2444YrdN5s2bpxdffFHPPfec6uvrtXnzZpWXl+vd7363zjnnHJ199tkyMw9PBhgcghgAwLsxzzyjPb/0JY159tndl61Zo/E//7m2HnWUOpcu1bbZs/uWHXvssTRsxYjmfY6YmU03s1vM7K9m9rqZbTGzV83sj2b2MTMb47tGAED2jF25UnstXKgxzz4rl2IdJ2lsfb2mnHmmxjz9dC7LA7LKexCTdJCkj0jqlPSgpOsl/VbSAZJ+JOn3ZsbIHQAUoNH/+IcmX3SRRnV3S5JSHUSM7h8Vi2mvCy5Qycsv56Q+INvyIeD8WdJk59yO+HFuPHEAAAvbSURBVDvDkbDfS5ovaaGke3JfGgAgmybeeKNGbdqU1jajNmzQhB/8QF1LlmSpKiB3vI+IOee2Joaw8P5eBSNkkjQrt1UBALJt1JtvqnT58pSHI/tTdt99so0bM14TkGveg1gqZlYi6X3hzdU+awEAZF7pgw/Ktm5NeTiyP6M2blTp736X8ZqAXMuHQ5OSJDOrkHSJgqkAe0s6TdLBkn4uafkg91GfYtHsFPcDADwZ7jwv5omhEORNEJNUIenrcbedpOskfdU5N5SRawBAHrOtW4e3fW9vhioB/MlIEDOzVgWfchysu5xzH42/wzm3NtiVlUiqknSWpG9KOt7M3u+c6xhop865o1LUVy/pyDTqAwBk2Y7Jk4e3/aRJGaoE8CdTI2IvSupJY/1XUy1wzm2X1CbpRjNrl/QLBYHskmFVCADIK1tOPVV7fO97ckrdtiKZaP0tp56ancKAHMpIEHPOnZKJ/STxcHg9P0v7BwB40vvOd6r38MOTdtPvj0nacvzx2jaLD9Rj5MvbT02GqsLrbV6rAABknpk2fupTkjToFhbReps++cmslATkmvcgZmZzzWx8kvsnSroxvMlnlAGgAPWcdZY2XXCBTAOHseiQ5MbPfEZbTjst+8UBOZAPn5r8iqT5ZvaEgrlhmyVNl3S6pEkKOu//j7/yAABZY6aub39brqxME2+9tf9VJcUuv1wbL7ssN7UBOZAPQew2SZskHa1gLth4SW9LqldwWqMfOec4NAkAhWrUKMWuvlrdCxdq/E9+orL77+8796Qk7Zg4Ud3nnqvNF1ygbdXVHgsFMs97EHPO/U4cegSAorftsMPU9Z3vKHb11Rr94ouyTZu0Y+JEbT/4YLnxu81gAQqC9yD2/7d3/yGW3eUdxz9PTI3UtFGidilKFttooEKkSitaiDFgA2Ibi+I/iW5aC7aBWDHUIpRoQbC0tNXQ2l9pYppIbStRRKsWzVpjkIJmDRJ/TCJrlcTY/EBrujbWPv3jnKXbyYzJOnPv986d1wuWkzln5vLkMOx977nfey4AnKhPPz3fO/fc0WPAUgxfrA8AsF8JMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIOsZIhV1dVV1fOfnx49DwDAIqxciFXVS5P8apLvjJ4FAGCRVirEqurJSf4qyXuSfGbwOAAAC7VSIZbkL+ftZUOnAABYglNHD3BcVR1KclGSl3X3fVU1eCIAgMVaiStiVXVWkrcnub673zd6HgCAZRh+RayqTknyrkyL8y/f4WNtt67s3I2NjVx44YU7eXgAgCTJxsZGkhzc6ePsSohV1dEkZ53Ej9zQ3RfP//36JOcleUl3P7Ab82zhlGPHjn3/tttu+9yCHp/knHn7xaFTrD/nefGc4+VwnhfPOV6sg0m+vdMH2a0rYncm+e5JfP9dSVJVZyd5a5JruvtDOx2iu5+z1f7jV8q2O87OOcfL4TwvnnO8HM7z4jnHe8OuhFh3X/BD/ujPJDktyaVVdek237MxL9x/mfVjAMA6Gb1G7GiSq7c59pIkB5L8Q6ZLf0eXMxIAwHIMDbHuPpLkNVsdq6rDmULsTd19xzLnAgBYhpW4fQUAwH4kxAAABqnuHj0DAMC+5IoYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIPsuxCrqrOr6o1V9fGq+lpVPVRV91TV+6vq/NHzrYuq+pGqel1VXVNVR+bz3FW15Uda8YNV1VOr6m+q6q6q+q+qOlpVf1JVTxw92zqoqpdX1VVV9cmq+vb8u3r96LnWSVWdWVWvqaobq+qOqjpWVd+qqpur6teqat89Hy1CVf1+VX1sfn47VlX3V9WtVXVlVZ05ej4ebt/d0LWq/i7JK5PcnuTmJPcneWaSX0rymCSv6+53jJtwPVTVE5I8MH95T5KHkjwtya93918PG2wPqqqfSnJLkqckeX+SLyb5uSTnJ/lSkhd0933jJtz7qupIknOTfCfJ15Ock+SG7r546GBrpKpem+SdSe5OclOSf0vyE0l+JckZSd6b5BW9356UdllVPZTks5me476Z5PFJnpfkuUnuSvK87v7auAnZbD+G2KEkn+vuWzftPy/JPyfpJAe7++4B462NqnpskguSHOnuu6vqzUmujBA7aVX1kSQvTnJ5d191wv4/SvL6JH/R3a8dNd86mK+Gfz3JHUnOyxQKQmwXVdWLMkXBB7v7f07YfyDJv2b6h9rLu/u9g0ZcC1X1uO7+7hb735rkTUne2d2/ufzJ2M6+uxTc3ddujrB5/yeSHE7y2CTPX/Zc66a7H+rufxK0O1NVT88UYUeT/Ommw1cmeTDJJVX1+CWPtla6+6bu3nA1ZnG6++Pd/YETI2ze/40kfz5/+cKlD7Zmtoqw2d/P27OXNQuPzr4LsUfwvXn730OngP/zonn70S2ewP4jyaeS/Gimlx5gr/J37+K9dN7eNnQKHubU0QOsiqo6K9NLaf+Z5F8GjwPHPXPefnmb4xuZrpg9I8nHljIR7KKqOjXJq+YvPzxylnVSVVckOT3T+rvnJvmFTBH2tpFz8XBCLElVnZbkhiSnJfnt7n7gEX4EluWMefutbY4f3/+EJcwCi/C2JM9K8qHu/sjoYdbIFZneDHHch5Mc6u5/HzQP29iTL03Ob93vk/iz7dvQq+oxSf42yQuSvCfJHy7r/2PV7eZ5ZmFq3lrbxJ5TVZcneUOmdwJfMnictdLdB7q7khzI9M7Upye5tap+duxkbLZXr4jdmWS7BYlbuWurnXOEXZ/kFZkWMl5sse7/syvnmR05fsXrjG2O//im74M9oaouS/L2TLdZuKC77x880lrq7nuS3FhVn820xOG6TFcgWRF7MsS6+4KdPsa8LuHdmSLs3Ule1d3f3+njrpPdOM/s2Jfm7TO2OX78HVDbrSGDlVNVv5Xkj5N8PlOEfXPwSGuvu79aVbcneXZVPam77x09E5M9+dLkTs33uPrHTBF2XZJLRBgr6qZ5++LNdx6vqh/L9JL6sSSfXvZg8MOoqjdmirAjSc4XYUv1k/PW890K2XchNi/MvzHJLye5Osmlm28LAKuiu+9M8tEkB5NctunwWzLdIPO67n5wyaPBSauq3820OP8zma6EuSqzi6rqnPkGuZv3nzLf0PUpSW7xhrTVsh/vrH9NkkNJ7k3yZ9l6kfPh7j68xLHWUlX9TqaPikmSZ2f6CJlbMt1yIUludpf9R7bFRxx9IcnPZ/qIoy8neb6PONqZqrooyUXzlweS/GKSryT55Lzv3u6+YsRs66KqXp3k2kxXY67K1usaj3b3tUsca63ML/n+QaZbMN2Z5L5M75w8L9Ni/W9kCuDbhw3Jw+zHEDuc6ZfyB3lLd7958dOst0dxrt/V3YeWM83eVlVPS/J7SS5Mcmamz+t7X6bfVYucd+iEj+Dazle7++BypllPj+IcJ8knuvuFi59mPVXVs5L8RqYlC0/NdFubBzP9g+2DSd7h74vVs+9CDABgVey7NWIAAKtCiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABhEiAEADCLEAAAGEWIAAIMIMQCAQYQYAMAgQgwAYBAhBgAwiBADABjkfwEH2lRIkqnjNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pi58Or6PGmCpll+yZ3JJy24CC8WipyyfbdroKve/kEZTr0kKYJCm87UfhrzmFIRtMh5GcmPX9462bxTfD65ONMcXqKS8pBLHS9CYF/7QfkfRua+391trhtHWyfbrfGl435rC/qbSRgm+hSWPjDDKZTO9IRsaYIxV8s2ZUwQSHt9m0eYGU38dB0nNjem5X0IuSnO05+QYzlfFsr1AwXm2bgqBydzjeKtVkemtK2TPh9QudVrG/ZF3HGGMKdQQg+WHg+9baz1trn8jQ61So5zfZUzfe67whvO4d5xBkucl2CPKRlJ8zvhaNMfUKvvG3z/rhY7M2/DXbrPup231knHVyUoR9Lwyv14+zzrrw+qgcty2N9chmmpV/sm2n2r7sEcRKU/KN8yFr7d70hcYYo2A6h0z+HF6/KYf9Jdu05nicfnt43ZBpoQlOd1GXw/bSJbf77DjjvF6f5fap3qek5KD9c4wxL1YwnmFEweHiXCXvR3fYnZ9JtvshBYelpen1puRjG+NJ9hK+s0Dbz+S5v43wbyKTZF0HSkofT5Qvyef3gUwLjTGNCnrJMpnu8/K38Pq146yTfK/42zjrlI3wuX5p+OuGtMVrNRa+s33xInn7HgXfqE11R9o66fuuUnBaHyk4fVM+FXLfydfZkeOskwzz4x2qzmZ+eD2Vw7XzU37O5+HeskEQK0394fWiLP9gPqjsnxySE7kuMMZ8aJL7+4OCTyWzJS3Poc414fXJWZZfmsO2Mkk+DjFjzKHpC40xL9LYbNTppnqfkn6p4BudCxXMyyZJt1hrn8neJKvk/Tgm0+GScMDxeP9IB8Lr6YTafGxjPKvC65caY84ab8XxBgPnaCDl54z3y1r7qMZC+VdMlhn0w7qqjTFTOcSXfH5flGX5l5Q9aCXvw1R7jpPfiHyTMaYtfaEJzqeY/GZlpm8ZlpxxQnXShzTWa3NL6oLwg+v/hr9+NP35Dmfe/3j4629sMKN8quS39xYYY96aYd8fVPBcJTT2RaF8KeS+/x5en2mM2e8bl+FtyS+s/CVt2bg9yWEP4znhr3fn2HaWxoZlPKvgxPYzTyHnxuAytYuCk6Em5wJbqbFJNSMKBqkOK/j6sFUwXUB6+++Ey5ITuh4a3j5bwYSuyyR9OK3NGRqb1+VnkhakLHuegjeBb6S1SZ2z7OspdR6qYPLS3Rqb4XtJWttl2epPWWeWxuYCu0NSc3i7p2Cm9K0pj8OGDO1zvk9p7VektLfKcP63ST6fdSmPw88kPS+8vVrBIc/BlPtxZ4b2/5PSNusklRPU8MVwG3crnFA2wzpnZ6thMs+bpJ+nvO4+n7yf4bKDFIw9+ZWkH+ZY+53KMgeaxub/unCc9i9VMOjcKugVer3CCUrD19ixCuZHelrBCaJT2yaf+6PG2f55GpvL6/0am9D1SAVjZ/ZqbAb9s9PaHqCxeb6yzmCf7THQvhO6PhneNxMum+yEruP9Da4K11k2hdfcQQq+fZy8JB/L09Nu99LarVTwfvIqpczdpuAbrV/W2KTLt2fZ72EaOzvAbQone1bwxYbrwtt3Szo2S/vrw3V6FE4yquC98yyNTYr6xQker/3ejyb5mE1n38nXSKb3kDNTHv97FHyDdnZ4eYnG5tqzkt6Q1vay8H6dqJRZ+cPX7imSujX2+l+c1naJgmEepyvl/JgKvij4So1NTm4VTIGR82NWCRfnBXDJ8sQE50NLDQHbUt6AVmtshvdVGdrOS/mDTl76NPEpji7U2Ol0rIKAkPUUR1nqTJ7aZUTBP/YNmmIQC9d7R1pNqacGelLSe8d745vKfUppe2zKels1jdnFJZ2f9jilnnLqAQWDvbM9xq9LabdbQTjdIOl/c9j/gpTHbVhBgNkg6Z6Udc6exGOS9XlT8Mb8S+1/P/vTbvthjo/dncoexD6fst0d4X3aoLTTMCk4VJ96qqbdCv7Z7UmrrTGt3WSC2FwFh0CT66aeqssqOF3UePfh2rTHK3kfTp3kYzCZUxy15PJcpqyzSlMPYqk1jXdJf29YlbJsVMF7X/pr6E5lmTg43MZJaY/Bdo19aByW9N5x2ka07ymrdmosyFsFcxdmfC/Q9IPYdPadfI1k/PvV2MnQk5ehtG3vVeaJnJelrbNdwdGC1PfVfkmnZGi7JG2fOzR2poTU5zhjuJwpFw5Nlihr7YUKPmk/oOCfxhwFX/e9QMFpJbLOvWWt3W2tPUNBD8RvFIyZOEDBP54/K5hA7+oM7f5bwVioHyp4E/UU/KE+pOAT6sfT20i6SNJHFXwqT/5R3ybpddbaVTnd6cz35ZcKgsjvFIQoT8E/lq+GtW7K3nrK9ynZ9h8KPu1JwbeNxp3vbII6vqHg0+OfFATBOQq64f9LwSfDrOMyrLW3Kwikdyk4LHG4gvEch2Vrk2Ebjyr457RawZvmYeE2Mo7vmwpr7U5r7TsUzEv0CwVhr1pBUHlcwaShpyp4veTLFxR81f4hBYf/GsPLPocqrbW3SmpR8AHmbwpeA3UKgn2ngq/2L7TWPplrAdbaPQp6or6sYMBz8oPI7xTMkn75BJv4sILTmT2m4ENU8j5MatJOa+3jCuYp+4KCnq+khyVdruB0Xd2Z2paoqxT8fXcq6KWsUvC4PKUg6J+u4P0l28TBstb+TsHkuT9U8B5RreB98GeSjrfW/nictgMK/iYv1Vhv424F750fUtAzPuX3gvEUct/W2gsU9Gpdr32n9dmgoNf9BGvtFzM0/YGC/zu/VvB3bBQExm0KetI+K+kF1tpfZGh7v4LJnq9T8HpMKPi726Xg/9lKSW3W2s9M5T5VimQXNoA0xpgjFLxJzVLwT3pmjl8AABQMPWJAducp+Bu5mxAGACgEghiQQfgNtOQkiPuddxEAgHzg0CSQIjxdR5OCMVRG0h8VDCbmDwUAkHf0iAH7alAwtcW/FJzq6BRCGACgUOgRAwAAcIQeMQAAAEcIYgAAAI4QxAAAABwhiAEAADhCEAMAAHBkjusCisEYs17BubE2OC4FAABUhqMkDVhr509nIzMiiEmKHHXUUdFjjjkm6roQ7Ovwww/XAw88IKZRAQCUk3/+859KJBLT3k5JBDFjzMGS3iHpLZJeJOlwSXskrZH0Q0k/tNbuncYuNhxzzDHR1atXT7tW5Nf999+vvr4+vehFL3JdCgAAk9bR0aGHHnpow3S3UypjxE6TdLWkl0v6i4Jz+/1c0iJJ35f0M2OMcVceCqWhoUF9fX1as2aN61IAACi6Ugli3ZJOltRgrX2PtfZT1tr3S1og6SlJ75R0issCURixWEzxeFzbt29XT0+P63IAACiqkghi1trbrbW/ST/8aK3dKumq8NclRS8MRRGNRhWNMnwPADDzlEQQm8BweD3itAoAAIA8K4nB+tkYY+ZIOiv8dcKR9saY+7MsWpC3ogAAAPKk1HvEvqxgwP5vrbW3uS4GhWOtVXd3t+syAAAoqpINYsaY8yVdJOlRSUsn08ZauzjTJdwGSpTneWpvb1ckElFnZ6frcgAAKJqSDGLGmH+X9HVJj0h6rbV2m+OSUGC+76u9vd11GQAAFFXJBTFjzAWSvinpYQUhbKvjklBEo6OjTGMBAJgxSiqIGWM+KWmFpAcVhLB/OS4JRVRVVaX58+dr7dq1hDEAwIxQMt+aNMZ8VtIXJN0v6Q0cjpx5PM9Ta2urJGn9+vWqr693XBEAAIVVEkHMGPM+BSFsVNLdks7PcEajDdbaVUUuDUXmeZ4aGhq0ZcsW16UAAFBwJRHEJM0Pr2dLuiDLOndJWlWUauBcIpHQunXr1NTU5LoUAAAKpiTGiFlrl1lrzQSXJa7rRHHEYjG1tbVp06ZNWrdunetyAAAomFLpEQP20dzcLEnasGGD20IAACigkugRAwAAmIkIYgAAAI4QxFDShoaGXJcAAEDBEMRQsmKxmBKJhLq6ulyXAgBAQRDEULJ831dHR4eGhob49iQAoCIRxFDSqqqqmEsMAFCxCGIoaZ7nyVqrrVs59zsAoPIQxFDyWltbFYlE1NnZ6boUAADyiiCGkud5nuLxuKLRqHp6elyXAwBA3hDEUDZGR0ddlwAAQF4RxFAWPM9TbW2t1q5dS68YAKBicK5JlI3FixdLkrq7u1VfX++4GgAApo8eMZSVlpYW1yUAAJA3BDGUnZGRESZ4BQBUBIIYyorv+2pra9OmTZsIYwCAskcQQ9lpbm5WW1ubent7XZcCAMC0EMRQlnzfd10CAADTRhADAABwhCAGAADgCEEMZammpkbV1dXq6upyXQoAAFNGEENZ8n1f7e3tqq6u1po1a1yXAwDAlBDEULZ831djY6PrMgAAmDKCGMre4OAg558EAJQlzjWJstbY2Kj+/n51d3dLEuegBACUFYIYyprneWptbZUxRgMDAwQxAEBZ4dAkAACAIwQxlD3P82St1ebNmzn/JACgrHBoEhVh8eLFkqSNGzcqEolwiBIAUBYIYqgYLS0t2rFjh+syAACYNA5NAgAAOEIQAwAAcIQghooyMjKi9evXuy4DAIBJIYihYvi+r0WLFimRSHAycABAWSCIoaLEYjHF43HXZQAAMCkEMVSk4eFh1yUAADAhghgqTk1NjSKRiDo7O12XAgDAuAhiqDi+76u9vV2RSERr1qxxXQ4AAFkRxFCRfN9XY2Oj6zIAABgXQQwVbXBwUD09Pa7LAAAgI05xhIrV2Nio/v5+dXd3SxLnnwQAlByCGCqW53lqbW2VJA0MDBDEAAAlh0OTqGie57kuAQCArAhiqHi1tbXavHmz1q1b57oUAAD2waFJVLzm5mZJ0oMPPqhIJMIhSgBAyaBHDDNCY2OjotGo6zIAANgHQQwAAMARghgAAIAjBDHMGNZarV+/3nUZAAA8hyCGGcHzPLW3tyuRSKirq8t1OQAASCKIYQbxfV8dHR0aHh52XQoAAJIIYigBN954ow4//HAdfvjh+slPflLw/fHtSQBAqSCIwamnn35al112mQ444ICi7K+qqkojIyPq7Owsyv4AABgPQQzOWGv18Y9/XAcddJCWLl1alH16nqd4PK5IJMJYMQCAcwQxOHPNNdfoT3/6k1asWKGampqi7dfzPC1atKho+wMAIBuCGJz45z//qS996Us699xzdfzxxzupYWhoSD09PU72DQCARBCDAyMjIzr//PN1+OGH61Of+pSTGmKxmObPn6+1a9cSxgAAznDSbxTdihUr9PDDD+umm25SVVWVszoWL14sSdqyZQsnAgcAOEGPGIrqgQce0MqVK/WhD33ouSDkUm1tresSAAAzGEEMRZM8JNnU1KRLLrnEdTnP6evr07p161yXAQCYgTg0iaLZtWvXc4Fn/vz5Gde5+OKLdfHFF+sDH/iAPv/5zxe8pubmZknSgw8+KElqamoq+D4BAEgiiKFo5s6dqzPPPDPjsjVr1ujhhx9We3u7jj766KIetmxublZ/f7/27NlTtH0CACARxFBEVVVV+upXv5px2ZVXXqmHH35Yp512mt797ncXuTIAANwgiGFa9u6V/vhH6bHHpKEhqa5OWrJEamx0XRkAAKWPIIYp2bFDuvpq6aqrjB5/3OyzzBirN79Z+o//sDrpJEcFTkFvby9jxAAARcW3JpGzp56STjjB6BOfmLVfCJMka6VbbjHq6JilSy4x2rt34m1edNFF2rx5s7PDki0tLUokEpx/EgBQVAQx5KS3V3rDG4wefnj/ADYmuczqyiuNLrtsvHVLg+/76ujo4LRHAICiIoghJxdfbNTdPdlgZSRZfeUrRvfcU8iq8qOqqkrRaNR1GQCAGYQghknr6ZH+938lyebQKght3/526feKSZK1Vt3d3fSKAQCKgiCGSbv2Wmn3bqOxQ4+TZfWLX0jPPFOIqvLH8zzF43FFIhF1d3e7LgcAMAMQxDBpd9891V4to+Fho7/8Ja/lFITneWpvb3ddBgBghiCIYdIGBqbXvr8/P3UUw+joKOefBAAUHEEMk1ZdPb32BxyQnzoKzfd9zZ8/X5s3byaMAQAKiiCGSVu0aKotg8H9L3xh3kopuMWLF2v+/Pnq7e11XQoAoIKVRBAzxpxqjFlpjLnbGDNgjLHGmB+7rgv7Ovfc5Lclc/nWpCQZxeNWCxYcQx7AAAAgAElEQVTku6LCamhocF0CAKDClUQQk3SZpI9JOk7SZse1IIuWFun1r7fK7VuTQWj78IdzDW8AAFS+UgliH5fUIiki6SOOa8E4li+38v3JhqogtJ10ktWppxayKgAAylNJBDFr7R3W2n9aa+k2KXGtrdJNN1lFIpM5TBkckvzZz6xmzy5GdfmXSCS0Zs0a12UAACpUSQQxlJclS6Q//cnq7W+3mpXlFXTIIVaXXWa1erVVJFLU8vImFospHo+rr6+PMAYAKIg5rgtAeXrhC6Wf/9zqqaeka6+16u42SiSkujrpta+1euc7pXnzXFc5fbFYTG1tbdqwYYPrUgAAFaiigpgx5v4si8rs+3rl44gjpMsuk3L/JmV5GRoacl0CAKACcWgSmEAsFlN1dbW6urpclwIAqDAVFcSstYszXSQ96ro2lC/f99Xe3q6amhpm2gcA5FVFBTGgUKqqqlRXV+e6DABAhSGIAZNkrdXWrVvV09PjuhQAQIWoqMH6QKF4nqfW1lZJUnd3tySpvr7eZUkAgApQEkHMGPN2SW8Pfz0svH6FMWZV+HOPtfYTRS8MSOF5nlpaWrRjxw7XpQAAKkRJBDEF55h8X9ptTeFFkp6URBBDSRgdHdXAwEDJ94ht2bJFy5cv1x133KG+vj7FYjF1dHTowgsvVG1trevyAAAqkTFi1tpl1lozzuUo1zUCUvANyiOPPFKbN28u6W9QPvnkk+ro6ND111+vtrY2nXfeeTryyCP1/e9/X29729vU19fnukQAgEokiAHlpLm5Wccdd5x6e3tdl5LVpz71KfX09Ojyyy/XD37wA33605/WDTfcoPPOO09PPPGEvvKVr7guEQAgghgwJb7vuy4hq40bN+quu+7SEUccobPPPnufZRdddJFqamp04403ateuXW4KBAA8hyAGVJh77rlHkvSa17xGs9LOyn7ggQfqZS97mRKJhP72t7+5KA8AkIIgBlSYJ554QpLU1NSUcfn8+fMlqaTHuAHATEEQA6agpqZGiUSiJM8/OTg4KCn74dNIJCJJ6u/vL1pNAIDMCGLAFPi+r3g8rkQioTVr1rguJyfWWkmSMcZxJQAAghgwRbFYTPF43HUZ+0n2hCV7xtIlb0/2jAEA3CGIAdOULfC4cvTRR0vKPgZs/fr1krKPIQMAFA9BDJiGmpoaRSIRdXZ2ui7lOSeccIIk6a677tLevXv3WbZjxw51dXWpqqpKL3nJS1yUBwBIQRADpsH3fbW3tysSiZTMWLHGxka95jWv0VNPPaVVq1bts+zKK6/Url27dNppp6mmpsZNgQCA55TKuSaBsuX7vhobG7Vhw4bC7GDPHlXdeqvm3X23zPbt0rx5Gmlq0q4zztDehoaMTa644gqdfPLJ+uxnP6t77rlHxxxzjP72t7+ps7NTTU1N+uQnP1mYWgEAOSGIAXmyfft29fT05O9k4Hv26MCVK1Vz3XWa/eyz+y0+cMUK7T7pJA1ecolGFi7cZ1ljY6NuvfVWLV++XHfeeaduv/12HXrooTr33HN14YUXqq6uLj81AgCmhSAG5EFjY6P6+/u1du1aLVy4cNphzOzcqYPOOUfzwlnyM9q7V1W33aa599yjvmuu0Z60b3A+//nP14oVK6ZVBwCgsBgjBuSB53lqbW1VU1OTBgYGprexvXtV95GPaN4998iOs1pyFrBZO3fqoPe/X3NKZIwaAGDyCGJAHiUnS52Oebfdpqrf/15WY2FrIrN27VJk2bJp7xsAUFwEMSBPPM9TbW2tNm3aNK3zOB4QftMxl3nvraR5996rOd3dU94vAKD4CGJAHjU3N6utrU1bt25VT09Pzu1nb9igeXffPe4hyUySoa3mxz/OeZ8AAHcIYkCexWIxRaPRKbVN9mhN9SyQcx57bIotAQAuEMSAEmISiem137UrT5UAAIqBIAaUEBuesHuq9nIibwAoKwQxoABGRkaeO7l2Lva8+MWyc+fmPEbsufYvf/kUWwIAXCCIAXmWPP9kIpFQV1dXTm3twQcr8ba35TxGzEqynqfEmWfm2BIA4BJBDCgA3/cVT5vpfrJ2vf/9kpRTr5iRNPTWt2rvIYdMaZ8AADcIYkABDQ8P596mrU2DF1wgo8mHsZGjjtLAF76Q874AAG4RxIACiUajikQi6uzszLntjosv1o6Pfey5Q5TjBbLhY47Rtuuv196DD55SnQAAdwhiQIF4nqd4PK5IJKI1uZ4H0hgNfvrT6r3+eg298Y3SrP3/VEcaGzXw2c+q9+abNXrEEXmqGgBQTHNcFwBUMs/z1NjYqA0bNkyp/Z5Xv1p7Xv1qzdq0SfM6O2X6+6V58zQyf772nHBCxoAGACgfBDGgCLZv366enh7V19dPqf3ehgYlTj89z1UBAFzj4zRQYM3NzZo/f77Wrl07pfNPAgAqFz1iQBEsXrxYkjQwMDDlXjEAQOWhRwwAAMARghgAAIAjBDGgiHbu3Om6BABACSGIAUXS0NCgvr6+3OcUAwBULIIYUCSxWEzxePy5qSwAACCIAUUUjUYVjUZdlwEAKBEEMaDIrLVav3696zIAACWAIAYUked5am9vV3V1tbq6ulyXAwBwjCAGFJnv+2pvb9fw8LDrUgAAjhHEAIcYtA8AMxtBDHCgqqpKkUhE3d3dhDEAmMEIYoADnucpHo8rEokwcB8AZjCCGOCI53latGiR6zIAAA4RxADHhoaGtG7dOtdlAAAcIIgBDsViMc2fP1+bN28mjAHADDTHdQHATLd48WJJUl9fn+NKAADFRo8YUAJqa2tdlwAAcIAgBgAA4AhBDCgRQ0NDrksAABQZQQwoAb7vK5FIcP5JAJhhCGJACYjFYorH40xlAQAzDN+aBEpELBZTU1OTdu/e7boUADNIX1+fbr31Vv3hD3/Q2rVrtXXrVs2dO1cLFizQGWecoTPOOEOzZtFvUygEMaCEWGvV29urpqYm16UAmCFuvvlmXXrppTr00EN1wgkn6PDDD9ezzz6rW2+9VZ/4xCd0xx136Lvf/a6MMa5LrUgEMaCEtLS0aPv27erq6tLLXvYy1+UAmAGampq0atUqnXjiifv0fF166aV6y1veoltuuUW//e1v9Za3vMVhlZWLvkaghPi+r/b2dtXU1Kinp8d1OQBmgBNOOEEnnXTSfocfDz30UC1dulSSdO+997oobUYgiAElpqqqynUJACBJ8jxPkjRnDgfQCoUgBpSg2tpadXd30ysGwJmRkRHdeOONkqQlS5a4LaaCEXGBEuN5nlpbWyVJ3d3dqq+vd1wRgJnoS1/6kh599FG97nWvI4gVED1iQAnyPE8tLS2uywAwQ11zzTX67ne/q+bmZq1cudJ1ORWNIAaUsNHRUSZ4BVBUq1at0uc+9zm1tLTohhtuUF1dneuSKhpBDChRvu/ruOOO0+bNmwljAIri6quv1mc+8xktWLBAN9xwgw499FDXJVU8ghhQwpqbm3Xcccept7fXdSkAKty3vvUtLVu2TMcee6xuuOEGxqcWCYP1gRLn+77rEgBUuK997Wtavny5Wltb9dOf/pTDkUVEEAMAoBIND0vGSBPMAXbDDTdo+fLlmj17tl7+8pfrmmuu2W+dI444QqeffnqhKp3RCGIAAFSIOQ8/rAOuvVZVN9+sWf39kqTRQw5R4h3v0K6zztJohvPYbty4MVhvdFRXX311xu2+4hWvIIgViLHWuq6h4Iwx95900kkvWb16tetSgJwNDg5q9erVqq6u5vyTADIy27bpoH//d8276659breSUk/VnXjHO7T9q1+VqquLWl8l6ujo0EMPPfQ3a+3i6WyHwfpAifN9Xx0dHUokElqzZo3rcgCUGNPbq/q3v13z7rpL6V0rqSHMSqr+5S918JlnSolEESvEeAhiQBnwfV9tbW2uywBQaqzVQR/8oOY8/rikfYNXOqMgjM297z7VXnppMarDJBDEgDIyODjougQAJcS77z7N+/Of9+sJyyYZxqpvvFGzn3qqgJVhsghiQJlobGxUJBJRZ2en61IAlIgDVq2SNH5PWDojyVirmh/9qBAlIUcEMaBMeJ6neDyu2tpaZtoHIO3erarf/nbSvWHpqn75y7yWg6khiAFlhokWAUjSrL4+meHhnHrDUs3+17+kGTBzQqkjiAFlxPM8WWu1efNm9fT0uC4HgEvTDVGEsJLAhK5AmWltbZUkdXd3SxLngwNmqL0HHSQ7e7Y0OjqlXrG9hxwSzLwPp+gRA8qM53lqaWlRNBp1XQoAl6qqNPTGN0750GTi5JPzWg6mpmSCmDGmwRjzA2PM08aY3caYDcaYrxljDnJdGwAApWjX+96Xc5vkAcldS5fmtxhMSUkEMWPM0ZLul3SOpPskrZC0TtJ/SrrXGHOww/IAAChJe171Ku3JcbJnIynx1rdmPO8kiq8kgpikb0s6VNL51tq3W2svtda+TkEge4GkLzqtDihBIyMj2rJli+syALhkjPquuUYjRxwx4arJnrA9ra3q/+//LmxdmDTnQcwY0yTpDZI2SPpW2uL/krRT0lJjzAFFLg0oWb7va9GiRerr6+P8k8AMt/eww9T7619rz+Lxzz1tJA29/vXadsMNsgceWJziMCHnQUzS68Lr/7PW7k1dYK0dlPQnSTWSji92YUApi8ViisfjGhoacl0KAMf2xmLq/fWv1fuLXyhx8smynje2rLpau979bj27erX6rrtO1vcdVop0pTB9xQvC6+4sy/+poMesRdIfxtuQMeb+LIsWTK00AADKhDHac/zx2nP88cGUFv390qxZspGINKsU+l2QSSk8M7XhdX+W5cnbmU4cSFNTU6NEIqGuri7XpQAoJbNny0ajsnV1hLASVw7PTnKKlAmnALbWLs50kfRoYUsE3PB9Xx0dHUokEowVA4AyVApBLNnjVZtleSRtPQApfN9XW45fXwcAlIZSCGKPhdctWZYfE15nG0MGQNLg4CDnnwSAMlMKQeyO8PoNxph96jHG+JJOkJSQ9OdiFwaUi8bGRkUiEXV3dxPGAKCMOA9i1tonJP2fpKMk/Xva4s9LOkDSddbanUUuDSgbnucpHo8rEoloYGDAdTkAgEkqhekrJOmjkjolfcMYc6KktZJeLum1Cg5JfsZhbUBZ8DxPdXV12rNnj+tSAACT5LxHTHquV+ylklYpCGAXSTpa0jckvcJa2+uuOqB81NbWavPmzRyeBIAyUSo9YrLWPqXgpN8Apqi5uVn9/f1au3atFi5cqPr6etclAQDGUTJBDEB+tLa2qr+f2V4AoByUxKFJAACAmYggBgAA4AhBDKhAtbW12rJli+syAAATIIgBFcbzPDU0NKivr4/zTwJAiSOIARUoFospHo9z2iMAKHEEMaBC1dTUKBqNui4DADAOghhQwUZGRrR+/XrXZQAAsiCIARXK9321t7erurpaXV1drssBAGRAEAMqmO/7WrRokesyAABZEMSAGWB4eJhB+wBQgghiQIWLRqM68sgj1d3dTRgDgBLDuSaBCud5nlpbWyVJW7Zs4UTgAFBC6BEDZgDP81RbW+u6DABAGoIYAACAIxyaBIrk5ptv1p///Gf94x//0COPPKIdO3bolFNO0cqVK12XBgBwhCAGFMnXv/51PfLIIzrggAP0vOc9T48//njRa0ief/JFL3pR0fcNANgfhyaBIlm2bJnuuecePfbYY7riiiuKvv/m5mbF43H19fVp3bp1Rd8/AGB/9IgBRXLCCSe4LkGxWExNTU3as2eP61IAAKJHDJiRent7XZcAABBBDJhxGhoalEgkOP8kAJQAghgww8RiMcXjcQ0NDTHTPgA4RhADZqBoNKpoNOq6DACY8QhiwAxlrVV3d7frMgBgRiOIATOQ53lqb29XJBJRZ2en63IAYMYiiAEzlO/7am9vd10GAMxoBDFghhsdHWXQPgA4woSuwBTt3CndcYfU0yPNni01NEjxePBzJqtXr9bq1aslSc8++6wk6a9//asuuOACScEA+s997nNFqT2pqqpK8+fP19q1a7Vw4ULV19cXdf8AMNMRxIAcPf649K1vGV17rdTfb/ZZduSRVh/6kNUHPygdfPC+7f7xj3/ohhtu2Oe2jRs3auPGjZKC+b2KHcQ8z1Nra6skaf369QQxACgyghiQg5//XFq61Gj3bpNx+caNRp/5jNG3vmV1881WL37x2LKLLrpIF110UZEqnTzP89TQ0KAtW7a4LgUAZhzGiAGT9OtfS+96V/YQlurpp41e/3ojZocAAIyHIAZMwvbt0llnGe3dO3EIS9q2zWjpUiNrC1gYAKCsEcSASbjuOmlwcPIhLGD1178a3XdfQUrKu0QioTVr1rguAwBmFIIYMAFrpauuyjWESVLQ5tvfnkrb4kqef7Kvr48wBgBFRBADJrBli/TYY1MPU3femb9aCikWi6mtrc11GQAwoxDEgAls3+62fbENDQ25LgEAZgyCGDCB6urpta+pyU8dxRCLxZRIJNTV1eW6FACYEQhiwASe/3zJ96f+1ccXvCCPxRSY7/vq6OjQ0NCQ1q1b57ocAKh4BDFgAvPmSUuXTr39Bz5QXvNXVFVVqampyXUZADAjEMSASfjwh5NhKrdQVV9vdeqp+a+n0Ky12rp1q+syAKDiEcSASTj2WOmjH7UKpqSYTBgL1lm+3KqqqpCV5V/y/JORSESdnZ2uywGAikYQAyZpxQqrd70rGcaySYY0o//3//bqrLOKUFgBeJ6n9vZ2RaNR9fT0uC4HACoWQQyYpDlzpB/9yGr58r16/vOz9YoZtbZa3XjjXpXg+b1zNjo66roEAKhoc1wXAJSTWbOkCy+U/uM/rH7zG6ubbjJ69llp9mypoUFautTqla+UTOlPpj8h3/dVW1urtWvXauHChaqvr3ddEgBUHIIYMAWeJ51yinTKKeX1jchcLV68WJK0fv16ghgAFACHJgGMq6GhwXUJAFCxCGIAAACOEMQAAAAcIYgBGFdNTY0SiYTWrFnjuhQAqDgEMQDj8n1f8XhcfX19hDEAyDOCGIAJxWIxxeNxDQ0NuS4FACoKQQwAAMARghiASampqVF1dbW6urpclwIAFYMgBmBSfN9Xe3u7qqurGSsGAHlCEAMwab7vq7Gx0XUZAFAxCGIAcjY4OKienh7XZQBA2SOIAchJY2OjIpGIuru7CWMAME0EMQA58TxP8XhctbW1GhgYcF0OAJQ1ghiAKamrq3NdAgCUPYIYAACAI3NcFwAgN1/84hf197//XevWrdO2bdtUVVWlhoYGdXR06JxzztFBBx1UlDqstdq5c2dR9gUAlYoeMaDMfO9739OuXbsUj8f1gQ98QKeccormzJmjK6+8UieeeKKefvrpgtfgeZ5qa2s5/yQATBM9YkCZ6e7u1rx58/a7/ctf/rJWrlyplStX6oorrih4Hc3NzZKkNWvWqKenR/X19QXfJwBUGnrEgDKTKYRJ0sknnyxJWr9+fdFqicViikajRdsfAFQaghhQIX73u99JkhYuXFjU/Y6MjBQ1/AFAJeHQJFCmrrrqKu3cuVMDAwN66KGHdN9992nhwoX62Mc+VrQafN/XokWL9Mc//lFdXV162cteVrR9A0AlIIgBZeqqq67Ss88++9zvr33ta7VixQodfPDBRa0jFospHo+rq6urqPsFgErAoUmgTD344IPavHmzHnzwQX3/+9/Xk08+qTe84Q18ixEAyghBDChzhxxyiN70pjfppz/9qfr6+nT++ecXvYaamhpVV1fTKwYAOSKIARWioaFBLS0t6u7u1rZt24q6b9/31d7erurqanrkACAHBDGggjzzzDOSpNmzZxd9377vq7Gxsej7BYByRhADysjjjz+uf/3rX/vdvnfvXn35y19WT0+PXvrSl6q2ttZBdYHBwUH19PQ42z8AlBO+NQk4NDws/frX0m23GW3bJs2dKzU1Se97n9Uxx+y//h133KHLL79cxx9/vI466igddNBBevbZZ3Xvvfdq48aNOuSQQ7R8+fLi35FQY2Oj+vv71d3dLUnMtg8AEyCIAQ6MjEhXXil985tGTz9t9lt+xRVGJ51kdfnlVqlTc7361a/We9/7XnV1demRRx7RwMCAqqurdfTRR+vUU0/Vueeeq7q6uiLek315nqfW1lZJ0sDAAEEMACbgPIgZYzxJH5V0nKQ2SS+U5En6oLX2+y5rAwphaEg6/XSjW27ZP4CNsfrd74z++EfpJz+xevvbg1sXLFigL33pS0Wpc6o8z3NdAgCUjVIYI3aApK9JOlvSYZK2Oq0GKCBrpXPOSYYwO86aQUjbvdvozDON7r67KOUBAIqsFILYLklvlvR8a+1hkn7guB6gYO64Q/rZz5IhbLwesTF79hhdcIGRHS+3laCdO3e6LgEASp7zIGat3WOtvdVau8V1LUChfec7yfA1uRAWsHrwQaO//KUQFRVGQ0OD+vr6mFMMACbgPIgBM8Uzz0i/+pU0/iHJTILQ9r3v5RLe3Eqef3L79u1MZQEA43A+WD+fjDH3Z1m0oKiFABk89pg0Ojr1MPXII3kspgii0aii0ajrMgCgpNEjBhTJrl3Ta1+OQ66stVq/fr3rMgCgZOUliBljNhhjbA6XH+djv+mstYszXSQ9Woj9AbmY7mT3DifLnxLP89Te3q5EIsHJwAEgi3wdmnxC0lAO6z+dp/0CZaO1VYpErAYGpnZ48tWvznNBReD7vjo6OvT73//edSkAUJLyEsSstSfmYztAJTvgAOmss6RvfjPXllbGSOedV2bzVwAAJsQYMaCIPvxhK2Ny/9bkm98szZ9fkJIKrqqqSpFIRJ2dna5LAYCSQxADimjhQmn58mQQm1wga2iw+s53yrc3zPM8xeNxRSIRxooBQJqSmL7CGHOpxqaYOC68PscY86rw53s47yQqxQUXSMPDe/WpTyU/B2WfZb+pyeqWW6wOP7xo5RWE53latGgRQQwA0pRKj1iHpPeFlxeHt70y5bZXZWkHlB1jpEsuke6+e69OP91qToaPQ42NVl/84l7dd59VS0vxayyUoaEhJngFgBQl0SNmrV3iugag2F75SumVr7TaskW6/XarbdukuXOlpibpda+TZs92XWF+RaNRzZ8/X2vXrtXChQtVX1/vuiQAcK4kghgwkz3vedJ73uO6isLzPE+tra2SpC1bthDEAEClc2gSwAzgeZ5qy21mWgAoIIIYAACAIwQxAAAARwhiAIrK93319fVpzZo1rksBAOcIYgCKKhaLKR6Pa/v27Vq3bp3rcgDAKYIYgKKLxWKaX67nbAKAPCKIAXCmt7fXdQkA4BRBDIATLS0tSiQSnPYIwIxGEAPghO/76ujo4LRHAGY0ghgAZ6qqqhSNRl2XAQDOEMQAOGWtVXd3N71iAGYkghgAZzzPUzweVyQSUXd3t+tyAKDoCGIAnPI8T+3t7a7LAAAnCGIAAACOEMQAAAAcIYgBKAkjIyOc8gjAjEMQA+Cc7/tqa2vTpk2bCGMAZhSCGICS0NzcrLa2Nk57BGBGIYgBKBm+77suAQCKiiAGoKQkEgmtWbPGdRkAUBQEMQAlIxaLKR6Pq6+vjzAGYEYgiAEoKbFYTG1tba7LAICiIIgBKElDQ0OuSwCAgiOIASg5sVhM1dXV6urqcl0KABQUQQxAyfF9X+3t7aqpqWFeMQAVjSAGoCRVVVWprq7OdRkAUFAEMQAly1qrrVu3qqenx3UpAFAQc1wXAACZeJ6n1tZWSVJ3d7ckqb6+3mVJAJB3BDEAJcvzPLW0tGjHjh2uSwGAguDQJAAAgCMEMQAAAEcIYgBK3sjIiLZs2eK6DADIO4IYgJLm+74aGxs5/ySAisRgfQAlr7m5WZL06KOPOq4EAPKLHjEAZcH3fdclAEDeEcQAlIWamholEgnOPwmgohDEAJQF3/cVj8eVSCQYKwagYhDEAJSNWCymtrY212UAQN4QxACUncHBQdclAEBeEMQAlJVYLKZIJKLOzk7XpQDAtBHEAJQV3/fV3t6uSCSidevWuS4HAKaFIAag7Pi+r7q6OtdlAMC0EcQAlKXa2lpt3rxZPT09rksBgCkjiAEoS42NjZo/f77Wrl1LGANQtjjFEYCy5HmeWltbZYzRwMCA6uvrXZcEADmjRwwAAMARghgAAIAjBDEAZc1aq507d7ouAwCmhCAGoGx5nqeGhgb19fVx/kkAZYkgBqCsxWIxxeNxDQ4O8u1JAGWHIAag7NXU1CgajbouAwByRhADUBFGRka0fv1612UAQE4IYgDKXvL8k4lEQl1dXa7LAYBJI4gBqAi+7ysej7suAwByQhADUFGGh4ddlwAAk0YQA1AxotGoIpGIOjs7XZcCAJNCEANQMTzPUzweVyQSYV4xAGWBIAagoniep8bGRtdlAMCkEMQAAAAcIYgBAAA4QhADUJH6+vq0bt0612UAwLjmuC4AAPKtublZkvTAAw9IkpqamlyWAwBZEcQAVKTm5mb19/drz549rksBgKw4NAmgou3cudN1CQCQFUEMQMVqaGhQX18fc4oBKFkEMQAVKxaLKR6Pa/v27erp6XFdDgDshyAGoKJFo1FFo1HXZQBARgQxABXPWqv169e7LgMA9kMQA1DRPM9Te3u7EomEurq6XJcDAPsgiAGoeL7vq6OjQ8PDw65LAYB9EMQAzCgM2gdQSghiAGaEqqoqRSIRdXd3E8YAlAyCGIAZwfM8xeNxRSIRBu4DKBkEMQAzhud5WrRokesyAOA5zoOYMeYYY8wnjTG3G2OeMsbsMcY8Y4z5lTHmta7rAwAAKJRSOOn35ZLOkPSIpN9K2ibpBZJOlnSyMeY/rbXfcFgfAABAQTjvEZO0WtJLrLXHWms/ZK39lLX2FEknShqWtNwY8zy3JQKoJIlEgvNPAigJzoOYtXaVtfaBDLffJelOSXMlvbLYdQGoTLFYTG1tbZwMHLm5DHEAABf2SURBVEBJKIVDk+NJzr444rQKABWlublZkrRhwwa3hQCY8Uo2iBljGhUcntwl6Y+TbHN/lkUL8lUXAABAvjg/NJmJMWaepP+RNE/SMmttn+OSAFQY3/c5PAnAubwEMWPMBmOMzeHy43G2NVvSjySdIOl6SV+dbB3W2sWZLpIenfadBFBRYrGY4vG4tm/frnXr1rkuB8AMla9Dk09IGsph/acz3RiGsB9LOk3SzyS911prp18eAOwvGo2qqalJu3fvdl0KgBkqL0HMWnvidLdhjJkj6ScKQthPJJ1lrR2d7nYBYDzWWvX29qqpqcl1KQBmoJIYI2aMmSvpRgUh7DpJSwlhAArN8zy1tLSourpaXV1drssBMAM5D2LhwPxfSvo3SddIOsdau9dtVQBmCt/31d7eLt/31dPT47ocADNMKUxfcZWkN0vqkbRZ0ueMMenr3GmtvbPIdQEAABRUKQSx+eF1vaTPjbPenYUvBQAAoHicBzFr7RLXNQCY2aqqqjQ6OqqBgQHV19e7LgfADOJ8jBgAuOZ5no488kht3ryZOcUAFBVBDAAUnH/yuOOOU29vr+tSAMwgBDEACMViMQ0PD7suA8AMQhADgBQjIyOcfxJA0RDEACDk+77i8TgnAwdQNAQxAEiRPBn40FAup88FgKkhiAEAADhCEAOANDU1NUokEpx/EkDBEcQAII3v++ro6FAikWCsGICCIogBQAa+76utrc11GQAqHEEMAMYxODjougQAFYwgBgBZxGIxRSIRdXZ2ui4FQIUiiAFAFr7vq729XbW1tZyDEkBBEMQAYBxVVVWqq6tzXQaACkUQAwAAcIQgBgATsNa6LgFAhSKIAcA4PM9TbW2tNm3axDgxAHk3x3UBAFDqmpubJUlr1qxRJBJRfX2944oAVAp6xABgEmKxmKLRqOsyAFQYghgATNLIyIi2bNniugwAFYQgBgCT4Pu+Fi1apL6+Ps4/CSBvCGIAMEmxWEzxeFxDQ0OuSwFQIQhiAAAAjhDEACAHNTU1SiQS6urqcl0KgApAEAOAHPi+r46ODiUSCcaKAZg2ghgA5Mj3fbW1tbkuA0AFIIgBwBQNDg66LgFAmSOIAcAUNDY2KhKJqLOz03UpAMoYQQwApsDzPMXjcUUiEc5BCWDKCGIAMEWe56murs51GQDKGEEMAADAEYIYAACAIwQxAJiG2tpabdq0iXFiAKZkjusCAKCcNTc3S5IefPBBRSIR1dfXO64IQDmhRwwApqmxsVHRaNR1GQDKEEEMAPLAWqstW7a4LgNAmSGIAcA0eZ6nRYsWqa+vj/NPAsgJQQwA8iAWiykej3PaIwA5IYgBQJ7U1NS4LgH/f3v3Hlx3ed95/P01nMQSPhII0cN0DcLuwTBZ41jrVhTIOASS1m2nTeKQyR/LLQ1Jm2WHNpBJd5PZpO1MumzTZEOTbdJLLiUJ3bJhQqfQSzYl5LJMuh4TpcpwsbERIGNC5Ui+HlmSefaPc5wltuRLdM55zuX9mtH8OL9zmY9/40EfP7/nPI/UZixiklRHfX19bNmyJXcMSW3CIiZJdVIsFhkZGaGnp8cyJumUWMQkqY6KxSJr167NHUNSm7CISZIkZWIRkyRJysQiJkkNMDMz4/6Tkk7KIiZJdVYqlVi1ahW7du2yjEk6ITf9lqQG2LBhAwBTU1OZk0hqZY6ISVKD9Pf3544gqcVZxCSpgdx/UtKJWMQkqUHK5TLDw8NMT087V0zSgpwjJkkNVC6X2bt3L7Ozs7mjSGpBjohJUhPs2bMndwRJLcgiJkkNtnLlSiqVivtPSjqORUySGqxUKrFx40ZmZmaYnJzMHUdSC7GISVITDAwMMDAwkDuGpBZjEZOkJkkpsW3bttwxJLUQi5gkNUGhUGBkZIS+vj7nikn6EYuYJDVJsVhkZGSEubm53FEktQiLmCRJUiYu6CpJamuXX345ExMTCz533nnnMTo62uRE0qmziElSkx05coSdO3eyevXq3FE6Rl9fH7fccstx588666wMaaRTZxGTpCYqFousX7/+R6M0lrH66Ovr44477sgdQzptzhGTpCYrl8usX7/ebY8kOSImSTkUi8XcETrK7Ows9913H7t27aK3t5dXvepVXH755Zxxxhm5o0knZBGTpEwqlQpjY2NcdtlluaO0vRdffJHbbrvtx85deOGFfOxjH+OKK67IlEo6OW9NSlIGR/efnJqaYmxsLHectva2t72Ne++9l9HRUZ566ikeeughbrjhBp577jmuv/56HnvssdwRpUVZxCQpk1KpxPDwcO4Ybe/222/nqquu4rzzzqOnp4dLLrmEO++8k3e9613MzMzw0Y9+NHdEaVEWMUnKbGZmJneEjnTjjTcC8J3vfCdzEmlxFjFJyqhUKlGpVNx/sgHOPfdcAA4dOpQ5ibQ4i5gkZVQsFtm0aRMzMzPs3Lkzd5yOsnXrVgCGhoYyJ5EWZxGTpMyWL1/uwq4/oSeffJLp6enjzk9MTPCBD3wAgM2bNzc7lnTKXL5CklpASokXXnjBQnaaHnjgAT75yU9y1VVXccEFF7BixQqeeeYZvva1r3H48GGuueYa3v3ud+eOKS3KIiZJmRUKBdatW8f09DSPPPIIV155Ze5IeaRE4dFH6f3CFyiMjREHD5JWrGBu/XoO3ngj8+vWHfeWK6+8kh07dvD973+frVu3cujQIfr6+hgZGeG6667jLW95CxGR4Q8jnRqLmCS1gEKhwMjICI8++iiTk5MMDg7mjtRUhe99j/73vY/CAmuqFR57jN577mF2wwb2fuQjzF966Y+eu+KKK1ywVW0t+xyxiLggIv4kIv45Il6IiMMR8XxEfCsi3h4RhdwZJUmN84pvfpOBzZspjI2RFnlNAl6xdSvnvvGNFPyGqTpI9iIG/Azw74G9wP3AR4G/BYaAzwJfjQhH7iSpA525fTvnvOMdLKtUAFjsJuLR88v272fgpps447nnmpJParRWKDiPAOeklF56+cnaSNhXgauBzcC9zY8mSc01Pz/Pvn37uubW5Iq77mLZwYOn9Z5l09Oc9alPse8P/qBBqaTmyT4illKaPbaE1c7PUR0hA7i4uakkqfmKxSJDQ0NMTEx0xZpiyyYnWf7AA4vejjyRni9/mThwoO6ZpGbLXsQWExFnAL9ce/gvObNIUrOUy2WGh4fZs2dP7igNt/z++4nZ2UVvR57IsgMHWP7gg3XPJDVbK9yaBCAiBoH/SHUqwHnAG4AycA/wwCl+xtZFnrp0kfOS1HKKxWLuCE2x1HlezhNTJ2iZIgYMAh962eME/BHw/pTSTzJyLUltq1KpMDY2xmWXXZY7SsPE7OzS3j83V6ckUj51uTUZEeMRkU7j54vHfkZK6YmUUlAth0PAe4B3Ad+MiIFTyZFS2rDQD/BEPf6cktQMpVKJjRs3MjU1xdgC62p1ipfOOWdp7z/77DolkfKp14jYDmDmNF7//GJPpJSOAM8Cd0XED4C/An6f6m1LSeoKpVKJ4eFhxsfHc0dpmMOvfz3Fj3+cxOLLVizk6OsPv/71jQkmNVFdilhK6dp6fM4C/r52vLpBny9JLW1m5nT+jdte5oaHmbvssgVX0z+RAA6/5jXMX+wX6tX+WvZbkzX/pnacz5pCkjIolUpUKhW2dOpK8hEc+I3fADjlJSyOvu7gO9/ZkEhSs2UvYhFxeUT0LnB+BXBX7aHfUZbUdYrFIps2baJSqXTsumIzb34zB2+6ieDkZezoLckDt97K4Te8ofHhpCZohW9N/mfg6oj4BtW5YYeAC4BfAs6muvL+f80XT5LyKRaLnT1XLIJ9H/4wqaeHFZ/+9IlfCuy/4w4O3H57c7JJTdAKRezPgYPAz1GdC9YLTAFbqW5r9NmUkrcmJalTLVvG/g9+kMrmzfTefTc99933o70nAV5asYLKW9/KoZtuYn7NmoxBpfrLXsRSSg/irUdJ6nrza9ey7w//kP0f/CBn7thBHDzISytWcKRcJvUeN4NF6gjZi5gk6eSmp6fZuXMnq1evzh2l4dKKFcy9+tW5Y0hNkX2yviTpxMrlMqtWrWLXrl1MTk7mjiOpjhwRk6Q2sG7dOiKCffv2MTg4mDuOpDpxREyS2oTb7kqdxyImSW2gUCjQ39/PxMREx64pJnUjb01KUpsol8sAjI2N0dfX5y1KqQM4IiZJbaRUKjEwMJA7hqQ6sYhJUpuZn59n9+7duWNIqgOLmCS1kWKxyNq1a5mammJsbCx3HElLZBGTpDZTKpXYuHEjMzMzuaNIWiKLmCRJUiYWMUlqQ729vfT09LBly5bcUSQtgUVMktpQsVhkZGSEnp4e54pJbcwiJkltqlgsMjQ0lDuGpCWwiEmSJGViEZMkScrEIiZJbW56etr9J6U25V6TktTGju4/OTo6CsDq1atzxpF0mixiktTmyuUye/fuZXZ2NncUSafJW5OS1CEOHjyYO4Kk02QRk6QOsHLlSveflNqQRUySOsDR/Senp6eZnJzMHUfSKbKISVKHGBgYYGBgIHcMSafBIiZJHSSlxNNPP507hqRTZBGTpA5RKBRYu3YtlUrFzcClNmERk6QOcnSu2NzcXO4okk6BRUySOkxvb2/uCJJOkUVMkiQpE4uYJHWgI0eOuIyF1AYsYpLUYZYvX86qVat4/PHHLWNSi3OvSUnqMIVCgXXr1gHw9NNPMzg4mDmRpMU4IiZJHahQKLBy5crcMSSdhEVMkjpYpVJh586duWNIWoRFTJI6VKlUYnh4mImJCcuY1KKcIyZJHaxcLgMwPj6eN4ikBTkiJkmSlIlFTJI6XLFYZGpqirGxsdxRJB3DIiZJHe7o/pPT09POFZNajEVMkrrAwMAAq1evzh1D0jEsYpLUBQqFAikl9uzZkzuKpJexiElSl1izZg2VSoUtW7bkjiKpxiImSV2iWCyyadMm5ubm3INSahEWMUnqIsuXL6e/vz93DEk1FjFJkqRMLGKSJEmZWMQkqYsUCgX6+/t5/PHHnScmtQD3mpSkLrNhwwYAtm3bxuDgYOY0UndzREySutCaNWtyR5CERUySutb8/LxbHkmZWcQkqQsVi0WGh4eZmJiwjEkZWcQkqUuVy2WGh4fd9kjKyCImSV2sWCzmjiB1NYuYJHW5SqXC2NhY7hhSV7KISVIXK5VKbNy4kampKcuYlIFFTJK6XKlUYnh4OHcMqStZxCRJAMzMzOSOIHUdi5gkiVKpRE9PD1u2bMkdReoqFjFJEsVikZGREXp7e11XTGoii5gkCYDly5dz9tln544hdRWLmCRJUiYWMUmSpEwsYpIkAAqFAikldu3a5TwxqUnOzB1AktQ6NmzYAMCzzz5LX18fg4ODmRNJnc0iJkn6MWvWrOHAgQO5Y0hdwVuTkqTjzM/Ps3v37twxpI5nEZMk/ZhiscjQ0JD7T0pN4K1JSdJxyuUyAE888UTmJFJnc0RMkrSgYrGYO4LU8SxikqRFVSoV95+UGsgiJklaUKlUYuPGjVQqFeeKSQ1iEZMkLapUKjE8PJw7htSxLGKSJEmZWMQkSZIysYhJkk5q//79TE5O5o4hdZyWLGIR8ZmISLWfcu48ktTNhoaGuPDCC9m2bZtlTKqzllvQNSJ+Ffh14ACwInMcSep6hUKBdevWAbBv3z43ApfqqKVGxCLiPODPgb8GtmaOI0mqKRQKuSNIHamlihjwZ7XjrVlTSJKO09/fz65du9i5c2fuKFLHaJlbkxFxM/Am4M0ppT0RkTmRJOnlju4/OTo6Sl9fn7copTpoiRGxiBgC7gK+mFK6P3ceSdLChoaGGBgYyB1D6hjZR8QiYhnwl1Qn59+2xM9abF7Zq7dv386mTZuW8vGS1PX6+vo4cuQIO3bswDsX6mbbt28HuGipn1OXIhYR48DQabzlSyml62v//R7gtcCvpJSm6pFnAcvGx8ePjI+Pf69Bny+4tHZ8ImuKzud1bjyvcXN4nRvPa9xYFwH7lvoh9RoR2wHMnMbrnweIiIuBDwOfSyn93VJDpJQ2LHT+6EjZYs9r6bzGzeF1bjyvcXN4nRvPa9we6lLEUkrX/oRv/bfAK4G3R8TbF3nN9trw95udPyZJkjpJ7jli48BnFnnuV4Dzgf9FdehvvDmRJEmSmiNrEUspjQK3LPRcRDxMtYi9P6X0VDNzSZIkNUNLLF8hSZLUjSxikiRJmURKKXcGSZKkruSImCRJUiYWMUmSpEwsYpIkSZlYxCRJkjKxiEmSJGViEZMkScrEIiZJkpRJ1xWxiLg4In4nIh6KiOciYjYifhARfxMRr8udr1NERCEifisiPhcRo7XrnCJiwS2tdGIRsTIiPhsRz0fE4YgYj4iPR8Q5ubN1goi4LiI+ERHfioh9tb+rX8ydq5NExLkRcUtEfCUinoqISkTsjYhvR8Q7IqLrfh81QkT8t4j4p9rvt0pE/DAivhsRH4qIc3Pn0/G6bkHXiPifwNuAx4BvAz8ELgF+DTgD+K2U0h/nS9gZIuJsYKr28AfALHAB8M6U0l9kC9aGIuJngEeAnwL+BngCGAFeBzwJXJVS2pMvYfuLiFHg1cABYAK4FPhSSun6rME6SET8JvApYDfwdeBZoARsBvqB+4C3pm77pVRnETELPEr1d9yLwFnAzwM/CzwP/HxK6bl8CXWsbixiNwPfSyl995jzrwX+N5CAi1JKuzPE6xgR8QrgWmA0pbQ7In4X+BAWsdMWEf8I/AJwW0rpEy87/zHgPcCfppR+M1e+TlAbDZ8AngJeS7UoWMTqKCKuoVoKHkwpvfSy8+cD/5fqP9SuSyndlyliR4iI5SmlmQXOfxh4P/CplNJ/aH4yLabrhoJTSp8/toTVzn8DeBh4BXBls3N1mpTSbErp7y20SxMRq6mWsHHgfxzz9IeAg8ANEXFWk6N1lJTS11NK2x2NaZyU0kMppb99eQmrnX8B+HTt4dVND9ZhFiphNffWjhc3K4tOTdcVsZOYqx3ns6aQ/r9rasevLvALbD/wf4BeqrcepHbl/3sb71drx3/JmkLHOTN3gFYREUNUb6UdAr6ZOY501CW147ZFnt9OdcRsDfBPTUkk1VFEnAncWHv4DzmzdJKIeC+wgur8u58FXkO1hN2ZM5eOZxEDIuKVwJeAVwLvSylNneQtUrP01457F3n+6Pmzm5BFaoQ7gbXA36WU/jF3mA7yXqpfhjjqH4CbU0r/mimPFtGWtyZrX91Pp/Gz6NfQI+IM4AvAVcBfA3/UrD9Hq6vndVbDRO3o3Ca1nYi4DbiD6jeBb8gcp6OklM5PKQVwPtVvpq4GvhsR/y5vMh2rXUfEdgCLTUhcyPMLnayVsC8Cb6U6kfF6J+v+mLpcZy3J0RGv/kWe7zvmdVJbiIhbgbuoLrNwbUrph5kjdaSU0g+Ar0TEo1SnONxNdQRSLaIti1hK6dqlfkZtXsI9VEvYPcCNKaUjS/3cTlKP66wle7J2XLPI80e/AbXYHDKp5UTEbwP/Hfg+1RL2YuZIHS+l9ExEPAasj4jBlNJk7kyqastbk0tVW+Pqy1RL2N3ADZYwtaiv146/cOzK4xFRpHpLvQJ8p9nBpJ9ERPwO1RI2CrzOEtZUP107+vuuhXRdEatNzP8K8EbgM8Dbj10WQGoVKaUdwFeBi4Bbj3n696gukHl3Sulgk6NJpy0i/gvVyflbqY6EOSpTRxFxaW2B3GPPL6st6PpTwCN+Ia21dOPK+p8DbgYmgT9h4UnOD6eUHm5irI4UEf+J6lYxAOupbiHzCNUlFwC+7Sr7J7fAFkePA5dT3eJoG3ClWxwtTUS8CXhT7eH5wC8CO4Fv1c5NppTemyNbp4iIm4DPUx2N+QQLz2scTyl9vomxOkrtlu9HqC7BtAPYQ/Wbk6+lOln/BaoF+LFsIXWcbixiD1P9S3kiv5dS+t3Gp+lsp3Ct/zKldHNz0rS3iLgA+H1gE3Au1f367qf6d9VJzkv0si24FvNMSumi5qTpTKdwjQG+kVK6uvFpOlNErAXeTXXKwkqqy9ocpPoPtgeBP/b/F62n64qYJElSq+i6OWKSJEmtwiImSZKUiUVMkiQpE4uYJElSJhYxSZKkTCxikiRJmVjEJEmSMrGISZIkZWIRkyRJysQiJkmSlIlFTJIkKROLmCRJUiYWMUmSpEwsYpIkSZlYxCRJkjKxiEmSJGViEZMkScrk/wFS61Bxd7NZxQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sTDtVG8LrpkwLLZhcd36mZVOU2u+6Cfp5nZzl/nwfU0qq0/65ZvYyBcOIjCk4XZyr1OPodc5tzbJOtschBaelpem1phRiHxNJtRL+U5H2n8mLn40MA3OmpOraW8GI7sWQen0fybTQzJoVtJJlMt3X5eHw+jUTrJP6XfHwBOsUnJnNUtDpPjWG22m5tiZn2e9e2hUoVo1bfL92nQ7O9plKvQ/WaFdASUn1tcv4pY3wd0nq2L+bQrnlYrLHVSPp1eHNSnpcZYMgNvOkJvZdlOUPzPsVdPbOJDWQ6xFm9oEpHu93CvqYzJa0NIc6e8Lr07IszzSFSC5Sz0PcMky7YWYv1a4Ro8fL9zGl/EzBNzqPVDAumyTd5pz7W/ZNsko9jsPDX3i7MbPXaeI/pMPh9XRCbSH2MZFl4fXLzeysiVY0s2l3/A4Np/2c8XGFHblTofzL2UbQD+uqNbN8TvGlXt+XZll+ubIHrdRjyLflOPWNyDdYMI3NbszsKO36ZuVNeR4jZ+Hvre8o+Hxul3S6c26iLxSM33Yin9auscB2+1KSc25j2n0XhmEwfd97KRgvTQqGtRnfopb69ujrwn/AxrtQwWu5RhN/QaLcpCZXP8LM3pRh+fsVvAeTCn73IUcEsZnnfxX8klkk6RvhtB2paUwuVhAM1mfaMPy6+rfDm98KpzHZP9x+tpkdHt73wbRtRiVdFN58l5ndFH5jU+F2B5rZ+8MOyeluCet8qZl9Pa3O/cN1l2jXV6LzsVJBR2OTdGPYwiYzi5jZ6QqG8MjYsXQajym1/TYFoVbaNaREvsNs/F7B87CvgomODwxrqDWz9yoYpDLj6xn6S9rjmOg08ERS+zg925Q30xEOQ5D6hul3w6l1Uh3lZWb7mNlbzOwXkr5aoGNu0K5+PedOsOqHFXzJZZGk+8zs5NRpSgumZDrKzC5VMFbYgRPsJ5vUUDIfMLP3hn2iZGYLzOx6Bd9YHMqy7V8VtODUm1k+rYk3KpgVQJJ+Hj42C49/koJQElHw+v8wj/3n66sKvhU5JuntEwxTkclNZvYFM3u5pc3naGb/YGbXSPp4eNf1zrlMp9H+U8Fz2ilpmZk1htsvUPAeXaCgNf/LGbb9hYL+fLMk/czMjgu3nWdmF0m6IHUM59z28Rvbrqmo7s7h8aZvv4+ZNaYuaYti6ffbnkPrpE8nt2z8MufcI9oVxJeZ2RvDbWaH/zilnosrnXOl+DbzzFOsAcq4+Lso+EWWPoDhC9o16vsd2jXC+7IM287TrtGfU5chTT7F0YXaNZ2OU/BtqqxTHGWpMzW1y5iCAUJXaeIBXfeof9x6bxtXU/rUQM9Ieo8mGBAzn8eUtu1Raeut1TRGF5f0kXHPU/qUU48oCAvZnuPXpm23TcFAtask/U8Oxz8i7XkbVdBauErS/WnrnDOF5yTr66bgG4E/056Pc+O4+76X43N3t7IMRqvgG3Sp/W4OH9MqjZuGScGp+vSpmrYp6A+0fVxtzeO2S91/6AT1zVVwCjS1bvpUXU5BC85Ej+H6cc9X6jGcMcXnYCpTHC3M5bVMW2eZsvy+mGCbBWnH3q49p27a7TLB6516LtdrzwFdb9a4mQLG7eNs7fp87Rz32m+W9NoJtm2S1Je2/ibt/rvzv6fwXs36GZrkuUt/HSe6nDjBthlfTwXfyk6fimuLgm/Fpm7/SgWeQaGaLrSIzUDOuQslna/gj/Q2BcOUrFDwH9mp2tVRPtO225xz71Aw3MKvFHRY3kvBH54/SPoPBd/KHL/dVxX0hfqegg91RMEH9VFJX1cw7dJ4F0n6VwXTrKQ+1L9R8ItuWU4POvNj+ZmCIPJbBb8QIwr+sHwlrHV19q3zfkypbf8iqTe8eYObZLyzSer4hoK+MqnWsTkKvnb/nwrGuso6hIBz7k4FgfQeBacODlbQOfuAbNtk2McTCvqH3KEgGB0Q7iNj/758OOe2OOfepmC+v58qCHu1CoLKUwpO+5yh4P1SKJ9T0ELyqIKW0+bwstupSufc7ZIWKvgH5mEF74H5CoL9ckmfUTAF1jO5FuCClpGTFUyf1Kdd/4j8VsFI5p+fZBcfVDCd2ZMK/olKPYYpDazpnHtKwajwn9OubxMq/PnzCqbr6s20bZGk/02KKPiiwkSX8S6XdJWCaZD+ruB31ywFszb8WMHQF2e6oNU6I+fc9Qq+JHOTgt9/tQr+gfmugnls75xg29UKBt69XMFndI6Cz+ddClr3Jhsnryw554YV/K75hHZNi7VNwd+EDyjow5f377hqZ2HaBVBAZnaIgvA2S8Ef6Scm3gIAUI1oEQOK43wFn6/7CGEAgGwIYkCBhd9A+/fw5h7zLgIAkMKpSaBAzOx+BaN1H6Cgz9G9CjrG8iEDAGREixhQOE0KhjD4u4Kpjk4nhAEAJkKLGAAAgCe0iAEAAHhCEAMAAPCEIAYAAOAJQQwAAMATghgAAIAnc3wXUApm1q9g0tJVnksBAAAzw6GShp1zLdPZSVUEMUmxQw89tOHwww9v8F3ITBSPx7Vu3To9//zzMjPf5QAAUHR//etflUwmp72fsghiZravpLdJOlXSSyUdLGm7pB5J35P0PefczmkcYtXhhx/ecMcdd0y7Vuxp06ZN6u7uVjweV2Njo+9yAAAouq6uLj366KOrprufcukjdqakayS9QtIfFczP9xNJiyRdK+kmo6mlbEWjUdXX12vlypUaHBz0XQ4AABWjLFrEJPVKOk3SbektX2b2KUkPSvonSacrCGcoQ4sXL5Yk9ff30yoGAMAUlUWLmHPuTufcr8affnTOrZV0dXjzxJIXhpw0NTX5LgEAgIpSFkFsEqPh9ZjXKgAAAAqsXE5NZmRmcySdFd6ctKe9mT2UZdERBSsKAACgQMq9RexLCjrs/9o59xvfxWBidXV1SiaT6unp8V0KAAAVoWyDmJl9RNJFkp6QtGQq2zjnFme6hPtAkUWjUSUSCQ0NDRHGAACYgrIMYmb2b5K+LulxSa9xzr3guSRMUTweV0dHh+8yAACoCGUXxMzsAknflPSYghC21nNJyMPIyIjvEgAAKHtlFcTM7OOSrpS0QkEI+7vnkpCHeDyu2tpadXd3+y4FAICyVjZBzMw+raBz/kOSTnLOMUR7hYpGo+rs7FRtba36+vp8lwMAQNkqi+ErzOxsSZ+TtEPSfZI+kmFGo1XOuWUlLg15ikajam5u1rp163yXAgBA2SqLICapJbyeLemCLOvcI2lZSapBwaxdu1axWIxpjwAAyKAsgphz7jJJl3kuAwXW3NysjRs3qre3V5IIYwAAjFMWQQwzUyQSUXt7u8xMw8PDBDEAAMYpm876AAAA1YYgBgAA4AlBDEXnnNOWLVt8lwEAQNkhiKGoIpGI6uvrmX8SAIAMCGIoura2NnV0dGjTpk0aHGScXgAAUghiKIl4PK6GhgbfZQAAUFYIYiiZsbEx9ff3+y4DAICyQRBDSUSjUS1atEjJZJLJwAEACBHEUDLxeFyJRMJ3GQAAlA2CGEpudHTUdwkAAJQFghhKqq6uTrFYTMuXL/ddCgAA3hHEUFLRaFSdnZ2KxWKMKwYAqHoEMZRcNBpVc3Oz7zIAAPCOIAZvGOAVAFDt5vguANWpublZGzduVG9vrySpsbHRc0UAAJQeQQxeRCIRtbe3S5KGh4cJYgCAqsSpSXgTiUR8lwAAgFcEMQAAAE8IYvBuy5YtvksAAMALghi8ampq0tDQEGOKAQCqEkEMXqXmn9ywYQNDWQAAqg5BDN41NDSooaHBdxkAAJQcQQxlwTmn/v5+32UAAFBSBDF4F4lE1NnZqWQyqe7ubt/lAABQMgQxlIVoNKquri6Njo76LgUAgJIhiAEAAHhCEEPZqKmpUSwW0/Lly32XAgBASRDEUDYikYgSiYRisRh9xQAAVYEghrISiUS0aNEi32UAAFASBDEAAABPCGIAAACeEMRQlpLJpPr6+nyXAQBAURHEUHbi8bg6Ojq0evVqwhgAYEab47sAIJO2tjZJ0qpVq/wWAgBAEdEiBgAA4AlBDGUrGo1qaGhIPT09vksBAKAoCGIoW/F4XIlEQhs2bKCvGABgRiKIoaw1NDSotbXVdxkAABQFQQxlzzmn9evX+y4DAICCI4ihrEUiES1cuFDJZJL5JwEAMw5BDGUvGo2qq6tLo6OjGhwc9F0OAAAFQxBDRaipqVFDQ4PvMgAAKCiCGCrG2NiYent7aRUDAMwYBDFUhEgkokQioVgspv7+ft/lAABQEAQxVIxIJKLOzk6Njo76LgUAgIIgiAEAAHhCEAMAAPCEIIaKMzY2xpRHAIAZgSCGihKNRtXR0aHVq1cTxgAAFY8ghorT1tamjo4Opj0CAFQ8ghi8u+WWW3TwwQfr4IMP1o9+9KMpbRONRotcFQAAxUcQg1fPP/+8Lr30Uu211145b5tMJtXT01OEqgAAKA2CGLxxzumjH/2o9tlnHy1ZsiSnbePxuBKJhIaGhghjAICKRRCDN9ddd51+//vf68orr1RdXV3O28fjcXV0dBShMgAASoMgBi/++te/6vLLL9d5552n4447blr7GhkZKVBVAACUFkEMJTc2NqaPfOQjOvjgg/XJT35yWvuKx+Oqra1Vd3d3gaoDAKB0CGIouSuvvFKPPfaYvva1r6mmpmZa+4pGo+rs7FRdXR3jigEAKg5BDCX1yCOP6KqrrtIHPvABLV68uCD7rKmp0fz58wuyLwAASokghpJJnZJsbW3VJZdc4rscAAC8m+O7AFSPrVu3vnj6sKWlJeM6F198sS6++GK9733v02c/+9lSlgcAQMkRxFAyc+fO1bve9a6My3p6evTYY4+ps7NThx12WE6nLSORiGKxmFasWCFJam1tLUi9AAAUG0EMJVNTU6OvfOUrGZddccUVeuyxx3TmmWfq3e9+d877bmtrkxQEulgspsbGxmnVCgBAKRDEMC07d0r33is9+aQ0MiLNny+deKLU3Fz6WuLxuAYGBkp/YAAA8kQQQ142b5auuUa6+mrTU0/ZbsvMnN74RunDH3Y65ZTS1jU2NqY1a9bQIgYAqAh8axI5e+456fjjTR/72Kw9QpgkOSfddpupq2uWLrnEtHPn5Pu86KKLNDAwkNdpyZRoNKpFixYx/yQAoGIQxJCT9eul173O9NhjewawXVLLnK64wnTppROtW1ipycCZ9ggAUAkIYsjJxRebenunGqxMktOXv2y6//5iVgUAQGUiiGHKBgel//kfSXI5bBWEtv/6r9K1itXV1SmZTDL/JACg7BHEMGXXXy9t22badepxqpx++lPpb38rRlV7ikajSiQSSiaT9BUDAJQ1ghim7L778m3VMo2Omv74x4KWM6F4PK6Ojo7SHRAAgDwQxDBlw8PT237jxsLUkYtNmzaV/qAAAEwRQQxTVls7ve332qswdUxVPB5XLBbT8uXLS3tgAACmiCCGKVu0KN8tg879L3lJwUqZkmg0qs7OTsVisRcnGwcAoJyURRAzszPM7Cozu8/Mhs3MmdkPfNeF3Z13Xurbkrl8a1KSTImE0xFHFLqiyUWjUc2fP7/0BwYAYArKIohJulTShyQdLYnJAsvUwoXSySc75fatySC0ffCDuYY3AABmvnIJYh+VtFBSTNK/eK4FE1i61CkanWqoCkLbKac4nXFGMasCAKAylUUQc87d5Zz7q3OOZpMy194u/fznTrHYVE5TBqckb7rJafbsUlSXWX19vVavXk0/MQBA2SmLIIbKcuKJ0u9/7/TWtzrNyvIO2m8/p0svdbrjDqdYrKTl7aGtrU0dHR0aGBjQ4OCg32IAAEgzx3cBqEwveYn0k584PfecdP31Tr29pmRSmj9fes1rnP7pn6R583xXuUtzc7OeffZZ32UAALCbGRXEzOyhLIs8fF+vOhxyiHTppVLu36QsPeec1qxZo8bGRt+lAAAgiVOTqBKRSESLFi3S0NAQ808CAMrGjGoRc84tznR/2FJ2TInLQZmJx+NKJBKMtA8AKBu0iKGq1NXVqaGhwXcZAABIIoihCo2Njam7u9t3GQAAEMRQXVLzTyaTScIYAMC7sugjZmZvlfTW8OYB4fUrzWxZ+POgc+5jJS8MM1I0GlUikSCIAQACQljrAAAgAElEQVS8K4sgpmCOybPH3dcaXiTpGUkEMSAHa9as0dKlS3XXXXdpaGhI8XhcXV1duvDCC1VfX++7PACAyuTUpHPuMuecTXA51HeNQCV55pln1NXVpRtvvFEdHR06//zztWDBAl177bV685vfrKGhId8lAgBUJkEM8GFkZGTGTnn0yU9+UoODg/r85z+v7373u/rUpz6lm2++Weeff76efvppffnLX/ZdIgBABDFUqXg8rpaWFq1cuXLGhbFnn31W99xzjw455BCdc845uy276KKLVFdXp1tuuUVbt271UyAA4EUEMVStxYsXq6WlRWvWrPFdSkHdf//9kqQTTjhBs8bNyr733nvr2GOPVTKZ1MMPP+yjPABAGoIYqtpM7LT+9NNPS5JaW1szLm9paZEk9fX1lawmAEBmBDFUvaGhoRkVSjZt2iQpGKYjk1gsJknauHFjyWoCAGRWLsNXAF60tbVJklasWCEpeyvSTOKckySZmedKAAAEMVS9trY2bdy4Udu3b/ddSkGkWsJSLWPjpe5PtYwBAPzh1CQQ2rJli+8SCuKwww6TlL0PWH9/v6TqaP0DgHJHEAMkNTU1aWhoSD09Pb5Lmbbjjz9eknTPPfdo586duy3bvHmzuru7VVNTo2OOOcZHeQCANAQxQMG4YolEQhs2bKj4ccWam5t1wgkn6LnnntOyZct2W3bFFVdo69atOvPMM1VXV+enQADAi+gjBoQaGhrU0NDgu4w9bd+umttv17z77pNt2CDNm6ex1lZtfcc7tLOpKeMmX/ziF3Xaaafp05/+tO6//34dfvjhevjhh7V8+XK1trbq4x//eIkfBAAgE4IYkMY5p/7+fjU2NvouRdq+XXtfdZXqbrhBs9et22Px3ldeqW2nnKJNl1yisSOP3G1Zc3Ozbr/9di1dulR333237rzzTu2///4677zzdOGFF2r+/PmlehQAgAkQxIBQJBJRZ2enHnzwQXV3d+vYY4/1Vott2aJ9zj1X88JR8jPauVM1v/mN5t5/v4auu07bE4ndFh900EG68sori1wpAGA66CMGpIlGo+rs7NTo6Ki/Inbu1Px/+RfNu/9+uQlWS40CNmvLFu3z3vdqzgz4ogEAVBuCGFBm5v3mN6r53/+V066wNZlZW7cqdtllRawKAFAMBDGgzOwVftMxl3HvnaR5DzygOb29xSgJAFAkBDEggx07dniZf3L2qlWad999E56SzCQV2up+8INClwQAKCKCGDBONBpVS0uLBgYGSh7GUi1a+c4COefJJwtXDACg6AhiQAaLFy9WS0uL1q9fX9LjWjI5ve23bi1QJQCAUiCIAVk0ZRkstZhcOGF3vnYykTcAVBSCGDCBZDJZ0vknt7/sZXJz5+bcR+zF7V/xioLWAwAoLoIYkEU8HldHR0dJJwN3++6r5JvfnHMfMSfJRSJKvutdxSgLAFAkBDFgAm1tbero6CjpMbe+972SlFOrmEkaedObtHO//YpSEwCgOAhiwBSMjIyU7FijHR3adMEFMk09jI0deqiGP/e5YpYFACgCghgwiWg0qmQyqe7u7pIdc/PFF2vzhz704inKiQLZ6OGH64Ubb9TOffctRWkAgAIiiAGTiMfjSiQSGhkZKd24Ymba9KlPaf2NN2rk9a+XZu35UR1rbtbwpz+t9bfeqh2HHFKaugAABTXHdwFAJWhoaFBra6u2bdtW0uNuf/Wrtf3Vr9as1as1b/ly2caN0rx5Gmtp0fbjj88Y0AAAlYMgBlSAnU1NSr797b7LAAAUGP9OAwAAeEIQA6bIOae1a9dqcHDQdykAgBmCU5PAFEQiEbW3t0uSesOJuRsbG32WBACYAQhiwBRFIhEtXLhQmzdv9l0KAGCG4NQkkKMdO3ZoeHjYdxkAgBmAIAbkIBqNasGCBRoYGCjdmGIAgBmLIAbkqK2tTUcffbTWr1/vuxQAQIUjiAF5iEajvksAAMwABDEgD3V1dUomk+rp6fFdCgCgghHEgDxEo1ElEgkNDQ0RxgAAeSOIAXlKTQYOAEC+CGLANI2MjPguAQBQoQhiwDSk+op1d3f7LgUAUIEIYsA0RKNRdXV10XEfAJAXghgwTdFoVB0dHb7LAABUIIIYAACAJwQxAAAATwhiQIFs2LBBg4ODvssAAFQQghhQAM3NzWppadHKlSsJYwCAKZvjuwBgJohEImpvb5eZaXh4WI2Njb5LAgBUAFrEgAJyzvkuAQBQQQhiQIFEIhHV19dr9erV6uvr810OAKACcGoSKKC2tjZJUk9Pj2KxGKcoAQATIogBBRaPxzUwMOC7DACYkqGhId1+++363e9+p5UrV2rt2rWaO3eujjjiCL3jHe/QO97xDs2axQm0YiGIAUUwNjamNWvW0CIGoOzdeuut+sQnPqH9999fxx9/vA4++GCtW7dOt99+uz72sY/prrvu0re//W2Zme9SZySCGFBg0WhUixYt0r333quenh699KUv9V0SAGTV2tqqZcuW6aSTTtqt5esTn/iETj31VN1222369a9/rVNPPdVjlTMXbY1AEcTjcSUSCY2MjPguBQAmdPzxx+uUU07Z4/Tj/vvvryVLlkiSHnjgAR+lVQWCGAAAyCgSiUiS5szhBFqxEMQAAMAexsbGdMstt0iSTjzxRL/FzGAEMaCIRkdHmfIIQEW6/PLL9cQTT+i1r30tQayICGJAkTQ0NCgWi6m3t5cwBqCiXHfddfr2t7+ttrY2XXXVVb7LmdEIYkCRRCIRJRIJxWIxrVmzxnc5ADAly5Yt02c+8xktXLhQN998s+bPn++7pBmNIAYUUSQSUXNzs+8yAGBKrrnmGv3Hf/yHjjjiCN18883af//9fZc04xHEgBLYsGED808CKGvf+ta3dNlll+moo47SzTffzIDUJcL3UYEia2tr08aNG9Xf3y8pGDwRAMrJ1772NS1dulTt7e368Y9/zOnIEiKIASWwePFiSdL27ds9VwKgaoyOSmbSJGOA3XzzzVq6dKlmz56tV7ziFbruuuv2WOeQQw7R29/+9mJVWtUIYgAAzBBzHntMe11/vWpuvVWzNm6UJO3Ybz8l3/Y2bT3rLO3I0CL/7LPPBuvt2KFrrrkm435f+cpXEsSKxJxzvmsoOjN76JRTTjnmjjvu8F0KqthTTz2lRx55RE1NTZyeBFBQ9sIL2uff/k3z7rlnt/udpPSpupNve5s2fOUrUm1tSeubibq6uvToo48+7JxbPJ390CIGlEhbW5skacWKFYrFYnSEBVAQtn69Gt/2Ns156qk9glf6z05S7c9+ptkDA1r/4x8TxsoE35oESqi5uVkNDQ2+ywAwUzinfd7/fs156ilJuwev8UxBGJv74IOq/8QnSlEdpoAgBpSYc44BXgEUROTBBzXvD3/QVDsZpcJY7S23aPZzzxWxMkwVQQwooUgkokWLFmloaEg9PT2+ywFQ4fZatkzSxC1h45kkc0513/9+MUpCjghiQInF43ElEglt2rTJdykAKtm2bar59a+n3Bo2Xs3PflbQcpAfghjgQV1dne8SAFS4WUNDstHRnFrD0s3++9+lKhg5odwRxAAAqETTDVGEsLJAEAM8Ghwc9F0CgAq1c5995GbPzvvU5M799gtG3odXBDHAg5qaGi1YsEC9vb2EMQD5qanRyOtfn/epyeRppxW0HOSnbIKYmTWZ2XfN7Hkz22Zmq8zsa2a2j+/agEKLRCJqb2/XggULXpwMHABytfXss3PeJtWCtnXJksIWg7yURRAzs8MkPSTpXEkPSrpSUp+kf5f0gJnt67E8oCgikYiampp8lwGggm3/x3/U9o6OnLYxSck3vSnjvJMovbIIYpL+S9L+kj7inHurc+4TzrnXKghk/yDpC16rA4poZGREfX19vssAUInMNHTddRo75JBJV021hG1vb9fGr361uHVhyrwHMTNrlfQ6SaskfWvc4v+UtEXSEjPbq8SlAUUXj8d19NFHa2BggDAGIC87DzhA63/5S21fPPHc0yZp5OST9cLNN8vtvXdpisOkvAcxSa8Nr/+fc25n+gLn3CZJv5dUJ+m4UhcGlEJbW5uOPvpobdmyxXcpACrUznhc63/5S63/6U+VPO00uUhk17LaWm1997u17o47NHTDDXLRqMdKMd4c3wUoOPUoSb1Zlv9VQYvZQkm/m2hHZvZQlkVH5FcaAAAVwkzbjztO2487TtqxQ7ZxozRrllwsJs0qh3YXZFIOr0x9eL0xy/LU/fNLUAvgDfNPAiiY2bPlGhrk5s8nhJW5cmgRm0xqiJRJx6xzzmU8QR62lB1TyKKAQmpra5MkrVixQn19fWrl20wAUBXKIYilWrzqsyyPjVsPmJHa2to0PDysbdu2+S4FAFAi5dBe+WR4vTDL8sPD62x9yAAAACpSOQSxu8Lr15nZbvWYWVTS8ZKSkv5Q6sIAAACKyXsQc849Len/STpU0r+NW/xZSXtJusE5x3f7MeM557R27VrfZQAASsR7EAv9q6S/S/qGmf3czL5oZndK+qiCU5L/4bU6oEQWLlyoWCym5cuX+y4FAFACZRHEwlaxl0taJukVki6SdJikb0h6pXNuvb/qgNKJRqPq7OxUfX29BgcHfZcDACiycvjWpCTJOfecgkm/gapWU1PjuwQAQImURYsYgN3V19dr5cqVtIoBwAxXNi1iAAKRSETt7e2SpN7eXjU2NnquCABQLLSIAWUoEolo4cJsQ+sBAGYKghhQxsbGxtTX1+e7DABAkRDEgDIVjUbV0dGh1atXE8YAYIYiiAFlrK2tTR0dHVq/nhFcAGAmIogBZS4ajfouAQBQJAQxoAIkk0n19PT4LgMAUGAEMaDMxeNxJRIJDQ0NEcYAYIYhiAEVIB6Pq6Ojw3cZAIACI4gBAAB4QhADAADwhCAGVJBNmzb5LgEAUEAEMaBCNDc3KxaLafny5b5LAQAUCEEMqBCRSESJREL19fWMtA8AM8Qc3wUA1eLWW2/VH/7wB/3lL3/R448/rs2bN+v000/XVVddldN+5s+fr23bthWpSgBAKRHEgBL5+te/rscff1x77bWXDjzwQD311FM57yMSicg5p4GBAcViMTU2NhahUgBAqRDEgBK57LLLdNBBB+nQQw/VAw88oDPPPDOv/SxevFiS1NvbK0mEMQCoYAQxoESOP/74gu1r4cKF2rx5c8H2BwDwg876QIUaGxvT8PCw7zIAANNAEAMqUDQaVXNzs1avXs03KAGgghHEgArV1tamjo4OrV+/3ncpAIA8EcSAChaNRn2XAACYBoIYUOGSyaR6enp8lwEAyANBDKhg8XhciURCQ0NDhDEAqEAEMaDCxeNxdXR0+C4DAJAHghgAAIAnDOgK5GnLFumuu6TBQWn2bKmpSUokgp8zueOOO3THHXdIktatWydJ+tOf/qQLLrhAktTQ0KDPfOYzJakdAFAeCGJAjp56SvrWt0zXXy9t3Gi7LVuwwOkDH3B6//ulfffdfbu//OUvuvnmm3e779lnn9Wzzz4rSWpqappWENu0aZMGBweZ8ggAKog553zXUHRm9tApp5xyTKo1AsjXT34iLVli2rbNJlzvoIOcbr3V6WUvK01do6OjuvfeezU8PKyFCxcSxgCgyLq6uvToo48+7JxbPJ390EcMmKJf/lJ65zsnD2GS9PzzppNPNoXzchddJBJRIpFQLBZj2iMAqCAEMWAKNmyQzjrLtHPn5CEs5YUXTEuWmErV6ByJRDR//vzSHAwAUBAEMWAKbrhB2rRp6iEs4PSnP5kefLAoJWVUX1+vgYEB5p8EgApBEAMm4Zx09dW5hjBJCrb5r//KZ9v8tLW1qaWlRQMDAxocHCzZcQEA+eFbk8Ak1qyRnnwy/zB1992Fq2Uq2tvbtXHjxtIeFACQF1rEgEls2OB3+3zU19drzZo1pT8wACAnBDFgErW109u+rq4wdUxVJBJRfX09808CQAUgiAGTOOggKRrN/6uP//APBSxmitra2tTR0fHiIK8AgPJEEAMmMW+etGRJ/tu/731+Bk2Ox+NqaGjwcmwAwNQQxIAp+OAHU2Eqt1DV2Oh0xhmFrwcAMDMQxIApOOoo6V//1SkYkmIqYSxYZ+lSp5qaYlYGAKhkBDFgiq680umd70yFsWxSIc30f//vTp11VgkKm8DY2Jj6+/v9FgEAyIogBkzRnDnS97/vtHTpTh10ULZWMVN7u9Mtt+zURReVtLw9RKNRdXZ2qra2Vt3d3X6LAQBkxICuQA5mzZIuvFD68IedfvUrp5//3LRunTR7ttTUJC1Z4vSqV0lWusH0JxSNRrVo0SKCGACUKYIYkIdIRDr9dOn00/18IzJXo6OjGhwcVGNjo+9SAABpODUJzHANDQ1asGCBent7GVMMAMoMLWLADBeJRNTe3i5JWrNmDa1iAFBGaBEDqkBq2iMAQHkhiAFVZMOGDerr6/NdBgAgxKlJoEq0tbVJklasWCFJam1t9VkOAEAEMaCqtLW1aePGjdq+fbvvUgAA4tQkUJW2bNniuwQAgAhiQNVpamrS0NCQenp6fJcCAFWPIAZUmXg8rkQioQ0bNjCuGAB4RhADqlBDQ4MaGhp8lwEAVY8gBgAA4AlBDAAAwBOCGFClnHPq7e31XQYAVDWCGFCFIpGIEomEYrGYli9f7rscAKhaBDGgSkUiEXV2dvouAwCqGiPrAxXmC1/4gv785z+rr69PL7zwgmpqatTU1KSuri6de+652meffXLa344dOzQ4OKjGxsYiVQwAyIYWMaDCfOc739HWrVuVSCT0vve9T6effrrmzJmjK664QieddJKef/75Ke+rpqZGLS0tWrlyJWOKAYAHtIgBFaa3t1fz5s3b4/4vfelLuuqqq3TVVVfpi1/84pT2FYlE1N7eLknq7++nVQwASowWMaDCZAphknTaaadJCgJVLiKRiJqamqZdFwAgdwQxYIb47W9/K0k68sgj89o+mUyqr6+vkCUBACbBqUmgQl199dXasmWLhoeH9eijj+rBBx/UkUceqQ996EM57ysej6ujo0OPPPKIJKm1tbXQ5QIAMiCIARXq6quv1rp16168/ZrXvEZXXnml9t1337z219bWJklatWpVIcoDAEwBpyaBCrVixQoNDAxoxYoVuvbaa/XMM8/oda97nXp6enyXBgCYIoIYUOH2228/veENb9CPf/xjDQ0N6SMf+YjvkgAAU0QQA2aIpqYmLVy4UL29vXrhhRfy3s/IyEgBqwIATIQgBswgf/vb3yRJs2fPzmv7eDyuZDKp7u7uQpYFAMiCIAZUkKeeekp///vf97h/586d+tKXvqTBwUG9/OUvV319fV77j0aj6urq0sjICENZAEAJ8K1JwKPRUemXv5R+8xvTCy9Ic+dKra3S2Wc7HX74nuvfdddd+vznP6/jjjtOhx56qPbZZx+tW7dODzzwgJ599lntt99+Wrp06bRqqqmpUWtrq7Zt2zat/QAAJkcQAzwYG5OuuEL65jdNzz9veyz/4hdNp5zi9PnPOx177K77X/3qV+s973mPuru79fjjj2t4eFi1tbU67LDDdMYZZ+i8887T/Pnzp12fc05r165VLBZj2iMAKCLvQczMIpL+VdLRkjokvURSRNL7nXPX+qwNKIaREentbzfddtueAWwXp9/+1nTvvdKPfuT01rcG9x5xxBG6/PLLi1pfav7JDRs2qLe3V5IIYwBQJOXQR2wvSV+TdI6kAySt9VoNUETOSeeemwphboI1g5C2bZvpXe8y3XdfScp7USQSUWdnpxoaGkp7YACoMuUQxLZKeqOkg5xzB0j6rud6gKK56y7ppptSIWyiFrFdtm83XXCByU2U24pkx44dpT8oAFQR70HMObfdOXe7c26N71qAYvvv/06Fr6mFsIDTihWmP/6xGBVlF41GVV9fr5UrV2pwcLC0BweAKuE9iAHV4m9/k37xC2niU5KZBKHtO9/JJbwVxuLFi9XS0qL+/v6SHxsAqoH3zvqFZGYPZVl0REkLATJ48klpx478w9TjjxewmBw0NTVpzRoarAGgGGgRA0pk69bpbb9lS2HqyFVdXZ2SySQDvAJAERSkRczMVklqzmGTHzrn3lOIY6dzzi3OdH/YUnZMoY8H5CLPwe4Ltn2+otGoOjo69Mgjj0iSWltb/RQCADNQoU5NPi0pl5mCny/QcYGK0d4uxWJOw8P5nZ589asLXFAO2traJElPPPEEQQwACqggQcw5d1Ih9gPMZHvtJZ11lvTNb+a6pZOZdP75HsavSBONRr0eHwBmIvqIASX0wQ86meX+rck3vlFqaSlKSQAAjwhiQAkdeaS0dGkqiE0tkDU1Of33f/ttDQMAFEdZDF9hZp/QriEmjg6vzzWzfwx/vp95JzFTXHCBNDq6U5/8ZOr/oOyj7Le2Ot12m9PBB5esvKzq6upUW1ur7u5uHZs+EzkAIG/l0iLWJens8PKy8L5Xpd33j1m2AyqOmXTJJdJ99+3U29/uNCfDv0PNzU5f+MJOPfig08KFpa8xk2g0qs7OTtXW1qqnp8d3OQAwI5RFi5hz7kTfNQCl9qpXSa96ldOaNdKddzq98II0d67U2iq99rXS7Nm+K9xTNBpVc3OzVq1a5bsUAJgRyiKIAdXswAOlf/5n31XkZtOmTRocHFRjY6PvUgCgohHEAOSkublZGzduVG9vryQRxgBgGghiAHISiUTU3t4uM9Pw8DBBDACmoVw66wMAAFQdghiAnEUiEcViMQ0MDDAZOABMA6cmAeQlNf9kT0+PYrEYpygBIA+0iAHIWzweV0NDg+8yAKBiEcQAAAA8IYgBAAB4QhADMC1jY2Pq7+/3XQYAVCSCGIC8RaNRLVq0SMlkUt3d3b7LAYCKQxADMC3xeFyJRMJ3GQBQkQhiAApidHTUdwkAUHEIYgCmra6uTrFYTMuXL/ddCgBUFIIYgGmLRqPq7OxULBZTT0+P73IAoGIQxAAURDQaVXNzs+8yAKCiEMQAFNSGDRs0ODjouwwAqAgEMQAF09zcrJaWFq1cuZIwBgBTwKTfAAomEomovb1dkjQ8PMxE4AAwCVrEABRUJBLxXQIAVAyCGICCq6+v18DAgPr6+nyXAgBljVOTAAqura1NkrRixQrFYjFOUQJAFrSIASiK5uZmNTQ0+C4DAMoaQQwAAMATghgAAIAnBDEAReOcU39/v+8yAKBsEcQAFEUkElFnZ6eSyaS6u7t9lwMAZYkgBqBootGourq6NDo66rsUAChLBDEAAABPCGIAiqqmpkaxWEzLly/3XQoAlB2CGICiikQiSiQSisVi9BUDgHEIYgCKLhKJaNGiRb7LAICyQxADUDIjIyMaHBz0XQYAlA2CGICSiMfjamlp0cqVKwljABBi0m8AJbN48WJJ0po1a5gIHABEixiAEquvr/ddAgCUDYIYAACAJwQxAAAATwhiAEoqGo1qaGhIPT09vksBAO8IYgBKKh6PK5FIaMOGDerr6/NdDgB4RRADUHKpoSwAoNoRxAB4s379et8lAIBXBDEAXixcuFDJZJL5JwFUNYIYAC+i0ai6urqY9ghAVSOIAfCmpqZGDQ0NvssAAG8IYgC8cs6pt7eXVjEAVYkgBsCbSCSiRCKhWCym3t5e3+UAQMkRxAB4FYlE1NnZ6bsMAPCCIAagLOzYsYMBXgFUHYIYAO+i0ahaWlo0MDBAGANQVQhiAMrC4sWL1dLSwiCvAKoKQQxA2WhqavJdAgCUFEEMAADAE4IYAACAJwQxAGUlmUyqp6fHdxkAUBIEMQBlIx6PK5FIaGhoiDAGoCoQxACUlXg8ro6ODt9lAEBJEMQAlKWRkRHfJQBA0RHEAJSdeDyu2tpadXd3+y4FAIqKIAag7ESjUXV2dqquro6R9gHMaAQxAGWppqZG8+fP910GABQVQQxA2XLOae3atRocHPRdCgAUxRzfBQBAJpFIRO3t7ZKk3t5eSVJjY6PPkgCg4AhiAMpWJBLRwoULtXnzZt+lAEBRcGoSAADAE4IYAACAJwQxAGVvbGxMa9as8V0GABQcQQxAWYtGo1q0aBHzTwKYkQhiAMpeajJwpj0CMNMQxAAAADwhiAGoCHV1dUomk8w/CWBGIYgBqAjRaFRdXV1KJpP0FQMwYxDEAFSMaDSqjo4O32UAQMEQxABUnE2bNvkuAQAKgiAGoKLE43HFYjEtX77cdykAMG3eg5iZHW5mHzezO83sOTPbbmZ/M7NfmNlrfNcHoLxEo1F1dnYqFoupr6/PdzkAMC3eg5ikz0v6kqS4pF9LukLS7yWdKulOM/uIx9oAlKFoNKr58+f7LgMApq0cgtgdko5xzh3lnPuAc+6TzrnTJZ0kaVTSUjM70G+JAMpNfX29BgYGNDg46LsUAMib9yDmnFvmnHskw/33SLpb0lxJryp1XQDKW3Nzs1paWrRy5UrCGICKNcd3AZMYDa/HvFYBoOxEIhG1t7fLzDQ8PKzGxkbfJQFAzso2iJlZs4LTk1sl3TvFbR7KsuiIQtUFAABQKGUZxMxsnqQfSpon6RLn3JDnkgAAAAquIEHMzFZJas5hkx86596TZV+zJX1f0vGSbpT0lanu1Dm3OMs+H5J0TA71AagQzjlt2bLFdxkAkJdCtYg9LWkkh/Wfz3RnGMJ+IOlMSTdJeo9zzk2/PAAzUSQSUVNTk/r6+tTT06OXvvSlvksCgJwUJIg5506a7j7MbI6kHykIYT+SdJZzbsd09wtgZovH40okElq+fLkGBwfptA+gopRFHzEzm6ugBewtkm6QdK5zbqffqgBUirq6OjU0NPguAwBy5n0csbBj/s8UhLDrRAgDkIexsTH19/f7LgMAclIOLWJXS3qjpEFJA5I+Y2bj17nbOXd3iesCUCFS80/ecccd6u7u1rHHHuu7JACYknIIYi3hdaOkz0yw3t3FLwVApYzx8FwAABaFSURBVIpGo0okEuru7vZdCgBMmfcg5pw70XcNAGaO0dHRyVcCgDLhvY8YABRKQ0ODYrGYli9f7rsUAJgSghiAGSMSiSiRSCgWi6mnp8d3OQAwKYIYgBklEomouTmXiT4AwB+CGAAAgCcEMQAAAE8IYgBmpKGhIfX19fkuAwAm5H34CgAotLa2NknSI488IklqbW31WQ4AZEUQAzAjtbW1aePGjdq+fbvvUgAgK05NApjRtmzZ4rsEAMiKIAZgxmpqatLQ0BBjigEoWwQxADNWPB5XIpHQhg0bNDg46LscANgDQQzAjNbQ0KCGhgbfZQBARgQxADOec079/f2+ywCAPRDEAMxokUhEnZ2dqq2tVXd3t+9yAGA3BDEAM140GlVnZ6dGR0d9lwIAuyGIAagqdNoHUE4IYgCqQk1NjRYsWKDe3l7CGICywcj6AKpCJBJRe3u7JKm/v1+NjY2eKwIAWsQAVJFIJKKmpibfZQDAiwhiAAAAnhDEAAAAPCGIAag6yWSS+ScBlAWCGICqEo/H1dHRwWTgAMoC35oEUHXa2tokSatWrfJbCICqR4sYgKo1MjLiuwQAVY4gBqAqRaNRJZNJ5p8E4BVBDEBVisfjSiQSGhkZUV9fn+9yAFQpghiAqtXQ0KDW1lbfZQCoYgQxAFXNOae1a9f6LgNAlSKIAahakUhECxcuVCwW0/Lly32XA6AKEcQAVLVoNKrOzk41NDRocHDQdzkAqgxBDAAAwBOCGAAAgCcEMQBVr6amRjt27NDw8LDvUgBUGYIYgKoXiUS0YMECDQwMMKYYgJIiiAGAgvknjz76aIayAFBSBDEACMXjcd8lAKgyBDEASDM2Nqaenh7fZQCoEgQxAAhFo1ElEgkNDQ0RxgCUBEEMANKkTwYOAMVGEAMAAPCEIAYA49TV1SmZTKq7u9t3KQBmOIIYAIwTjUbV1dWlZDJJXzEARUUQA4AMotGoOjo6fJcBYIYjiAHABDZt2uS7BAAzGEEMALJobm7W/2/v7oPsruo7jr+/CVezIXcXlqWXKYGQ7Q1Qu41sUxcBZ0HQNq3TKkjHPxqeKmotHdqCY1udatsZW1qrLdVW+2C1PjCVyohTaJVaRLEZ253o2nVAFpIssiGIG3bzsOySbDj9495tY7Kb7GZ377n37vs1k7m5v/swn/wmk/3k/M7vnNbWVrZu3Zo7iqQmZRGTpFkUCgV6e3tpa2tzD0pJS8IiJkkncNppp+WOIKlJWcQkSZIysYhJ0gmklHJHkNSkLGKSdByFQoG2tjaGh4edJyZp0Z2SO4Ak1btyuQzAwMAAra2tdHR0ZE4kqVk4IiZJc1AqlWhvb88dQ1KTsYhJ0hxNTU2xe/fu3DEkNRGLmCTNQbFYpKuri9HRUfeflLRoLGKSNEelUone3l4mJydzR5HUJCxikiRJmVjEJGkeVq9ezcTEBH19fbmjSGoCFjFJmodiscjmzZuZmJhwrpikBXMdMUmap2KxSHd3N0NDQ7mjCLj44osZHh6e8bUzzzyT/v7+GieS5s4iJklqeK2trdx8883HHD/11FMzpJHmziImSWp4ra2t3H777bljSPPmHDFJOkljY2PuPylpQRwRk6STUC6X2bt3Lzt37gSgs7Mzc6Ll7eDBg9xzzz3s2rWL1atX87KXvYyLL76YlStX5o4mHZdFTJJO0qZNm4BKCVBezz77LLfeeusPHTv33HP54Ac/yCWXXJIplXRiXpqUJDW0N73pTdx999309/fzxBNP8OCDD3Ldddfx1FNPsWXLFh555JHcEaVZWcQkaQHa2toYHh52rlhGt912G5dddhlnnnkmLS0tXHDBBdxxxx289a1vZXJykg984AO5I0qzsohJ0gKUy2W6u7vZtWsXIyMjuePoCNdffz0A3/jGNzInkWZnEZOkBVq3bh3t7e25Y+goZ5xxBgDPP/985iTS7CxikrQIUkrs3r07dwwdYdu2bUClKEv1yiImSQtUKBTo6upidHTU/Sdr7LHHHmNsbOyY48PDw7z73e8G4Jprrql1LGnOXL5CkhZBqVSit7eXrVu35o6yrNx33318+MMf5rLLLuOcc85hzZo1PPnkk3z5y1/mhRde4Morr+Ttb3977pjSrCxikrRIVq9enTtCY0uJwje/yepPfYrCwAAxPk5as4ZDF13E+PXXM7Vx4zEfufTSS9m+fTvf+c532LZtG88//zytra309PRw7bXX8sY3vpGIyPCHkebGIiZJi6i1tZW+vj5e8YpX5I7SUArf/jZt73wnhRku7RYeeYTVd93FwU2b2Pv+9zN14YX/99oll1zigq1qaNnniEXEORHx1xHxXxHxTES8EBFPR8TDEXFTRBRyZ5SkuSgWi/T09NDS0kJfX1/uOA3jJV/7Gu3XXENhYIA0y3sS8JJt2zjj9a+n4LlVE8lexIAfA34Z2AvcC3wA+BdgHfAPwAMR4cidpIZQLBbp6urKHaNhnPL445z+5jezYmICgNkuIk4fX7F/P+033MDKp56qST5pqdVDwdkKnJ5SevHIg9WRsAeAK4BrgLtrH02StJTW3HknK8bH5/WZFWNjnPqRj7Dvj/5oiVJJtZN9RCyldPDoElY9fojKCBnAhtqmkiQttRUjI6y6775ZL0ceT8vnPkccOLDomaRay17EZhMRK4Gfrz79n5xZJGm+Jicn3X/yBFbdey9x8OCslyOPZ8WBA6y6//5FzyTVWj1cmgQgIjqAX6cyFeBM4LVAGbgLuG+O37FtlpcunOW4JC26UqnERRddRH9/PwCdnZ2ZE9Wnhc7zcp6YmkHdFDGgA3jvEc8T8GfAu1JKJzNyLUnZlMtlAIaGhvIGqWNx8ODCPn/o0CIlkfJZlCIWEUNU7nKcq8+klLYceSCl9N3KV8VK4GzgauAPgVdFxOtSSs+d6EtTSptmybcN+Kl55JMkLbEXTz99YZ8/7bRFSiLls1hzxLYDj83j19OzfVFK6XBK6XsppTuBtwGvpFLIJKmhFItF9588jhde8xqAeU/Wn37/9OelRrYoI2IppasW43tm8G/VxyuW6PslaclM7z/58MMPs2PHDueKHeVQdzeHfvInZ1xN/3gCeOFVr2JqgzfUq/HV7V2TVWdXH6eyppCkk1QqlVi/fn3uGPUpggNvexsw91Gx6feNv+UtSxJJqrXsRSwiLo6IY3bKjYg1wJ3Vp96jLKmh7dmzJ3eEujR59dWM33ADwYnLWKIyGnbgllt44bWvXfpwUg3Uw12TvwtcERFfBb4HPA+cA/wccBqVlff/OF88SVqYtWvXsmPHDjcDn0kE+973PlJLC2s++tHjvxXYf/vtHLjtttpkk2og+4gY8HdURrx+HLgeuA14DbCNymT9y1NKLp8sqWFNzxWbnJxkZGQkd5z6s2IF+9/zHn7wwAOMb9nCiy0tP/Tyi2vWMH7TTfzgoYc4cPvtECezBKxUn7KPiKWU7sdLj5KaXHt7O+3t7blj1LWpri72/emfsv897+GU7duJ8XFeXLOGw+UyafUxM1ikppC9iEnScpFSYnBwkI6OjtxR6lpas4ZDL3957hhSTdTDpUlJanqFQoGenh5aW1vp6+vLHUdSnbCISVKNFItFenp6OOTWPJKqLGKSJEmZWMQkSZIysYhJUo1NTU2xY8eO3DEk1QGLmCTVULFYpLu7m+HhYcuYJIuYJNVauVymu7vbbY8kWcQkKYdisZg7gqQ6YBGTpEwmJiYYGBjIHUNSRhYxScpgev/J0dFRy5i0jFnEJCmTUqlEd3d37hiSMrKISVJmk5OTuSNIysQiJkkZlUolJiYm3H9SWqYsYpKUUbFYZPPmzUxOTrqumLQMWcQkKbNVq1bR2dmZO4akDCxikiRJmVjEJEmSMrGISVJmhUKBlBK7du1iZGQkdxxJNXRK7gCSJNi0aRMAg4ODAHR0dOSMI6lGLGKSVCfOP/98Dhw4kDuGpBry0qQk1ZGpqSn27duXO4akGrGISVKdKBaLrFu3juHhYdcUk5YJi5gk1ZFyuUx3dzd79uzJHUVSDVjEJKnOFIvF3BEk1YhFTJLqzOrVq5mYmGBgYCB3FElLzCImSXWmWCzS29vL6OioZUxqchYxSapDpVKJ7u7u3DEkLTGLmCTVscnJydwRJC0hi5gk1alSqURLSwt9fX25o0haIhYxSapTxWKRnp4eWlpaXFdMalIWMUmqY9OLvI6Pj+eOImkJWMQkSZIysYhJkiRlYhGTpAYwNjbmPDGpCVnEJKnOlctl1q9fz65duxgZGckdR9IiOiV3AEnSiW3cuJGIYN++fXR0dOSOI2mROCImSQ0ipeTdk1KTsYhJUgMoFAq0tbW5/6TUZCxiktQgyuUy3d3d7N+/37liUpOwiElSAymVSrS3t+eOIWmRWMQkqcFMTU2xc+fO3DEkLQKLmCQ1kGKxSFdXFxMTE24GLjUBi5gkNZhSqURvb2/uGJIWgUVMkiQpE4uYJElSJhYxSWpQhw4dchkLqcFZxCSpAbW3t3PuuecyODhoGZMamHtNSlIDKhQKbNy4EYDdu3e7/6TUoBwRk6QGNb3tkaTGZRGTpAY3NjbGjh07cseQdBK8NClJDaxcLgPQ398PQGdnZ844kubJIiZJDa5cLrN3714OHjyYO4qkefLSpCQ1ifHx8dwRJM2TRUySmsDatWsZHR1lYGAgdxRJ82ARk6QmML3/5NjYmOuKSQ3EIiZJTaK9vZ329vbcMSTNg0VMkppISomdO3fmjiFpjixiktQkCoUCPT09TExM0NfXlzuOpDmwiElSEykWi2zevJlDhw7ljiJpDixikiRJmVjEJEmSMrGISVITOnz4sMtYSA3AIiZJTWbVqlWsX7+eRx991DIm1Tn3mpSkJlMoFNi4cSMAO3fupKOjI3MiSbNxREySmlChUGDt2rW5Y0g6AYuYJDWxiYkJduzYkTuGpFlYxCSpSZVKJbq7uxkeHraMSXXKOWKS1MTK5TIAQ0NDeYNImpEjYpIkSZlYxCSpyRWLRUZHRxkYGMgdRdJRLGKS1ORKpRK9vb2MjY05V0yqMxYxSVoG2tvb6ezszB1D0lEsYpIkSZnUZRGLiI9FRKr+KufOI0mStBTqrohFxC8AvwIcyJ1FkppFoVAgpcQzzzzj/pNSHamrIhYRZwJ/B3wW2JY5jiQ1lY0bN9La2srg4KBlTKoTdVXEgL+tPt6SNYUkNaFCoUBvby/t7e25o0iqqpuV9SPiRuANwNUppT0RkTmRJDWnw4cP544gqaouRsQiYh1wJ/DplNK9ufNIUrMqFAq0tbXx6KOPenlSqgORUsobIGIF8CCwAehKKY1Wjz8EXA5sSCk9Mcfvmm1e2cvPO++8lRs2bFiExJLU+M4++2wGBwc5cMD7oqST8fjjjzMxMfFcSumMhXzPolyajIghYN08PvKZlNKW6u9/i0rhet10CVsCK4aGhg4PDQ19e4m+X3Bh9fG7WVM0P8/z0vMc14bneel5jpfWecC+hX7JYs0R2w5MzuP9TwNExAbgfcDHU0r/utAQKaVNMx2fHimb7XUtnOe4NjzPS89zXBue56XnOW4Mi1LEUkpXneRHfwJ4KXBTRNw0y3ser07cv9r5Y5IkqZnkvmtyCPjYLK+9DjgL+GcqQ39DtYkkSZJUG1mLWEqpH7h5pteqk/XPAt4118n6kiRJjaQulq+QJElajixikiRJmWRfR0ySJGm5ckRMkiQpE4uYJElSJhYxSZKkTCxikiRJmVjEJEmSMrGISZIkZWIRkyRJymTZFbGI2BARvx0RD0bEUxFxMCK+HxFfiIhX587XLCKiEBG/EREfj4j+6nlOETHjllY6vohYGxH/EBFPR8QLETEUEX8REafnztYMIuLaiPhQRDwcEfuqf1c/nTtXM4mIMyLi5oj4fEQ8ERETEbE3Ir4eEW+OiGX382gpRMSfRMR/VH++TUTEcxHxrYh4b0SckTufjrXsFnSNiH8C3gQ8AnwdeA64APhFYCXwGymlv8yXsDlExGnAaPXp94GDwDnAW1JKf58tWAOKiB8DtgI/AnwB+C7QA7waeAy4LKW0J1/CxhcR/cDLgQPAMHAh8JmU0paswZpIRPwq8BFgN/AV4HtACbgGaAPuAX4pLbcfSossIg4C36TyM+5Z4FTglcBPA08Dr0wpPZUvoY62HIvYjcC3U0rfOur45cC/Awk4L6W0O0O8phERLwGuAvpTSrsj4veB92IRm7eI+BLwM8CtKaUPHXH8g8BvAX+TUvrVXPmaQXU0fBh4AricSlGwiC2iiLiSSim4P6X04hHHzwL+m8p/1K5NKd2TKWJTiIhVKaXJGY6/D3gX8JGU0q/VPplms+yGglNKnzi6hFWPfxV4CHgJcGmtczWblNLBlNK/WWgXJiI6qZSwIeCvjnr5vcA4cF1EnFrjaE0lpfSVlNLjjsYsnZTSgymlfzmyhFWPPwN8tPr0ipoHazIzlbCqu6uPG2qVRXOz7IrYCRyqPk5lTSH9vyurjw/M8ANsP/CfwGoqlx6kRuW/vUvvF6qP/5M1hY5xSu4A9SIi1lG5lPY88LXMcaRpF1QfB2d5/XEqI2bnA/9Rk0TSIoqIU4Drq0+/mDNLM4mIdwBrqMy/+2ngVVRK2B05c+lYFjEgIl4KfAZ4KfDOlNLoCT4i1Upb9XHvLK9PHz+tBlmkpXAH0AX8a0rpS7nDNJF3ULkZYtoXgRtTSj/IlEezaMhLk9Vb99M8fs16G3pErAQ+BVwGfBb4s1r9OerdYp5nLZmoPjq3SQ0nIm4FbqdyJ/B1meM0lZTSWSmlAM6icmdqJ/CtiPipvMl0tEYdEdsOzDYhcSZPz3SwWsI+DfwSlYmMW5ys+0MW5TxrQaZHvNpmeb31qPdJDSEibgHupLLMwlUppecyR2pKKaXvA5+PiG9SmeLwSSojkKoTDVnEUkpXLfQ7qvMS7qJSwu4Crk8pHV7o9zaTxTjPWrDHqo/nz/L69B1Qs80hk+pORPwm8OfAd6iUsGczR2p6KaUnI+IR4KKI6EgpjeTOpIqGvDS5UNU1rj5HpYR9ErjOEqY69ZXq488cvfJ4RBSpXFKfAL5R62DSyYiI36ZSwvqBV1vCaupHq4/+vKsjy66IVSfmfx54PfAx4KajlwWQ6kVKaTvwAHAecMtRL/8BlQUyP5lSGq9xNGneIuL3qEzO30ZlJMxRmUUUERdWF8g9+viK6oKuPwJs9Ya0+rIcV9b/OHAjMAL8NTNPcn4opfRQDWM1pYj4HSpbxQBcRGULma1UllwA+Lqr7J/YDFscPQpcTGWLo0HgUrc4WpiIeAPwhurTs4CfBXYAD1ePjaSU3pEjW7OIiBuAT1AZjfkQM89rHEopfaKGsZpK9ZLv+6kswbQd2EPlzsnLqUzWf4ZKAX4kW0gdYzkWsYeo/KU8nj9IKf3+0qdpbnM41/+YUrqxNmkaW0ScA/whsBk4g8p+ffdS+bvqJOcFOmILrtk8mVI6rzZpmtMczjHAV1NKVyx9muYUEV3A26lMWVhLZVmbcSr/Ybsf+Ev/vag/y66ISZIk1YtlN0dMkiSpXljEJEmSMrGISZIkZWIRkyRJysQiJkmSlIlFTJIkKROLmCRJUiYWMUmSpEwsYpIkSZlYxCRJkjKxiEmSJGViEZMkScrEIiZJkpSJRUySJCkTi5gkSVImFjFJkqRMLGKSJEmZ/C+52UdWx8ZkNAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 305
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_1 = train_neural_network(data, labels, 0.01, 2501, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can inspect the result by comparing the real label of a data point and the predicted label:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "code_folding": [
     0
    ]
   },
   "outputs": [],
   "source": [
    "def show_prediction(train, data, labels):\n",
    "    A, B, C = train\n",
    "    for i in range(data.shape[0]):\n",
    "        X,Y = data[i]\n",
    "        label = labels[i]\n",
    "        output = A*X + B*Y + C\n",
    "        predicted_label = 1 if output >= 1 else -1 if output <= -1 else 0\n",
    "        print (f'data point {i}: real label : {label}, pred. label: {predicted_label}, {(label==predicted_label)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data point 0: real label : 1, pred. label: 1, True\n",
      "data point 1: real label : -1, pred. label: -1, True\n",
      "data point 2: real label : 1, pred. label: 1, True\n",
      "data point 3: real label : -1, pred. label: -1, True\n",
      "data point 4: real label : -1, pred. label: -1, True\n",
      "data point 5: real label : 1, pred. label: 1, True\n"
     ]
    }
   ],
   "source": [
    "show_prediction(train_1,data,labels)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}