docs/source/examples/lecture3_lotka_volterra.ipynb

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   "source": [
    "# Lotka Volterra"
   ]
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   "source": [
    "The Lotka–Volterra equations, also known as the *predator–prey* equations, are a pair of *first-order* **nonlinear** differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.\n",
    "The equations provides a mathematical framework for the description of **ecosystem** dynamics in which 2 species interact each other.\n",
    "\n",
    "The equations represent a syntesis among the population dynnamic (provided by Volterra) and the theory of autocatalytic chemical reactions with oscillating creation of chemical products (provided by Lotka).\n",
    "The equations describe an ideal system in which the increasing amount of \"food\" (prey eaten) leads to a growth of predators (reproduction)."
   ]
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   "source": [
    "Given $y(t)$ as the number of *predators* at time $t$ and $x(t)$ the number of *preys*, the Lotka-Volterra system of equations is:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\frac{dx}{dt} &= +\\alpha x  - \\beta xy \\\\\n",
    "    \\frac{dy}{dt} &= +\\delta xy - \\gamma y \\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "where the sign $+$ identifies the \"birth\" terms (preys grows up autonomally, while predators need preys) and the negative terms ($-$) identifies the \"death\" terms (vice versa between predators and preys)\n",
    "\n",
    "The $\\alpha x$ term is analogous to the logistic growth: more preys and more preys birth.\n",
    "The terms $\\alpha$, $\\beta$, $\\gamma$, and $\\delta$ are the **interaction terms** between the two species and they weight the growth of predator-prey populations.\n",
    "\n",
    "The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism. "
   ]
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    "Lets try to deduce some characteristics of the model looking the form of the equations:\n",
    "\n",
    "* The growth of predators ($y$) is strictly related to the number of preys ($x$).\n",
    "    * if $y > x$ only a portion of the predators will have enough \"food\" for their reproduction with a consequent decrement of their number.\n",
    "    * if $y < x$ the preys can increase their number since they are prevalently \"safe\"; however all the predators have (more than) enough \"food\" for their reproduction and they will tend to increase.\n",
    "    This behavior leads to an **oscillating regime** of the system!\n",
    "    \n",
    "* The main assumption behind this model (i.e ideal factor) is the **unlimited growth** of prey population when the number of predators is 0 ($y = 0$).\n",
    "    An improvement of the model can be achieved including (as for the improved Malthusian model) an extra term $-\\xi x^2$ which reduce the ideality of the model.\n",
    "\n",
    "* An analogous argumentation can be applied for the exponential decay of the predators when the preys are zero ($x = 0$).\n",
    "\n",
    "* Further correction factors can be included considering genetic terms which model the adaptation of the species in the environment."
   ]
  },
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   "source": [
    "Starting from the implementation of the model in Python, we will try to perform a numerical analysis of the dynamic of this simple system.\n",
    "\n",
    "As always we will use the *odeint* function of *scipy* for the numerical integration of the 2 ODEs."
   ]
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   "source": [
    "import numpy as np\n",
    "\n",
    "def lotka_volterra (xy : tuple, t : np.ndarray, \n",
    "                    alpha : float, beta : float, \n",
    "                    delta : float, gamma : float) -> tuple:\n",
    "    '''\n",
    "    Lotka-Volterra ODE\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "        xy : tuple\n",
    "            List of x and y Lotka-Volterra signals\n",
    "            \n",
    "        t : array-like\n",
    "            List of time points\n",
    "        \n",
    "        alpha : float\n",
    "            Preys growth factor\n",
    "        \n",
    "        beta : float\n",
    "            Preys decay factor\n",
    "        \n",
    "        delta : float\n",
    "            Predators growth factor\n",
    "        \n",
    "        gamma : float\n",
    "            Predators growth factor\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "        xynew : tuple\n",
    "            Next point of x and y dynamic\n",
    "    '''\n",
    "    \n",
    "    x, y = xy\n",
    "    dx = alpha * x - beta * x * y\n",
    "    dy = delta * x * y - gamma * y\n",
    "    return (dx, dy)"
   ]
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   "outputs": [
    {
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       "<matplotlib.legend.Legend at 0x7fdae4b7f090>"
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab as plt\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "# initial conditions\n",
    "xy0 = (1, 2) # (x0, y0)\n",
    "alpha, beta, delta, gamma = (1.2, 1.4, 1.5, 1.7)\n",
    "\n",
    "time = np.linspace(0, 30, 1000)\n",
    "xy = odeint(lotka_volterra, xy0, time, \n",
    "            args=(alpha, beta, delta, gamma))\n",
    "dx, dy = zip(*xy)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 6))\n",
    "ax.plot(time, dx, label='$x(t)$')\n",
    "ax.plot(time, dy, label='$y(t)$')\n",
    "ax.set_xlabel('Time', fontsize=24)\n",
    "ax.set_ylabel('Lotka-Volterra', fontsize=24)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "58JRAN0cclhh"
   },
   "source": [
    "## Stability Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ox7ve1XUMreO"
   },
   "source": [
    "Given the Lotka-Volterra system of equations, we can determine its stable points (points of *equilibrium*).\n",
    "We have a stable point when the level of both the populations remains **constant**, i.e $x(t) = x^*$ and $y(t) = y^*$ for each time $t$.\n",
    "As consequence, both the derivatives will be null, i.e\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\alpha x^* - \\beta x^* y^* &= 0 \\\\\n",
    "    \\delta x^*y^* - \\gamma y^* &= 0 \\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This system of equation is very simple to solve, *but* unfortunately we are very lazy persons and we prefer to obtain its solution by the computer...\n",
    "\n",
    "To this purpose we can use the *Symbolic Computation* provided by the **SymPy** library in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 463,
     "status": "ok",
     "timestamp": 1632142590863,
     "user": {
      "displayName": "nico nico",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
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    },
    "id": "xlLZYPv1M9Dc",
    "outputId": "ac6da321-4e8b-4ebc-c316-1ac3540f85e7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(𝑥∗, 𝑦∗) = (0, 0)\n",
      "(𝑥∗, 𝑦∗) = (gamma/delta, alpha/beta)\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "from sympy import solve\n",
    "\n",
    "x, y = symbols('x, y')\n",
    "alpha, beta, delta, gamma = symbols('alpha, beta, delta, gamma')\n",
    "\n",
    "dx = alpha * x - beta * x * y\n",
    "dy = delta * x * y - gamma * y\n",
    "stable_points = solve([dx, dy], (x, y))\n",
    "\n",
    "print('\\n'.join([r'(𝑥∗, 𝑦∗) = ({}, {})'.format(*x) \n",
    "                 for x in stable_points]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q0q49OD6NA3H"
   },
   "source": [
    "We have found 2 points of equilibrium: the 1st ($0, 0$) is related to the extinction of both the populations; the 2nd $\\left(\\frac{\\gamma}{\\delta}, \\frac{\\alpha}{\\beta}\\right)$ corresponds to a perfect equilibrium between preys \"eaten\" and preys \"produced\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DbYbjfE9NCTB"
   },
   "source": [
    "A second analysis can be performed studying the stability of equilibrium points.\n",
    "This can be obtained studying the determinant of the Jacobian matrix associated to the system, i.e\n",
    "\n",
    "$$\n",
    "J(x, y) = \\begin{bmatrix} \\alpha - \\beta y & -\\beta x \\\\ \\delta y & \\delta x - \\gamma \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "The matrix is obtained considering the dependecy by $x$ (first column) and $y$ (second column) of the two ODEs, independently.\n",
    "Now we can substitute the equilibrium points obtained above into the matrix and compute the corresponding eigenvalues.\n",
    "\n",
    "* 1st point: $(0, 0)$\n",
    "\n",
    "$$\n",
    "J(0, 0) = \\begin{bmatrix} \\alpha & 0 \\\\ 0 & -\\gamma \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "* 2nd point: $\\left(\\frac{\\gamma}{\\delta}, \\frac{\\alpha}{\\beta}\\right)$\n",
    "\n",
    "$$\n",
    "J\\left(\\frac{\\gamma}{\\delta}, \\frac{\\alpha}{\\beta}\\right) = \\begin{bmatrix} 0 & -\\beta\\frac{\\gamma}{\\delta} \\\\ \\alpha\\frac{\\delta}{\\beta} & 0 \\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nskGY5KhNN6x"
   },
   "source": [
    "For the computation of the eigenvalue solutions we can use the Symbolic Computation as performed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 7,
     "status": "ok",
     "timestamp": 1632142590864,
     "user": {
      "displayName": "nico nico",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "04264570794863623616"
     },
     "user_tz": -120
    },
    "id": "VdI10723M-Pm",
    "outputId": "ab32678c-c2fc-46a6-dcd3-9098d700b5ae"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue 0: alpha\n",
      "Eigenvalue 1: -gamma\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "from sympy import Matrix\n",
    "\n",
    "x, y = symbols('x, y')\n",
    "alpha, beta, delta, gamma = symbols('alpha, beta, delta, gamma')\n",
    "\n",
    "J = Matrix([[alpha - beta * y, -beta * x], \n",
    "            [delta * y, delta * x - gamma]])\n",
    "\n",
    "# substitute the 1st stable point\n",
    "J_1st = J.subs([*zip([x, y], stable_points[0])])\n",
    "\n",
    "# compute the eigenvalues\n",
    "print('\\n'.join(['Eigenvalue {:d}: {}'.format(i, k) \n",
    "                 for i, (k, v) in enumerate(J_1st.eigenvals().items())]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "z-2FAauaNSSl"
   },
   "source": [
    "The two eigenvalues are always different and therefore the point of equilibrium is classified as *saddle point*, characteristic of an **unstable equilibrium**.\n",
    "\n",
    ">⚠️**Note:** A little change in initial condition, in fact, leads to an oscillating dynamic!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MeQqwTlNNTIA"
   },
   "source": [
    "Lets move to the 2nd point of equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 5,
     "status": "ok",
     "timestamp": 1632142590864,
     "user": {
      "displayName": "nico nico",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "04264570794863623616"
     },
     "user_tz": -120
    },
    "id": "4fxQRsiNNQBl",
    "outputId": "ad50eeb0-872b-425d-8878-b9ce641eb8be"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue 0: -sqrt(-alpha*gamma)\n",
      "Eigenvalue 1: sqrt(-alpha*gamma)\n"
     ]
    }
   ],
   "source": [
    "# substitute the 1st stable point\n",
    "J_2nd = J.subs([*zip([x, y], stable_points[1])])\n",
    "\n",
    "# compute the eigenvalues\n",
    "print('\\n'.join(['Eigenvalue {:d}: {}'.format(i, k) \n",
    "                 for i, (k, v) in enumerate(J_2nd.eigenvals().items())]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OfCTbj4tNbD8"
   },
   "source": [
    "The two eigenvalues are complex (**note the minus sign under the sqrt!**) with a real component equal to zero.\n",
    "This identifies a **stable equilibrium** with consequent oscillating orbits around it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XgA5P3UxNbyN"
   },
   "source": [
    "We can better appreciate the results obtained by our analysis plotting the phase space of the system under different conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
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   "outputs": [
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       "model_id": "02f848edf443468282918983cd2cedb7",
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       "interactive(children=(FloatSlider(value=0.6, description='x0', max=1.1333333333333333, step=0.01), FloatSlider…"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "xy0 = (0.6, 0.4)\n",
    "alpha, beta, delta, gamma = (1.2, 1.4, 1.5, 1.7)\n",
    "\n",
    "time = np.linspace(0, 30, 1000)\n",
    "\n",
    "@interact(x0=(0, gamma/delta, .01), y0=(0., alpha/beta, .01))\n",
    "def update (x0=xy0[0], y0=xy0[1]):\n",
    "    xy0 = (x0, y0)\n",
    "    xy = odeint(lotka_volterra, xy0, time, args=(alpha, beta, delta, gamma))\n",
    "    dx, dy = zip(*xy)\n",
    "\n",
    "    fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(20, 10))\n",
    "    fig.subplots_adjust(top=0.95, bottom=.15)\n",
    "    xt, = ax1.plot(time, dx, label='$x(t)$')\n",
    "    yt, = ax1.plot(time, dy, label='$y(t)$')\n",
    "    ax1.set_xlabel('Time', fontsize=12)\n",
    "    ax1.set_ylabel('Lotka-Volterra', fontsize=12)\n",
    "    ax1.legend(loc='upper right')\n",
    "    ax1.set_ylim(-.5, 12)\n",
    "\n",
    "    xyt, = ax2.plot(dx, dy)\n",
    "    ax2.set_xlabel('$x(t)$', fontsize=12)\n",
    "    ax2.set_ylabel('$y(t)$', fontsize=12)\n",
    "    ax2.set_xlim(-.5, 12)\n",
    "    ax2.set_ylim(-.5, 12)"
   ]
  }
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AAIA9kKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQ2pMnJpZTjk/xGkvFJypbjtdbP9/JcAAAAAAxgPV6pVEq5IMkvkrwxyaeSHJfkT5K8sm9GAwAAAGCganL72yeTnF1rfUeSdd0/vzPJxj6ZDAAAAIABq0lUOrDWemP3x5tLKYNqrT9N8rY+mAsAAACAAazJnkqLSylTaq2LksxPcm4pZWWSjj6ZDAAAAIABq0lU+kKSo5MsSvJnSa5MMizJx3p/LAAAAAAGsh5FpVJKSTI7yWNJUmv9aSll/yTDaq3P9+F8AAAAAAxAPdpTqdZak9yXZPMLjnUISgAAAADtqclG3XclmdZXgwAAAACw52iyp9L1Sa4qpXwjyeNJ6pY3aq2X9u5YAAAAAAxkTaLS65M8kuQNLzpek4hKAAAAAG2kpxt1D07yf5N8q9a6vm9HAgAAAGCg6+lG3Z1JviwoAQAAAJA026j7h6WUt/XZJAAAAADsMZrsqTQ8yZWllFvy0o26P9DbgwEAAAAwcDWJSnO6fwAAAADQ5noclWqtF/XlIAAAAADsOZrsqZRSyptKKV8vpfyw+/XMUsob+2Y0AAAAAAaqHkelUspHk/xDkgVJZnUfXpfkz/tgLgAAAAAGsCYrlf44yZm11ouTbO4+9mCSo3p9KgAAAAAGtCZRaVS6nvqW/PrJb0OTdPTqRAAAAAAMeE2i0uwkn37RsY8lua73xgEAAABgT9Djp78l+WiSH5ZS/iDJqFLKvCSrk7y1TyYDAAAAYMDqcVSqtS4rpZyU5KQkh6frVrhba62bd/4rd66UMjbJPyeZka7b6j5Ua71ld35PAAB2zjUYALC7mjz97fu1y6211v+otf6y1rq5lPKd3Zzhb5JcVWudnuTVSR7Yzd8PAIBdcw0GAOyWJre/nb6D47/5cj95KWVMkllJfi9Jaq0dsfE3AECfcg0GAPSGXUalUsqfdX847AUfb3FEkkd34/NPTbIiyb+UUl6d5I4kH6+1rnnRDBckuSBJDjvssN34dAAAxDUYANALenL726HdPwa94ONDk0xO175K79qNzz8kyYlJ/qHWekKSNXnpE+ZSa/1arXVmrXXmhAkTduPTAQAQ12AAQC/Y5UqlWuvvJ0kp5eZa6z/18udfnGRxrfVX3a+vzHYuaAAA6FWuwQCA3bbTqFRKOeIFL6990eutaq0LX84nr7U+UUp5vJRyVK11XpIzktz/cn4vAIC9QSnlwCS/la7Ns8cmeSbJPUmuqbU+0RufwzUYANAbdrVS6aF0PWK27OScmmTwbszw0SSXlVKGJVmY5Pd34/cCANgjlVKOTvK/0vVwlDvS9TS2J5KMSvL+JH9dSrkuyedrrb0RgFyDAQC7ZadRqdbakz2Xdkut9e4kM/v68wAADHDfSPJXSd6XZGOtdfML3yyl7JPk7Um+nuS1u/vJXIMBALtrl3sqvVgp5bAkh6TrPvzHe38kAID2U2s9ZcvHpZQVSSa86P0NSf6j+wcAQMv1eCVSKWViKeWGdN0S950kD5dSZpdSJvXZdAAAbaSU8upSytAkw3fw/mP9PBIAwA41ub3tH9K1SeT+tdaJSfZPcleSr/bFYAAAbehHSZ5PMryUcnkp5VOllLNLKQd3/4+8MS2eDwBgqya3v52WZGKtdWOS1FrXlFI+mWRJn0wGANBmaq2HllLGJ3ksyY3pegLc+UlmpGv1kv+ZBwAMGE2i0tNJjknXaqUtjkrXY24BAOgFtdaVpZTjaq0PbzlWSilJRtRa17ZwNACAbTSJSl9I8rNSyteTPJrk8HQ9evZzfTEYAEC7emFQ6n5dkwhKAMCAsss9lUopxyRJrfWfkvx2kvFJ3tb983trrV/r0wkBANpAKeVjpZR9dnHOPqWUj/XXTAAAO9OTlUp3lVLuTfKvSS6vtf68j2cCAGhHByd5qJTykyQ3JJmXZHWSUUmmJfnNJG9O8m+tGhAA4IV68vS3SekKSu9PsqSU8t1SynmllCa3zgEAsBO11v83yQlJFiT5cJKfJpmT5CdJPpTkwSQn1Fo/27IhAQBeYJdRqda6qtb6lVrrKel6Asn9SS5JsqyU8n9KKSf19ZAAAO2g1rqy1vrFJG+vtR5Yax1Waz2o1vqmWusltdZVrZ4RAGCLnqxU2qrWOq/W+pla69Qk703y1iS/7JPJAADa14JSyh+VUga3ehAAgB1pFJWSpJRyainl75NcnmRzkj/r9akAANrbWenaP2leKeV3Wj0MAMD29CgqlVIOL6V8tpQyL8lVSYYleUet9RW11ov6dEIAgDZTa51Ta31buvZS+ngp5c5SylmtngsA4IV2udl2KeWGJK9Ncl2Si5J8t9a6rq8HAwBod7XW2UleW0o5P8lXSymPJPl0rfW2Fo8GALDrqJSuJ468t9a6ZMuBUsp7aq2X991YAADtq5RyUJITX/DjNUkOTrIqyZWllJuSfLTW+lTrpgQA2l1Pnv72ly8MSt3+sY/mAQAgWZLkC0lemeTaJO9KMrrWelL3sUVJvtOy6QAA0rOVSttTenUKAABeaEytdc323qi1bkzymVLKM/08EwDANho//a3bjb06BQAAW+0oKL3I6X0+CADATrysqFRrfUtvDwIAQM/VWu9q9QwAQHtrdPtbKeX4JL+RZHxecAtcrfXzvTwXAAAAAANYj1cqlVIuSPKLJG9M8qkkxyX5k3RtFgkAAABAG2ly+9snk5xda31HknXdP78zycY+mQwAAACAAatJVDqw1rplg+7NpZRBtdafJnlbH8wFAAAAwADWZE+lxaWUKbXWRUnmJzm3lLIySUefTAYAAADAgNUkKn0hydFJFiX5syRXJhmW5GO9PxYAAAAAA1mTqPTNWuumJKm1/rSUsn+6olKjJ8gBAAAAsOdrsqfS5aWUsuVFrbUjXVHp570+FQAAAAADWpOotCnJP295UUo5MMkNSX7c20MBAAAAMLA1iUrvT3JQKeWSUsrBSa5PckWt9XN9MhkAAAAAA1aPo1L3fkrvTHJCkrlJLq21/nlfDQYAAADAwLXTTbZLKf83SX3R4WfTdSvcq0op/5YktdYP9M14AAAAAAxEu3py20M7OH5nbw8CAAAAwJ5jp1Gp1nrRlo9LKQfXWp948Tnd+ysBAAAA0EaabNQ9fwfH7++NQQAAAADYczSJSuUlB0oZnWRz740DAAAAwJ5gV3sqpZTyeLo26x5RSnnsRW+PS3J5XwwGAAAAwMC1y6iU5HfTtUrpJ0ne/4LjNcmTtdZ5fTEYAAAAAAPXLqNSrfWGJCmljK+1ru37kQAAAAAY6JrsqbSxlHJRKWVhKWV9988XlVKG9dl0AAAAAAxIPbn9bYsvJDk5yf+T5NEkhyf5XJLRST7R+6MBAAAAMFA1iUrvSvLqWuuq7tfzSil3JrknohIAAABAW2ly+1tpeBwAAACAvVSTqPQfSX5YSvmtUsrRpZSzk3wvyb/3zWgAAAAADFRNbn/7ZJLPJvm7JJOSLEny7ST79MFcAAAAAAxgPY5KtdaOJJ/v/pEkKaUMT7ImXcEJAAAAgDbR5Pa37amxpxIAAABA29ndqJR0hSUAAAAA2sgub38rpbxxJ28P68VZAAAAANhD9GRPpa/v4v3HemMQAAAAAPYcu4xKtdap/TEIAAAAAHuO3thTCQAAAIA2IyoBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANDYgolIpZXAp5a5Syo9aPQsAQLtwDQYA7I4BEZWSfDzJA60eAgCgzbgGAwBetpZHpVLK5CTnJPnnVs8CANAuXIMBALur5VEpyV8n+WSSzTs6oZRyQSnl9lLK7StWrOi/yQAA9l6uwQCA3dLSqFRKeWuS5bXWO3Z2Xq31a7XWmbXWmRMmTOin6QAA9k6uwQCA3tDqlUqvT/L2UsqiJN9O8sZSyjdbOxIAwF7PNRgAsNtaGpVqrX9aa51ca52S5HeS/LzW+rutnAkAYG/nGgwA6A2tXqkEAAAAwB5oSKsH2KLWen2S61s8BgBAW3ENBgC8XFYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUoAAAAANCYqAQAAANCYqAQAAABAY6ISAAAAAI2JSgAAAAA0JioBAAAA0JioBAAAAEBjohIAAAAAjYlKAAAAADQmKgEAAADQmKgEAAAAQGOiEgAAAACNiUottn5jZy771aP55i8fzfqNna0eZ8Dp3FzzvbuW5Os3PZKn13S0epwBp9aanz/4ZL56w8NZ/PTaVo8zIN3x6FP5u+seyrwnVrd6lAFp/pOr83fXPZRbH3mq1aMMSEufWZev3vBwfnb/k6m1tnocAAAYUIa0eoB21rFpc97/9V/ltkVPJ0l+cPfSXPYHp2ToYK0v6Qomn7ji7vzgnqVJkm/+8tF8749enzH7Dm3xZAPHV37+UL50zfwkyVdveDjf+6PXZ8r4/Vo81cDx/buX5OPfvjtJ8jc/W5Bv/rdTcvLUA1o81cDxq4Wr8v6v35qOzs1Jkr/+7eNz3gmHtHiqgeORlWvyrq/ekpXPb0iSfOLMafn4mUe2eCoAABg41IsW+uLV83Lboqfz5Xe/Ol9816tz66Kn8m+3PNrqsQaMb9/2eH5wz9L88ZlH5vI/ODWPPbU2l/xsfqvHGjBufnhlvnTN/LzjhENy9SdmZfPmms98775WjzVgPLJyTf7Hlffm5KkH5MZPnp5JY4fnk1fek43dAaXdPbt2Yz56+V2ZvP+I3PjJ03PylAPyue/NyTNrrQhMulZJ/vdv3ZnNtebHH6zMmwcAACAASURBVDst559wSP762vl5aPnzrR4NAAAGDFGpRRY/vTb/8otH8u6Zk3P+iZPzztdMzilTD8ilNz2STb7pzdqOTfnS1fNy8tQD8rE3HpnXvmJczj/hkHz7tsfylNvgsnlzzZ//6IEcMnZE/uL84zLtoFH52BlH5hcPrcqcJc+2erwB4YtXz8uQQSVfee8JOfSAffOnbzk6i1atzc/uf7LVow0I/3TjwixfvSF/+56ur89F5x6b1Rs25fJbH2/1aAPCf96xOHOXPpeL3n5sjp00Jp855+jsM2RQ/vGGh1s92oBw+6Kn8uN7l/nvFQBAmxOVWuQfb1iYkpI/PnPa1mO///qpWfLMulz74PIWTjYwfOtXj2Xl8x355G8dlUGDSpLkD2YdkfUbN+ffb/dN7w3zV+T+Zc/lT86aluFDBydJ3vWaQzNsyKBccZuvz0PLn8+P712WD582NQeOGp4kOfPog3LI2BFWAyZ5dt3G/MsvHsk5r5qYGYeMSZIcPXF0Xv/Kcfm3WxZl8+b23jto8+aaf7jh4bxq8pi89VUTkyTjRu6Td888NN+7e0meXbexxRO23t/+/KH82Y/mpr3/TQEAQFRqgXUdnfneXUvy1ldNzKSxI7YeP/PoAzNuv2H58b3LWjhd69Va881fPpqTpuyfmVN+vf/NtING5VWTx+SqOU+0cLqB4Rs3L8qBo/bJ2149aeuxMfsOzZtnHJzv372k7W/x+uYvH82wwYPywddN2Xps8KCSd888NLcsXJXlq9e3brgB4If3LM2ajs784awjtjn+7pmHZtmz63PP4mdaNNnAcMOCFXlk5Zp8+LSpKaVsPX7eCYdkY2fNdW0e/h9ZuSaz56/Ie08+3B6AAABtztVgC/zkvmVZvWFTfvukQ7c5PmTwoJw+/cBcP295W99ScMvCVVm0am3ee8phL3nvrGMOyt2PP5Mnn2vfKLDkmXW5Yf6KvPeUw17yDd3Zxx6c59Zvyl2PtW8UWL+xM/955+K8+biDM37kPtu8d+YxByZJrp+3ohWjDRj/fvvjmX7wqBzXvUppi9+cdmAGDyq5ps1vEfz32x7P+JHD8uYZE7c5fvzksTlo9D5tH7a/fetjGTKo5D0nH7rrkwEA2KuJSi1wxW2PZ+r4/bb7FKozjz4wz63flNsffboFkw0M371zSUbtM+Ql39AlyVnHHpwk+XkbrxT48b1dT8N7x3ae0vW6V47P4EElN8xv36/P9fOWZ/X6TXnnaya/5L1jJo7OwaOHt/VKkweWPZd7Fz+bd888dJtVOEnXardTph6Qax9o36/P6vUbc+2Dy/PWV03KsCHb/idy0KCSM48+KLMXrGjb1YC11vzo3mWZNW1CDhw9vNXjAADQYqJSP1vyzLrcuuipvPM1k1/yDV2SvP6V4zOoJDc/vKoF07Xexs7Nufr+J/OmYw7aulfQCx154MiMH7lPbn3kqRZMNzD84J6lefXkMTl83H4veW/MiKE58bCxuWF++67E+eG9yzJuv2F57RHjXvJeKSVvmDYhNz20sm33Dfre3UsyZFDJeduJkknyG0dOyLwnV7fthvj/NffJdGzanLcfP2m777/2FeOytqOzbTfEv/OxZ7LkmXVb95oCAKC9iUr97Oq5XbdNvHnGwdt9f9TwoTlm0ujcvqg9o8kvHlqZZ9dtzFuO2/43LKWUnDL1gLaNSgtXPJ85S57bZi+lF3vtEeNy/9Ln8vyGTf042cCwtmNTfv7A8pw94+AM2cFeLydNPSCr12/K/OWr+3m61qu15r/mPJHXvmJcDthv2HbPOWnK/kmS29r076Af3LM0hx4wIiccOna7729ZYfqrNv076If3LM2wIYPypmMOavUoAAAMAKJSP7tqzhOZdtDIHDFh5A7PmXn4AbnrsWfa8vaKn9y3LCP3GZLTjhy/w3NOnnpAljyzLoufXtuPkw0MV3VHyXN2skrgxMP3z+aa3Pt4++2rdN2DK7JuY2fe+qodR7eZh3dFk9sXtd8tpvOffD6LVq3Nbx27/aidJMdNHpNhQwbltjaMJs9v2JSbH1qZtxw3cbsrSZPkwFHDc8SE/fKrhe23mrTWmp/OWZbTj5qQUcOHtnocAAAGAFGpH616fkNuW/TUTr+hS5KTphyQdRs7c//S5/ppsoGhc3PNzx5YnjOOPnC7t75tMbN7JcUdbbjv1Oz5K3L0xNGZOGbEDs854bD2/fpcP295xowYut39yrY4fNy+GT9yWFt+ff5r7hMppWvD+x3ZZ8jgHH/o2NzWhl+fWx5elU2ba94wbcJOzzvp8ANy9+PPpNb2uoVy3pOr8+RzG3LGdKuUAADo0tKoVEo5tJRyXSnl/lLK3FLKx1s5T1+79sHl2Vyzy6h0/GFdt13c22Z7dsxd+myeWtOR0486cKfnTTtoVIYNGZS5bRbd1mzYlDsefTqzpu14FVfSta/SkQeOzJ2PtVcUqLVm9oIVOa17s/IdKaXkxMP2z91tuJLr6vufyAmHjt3lBsuvnjwmDyx7ru1WS86evyL7DhucmYfvOEomyYxDRufptRuz9Nn2egrl7O692n5jF38HsWdot2swAKBvtHql0qYkf1JrPSbJqUk+Uko5psUz9ZkbF6zM+JH75NhJo3d63qQxwzN236G5f2l7RaUbF6xMkp3e+pYkQwcPytEHj2q7jXJveXhVNnbWzDpy56sokuTVh47NfUvaK7rNf/L5PPnchl1GtySZcciYLFq1JmvaaN+plc9vyJwlz+WMo3e9yuTYSWPSsWlzHl7xfD9MNnDMXrAirz1i3Eue+vZiMw4ZkyRt93fQ7PkrM+2gkTtdKckepa2uwQCAvtHSqFRrXVZrvbP749VJHkiy/UcS7eE2b665acGKzDpy/A736tiilJJjJ41uu5U4N8xfkWMnjc74kfvs8txjJo3JnCXPttXtJ7MXrMiIoYO33v63M0dPHJ2Vz2/IitUb+mGygeHGBd2rKHoQ3Y6ZODq1Jg8+0T5/xn7xUFe0/Y1dRNukayVOksxtozD56Ko1eXTV2szaxa1vSdefr8GDSua2UVRa19GZWxc91aM/X+wZ2ukaDADoO61eqbRVKWVKkhOS/Kq1k/SNuUufy9NrN/b4toFjJo7Og0+szqY2uf3k+Q2bcuejT/f4G5YZh4zOc+s3ZfHT6/p4soFj9vwVOfWIA7LPkB3vN7XF0RNHJUkeWNY+UeCG+SvyygNHZtLYXa+iOKZ7tWA77Vs2e/7K7L/v0Bw7acwuz506fmRGDB3cVmF7y61dPYlKw4cOzisnjMycNvr6/OqRVenYtLlHXx/2PHv7NRgA0HeGtHqAJCmljEzyn0n+uNb6kqv0UsoFSS5IksMOO6yfp+sds7tXUbz+lT2LSr++/WRNjjp41K/fWPtUcse/JMPHJie8Pxmy/ceC72m2bJDbk1uXkmRG9zfGc5c+m0MP2PfXb2xcl9zxr0lnR/Ka30uG7/xWwz3FY6vWZtGqtfng66b06PxjJnZHk2XPbftN4ObO5J7Lk+eWJSe+Pxm18/299hTrN3bm1keeyvtOObxH508cMzz77zv0pdGk1uTBHydP3Jsc965k/JF9MG3/q7XmxgUr8vpd7De1xeBBJdMnjsrc7d2C++jNycM/T6adnUye2QfTtsYN81fm0ANGZMq4fXd9cpJjDxmdm7pv2d3Gk3OTud9NDj0lOfJNvTxl68yevzL7DBmUU3ayCT57pna4BtsdV9z2WD71n/ft9JzfPfWw/K9zZ+xyJToA7I1aHpVKKUPTdTFzWa31O9s7p9b6tSRfS5KZM2fukfc73big66ldB47a+Qa5W2zZd2nu0md/HZU2PJ9cenaycl7X6/lXJe+5Ihk0YBacvWw3dt/a9ZrDd31rV5IcdfCoDB5UMmfJczl7xsSug5s7k8t/J1l4fdfre/89+fDVybCefZM4kG2Jkj1dJTB232GZNGb4S1cq/fRTyW3/1PXx7V9PLrghGbXnP8np1keeyoZNm3u8ErCUkmMmjc79L/763PJ3ydWf6fr45q8kv/+TZNLxvTxt/5v/5PNZvnpDj/bj2uLYSaPz/buWZvPmmkFbQtQDP0yueH+Smtz4peR3vpUc9ea+GbofdWzanFseXpnzTjikx98Uzpg0Jt+5c0mWP7f+1xufPzEn+eczk03dKyjf/FfJKRf00dT9a/aCFTl56gE7fTIne552uQZr6tyv3JR7Fvf89tZv/vKxfPOXj219/b/fMaPH/5MDAPZ0rX76W0ny9SQP1Fq/3MpZ+tLWp3b1YC+TLaaO3y/7vPgJZ7/8+66g9P7vJmf/ZbLg6uTuy/pg4v5344KVPb61K/n17SfbRIG7L+sKSm+9pCu2PXlfMvsLfTNwP5s9f0UOGTsiR4zfr8e/5uiJo7e9vWvxHV1B6eQ/TP5wdteqtx9f2AfT9r/Z81dk2JBBOXXquB7/mpfcYrr6ieTnf54c9Zbkj+ckI8Ym3//vXbFyD7dlv6ldbYL/QsdOGpPVGzbl8afXdh3Y8HzyowuTia9O/mR+ctCM5AcfS9bv+fsK3fnY01nT0dno1q6tt1Bu+Tto8+auP0/D9ks+MbdrJdc1n0tWPtQXI/erpc+sy0PLn28UJRn42uUarIkpn/5xpnz6x9sNSm+cfmB+8ek3ZtHF52TRxedk9v84PWfv4Gm+n/nunK2/11NrOvp6bABoqVYvcXl9kvcneWMp5e7uH29p8Uy97lePdD+1q8E3LEMGD8r0g0f9eiPh9c8lN/+f5Khzkle8MTnlD5PDXpv87P9LOtb2zeD95PGn1uaRlWsa79Ux7eBRWbB8ddeLWrtWmUw8PnnN7ydHnZ0c/76ur9mzi/tg6v6zsXNzbn54VWZNm9Boaf0xk0Zn4co1Wb+xO4rc8JfJfhOSN362Kwz85qeTB3+UPLbnb6Exe8GKnDzlgIwY1vNVFMdMGp2OTZuzcOWargM3/XWyeWPyW/87GXtoctafd4XJey7vo6n7z+wFK3u839QW07tXSM5/svsJcHOuTNYsT86+uGt129v/NlmzouvrtoebPf//Z++8w+O66vT/mRmNeu+9y5ZkW+4lLnGJnTidJCQEAmxCqD/aspTNsruwsIQElhrKQoCwKYRAQiDFceLYiS33FstFvXeNZiSr1ym/P45GlmOVe2fuaCT7fJ6HZ2T73nMPJ3eu5rzzft+vGR+9jvVZykXJBXFifarax9anrhAaj8MN34KwZLj952DwhXe/54kpzyoHVTolJfOGa+IzmBL+fqaJ9Ed2XfZ3txYkjAtIdY/fylMPriZpwjM0NSqQ33xs5WXHlH9v5xVjr/jvt0l/ZNfk5bISiUQikVwFeLv72yGHw6FzOBwFDodj2dj/3vDmnDxBYYUFf6NecWmXk+zYkEsblrJdMNwDG/9Z/FmnE+LAgAXOv6jxjGeXQhVduyaSExtM08VBBkas0HQSzGWw6hNibQA2/ys47HDiSa2nPKucaeiib9iqyukGkBsfis3uEPdQXztU7YXlH72UM7X2MxAQAYd/7oFZzx5t3UNUmPoUdTWbiFMUqDT1gW1UvI9yb4PITHHAorsgfokQK+dxl8GhURvHazpUr092bDDAJeH29P9BbD6krhN/TlwOebfDqafmvbBdWGlmRWoEIf5GxedEBvkSFeR76Rl95k/gHwYFHxJ/DomHVQ9ByStwsU77Sc8ihRUW4kP9WRAX7O2pSDTkWvkMNhPpj+ziK385O/7nn35oKXWP38qvPrJC9Vh+PoZxgenUf2y/7N8++ofjpD+ya/KsOolEIpFI5jHedipdExysNLM2I0p1FkVOXDCmnmF6hkah+GUIS4Xk1ZcOSNsgSlBO/E7jGc8uztKurBjlpV0gRCWHA2rM/XDuL2AMhMV3XzogIk1sek8/DdZhjWc9exRWmDHodaxXGPLuJGdsA1jV3gfnXwKHDQruv3SAb5AQ4crfgJ4WLac8q6jNm3KSFROMTjcmmtQcEALtknsvHaDTiVLB9hKoP6zllGeVU3UXGbbaVZcuhfgbSQjzp8rUBx3V0HIGVnz8kmgLsO5zMNQlXEzzFEvfMBeaexQ3CZhIdmwwle19ojSw9DVYfA8YJ+Tmrf0soINTf9RuwrOMze7gUJWFTTnRMoRYctXxfndS3eO3ctfyZE3Gjg72GxeYJnLrE4dIf2QXdvv8/bJCIpFIJJKJSFHJwzR3DVJt7lftEgDIjhGiQE1Tq+i2tOgDl2/odDrR4cx0HtpLNZrx7GK12TlS1eHShsUpmlSaekS+VOYW8Au5/KDlHxOb3qp92kzYCxRWmlmWEk5YgHIXBUB6VBAGvU6IShVvQkwexOZeftCyBwCHEOXmKYUVZmJC/MbLtZTibzSQEhEo1qfsNfANubJb15IPir+fx+tzsNKM0aBjbab6rl3joknlHvEX7w/lTr0OorLntVvSWZKi1ikJ4hlUaerFUXdQhHPn33n5AaGJ4p46/+K8zeY629RF9+Aom2Tpm+QqY6Kg9Ohdi68Qf7RkMnEp85tvsPNnhR67pkQikUgks4UUlTzMITeyKJyiSW/ZAbBbIefGKw/KvxN0ergwadOWOc/Zpi56h60ubejSooLw0euw1JdCVwNk33DlQZlbICBy3jopOvtHON/c7VJArq+PnrTIQOrbLNBwbPL1icoSrc/Pzk/RxF0XRXZssBCVavZDxibw8bv8AGOAEFJKXxMlcvOQwkoLq9IiCfRV3+wzOzaYanMfjsq3IXoBRKRffoBOJ9w5tQdF0Pk8pLDCTESgkcVJYarPzYkNoWfIymDpHvAJgJR1Vx5U8CHoaYa6gxrMdvY5WGFBp4NNKp2SEslcZqKgtO+rm2etU1vd47dy9luXPsuVtfWS/sguBkfmp+gskUgkEglIUcnjFFZYiAv1IydWfRZFckQgvj56fBsPgY//5aVvToJjIX2jKI+bh7kvByos6HWwIVt5QK4To0FPRnQQwU37xV9kb7/yIINROLzKd8NIv3uT9QKHqiw4HLhUmgOQFRtMkOkE2IYhc+vkBy26G8yl87JL1YXmbroGRtnsoosiJzaYEUutyLzJ3DL5QYvugsGLUHvA1Wl6jfbeIUpbe9jk4v2TExuCdWQI6g5N/v4Ccf/gENlB8wy73UFhpYWNOTEY9OpFSedzXVf9jngOTyx9c7LwZlGaW/qau9P1CoWVZgqSwogI8vX2VCQSTZgoKB34+hayYmY3Kyws0Ejd47dyz4pLZXZ533qTr794dpqzJBKJRCKZu0hRyYNcclGo69rlxKDXkRUTTELnCeEmmWzDAmJT11EFbefdnPHsc7DSTEFyOOGBrm1YcuKCie8ugrCUK10UThbfA6MDl0p45hGFFWbCAowUJIe7dH52bDDpve/h0Bshbf3kB+WONfsp3zX5v89hCiuEE3CDiy6KrNhgVjnG3jcZm6c4aBv4hcKFv7t0DW9yuEqUdrnaCj4nLphFujp0tuGp75/YXJHtNg/dkqVtPVj6hlWH4DvJjgsmhi4Ceusg4/rJDzIGiHuofPe8E/67B0cpauySXd8kVw2fe+70+M9PPbiKtCh1WY5a8uP7llLz/UvN9l48fWUHOolEIpFI5gNSVPIg55u7RRaFixsWgMVROpJHa0Uo91Tk3Q7oRG7OPKJ7YJSzbm5YsmOCyRktx5a0auqDUq8TXc4q33b5Ot7A4XBwsNLMxuxol1wUINangCqGo/PBN3Dyg8JTIb4AyuZf05+DlRYWJ4USHew388GTkB0bzEpdJSO+4RCzcPKDjP6w4Cao2A12uxuznX0OVliIDPIlPyHUpfOzY4JZoa8Uf5jMKekk9zZoOgEDnS5dx1sUVoyJbi4+g2KC/VjvXyf+MN36LLxFlMC1Frl0HW9xpMqCze5wqTxZIplrDI7Y2H1BlOlmxgSxLTfOyzMCvV5H3eO3EhF4KTMx/ZFdDI3KcjiJRCKRzB+kqORBDlaY0elgoxtZFNcFNKLHwVDcsqkPCooW7b3nmWhyuNqC3YHLLgGARWGDJOssWMKWTH2Q3gBZNwin0jwSBcpNvZh6hl0ufQPIig5gib6W9pBF0x+Yeys0Hoe+dpevNdv0Do3yXsNFl104IESlAn01bcH5l4fgv5+cG2GgA1rPuHyt2cbhGCvtyo5G76IoGRHky1rfGjqN8RASP/WBOTvAYRcNBeYRhRVmcuNDiAudwgU6Azqdjs1B9djQQ8LSqQ9csFNk380z4baw0kywnw/LU11zSkokc4m8b1364u2dr27x3kQm4cy3buTl/3fJDZr7n29yrKbDizOSSCQSiUQ5UlTyIAcrLSxODCPKRRcFQL5D5NzU+i6Y/sCcG6H51LxyChRWmAnx82FZiusblnxbBQAVxtzpD8y5EfrN88op4CztcsfJlaNvIUQ3SIXPFC4cJwtvBhxQtdfla802R6o7sLrpogjVj7BA30yZPnv6A7NuAHRQOX/Wp6ytF0vfsFtOSYAV+kpK9DM8fxKXQ2DUvCoxHRixcqq+0+3SrgJdFeWk4TAGTH1QUJQI8a7Y7da1ZhOHw0FhhYX1WVEYDfKjgmR+c+cvD43/PLHkbC6xIjXisrnd/+QxvvtaiRdnJJFIJBKJMuQnRQ/hdFG4u6FLGiilwR5DWc8M7eTnmVNAlHZZWJ8dhY8bG5aE3guMOAy8N5Iy/YHZTlFg/ri5Ciss5MQGkxA2zWZ1BoLMQkQ7OZo5/YFxSyAoBqrfdflas83BSjNBvgZWpkW4PkjrWQzYOTGcPv1xQVGQtAKq5s/9c3Cs86RbpUs9LUTbzBwezsAxXR6Q3iCCvKv2zhs34LGaDkZtDrecbthtpA6WcdqaRUf/yPTHZt8gcu/6zK5fbxapsfTT3DUo85QkVwVnm7oBuGdFssvOzdnAWQ7n5KnDtWz8wfz4XCeRSCSSaxcpKnmIYzWdbrsoAII7znHekUWlqW/6AxOXQ0DkvBFNnBsWd9fHp+U01YZMyjtmaPceFA1JK+eNk2JwxMaJOvddFDSfpl8XxLHuGdxger3oDlfz7rwRBQorLFyXFYWvjxuPseb3AHi7O2l60QQgewc0zR834MFKCwvigokPc620CxD/f4Fjw5m09w5Pf2z2DlEi2DI/SgQLKyz4G/WsSndDlLRU4Gvrp8ieTVX7DM/orLHuizX7Xb/eLDLulJR5SpJ5zsTw6x/fN02Z6hxiorDUdHFQBnhLJBKJZE4jRSUPUVhhJtDXwIo0N7Io+i3ouhtpDMydecOiN4hvwueJU8C5YXG1FTwgOim1nqU1KG/m9YGxEsHT0G9x/ZqzxPHaDkasdk1EpbbgfKrMAzOLJlnbRImg6YJ715wF6iz9NHQOuB8g3PIe/f7x1I+E0No9NP2xOTsAx7xwAw6O2Dhe28nGbDfXp+08Dp2eEkfazO+xcTfg/BBuCyvMrMuMwt9ocH2QMVGyyJE18/okLBMNA2rmhxuwsMJMelQgqVFTBPxLJPMAu/3S772/fHqdF2einrrHbyVhwpcCUliSSCQSyVxFikoe4kCFmfVZUfj5uL9h6Y9aQpVZgWiSvQMGLPMiN+hgpYX0qEBSIt3YsHQ3wkgvw1F51Fr6sdpmENOytwOOeeEUKKyw4OujZ21GpOuD2EbBXMZg9GL6R2wziyaZW8TrPBBNnKVdbotuLWcYiikAoHqm99g8cgM6RcnNC91cn/YSbOGZDOM7s2gSGAnJq6B6n3vXnAUaOweosfS778JpL8Hh44/JmKxM+M/cIt5fMwm8XmbYauNYjQZOSYnEy2R+81I4/trMKC/OxDWO/tsNl8UoSGFJIpFIJHMRKSp5AKeLwu0P5KbzABiTllLfMcCIdQbRZLy8Ym5/Ez5stXG0usN9l4lJBFj6JS5i1OagoXNg+uMTl4F/+LzIDSqsNLM2I9I9F0VHNdhG8EsUnfFmFE1CEyA2f16ISgcqLKREBpDujotipB86a/FPFuUQikSBrLESwTkuChyoMOPnrigJ0F6CIT6fED8fZW7ArG3CDTh40b3repgD4yH47mXeYSpGF7OQjJjQmd9fIEpMe1vBXObedT3M6bqLDI7aZOmb5Krh7a9c7+0puMyzD6/lliWXum9KYUkikUgkcw0pKnmAA1qUdgG0l0JoMimJCdjsDuo7+qc/PjgW4pfMedHkZK3YsGxx20VRDEBU5jJAoSiQuWXOOwWaLg5Q1d6nwf0jRLeoTIWiCQhRoOEojMwg0HmREaudo9UWNuXEoNO5EbhqLgMcBKYsIdRfoWiSuRX6TONrO1c5oEVp15jopotbRFZssPL7x2GH2kLXrzsLHKgwkxQeQFZMsHsDtZdC7CKyFa/PmPA/x4Xb/RVmjAYd67Lmn7NDInEyUXzJiQvx4kzc59cPrLzsM8H6x+a+I1QikUgk1w5SVPIAhRVm0qICSYsKcm8gUwnE5ZMdIz4MKRcFjsGwgmO9xP7ydnwNeq5zd8PSXgphKWQkJwIoKxHM2gq9LWAud+/aHmR/uRAl3RfdSkBnICJ1EWEBRuWbXtsI1B9x79oe5FRdJ/0jNrYujHVvoDGnmy5usQuiwNwVbhs7B6gx97vvlDSXAw6IzRfro+T9lbQS/ELntGgyYrVzpMrCloVuipIDndDXBrF5ZMcG09o9RN+wdfpzwlMhKmdO3z8gntGr0yMJ9vPx9lQkErd59K7F3p6CJjz9iTXEhfoB0NI9xLdemfv5hxKJRCK5NpCiksYMW20cqe5w32ViGwVLBcTmkRUrxCnFopJ9FOoPu3d9D7K/wszazEgCfd3csJhKIDafUH8jcaF+yp0mMKc3vfvLNXRRRGWhMwaQHRtMpZL1SV0PBr85vT7vjomS67UQJX0CICKd7NhgZeVLYckQvWBOr09hpVZOyTE31pioZO4dpntwhi6LBiNkXA9Vc9cN6BQlt7grSjrXJy5//L1ao1TYrjsE1hm66XmJlq5BJ7R9aQAAIABJREFUKkx97ovaEokXOVJ1qSHHA2vTvDgTbTn+ze3jPz9ztJ7DVXO/8YhEIpFIrn6kqKQxmmVRdFQJcSh2EYG+PiSFByhzCqSsExvlObrp1ay0a4LoBghRQIloEpEGUdlzdn2EKKmBiwLAVHxpfWIUro9vIKSum9Nh5vvLzazOiCDIXRdFezHELAS9gezYYCx9I3QNjMx8XtY24eQanSH43EscGBclNXBK+gRAZAbZY6KJMuF2C3Q3QGeNe9f3EPsrzNqIkian6CbK30Dp+mwF6yA0Hnfv+h7C6ZR02wkokXiRj/x+br6/tKDu8VvHf37g98dndkhKJBKJROJhpKikMQfGsijcL+1yblguiSaVJgUbFqM/pG+Ys6KJM2/K7W/BnaJb3CJgTDQx9+NQ4o7I2iacXHPQKXCq7iIDWrgoRvrhYh3Ejq1PbDAd/SNc7FcgmmRuEYJLr8m9OXiAposDVLb3abPhNZWM3z9Op4nisGXrIDQec38OGjNqs3OkuoPrF2ggSraXjItuOXFj66PULQlz9hm0v7xdO1HSPxxC4kmLCsRHr1MmKqVvBJ1hzpbA7S9vJyk8YFwok0jmM5WP3uztKXiEicLS4m+/5cWZSCQSiUQiRSXNOVBhZlVapPsbFpPIwyFmISBEgRpLH3a7QtHEUgFdje7NwQNoVtplEiHdxOYDYn36hq209Shwj2Rtg9GBOekU2K9VaddYCPW4KDkmCijOnQKoPeDeHDyAZnlT/Rbob7/s/gGFTpP0jaA3zklR4L36i/QNW913AoIQlcbWJzkiEF8fvbL7JzITwtPm5Po4S7u0WZ9SIUrqdBgNetKiApXdP/6hkLx6TroBR6x2DldZ2KyFU1Ii8RL//fqlRgpGw9X7Mbf2sVvGf5Yd4SQSiUTiTa7e37ZewNQzRFlbL5u1yKJoLxVlWj4ilDE7NpihUTvNXYMzn+t0CtTMrU2dZgG5MB5CTXQOAFmqRQGfOemk2F9uZk2GBqJke6l4neDkApS53eILICBiTooC2uVNXe4EHBdNlNw/fsGQsnZO3j8HKsz46HWsz3ZTlOzvEF3u4oSoZNDryIwOUrY+Op14BtUWijLVOcQlUdJNp5vDMdb5LW/8rxSHmYNwA7acEWHfc4hT9WN5U1qIbhKJl/jDoVpvT2FW0Ol07Pvq5vE/b3h87v1OkkgkEsm1gRSVNOSdsnZAAxcFiNKK921YQKFoEpMLIQlzbtPr3LBo4hIwlQhBaYLoBgrXxy8EktfMufVp7hqksl2jgFxnHk5EOgBJ4QEEGA3K1kdvgIzNwkkxh8KWnXlTW3O1yJtyhiwL0U2VaAKQtQXazgnH0xzinbJ2VqRFEOpvdG+gCSHdThR3yAMhKo30QtMp9+ahMQcq2kkM8yfH3dKu7iYY7rlifeo7Bhix2mc+P2sr4IC6g+7NQ2P2l4vy7fXZ0d6eikTiNhOdPFcrWTHB7FwUD4jPEBWmXi/PSCKRSCTXIlJU0pC9JSaSIwJYGBfi3kDOPJyxDS+gLihXpxO5LzX7wW5zby4ackDLDcuE0hyAmGA/Qv191G16W8/OKVFgf7mWouSlPBwAvV5HZkyQcidF1lbobRFllHOE8bypBRrkKbWXQEAkBMeN/5XoANev7PxxN+B+9+eiEY2dA5S19bIjL27mg2diClGp8eIAQ6MKnikZ14NOP6eEW1Ha1cHmhbHaOCXh8md0bDA2u4P6DgX3UNJK8A2Zc27A/eXtrE6PJNhdp6RE4iXeHfs9ClwzJZy/+djK8Z9v/GmhF2cikUgkkmsVKSppxMCIlUNVFrbnxWmwYSkTrxOcShFBvkQH+6oTTQYvQmuRe3PRkLdLTazNiHJ/wzLcC13146U5ID48qnZSwJwSBd4ta9emtAuuEN1ARYc8EOU5MKc2ve+WjeVNuVvaBWJ9xvJwnGTFqBBNEpaJkOY5JJrsKxXB6tvzNRCVTMWiBDIkfvyvsmODcTigRonwFhAOSavm1PqcrOukb9jKVq1EWxCu0DGyY8SXCYrC3g1GUYY7h0qUm8fypjQRtSUSL/HQH096ewpeYWJwt8xXkkgkEslsI0UljThUaWHYameHFhu6SVwCIDa9qjI7YM6IAlXtfdSY+7lxkRbr4xTdJhFNlK5PolMUmBvr0z9spbDSwo58DURJZx7OBFEShNutuWuQfiXthyPSISJjzohuDoeDPSUmrsuKItDXTVHSbr8iDwdUiiZ6g3iPVb87Z0oE95a2kxUTREZ0kPuDtZeKzoET7sXxElM1breW94S4PQd4q7gNf6OeTTkalZeGJgvxbIysWLHuyoXtrcKR2jk38l/2FLcBsCM/foYjJZK5z64vbfT2FGadf3x+w/jPb5fMve6tEolEIrl6kaKSRuwtNRHi78OajEj3B2t35uFkXPbX2bHBVJp6cSjZxAbHiMDlOSKa7CkRG5btHirNAbE+lr4RugZGZh5Db4DMzcJJMQdEgYOVZkasdm5apMGGbrw05/L1GW8Lr0aYrDs0J8KWy029NHQOaLM+3Y0w0jfp/QNqRJNtokTQXO7+nNykZ2iUYzUd2riUJgmhBsiIDkKvUyOabAOHXQR2exmHw8GeYhPX58QQ4Gtwf8D2kivWJ9DXh6TwAOXrk7lFvM4R4XZPsYmc2GBtREmJxMssSgzz9hRmnWUpl0TuTz0zt/LsJBKJRHJ1I0UlDbDbHbxT1s6WhbHatK9tL4HYXNBfPlZ2bDA9Q1bMfcPKxsnaBo3HRbmYl9lTbKIgOYzE8AD3B2svAWOQaFs+AVVh3TCnRIG3ik1EBBpZnR7h/mDOzm9TiSZqnBQjvdB82v05uclbF0zodLA9X6M8JbgsDweEaKJTJZpsFa9zoITpQLkZq92hTZ5SV4P47/4+UdLPx0BqZCBV7QqfJ0krwS90TpTAnW/upq1niBu1ECVtoyJr7H3rA6ILpWJRMnoBhCTOifvnYv8IJ+o6tRFtJRIv8eKpRm9PwevIMjiJRCKReAMpKmlAUVMXlr4RtudpsOEFUVoRu+iKv3ZJNLGPQt1hbeblIqaeIYoau7hRCxcFiLyXyUQ3NZkmIMLMweub3lGbnX2lJm7Ii8NHE1GyWJT2hSRc9tdpUUH46HXK75/0TYBuTrjd3ipuY0VqBLEh/u4PNkkeDoC/0UBKRKDy+yc8FaKyvX7/gHBKRgX5sjxVS1Fy8meQ4vvHYBSB3VXedwPuKTZh0Ou4IVeDZ3RHNdhGrhBtQZSYVrf3Y7cr+P+r0wlhsrbQ6w0V9paasNkdUlSSzGu+/tI5b09hTvDUg6vGf+4Z8r7TWCKRSCRXP1JU0gDnhkWTrlT9Fuhvv6K0AiAndkw0UbqpS10nyui8vOl11vZr4hKAsdKcKzd0SREB+PnolW96I9KEKOBlp8Dxmk56hqzaiW7O9XlfNpPRoCctKlD5+gRGQuJyr5fnNHYOUNLaw01a5HGBWJ+wFPAPveKfcsZKTBWTuVWUCFoVugc9wIjVzrtl7WzNjcWg16DbUXuxeJ3kGZQVG0ytpR+rza5srKyt0N0AnTXuz8sN3ipuY016JBFBvu4PNkX5LQjRbXDURkv3oLKxMreMNVQ46/683GBPiYnEMH8WJ135npBI5hvPf2qtt6fgVbblXvpdWfBfe7w4E4lEIpFcK0hRyU0cDgevn2thQ3Y0YYFG9wecIg8HIC7Uj2A/H+WigI+f6DDkZVFpT4mJ9KhAcmI16GrW1w4DlitKlwAMeh2ZMcFUKl0fmBOiwJ4SDQOEnXk4k9w/AAviQqhQJZpsgaaTMNTj/txc5K2xAGHNXBSmKzvjOclNCKHG3M+wVaFzJGsbjA5A4wlt5uYCh6ss9AxZuXmxhuszheiWHRPMqM1BQ+eAsrGcXRa9+AyqMfdR2d6nTZMAEM9onUGUr70Pp5tU8TMoc8vYJL0nbA+MWCmsMHPjovhrpgW75OpmfVa0t6fgdaoevXn854OVZi/ORCKRSCTXAlJUcpNzTd00XRzktoKEmQ9WwhR5OAA6nY6sWJWiSdY26KgUOSleoGtghKPVFu02LCani2Iq0SSYijYVosm4KHDc/bm5gN0uAoQ3L9AoQLi7CYZ7JnWZAOTGh1LfOaCsAxwIp4nDBvXeK6HcU2wiNz6EtCgNAoSdeThTrE9eQihWu4NKk9ISwY1CYPCiaPLauRZC/X20ESVhSicgQE6ccEtWKF2fyEyRfebFEsq3ioVTUpPOnCBEt6gsMF5ZirlwbH3KWhU+g4JjIW6xV92AhRVmhq127UQ3icQLKCo5vYaYWEr/sT9470sPiUQikVwbSFHJTV4/14LRoOMmrdowm4ohIBKCJ/+AnxcfQlmbwg5wMMEp4J1N3e4LbYzaHNxekKjNgFOELDvJSwilpXtIWQc4EKKA3sdrosDJuk7aeoa4ZYlGouS46Db5+uQmhOBwiG5qikhZO1ZC6Z37p617iJP1GgYId1SJnLFp7h+A0laFziz/UEhZ4zWnydCojbeLTdy0KB5fHw0e59OEUIMQTfQ6FesD4hlUW+i1LoKvnm1hWUo4yRGB2gzYXjzl/RMWaCQpPEDd+mRugYZjMKLQ/aUxr51rJSrIlzXpGnQulUi8xDf+JvOU3s/E0O5Xipq9OBOJRCKRXO1IUckNHA4Hu861siknRpvSN5gyD8dJXkIonf0jmHoUlmvFLBQdhrwkmrxa1EJGdJB2WR2mYgiKhaDJ7e35Y6JAiRpRIHmN99bnbAsBRoN2LgpnHs4UooBzfRQ7KZwllJV7vBK2/Pq5FhwOuHOZxqLkFE6l9Kgg/I16SpWuDwjRpKUIBjo1mKA6CivM9A5buVUrp6SlUohuUziVAnwNpEcHqReVRnqhafZbXFeaeilt7dHu/hnuhYt1U4q2AHkJISrXZ6sI/q475P78VNI3bGVviYlbCxK0aRIgkXiJl043eXsKc5ovv1Dk7SlIJBKJ5CpGfop0g/caumjpHtKu9G2GPByA/ESnaNKtbExnh6Ga/bPeYcjUM8Sx2g5uX5qoXVaHqXja9bnkNFEpCrSeEyHps8iI1c6u863syI8j0NdHm0FNxRCWCv5hk/5zUngAwX4+6ja9C26Ci7XC5TPLvFLUQkFyGJkxGuRxgShdmiIPB0Qu18L4UJVOk62AwyslTK+fayUi0MiGbI0yREwXxGvc4ikPyU8IVS7agugAp9N7Rbh99WwLeh3aiW7tZeJ1CqcSiBLTGks/Q6MKn7dpG8EYCBVvajBBdewpbmPYatdOdJNIvMy3bpv688G1yES3Ulmb97IRJRKJRHJ1I0UlN3j9XAu+Bj3btXKZdDeKb/SncFEA5MaLzA7VoslQl3BTzCKvn2vF4YA7lmq0YbHbwFw27YY3JsSP6GA/9U4BL4gCh6rMdA2MaruhM5VMK7rp9Tpy40PUfbhccJN4neVNb7W5j/PN3drdPyBE26hs4cCagvyEEErbepSXmCYuFyLeLIsmgyM29paa2Lk4HqNWLhPTBTD4QnTOlIfkJYTSdHGQ7kGF5WwB4ZC0atbXx+Fw8OrZFtZnRRMbcmX+kUvM4AQEsT42NblcRn8hTFa8NetuwH8UtZAcEcCK1IhZva5E4ike2pDu7SnMWXb+7KC3pyCRSCSSqxQpKrmI1Wbn9XOtbF4YQ6i/RqVvJmdpztTfgof4G0mNDKSkRWVmB0DN7G7qXj3bwqLE0PGOSG7TWQvWoSlLc5yoLj8ZFwVmNxfnlaIWwgON2gUsW4fH8nCmvn9AbHrLWlXkcoWninuy4i0NJqmcV4pa0Ok0FCVBiALTiLYg1qdrYJS2niFlYxp8hBunZv+sigL7ykwMjNi4Tau8MhBOt5iFYJj6mXaphFJlCVzLezB40d0ZKuZsUzf1HQPa3j+mYvANFm7AKchLGBP+1Qi3C3dCT9Mlp9gsYO4d5nCVhTu0dJJKJF5G3stXMrETnEQikUgknkCKSi5ysNKCuXeYe1YkazfoeN5L7rSHqS4/CYqGhKWzKprUd/RztrFLe0EApnUJgFifSlMfoza7snH1BiG8Vb8za6LAwIiVPcUmblmSoE3AMghByWGbUVTKTQihd9hK08VB5WMv3An1R2ZNFHA4HLxS1Mz6rChiQzVymYz0izwcBaIbuBBG3d0onHSzxIunmkgI82ddZpR2g5qKp3UCwqUSXNXr47CLwO5Z4tUi4SS9abFGIe8ghP/YfNBP/Z5NiwoiwGhQtz45s+8GfON8Kza7gw8sT5q1a0okktlnYl5a+iO7vDgTiUQikVytSFHJRV483UhkkC/bcmO1G7S9BMJSpszDcZKfGEpdRz99StvCg9jUNR6HIYVZTG7y0ukm9Dq4Q9PSrmKRzRIzg+iWGMqIza68/AQg6wbobZk1p8CbF9oYHLVxp9YuCpjW6QawJEncX+ebVdwLC3YKwapqn6uzU8WZxi7qOwa4c6mGG16n4DODU8mlEtMFY98El77uysxU09Y9xMFKM/esSMag1+ib+f4O6G2dUXSLDfEjMsiXYjVuyaSV4BcmAt9ngRGrnVfPNrM1N4awAI2cpA7HWOe36UVtg15HXkIIF9S8v0LiIHEFlM+eqPTymWZy40NYEBcya9eUSDxBnaXf21OY83ztxslzBCUSiUQi0QIpKrnAxf4R9pa0c+eyRO1cJjDW+W36DS/AosRQHA4oViUK3Ax2K1R4flNnszt48VQT1y+IISEsQLuBTcUQmQnG6ccsSA4H4FxTl/KxF94C6KD0NTcmqJwXTjSSHhXImgwN23ibikUeTlT2tIflxofia9BztlHF+iSthMCoWSuB+8uJRgKMBm5eorHLBGYsn3SWmBa3qHh/hSaILoJls3P/vHymCbsDPrhSQ6ekgpBuEOUli5PCONekYn0MPrDgRih7A2wqxHAX2VdqwtI3wv2rpy5TU01vq3DqzSDaAixNCedCcw9WpW5JgIU3Q/Np6Gt3Y5LKKG3t4WxjF/euSvH4tSQST/ONl855ewpzni9su5STp7j0XSKRSCQShUhRyQVePdvCiM3OvSs1/EBuHQFz+YwbXoBlKUI0KVIjCiSvhpAEKPmHqzNUTGGFmbaeIe5frfGGpb1kRhcFQHpUIGEBRnXrExwDaeuh5FU3JqiManMfJ+o6+dDqVG3zH0zFwsVlmL6TnK+PnrzEUHXrozeIEp3KPR4XBXqHRnn1bAt3LE0kRKu8MhCiiTEIItJnPHRpSjhFDSrWByDvNmg9C10Nrs1PIQ6Hg5dONbEmPZL06CDtBnY63WYQlQCWp4RT0d6rzi2ZdwcMdkL9YRcnqJwXTjaSEObP9Qs0yiuDS6KkgmfQspRwBkdtVKhxSy64CXDMipvrhRMN+Br03C1L3yRXASfqOr09hXlFxr+94e0pSCQSieQqQ4pKKnE4HPz5RAOLEkPHs0U0wVwK9lGRfTQDUcF+pEYGckbNplevh9zbRPnSiGet4i+cbCA62JdtuRp1xQMY7hVB3Qo2vDqdTogCakQTEJtecylYKl2cpDL+crIRH72Oe1ZqvKEzFSva8AIsSw7jfHM3NruKbyxzbxVdBOs8m4vz6tkWBkdt3L9GY1Gy9SzELxEC2QwsTwmnpXuItm6FYd0g3l/g8RK4E7Wd1Fj6+eAqDV1KIES3oFghsM7AstRwHA6VbsDs7eATAKWeFW6buwYprDRz76oU7UoDAUznxesM5W8AS8fckmfVrE98gSh/9rBbcmjUxt/PNLNzcTwRQb4evZZEIpk73LokwdtTkEgkEslVihSVVHKy7iJlbb18bF2atgO3FIlXBaISiG/CVYsm+XeCdRAq31Y5OeW09wyxr7Sde1Yka1sa2HoOcEDCMkWHL0sJp8LUS78qJ4VTFPDcpnfEaudvp5u4IS9WuzbnAL0m6GsTG1MFLE0JZ2DERlW7CidF9g2i81WxZ91uL5xoJDc+ZNyRpwl2u7iHFL6/lqc63YAqgsmjskRpVJlnRaVnjtUTFmDkdi27voEQlRSLki64JX0DIWe7EN3sKsrCVPLXk40A3KtlaSCIZ3R4GgREzHhoWlQg4YFGdSWmOp14Rle/A4Mqn+0qeON8Kz1DVu1FW4nEy3xiQ4a3pzCn+dUDK7w9BYlEIpFcpUhRSSVPH60j1N+HO5dp7DJpPSuCbCMzFR2+PDWctp4hWrtVdPBKWw+B0R4VTZ47Vo/N4eDDazTMMgFoHRPdEpWJSstTwrE7VIZRhyWL7CAPOgV2nW+ho3/Eg+uzXNHhS1NccFIYA0Rgd+lrHiuBO9NwkfPN3Xx4jcalgZ3VMNqvWFTKTxS5U6rcgCCEyfoj0Gd2YZIz09Y9xFsX2rhvVTIBvjM7rhRjHRGZbvEzOwEBIoJ8SY8KdKFE8E4hfjadcGGSMzNstfGn4w1sXhBDSmSgtoO3Fil+/uh0OpYmuyD8L7oLbCNQvtuFCSrjmaP1ZEQHsS5Dw66BEskc4JObpKikFJmrJJFIJBItkaKSCkw9zg1dirYbOhAbloQC8W21Apanim/LVW3q9AZRwlTxFoyqKOtRyNCo2NDdkBurbdYLCJdASCIEK+u2V5AsOpy5VALXcsYjuTgOh4M/HKolKyaI63M0zHoBMWd0orxLARlRQYT6+/BevQonDohN72Cnx0rg/nColhA/H+7R2mXSela8KhSV/HwMLEoKVS8q5d4GODzmVnr+RAM2h4OPau2UNF0QYkai8m+ynW5JVZuTBTeJMHkPZZe9frYVS9+w9o6FgU64WKfYKQlCuK0wqcydSlopSuA8lH13uv4iRY1dPLg+Hb2WpYESyRwgMVzDxiBXOf/9eqm3pyCRSCSSqwgpKqngT8fqsdo9sKGzjULbBcUbXoC8hBB8ffScVisK5N8BI31QrX1r+FfPChfOQ56woLecUewSAJE7lRkdxIlalQGeebeLVw+UeJ2qv8iF5h4+sTFD+w1dyxmIWQh+wYoO1+t1rMmI5Lja9fFgCVxz1yC7L7TxodUpBPtNHzaumtYiMPiJNVLI8pQIzjV3MWJVUaoVvwSicuD8Sy5McnqGrTaeP97A1oWxpEVpLdq+J16TVio+ZUVaBO29wzR2qnBL+odC5lYoeUXzEjiHw8FTh2vJjg1mU060pmOPi5IqnkFr0iOxO+CkmhBhZwlc1T6PlMA9dbiWUH8fbbsGSiSSecdTh2u9PQWJRCKRXEVIUUkhfcNWnj5az435cdq7cMzlYBtW9S24n4+BFanhHKnuUHetjM2iBO7cX1ROcnocDgd/PFzHwrgQ1mdpXFYx3AsdVarWB2BdVhQnajvVtfWOyoKkVZqvD8BTh2oJCzBy93IPbOhaitSvT2YUtZZ+dWHUxgDR+rz0VbAOq5zk9DxzpA6Hw8GDG9I1HRcQokDcIjAo7ya3JiOSoVG7uhJBnQ4KPgT1h6Cr0YWJTs3fTjd7xoUD0HwGAqMgXHlZ5nWZ4n1+tMai7lpL7oWeJmg4ou68GThR20lxSw+f2JChbekkXCovVfEeW5kWgdGg45jaZ/Siu0XTBo3dbs1dg7x5oY0Pr0klSGvRViKRzAsytf78KpFIJBIJUlRSzAsnGugeHOWzW7K0H7zljHhV4VQC2JAVTUlrD539I8pPMhjFpq58tyjp0Ih3y9spbe3h4U2e2NCNhXSrcAkArM+Kom/Yqi5XCWDp/aIcqO28uvOmoaq9jzeL23hgbar2pZM9rSKnRmGekpN1Y6LAsRqVm96C+2Hwoiij1IieoVGeP9HAzYsTSI7QOAvHbhOim8r757rMKPQ6OFSpVjT5oHg9/6K686bBZnfw28JqCpLD2JDtgSyclvdE6ZuK9252bDAxIX7qhe3cW4XbrejPKic5Pb/eX01kkC93Ldc47w7EMzo8DQIjFZ8S4GtgeUoER9W+v5JWQGSW5uvz+4M1AHx8fbqm40okkvnDv92S5+0pSCQSieQqRIpKChi22vjdwRrWZUayInXmzj+qaTwO/uEQla3qtPXZosRDtSiw9H6Rn1L8d3XnTYHD4eCJfVUkRwR4ZkPXfEq8uiiaqN7ULbob9EY4+4K686bh1+9W4e9j4OGNHioNBNWiSV5CKKH+Purvn6ytEJIARc+rO28a/u9wHb1DVj7nCdHWXAbDPZCyVtVpYYFGFieFcaRapagUmQEp64TbTaMw1DfOt1LfMcD/25KlvWg70i/WKEldZyCdTsf6rCiOVHeoy1XyDYT8D4jcoJEBlZOdnLONXRyoMPPJTRnai7YAze+pfv6AcEteaO6mZ2hU+Uk6HSz7iHC7dWpTotLeM8Tzxxu4e3kSSTJ3RiK5Zrl+gcalwRKJRCKRIEUlRbx0uglTzzCf26JO9FFM4wmx4dWr+89RkBxGkK+Bw1UqN70JSyE2H85q8034wUoLRY1dfG5LFkaDB26phmOiK57CkG4n0cF+LIwL4ahaJ0VQlAgUPv+iJl3Oai39/KOomY9dl0ZUsJ/b411B4zERfqyy/M2g17E2M0q900RvECVelXugr13duZPQMzTK7w/WsD0vjsVJYW6PdwWNx8WrSlEJYEN2NGcauuhXE7YMUHCfEGqcZVNuYLc7+NW7VWTFBHFjfrzb411B61lw2FWFdDtZnxWFuXeYanOfuhOX3i+y3cp2qb7mZPzinSrCAox8/Lp0Tca7jO4m6G6E1HWqT70uMwq7A07UqHSFLv0woNPsGf1kYQ1Wu4PPb/XQ7zCJRDIv8PXEZzSJRCKRXPPI3y4zMDhi44l9laxMi+B6rcNfQZSgWcohZY3qU40GPWszo9SLSjqd2NQ1nQRzherrTsThcPDzfZUkhPl7JvzV4RCiUup1Lp2+PjuKk3WdDI7Y1J249H7oM0HVXpeuO5FfvlOF0aDnU5sy3R5rUuqPCheF0V/1qZtyomnoHFAvCiz7CDhscO6vqq/5fp4+XEfPkJUv35Dj9liT0ngCgmIhIl31qRuyorHaHRyvVSm8Lb4bfPxUxl6iAAAgAElEQVTh9NOqr/l+XjvXQllbL1+6IcczHbsajorX5NWqT12fJZ6JB9WWCKZtgLBUKHpO9TXfz4XmbvaWmnh4Y4b2Ae8gnj/gkqi0PDWcAKOBAxVmdSeGJQlHYNGf3Q40N/cO89zxeu5clqh9HqBEIplXNF1U0VhBIpFIJBKFSFFpBp4+WoepZ5h/3ZmrfdkJCGEHXNqwAGxZGENdxwBV7b3qTiy4X5R4nXrKpes6eavYxOn6i3xxWw5+Ph4oO7FUihb2LrhMALbnxTE0audgpcpN3YKdEBwPJ3/v0nWdlLb28PKZJj5+XRoxIR5wKY0OivI3F++f7XlxALxdYlJ3YsxCEWj+3tNulXh19A3zZGEN2/NiWZLsAZcSCKdSyhpVeUFOVqVHEGA0sK9UpSMrIAIW3yNEt6Ee1dd1MmK18+M9FeQnhHJ7QaLL40xL3WGIyRMOPZWkRAaSHRvMnmKV949eDys+BjX7wVKl+rpOHA4H33+jlIhAo2cC3kHcP8YgiFui+lR/o4HrF0TzdolJXYkgwLIHoLsBavervu5Efr6vAqvNwRe3eUi0lUgk84bfFlZ7ewoSiUQiuQqRotI0dA+M8r/7q9m6MIY1GcoDWlXRcAx0BpdKT4Dxcpi31G7qQuJE6+qi52FYpUtljFGbnR+8WUZObDD3rfJQi+pGp0vANafSmoxIQv192KNWNDEYYeWDwqnUWePStZ0b3rAAI1/Y6qENXfNp0Skqdb1LpyeGB7AoMZS9atcHYPUnwVIhhAEX+dneSgZGbTxyc67LY0xLn1n893NRlPQ3GtiaG8NbxSZsdpWiwKqHYbQfzrvu5vrziQYaOgf4xs6FnnEp2axCNElz7f4BuGlRHCfqOrmopmEAwIp/GhO2/+DytfeXmzlS3cGXb8gh1F95Zz9VNByF5FVgcM0FtSM/nraeIfUNA/Juh6AYOP6kS9cFqDT18vzxBh5Ym0qGdClJJNc8zx1r8PYUJBKJRHIVIkWlafjRnnJ6h0b5xk4PbXhBbFgSCkR4rQvEh/mzPDWcNy+0qT95zadguNvlTe/zxxuotfTzb7fk4uOpOv2GYxAQCdGuiTJGg54b8uLYV2rCalNZRrLyn0Cnh1N/dOna+yvMHKy08KVtOYQFenDDCy6VTzrZkR/H6YaLWPqG1Z24+G4IjIYTrm16K029PH9CbHizY0NcGmNG6g+LVxedXAA3LYrH0jfMmYaL6k5MWgHxBXDyKZfcXJ39I/x0bwXXZUaxeUGM6vMV0XZOZBu5JSrFY7M72FvqirB9B5z5kwgLV4nVZuf7b5SSER3EA+vSVJ+viKFuMBW7LGoDbMuNRa9zwQ3o4wcrH4KKN10O7P7+G6UE+fnw5e0LXDpfIpFcnSxNCff2FCQSiURyFSFFpSk439TNc8fr+fh16eQlhHrmIkM9ovwtc4tbw9y0KJ7zzd00XVTZSSllLcQvgRO/V73pbe8Z4kd7ytmYHc3WheoCtBXjcEBtodjwulF6eGN+HBcHRjlRqzIsNzRRtD8/86zqLlVDoza+82ox6VGBfNRTG164VLqkotX5+9mRH4fDgXph0sdPuLnKd8PFOlWnOhwO/uu1YgJ9DZ7LUgKofgf8wlx2AoIQBXwNenarXR+dTri52ouh7qDq6/5gdxl9Q1a+c+ciz5TeAtQfEa9pG1weYklSGIlh/urdkgCrx4RtF7K5njpcS2V7H/92c65nGgSAELUddkhzXVSKDPJldXokuy+0qS+BW/UJEYzvQhnu3hIT75ab+eK2bCKDfFWfL5HMNxo7tekmeS3w0mddf6ZJJBKJRPJ+pKg0CTa7g/985QJRQX58ZYcHv+GtOwR2K2Rtc2uYWxYnAPCPM83qTtTpYM1nxKa3+h1Vp37ntRKGrXb++wOLPbfhtVSKrkturs+WhbGE+Pnw0ukm9Sev+xwMXoQz6gKFn9hXSV3HAI/etQRfHw+9zUYGhCjg5vrkJ4SyMC7EtfVZ9Qnh5lJZovPS6SYOV3XwrztzPdMRD4QoWfMuZGxyuXQJIMTfyPULonn9XIt6t1vBh0RI+KGfqTrtdH0nfznVyMMbM1gQ5yEXFwixKzITQhNcHkKn03FrQQIHKtrVu91S1wk319Ffgl15mH5j5wA/ebuCHflx7MiPUzljFVTtBWMgpLjudAP4wPIkqtr7KGrsUndiaALk3QHvPQvDynPzeodG+Y9/XCA3PoSHNmSonK1EMj95bHept6cwp+keHB3/2WNCvEQikUiuSeRvlUn43cEaihq7+I9b8wgL8FDZEgghxxjoct6Lk9SoQNZnRfHnE43Y1ea+FNwHIYlQ+CPFp+wtMbHrfCtf2pbt2ZyO6n3iNfsGt4YJ8DVw5/JEdp1vvexDlSLS1ovSl8M/B6uyzJjS1h6eLKzhgyuT2ZDtgY6BTuoOgW3Y7fXR6XTcuyqZosYuKk0qA9/DkmDJvXD6j9CvrAOYuXeY7+0qZU16JB9Zk+rCjBXSWQNdDW47AQHuW5WCqWeYd8pUBnYb/WHdZ8W93HpO0SmDIza+/uI5EsP8+ZInXVyjg1BzALK3uz3Uh1anMGpz8De1wqROB5v+BTqqoPRVRac4HA6++ffzGHQ6vutJFxcIUSl9k0udFSdyW0ECAUYDfz3VqP7k9V8Qbi4VbqUfvlmOqXeIx+8pkJtHyTXDG+ddiAG4hlj6nT3enoJEIpFIrlLkp833Udraw0/2VLBzUTx3LvNQtyUnNe9C+kZRRuQmH16TSnPXIAerVLb29vGDDV+GhiOXSmGmob1niH/92zly40P49PVZLs5WIVX7ICrbpVbw7+dDq1IZttp5tUilmwtg01ehpwnOvzjjoUOjNr78whnCA438+y15LsxUBVVvC1HSjdIlJx9YnoSPXufapnfTV4VAcfSXMx5qtzv4xktnGRy18dg9SzwTPu3E6b5z08kFogQuPtSf50+4EHK66mHwDYHDytxKj+0upcbSz4/uXUqQn+sOqxmpOwTWQci5ye2hsmNDWJUWwV9ONqov8cq7A6JyoPDHispw/+9IHQcrLTxycy4JYQEuzlgBHdVCmNRAdAvxN3LLkgReO9vKwIhV3clJKyF7Bxz5haLsqXfL23n2WD0Prc9gmcxNkVwDRAfL8k41vPnPm7w9BYlEIpFcZUhRaQIDI1b++YUiQgOMfP/uJZ79BryzRnw7n7lVk+FuXBRHZJAvzxypU3/yio+LwOXC/5n2MLvdwb/89Sz9I1Z+8eHlnivrAhgdEpveLPdcOE4WJ4WyKDGU/ztSp76LV/Z2kT116CeiW9Y0fPf1EipMffzkvmVEeDrHRCMXBUB0sB83LY7nhRON6t1cMQtg0V1w4ncwMH1u1e8P1fBuuZn/vDWPrJhgN2asgMq3ITxVlHe5iY9Bz32rUzhQYaa+Q2WodEA4rH4Yiv8OppJpD32nzMQzR+t5eGMG6z3pcgMRAG0MFMK2Bnx4TSo1ln4KK1UK23oDbPwKmM5DxVvTHnqhuZvH3ihje16sZ7PK4JIo6aYT0MmH16TQN2zlLyddEG43fwMGOuDUU9Me1tY9xFf/epbc+BC+sXOhizNVSJ9ZVUmeROIpXv+iFElmIv2RXeM/58Z7KCdUIpFIJNcsUlQaw+Fw8PWXzlHZ3stP7lvq+WDTklfEa+6tmgzn52PgwfXp7Ctr53yTytbVvoGw4UtiE1VzYMrDfra3gkNVFr59+yJyPJnzAkIwsQ7Cghs1GU6n0/G5LVlUm/t543yr2pNhy78JEfDMM1Me9vczTTx/vIHPbM7kek9163JiLhfCZM4OzYb83OYseoetPHu0Tv3J139ddBGbxo1zsq6TH75Zzs2L4z0vCAx2ifs57w63Qt4n8tG1qfga9PzinSr1J2/4snAr7fvulIfUmPv48gtF5CeE8vWbPCwIOBxQsUeUBmogSgLctjSBxDB/nthXqd6tVHAfRGTAvu9Mma10sX+ELzz/HhFBRn74waWeFf0Byl6HyCyI0saRuSo9kjXpkfz2QA3DVuX5UYDo7pi5RWRzDfVMesiI1c6X/nyGwREbv/zICvyNBrfnPC2FP4SfLlZcFiyReIr4MG2eYVcrI9ZLWYCP373EizORSCQSydWKFJXG+M2BGnada+UbO3M9LwiAcC0krYQI7TbXD21IJyzAyM/2Vqg/ec1nICwF9vw72K8MI/7HmWaeeKeKe1cmc//qFA1mOwPFL0NgFGRs1mzImxcnkB0bzC/eqVTvVlp4i8hWevexSb+dP1Hbyb++dJ51mZF8dYeHBQGA8y+JgOy82zUbcnFSGFsXxvCHQ7X0Dql0K8Xlw9IPw7H/nbQTXK2ln08/c4qUyEAev7vA84JA+W6wj0L+BzQbMjbUn4+tS+Pl95qoMfepOzkwEjb+M1TsnrTMtHtwlE89cwqjQc+TH1/peUGg5Qx0N8CCnZoN6edj4HNbszldf5GDat1KBiNs/y9oL4GiP13xzyNWO5997jQtXUP86iMrPC/697WLzpOL79Z02C/ekE1bzxB/PeVCKP4N34YBCxz88RX/5HA4eOTlc5yo6+Txe5aQHethF6DdJr4YydgEPrL0SDJ36FH7u+saYMF/7B7/+X5P5hhKJBKJ5JpFikqID+QlrT3cVpDAZ653v1RmRjproPWsKBnSkBB/I5++PpN9Ze0UVpjVnWz0F5uWtvNw7oXL/ulQpYVv/O0cazIiefQuD5cFgsgNKd8tXCYG7YLSDXod/7w9hwpTH386Xq/uZJ0Obvwe9LfD4Scu+6cKUy+fefYUyREB/OajKz1bFgjCZXLhJVG2FBKv6dD/smMhXYOj/HiPC8LkDd8CvQ+8/e3L/rq9d4iH/ngCnU7HHx9cTVigB8PvnZT8A0KTIXmVpsN+dksW/kYD33+jVL0bZ+1nISQB3vr3y9w4/cNWHvrjCRo6B/jVR1aQHBGo6Zwn5dxfwOAL+XdoOux9q5JJCg/ge7tKLvt2XBH5d0LyGnjnezB8SbSz2R18/aWzHK/t5IcfLGBVeqSmc56U4n+Aww6L79F02I3Z0axJj+Qne8rp7Ffp8ElaAUs/Asd+fYVw+5O3K3j5vWa+sn0Bdy5L0m7CU1F/GPpMsEhb0U0icZeC/5Jh1BOZWPZW9t/afYkgkUgkEslEpKiEKI164v5l/Pi+WSipALjwN/Gaf6fmQz+8MYPM6CC++ffz9A+rDIRdfA8krhCiwOBFQAhKDz99kszoIH47G4IJiKyX0QHNN3QAty5JYFNOND98s5zW7kF1JyevEnM6/HOwVAJQ3tbLh588htGg56kHVxMeOAvf2recEcLkkns1H3pJchgfW5fGM0frONektv15oijzKvmHcHkApp4h7n/yGKaeYX738ZWke7JboJP+DlH6ln+nZqVvTqKD/fjK9gXsLW3n1bMt6k72DYQd34WW98azcQZGrHz62VMUNXbxxP3LuS4rStP5ToptVDjdFuyEgAhNh/bzMfDdOxdRYerjNweq1Z2s08FNjwqxYv9jYqp2B1978SyvFLXw9ZsW8oHlsyCYgHhGx+ZDrLZh+zqdju/dtZjeISuP7nKh/blTuH3r38HhwOFw8JM95fzinSruW5XMl27I1nS+U3L2L2AMggXuh7xLJFrwtRsXeHsKc46tP9o//vMDa1M974CVSCQSyTWLFJXG0Ol0+PnMwi9cuw1OPy0ClsO1tyH7Gw384IMFNF0c5N//fl6dm0Kvh9t/JgJh3/oPXilq5uGnT5IRHcSfPrnW88HTTk4/DaFJkLZe86F1Oh2PfmAJNruDLzx/Rn22yU2PCVfXa1/meLWZ+588io9BxwufXjc7ggmI8iCDr6albxP52k0LiQ3x5/PPv8dFtW6K9V8SwdivfpHqZhP3/fYopu4hnnl4DSvTZsFhAlD0HNhGYMXHPDL8JzaKrlrfeqWYWovK0O4l94psnH3fxdJax4d+e4yj1R386N6l3LwkwQOznYTqd0QZ1dL7PTL8DXlx3FaQwBP7KjlW06Hu5JQ1sPJBOPZrBmtP8NnnTvP3M818/aaFfH7rLAkm5nJoPAZLPuiR4RfEhfDZzVn87b0mXjqtsgwuNAE2/yuUvY7t/Mt857USnninig+tSpmdslIQXzhc+BsU3Au+s/TMk0hm4AvbcsZ/ttpUuiSvQnL/c/dlv58evUtmKUkkEonEc0hRabapeAu6G2HNpzx2idXpkXztxgX8o6iFn+5VGZqbsBTbdV+Eoud48a/PsjQ5nOc/tY6oYD+Pzfcy2sug9oDolqX3jMiXGhXI/9xbwOn6izzyt/Pq8pVC4nDc+D2oP8yuP36fiCBf/vLp68j0dCczJ4NdUPRnWPxBzV0mTkL9jfzvR1dg6h7ms8+dVud48w2EO34JF+s48uQ/0z9s5dlPrmX1bJQsgcgDO/UUpG3Q3GXixKDX8fP7l2HQ63jojyew9A0rP1mng1t/gn10iLLffZKq9l5+9/FV3L0i2SNznZQTT0JQrGhT7yEevWsJaVGBfPa501S1q+wQtuO7WANjaXv2UxwsbeLbt+fPnqAEYn0MfrDinzx2iS9vz2F9VhTffPk8R6pV5k9d9wVG45fT/4+v8OqRczy8MYPH7l6CXj8LghLA2RdEE4VVn5id60kkKsn+990zH3QVk/7ILoZGLwlrdY9r0xBGIpFIJJKpkKLSbHPydyJXZaFnf8l/fms2965M5ol9lXzntRJGFX5zd7axi7tLNlFtT+DXgU/y3P0Zng/Fncj4hu5Bj17mtoJEvnbjAv5+ppn/96fT9CkUTmot/TxwKodC2xL+w/gcr94bMXsOJYAzz8JoP6z7rEcvszw1gv+5t4CTdZ189A/HMfUMKTrP0jfMl44G8rR1Bw/odvPWbSOsSPWM+DUpVXtF3oyHN7xpUUH87uMrae0e4u5fH1EsnPQMjfLY8REeHfkQG+0n2bexnBvy4jw618swlYg1WvtpjwYshwUY+cM/rcZHr+ODvznKcYWOpRGrnd8et/CFno+RYa9j35J3eGhDhsfmeQVO0XbJByEo2mOXMRr0/OojK0iLCuTBP57kNYWllHa7g5eK2ri/7aP42/p5Pe0F/vOW3NkTlOw2OPl7SFoFCUtn55oSiUJe/+JGb0/Bq9jsjssylEAKShKJRCKZHaSoNJs0nhSlJ2s+BQYfj15Kp9Pxg3sK+OTGDP7vSB23/+IQ+8vbsU/iyrHbHRyptvDJp09y568O09IP7Tt/Syj9+L7yqSlbfGtOTwsUPS9KhII8ny3zhW05fPv2fPaUmLjxJwd4pah5UvHN4XBwvqmbf/lrEdt/coBzzT1YdjyBMSiC4FcevixU2KOMDsGx3wgXzixs6O5clsSvH1hJSUsPO35ygKeP1DEwMrn4Vmvp57uvlbDpB++y+0IrvZu+BbF5RL31eehq8PhcARFgvv8x0cUwT9sA6slYmRbJnz+9jv5hK7c+cYif7a2YMny5uWuQJ/ZVsvmH7/Lbwhr6ln4Ka/ZNJJ54VGRkzRZHfgHGQFj1sMcvlR4dxMuf20BEoC/3/+4Y33rlAs1dk+eYdQ2M8PSROrb8z7s8trsMe85OBpZ/iqSKp0Vo9mxx4ndCtF37GY9fKiLIl79+5joWJ4byxT+f4fN/eo8K0+Ti5MCIlZffa2Lnzwv52otnIS6f7k3/SaJpPxz+qcfnOs6Fv0FHFaz/wuxdUyJRyOKksPGf3y+uXO184v9OkvXNN8b//MVt2VJQkkgkEsmsoVPdwcjLrFq1ynHq1ClvT8M1nr4d2kvhS0XgN0vlUsCe4jb+69ViWrqHSAjzZ2VaBHGh/tjsDpq7BjnTcBFL3whhAUY+uTGDf9qQTqi/Ec48B698Hq77ggjQ9TSvfkmISl88BRHpnr/eGKfrL/LNl89TbuolItDI6vRIkiMC0emgrXuIosYumrsG8TfqeWBtGp+5PpPYUH+oPQjP3CECj+971uNCIYd/Dm9/Cz7+KmRu9uy1JlBj7uORl89zoraTIF8DqzMiSYsMxGjQY+kb5nxzN9Xmfgx6HR9YlsTnt2aJcsCOanhyi8hYenCX5+/5sjfghQ/DHb+AFR/37LUmYOoZ4ruvl7DrXCu+Bj0r0sJZEBdCgNFAR/8IJS09lLb14HDA5gUxfP2mhWLz098Bv71edBn75F4I83AItakYfrNRdKHb+ZhnrzWB3qFRfvRWOc8eEx0XC5LDyU8MJcTPh56hUcrbejnf3M2ozcGK1HC+vH0B1+dEo7ONwh93ioyjh3ZDQoFnJ9pvgZ8vg4zr4cPPe/ZaExi12fnN/mp++W4Vw1Y7ufEhFCSHERHoS9+wlWpzH0WNXQyN2smJDebzW7O5Y2kieh3wt09C8cvwkb9CjufKGQGwWeFXq4Uo+ZmDIoPPg+h0utMOx/9v787D5KrKPI5/X7ISyEKGEEIgBkgghAQSQHYxrAmEzY1FURQd0EGFmUGHRUZhEEEQcFwYFTEoQgRk1bDLJgoxQNjCFkhCErJvZN/6zB+ngk3S3Umlq7q6Ot/P8+Sh61bV7bcPt6rO/dU556bSXr5Rjdbc+2BvTF/I0OvyhSJGfOmjDNl1mwpXVF5vzVjIkdc++aFtr14ylC3albk/IklqsTamD2ao1FTeeABuPRmGXVn2qUt1Wb5qNQ+8Mp0HX53OS1MWMHfxCjaLoHunduy5fReG9NuGI3frzuZt11rHaNS3YfQv4KjL4MBvlK/Ama/B9QfBR78Cx/ywfL+nHjU1iSfenMV9L73H2HfnM+P9ZSTy1b4G9OzEIX27MWzAtute3W30r2DUebD3l+DYa0t+tbEPLJ4D/zsYeu0Hn7u9PL+jASklnps0j7vHTuUfE+bx3oKlrFxdQ9cObenXoxMH9dma4QN7sG3n9h9+4hsP5KBnp0Ph1JHlm3K1chn84mN5VN3Zo8sf8NXhjekLuX3MZEZPnMukOUtYunI1W3VoQ59ttmT/Hf+FEwf3ZIeuHT78pOmvwI3DYKuP5OCkfafyFJcS/PYEmPYifPMF6NBEa1zVMmXeEm4bM4W/vz2bt2ctZtHyVXRq35odt96CfXp3ZfjAHuy+XacPLzb9/ntww5FQsxK+/FB5w+ZR38pTu/7tGei2a/l+Tz3mLl7B7WMm89Rbs3lzxkLmL13JFm1b0atrBwb32oqhu2/Lfjt2/fBUt+WLcvA25234wj15ofNy+fvP4cEL4JRboF/5R0AYKjVP1dAHqz1K6fX/GdYir3o2Z9Fy9r7skXW2OzpJktRYhkqN8dYj+UR0pyGl3/fSefDzA/LCymc+Dq2baNHrUqhZDXeckS8TP/xHOfQptdUr4YYj8gLmZ48u61omZfHI9+Cv1+YRXUddVvpgKSW4/fQ8EuesJ6F7/9Luv9ye/x3c+3XofwJ88obyBEuPXAJ/vQZO+yP0OaL0+y+n8Y/CLSflKY2n/bE8C7C/OBLuOguO/mGTTO0qqZmvwY1DYfOuOTjZ6iOl/x0T/wojjs3vb8OvLv3+y2nhjNw+S+fl9tluUOl/x9wJcP2B0PvgPCqqCa4yZ6jUPFVDqAQtN1i678X3+Mat606ZnvCDY5rm6o+SpBZvY/pgrqkE+aT9iSvh5k/lRVpLqaYG7jsXFs2EE35WXYES5CuwffKXeYrXn/8Tnrgqt1cpPX4FTBsLw6+pvkAJ4PDvwr5nwd9/Cvd9M08TKaWxt8C4e+DQC6svUALY6/Mw9PL8N9xyEiwv8mpg6zPhqTw1cNBp1RcoAfQ5PE+fnP4y3HQ8vD+ttPuf83Z+7fY6sEnWUiq5bXaD0+6EpXNzeDLztdLuf8lcuPtreRTUkZeUdt9NoWN3+MLd0K4jjBgO7zxe2v2vXAZ3ngnRqryjMaUSmvCDYz74ud/FD/CX12dUsJrGWbW6ht7n/5ne5/95nUBp3KVDmXjFcAMlSVJFGSpB7iR/7nb4yIFw91fzyJPVK0uz78cvz6N8Dr8Yeu5Vmn02tdbt4OSbYY+T4bHL4I8lXJz6hd/DU1fD4NNg9xNLs8+mFgFHXwmHfAue/22eZrSwRB3Yd56A+86B3h+Dg84pzT4r4YCzc6g64ck8nWnWG6XZ7+zx8IfT4F/6wLDLS7PPSuh3DJx66z/XoXr32dLsd9HMHOS1agOf+lVFpgWWxPb75OmBqSYfP6VavHvlUrj1VFg4HT75K2jbhFdyLKWteufpgV16wc2fhmeuL034X1OTg/Ipo+GEn0Dn7Ru/T6kJRATvXP7PYOmMEWOqavHueYtXfBAk9bno/nXun3jFcCZeMZwObav0PV2S1KI4/a22VSvy+jjP35QvmXzizzd+bY2U4C//A0/9KAcmx/+0+r/hranJU4we+35efPm4H+fpEBvruRHwp/+AHT8Gn729rJc4bzIvjswj09p1zGtD9T9x4/+/v/VInvbWeQc44/7yTItqam//JS8uvHJZHhWyzxl5NNzGmPZSHl2YVueFrrvuVNpaK2HGOBj52XzFvIPPhUO+DW3ar/95dZk/GW45GeZNgM/fBb32L22tlbBgCtx2OkwdA3udno+hjX1dLJ0Pt30+B52f/g0M+GRpa62EpfPgrq/Bm/fn0aXHXA1ddti4fa1emS/U8NIf4NDvwMe/Vdpa18Ppb81TtUx/q62uMKm5TRerqUn0/c79rK7jCr1r/OTUwRy353ZNWJUkaVPkmkql8updORhYvhD2/Vc46Fzo1GPDn79wRh5d8ub9+cRn+DXVO0KgLhOezCcb89+FgZ/JJ77ddtnw5y97Hx6+OIdKfY6Az4zIIUxLMeNVuOurMP0l2PlwOPQi2H7vDX/+qhU5vHviSui+ew7cijn+mrv3p+URge88Dj0GwWEX5ylgG9rBTykfOw9eBJt3yYFJBRZWLpul8+CBC+HFW2CrHWHIBTDw08WFb6+Pgnu/AatXwEm/hZ0PLV+9TW3VihzY//1necHxQ76Vr/bXZvMN38e7z6tGGBcAABAPSURBVMI9/wbzJuWrBQ46tXz1NrWU8kilRy/Nr6mDzoX9ziwufJs9Pq/BNXUMHPYd+Nh5Tf6liKFS81SNoRLA0+Nn87kb1h0B2qFtK8ZdOqxJa0kp8d/3vPrBFTEbcvknBvLZ/Xo1QVWSJGWGSqW0eHYekfPciLyWxO4nwoBP5YW86zt5mf0WvPA7GH1DHj1x+Hdh/69V/wiluqxYAk9elU9eVi2DXYbCHiflkKh957qfs2AqvDQyP2fJnDwl6vDv5qk5Lc3qVTD6l7mNls7N69nseQrsejRsWc8ljpfMzZcH/9tP8+iSgZ/Ja5i0pMBtjZTy3/rQxfD+VOg+APY8NS/mXd/IihWLc1jytx/n9Yd2GgInXg+dWug3t+MfhYf/G2a8kqc1DTott0+3Xet+T1m1HN5+DJ75OUx4ArbpD5+5qbjAt5pMewkeOB8mPQ1bbJPffwZ8Ki94XlcAV7Ma3n0mX81y3L15Ktcn/q9xoy2bs3mT4MEL4fU/Qdstc/vs/gnodUDd77kp5asDPvcbeOHmPBXw2OsqNoLLUKl5qtZQaY17xk7lnJFjG3zM4F5d+M0XP7ru1V6LsGDpSi6571XufH5q0c996/tH06aVq1NIkirDUKkc5r4Dz/4iL+C9fAG0agvd+uU1XNp3hppVOSCZ8UoeuUPkTviQC2HrPk1XZ6UsmgXPXp/bZ+F7QOST2a47whbdcri2dF5eXHfO+PycjRm9U62WL4QxN+a1ltb8/V13hq37Qsdt84nc8vdh1psw6/XcXj33zqNT+h5Z2dqbwqoV8PLt+UR/2ot5W8ft8gitjt1hszawYlEObGeOyyNvuu4EH/8vGHgSbNbCO941NfD6ffCPX+egCHKAsk0/6NwrhwOrluWrc01/GVYuho494MBvwL5ntszAdm0Tn86jlt56CGpWQrtOsO0eOTRq2yEfY/Mn5fZZNh/adYZ9vwIH/3vLDGzXNv0V+NtP4LV7YeUSaN0+t0+XHaB9l3z8LJqRX3+LZ+XX3N6n5xFgHbetWNmGSs1TtYdKtQ383oMsXFbiC2sU6byjduHrh/WtaA2SJNVmqFROq1bAxKfyid30l/O3wMsWwGat8xSMrXfJ3wD3P77ljpxoyJpRABP/mqdMzJ8Mi2fmE5R2HfPoip57w27Hbxph29pSyle4m/AkTB6dj59F0yE2gzYd8vHTY8+8YHOPQS1zdNv6zB4P4x+GKWNg9hs5sKxZlUdMbNU7Xyq979D8OmvpYVJdFkzJI5EmPZ0DygVT8uuuVdvcPtvslkcK9jl80wiT1rZkLox/BCb9LQeQ77+XF+Ju3S6/J2+zWx7d1ncotNuy0tU2vRWLc/u8+2x+L1o4PQf+bTrkqXE99oAd9oPdjsufaRVmqNQ8taRQqbaUEmff8jyjXp5elv1fdMxu/OshLWDdP0lSi2eoJEmSqp6hUvNkH0ySpJZtY/pgm+DX/ZIkSZIkSWosQyVJkiRJkiQVzVBJkiRJkiRJRTNUkiRJkiRJUtEMlSRJkiRJklQ0QyVJkiRJkiQVzVBJkiRJkiRJRat4qBQRwyLijYgYHxHnV7oeSZKkTYF9MEmS1FgVDZUiohXwM+BooD9wakT0r2RNkiRJLZ19MEmSVAqVHqm0LzA+pfROSmkFMBI4ocI1SZIktXT2wSRJUqNVOlTqCUyudXtKYZskSZLKxz6YJElqtEqHShskIs6MiDERMWbWrFmVLkeSJGmTYB9MkiQ1pNKh0lRgh1q3ty9s+5CU0i9TSvuklPbp1q1bkxUnSZLUQtkHkyRJjVbpUOkfQN+I2DEi2gKnAPdWuCZJkqSWzj6YJElqtNaV/OUppVUR8XXgQaAVcGNK6dVK1iRJktTS2QeTJEmlUNFQCSClNAoYVek6JEmSNiX2wSRJUmNVevqbJEmSJEmSqpChkiRJkiRJkopmqCRJkiRJkqSiGSpJkiRJkiSpaIZKkiRJkiRJKpqhkiRJkiRJkopmqCRJkiRJkqSiGSpJkiRJkiSpaIZKkiRJkiRJKpqhkiRJkiRJkopmqCRJkiRJkqSiGSpJkiRJkiSpaIZKkiRJkiRJKpqhkiRJkiRJkopmqCRJkiRJkqSiGSpJkiRJkiSpaIZKkiRJkiRJKpqhkiRJkiRJkooWKaVK11CUiJgFTCrT7rcGZpdp3y2VbVY826x4tllxbK/i2WbFK2ebfSSl1K1M+9ZGKkMfzNdd49mGjWcbNp5tWBq2Y+PZho23a0qpYzFPaF2uSsqlnJ3MiBiTUtqnXPtviWyz4tlmxbPNimN7Fc82K55ttukpdR/MY6jxbMPGsw0bzzYsDdux8WzDxouIMcU+x+lvkiRJkiRJKpqhkiRJkiRJkopmqPRhv6x0AVXINiuebVY826w4tlfxbLPi2WZqLI+hxrMNG882bDzbsDRsx8azDRuv6DasuoW6JUmSJEmSVHmOVJIkSZIkSVLRDJUKImJYRLwREeMj4vxK19PcRcTEiHg5IsZuzArxm4qIuDEiZkbEK7W2dY2IhyPircJ/t6pkjc1JPe31vYiYWjjWxkbEMZWssbmJiB0i4rGIGBcRr0bEOYXtHmf1aKDNPNbqERHtI2J0RLxYaLNLCtt3jIhnC5+df4iItpWuVc2ffa7Gq+99TMWLiFYR8UJE/KnStVSjiOgSEXdExOsR8VpEHFDpmqpNRPx74XX8SkTcGhHtK11TNfA8q/HqacOrCq/nlyLirojosr79GCqRP0yAnwFHA/2BUyOif2WrqgqHppQGednGBo0Ahq217Xzg0ZRSX+DRwm1lI1i3vQCuLRxrg1JKo5q4puZuFfCfKaX+wP7A2YX3L4+z+tXXZuCxVp/lwGEppT2BQcCwiNgfuJLcZn2AecCXK1ijqoB9rpJp6H1MxTkHeK3SRVSxHwMPpJT6AXtiWxYlInoC3wT2SSkNAFoBp1S2qqoxAs+zGmsE67bhw8CAlNIewJvABevbiaFSti8wPqX0TkppBTASOKHCNakFSCk9Ccxda/MJwE2Fn28CTmzSopqxetpLDUgpTUspPV/4eSG5M9cTj7N6NdBmqkfKFhVutin8S8BhwB2F7R5n2hD2uUrA97HSiIjtgeHADZWupRpFRGfgEODXACmlFSml+ZWtqiq1BjaPiNZAB+C9CtdTFTzPary62jCl9FBKaVXh5jPA9uvbj6FS1hOYXOv2FPxgXp8EPBQRz0XEmZUupsp0TylNK/w8HeheyWKqxNcLQzBvdBhr/SKiNzAYeBaPsw2yVpuBx1q9ClNExgIzyd9ivQ3Mr9Xx8LNTG8I+V4nV8T6mDXcd8G2gptKFVKkdgVnAbwpTCG+IiC0qXVQ1SSlNBa4G3gWmAQtSSg9VtqqqZv+3tM4A7l/fgwyVtLEOTintRR6+fnZEHFLpgqpRypdf9BKMDbse2Jk85WYa8KPKltM8RcSWwB+Bc1NK79e+z+OsbnW0mcdaA1JKq1NKg8jfWO0L9KtwSdImr6H3fjUsIo4FZqaUnqt0LVWsNbAXcH1KaTCwGKcbFaXwBdYJ5IBuO2CLiDitslW1DPZ/GyciLiJPtf79+h5rqJRNBXaodXv7wjbVo5Cqk1KaCdxFPsHQhpkRET0ACv+dWeF6mrWU0ozCyWwN8Cs81tYREW3IJxW/TyndWdjscdaAutrMY23DFKY2PAYcAHQpDNcHPzu1YexzlUg97/3acAcBx0fERPI0zMMi4ubKllR1pgBTUkprRsndQQ6ZtOGOACaklGallFYCdwIHVrimamb/twQi4ovAscDnCuFcgwyVsn8AfQtXsWlLXhzt3grX1GxFxBYR0XHNz8BRwCsNP0u13AucXvj5dOCeCtbS7K35YCj4BB5rHxIRQV7L4LWU0jW17vI4q0d9beaxVr+I6Lbm6h8RsTlwJHkNl8eATxce5nGmDWGfqwQaeO/XBkopXZBS2j6l1Jt8HP4lpeQIkSKklKYDkyNi18Kmw4FxFSypGr0L7B8RHQqv68NxsfPGsP/bSBExjDwt+PiU0pINes4GBE+bhMKlo68jr7h/Y0rp+xUuqdmKiJ3Io5MgD3u9xfaqW0TcCgwBtgZmAN8F7gZuA3oBk4CTUkouTk297TWEPB0pAROBs2rNld7kRcTBwFPAy/xzTYgLyWtreJzVoYE2OxWPtTpFxB7kBS9bkb+Qui2ldGnh82Ak0BV4ATgtpbS8cpWqGtjnarz63se8auXGiYghwHkppWMrXUu1iYhB5IXO2wLvAF9KKc2rbFXVJSIuAU4mTzV6AfiKn6Xr53lW49XThhcA7YA5hYc9k1L6aoP7MVSSJEmSJElSsZz+JkmSJEmSpKIZKkmSJEmSJKlohkqSJEmSJEkqmqGSJEmSJEmSimaoJEmSJEmSpKIZKklqFiLi1cIlfSVJkiRJVaB1pQuQtGmIiEW1bnYAlgOrC7fPSint3vRVSZIkSZI2liOVJDWJlNKWa/4B7wLH1dr2+0rXJ0mSpCwifhAR5zZw/+iI8AtBSYZKkpqHiJgYEUcUfv5eRNweETdHxMKIeDkidomICyJiZkRMjoijaj23c0T8OiKmRcTUiLgsIlpV7q+RJEmqThHRDfgC8Iu1tk+JiMGFm1cDlzZ1bZKaH0MlSc3VccDvgK2AF4AHye9ZPcmdmNodnRHAKqAPMBg4CvhKE9YqSZLUUnwRGJVSWrpmQ0RsDXQHxhU23QscGhHbNn15kpoTQyVJzdVTKaUHU0qrgNuBbsAVKaWVwEigd0R0iYjuwDHAuSmlxSmlmcC1wCkVq1ySJKkZi4gfRsTdtW5fFRGPRkRb4GjgiVr39QEmk88d50TEHPKXec8BQ5u2cknNjQt1S2quZtT6eSkwO6W0utZtgC2B7YA2wLSIWPP4zcidH0mSJK3rSuCdwnS2/YBhwMEppRURMRB4Y80DU0rjI+I84JCU0slrtkfEa8CeTVy3pGbGUElStZtMvpLc1oVRTZIkSWpASmlORFwL3AR0JgdKCwp3dwEWrvWUPYGxa21bCPQoa6GSmj2nv0mqaimlacBDwI8iolNEbBYRO0fExytdmyRJUjP2AjAQuCClVHuE9zyg41qPHQS8uNa2jsD88pUnqRoYKklqCb4AtCUvHjkPuAO/OZMkSapTYYrb9eSRSmesdfdLwC61HrsZMIB1RyrtxrpBk6RNTKSUKl2DJEmSJKkJRERP4Gngm8AjwATg5JTS44X7/wPol1I6s3B7C2ARsENKaUphW3vgPWBASum9Jv8jJDUbjlSSJEmSpE1ARHQCRgHXpJTuTSktAa4Cvl/rYb8FjomIzQFSSouB/wPGRcSUwmOOAx43UJLkSCVJkiRJ0gci4nJgZkrpunrufxb4ckrplaatTFJzY6gkSZIkSZKkojn9TZIkSZIkSUUzVJIkSZIkSVLRDJUkSZIkSZJUNEMlSZIkSZIkFc1QSZIkSZIkSUUzVJIkSZIkSVLRDJUkSZIkSZJUNEMlSZIkSZIkFe3/AXsnlbDVno9NAAAAAElFTkSuQmCC\n",
         "text/plain": "<Figure size 1440x720 with 2 Axes>"
        },
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