{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:05.512001Z",
     "iopub.status.busy": "2026-07-28T19:06:05.511804Z",
     "iopub.status.idle": "2026-07-28T19:06:07.008867Z",
     "shell.execute_reply": "2026-07-28T19:06:07.007336Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:07.012520Z",
     "iopub.status.busy": "2026-07-28T19:06:07.012005Z",
     "iopub.status.idle": "2026-07-28T19:06:11.007204Z",
     "shell.execute_reply": "2026-07-28T19:06:11.006626Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.iolib.table import SimpleTable, default_txt_fmt\n",
    "\n",
    "np.random.seed(1024)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WLS Estimation\n",
    "\n",
    "### Artificial data: Heteroscedasticity 2 groups \n",
    "\n",
    "Model assumptions:\n",
    "\n",
    " * Misspecification: true model is quadratic, estimate only linear\n",
    " * Independent noise/error term\n",
    " * Two groups for error variance, low and high variance groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.010183Z",
     "iopub.status.busy": "2026-07-28T19:06:11.009808Z",
     "iopub.status.idle": "2026-07-28T19:06:11.026408Z",
     "shell.execute_reply": "2026-07-28T19:06:11.025752Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "x = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x, (x - 5) ** 2))\n",
    "X = sm.add_constant(X)\n",
    "beta = [5.0, 0.5, -0.01]\n",
    "sig = 0.5\n",
    "w = np.ones(nsample)\n",
    "w[nsample * 6 // 10 :] = 3\n",
    "y_true = np.dot(X, beta)\n",
    "e = np.random.normal(size=nsample)\n",
    "y = y_true + sig * w * e\n",
    "X = X[:, [0, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WLS knowing the true variance ratio of heteroscedasticity\n",
    "\n",
    "In this example, `w` is the standard deviation of the error.  `WLS` requires that the weights are proportional to the inverse of the error variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.029392Z",
     "iopub.status.busy": "2026-07-28T19:06:11.029161Z",
     "iopub.status.idle": "2026-07-28T19:06:11.065203Z",
     "shell.execute_reply": "2026-07-28T19:06:11.064736Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.927\n",
      "Model:                            WLS   Adj. R-squared:                  0.926\n",
      "Method:                 Least Squares   F-statistic:                     613.2\n",
      "Date:                Tue, 28 Jul 2026   Prob (F-statistic):           5.44e-29\n",
      "Time:                        19:06:11   Log-Likelihood:                -51.136\n",
      "No. Observations:                  50   AIC:                             106.3\n",
      "Df Residuals:                      48   BIC:                             110.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2469      0.143     36.790      0.000       4.960       5.534\n",
      "x1             0.4466      0.018     24.764      0.000       0.410       0.483\n",
      "==============================================================================\n",
      "Omnibus:                        0.407   Durbin-Watson:                   2.317\n",
      "Prob(Omnibus):                  0.816   Jarque-Bera (JB):                0.103\n",
      "Skew:                          -0.104   Prob(JB):                        0.950\n",
      "Kurtosis:                       3.075   Cond. No.                         14.6\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "mod_wls = sm.WLS(y, X, weights=1.0 / (w**2))\n",
    "res_wls = mod_wls.fit()\n",
    "print(res_wls.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS vs. WLS\n",
    "\n",
    "Estimate an OLS model for comparison: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.067553Z",
     "iopub.status.busy": "2026-07-28T19:06:11.067359Z",
     "iopub.status.idle": "2026-07-28T19:06:11.080057Z",
     "shell.execute_reply": "2026-07-28T19:06:11.077574Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.24256099 0.43486879]\n",
      "[5.24685499 0.44658241]\n"
     ]
    }
   ],
   "source": [
    "res_ols = sm.OLS(y, X).fit()\n",
    "print(res_ols.params)\n",
    "print(res_wls.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the WLS standard errors to  heteroscedasticity corrected OLS standard errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.082307Z",
     "iopub.status.busy": "2026-07-28T19:06:11.082119Z",
     "iopub.status.idle": "2026-07-28T19:06:11.100019Z",
     "shell.execute_reply": "2026-07-28T19:06:11.099543Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "          x1   const \n",
      "---------------------\n",
      "WLS     0.1426  0.018\n",
      "OLS     0.2707 0.0233\n",
      "OLS_HC0  0.194 0.0281\n",
      "OLS_HC1  0.198 0.0287\n",
      "OLS_HC3 0.2003  0.029\n",
      "OLS_HC3  0.207   0.03\n",
      "---------------------\n"
     ]
    }
   ],
   "source": [
    "se = np.vstack(\n",
    "    [\n",
    "        [res_wls.bse],\n",
    "        [res_ols.bse],\n",
    "        [res_ols.HC0_se],\n",
    "        [res_ols.HC1_se],\n",
    "        [res_ols.HC2_se],\n",
    "        [res_ols.HC3_se],\n",
    "    ]\n",
    ")\n",
    "se = np.round(se, 4)\n",
    "colnames = [\"x1\", \"const\"]\n",
    "rownames = [\"WLS\", \"OLS\", \"OLS_HC0\", \"OLS_HC1\", \"OLS_HC3\", \"OLS_HC3\"]\n",
    "tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt)\n",
    "print(tabl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate OLS prediction interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.102116Z",
     "iopub.status.busy": "2026-07-28T19:06:11.101932Z",
     "iopub.status.idle": "2026-07-28T19:06:11.111490Z",
     "shell.execute_reply": "2026-07-28T19:06:11.111048Z"
    }
   },
   "outputs": [],
   "source": [
    "covb = res_ols.cov_params()\n",
    "prediction_var = res_ols.mse_resid + (X * np.dot(covb, X.T).T).sum(1)\n",
    "prediction_std = np.sqrt(prediction_var)\n",
    "tppf = stats.t.ppf(0.975, res_ols.df_resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.118160Z",
     "iopub.status.busy": "2026-07-28T19:06:11.117967Z",
     "iopub.status.idle": "2026-07-28T19:06:11.129895Z",
     "shell.execute_reply": "2026-07-28T19:06:11.128295Z"
    }
   },
   "outputs": [],
   "source": [
    "pred_ols = res_ols.get_prediction()\n",
    "iv_l_ols = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u_ols = pred_ols.summary_frame()[\"obs_ci_upper\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare predicted values in WLS and OLS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.136449Z",
     "iopub.status.busy": "2026-07-28T19:06:11.136266Z",
     "iopub.status.idle": "2026-07-28T19:06:11.766598Z",
     "shell.execute_reply": "2026-07-28T19:06:11.765597Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcda4fcf4d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YsmVLhuckJyezatUqevToQc+ePfntt9+eeqB5waxZs6hUqRLbtm0jX758BAQE0LJlS/r160diYqLpvF27drFixYrHXmfLli2UK1eOP/74A3t7e44cOUKbNm1YuHChNX4MIYQQIk+JT4onMj7SdPulqi/h5uDGJP9JBI4OZFHnRRJoPoUszWwuX76c2bNnM2jQIObNm8fAgQPTnZOcnEyXLl24ePEi7777LkWKFOHrr79Gp9Px/PPPm2vcuc6vv/7KxIkT+eWXX3jxxRdNx8eNG0fdunV5++23mTVrVqauNWHCBF5++WVWrlxpOpaYmMjZs2fNPm4hhBAir4pOiGbZ4WXM3jubfjX6Ma3NNABalmnJtTHXcHdyt/EI84YsBZvdu3dn4MCB6HQ6JkyYkOE5S5YsYceOHZw9e5ZSpUoB0LlzZ6Kjo59+tLnYtGnTaNWqVZpAE6B8+fKMHTuWqVOn8n//93/kz5//ide6efMm3t7eaY7Z29tTo0YNs45ZCCGEyIvuxd4zdfsJjQ0FYN35dXzS+hP0Oj06nU4CTTPK0jK6h4fHEzfFfvXVV3Tr1s0UaKbIly9f1keXFdHRj/+Ki8v8ubGxmTs3C2JjYzl8+DAtW7bM8P4WLVoQFxfHoUOHMnW9559/njlz5jB58mT++ecfIiIisjQeIYQQ4lkUEhXCpC2TKPVpKd7b9h6hsaGUL1ie5V2Xc3TIUfS6LO8uFJlg9gShU6dO0bNnT2bOnMnWrVspWrQoPXr0oGvXro99THx8PPHx8abb2QqeXF0ff1+nTrBxY+rtokUhJibjc5s3h23bUm+XKQN376Y/T9MyPbSIiAg0TcPT0zPD+728vAC4f/9+pq63cOFCqlatyvfff8+cOXMAaNmyJZ9++im+vr6ZHpcQQgjxLPlkxycsPKjyG2oUq8GUJlPo4dsDO73kS1uSWUN4TdOIj49n5syZBAYG8uabb1KtWjV69erF3LlzH/u4adOm4e7ubvrKa1nVBQoUwGAwcP369QzvDw4OBqBw4cKZup69vT0jR45k7969REVF8ccff3Djxg06dOhAQkKC2cYthBBC5GZn7pzh/N3zptvjGo+jaammbOi9gWNDjvFytZfzRqB59Sp07Ahr1th6JBky69+wTqejQIECVKpUicWLFwNqv+a9e/eYM2cOY8eOzfBxU6ZMSXNfRERE1gPOqKjH32d4pD/p7duPP1f/SPwdGJi1cWTA0dGRRo0asWnTJt5///1092/atAlXV1fq1q2brWu3bduWWbNm0alTJy5duiSzm0IIIZ5pKd1+fjv3Gy9UfoFfe/0KQJkCZdjx+g4bj84CPDxg/34IC4MePWw9mnTMHs7XqVOHQoUKpTlWsmRJwsLC0DQtwz2fjo6OODo6Pt0TZ2VPqKXO/Q/vvfce7du3Z+nSpQwZMsR0/MiRIyxcuJApU6bg4uKSqWutW7eOzp07Y2eX+vIdO3YMg8GQ52aFhRBCiMzQNI1tgduYumsqf1/523Rcr9OTZEzKGzOYAImJ8P33anvgDz+ATqe2En79NVSpYuvRZcjsf/MDBw5k+PDhBAYGUqZMGWJiYvj2229p0aLFM11xv23btnzxxReMHDmS7777jlq1ahEcHMymTZsYMWIEb7/9dprzQ0NDGT9+fJpjXl5ejBs3jg0bNjBmzBj8/Pzw9PTk/Pnz7Nq1iwULFuDm5mbNH0sIIYSwub+v/M3/bf2/DLv9+BbJI6t90dGwciXMmaOWzQFee03lpQB06WK7sT1BloLNw4cPM27cONPtTz75hBUrVtC5c2dTKaRevXpx/PhxatSoQeXKlQkICKBixYosX77cvCPPhV577TWef/55/v77b65fv06dOnWYN29eusz9jh07UqBAgXSPT5kxXr58OTdv3mTPnj2EhITQvHlzvv32W4oWLWqNH0MIIYTIUc7cOcO+4H15s9tPWBgsXAiffQahqkwTxYrB2LHg72/bsWWSTtMyn1Z97949jh8/nu64l5cXlSpVSnPszp07XL58GS8vL0qXLp2lQUVERODu7k54eHi6upNxcXEEBARQtmxZnJycsnRdkZ78fQohhMhN4pPi+er4VxR3K06Ximo2LyYxhum7pjO83nA8XTOu/JIrnTsHdeumllwsVw4mTlQzmjngd/Z/xWsPy9LMZsGCBWnRokWmzi1SpAhFihTJyuWFEEIIITIUlRDFssPLmLN3Djcib1C1SFU6+XRCr9PjYu/C/1r+z9ZDNI/wcHB/UFC+UiUVYBoMMHkydO8Odrlv72nuG7EQQgghnhlhsWEs2L+Azw58RlhsGAAl3EowoPYAko3J6A15pBD7gQMwfTrs2gUBASpBWaeDLVtUffBcnPciwaYQQgghcqRlh5cx7q9xRCWo8oYVPCowyX8SfWv0xdHuKavY5ASapoLJ6dNh69bU43//Dc89p74vVsw2YzMjCTaFEEIIkSOVci9FVEIUNYrV4O0mb9PDtwcGveHJD8zpkpPhl19UkHn0qDpmZwevvgoTJkAeq5ctwaYQQgghbO707dNM3z0dHw8f3mv+HgDty7fnn37/0LJMy7xVPvHKFXj5ZTWz6eICgwfDmDHwSHWavEKCTSGEEELYzP7g/UzbNY1159cBUNCpIBMaT8DZ3hmdTkersq1sPEIzCA+H7duhWzd128cHBg6EEiXgzTfhkWY4eY0Em0IIIYSwKk3T+DfgX6bumsq/Af8CoEPHi1VeZEqTKTjbO9t4hGYSEgLz58Pixaqt9sWLKrscYNky247NiiTYFEIIIYRVTd05lXe3vguAnd6OV2u8yiT/SVQuXNnGIzOTy5dh9mz44guIj1fHqlSBW7dSg81nSB6pFyCEEEKInCrJmERoTKjpdq9qvchnn483673Jpbcu8cVzX+SNQPPGDejdGypWhM8/V4Fmw4awbh2cOgWNGtl6hDYhwaYV3Lhxg3/++Sfd8YMHD7J37950x7dt20ZQUBAAly9fZs+ePU98jqCgIPbs2cO1a9eefsBCCCGEGcQlxbHk4BIqLqjIiD9GmI5X8KjAzXE3WdBpAaULZK3LYI7m6gqbNoHRCB07qn2ae/aovZr6ZzfkkmV0KwgMDKRNmzacOXOGKlWqAGA0GmnXrh2xsbHcv3/f1Cryxo0btGzZkt9//53SpUvzxRdf8MMPP3Dp0qUMr33t2jV69+7N6dOn8fX15caNG3h4eDBnzpxMd3sSQgghzCkyPpLPD33O3H1zCYkKASA2KZbI+EjcHN0ATH/mWkYj/P47bNgAy5erouv586u9mJUqQc2ath5hjiHBphXUq1ePfPnysXXrVlOwefToUQwGA6VLl2bPnj20aqWy7bZu3YrBYKBZs2aZuvagQYPQ6/Vcv34dFxcXAE6cOMGpU6cs88MIIYQQj3E35i6f7f+MBQcWcD/uPgAl85dkQuMJDPAbgIu9i20HaA4JCfDttzBzpupdDmrpvHVr9f1LL9lubDnUszuna0X29vY0adKEbdu2mY5t27aNZs2a0bJly3TH/fz8cE/pi/oEhw8fpnPnzqZAE6BGjRr06dPHXMMXQgghMuWrY1/x0Y6PuB93n0qFKrGq2youjbzEWw3eyv2BZlQUzJsH5cvDG2+oQNPdHd5+G6pXt/XocrQ8M7MZnRD92PsMegNOdk6ZOlev06cpufC4c/M55MvS+Fq2bMmcOXPQNA2dTsfWrVtp164dRYoUYfHixabztm7dSo8ePTJ93Ro1arBq1SoaNGhAkyZNsLPLMy+pEEKIHO5i6EXuxd2jfon6AAyuM5g/Lv3BsLrDeKHyC3mj2w/A+fMquefePXXby0sVYR8yRC2di/+UZyIT12muj72vk08nNvbZaLpddHZRYhJjMjy3eenmbOu/zXS7zPwy3I25m+487X0tS+Nr1aoVkydP5vTp01SpUoWdO3cydepUChcuTP/+/YmJiSE0NJTLly/TsmXLTF931apVDBs2jDZt2uDg4EDdunV5/vnnGTFiBI6OeaBvrBBCiBzneMhxpu2axs9nfqZGsRocGXwEnU6Hm6Mb//RLnxCbK8XGgvODyScfH9WjvHBhmDgR+vYF+R2baXkm2Mzp/Pz8yJ8/P1u3biUmJgZ7e3uqV6+OTqejVKlS7N69m5s3b5qW3DOrdOnS/PHHH4SFhbFv3z7++ecf3nvvPTZu3Mjff/+dt9p7CSGEsKndV3czbdc0Nl5MncAp4VaC8PhwCjgVsN3AzOnUKbUf899/VRF2Z2eVSf7nn6rjjyGPzNZaUZ4JNqOmRD32vken8W+Pv/3Yc/W6tNtYA0cFPtW4TGN4kPSTEmw2a9bMFAg2b96crVu3cvPmTRo0aEC+fFlbogfw8PCgU6dOdOrUiRo1atC/f38CAgIo9wwWjxVCCGFee6/tZfI/k9kRtANQvytfqvoSk/0nU9Mzj2Rd79oFM2ao7PIUmzfDCy+o7/No33JryDPBZlb2UFrq3Cdp2bIln3zyCdHR0XTu3Nl0vHnz5ixevJibN2/Sr1+/LF0zNDSUQo/0VHV+MO2fUk5JCCGEeBp3Y+6yI2gH9np7Xqv5GhP9J+JTyMfWw3p6RiP88QdMnw67d6tjOh107w6TJkHdurYdXx6RZ4LN3KBly5aMGzeOv//+m1mzZpmON2/enP79+2M0Gk0lkB4WGxvL33//neaYq6srDRs2pHXr1tSqVYsmTZrg6enJ+fPnmTFjBi+99BLFixe3+M8khBAib0lITuDbE9+SZExiUJ1BAHSu2JmprabSt2ZfvPN723iEZnThAnTtqr53cIDXXoPx41UHIGE2EmxaUa1atUwzmtUfKpNQqlQpunfvzv3792n0SCurChUqUKVKFaZPn57meNmyZWnYsCEHDhzg559/Ztu2bYSEhFC0aFE+++yzLGW0CyGEEDGJMaw4soLZe2ZzLeIahZwL0ad6H/I55EOv0zOl6RRbD/HpRUerGcx27dTtypXhlVfUXszRo1WWuTA7naZpWUurtoKIiAjc3d0JDw8n/yMlBeLi4ggICKBs2bKyTGwG8vcphBDPtvtx91l8cDHz9s0zVV/xdPVkXKNxDK83PPfXxwQIDYVFi+CzzyA8HC5flj2YZvBf8drDZGZTCCGEeEb9cuYX3vj9DSLiIwAoW6AsE/0n0r9W/zT1qXOtq1dh7lzVTjLmQcnDcuXg2jUJNq1Igk0hhBDiGZLSXATAt4gvkfGRVC1SlSlNptCrWi/s9HkgNLh5EyZPhu++g6QkdaxWLZX006MHSAMUq5K/bSGEEOIZcPbOWabvno5BZ2DVc6sAqFKkCnsH7KVeiXrpSv/lak5O8OuvKtBs2VIFnm3bqkxzYXUSbAohhBB52MHrB5m2axprz61FQ8OgM/BJq0/wclPJMA28G9h4hE9J02DTJvX12WcqoCxYEBYvhkqVoH59W4/wmSfBphBCCJHHaJrG9qDtTN05lS1XtpiOv1D5BaY0mWIKNHO1pCT48UdViP3kSXWsZ09o1kx937ev7cYm0si1wWYOTKLPleTvUQgh8p4vjn3BgN8HAGDQGehTvQ+T/CdRtWhVG4/MDGJiYNUqmD0bgoLUMVdXGDpU9TAXOU6uCzYND3qSJiQkmDrliOyLeZCdZ29vb+ORCCGEyK4kYxIhUSGmguvdq3Tn7X/epnuV7kzwn0CZAmVsO0BzOXcOmjaFu6pEE0WKqPqYw4appXORI+W6YNPOzg4XFxfu3LmDvb09en0e2tBsRZqmERMTw+3btylQoIApiBdCCJF7xCXF8dWxr5i5ZyaFnAuxf+B+dDod7k7uBI4OzBvli+LiVMIPqJnLAgXAzU11+nn9dZCJpxwv1wWbOp0OLy8vAgICCEqZPhfZVqBAATw9PW09DCGEEFkQGR/J0sNLmbN3DiFRIQBExEdwLeIapdxV/chcH2ieOQMzZ8LWraqtpKMjGAzw55+qRqaUL8o1cuUr5eDggI+PDwkJCbYeSq5mb28vM5pCCJGLhMaE8tn+z1hwYAH34u4B4J3fmwmNJzCg9gDyOeSz8QjNYM8elfTz+++px/78E7p1U9+XK2ebcYlsy5XBJoBer5f2ikIIIZ4p2wK38b8d/wOgYqGKTPafzCs1XsHB4GDjkT0lTYM//lBB5s6d6phOBy+8oAqxS/miXC3XBptCCCFEXncx9CKX712mQ4UOALxQ5QVeqvoSPX178kLlFzDo88jq1OnT0KWL+t7eHvr1gwkTVJ1MketJsCmEEELkMMdCjjF913R+PvMzRVyKEDAqAGd7Z/Q6PT/2+NHWw3t60dGwdy+0aaNuV6umamSWLq2yy0uUsOnwhHlJsCmEEELkELuu7mLarmn8cfEP07G6xesSFhtGCfs8EICFhsLChbBgAURGQkAAFC+u7vvpJ9uOTViMBJtCCCGEjR25eYTRm0ez86rar6jX6Xmp6ktM9p9MTc+aNh6dGQQFwdy5sGKFKsoOKtEnKCg12BR5lgSbQgghhI3Z6+3ZeXUnDgYH+tfszwT/CVTwqGDrYT2969dhyhT4/nvVXhKgdm2YPBm6d1eljESeJ8GmEEIIYUUJyQl8c/wbrkVc44MWHwBQvVh1lnddTiefThR3y0MzfY6OsGaNCjRbt1aZ5W3aqExz8czQaTmwOXZERATu7u6Eh4eTP39+Ww9HCCGEeGrRCdEsP7KcOXvnEBwRjJ3ejisjr1DSvaSth2YeRiNs2AB//w2ffZZ6/MsvVQJQ3bo2G5qwjMzGazKzKYQQQljQvdh7LDywkPn75xMaGwqAl6sX4xqNo6BzHujnnZCglslnzlRdfwB694ZGjdT3/fvbbGgiZ5BgUwghhLCQv6/8zQs/vkBUQhQA5QuWZ5L/JPrV7IejnaONR/eUoqJg+XKV+BMcrI7lzw/DhkmXH5GGBJtCCCGEGSUZk7DTq1+vfl5+aJpGjWI1mNJkCj18e5juy9VOnoTmzeGeapmJpyeMGQNDhoC7u23H9ohko8aBgDBuR8ZR1M2J+mU9MOhlz6g15YF3vBBCCGF7J2+dZPru6VyPuM62/tsA8HD24NDgQ1QqVAldbk+KiY0FZ2f1fZUqKqgsXBgmToS+fVUyUA6z+dRNPlx/hpvhcaZjXu5OvN/Vlw7VvGw4smeLJAgJIYQQT2Ff8D6m7pzK+gvrTceODz1OjWI1bDgqMzp2TPUs378fzp9X7SRBFWQvVSrHli/afOomw1Yf4dEgJyXkX/KqnwScTymz8ZreimMSQggh8gRN0/jr8l+0/KoljVY2Yv2F9ejQ0dO3J4cHH879gaamwdat0KGDqov5ww8quPz339RzypbNsYFmslHjw/Vn0gWagOnYh+vPkGzMcfNteZIsowshhBBZ9MfFP+jyfRcA7PR29K3Rl0n+k6hUuJKNR/aUkpNh7Vo1k3nwoDqm10OvXmq5vFYtW44u0w4EhKVZOn+UBtwMj+NAQBiNyhey3sAsLDgimIuhF/Ep5IN3fm9bD8dEgk0hhBDiCRKSE7gUdgnfIr4AtK/QnhrFatCyTEvGNRqXd2plnjgBPXqo752cYMAAGDdOzWLmIrcjHx9oZue83GDlkZUM3jAYo2ZEr9OzrMsyBvgNsPWwAAk2hRBCiMeKSYxhxZEVzN4zm2QtmSsjr+Bo54id3o4jg49g0OfMZeRMCw9XezHbtVO3a9eGnj2hcmV46y0oUsS248umom5OZj3PXCyVGf/PlX8YtH4Q2oNNAkbNyJANQ2hfoX2OmOHMVrB55MgRjhw5QsuWLSlfvvxjz7t79y5r166lbNmytG7dOtuDFEIIIazpftx9Fh1YxKf7P+VuzF0APF09uRB6gerFqgPk7kDz5k349FP4/HNVlD0oCIoWVff99JNNh2YO9ct64OXuREh4XIb7NnWAp7sK9qzFEpnx+4L3MX3XdNadX5fuvmQtmUthl3JEsJmlBKE9e/bQoEED3njjDQYNGsTevXsfe66mafTr14+33nqLJUuWPPVAhRBCCEu7HX2byX9PptS8Ury79V3uxtylbIGyLOm8hIBRAaZAM9e6cAEGDYIyZVTHn4gIVYA9pSh7HmHQ63i/q9ry8Oi8Ycrt97v6Wq3eZkpm/KP7SEPC4xi2+gibT93M1nXH/zU+w0ATwKAzUMGjQraua25ZCjaTk5OZP38+x44de+K5c+fORdM0WrVqld2xCSGEEFYVHBHMjN0ziEyIpFrRaqx+YTUX3rrA0LpDcbKz7pKrWQUGQvfuanl8xQo1m+nvD7//rgq0+/nZeoRm16GaF0te9cPTPe3r5unuZNWyR0+TGR8cEczWgK0ERwSTbEzmp9M/ERoTarr/nabv8Hqt1zk74iwruq7AoFOz7QadgaVdluaIWU3I4jJ606ZNM3XeoUOHmDdvHocOHWLgwIHZGpgQQghhaadvn+bgjYP0r9UfUB1/xjcaT9PSTelSsQt6XR6pEOjsDBs3qpJG3bqpzHJ/f1uPyuI6VPOira+nTTsIZTcz/uGEHx06CrsU5k7MHT5s8SHvNX8PgI4+Heno0xGAyoUr075Cey6FXaKCR4UcE2iCBRKEIiMjefnll1m8eDGenp6Zekx8fDzx8fGm2xEREeYelhBCCGGyP3g/03ZNY935dTgYHGhXvh3F3YoDMKvdLBuP7iklJal9l3v2wMKF6lixYrBsGdStC76+th2flRn0OpuWN8pOZnxwRLAp0ATQ0LgTc4cCTgXI7/j44une+b1zVJCZwuzB5pAhQ2jTpg3dunXL9GOmTZvGhx9+aO6hCCGEECaapvFPwD9M3TmVrYFbAdCho2vFrsQnxT/h0blAdDSsWgVz5qiEH4DXX4c6ddT3/frZbmzPsOxkxv/fv/9nCjQf9t2L35lmMnMTs64PbNu2jV9++QVfX19WrFjBihUruHbtGoGBgaxYsYKoqKgMHzdlyhTCw8NNX9euXTPnsIQQQjzjTt0+Rf0V9Wn7TVu2Bm7FTm/H67Ve58yIM6x5aQ1lC+auOpJp3L0LH3wApUvDyJEq0CxSBD7+WCX/CJtKyYx/3MK9DpWV/nBmfExiTLrzDDrD4xPU7t6FsWNh+/anH7AFmHVms0CBAvTt25cTJ06Yjt27dw+DwcC+fft44YUXcHV1Tfc4R0dHHB0dzTkUIYQQwqRovqKcvn0aZztnBvkNYlzjcZRyL2XrYT29AwegRQuIjVW3y5WD8eOhf3+1T1PYXEpm/LDVR9BBmkQhHZCgCySf5zZO3ylianP6cauPKeRSiGWHl5GsJWcu4efzz+HsWWje3JI/TrboNE3LVmNQnU7HN998w6uvvvqf53Xp0gUnJyfWrFmT6WtntrG7EEII8aiYxBhWHlnJwRsH+fqFr03HN17YSP0S9SmSL3cWKjeJiICU340JCVC+vKqROWmSyjjPIf3KLVXAPLdKqbN5LTyYJP0NjEST5PQv9zRVRvKV6q+w+sXVaR4THBGcPuFH0+Dvv+Gvv2DWQ/uLFy9W74X27a31I2U6XsvSzOaNGzf4448/TLe3bdtGXFwclStXpkmTJtkfrRBCCPGUUgqxz98/nzsxdwAYXm84Db0bAtC5YmdbDu/paJpaIp0xA86fV/Uy7ezAwQH27YPixUGXcwI5SxQwz4myElB3qObF1bgNDN04xNTpB03tG+7u253RDUene0yahJ/ERPj5ZxVgppSg7NEDGjRQ3w8fbt4fzoyyFGyGh4ezb98+AAYMUP029+3bh729/WODzfbt22Nvb/+UwxRCCCEydivqFvP2zWPxwcVEJkQCULZAWSY0nkAtz1q2HdzTSk6GdetUkHnggDqm16sAM+X3bokSthtfBlIKmD+6bJpSwNyaNS4tKasBdXBEMEM2Dk5zTIeOra9tpXmZ/1j6joqClSth7ly4elUdc3GBgQNz3Gv/ONleRrckWUYXQgiRGQeuH6D5l82JS1K/8KsVrcZk/8n0qtYLO73ZC65YT1wcfPMNzJ6tZjEBnJxUdvm4cWq5NAdKNmo0mfHvY+tKprSJ3DWpVa5eUn9cQJ3yE6UE1HFJcdjr7THoDWwN2Eqrr9M3utn62lZalGmR8ROdOKH25N67p24XLap61g8bBoVsV84phUWW0YUQQghbi4yPxM3RDYDanrUplq8YXm5eTGkyJe8UYj96FAY/mAUrUABGjFCZ5in9y3Oo7BYwz02e1BFIB/zf7wc5dv8s8/d/yqJOi3ixyov4FPJBr9OnKWmUYUvJqChISaauUkXtzy1SRH3I6NdPfejIZSTYFEIIkSukFGI/FnKMi29dxN5gj73Bnn0D91EsXzF0OWjPYpbduAGHDqnuPgCNGsHLL0P9+mq51M3NtuPLpOwUMM9tHg2ok7hLkv4Gdsbi6DAQYfc7QQl/cOifaAC+Ov4VL1Z5Ee/83izrsowhG4ZknGG+e7fqV3/sGFy6BPb26mvrVlXWSp97P0RJsCmEECLH0jSNv6/8zbRd09IUYt95dSetyqolSU/XzHWry5HOnVMJH998owKLq1dTl0e//962Y8uG7BQwz20eDpQjDX8RZr8AdNqDmkYG0CUD4O3qw8et36F39d6m8wf4DUjbUjKfF/z2m3oP7N2b+iQ7d0KrB0vuZXNxDdgHJNgUQgiR4xg1I2vPrWXarmkcunEIADu9HX1r9GWi/0QqF65s4xE+pX37VNLPunUq0xygYUO4cydH7MXLrpQC5iHhcRkuM6fs2Xy4gHlukxIoJ3E3NdCEBxs2k7E3lqNAYh9+eGUk/hXSl9nyzu+Nt30h+Ppr1e3p4kV1h4ODWiYfNw4q5/L39yMk2BRCCJHjHLl5hO4/dQfIW4XYT59WyR07d6Yee+45VSOzUSPbjctMnlTAHOD9rr65OjmoflkPXN0ucSc6NDXQfIhH4kDKutWnYbnCj7/I6dMwdKj6vkABVbborbfAMxfP0v8HCTaFEELYXExiDAevHzSVgKlbvC4vVH4B3yK+jGowKvcXYk9RoICa1bS3h759YcKEPDeL1aGaF0te9UtXFsgzl9fZ1DSNTZc2MW3XNE4n7SK/vjtourQBp6bH3lg8fUAdGAgHD0LPnup23brq9ffzgwEDcs2e3OyS0kdCCCFs5uFC7JEJkQSNDqJovpydcZ1pkZGwfDmcOQMrVqQe/+kn8PfPNTUSsyuvdBBKMibx8+mfmb57OiduqXbcDgYHnq8wmEOXHLmSNA90RtD0lLMbw6Lnx6UG1EeOqP2YP/+sPmAEBeX4igJZIaWPhBBC5FghUSHM2zuPJYeWpCnEHnAvIPcHm7duwWefqfaB9++rY2+9BTVrqu9feslmQ7Mmg16Xa8sbBUcEczH0IgdvHGTp4aVcuXcFAFcHV4bWGcqYRmMo7lacZKPGhlOvcfL2OaoXrUyXatUw6IA//1SZ5f/+m3rRVq3U+yEPBZuZJcGmEEIIqwmJCuF/2//HqqOriE+OB/JQIfZLl1QR9i+/hHj1s1Gxoloqr1TJpkMTmbfyyEoGbxicph5mYZfCjGowihH1RlDQuaDpuEGv47ka1XmO6urA0aPQv78qxg6qT32vXjB+PNSubcWfImfJxf+qhRBC5DaappkCzUbejZjSZAqdK3bO/YXY//4b2rcH44MApUEDlfTTrZsKOESOdyvqFv/b/j8+P/x5mkBTh449b+zBp5DPky9SvLjqXZ8vHwwaBKNHqxqZzzgJNoUQQliMpml8eexLXq/9OgBebl7MbT+XqkWq0qx0s9xbiF3TICQEvB7szWvSBIoVU7NXkyZB06aQW3+2Z0zAvQBm7ZmVZrb9YRoa1yOvpw82b95U2yUuXoQ1a9SxYsVU3cyGDaFgwXTXelZJsCmEEMJiAu4H8Mbvb1DMtRgdK3REp9MxvN5wWw8r+5KSVILPzJkQEwNnz6qZSycnlQhUoICtRygy6eStk0zfPZ0fT/1IsqYKsdf2rM2xkGNoDxVtStdS8uxZtV1i9WpISFDHjh9P3ZPbsaO1foRcI5evWwghhMjJDt84DMAH2z7IvbOYANHRsGAB+PjAK6+o4OLGDVUvMYUEmjlWcEQwWwO2EhwRDED/tf2p8XkNvjv5HclaMh0qdGDba9s4PPgwy7sux6BTWx9MLSXdSsCOHdC1K/j6wqpVKtD094e1a6F6dRv+dDmfzGwKIYSwmMM3VbBZ2zOXJkeEhqogc+FC9T1AkSIwcqQqxO2RezvhPCseTvjR6/Qs67KM8gXLo9fp6enbk0n+k6jtlfr+TNdSMr+36vT0/PPqBJ1OfT9hQp4oxG8NEmwKIYSwmJRgs07xOjYeSTadOgUffqi+L1dOZRX37w/OzjYdlsicwPuBDFo/yLQsbtSMDNkwhONDj9O7eu+0y+MP8bYvhHfUfSjjrQ507Ajly0ObNjB2rKoyIDJNgk0hhBAWoWmaaRm9jlcuCTaPHVN7L/v0UbebNVMdXtq1gxdfBDv5tZkbxCbG8sWxL/jf9v+l2X8JkKwlcyfmDi3KtEj/wLt3VX3UhQvB1RUuXFCvuYOD2qtpb2+dHyCPkX81QgghLCLwfiD34u5hr7enWtFqth7O42maKr49cyb89ZcKMjp1Unswdbq03X+eYbmhI9D9uPssObiET/d/yu3o2xmeky7hB+DKFZg7V+3FjI1Vx/LlU20mKzw4VwLNbJNgUwghhEWkLKFXL1YdRztHG48mA0lJ8OuvKsg8rMaKXq+SQKKjJeHnIZtP3UzX69zLxr3OU7r8+BTyUfsqged/eJ7tQdsBKO1emvGNx2PQGXhr01ska8mpCT8PzufsWfjgA1W6KKVGqp8fTJwI3bvLTLaZyN+iEEIIi8jvmJ/25dtTs1hNWw8lvd27oV8/NaMFag/mgAFqP17ZsrYdWw6z+dRNhq0+8shiNISExzFs9RGWvOpn9YAzo6SfAX4DGF5vOHdj7jK5yWR6Ve2FvUHNRnat1DVtwk+Ke/dUKStQRfknToSWLaVGqpnpNE179P1jc5lt7C6EEEJkmqalBhFXr6qEnwIFVN/yESOgcGGbDi8nSjZqNJnxb5oZzYfpAE93J3ZNamW1JfXgiGBKf1o6TZcfg85A4OhAirsVB8i4I1VCAnz/vdqXOW5c6vH//U9ll9eoYeGR5z2ZjddkZlMIIUTeFhQE8+bB7dvw3XfqWKlS8Mcfqk5ivny2HV8OdiAg7LGBJoAG3AyP40BAGI3KF7LoWDRNY9fVXUzYMiFNoAkq6edS2KW0s5YpIiJg2TL49FO4fh1cXFRFgUIPxvveexYdt5BgUwghhAVEJ0QTnRhN0XxFbTeIEyfUfswffoBk1SGGDz5ILVvTrp3NhpZb3I58fKCZnfOya+OFjUzdNZU91/ZkeH+GST/Xr8P8+bB0qQo4QbUXHTVKZZcLq5EOQkIIIczuj4t/UGx2Mbp818W6T6xpsHWrqotYsyZ8+60KNNu0UZnmPj5PvoYwKermZNbzsuubE9+w59oeHAwODKkzhKmtpqbv8vPwrOZPP6m9t7NmqUAzpetPQIDqXe/mZtHxirRkZlMIIYTZpWSil3ArYd0n/vFH6N1bfa/Xw0svqU4vfn7WHUceUb+sB17uToSEx6VLEILUPZv1yz59J6WU7HLv/N78dfkv2ldob5qtnNxkMqXdSzO64Wi83FQyUt+afVOTftxKqKAyZd+gv7/6s1kzlfTTsaN6PwibkGBTCCGE2Vmtc1BsrNqTWbmyuv3cc1C6NHTpojLLy5Wz7PPncQa9jve7+jJs9RF0kCbgTEkHer+r71MnBz2cXZ5isN9glnZdCkAtz1rU8qyV5jHe+b3xdvFU5atmzVIJXps2qTtLlIDz56WyQA4hwaYQQgizskrnoLAw1enls89UkHHqlJq5cnaGixelALcZdajmxZJX/dLV2fQ0U53NwzcOp2kpmaK8R/nHPiY5Kpqg2YsotnIx+YKD1EFnZwgJAU9PdVsCzRxDgk0hhBBmZdHOQSmZ5StWqMLroLKLr11TM5oggaYFdKjmRVtfT7N3EJq0ZRJz981NF2gC1C9RP/0D7tzh0nvTKPz1SsrFqKSfMOf8/NroOcq+P5HWKYGmyFEk2BRCCGFWFukcdP48fPRR2szyWrXUfryePaXTixUY9DqzlzdytHMkyZiU/rkyyi4HTi36imqfzwPgqnsxltd/gZ+rtyHe3gn+CGKJRyGbdTQSjyf/OoUQQpiVRZbQr11TmeWgMssnTlR/SqeXHC0l6aeCRwWu3LvC9N3TGdVgFB0qdABgZIORtC3XlguhFxiyYUj6lpL796vEn7ZtSTZqjNBX5YNydVhTrQ2bKzUmWW8wPZcO+HD9Gdr6eua4nu3POgk2hRBCmFWLMi2IiI+gXfls1rFMTlZJH/fuweDB6ljr1irAfOklqGPhpCNhFhkl/QDEJ8Wbgs3CLoVpWropTUs3pX2F9iq7vEA5vHedgNHNYOdOVa7q7FkOBN4nKMbI6z0/zPD5rFlgPidJSFAlZffvV19duqh/JjmJBJtCCCHMqn2F9rSv0D7rD4yNhS+/hDlz4PJlcHeHl19W5Wx0Opgxw+xjFZYRcC8gw6SfvjX68kGLDzJ8jLdjEbz//QtmD4ezZ9VBe3to3BiionJMgXlb0jQIDEwNLPfvhyNHID4+9RyDQYJNIYQQIq3QUJVZvmAB3LmjjhUqBG++adtxPQOSjZrZk34AXl7zcoZJP2/UfoNyBTMoR/Xrr+r1vnlT3c6fH4YMUd1+SqharUXd0u/tzIilC8xbU3g4HDiQGlgeOKC6rj6qYEFo0EB9tWlj/XE+iQSbQgghzOZS2CXuRN+hpmdNXOxdnvyANWvgtdcgJkbdLlNG1cd84w3pWW5hm0/dTFfOyCub5Yzuxd7D0c7R9Jq/UuMVDtw4kOacdEk/mpa659bDQwWaJUrA6NEwaJCa2X6INQvM24KmqTy4vXvV1549cOaMOv4we3uVG5cSXDZoABUqgFFL/eCw97L5PjiYgwSbQgghzGbV0VVM2zWNQX6DWNZ1WcYnJSSk9qauXRvi4tSfEydCjx6SWW4Fm0/dZNjqI+mCtpDwOIatPsKSV/0yFXDeiLzBvL3z+Pzw53zS6hNGNhgJwPB6w7HX2/PWprfSJ/2cOAGzZ6vActo0daHmzeG336BTp8f2LbdWgXlriYxUM5UpweXevWqb8qPKlk0bWNauDU6PTN6a84ODJeg07dGY2fYiIiJwd3cnPDyc/Cmtp4QQQuR47b5px5YrW/i88+cMqTsk9Q5Ng3/+gZkz1RLpmjWp9508CdWqSWa5lSQbNZrM+DdNYPKwlBnCXZNapQvcUrLL7fR2fH38a74+8TUJyQkAdPbpzIY+G9KdfynsEhUKlsf78EX1+v/5p7rTzQ1u3ABX1yyNP6cHVhlJ2Wu5e7f62rtXve2NaXOncHKCevWgUaPUr2LF/vvaj/vgkPLKZfaDQ3ZkNl6Tj49CCCHMQtO09G0qk5JUYDlzJhw9qo7Z26uNZ0WLqtvVq9tgtM+uAwFhjw004fFZ3Y/LLm9SqglTmkyhY4WO6a7l7eKJ9x+7YNY4lckCqtNTjx6qZ30WA02wXIF5c0pKguPHVWC5a5f688aN9OeVLp02sKxZ87ETuxlKNmp8uP5MhtsKNHJOOSgJNoUQQphFUHgQYbFh2OvtqZ6vHCxcqDLLAwPVCS4uMHAgjBmTGmgKq8tOVndwRHC6QFOHjjUvreHFKi8+/iIffQT/+5/63tlZ7cU1Q896SxSYfxqRkbBvX2pguW9faoOrFHZ2qmqXv79KsG/UCIoXf7rnze4HB2uTYFMIIYRZpBRzr1a0Go7ffAdvvaXuKFxYfT9ihMoyFzaV2Wztwq4OrD23ltqetbly70q6GU0NDQ/nR5Jxbt+GqKjUYPKNN2D5chg6FIYPV++FPOD2bRVY7tihvo4fT78k7u6ugsomTVSAWa+e+rxl1nHkknJQEmwKIYR4epcvc/jwegDqFq8LLfvD11/D66+rbHNz/5YV2fakrG5Iws51D4P+nMDZu2cZUW8Ek5tMRq/Tpwk402SXX7yoZrG//BLat4d169Tx0qXh6tVcn/QVFKTqy+/Yof48dy79OWXKpAaW/v5QtaraMWBJmf3gYOtyULn71RdCCGFbhw7BrFmwZg2HhrhAsQdtKl1dVaqtyHEezepO5C5J+hvojYWINxwm3O43kpPvwF3I75ifovmK4p3fm2VdlqVvKXn6GswaCWvXptbouX1bVRl3dFS3c1mgmVKCKCWw3LFDxcuPql4dmjaFZs1UkPmgHKhV5ZZyUJKNLoQQIms0TWUUz5oF//5rOry/R0P2DutKl1ovpa2nKHKkzaduMmLtHK4kzQWdlppRAhTLV4wxDccwtO5Q3J1S612assvP3sJ76kK1lpyiSxeV9NO0aa6qLKBpaqZy27bUr0cLpxsMar9ls2bqx2vSRJUGzQlSstEh43JQko0uhBAid9myBcaNU3VbQM1avfwyTJhAgxo1aGDb0YksqFYqmUDjPBVogik6mdpqKmMajcHJLv3Sq3d+b1Ur84/FKtC0t4e+fdV7wtfXiqPPPk1T3TBTAsvt29MHl05O0LBh6sxlw4bZSpy3ig7VvFjyql+6clCeOagclASbQgghMi8xUQWa+fLB4MGq20upUrYelciCC6EXmLl7Jr5FfNMl/QA0KtkobaB57x58/rlqU9OzpzrWvz+EhKjEn6dNqbawR4PLbdtSu6KmcHJSyTwtWqiv+vVTdwHkBjm9HJQEm0IIITIWEqL6lRcsCOPHq2MdO8KiRdC7tzr+wMYLGwmLDaNl2ZZq5kvkOIdvHGb67un8cuYXNDSalGry30k/V6/CvHkqmzw6Ws1cdu+usl5cXFJLGuUwmgYBAWqHR8rXrVtpz3F2Thtc1quXu4LLjOS0clAPk2BTCCFEWufPq8zir79WiR4eHjBsmJrN1OlUCZtHfHbgM/66/BdLOi9haN2hNhi0yIimaWwN3Mr0XdPZcmWL6XjXil2Z5D+Jc3fPpU/6CQiFWZPhhx8gOVk9oHp1tR8z56V5AHD9OmzdmhpcBgWlvd/JSWWI56XgMjeRYFMIIYSyd6/q9LNuXWpQ0bAhTJqkpoIeQ9M0U43NOl51rDFSi0s2ajl2SfJJUlpK+hTyYfLfk/n25LeAmrXsXb03ExtPpHox1bXJv5Q/7Su0V0k/HhXwnvk5fDIw9WKtW6sgs127HJX0ExqaNrg8fz7t/XZ26q3bqpX6athQgktbkmBTCCEEzJgBkyen3u7aFSZOVNNBTwgyroZfJTQ2FDu9nSmIyc1yY+/tFEsPLWX4H8Mxakb0Oj39avTDyc6JAbUHMK7ROMoWLJv2AYmJeBsK4l2mhbrdvDlMnw4vvaS2Tvj5Wf1nyEhcnOrMs2UL/P236nz58CSrXq+GmhJcNmmiJuJFzpDt0kdxcXE4ODigt0DFUil9JIQQFhYfD+HhqW0jz59XjZlfeUUFGVWqZPpSv579le4/dae2Z22ODDlioQFbR0oZmUd/MVqjjMzTiE6IZvae2Xyw/YM0xw06AwcHHaS2V+20D4iKghUr1J7MV16BqVPVcU2D4GAoWdI6A38MoxGOHUsNLnftUgHnw6pWVROvrVqpjPGHthALK8lsvJalSDE8PJwFCxZQtWpVnJ2d+e6779Kds2fPHp577jkKFiyIq6srLVq0YP/+/Vn/CYQQQpjf/ftqFrNsWRg1KvV4pUpw8yasXJmlQBPIM0voyUaND9efybA4dsqxD9efIdmYc/YthsaE8uG2Dyn1aal0gSZAspZMeHx46oGQEHj7bRVMjhmjkoB+/TW116JOZ7NAMyAAli1Tk6pFi6q6lpMnq2AzLk4lvb/2GnzzDdy4AadOwfz58NxzEmjmdFlaRv/uu+84f/48P/74I9WrZ7xUMmfOHAYOHMhXX32FXq9nypQptGvXjlOnTlHSxp+UhBDimRUcrH4zL10KkZHq2N69EBubuh8zm7+xD908BECd4rk72DwQEJZm6fxRGnAzPI4DAWE2z/oNjghm7t65LDu8jOjEaABKu5fmavhVtIfCZVN2+blzqUlfCQnqzooVVX3Mfv0s31cxA5GRat/lX3+pHgGXLqW9380NWraENm3UV+XK1tk2mpv36+ZUWQo2hw0b9sRzfvnllzS3582bx7Jly/j77795/fXXszY6IYQQT+fMGZX08+23kJSkjlWtqpI+evcGB4enurymaRy5qZbOc/vM5u3Ixwea2TnPnB5O+vHO782bf7zJuvOq/3gtz1pM9p9Md9/ufHXsq/TZ5fm9YcoItWwO0KiR2o/brZtVg8zkZLXX8q+/1NeePalvSUhN6mnbVgWX9eqpmvHWlJv36+ZkFk8QunPnDsnJyRSUOW4hhLC+jRvhq6/U982bqyCjY0ezTRHpdDqODz3O4RuHqVGshlmuaStF3dJ3zHma88xl5ZGVDN4w2JT0s6zLMiY0nsC9uHtMaTKF9uXbo3vweg7wG0D7cm25tP4rKlRsiLdfW3WRsWPV2vP48Srpy0qCg9W+yz//VMvhoaFp769QQSW6t2unZjFtmabxuP26IeFxDFt9JMfu180NLBpsaprGW2+9RZkyZWjfvv1jz4uPjyc+Pt50OyIiwpLDEkKIvCk5We2/K1hQTQ2B6vJz/DiMHKnaolhAcbfiFK+Us7vIZEb9sh54uTsREh6X4b5NHaoFYP2y1mmKrWkaP5z6gYHrU0sRGTUjQzYMIXB0INv7b0/7gLg4+PprvOfMwfvCBejRA35+EGyWLw+//WbxMSckqGSeTZtg82a1r/Jh+fOrhJ727VWAWa6cxYeUKU/ar6tD7ddt6+spS+rZYNFgc/z48fz7779s27YN5/+o0TZt2jQ+/PBDSw5FCCHyrpgY+PJLmDsXLl9WmRUHD6rZS3d3WL3a1iPMFQx6He939WXY6iPoIE3gkRJevN/V1+LBhlEz8tvZ35i+ezqHbhxKd3+ylsylsEupnZrCwmDxYtXtKaXJd4ECapOjpll8o2NgoAosN22Cf/5RzYZS6PVqObxdOxVg1q9v/aXxzMhN+3VzI4sFm5MnT2bFihVs2bKFWrVq/ee5U6ZMYezYsabbERERkkwkhBBPcveuah25cKH6HlS3n06dVA/zp9yPmRnvb30fgP61+qev4ZgLdajmxZJX/dLt2/O00r69705+x/+2/4/zoapKuZPBifjk+IyTfgCmTYOPP1YfOED1qR8zBgYMUBk2FhAXBzt2pAaY586lvb9YMejQQX21bQuFckFslpP362ZKbKxK02/USHV7ymEsEmy+/fbbLFmyhD///JP6mVi2cXR0xFFK+wshROYtWKA6+8TGqttlyqjM4tdft1o1a03TWHxoMXdj7tK5Yuc8EWyCCjjb+npaNCP50YSfFIdvHOZ86HkKOBXgzXpvMrLBSH4///sjST+fpz7G2VkFmrVqqaSvnj0tMnV49ara/rtxo8ogT4ltAQwGFeN07KgCzFq1bJLc/lRy6n7dTLt5U7WU7dNHBZ05TJaCTaPRSEJKyQQgMTGRuLg47OzssLNTl3rvvfdYsGABGzZsoFatWsQ9qML68DlCCCGywWhM/S1eqpQKNOvUUUFG9+4qndeKrkVc427MXez0drk+OehRBr3OYsulDyf86NAxuclkprZWRdXHNhqLl5sXQ+oMwc1RzUwO8BtA+/LtuPTn91T48ne8yztDSmOfgQNVdYE2bcy6XJ6UpLLFUwLM06fT3l+8uAosO3ZUT12ggNme2iZy2n7dJzp1CrZvhxEj1O1y5eCtt8DHx7bjeowsdRDaunUrHTt2THf89ddfZ8mSJQAUKFDAFGA+7N133+Xdd9/N1PNIByEhhHhA09R65axZKrMi5f9Ro1FlYjRtarOe1b+d/Y0Xf3qRWp61ODrkqE3GkNsERwRT+tPSGDVjmuPXxlxLM8NpkpgIP/wAs2fDiRPqWJ06cCj9Xs6ndeeOeqtt3Kiyx+/fT71Pr1ezl507q10aNWrkqFbpZpGSjQ4Z79e1eTa6pqnU/rlz1Quk08GFCyql30YyG69l6WNwy5YtMwwkH3b/4XenEEKI7ElIUEHGrFmpKb0XLsCUKWrdUq9XPfpsKCV5JTfU18wJhbrP3T3HmM1j0gWaQNqEH1AVz5cvV+0kg4PVsXz5YNAgGD3aLOPRNFWoYMMGFWDu35+237iHh5q57NxZJfjkhr2XT8PW+3UfKz4evvtOBZkp/xfo9fDii6mdn3I4WdcWQoicJCJC9ez79FO4fl0dc3VVJYxGj1aBZg5x+GbuaFOZEwp1j9k8hvn756dJ9EmRJuEnRZ8+KgoElXEzcqTak/eUNavj4tSey/Xr1eWvXUt7f61aauayc2do0CBHvd2swhr7dbPk0CHo0gVu3VK3XV1V8tfIkTmnblQmSLAphBA5yYQJKtgE8PRU/cuHDs1xm+I0TUsNNnNwm0pbFerWNA2jZsSgV9Fa5cKV0dB4vvLzVClchZm7Z6bt8nM9EhJDU6cPhw6FixdVEfZXXwWn7Cem3LqlZi7Xr1ersA+XJnJ2VhnjXbqoILNEiaf5qfMGS+7XzZS4uNTXu3JlNbPp7a3+Lxg4MMf9X5AZWdqzaS2yZ1MI8cw4c0b9YkmZpTh9WmUUjxungowcWqnjdvRtys0vR3xyPJFTInGyy3lZuslGjSYz/n1s/cSUpI9dk1qZZeYqOCKYc3fPcTnsMsuPLGdY3WEM8BsAQFxSHFfuXcG3iK/p3EuhF6lwMRTvBV+pacb33oOUmtOapr6ykdataXDypAou16+HAwfSLo+XKKGCy65d1Tbg/yiDLaxF01TCz9y5KvX/6NHUTbHHj4Ovb44sUGqRPZtCCCHMQNNUocJZs9SUU79+qS0lq1ZVAWcOz74omq8o4ZPDCQoPypGBJli3UPfnhz5n+MbhaZbJFx5caAo2neycTIEmycl4/7UP71mzVCQI6vW+cSP1gjpdlt4DiYmwcyesW6e+goLS3l+3rgouu3SB2rVz/Nvr2ZGYCD/9pILMIyo5CZ0Ojh1TLxRAzZo2G565SLAphBDWkpysWgY+GmTExaUta5RLIgGD3kC5gjl335g1CnVHJUQxc/dMPtrxUZrjOnR8+dyX6R+wahVMnao6PYGaue7fX/Uur1gxw+d4XHJTZKRKSl67Vn1meTg/19lZlSTq2lXtvyye+7uJ5i3376vtMp99lro329lZvRdGj37seyG3kmBTCCGs4dtv4f330wYZr7+ugowcWhsvt7NGoe7+a/vzy9lf0h3X0LgXdy/9A/buhcuXSSxQkCs9+hExaCh+dSs9dhn/0eSmpChHHIK9KRRahhMHnHio9DWFC0O3bvDccyrQdHHJ9o8lLG3vXtWUAdTe7DffVPt082jKvwSbQghhDUFBKtD08FCFmN98E4oWtfWoskXTNJp80YSyBcoyt/1ciubLmT+HJQp1Xw2/iou9C4VdCgMwot4Ijtw8QuD9wPQtJSPt1es8YIBpSXTHc69xMMSRFT4tiXVwgl8v4/XP9Qwz41OSmxJC8xFzoTwxF4uRcFNlowc8OKdCBXj+eRVgNmr07GWP5xp796q9mL16qdsdOkCPHmrauXfvHLs321wkQUgIIcztyhW1B6t9e7WOCXDvHqxeDW+8YbV2kpZyNfwqpT8tjZ3eLscmB6V4mkLdD7eUjIyPZMbuGXx78lvGNhzLjLYz1DUfZJ1/eezL1JaS6Fl63Y8BK4+o7RG9e8N33z02M/7RsWgaHDio8eLEIG6fLExSmGua8x287uHic4tSte9zeE4D7Ay5Y9vFMydl28ycObBvn/qgee1anppylgQhIYSwtoMHVaeXNWtUkHH4sMrI0OlUfcS33rL1CM3i8A1V8qhqkao5OtCE7Bfqfril5KMuhF1A0zR0Oh06nQ6DzsCA2m/Q/qo9l76aS4V/j+Md8aDDT4cOMGgQyUaND9efyXCGVQMw6hg7/wZ/OHuydq2Oa9d0QBl1gt6IU+m7uFS8hXP5W9i5xQMQDhwMfPrkJmFmkZFqb+78+RDwYA7awQFeeEHVnbJQsBkZH4lepyefQ877MCvBphBCPA2jETZtUkk/27enHm/fHiZOtN24LCAxOZFvT37Lxzs+BnJ+MfcUWS3UHRwRzOD1gzGSNtDsUL4DH7b8kPol6qd/UMeOeP/5J96getT37a1qZNZQPeMPXA5NlxmvJemJDSxMzAVPYi8VwxjrwNkH9zk5G9GXuoVLxRCcy99G75iU4VifJrlJWMBvv6m92OHh6nahQjB8uNo6U6yYRZ7yVtQt5u+fz+KDi3m32buMbzzeIs/zNCTYFEKIp9Gvn0r+ARVk9E4bZOQV686tY+TmkVwNvwpAQaeCjGww0sajyrysFOq+GHoxXaAJMKnJpNRAMzxcbYewe/BrtHVr2L0bhgxRxbdLlkzz2JSg0JhgIPZKEWLOexF7pShaQuqvYb1TAi3aJTJqQD7yl79H/2+OPHGsT5PcJMwkPj51z6Wvr3pvVKyokv/69rXYTObF0IvM3jObr45/RXyymu3edGmTBJtCCJHrhYerLAzXB/vounWD339X7SQzCDLyChd7F66GX8XT1ZNxjcYxpM4Q3BzdbD0ss4hPiuebE9/g5+WHn5cfPoV80Ov0aZbQTS0lg4PV8ujSpbBiBbz0kjph2DDVtzyD7i4REXBsa37u/OanAsyk1Cweg2usWh6vGIJTyTA+HtKARuXzkWw0f3KTMCOjUdWbmjtXzVj+8IM6XqmS2p9Zr162CvJn1sQtE5m9Z7YpKa2hd0Mm+U+iW6VuFnvOpyHBphBCZEZwsOpXvmwZvPtu6hJ59+7Qrl2ubCH3OHdj7jJ/33xcHVyZ1ESVZ2lTrg3fvfgdL1R5Icfv08ysyPhIlh5eyty9c7kZdZPnKz/Pb71+wzu/N8u6LEtN+NEZWFr7PbxHvgvffacKcYMqcJkSbLqmTeK5d099BvnlF1ULMyHBDVDBuV2BaFwqhuBSKQQHr/uqfjtpg0eDXsf7XX0ZtvoIOjJObnq/q6/tenY/q2Ji4OuvYd48uHBBHXNyUi94St/6Bg3M/rSPtj+tVKgSGhqdfToz0X8iTUs1RZeD6/NKNroQQvyXkydV0s9330HSg31zbdvCX3/ZdlwWcD3iOnP2zmHp4aXEJMbg7uhO0Ogg3J3cbT00s0jJLvdw9mDNmTUsPLiQ+3H3ASjhVoIJjScwssFI0y/t4PBrXNr6CxW+/B3vdVtTL9Ssmfqw0bFjmtmru3dV/PnLL/D336lvF1ATXrWbRbI98RgORSNSI0b+OzP+0TqbAF5PSG4SFhASAosWwZIlEBqqjrm7q20Tb72lepdbQJIxiZ9O/8TM3TMZWncoQ+sOBdRs/IXQC1QvVt0iz5tZmY3XJNgUQoiMbN0KM2aoaakULVrAhAkqyMjBswhZdSnsEjN3z+TLY1+SaFSzdnW86vB207d5vvLz6HWWWw60lsdll1cqVIlJ/pN4pcYrOBgc0j/Q3x/27FGvd/fu6vWvn5ogdPeuygn56Sf1lklOTn1otWqqlGKPHmorn06XveDxcR2EhBXNmaP2YgOUKaO6/LzxBrhZZitJTGIMK4+sZO6+uQTeDwSgZrGaHB1yNEfNYEqwKYQQT+OVV9Rspl6fGmTUq2frUZndo0FYs9LNeKfpO7Qt1zZH/VJ7GsERwZT+tHS6QHNZl2W8UfsN09Ik0dHw5ZcqycvjwV7IjRvV19ixqoI6amJr7VoVYP7zT9oA089PvV26d1ezmRmR4DGH0zQ1NW1vrz5ggtqr3aOHmsl8/vnUxDAzC40JZeGBhSw4sIDQWDWDWsSlCCMbjGR4veF4OOesPbpSZ1MIITIrKgpWrlQ1EVMihAkTVMAxZgyUy7n9v7MjPikeRzuVPduiTAt06Ojk04kpTabQpFQTG4/OfPYF72P6run4FvHNsF6mTyEfFWjeuQMLF6pl0tBQ1bf6nXfUSZ07Q+fOhIXB2lWpAebDS+R+ftCzp/oqX/7J48pKZrywooQE+P57lfRz4gTUqaNq5+p0asl8yxaLD2HwhsH8evZXAMoWKMv4xuN5vdbrONs7W/y5LUmCTSHEsyskBBYsUPuw7t1TbQVXrFD31aql7ssjNE3j34B/mbprKh7OHvzc82cAynuU58qoK5RyL2XjEZqHpmn8eflPpu+azvYgVff03N1zGWeXRxhUDcQvvoC4B8va5cpBKfV3ce8erFunAswtW9IGmLVqqdygnj1NE54itwoLU9UFFiyAmzfVMRcX1f8zPl4lAFnIiVsnKOJSBC83tYVidIPRBNwLYJL/JLr7dsdOnzfCtLzxUwghRFacO6f2YH39tZrNABUxNG5s23FZgFEzsuHCBj7Z+QkHrh8AwMHgwO3o26ae5rk50ExJ+ilXsJyaydw9nWMhxwCw19vTt0ZfJvpPZNfVXWmzy2/WwbtWc7VkCmqLxIQJRLV7kd83GvihG2zenJp4DlCzZuoMZsWK1v9ZhQUsWqSSvWJi1O3ixVXCz5AhqdnlZqZpGtuDtjNj9ww2X9rMmIZjmNt+LgBNSjXh8ODDeWYLSwoJNoUQz5YBA1QruRSNGqkl827dVP3MPCIli3Xarmmcun0KACc7Jwb5DWJ84/GmQDM3W354BUM3DElXgD2ffT4G1xnM2EZj8c6vsoQrFapI+wrtuRR2iQoeFVQZI+0AdOpE/MgJbIxqzg8/6tjwGsTGpl6rWjXo1UsFmI/bgylyEU1Tm2xT9lx6e6tAs0YNGDcOXn5ZtZa0gGRjMuvOr2Pm7pnsv74fAL1OT0R8hOmcvBZkppBgUwiRtyUnqz1XKSVqSpZUt7t1U0Gmv79tx2chK46sYNjGYQC4Obgxot4IRjccTTFXy7TMs7Zle3YwZMtgeKTk+Qs+Q1j+/CcUcnmwJzI+XnV4mjMH7x9/xLtaCwASprzPvvrjWbGvGmt7qnbWKXx8VMzx8ssqi1zkAUlJqmzAnDlqH+7//Z863qULbNumyllZMND75vg3fLzzYy6EqtqcTnZOvFHrDcY2Gkt5j0xs9M3lJBtdCJE3xcaqzOK5c1UB5i5d1PGwMJUQksemqaISogiOCKZy4cqm23WX1aVvjb6MqD+CAk4FbDtAM7kdfZtRG6by49mlaLr0fcGLxU/lyz796eDtrPbhzZ9v2odnHDiIbb2X8cMPqhZmWFjq40qWTA0wa9fOU5Wtnm2RkSr5b/58CAxUx0qVgoAAi3b4edTYP8cyb988CjoVZES9EbzV4K08sbog2ehCiGfT3btqH9bChep7UEFHSrDp4ZFa1iYPuBd7j4UHFjJ//3xK5C/BsSHH0Ol0uDq4cnbE2TyzLBd4P5A5e+aw8uhKYpNiMbXVefjH0/SUiHAkbNhItON/onswXZlQtASbKo1mwu+DuLgi9fRixVSSz8svQ8OGVo09hKUFB8Nnn6mOX+Hh6lihQjBihEoKs+CLfSPyBp/u+5TnKz9P45JqH/iYhmMomb8kg+oMwtXB9QlXyHsk2BRC5A2XL6tZzC++SN10V6aMKl30xhs2HZolhESFMG/vPBYfWkxUQhQABZ0LciPyBiXylwBy5/6vlIQfn0I+eOf35tTtU8zYPYPvT35PsqYKWjoYfXBP7EmyLoIw+8WgM4Kmp3DCcNZ/PY3ikepDxu0iVZmjn8C8W71JvK324RUsqMolvvwyNG+ep7bpioe9/37q3uyKFVWd1H79wNlyJYTO3T3HrN2z+ObENyQaEzlz5wwb+mwAoKR7ScY0GmOx587pJNgUQuQNvXrB4cPqez8/tR+zRw+LFV+2lavhV5mxawYrj64kPjkegBrFavB2k7fp4dsjtUB5LvRwgXm9Ts+yLss4eOMgq0+sBlR/9maeg1jxjws6dKBpNAp241BxV+y0EhBZglWF9TSJP8LMhClsutMR0OHsDN2fgz59oH17i+V/CFsxGmHTJlXktLLaRsKYMeoD6Lhxao+mBWcy9wXvY8buGaw7tw7twR7iJqWaMKzuMIs9Z24jezaFELmP0ai6urRokdou7rvvYPVqFWS2aJFnN91tvLCRLt+rLQGNvBvxTtN36OTTKVfOYj4soy4/Bp2Bbf23MX//fCb5T6Ju8brsvRzKq0t30+ncLoYc+JVqty7Tt/Y81oS9SlxQIXRoaOgxGDTatdPRpw8895zFugoKW4qNVf/m585V5cz69YOvvrLqEPqv7c9Xx1Ofs1ulbkzyn2RaPs/rZM+mECLviYtTv1zmzFG/XObOVTMYoKat+vSx7fgs4OD1gwSFB9HDtwcAnXw6MazuMHpV7UWz0s2sHmRaotVikjGJpYeWpuvyk6wlk2RMMhWgJzqaBhtWs3P5dIrfDwEgBmcKHtUTR2EAHErcw6vObfYuq4Rn3ki8F4+6fVs1Yli0SCX7AeTPDyVKWPypE5NV4VV7gz0ADb0b8t3J73i1xqtMaDyBKkWqWHwMuZEEm0KInO/ePfXL5bPP4NYtdSx/fjXDmQelFH2eunMqW65swcPZg7bl2nPmegK3I+PoW/kj6pfysHqgufnUTT5cf4ab4alZ4F7uTrzf1ZcO1byyfL24pDi+OvYVM/fM5Mq9K+nuN+gMVPCoAImJaB/+j6QFi7GPCKM4cIfCfMZIFjOcyMIOFPA9R74qN7AvEMuSV/3wLJb7g3CRgXffhdmzVUkrUJnlo0er+rkWXAmNSohixZEVzN07l/ebv88AvwEA9K/Vny4Vu5jquYqMSbAphMi5NE3tuVq2DKKj1bGSJdUvl4EDLfrLxRY0TWPDhQ1M3TWVfcH7ABVw1S7SmlZz/yQ0IjW54WmCvOzYfOomw1Yf4dF9VyHhcQxbfYQlr/plaSwrjqzg/7b+HyFRaoaykHMhmpRqwoYLG1K7/HRZSkyIN+99o9Fj9mZqxIdxifLMZjzrC7+KVjkUR5/TuBaJRKdL+TvJ2jjMwdxBuHhIyk6/lA9WLi4q0KxbV/3fYOF92Xei77DgwAIWHVxEWKyqlfX1ia9NwaaTnZMEmpkgwaYQIufS6eDaNRVo1qwJ48erRCB7e1uPzOz2XtvLkA1DOHn7JACOBkcG+g2kXqF+fPDbHbMFedmRbNT4cP2ZdGOA1OpDH64/Q1tfzwxn8x7NMAeIjI8kJCqEkvlLMr7xeAbUHkA+h3wERwRz9I91uC/cwgfrejDwCICO3UzH0/E+9j2f55V+Bha1AnT5OBDgatPZRHMH4eKBxET4+We1Zeadd+DFF9XxoUOhSRNo2tSi+7ID7gUwZ+8cVh1dpUptARU8KjC+0Xheq/WaxZ43r5IEISFEzqBpqhn1nDnw+eeqVznAqVOqKHebNnk26Qfg/N3zVFlUBVcHV4bXG87ohqMp4lKMJjP+TTNj9jAd4OnuxK5JrSwaZO29HErv5fueeN73gxrSqHyhNMcezjDXoWN51+UM8BtAVEIUv5z5hd7Ve+NgcCA+1sjhD9ZTYPksfO/tBmACM5lnmEC7dvDqqyrRJ18+i/yI2ZJs1HLE65OnhIfD8uVqy8y1a+pYq1bwzz9WHUbHbzuy+dJmAOoWr8sk/0m8UPmFXF3twRIkQUgIkTskJKhM8tmz4fRpdWzuXFi8WH1frZr6ykOiEqJYfng5wRHBzGk/B4BKhSvxY48faVOuDQWdCwIqyHtcIANqVvFmeBwHAsLSBXnmdDvy8WP4r/O2XN7CwPUDTbc1NIZsGEL7Cu3xzu9Nv5qvcXBnHBfeW0H9nbNpbDwPQAL2bCrcl+oDu3B9tCq+nhMdCAjLEa9PnnD1qurys3x5au/QokXhzTdhmGVLCGmaxrbAbVQpUgVPV08AJjSegFEzMsl/Ei3LtMz11R5sTYJNIYRt3L+vOvt89hncuKGOubrC4MEwapRNh2YpYbFhpm4/YbFh6HV6htcbbuqN3LNqzzTnZzfIM7eibk5ZOm/31d1M2zWNjRc3pjsnWUtmz7lLXPrbmx+/jGXDxYrUJxiAcJ07RxsMpfi0kTzXorj5fgALySmvT57Quzfs2aO+9/VVRdhfeQWcMvfey45kYzK/nfuNmbtncvDGQSY2nsiMtjMAaFW2Fa3KtrLYcz9rJNgUQlhfcjLUqgVBQep28eIqwBw8GAoUsOXILOJm5E3m7p3L54c/N3X7qeBRgcn+k/8zuSCrQZ6l1C/rgZe7EyHhcRnu20xZLq5f1oNRm0bx2YHPHnstnWagV9sKEAHgzF5DU5wddxHWdzTlpw+iRYHcUxAzp7w+uY7RCBs2qH2XBdUsPqNHq+4+48ZBhw4W3TITlxTH18e/Zvae2VwMuwioRB+9TvqVWor8zQohrOPUqdTMUoNBzVpUqwZffgkBATBxYp4MNP+89Cdl55dl9t7ZRCVEUbNYTX7o/gPnRpxjgN8AHO0cH/vYlCDvcb92dais5/plLdvr3aDX8X5XX9NzJnGXOP0JkrgLJGMknve7+mLQ62hXvh32ensG1h7I2eHnmVBpBTpN7XPTG3Us+R0qRUTRooXqLNrp0mcUvn+Zip+PxZCLAk3IOa9PrhEbq1YzqlRRG3CXLUu9r0cP+Ptv6NjRooHm/H3zKTu/LEM2DOFi2EUKOhXk/5r9H1dHX2Vam2kWe95nncxsCiEsR9Pgr79g1iy1wf/PP6FdO3Xf//0ffPxxnkz6iU2MxdlelSlqVLIRTnZO1Cleh3eavkPHCh0zvf8rJcgbtvoIOkgzq5hyhZQgz9I6VPNiyat+jFg7h+tJc0GngabDTufGy76D6VBNZQt38unE7h5BbPrZi06jNCoEBrI6fyOKe+yiQpiGd0QyPd/eiMcnD9oKPijGnhvlpNcnR7t9WxVgX7wY7qq+9bi7p20haaX/By6FXTJVQRjXaBwD/Abg6uBqled+lkk2uhDC/BIS4IcfVNLPSVXKB4MBPvkEJk2y7dgsaF/wPqbtmsbNyJvsH7jfFFReC7+Gd37vbCcZ5JQ6jhm1lAQoX7A8xwdc5LffdHz5JWz/J4mX+JEJzKIWxwHQDAZ46SV048er3vV5SE55fXIcTVMJPitXphZhL1NGLZm/8YbFe4ieu3uO2XtmM9BvIA29GwIQdD+IHUE7eLnay6YuQCL7JBtdCGF9CQkqo3T+fLh+XR3Llw8GDVJ7MsuUsenwLEHTNP4J+IepO6eyNXArADp0nLh1gpqeNQEo6V7yqZ6jQzUv2vp62rRDTUhUCBP/mpgu0ATwubiQ4sV1RESo284ksNh+FO6JoWguLugGDkQ3ZkyefP0hZ7w+OZJOp0oZxcdD/fqqTu4LL1i0CDuoD30zds9g3bl1aGiExYbxa69fAShdoDR9C/S16POL9GRmUwhhPpqm9mGeOQOenirAHDIkNQkgDzFqRtadW8e0XdM4eOMgAHZ6O/rW6MtE/4lULlz5CVfIXQb9PogVR1ekv8NooPCnB+gXsZW1Zcbw2ut6XnsNSq+dD1FRqmyNh+xZzPNSirDPmwdffaUyygHOn1f9y/39LbpUrmkamy5tYsbuGewI2mE6/lyl55jkP4lGJRtZ7LmfZZmN1yTYFEJk3/Hjah/W3Lmp1bZ//x1CQ6FPH3B8fPJLbrfp4iY6fdcJAGc7Zwb5DWJc43GUci9l45GZx4lbJ3Cxd1G9yYFTIefp8c3rxAf4EVjkc9Ang1FP/43+LDu6H3tjAsbfN6Dv2tnGIxdWFR4OK1ao1YyUIuxDhqjGDFbU7fturL+wHgB7vT2v1niVCY0nUKVIFauO41kjy+hCCMvQNJU1OmsWbNmijtWsCcOHq++7dbPd2CwoNjGWs3fP4uel9hu2r9Ae/5L+tCjTglENRlEkXxEbj/DppLSUvBd3j1VHV7Hx4kb6VO/De1W/ZdUq+OqrSty6peog1snfmn6lZ/Ni0B68I3aqCzRqhN49d2WTi6fwuCLsb72lWkpaWHRCNA4GB9O+y7bl2rI1cCtD6gxhdMPR0q88h5GZTSFE5iQkwI8/qqSfEyfUMYNBlSyZPFnVzcyDwuPCWXJoCfP2zUPTNAJHB+Ji7wKopbu80FlkxZEVDF4/GO2hfGodegrffJk7y74BTWUNVyocymaHrpS5sTf1wc89BxMmqGVS8WxIToaSJVUbWbBaEXaAuzF3WXhgIQsOLGBe+3n0q9kPUB8G45LiTN23hHXIzKYQwnyioqBqVTWbAWrJfOBAlVWaR5M+bkffZv6++Sw6uIjw+HAASruX5nLYZaoXqw6QZwLNQesHpT2o6dC+2Madq03R6zQ6dlYvd+dOHtjXj4G7DtCvnyrAXTlv7U0VGTAa1SpG27aqXJHBoBow7Nql3gPt26ctY5QNyUbtPxOsAu8HMnfvXFYcWUFsUiwAP5/52RRsOts7m8qNiZxHgk0hRMbu308tsu7qCrVrq9nNkSPVMlkeTPoBuBF5g2k7p7Hi6AriklQpmyqFqzClyZQ8WS5lx5UD6Q/qNHyK32N5xY9pHLAa++8PPihTo1OV2L28VAKYyNtiY+Gbb9Se7PPn1X7srl3Vfe+999QBZor/Kh1VvMgdZu6eyQ+nfiBZSwbAz8uPSf6T6F6lu1meX1ieBJtCiLSOH1dL5WvWwNmzqTOXn3+uAsw8nPQDcC/2HgsPLgSgXvF6vN30bbpV6papVnZPmp2xtftx91lycAk1itXE9WYnli+Hn7aOhkErVJH2Bwyajn+u9KLk7Qe//FevVlnloD50iLztzh2V+LdokfoeIH9+CAlJPceMgeaw1UfStUENCY9j2OojuJeazvE7uwC1L3OS/yRalW2VJ1YVniUSbAohVNLPli0qyExJ+gFYv15t+Ic8O5N16MYhDlw/wPB6KsGpatGqfND8A5qUapKlX2o5rbB3SsKPTyEf7PR2fLrvUxYfXEJkQgSOoXWJX9AR1efGF++jy7heewiazojBCEvXayrQrFVL7cfs2dPq4xc2EBsLY8ao0kVxD97HpUqp7TIDBqiA04ySjRofrj9jCjQ1jMTq9+Fo9MVAAXRA/L0uvORbgklNJpqS80TuI8GmEM+yxMTUTj8pST96vQouxo+HunVtOz4L0TSN7UHbmbpzKluubMFOb0dnn86ULlAagPdbvJ+l6z1pdmbJq35WDThXHlnJ4A2DMWpGdOjQYyCZJHXn7arE7xqJSz6NV/roqNrqLn8fdWPXPI0AD6gQBteL1uHg0vHUG9QrT7YTFY/h5AT796tAs04d9X9Ajx4WK8J+ICCMm+FxaCQSZdhKhN2vJOmDyZ/Yi4JJfdGA2MhqjPYbiJ9XIYuMQViHBJtCPMtiY1U7uYiIZyLpx6gZ2XBhA9N2TWNf8D4ADDoDvav1zvY1H52deZiGmjv8cP0Z2vp6WmVJPTgi2BRoqjFoKtC84QfbPqCue2eGDE2mT5md7ChZUQXJOleOl2hKsk7P4BYvcrZYObgCS06HPNvtFvOypCT49VdYtkz9mT+/+mAxb576s1kzi3/QCAy7Q7jdGiLtfidZFwaAXsuHnrSJPrcj4zJ6uMhFshxs3rhxgxUrVnDkyBHGjBlD8+bN050TGBjI4sWLCQoKwsfHh5EjR1K0aFGzDFgI8RSuXYOfflJlSnQ69QtmyhS1jD5kSJ7u9HLi1gle+fUVTt0+BYCTnRNv1HqDCf4TKFOgTLavmzI78zgacDM8jgMBYTQqb7nZGU3TSEo28v1fFzNsKfmcy2w++qIu1fd9ClPnod24wYoxX6LZqdd8VNfxaA/tS7V2kCysJDJS9Sr/9FMIClLHVq5Uy+cALVpYZRgfbPuA2XvmEm2vanQatELkT3oO16QO6HFJc25RN8uWUxKWl6Udvt988w0NGzYkISGBdevWcS2lW8BDAgICqFOnDleuXKFDhw4cOHCAunXrcvfuXbMNWgiRRceOQd++UK6cWhrbvj31vsmTVcCZhwNNgJL5SxJ4P5D8jvmZ7D+ZwFGBLOq86KkCTcj8rIulZmeMmpHVB9dT9uMmePaYycQBPmBM+1+7QWdgoePPVO9UUpWqCQ4msVBhXK4GmM7RHkmAejhIFnnA9eswaZKqjzlmjAo0CxeGDz6AV1+1+nBuRt4kOjESJ0pRKGEUJeJWkD/pxTSBpg6177l+2bz9f9OzIEszm61bt6Z3797Y2dnxySefZHjO//73P8qUKcNPP/2EXq+nT58+VKhQgblz5zJ16lSzDFoIkQkpST+zZqmOPylatgTnvF2PLiI+giUHl7Dv+j5+felXdDodBZ0Lsu7ldfh5+VHAqYDZniuzsy7mmJ15OOmnqEsxPvzlRxYdm0G4k5qtpWwwbtsmUjd6KdvdhmIkGYOm4/MN4H1oiTqncmUYP54/q7dkx69nn/icsoSZu2RYEeH+PahQITXpp2JF9aGjb1+r/F9w6MYhZuyewWT/ydQpXgeASU0m0cmnE/aJdRnx7TGANFtRUubS3+/qKzPreUCWgs3ixYs/8ZxNmzbx5ptvon9QFsHR0ZGuXbuyadMmCTaFsJbr16FjRzh5Ut02GOCll9QvmDp1bDs2C7oTfYf5++ez8MBCUyH2nVd30qx0MwBalW1l9uesX9YDL3cnQsLjMty3qQM8zTA783DSD+gwxHmQ7BQKTkC8G57Bw5jQdDTl/rrDjH/K4hW+ErvkAP74cia+d2MJ86uPx/vvQJcuoNdT+HJopp5XljBzD1NFhPuxVL19hdPFyqdWROjSBW7fVisbnTubrXTR42iaxpYrW5ixewb/BvwLgF6n58cePwJQrmA5yhUsB8CSV/XpKjl42rCSgzA/syYIxcbGcuvWLUqWLJnmeMmSJfnuu+8e+7j4+Hji4+NNtyMiIsw5LCGeDcnJKqgEVXQ7Lk4VYx80CEaNgtKlbTs+C7oafpXZe2an6S5SuXBlJvtPppF3I4s+t0Gv4/2uvgxbfQQdlpmduRYezOD1gzGSshdTU4FmrAf1Escxu9dwmtVx4+j8VVwe8CM3O43GTlcYDIX5vNGbBLsX5WiJKiwp50eHB0GGtYJkYR2bT91k1Jf76Xp2OwMOrqXSnSBaDl7KVYozbPURlk6eSbs6ZS0+jiRjEmvOrGHm7pkcDTkKgJ3ejt7VejPRf2KGj+lQzYu2vp45ukateDpmDTZTAkYXl7Sbe11dXYmLe/xSzLRp0/jwww/NORQhnh1BQTB/vqqJefKkKl+i16tEoDJlUrsA5VEHrh/Af5U/SUZV2qde8XpMaTKF5yo/l6lC7ObQoZoXS171M/vsTHQ0LFl9k0Xr92Cslz7p59c+3/GCTzP48ku0PnOoffkytYG1vi3YVVYVX//dVyVxPprwY40gWVhHcmgYV8b/Hzt2/0axKLXHNsrBGd9bVwgqWBwd8P5fV2hdu4zFX8/WX7dmR9AOAFzsXRjkN4ixjcZSyr3Ufz7OoNdZNIFO2JZZg01XV1cMBgP37t1Lczw0NJSC/9HabsqUKYwdO9Z0OyIiIt3sqBDiEUeOqPqYP/2kZjUBfvsNej8o41Orls2GZmmhMaEUclG/mOp41aFsgbKUdC/JlCZTaF22tU26i5hzdubsWZi+7BI/XJ1Fgu+X4PycSvrRpwacBp2Ber/9CQtfhbt30QH3nNz42q8zZ4umn8HKKCveUkGysJKwMPjwQ1ixkuEx0QCEuHrwRd1ufF+zAxFOroBlKyLci72Hm6MbdnoVTnSr2I3Tt08zssFIRtQbYfp3Kp5tZg027ezs8PX15fjx42mOHzt2jBo1ajz2cY6Ojjjm8RZ4QpiFpsGmTSrI3Lo19Xjr1movVvv2thubhWmaxr8B/zJt1zTO3DlDwKgAHO0cMegN7B+4n4LOtu/V/jSzM4mJsG4dzPj6KIccZ4Dvz1BDBZfla95hRNPPmbB9GMlaMgadnqV/6PHeP089uEwZTrz0Br0SfYl1+O89lo8m/MgSZi7m4ADffIMhJpqzRcqwrP6LbKjSlESDfYanmzPZKzgimHl757H08FKWd11O7+rqQ+7wesMZVm8YLvYuT7iCeJaYvah73759mTlzJpMmTaJUqVKcPHmSP//8k+XLl5v7qYR49pw/rzb3g9qf+fLLKuknD/erNmpGfj//O9N2TePA9QOAmtXbfW23KeEnJwSa2REcEcyecxfZu9GHb34PIrTqx1Bns+n++gU6MfO5yTQv0xRu36Zn7Y5cCrtEhQLl8P6xI/g5wcSJ0L070UHhxC7f98TnzCjhR5YwcwGjETZsUJ9IVqxQdXJdXeHTTzmDK51OOzyxCLs5kr3O3DnDrD2z+PbEtyQaEwFYf2G9Kdh0ts/blS5E9mQp2Dxx4gTvvfee6fann37KmjVraNu2LSNGjABg9OjR7Nu3j5o1a1KjRg0OHz5M3759eeWVV8w7ciGeBWFhsGsXdOumbleuDL16QYkSqtNPHt5ukpicyPenvmfG7hmcuXMGUIXYB9QewPjG45+6PqYtaRpM/H4lsy8MBp0R0EOlruCzGZ2mp1v5l/mw7URqFquhZrJfbwmnTuEdFIR3mRbqIlu3QpEipgBDEn7yqNhY+PprmDsXLlxQx3r1gnbt1Pf9+lHJqOE141+LvvZ7ru1hxu4Z/H7+d9Ox5qWbM8l/Eh0qdMj2dcWzQadpWkbvzQzduXOH3bt3pztepkwZaj2yP+z06dNcvXqVChUq4OPjk6VBRURE4O7uTnh4OPnz58/SY4XIEwICVIePlSshPl7d9va29ais6njIcWotrQVAfsf8jKg3glENRlHMtZhtB/YUIiNh9WqYuyqAS53Lgy71v189Bl6p3pcPWv4f5fJ5w3ffqe0Sp0+rE+zsVODZps1jr5/Sox0yTvixdo928RTu3IHFi2HhQkhpiuLuDkOHquoSXmlfR0u/9k1WNWH3td3o0PF85eeZ5D+JBt4Nsn09kTdkNl7LUrBpLRJsimfWgQMqwPjlF7VsBlCzpgo683B9TID7cffZfXU3nSt2Nh17fd3rVCpUiWF1h+Hu5G7D0T2d8+dh0SL4YnUMUT6roNnH4Hor3Xlbe2ygxR9nVHWB69fVQTc3GDxYBRiZmMk21Vp8KOHHSxJ+cpczZ9S/95QqLqVLq5WMAQPU++ExzPXaJyYn8sOpH+jk08mU4PPHxT/49eyvTGg8gUqFK2XrxxJ5jwSbQuQm58+repg7d6Yea99eJf20bv3EvVi5WUhUCPP2zmPJoSXEJcURMCqAEvlLWOz5MuywYoFkmORk2LhRTUxt2XkP6i+CBvMhX8atew06A4Fd/sa7Tkt1wMtLBRiDB2e5fJW1fkZhJpqmPlykrF5oGtSoobr7jB8PL76oZrYz4Wle++iEaFYcWcHcfXO5Gn6VD1t8yHvN33vyA8UzK7PxmtkThIQQ2VCkCBw+DPb20KcPjB2rftnkYVfuXWHW7ll8cewL4pNVjd6qRapyM+qmxYJNa8z6nQgMZuF3F/ljtQ/Xz3pDvUUwZjI4RgFQtkBZJjSeAMBbm94kWTNi0BlY2mUp3n4tVN/q6tXV+yCbVTok4SeXSEqCX3+FOXPg0iW4ehXy5VMfLrduhUKFsvxBMzuv/d2YuyzYv4CFBxcSFqvqdBbLV4xCzvIeEuYhM5tCWNvdu7BkiQou165NPf7772rprITlZvVyguCIYCb9PYkfT/1IsqbqgzbybsSUJlPoXLGzxQqxp+xpe/Q/PHPtaTt+HN5cuZJdBQerephGPfn+XUarpq6sd3yZGsVqMNl/Mj19e2C3YxfMmkXw7k1cKqynwvrdePs2zPZzi1wmKgpWrYJ58yAwUB1zdFR7clu2tOpQxv81nsUHF5s6b5UvWJ4JjSfwWq3XcLKTVqXiv8nMphA5zcWL6pfLl1+qDFOAvXuh0YN2iikZ53mck50Ta8+tJVlLpn359kxpMoVmpZtZtBB7slHjw/VnMszU1UjfXSezkpJUJZrPPoMdx4Jh9ODUwut6I3Fth7Bg5GXeDP2TtqVaovvtN3ijMRw6BIC3Xo93uxfBschT/4zWdD3iOvuC99GlYhcc7cxXIznPL//fuaP+D1iyBO7fV8cKF4YRI2D4cCha1OpDCosNIzYpFj8vPyb7T+bFKi9i0BusPg6Rt0mwKYSl7dmjkn7WrlV7sQD8/GDCBKhXz6ZDszRN0/jz8p/8eelP5nVQBcgLuxRmSeclVCtaDT8vP6uM40BAWJql83TjJGsdVsLCVKnDRYvg6lUNymyHXhPSdPgBSNaSCbgfQLuIIqps1ZUr6g4nJ3jjDbVdonz5p/nRrOrsnbPM2jOL1SdWk2hMNOuevmcisSksDKZPV/8P+PioLROvvQYuli+ArmkaO6/uZMbuGUxrPY0axdQ2nXeavkOf6n1s1nlLPBsk2BTCkv76K21Xny5dVBH25s3zdNJPsjGZNWfWMH33dI6FHAOgZ9WeNC7ZGIB+NfuZ8bmePBuW2c4pTzrv5ElYsECVL4qNM0LF9dgNnUaS5/4MzzfoDFTwqAAF3dSsVqFC8OabaiarSO6azRywbgCrjq1Kc2zzpc1mCTYft8UhJDyOYauP5M6STZqm9l0ePqw+WAJUqgTvvAN160LXrqC3zJaRh6U0RZixewb7glXR/4JOBVn94moAynuUp7xH7vnAI3InCTaFMKfoaJVZ7vdgxq5VK6hSBfz91SxWlSq2HZ+FxSfF89Xxr5i5eyaX710GIJ99PobUGWKRIuyZnQ3LbOeUjM5LTob169VS+cMdQou8Op47FeaRhNoa8EatNyjpXpJ3/31HJf1osLTr53jnf5BhvGmT6vRkhVksczBqRnToTLNdJd1LmmosvlztZXqt6cXBGweJTogmn0O+bD+PpbY42ExiIvz0k1rNOHZMdfrq2RPKlFH3f/SRVYaRkJzAtye+ZeaemZy7ew4AR4Mjr9d6nXGNx1llDEKkkGBTCHMICVE1bpYsURv9AwNV32I7OzhxItNlS3Kzc3fP0eqrVtyMugmAh7MHI+uP5M36b5pq9ZlTVmbDstNdJyJC5XDMXRHMteiLEOGN3rUg3TsWZuRIcCnXl1Zfr2JEvRGMbDCSYqcDYdYsXt1i5JIHVAgD747VU5/E39/cfwUWkZCcwHcnv2PWnlnMbDPTVPd0ZIOR9K7Wm0qFK6FpGm8XfJtirsW4FX2Lcg7lsv185t7iYDMREbB8uWrGEBysjrm4qO0SDg5WHYqmafiv8ufQDbU32N3RneH1huf6pggi98r7vwGFsKQzZ1QbuW++gYQEdax8edXxp9KDwsd5ONBMNiabkgkqeFTA0c6REm4lGNdoHIPqDMLVwdVCz5u12TCDXsf7XX0ZtvoIOjLusPJ+V18Meh2XL6ul8lWrILLCSuj+IOlHg7qeTflp6I4Hj6jNjTHBuGzZBp1fgh3quDfg3aSTWjqtX98iP78lRMRHsPzwcubtm8f1SFVQftHBRaZg08PZAw9nFYzrdDrOvXkOO/3Tv7fNtcXBprZvVwl+ERHqdrFi8NZbqttPIesEyLejb1PIuRAGvQGdTkf3Kt25EXmDMQ3HMLjOYPI7SmUXYTt597egEJZ08iRMngx//JF6rFEjVYD5uefU0lkedjX8KnP2zOHPy39yYtgJHAwO2Ont2PTKJsoVLIeDwbIzOdmZDetQzYslr/qlW3b3dHfivS6+OId68fzzqgKVpgFeB6HboNSWkjo4cGsngfcDTVsCXP7dqfbegaqR+sor6j1Qtar5f2gLCYkK4bP9n7H44GLC48MB8HL1MgUpj2OOQBOebouDTUVHq5qYALVqqTdNlSrq9e/TRyWBWcGVe1eYvWc2Xxz7gm9f/JYXq7wIqJnoMQ3HmLVagBDZJcGmENmRnKwCTZ0OXnhBJf00bmzrUVnc2TtnmbF7Bt+e/JYkYxIA68+vp7tvdwAqF65slXFkdzasQzUv2vp6mhKKCjg4cWW/B2/303Hs2IOTCl3Au9dMbhT9EmMGc6eBuzdSpvMIdaNdO5Xs0bKlaieZC2ukPv/D8+y/rhKcKhWqxET/ibxS/ZVMBynhceG42Ltgb7DP1vNnZ4uDzWiaSvqbPRvu3YODB9X/Ae7u6nsfH6sk/QAcvXmUGbtn8POZnzFqqgrCpoubTMGmi33u2Bssng0SbArxJBERqs7NvXupm/tr1VJ7szp3hgoVbDk6qzhw/QDTdk1j7bm1pmOtyrZisv9k2pRr88THm7t+4tPMhhn0Osq7FWLLt7B4Mdx60KLc2Rn69wet5Td8fmZlhtczGKHCyA+g9QA1c2UwqH72uaiywMHrB6lSpIppi8PIBiNZcGABk/wn0a1StywV1e/yXRc2XdrEP/3+oUWZFtkaT1a2ONhMQgJ8/73q9HPypDpmMMDZs+Drq25Xsny/cE3T2Bq4lRm7Z/DX5b9MxztU6MBk/8k0K93M4mMQIjsk2BTica5dUynIy5apgNPBQZWs8fRU948aZdvxWcnZO2dpsKKB6fbzlZ9nsv9kGng3+I9HpbJE/cTszoaZttiuCybB9SLEVqBwvUu89IILHw1pgIcH3IkeyW3tDOMajeP0kb8YdvR/JOs0DEZYuh68XTzVe8PH58GTZS8IsmYB85R6pzN2z2Bb4DbmtpvLmEZjAOhdrTe9q/XOVo1FN0c3jJqR7YHbsx1swn9vcbBpnc3792HpUvX/wI0b6li+fDBokPr3n5JhbkVT/pnCgesH0Ov0vFztZSY2nkhNz5pWH4cQWSHBphCPOnpUzWD8+KNqEQOqIPe4cVCggE2HZg3JxmRO3j5JLc9aAFQpUoUOFTpQLF8xJvlPokqRzJdvslT9xKzMhmka/POPekk3bwZqr4ThqZ1+7gKnvZrj4bENgCL5ivBLlQ+403skjXdvo2N+uOQB4U6V2d6gL5vH9aeDT/Esj/lh1ipgnmRM4sdTPzJzz0xO3DoBqL2Wt6Jvmc55mkLezUs354dTP7A9aPtTj/XRLQ45ooPQ9u1qbzaAl5cKMAcPhoIFrfL08UnxfHPiG3r49qCAUwF0Oh3vNn2XPy//ybhG4yhbsKxVxiHE05Le6EI87Msv4fXXU2+3aKE2/HfsaLW9WLaSkJzAN8e/YeaemVwNv0rgqEBTmZSHs84zK9mo0WTGv49N5EmZfdw1qVW2A4r/Ctpa+njxww9qJvPEiQd3FrgCoyqkJv088FrN11jedblp3+GuX/+lSffWJOv0bKrkz9L6L3LSy8csfdQt3aM9xeKDi5m5eyZB4UEAuDq4MthvMKMbjqake8mnvj6oWW/fxb442Tlxf9L93J+McviwmrV+/nl122iE7t3V7d69rVbCKDwunKWHl/Lpvk+5GXWTaa2nMbnJZKs8txBZIb3RhciM+Hi4fRtKPvjl27kzuLqqDONx46BOHduOzwqiEqJYdngZc/fONZW8KehUkBO3TtDWtS1AtnolW6N+YkazYeXze7B8mY7XF6ryp6BWPpsO+4EDhUYSFp/+83X/y27Yv/cBfPIJyUaNCec12rQdyrZydblWwDPNmJ+myLg1C5hvDdxKUHgQRVyKMKrBKIbXG05BZ/POyFUuXJkiLkW4E3OHgzcO0qRUE7Ne3yqMRjXlPXu2qtpftCh06KD25Or18NtvVhtKSFQIn+77lCWHlhARr8ooeef3pmg+6/dMF8KcJNgUz6awMLUXa8ECqFgRtm1Tx4sUUQWZ3d1tOjxruB93n3l757HgwALuxd0DoLhbccY0HMOQOkNwc3R7qutbq36iQa+jUflCXLwIn86FL76A2Fh1X4kSMHKk2mK38VoSm3+7k/7xRqjwv4UQaw/Dh3Mgzomb4XF849clw+d7miDZUgF44P1A5uyZw6iGo1R7TFTP61ZlWtG/Vn+c7Z2zNM7M0ul0NCvdjF/O/sL2wO25K9iMj4dvv1X7K86cUccMBmjbVu3RtlLpIlB7at/a9BYrjqwgPjkegCqFqzDJfxK9q/e2eCkxISxNgk3xbLl8WWWRr1oFMTHqmF4Pd+9C4cLq9jMQaILaDzZzz0zikuLw8fBhov9E+tboa7alUGvVT9y9Gz6aH8yfhy5CqA/EelO1UTCles2ja6PKDKs/CIBe+XuRbEwm9nogbx78MG3ST5HyaruEhwe3z4dl6nmzEySbOwA/HnKcmXtm8uOpH0nWkknWklnceTEAtTxrmfbdWlLz0s1VsBm0nXd4x+LPZxYbN8LAgalT325uai/myJFQqpTVh6PT6QiPDyc+OZ5G3o2Y3GQyXSp2yVJlACFyMgk2xbPh6FH45BO1JGZUiSHUrKmWynv1sno7OVs4d/ccv5//nYn+EwEo5lqMj1t+TCn3UrxY5cVsLZX/F0vWT0xOhnXr1Mrn3riV0HUwVDWCpqeae2POR+3n9P1ETu0uycA6/bE32GNvsOe1C87w8od0cdNUS8nStfB+5121J+9BIX5LBsnmuLamaWwL3MaM3TP48/KfpuNty7Wlp2/PLI/pabUp14be1XrTvnx7qz93lhiNqfuuy5RRgWaJEjB6tJr6ttKHTE3T+CfgH2bunsn8DvNNCXfvNXuPwX6DaVKqyVMlbQmRE0mCkHg2fPstvPqq+r5DBzWL1apVrqqPmF0Hrx801cjU0Dgw8AD1StR76utmpnRPSjIMZJwxntVkmNhYlcM1dy5cugTkD4bRpU2Z5Q9rXro5U/wn0c6tNrqUclVhYVC6tCrCPmECNGmS7j2Qktj0pCA5O4lNT3ttTdPo+G1HU5Cp1+l5qepLTGg8AT8vvyyN5Zlx6BDMmqU27q5alXp8yxZo3txqHzSTjcn8cvYXZuyewZGb6t/E67VeZ9Vzq57wSCFyLkkQEs+umBj46iuV6NO3rzr20kuqw8fAgVCtmm3HZwWapvH3lb+Zvns6/wb8azr+fOXnzdJZJLOle8xVP/HOHVWAfeFCteMBVPWZTiMu8m0GgebCNvMYcSYfdB2jelPv3q3u8PBQfetTtkxkwJJFxrNz7fikeBwMDuh0OnQ6HXW86rA9aDtv1HqDcY3HUa5guSyPI88zGlWHr9mzVfkiUO1EZ85Mfe3btrXKUOKS4vjy2JfM3jOby/cuA+Bs58xAv4GMbTTWKmMQwtZkZlPkHbduwaJFKioJDVV7ry5fBrtn6zNV0P0guv/UncM3DwOqruIr1V/Jco3Mx8lO6Z7sFjC/eBHmzVNJP3EPYtXSZYy8OSaGoW+4ct8YTOlPS5va9QEY0BH4dSG8rzyISt3d4dQp8PbO8s9pqVqYmbl2eFw4Sw4tYf7++Xz1/Fe0K98OgLDYMJKMSTkqQ1nTNM7cOcOVe1foWqmr7QYSFwerV6ukn3Pn1DE7O9WrfNw4qFHDqsPRNI0an9fg1O1TAHg4e/BW/bd4s/6bFHZ5/AceIXILmdkUz46UtjCrV6sMU4CyZWHMGLW57xkLNr3cvLgVfQtnO2cG+Q1iXONxlHI3T9JDdkv3pGSMZ9aBAzBjhtpim/JxuHbdBBoM/JatiTMILNcGV9eFuOLNsi7LGLJhMMma8UHCj6YCTW9v9R4YNEglgGSRJYuM/9e1b0Te4NN9n/L5oc+JTIgE4MtjX5qCTQ/nHNAj/BHHQo7ht8wPNwc3wiaFYae30b+5hQvV9giA/Plh6FB4660sf9B4GiFRIRTNVxS9To9Op+Ml35cIjwtnXKNxDPQbSD6HfFYbixA5hcxsitxtxozUDh8ADRuqGYwXXjAlfORlkfGRLDu8jN/O/ca2/ttMv+T3XtuLTyEfs8+e7L0cSu/l+5543veDGma5LJCmqXKHM2c+qESVPxg8LtKsdnGqvfgH627PMdUB9XL1ImBUgClzPvjbJVx6dzgVwsC7dHWYOFElftnbZ/VHtJnzd88za88svjnxDQnJCQBULVKVif4T6V2tt6ngfE6UbEym0MxChMeHc3DQQeoWr2udJ75yBcLDoXZtdTssTO3DHThQfVnx98eF0AvM2j2Lr098zZqea0wzvDGJMdjr7XP06ydEdsnMpsibEhMhOjq1bWSLFirB4/nnVdJP48Y2HJz13Im+w2f7P2PhwYXcj7sPwC9nfqFXtV4ANCrZyCLPa4namUlJqjPozJmpnX70dVdi7DwYdEZ2ADvUVje8XL0Y23AMQyIr4rhug+ruAnj3GoT3n3vhlVegXbtcl/ilaRo9f+7JydsnAWhSqgmT/CfRyadTrih/Y9AbaFKqCRsvbmRH0A7LB5sHD6qkn19+gQYNYM8eddzDA06fturrf/D6QWbsnsGvZ39FezDn/9flv0zBpjn2SAuR20mwKXKH8HBYtgw++0x191msagnSoAEEBaV2AMrjgu4HMWfvHFYcWUFskqpcXrFQRSb5T+KFKi9Y/PnNWRYoOlolB8+Zo15CUAnDvYcEs8p9MGhpE39mtJzGqKueOL45H44dU2VrunZV2cR2dvD111n9cWxG0zQ2X9pM8zLNcbF3QafTMaHxBNacXcMk/0k0Lpn7PjQ1L92cjRc3sj1ou2USX4xGVR9z9mzYsSP1uLs7REWphECwSqCpaRpbrmxhxu4ZaRLwulTswmT/yfiX8rf4GITITSTYFDnb1aswfz4sXw6Rav8amzerGc6UJdJnJNC8FHaJygsrk6wlA1C3eF2mNJnCc5WeM3uNzMcxR+3Mu3dVHteCBSqPC1Tjpj4jz9HjpUQS7e+y4uv0Geb1J8zD8cBtdcPFRc1qxsbmqhqpScYkfjz1IzP3zOTErRMs6LiAN+u/CUDfmn3pW7OvjUeYfc3LNAdgZ9BOjJrRvDOyGzaovZiPJv2MHw/Vq5vvebJg8t+TORpyFDu9HX2q92FC4wlUK5r3K10IkR0SbIqc6cgRtUz2888qyQfA11ftx+zTJ1ftxXsaV8OvmpJ7KnhUwL+UPw4GByb5T6J12dZWL/78NGWBgoLULObKlanNm8qVgx6jDnK+yHQ+u/AbZ/a3YdVzq9Dr9GkzzI1Q4dxt1bd65EgYNkwtmeYSMYkxrDyykjl75xAUrqZxXR1ciU2MtfHIzMfPyw9XB1fuxd3j5K2T1PSsab6Lx8WpQNNGST+xibF8c+IbelfrjZujGzqdjv9r9n/sCNrBmEZjzJaAJ0ReJcGmyJnWrIEfflDft26tZjDat891e/GyI2WJdfru6Ry6cYig0UGmRJ9Nr2yy+R6wrNbOPHNG5XF9uz6YZPeLYOdDrdol6PTm3+w1TGdm4L+gWrOTz+H/27vvsKiup4Hj392lqoBdELBXsHfFxN5ii9FYoz+jMbbYuynGxNdu7AUTozFGk5hYYoqa2KJi78aKHcWCVOmw9/3jyCIKisqylPk8j4/uZe/usCDMnntmJicF7PKxrLU3A/4YgFGLx2CEZYcL4TbrC+jVK11nVr8uTdOY8u8U5h+az8NItYxbIEcBhtUexqCag8hjn8fCEaYdK70VXu5ebLuyjT039rx6snntmuouUbq0emMBquBvyRK1Jzcdi36Co4JZemQp8w7N4374fcKiwxhVb5QKqXyHdNm6IkRWINXowvIiI+H779XKZf366pi/P0yYoEbJValiyejSTZwxjvX/rWf6/umcvqcqZaz11qx/dz3ty7W3cHTPelHvzMOHYdo02LQJqPp4pKTeiA49RZzcTSt8CX1Ax9o3xWPJem7aOtGl6v+4FeJHnP4ONW6HEVimEZ+1r/Da/S0t4e0f32bzxc2UyFOC0XVH07tKb+yt7S0dllnsvr6bqLgo6rnXw9H2JX92Hzmi9mP+8ovan+niAtevW2SbxJ2wO8w9MBfvY96m9lNFnIrwZaMv6VW5V7rHI0RGldp8TZJNYTn376vViiVL1IiYZs1g+3ZLR5XuouKiWHliJbN8ZnEt+BoAOa1zMqDGAEbUGYGro6uFI0w9TYMdO1SSuTOhbsLRD0YUBV3SfZh2Bjs+rNaPUWEVKDJ/FRw4AECklS21PlpNmG1iP8JXHW+Z3s7eP8ssn1l80fALiuYuCsAJ/xNceniJjh4dLdd/MqNKbtIPqKsYY8ak+0hZTdMY8PsAVp1aZWo/VaFgBcZ5jaOLZxdpXyTEU6T1kci4Ll5Ul8m++y6xCXvRotC6tcpWssGl8icFRgYyfNtwYuJjyJ8jv+kSa0Zs3p0So1GtYE6frhaoQNVwdH4vjPgm/8dPV54t+PnRoTfth2+FywsB0Gxs+K1SExZUaZck0YTnN4zPCPbd3Mf0fdP54/IfAOS2zc38VvMBqOpSlaouVS0ZXsY1bpxKNMGik34S6HQ6gqODiYmP4Y0ibzC+/nhalWqV7nujhchqZGVTpK+RI9X8wQQ1a6pfLh07ZptJP/5h/vxx+Q8+qPaB6dhnuz4jf478fFDtA4vtyXyVkZKxsfDDD2pPZkKhsL099OgXQI5GC/j+4iKCooKeOc+AjutfabiFonqmDhrE0bY96LTp2gvjfJWG8eZg1Iz8ful3Zuyfgc8t1edRh45OHp0Y5zWO6oWrWzhCyzh8+zC/nvuVOm51nt3TGBgIMTHg7KxunzwJDRpA//5qf2Y6Fv0ktC+auX8mS1svpXS+0gBcCLhAYGRgpmw/JUR6k5VNkTHExqplL1s16YWKFdXKZdu2Ksl8441ss5LpG+jLrP2zTJfoahauaSqi+KLRFxaN7WXngEdGqh6ZM2eq7lSg2h32/Ogm0dXmsOb810SeUpXWpfOWpl6eSqy5ulGNlNQZ8G4wG7cfveGLAdC3L+TKxe2Tt1MV68s0jDcXTdPw+taLg35qmpKtwZb/Vf4fo+uNNiUt2dU2323M9JlJZ8/Oicnm9evqTeaKFdCtm2plBmo/tr+/amWVTuKMcfxy7hdm7p/JibsnAJjtMxvvtt4AlMtfLt1iESK7kGRTmEdICHzzjeqROW4cDB6sjnfvDl5eUKaMZeNLR8fuHGPG/hn8ev5XUzufeu71iDXGWjgyZetZfwauOf5M38y7IVEMXHM8yT7JsDBYtky1MLp3D3D0I0/VywzoUpo8dTYy8d+RxJ2JA1QrnAmFu9Dhh2MY1v/KlKa18F02jVJ5S+Hm6AbnhiV5o5GWDePNITwm3NSAXafTUd+9PucenGNQjUEMqzMM51zOFokro0not7nn+h60o0fRzZ6tWpgZH2+lOH1atTNLGCebTolmZGwkq06uYvaB2VwNugqovdH9qvVjRN0R6RKDENmVJJsibSXXhP2HHxKTTVvbbJNo3g69zfub3+fvq3+bjrUu3Zrx9cdTv0h9C0aWKN6oMXnLuWQbtD+5T7KGizNLFuuYNw+CHl8Vz9tkBUFvfEgQRmZE6xkbO5Y4YxyNizVmvF0Tmi7/B93OcabHc9MccStYKzG5eGpFOy0axpvDg/AHLDy8kEWHF7GhywYaFmsIwMQ3JvLJm5/gZOeUrvFkdLVca2Grs+Ze+D0utaxJ2ceN+2nWTBX9NG2a7lczjJqRasurcSFA7fXIZ5+PobWHMrjmYPLlsPyWDCGyOkk2Rdo4elQtdz3ZhL18eXWpvEcPy8ZmIflz5Ofs/bMYdAa6VezG2HpjqVjIMtNOUnL4WmCSS+dPiwu34dzuohT9P42IcJUglCqt0XjoWpY/TNxzatSMzPKZxd9lptB02k9w5mP1AYMBunZVSUbl5/ddfJ2G8eZwLegacw7M4dsT35pGg645vcaUbGalHplpyc7KjjrGwuzR3WBPCT1l3+qhfg684Ouf1u4+ukuhnIXQ6XTodXo6le/E6tOrGVV3FH2r9iWnTc4XP4gQIk1IsinSxpQpsHmz+nfjxuqXS8uWoE/DkXUZWHRcND+c+YEN5zewuetmDHoDtla2rO6wmlJ5S1EsdzFLh5islPY/xoXaEXq4BI9OFUGLU5c7K1aKp8lHG/jXOJ3ld48/c068Fo/Vowg4c0YNOf/wQ9UntUjqp6u8bMN4czh97zQz9s/gp7M/JRkNOt5rPG+Xe9vsz5/pBAeDtzdUr65WLYE3a3Zkz9Gv2DOkHR/2TN+Z9RcDLjLLZxbfn/6ezV0307JUSwDG1x/PZw0+k/ZFQliAJJvi5UVGwurVqhdesWLq2OjR4OCgqs2rZp82L2HRYSw/tpyvDn7FnbA7AGy8sJFOHp0AaFqiqSXDe6Gn9z/GBuUg9GBJHp11A6N6o2Dtepd2o9dz2rCQeXcuA2r1KjouGu2J9UeDzkCpdz6AR/mhd2/I82orfy0ruNDMw/mlK+PTgqZpvLv+XS49vARA85LNGec1jkbFGkn7m6fduAHz5qm92Y8ewZtvmpLNBuXf4sujX7HnwRE0TUuX1+7I7SNM3z+djec3mr4vt/puNSWbspIphOVIsilS7/59WLxYNWEPCIBhw9QvG1CTf+pnjH2I6eF++H0WHFrA4iOLCY4KBqCwQ2FG1hlJi5ItLBvcS0jYJ3nrqoHgg6UIv2mEvFcglx7b3PbkrnsZK8/F/BqyBoA8dnkYUqIrQ7YFs/nUz/R/K554vUo0vdt445avOIx4/WILg16XLu2NEtoXNS/ZHDsrO3Q6HeO8xrH9ynbGeY2T/pjJOXECZs2Cn39O3DJToQL06WPqk1vXvS7Wemti4mMIiAigQM4CZgkloX3RjP0z2Hltp+l42zJtGec1Dq8iXmZ5XiHEy5E+m+LFzp9XTdi//z5pE/YJE1R/vGzmatBVPJd4EhWnLvOWyVeGcV7j6FGxB7ZWthaO7uX89x98NCaS3VvtoMq3ppGSaDryxQ7BIb45X3Z04TOfTnyUrxUfrr9Krt+2ms73a1IT3z5vU+qt93DLnfrL5ZYWEx/DmtNrmOUziwsBF/Bu482H1T+0dFgZ35AhsGhR4u3GjdV+3BYtnin6uR58naJORc26qmnUjFReVpmz989ipbeie8XujK03Fs+CnmZ7TiFEIumzKdJGjx6wdm3i7Vq11H7Md97JNk3YQVUkJ6zOFM9dnCrOVYg3xjO+/njal22PQW+wcIQv59Qptc32l18A7NVIyXYfJo6U1Gk8tFnE3Fa9eK9mNbpv6Ix++IzHH9NBhw4wZgxudeqQfm24X1/Ctoe5B+dyO0z19XSydSI6LtrCkWVQMTGqZZHd4+0WderA0qXQubPaOlOtWoqnmmOfclRcFKtPraZHxR7ktMmJXqfn0zc/Zf/N/YyqN4oiTpnnDY8Q2Un2yRZE6sTGqiQyYTXCxUX9u317lWR6eWWbJuyapqkxhPuns/fGXm4Mv0Ee+zzodDr+7P4nue1yp/s+vleZ8vOkY8fgyy8Ta7kAmnX/jzCvkRx88PRISSPuBVX7Kv3bHWDuPLUXc+TITNe+yqgZmbRrEouOLDJte3DJ5cLIuiP5sPqHONrKFZQkQkJU+7J589T/+4StEZ07q+0yRYum+qHSYs9mcFQwS48sZf6h+dwLv0dUXBRDaw9VIXl2prNn59d6fCGEeUmyKZTgYPXLZcECVfzTqJE6Pnq0ulReOvtMRUnYxzd933QO+B0AQK/Ts/PaTjp6dAQs0/bmZaf8POngQZVk/vmnuq3TQbNex4it9yV/+2+GB8+eY9B0lMpbSt2oXRvu3IG8mWde+5P0Oj3H/I8RHBVMmXxlGFtvLO9Vei/TbXswOz8/1Sd3+XIIDVXHfvwxMdm0tk51oqlpGr029eKfq/+wuOlfGLQCL/0G6U7YHeYdnMeyo8sIi1FvfNwd3cljJ22nhMhMZM9mdnf9ulq9WLFCVZSCunS+Zo0lo7KImPgY1p1Zx0yfmZx7cA5QYwh7V+nN6HqjExMvC0hpyk/Cr+wnp/w8af9+mDwZ/n7cV16vV1/eiRPh3/Dl9P+9Pzp0dCjSnPLnA5huf0wV/BjB+5gLfTffSpz0komcunuK2QdmM73JdFwdXQE4eucoN0NuZsptD2Z35gzMnq22zMSpCVCUL6/ebPbokThu9iWVW1CNi0EnyBczglzxTYDUvUEyakYG/TGIlSdXEhMfA4BnAU/Geo2lW4Vu0r5IiAxC9myK5zt0SDVh//XXxDFyFSqoS6Tdu1s2Ngu5++guH2z5gDhjHI62jhlmDGFqp/w083A2rRjt26eSzH/+ARz90Je6QK23LtG7gxv9G7YDoFhcL86e3cmgv4Mp98XfYDQywBF8a5emVK/huH36YaZKNDVNY+/NvUzfN52/fP8CoFDOQsxuPhtQvTJrFK5hyRAzri+/VAMZABo0UEU/rVq9Vp/crWf98b9fHKxPEKU/a0o2kxuD+jS9Ts/98PvExMdQz70e473G07pMa/S67NG3V4isRpLN7MhohP/9Dy5eVLebNVP7spo3zzb7MQECIgLY5ruNHpXUhKMiTkUYXns4BXIWoH/1/hlmDOGLpvxogH9IFIevBRJ3Jx+TJ8OOHepjuprL0N4ahFGncRC4drQQH7zZGoPegJ2VHQsuFIcfpqs7t2yJ25gxuDVqlKm+D4yakd8u/saM/TM46HcQUMnKux7v0qNi9pxe9VxxcaoyrFYtKFFCHRs9OvHvWrVe+ykS3iDZGisCG4jWnzV97Ok3SHod7Li2g1k+s1jWehnF8xQH4MtGXzKy7sgMM9pVCPHqzJJsxsXFcfz4ce7fv0/hwoWpWrWqNES2pPBwdVm8Vy+wt1erFWPHwr//qpXMSpUsHWG6uhF8gzkH5vDN8W+IjIukinMVU6uUWc1nWTi6Z6U05edJUbfy0L97Ts4cVrcNOUIp2nsKVwvMSrzWDtx7dI8Nq77h3T6PW1YNHQr+/pn2+8CoGan9TW2O3jkKqG0P71d5n9H1RlMyb0kLR5fBPHqktsvMnasasg8cqHrmgkowf/45zZ4q4Q2SHR6g6YnT+xPHQ6xQvVM14E5IONN3r2Sj7xKO+R8DYM6BOSx6S7VWkvZFQmQdaZ5snjt3jtatW2MwGChXrhynTp3C0dGRbdu24eaWmZqkZAH+/rBwISxbBkFBKsns1099rE8f9ScbOXPvDDN9ZrLuzDrTGMKqzlVNhQcZ1dNTfp4UdSsvwftKE30zP/dQ9Rv1B3/PoXxDuBof8uwJOvD/ejZba7VTlzBdXGDVKrPFbg6RsZHYW9sDagXTy92LSw8vMajGIIbXGU6hXIUsHGEGc/eu+jmwdKn6OQBQoEDi9C8zSHiDpCcnNlpxYnRXiDacxSq+ARoxPDLsJNTqVz7Z6w+AvZU9/ar1Y2TdkWaLSQhhOWmebE6cOJHChQuzd+9e9Ho9UVFRVK5cmSlTprBs2bK0fjqRnNOnVRP2tWtVKyOAkiUhmxZb3Q69zYA/BvD7pd9Nx5oUb8I4r3E0LdE0zVfdX7c90dMSpvzcDYky7duMupmX4P0qyQTAEE//D/RMnKjjcpwbTb8PwTauIDGG+2hPPLXBCHecqrHut/+S7PHMDAIiAlh4aCELDy9kS7ctpukwn775KZMbTs4w2x4ylDFjVIeJGFVkQ+nSastMwlUOM3nyDZKtsQIx+itE6c+QI/4N7tgOJU7vB4CjTR6G1xnCkNpDyJ8jv9niEUJYVponm5GRkRQvXhz9443ldnZ2uLm5ERX14kuB4jXFxEDbtrB9e+IxLy/1y6Vdu0xV7JGW8trn5ZDfIXTo6OjRkXFe48xWKPI67YlSYtDrmNTWg4FrjhPtl4fAY7mIiXoIwVFQ6DRWbT6nVZ0iLPtgHgB+vhXpf6wR8/74lx8qQ/+2EK8HnaYjX8wgfqzSCkKjOXwtMF1GQr6up7c9AKw+tdqUbObLkfE/h3ST0Fwk4Q2UtbX6uVC3rko80+nnwJNvkOziKxOtP4e15ooOPTni6xDObtys3+XUiBk42TmYPR4hhGWlebI5ZcoUOnfuzMcff4yHhweHDh3i9u3beHt7p3hOdHQ00dGJEzxCE/q7iReLj0/85WFjo/6t10PHjirJrF3bsvGls9j4WNadXcemC5v4pfMv6HV67K3t+e7t7yiZtyRl8pmvGXlK7YlSU337Ik5hLuT5tyknotZA54SRkoAO4oDdDxx4FDmZXPZOPHgUjUNcReyMu/AMqMA7l5rxb7H8WGmuWJG4epSavaCWdPb+WWbun8naM2tN2x6qu1RnfP3xdCjXwcLRZTDx8bBpk2pfNHmyKvYDGDYMWrdWbzrT0ZNvkHIaa5EjOrHoKHdcF/LE9WDZu7Ul0RQim0jzZLNIkSLUrFmTdevWUa5cOc6ePUuLFi0oVCjlfVTTpk1j8uTJaR1K1hYQoPZiLl8OPj6QsB92zhxYvBiKF7dsfOksPCacb45/w1cHv+JmyE0Afrv4G2+XexuAVqVbmfX5X6U9UWocPgyTJsHWrYDjfRjRD3QJq1fqr1Y5q/DFX1HkcvoBBg2ioIMdmz0acSl/UU4VLguAXTKBPW8vqKUZNSPtf2zP1aCrADQt0ZTxXuNpXLyxFBs+KTJS7bn96ivw9VXH5s1LTDYLFVJ/LKBlBReWvlftmZX+wk55XmulXwiR+aR5U/eGDRtib2/Pli1bsLKyIjIykjfffJMyZcrwww8/JHtOciub7u7u0tQ9OZcuqWrS775Tv2hArWR89pll47KQgIgAFh1exMLDCwmMDARUb8XhdYYzoMYActvlTpc4Dlx5SLevD77wfuv61UnVpevjx1WS+fvjbaYGA5Qc8QGXcq145r67VkHD66g+qadPE69B/Rk7k+zxfJIOcHayY9+4xhlmz6amaWz13UqTEk2wMdgA4H3Um7+v/s34+uOlP+bTAgLUm8pFi9S/AfLkgUGDYMgQiyWYyUnrPcxCiIzDIk3d4+Pj2bt3L8uXL8fKSj20vb097du3Z9GiRSmeZ2tri+0rTqjIFjRNtSmaM0dlHwnvD6pVUy1rOmfPucCXH16mincVImIjACiZpyRjvcbSq3Iv7KzSd9UutZekX3S/kyfh888fzy63ikLnGESvDi58+ik8sPmAut8mTTYNRihlzA2ThsHgwaDTYdBhuoSpgyQJZ8Kv+EltPTLEL/w4Yxw/nf2JGftncOb+Gb5t9y3vV30fgP41+tO/Rn8LR5hBvfUWHDmi/l2smBon2acP5Mpl0bCSY9DrMsXeYCGE+aRpsmkwGHB2duZiQrPwxy5cuICrq2taPlX2Ehqq9l2Fh6vbbduqJLNBg0zVfDstPIx4aCoIKZW3FOXzl0dDY7zXeN4p/47FxhCm9pJ0Svf757AfXyy+zN5NpSHaEbyWYddoLl5Fa7Pqg00AlKQOS/yqMKTwycSRko7dcTv/NeTIkeTxUrqE6fyaxUppJSI2gpUnVjL7wGyuB18HIJdNLkKjZb92so4cAU/PxK/zwIFqn+aYMdCpE1jJfA4hRMaV5pfRlyxZwogRIxg6dCiVKlXi4MGDeHt789NPP9GxY8dUPUa2n40eEqI2+/fqlZhMjh8PwcFqBaNsWUtGl+40TWPfzX1M3z8dn1s+3Bh+A0db9X0REBFAPvt8Ft/HF2/UXunS9aVL0HPuCg4XTCj60WHQ7IjXqy0SReycOdt5Nw7FH3/N9+7F7+Mh+PZ5m1Lt38ctT9EXxpWRLmEaNSPT9k5j/qH5PIh4AECBHAUYXmc4A2sMJI99HovFluEYjfDXXzBrFuzZoy6ZDx6c+DGdLtu92RRCZCwWm40+aNAgKleuzMaNG9m+fTuurq4cPXqUKlWqpPVTZT03bsD8+fDNNxAWBqVKJVaRTp9u2dgswKgZ2XJxCzP2z+CA3wEAdOjYdW0X7cu1B8gwvfmerL5NzaXr69fhiy/gu41+GIc+TjQBdBrxukhK2brwyXEHum24hM3dZWqfLkD9+rjtOYFbKpOMjHYJU6/Ts/vGbh5EPKBY7mKMqTeG96u8b2rSLoDoaNUjd/ZsOHdOHbOygjt3Eu/zGjPLhRAivZnl2ouXlxde6dxqI1M7fFjtx/z1V3VpDMDDA7Jpb9KY+BjWnlnLzP0zOR9wHgAbgw29K/dmdL3RlM5X+rWfwxwrfqm5dH37Nvzf/6n3E7GxQLHLiYnmE7y9/Wl83V/1SYyLS/xAJlvJuhhwkTkH5vBFoy9wzuUMwBcNv+D9Ku/T2bMzVnq5/GuiaernwFdfqelfAA4O0L+/amEkE9iEEJmU/KS3JH9/Vdyzb1/isaZNVX/MFi0yXWKRVm6H3qbvb30xakYcbR0ZWGMgw2oPw8UhbfYZmqPxeoKWFVxo5uH8TCL7MEDHqFFqFHVUAR9wi6JqIS/8ygbzQNMltjNC7cV0CbPj6vt9KPHlRMiE+52P3D7CjP0z2HB+Axoa+XPkZ2qTqQDUda9LXfe6Fo4wA9Lp1M8Cf38oXBiGD4cPPwQnmYwkhMjc0nzPZlrI0ns2NS0xiYyPV+Pj/Pyge3e1H7NyZcvGZwH3w+/zz9V/6F6xu+nYiK0jcHFwoX/1/mk6hjClxusJaf3rNF5PTlCQuho6b75GROG/oP50KLqXojk8cI6dx93QGMIM2wm2WohRr2EwQttL9fF1HkqugnkzVHuiF9E0jR3XdjB933R2XNthOt6ubDsm1J9AHbc6FowuAzp9Wq1kTp6cOKf82DE4c0b9PLCxsWh4QgjxIqnN1yTZTC937sDChbBli2qimPCLxMdH/aIpXNii4VnC1aCrzPGZw7cnvyU6Lprzg89TNr/5ip8SinieXNF8Ulr2n7xwx48Z31zml6+L8yj3AZVkOp8GwFpnRZcH7jwK6s0Jt+oA5Hl0idIBPhwp0gJNn5jsprYvp6UZNSMNVjVg3021Sm+lt6J7xe6MrTcWz4KeFo4uA9E02LlTFf1s26aODRumGrELIUQmY7ECIfGUU6fU6sWPPz7epAds3Ahduqh/16tnudgs5OTdk8zYP4Of//sZo6b2K9ZyrUVYTJhZn/fwtcAUE01QRT3+IVGvNTM8MhJ6z1/Bz5GPi376Ylo2zaW3p79fIUasu45r2DV2lPydvp1UshmUqwyHcz07SjMjj5SMjY/F2mANqMKfSgUrcezOMfpV68fIuiMpmvv5lfLZSlwc/PKLSjKPH1fHEsbKvveeZWMTQggzk2TTHIxGNV/wq69gR+LlRN54Q/XHbNvWcrFZ0M2Qm/Tb0o/tV7abjrUs1ZJxXuNoULSB2dsXpVXj9eTExqqpgZ/N9uNu1yery9Vfoy8XZMKG++SNvA56PQFvtWVe/oYvfNyMOFIyLDqM5ceW89XBr9jUZRM1XWsC8FmDz5jcaHKG6RCQYRiNUKOGeuMJYG+vGrCPHAklSlg2NiGESAeSbJrDuXOqCTuoOYOdOqlfLLVqWTYuC8tnn4+jd46i1+np4tmFsV5jqeJcJd2e/3UbryfHaISffoKJU+9xvdA8KPMw2ery1vvvkxd7+KgvjBhBnmLFCZixE90L+nLWKp431bGY24PwByw4tIBFRxYRHBUMgPcxb1OyWShXxhmRaHEBAZAvn9qfrddDs2Zw+7YaJTloEOSXhFwIkX3Ins20cP8+HDgA7dsnHuvYEYoXV79cima/y4lRcVGsPrWarb5b+bXzr6ZVyz8u/UH5AuUpkSf9V3RetfF6cjRNTQ4dO/UaF/LNgqrfglU0duQiRhdh2h4Aqrr8umEUboMnqATksYRiJUi+L2daFyu9quvB15njM4cVJ1YQGaeazZfJV4ZxXuPoUbEHtlYyatbk0iW1bea779TVjYYN1fGQELVP2176iQohsg4pEEoP586pZtvff6+yjxs3wNnZ0lFZVEhUCEuPLmX+ofncfXQXgD+6/8Fbpd+ycGTK6yR4fqF+XH54mYBLpZkyJ5DTDjOgwk+gV71Ra0UXZOKWQO737cbA0LXEa/EYdAa8Wyykb+2BKcZjrjZMacGoGSm9sDRXg64CUKNwDSbUn0D7su0tNho0QzpwQO3H3LRJ/SwA1V3iq68sGpYQQpiTFAiZS0I16Zw5apRcgpo11QpnNk0274TdYd7BeSw7usxU6OPu6M7IuiN5s+ibFo4u0avODF9xfAUfbvkQI2qkJF6JqWqz4IJM3HSfBtfvq6T1qJFWS67jG+hLqbylcHNMuRl3Sn05Ldnu6KDfQaq7VMfaYI1ep2dY7WFsubSF8V7jaVy8scVHg2YYRqNa3p41K2mv3DZt1MzyN96wXGxCCJGByMrmyzh1Ss0rP61a2KDTQYcOaj9mvXrZtgn7f/f/o9ryasTExwDgWcCTsV5j6Vahm6laOaN5mQlCu4/fotFvxUD3xF5MDVrfy8OXm4KoevfxsbZtVZJRv36m+17QNI2tvluZtm8ae2/uZU2HNfSo1MP0MUkwk2E0Qvny6tK5tbWqKh89Wk3/EkKIbEBWNtPKk03YXV3VL5YcOaBvX9Ufr2RJy8ZnIXcf3TWNH/Qo4EG5/OVwtHVknNc43ir9Fnpdxp7dnJqZ4ddvxtFnzs/s4hPI+1TRjw5Gbw2iaqAN9HmcZJQvb8aIzSPOGMcv535h+r7pnLqnqqWt9dZcD75uuo8kmo8FBcGKFfDRR2Bnpwp/Pv0Uzp6FoUOzZa9cIYRIDUk2U3L5stqPee1a4uXy/PlVj8zatSFPHsvGZwEJq18z9s/gzP0z3Bh+g1w2udDpdOz+327y2GeN1+T2/Uh6z1vJjshZaHmvq4MaiRs7AQN6SnUdAEM/ARfL7618WZqmsfzYcmb6zDTtx8xpnZMBNQYwos4IXB0z34hMs7l1SzVdX74cHj0CR0c1RhKkR6YQQqSCJJtP0jTYu1ftx9yyJXGj/+nTUKmS+nfLlpaLz0Ji42P56b+fmLl/JmfunwHU6pfPLR+al2wOkCUSzTuBIby/ZAl/h85Dy3kfbMEx0p7RR+JwehTLyFY64nWaKvpp441btb6WDvmV6XQ61p5dy9Wgq+Szz8ew2sMYXGswee0zTqslizt9Wu3H/PFH1ZQdoEKFTPnmQgghLEmSTVAdudevV5Wjx44lHm/TBkaNgooVLRebBYXHhLPixArmHJjDzZCbAOSyyUX/6v0ZXmf4cwtfMoOE6vJijqXZtt6NsRtWEuY1EXJCwdCcfLovgj4nIskRC1rFilTO04u9nkWpWLAcbSpUsHT4L+Xeo3ssOLSAEXVHmJquT244mTP3ztCnah9y2uS0cIQZSEyMamO2dWvisUaNYOxYaNEi0+3HFUIIS5NkE1S7kh6qGAI7O/jf/1TbkrLmm9OdGdwOu83wrcPR0CiYsyDDag9jYI2BWWIVc8XxFXz4+4eqH6ZRD1uWw399qVBkCuOOPKTL2XCsjUCTJhx9ty9DHhbA3z8a/AFuMt3pfoZpT/Q814KuMdtnNt+e/JaouCis9FZMbjQZgIbFGtKwWEPLBphRPLk328YmsRl7p06q6KtGDcvGJ4QQmZhUo4Na2axXT61mDBiQbad7XA++zq5ru3i/6vumYyO3jaRMvjL8r/L/sLfOGg2pt/tup8UPLZIeNBr4Iu91Jl6aicF7CXTuDKNHs9XGhYFrjj/TBD6jNV5/2pl7Z5ixfwY/nv2ReE31Aa3tWpvPG35Oy1LZbytIisLD4dtvYdEiNVrW7fFq/fnzYGsr4ySFEOI5pKn7y3pyZSObOXX3FDN9ZvLT2Z/Q0Lg85LJFJvyYk6Zp7Lu5j4l/TWffvT+Tvc+u/+2ioW1ZiI6GYsVME4ee7Mf5pJeZOJReNE2j0/pObDi/wXSsRckWjK8/Pl3mz2ca9++rBHPxYggMVMcmToT/+z/LxiWEEJmItD56Wdnsl7Cmaey+vpsZ+2ew7co20/HmJZsTGRtpwcjS3v6b+xn2+1iOPfBRB4yoTPHJ6nKdgVJ5S4Fj4irl4WuBKSaaoArU/UOiOHwt8IVtlMzpyT6YOp2OfPb50KHjXc93Ge81nqouVS0WW4bj66sKAFetgqjHX9sSJVTrqv/9z6KhCSFEViXJZjZ0MeAiPTf25MidIwDodXo6e3ZmbL2xmToxiTdq/H72LGfunadiofK0qVCB4CAdsxYFcSynD1ZxenqfhPH7jewuBv3bQryexOrypwqe7oelnGi+yv3SWpwxjvX/rWfG/hmsbL/S9LX79M1PGVNvDKXzlbZIXBlWRARUqwZhasIVNWuqop8OHcAgozeFEMJcJNnMhlwcXLj08BJ2Vnb0rdqXkXVHZvrL5lvP+jN40xyuxn0FOg00HXlm/x8xm8YRHtaK8fXyMvR0IC6PgHr1KDlmDC0aVsM3+GqKIyULOtil6rlTe7+0EhUXxaqTq5jlM8vUI3Puwbms7rAaAHcn93SNJ8PSNDVGMmFsZMIwhkuXVJL55pvZ7oqGEEJYgiSbWVxwVDBLjyxl7829/NH9D3Q6HY62jqx/dz1VnKtQIGcBS4f42rae9afPmo34281JvDSu0wgq/inoelKibCF6VvkC5wJ/q8piLy8A3AC33EVSfNxaxfPi4mTH3ZCoZwqEIHHPZq3i6dObMjQ6lKVHljL34Fzuhd8DIH+O/AyrPYxBNQelSwyZQkwMrFunemT+959KOB9/zZkzR1WZCyGESDeSbGZRfqF+zDs4D+9j3jyKeQTAzms7aVKiCQDNSjazZHhpxi/kDn02jsDfblOSPZgA6ONxbL2VAp7FKTt+IDrD4Jd6bINex6S2HgxccxwdJEk4E55qUluPdCkO0jSNOt/U4XzAeQDcHd0ZU2+M9Mh8UmiomvIzbx7cvq2OOTjAlSuJyaYkmkIIke7kJ28Wc+7BOXpv6k3x+cWZc2AOj2IeUbFgRb7v8D1vFn3T0uGlqe9PfU+JBcXxN/4MuhieXn7UaTocilhzNyyKw9eDXuk5WlZwYel71XB2Snqp3NnJzuxtj24E3yDeqNoW6XQ6+lTtQ/n85VnVfhVXhl5hSO0hkmiCal80fjy4u6uV69u31ZSfGTPUqMlevSwdoRBCZGuyspmFHPQ7SN0VdU23GxRtwDivcbQs1TLTtrxJmPJTOl9p3BzdiI2PxdpgDUDhuKrExcdQ55aej/cZuZsTBjwu+kHTkyf2I6xQPVNfp4inZQUXmnk4c/haIPfDoijooC6dm2tF8+z9s8zYP4N1Z9axtuNaOnt2BmBo7aGMrDsSvU7eIyZhaws//6xWNsuVUwlnjx7quBBCCIuTZDMTM2pGrgapAheAWq618CzgSdn8ZRlbbyy13WpbOMLX8+SUH71Oj0cBDyoXqszCRmuYOhUWLKjAN4616RNwiFN2nmz1aodbZEmirO5jZSxsSjTh9Yt4DHqd2dsbHbh1gGn7prHl0hbTsf0395uSTRuDjVmfP1PQNNi/H775Rl0yt7EBKys1alavVyNm5VK5EEJkKNLUPROKjotm7Zm1zPKZxYOIB9wcftM03ScyNjJLTPrxC/Wj6LyiapzkE6zjocjy/7hyzwOAgTUOEet6mH/KFkdLZvU2IzZef5KmaWy/sp1p+6ax58YeAHTo6OjRkfFe46leuLqFI8wgjEbYvBlmzoSDB9WxlSuhd2+LhiWEENmZNHXPgkKjQ/E+6s28Q/O4E3YHAEdbR07dO0UdtzoAWSLRjI2PZfHhxc8kmgCrNsLVe2v5qcIUZs6Eli1rs+2/IvyTAYp4XtXnez7noN9BrPXW9KrcizH1xlA2f1lLh5UxREXB99/D7NmqZRGoy+O9eiUW/QghhMjQJNnMBO6H3+erA1+x9OhSQqNDASjsUJgRdUbwYfUPcbTNWqu/S48uZfr+6c8cNxjh5oMPKDXjQ06OSuzDnVDEM3nLuSQTf5yd7JjU1iNDzS6Pjotmzek1vFP+HfLY50Gn0/HZm5/x99W/GVl3ZLL9PrOthw+hQgW4e1fdzp0bBg2CIUPA2dmioQkhhEg9uYyeCZx/cB6PJeqycbn85Rhbbyw9KvXIMnv4giKDuPvoLuULlAcgJOQ+tSYVpoJ/PJvLqYIfnVFHJ+M8Vo4fSs4UCrDjjVq6FfG8rEcxj1h+bDlzDszhTtgdvmz0JZ+8+Ymlw8p4QkPhyf/zTZuqFc2RI1VDdgcHy8UmhBAiCbmMnokd9DvIkdtHGFJ7CADlC5Tn4zc+ppZrLdqUaZPpq5ETKswdbB346exPLDu2jHIOxTk8+BSBgTq+/LIgIxf05U3tX2wd+xDZszKfjfCgasnnr/qlRxHPy3oY8ZAFhxaw8PBCgqJU+yVXB1ecc8nKXBKnT6sm7Js2weXLiSuXq1dDgQJgbW3R8IQQQrw6WdnMIIyakb8u/8WM/TPYe3MvVnorrgy9QhGnlCfcmIs5VwifrDB/UsV7MNBuOxNXNiM4GHLyiIatcjBzth4PjzR56nSlaRrj/hnH4iOLiYiNAKB03tKM8xrHe5Xew9ZK2vKgabB7tyr62bo18bi3N3z4ocXCEkIIkTqysplJxMTHsO7MOmb5zOK/B/8BYK23pmelnuieGYljflvP+j+z99EljfY+/nP1Hz7Y8kHSg5oq+nnvNIzmLME0o1IlmDMnF02bvtbTWZROp+N++H0iYiOo6lyVCfUn8E75dzDoDZYOzfLi42HjRpVkHjmijun10KmT6pFZo4Zl4xNCCJGmJNm0oMO3D9Px5474hfoB4GDjwIAaAxheZziFHQqnezxbz/ozcM3xZ+aA3w2JYuCa4689Mcfn+t5nD+rgZGhbpjCHcJfSrJgC//ufKv7JyHswn3bszjGm75/O5w0+x7OgJwCfvPkJ3Sp0o3nJ5pm2qb5ZBAZCz56q0tzODvr0UXsyS5a0dGRCCCHMQC6jp7OEBuUAwVHBuM91x8HGgeF1htO/en+c7JwsEle8UaP+jJ1JVjSflFK/ypQSQqNm5LeLv/Eo5hHvVXoPgJsPfCm2uDTak3mX0YDdsuuMHeDGmDGQK5c6bM4V1rSiaRq7r+9m2r5p/H31bwB6VurJ6g6rLRxZBvPwIWzZkrQn5iefqHcUH32k9mQKIYTIdOQyegZz6eEl5vjM4eLDi+z63y50Oh257XKzo9cOKheqbPE9fIevBaaYaILqX+kfEsXha4GmIpyEhPBWiB9x+jtYGQvj6uhM/coX+Ou6N+cDzlNQy0HH0u2xt3cgt20p+l9/H++iq9D0GhgN1Av05ufjbri6Jj6XuVdYX5dRM7Ll4ham7ZvGoduHADDoDHSr2I2xXmMtFleGc/26muyzYgVERICnJ9SsqT42ZYpFQxNCCJF+JNk0s0N+h5jpM5ON5zeiPU6fjvkfo0ZhtS+tlmstS4ZnktrZ4Qn3S0gIQw3bCbRbCDoNNB13onNy+OgjAByjoO+RCKJL/syaqL588gncv/8tOH5B1Sa+TBtTihZ1k1aYxxs1Jm8590yiCSrh1QGTt5yjmYezxS6pN/u+GTuv7QTA1mBL36p9GV1vNMXzFLdIPBnOiROqsvznn9X+TICqVdVlcyGEENmOJJtmoGkaf17+k5k+M/n3xr+m423LtGWs11iqu2S8EYSpnR1e0MHOlBDGEkCg9eNEE0CnoekekT8cRvvAgKMQW6klH31RgR981V1Kl4bZs91o29aN5LYxvsoKq7lFxkZia2Vr2v7QpHgTjt45yqAagxheZziFchVKlzgyPH9/teH2778TjzVrBmPHQpMmJPsFF0IIkeVJsmkGf/n+RZt1bQBVWd69YnfG1BtjKhzJiGoVz4uLkx13Q6KSXVVM2LNZq3heDl8L5E5IJHH6O4mJ5hO+26AjXN+MoVWmsfpQNUANf5k0SQ2AsXlOL/qXXWE1p5CoEJYeXcrcg3PxbuPN2+XeBmBo7aEMrjnYYvtrM6z8+eHCBbUXs3NnVVletaqloxJCCGFhkmymgbDoMC4EXKCmq9qP1qJkC6q5VKNxscYMqzMsU4wgNOh1TGrrwcAXzBi/EnSZz/6dRLBVIA5x3UHTJUk49UYdQ/P/wpUjb8NlPQaDSjAnTYJ8qViIfJkVVnO5H36feQfnsfjIYtN40NWnVpuSzVw2ucz23JlGRASsXAm//ALbt6um69bW8N13UKwYFJctBUIIIRSpRn8Ndx/dZcGhBSw5sgR7a3uuD7tuKvR5suo8M0mpCrx7/Tj+vfsNv577FQ0Nq3goG7IY/1wXCbReBDojaHp0fy1BO9wfgLoNY1ixxIby5VP//AlV8S9aYX26Kj4t3Ai+wSyfWaw4sYKoOPX5l89fnvH1x9OtQjesDTLFhoAAWLwYFi5UVeYAa9dCt26WjUsIIUS6k2p0M7r08BKzfWbz3anviImPAaBQrkJcD75O2fxlATJlognQsoILzTyc+f3sWU7fO4+mD+Hf2z8zdOc/pvu0vQjj98HfZU6xskY7dFebEvSfFcYbFdFC3bDOH0bJtr7s/aYKhpd8GVK7wmqO4qCuv3bloN9BQBVuTag/gXZl22Xar2WaunYtsbI8MlIdK1ECRo2C9u0tG5sQQogMTZLNl3Ah4AIf7/w4SWV5Hbc6jPMal6WSklUnv31mpKTBCN3OwNj9ULF8A46N78vXx10JXF+ByKsFAdDbR5O7+RkcKt9ibq+qr5wQtqzgwtL3qj2zwuqcxn02D98+TLn85XC0Ve/GRtcdzbJjy5hQfwKNijWSRuwJrlyBMmXA+Pj7oXp1VfTzzjtgJT9ChBBCPJ9cRn8Jp+6eoop3FSCxstzL3SvLJCUx8TGc9D9J3W/rJkk0dRrs/xbq1lbjBIPL1GLyZFi4SCM+Tgd6I47Vr+NU7zKuhazSLCE0xwQhTdPYeW0nU/dNZee1nUxvMp1x9ceZPpZVvpavRdPg8mWVYCZo2FBN+xk7Fho1kspyIYQQchn9dSXMLL8ZcpNPG3wKQGXnysxpPoeWpVriUcDDwhGmnfCYcL4+/jVzfGbjGKNPkmiCqgGKXreG+Do9+Ppr+LS12roHOtq00eg5PATbfLYUdKiRpiMlDXpdmrU3SphoNHXvVI7cUfO4rfRWBEQEmO6T7RPNuDhYv171yLxwAW7cSJzu89dfYG9v2fiEEEJkSpJsPiU0OpSvj33N3INzuR12G2u9NX2r9TXNKh9Zd6SFI0w7DyMesujwIhYcnE9gdBAABR6BPpceI09cQtcZuB/WgGrV4PRpdax8eZg7F1q00AF5Hv/JmH44/QNT903l3INzANhZ2dGvWj9G1R1F0dxFLRxdBhAerirL58xRU38AcuSAo0ehVSt1WxJNIYQQr0iSzcf8w/xZcGgBS48uJSQ6BACXXC4MrzMcBxsHC0f3+vxC/bj88DKl85VGh445B+aw/Kg34XERAJQMVPsxe4UU44fP36H/lfnEa/HodQYq3/SmyyTVvil3bvjiCxgwQHW6yQz+uPwH5x6cw8nWicE1BzOszjAK5ixo6bAsLzgY5s2DRYsSK8sLFIAhQ1S/qtT0qhJCCCFeQPZsAlsubqHT+k6myvJy+csxtt5YulfsbvGZ5WlhxfEVpoIfvU5Pv3I98D7/PQCV78KEvdAxZw2sRj8u+jAYuHDHjy8X+7LeuxSxD93Q62HgQJg8OWPnICFRISw5soSOHh0pk0/tOTx7/yy/X/qdgTUGSiP2J/n7q56YMTGqsnz0aOjdW1YxhRBCpEpq8zVJNlGXk4vMK0JV56qM8xpH6zKts0xluV+oH0XnFU1aWa4z0O6KFR/6RNOiTCt0Y8ZCgwag02E0wpo1MH68ykVATRqcNw8qVLDM55AaTzdi71OlDyvar7B0WBnL8eOwdStMnJh4bMYMlWg+fpMhhBBCpJZFC4T8/f35+OOP+fPPP9HpdHTv3p0pU6Zgn0FXTPLlyMe5Qeey1P69hKrrMdtHP1PwE6/FM7TllzQc2w48E0doHj2qrqAeVK0mKVFCtVZs1y7jFh/fCL7BbJ/ZfHPiG1Mjdo8CHjQt0dTCkWUQmgY7dqik8p/HvVJbtUocIzlunOViE0IIkS2kebIZHByMl5cXHh4e7Nu3jwIFCrB69Wq2bt1Khw4d0vrp0ow5Ek1ztO55EaNmZNOFTUzf838cuXdcHdRI7IiOWtks1bonPB6jef++Wuz69luVm+TMCZ98AiNGgG0G3kUwYusIFh1ZRJwxDlCN2CfWn0jbsm2zzMr0K4uLU6MkZ86EEyfUMYMBunSBXDJuUwghRPpJ82Rz+vTpRERE8PPPP5MjRw4AhgwZktZPk+GlNPYxLXtQ/n72LGfunadiofK0qVCBvTf3MGDTB1wMuQKAXSx8cBzccWRi7TDi0TDoDHi38cbN0Y3YWFUb8vnnEKpGgPPee2oRrHDh1w7R7HLb5SbOGEeT4k2Y+MZEacSe4Px5aN1aTf0BVVnety+MHKn2aAohhBDpKM33bJYtW5bGjRuzdOnSV36MjNrUPbW2nvVn4Jrjz8z2TkiDlr5X7bUSzq1n/Rm8aQ5X475SHdc1HSWsRjKxdHk+uPABuSNh8BEYGlKOgkMnQNeu+EXdxzfQl1J5S+Hm6Mbff8OwYSovATUUZsECqFfvlcMyG03T2H19N9P2TWN4neG8VfotAAIjA/EN9KWWay0LR5gBxMcn7rmMjobixSE2FoYOlcpyIYQQZmGxAiFra2smTJjAyZMn2bVrFwULFqRTp05MmjTJtNL5tOjoaKKjo5ME7+7unimTzXijRv0ZO5OsaD5Jhxq7uG9c41e6pL71rD/91mzHz+59lWgm0PS4Ra3gi9Nf0DHWDceRE6Bly2c2W169qsZZb9qkbhcoAFOnwvvvZ7z6EKNmZMvFLUzbN41Dtw8B8GbRN9nTe4+FI8tArl9XG2t371aXyxO+iCdOQNmyalVTCCGEMIPUJptpvrHNaDQyY8YMunbtip+fH2vWrGHt2rWMGDEixXOmTZuGk5OT6Y+7u3tah5WieKPGgSsP2XzyNgeuPCTe+Hq59+FrgSkmmqC2T/qHRHH4WuBLP3a8UWPib7sJtPZOmmgC6IzE6v35vtYCcm7bo4pAnkg0w8PVPkwPD5VoGgwwfDhcugQffJCxEs04Yxw/nP6BSksr8fZPb3Po9iFsDbYMqjGI797+ztLhZQwnT0L37lCqFCxcCGfOwLZtiR+vWlUSTSGEEBlCmu/ZdHZ2plq1anTv3h2AunXrMnz4cKZMmYK3t3ey50yYMIGRIxMn8ySsbJqbOfZV3g9LOdF8lfsluBBwgTFbPuNU9K8YrYzP3kHTY2UszNUoHYevBZrGPGqamkA4ahT4+am7NmumWhl5ZNCJmx1/7shvF38DwMHGgUE1BzGizggK5Spk4cgsTNNg1y61qXb79sTjzZqpmeVNmlguNiGEECIFaZ5senl5JbkkDi+eOW1ra4ttOpc9p7Sv8m5IFAPXHH/lfZUFHexe6X7Pq1xfd2A5Pbb1R9MBemh4DcoF2OBdIxZNp4GmJ2/sR1iRH0hMZP/7T7Uy2rVLPUexYirJzGitjMKiw7DSW2FvrVpjdfXsis8tH0bUGcGgmoPIbZfbsgFmFMeOJSaUej107qySzIQ2RkIIIUQGlObJ5qhRo2jYsCEbNmygdevWnDt3jgULFtC1a9e0fqpXFm/UmLzl3DOJJiR2CZq85RzNPJxfel9lreJ5cXGy425IVLKPn7Bns1bxvKZjCSust0L8iNPfwWB0obBjbr5sV5uWFVxolq8WOWKh6VXodSofR4t05VfPxhSOCiNOfwcrY2FTogmQA3tGjlQFP/HxYGcHEybAmDEZazjMw4iHLDi0gIWHF/Lpm58yoq7aavGu57u0L9eeHNbZ/DJwZKTae5lQtVW9uko2y5dXleXFi1s2PiGEECIVzDJB6LfffmPChAlcunQJZ2dnunXrxuTJk1Pd1N3c1egHrjyk29cHX3i/df3qmC5Hv4yEVVMgScKZXDV6wn1DDdsJtF74uLoc8kc4kku/1nTfB//3MXnLVuPNiw7cCYtNNpFFA6urxXi014N799Szdeig6kcyUseb26G31Wz2Y8sJjw0HoHHxxuzotcPCkWUQgYGwdKl6txAeDrduQZ486mOalrGWpYUQQmRbFp0g1K5dO9q1a2eOh04T5tpXmaBlBReWvlftmf2gzk/tB01YYY3BPzHRBNBBQI5Qit/bw+QtdjTzcKbAx/8HwKePk1MdSRPZmLuOBP5dgeg7KikpW1blKs2bv9KnYBa+gb5M3zed706tJs4YC0BV56pMfGMiHcpl3Ib/6ebWLZg7F5YvV0kmQJEi4OsLNWuq25JoCiGEyGTMkmxmdK+6r/JltKzgQjMP5+dOENp96SZXQtcQZvgxmepyiLSBsMeV6wkrrE8nsvGR1gT/W5ZHp4qApiNnTpg0SfXQtLF55fDN4v0NI9h3+3cAbOM9cYrrjM3DeuQyemLQZ6By+PR28yZ8+imsXasm/wBUqqRGSb77LlhbWzY+IYQQ4jVky2TzVfZVvgqDXvfcy/C79izhgd0qdeOpkZJoeoLsPbHi2RXWlhVcaFzWmU9nhLN0WQ4ehagOVt27q+mErq6vFXaaOXDrAK6OrhRxKsLWs/5cudIUe+u7OMa9i51RzWS/Fxr9WgVZWYJOl5hoNmqkkszmzWUVUwghRJaQLQdIG/Q6JrVVfX+e/nWecHtSW480mWPuF+rHrmu78Av142bITfb4/mP6WKt6A2l0zcCsbbloe9kLtMdfjqeqy59eYT18GOrV1THz01yEheipWBH27IEffrB8oqlpGtuvbKfRd42o9209pu6datouYKOVomDM56ZEExK3Akzecu61e5xmCkYjbNwI48cnHnN3h/nz1Rd2505o0UISTSGEEFlGtlzZhNTvq3wdK46v4MPfP8SoGdGhrpS7RlrjOyUUG2s76ngWxcVpGd5eBYg1WOEaFZCkuvzpFdaAAJg4Eb75RtWJODrCl1+qaYRWz/lKPq+tUloxakY2XdjE1L1TOeZ/DABrvTUGnYFDVx+mutH9qxRkZQrR0fD99zBrluqkD2oQfYUK6t+DBlkuNiGEEMKMsm2yCanbV/mq/EL9TIkmqIRK04FbQCwP9vyFa9MOGPQ6evZrjc/jgh8r8mNlVKuZT66w6tCxfLlqXxT4ePBQr17qknmhF/Q5N0fj+qet/289n+3+jAsBFwCwt7Lnw+ofMqruKNyd3Nl88naqHudVC7IytJAQ8PZWDU79/dWx3LlVcvmiL54QQgiRBWTrZBNevK/yVRy/dZi+379rSjSfNLWLN65NEyuvX7TCmi/ShTp14MgRdbxiRVi8GN5448VxmKtx/dNO3TvFhYALONk6MaTWEIbWHkqBnAVMH0+PgqwM6eBBdUk8NFTddnVV/TH79QMHB8vGJoQQQqSTbJ9smkPc8aOcjL35TNGPQWegVJ23nrl/ciusJR3z8tmnakUz4ZL5F1/A4MHPv2SewFyN60OjQ1l6ZCl13evyZtE3ARhWexgONg4MrDkQR9tn+2ylV0FWhhARkTiTvHJl1VHf1VVN+unePeO1CBBCCCHMLFsWCKWl6Lhovtk1h2nfvm86VqvdQBZe92CmvgUGnWrpY9AZ8G7jjZujW7KPk7DC2raSK//tyodHeR3e3irRfO89uHBBtTNKTaIJcPhaYKr3SaZGQEQAn+78lKLzijJ+x3g+3/256WMFchZgXP1xySaaCZ9behVkWczBg6qDfo0aqggI1LgmHx84exZ695ZEUwghRLYkK5svyS/Uj8sPL+OSy4U/9q/kq+OLuGOIwC4O+vh/TCGXUqDT8dHK/wDoFuqHb6AvpfKWSjHRTHD8uNrKd+iQul2hgrpk/uabLx9nWjWu9wv1Y47PHJYfX05EbAQA5fKXo3eV3mia9sK59wnSoyAr3Wka/Pmn2jz777+Jxw8dgrp11b9LlrRMbEIIIUQGIcnmS3iyutx0LdoArqEw6k4xcgWHw1M5k5uj2wuTzJAQ+OQTWLJELYo5OMDkyfDRR6/ezzst9klO+XcKX+z5gtjH036qu1Rn4hsTebvc2+h1L78obs6CrHQVGws//qiSzLNn1TFra+jZE0aPVrPLhRBCCAFIsplqfqF+9NvSD43EkZJoMOuOJ0N6LcK2fsOXfkxNg3XrVM3IvXvqWNeuMGcOFC78evG+6j7JJ1crizgVIdYYS4OiDZj4xkSalWiW6pXMlJijICvd7d+v2gGAemfQvz8MH275JqdCCCFEBiTJ5gvExMdgY7Dh8sPLiYlmAh3UmLgI22INX/pxL1xQl8x37VK3y5RRK5tNmrx+zJC4TzK5OerJ7ZM8cOsAU/dNpVWpVgyqqXo+dqvQjdJ5S1PXvW7aBJVZPXgAJ09Cs2bqdoMG0KYNeHnBgAGqlZEQQgghkiUFQik4+N823p5cnjaflACgdL7Sz1w6NugMlMpb6qUeNyICPv5Yjb7etUsVK0+ZAqdPp12imSBhn6SzU9JL5c5Odix9rxotPJ35+8rfpmk/v1/6ndk+s00tm6wN1tk70bx6Ve1lKFoUOnVS+x1ATffZskVNAZJEUwghhHguWdkkseinVN5SnDuzk+l/fcxuG9WIXGcLV47voGS1Jixvs5z+v/cnXot/YXV5crZsgSFD4MYNdbt1a1i4EIoXN8dnpSS3T7JGsdz8fuk3an0zlaN3jgJq2k+vyr0Y6zX2lfZjZiknTqj9mD//nFhZXqGCasru5GTZ2IQQQohMRqdpWoYbSB0aGoqTkxMhISE4OibfTietJFv0A1jHQ0+/vIxpMIFyPYabeg75vUR1eYLr11Xbot9+U7eLFIEFC6BdO8uMwP7oz49YfGQx8Oy0n2zt3DkYMQK2b0881qIFjBsHDRvKvHIhhBDiCanN17L1yubTIyUTNjd+cM+VSW1m4Ta5a5IEI96oceuBPSFhpbkVb4dLLu25ldQxMfDVV6oZe2SkyldHj1aV5zlzmvmTe0JUXBRRcVHktssNQM9KPVlzeg0f1fqIYbWHJZn2k63lyAE7doDBAF26qEbslStbOiohhBAiU8vWyeblh5efHSmpgx7j1uD2VNHPy84Y37tX1Y6cO6duN2yoemZ6eKTxJ/EcYdFheB/zZs6BObzr8S4LWi0AoLZbbW6PvE1Om3TMeDOaqCj47jtVqTV3rjpWrBh8840qADLn3gYhhBAiG8nWyWZC0c+TCWdyRT8vM2M8IEAtiK1cqe5ToIBqZfTee+l3FTYwMpAFhxaw4NACgqKCANh+ZTtxxjis9OpLnm0TzeBgWLoU5s9X/aZ0OvWuoGxZ9fHevS0ZnRBCCJHlZOtKEDdHN5a3Wf7ckZIvmjEOasZ4XLzGqlVQrlxiovnhh2rhrGfP9Ek0/cP8GbN9DEXnFWXynskERQVRJl8Zvm33LacHnjYlmtnS7dtqD4O7O0ycqBLNIkXUqqZb6ou8hBBCCPFysnH2ofSt1pcWpVqkWPSTmhnjN65YUbNuHCePqHE/FSvCsmVQr545I3/WvIPzmH1gNgCVC1Vm4hsT6Vi+Iwa9IX0DyWj++QfeektN/gFVWT5unNqX+aojmoQQQgiRKtk+2YTnj5R83uxwY6yekAOlCT1UAn+jnhw54PPP1TCZ9Mhhzj04h1EzUqFgBQCG1xnOkTtHGF1vNK1KtXrtaT+ZWnBwYg/MunXB0VFtmB0/Hlq1kspyIYQQIp1IsvkCKc0Oj7xagMDtFYgLyQFA/cYxrPnWhqJFzR/T0TtHmbp3KhsvbKR5yeZse28bAC4OLuz8307zB5BRaRr8+SfMmAFBQapTvk6nSv/PnAGXZwu5hBBCCGFekmy+wNMzxuPCbAna4UHERTW83OAQScn2l9j9XSUMZtwBq2ka/974l6n7prL9SmIfyJzWOYmOi8bWytZ8T57RxcbCjz+qRuxnz6pj1tYqwaxUSd2WRFMIIYSwCEk2XyBhxviA1ccJO1mUoD1l0WKsQWfEscZ1cte/xPw+lZ/bb/N17b6+m092fsL+W/tVTDoD3St2Z3z98XgUSMdeShlNeLhqVfTVV3Dzpjrm4AD9+6u9DK6uFg1PCCGEEJJspkphowt225px47QNADYuQeRrcZaiZWKY1LZysn0205JvoC/7b+3HxmBDnyp9GOs1luJ5pA8ke/eqpBKgUCH17wEDZF65EEIIkYFIsvkcERFq+s+cORAXZ4ODg0a/ERF4tYvAJbcHtYrnTfMVzdj4WNacXoOjrSMdPToCauLPrZBb9K/Rn8IOhdP0+TKV69fhv//UUHlQoyTfeQeaN4f//Q/skt9fK4QQQgjLyfaz0VOybRsMHAjXrqnb77yj5pmb68psZGwk3574lpk+M7kZcpOSeUpy4aML2bs3ZoJTp9R+zJ9+UlXlN29CrlyWjkoIIYTI1mQ2+iu6dw9GjIB169RtNzc1ZrJdO/M8X2h0KMuOLuOrA19xL/weAIVyFqJ/9f7EG+Ozb7KpabBnj6os37o18XiNGmpMkySbQgghRKaQTTOZZxmNsGKFGjUZHAx6PQwdqi6jOziY5znXnlnL4D8HExwVDEBRp6KMqTeGPlX7YG9tb54nzQyOHYPBg+HQIXVbr4d331VfnGrVLBubEEIIIV6KJJvA+fNqtOS+fep2tWqwfDlUr27e53V3dCc4Kpiy+coyof4EulfsjrVBJtrg6AiHD4OtLbz/vhozWbKkpaMSQgghxCvI9snmtm3Qtq1q1ZgzJ3z5JQwZAlZp/MpcC7rGLJ9Z5LXPy5TGUwB4o+gb/N3zbxoVa5R9R0qGhqrM/tYtmD9fHStdGtasgSZNVJW5EEIIITKtbF8gFB4Onp6q9/eiRVCkSNo+/vkH55m+fzo/nP6BeC2enNY58RvpR2673Gn7RJnNvXsquVyyBEJC1KXyixehVClLRyaEEEKIVJACoVTKmVNdsS1QIG3HZR/3P87UvVPZcH4DGiqfb16yORPrT8TJ1intniizuXIFZs+GlSshOlodK1sWxo1L+0xfCCGEEBaX7ZNNgIIF0/bxlh5ZyqA/B5luv13ubSbWn0hN15pp+0SZzZYt8PbbqhoLoHZtGD9elfrrzTjrUwghhBAWI7/h04CmaYRGh5putynTBnsre96r9B5nB55lY5eN2TPR1DTVpihBw4bg5AStWsHu3XDggEo+JdEUQgghsixZ2XwNRs3IpgubmLp3Ki4OLmzptgUAdyd3/Eb6kdc+r4UjtJD4eNiwQfXINBpVKyOdTvWQunQJ8ue3dIRCCCGESCeSbL6COGMcP579kWn7pnHuwTkAcgbk5N6jexTKpaqns2WiGRUFq1fDrFng66uO2durBLNsWXVbEk0hhBAiW5Fk8yVEx0Wz6uQqZuyfwbVgNcfSydaJj2p9xLDawyiQs4CFI7SQkBBYtgzmzlVV5gB58qgeUh99pKqvhBBCCJEtSbL5ElafWs2APwYAUCBHAUbUGcGgmoNwssvG1eUA//6rCn0A3N1h5Ej44AMZKSmEEEII6bP5PMFRwdwIvkFl58oARMVF8cbKN3iv4nv0q96PHNY5LBabRV2+rC6Nt26tbhuN0Lmz6o7frRvY2Fg2PiGEEEKYXWrzNUk2k3E//D5zD8xl8ZHFFHYozH+D/jNN+NE0DV1aNuTMTI4eVUU/v/4K+fLBjRuQI5sm3EIIIUQ2J03dX4FfqB+z9s/i6+NfExkXCYCV3oo7YXdwd3IHyH6JpqbBjh0wfbr6O0Ht2hAYKMmmEEIIIZ5Lkk3gevB1/u/f/+O7U98Ra4wFoGbhmnz8xse0LdsWvS6b9oE8dAgGDYLjx9VtgwG6d4exY6FCBcvGJoQQQohMQZJN4ErgFb458Q0ADYo24OM3PqZpiabZbxXzaY6OKtHMkUMV/IwcCUWLWjoqIYQQQmQikmwCjYs3ZlTdUXQo1wGvIl6WDscyEtoX3bsHX32ljpUvDz/8AM2bS39MIYQQQrwSKRDK7vz9Yf58WLoUQkPVpXJfXyhWzNKRCSGEECIDkwIh8XyXL8Ps2bBqFcTEqGOenmo/pqurRUMTQgghRNYhyWZ2tGEDdOqkKs0BvLxg3DjVN1OfTYuhhBBCCGEWZs0sTp8+Te/evVm8eLE5n0a8iKbBw4eJtxs3BgcHaNMG9u6FfftUQ3ZJNIUQQgiRxsy2shkeHk7Xrl0JDg7m0aNHDB482FxPJVISH69WMWfMUHsxDx4EnQ5y54YrV6ToRwghhBBmZ7Zk86OPPqJVq1ZcvHjRXE8hUhIVBatXw6xZqtgHwN4erl6FkiXVbUk0hRBCCJEOzHLddO3atRw/fpypU6ea4+FFSkJCYOZMKF4c+vdXiWbevPDZZ3DzZmKiKYQQQgiRTtJ8ZdPX15fhw4ezc+dObG1tU3VOdHQ00dHRptuhoaFpHVb2sGOHKvQBcHODUaNUM/ZcuSwblxBCCCGyrTRd2YyJiaFr16588sknVHiJcYbTpk3DycnJ9Mfd3T0tw8q6rlyB7dsTb7dvD+3aqXZGV67A8OGSaAohhBDCotK0qfuWLVvo1KkTXbt2NY163LFjBwaDgYYNGzJ79mzyJ7NXMLmVTXd3d2nqnpITJ1TRz/r1ULAgXLsGdnaWjkoIIYQQ2YhFmrpXrlwZb2/vJMdOnjyJtbU1DRs2xC6FhMjW1jbVl9yzLU2D3bth+vSkq5lVq6q2RtKIXQghhBAZkNnHVbZp0wY7Ozt++eWXVJ8j4yqfcvgwDBmi/gbVD7NrVzXtp3Jly8YmhBBCiGxJxlVmJXZ2KtG0s4O+fVXhT/Hilo5KCCGEEOKFzJ5sjhgxAoPBYO6nyTrCwuDrryEgABJaR1WqBCtXwltvqT2aQgghhBCZhNkvo7+KbHkZ/cEDWLgQFi2CoCCwtlZN2N3cLB2ZEEIIIcQz5DJ6ZnH9OsyZAytWQGSkOlamjNqPWaCARUMTQgghhHhdkmxa0saN8O67aoY5QI0aqil7hw5qlrkQQgghRCYnyWZ6Cw2FhKXmN99URT/16qkks3FjeNyfVAghhBAiK5BkMz0YjfDnn6pHpk4He/eq4/nyweXL4OJi2fiEEEIIIcxEkk1zio2Fn35S037OnlXHbGxU4U+JEuq2JJpCCCGEyMLSdDa6eCwiQlWVly4NPXuqRNPBQRX9XL+emGgKIYQQQmRxsrJpDlu2qIk/oPpiDhsGgwZB7twWDUsIIYQQIr1JspkWbt8GX19o0EDd7tgRmjaFd96B3r3B3t6i4QkhhBBCWIokm6/j4kWYNQtWr1YrmFevqj2ZVlbw99+Wjk4IIYQQwuJkz+arOHIEOnWC8uVVM/bYWChZEu7ds3RkQgghhBAZiiSbL+PECXV5vFYt+PVX0DRo1w7274c9e8Dd3dIRCiGEEEJkKHIZ/WUYjbBjh5ru06OHqi739LR0VEIIIYQQGZYkmymJjobvv4e7d+GTT9Sx6tVVS6M2baBoUcvGJ4QQQgiRCUiy+bSwMPD2hq++An9/sLWFDz4AZ2f18cGDLRufEEIIIUQmIslmggcPYMECtXIZHKyOubrCqFGqIbsQQgghhHhpkmwC/P47dO4MkZHqdtmyaj/me++pVkZCCCGEEOKVSLIJqrpc06BGDZgwAdq3V0VAQgghhBDitUiyCaoh++nTUKoU6HSWjkYIIYQQIsuQZDNB6dKWjkAIIYQQIsuRpu5CCCGEEMJsJNkUQgghhBBmI8mmEEIIIYQwG0k2hRBCCCGE2UiyKYQQQgghzEaSTSGEEEIIYTaSbAohhBBCCLORZFMIIYQQQpiNJJtCCCGEEMJsJNkUQgghhBBmI8mmEEIIIYQwG0k2hRBCCCGE2UiyKYQQQgghzEaSTSGEEEIIYTaSbAohhBBCCLORZFMIIYQQQpiNJJtCCCGEEMJsrCwdQHI0TQMgNDTUwpEIIYQQQojkJORpCXlbSjJkshkWFgaAu7u7hSMRQgghhBDPExYWhpOTU4of12kvSkctwGg0cufOHRwcHNDpdGZ/vtDQUNzd3bl16xaOjo5mf77MQl6XlMlrkzx5XVImr03y5HVJmbw2yZPXJWXp/dpomkZYWBiFCxdGr095Z2aGXNnU6/W4ubml+/M6OjrKN24y5HVJmbw2yZPXJWXy2iRPXpeUyWuTPHldUpaer83zVjQTSIGQEEIIIYQwG0k2hRBCCCGE2UiyCdja2jJp0iRsbW0tHUqGIq9LyuS1SZ68LimT1yZ58rqkTF6b5MnrkrKM+tpkyAIhIYQQQgiRNcjKphBCCCGEMBtJNoUQQgghhNlIsimEEEIIIcwmQ/bZTGtGo5HDhw9z9+5dPD09KV26tFnOyWyMRiNnzpzh5s2blChRAk9Pz+fePzw8nC1btjxz/M0336Rw4cLmCjPd7d+/n1u3biU5VrBgQRo3bvzc8+Li4jhw4ACBgYFUrVqVIkWKmDPMdHf8+HEuXbr0zHG9Xk/nzp2TPefhw4f8/fffzxxv0aIFefLkSfMY09P9+/fZvXs3pUqVolq1asne58qVK5w5c4aCBQtSp06d5zY9fp1zMhJN09i1axf379+nc+fOycZ/69YtTp8+Td68ealatSp2dnbPfcxt27YRFBSU5FjJkiWpWbNmmsZubrdu3cLHx4eKFSvi4eGR5GM3btzgwIEDz5zTsWNHrK2tn/u458+f58KFC7i7u1O9evV0GYaSluLi4vjnn3+IiIjgnXfeSfKxe/fusWvXrmTPe97vns2bNxMZGZnkmKenJxUrVkyboNPBo0ePOH78OJGRkVSqVAkXF5dk73fq1CmuXr1KiRIlqFy5cqoe+1XOeR1ZPtkMDQ2lVatWXL9+HU9PT3x8fBgwYACzZ89O03Mym507dzJ06FCsrKxwd3fn0KFDeHp6snnz5hQbwT548IBu3brRunVrcuXKZTpetmzZLJVszp07l5MnT1KjRg3TMQ8Pj+cmm3fv3qVZs2Y8evSIEiVKcODAAT7//HPGjh2bHiGni1OnTrFt27Ykx3bu3EmuXLlSTDYvX75Mt27d6NixI1ZWiT9uatWqlWmTTX9/f0aNGsWePXuIiIigR48eySabn3zyCXPnzqVevXqcP3+ewoULs23btud+3q9yTkbi7e3NrFmzAJU0v/3220kSybt379KvXz/OnDmDp6cn169fJzQ0lJ9++ol69eql+Ljjxo1Dp9NRtmxZ07HGjRtnmmTT19eX0aNHc+LECQICApgwYcIzyebevXvp168f7du3T3K8Xbt2KSabmqbRv39/fvzxR+rWrcuJEyeoUqUKmzdvxt7e3myfT1qaMWMGS5YswWAwEBgY+Eyy+eDBAzZt2pTk2MWLFzl58iSnTp1K8XdP//79KV68OEWLFjUd0+v1mSbZnDZtGosXL6ZEiRLY2dmxb98+Ro0axZdffmm6T1xcHN26dWPHjh3UrFmTI0eO0KRJE9atW5fk5+2TXuWcNKFlccOGDdNKliypBQUFaZqmaT4+PppOp9O2bt2apudkNn/++ad24cIF0+3AwECtWLFi2pAhQ1I859q1axqgXb58OT1CtJiOHTtq/fv3f6lzunTpolWvXl2LjIzUNE3TNm7cqOl0Ou348ePmCDFDCAkJ0XLkyKFNmTIlxfscOHBAA7SwsLB0jMy8Ll68qK1Zs0aLiorSateurQ0ePPiZ++zatUsDtH///VfTNPValSlTRhswYECKj/sq52Q0y5cv13x9fbX169drgOn/QwJfX19ty5YtpttGo1Hr3bu35u7u/tzHrVy5sjZr1iyzxJwejh49qm3YsEGLi4vTihYtqn355ZfP3Of777/XChUq9FKPu27dOs3W1lY7c+aMpmma5u/vrzk7O2uff/55msSdHhYuXKj5+flpCxcu1JycnFJ1TuvWrbUaNWo89z6FChXSvv/++zSI0DJWrFihhYSEmG7v3LlTA7QdO3aYji1cuFDLnTu3du3aNU3TNO3KlSuao6OjtmjRohQf91XOSQuZ6/rMK/jhhx/o06cPuXPnBqBu3brUrVuXNWvWpOk5mU2rVq2SrBLkyZOHRo0acfLkyReee/DgQbZs2cKFCxfMGKFl3b9/n02bNrF//37CwsKee9+IiAg2btzIoEGDTKs4b7/9NsWLF2ft2rXpEa5FrFu3jujoaN5///0X3nf37t38/vvvXLlyJR0iM68yZcrQo0eP5/axW7NmDTVr1uSNN94A1Oi4Dz74gLVr12I0GtPsnIymX79+lCxZMsWPlyxZkjZt2phu63Q6OnTowK1btwgMDHzuY9+4cYONGzdy+PBhoqOj0yzm9FC9enU6dOiAwWB47v3i4uLYtm0b27Zt4/bt2y983DVr1tC8eXMqVKgAgLOzM927d89Uv6s++ugjXF1dU33/O3fusHXrVvr16/fC+168eJFNmzZx/Phx4uLiXifMdNenT58kVxkbNWpEnjx5kvyOXrNmDR06dKBYsWIAlChRgrfffvu5X/9XOSctZOlk09/fn4CAANN/xAQVK1bkzJkzaXZOVhATE8O///77zOf9NJ1Ox/z581m0aBG1atWiZcuWz+ylygp8fHz4+uuv6devH8WLF2fDhg0p3vfixYvExMRku++ZFStW0Lp16xduobCysmLq1KnMmzePihUr0rlzZ6KiotIpSss4c+ZMst8PoaGh3Lx5M83OyQr++ecfXFxcyJs373Pv9/vvv7NixQo6d+5MuXLl8PHxSacI009ERAQzZszg//7v/yhRogTDhw9He04r7JS+Z3x9fZ/Zr5hVrFq1Cjs7O7p16/bC+/7888988803tG3blsqVK2fqn8fHjx8nKCgoydc7pa//8z7PVzknLWTpPZshISEAz/wQy5cvH8HBwWl2TlYwatQoAgMDGT9+fIr3cXBw4ODBg9SqVQtQiXndunUZPnw43333XXqFanYDBgxg3bp1pn1Sn3zyCT179qR69epJ9v8keN73zH///Wf+gC3gzJkzHDlyJNmCsSc5Oztz+vRpypcvD6h9fLVq1WLSpEnMmDEjPUK1iJCQkGS/H4Dn/ux52XMyu23btrFkyRJWrlz53PtNnz6dFi1aoNPpiI2N5f333+fdd9/l0qVL5MyZM52iNa+EJDHhzZuPjw8NGzbE09MzxVW8533PhISEZJp9m6mlaRrffvstXbt2xcHB4bn3XblyJa1atQIgMjKSd955h65du3LmzJlMV3QXGhpKz549adKkCc2aNQPUKnhERESyX//w8HDi4uKe2YP5Kueklcz1ir+khMtcjx49SnL80aNHKVY/vso5md0XX3zBypUr2bx583MrqPPly2dKNAFcXFwYPHjwCxOOzKZp06ZJNuR/9tlnxMbGsmPHjmTvnx2/Z1asWIGrq6vph3lKihUrZko0QV1G7d27d5b7nnmara1tst8PwHN/9rzsOZnZ/v376dSpEx9//DE9e/Z87n1btmxpqrC2trZm0qRJ3Llzh2PHjqVHqOmicuXKSa4S1KtXj1atWj33/0p2+57Zs2cPV65cSdUl9Cd/Ntnb2zNx4kTOnTuHr6+vOUNMc+Hh4bRu3RobGxvWr19v+n9gZWWFwWBI9utvZWWVbNL4KueklSydbLq5uWFjY/PMJagbN25QokSJNDsnM5syZQozZszgjz/+MO0VexmOjo4EBwdnuv0wL8PGxgY7OzsePHiQ7McTvi+yy/dMTEwMa9asoU+fPi/cg5YcR0fHFF/LrKJkyZLJfj8YDIZkV8df9ZzM6sCBA7Rq1Yphw4YxefLklz4/YS9bVv8+etH/lZS+Z/LkyWOqOchKVqxYQcWKFaldu/ZLn5sZv2cSEs3Q0FD++eefZ7pSlChRItmvf/HixVN8zFc5Jy1k6WTT2tqaZs2asX79etOxwMBA/vnnH1q3bm06dvToUf7888+XOicrmDp1KtOnT+ePP/6gQYMGz3z80aNH/Pjjj9y5cwdQl82ftmHDBqpUqWLelgnpKCoq6plLln///TdhYWFJ2qzs27ePnTt3AlCoUCGqV6+e5Hvm2rVrHDlyJMt9zwBs2rSJoKAg+vbt+8zHAgIC+PHHH037eJ/+nomPj2fz5s2ZpmXNq3rrrbfYtWsXAQEBpmM//fQTjRo1Ml3avHv3Lj/++KOpAC0152QFBw8epGXLlgwZMoQpU6Yke5+tW7dy5MgRAIKCgp7Z47thwwb0ej3Vq1c3e7zp5en/K6Ghoab2NAmuXbvGjz/+SGxsLKC+Z/78808iIiIA1Tv5l19+yZI/d0JCQvj1119TXNXcuHGjad/hgwcPnlkA2bBhA3Z2di+sS8goIiIiaN26NUFBQezYscO0PeJJb731Fps2bTJ9P8TExLBp06YkX/+LFy/y888/v9Q5ZmHWWvcM4PTp01quXLm07t27a4sXL9aqV6+uVa5cOUlLjv79+2tly5Z9qXMyO29vbw3QBgwYoK1bt8705/fffzfd5/LlyxpgalUya9YsrVmzZtrs2bO1pUuXas2aNdMcHR21PXv2WOrTSHMBAQFauXLltLFjx2orVqzQxo8fr+XKlUvr2bNnkvu1b99ea9Cggen27t27NRsbG61///7awoULtXLlymmNGjXS4uPj0/kzML/mzZtrLVq0SPZje/fu1QDtyJEjmqZp2ujRo7X27dtr8+fP1xYuXKjVqVNHK1iwoHb69On0DDlNxcbGmv6/lCpVSmvevLm2bt067a+//jLdJzo6WqtZs6ZWpUoVbdGiRVrPnj21HDlyaEePHjXd56+//tIA7fz586k+J6M7cuSItm7dOm348OEaoK1evVpbt26d5u/vr2mapl26dElzcnLSatSokeTnzrp167Tg4GDT43h6emp9+/bVNE3TTp06pVWoUEH77LPPtBUrVmiDBw/WbGxstEmTJlniU3wlYWFhps8zf/78WufOnbV169Zpu3btMt2nY8eOWs+ePbUlS5ZoX331lVa2bFmtdOnSptdO0zRt5cqVGmBqyxcSEqKVLl1aq1+/vrZkyRLt7bff1vLmzav5+vqm82f46vbu3autW7dOe//997UcOXKYXqeEzzHBkiVLNDs7Oy0wMDDZx8mXL5/28ccfa5qmaTt27NCqVq2qffHFF9o333yjvf/++5qNjY3Z2/ukpVatWml2dnbaokWLkvw/OXHihOk+/v7+mqurq9a8eXNtyZIlWrNmzTRXV9ck3zOzZs3SDAbDS51jDlljOeo5KlasyIkTJ/j66685dOgQXbp0YeDAgUn2s9SsWTPJJvPUnJMVdOnShaCgoCQNc52dnU3vcBwcHOjSpYupLcXo0aOpW7cumzdvJjg4mObNm/PDDz9QoEABS4RvFvny5ePAgQOsWrUKHx8f8ufPz8aNG2natGmS+73xxhuEh4ebbjdo0IAjR46watUqjh49yuDBg+nXr1+m24j+IpGRkeTPnz/ZVU2AAgUK0KVLF9MG9FmzZrF9+3a2bt1KZGQk3bp1o3fv3ikODsgM4uPjTf9nElbWNm3ahLu7Oy1btgTU1ovdu3ezbNkyDh8+TKFChTh+/HiSdmMuLi506dLF9Fqk5pyM7tSpU6aJUV26dOGPP/4AoHz58jg7O/Po0SPTa/R0o+769evj5OQEqP12CVPbKlWqxNatW1m9ejX79u3D1dUVHx+fTLWqGR4ebvp8mzRpAqjPv2LFijRs2BBQldO//vore/bsQafTMXr0aHr16oWNjY3pcYoXL06XLl1MxxwdHTl06BBLly7l4MGDeHh4MH/+/Ew1vezQoUOmVey2bduaXqe6desm2QoQGBjI5MmTUxxw8M4771CpUiVANfxfv349a9aswcfHh6JFi3Ly5Mkk+8czOjc3N9q3b8/evXuTHG/bti1VqlQB1O/rY8eOsXTpUg4cOEC9evX4/vvvKVSokOn+5cqVo0uXLqbbqTnHHHSa9py+CkIIIYQQQryGrLXsIoQQQgghMhRJNoUQQgghhNlIsimEEEIIIcxGkk0hhBBCCGE2kmwKIYQQQgizkWRTCCGEEEKYjSSbQgghhBDCbCTZFEIIIYQQZiPJphBCCCGEMBtJNoUQQgghhNlIsimEEEIIIcxGkk0hhBBCCGE2/w+CeF/pl+MPFQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_wls = res_wls.get_prediction()\n",
    "iv_l = pred_wls.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_wls.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(x, y, \"o\", label=\"Data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "# OLS\n",
    "ax.plot(x, res_ols.fittedvalues, \"r--\")\n",
    "ax.plot(x, iv_u_ols, \"r--\", label=\"OLS\")\n",
    "ax.plot(x, iv_l_ols, \"r--\")\n",
    "# WLS\n",
    "ax.plot(x, res_wls.fittedvalues, \"g--.\")\n",
    "ax.plot(x, iv_u, \"g--\", label=\"WLS\")\n",
    "ax.plot(x, iv_l, \"g--\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feasible Weighted Least Squares (2-stage FWLS)\n",
    "\n",
    "Like `w`, `w_est` is proportional to the standard deviation, and so must be squared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:06:11.769018Z",
     "iopub.status.busy": "2026-07-28T19:06:11.768676Z",
     "iopub.status.idle": "2026-07-28T19:06:11.814094Z",
     "shell.execute_reply": "2026-07-28T19:06:11.812742Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.931\n",
      "Model:                            WLS   Adj. R-squared:                  0.929\n",
      "Method:                 Least Squares   F-statistic:                     646.7\n",
      "Date:                Tue, 28 Jul 2026   Prob (F-statistic):           1.66e-29\n",
      "Time:                        19:06:11   Log-Likelihood:                -50.716\n",
      "No. Observations:                  50   AIC:                             105.4\n",
      "Df Residuals:                      48   BIC:                             109.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2363      0.135     38.720      0.000       4.964       5.508\n",
      "x1             0.4492      0.018     25.431      0.000       0.414       0.485\n",
      "==============================================================================\n",
      "Omnibus:                        0.247   Durbin-Watson:                   2.343\n",
      "Prob(Omnibus):                  0.884   Jarque-Bera (JB):                0.179\n",
      "Skew:                          -0.136   Prob(JB):                        0.915\n",
      "Kurtosis:                       2.893   Cond. No.                         14.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "resid1 = res_ols.resid[w == 1.0]\n",
    "var1 = resid1.var(ddof=int(res_ols.df_model) + 1)\n",
    "resid2 = res_ols.resid[w != 1.0]\n",
    "var2 = resid2.var(ddof=int(res_ols.df_model) + 1)\n",
    "w_est = w.copy()\n",
    "w_est[w != 1.0] = np.sqrt(var2) / np.sqrt(var1)\n",
    "res_fwls = sm.WLS(y, X, 1.0 / (w_est**2)).fit()\n",
    "print(res_fwls.summary())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}