Chapter 3, Risk.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3: Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Important Lessons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Risk defined as the standard deviation of return\n",
    "- Risks are not additive\n",
    "- Many institutional investors care more about active and residual risk rather than total risk\n",
    "- Active risk primarily depends on size of active position not size of benchmark position\n",
    "- Risk models identify the important sources of risk and its components"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Properties of Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Source of Risk\n",
    "\n",
    "Risk comes from the probability distribution of returns. We can get a sense of the distribution via a histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas.io.data import DataReader\n",
    "from datetime import datetime\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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P7U7Fr6smWXpK8dNrrQtxwv0FKn79g0KKnzFmG2NMQ8f/440x5xhjhnVv0dY9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\nAAAw4Qj8AAAAAGDC/X/t5voZvFykiAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f729986ed30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "jpm = DataReader('JPM',  'yahoo', datetime(2006,1,1), datetime(2015,1,1))\n",
    "jpm_returns = pd.DataFrame(np.diff(np.log(jpm['Adj Close'].values)))\n",
    "jpm_returns.index = jpm.index.values[1:jpm.index.values.shape[0]]\n",
    "jpm_returns.columns = ['JPMorgan Returns']\n",
    "\n",
    "plt.figure(figsize=(15,5));\n",
    "plt.plot(jpm_returns);\n",
    "plt.ylabel('Returns');\n",
    "plt.title('JPMorgan Returns');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J/l6Sb0nyo1V18RixsB72798/dgisEPnCcHJlMb6YyTLScR6TftlTZ25hKLnC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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f72998dba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "jpm_returns.hist(figsize=(15,5),bins=20, normed=True)\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.xlabel(\"Daily Returns\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining Risk\n",
    "\n",
    "Rather than using the entire probability distribution to inform risk, the authors try to capture the essentials of risk. This creates some shortcomings. If we assume normally distributed returns, then all the risk measures are products of the mean and standard devation.\n",
    "\n",
    "Standard deviation was Markowitz's definition of risk. Knowing just standard deviations and covariances, we can calculate portfolio standard deviations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limitations with Standard Deviation\n",
    "\n",
    "One criticism is that standard deviation measures the possibility of returns above and below the mean. Most investors would define risk as small or negative returns. An alternative measure is **semivariance** or **downside risk**.\n",
    "\n",
    "Semivariance is calculated similarly to varaince but only using returns belowthe mean. If the returns are symmetric then the semivaraince is exactly one-half of the variance. Downside risk has varying definitions but many just assume it is the square root of semivariance to give an analogy to standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JPMorgan Returns    0.000815\n",
      "dtype: float64\n",
      "JPMorgan Returns    0.000489\n",
      "dtype: float64\n",
      "JPMorgan Returns    0.599876\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "jpm_variance = (jpm_returns.var())\n",
    "jpm_semivariance =(jpm_returns[jpm_returns<0].var())\n",
    "print(jpm_variance)\n",
    "print(jpm_semivariance)\n",
    "print(jpm_semivariance/jpm_variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For JPMorgan returns, the semivariance is 60% of the variance. This is because the distribution is skewed to the left (negative returns) so the semivariance is more than half the variance.\n",
    "\n",
    "A variant of semivariance is target semivariance which focuses on returns below a target.\n",
    "\n",
    "There are some problems with downside risk : its definition is not as unambigious as standard deviation or variance nor are its statistical properties well known. It is also computationally challenging for large portfolio construction problems, and aggregating semivariance form assets to portfolios is extremely difficult to do effectively. In a larger sense, if returns are reasonably symmetric then most definitions of downside risk are simply proportional to standard deviation and contain no additional information. Active returns (relative to a benchmark) are symmetric by construction. Return asymmetries are also not stable over time and may be difficult to forecast - so past downside risk may not be a good predictor for future downside risk.\n",
    "\n",
    "**Shortfall probability** is another risk definition. It is the probability that return will be below some target amount."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of daily return below -1% is 25.53%\n"
     ]
    }
   ],
   "source": [
    "shortfall_prob = jpm_returns.values[jpm_returns.values<-0.01].shape[0] /jpm_returns.values.shape[0]\n",
    "print(\"Probability of daily return below -1% is \" + str(round(shortfall_prob*100,2)) + \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forecasting can be particulary difficult for lower shortfall targets, as the shortfall can be influenced by just a few observations.\n",
    "\n",
    "**Value at risk** is similar to shortfall probability, but it starts with a target probability (e.g. 5% lowest returns) and equates that to an associated return:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The worst 5% of JPM daily returns exceeded a -3.91% return\n"
     ]
    }
   ],
   "source": [
    "print(\"The worst 5% of JPM daily returns exceeded a \" \n",
    "      + str(round(np.percentile(jpm_returns.values,5)*100,2)) \n",
    "      + \"% return\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use a normal distribution then the distribution is completely defined by its mean and variance. But the evidence on financial time series suggests they are heavy-tailed, which is why many look beyond standard deviation as a measure of risk.\n",
    "\n",
    "The authors focus on the normal distribution and standard deviation as a measure of risk for tractability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Deviation Properties"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Does not have the portfolio property: the standard deviation of a portfolio is not the weighted average of the standard deviations of the constituents!\n",
    "\n",
    "Let's load data for another stock:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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faPHbYgv3XsuY1fbWr3fPZO1aF78IlH/meo+HHpp/XKX87nfxmMY99pD9B7OY\nP79zBZsTTgCGD2//eYwBnn02+Vklc0T4LI0pr3zT1bNz8Z9ffb3UdVMT8N3vpp81IPtsKrpQA1Q2\nbk+e7GSBp54CRo9OlqG1VbxB/vpX+cwfQyZMkJjk9jBrFvDCC+07Rx7nny/7TwIi13T0gvYjj7Rv\n/m9t7frtktpDQ4Ms7nUWc+dWHntMNnzWrSs+rxa1+N0HoMUYsyOAmwFsC+CONpWuh9HSIgJZ6J7R\n0JAv/GYJEC0tYlnJUxpD9NobQizPVlsVyxgZTg7XXSf7mGXRr1/7ytUZtLTkx8/5k80HPiCvKtT5\nx8ycCbz9dvwad90FnHxydhlUGdBnnxdj5rc5/31jY/o+YopYRyl+/rVUyCmq+A0dGi+Tr/iFVtTQ\njVKPr61Ntis/7i52jSz8TJ5a/3qP/gQeKn5jx8r7hobyrp5vvumsaGvXAi+/7M6Xt+DT3Axccom8\nnzs3/z4qZe3a+JjzzjtxS6By8snARz7SsWXx6UihZsYMsdjqc8lKorTzzsDZZyc/i40N6nKYBV09\n209ra/b86fflpUvltaUFuPxy2Ux95UrpV1muf2119VRCTwg/uUvM++Pll/P7UpGsnp29IHz11RLG\nApRv3z5TpxZb5Pif/wEuuqhtZQOAo48GPvWp+HcdlaSnLfgxpD7r13esYSBkhx06d/wl1eHnPy/+\nXIsqfq3W2vUAjgbwC2vttwBs2bbibbi0ZaVKB9Vwsm5oiLu7NTTIKl7WQFNbK/um6X5jlZRhQ/FT\nX768/DFhXZ97rqwchmg9daXiFyomWauFm23mYup0xROIK35a/ksvTR/z61/Lnkwx7r/fbeodIxT+\niyp+vjBQxNUz/H0e5TIThgoY0HbFz6/HsHyhxS909aypScbnWRvfU7ASoSBvZTnM6qntrKEhXcaw\nf5xzjnu/dq0Irb/+dfyavrI5a5ZbBWxulv/DDaPbypo12YtNeWNpZy9QVbIv5LHHlk+MdPPN7v+s\n5ztzZjp+O+YNUG6Ooatn+3n8cWD//ZOfhWPg44+L6ziQHAuHDZN4zizBuy3JXfx+H7p0l0vusn59\ncbfpail+QNrL4ve/L9/WDzxQttgpQnvm/0mTgCeecP/fdBNw553yvqOS9LSFIUOA115Lf97c3LmK\nH9C+5G1kw6SSebWo4tdsjDkewMkAHi59Flkb37BYsya+r1ZHooNqqORlKX7TprkV+CxWr65s0+XO\nsvjNmdP5K6OFAAAgAElEQVS2SSMm8Picf37a5SlLuNZJs1qB62PGSGxmDD8u4JvflNdnnokrYfps\nLrss+Z21cWvxI4/Ie98tKEYRV8/Y5FbO1VNXcH3aa/G77jpZvY0pflmLFmFb2iRwMPfvO0uA0rYT\nXremJimIWRsXMML4j7x6CFfvfUKLn7+XX7k+o9TUJC1//jUBUfJ0T0Ag2W/Wrwd22kmyTfqsXdu2\nPUCzLH7l8H/TFuvc3/8u7pxZVCIk3ntvcixavjytNPj1mzceht/Fxqxy41h7LX7Nzfnt09psRffJ\nJ7vWpb6zyHPX1lc/zEDbo/5u7tzyMV/h+ebMKRYjHI43WRu4/+Y3wDXXVKb4ZdFWxW/VquS4dO21\nwIIF8WNV1tG2+69/FbuG7yafR8wToxIGD3bvX3nFedgUTZDVWcRikbtC8autzf/+pZdkayHSuWi8\nfkdQyQJ1UcXvFAAHAfixtXaOMWYHAL+rvGhdy0UXpffE6miyLH6NjfEJXCeZPCtMY2P+KnRWGTra\n4jd6dL61KYtyQuzVVxf3RdaVKV9YbG3tumDsefNkXz9lwgRxVQs7a12ddOIPf9g9O39Cz9t8OxSe\n//AHUZAAYMuSXd1fRHjvPUms4Z83bFdZ1wo/A+IDT8xdt9yq6JIlcv0s4fWOO0Sh9c9TqatnqPj5\nCnSWxU+JWfz88/uxdv4zmTixeLKQvDqKKX66B2N4n1kKQr9+ThDUMvpCS1bWU//4sK6POw4YMSJ+\nvXXrJP4phip+b70F/PGP8WMGDXIJfMJyLFgAbL11/Hd5PPSQ9JEsiip+oXW1tVW2zQjdBGPtVfH7\ntd7XX/8KPPdc/JpFFL+GBnmNWQPK0a+fLLBk8atfZVtEP/7xyjOXZnH77cU8PzqCSZOS/2u23Bjl\nvB8AeUbl5pdwTB09On8PTxW09bW+Xvqhjpc+69cDF1wAnHeevC9qneloi9+iRcl6Ovdc52UQouO9\nzlO+J0UeMaX2oYfS99Jexc9PwLVsGfCDH8h7rZtqhcnEnk1nu3oC5evzu98FTj+9c8tAJOGfWp/b\nS4crftbaf1trz7bW3ln6f4619idtK17XkZVZsCM7eaWunqFlxhcqVCCrq+s8i19TE/CJT7g01eX4\ny18qdwsoYr2ICcix34UZGgFxrwwVgBgrViTPuWKFKGePPpruJPfcA3z5y/I+nHT8Z3H11dJRJ05M\nHrN2rRusdRUzb8uEPMUvTDgCiIuectllwGc/K++1zey9d/L4rGuF59XrFRk0yh2zxRaStCcrq2fM\n8lZO8dPfaB35E7j/+0pcPfU7Y9KKn2+FA0SIPOKI5FYcsXrYeONkeWL3Grp6traKgFQkxk/p2zet\n+Ol9rl2bFqRiil947oUL49cCgFGjJP4phrp6XnAB8L//K7F9uiCh16ivlzglH3+BK4u77073MSVL\nSVWKKn6hdfaii4BDDkkfl9WPX301eS093yc+IQs3YdsCilv8fvMb16crRbPIhtTWlhcywv7VVq6/\nPv3cO4Mf/AA46qhk39JnEhvv8hQ/fTZ5ip+6Sevv//Y3t+drXnvWdqP9/Oyz0+6RfoyfHlfO4rd+\nvSwE+uUPaaviF1tIbmmRZ7vNNsnP9V70tWgfjN3bK6+kP/PP949/5Mc9xtDxGXD11djo6ubNN8uf\nY/lyUUorpa4uexuvd95Jf9bcLDJEZybAKmfxa2/M4/33A7vv3r5z+Lz+eseda0Ni7Vq3QNbUJItv\nXUHRrJ4HG2OeMMbMMMbMNsbMMcZ0UKRI5xH60wPScduzerRgQXIltlJXz1BJi1le6urEHbLonn+V\nWPw++UlZkS46gN11F3DVVdnfGwP8+9/Jz0IF7v77gSuuSH6mA4sv8OcpfuvXiwvOkiXF3MOmT5f4\nAX8A23tvceM64oj0s7nxRreaGU6gfsxNS4tYMULhqq7OCQtaviyL34IFxRU/fbZ+zKf+dvHiZJsJ\nrxkeX4nFL0aRyWDlSjn3ihXAxReXP4+WI7Zo4bsaZWU5y1P8yrl69umTftZhEo/WVuDznwcefDB+\nfWXTTZPXVPznHrP49e8fd/XMs/jpsw7dlI46CvjiF8ufJ/wsNk4qfgKMELX4aZ398IduQQIAjjnG\nldlHn3XeAtGJJwJf/3r8O7XoHHGEvL7yStJ1r6jQ6W+FAmQnWMpy9Qzd1Pw2XFvrntOUKcVdyjTG\nLyYQ+oJqHlmLYi0t5QVcX0BuD42NnZuZUPm//5PX2Gbrsfm3vj5tnQ7HnpqabMVPPWB03Lr0UrGE\nAWkrjcZz+2hfW7rULRbHXNRVMG9pyVf8fv5z5xXyt7/Fj9E286EPZZ8nRkyeaG0Vq3C4WBQqfjrG\nlJtbYp4hsev6MttHPiIJW0Jefjl7kdp39VS39jvuENkEcNtsxZg8WbYRuuYa2YKoUm64AfjYx+Lf\nnXpq+rPmZuC22zo3AUue4jdqVLYL7sKF2e6+Po8/npYL28Nee3Wu8vf009VJ8NPU5MaNdevE3b4S\nbz+fznD1vBXA1QAOAXAAgP1Lrxs0McHijTfad84jjkiuxFZq8Qu3XvAnct/i19RU3NXHVyZ9geG2\n29KTgQpIeR3/2WeB005z/5eLMXjxxeT/oWD53e8C3/lO8jM/CDz8XUuLO6fv6rnDDsB//7cT7Fas\nyHYneukl2TvP5513nHCXpyTnWfzWr5frx1z/tAPrqz6/Sy5Juo9tu63EKQHpGD9rk/FW+p3/XLWD\njxiR3rA9FCJefz2+yOC/L5pMwrdaZNW73678yXTWrKRLXViO9eslm+1557nvNtnETTLqwpil3OVZ\n/ELFT61teRY/X/HbZpvyQqymei+6P+PEiUnFL1S+slxGYxY/vUYsPisWT6z18dprwPbbu2f29a8n\nBWh/cSPsL83NUkd+2w37jQpVoWthnkIeXi+vnz76qLzeeae7FuCeRZ4HxJQprg3rcX66fh/fbfMn\nP3H7cYbPLKsuxo1z311/vSwkxJgzRwSrhgancPuMHCnbVDz3nFg81q5144ivgOdZFfPcIAGn+D37\nbPvinpqaOmbfyDvuKLag6bdbLXfWvPX1r7fd1VMVkFjSMX/rhyx0vKmtdTJDzNVT+2Q5V09/Hiqn\n+D3/vLStovHyvgC6aJG8+uOSX0cq6+jcp2Uu5yLf3CyL3H57j/XbcDEnbBP9+wP77SceSj6xPqGZ\nR0891WXMVrnwttskPvHVV91v586VBXBdZCjCtGkui7L/fNW9358/Y88/j8cei8uxO+6Yvv8s8owf\n8+dnLxAdfLBcp7N4/HFR8mJ05hYU48dXZ4sLX/HTvhUb+4vQGYrfKmvtY9baxdbaZfrXptJ1ITHF\nr0jg/PTpMrAMHSoC9yWXuEoNH0qWxU9j/LIG7Zjip8KmDrhFG6IOFM3NkqlME9qcckp6c3kdAEPF\n7957ga9+Vd7ffjtw663uuyzFQMsebjcQTix63IUXuvrQ+vSfhz6v++8HDigtK/gWP0CECY0fOPhg\nYLfdssuWl1q6ksx5ocWvf//4hKYB7Xr8kUfK64QJ6WNVkQgtfvfck7SOat3pxKu/UUJhv7VVYq6U\nvfZy1t0iFj9jkr/3sdZNuFn1V1OTbFvGyDPfaSe3j2GWxe93v5NVVR8dFFWIDBUiX0ErmtxFFbxY\njF+o+LW0SHsLrXUhavFrbU0m+MkTnlXxi8X46ab1IbEYP71vXxF5+WVpo7FYuJoacUW84gpR7vR5\nTZyYdLPafnv3/rHHRMnQetEyZMX/+Xzve8n/tdy6P1lYR/5zjPWdUDB6773k81EF7tBD4ynTrRVl\n7Mwzk+eLWT7r6pLWxGuucZkIw2fm30eYLEevcdNN4sYaQ8fc+vr45L9ypfydcgqwyy4ytn/0o9Kv\n+vZ11qg8Ramc4qeunqeeWpmr5tq1yWcQU/yGDs1OYZ/FGWe48eu997L3tPPPG4tl9fvsgAFtd/XU\nvqJWvizX2Kx+7ysiYRhDzNVzypT8hdciGWz9/qLzbREhUevPWtmmCUj2TV1E7dvXfa6WIi1zlhCr\n11+1Khnz//DDwE9/mj4+VFQGDEguTGlZ/XkScHX80ksuVj+2ILFqlZTplFNkkXrffV2m7aLx3T57\n7OHaiC8Paf347TVcRM3rvxMnyuL3F74g86XP22/nu4e2tLjr1tQAhx+efWxWGVpbi3kItTUZ31/+\nkm3Za0sCshjr1iXLp22x6Nj06KPp+xs7trKtTJTGRndd7UP33pvMJJ3H5Mlx1+hyFFX8njLG/MwY\nc5Ax5gP6V/nlupa2Kn677eZSOu+xhwgf+rtQkVPlTL9/8klZeWtpkbigLNeZPItfeG5l2rS4JSB0\n9fQnilBA1warE4sO3pde6oTNUCmsr5cOGTb2rBXdmhoZmELr5rXXuoHPd/XUcodCN5BW/Fpb3erf\n4sVpl4Rp06Rc5VarGxvFnSxcIbv0UqdYavkXLBC3BY1fy7L4qWtaEaXSt1SFcUM+69eLhdCf0PxJ\nOxysnnzS7Q+naHvIilUKY/zmzYtvwN3amu/6B0i7CgVorSt9zrFkGS+/HFc49XudHLMEljyLn/aj\nIsld9JjHHpO4tdZWEZbLuV/4rp4f/rD7PG/1NubqqdfPmvx8xS8cQ/x+u99+2fFcxkiSHf3ef15Z\ncdGf/ay0iQEDRDDyrRtF49cUrZNjj5XXsG59L4Asl0efRYuS59D6ePppGYtDYVCFI63jCy4QZT0W\nW5tHOL/kPWt/ca4czz4rC0DKww8n3ab1GWnd6IKKCsK+wN7SIq79OiZlKQraVwYNkteGBldvn/tc\negExZJNNkl4iMcVv9eriWRyVxkaxkgLynA48MH6c72ZZLoZ04MDk8w2fWxHFb/p0ec1S/LLiZv14\nPpUZtJx+hma/L+cpfjG35paWZDvzx+pwTo6xZIksmviLarFzqRKubQZIKzb+PPnDH6b7gSbE0XM8\n+6w7/nOfc9mt9T59ucFfmFL8vt7cnExOt2RJfvItjf1TtE2Fc/3ChS45TB76DP1xUb2A/Ge6eLHM\nby+84Modon1p8mR5ff114KST0lbePE+uCRNkCwlA+vfjj6fbfiwG1mfzzbPP71NpP89i3Tq38FPJ\nYv23vy2x1j66cO2Pj4Crg6w+H1o/YyEBb70lsltdXf5+uT/7megWSlOTtFk/g/7558uC1+OPJ3ML\nxLjnHjdXdIbFbxzEvfMyAFeV/gruwFI9YoqfDmaXXy4dZ8YM4PvfTx+nqWy182tjCRuHZl/Uyn/i\nCZdlLC+rmQ5w2pH9sinPPJPcCHqPPdIm/u9/3w0mMeG4oUF+oxO3dp7aWrmXHXcUgUGFIGvTgntD\nQ3LVW/EHRM1QBkiZ77zTXctXTMOMl42Nrk71O3+gzMrqCbjnu3Sp+/7880VQig3w/nkbG0XADN1B\nf/hD91v/We++u8tyVVubvwpYZIBSoS1U/MJVrVmzxNXw3Xel/NOmJZ9vGFcSEz7VauLXiT9hhO1u\n4ECJiQjT/vtuqFkCbEzxUyEgL7mLbwXxF1f0e7UaZU3ceTF+YfIE/SzP1fPXv3axQP37l1f8NK4q\nlpo9C2tdcpei2znkuXqG9Z4l5OfF+B19dHkF7oYbZGwqd94sQqHz7beBPfd026aEHgQhYXsNLX6X\nXy6LJYBY9dRa4V8PcG34wQdFufDPUc7davlyUUR8imz10Jb9wq68Muk2rf1DhUGtDxWeVTG86CKx\nfn7iE+KqFrv+woUylun439IiY838+W7B5L773O+vvTYu+LS0yByhLvp+jJ8/N1TiPtraKs9Irdcq\n1Mbm1XIWP58BA+LKTCUWPyW0oGqbUmXcZ9my5HX1Oel8oXHEWYrftGnuOSih4veLX0hs2Cc/6T7z\n61zLlzeezZgh11LF1N/30y+/egj5dfDPf0r9hRa/hgZZVPXbhE8sDOC++5x8pfO0Phd/gcqfb33F\n769/TQrZ5bK1qjL/2GPyqv0qnOv/8Adx+/zXv+QaWeiYHlP8/HIsWSJjyUEHyf/h2PPUU25hMVzo\nPfTQ5P9h+/zZz4APflDe+7KjtoPQEBI+l7ffTsaqFlX8ysXEF+Wuu1xcZZHYt2XLpL5//ev0s5k0\nSSy6Wr/abvzn/O67ztsMkPFx113l/bp1opxnZaxdvlzmmx12kEURfyFb9YKrrpL50xhRjpuaZHFj\n9Oj0Qu7hh8viRx51demEU0UoK24YY2oA3GCt/a/gLyNctbpo/MTcuckVHGulIrUT3nKLmMp32UVi\ni4B8wcUfXGKN/4475LWpqZhrgFqHjjoqbunSewCkk+ok7A94S5dK9jdtYDE//NZWaYS33CKDrjb6\nvn2dsOqvnNXUpFcs6uuTq7daXv8+V6yQSQdwDTdU/ID0aktTU/5grPergo+/Uqr3svnmbn+8N95I\nJ0FYvFju3Reuw6QoseyL4XPU9tSnT/4z/vOf3fusNqUTQBjjF7on/e53ci19tkuXZsdZlCNL6Azb\nna6MhZul+4pf1kphuDce4AS1mMUvlnjG33tTy6BuZ0UVv3790seGWz/kWfy03dXUyLnWrEm6SYXb\nEOhkUIlgqxa/2GJLVrvx9/ELXT3DST/Lehcqmf6127N5uF/mWPlXrZKxNmw7l14q/fZnP3P3opk7\nw7K+/HI6UVSo+AFO4AxX8QG36BJa+PxzxNqqz7PPurjdcOU4RnsySfuJKQD3XEPFTwVwHdNeeMGN\nDyow+paWGTNkUWn//YF99nHfqwus73GyZo0Ixueem51t9a23nNDkW/z693flqCRbdVOTzFMbb5wc\n09UFzyem+GVZcLNcPf2st1lWtrCPhe1Txwhf8VOrYLhnnx4bLt75rp6Ae54/+IEkGTngAOCcc+Sz\nUPE7+2yJAfWFU39MCq2MIStWyELwe++5cXjnnd33sf7gW/wWLpQcCFp/xx4rda0WUL1+uHCYlehG\nUWu2tkk/5trv47fe6rIQa3/2FbC8uNPQsvP++/LbcK7XkI6//CU/S25sMU/nff+ZX3edq2vfA0rR\nsey+++LuiI8/7t5r+9xhBzFePPyws6r6Y7ta5M44I9kXQkXwySdlMVyPGT7cfffSS+lx/s47k4sO\nMWbPTobovPiiLE5rkiLFWpdpHchus8a4hWz1ttH2t2qV9OuHHxYFcvHitNKrSWiWLxdF98UX3f3q\nsevWiTJ50EHZi7TLl7t+f+CB4jGkHHecyPr+ovaKFcl7qnRR0FppR7FFpnKUVfysta0AMraw3vBo\napLVyx12cAH/W24plfr449mCWblKX7jQKUT19dnadVHFz0cffpbQdeGFLjWuHtPaKgrPu++6wUAT\nYfgCTEODyxzlKyR5mfxCM/2KFS5Ne0uLxGutXJlceV261NW31vEvfylCWiyOUeu7uTmdOMOvWxVy\ndCXZV/z88771lpxn4UK5hv88t9pK/OL9QUoDiGMTvHb2LKWqT5/8ZB8xwSTE3/LBFwr93+oAM2iQ\na3sDBiQHnqwyLluWDpJuaYkHhYcDakODtKFYdsAsi5+2uWXL0gqH/kavE4vx8z8bN849lzC2o6ir\n54AB6b4eXreI4tenjwhX776btICG1jRtW/62Gz4x65sqfkDa1TNL8WttLWbx+8QnsttoeO6Ye1Ce\nApul9Jez+D3xhHgohL/3x6vGRvFsULdzPeeZZ8ri2oQJyXHyiSdk7GlqEgvE+PHyeags+cTGyVDx\niyVE8vGF3SLxnB2p+Gk/UiE2FGZVuPD7aOgy/7OfOYHHX+jzN4APQw1UWPPb8pw58eeuip/W37Bh\nyXLEaG1NjmeNjXKtPn2kbpuaZM676650yIXGaAHuOey3XzwuKFT81IKpbv81NdnPKxyPwnvXucmv\nU7U6NTW5so0dK3MSEI/x8vuy9vcddpDXF1+UbJ6x8igjR7r3frvU+te2ftttLk589myxLKmiEIvf\n9fvD9tvLM/Itgs3NMm/48+pvfuP63MqVUkdhLHdM8YuNS9omVeZ5+mlXL4qWW+9RlZVyip+fORsQ\nmcfadJI9XeRfu1bO9/778Yy5MYvf22/LM/MVvwcflN9usYW07XAc0fP84Q9xecVfCNM6mztXZIms\nRT09z513JpW9sH/qYtLKlVIXGjO+fn3anfnRRyXEJ5Zgxh9Lnn3WWVcBWci45JL0Il3Yd88/X15n\nzHDxdFpXb78tcr6eV+9pn33EKqpx2WvWuHYxcaLc/7hx8v/y5a4/aTvR8yxZ4rz6QnlGX5cvTyrm\nW2zh3msb8J9fbW08RKEo11wjbSe0+BUKUyh4jb8aYy4wxmxrjNlU/yorZhxjzOHGmDdLW0VclHHM\nz40xM40xrxpj9sk73wMPJOMjAGlQOlFkxfhpw85i//1lgBk+XB5eLPFKa2vbFD9tDFm/8wcebWT+\nfajFUjvOc885C5Hf2f001nm+4OEK5JNPulWFV1+VTrZ8ufO/B6TD6aqVNuAf/lDigfIsftOnJwXU\nLCFGsdatgPnlXLjQrcSFFr+WlrTFT4kpTrF4Qp/2ZoZVtt46rfjF2lVtrRuQm5uTrjVZit/q1WmX\nrNtvF5e6kJjiV87ip0JlY6MMampx/fKX0wNYaJmIuVmFfc/PDuen9S9q8Qvdufxr5GX1VLTfqMUP\ncJZ1X2ELydpfKna8JgoCilv8pk9PW9KXLJH3GnNzyCGiPGUJOUW2c9A+FroS+dfNO2+WMhD7va+g\nNDZKW9dFh5UrJdPrjTfK5B2298MOc+e+7z63P2nW83nxxbjFT8fusExZ9+r3Qd8dPWsOyVIk7rhD\nFtJiqKVI43JCdA5QAUyVgbo6EeY1ZghwY4GW45//zN5DTJ9dVnKxyy93iWiyYtlU8QsXiELB8pFH\n3HO48cbkYtOqVU5JmzTJLUbdd5/MLT6nnebS3/t1PWKEjCX+sw4VP3Wn8l3Ss8aZcvuf6f35c5oK\nk01N7ry+wqbzvpZ7yZLkPah8EPM0ytq6JCvGz7cW19WJUqbJIXRsz9vjN0wK5i8max/SJD4618yf\n7xS/vfaSBfhLL00+ay2X/1zCPtzUJOOfv4egLvTE0P6syZ7KKX6h3KP1ECqEiu7BNnKktAt1CVTC\nxbwpUyTBzC67pGW9gw+WxHyhm/tNN7nx2Zi4xc9f9PDHcvVqUbJkX1/GCo/RkKSpU4FvftN9ft11\nLkZbF3WeeCJ9bs2gu/XW4rU1c6a7h9jYevXV7v3o0fHy7r67e+46rq1YEffumDtXnqNec80aF4s8\ncWIygdXy5a4d6mKM1sf8+fL8jHELC3qsWtcXL062ob/9zXmqZSV5jG3dFZLlfaALDereqn3etwBn\nUVTxOw7A1wH8HcBLpb8Xc39RgJIb6fUAPglgdwDHG2PGBsd8CsAYa+1OAM4AcGO58/ppd3VfqYtK\nKmUYs6cUzciz996iAMb8jZua5C9cwXv55fwBp1wGLP98KvSFE+jvf++sSN/7XjquBRDFSFchwvgU\nH62j2DnUpP7MMzJRK6+8kp34I2bx04HqvvuSwqXv5jdlStqMbW08bf3TT8tqk14jnLiXLo0Lo7G4\nSN/NK8ufuyMYOjS+j1+IL2w0N0t9ZqWEV9avT7eRMHGMsnx5WumJWfzWr3dtTMuszyfP5SUc9PzM\nfDGLn3/+NWtEiQmPDwmzeg4cmK346fssi5+vEI4cGReushSLLME/dnxjo2tfoZBQZNVO6+iww5Lu\ndzU1Ili2R/FTi0G4iOaXVdGYGD8TWczaGO6bF34OSJ3U1blFhylTnHVgwQK3fUHs3P4kGpZRExMd\ncIBTeMIx3BeWVajJam/++bWftLTExyYgHS8LyH1+8YtiJf7lL5Pf/eAH0u/PPTc7wysgQpcqaLro\nUFeX3mdUY6S07hcsiJf1yivTSZFinHaauGDG2lhLi/ytWJGuYx0Lpk4VK+7//I+LBwrH+lGj5Jkt\nXAh84xvJxairr3YxZorGnYbta9gwSeSlhIqfX25A5uMsIazcxuG69Yc/9sYUP7+My5aJBVmvuXBh\ncg80rbN169IxP1mK39tvi/Vo/fp4Vs9ddxWXvDVrXFl1UUUXUGOEi7j+wrJuQzV0qNShLo5cckly\nfrjqKhkPNWbev0e/v4Vj5jnniCvrqFHZ5VNOP93JI9ttJ681Ndlj4oAB+dtmxFizJn2+FStcQg4/\nPwMgliVr5dmGyWGGDYvPEV/9qhtramriit8rrzhvq9Wrk3OqymurVrnnHM7rdXXSLh54IK34qYz3\n0ENuYQmQ8ut4u3KljMuxRZGJE508efHFUgeqQIb7afrcfnvcO6CuTtrzv/8t962xyVkZOXW80Ge7\nZo2L/Vu0KKmo+Yqfnk//nztX+qg/btTVJdvre++ly3HlldIm/LhB5eyzi1n8Bg+WvhSeO4wvbmoS\nL4LTTy+fRKyQ4met3SHyl6GPV8SBAGZaa+dZa5sB3AXgqOCYowDcXirHPwEMNcaMKHoBXXXSBqwd\nVStRM/8U3TtjzBgZbO+/3wXjKo2NzuLnW0v22y89SfmsWiXCSFYZfAtTfb2UPRyktt46ucIbY+HC\npPk5xogRbgLwV9YU7TR+9i0gmewhbKDaoGtq0sldFB3cpk51nW3cOEkm4NPcLAKLJm/wefddWR1X\ni5+/Ur5kSdziF7Oy6iTV2losXXYRfHcYpabGxdPl4QvmTU1uL8E8YufM8pG/5JJke8qy+M2a5eKa\n9Pw6cGZtq+EfEytHlsVPBYq1a9OrmDEqcfUsl9Vz4EA3aW+3XbKuzzhDXrPaRdbgHTu+qSmt+IVu\ng/734T5hvkB39tnuvSp+Wa6etbXybL/0Jfk/z+071s7KjSEx7r8/HvMLJCc/nXy17fmTW97i3J/+\nlBx3wvHlgQecchxTeDQDpqIu11mKX2yxRrfyiBETOH3F6hvfSH43YIBco5yXxogRaavb5MnZmz/7\ndZi1Yb0+j3fecfFSMerq4nOO1u+sWcmsioB4p7z8sij0OiffdJP0t1j2SZ/6+qTQ+qc/JV0atezh\n/AaDUo8AACAASURBVNPamnTB1iyBWYwcWdztKlxEOeEEefXHU31uDQ3JEAdl+XLxJFq/Pj5OrF0r\nguell6b3UMsaD59/XuIBH3gg7vILyDl9xa/cXqVA2uLnK35TpyZdPX13aN87SDPo+ts2aLv0zx/e\nqy5mqCKXx69+5RQMtai3tmYn3Bs8ON8N2eerX5XntWBBul9vuqlTzvVeHnkkuUfoz3+eljv69s2e\n03Vu+OMfs8dAvebFF8cTq2yyiVOSQoWhrk7ayWc/m20VDON6w+M++lHnThnij3O+F8Dzzzu34hB/\nUcDHH7sXL5b7HjgwW2lXGVDrMBwb/P9/8QuxZAJiTVu3zsUMzp+frrfLLksuYi9YkJbh+/aVfrjL\nLpJYxuexx5JzX2trWubWXQEaGmQ8njFD3G1feMH1B1UqGxqAT31KxpDvfS8dC+9TSPEzxpwU+yvy\n2zJsDcB3OFlQ+izvmIWRYzLZcUeZWFSA0o6qwujcuVK5S5YUy0rX3Cwd9Jln0pOeWvxWrnTmbyW2\ncq5ce60MZlmd2hcyjj9eGvO6dTKwqkKZtfmwT329lCuWmltdNnbe2XWiTSPOvE88IauF/qbGxx6b\n7MDh3luqSG6/fdrVU9FV0fPOc8K1j56zvl46YZZ71L77upVVP7gWiD/fvO09slw9Y8Ti4Xxi56mp\nEQGjnMWvLYpf7Jx5iRX8AbC+Xtp56Fr0zDNO8ff3VQTSKfN9QteDLOuqj1row7TwRV098yx+ea6e\nmmlTyxUqfjff7I7x0bZVqeIXxviF5/PvL2/D8PC3tbXZq9ubby5jx7e/Le6EeYpfLIZIBURNCFKE\nY45xSUPCRQnfirfbbtJOdfz0J9uifRFIP4fHHnNbIsRWh++/P+7FUYniB8iCWJEMrcYkMw4CyfZb\nUyPjsB/nErvmyJGVbTyswu2QIaIMhfFRgKuH5cvTcV7h9kSxffUOOsg9t1Ch/ec/0/FdTz0lrzpP\nXHmlWEJDFi1KLka1tsq1Pv5x99lxx8WFxqIZZ0eMcJ4Y7cFXIrQ9+Iqf/ywbGpzil6XI6XMK55ly\n5Vy9Olvx23JLl7Tqpz91zyEPvd7//V/a4vfqq87it3hxUvErx4IFcv96/iOPTGcS17EoZvHLcgsE\nXIxsc3P2mDh4cFx5iPWPj39cBPzHHsv35Hr+eelj770nrpyKKiMjAvNF0fEtlGtCQu8Rn4kT0/KZ\nr/DX1xdTrIFkeXURMUbWovB117mMoyGxsfjQQ5OeDCq7jRmTrfipoq914j+vj340/fxUvvnCF5L1\nMG9ees6/4YZk+X2ZWNl2W5F/br3VLWT4C3jhIriOrzo3+EnkHnlEPC1OOEHGvYceEpd3lYXXrZNn\nssceosRmbQkFFHf1PMD7+zCACQA+nfeD6jHhP3+77joZxx8vE8GnPiXfhu5uM2fKAPiPf+QrZ8qe\ne0rlxoRotfgBcaUpC3Wfq2QDyHXrRAHTwXCPPUQheuMNt52Ecs89zhXguefigokGQPsKVdY9jBzp\nrJC//71YyIpkaxs7Nvu4vBXWI45wQptmafIHTb8jbb65rFLffbcTHlWwzVMasj4vmiL31ltltSar\nzmKCf21t2hUnRszV0x90Y+euxOIHJAUj3XYjZlVVdHVv5UpRHvKEzzAm0lpXT+Eejoq/avmi51Te\nURa/PFdPfwVxu+3iilHWJJ31LGN9zlf8wmuo4Ow/l9Di48fXhNdatiy5me9PfuL6zPDhUu+DBslr\nXtxSnuKXJ2zlUS5z6OjRbpL17z9rT9QY/rPfZJOkEBkKXIqfcCB2Hh//Oft19Mc/xvfAjBGmG4/1\n2ZgA5FvhRoyoTPEDRGEfMECEUt+qospWXmIcFeLUWvP66+n28/772fvbAfIswjaw3XZOifS3j/Cf\n+TvvJBWflhaxVPhjbtYG1kUVv2HD5NlWmmghxBdEtW/X18cVP0DmrTzFT1HFV1f5yyl+jY3Zip9m\nL123Thba8lyKFfWC+eY3k4rfxz4m9+lnpQwVP02iEY4bAwdKrOFRRzmX5733Tl9b21RMMclTMrV/\n5il+Bx8cVx6OOy67HEB2/NUxx4iXz4wZIpv5sp226dC6kzWn5FkiNZO6/n633Vz9x+TZ005z9XfM\nMfL6kY+4vj9zZlzZjeGPE34Cnc5i1CgnxwPuWX7uc8lnd8stzpvBzx4fctllopzvtJPbK9THt8o+\n+GAyYZOf6TaGyuC+d8zAgRKf6BtpfAv07ru7uD2Vw32PhgsvTI9vixa5uXLdOmD27MloaJiAhoYJ\neOGFCZnlK+rqeZb3dzqADwCoYBrOZCEAvxtvU/osPGbbMsd4ZZ0AVfyOPHI8+vSRxhi6hPhsuWUy\nqNTnxz9OWsjOOUc6mMa1+Dz2mHvgocUPkAf+rW/FfwfEg1OzuOMOacx+5qhtt5XGc+SRyWMPO8wN\npGGqaEUbj9+gfYuPv9LqT/SaZTJUPsLUvIBM2lnKR2wC03N84APJz/v3T66++CtKasmdOrV4woz3\n30+7I2qZsibW0A0SEMEkywoSG9T79pVBui0WP7++VfD505/cZ/vvnz5PnuLnKybNzfIXc/VVtJ2v\nWCETeZ7Fb9Wq9GStg1+W4ufjr/D+9rfxybYSi58en6X4DRjgJtvttku3mzBoHihv8ctKdhK6eiph\njBYQT8YRo6YmHYs0bJg8o298w2UTGzRI2lKexc+Y4tftCHbeWRaSVFgr1zd23915G/j7Tfm/Gzo0\nufq53XbJffGUWF/Patd6/qFDxY3HP4e6+1XK2rWSbbMcvmC29dbJMhbZP2vtWilnfX1SCD/pJHne\nQ4ZI6vIYusKtQt+yZXFBPM9FfsaM9Hg7f35yL1lAxh9fUF+7Nqn4qTDtj8Uq4B1/vFM0gLgFPcaw\nYS5GsT34wrr2r4aG5J62PpttJt+F5fLdIQF3r7q/XUtLUhgOrRI6X/jl2mgjcbOtq5O/oi6OgLhQ\n6rjVt6+zng8aJOfx7yGscx3zwzKqrPToo+4zbV9+29LP/MUKVfjyBHGde595RuozXEDabz9JQvfP\nf4rM8e1vu+9iHkF5ixqKxggvWCBzkZ8pXftGqKxm9Znw+fhtM8xUvtde+S5+ffu6elRrvt/mTjst\nLtvE8OcNfbZqzRw9WuJqb77ZKTEHHljsvEDarRJItoVDDxWlaY895J59xe/AA+X6O+3k6mq77dKW\nzj33FNnkkEOc59xJJ8k4EyY1W7JE6un3vxdXy5ibvL838hFHyLj86KMuEVVLiyiYRTa3N0Y8Yfbb\nT/7XPnLIIcBZZ8n7Z5+VZ62yQ10dsNde4/HLX07AQQdNwJAhE1LnVYpa/ELqABRcF8hlKoAdjTGj\njDH9AHweQGCvwiQAJwGAMeaDAFZaa3OrThuu34B9wWrs2OTxsZVWFXqHDEk22JqabAVCg3qB+Kpp\nTY24MmYRW7n1B4cttnDluuYamSizhLYxY6Tx6T34g0qeBcMXKnxl2Xe98YPwVUDT+COdmOvqkoPx\nv/8tAlJWgpHPfc5t1Klo9qVLLkkfnzVI+oJMuGF41m+22splNvPxFb/QLSsM1tVrxBTerGsXtfiF\n1rjQ4rfppjKZxZLx+OQpfn62RLX4bbFFeUFSFb9ygpK/tYS1boWwyKasau0FZDDVrUV8QiW9SIxf\nlqunP+kUSSTgk+d+GeJb/EK3phiaGU/J2ky3piYtQNbWShnOPlsWRVavdplP/XryE2MpOuaEMYad\nwYgRsniiY5TfZmOWwpoaN075fcy//zAr5r77yrYSIbHFnzDpiqL9pa4uef5BgySWQ8d5fx8qINtF\nHRAhWu8hrz8NH+7cZrffXtrs3ntLOXy3x7zrLF0q8+OQIW4MHzZM3k+Z4rYP8mludjEvKvw2N8cV\nP3982nHHtLD/ox9l9y2dj4cOTVsTY0Kplt8YJwDOmpXs22H/88cdv6ybb550ySxHbMGqX7+khaeI\nxW/TTZ2ro79oF8omKldovaj3i46noYU+3Beuvh740IfEQqfxSHnhDln06SPn1SQlqgT27ZveGBsQ\na4m2mVD+iC2Sq3Lm7xu3apWk9PfbjdbHlVdmu7Zpnge1aIYLmrNni0z4zW9K+I5vpYkpxTHFb6ed\nkvshH3us9KG5c2U+OeWUdFsO66Goxc9vm34b13K9/HI8G7Oi49WoUXG30VAhzfKQ8Muv45b289df\nl/je00+XvACTJ+fnuQjxlW/Fl6369xfFb6ON5M9X/LTt9O/v2uCqVdLmfQYPFhn14IPdvQwYIOfz\n69WPXfziF8UN9Kij0llcVXZ+4QU3L9XWOvm1pSV7+5UQa2WsvfxyuQdtk//4h5OLx42TcUPHNnX1\nHDNGPCbyPAiLxvj9yRgzqfT3MIC3ABRYW8zHWtsC4BsA/gJgGoC7rLXTjTFnGGO+UjrmUQBzjDGz\nANwE4GuZJyyxaJE8fH910H+Q4UCjK7Zhw5w+XT77r/9Kfh4G06tF0R9AY9kg167Nd6uKpcbWcl94\nodyXr1z26ZOddXLGDBGQf/QjKZ9/XGyy0g7iD7R+/fnC8D77uMFTG3LoTrl6tZitf/c79/s998ze\n52yPPVwig1/8Qsr4oQ/J/+GkvXZt8n7efdfFhP38584ipKuR5RS/GH37JoXiUHisqYlvnPn97yf9\n+f3zhejeMOUUP1Vm+/ePx/htuql8V25QiSl+n/60PJtVq2QlaexYZ/Hr108GuCzefFPaYxGXP3+Q\nbG52wvq998prXh2E95WVWKPodg4TJ0rmujyLn143lo0LyN9nr+jxvuKXlRbfR5+5Tuo6loQpzbMU\nP0AEFO0r/frJ5/64dfrp0mc1Q65y550uM6RSiVtPmKhB8RWhP/0p7XLjK3sxAXX9ejdO6XM77jgR\n8u6+W/4PBbWNN5ayh/ElRd26AZdVd/36ZBsaMEDO/Z3vyP8ao3FSKSJ+2LDsNrJ2rWsPWfF8gPxe\n73n4cLnewQfLtcrFVV10kVNKN9lErqdeCkOGSJtcujTtZQEk5y6/T/pxKIo/Ng4ZEo+B9r0jfGFc\nty+KCdix8/gxTQMHiiXj5JOT7TNU6puaxPrz29866wwgwvuyZcUtfrFF4+bmpMU9FuOn5dHYKLW+\nWyuWKY17Dc+vY4Ces7nZJQkD0mNlY2NyUXPKFBH4Bw508aOVWPz8Mvjo3nT9+rm5Uueb2bPlmuef\nLxbDMBwipvgdcUTaWnn33fJs/HaoQv5GGyWzPwMyZu2wgwjIJ5zgxpILLnDxWLvvLmUzRhbTt9vO\n9aGpU0XuCjNw+hZDfT9mjFiDfEaMcNkgv/99l8xIn5U/JhqTrfj52xnNmpVcRA0VP/UaCxOJ+Oji\nyaBB8T4WWtu22Sap/H3pSzJ/+oqflsNXoJTBg8X9/dOfTlqnY5x1loQlxYwT+lyGDpVx67LLRG7J\nU/yU5cvjsvJ11wFHHy3vX3nFWdj1Gf3v/8YTZd17b3Lbk09+UtqatUlPA5/164srfkq/ful2sd12\nIhv723wATvEDZAGr3YofgCsBXFX6uxzAR6y10T33KsVa+2dr7S7W2p2stVeUPrvJWnuzd8w3rLU7\nWmv3tta+nH02YeBA+fMnCa2cn/403ZF1Y8hPfjI5cY4dK4PM6NEyQSihG1ZLi3QOv/HFlIz6+ny3\nKl2Bq6kRX+uhQ92E2NAgn4eDW5bip5n99F798vjl1AyWW28tA4oOBF/4QtJl1F9pveMOFw+jA0Is\njs4YZ3Xs108Elyx3Vj+WSgW8ULB86SW3ma+W8/jjZcNQf+LT78I9v2LP5MQT4/EEzc0iIOn9hINh\nTU1yhU8Hm7Fj45n9YjFeM2aIoFtO8dNMUwMG5Ct+5YLDY4pf//5S37W1ojQfe6yz+Okg9fGPp1fL\nAFHmXnqpmOLnt5/GxrR1Ms8aGQ6WMaEsVPxqa7Mtftr+y1n8zj03uRCixDLBqtWjUlfPShYj9Pnq\nRHXLLbJYErYfXxBU/NVSFZz69k1vJrzFFiIkhau8n/9827J5qnCTFfvqK3Yf+lBSqAGSyl5MMWtu\ndn1P28ldd8mEfeyxIiyGyqTW49//Xl4QKYLfhvR5Dh8u19fthL73PXkdOjRbYY5Z/DTrNCBhB1On\nSn/U7zfbTFzdhw+XuaJcYpkrrhBhFpC5rn9/Z0FR68lZZ2UvUKqlzJ93shJbaWxu//4SwzV2bFIo\n8n83bZpb/NBFh5gSG5s//XseNEjq6etfz1+YaGyUc+l8ooweLfNwUYtfEWuZlk8tfttsI/fbt6/U\nCyB1pEpe//7Oshr2bb1/Pef8+cn+HlpE6+pcvCQgc/dppyXns1h8Ux4x4bVPH7GO19U5a7pmIFdL\nyLhxYgH/4x+TinHsmW60kVwnvP+GhuT1da73P9Oxbq+9ROkcMSKZfG7nnaUsY8fK5+EWMdru9t9f\nxq8wWZCvLPlj4sEHu8VqQK47Z046Xlvb1vXXJ/eLK5LcZcwYcVnUtmKMc/VetMi5Rue1fR0v1boV\nEso6W20lz0tju3feWep21Chpewcc4Ly79N5i49BmmyXdeWN85zsyv332s2mXeR1zNt3UzRvz52cr\nfv4Y9d57yf91O7PDD3dz0z77uP6j/en2290z9sMDamqS41OeXK+0tOTHT/uEc90Xv+jcuzfZJJlV\nX591XZ1rQwMH5iuZRRW//7bWPl36e9Zau8AY85OCv60KffvGXT2/9a3kZKrHAjLgZmUHypsIdLXG\nXzkLH5y6ZdXWio+wEttPr29fGXBeeUWCT5cscQH9gwY5hSaWXTAL/zg/RkrrZdgwWcXRxrzZZsnJ\n3xfu+/aVzrV6tVsZ1vNoPanAPGyYTDYjR0oMou/q6ftc64q4X77x453FEJBr6TNVq8Wuu4rrVkwo\nDScNayVjqD/YHXNMtrD02mtOKMiagAFRHHUj6bZQTvHTzqzZJkNXzyFD4itDITHlStu+rtJq3KFa\n/ABRrP3NWVeuFKVIKaIQ+INkQ0Pa3ToW06aEz6eIxa+2Nt1nY1uI5Cl+WcKv7gmmMZWTJjnrRZbr\nalsUvzFjkq57+qy0XEccIe03dIGMxQr5rj9+PWXt95dl/fL7aRFefVWEL41tDhVAv03GJs9yE6XG\nOb/8clwBOfZYiZPws09qu+7bt2O2a/Gfrd+e7r7bLSrpmOMrtjqRKzGLn8ae/+IXwKmnijDqW3TH\nj5cV8r5945a3PAYNkrY+YoS0oa22kgzTuhAaQ9v3kUc6q2dWzJPe+6mnioA1fXoyw+/y5W4RY8gQ\nZ/lRITLWHmKLTL5VvmiCtNdey1b8liwpbvErsvebH+PX2ipWpjApjip+5cY6f083QNrM9Omuvz79\ntFhClFiymwMPjMdQAenPYxkZY/OMzsuf+Yxrw01N8YRMw4cnLf2xMVPni/D+Q5d+Pb9fl2rB9evy\nwQfFVV5d6GpqpN422ig9xoQLDmE71Gv+8IdpTwY/vEUtfmGd6nzZv79r84sXF8/qqVmbgaSr+7x5\nSYUwRLdiGjpUQleMiS+u+IsZ778vCwdDhqQXFR55RJTNKVPEaAKU35oqjwMOcEr7rrs62e+//1v2\nftT5b9AgZ7FVV08/M2moaP/Xf4lsrjLwHnuUj6VW+XXAACe7h/kbyoVPhbS0yH1pXw2fkR8rHvKD\nHyRzOPj4Fj9f2cvbtqao4veJyGcdsFbaefTtm+3qWVsrwoC6FlorWe98k24o+JRzA1LLiRJOHL5l\nzHej0pgaXzHT3+6wg9zD8OHJDuq7HRbZxgFwA8UmmyQnq3Ci0Um8psb95sQTRQANYzn8ATO0+Pmu\na8cfL+fbZpvk6qJee5NNkp1AFb/+/dOrPnpNfdXrnXCCW1VXwmewZo0IIeEKcZ6b3erVYu0KE+b4\nHV3drdrKW28VO66+XpILhRY/FWCzJg7NMhhT/LTcOliq4udb/EIFqV+/5CAYc9UJ8YXDhgaZMNVX\nPcbgwdmpnotY/NRV1yfsw+VcPcslPVGrZf/+rh6LZLfVsclP7uLvc3XAAWI1njUrudqszzcsV7g9\nQUODiwGL4deDvwG4T9ZCV7jA8fDD2dc55hjpXzvs4PprmDHOv06oaF9xRfkJVQWNffeVOOGsWMn9\n93f36U/YlfbbchanGBttJOP0ihXJxAthHf/738ksry+84ATksG60D/TrJ8Lmbrsls4medVa+NXPC\nBFk8O+UUGTf1uueck3Zr91EhvU8f5wWQpfjV1kr7OPVU95m24S9+UWJ3/fvyFXL/FZD782ODlXff\ndbHhlbhRvfiim+N85UItfllJ0EKKuEnqeWbNEkvfZptJv1d54a67RFlZsSJdl83NycXSUPEDZCFY\n+/S22yZDDWIp5sPQD59Jk5yrLRBP0+/X8wkniHKjSr5mDweKjYVanqefTs6DWj59NrrVREuLLB6p\nwqXjil+mWHKZ3XYrvjCSp/j17+/myrFj04qt36dHjBBLU6j4jRuX9LJ45RXgttsq2/5C0Xu87TaR\nrWKKn77XuF21zgLJ9jZtmryuWeMWynTrHx/fuqxKrLbHUaPEzbotZGVI3Xxz8b7S++jfXxZFARkz\nNtoomR1Tj1Mrry6wqVJZbqEdkKQ0msUzaxHCH7vyYiqVvN8DyWdRSdiB1v3ixcmF1bx479wpyxhz\npjHmdQC7GGNe8/7mAHgt77fVZuDAZCWEE/xll7kBsrlZ3F/yKt7/f8mSdBKPfv2Sip8+5AED5AFr\nWfyHPWKENOIFC9yqfTgRZdGvn5z75JNFYCjC/PkyqMdSTSu+4qff3XSTrCrlpVMPFb8sJcQ/R0xg\nOvNMt5Icw1c2VYEHpC7DxBRajxpftnKldOJnnnH7S/mxDllMmuRWlTUTlpZ9443zEzb4TJzoVudi\n1qS8bFyAG9RDxa9Pn2zFr18/1/byJuJQ8WtuzhakamuTinBM8Quz5Pp9q64uqSzFyr1mTdrtT4kp\nfpqwxS9jlqunErp6ajtQoSMvHld/r8freYpY/IYOdVub6LV8YXuvvdzY5P9OJ6Att5SJXgnjlxob\n42nIFb+eNttMxrPwGWQpfmGdHnFE9uLTBRekn7Eqfrr6nLdqWlsbj6P18VeYa2uzYzIBN2b7x1Sq\n+MVWZcudQ2OSN9kk2aZaWyXpgVpV1NVz6lRRysaNS8d0KeFz+Oxnk0L6iBHiVhXGGCoXXyzusJtu\nmp2Qykef17hxzqqhC6t++MGcOcn4wCOOSJZdx5QzzpCx+5xznOtp6Mbo15W+D/vkFlvI2DJkiLgR\n+lbUcs8lZvHbaitpU3V12ePf/fe7hdwiFg69nxtuEDfUPn2SlqLjjpMxob4+HR/U3OyUqnPPdYnm\n/HtraUmObbGYJEDmKU3SlrVYse22LhkK4OrbX4ANx4pRo1w788tVRPF77TWJl/rIR1y7uuQSV75f\n/lK2StI45tZWkQFmzpT/QzdvwNVFkQXJGKGbuz8u3XBDchE9tBb646YuUsTkJv93++wji+oXXphe\nYPa59tr0Z1pPJ58sC+zaHnXO32knZ42LzWc6L++0k4xDV10l5dC5JtaH8pSSAQOSc1OMcHsnJUsO\n862bgIyRU6bI4tWPfyz3EFMaNRmVjvf6HIrI14MHp5NPxfZ/BcSAdPbZ+ec76KD0omm4ENEWxR9I\nunqWS/CnlLP43QHgSEhmzSO9v/2stW1MWt01PPJI0p0sHOgOO8wJ4TEXofAzv7EPHy4rjb7QErqJ\n6vUGDZI/Fez8QURNyNoAhg8vlioYkM6jAbZhdqEstt1W/mKbyyra+HzFT1+feCKdJl75znck5qhc\nbIR/vZoaser48WMTJ+YLb/6A2dycdpfy0Qn97LOdcDVokAjWeo0iq7p+mfv0EUVQFZtly4rHSBx0\nkJtUYkJFuf1ztL2tXZtW/Pr1y4690IGzqOI3e3baGgbIKhgg5/Mn1dgE67uCAslBTS1deXvsANkC\nabghPCDtzo/VbIvFb/58mVCKWvwUX4ktktxFLQ2+q6e/KpwlsOozr61NrqqGyYTK7ZPnowJCOGEU\nVfwAGYdi+PekbVMF3n33lVe/HYeCSTmlD6jctcjapKt/nnIQJri55BJRmHz3t+nT87NH5tHSIlY6\nP2t0ba1YJ1VIydomJM8Vcd06lxVP55Nx4ypPLOCj8cx77+0sM+r6tc02Tijdbrv8leZwTjn4YPG2\n8dF+GlP89tpLEkpZ69w1a2rEze2GG5LuULFn4Qv1McVv8GCZhxcvzl74Ofro8lZeQBYJ9tknPu6E\nLoJ6rbAv6/hgrcw52qdGjnT7sBXdb/bII9MJSHwOPDC9iKn901+EiylZRx6ZHneKKH577pkee/zz\nH3540mIcjktaHzHPjbbEJAOycOFvYRMmMdFrDR2ar/hp2Yq6cG62Wfa2Y8OGySKJz9FHp2PvdTw8\n9FDxZJoxwyWaysvmrn36vPNENsobX/LaWpHYWLU86qK9trlY7DyQdt3cd195BhdfLPNglkHi1VfF\nxffDHxaZRq99yCHlyxhywAFxufSOO/IT4CnPPZfe33WvvZKyeFstfj6xnAQxcocva+0qa+1ca+3x\nkL30PmatnQegxhjTEds5dBqjR2fHXvhYm96oeu5c4Mknk5/FYkH8c775ZnLVQRXHkSOl4eoAob+Z\nPTu9ge+HPiR+46HQHGOnnbIz5ZUjz9XTV/x0MtIBY6utsq1bY8aI616lit/zzyczlZajkk2cdWWn\npiaZyQooHrwPJAfM1laZ5FRJ69evmPKo5dABNSaElevsWncrV6YFZt/id/zxybLHUuOH+IPrpEnx\n+gmFUSVrZTUWhK/4il8WsTTxQDxAPJbFspzFL6bcvvGGExiKWvz69y8vCIauN337iuLnx28qWSuS\nYQZd5d57k/daTvHzn4VaAMIxMKt/7L13uu36wo/fLv17UoFkm23kGK0P/7rhfWksJZCtTOQtEhUh\nT1H7wx+SVrRNNxWXPD/d/tixyWeflcQmRmyrmCwXvLBN5MU+Dhzo6lLHu699rdjWKSH6rGPCNObK\nQQAAIABJREFUq85xtbVOcKypkZX4rFX9IopxLEOlv+qvCXN8y1RWgpkQf8EkpvjpWDpjRn7/L3If\nL70kSRhi407ozRBT/KZNS25l47PXXi5UJbT4KaGLYbnx7IEH0uPYyJFilY6564aEMlJRV8+QvLoN\nx6UhQ9J7rbZVaPbxs8z69ab7Quu1Q3nIL5/Ow5XsCekvkJ59tuvHsTjs++9PW6V8V09VqPPqMyve\nrC2K31NPJXMylOOOO8Sd/dlns5X0F18Uq55fRk12p2TJX3vv7cZjlddefz17j9I8pkyJG1iOP758\nv8pin31cIkrAPfv7788PgwnRPuuP+2V/U+QgY8zFAC4CUFo7QD8AOWtHGx5FVuiUUaPiWe3U3UXx\nKznc0PGQQ2Q1+KqrnMXPHzR22CF9jW22kRWXrM3kO4pws0vfaqb35G8OX0ndlVOoiijjeRTNigS4\nwcsYsbYBaXN6VhyZj1/OShRGTWPsn0cH5thgEQp36o6qqGU4VPzU4qefqSJ20UVJi19M8PPdFYHs\nrKtAesDXwSlrw1ffghlT/PJYuLCYkq/3Flp+Yha/8H/f1VODvZub3UpkuUHUV/zKCYL+9336uPLF\n+pjvMl60v/jflVP8vvpVt+fVl74kruZh0oysyf0DH0i3I99N1U9u4D9jTUg1bJgTEBcskBVZzRAc\n1uG4cdIHdtstuTm7stVWwGOPxctZFL2mnzI99j3g+qcKVDphn3iipCo//PD0fp95aHs84ACX8THL\nTc/PIAzIAmGW94VPUWtDFn7isxBVtvr2lfhKvfdBg+L7APoUEUZjFr9KuPLKtJDnK4vq1RIKuWpp\nbqvi96lPiVC70UZSF2FfWrlSrDD+Rs6aYdefj3b7//buPXqSsr7z+Of7m99v+A0zAxmQGWBmUIbL\ncFNucdBwOWPiYAIuM2QE8bYg7uKBRdBNzIJnxEENMiYhAolhkRhJTlhlJ0FZVuUiDIsYkRVYJ4KA\nh6iIMOzxEsICcnv2j+qHerq6qrqqu7q6q/v9OmfOr6d/fal+fl1Vz7e+z/N9DkgfAeRce/umZfy+\n/e2oIqEUj0hJu9g4f34cvKT9fvny6BwWXtwLv1N5QVYdgd/cue2FwT7zmc7MWL/CdgnPCQsXds6l\nDtdW9cfkMoHfuefG2fOZmeIdee/KK+NKsV6RfS0pr5+T9ZzVq4snI558Mq6uussu2YHf4YfH55ej\nj46CwLT90l9A/LM/y39fs/7qMVTlhRfi4oZ+xIw/X554YnafKo3/PFnLSKQp2vU+UdIJihZul3Pu\nZ5JKdMGHb+3a6MTcq+npzrWNwqqU4c791FPRMKH99ot2hCVLoi9v3olk8+boZF6HMOBcsiS9WtCz\nz0YHnoULq91Rwg5qmQOi12vGzxc68J21rCtdacKDb5ltfv759gPonDnxNqUd0P3vfCc0PMG++GJc\nUCU5J8tfpfYXFvz3bMWK9sAvj98eP0k6uVi41Hky8IVH5syJrvQlrz6GwUQy4J43r/0Eklx8d/fd\ni530/GOS8wPKZvx8sCfFQ0a7dfzKZPzCzoNfakWKhmZ84APtj80K3LIWf07q1uGamWmfl7V0aeeJ\npsgFjnDf8cUXwueFgd/q1dFQyZ12ir+7S5dGHcq8OWaXXx5lPtK+C0W/23n8ZwjLsIfCv6u/uOC3\n15dRf/e7owpqX/taFAAVlWyrrGPRc891zv2ZN6/Y3OKyHces56e1s//OTE9HQ86yFrsvq6rAb9Wq\nqHhNskCYl5bxC+UNjc07byxf3j7qIumuu6JjRtjZnTcvmrdW5sKmlxb4HXFENBT0vvvi80ny82zd\nGmVb/P1pQabvUE9NxeXsiwwZvueezmUSqpBWmTl07rntF5+qkHaR8phjomxosi0+/en2YaJSPAc6\nbdmopD33jAPX6el4/0smFrKsXdtZkKdMIO1lTTnabrv+R1lI7QGyVGxY7oIFcY2FJP899WuUjrrp\n6c7pIb0Oxff7QHK1gtznFHzc8845J8lJkpkVnIk2Oo44ov+rw0l/8AfpO054dXTvvaPxvQsX5p+E\n16/vzAAOyk03RUNx3v/+7Mf4dQOThSOKKJqZ8BO0yzj33Hj+Sjdhxu+oo6LOrt+5ymTuwgNnmec9\n/3x7p2JqKu60p3Vk/GN9G2VdaQyXWvC/81knvyi3FB1MDzqo2FU4/xn9z7QKaMnORTg3493v7qxs\nlZfxSxYESa5PKUUnym6Bvm+r5Mk2bTmHtMAv+bml+Apjt1L//jkzM90vIISdB5/x89t52WXtz89a\nG8xvf7eLD2Xm+HnJoXJlvudSe/EFL7nW2wUXxGtOhnbcMb36YCjt2Fl2G9P4ds+aGxH+XXzg9653\nRfPSylyVTVN0+/tZcqLfwNj/DdO+3/7z99JhKdIZTRvq2YusDIUP/JLrvfrOY9GMnx+S7Od+Js9/\nyff36/UmJS+cFZU11NOsPdhIfp6DDop+76eopBWXSOuThFnTLIce2rlkT1F5wW+3wG/Q/Pn79tvT\n98vZ2fZhoj/7WVR0SIouLhYdhnrttdH30B/3iqyVmyWvjbKOYStXphdbee65atY+Tepl3l0obPOm\n8efzXqduXXCBdNVV8RJnRRTdba41s/8q6TfM7D9KukXSVeU3cfyEJ4CwQEbyMd0yfnXaYYdoqMgV\nV2Q/ppfOo1c08PMTbss47LB4TcNuwozf7Gx7VumQQ+K/nV/EvoiinbXp6eggH2ZnkoHfd78rff3r\nndsbBhQhf9K46ab2DJUf6im1zzlcuTI6QZ13XjzUNSkZ+GzaFJUdT5P87MuWtZ/IkgFLOPE8Gfgt\nWND9JLj33tmVtDy/T91zT+f9Zap6ht9L39ntNkzOt9n0dPcOSBgEhRm/tMAz3PfS5q50y/j55zsX\nnRSKXKHtJeOXJmzztLXCdt89PcjK+n56/jsdzvurYi5Pt8Av/Lv6jPvOO8eVKPvRy4iHsvo95yQz\n86HZ2ajzW/Y9TjklfX24pDoCv+npztENfj5p0cAvORIoL6i9996oHkCVkmvbZcn6PFmBqNT+/f/9\n34/2Pz+U8Kqr4sXaq3L//dIZZ2T/PrnP1BX4+Sxi2X12t91628aTToou3Fbx+fK+j6edln2+T2bl\nBuljHyu2JmaWIseTUeX/xh/5SPpczm4WLYouLpQZ3VHocOqc+1MzWyPpKUkrJV3gnLu5y9Mmyj/8\nQ3Sl6sor03e0bhm/UZOVdSiiSOB31129V90qKplBCx1+eHyyPOWU/KE5oaId4s2bo4xfWLEunOM3\nZ07UYQg7HWGGUsoO/N785vYFS/1QT/8cH3R6c+a0t/Xjj3cOr/PvuWBBdpatW0fbdyB8gP22t0WZ\nw8ce67yaXNXwYd+ZWb26fcHS6enOeX95Qz39z5//vD2ITjNvXvv2h8M2svihuC+91D3wy9r3ehnq\neeGF0b9uymb8vvGN9KUNwgAyLRO0bFnnXOki/LHz6KPLFRDopmjg9+KL1R6/d9ut3JyMXlU1FDbL\n0qXFK1F73S60VTXUM/l6ST7jl5zXnLaOoBQFhGlZveQ+nHf+e/Wre19mIEvRqp5ZmdlnnimWVT7w\nwHjeoBRnsqrUrUJ5cj+tK/B78MHo71tkKYAqVXHMWbky+8LanDnxmnjDNDXV+3IGUhQ05S1hNMpW\nroz6w3PmFC9S1a/Ch9NWoHezJJnZlJm9yzn39wPbsobxlcayxtmOUsaviF4zfmefnX6l3/MH6kMP\n7a+8eDerVkVDEv7pn6qdo1j0ip8v8XvRRfF9c+fG7eoP6GEbJDN+ed+X5BIT/sQdDvUMhZmz8D3T\nAo8s3YIBX445HLbpP2dWkYKi753Fv/5RR7UHfjMznWv75AV+fhvmz49fMyvwSwboRTN+MzPxwtBF\nM35p25/1HXzkkWhIUC+ZpGTG77jj2hdyTkqWEZeiIgvbbx9fKc76u/ZyHPR/kyVLonYwqzbjl3XM\n8n/Xqi/aPfZYPUUGBn3O2bq1vw5bGueiCpNhYOyzrb2+XtrtcMmikN/vDzqovYDOZZfFgV9a0aWs\nwC98z0F07PoN/KR6szu9evTRzvar+2J6WuD3h3+Yv4RJP6oIbBct6j6UvulmZnofWjxsZu1L+tQh\n92tlZjuY2flm9hdmdqxFzpb0iKST69nE8TApGb/LL48mOGcpclW0CnfdJX30o9Kb3tS5NlKak04q\n9rplh8CFJ4r58+MALLlURvhY30bJq59hZT//vIcfjl4rzFKldfaSFeS8KgO/tCFDvkOSN2yyn7la\nvh2S219kjl/aUM+wYEjad9Rf9Q2Lu4QZv/Bzht+72dn2v3nRjF9yfumll8YL8ibtuWfvnfCjj25f\nj+jkkzuHz3azxx7F1xEqy/+dwwCtisCvW+XiQR2n6qos96EPSR/+8OBev+qgT4qC+3Xr4lEJv/51\nelXXorpl/KRoCKMv1uP3zQ0b2tdVC4+rp58eH4+T35Hk8de///r1g/m7v/RSFCh/+cv5j8u7CJDc\nb6+7rveqnIOybFnnaJS6KzSmBX5/8if9FQ7M06Q+I5qj22nt7xQN7dwq6T9Iuk3SSZLWOecKLFsI\nb1Iyft0kr44O2q23quvC6FJUqKeIskFKmH0JS3v770I4xCaZqdlvv/ZOy8aN8Rhw34577lks45cV\n+JXRraOdtgBr2F5h2f8ir1eE/6xFAr/rrmv/f1rGLzzRpm2fc/HrpmX8whLcYcZidjYOCsNhLWmB\nRV7G75xzOtsx1GshkMWLu3cch8m3aThXssriLlnVHfst4DJsa9bkX4jrpop9tIxt2zqHEM6d218A\nnvwMd98d3/YXElaujIO8cKhneKEhPG5u2BAfT5LblnWc8+vuVe3ll6MMfbeFpMtk/Nat638pkDoM\nq7hLXQj8MAjdQpEVzrnXSpKZXSXpcUl7OOcGFBaML7+OX1OMS+BXlO/0vfa1nUsLhMpud9iZDDvl\n/ruwcGG0hMJOO3WeVNKCGT/UxT9/aioaZuKHNWYtKB9m49ICwzILK2d5+unOzkXYOZ8/P6oSW2ZJ\njm6yMn55Zdq9MPBLG3ba7fOmVfX07f/UU+3DW7fbrn0Bdv+7XoZ65um2PmId/vzPo0xTlQaV8QsD\nv7R9YMOG9oIyGKxBzPtOXiD4zd+Mfj77bFxBMszs+YAneRxNHjeTFU/9z7ovFpQpOJalCUM909Td\np6qjIFPowx+O15UEqtIt8HulPIJz7iUz+ylBX29WrKimElxdBhX4lRlaWKfDDosW/zz++Oyx4nfe\n2X3yeVIYzIWfOVxrx0/29yeVIh3asB3Dqo2+uEvSpk1RwHXWWe0nrzJ/jxNOkH70o+zfH3VUZ0ny\nM86IF9j1wY4PXo84QvrSl+LH7r9/vJh30jnnRIsxJ+ft5QV+3TpE4VDPtMfmPT98vzlz2jN+c+dG\ngV8YhIVDPaemigd+a9ZEhaPWry/WwRuFwC+5wHsVfNuFn29Qgd973hMP3ZqdTS9iMylG7ThdpazA\nz1+gSe5LyYta/vfJrFMy8Bt01rRoMJKV8bvttvYF4ZtkFIZ6DlLVF9AAqXvgd7CZ+ZXcTNK81v9N\nknPO5Qw6QmjevKjT3QTnndc+n6xKo9qRmJ2N1s15+eUoGEmrEJW1yHOerJNy8oB+ySXRPMMNG4p1\nFKanpX/8x877s4Z6hhcdkh2VSy4p9tl23bW9WE3SHXd03rdxY3zbD2/0gd+ZZ0b/vPvvj94jHJbq\nXXppND/SlxL3soZ6Tk31lvELdfs7hEVewuxfWjVZX9zF358X+IVz/GZm4sJRRb4XRx45/Lk5gwj8\nli6VTj01vrBw443VZI7T5hwfcID0znf2/9oYDVn7TbfAL5kF6xb4mUUXp972tv62t4wvfjG/mFoo\nK/Dza3A2UZ1DPS+4IKoADjRdbuDnnGvQ4ERUpeg6eeNoaioqbOEDvzJr/KU57jjpn/85/v/ixekL\no6Zd2csLks2kE0/svD8r8Mt73bquKvpgJ6/6Vl5wk1yeQeov4xcGfmUzflJ65nTu3PTAKwz8ug31\nzApYi8zf+8IXqpn71o9BBJ5TU9Fn8449tprXTZvb2aQh+ejupJOirHnSs8/G+2S4xILP6iQrESeP\nqz7gCoOP9763830GmfErWsJ+7dr+F8keRXXuq0WWxQGaoEHlRoB6LVrU/xW+z362/f9r10qf+1yx\n5/aSHS0S+PX7Hr2aPz8acnr22dmPyeskpX2urMBvaqr7sJxwqGfyfX/rt/IXFTdLD/xmZuKMV9gh\nTM7x89mqZOB3+unpJd+///1iFTPDSoXDstNOw33/MtICv7oLRoyqPfaI58M12dvfLl18sXTffe33\n+4zejTe2FwBbvDj6nVn7RZSsjF+3Y2jdBXLSjHLhpn6wrwLlEfihVqM61DPNILb19NNHK/Cr0/bb\nS7vvnl8CPq+TdMklUacsrFKY9VmLBH55Gb8772z//913t8+llNIzc+HSDuHfb3Y2ziDkDfX8xCei\nNkry64c1wQc+0LyhkmEHks5k5OGHx6ctktnyX/0qrr6ZzB7vvHM8KsPPT5Y6jzXJqpdVrluJYsbl\n+wnUid0GtZr0wO8Nb+gekKQtdl5UVlXPUbDXXt2rx+UFfosWdWYg8oZ69hP4JSXfNy/jl9YZmZ2N\nr7qnBX7J12my6eloLbYmSPu705mMjPJFpLKSQdqOOxbf1445JvqZbAv//G5zWt/3vvT5z+gf+ypQ\n3pgc1tEUTerYDmpb8wKz+++PCutcdFFv759V1TPp8sujghnJLNYgXXJJ98d0GxaV/GxZbbnnnvnL\nckj5Qz2LSAssw4xfmGWYnY0zeXlz/Jq0f4yDtL87ncnx4/fFXvbzE0+UvvWt7O9Ft8BvdnY859eN\nAvZVoDwCP9SqSR3bYWxr2eUiko44IsqsdZM3z26YunXMstbWSnYA9t1XevTR/Ncqk/FLk5fxe+CB\naAmXdeuiSpRhENitqifqQ8ZvMhQpjJTmxz+Wli/Pr3q8dGn0k324fuyrQHkEfkCKPfaIgoemadJa\nkWm6BWDJjF/Wcg5Z1TVDYcYvuf5gN2Zxhy+5PWZx5dLkmmDr10frIfriLmEp+LTPgcEi8JsMyaGe\nRe2xR/Rz1ar034cXqth368e+CpRH4Aek+MEPhntSOf749MBi3FU11HPu3PaF0NOEC6/vvXf5YWB7\n7RU/x3f6wqGe4fb6wG/z5uinLx7BUM/hSgv8RnWOLHrXa8YPo43ADyiP3Qa1akrHdt684XYWbrih\n+MK842TzZum667J/nxX4pWX8ugVy4VDPqiSLu/jtTX6XmOM3GtK+I/wNxs/GjcPeAgwCgR9QHhk/\n1IpOFfKsWZP/+2Q2JivwS665lSYM/Mp+L/NKt4e/Sw719HxQnww82D/qxVDPybByZfRzkGvqse/W\nj30VKI/dBrXi5Ih+JDN+WYFbXofggx+Mn9Nr4JdlZiZ/qGdy+559ttr3RzkM9QSay6/FCKA4Mn4A\nGqPoUM88++wT3+51iGXW+nvT0+lDPZOBn/fMM/1tB/rDcg6oCvtuvR56qFgFawDtOMWhVpwc0Y+s\nRZTzhMsuJJX5PhYJCJJDPX1gmlVVkMBvuAj8gGbaZx/2VaAX7DYAGiMM/B56KH+opr8v2TkIO/tl\nOg55JeHDdfzCbQkzgUmvf7108MHtjyPwqxdz/AAAk4ShnqgVHVv0I5x/FV7xTVtgeXpaeuGF/Ncr\n832cmYmXiMgr7pIWOKTNG/vOdzq3g/2jXgR+k4XiLgAmHac41IqTI/qRNcfvgAM6H+uctGRJ/uuV\n+T5efLF05pn5r5PM+EnRou2LFxd/H9SHwA8AMEnI+AFojDJz/B55RHrVq6p777POkrZtk/7qrzp/\nt2RJ9C85x0+KF23PQ8ZvOJjjN1nYvwBMOk5xqBUnXvQjazmHNMuXx+vlZSn7fcyqIrpggfTEE50L\nuBdF4DccLOeAqrDvAmgCAj/UipMj+pG1gLu3aJH02GOdz/vmN+PbvRZ3KfL4tIxfEQR+w8FQT1SF\nfRdAEzDUE0BjdMv4mUm77975vCOPTH+9qjJ+4fYR+DUHgd9kGVRxl2uukfbeezCvDQBV4hSHWh14\noPT+9w97K9BU3QK/vI7d2Wd33tdr4Jel36GeqBdz/FCFd7wjWp4FAEbd0E5xZrbIzG4yswfN7EYz\n2zHjcX9tZtvM7Ht1byOqN3++dMUVw94KNFWZOX5Jn/pU9DPs7Fcd+JHxaxYyfgCASTLMU9x5km5x\nzq2UdKuk8zMe9zeS3lLbVgEYWcnAq0zGL03VQz3TlnMY5PagPwR+AIBJMsxT3FpJV7duXy1pXdqD\nnHPflPTLujYKwOjqJ+OXFlQNorgLVT2bg8APADBJhnmKW+yc2yZJzrknJLHEMYBcVQd+DPWcbGkZ\nYpZzGF+DKu4CAE0x0KqeZnazpCXhXZKcpA0pD+eQDCDXsAM/s/hfml6HehLwDUcy4/dHf0SRDgDA\n+Bpo4OecW5P1u1bBliXOuW1mtqukJ6t4z40bN75ye/Xq1Vq9enUVLwtgBCQDvTJz/KoI/KT8jBBD\nPZslGfht2jSc7QAAoB9btmzRli1buj5umOv4XS/pNEmbJJ0q6Ss5j7XWv67CwA/AeOsl8OunqqcU\nBX6DyvgR+NWLoX8AgHGQTHZdeOGFqY8b5hy/TZLWmNmDkn5H0sWSZGa7mdkN/kFmdo2kb0na18x+\nYmbvHcrWAhg5vWTXwizPqGT8+tke9I7Ab7IsXDjsLQCA4Rpaxs859wtJb065/3FJbw3+/846twtA\nc/QSZIWd/V6en/ccMn7NklbVE+Pphz+UVqwY9lYAwHANc6gnAPQlGYS99FL35wxyqGe/VT1RLwK/\nybHXXsPeAgAYPlYsAtBYycDvhReyHzszIx11VDWBXxaKuzQLgR8AYJIQ+AForDKB39SUdMcdFHdB\njDl+AIBJQuAHoLHC7JtZsY784sXtz+nnPZNYwL1ZyPgBACYJgR+AxgoDpZmZYs95z3ukJ1urhlZd\n3OWgg6T168u/pkfgVy8CPwDAJCHwA9BYYRA2XbBUlZm0yy7x7bLyhnq+5jXSGWeUf00CvuEg8AMA\nTBICPwCNFQ67LJrxC1U91LNXBH7DwRw/AMAkIfAD0Fhhxq/Jgd/UFEHIMJDxAwBMEgI/AI3Vyxy/\nrOcXlTfUE81C4AcAmCQEfgAaq9+MX7/viWYj8AMATBK6MAAa5Zxz4tvhsMsVK8oHZb0EcWT8xgfD\nawEAk6RgHTwAGA1hZ/3AA+Pb118vPfdcudcalTl+GA4yfgCASULgB6CxTjghDgQXLoz+lUHgN9nm\nzh32FgAAUB8CPwCNUuXwPIq7TLZbbpGefnrYWwEAQD0I/ABMLDJ+k2358mFvAQAA9aG4C4BGqTLj\n10txF6p6AgCAJqILA2BiMdQTAABMCgI/AI0yCnP8AAAAmobAD0CjVDnUkowfAACYFAR+ABrl4x+X\nbr+9mtci4wcAACYFgR+ARlm0SDrmmGpei+IuAABgUtCFATCxGOoJAAAmBYEfgInFUE8AADApCPwA\nTCwCPwAAMCkI/ABMLIZ6AgCASUHgB2Bi9RLAUdwFAAA0EV0YABOrlyCOjB8AAGgiAj8AE4s5fgAA\nYFIQ+AGYWAR+AABgUhD4AZhYFHcBAACTgsAPwMQi4wcAACYFgR+AidVLcReqegIAgCaiCwNgYjHU\nEwAATAoCPwAogaGeAACgiQj8AEysvfYq/xwyfgAAoIkI/ABMrFWrJOfKPYeMHwAAaCICPwAogeIu\nAACgiejCAEAJDPUEAABNNLTAz8wWmdlNZvagmd1oZjumPGaZmd1qZt83s61mds4wthUAPIZ6AgCA\nJhpmxu88Sbc451ZKulXS+SmPeVHSf3bOHSjpjZL+k5ntV+M2AkAbAj8AANBEwwz81kq6unX7aknr\nkg9wzj3hnLuvdftpSQ9IWlrbFgJAAkM9AQBAEw0z8FvsnNsmRQGepMV5Dzaz10g6RNJdA98yAMhA\ncRcAANBE04N8cTO7WdKS8C5JTtKGlIdnFlU3swWSNks6t5X5y7Rx48ZXbq9evVqrV68uvsEA0AUZ\nPwAAMEq2bNmiLVu2dH2cubKLWFXEzB6QtNo5t83MdpV0m3Nu/5THTUu6QdLXnHOXdnlNN6zPA2Ay\nbNok/eQn0l/+5bC3BAAAoJOZyTnXcZl6mIOWrpd0Wuv2qZK+kvG4z0u6v1vQBwB1oLgLAABoomEG\nfpskrTGzByX9jqSLJcnMdjOzG1q3j5T0Lkm/bWb3mtk9Zva7Q9tiABOPoZ4AAKCJBjrHL49z7heS\n3pxy/+OS3tq6fackrq8DGBlk/AAAQBMNLfADgCZ6y1ukww8f9lYAAACUM7TiLoNAcRcAAAAAk2wU\ni7sAAAAAAGpA4AcAAAAAY47ADwAAAADGHIEfAAAAAIw5Aj8AAAAAGHMEfgAAAAAw5gj8AAAAAGDM\nEfgBAAAAwJgj8AMAAACAMUfgBwAAAABjjsAPAAAAAMYcgR8AAAAAjDkCPwAAAAAYcwR+AAAAADDm\nCPwAAAAAYMwR+AEAAADAmCPwAwAAAIAxR+AHAAAAAGOOwA8AAAAAxhyBHwAAAACMOQI/AAAAABhz\nBH4AAAAAMOYI/AAAAABgzBH4AQAAAMCYI/ADAAAAgDFH4AcAAAAAY47ADwAAAADGHIEfAAAAAIw5\nAj8AAAAAGHMEfgAAAAAw5gj8AAAAAGDMEfgBAAAAwJgj8AMAAACAMUfgBwAAAABjjsAPAAAAAMbc\n0AI/M1tkZjeZ2YNmdqOZ7ZjymO3M7C4zu9fMtprZx4axrQAAAADQZMPM+J0n6Rbn3EpJt0o6P/kA\n59yvJb3JOXeopEMk/Z6Zrap3M5Fly5Ytw96EiUOb1482rx9tXj/avH60+XDQ7vWjzUfHMAO/tZKu\nbt2+WtK6tAc5555p3dxO0rQkN/hNQxHsyPWjzetHm9ePNq8fbV4/2nw4aPf60eajY5hjKxBLAAAG\nkElEQVSB32Ln3DZJcs49IWlx2oPMbMrM7pX0hKSbnXN317iNAAAAANB404N8cTO7WdKS8C5FGbsN\nKQ9PzeQ5516WdKiZ7SDpy2Z2gHPu/so3FgAAAADGlDk3nJGTZvaApNXOuW1mtquk25xz+3d5zkcl\n/T/n3CUZv2cYKAAAAICJ5pyz5H0Dzfh1cb2k0yRtknSqpK8kH2Bmr5L0gnPuX81snqQ1ki7OesG0\nDwgAAAAAk26YGb+dJF0rabmkH0s62Tn3KzPbTdLnnHNvNbPXKir8MtX69yXn3B8PZYMBAAAAoKGG\nFvgBAAAAAOoxzKqeGDFmtszMbjWz75vZVjM7p3X/IjO7ycweNLMbzWzH4Dnnm9nDZvaAmR3bum+B\nmd1rZve0fv5fM0udlznpqmrz1v3vMLPvmdl9ZvbVVlYdCRW3+dvN7P+0XudTw/g8TVC2zc1sp9bj\n/83MLku81mGt7/lDZvaZYXyeJqi4zT9pZj8xs6eG8Vmaoqo2N7N5ZnZD63iz1cwuGtZnaoKKv+tf\na/VbtprZZ82MKUQpqmzz4DWvN7Pv1fk5JhEZP7zCoiI7uzrn7jOzBZK+q2i9xfdK+rlz7tNm9l8k\nLXLOnWdmB0j6e0mvl7RM0i2S9nGJL5WZ/W9J5zrn7qzz8zRBVW2u6CLOzyTt55z7pZltUlQI6eND\n+FgjrcI2XyTpXkmHOud+YWZ/I+lvnXO3DeFjjbQe2nx7SYdIOkjSQc65c4LXukvS2c65u83sq5Iu\ndc7dWPuHGnEVt/kqRVMyHnbO7VD7h2mIqtrcopoGq5xzt5vZtKRbJf0x3/N0FX/XFzjnnm7d3izp\nWufctXV/plFXZZu3Xu9ESeslvc4597paP8yEIeOHVzjnnnDO3de6/bSkBxR1dNcqmmup1s91rdsn\nSPqic+5F59yPJD0saVX4mma2r6RdCPrSVdjm/qrkwtYVyh0UBYJIqLDNV0h6yDn3i9bjvqHoxIWE\nsm3unHvGOfctSb8OX6fV2VgYrOf6t4r/TghU1eat333Hr7uLbFW1uXPuWefc7a3bL0q6p/U6SFHx\nd90HfTOS5ipjqbFJV2Wbm9l8SR+S9MkaNn3iEfghlZm9RtHVmW9LWuJP+s65JyQtbj1sqaRHg6c9\n1rov9HZJXxrkto6Lftq81Tk4S9JWST+VtL+kv65lwxusz+/5DyWtNLM9Wlfl1ykqVoUcBds8y1JF\n32/vp+o85iChzzZHD6pqczP7DUn/TtGFJXRRRbub2dclPSHpKUmbB7KhY6SCNv+EpD+V9OyANhEB\nAj90aKXtNysanvm0Oq94lbkCdoqk/1bVto2rftu8FXicKelg59xSRQHgRwaxreOi3zZ3zv1KUZtf\nK+l2Sf8i6aUBbOrYqPjYggJo8/pV1eZmNkfSNZI+0xptgBxVtbtz7ncl7SZpO0m/XelGjpkK+i4H\nS9rLOXe9opFLzKkcMAI/tGkFEJsl/Z1zzq+tuM3MlrR+v6ukJ1v3P6b2DMey1n3+tV4naY5z7t6B\nb3iDVdTmh0hyQefgWklvHPCmN1ZV33Pn3P90zr3BOXekpIda/5CiZJtnyT3moF1FbY4SKm7zKyU9\n6Jy7vPotHS9Vf9edc88rWm96bdXbOi4qavM3SjrczB6RdIekfc3s1kFtMwj80Onzku53zl0a3He9\npNNat0+V9JXg/lPMbK6Z7Slpb0nfCZ73DpHtK6KKNn9M0gFmtnPrcWsUjblHukq+52a2S+vnIkVD\nba8a/KY3Vpk2D71yBbg1dOhfzWxVay7rv894DiJ9t3nB+xGrpM3N7JOSdnDOfWgQGzmG+m53M5vf\nClZ8UHO8pB8MZGvHQxXH9Cucc8uccyskHaXoQgdZ1gGiqideYWZHSvpfioYJuta/jyjq5F6r6Er7\njyWd3BrmJjM7X9L7JL2gKNV/U/B6P5R0nHOOLEiGKtvczM6Q9EFJz7eec5pz7pe1fqAGqLjNr5F0\ncOs1LnTO/fd6P00z9Njm/yJpoaICC7+SdKxz7gdmdrikL0ialfRV59y59X6aZqi4zTdJeqei4W8/\nk3SVo2Jwh6raXNK/KZpX/ICi47mT9BfOuc/X+XmaosJ2/4WkG1r3TUm6TdKHnHMv1/l5mqDK40vw\nmq+W9D8cVT0HisAPAAAAAMYcQz0BAAAAYMwR+AEAAADAmCPwAwAAAIAxR+AHAAAAAGOOwA8AAAAA\nxhyBHwAAAACMOQI/AAAAABhzBH4AAAAAMOb+P0ZlCmBidBVLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f72998dbd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gs = DataReader('GS',  'yahoo', datetime(2006,1,1), datetime(2015,1,1))\n",
    "gs_returns = pd.DataFrame(np.diff(np.log(gs['Adj Close'].values)))\n",
    "gs_returns.index = gs.index.values[1:gs.index.values.shape[0]]\n",
    "gs_returns.columns = ['Goldman Sachs Returns']\n",
    "\n",
    "plt.figure(figsize=(15,5));\n",
    "plt.plot(gs_returns);\n",
    "plt.ylabel('Returns');\n",
    "plt.title('Goldman Sachs Returns');\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us calculate the variance and the correlation between this stock and our previous stock:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation is 0.738516966615\n",
      "Weighted average std is 0.0273508317976\n",
      "Actual std is 0.0255039700001\n"
     ]
    }
   ],
   "source": [
    "gs_std = (gs_returns.std()).values[0]\n",
    "jpm_std = (jpm_returns.std()).values[0]\n",
    "returns = pd.concat([jpm_returns,gs_returns],axis=1)\n",
    "corr = returns.corr().iloc[0,1]\n",
    "\n",
    "weighted_average = 0.5*gs_std + 0.5*jpm_std\n",
    "\n",
    "actual = np.sqrt(np.power(0.5*gs_std,2) + np.power(0.5*jpm_std,2) + 2*(0.5*gs_std)*(0.5*jpm_std)*corr)\n",
    "\n",
    "print(\"Correlation is \" + str(corr))\n",
    "print(\"Weighted average std is \" + str(weighted_average))\n",
    "print(\"Actual std is \" + str(actual))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two quantities above will only be equal if both stocks are perfectly correlated. Else, $\\sigma_{p} \\leq 0.5\\sigma_{1} + 0.5\\sigma_{2}$. This is the key to diversification: the risk of the whole can be less than the sum of its parts. We can visualize the effect of diversification for a two stock example as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f8/jj3pYtc+bMAWDhwoVs2bKFv/71r8De2cq8vDzOOuss+vbty/r165kyZQoXXnghy5Yt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\n/x9aQehuS/H6FgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f72967562b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def portfolio_std(s1_std,s2_std,corr,s1_h=0.5):\n",
    "    return np.sqrt(np.power(s1_h*gs_std,2) + np.power((1-s1_h)*jpm_std,2) \n",
    "                   + 2*(s1_h*gs_std)*((1-s1_h)*jpm_std)*corr)\n",
    "\n",
    "portfolio_risk = [portfolio_std(gs_std,jpm_std,corr,h/100) for h in range(0,100)]\n",
    "perfect_corr_risk = [portfolio_std(gs_std,jpm_std,1,h/100) for h in range(0,100)]\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.plot(portfolio_risk,label=str(round(corr,2)) + \" correlation\")\n",
    "plt.plot(perfect_corr_risk,label=str(1.00) + \" correlation\")\n",
    "plt.xlabel(\"Goldman Sachs Holding (%)\");\n",
    "plt.ylabel(\"Standard deviation\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have a portfolio of $N$ stocks each with risk $\\sigma$ and uncorrelated returns. What would the risk of an equally weighted portfolio of these stocks be?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma_{p} = \\sqrt{  \\sum_{i=1}^{N}(\\frac{1}{N}\\sigma)^{2} } = \\sqrt{  N(\\frac{1}{N}\\sigma)^{2} } = \\sqrt{  N} \\frac{1}{N}\\sigma = \\frac{\\sigma}{\\sqrt{N}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately it is quite difficult to find uncorrelated stocks. Let's assume the correlation between the returns of all pairs of stocks is $\\rho$. The variance of an equally weighted portfolio is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\sigma_{p} = \\sqrt{  \\sum_{i=1}^{N}(\\frac{1}{N}\\sigma)^{2} + \\frac{N(N-1)}{2}2\\frac{1}{N^{2}}\\sigma^{2}\\rho}$$\n",
    "\n",
    "$$\\sigma_{p} = \\sqrt{    \\frac{1}{N}\\sigma^{2}  + \\frac{N(N-1)}{2}2\\frac{1}{N^{2}}\\sigma^{2}\\rho}$$\n",
    "\n",
    "$$\\sigma_{p} = \\sigma\\sqrt{    \\frac{1}{N}  + \\frac{N(N-1)}{2}2\\frac{1}{N^{2}}\\rho}$$\n",
    "\n",
    "$$\\sigma_{p} = \\sigma\\sqrt{    \\frac{1}{N}  + \\frac{N(N-1)}{2}2\\frac{1}{N^{2}}\\rho}$$\n",
    "$$\\sigma_{p} = \\sigma\\sqrt{ \\frac{1 + \\rho(N-1)}{N}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As $N \\to \\infty$, $\\sigma_{p} \\to \\sigma\\sqrt\\rho$. Let's get a feel for this by loading a large set of stocks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MsRMYY0cAPAjgCcZYMWPsuPSVmpD6Cc34RcZ4yWT8li8H3nsvpUVre0yCLM6a\nqKmn3w+sW2c8PPTUIZR/XN5470cIISTtaHAX0hykO+MHzvliAGdELJsR8v9jAPo0dbkISRU5mEiK\nmfHj2nQCnPOY2Z9du4CNG1NdyrbjtuuBN0Q3Okc+kaamntLanZAqs4E7ezbZexJCCGlaNJ0DaQ5o\ncBdCGpmkTUQiy7H7+ImCumLofHJW25Njr0JiyDsX2OLZH/0ES+10DkeOxF8HAPiy5eDzvmzw+xFC\nCGm+KOOXPM5l1NYuDz6mZrINRoEfIY1MFNV/FSX2qJ6yrAZ+8S4KokgDwTSU6aXDFhL4NTDjt3Yt\n0Ldv/PUAQEEGOJ2K2wzOOX731u/SXQxCSBPTr+0UvCSupmYpCguHprsYrQrVNghpZKEZv1jz+Mla\nGi90InGr7VHGr2F4nOC6oYO7eDzaf955J35ZYAfndCpuK2QuY3/NfrrrT0gbozfxpGM/cZxLCa+7\naRNw4EAjFqaVoNpGC1LpqUSZqyzdxSBJSjjjpzXxjHdRoMCv4YY9diF8MZJ6DW3qmaH3np44Me66\nHBkAszfo/RqksBD4+uv0vX8box/f8W7wEJJONMpw6tF0DvWReJD88cfAt982YlFaCQr8mhOPB9i6\n1fLpDzd/iDfWvWH5/MrOK1H0UlFjlIw0gFkfP9NRPfWMX5w+ftTUMxU43G7rZxva1NOeRBynZvzS\nWMm6+25g1Kj0vX8bowd+kpL4nWxCSMtH0znUR+LflSwj5g1doqLArzn55Rfg4Yctn/ZLfoiyaPm8\n7JThXOtsjJKRBgjN+MWex08L/OKk8yjjlwIs9sXEV1oMVFQYjwsLgX37Et+8LYkzK29gH78lNTV0\nB7kFocCPkLaJBndJXjLXNkVRZ0tqS5zrnKheVJ3Uayjwa04kCfB6LZ8OyAHLykKJswRDpw5NJisO\nAFi5EpgyJbnXFBwsoIpmiGPHYj+f6Kiektb0S5YaN/D79lvgkkuSe40se+Kv1KJw9dbgiy+aPuvb\nuwNYtcp4fO65wGWXJb51valnFf6UQEka1sdvxMatKA4E6v36qPQzaVQU+BHSNhmDu9A5NwnJZfza\nWuBXt6IO1Qsp8EvIpk3qXfxmRVFiBn6CLFhWFg7XHQaQ/AmltFSdFy4Zw2cOx57qPcm9KBkFBcDm\nzY23/RQbNAgoi9H1MuGMn5x4xq8hTT2//jospsERxxG4Aq6Yr1m58jh4vUmkvFqCsjLg3XdNn/Ir\nQoO+ZL2fbCP8AAAgAElEQVSpp2XgF9J/RkEGGnIq/vFKQK60bglAGmC/ybQfDaT37aPAjzRnDNTH\nL9VocJfG1RabenKJgweSq/e32cBv3jxgwYJ0lyKCLMcM/OoEHxyi+Z19u02raZr8/tULq7GcLbd8\nS7M7JCu7rIR7q3knqJNrLIuYGl99Bfz8cyO/Sep4vYjZXyzRjJ/ety9exk8UG5bxi3zvp35+CvN2\nzov7Okmqq/+bNjdMy/hZBHc+RHekTKb5pr6uDfGvQmpTz4YN7qJ4GrBD0N1nc7W16l2dFKOMH2kJ\naHCX1DMGd6E+fkkI/65iJTfaWlPPqm+rcOjxQ1ACyd1IaHOBH3uWYc2RNWrTuuZ23Y0T+G111WGr\n22H6nI1pP6V2TOx/aD+237AdAODZZd1Mzyrwkx0y3FvMo5mDbwJZhxKcnbo+vN4W1YlNktTAzYr+\nUeKO6qlnAuTYO2ZDm3pGvlaQBTj85vtVuNZUEeBQvP4YgV/0l1y/epCQQEns4A36bhXAGePOQ9wC\nUCXElN+vHpgpZozqGWcQp8bQwk6thLQqlPGrDxrcxUrJuyUAQIFfIvZW74UgNMPAL15TT8ELWTCP\nMPTAjyvqQVLydgmqvqpK6C3r0z2INeZtlRZWO0k08Audx890VE99Ogcp/nQODWnqGflamctwBtrY\noECMQ6msNv0i2yt2+Jgc9RzzWR+bkYzRWxG/CWZDM35DMAy24uJ6v54CPwtCw5r7Wklnxu+ee4Dv\nv2/ytyWkSXEOrFiR7lJEo+kckpfMd9XW+vjpWXnFT4FfXJzz5pvxi3G7QqiugFxdafqcXZsHzBgu\nWOCwd7Ru/hn6lpYHikkSQt8+UxrxxBWjCV5zJIqxAz99P4uV8QsN/KQ4O2ZDM35RgZ8iwyXE7uMH\ntL6mP3JVnel+1oFnwGeLDvxstYl3oDb6ciYU+NlR32yqcTy6Y/9+QqVg3BQy2Ui93rvVs2hT7fEA\nt9xS/83qmb50BH4uF1Cd3DgAhLQ4TidwxRXpLkU0/aZPW8v4ORy/Yv9+6xHrY0tuVM+2lPHTIzjK\n+CWoWWb89KaeFhUxQREtmwfpd5JCJwXOOiErobc0C/yO5B4xPTmJiqi9rhEHk2jFGb9YTT0VfVTP\nOBM7N3Qev8jXKlxpexm/q++Hp9Jr+kVmK3b47dykqWcSdx5F7XiEjOqfynDo5e3hK0QM7lLfjN+Y\n58cAAHicfqFreqxB6Xul9XqPNssi47d/P/DZZ/XfbDozfqKoBq6EtGb6NVlsZmNetdV5/AKBo/B4\n6juaImX8LGnViDY/uItPljE/ZP4tMxy8WQR+W8q2YPH+xcEFeiXDYs/1Sl54JfPmZnolQgjpU5TZ\nI1P9jyyiAw6Yvs7qQLl10q1Y6F0YtVyfR1CJ0w+tQVIU+E2aBHz5ZQrKE0fMwM/thvyPhwDEHtUz\ndHCXRJp6pjTjl3BTz1aU8cvdhxqveVPPHNkGXwaim3omcQES3VoQjwzMfftBPL7yVst1GzKB+wqX\n2p5JluPfCQiUWeykFjeaDj55EFuGbKlXuRImy8Dy5Y37HhpFAa67LokXWGT8Gpr4TnfgF6M3ASGt\ngn7Yxhp0LR3aalNPziVIUvxWRRavjnhk/d21tT5+zKY19WzrGb8dHg+ePnw45jrNpannuPnjcPVn\nVwcX6GcriyuzxCUoMK/xGwODIPihMrqok4kdt24u/oi7TF8XaxQklxJ9oOqVFVlKbtCDbdtMFno8\nwEUXRS/3mmdiklVTo05X0Zj0YM4y8KuqgrR9N4AEMn5omgnck23qyY25hxq3ecquyiTnFYmwYPcC\nLD2wNO56P38C5HoA0W8+uEsHEfBlIrqpZxKTZIou9QcSkIkafw1c7axvPYdO4O52A0VFCb8NBJt6\nHCpiAjtEknWNqq+r4PglkUF/GmD1amDoUDWFVhW/T3JDCAKwcGES47VYZPzMAr/vvgO++Saxzern\n6s1Xb8bRt48mWJjUaKyMX21BLTy7KZXYmrTk6Rz0w9ZV31ijkbTVwV04lyDL9YvCaQL3GLRDtM0H\nfnWSBDmBHaU5ZPyi7lzECfwY88NuM7+doWeLVtW2C66v3Q1govUtEFm2DloUk4quKKu1JllMPPCr\nrATOOcfkiZISYP366OUpyvjJMuBo5Hqrvg9ZBn5OZ9ionmYZP32wFqOpZ5zP3tCmnpGbj5fx41w/\nUBqv+W2lpxL/+/H/Nmgb139+PUbPGx13vSFFwNkVgOQLmDf1FDgEe3RWO5mMnyKo64rIhN/GIdq5\nZfZZbeapnoonTQL690/sPTjnEOzqVU4W6hf4eXZ4cLTykuACZ8h+0BT1vkytVcIttwAfftiob6Uf\nqwkHPqKoHrAJXE/Wr1fnxqwtqIX/SOyah17p85X5IB5r2rZoktQ4gV/h8ELsHr879RsmTa41NEfU\nr3HNKfBb7XDg6UMHAbTs77Y+1MAvNRm/WNpaxs8I/Nr64C4OWY4b+HGoGb/ICvD/++03uJswGoy6\nk6FXQi0Cv3Z2J3IyzCMZPRP3fVWH6PeJUYOL1SZaNqnoi9o8gkoSgV+yX6mn2odD+8PfWxSTb68v\nSeH12MYQN/BzueL28dMzEEbGT+uv9d2e73D/ovtN3zPVGb9EAj/eiMPPuwU3fFLwjL1k/5J6NYVL\n5i615DUP/GySjHYS4JfDf1Q98Ht19avIeC4j5rb1bpoSsuBnCkQbMHp0yO8WkjbiyADn6qm4Jok5\nMmWPDNGuHY+B2LX5z9AXR+qiy+za5EKN6/fqg8OHgc6djeeaZDCf9u3N/98I9O8+4cDHODDNL6qh\np++zN+fj7PUfo/S/pXCsMD9Hr1qlNWbQp3OwycEBuJpIY/bx41KcCtqsWcCjjzbOm4dYXbw67vFJ\nrLWGAUiaY+BXLgio1upNLfm7rY+GZPyoj581auqpcUhSQnmJyIzf6O3b8XNdHYoTmNtgytIpKHOV\n1b+QGsuMn8UtC4UrUCyCWmNAEFtIQKbV20pifCZFsR613DTjJ6pHld+X/Bk1qugWn4V7vKg8Fnzv\nESOAJ58EXnstufeTZYvAz+FoWK/vadOMzoMJBX5ahSh0VM/Qj66/1gj8tN+y3F2O7RURg4Kgcfr4\nuQKxmnpKYf82Bq/oRUAKGDdD7v7ubuyv2Z+Sbe/eDRyJmHaSARAC5oEfkyS0Nwn8OFcHS1pfuj7u\nHGx1Yg3w5zshIgM+G4doUz+XWTNDJaSpZzKTxPucPtj1DLIYe6jGD3EKvijsGLVcrBHBuRZ8RJ53\nmiLjF/qBs7MbvDlJkeAVLZrKa7tvwv1+9B8r4mDTtxN6CulavQ+5x3aCS9zyIvzoo2pmMDTwkz0p\nupmyezfw+edxV0tr4PfSS8ArryS30XnzgKXxm2+H2lS2KS1zJLYWLSXwq/RUYl/1PtPnmmPg55Nl\nSEa3ibaY8Wv8wK/NjepJg7uoHAk09eQ8enCXL5PoX7Jo/6KUVUrDxGnqKUOGYnEQyFzGz58AV/qi\n25MFYky9oL+lWeBiFvjp8whW1yUe+Orfc1Tmz2JSuywpvKnn998DK1cmlw0BYjT17NIl7M7zjBlJ\njmj/8MPAU08BSKypp6Rlc0Ln8TPN+EVM5yDIAo46o/sApXwev2aQ8fOKXnBwY9RYR8ABv5T8rTuz\nLNVbb4XUifXpDzgQ8AfveIReiG2ShGwJ8CnhP6qodAEAOJ3xd5Z9vi3AwI+Npp6CFqGZ7SeCvR0q\njlMzbVJF4pNquuvcRuAneONfVM3Oi1K1BEUP/Ozav/pOHSvw8/uBYcMSLqul0JNCu3bW68Xx6upX\nsbF0Ix5Y9AA6/Du61UPoWyXV1BOIOmD0xWH3jkQJ8HnVwE8wPzglSRsvRjuOUhr4jR0L3HgjcPfd\nwLhxlqs1auAnxzku6nPSWrYM2LgxoVWH5Q8zBh9rUd57D5g/P92lMBiDjDXzwG/k5yNx+tunmz6X\nyj5+bnfi/Xdj8SkKRCXxoHpl0UoEpHpMstwsyeBcgKIkNzYEENL0OIFKWjozfsIxAcc+O9ak76ln\n/OQ239RTkiyzYjq9qadZE0QOAGvXAjEmRJYUCY5AwzuPJdvUU+GKaTCml2lIEXCp+IPJs8Ea3Kuv\nhldY9Pgq9GDRy2V211TP+CXT1NO0ogQEf4DQO+qKgizZDx4xSqEgJD8anWXGDwAOBEc5/fvf6zH6\nV04OgAQzftpQ/Vbz+Omv1QdPUbQn9cAvcj+xGGwwYcGsI8e/V/47bh+/BXu+w2t7Gz/jBwABKQCF\nK3AFXPUK/Mw4nebfl9NTZzyhB5wA4FP6IFtk8EW8v97Uc8cO8/PLhpINRvPUo0VqUzMJmQjYZUg2\n7TcVAB9OhCzZIHOOk2begncv/xCVGWqwEvg19sgulZXBVqIepwd2fSBgX/zafIk/+pgVa0RwRQv4\n9ANUOxhyarcgF6vNN+Z0qpVykxSmc4MTgZIEKyyhJ+EEWltYWX1kNXZU7MCOyh2W69S7qWcCGT9I\nEux+D7jELe++yrLWuiIk46d4UlO55tu2Q0GmOkjOF19YrpfWwK8+WQ6HI+G+Ar8c/iUl1+Umt2kT\nsM88c5UOLSXjF+u3TmXGr7AQePbZhm/HpyjBjF8CWawHFj+A1Ucszr/N3PqS9fjxwI/GY73uUL+s\nn37+jb8/pjPwq1tRh1237ILvkJpyfHj/fixq7ElTtbpAmw/86hJo6mmW8Qszfbo6/JsFURYtK8qc\nc3yy5ZOE7k4kO7iLnEhTTxayA5jcsZ8yJSzmMYKAsDqXtmxvafQGJL2PnxD/6BoxQp3zyrSiBEBy\nCPiVzQx/Qs/TR1S2AoH6BX6Wg7vod960YCzpC4TWLC2ZwC/RPn6KHAz8fJIPdf66sE1GNvWU/XL0\n/jZ/vmVlQn9vURHxxLInIMoiREW0vLv4wZZPsbAsuYyfwhU8ujTx/jx64OeX/PAIHnBw+GIMSmRF\nEhl27gxfFlZ31DN+ABze4ATughwMYETeHXapG3yhdye7HIJ8XLm6CYuL9qjPR2HbMW34WlkN/ARk\noi7LBk+Wug8IArAOc3B4w1nY7vGg7OBnWHTuYijadA4sTlZEz3pzDrjq3MjQVnfWxnxZ6EcPI9WE\nZPz0HVEL/DqWrUR3rDLW3VCyAbcvuD183crKqG0enX4UVd8l2IIi9CScRBsdmXN4Qw4CSZHgElwx\nK1RmGb91R9fhm90Wt/OTyfi5c5DpzY6b8QsEGqepZzFuxgr8GLwr8NBDlmWo73QOgQDQvbv183Gb\netY38EuwWb5+w6gxm9FxzpOe8/TYsWPYvHmz9Qp1dc1qwrmWEvjF+p1TGfj5/UmMBByDT1EgmbQw\nsSIqIkqcJQ1/4xSq8SXW7GrU56Nw5awrjccNCfz0ekcio4orinaOTcOuq5//9Kb+S1aswMfbo7vq\nxOJy/ZZcVlSL4LjFNSfOy1oP08FdfL6oI9c043fnBXDWcaC2Vj0ZW5AUCQ6/eUThFty449s7EJDj\n372OOvgTCfwiKzbr1gHz54dk55KrSJhm/LQd2FUWXZuUtKaePIG784cOAeXlwWta5MmzptQPgR8f\n/kPonz0i8KvySdhRrVYMnU7g11/jvr3l4C47jgfqWCDsbdxuwLPLg6U3LI264MlydB+xZAI/CRmw\n27nlqJ6RffwkWUJBAfDRp+oXFtncM7Kp566bd6Hu54j9dcwY4J//NC2S/pmdbrXw+qAqVhUaPfxP\nJuPnCrjwyprE+vPsr9kfzPjJAaMcesZPUiSsObLG8vVVC6qwb5Ia5LpdDLfdFv680xlSrwo55gRJ\nMUZtDA16bVBwvKsDqo6EHGv/OAXlt12nbSL6ou0oO4yjrqMQi9RR22xaMCUhA3V2BrfWl03/rSV/\nFlZq55hbtuTg+MBe7b1jd6zTXx8IABU1waaeAV/8454dPQqsCf8ew/r46QeoVltikGFHMBir9FZi\nR8WO8IKYzJmqeBXIjgTPQ6HHeRK3ah87eBAdVq40HouKCLcQu1JhFvitKFqBH/aZtZKAdcbPqy4P\nrasHnMcjIPSN7uMXCAAjRxqbicz4pSrwc0Fr8qYHfhZZv9CM308/JReLOatFxLqB3WgZvwSCIs45\nOHjMaWlSYVPZJlw3O5nJIIFFixbhxRdftF5BC/xeeglRN62SpYgKvHsaNlFjiwn84sznBqQm8PP5\nGtQYIbgdWYaYxHQOgiygxNV8Aj+f6MMpb5yS0LrtMsKb7QcDv/qMDRGe8Usk4E/F75Usvd6s/7vt\nzjsxeepU4/lrrxURCAC+gz7L8/6mTeehtHRGwu+pKNr5XuBJ3fBqfYGfWR+/fv3U/g8aywncS7Lh\ncEI9EccI/ERFtGxmcMyjtvH1CPHb00SduLTavNPibNW92obckoiR7zZsABYtMpqYcRb941ezcssy\nxAr8FJO5+mI19Xz77fA6kiColQyrpp6BmmO4FFeZZvx4SEYOUOPBKpf6YMUKy5gm6rOZBX5nTwBu\nO7kwrEwuF1DzbRnyAvdh+eHlYevPmAH07RuxkUQDP6cTMuzIzExuVM9ZL5Zj3yF1o5En/8iMn+SU\njKZ1u6vMh1T/bdhv2DF2R9h779mnBX6ieeC3ZUvk1GqJV1KTmaj2d2/9DoXH1N/DL/mNcugB6fyd\n82NO9SBWiSFD6LOoGwxmrcUYB5xZ2sWJ87CMXw1vj9cKKpCz60DYa5Qsd9hnC7Xz6b9h6EFAqFID\noVx3NUpfA8ZNfQqnlDlxa6FaY67d6tG2AfxSp95YufggQ5WrVit9uK8rK3EoJBOmnxqcTqCqNtjU\nUxHiX+m+r7oAh9eG980Vix3gAe13jcj4MSbDjuCJQVZk1Pprw9cNDfxkGWAMskeCVKd+4aIsWg62\nAqDeGb9ddW50CjkFS4oEt+BOqFIQ2qzbGXBa36SzGNVTrFF/hNDT1vNn7cIzgw+qTT2FkDK43cCC\nBYCiQJLUTeqtMxSbEqwAVFWpzSPqSYG2L+uBn0VzltDA7/LLgR07ANdvLgRKE7hRWaP+9h6PeZ+n\nxsj4VVZVYUeMa7FOv/EZa5CqVHALbpS7ra+nZgRBgCPWvEJa4LdsWT0Cv99+C9s/Hasc2HPXniQ3\nEi7RwK+wMGaPmNRZuRJ4992oxYGKgOW4H6ns45eywE9RIHEZdjmxpp6i3LwyflXeKjgCjoSu6e3s\nVoFffTJ++hgDiTX1BNIzwAsXte9FDo4pkOX3I1ASQO3yWixZAhQVubHu1HXGjWozm5zRrWisSCFV\nsrDrThxtI/CrrAS2bw87oUVl/DiAgB1ePywzfmvWqBOCmzX19PkOQlEk46LwzP74Z3CrjN8Lu3ah\n0uRMc8tmGbf9KkS/xueL2dTzmBK+I1V6gp8tVuDHI9pUr1gBPH6tui0eiL47P2lSeGZM75dnFfiJ\nPrVCyENr6hEZP/2pgIcZB7MgqD9RPLGaeq7pqg+koj52uYAOa2dj1sKDURk20/dKso9fVmZ4xi9y\nVE/GAK4FVq7tLlQUOAB7MOO3r3ofqr1q8BDZx49LHFKNWpAB7wxAlTe6mV3dsjrULFabaSgKcAlW\noK5WLbRVxm/gQGDiRABGEJd4xk+/ERHady6WWp/6JQek6IxfaFBmhkscsjZhOnh04Od0mjf19LXX\nJ8FRwir/h3hnnForQopozsy0QXqM40L/EffuxY79a/DeQqBii5qKPrF4K3pq17iTnU6cXaPu15XL\nHEY5f6lQA0u7LGNvoKtRrlB55eVYHnIu0isyLhdQ5fAGB3fxJ/Y9r9mTG/ZYqvBCgTb0vb4T6xk/\nFp7xU7hi/E6mGT/tJKJU1BiB38ytMzF5yeTogsxUm3jLkoSl558PHH98UlfrU5YJmPh28LEoi3Er\n/WYZP6fHCa8nJDB95x3gqHb86yeskINt8f7FEP1S2NNln5TBa7PDne2DEtnUU5LU/USbz1PP+HUI\nAHccfjvYx2/ePOD55xP+/FGfLTLws+gEbNbHb9N5m7BzXPzrlexTD6wNv8oIuZFt4BIH3ngDKLMY\n+Mui/dVd+aPxxw/+aP6aujp4EsgE69e/eM19Gyrs5keCAoFAQoGfICTe11wQKtUmYTfeCGzdGiyf\nU4acQPY/lkQDv3PPBa5LLvmZkJdWvYQ3170ZXLB9u2kTn+J3igGLn8JoPFUnJDw4kBW/P7nAT1Ek\n+P3Rg7LpTT2l54HOJq2pIomKiKOu6O2YcQvuYGuMCIypg/42VLVPrX8kkq1snxGeoNDrDpLU8Ixf\nLPopJuqUceGFxoB8uoAUwL9W/Cvp8ljRAz8ucfhuvA2A2nVj36R9+G1oIWQ5E4cPq9dyocK6TrPR\nlXhT8v96t+HuId8CSG5Kh1YX+NVJEnKcHBXzIpogMRasjMpidMbv6GIg0wuvT2vqaXKifu01tXmM\n3tQzNBuybt2pKCl5ywj8ZpUeNp77YscXeGDRA2qaKi/PWM71iEKWUTL/E8zc8qm63OtFj5fah1d4\nJQk5goLMyIunNn6tMRKXdt13Zgd3nrq6TmEvufferLCXA+EnNkVUF9baOepEEWz5cgBqt7GdTM10\nKRaN3kMXx8v4CdrZWfZGB35Me04vl+CxIeBjxrJEAz+n0/xGc41NvcKGDfGuFbDUVRq2rj10qi19\nYxEZP6czbGq2oJDAT5YBvcVPZMYvOzuY8RPqBASQBdgFHJd1HI46j+L0t0/HjV/eaLxn6Ou5xCHW\nBL/ceIGSogAf4w7wbWr7c6/oRcesjqbNpBQlOKhJMn38At5AQmXRhfbx07PpeuAX7w4jl0MCPwBi\nbfjnMOvjBwD+jAzk4VZAUdRyyupk4p0ECT18MkTF/Gqvl+fQnF+NN9jetz26+YC6Kq15akjFu4Mo\nIFO7WAa86mt/7dYN3FcKhhwcZ6uDLUNvXhm+E/kVBVUhB05oxq/W5TUyfgEpdtBUgpNwJRYHJxjU\niG4bJKadDyIzfhFNPWUuo85fB845yksVHMrKDe/jp11teeEOI/BzBVw4UBueOQUA3HorsHEjlnOO\nK157TZ2vJYmmnpm1fmRpxa2rC2b8YjEL/A5tOYzSwpBA5f33g7Ukk4zf2HljcUyr1OlPH33jKCSb\ngkCmADkQMbiL/qa1tUbGT+EKcn1Az0A5ZLe6ES4I4MfqPyJcadcT1P/ECfwiJ3DXV9dv9jn8DhQ7\nzNM4olM9RitKRPM+TzKADz+0TltZHMc//vYlNpZGV84552jndKO6PP4NJ/36Z99SiI7lyQVmce3a\npc7DAXU/q/HVJNUMMm7Gr7bWCPz036Z6cTWqvrfuJ7tnz92orv5BvVkScgxKLinpod0jb2QbGekE\nPmN9pz2es20OnvvlOdPnHit4DP/8Kdik59cDK7D2wC/G43+t+Be2V2xXb7BYXF70KZR+v30+8EeL\nmwoJSjbjV1LyNn79tU/0dhQFknYMtHfFv8mVTMbvsZ8ew9nvnW35fGmp5VMJ0/v3JTK/rnVTz/oP\n7pJI/cMy47dhA/BDeJP+ElcJpq2dVo/ymDMSJjLHbVDr+YxzMDuDrF3XjxzRkh0xjlG/nPi5ZV6P\nWdg/5D8AGiHwY4ydyhhrp/1/CGPsfsZYl4TfpQl12B3AsO85do6NuPgwZpzQJEWKDvwOvgwudoBc\nVmnZ1NPp1IIZwYNjnmM4/vjgHTqXqwsEodoI/JiiD4KioMpbhU2lG9V+FyEXdyNrduAAuvx9Mo6W\nqRfcHK0CFDqqoeJ2I1viyFQUlJSENHtQFMDrDWnqqYBzjr88+hccaKdWuDKgVmh9WnOwXZtyogbU\nNMv4yeCo8cnAS+oEz9nZgN2mfy7zM2Hod6pn/CIHd1m8ezGeXPQkBO0OcqAmpKKuBX6KImF18Wrj\nhNtbPoIezmCFSx/kwif6LPtcFPf7N5STf4wexS7jOMhcnTMuNOOnV/Ai52jMCJ0LOKJyqr9eT1RG\n1W20Pn5ZmRxlZcFzT2Qfv/btg9NnCE4BAWQCdgGndD3FOPnr2ZbIpp56xk+/UDtcFtkfBgRqAxAE\nBe3hx8alaoXBK3rRpX0XOANOMKb2zTT77FYZv+JitS9nKCGg/rZCSJPgJ5+EZR8hj6j+SKF9/PQm\nqPod/KKif5u+NizjBwahLnjW5zw88FO0qU2WzgSqeRf8M/thNeMnBQBRDeYHONQfsxYRd96MjJ+6\njb/+X3Dwjx3HedHVB7Aq9b0DGZnGy46TBGRoP3jAD/y3fU/s/d1e9JaqwYsvwHGSDJy2UCt9eOBX\nvO1X7C0PVsRDM34Oj88Y3MWrBHfyl985hupqbfqIkgDEOhEnoQyXdfkEczoG+w8okgJZyMKm9r0x\nD6Oj+vjZIpp6KlyBzGW4BTfO+mt/nPYAgIoKjB9Wip0bPMHAD3Yj8BNkAUcckR1kNZIERd+R27dP\nKuPH9h6CTVHrzF27an38RHdC/X5CzweHXVWoFEIyfiUlxs4iSBL+MWECar3V8Et+FNUVwS/5UeNX\nK+Si1rTG1s4GySZDyBQgCSYZPwCorQ3L+OmlZE71gNhYvBbFezck/PmjPluGDIADjEFAV0iS+dQY\nkRk/42aV9u/YWX9Bv+n9TF/rPaL+PpXlsmngxyWuBiFWo8eYBX6iCMWiGlLu86GTzwN5r3qeqvPX\nobC80HRd/dx3xltzcMrKkAEVYu1TsmzeF7KkJPz6/+23wMcfA1DrDvogMomKmfHj3DTjV7e8DrVL\na/HjgR9RVBc90q8glKmV6EAgLPCT3TJOKgnJWifgix1fhGXlIzN+Jc4So7VJmasMK4uCfWvr022z\n8N/Tsa+wEIfqDsVfGcCWw2tQVhM8By4vWo4dFTvUPqVWgZ9D/SKrJK2aWt8IFaZDRMQkiuYBu0+W\nIWp1UL0ri1/yY93RdQDU5oH6OUoUAb8oJtzHr8qX2GBaK1equ3c8Dy15CC+uDO+Xqu8DCQV+9nbo\nXwtjP0zl4C6JnONN7yFG3Jmv9dUm3CIpEXrCJKzJO+dgGQwSgFX4X5QeVM8bsYI0b4zp1yLZheDc\nvMT6pUQAACAASURBVI2R8fsSgMwYOw3A+wD6AJid8Ls0od+vkFHT1eSLY8w4WUuKZDmdA0qPqXuP\nSeDncKgngG/yBWTuUwdxqHOrF5Y//7kWc+ZcYAR+jt8ewXsb3kPh5YXwHPFA3LNLrVGHpr1YcMMZ\nHhk3rRkHKTsbOVpAGDrghM/tQI4IZMkcRYeD6WnBweCtyTaCWs64kRGvzKgEXC4oPvWzHKkrxxcY\ng/bwGQeG2YEiC9q27D6UlzFgyYngnCMnB7Db9DvUkZNbq/+Gfjyrpp7bC3ZiXcFGSFpwMO4edQ6z\nXbsAxa1WGtz8IC7+5GLjhHs3PsBdVWqlNRBQKy+vrHodk36YhB/2/QCFK6heVA3Jpf6ov5X/BmeH\nzUC/X6L7+XU4FQCw/PByCD71y3K7Ab/WtK/UHX57zK1nrTZtCl4BtH8jm3pGjUOg9/HL4CgMqbMo\nMscRxxHc+929EAS13qs39RSdIgLIMAI/vbmHflfbrKmnWC0ac1g5PNaZk1HPjUJV1hK0QwC8Wo2e\n/ZIfXbO7GgFXaL+NzEwAcTJ+b7wBvPxy+DI98Av4gvvJ9Onqumb0wC+0j59TywKKTvVzHTr0hOlr\nucSN3x2cQdAyWAt2L8BjS5+CJIUGfsGToyenApV3/znY1FNSA78z69SyHLVHBn7qAatfeLrmaqlg\nWUZROz8yOCBpQaegnVrtMtBJEJCpfXd+L8fn/jOwtaoz6sr3AiXn4zgByPSpJ/DQS1OgJICKH75G\nwdfrjWWhGT+nN2QC95DG/lMPjMDXa38DABT9qwjH8tWbTRlZDuxpF2wOJNWI4EzB2/6zMBbzQtpV\nq7/ZUTkbgZCalX6O2VW1CzXt90DpUA13ZQlmLTsJC55YH+yfGxL4iYqIYkexedZWkozMPrKzkwr8\n7LIdNiV43pIUCa6AC+cvPx/PzzFvMmmW8fPLfsgIOYirq42mikf9fjww/wsMXvBnPFHwBPq/0R+i\nIqLKpVa0Rb9adluWDTLjELIC8AVk+H0hFxbtTYtL96HmnCcQCHDIXDYCdtmptkzx7duFjKoa+EQf\nPvpI7boVy+ayzWHf6V8qx+N4/Axwjg34EFtc5jdJZIFDFIM/dWTgd2C39SBKgtOPdvCjolwxD/xk\njh3H/gbPXov0iFZeSQK++kpbVl0Ngann/znb5oStvkO7m8S9HG43sPTAUjyz/Bnzz6XIAAe6bz8A\nm34sbN+uNsnXT2jl5XCtqw0G5qWl6lw+kXr3BkaNMh7WbM8Gr1Qr1vo5OObohi5XWCVTD/zcbuD8\n8yPKXelU7wIKQljgJ7tliJUirpx1Je5ffH/UW4hiJRTFrx4AoYGfS0av2ryQLzi+On+dcf4FogO/\n3v/pjStmXQEAmLhoIi799FKAc9xUzyqgo+97yDx2MGbf39DKfabIkRU6doAsqNcIGYBFvT3g9wGX\nPwKPR9tO1Ohsieuz8Wuc5D9oHuSOHh2V4WYsWK0WZRETFk4AoGb8vIUPAwh+vnVH1+He7+8FoLba\nXaUNovyf/wAOl4Byd3lCgVa8EbD13fHSYV7cc2/8zNnrv76O19a+FrZMb+ppWh6nE3j8ceNhu4x2\n+PsGqAMkIFh3SMXgLrEoinqz2vRSEhn4+WsTnvdT4Qo+2PRB7HKGZPyMt1QUwA5IjOMirINrv3oe\nsRr5GQB8ivXvo0gKdv11l/E4LPBLYkqHRAM/hash+0gAb3HOHwHQM+F3aULMq8CpfRdhETBjmL5u\nOgBAEGXIdjfWX3Z88Hntt6qpq0AAuZBrok9KDodaN+hfB3Q9oh4E180aaTxfVNQVx9zHcPdGgAt1\neH/z+/Af8kPwChi0LWJQBABitj68ohN2QQKDjECHDkbGzyME995qRxU6iIBdViBUBQ+8ysKuOHJ4\ncHBUT6aAa3cM3MwNrFqFTEk9qR+oLMEYzEfPQY8YFSazNtGi1udFzq6Ez69lDiSuZvxYSOATEn2Y\nbUdvunLf5vOBLLfx0TftAbbVSpD9agVhy292CAJw5pnA5tXqZ67J2IDTqoMBVTsE0E2oDvsKv/z+\nZaxc+hE4OBx+B7Zdsw0l76i3s86bcR5cUg1w/M7owI8r6N1+EF5Z8wq23652hHe5gKN1agV5X3l4\n4Ld13WEAHMLBarzzXztex4NRgZ/+uX1lETcM9KaeGdoOdvr3gE2C8vgT2FK2GSuLV0Zn/FwCRNgB\nu4CTu5xs9DnUT7hWTT19gnoSq3ZZV0pqlBoI9lq0QwBZnmD6rUv7LsaNEVvIWSErK7Spp/r+245t\nwyWfXGKs4/cDq1erJ7M77tDub2h9zgLab+z1quu9+655v0t9MCS/EAz8nj+ojnRZ9lXswQrCM36A\nqGW4X1z1Il5e+wKAkCkjpeAXl2E7io1zjgabemoZvzMdHihgcNssMn5aDSArWw386vx1sIvq+3uO\neoCSEqPSlC0BnUURGdoxua9Ob75qQ03FAaDyTHR0dEWmpG5rOL7EMgxVy+qTIR7nRLva4Ik+NOPn\nFnxGU8/QeS+VLrXY4lCDF8WvQHKqHz4DIioytX37+ushTXkBgewAJL3Wrx9Y2t2L/fJxsEX08QOA\niz68CLjrTwCAY3XqvskU2TLj55N8qPHV4Mx3zsQ7698Jfp+hqeskAz+bZIM95PooyuqongNXDcTF\ney42fY1Z4CdyP2T9nKYHCEVqhsXudOKk6lqUeStQ6Q1WrqvqtMDPq35PH5aeiMO2dhCzPagVBBS7\nQk6CkoTa447DZ2uWwX3Bv1FbuxUKV5Cp/VyZ2nblgB/He4AlBTNw113AM+bxjeH898/Hnurw42JP\nry3gPj8AGzy8f9RrPDs9WCT+guOOC+5HSrGWGdJ2gXFbRHw9J+qlAIDqqlr4kY3KCgWiCKwuXo3X\n1rwGZ8AJX5YPsktGLf4HQrmg9smymKd240bghhu0ZRUVRhX/lq9vCfZVB3BQax3jKD8en3+unv+y\nq8wHepG5jL4OIKfWHQz8Dh9W/9Wbh/TsiU2DClH2kdaiIxCw7lS3K3jMbZ11DtyH1XOKfg6O7Of3\n0qqXsKdK/T0qd74f9pwgCPD5fNi2TYI+q8PcuUDVURkrT9iCqpyTAFEMy8bKLhlilbp/RbYCAEIC\nv0AgbAQu2a1+dm/AHvWaSF7vHmzdeh18kg+iJAAvvQRwbtrHr9Kj7qd2pm23vByz8X/1yvhluP1Q\n3LWxB30K0U5SwgI/vR84l7ll4Of21QH/+xoCPvXmQeH675IvqGbUrFF4Ef80TxR8+SXw/fdhi5zO\nbKxfr05lUOIqwQeb1YDBF3LRVrT93Ct6UeGpMOo5d92lHjZVVQDsIjpmdcQxd7CV2I8/vofaxx+M\nKkbVltgZPyPm+Wdn7OgXfSMBADB8eFh/SBsLDw8iM35//jNw8KD25I4dOPbFx8a6WfYs9TfTbqKp\ndQdbo0/nIMtAhw6JZfxqfDUJZ/wcfgfu/f7emIHiccveRxZqwuoidlFRm3raZGRARuBIHao6VuGN\n0yzugAPwS4pl9xbZIRs3cgEg09MOxa8DGXAk1cQ70cBPZIzdBOCvAPS9PDPG+mnT3g9j8MGwkcps\nNmOHDQQU9Oy8Bt1CUvL6icXpKMVafI7tRXdEbbv0jKew07cM7SUgu0I9ae0sO2g87/NloMpRive/\nB05wqwe1UC5AEiVctR9wnXYqpOqQyo1+t76uBjZZBAOHJycH2VrG78Pn9hqrVtUdRY6oVt5+qAhp\nyiZzyII95C6MmvHjUwG7fw/AGGxd1IvUjsPqhUnpUBUz4ydpVx9REVBboh6oDi9HRgZHhtbUs8+u\ncqBzZ+M18oHD2ncQ3I4oqhX+/d7NwGmLjWzYfqcDXnghacFB5vCJxoB2x748CgUM1+8WsO+tYOCX\nBQHdZfX30pd9OaMaC7TRk2p8NViLbnD5GPDJJ5j0K8BtAliPnaitUiBUBgNuJkvo224wNpdtxu4t\nan8etxuo9KjNo8pcZXAFXEbTyq//5wzgordwcBNHeRnHUfQ2ChEV+P3rdYRxuSDZ2iErQ1HPO9fd\nC3Q9AMXhQknxTvhsHYw+fkbGzxWe8dObelZ4gu9p1tTT8f+ZO+9oyaoy7f/OqXjr5s65CU1GCQoC\nioKOYk4YRkdndGYcw5gDGGfGgKKCIiJRFCVIztANTaYDnXPfnGPVrZxOPvv7Y+86597uRpm1vm/m\nO2v1gltVp+qEffZ+n/d53udVdXUTMy/TBFyDolPE8uoksGialbXuTIaM32zgF1NP+bIy9PW1APDQ\n0ItsGA37u1kW7NopeCKxgT/+EZ54AsqGMmZRct6ZGVi2DN7xjrkGbY0JrpFxHrphSB2HTmJ9kq98\nBbIT0gGrbT9H1NwIVwQBD2g4qiH57IUrAH6zZBSLnWmW1rxA6vnhLodfPAmnlir0RFexrGAEFzrq\nQcQH0xzH8+UzYasAc6g2wXFlOXaON6dhxQqEkGO72YYOxwlq/OqG4Cd8j9MyXZzVMwGFo2lxPGKK\nWTufx7iQ5+QB+uDpLq5fpljcgO+7QcBeq0HVCs1d/FkDYn7BoTqojHwsP1iIoppDKVqUtXAPPYTz\np/tpSu7kZ+KLAFQdh4/8538G17hNM2mhyvTMU9y448ZZLWPCbUjJHjXhzwJ+0TmungBj5TG6sl08\nPxLW6syxuW1qkvv/9Kdz7nF1f5WxXx+erdc9Hd2fpSbwZI1f3Arrl4UQoUxucvKIrp62ZuBpanA8\n84z8LvX7vUMJEq5LzawwNHmQhmFy2ZDPo6OYvXXpTtA93EQdXBEwgQBl2+a4224jpc6zXqniCz9g\n/JKWZPw81ybuw2OPyvlDfwUr86H1s3vaPIrOSTgcuQrDnJSfb22FkgIVrqf6R6qg6CMH4P0KT+7Y\nMTdWsvMyYzOTkbdoX2Yf6/rXccq1p/DVT30VgFP4D/p3TCLe/ObD9N8LxvYyxqpZHkK2BH4NjyXh\nk6mFtfk1BdhiONKgyXf5y5eeP6LRh+d7nKUkbAHwa2SYZj0bz7IwEPOIhmvHkdpFHHLsfqEa/A7A\n48/ewk9/+kn5pmGw4+rvcN3D1+EaLiN7v6l+QHDccdCrGNDNv384OJzLL4e9f5LnNzTvlMOknrOB\n32Hn6pl4XhXfM+YyfpVKMA9+4xI5gA4suZbh86474vfk8+vI5x/DcAxWDmbhO9+R0tsjAL8GQxWL\nqAVBPSPaX2Engn3FXKv5U381zYrR9F8HfrNi2JZKlM56U/B3g/ET7ssDP6Mg5yIDWe6yd1jKKSmV\nYOl/n7PQ8V++zu+QIP3mm8/l0kvXAdIvwPEdhBBzgF+tLNe7ql0lXU1TKMr3+vsl6HMcQHc4uvPo\nOXLPizZ/gV9uveqQnxdU80cGVI1Dsxv3KeIy077uyOfx9NOwLnzv0IRD9hDgt3NnOPT2923k3PeG\nybFkNClj6gZrL1yi0Y5XDPy++aNxFr5GNq/3LUf2rX0F/TMbwK9YnGJ8/Ldz3zyC1NMX/iuqZXV8\nB4H4q46+89ZexiKemuO3sGDURYtq+Lq8Zv50lc3Hb+bW42592e85oRuqL1OjfShiixtNrCxDkpn/\nJ1LPTwPnApcJIYY0TTsaePkj/1/c2kzQGzrpzGxZpRZYzHY8nmZP7sNsU4k5IQRNjXKdSg2IcJr9\nNVnoP2szFm5k0jlI0oXOgkQ4uhdOSIYRpZKVGfXj8lC36ghHIOp13jAKu6JLqe8P6Y7GdCFKWXTh\nouFSakqSMk0+sh8KDz7Ml3Y8zAvpfgrVKZptjZgPd2XDCVN4As+JMjbRYPxEQDU7lT7QNDQV7Hb1\nSslYIkzOE68VOJ1dcyY1u1zltRMgPIfyeJFr+HeKVZ9atRAwfudsn5iTOs988Y0AcwCl70OlYVe+\n8ECwvhq2jRc1KFty4Ws65lEOHFSa994iNT1OQu3WiAETWCz0cvhCBK89cP7b2LhQSnXyj93Ld3k1\nD+xshqEhVpaBiIPoHGD/r4fZtEhKmHzfZk2fyxnPLWRl20pKKXk/KhUwFGuSdya5adM1XPGULD7X\nfFjQvpWTfn4RjuVTJ3UY46dVVV3aorA+Zv16eMvIzXzZv4rF8xze8Q4gUYaIw0Iy7E1nmVj9RSxL\nAT9N1aBWXGwiELFY2rIUW7XQyKj5/yvp79LkhOPIPWY7tpUlU5HjomiEbQcai+ty7mWh/Sg2Np5v\nk8AmNStrPVvqqeuwc3IXIGUTGoKJX4E4MMHWcpkf5F7F7M00ZQC5Rvsub2Y9ySRYSupZq8tjH95c\nZ+FCwaWXyrYfja0x6VbMMm8chspohbJVps1op5yOcfXVUErKQsMTrkD2rTxkE65MdnxyN3yw18T2\nDgd+f/iDlJn6s5ixJU5eLk6K8XvHsMG3NsEppQpdzUfzT7vLQW3Pvmvh7sfT9KeforhA1rhkFsr0\nveM7dBjyN4NaPiUTTTnQabnE1euFPHyPn/L9Xdfyp4fGiRZW0OI5RAlZueC8PIGnOzjU2b37fHK5\nRwLg53lQ9yoBgBC+x+NPXEN//1Z8zaNcU2PADtnQxncPFmSyyqWNeHyExcg566Cmcc8FFwSBcAsm\nEXzWbf4dX7zvB5je4SnvXl1lenwfvy7nAx9wSyHjBwSGIU2xcL6ck8Fo1Pj98pdSlqWer/qBOqM/\nHw1UDI1N9yOHAD+Hil3hQOUAjjrPZ4ae4ajfHCU/8KY34Y7K85zN+FkRAw8bHnggAH4HXLn/jU+8\nVh7mj6He3xUAlJJQ7roK+PmaBrqLF7VwbA171gJcc11y7e1ElamPWdTnAL8mbxLf9fHVb+6yJciN\n/G3CJgxYVE2d1VliD1e97Ocbty+VgupoHt79Oaqm3LfWVePgR/fPYVZmkV4AGKYcfJkZ6ZxbtsqM\nl8cZL48zMU9OTjUq/PTZY9EMI2Ta1JYVHfRwbhAsvvTSz2FmBs0XAXs7O8jVuyUbGVvzENXqLIfg\nIzh7ecLj7Amw45EA+Dk5FSjOomp+xCnctbUZgHSD4T2sCDzcfOHzwW9+kLJywm4EvTf8+Ua+973b\n5Ifuu4977gF3rUtxQ5ZoQ83mefT3w/CwHMuXZZYDUK8Lcjmoq8R0JnXsXOCnaXiZasj4zQ5YXRfH\nVCyKqk210pOylqqtLXjWG3WTM+mTmd7aOeec3Opce3zDNTjxoATcYrZR3Gzgp2KKmB6bc82S4mVY\n+llg6AN3fYA3/PEN/HLL9bw4tgXd9JlXrf1VeeLsIPa0Has4fjrsH2d5FkWzKAOol6m9s5XSxInJ\nOsJSRvXtnRhg71f+e+044L8H/BIJeew7d4ZGcY7vYHheEPRlK3L93jO9Dx+ffTeNsarN5swzof+g\nS2FfBXSfVe2rDjN4iRwS31sTFpbqS8xnPzvnvcbQ/+DeUOJfT8j5f3D/i2we2zz3y2ZNPNohQCld\nls+z47kIIQ2dG7HYtvEtlOLhgTUYPzGL8ZPA75VJPf9Y+BTZ90rlhjFUo7cK77rzI/K4ZgPSE0+c\n01vG9yXwm5h4jP7+Q5jNI0g95fnIlkPDxeGXPZ7fbpEg8lDjv0Yf4NmbWwjnG90T2JrA1+SzHMnV\niHl/nTNrqUqTyjnb+vVwySVQUet6w51cfZcVd/7vAz8hxEEhxJeFEH9Rfw8JIX7+t/b739ja6g7n\n9G6D9z+AbYdSNsOzAqeh/TtexUK/zKqynPxc36epUSJUnTUZ7dgh//vkk9iWwE9NU7bzJF1YVFG1\nbqnTOKgmQcOIUc3JSWVNHupqYl7VNcSeJTDi1YmP7AkGoK8aJ4uSXFR0LIrxJK2WxV33wgunruGO\nzAyPTHRRrKVJWTpxD1oj4W3L2gZVkvz0Z4oOhyBIMjFVnwD59+S4DFQTGAEzt2zyPv5hxb/PYfxq\ntSLbboK3DmaIdnXxr/yectmlXBoPavxyzSqz7nngOHT9Q1FdA/lyYBBYdzh/GNBdHEf2ZDtwwuV4\nsTp32XLhTGKz9aCcIDTPoBILHUW8a67id9F/lowfWXKGG0zAH9qwlX/pkvRRfkymqTuapNlN1Ee2\nQ9A9+ssD6lANXnrpKLyYQ3shSiKawIrIB7JSCd2UIiJJ+01bOem30iTgX3bBzJO3A+BYHjWagxMs\nmiWY3wuK4TKs8N689BK0e3KyPG1NjYcf8SBRJa5X+XvuJp8p4uvxoMYvb+b4t+1g12xO5yWa/TpJ\nEeGUEXVRhY8nBJd4P+NMQzJujgPbjt2Ds2wHGZXKLhsVZlLwZEuGj977UQCO43ccZ1yFo7tElXyv\n1QoDqI5ER+DqWfeLvOamM4GG+Y0cP8Vymi2bLXj3+bDuQbbtazDosHKhx3FiIxcv/f5c4Kdq/Nb/\n6xb0ts0cc8zcuK0RZLRNF3j+Fsh6VUpmiTajE6LymmqNvpJ5uOzuL3HezefNqTNoaOv//CDc+WgJ\noQK/iB4uYkJIt3x7VnZ/VcUi4Ymgxm8mIUHJyrpJbeVco5MTc/DatM2OqV3h/b1YLiyWV6RDAbeG\n665Qx5dyoMP2ifmCS/g5r8/dA0DCs1he9flAaQctvkVM7R/RZkXePni6g62p2jnhUalAS4tc0C29\nGvbxEy7X3HsJG9begK95VNS9PZTxAxjIy+fBoY1oJENcRU+G64I1wz/UZE4v4svXd+yewtErfGbP\n4ZLboZi8v5rvYVVVMkKzEI5sZN4Afg2Dl6aovMaPHA+uY+G4FmSeRTSAn+vKWpErZH2Jb/s4aYfq\n3rmZYt3VEZ4WAj/l6vmT8k/YgHw2cjtDEwqKxaDxeiPOd3wfK1KnGjHQ9n6QoSf7yCci7BpVc3gq\nZBqL0XC8VZAs58L1t8PoqHw6NA8vanBz4TgeMIYDh9GeM0vEbPAb86IZwfM9Yo3kpD6JX/PxvHC8\ngPirjF/QAL6RxVeOSdFDGFkhhOyxo9wcLNdj65qtNDdDfTwPr72BfiVPdHMuMw/l5gC/Qzerpub+\nvJz+KlYlkKFHFMveRp6VqOuWP1xynsAKOoCMj9chk+H6tTUOKgXwZGVSash272bVs1IGEtUtqtVZ\ntUUqWdDb+wVyucd4ZugZvv/M9zlrEgbWzEd35OcG9ihq75AgSqjA0VLPtjEzQ/S559h2hKavG0Y2\nUGgpULArIEQIimZ55zTaEbXUWqgP5Yip2HbLBocHLzuGJlfWgL32UblToWJJ4KcSB6uKXfyqtXWO\nq6eVLQcqlTmB7jnn4HzuY/J3DRV3jI0GC2+D8fMI577TvS/jX/FLuY8QvLT6JXqmynxzQCqKDMcg\nrhxb7Vr5iIyfnZXHEtXV2qyoyaRfZ+PoxmCdAWR7iVkD+Im+h9g0tolf7riFG3qfRfd8Oi2HmeIr\nq/GL+g4a4T20PZui8i14OcavoTQRSTkWM6NqjhMT5M/hv+1Ko3OEutZDXevUllBZ6z17QqBgezaG\n71O8XH6mZsnrt39IZkGG/1KkqWyyejUcfLhGdkcBvBjLW5cf1l4qekh8X9tXw4qqoOgQssK2gWXb\nqBkyqUV1UfBe5xsv4uKrzptzn71ZQ+1Qxi9TlfOM5boNP6Lgmuws9VCPzt33yMDvlUo9Bf+yA/je\n9xB4VF3oyfWrdwTHNcR6PT3Sar9x/J5cH03zCJmzIzB+IEH5g90P8rUnQgmtZ3hBssMXPj95UZaM\nBMBv507wPMTZZyEuDsu9rn/rdWwaC+ukNeHzQrmMqavSj2oV3ZvtFhhu1Sp4nk7MOQLwe9vbSF93\nH/QpaVyjVKCxdjdV/5+4er5e07T1mqb1apo2qGnakKZpg397z//57ahsL195/Cr4ytWU3fWBi+Bw\naSRgAFwnXN26uv6JbP4xteCCXzlEqwhw0UWUdg9ByxRVt0jShcVVBxB4LefxmPqRuhHFKsoRubQS\nytc601mGF7WRbSsRm5Zp1L68JTPFACU5ANef9jAF6sxXyKaeEpRH7mQ4t5+ymZeMnwdtjUm1r489\nRZPBthWgN6gnPxgUPsYc4GcX5USf0MwA6PW07OG2t+6bA/zKNblgJzwHt2cvCWxKOQOz7gSunjdf\nuFhOzeUyTE9jNcnBfCjwqxkWL9wCHV4Vx4GnB58GwIsZLLBlm4mkC1v6BtTxO1Tj4aTcu+FOli18\nUjJ+zDCQq7DXvU+davggTyljlua4D4ZB7jXHQ8QhYaxmuEl+t+vmse0p3NXDLHjTWuKROHZEXrdq\nNWT8mq2l5Pti0C0zw4tm1wRZgjopdm6RJ3jH6M/hSycEVKdhhsdUq/ic5kugMLM2tMyOa3LBe/et\nHfzwh/NUjZ9gkRvlhkfBqTncy0V8pW+Arc+4nBqonzym1YLmeIIZ22brVvjq+rcwGZsgoxqCl40i\niy6BLyzfPcehVMPDjXpEhPyOdkcungkH5sXbKZny+KqOCoDiNYaum8JRYKYoXNJ7n5DvvfQ+fnOH\ncp814fUnKLfXtnESCTBUkF1RA+Ked/+U7Re8nkgEnM4DwQQamBKp3jV2LU3ZLtNW68RXi1nCNPni\nFmiqwetjx7AnvYdceRbrPctFK+bD75DF9IfWKOg6uLNMUI4uSva7IfVsU8+ApessXKUkgrNsTX0N\nDnTp0BVO9I4DNW+a+b6NrevEvUY9gjz/lAMdlgR+P+fbfLgo7aMjCKZTOl8XVxMTPjElDfXa5e9O\nTKzn2As1fM3FjqgWJ5pGpQIdHXKBs/VaKPU0LcZjBrZtyH1MeX192w8y/FElJR4oDICuY2ttNHlp\nYhE5wOu+D4Ud3OFLZxFNfX4qm4eYwfl3zV2wlpVhtEO+pgkfS9Vk+pEy0XYdt+Tym3dezTn24pDx\nizbhuYL3fhzeuufHbK/uha4f4TZq/FwXkU4jdu/mwAH40nVyjmh7qG1Of8oNEyv57t7zsAzBRxkN\navxmb+6Pfhj+UangWh7JZBhcT9k2ZsygkirQbMGSUjfPHuNRV8mKOCEzUFCI6B29kNflc7bkxXtg\n+/aA8fOjBrYX4ZlX/5yNoxsRQlBuKuNsvpCKqr9NR/oCxs+KQFyM49U8KipZt7gG6B5eJqQXb1Aj\nvwAAIABJREFUZtf4QMiiTmYeIZt9BD8tg8cYDuCzBpmdrtccSa+rGqRNxc1c+olLZQ3MlJzjqyPh\n77i2+1eBn6uSW/m8ZPy2TGwN1jhNaGg4tFEOgV+hEGTEG8nIdPs8Cfy+sZR7J/fAzAxnT7gcrzDi\nZGUSBgYgk2Hc2kwhFifmy/yL67vsXApCPWNmsR8jm2b39G4KOzZy5hQcXNMGCviZ2TynsJ9S/hBA\n3ChpVcAvNzKC55S5b/CFw/BA94wsBTD0CH3DO/nkA1LeORv41Q05dwlLUB/NE1X5j43Pu7SfN0RK\nU21zVJJxdLqGYYBheJhxwarSQaKlEt8tXRpIPUuFKsI8AjjZsQN7UrI3wpTXXp/MkTbkZ3Ojyj1x\nFvBLMsPgQ7fI12sebt6ld18RnZDxE/WXB35JByKWmkMU8BPq2iV8g7sP3M3dB2a5o84yxhNC0PC6\nKFbHyRtFNE/QbrlkCrOA33e+czjFrLZIqoSulDk8/zyWWfubwO/JJxTD0izHYtRSyTNlmLdj6KU5\n7bgAioXn6Nv0D6xdC5//vHzNnrG5DOih93DGryElPoSBTibleGt18ocBv/bABE7euwWPxtB9na7S\nFC24tB7I0rvFxvIc8GIsTS5lYmII3vnO4PuPBPwKMZcVJejn8zjFWa2dDI/293wE8d2vcajZQWvZ\npNWeawyzeWILTE5yVOFwxi+rPAEM0w2SNwHw88YxY2HtouXZxD3QMhkJkIRLNNp5GOP3i/cvYv/+\nZzl0azcdzh8FenoQwsP2oWiVZNLSsmWiqBG0znpoG1JP60g1ri/D+C29cilTlak568ee1LWMfFmy\nobMlyYEi4e//HrZvR9u+A/PpsMZTAzYNhsDP9+Gx/Yv4hnk2ACti49izVIKzt9ZW+Mtfvk3MgcIR\nCkorThIxqYC0inmSqnuAiJcZ8T53xO890vZKpZ43A78C3gCcBbxW/ff/u21eZYYWlU2Juou44+uy\nWFVoGuWyvCGGMLFVULhtxyLGxicDqacoG7ixWUYsX/860ePvZ7AnB8kiNa9AwoWlFQ3OuwLf3UJO\nAcS+4gBtthxwMR8sobLh5Qqa2UF2URkUuLjw1g9TUBn4BuOXcsDQ67SqYHm+UcQzpigZWWpOkZQj\nsyjNWpRdu2DLW77DpumTuaN0KgRMgcBzGuyfoaSeKtugJssEEvhtndjK9SdfQ9dKF8MIH55STZ6/\nRp3FY/sAqKaLzBRLRGJlti6DDUurFJJALsdU92bcuDzvQ4FfXUkaElg4DuTyPouq8Kp8mSYlj0u6\nsH9ygO/zYz4ofkG1KZy44u4USSwSWHRQ4q7tj/FA7EMA6L68hwurMGQ0jE80qNf5uw/1EoladJpn\nMIE8B8cpcNtt3yGRSdGcypLwNGyVyR8eRtZMAKnqYjS/TJup6jpmzRcNqadTs8nnYWFUSjttIYOz\nBvC7btt13Bq9gM64cqYsisAVK67L146ZzLJiIiqvlV7B01WGSVMzu+bxwvNJljXmSt2lX2WBPXTy\nrkv29+Nw1u94tGWGQkZe68YENhEzmClm+VyPzOrreLi6Q0yTE2a7Kz//27XwuhcGuPfgPRCrs/tS\nZSmYKGGjU7LlNap7EWrZUOqQr5t4SQ2zanDyAgX8miokk2FLiVrdwqt5mErLFa0WuavtVN5z7Xvk\n/VJZ/GRZXvt57jhFs0S6vAJUoHTi9Ay/XSsXvJX5JMlIkpe2yfpSIURgXtLYTkIGELoyY2luVrb7\nOjh2+NmjC0jg5DjYnk2rGrMC0JVch2h0TjCYzpsY9zzERbLskEIBchVBdKadfDKB7zrsBFDn1WZB\nqw0xFfiKWVPuY0d3cg5Sutpg/PyEDOI3bfoP0jMp/IgTAL99mf0MTGdC4BcN+/jpwmW8Q1fAz0eo\nRrnCErizpJ4dRqtcPNvbKSUW0WlOE1egs+L7MKvYPaKOqapqS2PlMDvUbkDPb2FaAT98H/M5mXn1\nV/UQWZUL6vzOMxcysutZfvAcnHgww+vP9Wk3oLu6h9G6jCCcRo2f4zDdUyLzzAEeu6PEvZtT2MfK\nG9NIGgE8/fdn4y7fip2x+RyDYR8/bTVD8yVYtKLqZjoOWBae5dLREQK/gUIJN+qA7nH+KAzP76CY\nBL+/D4aG8BIhw1lT9QN33wNNKjGG7UhEIgDdw4+auGgYcWkTLlxB9wrJ9mR9eT/WnfKJwNylawEs\nFmN4FYeqmrMXlWVtb/l5OVff+luDJVcuCZ7pRx6BtGJfCtV9FIvP42bywf2KUmcF96Njky2oKLPR\nnkKtU80pgT0t97GUJPccPkpr4sEA+B3JXMBUbsHlqpzj1vc8E7ynaxGKyKTFKpSEMp+Hk06Cr3wF\nT0n+t5+zWgaNrdP0u8OQyczhFSYrk3I/08Rx02SbZLKzUhVEu6K85rPwVHkXdHXx6tetp+8nA0xV\npjhrZ5o/nwaTKYFQLWScXJaDnMLo2KHmKPLvBvDLj45y9pP/wZX3v4ep6RAkbp/czp277wTAiCbo\nGdkRvOfEws9V1HiwfAtzIE1MxdflvAKgnkrkniYbrfcNGbByI7cs+A+qi4dpt2Z4/8aNfMX6BTl3\njN1LwDciwTpwaADuLFBGM0YZnyixUok9vYrVzcpxoh/igNhXHqbnsz3U9qn6/QGT33z8Lyx7ELxa\nBc2oU+KUIwK/rmvgjw+rmEoBv7uVq0fCN0IWsLG1yFpwPI890ztQfa1xa9M8cTVoLjQbFg6zgN/l\nl8NN0gQl7kJsljNibPUI2oJpXBeu+vYFjNWnwr6Djmz95Ls+vu9jOFLNdGBXjZvuTxBLyUA5WpAo\nT1g1Jgy444HB2catjP9mnPG7vsXqd9/BzddZXH+9fH3w24N8DzgtUjwMKAYAN5/HmrYwx+XzEbdl\n/JTM7AmAguM5c2r8HGVmlnQz+LrPtF+lBZe23gKD3T6W64IXp3lHM5PPHIC1a4N66Mghj6Zk/Bze\n1QtruA57d6hUiNxwLX9+Sh6DME1JDACYJlFPkHSldHb8t3Ifw7fgD3/gG5sAG4yhEBTm6zMgNEzL\nJp2Gt/IkbtXEv/FG9iWKRPwwCWK4Cvh5HmSzIeNXmERs2cIu9exd8tAM0zcdXoP6zsEZ/mkPUsIs\nXFSnBM696dW0WhAVhM0J1Vw1NjbGcfUdHKMNzQF+JVMB9ENkFA3gV7Wr+N1dvPH54eC9M/kyLfdK\nIDW7dUvA+JXLgXlUdVYyeUUZOsfD78lZcdZ2HcP7kXLU5YkhKkI+vz3ZHp4aeArth2GP8YmJYwPG\nL5fLcfbZZ8M9UiXkuBpMKOCnno8m9Qy5q6co6vf9zZ7Hje2VAr+SEGKtECIjhMg1/r3Cff9Ht3Zj\nhmazCgKEC8vWyRodoUG1IgPaOiaOGgR/uOXdrH18QSD1jPoT3BuVxfFWrQbXXIP3oU/yTN9+brsf\nLuw5iA4yGH/bJWju7bLB8gkPYaWmmG/ImzprXUCbqhKJLmQmVgBHLgINvTSAKMwCfjGfZuWq2WEV\n6BA5dCdD2SjTrGyN9+39O8bHwax61L0EZS8ZFjYCrur/FxEuY/YM450y+Jhfl2nKZKxIqWbwcI8s\nNrd1k6wZZrfLCiD6VFidltnFWrqXdKlINFHA02H9MpNaDCgU2LH9fvaUPIhYhwE/ryofrmZhYNuC\nfXs93t0L395WRVdB+Pu7oSAG+TBygFcS4bmsqeRICCeQo3kz8tw6O0FTgf3Qb2Ba1ZKZjhegzy/t\nzvKFfR7TzUrO5Ba5+eaf0ntFndc/PE3sqecCxq+/H+yUpNHj+UX4iafojMiF3p31lDi2oKa1Esfm\n3/f307x3A2/rB0P9RuP81/avZTLxIs1NSpaFxq83y0abcVUXVVl+kKir8bvfQcHpx1dygMDkJepj\nlXWSDayiewxONaR1PgXHYfKWNCTKDKbylHJygqraVdpM0PwI2VKOG6amgpoPJ2oTF/JazVPAb0Ed\n5o3nqDpVWL6V7LQqwklK4OeooLRqQbUQBv/2iMXuX0O2sI92Vfvpx+okElCrWDx+G4xM2lhTVpCY\n1W/9E+/sg/KQXCAa0qlOdd1WLN1Cxiji1BbDabfC2ddQj4WBjzaYJoKO64PrCsavGmfyd3N1941z\nNbpVHW67vIC6LusTGttKFTv4dQPDtWi1w0nTrau6mFgsAApCk+1bkr7PJ+5/L01EKBRgMh8jkW+h\nnIxSMPK8BtAUgGqA9oaLoy/CwVTWUsH/N4BfkM11T5e/GbFwFfDrnukmnavTNr/GBuMG3IgZfN7V\nLApxH+fhB/F1D0+EfUTdcgP4uSzJz2egMMAFlUe4VryPBdVpEoqdLGgaiNnATxmAqCCllgip7w4T\nWhzwGjWTvk+lIueNSy64GXH+MwHwWx6fz4HhbfzoOXjDzU/Rtd/jsTtg6krorsgA0kkk5MPjecTq\nJQy7m/f8fhkA1b+TQeeuiVBmK2/gZgqGHMOB21rsam7NfQOAi/s0rnwCqFZxiOLaPu3toYHG4HiG\niKoHvWAYnl0tsCMghAZbthBNhBKrNgsQco5O2XLgaKooyzcMTi9nODNbxY34WMkijucgHJ/e1ZLt\nGU+GUaMvfGITp1FIapQiKfzBUbA1yrEky8sRInodXUndLvlPuU7krr4cnnySyy+HTVvkvTUcA9ue\nwlbtR2K+Q0QFAjGK5EqNSVjef9ua4u190NYksFXvVFMlTZJkaE/tJOHKZ23mCIYnblleuGMZ4E4+\nylc3hkY6utApypRHwPjl+ialFOu3v8VTLVmSjkdmWtVzWxoBdaC2ycqEzKaYJlGrRrZZEPOhXLNI\nHJC/Nz2RkRbQgJZzGOvaRbJQYbIVeswqg406mJIMUYSq9/IVC9bo5VkalddgarCHLVfs4YJhGMvN\nYpVHN9CdUYxfJI5QjElEi+BEwzVqYnQYgJpnsjW/kbIqp8qUxujYDalqirgep16XCpI77jbgtdfz\n3II76IhtxtXitJTlMWabn+OMz8GfXnM/G0+QJjbbJ7azY3IW6Jyvo+lNWNUiJp0kjBp6Q6WhVB+x\nQ6iwol8nddsl1J7qJUId/8VhFk1VmL8ZXrWxn2glyi6uwZiaC/y++U04qgSnp+U4mVJsal9GJjqT\nIgR+27apGLwBcAoFHuoO20oI3cOPVdFcaDItrEhurkGRAgNbboJ1t4fz9LRhU6pJQvBrb5evlSz5\n3J+QgKGhH/Bc7Dme/8bzvO/O95HPQ6tW5l/3WiwsShAacywQgqEvfYpPbIWB0RhDL9bJr5fPV/9X\n+3lyzwjxApw1KeMQY8jAHFZKniUuTzwBwz8exmuYNzWA3+bN7LlwFy+tkvfrVZvXsooR+mMOEwUJ\nuj7wjQ9Qali6Aq5i2Wofku50hWSdFlyWYDJRjOJEXPBjzEvPo16XwX76z8MsL0mjsdlbdW8Vo206\nSNpU9k9x6mezeIZH8vabOX1GjgXbmAiBnzr2Jgcq6QpD35LjfMRtJd3VxcI6+HWf3MM5agdrTN08\nRcnOQ30+RrlGJi24jU/Q1L8X7XOf46I+aDFi1FUt7MCwS0Il5pmeDoDfPZte5LYvvI037t4dgBS7\ndDi71aIUEoyNIfBIqMdyxqwHCdpDGxKefvrpfGjmKv6l/9uB1NN0TFb+eiVbf9DOxOumqVRkq5wt\nJ24hVw4hzIKt+3njtgz93+gP+vEVXEkYBOwy0DP1BN3dO/HLJfyGa/AsrPW+bnjnaHfwd+Mc34As\nO1gYG6SgFu2fbfgZ1+2QoHc22xhzgInv0N/fzbZt27BVY2XXAzGlzHIU49eUkMfmteXoHzgFz3v5\neuXZ2ysFfs9qmvZLTdPO1TTtzMa/V7jv/+jWZmSJCB/dBN+zWVQIb8JDj/8dADZOYFHvlSsM7XMC\nxi+dbeYGQ9qpr9/4HDgOg9fWGJrZxnt6YEkxixGBRTWB5sOKkk7OdeFj76f82t/QVgsZv8bWVHDo\nWdKEr6VoqBPdzDnhB0qhEURWLxBXVuwdVolmUSLupUnnDVKuIJY7mkKlk2oVpt15bLEXU0plOV7Z\nFvsILCVBiOLQY4wFrMCismRJEgv2cv/479g2ETYMji39Jz71KZ9f/hJKyhgiKuocnR+kTCu1XD8n\nZfv5Q/fDeCKGqRnU4yDyeQa7BrhsqAg/SJIzcmz/t3cz8pjM3tlFGQQ0+yb5lyq43WWOz8E80yOi\nFpGvbIHEsn7iSXkONa05OK6TsjWSvksCuTDqMzWiHpw6f5KGvX6zAx3DEqz0zYwE6Os9g3W+9eKT\nvH9MMkCuG0oyJvYfR7x5PnbEIar5GAbocQV4sguICo92vwj9/XiNp+SMP2AagmKLzT98tovH7Qwf\nfnAdT9wG9Wb5cBqWDgMDdIzJ70rF6/w++nE2X/wlhkvDQMj4HTc9RczVGBwUaFqJBYEMQg5GJ+Jh\nVqJBUgLNY3q9/J0mTIqui4cGyRLTzRnqSjpTd+qULoefPO1Tj1dZIXQ85OJsRS1ivo1DlE5fjpNm\nG1aUVRAndOpJNXkoxs9UUik/V6JUmB9cw0LOoXISWLZGmzKnaIxvu1ThHf3wg5/FsCZtNA8W1EB7\n5GG5QKnJsiH1nKeAX8z0yZklInX1O+/8EvFZYC0xmUEXAkdAtWqT2Xl4bwiBJhVmVcX0tcn9i/5+\nNnWHTrmNzKlbNanUbFqd8KFNeoo1wgtiUw+NeEZOtGvsKRx8prJ1LNemw/QppKI0ct+aArRHFaXy\nupEI8rVwlSibYQ+euHDx/XANMfLqWCI2Tkw+j4ZrYdZjxBYP8KxzOU7UCs7BjlW55UFYXYTP7DBo\ntspgmpy56TV4Sur5sekejs01M1AY4Hn39Wz1jibhmkFSJe1oAeMnhEBXYFT3S1BeRj1ZpSkmA6kW\ntfg2V0xAYHoez2nyfGI+sHQCtyC/a7neQfcCdV4FD8d0Wa3W0mS2B/Ff8O3LYmSdEl0LIGmVKKV8\n2lQyZ3+TnEMa7RMATspAPD5DRaE4y7FIRpIQDxfptqrgrEmgWiWOw/YDTbS1hYzfyGSahCEBfqcB\nBxdm8Z02NKHjORrM2xt+lyWDJB1Y4MnfsEsG1YkSvg+fHhngs7scjLiJkyjh+A6ffvhT3PwGWRs8\n3RLKNT3hEXXiuJpOn76MPQ8PgO9TaE7y3c0Wf3I/GwA/0SYjnuk7b4GdO7FtmM7KubA0UqY6NoyV\nU8BPuAHwm8dWiqW5zUUX7NrA2tuhpcnDqBock4d6NQy83XkGcQX88kcCfkoBcT4v8lHu5ssvLeUD\nmRMBCfzEAvldDcbvL0/cxdgCWVM0fVC+5jdtJL1DMoO2aviuzYqcJovjsmjYNGmq1pnosIl5sHBq\nGxc8IRtKm5PD4UFpHsPTEzSZLsUk2GWBNaOYJCUNtmqGNB9CJj6NmuDjH4dHnpdgqvCiDL7tCGSL\noZ5vZtNTlOpKRRGP0rVhM394EOan5qNHBIrXIjMlA9Df68u4s2WMhQfkNezzHuD0r8FHCxU64wmu\nGL2Gx3gnb99+LR1NGVYX4OjSRnK8jpaGyU5EJhv+cvaj3HPCi3xsL4yOCm56KpSTOZ061VITk6MD\n+KRw4lGsLlmX21+RToiN9bKx2RHotJ5H7O7iXD5C/AW5JkZrsOZgmlRFGc/0GnOA39VXy/0bCab9\nivWd6pUMRtw3qBsy6fnJ153K7q3ZgGEe6t/OYKF/znGQKCHsCIm6ja+bXPOW0OJ5U9d6hgpDnJ6G\nc8fgjOvPACBtu3gO7NkZrt+TSpUU8aPc/tAf+Qyfod5Xp2f6AAvOO55lQsYSJ08lAdAdjz++cA2u\nmqAPFBdTJkbtQBgor6vOYOtw0fCN8F8aj532GHq3BHO60Nm6x2XsijGMfrVYFYtw4YVw1lk8PRxh\nnVgMts3p25/lLLZRMAzGJuXc1bWnC2PXLPCugJ+amjnJ3co/ciVLMMkkUzgJH7wYnROd2I6MJeov\nzTD+azi3dz5Gr4wZfcdncErGBImqJCyG9k5y4GP7GXrX/TAxyaqGwtN2QoJAAb+Xbob+6w+Qj8rn\nc8JsYmjnThbVQBOyPdHuL+2m6zNd1Pwy1BZhVusY3SMsYobe6YfRhODd+9ooO0uY3jaFLwQV06ZZ\n6DJ2uu020vUq//TsEzw8INi8KM5x27ygjs015X/z997K+298MwDNjXKsqSlS2we4dFa7zdbG0FbN\n4fu7HdJ/SVMsFGnC5Nyp+9G6JaC/Y/8dVOwK+84u8ZYFQ3z3u3DGGWD0G+RKOdpMiLkQm0qjmx7j\nvx7HU4nSZRXwB4bIVUKAOJTt5qtf3svjJ5iMHZAKQjFLs5B0Yak7FB6smttWacMAtLsZtsSkXOi+\nrvukSRGKVWzKs24iSTq9mNTMLbzjHccDUSYVSVVjkewzTsj4JdV8nzc9vvzlDbgqmV98sTinn+Ch\n2ysFfq9Dyjt/Clyp/l3xV/f4X9pStpzsu186F99xOcaVk5LQNKqGDG6F65NqZEE9j6Hx9iC4Nkut\nnHbxtwDw6yYeshZodc/ztNnQYtYox3XK8QjnjcHI1RYFs85RBXDbh0gW5AzZCPSKLYImzyZ5VCeu\nuRBUMJXoXR4edFkG/CkHBJ20GHLRbTcrvOmATXu2TKZo0ez4xH0PoTvUanBd/dP0r3mB4bd9n54d\nsi9I3fWozygbbN9hspYPJu1FBQmoEi70VcbmGGSUU+v50590rrsOiqpB8clpjYzWST7agVPMs7ia\n5cRaEVfE0fwo9RhMjXUzqqVwVEBbNqoknnmB/EG5AIm6PJZUtEjdsvlC/0Eu3QjzDXDcUEYQWdBH\nPCl/t0bYJiLuQ8J3iWPjobMqvYnv98M9Y2cTT4VB/4kDMjp3LY3CSDcrfwFvHrO5+6Iv8MGBAj9e\nlaRWCzP4tXobwk/hRC2a23I4jk+80bMsO4+4B50mMDQUMn4XfY0NewzyLWW6llqUtTJOXbI2tXbJ\nXNRMDS6/nM5n5YKx0B/kYu5n4lUPYbsyMIrF8wy3aSzJz5B06oBPxJ+iZ4vM/jQCbj/iYdVicxi/\nxBVywWsSBgXXlYKeRJlcMoNVkTOiqfo2HqPWyeNHjKDmQxOyCfM0S+hQbQmaHaiNTnJecTHoDvWE\nkgutWSsbkavgULOzjIyE+R7NVvIifHQlb/E1jUqlhK3YgRa/xOSoz3/t7GPmlyB270YHIgohNsZg\nZ8Nl1hQc058lqodsQszzyDbBr86BVGmGuuvg+lAu17lRu5ufv2+uz5RAo1gMpZ5+mwPHPomT3MD6\nHXM7Y9s6ODWTXMmibZYMNB6T12vELAcuhEKDjnSR4eYWzvG28a4DGoMzsjZgnuWRbYkRUxO9r7T3\nZ0xDvgniSi9sx0LG1PRD2/2YcDGMMGFkZFRAHrHwYlWq1XYs18A2EqTaDSwqOFGLx29X5xGv8ZZB\nsFck+eQ+h9XZIhVlpe0XQ6nKe2eq0ixAd1imjVNvbSOuGL+s0IipFit134eoQZUULdVWaCqw73W3\nEmMeQJB1XVyswHlX8h/v/DDT0zIUjnvgL5rAnpDjMJWJB8kTVxNE8FCqZqKKYbn+1nl89o0lTv4i\nVGMpzEiMVtXktkuXQUmlHAazB6+FP/Q+QGmwi8qK72F7FlE3CksPwlnXMqIc2nwNqFT4M59kX/VB\nfPFs0NR5Ij1D1JT3IOqDGfOIGItBc6mWfZoIs7DtJkEd+GLLYJ42TaSaIfvcblaLQT4+OsrJM1Bq\nnwZNYHs2DwyEbnMzTXkorqK1cCrFkqzxc7QI3azg9uvH8JwIxXY55s8Ue9GBzLTg+MhWLhiCLck2\n2ezchpm8cjytGdjOFN39MjMd9TyiKhA4gSspFdVNakg9DXmtT6q8wLGP/4KBqyE+HSZCcv6ENDsC\ncq7L/bMag+P7GKKhBJFj+bIPfY76om/x9U3wiV0GO2z5bK1ggnRsARGvj7IqQbjrd7cA0N30NJN2\niZgrTcjMsVDqqfswWZJztGFZdJgWE23y3iwu7KdNNVGnELarMTyY8Eq0m1CMJnCSBtq0PE5ztfyu\nH6//MV69hkcC4lWe2t/D9J40laJMCreOynHV5MDMVPistG3YFtTLF5MJWnZ28+ndMC+R4JqNUAE+\n9jHwVH05UZPJVIYlVcF4K9QcOT8asRqLj7J5V30j72Qtb516nI+V9nPtY7Ci2MN48mziKtlnxpRM\nL5Xn1NIINz4CTJxF9jP/SP6JPHk6GSZCc+9RNA1q5GnBao4RG5f3atqR6p5GMueyd0tTCl+DJq9M\nYdt6otRoi8tntZ7u4MTeGVLaEpr1XRj9TpCM84Uf+Jc0kscdI/J7E+k9ACS9GsXaMAA9Kw+w7tlb\nqR+USOPWZ68iums/FysGtLPYytdrt6G5grhCPA/F7wkC1Ho+zZYJKX2PCnj/52/Dci2SLsQd+P1P\nNoGAJRUoKyMypwLXXZFmmGEq8QrH75skMdrHcUIG1yeU5JquGRE23vsMThReMwFixqZCFNvx8Ms1\nVnEDKQeeXgpHVfaxqgjEhjh5UqoHND/K+v0Wfs3DGrPwPNixXUjp0fXX813zLH7OSfCxj9FRyzGP\nPGXLYcqcorPaSdSJ4o6Ethi+byCEoG/sKAA+XHySj/Ar9vMok7hMn34n+DH2b+jAUQZxU93Sq+D1\nuRzWb+TEb41abD1hG8vHjiGp7ls8M8Pbs1tp636AgWM/TJDTtauHMX4APbftZOLtMk5usizcTIaF\nNUBoPL/9ecZ6xqglaqScBJk/9JIZL9N75wsAvDhxGQDnjUYQTgt7H36BG4f3YCXX0wJk2jX8G27k\nge4ZFjS1s+UWuHZdltN3Q/E+6dXwqpd2QT7P2h99mkemnsf13RD4CUHkOVmu9WolSmtrLAOK8csd\nmKa8s4KGRgqTfGQhr9/7GM09sGm7jAunTeixfTLFRr8UKfUsXQ5Xr5UExsp0BAT4Y9PU9DjNDlzz\n+T3ka6E6L+/U6WjK8Z73w6MJOVbFLCl2woOFuTCZlkKO06VMkU9Cp1VhVJMJqKpdDWTZXmVpAAAg\nAElEQVSoZasMKzbDeVewd/R4arV2Cq4DF7YwWJDrqEUHYjoEfnWnTpNSb43MtGOazTy+936EEOx/\n337q3S9vnvQ3gZ+maTpwnRDiwkP+vflv7fu/saWElH1t+9GnsfpHWK7+Fho4KvhKYFKMR3A18HyX\nsfTigPF7XXyU/LF3ANBk+tSVjOGN/YPYOnSYJlZEZ7IpyUfUhHbOo48y9BsQEYdEWf5Gg3b/uraG\niOditzVhW/OJKeq3eXhBcMx+MWT8XjV2QTCw250Kn3nR4+S9aUpFh5gQxIRgnlOhXHYwhE2zViI1\nP7TkFQhqaoGMey53b94dAL8zphTo9OBgaRrhq/SXFmG4BiSLONSxfDnBnD2uszu1DDsexa1USKr+\ngp4fZ2H6VOqRCP033ETn8Gjw+w+tt1mSruHXqrLmROmjm1ev4/nIH2lT9RfzDGQDWrV10h9cM1OE\nAXE1BknfJ5GcJpto5oTiAd5OE/PtNFpMno8RhbOnMixhkif7jmN6Zoxj16rvOvYskr6LM2pz7jnf\nDK+TiFC05/OXV7+AHjXxPI8Y8ng6rNXEPXmMYmo6YLG0eJnRVz9CZokaLOYUbkRew+oCGWSU6j4I\nQdKSAXJSHyCusq8NWUv89ZdhxAT7Fwla3IOco29kpRUuChHl4pjAJjftk3Shw4Crnq7glVW9ppCM\nnxuzIVGiksixfvMtiP8C15grn1o8UMJVbTfvuk/wLvdx8loHETySjmRvUmMTuE02RJyA8fMv+DE2\nOkklu9D8Mt3dYSsHo57A8yB70u+5r1OCVl+DRx65E6cqF5Z2UaJnUGexMswQZQkQG/faNiwiXsj4\nvWafwZ/+lGOeBUcp4BrzPO47Ga44D+LVKikfXAGFQp4bj/0x685YR5mwcN1HI5PxgzYmTosNn7wI\n8eZrKM4q1DC1COkWsKt10lmTVhXlCA0SamocrxRC4Cc0tJrJZJNkiR68xyfv/COFaDfzLIceTSOq\nIkVNNbt/zSRkm/WQ8dPDLJzpzQv+P45LvS4TRkYEtMkaSQyIWoh4lfe8N0/tzjW4RhPJ1jqWqNJZ\nr9CshuJyo8iKCtBhEvEFLWadkqIqvUKY8Fg55bA42Qrto6xu2s9IyyrJDnzi7WRGY3z4LnkjZuo1\nam6ZQiRFc3EJxOTrRnohEDJ+y8o1OEoW50eUjD3mgd05zsDnJWOWyNfpbJgAaz5R3ICpbNQfJ6IF\nTF1m528/+fOY0QXqNwSD0d0sLCxmx8wO+vMhg3Cq14c98HveObEJoSv30rfcAe/6d868QbIFvgZe\nqcTF3Mfg4q/B/H3UalL+19J9EByZDIv50Fxdgkj56DGTTNam3QjrRNosgmt9zkicnFhKttWkPz/K\nL/gqC2ybU2ag2iqjE8uzqbohmzATq0HhWBxh8/g6n5in4WoReiJHcTy9RHGptitr7oSB0TnMBRfA\njeP/xbN/gt2rToB8ntTMCJOTMtFo+RZePEMtH0pPe2ct6aMKAFWV5HbEkCBvkXkwWNcaZmQAwqkS\nQeAD2yZ3MjQlx8/Bg5/HGt4RyBuXRWXAtXQ6zbyplVz5JHx/YwVndQgi9+sr6XQMqnGZLa9MyHU4\n6cKU2Yr9E7hk4wze9EzQH3FhpYPJmlS75B2H+abLRKu8N20z/cRMOeiaCmEG/tax88jFSnSYUIik\ncGIWMfV9tQUyyIt5CQrpHBt5A5zwED1//wHeFvlnlmbkNYip29RRb8bOh+1i2kYzdCQ6+PJLUI5p\nlHvkeTeTZY2abh580MFXdQ2fn9yCE5+mnACLBKZqk1LQIXJmmLQQsSzzJpp4VQZG2j16l4fjRI+H\na+l7JiZoccC9935O19dx2/dv4+hTfsE/3/w0Z17Rz5r1E0zTQjHeSlyNgaon949j88ADD/DUa2Vd\n7MpKggiCyYhsZN6m+g8vzRZJVVPwu2c5y/86tb48qSslzecLH6EmrqgPmRczxPbt57gszFPGMwlR\nJ63YN/4Zfmb+iMyYvE7ZsR7OeHGY96lS2Yt2LefKJ0H3fGJFuf8LkU14hvqNmsWBzAEcNYTfyBfp\nnRki4coE8FjLAG/vlxJxX7Us6tvqcuIJ0K638LqNP+S3j4OvR1jly2NYU61iRiAmbKzuCstG4CfP\nwCd6H0Cg8XT/VtxfXM8x3EmzA4UE9LQsYE0ezqveiKt4XV3AN3t/yZu8CzH293HPfS7vuN2Fjg78\nVAsRPFh4kJd6t9LkGCxlCnfMwNVcknYSHA0mw3sb8zRM12QkswScJrIxCQZS/Aht+Q4mzv8peDH2\nT6+gVYVJ67ruC/afUu2jvLrH1hVb+PDzMX68ScZascl9XLrgUhKRZxnxBCMqnDIrgwHwq+8P14Sx\nBd0saJGvpwoV9FKJRTXZG7Y2VsfLLeC9qZM4Jt3CQtMlv32Kjpm/AHLdHmuDFtfnBLr45LLvcNdz\n/0nWhjbfZ6xdsHPRGv78xHLOW35yo7yWjiJ0fkOC6qNHxsmte5BPXOzh4zNSGqdlVhL2wc0fB+Ah\nWW4bSj0V42cJl3+1voR/vk9zpMj9y97GO/of56zPwe33yXEylpNrbd8zG4PvLSpzuyVV0AsdLC1F\nWMoj+D+7gqrqVzkhIhRKIdOctaCtSQYEVrN8fTavlnChYQ8AsEBVxHVQZLIVFtoemr6Yt/bDefFz\niG/ZAVOv4t674tA6KWNwzaVSbYWLPwbnVOgbluep4SKm0iSZJr4wwUB+AF3F5IVcO0L4fOML12NN\nWLgF96+6fP5N4Cdks5dL/tbn/n/ZmpTk7ib+Das7fNDQNBwVCEYSLrmkjhUFqx5jMr0syObOp8DP\nH5cTdqsnqERkxHL+uMlTK1rptGzMiM5Uolm6DgFJBbRiLjQZESq6dCLTfBia30/CdXFHBvA3fys4\nnGVNDueNwocOQC47gUuCZgdaKq3BTZnnlWivg+a42Ip+frU5xvTDD7Nr1xP0+EU+kdvKD7fNDfSL\nMyrgMzUGunuDIOusbJ7BxDwSLuSdDOPdUoaTSC1iuA58YxkzF34IPSEX32MrDgdWe2h2Eq9SJx5Y\nRi8n9/hbqEcjvHH7Ab73wjD/ugM+ug+ix+5nYdWnnCnToZeJqh50zTZk/IGAPZtfB19YXDfvAoY7\nFrCkZgZgwCIMiA/Oj5HwPOItY4zNq9ExVGPZ0HwiwgVXBmabFrdwSrHKFMsZLaRYlQkzLk2Lj6LZ\ndXmBN7Fqus7bUK6UQifrLMBb8xSltj5cfBKqLmqxfaIMBB3YucUOgvb2kbMRJ/wRR8lIqE5gxVQ9\nWadcaKZs6WJXFK8DoNPOBOf1f3h7zzC57vLu/3PanOmzs321Wu2uqmVZlixZ7kXuFdtgElcMmPYA\nIZSQ8EDiQMAhccAU0zGEQDCY2MYF927LXbJ6WZWt2r47O72c/rz4nZ2z4g/Br/7nuvbS7Oq0+ZW7\nfu/vnX4tzQ8fhU4ng6lI9C1Kc7jnl6yT9rHMGAqWql/TFXFNqkaKTLKFpVn49Nsm3YhIW4Qqw/k5\nzFiJXz3ocsXuGLN+tPhwZZt/J7HxG4ZzWL7jd/oonJsbwY7PMicnSFfF3DRNTWOmaiLjFy7W6wjM\npIJmiM0xM7UIzQvGtlqOceEVcEXmDdpnBYW+J3nYtkkm/4wYMylP34CM4cMVDFUhrwvnwLVctu64\nBPtrsHYKCiFYedSiO+/x1LYfMCiS2KiuRTEE0zEIG1Uaay5XfxzmZgL43DeVBf3LJIvx8UkkH5ZU\nixkcNwONVYvcXCDEJ7xFtJcg/MXPMTVXJuFnZCUPCj6RSSmfY2rKh91JoNQsCh7cyXVsTSvMVF5j\nPFckbdiMeemg1NazyYcUlhRgNizXM3n2MY5fuJ49UT2bStFBc+H1RSEats1RJcodzxuc1R8GPU91\nqgPHCKPHKziSwcbxwAA+bUoouFBeQ3M9klaZjG9sO7UgQ5KcNGhTTRYl32SVc4D+UCe6VIHlT5HY\n8QLrq7/hksPw0puvouGSDWlE51rq1zt5AcGdh9v05CRoEtH1Fr/eTnOhGp1C8pnrlNkCrcKnw5Jd\nIuTrGYQm3+FvUUcJGeLe3zj7LjqzBWQgSoVdUwrLsjW2l9/gztfurL+LK4Ha8hCKJ7I11VwV/Hct\n+06CB+T6x4lSJWHA7pP/EVl1cO78Dt/99u1giYy95kDSTeOqMgo2M1mLRC1QjylD7BOA3pyYs7Dr\nYFdLGD6EUPZgrfQaMQOK1kKa5E7mpBoYCVzZplB0UF2wUTisL6s7fhXf8TMTs0x1v8mhI1DzW/dM\npJqY7svwralrkbc8xFt3w9jEJE9ly2QKYt9LtsnwAtjRvsPCuD/SL97Fqmf4R6n6ho2qB/uh5Au6\nigZfe/x9eHPivqOjvyAz9CCGJuRAuyJkXUUZYdUBrX5Nc6pWN9oPtdo0ZRvrsjPsF9T+80vwIfMX\nAKyZqqJatfobf+oNjZxZxFRgyjBprTqMJcXcNFbH0QyLnz4CLWNBkKegHcCSLRpqUJbimJpVz7r3\ndXZQ0iR0zeFrd1jcxM8gdRSrYYIfSs8zURbfJ27MOzcmz5l/V7/3snKaZr2J7z4JUbtIwRRrK6HU\n5lUPtdp2cn4G9ocHnkdVJ8mGwXbDOJLPqCx307jABlNlhZ5yha4C7GuFI4sDOyUaPUJjBVbNwGUj\nBaZiApLeaf+BPeqXuVn6BVO5JSQnC3TsylMmwozSSDgj5rbmwzT1yDg///nP6/dtKQsHZlU2jytB\nODxEhQiTtJGJLOKwL0orh19i8XcEL0KhVIKIGJuw4/Glr/9f/rp/D4e+Dzf1RRiL6ITcKuPFMTb6\nzoVj23xvXNSyx2suq0eqddtKKwu9rrkeWsH3QUJ6nXU4aXrsmwkcvzN4jWdfmBQZP0disv0A5x4W\njIiP/Mbg9DB8NApfnJQwbqnRO93HcRnYdtKZLA+JtR9zbIo6KHKV4yfbWDIMm8Zh8/jr8N7r+X3r\nF5F+KFpdpGpiHY+HJHqz0GIN8bvjhUw6f3aST3g/Zrq5hdzsZv71R88xc8n7Kbud7LxzkjYycO1f\n84kzhJH+L3yFVTu30aa1UXNreI4LE4GzFTI1CkYBM5SH6TVMqkIOfRKIdvgM506Io26MdFkIz1w5\nqGUv2Cb/ekeNf/uxwa5FO/j2kYCISsnN4XjgWrNkN+9k2AdQjQ0Fjt/M4wHypS+9g70DYk9HDpVJ\nOQ5NVajWClgzG/hBLcW7eJDeCTH2+7c+yybldbJhYccVQzC4JlV38IcmRb9oN+dyJAXVZI2CPk6v\n1VPf69nB7URnAru174l94MEJU7BldC9xP+PnSNDgE8b05ESf7oQBtkQ949eX2st+6SBeu0c0dYSX\newPSqUi3QF4NTQtbt9gidJUtOZQ9oZ8KOliRJpRQnlV8C7tvDEMRb5qX80z7nAdhW8XywEsMATDX\nHOiYedbicOCvApD0M36NXp6SEqKiwfnGIZ7+NVz1/Am89p+wjj1seS5EbtenuKl/ClNx+cSRET4y\ndAhJddg/IxAdCgZMTZNLit8Hc4OEfeKo1tgQkKdakinuLPLBT3yQ4QXIiD8+3inU81lJkj4vSVKX\nJEmN8z/v8Nr/9ZAk6VJJkvr8VhFf+DPn3CVJ0mFJknZKkrT+f7ufXgwia8bho5i+wetJYM83PVQk\n5iJQU2FiYjmGrdeFk6Mf5gZRj4/dpPDthiDq+2pLB2nToqZITITidShd24jY0MvnIGYozKkxlmah\nervElsytLK6UMJ0KWSOo6Tmp6zC/eMgn7CmVKGoRIjZorYEiDlOloQKybWOXjq3o1Q69xB3STwlT\nE2l5//Akj117xcKQTIdKzahn/OJOlTc4XVDYe1mqPrFBMtYiMn5aFTsxgJsMDOpdvXnKrgrVKnpV\nOCROtZm22cuo+M0+b7gW/uMZuPcB2GCLbOnEQAYvbqP42aKYBdPeKLafFo9bIiNpEqLaOMviaqoO\nh7PtIBu6N9aC7rrocokZvYEzXxmm641RJCDip9TnlFhdWZzc8itiPsvSrVfBmAyr5sS8p4CnENXh\n4XCVaVM8J5IexZUrhP36FlW3iR65AICDB7N1x6194HxIHeYjtT9w7iBc9ODRoKhNO8q3+TTb7aNQ\nLpM0K5w3AD2lIqonYEyp/gQf3wY37AHTSlNOryJtDfACGsvKC5i4/Ka4Udei7DVTm/oUqRpYMlzM\nT8R4SiXM7dOU4zmWZ2Q+8ZaHqgnD+/TiieJ7WR6rZuBnb3Ri+Fu9qQoXD8DG4iRzukpjVcyN7Lmo\nI7Jg0lSyjH5DAw9yoTk0PxM2MLiCDjWI6hcKYSo2vG9sL2dOCkXrSmDbVaIRIZRTXoHd/Sqm7/jt\nWZTEUIQxZ1cMKpa4X28OxlSRSZuNQLchginfeQKqoSlKIXAUKOkR1k25pI9CfnwU2e8fdlQKlKon\nWRzc2U/NnU+d2xz4Adz96jjZBcpmgk40FyLbtzJdKJK0A6f2968LGNjs/TsZnSnUv5tmW1SR+AEX\n0WxIfOtu2LpNotG0mA231rMNsmczHhEOwbQOzdV55zHYx1Vbq9cHhFyXclYwob22KMQKv3n1P7wG\nn3xLgnAOs5JEUkwkP/t2+mQAdV437TEdh8K4h+pCqlbj8IAIgjlyMDa9tRLhisHY8E18qvwj9pqr\nCMtV5HIz95//3/z9a/DRt+HORx8Sjp+uEC/FUf3MmFsMMn55XaZ7Tqs7fp2VOWqKyOYalRRKsw8F\nHuoj7E/FlBTjKflymn2Hry0v5HOLMkYhJJ4hl1IsrlTIhiFOEU8f49l78qSq8GT/k/WCeQ+o+eyq\nCRMwAMWAWpKQG63PWfbAUP2dLa3EbeHP4z0pAkAdWZU1UyKjsTgRw5FCyNjM5k3iCxy/RUUBLwVY\n6kOfW2smrpOhiwGOv/IsdrbDS4fu4NtPQd53/JbkgPwSPMkDM44n2RzMVNFcsFA5GOpmBYdFxi8i\nDDxbs5mOGDiORKuTZzwOJwwMMXioQJc3RjKzl1QNDk1nuH8UXrcFvCHkucQo8V/Ry9nbAtXdoo7r\nwJ7t3H47qJZYa5nSfr632EcftAQECSVdjGs2LFExdT6Y+wmLOYplhfim189AYcKfKyGrbNeledc8\nnBE6J9KMeYsBOHhcH63lUL2EItEulNTyLHyhJmSYDHz5ps/XQ+afe2uWNjXFbefBxsJnaa14TERF\n0KTFmUKtWXxkO5zaF5QI/Mv+u0hXmmioQSHsYSkeWoPQoa+MnSZg7Pl2fnZPB9NSEyRH0UfXoG0y\nkX34e8qvZ9RdiwcX7Kkl5RiS4VOvS069D8T4IQ/LNwtW0U9xQVuCpFckGwHbieJpvh5VVNLVALpe\n0WV6S+Ka6Rj0twRZ7FhskOd+CX0/gB0dsMdvuxZxy/zt4TynFsaxFrAIGoToL3URyYn1lvBWi3mN\njbJ36158UAzthnhedx5eXSwzHdmKi8zf91xGvDaF3xEE0xiqZ+Hz+XtAdrEl2N2i8Mndf2Ced81J\nNfJcZxypMoPtuqwJi71yYinEQEXI9GjFYsMERP1g0dLRoIdczhEEUejnMjgu5FRTFbaObK2PrY7J\nwSfG0R3hLFabBuidSvLhd8GbHRpfaoOOTXBxn8eVfl/loSaF+6YGaS0HbYwKOiAX2Ticrj9nY+0g\n6urf0bN9mB1WmCJxGqvC8ZvUhXOY1xo4vEgEeaOOw51L38ebx/Wi7dQ5XNsP8Wn2zMSQ/vVzjNHG\nF7cW6QkQlIQLRwnrYbLVLG6tBgTzphoKhVoeI5Sl2U2JnsPAdsBL+G0tXI2RmEfKJyqpKAH0eqCy\nnX+qRfh6azPdCwjXCpEoejXD6Ax4BZs5p62e8Zs8erTu+OV39QfvEteYnjZxgWjJoFGSkDyIGiYj\n5WY28TSPzP0DGybEPjGGt7Ahk+et5rQYs+JKrBNC3PYSeF+B8YpY92YextMgzzl40VnG74zVs2MT\nRx8lZAVe0tE3R1g+By/9Al7Z/TpRP+M3nJRZKQVtPv7tOcFC3t8IMwd951Wr0Lx9NSttiLoGAysD\nW8qMDPCVp1VCR8T6LLaKtXltQy8xI1RfH8PnzaD4Nf7m4VnmSUG7hl7krR0+F4bs0qjI5JLC1tk/\nD6GVJGo+i/mfcqjmlCgKLhYqmajEKZJwjNt2C3mSNODg21lSjsGvH63QeuAt7r7P5acvTnJ5n8b0\nnFCeZ/I0GFUKMTG+hzNHiPlj2KCPcgYvshyZZ7c/y1DrEPv/Z8+feBv+7Hv+qeM6RDDiZeBt/2fb\n/3rFOzh8GOn3gUuANcANkiQd90fnXAYs8zxvBfAx4Mf/2z0dRWVd5FaOsphQZpL9CEHoAa5vdIVL\nJTJRl5oCYamMpBh1eOXlQxPc1xVie6uKG3J55aoA82/IKZpqNoYqMx5T6j1ZVjz7IgCdRUhYGnNa\nmPYSHI0mcPUibbUqlWV2PesCsI6n6r2LwlWLQ605oiZkVg3Vz9Eci3QVpoby1LIO5gIscfP0FjZx\nEFWyaCoHdMqeBNsOCPaokOlSKJbr0fUDrCKDyPjhzVLwGfmSmky9taEjU50NHNQtyweZ6dmDV7XQ\n/V44jhsmFVpGxYc5bu+A8ah4t8VDgnlPMitUmmR0J+hnNquMYMvBd0jXbExk+muwyIwR8rH+tiMk\nlSPBHmW5H/GDmrumfq2rgeaTfhS9JL2fhrEEnOe+Sibs11MpMFTaV79mEcGRiJSZqgpF5IYzSPFp\ndFPMz7WF7yGXhJJ4dnikruwuGz3AycNhftr3DF94OcSEtZ0jtrA8Lxiu8im+zxPn3c6OAYf37dvL\n87+C0aTYYnc8A7rPuPSeA2BlV5E1Yqycq3HIUdk0G2xSzafiP3XSwK2k0ewQKQOeXipRlcSYRzq2\n0LL/EJVYnlRN4sLJIktloQBWTHaJdxqE3zwAofBsHeq58MhGXD7zhjCIh7UwygEJZItmd4K2moii\nz956EjVJaLPxXIy22DTXn3M8bPw6UqZGxIEzjsJKH4fu4ZHZO4HkG80NXoEnt7vY/t57u1zDk+CM\nmcM8euC/kfysZGMVJlVhIDyxLAi23LpdwpHyFHXAVpiRm1jtC0JnYqhexzflLWhyK5n87Ocvsc1v\nnEzSDz7YLsUFUM8xFtc/5/O5eo0EwOlLxdpITkkMZ3xcveShWTYlXJKsYVHNwdFhakai0TQZlzrR\nPVAQ5C6ZkNAMUz724/7lYcILiGpqtlx3/FTPYWq0jObAa4tkTqoFEVzJ1iCcQ8p0EsHG9smBzhk/\nFsP/5koJq2CjudBgGIwP+KQochApbnBsCtvD9d/fcjrRHJfoQ7+j5DOF5eIyh996DV1ymY0oNFdd\nLtj3Zd7VBz2zYv0lTDjUEqInB9fuE+0dllTmKIdEMGs618zbITE3nmKR8ofdkx2WExgdLVkxRi3S\nJJMxj0uflejKSAw2iOBcQp7jBHOQmCOybkO5IQ5M+2NTSxP2v1rSgChxPjw8yUUvnEFFFsLVlWB0\nn1D2cVMw4n2ycjeT+wTL2r0v7Gbvj0CrpMB2Ma0ksmdzNJclYUhccAv8cF2E9yxoMbbYR18kLQfN\nMohTJq/vYJ+fGG2oQdasgAfD34HwfMbUjOPJNrPTc7TVTGxJZby1Spc0TNSxqchhvn6BxhljDqsq\n/SjYNFtl7jg5yUV9e/nOeVO0M8ny8gQhFz65Fb5egMXVJFUVQq6DSplCax8zMXD6RQQzd2SGb3/L\n8/tbwMOZIzxxnfhCmhroN9ln5u0qenzoxVnO3rmP83kee7aFJS++jum3o2kMiUjy8OEOPpf/qpgK\nFVqrCqOeaG9z4O3zaa6ViJSS5EIaoUoQ0MzIwpnyPInt9pn1ek9PgkVSksd7RaCssQqZiI7mQLs7\ng+Lrq4YFydSN1gxO2SZlQDFmYskBjHwsK2R4xk1x5nX/QMwrc23+LZq330gh4aL7cqHB11E375ZZ\nNyok0qevDLN0fIKWgjD8dc+mGBHv/aX/idZrVh9SP49dDJznhqlOsmGw7ASy7geZegZILSCOshyF\n3pLQpUalg/54EJmP2TbrfX9xyxLhGAJs9vaxNuPRZFcCJl2g1vMa/elZpGlxv9NCYkOcXT7IadPD\nxHynoWlBf+JHjBuR5SNEqPDgOXtoKs1w+AkR6KxoB0TLKAPGJ6BNGsOW4ZT3hShZXr2nbN/mBqph\nk1DZxrAlJrefzw27IWyVsP0sxKJ9M6RrcPI4nDQO7bmgVqoSbRD9cXWDo2NDgOiXO1EarwdxAYzd\nGaH/XfCaDpIoR5lIwDOdSdKOyLI/tgK+75d2vO+9N/Dq6AQn1DKUVHGjgg4huUZvUjynpsCg0s5J\nE3DLTo+7pZOp6QaNVTBCEhMRl1PGIKMnGGgIPLl9DTmety4ksi2C3iUY0Q9PP0sq/ya/0j9EZ61E\n7wLHb6a2l4GjR8GBgltF7Q70jWpq/J+/meOvjszwiwe2kSLP71oisFgi6+7jpHF45IkBxsotNFTF\nvrXUYA897T1C1IRDd8HmQ7BLE/tuTm9Azx/m/deJzNjdL17FkO/4leYmuHmPzYmTkF+w7wtHLmSF\nM8LuNohaNdIejKSgyYwy5DRQQMivzbNjOBKcWysxEdXJxDSaqmCgMDRySx1Zdk2fxzlDEPIk5lLg\negeh6TAHpCZMU+yh48ML6oeB8Ew/rWVorMHrb7xJxHf8jjS5rFJ21c/7xFbR6/RAM9ijIlMuRea4\n6mCNL+2DmGsSml1WP3+JeZQvv2bzyK/2s2wOyq37aWWKguQS9yL19fHrpikkD2xi1PTuesnGPx76\nOfc/L3pU1iyXZDXKXHSSL70MmXGhuz2gkguCxmPxY9uvDPtRThOZcijCibURsqrM0jlB9tNcgdx4\nT/38n4z9mOv2QZkon3sDSkawd2ebmhltEPpv98R+uqplAWWuZXiV93LX6DBP7riLs4Zh+NnAAf7j\n4x05fp7n9f6Jn6Xv5Nq/cJwCHPY8b9jzPAu4F7j6j865GviV/x5vAilJktr+3C/l3ckAACAASURB\nVA0tOcrRWogERWLZLLvwadEBFIN/fwZ6xgaZjbkYikRYKtPYMkBDTQDjUgb8Iwk+e7nNWRMmr/to\niS9cCJVynFUZwZw5lQgMuOMdlaoq4EZxS6WgacRNyLpphv06gz21nmMcv08+HizmpAEzUZF5efnw\nOfW/q1WDlAGFqSrVWYdsKLhecfpJxiZRsWgsBA0hZTz2DYlshWK7FGulesZvK6diuFFBMS8VKfjZ\nkkSlgCnI+ThlvMZkvonJiIqEx5wco6rCW4U3ifiOi+3pzBgNdRhsXgfPj56eOD2CoUDYruJFHWJ+\nqjtmQiE8QlEJ0pOtVQdHVjmYk1i0d6weUT3qR+++fX6Yh0Or0R1Rl1hU2+vXlnqDOS95SfJhMY7n\n1XbwdK+4j6HC8Uvvrp/XGQqWu2vqXJ3Zz/ceg6o6ixqfIWzK3Eg366ff5q+4H4DBSlE4ysC3Bh/m\n1t3CWJi1uphMDWH6tTLv3h9BwUWXDL5WbakXyG/pFv9+/nWIu5Psa4EGQ0DYdg/aJA2PRZTpLgWC\nMGkJAb95GC5xXmWN9ywP/g5m5RTfS18GQLjnSWaHXyajzpEyPZ5IH8en/DJBOxMwy544BYnwOCZi\nrhb2NZW0Ch/eIYz4PUaFJWVAMWmJ+fUfRUCyMX3CCCk+wQlSP799+QCnrPkqq/0G1ylDPAfg5r0u\nijHJ4H4xBymvSL4SJ+STuLyYrdJWhm89DduGXuchv+9vWwkmVYFJeX5psJ7HQ0kSBpRCILsSI9Yi\nVvi9tuzJMWRXImRD1QmEoySZ5PNqAL5PBgyFhZkFzHALQgHG7CRlP4PtAYmYL9Qlm9GcT6EsQdiy\nyXsGCeKUVI1mHUJ4aJ5LVkqxsQgHEI7frD7v+IkX2dNhk7AC57LmyMdk/Pr7s2gubO0Q0cH5Y1XW\ngv+zgcHkgHD8KNOZhwbTPcZIenuJxkeOijYVyarBc/eLOowZv2fpZTfBYCSNOhiQlhw6/248CUJT\nq9nk0xRmXBd36DAR2eW5jiQX5Q+h6gqP3As7X72XlbPwg8dhRpNYna1x/31w044w3dU5av5rHyy3\n8Ss/uuzJGspT4j8aTZOIGyjJ9YPi3RYzymiswpOTP6O3PMu+FpeSBhtP+hobffr/uAlhVB59/WEA\nZEujxUe7JgxotBq4+7UMf3dkPwllvicmjB/qr19/7hA0WhXwHfCkPx/a0VN47mWPsZkSkmNxKD9M\nwhQwprysi73gHwtb9YQdGw0bU62y3/fvLBkOjQ3UoaF6zl/PZgJXNvnYoZf50oED2IBx6t2MxWVW\nZW3cWph7zxBr9eaZt2kL9zEbCnNPx2pOmZiir3EY1YN1JWF937gHTno5RNi0KegghwrQeoBi1wAz\nUWiqimCIKi2jkP17an57h1G7ve4cyUaZfEJ45W0lmEBYid9/uoBmOPQwRM8vojzywhhtcZHBTiPO\nlyWbVdGPAKLOOlZoIYMI3kxYW0haVSKOw3hIIzYSZGCWO/5+shTeun9TvcbPlSQ6nCiDMQEhy+oK\nihJDdaHTPbaJ/cKje9IkbkIpbGEqsHpGOC5zs+J9U91PElMfo0CK+1/dykkzEt98DD5XG6ZAgka/\nqfd5wy5P/FbmoePgrpNrlNUoPUfEmCmuieLDKK+Ztplnqu91p7g5E8ie9EyTn/GLoJl+gEX2aFiQ\n3bBslSV+1tgsdzERD1BKsXxQ3161U/jdoWj3MvxhJTSZNTSC5xmRCpn2cdSK2NNXmy9z7xo4s3qQ\nq4CThgU7sWr78DjgiZmbWTepUVUlyrESTy91ufyIyLot8uueSv8Gk1OLWKq9yWAaXLnKUFzohF16\nN9ULB6mEDdYqu5mr6Dz95Jf5ze9h7c5F9f1x1pjNTEyhhQzbfwpXWPuZU32EhtUrHL/lL7Fl6A0q\nqgge9BSSmAt0lDZMXf+GIlOkqjIFHUq60KOyB7tatXrQ5ZWf/Df7/IBef0qMf0GHRsOiXX8MEHJ8\nS/R4fvQYrMh63BddgRGy6o7fZNzmpEk40lCjOA/hAPLqc/x49bPES1k63L1QTtFnjPAGEaZWVEl5\nJXqz8Htphb82ajiTYXBOxlFcpJ5A36imyvN7RvnwDokrc3nOyo0zurxKWPNwYwNcOADvGi7yd963\n+NJWYRvYcgBx7nRc2kuwYg7OH4vxqCIavB8qJ8kWhUM0G4VdS1/jF+thPKIzNz3Hfz/s8P3HwXAX\nEFd5c6x3+tnVDk1GDkmWGElCq11jUAoT8hXphtEQW5tSLK0ZTIZDOJoIzuRMi8dfOcB9DWcxGpf5\nyBtwzwOwyvF4e+r4uuz8z+eP4vo2Z0PHXhYey5XddeRa6vA4UZ9kbEjpock+lqEWoL9RoiU3vzdh\naSVKmwlRx6bBRw4BnHck0KPXvS3x0ZnnmKKdgfw53P64WKiG2YRdE7q6KslMJHsJOwuEvDofKJVo\nPAAVK8PHt8KGfcG9q/lgT+5rCFjpAYYbfK4BSSEfjrNu1uTphjWst0XwraMEV7pPHHPN0vecRjOz\nnDZh4xWDNTiYTFNVxffeO7Wf7kqFH58MV02K4NOGcp5/f+YNnvxviRhD/59xmz/ekeMnSdItf+rn\nnVz7F45OYKFbOur/7X87Z+xPnFM/KkaYfMcMCSlPopBjNwL25gIoNT6+Fc6uDTEbhZoso0s1kulB\nUgZMJODxZTBebubVLjj7egk/2MJ/nAUzUwkiNhyJ6xSVIGq+yMpyoBkiNjQiHL+EARUnjRESk3Qo\nuxhFDwye34QDpKwlQzYiDPWhsSDh2ehTPKsSRCWJghY4fgmjkZRto2LV62QAFM/jaEYoWdkBRZEX\nOH6biLkG//dViLtF0jmfKGSvxYu/VlgzDS8+NMSE01ivyXIHPaoatKYPE/X8gmIU5owkE34ENPfA\nY/UeSeuzFn2pMGHHxNy/g4Tk9/GzwAnnMdRgDNoqHrascPmli1ntRef9PuY5Fe6Z/gSj400i4mdD\nQQ2U4qsLZEFrtUSZCFELNtaO8GqPn7JXYDguspdVFVaEA7ZQxcjxyZE9/M1WIJblG7Nf5/zxCsPI\n3IkgMHEkSOhO3UgCuPFQkbtOgSUZnWLSwZIFicSVgyUMRRigzy7JE/XhMiPBI1mVH+Gg36VAx2Bf\nLkncgmtxeLInXj8vpO+i4q+703mDd/WLxtiWleS7S9bw9xeJDOr+3E5+mX+UBsPh9/GzOcdPejnF\nIOKkerCePfWM31v+zrl0zQdIugsWjryM64428TdzT9JhCWt6/w/htmcSRH8nosHKkpc4zifX+P6z\nBpdrj9cv920slhTgosJeyrNi/aT94uaUbVAMgXtGsG9eeO15XngseM9Jf36nkyq/j50FwAxtwggM\nQ1hSOGp1sWJMfL/C4ACfeNPEuB0gQIk7nonrJeuOnxzz+3h5UM0HIdkHuLb+WckXKC/YX5FmMR+2\nW2XEZxp0JY+wY5H1Siwixkw4yWIJ0q5LVtOIS36bDoTjV5H9vmGqGJyjaZuovaDGz9W4SbubL0Y/\ni+a5DIwURbPqkM1uZRUAEzGZVYUa7UU4YI0he1VmXx5n7bTItM/LJ/U2mA0FY5uuWuTnfFZPpYQt\nwTNL4XCinVNdvQ65nkkmkYAua4zTHxHvGTMguaSRkOzyfLdMjzlLomozHYWUY3DVLrGnnAXZy8v7\nTVzZrdfwPnvvAJHOFymEYONogS8dEJtoSeXYLGW3rfL1E7pZ5g2xJjvHi4N38/NnMxxIS5Q0GJu8\nl03D4qYJAxpmXJ6+X9DvR21YVhaBp4QJV84IhR9zHKRysz9nMDksMiotFbh5t2Bync8yzf+bcKsk\nVp4Pio4l59lV2kvS9CjqUApFhJH6J464YxPCoqnT5UCjMB5kV+aVFx6tE+A0+C0j5FqMBsMgUauS\nsG0UtYyx5FUmYwodJY+418JkNcaZt8LNU3sYq60l6tXIVFexpV3ls6+L6O6Jhvg+igflLSazc44Y\ng3ya4uKXqKkwE4M2W2RYesK7QP0cFZ9x+r2awYM+UYI1azG7Qhhh7SWYighHoaqAbllcywOse2kv\nuw+4NLb4xFxWiYoKUblIlx8UqmrQbJeJ+r+v6Oom4jrEnBqPNjVw3ttB1jmrCBiujEfeaa7X/XhA\nypKpRFTayjAdVtHVJLoDbc6CWkRJ5ez3BzLuYruRqAWlRAFLgaU54bh0+4QnxxmTXLojgHgvK5e4\n6GiEDtNmjkYiCzL9nS2PcO314vNhdxGr+sUGW5adJOo7bynHZLFvg399YyMNC/TDiXM2cwevxfIi\nqMWgZKF5wbJfZBZEA2rA9hRKPmSsj1U05AOFYRmxeiAF4CenwWmzBT4u/6T+t5oqIVfW0ez3sdza\nrvJcs3AwGoGrBmrslgXqaSAZYrABvNX/Q8oxcRQX2g7yTHMDV0+LYN/q6WBcS9VW2k79W/rTgASF\neIXOIvw6cR4jz7+bqm5xq/NfXL7XQs2KZy7qW1u3N1Zm4a3mBRVBssKeTvH9cnqcNX6s86WJZ6ip\nEoNyOxtGo8c4fk3lfL1u6vWfw5nlfoohKMgO6arYv5LUxMPzZpPkUPjKEACG5DEdVino8J6DMD0r\nWmh5wLZ0hI0T8NErJQopHUMVzNK5hEvOh3ceaZnA9hEln9sE/dNHqbUe4j/OcLmtL8PQXQaXTI9R\nVaNsj24jZZssm4P/6k1z5Q2QkCykqXPBaQOlk4aWBRk/Q4PGw6QrCrsTJ7GoajCaFM6sms7UEWj/\nxhcBYb/qaqA71DmpTkh44ViRB2ofBOCo08RSTSyo6bAKx99HJgYHk1Hu/41wSNpKUDKD+vBTGu9l\n03ieB1ZDp13ACGtMRzRa8hGOhG3CPuldzDXZlm6gx3AEg64qAjRlr8xjPMqn9dPpunktl64/m69s\nFvee1Y6n3fcxw6kLgqUQmDsALMs79fOWWWUSlviug1rQ63Z3EA9mLuJR8dW17kCPOUd7BaKuTaOc\nZvP7xf+dc3iBnDgc5mPb4Icnw8dOeA8zcTFOmuNx/rZLxNrw4JnaHPoCmYASo60ID98v88oDJa7c\nWqG5Auf7CG0PicxkEJjabS1o1QYM+89xZIWslmDlHLycWEbYZ2/vLMBt4U+zo0Vs9qtPgkF3JTUi\n7E1HWZsLIA4TZZkJT8iy4ck+essVfr8a9r0nWBtXbl7EoXQMSf7zrdbfKdRz04Kfs4GvAFe9w2v/\nfz3+3c3jJV/kn4FD5Tl2+z6ig0enmSdpwmp7mlxYw1Alwuf8E+WWR2muwDfOgPdvhHe/91IcBXZF\nOzDnoYmuTMwTQuvLp7ZS3fGhY57b1yyM8YQDZVUjYUINHd2XYrnZDnQ/svplvsKX7UAglsOQ08Vz\nitXg7201YZhrQAyJghbUCXS4VVKmg4ZFkxUY8LLr0NMgwl+KC/FQHMWDo+EQT3MxG1yh5NdOS5Qt\nEQm/+akY5446LM1CyPU4ffckhk8q0LN1Bdf0CVx1QioxHlVxUHA9mUxIGIqKU2WerumEWRhoTBKN\nT+J9/npOMQ4wmgiIEaxooAE7iuDKKl6kg3WOguKHUds6BczO2PMhWsMKiiucandBFuSZ5eLfB4+D\nN+In4tWaUDxodKp1Z8t89Yv8YO/ZADyyCi5b0AfMtXYiz2PuVYvNpoBa1nDI+f2qZkIRGvQCuqFz\nL8fxUa4gZbq80AsrqxnCWpFNPsxnNBpmJAXJYoTiqheJ+BmuwgKE5QlTY3XYhcY0m5eeSMKCq3mY\nh5YHAmpJzq0bpJ8g6HPUUFaopqcYSwgjbbc9iap4hB2PIbeHRb7gdMsLNCewyTiAHREOz8sCEcJz\n1WtILYBMKdoSrp0Y5nujv2FDX/Afl4/muPwUobD0SowHrvkZ29thzTR81P553TAZigeS3LUMYr5k\nSfqRxaRtcdlNcNp7gzmwMlNEpSfrv08qwkBe3VPiY81f4vazYUpuYsW0wpFGaNRVJljCSp9s5dUD\nz9QJliTp0vp9bMfElFLgCUeowwuyDSyIHm4hyK6HKga1kD9uEqz/0MX8dL2G6dmM54Sh7UoQsU0U\nL0JcdphS21kdh0bXJR/SaF7QQ07CYd7Hi/iF+9kIdWUFYDghnrQu5QHlCjTXY2SmTMgBL2yzPSoA\nFWVVZiISYeJO6J0cp+yMs7+yk8UFGE1S36eOAkU7uHmzYZNoF2sqEh1C9cCRYUhLscbRmQuJiTux\nfCUFTWFndRP/8pLCHHFSBixOeCSdAlPpEk/pZ3DS5CGO+vsq+db7+cYZcOPxYv9kSHPGmMtIyqPJ\n3976rE20EmNLNyxObuZ039HsKgXO4gNcwj1XX8yeRBPL3e1c01/lXOcNYhYcSYksbyIOp8zYFOQQ\nCROm3+xgoFHIsJjr0JuFne0i23/r/lm+eZpCm1GhNnZCfc5a7RrjcfjGM/CBXfDU8oCefv7fs3kF\nu7sHyY0TUg12pvaSsFyKIShpoWMM9/l6VYC46xDCJN4Ku5rjHElLtBY0ipWZOvtcohrnkkMS9+x7\nhMxdRSKmSdRxcCUF2Q5T1gVUMaolaIh08FoXrLvidA43iqwuuV6+esoSbtkNe1oUUgsCNmtcmSYE\nLLZhrgFJnxCOXxQWyxXmwrDSmOKytnuIh8X6+MzkDi720QFLJ6u8HRHMj+0lyLQKp76kgV6zmUbI\n4s+dAgUf4tlcdZkJhfjM1As8WBVQz9UzsL42yK+5md9yPeecdAolJOKuw38sX0TUCAyTvohwEmTP\nQ5Ufqzt+tgSZYh5QaS3DrK7SkEzQUoacElh9g9JxvNLWyA+1WziQSnLmnERNBVt2jsmA31QQUKo7\nn4a/3hvItFNq+1jk69astCAyB5i5k8UHV+GAdRxnzua4r6eJddkZus1g3Ff50OXnVpW5c3Ug+z7T\nf4j/dC7GRiVUDkomWhasn+5angk/KaCFakypDSz7q3XsxaQ7r9fPqxaVemDn3qWdHGITAN91v8q0\n3/LI8kIQD9NUEwv5q5tDGNPiOzRLCSKuwbQnkDJ94TD7W+Ddt/jBOF8UjuWuqLfTSVvBPEl5h2Wl\nIv2NQEQEWHQHSnKY+x8wqEnCHjlxyiZdErL2w7ln6VyQHX/K2lz/fG/TZtSoeM+erhl+9Bh05WCu\nepCqCr+3PsB7dtaC9knAcbFt6I54dqrqB/x0mDAM0jXh+BVjSe7avoMTPhKCJa/Ur1VdGNAcfOoA\n7usRgT5Pgt+ucdl0HTy0PIa3qEZNFdmr9QeW4+wTDkoxBs5BAUD79hUw9dc2jC/lR8uWcemAR7dR\n49SZMpW1e5hOz5Aa76EnqzLepFEOQTRUxCtcjqJOwbtn6Gzsqr+bYoYgPUBzBQ6G3k0hBMMpSBgK\nHxwt8k9bBBHoNyI3ADAZh85YIN8zh1fU58+UJZweIRMnmpPEfeb0KZrQZHGSJcOalUErHlMO4MlX\n7TF4dr3CWBI6nTxGREfyZO57uIwTn6o7fi4SOxqSdNUccqpG2ZJpqsLa0/Kcu/F6cmOjcPBdsPs2\nJvylv+YMUYe3JAebK3N1ZNiyHBTCgT07q8qcPC4c3N5qgYQt1kmfG9hF+8PB54omglsgMsK93ijt\n+RAx2yFtdfJyt7jX5okg0XBKxuA7p8Enr4AXpUPc1jvLFy8A1fYYGlCoyRJRKjxTe4PwAjj1IifM\n5J1w8YDDdesv4sJ9Eoorce64zwIO/OHegHH1YOYKFh4VTcy7I6uUtCSKByNqC0cQmeHPvwa5pgwP\nrxbP3LIGKBRgTT9vN6a5xA42VH7S4qAh9q9rVFheKXKkEbZcAx9c/UE2nbCSHY/fwB1liV/MPcmf\nO94p1PNTC34+AmwA4n/pundwjAFLFvy+2P/bH5/T9RfOqR8fTjl412f4Vw82A2Xdb0HgeBzn0w6v\nMLLC8VMk9MgE108+z017RHYmt0fi/e8/F4BK/vh6oTE/2U6jJCY62ygRcoNXmlCayIUFdXvU8Khq\nIXQHDI4Qc4TRV5nrwNJFzZGBTvuCpKUVkck5wlmb77cG0Olj5RvjClEkKr7jZ8gS3U6JkOsRd2vo\nXmBMKZ7HqkahWBXHI6oKqMy3Tu5liF5+yP8B4LT+OKY6yfHTcO3EMIWQxOICWJLEVTv3YfjZiptH\n3ssjIvlASirRH4/U39HwMfRhLdhcAKOhpUQcD6J5Lqzs5aGViiDPsXWcmNCAeR0WF8CUdaSG5bSU\nqoT8LFk0Jna0FHqKK859EEMRht24EkTM9vgf//4ieC12AZgiUp0NqXVnxPAiWF8XfWb6mmEyIt77\n2V5YSxv4UR1dKrPGFBFpW3Yg7ZNySM00Nb1ByJZ5iV6eZAP70jrPLoUjrODodx3OzonrXlH+moIO\niZluwpJExGcIzS7og7w+C0PzUSYMhmOLCTnQyRgHFmDJusYj3LGqkaoKzWQo6kLgN1kuXsMEby6G\nU8dgyjNIyg4FTaaoBtvRqwYO8uGkxqbsBIXGGd7shAn/NHt6A9sWwY5Wha7PQvI44XRtjS1h04zF\niCai1b1Fg2XDQtAsPnIqCXMJ0zFRe/JC/GymouLd8lrA/Ki7Nqf5LUqSXom0fBqNpkkuDH+Qg6xU\n0jCJEqRSphShmFYttglZGq93Qdw1WDYHh5sgpSjktRhJU2Rjj2tN01YRa1DaGNCwe7JJpdoMntgH\n6nMC8ugBsvSnRV7C9bD0ecXqoatRRmMqI9bllDwRmvYkj6hn4DYkUVNZJr1uGosQw6OkqqhSoMis\nWg3DT2FH/b8XQ4haRf8wZB0bD8toRvMcpv3eh1LY48drg+h0X9I3Tu0QFabIaON0FkRN6zz7WOSO\nEdRsEKVsqTkkG2XKGiySa8L4keBotJFuQ+VQs8cXNvawsrtKg+ngInEBz/NFbqOhBt/sm+JnjR8g\n35jnKflsLhl+qQ4TXuGMMBWDjV099LGKX3It6RqMRGLE/fV+k9ZKvCpYzC6OX0UpLb5DzA4U6geU\n3zKRP4sBvYVlXoaTx4J1O9ggk0vJvGcjrMrZvBldyYYJ2CC/C33aoRCCNitHWRPjcNYILC/O8c0z\nHVrNCsZowAG2RKpywF+e31ZvZH8L9XqUFqPKq5wBQCWhohRauXUndBtlEpZDQYdCSEIG7lkLJ599\nPWYomOe4LYJvNRlKWoJrrvdoL0nIi3XS8xk/yePJ33hcnxFGUNQnE5EklY6JsymHxe/lcpqwEgEJ\nBtZu5ewPwqaPANml9C8Tntp4XGZKTdaf7yFzUs5iqAFazAq6IyBz0zFYbJfJRuDB1Emc1X4n8Yjw\nVlzZIetvw+aQxN++KYzlpAmLu1rqa1UzbGL+/nzfXgndhz+FXJiR45xcGuOnKy/g8eXQWgEVlyf0\nS7iR37Ly5OPI+Sn3TEThZ5tCvNIF6z8G5V6RiZTxsN3vBlBPYPdcBU9xaS1DVlcJNbfhyDCmpTjt\nQ/C1cyAXbgEzxif/8Vd8+aICq0fLlEJg2QT6GnhXcXf981tNgdF4TeUpplp8JyJ0LCyrKw2Ju/8L\nJJcBaQ2nT5fYkwzzQnMjH54LavHmpUi5spKfXBqs26c2djKwdik2KnpBDLLiHpvxC7keI/F50pgo\nfO8OBv7wIq8wwcWjgTyslgt1Xfap82L0b/07/53hqC+fLUIUQ50oHtx3PJTaVmNaQpY3ShF0W6Lg\nt0eavKqZI1ekWb1SCKHZiJB3HSuDemKAH4eEs7Gk3M4l/Q4v+cHCSlZ8KKkqlUIbFU/cZ82UQqNX\noK8JfhmpcudTYv0AbDEerN/3ubXXk0iL4Ngi3zE4bwhcO09V8/hP+0YuHajUEUymDC3WQXQbjv8k\nfHO5QG/dYZ9ASBLjGrVArYQJO13sczrgxF/Xn6e6sKfnTP7pfGi95lz2dgo95gHW8q1sy4BmJGDx\nW5iqJDKImRbcEdGrtqrBAel4/smPxR/3cDORpy+jUFvK7zYKRWrJUA3bzPVkOac0xOo5m3LjEsoa\nxCizonwQmg5CxCRuBnOrmjF+3Pc4S8oGiaYVrP0EbO2EjqLDV18SguP2E5Yze6qY56eXwYULCP4i\n5VPqgduaIvFXHd8DYHRTABmcVlOsddaBK2MqEm0xsQ5sGWILYKMrSy7fPcnCKoQIeQ75eIhvbBTy\n+la+xwkIp3KEJUz5OjKnKhQcieYKxMZX8/Ev/B18/jg6ll/PmqKJ39KV6y44hck4fGwbPGHeQAOC\nPGlFBg6lgj1phOCiAdjfqLGsVCBmzbf56amfM6y28x0+LeZGhVkfSROxodsdp7lmE7OgPboSTxZ7\nVHZhpqONV7ug+b3reLKcgHIrllri7HVhTAWinsxAcYJMWGUw7RKrbifsuLzrqiXMRHQuyfslCxIM\nN4XYOO0xGdbZ6RececCBvUE7rs3pndxx5rvrv5fjYg5TxS6qmpDdk1qUPdKJlIgScuGnDYuoIHyF\n6mIg/xB8fgu7UwnOquS4ewNcfy10aHn0uFify/d1EXYdJhIC3fbCqga2Nd/Aezbv56JkB+uaj00A\nLDzeacbvj48y0PsXz/rLx1ZguSRJ3ZIkhYDrgUf+6JxHgFsAJEk6Dch5nvdnAf8Xt9xFS1U4VZNq\nmGjSbyzteKyuBZH/vK5TU2TC1NhgCaM7HxYMUccvEx67PHl2HRLF1DrSfrYgYjag+jTgOV1iJpyi\nKun8zVY4szBELSSEerxF4pmlK7j9bPCy7UxnRF2fgU7j6Wn+RpRrYakaue2iY4a7YEpaK36zVEkm\nhktJ0/lB+HpyusxinzWu2ToWOqV6LksTIsIX8lxichzVhY7CSpJU+ZX3IU5b9F0+t61KJFRm/SQ8\n39BC3nf8Hl3SwMpKqZ5JOItT+fgVkIlAyqvQH4tj+5m3qajYeCFFPeYdpsPdRC04YRqqisq+RtGq\nQit2Ivl1P7NRwexZUyPEl59OLFvFlhXWsptys8BDfuFDd/ORcxQijsgnjlcl/pGvAbB4hYKhiDq+\nqBFF9RX4WNJD8Y1h04twliSMOkOBB08SQufa6yBBiTa/8e6J5cl6Me9pdAJMBgAAIABJREFUobXE\nW4XQe8s4n1Nnc+iWjIlOb6yRE27qpqTDP/PVOhwBgHePU9Hgtu2TPH6PREvNJxLSA0s/ZlFX+ImQ\nzVipm1IImpmhGgmc9y5yvNqi89lL4C028c2Pf5oXeuD11GpoPsxAGmIVne5miRQ2eU3F0IOIeKgU\nRAZfaG/g5BlhaH3m7OZ6JlE3O7jx0mY23dDBaAqSt9/ClRveRUaN0Gh4vL/jqyS+CB+7sJubDj4K\nQHfHY4StEuUQ/PN58F/tt6D7hSNhZXn9mdcoM3xqSsRm0l6FK5NL6ajAci/ERV0r6uc11bw6NCwX\ngiriOyhhCJuibnapIZqplnRozUtorcIwHUhDoyvgPgDrlwaZUVWzKJdbwRPrcvglwUN1yWSFWzk2\nSDF/pDwPMxSs44SzDEtW0CQDz8+WepJHzDGJRRppi2Q4aqyivQgaLrYko6rBXBcKRSRF4dcnqLy0\nXCjcgh4YRABH1EW4eBhmC2FLYto9hKkIdEJmVZA9PJQSWvTm8n7+QXsANDPI+PnBF8NI8kjNZsZH\nxjTXHBZ364wlJJrNUj2KXk4sZXHZQ8Pm5cQKfvcz0XZjiB7eljZykNVcMQopG37ZdB2eXuRRo5fe\nKRGddoG1zkFKIdCHTmc1fdyJwNWMKe0841d+S1obTU6RTATC1V7BxvRHRzScY+cL72Xaa6PVqbBu\nOnAKx1siTKRk1u+GmWSEKaWJL78Iv975CK05mdkoqDgMpiXm5ARfeBVeutxmKg4R1yI9I+KJYUth\niVdl1PeVvu18BdcL1+FoOSXG/bxXjKHmYfq21WlFF0eSKYUg72eCR1IwmOwgZgXRnKTliBo/CVQ3\nylQcOssWbVj49jLNyrGMzFG/xrGrtJS1M1dTDolNWZYdpPn8l1ZlVo+wrRPI9tYDBiXdZTiaZsZH\nW+yLrGHDrMlgGlqdAmFbyLqZvk0sqlUwFXhicSNnTk/VIXM/Wa/V1+EHrt7AcQsoyFNLRUStqoFi\nVIgnDnEPN1JF4W/fCL5HMSr26h7vIr67ANnk+etvzanHM9+oQQ638W+nxrn8JtjVAdlWgcs7b7zM\nhgufqzN/upLE2FAjqCatZShG4LrlFzMdgbFQlDe7BJFHNbG43oZjTxt0jc0JuKTMsTBBp8x0FD51\nGfzkxBRX3Ah3nAlRavxhqcgIFyLHZvw+c0GNDWNHwPWodYrvO0yKH7ZG+VNmVNVezWBS6JX+cIyZ\nf17H0qsyWGj/j7jzDpOkLvf951exqzp3z3TPTE+OO7M5syybgAV2iRKWrCIoIijokeMxIKKYzvGY\nDqJcBAyHIGBAMSCgCIKAkmEXlo2wu7OzYVJP566q+8evpnvWc/R6n+c+99TzzLO9M1XVVb/4fr/v\n+35fgjk55k0HGnPUCmkDjJvSGPS0IOQPQzHG47isH66bNq5TreX4FRJvkR5wuXWRBDxv9chonZLQ\nGdc7AXBKFktf+yjFqhzscaYwpmJkkSirY94+4sc2EUon+M/+d/KVYyV5PWrVw2gPYHFFeSXPRNOc\nMLmPxSMOD/lLe8KQ4mpTumCjeBcFT77Q7IOQYJTRbA/fV2IowKgF+0Kw15XnnL3qZoaWrMVPNcc9\nSkbiLNzSTuukSUFTGPYe55faupr38WAQOqtSXGZfUKNiyTm96tx7WJ+vMmb59V9zCZqWjnG8bSPm\n3EvjfslU6y7sVQe5yTidcTfGcyUJcD1Xp+/O/0X0WUEo1wCtf0ZRPRryUC4spOjK9itq0Joo8/kx\n4CZYMzyPtqIN4x082RnjABqhClRevpSkVu/cMUMjr8v9/v3vSTF8S5ZYAd4M/KJ2jlpJcvmbkjRu\nHuznrRhM7Jbky89nq5wyC+6e+iSiXY6te+bAioP1iRoodtQ8flUFurqbam1W60ulgWObz4CpJBUF\nrH1SMTtWhFjW4s7ek3gxDc8lBYczzRTyfnSaavFMKsy7l8/nssrdXMx/MmHCNnoZ9/ebYrDKlOIR\nL0Koay3HndwNJ69m+PyDnB46UAN+i7qPwTXg6D/Cz1sz5HxwM3QQXm2qR9+82ejSMQG3rojRO6oQ\n8pVrexyJrh7q0PlC61J+IKEAeR32eDIaoWMcPENQ9pfO3sb1tfuOGBkqj+/guHeCSJTptRUIHYCV\nrxBRIlQUiFddMpXTmLCrfOo4j4/h4CjwYrqJHbEgJ47WowWsDh3Nk6TUw53SXvCEYMfOumjcrGCe\nilZfLQ76JQNMPIp+hMEwGV5mDn9mGQBPb4Xo22tl2wZAzeoQj7PLCqJ5HnsDNtsSkDH20tbyBwC6\nXurjjQZQhKDqQjW8lx63mRWz+jmsqCSi9fb96+MfzfH7hRDi5/7Pg8AbwM/+kWv/3uF5ngNcBfwW\neA24x/O8LUKIy4UQ7/PP+RWwUwixDbgF+MDfu+fbxTkMPf01HkvH+GRsCfG4X4IAGMwd5NWonBmT\nRkCKu3glDFE3Br/qgWUY8PkpWp+65ojQETO9gMxHIDTZgvAVgQ4HVLKBAMxg+wt+nkSw3EPJSnDd\ncaCbReLHye8pYXLqF4/nW7LUG0pVYdxPqp/p8YuW/Rw8RcH2PEqqwVX25yip0FIs4QLJmfWiAA1P\nFmgGdA/aNIdzX4P2fBPTa8Iz+z7EU40JPvpGFrsCJV2lokjg90o8yLMtcUqu5d9PpaRJd3rYLfBq\nKE6WMKEQ/LEpReYjYBnKEUUsy6aFVYH12+HxeC95TYrdhMqJWj2zMd+YKio24WUnopY9KqrBq8yl\n0a+U3JUuE61IoPBQD/xxZD9FHxxMRuKcFfwWe8MQKlnM65Zm1ncXO4TK8k1Lns2GJpnfUNJgawKq\nSAN8T3CQORNybCyerAurnF3ZQFNQtt9DbGD9DoFdEZQIkGktgSbb+zHW8UJcnve5FUfTe84jDB2E\nM3aPo7Wn6P2gvN8ph+tx7QC7bLki2kaFg3v7yRqQYIyAqDu+dRwOxyx+NAcu5oeI5EKOfTc8oq6C\nxtcQ5SD7RBMZE2KiwqShUZwB/Irj9XDh3fEGVOHQPgHVSqQG/DRcAhPdOFX5DiIzxC+TsxjV5X22\nlhczZcIj3fVwpf2jo2SmsuR0+OECKAZiPJhp4tF4K+HwUO28lgMzEsfJc9+Vd2NVoV0vc97g8bW/\n9eTBPvViAEYNKPmhmZoFekknr0NfdR/7gkmaDi/kYz+eID5XWiGbGyFSzlL1XTdP3VdX9TTNCqVS\nsgb8Fr2nzm6uUI4stHP9cjnvYp5DVa/PPUU1qQgFXZTlRoHM8Qs6ZRJWjPb4OG+W+slkQVddHEXB\nnOEJakqGCZg6V20I8nZCjsedcZiasSGUlCAuMEqCRBFy1itUVHBwaV0oVSc9AW/E5HpyRm4z/+T+\nFFUpk8nC3ghUpnNxXZeO2UfxgO+ddwU0lz32GmHSxWIt3KmUOpqW0QpmFYqFJvrmnsqnelfwaW7g\nHZ3PcxCJ3K46JUqxbINW5ijnaP6oaPSPwvaAwYC3jZwBux3pWXD8/NED1V5OeKc0zh0rRNKd5PDo\nckL7DZRy3Us1vaZGmrbyRi7JQaeFTL5Qy6V9KtXM6vwmRqIaS1+FA8kwBUPHroLuutz7hMuYP9z3\nRAy+kjyVx5c08Vj+YhCwOxDjxmFZyylYVmmuFLlnDtyxACqNFgp2rXzPbi1Vq8NXMkv0+uFH5wzD\nw6k2PAUmNPl+RQ10YSD+iswpqfBmDnRsSZBVHB79nkubv9YNlfazPVKfn9Ne7rAZJx2zyPnDpqAr\nCE0gfE9xV1aCE6aaanXjXNVhlx1iqyXJsSfN1YQqHm9HIOYWCO2ax9ygxeh4A635AiUV/nDcb5g7\nIkM5b5+1hG/s/WWNCBi3XmCGKDRmp+z/kgZhioTUUaYIsenEKOUZfThhyjGd79p/RB5aNCKZmEhn\nppZX7Co6U6Yg63sZgyf3MaXDC03w4FMu3z9K3tdDENZkfnUqB+UwXLDxGkpxlT22fOBn2sAbP7lG\nJLyZAITLlAG6AYpTf5jN4TDPtMJNC4N0LF/Cr/plXuwhkeBPzrEA5Oz6+gYwVxtjTm8DODAyR65j\nw47Nk4NzOH/oXAC2B6Xxev/S2ZilubJUB7BZb+KUecfxvQvbWLz8YZL+QA9UoSGncLiersSEJg1a\nxTAw/NzclyjXCAmATDpVa1vP6eJ9p43yeAcEq7JoNkBZqBSsZgCqRRtFbaKqybUw7uaxp4I14Gd3\nF9kZTNKU7qL31u3sXeurNdv18fyWkgG24RiN/MurW7l/UCVvwANPN/BCaoXsc01nsuRQ9IFfz4TD\nU6xkSXk7nT6gfjYD158gOHqVbOftaw1WLIwhfEJ55LqP8MH3NNH1Rhfv/bXB71ts4Eb+w6kHcx20\nob+SlWK0VYv2Bkn6BRfOxstEGQ/I0gxTh2J0Nv2Upjfn4pmTJF+WxL3mws5YHoRHo6GwzZJSER6C\nWckKHz61l6ZsBAJTjI7KMeeSIO/3R/HlS1k2u0W6dA7Be05YwLmnz4FnriatZvgC8rxsroOPrZS2\n3bwTjidrTZAzZHrLPiVPYx7OexXaqsnau2kVh+muDg/KPWhhJciP56jcvsLiyf2QKw0R6JLzaVso\nxAsN9X6KugXu9qMLHUWQ6ZOETVEDxye+R5RGTpt3DRtHLqeiQtPoKC80Sy9pQ9GhdfEAv+uCj22E\nLmUxWX/dOUwMHIPvx9bxgY3yHZ9vEvyBNbghv6xPuFJzDiTeNRvL9AeqAOPdvTU1WjPcgbpBRt9t\nTSYI+kSvXYVRUScDbzizh8Er4cXZEfpHwap6rHsXuPEkZ502lwvOraDrTTVyuPDWel739TsGDkPJ\ntHlqIMk9s2HNcZ21+46JARrabUo6BDyTltSp8g/xKXJ5jbIKF28e48bR+5gIePx0FgwAJUUhWA5y\nIKQzZ0aJuFi7nHiuCvv9fcADiuN1u8IggqvVgUOsLFNKOtSduG4MFxhR0vy+4Xi+xL9wjX4l+Y4A\nm1L7a9d8p+9mAvE4+2MWU5rCcLWLtx98kKHcIb7t6yIMZA/xRhJ0oeK6FnZkmI1FwYlnnMtoRSOp\nHekUmnn8ox6/rwD/7v98EVjted5/W3Pv//bwPO83nucNeJ7X53nel/zf3eJ53v+acc5Vnuf1ep43\n3/O85//e/VpKNq+/vpR1x63k9sQyEklpTbiKy8Ao3N8iAUJWtymrApMK/aMuf2yTG9EAoKpAJYjp\nQWVG+YEVwYXsu+9J5v3+owhFLnqjpsaeeBVjxqZYisqJrBChr0EyeG3tAQ6ZdeB31pwzaudrpf8e\n+E0fMRtaI1BWdXAMShqEqi57w5D4K+BnKh6eXxZBd13afN3pvS3NhKjvKt/oH+KCLTnsCigRnbIq\naJ6CQ4bJQ4MhSn64iBqWnjXTgYhb5LuZfq7mG6RSECxH2ReBhsiRHj8vIOsiHr8Dnkp2UlRMLnwF\nPvxCXWF0WqG0pAQIze2iHBNU/Mlihf3wvRdWEa+sYHtc5475kC1na0baQSPGLzkVT4FgKcgjG7/M\nqovO5xtHQXxUtmXZsWlWZL2ufWGwGxXWCbi6ATavX1573sVjh3k9LK/RHZ2Mv6AdEjFGvUZW7xaU\nsIm1VWrAD+CslZKtKWtRLFVuQjkdrFX9Mi8CWPmeK49om10+w6y5LgdGW5gyBAoeDYE5R5wXXzTE\nuAVbGaBbOYH1f/4ErTtawMjjCY8RL0NDqUq7XmHMMlHs+jhtnTGECkTZlnRpmYKKma+LWrhVrKkB\n8EHy2HgVXalSsarsDcNkThqAquryth9pfWB4mIwareWpxahy+eJFfObY0ymlImz5qPz97xZ0UPTV\nTmNOjuaszFHQNLCs/tqzzTpMzQAfN0w8IR9cMyCXytS+ZyyRYdOfv8OJ2yE6Xz7X5kYI5ao4/gs9\nHO+h5NPJ5WgR1BAIha/9Gt5K1YG9/leOp+8NxciGDOxKFVeb8UdFoYKGLkqoURkp4AmwXYds/7F0\ndeoMKxlaJ0HXq1SFSsCsAz/V83BRUF0VXfcQJ3yEQ0FqolDHXwyaInCRpEIJhWr+MSqK9PlEd9UN\noEebm7hntjTsY+4UJ2bHaB1X2BMS/CljsyMGs2c/SG/Xe2sy8yNBwTUPFZgiTLxcrRn6P3hiBeFi\nkVgR5s99iVkdl/HDZafzU87khP632cxsGo3tvNZaYqLlMYSr0uFVGffk2rXNMtFwmDLgLWJ8nyf5\njFYmrwnGy7OwBj/CmGahKFV67F009m5juxblW+Wr2OX7wN72S5wEUk8yhU6ukqKkwRtpSYo8Lr7J\n2fHzGAnL/siFQ5R9oujTvRczoRvsC4ODwrAVYrfexG9PXEdIk6G9z0fbeefYI7z7NIP2SZesofKb\nPnjPGfB97XF67FCtRMt2tbW2pkwFxon54fTHj8AvGySKnpwmqTQIaAZYFtMl/nJ63csUUIL4WhAM\nHoIl/j4+N/sWW8JHs0Z5mMfbFGy/cLAdiNKWdshNe3UMBbfiEiaMLWwW/fxj8PTVDGZmZDZ4gh3J\nCvto4UN8gydVPy1Bh1E1ROeoxeLYSobahohUXEoalEJZXu6wOXkrvBVtIG6FqfpG+/l3fZzRGYBE\n726rvZftOYRLUv7+pVSJBz/ay8FWcBSFvK9090brbyltlmoo/2a/i1hEGhtGNEZDLYe6QFXxyaDD\nfeye1cx3lsDNSyFUEaz+7K/ZGZOG+uW7CpzzKnzoGahGo6CqmO0D7G2qlwJ4c/AjYEuG3VFhJOPJ\nUE9ULn/wmNp5D8zNMVVO8/n0An7d4oBq8fMBqHzs02wdkYTi4XbpdXk23MhtQOWtEstSS4iYCvmu\n3VyxupvY0bPQMm9wzyYpKrQzGKQEROMNtBYGakBdKFVCoQWEbRtPhYxPSplVGeo509s/oUoPjR5W\nWLlSetJcYEt8gCkhO2RgYC7lZ2W+3saeS1nQkKmNlZFJ3wAVCuWQ3KsrqoMXcLAjj9a+p2nKJEuY\nMjqODXsPbKbdToExgunJgTvpa9BsNVvYJfqAN5kUjaRyFb43Xz70qT/YTF7I78zuOpXHzCCVvyJx\nnwfmHiM9eYcteHKBzVlnbwKgeOMKFiwAc49s96pbZX+jzen8ge6xJq4fXMqv7j/ETddu4UnpgCev\nS9Evw4HkU18js+4EACwLYsedUisgrmoK+fJPaDrYjlIKUs7KdBbN8/jUcdfDo8exsKsVx1d39hC0\nRyZZ09VGW94GV1DMS2M4FHGINUoStrh/BQsXyOixvatWseyitfzzzaehTvRwf2Y7OVu2TZ4ghh9K\nvtnMULBlCHqwAme9soWqAvHdQyzcUxcTM5wsD/bDvzevxuq3aJhsoBSPcfbZDpHJIhs3wgc/eB6z\n1sj5NOXEeWigHmmwiXvrg6kUQ0lLUKl4UNLknr5NbcMMBbj+y6fiaVU68m/zZlxhwoSOXIlla+by\nVgwe7fHIPpMl75Oiw9UGcAx46Gt8M3ctAPfOMriR68iG/ZB926Go+XZfsyQe9q5YQbtpol/WQfVf\nYWzXLgKhft6+SJ5WmV0vs1BWoXmGNPvA0St5vREOJjTCZZe8Do91QTBmMa43MmqDyLVR9MF2/vmr\neSpa9+w6VoRDn7Y4f/cwwQGbr9/xdQBG+09kmo9VHJ1wuC4Q2ByZWwsNP6b8AuMBqGjw036ZLuSq\nEUYsnd5c3eZrT8nrx0M6FZ8AQgj0Gak26BaodXuss7oEx4Tmw2OISoJDNnieTTZt8ltO5NdeL62T\nTagz4FjvwV6CikKwIcwz6QB7rBD5sbU1+w1gUXWSNxpAR8PzbDD3M39UZei4pfT3x5jzp0X8reMf\nBX4bPc/7g//zpOd5e4QQX/4Hr/3/ejRrZUZGOqFigR4hOj3Z1SodYyo/au0EYNIIUVIVLLfKwCE4\n+UIY8/txejyHdJfKjA5sSOnw9tEoB9rQ45J5eD5p85euMvFcfUCpDZJ9EapFty9R39wMVqaPF5nP\nFgZpDjfXzjdLXg34edTDLkDmMpUdDd2pUlFNqJo1Q2NvBEJO5YjzVTyISYtD9zziisZfmkJMpRVi\nZn0AT4gO+g/Dpc9DWdEpK4JYEfKqzk19AW7UZT6BmTGpqDK8xHAdCo5NFZ3GRghmJbrRhKgpch73\nThC6jVWVISAvpw0KvrF78o7xmtTzqB+qVNQstLBGKRSg7Dd8t8+0ug+cj9V8FNdcFGF/BNbbrbWy\nBHPaV0PZ956VQ8S7u6l6SRDQkJcdWXKDDA7vpfk0GSrR3JTgjx6ctmATjafWq4Zctm2YF5Jy5RZA\ny7jc4MKGy9uJFbSUs5T5KeGEAK3O/uSEH9LblObm7TIH6PZF0NDQPq11Q2J1R+380QCUfY+fWoBk\nqMSULk9c1NdZOy9LiKb+eg5olSCNv3wfLzecBFUTjDyHaad5ssqyngKHAwHClmzY/abNhcZ/8mSP\nXBSFG6oJylTNPI92y/pQilMheehS2HImAIcOlfGqAXZ1v8qOOOT98VzA5k4uBCDd0ABTpZqHIjYW\nw8XFcFWIFxF+gehvrJ3LCcvfydkbU4SZIJOVirmLFoFl1UNCBw+KGvA7rIcZDEqANrrjXBynLmWe\nberF8gvcNs6VBtPmRojk3JrU9yOhOQzZMgRCqFUu69vExM83c80zMH9v3aNv6jN90+B5CngQqpZx\n1RkJeIpCRajolBHBOvALVqsYyRb6jQIFK05mUkHXHByhEjbrcTbCc3CFguIpmIqHGpcqNFm/htnv\nuiBoGni+rzxrhsiED1BRQEPhL5Yf8uUJksN9bPOJhN/3L+GKPXlaJwV7bYsvr0jScw2cecEjvPZU\nmulc+JKvABctCnI6NUD4xK8bOWTG6JyAwe63+NIX2ghNLCPEFMcukh6AQ+Vu3tc2h4NrP4GnVrkw\nPlyjjPaZcvxPGTA0FMNru5sW7UVGq80IbRaF1KncYb+LTS/9jrZcFj2R5WVniM+Ur+bdfA+A3WE5\nz0X7n+RNiwkO2lKYoI+t5PUMwXlBdqR8cigcxnX9nJo2l4GTTuK0C2Ro8H6lESo2IyMd2BE5Z36Z\nWcifuq5D2fNFMlNV9oTrgN6YiNCTrufT7hGZGvDLGxM8njqBb/e1UhXwm8h82Tf+HC1qoAoV2tr4\neYt8nqxR92Da4sh8sfVPyetmT+5hd3IhVddCdQVhX/3VNiOsGthYm08VPJyKQ7fezQ3pGxC7l8Jv\nvs6fnqgjBuGqPDYwzrPeCv6DD/GcWOL3NxzSm+kRO7DCCrFmue5M7xUjbRaaB0KBTHS4Vk/1wPz3\nMzpDLc/o7+GrrZcjfM9nqAyl9FbmZWcxd9E4VbMZx43i+t68Q8F9lHZKKfk79HMZmC33HlW1iSIY\n1QwITMjC0T+6H169gENamWtPhLvnwPkXd5BZ0M+cD0hjZOnBUe69XwpQRHvkO0QXHcNrvfVQKlXb\nB6b04mselPvjMtTT88jOqLXxQPbzfD+2iU/Ou5FYwOb9C95FUYfmL16NGpB7xIM9TwLw58bFPHPx\nzyi/VULoAlMIzNRLfGfTPOYfJbhnQT2KoaQqfE0IuuYtpbW1GXvSj292TKLRVUR94NflC7aFyhAu\ne9QtCWjrl2JUakrlhhtOqP3+xeZZHNbkZG/vG8T1S0jcvPy92KZN/gE5d0aHfcVvVeO8Ruk91Pc1\nEw2ptX0UoKlY5MTQHvxKNRzIjqLrcSqVEVRXnufE5Vrxpt3KdmcuQmzjsNnM4x0BXkt7nKatRzQ2\n8qp1FNfwNbaqg4wEO8hWZV+/mIyQEzZ774OFa6WxaeTC3LTlZi6+WEZ0rNnUQk8PWGEJUiXwkwPv\nF23n8u17PosohagsqHBP/6l8cANcdyxMGQLTgZ985hIyi9aQuLwNTYOOhh7GLEm2nrRB59NHfZre\n4V469x7H3m0SUOiuh6mb8Mo8Vi+4CD3pbzaKx7r5j0AuSDQfJVROML2rN7SOEkp2AlAkQNono1ru\nugs2biQUgj+8sIdHPvIklVY/LBoLTwOBh1OJ4dmHpbhLBZY+8zQHV0F0y0lse2lFrV8sbxTVg9LQ\nIex+m/u+eh9nHSvz1zLRNj4dgaOO2sm8jhO4Gp2DWoi759XHdht7akSnV45hpKQ96QEYCt/tbeYn\nwTVo/ppVFh79znZ2xFTGAxBwXay5A5hVWBydzXO/e468r2ExXEmCo9PDFL1rJVgrKho2Ffaqcdad\nleaVjhZK0+FbPvBrMU0adJ2MYeAVPeIdHdh2L8Wvf5iH7wuy/8Iz4PNSc6EqBFuG69FQVy29Sn4w\nFQ7a4ZrSbetlfTRm5H+qk50UkfM+j83Y7JMIfdy/QSxBKv02V6ZfRItozN89ny52oK26oPYdXfPh\nxhtvBEeuXWvmnEO0Ir3hz825ku8uArLNPLi4g81JnZjazm41gelrTwgPOpKSXNyy2EGN15094XC0\nljct9GBtvwI4vrWfP39X4bnvQLGc4eQLIVBuoNv3jjdVD9MW6yC9TJJWIc3C2GsQVBQyA92cfk6A\n19qjfHrDi+wP1jUS5lTGeb0BAloAz7M5rB2mOdaMomqMtC/H5khbZ+bxjwK/9f/N7zb8g9f+fz3O\nHvIN7aqFEQzR4Iee6C60TlXYZUUw3r2c8UCUsqrQO+rn3gRUzrVX8pkvnFBbJC3VrXn8Pslmgoky\n13Enp7GPaIs0jK9f2MFdy3LkW+qDwI358t2mScKPcT/vzBArh9aykBf5ky8mcOhauZmZFZfdPhvu\nHVG5QoY7iCoEKg6OGuD2e75KSfM4bAkZTuBUcPwt5VOLjkPzXNx2mWhquB5RxaOgaST3N9LYqSPw\nuP12EMEWFGDeASgpBhUVokWoRCfIZ4aZdYGUBzYyBghpQExqBsKvTZRKQSAr20BT6+Dzd92gmEFC\nZb/mz9KfoY9KV/e8gwdqidujPutf8sFT2bQp+oZ3qFG2mYuGWLoA25AM/boF6VrdMzGyGirS0LJ9\nr1V0UoKdeFHep+wGCcdi7LcAAamU7KPlC29n7qa1TAXqhv5zCUnMP3BvAAAgAElEQVR7OprA3L4W\ngPXNb9C2QrJ/Q53dnH3GWsg3gC/PnvOFSuxQkPv2wEVnwQ/mQUOzXCxfvfNrMFQPgdwVg2klA+FB\nR1OJKV22w2BTnQ3bRwuXLLkIXjkfXYeCo1BF4YKPpuX3A+OBFtonLMx8lsMBi0REqmb+tHE2rYX9\nfLMq3W/pUmUG8CvwchOsfg+oukpPeA1sk9N4eHg3bjXAIRu2x8EwfJLAVfg4X+DPjatpb23FnSrU\nWOdgzgK1jF7VsdY6KGX5h62E2R3ReNnK0JnLc/NDCgcHW+jr6yMYlOx2lhADo3WP34Rh0uwbxG++\n/u+MHgjXPH4j0VnYqtya22eH+X2bxmuNkCzUgV8h385+pAEUERk2Vp4g4guJnLyj3s9HSGJrUEan\nVLCIegUcT44jTwBCUBEauijT5qtoqa4gWAEr3URyfpFkLkrbpIehVqmqgsgM6WnVc3GFgvAUbE/h\n/HVZmrMwpVi4gKeAYVADVAUaaPKyVBSBisD2FW49AYte24A7IkHIbxYvY8nBHFbV47Bm1WqLffzD\n3+fVzdX6Uu8zMS3FAocsUfP4HX1MgIN+ftGi1itIpwWRw+t4lqX0DNYBxinpHMLPo9IbdfwgAoLh\nTkB6hL75zyvYdHkj3cXn+DL/gjd3MQB/4Bx+22Fy3FsHcC2XvuBeQmaZMzZ9k5wI1bz9373882TI\nQyHBgSBMpmJsow/T9YhGIkz65WJMRacU8MkYJYfqrwFFAhT2nERPuYfXtyzjjyMy52NfoJGKsYAJ\nQ6ogvtJY3+Z0pgiE6kb8sEizYo2sC1iNRBho2cdfklGeaBOMuvJ+k3rd46crOnR18WxUPtuUrtTA\nVcQvU/CtObO44mRoPCwbbdb4HmLdy6iioTmCkCLnlm2FOXpZtDafHNelOFWkPdLOJR2XMOobdtHo\n0bXnVVyVh+Ye5CuFLwJwoJpmT9SgpMKuShcp7yCaZdM01FV7ZgC/5Cqa4tKROIjjixw9/bzN51bD\nc/6epfb1U0pBY06+X8CBUuYpjn19BZH4QjyhUSVUC+9Nl1ZQdGTfTLoJPv7Jn/OTn6RQlACvKLfx\n9eWXQnAEUY6wJnUWN93YwfCUJFJyJrzUEyIYjpI3IHn6uVzc+gkapJOBprAM0w/9xy38rK1eGuGs\nLYAhvaaNHgTnt/mGosvTpyzkKqTQRXrf6Rx+Q97sN+f9lLhVr+/V1+UPaF84KVLuYMW8Xow9VYSh\nYArYFShArJ1Xi5uo3vyh2rWuUNm0YQM9V19N/8I27OevAMDUDyKEQA/ZeBpojg8aspA1jZoYR1Uo\nDK6QYK8h0M2AH56ded/7eHbOMdzWKF0kqfZuvAm5JllhDU3TyJXkglfy1ypTMxiY20EOm6HqIMl0\nlOoMtcQm7wBPrB7kgUtkZk6uCqoaxXGyBJrkeVpIQ3wGbm0/hR9wEYY2jDF+Bv929kks3dnPLT3S\nezIQHuIbXIMWT3PDDUGK/ur1ZirMiJYi2QCzZ8v1PehCW6MPdDyP79wTQ1EgvkquERWnQiEcoPuu\nO7j/o8tojT7CgbEuSmnobriFm5bDY92i5o0ORRQawzHGbpEE2oHcgZrHLxTSWRhfyMDwAO/Y+s+U\nfHEzzfNqFu6yvg6ckCQWhfAIdu6BXJBYMUZrsJ1pSvzZnovJiWnS02LdunXceuut0NrKtGG4cnYX\n/cl+nEbpZbv0xAqT9/qRPaUI2IdkXcsKMDHGgb5e4t4UO3cN1volqB7CrELIjGP1ybm2qkt6SzOD\nyxj4DmR3tZOMr+CW5RUiif283gg/b2tiiiDZcDMhpvzmVZg9azUr3wO/7oPnY5PkE8NQsdB1UBWV\niip1DXbGtBrRRH8/i4fhnxZ9gObmZhzhURYqw5Vm5ihv81VeJL5YErVldEKqQ3bK5LGeClOHhwj4\nIIjeOpk7YNsMBo8kwIo9I5wSfoBIPAGf+AQg8xIf4Hq2+6kFSzNyrUaHca2hBvzSc5LMX+wLKeZ7\nKCljtb45a/V6vJfXMmGCkm5GUTzObnwB4RMud7Cb+b0z8qtNj2g0yvbLpNZGR3cnn4h9AQC1fwE/\nGQLr8Gx+byZZd1GMoNbALr0OtADaYh0Yn4Inl9jsC017kOHy4mvcN+jbpmaQLrMeduVqYUotGtkB\nMLH5SwYClSRNTRo//PhBTifJKce/g6CvZt8R66a8t8xVn3HoWTibXHQMXdGJVBVGrbqoZHf5AG8k\nIWQpVL0AE+YESUOOyblvncU6HuJvHX8X+AkhrhBCvAIMCCFenvGzE3j57137P3X0tvgLesWi7AZp\naIAfzpO1Mia0AEURoBIax3QsSqrCwmF4M6kTUztZvfYC3KOW14CfKLvcMRTm/kE4ngMEVnRwSWYL\nLRRZvdpX2PQC7NcP0R2XLF1BGASTcrAITSfWK1H9wqEw71x87hHPqioqOV2WfdhBN8fwBI/z9Vo+\nDsBIUKFxzAd+WoBY4jjKmstBW4bghKoVxnS5wWi2heF6eL+QDKzuekSFIKfq2BWN1tVRzj7d5ZJL\nIJ5I1b6jpOhUVEG0BLnIMIszC3EqcvE0Mz6IUmFC1xFluUg1NkKgIt9TUeohpCvbVmIEInRMSAGX\nxrEz0UoyFjuv25y0Db4/H348KD1sZcX3zkVVok0j8AkbU5lemRQUXSFkxwhUoWPAQvim7c4XZhMM\nFOC5y7Cnnyk6Dnc/wOAhucGX3CBaS71oatoPhzBNk0BI58ke+QyXbmxkLOxPYkOg+fmNs0/L0Pd1\nuaB/8YxVDCwfgNuegptk4c3peHNFt6SH2T+CGWl0ja5cBL440CspuOhMWKFfXjuvs80hq8t2HkrU\nwx72iSaO6z0GfnwXkQjkCoIqAsMQcmMB8okMreMmwUKOUcOmubHCb/ogJ0IUett4NHsyJ14EP+5v\nZzgkB3TFqAN0RRMsWwbsnw8/fIgdO/bjVk2+twD+eT20t78OyJBFGbiv0J7J4E0Va4BMeDnQSrhK\ngMCqvSh+3MQuzaWiFziYinHXXHjmeJXnV72f5cu3YvgxMftpQkHh4peldLxIZzGFXKRHxxsYmluo\nfc++8Gx8DEBXt+DYiw32RiA1JTAdwX2cyZax88mXMlz0/rmYmk04J8ftpKFw0vY68DNmAD/LgrKn\no3geUaeENyNcG8ehGh1Gz/yRM193mWAOuiMIlgWxTAJ7cRPtgUkmDZXecpmqaxCdoRCoeDLvbyLh\nYbsqt8+7jp1fh5ywa+ElhuFLbQJFp4HmKahoLpoQXDhazwcJmg7hkp9/kcjx0Q0qu8IxcCw0HyBa\nFhxz/DjuTLcCkKgWGDX1IyTSJ3U59+d1STbU86R6LKn6mlDw3sbzQ8H0Br0GUItRCa4H430saVmC\ndeLJlNjCTXyQxCyfdJuYw0dOzHPA1imZgpXp7UyVDI6+12HY7Ef4D7lgzgIWMg6FJNeeAJO9kmRx\nFY1QKERyz1yu3AiHBnop+Yp0CdXB8N/xEdbz+v5z2LDweTZvXsFTb8k20x0Fq2qxvyHC1miAX8xQ\nL5kX/zaCugdwREkxtEh6fZRohNZYjF/1xbnkbHBLYXh1E94WqXJY1MBQVYhGqfj9ltX0GvBrDsjv\n/17z8dzqR9lsi4PuuYy1L8BBRXMFQccvPGwGUINqzRCbKEwxNT5FV6oLLaJxIvu59OiJI/pTOCpm\nobNGehUKOr8YbGZrEt52ZPsrts3shTKkrhZeOCxz5zRNoa8ri+s//8gI/Hg2fHKuJKhEopFQbJTw\n1IzixOEysw/Oo33hFbjFBioiVPP4oYQo+YouWSdBIKASjx9EUSzybjtjohlCI1hKhEgEelMt7MvW\na/rNaW9F9cXB3JJFOqBwOAi/6+ui/9x6mLx5cKD2edF19XF6cVlj/PgEtyyV7/O+8z5b2yPmt4/R\nbErvrq2qaEr9nU5eLdfCYtQvSaTqHDurETsPii4IlS1eqxbA7qQ0sYLis/XSL0J4dP/yl4jWVtra\nW8g+I9d0XZfwQVFNPBWKFbkvZ7KQC1s10ZJxbwFmm/Q0lNNDpFJyDl573XVYzWGeTsjasAPz5rG0\nWaYTaLaCrus1DWQvLttAoJNsMRknRgCdWakQ1YBPpiqCACW8QII3ujfy/geO5ncHQPOjkDQ/X8v2\nCavdqQQjyRaMsMbDpzRyrfN5vvSXf8fulp70z31C5d3vhptvhksvheYuObje6k6wV2uDnM2Aj2ID\n5Oj+cjd/fShXXMnHN+hU3Sq6qjOaDPPakE3S+gGTnvye/n5fnE41mfCFj5JJmD0brvVJgfnp+YwH\nZN07oekkTkzQfolO+pSlte/SXbcWebN4sBFHk94iRQGSkzAVYp4yj1NnnVjz+N3wi0U8/YrstyIB\nAoEAl1122X95D4Drb7oJgMG5AU67WX6mFAHrMJ4CeQ2yy2NgdRLQchzO16PCgpQwHIjHmtEbddSo\niuXn6WfmH8NIEPZvn0MkOEBpA7S3tmHrNqf+5lH2/voV7Ltu4xwkgeKiEG7p5Kl2uPI5hYRryr2z\nYkvgJ9RajvCuqF7fIxoa2PQanL/wYtlvrkdeMZg0bWLCJUIV0SrXe62qEUkouHoW7FGikxGe+PBX\n6L7zTpgB9O4aGmJx+Mi8WSNlEMtNkGpoqv3OcQ3e0V3heY4MR/TwqNjttXXLUA06YnJdM2mjqkkS\nNo/N8uWgOBb7Q+C2+fZT2UAJKBy1SypOCa2+IbZFJGhKNcl/41YcPSOfXTNk36w0ZlNO7CAUKRG2\n4jUV9OmjNdVKRQPN0YgnJZDvypZZU3iT646TY1XRYgRn5PtLblZuwLrvbLC9GOk0rJ7nsIgFLOtd\nAueey5uXnUl3Qs6bpr0e0XgYhEfADBIpCrKtMwscSLXzgGrwdtEhMZUgEJI2eYswAYu/dfyfPH53\nAacilTVPnfGz2PO8i/4P1/6PHE3TqvJVC7QCrWmH/1gGbZPwtp4ET4XAGGY1SFFTWTwMe6JBFFSu\nWHIFN6y9oQb8VDy+sSjOOT5es47ugvfI+n3rv9SCp6rkCOLisSwoGcmCFkALyc4VRoDoJZIN1BSt\nll/029/KfxWhMHQlnJv6JjE1x5McQ4nhIxy0I5bGGVtyvPfN7aimSUtDipIqGAl5lAgQqriM6XKi\njcfa6Zgs4U5Mi7t4BFWHvKqjCZdESkEPypfLpOry+2VFGi/RomTyl2eWU/VtJXvQB2aaNKKjjhxM\n69ZBcLH8LITL3f0JftEPT1zyBFpQzpbhoMV67Rt4Afn/bU3z6RqXCfZFW25cFdeXGJ7oxhtL8vQV\nv8ecUeRaGIJwuo1AFbRYuLap51/to7PzVfjFrTVD8F3vuoEfnvJhItO5Xq6N3lovAZFON6JpkjkF\nWBJPU9Dg8R6HQlQKeDT1Bhg07pRt1NkMnZ3yYs8j1BZHySW57UtZHn4YXFf2s+YKyNXbU/hgM1uq\nh5Q5QmNLCh75t0slexiL0dEhyOqCogpz7XpI6EGzbthEo1DwFKoIuYj7im2FhjZaxwXhQoExwybd\nKH//dHiIyvXfoFJNMtKyEHtqJVpOquhVFVB9RVYlaPnrtYDtJ7B1q4GilZgy4WAIOjNbAQj6cf9C\nVWhtbiZQduuMoZcDtYy7r5vxiZ/j+qqYpcB2KkaBSkMTV2+El3Z/GtxzmHlU0dgTiLNhG7zrHfD0\nggZURRrEew4YrFxdIa/DlLDYF5qLdcIqeOklIhFAL8i6ZUUPuwIf4DuEgx44BmtS52JVKnRl5b2e\ntFfQdaguo63PyNm1bXA9DRWHsFPCqcxQ+KtWqSigWwc4c4vCAdahO2BXBI2ZGPT3c7T+K16JhVia\n9aigE5lRQF1BhnoKBEFXQddNTEfmg0yDsEDAY3oJLisR2sdk8eIlWoxL9/uCFwKCDVN8qmcNzUs/\nwSvB59k+p4NTj74UUQ3wpZ9ewa3fvhWAe75yVC3kelod8pTBDzKum5JMetJPwgxIYiTaKNcJz/Nz\nixvrY/iphy+u5RPojTqzfM/1WERec9vC6zFUA5YsYZH7DKoqjbP//Pzn6S65jE0Nsfz9IawXK6yc\nJ+dBhBLf77q39s56QufDYivsXcpjXRANBrlefZU28gRsg+7Jfm5eBkZjBM8XuOm0BJqfC/xO7uR1\n+liw4DG8qoKqyAVWd1T0kkFH9QADJ23gvvn1EPdQfjNuWa5pj3bBG/oQI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aZWtVTqV+Ga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ED/2SvG6cHlQDBAHdxlKo2PhzEL8rF/4UW1dGzZ2cY9nlStWJ+mgKlYPUan3pGh2mXK4PbTX1\nxh061t8WBqVCLPeuVDNIEglwfIGPoGMaUtWwaAiwbBmDW58hUUyy8PE+EjzOtBSRswiA8XEsXQCk\ngsRIO9zZ72KZ0yCKyGqSzU8nGDXyNeLnZqhU1GLveRbhQLfzygh5hoIqrKENgvCnryxW4YEz6U44\nbPqg2mfBECqEIBZrtmjgEQBcnWNTqjrs6F7CtBW7T11ddflkcYRzneEa9cRPv+RVCfz850QJH3FY\nYVihFy/62ewsdX91dNQux8pb0XXImLPFyqrzWdLiPf+xhRfeJzDxWZBtJH5L/Umqu6sYBpy8YDfX\nbBcE8WIT+jofT2vHSnzA3XgjgafG7foN+p6ZFss6VW5x6JAytFOr064SeEr1lYZkZc9Ksvfczru/\nexwdNzzAb456B4lFunHzLkVsRChJaHLvDDrR745j4QcWklwVG7tNyE0+D1XfIN/nEgQVJhcIhKgZ\naeEa5nar8WWHk+UsS5qj39tJW/3+Cavm5BKmCkFdtuCXauOqw8ol5ej+zQz1BFXMY6biFxE/X23/\nxYu+yGdeqHK8uxJddduDmge7rFp7HCEEwodysoppdsw71NPQVX/NkU7GB2+jY426T/kz8mSOaqKG\nJLUtYJcbgoOisR57D628hb1Vjd8SHbW2QHFcdVXNe9oC8VdwpuJ318vv4lVHvAphCI6dPjZ61ps3\nq5xVZ5GK4Agsu6XiZxqmVvxC4teaaM1EWIykWahnM3sqxMbBjRSrRSzDmlPxi0hME/hmc+Knfz7F\nSnHmLiSsRE19Mfd+mYqQ+N182s088jo1F2OalCX0GhZ+aPQvUIu80STSbD644QZVBK7uGkSNFIXF\nXSynyvqjdpF21G82Fi5iJgQCX/iUd+/EQpJeq7Y9bdFpvHXzWxt/6x5d+dx29ZreNZGjLZy2br31\nffzPvffyGs16ejNq/hCm4LhTd2C59Q72uXL8OOkkeFg5Ejf0b4hCzW8+/eZok6ENQw0CRNWo4hgG\ngZlAPLUC//vX4RU9hLbejTB0vNvFn/Cfk+KHJXhmnPFVRQAAIABJREFUW5FEOYljOpgZk44Jtd3Z\n7gOcdRY8/aanOWVMtQlIr0nj9M9uc4WYlfgJITJCiDcLIT4shHiBUHgV8Buoqyhw0CC1MsULhu/n\nqpecyic3/wvnLjmXSiHJOzNvZu1ySXKN8txmE2lERatOfd2RoRWHEZYLnsMzAbUBZjsw0Kc9Smab\nr4Yv6RisqXLxHD87RvxM3SSechK/PMDCxcrr6qQtZbRIyTWHv4T7Ej1MGxad0wHTtuDZTPOk4Oi4\nHZJKmHjSZCKyPUnRMNhlmvz96V/lGV3hNlyHZkaN2WExEZ146+vwn/DlcSuQdj2YypHLtiB+bTiT\nagojdf9jaO+2eN9NUV8ho1kGPsrgAJV3ECGfr5U/Bfj3f4dTT208v1FT/G6/fe7rbYlFtUlYzHDf\nhYrfTAEykYAnHUXoZSodNTifuYZWUoLe3svpXaaaDIfE7+KLa486CBTxs231TD0P1v7XWvpfrhwN\nH/tEmny/A489xkReE5JA4KSArePYYRG6YQcByMCBv70Pkq0Xbauwi96RMn/+jT/iP1/8nyz/Qi2e\nJ37rZ0P+mKXRGAtvWzgUs2FvJSF5ekWNSfvlmorkeWD6Br4QJCpgVyej7zjlFJJf/CKrH1nL8E97\n8NhCSRoU40bGwABm2I9SWBgph5HHV2GISQTTiGKW997TxUKzK3pJyh2L+CzKZ5ZKOYQD3etWD3pX\nWFk0nI9030y7rMhFkM5g6vDYBaNSdVN+opav0VdQ85unO/aWfIfq0AKm3Jhx1tfXUoGOlHZbNFX8\nRGqWOU1KePBBLNeclfh9aO1beeOFzcOWpCdZ/sXlKrIiFuMbEgXLsDiy0sMXbguQBIx2awnMdbGn\nFHG3fYOpB1RIkLleh5zFiZ+eh55K6vcrbqSm0yTyWUTZITlaq66X61JesPCeiN26Wuhjw5j+DJVd\nqPfz6FyW0ZFTG6MWwjh7/YxXf2s1yWWNzyN/Rr6uF9rFyy9uMMBCrpFxJEFQwfdLGLqU+Lofros8\nwB260Ifl1CoZtkKo+E15mvjZtblOSIFMS2xDG1wIlo7HyV5jZMRsxC9cG85fej6nH6Yq5H35xV/m\niIEjGo4Tv+bx/DhUoZysPCfFz0hq0vCKK7B7XIQuFJI/M0/+9EYFSyYlyekkK7MrG77767+Gqfsf\nqlVOQ4V6Gs+oueYePtgYstEm0snaehAnful0mnV966KqqCHpC/GTl/+IE0/4EzUYTZPJyfrobNPM\nIoQTU/zCUM/5E5EGcnb//fDZz7bcfjw/Ts5VBXpGXbeu8Necx47B120cZhK/EM0Uv2s3XEtPqh8p\n05HytzchhSRpJck62bowd5np5K9OeHlUZEuGa/4sBLkdvPvdDQVV69R1IdTcGYgqdmoXaV0Bvtn7\nLwOJb/hsLW3HpTbW8ol80/dxTxW/zFGZtuw8qI3d0dFOjl65kkFtvCzIh32GWxxoruMLQUMeVBuo\nGlWkEKzKFUh/6r8J7r2cGz93Q/R92GLELoTvk1b8smYdY46q9jbjGJagutsnWUrimi4yI8no1P/F\n9jP09Sk1dra5vBXmkqQ+DWwD7gCuAd6CupXnBUHQujvgAcY3H15a97eXmeKY/3sL3o4Xgqcm0kzK\nIxHoPLNTT4HTG2X0SPFrEYs8E2/hPk5dmWHa0yGO9tyKX27rInYVPdyO2oSrykWr63RiLNDVeUvi\nztfgJYZZcNg/wi9BuJayNITg2GPhc09dxArvHuC7/GQgSWqOcAI7b+OV9QLThCA5CckdvQl+2VHG\nzTq4el0MCV8rxe/hjLLg+7PLeMmyU2q/owK2I+CvH6XzU80J2ZyeGpoofjOIn3HRBU32qoclLe77\nk/tqcfHzQKj4ZZxMdC1Bk1zAORGGmjVBSPzieX+g7PYnrAWUhIWwrchxPDOtzteEPjS04sU2om18\nFdr71FMNXwGa835DqlDPlepCjMDAS6lnFw6vnst6GPxeQLEI7BgF+WjL3yUk5DcGHP/A/+Itflv0\n+c6dczrBIyw7rpvyv7nw6xrxCxW/jB1WlrVJjnRy/sXwr/8CTrVG/BIJkDsMbK1SmGUdzhduYJr8\n6Vevx5UWNlvZJS1KRuwGC4HZp4hFRZiItMvYlpVIfkS6VObJXaNQ+JF6KPplkdksfyP+DALwPIdw\nQUh0hsaLPrtWgwzdjoBikUv5DEMDPo+GxG9MqJcv9gKGnkWvYoIFxarDkhP7Kd0bm4sKBbj33qb3\nNGxXE+XVhtDnSB4+h5d8bIxcLuoM0BTld53AB7av5a9afN91vhpjrz3+eI7RKllEuIRQbOehh3gZ\n97F8gS6R7nlY+S7gaT72MoOXLVOGdnJlk/d661YAfEO/X7lc5PUFGM56uCUzFp5HFNoaOpBERR13\nYnoVXU+cz1NvfF/DaW5btqwJDdLHOv/8eRt9A5kB3nNifZxhSPwcJ8nOnXdQqWyPFL/MhhrZMrWh\nZLWh+Jm6GFQpEQv1lDHil5KktAOlt1fg9taqOiYSS5mJmcQvHurpB413KFQlZiLuiOj0OnnKh6r7\nHBU/y+D44Hj1xwtfCOOtc9JAtdX48nu+zIYfNYb09/UBffVRNWanGaWdVGgvj6sZ/ugtCUaffRBY\nGBG/O+64Y05jb3XfejWx/8VfYASCqamZueNr8LyxSPETQo1FKdtX/KIxMfNaYiGvzSCEYOPgRizD\n4i0js0cjzUb8qiHxsxpzycfz42SdxlDOxYXF3PNYkqA8S5jnHsC2lT1gzSCjdkcHdrnCY2Fhr5Ur\n8Q0Do0Wu9Z5gODvMx8Z28jL9tzQkFb/C7tJu8lk1YTTLiTUw2Ont5NYFW/nWQ43v8UycmMvxk927\n59yuFbrO6+J4//i2tg2nrZmm7HniPJ6444mmitnYe8fIn9Ws8tKeo6odX59evYwF5m4ca5q+3bHq\n4dp+NbvCXOZw/ZdtK37CFiQmwa8kcaSDTEtyEzrHUDZdWdrGXFLWWBAEVwZB8H+AS4BlwKkHM+lr\nirIgnd5OKp3FT6kblk56bM338qXFYCW8pqFLpqsfShuhngCn8JQyJsPk4TZCPc/7+j/Q4U/XER0/\n9lTcMLTobdCZ1FXgHjsKOTGIk1HGR+AvUvX+UbbKQ84aJgIlEX2vz6XLbNK4Bfj85/X/iICRna0H\nkuma3LS+i3sKmTqlICQ7jcTPRBBwd49OyDVtPv2ib0Xfb8mAYwPlZJSI3YA2gpBrOX7RidWuOa34\nJWcvLhJiadfck1zT8+vJvVk563khnmA8gziGt7up4mcvpBJYmGZNvZu5jmRijUGhFp4T4mtfUxUZ\nh4fhda+b5RqlhC1bmNChniIQeBk1NnODuvy9EEjbYGICXA/+fjbpTgTI3k68zum6j9PplnVHGmAe\nNoo3Vj+2ZUT81BjYfHGaJccs4SuL4TWngevX7nUiQaTW7LbALD5Tdywsi2SlSGLEQnR3UzIMKrLe\nWO/01PnLhsTIeHiVBGZQZe3vBI87K9TL4Tg14pSoOfxs2wWu541HfxVX98oSYf6bXuECXYWYW27h\nM19MkOhOYeoS8WMLG+elzA51PV5Z7ZfxoWtVH/5Mw7i7ebW+oFobf01z/OTcL+aHP6wU5Va4cWSE\ndzULfZuBhJRs1hNE0k5yx9U6V06znbP5LdkwVcV1EUPKc/ubsYD8mWqbvqv7OOrpo8hmY/dq0yY+\nd4bqGRrVVoh5fZf2TNBdmaBucvp7XctMHyZUCyY4jG3yXLqSMzwzgGkY2M0iDZJJ+OIXW8cwzwOR\n4pdZxNjYe5X6JRvJrqnnxvDf2eZXqQtuVVLq909YMeKtiZ/zOzXORkdRk5OetwYHr+PYY+tD7N57\n8ns5abTWgmIoOxQpVdUmoaGtIGYYqyKsjmrlOH/J+Rw3clyTvdrA9dfX4t5bwEgaSF9GpHguGJaB\nzOy5UZ8YcTn1cypkM0xXGGxSIbr5RRhw/fUYBg2hnsPD11MonBNT/Ex6ei6vCxOeC2t61/Dw6x6e\ne8Mm2DS4qSGPsxnOWHQGox2N9REAfNk81BNUfth/X/nfTfcTQs6e3/cc8dOfwne+0zxHlUwGtm/H\nN2qKn7GHat9sSMgaQ5JCUvWr7CrWQj1FE8+PRPL5TZ/nvPt9Vpfmrnj6hqEhHjvqqL130bPAtpvb\nBmNijFd+85VNhYLhPx2O2qbsbWRO1XaQKTBlmYQ7gTBqa2doTdtdoaO9RajnLDl+IfG75Gd/xKah\nTZgZE3eXduS3m0bWAnOt4pGVFKjg/S1BEEzPsv3BiaqAskkyk8RPKPk/kTYpeR2cfwlIq/kELbXi\nZ9jzqBgma4uktOee+C3p0yF31X0WN/2f9lSCeWBAV0Yn5gq1ziZ0sRfD9FR1Do0to+fz/o6/AODb\nIxOMysObnvsCLYgJAQt2tF6AhTQQvsQuJ+uIXyvFTwh1nUty9SWDAZia4p9W1jw4rYhfO/J1S8Uv\np6w5kdx3EyvUwp+aeRbnhRmVpeJoRfySSXhALuWbG96ClDUbMl6NFeAY3YstvNaZit8ZZ8wqONZg\nGFAsMlnQykdg4HrqpMMv663bbGICMgmDq/v6mh4KUJPkhg1K+XiuWLYMvvlN/vZv1e+AmuLXpQsO\njF83jJt18Q343jC4McXvRS8Cu6LGzKQlsKae5Oir4ISL9M02TYTwSQz40NND2TCoGPVjqiPRyYQF\n0+5ujLRLomKTLlcY2hnwhD2mbkhM8UslA6S2WE3TBW7hNZ9cgpFWx30aTSDC4i5hiOKyZepedXRg\nUcLCp3+oyWJxhEo2Te5Sz/n1xoPKA79wUYNq3BSxaeDWM2/lk+d+Uv0R9vFrYyoUYnZOc3wux41t\nEL+Z2DioE2m1k27I/CKJMT0JuC4MhaFVNSeWEAK7YLMwTpK7u7n5GkUSmkW8WoZFMlDh85s36yG6\nQhUZCEMKq44ukmT7dQt+W2hX0m4DIfEzTejpuZSjjtqClI3HF2GIZ/jvLBEVIbnxs7VQzxA9l/eQ\nPzOPsUvNsS97ef1vF0JEoaYh1vWtq1PxxnJjfPfK76pzNFH8WmGkPONh6bFqmh188LQP8l9X/lfb\nx5ovonYOTvu2wN42OufKV2+FZsQvOqZW/ACWLv3UvMPGhrPzD5MDeO3G13LjcTfOud1lqy7jN6/9\nTdPvglDxa9LkPWElWhaGEUJimnvorG2CFSuUIyTjZKL1NkI6Ddu3Uw2Hz6JFzynEsF3EH6M0JNWg\nyq5SLdSzqeKnK3m++n9p3/u6n2DbDfXODhg+96LP8eY3qsRKYQosWSbhTiKMWC9uUa/4LfA/xZo1\n/91A/KJ2Ds2In2WQmIQjt26kkCggM5LK9gpWr8WJ3zhxj37DXLRxtRAi7DopAE//LYAgCIKD5FHM\njnIgYNrF6pNUbWVkV6TEQsuwLeKDxTyKu0T7xB5gO/uZZkDWmqz7LJ7j942+k0kMTgAfwEqGoRWq\naJaZ15PXDC/8MUvKfPNuj0+sgXu6HTaVBpgNWaOff19gUSgVaRocKQTClziBbKr4zZwjNm7s4p38\njJTVpLSs64KApM4j2RuKX11xF0B0pFjEzQjnC3MfZA9QrCrPdjyso2k7h9nw0pfCRa3TZW1bVTyc\nOeklErBtyuXrR7yVI2Jv8czcqrCoxWyhnm1BP+SpfBYmleLHhCJRthcLNRSK+M1l25oGKrxqjhCr\ndhD2IoMa8VvZo0L9pCGjRa4owfNrzGbt2hrxmzIFycmtfH8YrGk9oC0LQQWvUIJKgektDzHVUR9r\n4iUsdjhQFiZGxiVR8XD8gJ8WUmBoRh4jfsm0iIa21OqhlUphZHcywkNsp8A7jHc0zTkGoKODHNtY\nzXbMJtV6wxvf8ygwAJkKMD7O0A8+R4tI3joEldr4PW7BcRyHVlHCPn5tHGOfQ7OdIfcrkFPFmeqI\nXxMycfTQ0TyxO+6IUr+zWTV1S1qkhHpPvvvd+u9SK9QOgR5TVgZEa79Nc+wD4jcXF0iGIQF6w4Xv\nX8jue5uHaVk6VUF0KCfPVGx+yR6lPtuhb/FzdTyPdIzwb5f8G5sGN7W9z01PruD6f/w16LpbYnAY\neARzRu/SfYHnQvzMvAkPwUI+DBy/x9cQEj+zRWGmVpCSugbucVjSaogC2R/IOJmGAj7zRTXs4Sbn\nOwjl7K0c9hA5L9dIOjXxi2y7XE71adpHiBM/0zCV4leKKX7Ncvw0C0mVOCiJX7NC0gcCFy6LJVX6\nYBkVpBUgRIz4acea1a3mXU8upaMjR7GniJmrjdfZFD/DFnhTYOo8bzOtwscL5xfIrtqzmzHrGxNE\nXW+f35ioJuGxAeRhkpf05/nkE7B0CVh3a+LXwvsp5xnqCfUk0hube0I1JWR1b5IIRizHz3V5Wjev\nDEt7G4ZS/PwRnUhj1Bs652+cZoN4ks2rIb19Dan0LNf/FztY/Rdprj0tCV6xJW0xfAMvkHVGSyvF\nz/PgWJ7BLjRvwHPnNXcynl7HS2lN/JyBudW6VoqfyGYYvH5xfe7TXgirmomJ0sTcG82FqJRoa7zt\nbY2fJZMwOakUvvgcfeml9duFhRFDcrrHxK+rAx5W3kF/pyJR8ejUUPHzZhn6qXTAqUfv/YpqUAv1\nXJBRoWilaikKa5luMttFip8psVDKezanyaFlIYSPl90FlQJTro1fqJ9wTRe2TywmseVkhGvgldUP\n/2m2gONXGxW/jBEpfmBi2za2bSM7XB5hBJey2raVe7Ojgz6e4v3ci+Ee0/I+dKP8dY4/P6OoZY6q\nvv6qmKdjY1/ghhtUUuq119YcUZ6niN8k0GQWu/m0m7n5tFqltsM8h+/RfP6xnARJuzk5C51vpna2\nWYNpguo8c7j2keI3G1LhOTXxS69Pk17f/B0MFT8zHbZKadwm0BZsvMn5fBFWVG4XlrQoxHyk4iMf\nhZ+euU/Um5mIiJ87D8Uvb2GnpxnatXcckM+V+LWr+D3fELQyQOaACvXce+/gTHzi3E/QlZgRXtHd\nDY88UlP89jHq0rOFQUDAzuLOWnGXJqGeYW9Op8JBR/y6u+dMHT0wEGAaFRJ2FSNmh6d1FJjVVR9h\n4Qw4rL9rfW132ZpjSFspfpZ2rIeh4+3Uv5gL+2kYHljcnx+FV9yKTEkymllbaQNLzO4mNUwDwzPm\nFeoZZ+6dL5g7TtqUAR1uffRsOUYe+9KpqPdgSIbSabXQ+7ruf4b6ME0zK/Fs3b9u6/qmXu0IxYwi\nRWJ2X77hGzglq60cvxDdyeZ5RIcPHE4qbIjbwnGROzHHMbtaG7ZQm5uidTBkgIkE/OVfzrrv3sBE\neS8Qv+eIREIRrGq1dh+CQKlYADt0scOQ+EU5fs91kQ+JX0EZWSIQVHZUovOGaIf4PfmE4LOf3jdT\nT6j4JaXk0eseZXXP6kjxa0b8Rnt/DEDJMDA18fNrMWQYVPC8Z6FQYGhgiDWr6vMWLcdgR5CjEjgY\npoFVVgbFXdYovcViA/FLZgSGJk/VKrzrXe8ik8lgdOgKuAi1bSvFL5uNQgtnM0KzGfXu2dX5hYWN\nvGWE1JomE0ao+O2FRWeP0dsLL36xuk/hfNTVFVkGbxpszGmeWaxmUJeiXbeu8fDW+sNJLm/8Yigz\nxKoe1aNyNK8LAuUtDGeeRtJeJH62rVTLOaP/wg3aCBO0EtpJlG6dg2Ue1k2JDtb0rmn3Uvccb3mL\nKqGpIaJG3Pue+EXtHJz2x7/VaTHPvvKzX8McFapb79da8cs4mebtGJ4HqO4B8duXil9/ur+huAsb\nN8J3v0t1Hzigm2HmaaSQbJ/eXmvn0GRgSq3z2FUOOuK3bBl8Yd8GcD0neKMeXicknQqiI62ckkAu\npdJFrB790sVuZ7yC52yKX0j8bK34ybRsONZzxR8E8Vv0uKouKFMyKvErExI7mDu52MpbbVf1BPUA\n56MumSZkvfpYoR9+5n1c/z4lJ49kM/Cdd/Hxv/14zeuoJ3K7oF7irFtvJKZWp8gdocJfnr1zc6vK\n7XXX0MxLHofhG3hFs61QzxCJJa0NHCnhf/5ndoJgpmb3bAoBn/xkrANFnPjtB5Sr843xagNtVgVN\nJJTiVy43t+VCwSjso9sqx69t6ETCYr6W4zd8/TC3XvpUXV0EIdR1zfZcE4nn1Bu3vcvU715KSgYz\ngyrnaBbil/ijPwJ0cRZdNCXsLYZlMVr4Eunko1AokM/30NlVn7doewY7yFLSTiS3ksAH7jBXYhhB\nQ6hnukNGk26lAtdffz2maSLjxM8wZlX8hGOCaBGJEPYxvEFVfzTaScqLoXBOgQ13N1YujHL8DgLe\nF8EwarGaH/84nKUUpMPbaIpcqxLa+J1teaQSjYbhI9c9EjWkTyS04pe35hURgpR7fX7K5+dW/KIf\n2sbaFIZ6OpnW62NqQxc229u9xL2DNWvguutiH+gS6QdxqKfIZeG3v91r1zE2NoY32+TaBCEvmlnx\nGVQ7oyMHjtwLV7b/EZKozuT8mnbvq+Ius2LzZnjwwf2m+M2ENCQ7pneQstV82aqqJ6AKLx1kxO9g\nhu0FJN0AkXRVfw1A6MbuVmH2qMLZqnpatkG+ZES1RsyMOeux5oM/COL3oQ99EFCTd0T8UhKzo7ki\nFUIIWP6vy/EWtj/Rtuwn0gKmCdlUfUWO8894PS885/0AHLneg1Ka0adqla2i0I2E4Hb+jezCVXX7\nZzdlGX7dEGbV5O3vXMgLX9j6/N/+Nlx99dzXaQQGiWmjreIuAMeWj6Xv6tbFPaDNoiJz4IorYrZM\n2M+sSYW2fRHq+caj3sj3rvpe9PcRA0dwxqIz9vp5msFxFHGYmpqdRM1U/PaI+BUKiDCcNhDkTsrx\nx5/prnv+7Sh++xKR4he7qP60UoCKTYxjz1L3oxIbH1GlQcui27sTueNpVV3HcRqMdss1eIDD2Goo\n48Mtu3xpCfzMX62UvVDx09ezdDFcV3iIa6+NeApQq0S7Vj5Zp/hlmdGEuK8P8cJzMVyj+ZjWY78j\nr/J6zfKeVf+KcDASv7jiF6soM5iZu+rhG496Y8uqf+csPod3Hv/OWfcfHtaLcc5sn/j99rfqZT2Q\nxK8NhKGe1sDs/V8PNPan4ieTUjlbmjVabgHlFDCaN29/jnjwwQefU6gnNFf8VCuHg+mlbh9+2Ft0\n3iRl3yp+TbF0KeTzVPfTrd64sdbIHtT6v21626zFXULFz8nmDxG/ecB1BRm3fh3wDtMtxRzZ0MIh\njtkUP8eVvCTZFUX2RFWC9wJr+4MgfoIKgjKGZVDyFfFzBhwsd/aXXwjVC2leCl6HOWvvmZnoz+xm\nYdeuhs9tPblfcanH0ye/nQw/j76LiJ8rqJKqK8EeQgrBWY//HRefMcwsxRU56aTQSJ9L8RMkpmg7\n1NMwWxim+xIXXgj/9E9tWEF7B2knzVFDtXLG/3vN//LnJ/35fjl32CR6x472iJ8lLQSisdpYu5AS\nenujBcNolvjDgSd+EnANAzM2KPvSfZxy1182VfxCIlzRRuRL8ydx9VrtCTFNJak+84wifq7bUAYy\n6Rm8hg9xu6OqbLkllwteDP5kn0rVnRHq6XTYbErt5KMf1aXwNUTC43N8nw+5/xnl+G1nFYGckUPl\nOIjrXtM6zPOKK6BYjCrNSn8vLeD6fq7s34+hfXPBshqqs1TfVmXT0NwFQ9JOmmNHmjeRz3k51SB8\nFoQ5MmZ2HsRvwQI1pvYy8SsUmqs5dejthY99rK3j2WmH0/h/cMYZvO+fX918o4OALNSI3/5R/Axn\nfmua1WnN2xG8LzAb8Xs+I2yGfrCFerY4KRxzTNOeg/sCw8P1haksw2KyPDlrcZcQZuch4jcfdHQs\nIWeN1Bd2jN1fq2C1DM+cLcdPWAJztx9FGZhps26fPcH+sZAPMARVpFAFVELFDyArumblO/Nd2478\n9ZG4Yy55kWfLdVva2ueVp/yqaXifZaqRks+6GEOPUuBdwCsBNc/5fm2xb0b8hBDc/7JljCbatMDn\nKNogA4PkRNBU8Tto5ojh4X1aIvlgQzLZPvEzDRPXdJ87GTcM6OurhcgFzY9zoImfKQSpJgPSEAYV\nQ3V2kbGhHla08311Ez++8A1w2unqS8uqJ379/eq/GDI67t7XPrTjf3M83ApLJ31EImggfkayxSJg\nmhQoYeJHit9PuJmU9SgzM9aEJVoTPx1aGvaWtJy9FFOrr//CFa0r0O53fP3rMKMBdDNP9r5A+B6Z\nWbMuZ2NO7INQz1tuiXWyaAXDgGuuaet4lgXf5DQ6crCj0CJsts2Q9H2L/aj4ZeS8+/KZeXOv5OPs\nKcLp8PeO+D1HA6S39woc5wDYCZs3s2RiF4+//sf7/dSO6UCxtt41myerOrddHCJ+84JtCzIdArG7\nuU00/KZhvEUtDKJZ2jkYtkF1dxUrr/tVpvdecZc/COJnsYMu+07gnLq8rMXGkfC+x6Ly0HuKeEjo\nQGb2FgoR3vCGph93ZEyk72I0ecgNMfst6rL84sh5xO5bsxcqkb4gVawnfvN0tB1CO5iHQTUfxS/r\nZHnDpuZjrS1IWUf8Wil+YTuHA0n8kk0GpsAAofL8krHUzFDxc3b1A1vr1WLTVPG0IfH74Acbjpvq\nVtvb2guX0j0k/3jyHpb0L6zl+Onmm872Mj2XNAmh00RCiulYVc8p6GxUM4Q5C/HTyOpohiO+d8Ss\n27WNeeSI7TesXHnATh3mw8xL8QM1puZKup4nFi+ee5v5IFxXDpby6a2wP0M9rZzFhnua5L7Otk/+\nkOK3L1EJf9g8DZFcbs96oD1nXHQRsreXvvTsKTD7AmG15tBh1ayqZ0XnuJM/RPzmA8eBbEYgnmj+\nrvf/cWOxsRBzNXCvPlHF6VcvrmEbqrjUoVDP9mAyxeL8JwAiTzjAkcvLXLGrSa85jf1i47TodlxI\npzlv+ZlNd5lJ/JopfvOGMXtVTxkYpIqiqdHiHxTNvVrjpptu4sILL5x7w+cZEgnYvr39UM93n/ju\n536yk06Cyy8/6BW/hZ7Hh5vkeIYOlKKEO7s45G68AAAZWElEQVRrYzgkfkFVqzBx4hcqfk/rHL8m\nEFqZd0LiZkpe8/VXc+qu37Aoub2m+IWH7LBY8PYFLa9fMq32CQuUdPc2bOMMOwy8ZnbHki3VObML\nD3Lr/XmKKNQzZ86r4Me+CPXc23AcePWrY0WzDlIIYSBlCsPYP/5rp3d+zMnus6OiMAcSv6/Ez5+t\nyMDBiKEhuOyyA3JqP9bb1DIsjhxsFAV8W2/zfCJ+B0HgQToN3aMSu3f+YbyzFXcxLIPqrmqdk9fM\nmIdCPecFvYrdcvotvOP4dwCQLUiu5CFgQdNdDqRz2zVdPn/R55t+10D89gPxGvnZySx/9MdNV4+D\nIupnFrz5zW8+0JewTzCfUM89xhqV22Xc+3/Vv3Pk+B0o29YyDM5qRtL05U6b9WtFSPyqviZazYhf\nqPg1g95+x2it4tb5PzwfEfyL6sd5zLH1yXxzQDKllKyeHmjRct1MmQy9bq7YPgjevhdfzINJ6TsI\nECp++XPyZI6cRyPqfRDqubdhGCp89OCH3C/5fc8V6TVpVn1j1dwb7mP8vhK/07t0r7znC/E7gIgT\nv9KNzcWO9Ilp+D7Q2QnFYtNtDqERH/gA2LaHZc0/AiVS/Jrl+NmCys5KXQsZmZF7Ra77wyB+P/5x\nFLeSslNRSdvsMVmO+GXrUKiDxtaZwazCec6yYOFLdpC+8rQ9PoVAEMziPrl4i83m0tamN+VgJ37P\nK8wz1LNanZ347W3HXTuK39TUgVP8WkHqCXbarK9MKQ2doxdoFXBmqGcoX7Yy1vX2pdjELQzwq7bq\n4XXTTfO7TqbgW9+a1z6HsP8RjhszZc7ZdqYOzwPF7/kC08ziOG2mVBwghCXYDyRma+fwfMblA/rZ\nHyJ+c8JvQx3wTb3NmjWwbds+vqLfHzSN3G+TPMyq+Okcv3hEiZk2D+X4tY2wq/UMCCFIjLdehFu1\n0jrQkFIZ+4YBQ58+d68c05Y2xWprL88bC5+EnTubfneI+B0YhBNOK+J3xx17Pw1K6rya2XL84OAj\nfp6r3N3Tpu6VpzFZngSgIvRUOFPxg9ZqX2z7SowIOwWfqSf7mU8EYIhkR/2CGxwsL9dB4wU7OHBm\n6kz+6lN/Nf/88OeB4hfHWG7sQF9CSyQSh7F27f8c6Ms46PH7qvjxHHP8/hDRDvGr+DrH7+KL9/HV\nHEKIOXP8ZoR6HlL89jF++UsYnLsd1P7BDKNrRtrQXsFsah9Q3zNr5r4HiW36h4bQfmxF/DZu3Pvn\nbEfxg4OP+AVSVSybNoHYtRcrytlR1Q3Y64hfKJfORfxe8jALT6gAKn84NQY7n1xIzphfg+tjOAO5\n/Lh57XMIBwaWsFj/m/Xz3/F5pvhdtfYqLll5yYG+jJYIC7wcQmv8vlb1nLWR8CHUYU77jhjxO4T9\nhlC9a5a3JyyBP+XXK357Kcfv0BvTAuPjB9H63CTUc68Tv7nY2yHid9BhLsVvX6CdPn5w8BE/oXs4\nFGeEel60XLUnGLT1ohePjRVCGeqzET8pWXPst7jk1FoljOS4SYmueatkJlOI3oO7afYh7CGuuw4W\nLjzQV9E2hBDz6kt7CAcffm8Vv0PEr23MS/E7hP2KI397ZNOWQIatba0Y8ZNpeSjU8w8GM3tV7QPi\n153sZqI8S0uHWUKUDvaqns8rzDPHDw4M8Suc3qLK5UEa6tmnbYRpE2Q1FpZpKmtImE1CPUHd3NmI\nX7XK3S9/ed1zSy7zgEnm3VJuyRK44IL6zw45VX6/8IpXHOgr2Dvo7j7QV3AIbeIQ8TuEQ8Tv4IW3\noLmxJGytBh4q7vIHihtugNe+NvpzXxC/u15+1+zhALP0nzqk+B0YHEjit+pfm1erO1gVv7BdybSE\nZpdWNbRVNF/iVy43fJRclQImVVXP+eD+++e3/SEcMKQ3pHEXHuT9DvYl/vRP4corD/RVHEIb+L0n\nfs+X1gMHEO0Qv3bCQQ82DL52kNTa1IG+jH2CUAWsa+eQPtTO4Q8Hpgm5WtnqfUH8elJzhJgdCvU8\n6HBAQz1byFkHK/HzPfXC/P/27j3Izrq+4/jnc86ezRVCLCTcxBTkGgSD0sKAuioZ0FFIC8OMVg1U\np446lsHaESpq0tqZQMfenHrB29CxeKmOELESyMAypQxQwkWQmGqrJaYQptxGq4SQfPvH85x4sjmb\nTXafc37P5f2a2cnZc5599vf88tvd83m+v+f3bGu3NbvPzWt3tDvZz9nE4DfVVM8+76bmnLRA1s/3\nv+I3wdJvLdWsl5bk3RqLu+xm7rFzdcZPBnARbVV0OtIR5V5RE5naBj8Wd9lnG/5og3bs3LHXbVaP\nrd516UNVdF7S0SErDkndjD0dMvM2dSt+vVM9F7y2mPvyEvwqaBDBb0oEv8H78pf3649Yyopf1YLf\nyTpXGv+4trfWKCaEmId0jR5ZNKZXvPDN/a/4LV0qbdmy21Otgw7QPP1MmuGNpQ+5sIR/0ABUSm2D\nH1M999nJi06ecpuFcxbq7KPOHkJrGmDJkhm/Me53jd/Bb93Le5H92Xche8FQlS34cY1fQS69VFq5\ncp83T1Hxcx6aPEkFqPt0aRZGys3TQml8tV5otxTe/RfyMzpd20YPko49VjrggN2/cKqKnyQdfviE\nbzZPB+hHas/mjAiAtLr5qG738SP4oc66N3XvnepZFH5iKqhswY+KXxopKn7uM02yV1krfjvzWzjs\nHGlrtLXnmYqwpfvu221KtaSpK379tNs6dva1Wrzsqek2t3yY6glUEhU/oHr6TfUsClM9K6jV2nNG\n2sCxuEvppAh+Uylr8OsO0e3t9h4VP0mKyS6YnjVrWvP1W/PnSCO8IQGQFsEPqJ7uVM/eVT2LQvCr\noLJV/JjqmUb3v2PoJwH2oqzBrztGX2yNKLT7stXrtFhzTphkefrvfCe7zcL+mj+/Xm9IqPgBlUTw\nA6pn11TPAVT8kv3E2F5o+xbbm2yvs913uRrbX7K91fYPht3Gsmq3yxX8qPilMXdu9t9SpvfkZb2P\nX/fcxM5WWxPPU6zRifrFoQdM/JLMiSdOr4PrFvwAVFJtgx+reqLGdi3uUrNr/K6QtD4ijpd0m6Qr\nJ9nuK5LOHVqrKqDVSvBLnOBXOvPmlWuap1Tiil8+Rne0R/oGucLD8/z55UrkABqpWxirXfCj4oca\nG+Q1fil/Yi6QdF3++DpJK/ptFBF3SnpmWI2qgiRTPUdGJl2qkeCXxty5BL99Fd3FXdojw7lNLRU/\nACXQamUZqXb3OecG7qixfrdzKErKq4MWRcRWSYqIJ2xPcpENJkoS/D784Wy5+z64xi+NMlb87Ozv\ncNna1a34tdSS+kS/wotz8+YR/AAkl+T9wjBQ8UONDfJ2DgMNfrZvlbS49yll77qu6rM5daN9lOQX\n+VlnTfoSFb80Dj5YOvPM4X7Pye7f19Vqle8efpI0J/95mR1WexhnKupW8WPaKlBJSS4NGQaCH2qs\nO9Wzcqt6RsTyyV7LF2xZHBFbbR8q6ckivueqVat2PR4bG9PY2FgRuy2Vsp3BI/ilceCB0k03pW7F\n7lqt8k3zlKTly7bpK7pXO9VS9LkXYeG5ZulS6YgjCt5pQgQ/oJJqG/y6gY/fTaih6Uz1HB8f1/j4\n+JTbpZzquVbSJZKulrRS0o172db5x5R6g19dlS34TTIDFA1U1uA395jZWqJf6V+XWBvmb9fY5gF/\nwysnW6uqombPTt0CANNQ2+DXxZln1NB0bucwsdi1evXqvtulrJFfLWm57U2S3ihpjSTZPsz2rjqG\n7esl3SXpONuP2b40SWtLpEzB79e/li6/PHUrUBZ2OYPfgjMXaOzqe9UZkR4/6Pk9Xuek8RTe9jZp\nw4bUrQCwn9ptgh9QNa3Rltyx3KrYVM+9iYinJZ3T5/nHJb2l5/O3D7NdVVCm4EchAL3KWvGTJHU6\nmrM95D7vEwh+UxgZkU47LXUrAOynkZGa/50m+KGGPOqBrOgppa34YZrKFPyAXqUOfqOjmrttzyv8\nLr5YuvDCJC0CgIE6+WTpa19L3YoBKuNqYsAMueOBLOwipb3GD9NE8ENZlTr4dTqas32nPOF01ze+\nkaY5ADBorVa21lQtUe1DTc06bJaO+9xxA9k3wa+C2m2CH8qprNf4SZI6HS3fMkdHF7J+MAAAQPHc\nthZdNJjbmxP8KoiKH1LxFIvrnn56+W7evkuno8W/2KnF/9OWvrc2dWsAAACGiuBXQQQ/pDKns/dy\n3pIl2UcpdTrS9u3SsmXSm9+cujUAAABDxeIuFVT7+/KgtF5z1Gu08QMbUzdjejod6YUXUrcCAAAg\nCYJfBZ11lnTSSalbgSayrRMOPiF1M6anG/y4dwMAAGggpnpW0Pvel7oFQAUR/AAAQINR8QPQDEz1\nBAAADUbwA9AMVPwAAECDEfwANEOnI+3YQfADAACNRPAD0AylvcEgAADA4BH8ADRD9+aXVPwAAEAD\nEfwANEO34kfwAwAADUTwA9AMTPUEAAANRvAD0AxU/AAAQIMR/AA0A8EPAAA0GMEPQDMw1RMAADQY\nwQ9AM1DxAwAADUbwA9AMBD8AANBgBD8AzcBUTwAA0GAEPwDNQMUPAAA0GMEPQDPYUrtN8AMAAI1E\n8APQHEz3BAAADUXwA9AcnQ4VPwAA0EgEPwDNMTpK8AMAAI1E8APQHEz1BAAADUXwA9AcTPUEAAAN\nRfAD0BwEPwAA0FAEPwDNwVRPAADQUAQ/AM1BxQ8AADQUwQ9AcxD8AABAQxH8ADQHUz0BAEBDEfwA\nNAcVPwAA0FAEPwDNQfADAAANRfAD0BxM9QQAAA1F8APQHFT8AABAQxH8ADTH6CjBDwAANFKy4Gd7\noe1bbG+yvc72gj7bHGn7Nts/tP2w7T9O0VYANcFUTwAA0FApK35XSFofEcdLuk3SlX22eVHShyJi\nqaQzJX3A9glDbCOAOmGqJwAAaKiUwe8CSdflj6+TtGLiBhHxREQ8mD/+paSNko4YWgsB1AvBDwAA\nNFTK4LcoIrZKWcCTtGhvG9teIumVku4ZeMsA1BNTPQEAQEONDHLntm+VtLj3KUkh6ao+m8de9jNf\n0rckXZZX/ia1atWqXY/HxsY0Nja27w0GUG9U/AAAQM2Mj49rfHx8yu0cMWneGijbGyWNRcRW24dK\nuj0iTuyz3YikmyR9PyL+bop9RqrjAVABl10m/exn0o03pm4JAADAQNhWROxxpjvlVM+1ki7JH6+U\nNNk7sS9LenSq0AcAU2KqJwAAaKiUwe9qScttb5L0RklrJMn2YbZvyh+fJekPJL3B9gO277d9XrIW\nA6g2pnoCAICGGug1fnsTEU9LOqfP849Lekv++N8ktYfcNAB1RfADAAANlbLiBwDDxVRPAADQUAQ/\nAM1BxQ8AADQUwQ9AcxD8AABAQxH8ADTH6GjqFgAAACRB8APQHFT8AABAQxH8ADQHwQ8AADQUwQ9A\nc7CqJwAAaCiCH4DmGB2l4gcAABrJEZG6DYWxHXU6HgAFe+YZafNm6ZRTUrcEAABgIGwrIvY4003w\nAwAAAICamCz4MdUTAAAAAGqO4AcAAAAANUfwAwAAAICaI/gBAAAAQM0R/AAAAACg5gh+AAAAAFBz\nBD8AAAAAqDmCHwAAAADUHMEPAAAAAGqO4AcAAAAANUfwAwAAAICaI/gBAAAAQM0R/AAAAACg5gh+\nAAAAAFBzBD8AAAAAqDmCHwAAAADUHMEPAAAAAGqO4AcAAAAANUfwAwAAAICaI/gBAAAAQM0R/AAA\nAACg5gh+AAAAAFBzBD8AAAAAqDmCHwAAAADUHMEPAAAAAGqO4AcAAAAANUfwAwAAAICaSxb8bC+0\nfYvtTbbX2V7QZ5tZtu+x/YDth21/IkVbAQAAAKDKUlb8rpC0PiKOl3SbpCsnbhAR2yS9PiKWSXql\npDfZ/p3hNrNZxsfHUzehdujT4tCXxaI/i0V/Fov+LBb9WSz6szj05fCkDH4XSLouf3ydpBX9NoqI\nX+UPZ0kakRSDb1pz8cNXPPq0OPRlsejPYtGfxaI/i0V/Fov+LA59OTwpg9+iiNgqSRHxhKRF/Tay\n3bL9gKQnJN0aEf8+xDYCAAAAQOWNDHLntm+VtLj3KWUVu6v6bN63khcROyUts32gpBtsnxQRjxbe\nWAAAAACoKUekmTlpe6OksYjYavtQSbdHxIlTfM3HJP1fRPz1JK8zDRQAAABAo0WEJz430IrfFNZK\nukTS1ZJWSrpx4ga2D5a0PSKesz1H0nJJaybbYb8DBAAAAICmS1nxe4mkb0p6qaT/lnRxRDxr+zBJ\nX4iIt9h+hbKFX1r5xzci4i+TNBgAAAAAKipZ8AMAAAAADEfKVT1RENu/mOL1222f1uf5r9r+ke0f\n2P6i7XbPa39v+8e2H7S9rOf5L9neavsHE/a10PYttjfZXmd7QRHHNmxT9eU+7uNy2z/M++5W2y/t\neW2l7f/I++ldPc9/IO/vHXk1vPv88bbvsv287Q/NtG0plGR8XmT7kbx/9/heVVHC8fl22w/lH3fm\nszQqpSTj8xrbG/Ptv50vZlY5JRyf5+dj8wHb99o+a6btG7aSjM8/7+nHm52ty1A5ZRufPa+fbnu7\n7d+fafuGrQzjs+f1P7G9s18f4zcIfvUw3bLtVyPihIg4RdJcSe+RJNtvknRMRBwr6b2SPtvzNV+R\ndG6ffV0haX1EHC/pNklXTrNNqRVRAr9f0qsi4pWSvi3pr6QsHEv6uKTTJf2upE/4NwH5TklvVDbt\nuddTkj7Y3UdFlWF8Pizp9yTdMc22lEXZxud/SXptRJwq6ZOSvlBA+4atDOPzFklL8/+TH4vfn0WN\nz/URcWpELJP0bklfLKB9w1aG8XlNTz9+T9Inptmm1Mo2PmW7pWztinUFtC2FMoxP2T5S2Toge/Qx\ndkfwqwfbfp3t7/Y88eneM079RMTNPZ/eK+nI/PEFkv4x3+YeSQtsL84/v1PSM312d4Gy6zGV/7ti\nOgdSBrbn2l5v+778LOf5+fMvs/2o7WudVY9utj1r4tdHxB0R8Xz+6d2Sjsgfnyvploh4LiKeVfZm\n77z8ax6KiMeU3fKkd1//GxEbJL04mKMdiuTjMyI2RcSPNaF/q6hk4/PuiHiuz76qpAzjc31+6yIp\n68cjJ25TFSUbn7/q+XS+pJ2qnjKMz1/2fDpP1exHSeUan7kPSvqWpCeLPdKhST4+c38j6U+ndwjN\nQvCrj9A0z7zYHpH0Tknfz586QtLmnk22aOo3dIsiYqskRcQTkhZNpy0l8bykFRHxaklvkPSpntde\nLunTEXGypOckXTjFvt6tmfVrXaQen3VS1vH5np59VU2Zxucfqrr9KJVsfNpe4ez2Ud9V1rdVlHx8\n2v6k7cckvV1ZZauqSjM+bR+et+WzqvZJyaTjMw/vmyPi4em0oWlS3s4B5fEZSXdExF0F7rPKqwZZ\n0hrbr1F2ZvNw290g+9OeXy4bJC2ZdCf2OyS9StLrBtjWJhjE+Kyy0o1P26+XdKmks2e6rwoqbHza\n/qiyWxhdP/NmJVOq8RkRN0i6wfbZyqYjL5/J/iqokPEZEVdJusr2R5RVqVYV0LYUyjQ+/1bSRya0\nrWlmND6d3ertz7T7z3UT+3GfUfGrjxcltXs+n70vX2T745IOjojehUO2KLvNRteR+XN7s7Vbjnd2\n4Xdlpy1Ieoek35K0LL+m4Un9pj+39Wy7Q5OcPLF9jrLrdN4aEdvzp7dIOqpns379WuXAvDepx2dd\nlG582j5F0rWSzo+IyabhlF3y8Wn7EklvVlZRqarSjc9dL2TTxI6u6MIPycdnj+s1dSWsrMo2Pl8t\n6eu2fyrpIkn/0J16WjEpx+cxygL6Q3k/HilpQ0+YxwQEv3oIZRe0nmS7Y/sgZRcS75Xt9yibl/62\nCS+tlfSufJszJD3bncbZ/VLteUZlraRL8scrJd24n8dQJgdKejIiduaVjJf1vDblmSRnq1B9Ttkb\n4ad6XlonabntBc4uBF+uPS/o7te3+/y9S6oM41MTXq+y0oxP20cpW+DgnRHxn9M6mvSSj0/b5ym7\nPuX8iOh981lFZRqfx/Q8Pk3SaEQ8vb8HlFgZxufLez5dIWnj/h5EiZRmfEbE0fnHbyu7zu/9EbF2\nWkeVTtLxGRGPRMShPf34c2WhvqrFh4Ej+FWcsyVwt0XEFknflPSIpK8rW3mqa7KzoJ9Vdi3e3bbv\nt32VJEXEv0j6qe2fSPq8pPf3fL/rJd0l6Tjbj9m+NH/pamW/9DYp+6FfU9QxDkvel89L+idJp9t+\nSNnZwd4/cvtSkbtG2QXw/+xs+esbJCmvhvyFpPsk3SNpdX4RuGx/0PZmZXPZH7J9bf784vz5yyV9\nNO/z+QUc7lCUZXzm1/lslnSGpJtsV+4aqjKOT0kfk/QSSZ/J93XvTI9zmMoyPiV9WtniI7fm+/pM\nYQc5JCUdnxc6W6jjfmV9fPFMj3OYSjQ+1zhbdv9BSedIuqywgxySko7PXpWb7VOi8dkrVP2TuwPF\nDdwrzvapkj4fEWekbkvV0ZfFo0+LQ18Wjz4tDn1ZPPq0OPRl8ejTaqLiV2G236vs7NVHU7el6ujL\n4tGnxaEvi0efFoe+LB59Whz6snj0aXVR8QMAAACAmqPiBwAAAAA1R/ADAAAAgJoj+AEAAABAzRH8\nAAAAAKDmCH4AAAAAUHMEPwAAAACouf8HvuAdzxrVzFsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f72966ef128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "list = ['ACN','BA','BAC','CAT','HP','INTC','KMB','NVDA','UA','XRX']\n",
    "stocks = DataReader(list,  'yahoo', datetime(2010,1,1), datetime(2015,1,1))\n",
    "return_df = pd.DataFrame(np.diff(np.log(stocks['Adj Close']).T).T)\n",
    "return_df.index = stocks['Adj Close'].index[1:]\n",
    "return_df.columns = stocks['Adj Close'].columns\n",
    "plt.figure(figsize=(15,5));\n",
    "x = plt.plot(return_df);\n",
    "plt.ylabel('Returns');\n",
    "plt.legend(iter(x), return_df.columns, ncol=3);\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain the historical covariance-variance matrix as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ACN</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAC</th>\n",
       "      <th>CAT</th>\n",
       "      <th>HP</th>\n",
       "      <th>INTC</th>\n",
       "      <th>KMB</th>\n",
       "      <th>NVDA</th>\n",
       "      <th>UA</th>\n",
       "      <th>XRX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>0.000211</td>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.000134</td>\n",
       "      <td>0.000162</td>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.000044</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000146</td>\n",
       "      <td>0.000142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000236</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000154</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000106</td>\n",
       "      <td>0.000054</td>\n",
       "      <td>0.000159</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000581</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000275</td>\n",
       "      <td>0.000151</td>\n",
       "      <td>0.000061</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>0.000134</td>\n",
       "      <td>0.000154</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000302</td>\n",
       "      <td>0.000250</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000191</td>\n",
       "      <td>0.000187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>0.000162</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000275</td>\n",
       "      <td>0.000250</td>\n",
       "      <td>0.000545</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000256</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>0.000226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.000106</td>\n",
       "      <td>0.000151</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000217</td>\n",
       "      <td>0.000042</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.000044</td>\n",
       "      <td>0.000054</td>\n",
       "      <td>0.000061</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000042</td>\n",
       "      <td>0.000077</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000159</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000256</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0.000576</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>0.000146</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000191</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000612</td>\n",
       "      <td>0.000208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>0.000142</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000226</td>\n",
       "      <td>0.000141</td>\n",
       "      <td>0.000059</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>0.000208</td>\n",
       "      <td>0.000358</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           ACN        BA       BAC       CAT        HP      INTC       KMB  \\\n",
       "ACN   0.000211  0.000115  0.000161  0.000134  0.000162  0.000100  0.000044   \n",
       "BA    0.000115  0.000236  0.000194  0.000154  0.000176  0.000106  0.000054   \n",
       "BAC   0.000161  0.000194  0.000581  0.000234  0.000275  0.000151  0.000061   \n",
       "CAT   0.000134  0.000154  0.000234  0.000302  0.000250  0.000132  0.000052   \n",
       "HP    0.000162  0.000176  0.000275  0.000250  0.000545  0.000150  0.000058   \n",
       "INTC  0.000100  0.000106  0.000151  0.000132  0.000150  0.000217  0.000042   \n",
       "KMB   0.000044  0.000054  0.000061  0.000052  0.000058  0.000042  0.000077   \n",
       "NVDA  0.000150  0.000159  0.000248  0.000204  0.000256  0.000174  0.000045   \n",
       "UA    0.000146  0.000153  0.000230  0.000191  0.000244  0.000132  0.000053   \n",
       "XRX   0.000142  0.000157  0.000234  0.000187  0.000226  0.000141  0.000059   \n",
       "\n",
       "          NVDA        UA       XRX  \n",
       "ACN   0.000150  0.000146  0.000142  \n",
       "BA    0.000159  0.000153  0.000157  \n",
       "BAC   0.000248  0.000230  0.000234  \n",
       "CAT   0.000204  0.000191  0.000187  \n",
       "HP    0.000256  0.000244  0.000226  \n",
       "INTC  0.000174  0.000132  0.000141  \n",
       "KMB   0.000045  0.000053  0.000059  \n",
       "NVDA  0.000576  0.000230  0.000212  \n",
       "UA    0.000230  0.000612  0.000208  \n",
       "XRX   0.000212  0.000208  0.000358  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov = return_df.cov()\n",
    "cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance of a portfolio is calculated as $h^{T}Vh$ where $h$ is a $(K,1)$ vector of portfolio weights. We will assume an equally-weighted portfolio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Portfolio standard deviation is 0.0133005349906\n",
      "Equally weighted standard deviation is 0.018593356928\n"
     ]
    }
   ],
   "source": [
    "h = np.ones(len(list))*(1/len(list))\n",
    "p_std = np.sqrt(np.dot(np.dot(np.transpose(h),cov),h))\n",
    "equal_std = np.dot(h,np.sqrt(np.diag(cov)))\n",
    "print(\"Portfolio standard deviation is \" + str(p_std))\n",
    "print(\"Equally weighted standard deviation is \" + str(equal_std))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our equation implies an average correlation between these stocks of around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.511708472128\n"
     ]
    }
   ],
   "source": [
    "print(np.power(p_std/equal_std,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While standard deviations (defined here as risk) don't add across stocks or time, variance will add across time if returns are uncorrelated from one interval to a next. This would mean variances would grow with the length of the forecast horizon and standard deviations will grow with the square root of the forecast horizon. So a 5% annual active risk is equivalent to a 2.5% active risk over the first quarter or a 10% active risk over four years. The variance (6.25, 25, 100) remains proportional to the length of the horizon.\n",
    "\n",
    "To annualize risk we calculate: \n",
    "\n",
    "$\\sigma_{annual} = \\sqrt{12}\\sigma_{monthly}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relative and Active Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Active Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In practice a manager might be judged on their return and risk *relative* to a benchmark. We define:\n",
    "\n",
    "- Active return $r_{PA} = r_{P} - r_{B}$\n",
    "- Active risk $\\psi_{P} = Std\\left(r_{PA}\\right) = Std\\left(r_{P}-r_{B}\\right)$\n",
    "\n",
    "Where $r_{P}$ is the return of the manager and $r_{B}$ is the return of the benchmark. The active risk is sometimes known as the tracking error of the portfolio as it describes how well the portfolio can track the benchmark.\n",
    "\n",
    "To see an example, go back to our dual JPM/GS example and assume our benchmark is 60 percent GS and 40 percent JPM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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PP/+PLTqOuP7661m2bBkff/wxhw8f5sUXX+SPP/5I87mn9TPbs2cPxYoVI1euXMyfP59J\nkyal+9xQUpEYIpdcAjNmwNNPw2OPwbXX+u0zRERERCQy3HjjjRQuXJgiRYrQr18/JkyYQJUqVQAY\nNmwY559/PnXq1KFo0aJcd911rFix4rj3dfQo24gRI6hevTqXXnopJUqUoFevXinTJY83GpdeR44v\nWLAgI0eO5Pbbb6d48eJMnjyZ5s2bp/t+rr32WsaNG8dNN92U0uymUKFC/2rickSxYsWYMmUKw4cP\np2jRosTGxjJlyhSKFy8O+M6s5557LhUqVOCaa66hV69eNGrU6B/38fTTT9O6dWvKli0L+D0St2zZ\nQqlSpShfvjwtWrQ45mP36NGD5557jtjYWMqUKUOZMmV48MEHiY2NpV69egCMGjWK/Pnzc+6553LV\nVVfRunXrfxWp4Kevvvfee/Ts2ZOSJUvy66+/cuWVV6b5vUrrZ/bKK6/Qr18/ihQpwlNPPcWdd96Z\n7nNDycJhODNUzMyFw/M7dAhefx0GDYJGjWDIEEg1dVlEREREjmJmYTHtTiSrON7/meTrT6q61Ehi\nJsiZEx54wDe3qVABatWC3r0hHdPSRUREREREMpWKxExUqBA8+SQsWgSbN0PlyvDSS5A8xVxERERE\nRCRwKhIDcNZZ8MYb8OWXvsHNhRfCxx+ruY2IiIiIiARPaxLDwJdfQvfufhuNESPg8suDTiQiIiIS\nLK1JFDk5WpMYYRo3hoULoX17uOUWaNkSVq8OOpWIiIiIiGRHKhLDRI4ccM89vrlNdDRceqnfOmPb\ntqCTiYiIiIhIdqLppmHqjz9g4ED48EPo1Qseegjy5Ak6lYiIiEjmqFixImvXrg06hkiWUaFCBdas\nWfOv609luqmKxDC3bJkvEpcsgWeegdtvh0zaQ1NERERERLI4FYmpREKReMSMGb65Ta5cvrnNlVcG\nnUhERERERMKdisRUIqlIBEhKgkmToG9fqF3bjyxWqhR0KhERERERCVfqbhrhoqKgdWuIj/fbZNSr\nB126wJYtQScTEREREZFIoSIxC8qXD3r2hOXL/frEqlX9qOK+fUEnExERERGRrE5FYhZ2xhkwciTM\nmQM//ACVK8PEiX5aqoiIiIiIyKnQmsQI8v33vrlNYqJvbnPNNUEnEhERERGRIKlxTSrZrUgEcA7e\nf99vm1GlCsTGQnR00KlERERERCQIalwjmPm9FJctg2uvhQYNoEMH2LQp6GQiIiIiIpIVqEiMUHny\nQNeukJAAhQvDhRfCoEHw999BJxMRERERkXCmIjHCFSvm1yf++KMvGCtVgtdfh8OHg04mIiIiIiLh\nSGsSs5kffvDNbbZt8+sVmzTxU1RFRERERCTyqHFNKioSj805mDLF77V49tkwfDjUqhV0KhERERER\nyWhh2bjGzJqYWbyZrTCznsc5ZqSZrTSzhWZ20VHXjzOzzWb2S6rji5nZV2aWYGZfmlmRUD+PSGIG\nzZvD4sXQooUfTWzXDtavDzqZiIiIiIgELaRFoplFAS8BjYFooJWZVUl1TFPgPOfcBUBHYPRRN49P\nPje1XsB051xl4BugdwjiR7xcuaBTJ1ixAs48E2rWhL59YdeuoJOJiIiIiEhQQj2SeBmw0jm31jl3\nEJgMNE91THNgAoBzbh5QxMxKJ1/+Hth+jPttDryV/PVbwM0hyJ5tFC4MQ4fCwoWwYYNvbvPKK3Dw\nYNDJREREREQks4W6SCwHrDvq8vrk69I6ZsMxjkmtlHNuM4Bz7g+g1GnmFPz6xDffhC++gA8/hOrV\n4ZNP/BpGERERERHJHnIGHSCDHLeMGThwYMrXMTExxMTEZEKcrK1WLZg2zReLPXrAc8/5bTQuvTTo\nZCIiIiIikpa4uDji4uJO6z5C2t3UzOoAA51zTZIv9wKcc27YUceMAWY4595NvhwPXH1kpNDMKgD/\nc87VOOqc5UCMc26zmZVJPr/qMR5f3U1P06FDfnRxwAC4+mo/LbVixaBTiYiIiIhIeoRjd9MfgPPN\nrIKZ5QZaAlNSHTMFaAspReWOIwViMkv+SH1Ou+Sv7wY+yeDckixnTrjvPkhIgMqVoXZtP7q4/Vgr\nRUVEREREJMsLaZHonDsMdAa+ApYCk51zy82so5l1SD7mc2C1ma0CxgKdjpxvZpOA2UAlM/vdzNon\n3zQMaGRmCUBD4JlQPg+BggX9aOKSJbBzpy8YX3gBEhODTiYiIiIiIhkppNNNg6bppqGzdCk8/rgf\nYXz6abjtNr//ooiIiIiIhI9TmW6qIlFOy9dfQ/fukC+fb25Tr17QiURERERE5IhwXJMoEa5hQ1iw\nAB54AFq29COKK1cGnUpERERERE6VikQ5bVFR0Latn3pauzbUrQsPPwxbtwadTERERERETpaKRMkw\n+fJB796wbBkkJUHVqhAbC/v3B51MRERERETSS0WiZLhSpeCll2DWLJg713dCffttXziKiIiIiEh4\nU+MaCbnvvvPNbQ4d8s1tGjQIOpGIiIiISPag7qapqEgMH87Bf//rp6NGR/tpqFWrBp1KRERERCSy\nqbuphC0zuPNOWL7cjyRefbXviLp5c9DJRERERETkaCoSJVPlyQPdukF8PBQo4EcVn3wS/v476GQi\nIiIiIgIqEiUgxYvDs8/C/PmwdKlvbjN+PBw+HHQyEREREZHsTWsSJSzMm+eb2+zc6ZvbXHdd0IlE\nRERERLI+Na5JRUVi1uIcfPwx9OwJ55wDw4dDjRpBpxIRERERybrUuEayNDNo0cJPP73xRj+aeM89\nsGFD0MlERERERLIPFYkSdnLlgs6dISEBSpf2o4n9+sHu3UEnExERERGJfCoSJWwVKQJPPw0//wxr\n10KlSjBmDBw6FHQyEREREZHIpTWJkmX89BP06AEbN0JsLNxwg5+iKiIiIiIix6bGNamoSIw8zsHU\nqb5YLFXKd0KtXTvoVCIiIiIi4UmNayTimUGzZrBoEfznP77BTevWfjqqiIiIiIicPhWJkiXlzAn3\n3w8rVsB558HFF/utM3bsCDqZiIiIiEjWpiJRsrSCBWHQIFi8GP76CypXhpEjITEx6GQiIiIiIlmT\nikSJCGeeCa+/DtOn+zWL0dHw/vt+DaOIiIiIiKSfGtdIRJo2zTe3yZ8fnn0W6tYNOpGIiIiISOZT\n4xqRZI0awYIF0LEj3HEH3H47rFoVdCoRERERkfCnIlEiVo4ccPfdkJAAF10EderAo4/6tYsiIiIi\nInJsKhIl4uXPD336wLJlcPAgVKkCw4fD/v1BJxMRERERCT8qEiXbKFUKXn4ZvvsOZs3yxeKkSZCU\nFHQyEREREZHwocY1km3NnAndu/sOqCNGwNVXB51IRERERCRjnUrjGhWJkq0lJcG77/rpqDVqwLBh\nfoRRRERERCQSqLupyEmKioJWrWD5cqhf33906gR//hl0MhERERGRYKhIFAHy5vVTT+PjIU8eqFYN\nhgyBvXuDTiYiIiIikrlUJIocpUQJeP55mDcPFi2CypXhzTfh8OGgk4mIiIiIZA6tSRRJw5w5foTx\n77/9thmNGgWdSEREREQk/dS4JhUViZIRnIOPPoKePeG883yxWL160KlERERERE5MjWtEQsAMbrkF\nli6F66+Ha6+Fe++FjRuDTiYiIiIikvFUJIqkU+7c0KULJCTAGWf40cT+/WH37qCTiYiIiIhkHBWJ\nIiepaFF45hn46SdYvdo3t3n1VTh0KOhkIiIiIiKnT2sSRU7TggW+uc3mzX69YrNmfoqqiIiIiEjQ\nwnJNopk1MbN4M1thZj2Pc8xIM1tpZgvNrNaJzjWzmmY2x8x+NrP5ZnZJqJ+HyPHUrg3ffAOxsb5Y\nbNjQjzKKiIiIiGRFIS0SzSwKeAloDEQDrcysSqpjmgLnOecuADoCY9JxbiwwwDl3ETAAGB7K5yFy\nImZwww2weDHccYdvcNOmDfz+e9DJREREREROTqhHEi8DVjrn1jrnDgKTgeapjmkOTABwzs0DiphZ\n6ROcmwQUSf66KLAhtE9DJH1y5oQHHoAVK+Ccc+Cii6BXL9i5M+hkIiIiIiLpE+oisRyw7qjL65Ov\nS88xaZ3bFRhhZr/jRxV7Z2BmkdNWqBAMHgy//AJbtkClSjBqFCQmBp1MRERERCRt4djdND2LKh8E\nHnHOlccXjG+ENpLIqSlXDsaNg2nT4LPPIDoaPvwQ1E9JRERERMJVzhDf/wag/FGXz+LfU0M3AGcf\n45jcaZx7t3PuEQDn3PtmNu54AQYOHJjydUxMDDExMSf1BEQyQo0a8MUX8NVX0KMHPPccjBgBdeoE\nnUxEREREIklcXBxxcXGndR8h3QLDzHIACUBDYBMwH2jlnFt+1DHNgIecc9ebWR3gBedcneOc29I5\nF29mS4FOzrlvzawh8Ixz7tJjPL62wJCwc/gwTJgA/frBFVfA00/DuecGnUpEREREIlHYbYHhnDsM\ndAa+ApYCk51zy82so5l1SD7mc2C1ma0CxgKd0jg3Pvmu7weeNbOfgaeADqF8HiIZKUcOaN/eN7ep\nXh0uuwy6dYNt24JOJiIiIiIS4pHEoGkkUbKCzZth4EB4/33fCbVzZ8iTJ+hUIiIiIhIJwm4kUURO\nrHRpGD0aZs6Eb7+FKlVg8mQ1txERERGRtK1eHZr7VZEoEiaqVoUpU2D8+P9ravPdd0GnEhEREZFw\ns24d3H031Kvnt1vLaCoSRcJMTAzMnw8PPwxt2kCLFpCQEHQqEREREQnarl3Qty/UqgVnn+1fI55x\nRsY/jopEkTAUFQV33QXx8f4doiuv9GsVQ/FOkYiIiIiEt4MH4ZVXoFIl2LgRFi2Cp56CwoVD83gq\nEkXCWN68fl/F5ct9V9SqVWHoUNi7N+hkIiIiIhJqzsHHH8OFF8JHH8GXX/qlSWedFdrHVXdTkSxk\n1Sro3RvmzYMnn/TTUaP0Vo+IiIhIxJk/H7p3h+3bYfhwaNwY7KR6lHqn0t1URaJIFjR7tv+lsW+f\n/6Vx7bVBJxIRERGRjLB6NfTp4zvfDx4M7dr5GWWnSltgiGQT9erBrFl+4fIDD0CzZrBkSdCpRERE\nRORUbd/uBwEuucQvMVqxAu699/QKxFOlIlEkizKD226DZcv89INrroH774dNm4JOJiIiIiLpdeAA\nPP88VK4Mu3fD0qXQvz8UKBBcJhWJIllc7tzwyCP+3aZixfzC5oEDYc+eoJOJiIiIyPE4B//9L1Sr\nBl9/DTNmwNixUKZM0Mm0JlEk4qxZ46ehzpgBgwZB+/aQM2fQqURERETkiFmz/NTSAwdgxAg/IyxU\n1LgmFRWJkp39+KP/5bN1K8TGQtOmp9YRS0REREQyxsqV0KsX/PADDBni98UOdad6Na4RkRSXXOJH\nE4cOhW7doFEj+PnnoFOJiIiIZD9btkCXLlC3Llx6KSQkhPdWZmEaS0QyghncdBMsXgy33uq7oN59\nN6xbF3QyERERkci3bx8884zvVgqwfLkfScyXL9hcJ6IiUSQbyJULHnzQN7cpXx5q1fL77+zaFXQy\nERERkciTlARvvw1VqvippbNnw6hRcMYZQSdLHxWJItlIoULw5JOwaJHfKqNSJXj5ZTh4MOhkIiIi\nIpHhm2/8lNKXXoJ33oEPPvCvubISNa4RycYWLYIePWDtWhg2DJo3V3MbERERkVOxbBk8/rj//Mwz\ncPvt4fG6KiSNa8z+/dTMLM/JPIiIhKeaNeGrr2DkSOjXD66+GubPDzqViIiISNbxxx/QsSPExEDD\nhn7d4R13hEeBeKrSM9103NEXzKwg8Hlo4ohIEBo3hoULoV07aNECWrWC1auDTiUiIiISvv7+2y/j\niY72S3oSEqBrV8gTAcNp6SkS15vZKwBmVgz4Cng7pKlEJNPlyAH33OOb21St6rfQ6N4dtm8POpmI\niIhI+Dh8GN54AypXhqVLfWOaESOgWLGgk2WcExaJzrn+wB4zG4MvEJ91zo0PeTIRCUSBAtC/v/+l\nt3u3/wX4/PNw4EDQyURERESC9eWXcNFFMH68b0gzeTKce27QqTLecRvXmNktR18E+gHzgS8AnHMf\nhjzdaVLjGpHTt3Qp9OwZfouwRURERDLLkWZ/a9ZAbGzWavZ3Ko1r0ioS0xotdM65e07mgYKgIlEk\n43zzjZ8GeFeHAAAgAElEQVR+mju3n1Jx5ZVBJxIREREJrfXrfXO/qVP95w4d/P7TWUmGFomRQEWi\nSMZKSoJJk6BvX6hd248sZrV9f0REREROZNcuP2I4erTvXNqzJxQpEnSqUxOqLTBizaywmeUys6/N\nbIuZtT71mCKSVUVFQevWEB8Pl18O9epBly6wZUvQyURERERO38GDvjCsXBnWrfPd34cOzboF4qlK\nT3fT65xzu4AbgDXA+UCPUIYSkfCWL59/Ry0+3s/Hr1rVjyru2xd0MhEREZGT5xxMmQLVq/uGNJ9/\nDm+9BWefHXSyYKSnSMyZ/Pl64D3n3M4Q5hGRLKRkSRg5EubM8e2fK1eGiRP9tFQRERGRrOCHHyAm\nBvr08R3dp03zHUyzs/QUiZ+aWTxQG/jazM4A9oc2lohkJRdc4N91+3//D15+2e+x+M03QacSERER\nOb41a+Cuu3yn0jZt/NTSpk2zTtfSUEpX4xozKw7sdM4dNrP8QGHn3B8hT3ea1LhGJPM5B++/D716\n+WmosbFQrVrQqURERES8HTv8OsNx4+Dhh+Gxx6BgwaBThU6GNq4xs2uSP98CxADNk79uAtQ7jZwi\nEsHM/F6Ky5ZBw4Z++kbHjvBH2L+tJCIiIpEsMRFefNF3Zt++HZYsgQEDIrtAPFVpTTe9Ovnzjcf4\nuCHEuUQki8uTB7p2hYQEKFQIoqNh8GD4+++gk4mIiEh2cmSWU7Vq8OWXfknMa69B2bJBJwtfaU43\nNbMo4Dbn3H8zL1LG0XRTkfCxerVfED5zpi8W27WDHDmCTiUiIiKRbPZs6N7dd2AfPhyuvTboRJnv\nVKabnnBNopn96Jy75LSSBURFokj4mT/f/7Levt3/sm7cWAvERUREJGOtWuX7I8yfD0895fd5jkpP\ny84IlKFrEo8y3cy6m9nZZlb8yMcpZhSRbO6yy+Dbb/0v7Ecegeuu893ERERERE7XX3/Bo49CnTpQ\nu7Zf9tK2bfYtEE9Ver5ddwIPATOBBckfP4YylIhENjPfbnrJErj5ZmjSBNq3h/Xrg04mIiIiWdH+\n/X6GUpUqcOiQb6DXuzfkyxd0sqzphEWic+6cY3ycmxnhRCSy5coFDz3k3+UrWxZq1oQnnoBdu4JO\nJiIiIllBUhJMmuSLw9mz4fvv4aWXoFSpoJNlbRp4FZHAFSni9ytauBDWrfOtqUePhoMHg04mIiIi\n4Souzi9jeeEFmDgRPvoIKlcOOlVkOGHjmqxMjWtEsqaff4YePfz009hYuPFGNbcRERERLz4eHn8c\nFi+Gp5+GO+7QmsO0hKpxzWkxsyZmFm9mK8ys53GOGWlmK81soZnVSs+5ZtbFzJab2WIzeybUz0NE\nMs9FF8G0afD8837bjJgY+OGHoFOJiIhIkDZvhgcfhPr14eqrfbHYsqUKxFA44bfUvNZm1j/5cnkz\nuyw9d568z+JLQGMgGmhlZlVSHdMUOM85dwHQERhzonPNLAa4EajunKsOjEhPHhHJOsygaVM/BbVN\nG9/o5j//gTVrgk4mIiIimWnvXt8VPTraN6KJj4fHHoM8eYJOFrnSU3e/AtQFWiVf3g28nM77vwxY\n6Zxb65w7CEwGmqc6pjkwAcA5Nw8oYmalT3Dug8AzzrlDyedtTWceEclicuaE++6DFSv8OoPatf1U\n1O3bg04mIiIioXT4MIwf73sVLF4M8+bBc89BiRJBJ4t86SkSL3fOPQTsB3DObQdyp/P+ywHrjrq8\nPvm69ByT1rmVgKvMbK6ZzTCzS9KZR0SyqIIFYcAAv23Gzp2+YHzhBUhMDDqZiIiIZLSvvoKLL4Zx\n4+D99+Hdd+G884JOlX3kTMcxB80sB+AAzOwMICmEmdKzqDInUMw5V8fMLgX+CxxzW46BAwemfB0T\nE0NMTEwGRBSRoJQtC6++Co884hetjxoFzzwDt92m5jYiIiJZ3S+/+L/vv/4Kw4ZBixb6+36y4uLi\niIuLO637OGF3UzO7C7gTuBh4C7gNeMI5994J79ysDjDQOdck+XIvwDnnhh11zBhghnPu3eTL8cDV\nwDnHO9fMpuKnm36bfNsq/IjnX6keX91NRSLc119D9+6QNy+MGAFXXBF0IhERETlZGzZAv37w2Wd+\nz+SOHSF3eucuSppC0t3UOfcO8DjwNLAJuDk9BWKyH4DzzayCmeUGWgJTUh0zBWgLKUXlDufc5hOc\n+zFwTfI5lYBcqQtEEckeGjaEBQugUydo1QpuvRVWrgw6lYiIiKTH7t2+OKxRA0qX9j0IunRRgRi0\n9HQ3HQkUd8697Jx7yTm3PL137pw7DHQGvgKWApOdc8vNrKOZdUg+5nNgdfJo4FigU1rnJt/1G8C5\nZrYYmERykSki2VNUlO+AmpAAl1wCdevCww/DVrW0EhERCUuHDsGYMb4pzZo18NNPfs/DIkWCTiaQ\nvummd+Onm1YGPsIXaz9mQrbTpummItnTn3/C4MEwebJf1/Dww346qoiIiATLOfj0U//3uWxZGD7c\ndy6X0DmV6aYnLBKPuvPiwK34aZ/lk/c1DGsqEkWyt4QE6NXLvzs5dKifjqoNd0VERIKxYIHvI7B5\nsy8OmzVTU5rMEJI1iUc5H6gCVADiT+ZBRESCULkyfPQRvP02vPgiXHopzJgRdCoREZHsZe1aaN0a\nbrgBWrb0HUyvv14FYjhLz5rEWDNbCQwGlgCXOOduDHkyEZEMUr8+zJ0LPXrAvffCjTfC8nSvrhYR\nEZFTsWMH9Ozp9zs87zzflKZjR8iZnk34JFDpGUn8FajrnGvinBvvnNsR6lAiIhktKsq/e7l8OTRo\nAFddBQ884Ke8iIiISMZJTISRI/2Mnr/+gsWLYdAgKFQo6GSSXsctEs2sSvKXPwDlzezioz8yJ56I\nSMbKkwe6dfPrFQsUgOhoePJJ+PvvoJOJiIhkbc7Bhx/6v61Tp8L06fD663DmmUEnk5N13MY1Zvaq\nc66DmR1rBY9zzl0T2minT41rROREfvsNeveGWbN8R9S774YcOYJOJSIikrXMmeOb0vz9t29K06hR\n0InkiJB0NzWzvM65/Se6LhypSBSR9Jo3z/9x27nT/3Fr3DjoRCIiIuHv11/9m61z5sBTT/kGNXqz\nNbyEqrvp7HReJyKSZV1+Ocyc6ddMdOnii8Rffgk6lYiISHj66y/o2tX//axZ0y/j0GycyJHWmsQy\nZlYbyGdmFx21HjEGyJ9pCUVEMokZtGgBS5f6DqiNGkH79rB+fdDJREREwsP+/X7GTZUqcOCA/5vZ\nty/kV3UQUdIaSWwMjADOAp496qMr0Cf00UREgpErF3Tu7Ft1lynj3yF94gnYvTvoZCIiIsFISoJJ\nk3xx+P338N138MorULp00MkkFNKzJvFW59wHmZQnQ2lNoohkhN9/90XitGnQvz/cf7/2eBIRkezj\n22/9un3nYMQIiIkJOpGcjFCtSaxtZkWPepBiZvbUSacTEcmiypeHCRPgs8/gvfegenWYMsX/sRQR\nEYlU8fHQvLlfa9i1K8yfrwIxu0hPkdjUObfjyAXn3HagWegiiYiEp4svhq+/9u+i9u4NDRrAjz8G\nnUpERCRj/fkndOoE9evDlVf6YvE//4Go9FQOEhHS86POYWZ5jlwws3xAnjSOFxGJWGZw/fWwaBHc\ndRfcdJP/vGZN0MlEREROz969MGQIVKsGefL44rBHD8ibN+hkktnSUyS+A3xtZvea2b3ANGBCaGOJ\niIS3nDn92sQVK+CCC6B2bXj8cdix48TnioiIhJPDh+HNN6FyZVi4EObOheefhxIlgk4mQTlh4xoA\nM2sCXJt8cZpz7suQpsogalwjIpll40bf1OZ//4M+feDBByF37qBTiYiIpG3aND9amD+/X05Rr17Q\niSSjnUrjmnQViake5EqglXPuoZM6MQAqEkUksy1e7EcUV66EZ56BW2/1U1RFRETCydF/r4YNg1tu\n0d+rSBWq7qaY2UVmFmtma4AngfhTyCciEvGqV4epU2H0aHjqKbjiCpgzJ+hUIiIi3saNcO+90LAh\nNG0Ky5bpDU35t+MWiWZWycwGmFk8MApYhx95bOCcG5VpCUVEsqBGjWDBAujYEe64A26/HVatCjqV\niIhkV3v2wIAB/s3MkiX9mvqHH9bSCDm2tEYS44FrgBucc1cmF4aHMyeWiEjWlyOH31sqIQFq1YI6\ndeDRR+Gvv4JOJiIi2cWhQ/Dqq77J2qpV/g3MYcOgaNETnyvZV1pF4i3AJmCGmb1mZg0BDUSLiJyk\n/Pmhb19YuhQSE6FKFRg+HPbvDzqZiIhEKufgs8+gRg2YNMk3VnvnHahYMehkkhWcsHGNmRUAmgOt\n8COLE4CPnHNfhT7e6VHjGhEJR/Hx0LOn32tx6FBo2VIbFIuISMb56Sfo3h02bYLYWLjhBq05zM5C\n3t3UzIoBtwN3OucanmS+TKciUUTC2bff+j/i4NuOX311sHlERCRr+/13eOIJv63FgAFw331+X1/J\n3jJlC4ysREWiiIS7pCR4913o3Rtq1vTrRKpUCTqViIhkJTt3+m2XXn0VOnXyW1sUKhR0KgkXIdsC\nQ0REQiMqClq18lNQ69f3H506webNQScTEZFwd/AgvPQSVKrk/24sWgRPPqkCUU6fikQRkTCQN6+f\nehofD3nyQHQ0DBkCe/cGnUxERMKNc/DRR/5vxf/+B199BW+8AWedFXQyiRSabioiEoZ+/RX69IHZ\ns/27wm3a+C01REQke5s3Dx57DHbv9p2yr7su6EQS7rQmMRUViSKS1c2Z40cY9+zRiwERkezst9/8\n+vVZs/ybh23b6s1DSR+tSRQRiTB168L33/sudQ89BE2awOLFQacSEZHMsm0bdOsGl14K1atDQgK0\nb68CUUJLRaKISJgzg1tugaVL4frr4dpr4d57YePGoJOJiEioHDgAzz4LlSvDvn2wbJnf3qJAgaCT\nSXagIlFEJIvInRu6dPHvIp9xhn9HuX9/vy5FREQig3MwebLfDunbb2HmTBg9GkqXDjqZZCcqEkVE\nspiiRf1+WD/9BKtX+3eZX30VDh0KOpmIiJyO776DOnVgxAgYPx6mTIGqVYNOJdmRGteIiGRxCxb4\n5jabN/vmNs2a+SmqIiKSNSQkQK9e/s2/oUP9/rlRGsqRDKLGNSIi2VDt2vDNNxAbCz16QMOG/oWG\niIiEty1boHNnuPJK36gsIQHuuksFogRP/wRFRCKAGdxwA/zyC9x5p/+6TRv4/fegk4mISGr79sHT\nT/uppDlywPLl8PjjkDdv0MlEPBWJIiIRJGdO6NjRvxt9zjlw0UV+CtPOnUEnExGRpCSYMMGvJV+w\nwO+F++KLULJk0MlE/klFoohIBCpUCAYP9iOLW7ZApUowahQkJgadTEQke/r6a788YMwY3730/ffh\ngguCTiVybCEvEs2siZnFm9kKM+t5nGNGmtlKM1toZrXSe66ZPWZmSWZWPJTPQUQkqypXDsaNg2nT\n4LPPIDoaPvzQt1gXEZHQO7LHbceO0LcvzJoF9eoFnUokbSEtEs0sCngJaAxEA63MrEqqY5oC5znn\nLgA6AmPSc66ZnQU0AtaG8jmIiESCGjXgiy/g5Zdh0CCoXx/mzg06lYhI5Nq0CTp0gAYN4LrrYNky\nuO02dZ+WrCHUI4mXASudc2udcweByUDzVMc0ByYAOOfmAUXMrHQ6zn0e6BHi/CIiEeW663zn0/vu\n8y9W7rwTfvst6FQiIpFjzx7/ZtyFF/p9bVesgEcegdy5g04mkn6hLhLLAeuOurw++br0HHPcc83s\nJmCdc25xRgcWEYl0OXJAu3b+hUv16nDZZdCtG2zbFnQyEZGs6/BheP1135QmIcE3pomN9YWiSFYT\njo1r0hyEN7N8QB9gQHrPERGRf8ufH554wq+X2bfPv7B59lk4cCDoZCIiWYdzMHUq1KwJEyfCxx/D\npElQsWLQyUROXc4Q3/8GoPxRl89Kvi71MWcf45jcxzn3PKAisMjMLPn6BWZ2mXPuz9QBBg4cmPJ1\nTEwMMTExp/ZMREQiVOnSMHo0PPww9OwJL73k9++6806tnRERScvChdC9O6xf70cNb7xRvzcleHFx\nccTFxZ3WfZgLYYs7M8sBJAANgU3AfKCVc275Ucc0Ax5yzl1vZnWAF5xzddJzbvL5q4GLnXPbj/H4\nLpTPT0QkEsXF+Rc9UVEwYgRcdVXQiUREwsu6dX4mxpdfwoABfp13rlxBpxI5NjPDOXdSb1+EdLqp\nc+4w0Bn4ClgKTHbOLTezjmbWIfmYz4HVZrYKGAt0SuvcYz0Mmm4qIpJhYmJg/nx49FFo2xZuvtmv\nrxERye527YI+faBWLTj7bL+2+8EHVSBK5AnpSGLQNJIoInJ69u+HUaP8NKo77vDvmJcqFXQqEZHM\ndfAgvPoqPPkkNG3qP591VtCpRNIn7EYSRUQka8ubF3r0gPh4/055tWowdCjs3Rt0MhGR0HPON6K5\n8EL/+csvYfx4FYgS+TSSKCIi6bZqFfTuDfPm+XfS27TxaxdFRCLN/Pl+ffb27TB8ODRurKY0kjWd\nykiiikQRETlps2f7F0/79vkXT9deG3QiEZGMsXq1X3c4cyYMHuz3lc2RI+hUIqdO001FRCRT1KsH\ns2ZB377wwAPQrBksWRJ0KhGRU7d9u3/z65JLoGpV35Tm3ntVIEr2pCJRREROiRncdhssW+anYTVs\nCPffD5s2BZ1MRCT9DhyA55+HypVh925YuhT694cCBYJOJhIcFYkiInJacueGRx7x22QUK+YbPAwc\nCHv2BJ1MROT4nIP//tc35Jo+HWbMgLFjoUyZoJOJBE9rEkVEJEOtWeOnoc6YAYMGQfv2kDNn0KlE\nRP7P99/7qaWJiTBiBFxzTdCJREJHjWtSUZEoIhKcH3/0L8K2bvX7LDZtqs6AIhKsFSugVy//+2nI\nELjrLnVolsinxjUiIhI2LrnEjyYOHQqPPQaNGsHPPwedSkSyoy1boEsX33Trssv89Hht4SNyfPqv\nISIiIWMGN90Eixf7JjfNmkHbtrBuXdDJRCQ72LcPhg3z3UrNYPlyP5KYL1/QyUTCm4pEEREJuZw5\n/VYZK1ZA+fJQqxb07g07dwadTEQiUVISTJwIVarAvHl+b9eRI+GMM4JOJpI1qEgUEZFMU6gQPPUU\nLFoEmzf7lvMvvwwHDwadTEQixTffwKWX+t8t77wDH34IlSoFnUoka1HjGhERCcyiRdCjB6xd66eE\nNW+u5jYicmqWLYPHH/efn3kGbr9dv09EQN1N/0VFoohI1vDll74TatGivh395ZcHnUhEsoo//oAB\nA+Cjj/w09k6dIE+eoFOJhA91NxURkSypcWNYuNDvqXjLLdCyJaxeHXQqEQlnf/8NgwdDdLSfyp6Q\nAF27qkAUyQgqEkVEJCzkyAH33OOb20RH+y00HnsMtm0LOpmIhJPDh2HcOL/OcNky+OEHPwOhWLGg\nk4lEDhWJIiISVgoUgH79YOlSP1JQpQo89xwcOBB0MhEJknPwxRdw0UXw1lt+eunkyXDuuUEnE4k8\nWpMoIiJhbdky6NnTF41PPw133KFmFCLZzcKFvsnV77+ryZXIyVLjmlRUJIqIRI4ZM3xzm5w5/dSy\n+vWDTiQiobZ+vZ9ZMHUq9O8P998PuXIFnUoka1HjGhERiVgNGvi1Rw8/DK1b+wY3K1YEnUpEQmHX\nLnjiCahZE8qW9U1pOnVSgSiSWVQkiohIlhEVBXfdBfHxfpuMevWgSxfYsiXoZCKSEQ4ehNGjfVOa\ndev8NNOhQ6FIkaCTiWQvKhJFRCTLyZfPr1OMj/frkqpW9Ztn79sXdDIRORXOwZQpUL06fPCBn176\n1ltw9tlBJxPJnrQmUUREsryVK6FXL/jxR3jqKT/aGKW3QUWyhB9/9OuNt26F4cOhSRM1pRHJSGpc\nk4qKRBGR7OX77/2LzYMH/YvNa64JOpGIHM+aNdC3r29KNXgwtGvnG1OJSMZS4xoREcnWrrwS5szx\nU1Hvvx9uuMFvoSEi4WPHDnj8cahdGy64wDeguu8+FYgi4URFooiIRBQzv5fismXQsCHExEDHjvDH\nH0EnE8neEhPhxRd9U5rt22HJEhg4EAoWDDqZiKSmIlFERCJSnjzQtatvnV+oEERH+yltf/8ddDKR\n7MU5eP99qFYNvvwSvvkGXnvNb20hIuFJaxJFRCRbWL0a+vSBmTNh0CBo3x5y5Ag6lUhkmz3brxPe\ntw9GjPCj+yKSudS4JhUViSIiktr8+f5F6/btEBurTooiobBqle84PH++7zjcurU6DosERY1rRERE\nTuCyy+Dbb/0L165d4brr/IbdInL6tm6FRx6BOnV8Y5qEBGjbVgWiSFaj/7IiIpLtmEHz5rB4MbRo\n4UcT27WD9euDTiaSNe3f70fmq1aFw4d946jevSFfvqCTicipUJEoIiLZVq5c0KmTb8FfrhzUrOn3\nbdu1K+hkIllDUhK88w5UqeK3n/n+e3jpJShVKuhkInI6VCSKiEi2V7gwDBnip51u2OBb9L/yChw8\nGHQykfAVF+enb7/4IkycCB99BJUrB51KRDKCGteIiIiksnChb26zfj0MGwY33aTmNiJHLF8OPXv6\n6dpPP+33JdWaQ5HwpcY1IiIiGaBWLZg2DZ5/3k8/jYmBH34IOpVIsDZvhgcfhKuugquvhvh4aNlS\nBaJIJNJ/axERkWMwg6ZN/ahimzZw883wn//AmjVBJxPJXHv3+m7A0dG+EU1CAjz2GOTJE3QyEQkV\nFYkiIiJpyJkT7rvPvzCuXNm39e/Rw++zKBLJDh+G8eP9Gt3Fi2HePHjuOShePOhkIhJqKhJFRETS\noWBBGDAAlizx3U8rV4YXXoDExKCTiWS8r76Ciy6CN96ADz6Ad9+F884LOpWIZJaQF4lm1sTM4s1s\nhZn1PM4xI81spZktNLNaJzrXzGLNbHny8R+YWeFQPw8RERGAsmVh7FiYMQOmT4dq1eC990B90iQS\n/PILNG4MnTvDwIEwcyZcfnnQqUQks4W0SDSzKOAloDEQDbQysyqpjmkKnOecuwDoCIxJx7lfAdHO\nuVrASqB3KJ+HiIhIatHR8OmnvmAcOhSuuAJmzw46lcip2bAB7rkHGjWCG2+EpUvhllvU1Vckuwr1\nSOJlwErn3Frn3EFgMtA81THNgQkAzrl5QBEzK53Wuc656c65pOTz5wJnhfh5iIiIHFPDhrBgge/6\n2LIl3HYbrFoVdCqR9Nm9G/r3hxo1oHRpWLHCjyLmyhV0MhEJUqiLxHLAuqMur0++Lj3HpOdcgHuA\nqaedVERE5BRFRfkOqAkJvrFNnTrwyCOwdWvQyUSO7dAhPwpeqRKsXg0//eT3PCxSJOhkIhIOcgYd\n4BjSPbHBzPoCB51zk453zMCBA1O+jomJISYm5nSyiYiIHFe+fNC7N9x7LwweDFWr+k6oDz8MefMG\nnU7Er5397DN4/HE/cvjpp/6NDRGJHHFxccTFxZ3WfZgL4Up7M6sDDHTONUm+3AtwzrlhRx0zBpjh\nnHs3+XI8cDVwTlrnmlk74H7gGufcgeM8vgvl8xMREUlLQgL06uVHaYYOhVattPG4BGfBAujeHTZv\nhuHDoVkzrTkUyQ7MDOfcSf1vD/Wfqh+A882sgpnlBloCU1IdMwVoCylF5Q7n3Oa0zjWzJkAP4Kbj\nFYgiIiJBq1wZPvoI3n4bRo6ESy/1XVFFMtPatdC6tW9I07Kl72B6/fUqEEXk+EJaJDrnDgOd8d1I\nlwKTnXPLzayjmXVIPuZzYLWZrQLGAp3SOjf5rkcBBYFpZvaTmb0SyuchIiJyOurXh7lz/RS/e+/1\nL9aXLz/xeSKnY8cO6NkTLr7Y73GYkAAdO0LOcFxsJCJhJaTTTYOm6aYiIhJuDhyAl1/2TUJuvdXv\nRVemTNCpJJIkJsKYMTBkiH9DYvBgOPPMoFOJSFDCcbqpiIiIHCVPHujWzY/qFCjg91t88kn4+++g\nk0lW5xx88IH/NzV1KkyfDq+/rgJRRE6eRhJFREQC9Ntv0KcPfP+9H/G5+27IkSPoVJLVzJnjm9L8\n/bdvStOoUdCJRCRcnMpI4v9v787DrKjOPI5/f4BIXIIYJ5hoBDcWQQEVoiFGjSJKDLhkWGIMqEnc\n10RBwT0hbsQobnHcUCegiSHiqBE3hERwYW2BBlSiRhE0jo6gGJZ3/jh14abphm7o7mq6f5/n6cdb\np+pUvVWe59Jvn1PnOEk0MzOrA156Kf2S/8kn6Zf8nj3zjsg2B2+8kZZdmTwZfvnLNEGN/8hgZsU8\n3NTMzGwz9c1vwsSJcOWVcPbZKUmcNSvvqKyu+uc/4fzzoVs36NQpDV92L7SZVRcniWZmZnWEBMce\nC7NnpwlHevSAk0+Gd9/NOzKrK5YvhxtugHbt0iRIc+bA0KGw1VZ5R2Zm9YmTRDMzszpmiy3grLNg\n/nxo2RL22QcuvRQ+/TTvyCwvq1fD6NHQvj1MmpR6nW+7LbUPM7Pq5iTRzMysjmrePC2VMX16WhC9\nTZu0tMHKlXlHZrXphRfScOTf/Abuuw8efTQli2ZmNcUT15iZmW0mpk2DCy+E996D666Do49OQ1St\nfiothcGDYebM9MeCfv2gkf+8b2ZV5IlrzMzM6rF9901r340YAUOGwKGHwquv5h2VVbclS+DMM+Gg\ng9JPaSkMGOAE0cxqj79uzMzMNiMS9OqVepdOOAF6907LHrz1Vt6R2ab67DMYPhz22guaNk3J4S9+\nAc2a5R2ZmTU0ThLNzMw2Q02awE9/mia32X331Ms4eDB8/HHekVlVrVoFo0ZB27YwY0ZaM/PGG+Er\nX8k7MjNrqJwkmpmZbca22SatrVhSktbOa9sWbr4Z/vWvvCOzynjmGdhvP7jzTnj44fSz++55R2Vm\nDZ0nrjEzM6tHSkrgoovg9dfhmmvguOM8uU1d9NpraRKiBQvg2mv9/8nMas7GTFzjJNHMzKweevrp\nlGCiH5EAABHNSURBVIRsvXVafP3AA/OOyAAWLYLLLkvLWAwbBqedlt4/NDOrKZ7d1MzMzADo0QOm\nTk3vLfbtm37eeCPvqBqupUvhiiugY0do0SK9S3rOOU4QzaxucpJoZmZWTzVuDIMGwbx50LlzWpD9\nvPPSu4tWO1auTO8btmmThgBPm5bWuNxuu7wjMzOrmJNEMzOzem6rreCSS2DOHFixAtq1g+uvh+XL\n846s/oqAxx+HTp1g9GgYNw4efBBatco7MjOzDfM7iWZmZg1MaSkMGZKWWxg+HPr390Lt1WnatLS+\n4aJFqdfw6KM9KY2Z5ccT15ThJNHMzKxiEyemZCYiTW5z8MF5R7R5e/ttGDo0LWtx+eXwk5+k9SzN\nzPLkiWvMzMys0r7zHZgyBS64IL272KdP6mW0qvnkk9Qz26ULtG6dJqU57TQniGa2+XKSaGZm1oA1\nagQDBsDcuXDQQennjDNgyZK8I6v7VqyAW25Jk9IsWQKzZsHVV8O22+YdmZnZpnGSaGZmZjRrloae\nlpbCllvCXnvBr34Fn32Wd2R1TwSMHQsdOsBjj8H48XDPPbDTTnlHZmZWPfxOopmZma3jjTfg4oth\n8uTUO3biiWlJjYbupZdSMv3JJ2mG2J49847IzGz9PHFNGU4SzczMNs3kySkpWrYsJUU9euQdUT7e\nfDMlzX/7G1x1FQwc6KTZzDYPnrjGzMzMqtWBB8Jf/wqXXpreVTzqKCgpyTuq2vPRR2lin65doWNH\nmDcPTj7ZCaKZ1W9OEs3MzGy9JDj+eJg9OyWJhx+elnd47728I6s5X3wBI0ZA27bw+ecwZ05KlLfe\nOu/IzMxqnpNEMzMzq5SmTeGcc1Jv2g47wN57w2WXwaef5h1Z9YmAMWOgfXt44YW0luTtt0PLlnlH\nZmZWe5wkmpmZWZVstx1ccw1MmwYLF6bett/9DlauzDuyTTNpEhxwANxwQ5qtdNy4lCyamTU0nrjG\nzMzMNsnUqWlym8WL0+Q2vXqlIaqbi/nzYfBgmD49LfsxYEBaP9LMrD7wxDVmZmZW6/bbD557Dq67\nLiWLhx2Wehnrug8+gLPOgu7d0wQ9paVwwglOEM3M/DVoZmZmm0yCo49OM5/26wff+15aW/Htt/OO\nbF2ffw6//nUaStq4McydCxddBM2a5R2ZmVnd4CTRzMzMqk2TJnDqqWkI5667QpcuMGRIWnw+b6tX\nw/33p3cop05Na0DedFOahMfMzNZykmhmZmbVbttt06Lzs2alYZ1t2sDIkbBiRT7xPPss7L8/3HYb\njB4Nf/wj7LlnPrGYmdV1nrjGzMzMatysWWlI55tvpplRjz22dia3mT07Xbe0NF33Bz/YvCbVMTPb\nVBszcY2TRDMzM6s148fDhRemnsYbbkhLTtSERYvg8svhz3+GSy6B00+HLbesmWuZmdVlnt3UzMzM\n6rQjjkgzn55ySurV69cv9S5Wl6VL4coroWNHaN4c5s2D885zgmhmVhVOEs3MzKxWNW4MJ52UJrfZ\ne2/o1g3OPx8++mjjz7lqFdx1V5qUZt68NDHN9ddDixbVF7eZWUNR40mipCMllUqaL2lwBcfcLGmB\npBmSOm+orqQWksZLmifpKUnNa/o+zMzMrHpttRUMG5beG1y+PCV4I0bAF19U/hwR8OST0KkTPPBA\nGl76+99D69Y1FraZWb1Xo0mipEbALUBPoAMwQFK7MsccBeweEXsCpwJ3VKLuEOCZiGgLPAdcXJP3\nYVbdJkyYkHcIZhVy+7Ta1rIl3H47TJwIL7wA7drBmDEpASxWtm3OmAE9eqReyOHDYcIE6Nq11sI2\n+zf+7rT6pKZ7ErsBCyLirYhYAYwB+pQ5pg9wP0BEvAQ0l9RyA3X7AKOyz6OAY2r2Nsyql/8hsbrM\n7dPy0r49jBsH9967dlKbSZPW7i+0zXfegYED4cgj4fjjoaQEevf2rKWWL393Wn1S00niTsA7Rdv/\nyMoqc8z66raMiMUAEfE+8NVqjNnMzMxydMgh8PLLcO65cOKJabmM+fPTMNShQ6FzZ/jGN1LZ6afD\nFlvkHbGZWf3SJO8AyrExfwf0OhdmZmb1SKNG8MMfwnHHwciR0L07LFsGffvCzJmw8855R2hmVn/V\n6DqJkg4AroiII7PtIUBExLVFx9wBPB8RD2XbpcDBwK4V1ZU0FzgkIhZL2jGr376c6zt5NDMzMzOz\nBq2q6yTWdE/iK8AekloBi4D+wIAyx4wDzgQeypLKj7Pk78P11B0HDAKuBQYCj5Z38ao+DDMzMzMz\ns4auRpPEiFgl6SxgPOn9x7sjYq6kU9PuuDMinpDUS9LrwDLgpPXVzU59LfCwpJOBt4C+NXkfZmZm\nZmZmDUWNDjc1MzMzMzOzzUtNz26aC0lnS5orqUTSNUXlF0takO07Is8YrWGT9HNJqyVtX1Tm9mm5\nkXRd1vZmSHpE0peL9rltWu4kHSmpVNJ8SYPzjscaLkk7S3pO0uzsd81zsvIWksZLmifpKUnN847V\nGiZJjSRNkzQu265y26x3SaKkQ4DvA3tHxN7ADVl5e9Kw1PbAUcBtkldUstonaWegB2modKHM7dPy\nNh7oEBGdgQXAxQCS9sJt03ImqRFwC9AT6AAMkNQu36isAVsJXBARHYADgTOz9jgEeCYi2gLPkX2P\nmuXgXGBO0XaV22a9SxKB04FrImIlQER8mJX3AcZExMqI+Dvpl6Bu+YRoDdyNwIVlytw+LVcR8UxE\nrM42pwCFBQZ647Zp+esGLIiItyJiBTCG9L1pVusi4v2ImJF9XgrMJX1n9gFGZYeNAo7JJ0JryLLO\niF7AXUXFVW6b9TFJbAN8R9IUSc9L2i8r3wl4p+i4d7Mys1ojqTfwTkSUlNnl9ml1ycnAE9lnt02r\nC8q2w3/gdmh1gKTWQGfSH9daRsRiSIkk8NX8IrMGrNAZUTzxTJXbZk0vgVEjJD0NtCwuIj2IYaR7\nahERB0jqCvwB2K32o7SGagPt8xLSUFOzWreetjk0Ih7LjhkKrIiI0TmEaGa22ZC0DfBH4NyIWFrO\n+tyeHdJqlaTvAYsjYkb2Cl5FNtg2N8skMSIq/CVb0mnAn7LjXpG0StJXSH/93qXo0J2zMrNqVVH7\nlNQRaA3MzN7p2hmYJqkbbp9WC9b33QkgaRBpiMp3i4rfBb5RtO22aXnwd6TVKZKakBLEByKisF73\nYkkts/W+dwSW5BehNVDdgd6SegFfAraV9ADwflXbZn0cbvpnsl9wJLUBmkbEP4FxQD9JTSXtCuwB\nvJxfmNbQRMRrEbFjROwWEbuShkt1iYgluH1aziQdSRqe0jsivijaNQ7o77ZpOXsF2ENSK0lNgf6k\ntmmWl3uAORFxU1HZOGBQ9nkg8GjZSmY1KSIuiYhdImI30vfkcxFxIvAYVWybm2VP4gbcC9wjqQT4\nAvgxQETMkfQwaaafFcAZ4UUiLV9BGu7n9ml1wUigKfB0NnnplIg4w23T6oKIWCXpLNIsvI2AuyNi\nbs5hWQMlqTtwAlAiaTrp3/NLgGuBhyWdTJrBvG9+UZr9m2uoYtuU/603MzMzMzOzgvo43NTMzMzM\nzMw2kpNEMzMzMzMzW8NJopmZmZmZma3hJNHMzMzMzMzWcJJoZmZmZmZmazhJNDMzMzMzszWcJJqZ\n2RqSjpG0WlKbShw7UNKORdt3SmpXDTE0ljRc0nxJ07KfiytR79MKyu+VdNymxlVZktpIel7SdEmz\nJd2xked5XtK+G1l3oaTti7YPlvTYBuoMlDSygn2fZv/9WrZuZrWQ1EfSsOzz2ZJKJP2PpCZZWXdJ\nI4qO30HSk9V1fTMzK5+TRDMzK9YfmAQMqMSxg4CdChsR8bOIKK2GGH4F7Ah0iIh9gYOALSpRr64s\n/HszMCIiukREB6DcxKuGlfcsKvN8KjomACJiUURU5wLhFwG3Zp9/GBF7A5OBnlnZpcDVa4KI+BB4\nT9KB1RiDmZmV4STRzMwAkLQ10B04hTJJoqTBkmZlvWPDJR0P7A88mPX0NSv0fEk6VdJ1RXUHSro5\n+3yCpJeyOrdLUpnrfAn4CXBWRKwAiIhlEXFV0TEXZD1OsySdW8G93CJprqTxwFeLyhdm8U+X9LKk\nLpL+ImmBpFMLz0HSM5JelTRTUu+svJWkOVmP6WtZvS3LufyOwLuFjYiYXVR/YnbeVyUdUNHzLTpX\n3+x5lUrqnh27V9EznCFp9/IeQUXbklpIGpvd24uSOpbz/Fpn+2ZKurqovJWkkuzzQEmPSHpS0jxJ\n1xYdd0pWNiV7XjeXc409geUR8b9FZU2BrYAVkn4EPBERH5ep+ijwo3Lu2czMqomTRDMzK+gD/CUi\nXgc+lNQFQNKRwPeBrhHRBbguIh4BXiH1/uwbEcuLzvMIcGzRdj9gTDYUtR/wrayHcDVwQpkY9gDe\niojPygswG345EOgKHAj8VFKnMsccB+wZEe2zY79V5jR/z+7jr8C9wHHZua7M9i8HjomI/YHvAiOK\n6u4BjIyIjsAnwPHlhPlb4HlJj0s6T1LzrHwxcHh23v5kPYySjqLM8y06V+OI+CZwPnBFVnYa8Nvs\nGe4P/KO8Z5XFME3SdOC/isqvBKZFRCdgKPBAOXVvAm7NjllUZl9xb2Mn4D+BfYB+knaS9DVgGNCN\n9EeHioYgdwemFW3fCkwBdgZeJPVU37puNV4l9S6bmVkNcZJoZmYFA4Ax2eeHWNubeDhwb0R8AVDU\nsyPW7bEqDAl8Q1K37L24thHxInAYsC/wSpa4fBfYbX0BSRqU9a69JWkn4NvA2IhYHhHLgD+xbsJw\nEDA6i2UR8FyZ/YV380qAlyLisyzm5ZK+nN3TryXNBJ4Bvi6p0Bu5MCJKss9Tgdbl3P99pMToD8Ah\nwGRJWwBNgbskzcr2tc+qHEb5z5fs/grXapV9ngwMlXQh0LpQrxyHZAl8F1LvbMG3yRLDiHge2F7S\nNmXqdmdtWygviSx4NiKWZjHMzmLsBkyIiE8iYlV2r+X5GvBBYSMiHsziHUhKim8Gekn6Q/F7icCS\nrK6ZmdWQJnkHYGZm+ZPUgpS0dZQUQGNSj9FFG3nKh0i9hqXA2MJlgFERMXQ99V4HdpG0dTbM9D7g\nviyxaryRsZRVSKpWF30ubDch9W7uAHSJiNWSFgLNytQFWFVU/m8i4n2gEHsJ0BHoDbwfEftIagx8\nXoVYV2WxERGjJU0BjgaekPSziJhQTt11EvgKlHdcsLbHcH3nKe/5VfbanwNfXicY6eukXtWrJU0A\nDgUulXRYRDxLeuaVeXZmZraR3JNoZmaQhgzeHxG7RsRuEdEKWCjp28DTwEnZ+4KFhBLg/yjnl/zM\nWNLw1f6s7ZF6FviBpP8onEfSLsWVIuJz4G7glsL7fllC1TQ7ZBJwjNI7kFuThrVOzPYVEpOJpKGP\njbKhj4dW8hkU6jcHlmQJ4qGs7cErPqbik0g9tXZ2zh2B7UnvKDZn7dDNH7M26a3o+ZYbn6RdI2Jh\nRIwkvZ+3TyXvr2AS2Tt9kg4BPoiIpWWO+Rtre5LLDgnekFeA70hqnj2H8obkAswF9iyn/CrShDWw\nNglfTXpXEaAN8FoVYzIzsypwkmhmZpB6/caWKfsTMCAiniIN0XxV0jTg59n+UcAd2XtvzSh6Vy0b\nMjkX2CUiXs3K5pLeVRufDeUcT5rkpaxhwPvAa5KmAi9k13ovIqaTeuheIQ27vDMiZhUum11nLKlH\ncnZ27ItF517fDJ+Fff8NdM1i/FF2H5WpX3BEFvt04EngFxGxBLgNGJSVtwGWZfE+BYxj3edb9lqF\n7b7ZxDnTgQ7A/eu5l/JcAeyX3d9wUsJa1nnAmdkxlR3aWXj+72XnfZmUkC4kvb9Z1kSgc3GBpM7p\nFDEzKxpNGhb8LeAvWdmhwOOVjMnMzDaCIurKjOFmZmZWHxSGC2e9wGOBuyPi0XKOuxF4LCLKvje6\nvnNPAPpERHmJp5mZVQP3JJqZmVl1uyLr6SwB3iwvQcwMZ+0w0g2StAPwGyeIZmY1yz2JZmZmZmZm\ntoZ7Es3MzMzMzGwNJ4lmZmZmZma2hpNEMzMzMzMzW8NJopmZmZmZma3hJNHMzMzMzMzWcJJoZmZm\nZmZma/w/OzqfMBhtfbMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7296657198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "benchmark_weight = 0.6\n",
    "portfolio_risk = portfolio_std(gs_std,jpm_std,corr,benchmark_weight)\n",
    "benchmark_returns = benchmark_weight*gs_returns.values + (1-benchmark_weight)*jpm_returns.values\n",
    "active_risks = [(((h/100)*gs_returns.values+(1-(h/100))*jpm_returns.values) - benchmark_returns).std() \n",
    "                 for h in range(0,100)]\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.plot(range(-60,40),active_risks,label=\"Benchmark: 60% Goldman\")\n",
    "plt.xlabel(\"Active Goldman Sachs Holding (%)\");\n",
    "plt.ylabel(\"Active risk\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Residual Risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Residual risk is the risk of return orthogonal to the systematic return. The residual risk of portfolio $P$ relative to portfolio $B$ is denoted by $\\omega_{P}$ and defined by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\omega_{P} = \\sqrt{\\sigma_{P}^{2} - \\beta_{P}^{2}\\sigma_{B}^{2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This comes from the model $r_{P} = \\beta_{P}r_{B} + \\theta_{B}$ and the lack of correlation between the residual and market returns. Let's calculate the $\\beta$s for the return data we have. We first need to convert to excess returns by subtracting the risk-free rate and we need to load the benchmark (S&P500):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "one_mon = DataReader('DGS1MO', 'fred',datetime(2006,1,1), datetime(2015,1,1))\n",
    "one_day = np.log(1+one_mon)/365\n",
    "\n",
    "spy = DataReader('SPY',  'yahoo', datetime(2006,1,1), datetime(2015,1,1))\n",
    "spy_returns = pd.DataFrame(np.diff(np.log(spy['Adj Close'].values)))\n",
    "spy_returns.index = spy.index.values[1:spy.index.values.shape[0]]\n",
    "spy_returns.columns = ['S&P500']\n",
    "\n",
    "excess_returns = pd.concat([one_day,return_df,spy_returns],axis=1).dropna()\n",
    "excess_returns = excess_returns.subtract(excess_returns['DGS1MO'].values,axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we calculate the betas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Betas</th>\n",
       "      <th>Total Risk</th>\n",
       "      <th>Residual Risk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>1.001259</td>\n",
       "      <td>0.014493</td>\n",
       "      <td>0.010495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>1.126470</td>\n",
       "      <td>0.015354</td>\n",
       "      <td>0.010454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>1.746524</td>\n",
       "      <td>0.024121</td>\n",
       "      <td>0.016669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>1.359794</td>\n",
       "      <td>0.017348</td>\n",
       "      <td>0.010802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>1.603451</td>\n",
       "      <td>0.023260</td>\n",
       "      <td>0.016876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.971528</td>\n",
       "      <td>0.014755</td>\n",
       "      <td>0.011119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.470336</td>\n",
       "      <td>0.008792</td>\n",
       "      <td>0.007434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>1.424608</td>\n",
       "      <td>0.024022</td>\n",
       "      <td>0.019360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>1.377694</td>\n",
       "      <td>0.024729</td>\n",
       "      <td>0.020552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>1.350762</td>\n",
       "      <td>0.018959</td>\n",
       "      <td>0.013327</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Betas  Total Risk  Residual Risk\n",
       "ACN   1.001259    0.014493       0.010495\n",
       "BA    1.126470    0.015354       0.010454\n",
       "BAC   1.746524    0.024121       0.016669\n",
       "CAT   1.359794    0.017348       0.010802\n",
       "HP    1.603451    0.023260       0.016876\n",
       "INTC  0.971528    0.014755       0.011119\n",
       "KMB   0.470336    0.008792       0.007434\n",
       "NVDA  1.424608    0.024022       0.019360\n",
       "UA    1.377694    0.024729       0.020552\n",
       "XRX   1.350762    0.018959       0.013327"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "def get_beta(stock,market):\n",
    "    exog = sm.add_constant(market, prepend=True)\n",
    "    mod = sm.OLS(stock, exog)\n",
    "    return mod.fit().params[1] \n",
    "\n",
    "def get_residual_risk(benchmark_std,stock_beta,stock_std):\n",
    "    return np.sqrt(np.power(stock_std,2) - np.power(stock_beta*benchmark_std,2))\n",
    "\n",
    "def get_risk_measures(excess_returns):\n",
    "    tickers,betas,total_risk,residual_risk = ([] for i in range(4))\n",
    "    tickers = []\n",
    "    for stock in excess_returns.columns:\n",
    "        market_risk = excess_returns['S&P500'].std()\n",
    "        if stock not in ['DGS1MO','S&P500']:\n",
    "            beta = get_beta(excess_returns[stock],excess_returns['S&P500'])\n",
    "            stock_risk = excess_returns[stock].std()\n",
    "            total_risk.append(stock_risk)\n",
    "            residual_risk.append(get_residual_risk(market_risk,beta,stock_risk))\n",
    "            betas.append(beta)\n",
    "            tickers.append(stock)\n",
    "    results = pd.DataFrame(np.array([betas,total_risk,residual_risk]).T)\n",
    "    results.index = tickers\n",
    "    results.columns = ['Betas','Total Risk','Residual Risk']\n",
    "    return results\n",
    "\n",
    "risk_summary = get_risk_measures(excess_returns)\n",
    "risk_summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance in the book measures the cost of risk. The cost of risk equates risk to an equivalent loss in expected return. The book associates the cost of risk with active or residual return. An example for a risk aversion coefficient of 0.1 is shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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RJElSW2bMgPPOgzPOgH794Gtfg7//HVZaqezKJNWbavrk7dRqvw+wN/AgYMiT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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7294485f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "risk_aversion = 0.1\n",
    "active_risk = np.array([i/100 for i in range(0,600)])\n",
    "return_tradeoff = risk_aversion*np.power(active_risk,2)\n",
    "plt.figure(figsize=(15,5));\n",
    "plt.plot(active_risk,return_tradeoff);\n",
    "plt.title(\"The Cost of Risk\");\n",
    "plt.xlabel(\"Active Risk (%)\");\n",
    "plt.ylabel(\"Return Tradeoff (%)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So a 4% active risk produces a 1.6% loss in expected return (given this investor's preferences over risk)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elementary Risk Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a significant problem in calculating portfolio risk. As we increase the size of the portfolio, we the number of covariance estimates we require increases exponentially; specifically, we need $N(N-1)/2$ correlations. The 505 stocks on the S&P500 are highlighted (127,260 covariances are needed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iR2bOAS6OiL8Dx9Y3NEmSJKnxMostQ44/vqhWnnYa7LwzRJu2k5e6ltYklm9H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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f727ffd7c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stock_no = np.array([i for i in range(0,600)])\n",
    "correlations = np.array([i*(i-1)/2 for i in range(0,600)])\n",
    "plt.figure(figsize=(15,5));\n",
    "plt.plot(stock_no,correlations);\n",
    "plt.title(\"So Many Covariances\");\n",
    "plt.xlabel(\"Stocks\");\n",
    "plt.ylabel(\"Number of Covariances\");\n",
    "plt.plot([505, 505], [0, 500000], 'k-', lw=2);\n",
    "plt.ylim(0,180000);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a challenge to estimate so many quantities accurately - since we will perform portfolio optimization, even if only a small percentage of the estimates are wrong, they will severely impact the choice.\n",
    "\n",
    "** The goal of a risk model is to accurately and efficiently forecast the covariance matrix**\n",
    "\n",
    "There are three elementary stock risk models:\n",
    "- The single-factor diagonal model\n",
    "- The commmon correlation model\n",
    "- The historical returns model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Single-Factor Diagonal Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The single-factor model of risk was a precursor to CAPM but both models are distinct. It analyses returns as:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ r_{n} = \\beta_{n}r_{M} + \\theta_{n}  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where $\\beta_{n}$ is stock *n*'s beta and $\\theta_{n}$ is the residual return. The single-factor risk model assumes that the residual returns $\\theta_{n}$  are uncorrelated and therefore:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ Cov(r_{n},r_{m}) = \\beta_{n}\\beta_{m}\\sigma^{2}_{M} $$\n",
    "$$ \\sigma^{2}_{n} = \\beta^{2}_{n}\\sigma^{2}_{M} + \\omega^{2}_{n}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the covariance matrix for the stocks we had earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ACN</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAC</th>\n",
       "      <th>CAT</th>\n",
       "      <th>HP</th>\n",
       "      <th>INTC</th>\n",
       "      <th>KMB</th>\n",
       "      <th>NVDA</th>\n",
       "      <th>UA</th>\n",
       "      <th>XRX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>0.000210</td>\n",
       "      <td>0.000112</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000136</td>\n",
       "      <td>0.000160</td>\n",
       "      <td>0.000097</td>\n",
       "      <td>0.000047</td>\n",
       "      <td>0.000142</td>\n",
       "      <td>0.000137</td>\n",
       "      <td>0.000135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.000112</td>\n",
       "      <td>0.000236</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000180</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000160</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.000152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.000237</td>\n",
       "      <td>0.000279</td>\n",
       "      <td>0.000169</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000240</td>\n",
       "      <td>0.000235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>0.000136</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000237</td>\n",
       "      <td>0.000301</td>\n",
       "      <td>0.000217</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000064</td>\n",
       "      <td>0.000193</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>0.000160</td>\n",
       "      <td>0.000180</td>\n",
       "      <td>0.000279</td>\n",
       "      <td>0.000217</td>\n",
       "      <td>0.000541</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.000075</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>0.000220</td>\n",
       "      <td>0.000216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.000097</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000169</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.000218</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0.000138</td>\n",
       "      <td>0.000133</td>\n",
       "      <td>0.000131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.000047</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>0.000064</td>\n",
       "      <td>0.000075</td>\n",
       "      <td>0.000046</td>\n",
       "      <td>0.000077</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.000063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>0.000142</td>\n",
       "      <td>0.000160</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000193</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>0.000138</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000577</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.000192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>0.000137</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.000240</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000220</td>\n",
       "      <td>0.000133</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.000612</td>\n",
       "      <td>0.000185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>0.000135</td>\n",
       "      <td>0.000152</td>\n",
       "      <td>0.000235</td>\n",
       "      <td>0.000183</td>\n",
       "      <td>0.000216</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.000192</td>\n",
       "      <td>0.000185</td>\n",
       "      <td>0.000359</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           ACN        BA       BAC       CAT        HP      INTC       KMB  \\\n",
       "ACN   0.000210  0.000112  0.000174  0.000136  0.000160  0.000097  0.000047   \n",
       "BA    0.000112  0.000236  0.000196  0.000153  0.000180  0.000109  0.000053   \n",
       "BAC   0.000174  0.000196  0.000582  0.000237  0.000279  0.000169  0.000082   \n",
       "CAT   0.000136  0.000153  0.000237  0.000301  0.000217  0.000132  0.000064   \n",
       "HP    0.000160  0.000180  0.000279  0.000217  0.000541  0.000155  0.000075   \n",
       "INTC  0.000097  0.000109  0.000169  0.000132  0.000155  0.000218  0.000046   \n",
       "KMB   0.000047  0.000053  0.000082  0.000064  0.000075  0.000046  0.000077   \n",
       "NVDA  0.000142  0.000160  0.000248  0.000193  0.000228  0.000138  0.000067   \n",
       "UA    0.000137  0.000155  0.000240  0.000187  0.000220  0.000133  0.000065   \n",
       "XRX   0.000135  0.000152  0.000235  0.000183  0.000216  0.000131  0.000063   \n",
       "\n",
       "          NVDA        UA       XRX  \n",
       "ACN   0.000142  0.000137  0.000135  \n",
       "BA    0.000160  0.000155  0.000152  \n",
       "BAC   0.000248  0.000240  0.000235  \n",
       "CAT   0.000193  0.000187  0.000183  \n",
       "HP    0.000228  0.000220  0.000216  \n",
       "INTC  0.000138  0.000133  0.000131  \n",
       "KMB   0.000067  0.000065  0.000063  \n",
       "NVDA  0.000577  0.000196  0.000192  \n",
       "UA    0.000196  0.000612  0.000185  \n",
       "XRX   0.000192  0.000185  0.000359  "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas = risk_summary['Betas'].values\n",
    "market_risk = excess_returns['S&P500'].std()\n",
    "residual_risks = risk_summary['Residual Risk'].values\n",
    "\n",
    "def single_factor_covariance(betas,market_risk,residual_risks,tickers=None):\n",
    "    beta_vector = np.array([betas])\n",
    "    cov_matrix = np.dot(beta_vector.T,beta_vector)\n",
    "    cov_matrix = cov_matrix*np.power(market_risk,2)\n",
    "    cov_matrix[np.diag_indices_from(cov_matrix)] = np.diag(cov_matrix)+np.power(residual_risks,2)\n",
    "    results = pd.DataFrame(cov_matrix)\n",
    "    \n",
    "    if tickers is not None:\n",
    "        results.index = tickers\n",
    "        results.columns = tickers\n",
    "        \n",
    "    return results\n",
    "\n",
    "sf_covmatrix = single_factor_covariance(betas,market_risk,residual_risks,risk_summary.index)\n",
    "sf_covmatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem with this model is that residual returns *are* correlated. The market-weighted average of residual returns is exactly zero:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\sum_{n}h_{M}(n)\\theta_{n} = 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a result the residual correlation between stocks must be in general negative. To se this assume there are two stocks with equal market capitalization. The equation above implies $\\theta_{2} = -\\theta_{1}$ so there is 100% negative correlation. As the number of stocks $n$ increases the average negative correlation decreases towards 0. In practice, we should expect positive residual correlation among stocks in the same industry. The reasons why this simple model may still be attractive:\n",
    "\n",
    "- It isolates market and residual risk\n",
    "- It gives a conservative estimate of the residual covariance between stocks (0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Common Correlation Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model requires an estimate of each stock's risk $\\sigma_{n}$ and an average stock correlation $\\rho$. This implies that the covariance between any 2 stocks is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ Cov(r_{n},r_{m}) = \\sigma_{m}\\sigma_{n}\\rho $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's just use the risk estimates from the historical covariance matrix we estimated earlier along with the implied figure we had for average correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ACN</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAC</th>\n",
       "      <th>CAT</th>\n",
       "      <th>HP</th>\n",
       "      <th>INTC</th>\n",
       "      <th>KMB</th>\n",
       "      <th>NVDA</th>\n",
       "      <th>UA</th>\n",
       "      <th>XRX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>0.000210</td>\n",
       "      <td>0.000114</td>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000173</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.000178</td>\n",
       "      <td>0.000183</td>\n",
       "      <td>0.000141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.000114</td>\n",
       "      <td>0.000236</td>\n",
       "      <td>0.000190</td>\n",
       "      <td>0.000136</td>\n",
       "      <td>0.000183</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>0.000189</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000190</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.000214</td>\n",
       "      <td>0.000287</td>\n",
       "      <td>0.000182</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000297</td>\n",
       "      <td>0.000305</td>\n",
       "      <td>0.000234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000136</td>\n",
       "      <td>0.000214</td>\n",
       "      <td>0.000301</td>\n",
       "      <td>0.000206</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>0.000078</td>\n",
       "      <td>0.000213</td>\n",
       "      <td>0.000220</td>\n",
       "      <td>0.000168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>0.000173</td>\n",
       "      <td>0.000183</td>\n",
       "      <td>0.000287</td>\n",
       "      <td>0.000206</td>\n",
       "      <td>0.000541</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000105</td>\n",
       "      <td>0.000286</td>\n",
       "      <td>0.000294</td>\n",
       "      <td>0.000226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000182</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000218</td>\n",
       "      <td>0.000066</td>\n",
       "      <td>0.000181</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.000078</td>\n",
       "      <td>0.000105</td>\n",
       "      <td>0.000066</td>\n",
       "      <td>0.000077</td>\n",
       "      <td>0.000108</td>\n",
       "      <td>0.000111</td>\n",
       "      <td>0.000085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>0.000178</td>\n",
       "      <td>0.000189</td>\n",
       "      <td>0.000297</td>\n",
       "      <td>0.000213</td>\n",
       "      <td>0.000286</td>\n",
       "      <td>0.000181</td>\n",
       "      <td>0.000108</td>\n",
       "      <td>0.000577</td>\n",
       "      <td>0.000304</td>\n",
       "      <td>0.000233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>0.000183</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000305</td>\n",
       "      <td>0.000220</td>\n",
       "      <td>0.000294</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000111</td>\n",
       "      <td>0.000304</td>\n",
       "      <td>0.000612</td>\n",
       "      <td>0.000240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>0.000141</td>\n",
       "      <td>0.000149</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000168</td>\n",
       "      <td>0.000226</td>\n",
       "      <td>0.000143</td>\n",
       "      <td>0.000085</td>\n",
       "      <td>0.000233</td>\n",
       "      <td>0.000240</td>\n",
       "      <td>0.000359</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           ACN        BA       BAC       CAT        HP      INTC       KMB  \\\n",
       "ACN   0.000210  0.000114  0.000179  0.000129  0.000173  0.000109  0.000065   \n",
       "BA    0.000114  0.000236  0.000190  0.000136  0.000183  0.000116  0.000069   \n",
       "BAC   0.000179  0.000190  0.000582  0.000214  0.000287  0.000182  0.000109   \n",
       "CAT   0.000129  0.000136  0.000214  0.000301  0.000206  0.000131  0.000078   \n",
       "HP    0.000173  0.000183  0.000287  0.000206  0.000541  0.000176  0.000105   \n",
       "INTC  0.000109  0.000116  0.000182  0.000131  0.000176  0.000218  0.000066   \n",
       "KMB   0.000065  0.000069  0.000109  0.000078  0.000105  0.000066  0.000077   \n",
       "NVDA  0.000178  0.000189  0.000297  0.000213  0.000286  0.000181  0.000108   \n",
       "UA    0.000183  0.000194  0.000305  0.000220  0.000294  0.000187  0.000111   \n",
       "XRX   0.000141  0.000149  0.000234  0.000168  0.000226  0.000143  0.000085   \n",
       "\n",
       "          NVDA        UA       XRX  \n",
       "ACN   0.000178  0.000183  0.000141  \n",
       "BA    0.000189  0.000194  0.000149  \n",
       "BAC   0.000297  0.000305  0.000234  \n",
       "CAT   0.000213  0.000220  0.000168  \n",
       "HP    0.000286  0.000294  0.000226  \n",
       "INTC  0.000181  0.000187  0.000143  \n",
       "KMB   0.000108  0.000111  0.000085  \n",
       "NVDA  0.000577  0.000304  0.000233  \n",
       "UA    0.000304  0.000612  0.000240  \n",
       "XRX   0.000233  0.000240  0.000359  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residual_risks = risk_summary['Residual Risk'].values\n",
    "\n",
    "def common_correlation_covariance(stock_risks,correlation,tickers=None):\n",
    "    stock_risks = np.array([stock_risks])\n",
    "    cov_matrix = np.dot(stock_risks.T,stock_risks)\n",
    "    cov_matrix = cov_matrix*correlation\n",
    "    cov_matrix[np.diag_indices_from(cov_matrix)] = np.diag(cov_matrix)/correlation\n",
    "    results = pd.DataFrame(cov_matrix)\n",
    "    \n",
    "    if tickers is not None:\n",
    "        results.index = tickers\n",
    "        results.columns = tickers\n",
    "            \n",
    "    return results\n",
    "    \n",
    "cc_covmatrix = common_correlation_covariance(risk_summary['Total Risk'].values,0.511708472128,risk_summary.index)\n",
    "cc_covmatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is \"quick and dirty\" - it ignores linkages between stocks in similar industries and those with similar attributes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Historical Covariance Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This approach relies on historical variances and covariances. This approach is not robust for a large number of stocks. If the length of the time series $T\\leq{N}$ we can find riskless positions. This is because a $N x N$ covariance matrix with $T$ periods of return has rank equal to $\\min(N,T-1)$. (With $N$ stocks and $T$ periods we have $NT$ observations so we require, for a minimum of two observations per estimate, $T\\geq(N+1)$). If we had monthly returns then we would require more than 40 years of data to construct a monthly historical covariance matrix. Even if these conditions are satisfied, the historical approach has problems:\n",
    "\n",
    "- Historical risk cannot deal with the changing nature of a company due to mergers and spinoffs.\n",
    "- Selection bias as takeovers, LBOs and failed companies are omitted.\n",
    "- Sample bias can lead to gross misestimates of covariance. For a 500 asset covariance matrix, with 125,250 independent numbers, if 5% of these are wrong then there are 6,262 poor estimates.\n",
    "\n",
    "We reproduce our historical matrix below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ACN</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAC</th>\n",
       "      <th>CAT</th>\n",
       "      <th>HP</th>\n",
       "      <th>INTC</th>\n",
       "      <th>KMB</th>\n",
       "      <th>NVDA</th>\n",
       "      <th>UA</th>\n",
       "      <th>XRX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>0.000211</td>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.000134</td>\n",
       "      <td>0.000162</td>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.000044</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000146</td>\n",
       "      <td>0.000142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000236</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000154</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000106</td>\n",
       "      <td>0.000054</td>\n",
       "      <td>0.000159</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>0.000161</td>\n",
       "      <td>0.000194</td>\n",
       "      <td>0.000581</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000275</td>\n",
       "      <td>0.000151</td>\n",
       "      <td>0.000061</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>0.000134</td>\n",
       "      <td>0.000154</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000302</td>\n",
       "      <td>0.000250</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000191</td>\n",
       "      <td>0.000187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>0.000162</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000275</td>\n",
       "      <td>0.000250</td>\n",
       "      <td>0.000545</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000256</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>0.000226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.000100</td>\n",
       "      <td>0.000106</td>\n",
       "      <td>0.000151</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000217</td>\n",
       "      <td>0.000042</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.000044</td>\n",
       "      <td>0.000054</td>\n",
       "      <td>0.000061</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>0.000042</td>\n",
       "      <td>0.000077</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>0.000150</td>\n",
       "      <td>0.000159</td>\n",
       "      <td>0.000248</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000256</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000045</td>\n",
       "      <td>0.000576</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>0.000146</td>\n",
       "      <td>0.000153</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000191</td>\n",
       "      <td>0.000244</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000053</td>\n",
       "      <td>0.000230</td>\n",
       "      <td>0.000612</td>\n",
       "      <td>0.000208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>0.000142</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.000226</td>\n",
       "      <td>0.000141</td>\n",
       "      <td>0.000059</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>0.000208</td>\n",
       "      <td>0.000358</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           ACN        BA       BAC       CAT        HP      INTC       KMB  \\\n",
       "ACN   0.000211  0.000115  0.000161  0.000134  0.000162  0.000100  0.000044   \n",
       "BA    0.000115  0.000236  0.000194  0.000154  0.000176  0.000106  0.000054   \n",
       "BAC   0.000161  0.000194  0.000581  0.000234  0.000275  0.000151  0.000061   \n",
       "CAT   0.000134  0.000154  0.000234  0.000302  0.000250  0.000132  0.000052   \n",
       "HP    0.000162  0.000176  0.000275  0.000250  0.000545  0.000150  0.000058   \n",
       "INTC  0.000100  0.000106  0.000151  0.000132  0.000150  0.000217  0.000042   \n",
       "KMB   0.000044  0.000054  0.000061  0.000052  0.000058  0.000042  0.000077   \n",
       "NVDA  0.000150  0.000159  0.000248  0.000204  0.000256  0.000174  0.000045   \n",
       "UA    0.000146  0.000153  0.000230  0.000191  0.000244  0.000132  0.000053   \n",
       "XRX   0.000142  0.000157  0.000234  0.000187  0.000226  0.000141  0.000059   \n",
       "\n",
       "          NVDA        UA       XRX  \n",
       "ACN   0.000150  0.000146  0.000142  \n",
       "BA    0.000159  0.000153  0.000157  \n",
       "BAC   0.000248  0.000230  0.000234  \n",
       "CAT   0.000204  0.000191  0.000187  \n",
       "HP    0.000256  0.000244  0.000226  \n",
       "INTC  0.000174  0.000132  0.000141  \n",
       "KMB   0.000045  0.000053  0.000059  \n",
       "NVDA  0.000576  0.000230  0.000212  \n",
       "UA    0.000230  0.000612  0.000208  \n",
       "XRX   0.000212  0.000208  0.000358  "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Which model performed better out-of-sample?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at squared losses for each matrix out-of-sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FykclN9KZQs1TKMVEfQpFRGTAHEfZGck/x4GJE3UsSm64njKFUnwG2qdQmUIR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\nMJtv28yWe7bQcH8DjY808nz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0hAdQUpahtWvhggu6vG6XPoXp0lGAKbuMPprYlprQfKiD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Q0t07nfxx3i2oI+twOlvs51dnK4XprWlcC49PjrAh+2RwRsFdq1zVu+s5mjxK8Iog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\nCIIgCIIgCIIgx/wPlddkLcdHhLkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7296770be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stocks_oos = DataReader(list,  'yahoo', datetime(2015,2,1), datetime(2016,6,1))\n",
    "return_df_oos = pd.DataFrame(np.diff(np.log(stocks_oos['Adj Close']).T).T)\n",
    "return_df_oos.index = stocks_oos['Adj Close'].index[1:]\n",
    "return_df_oos.columns = stocks_oos['Adj Close'].columns\n",
    "\n",
    "plt.figure(figsize=(15,5));\n",
    "x = plt.plot(return_df_oos);\n",
    "plt.ylabel('Returns');\n",
    "plt.legend(iter(x), return_df_oos.columns, ncol=5);\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ACN</th>\n",
       "      <th>BA</th>\n",
       "      <th>BAC</th>\n",
       "      <th>CAT</th>\n",
       "      <th>HP</th>\n",
       "      <th>INTC</th>\n",
       "      <th>KMB</th>\n",
       "      <th>NVDA</th>\n",
       "      <th>UA</th>\n",
       "      <th>XRX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ACN</th>\n",
       "      <td>0.000182</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000145</td>\n",
       "      <td>0.000110</td>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000114</td>\n",
       "      <td>0.000074</td>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>0.000152</td>\n",
       "      <td>0.000130</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000087</td>\n",
       "      <td>0.000120</td>\n",
       "      <td>0.000119</td>\n",
       "      <td>0.000147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAC</th>\n",
       "      <td>0.000145</td>\n",
       "      <td>0.000152</td>\n",
       "      <td>0.000329</td>\n",
       "      <td>0.000165</td>\n",
       "      <td>0.000223</td>\n",
       "      <td>0.000147</td>\n",
       "      <td>0.000080</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAT</th>\n",
       "      <td>0.000110</td>\n",
       "      <td>0.000130</td>\n",
       "      <td>0.000165</td>\n",
       "      <td>0.000283</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>0.000126</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000092</td>\n",
       "      <td>0.000123</td>\n",
       "      <td>0.000155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HP</th>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>0.000223</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>0.000784</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.000073</td>\n",
       "      <td>0.000118</td>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INTC</th>\n",
       "      <td>0.000114</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>0.000147</td>\n",
       "      <td>0.000126</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.000246</td>\n",
       "      <td>0.000068</td>\n",
       "      <td>0.000180</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>0.000123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KMB</th>\n",
       "      <td>0.000074</td>\n",
       "      <td>0.000087</td>\n",
       "      <td>0.000080</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000073</td>\n",
       "      <td>0.000068</td>\n",
       "      <td>0.000117</td>\n",
       "      <td>0.000066</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NVDA</th>\n",
       "      <td>0.000132</td>\n",
       "      <td>0.000120</td>\n",
       "      <td>0.000164</td>\n",
       "      <td>0.000092</td>\n",
       "      <td>0.000118</td>\n",
       "      <td>0.000180</td>\n",
       "      <td>0.000066</td>\n",
       "      <td>0.000522</td>\n",
       "      <td>0.000111</td>\n",
       "      <td>0.000143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UA</th>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.000119</td>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000123</td>\n",
       "      <td>0.000179</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>0.000067</td>\n",
       "      <td>0.000111</td>\n",
       "      <td>0.000574</td>\n",
       "      <td>0.000141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XRX</th>\n",
       "      <td>0.000125</td>\n",
       "      <td>0.000147</td>\n",
       "      <td>0.000176</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>0.000226</td>\n",
       "      <td>0.000123</td>\n",
       "      <td>0.000084</td>\n",
       "      <td>0.000143</td>\n",
       "      <td>0.000141</td>\n",
       "      <td>0.000399</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           ACN        BA       BAC       CAT        HP      INTC       KMB  \\\n",
       "ACN   0.000182  0.000116  0.000145  0.000110  0.000129  0.000114  0.000074   \n",
       "BA    0.000116  0.000234  0.000152  0.000130  0.000157  0.000116  0.000087   \n",
       "BAC   0.000145  0.000152  0.000329  0.000165  0.000223  0.000147  0.000080   \n",
       "CAT   0.000110  0.000130  0.000165  0.000283  0.000312  0.000126  0.000067   \n",
       "HP    0.000129  0.000157  0.000223  0.000312  0.000784  0.000164  0.000073   \n",
       "INTC  0.000114  0.000116  0.000147  0.000126  0.000164  0.000246  0.000068   \n",
       "KMB   0.000074  0.000087  0.000080  0.000067  0.000073  0.000068  0.000117   \n",
       "NVDA  0.000132  0.000120  0.000164  0.000092  0.000118  0.000180  0.000066   \n",
       "UA    0.000115  0.000119  0.000179  0.000123  0.000179  0.000086  0.000067   \n",
       "XRX   0.000125  0.000147  0.000176  0.000155  0.000226  0.000123  0.000084   \n",
       "\n",
       "          NVDA        UA       XRX  \n",
       "ACN   0.000132  0.000115  0.000125  \n",
       "BA    0.000120  0.000119  0.000147  \n",
       "BAC   0.000164  0.000179  0.000176  \n",
       "CAT   0.000092  0.000123  0.000155  \n",
       "HP    0.000118  0.000179  0.000226  \n",
       "INTC  0.000180  0.000086  0.000123  \n",
       "KMB   0.000066  0.000067  0.000084  \n",
       "NVDA  0.000522  0.000111  0.000143  \n",
       "UA    0.000111  0.000574  0.000141  \n",
       "XRX   0.000143  0.000141  0.000399  "
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "realized_cov = return_df_oos.cov()\n",
    "realized_cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Squared Loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Historical Covariance</th>\n",
       "      <td>3.422721e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Constant Correlation Covariance</th>\n",
       "      <td>5.651894e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Single Factor Covariance</th>\n",
       "      <td>3.100398e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Equal Ensemble Covariance</th>\n",
       "      <td>3.815464e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Squared Loss\n",
       "Historical Covariance            3.422721e-07\n",
       "Constant Correlation Covariance  5.651894e-07\n",
       "Single Factor Covariance         3.100398e-07\n",
       "Equal Ensemble Covariance        3.815464e-07"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equal_ensemble = (1/3)*cov + (1/3)*cc_covmatrix + (1/3)*sf_covmatrix\n",
    "\n",
    "historical_loss = np.power(realized_cov-cov,2).sum().sum()\n",
    "cc_loss = np.power(realized_cov-cc_covmatrix,2).sum().sum()\n",
    "sf_loss = np.power(realized_cov-sf_covmatrix,2).sum().sum()\n",
    "ens_loss = np.power(realized_cov-equal_ensemble,2).sum().sum()\n",
    "\n",
    "loss_results = pd.DataFrame([historical_loss,cc_loss,sf_loss,ens_loss])\n",
    "loss_results.index = ['Historical Covariance','Constant Correlation Covariance','Single Factor Covariance','Equal Ensemble Covariance']\n",
    "loss_results.columns = ['Squared Loss']\n",
    "loss_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **single factor** model had the best performance!"
   ]
  }
 ],
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