lectures/L07_frequentist.ipynb

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    "# Classical/Frequentist Statistical Inference: III\n",
    "\n",
    "*Davide Gerosa (Milano-Bicocca)* \n",
    "\n",
    "##### Reading:\n",
    "\n",
    "- [Ivezic textbook](https://press.princeton.edu/books/hardcover/9780691198309/statistics-data-mining-and-machine-learning-in-astronomy) Chapter 4. \n",
    "- [David Hogg's \"Fitting A Model To Data\"](https://arxiv.org/abs/1008.4686)\n",
    "\n",
    "\n",
    "This course is based on previous work by many people. See [here]((https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/README.md) for credits.\n",
    "\n",
    "\n",
    "\n",
    "---"
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    "## Hypothesis Testing <a class=\"anchor\" id=\"one\"></a>\n",
    "\n",
    "A common problem in statistics is **hypothesis testing**, i.e., testing whether an observation or observations agree with a certain hypothesis. \n",
    "\n",
    "The simplest example is whether a measured value $x_i$ or an entire dataset $\\{x_i\\}$ are consistent with having been drawn from a Gaussian distribution, $\\mathcal{N}(\\mu,\\sigma)$. In this example, $\\mathcal{N}(\\mu,\\sigma)$ is the ***null hypothesis***, and we are trying to reject it in order to claim that we have measured some effect. \n",
    "\n",
    "A great example in astronomy is ***source detection*** in images that suffer from a substantial noise background (e.g., atmospheric fluctuations in optical images).\n",
    "- Since the background fluctuates, we need the source flux in a given image resolution element (e.g., pixel) to be substantially larger than the background variation in order to give a robust detection.\n",
    "- Here the null hypothesis is that the flux in each pixel is caused by background fluctuations, and if we can reject it then we can achieve source detection. \n",
    "- But note that *rejecting the null hypothesis is not the same as favoring the source hypothesis*! Our understanding of the background could be poor or incomplete, rendering our model of the null hypothesis similarly lacking.\n",
    "\n",
    "In the image below (from the [photutils](https://photutils.readthedocs.io/en/stable/background.html) package) we have sources embedded in Gaussian image noise. \n",
    "- Ideally we would like to be able to find the real sources in here and assign a number that says how much they reject the null background hypothesis. \n",
    "- We would establish a threshold in these numbers above which we could accept sources, knowing that we might be falsely rejecting some real ones, but hopefully not accepting too many spurious noise sources."
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    "![https://photutils.readthedocs.io/en/stable//background-1.svg](https://photutils.readthedocs.io/en/stable//background-1.svg)"
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    "The same applies to time series data. This is a famous plot from gravitational-wave astronomy (namely the very first event detected in 2015). These data have already been filtered, but one can clearly see some noise and then a signal popping out of it. Now, what's its significance? \n",
    "    \n",
    "![](https://gwpy.github.io/docs/1.0.0/_images/gw150914-8.png)"
   ]
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    "Imagine we have data $\\{x_i\\}$. This could be signal strength in time-domain data, or pixel brightness in image data. Under an assumption about the null background distribution, $h_0(x)$, we can compute the probability that a data point would have a value as large or greater than that observed. This is called the ***$p$-value*** of the data:\n",
    "\n",
    "$$ p_i = \\int_{x_i}^\\infty h_0(x)dx \\equiv 1 - \\int_{-\\infty}^{x_i} h_0(x)dx = 1-H_0(x_i),$$\n",
    "\n",
    "where $H_0(x)$ is the CDF (cumulative density function) of the null distribution.\n",
    "\n",
    "In the image below, we show the distribution of a statistic $S$ under a null hypothesis $\\mathcal{H}_\\mathrm{null}$. The $p$-value of the observed statistic $S_\\mathrm{obs}$ is shown graphically.\n",
    "\n",
    "\n",
    "\n",
    "Typically, a threshold $p$-value is adopted, called the **significance, $\\alpha$**. In a classification scheme, data would then reject the null hypothesis if $p_i\\leq\\alpha$. If $\\alpha=0.05$, such data would reject the null hypothesis at the $0.05$ significance level. \n",
    "\n"
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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![download.jpg](attachment:download.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**NOTE**\n",
    "- If we can't reject the null hypothesis then it doesn't mean the data belongs to the background. It could be that our sample is simply not large enough to detect an effect. \n",
    "- Rejecting the null hypothesis does not necessarily mean that we've proven a signal hypothesis. Our model of the null hypothesis could be bad, or there could be many other things we have not considered.\n",
    "- There is ***a ton*** of mis-use and abuse of p-values in the scientific literature. Read [this](https://fivethirtyeight.com/features/statisticians-found-one-thing-they-can-agree-on-its-time-to-stop-misusing-p-values/) and [this](https://www.wikiwand.com/en/Misuse_of_p-values) in your own time. \n",
    "\n",
    "**EXAMPLE**\n",
    "\n",
    "Let's flip a coin 10 times. \n",
    "- Defining HEADS as a success event, use `scipy.stats` to define a binomial distribution over $20$ coin flips, where the intrinsic success probability is $0.5$. \n",
    "- Plot the probability mass function (the analog of the probability density function for discrete distributions).\n",
    "- If we get $14$ HEADS, what is the $p$-value with which we reject the hypothesis that the coin is fair?</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import uniform\n",
    "import scipy.stats\n",
    "from scipy import optimize\n",
    "from astroML import stats as astroMLstats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1299f04c0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=20\n",
    "\n",
    "ks = np.arange(0,n)+1\n",
    "draws=np.array([scipy.stats.binom.pmf(k, n, 0.5) for k in ks])\n",
    "\n",
    "plt.scatter(ks,draws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05765914916992186"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p-value of 8 tails in here.\n",
    "np.sum(draws[ks>=14])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In 20 flips, we get a result with $p$-value of $1$ in $10^3$ (i.e., $p = 0.001$). How many HEADS did we get?\n",
    "\n",
    "Let's check the properties of the `scipy.stats.binom` object for useful functions for this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "?scipy.stats.binom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.0"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.binom.isf(1e-3, 20, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When making these kinds of classification decisions, we make two types of errors. These are quite literally described as **Type I** and **Type II** errors by *Neyman & Pearson*.\n",
    "\n",
    "**TYPE I ERRORS**\n",
    "\n",
    "- The null hypothesis is true, but incorrectly rejected.\n",
    "- These are ***false positives*** (or false alarms).\n",
    "- False positive probability is dictated by the significance level $\\alpha$. \n",
    "\n",
    "aka *That pixel was just background but I think it's a real source.*\n",
    "\n",
    "**TYPE II ERRORS**\n",
    "\n",
    "- The null hypothesis is false, but not rejected.\n",
    "- These are ***false negatives*** (or false dismissals).\n",
    "- False negatives probability is dictated by a variable called $\\beta$, related to $(1-\\beta)$, called the ***detection probability***.\n",
    "\n",
    "aka *That was a real image but I missed it!*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at Fig 4.5 of Ivezic, v2. We have two Gaussian distributions; one describing the background noise and one describing the source. These distributions overlap, as they often do in real life.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xIx0AAAAAAAAAgAQo0gEAAAAAAAAASIDRLgAAIK1Ya7Vv3z41NjZq//79CgQCys/PV3FxsbxeryoqKuIPLQUAAAAAIBko0gEAQFo4cOCAampqtGnTJrW0tCgUCikcDscfLJqbm6v8/HyVlJTo+OOP18qVK1VSUuI4NTA6y5cvdx0BAAAAQAIU6QAAIKX19fXphRde0KuvvqrOzk719PQoPz9fXq9XxcXFKigoUDAYVEdHh5qamlRbW6umpia9/PLLWrFihc466yxNmzbN9a8BJFRTU+M6AgAAAIAEKNIBAEDK2rlzpx577DE1Nzerq6tLCxYs0PHHH6/q6mrl5Bz6qBdrrfbs2aPNmzfr/fff10svvaR3331XF110kZYuXergNwAAAAAAZAKKdAAAkHKstXrhhRe0bt06dXR0qKSkROedd54qKysTXmeMkdfrldfr1YoVK/Tiiy+qoaFBDz/8sE499VSde+65ys3NnaTfAgAAAACQKSjSAQBASgmHw/rd736njRs3qqOjQytWrNCKFSuG3IGeSElJiS655BJt3rxZ69ev10svvaTW1lZdccUVKiwsnKD0AAAAAIBMRJEOAABSRigU0iOPPKK3335bPT09Ov/88zV//vzDXs8Yo+OPP14VFRV66qmntHnzZgUCAX3605/WlClTkpgcGJ81a9bEP69atcphEgAAAABDMdZa1xmQRMaYmuXLly/ngVUAgHQTDof1yCOPaNOmTQoGg7r44otVUVGRtPXb29v1+OOPy1qro48+WldffbUKCgqStj4wHsaY+Gf++xwAAACIWLFihTZu3LjRWrvCdZax/RtpAACACWCt1dq1a/XWW28pEAjokksuSWqJLknFxcW67LLLZIzRtm3b9D//8z/q7+9P6j0AAAAAAJmJIh0AADj3l7/8RX/961/V3d2tCy+8UOXl5RNyn5kzZ+riiy9WKBTSO++8o2eeeWZC7gMAAAAAyCwU6QAAwKlt27bp2WefVUdHhz760Y/K6/VO6P1KSkp0/vnnq7OzUy+//LLeeOONCb0fAAAAACD9UaQDAABn9u/fr9/+9rfq6OjQBz/4QS1cuHBS7ltVVaWPfOQj6ujo0Nq1a9XU1DQp9wUAAAAApCeKdAAA4ER/f78effRRtbS0aPbs2Vq+fPmk3n/JkiVavHix9u/fr//5n/9RMBic1PsDAAAAANJHRhTpxpg5xpifG2MajDF9xphaY8y/G2NKxrhOafS62ug6DdF15wxz/v81xjxnjKk3xvQYY/YZY94wxtxujCkb4vwFxhib4PXw4f5vAABAunnppZe0Y8cOGWN01llnyRgz6Rk+/OEPq6ioSH6/n3npAAAAAIBh5bkOMF7GmCMlrZdUKelxSVslnSTpy5LOM8acZq1tHcU6ZdF1FktaJ+lhScdIuk7ShcaYU621Owdd9lVJGyX9UVKzpGmSTpG0WtIqY8wp1tr6IW63SdLvhvh+80g5AQDIBE1NTXr++efV0dGhiy66SFOnTnWSIz8/Xx/72Mf06KOP6tVXX9WSJUt05JFHOskCAAAAAEhdaV+kS/qJIiX6TdbaH8W+NMb8UJGi+3uSPj+Kdb6vSIn+Q2vt1wesc5Oku6L3OW/QNTOttb2DFzLGfE/SbZJulfTFIe71prV29SgyAQCQccLhsB5//HF1dHRo6dKlmjt3rtM85eXlWrlypTZu3KgnnnhCX/rSl1RQUOA0EwAAAAAgtaT1aJfobvRzJNVK+o9Bh2+X1CXpamPMtBHWmS7p6uj5qwcd/rGk3ZLONcYc9AS0oUr0qEei74sS/wYAAGSfV199Vbt371ZBQYFOPfVU13EkScuWLVNxcbH27NmjP//5z67jAAAAAABSTFoX6ZLOjL4/a63tH3jAWntA0suSihQZt5LIKZKmSno5et3AdfolxYamnjn4wmFcHH1/a5jj1caYG4wxt0XfTxjlugAApLX29natW7dOBw4c0Omnn678/HzXkSRJubm5OuOMM9TV1aX169drz549riMhy1x00UXxFwAAAIDUk+6jXY6Ovm8b5vh2RXasL5b03DjXUXSdQxhjbpY0XVKxpJWSPqxIiX7nMOt9LPoauMafJX3GWluXIOfA82uGOXTMaK4HAMCFZ555Ru3t7TriiCM0b94813EOUllZqaVLl2r79u168skndd111zl5ACqy09q1a11HAAAAAJBAuu9IL46+tw9zPPb9rAle52ZFRsl8RZES/WlJ51hr9w46r1vSdyStkFQSfZ0u6XlJZ0h6bqQxNAAApKva2lq9/fbbCgQCOu2001zHGdJJJ50kSdqxY4feeecdx2kAAAAAAKki3Yv0lGCt9VprjSSvpL+RtFDSG8aY5YPOa7bWfstau9Fauz/6elGRXfOvSjpK0t+N8p4rhnpJ2prUXw4AgCSw1urpp59WZ2enTjzxRE2fPt11pCEVFhbq5JNPVmdnp5599lkFg0HXkQAAAAAAKSDdi/TYTvHiYY7Hvt8/GetYa/dYax9TpBgvk/TLEe4buy4k6d7ojx8ZzTUAAKSTt956S/X19SooKNCyZctcx0loyZIlKi4u1t69e/Xaa6+5jgMAAAAASAHpXqS/F30fcna5pEXR9+Fmnyd7HUmStXa3pHclLTXGlI/mGkmxMTCMdgEAZJRQKKTnnntOnZ2dOumkk1LmAaPDycnJ0amnnqrOzk69+OKL6unpcR0JWWD16tXxFwAAAIDUk+4PG30++n6OMSbHWtsfO2CMmSHpNEXmkm8YYZ0NknoknWaMmWGtPTBgnRxFdpgPvN9oVEffw6M8/5To+84x3AMAgJT3+uuva+/evZo5c6YWLx7u76xTy9y5c1VVVaX9+/fr5Zdf1kc/+lHXkZDh7rjjjvhnynQAAAAg9aT1jnRr7Q5Jz0paIOlLgw7focju7gettV2xL40xxxhjjhm0TqekB6Pnrx60zo3R9Z+x1sZLbmPMYmPMIaNgjDE5xpjvSaqUtN5a2zbg2PJoMT/4mrMlfTX640MJfmUAANJKIBDQiy++qK6uLp188snKyUmP//QwxuiUU05Rd3e3NmzYoM7OTteRAAAAAAAOpfuOdEn6oqT1ku6OFtJbJJ0s6UxFRrF8c9D5W6LvZtD3t0k6Q9LXjDHLJL0maYmkSyU169Ci/gJJ/2KM+YukXZJaJXkkna7Iw0abJF0/6JofSlpkjFkvyRf97gRJZ0U//7O1dv1ofmkAANLBX//6V+3bt09lZWVasGCB6zhj4vF4NG/ePO3du1d/+ctfdN5557mOBAAAAABwJD22hSUQ3ZW+UtIDihToX5d0pKS7JJ1irW0d5Tqtkk6VdLeko6LrnCzpfkkrovcZ6E+S7pNUIelvJH1D0ick7VNkN/xSa+27g655UNIbkj6oSMn+RUXmrz8i6SPW2u+O9vcGACDVBQIBvfzyy+ru7tZJJ50kYwb/HXbqO+mkk9Td3a2//vWv7EoHAAAAgCyWCTvSZa2tl3TdKM8d9k/x1tp9kr4cfY20zmZFxr6MmrX2PkXKdwAAMl5NTY3a2tpUVlamuXPnuo5zWMrLyzV//nzt3btXr7zyij72sY+5jgQAAAAAcCDtd6QDAIDUEwqF9PLLL6urq0srV65My93oMStXrlRPT49ee+019fT0uI4DAAAAAHCAIh0AACTdpk2b1NraquLiYs2fP991nHGprKxUdXW1Ojo69Nprr7mOAwAAAABwgCIdAAAkVX9/v9avX6/u7m4tX748rXejxyxfvlw9PT3asGGDgsGg6zgAAAAAgElGkQ4AAJLqvffeU1NTk6ZOnaqjjjrKdZykmD17tsrKyrR//369+eabruMAAAAAACYZRToAAEiqV155Rd3d3frABz6gnJzM+E8NY4yWLVum7u5ubdiwQdZa15EAAAAAAJMoz3UAAACQOfx+v3bt2iVJOuaYYxynSa6FCxfqlVdeUVNTk7Zt26ajjz7adSRkkOuvv951BAAAAAAJUKQDAICk2bBhg3p6enTssceqoKDAdZykysnJ0fHHH6+amhpt2LCBIh1JtWbNGtcRAAAAACSQGf/eGgAAOHfgwAFt3rxZvb29Ou6441zHmRBLlixRf3+/3n//fTU3N7uOAwAAAACYJBTpAAAgKWpqatTd3a0FCxZo5syZruNMiMLCQh199NHq7e3Vq6++6joOAAAAAGCSUKQDAIBxC4fD+utf/6qenh6dcMIJruNMqOOPP149PT3atGmTent7XccBAAAAAEwCZqQDAIBx27p1q9ra2jRz5kxVV1e7jjOhSkpKVF1drY6ODm3atEknn3yy60jIAKtWrYp/Zl46AAAAkHrYkQ4AAMbt9ddfV09Pj4477jgZY1zHmXDHHXecenp69Prrr8ta6zoOMsA999wTfwEAAABIPRTpAABgXFpaWrRjxw719/dr8eLFruNMigULFqigoECNjY3avXu36zgAAAAAgAlGkQ4AAMalpqZGPT09WrRokQoLC13HmRS5ubk69thj1dPTo5qaGtdxAAAAAAATjCIdAAActlAopDfffFO9vb069thjXceZVMccc4wCgYDeffdd9fT0uI4DAAAAAJhAFOkAAOCwbd26Ve3t7SopKVFlZaXrOJNq5syZmj17trq6urRp0ybXcQAAAAAAE4giHQAAHLY33ngjvhs9Gx4yOlhsvMvGjRt56CgAAAAAZDCKdAAAcFja29v1/vvvKxQKadGiRa7jOLFgwQLl5eWpsbFRjY2NruMAAAAAACYIRToAADgsmzZtUm9vr4444ghNmTLFdRwncnNztXjxYvX29uqNN95wHQcAAAAAMEEo0gEAwJhZa+MPGT3mmGNcx3HqmGOOUW9vr9566y2FQiHXcQAAAAAAE4AiHQAAjFl9fb2am5tVWFioOXPmuI7jVHl5uUpLS3XgwAFt27bNdRwAAAAAwATIcx0AAACkn9hYl2OOOUY5Ofy9/NFHH63XX39dmzZt0rHHHus6DtLQ7bff7joCAAAAgAQo0gEAwJgEg0Ft3rxZvb29Wrx4ses4KWHRokV65ZVXtG3bNnV1dWnatGmuIyHNrF692nUEAAAAAAmwhQwAAIzJtm3bdODAAZWVlamsrMx1nJRQVFSkuXPnqqenR5s3b3YdBwAAAACQZBTpAABgTN566y319vbq6KOPdh0lpSxevDj+0FEAAAAAQGahSAcAAKPW09Oj7du3KxAIaNGiRa7jpJQFCxbIWqv6+nq1tra6jgMAAAAASCKKdAAAMGrvvPOOuru7NXv2bBUVFbmOk1Ly8/O1cOFC9fb26u2333YdB2nm4osvjr8AAAAApB4eNgoAAEbt7bffVl9fHw8ZHcbixYu1c+dOvf322zr99NNljHEdCWni97//vesIAAAAABJgRzoAABiVjo4O1dbWKhwOa+HCha7jpKQ5c+YoLy9Pzc3Nampqch0HAAAAAJAkFOkAAGBU3nnnHfX29mrevHkqKChwHScl5eTk6Mgjj1Rvb682b97sOg4AAAAAIEko0gEAwKhs3rxZfX19PGR0BIsWLVJfX582b94sa63rOAAAAACAJKBIBwAAI2pra1N9fb2stZo/f77rOCmtqqpKU6ZMUWtrq/x+v+s4AAAAAIAkoEgHAAAjevfdd9XX16cFCxYoPz/fdZyUZozRUUcdpb6+Pr3zzjuu4wAAAAAAkoAiHQAAjOidd95RX1+fjjzySNdR0sLChQvjRTrjXQAAAAAg/VGkAwCAhNra2uTz+WSt1bx581zHSQter1dTp07Vvn375PP5XMcBAAAAAIwTRToAAEiIsS5jZ4zRkUceqb6+Pr377ruu4wAAAAAAxokiHQAAJLRlyxbGuhyG2HiXd999l/EuAAAAAJDm8lwHAAAAqau9vV11dXWMdTkMXq9XhYWFam1tVUNDg2bPnu06ElLYz372M9cRAAAAACRAkQ4AAIYV240+b948xrqMkTFGCxcu1M6dO7VlyxaKdCS0atUq1xEAAAAAJMBoFwAAMKxYkb5w4ULXUdIS410AAAAAIDNQpAMAgCF1dXWptrZW4XBYCxYscB0nLVVXVys/P1979+7V3r17XccBAAAAABwminQAADCk9957T319fZozZ44KCgpcx0lLOTk5WrBggfr6+rRlyxbXcQAAAAAAh4kiHQAADCk21uWII45wHSWtxca7bN261XUUpLAVK1bEXwAAAABSDw8bBQAAh+jr69OOHTsUDAYp0sdpzpw5kiS/36/9+/dr1qxZbgMhJW3cuNF1BAAAAAAJsCMdAAAc4v3331dPT488Ho+Kiopcx0lreXl5mjdvnvr6+vTee++5jgMAAAAAOAwU6QAA4BDvvfeeAoEADxlNkiOOOEKBQIDxLgAAAACQpijSAQDAQcLhcPxBowsXLnQdJyPMnz9foVBItbW16unpcR0HAAAAADBGFOkAAOAgdXV16uzs1KxZs5jnnSRTpkxRVVWVent7tX37dtdxAAAAAABjRJEOAAAOwliXibFgwQL19fVp27ZtrqMAAAAAAMaIIh0AAMRZa+NjXSjSk2vBggUKBALavn27wuGw6zgAAAAAgDGgSAcAAHEtLS1qaWlRfn6+PB6P6zgZpbi4WLNmzVJnZ6d2797tOg4AAAAAYAwo0gEAQFxsrMv8+fOVk8N/JiQb410AAAAAID3xJ2QAABC3bds2xrpMoNh4l/fee0/WWtdxAAAAAACjlOc6AAAASA3d3d2qq6tTOBzW3LlzXcfJSB6PR/n5+WppaVFra6vKy8tdR0KKeOKJJ1xHAAAAAJAARToAAJAkvf/+++rr61NVVZUKCgpcx8lIOTk5mjt3rhobG7Vt2zaKdMRdfPHFriMAAAAASIDRLgAAQJK0fft2BQIBxrpMsNh4F+akAwAAAED6oEgHAADq7+/X9u3bmY8+CebOnatgMKjdu3ert7fXdRwAAAAAwChQpAMAAPl8Ph04cEAzZ85UcXGx6zgZbcqUKfJ6vert7dWOHTtcxwEAAAAAjAJFOgAAiI91mT9/vusoWWH+/PkKBALavn276yhIEdXV1fEXAAAAgNTDw0YBAEC8SJ83b57rKFlh3rx5eu2117R9+3ZZa2WMcR0JjjU2NrqOAAAAACABdqQDAJDlOjo61NDQIGstu2EnSVlZmaZOnar29nY1NTW5jgMAAAAAGAFFOgAAWe79999XIBDQnDlzlJfHP1abDMYYxrsAAAAAQBqhSAcAIMvFinTGukyuefPmKRAI6P3333cdBQAAAAAwAop0AACyWDgcpkh3ZM6cOQqFQqqrq1NPT4/rOAAAAACABCjSAQDIYn6/X11dXZo5c6aKi4tdx8kqBQUFqqqqUl9fn3bu3Ok6DgAAAAAgAYp0AACyWGw3+vz5811HyUqMdwEAAACA9ECRDgBAFosV6XPnznUdJSsNLNKtta7jAAAAAACGQZEOAECW6urqkt/vl7VW1dXVruNkpbKyMhUWFmr//v3au3ev6zgAAAAAgGFQpAMAkKV27typQCCgqqoq5efnu46TlYwxmjt3LuNdAAAAACDF5bkOAAAA3GCsS2qYN2+eamtrtWPHDn3oQx9yHQeOvP76664jAAAAAEiAIh0AgCxkrY0X6fPmzXMdJ6vNmTNHwWBQtbW1CgaD/OuALLVixQrXEQAAAAAkwGgXAACy0J49e9Te3q4pU6aotLTUdZysVlRUpPLycvX09Gj37t2u4wAAAAAAhkCRDgBAFtq5c6eCwaDmzp0rY4zrOFlv7ty5CgaD2rlzp+soAAAAAIAhUKQDAJCFduzYwXz0FDJnzhwFAgHt2LHDdRQAAAAAwBAo0gEAyDKxedyBQEBz5sxxHQeSvF6vrLVqbGzUgQMHXMeBA8aY+AsAAABA6qFIBwAgy9TV1am3t1fl5eUqKipyHQeS8vLyNHv2bMa7AAAAAECKokgHACDL7Ny5k93oKSg23oUiHQAAAABSD0U6AABZJlakMx89tcydOzdepFtrXccBAAAAAAxAkQ4AQBbp7u6W3++XtVZer9d1HAxQWlqqwsJC7d+/X3v37nUdBwAAAAAwAEU6AABZZOfOnQoGg/J6vcrPz3cdBwMYYxjvAgAAAAApKiOKdGPMHGPMz40xDcaYPmNMrTHm340xJWNcpzR6XW10nYboukMOkTXG/F9jzHPGmHpjTI8xZp8x5g1jzO3GmLIE9/mQMeap6Pk9xpi3jDFfMcbkjvV3BwBgLBjrktoGjncBAAAAAKSOtC/SjTFHSqqRdJ2k1yT9m6Sdkr4s6ZVEhfagdcokvRK9bkd0ndei69YYYxYOcdlXJU2T9EdJd0n6L0khSaslvWWMOaSlMMZcKulFSR+R9JikH0sqiN7v4dFkBQDgcMV2pPOg0dQ0Z84cBYNB7dq1S+Fw2HUcAAAAAEBUnusASfATSZWSbrLW/ij2pTHmh4oU3d+T9PlRrPN9SYsl/dBa+/UB69ykSEn+E0nnDbpmprW2d/BCxpjvSbpN0q2Svjjg+5mS7pEUlnSGtfb16Pf/LGmdpMuNMVdaaynUAQBJ19bWptbWVuXl5am8vNx1HAxh+vTpKi4ujs+ynzdvnutIAAAAAACl+Y706G70cyTVSvqPQYdvl9Ql6WpjzLQR1pku6ero+asHHf6xpN2Szh28K32oEj3qkej7okHfXy6pQtLDsRJ9wDr/FP3xC4myAgBwuGK70WfPnq2cnLT+T4CMNnBXOgAAAAAgNaT7n6LPjL4/a63tH3jAWntA0suSiiSdMsI6p0iaKunl6HUD1+mX9Myg+43k4uj7W4O+Pyv6/vQQ17woqVvSh4wxhaO8DwAAoxabjz579mzXUZDA7NmzmZMOAAAAACkm3Ue7HB193zbM8e2K7FhfLOm5ca6j6DqHMMbcLGm6pGJJKyV9WJES/c7R3sdaGzLG7JK0VNJCSVsS5JUxpmaYQ8ckug4AkJ2stfEd6TxoNLXNnj1boVBI9fX1CgQCKigocB0Jk8Dv97uOAAAAACCBdC/Si6Pv7cMcj30/a4LXuVmSZ8DPT0u61lq7N8n3AQDgsDQ3N+vAgQOaOnWqiouLR74AzkyZMkXl5eXq7e1VXV2djjrqKNeRMAmqq6tdRwAAAACQQLqPdkkJ1lqvtdZI8kr6G0V2lL9hjFk+gfdcMdRL0taJuicAIH3t2rVLwWBQc+bMkTHGdRyMgDnpAAAAAJBa0r1Ij+3gHm5rXez7/ZOxjrV2j7X2MUXGyZRJ+uVE3AcAgLHatWsX89HTSGxOOkU6AAAAAKSGdC/S34u+Dzm7XNKi6Ptws8+TvY4kyVq7W9K7kpYaY8pHcx9jTJ6kIySFJPF0MQBA0vT39x+0Ix2pr6qqSv39/WpoaFBPT4/rOJgEDQ0N8RcAAACA1JPuRfrz0fdzjDEH/S7GmBmSTpPULWnDCOtskNQj6bTodQPXyVFkh/nA+41GbNBleMB366Lv5w1x/kckFUlab63tG8N9AABIqKGhQd3d3Zo5c6amT5/uOg5GIT8/Xx6PR4FAQLt373YdB5Ng9uzZ8RcAAACA1JPWRbq1doekZyUtkPSlQYfvkDRN0oPW2q7Yl8aYY4wxxwxap1PSg9HzVw9a58bo+s9Ya+M7xY0xi40xh4xoMcbkGGO+J6lSkVK8bcDh30hqkXSlMWblgGumSPpu9MefJv6tAQAYG8a6pCfGuwAAAABA6shzHSAJvihpvaS7jTFnS9oi6WRJZyoyiuWbg87fEn0f/KS12ySdIelrxphlkl6TtETSpZKadWhRf4GkfzHG/EXSLkmtkjySTlfkYaNNkq4feIG1tsMYc70ihfqfjTEPS9on6RJJR0e///WYfnsAAEZQW1vLWJc0NGfOHL355psU6QAAAACQAtK+SLfW7oju7v62IiNTLpDUKOkuSXcM2hGeaJ1WY8ypkm6XdJmk/6NIOX6/pG9Za32DLvmTpKMkfVjSiZJmSepSpLx/UNLd1tp9Q9znd8aY0xUp+D8haYqk9yV9LXqNHfUvDwDACMLhsHbv3q1AIKDq6uqRL0DKqKyslLVWTU1N6urq0rRp01xHAgAAAICslfZFuiRZa+slXTfKcwfvRB94bJ+kL0dfI62zWZGxL2NmrX1ZkcIfAIAJ5fP51NPTo9LSUhUVFbmOgzHIy8uT1+vVgQMHVFtbq6VLl7qOBAAAAABZK61npAMAgMRiY13YjZ6eZs+erWAwqNraWtdRAAAAACCrUaQDAJDBeNBoeuOBowAAAACQGijSAQDIUKFQSPX19QqFQhTpaaqyslLGGDU3N+vAgQOu4wAAAABA1qJIBwAgQ/l8PvX29qq0tFRTpkxxHQeHITc3V1VVVQoGg9q9e7frOAAAAACQtSjSAQDIULH56OxGT2/MSQcAAAAA9yjSAQDIULW1tQoEAjxoNM1VV1czJx0AAAAAHKNIBwAgAw2cj06Rnt4qKipkjNHevXuZk57BrLXxFwAAAIDUQ5EOAEAGis1HLykpYT56mhs4J53xLgAAAADgBkU6AAAZiPnomSU2J50HjgIAAACAGxTpAABkIOajZ5aqqioFAgF2pAMAAACAI3muAwAAgOSKzUcPBoMU6RmisrJSktTc3KzOzk5Nnz7dcSIkW01NTfzzihUrHCYBAAAAMBSKdAAAMozf71dvb69KS0s1depU13GQBLE56R0dHdq9e7eWLl3qOhKSbOXKlfHPPHAUAAAASD2MdgEAIMPE5qOzGz2zVFdX88BRAAAAAHCEIh0AgAyze/duivQMNHv2bAUCAR44CgAAAAAOUKQDAJBBwuGw6urqKNIzUEVFhSSpqalJ3d3djtMAAAAAQHahSAcAIIM0NDSop6dHxcXFKioqch0HSZSXlyev16tgMMiudAAAAACYZBTpAABkEMa6ZLaqqiqKdAAAAABwgCIdAIAMQpGe2XjgKAAAAAC4QZEOAECG6O/vjxfpVVVVruNgAng8HvX396upqUm9vb2u4wAAAABA1qBIBwAgQ+zZs0fd3d2aPn26ZsyY4ToOJkB+fr4qKioUCARUX1/vOg4AAAAAZA2KdAAAMgRjXbJDbLwLc9IBAAAAYPLkuQ4AAACSgyI9O1RXV2vz5s0U6RmGcUwAAABAaqNIBwAgA1hrKdKzhNfrVSgUks/nUzAYVH5+vutISIKGhgbXEQAAAAAkwGgXAAAyQGtrqw4cOKDCwkLNnDnTdRxMoMLCQpWVlSkQCMjn87mOAwAAAABZgSIdAIAMMHA3ujHGdRxMsKqqKuakAwAAAMAkokgHACADMNYlu1RXVysQCKiurs51FAAAAADICsxIBwAgA9TV1SkQCPDAwixRVVWlUCikuro6hcNh5ebmuo6EcVq7dm3888UXX+wwCQAAAIChUKQDAJDm2tvbtW/fPuXl5am0tNR1HEyCoqIizZw5U729vWpqatLs2bNdR8I4XXLJJfHP1lqHSQAAAAAMhdEuAACkudhYl6qqKuXk8H/as0V1dTVz0gEAAABgkvCnbQAA0hxjXbJTVVUVc9IBAAAAYJJQpAMAkObq6uriO9KRPaqqquI70hkFAgAAAAATiyIdAIA01tPTo6amJklSRUWF4zSYTDNnztTUqVPV2dmplpYW13EAAAAAIKNRpAMAkMbq6uoUCoVUWVmpvDyeIZ5NjDHxXemMdwEAAACAiUWRDgBAGmOsS3ajSAcAAACAyUGRDgBAGqNIz27V1dXxOekAAAAAgIlDkQ4AQJoKBoPy+/0KhULyer2u48CB0tJS5eTkaN++fero6HAdBwAAAAAyFkU6AABpqqGhQX19fSotLVVhYaHrOHAgJydHXq9XwWBQ9fX1ruMAAAAAQMbiqWQAAKSp2FiXOXPmuI4Ch6qqqtTS0qK6ujotXbrUdRwcpuXLl7uOAAAAACABinQAANIU89EhRYr0jRs38sDRNFdTU+M6AgAAAIAEGO0CAEAastZSpEOSVFlZqXA4rMbGRvX19bmOAwAAAAAZiSIdAIA01NzcrK6uLk2bNk3Tp093HQcO5efnq6KiQoFAQD6fz3UcAAAAAMhIFOkAAKSh+vp6dqMjrqqqSsFgkPEuAAAAADBBmJEOAEAaio118Xq9rqMgBXi9Xr377ruqr693HQWHac2aNfHPq1atcpgEAAAAwFAo0gEASEN1dXUKhULsSIekyI70UCik+vp69ff3KyeHf3SYbm644Yb4Z4p0AAAAIPXwpywAANJMR0eH9u3bp5ycHJWWlrqOgxRQVFSkGTNmqKenR01NTa7jAAAAAEDGoUgHACDNxOaje71edh4jLjYnnfEuAAAAAJB8/OkbAIA0w3x0DMXr9fLAUQAAAACYIBTpAACkmdiOdOajY6CBO9Ktta7jAAAAAEBGoUgHACCNBAIBNTY2KhwOy+PxuI6DFFJSUqL8/Hy1tbWpvb3ddRwAAAAAyCgU6QAApBG/369AIKDy8nLl5+e7joMUYoyR1+tVKBRiTjoAAAAAJBlFOgAAaWTgg0aBwWJz0inSAQAAACC5KNIBAEgjPGgUifDAUQAAAACYGBTpAACkCWstO9KRUGVlpcLhsJqamtTX1+c6DgAAAABkjDzXAQAAwOjs3btXXV1dmjZtmmbMmOE6DlJQfn6+Kioq1NfXJ7/fr4ULF7qOhFG66KKLXEcAAAAAkABFOgAAaaK+vl6hUIjd6EjI6/Vqx44dqquro0hPI2vXrnUdAQAAAEACjHYBACBNMNYFo8EDRwEAAAAg+SjSAQBIEzxoFKMxsEjv7+93HQcAAAAAMgJFOgAAaaCrq0stLS2SpPLycsdpkMqmT5+u6dOnq7u7W83Nza7jAAAAAEBGYEY6AABpIDYf3ePxKCeHvwdHYl6vV42NjfL5fPwLhjSxevXqIT8DAAAASA0U6QAApIHYfPSqqirXUZAGvF6v6uvrVV9fr5UrV7qOg1G444474p8p0gEAAIDUw5Y2AADSAA8axVjwwFEAAAAASC6KdAAAUlw4HJbf71cwGJTH43EdB2mgrKxMktTS0qKuri7HaQAAAAAg/VGkAwCQ4pqamtTX16eSkhJNmTLFdRykgZycHHalAwAAAEASUaQDAJDiGOuCw+H1ehUKhSjSAQAAACAJKNIBAEhxsSKdsS4YC3akAwAAAEDyUKQDAJDi2JGOw+HxeBQMBuX3+xUOh13HAQAAAIC0RpEOAEAKa29v1/79+5WXl6eSkhLXcZBGpkyZolmzZqmvr09NTU2u4wAAAABAWqNIBwAghQ3cjW6McR0HaYbxLgAAAACQHBTpAACkMJ/Px3x0HDaKdAAAAABIjjzXAQAAwPCYj47xiM1J9/l8rqNgBNdff73rCAAAAAASoEgHACBFBYNBNTQ0KBwOsyMdh6W0tFR5eXlqa2tTR0eHZs6c6ToShrFmzRrXEQAAAAAkwGgXAABSVENDgwKBgEpKSlRQUOA6DtKQMSa+K53xLgAAAABw+CjSAQBIUbH56Ix1wXgw3gUAAAAAxo8iHQCAFFVfX69QKESRjnHhgaMAAAAAMH7MSAcAIAVZa9mRjqTweDwKh8NqaGhQKBRSXh7/+ZeKVq1aFf/MvHQAAAAg9fAnKQAAUtD+/fvV3t6ugoICFRcXu46DNFZYWKiSkhL19fWpsbFRc+fOdR0JQ7jnnnvinynSAQAAgNTDaBcAAFKQz+dTKBSSx+ORMcZ1HKQ55qQDAAAAwPhQpAMAkILq6+sVDAbl8XhcR0EG8Hq9CoVCzEkHAAAAgMNEkQ4AQApiPjqSiR3pAAAAADA+FOkAAKSYYDCoxsZGhcNhdqQjKUpKSpSXlxefvQ8AAAAAGJuMKNKNMXOMMT83xjQYY/qMMbXGmH83xpSMcZ3S6HW10XUaouvOGeLcMmPM3xljHjPGvG+M6THGtBtj/mKM+Zwx5pD/bY0xC4wxNsHr4fH87wAAyAwNDQ0KBAIqLS1Vfn6+6zjIAMYYdqUDAAAAwDjkuQ4wXsaYIyWtl1Qp6XFJWyWdJOnLks4zxpxmrW0dxTpl0XUWS1on6WFJx0i6TtKFxphTrbU7B1zySUk/ldQo6XlJdZI8kv5G0r2SzjfGfNJaa4e43SZJvxvi+80j/sIAgIwXG+tSXV3tOgoyiMfjUUtLi+rr67V06VLXcQAAAAAgraR9kS7pJ4qU6DdZa38U+9IY80NJX5X0PUmfH8U631ekRP+htfbrA9a5SdJd0fucN+D8bZIukfSktbZ/wPm3SXpN0icUKdUfHeJeb1prV4/mlwMAZB+fz6dQKMR8dCSV1+vVm2++yY50AAAAADgMaT3aJbob/RxJtZL+Y9Dh2yV1SbraGDNthHWmS7o6ev7qQYd/LGm3pHONMQtjX1pr11lr1w4s0aPfN0n6z+iPZ4zh1wEAQNZa1dfX86BRJJ3H41E4HFZDQ4NCoZDrOAAAAACQVtK6SJd0ZvT92SEK7QOSXpZUJOmUEdY5RdJUSS9Hrxu4Tr+kZwbdbyTB6Ptwf0qtNsbcYIy5Lfp+wijXBQBkuPb2drW3tys/P1/FxcWu4yCDFBYWatasWerr61NTU5PrOAAAAACQVtJ9tMvR0fdtwxzfrsiO9cWSnhvnOoquk5AxJk/SNdEfnx7mtI9FXwOv+7Okz1hr60a6R/T8mmEOHTOa6wEAqSk21sXj8cgY4zoOMozX61V9fb3q6+s1Z84hz1KHQ7fffrvrCAAAAAASSPciPbZVr32Y47HvZ03SOpJ0p6TjJD1lrX1m0LFuSd9R5EGjsQeXnqDIOJkzJT1njFlmre0axX0AABko9qBRj8fjOgoykMfj0c6dO5mTnoJWr17tOgIAAACABNK9SE8p0QeTfl3SVkVmrh/EWtss6VuDvn7RGHOOpL9IOlnS3ynycNOErLUrhslQI2n52JIDAFIF89ExkTwej4LBIEU6AAAAAIxRus9Ij+0UH26IbOz7/RO9jjHmRkUK8HclnWmt3TfCPeOstSFJ90Z//MhorwMAZJZQKKTGxkaFw2FVVla6joMMVFpaqtzcXLW1tamjo8N1HAAAAABIG+lepL8XfR9udvmi6Ptws8+Tso4x5iuSfiRpsyIl+uE8wWtv9H3aYVwLAMgAjY2N6uvrU0lJiQoLC13HQQYyxqiyslLBYFB+v991HAAAAABIG+k+2uX56Ps5xpgca21/7IAxZoak0xSZS75hhHU2SOqRdJoxZoa19sCAdXIUeWDpwPtpwPF/VGQu+puSPmatbTnM3+WU6PvOhGcBADJW7EGjc+fOdR0FGayqqkptbW3y+XxasmSJ6ziIuvjii+Of165d6zAJAAAAgKGk9Y50a+0OSc9KWiDpS4MO36HI7u4HBz680xhzjDHmmEHrdEp6MHr+6kHr3Bhd/xlr7UEltzHmnxUp0WsknT1SiW6MWR4t5gd/f7akr0Z/fCjRGgCAzMWDRjEZmJOemn7/+9/HXwAAAABST7rvSJekL0paL+nuaCG9RZGHdp6pyCiWbw46f0v03Qz6/jZJZ0j6mjFmmaTXJC2RdKmkZg0q6o0xn5H0bUlhSS9JusmYwUuq1lr7wICffyhpkTFmvaTYn15PkHRW9PM/W2vXj/QLAwAyE0U6JsPA0S7hcFi5ubmuIwEAAABAykv7It1au8MYs1KRUvs8SRdIalTkwZ93WGvbRrlOqzHmVEm3S7pM0v+R1CrpfknfstYO3rZ1RPQ9V9JXhln2BUkPDPj5QUkfl/RBSedLype0R9Ijkn5srX1pNFkBAJmno6NDbW1tys3NVWlpqes4yGBTp05VcXGxent7tWfPHlVXV7uOBAAAAAApL+2LdEmy1tZLum6U5x6ybXzAsX2Svhx9jbTOah06Bmaka+6TdN9YrgEAZIfYbvTKykoN8S+cgKTyeDxqaGiQz+ejSAcAAACAUUjrGekAAGSKWJFeVVXlOgqyAHPSAQAAAGBsKNIBAEgBPp9PoVCI+eiYFF6vV6FQiCIdAAAAAEaJIh0AAMfC4bD8fn98tAsw0crKyiRJLS0t6u7udpwGAAAAAFIfRToAAI7t2bNHfX19Ki4u1tSpU13HQRbIyclRZWUlu9IBAAAAYJQo0gEAcCw2H52xLphMzEkHAAAAgNGjSAcAwDGKdLhAkQ4AAAAAo5fnOgAAANnO7/crFArJ6/W6joIsMvCBo9ZaGWNcR8pqP/vZz1xHAAAAAJAARToAAA51d3dr7969kqTS0lLHaZBNpk2bpmnTpqm7u1stLS2qqKhwHSmrrVq1ynUEAAAAAAkw2gUAAIdiu9ErKyuVm5vrOg6yjMfj4YGjAAAAADAKFOkAADjEfHS4xJx0AAAAABgdinQAABzy+XwKhUIU6XCCIh0AAAAARocZ6QAAOGKtZUc6nCovL1d/f7/27Nmjvr4+FRYWuo6UtVasWBH/XFNT4zAJAAAAgKFQpAMA4EhLS4u6u7tVVFSk6dOnu46DLJSfn6/y8nIFg0E1NDToiCOOcB0pa23cuNF1BAAAAAAJMNoFAABH2I2OVMB4FwAAAAAYGUU6AACO+P1+inQ4R5EOAAAAACOjSAcAwJHYg0a9Xq/rKMhiXq9XoVBIPp9P1lrXcQAAAAAgJVGkAwDgQCAQUFNTk8LhsMrLy13HQRabOXOmCgoK1NHRofb2dtdxAAAAACAlUaQDAOBAQ0ODgsGgysrKlJ+f7zoOspgxRh6PR6FQSPX19a7jAAAAAEBKokgHAMABHjSKVBKbk+73+11HAQAAAICURJEOAIADfr9foVCIIh0pobKykgeOAgAAAEACFOkAAEwya218RzoPGkUq8Hg8CofDamxsVCgUch0HAAAAAFIORToAAJMs9lDH/Px8FRcXu44DqLCwULNmzVJfX5/27NnjOg4AAAAApJw81wEAAMg2fr9fwWBQlZWVMsa4jgNIiox38fv98vl8mj17tus4WeeJJ55wHQEAAABAAhTpAABMMh40ilTk8XhUW1srn8+nk08+2XWcrHPxxRe7jgAAAAAgAUa7AAAwyXw+Hw8aRcrxer0KhULy+/2uowAAAABAyqFIBwBgEoXD4YNGuwCporS0VJLU0tKirq4ux2kAAAAAILVQpAMAMImam5vV19en4uJiTZ061XUcIC4nJ0eVlZXsSgcAAACAIVCkAwAwiWLz0dmNjlTk8XgUDAYp0h2orq6OvwAAAACkHh42CgDAJIrNR/d6va6jAIfweDx699135fP5XEfJOo2Nja4jAAAAAEiAHekAAEyi2I50HjSKVBTbke7z+WStdR0HAAAAAFIGRToAAJOkp6dHe/fulSSVlZU5TgMcavr06SoqKlJ3d7daW1tdxwEAAACAlEGRDgDAJPH7/QqFQiovL1dubq7rOMCQKisr47vSAQAAAAARFOkAAEwS5qMjHQwc7wIAAAAAiKBIBwBgkvj9fgWDQVVWVrqOAgzL6/UqFArJ7/e7jgIAAAAAKYMiHQCASWCt5UGjSAsVFRUKh8NqampSMBh0HQcAAAAAUgJFOgAAk6CtrU2dnZ0qLCzUjBkzXMcBhpWfn6/S0lIFAgE1NDS4jgMAAAAAKYEiHQCASRDbje71emWMcR0HSCg2J53xLgAAAAAQQZEOAMAkiD1olLEuSAcej0ehUIgHjgIAAABAVJ7rAAAAZAMeNIp0wo70yff666+7jgAAAAAgAYp0AAAmWCgUUmNjo8LhMDvSkRZKSkqUm5urtrY2HThwgLn+k2DFihWuIwAAAABIgNEuAABMsMbGRvX19amkpEQFBQWu4wAjMsaosrJSwWCQ8S4AAAAAIIp0AAAmnN/vZz460o7X62VOOgAAAABEUaQDADDBfD4f89GRdmI70pmTDgAAAAAU6QAATDh2pCMdeTwehUIh+f1+9ff3u46T8Ywx8RcAAACA1EORDgDABOrq6lJra6uMMSotLXUdBxi1oqIiTZ8+XT09Pdq7d6/rOAAAAADgFEU6AAATKLYbvbKyUjk5/J9dpJfYrnTmpAMAAADIdvyJHgCACcR8dKSz2Jx0inQAAAAA2Y4iHQCACRQr0pmPjnTk8Xh44CgAAAAAiCIdAIAJY62Nj3bxer2u4wBjVlFRIWutmpub1dfX5zoOAAAAADhDkQ4AwARpaWlRd3e3ioqKNG3aNNdxgDHLy8tTWVmZgsGgGhoaXMcBAAAAAGco0gEAmCB+v5+xLkh7sfEuzEkHAAAAkM0o0gEAmCA8aBSZIPbAUeakAwAAAMhmFOkAAEwQ5qMjE3i9XoVCIfl8PllrXccBAAAAACco0gEAmADBYFBNTU0Kh8OqqKhwHQc4bMXFxcrPz1d7e7s6OjpcxwEAAAAAJ/JcBwAAIBM1NDQoEAiotLRU+fn5ruMAh80Yo8rKSrW3t8vn86m4uNh1pIzE6BwAAAAgtbEjHQCACcCDRpFJeODoxKuuro6/AAAAAKQeinQAACaAz+dTKBSiSEdG8Hg8CoVC7JoGAAAAkLUo0gEAmADsSEcmqaysVDAYlN/vVzgcdh0HAAAAACYdM9IBAEiyAwcOqK2tTbm5uSopKXEdBxi3qVOnqri4WH19fWpublZVVZXrSBmnoaEh/pnxLgAAAEDqoUgHACDJfD6fgsGgKisrZYxxHQdIisrKSjU2Nsrn81GkT4DZs2fHP1trHSYBAAAAMBRGuwAAkGR+v5/56Mg4Xq9XoVCIB44CAAAAyEoU6QAAJFlsRzpFOjKJx+OJz0kHAAAAgGxDkQ4AQBL19/ezIx0ZqaysTJK0d+9e9fT0OE4DAAAAAJOLIh0AgCSKlYzTp09XUVGR6zhA0uTm5qq8vFzBYPCgB2MCAAAAQDagSAcAIIl8Ph+70ZGxPB4Pc9IBAAAAZCWKdAAAksjv9ysYDKqystJ1FCDpmJMOAAAAIFtRpAMAkEQ8aBSZLFak19fXy1rrOg4AAAAATBqKdAAAkqSvr0/Nzc3q7+9XRUWF6zhA0s2YMUOFhYXq7OxUW1ub6zgAAAAAMGko0gEASJKGhgYFg0GVl5crLy/PdRwg6Ywx8nq9CoVCjHcBAAAAkFWSWqQbYz5mjPlXY8wGY0yDMSZgjGk3xmw3xvyPMeYLxpjZybwnAACpgrEuyAaVlZUKBoM8cBQAAABAVhl3kW6MKTLG3GKM2SXpaUk3SzpJ0ixJzZJCkhZK+oSk/5C0yxjzqDHm1PHeGwCAVMKDRpENYnPSKdKTy1obfwEAAABIPeMq0o0xn5W0XdL3JfVIukPSxyTNstYWWWvnWGvLJOVJOlbSZyU9Kul8SX8xxvzaGDNvPBkAAEgF1lr5fD6FQiF5vV7XcYAJU1lZqXA4rMbGRoVCIddxAAAAAGBSjHdH+r2SXpV0srX2WGvtt621z1lrOwaeZCO2WmsfsNZ+SpJX0lckfVjStePMAACAc+3t7Wpvb1d+fr6Ki4tdxwEmTGFhoWbNmqW+vj41NTW5jgMAAAAAk2K8RfpKa+3fWGv/OpaLrLUd1tofSTpS0iPjzAAAgHN+v1+hUEiVlZUyxriOA0woj8ejUCjEeBcAAAAAWSNvPBdbazeO8/peSVvHswYAAKmAB40im1RWVmrXrl3y+/2uo2SMmpqa+OcVK1Y4TAIAAABgKOMq0gczxnzfWntbMtcEACAdMB8d2cTr9bIjPclWrlwZ/8wDRwEAAIDUM97RLoPdYoz5SZLXBAAgpYXDYTU0NCgYDKqystJ1HGDClZaWSpJaW1vV1dXlOA0AAAAATLxkF+m/lPR5Y8x/G2OG3O1ujDnNGLM+yfcFAMCZPXv2qK+vT8XFxZoyZYrrOMCEy8nJUWVlpUKhEONdAAAAAGSFpBbp1tprJf2bpCslPW6MibcJxphFxpjfSnpR0snJvC8AAC4xHx3ZyOPxKBgMMt4FAAAAQFZI9o50WWu/LumfJJ0v6VljzGJjzH9I2izpMkk1ks5J9n0BAHDF7/crFApRpCOrUKQDAAAAyCZJL9IlyVr7fUl/L+nDkrZI+ryknZI+aa09yVr7XDLvZ4yZY4z5uTGmwRjTZ4ypNcb8uzGmZIzrlEavq42u0xBdd84Q55YZY/7OGPOYMeZ9Y0yPMabdGPMXY8znjDHD/m9rjPmQMeYpY8y+6HVvGWO+YozJPZzfHwDgVmxHOg8aRTYZ+MBRHo4JAAAAINMNOcd8PIwxRtLVkr4W+0pSo6QPW2tbJ+B+R0paL6lS0uOStko6SdKXJZ1njDltNPc1xpRF11ksaZ2khyUdI+k6SRcaY0611u4ccMknJf1Ukd/teUl1kjyS/kbSvZLON8Z80g76k6Ux5lJJj0rqlfRrSfskXazISJzTousCANJET0+P9u7dK+l/H8AIZINp06apqKhIPT09amlpUUVFhetIAAAAADBhkroj3RjzcUlvS7pfUpWkOyV9XZJX0p+MMZXJvF/UTxQp0W+y1l5mrb3FWnuWIsX00ZK+N8p1vq9Iif5Da+3Z0XUuU6SQr4zeZ6Btki6RNMda+2lr7a3W2s8qUr7XS/qEIqV6nDFmpqR7JIUlnWGt/Zy19huSlkl6RdLlxpgrx/brAwBcio11qaioUG4u/7AI2YXxLgAAAACyRbJHuzyqSJH8S0mLrbW3WWv/TZEd6sdKetkYsyBZN4vuRj9HUq2k/xh0+HZJXZKuNsZMG2Gd6dGMXZJWDzr8Y0m7JZ1rjFkY+9Jau85au9Za2z/wZGttk6T/jP54xqC1LpdUIelha+3rA67pVWSuvCR9IVFWAEBq4UGjyGYU6QAAAACyRbKL9D9KWm6tvc5aG/8TlbX2vyV9XFK1pL8YY5Ym6X5nRt+fHaLQPiDpZUlFkk4ZYZ1TJE2V9HL0uoHr9Et6ZtD9RhKMvocGfX9W9P3pIa55UVK3pA8ZYwpHeR8AgGM+n48HjSJreTwehUIh+f1+11EAAAAAYEIldUa6tfbcBMeeMsacK+n3kl6QVJ6EWx4dfd82zPHtiuxYXywp0QNOR7OOouskZIzJk3RN9MfBhfmw97HWhowxuyQtlbRQkYe0JrpPzTCHjhkpIwAgOay17EhHVquoqFA4HFZTU5MCgYAKCgpcR0pbVVVVriMAAAAASCDZO9ITstb+RZFxJ8ERTh2t4uh7+zDHY9/PmqR1pMhc+OMkPWWtfWbQsWTeBwDg2L59+9TV1aWpU6dq+vTpruMAky4/P19lZWUKBoNqaGhwHSetNTQ0xF8AAAAAUk9Sd6SPhrX2TWPMhyf7vpPBGHOTIg9X3arIzPUJY61dMUyGGknLJ/LeAICIgbvRjTGu4wBOeDwe1dbWyufzacGCBa7jAAAAAMCEGNeOdGPM1MO5zlq7Y7xrRMV2cBcPczz2/f6JXscYc6OkuyS9K+lMa+2+ibgPACB1MB8d+N8HjjInHQAAAEAmG+9ol13GmC8fzsMxjTEfMMY8Lunmcdz/vej7cLPLF0Xfh5t9npR1jDFfkfQjSZsVKdGbxnqf6Gz1IxR5QOnOEfICAFIA89GB/33gqM/nk7XWdRwAAAAAmBDjLdKfkfRDSY3GmJ8aY85MtMPcGLPQGPMFY8wrkjZK+oCk58dx/9i15xhjDvpdjDEzJJ0mqVvShhHW2SCpR9Jp0esGrpOjyANLB95v4PF/lPRvkt5UpERvTnCfddH384Y49hFJRZLWW2v7RsgLAHAsGAyqqalJ4XBYlZWVruMAzsyaNUv5+flqb29XR0eH6zhpa+3atfEXAAAAgNQzrhnp1trPGGN+LOl7klZFX2FjzBZJjZLaJE2RVCbpaEnlkoykZknflPRv4ymNrbU7jDHPKlJ0f0mRXeExd0iaJuln1tqu2JfGmGOi124dsE6nMebBaP7Visw5j7lR0gJJz1hrD9opboz5Z0nfllQj6ZxhxrkM9BtJ/1fSlcaYH1lrX4+uM0XSd6Pn/HTk3xwA4FpjY6MCgYBKS0uVn5/vOg7gjDFGlZWVam9vl8/nU3HxcBPskMgll1wS/8zOfgAAACD1jPtho9bavyqyI3yRpM9JOlvSMknHDzp1r6TfSnpU0qPW2uB47x31RUnrJd1tjDlb0hZJJ0s6U5FRLN8cdP6W6Pvgp8LdJukMSV8zxiyT9JqkJZIuVaT4/9LAk40xn1GkRA9LeknSTUM8aK7WWvtA7AdrbYcx5npFCvU/G2MelrRP0iWK/EXDbyT9etS/OQDAmdhYl+rqatdRAOc8Ho9aWlrk8/m0dOlS13EAAAAAIOnGXaTHWGu3S7pFkowxRZJmK7ITvUdSs7W2MVn3GnTfHcaYlYqU2udJukCR3fB3SbrDWts2ynVajTGnSrpd0mWS/o+kVkn3S/qWtdY36JIjou+5kr4yzLIvSHpg0H1+Z4w5XZGC/xOK7Nh/X9LXJN1t2YIEAGmBB40C/8vr9WrTpk08cBQAAABAxkpakT6QtbZb0vboa8JZa+slXTfKcw/ZNj7g2D5JX46+RlpntSJjYMbMWvuyIoU/ACBN8aBR4H9VVlYqGAzK7/crHA4rNzfXdSQAAAAASKqkF+nGmDmSbpJ0rKR8SXWKPJT0CWttINn3AwBgsnV0dGj//v3Ky8tTSUmJ6ziAc1OmTNGsWbPU19enPXv2MPIIAAAAQMZJapFujDlD0pOKjCsZuPP7s5LqjDFfsdY+nsx7AgAw2WK70SsrKzXE8zGArFRZWamGhgb5fD6KdAAAAAAZJyfJ6/1fSVMl/VjSByTNkfTh6PfTJf3WGPONJN8TAIBJFZuP7vV6XUcBUobH41EwGJTPN/ixMgAAAACQ/pI92uUDkv5orR04Y7xB0npjzA8k/UrSncaYjdba55J8bwAAJsXAHekAIrxer0KhEEU6AAAAgIyU7B3pvZI2DnXAWtsm6ROSGiX9Q5LvCwDApAiHw/L7/TxoFBikrKxMktTS0qLu7m7HaQAAAAAguZJdpL8l6ZjhDlpruyQ9LumUJN8XAIBJsWfPHvX19am4uFhTp051HQdIGTk5OaqsrGRXOgAAAICMlOwi/SeSLjTGnJrgnD5JNsn3BQBgUsTGurAbHTgUc9IP3/Lly+MvAAAAAKkn2TPST5X0vqSnjDE3Wmv/a+BBY0yRpEskvZzk+wIAMCliDxqlSAcO5fF49M4771CkH4aamhrXEQAAAAAkkOwi/e8HfP6lMeZ7kp6RVCtplqTLo8duSvJ9AQCYFMxHB4Y38IGj1loZY1xHAgAAAICkSHaR/iFJKyQtj76OlXR99JiVZCS9Kelrxpg3JL0h6W1rbSDJOQAASLru7m7t3btX0v8+WBHA/5o2bZqmTZsW//8rlZWVriMBAAAAQFIktUi31m6QtCH2szGmQNLx+t9ifUX052WxSySFjDFbrbUfSGYWAACSze/3KxQKqaKiQrm5ua7jACnJ4/GoublZfr+fIh0AAABAxkj2jvSDRHea10RfkiRjTK6kpTq4XD9hInMAAJAM9fX1CgaDOuKII1xHAVKWx+OR3+9XfX29TjzxRNdx0saaNWvin1etWuUwCQAAAIChTGiRPhRrbVjSW9HXA5JkGKAJAEgDPp+P+ejACDwej4LBIA8cHaMbbrgh/pkiHQAAAEg9Oa4DSJK11rrOAABAIv39/fL5fAqFQvJ6va7jACmroqJC1lo1Nzerr6/PdRwAAAAASIqUKNIBAEh1LS0t6u7ujj9MEcDQ8vLyVF5erkAgIL/f7zoOAAAAACQFRToAAKMQ243OWBdgZB6PR6FQiPEuAAAAADIGRToAAKPAfHRg9JiTDgAAACDTUKQDADAKFOnA6MWK9Pr6evEoHAAAAACZgCIdAIAR9Pb2qrm5WdZaVVRUuI4DpLyZM2dqypQp6uzs1L59+1zHAQAAAIBxo0gHAGAEDQ0NCgQCKi8vV15enus4QMozxjDeBQAAAEBGoUgHAGAE9fX1CoVC8nq9rqMAacPr9fLAUQAAAAAZgyIdAIARMB8dGLuBc9IBAAAAIN3x79MBAEjAWqv6+nqKdGCMKisrFQ6HtWfPHgUCARUUFLiOlNIuuugi1xEAAAAAJECRDgBAAvv27VNXV5emTJmiGTNmuI4DpI38/HyVlZUpEAiooaFBCxYscB0ppa1du9Z1BAAAAAAJMNoFAIAEYrvRvV6vjDGu4wBphQeOAgAAAMgUFOkAACTAfHTg8FGkAwAAAMgUFOkAACTg8/kUCoXk9XpdRwHSTlVVlUKhkOrr62WtdR0HAAAAAA4bM9IBABhGIBBQU1OTwuGwKioqXMcB0s7MmTNVUFCgjo4O7d+/XyUlJa4jpazVq1cP+RkAAABAaqBIBwBgGH6/X8FgUOXl5crPz3cdB0g7xhh5PB61tbWpvr6eIj2BO+64I/6ZIh0AAABIPYx2AQBgGMxHB8bP6/UyJx0AAABA2qNIBwBgGPX19QoGg8xHB8aBB44CAAAAyAQU6QAADMFaGy/S2ZEOHD6Px6NwOKzGxkYFg0HXcQAAAADgsFCkAwAwhH379qmzs1OFhYWaOXOm6zhA2srPz1dpaakCgYAaGhpcxwEAAACAw0KRDgDAEGLz0b1er4wxruMAaS023qW+vt51FAAAAAA4LBTpAAAMob6+XqFQiPnoQBLwwFEAAAAA6Y4iHQCAIQzckQ5gfLxer0KhkOrr62WtdR0HAAAAAMaMIh0AgEH6+vrU1NSkcDisiooK13GAtFdcXKyCggJ1dHRo//79ruMAAAAAwJhRpAMAMEhDQ4OCwaDKy8uVn5/vOg6Q9owx8fEuzEkHAAAAkI7yXAcAACDV1NfXKxgMau7cua6jABnD4/Foz549qq+v1wknnOA6Tsq5/vrrXUcAAAAAkABFOgAAg8SKdOajA8nj9XpVU1PDA0eHsWbNGtcRAAAAACTAaBcAAAaw1saLdI/H4zoOkDEqKysVDofV1NSkQCDgOg4AAAAAjAlFOgAAA7S2tqqrq0tTp07VjBkzXMcBMkZ+fr7KysoUCATU0NDgOg4AAAAAjAlFOgAAAwwc62KMcR0HyCg8cBQAAABAumJGOgAAA/h8PuajAxPE6/Vq27ZtFOlDWLVqVfwz89IBAACA1EORDgDAAMxHBybOwB3p1lr+1ccA99xzT/wzRToAAACQehjtAgBAVG9vr5qbm2WtVUVFhes4QMaZMWOGpkyZos7OTrW2trqOAwAAAACjRpEOAECUz+dTIBBQRUWF8vL4R1tAshlj4rvSfT6f6zgAAAAAMGoU6QAARA180CiAicEDRwEAAACkI4p0AACiKNKBiUeRDgAAACAdUaQDACCpv79f9fX1CoVCFOnABKqoqJC1Vs3Nzert7XUdBwAAAABGhSIdAABJzc3N6unp0fTp0zVt2jTXcYCMlZeXp4qKCgUCAeakAwAAAEgbFOkAAIixLsBkYrwLAAAAgHRDkQ4AgMRYF2ASeb1ehUIhinQAAAAAaYMiHQAAsSMdmEwDd6T39/e7jgMAAAAAI8pzHQAAANc6OzvV2toqY4zKyspcxwEy3rRp0zR9+nT19PSoubmZv8CSdPvtt7uOAAAAACABinQAQNaL7Ub3eDzKyeEfawGTwev1qrGxUfX19RTpklavXu06AgAAAIAEaAsAAFkvVqRXVVW5jgJkDR44CgAAACCdUKQDALJe7EGjHo/HdRQga1RVVSkYDKqurs51FAAAAAAYEUU6ACCrhUIh+f1+hUIhxksAk6i0tFS5ubnat2+fDhw44DoOAAAAACTEjHQAQFZraGhQX1+fSkpKVFhY6DoOkDVycnLk8XjU0dGh+vp6HXvssa4jOXXxxRfHP69du9ZhEgAAAABDoUgHAGS12Hz0+fPnu44CZB2v16vW1laKdEm///3vXUcAAAAAkACjXQAAWS1WpDPWBZh8PHAUAAAAQLqgSAcAZC1rrerq6hQKhVRVVeU6DpB1vF6vwuGwGhoaFAwGXccBAAAAgGFRpAMAslbsIYcFBQWaOXOm6zhA1ikoKFBpaan6+vrU0NDgOg4AAAAADIsiHQCQterq6hQMBlVVVSVjjOs4QFaKjXepq6tzHQUAAAAAhkWRDgDIWsxHB9yrqqpiTjoAAACAlEeRDgDIWgN3pANwY+COdGut6zgAAAAAMCSKdABAVuru7lZzc7MkqaKiwnEaIHvNmDFDRUVF6urqUktLi+s4AAAAADAkinQAQFaqr69XKBRSZWWlcnNzXccBspYxhjnpAAAAAFIeRToAICsxHx1IHcxJBwAAAJDq8lwHAADABeajA6kjVqRn8470n/3sZ64jAAAAAEiAIh0AkHVCoZD8fj870oEUUVZWJmOMWlpa1NnZqenTp7uONOlWrVrlOgIAAACABBjtAgDIOo2Njert7VVpaammTJniOg6Q9XJycuTxeBjvAgAAACBlUaQDALJObKwLu9GB1MF4FwAAAACpjCIdAJB1KNKB1OP1einSAQAAAKQsZqQDALKKtZYHjQIpyOv1KhwOq6GhQcFgUPn5+a4jTaoVK1bEP9fU1DhMAgAAAGAoFOkAgKzS2tqqzs5OTZ06VTNnznQdB0BUQUGBysrKFAgE5Pf7tWDBAteRJtXGjRtdRwAAAACQAKNdAABZZeBudGOM6zgABojNSd+9e7frKAAAAABwEIp0AEBWYT46kLp44CgAAACAVEWRDgDIKsxHB1LXwAeO9vf3u44DAAAAAHEZUaQbY+YYY35ujGkwxvQZY2qNMf9ujCkZ4zql0etqo+s0RNedM8z5lxtjfmSMeckY02GMscaYhxKsvyB6znCvh8f6uwMARq+zs1MtLS0yxqi8vNx1HACDTJ8+XdOnT1dPT4/27NnjOg4AAAAAxKX9w0aNMUdKWi+pUtLjkrZKOknSlyWdZ4w5zVrbOop1yqLrLJa0TtLDko6RdJ2kC40xp1prdw667J8kfUBSpyRf9PzR2CTpd0N8v3mU1wMADkNsN7rH41FOTkb8XTKQcaqqqtTQ0KC6ujr+5QgAAACAlJH2RbqknyhSot9krf1R7EtjzA8lfVXS9yR9fhTrfF+REv2H1tqvD1jnJkl3Re9z3qBrvqpIgf6+pNMlPT/KzG9aa1eP8lwAQJLs3r1bwWBQ1dXVrqMAGEZVVZV2796turo6nXzyya7jAAAAAICkNB/tEt2Nfo6kWkn/Mejw7ZK6JF1tjJk2wjrTJV0dPX/1oMM/lrRb0rnGmIUDD1hrn7fWbrfW2sP9HQAAk4f56EDqG/jAUf4TCwAAAECqSOsiXdKZ0fdnrbUHPZHKWntA0suSiiSdMsI6p0iaKunl6HUD1+mX9Myg+41XtTHmBmPMbdH3E5K0LgBgGH19fWpsbFQ4HJbH43EdB8AwSkpKVFBQoP3792v//v2u4wAAAACApPQf7XJ09H3bMMe3K7JjfbGk58a5jqLrJMPHoq84Y8yfJX3GWls3mgWMMTXDHBrtnHYAyCo+n0+BQEAVFRXKz893HQfAMIwx8nq9am1t1e7du1VSMqZnxwMAAADAhEj3Ir04+t4+zPHY97MmaZ2RdEv6jiIPGo09uPQERcbJnCnpOWPMMmtt1zjvAwAYJDbWZcGCBa6jABhBVVWVmpqaVFdXp2XLlrmOMymeeOIJ1xEAAAAAJJDuRXpasdY2S/rWoK9fNMacI+kvkk6W9HeKPNx0pLVWDPV9dKf68nFGBYCME3vQKPPRgdRXVVWl1157TXV1o/qHehnh4osvdh0BAAAAQALpPiM9tlO8eJjjse/3T9I6h8VaG5J0b/THj0zEPQAgm4XDYdXX11OkA2mioqJCktTc3KyuLv6hHgAAAAD30r1Ify/6Ptzs8kXR9+Fmnyd7nfHYG32fNoH3AICs1NDQoN7eXpWUlGjq1Kmu4wAYQW5urrxer4LBYFbtSgcAAACQutK9SH8++n6OMeag38UYM0PSaYrMJd8wwjobJPVIOi163cB1chR5YOnA+02EU6LvOxOeBQAYs9h8dHajA+mjqqpKwWBQu3fvdh0FAAAAANK7SLfW7pD0rKQFkr406PAdiuzufnDgwzuNMccYY44ZtE6npAej568etM6N0fWfsdaOq+Q2xiwfXPhHvz9b0lejPz40nnsAAA7FfHQg/cSK9GzZkV5dXR1/AQAAAEg9mfCw0S9KWi/p7mghvUWRh3aeqcgolm8OOn9L9N0M+v42SWdI+poxZpmk1yQtkXSppGYdWtTLGHOZpMuiP3qj76caYx6Ifm6x1t484JIfSlpkjFkvyRf97gRJZ0U//7O1dn2iXxYAMDbWWnakA2nI6/UqHA6roaFBfX19KiwsdB1pQjU2NrqOAAAAACCBtC/SrbU7jDErJX1b0nmSLpDUKOkuSXdYa9tGuU6rMeZUSbcrUo7/H0mtku6X9C1rrW+Iy5ZJ+syg7xZGX5K0W9LAIv1BSR+X9EFJ50vKl7RH0iOSfmytfWk0WQEAo9fc3KzOzk5NmzZNM2fOdB0HwCjl5+eroqJCfX198vl8OvLII11HAgAAAJDF0r5IlyRrbb2k60Z57uCd6AOP7ZP05ehrNGut1qGjYBKdf5+k+0Z7PgBg/BjrAqSvqqoqbd++Xbt376ZIBwAAAOBUWs9IBwBgJIx1AdJXdXU1DxwFAAAAkBIo0gEAGctaG9+RzgP8gPTj9XoVDAbl8/kUCoVcxwEAAACQxSjSAQAZq62tTfv371dBQYFKSkpcxwEwRlOnTlVpaal6e3vl9/tdxwEAAACQxSjSAQAZa+B8dGOGfUQGgBRWVVWlYDCouro611EAAAAAZDGKdABAxmKsC5D+mJMOAAAAIBVQpAMAMhZFOpD+Bhbp/f39ruMAAAAAyFIU6QCAjNTR0aHW1lbl5OSorKzMdRwAh2natGmaMWOGenp61NTU5DrO/9/enYdHWd77H//c2fewL2EJuyAIsoi4lEW0UBWk1brX2vrTtrbH2uqp2vZUsLW1x3M8tee01t26VIsLLhVFLYsLILIvQoCEsISd7MvMJDP3749ZGkISskzyzCTv13XNNZN5tu8wD5PMZ+753gAAAAA6qTinCwAAoC3U7o8eE8PnxkA0y8rK0oEDB5Sfn99hv2Gydu1ap0sAAAAA0AiCdABAh0RbF6DjyMrKUl5envbu3avzzz/f6XLaxMSJE50uAQAAAEAjGKIHAOiQ9u7dK4/Ho759+zpdCoBW6tu3b6hPurXW6XIAAAAAdEIE6QCADqeiokJHjhyRJPXq1cvhagC0VkZGhlJTU1VeXq6jR486XQ4AAACAToggHQDQ4QTbuvTp00exsbFOlwOglYwxJ41KBwAAAID2RpAOAOhw6I8OdDxZWVmqrq5Wfn6+06W0CWNM6AIAAAAg8hCkAwA6nPz8fIJ0oIPp169fKEinTzoAAACA9kaQDgDoUKqqqnT48GFZa9W7d2+nywEQJpmZmUpMTFRZWZmOHz/udDkAAAAAOhmCdABAhxJs69KrVy/FxcU5XQ6AMDHGhEal0ycdAAAAQHsjSAcAdCh79+6Vx+NRv379nC4FQJj17dtXHo+nw/ZJBwAAABC5CNIBAB1KsD963759nS4FQJjVHpFOn3QAAAAA7YkgHQDQYbhcLh06dEg+n099+vRxuhwAYda1a1clJCSouLhYhYWFTpcDAAAAoBMhSAcAdBj79u2Tx+NRz549FR8f73Q5AMLMGKOsrCxVV1fT3gUAAABAuyJIBwB0GMG2Lv3793e6FABtpF+/fvRJBwAAANDuCNIBAB1Gfn6+PB6PsrKynC4FQBupPSKdPukAAAAA2gtBOgCgQ3C5XDp48CD90YEOrlu3bvRJBwAAANDu4pwuAACAcAj2R+/Vqxf90YEOLNgn/dixY9q7d6+6d+/udElhUVBQ4HQJAAAAABrBiHQAQIcQ7I9OWxeg4wv2Sd+zZ4/TpYRNVlZW6AIAAAAg8hCkAwA6hGB/9H79+jldCoA2Rp90AAAAAO2NIB0AEPXojw50LvRJBwAAANDeCNIBAFFv79699EcHOhFjjPr16xcald4RHDx4MHQBAAAAEHkI0gEAUS/Y1qV///5OlwKgnWRlZXWoPun9+vULXQAAAABEHoJ0AEDU27NnDxONAp1M7RHp9EkHAAAA0NYI0gEAUa2qqkqHDh2Sz+dT7969nS4HQDvp2rWrEhMTVVJSouPHjztdDgAAAIAOjiAdABDVgm1d+vTpQ390oBMJ9kn3eDwdpk86AAAAgMhFkA4AiGr5+fm0dQE6qWB7l47SJx0AAABA5CJIBwBEtWB/dCYaBTqf2kE6fdIBAAAAtCWCdABA1KqoqNDhw4dlrVWvXr2cLgdAO8vMzFRycrLKysp09OhRp8sBAAAA0IERpAMAolawrUufPn0UFxfndDkA2lmwTzrtXQAAAAC0NYJ0AEDUoq0LgP79+8vj8RCkAwAAAGhTBOkAgKi1Z88eeTwe9evXz+lSADgkKysrNCLd5/M5XQ4AAACADoogHQAQlUpKSnTs2DHFxMTQHx3oxDIyMpSenq7KykodOnTI6XIAAAAAdFAE6QCAqJSfnx8ajR4Tw68zoDPrCO1drLWhCwAAAIDIQ/IAAIhKeXl5qq6uVlZWltOlAHAYE44CAAAAaGsE6QCAqGOtDfVHZ6JRAP369ZPH49HevXtVU1PjdDkAAAAAOiCCdABA1CksLFRRUZESEhLUvXt3p8sB4LCUlBR169ZNVVVVOnDggNPlAAAAAOiACNIBAFEnLy8vNBrdGON0OQAiQLT3SV+3bl3oAgAAACDyxDldAAAAzbVnzx5VV1erX79+TpcCIEL069dP27dvV15enmbMmOF0Oc02adKk0G0mHAUAAAAiDyPSAQBRxVp70oh0AJD8QXpNTY0OHDggt9vtdDkAAAAAOhiCdABAVDl8+LDKy8uVlpamjIwMp8sBECESEhLUq1cvud1u7d271+lyAAAAAHQwBOkAgKhCf3QADQn2Sc/Ly3O6FAAAAAAdDEE6ACCq5OXl0R8dQL369++v6upqgnQAAAAAYUeQDgCIGjU1Ndq7dy/90QHUq3fv3rLWhlpAAQAAAEC4EKQDAKLG/v37VVVVpW7duiklJcXpcgBEmLi4OGVlZTEqHQAAAEDYEaQDAKJGsD/6gAEDnC4FQIQK9knfs2eP06UAAAAA6EAI0gEAUaP2RKMAUJ8BAwbI4/EoNzdX1lqnywEAAADQQRCkAwCiQlVVlQoKCuTz+ZSVleV0OQAiVPfu3ZWQkKCioiKdOHHC6XIAAAAAdBBxThcAAEBT5Ofny+12q0+fPoqPj3e6HAARyhij/v376/Dhw8rLy1OPHj2cLqlJ+vbt63QJAAAAABrBiHQAQFTIzc1VdXU1bV0AnFb//v2jbsLRgwcPhi4AAAAAIg9BOgAgKjDRKICmCvZJz8vLk9frdbocAAAAAB0AQToAIOIVFRXp2LFjiouLU8+ePZ0uB0CES09PV0ZGhioqKlRQUOB0OQAAAAA6AIJ0AEDEC7Z16devn2Ji+NUF4PQGDBgQde1dAAAAAEQu0ggAQMQLtnWhPzqApgq2d8nNzXW6lCZ55513QhcAAAAAkSfO6QIAAGiMz+dTbm4u/dEBNEu/fv1UU1OjAwcOyOVyKSkpyemSGjV37tzQbWutg5UAAAAAqA8j0gEAEe3gwYOqqKhQenq6MjMznS4HQJRISEhQnz595Ha7tWfPHqfLAQAAABDlCNIBABGN0egAWira2rsAAAAAiFwE6QCAiEaQDqClCNKd9eabb8oYo6SkJBUUFDhdDsIkPz9fxhgZY3TzzTc7XU6baerj9Hq9euyxxzR16lR1795dsbGxoe02btzYrH21t+eeey5U13PPPed0OUCzvfjiizLGqEuXLjp69KjT5QDoBAjSAQARy+Vyaf/+/aqpqWGiUQDN1rNnT8XFxen48eMqLCx0upxOxeVy6Sc/+Ykk6bbbblO/fv0crggIP5/PpyuuuEK33367PvnkExUWFsrn8zldFtBpXHfddRoxYoRKSkp03333OV0OgE6AIB0AELH27Nkjt9ut3r17KyEhwelyAESZmJgY9e/fX9XV1YxKb2d//vOflZ+fr6SkJN17771OlwO0iTfffFPvvvuuJCk7O1sPP/ywFi5cqEWLFmnRokUaPHiwwxUCHVtsbKx++ctfSvJ/w2L79u0OVwSgo4tzugAAABoSbOtyxhlnOF0KgCg1YMAAHThwQLt379Y555zjdDmdQlVVlR566CFJ0s0336ysrCyHKwKab9CgQbLWNrrO4sWLQ7dfeeUVTZkypcX7AtAy119/vf7jP/5De/fu1YIFC/TKK684XRKADowR6QCAiGSt1e7du+mPDqBVBg4cKI/Ho7y8PHm9XqfL6RSef/55HTt2TJJ00003OVwN0Hb2798fuj1+/HgHKwE6r9jYWN1www2SpNdee0379u1zuCIAHRlBOgAgIhUWFurEiROKj49Xz549nS4HQJRKS0tTly5dVFlZeVLohbbz2GOPSZKGDh2q8847z7E6/vSnP9HSB23K7XaHbicmJjpYCdC5BYN0r9erJ554wuFqAHRkBOkAgIgUHI3ev39/xcTw6wpAywVHpe/evdvpUjq8LVu2aNOmTZL8X7dvzMUXXyxjjIwxevnllxtcz+v1au7cuaF177777ibV8vDDD2vYsGG68MIL9cQTT6i4uLjJj6O12vqxhUtlZaX+/Oc/6/LLL9eAAQOUnJys5ORkDRkyRN/4xjf0xBNPqLS0tEX7Li0t1UsvvaRbbrlF48ePV5cuXRQfH69u3bppwoQJuuuuu5r0QYfX69ULL7ygOXPmaMCAAUpKSlJycrIGDBigCRMm6MYbb9Rf//pXVVRUhHX7/Pz80PNy8803h+5fvnx56P4VK1aE7g/eF7zMnz//tPuqT3l5uf7whz/okksuUVZWlhITE9WtWzedc845+tWvfhX6tkdT/OMf/9CcOXPUp08fJSUladCgQbrhhhu0atWqJu+jqSLl+W6KcB1j+/bt+vGPf6wxY8YoMzNTycnJys7O1tVXX61FixY1uu38+fND58Ty5ctbtW7tczJ43uXk5OjOO+/UqFGjlJGRIWOMnnvuuXr339rXgXCcs619Ts4880ydffbZkqQXX3yRVkoA2gw90gEAESkYpA8cONDpUgBEuQEDBmjbtm3Kzc3VxRdf7HQ59ZowYYLTJYTFm2++Gbo9Y8aMRtd96KGHNHnyZFlrNX/+fF199dWKjY09Zb0f/OAHeueddyRJ3/rWt/Twww83q6bPPvtMn332mX784x9rzpw5uummmzR79mzFxbXdW6H2emyt8f777+vmm2/WkSNHTlm2Z88e7dmzR4sWLdKqVav07LPPNmvfHo9HvXr1OmnEdlBRUZGKioq0YcMG/fGPf9Qf/vAH/fCHP6x3P8ePH9ell16qL7744pRlBw4c0IEDB7Rhwwa99NJLyszM1Lx588K6fXt77733dPPNN+vo0aMn3e/xeLR27VqtXbtWf/jDH/Tiiy9q7ty5De7H6/Xqlltu0V//+teT7t+7d6/27t2rV155Rb/73e/Uq1evsNQdKc93U4TrGPfff78efPDBU1qG7du3T/v27dOrr76q6dOn6/XXX1e3bt2aXWdrPP/88/r+97+vqqqq067b2teBcJyz4XpOZsyYoY0bN2rv3r3atGlTKFgHgHAiSAcARJyamhrt2bNH1dXV9EcH0GrByS4LCgpUXl6utLQ0hys61bp165wuISw+/PBDSVJMTIwmTZrU6LqTJk3SVVddpVdffVU7d+7UCy+8cMpo3fnz5+vJJ5+UJM2ePVtPP/20jDFNqmXRokV6/vnn9fLLL+vIkSNyuVx69dVX9eqrr6pXr166/vrrddNNN7VJb+u2fmyttXDhQl1//fWhEHDs2LG68sorNWzYMBljtH//fq1cuVJLlixp0chOn88nt9utrKwsXXLJJRo7dqx69+6tmJiY0L7ffvtt1dTU6Ec/+pGysrL09a9//ZT93HrrraFwbdiwYbruuus0YsQIJScnq7S0VDk5Ofr444/1+eef11tHa7evz5gxY0KjjX/5y19q27ZtknTKCOSRI0c2eZ+S9Prrr+uaa66R1+tVfHy85s6dq+nTp6t3794qLS3VsmXLtHDhQpWVlenrX/+6PvzwQ1100UX17uuOO+4IhegJCQn69re/rQsvvFAxMTFas2aNnn76ad1zzz1h++AgUp7vpgjHMe67777QhMqxsbG69tprddFFFyk5OVlbtmzRM888oyNHjmj58uWaMWOGPv/8cyUlJbW45ub47LPP9OCDDyo2Nla33HKLLrjgAiUlJSknJ0d9+vQ5ad3Wvg6E65wN1/Nee7LfJUuWEKQDaBOGr7x0LMaYdRMmTJjQUd6MAeiccnNz9cwzzyg2NlbXXHON0+UA6AD+8Y9/qLi4WNdee63GjRvndDkdktfrVUZGhiorKzV69Ght3br1tNvs3LlTo0ePVk1NjQYPHqycnBzFx8dLkp566indeuutkqTJkydr6dKlSk1NbVFdH374oV544QW9+eabqqysPGn5mDFjdNNNN+mGG24IfegSDu3x2FoiLy9PY8eOVUVFhWJiYvTII4/ojjvuqDfELyoq0qZNmzR9+vTQffn5+Ro8eLAk6dvf/na97SKC/+azZs1q8MOBzZs3a9asWTp8+LCGDBmiXbt2ndTK7ejRo+rTp4+stZo0aZKWL1/e4L/R3r17JUnZ2dlh274pj3P69Omh9i6Nva8+3b7279+vMWPGqLS0VAMHDtQ//vEPnXXWWafsZ82aNfrqV7+qkpIS9e/fX3l5eaFzKuiTTz7R1KlTJUldunTRRx99pIkTJ560Tk5OjqZPn67Dhw+H7nv22WdP23amIZHwfDdFOI6xatUqXXDBBbLWKjU1VYsXLw79ewcVFhZq1qxZWrt2rSTp7rvvPuXbJvPnz9eCBQskScuWLTvp/1hdp1s3GNgH9enTR//85z915plnNrjP1r4OhOucDefzvnfvXg0aNEiS9PWvf11vvPFGg48fQHSZOHGi1q9fv95aO/H0a7ctms4CACIObV0AhBt90tteXl5eKKQ+44wzmrTNiBEj9N3vfleSv43AM888I0l655139P3vfz+0zrvvvtvioDk2NlazZ8/WSy+9pCNHjuivf/2rLrnkklCrla1bt+pnP/uZBgwYoFmzZumll146JWxvifZ4bC3x0EMPhfoM33PPPfrxj3/cYPjZtWvXRgO+hgT/zRsbYT927Fj99re/leQ/d1auXHnS8ry8vFA4ff311zf6b5SdnX1KuNba7dvTww8/rNLSUsXGxuqtt96qN5CU/B+6PPLII5L8LS9effXVU9b57//+79DtP/zhD6eE6JL//+dTTz0Vpuoj4/luinAc4+GHHw7t4+GHHz4lRJekbt266bXXXlNKSook6S9/+Uu7ztHw+OOPNxqiS61/HQjXORvO5z07O1vJycmS/B/cAEBbIEgHAEQcgnQA4VY7SPf5fE6X0yEFRwtKalZP4Pvvvz8UfvzmN7/RihUrdO2118rr9apv375asmSJevToEZYa09LSdNNNN+mDDz7Q/v379V//9V+hr//7fD598MEHuvHGG9WnTx995zvf0bJly1o1aV17Pram8Hq9+vvf/y5JSk9P13333ddux67P+eefH7pdt21DMISUFGqf0hyt3b69WGv10ksvSZJmzpx52nYU11xzTai//wcffHDSMrfbrffee0+S1Lt3b914440N7ueyyy7TqFGjWlF587Xl890UrT2G2+3W4sWLJUndu3fXLbfc0uC62dnZuu666yT5J+Os+1y1lezsbM2ZM6fRdVr7OhDOczbcz3vXrl0l+UfM030BQFugRzoAIKKUlJToyJEjMsac0ssRAFoqMzNTqampKisr08GDB9W/f3+nSzrJE088Ebp92223OVhJyxUWFoZuNydIz8rK0h133KHf//73OnDggGbOnCmv16vMzEy9//77oa/qh1vfvn1111136a677tK2bdv0wgsv6G9/+5v279+vsrIyPffcc3ruued0zjnnaM2aNS06hlOPrSGbN29WaWmpJP/EfOnp6W16vPz8fP31r3/V8uXLtWPHDhUXF8vlctW77oEDB076efTo0crKytLBgwf19NNPy1qrW2+9VZMnTz6pJUhDWrt9e9m2bVvo/056evpJE/Y2JC0tTcXFxdq+fftJ92/atEkej0eSNG3atHonuK1t5syZp+yjNZx8vpuitcfYtGlTaELV6dOnKyEhodH1v/rVr+rpp5+W5P/g4Oqrr279gziNCy+88LRzLbT2dSCc52y4n/fu3bvr4MGD8ng8qqioiMg5UQBEN4J0AEBE2bVrlzwej/r373/aN4AA0FTGGA0cOFD5+fnavXt3xAXp3/ve90K3ozVIDwZMkpodzNxzzz164oknVFRUJK/Xq8TERL311lsaO3ZsuMus1+jRo/XQQw/pwQcf1AMPPKAHH3wwNAHf0aNHW7Vvpx9bbbXDy7YejfyHP/xB995770nnRWOCwV5QbGysHn/8cV155ZXyeDx65pln9Mwzz6hLly4677zzdOGFF2rWrFn1ti4Jx/btJT8/P3T79ddf1+uvv97kbYuKik76+eDBg6Hbw4YNO+32TVmnqZx+vpuitcc4dOhQ6PaIESNOe7za69Teti3169fvtOu09nUgnOdsuJ/3jIyM0O2qqiqCdABhFzkfxQMAINq6AGg72dnZ8ng82rVrl9OldEiJiYmh23VDstM5cODASS13rr76ak2bNi1stZ3Oli1bdM8992jQoEF64IEHQiG6pFZ/6OL0Y6ut9vPSlgHTSy+9pJ/85CehUPUrX/mKfvnLX+qpp57S3//+dy1atEiLFi3S448/Htqm9r950OWXX641a9Zo3rx5oQkKi4uL9d577+kXv/iFJk2apLPOOkvvv/9+vXW0dvv2UFJS0uJtg6PPg8rLy0O3a7fMaEi4evNHyvPdFK05RllZWeh2U/7tav8fq71tWwq2kmpMa18HwnnOSuF93mvX1pR/CwBoLkakAwAiRk1NjXJzc+XxeByd9AtAx9SvXz95vV4dOHBAFRUV7TrBY2dQu51L7TYvp7Nv3z7Nnj37pABk4cKF+s1vftOmH6oWFBTob3/7m1588cVTJqbr2rWrrr76at10000n9XVuLqceW0Nqj9asHbqG23/8x39IkuLi4vT222/ra1/7Wr3rNaUn8rhx47Ro0SKVlZXps88+08qVK/Xxxx9r5cqVqq6u1tatW3XppZfqhRde0A033BD27dta7SDzV7/6lRYsWBCWfTVlwtzgZJOtFUnPd1O09Bi1v2nTlH+72v/HWtNGKdzzerT2dSCc52xQuJ734O+ehIQEfscDaBOMSAcARIx9+/apsrJSXbt25auYAMIuPj5eWVlZ8ng8ys3NdbqcDqd2v++mBuknTpzQrFmzdPDgQcXExOimm26S5G8T86tf/SrsNZaWlurZZ5/VzJkzNXDgQP3sZz8Lhejx8fGaM2eOXn31VR06dEh/+ctfWhWih+uxFRQU6J577tFZZ52ltLQ0ZWRk6Oyzz9Z9992nEydONKum2qPrw9kbu7a8vDzt2bNHkjRv3rwGQ1Xp5AlqTyc9PV2zZ8/WAw88oOXLl+vQoUP6yU9+Isk/+eFPf/rTekc5h2v7tlK7FUfdvuHNlZWVFbq9e/fu067flHVOJ1Kf77Y4Rt++fUO3m/LNptrr1H5upJO/wVPfKO3ajh8/ftpjNUdrXwfCec7W1drnPfi7Z+DAgaftFQ8ALdEhgnRjTH9jzDPGmIPGGLcxJt8Y8wdjTNdm7qdbYLv8wH4OBvZb7/c5jTFXGWP+1xjziTGm1BhjjTEvNuE45xtjFhtjCo0xVcaYzcaYO40xNAMG0KkF+6MzGh1AW6G9S9sZPHhwaARgTk7OadevrKzU5Zdfrh07dkiSHn30UT377LMaM2aMJOmFF15o0gjW06murtbbb7+tq6++Wr1799Z3v/tdLV26NDTKc+LEiXr00Ud18OBBvf3227rqqqtOCrlaIlyP7a233tKoUaP0n//5n/J6vbr88ss1c+ZMHTlyRA899FCT+1EHjR07NjQaddmyZW3SbuLIkSOh20OHDm103SVLlrT4ON27d9cjjzyiSZMmSfL3sm/O/+vWbh8u48ePDz0n//znP1s1+njcuHGhCTBXrFhx2qD5n//8Z4uPFRQtz3c4jjFu3LjQa8Py5ctVXV3d6P4++OCD0O3JkyeftKxLly6h27V729fn888/b1L9TdXa14FwnrOn05znPT8/PzS5rRNzUADoHKI+SDfGDJW0TtJ3JK2R9D+S8iT9WNIqY0z3Ju6nu6RVge1yA/tZE9jvOmPMkHo2+6WkH0k6W1JBE49zhaSPJU2VtEjS/0lKCBzvlabsAwA6KoJ0AG0tOztbbrdbu3btatM3/51RbGxsaEK4HTt2NNonvaamRldffbVWr14tSbrvvvv0ox/9SDExMaE2AT6fTz//+c9bXM/q1at1++23q2/fvrriiiv06quvhkKW/v3765577tG2bdu0du1a3XHHHerRo0eLj1VbuB7b8uXLdfXVVyshIUGLFy/Wl19+qVdeeUWLFi3SgQMH9Nprr50yyvV0YmNjdd1110ny92z+3e9+14JH2Ljavbkb++bH/v379eyzz7b6eLW/CVFTU9Pu27dWbGxsqFXF3r179dRTT7V4X4mJibr00ksl+QPuv/3tbw2u+95774XlWwnR9ny35hiJiYm67LLLJPlHiT/33HMN7mP//v16+eWXJflbocyaNeuk5WeeeWbo9tKlSxvcz2effab169c3p/zTau3rQDjP2aZqyvNe+wOHc889t61LAtBJRX2QLunPknpJusNaO89ae6+19iL5g+kzJD3YxP38VtIISY9Ya2cG9jNP/mC9V+A4df0ksE2GpB+c7gDGmAxJT0rySppurb3FWvvv8gfxqyRdZYy5ton1AkCHUlRUpKNHj8oYo969eztdDoAOKjMzU+np6SovL1dBQZPGQaAZLrnkEkn+oHjt2rUNrnfrrbfq3XfflSTdfPPN+u1vfxta9vWvf10TJkyQJL399ttatWpVi2q59tpr9dhjj4Xan6SmpurGG2/Uhx9+qL179+qhhx46KcwKl3A8tqqqKt10003yer164403TmmXERsbqyuvvLJF9d1zzz2h9mm///3v9eijj8paW++6xcXFWrFiRbP2P2rUqNA3E9566y2tWbPmlHWOHDmiefPmNToSdsmSJXr00Ucbndhw9+7d+vDDDyX5w8raI6Jbu317+vnPfx4aoXzHHXfo+eefb3T9o0eP6te//vUpvf0l6a677grd/vGPf6yNGzeess6uXbt0yy23tKrmoEh5vpsiHMf493//d8XE+GOUu+66S5999tkp+ygqKtJVV10V6qP+/e9/X5mZmSetM2XKlNBz/sorr2jdunWn7Cc3N1c33nhj0x9gM7T2dSBc52w4n/faQXrdDy4AIFyierLRwGj0r0rKl/SnOovvl3SbpG8ZY+6y1jY4G4gxJk3StyRVSJpfZ/H/SfqppFnGmCHW2rzgAmvtslr7aErJV0nqKel5a23onYW11mWM+aWkf8ofyDMyHUCnExyNPmDAAMXG0ukKQNswxig7O1u5ubnatWuXBgwY4HRJHcq8efNCEw8uX75cF1100Snr3HfffaGRnJdeeqmefPLJk5YbY/TrX/86NPLz3nvvbXaYGxQTE6Pp06frpptu0pVXXtnm82+E67E9/fTT2r9/v77zne9o6tSpYa1x8ODBevrpp3XdddfJ5/Ppzjvv1DPPPKOrrrpKQ4cOVUxMjAoKCrRq1Sq99957+uY3v6lp06Y1ef8JCQn63ve+p0ceeUTV1dWaOnWqvvvd7+qcc85RfHy81q9fr2effVbFxcW66aabGgzgDh06pDvvvFM/+9nPNGPGDJ177rkaMmSIUlJSdPz4cX3xxRdauHBhKKy88847lZycHLbt21P//v31yiuvaO7cuXK73fr2t7+tRx55RHPnztXw4cOVnJyskpIS7dy5U6tXr9Znn30mr9erGTNmnLKvCy+8ULfffrv+/Oc/q6ioSFOmTNG3v/1tXXjhhYqJidGaNWv09NNPq6KiQvPmzdObb77Zqtoj5fluinAcY8qUKbrnnnv0u9/9TmVlZZo2bZquu+46XXTRRUpOTtbWrVv11FNPhVrejB07Vg888MAptSQmJurf/u3f9Otf/1rV1dWaPn26vv/972vSpElyu91atWqVnn/+eVlrNXfuXL399tvNeqyn09rXgXCds+F83pct88czgwYN0rhx48L67wUAQVEdpEsKvgp/YK096bu51toyY8xn8gftU+QPqRsyRVJyYD8nfUxurfUZY5bIH8rPkL9tTEsF30m8X8+yjyVVSjrfGJNorW1ew0MAiHK7du2S2+2mrQuANpedna3t27dr165d9Qa9aLkxY8bo7LPP1saNG/W3v/3tlADpj3/8ox566CFJ/p7BCxcuVFzcqW9JLr30Up1//vlauXKlPv74Yy1evDjUsqKpfvnLX2r27NknTazXlsL52N544w1J/tHtbeHqq69WSkqKvvOd7+j48ePavHlzvaObJYVG3zbHgw8+qA0bNmjZsmVyu9167LHH9Nhjj520zve+9z397Gc/azBYDQ5U8ng8WrJkSYP9tY0xuuOOO0Jtc8K1fXubNWuWVqxYoRtuuEF5eXnatGmTNm3a1OD6aWlpp4xyDvrjH/+osrIyvfDCC3K73XriiSf0xBNPhJbHxMToP//zP9WzZ89WB+lSZDzfTRGuY/z2t79VXFycfvvb38rr9erFF1/Uiy+eOlXatGnT9PrrrzcY/P7iF7/Q6tWr9eGHH6q8vFz/9V//ddLyjIwMvfTSS1q7dm3Yg3Sp9a8D4Thnw/WcbN++PfTti7YaxQ8AUvQH6WcErnc2sHyX/EH6CDUepDdlPwrspzUaPI61tsYYs0fSaElDJDXasM4Yc+p3v/xGtqpCAHBAdXW18vLy6I8OoF1kZWXJWquCggKVlZUpPT3d6ZI6lNtvv1233XabcnNztXLlSp1//vmSpIULF+rOO++UJA0fPlzvvvtuqCVEfX79619r5syZkvwjvWfPnt2sUPf//b//1/IH0UzhfmwbN25UTEzMKRMUhtPll1+uvLw8PfXUU3r33Xe1detWFRYWKi4uTllZWRo/frwuu+wyffOb32z2vpOSkvTBBx/oySef1AsvvKCtW7fK4/GoT58+Ovfcc3XLLbfoq1/9qvLz8xvcx0033aRRo0bpo48+0urVq7V9+3YdOnRILpdLaWlpGjx4sC688EJ997vf1fjx48O+vROmTJminJwc/f3vf9fbb7+tL774QseOHZPL5VJGRoaGDBmi8ePH6+KLL9Zll13W4DkWGxur559/XldffbX+8pe/aM2aNSotLVXv3r11wQUX6N/+7d903nnnNdrjuzki4fluinAe44EHHtC1116rv/zlL/rnP/+p/fv3y+PxqGfPnjr33HN1/fXX6xvf+Eaj+0hMTNTixYv11FNPnfTv1r9/f1166aW68847NXjw4EbbZLVWa18HWnvOhus5CX6QERsb22YfQAKAJJmG+mBFA2PME5JulXSrtfaUGS6MMQ9K+rmkn1trG5xBwxjzc/l7qT9orf1lPctvlfSEpCestd9rYB/TJS2T9JK1tt6PQI0xOyUNlzTcWru7nuWfSTpf0vnW2kabQTYWpE+YMCGlvh5rABCpdu7cqeeee06JiYm66qqrnC4HQCewePFinThxQldffXWoZ7WT5syZE7r9zjvvOFhJ67lcLmVnZ+vo0aO67bbb9PjjjztdUlTxer2Ki4tTSkpKqJ0BAKB+Xq9Xw4YNU35+vq655hq98gqdcoGOZuLEiVq/fv16a+1Ep2vpCJONdkrW2on1XSTtcLo2AGiunTt3yuPxaODAgU6XAqCTGDhwoDwej3bubOgLie3rnXfeCV2iXVJSku69915J0vPPP6+DBw86XFF0iY2NVVpamiorK3XgwAGnywGAiPbyyy8rPz9fMTExuv/++50uB0AHF+1BenBq5/qbw/3r/uJ22s/ptNdxACBqWGtDE40OGjTI6XIAdBKDBg2Sx+NRbm6uampqnC6nw/nBD36gwYMHy+Vy6Xe/a/CLoWhAsHf/3XffLZfLddKyL7/8UmvWrHGiLACIKF6vV7/5zW8kSTfffLNGjRrlcEUAOrpoD9JzAtcN9S4fHrg+3VCjcO3ndBo8jjEmTtJgSTVq3YSmABBVjhw5osLCQiUkJKhnz55OlwOgk0hLS1O3bt1UWVnZaN9etExSUpIeeeQRSdKTTz6pgoIChyuKLg8++KDS09P197//XUOGDNHcuXM1b948jRo1SqNHj9b+/fudLhEAHPfyyy8rJydHmZmZfGgLoF1Ee5C+LHD9VWPMSY/FGJMu6QJJlZJWn2Y/qyVVSbogsF3t/cTIP2Fp7eO11NLA9ex6lk2VlCJppbXW3crjAEDU2Llzp9xutwYNGiRjjNPlAOhEBg0aJLfbHTHtXTqaefPmyVorl8ulfv36OV1OVBkzZozWrVunm266SbGxsXrvvff0ySefKCUlRffee69mzJjhdIkA4Lgbb7xR1loVFxerV69eTpcDoBOIc7qA1rDW5hpjPpA/6P6hpP+ttXiBpFRJj1trQ7P0GGNGBrbdUWs/5caYFyTdJmm+pLtq7edHkgZJWmKtbe1I8dck/V7StcaY/7XWrg3UlCTpN4F1HmvlMQAgqgT7o2dnZztdCoBOJjs7Wxs3btTOnTv1ta99zdEP8+bPn1/vbXRew4cP11//+lenywAAAEBAVAfpAbdLWinpj8aYmZK2SzpX0gz5W7H8os762wPXdd8p/VzSdEk/NcacLWmNpFGSrpB0VP6g/iTGmHmS5gV+7BO4Ps8Y81zg9nFr7d3B9a21pcaYW+UP1JcbY16RVChprqQzAvf/vUmPGgA6gIqKCu3fv18+n08DBgxwuhwAnUzv3r0VHx+vEydO6NixY46OZluwYEHoNkE6AAAAEHmiPkgPjEqfJOkB+VumXCrpkKRHJS2w1hY1cT8njDHnSbpf/nD8K5JOSHpW0q+stQfq2exsSd+uc9+QwEWS9kq6u/ZCa+2bxphp8gf8V0pKkrRb0k8l/dFaa5tSLwB0BMG2LllZWYqPj3e6HACdjDFGgwYN0v79+5WTk8PXwgEAAAA0KOqDdEmy1u6X9J0mrtvgd3attYWSfhy4NGVf8+VvBdMs1trP5A/8AaBTC7Z1GTRokNOlAOiksrOzlZubq507d+orX/mK0+UAAAAAiFDRPtkoACBK1dTUaNeuXQTpABw1cOBAeb1e7du3TxUVFaffAAAAAECnRJAOAHDEnj17VFlZqW7duik9Pd3pcgB0UvHx8erfv7/cbrd27tzpdDkAAAAAIhRBOgDAETk5OfJ4PBo8eLDTpQDo5LKzs+XxeJSTk+N0KQAAAAAiFEE6AKDdWWuVk5Mjt9tNWxcAjhs8eLA8Ho92796t6upqp8sBAAAAEIEI0gEA7e7QoUMqKipScnKyevbs6XQ5ADq5tLQ09ejRQ5WVldqzZ4/T5QAAAACIQATpAIB2F2zrMmjQIBljnC4HADRo0CB5PB7t2LHD6VIAAAAARCCCdABAu9uxY4fcbjf90QFEjMGDB8vtdisnJ0fWWqfLAQAAABBh4pwuAADQuRQVFenQoUMyxigrK8vpcgBAktS9e3elpqaqpKREBw4c0IABA9r1+Lfeemu7Hg8AAABA8xCkAwDaVXCS0ezsbMXF8WsIQGQwxmjw4MHavXu3duzY0e5B+hNPPNGuxwMAAADQPLR2AQC0qx07dsjj8dDWBUDEGTx4cKhPOu1dAAAAANRGkA4AaDeVlZXas2ePampqNHDgQKfLAYCT9O3bV7GxsTp69KiOHz/udDkAAAAAIghBOgCg3eTk5Mjj8SgrK0uJiYlOlwMAJ4mJidGgQYPkdru1Y8cOp8sBAAAAEEFoTgsAaDc7duyQ2+3WkCFDnC4FAOo1ePBg5eXlafv27frKV77Sbse97bbbQrfplw4AAABEHoJ0AEC78Hg82r17N/3RAUS0AQMGyOfz6cCBAyopKVFmZma7HPfJJ58M3SZIBwAAACIPrV0AAO1i9+7dqqqqUq9evZSamup0OQBQr/j4eA0cOJD2LgAAAABOQpAOAGgX27dvl9vtZjQ6gIg3ZMgQeTwebd++3elSAAAAAEQIgnQAQJurqalRTk6O3G63hg4d6nQ5ANCoQYMGqaamRnv27FFFRYXT5QAAAACIAATpAIA2l5eXp/LycnXr1q3d+g0DQEslJiaqX79+crvdysnJcbocAAAAABGAIB0A0Oa2b98uj8ejIUOGOF0KADTJkCFD5Ha7ae8CAAAAQBJBOgCgjXm9Xu3YsUNut5sgHUDUGDx4sKqrq5WbmyuXy+V0OQAAAAAcRpAOAGhTe/fuVWlpqTIyMtStWzenywGAJklJSVHfvn1VVVWlnTt3Ol0OAAAAAIcRpAMA2tSXX34ZmmTUGON0OQDQZEOHDpXb7daXX37pdCkAAAAAHEaQDgBoMz6f76QgHQCiyZAhQ+TxeLRr1y653W6nywEAAADgoDinCwAAdFz79u1TSUmJ0tLS1L17d6fLAYBmSU1NVe/evVVZWaldu3ZpzJgxbXas+++/v832DQAAAKD1CNIBAG1m27ZtcrvdGjlyJG1dAESloUOHau3atdq2bVubBunz589vs30DAAAAaD1auwAA2kTtti7Dhg1zuhwAaJGhQ4fK4/Fo586d8ng8TpcDAAAAwCEE6QCANrFv3z4VFxcrNTVVPXr0cLocAGiRtLS0UHuXnTt3Ol0OAAAAAIcQpAMA2kSwrcuwYcNo6wIgqg0dOlRut1vbtm1zuhQAAAAADqFHOgAg7Hw+30lBOgBEs6FDh2rVqlXauXOn3G63EhMTw36MOXPmhG6/8847Yd8/AAAAgNYhSAcAhN3evXtVUlKitLQ02roAiHrB9i4VFRXKycnR2LFjw36Mf/zjH2HfJwAAAIDwobULACDstm7dKrfbreHDh9PWBUCHMGzYMNq7AAAAAJ0YQToAIKy8Xq++/PJLud1uDR061OlyACAshg4dKo/Ho127dqmqqsrpcgAAAAC0M4J0AEBY7dmzR6WlpcrMzFT37t2dLgcAwiIlJUVZWVmqqqrSjh07nC4HAAAAQDsjSAcAhNWWLVvkcrk0bNgw2roA6FCGDRsml8ulrVu3Ol0KAAAAgHZGkA4ACJuamhpt37491B8dADqSoUOHqrq6Wrm5uaqoqHC6HAAAAADtiCAdABA2u3btUnl5ubp3764uXbo4XQ4AhFVSUpIGDhwol8vFpKMAAABAJ0OQDgAImy1btjAaHUCHRnsXAAAAoHMiSAcAhIXL5VJOTo48Hg9BOoAOa8iQIbLWKj8/X8XFxU6XAwAAAKCdEKQDAMJix44dqqysVJ8+fZSWluZ0OQDQJuLj4zV48GC53W5GpQMAAACdSJzTBQAAOobNmzfL5XJp/PjxTpcCAG1q+PDh2rNnjzZv3qwLL7wwLPt8/PHHw7IfAAAAAG2DIB0A0GplZWXKzc1VTU2Nhg4d6nQ5ANCmBgwYoNjYWB06dEhHjhxR7969W73P2267LQyVAQAAAGgrtHYBALTa1q1b5XK5NHDgQCUlJTldDgC0qdjY2NCko5s3b3a6HAAAAADtgCAdANBqmzdvltvt1hlnnOF0KQDQLkaMGCG3263NmzfL5/M5XQ4AAACANkaQDgBolWPHjunAgQMyxig7O9vpcgCgXfTp00cpKSkqLCzU3r17nS4HAAAAQBsjSAcAtMqmTZvkdrs1dOhQxcUx9QaAzsEYozPOOENut1ubNm1q9f4mTpwYugAAAACIPATpAIAWs9Zq8+bNcrlctHUB0OmMGDFCLpdL27ZtU3V1dav2tX79+tAFAAAAQOQhSAcAtFh+fr5OnDihlJQU9e3b1+lyAKBddenSRT179lR5ebl27NjhdDkAAAAA2hBBOgCgxTZu3Ci3260RI0bIGON0OQDQ7oLtXTZu3Oh0KQAAAADaEEE6AKBFPB6PvvzyS9q6AOjUhg8frurqau3evVulpaVOlwMAAACgjRCkAwBa5Msvv1R5ebl69eqlLl26OF0OADgiKSlJgwYNksvl0ubNm50uBwAAAEAbIUgHALTIxo0b5XK5NHLkSKdLAQBHjRw5Ui6XSxs3bpS11ulyAAAAALQBgnQAQLMVFRUpLy9PPp9Pw4YNc7ocAHDUgAEDFB8fr8OHD6ugoMDpcgAAAAC0AYJ0AECzbdq0SS6XS4MHD1ZiYqLT5QCAo2JjYzVixAi5XC5t2LDB6XIAAAAAtAGCdABAs1hraesCAHUE27ts2bJF1dXVTpcDAAAAIMwI0gEAzbJnzx4dO3ZMKSkp6t+/v9PlAEBE6N69u3r27KmysjJt377d6XIAAAAAhFmc0wUAAKLLhg0b5HK5NGbMGBljnC4HACLGyJEjtXr1am3YsEFjx45t1rZvv/12G1UFAAAAIBwI0gEATVZVVaUvv/xSHo+Hti4AUMfw4cO1cuVK5ebmqrCwUN26dWvytnPmzGnDygAAAAC0Fq1dAABNtmXLFlVUVCgrK0sZGRlOlwMAESUxMVFDhgxh0lEAAACgAyJIBwA0ibVW69atk8vl0plnnul0OQAQkc4888xQkO7z+ZwuBwAAAECYEKQDAJrk4MGDOnjwoGJjYzVo0CCnywGAiNS3b1+lp6erqKhIu3btcrocAAAAAGFCkA4AaJL169erqqpKZ5xxhuLimGIDAOpjjNGoUaNUVVWldevWNXm7rKys0AUAAABA5CFIBwCcltvt1ubNm+VyuTRq1CinywGAiHbGGWeopqZGOTk5KikpadI2hw4dCl0AAAAARB6CdADAaW3ZskXl5eXq06ePunXr5nQ5ABDRUlJSNHjwYFVVVTHpKAAAANBBEKQDABplrdXatWtVVVWl0aNHO10OAESF4KSj69atY9JRAAAAoAMgSAcANKqgoEAFBQWKiYnRkCFDnC4HAKJCv379lJaWpsLCQu3cudPpcgAAAAC0EkE6AKBRwdHoI0eOZJJRAGgiY4xGjx6tqqoqrV271ulyAAAAALQSQToAoEFVVVXasmWLXC6XxowZ43Q5ABBVRo4cqZqaGu3cuVOFhYVOlwMAAACgFQjSAQAN2rhxoyoqKtSvXz9lZmY6XQ4ARJWkpCQNGzZMLpeLUekAAABAlCNIBwDUy1qrL774QlVVVYxGB4AWGjNmjKqqqrR+/XpVV1c7XQ4AAACAFiJIBwDUKzc3V0eOHFFSUpIGDRrkdDkAEJV69+6t7t27q6SkRNu2bXO6HAAAAAAtRJAOAKjXmjVrVFVVpdGjRysmhl8XANBSZ511lqqqqrRmzRpZa50uBwAAAEALxDldAAAg8hQWFionJ0c1NTUaNWqU0+UAQFQbOnSoVq5cqX379unAgQMaMGDAKevQQx0AAACIbATpAIBTBHujDxs2TCkpKU6XAwBRLT4+XqNGjdKOHTu0Zs2aeoP0iRMnOlAZAAAAgKbiu/oAgJN4PB6tX79eVVVVOuuss5wuBwA6hDFjxsjlcmnLli0qKytzuhwAAAAAzUSQDgA4yaZNm1RaWqqePXuqV69eTpcDAB1Cenq6Bg8erKqqKn3xxRdOlwMAAACgmQjSAQAh1lp9/vnnqqys1Lhx45wuBwA6lHHjxqmyslJffPGFampqnC4HAAAAQDMQpAMAQnbv3q1Dhw4pKSlJQ4YMcbocAOhQ+vTpo27duqm4uFhbtmw5aZkxJnQBAAAAEHkI0gEAIatWrVJVVZXGjBmjmBh+RQBAOBljNG7cOFVVVWnVqlWy1jpdEgAAAIAmIiUBAEiSjhw5ol27dsnn82n06NFOlwMAHdKwYcMUHx+vgwcPKi8vz+lyAAAAADQRQToAQNK/RqOPHDlSiYmJTpcDAB1SbGyszjrrLFVWVmrVqlVOlwMAAACgiTpEkG6M6W+MecYYc9AY4zbG5Btj/mCM6drM/XQLbJcf2M/BwH77h+vYxhjbyGV1cx87AIRDWVmZNm/eLLfbrbFjxzpdDgB0aKNHj5bX61VOTo6OHDnidDkAAAAAmiDO6QJayxgzVNJKSb0kvSVph6TJkn4sabYx5gJr7Ykm7Kd7YD8jJC2V9IqkkZK+I+kyY8x51tq8Otu09Nh7JT1Xz/0HTvuAAaANfP755yovL9egQYOUmZnpdDkA0KElJSVp1KhR2r17t1atWqV58+Y5XRIAAACA04j6IF3Sn+UPsu+w1v5v8E5jzCOSfiLpQUnfb8J+fit/iP6ItfauWvu5Q9KjgePMDtOx862185tQEwC0ObfbrS+++EJVVVU6++yznS4HADqFsWPHatu2bdq0aZMuuugip8sBAAAAcBpR3dolMCL8q5LyJf2pzuL7JVVI+pYxJvU0+0mT9K3A+vPrLP4/+UeQzzLGDAn3sQHAaevWrVNJSYl69+6tPn36OF0OAHQKmZmZGjJkiCoqKrR6Nd39AAAAgEgX1UG6pBmB6w+stb7aC6y1ZZI+k5Qiacpp9jNFUrKkzwLb1d6PT9KSOsdr7bG7GGO+a4z5uTHmh8aY09UHAG3C6/Vq1apVqqys1Pjx450uBwA6lfHjx6uqqkpffPGF06UAaIHvfe97MsbIGOPofAdvvvmmjDFKSkpSQUFBmxzjxRdflDFGXbp00dGjR9vkGAAARLpoD9LPCFzvbGD5rsD1iDbYT2uOPU7S0/K3fvk/SauMMRuNMWedps4QY8y6+i7y93UHgCbZvHmzTpw4oczMTGVnZztdDgB0Kj179lTfvn1VVlZ2+pUBRJwNGzZIkrKystS7d29HanC5XPrJT34iSbrtttvUr1+/NjnOddddpxEjRqikpET33XdfmxwDAIBIF+1BenBGvJIGlgfv79IG+2npsR+RdIGknpLSJZ0j6TX5w/Wlxpi2+csHAOrw+Xz69NNPVVlZqbPPPlvGGKdLAoBOZ8KECaqsrHS6DADNVFNToy1btkjy/z92yp///Gfl5+crKSlJ9957b5sdJzY2Vr/85S8lSc8995y2b9/eZscCACBSRXuQHnWstXdZa1daa49ba8uttWuttd+U9LqkHpLubuJ+JtZ3kbSjLesH0HFs375dhw8fVlJSkkaMON0XdwAAbaF///7q3r27fvjDH+qdd95ps7YMAMJr+/btcrlckuRYe7yqqio99NBDkqSbb75ZWVlZbXq866+/XtnZ2fL5fFqwYEGbHgsAgEgU7UF6cNR3ZgPLg/cXt8F+wnXsoL8Erqc2cX0AaDFrrT755JPQaPSYmGj/dQAA0ckYowkTJigmJkY5OTmOtYcA0DzBti6ScyPSn3/+eR07dkySdNNNN7X58WJjY3XDDTdIkl577TXt27evzY8JAEAkifbkJCdw3dBQyuGB64b6mLdmP+E6dtCxwHVqE9cHgBbbtWuX9u/fr9jYWI0aNcrpcgCgUxs8eLAyMzN14sQJbdq0yelyADTB+vXrQ7edGpH+2GOPSZKGDh2q8847r12OGQzSvV6vnnjiiXY5JgAAkSLag/RlgeuvGmNOeizGmHT5e5FXSlp9mv2sllQl6YLAdrX3EyPpq3WOF85jB00JXOc1cX0AaBFrrT7++GNVVlZq/PjxiouLc7okAOjUgqPSKyoq9PHHH8vn8zldEoDTCI5I7969u7Kzs1VdXa0XX3xRl156qfr376+EhAT1799ft9xyi/bv3x/242/ZsiX0wdv111/f6LoXX3yxjDEyxujll19ucD2v16u5c+eG1r377lO7jp555pk6++yzJUkvvviirLUtfxAAAESZqA7SrbW5kj6QNEjSD+ssXiD/6O4XrLUVwTuNMSONMSPr7Kdc0guB9efX2c+PAvtfYq3Nq7VNS4491hgTX/dxGGPGSnow8OOLDT1eAAiH3Nxc5efnKyYmRqNHj3a6HACApIyMDPl8PuXm5mrz5s1OlwOgEdZabdy4UZJ/NPrGjRs1ceJEfetb39J7772ngoICVVdXq6CgQM8884zOOeecsIfpb775Zuj2jBkzGl33oYceCk0qP3/+fHm93nrX+8EPfqB33nlHkvStb31LDz/8cL3rBY+3d+9evkUDAOhUOsIwxNslrZT0R2PMTEnbJZ0raYb8bVV+UWf94PTips79P5c0XdJPjTFnS1ojaZSkKyQd1alheUuO/VNJc4wxn0jaL8ktaaSk2ZJiJT0pqeEhAgDQStZarVixIjQaPT7+lM/2AAAOuPjii0O3hw8frrFjxzJ/BRChcnNzVVpaKkmKiYnRjBkzVFFRoeuvv17Tp09XWlqatm3bpj/96U8qLi7WkSNHtGDBAj311FNhq+HDDz8MHX/SpEmNrjtp0iRdddVVevXVV7Vz50698MILuvnmm09aZ/78+XryySclSbNnz9bTTz8dCt/rmjJlSuj2kiVLQiPUAQDo6KI+SLfW5hpjJkl6QP5A+lJJhyQ9KmmBtbaoifs5YYw5T9L9kuZJ+oqkE5KelfQra+2BMBz7TUkZksZKukhSUuAY70l60lr7dtMfOQA0X15envbs2SNjjM466yynywEA1OPw4cPavHkz4RQQoWpPNPrBBx/ozDPP1BtvvKEzzjjjpPWuuuoqnXPOOaqpqdEHH3wQtuN7vV6tW7dOkjRq1Cilp6efZgvpN7/5jRYtWqSamho98MADuuGGG0IDKp566iktWLBAkjR58mS99tprjQ62OPfcc0O3P//889Y8FAAAokqHGOZird1vrf2OtbavtTbBWpttrb2zvhDdWmustfV+tG6tLbTW/jiwfUJgf9+tL0Rv4bHftNZ+w1o7zFqbUesYcwjRAbQ1a62WLVumyspKnX322YxGB4AIVVFRoRUrVjTYfgGAs2pPNNq/f38tXbr0lBBdks4++2yNHTtWknT8+PGwHT8vL0+VlZWSVO9x6zNixAh997vflSTt2bNHzzzzjCTpnXfe0fe///3QOu+++65SU1Mb3Vd2draSk5MliVZUAIBOpUME6QCA09u9e7fy8/MZjQ4AES41NVVHjhwhoAIiVO0R6Y8++qh69+7d4LrBwLkpo8abau/evaHb3bp1a/J2999/f6ie3/zmN1qxYoWuvfZaeb1e9e3bV0uWLFGPHj2atK+uXbtKkvbv38+EowCAToMgHQA6geBo9IqKCnqjA0CEmzRpkioqKrR8+XLV1NQ4XQ6AOoJBenZ2tubNm9fourt27ZIkDRo0qMF1jh49qvnz52vy5Mnq0qWLEhMTlZWVpcmTJ+vuu+/WmjVrTlq/sLAwdLs5QXpWVpbuuOMOSdKBAwc0c+ZMVVZWKjMzU++//36jNdbVvXt3SZLH41FFRUWTtwMAIJoRpANAJ7Bjxw7t3btXcXFxGjNmjNPlAAAaMXz4cKWnp+vo0aMntZAA4LyCggIdPXpUkjRr1qxGJwU+evRoaN3Ro0fXu86SJUs0atQoLViwQIcOHdKUKVP0jW98Q4MHD9bmzZv13//933rrrbdO2sbtdoduN3ek+z333BMaTe71epWYmKi33nor1IKmqTIyMkK3q6qqmrUtAADRKuonGwUANM7n82np0qWqqKjQlClTGI0OABEuJiZGkydP1kcffaQVK1bwTSIggtRu6zJ58uQmrzt+/PhTlm/dulXz5s1TTEyMnn/+eV1//fWKjY0NLS8tLdXLL7+sUaNGnbRdYmLiSes0x4EDB+Tz+UI/X3311Zo2bVqz9iFJJSUlodvBdjEAAHR0jEgHgA5u8+bNKigoUFJSks4880ynywEANMGQIUPUrVs3nThxQp9//rnT5QAIqP0tkfrC8dpqB+kTJkw4ZfmCBQvkcrn0wAMP6Fvf+tZJIbrkH/X9ve99T1OnTj3p/trtXGq3eTmdffv2afbs2SeF4AsXLtS+ffuavI+6x01ISDjt5KQAAHQUBOkA0IHV1NSERqOfc845p7xBAwBEJmOMpkyZooqKCn3yySe0TgAiRDAcj4+PP227vOC6xhiNGzfulOXLli2TJF144YXNqqF2L/OmBuknTpzQrFmzdPDgQcXExOimm26S5G8T86tf/apZx6993IEDB8oY0+ztAQCIRgTpANCBffHFFzp27JgyMjI0YsQIp8sBADTDgAED1LdvXxUXF+vTTz91uhwA+teI9NGjRyshIaHRdYNB+vDhw5WWlnbKcpfLJUn65JNPmlXD4MGDQ6PAc3JyTrt+ZWWlLr/8cu3YsUOS9Oijj+rZZ58NfRDwwgsvaNu2bU0+fn5+fqj25vZWBwAgmhGkA0AH5XK5tGLFilBv9MYmwwIARKbzzjtPFRUVWr169UntGAC0v8LCwlAblPpatdRWVlam3bt3S2q4BcwFF1wgSfr3f/93zZw5U4899pi2b99+2jpiY2M1ceJESf4J5Rvrk15TU6Orr75aq1evliTdd999+tGPfqSYmBgtWLBAkn8+nZ///OenPW5Q7XZT5557bpO3AwAg2pGqAEAH9emnn6qoqEi9e/dWdna20+UAABqxdevW0KW2Xr16adiwYSotLdXSpUsdqg6AdPrJQ2vbtGmTrLWNrvuXv/wlFMgvXbpUt99+u84880xlZ2dr/vz5jQbkl1xyiSR/CL527doG17v11lv17rvvSpJuvvlm/fa3vw0t+/rXvx46/ttvv61Vq1Y1+piCagfps2bNatI2AAB0BATpANABFRcXa9WqVaqoqNB5551H70oAiGKTJ0+W2+3Whg0bdOjQIafLATqtlk402tC6gwcP1rp167RixQr95Cc/0ejRoyX5JwVdsGCBJk+erMrKynq3nTdvXuj28uXL613nvvvu03PPPSdJuvTSS/Xkk0+etNwYo1//+tehn++9995GH1NQsLf7oEGD6u39DgBAR0WQDgAd0D//+U+VlpZq2LBh6t27t9PlAABaITMzU2PGjFFFRYWWLFkSGuUKoH0Fw/GYmBidffbZTVpXOn3oPnXqVD3yyCPaunWr9u/fr3vuuUeSv//5E088Ue82Y8aMCdXwt7/97ZTlf/zjH/XQQw9J8n8Yt3DhQsXFxZ2y3qWXXqrzzz9fkvTxxx9r8eLFjda6fft2bdy4UZJ04403NrouAAAdDUE6AHQwBw4c0MaNG+XxeOhbCQAdxMSJE2Wt1e7du5s0uSCA8Ks9eWhwss/TrduvXz/17Nmzycfo37+/HnroIU2bNk2STmn3VNvtt98uScrNzdXKlStD9y9cuFB33nlnqNZ333230Xprj0q/77775PP5Glz3xRdflOTv037rrbee/gEBANCBEKQDQAdirdV7772niooKjR07VhkZGU6XBABogm3btoUu9UlKStLkyZNVXl6uJUuWqKampp0rBLB9+3ZZa7Vjx47TrrthwwZZa3XgwIEWHatfv36S1GgA/q1vfUu9evWSJP31r38N3X/11VfL5/PJWqudO3eqR48ejR7roosukrVW1lpt2rSpwQnqvV5vaPT7VVddpYEDBzbrMQEAEO0I0gGgA9m8ebPy8/MVExMTmjwKABD5rrnmmtClIWeeeabS0tJ0+PDhkyb7AxBdTteeqaKiItSHfObMmQ2ul5SUFOpr/vzzz+vgwYPhK7IeL7/8cujvzPvvv79NjwUAQCQiSAeADsLtduuDDz5QeXm5zjvvPCUkJDhdEgAgjGJjY3XBBReovLxcy5cvV1lZmdMlAWiBe+65Rz/96U+1d+/eU5Zt375dc+bM0aFDhzR16lTNmTOn0X394Ac/0ODBg+VyufS73/2urUqW1+vVb37zG0nSzTffrFGjRrXZsQAAiFQE6QDQQXz88cc6fvy4unXrpjPOOMPpcgAAbWDgwIEaOHCgiouL9eGHHzpdDoAWWLlypf7nf/5HgwcP1llnnaWrrrpKV111lSZOnKgxY8Zo2bJlmjlzpt566y0ZYxrdV1JSkh555BFJ0pNPPqmCgoI2qfnll19WTk6OMjMz2zSwBwAgkhGkA0AHcOzYMX322WeqrKzUV77yldO+6QIARK8LLrhAHo9HGzZsqHdEK4DI9uSTT+rhhx/WJZdcIrfbrSVLlugf//iHjh07pnnz5mnRokX68MMP1aVLlybtb968ebLWyuVyhXqrh9uNN94oa62Ki4tDfdkBAOhs4pwuAADQOtZaLV68WGVlZRo5cqR69+7tdEkAgDaUmZmps88+W5s3b9bixYv1ve99r8HJAQFEnlGjRmnUqFG6++67nS4FAAA0A39xA0CU27p1q3bu3Clrrc4991ynywEAtIPx48crMTFR+/fvZ+JRAAAAoB0QpANAFHO5XHr//fdVXl6u888/X8nJyU6XBABoB/Hx8Zo6darKysq0dOlSlZSUOF0SAAAA0KERpANAFPvoo490/Phx9ejRQyNHjnS6HABAO8rOztagQYNUXFysxYsXy1rrdEkAAABAh0WQDgBRat++ffr8889VVVWladOmMcEoAHRCF154oWpqarRt2zZt377d6XIAAACADosgHQCiUE1Njd555x2Vl5dr/Pjx6t69u9MlAQAckJaWpnPPPVdlZWV69913VVVV5XRJAAAAQIcU53QBAIDm+/jjj3XgwAGlpKRowoQJTpcDAGilnj17tnjbMWPGaOfOnTp+/Lg++OADXXHFFWGsDEBbsNbK6/WedPH5fKFrn88na23oOnipjzEmdImJiQldx8TEKDY2NnRd+8I3GQEAaD6CdACIMocOHdLHH3+s8vJyXXHFFYqL46UcAKLdsmXLWrytMUYXXXSRFi5cqLVr12rMmDEaOnRoGKsD0Bw+n0/V1dWnXGpqak66OMUYo9jYWMXFxSkuLk7x8fGh6+AlISGBsB0AgDpIXwAgini9Xr355psqLS3V6NGj1bdvX6dLAgBEgK5du2rSpElav3693nrrLf3whz9UYmKi02UBHZa1Vh6PR263+6Rrj8fjaEjeFNbaJoX5wUA9eElMTFRiYqLi4+MJ2QEAnRJBOgBEkY8//lj79u1TYmKipkyZ4nQ5AIAIMn78eO3Zs0dHjhzRkiVLNHfuXKdLAjqE6upquVwuud3u0LXb7W6w1UpHERxJX1FRcdL9MTExSkhIUFJSkhITE5WUlKSkpCS+JQkA6PD4TQcAUaKgoEArVqxQeXm55s6dq/j4eKdLAgBEkJiYGF100UV67bXX9MUXX2jkyJEaMWKE02UBUaWmpkZVVVWhi8vlivgR5u3N5/PJ5XLJ5XKddH98fLySkpKUnJys5ORkwnUAQIfDbzUAiAIej0evv/66SkpKdNZZZykrK8vpkgAAYbR8+fLQ7enTp7d4P926ddM555yjL774Qm+99ZZuv/12paamtr5AoAOy1srlcqmyslKVlZWqqqpSdXW102VFreAI9rKystB9CQkJSk5OVkpKilJSUpSYmEhbGABA1CJIB4Ao8MEHH+jgwYNKS0vTueee63Q5AIAw+9GPfhS6vXXr1lbta9y4ccrPz9exY8f0zjvv6JprriG4AuQfSR0MzYPBuc/nc7qsDi3YN76kpESS/5szwVA9JSVFycnJiomJcbhKAACahiAdACJcTk6OPv/8c1VWVurKK6/kK7IAgEbFxMRo5syZWrhwobZs2aJhw4Zp0qRJTpcFtDufz6eqqipVVFSooqJCVVVVHb6veaTz+XwqLy9XeXm5JMkYo5SUFKWmpio1NVXJycl88AcAiFikMQAQwUpLS7Vo0SKVlpbq3HPPVY8ePZwuCQAQBTIyMjR16lQtXbpU77//vrKzs9WzZ0+nywLalLVWbrdb5eXlqqioUGVlJSPOI5y1NvRBh+T/IDAYqqelpSkhIYFgHQAQMQjSASBC+Xw+vfHGGzpx4oT69u2rcePGOV0SACCKjBgxQvv371d+fr5effVV3XrrrUxUjQ6npqZGFRUVoVHOTAwa3Xw+n8rKykJ91uPj45WWlqa0tDSlpqYqNjbW4QoBAJ0ZQToARKgVK1Zo586dstZq5syZjMYBADTb1KlTdfjwYe3bt0/vv/++5syZ43RJQKsER52XlZWpvLxclZWVTpeENlRdXa2ioiIVFRWF2sCkpaUpPT2d0eoAgHZHkA4AESg3N1fLli1TWVmZLr/8cqWkpDhdEgAgCsXHx2vWrFl644039Pnnnys7O1tjx451uiygWXw+X2jUeVlZmaqrq50uCQ6o3QbmyJEjSkhIUHp6utLT05WSkkKoDgBocwTpABBhSkpK9Nprr6mkpEQTJ05U//79nS4JABDFevTooQsuuECffvqp3n77bfXp00e9evVyuiygUV6vN9Tio7y8nF7nOIXH49GJEyd04sQJxcbGKi0tTRkZGUpLS1NMTIzT5QEAOiCCdACIIDU1NVq4cKGOHTumvn37atKkSU6XBADoAM4880wdOnRIe/fu1SuvvKLbbrtNSUlJTpcFnKSmpkalpaUqKytTRUWFrLVOl4Qo4fV6VVJSopKSEhljTgrV4+KIPQAA4cHHtAAQIay1Wrx4sfLy8hQXF6eLL76Yr6gCAMLCGKNp06YpLS1NBQUFWrRoESElIkJ1dbVOnDihPXv2KCcnR4cOHVJ5eTnnJ1rMWquysjIVFBRo586dys/PV2FhIRPRAgBajY9mASBCrF27VmvWrFFlZaW+/vWvKzk52emSAAAdSHx8vGbPnq3XXntNW7ZsUZ8+fTRjxgyny0InVF1drZKSEpWWlqqqqsrpctCB1e6rfujQIaWmpiojI0MZGRmMVAcANBu/OQAgAuzZs0fvvvuuSkpKdNFFF6lnz55OlwQAaEdnnnlmuxwnMzNTl1xyiRYvXqylS5eqV69eGj16dLscG51bdXW1SktLVVJSQngOxxCqAwBag98WAOCwEydO6O9//7uKi4s1duxYjRgxwumSAADtbOHChe12rIEDB2rKlCn6/PPP9cYbb6hLly7q169fux0fnUew53lJSYkqKyudLgc4Sd1QPTMzUxkZGYqNjXW6NABAhCJIBwAHVVVV6aWXXtKxY8fUr18/TZkyxemSAACdwLhx41RUVKTc3Fz97W9/02233abMzEyny0IH4PV6Q+F5RUWF0+UATVI7VE9LS1NmZqbS09MVE8O0cgCAfyFIBwCH1NTU6OWXX9aBAweUmpqqSy65hD/WAQDtwhijqVOnqrS0VEeOHNFLL72k7373u0pKSnK6NEQhn8+nsrIylZSUMFEoolpwotKysjLFxMQoPT1dmZmZSk1N5e90AID4TQAADvD5fFq0aJF27twpSbrssssUHx/vcFUAgM4kNjZWs2bNUlJSkvLz8/XKK6+opqbG6bIQJYKB44EDB5STk6MDBw6orKyMEB0dhs/nU0lJifbt26edO3fq4MGDqqio4BwHgE6MEekA0M6stXr//fe1YcMGud1uzZs3T2lpaU6XBQBw0Kuvvhq6/c1vfrPdjpuUlKTLLrtMb7zxhnbs2KE33nhDV111FSMvUS9rraqqqlRSUqKSkhJ5vV6nSwLahdfrVVFRkYqKihQfH6+MjAxlZmYqKSlJxhinywMAtBOCdABoZytWrNBnn32m8vJyXX755erRo4fTJQEAHLZgwYLQ7fYM0iUpIyNDl19+ud58801t3LhRKSkpuuyyywiHEOJ2u0PhucfjcbocwFHV1dU6ceKETpw4ocTERGVmZiozM1MJCQlOlwYAaGME6QDQjlavXq2PPvpIpaWluuSSS9SvXz+nSwIAQD169NDXvvY1vfvuu1q1apWSkpI0c+ZMwvROrLq6WqWlpSouLpbL5XK6HCAiud1uHT16VEePHlVKSooyMzOVkZGhuDiiFgDoiHh1B4B2sm7dOr377rsqKSnRtGnTNHToUKdLAgAgpF+/frrkkku0ZMkSLV++XPHx8Zo2bZrTZaEdeb1elZWVqbi4WBUVFU6XA0SVyspKVVZW6vDhw0pLS1NmZqbS09NplQUAHQhBOgC0gw0bNuitt95ScXGxzj//fI0aNcrpkgAAOMXgwYM1c+ZM/fOf/9SHH36o2NhYXXjhhU6XhTZkrVV5eblKSkpUVlYmn8/ndElAVAtOxFtWVqaYmJhQP/XU1FS+5QMAUY4gHQDa2IYNG7Ro0SIVFRVp8uTJGjt2rNMlAQDQoOHDh8vr9Wr58uV6//33JYkwvYNh0lCgffh8PhUXF6u4uFhxcXHKzMxUly5dlJiYSKgOAFGIIB0A2tDatWtDI9EnT56sCRMmOF0SAACnNXLkSEkKhek1NTWaNm0awU+UY9JQwDk1NTVMUgoAUY4gHQDayMqVK/Xee++puLhY5557rsaPH+90SQAANFntMP2jjz6Sx+PRJZdcQpgeZYKThpaUlKiqqsrpcgCISUoBIFrxKg0AYWat1dKlS7Vs2TKVlJToggsu0FlnneV0WQAANNvIkSMVFxenjz76SCtWrJDL5dLll1/O5HkRzuv1hsJzJg0FIhuTlAJA9CBIB4Aw8vl8euedd7RmzRqVlpZq+vTpoRF9AABEo2HDhik+Pl5LlizR6tWrVVlZqSuvvFLx8fFOl4ZafD7fSZOGWmudLglAM9Q3SWlGRobS0tL4JhAARAiCdAAIE7fbrddee01bt25VZWWlZs+erUGDBjldFgAArZadna05c+Zo8eLF2rhxo8rLy3XdddcpNTXV6dI6NWutKioqVFJSotLSUvl8PqdLAhAGtScpjY2NDfVTT05OJlQHAAcRpANAGJSUlOjll1/Wnj17VFNTozlz5qhv375OlwUAiBLTpk1zuoTT6tu3r77+9a/rH//4h3JycvTkk0/qhhtuUM+ePZ0urVOx1qqqqioUntfU1DhdEoA25PV6VVhYqMLCQsXHx4f6qSclJRGqA0A7M3zlr2MxxqybMGHChHXr1jldCtBpHDhwQC+//LKOHDmihIQEXX755crMzHS6LAAA2kRFRYUWL16s0tJS9ezZU9/85jc1bNgwp8vq0Ky1crlcofC8urra6ZIAOCwhISE0Uj0xMdHpcgCgzUycOFHr169fb62d6HQtjEgHgFbYsGGD3n77bRUXF6tnz56aNWuWkpKSnC4LAIA2k5qaqnnz5umjjz7S/v379cILL+irX/2qzj//fEZHhpG1Vm63OxSeezwep0sCEEE8Ho+OHTumY8eOKTExMTRSnVAdANoOQToAtEBNTY3ef/99rV69WqWlpRo1apQuuOACxcbGOl0aAABtLj4+XrNnz9YXX3yh9evXa/HixSooKNAVV1xBiNMKwfC8tLRUJSUlhOcAmsTtduvo0aM6evSokpKSQhOV8noMAOFFkA4AzVRUVKRXX31VeXl5qqqq0tSpUzVq1CinywIAoF0ZYzR58mT16NFDS5cu1bp163T48GFdc8016t27t9PlRY1g25aysjLCcwCt5nK55HK5CNUBoA0QpANAM2zdulVvv/22Tpw4ofj4eM2bN0+9evVyuiwAQJT705/+FLr9wx/+0MFKmm/IkCHq1q2b3n//feXn5+vxxx/X1772NU2aNIlWLw0IThhaVlZG2xYAbaZ2qJ6YmHhSqM7rMwA0H5ONdjBMNgq0Dbfbrffee09r165VaWmpBg4cqBkzZtAPHQAQFmPGjAnd3rp1q4OVtFx1dbU+/fRT5eTkKCMjQ2PGjNHcuXOVmprqdGkRwVqryspKlZaWqqysjAlDATgmISFBGRkZSk9PV3JyMqE6gIjGZKMAEEX27NmjN998U4cPH5bL5dIFF1yg0aNH8wcnAAC1xMfHa8aMGRowYICWL1+u9evXa//+/ZozZ06nbYHm8/lUXl6usrIylZWVyev1Ol0SAMjj8ej48eM6fvy44uLilJ6eroyMDKWkpCgmJsbp8gAgYhGkA0AD3G63PvroI61evVplZWXq0qWLLr/8cnXr1s3p0gAAiFjDhg1T7969tXTpUhUUFOill17S2Wefra997WudYnR6TU1NKDgvLy8X3wAGEMlqampUVFSkoqIixcTEKC0tTenp6UpPT1dsbKzT5QFARCFIB4B67NixQ++++66OHj2qyspKTZw4URMmTOCPSQAAmiA9PV1z587V1q1btWrVKq1Zs0a5ubmaNWuWxo0b16G+1WWtldvtDoXnVVVVTpcEAC3i8/lUWlqq0tJSGWOUkpISCtYTEhI61Gs3ALQEQToA1FJUVKT33ntPX375pcrKytStWzddeuml6tGjh9OlAQAQVYwxOuusszRw4EAtX75cBQUFevXVV7VhwwZddtllUT1Zt8/nU0VFRWjUOf3OAXQ01lpVVFSooqJCR44cUUJCgtLT05WWlkYLGACdFkE6AMjfJ/DTTz/VZ599ppKSEnm9Xk2ZMkVjxozhj0QAAFohMzNTc+fOVU5OjlauXKmtW7dq7969OvfcczV9+nQlJyc7XeJpWWvl8XhUXl6u8vJyVVRU0LIFQKfi8Xh04sQJnThxQjExMUpNTVVaWprS0tKUkJDgdHkA0C4I0gF0aj6fTxs3btTSpUt1/PhxVVRUaOjQoTr//PM7RR9XAADagzFGI0eO1KBBg/T5559r+/btWr58uTZt2qRp06bpnHPOUVxcZL018Xq9qqioCIXnjDoHAD+fzxdqZyVJCQkJoVA9NTWVgUgAOqzI+msVANqJtVbbt2/X0qVLdfDgQVVUVKhbt266+OKL1bdvX6fLAwCgQ0pKStK0adM0evRoffbZZzp48KDefvttrVq1SjNmzNC4ceMcC2B8Pp+qqqpC4Tm9zgGgaTwejwoLC1VYWChjjJKTk0OhenJyMr3VAXQYBOkAOhVrrXbs2KEVK1Zo//79qqioUFJSkmbMmKFhw4bxRx4AAO2gR48emjt3rvbt26dVq1Zp7969evXVV/Xpp59q6tSpOuuss9o8ULfWyuVyhXoAV1ZWyufztekxAaCjs9aqsrJSlZWVkhRqAxO8JCYm8p4LQNQiSAfQKXi9Xm3btk2ffvqpCgoKVFlZqbi4OE2ZMkVnnnmmYmNjnS4RAIBOxRij7OxsDRgwQLt27dIXX3yh3NxcHTp0SMuWLdOFF16ocePGKT4+PizHqx2cB0Mer9cbln0DAOpXtw1MbGysUlNTlZKSQrAOIOoQpAPo0Fwul9atW6fPP/9cx48fV2VlpRISEnTuuedq1KhREdePFQDQOV111VVOl+CYmJgYnXHGGRo+fLh27typdevWac+ePTpy5IiWLl2qyZMna9KkSUpLS2vWfoOtWoKhOSPOAcB5Xq9XpaWlKi0tleQP1lNSUkIXWsEAiGSG2eY7FmPMugkTJkxYt26d06UAjjp8+LDWrl2rjRs3qry8XJWVlUpPT9f48eM1YsQIRqADABChfD6f8vLytH79ehUVFSk5OVmpqakaM2aMzjnnHPXv37/ekKWmpiYUmFdVVamqqkq81wGA6BITE6Pk5GQlJyeHgnUGPwGd28SJE7V+/fr11tqJTtfCqxGADsPtdmvr1q1av3699u3bJ5fLpaqqKmVlZekrX/mKsrOzGd0AAECEi4mJ0bBhwzR06FAVFBRo8+bN2rdvn1auXKn169crKysr9MG4pNCo8+rqaocrBwC0ls/nC81dEZSQkBAK1ZOTk5WUlMT7OgCOIEgHENW8Xq/y8vK0efNmffnll6FRaMYYnXHGGRo9erS6devmdJkAAKCZjDHq37+/+vXrp6KiIu3atUsFBQUqKSnR559/rg0bNqh79+7q3bu3unfv3uaTkwIAnOHxeOTxeFRcXCzJ//shGKgHw/WEhATCdQBtjiAdQNTxer3as2ePvvzyS3355ZcqKyuTy+WS2+1W3759NWnSJA0dOjRsk5MBAID2Ya1VTU3NKRdrrQYPHqxBgwapqKhIJ06cUElJiVwul44cOaKEhAT16NFDPXv2VNeuXWnhBgAdmLU21MorKCYmJhSsJyUlKSkpiYlMAYQdQTqAqFBVVaXdu3dr586d2rlzp8rLy+V2u+V2u5WZmamxY8dqxIgRysjIcLpUAACabf78+fXe7qistfL5fPJ6vScF5l6vt9G+5sYYdevWTd26dVN1dbUKCwt14sQJlZWVqaqqSgcPHlR8fLy6d++ubt26qXv37kpISGjHRwYAcILP5zslXDfGKDEx8aRgPSkpiZ7rAFqMVw8AEcnr9aqgoEB5eXnKzc3V/v375Xa75fF45Ha71bVrV40ePVpDhw5V9+7dnS4XAIBWee2110K3O1KQXjswrx2ae71e+Xy+Vu07Pj5evXv3Vu/eveV2u1VUVKTCwkKVl5erqqpKhw4dUmxsrDIyMtS1a1d17dpVmZmZtIABgE7CWiuXyyWXy3XS/XFxcUpMTDzlQsAO4HR4lQAQEaqrq3Xw4EHt27dPe/fu1d69e0MTh3k8HtXU1CgrK0vZ2dkaPHiwMjMznS4ZAAAEWGtDYXkwMA/ebm1g3hSJiYnq06eP+vTpE+qjW1JSotLSUrndbhUWFio2NlZxcXHKzMwMXTIyMmgDAwCdTPBD3doTmkpSbGxsKFRPSEgIXdN/HUAQQTqAdufz+XTixAkdOnRIBQUFOnDggA4dOiS3263q6urQpUuXLho8eLAGDBigfv368dVsAAAcVDcsr33x+XyNtmRpTwkJCerVq5d69eoln8+nsrIylZaWqrS0VOXl5aqsrNTRo0cVGxur2NhYpaamKiMjQ+np6UpPT1dqaiqBCQB0Ql6v95T2MJK/RUx8fHwoVK99iY+P55tOQCfSIYJ0Y0x/SQ9Imi2pu6RDkt6UtMBaW9SM/XST9CtJ8yT1lXRC0vuSfmWtPRCuYxtjzpQ0X9J0SRmS9kp6RdJD1tqqptYLRIOqqiodO3ZMR48e1ZEjR3T48GEdPnxYLpdL1dXVqqmpUXV1tbxer7p27apBgwYpKytLWVlZSk1Ndbp8AAA6DZ/PF2rDUve6vUaWh1tMTExo9LnkH4VYVlam8vJylZWVqaKiQlVVVSosLFRMTIxiYmIUFxentLQ0paamnnThA30A6JystfJ4PPJ4PPUuj4uLCwXt8fHxp9wmaAc6jqgP0o0xQyWtlNRL0luSdkiaLOnHkmYbYy6w1p5own66B/YzQtJS+YPtkZK+I+kyY8x51tq81h7bGHNuYP/xkl6TtF/SRfIH+DONMTOtte6W/FsATqmurlZRUVGoN+mJEyd0/PhxHT9+XKWlpfVOJJaSkqKePXuqd+/e6tWrl3r37s0bVAAA2oC19qRe5cHAvL6fO7q4uLhQv3TJ/+FBRUXFSZfgqPVgsB4TEyNjjBISEpSSkqKUlBQlJyefdKE9DAB0XsH3uVVV9Y+LjI2NVXx8fChwr307Li5OcXFxio2N5dtQQBSI+iBd0p/lD7LvsNb+b/BOY8wjkn4i6UFJ32/Cfn4rf4j+iLX2rlr7uUPSo4HjzG7NsY0xsZKelZQi6Qpr7duB+2MkLZR0ZWC7h5rywIH24PP5QqO2ysrKQv1GS0pKVFJSouLi4lBYXt/FGKNu3bqpd+/e6tatm3r06KHu3bsrJSXF6YcGAEDUqh2O173Ud3+ktF2JNDExMaGWLkHBMKSyslJVVVUnXcrKykLBeu3rhIQEJSUlKSkpKXS7dp/dhIQERiQCQCcVfG/cGGNMKFSvewnO8RG8TegOOMdE8x/VgRHhuyXlSxpqrfXVWpYuf5sVI6mXtbai3p34102TdFSST1Jfa21ZrWUxkvIkZQeOkdfSYxtjLpL0T0kfW2un1alhiKRc+du8DLYtfGKMMesmTJgwYd26dS3ZHB1c8CtpLpdLVVVVcrlcoTeJlZWVqqioCF2Xl5ervLxcFRUVDY5eq/0HQXp6ujIyMtSlSxdlZmaqa9euoUm8+CUPAED9goH42LFjQ/etXbs2FIY3dN0ZRo9HmuDfUC6XS263O3TtdrtlrQ0F68FL3Z9r99et+9X/uqMUGZ0IAGhMMFwPBuunu8TExPB7BVFr4sSJWr9+/Xpr7USna4n2EekzAtcf1A6yJclaW2aM+UzSVyVNkT/AbsgUScmB/ZTVXmCt9Rljlki6LXC8YHuXlhz7osD1+3ULsNbmGWN2yj8qPhiqo5OpPYlXsAVK7ZYotXuKB297PB5VV1efdO12u0PXwUvwjV/d0Wq135A3NIItKSlJqampyszMVGpqqtLS0pSWlhaamCs1NZVRVgCATiE41iEYgDf1EvydWt99dZWWlrb3w0ITBEPwjIyMU5YFe+cGJ04PXgf/Pquurpakk4L1upfay4O36xuR2FA4Uvt27bY0DV1qHwsAEF2aMsq9PrV/T9T+fdHU3x38HkFnF+1B+hmB650NLN8lf5g9Qo0H6U3ZjwL7ac2xm7LNiMClxUF6UVGRHn/88UbXCec3EZqyr8bWqW9Z3ftq/1zf7caW112nvjfAdX+u79IeTldrfXU2Vnt9b9obeiyJiYlKSkoK9fqs3QO0vl+ONTU1KiwsVGFhYdj/HQAAiFTt8Ybx2LFjbX4MtJ3Y2NhTWthZa08ZDFF7kERD6gbrDd1Xd3lj99X3c1ur7zHUraMptTZUd333N/YYm/v4nfr3AoBId7p8pqF1mvpzc+5Dx3X8+HGnSwiJ9iA9M3Bd0sDy4P1d2mA/7bVNvYwxDfVuGbd//34tWLDgdLuIWpH6gtnSuiL18QAAnBVpQUq46om0xxWJ7rzzTqdLQCcS7v+T/B8HAESytsxgyHfaRmCQySCHy5AU/UE6TuWtqakpOXToUL7ThXRgIwPXOxytAmg9zmV0FJzL6AhC5/GhQ4ccLQRoJV6T0RFwHqOj4FxGRzBOUprTRUjRH6QHR3BnNrA8eH9xG+ynvbapVyQ02O+sgt8G4DlAtONcRkfBuYyOgPMYHQXnMjoCzmN0FJzL6Aga6crR7qJ9dsCcwPWIBpYPD1w31JO8Nftpr20AAAAAAAAAAA6K9iB9WeD6q8aYkx6LMSZd0gWSKiWtPs1+VkuqknRBYLva+4mRf9LQ2sdr6bGXBq5n1y3AGDNE/oB9r6S809QLAAAAAAAAAGgnUR2kW2tzJX0gf8P5H9ZZvEBSqqQXrLUVwTuNMSONMSNrr2itLZf0QmD9+XX286PA/pdYa/NqbdPsY0taIWm7pKnGmLm1aoqR9PvAj3+xzE4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      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 428,
       "width": 745
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load ./code/fig_classification_example.py\n",
    "\"\"\"\n",
    "Example of classification\n",
    "-------------------------\n",
    "Figure 4.5.\n",
    "\n",
    "An example of a simple classification problem between two Gaussian\n",
    "distributions. Given a value of x, we need to assign that measurement to one\n",
    "of the two distributions (background vs. source). The cut at xc = 120 leads\n",
    "to very few Type II errors (i.e., false negatives: points from the distribution\n",
    "hS with x < xc being classified as background), but this comes at the cost of\n",
    "a significant number of Type I errors (i.e., false positives: points from the\n",
    "distribution :math:`h_B` with x > xc being classified as sources).\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate and draw the curves\n",
    "x = np.linspace(50, 200, 1000)\n",
    "p1 = 0.9 * norm(100, 10).pdf(x)\n",
    "p2 = 0.1 * norm(150, 12).pdf(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "ax.fill(x, p1, ec='k', \n",
    "        fc='#AAAAAA', alpha=0.5)\n",
    "ax.fill(x, p2, '-k', \n",
    "        fc='#AAAAAA', alpha=0.5)\n",
    "\n",
    "ax.plot([120, 120], \n",
    "        [0.0, 0.04], '--k')\n",
    "\n",
    "ax.text(100, 0.036, r'$h_B(x)$', ha='center', \n",
    "        va='bottom', fontsize=15)\n",
    "ax.text(150, 0.0035, r'$h_S(x)$', ha='center', \n",
    "        va='bottom', fontsize=15)\n",
    "ax.text(122, 0.039, r'$x_c=120$', ha='left', \n",
    "        va='top', fontsize=15)\n",
    "ax.text(125, 0.01, \n",
    "        r'$(x > x_c\\ {\\rm classified\\ as\\ sources})$', \n",
    "        fontsize=15)\n",
    "\n",
    "ax.set_xlim(50, 200)\n",
    "ax.set_ylim(0, 0.04)\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$p(x)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have data $\\{x_i\\}$ drawn from an underlying distribution\n",
    "\n",
    "$$ h(x) = (1-a)h_B(x) + ah_S(x)$$\n",
    "\n",
    "where $h_B(x)=\\mathcal{N}(\\mu=100,\\sigma=10)$ is the background distribution (normalized to unity), $h_S(x)=\\mathcal{N}(\\mu=150,\\sigma=12)$ is the source distribution (normalized to unity), and $a$ is the relative normalization factor that accounts for background noise being $(1-a)/a$ more probable than sources.\n",
    "\n",
    "- ***If we set a classificiation threshold at $x_c=120$, calculate the Type I error (false positive) probability, $\\alpha$.***\n",
    "- ***For the same $x_c$, calculate the Type II error (false negative) probability, $\\beta$.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a sample of size $N$ (containing background noise and sources), the **expected number of spurious sources (Type I / false positives)** is \n",
    "\n",
    "$$ n_\\mathrm{spurious} = N(1-a)\\alpha = N(1-a)\\int_{x_c}^\\infty h_B(x)dx$$ \n",
    "\n",
    "and the **expected number of missed sources (Type II / false negatives)** is\n",
    "\n",
    "$$ n_\\mathrm{missed} = Na\\beta = Na\\int_0^{x_c}h_S(x)dx.$$\n",
    "\n",
    "The **total number of classified sources** (that is number of instances where we reject the null hypothesis) is\n",
    "\n",
    "$$ n_\\mathrm{source} = Na - n_\\mathrm{missed} + n_\\mathrm{spurious} = N[(1-\\beta)a + (1-a)\\alpha].$$\n",
    "\n",
    "The **sample completeness** (or **detection probability**) is defined as\n",
    "\n",
    "$$ \\eta = \\frac{Na - n_\\mathrm{missed}}{Na} = 1-\\int_0^{x_c}h_S(x)dx = 1-\\beta$$\n",
    "\n",
    "Finally, the **sample contamination** is\n",
    "\n",
    "$$ \\epsilon = \\frac{n_\\mathrm{spurious}}{n_\\mathrm{source}}$$\n",
    "\n",
    "where $(1-\\epsilon)$ is sometimes called the **classification efficiency**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "false positive 0.019900194921703387\n",
      "false negative 0.0006166506405920415\n",
      "completeness 0.999383349359408\n",
      "contamination 0.15197625641588255\n"
     ]
    }
   ],
   "source": [
    "xc=120\n",
    "alpha = np.trapz( p1[x>xc], dx=x[1]-x[0])\n",
    "print('false positive', alpha)\n",
    "\n",
    "beta = np.trapz( p2[x<xc], dx=x[1]-x[0])\n",
    "print('false negative', beta)\n",
    "\n",
    "print('completeness', 1-beta)\n",
    "a=0.1\n",
    "print('contamination', (1-a)*alpha/( ( 1-beta)*a +(1-a)*alpha) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The threshold depends on what you care about**. \n",
    "\n",
    "- Say you're looking for a very rare type of star and you're designing a machine-learning stategy to filter a large number of images. Those that are left will need to be analyzed visually (which is painful and time consuming). In this case, you might be willing to accept some contamination, as long and the filtered sample is very complete (better do a bit more manual work than lose a Nobel-prize-worthy target!)\n",
    "\n",
    "- Say you're testing a safety protocol for your computer cluster: you don't want it to explode while you run your very complicated astrophysical simulations. In this case, the contamination needs to be extremely low, even if then the sample is less complete (i.e. you end up discarding many potential builds that would not blow up your cluster after all as long but you're sure that the one you pick is very safe)."
   ]
  },
  {
   "attachments": {
    "0__zFg_-LPurj7FbPL.png": {
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"
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   "source": [
    "## Comparing Distributions <a class=\"anchor\" id=\"two\"></a>\n",
    "\n",
    "Hypothesis testing is strongly linked to the **comparison of distributions**. Common questions are whether two samples are drawn from the same distribution, or whether a sample is drawn from some known distribution (like a Gaussian).\n",
    "\n",
    "Sometimes we may be only interested in the location parameter of some underlying distribution. For example, do two gravitational-wave detectors with different measurement uncertainties and local effects measure consistent masses of a merging system of black holes?\n",
    "\n",
    "There is enormous variety in the nonparameteric and parameteric statistics to compare distributions, and we'll only look at a few. See the textbook and wider literature for further examples.\n",
    "\n",
    "### Kolmogorov-Smirnov (KS) Test\n",
    "\n",
    "By far the most popular nonparametric statistic to compare distribution is the KS test. We compute the empirical cdf $F(x)$ for two samples $\\{x1_i\\} = (1,\\ldots,N_1)$ and $\\{x2_i\\} = (1,\\ldots,N_2)$. *Recall that the empirical cdf can be calculated by sorting the samples and dividing by the sample size.*\n",
    "\n",
    "![0__zFg_-LPurj7FbPL.png](attachment:0__zFg_-LPurj7FbPL.png)\n",
    "\n",
    "The KS test is based on a statistic that measures the maximum difference in the cdfs of our two samples\n",
    "\n",
    "$$ D = \\mathrm{max}|F_1(x1) - F_2(x2)|$$\n",
    "\n",
    "where $0\\leq D\\leq 1$. \n",
    "\n",
    "> The core idea is to know how often the value of $D$ computed from our data would arise by chance if both samples were drawn from the same distribution (which is our *null hypothesis* here). \n",
    "\n",
    "Amazingly, ***this does not depend on the underlying distribution we care about!*** Kolmogorov published the following result in 1933 and Smirnov published numerical tables in 1948. The probability of obtaining a value of $D$ larger than that observed in our data is\n",
    "\n",
    "$$ Q_\\mathrm{KS}(\\lambda) = 2\\sum_{k=1}^\\infty (-1)^{k-1}\\exp(-2k^2\\lambda^2)$$\n",
    "\n",
    "where \n",
    "\n",
    "$$\\lambda = \\left(0.12 + \\sqrt{n_e} + \\frac{0.11}{\\sqrt{n_e}} \\right)D $$\n",
    "\n",
    "and the ***effective number of data points***, $n_e$, is\n",
    "\n",
    "$$ n_e = \\left( \\frac{1}{N_1} + \\frac{1}{N_2}\\right)^{-1} = \\frac{N_1 N_2}{N_1 + N_2}$$\n",
    "\n",
    "If the probability that $D$ were drawn by chance is very small (low $p$-value) then we can reject the null hypothesis that the two samples were drawn from the same distribution."
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For large $n_e$ we have $\\lambda\\approx\\sqrt{n_e}D$. In fact, for $n_e>10$ we can bypass $Q_\\mathrm{KS}$ entirely and compute the value of D that would correspond to a given significance level $\\alpha$,\n",
    "\n",
    "$$ D_\\mathrm{KS} = \\frac{C(\\alpha)}{\\sqrt{n_e}}$$\n",
    "\n",
    "where $C(\\alpha) = \\sqrt{-\\frac{1}{2}\\ln(\\alpha/2)}$. Some instructive significance levels are shown below (from [here](https://www.wikiwand.com/en/Kolmogorov%E2%80%93Smirnov_test)).\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The KS test and variants can be accessed in the `scipy.stats` modules `kstest`, `ks_2samp`, and `ksone.` Let's look at a simple example for comparing a Gaussian sample to a Gaussian null hypothesis distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KstestResult(statistic=0.003832961769962062, pvalue=0.10562314655566618)\n"
     ]
    }
   ],
   "source": [
    "# the kstest function is appropriate for this\n",
    "x = np.random.normal(loc=0, scale=1, size=100000)\n",
    "print(stats.kstest(x, 'norm'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compare a Student's $t$ distribution with $100$ degrees of freedom to a Gaussian distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KstestResult(statistic=0.1094480639463396, pvalue=0.1690763484589463)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "print(stats.kstest(stats.t.rvs(df=100, size=100), 'norm'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can I tell if two samples are extracted from the same distribution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KstestResult(statistic=0.0595, pvalue=0.8542805100790792)\n"
     ]
    }
   ],
   "source": [
    "print(stats.ks_2samp(stats.t.rvs(df=100, size=10000), stats.t.rvs(df=100, size=100)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other nonparametric tests, in particular the **Anderson-Darling test** to check whether a sample is consistent with having been drawn from a Gaussian distribution. We don't have time to do a deep dive here, but see the textbook for further details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametric Modeling & Histograms <a class=\"anchor\" id=\"three\"></a>\n",
    "\n",
    "Imagine you have some one-dimensional (\"univariate\") data that you would like to try to understand.  Where by \"understand\" we mean \"know the distribution in the measured space\", i.e., you want to know the probability distribution function. Our constant friend is the histogram, and it's usually the first thing any of us do on new data. Simple, right? Not quite...\n",
    "\n",
    "Let's work through some examples to see what problems we encounter and how we might overcome them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute this cell to generate a univariate data array, x\n",
    "# this is the same data used in Ivezic, Figure 6.5\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate our data: a mix of several Cauchy distributions\n",
    "#  this is the same data used in the Bayesian Blocks figure\n",
    "np.random.seed(0)\n",
    "N = 1000\n",
    "mu_gamma_f = [(5, 1.0, 0.1),\n",
    "              (7, 0.5, 0.5),\n",
    "              (9, 0.1, 0.1),\n",
    "              (12, 0.5, 0.2),\n",
    "              (14, 1.0, 0.1)]\n",
    "true_pdf = lambda x: sum([f * stats.cauchy(mu, gamma).pdf(x)\n",
    "                          for (mu, gamma, f) in mu_gamma_f])\n",
    "x = np.concatenate([stats.cauchy(mu, gamma).rvs(int(f * N))\n",
    "                    for (mu, gamma, f) in mu_gamma_f])\n",
    "np.random.shuffle(x)\n",
    "x = x[x > -10]\n",
    "x = x[x < 30]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next few cells, I plot a normalized histogram of this data with 10 bins, 20 bins, and 100 bins. It starts off looking unimodal and Gaussian-ish, but clearly when more finely binned the data breaks up into several modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x,bins=10,histtype='step', density=True); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x,bins=20,histtype='step', density=True); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x,bins=100,histtype='step', density=True); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How would you characterize this distribution?  Could we reasonably think of it as a normal (Gaussian) distribution that we could characterize by some mean and standard deviation?  Maybe, but even just by looking at this plot we see that it wouldn't be a particularly good description of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that small changes in the (hyper)parameters of the histogram function *significantly* change the PDF.  That's bad, because the underlying data clearly have **not** changed. One of the problems with histograms is that some bins end up with little (or no) data.  We can fix this by making **variable-width bin sizes** that have the ***same number of objects in each bin***.  How can we do this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14. 15. 16. 17. 18.\n",
      " 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.\n",
      " 37. 38. 39. 40. 41. 42.]\n",
      "[ 1.  3.  5.  7.  9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35.\n",
      " 37. 39. 41.]\n",
      "[ 1.  4.  7. 10. 13. 16. 19. 22. 25. 28. 31. 34. 37. 40.]\n"
     ]
    }
   ],
   "source": [
    "#Execute this cell\n",
    "a = np.linspace(1,42,num=42)\n",
    "print(a)\n",
    "print(a[::2])\n",
    "print(a[::3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are familiar with slicing, then you know that `[::2]` and `[::3]` say to take every other index of the array or every 3rd index of the array.  So, if your array is sorted (like `a` is), then you could use this to instead define the number of values in a bin.  That is for any given value of `M`\n",
    "\n",
    "    bins = np.append(np.sort(x)[::M], np.max(x))\n",
    "    \n",
    "would give bins with `M` objects in each bin.  \n",
    "\n",
    "*Note:* you need to add the maximum value to set the right edge of the last bin.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11 34\n"
     ]
    }
   ],
   "source": [
    "bins100 = np.append(np.sort(x)[::100], np.max(x)) \n",
    "bins30 = np.append(np.sort(x)[::30], np.max(x))\n",
    "print(len(bins100),len(bins30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-6.92142972,  5.2432259 ,  6.49176043,  6.87252468,  7.21447313,\n",
       "        7.9733059 ,  9.01101366, 11.08945533, 12.05155804, 13.82703299,\n",
       "       26.91818424])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Note that the underscores and the semicolon at the end both suppress the array output so that we just see the plots\n",
    "_ = plt.hist(x, bins=bins100, density=True, histtype=\"step\") #Complete\n",
    "plt.hist(x, bins=bins30, density=True, histtype=\"step\"); #Complete\n",
    "plt.xlim(-5,25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, this can look pretty different depending on what the number of objects you choose as the minimum for each bin and compared to the plots above.  And it looks a lot different from the plots above.\n",
    "\n",
    "So, what is the \"right\" way to set the bin size? There is no \"right\" way, but there are some useful rules of thumb."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**\"Scott's rule\"** suggests that the optimal bin width is \n",
    "\n",
    "$$\\Delta_b = \\frac{3.5\\sigma}{N^{1/3}}.$$\n",
    "\n",
    "That's great, but what if we don't know the standard deviation, $\\sigma$ (e.g., if the distribution isn't really Gaussian)?  \n",
    "\n",
    "We can then instead used the **\"Freedman-Diaconis rule\"**: \n",
    "\n",
    "$$\\Delta_b = \\frac{2(q_{75}-q_{25})}{N^{1/3}} = \\frac{2.7\\sigma_G}{N^{1/3}}.$$  \n",
    "\n",
    "Let's try that. Remember that you can compute $\\sigma_G$ using `astroML`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6731977984018402\n"
     ]
    }
   ],
   "source": [
    "from astroML import stats as astroMLstats\n",
    "sigmaG2 = astroMLstats.sigmaG(x)\n",
    "print(sigmaG2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now set the bin size accordingly, using [np.arange](https://numpy.org/doc/stable/reference/generated/numpy.arange.html) and plot.  Make sure that you don't throw away the last object in data set (append that maximum object to the end)! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9917634055684971\n",
      "36\n",
      "[-6.92142972e+00 -5.92966631e+00 -4.93790291e+00 -3.94613950e+00\n",
      " -2.95437610e+00 -1.96261269e+00 -9.70849286e-01  2.09141194e-02\n",
      "  1.01267752e+00  2.00444093e+00  2.99620434e+00  3.98796774e+00\n",
      "  4.97973115e+00  5.97149455e+00  6.96325796e+00  7.95502136e+00\n",
      "  8.94678477e+00  9.93854818e+00  1.09303116e+01  1.19220750e+01\n",
      "  1.29138384e+01  1.39056018e+01  1.48973652e+01  1.58891286e+01\n",
      "  1.68808920e+01  1.78726554e+01  1.88644188e+01  1.98561822e+01\n",
      "  2.08479456e+01  2.18397090e+01  2.28314724e+01  2.38232359e+01\n",
      "  2.48149993e+01  2.58067627e+01  2.67985261e+01  2.69181842e+01]\n"
     ]
    }
   ],
   "source": [
    "binsize = 2.7*sigmaG2/(N**(1/3))\n",
    "print(binsize)\n",
    "binsG = np.append(np.arange(start=x.min(), stop=x.max(), step=binsize) , x.max()) #Complete\n",
    "print(len(binsG))\n",
    "print(binsG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.0, 25.0)"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 391
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(x, bins=binsG, density=True, histtype=\"step\") #Complete\n",
    "plt.xlim(-5,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did you find that tedious? Me too. Try the following shortcut."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.0, 25.0)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from astropy.visualization.hist import hist as fancyhist\n",
    "_ = fancyhist(x, bins=\"scott\", histtype=\"step\",density=True)\n",
    "_ = fancyhist(x, bins=\"freedman\", histtype=\"step\",density=True)\n",
    "plt.xlim(-5,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that even those don't yield quite the same results!  But we can do better!\n",
    "\n",
    "An obvious thing to do is to simply show all of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12bb97250>]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 375
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# execute this cell\n",
    "plt.hist(x,histtype=\"step\")\n",
    "plt.plot(x[:100], 0*x[:100], '|', color='k', markersize=25) #Note markersize is (annoyingly) in *points*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is called a **rug plot** and now we have a better idea of where most of the data and where the gaps really are (as opposed to where the binning makes them *appear* to be).  However, the markers are all piled up, so we have lost all sense of the relative numbers of objects.  Are there ~10 at x=5 or could there be 100?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel Density Estimation (KDE).\n",
    "\n",
    "\n",
    "This is where **[Kernel Density Estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) (KDE)** comes in:\n",
    "- In short the idea here is to represent each data point not as a delta function, but rather as a distribution (e.g., a Gaussian).  \n",
    "- Those individual distributions (\"kernels\") are summed up to produce the PDF.  \n",
    "- One of the advantages of this is that it combines the best of \n",
    "    1. the histogram (tells us the relative height of the distribution) \n",
    "    2. the rug plot (centers the data points at the actual location of the data instead of within some arbitrary bin)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just about any distribution can be used as the kernel, but the most common are a **Gaussian kernel** and an **Epanechnikov kernel**.  One downside of the Gaussian kernel is that the tails are technically infinite in extent.  So each point has some finite probability of being *everywhere*.  The Epanechnikov kernel has truncated wings.  \n",
    "\n",
    "One still has the problem of deciding the width of the kernel (e.g., for the Gaussian the \"mean\" is fixed at the value of the point, but how wide should you make the Gaussian?). For now, we'll just play with the widths by hand to see what might work best.  N.B. the widths of the kernel distribution are referred to as **\"bandwidth\"**.\n",
    "\n",
    "In practice, the bandwidth is almost always the key parameter of a KDE representation, the exact shape of the kerne doesn't really matter too much "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the KDE module\n",
    "from sklearn.neighbors import KernelDensity\n",
    "xgrid = np.linspace(x.min(),x.max(),1000)  # Use this instead of 'x' for plotting\n",
    "\n",
    "def kde_sklearn(data, bandwidth = 1.0, kernel=\"linear\"):\n",
    "    kde_skl = KernelDensity(bandwidth = bandwidth, \n",
    "                            kernel=kernel)\n",
    "    kde_skl.fit(data[:, np.newaxis])\n",
    "    log_pdf = kde_skl.score_samples(xgrid[:, np.newaxis]) # sklearn returns log(density)\n",
    "\n",
    "    return np.exp(log_pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we try the Gaussian and Epanechnikov kernels, let's first start with a tophat using `kernel = \"tophat\"`, which will produce a plot much like the rug plot.\n",
    "\n",
    "Start with `bandwidth=0.001`.  See what happens when you adjust this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12badb040>]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PDFtophat = kde_sklearn(x,bandwidth=0.1,kernel=\"tophat\") #Complete\n",
    "plt.plot(xgrid,PDFtophat) #Complete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The defaults give a result that is essentially what you would get if you made a histogram with a really large number of bins.\n",
    "\n",
    "Now let's compare what happens when we adjust the bandwidth (which is just the width of the kernel function).  Try \n",
    "`bandwidth=0.1` and `bandwidth=0.5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12b9d7790>]"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fiIjUDgX1IiJVkMvUt9GbXxdomEqHdTL39flMvbf8phoDZf3aVyqmFxGpHQrqRUQq6Bf3rOLZTV286/gFALSanvw20ziVdpwAvj6RydRHQ96gvhqsb029onoRkVqhoF5EpEIeXbuTb978AgAPrW4HYApOUB9snEqHdepe6hKdQHG5TSLlUxtTZn5ZeU0+JSJSO8o2+ZQxZp4x5ipjzCZjTMwYs9YYc7kxZsowj280xrzNGPMHY8wLxpheY0y3MeYxY8wlxphIiePsIH8eKtfXJyIyUrc/vzW/vL070/WmzZWpDzZMpZMm0jYTxNcldkEqWdSnPpmqfHDtVz/vNyGViIhMTGXJ1Btj9gEeAGYCNwAvAEcDHwPOMsacYK1tH+I0JwG/A3YCdwHXA1OA1wLfA841xpxurR3wOXYdcLXP+o0j/mJERMrErxbeHdSHm6aRYiu7aHQy+P0dBAPefEs1MvX+5TcVv6yIiJRJucpvfkomoL/YWvvj3EpjzGXAJ4CvAx8c4hxbgLcDf7HWxl3n+BRwN3A8cBHwfZ9j11prvzKG+xcRKbtQsPjD0DZX+U2gcSoAO20zU3LBft8OwgWZ+kQVMuYqvxERqW1jLr/JZunPANYCVxRs/jLQC1xgjGkc7DzW2qestb93B/TZ9d04gfwpY71fEZFqKayNjxKn0WQnnwqEINoCwE6anZ362otmkE1WIVPvW36joF5EpGaUI1N/avb1Nmut5zePtbbbGHM/maD/WOCOUV4j18g5WWJ7mzHm3cBsYBfwuLV2RPX0xpjHS2xaMpLziIjkFJbfzDQdzpumWZAN3nfaFmd97w5Cgame4xJVqKn3n3yq4pcVEZEyKUdQv1/2dUWJ7SvJBPWLGX1Q/+7s6y0lth8C/D/3CmPM08AF1tpnRnlNEZGymkmn86Z5dn5xp/Vm6qc3Rz3HJf1mhiozv6S8BsqKiNSOcnS/ac2+7iqxPbe+bTQnN8Z8BDgLeAq4ymeXy4ATgBlAM3AUcB2ZQP9OY8zc4VzHWnuE3x8yg35FREYslvQG47PcmfrmOfnFwvKbC45d4DmuKt1vfDP1CupFRGpF2VpaVoIx5lzgcjKDaN9grWs+9Sxr7SXW2gestTustT3W2sestecBfwWmA5+q6k2LiGTFkinP+5mm03nTNCu/WJipb4yG+OUFR+RXVadPvcpvRERqWTmC+lwmvrXE9tz6zpGc1BhzDvAnYBtwirV29Qjv6+fZ15eN8DgRkbKIJYaZqS+oqQeY0uhMzZGsQnRdKimvEhwRkdpQjqB+efZ1cYnti7KvpWruixhjzgP+AmwFTrbWLh/iED/bs6+Ddt0REamUwkz93maL86bFCeo7POU3maDe3TmnGpl6v+43oBIcEZFaUY6g/q7s6xnGGM/5jDHNZOrd+4BhdaMxxrwN+COwiUxAv3KU93Vs9nWkGX4RkbIYcGXqDWmODixzNs51ymva3Zn6vsw8fWFXj/vx6n6TWV/xS4uISBmMOai31q4CbgP2IjM5lNulZDLl11hre3MrjTFLjDFFrSKNMe8EfgusB142VMmNMeZgY0zYbz2ZCa8gM0utiEjVuTP1+5hNTM1NMNUwHWY4PwI9mfre4qC+Gn3qSwXvytSLiNSGcs0o+2HgAeBHxpjTgWXAMWR62K8A/rdg/1y6Kv/5sjHmVDLdbQJksv8XGlM0xXqntfZy1/tPAq8xxtwLbABiZPrKnwUEgSvJZP1FRKrOnanfw7Q7G2YdkO9R/8lXLOZn/x5wtvW1g7WEXLPKVqOmvlTtvIJ6EZHaUJag3lq7yhhzJPBVMgH12cBm4IfApdbajsGOz1qA88nBu0vss45MN5yc64EW4GDgNKAOaAduBq601v5jRF+IiEgZuTP1bfQ6GxqcyaU+cuq+HLlnG/ZPdZjUAKRiEO8hHAjm9xmv7jeZ9RW/tIiIlEG5MvVYazcAFw5z36IUvLX2auDqEV7zejKBvYjIhOPO1LfmSm8A6qfkFwMBw/GLZkDjdOjamFnZ104o6LS8rEaf+lLBe6kBtCIiMrFM6D71IiK1zJ2pn4J/UJ/nyt7T215QfjN+mXqr8hsRkZqgoF5EpELcmfo2T6Z+avHOjdOd5b52wgHnx3M8WYWgvmRNfcUvLSIiZaCgXkSkQtyZ+lLlN3kN05zlvh2EQ67uN9UYKKvyGxGRmqagXkSkQvpiJcpvGnwy9Q3eTL178qnqBPUqvxERqWUK6kVEKqQ3nswvt40kU9+7A3dH32oE1up+IyJS2xTUi4hUQDKV9tTUT6PL2ehbU+8K6u+/nKBrUzVKYEoF9Sll6kVEaoKCehGRCuiNO6U3AdLMcU8+1Tqv+ICmWZ63wfX35ZfTtvLZ+lKt8EsNoBURkYlFQb2ISAX0xpzSm1l0EDGZID9VPx0iDcUH7HO6563pWOspwal0bF3qoUGJehGR2qCgXkSkAtxB/TyzPb+cap3vf0C4Dk74mOsE2wi6ovpKl+Co/EZEpLYpqBcRqYCeEkG9bd2z9EHuEpye7QRcHXBKBd3lUrL8RkG9iEhNUFAvIlIBva52ljNNp7OheU7pgxpnOss9Wwl4ym8qHdT7R/VqaSkiUhsU1IuIVIA7U19vYvnlYF1z6YOaXEF97/aqlt+kSk4+VdHLiohImSioFxGpAHdNfT1OUB+INpU+yB3U92zzlt9UOLgu1eVG5TciIrVBQb2ISAW4J55qcAf1fp1vchq9QX3QFdRXesBqqU8CFNSLiNQGBfUiIhXgrqmvN3Fnw2BBff0UCIQyy7Fd1JPIb6p8+U2JoF7lNyIiNUFBvYhIBQwkXEE9A86G8CBBfSAAjTPyb6cFnFloKz9QVpl6EZFapqBeRKQC3MHwfHcZ/WBBPXiC+pnsyi9XPFOvoF5EpKYpqBcRqYCkK0ieFnGy9oOW34CnV/00OvPLlQ6uS51fQb2ISG1QUC8iUgHubjLhdL+zYahMvasDzjTjZOorXdteOlNf2euKiEh5KKgXEakAd5AcTo0gqHeV30x3ZerHrfuNonoRkZqgoF5EpALcQXgo7RooO1T5TcPU/GILfc75qlhTX81WmiIiUh4K6kVEKsBTfpMaZvcbgEhjftHdNafi3W9c5w8HnaBeMb2ISG1QUC8iUgHugbKhkZTfhP2D+kpn6j0PIQHnV4MGyoqI1AYF9SIiFZALhg1pb/nNCDL1DeOUqQ+5MvWVfpgQEZHyUFAvIlIBuWC4DtdssqG6zARTg3EF9XU2ll+ufPcbZzkcdO5RiXoRkdqgoF5EpAJyQXIbvc7KurahD/TU1DtlO5XvfuNE9e6gXuU3IiK1QUG9iEgF5IJhd695GqcPfaA7qLfVq6n3tOB0ld+o+kZEpDYoqBcRqYDcQNlppttZOcKgvq6KNfXu4N2dqVdNvYhIbVBQLyJSAbluMtNwZeobhhHUh9019eOTqQ95auoV1IuI1AIF9SIiFZALkqeOJVNvnZr6Ss/sqvIbEZHapqBeRKQCUvma+i5n5XCCelfLyzobw5AZwFrp4Nob1LvKb5SpFxGpCQrqRUQqwCm/cQX1wym/CQQ8gX19tiVmxbvflJxRVkG9iEgtUFAvIlIBuYGy0z3db2YM72DPBFSZXvWVLr9Jl8jUq6WliEhtUFAvIlIBuWB4lulwVjbPGd7Bkab8YpPpA6owUNaWKL+p8KRXIiJSHgrqRUQqIBeEzzSdzsrm2cM7uL4tv5ibvKri5TcpV/ebgHugrDL1IiK1QEG9iEgFpNKWEElXTb2BppnDO7h+an6xzfQAVeh+UyJTr5p6EZHaoKBeRKQCUmnLdHYRMNmguHEGBMPDO7h+Sn6xlUxQX/FMfYmWliq/ERGpDQrqRUQqIGVtQenNrOEf7Arqp+Qy9RVOmKdLZOpVfiMiUhsU1IuIVEA6bZnq6VE/zNIbgIZxKL/RjLIiIjVNQb2ISAWkrKUx244SgGhT6Z0LecpvsgNlKxjUW2s9nwS4y2+SmlJWRKQmKKgXEamAVBoazICzItxYeudCnvKb7sz5Kpgxdz8wBAyEAgHfbSIiMnEpqBcRqYBUOp2fOArwTCg1JHdQT+XLb9wPDMGA8WTq4xopKyJSExTUi4hUQCptacSVqR9JUF/Xml9sMv2Z81UwU592xe2ZoN751ZBMKVMvIlILFNSLiFRA2kK9GWWmPtqcX2yiP3++SvFk6o0h5K6pV6ZeRKQmlC2oN8bMM8ZcZYzZZIyJGWPWGmMuN8ZMGfpoMMY0GmPeZoz5gzHmBWNMrzGm2xjzmDHmEmNMZJBj9zfGXGuM2WaMGTDGLDfGXGqMqS/X1yciMhJjytRHnEG1jdm6/IqW37iy8YGCTH1CNfUiIjUhVI6TGGP2AR4AZgI3AC8ARwMfA84yxpxgrW0f4jQnAb8DdgJ3AdcDU4DXAt8DzjXGnG6tHXAfZIw5BrgTCAPXARuA04AvAadnj4khIlJFqbSlYbRBvStT30xf/nyVUlhTHwooUy8iUmvKEtQDPyUT0F9srf1xbqUx5jLgE8DXgQ8OcY4twNuBv1hr465zfAq4GzgeuAj4vmtbEPg10AC8zlr7j+z6AHAt8Ibs9b81ti9PRGRkUmlLg7v8ZiTdb1xBfSbbbys6CZT7gSFTfuPK1KumXkSkJoy5/CabpT8DWAtcUbD5y0AvcIExZtDfaNbap6y1v3cH9Nn13TiB/CkFh50MLAX+kwvos8ekgc9k337QGGMQEamilB1Dpj4YhmAUgJBJU0e8opn69CDdb5JpZepFRGpBOWrqT82+3pYNpvOyAfn9ZDLpx47hGonsa7Jg/WnZ11sKD7DWrgZWAAuAhWO4tojIiKXTBZNPjSSoh4LBsgNV61OfKb9R9xsRkVpTjvKb/bKvK0psX0kmk78YuGOU13h39rUweB/OtRdn/6wa7ALGmMdLbFoynBsUEXFLWUu9GWWmHjIz0PbtAKDJ9FV2oKxn8ilv9xv1qRcRqQ3lyNTnGirvKrE9t75tNCc3xnwEOAt4CriqmtcWERmtVBkz9Y0MVLalZUGmPqI+9SIiNadcA2UrwhhzLnA5mUG0b7DWJgY/YvSstUeUuIfHgcMrdV0RmZxSaUtjduIoAMINIztBxNUBx/RXt/uNaupFRGpOOTL1uWx4a4ntufWdIzmpMeYc4E/ANuCUbI18Va4tIjJWqXSa6e4PERtnjOwEnkx9f0W736Q95Td4aurV/UZEpDaUI6hfnn1dXGL7ouxrqbr3IsaY84C/AFuBk621y0vsWvZri4iUQ6vtImJSANhoC0RGmKmPOhNQNVG9TH0oEPB2v1FNvYhITShHUH9X9vWMbH/4PGNMM3AC0Ac8NJyTGWPeBvwR2EQmoF85yO53Zl/P8jnPQjLB/jrAL8svIlIx022H86Z5zshPEC0ov6lgpj5ZMKOsu099UjPKiojUhDEH9dbaVcBtwF5kJodyuxRoBK6x1vbmVhpjlhhjirrKGGPeCfwWWA+8rETJjds9wDLgZcaY17rOEwC+nX37c2sr+NtQRKSAtZYZuIP62SM/ScTJ1DcyUNHuN94+9RB2zSibUKZeRKQmlGug7IeBB4AfGWNOJxNoH0Omh/0K4H8L9l+Wfc3/5jDGnEqmu02ATPb/Qp85ozqttZfn3lhrU8aYC8lk7K8zxlxH5oHgdOBIMj3yf1CGr09EZNhSactM4wT1ZjRBfbQlv9hk+umoYGw92Iyy6n4jIlIbyhLUW2tXGWOOBL5KphTmbGAz8EPgUmvdn0OXtADnk4N3l9hnHZluOO5rP2yMOYrMpwJnAM3Z/b4KfMtaGys8iYhIJaWsZaZ7fH7TrJGfpKCmvr2SA2VtYfmNMvUiIrWmbC0trbUbgAuHuW9RCt5aezVw9Siv/Txw3miOFREpt3Qa5pntzoq2PUd+Es+Msv1UsorQXdkTNN4+9ep+IyJSG8oxUFZERFxS1o49qHfX1JvKTj6VHmRGWfWpFxGpDQrqRUTKLJUuQ1Dvrqmnst1v3A8MpqBPvWrqRURqg4J6EZEyS6VSzDU7nBWt80d+EndNvals+Y373Mbg6VOfUKZeRKQmKKgXESmzbZs35Cee6qTJE6APW0FNfSVja/fjQmCSdb+x1vKzu1fx1Rufp7MvPt63IyJSMWUbKCsiIhnX3v88X8oud9FE22hOUlRTX6XuN8YU9Kmv7aD+n89s5tu3vABkPoH43NlLx/mOREQqQ5l6EZEyi/d355djgbrRncQ9oyz9lR0oW1hT75lRtrbLb350hzMp+S/+o8nFRWTyUlAvIlJm4VR/fnnmtGmjO0mkMb9YT6zCLS0LMvXumvpkbQf1vbHUeN+CiEhVKKgXESkzd1BvQw2jO0kwgs1Ouh02KUgnynFrvooHyrr61FfyI4Iq6I0nx/sWRESqQkG9iEiZRdJOUJ92ZdxHxBhSQad0J5Cu3CBPd4VNwBhCrpr6ZI3PKNsbU1AvIrsHBfUiImXmDupteJSZeiAVjOaXg6mBMd3TYLzdbyDoCurT1js5Va1xD/Q1RXOZi4hMHgrqRUTKLFKO8hsgHazPL4fTlQvq057yG4MprKuv0cGyheMQGiNq+CYik5eCehGRMotYJwC3oy2/wZupD6ViY7qnwVjPQNnMqydbX5sxfVE7zkoONhYRGW8K6kVEyizqKr9x95sfqbSrpj5U0Uy9sxzI1qgY3CU4tRkMx5Lezje98VRNlxKJiAxGQb2ISJlF033OmzHU1HuD+goOlLXFdeeuRD21GgYPJIo/YuhPqMWliExOCupFRMqszrpKZcZQfpMOVT9Tb7JRfcDUfqZ+wCeAVzccEZmsFNSLiJRZ1DrlN6ZsQX21auqz5TfuTH2N1tTHfCbO6lFQLyKTlIJ6EZEyq3MNlCU6hqDeVX4TrmhQ7yznym4CgcmaqVf5jYhMTgrqRUTKrMn25JcDda2jPo91B/W2ckF92idTPxnKb/wy9aqpF5HJSkG9iEiZtdru/LJtmDrq84xPTX32tcT2WhLzCeD9svciIpOBgnoRkTJroyu/HGicPurz2JC7/KZK3W/I1dQ7Yb2t0f43fpl6v3UiIpOBgnoRkXJKp2nBVX7TOG3Up3KX35zUd/uYbmvQ6/hMPuVpaVmbMb1vVl6ZehGZrBTUi4iUU2wXITLZ4G5bTzAcHeKA0mwwkl/eK7kaeraN+fZ8r+Mz+dRkqKlftrmraJ0y9SIyWSmoFxEpp76d+cUO20TInfIeoaBNeFfsXDPqcw3GM6Ns9reC+7Zrsaa+ayDBj+58sWi9MvUiMlkpqBcRKae+9vziTpoJjiGo755zrHdFrDjzXA7eGWWLa+rTNRjV3/rsFt/1ytSLyGSloF5EpIysK6jvtM0EzeiD+t65LyNlXccP7BrLrZXkV1NvarymPhLy//WmTL2ITFYK6kVEysj2OkF9B82eSZxGKhAI8KfUac6Kgc4x3FlpnpaWFNfU12L3m4ZIyHe9MvUiMlkpqBcRKaO0K6jvpHlM5woYQxcNzooKZerTQ3S/qcHqG2JJ/4y8X+96EZHJQEG9iEgZWddA2U5axnQuY6DLNjorKlZ+477m5Oh+E0v4Z+SVqReRyUpBvYhIGdm+HfnlLlOLmfrcQFlnu63BoH6gRKZeNfUiMlkpqBcRKSPjytR3BcaWqQ8EoMtWPqj39qnPvboz9RW5bEUpUy8iuxsF9SIi5eTqfrPLjDGoN4YuKl9+48nUB4oz9bVYfqNMvYjsbhTUi4iUkenvyC93B1rHdK6AqU6m3tv9JndtV/eb2ovpGXBl6g+a2+par6BeRCYnBfUiImVk+p1MfU+g9mrqfSefqsGo3t39prU+7Fqv8hsRmZwU1IuIlJGJ9+aXBwKNg+w5tIAxVel+472m9xVqM1Pvrql3B/XK1IvIZKWgXkSkXNJpAqmB/NtkIDqm0/lm6isQYafTxd1var6lpStT36JMvYjsBhTUi4iUS6Ivv9hvIwSDwTGdzhiIESFms0FpKg7JgcEPGoW0b/cb/+21wl1T31LvzC6roF5EJisF9SIi5eIK6vuI5jvJjFbu+ErX1fvV1DOJMvXNUSeoT6YU1IvI5KSgXkSkXNyZeqKExhrUZw/3dMDp7xzTOf1YT1DvvXZme9kvWXHuTH2TK6hPpGrwixERGQYF9SIi5RJ3ZeptlOCYg/pcpr6yg2W95TfFNfW1OKOsO1PfVOfU1CfTytSLyOSkoF5EpFwKMvVlC+or3Kve4h4o632F2q+pb4o6YxuSytSLyCSloF5EpFzKHtRnXitfU+8sT8Y+9U1RJ1OfUE29iExSCupFRMqloPxm7DX1uUy9u/ymc0zn9OMO2nPXNCW21wp3n/oGV6ZeNfUiMlkpqBcRKZeEM/FUPxFPXfpoODX1FS6/8W1paXy314qk6+OHhoir/EY19SIySSmoFxEpl0R/frGfOkLBsQX1JvsTeleFZ5V1Tz6V737j+u1Qi0F93NWPvi7kzdTX4sBfEZGhKKgXESmXou43Y/sRO1G639Ri+Y07Ix8JBTzjG1K1OPJXRGQIZQvqjTHzjDFXGWM2GWNixpi1xpjLjTFTRnCOVxhjvm+MucMY026MscaY+4Y4xg7y56Gxf2UiIsNUUH4zxkS9f5/6Cne/mSwDZd1dbsLBgGd8Q1JBvYhMQqGhdxmaMWYf4AFgJnAD8AJwNPAx4CxjzAnW2vZhnOoi4HXAAPAiMHWYt7AOuNpn/cZhHi8iMnae8ptyZurHo6bef3utcHe5CQcN4WCAWLYkJ5FKUxcOljpURKQmlSWoB35KJqC/2Fr749xKY8xlwCeArwMfHMZ5vg38L5mHgvnAmmFef6219isjuWERkbKLO5n6ynW/qUT5zeTrfuPOxoeCAc/4BnXAEZHJaMzlN9ks/RnAWuCKgs1fBnqBC4wxjQzBWvugtfY5a21qqH1FRCaceE9+sZf6GupT7zf5lLv8puyXrDh3+U0oYAi5PjVJqle9iExC5cjUn5p9vc1a6/lJaa3tNsbcTyboPxa4owzX89NmjHk3MBvYBTxurVU9vYhUV8wJ6ntsXRlnlK3eQFl8auprsVtMIu0uvwkQdmfqa/EpRURkCOUI6vfLvq4osX0lmaB+MZUL6g8B/p97hTHmaeACa+0zwzmBMebxEpuWjPHeRGR34crU91FH8xiD+lxc3U29s3KgM1PkPsYe+G5D1dTXWgycStv812QMBAPGU36jTL2ITEbl6H7Tmn0tlT7KrW8rw7X8XAacAMwAmoGjgOvIBPp3GmPmVui6IiJe7kw99QTGHNQbjIEYEXblOuCkk9C1aUznLWR9auoDNZyp9w6SzfyaC7vKb1RTLyKTUc33qbfWXmKtfcBau8Na22Otfcxaex7wV2A68KlhnucIvz9kBu2KiAwt3p1f7LV1Yx4oC05wvdLOc1ZuXzbm87r51tQH3NvLermK8wT12S8oF9yDZpUVkcmpHEF9LhPfWmJ7bn1nGa41Ej/Pvr6sytcVkd1VzD1Qduw19eAE2SvSrg8dt5U31+AO2vN96nEPlK2tqN4zSDYbzHu63yRr6+sRERmOcgT1y7Ovi0tsX5R9LVVzXynbs69Ddt0RESkLV0vLHjv27jfgZOpfdGfq21eO+bxuvi0tjf/2WuAdJJv5QkKuTH1CmXoRmYTKEdTflX09wxjjOZ8xpplMvXsfUO1uNMdmX1dX+boisrsqGChbzqC+3TY7K2PdJfYeHXfMnrvjQBkH4labt51lrqbe+G4XEZksxhzUW2tXAbcBe5GZEdbtUjKZ8mustfkUljFmiTFmzF1ljDEHG2PCfuvJTHgF8LuxXkdEZEjpdEGf+nLV1Gde+4k6K+N9Yz6vm2egbMB7Xai9TL23/MZ4XjPblakXkcmnXDPKfhh4APiRMeZ0YBlwDJke9ivIzBLrlhvl5fmNZ4w5EXhv9m1T9nWRMebq3D7W2ne5Dvkk8BpjzL3ABiBGpgXlWUAQuBL44xi+LhGR4Ul4Z5NNExhz9xtwMuZ91PleqxzSnpaWxd1vaq1axV1eE8l1v/GU39TWQ4qIyHCUJai31q4yxhwJfJVMQH02sBn4IXCptbZjmKfaF3hnwbqZBeve5Vq+HmgBDgZOA+qAduBm4Epr7T9G9IWIiIxWwSBZoCyZ+lxs3WddmfpE/5jP6+bOxBufyacmRaY+oEy9iExu5crUY63dAFw4zH19f9NZa68Grh7BNa8nE9iLiIyvuHc2WYBgYOzDlnLZ/gEirmuVu/zGdb3sT2d3SX2NxfSelpb5mnp3pl5BvYhMQjXfp15EZELo78wvdmWbbgXLMNjUKb9xZ+rLXX7jN/mU//Za4J18qrhPvSafEpHJSEG9iEg5DHTmF3fZTFDvHpw5Wvmg3rpr6itYflNwXYBaC4GT6cH71GvyKRGZjBTUi4iUg1+mvma63zjLk6Gm3lt+k6upV6ZeRCY3BfUiIuXgytR32vKX3/S7a+oTvWUtdE/71NR7y2/KdqmqcA+UjYRyNfXqUy8ik5uCehGRcuh3mnztqkCmPkkIG8hOy2HTkIqP+dw51rem3vhurwXu8pp8pl7lNyIyySmoFxEpB1f5TTlr6t1lMDbc4GyIl2+wbNpn8in3hwzpGkvVJ1LFNfXugbLxpIJ6EZl8FNSLiJSDe6Bsdu68QDnKb1w/pdOheudNGQfLpn1q6j2TT9VWTO/b/Sai7jciMskpqBcRKQe/TH0ZZ5QFsCFXpj5RvsGyft1vPH3qy3al6vBMPqU+9SKym1BQLyJSDp5Mfflq6t2DbdNhV6a+jOU3bpOhpt7T/SaXqQ8pqBeRyU1BvYhIObhbWtryBfWe2vZwk/Mm1j3mc+fPO8kmn3L3qQ/7ZOpVUy8ik5GCehGRcvBraVnm8ptk3VRnQ9+OMZ87x90MxmlpWbs19Ul3TX0oN6Os8/XElakXkUlIQb2ISDm4a+rJ1dSP/UesO7hO1E1zNvSWMah319TnrlfDmfqET019VOU3IjLJKagXERmrZDwzIRSQIkAPmdr3YBl+wtZFgvnlWGSKs6GMQb31nXzK+G6vBX3xZH65Ifv9U/mNiEx2CupFRMbKVXrTF2gil+YOliFT3xR1gvrekDuo3z7mc+f4ZerdlUO1NlC2J5bKLzdGQ0DhQNna+npERIZDQb2IyFi5Sm96A85g1nK0tGyIhPLLPaFWZ0MZa+rdIe5kqKnvjTmZ+kZl6kVkN6GgXkRkrFyZ+t5Ac345UIagvinqBPVdps3Z0Ns+5nPn+GXqjSeor62ovtdVfpPL1HuCetXUi8gkpKBeRGSsXJn6HlPeTH2jq/ym07Q4G8rZ/ca3pt5/ey1wZ+pzD0UaKCsik11o6F1ERGRQ/Tvzi+6gvhwtLRtdmfqOtGvyqXL0qV/3IGxfRii9V35VruzG4B4oW1tRfa9PTb3Kb0RkslNQLyIyVu0v5he3BWbkl8sR1De5auo7Uq6gfqBrbCfuWAdXnw02zUWRU3k37wMmx+RTPbHi8hvNKCsik53Kb0RExmrbsvziuuCC/HK5M/WdybCzId7tnTVqpDY8DDZz/Gnxu9jbbAacGWzd4wFqLKb3DpSN5gbKuiefqrEvSERkGBTUi4iM1fbl+cW1gfn55XLX1HfHgYhT3kO8Z/QnLuhzf1zgecAJ6s0kqalvjKj8RkR2DwrqRUTGIhmDnavzb9eaeflld1vI0XJn6vviSYg63XXGVFffvdnzdpHZCLjLb2q3pr5HA2VFZDekoF5EZCx2rASbHZjZtoA+G8lvCgXLG9T3xJIQdXXAiY2hrr5nq+fthaFbiZCo+Zr6Xf0JugaGaGmpTL2ITEIK6kVExmL7C87yzKWkXLUq5Si/cfep742VKVPftQn+++ei1XdGL6F+6+OAt/tNLZXf/PyeVfnlcNDkB8hqoKyITHYK6kVExsJVT8+M/TxBfTnKb+pCTk19LJkuCOpHkanv74QrT/fdNM/sYP71r4c19xbU1NdOVL96uzPOwP0w4s7UK6gXkclIQb2IyFh0b3KWp+xF0pOpH/uP2HDI1bWlKKgfRab+0Su991zA2DTc9fWCmvqRX2a8xFylNVecf3h+OeIK6mMqvxGRSUhBvYjIWLgD67pW0q6gPliGmvpIYYa5zlVTP5pe9Wvv874/6r2sNHt5161/kEiqN/+2lgbKDiSciada6pzSJZXfiMhkp6BeRGQs3EF9tNWTqQ+WofzGWzZixz5Qts+Z/ZY5h8Arvsp3wh/ijtRhnt2m9K3JL9dSTb07Cx8NO6VL7j71CfWpF5FJSEG9iMhYuLPl0WZPTX05Jp9yt2KMJdNQP8XZ2N8x8hP2dzrL5/0GIo08wyLek/g0N6WOyW+a0uu06aylmvqBhCuod33vQsFAvqNPKm09f08iIpOBgnoRkbHwZOqbSdnyBvVFAzzHHNS7MvXZc+XueWXa6bE/fdcz+eVain9jSaf8ps6VqQe1tRSRyU1BvYjIWBQE9f1xd1A59h+x7lrw+Fgz9cm4MwutCUJdK0B+HMBjdnF+18Ub/sJs2rPvaieqj5XI1APUR5wgv99Vey8iMhkoqBcRGQtXUJ8MN+Vruo2B+oJM8WgMmql318cPx0Cns1zfRq5vZS5Tf3/6QJKzDs7v8lDdR5lNO+kaSmoPlqlvjBT0/BcRmUQU1IuIjFY6BXEnqO+lPr/cGAlhyjJQ1jlHMm1J140hU99XXHoDuOrLDbETPuM55K2hO2u3pr7gk5LGqBPk98YV1IvI5KKgXkRktOLOREdEmuhNOMGvO4AcC2OMt61lpNXZ6B70Ohzuh4D6qflFd8yeXnQmTF2Yf/+x0N+pS+wa2XXGkbulZX7iro518I+P8ur0XfltytSLyGSjoF5EZLQK6undgWJjNORzwOi4s/XxSJuzYaSZek9Q75zHMwtuIAAX3uI57NQdvx/ZdcZJMpXOtxQ1Jvt9sxaufQc88Vsu7v4B+5qNAPTEVFMvIpOLgnoRkdHyBPUt9LoGyTaVMaj3DJYNNmYGuUKm9CcZH/6JCu43p6hjT/MskkGnlGiP2KqR3/Q4cPeorwsFM+VPa+6BzU/l158TvJ8FZosy9SIy6SioFxEZrYIe9e5AsSFSnvIbKBgsmwYaZzgbuzcP/0QJZ5ZYIo35RfcsuIHsOIAHTrgqv64lsWP41xhH3omnst+zLc969vlI6AbuiX6Saav+Vs1bExGpOAX1IiKjVVB+0+MK6suZqS/qgNO2p7Oxc/3wTxR3B/VN+UW/3vqxprn5dS3JdmqBbz19zxbfffda8+dq3JKISNUoqBcRGa1Y6Ux9OWvqi2aVLUtQ3wCAtdYzUDY3X1aybhpJm7luU7oLkrER33e1+Wbqu/2D+lm7nq7GLYmIVE35fuuIiOxu3Jn6upYKDpStRKY+U37jGSRryLfhDAZD7KCV2WQH1/Zs9V53Aspl6g82qzg/+TTc/ww88xfffeOBeiLW5nv1i4jUOmXqRURGy5WpT0ea+eczTn17xQbKli1Tnym/SXuy9E6AGwoatlpXT/yuEdTuj5NYMk2UOFdFvstbYtfBv79Yct9Iuh9e+GcV705EpLIU1IuIjJYrU//wSwkeWu1M7lTegbJOsJ1IpaFplrOxbwSDWN1BfThTfuOeWCoQcK4TMIbNdpqzf9fG4V9nnAwkUhwVWM500+W7/V+n3szatOt79+e3wXPXV+fmREQqTEG9iMhouYL65Z3eTfvPaaFcijL1rh7zI5qAyqf7jbv8JujO1AcCbLTTnf1H8onAOEn3tvO7yDdLbrdte3F/+kDvyjv/D1JqbykitU9BvYjIaLlaWnbbhvzyW4/ek5cvneV3xKi4a+rjqTTUtbnuoXP4J/Ipv/HrfJNbfqnGgvq5z/+y9MbTvkBdJMj3kufxq+QrnfXtL8Kz11X+5kREKkxBvYjIaLlq6rtsXX75gmMXeEpZxiriGShrR5+p9+l+ky4YKJsTCho2Wlc//Ike1D//DxYsu9K7riFbPnTEu+D4i4mGgnTQwteSF/CX5guc/VSCIyKTQNmCemPMPGPMVcaYTcaYmDFmrTHmcmPMlKGPzp/jFcaY7xtj7jDGtBtjrDHmvmEct78x5lpjzDZjzIAxZrkx5lJjTP1Qx4qIjJqr/KYr7fy4cZfLlENR+U1hpt7dk3Iw8T7XSX3Kbwpq6j1B/aYnJ25by+0r4FonSI/ZMB/e53b4zGr4yi54zQ8hFKUu7HwfHw0f4RxfA+MFRESGUpbfPMaYfYDHgQuBR4AfAKuBjwEPGmOmDXK420XAJ4HjgU3DvPYxwKPAOcDtwA+BLuBLwL+NMdFhfyEiIiPhCupX7nICYndmvRyKWlqG6yGY/dGWikOif3gnivfkF1OhRp7a0MlTGzrz69xBfShgWGnnst22Zlb0tcOzE3QW1od/5nn7rN2LUKi4+1A05Axe3pJuczaU6GUvIlJLyvWb56fATOBia+051tr/sdaeRia43w/4+jDP823gQKAJeM1QOxtjgsCvgQbgjdba8621nwWOAf4KnAB8YqRfjIjIsLjq2btwauornqk3xluCM9y6+oSTqf/2nRs454r7ec9vHsuvM8ZbU58kxO9TpzvHv+TsO6Fs/q/n7W+SZxAKFpc/uTP1W1KtQHaf3h2QSlTyDkVEKm7Mv3myWfozgLXAFQWbvwz0AhcYYxqHOpe19kFr7XPW2tRQ+2adDCwF/mOt/YfrPGngM9m3HzRGs4uISAX0d+QXO21zfjnsE1COhTuoj6Wys6a6S3CGW1fvqqn/45PFrTCDBUE9wNPpfZwdtr0wvOtUm6ve/yuJd/CP9PGEA8W/3tyZ+r4k0JgrL7LQs63CNykiUlnlmB3l1OzrbdlgOs9a222MuZ9M0H8scEcZrud2Wvb1lsIN1trVxpgVwGJgIbBqsBMZYx4vsWnJmO5QRCandNoT1O/CyVuEy5ypj7qD+uysqd7Bsh0MyVpPUN9LXdEuheU3ACvtPGeH7cuGd8PVlOiH3kxAnjYhrkm9AjBDZuoHEmmYPit/LD1boHVuNe5YRKQiyvGbZ7/s64oS21dmXxeX4VoT6doisjuLdUE2j9Ft60m4ciTlrqmvCzsZ5ljSJ1M/nPKbRD+QGRSbDtaR9vnx705u5wL8l+w0+nMPAH3t8FKp/Mc46dyQX+ytm0WKzPcq7PN34M7Ux5IpaJ7jbKyBGXNFRAZTjt882VFU7CqxPbe+rQzXqti1rbVH+P0BJujnzSIyrvqd2WPdWXoof1A/dKa+c+iTuLL0qVCD7y5+5TeWAPcFj3J2uuc7Q1+rmlylN91RJ0gP+bQUjYbd38c0tLo+hdi1oWh/EZFaoj71IiKj4amnb/JsKmePevBm6gdGm6l3db5JBP27/QYCxUE9wG+CbyQ/qHTFLbD1uaGvVy2uv4eesNNoLeSbqfdO4pVu3dPZONH78IuIDKEcQX0uG95aYntufWcZrjWRri0iuzNXMNlRENSXW1ky9a7ONzFTXE8P3kx9yFWLs5J5sPTVzo4r/z309arFNQFYLOjqQORTU2+M8Xwvk82uTL2CehGpceUI6pdnX0vVrS/Kvpaqe6/Va4vI7qzPXX5T2aDek6lPjDZT75TfDJSYly/gCurd9fWpNLDoTGfF2iHnBKweV1A/4Gqy5peph4LxCU2uoL5jXfnvTUSkisoR1N+VfT3DGOM5nzGmmUyv+D7goTJcq9Cd2dezCjcYYxaSCfbXkZkIS0SkfNbck1/cYVsqeil315ZYMpepd03WPayaeqf8pr9Epj4Q8M/Up9Jp2OsEZ8eNjwx/FttKc00A1ufK1Pt1vwHvpx79Da5uN8rUi0iNG3NQb61dBdwG7EVmRli3S4FG4BprbT5NZIxZYowpR6vIe4BlwMuMMa91nT9AZiIrgJ9bO1F++4jIpJBOwTN/zb+9NX3UIDuPnbtrSz5TP9LJp+JO+U2/TztLAPdQAHdNfTJtYcreEM0+vAzsmjizsLqC+n5Xpt6vTz14M/X9kakQyn4vYruG3+9fRGQCKkefeoAPAw8APzLGnE4m0D6GTA/7FcD/Fuyfa3bsSaUYY04E3pt9m/s8e5Ex5urcPtbad7mWU8aYC8lk7K8zxlwHrAdOB44E7iczq62ISPnEuiHZD8AAER5M71/Ry/lm6kc6+ZSr/KaPqO8uaVf6wx3Up9M2M4vtjP1g46OZlduXQcscxp0nqHfKioaTqR9IWmjbE3ZkKzQ713sflkREakhZut9ks/VHAleTCeYvAfYBfggca61tH+ap9gXemf3zhuy6ma517/S59sPAUcANZCa5+gSZAbJfBV5hrY2N6osSESnFNei0xzRSkJ8ou8JMfddAYhSZeqf8psf6Z+rTrqg+VJipB5jh+oB1oswuO+DU1Lcnna9rWDX1yVQmqM+ynaqrF5HaVa5MPdbaDcCFw9zX9zegtfZqMg8GI73288B5Iz1ORGRUXFnvUqUs5eTO1D+4up3DvvpvvnH6VN6cW+kKbEtyPYj0piO+uyTTzqTg7kx9KhfUT1ng7NyzdehrVoNroOxda/vzy37db6AgU59I01O/R/5j4T/cej/nL3k1xlT2IU1EpBLUp15EZKRcWe/eElnvcnJn6iETZH/j366scrKfIbkeRLrS/uU3KVem3t3eMpUblhRydc1JxYe+ZjW4ym+6rWug7DBq6gcSKZ7rdToi9+9Yy/qdfX6HiYhMeGXL1IuI7DZcg05L1aeXkztTnzOAK9ueGE5Q7zyIdKX8M/UpV0+BQMBgTKbJjbWZ0pxAyPW1JidIZaMrqO9h6Jp67/iENP3GCeqnmm529ScqcJMiIpWnTL2IyEi5st7jkakHiBHG5mr5U/FMR57BuB5EdqXCvrukUt5GYUV19UHXw0BqAgT18V7YtTH/tts6QX24RE29d3xCil2Btvz7aXTRGxvi+ygiMkEpqBcRGSnPoNPKZ+qjPpl6MFh3OcxQ2XrXg0hHcuhMPRR0wLEWPJn6CVB+8/Sf8g8XG+10ttOW3+R+IHGLFmTqO40zx8BU00VvLFmZexURqTAF9SIiI+UedFqFoN5dB+6WCro+JRgyqHceRDqTmXsuHA+aSnvfu+vqJ2Smfutz+cU/Jk/D3YVouJn6nTjlN9NMV6azkIhIDVJQLyIyUp7ymypk6kP+P6q3x1zBfmKIAZ4J9+RTmXtujHiHVaXS3qje0wEnZZ2JmmBi1NS7JsBabb0984dbU7+T5vz7aXTzyWuf4id3rizzjYqIVJ6CehGRkfJM5OStqV8yu7lw7zGLBAOeADvH05pyBOU3uQeRhoj3E4BkuqCm3pXtTlkLIdf1JkRQvzm/uNVO8Wwabqa+Kxml32a+rqhJ0MgA37ttRQVuVkSkshTUi4iMlDuod2XqD53fxk/OP7zslzPGML2puA5+ANeA16Ey9T4PIvWR4laZbgFP+U0agq5PJSZCS0tXr/xtFAb1w8vUx1Jp2nHq6meaTgBswfgCEZGJTkG9iMhI+QTI05uiXH/RCew7s6nUUWMyq6W4y06/u53mCDL1uTachWU9hUF9qHACqonU0jKd9pTfbLetns2l+tS7M/WxRIqBRJp16Vn5dfuYTUDxpxYiIhOdgnoRkZFyTz6VDepLzWBaLjObi2v3B+xoy28y91w4ADc9SPeb1EQbKNu3A2ym/WSXaSaG95OM4dbUx5IpVtq5+XWLTaZFZjyZLjpWRGQiU1AvIjJS25blF3MZ4kiJwazlMnPITP3Iy28KM/WF2emioH4itbR09advD0wr2lyqpr5wRtmBRJqVdl5+3b6BlwBIFLYCEhGZ4DSjrIjIEFJpy0f+8AQvbOnmsnMWctimJwGwGB5L7weUDiLLxS9T3z/cWWXTad/uN4WZ+sIy8gk9+VTn+vziFjOzaHPJPvWuB5mBRIqBZIpVdo/8uj3NNgDiIwjqe2NJ3n31ozy8ZicAR+81lf/3riNprvOf5EtEpBKUqRcRGcKNT2/i5me3sGZHL9+86i/5so+BqUvZRaaG3n+CqPKZ21ZftK7fDjNTn+wHbPaYCOnsj/5oKOjbVSfHM/lUeoK1tHQF9ZuYUbS51Ccn7geZWDJNLJFmh3UGyk6hGxhZ+c3P7l6VD+gBHlm7k388vWnYx4uIlIOCehGRITz70q788nQ688vd9U4t9rTGyvarP/ugORyxYAruGHzAnalPDpQ+2F1P72rBGQ37t8rMCRZm6ifSQFlXUP+SLQ7qpzf5/30UZupjyRQd1mlDOsVkgvpEavgDZW99bkvRuo0dQ4xxEBEpMwX1IiJDcGd3p2aDPoBdAafjyqyWygb1jdEQf/3Q8az8+tmceUCmW4unpt4VuBdxbXNn9+tCwZJlKjDUQNlxrql3BfUbfIL6UrPw+mXqO3E6FrXRS4D0mAfKbu0a5CFLRKQCFNSLiAzBnd2dRld+ud1VtjGzuXggayUEAybflrHDutpn9mwrfVDMeRAZSaZ+Qre0dAX169PTh32YX019iiCdthGAgLG00jPmgbLbuyfA5FwisltRUC8iMgR3dneacYL67WmnbKPSmXrv/WR+dG90Z6hdQW4RV1DfjVObXzdETX1gsIGy6URmAO54sNbz9a5LDT+od/9d9sVT+TIb9wPSVNNNbASZ+sJWoKBMvYhUn4J6EZEhuAfBTnUF9Zvijfllv5aTFbufbKbeHdSnOtbxvt8+xjuueqQ4S+wO6m2Dc55wgKAZQabemIlRgtO3ExKZkqJ+08CWxPC/9+5MffdAMr+8yzifurTRw7WPbuBVP7qXPz86yMMSsHZHL6u2F5c+be0aPFP/zZuX8bor7uextTsH3U9EZLgU1IuIDMHdrnK6K6jfEHMC5Bk+LScrxcnUOxnqZPta/v38Fv6zYjtf+cdz3gNcQX2PK1MfDQU4YsGU/PtFBbPhegbK5spR3B1wxqutZee6/OLa1DTA+2By4NwWSnFn6nf1J5xlV1A/1XTz58c28NymLj7712eKZtp1u/qBtb7rd/UniCVTvtseWLWDX9yzmqc3dPL+ax4veW4RkZFQUC8iMgT3pEwzXN1vtrnKb5qi1Zv2IxeYdtBMPJAJ0qPpPlrJZIz/+cxm7wExp3tPj3WC+oAxfO2cA5k/tZ6ZzVF+cv7hnsMaIs7X1BfPBqjuTP14TUC1c3V+cWPBINmZzVF+8tbDC4/Ic2fqe2JOpr4n4Gpr6RoMDZna+1IGK7MZSPiX8Nz/4o788s7ecR5wLCKThiafEhEZQiqbpZ5CF/sEsgFzIMSalBNQ1oX8u61UghOYGnrDU4nEMrOgTjHd7LJNxQeUqKlPpS0zW+q451OnkrK2aAKtRteDSm88GwB7BsuOU934+ofyi8vtfM+mBz93+qDjBKIluuJ0B1ogG4NPxRvUx5JpSnUsdT8Y/PKCI/j8359lR0/mE4xYIgX1xRNQdfQlitaJiIyVMvUiIkPIZeqPDrzgrNzjcDpTTqRX6cmn3NwlJP1BJ4hvocQEVCVq6pPZga6BgPGdEbcp6lwnH7x6JqAap6B+7X35xQfT+3s2DRbQg1O6VKg36LQnHUmmvtcV1E9pjHg+CSg12LazT9l5ESk/BfUiIkPI1VTvH3BqudnzWE+wNz6ZeugPuIJ6UyKoH3DGAbhr6pOD1IqDt/wmH7xGnMHBg/bGrxRrYceK/Nsn0otGdHgkGMBvbHB/2BXU0+PZNnhQ72xrjIQ8Dw2ljuvoVaZeRMpPQb2I7Pae3tDJu379CFfdtwaA3zywlnde9QhPrO8AnOB3ntmeP+bXLwQ93VOqmal3l5As3+Ust+AE2S9scQL5UgNlk0PMmuopv8kFr+MU1N/8zGZe/9P7+dTv7gWbuZduW08/I+s6ZIzxPBTl9Ifa8suFmfrzr3yYx9d1FB3z+LoOlm919m2KhvKdiaB0pr5DmXoRqQDV1IvIbu+C//cwXQNJ7l6+nb2nN/LlbPeY5zbt4rEvvCIf/M4zzgDHO7Z4g0m/QLFSGl0Z9C5XOY07U/+1P97J7w57AeYfU1B+4wT1c1oHD4jd5TfjmalPptJ84tqnGEik2WG2kptIdxeNgx9YQjQULBrEOhBpyy9PLQjqt3QN8P7fPsbjX3yFZ/37f/uY531jNDisTL27646ISLkoqBeR3V6XK+P+mwfX5pd39GQyqql0mgBpjnHV1LvbSUZDAcwg/d7L7WWLnWt3uQJbd6b+rTuvgLsfydTAtzqDSXOZ+r2mNfD2YxcMeh3fgbLuoD5RnaC+vTeeD8LbXF9jh9+g4GGoCwfY1e9dFw87rT2nFAyUzd3DUOsah5mpTwzxCYmIyGio/EZExKWwJ/lAIkUileazoT/m16WtYVNBUF9NzXVh3nlcJiB3Z+r3Mlvyy68KPpJZSA5A+8r8+i12Ks3REHdccopnwK0fd5vOnlz5Tbj6mXp320h3aUznKIP6iM/fVzzall8uzNQPVzQUGFam3vrMQCsiMlbK1IuIuBTOxrq9O8ZJ66/g+NA/8+s2MY04TqvCoYLjSpg7JZNx78IJ6s8P3UUPDXwv+SbfY+I2yDo7iz1bokN2iQFvmc94lt+4Z2d1Z+p3MbqgPu2TQE9Fp5AmSIAUbaaXKHFiRDz7WGsH/UQmU68/dKa+cIByOm0JDOPvQ0RkMMrUi8huLT9TatamTm9dRtf6/3L85ms86z4Q/4TnfTUHyebMbM7Uw3dZb135+0P/ZL7Z5nvMarsHSUJEfNpX+mnwa2k5DkH9tm4nU99qnM40oy2/SfpE9ZFImJ7orPx796DonFKTSbkNJ1MfLwj2E35PGSIiI6SgXkR2W9c8tI4P//4Jzzp3fT1A5IXrPe/XNRzEc3Zvz7pqtrPMmdmSGS3a6ZOtPi7wvO8xuYma/HrS+3GX3/T51dSPQ6be3W7S72sfjsISK8j8HfbU75F/P9c1KDonP65gEO5Mvd9DgLWWgaQ32P/c357RzLIiMmYqvxGR3dJzm3bxxeufHXK/aPsyz/v7514IOwv2GYdM/ayWTKb+sfTiom1nBB4rWhevn8FVnWcB/jXlfiZKS0t3SZS3pn503W/8BqrWhQP0NuwBnZn38/yC+liS6U2Zh6lSdfHuTH0sWZypj6fSFB76tydeIhoK8s1zDxrmVyAiUkyZehHZLd30383D2q+lZ1V++VWxr7Nx2glF+4xHpn7vaZmAtocGvph4l2fby4LP5JdvnPVh+MI2Hnv9/Txt9wUgHBxe/bZ3oOz4db9xz9o6w+zKL++wrZ79vn/eIcM6n1+mPhoKEmucl3+/xKwv2qfHdR+F5/jCq5ZmzhMePFNfqs7+j48UX09EZCQU1IuIlFDPAG39GwBIWcOLdq7voNjxGCgbCJh8IHlN6gx+kHiD737PhA+GUJS4dQL54ZbfeDP12YB2HLrfuGvTZ5jO/PI2Mm0oD9+zjXs/cypvOGJe4aG+/Grq68IB+qYfmH9/bvBemvDO0OuePTZeMBbjvSctzJwnNHimfrDZaUVExkJBvYjslgoHyBZqpJ9lde/Ov19rZxMj4imvyKl2S8uclnqnA88VqdexPj3Dsz1mw7xApvWle3DmcO+3wfWw0hdPkU7bcSm/cWe3Z+HM7LrNtgGZ78P8qQ2Fh5Xkn6kP0Dv/NNamM4Nlm8wABwXWePZxf2KQSDrnaK5zHn6GzNQPY7CtiMhoKKgXkd1SYevKQqcHvANon0gvArwDIXPGI1MP3vKYJCHel7jEs/1nqdfQE88En+468uFm6gMBQ0PENatsPDkuQb2T3bbMMu6gPpOpD42wHaR/TX2Qxvooj6SX5NctNhv5UPAf3Bn5JHdELmHmc7/Kb4ulnIy7+yEpOkSm3m+diEg5aKCsiOyWtg0S1EdI8KPIFZ5196UzpRkTKVPvLo8BWG735NTY9/lO+BdssVP5efI1LIil2No1wP/d5HTEGe5A2dw1+uKZQLQvnqK5ikF9Km25+oG1PLwmMzK5mX7qTaZLTJ+N0p2dHXc4PfeHEg0HaIwGWWGdEp5TA09xSvBpZ6dnvg1tKZi+iPp1TzKDg9lOm+chaahM/XDaYoqIjIaCehHZLblnKS306dCfi9bdlj4S8M/UR8ctU1983TV2DufFv5J/3xtP8q2bX2CL6+sdbqY+c41Q/lONnliSWVUM6m97bovnYWSR2ZhfzpTeZIL5UGBkD1XTm6Ls6PE+1NWFgjRFQ6x0BfWegD7n3u8B0Ax8KnQKn02+3/OQ5Kmp96mfV6ZeRCpF5Tcislvqj/sHV7Np532hf3nWvSd+Cf1kWkj6ZepP2W9G0bpqKMzU++mNJfn7ky951o0kqG90PTj0xgrKbxJ9PkeUz9f+6W0n+qHQjfnlJ+yi/HJomN18cn5y/mGe93XhAEfvPZXGaIin0vswYMMljvR6c+huwPv9dAf4hYNpQZl6EakcZepFZLfkDri+8KqlHDi3lVD3Sxz59/OL9l1vnZlG/TL1Zx4wuzI3OYTGSPGP8Js/dhK9sSRv/PmDgLdjS85IyoXc1+iJJWGKO1Pf43NE+bjr+Q8wa3hF8PH8+58nX5NfHmn5zbELp3H7J0+moy/Otq4YR+09hWlNUfrjKXbRxJ9Sp/Ku0G3DPp+n/MYd1Pu0ryyVqS9DBZGI7OYU1IvIbskdcJ13xHxau5bDb08q2q/H1rHBOpn4wnr0qY2Ryt3kEPwy9XOn1NMcDREMGFJp65stHm6f+sJr9MZSEHH1hq9w+U1jNIQhzc/Dl3Nm0JlQ66bUMazIzo4LIx8oC7DvzOLZaHOfwtyVPox34Q3qH00v5qjAiqJjWuglEmrLv3cH+IkRZOr9HhZFREZC5TcisltyB7vhkIFHr/Td71OJDzJANP++MIAMmPFLsTYW1NTXhQM0R0MYY2iMlA4SRzpQNqc3loRQFEz23Kk4pBIju+kRaIqGONos9wT0AD9Knut5HxxhTX0pJvt3+Vh6MUnrPedD6f19j5lnthNxPSS5v7d+XXZKZerHY1ZiEZlc9FNERCateDLN7x5ax7dufoEVW7s929wBVyQYgP/+pej4D8cv5pb00Z51hfXb41k2UZjdbauP5APTpkHq7Uc2ULagpaUxZW9r+dSGTr7+z+e54amXMr3ws6KhAEsD6zz7/it1tCdLDyP75GE4eqlnvZ3pWXdn6jDffeebbZ5A3v299Su/KZ2p169jERkbld+IyKT158c28MXrnwXgxqc38Z/PnJovS8lMQGQ5OrCcYMdiaJwOnU6Aujo9mzvShxedszArPJ6Z+kJtDc4Az8EG0Y5ooGzEZ1bZSCPEujLL8V6obxvRfbr1xJJc8KuH6c6eu6U+zKn7ZQLq/kSKfY13kO93km8uOkc5WloWWm7ns5At+fdP2n15OL2EYwIvePbb12ziuWCJoN63/MY/Uz+ST09ERPzop4iITFpPrnMmKnqpsz/fmjHRt4sGBnhv8F9cG/kq5qfHQaeTEX7m9bdzRvw7xCiuly8sv6lEQDkSrzzQGaR79kFz8ssNgwT1xy6cOuzzuwer9sezQWoZO+Csa+/NB/QAz2/qyi/3xpIc4MrUfyT+UdbaORQaTU19KW87Zk8AfhM6D2syvyK/bS4EDG+Jf4HODzwJr748v/8hgVUjGijbV6LrkmHiPByKSG0qW6beGDMP+CpwFjAN2AxcD1xqre0Y5NDC80wFvgScA8wB2oFbgC9Zazf67L8WsvOgF9tqrR2fthQiMu62dnt70W/tGmD2S7dRd+0FPF/n2pB21YU3ziA1dRFJtvmes7D8ZrwT9d877xDOOGAWjZEQpy5xSkb8etgD3HDRCRw8r9V3mx/PZEq5evBwg7PDGDvgFHbncWeyZ/et4LDAiwCkreFh12yvbuWqqQf44qv356RFMzhw7qmYvqOgZxt/vdYASSwB4k17wMyl+f3PCD7OM4nngMw8BkMNlO11PcDMbavnpc7+kvuKiIxEWYJ6Y8w+wAPATOAG4AXgaOBjwFnGmBOste3DOM+07HkWA3cCfwKWABcCrzLGHGetXe1z6C7gcp/1le23JiIT2tauWMH7AbjhQ4MfNGWvQWu0J9JAWciU2bz+sHnF633aXTZGghwyv21E5496JlPKZepdnWPGWFPvDnIBYq7s9sExp4Xlbekj2c4U33OUs6a+LhzkrNynH1My5VfB0B1A5j4TKQszl5IKhAlmHwbftP0KsO8AY4bsU+/O1L/6kDn84p7VznlFRMagXJn6n5IJ6C+21v44t9IYcxnwCeDrwAeHcZ5vkAnoL7PWXuI6z8XAD7PXOcvnuE5r7VdGffciMiltK5g1dmdHx9CZ5fnHDDposXD20onaX9xvoOxoZr71zdR7BsqOrfymN+4N6t2Z+inJHblJY3k0vbjkOSpdAuX+dCaZSkNdK/9dfDGHvfB9AOYPLIetz8Lsg/IPGGcFHuH8/gfgG2+Hg94Ip38ZGqZmev1ntdU75V3JtDL1IjI2Y/7MMpulPwNYC1xRsPnLQC9wgTGmkUEYY5qAC7L7f6Vg80+AdcCZxpiFY71nEZn8BhIpuga8AWPzun8PfeCCEwYdSFoYQI53pr4Uv4GydaMYjFnnm6kvZ/lNQaY+kaazL85vH1xLW3pnfv0265+lh/LW1PsJB9wlNZmM+jML3sFNqWOcndbeB2QGvM5iJz8K/5iXpR/JfH8evxr+9j7A+/VOcQ1sTg4zU59MpfnXM5t5YNWO0X45IjJJlaMQ8dTs623WWk+qwVrbDdwPNADHDnGeY4F64P7sce7zpIFbC67nFjXGvN0Y83ljzMeMMacaYzSTh8hubFtB6Q3AwRt/73l/a+pIzmr6CxyVCbhonQ8LTx60E8lEq6kvxS+oL1+mvnzlNz2FNfXJFJ+57r986YbnOCHwbH791kGC+nLW1PvxZOqzGfV4Mu3tXZ8L6oMBjg88R8QUDIh98XbY/F9Ppr613gnqh1tTf+1jG/nw75/g/Csf5qkNnSP8SkRkMitH+c1+2dfiqfYyVpLJ5C8G7hjjeciep9Bs4JqCdWuMMRdaa+8Z5Jp5xpjHS2zyH5klIhNaR1/c8z5KnLn9zo+Xd8U/w73pg1gUqoNXfhsOeStMXwSRRsLx4geCnBlNUc/7CZup95l8ajS90H0z9e6BsmPsfuOXqX9ifSdvCd5Jq3HOvZUpnHv4XP793FZPtxwof5/6Qu6Sq1xGfVd/gsfS+zk7bXkmey8Bjg0s8z/RqjvojTnzHrS6M/Xp4WXqP//3Z5zlvz3Dvz5WPAuyiOyeypHeyLVR2FVie259W4XO82vgdDKBfSNwEPALYC/gZmPMIUNcV0QmocJgcaHZTIBMUBprXsDd6UNJEcxk5QNBmHcE1LUApXuGX3jCXoQKSnPGu6VlKZXI1Md8a+rHWH5TWFOfTBFLpPhA8EbP+o+85gS++roDufaDx3Hxaft6tlX678D90JDLqG/rirHaznFmnu1cB/FeIqEABwdW+Z9o7X2egbLuTH0qbT0Tbw3Hzt740DuJyG6j5vvUW2svtdbeaa3daq3ts9Y+a639IHAZmXKerwzzPEf4/SHTyUdEakxvQT/wRcbpiNvXtii/HPGpn/dbB3DAHsWtIM0EzdT7DZQtX019BbvfJNKEkj3sHdjqrAyEOO/4JTRFQyyd08KFJ+ztOabSNfXuB7lcRn1r9wBxwqyzs5wdty8nRIqFZnN+Ver9/3G2r3uQ/gFn8HZTNOS598QIB8sWfu9EZPdWjqA+l0Ev1fg4t76zSufJ+Xn29WXD3F9EJpFcwLOfWc/nQ7/n46G/OttanKDeb1BsqYGyfr3fJ2ii3n+g7Cgy9XW+NfXugbJjLb/xPnz1JVIstS96d3rNDz1vo+HCT0sqXFMfKM7U59qlrrCudqI7VmB2riFqMv/2NtupJGYcCK17Zg/uZUHMKQFrjIYKOuuMLFPfE1dQLyKOcvwkXJ59LdVvLPfbs1StfLnPk7M9+zpo1x0RqV07emLc9twW+gqCm+6BBH9/8iUAfhr+Ie8P/ZOFgS357aumnpBf9iu1KVXO4RcoT9iaep8HkNHU1LsD6Hy7yTKW3zztGuwZIsn+3Q/wudAfnB0OOR8Oe7vnmLqQ92urdKbe/W8k1/0m1y51rXt+wyeugfUP5t+uTM/N9Krf68T8ugPiTk18UzTk6awznKDe/bVatbYXEZdyBPV3ZV/PMMZ4zmeMaQZOAPqAh4Y4z0NAP3BC9jj3eQJkBtu6rzeUXLcdv8mqRKTGJVNp3vizB3j/NY9zybVPe7a986pHuGfFdqaxi30Cmz3bemccyjv/7fyoGqx9ZSH/oH6EN14lvuU3o8nUh9w19eUtv1mzo5fVO5zjLwrewDcHvsZBgbXOTm17Fh0XKPimpyoc3boD6WQqTSKVpj1bz77RznB2XHcf3Hhx/u3D6aUkkt6g/rXBB4DMg2M0FCDsfmAYRvlN4b9Bq8heRLLGHNRba1cBt5EZmHpRweZLyWTKr7HW5n9yG2OWGGM8XWWstT1kOtg0UlwH/5Hs+W91zyhrjFnq1//eGLMXmd72AL8b6dckIhPfC1u6WdueKf24+VknCz+QSPHE+k4AFgc2Fh23svEIz/tIyD8qXzK7uWid3yythQHmRLFwRlPRurpwmTL1Zep+89Bq70TjZwQfK97JJ6gvlBxmO8jRctfUJ1KWzr5E/n1nZLbfIfTbCNekXl6UqV8aWM+bgneRSluMMQUPDEMH6IUfDBXOxSAiu69yzSj7YeAB4EfGmNOBZcAxZHrKrwD+t2D/XL+vwt+GnwdOAT5pjDkUeARYCrwO2EbxQ8ObgUuMMf8hMzlVN7AP8CqgDvgX8L2xfWkiMhF1FwQzPbEkTdGQa/Cg5Y+Rrxcd90TEG9T3FwyozfnFBUdw4dWPsnq7k0n2K2mZmCE9TG2McMSCKTy+riO/zu+ThqH4Z+rd5Tejz9S7B3oGSLOP2VS8U9v8Ic8z3HaQoxUu6FPvLvfqjM6BgeJjHk3vRxdNJJIWpi2A+qnQn5lM6/zgHSw+68PZc7sfGIZ+OCkcHLuta8DTRUdEdl9lGV2UzdYfCVxNJpi/hExw/UPgWGtte+mjPedpB44DfgTsmz3PMWTaVh6RvY7bXcBN2WudD3wSOBm4D3gn8GprrXp+iUxC27q9kVSuxrk3liJIimsjXy065ofJ13N3v7cdYocr6+q2YFojn3vlUs86v5KWiVpTD3Dakpme9373PxT/mnp3+c3oa+rdEzHNN9uoMz5/F1P2GvI8qQoH9YV96t333R2d43vMQ+nMv514Kvs9e/Vl+W2LzEssmZX5JMg7sdXgX0csmcrX9Ods6y49p4KI7F7KlanHWrsBuHCY+5b8LWit3Ql8LPtnqPPcAwxrcikRmVwKZ4zd2hVj4Ywment7+HPk/zgy4B1Tf8jAL9lFE/N2eDPLnX2ln/sLM/O+NfUTtPwGioP4cmTqrbWYMnW/cWedTwg859nWaRt5oO5kzh5O+U2lg/qCPvXujj3hukY45NPwn+96jrkxfRwA8WT23vY/h27TTLPtptHEaIlvBmYU1esPpi9W/KnS1i6fjwlEZLdU833qRWT3s2ZHL396dL1n3c6d22H5Lcy+46NFAf1f5n2OXWSyyxs7+j3bSmXqwZuhBf9BtRM4pi8K4kcT1AcCJt+331oyNeKu8pt0vIenNnSOasBmjytIfXfw5vzyNxNv5dDYL7mq7aPDOk+la+o9HWrS1vMw0hgNwWlf8Oz/RPhwNmT718dz92YM64LOA0pbe2Zwt/vfVHyIr6PHpy+9MvUikqOgXkRqygMv7uDU793NKlete5gkx979dvjjm5my7paiY/r3PLXk+Xb1lw7qh2Mil980RryfNPj12R8OdyvMWDLNjcu68u+7dnVyzhX384PbV474vLna9LlsZ99App6+z0b5XerlgBl2t55qZuqTqbQnuM5/T3NtNyNNXNnqPIy46+T/G3D6Q8xYdrXPuQf/Ogpn3wVl6kXEoaBeRGrKHS9sK1p3bvBepvX6B5WvSXyTA/YrNf0F/N85B5bctmSO0wFn4QwnO/32Y52M6/tetnDQ+x1PhZn5Bp/uPcPhrquPJdJ84oZVJG1mXZvppZ4BfnTHyIP6XMb72MCy/LrH0ovppR4YvFvPSYum55dffbB/XXu5hAu637gHyuY7Ir3yu/D6X8B7b6enfm5+e/eA89D4Z3N2frluy+MQ7yPqNxC5hD6fQd2FZWgisvsqW029iEg19Pi08Htt4AHffc+NfYUPn/969vVp75hz3hHzSm5rqQtzzXuO5o5l2zyB/KfPWEJrfZjZrfWcsnhGyePHW2FQP5qBslAwUDSdJkmIdXYW+5jMHAD7mE08a0f+cDMw0McV4ct5VfCR/LrcAFPAE/AW+u4bD+FX967m4Plt7DuzuP1oOYULaup7XHF0/nscaYBD3gLAzGZn3gR30P1SqpXV6dksDGzBYGHHChpcn6YUdrYplB+o7FI4YFxEdl8K6kWkpvQUlCBESHCEq4Y+FmpmRXwaX0m8k4OOfQWvPGhOyVaBH3/5oiFLPE5aNIOTFnkD99aGMJ8+c0mJIyaOcgyUBf8SkRV2HvuQCeoXm408axcSS6YGDcQLHdV1hyegj9kQf0udlH8fHSRTP7u1ji+8ev9hX2ss3H3qk2lLLOmuqS/+eme1RPPLW11BfSyRZqWdx0Ky8ypsf4Gm6KL8dr/yGje/TP5WZepFJEvlNyJSU/oKspmHmFVOK8SpC/nlcXfxmvg3eNzulw9iw8EAkVDxj7vRZq5rRWHAOdqaer9e6ius8wnHMYEXgBGWgmx7gY/1/tCz6s+pU9nCtPz7kTwgVFI4UNj9pmCgbIGZzU5Q786kDyRTnu8b21/wHJ8/b99OePJ30OkdDB7zydRv7RrQrLIiAiioF5Ea01vQ1u/s4MPOm71O5OmNu/Jv3QGTXwA/2sx1rShbpj5Q3Ev9wfQB+XXnBO+jjW5PJ5ZU2rJ2Ry9rdvSyYWcf/fEU69p7M51qenfA/3tF0XWuSL7O8340M+BWgjtT/+K2noKBssXf01ktdfnlXCY9lbYkUpaVaVdQv+0Fz/HPvLSLdCoNf3gT3HAR/L8zIem0XPXL1MeSac0qKyKAym9EpMa4A6r9zVouDN2af399x0JuX7Y1/97d/aUxGmRnweSnDZGJkQmulMKBsaMdKBvyydQ/lF7KsvR8lgY2EDVJDgqsyU8AZq3ljT9/gCfXdxad68C5LfzjpI0EYl2e9Vcfdwtb79rpWTdRMvXu8qOb/rvZs63R53s6s6U4Ux9LZh5GV1pnEC3bl9E4zfkaf/fQeqa/dCcf3/5oZkX3JuhYAzP2A/xr6kGzyopIxsRIg4iIDJO77vg1wQc9276+zFv7vmC607HGL/jaa1pj0brJpLDkqLDF5XB5B4rmSj0MT6ad2XkXm43s6M1klZdv7fYN6AGefamLbc/c4ZzPBjk19n3227e4Q9GeUxuK1o2HcKD0r0q/Tz+mNTpBfUd2crNYIvMwtNrOIUX2+9mxjpagt6Xq1M33ek/mKsEp1R1HdfUiAsrUi0iNcdczH9bSDdkJTf+TOojtTMlve8+Je3Oya4CrX/B1yPy2it3nRPGH9x7D7x9Zz3lHzPNk3Eei1KynK1314fual+jK/t2kh5gLqn7r4/nlt8b/l82huRy7cCqfPnM/7lmxHSwcOLeVcw7bY1T3W27uTH0hv4Gy7gG+ieyMsgPZTH2MCBuYw15sAizz46sAJ8u+OLDRe7LOdfnFkpl6dcARERTUi0iNcZffHNXmBPU/SZ6TX98YCfLFgs4ohUH9p84o3bt+Mjl+3+kcv+/0oXccRKigT3uOO6hfHNjIPdm/m1TBZFAB0rw1eCdhkvwxdRrNvU72+Xm7F03REMYYLjp1Xy46dV8mmsEehvweFv1mic1l6gGeCy5lr1Rmsq3Tn/o4FwVfwZN2X6bS7enZD3gz9Qll6kWkNAX1IlIzUmnLQDawCZo0wU1OxnejdbLy7oGKOYWdX2b67CP+3OU3SVcafoVr0Ocis5F/Zgds5rLSOa8MPMLXw1cBcGRgOQGb2W+jnU4fdcyY4AOW3d1vCvkNlPV0C8qWzLi/J8+GD+JVqUwJUjTewafD15a++Ob/5hfd52iuC9Gd/X4rUy8ioJp6Eakhq7b35JcviVyfX07YIFuYmn8/w9VSMKewpn6mzz7izz35lHvyr220sctm6t5bTD+h3s0Q7yM+0J/fJ0yS84L35N+/2tWtKPdQ4DfeYSIZaaY+GirO1A+4suz/rT96+BdffRdsX150jgXTnPEGQ7USjSfTQ05sJSK1T0G9iNSEr974PGf84D/596cGnswvb2UKadePM79MfWHw5beP+HNnnj/0+ydcW4ynBOfQ7dfD9xZx5N9PYh/zEs30cXvkU5wSfBo/z2RnofWrS59IwoPU1Df5PJAUlt9Yaz095uPRKfCBe4uOy3lqypmw98nOipW3AU4HHfAOIt7aVTpTv617gOO/dQdHfu12Hlu7s+R+IlL7FNSLSE34/cPOgMFzA/9hqV2Vf39x/COefRfOKO5qM7et3vt+Sn3RPuJvsKB2Zdpp0Xj2zmsg3kM01s7nQn/grOAjLAhs8z0uFYjw++TpwMSfL2CwB8AGnweSYMAQzJbsWJspG+t3BfXRUBDmHAzvv5veg9/JS9aZcCtug1zd+mE48A3OCdfeB3gz9fOmOEH9zl6nl32h796ynB09cfoTKS76wxMl9xOR2jexf5KKiJDpuJJr5/e+4E38b/gPnu3HnfJKup/bStpaFs9q5oJjFxSd401HzueZl3bx4rYe3nHcAlrq1Nd7uAYrP9lgZ/quf3nwSfYxm0oe9/QhX2bbg5luRRM9qD9m76m898S9+dV9a4q2hUt8b8JBkx8wHE+l6Ys7QX3+k4k9DqPx3MP444yP89jNv+E9oX9xbeoU1vWFYa8TnZOtewDSKU9LS3df+lJdcQCe2tCZX9aAWpHJbWL/JBURAQaywcz7gzfy+fAfvRtnHsCnz1zCp89cMug5WhvC/Oith1XqFie1wQaKvvWME+GuP/tu2zuwtWhdv43wmdSHOHb2a4BnAf8SlonEGMMXXr0/9724gxe2dA/rmHAwkM+sJ5LW07Wp8CHmvSct5BX7f4aTv5uptZ/bFYOpC6F5j8wEVLEu2Py0J1PvDupL9a8Xkd2Lym9EZMKLJVIcaFYXB/QAR7+v+je0mxmsT3twavGnIqX8NXUiB8Su4sbkMbzU4QymneiZ+hz3xGdDKRws6x6o6tcxZ2azU+KzrXsAC7D3Sc4Oa+8bVaZeRHYfCupFZEzckxFVykAyzWmBp7wrz/k5XPQoHHlhxa+/uxus/CYyba+idZtbDvG8X5eeydmxb/CpxAfzA5rdZSGF7UYnqt7Y8IPnwsGyvYNk6gHqI0Ga6zLrEylLR18C5ru65Gx91hO8tzUML1NfuC2urL7IpKWgXkRG7canN3HIpbfxzqsewVo79AGjkYwx5bo38snwdc66Q98Gh74VZuweE0iNt8HKb+qnzila9/b459hsnRajv06dxfN2L6zrV84Dq9rzyw21kqkfQVvIwl71ve6a+oj/Q4x7QO73b1sOM10TqG1b5gnQG6Mhcn8tybT1fbh+cn0H63f2edZdee/qYX8NIlJbFNSLyKh99I9P0htPcc+K7fxn5Y7yXyAZg+8voWHjfd71h729/NeSkkpl6ue01tEQDXMVr82v+2vqRFZ1pjkldhk/T76aJ+a9gz+kTh/0/KWC3InmTUfO97x3t5UsFBmk/KZUudGsFmfuhFuf2wIzXONEdqwgHnO63NSFgpkuOll+2fo/PrK+aN1fn9hY8p5FpLYpqBeRsti6qwKzWv73Wuj36a09Y/BBsVJefjX1B81t5advOxxjDK1nfp5/p47g6fRCrkieA0CMCN9Kns+TSz5JnME7DdWFayOo//jLF3HivtMBmD+1np+cX3rgtaf8JpkedKBszsWnLcovd/QlSNdNgcZsd6HkAD/rvogDTSbT3hQNURd2ruFXV9/RlyhaN1j7SxGpbbXxmaeITDiFH/fXVSLburl40qLOwBTaGqb67CyVEg548z83fuREDprXmn//huOWsuuQWznkq7cVHeseMJpz3MJpPLjaKb+J1khQP60pyu/ee8yw9nVn6hPDGCgLcMzCabQ1hOnsS5BKW9p748xYcjY8fjUAe9mXuCn6BV4d+xqN0ZdnM/WZwN0vU9/nM7C3sy/BQCJVMw9SIjJ8ytSLyKi0F2T8KjIAb/sLnrcJG+Qn0/63/NeRQRX2YvebAdZvEibIZOELS/KjYe/56nwC/1oXcX26EU+mPYNsB+v2M7PZKcHZ1j0AJ34Soq2efW6KfoHG2FbqwgEMaebQTmLneuhYBxsfz/zZtozegeJMPcD2bvWrF5mMlKkXkVEpnJp+JIMIh8Va2Pps/u1H4x9hmd2TvZvVa77aCstv/ILScDBAJBQoeriLhgKEAgHirk926kLeB4DJmDX2DJRNWU87zMHGEMxqqWPF1h4AtnXFOGCPBfCh+0j/4+MEVt+R3y/68E+Ihl7Nt0K/4s2hu+G3xef6SPhk3ssHAKgLO33zt3UPMH+Q8QAiUpsU1IsItz+/lc/9/RmshW+8/kDOOGD2oPsv39LNa39yv2ddzxiC+q/d9Dy/fWgd8WSaaCgTHP748M2c0t8BQCLUxE0Dx2IJsGQSZnUnuvAwgnrIlJXsTHo/wakLBwkFDa7mL0WZer8SnVrnLr/52j+f90xaNXim3umAk39wbtuTXef+kXu//TpeG3wQAPPivzmUfTMBfQkvT9zD4eZUnrCLWTi9iec3dwHwhp89yD8vPpED9mgteayI1J7J95NUREbsu7cuZ3t3jB09Mb59ywtD7n/1A2uL1o02U7+1a4Bf3bcmn+GNJdN0DySJPfb7/D6r578h3w5xMmZ1J7qA8Qb1DSX+DvzKcurCAc50PSSetGj6bpepL5yFdlpjpORxM1vc5TdOmUxPPMVnEu8nbbN/Fx1reWX81iHv41XBhwHYe0ajZ/37fvPYkMeKSG1RUC8iLN/qBB2rtvcOuf/Gjr6idaMN6je6ZhbNMaQ5yjyff//CHk7LxMmY1Z3o4gWDogMl+tanfYZVTG+K8sVX788h81pZMruZb7z+oOJMfXjy/Z1GSvw7ffcJezPT1Y++0CxXTb27xK03nmSAKOttthuOTXP8wH+Kjv904v2k3nRN/v1iswGA2QXX3FSJblUiMq5UfiOym/ObtCaeTJcMSiBT61uoZwSzbXrPVRxcHGpWMdVk6oppmM62yN5A5hOEyZjVnehiieENgvbrtjKrpY6pjRFu+MiJWGsxxhT9HRZm7ieDiE9v/6VzWvjSa/b32dvhnoBqq+v/WW6g7Uo7j73YmrmGzZQ6xWyYg2NXEiPzCcD/NO7NtOxxiwMbiQQDtNUP3lZURGrf5EuPiMiI7Ogp7lu9vWfw7hjbuosD8dFm6rf5dOL4QOgm582iVzDgGnypTH31FWbqS+n1ebCb0uAEkyZbxlP4dzgZM/WF4xAAmocxc667/Ga76/9Z7v/X7enDi465NX1kPqAH2ByYjQ1mzjPLdDIn0jdoHb+ITA76Xy6ymyvsYpNbN7et3nf/WDLlO6lNr0+WdjTXD5Pk5ICrP/0JHyP2pKtzijL1VTfcTL1f8G9McXC7W2TqfR4+S7X9dPMOlHVn6jP/v65Nnczc+Xtz8SGGG55+ibvXp7gtfaTnHFt7Eiyaupjo9mcAOCq8mqbo0UXX6oklS/bMF5Hao//NIjUimUrzqb88zX0v7qC1PsznXrmUl+8/a8zn9Qvqz/3pA7zjuAVc+toD2NWf4Opf/4xXbr+Ku8zRfC92ju95BlY/yPNfeh/Ppvfi5r3/h6++/lC+cP2zJNNpLn/zYcxw1Qp7r58JXAxppz1f1tr0LNr7Z/GTux7Mr6ubhFndiS6WHF1pVSm7R6a++GsaTrbcnanf0jXAXv/zT2Y2R/OfaFkCrJ1yAhx3KI9seYa/r11fdI73/OYxblt6KIuzQf3RZpnvtf/86Abec+Leg97Pd255gb8+sZFkKlM6deYBs/jaOQfyq3vX8Ov715C28Naj9+RjL3dmw31s7U6+eMNzbOsa4JD5bfzorYcN++HhB/9ewZ8f3UAilcYYw2lLZvCtcw8uOY7j709u5Bf3rOb8Y/bkHcftNaxriExWk+8nqcgk9Z+V27n+qU3s6Imzansv3xpGl5rh8Ct/Afjtg+u4d+UO/nvTT/n49i+xH2v5oL2WHwd/AFgONyv4TvT/cbhZAcCngn9k/8A63hS6h7mrr+Wk79zFPSu2c/+L7YN21MmV8pwYeLaoPd/D6aV8+i//9axrrlNtcLXtM6NpWPsdtmeb531znX8gVxjUT8ZMvV+pTVNk6MA2GgoyvcnbHafw/2hbQ2b7YJ9a/WL9Hvnllyfu4tD/XsprAg949rnyP6sHvZe1O3r56d2r2NoVo703zo6eGL9/eD13r9jOt295gU27BtjSNcDld6xgi2vg7eW3r2TZ5i7ae+Pc+cI2/v7kS4N/0VmbOvv54R0r2dI1kL/etY9t5KE17b77W2v5xJ+f5oUt3Xzphud8x3SI7E4U1IvUiC27vL/Y17f3Ya0d83n9BqoCzKCT5js/x8ue/7Jn/SuDj3JP5BP8LfoV3mTu4G/Rr/DF0DUcE3AC94+H/uo55rrHNw5y/czXtb9Z51m/w7bwq9TZrN7h7cZz1hA99KX83nbsnhwyv43W+jC/e88xJff71rkHewL5K99xpO9+hSU5pbKwteycw+YWrRtuXfsHT95n0O3nHTkvc75BJrH6d+8++faXU9M7mfviH/lx5CdcEb6cuWwHYFd/Art9Bdx3OTx3fWbCN5d1O4u7XAE8uKqdZNrZ11rY4OqItbbd+392ffvQHbUA1pe43vp2//XdBeN4tvoM4BfZnaj8RqRGFGah4qk0nX0JpgzS83o4/H4RBkjzm8i32X/LOp8jYEFgm+f9e0I3e95PN12cEXiUHbaVXurYkGvDl9O9FbY9D3UtbO/K/MJfHHAC/xvbLuDjW84ghTdoOXnxjDF/vTJy0VCQ6z98PMm09S0rydlvdjNPfvEVBIwhZQffd7JbOKOJo/eeyiNrdubXNQ2jph7gvSctZMuuzPwNhQ6c28LSOS1A8UPCYXu28eT6TgC6aOJ5u4ADzVrPPq8KPsJSs56z4t/mmNSTmCve7Np4GRz1nvxbv9I8gGc27ipal9vXWlvUHWu4wXap65U6vjAhsa1rgL2nN/ruK7I7UFAvUiP8Zmzd1h0bc5Dr18nm1YGH2D/gDeh/mnwtHw79Y9jn/WXkB/nlZek9oe9UCNXBztXwy1MgnRls+9nkKXyW97Nftp82QPec40htKQ6AmkqUc0jlGWN8O7oUCmUD+QCTL/s+Unu0envDj6QDzV4lgtM9Wp0B7IXnm9Nax5Ou9zenjubAwNqicywMbOH+6EeZYbq8G+75Dhx6PoQz19juKvsxxknkP/tScVCfC+R39SeKBkz7/YzxU+p6pY4vfHgoVUoosrvQb0iRGuHXMnJr1wD7zW4e03ndWbCGSJCBeIKLQ3/Lr0sQ5p3xT/NA+kD6iXJJ6C/5bavmvZ599l4IwPIt3dQtv74oiw+wNLAevuM/IO/Nobs9tfQpa2iYdzA8WTwAcLByA5GJZlbBhE8NIwjqC4/1W184g6+7cw7AlalXsYNW3rkUFtb1UvfsH/LbigJ6gJ4t8PjVcOyHAG/m/KC5rfw3m6EvLHsB2JoNvP2y6n7zWvgpdb1SmfqtBcF+qUy/yO5CQb3UhF/fv4ZrH9tIKGB45/F78cYj5uW3PbZ2J9+9dTk7e+M0REN86OSFnHXgnHG828rwm9zpx3eu5GWLZ4zpvNu6BzjEvMjnwn9kdqgHS5y9A5nJbbpsPSfFfsguMgMlb51yPuGOBE0M8N3km7jixBPZZ0mmA8/m5dv44DPH8dnQn1hkNnJi8LlR3c+N6eNomz4L8Anq1X5PakjhzLHDLb8BmFmiW9QsV3ecxoKBt4UPAnHC/Dl1Kq886igWLpzGZ59s5NvhK4tP2rwHdG8CoOv27/CBJ5aQDER5dG1HfpcDs0F2gDRfDF3D8YHnMGRS6R00c9/WS4Cl/PbBtUWnH26w7Q7eD3QF9dtLZOq//k/vAPyv/XMZ7z1pYdF+T6zv4Du3vEB7T5yGSJD3v2wfXnXw5PsdUU4DiRRf+cdzPL7O+TewcEYjX3ntAcxp9W93LONPvyFlwtuya4D/u+l5cuOyvnD9M5x90Gwasr/Qvv6vZfk6UoDP/e0Zzjxgtm9/7Frml6l/dG0Hu/oTtI5ytshEKk17b5xfha/m0MBqSOMZPv/r1Fn5gB5g4cxWLtv+pvx7dxAxrTHKAFEuTb4TgOmJXfw88gOODKzwvfYNqeN5XfCBovU/Tr6eK1rraIwE6Y17H2TUU3tyKBWwTjazC4LslhF0bprW5F9W5/4/V/j/YVpThICBtC0+JhoKcH3qBM4IPMaxgecBWG7n84H4J7nr06+j6edHQvdmWpI7+eO2c3gyvS8rQ85g3yPbp3BwqJM9TDsvCz5TdF/HrH0f9g9/Ze2zhwEHebb1xlPD6onvLrM5aG5rftkvU79hZx87fCbJe2bjLg6a1+pZ961/vcAja52xDZ/7238584BZ+VIxKXbLs1v406MbPOtWbuthr2mNfO7speN0VzIU/YuWCW9te6/nl9RAIs2mTueH/6ptPZ79O/oSvpMj1bpSM7a+1NE/6nPu6InRbHs42BQPyFudns3/S77Ss+7NR8+nLTtD6JELprB0dkt+24FzWzhp0XTn3LTyxvhXeE/8EuI2yE7bxHab+WX7lcQ7+FjiIxw9cAUbrXPMj5PnsNd+h7FkdotvVl6Z+snh5Utncej8NoIBw9fOOXC8b6diTtlvBvOnZrKae09v5IR9pw9xhGPelAbOPMA7D8XsljrO2N/p/lT4/6E5GirK3kMmqDfGcP4Ji3lP4tO8adpfOSD2a86Nf5XttLGpx8KJn/Qcc1jgRd4Uuif/Z+HG63lL6G7fgD7HrLiF30e+yXnBu4u2eQa1xnvh2b/C8zdAMu7ax5Wp38MJzLf3xEgVPKkUdtjJWb2jp2jdqu3edV0DSdp7i2fSFsfGDv+OQxs7R//7RipPvyFlwvMb/LSte4B9ZzYxkEjRNeA3gHSAqZOsS0qpGVu3dQ+wPy2+2wY10EXXmmd5b+hfBEz2F+bsg0i87hfEUrC+u42u3zzlOWTxrGYe+tzpbOrsZ+/pjZ5PQ4wx/PbdR9PZl2AgmaJ7IEkileZVP4LDYr8kSZB9Z7USSg/w9PbM9bYxhdNi3+crZ+3N+cfsydvTjXwk+9DQFA0V/d0rqJ8cAgHD3z98PLv6E/me65NRYzTEXZecwtr2Pvae3khwhK07f/72I+jsy3wSt6a9lz2nNng6ChX+f2iIhmiMhjw17+GgYUr2/9SXX3MAF5+2iCmNEV77k/vy5S3bumIsPvwdrL/5MvZk87Durd02Y95xA/dc/UVeH7zfs+274V+yR12Cja1HcsumOnqpZ1t3jIW5+Q7++j5Y/s/M8uHvhNf+KHMfrv/ve05toK0hTGdfgmA6zq61TzK1IQwmCNMXl6zTL1yf+zTSb79S4xYEz6ek+89p4fnNmTEYfSWSSzIx6DekTHh+fdRzP7hL/WDf2hVjySRrZ97rqqnfZ0Yjq7ZnMlXDHYTmsfm/cNVZ7JfoZT/3T4FFZxCecwBh4Gifh4jGSJC6cND55VzAGJPvxjOnlXwf/V4y2cqpLY0ETBNs354/Jk6YaTNmQf0UprjO1eBTf6yBspOHMWZSB/Q5oWCAfWcOb/KuQu7/T34TgBWWszRFg76DZ90P37nzLZjW6BqIOgDh6bwn9HXePPAX3utqUdv5istoq49A5zr4z3fz669Mv47PLjycz6QvIkyKVwcf8lz3E6lfw85fc2m0jvPiX2Zr16GZDesfcgJ6gCevgeM/Sk/z3vkOX5FQgJb6ELOa6wj0tfOP6BeY+tsdzjGzDmTH4l/4fs8K6/e3l+iIs7VrgINo9d0m3k+G95zakA/qe33GdsnEoaBeJjy/QVa5dYXdDwY7pta5f8juPb0pH9SP6mv995cg4f34OmEihI96X/59QyREUzTkaaU50ky537gG90C/HL9aW78yAmXqRRyFD76N0VDR/6WZPv/fAGa5xjXkfo52mla+lryAu9OHcphZyW/SZ/L4sW+E7KcDb7k9ytmBh1ljZ/MHXsn/GMPM5no+0vlR7kodyv+0/psZ/as812kyA3w29CdWdp2VWXH3t7w3YtPwkyPpeMudzr21RDHGsF9DF7fWfbD45rc+ywe2nsDLI3P4cOJjBGcfmA86txYE8SV73w+zzebuyv1z3/0z26+1skwc+g05QX3+78/ka8UP23MKnzpjMU9v3MXP71lFV3+mXjwSCvDGI+ax3+xmfnzHi/lBQ8GA4eyD5vD2YxeM6R6e3tDJT+9+kc5sfXo4GODcw+dy7uHzhjiyfB54cQdX3ltc733rLf/gLS/ey5T2dv4UyXzdnbaJ7ybfxCo7l89c91/+6prF9KC5rXz6rP2IDjEdvbWWK+56kfte3JHvkTy3rZ4zD5zN9U++xM7sx7ihoOF1h8zlTUfN9xzfH0/x3VuX89wmp4/zfrOb+fSZ+9GcHST34Kp2fnXv6vwPx2g4yNuO2ZM5rXX89K5VLGq/k5f3/YsISWY0Bpne8SQ7phzGN7oGIJvYnLOjjpND0/ha8u18/98ruO/FTBarKRrivSct5Lh9pnm/sJ1r2PzXz9K5YzOkUyxNZDrTpKxhhZ3PABE2Lnk3r2nxdoRorQ97foiXYzIhv4+8/YJ1v0BfA2VFHIUPvo2RUNH/pVKDkt3B/nduWc49y7fT2Zf5+XZf+iDu4yDqwgHP//mH0vvzUHp/ACLZ9TOao7zU2c9f0y/jpu5TeEX6ft4Tupk9mmBG32oCpDkl+DQzbz+HZfc25X/2FJr/p9P4UyQzADOUbIbf/5wfbb510K9/n8Bm/i/8a/66x5Xsv+1GzgncR2hZmp0/aWJqY+bra93Rw6dCC7gseR5p1zDCH/x7JW87xv935PbuGN+7dbmnbv+IBVO45Iz9RlxCVW7Vujd3EsndxalUGehQHl27k1/cs5ruASd+efNR83n1wXuM7UZLeGJ9Bz+/exW7CuKl1x1aPNNzoV/du5o7lm0jbS2N0RBXveuoitxjJeg35AT13Eu7eDr70ejDa3ZywB4t/PjOlazY6h3w8/CanSya2cRzm7w9hx9Y1c4J+04f0+x6/3v9Mzz7kve8D61u58R9pxe1aqsEay2fvPZpAA4xL/Ly4BOESFFHnAtDt8IGaAX2dcWZZwUf5afJ13Jn6lAeXrMkv/7hNTtZPKu5KAgv9OCqdr53W3G3lr89+ZLvvicsms7cNqe913WPb+Cq+70PIQ+v2cnctno+cPI+WGu55Nqn2LTLmyV6fO1O5k6pp2/bGn4U+SYRk/2IM1sKOr3jSaa74+luuCAEF4Ru52fJ14CrScGLG0Icd+wC2OMwOOAcsJbkde9jzqZHKWzidn36RC5JZHpSf21h8YDF6U0RXirjwKi9pzf6Bhl+rf6afSaaUlAv4igM4qKhQFFQP5x+95D5OVVoWqP3/+rCGY2szn5CeMDclux5nH1iyTQ3cRw3xY/jS8fvz+nLvsiCl24EyExm5+pfcF3qZRwwfzpLNzlzYhwbWJZZiAMrvfeyvu1o9rzoRuyfzsesuiO//ujAcmbt+CoLwrc7O+/I/gEWAh8JPcXxged4Y/wr+cB+R0+M1dt7fEsJf/mfVfz5MW/nl4fX7OSgua288qDxbYVZrXtzl9m4/62UatgwlM9e919W7/B+OvzImp2ctGjGqLu3Debzf3uGF7Z0e9Y9vHonJ+47nWlNpbtvPfvSLr72z2X5936/hyaysnW/McbMM8ZcZYzZZIyJGWPWGmMuN8ZMGfpoz3mmZo9bmz3Ppux5S6aHy3XtiWzZ5i6C25/nzMCjnj+HpJ7n+U2dvses3Nrtu344rLWs2FLcRSCZtkX/MSulqz/Jlq4Bjg08zw3RL/HR0PV8KHRjJqAfxIdD/+C66Ff5cPB6z/eKF26CXcXBudvyYX7PprGL08zj7HzqnxBzvk+ljs+t7+3Ywv7d9+fv6fjAs4RJ0htPkd72AtdFvuIE9MP0odCNnj8XpP4O918Of3knPPd3WHUnoU2PFh3XaRu5PHlu/v0Z+88q2sedyXrX8XuN6L5yfva2wzEm05nj4tMX+T4Q+mXqX3XwHrhjloXTGzlgj1EMCBaZxN56dCZRcdKiTLJlWkGDgFJBfeFEVX4K/89f9qZDCQUyMwt/89xM28pzSmQ+Z7XU0XrW50nZ4uxx7mfPr9o+zsb93jXkfdyUOpZfLLgMwnXsOOeP7DdwNf9OHZ7fvmDr7YMcnXF44EUen/UN9jRb8+s2rFkOy250/bkJOjewfGvx7z4Y/u+HSqrWvbk/oXUnYkZTfhNPpn3jhlgyzYad/l12xiKVtqzcVvx9iqfSJbsm5SzfMv5/x2NRlkcQY8w+wAPATOAG4AXgaOBjwFnGmBOste3DOM+07HkWA3cCfwKWABcCrzLGHGetXV2Ja0803zxzD37/YB//fj4zO+fsFb/j5siPffe9LvUyvpN4M8bACftM474X2+kjOqYps91TfTdEghw8r5WHVmcyORWbijuVhF5nAGX7jh5ODTzJryPfLXnI31Incm3qFD5b93cOS3s/1v1M+FrvzquAH/wPXPQItO0J/Z2Z9dFmiDaBtfS0b2Immck2Tlo0jXtXev/pRIKGk+cZvrjlYupMAu4GntoTLrwZTJDYzpeYSQc7aeaM/aby2PJ1AMQ7DGwN03Dlafwq4s3S35c6gBvSJ/Dd8C8967+YeBf/F746//4d8c/S2tzED990MOZ352LsMIL/u74Bdc5gsL+nTuDxqa9ha3eMR/rm5HvQv/aQPXyD7TcdNZ9jFk6lL55iyShnrn3lQXO477On0VofpikaGnb5zSv2n8V9nz2Nde19hIKGQ+a1qa+0SIFvvP4g3nfSQvaalvlUtvCTsBnDKL/J+djpi3jF/rOIhAIEA6ZocO6h89t48HOnEwyYfHexVx40x7c3/syWKG3z9+fRqWdzVEdmYGzMhvnRnG/yu7Ut7KKJvbsHePDgS7jqv/vRanqZ2hDh+3s/Qv3Km/LneWv8f3k4vZTTsg0BtnYNECPCnenDeEXwiaKv4cuJd7LczufzZy+hnjiLbn93ftuUXc/zn+gneH/8E/RSx8n/Or/4GxNpIhL9DtAGwMuXzuT2Zduy167Q774RcDeOcN/bqH8vx3thoHh24br+rcwkE3DPNh3534skINn5EqGA62exMdA4EwL+P5+3u+YTmNYYYd7UBp7e0Jm97wEo84Dlnb3xfAvU5roQS2Y35ydSyzeWSAxAvzOxFo0zIOjtuHbg3Ba+/JoDynpvlVauzxV+Siaovtham488jTGXAZ8Avg74jHYp8g0yAf1l1tpLXOe5GPhh9jpnVejaE8r+d72Hr296gq/n4p/iT0bz3hj8D28M/ifzZiNQl6mVvm/ZxXDsV0d1ffcPr9ktdew3q9kJ6isxCHX7Crj6bE9QvxD4dWFzjH1O58oNe7CzN8EqO4fb0kcChiv3PpmfHrKW5Xf/nv123j34ta442vveBOGsb8Gyf/DRtffy0dz3fAPgl8zaCriTT53r4QeZ//jfxXXMOtfyZuBn/h+NnRh8rmj21bVNh3HNjjO4OXUMr2p4nn/27c8OWnn3gXsT2Gd/Bj62jK9/9xs0kfm72G9OMz0DSV7q6Mdg+WTDPwklemCHU0oUsyG+nXgLJ847hC1butnV59T9L5xRukxrwbTRl3DluEuU/MpvGsL+Yx32aKtnD9exIuJljPGUkBQ+nA+3/AbguH2mceDcwQMsv4eEw/ac4pl5FGBW9pOApw/6AtfeMZcoCW5KHcsnDzmWXWszP++2dcXY1hNnmV0AFj5w+ELqX3kxLPsHdG7gmeYTefD3mU9XcxNT5brZ3Js+mCRBQjjJjV/O/Qa/WbUXACvqD6ExEuTC2OXcF/24595+GflB6S8w3sN5id9xOx8B4GWLZ+QD51Iz21aTO+h039uofi8/+1e4/sOQLD72T+D8/vo9POL+53K5z7mmL4YLb4HGaUWb3IOV92irZ9HMpnxQX4kHJff15rTWsWiWE9Rv7RqAtffD78/zNotonAkX3uy5n9cdMpej9ppa9vurpDEH9dlM+RnAWuCKgs1fBt4PXGCMucRaW/JzD2NME3AB0At8pWDzT4BPAmcaYxbmsvXlunateT56KJHGVvbdeU/JfYLGcvK6H8I3fw3RgpKFqXvDuVdC82y47QuZH6DptGeXBckU90czBd3R/gDR5wO8P5r52K3p3hA8WlADF22G078ES84e2ReTSsCNH4enfjf0viddAqd/ibuufIgHurwZ9JmtjXDwm3ig+yiu+OevOCv4CEHSHLP31MyYhMBa5pkd/ue1Kbj50yO77zEasOFMpt/Hw9ETWHHQF+CuDnbQym/6jstvy9Wv1rXN4prUGfn1r58xl1gyxb92bAHgtQunsmT5zzzn/VPqVLYwjVktUToK+jZXs19zYVAQCQaUgRcpk8L/y37dpiAzPqVw1ubR/hzwu0buk4DpU1r5WuqU/Hr3Q8O27gFPMDqzpS6T9d3/dQBM6egDskG9K1MPsNHO4Pfzvsw7Wx7PJGYOfwc7ls+GVavz526MhNhoZ3Jq7Pv8atrv2aenOLMPwNR9MkHpikwrzzPtA9wfXY4Bpt0X5fRo5tqRdQG4zOf72TgNXvUDmHfEEN+pYXr6T3Dv9yHuLU2xWG5MDkCUkd3bq38Ac33u7d7LfAP6UdmxAm74MPS1Q5d3roOlCSeeqOsMEO4O8IlsPNFyRwju86mpn3MwvP4XUFei5DKdhls/By/8K9NByWVfd/zSEyD6QoCLstdrvicI8W3F5+vdBj85gotDM3lfNPN/YsqDYXhmClz0UPH+E1Q5MvWnZl9vs9b7nbXWdhtj7icTeB8L3FF4sMuxQH32PJ6iJmtt2hhzK5kg/VQgV4JTrmtPPA3TSDXO8kyD3WPr+U7yLbQc8HoO3bOND11/C98P/4xZJvMEGgkFaAgHiQ442W5iXZk/bl0b4bIl9AcaqU/7P+vUAXNz2ehU5k9z7n2c/ABOjz+9lecbjmQg0DDsL/Pwnv/4ru8MTiOVtiTTaWI2zLIFb+fM078E+Gd6c4FiQyTIP9LH84/08QA8/ZYz+MBXbwPgy+FruDB4c9GxfrbaNqY2RujqT5J0PfBEQ0HqwgF29qe4O3UIe0T6ONS8mN/emOwkXFATv9M2kSBENBQkkTbclDiCryYv4KNHNfOW9ZcS7Mz8c+61dVyefCPpxW/gtBkzAW/mC0q3p8t8X5xfyJ/bejpfanyWvQcy08GvYE8uGzgvv9/O3kTBsaXPW26FHXRyZV4iMnaF/5cHq52f0Rylt73Pte/ofg4UXqOlLkRd9tO36QWDEpfObiEYMKTSlo6+BP9+fqvrPKVLh7Z1D/Dh3z+eH6gLsGXemXDWx5zjNznVudc9tjE/kHiNncONh/6Cj7f+h767L6e7JxNipEyEh6afw+1T3gIWPtTYwUG9mQBurskmjnpdvwvTQHGlSuZ36q9O46nGE0mbsSUoWpI72XfgWd9tBte9jOTervS/t8N7ns0eaugKejPSsaTze2xmcx3tvc6svpFQAJP9uDpAmpZU9nfVilt877ue4niiJfc+lv3jd9/fms8TTS/zPecBvY8Qtf4PJEPGL4OYmtzmfBLfD6RrawbdcgT1+2Vfi1uGZKwkE1gvZvDAejjnIXuecl8bY8zjJTYtKbG+st5+HTaV5tgv3JxvrZhzUUuUWc11rLTzeG386/n1bzpoHm87ZgGX/vTX/DbyLZrM4E/gpQL6sdi/77ExHf/L5Kv4RvJtRes/v8j5a/DLJuV+GbTUeZ/4W+pD1IUDDCTSXJq4gM50A58I/5WkDfDZxPvZzFSuCn83nzX/b3pv3hz/Iv3U8cinTueTf3463y4S4B2HL+Dsg+bwll9mn9x9xgx9MnQtF4euh0CILwcu4jc9x2Q2FPzgqp82n0cW/o6P//kpz/p3N9eNeHDbzOaoZyKfJ7fEeT0fKrlvR1+8YF11Z1ac3hTNP7BGQ8rSi5TLtCZvzWJuNlk/rQ0RcAX1o50HojDZ4C4BKuweUh8JMqMpypZsxt3dCawwqI+GgkxpCNPRlyBt4V/PbPFep/ABxnXdwoGZM5vr4Kj3snL2G3ndFa4ZcDcCGzPnXW7ewLWR55hmRjdY8tDe+0Z1XDUMdm9PpvflDQOX+m4LBw0rP3U273bNQOz9XWb5Z+TzHBBYV76bdSmV+BurlDV8NfkOfpM6ky+ErvFMuFbLyhHU5z5L21Vie259WwXOU65rT0ihYIDTl8zi9mVbPetfsf9sFs5opLU+nO/BCnDG/rNZOqeFra2HcETnz5nm89j+g8hPOSbwgmdd3AY5N34pO63/x1w/fdvhLJ7VzHk/f4COvuKSkVcGH+GL4WGUzwyiyzZwZuzbbKa4Hi9g4LQlTmeWV+w/i1/8x8nIREMBTl48A4BTl8xkTmsdm3cN8P6XLcQYwxn7z+YfT28C4IepN3B16kxSBOgh84nCobFfMpVu0hi2MBUwHLZnGzOaopxxwCxPUH/G/rM5dH4bM5tLD0S+LPkmth/wXv7v3EPhlnXwYPEPu4DJDHJqa4hQHw7Sn3CyImccMIuD57UyvSnCjh4n+J7eFOGwPdvy77/6ugP40g3PUR8O8r6XLaSjN853b32haMCaW3M0xHH7TGP+1AYuvz3znLzn1AaWzBndINjRetsxe/LDO1Zml8c2n4KIOOa21XPIvFae3riLVx00x3cCuJzXHrJHvrb53MOG7t9dysuXzuJ7ty7P/+xxd9I6cG4r+85s4sVtPZx3RKaJ3RkHzOK3BT8XZ7VEOWR+W9G5z9h/dlELR4BQwHDakpmedSfsM62opAgymeVT9sv8jlg6p4V5U+rZ2FGcgV1l53JM7Apm0gnAe09ayLtP2ItL/vI0D67y77fx/tBNvCt0m++2sbok/kEezM4LUOh9Jy3kwiHu7QOhG3ln6N9DXue6lH82HOD07O/e05bMdIJ6D8M3k+fz2/C3CJjMP4CbUsfwjURxcg7g1xcexezWOt74swd922MaLL+LfIO9A1t9ji4Ws2HOjV9Kh/WftfkX7ziCvac18safP0BXv3O9bhrozsYAX0tewBXJ11HvSuPvNb2Ra95zNMESg38nKmML08AjPYExvwTeB7zPWvsrn+1fBz4PfN5a+81BzvN5MoNav26t/YLP9vcBvwR+aa39QDmvPcTX9/jhhx9++OOPl0rkV1Y8mebB1e30DGT+MR44tyU/cHFnb5yHV7eTtrBoVhOLZ2UCs+6BBA+saieZKv67DaTiTN3xSGYQJYAJsHPa4cTrpvtef+mc5vwgrM6+OA+tbsevWqKl83kaetaP6mu0gTA7px9BItLmu/3QPds8Ay0B1uzo5flNXRgDR+41xZNp7hpIsHJrD4fNbyMQMCRTme+h+z/0YOojAY7fZzp14SDWWp55aRcbdvaz3+zm/HTvu/oTPLiqPf9xpFtbQ5hj9p5KKBgglbY8smZnftKqnEPmtzJvSuYHyvbuGI+u3Ym1sGROc77jxK6+BA+u3kEqnZnQ8biF02l1Zd2stTz7UhezW+vyH1Nv7Ojj6Q3+z7gBA0fvPTXfo3fDzj6e39zF8ftMy0+MVS3WWh5f10EybTl6r6kExnlCF5HJpD+e4tlNuzh0ftugE8ZZa3l64y56BpIcu3DqmMa25H72zGiOcuSCKZ7/072xJMs2d3HYnlPypTcPr2mnI1sGGAwYjttnmm+/8lTa8tDq9vwkiDmHL2hjTmvxIPodPTEeWbMz/wm3MZnJmdyffg72OzJndmuUw/ecgjGGeDLNA6t2eHq351nLlPYnvGWvZdDTsi89LftW/N76G+aya8qBmW9Ugea6TBIoHAxgreWJ9R1s2eWfzGrqWklT1yoS0Tbapx+VGedQ4OB5rcyfmvm91579e/JLQgWTfUzb/giB1BD1/ibAzmlHEK8rTgYCHLBHC3tl5+rp6I3z8Br/+KVQJBTghH2n0eAzq3k1HHHEETzxxBNPWGtHPEijHEH9d4FPAZ+y1n7fZ/tPgIuAD1trf1a43bXfRWQGxP7EWvtRn+2fItNc5DvW2s+W89pDfH3jGtSLiIiIyO5hLEF9OT5XWJ59XVxi+6Lsa6m697Gcp1zXFhERERGpWeUI6u/Kvp5hjHdotTGmGTgB6AOG6gn0EJmxxidkj3OfJ0BmwKv7euW8toiIiIhIzRpzUG+tXQXcBuxFptTF7VKgEbjG3SfeGLPEGOPpKmOt7QGuye7/lYLzfCR7/lvdM8qO5toiIiIiIpNNuUYBfBh4APiRMeZ0YBlwDJk+8iuA/y3Yf1n2tXBkxueBU4BPGmMOBR4BlgKvA7ZRHLiP5toiIiIiIpNKWXr1ZDPmRwJXkwmoLwH2AX4IHGut9e+3VHyeduA44EfAvtnzHAP8Gjgie52KXFtEREREpFaVrV+PtXYDcOEw9y3Zv85auxP4WPZP2a8tIiIiIjLZ1FZXfRERERERKaKgXkRERESkximoFxERERGpcQrqRURERERqnIJ6EREREZEap6BeRERERKTGKagXEREREalxCupFRERERGqcgnoRERERkRqnoP7/t3f/oXrVdQDH3x8ydI1ctrIRGddMc/RDSindQDdHy4hqxhYFmoVCRmFGQX+U6co/+susGSaEGStYMDGJVgpuudWsaFFjNKezXSX81bY2zW3W7NMf51y93J7nufc8997n9H3u+wUPh+d7zrl89uHD2ec5z3m+X0mSJKlwkZltx/B/LSIOzJs379WLFy9uOxRJkiQNsd27d3P06NGDmbmw6bk29ZOIiH3AycBoy6G06ex6+2CrUQw/8zwY5nkwzPNgmOfBMM+DYZ5hBHgmM09veqJNvSYVETsAMvPctmMZZuZ5MMzzYJjnwTDPg2GeB8M8T4/P1EuSJEmFs6mXJEmSCmdTL0mSJBXOpl6SJEkqnE29JEmSVDhnv5EkSZIK5516SZIkqXA29ZIkSVLhbOolSZKkwtnUS5IkSYWzqZckSZIKZ1MvSZIkFc6mXpIkSSqcTb0ai4iRiMgerw1tx1iSiHhDRNweEY9HxPMRMRoRN0fEKW3HNizqnHar1yfbjq8kEbE6ItZFxLaIeKbO4Y8mOWdJRGyKiIMRcTQidkbEtRHxskHFXZomefaa3L+IWBgRV0XEXRGxt67PwxHx64i4MiI69knWdDNN82xN9+eEtgNQ0f4M/LTD+K4Bx1GsiDgD2A6cCtwNPAi8G/g8cElELM3MAy2GOEwOAzd3GP/ngOMo3VeBc6jy9jfg7F4HR8SHgTuBY8BPgIPAB4FvAUuBNbMZbMEa5bnmNbm5NcCtwBPAFuAx4HXAR4DvA++PiDU5bqVOa7ovjfNcs6YbcEVZNRYRI8A+4IeZ+cl2oylbRNwDrASuycx148ZvAr4A3JaZV7cV37CIiFGAzBxpN5LyRcRyqiZzL3AR1X/QP87Myzoce3J93AJgaWb+oR4/CdgMXAB8PDO96zZBwzyP4DW5LxFxMTAf+Hlm/mfc+CLg98BpwOrMvLMet6b70EeeR7CmG/PxG6kl9V36lcAo8N0Ju68HngMuj4j5Aw5N6iozt2Tmwx3uqHWyGngtsGGs+an/xjGqO9EAn5mFMIvXMM/qU2ZuzsyfjW806/Enge/Vb5eN22VN96GPPKsPPn6j6Xh9RHwaWAgcAB7IzJ0tx1SS5fX23g4Xumcj4jdUTf/5wH2DDm4InRgRlwFvpPrAtBPYmpkvtBvWULu43v6yw76twBFgSUScmJnPDy6soeU1eWb9u94eHzdmTc+8TnkeY003YFOv6Xhv/XpRRPwKuCIzH2slorK8pd4+1GX/w1RN/VnY1M+ERcD6CWP7IuJTmXl/GwHNAV1rPDOPR8Q+4K3Am4DdgwxsSHlNniERcQLwifrt+Abemp5BPfI8xppuwMdv1I8jwDeAc4FT6tfYM5/LgPt8ZGRKFtTbw132j42/avZDGXo/AFZQNfbzgbcDtwEjwC8i4pz2Qhtq1vhgeE2eed8E3gZsysx7xo1b0zOrW56t6T7Y1M9Rk0zx1+n14lRqmfl0Zn4tM/+YmYfq11aqu8q/A94MXNXWv02aKDPX1s90PpWZRzJzV/0D5JuAecAN7UYo9c9r8syKiGuAL1LNRnZ5y+EMrV55tqb7Y1M/dz0C7GnwenyyP5iZx6mmpgK4cOZDHjpjd3QWdNk/Nn5o9kOZs8Z+oGW9zg5rvEVek5uLiM8B3wb+AizPzIMTDrGmZ8AU8tyRNd2bz9TPUZm5Ypb+9N/rrV+LTW5PvT2ry/4z6223Z+41fdbr7NoDnEdV4zvG76ifpT2d6sdxfx18aHOGNT5FEXEt1Vzzu4AVmfl0h8Os6WmaYp57saa78E69Ztr59dYL2uS21NuVHVbTeyXVIiZHgN8OOrA5xHqdXZvr7SUd9l0IvALY7iwhs8oan4KI+DJVo/knqjvH3RpNa3oaGuS5F2u6C5t6NRYR7+q0dHZErKBaMAmg57Lxgsx8BLiX6sean52wey3VXYj1mfncgEMbKhGxuNMPqurFTW6p31qvs2MjsB/4WEScNzZYL9RzY/321jYCGyZek6cnIq6j+sHmDqo7x/t7HG5N96lJnq3p/riirBqrp5M6E9hOteIhwDt4af7e6zLzxg6naoJ6AartwKnA3VRToL2Hag77h4AlmXmgvQjLFxE3UP0YayvwKPAscAbwAeAkYBNwaWb+q60YSxIRq4BV9dtFwPuo7phtq8f2Z+aXJhy/ETgGbAAOAh+imhpwI/BRF1j6X03y7DW5fxFxBXAH8AKwjs6z2oxm5h3jzlmFNd1I0zxb0/2xqVdjEXElcCnVNFSvAV4OPAU8ANySmdt6nK4JIuI04OtUX+cuBJ4A7gLWZuY/2oxtGETERcDVwDt5aUrLQ1Rf/66n+jbEC+EU1R+Sru9xyKOZOTLhnKXAV4ALqD5I7QVuB77j4l+dNcmz1+T+TSHPAPdn5rIJ51nTDTTNszXdH5t6SZIkqXA+Uy9JkiQVzqZekiRJKpxNvSRJklQ4m3pJkiSpcDb1kiRJUuFs6iVJkqTC2dRLkiRJhbOplyRJkgpnUy9JkiQVzqZekiRJKpxNvSRJklQ4m3pJkiSpcDb1kiRJUuFs6iVJkqTC2dRLkiRJhbOplyRJkgpnUy9JkiQV7r+8+Vyq2wytNwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PDFtophat = kde_sklearn(x,bandwidth=0.1,kernel=\"tophat\") #Complete\n",
    "plt.plot(xgrid,PDFtophat) #Complete\n",
    "\n",
    "PDFtophat = kde_sklearn(x,bandwidth=0.5,kernel=\"tophat\") #Complete\n",
    "plt.plot(xgrid,PDFtophat) #Complete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see what we get with the Gaussian `kernel=\"gaussian\"` and Epanechnikov `kernel=\"epanechnikov\"` kernels. Let's play with the bandwidths until we get something that looks reasonable (and roughly matches) for the two kernels.  They need not be the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1284ee970>]"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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   "source": [
    "PDFtophat = kde_sklearn(x,bandwidth=0.3,kernel=\"gaussian\") #Complete\n",
    "plt.plot(xgrid,PDFtophat) #Complete\n",
    "\n",
    "PDFtophat = kde_sklearn(x,bandwidth=0.3,kernel=\"epanechnikov\") #Complete\n",
    "plt.plot(xgrid,PDFtophat) #Complete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's nice (and still pretty different from the histogram that we started out with). We'll see later on how to select the optimal bandwith using cross validation. \n",
    "\n",
    "**HISTOGRAMS TAKE-AWAY MESSAGE:** \n",
    "\n",
    "Making a histogram is the first-cut we make of data, and it's certainly one of the most sensible things to try to get a feel for the data. But we can't just do it without thinking. We need to explore bin sizes and KDE smoothing bandwidths to tease out the structure in the distributions, and overcome any finite sample effects in bins by potentially having variable bin widths.\n",
    "\n",
    "Finally, the normalized bin height of a histogram can simply be understood as\n",
    "\n",
    "$$ f_k = \\frac{n_k}{\\Delta_b N}$$\n",
    "\n",
    "where $k$ indexes the bin, $n_k$ is the occupancy number of the bin, $\\Delta_b$ is the bin width, and $N$ is the total sample size. If we want to assign **uncertainties** to each bin height (not often done, but its good practice) then we can quote\n",
    "\n",
    "$$ \\sigma_k = \\frac{\\sqrt{n_k}}{\\Delta_b N}$$\n",
    "\n",
    "(this relies on approximating assuming that binning is a counting experiment, which is Poisson-distributed)"
   ]
  },
  {
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   "source": [
    "### Time to get your hands dirty! The irreducible mass of black holes.\n",
    "\n",
    "This is an example that comes straight out of my research in general relativity. This paper:\n",
    "\n",
    "Gerosa, Fabbri, Sperhake (2022) \"*The irreducible mass and the horizon area of LIGO's black holes*\" [arxiv:2202.08848](https://arxiv.org/abs/2202.08848) \n",
    "\n",
    "(some of the calculations there were first worked out by Cecilia Fabbri in her BSc thesis with me).\n",
    "\n",
    "Consider a rotating black hole. In [1969](https://ui.adsabs.harvard.edu/abs/1969NCimR...1..252P/abstract), Roger Penrose (now [Nobel Prize in Physics](https://www.nobelprize.org/prizes/physics/2020/penrose/facts/) for the theory of black holes) discovered that one can extract energy from a rotating black hole:\n",
    "\n",
    "![](https://inspirehep.net/files/268d28446b405e134199d84f67c23792)\n",
    "\n",
    "(figure from [Harada, Kimura 2014](https://ui.adsabs.harvard.edu/abs/2014CQGra..31x3001H/abstract)).\n",
    "\n",
    "Maybe some of you has seen this already in your GR class? In any case, a rotating black-hole has a region called ergosphere such that infalling particles have negative energy. Penrose imagined a particle that enters that region and decays: half will fall in and half will escape to infinity, carring some energy with it. In a nutshell, we've extracted energy=mass from a black hole! It turns out that one also has to extract angular momentum, not just energy (and here you'll need some GR do to this calculation, see e.g. the famous textbook by [Misner, Thorne and Weeler](https://press.princeton.edu/books/hardcover/9780691177793/gravitation)). But angular momentum runs our first, such that a repeated series of Penrose processes leaves behind a non-rotating BH with a remnant mass which is called \"irreducible\". This is a famous result by [Christodoulou 1970](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.25.1596) and is closely related to the even more famous area law by [Hawking (1971)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.26.1344) (which in turns is the foundation of black-hole thermodynamics).\n",
    "\n",
    "\n",
    "For a BH of mass $M$ spin $\\chi\\in [0,1]$, the irreducible mass is \n",
    "\\begin{equation}\n",
    "M_{\\rm irr} = %\\sqrt{\\frac{M^2+\\sqrt{M^4-S^2}}{2}} = \n",
    " M \\sqrt{\\frac{1+\\sqrt{1-\\chi^2}}{2}}\n",
    "\\label{mirrdef}\n",
    "\\end{equation}\n",
    "For convenience, let us define $f= M_{\\rm irr}/M$\n",
    "\n",
    "Suppose you have repeated measurments of $M$ and $\\chi$. This is just because we're still frequentists for now. When we will put our Bayesian hat on, these distributions will be the *posterior samples* from a single measurement.\n",
    "\n",
    "Let's assume that\n",
    "\n",
    "- the spin $\\chi$ is uniformly distributed between 0 and 1.\n",
    "- the mass $M$ is normally distributed with mean $\\mu$ and standard deviation $\\sigma$.\n",
    "\n",
    "These are simplistic assumption that, however, are not too far from what we are now measuring with gravitational-wave detectors. It's a toy model, but not a totally unreasonable one.\n",
    "\n",
    "**Tasks**:\n",
    "\n",
    "1. Start with a value of $\\sigma=0.02$. Note that $\\mu$ is a scale and not a parameter: you can normalize all quantities with a dimension of mass by $\\mu$. Just set $\\mu=1$ in your code and remember that all masses in the problem are measured in units of $\\mu$. \n",
    "\n",
    "2. Plot the resulting pdf of $M_{\\rm irr}$. First try an histogram with one the rules of thumb we've seen above.\n",
    "\n",
    "*Hint*: You don't know the functional form of the pdf of $M_{\\rm irr}$... but you don't need it if you just want to generate samples! That's the nice thing about numerics!\n",
    "\n",
    "3. Using the same samples, plot the distribution of $M_{\\rm irr}$ using a KDE.\n",
    "\n",
    "4. Compute the KS distance between ${M_{\\rm irr}}$ and ${f}$ as a function of $\\sigma$. Discuss the limits at large and small values of $\\sigma$. \n",
    "\n",
    "5. Compute the KS distance between ${M_{\\rm irr}}$ and $M$ as a function of $\\sigma$. Discuss the limits at large and small values of $\\sigma$.\n",
    "\n",
    "6. You should find that (i) $M_{\\rm irr}$ is distributed like $f$ if ${\\sigma}\\ll \\mu$ and (ii) $M_{\\rm irr}$ is distributed like $M$ if  $\\sigma\\gg \\mu$.\n",
    "\n",
    "\n",
    "7. (At home...)  Compute the pdfs of $M_{\\rm irr}$ from their mathematical definitions, plot them, and check they agree with your KDE.\n",
    "\n",
    "*Hint 1*: First compute the pdf of $f$, that is just a change of variable. We saw how to do this in a previous lecture. The answer is:\n",
    "\\begin{equation}\n",
    "\\pi(f) = 2\\frac{2 f^2-1}{\\sqrt{1 - f^2}}\\,.\n",
    "\\end{equation}\n",
    "\n",
    "*Hint 2*: Then compute the pdf of $M_{\\rm irr}$, you want to use [this theorem](https://en.wikipedia.org/wiki/Distribution_of_the_product_of_two_random_variables) for the product of two random variables. The answer is only semi-analytic (unless you know how to solve that integral? If so please tell me!)\n",
    "\\begin{equation}\n",
    "p(M_{\\rm irr})  = \\frac{\\sqrt{2/\\pi}}{\\sigma} \\int_{1/\\sqrt{2}}^1 \\exp\\left[{-\\frac{(M_{\\rm irr}/f -\\mu)^2}{2\\sigma^2}}\\right]  \\frac{2 f^2-1}{f \\sqrt{1 - f^2}}  \\,\\, {\\rm d}f\\,. \\label{pmirr}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[My solution](https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/solutions/S07_irreduciblemass.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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