FIN5615_Project_2E_Mark_Shust.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<h2>FIN5615 Project #2E\n",
    "    <p class=\"text-primary\">Bond Spreads</p>\n",
    "</h2>\n",
    "\n",
    "<div class = \"alert alert-block alert-danger\">\n",
    "    <b>Due Date</b>: October 23rd, 2020\n",
    "</div>  \n",
    "<div class = \"panel panel-success\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:black\"><b>Project Introduction</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    A corporate bond's yield compensates an investor for risks inherent in lending a corporation money. Naturally, investors demand a return on their investment higher than the risk-free rate, but by how much? \n",
    "    <br><br>The credit spread represents the extra yield an investor demands above the risk-free rate to compensate for the risk of the corporation defaulting on their debt obligations. The higher the credit spread, the cheaper the bond price due to the perception of higher risk by investors. The credit spread can also be interpreted as the probability of default for the company. \n",
    "    <br><br>Here we will estimate the credit spread on a corporate bond issued by GE, by first simulating the floating risk-free rate then applying a credit spread on top in order to match market observed prices. \n",
    "    </div>\n",
    "</div>\n",
    "<div class = \"panel panel-info\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:black\"><b>Instructions</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Please code you solutions directly in this Notebook under each task in the cells provided below. Include all code used to produce your results, and support your answers with textual explanations if neccessary. You may feel free to add additional Code and/or Markdown cells as needed. Code must be written using **Python 3**.  \n",
    "    \n",
    "    <br>Please order the cells in your Notebook in the order in which they are intended to run! It is expected that your Notebook is able to run in sequence from start to finish without any errors (before submitting check by: `Kernel > Restart & Run All`).  \n",
    "      \n",
    "    <br>Once ready, please submit your assignment as an **.ipynb file** (`File > Download as > Notebook`). You must name your files in the following format: **`FIN5615_Assignmnet_1_Richard_Lee_tuc12345.ipynb`**.\n",
    "    </div>\n",
    "</div>\n",
    "\n",
    "---\n",
    "<div class = \"alert alert-block alert-warning\">\n",
    "    <b>Note</b>: Add any additional libraries that you plan on using to the import statements in the code block below.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
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   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 1</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Before we can estimate credit risk, first we need to estimate the amount interest-rate risk impacting the overall bond market. \n",
    "    <br><br>\n",
    "    We can do this by simulating future risk-free interest rates, which we will treat as the 1-year Treasury rate, and we will assume follows the below random process (specifically, a Cox-Ingersoll-Ross model, but do not need to understand the math here, we only need the below formula):\n",
    "    <br><br>\n",
    "    $$r_{t+1} = r_t + a(b - r_t) + \\sigma\\sqrt{r_t}dZ_t$$\n",
    "    <br>\n",
    "    Note that $dZ_t$ represents just a random draw from a standard normal distribution.\n",
    "    <br><br>\n",
    "    Simulate 1000 trials of interest rates for the next 15 years in 1-year increments <i><b>using numpy arrays</b></i>. Assume the following parameters for the random process, with a starting interest rate ($r_0$) of 2.66%:\n",
    "    <ul>\n",
    "        <li>$a$ = 0.150171427</li>\n",
    "        <li>$b$ = 0.013625329</li>\n",
    "        <li>$\\sigma$ = 0.00288994</li>\n",
    "    </ul>\n",
    "    Plot 100 paths from the simulation as well as the average path on a single line plot. Label all axis and provide a title for the plot.\n",
    "    <br><br>\n",
    "    Set the random seed to 5615 at the beginning of your code (<code>np.random.seed(5615)</code>).\n",
    "    <p style=\"text-align:right;\">[15pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
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RfvXjH/PDu2/FURHklu+8gCs0Tl2lk+Y6N3Wt5+OstWE0qx5A5eSye/duZs+ePdXN+Mh54IEH6OjoeMeZyWQ51N9QCLFJSrnk4LqT2VVVDwxOmB4qlR2yjpQyB4SBg0d3VgObS6HhLJV9VwjxlhDiN0KI6kNtXAjxWSFEhxCiw+v1ftB9AaCp1sHsudO48pr/ZWy4kacfaSFTXYc3lKTPl2Ro75N4BzxEfEl12a6iKB9Zkxkch3r4ycGfpu9aRwgxl2L31edKRTqgAVgvpVwEbADuPNTGpZT3SimXSCmXVFb+xU/mvm9nX3w1Zy/oYdniV9jw/Lls354j764mGAjSFzYxOvA8gZEeAqNxspkP1leqKMrJ7dOf/vSHcrZxtCYzOIaAxgnTDcDBt18fqFPqqioDAqXpBuAJ4JNSyu5SfT+QKJUD/AZYNBmNP5z6ahu1087h8o89Tm3FMI/+9FoCmXEKFVXEwkF6wxb8/u34h7cQ8SWJh9TjSpSTgzrLPnEd7d9uMoNjIzBTCNEqhDAA1wEHPzJwDcXBb4BrgBellLLUJfU0cJuU8sDtlKWxj6eAlaWi84G3L4T+kCw98yyazGVc+df/TTaj5/7vXULeFkKWO8lGonSFtKQSQUb7XiSdSBPyJCjkCx92MxXlQ2MymfD7/So8TkCy9HscEy9Dfi+TNoorpcwJIW4BngW0wH1Syp1CiO9QvBtxDfBr4CEhxD6KZxrXlRa/BZgB3C6EuL1UdpGUchz459IyPwa8wP+ZrH04nPpqG1VzVzGfR7nsgsd54k/Xs+bBLq79bBKhtaCJJtmuFSysKGew90/U1p1FxCcxWvWYbYYPu7mKMukaGhoYGhriWI0nKh+u/b8AeKQm7aqq48mxuqpqomFPnLW//QX74v08ee/fsK13Af/wLz9n3oo2LHE/2qggZTWwuLqBlOynyrEAW3ULAI6Kd7/hR1EU5XgwFVdVfaTVV1upmn8ZzUYjl177W5yWMA/88EainjeIWRvROCTWZIFN40OYdG344l34BzYjCxANqN9lVhTlxKWC4wOY3d6EzT4dV12MG67+b4IBB//1k2sw5tcStExH58zhSGnYMtaLRtNCmgSjPevQaAWxoAoPRVFOTCo4PoCGahuVcy+lXpqpWtjHJcufpeP1uTz/+ELc+tcY189AX57Ckdawe7SbqHQj9AX6Ozei02vVFVeKopyQVHB8QNOb3Zir5lJtFZy1ah0za7t55Ner2LLZSINtJ2OaGejcKWx5PcOeQQIhA1pHgf6eHWi0gnhYhYeiKCcWFRwfUEONjcq28ymTdrSVWW685mF0Isd9P7yWnmEP0ypG8RZa0ZQnMOV1jEbDZHw5pCbByHgPQggSEfWQREVRThwqOI6BpjoHtppTaNBqMTZFuXHVI/T3V/Hkry+ie2QPTdUpwoUmdK4YhryezpFBTFYLuVAET3wUKSXJmAoPRVFODCo4joGGaivuaSvQ68owu3TMXrKPc+dv4NmnF7FrfTtDY29S5TYRLzRgcGRxmCp4Y/2buFrKyI+OMZ4Jkc9KUvHJfRSyoijKsaCC4xgQQlBdZcXeeBr1+QK5CsnVVzxDfYWHX959MZHhMiLhdVicLsJaExZTGRX2Mp5fvxFXQxViZB/jJMim86QTKjwURTm+qeA4Rppq7FTWz0VnqqTcbECUSb5w1f+SSOj4xZ2XEYmAMfcyWGoZy0ZpbpqHOxDnuZ4d2NxtGEd34dVlSSdzZJKH/pUxRVGU44EKjmNECIHLZcLWfDbl+QKaCknZ9CA3rPwj27bV88z/nEafv8AM5x68Rh3dw1EWn3s+9m29vOx7C6NjLqbhbXgNxS6rTEqFh6IoxycVHMdQc62dispm9LY63DoT0iE57ayNLJ6xm8ceXsTo1jp2DflY2a5nV2aMQY9k+bLTEZu72RTdhsM9F8vIDsbNkIik1WPZFUU5LqngOIaEEDicRuzTzsMqC1hcBoTFzM1XPY7DEufuO89F5zeyq28ny2bZ2TTQidfg5sz5S4i8uYWNvj7Ka2ZgH9vDuEVDLJAil1XhoSjK8UUFxzHWUmvHYa9Ab2+gqqAn604jqwp88arHGfPYuOeeC8h6CiTTY0hLhtHxITxpPSsWr8S/bR2vj/ood9fh8vXisWkI+5Lkc+qR7IqiHD9UcBxjQghsdgOumRegFYIKkw2DXUt9ew8fO2M9a19q5eVnlzE+MMbsxgI7gjG0NkEomKa9aRHh3S/yujeGw26jMjyK164l6FW/56EoyvFDBcckaK2zYzZY0Ja1YMsXkGUSYS/j2vNeZPGsfdz762X0vDGP3p5d1JsDbAlnMRnSYHFRYW8hted1NiUKWHV5ahJ+fHYtPk+CQuGj/wh8RVGOfyo4JoEQAqtNT+2sc9DrjFTozOQcCcJ2LV9Z/RT11UF+cPe5RAdOJVXoIdG1jXFDNdbYONa6ZgoaO/mdW9guTWjTQeqzMYJ2LeNjcaQKD0VRppgKjknSWu9AU9ChdbZhLuRwltlw2GwkK5J8+brfAHn+/++fRT7WhKiL07NvC1HpxOUbobyyGn8O2LOTvUYnudAADWQIO7SMjcbUz3MqijKlVHBMEiEEJque+rbT0OvMWLNaYo4Ydn05VTOSfPb6pxkatfOLf70Abd5ATO/HLzIkzFU0Wy24NQUGvSl0A50M26pIjHXSrIWYQ8eoCg9FUaaQCo5J1FrnoJCViMpTsGjT1NmdpG0BDNEsS5d4+MQVr/Dmtjr+eM8ZgKArsJmc1BHKaVl8zsVUOAp07wqh2buJkL0K38A2mo1aknYdwyo8FEWZIio4JpFGIzBadDRPXwDCBilB+cxm8m4w+H2cf1EnF562md88PZ+uZ1tJSiO7wjtI++J4wxEWrzgPZ6OJvmEDheFtZNIFBrevp9msJ2vXMzwam+pdVBTlJDSpwSGEWCWE6BRC7BNCfPUQ841CiEdL898QQrSUyi8UQmwSQmwv/fe8Qyy7RgixYzLbfyy01jlIJwpo65dj02WxRjXY5k4jW17AnfFz2er1zJ/Ww89/dR6eN4yM5mMEjCl8nYOk8wUWzJqHqdJMz5AG6QKT3U7XGy9SG/SStQj6hiPq2VaKonyoJi04hBBa4OfAJcAc4HohxJyDqv0NEJRSzgDuAr5fKvcBV0gp5wOfAh46aN1/BZwQX7c1GoHBomVaywwkZaQ1ehpyFnQtS4lrwzS5DNz4t3+kwh7i3p9ehnezlq3pLhwaLb09w5jLqmhrLMNkq6Jnp5+UNU9tSy3dMS910RDppI9kJkfYmyTsTRIPp1UXlqIok2oyzziWAfuklD1SygzwCHDVQXWuAh4svf8tcL4QQkgpN0spR0rlOwGTEMIIIISwAbcC/zKJbT+mWuocxCI5DK2nUyXH8STizKu0kq9ZQTKyg9m1zXzm7/9AOmPgsZ+fQ2Bngedy26lN5tnd1UNVwxyaGvKYdM307fXhJ0GTRbInHWZ6Qx2j4yOUVZopqzRjMOuI+lOEvUki/iR5deOgoijH2GQGRz0wOGF6qFR2yDpSyhwQBioOqrMa2Cyl3P/j3N8Ffggk3m3jQojPCiE6hBAdXq/3/e3BMaLVCPRmLS31DfitC2kwhBkY9bK02Ua85jTC4Vc4r9XFJ296mu6RJv78q8WE9o3zjP9VKoWRzj1d1FTPpKolj7XQxFBPhDF9mpkixM6RQSrcFYz1Fw+13qDF4S6GiM1pJBHOHDgbUU/cVRTlWJjM4BCHKDu4D+Vd6wgh5lLsvvpcaXohMENK+cR7bVxKea+UcomUckllZeWRt3qStNY7CIXStLTNxm+cR50jzujYOMvqyghbp+NLdnDFWXGuvHwdr25bxPbfL8cb0vDalseBNMM9u3EZ9VjrbTg0tYwO5hk0QVO6n2A8RkinJzXmecc2NVoN9nITZZVmHG4TuUzhQIgkIhnVpaUoyvsymcExBDROmG4ARg5XRwihA8qAQGm6AXgC+KSUsrtU/zRgsRCiD3gVaBNCrJ2k9h9TWo1AZ9RSZbbirC4nZl6KuzxLeGSMU6bVMy4rMcYHueGGfSw9dRePPHMOvtcaGDFWMdrVyUi4QGpkCEt2K9JuwCHKCI4ZGLTr0AW3UK7JsC+RIhcIHHL7QggsDsOBLi2dQUPEV+zSigZS6llYiqIcsckMjo3ATCFEqxDCAFwHrDmozhqKg98A1wAvSimlEMIJPA3cJqVcv7+ylPI/pJR1UsoW4EygS0q5chL34ZhqrbfT44nS5GpEZ8qTsS3DVqdB2zPOnMXT6UlZqU308pnPb6K1ZYRfPLiK7C4Le1MpyqxmtqXNGPu0uEQfwqyBeJhCwEHcVc5IcCe57AD9417ykch7tsVg0h0IEUuZgVgoXRwX8SXVmYiiKO9q0oKjNGZxC/AssBt4TEq5UwjxHSHElaVqvwYqhBD7KA54779k9xZgBnC7EGJL6VU1WW39sOi0GqY3ORlJZKgrqyVX0IJ9AfnaPMYd47iXNzCaamCWbjuf+vSfMVnT/PhnF6EdN7C1Zw/Ty6vYMb2Rwl4/Gu8IlTXzSQaCaAMSra2OmdWtjOX72LZrPZHQ+BG3S6vV4KgohYjDQCyYfu+FFEU5aYmT4dvlkiVLZEdHx1Q344BMrkC/P4YhNspYwIpeM0Kk83UMRicjZTGMg1Yssps129u55xcfp71hmK988Tns0xtoa5vNuD5K3b49BPP1VFc5GU0GKTOlKDhstE1bxqi3j3jnZoztczHZHFRbqtFqtEfcvrA3ib3ciEar7g9VlJOZEGKTlHLJweXqk2EKGHQaWt020tYaKp1RCrIea8sC4tEI1dpm0q5hMDRydnMfH7/hT2zvaeHBRxYRHRgg0D2MM+/CN2s2LuMw42kDjqwgpLUTD0YZ2/MGRlcj9ctWYd/XjTmeZSwxxmB0kGAqeETtc1SYiPhTk3wUFEU5UangmCI6rYYZVQ6yVgtOVwGjdSbGsnrCgz20156GxziO2+Vi1fwdXHjJa7zw+hJefL6VrvE9aHt8aJNlpGbOxJrbTsHVgmUkS9xsYjgTJbv7LTwFDRWnrYLBfsxePw3WenQaHYPRQQajg6Tzh++OEhqB3qBVl+8qinJIKjimkEYjaKttImsIozUacM1aglGUs2tfN2fVz2O0LESlqYwbLl3PglO7eeD3F9LT4WaLr4Oy4TixpBtDQyO5+KuYGxpxDmkIWRwENV7Y18lQMIxzwQqMGT2+fZsxZzI02htpsDUQSoUYjA7iiXsOORhuLd0DoiiKcjAVHFNMCEFb3Qy01gAFzFS0zsahNbF5IMw8SzUBd5xqneDmG5+kvjHMj359Mf7hOvZ41lM2nCIkG6l0zyUmt2KqMGPvjjNc1oRRN0zv8AiR0TFMjc04zFWEA36SI7sRQLW1mkZ7I06Tk6HYEIPRQaKZ6DvaZrbrSURUeCiK8k4qOI4DWq2Jlko7FmseWdFAmauFhA4iAQvTrSbCZg2t5Xq++NlH0eoE37tzKV5a8Yy+im4gyqihgtpCA9o6HU67mfSeLoZtdcx3JXg5kSbW24vGZMJhcJCzVBPu3wbJ4niHUWuk0d5Io72RXCFHb7iXTL4YFkaLnkwypy7PVRTlHVRwHCdMpjrq3QnsRj1Zq4vWugX062Lk/S6qXBZiyTCt0wS3fv55vP4KfvydJobK68gPvY5tKM0+awWW/ijOeU1MtzbTtXcfnpSfM2v0dDgr8Xk8pP1+zLkCptpZ+LxeCr59UHj7xj+XyUWLo4Xh2PCBMnu5iWhADZQrivI2FRzHEYPBTXN9lmp3DaFAgqqZK/DbkpgDOezuGeRCo7QvH+Dzn9rMzt0zuf+HFfS21xLo2UjjXi9deie5Xf00zJ5Ou6WeLSM5xgbX0WxO4W9uJV7mxLttOyIcprxhBoG8ncx4FyTevttcCEG1pRpPvPj4Eq1eAxL1sERFUQ5QwXEc0ens5PNJpk+3U+muIuMvYGpZgs+mxxnvwWqfQdob5/yPbebKC/fw0vNLePw/tcQXldNbiNJS0NHtyeDr6GBB61yMBgeDMSfJ/nVoUv1EnHZsZ56Jf8dOAns6qaiqImGqIRaLgb8bCnkALHoLeZknlSueadgrTER96qxDUZQiFRzHGeLNkiIAACAASURBVLO5kWx2hNnzmnBmcgTyNuralxDRmqk2eLBkzfgDUf7mC1tZNHuA3zx4Fv/7X1lozBDwjVN19iL68w5G1r3G+aZaYnkr/rSeuGcQU87PSHwI61lnYkyn8HR0oNVo0NjcBChDBnoh7geg1lrLaHwUKJ6F6E1a9YNRiqIAKjiOO0Jo0Ons6IxJGluracwW6I4ZqFtyDv6gj5kzTFhDerypAP/8zY1Mq/Xz3z+6kP+8r8BQuR9Hxx5qV8xiR7ULXyjDwrwT3ZCWpHeAPcOjNFrq8MQGic2oxOl0IgcHiY+PYzCa8Mkycvk8BHoRQI21hrH4GADWMqO6wkpRFEAFx3HJYKggmw1Q31aPNZGkuraaIb+W8mWX4untpKVOYIqniYsc//6jV5nd4uG3P7+YR39Z4EXRR3lXP6fNa2OzNkLOWo65fTFObw2m3S/x6tY3qbU0UdCW4anUoNGncVos5IaLA+L+pCRnrgRfF2ahAyCRLf70icVhIB5Wz7FSlJOdCo7jlMlURyo1TOMpjbiGgjjraojmyhENc4n5vdTnC5gtfqJ5M3f9rIMFc708+uDH+NMDBp7q/CORrj1cOL2J3vQ4aQxk5s/DZT8D48gWtm58Gf2QF7OpgUB1PfHgHiwNldijUXS5HKO+ILjbIDRAjdaMJ1G8SdBg1pFN5dXluYpyklPBcZzSaIwIocHusqDXZHBpTJRZzVgbzybjFOSlpLx3HHtdmoGIhfvu2sDSxSM8+sjH+NMzZ/Ny13P0dW1idngAQ8RD2GInXNuI09JILO1hLBUh3dmH2Z8g7JxDZqyPQo0GWyGHMZvFMz4OFdMhk6CuoDkw3mF3m4iq51gpyklNBcdxzGSqI50eo2FuE7mBMeobatBo8phbryFmGEWvq6SscwONM/RsCDp5+HsvcvYZgzz+6Bk89fiVrPNuIT1nPpr+zTh2bcRlyOGrmo8tnmcwO0DYmiOcteFIJRmL6RG9cfIVYNPlSAeDRCIRcNRiNJWhCw8Tz8TQajUgIJ9Vl+cqyslKBcdxzmBwozelsTly+IZizGupQacx4J63inH6MaZnIHc9w/xZZv4QbubB2//MpRf0s2bNIv74q2t55q3/pvzsZeSSefoSSU7XjmIyusjvGcUTHyVfEWIkpaGiqoV+rYnCbh8FU5ZKk47A6CjxeBzMTqpqFjI+/CYym1I3BSrKSU4Fx3Fu/70dldPqMSaCBKKCtkYnhXw9dfPm0FcYwRKfTmL7n1jWYmRNvJk7/2kd11++l2demMNTP/40T2x6irJ5Bqo7B1ljm8ap513AwqY6Um++RU9HB2XuLL35AJWuaobMVRS6o2R1YcqlJBIIFO/z0OqpbzyDYc9mRDKIwawjnchO9eFRFGUKqOA4AZjNjWi0IQymPKl0FrPeSkOlE6NzHo3Ta+hOeSiLuBkdeI5ZtTpeDbj50he38flrdvLnV6fz5L/dwHM9e8m0jNP85mb+7AljXnYx8886G1M0z1sbXsHm3Uf36BbstS7G6tugJ002M4zW6yWXyRCLxTDojBjLZxBNBbHIcZJRFRyKcjJSwXEC2H9vh7vJBUEvgVQBu91ApbWZsumnsmBuK7sTXqo9LrKhVzHPNLEzYOKqGzv5ynVbeeXNJh657a/YGNaRcvah37yBoUCIZN08ama7qTE10Z3SYbJZGdy2BkshjnfOfPT5KkR6lMT27RTyeWKxGJWWSvxaLdJYhiXXTzyYnOrDoyjKh0wFxwnCYHCj1aUwmgvkClk0eSMin6HaNQ3ROJs57W2MZMdxD5uo8G5GW5cnbHAw79q9fOOTm3hjSy33f/kydlBFMuMhvuMFNLE42roVZNwR6gtGEv4Cxrbz6Ox9BYdMEJg5A5O9BY0+T/qNN8mn08RiMert9QxlQhhq28iPdyHT8ak+PIqifIhUcJxATKY6XLV6suPj5O16jEYzJAU17mr00+dTW9/GcCrFdI9kWrYbjxylylZJ25VdfO0LHWzdVcF//N0F9GjL8UUKePasQUQjNNYsIuiMoJVZNGNBbK3nsHvzH7Hl4wSnz8DiriJtNqHp6iIzMkIqnsKsNxPOxrDNmE90aBhi3qk+PIqifEgmNTiEEKuEEJ1CiH1CiK8eYr5RCPFoaf4bQoiWUvmFQohNQojtpf+eVyq3CCGeFkLsEULsFEJ8bzLbf7zRaIyYzBZM1gxhfwxnhY1ENIXNUEGdy4Zx5gKqa6vZndXiHtax0hFmRGynsqyW9uW7+eY/bqKzp4wf3noxvSEd4WgVQz3PEPH7qDZWY6qB8WQAbTAJ086jZ+Mf0OdixJracDTZCcdzWDQ6soOD6LyJ4m+Ya0C4msjlJAT7pvoQKYryIZi04BBCaIGfA5cAc4DrhRBzDqr2N0BQSjkDuAv4fqncB1whpZwPfAp4aMIyd0opZwGnAmcIIS6ZrH04HplMdZRV6smEfKQ0kqp6NwNdY5Q7G2ms1KNpnEelw8I+YUHbD2eaDSTNO2id5mbmrK3ceusmhoZs3PXtK3hjIIYpNRP/2E4Co0PISIr5sypIZrzkogWSdWfi2/QM+UyYRPUc9DOMRAfHsRptCIMBy1CUfk8XNpeRWNoGtmrwdkJePQxRUT7KJvOMYxmwT0rZI6XMAI8AVx1U5yrgwdL73wLnCyGElHKzlHKkVL4TMAkhjFLKhJTyJYDSOt8CGiZxH45LDkcDZlMI32gEu8tE08waOjcN4na301RvoFDeQoXZQK++gsxwhgUZI2mLl7qZBi6etZF/+Mc3Gfea+PW/r+bJnUPkbS2ENBqGe/YS7OylpsWKO+MhkdXjsS8itXstyXQATc1cUo1aMp5xDKEM5qYWiKbxdu/AYBSkMjqomAnBXkhFpvowKYoySSYzOOqBwQnTQ6WyQ9aRUuaAMFBxUJ3VwGYp5TuerieEcAJXAH8+1MaFEJ8VQnQIITq83o9W/7tOZ8dZ5SQT9xGKprA6TLTOq6Jz4xCVFXNobi+nYNDjMjvo1dSSDCRpDuZwVLrJtUoun/YqX/vn1wlFdNz3/et46s97cNlr0M5aypt9Oyh09pOvyTEjOUpGZ6VPzoTuNwkmQxhqpxOtN1EIj6EdDuF2t+KzaBARD7GeYaQQ4J4J6ShEx6b6UCmKMgkmMzjEIcoOfjreu9YRQsyl2H31uXcsJIQOeBi4W0rZc6iNSynvlVIukVIuqaysPKqGnwiczplYzAFGPCFyoRQWm4W6tjKG9gYod7RR296CNh/C7aygW7aSDvoxj8eZ1biA2HQ959au5fZ/foVMVsNDd36Khx7fQj6c5fSV1/Oyd4R0t5eAzUNbYghhqaAn04h+YCveVIyc2UpuZj0yPII+FKdO1NCrT2BvqSK4vZtcMAhl9aAzQqAH1EMRFeUjZTKDYwhonDDdAIwcrk4pDMqAQGm6AXgC+KSUsvug5e4F9kopfzwJ7T4hCKGhvKoZY2GEfYUMuUAKmzRgskE0mKfM3oy9phxtNkh1WRm92gXg6yTsSbK0ZRnx6SbOqNzIN2/7A1IjefiuT/LMM9283tnLubMWscdkJzZuoz+3g8rwbkyWckZTNehHdhMS4I0FMJw6j9xYHxYkjrgFT8qLtrYOKSHT10cBEzjqwdelwkNRPkImMzg2AjOFEK1CCANwHbDmoDprKA5+A1wDvCillKVuqKeB26SU6ycuIIT4F4oB8/eT2PYTQllZA2abDlNgL10ihbbcRJXbRTYcQZcy46xqw2jMYDJLyrSCQf1ydIG3GB6Jc0brmeRbCywqG+DbX38SnSnH/Xdey5aXgvx+YIRzSOJraURrPwdvYYRE34vkhZFcphrh6SaoMzDk6cKyfCmZnk6qK5wkfFFy+QSJvBFDSwv5cJjMiAfpai0OmhfUgxEV5aNg0oKjNGZxC/AssBt4TEq5UwjxHSHElaVqvwYqhBD7gFuB/Zfs3gLMAG4XQmwpvapKZyFfp3iV1lul8s9M1j6cCOrqFuAor0Hn2crW0QG0NgN18+qJ5BI4DVXYy5rJBzzUt1SjTaUZZQH6ZA/9YzGWTDsPU32QdssIX/3G85Q5M/zi+5cT2VjL/f09VA2/QrjSRa78NCqntRMa2YA3OII+YkX6h+hPF/AFu7CefjqpHduZXtfAeGyMpC9CNp1HX1ODvr6ezMAQsmJ68cxDhYeinPDEyfCjPEuWLJEdHR1T3YxJVSgU6OnZxGg2xRntp5PJZPGNRKhtdNPb8Qd8w1qaZ85gy659GExJqisFJm0ZVa4y9m5/Ck/MRldyET/70Wn09Vr42tcGKW96jIb5Lgo1p5ELJllud7J3z2Yc5hhu0zSGNWFiZjvnzmzFamkivn492VktRLJZtKM66hfUI3QaCuk0ufFxDPV14NtbHDzXaKf6kCmK8h6EEJuklEsOLld3jn9EaDQaZsxYyuzq2by09UWyWR8Ot4nx4SCtSy+lsj5M3+AQi2ZNpxC24B0vECNDKJ2iZfZlNBoTNJW9zm3/vJFTF8X47r800fn6DYR3BtF5OrG5nTwb6sU8bQbJ1HSS2W6adBocqSi/37adQKAf6+mno+8cgEISba0Rb/c4+VgGjdGI1uEg6/MXf1nQt1fd66EoJzAVHB8x7nI3Z847l47eMcKhTjBGCYwlaJh7AVVVQYYDQWadUk8uYyE8nmHUlyCvM1DVdi6zcwVMrpe55QvruWiln3vuq+XJx64n1zlMZGgnje5ZDOUk6UYze0PlaNBQU/DSIHL8aXAX494h0jNn4OwLkciMkDNoicZiZH1JNFY7SMjHYlDZDoFuyKun6yrKiUgFx0eQUa/jjLmLGMlVkkmFCMS2k0iacLnqsLqipISB5ion2ayOtMizdziAyVaHpXIJixNG3I1buPxvn2P1ZV384bl67rz74+j3jZLt3UYGSAs7FXMWsXMoT8YyHRdjVHkGeXZ8C7ZyB4WZM9B0jZJIDZLOQUQkyIZTCL2DXDBIIZstnnkEeiGXmerDpSjKUVLB8RFl0GpY1NJMwFhNmbWBobHN5KzVlGnT5Avj2KY1U6XVkY7qKegzbA+OUr18KXpTG9OHdSw2hrjsHwa46caNbHrLzW13fJzRwRFaIjH6/T0EUxkMsxaSHtRTbjmTmrpyXP1v8astD0OZk+YzzqHgHSMy1IdepycmUkRlAmFxk+7sQ0pZHOsI9kEu/Z77oyjK8UMFx0eYXiOYV1ODz2il0tlMKJwhobVh0fmI+AdoOnMJFWE/ybgLmYuzed9emq++HGv9KVQER5kX7GbVtYJ/vG0LI0M2vvvl61jX0U2bxcCAfxNjgQjjjY0Eh6LU5eexbOEnmBsa46ENP6AjNsS0U85AaAKEdvch0GJz2IlqUmQqy0ls20chnS+GR2gQsup3PRTlRKGuqjoJZAoFusNRzOMjmExuIiOvUzCH0dBGTetMeh7/PaPV8zHbPJjNZSxbcjr+vT2MrX0AqmwMy5Vs263nX783l4KEW7+0hsXnWRg0BIikmpijq6U9FcBVYUI2VuDvf4HOtJ9c3anMkmYs0TSGpB1jyzSq6stJp9NEvF50oSS2mgZ0LiMi1Av2WjBYpvpwKYpScrirqlRwnCQyhQK9iSTa/l4c1hqS41sJaYfRinrqq2cyun4dA5Y29GUBHAYTc+bMxyBM7PjdT9FqfGRqV7N7U45/+vEiggEjX7xlHaefNoS+SsumnJO6TAVL4jEqqmw45rcx1Pc8kbQXUbWYHFlMY15cCTuWprnUTq9BaATRkRESySQ2ixuj0Yi2MIRw1ILBOtWHS1EUVHCc9MEB+8MjhXagF3NWg84UI5D2kUzmqTEaiY3nGci4MbgzGA1ZGi12qlvnsO3ZR0iO7aSq9Sx6epz83zvn093t5DNf6OK8s7ZQZSyw3WzGaKhgiS9BXp+m5exljA+/SSjrp9w1D+FwkBoeINc/Sm3zGdS0t6A3asmOjJDS6UijwZI3YMyNo62qBqN9qg+Xopz01H0cCgaNhlaLiVxDC1mLjthojHJ7IzXV9YznDBS0Q7S6EmQjZeSSDkYyKXo636Bt6Xk421fQ27eNWdZNPHbnDpYvGuGXP2/n4afOoV+n59SEDcuwh/V2iVGvY+D1zThscxA5Ex7fDpL+IeyN02k6YyV7e55jX8cG4uE0+ro6DPE4FeVOclYIahyk+kcohINTfbgURTkMFRwnGYNGwzSbmVhFJebmFgJdAyChvqYGbe1S4pFOppcHyEkLiWQ1oZyZ0dAAzooGps2ezU6po3L0Ve7/xpusvmgPa/6nhv/48QXssCdobGpgZn+addEc/niK2Fg3c2uWUincDI3upq/nDUKkOPvKm4nkPHSsfQjvaBh9czOZ/n7sdjsVdZWkqqoJDfWTGRpD5j/6Z8SKcqJRXVUnqUyhwE5fgPqQh/EBDxUzHSDtFJJxAn07cNS049PUEU0msTq1uLVekqEoer+Xbl+YeXojkXSC//zTYu5++DSmL4jy+e++ydyZVbh2BNkd9lHIhrnwnGWYKwV6f5S3PLsZyPtYMGsls6vm4R3so2fj85S1r2D2tLmIoA9DUxNQfIRKeGAHMmXBXl2PzmlCiEM9hV9RlMmixjhUcPyFTKHA1tFxmsb78CcKVLQYKKQd5PMZIrs3YKqfi6ycTe+gh/JaJ+XGEEF/N7k9AaIxP3ObZzPet4vfvjmNf7//Slz1KW765lucsaKK5lCQ3r0xerx7uHjZcmrm1WBIjOLzBFjr2YylvoVV7ZeSi2cZ3fgiIZ2gvnU+dVYn+uqqA23MBfrxhKLEUwKzy4qw6cjLPHaDnXJT+RQePUX56FPBoYLjkNL5PFsG+qn1ekkLQVmdoJApJ5lKk9y7AZ27BfusFWzfM0ZdlRGz3UQ0vpHQW170oRAzGtrx+/fxx41WvnvfXyOMBa765k6uXm5ngT1K7/YIe8Z6mW63sPjic3GYvaTGPHQM9bPLEOSCORdRb2gg1tvJuGeQvM2Jq6kSo/PtULAmw1gNFUTiGvQ5DfYaFxEZJZKJ0GhvVGciijJJVHCo4DisRCbDjp5dVES1GKwCgyNNIaclHMwhPD1Io5naxefzxm4fLVUasloj2VwX/u0bcWRdVCZN5MszvLA+xB333UwkpuPcr+/hhnPNnObI4x0Ms6O3h0QuyrLqNpraq8kyQCKR4ZVEH3m7gTOql6KPZwiPdJOLQeXSU2munoZBayg2MjIKWj0prY2YJ4ymANYGJyOJEaot1Vj06v4PRTnWVHCo4HhX4XiCzn3bKM85cZTrQZenQJjRvgD2giArU7Sesoy1e3PMbbAQTiYIxjww8hoWRxmOLoG+3MSGnf3c/qvP0j9o46y/38fHr9dwRaUO72CWxMAIb2U7cRTMLKyvJp/xgE1LKGdnS6qfxTWLaLPWkY+O4evrwXzqfMxVTupt9WiEBqIeEBqwVZLL5ggP+pBaQcyaxGw2U22tnurDqCgfKSo4VHC8J99YPz2+AJXCidkMQiPRGjJ079iEy1JLXpOjbUYrL/QbmddcTjwVonfXLsrLEgjhwzqgwWxwsbe7l3/6r79m67YqzvnUPi78XJyrm9L4B3ToBwvEtAP4NDqm1bqpCI0hjVmMTicvB/vBXM7yijYcgTyDQz3YyhsotJZhNlhoqqxHl/EXG2srjoMU0nkS3gghGSNQCNJW24bJYJrCo6goHx0qOFRwHBFv9xb8BichXxKDUUO1Aax2J52bnsfhcCAsZbQ11rG2u8C05lq0MsG2N16naXol+VQ/hdFxyu0z8O/Yxz8+djkvr5/B0otGuPkbQZbVgz7jIjoQpxDuIW4BbXUlZdlxzLEkOpOZgVQ//QUD06a1c0oyRyQtiSXz1LbPxpOLYRM27OkcNpcRnfPtQfR8NEM+maU71Y9Zb6HcWo7dblfjH4ryAXzg4BBCnAnMlFLeL4SoBGxSyt5j3M5JoYLj6AQGu7Do8gRiRvrDUbQmLSazhVzndrS2Akanjvbpp7Nu6yDVtU2Ys2F2D/ZR5dRgz2cY927B7ZwGI3Fuf6CNx/64gsrmON//YS/ts5OIiIN4WoczOkwil8ToLidmSdEscgjhpH9gE+F8ioy9hlMcNirMVsbSGmqs5ehaaghnwjgCeYxmG9aat7unpJTkg2mCmRAxfYIy4QTAYrFgMqmzEEU5Wh8oOIQQ3wKWAO1SyjYhRB3wGynlGce+qceeCo6jFwqFMKSDiFSa8WCeVD5BQGcgMTKCUa+jvNLPzNmreGtrP2aTA2vUy2j5/2PvvcM0u+46z8+5+c05Ve7crW7lYBNsLBkHDB6CDbaXYA/LQxwDMwOzhGGXwcOYMLPLYh7gYUiLgWHAO8aadcZB2NiSJVlyS92tjtWV33pzvO/NZ/+o6la31JaMrez38zz1VJ37nnPr3Fv13u97fulk0TrLzEidVX+NhBiTipb42w86/Oc/+Q6GtsYv/8JFXvOWOtlBjtODgII3IFLHlIwsTa1PMmdxZPF6Hj75j7Tr63SCiKwwWEgbTGZrqA2bmcNHIBFD7/SIq1Uys2WE8vjKQvoRTmdEPWpQLc0SOiGe5yGEIJ1Oo6rTbWunTPlK+FqF42HgZuCLUsqbd48dl1Le8IzP9FlgKhxfHYPBAEUILLdHZ7OLHUyY2BMmI4cOSczKFktLN9DcEPitIYWEy6S2D3vlYdJjD7uUwe1/kdmoxr3rAe/6nddx4qEir75zk5/8j49QI83GYAKTMXbUppSoYTk9gkKcxMwisZjHcPk87eaAsK+wUEhTns3S7k9IzcySqFXxOiukxV5S5SKGpV01/3Dss93eRMtalNMVoihiMBgQRRGGYZBMJp+nOztlyouDr7VWlSd3FEbunuwrKl8qhHi9EOK0EOKcEOIXrvG6KYT477uv3yeEWNo9/hohxINCiEd2v991xZhbd4+fE0L8rpgasZ810uk0CIFtZCgePUYmVaKYMYj8MdVwQKo3R3t1mUQ1pF/WOHt2hOkuk957O0rOIlhvUqp9K9tmyP7MMv/pN/6CO99+kk//Y5Wf+J5X8sjDfebKBaxSnkKqwmC0xpql0tvsEp47x3ZTwS3Mkj80S/xQxKPtZT5/8gKbWp9wbZnRA6cRmVlGnKPZ2mTUda6av5rQqc0vYDoaF1fOEcmIbDZLPp9H13U6nQ6dTgffn25hO2XKP4evdMXxc8AB4DXAu4EfBv6blPJ3n2KMCpzZHbMO3A+8TUp58oo+PwncIKX8cSHEW4HvllK+RQhxM7AtpdwUQhwDPiqlnN0d8wXgZ4B7gQ8Bvyul/PBTzX+64vjamEwmuK5LNpul37BRJ+ucu/+zuGEcq7aEkemz59AdPLy+wtbnLpC6PU8xdSPVxr2c3PLZv+cg8Rhw4gvU8yG/9+BBPvjbt7O5ofOzP/IYP/a9Ht1qHs0PSTZOshnX6G63qSga6X130NZsEsKmkuixfHaV4RY0ZuA1cwfg3JhW2aJS1piYRXJylmw5jqJe/ZkoDALW1y+STuXIFQqXj0spGQwGAGQymefytk6Z8oLnmXCOvwZ4LSDYeZB//Gn6fwPwq1LK1+22fxFASvnuK/p8dLfP54UQGlAHSvKKSe2uKFrADJAHPiWlPLz72tuAV0kpf+yp5jIVjq8d13UZjUYUCgXGPRcpQ7a+8EG21zskFg5gFBz2XfcKzp2+QHtrg6CqkchcR77+IOf7ccrpPAuLedQH7mU1b3L3IM59f3QHH7o7z223d/nDX9hkUgoQRoy9yoB+XLC+vYrV6iJLNzGJmXhixLGsSmv0EO0LJlvS5mXf9I3MtkJWhz0Sso08eBQzKFDI5rAS+pOuo9ndxh1OqFXmUM3HTVuO4zAej8nn89NIrClTdvmaTFVCiN+UUn5cSvnzUsqfk1J+XAjxm08zbBZYu6K9vnvsmn2klAHQBwpP6PMm4CEppbvbf/1pznlpzj8qhHhACPFAs9l8mqlOeTpM0ySdTtNsNolnDDRDp3TzG1g8dgPO9jrj1T6nHvgYew8skDGqWGGOoH+cTO0gh6oKsr/GiYceYbhnlrl2wCtjLt/1S2f51f+yzokTae764YNcfDCPbmo81BdkmmOOLh0l2DfLHn2ZnN9HHQruOT8kjG4jURtRNkNOf+I+zpg6pWKexN6X4Zz4Ik7rPKvb5+k37SddRylXoThTZaW5jN3sI6OdzyiWZZHJZGi1WkRR9Fzf3ilTXlR8pT6O11zj2Lc9zZhrfWx74vLmKfsIIY4Cvwn82FfS/6qDUv6RlPI2KeVtpVLpaaY65StB13Xy+TzNZhMjppLMWsRmr2Pp6FEUtQxdn0c+/tfMH84QH1no+mFO9LaJpXRK1+2jmshxvh/nbDrOsX6f1MZJXnPXWf7y40Pm511+8F/P855fM1ha3Ms9Vg3v/BpH/DRnrCT7s2Nu25vmZUuznFyt05Q3YtaKOMk6g3/6POs9Sauxyd4bX4tQh8jBhLWNB1g7cZ7Qv1oILM1iz+x+OsaA5tYW4cBFSommaRQKBdrtNp7nPU93ecqUFz5PKRxCiJ8QQjwCHBJCHL/iaxk4/jTnXgfmr2jPAZtfrs+uqSoDdHbbc8D7gR+SUp6/ov/c05xzyrOIqqoUi0Xa7TYokvxMGjW/h/mZPHpqH2bqABce+CiJ3peIq3HSsUUe6adZ315lWJPMToYU567jc1aV2+OLnDhf5xvin+Sv/naZt799nb98/xzf+XpBraXxucphmlaG60cmpzojZO8s1ZTGm77lVmITWO0WiO+7gYu1Ds6Jz+Gs9zn52Gni8QOUCg5arsZIGXP64fsZnF3lSrOsEIK5zDxmMcGau8GkNSBoT8CPKJVKjEYjbPvJK5YpU6Y8/Yrjr4E3Anfvfr/0dauU8geeZuz9wAEhxB4hhAG8dfc8V3I38Pbdn98MfFJKKYUQWeCDwC9KKf/pUmcp5RYwFEK8fNf38UPAB57uIqc8syiKQrFYpNfrEQQ+kaEwMgAAIABJREFU5cU8FObIaYJMaR/SXMIrZfDuez+W0+eO/fvJFg4x6Iw4lelx7vhxbtq/wBnpUY3KfGRD45DV4Vf+i8Hv/sEJur0Er3vzPOf+co1lDE5Wl9iT3sOWY9A58TH0yOflN+7jRsNgtKwTlY9wcr+L66zQ39hm48SjbK+pzBsOeiWBVZ3lXNil/vBp3JUV5BVRVBkzw2JxD4P4hC29RWfYJmhPSBPH9/zLjvMpU6Y8zj+r5IgQogxcTsGVUq4+Tf83AL8DqMCfSil/XQjxa8ADUsq7hRAW8F52ckQ6wFullBeEEP8e+EXg7BWne62UsiGEuA34cyAGfBh4p3yai5g6x589Op3O5czs7Yt1nJUNYvuXuPjovSTVCa5rIvJpDt9wG4owaFz4Emtym60LXWaKNdxxwGc2Iqr5gB88ZtHP38j9Fwb8xr9e4LOfMXjtqy7yMz97H4mZCjPSIMwkUC7ej5krkC7O0GsNObU+4GIqwjL7HJ6E+EENYTvEg4jZ6/cTLVaRPvQ6I9RAY9E00FSJmi+gJq+OLB95I7pOFyGhFObxJh5e5JOfK02d5lO+7vhaEwDfCPyf7EQ2NYBF4JSU8ugzPdFng6lwPLv0ej0MwyAej7N9fpXRapfSTfs4//C9KM0NRK0IyRnmKmVShQJhc5Xt3pCTjSYZ0WI8DvlUo8yc0uHORYGd2kdDC/nwn+znD/6wRLHo8os/dw+Hr98kKw3yySQZJYUoz9J32/QGm3Q7HueFy5wqyNkdJloaI7GEcvECVrnKzE234yQddDfGxmaDg7N7SQmHyLZR4nHUfB6hPL4AD6OQul0niiKs0ES2fLK5HFrSQHlCouGUKS9Vvlbh+BJwF/APUsqbhRB3spOT8aPP/FSfeabC8ewzGAxQFIVkMknj9FkGmwG125e48MX7GJ8+Q5gRaHuOMJ8pEPgeSWVCrzNi2U2xqLY50znDxyYHuN10+JYDMfTEDMfROPXZMr/1y3nqdZV/+SPrvPX7z6AZE+KRwrw7JL5wK7FMjovnHmTD9vmC12ffXI75zQ7RcBNPi2M1h4SpKmrpMIW9KXLlGmvr2+iOxeEji+A5hN0uT3wrCFVBTafpKx4Dd8C4P2ZvZhEtVEAI1IyBUL/S+JIpU158fK3C8YCU8rZdAblZShkJIb4gpbzj2ZjsM81UOJ4bRqMRURSRSqVonHiUUSfGzK3z9Potmp+/j3GvS+qVt3FgYQ53GBJ21wkchxVjjvJwyNbG/XxUlNnj9SjkI14xX6NVmGNtrciv/0Kcj30kxrFbB/z7X1qhlD1DIC2W4goSg4WDh6jXlxl2PT7f7HLwln0E9RaWO2Ss2STOb5Awkwy1LElFUjw4S2zmMMsXmhyo7SVfe3L5ERkEhIMBkT0BwA89Lm5fxLRMSvkZ4kYeoeoITUFJG1NT1pSXHF+rcPwD8F3sZI0X2TFX3S6l/MZneqLPBlPheO64lGWeTqVoPHIc1y+Q21vCCYd0L15g+wtfovRNd7B4KIeu5RivrtCtr+Puuw2rPeT4Iw9i12aYCzY57wYcTk6I7z9EFBzhg39t8uvvSqCZIf/7L7e48WUnaLY22VuYw5AWhtpHMSLGaowTp9bZd+Aws+U0g3qXnr6J315HuCr64h04FzewhuscvPl6Gr5HQptjfv+BJ9W7upJIRjiBw3Znm+ZoC9wxeiTIqlmEvfs+MgUiG0NJpUARFGNFYlrsObr7U6Y8s3ytwpEAJuxEYX0/O2GzfyWlbD/TE302mArHc8ulLPN0Kkn74ROo2Rn0bIpur4sSdDj3ueOUFxfY/7J9SM1D7Uesnz+JUzpISo/zsc8/yKHqPPuyHY5PesjOkNKhORyxh82zcd79KxUefkjjW19l85/e1cJ2P0Mk4mjZWxiOz5OljZtP0jw/JivKXJdXCaM49ahPJlyn3R4yOXwdk5hJ9MgyCTdEVDQQHpXaDWSqhauq7V5CEQqWZhHTYoROSBAEWEmLpr2TYFpJVFAmEPXGhIM+UkZ0lCFRKYFiWlTiFXT1ydnsU6a8UHlGN3LarUP1VinlXz0Tk3u2mQrHc4/v+/T7fZIxi/7yGmpokCrGqNuSoLfF8kqHtBZy4y1HiYoq/lad0aTL2Fxk0utzz3KL76gVMImwZ2zOPXYCI3eAfOkoQ9Xm7j/O8fvvKRD58FPv7PN93/k5MnTJVe/isfEa9UYDJRHi9HsI7TruKARUxhHLqTRicpZYa4i+8CpWrS5Nu0dlvUMyWcSND8iIGJnKYaz04xFXiqJgWRaG8bhJynVdhsMhhd3aV9v2Nn7okzAS5K08MpKEY49gq0nou7TdLlHMRMtnqBRq6NpURKa8sPmqhEMIkQZ+ip2yHncDH99t/zzwsJTyO5+d6T6zTIXj+SEMQ9rtNulkgkGzg6okSTGiOxhgjzqsdhO4nQ2++Y4j6KkUzmCLrnOG2Nxr+dJDj/BYa8j3L+XxXIk3m2Z780E6E49E/jXEF0wuPDLkD357nk98xOLIYY+f/dlHuWnxPmLFO0mkB6wNh7ixGIPWGr1mCmu+ys3tLulckr63Rbh2gcLSKyGV4FG/i9JvkZUW8VIBTRtQ1cqklg6hGhphGOI4zpMyysMwpN/rUS6kSeCiEDL2bfpenzBVRVENClYBS9uJYg97Pdx2h2a/RaRqGPkCpXgJRVNREzv+kilTXih8tcLxAaALfB54NZADDOBnpJQPP0tzfcaZCsfzRxRF9Ho9ZBTiD8YYVoFsNUHnzGmGW+fppw5SP3mW667fRzGpQxDS9B8gtfCN/MPD2wTDHnfGLZIZjXGlQGdzg/7wMez4HVTm93NquM3yJ9O8590VNrYUfvAHhvz49/wdxX0307YHdDUFOR5gosCmTSMGi5GJIzUMdYgXjZnfc5hMfImtboO6vU0QtNlXPYavj0iFEcVEmcTCPkTowaQLofuka6x3R2jJIrq548/QFEFKDohCnzYhjrF7XGgU40V0RSdyXSbbmzScFlJCLF6iGK9c5WRX4hrCVKeO9ynPC1+tcDwipbx+92eVnSq1C1LK4bM202eBqXA8/1z6ZN7ZqpNOz1CazzLYXqWzscFE5uieO09uvkIlWUK1W4zMDVJLh/jzL2xxUzbBvr6LrnaI33GMzuqQ7e1HcXSFWm4/9wQqqbHPJ//sIP/1z3JUSgH/9vs/xNve5NB0DGS+TEd3MYMkomdxyq5zWwL8Qhmxfp6tzoh4PM7+oy+ju9VksL1BT6xg5vIcKFUZOQPmMEkUK5jzR0G/9ja0vV4PXddJJBLYto3neWSzWbA74PRA0fCTZdpuDz/ayV43VZNirIiIJOP6Bo1xHSkhWahQys8jJyHSDZFhhJa3puG/U55Tvlrh+KKU8pYv136xMBWOFw5hGLJy5iyBZ7Dv2CL21hlajoKnF3AeOQl+k7nDLyfst+h3jlO941W8577TvHFfmkonjt9+FOuWg0w6I5otha7f5qjm849ykUC3CZdT/PZvHeT4ySSv/IYV3vW/fZrYQplcej9rco09WhVlILiv3eegqRDKEeNxC0O49DY6LM0cILXnRpbPNDGiBivJLsViBSsCfRxRNWOU9u3ByFaveX2j0YgwDMlkMpeDBC6Xag8DGKyDjCBeBCuNG7q0Ji0iuVOIMaEnyBpZxu06ze5OIehUIk+htpeo46LENZT41Dcy5bnhqxWOEBhfarJT5sPe/VlKKdPPwlyfcabC8cKjW9+mvt6jsreEPlyjESQJEyWs7oDuuYeoJEoklspsPnIPsnAT/9OZ8G0zPjWvhtJbwTN9ghj0ybOlGBxTBjzmx5GZCsPOkAfeV+A/v6cCRLzzHf/Ev/ihOvPlQzw4OM7NucMETZvTw4g9hVmWYhEPNzaJ9JC+Lyh1A9KxDANRQnaaxGd8trIexXQBMXQxuxHZhIpVroG58xYwTRPLslAUBcdxLhdI1DQN13UpFAooV2SmM26BOwDVgPQs7JqiRt6IntsDQCLJmTnCyYSt9VPsn70BocSRkUTLms/p32vK1yfPaFTVi42pcLwwGXV7tDcHJAsGbneVoZpFydTIeh6d9QvotkdpLk9n+V7OuntYjaW5uTZhRhqk0vNMRueRbo9e/Ajr4Yia0aM+GHPdzF4eHUg2Tjm89z17+din0hw9sM3/8R9O8613HeIz7QdZMI4QtNss1zdQUwUOJyP8ice4cw6xdB0imSOz0mXU8ulaGQ6oI/pHk4yli2aqpEcWKVtSrsbRi3O4kcpkMrnq+i5FYNm2Ta/XI5fLkc1mUVX18U6BC4NNQEKyAsbjkVxSSnpuj7E/xo986pvnuD6+j1hlnmjooxVi1wwbnjLlmWIqHFPheEEyGY3ZvtBgbjHBdrPJ1sAjXdtLRVfpXFgl8kfk5svYF+/lU2splio5RCZOVU4o18oEkwi39SWC7BHqSgndsOn2H2NvPoFrw4PbCo9+IsEf/v4Rej2dt775PD/77xxGxS5HE4fxxzbrK8s0wgQzKQkpi42HPsuMqhPV5snuv4Xgcyc433EpJ3RmDhdoZCIiK8LzXaqjAnHfpjKbRsktgmZcvjbHcS6LiZSSfr9PPB5H13dMTbFYjFhsNzlQShhtg2+DFoNU9fIq5BIjb8S5xilyXQ9RLqO7JsVSFT1mMGXKs8FUOKbC8YLFcz3WT62yOKsw0dKcPLeCka9ysJSneXINNekREmLQ4H2PKbypoNHTNAajiHBPkvTAx+s30bIl2hOdcbKEKjrcXBNk9IjNTpfjp4a8948P8/f/8wBzVZv/8K5ljn77iBvzN9Lr9HDHI06MhuRGE+YKMR6on0M0WmRCSfXoy9AmOvXjF7AVyVI5T7A3jszFGCtjFF9Q6GbIGCMKlTxkF0F5shPb9302NzcxDAPLsnBdF03TUBQFVVVJJpM7qxHPhlF9Z1Bq5ipnfN/t4wQOuW5AqAk6UUBEiEjpxPU4OTM3jcCa8owxFY6pcLygCYOAleMXmau4hPm9nL2wgrCSlOMmk/NdEosmrdWLSGPMZztZqqbKTCKBtlnHnM0hkkPaGw4z+45gtzoMjRi2lebm9JBkoYJ0bY4/9gD3fKLP7/z+v2B9NcPrX7fBv/nNLV59/S00m02yMsFjckCv2aEaCwhwWW4N0NZOksuX8NS9hMsNFH9ILJRYs7N4ByzS1SJtt01sYpEcmJRTDqnqPCSK17zWSwUhY7HY5fpeYRhi2zaWZaFp2k6petPcMWOFLig6JEqgW7QmLRShkPE0glYbrTyDdCKcdHjZPwKQs3Ik9MQ15zBlylfCVDimwvGCJ4oiVo+fo1IIkIUlzq9ukClUiIUe7VPblK8r0lg+y9hrEk8t4fWGBNU5/FEX6RkklFWWRxEyv5+xMIj7Q4jHuCtnoWUj4okFeu0tPvOZ/5e//ftv5G//+hZMK+Df/MpFfuzHMghHUlQz9HTB1sBGc+uM7Qv0tb3obo/86ATp7EEeO5+g7XfY31jFcyKiuEL6zutJlAuMgzGiIzCGHfLZJMV9t6Aq6pOudTweEwQBmUzmqusfjUYEQXA52TAWi2FZFqlEDGXSgcABoGk3ielxEokq3nYfNZtHBgZazkToKlJK2pM2A2/AyB8RRAEFq4Cmapd/V0yPUYxdW9ymTIGpcEyF40WClJKNh0+QKcdRshXOrW5SqlQpqhoXT62iZ8AyFbY2ThKRpBwk6HkqfiYkpReI9y7QDYcgU2xXrqMZurSweYWlYxY19FgaIRROPPQpzpzN8Bf/1008cqLCwYN93vnOdV7xWpdsIoMjBJsBVAOYRGfYbBmE8QJle5MDKQ+3neaLyUXoNajYNoNT5wgSE7L7S1izc8zOHWG0VcfpryCKs8RyWVT96jBaz/VwJg7FfJG4Hiemxa4SGSkltm1j2zbD4ZB4PE65XL4cnbXcvUAiCpFOj6DbQfo+ilkA00AWC6DqmKpJUk+iCY2W07qcP2KpFpZq0XE7FGPF6cpkyjWZCsdUOF40SCnZfughrGoJLZ3j/Po21UqZgtTp9Ac0tjfJZDRsf0B3uM3RTI3ATrOldXHVBLOBRyNQcDcv4AZV3GyJraLOwqRPPiWozCZBCRm2WpxZ6fKBj9T4H399iPpmmgOHR/zUT9Z5+7cbGCLNBV2iezZSX6U+9Dnd6qLJIUdTSdIdDyVXYtnMMxNayFafleUN9OQAQ+9zw62vI5kq4zdWkfkKSImZTBJLpi5fq+/7NDtNYukYTugQyvCqe3HJXyGlZDgcMhqMSCQSKIpCKpWi43U4lDuEoRpErou/sYGSzCAmQ9SUvMLfISCWAzMFQjAJJrQmLQC80ENXdGaSM2jKdJOqKY8zFY6pcLyokFFE80sPoRSrmNk05zdb1Mp58r5OlNbZXN1G8XzG4zGrnQvU7AaV4s3IkmCrtUEiUUGNV5BKm/ZqC9XJEi3lyVgGDFo4iQntsMXh2BHslTM85qh86O4Y7///bmN7PcnB6yb89M93uOubB7TMInkb8tE2scwMj211uehcIC+75Nw0cWvMiiUJzQwLRp7Ooys0JjqKsUIxkeDlR16Bu7GMzO/FrGbxPA9V10nmCwghCMOQTqdDPp+/OlT3GnieR7/fJ5vNMh6PCaOQ9dE6x2aPoao7Jip/YxOhaqCm0Aq72eZRtFMuxdst+hCFkJkHzaDv9um5PbbtbSrxCovpxefgLzzlxcBUOKbC8eLDd2idO08YS2JlM1xs9JnJp8lGJlKBXq9LLG4QIll3fYxz9yBGWcxDBxlcvJehbTLOLzFXStG0N4mLPIqvkzAFlYSJkmxz//gkS7XvQFk5Tdx2OHd2jfeeuJ3/8VfzNNbTHLne51/9xCY3f5eDJI3Z75Iu1Gi0fcb9NuHgMQqjFMW8hVlUaIQT1NkF/JVVNo9vo+YThGqDvYduoeRMCOwkqWwGzYBRv4eaTJJeWETV9J2CkOk0hvHU4bVSyst7vcdiMdzA5czWGWYTswghSKfTMB7jt1qoyTJq0nxytrmU0FvZDf2tXD7v+midjdEGWTPLgeyBa/pnpnz9MBWOqXC8OBk16TZdPBmipROsdidUMyaWrhMEAcPuABOBb7t0pEmqfx5/e53EgTuIvFV6GwFbto5npvC9JsmMgmkUSCsRcU0nbvRoW1sUMgdxRA7ZHyDWzzLRZvjjz1R5/18tsLWW4uh1Pv/rv+tyw7e2yQxaxDJHGasqddtl2Fkm35gQD1VqJYlvD6G6QEtK2o8+jBOEJL02+2+6iVhCwRBzBDJJImeSlBHj+hZRGGIlEjgSkrUasVTq6W/NriM9m81i+zYdp8NMYobhcEgYhggpsXo91FgWJZ68dra504dRA3JLcMVeIU27yXJ/mWKsSMpI7dTTmob5ft3xvAiHEOL1wP8NqMAfSyl/4wmvm8BfALcCbeAtUsqLQogC8D7gduDPpZT/6ooxbwN+CZDAJvADUsrWU81jKhwvcjoX6HkFPGdAZKqMlQS6pmPqChljZ9fBmKHjjsd0lSSpYZ9w7R6o7cVkhKPO0K+PaXsmG5OAubhDFOikPQvHnWDZF5HJMVL3SWQLBKSZ+A4pYpzvwacfWuDP/7TK1mqK6456/MQveXz7Nz2AGxSIsrOsj0Jadp/kZh0xcNBKBqoYcWOhyDiWYvXEY6wR4W6usFfPYS0ZhOkMuphDhDpGIokiBKEzQYtCJoMusUyGeCqJUARKMomWTDJnPXl72kumq3w+zygY4QQOlcTOCiKKIobDIV6zSWR7pItzWNXUk7PNpYTuMhgpSJauOCypj+uMgzGGsvO7M2aGtPGiqDQ05RngOReO3Wq6Z4DXAOvA/cDbpJQnr+jzk8ANUsofF0K8FfhuKeVbdnccvBk4Bhy7JBxCCI0dsbhOStkSQvwWYEspf/Wp5jIVjhc5UkLrLAMxjzfpESghRiyOalgMPJg4DlHgM59PENgjhnoaqzfB7D6EnwqQkwAvM489TqO4HvetdCjtTVFKSGb0FM1ejEmvh55toAwHRJ01bNvGdFRqs0dZmRiMrBif/FyaP/uTWTbXkuw9POKnf3KZb3/FBCMh6bgajShGMBhSkCbDSZvupEe5mOPovsM0HjvNxcEWdbnBdX2TomYh9laYVCrEfJ18LotmKYxGE6Sj0msM0ITKwtIBhD1h0uuxqSvUsnGytSriigTDK01XY8YoQiFv5a+6haHj0Dl7FrQMai5OqpC5nMF+mUkXxm3I74ErTFR+5LM12iKux9GExtDf8ZOU42VMdVoz66XM8yEc3wD8qpTydbvtXwSQUr77ij4f3e3z+V1RqAMluTspIcQ7gNuuEA6dHeG4DVgF/gD4opTyj55qLlPheAngT2DUYBCVicIJMpwgdQMUFV3XCSU0Bu5OkcFhn2ShhNV3yXh1pLWJOx4wMEq4bo10qcyXHjyDEvMw58rsT3hklVkayyO8mofn9wkdjY3lzxI1lqlkiljODHa8hD9xef/nKvy3D1zH1laKA/u7/PQP13nzG0IctUdz4tGvu+w3LAaazpYzwgls9t5yK/NSZ61hc693mjlcDjdtLOHhFDL0Yyli2iylUg5w8P0B/eGY9uY2McsgV1lgbvYIG+0hrtNnwVIRiopeKSN2BeCSicrRHRJ6gpRxtbnrkuM8csGJWcjYjvgIIUgmk2iatuNE7y6DlYVE4arxQ29Ix+lQipWIaTEadgMv8lCFSiVemfpDXoI8H8LxZuD1Usof2W3/IPCyJ5idHt3ts77bPr/bp7XbfgdXCMcV5/1Tdqr2ngXulPIJMYxPYCocLxFGDVA07CCJ74Y4owGa4WNlMrief7mEuaFrLK/UsY00Uc9l0RqTjnXw3XW6WpFeM0aitp+N7hitu0kgQjS3xWw8id3SSOVUAtkhVigw6kcsP3oPaHUcc4Fk+hCZ/Ayxicd//YDkve8/xvZWmsOHbH7k7Vu85c0WA79FR4nQ7QnJxk69qs1OBzVvUtg7S9FJci4Ja4OLvCJWID60SWSrBO4GHUUhkyxSm1lAJIp4u1vwDhrnGA+6XP/yb8Ppu6yNXSo5k3i/iwwCALRSiUBR6Pf7jPQRtWTt8s6DVxIOBngbDfTqLFoudtmkFUU7pd2FEKQUD9UfQm7Pk8qnNOwGTuAwm5xFVVSCKGDb3kZKiUSS1JNkzezUJ/IS4PkQju8FXvcE4bhDSvnOK/qc2O1zpXDcIaVs77bfwZNXHB8BfhS4ALwHqEsp/+M1fv+P7vZjYWHh1pWVlWflOqc8x7TPQ3YBVJ0ojBh2HcbdLkIJKS3U2NzaQtd10qkUTr8LsQJbzTFWMEBniME6Ip2g144x9IqIUg6LiEBTcPweSzqokzy5uRTBqIPnt9BSVVoXW6jrH6Ye9BiqMzQzB9k/ewBjc8Lv/V2L9/33I7TqaQ4fHPGj/3KZl7/GJ5MoE+pDDCNCtpo0Lg4YtVy0YoHI9ckdTPFob4XZQoZ9rS3Y+1oqmoI9atEa9SkVk1QyOcIooj8J6E8imquPcuzlrySWKLPZGONEEXvKO76QoNlEuu5OQcUooh2bcKB04Jq5GTKKcM9cRMTimItX7y0ShuFOKZTAh/46SjxHsjR3VahwJCM2Rhvoik41cfX4K0vDA8S0GHkrPxWSFyEvFVPV7cBvSClfvdt+JfALUso3PNVcpiuOlxC7/g7SM2AmLx92bZ/mah0pJXrGxIqb+J6H3e2Qys3ScyPmNZvJuEEviug5a/hKgVEvj5Yw2Ttf5mLfoRXaZMctSmqNRC0NCtitNTxnQhClUOwmYnQa1/dY8wVh+RDzVh4/VPm9vxnxyb85SmsrzuLihO/6tjXuvKtOLg6VRBY9PmbY32Br+SymmQG3hptK0HAvUkhWqKrnSGT3IOcPULFgUK/T9ySVYzdSNRNEoyaNZpPlU8eZO7jA3JG78EOFi40hBUsnn49dfjgH3S79+hZrwzWO7rsNLX/tB7e32SbsdrEOLl42eT2RsF9n1GsSpXb2DVEU5XJBxkkwoWE3yJpZMmbmmuMvRXxJdp41MS1GwSpMheRFwPMhHBo7zvFXAxvsOMf/FynliSv6/BRw/RXO8e+RUn7fFa+/g6uFYwZ4kB2HelMI8S4gLqX8t081l6lwvAQZbELo7VSiveIBFIYBjQubdLtDakuLxJIqmxfPo2tZJrEEe0wfuhfQF6+jsf4AK+MxHfcYo8GY2ZSBrij0shadQYNbzTK1PWWsuE4UefTWT+GPNEJXI62tYVlxNtbPsi5iqGqJwmKVM9017rl7kbv/psaZUxl0Q/LK19vc+b0NvvnmCTORRS6W48LFh9nYOIUV6aSqBzjvDzD9DLOso0488rXrMctpCvqY5vnTtCdNjnzzm0hVZ/A9j5Of+zQGDQqz8xTz87RI0XcM9qQttNTjDuvxZMzp5Yc5Ep9FVVWEYaKVS1c9tIOBS7C1hZZPoJVKXJPQh+4KJEsEWoLRaMSlZ4eiKPi6zzgYM5OYQVefeofCS0JyCVM1KcQKKGK6Le4LjecrHPcNwO+wE477p1LKXxdC/BrwgJTybiGEBbyXnQiqDvBWKeWF3bEXgTRgAD3gtVLKk0KIHwd+BvCBFeAdl0xbX46pcLxECTzore44cWO5q1/yPS48doaklSOezjDuNVAigw0VDiYFsd4y+pFvYrR5kvbwBFr+CFvDOP7EQhl6WPicilqkpMW3HDtCMruzb8agu4bd2iIc5rDcTXJLJfzOiC2nQXfgYSbLrOl9okyVlQdV3veXKT7/DwvYY53aosur3jLk297c50Beorg+an2Tze1NTEXDT4UMiVO18njtbRS1QDa3H11VWTyQ4ewX/45CfIlsfp7YQpmNzTUMNSBSXVJWBksVNFxJOpDkKrMo6Z0VwMgdcbFxkX3FfZiKQtBsQhCgzcyg7CYbhgOP0B4jJz2M2VnEl0tCHNZ3Ci1eIdhBEFzOKZnoE1RVpZaofcUrCidwaDvtyz6fjNMOAAAgAElEQVQSUzUpWIWps/0FwDQBcCocL11GDXCf7MiNoojtrU1MAQiTYWNATE2yYUGVPmZvndytd+L02/Qax8mmkvR8hbZM4ToBQdfHjbqc7cPh6gLX1eJYiQRSSsbDi7iugtnwyOR1hCqZeBoNt4URjphoKiPVQE3lObc15p73m3z6Q/t49NEcqhpxx109vuttLfYe3WTUHuKNxgzMAiEOkdeglskyY3h444hEcZG0UyWmx/CjRzEMkxTzRLZNc3uDzNIcwpygJVIIkWYQRIjJiFrkoCVNhKYw0ON0bZuckSOVSoEApdfEzMTRizsVcsOBi1QEUa+B0A30Svna9ztwdwQ7Vd2pfbWLlJJut0skIsbqmLSRJmflrn2Op+DSPux+6DOfmp8KyPPIVDimwvHSJgqhexGszFX7YARBQK/XIxWPM+51sLt94kaZtUhQjLpo/TW0Azei6zqDwQbZZIKklHTGHn03wvaSeOMm54drmMkqtbRBKfJ2KtRKlch0iE8MkloKLbIJA0nTLBCOzhN5DoYf4hVK+JkiJ7odJmcc/v59C/zDh2fpdVXm5iJ++AcmfMcbzkL9PiaKSn+pwtbaFtItosQmqEmNwbDHAln2VG9DU1uoUZ3Dt72RKIw4+4+fx1RUwCF3pEgiv5f+0GNj4lJSLCq6jmoM6NrbhH6AGpqkawfwfZVJo0M0GqHPzOzUzRp46AkdwwqQ7Tb67AyK+WVyNQabEAU7Na+uWF14nsdgMCAyImxpU0vWvqp8j0hGrA3XyFm5adLh88RUOKbC8fWB3dn5yi1eLqHheR7j8ZhcLoc96NN47Bz5mQVahoXV3EIfjqA6jxtF9HrrICCXn8cwNHyny3DoIvoeG/qQblRiz74qmjcmNdrCGQ8JtQ56MCGuFqiUDxNtbRIlqng5SUeGBNsNvF4DYSZpJipIX8Uab/GBT1T58Ef38aX7EiiK5PXfYvN933SKYzOP0juUZdvoUNTKWBsNnPwsF9U+G3WHQzKHHgfRX+PosVcQX1yg0WmjRgK51cT3OmRyaYqHb6JtO4wchwVfkMtmaRk94opB1NhEVSCVTEIEXtdDn5lDSSRwmjaeHyF1hWB7GzRtZ1UiwIzrGJb6uBnKn0B/fSdYwbi6NPtwOMTzPBzdQQrJbHL2q3KItyYtvNBjJjnzNf97TPnnMRWOqXB8/SDlzupDsyBdA3b2/3Zd9/LGSRsPnUCLG0yyRTJ+i6RUkVJDn51lOG7Q77XJpJawxxPCIKLdd2idb5KI99iY6BTnqqipHLHQJTUJcMMIEa4T9FZJVPeQVoeYagoiCxl3Sc/fxnZzhfb6ScZWghN9m8OWSjHw+MyZOB/4xDHu+3iNRkOlWgr57ped443fO8GYWUFPFvCjAdlBQLdscao/wQqTHEo7rK0+yJJS5WB1P0N7jAwD0pkaAz/Aj2wUK49MZNku5lBch7gTMVSHzFTnUKSKPRpRMTRKmkOwvQmAXioT+BmUdBLF0ojGY/ztBlq1ih9peE7wpFuuThrE4yFCv3q/9CiK6PV6CE0wYEBST1KIFZ40/hJDx6dn+5fbc7mdSLFJMGFrvMV8cv5pne9TnjmmwjEVjq8/nAGMtiEzB3qM8XhMFEU7Nn6g89gKUQI6HqQ0l2qxhN8eIjQNWUzQbK5RKOzHsh5Pojv9pS1adoeR3cJMx0lqKnXHY65WY0a1UByP4cojOH6ObCVFtjLBi+KM6w8TV+LE4jWGTPCIOBUlqff7LKkuycjkhB/j3i/OceIjNT79cZMoEnzDjV1e+52rvPambYKZGDV7hMuYdU/j/nGBfdkMC+IszjikWDuEGvkkkOTjJr21i4jIRZEBsg1jw2SSzVLIZeiOhmiVLKQNBkJh5HnoqkZC0SgPh5TLGbSRRIupKKYC8QJ+e6fUiD7z5E/+gRcy7nsQuKT07o6rSdEgVQNVw3EcxuMxmDAMh5TjZTRh0Rq5hNHjz6CEqZGL6wghcIOQtc6E+XwMU9spGb8+XCdlpMha2Wf3f2cKMBWOqXB8vSLljikFIDPHcDRCVVXi8ThSSnqn1zGqKVqdLoEM2FPJgZYkqNeRCY1eNMDQa2TiKSIn3Emc27ZZ79s0BluYhRr7ynFWz55iPYyIpXRu3bvEYPMcowtn0WSWfCZNZmmRcThCigBV+ghFMPJGDM0Ua0qNTLCN7G2Q8jXun1isTspc/MdZPvSXKep1k2w+4HveuM6r7zpO8bAgKRw0Y8zJVYOTao1Zq0F51GZm750Y7gDhjVk6doS0jOOMBphpD9U3cDdtli+uIyZDcpGClk1ASiDiedRCkZ5j05EhbreLmk2iqnEySZWMHKAEEyLXJWy3ETN7UDIlJKApGjEttuOHkDDsOkShJJFS0N0GRCES6KhFtvsTwiDA132kCDhWXcTUrk5QDCNJc+jihxFSSpojl2zMoJa1MDWVvtdl7I+ZS85Nc0GeZabCMRWOr2/8CfQ3IFWh70SYpollWcggYrjSwA9deo0G/VBSy1jkZ/bAxCHotrCtCVGiRqFSQjO0nZpPDZtxKDmzeoGeHmN+ocKc4tEYTlgeDikkTJaSeeoXTqNEdYKuQ7I8h5JMk1AMEmqFwGnjuHU27FXOxxOo6UPE9AgxbJJxJpzrKJiZBCv3Z3jf/5Pl3i/Ooqrwuld1eOMbTvCNLxsSVGOo2zaPDuI0MibJ7YeYr93MUGp4rTqze7JYKZN+o48VT6HoIanYArqZZlDvkF/vEuoxlIwk6XcRXkCogxcYMHYwVHASBUaWijAUhGmRz+coDeoo7hC9UiaQIY4QdFUNS49RjpcZuz4b9TG+H2JaGmZMJRd2SGohYRjRCwz0ZIae7GEqFkRpvOBSyRMopUxMbSeayg8j6n2H9tilmDSRErzQp25vUYlXMdUvv3+JqggsXcXUFCxdRX1iZeApT8lUOKbCMQVgsAWBQ4cMyWQSwzCQYbRrk5d0NjcY+j44A3KFnVIaXnObyfgC5K4jX50hmUohI0nQtAniGhvn1unoHm2R44Y8mEIyVk1WPEHF0kk0u6RzGpPGWVrtLQaFCpGIY8VmUbyIlB8RG7Ro9M4xUGBm72FspYWmWUz6kr4bMquZPHZc8scfnONTH61hjzWuO9znTa8/zqvedI5hIs6krjFIWgzbyyzqB0mUF1lfq5NPlUimJR514lqAnvTRFANPyTFUNPb2XUR7iJfKkN5zCGFHCL9DXHEYOkNEq00mdz1qPkfkO3TaTbqjNnrYh/EAM5nCCANM4WLPHqAfeaSLCxwozqAoAmfs44x9dFMlnjaQkaTd3GDU6zBxXJR0GpExmEtXnnLv82uZrjbHm5iqSTFWvOYYP4xwgwjHD3H8kCc+7tKWTjqmTVcuX4apcEyFY8oldrOgWxNBtra4UxV2Fyklnc110HUGwz5Lew8ihCCKAjpnP4PdjyNzWTLpHbNM0HEwqxlam2OMxIjTdhYlHDGfUGhNJtixNE2pkx7ZzOXjLBZy+Kc+hzS7OMkklnULmohjCYkf+nTGTU6dehjTM6jOFhnIPkIJiUIX2wnp+ylaQYJP313ino/uZX01RjE/4Ttf+wivf8syI12hK0LsaIWSq1Mt1pB+RKZQJhnEsN2IodtDpCxqKUkqlWTDU0h7CbSBzaS9SZDRcfNZBpOIaBxihpJi5zGqCZP0viKoCn1ZZRimCfwIp9MjFAHEcuzrXySWzaOWkvTDEUkzQ7pwkOYkYjz2cYc7ZrqFuRQxc2f11m+sIicDQt3FURSq5evRvowDXErJendC3FApJHdCfPtun77bZz41/88SACklg0nAwPGvOq4qgnzCwNJfuPkjUkrcIGLihThBSBBe+zmejeukrK8+mGAqHFPhmPIE5KhJa2uNwv/P3pvFSnbf+X2f/9nPqXNO7Xfre/v2wm42d1GiNBpNJnYmE88kAZyMMY6dBAbGSGAEifOStyB5SAIEyWMC5MkInMB+yGI7AQaBY4+TzKKZ0VDUaKNIkc1m992X2qvOvv3/eahWk5RIySYpySPdD3Afqup/qs6999T/e377zRfQjPe+XEop5uenOC2Hs8sR1/bvPtnkkuXbMFbESqd/8ya60MjOl9R2xeQ0oiwvwetwXll0PROtzrnWC3iYVhyeTrhrG9y4tUU+mVFdHmDtRLj9uxRlB10foucSt2VwVC05eOubbJoWHa/LxKgIohluWXHpbfGu7jE6X/Loa33+yT+6xre+GmAaDf/Gr57x7/3GjOA5eKM+Qs0v2Pav0YkywqdeoLO5Q1jWRKszjrIli3iG3TIonJK7nV22cNGTFG0ZYbRsjI0BC1nznVnJo3cvaUYz6r1N+kPJ9TCk5wQIzcQQbbTxI0auw2a6ZHk8p7D66FsBjTZnLwwZtNrgb9JoNvGsABR+10E3tCf1Nq4hWa4eYOomw94dcD88CD5LSuK8Zu9xf65KVpxEJ2x6m3im94mui7qRzNKSopIfeN4xdXot61Nzd0mpqKSkkYqqUdSNpGzkR4rA92ObGq6p45g6pv7jaddyJRxXwnHFhyCbhumjb2NZFp7nYXaugbH2mc/PT/EDn4uLE9yNWwxCF6UUWXaAXnosj0c4wyHBYIN6nmMOPZaTjNnFCX5PQNOh1hVHlyOE0LixEfK1kylJVPLLd7ewdIgPD1HaJa7fQlkOlebRFD5aaWO0WhzLmHp5QiurKA0PZUQMLlN6N5+jdFocyYb6bMzBRY+/8784/O7vDMkLg+fvTfl3f3PCS//mnIPpO9C7SX98wK6w8G5/kXa7S1sKAlFzcfIuyyLicHmI0Eq6fg+zO6BONdpS4dh9hrdv4fsuTVWx+qM3SUObS0ej8QVK1JTljGWaUc0jEtHmX7jZo1fMWaw2qeOU3Kiw726wLQQu641XuV3izEE2EjewsByDJEnIsgzbt1nN7yPQkP4Qx3DoOb0P9LP6nutqt+s+sQ4ukgs0obHhfbDqXWYZMkkwBh/u0vqnISsbZmmJlJ/OnikEmLqGoQkMTcPQBZah/dhE4ONwJRxXwnHFD6FpGpJoRbO6WFdDAwhB2Zh0NrZIpyes3D2uD4N1XUF2jGl2yC5XJNMpg5tPQSEwBi5ZXLKapChtThZnuKFNq7PB4WhFKwip0pi3Rgkb/ZDnehbl6IR4eozV8XGFRaWX1KZFtqpRWZtJLZB1RLu4JBtNMa4P2FjMad/6ZaqOw6jbpbeck0YNh6XG//E/Sf73/63P6ZnHoJ/zr/7FE774q68x6HQ4FBrD+D4tCmzvOtu7txj092kJm3GUc5YXXK4m3K4W2K4GmiLctBDxAuqG9t4z9Hq3KN46pbFqUs3GNEzagw6aZ1I2JWejB/zpwdt02i2c5CFBZ5sb/S8y/+4x83yJ2mzz9J1n8eoMihUASWFR6x1szwJb8O7pGCkV+4EiNGqyYGPdYfd9+1VgBQRmwOki/4DrKiojJtElO7mDkAqEQFgWmudRj8eYm5to3iezSn5euBKOK+G44p8R1TRk02OmZ0dYto2WjjlynuLmtR06oU9ZXqDrHkL4TO7fx9NM3ME1zIFHU0lW04xWxyaeJ8zHp9i+QHMEprfLdBFxOcvIPI8bfZ+nuxaLh98iFYpWeweVTKmkJFUlVVlQ5D6jSsM0LKzDbxPNzrCYcveZ30BoBvNnbrFraCwfPKIpBatqzp/8juBv/8N7fOVrAyyr5qV/8T6//pdO2Xx5SK0EyeqEOk7o9G5huQ5B6NGxTNxCMskb7jkuXaNksTxDVg2D3W3qxTFVs4J2C7UyaYqCYGOfIirohkOCTge9baNQPHh0yCAMyPNzDsZfp3B8PNvHiwST0RLXG3Dr9kv0Bm3ieEkyv6QqarLawNnYRfdNzmYRZbSk0yzob9+kGwY4pokAVuWKqFzXlizikuxiyt1OB9d0kQJOrYzQ7GCo92JYnU6H+vISVdeY1z5eJfuPA6UUi2KBJrSPbE//0+BKOK6E44pPwGoywrRsnMVbvBuZ6LpOx9Eo9Rphh9j2gLoskacjAi/EubsHQDTL0TRBq2OznKTMLqak1RmaBZ4bcDFVTJRJYWnc6/psixnJ6pTe9S/huTqsTlFCo3AslJAUqcPblxOqKKL57jcop9+md/0VwnKTcb9Hfxiiq4JK1pzZJX405ews4P/8By/w9367R55rPP/cGb/21xv+wq9UrIoxJ6dvUBlt+m6PWgkcL0QEHnFRoKISs5I4bQszWeIYJbYBPWVhlDkaOnJQYwUWZaEz0Dfpe0Mcr4UWWJzMZ5hJzNbOABGdM7MCDuYXTIoll5NkHYyvTXq7d9kb7DDsDghNhRePkFFO5fSprYB5mjEbH5OabXzHxNDBqQtcIamqEtlIijDkYZzQ9hSmoYGAgpJuq8O2v01VN5hpxO5wiGgaypMT9E4Ho/vP3ojxk/I9oUiq5MlzHbuDRLIslgBoQmPgDn6qc92vhONKOK74hETTCbpp4jVzpk2LVHjsOjlVckTVVDR1i7QxiBYVLBN0XcexLOpSkecNrcBA03SaWkMqSVZOMcwa02rImm0ODJNV2fAFX+Fkb6CMO7QHQ3TRQHKBUjV5M0E3OjibL3DSSI7fepv46/8Xrbt7tOgw7z9F0G9jNjXGZURZCcp0Rk8tqcxb/P3fvcvf+rseF+cWtt3w0i8kvPJLGc/fu8/m8ACzewcXg0mcMZcaC9NkGITs5CYLSycvKly9pmSFBbh5TO8yQ4UmpSOZFiPKKudauEkQ7OI6HZayoYgX9MKAPLrEcDvYtkdgrFjmEiQsT95ENgWqFeK0trDtFn6rxVNbA5p0QYZDXRvUB28wlQGNbmF6PsIyMQ0LwzBwXRfLtDhdrl1XPc9CioZRdcmkvmTH32FWC6aLiDsb19gPOjSLBc1igbW7+4FBVt8fuG7kOnhdS/WBSnfb1Oi37B8ZMP8oofAt/yOPkUoyTseUslx/1uO045/k3JIr4bgSjis+BeL5DE3T8EjIlcVJ6bDfb4Fc0jQZjvKQ2RyloKpqsrxA6RY4HZrSxvddbFsjWxRki5xaZFRJTVVOQDewuzbfyQLyQvGs/g5tM8QZPkMw8NZV8ArK5Jxq9RDb6LOsCt5JUk5e+zIqdNjXu5TeBo7ocf3aNpapk6cZkyzBuryP3rSJpcfv3e/zB39i842vbXBwut68tq6VfObzp9z8UsTnfsnlV5/qYFUV3zy64DRLeUqzCDZ6zGYFZqWzdatPaSgOVhOyywjXho5p0xUa75y+g6gXaLnCEwbKH1A6A57f6mN2TIQsaYJdTF1CdUFV5iwSi+nFEfXsEleFZLoiW04Z9HfYMQK8lkQbbiJlRa23GNUtVkWFENBzTeqyoKrWm2xUNkjdZtPUaGYr6rJmlkzxew4b957m4fSMlS6wLYOBDvrFCM2yCXZu4Rjuk8C1rglMTUPXxeMgtkDXxBMX14cFzA1d0PMssiYiqtauNIH4kULxo8jrnEk2eTJJsWt3P9H7/dNwJRxXwnHFp0SymKOUwjcqlJIcliEdz8S3CqpqgevuffCAKkclE+I4Il6VVIUi7JkE7Q5JEZIUOYZZoaORpwZlMcYYWLydKqrpgp16ynbnsxiWhQKmxYRVU1E3c9otj5vtPfRswvlrv89RuaBs7zLcv8titmQoLOxeH4Uk1wRyesS2FSKcDnllc17NmL+Z8+p3b/D7X2vzx19tEcc6ui65eW/G5/5cwa/8xYCnXqhZzab0Zitato4d2IwnDfGqRg8MLEcjyCsWLcVMN+m6Pk3d4IUNWpVinkfkk1OySnI7muJ0fBxLo9l6hsYNUWGXUsTMj2OkbjBtIlQ6p98KSFeSMmxwW112rCFuOcaqVrib17A391ESRlFBU5V0ixhPXzdXnEUJp5lkd3dI4Hu0Wi2OH1wwOXnEdj/E9BzMrW0WuoECukVKdvGIqhcgXPfJv8/QDDp2B8dw+CiUUiyLJXEVUzWSeVri6SEtc72xCwED3/7UakO+Z8HEVQyALnSG3hBT+3QbQF4Jx5VwXPEpkq6WNHVFYAuoM0bagKpRbAWKohjhuvsfGXhtGsn8IkYRY8gVVVaSRTWalhH4Ll57g+nSwWoJRuWM83pBNn5AY2xz68YeO+E2PdtDSUWR50SLE4RoYdQO+aPvMJ0ccpFnuLc/Ry1zdvKURmlo7ZACSVTNaEc5be8ajdRYpBHpKmK7vYewQr7+wOWf/KHgD171eOPtEKUE7XbFZz4/49YrM55+PsKzYzqW4l7fp86hsW3GywhVVXRsk6zVoISGqHU6WwNKp0FoQGFyKXWezjNslbJZHKFsj8kpGKXF8HoXo+tQyRVNI3m7jqn1KX4+QK9tYqchCFw2jT7m0ZuIJKLpv4xmOXg9j6UbkEmBbehshjZNLbl/uMRAYlMBEl1YlEZBlq7w4xrfNwmHQ6ZBm1xKvPGYjlCYu7tPakSWxZK8zj/wf9TE2uX4Pdp2m8AK+DAaqZgmxQ/UhnRbFi1L/8RB+lrW6+FXcl3M+GnNdb8SjivhuOJTJosjqjwn9C3I5qStXc4WOde7OnU1QgiBbW+jfcRdYDzPUQqCnkOe54zPZkxHI1qe4vp2j3RW0gp18qwhrUqq4ojLVYXpX6PXDtE12PBNDE1Q1RFVvcCoWnB5RtxknBwdI/fuMe3ucTudIC7GJHFCXNaUoY+sU1xHY7O/hVI9zqZHhAoGN15GpBJVVIxHMf/vdwN++/c8vvH1LebzdaD29q2Uz31mzN0XRzz1fExYr7izMcCrTaZFCoaFNwzI3IzTSYyvh3RDH6UtmZcl54WFu0pIFg0tQ3KtDcFGiK0yVJyuXTvtIZ7jUTUax0evk2o6mjCxrTaFXmIPPIaWjz76DkZnC2ltoQyHplasoppICnRDcH3bIW8UUV5xe3OPJKoZnUypygZ9q6GOFX5jsuXrCCD2A5aGiX5+xvZwiNn78OB5I5tPNJ1QSsUiq0iKdfq3UtB2TdreJ7cavjfX/ZO6x66E40o4rvgxkCcxZZoStluwOkd2b3E4zzA0AUgMNcO1GlpOF9P8wSroMq9JFgXhwEU3NJpKcvj2EWk+Z+fWPvG8wHZMhts9VAPz8SHJYkJWeQxu3qSQ4ol/3dAEoTVDRQusWCItyeH9d1CmS/zsl/Bdh0AJ2qNHLMcPqZuMNLK4WERQTXAClxILVg07u7dQnT6aNkBN5wyu2chOyT/8us5rv9/l63/c5qt/YlJVGo4t+fxnI249PeLuszEvfU7jWdsmi6aklUT3HTJnSdI0tFq7UBss8yW5Jtlvh7jTMXHgkcuKxN4ATdArIozZCSJP2HQtWte2ifWE5SRFFjXCF1RBj6Qp6bcC+tmCOK7RkGitHuHWFmk0p2lS5nmFEhqmDXmt2GyHbPZfoCoEx+9couz13XpgBuxtXMfTckhjSqUYSaAo2L55A9f+6GaKnxbjqCArmycV8T9troTjSjiu+DFRpClZtKLT764HSPXvgKYhpSKtGqK8IiuW1FWEEDq2vYF4nBkjBLQsHRnXeJ6JG6w3p9HxJaOTc+59/gXypGQ+XdDq2LTbbZRKiRenzE9KEtFib/8a7Y5DUTeMo4KmqUjG9/GbmmubfS6PjpksVnDzOTav3SSTEpHXqFVCxbsoJLW+yfJowdnFJcXqgCqb027t0t+7Ttt30VOolhnSz0llxjkdnJ27vPHtDq//3/CVP3J49O76Ttm2G+48teSZF2J+4UuCz9yd0XGgaXRWyRmWodP1QurA4UTLEI7FZ6UJx8fotkRzdrj0tziTkkpUNM2Kni4IqhqrBbGAuAxwlhOUZrIoIiJrzjW74pnr9zBVQ764RHc2EP4+QRDQJCXziwUTuWCULKiaBTe7Lm3vOuWqg9s2eff4gOlixPXeLfr9PmHfQU8WqCLl8nKE2tiks79HzzQom5JVuaJrdz+VmehSKqLHA7IcU+NkkbEZOvi28SOO/PFyJRxXwnHFj5Eyz0gWc7obmzB9AP7mev759901SllRFOcopbDtIQiXuKhJipo0KinymqDrIDRBliQcvn3I7s19rm2ENEkNdomUkjAMqKpTzFrn9CQiFX22eiF+e926A2B6+Daj5Tlua0g+mzOPVujdDtdvPsdWp41qFOkoZiYUZfQuQsVsbl/DMLdYHI548M3fYTk6wTa6tIIug9ubbJYu5v5tEmPG+cWCi1hHb7e54wdkc5dvHgz5x7+b8JU/tvnu6yZKCXRdcvduybPPLXnxuZi7f17y/D2BuUqwxwWX85rjPCGwdHzZsNHKcFsa3We+hNG4XIxWHM/nOBsuIpsSpOfoak7RbJLbGtevbaPNSg6nFxxOjij8kOv9Z3D1CpHPyWpF5QwQjoNf5rRkQ1KOOYhKPE3iGCmyDLm5t0G4cZu3jh6C0vHqEM3V0QOJ0ECeHpNMZqx6A9ydPW57HRbVHIliszugH3zQpaWUQpUlqijWP2VJ3UiWRUPyJNax3n+busGsUpAN2o07aLqxvglQiq3Qoe2ZBPZPvovvT0U4hBC/Dvz3gA78j0qp//b7XreBvwN8DpgCf0UpdSCE6AN/H/g88D8rpf7m+46xgP8B+POABP4zpdQ/+GHncSUcV/wkqMqCaDKhu7WNKJaQLz+4wA7B7YIQKKUoywlNk6LrDpa1se7C20hWkxwvtLBcgyrPObj/kJVqgW5hVhp713ySOKKREsfJ0DWBkVacRhVSH9K11xP0vNBCTi6pOUU3FXni8s7ZnIkp8e0++7aH7doM7BZGx0f3DZqD16maMcrroDktMjY4fvCnuE1NPl1R1iWGZmM4LVq9DuH+FqcrjUfzin23xWZR0Gq76O0W52cz/vS7G/zu78PXvqLx1kFIVa8treu7C55/KeLFV5a88otTbu0apDgMZcZiusCpLGT8kLqO0UyXujaJlgXCCKn8Hpot8M053dxjlSv0dpsbr7yMAOTpfd69vE9ldtncvcet/WgFVj4AACAASURBVD30+AIQTBtF1ChcTdAXiofjU9JyiaZiLs4SDK1ANTVVITE0Hafx0SsbXUB3GGJ3fJplRLOMmW9u0x7soukm02jBqogRaGzZPTylo3QQjoNmW2CaSCGo6hLf0vAsA5mmyMUCANMwcIIAWdcs77+DFgRofotSwsjwGGwMQHzQshECOt6nE1z/KH7iwiGE0IH7wL8CnACvAf+2UurN9635D4EXlVL/gRDirwK/oZT6K0KIFvAy8Dzw/PcJx38J6Eqp/1ys7f2eUmryw87lSjiu+ElRVxXL0QXhcO2O0jQNIR7n/RcRZHO+d5cJgNmicTyKcvI4mL6FplkkiwIpFUHPoSpyoskEIwiZrTJOzlJ2drvc2ApZrVaU5QrHyQmcaxTTU86bgCDs4jTQ1Ir68pJgQ1A3R2hah+RwwvHWJqOqQYtTnqst7KSGQmLs9EDoqOiCsiyJpUYtFRdnR0i9TWgPqJIjjDJGldC0u+jdHNWCY3yoe2xIF+oVwy0XxxdYJOi5z+VBye//kcVrD4d856DLm98KyPK1dbSzG/PiS1NuPzflX3p+zs2dCVoBorHJsiWOELRbfXJpUxQFsoQFDYUVYRo6TtFQLROCdofg2i7Kc5HljLMoJVlFbPhb9G8OcDc6CE0jaxTTSqJrgk3dZbVasNvVKZY1tmvRWB1Ozh5QaTWVrrjVfprl4YJiGdH2Bd1AJz09ZTW/IK1qxMYGxvZNct3jPLogVxLfbROabQQClMLIc3xqnJYNAnTPwx/0CQzjcUzsfdfRdLpuyri9TTke8+h4hC4U3ZaF0HW0bhcnbJPWkH1fppYQ0GtZeNYnd3P9NITjF4H/Qin1a48f/6cASqn/5n1r/vHjNV8RQhjABTBUj09KCPFbwCvfJxzHwD2l1HslmD+CK+G44ieJbBqyaIWSEiklKMVHfs+qFJHPQa3XlfUEpelorV2gS7Ks8LsmSlVURcHG/i0QgoMHY+ZNiWnr3NrqUhUZaXZAr3sDt6lZLhfMzC2GbQ/P0Jh/5yF64IK8xAjBPJuiwn0KL+Bb+YJkVeJXii3p4XQC0AS6LmgbC1zXRAUbzC/e4nh0RM+/ByuHKj1HHX8D3TIxqjZJuuDCz7jUXIYplJWGUhVBP6A1dBmEPQxlUc8z8mnDsbL51nSL737T47v3e7z+us9qvrZIesOaL3yh5Au/WPHFX6rYvp3QJGP0fIoQUKeKbmcLtVDk8zGyZVHoHqv5iLCS7BkNLVOg6TmZ0+GgmBLNUhqzz/7WkGGnhxOENMBZrcBxaISJp89x6gohNFptl7IMkKrkndk7TFYZlgxoIh8Zxyhq+jshPc+kOT2lHJ9gygI/8PGGmySVIpYVwnXoOl2MsENtulR5gyY0NMui1g1KQ8P0DJQAqWDftdCEQFUV5ckJRr+PHoZEecUoKtgLLdRsSh5FlNU6/VboOlqvh91qYTvu42ytCteWbPjhx76WfxrC8ZvAryul/v3Hj/8a8AvfJwLfebzm5PHjdx+vmTx+/Fu8TziEEB3gdeDvsXZVvQv8TaXU5Yd8/t8A/gbA9evXP3d4ePhj+T2vuOJTp8qolgfU5QzQqLIOhmkidcX0csLw9j28dpfVNEM3NU5WK/KioucZGEwBxaB/GzM6YVTapGaXnY6LOjpE63VILi8oPRvSCaIuEV6b9s7TLBEcJ1PENKLXNfFbIS4uRZaholNQoOw+x4++huy18GUfUfWQixhlnGMqiO+PkLXkdMNh23PQ6hbz2QrNylGDBro+rr+P1/jsCBeZJETxnMOyoUbnfOHz5TeGfPs1gwevecxG62SB4UbFZ7+w4qVfSHnp5Rmbm1PKdInhGgT+EE2qx9bAkGm8Iq4Vdm+XFy3opidovX2U6ZA9us+70xGR36I1aNMK1hX5WtnQCJ+sMohWCf16QpXnYBiUQkf4G/T6IamaUlUJiBYIl2wssDAJDA1bpXTaFlqeEY0uaVSMKxSarrNwbGrTxTFdQq+H0e+hWRZN01CXDXlSoRRIFDNPZ8N12Ql9NE2jnkyQWYa5uwvA0SylZRsM/Pd6WKmqoppOKZOULM+Y5DNGdcHTdz/LVrf3sS/Fn4Zw/GXg175POL6glPqP37fmjcdr3i8cX1BKTR8//i0+KBwDYAz8plLqHwgh/hPgZaXUX/th53JlcVzxZxUpa4rinDLLqZYNnu0SXTxA0zS6O7uU+fr76wUWo6hiskoxSdDUFDe8x6DbxSzmnKo+UrcZzs9x9nYQ0SkYznqwUrGkWj4ATaDCLXJlMFu4FKLB9XMMIbB1m6HdQy2PSZKU+ThmZOa0fZ98UVCvBHWj0d5xMMqKdq5zYkgsN+WprX3GY4P5oylFMSXcXNDd2eE0akhPU+oyJ69ijCTGD4dIJ6C5uUcU9nntLcnRqw4P/8TiG3+oMx2tLZLN7ZrPvRLxzHOXPP3KBTs3ahoFVVpSqjaNzBHVlLFukpsam0ZCD7jTexGvsakXcybxkpnRwvcDtKpgUi7ITUmlw0Wm6HoeW9qKwDFxCzCkTq9/k1oVRNkFgVajdJesVsRFTWG0yJMasy7oeTZBYCJMhYeFmSSEpkbWZESGoqJFoHxQ77molGlS2Q6WFpJ6Gou6YNfU19ZHXVOdnWMNB/jDIXGpmKclN/ottMdurloq3olnzPMZfWfADcvFBDTnoyvefxQ/E64qsY4AxUCglJJCiD3gHymlnvth53IlHFf8LFDXMfFyRJFWoECWAsf3sZwOTSMI++s2Gau0YLqYk8zeIpAVQjn0rQrLtriQHbTRiJ17NxFSQrEE0wHDXc8hqXOU6VLYOmUmOZkVxE5Nx3SpHjfb812Pa0jUbMmpavB29xm6faQskLKmLDPm8ynJ8QmLpKLyDLb0iqDXQlgbnL05Yrl4hOHV7Nx+hn5nm3qlmNkNx8cHqGWMnpUkRsRwsI82uM3DStIG5scer/2pz9dfc/nGqxaL2VpINrZyXv5CzC+8MuYLL7xDr7PNPNdoVEnY7XO5yIiKKUvrCD0I6KgWz5Zd+sWSRMvJgg0GvS4+Ek0IbMPguGx4VOm4dUw/GNPoGVmW0um0cd1dcnRcUSOblEHrGm1vj0YpJkXFyTxjOcsolhlFPsezUvp2jdcy6OjgFQvm1YyiLBCtAe3uTYzGRCQly9mCTGvhdHpEoUNb1+ga698zvxyRJQmi30c3Lc7SBulYOI5gKZds+X1cu/skitYzDQLj46cL/zSEw2AdHP+XgVPWwfF/Ryn1xvvW/EfAC+8Ljv8lpdS/9b7Xf4sfjHH8r8DfUkr9f49f/9eVUn/5h53LlXBc8bPGaj5jOT5GM0ocN0SWLXSrTXfLf5JhU9aSw/EJUtZ4OFRpRNDM0MMdpqMMIwjQA5eunuOLgqqqyOeXUMaIfIFoSvTWBlr7M0w6GpHM8DRB11DMygRNtGB6hDmJyG49ReD3f2BKXxLHHL35FhfxjGErICgr3K5NXflEi4bV/BEGDe1Wn5aycIcdKg+WszlNbTJNLkjLiO29p7A27nBRlGxrsCMUMi95877GH3zV5fdetfmDr9oso3Utye61mM+9MOGFp+fc2b2g3yvobXURyiUuR8y1JSOzxnT77Jrb7NoKQ0boRpteu0c7cGnIyJaXHMwbZklNezOk65SUcUav62N3e8xqyX64zzQ7I87OEEKj59+h43wwNfdynnL/IiaNchajCxqZ4Vgad3f6DPSYZHlCWWb0HB8vbFEmJdEqIS9B7W+DH7BlGVTAOMk4O79Atbz1/PdoRNNIdlo9bClxhHqcBq7Y3LrL1rXbH/s6+2ml4/5rwH/HOh33byul/mshxH8FfE0p9dtCCAf4u6wzqGbAX1VKPXx87AEQAhawAP6CUupNIcT+42M6rN1Wf10pdfTDzuNKOK74WUQpxeJyxWJ0xOCGTzybkq0s9p99Ft14L6OmqhIOxscY5g42NWpxglEn1GlGPV8SNZAIC73dwfM8LMvEs0w2QgsjGaNG36VeSvTQp7BN5maI0qCrpwihMWsK8pNTancTYZoYmk6ZZDRVSWh4tO2QUjM4OjrDNgva7R36hoFmlpSNzSRTxHKJ0HxkrDAxsDbAyDOkVJROh9H0lEJPCba2MYYvMpawa1vsvC8VtWkUX/1qzqtfsXj1VY+vvGqzWq3vtm/fzPnMswtevDfh889n7PUMKgqW1SXvljF5ZeDhoQcxHUsnUx622WHHb9OyLBZFwzKucdsGpVYilhcMPRvdd5lrU/Z7z+AZLkI1zOKH5HWCYfbwrJC2GZKtlshmnf1kOi3iuWSZ5hyOZqR5jjQbTMskJ0VH0bZNNFtDR1FeTKjKglGvS+C32fRCtiyLaH5CVWfsbt5GVwbTdO0ic0wDIUADgs0hrU8wLveqAPBKOK74GaWpak7eOiLcGOKEFaf336bVNult3cB21pvGelb6IauiRSE9VF0xCD1azrrmQ2YZ9WSyDtYKjcwPmMbFe7MnZIM+viA0K7xQRwqNi1oihGDHtfBERXL6TcaWTYXC9QJ2uk+T1QlJEYHQqIXB2TJnO04oWxZDZxtHgllHFHnFSimEZSEnMcVYgQNNNkeUc4y2QVxCJDRkq8DbbGNsvczKvcZeq8WeYz0RkDiOqesaUxh85Q/H/NFXPV59bciX/xDiaG0N7e0UfP6zMZ9/dsqvfCnj1o0ZB2nOJGkxrUq2OjUqWeCHe1jhNoEhKOYLDs8zng10lCN4mC0xigWd/h4XKsbVXdqta4BBoyry4piKnChWGE4f07DxDA/ZNBiOhqZrCE1DNgpR6+R5jBIWdVMSr6YYtUB3LUxLYGsm1sWMuFqx0FK8nkHf7WMJC5mk6L0+BD1GtUuldAaBDZVkt2Wz3fv4Y3KvhONKOK74GUYpxez0FCk9HN+lyCrq4hzNTvG7PUwzxDS7FMUYKUuEsUWU1+RV84PvVZbUs/V8b9exCHc2aTkmSsFsmrA6OaFQc6TuUBk+y3yJrVJafoCdntI4XYTlUDLCMgWO4bDhDHD1NlVV8PpqhD2/JMnn2H6XYFHSzgVeuSKvM4rBDmb/JiorsIMbCAT56Tmy5ZDPj7k8O6JIY6SYYfoN+mCD2N1CNxQdz6Xyu9Rum6yQeO2ApohI52d4rZs8eORy/6sar/2Ry9deDZnP1oHjfrfkiy+n/LnPx7zwXIS3V2IMbRbLc7RsRI7FjRsvc29/l68fLGg0xY6rmC9XlGfvsEFELiUZEl/romsdMDqUmoGwMxoipNTILQOvYyOEwNTWM9qVUmRFTVnBIokwZcDm9jaqycinC+zSpd1p4W9YHI5P8RoNWWkEuqC3vYXtOmTHx8g8xggt8kXGPCrodxzaN2/hdLc+9nV1JRxXwnHFzwGryQgwkY1NkdUEPYMiXaBEgRN8rxjRRMocIQwsq4+uf/gdqZSSaLZg/OARedOgNAOt20E3bYzKxPIVopqTVZDaQ3q+s7ZeludkecxCGkhZYOqKqJlRyxU+Oh1pMpYWjnIwFiOiXgt7Y4eiqLHSCn8xZlDOEZpOml0yxaHxN6BScP0eSunkWc7k7BKRxsT5lJICd3PAxuAut03Yy+eIMmaWFvi2haVLVtWCrPZJg20026Et4PKRw+/9scPvfsPi1W/1Ob9c1zz4XsELT4144YUpr3x2zi+/UHG6uM9JViLcPmHloFkhKMVKacQa1FZF4OW0lWTTbKNRYUgTGW6R6jqrckxdzJCVjvCu0ZgGhrZ2Kw26XTZ6fbQGltEl04sJtzu73Li9ySi95M1H72DEDteCbQxHI0kSChdWFyM6eULQG7C5cR1tvsC+uQW+y7vHY7qhx7D38WeYXwnHlXBc8XNCspgjZYPltJmdJTiBRdA1iGYTDMvCCSyqag6AptkoVaGUokhiZG1i6O/NlDAdF9cPEJqGKkuq0XhdrKhpCKuD3rIQtqCYHnMWlQxaBqFjQlOjyoS46bOIC0opkXXDUtQstAKlakpZ0fFDnrYb5pdH9G6+ghlsMI0jjkenFHGKkSjaxYogOUGV4C2XaIMOwlvHcJK4oShCArPP5fyU8+yI3HUQnbv4ls/tXg/D0KlyReDa2FqMMGOkVKjbz5PYNhqwY5kQlTx6KPl/vrziy3/Q8Cd/GvLocP23MM2aO/dmfPalJffuHbD59DGRbTD021jCpEpKVJaxiArGgaBxJmwG19lwarbKBT3dYSe8jWuENBik9YwqTzGNDho20yRmlaXogU833KCzOeT+8pjFRQKW4BeffYFVPYVcx84ClFRUeYWJYOpJmtNDytERDWBYFq7r0X/mGcJ2B+fPUjruP09cCccVP2/kSUwex3Q2t5idx2RRxcZ+CFRPxt8qJSmrEUrVmEYPL9xAMyuaJn7yPrruYZq9H+iFpOqa+vKSJq5ACezbO6AU54fnpGXNXmih0aCLFdrW02DYfD+LfMk700vemUbcsn2yywfURcJw/y4tv43vbdJt2egS4llGS5+QzC5RsU5reB3NDxBBTRkdcn52HyfXCVTAfHXB4fiQlWGT29exRJsNraKqStyWhyod3KCNWp4gUFiez7nrszBtbKFoNaArQWAJZkcZ3/q2zjff6PLqN7u89aCNlAJdVzx7J+app1fs3pizuTtm81ZFf6emWc6Z5TozOWdYu+RsIh2DUqS41Gy4DluioOdpGFqCpES3A5zODs1iwSJZMJI2tbRoWyGd1gZpYeF2fAxXUaxO8DMXu3aoDKgqgbbdoXBM7nYdkkePSOZziiRl6zMv4fX+DBUA/vPElXBc8fNIXZYsx5f0tq9RFZLpWYzjm4R9F00Dob2XNlsUY5omxTBaWNZ7WTh1HT+xTmBtoVjW4ElbeIAmLSkfnSFcE3NzQG0ZnCwyhoFNaBswfwROB7wP38DKuuabswPaRBTxgvzwAt9sIQODynDRnTtomkaxqkE1WPU5+mhCe/cG7cF1DN3A6rqkdcLl7JxO2UbkirI84eDk22TNHBX02RjcIMlr9NpA1RaF0BF6ja5B2/YYapBhkOKiO1220dAECFMjyVbIVcI0XfL6QcgfvzHgy182ePhOwHzx3uAl15E8davg7s2E61tTxNMpt+7EvLKb4gmbWAhOsyUzadDYW/T0Di3DpsmX6Mkltqgp9DlDs8aXGWOVscpqylinU+wipc3WvXuwaZE2MXeDa2iFRlE0WK7OUVkT6hqbLXvdF00pvK2rGMfH4ko4rvh5RcqG+dkZ7c0tQGM1ydAfF5P5HQfd1D6wvq4jynKKECaOs/0BgQBompyynPC9Ro3rOMkQIXSoJbJoUJVEyYbz1YqsStnxFSKfo2QNreFasAxBUTask7YEQticNSbb7TZSW3I2eYSYLugRIptLvGtD/M4eTWVQJAEYKdO3XiepdLTdW2iVTpVUaLoG1grTbtgyttYNDVXMg+kly9W7ONLEokWZL3FMh8aw0YSJo2eELZfr13ZpOQG1ajjLJHUJHb2Hu2xQtSSfR+RZSuMt2bgzQPmScRTw7v0+b79u8tZ9jbce6rx9X3Bw8N7fTdMUe3sZ927FPHWrZn+3YHtwiLc3QvPAsANq3cE1NEJ7i/nZhKSRWEhCUyc3a6bmMVsWNBcFdSbxA4O5oaF1LDbNTQZ1D1u30Ac+00IxLCThTh93cBXj+FhcCccVP8+s6z3O8cIOpu2wGGWEA4csqpCNRNM1/I6NeF+H1vfPDXGcLTTtB11N63UlZTlBqQZYF50BCKGjaQ6NcjmaloRCp6VStOSSJryJaMCx9CftMr7HqKzQgVDV5BScmhNkVWFfZBjZkiDwcTohuXAwbBN7dUx0lFAO7tHd3VrXlcwzSlVzWYwJLZ8OAZoh8EKQ2ZTR6l2U3qZZVTiJoMpT4qiiNKDxUtq9gF64HreqZMOyzJG6Q2AbDPUWqtLJLhJWcYSml+gCMHSUWSEMC6sOMDSLnDaPJgHvvFHznfsN3zkPOXrU4uhApyzfE+StYcmd/YjbeznXnlLcfTrh+duKtg2dImexmlFFCZFuMQ4kmW+gEZCuCoaqxNdrLosFSV1iuQE1Oju7XXLf5pn+dfZ72x/72rkSjivhuOLnnNVkjGGauGGbaJo/eb6pJemqBAWmo+O03nO9KKWo5QhNq7GcHrbdRjO0H9jwv0eZ1+RJ9YHO8bqhsVINtYLd0ETMH0LnOpjuk88okoQiXcdW5rWkMC120ShmMXlTUPQEmmdSJiX55JCgFHj6daJFSXsjxkyOKdpdlNOlt/00unSQcckimbPSIjbbu8SzilIqpJKIZkzH91lWJWVeYBQKNU6ZnI9IiktqbUGwG7J5fZt2MKCRJfNMMYlihBIEwkbLNLymRVuzqKwKEChNomoBDVCaUCo0R0dYinh+ybRVYwRP89ahzuSdipPjNg+Pfe4/gAePDKJkHfQ3dMmzz5Q8+2LJ85/Tee6zOs9vTRBnl4wmUxYdnWuDOyzjBfN5StBycFyX+fyMEJ3VPKNUNs9+8SZ37+5/7GvmSjiuhOOKK0hXS+qyJBwMP/T1IqvJ43VPKq9tY5jrEbiyVuTZlLJcgrIxtMGHDg8yLB3XNz9gvTx577rhZJ6xEdgY47eopI5y13EPu+XjtPz3zrORXBQVPVMn1ATLk0vieElhNHj+Bnmas8wfYQcWTtqnJwXG+AAt1IlaNlro0+p0133KY5vz6QF4FZvtHpodEOUrxssjZJNjW0Nsu6KQKUIZeFWHYtQQnU4pyxhJjdlSNFaFAkzdom65aLpGkseocBdH6yCVQagpPGuF6g4omwghQlQeIOc6opLI2ZhTccju9VssDY0sGrNRR9jGFqpuM110eP1Nm9e+lvHt7xi8/W6b1eM2KoahuHO34KUXMp7dH3N974h7L4VsPfsc4/GEKpvTCjQULqtVih8Z9Lpt9l/c/djXy5VwXAnHFVcA6xnpyWKObujohonlupi284FguVKKdFVSlw1CCPye88TKaJqMohghhIbj7KzjGz8EJSXJckFTrQXpMqowvBY3/QrRFGvr4yP4/9u79xjJ0rO+49/nXOtefb9M91x3xl7Wi2Mbe4NtJYoCTpYE2SSKYMlFloKEIuGEOImCESIKIEXOHSSQE8s4JokDhg1RVkgBDDhKTGxk49uud73r3bls9/T0tbrul1PnnCd/nJqZnp6e2enx9FaP/XykUldVnzr9q+quevo973nfdyeKacQJs76LtBPa9Qbt1ibDtM/i/GnCUp6N7W/S6EV4/iRT/QZVb0C/s043zeEXS+ROTOJ4OeK2sNNskMY9ZvwSZb+Eako7adFwllDJoyiJ1umndeL+gHRbiNoNcrkSE8EMQeDj57r0+jsMowGuG5CENdykzrQ3Tc9dZtOdR6JdxE2o5trkvAZO0SWsnCcfnGHnhVe4/M2XKM2fojK3zGoS47ltFsIWcVhExEWAeU+ordf40y9s8/LLk7y0Ms+Ll+f4ynMhtdG6JZ6XcvbULm95Y5u3PuFydr5OeXGV8pxSmVHOLbyFSuXEff+tWOGwwmHMLVSVJI6Jel3iweCOi02liTLogR/myBVzFKrZyGfVhH7/GqoJYTh7YyBhmibZWJI4BkDEIV+t4gc3+0n6w4Sr9R4LYUIx2oSpR8BxbvvZqkp7d8BWNyIpeSyVcxRchzRNuLz6It1ag5l8niAX0Io2aLVSnDimuLRMWfrk0hKdnS75YokglwcEp1xiJ8zTUyVACftrdBsvoprieVO0+w5OOIuEk7SSOmVf6V1p4ccxM8uL9AZC0onIhzmSfpv65hW8XEjN2aHiK4tE+FEJCRepzZ2i67q0W9tEuy8yoRuUSgUmZs5R34pxgipTuUWa3QbP1bu43TrzUwVmFxfpOQUSlCSJcbtt8smQ9vYaEvWpdWZ47qVZvvpCji8/6/LlbxRotLLX13VTzpxrcf5CjSfeGfBTH1yiWLy/vxErHFY4jLkvqko8jBj2evRaPXrtrCCEBZcg52bfj3dIdQCAOC75cmU00WLWSnGcENct4Lr5W87UutboEccxy+k1pLoEQZE0SYmHKf32MFs+dzI7+ytNE1bbG/TiHouhh+84iHhsNFu0Gg3mkimKpQrbW+vEjQ4zjy7T8tu47S1iKpTCOdrDNp36JnR72YqLKQzJE/gh05UACQfkcos4cQS9BoM4YbuvdJM+zSjBaQ+ZDH0WT5/G8SukniKdmMa1daqVKj3Z4lp7i5IfUPU8oksrBMkEhekFCm94AzuTBfqNLs0rX6VVv8qwvUOSxJxZeILpSplBucJmu0e72WRiOkdhZhHPLbEVxdSbDfK5kHNlh+0XPs/ubjagc+78BbzCLM+/2Obilyu88CfCV14Iee7iJJ2eT6sl3O8YQCscVjiMeaB6rYionyACxYnwxmm+1z/4kzglGX1VHZCkXdK0zy0958AgTrnWipnTGoV8Dre0SBCW8PNCmjb2bCkEwRSOk2d1MCRRZTkM8BxBVbnWXqO+s8msTOH0oXZphXw5z4l3vo1B4wr11lWKc49RDidu659J05S17RqDZpNguMFUWMQPpgDBKRagVCLtt1nfvMbljW1q69sUpcNCrswwLRCUqkS9HgwdCo7PLtv0ZYvFuUXcXo1we0jSGFKLpnDKRdyzC1SW5+l5Q1rdNTY3XuDRE29iLhZouUS5mJXNOq3mNXL5HfwgJfDydHsOawOP4tQpcoUCwbBPtLMFccTUXIXJ6RmGknKieJJkc4fNeImTb16679+xFQ4rHMYcCU2Vdn2AjmbSFUfwfAd3dHEcObAjfb9rjR5xa5vFsEVSnUNw8P3JOz42VWWln/WbnMxl63SnmnKtc41+t81EWqJ9cZ2o1qB67hSTJ5fxBleRIA93Oe7fjBO2utukcZ3TlUdwu12SZov9BW+tnbA6bOG5HaLGLrnmLrlBgh/DpDPDoC28mvQZzBbxqx7lksecV6NMDrft4AULuJUA8XOks9N85eJnaA+V6ggYFgAAEnxJREFUOGmRiwOQmJnpGdKNPMNuwlQ5prC8gOtUaTRbVMolOiq00xS/UKS33aZXWyeSmLiasjB5npOTM5RC7+Aneg+scFjhMObY6w8Trm7tssgWhfkL4L72h16cKquDCE+EpTCbJj5OYlZaayRJir8VU3t5Ba26lMMKM5Uy/rABhUmcfHU08aMD4iAOOK6LE3qkPlxpXUSCGWZyE1T9m1lUlbTZpL2yQv/aGmni0C5Msz1osd5LiKXLucUpHqlOMVjfpd7bwZvMkQxTulEHtMt0cUjFnyOsnMLzguwUXrKxI3E3ZhhBrbNLZ7qAuzjD7q5Pe3eT5UKXs2fO0Ivy+L5PoZBn0Omw225TH8YMo5jO2ibR4FVOn3+Us2fffN+/DyscVjiMeWis1TokjTUghbCcTVnyGiJN2RzEhI7DXOjhOoKSsN3dxAfyVwc0e1126zU8N2Sy7OAkXbQwS6oOWYtCSeMEjRVixUfwaBGnA9SdwnWESc8bLbCn+PkCvclZeo6QduoEDswWAwalCs9feolOr41fKrE8PUluN2WgQyrTBTo6YO3iRXqNTXSwSTFQ8hMncSbeRK4yj++FuJ5LQcDbbRNvbDLI10gl5ooWqCU+gdumUiyhwTRnpiYouDfPbuulKdu9mNlcjkUbOX5/rHAY8xDr7WYXcaCy/JqtkE6SsDmIKXkOs0E2BiJKIja6G8ios77fblC7toOkeUp+xMRUntLcefJ+Ac/J9q+qDOKU/jCh3e/S7V3D8efYTlwUmPY8fBFyeQ/Hc+in6Y3HUauhvR5Rt8MgSdktVNhpb8EwITeMOF0KObU4j1v1SJOU3ZXL7F59Eemv4XjgFqpoeYmB4zIUH9efJRcvkAuLiPYY1i7T68c0oz6h50GxSHXpMXw/e76uCLN5n3wpQNzbz1a7V1Y4rHAY83BLE2hehTSGsALFuy+J2owTtqOYCd9lyj+42ETRLvWtddo1cNM2w3wep1ImKN4+NkVVGQw28d2Acn6JTuqj4lHyPIqeSyC39uWopgyHdfq769QvXqZUreL6Ptupy2orolZvMluaZ3G+xNzMLOVylTRNaGys0F2/iNO4ipeW0aCIVIU0dInaA7QD5JQ0UKKBS6vdpZZ6DNo7LHoVJh//c2gYUPeF5XKe+dC/7bncKyscVjiM+fbRb0B3BxCoLIEX3HHT2jCmMUyY8F0mPPfAzvYoqtHc2UL6CTkR4nARvBBxoFi9ecYYwCCq0+xdBX+GOE2J05gkaRHHnX37FnyvjOMWEBHa29u4jkcYDSBOGA4GrPUb7LQhzFeJA3Adh1LoMJnLUXADfGdAKe7gNJS4XYf8DE7eA8kRlBbxZh26/Vfpru8wGPR4Jdqms7bCSekzXX4Hk4+8nerpBz9y/P67240xZlxy1eySpqNWyBCCEpTmbtt0yveY8j0aw5iVfnTj3KibUzKCJyWqs1X8pE67to3TukSxUsGbOku3GZHE2ZZh3iMsVpnxK/R6K9lhIFfw8st4XvnuZ4+Vlui1mgw6ndFsxXCqViNqNXj16iu4nYDJE6fRmSl2hz0aUZf2EDrJkJ63g1QSqrpGMXZBHaLV53G/DhPlClOLSxTK07wzCfAvFPlGa4OVrc/jyQpV7r9w3MmRtjhE5EnglwAX+Jiqfnjf90PgPwPfA+wAP6Kql0VkGngaeAfwCVX9wAH7fgY4p6qPv1YOa3EY8x1g0ILOVna9fAL8ex/1NkyVZpzQSRIUGA536e7u4LQ65KYXyU/OU/VcvChl0Lk+Iv7+YibDIa2dTUrTs3j+zZZSq7lD7dVXiDt9Js+cZGnhLE7g4pT80Uh9pdbepN5uQhQTJEI/jdjpCt3NbWK3RRAOcNMhrlbpuMrpU+d5w/Kj9xeUMbQ4JJvA5leA9wCrwBdE5BlVfX7PZj8G7KrqeRF5CviXwI8AfeBngcdHl/37/utAe//9xpjvYGE5u6hCcw2SAXh5KC+85qe87wjTgcf09Y/E/AKU5xn01uhefYlk7Tl6kyeI8vkbj1FVXBEWShWkOHfglCkHyzOxUKa5tYEXQKGSnfVUmVlm6dwyg1aXq89+g69e/b8UT81TLU4ylZ/CczwmSzNMl+dvrJviSInzA0WWi3S7PrVOSLPXIm3XKDbbVOoJR9DgONJDVU8AL6vqRQAR+Q3gfcDewvE+4J+Prj8N/LKIiKp2gM+KyPn9OxWREvCPgB8HfvPo4htjHkoiUB2Nlo662QqEAIVpSGKIe1kH+z0IvRzh8lsZaIfO+mUKzZjC8uOExWxeqEGastKq42y8TMV1qPgeOB6U5sG9c6e0iFCdW6DbbFDfWKc6N3/jMFdYLnDuXW/jdL/PzvOXaG5ssDvboLxUQXZSypTxE4giF82l1IdbIEIoRfLJNfKRj1fwYH6B/NK5+38d7+IoC8cSsLLn9irwZ++0jarGItIApoHtu+z3F4B/C3Tv9sNF5MfJigunTt159k1jzLexoABT57JWSG83+zDPVe9pYOFeIROE55YY9NboXf1jurJAYfECYcHnVHUKqlPsRDGXkwQnGXKiuY53fUQfAsXZLMs+hUqVIJentrbKxPwCrren2HgexXML+O0W7SsrNC5tEszMkswNiHMQVHO4LYf88CyCMPR28PNDSlMhnlslbgxwoy4UDl6E61txlIXjoLbh/g6Ve9nm5sYibwHOq+oHReTM3X64qn4U+ChkfRx3TWqM+fYmcsc1zw8jzJ8geGSRQfsi/bXP0nVmccvnQAQfmAK8fMBaOEcqUHQdZj0363vpbGY7UYX8RDaoUQQvCJg6sUxjc+OWI2qO65ErlylOTDK5fIqlwYD6S6+w+VIdd3qBYHqScELoeE3obOE0OpTK54lJ6cdd/KUpvHsYOHk/jrJwrAIn99xeBtbusM2qiHhAFajdZZ/vBL5HRC6TZZ8Tkf+tqn/hQYU2xpi7ERFy5UfIlR8haq+SNr8MIgTTjyNemUEvZqKbtTbayZDnkgTIsRhWqFYCPM+Bfh3qV27u08szMXt7P8kwSmhu927czp0+z4ULKb0rV2jVLtHrFij7KcXFM7jzE2z3tuknQ0gDwt021bJHWJ584K/BURaOLwAXROQscBV4Cvib+7Z5Bng/8DngbwB/pHc5zUtVPwJ8BGDU4vgdKxrGmHEJSstQWkbThMHO1yDugl+iPPXdiONQAU6QdaRf7UZs7HbxEmXeCxGZv7kfIsL6qyTDId24DGHWYe76DuWp3G0rKpbOLFHYWaG7uUs3DhnUIsJ+j0JQYaaSrc7YKXQYqvLgD1QdYeEY9Vl8APg9stNxP66qXxeRnwe+qKrPAL8K/BcReZmspfHU9cePWhUVIBCRHwL+0r4zsowx5lgQxyU3+1YA0n6NwfrnQMCdeAQ/v4CIsFwMoRjST1I2omwZ2mnfo+Q6DPs+rW6Am3MoO00kWoP85O2H14b9bNxKUMQ58V2UTkBhMKB7+RK9xjq6sERzO+tLKU7k8IK7r85438/XRo4bY8wRUGVYe5G4vw1BnmDyTbjerWNLtqIhnSTFAZZyAe7eTo5uLevQz09mU6w0XgU3yEbKH3B6cToY0Ll0iX40IH/qFGieIOcR5B/8tOo2ctwYY46CCP70o/iADtpE288yTCOonCAsnkYkm4Rxlmxq+KujUe03RrRLEckXkM3ncQYNdPoNJPkZ6Ee3jHq/ft0VwT/7CE4U0bxyiXgYMXX+DQSUHvhTs8JhjDFHTMIS4cI7QJW08SqDa59D/Rxu5TRBOIPnCKfye3ojVKGxmk2lcvLN2enDvV3ormatj9LsLftXVVIgViX2csRvfJRhf4Am9zZe5bCscBhjzOtFBGfiNLmJ0xB1iOsX6Q2/gZbnCIvLuG4BWusQdbJDUnunTclPZpd+A3ZeyUbJj+bmEhFcslZHCFmv8h1mBH4QrHAYY8w4BEW8ue/GU0Wba0RbzzNM+mhpFgpFAkc5sGv7+gSP/WZWQIISlOcP2vLIWOEwxphxEkGqS4TXp0khW8sjinaIopuTaLhu8dY12HOV7DJoZwXEL0Bl8XWJbIXDGGOOGRGHMLy1HyOOW/T7q3u28QiCWZywBGEpO7y18wp4OaicuP/pe++BFQ5jjHkIeF4ZzyvfuJ2mEVG0ierNObGCiUXcBKhdBC+846m733KWB75HY4wxR85xAnK5EzduqyrD4Q5R0oNCAHEfv7uBV1x44D/bCocxxnwbEBGC4NZ12FXTI/lZ97ryiDHGmIeMyNF8xFvhMMYYcyhWOIwxxhyKFQ5jjDGHYoXDGGPMoVjhMMYYcyhWOIwxxhyKFQ5jjDGHYoXDGGPMoXxHLB0rIlvAlft8+Ayw/Zpbjddxz3jc88Hxz3jc88Hxz3jc88Hxy3haVWf33/kdUTi+FSLyxYPW3D1OjnvG454Pjn/G454Pjn/G454PHo6MYIeqjDHGHJIVDmOMMYdiheO1fXTcAe7Bcc943PPB8c943PPB8c943PPBw5HR+jiMMcYcjrU4jDHGHIoVDmOMMYdiheMORORJEXlRRF4WkQ+NO89+InJSRD4jIi+IyNdF5CfHnekgIuKKyJdF5HfGneUgIjIhIk+LyDdGr+U7x51pPxH54Oh3/JyI/LqI5I5Bpo+LyKaIPLfnvikR+bSIfHP0dfKY5fvXo9/z10Tkf4jIxLjy3Snjnu/9ExFREZk56LHjZoXjACLiAr8C/ADwGPCjIvLYeFPdJgb+sap+F/C9wE8cw4wAPwm8MO4Qd/FLwO+q6qPAn+GYZRWRJeAfAG9X1ccBF3hqvKkA+ATw5L77PgT8oapeAP5wdHtcPsHt+T4NPK6qbwZeAn769Q61zye4PSMichJ4D/Dq6x3oXlnhONgTwMuqelFVI+A3gPeNOdMtVPWaqn5pdL1F9oG3NN5UtxKRZeCvAh8bd5aDiEgF+PPArwKoaqSq9fGmOpAH5EXEAwrA2pjzoKr/B6jtu/t9wK+Nrv8a8EOva6g9Dsqnqr+vqvHo5ueB5dc92K15DnoNAf498E+BY3vmkhWOgy0BK3tur3LMPpT3EpEzwFuBPxlvktv8ItkbIB13kDs4B2wB/2l0OO1jIlIcd6i9VPUq8G/I/vu8BjRU9ffHm+qO5lX1GmT/2ABzY85zN38X+F/jDrGfiLwXuKqqXx13lruxwnEwOeC+Y1n9RaQE/HfgH6pqc9x5rhORHwQ2VfVPx53lLjzgbcBHVPWtQIfxHl65zaif4H3AWeAEUBSRvz3eVA83EfkZskO9nxx3lr1EpAD8DPDPxp3ltVjhONgqcHLP7WWOweGB/UTEJysan1TV3x53nn3eDbxXRC6THer7iyLyX8cb6TarwKqqXm+pPU1WSI6T7wcuqeqWqg6B3wbeNeZMd7IhIosAo6+bY85zGxF5P/CDwN/S4zeI7RGyfxC+OnrfLANfEpGFsaY6gBWOg30BuCAiZ0UkIOuMfGbMmW4hIkJ2bP4FVf13486zn6r+tKouq+oZstfvj1T1WP2nrKrrwIqIvHF01/cBz48x0kFeBb5XRAqj3/n3ccw68Pd4Bnj/6Pr7gf85xiy3EZEngZ8C3quq3XHn2U9Vn1XVOVU9M3rfrAJvG/2dHitWOA4w6kD7APB7ZG/S31TVr4831W3eDfwdsv/kvzK6/JVxh3oI/X3gkyLyNeAtwL8Yc55bjFpDTwNfAp4le8+OfVoKEfl14HPAG0VkVUR+DPgw8B4R+SbZWUEfPmb5fhkoA58evV/+w7jy3SXjQ8GmHDHGGHMo1uIwxhhzKFY4jDHGHIoVDmOMMYdihcMYY8yhWOEwxhhzKFY4jHnAJPNZEfmBPff9sIj87jhzGfOg2Om4xhwBEXkc+C2yOcRc4CvAk6r6yrewT2/PJH3GjI0VDmOOiIj8K7L5r4pAS1V/YTTlxU8AAfD/gA+oaioiHyWb7iQPfEpVf360j1XgP5JNv/2LqvpbY3gqxtzCG3cAY76N/RzZiO8IePuoFfLXgHepajwqFk8B/w34kKrWRlOnf0ZEnlbV69OfdFT13eN4AsYcxAqHMUdEVTsi8imgraoDEfl+4B3AF7Npp8hzc/r+Hx1NOeGRzYL7GDfnzfrU65vcmLuzwmHM0Uq5uR6JAB9X1Z/du4GIXCBbKfEJVa2PZhHeuzxs53VJasw9srOqjHn9/AHww9fXkRaRaRE5BVSAFtAcTUf+l8eY0ZjXZC0OY14nqvqsiPwc8Aci4gBD4O8BXyQ7LPUccBH44/GlNOa12VlVxhhjDsUOVRljjDkUKxzGGGMOxQqHMcaYQ7HCYYwx5lCscBhjjDkUKxzGGGMOxQqHMcaYQ/n/MuAOG0UaE3AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.026600000000000016, 0.024683037003977167, 0.022993691449690826, 0.021671286922156537, 0.020442486713345073, 0.01942890096170794, 0.018552228339181232, 0.01785509859596102, 0.017306453744044648, 0.016705992396267695, 0.01632006162513225, 0.015986071371625922, 0.015633685781053463, 0.015299656135791217, 0.015078369664905436, 0.014800467391890306]\n"
     ]
    }
   ],
   "source": [
    "random.seed(5615)\n",
    "\n",
    "a= 0.150171427\n",
    "b= 0.013625329\n",
    "sigma = 0.00288994\n",
    "r0 = .0266\n",
    "trials = 100\n",
    "\n",
    "#trial portion\n",
    "#rate_trials = []\n",
    "#for trial in range(trials):\n",
    "\n",
    "sims=[]\n",
    "for trial in range(trials):\n",
    "    sim = []\n",
    "    for i in range(16):\n",
    "        if i == 0:\n",
    "            trial= r0\n",
    "            sim.append(trial)\n",
    "        else:\n",
    "            trial = sim[-1]+(a*(b-sim[-1]))+(sigma*(sim[-1]**.5)*np.random.normal())\n",
    "            sim.append(trial)\n",
    "    \n",
    "    sims.append(sim)\n",
    "#average price line    \n",
    "\n",
    "steps = 16\n",
    "average_path = []\n",
    "for step in range(steps):\n",
    "    average_price = np.mean([trial[step] for trial in sims])\n",
    "    average_path.append(average_price)\n",
    "\n",
    "    \n",
    "    \n",
    "# trials graph with billion lines\n",
    "    \n",
    "    \n",
    "for i in range(trials):\n",
    "    plt.plot(sims[i],alpha=.5,linewidth=.25)\n",
    "\n",
    "plt.plot(average_path,color = \"blue\",alpha = 1)\n",
    "plt.title('100 Paths of intrest rates')\n",
    "plt.legend(['Mean rate path'])\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Rate')    \n",
    "plt.show()\n",
    "\n",
    "print(average_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 2</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Back in 2018, General Electric (GE) was not doing well. Due to decreated earnings and increased losses, GE stock was down by over 50% for year-to-date, and they also abruptly fired their CEO. During this time on October 2018, a 15-year GE corporate bond paying a coupon rate of 5.25% was valued at \\$982.86.\n",
    "    <br><br>\n",
    "    Assume annual coupon payments, create a numpy array called <code>cashflows</code> to store the future cashflows of this GE bond for each year over the next 15 years (check that the array is of length 15). Plot the cashflows in a bar plot with appropriate axis labels and a title.  \n",
    "    <p style=\"text-align:right;\">[5pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cashflows=np.array([0,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,52.5,1052.5])\n",
    "print(len(cashflows))\n",
    "\n",
    "plt.bar(np.arange(len(cashflows)),cashflows)\n",
    "plt.title('GE bond')\n",
    "plt.legend(['Bond Cupon amount'])\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('$ Amount of cupon')\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 3</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Calculate the average net present value (NPV) of the GE bond's cashflows by discounting using the simulated paths of 1-year risk-free rates from Task 1. This average NPV is the \"fair value\" of the GE bond in the absence of any credit risk and assuming the bond's cashflows are gaurenteed. \n",
    "    <br><br>\n",
    "    Recall we can calculate the present value of a future cashflow at time t over a path of interest rates along times 1 to t by:\n",
    "    <br><br>\n",
    "    $$PV = CF_t \\exp{\\left(\\sum_{s = 1}^t r_s\\right)}$$\n",
    "    <br><br>\n",
    "    And recall that the NPV is then calculated by:\n",
    "    $$NPV = \\sum_{t = 1}^T PV_t$$\n",
    "    <br><br>\n",
    "    Plot a histogram of the distribution of the NPV of the GE bond. Label all axis and provide a title. Are there any scenarios from our simulation where the GE bond's fair value is at or below its current market price of \\$982.86?\n",
    "    \n",
    "    <p style=\"text-align:right;\">[15pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "average_path\n",
    "time_period = np.arange(0,16)\n",
    "\n",
    "NPVs = []\n",
    "for sim in sims:\n",
    "    negative_rate=np.negative(sim)\n",
    "    discount_factor = np.exp(negative_rate * time_period)\n",
    "    PV_Cashflows = cashflows * discount_factor\n",
    "    NPV = np.sum(PV_Cashflows)\n",
    "    NPVs.append(NPV)\n",
    "\n",
    "\n",
    "\n",
    "plt.hist(NPVs, color = \"Green\",bins = 15,density = True)\n",
    "plt.title('GE bond')\n",
    "\n",
    "plt.xlabel('Price')\n",
    "plt.ylabel('% of bonds in Price bin')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the rates we have , i even used excel with the simulated rates and mabey i did that part wrong but i get close to 1491. This is becasue its a super previum bond , it pays 5.25 while the market rates we had were at around 2 the lowest being ~1.48\n",
    "\n",
    "SORRYYYYY none of them are even close"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 4</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    Write a function that performs the same NPV calculation on the GE bond cashflows as Task 3, except it takes an additional input parameter <code>spread</code>, representing the credit spread, which is applied during the discounting, specifically: \n",
    "    <br><br>\n",
    "    $$NPV = \\sum_{t = 1}^T \\left(CF_t\\exp{\\left[\\sum_{s = 1}^t(r_s + \\text{spread})\\right]}\\right)$$\n",
    "    <br><br>\n",
    "    The function then returns the expected NPV, representing the price of the bond. Use this function to price the GE bond first assuming a 0% credit spread, and then again with a 10% credit spread. Verify that these two credit spreads results in prices that bound the observed market price of \\$982.86.\n",
    "    <p style=\"text-align:right;\">[10pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_path\n",
    "time_period = np.arange(0,16)\n",
    "\n",
    "def BondPrice(spread):\n",
    "\n",
    "\n",
    "\n",
    "    NPVs = []\n",
    "    for sim in sims:\n",
    "        spread_rate= [x + spread for x in sim ] \n",
    "        negative_rate=np.negative(spread_rate)\n",
    "        discount_factor = np.exp(negative_rate * time_period)\n",
    "        PV_Cashflows = cashflows * discount_factor\n",
    "        NPV = np.sum(PV_Cashflows)\n",
    "        NPVs.append(NPV)\n",
    "        \n",
    "        expected = np.mean(NPVs)\n",
    "        \n",
    "        return expected\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1487.932670649394"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BondPrice(.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "526.6595835728027"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BondPrice(.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 5</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    The market-implied credit spread on GE is the amount of spread that when applied to the NPV calculation on the GE corporate bond cashflows, gives us the market observed price. \n",
    "    <br><br>\n",
    "    Estimate the market-implied credit spread on GE using the <b>bisection method</b> on the function created in the previous task. Use 0% and 10% as the initial bounds for the bisection method. \n",
    "    <br><br>\n",
    "    According to this estimated credit spread, what is the probability of GE defaulting on their debt in any given year?\n",
    "    <p style=\"text-align:right;\">[20pts]</p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 6</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    The GE bond described in the previous tasks was not callable. For a callable bond, investors would demand some additional yield to compensate for the reinvestment risk associated with the bond being called away. (When a bond is called, the face amount is returned to the investor, and no more future coupons would be paid.) \n",
    "    <br><br>\n",
    "    This is because the bond issuer (i.e. the company) would favor calling the bond when rates are low so that they can reissue a cheaper bond and pay lower coupon rates. Bond investor do not like this because if the bond the called they must now reinvest in a low interest rate environmnet. For this reason, callable bonds tends to be valued less in the form of an additional spread added to its yield.\n",
    "    <br><br>\n",
    "    A 15-year callable GE bond paying a 6.25% coupon rate is valued at \\$986.45. Assume that the bond can only be called at the end of each year, and that GE would only call the bond if the 1-year Treasury rate falls below 1.5%.\n",
    "    <br><br>\n",
    "    Using the same set of interest rate paths simulated from Task 1, calculate the following:\n",
    "    <ul>\n",
    "        <li>The percentage of trials where the GE bond would be called.</li>\n",
    "        <li>Another numpy array storing the simulated cashflows for the GE callable bond under each interest rate path. The shape of this cashflow array should be <code>(1000, 15)</code>.</li>\n",
    "        <li>The average cashflow received from the callable GE bond at each year averaged across the 1000 trials. Plot this in a bar plot with appropriate axis labels and a title. Explain how this plot is different than the bar plot of the non-callable GE bond from Task 2.</li>\n",
    "    </ul>\n",
    "    \n",
    "    <p style=\"text-align:right;\">[15pts]</p>\n",
    "    </div>\n",
    "</div>"
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    "<div class = \"panel panel-primary\">\n",
    "    <div class = \"panel-heading\"> \n",
    "    <span style=\"color:white\"><b>Task 7</b>\n",
    "    </div>\n",
    "    <div class = \"panel-body\"> \n",
    "    As mentioned previously, for a callable bond, investors would demand some additional yield to compensate for the reinvestment risk associated with the bond being called away. This additional spread is known as the \"<b>option-adjusted spread (OAS)</b>\".\n",
    "    <br><br>\n",
    "    If we assume that the credit risk is equivalent to the non-callable GE bond, we can apply the same credit spread estimated from Task 5 when discounting cashflows for the callable GE bond. Any further incremental spread needed to match market observed prices can then be attributed to the call risk and is thus the OAS. \n",
    "    <br><br>\n",
    "    Rewrite the funciton from Task 4 to apply the credit spread estimated from Task 5 as a constant. Additionally, modify the input parameter to be the OAS instead, and then incorporate the OAS in the NPV calculation. Specifically:\n",
    "    <br><br>\n",
    "    $$NPV = \\sum_{t = 1}^T \\left(CF_t\\exp{\\left[\\sum_{s = 1}^t(r_s + \\text{credit spread} + \\text{OAS})\\right]}\\right)$$\n",
    "    <br><br>\n",
    "    Then estimate the market-implied OAS by calibrating the spread such that the NPV of the callable GE bond cashflows matches the observed market price for the callable bond. Use the bisection method with 0% and 5% as initial bounds.  \n",
    "    <p style=\"text-align:right;\">[20pts]</p>\n",
    "    </div>\n",
    "</div>"
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