examples.ipynb

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   "source": [
    "# Bayesian Nonparametric Market Segmentation Algorithm\n",
    "Reference: Nishi, Hayato, Yasushi Asami, and Chihiro Shimizu. \"The illusion of a hedonic price function: Nonparametric interpretable segmentation for hedonic inference.\" Journal of Housing Economics 52 (2021): 101764. https://doi.org/10.1016/j.jhe.2021.101764"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import BayesianMarketSegmentation"
   ]
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   "source": [
    "## Case 1: dummy is not included\n",
    "### Build toy dataset"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "K = 3\n",
    "\n",
    "mu = np.array([-1, 2, 5])\n",
    "tau = np.array([1, 1.1, 0.8])\n",
    "\n",
    "beta = np.array([0.1, 4, 1])\n",
    "alpha = np.array([0.0, -2, 8])\n",
    "sigma = np.array([0.8, 0.5, 0.4])\n",
    "\n",
    "def toy_dataset(N):\n",
    "\n",
    "    z = np.random.choice(range(K), size=N, replace=True)\n",
    "    x = np.random.normal(loc=mu[z], scale=tau[z])\n",
    "\n",
    "    y = alpha[z] + beta[z] * x + np.random.normal(scale=sigma[z])\n",
    "\n",
    "    return y, x, z\n",
    "\n",
    "N = 100\n",
    "y, x, z = toy_dataset(N)\n",
    "\n",
    "color = [\"Red\", \"Blue\", \"Orange\"]\n",
    "for k in range(K):\n",
    "    plt.scatter(x[z==k], y[z==k], label=k, c=color[k])\n",
    "plt.legend(title=\"submarket\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Model\n",
    "Infinite Gaussian Regression Mixture Model (IGRMM)"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = BayesianMarketSegmentation.IGRMM(\n",
    "    X=x.reshape(-1,1), \n",
    "    Exog=np.stack([np.ones_like(x), x]).T,\n",
    "    Y = y\n",
    ")"
   ]
  },
  {
   "source": [
    "### Inference\n",
    "`T` is maximum number of submarkets, and `maxiter` is maximum number of iteration in the variational nference procedure.\n",
    "\n",
    "This inference procedures are repeated `trial` times, and return the best result.\n",
    "\n",
    "Variational Inference depends on the initial values, so please try various initial values using the `trial`."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=5.0), HTML(value='')))",
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    },
    {
     "output_type": "display_data",
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     "metadata": {}
    },
    {
     "output_type": "display_data",
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    {
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     "metadata": {}
    },
    {
     "output_type": "display_data",
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     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "T=5\n",
    "best_model = BayesianMarketSegmentation.IterativeVI_II(model, trial=5, T=T, maxiter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.bar(range(best_model.T), best_model.π)\n",
    "plt.ylim(-0.1, None)\n",
    "plt.title(\"submarket ratio\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Get Segmentation Result\n",
    "It is fussy clustering"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = best_model.responsibility(\n",
    "    X=x.reshape(-1,1), \n",
    "    Exog=np.stack([np.ones_like(x), x]).T,\n",
    "    Y = y\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 360x1080 with 10 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(figsize=(5, T*3))\n",
    "for t in range(T):\n",
    "    plt.subplot(T, 1, t+1)\n",
    "    plt.scatter(x, y, c=probs[:,t], vmin=0, vmax=1, cmap=plt.cm.Reds)\n",
    "    plt.colorbar(label=\"allocation probs.\")\n",
    "    plt.title(f\"submarket {t}\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### confusion matrix"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "map_submarket = np.argmax(probs, axis=1)\n",
    "\n",
    "confusion = np.empty((K, T), dtype=int)\n",
    "for k in range(K):\n",
    "    confusion[k] = np.count_nonzero(map_submarket[z==k][None] == np.arange(T)[:,None], axis=1)\n",
    "\n",
    "sns.heatmap(confusion, cmap=plt.cm.Reds, annot=True)\n",
    "plt.xlabel(\"estimated submarket\")\n",
    "plt.ylabel(\"true submarket\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Coefficients"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0, 4, 1])"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "corespondance = np.argmax(confusion, axis=1)\n",
    "corespondance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.bar(range(T), best_model.τ.Regre.ω_[:,0].flatten())\n",
    "for k in range(K):\n",
    "    plt.hlines(alpha[k], 0, T-1, label=f\"submarket: {k}\", color=color[k])\n",
    "plt.scatter(corespondance, alpha, marker=\"x\", color=\"k\")\n",
    "plt.legend(title=\"true coefs.\")\n",
    "plt.title(\"estimated alpha\")\n",
    "plt.xlabel(\"segmented submarket\")\n",
    "plt.show()\n",
    "\n",
    "plt.bar(range(T), best_model.τ.Regre.ω_[:,1].flatten())\n",
    "for k in range(K):\n",
    "    plt.hlines(beta[k], 0, T-1, label=f\"submarket: {k}\", color=color[k])\n",
    "plt.scatter(corespondance, beta, marker=\"x\", color=\"k\")\n",
    "plt.legend(title=\"true coefs.\")\n",
    "plt.title(\"estimated beta\")\n",
    "plt.xlabel(\"segmented submarket\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Case 2: dummy is included\n",
    "### Build toy dataset"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "K = 3\n",
    "\n",
    "mu = np.array([-1, 2, 5])\n",
    "tau = np.array([1, 1.1, 0.8])\n",
    "\n",
    "p = np.array([0.1, 0.5, 0.8])\n",
    "\n",
    "gamma = np.array([-2, 0.3, 5])\n",
    "beta = np.array([0.1, 4, 1])\n",
    "alpha = np.array([0.0, -2, 8])\n",
    "sigma = np.array([0.8, 0.5, 0.4])\n",
    "\n",
    "def toy_dataset(N):\n",
    "    z = np.random.choice(range(K), size=N, replace=True)\n",
    "    x = np.random.normal(loc=mu[z], scale=tau[z])\n",
    "    d = (np.random.uniform(size=N) < p[z]).astype(int)\n",
    "\n",
    "    y = alpha[z] + beta[z] * x + gamma[z] * d + np.random.normal(scale=sigma[z])\n",
    "\n",
    "    return y, x, d, z\n",
    "\n",
    "N = 100\n",
    "y, x, d, z = toy_dataset(N)\n",
    "\n",
    "marker = [\"o\", \"x\"]\n",
    "color = [\"Red\", \"Blue\", \"Orange\"]\n",
    "for k in range(K):\n",
    "    for i in [0,1]:\n",
    "        mask = d[z==k] == i\n",
    "        plt.scatter(x[z==k][mask], y[z==k][mask], label=k, marker=marker[i], c=color[k])\n",
    "plt.legend(title=\"submarket\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()\n"
   ]
  },
  {
   "source": [
    "### Model\n",
    "Infinite Gaussian Bernoulli Regression Mixture Model (IGBRMM)\n",
    "\n",
    "`BayesianMarketSegmentation.NISHI` is an alias of `BayesianMarketSegmentation.IGBRMM`"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = BayesianMarketSegmentation.NISHI(\n",
    "    X=x.reshape(-1,1),\n",
    "    dummy=d.reshape(-1,1),\n",
    "    Exog=np.stack([np.ones_like(x), x, d]).T,\n",
    "    Y = y\n",
    ")"
   ]
  },
  {
   "source": [
    "### Inference"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=5.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f8d60783c996429f85b542c1598a78e2"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value='initialize'), FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "4331791cbfad411f9bc9a2e0d2e11fd8"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value='initialize'), FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "a63baab058614a89aa33cc40a4281a5c"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value='initialize'), FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2b0a9840c7734b29b908b6623dd8facc"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value='initialize'), FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "cb9fe820760b414fbf495b087d732d86"
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     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(HTML(value='initialize'), FloatProgress(value=0.0, max=200.0), HTML(value='')))",
      "application/vnd.jupyter.widget-view+json": {
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       "model_id": "cc7a83a32ab240c68d5325c65ddaf972"
      }
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     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "T=5\n",
    "best_model = BayesianMarketSegmentation.IterativeVI_II(model, trial=5, T=T, maxiter=100)"
   ]
  },
  {
   "source": [
    "### Get Segmentation Results"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = best_model.responsibility(\n",
    "    X=x.reshape(-1,1), \n",
    "    dummy=d.reshape(-1,1),\n",
    "    Exog=np.stack([np.ones_like(x), x, d]).T,\n",
    "    Y = y\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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crBPbiNo+aOViEOCJqebXymSjojjba2o0RAVrRmHRq0sEZFNk4ZpZJWrI8ApJBvzAzC5OOt4F13HiMAtRArULV7mJIHbNhK5YSHb90ly4XiuXQDYH0zulOv22b6Ss7q2kTwGPAi6Idr1R0nPM7NQk411wHSeOwuziKIFSIbIwmyQatBM1UClBpo042iVIyny4hwOPNQtfNySdT2itnogx9rY7TguqC1uNBNIMyjGWan2L9PpxbelDqsQkdVRrKaSo48PNwL41z/cBfp50sFu4ztKkVIhKHUZ+0UwuLFAl+StulmhQrbyVlCQLZ0sZiUwKqoVJ+gbhzbIzsFHST6JDhwE/THod/992lg6VSnARWCUI7oJjJZjbtrAubFxlrkyTP5tmzSTrmVy+ZN0E7TCMjLIG/HMvLuKC6ywNinOhSHczKmWY2RqEMJMJdQpquytUaRZZ0GwBLDcZRTqQ7gpdKSIttRTM7HvVx5J2Bw6Nnv7EzO5Oeh334TrjT6XcWmyrWCVYumYhWWFqRSSOmZrnTdrRVM9tRH4y9B7rNAliKdLEfzuMX6GkFwM/AV4EvBj4saS/STreLVxn/Cm1qkdQh1WCSGdzQVynlicfK4Xz52bmY3Ez2WAtu8h2RBos3BreCRxatWolrQa+DXw1yWAXXGcJ0MYi1o4hXRSEUSaIbj+bSS4RQpRCqn5/mToXwr204Slwl4Iz/iStF1tLL7rYDjF2aWyIohTitmSX0DGSbpa0SdJZMeccIekGSRskfa/RORGXS7pC0mskvQb4H+CypC/HLVxn/Mlkg+jWRybEkc2ntm34kqQLl4KkLPBJ4ChgM3CdpEvN7Fc15+wCfAo4xsxuk/TwmGsJ+DhhwezpBAN8naf2Ok49E9PBJ9so6kAZgttBQZg7sYid/iBQd9XQDgM2mdktAJIuBE4AflVzzsuAi8zsNoC4qAMzM0lfN7O/AC7qZDLuUnCWDtk8TK2EbNRwMZMNyQ7TK0OtgumVIZLA3QDpIqP4DVZJur5mq2/ouBdwe83zzdG+Wh4NPEzS1ZLWS3pVk9lcK+nQJseb4haus7TIVJsmprtxohOQhLJN7cItZra22SUa7KtfRc0BfwEcSXhj/EjStWb26wZjnwWcIulWYFt0fTOzQ5pNsvZGTZF0LnA8cLeZPTbatyvwX8Aa4FbgxWZ2f5IbOo7jtEV33zg2E+odVNkbuKPBOVvMbBuwTdI1wOOBRoJ7bDeTSeJSOA84pm7fWcBVZnYgcFX03HGGT6UMs9tg+4Mha6w4115tAyd1KJuJ3RJwHXCgpP0lTQAvBS6tO+cS4BmScpKWAU8GNja6mJn9HtiN4Ad+PrBbtC8RLWdsZtcA99XtPgE4P3p8PnBi0hs6Tk8xmxfUSiV0R6iU2NFcsTjbeKHMGQ3UxH+bIHrBzErAacAVBBH9ipltkHSKpFOiczYClxOqfv0E+JyZ/bLxdPQegubtBqwCviDpXUlfTqc+3N3N7M5osnfGhVFEEzwZOBlg3333jTvNcdqjXFrYQjw7ARZTOKZSCplfk+63HUUSWrKxmNll1MXKmtk5dc8/BnwsweVOAp5oZrMAkj4C/BT4YJK59D1KwczWmdlaM1u7evXqft/OWQqUo8petdlg5ULzSl3lwpi3Ex9T0lcQ91agtnrRJPDbpIM7tXDvkrRnZN3uCSSuluM4XVNsUgC8GeUy5DwSctRQCurh1jAHbJB0JSHa4SjgB5I+DmBm/9BscKeCeynwauAj0c9LOryO47RPnOugFR5fO3pIKF3Fay6OtipXtzM4SVjYBcARhADjzcB7CUL7FUmvB24jlCpznMGgLFiDrrit8HTd0aRLH24vMbPzW58VT0vBNbOTYg4d2c2NHadjJqZCNEI7JG1x7qSK4Kodn/83zzRzRo9MNnRlKM4mb2njC2YjilJl4XaLC64zmmRzkI36j5mFXmWlJpEKcV0YnNTjFq7jpAnVVPma2x7Et57c5ODn5XSPuo/D7SWSHg28FdiPGv00s2cnGe+C64wmVau2Ug4uhmqfsIlpmLP59jYA+anQS8wZTdIVpfD/gHOAzwJth8u44DqjR6UCcw8trJGg2dDgcUd7m0o4rowvlo0yrauFDZqSmX2608GpeiWO05SqVTu7dXFBGrOQ6ltFGY9MGBfSlWn2DUl/L2lPSbtWt6SD3cJ1RgOz4J+tNIm/LXcQm+ukm5T5cAmJXhD8uFUMOCDJYBdcZzQoFZqLrTOmJKsKNijMbP9uxrvgOqNBcTbBSen5w3R6hAhdOlKCpDzwd8Azo11XA58xswahMYtxwXXST9LkBo9EGE/S5Yf/NJAndPkFeGW07w1JBrvgOuknaccGj7UdQwTZVNXAONTMHl/z/DuSbkw6OD22uuPE0arojDIh1TdFXz2dHpG+erhlSY/cMT3pANqIx3UL10knlTKUisG6beZSmFrhVcDGmtRZuG8FvivpFsLHwX7Aa5MOdsF10kdxrvUiWTYfssrS5d9z+kGK/o/N7CpJBwIHEQT3JjNLXBHfBddJF9XGj60Y3ldKZ5CkJEpB0rPN7DuS/rru0CMlYWYXJbmOC66TDioVKM0lT16oeLnFpYFSIbjA4cB3gL9qcMwAF1xnRKg2hWwH99suDVJi4ZrZe6OH7zez39Uek5Q4GWL4r8RxamsgJEKQn+jLVJwUkq4oha812PfVpIPdwnWGi1kb3RgUCo/np7yg+BJBCKUgSkHSY4A/B3au8+PuxMK26U1xwXXSTX4qRCSk4GulMwSqcbjD5yDgeGAXFvpxtwJ/m/QiLrjO4LAKFGbnF8ZyE5CfhEyucWGa3GQ47ixhuo/DlXQMcDaQBT5nZh+JOe9Q4FrgJWa2wE1gZpcAl0h6qpn9qNO5uOA6g8EqMLN14b7SXKgCNrUiLJrVuxbSYdk4w6aL94GkLPBJ4ChgM3CdpEvN7FcNzvsocEWLS/5M0qkE98IOV4KZvS7JfPx7mjMYCnGx4Ras3kZ+3OKsh38tdapRCnFbaw4DNpnZLWZWAC4ETmhw3psIC2J3t7jefwB7AEcD3wP2JrgVEuGC6wyGZrVsK00q25UKvZ+LM0KoleCuknR9zXZy3QX2Am6veb452jd/B2kv4AWEXmWteJSZvRvYZmbnA88DHpf01XTlUpB0K0Hdy4ReP2u7uZ4zxkghPLxdEkcwOGNJ6zjcLS10p5E/ov6d+O/AmWZWTtCSvWodPCDpscAfgTWtBlXphQ/3WWa2pQfXccaZ3CQUtjc+ls03bm0OHv615Ok602wzsE/N872BO+rOWQtcGIntKuA4SSUz+3qD662T9DDgXcClwArgPUkn44tmzmDI5aEysdhFoGxzwU1afNwZX7oT3OuAA6NssD8ALwVeVntCbdscSecB/x0jtpjZ56KH15Cwj1kt3ZoPBnxL0voGvhMAJJ1c9a/cc889Xd7OGWkmpmFqZbB2c5Ohhu3Uco9GcOLpsh6umZWA0wjRBxuBr5jZBkmnSDql7elIH5a0S83zh0n6YNLx3Vq4TzOzOyQ9HLhS0k1mdk3tCWa2DlgHsHbt2k68eM44kcnARF1iTrO6CJ7Cu8TpPg7XzC4DLqvb13CBzMxe0+Jyx5rZO2rOv1/ScQQXQ0u6snDN7I7o593AxYQQDMdpjFlIeiiXFrbNkYK1W09uIiRFOEubdNVSyErakY0jaRpInJ3T8btZ0nIgY2Zbo8fPBd7f6fWcMaTaraFSCtEGpVo/rWByWaiNAOHn9E7Bl2sWnntFMEep6/jwn8BVkr5AcKm+Djg/6eBuzIfdgYujlb0c8GUzu7yL6zmjSKUcWayV+Z8oWKflEljcopeF7LLpneYtFUXjHKeWFH3wmtk/Sfo58Jxo1wfMrFV22g46FlwzuwV4fMsTnfHELJRVbBhdYCFtNwnloousE49SU4C8lp8RWqVb9DgxqXslzohQLsWHcrVD0hboztIlk43fBoykFwM/Af4GeDHwY0l/k3S8r0g4ndGrlNusvwWdFqQrbPCdwKFRoACSVgPfJmERcn+3Ox3SA8s0m0+Vf85JIelbNMtUxTbiXtrwFLjgOp2Rm0jQGkcsEmZlosWxSbdunWSkK737cklXABdEz19CXYxvM/wd73RGNg+ZYnwVsNxkEGWrhHOUCWPS9fXQSTsps3DN7K2SXgg8jWBRrDOzi5OOd8F1OkMKqbrlApRKYSU5Pzlvwe4g45as0x0p+5A2s6/RuJlkS/wvwekMqyzs0lAuh5jcqRXDnZczXqTEwpW0lcYLFwLMzHZKch0XXKczCjOLa9VaJeyfXDacOTnjSQosXDNb2YvruOA67VOtidCIXsTmOk6V9Fi4uzY7bmb3JbmOC67jOOkmHVEK6wkuhbgOEolq47rgOu0jxbc29+peTk9RKmK1a4uUd4P/daSdasUtq4RP+kw2FT4tJqZh9iEWrCNUIxccp1cIyKTg/V5D1GLnQBa2Sb8mfsQ8LrhpxqKKWrVtZjLZUDt22KKbycD0yuCzrZTDvDzO1ukHKbBwq0h6A3A6oTfaDcBTgB8Bz04yPhXOESeGwuzinl6VcoIMrwFRLac4MR1+utg6Padlm/RBczpwKPB7M3sW8EQgce8wt3DTTDmmQIxHAjhLBZEqCxeYNbNZSUiaNLObJB2UdLAL7qhi5halswQYWiudODZHTSS/TujjeD+L267H4oKbZmIjAVKycOY4/UakIg63ipm9IHr4PknfBXYGEne6ccFNG2bzGVz5qbBotiCjsM+RAFaJog1TZ1k4SxKlJQ53EWb2vXbHuOCmiUoZ5rbXpMxG4mplqFTCIkFusj9CaBWYm6mxqKN75/K9v5fjtEO6fLhd4YKbFsxgtt6aNShsD+FX/f6Un9teFxER3TuzYqze8M6IIaUuDrcbXHD7SbkYQrtqO9nmJhqHs5RLxHZRKBZgYmrhvko57LcoBrZaGrETKuXF4Wc77j3nxWic4TJGH/jpdI6MMpVy+Go+s7XOPRB1sp3dGizZ+uaJ9ZW3FhyrO7dcClle5UK4X6kQ7hcnmq1o1six2bwcp+9EPty4LckVpGMk3Sxpk6SzGhx/uaSfR9sPJfWtG/nStHBr02Uzue4DqKvXq5SCRdiKSmlxGcNmn+L1BbzjEh8KszC1vPX962nmE/baCM4wEagLC1dSFvgkcBSwGbhO0qVm9qua034HHG5m90s6FlgHPLmLWceytP6azII1WJxduD83ESICOlmMKpeiSIJ2xxUXxtLGdcFVXceE2iiGeuLa3TSjONfkQ0KQn2j/mo7TM7qOUjgM2GRmtwBIuhA4AdghuGb2w5rzryWk7faFrl5JK1M9VVTK4Wt3vdhCELu4+q61VAV79iGYeShYlJ2I7fwFQ/RBqRSfPdZOVEK7HxilYvT7aOBSyE6E7g0pDclxlhDZbPwGqyRdX7OdXDd6L+D2muebo31xvB74Zm9fwDwdW7gJTfV0YBb8qc1ae5fmWodAFWYWCmOpQ58pAAofAK2olIAaK1MKRWIaCXS2TWu00YdPlYkOLX7H6SWi1ftwi5mtbXGFehoKgaRnEQT36Ynn1ybdmC87THUzKwBVUz19WKX14k+l1fFyj2sYNBH/Whq92eKsznZ9XU1/Jwnn5zh9JaqHG7e1ZjOwT83zvWmQiivpEOBzwAlmdm9Ppt6AbgQ3kaku6eSquX/PPYmL6gyBFtZcEpdDPzCD7Q+GbW5mPiqhEc0s1kbEvmFFy9+H4wyK7qIUrgMOlLS/pAngpcClCy4v7QtcBLzSzH7d8/nX0M2iWSJT3czWEVb9WLt27XDMpmrr7mbhT630ZRhfr5VZaFWXC1ApEmt9Jg3h2iHaMa8p36dsNsdply57mplZSdJpwBVAFjjXzDZIOiU6fg7wHmA34FMK7/tSCzdFx3QjuIlM9Y6orsRXhbJbJJhY1t0CVzYPDKAObX4y3KtSCZle9TT70Kgeb/Y7K841t4Qz+TAHx0kLXWqAmV0GXFa375yax28A3tDVTRLSjeDuMNWBPxBM9Zd1NRuzxQtT3YRs1ZLNQX4aijGiWR/rWo8UVu3nGiQt9JJqVEKnLgyrgGIsAqu0djtUiuHerX4fjjMQ0tHTrFd0/FcVZ6p3NZvi7OKFqVIhWLq9sLpy+XjBTXL9TBamVgbh6nXnBWUWts7pOByryQdTUhEvzrngOulAjFVoYld/VY1M9S4u1mQxaK43gisFwSzUFGpRJlTFSvqfKgULsi8+zoSWc24KSg0s1Uy2RdZcwjn304J3nLYQSlE93G4ZETOmhwKQyQTXQFzd10ol3K+V/1iZ+HjY/FSDbLbJkLW1oARiDVYJCRXVymDNQtCqvcRqP6CUaV1kJqnV6tatkybcwu0DilL4Gq2098OHo8xCg6+6SFVbACY/1dyynpiGAjXiqJAwUK0KVq0AVq3XUC61Tr8tFcJ9m85dwR+dnwzz3REm08KClYLbotXioS+aOWlB7sPtHxNTUUZYHa0EqFuq7cjrxb44G7X/jvk1KSrSXZmoaRWemz9Wn7mWpLBN9et8LsZ6hpp7ZCDb5qd/NtdadD0kzEkTY/R+TJfgZvNBDIpzoc6rskGE+/0J1ywTrVSIF9yqUNdaxZnswsWv+vu0ovpaM7nGLov8dPdvwGpPtEa+2qx3eHBSRJdxuGkjXYILQdwG7UPstB5sYWZxDdpKOVjGjfqOZXPxC4Mw7xeGhdZzuciOAub1i2JWiQqRV6LfXT6Za6FhXLL6/23CcdrFfbhjRrP/0Lh6sGbxX/lLhcaCm58MFboaLQIqG/bPbg2iWe3g0OwDqFIOC21VykXQbLIqX9lciNgozUX90rJhUW+M3tzOmDBG70kXXGiSDKD4BaROQqcURUgU50KCgaKmkOViXRWyQng+tbK5tdrI320Wrp+ks28m098OwI7TNePVPdoFt1JpsjjV5Ot5s3Y2TS3mDExOA9Pz949L4S3NxX/Fb+p3LrqQOuODW7hjhDURzk6PteODbibc5TLkmXdflMtRq/QJmiYxjI9B4Cx1WtfDHSlccJtao01WR+PqFUB7fcCa9hPLBAt47qF5F0aZ4DLINYmVbbcQueOkGRfcMaJayLiRpZlrIlzZXOPQKqk9CzeTjU/4yE2E2g+L/MXWOLU3TMATF5wxYrx8uOPjHOmGyeULrdJqIZmmFm5UPaw2bjWbiyIE2niDSKHT7oJ7KaTpZrKdVQ0bozeo43TbJj1NuIUL86JnRlRgIZloJalfkOj+Leo7tHUtF1tnzBij97QLbi0acmuZ+voOEPyx5UbJEqJxt13PFHPGiGqNlTFhfF7JuDIxtfgNp2poWQNKc80jHxxn1Kh+42u0jRhu4aadqq+4Uo4K5GRChMRskxbrhdngInGcMUBjZOG64I4C1ciHavRDoUWbnKTNJB1nFBhBSzYOF9xRpFVN3aZdHxxnlBgvH64L7ijS6hPfK34544JnmjlDJzcZH5/bKn7YcUYNt3CdodKo5XsmG2KCx+jN6TjAWNUGccEdVfIToQ2PVQC539YZU8bLhzs+r2QpUm2w52LrjCtVH24XcbiSjpF0s6RNks5qcFySPh4d/7mkJ/X6ZVTxv1THcdJNF7UUJGWBTwLHAgcDJ0k6uO60Y4EDo+1k4NO9fQHzuOA6jpNimli3ySzcw4BNZnaLmRWAC4ET6s45AfiiBa4FdpG0Z29fR2CgPtz169dvkfT7ml2rgC2DnEMPGLU5j9p8wec8KAYx5/26Gbz+ZzdcoRW7rmpyypSk62uerzOzdTXP9wJur3m+GXhy3TUanbMXcGcHU27KQAXXzFbXPpd0vZmtHeQcumXU5jxq8wWf86AYhTmb2TFdXqKRGVxf9SnJOT3BXQqO44wzm4F9ap7vDdzRwTk9wQXXcZxx5jrgQEn7S5oAXgpcWnfOpcCromiFpwB/MrOeuxNg+HG461qfkjpGbc6jNl/wOQ+KUZxzW5hZSdJpwBVAFjjXzDZIOiU6fg5wGXAcsAnYDry2X/ORLeqX5TiO4/QDdyk4juMMCBdcx3GcAZEawZX0FkkmqVnM3dCR9DFJN0UpgBdL2mXYc4qjVUpj2pC0j6TvStooaYOk04c9pyRIykr6maT/HvZckiBpF0lfjd7HGyU9ddhzWiqkQnAl7QMcBdw27Lkk4ErgsWZ2CPBr4O1Dnk9DEqY0po0S8GYz+zPgKcCpIzBngNOBjcOeRBucDVxuZo8BHs9ozX2kSYXgAv8GvI0+BRv3EjP7lplVi9FeS4jZSyNJUhpThZndaWY/jR5vJQjBXsOdVXMk7Q08D/jcsOeSBEk7Ac8EPg9gZgUze2Cok1pCDF1wJT0f+IOZ3TjsuXTA64BvDnsSMcSlK44EktYATwR+POSptOLfCcbCqDSSOwC4B/hC5Ab5nCTvODogBhKHK+nbwB4NDr0TeAfw3EHMIynN5mtml0TnvJPwFfhLg5xbGwwsXbHXSFoBfA04w8weHPZ84pB0PHC3ma2XdMSQp5OUHPAk4E1m9mNJZwNnAe8e7rSWBgMRXDN7TqP9kh4H7A/cqFD5Z2/gp5IOM7M/DmJujYibbxVJrwaOB4609AYyDyxdsZdIyhPE9ktmdtGw59OCpwHPl3QcMAXsJOk/zewVQ55XMzYDm82s+s3hqwTBdQZAqhIfJN0KrDWz1FZdknQM8K/A4WZ2z7DnE4ekHGFR70jgD4QUx5eZ2YahTqwJCp+65wP3mdkZQ55OW0QW7lvM7PghT6Ulkr4PvMHMbpb0PmC5mb11yNNaEgw7tXcU+QQwCVwZWeXXmtkpw53SYuJSGoc8rVY8DXgl8AtJN0T73mFmlw1vSmPJm4AvRbUFbqGPqazOQlJl4TqO44wzQ49ScBzHWSq44DqO4wwIF1zHcZwB4YLrOI4zIFxwHcdxBoQLruM4zoBwwXUcxxkQLriO4zgDwgXXcRxnQLjgOo7jDAgXXMdxnAHhgus4jjMgXHAdIJTGlNS0DnCf72+SHjWs+zvOIHDBdUaaVkItaU9Jl0q6Izp3zQCn5zgLcMF1hkpUKL2fVIDLgRf2+T6O0xIX3DFD0pmS/iBpq6SbJR0Z7T9P0gdrzjtC0ua64YdK+pWk+yV9QdJU7bmS3ibpbkl3SjpR0nGSfi3pPknvqLn2YZJ+JOmB6NxPRMWuq8dN0qmSfgP8psFreLqk2yU9K3r+Okkbo3ldIWm/aP810ZAbJT0k6SX11zKzu8zsU4SOF44zVFxwxwhJBwGnAYea2UrgaODWNi7x8mjMI4FHA++qObYHoW/XXsB7gM8CrwD+AngG8B5JB0TnloF/BFYBTyW0+fn7unudCDwZOLjuNRwNXAC80My+K+lEQqPRvwZWA9+PjmNmz4yGPd7MVpjZf7XxWh1n4LjgjhdlQvufgyXlzexWM/ttG+M/YWa3m9l9wIeAk2qOFYEPmVkRuJAgpmeb2daodc8G4BAAM1tvZteaWcnMbgU+Axxed6//Y2b3mdlMzb4XAeuA48zsJ9G+N0bnbjSzEvBh4AlVK9dxRgkX3DHCzDYBZwDvA+6WdKGkR7RxidtrHv8eqB17r5mVo8dVkbyr5vgMsAJA0qMl/bekP0p6kCCSq5rcq8oZwFfM7Bc1+/YDzo7cEw8A9xFawO+V+FU5TkpwwR0zzOzLZvZ0glAZ8NHo0DZgWc2pezQYXttWfV86b6v+aeAm4EAz24ngElD9VBuMexFwoqQzavbdDrzRzHap2abN7Icdzs1xhoYL7hgh6SBJz5Y0CcwSrM6qVXoDcJykXSXtQbAm6zlV0t6SdiWIZKc+0ZXAg8BDkh4D/F3CcXcQ/L3/IKnq8z0HeLukPweQtLOkF9WMuQs4gCZEi3+T0dPJ6mKg4wwaF9zxYhL4CLAF+CPwcIJwAvwHcCNhEe1bNBbTL0fHbom2DzY4JwlvAV4GbCUsriUWbjO7jSC6Z0p6g5ldTLDSL4zcE78Ejq0Z8j7g/Mjl8OKYy84AD0WPb2LeJeI4A8XbpDuO4wwIt3Adx3EGhAuu4zhjjaRzo4SdX8Ycl6SPS9ok6eeSntSvubjgOo4z7pwHHNPk+LHAgdF2MiHKpi+44DqOM9aY2TWE+O04TgC+aIFrgV0k7dmPufS7cMgCVq1aZWvWrBnkLR3HGSLr16/fYmarOx2/j3I22zBkO7CFygZCCGSVdWa2rs3b7MXCRJzN0b4727xOSwYquGvWrOH6668f5C0dxxkikn7fzfg5jBexPPb4p9k6a2Zru7kHi5NyoHFiTtcMVHAdx3HaJaNGehjRG1nczMIsy73pPMuyKS19uJL2kfTdqDzeBkmnR/t3lXSlpN9EPx/Wjwk6jrN0EZBT/NYjLgVeFUUrPAX4k5n13J0AySzcEvBmM/uppJXAeklXAq8BrjKzj0g6CzgLOLMfk3QcZ7iUSyV+/o1vcutP1rNq//1Y+9IXMr3TTgO5d7cr+5IuAI4AVkU1oN8L5AHM7BzgMuA4YBOwHXhtl7eMpaXgRkp/Z/R4q6SNBIfyCYQXAXA+cDUuuI4zdsw8+CD//PSj2fK7W5l7aBsTy5dx8Vnv5S0/+BaPOPgxfb23ELlmLoUEmNlJLY4bcGpXN0lIWx8eUT+oJwI/Bnavmt3Rz4fHjDlZ0vWSrr/nnnu6nK7jLF3Ks7OUtm8f+H3/5wMf5a5f/4a5h7YBUNi2ne0P/IkvvOINfb+3gIzit1EjseBKWgF8DTjDzB5MOs7M1pnZWjNbu3p1x9EhjrNkmbnzj3zvhS/hon0eycX7Poqrjn4eD/5m08Duf/0FX6M0V1i404w7N9zEQ1vu7e/NBVkpdhs1EgmupDxBbL9kZhdFu++qBgdHP+/uzxQdZ+lSKZW46pjjuft738dKJaxc5t7r1vOdY46n+ODWgcxBmcYyYRjqs5kpgkjFbaNGkigFAZ8HNprZv9YcuhR4dfT41cAlvZ+e4yxt/vjt71C4736sXJ7faUZ5dpbbvnbxQObwlFefRH5qYQlhZTLs+6QnsHzXXft+/wFEKQyMJB8STwNeCTxb0g3Rdhyh7upRUefVo6LnjuP0gEqlwubrfspt37maSrGw6Hh5+wxbNw3GrXDsO97CPk88hMkVy8nm80yuXMHKh6/mdV/6XN/vHXy4it1GjSRRCj+gcSYGhELRjuP0kDt+diNfPPGlzD64lWVU2LVcZHu5Ql7iYbkMGYnc8uU87PGHDGQ+E9PTvPV/r+TX3/sBv7/up+y2Zl8Oef5x5CcnWw/ukmoc7rjgmWaOkyKKs7N8/ugTmLn/AcxCI7pqbI8InT0P3nkZu61axd4n/FXDa2y59ffceMn/kMlkeMIL/oqH7d19v01JHHTEMzjoiGd0fa12GUVfbRwuuI6TIm6+7AoqpRIQmtHVZq4aUAFuzUzwkqu+SbaBhfntf/sEl7zj/VQ7uXztre/mJR//J55xct9i+ftKsHDHx8Qdpw8PxxlJ7vzVTdxw0aX8cePNbL/3firRAlklOl7fBmvbQ9v4U4NwrLt+/Ru+/o7/j+LsLKW5uR3bl//uH7n9hp/3+2X0jXGKUnAL13GGRGH7dj5z4knc8r8/JpvPUS6W2O8vnoBVDDOjXJlvuYwZGSArKBWL/Oszj+Vt13+PXffZOzps/OfJp1OanVt0H6tUOPuoE/inP24ik80O7PX1AsktXMdxesDFb30Xv/3BjyjOzDD74FZKMzPc+pP1TO25O9trxTaiApQtiOvWe+/lgjeezk3f+R7//MxjePNu+/Gba/439l6zWx9iwxXf7uvr6RfjlGnmFq7jDIkfn/9lSrNzZKkJAyoUuOe3t8ZWHawApYphGL+64ipuuvr7FGdmY86ex8y4+ze/7c3EB4hHKTiO0zXlcpnizMy82Eai0kpbzGzet1upJBJbgNzEBHs97s87m+wQESLT8rcyOrhLwXEGzB0//yUfOOBxQWzFIrFNIi/KZqPBrclNTvDwAw/goGc9s4PZDp+s4rdRwwXXcVpgZvzvuf/Bux71eE5fuSf/fPix/O4nnbWKKhUKfPKoE3hg8x8aHq9qSNwfpklMrlzBznvuTm56KuasefLLpvnL172S/9/Vl6ERXHwat2ph7lJwnBZc8dF/47IP/BOFqDTipmv+l3971vG85QdXsO8TH9/WtW7+1ncoFRZHEtSTEWDzoWEAj/2rY9n70Cexx0EHcsgJz+Mb7/sw3z37nB3zAsjk8zzi4IPY/ymHcvjf/y17H/LYtuaXNsYtSsEF13GaUJyb45sf+tgCUQMozMzwjfd+mFMv/a+2rrftvvuxSqX1iQTRVSS6JrH60Y/iuHe9bcfxEz7wborbZ/j+uvNQRkgZjnvXW3nu284YSWs2jnH6Gu6C6zhNeGDzH7BGIQNm3P7TG9u+3qMOf9qOTLJWVO9rQDafZ9kuOy84nslmefG/f5QTP/xeHrzrbnZ+xJ4DqW8wSAQjWfc2jnH68HCcnrPTHrtjlfqI2MDqRx3Q9vV23W9fnvH3f8vE8mU79uWXTfOIQx7Lu275JUe9620gYRaEtnrnTDbL2pe/uOE1J5YtY9X+a8ZObKuoyTZquIXrOE144A93sGLVKu6/ffOC/fll0xz/3rM6uubz/+mDPOrwZ/C/n/k8hW3beeJL/4Ynv/pl5CYnOfb/eyePevbhfO7El2EWXA+VUpmXn/dpdluzX9evZxQZJ6vQBddxYnhoy7189ClHMvPAnxbsz01M8Novrus4zEoSf378Mfz58cc0PH7g4U/nQ3dt4jdXf59KscSjjng6k8uXd3SvcWCc/NEuuI4Tww8+ex7FmdlFxWMyuRyrH7l/V9c2q8C9d0E2ix62uP9qbmKCP3uul5sWMFrVH5rjgus4Mdz20xspzi7O5FI2w52/uol9ntBZAXC77ddUvnEuFObAKrDzbmROfCPabfdupzyWjJGBO1buEcfpKfs88ZBFvbwArFzm/tv/wKdOeCmffelr+NWV30l8Tdv6AJWvfQq2PQjFOSgV4d4/UrngX7FysuiFpURoIqnYbdRwwXWcGJ7+t68hPz21wIeYm5wkNznF/3zgo/z80stY/18Xcc4LXsZFb3t3omvaL38EjeJwS0W4ZUOvpj5WjFOUgguu48SwcvUqzrz2Kg468ggy2SwTy5bxmCMPpzQ3R2HbfCJEYdt2vvt/P8OW393a8pq29QFoZMlWyti2B3s3+bFBZBW/JbqCdIykmyVtkrQotETSzpK+IelGSRsk9a09hguu4zRh90cfyBlXXsKnSvfz8W1/ZLf91yzKOoPQNnzjld9teb3MvgdBvnG8rPZ6ZNfzHTeaWbeJivxIWeCTwLHAwcBJkg6uO+1U4Fdm9njgCOBfJE305AXU4YLrOG2wfNddyObzi/Znshmmd96p9QUOfDw8bDXkaq6Rm4BHHYJWP6KHMx0TmhSuSVi85jBgk5ndYmYF4ELghLpzDFip4DtaAdwH9MWh7oLrOG3w1Fe/jEyuQXCPxONi4moXnJbNknn5W9BfHgerHgF77Iue8yIyx49mk8dB0GLRbJWk62u2k+uG7wXcXvN8c7Svlk8AfwbcAfwCON2qWSc9xsPCHKcNVj/yAF75+U/yn284jUwuRIhmcjlO/cZX5pMTqnG7MT5G5SfQU46Gpxw9iCmPNNXyjE3YYmZrW1yinvrqGEcDNwDPBh4JXCnp+2bWc6d6S8GVdC5wPHC3mT022vc+4G+Be6LT3mFml/V6co6TRg476W94/POP5dff+wH5yUkOfObTgpuhXILCTIitBcjmYGLZeAWSDoEuf3ubgX1qnu9NsGRreS3wEQsZLpsk/Q54DPCT7m69mCQW7nkEk/uLdfv/zcz+udcTcpxRYHL5ch53XI2FWqnA3LaFJ5VLYd/UisFObozoQbWw64ADJe0P/AF4KfCyunNuA44Evi9pd+Ag4JZubhpHS8E1s2skrenHzR1nbCjFFBWvlMOWGacE1cHSjdyaWUnSacAVhCzhc81sg6RTouPnAB8AzpP0i+h2Z5rZlm7n3YhufLinSXoVcD3wZjO7v9FJkRP7ZIB99923i9s5ToppVlS8UnHB7YJuM8oid+dldfvOqXl8B/Dcrm6SkE6jFD5NcC4/AbgT+Je4E81snZmtNbO1q1ev7vB2jpNymgmqi21XSPHbqNGR4JrZXWZWjkInPkuIdXOcpUt+goZffrM5yPQ++rJSLrPtvvsoJ+weMapUq4XFbaNGR+8ESXvWPH0B8MveTMdxRhRlwuJYtuqlE+QmQ5RCj/nuJz7DW1bvz5l7Ppo377Yfl/+ff1lUQjKOe275HV/6uzP48Npnct6r38gdGzb2fH69RlLsNmokCQu7gJDutkrSZuC9wBGSnkCIZ7sVeGP/pug4I0ImA5P9LRT+wy/8Jxef+d4d6cWlQoHLPvgxshMTHPXmNzUd+4dfbOCfnnYUxZlZKqUSm2/4BT/96td50+UXc+Az/rKv8+6UUC1sfGj5WszsJDPb08zyZra3mX3ezF5pZo8zs0PM7PlmducgJus4S53/ef9HFncQ3r6dyz/8zy2t3P/3j29nbutDO5pYVsplCttn+PLf/WPf5ts1TazbsbRwHcdJDw/c8ceG+7fd/wCVUqlhnYcqv/3htQ33/3HjzRTn5lLbhDKbHT1hjWOcrHXHGXv2eMyBDffvuu/eTcUWYHrnnRvuz01Othw7LET6oxQa1G+IxQXXcUaIF/7zh8hPTy/Yl182zQs/9sGWY5/9D6cwsWzhIl5+eoqnvf6VZPoQSdETBJmMYreUkHgi7lJwnJQzu3UrP/riBfz8kst48O67mVq5gkwuS6VUZo/HHMjzP/juhWnGMTz3bWdw7+9v40fnf5n85CTFuTked/wxvPCfPzSAV9E5abFk4zCzzyQ91wXXcVLMn+78I+9/3FPYdu99i45NLFvG097w6kRiC5DJZnn5OWfzV+9/F3f/ehO77b8fD9sr3TV4BWmyZJF0OvAFYCvwOeCJwFlm9q0k41P6PcJxHIALT3tLQ7GFEJ1w8VnvpTgXU8chhp0evppHPf2pqRdbICpArthtCLwuKtv4XGA1UaWxpINdcB0nxfzif65oec49m/pS2ColxPtvh2T5Vm96HPAFM7sR9+E6zpjQ4k+5XCiy8uHjW6NEhCS+FLFe0reA/YG3S1oJJO4O4YLrOH2gODvLdRd+jQ3f/Ba77PUInvHG17HHQY1Duppx0BHPYMPl3254LDsxwcFHH8nK1au6nW56Ubp8uMDrCUW7bjGz7ZJ2I7gVEuGC6zg9Zm7bNv7pqc/hnltupbBtG5lcjmvOOZcnnPg8Nt/4S/LTUxz+d2/gqa99RctwrNf+52d5+95/RnF2duEBicc977m85ovr+vhK0kGaMsrMrBLVB3+FJAN+YGYXJx3vgus4zTALBcQtqmmboNTi1Z9cx92bfktxJohkpVSiUipx3QVf3XHOf53+Nm6++vu87j8+2/RaK3bbjf+zeSNfOeMsNnzzSiZXLOfJrzyJI047mZ13f3h3r20EEJBNkYUr6VPAo4ALol1vlPQcMzs1yXgXXMeJwyowu22+RxlAJgeTzfuUrf/KxTvENo7Ctu387GuXcOc73sKef3ZQ03NX7LZbS2EeW1KUURZxOPDYqP8Zks4ndPpNRLrc0Y6TJuZmFootQKUExeZhWEnTZKUMt/yo530Kx46URSncDNS2rtkH+HnSwW7hOkuXSgVKhVBWMZtfaEqZBXFtRKkAE1ONL1kus+V3tya6vbIZdt5z9zYnvbSo1lIYNpK+QShHuzOwUVL1k/Iw4IdJr+OC6yxNZh6C2YfYEXeVycCKh9UUEG9GfBnEjVd+h8L2mZZXUCbD1MqV/NlRz04236WKRCYd1cJ60qHcBddZGpgFy7TqJigWIq2NxLNShofuh5W7BfGVQgBovUsBgjUcw5bf/X5Hvdl68tPTZDIZKpUyqx91AKdc9CWyOf8TbMWQMsoWYGbfqz6OWqkfGj39iZndnfQ6/r/tjD9msO1PUJhhgXVqLIyqr5Rh+4OwbGWIRphcFlnBtQjyjd0JAPs88RDUINRrcsVyXvLxj7HmyWuZmJ5i1f5runlFS4YU1lJ4MfAx4GrC9P6vpLea2VebDoxwwXXGn3IRClGXhEaFVBd4CKLIhOlIdKdXBmu4GhaWm2jqVNz/yYey39onceuPr98RO5vN51mxehVrX/pCJupKKzotSF+UwjuBQ6tWraTVwLeBRILrUQrO+FOIQrTiKljX/kErA9QsmCkTFsgml0F+suVfvyTe9M2v8Zw3n8ZOe+7OilW78ZevewVv/8nVLrYdkrIohUydC+Fe2tBRt3CdpUMj61YKLgdYGKmQsAtuIyampznhg+/hhA++p+NrOIEQpZAqE/dySVcwn/jwEuCypIPdwnXGn8kWrcolyOWhdgErUbSC03eiKIW4LdkldIykmyVtknRWzDlHSLpB0gZJ34s5R8DHgc8AhwCPB9aZ2ZlJX46/q5zxJ5uDZTvDzIPheSOLqTZlNzeZuhJVS5ps5/8XkrLAJ4GjgM3AdZIuNbNf1ZyzC/Ap4Bgzu01Sw5xpMzNJXzezvwAu6mQ+/q5ylgZTy2Gn1SHkq57J5cGdkM2HxzFJDc4QEN22ST8M2GRmt5hZAbgQOKHunJcBF5nZbQAtwryulXRok+NNcQvXWTpkc7BydQgPK80Fq3ZimbsPUo1aWbirJF1f83ydmdWWUNsLuL3m+WbgyXXXeDSQl3Q1sBI428y+GHO/ZwGnSLoV2BYmiJnZIa1eCSQQXEnnAscDd5vZY6N9uwL/BawBbgVebGb3J7mh4wwVKfh0W/l1nVQQ8k+aWrJbzGxts0s02Fe/IpoD/gI4EpgGfiTpWjP7dYOxxzabTCuSuBTOA46p23cWcJWZHQhcFT13nPRg1lWkgZMelM3EbgnYTCgwU2Vv4I4G51xuZtvMbAtwDWFBbBFm9ntgN4Jb4vnAbtG+RLScsZldA9R3sTsBOD96fD5wYtIbOk5fKZdgZmtYIJt5MErldeEdaRrFTzcK8WvMdcCBkvaXNAG8FLi07pxLgGdIyklaRnA5bGw8Fb2HoHm7AauAL0h6V9KX0qnzanczuxPAzO6MW9VznL5iFjLAqnUPKmWY27bwnHIBZkswtSJ1KUtOAqSklmxDzKwk6TTgCiALnGtmGySdEh0/x8w2SrqcUGaxAnzOzH4Zc8mTgCea2WyYnj4C/BT4YJL59H21QNLJwMkA++67b4uzHSchxTko1hT5VpbYKl5WgbntIVLBGT26zCgzs8uoS04ws3Pqnn+MUCOhFbcCU0D1zTcJ/DbpXDr96LhL0p4A0c/YMAozW2dma81s7erV49td1Bkg5eJCsQWwcuPKXlUqpVD/1hktBMoqdhsCc8AGSedJ+gLwS+AhSR+X9PFWgzu1cC8FXg18JPp5SYfXcZz2adFxIZZKuXEcrpNu0uUKujjaqlzdzuAkYWEXAEcQ4t02A+8lCO1XJL0euA14UTs3dZyuaGbJNsPFdvTo0ofba8zs/NZnxdNScM3spJhDR3ZzY8fpmEwuuBXaQZlEHXedFJKierjd4ik2zuiRn+pAcMfnj3YpIZEqC7dbXHCd0SOTgamVwZdbLtKsx9gOfMFsRElfBfJucMF1RpNMBiangemow24ZSsUQdxt3vjN6pMzClfRo4K3AftTop5kl6gbqguuMPlIoQJPNQYHQLLKeJn3InHSTsgLk/w84B/gsUG53sAuuM5pUKqHiV6Uc9RqbDFZsfgpQOAbzLXK8IthoopbVwgZNycw+3elgfxc6o0elvLCbbqUcrNqpFVHJxamwmY2V/2+p0qJa2KD5hqS/J8Ti7ggIN7P6ejMNccF1RgezYLnGJT4UZoLoVnGxHX1E2izcV0c/31qzz4ADkgx2wXVGA7Ng1TZN323bpeaMAGny4ZrZ/t2Md8F1RoPiXOcZZs4Iky4frqQ88HfAM6NdVwOfMbNEgeEuuE76qboSWpEiS8jpEaFP+rBnUcungTyh6STAK6N9b0gy2AXXST9JLdvsRH/n4QwBQTZVKdmHmlltN4jvSLox6eD02OqOE0eijg2C/GTfp+IMge46PvSasqRHzk9NB9BGPK5buE76UQu7IJODiem0ffV0eoFIW5bgW4HvSrqFMLv9gNcmHeyC66QPs1AwvFgI7oQ4l4Iy3jpn7FGqBNfMrpJ0IHAQQXBvMrPEBZpdcJ30UZxtnJ5bS34KchMutuNOSixcSc82s+9I+uu6Q4+UhJldlOQ6LrhOuqhUWosthJhbF9ulQTr+nw8HvgP8VYNjBrjgOiNEuRRibZMmL3jr8yVCOqIUzOy90cP3m9nvao9JSpwMMXxb3XFKxdDevFIiUW1b8GI0S4VqHG56ohS+1mDfV5MO9netM1zMoDjT3hhlgv/WGXuEUAosXEmPAf4c2LnOj7sToW16IlxwneGTNM5WGcjlQinGdPj1nEGQjv/rg4DjgV1Y6MfdCvxt0ou44DrpZnJ5KLmYjj86Z9CkJErBzC4BLpH0VDP7UafXccF1BkelDHMzYNHCmLIwuSy4B+K6NLivdonTfRyupGOAs4Es8Dkz+0jMeYcC1wIvMbM4v+zPJJ1KcC/scCWY2euSzGX4Hx3O0qBaNNxqohCsDLNbo3jaBm9Fb/zoVC3cuK3VcCkLfBI4FjgYOEnSwTHnfRS4osUl/wPYAzga+B6wN8GtkAgXXGcwxBUNByjMNs4mKxe8xq3TbZTCYcAmM7vFzArAhcAJDc57EyEC4e4W13uUmb0b2GZm5wPPAx6X9KW44DqDoZlwVkrxx0qJyow6Y0sUhxu3wSpJ19dsJ9ddYC/g9prnm6N983eQ9gJeQGgO2YrqG/IBSY8FdgbWJH01XTnIJN1KMKfLhOZqa7u5njPGKNNZAXEvOr60aV0Pd0sL3Wk0uD4s5t+BM82snKC7xDpJDwPeBVwKrADe02pQlV6sSDzLzLb04DrOODMxtbDxYy25yfgC4x6dsMTpOtNsM7BPzfO9gTvqzlkLXBiJ7SrgOEklM/t6/cXM7HPRw2tI2MesFncpOIMhkw0lFOvJ5psvfvjCmdOdD/c64EBJ+0uaAF5KsEx3YGb7m9kaM1tDyBr7+0ZiG6aiD0vapeb5wyR9MOlL6VZwDfiWpPUNfCfVCZ1c9a/cc889Xd7OGWlyEzC9U4itnZiG6ZUhLKxZvVu3cJc2aunDbYqZlYDTCNEHG4GvmNkGSadIOqWDGR1rZg/UXP9+4Likg7t1KTzNzO6Q9HDgSkk3mdk1tSeY2TpgHcDatWu94shSR1ocW1tNbGiUceYpvE6XH7pmdhlwWd2+hgtkZvaaFpfLSpqs1sCVNA0kbjXSleCa2R3Rz7slXUwIwbim+ShnyVKpzEckZHPzlq0UrN657QsXyTzxwRHhAzk9/CdwlaQvEL7hvw44P+ngjt/NkpYDGTPbGj1+LvD+Tq/njAFmYav618xCBlm5FB2rCw2bmJ63YDPZ0L3BKuFcT+d1gJBplp73gZn9k6SfA8+Jdn3AzFolS+ygG/Nhd+DiaGUvB3zZzC7v4nrOqGEG5WIQ1EploaBm82F/s3KLhZnFlq5SZc04aSBdFi7Azwit0i16nJiOBdfMbgEe3/JEZzwxi2rYxiQ0lBMmLJRL7qd14lG6eppJejHwMeBqgsPj/0p6a5PaCwtwB5nTGeVib9JuvXOD04p0WbjvBA41s7sBJK0Gvk3CIuQuuE5nJOk7loRsvjfXccaXdPnyM1WxjbiXNsJrXXCdDunBH0F+MlVfF50Uoq4zzXrN5ZKuAC6Inr+EupCzZrjgOp2Rn4C5JkVnICyALYhMiGJwpeC3TddXRSetNEuMGTBm9lZJLwSeRrA61pnZxUnHu+A6nZHNx9RAiBY58pPhHKtAOWpp7qFeTrukz8LFzL5G42aSLXHBdTonPwlYENRMJiQq1LsIlIFceiwUZwRJwYe0pK00jnEUYGa2U5LruOA6nVHt4FClXA4hXlMr3C/r9I6UWLhmtrIX13HBdTqj0Ki1uYX9U8sHPh1njEmHhbtrs+Nmdl+S67jgOu1jFh+D26x7g+O0S0osXGA9waUQV9A8UW1cF1zHcdJNCqIUzGz/XlzHBddpHymqldAgfTfrabpOL1HqwgejFjsHsrBNeqIqiS64aadaIKZSDm+8bD4VPi0mpmG2vLCcYiYbWuk4Tq8QqaoWJukNwOmEVj03AE8BfgQ8O8n44dvqTjyVCsxuDQtRpUL4ObM1HW1npBCRUO3eMLk8bGn4MHDGi0w2fhs8pwOHAr83s2cBTwQSt7JxCzfNFGYaFHdJUSRAo+4NjtNT0lUtDJg1s1lJRJ0fbpJ0UNLB/teSZuJW/Cul+ULfjjPOpK/jw+aoieTXCW3F7mdxF+BYXHAdx0kxibvzDgQze0H08H2SvgvsDCRuvOCCm2ZiIwFSsnDmOP1GpCUOdxFm9r12x7jgpg2z+dY0+akQnVAbCaBM/yIBdiQ0VHuKpcp35ixJNFbvQxfcNFEuhs61teQmwyd8pRIWDzK5/li3lXJomVO7SJeb9DAvZ/iky4fbFS64/caMHRmBzYTSbLHYQih/mFsB+T52Rqjeuz4iojQXohA8EsEZFkpX195u8b+kfmEWBKtYUy82k4NcvrEPtlnTxVIhxLrWn1+ciyzfKOGgU0vAKgvdFrUU51xwneEyRhbu+DhH0kK5GMoWzjy4UGwhhHMVZkIyQzfJC8VCsEir/tZKKdyz3GHhmKaNHL3JozNMIh9u3JbkCtIxkm6WtEnSWQ2Ov1zSz6Pth5L61o18aZouVoFSMfzM5rvvRFCpBKEtl5JVyzKDwvaQqVVFTT7FaxstmkFxtvF5xVnIrmh8rBnNXrs3eXSGiUBdWLiSssAngaOAzcB1ki41s1/VnPY74HAzu1/SscA64MldzDqWpSW4lUoQpdqv76VC+Ko/uawz0S3OxQtg07mUFyYvFBvVlyXMbdEbLsbqbLdteVW84zrwKhN6jznO0Og6SuEwYJOZ3QIg6ULgBGCH4JrZD2vOv5ZQJ6EvdPVKWpnqqaJcCl/lG/lKK6Vkbb8tSqvd/mDYZrd1JrY77luJaiTMxYtlO9Z3u2/MUiHmdSuEpE2t8HhfZ/hks/EbrJJ0fc12ct3ovYDba55vjvbF8Xrgm719AfN0bOEmNNXTQVwEQC2lQtSjq9k1ti0Uxm6Lbc891Pqc+sUsKZRALDcQylyT+TdiUQPIHTcNlq2LrTNsRKv34RYzW9viCvU0/Ioo6VkEwX164vm1STcW7g5T3cwKQNVUTx9WoeXiT9OFI4LQtvuVvRcoE+bWan6d4ItlTupRt9XCNgP71Dzfmwa1DyQdAnwOOMHM7u3J1BvQjeAmMtUlnVw19++5J3EVsx6TwFJrZc0NQ2whWNEzD4atGonQyLoFKLXp3sjEfMGRSPQ7c5xB0F2UwnXAgZL2lzQBvBS4dMHlpX2Bi4BXmtmvez7/GrpZNEtkqpvZOsKqH2vXrh2O2ZSJ/nPiYk2BlhbdoNMLq5btAhdGublrJIkVXC1oXirEnz8x7e4EJx102dPMzEqSTgOuALLAuWa2QdIp0fFzgPcAuwGfUnjfl1q4KTqmG8FNZKp3RKVck8rao6DnyWUL23ovooWgZqOU2n58ta8lPx2SI8qlEDq2iASukWZiWZiNt5AhvM44y9dxhkGXH/5mdhlwWd2+c2oevwF4Q1c3SUg3f1k7THXgDwRT/WVdzabRwlQ3IVu1ZLIwsSxGxAgi1wwJJleE8f1yLygT5iG1sMabYJX4mN5KpbnYQuSyKLX+fTjOQEhfT7Nu6Fhw40z1rmZTmFksZpVSCL2qT23thGwu3rWQJN40kwmhUtWv+nPbup/TjrnlF36Vb+bCaGZpN/tgShpVUZpzwXXSgfBqYVUamepdXCy+nkCp2BvBrfbhKszM3yuTa99nqT586paLUM7PC10z10VusnH8bybXWqgdZ6QQSmk93E4YEWddD/2mUnBRNLyNzbevyeSa91KSgvA1imWdXBZ8pbWW9MR0uGZhJt7SLGyHzMpw32bWqKLEhFrRzeaCy6QZmYR+aE/nddKEW7h9oGo1NvKPDmIRp1IOmWO14p6baG5Z5yfDvEtzkUhnI2HNwnR+/rUoE51XbP21vlSIatA2s0YF+Ykwv+oiWRLrVQqddZsuHuLpvE566Me3ySGSro+OOHHrdxHs6mJdvSVdKjQvmygFccpPhZ+5iYWfxtXg7KoYxmZ2LZhM+NHMh1otl6ioo2k7roJMNiz+NcNdD06aqBoUjbYRIz0WLgQxmFoZhKla5zU/0f+vFNVCMo0oFuK/YlcqIT23dqxmoxoEDeacJKSsKqbZXLCg60s8Ti7v/o2WzcZ/m3Dr1kkTXcbhpo10CS4Ei60XC2Q9o4lIFmYWi6hZ8N828hNn882t3ExuYUhX1XIulwDNxwLXUilHhcjL4XhusrnvucrE9GIXijLhno6TJtyHO2Y0+w+Ns/iqC2yNiHND5CfDsUZhaZlsVEh860JfcLMSifU90KrVv6ZWthbdTBamV4ZrVL9NNBJ0xxk2LrhjRlwyhDLx7oROMs6qYWmlQrBalQkuk/r440o5LGxNr4x/s5nBXEwN3WKMhd1oPu5CcFLNaPpq43DBbVYFrFkt2mbRBs1WVaVg6VZLQTa7f7EQv2C4ozllAzptteM4acQt3DGiWQptp8faCWNp1tusKsSVSvD9lsvJFhLHyCJwljit6+GOFC64zXqJNYv/zeSAmAWwdhIHmvlaq5EEtXGz5XKoh9DsHu4mcMaJMRLc8bHVOyXTxE+bbyJccQWQkxdGrjk/Rtir/t1GxC3MuV/WGSuaxOCOoBC7hQshIqCYifp7RWm9E1Otv7ZPLg8hWVXxy+bns8/aYXLZwmaO1SgFZTpoDMlIvhEdJxb34Y4ZUhDYdjPaquPoMnZVCgLbMP5YtFVLIkkMruOMEmMkuOPzSsaVOPdA3JtwjN6cjtPUnTCC3+T8rzPt5CcX+5gzufiMsHLRw8Kc8aK7nmapwl0KaadaTrJSibo5RG+y2a3xY4qzkG1RoMZxRgSNoCUbhwvuqJDJsOMLSVzkQpV+911znIGhkbRk43DBHUXKLSIXvAmkM064hesMlUymuehW04YdZ9TxnmbO0KlWHVtEVBzHQ8OcccItXGeoZLIh6aIwM1/Tob7rr+OMBaMZ/hWHC+6oks2F8o3VBbIxelM6zgLG6L3t3z1HnRENAHecRFR9uF3E4Uo6RtLNkjZJOqvBcUn6eHT855Ke1OuXUcUF13GcdNNFppmkLPBJ4FjgYOAkSQfXnXYscGC0nQx8urcvYB4XXMdxUoy6tXAPAzaZ2S1mVgAuBE6oO+cE4IsWuBbYRdKevX0dgYH6cNevX79F0u9rdq0CtgxyDj1g1OY8avMFn/OgGMSc9+tm8Pqf3XCFVjxsVZNTpiRdX/N8nZmtq3m+F3B7zfPNwJPrrtHonL2AOzuYclMGKrhmtrr2uaTrzWztIOfQLaM251GbL/icB8UozNnMjunyEo38DvWpmEnO6QnuUnAcZ5zZDOxT83xv4I4OzukJLriO44wz1wEHStpf0gTwUuDSunMuBV4VRSs8BfiTmfXcnQDDj8Nd1/qU1DFqcx61+YLPeVCM4pzbwsxKkk4DrgCywLlmtkHSKdHxc4DLgOOATcB24LX9mo/MK0s5juMMBHcpOI7jDAgXXMdxnAGRGsGV9BZJJqlZzN3QkfQxSTdFKYAXS9pl2HOKo1VKY9qQtI+k70raKGmDpNOHPackSMpK+pmk/x72XJIgaRdJX43exxslPXXYc1oqpEJwJe0DHAXcNuy5JOBK4LFmdgjwa+DtQ55PQxKmNKaNEvBmM/sz4CnAqSMwZ4DTgY3DnkQbnA1cbmaPAR7PaM19pEmF4AL/BryNPgUb9xIz+5aZVbs0XkuI2UsjSVIaU4WZ3WlmP40ebyUIwV7DnVVzJO0NPA/43LDnkgRJOwHPBD4PYGYFM3tgqJNaQgxdcCU9H/iDmd047Ll0wOuAbw57EjHEpSuOBJLWAE8EfjzkqbTi3wnGQmXI80jKAcA9wBciN8jnJC0f9qSWCgOJw5X0bWCPBofeCbwDeO4g5pGUZvM1s0uic95J+Ar8pUHOrQ0Glq7YayStAL4GnGFmDw57PnFIOh6428zWSzpiyNNJSg54EvAmM/uxpLOBs4B3D3daS4OBCK6ZPafRfkmPA/YHboxaIe8N/FTSYWb2x0HMrRFx860i6dXA8cCRlt5A5oGlK/YSSXmC2H7JzC4a9nxa8DTg+ZKOA6aAnST9p5m9YsjzasZmYLOZVb85fJUguM4ASFXig6RbgbVmltqqS5KOAf4VONzM7hn2fOKQlCMs6h0J/IGQ4vgyM9sw1Ik1QeFT93zgPjM7Y8jTaYvIwn2LmR0/5Km0RNL3gTeY2c2S3gcsN7O3DnlaS4Jhp/aOIp8AJoErI6v8WjM7ZbhTWkxcSuOQp9WKpwGvBH4h6YZo3zvM7LLhTWkseRPwpai2wC30MZXVWUiqLFzHcZxxZuhRCo7jOEsFF1zHcZwB4YLrOI4zIFxwHcdxBoQLruM4zoBwwXUcxxkQLriO4zgDwgXXcRxnQLjgOo7jDAgXXMdxnAHhgus4jjMgXHAdx3EGhAuuA4TSmJKa1gHu8/1N0qOGdX/HGQQuuM5I00qoJT1P0g8kPSDpj5I+K2nlIOfoOFVccJ2hEhVK7yc7Ax8EHgH8GaHzxcf6fE/HaYgL7pgh6UxJf5C0VdLNko6M9p8n6YM15x0haXPd8EMl/UrS/ZK+IGmq9lxJb5N0t6Q7JZ0o6ThJv5Z0n6R31Fz7MEk/iqzKOyV9Iip2XT1ukk6V9BvgNw1ew9Ml3S7pWdHz10naGM3rCkn7RfuviYbcKOkhSS+pv5aZfdnMLjez7WZ2P/BZQqFzxxk4LrhjhKSDgNOAQ81sJXA0cGsbl3h5NOaRwKOBd9Uc24PQt2sv4D0E4XoF8BfAM4D3SDogOrcM/COwCngqoc3P39fd60TgycDBda/haOAC4IVm9l1JJxIajf41sBr4fnQcM3tmNOzxZrbCzP4rwWt8JpD2zhfOmOKCO16UCe1/DpaUN7Nbzey3bYz/hJndbmb3AR8CTqo5VgQ+ZGZF4EKCmJ5tZluj1j0bgEMAzGy9mV1rZiUzuxX4DHB43b3+j5ndZ2YzNfteBKwDjjOzn0T73hidu9HMSsCHgSdUrdx2kHQU8GrCB4bjDBwX3DHCzDYBZwDvA+6WdKGkR7RxidtrHv+e4Pescq+ZlaPHVZG8q+b4DLACQNKjJf13tEj1IEEkVzW5V5UzgK+Y2S9q9u0HnB25Jx4A7iO0gN8r8asKc3oK8GXgb8zs1+2MdZxe4YI7ZkQ+y6cThMqAj0aHtgHLak7do8Hw2rbq+9J5W/VPAzcBB5rZTgSXgOqn2mDci4ATJZ1Rs+924I1mtkvNNm1mP0w6GUlPBC4FXmdmV7XzQhynl7jgjhGSDpL0bEmTwCzB6qxapTcAx0naVdIeBGuynlMl7S1pV4JIJvGJNmIl8CDwkKTHAH+XcNwdBH/vP0iq+nzPAd4u6c8BJO0s6UU1Y+4CDiAGSY8FLgfeZGbfaO9lOE5vccEdLyaBjwBbgD8CDycIJ8B/ADcSFtG+RWMx/XJ07JZo+2CDc5LwFuBlwFbC4lpi4Taz2wiie6akN5jZxQQr/cLIPfFL4NiaIe8Dzo9cDi9ucMk3ExbbPh9FMjwkyRfNnKHgbdIdx3EGhFu4juM4A8IF13GcsUbSuVHCzi9jjkvSxyVtkvRzSU/q11xccB3HGXfOA45pcvxY4MBoO5kQZdMXXHAdxxlrzOwaQvx2HCcAX7TAtcAukvbsx1z6XThkAatWrbI1a9YM8paO4wyR9evXbzGz1Z2O30c5m20Ysh3YQmUDIQSyyjozW9fmbfZiYSLO5mjfnW1epyUDFdw1a9Zw/fXXD/KWjuMMEUm/72b8HMaLWB57/NNsnTWztd3cg8VJOdA4MadrBiq4juM47ZJRIz2M6I0sbmZhluXedJ5l2ZSWPlxJ+0j6blQeb4Ok06P9u0q6UtJvop8P68cEHcdZugjIKX7rEZcCr4qiFZ4C/MnMeu5OgGQWbgl4s5n9NKqUv17SlcBrgKvM7COSzgLOAs7sxyQdxxkyVoFiASolUBbyE5DJDuTW3a7sS7oAOAJYFdWAfi+QBzCzc4DLgOOATcB24LVd3jKWloIbKf2d0eOtkjYSHMonEF4EwPnA1bjgOs74UanA7EPMf38vQ7kAk8sh21+vpBC5Zi6FBJjZSS2OG3BqVzdJSFsfHpLWAE8EfgzsXjW7o58PjxlzsqTrJV1/zz33dDldx1mimEGlHLZBp+MXZ2noLC1s7/tcBGQUv40aiQVX0grga8AZZvZg0nFmts7M1prZ2tWrO44OcZylS6UMs1uDlTn7EMxshXJpcPePu5cZfVrMn0eQlWK3USOR4ErKE8T2S2Z2UbT7rmpwcPTz7v5M0XGWMGZBZBdYkgZz24JfdRA0Fbb+ip4IIhW3jRpJohQEfB7YaGb/WnPoUkK7EqKfl/R+eo6zxCkX448VC4OZQ26i8f5MroUY9+j2/Y9SGBhJPN5PA14J/ELSDdG+dxDqrn5F0uuB2wjV+h3H6QVmQWybug4G5MvNTQS3Rq34Z7IwuSx+TI8IPtwRVNYYkkQp/ID47w1H9nY6juNQKoYFqVb0OUJgB1IQ10oFrAzKDCwkrBqHOy54ppnjpAmzZGKbyYav9I3GV0pBtCFYp5lsb776Z4bjOR1FX20cLriOkyaa+WxrmVjWWEQLMwuvUS5CNj+Qr//9IFi442PiuuA6zjAxC35aK4cMrqRxrZVKZHHWUC41FuxyEUqF+MWvlOMWruM43WOVBiFfCSlsg8yKeV9qpQJzTVwRhZlg6Y6YtSi5hes4Ti+Ym+kuU2tue7Bai3MkilgoF0fSyh3FjLI4XHAdZxhUF7e6ukYlSrtt454jhkcpOI7TPcMQv0GFkfUQITJ9zmYbJKP3P+A4w2JH7QB15wstF5v7W/tBJjew2Nlekx0fvXXBdZyWmIWv7qVqKq0gPxVqwnZyrV6IbSYbsr9aoUzw246g7xbmq4WNCy64jtOK+thWDIozQQmy+fau1U2Vr+xEcAtkokyv4lxjH242H47nJkYuKqEej1JwnKVEtaZBI4pz7QtuN/UPBORq7pefDD9Lc2GeysDEVAdzSjej6QhpjAuu4zSjWQnESgflEbtZuGpk6eUn54V3DFlyxWscZ0mjJnlOnSxCKRP8v/WugGwOclMh46ww03jsiPphu8UzzRxnqdBsYWpiqrNr5ieDwJaKgM37XCUgGx7PbZ+3rpWBienm4j/GjI9964LrOPFUKqGzQiMml3cXZpXJwkTM+EwWplfOuyzUZRjaCOMuBcdZKpTm+nftatEaCNZuI1GpL06zRBmn34ILruPE0WzBrJt+Yo3CuQbQcnxUGScLd5w+PByntzQq8F2lXIKZB0MH3eJsG2UVy41jZ+e2jWStg36jFtuo4YLrOHE0SxwoF4NAWiVYrEmzx0pNGj8mLT6+xMgqfhs1XHAdJw4JplbMC68y8VZvpZQs1dZpEzX9l+gK0jGSbpa0SdJZDY7vLOkbkm6UtEHSa3v+MiJccB2nGdWQrOmdQuRAs9CsJGm7zfy0zVwYSxQpZFDHba3HKwt8EjgWOBg4SdLBdaedCvzKzB4PHAH8i6S+BD274DpOOzRbwEkSVZDJNRbd3KRHJcTQpQ/3MGCTmd1iZgXgQuCEunMMWClJwArgPqDLYsWN8Y9Ux2mH/ETjcDEpmYUqhQaQtf3HchMeoRBDSAVpKq2rJF1f83ydma2reb4XcHvN883Ak+uu8QngUuAOYCXwErNuwlDi8f9lx2kHZUIIV2H7fFRBdZ8UdXIoRwIck9gghSI0ufEqMtMvWkSFbTGztc2GN9hXHw5yNHAD8GzgkcCVkr5vZg+2Mc1EtPwOI+lcSXdL+mXNvvdJ+oOkG6LtuF5PzHFSSzYHUyvnt+mVwR1QLIRQsbltoTnkzNbOCtw4C8hEXR8abQnYDOxT83xvgiVby2uBiyywCfgd8JieTL6OJE6j84BjGuz/NzN7QrRd1ttpOU7KkaK6tNGfUKUcauTWYhWPr+2SagHyThfNgOuAAyXtHy2EvZTgPqjlNuBIAEm7AwcBt/TsRdTQ0qVgZtdIWtOPmzvO2FCMSQO2ShBj99F2TDdLiWZWknQacAWhtO65ZrZB0inR8XOADwDnSfoFQePPNLMt3c67Ed28C06T9CrgeuDNZnZ/o5MknQycDLDvvvt2cTvHSTHNrFi3cLsiabxtHNE38Mvq9p1T8/gO4Lld3SQhnX54fJrgXH4CcCfwL3Enmtk6M1trZmtXr17d4e0cJ+U0s2Cz49SzYLAIzzTDzO4ys3IUOvFZQqyb4yxdchONkyJyk/2pY2uVEFrWn+ilVDFOtRQ6cilI2tPM7oyevgD4ZbPzHWfsqaYBF+dCfK0UxLbXoV9mi5taZvNRgfIEElQuheI5lfLI9EAbp2phLQVX0gWEdLdVkjYD7wWOkPQEQjzbrcAb+zdFxxkRpKgLRIedIJJQFfRaykUoKohuM8qlhQXVrRKK7uSnO2v5PgBG1ZKNI0mUwkkNdn++D3NxHKcVcdXGSoXQK62ZNRjXK604GyzxNFqSEtmE8V+jgMeqOM5I0UXEQ6y/N91RFBojwfVqGY4zSsSmC2daW6hptGBbUJtf0mhLA1HoayJSMmXHcRIR56dt5b+FsIgXtz/FYiwpdksJiSfiLgXHSTuVSvCzlkss+vqfyYWFuiQdhPOR4Na2+MlNzu9PKZmUuxTM7DNJz3UL13HSTKUMs1ujyIQGvtZMpr127fnJ+WLq0zsFsU6PpbgIMd8lvtE28PlIp0vaSYHPS/qppMRZai64jpNm4iILqpQK7acOV9sFpVhodyDIZhS7DYHXRWUbnwusJlQa+0jSwe5ScJw0k6RPmlVA45o+nCpfLcz7a48DvmBmN6qNCbrgOs6o04/U4ZQQ6rinSnDXS/oWsD/wdkkrgcT51S64jtMPqu3Ty6WgGvnJzlJoM7nQETiOZq3cx4SUvbzXE4p23WJm2yXtRnArJMIF13F6jVVg5iF2LHIZIYUWze/LTbTODIMQ7jW7tfGxEYgw6AVpilIws0pUH/wVkgz4gZldnHS8C67jNMMsRAhUyiEaIJsgBbY4R+PsrZp9pUK4ZrUXWhyZTIgmKBWgVC2KM7Fk+qGFjg/pEVxJnwIeBVwQ7XqjpOeY2alJxrvgOk4clTLMbmOBUGoOppY395uWE3bYrpSTdYOouiSWgDW7CKXLwgUOBx5rFkJDJJ0P/CLp4PH1tjtOtxRmWGSpWgUKMe10dtCGQCyBerbdkqY4XOBmoLZ1zT7Az5MOdgvXWZpU25lXW5rXuwqqxxtRLgIxqbRmYAlCuaqMcYRBL5CUiigFSd8gfPruDGyU9JPo0GHAD5NexwXXWXqYhUWsBav/M8Gf2m2zx6TuBAhi206W2BIlJS7cf+7FRVxwnaWB2fzCE9b4q/zcttC1IZOtBoA2tnKbLVgldRG006VhCSNIRT1cM/te9XHUSv3Q6OlPzOzupNfx7zPO+GMWxLQ4G77uNxPF2YfmOypMLFssiMqEcK44mlnIE8uiOgY7wWSDazsNSVO1MEkvBn4CvAh4MfBjSX+TdLxbuM74UyklS5GtMrc9iGImA1Mr55s1ZrLz1m8c1dCx+jY4mWwQYxfZ9khflMI7gUOrVq2k1cC3ga8mGeyC64w/7fhVa8dU2860G/M6MQ3l3Hw7nGx+SWSE9YuU/doydS6Ee2nDU+CC64w/g/6L3ZGckM7GjKNECmspXC7pCuYTH14CXJZ0sPtwnfGnE+HrNlrB6RHx/tukPlxJx0i6WdImSWfFnHOEpBskbZD0vZhzBHwc+AxwCPB4YJ2ZnZn01fi7yhl/lAkhX7Utwpvh0QPpItu5XSgpC3wSOArYDFwn6VIz+1XNObsAnwKOMbPbJD280bXMzCR93cz+Ariok/m4hessDbK5sADWqG5sfioqBDMVznFXQHpQ11EKhwGbzOwWMysAFwIn1J3zMuAiM7sNoEWY17WSDm1yvClu4TpLh0wm1EGolEPkgjLJitE4Q0StLNxVkq6veb7OzNbVPN8LuL3m+WbgyXXXeDSQl3Q1sBI428y+GHO/ZwGnSLoV2EZUAs7MDmn1SiCB4Eo6FzgeuNvMHhvt2xX4L2ANcCvwYjO7P8kNHWeoSMHadR/tSBC6ATX9QNxiZmubXaLBvvpSbjngL4AjCTnbP5J0rZn9usHYY5tNphVJXArnAcfU7TsLuMrMDgSuip47TjowC2FdFS8MMw4om4ndErCZUGCmyt7AHQ3OudzMtpnZFuAawoLYIszs98BuBLfE84Hdon2JaDljM7sGuK9u9wnA+dHj84ETk97QcfpKcQ5mHgwLZLNbQyFwr8g12nRXLuw64EBJ+0uaAF4KXFp3ziXAMyTlJC0juBw2Np6K3kPQvN2AVcAXJL0r6Uvp9HvV7mZ2J4CZ3Rm3qhdN8GTgZIB999037jTHaZ9KZb7aV7XuQXF24TlWDqI7vdJ9taOIlNSSbYiZlSSdBlwBZIFzzWyDpFOi4+eY2UZJlxPKLFaAz5nZL2MueRLwRDObDdPTR4CfAh9MMp++O7IiB/Y6gLVr17bZz9lxGmAWatUuSJ+taV+zeECokTC9cgCTc3pOl6m9ZnYZdckJZnZO3fOPAR9LcLlbgSmg+sk+Cfw26Vw6Fdy7JO0ZWbd7Aomr5ThO15SLi2sVxIpt9XBlvk2OMzoIlK5Mszlgg6QrCW+6o4AfSPo4gJn9Q7PBnQrupcCrgY9EPy/p8DqO0z7FVh0XYqhUXHBHkXS5gi6OtipXtzM4SVjYBcARhHi3zcB7CUL7FUmvB24jlCpznHST8TyfkaNLH26vMbPzW58VT0vBNbOTYg4d2c2NHadjsjWVuJLi3RVGl3SVZ+wKj/52Ro/8VPDhWjtrsOPzR7uUkEiVhdstLrjO6CGFmgelwnxx8Jaxth6LO5oMrz1vP3DBdUYTCfKTYYMguKUSFGcan+/uhNEkZRaupEcDbwX2o0Y/zezZSca74DrjgTKQnwBscfIDNO9D5qSaYfQua8L/A84BPgu00bcp4ILrjCblUtQUshJKLuYnw2JafjKIb3E2+HgzWZiYcgt3VFHLamGDpmRmn+50sAuuM3qUSwuLiVsJ5kqhyHg2F3qQtduHzEktLaqFDZpvSPp7QizujoBwM6uvN9MQF1xndKhUguW6KMssojDj6bvjhkibhfvq6Odba/YZcECSwS64zmhgUT2EZim8XhVsLEmTD9fM9u9mvAuuMxoUttOyXoIzhqTLhyspD/wd8Mxo19XAZ8ws5mvXQlxwnfRTLSjeCqXnD9PpESJtcbifBvKEppMAr4z2vSHJYBdcJ/1UEkbfePPHMUSQTVWEyaFmVtsN4juSbkw62E0CJ/0ksXCUccEdV7rr+NBrypIeOT81HUAb8bhu4TojQIs/rFyUcZaur55OLxBpq/L2VuC7km4hzG4/4LVJB7vgOunDLNS8LReidbKYxbJsHiamXWjHGqVKcM3sKkkHAgcRBPcmM0tcoNkF10kfc9uh0mKRLD81X0fBGV9SYuFKeraZfUfSX9cdeqQkzOyiJNdxwXXSRaXcWmwhOscFd0mQjm8whwPfAf6qwTEDXHCdEaI4B6W55DVuPSR3iZCOKAUze2/08P1m9rvaY5ISJ0MM31Z3nOLcfLGZpHithKVBNQ43PVEKX2uw76tJB7uF6wwXiymn2IxMLiyYOWOPEEqBhSvpMcCfAzvX+XF3IrRNT4QLrpN+pCCyCHK58Dgdfj1nEKTj//og4HhgFxb6cbcCf5v0Ii64zmAxIzhgk3wlFEyvSHiuM5akJErBzC4BLpH0VDP7UafXccF1Bke5GEK+diCYXBYSF0oNQhknprw+wpKn+zhcSccAZwNZ4HNm9pGY8w4FrgVeYmZxftmfSTqV4F7Y4Uows9clmYu/m53BUCnXiS2AhULi2XxjYS2X2uzM64wdVQs3bms1XMoCnwSOBQ4GTpJ0cMx5HwWuaHHJ/wD2AI4GvgfsTXArJMIF1xkMzRbGCjONa9mWi8kL1zjjS3dRCocBm8zsFjMrABcCJzQ4702ECIS7W1zvUWb2bmCbmZ0PPA94XNKX4oLrDIZKk+Lg1kRU47o7OEuEKA43boNVkq6v2U6uu8BewO01zzdH++bvIO0FvIDQHLIV1TfkA5IeC+wMrEn6arry4Uq6lWBOlwnN1dZ2cz1njMlkodxBRwb3KCxtWtfD3dJCdxoNrn9X/TtwppmVE3SXWCfpYcC7gEuBFcB7Wg2q0otFs2eZ2ZYeXMcZZ/JT8dZqfqr9WFxnidB1ptlmYJ+a53sDd9Sdsxa4MBLbVcBxkkpm9vX6i5nZ56KH15Cwj1kt7lJwBkMmA5NRiFctucnmkQjN3A3O0qA7H+51wIGS9pc0AbyUYJnuwMz2N7M1ZraGkDX2943ENkxFH5a0S83zh0n6YNKX0q3gGvAtSesb+E6qEzq56l+55557urydM9Jks7BsJ5jeCaZWhp8TU81XmzPDzzJyhoha+nCbYmYl4DRC9MFG4CtmtkHSKZJO6WBGx5rZAzXXvx84Lungbl0KTzOzOyQ9HLhS0k1mdk3tCWa2DlgHsHbtWvfIOYutk0w2bI0iEryLg9Nl0ouZXQZcVrev4QKZmb2mxeWykiarNXAlTdNG2bquBNfM7oh+3i3pYkIIxjXNRzlLErMgqKVi8CrkJhZar5PLYG5mvjSjBBPL3MJd6oi0vQf+E7hK0hcI3/BfB5yfdHDHgitpOZAxs63R4+cC7+/0es4YYJUgqspEFmslLIZVSos7N5QKwX87ESXrKANTy9tM/XXGH0EmPe8DM/snST8HnhPt+oCZtUqW2EE3Fu7uwMXRyl4O+LKZXd7F9ZxRo9oKp1RgUaSNMo2TGWopzUWWbo0PV6JlDzNnaZEuCxfgZ4RW6RY9TkzHgmtmtwCPb3miM56YwezW+NTbVmJbpVyEjHducGJQunqaSXox8DHgaoJl8H8lvbVJ7YUFePEapzOKbXRnaIa7DZxWpMvCfSdwqJndDSBpNfBtEhYhd8F1OiNJ37EkZP0t6DRBXSc+9JpMVWwj7qWN8Fp/tzudoQwho7sLJqa9/KLTmnR9C7pc0hXABdHzl1AXctYMF1ynM3ITrQvLZCegXJh/nslGpRg1/9NxmpEyC9fM3irphcDTCD7cdWZ2cdLxLrhOZ2RzkJ+G4kzNTkUhYRnITwaBtamwgCa5Net0RsreN2b2NRo3k2yJC67TOdkslHMh9jaTjdJ066wRCZQeC8UZNZSKRTNJW2lcu06AmdlOSa7jgut0RrkUujVUqZRg9iGYXO4LYU7vEKlIfDCzlb24jv9lOJ1RmGm8vzgL2RWDnYsz3qTDwt212XEzuy/JdVxwnfYxi09s8JY4Ti9RalJ717Mj53wRRsLauC64To9JxR+HM06kwMI1s/17cR0XXKd9pBAWViosPublFJ2ekr7olqjFzoEsbJOeqEqiC27aqVRCkZdqJEBuMh255fmp4FqojcXN5kM4mOP0CpGqOFxJbwBOJ7TquQF4CvAj4NlJxqfgL9eJpVIOBWJKhaiWbCE8T4OfVAo1bKdXhsiE6ZXhuSczOL2muxY7veZ04FDg92b2LOCJQOJWNm7hppm4SIDCDEylJBJAGcj657bTJ1KWaQbMmtmsJKLODzdJOijpYBfcNBNnyVbK4eu8W5POUiBdPtzNURPJrxPait3P4i7Asbjgjiouts6SIF0Wrpm9IHr4PknfBXYGEjdecMFNMx4J4Cx1RGqNCzP7XrtjXHDTRrXRIoRV/0plYe3ZTC5ECPSDatSBWUjPTUH8o7PUSUcthV7hgpsminMhNbZKtefXxEqwcigC06+QsPraCEWC4E9Mp9bCcJYI6fLhdoULbr+pVKLyhJnmYmmVhWJbpVQIwpfNNxgTFS/qVhDNYG774v3lYqgG5i4MZ1ikL0qhK1xw+4VZCN9aUKQ7ytDKTyz+1C43aVlTLi6swGUWrN9i1C1XCm6GToWxUqZx5TmiduYuuM4QGaNvWONjq6cBMyjMwvYHYebBBh0RIqGc6TJ5oTgXtqpINhR3xxkHhDLZ2C3RFaRjJN0saZOksxocf7mkn0fbDyX1rRv50rRwK+X5rrPZ6Ctzp5+iZvMLXeUisZZiPXPbQ3ZWlWbuhloLs2rdNqIwC9MNXA/NMGvefdetW2eYiK58uJKywCeBo4DNwHWSLjWzX9Wc9jvgcDO7X9KxwDrgyZ1POp6lJbjlUrAEa0sLVkrha/PUiuSiW+s7Lc42Dt1qeY3KfPKCGczFZJVlJ5Kv0saVTIw938JCWZy1nck19h07zsDo2od7GLDJzG4BkHQhcAKwQ3DN7Ic1519LqJPQF7pyKbQy1VNFcS6ISyNRskr0Fb0FlUroajATuQy2P9iZ2FYpl4OlW/8hUEvDD4GYD4Z2w2eKs/FiO7ncayM46UCZ+A1WSbq+Zju5bvRewO01zzdH++J4PfDN3r6AeTq2cBOa6unArHEEQC2lQujJ1ewacw/Vff1O6D6Io7Ct9Tn1QryjNGKDD4hcm5W6Sk18vpmsi60zfNQyDneLma1tdoUG+xr+4Up6FkFwn558gu3RjYW7w1Q3swJQNdXTR5Kv2q3EpVxq7uvsF8oEK7T2/nHzSEMVMcfpNd1VC9sM7FPzfG8a1D6QdAjwOeAEM7u3J/NuQDeCm8hUl3Ry1dy/557EVcx6TA8stXb9o72iVAhujLltIbqhVIRyjBujXfdGnH9WGbdunXRQjcON21pzHXCgpP0lTQAvBS5deAvtC1wEvNLMft3z11BDN4tmiUx1M1tHWPVj7dq1QzARCREAmWx3FuBA0wujr1GVEgt/pQaFBgkKtcdbUXWvlJpEVEwuSz5Vx+k3XUQpmFlJ0mnAFUAWONfMNkg6JTp+DvAeYDfgUwqGRqmFm6JjuhHcRKZ62+zI56+EVNZsrjfW1uSyYCHG0eo/NZPtXrSTUG0zXipAoUkyRBytyjbObV9Ym6EeZccqldIZdbqvpWBmlwGX1e07p+bxG4A3dHWThHTzl9XSVG+bSiV0NCjMhKiBwvbwdboXX+eVaV60u1X4kxTEMDdB3xolVj9goHN/cbPfVaXcXGwh1GzoJvLCcXpNujo+dEXHFm6cqd7VbAozi4XGKiGgvxdfczPZEFtaLzrKQC5BvKkUirlMTEftbx7qfk5VcpMLoySafaor0ySMrMlnaFLrvFz03mROOpAWprWPOF29kkamehcXi7e+epmyOrksWHBVK67a+LDdT8umX7tFQ/9oM6GshnlVRbeZpZqbhGKDRIlWGXPuKnBGEI2gJRvH+Hx0JEUKAtvIgqtUIiG2IMTNYlGrBWMWxfdGrofS3PwHhTLBKs5kYXZb+NreiNJcsLQz2ebFbES4x47EhWpRnBZWaSbbXPSrtBvP6zj9Qng93L4gNf66D4NJLy0XF5YoLBXCfJplW+Unw5uhOBdELJuLrOUMZJctLp9YnIsX29r7tqpBq0y4V7bNRpISTC2PRL+J6I7RVzhn1NFYfTNL1ytpJDTKNM8A6wVx9WArpdbujGqd20YCWe/Yb5bZVU9c0ZjWmTfNUSZYx7HHR3MxwhljuovDTRXpMmUyGZha2Z+wsGY0W0xqVg+2fuGsUp4vhNOpKFat+Uw2WNe1HwTK9Ka+QSbT5NuEVwdzUsSYGQDpElyYrxWQGpr8ZxdiKnwVZhqHoOXyUGwi7tn8fPUwKTyf3mn+638jES8V5l0amWzwKydxCUxOL3YtZHIeneCkD/fhjhtNRDVO/Kt1cBsRtz83ERbD6i3LTHY+4aNcDPOZnJ4XYMW84ep7oFXKIQU4iYVdjUuulOfFeoze2M444Rbu+GBN0mUzuXhrsZNkDCm4BKoJCIq+2i8qGxn5lJsJZ7MKaHEWdqP5+AKZk2rUv8apQ8D/2qoWXiOa+Y+ahm01S1qIRK4qdOVSk9jcKGKhEc0y0SpDKrTjOH3BLdwxoolwNbVim4xrZ/U0iXCWS1HMbSV82uenmofKjJFF4CxxBGRccMeHZn7LZl+3s/n4LhHtLPo1vX+UADFXU6i86qdtNs4XvpyxYnwE100hZRpnVknNM64y2cYJGdUMtaRkMo2vU71/XCRE3MKcYq7nOCNJ5MON20YMt3AhJFZksiG11ix5fYWJaajkg6/VgPxEWARr+/7TUMouTCuu3r+TxpCOM1aMj4Xrglsll09WMayWaqxstxZls/oO1bjcpHholzNueGqvMzDi3BpxkRDCrVxnfGhWC3cEM9BccNNOoypgucn4hblygvoPjjNKNG+TPlK4SyHtVMtA5ibnU36t0rz4ebP6D44zYng9XGfw1H6FKsSEo1Vxl4IzNoxXeUYX3FGkVSaZh4U544RbuM5QyWahFBeHK098cMYH4RauM2Tyk40761YrgI2RReA44/R+dsEdRRQVai/OhqiEag3hVk0kHWfkGM3wrzhccEeVTKY3reMdJ+2MkeCOj3PEcZzxo+rD7SIOV9Ixkm6WtEnSWQ2OS9LHo+M/l/SkXr+MKi64juOkmy4yzSRlgU8CxwIHAydJOrjutGOBA6PtZODTvX0B87jgOo6TYtSthXsYsMnMbjGzAnAhcELdOScAX7TAtcAukvbs7esIDNSHu379+i2Sfl+zaxWwZZBz6AGjNudRmy/4nAfFIOa8XzeD1//shiu04mGrmpwyJen6mufrzGxdzfO9gNtrnm8Gnlx3jUbn7AXc2cGUmzJQwTWz1bXPJV1vZmsHOYduGbU5j9p8wec8KEZhzmZ2TJeXaOR3qE/FTHJOT3CXguM448xmYJ+a53sDd3RwTk9wwXUcZ5y5DjhQ0v6SJoCXApfWnXMp8KooWuEpwJ/MrOfuBBh+HO661qekjlGb86jNF3zOg2IU59wWZlaSdBpwBZAFzjWzDZJOiY6fA1wGHAdsArYDr+3XfGReWcpxHGcguEvBcRxnQLjgOo7jDIjUCK6kt0gySc1i7oaOpI9JuilKAbxY0i7DnlMcrVIa04akfSR9V9JGSRsknT7sOSVBUlbSzyT997DnkgRJu0j6avQ+3ijpqcOe01IhFYIraR/gKOC2Yc8lAVcCjzWzQ4BfA28f8nwakjClMW2UgDeb2Z8BTwFOHYE5A5wObBz2JNrgbOByM3sM8HhGa+4jTSoEF/g34G30Kdi4l5jZt8ysFD29lhCzl0aSpDSmCjO708x+Gj3eShCCvYY7q+ZI2ht4HvC5Yc8lCZJ2Ap4JfB7AzApm9sBQJ7WEGLrgSno+8Aczu3HYc+mA1wHfHPYkYohLVxwJJK0Bngj8eMhTacW/E4yFFn2PUsMBwD3AFyI3yOckLR/2pJYKA4nDlfRtYI8Gh94JvAN47iDmkZRm8zWzS6Jz3kn4CvylQc6tDQaWrthrJK0AvgacYWYPDns+cUg6HrjbzNZLOmLI00lKDngS8CYz+7Gks4GzgHcPd1pLg4EIrpk9p9F+SY8D9gdujFoh7w38VNJhZvbHQcytEXHzrSLp1cDxwJGW3kDmgaUr9hJJeYLYfsnMLhr2fFrwNOD5ko4DpoCdJP2nmb1iyPNqxmZgs5lVvzl8lSC4zgBIVeKDpFuBtWaW2qpLko4B/hU43MzuGfZ84pCUIyzqHQn8gZDi+DIz2zDUiTVB4VP3fOA+MztjyNNpi8jCfYuZHT/kqbRE0veBN5jZzZLeByw3s7cOeVpLgmGn9o4inwAmgSsjq/xaMztluFNaTFxK45Cn1YqnAa8EfiHphmjfO8zssuFNaSx5E/ClqLbALfQxldVZSKosXMdxnHFm6FEKjuM4SwUXXMdxnAHhgus4jjMgXHAdx3EGhAuu4zjOgHDBdRzHGRAuuI7jOAPCBddxHGdAuOA6juMMCBdcx3GcAeGC6ziOMyBccB3HcQaEC64DhNKYkprWAe7z/U3So4Z1f8cZBC64zkjTSqglPUvSLyQ9IOneqNPyyLQacsYLF1xnqESF0vvJr4CjzWwX4BHAb4BP9/mejtMQF9wxQ9KZkv4gaaukmyUdGe0/T9IHa847QtLmuuGHSvqVpPslfUHSVO25kt4m6W5Jd0o6UdJxkn4t6T5J76i59mGSfhRZlXdK+kRU7Lp63CSdKuk3BAGsfw1Pl3S7pGdFz18naWM0rysk7RftvyYacqOkhyS9pP5aZnaXmdW2FioD7rpwhoIL7hgh6SDgNOBQM1sJHA3c2sYlXh6NeSTwaOBdNcf2IPTt2gt4D/BZ4BXAXwDPAN4j6YDo3DLwj8Aq4KmENj9/X3evE4EnAwfXvYajgQuAF5rZdyWdSGg0+tfAauD70XHM7JnRsMeb2Qoz+69GL0rSvpIeAGaAtwD/lOSX4Ti9xgV3vCgT2v8cLClvZrea2W/bGP8JM7vdzO4DPgScVHOsCHzIzIrAhQQxPdvMtkatezYAhwCY2Xozu9bMSmZ2K/AZ4PC6e/0fM7vPzGZq9r0IWAccZ2Y/ifa9MTp3o5mVgA8DT6hauUkws9sil8IqwofITUnHOk4vccEdI8xsE3AG8D7gbkkXSnpEG5e4vebx7wk+zyr3mlk5elwVybtqjs8AKwAkPVrSf0v6o6QHCSK5qsm9qpwBfMXMflGzbz/g7Mg98QBwH6EFfNsLX9EHyfnAJQPwHTvOIlxwxwwz+7KZPZ0gVAZ8NDq0DVhWc+oeDYbXtlXfl87bqn+aYEUeaGY7EVwCqp9qg3EvAk6UdEbNvtuBN5rZLjXbtJn9sMO55YCHAzt1ON5xOsYFd4yQdJCkZ0uaBGYJVmfVKr0BOE7SrpL2IFiT9ZwqaW9JuxJEsqFPNAErgQeBhyQ9Bvi7hOPuIPh7/0FS1ed7DvB2SX8OIGlnSS+qGXMXcAAxSPrr6PeSkbSa0OL+Z5G16zgDxQV3vJgEPgJsAf5IsOSq0QP/AdxIWET7Fo3F9MvRsVui7YMNzknCW4CXAVsJi2uJhdvMbiOI7pmS3mBmFxOs9Asj98QvgWNrhrwPOD9yOby4wSX3Ai6P5vILoAK8oO1X5Dg9wNukO47jDAi3cB3HcQaEC67jOGONpHOjhJ1fxhyXpI9L2iTp55Ke1K+5uOA6jjPunAcc0+T4scCB0XYyfUz9dsF1HGesMbNrCPHbcZwAfNEC1wK7SNqzH3MZaPD3qlWrbM2aNYO8peM4Q2T9+vVbzGx1p+P3Uc5mG4ZsB7ZQ2UAIgayyzszWtXmbvViYiLM52ndnm9dpyUAFd82aNVx//fWDvKXjOENE0u+7GT+H8SKWxx7/NFtnzWxtN/dgcVIONE7M6RpPb3QcJ7UIyKmRHkb0RhY3szDLcm86z7JsSksfrqR9JH03Ko+3QdLp0f5dJV0p6TfRz4f1Y4KO4yxtMorfesSlwKuiaIWnAH8ys567EyCZhVsC3mxmP5W0Elgv6UrgNcBVZvYRSWcBZwFn9mOSjuMMmUoZCrPhZyYD+UnI5vt+W6HmFm6Sa0gXAEcAq6Ia0O8F8gBmdg5wGXAcsAnYDry2qxs2oaXgRkp/Z/R4q6SNBIfyCYQXAaEC09W44DrO+FEpw+xDC5/PbYf8VBDePtNtKJWZndTiuAGndnmbRLTlw5W0Bngi8GNg96rZbWZ3Snp4zJiTCbFt7Lvvvl1N1nGWKlYpw/YHwQyW7YSyA1x+Kcw23l+cg9wEdGmBNiP4cPt2+YGT+H9N0grga8AZZvagEv6SoxCNdQBr1671wg2O0ya27U9w1+9q92Cr9kE71ZcY7hOVcswBCx8AfRRcBEm1ZhRIZK1LyhPE9ktmdlG0+65qcHD08+7+TNFxli5WLsFdt4BVajaDLbdjxRjLs9c0E7w+i2HVwo3bRo0kUQoCPg9sNLN/rTl0KfDq6PGrgUt6Pz3HWeJs+xMNw0TNYOv9g5lDfqrx/my+74ILQaTitlEjiUvhacArgV9IuiHa9w5C3dWvSHo9cBuhWr/jOL2gXAy+07ntQVwbYZXBzCWXB5uCWos6m4eJ6b7fumUc7oiRJErhBzTOxIBQKNpxnF4yu20+KiCTgeU7w8QklMswszUsVinaPyjyk2GBzCrh3gMSQdHTeNuh45lmjpMm6kKwlMtjuTySsKwF4X3ogfA1f7JByqsZlOagVAzPcxO9iySQQNnur9MmuVh7b/RwwXWcNFEszD+ORFILfgpbuSus2G3x6r0ZzG1bGFVQnA3iO7V8YFZpL3EL13Gc3lGpBIu0UoZMlkXFARqIpCD4eDN1SQflUuMQLiuHe8QtfqUYjWg0QhwuuI4zLCplmHlw/nm5OK+3UvDf1n+dri6UzW0PvtRcPli2lTIUtsffqzgHucmRtHIz7lJwHKdr5iKBrFSjDQwQZHNRZIIWCmQ1ycAIPwszQaTLxWT3KxeDP3eEWLKZZo7j9BAzqJQisa11I0SPpcXWaFVsq05Nq0CpkNxqHdEO3e7DdRynOyrlGrGtKkoCQYwWzjpikPUXekQvqoWlidH7H3CcYVGJUmsz2e58oYWZeXdCM7GNq1NQuy/pPHIT0aLc6DE+cuuC6zitaRRulZsMyQDtCm+lUiO2TW8KqMZvW+fTzU0k891mclHt2tH8U19ymWaOs+SZ27443Ko0F6II2l2ESrrABeyweqvG70RUf7aa6VUuNhbv/FSwZru1xFOAetvZYei44DpOM6qLW42o1oPt/ySCyGIL3QLZfMg2K85GKbfZIMoj6jqIY5xejQuu4zSj6cp+B6v+sQKt+OspqouVafDnms1BdkX78xgRQqbZ+Ji4LriO04xmf+yNBDDJ9aZ3WpjwADCxDCanQ7bY9j+xw4dbvb80cjG0vWIUyzDG4YLrOM0oFWIOqPNU2VweVuwaXdsgOxFllREs1hUPg9ntUI7unc3D5LKR98d2yji9ahdcx4mjUl5YA7aWqeXzItkJUnwDRmVgesW8O2OJCi24S8Fxlg7FOOuWqKZB58s55d/+mtK110A+T/6ZR5HZ4xGLTxojoekGdyk4zpKgyaJYF2mys+v+neJ/fzUIeiZL4T/WMXnq25g45oSOrznOjJOFO04fHo7TW5olCxQLYXFr+5+at8Gpo7zxF0Fs52aj0oxFKMwx98mPUnngvh5NfHxQi23UcMF1nDiy+fiYVqtJhCgXQ5eGBKJb/N6VUJhbfCCTpfyT/+1wouNNVvHbqOGC6zhxSCGxYGI6hIBl8yGioBFWaVz8u55maVNj9NW5d6jpv0RXkI6RdLOkTZLOanB8Z0nfkHSjpA2SXtvzlxHhgus4zajGv04tD6FZzUgguPkjjg59yRaNrZB78tM7nOT4Uk3tjdtaj1cW+CRwLHAwcJKkg+tOOxX4lZk9HjgC+BdJfQl6dsF1nHZoFgqWIKU2++iDmfibVwbRzeXDz4lJJv9/70E77dK7eY4RXfpwDwM2mdktZlYALgTqVycNWKnQJG4FcB8Qk8/dHR6l4DjtkJsINRQW9R7LJK5hMPmqN5I/8tgoLGyC3NOfTWbXVb2f6xggINtcWldJur7m+TozW1fzfC/g9prnm4En113jE8ClwB3ASuAlZtVeRr3FBddx2kGCqRWhpm21qE02H/y8Evfdvpmbrvoe0zvvxGOPPYr8VONstMxe+zLxwlcMcOKjSwvX9hYzW9tseIN99aubRwM3AM8GHglcKen7ZvZg/cBuaSm4ks4FjgfuNrPHRvveB/wtcE902jvM7LJeT85xUkkmE3y6dVz67g9w5T9/nEw2hzJC2Sz/cPlF7P/kQ4cwyfGhyyaSm4F9ap7vTbBka3kt8BEzM2CTpN8BjwF+0s2NG5HEh3secEyD/f9mZk+INhdbZ0lz83ev4dv/+kmKs3PMbdvG7NaHmHngT3zieS+iXGynBq5TS0jt7XzRDLgOOFDS/tFC2EsJ7oNabgOOBJC0O3AQcEvPXkQNLQXXzK4hOJEdx4nhB589j8L2xcXAy8Uiv/n+D4cwo/Eh02RrhZmVgNOAK4CNwFfMbIOkUySdEp32AeAvJf0CuAo408y29PhlAN35cE+T9CrgeuDNZnZ/o5MknQycDLDvvvt2cTvHSS9zDcQ2IIozMwOdy7iRNN42jugb+GV1+86peXwH8NyubpKQTsPCPk1wLj8BuBP4l7gTzWydma01s7WrV6/u8HaOk24OfenfMLF8cZxuuVTkwGc+bQgzGg+EZ5phZneZWTkKnfgsIdbNcZYsT/qbE3nk057C5IqwmJbJ5chPT/OyT/87UytX9vZmZqFQeakQfrZbSMdsfhsBxqmWQkcuBUl7mtmd0dMXAL/s3ZQcZ/TI5nK86bKv8cvLvsWNl/4Pyx/2MP7yda9kj8c8urc3atRBWFHUhBLYT8W5hXHEnXYfHiDjVC0sSVjYBYR0t1WSNgPvBY6Q9ATC/9qtwBv7N0XHGQ0y2SyH/NWxHPJXx/bvJsXZxSnEVoHCbOvU42JhcUH10lwwFTvtXtFnRtWSjaOl4JrZSQ12f74Pc3EcpxVxLX/KxWD9NrMGSzHdK4pzwdJNoyUpkR2jPumeaeY4S4UR8dnWozESXC9e4zijRFyn4Ey2tYUa6+NNr6BJIbEvbksDUehrIlIyZcdxEhHna52Ybj027pz8VDrdCRGSYreUkHgi7lJwnLRTLoViOYsKWCmUeEwqmNlcKKheXXhTJozN5fsy7V6RSblLwcw+k/Rct3AdJ82UiiEMrGG1QAv727H0srlQ7WzZzjC9MvViK8LLi9sGPh/pdEk7KfB5ST+VlDhLzQXXcdJMfRhXPeVSjBiPCYJsRrHbEHhdVLbxucBqokpjSQe7S8Fx0kwSMTVL87pXl6TKVwvzv+njgC+Y2Y1qY4IuuI4z6iTJMBtRJMikq2jCeknfAvYH3i5pJZD4K4YLruP0g0o56gpRJixuTYQU2mpKbVKRzE3EJztA6tNye0HKXt7rCUW7bjGz7ZJ2I7gVEuGC6zi9plKG2YdqdlhIoS3Nze/KZGFiWetg0vxUvJ92YlnqF716QZqiFMysImkN8ApJBvzAzC5OOt4F13GacPem3/Kds8/hzl9t5IC/fDJHnHoyO++xe/NBxbnmxyGI8txDMLWyuQlX7aFWLoX0XWWC1ZuWqP8+Ezo+pEdwJX0KeBRwQbTrjZKeY2anJhnvgus4Mfz2hz/m7OeeQGmuQKVU4rf/+2O+98nP8vbrrmb1Iw+IH1hfXCYOs3ButsWfoaJ42yVgzS5C6bJwgcOBx0b9z5B0PvCLpIOXxsek43TAf/7tmyhs206lFLrzlubmmPnTg1x05nuaD2zHIhvnkK4ekaY4XOBmoLZ1zT7Az5MOdgvXWZKU5ub4+X9dxM3fvIKVe+7BYX/7Wh7+ZwftOD67dSt3/XrTonFWqbDxyu/GX7hqtSYlk21n2ksOSamIUpD0DcKK587ARknVjr6HAYmb1rngOkuOwvbtfOaZR3Pfb2+hsG07yma5/vNf5IXnforHvfBEAHKTk2QymYbxPlMrV8RfvNxGh95MzgU3ASlx4f5zLy7igussCbbfex/ffvf7+dXFl1Kam6M4O0epFCxRK5cpzszwlVedzPI99+CAv3wKuYkJnvTiF/DT//d1SnPzi2D5ZdMccVqH9faVmU9SyFbDxJxmCFJRD9fMvld9HLVSPzR6+hMzuzvpddyH64w9pbk5PvuM5/CzL36Z7ffex8zWbRSKJSpmWE2N2FKhwMeP/Cuu+vdPAfCyT/0rj3zak8lPTzO1807kpiZ54l8/n6Pe8g/xN4srnwihWteynWB6J5hId4WuNJGmamGSXgz8BHgR8GLgx5L+Jul4t3CdsWfjJf/NQ3fdQ7lQoFBXg9sAmZFRaMZdnJ3j629/H09+xUtYsWo3/vGq/+aPN/2ae275HXs99mB23Xef5jfLZILlWh8als27+6AT0hel8E7g0KpVK2k18G3gq0kGu4XrjD13/PQGCg89RDmm4YEBFTMqQBnI5nPc9J0d3yDZ4zGP5nHHHd1abKvkp0LsbG4iuA4mlwfr1i3ajkhZlEKmzoVwL23oqFu4ztiz24GPIr9sGYWHtsWeY8CDpWiJTGJyeYuGjK3IZJMVBXeaksJaCpdLuoL5xIeXAJclHewWrjP2PO7Ff01u+v/f3nnHSVVe//99pm6hKthABHsLNrBEoxg0gt3EGDVRYzSW2GONiSXFxMTkG/UXS7BijC1WTIy9oImooKKiogRRVpEmCLJl2vn9ce/A7O6UOzuzM3dmz9vXfe3ee5/nuWdw9jNnznOe8+TelVZVWZFIrc5ICAQCbLnP3pUxzihA7vit1xiuiEwQkdkiMkdELsrRZpyIvCkis0TkhRxtBLgW+CswGtgOmKSqF3p9NebhGnVPtH9/Tnz+Cf727aNYOPvDzjdFSAGR/s0gQiAQ4PR/P0A4ahkEviHYc79QRILAdcC+QAvwmohMUdV3M9oMAq4HJqjqJyKyTraxVFVF5GFV3Ql4sCf2mOAafYIhm2/K2W+/yqPnXMgrN08mFImgmqL/Outw1D2T+fzDOUT7NbPVPnsTikSqba6RRig1G2FnYI6qzgUQkXuAQ4B3M9ocDTyoqp8AFEjzmiYiY1X1tZ4YY4Jr9BlEhIOv/gN7nX8281+dTr911mGjr++CiDB8h9HVNs/IihTycIeIyPSM80mqOinjfBgwP+O8BdilyxibA2EReR7oD1yjqnfkeN7ewCkiMg9Y5RiIqqqnN1BBwRWRW4EDgUWquq17bS3gXmAkMA84QlWXeXmgYVSbgcM2YOBhB1fbDMMDIiD5BXeJqo7JN0SWa13zVULATsB4oBF4WUSmqeoHWfpOzGdMIbwER24HJnS5dhHwjKpuBjzjnhuGL1gy72Om/e1uZj3xNEm38IxRu0hAch4eaMEpMJNmOPBZljaPq+oqVV0CTMWZEOuGqn4MrI0TljgYWNu95omCHq6qTnUL7mZyCDDO/X0y8DzgeabOMHoDVeXeMy/gPzdPJhAKoZoi0tTEeVMfZ70tN6+2eUZPkIIhhUK8BmwmIqOAT4EjcWK2mTwC/EVEQkAEJ+Tw5+zmyKU4q8zSk2a3icg/VPU3XozpaQx3XVVdAKCqC3LN6rkGngScBDBixIhczQyjKFKpFO8//RwfTXuNgRusz05HHMa7TzzDf2/7G/H2NTvdxla18pvtv84vZ7/O2hvZ+68WKWXSTFUTInI68AQQBG5V1Vkicop7/0ZVfU9EHscps5gCblbVd3IMeRSwg6q2u7ZdCbwO9KrgesYNYE8CGDNmTI61PobhnXh7O1fvezAtb75Nx6pWwo0N3HP6uUggSLytrVv7REeMP+05gSvmzfLbDrBGIZzqNSUNoaqP0WVxgqre2OX8KuAqD8PNAxqA9Kd6FPifV1t6+koWisj6AO5Pz9VyDKNUnr32Bj6ZMZOOr1aBKvHWNhIdsaxim2bl4iV8NO3VnPcN/yKB3EcV6ABmicjtInIb8A7wlYhcKyLXFurcUw93CnAccKX785EejmMYRfPy7XflFddsBEIhVixc3EsWGb2GSKEshUrzkHukeb6Yzl7Swu7GmSAbIiItwGU4QnufiJwAfIITRDaMitCTsECiI8aoXfJlDxm+xUdhIFWdXEp/L1kKR+W4Nb6UBxtGT/n68T9gyqVXFOXlbvnNPRm4/nq9aJXRG3jIw60p6ueVGH2GcWeczKhdxhDt1+x5u/Dlny3oZauMXiMguY8aw5b2GjVHOBrlnGf/yQcvvMRHL7/Kl58vZNodd5OMJ4ityl6CsXXZlxW20igPgnj8UK0FTHCNmkRE2GLcN9hi3DcAOPyPVzB/5tv8v4nfYdWSpZ3aBsNhvnbgftUw0ygVwVeerIhsDpwPbESGfqrqN730N8E16oJgOMzIMTvyw8k3ctN3jyXRESOVTBJuaKBx4AAOuMQWQtYqPovh/gO4EbgJZ4OQojDBNWqSl++4mym/+DXLWj5lrRHDOfS3l7Pz0d/la/vvx4WvPMez11zP4jkfseX4vdjz1BPot/ba1TbZ6AlV3EsnBwlVvaGnnU1wjZpj6k23c9+Z55NodzZq/OLj+dz549ORgDD2yMMZtu3WHHPTX6pspVEufObhPioiP8HJxV29U6iqfuGlswmuUTN8PP11/nbiGbTMfLvbvVhrGw9f/EvGHul5x2qjFvBZDBdnoRc4cdw0CmzspbMJrlETfDG/hT/uOTFv7u3Sjz+poEVGZfDXSjNVHVVKfxNcoyb424mnF1zoEO3Xr0LWGBXFRzFcEQkDpwJ7upeeB/6qqnEv/U1wDd/TsWoV7z/9fMF2w0dv2/vGGJVF8Ly4pULcAIRxNp0EOMa9dqKXzia4hu/55PWZBEIhkrFYzjahaJR9zzuzglYZlUH8JrhjVTVzN4hnRWSm186+eiWGkY3mtdciEAzmvB/t18yW+4xj9IFdd4Iyap60h5vrqDxJEdlktXkiG1NEPq55uIZvSaVSaCpFKBKmoX+/7jFcEbbY+xvsfeapjD5oIgF/eUJGufBRDBcnO+E5EZmL83GwEXC8184muIbvaF2+nLtPO5fX73+YZDzhbLuaIaaBUJBgOMKhv7uc8WedWjU7jUogkOfbTaVR1WdEZDNgCxzBfV9VOwp0W40JruErVJWr9zmYT99+l2TMmfhVgOSab22BUJgjr/sjux9/THWMNCqH4AsPV0S+qarPisi3u9zaRERQ1QezduyCCa7hG2Jtbbz75LN8/v4HeSfIEu3tvPnQoya4fQLfeLh7Ac8CB2W5p6zZxTcvJrhG1UkmEjx4wSVMvfFWUsnEas82H5HGxgpYZvgCH3i4qnqZ++uvVPWjzHvuFuyesFkGo+o8cvEvefGvtxFva/Mmts1N7H7icQXbGXWA/7IUHshy7X6vnc3DNapKMh7n+etvItbaWrBtuLERVBn3kx+z9b6eyo8aNY74pAC5iGwJbAMM7BLHHYCzbbonTHCNqtL+1Vck47m92nBjI1vtO46tvjWeUCTCVvuMY8iokZUz0Kgu/llptgVwIDCIznHclcCPvQ5igmtUlLYvv+TjGW/SvPZaDB+9LU2DBtG81mBWfL6oW9vNx32Dnz73rypYafgKf8RwHwEeEZHdVPXlno5jgmtUjCf+cDWP/PxXpBIJwFmOe/wdf+XwP/2Ov/34dOKtaxY2BMNhDvrlxdUy1fANpWcpiMgE4BogCNysqlfmaDcWmAZ8T1VzxWXfEJHTcMILq0MJqvojL7b4wlc36p93n3ymk9gCJDo6uOnI41ln800Ytu3WSEbdUwkID154Kalk0buYGPVEOg8311Gou0gQuA6YCGwNHCUiW+do93vgiQJD/g1YD9gPeAEYjhNW8IQJrlERnrzqmk5iuxpV7jrlHD6b9R6a0tWXEx0xPnvnXd7595MVtNLwH66Hm+sozM7AHFWdq6ox4B7gkCztzsDJQOge2+rMpqp6CbBKVScDBwBf8/pqShJcEZknIm+LyJsiMr2UsYz65svPFuS8t+jDOVnTwTq+WsWHU//bm2YZtUB+D3eIiEzPOE7q0nsYMD/jvMW9ljG8DAMOw9kcshDpN+pyEdkWGAiM9PpSyhHD3VtVl5RhHKOO2f6wg1jw7uys99bZfFPmv/FW1nvR5qbeNMvwO1IwhrtEVcfkGyHLNe1yfjVwoaompXCYYpKIDAZ+AUwB+gGXFuqUxkIKRkXY97wzaRjQv9v1YDjMvueeieaI1a5YtLi3TTP8TgkxXByPdsOM8+HAZ13ajAHuEZF5wOHA9SJyaLbBVPVmVV2mqlNVdWNVXUdVvXjGQOmCq8CTIjIjiytvGKtpGjSIK+a9w9YT9iEQDoEI6265OT99/jGizU1E+zVn7bf4w7kVttTwFaWvNHsN2ExERolIBDgSxzNdjaqOUtWRqjoSZ9XYT1T14azmiPxWRAZlnA8Wkd94fTmlhhR2V9XPRGQd4CkReV9Vp3Yx8CTgJIARI0aU+DijlmkePJgz/929xsfiuR+RSnT3cEPRKCN32akSphm+pbQdH1Q1ISKn42QfBIFbVXWWiJzi3vfsnbpMVNXV+YqqukxE9scJMRSkJA9XVT9zfy7C2ad95yxtJqnqGFUdM3To0FIeZ9QpQzcexbYH7Ocs3XUREcKNDYw7zb449XlKrKWgqo+p6uaquomqXuFeuzGb2KrqD/Pk4AIERSSaPhGRRiCap33nl+K1YVdEpFlE+qd/B74FvNPT8Yz6JhGLMfXGW/jD7vvwp70m8srf7yWVSq2+f8Jdt7DveWfQb8jahBsb2faA/bjo1ecYuN66VbTaqDoCSCD3UXnuBJ4RkRNE5EfAU8Bkr51LCSmsCzzkzuqFgLtU9fESxjNqGFXlf/+ZxrxXZzB4xHBGHzSR+W/M5N4zL+CT199E3D+OdC7uxzPe4J3HnuSEv98CQCgS4eBf/YKDf+Xpm5nRZ/BNPVwAVPUPIvIWsI976deqWmixxGp6LLiqOhfYrmBDo25Z+OEc7v/pxbz/7FRS8bibgCOEoxGCkQixVa3E29sBUFKd+sZWtTLz4X/SMvNthm/nOW/c6Iv4oJZCF97A2Spd3d89Y7UUjB6x/LMFXLnz3rR/uQLVzmmN+XZryCSVTPHBCy+Z4Bq5KZyHW1FE5AjgKuB5HBfj/4nI+QXivqsxwTV6xLPX3EC8ta2b2BZDMBym35C1y2iVUZdUJ1abi58DY91EAURkKPA0HouQm+AaPeKjaa+R8OjJ5iIQCrL9oQeWySKjLvGZhwsE0mLrspQikg989dFh1A4bbLsVgVCBz+sssbdAKES0XzODhm3A2U9PIdJkS3eNApS20qzcPC4iT4jID0Xkh8C/gMe8djYP1+gR4885jZcn30UsSwWwSFMTwXCII669iueuuZ5P3niLxoED2OsnJzL6wImEGqJsuP1oPKxbN/o6PvNwVfV8EfkOsDtODHeSqj7ktb8JrtEj1tl0E85+6hH+fvJZLHh3NhIMsukeuzJs9Lasu/mmjD3qcJoGDWK3Y49CVU1cjZ7jrxguqvoA2TeTLIgJrtFjVn2xDAkECTU0sO4Wm7LfRT/Nurmjia3RcwQC1fdwRWQl3auMgePlqqoO8DKOvz46jJrh9Qce4aYjjqNl5tvEVq1i/uszueHQo3j7Mc854IZRGAECkvuoEKraX1UHZDn6exVbMME1esgD5/2cWMYeZADx1jYePP+SKllk1C2BYO6jQojIWvkOr+NYSMEomlQqxdJ5n2S9t/CDORW2xqhrpLKebB5m4IQUchU039jLICa4RtEEAgH6DR3CV4u7b/QxcP31qmCRUdf4IIarqqPKMY6FFIweccAlF3TLoY00NXHgZRdVySKjPhG/VQtLFx3fWUT2TB9e+5qH63eSCYi3Qyrl1P8MN0Cw+v/bxp1+MolYjH//5io6WluJ9uvHQb+8mN1POLbaphn1hOCrPFwRORE4C2ernjeBXYGXge7pOVmo/l+ukZtkAjpWrTlPJZ3zaBMEw9WzCyfVa99zz2T82afRvnIlDQMGECihMr9h5MRfaYVnAWOBaaq6t4hsCfzSa2cTXD8Ta8txvR0aqyu4aQLBIE2DBlXbDKNe8dlKM6BdVdtFBBGJqur7IrKF184muH5GU7mvq/rtk98wegd/rTRrcTeRfBhnH8dldN8FOCcmuL5GyLm4xcTW6BP4y8NV1cPcXy8XkeeAgYDnnW5McP1MOOpMmHW7Hqm8LYZRDQTfOheq+kKxfUxw/YQqpBIQd+vMBkMQikAio+5sKOocvUDb7A9YetfdJBYvYcC+4xl0wP4EIibuRjXxRy2FcmGC6yfi7Z3FNZWAQAga+jvnvVgD9IuHH2H++Rei8Tgkk6x45hmW3HIbm95/L4GGhl55pmF4wl8x3JKon1fiR1TdPNoO52e+7WhSyc5iu/p6AjTp5OB2FVtNOf1K2OYGINXWTsuFP0Pb2yGZdK61ttL2wQcsvc/TziGG0TuksxRyHTWGCW5voOoIV9tKJ2823u78bFvh/Ewlu/dJdi/knfOeKnS0OuO3f+WMG2vvsfCuevMNCHZ/K2hbG8sffbRHYxpG2fDXjg8lYYJbTlYL4Qro+IqsGQbJhCOSyXjn63nfPF3uxdu79090ZPeQPRBsbHJWsmW7169fj8Y0jPIgSCCY8/A0gsgEEZktInNEpNvacxH5voi85R7/FZHtyv4yXPpmDDcRd2f/1YmRhhucr+w9QdURukQsd95sNmJt0BBaI7T54lShjImr9POykehwMhuKQDs6CH/RQiAYoKv1gaZGhhz7g6LGM4yyIpQUwxWRIHAdsC/QArwmIlNU9d2MZh8Be6nqMhGZCEwCdum50bnpO4KbFqquaVbJuHM09PcmuqoZwiqOcKbyhAPyjZOu9pb2jLMRjnr/MCgypKArltN+4YnoiuUMG9FEy+w2UqkUEm1AkymG/OhHDNh776LGNIzyUnIe7s7AHFWdCyAi9wCHAKsFV1X/m9F+Gk6dhF6hJMEVkQnANUAQuFlVryyLVb1BvMPxAHOR6IBIY/4x0rUMSpykWmNTzBF7hewLHMj+LJHs14tMn4nd9Vd06WJIJog2hdl4+3VpXdFBaq11GXzNrUSs1KLhB/J7uENEZHrG+SRVnZRxPgyYn3HeQn7v9QTg30Xb6JEeC65HV90fqOYXW3DCDPkEV9WJvZaTQjaln5uJiBMCyVZnIVxc+lZy2gudJuREhOaBDcAqwgMsdmv4ACmYh7tEVcfkGyHLtazejYjsjSO4e3g3sDhKmTRb7aqragxIu+r+w0tstdCMZ9dJqkoRCHaPESdy2FKsjaE8n7c1mHJj1CmlZSm0ABtmnA8nS+0DERkN3AwcoqpLy2J3FkoR3Gyu+rCujUTkJBGZLiLTFy9eXMLjSqAc6SPlCiMUhTgx51ibc7SthFhH7phxEVkK2t5GcPd9uy8TDgQJbLsD0lAgvGIYlaD0PNzXgM1EZJSIRIAjgSmdHyEjgAeBY1T1g7K/hgxKieF6ctXdeMokgDFjxlRDtZwYUDBcmpcaDEFFnFy3wn0wlD3kkMhSW6EI9MtldPzlClIzX8PJ0shYUBEMwlpDiZ7xi5KeYRhlpYQsBVVNiMjpwBM4c023quosETnFvX8jcCmwNnC9OH8LiQJhih5TiuB6ctWLJpVyhCaVcr5OhyPlWdoXaYS2JHRLfnIplAkQCDoimG+BQjmINjvC18OcWjSV899LVWm/9HR0Qcua15FMdtoZTwAitpTX8Aul11JQ1ceAx7pcuzHj9xOBE0t6iEdKUbKCrnrRpJLQvtIRm1TCEd62ldlXZhWLCDQ05b7vpSBMpMkR7kCQ7A5+iQQja74m9TSEkadf6r2Z6JKF3T40Vr+SRAJdvpT4Ew/27NmG0RvYSjPHVQfSrvp7wH2qOqska/LtcFAOAsHOiwhWXw95+xQVcfo39IOG5vLY5GR2OxkGmZ5lIM+Xj3y25vk2oIsWFDYnFiP52n8KtzOMSiDifLPMddQYJVmczVUvYbDcnmxPFhbkItzgxHMTMeeZoYjzP67YT0sJkLNAuASyZEa4X426vRa3f7zdef2RRseWVJ6AcTiafaFEuCHv6wiM2jznEt5Olg5eq2Abw6gUUoOebC5qpJZCGf/B05+Y0SbHSw2F14hUMuEIWftXzkKJfF/rRZwxul0POHHYcNQdVxyBb+jnts/zWpLxNR86+cIoqs7KuGB4TZ5itKngst7ARpsQ2HZHNMMG7fIaVQKEDzgi7ziGUTEE5/2d66gx/CO4Irl3og1VYMPEeIeziiwtevF2R3jziW7QrVUbiji2RxodYU1vZ944AJoGOGIYCDjPyLWiLE06k0IKhA0CAWfcxgHOMz3u4hu94HcEd9kLTabQlIIqqoqmnJ+phBLcZgdPYxlG7+Nm7eQ6agx/Wbx6QiqDdHGZ3kQ1+1Y2miqcLZCuSZtKOAsS8nmmxaSl5dpGRwIlfbJLOEz0rEtIfBUjsWwViWWtJL5sJbmyjcQXq2Dg0B6PbRi9gtXD7SVE3Ampfk5GQHpyqrdjOD0VyWR8TX3b9PY4Hatyp455eR3pST0JuN5yxpsqEHKudRlHVdFEvFt4IBcSbSD8rYMg4oYgkoomUtDQSOSo4z2NYRgVIV+GQg3Gdv05zVfp+EwxtWgzyZU9EW+HYJZaBKEoxHJUBQMnLSzl5tGmY7MN/daENbIJ7cfvoJ/OcXaFCEeRUdsRWGdEntfj0HjWz6CjnfiLzzghm2SS6NHHE9nvoIJ9DaOi1GCsNhf+FNxKk88zzDUR1alMYxdyeczZNoVEnJoGiQQkY84BThgl/ewcHwipj96CBf9b87xYO/rhdDQUQdbKX+lLolGaLrmS1PJl6NLFBDYYjjTmyVM2jKpRe55sLkxw89WiDYZz5/rlTa/K8QYRceLUoagjkuJOCLRn2R0i3r5mdVs2s1PJzmK72q4kqU9mESwguGkCgwbDoMGe2hpG5ZGebw7gQ0xwU0mKqkW7ul+e3OBCX4ECgTVvomQi9/MTsTWCm2mLyOqt1LWtFdrboV9/JOxmKrSvyv98w6gpzMOtI3qhnk4xMad8op6+F2tbU/hcBCJNTlrXKy/CkoWOeKdS6CZbwGZbIc2DSjLfMHyDAAET3Poh3xLafPm/+aqHFZM3nC+1JRR2xDaz8LkqdKxCH74dlixyQhvp8MbcD6D/QAI77OP9+Ybhe+pHcOsnONJTRCCcpfZrIJh/MUEgmH1CLRwtzsOVQPY84/Tzs8SXtb0NnT2ze/w2mYRPW5D+tjTXqBdkTQgu21FjmIcLziKDdElE1TWTZYXy/NJ1GdJ5t0GPRXC6jRNds7ODquPZppftZsuEaG913mzZkiHaLH5r1Bv14+Ga4KYJBAtvIpmrXznyBHNVPwoEu3uyAwY7HxLxzqvgFEE22bZ0WwzDT9TgEt5c1M8rqVei3ctASiBA4MBjSQVDpFLOxFoimaKtPcbtk58gEeth8XLD8Bu20syoKOEoMGDNEuJAEKLNPP+fd3lt8ovss/Mohgxq4sNPvuDpV+fSmhReuPEWxp95arUtN4zyUEcergluLRCOdpqg+3Dqf3jogkuIt3dw00PLujV/+dY7TXCNukFqcHIsFya4Nciz19xAvD3LBpOGUXe4NaXrBBPcGmTFwkU574WiUXb70Q8qaI1h9CJCTaZ/5aJ+XkkfYvTBEwk3ZK8RvPFuY9nrlBMqbJFh9CaS56gtTHBrkD1POYFBwzcg3LhGdIPhMHufcTLnPPsvQpEcxcsNoxYJSO6jxrCQQg3SOGAAF8+YytQbb2HmI48xYN112PvMU9hi3DeqbZphlJna9GRzYYJbozQOGMB+F5zDfhecU21TDKP3sBiuYRhGJSkthisiE0RktojMEZGLstwXEbnWvf+WiOxYRuM7YYJrGIaPKa14jYgEgeuAicDWwFEisnWXZhOBzdzjJOCG8r6GNZjgGobhc0rycHcG5qjqXFWNAfcAh3RpcwhwhzpMAwaJyPrlsj6TisZwZ8yYsUREPs64NARYUkkbykCt2Vxr9oLZXCkqYfNGpXSe8cabT0i/wUPyNGkQkekZ55NUdVLG+TBgfsZ5C7BLlzGytRkGLOiByXmpqOCq6tDMcxGZrqpjKmlDqdSazbVmL5jNlaIWbFbVCSUOkc0N7rrNipc2ZcFCCoZh1DMtwIYZ58OBz3rQpiyY4BqGUc+8BmwmIqNEJAIcCUzp0mYKcKybrbAr8KWqlj2cANXPw51UuInvqDWba81eMJsrRS3aXBSqmhCR04EngCBwq6rOEpFT3Ps3Ao8B+wNzgFbg+N6yRzTfrrGGYRhG2bCQgmEYRoUwwTUMw6gQvhFcETlPRFRE8uXcVR0RuUpE3neXAD4kIoOqbVMuCi1p9BsisqGIPCci74nILBE5q9o2eUFEgiLyhoj8s9q2eEFEBonI/e77+D0R2a3aNvUVfCG4IrIhsC/wSbVt8cBTwLaqOhr4APhZle3JiscljX4jAZyrqlsBuwKn1YDNAGcB71XbiCK4BnhcVbcEtqO2bK9pfCG4wJ+BC+ilZONyoqpPqmrCPZ2Gk7PnR7wsafQVqrpAVV93f1+JIwTDqmtVfkRkOHAAcHO1bfGCiAwA9gRuAVDVmKour6pRfYiqC66IHAx8qqozq21LD/gR8O9qG5GDXMsVawIRGQnsALxSZVMKcTWOs5Cqsh1e2RhYDNzmhkFuFpHmahvVV6hIHq6IPA2sl+XWz4GLgW9Vwg6v5LNXVR9x2/wc5yvw3ytpWxFUbLliuRGRfsADwNmquqLa9uRCRA4EFqnqDBEZV2VzvBICdgTOUNVXROQa4CLgkuqa1TeoiOCq6j7ZrovI14BRwEwRAefr+esisrOqfl4J27KRy940InIccCAwXv2byFyx5YrlRETCOGL7d1V9sNr2FGB34GAR2R9oAAaIyJ2q6uddPFuAFlVNf3O4H0dwjQrgq4UPIjIPGKOqvq26JCITgP8D9lLVxdW2JxciEsKZ1BsPfIqzxPFoVZ1VVcPyIM6n7mTgC1U9u8rmFIXr4Z6nqgdW2ZSCiMiLwImqOltELgeaVfX8KpvVJ6j20t5a5C9AFHjK9cqnqeop1TWpO7mWNFbZrELsDhwDvC0ib7rXLlbVx6pnUl1yBvB3t7bAXHpxKavRGV95uIZhGPVM1bMUDMMw+gomuIZhGBXCBNcwDKNCmOAahmFUCBNcwzCMCmGCaxiGUSFMcA3DMCqECa5hGEaFMME1DMOoECa4hmEYFcIE1zAMo0KY4BqGYVQIE1wDcEpjikjeOsC9/HwVkU2r9XzDqAQmuEZNU4xQi8htJuxGNTHBNaqKWyi9Es/ZA9ikEs8yjFyY4NYZInKhiHwqIitFZLaIjHev3y4iv8loN05EWrp0Hysi74rIMtcbbMhsKyIXiMgiEVkgIoeKyP4i8oGIfCEiF2eMvbOIvCwiy922f3GLXafvq4icJiIfAh9meQ17iMh8EdnbPf+RiLzn2vWEiGzkXp/qdpkpIl+JyPdy/JuEgP8HnN6Df1LDKBsmuHWEiGyBIypjVbU/sB8wr4ghvu/22QTYHPhFxr31cPbtGgZcCtwE/ADYCfgGcKmIbOy2TQLnAEOA3XC2+flJl2cdCuwCbN3lNewH3A18R1WfE5FDcTYa/TYwFHjRvY+q7ul2205V+6nqvTle1znAVFV9y8s/gmH0Fia49UUSZ/ufrUUkrKrzVPV/RfT/i6rOV9UvgCuAozLuxYErVDUO3IMjpteo6kp3655ZwGgAVZ2hqtNUNaGq84C/Ant1edbvVPULVW3LuPZdYBKwv6q+6l472W37nqomgN8C26e93EKIyIbuGJd6/UcwjN7CBLeOUNU5wNnA5cAiEblHRDYoYoj5Gb9/DGT2XaqqSff3tEguzLjfBvQDEJHNReSfIvK5iKzAEckheZ6V5mzgPlV9O+PaRsA1bnhiOfAFzhbwwzy+pquBX6nqlx7bG0avYYJbZ6jqXaq6B45QKfB799YqoCmj6XpZumduqz6Cnm+rfgPwPrCZqg7ACQlIV1Oz9PsucKiInJ1xbT5wsqoOyjgaVfW/Hm0ZD1zliv/n7rWXReRoz6/GMMqECW4dISJbiMg3RSQKtON4nWmv9E1gfxFZS0TWw/Emu3KaiAwXkbVwRDJXTLQQ/YEVwFcisiVwqsd+n+EI5Jkiko753gj8TES2ARCRgSLy3Yw+C4GNyc3mwHbA9u4BcBDwkEebDKNsmODWF1HgSmAJ8DmwDo5wAvwNmIkzifYk2cX0LvfeXPf4TZY2XjgPOBpYiTO55lm4VfUTHNG9UEROVNWHcLz0e9zwxDvAxIwulwOT3ZDDEVnGW6Sqn6cP9/KSLrFjw6gItk26YRhGhTAP1zAMo0KY4BqGUdeIyK3ugp13ctwXEblWROaIyFsismNv2WKCaxhGvXM7MCHP/YnAZu5xEk6WTa9ggmsYRl2jqlNx8rdzcQhwhzpMAwaJyPq9YUtFCoekGTJkiI4cObKSjzQMo4rMmDFjiaoO7Wn/DSWk7VlTth2WkJqFkwKZZpKqTiryMcPovBCnxb22oMhxClJRwR05ciTTp0+v5CMNw6giIvJxKf07UL5Lc877N7CyXVXHlPIMui/KgewLc0qmooJrGIZRDAKEJJseupRHFlvovMpyOD1fZZmXgjFcEdlQRJ5zy+PNEpGz3OtrichTIvKh+3NwbxhoGIaPqELefkByH2ViCnCsm62wK/ClqpY9nADePNwEcK6qvi4i/YEZIvIU8EPgGVW9UkQuAi4CLuwNIw3DqDLJOMTaQVOAQDgCoSjk8z7LgCD5PVwvY4jcDYwDhrg1oC8DwgCqeiPwGLA/MAdoBY4v6YF5KCi4rtIvcH9fKSLv4QSUD8F5EQCTgecxwTWM+iOZgI7WjAsK8Q7n63ykodcfX2oqlaoeVeC+AqeV+BhPFBXDFZGRwA7AK8C6abdbVReIyDo5+pyEk9vGiBEjSjLWMPosqSQk4oBCMAzBCk6/xNuzX090QLh3vVwnhttrw1cczx8eItIPeAA4W1VXeO2nqpNUdYyqjhk6tMfZIYbRd4l3QPtXjsAlYtCxCmIVrL2TSuW+19sxXQERyXnUGp4EV0TCOGL7d1V90L28MJ0c7P5c1DsmGkYfJpXK7mEmYs5X/UoQyCMTvR7DdTzcXEet4SVLQYBbgPdU9f8ybk0BjnN/Pw54pPzmGUYfJxnv2b1yEs4Rp63ApBk4IpXrqDW8BIJ2B44B3haRN91rF+PUXb1PRE4APsGp1m8YRqmoOmKaiLlZAbmokIsXDEG0qUuWQhRCkYJdS6VgHm6N4SVL4SVy/58dX15zDMMg1ubNew2Fe9+WNMEwNFbweS5CWfNtq46tNDMMP5FKehPbcAMEgt2va8rxRNNjBCNO6lYNe4mhSnnyFcAE1zD8RCpZuA1k/zqv6mQzZGYOJGPQFofG/jUpuubhGoZRPlJJNzaaBAl6z6+Nt0OksfO1RCxHmpY6YYpoU5Z7/kZqNBshFya4hlEtkgknpzaNJiDlMdUrEQMJOJNXqSQkk7kXKIATYkil8qd4+ZSAhRQMwyiZUhcvxDs8ZDJkkIxDIFraMytMva00M8E1jGqg6l0ocw9S3EqvGozhgsVwDcMoBdXKrRLLpJL1F8pEOaqF+Yna+z9gGNVA1YmvqjrpWNlSsrwSb3dCAZUk3ODEfGuQ+pFbE1zDKEwqBR1d0q0C7uqrYr2vVKoMYuuu9Ip3kHfLAxEnfSwYqcnJMuiDK80Mo88Ta+0eK00l3PKERdaD9ZqFkI1QxPVUXQEKhpy8265EmiAYrFmPNhMp784OVccE1zDyoancixES8eIFt1RvLbN/IAgN/R3hT6Wc83CkLoQ2kxKCN77DBNcw8pE3CaAHtWADIZwvytn6BoA8mQuBLH+ugUD3BRB1hLPSrH5cXBNcw8iHCDkFMtiDYi4i0NDsbFmTmRYWaXKK0aRSzmKIriljEqjJLINyUE/+et/8P2gYXlB1V29lEVsJFB9OSBMIQkM/R1TTWQ9pLy4QcO7FO9wCNOpMevXyVjZ+xjxcw+gLpJK5MwqizaUJoIhTOyHXvUgD0PsbNPqd9PeLesEE1zBykS99K5XsearV6gLjcTfvKdKz8EQfIVhHimuCaxg9QtdsrliM8Ko68dvM9LBkwhHdOp78KgWpIx/XBNcwchEK5y4GHsuI7UrACTF4Ed5UjopgiZizR1iNLlDoLYT6mjSrp9diGOUlEMrzVT9jIk2zrETLRSLPwodSFkXUMQHJfdQaJriGkQsRZ/lutNnxPsMNTsZANtK1FgqOWV4T6x1BCOQ5PI0hMkFEZovIHBG5KMv9gSLyqIjMFJFZInJ82V+IiwmuYRQiGHKyBsIFasmmPJRbzLfTrU2cdUfchI4cR8HuIkHgOmAisDVwlIhs3aXZacC7qrodMA74k4j0ypbEJriGUQzBPAtNvSxMCAQh3HVyTEpPM6tjgkjOwwM7A3NUda6qxoB7gEO6tFGgv4gI0A/4AuiV+I5NmhlGMQTDIB3dV4IFQt5LNoYj7qqyBCCdFz4YnfCQhztERKZnnE9S1UkZ58OA+RnnLcAuXcb4CzAF+AzoD3xPteTq8FkxwTWMYhBxV4KltyIXRzxDUTeOm8y4nqcsooiFEDxSYHJsiaqOyXM/W++us5v7AW8C3wQ2AZ4SkRdVdUURZnqiYEhBRG4VkUUi8k7GtctF5FMRedM99i+3YYbhW0ScnNnGAc724+klvh2tTh2ERMyp4NW+svKFxusQyfOfB1qADTPOh+N4spkcDzyoDnOAj4Aty2J8F7zEcG8HJmS5/mdV3d49HiuvWYZRYyRz5NfG2orbd8zohOCsNMt1eOA1YDMRGeVOhB2JEz7I5BNgPICIrAtsAcwt24vIoGBIQVWnisjI3ni4YdQNeZcBJyx8UAKlRLdVNSEipwNP4JTWvVVVZ4nIKe79G4FfA7eLyNvu4y5U1SWl2p2NUmK4p4vIscB04FxVXZatkYicBJwEMGLEiBIeZxg+xua8eo1Sq4W538Af63LtxozfPwO+VdJDPNLTtLAbcILL2wMLgD/laqiqk1R1jKqOGTp0aA8fZxg+J19+bbbC4YYn0kt7cx21Ro/eCaq6MP27iNwE/LNsFhlGLRIIOaLbNbTQG/m16WpjqaRTxyEUKe4ZmnK35AnUxHY8fb4eroisr6oL3NPDgHfytTeMuieduRCKOBNo6bSvcotFth2E4x1OqlqhwjfpguqZHwrBsGO3j0XNv5YVT0HBFZG7cZa7DRGRFuAyYJyIbI+TzzYPOLn3TDSMGiIQ9L4AoifEs2U9qLOzcEO/An07unvgyTjExbelIUWkb3m4qnpUlsu39IIthmEUIpljxWkq6QhxPnHKlUmRiHXeft1n1GJVsFxYNN8w+gy1lw8sQKCOtnzwf8TcMIw15CoPGQgV9lBzhTok4FvvttRqYZXATX31hHm4hlELqAKasQtFhrcqAYh6iMFGGqH9q+zXfUzA/zEFzwaa4BqG34m1O7UZuuHu7us1GyK9PXu8w90EM+jU+O3NSb4yIH5xZXOgqn/12tZCCobhZ9KFcLKizv1iBCkQdHaxaOzv/PS92EIwIDmPytsjZ4nIAHG4RUReFxHPq9RMcA3Dz8Ta899PJb3tNFHD+CyG+yO3bOO3gKE4lcau9NrZQgqG4Wu8ZBbUXvaBVwTxW5ZC2pj9gdtUdaYUEfMwwTWM3iI90UUp7piQX1ClJpbn9hjxXQx3hog8CYwCfiYi/QHPXzFMcA2jN0jEnVq4abEMhp3FBemdW7xuqxOOOstxcxHx74KFcuGzLIUTcIp2zVXVVhFZGyes4AkTXMMoN8mEs9S207W4m87lIu7GkYUmrcLRjG17MggEnXQun096lQM/fZ6oasqtD/4DEVHgJVV9yGt/E1zDyEcy4XiYqZQrcg2FRS6eK6sgA1VoX+VkCxRSlGiT4xmni+J4WeRQJ6SzFPyCiFwPbArc7V46WUT2UdXTvPQ3wTWMXCRibljAJZVwFg5Em/Nvie55w1d1RDTkYTeIdBnGPojPYrh7AduqOhWERGQy8LbXznUcbTeMElDNnZKVL6Za/IPKOFb9IThVJ3MdVWA2kLl1zYbAW147m4dr9E005Xz1T39ND0WzeJo5xDCVzD1uKlWEh4vtBlEIEcQHIQUReRTnDTEQeE9EXnVv7Qz81+s49n/b6FuoOoLYvorVgqo4k1ypqBOjLUS+r7jZdu7NRShSNTetlvBJDPeP5RjEBNfoG6SSTjw2n3ea6HC93cian9lqyIaiPbNh9WSbQDhi3q0HBH/MD6rqC+nf3a3Ux7qnr6rqIq/j2MerUf+kMwLyiW2aePuaibJwQ/eJqnA0/+RVvu3QI41O8ZiG5t7ZfqceEScPN9dRcXNEjgBeBb4LHAG8IiKHe+1vH7FG/dO1nKGX9ulNFiON7oIF9baAP723WWZ2A9REVS6/4rMshZ8DY9NerYgMBZ4G7vfS2QTXqH+8eLbd+iQg4HqyxVZKCUUcDza9WCEQslhtD3GyFHwluIEuIYSlFBEpMME16p+eeJal1idIx4CN0vBfqYjHReQJ1ix8+B7wmNfO/nophtEbBMPF/dWK2Nd/3yBIMJDz8DSCyAQRmS0ic0TkohxtxonImyIyS0ReyNFGgGuBvwKjge2ASap6oddXYx6uUf+IOBNVHW2F07Yk4Kwk81fcsG9Twv8LEQkC1wH7Ai3AayIyRVXfzWgzCLgemKCqn4jIOtnGUlUVkYdVdSfgwZ7YYx6u0TeQgCO64S55toEQNPR3swf6O7UNLN7qH4RSPdydgTmqOldVY8A9wCFd2hwNPKiqnwAUSPOaJiJj89zPi3m4Rt8indalKXcyzMTV3xScsBwiItMzziep6qSM82HA/IzzFmCXLmNsDoRF5HmgP3CNqt6R43l7A6eIyDxgFW7BYlUdXeiVgAfBFZFbgQOBRaq6rXttLeBeYCQwDzhCVZd5eaBhVB0REIvR1gLierh5WKKqY/INkeVa1xzBELATMB5oBF4WkWmq+kGWvhPzGVMILx/vtwMTuly7CHhGVTcDnnHPDaP6qDrpWLE2p1ZCMXUNDF8iAcl5eKAFp8BMmuHAZ1naPK6qq1R1CTAVZ0KsG6r6MbA2TljiYGBt95onCgquqk4Fvuhy+RBgsvv7ZOBQrw80jF5DFTpWQUersyQ33g5tK53dF4zaxCmIm/sozGvAZiIySkQiwJHAlC5tHgG+ISIhEWnCCTm8l90cuRRH89YGhgC3icgvvL6cnsZw11XVBQCquiDXrJ5r4EnASQAjRozI1cwwikPVqX2QTDqTXKGIU/kr2yKHWCvQ5K3urOE7SllppqoJETkdeAIIAreq6iwROcW9f6Oqvicij+OUWUwBN6vqOzmGPArYQVXbXduuBF4HfuPFnl6fNHMD2JMAxowZY8U/jdLRlFMIXN23U4rsRWYyibVCcICle9UagldPNieq+hhdFieo6o1dzq8CrvIw3DygAUgXRY4C//NqS08Fd6GIrO96t+sDnqvlGEbJxDvWiG0xpJL5d2owfInPEkk6gFki8hTO5Nu+wEsici2Aqp6Zr3NP331TgOOAK92fj/RwHMMonmQRNWcz6YlIG9VFxPOKsgrxkHukeb6Yzl7Swu4GxuHku7UAl+EI7X0icgLwCU6pMsPwN+bd1iY+CgOp6uTCrXJT8B2oqkfluDW+lAcbRo8JR7uXPyxEIOirP1zDGx7ycGsK+8g3ao9gGELJwhNlmVg4oXbxV3nGkjDBNWqPdJHvUNSZCNOUI755FzmY4NYmgtRRbQsTXKN2ydwrOxx1dmlo/4qs4hq02rQ1ieArD1dENgfOBzYiQz9V9Zte+pvgGrVLegdeCbg1bN2KYO1fdW4nAUeQjZrEZzHcfwA3AjcBRW8lYoJr1B6qzrLdzBhuKOKUXgwEoXHAmhBDIORkJ9iEWW1S7PZGvU9CVW/oaWcTXKO2UHUyFJJd6iMkYs4fZrjB/Wkebb3gMw/3URH5CU4ubkf6oqp2rTeTFRNco3ZIxPKng8U7uhcYN2obn8VwcRZ6gRPHTaPAxl46m+AatUEyUXzurVEH+GulmaqOKqW/Ca5RG5jY9l18FMMVkTBwKrCne+l54K+q6qkGqAmu4X805a2QeMDeznWH4Lc95m4AwjibTgIc41470Utne4ca/iflcdcGmyirQ8RvgjtWVTN3g3hWRGZ67eyrV2IYWfFSny8UseI09Ujaw811VJ6kiGyy2jyRjSkiH9feoYZ/SaUAzb6LQ5pg2PFsA7YpZN3ioxguTnbCcyIyF+fjYCPgeK+dTXAN/5FKOXuT5YvbpuspBG3bnPpGIOifD1NVfUZENgO2wBHc91W1o0C31ZjgGv5CFTq+KlzdKxgxse0LCL7wcEXkm6r6rIh8u8utTUQEVX3QyzgmuIZ/SCWdFWReSinmCzMYdYRvPNy9gGeBg7LcU8AE16gR0tubFyOiPvB6jArhg//XqnqZ++uvVPWjzHsi4nkxhGUpGNUn1la8x2opYH0D/2UpPJDl2v1eO5uHa1QX1e6FaAqRrgpm1D3ikwLkIrIlsA0wsEscdwDOtumeMME1/I0EnPza9ASZ7U3Wt/DPSrMtgAOBQXSO464Efux1EBNco7KkJ8bAyTQQcUQ1WwpYIOQUFDf6Nj74gFXVR4BHRGQ3VX25p+OY4BqVQRVirU7VrzTxDmeFWKTRmTTrisVpjTJkKYjIBOAaIAjcrKpX5mg3FpgGfE9Vc8Vl3xCR03DCC6tDCar6Iy+2+MJXN/oAyXhnsU2TiLkTZlm8mFir7bbb10nn4eY6CnUXCQLXAROBrYGjRGTrHO1+DzxRYMi/AesB+wEvAMNxwgqeMME1KkMiz2KceAdZN37syYSaUWe4Hm6uozA7A3NUda6qxoB7gEOytDsDJwNhUYHxNlXVS4BVqjoZOAD4mtdXU1JIQUTm4ah7EmevnzGljGfUMXkd1Tw3bYGDkd+THSIi0zPOJ6nqpIzzYcD8jPMWYJfOw8sw4DDgm8DYAtakPYDlIrIt8DkwskCf1ZQjhru3qi4pwzhGPRMM5/FyhdyiW/0JE6OKSMEY7pICjl62N1DXN9vVwIWqmpTCYYpJIjIY+AUwBegHXFqoUxqbNDMqQzgKyVj2mGy4AeI5dnTwUnjcqG9Ky1JoATbMOB8OfNalzRjgHldshwD7i0hCVR/uOpiq3uz+OhWP+5hlUmoMV4EnRWSGiJyUrYGInCQi00Vk+uLFi0t8nFGziEBDfwhlZB4EQs61fJsEmuD2bUpfafYasJmIjBKRCHAkjme6GlUdpaojVXUkzqqxn2QTWwAR+a2IDMo4Hywiv/H6ckoV3N1VdUecGcDTRGTPrg1UdZKqjlHVMUOHDi3xcUZNIwKRBmga6BwNze4fTp6vjFZUvI8jJQmuqiaA03GyD94D7lPVWSJyioic0gODJqrq8ozxlwH7e+1c0rtZVT9zfy4SkYdwZgSnljKm0QeRgJOPm4h1uS6dPWKjb1LiSjNVfQx4rMu1G3O0/WGB4YIiEk3XwBWRRsDzm7THgisizUBAVVe6v38L+FVPxzPqFNU1YYF4bE2aVyjsxG7T8blwgxNiSHQ4fdI7OfhglZFRRQRvWyxVjjuBZ0TkNpyQ6o+AyV47l+Lhrgs85AaaQ8Bdqvp4CeMZtYgqoM5bLxl30rjSHmsyAfF2smYgpBc8RJvXJLGHws5hGKvxTT1cAFT1DyLyFrCPe+nXqlposcRqeiy4qjoX2K5gQ6N+SSZyrwbLt9AhTSrpHBanNfLhv285b+Bsla7u757xla9u1BCppLvvWIlLb21hg5EPKXmlWZnNkSOAV4HDgSOAV0TkcK/9zbUwekY8VriNF/wVnzP8iL/eIz8HxqrqIgARGQo8jcci5Ca4Rs/QMnimIhZOMPJTeKVZpQmkxdZlKUVECuzdbvSMQKi0cEAgCJEmP8bnDL/hr/fI4yLyBHC3e/49uqSc5cME1+gZ4XTebI4YrgScOreJGKQSgDipX2mP1l9/RIZf8ZmHq6rni8h3gN1xktYmqepDXvub4Bo9QwLQ0M+pgZBMuH8YYed6ILhmKxwLGRil4rP961T1AbJvJlkQ+2sweoaq472mi4qrrsm/Ne/VKBvii0kzEVlJ9q9zAqiqDvAyjgmu0TMSse65tvF256dtjWOUCwGC1RdcVe1fjnFMcI2eEc+xsCHeYYJrlBd/eLhr5buvql94GccE1yie9HLe7DcraYlR7/hn0mwGzps7V0FzT7VxTXCN4knXPsi2yswH3ohRZ/hgTkBVR5VjHBPcGiEZjxMIhfCwBUhlCDdALMsuDZGG7tcMo6f4x8NdjbvFzmZ03ibdU1lac0d8zn9u/RsXrL8Zp0WHcMH6m/HipNuqbZJDKALRpjUebSDoVP4KWrUvo8xIIPdRaVNETsSp+f0E8Ev35+Ve+5vg+piX77ibe884nxWfLwRVVi5cxD/O+Rn/ueWOapvmEAxDY39394Z+lnNr9AL+Kl4DnIWzs+/Hqro3sAPgee8wE1wf8+ilvyHW2trpWqy1lSmXXlEliwyjwghr5gyyHZWnXVXbAdydH94HtvDa2VwSH7Os5dOs179csABV9U881zB6DfHbSrMWdxPJh4GnRGQZ3XcBzokJro8ZMmoki+fM7XZ9rREjTGyNvkOJe5qVE1U9zP31chF5DhgIeN7pxj+vxOjGYVf+kkhTY6dr4aZGvv37X1bJIsOoMCJranNkO6qIqr6gqlNU1XNxaBNcH5GIxXjyqmu4dIsd+fmobfn4tdf5wU3/j3W33JxgJMI6m2/K8XdMYsz3vtMrz9eF80i+8k+SLz5AcvaraKy9V55jGEXhrxhuSVhIwUfceNjRzH7+ReKtTn7rM1dfz9BNRnHJzP8SikR69dmpOW+gH721phjNvBWkPvsfgT2+jdhSXaNa+DAPtxTMw+1F2leu5IUbbubOk8/k+esm0bZiRc62H09/nQ+ef2m12AIkOjr44pMW3nhwSrf2qsrHM95g+n0PsvCDD0uyU+Md6NyZa8QWnK3N4x3oJ++VNLZhlIyP8nBLxTzcMqOqzH9jJvPffIsHL7iUeHs7sVWtSCDAPWecz7pbbMahv72MHQ47qFO/j16dgaZS3cbr+Oor5rz0MmOPXLNP3aply7h2v8NY8O5sAsEAyXicbSbsy4/vvZ1guAcLD1YsdSYmuu7gkEqii1tgk+2LH9MwyoLvshRKovY+InzMikWLuWLHPfjjnhP4+8lns2rpF8RWOXm0mkqBKgvf/4DbfnAiL908uVPftTYcjoS6v7HCjQ0MGbVRp2t3/vhMWma+Q2zVKtpXrCTe1s6sx5/m8d//uWeGRxohi9gD0NDcszENo0yISM7DY/8JIjJbROaIyEVZ7n9fRN5yj/+KyHZlfxEufU5wO1pbeeCCSzhn8Ia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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(figsize=(5, T*3))\n",
    "for t in range(T):\n",
    "    plt.subplot(T, 1, t+1)\n",
    "    plt.scatter(x, y, c=probs[:,t], vmin=0, vmax=1, cmap=plt.cm.Reds)\n",
    "    plt.colorbar(label=\"allocation probs.\")\n",
    "    plt.title(f\"submarket {t}\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Confusion matrix"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "map_submarket = np.argmax(probs, axis=1)\n",
    "\n",
    "confusion = np.empty((K, T), dtype=int)\n",
    "for k in range(K):\n",
    "    confusion[k] = np.count_nonzero(map_submarket[z==k][None] == np.arange(T)[:,None], axis=1)\n",
    "\n",
    "sns.heatmap(confusion, cmap=plt.cm.Reds, annot=True)\n",
    "plt.xlabel(\"estimated submarket\")\n",
    "plt.ylabel(\"true submarket\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([4, 3, 1])"
      ]
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "corespondance = np.argmax(confusion, axis=1)\n",
    "corespondance"
   ]
  },
  {
   "source": [
    "### Coefficients"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.bar(range(T), best_model.τ.Regre.ω_[:,0].flatten())\n",
    "for k in range(K):\n",
    "    plt.hlines(alpha[k], 0, T-1, label=f\"submarket: {k}\", color=color[k])\n",
    "plt.scatter(corespondance, alpha, marker=\"x\", color=\"k\")\n",
    "plt.legend(title=\"true coefs.\")\n",
    "plt.title(\"estimated alpha\")\n",
    "plt.xlabel(\"segmented submarket\")\n",
    "plt.show()\n",
    "\n",
    "plt.bar(range(T), best_model.τ.Regre.ω_[:,1].flatten())\n",
    "for k in range(K):\n",
    "    plt.hlines(beta[k], 0, T-1, label=f\"submarket: {k}\", color=color[k])\n",
    "plt.scatter(corespondance, beta, marker=\"x\", color=\"k\")\n",
    "plt.legend(title=\"true coefs.\")\n",
    "plt.title(\"estimated beta\")\n",
    "plt.xlabel(\"segmented submarket\")\n",
    "plt.show()\n",
    "\n",
    "plt.bar(range(T), best_model.τ.Regre.ω_[:,2].flatten())\n",
    "for k in range(K):\n",
    "    plt.hlines(gamma[k], 0, T-1, label=f\"submarket: {k}\", color=color[k])\n",
    "plt.scatter(corespondance, gamma, marker=\"x\", color=\"k\")\n",
    "plt.legend(title=\"true coefs.\")\n",
    "plt.title(\"estimated gamma\")\n",
    "plt.xlabel(\"segmented submarket\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}