fibonacci.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Algorithms and Fibonacci "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This first Jupyter Notebook will serve as an introduction to algorithms, and will save Miles time from discussing it in class.  Hopefully this first notebook will be review for most of you, but it is a great problem to use as a refresher and introduction to the course and of what is to come.  First, let's clearly define the problem we want to solve.\n",
    "\n",
    "**Print the nth fibonacci number.**\n",
    "\n",
    "We can define the nth fibonacci number using the following recurrence relation:\n",
    "\n",
    "$$f_0 = 0,  f_1 = 1, ~~~~~ f_n = f_{n-1} + f_{n-2} ~~ \\text{for all }~~n\\geq 2$$\n",
    "\n",
    "Please note that the lecture slides may use a slightly altered definition, which starts at n = 1 instead of n = 2.  However, both definitions will lead to the same results for $n \\geq 2$, so there should be no issue! This recursive definition gives us a good idea to writing a solution.  We can simply use recursion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nth_fibonacci(n):\n",
    "    if n == 0: return 0;\n",
    "    if n == 1: return 1;\n",
    "    return nth_fibonacci(n-1) + nth_fibonacci(n-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the code for n = 10, 20, 30, and 35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nth_fibonacci(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nth_fibonacci(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nth_fibonacci(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's time the algorithm. Your computer may be faster or slower than mine so we will be interested in how the time *scales* as the input increases rather than the actual number of seconds elapsed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_elapsed(n):\n",
    "    t0 = time.process_time()\n",
    "    print(nth_fibonacci(n))\n",
    "    t1 = time.process_time() - t0\n",
    "    print(\"Time elapsed (in seconds): \", t1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Measure the time it takes for n = 10, 20, 30. Note that if the process is too quick then it may just show 0.0 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to get a better approximation, you can run the same process a few times then divide out by the number of times, essentially taking the average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_elapsed_average(n,m):\n",
    "    t0 = time.process_time()\n",
    "    for i in range(m):\n",
    "        x =nth_fibonacci(n)\n",
    "    print(x)\n",
    "    t1 = (time.process_time() - t0)/m\n",
    "    print(\"Time elapsed (in seconds): \", t1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try different values of m until you get a non-zero answer for when n=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed_average(10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed_average(20,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_elapsed_average(30,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot some results to see how the time scales as input increases. Let's pick a range of values for $n$ (say, 30 to 40) We will time each one and plot the points on a graph. (It may take a few minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_values = []\n",
    "y_values = []  #this initializes two arrays that we will use to store the points that we want to plot.\n",
    "for i in range(30,41): #if you want to iterate from 30 to 40 inclusive, you must include 41\n",
    "    x_values = x_values + [i] # this appends i to the end of the x_values array\n",
    "    t0 = time.process_time()\n",
    "    nth_fibonacci(i)\n",
    "    t1 = time.process_time() - t0\n",
    "    y_values = y_values + [t1] #this appends the amount of time to the end of the y_values array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x_values,y_values)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"time taken\")\n",
    "plt.title(\"Fibonacci algorithm time analysis\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the time it took to run the code seemed to take exponentially longer as we increased n. If you want to read more about the time complexity, you can view it here https://www.geeksforgeeks.org/time-complexity-recursive-fibonacci-program/\n",
    "\n",
    "From the graph above, there is good evidence that the time taken by the function ```nth_fibonacci``` scales exponentially as input increases. To get a better idea about the base of the exponential, we can plot the same points on a linear-log scale meaning that you take the natural log of all y values and plot them against the original x values.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_y_values = [np.log(y) for y in y_values]  #this takes the natural log of each value in y_values\n",
    "plt.plot(x_values,log_y_values)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"time taken (log)\")\n",
    "plt.title(\"Fibonacci algorithm time analysis (linear-log)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice now that this looks like a straight line. It is always the case that if you plot an exponential function on a linear-log graph, then the result will be a straight line. Furthermore, if $m$ is the slope of the line. Then $e^m$ will be the base of the exponential. What seems to be the slope of the line in your graph? What does this mean about the base of the exponential of the original graph? Can you find any explanation for this particular number?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Exercise 1** \n",
    "estimate the slope and enter it into the corresponding gradescope question\n",
    "\n",
    "## **Exercise 2** \n",
    "using the slope, estimate the base of the exponential of the original plot and enter it into the corresponding gradescope question."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You've probably already seen an algorithm for the fibonacci problem that scales linearly.  Before we consider it, let's first look at a recursive tree for our algorithm with n = 5, which is taken from our lecture slides."
   ]
  },
  {
   "attachments": {
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Vqd2Vu5XFUtqYKW0qlLzp1FSfuXy9e3DEZncyKN7IugefcyMIcl/g8TDdg6OvXS4Od146pD6voPWB7YyXmHSEXtMeH2LyHthXmJ2WIBLwA0kIsj5B5UYQZPMDbntCq//z2RsyW8k++VsR/DGS42HTQkLcXsroklXo9/YzezIz8gqy05QyMZuGIOsPVG4EQTY5bo9nXKO/UFJpGb25X/FWFH+IRzjZtLcB561zKZqMO/u8B6Lic4p2bgtXyUkCnyci6xG8LxEE2cwwjFejM1bUN04M1hRIr0TyRubKNkBwGBVXu0tWmUqeH+wuuV5ZPzyudThdbDKCrCfQcyMIspkxmm03qupbmkvyROe2y+po4g5ibPMIeizJV6dOqaOyju7OjwpTcWkaO3sj6wpUbgRBNi0ehrlQWnerqSyNurxffW3ms+0FcDH0qD3yrYnHKFnWoaK8rC0JJInVk8g6ApUbQZDNidPlrrrVWV5dmsS5lC+/IaVMbMKd8IZw3Aylcaqv6R6ycLPzduXnZaRwaQrHWUPWCajcCIJsQmx2R2f/8MXisljv5RzJjVDuJIeztLLO4yXHHRH1pqIxonBrWm7h9jSxUIDmG1kP4F2IIMhmw+F0DY1riqtrpY7KnZJiFVe7VNkGSI4nkj+SJ70ew1xrbLxZUtuk0RtdbjebjCD3DlRuBEE2FR4PM6bR3ayqNU/UHVSdVXM1i3y8PRdOiDeUN1mkuJ7Fv1hVW3K9onZyCsR7mUdDkNUCa8sRBNlUaHTGc8XVw903Hwx9OVY4uGzZngaKSDdDt5rSr0+dCIvNPVK4MzEmnE1DkHsBKjeCIJsEKM3MVvsb1ysn+8vyRW+kidsowg2+mU1eAd4QjoPhDttiy4wnHcKdR3bnbU2MpimKTUaQuwv59a9/nV1FEATZsDBer83uuF7dPNhdlcG7kiZu5ZP21WoLDsehOB4RZZGR43orp300hEPQcokYG5wj9wR8zo0gyIYH3LbFam9o72m6VZVM3dwqvgUqy6atHjzCEScY2C07L7VeK68ua2zr0hnNDIMTeyN3G1RuBEE2PA6nq2947EZ5eSxRtV1SJX97HrBVhyZc4byxo+o3w9zXSipvVjQ0Gy1WFG/kLoPPuREE2dhAIXara+BScQnPXP5YxMtiyryMPmBLwhvCcTF0iXZ/s31vbOKuhw7kSsUiAqvNkbsFKjeCIBub3qHxSyVlTk3FA+q/raQP2JIA8ba6he2WjDrLUZ5q+yOH8kMVMi6NbdaQuwEqN4IgGxUP4+u6faG40jVZkid+K1HYQ3LuasW12S3utyXVmg6QqoL9eTvjI8OEAh6bNj+M12u22Lhcms+l2U0IshTwOTeCIBsSt8ejN1pKaptN4/UZ/OtxgoG7LNuAmDInCzt2y866Jq5fKy1u6x00WWxs2jx4PMzwuLaiqcNsvcOeCDIfqNwIgmw8GMZnWyub2traancJz24Rd3CDzbp9F+CTdvD6x0PPcHSlN8pLGtu7rTbHfHWZINtGi/VCaV3XwKjZYme3IsgSQeVGEGTjYXc4mjr7i6uqC2XnU8SdAvJe+leCw0Twxx6KeC3ceelKacWVika70xVUuo0W29XKppbuQdBvp+sOM4UjyHygciMIssFwOF317X0VNSW7xNeyJA0CYvmyPWSLvWXM0rnk7OvlwgnxiinzXtX1POEbTbcqX7tcOqnVz+otZjBZ6ls7G5obk3hNtNeE458jywaVG0GQjYTHw7T2DDY0VYUz1TnySiFpBcvLpi0FxkuM2SOKpw5d1x4v1h6GddjCpi0LkuORUsZMSU2+6PRoX9Wlkoq+4YnpucUsNntjR19DU0UW/8pWyS2SsThdOO0YskxQuREEufeAAQWRY5g7dHVxuz29w+Ml1VV8a3W+/IaKq12ebHu8pMElr9TvtgpzQ+N3a3gHy/SHRuzRDubOLcMXAD6MlDZmS2tzhG9ph8qKqyp7h8btDpfD6eroH2lqrla5KnMVlQpaF8I4cMJQZNnguOUIgtx7zFb78LiWosgFRgJ3ezxTBtMbV0sZQ0Oh9EKscGB5Q5+Atza7JbXG/DbnkcN79xVmpymV4Q1D1JhFrKLH+aQN3POyB1WBN1KEJ5w3JiKmuifprjGXTCY3W2yXisvE1pI9yqtK7pSNEXZZMyOitsRFhrJvQ5ClgMqNIMi9x2i23qhp7hoYjY8K53GDi7fWYD57o3JiuPGY8pV4YT+x3IHS7Ay/2ZhVYjh1eHdRdmqiXCpSycVxkZENgyEdOpWI0Ku5mmUfPAB8fFBoFT02ZuRcbXa29gzJXTVF8qtRghFIBWffas4Kj0pNjMbZQpHlgMqNIMi9x+F0tfUOg3SD844KU/F5NEnc9ixPozOW1TV1dtQdU70aK+inCdfybLGT4d4ybq+zn9qelbt7R7pIwIMogeBwRAJ+Umzk6JSnc0rJuJ2hvAmSwyzbeQPwXiFpi+CNeBkn47IcVJ2P5I9SHA9EBG4v1WTIDo1ITYmLZPdGkKWAyo0gyL3H5fZ0D45oxztF7s7uCUYqlggFvOkJsA0mS/Wt9va2yp2Cc+mSFj7hWN4Y4R4v2WHe2uQ4GhabeyBvu0wiJvzxAYg3SRKg4mFqlc3F7dSKTXaOmqehOO6VmG/Qfh7pCOONRfMHw3njsO7byuF4vUSjcYcyPDU5LhJHO0eWAbZQQxDk3gMizaUoEWkqkJ53jt+4Vlrc7h+PzOv12hzOW5397e01sSEl2bJ636zby1JTcLqD1rhq81Fx2K69udtDlTKCuE01weVHh6l25+xITi3s9J6o1O2dcqpczIoGKAXtV9C6OGE/fOzAFk6Il0s4iBCP0+V2e7BjGLIcULkRBLn3UBRJ0TRNuOIE/cfUZ5ip0htlpbc6eo1ma1f/SHlttdpVkq8sF5FWUD72PUsBZFvvkl+beiBEklG4c2dMuIpNuB0w3+EqOdjxnB2Ft5wnSvWHtE71CsV7LiTHQ3FAt33SzW5CkKWAyo0gyL2HIgkuRTJeEiQ2gj/6UMRroc7L52+Wvn614qULJWpXaZ6s3NeZarkYXLKrmgdMdNbxfXuTYsPna74eQCoW7t217dThfYOcw5cnHxi1r/LTaDg5n7B73A5UbmR5oHIjCHLvASmlaYogaKe/R7WUMu1VXssTvdXf0xARUlOouKHiaQJ7LoMpp6rGsHvUm3vq4J6YCDVJkGzC/FAkuS0p9onj+wn1gfOax1tN21zMas7gySftjNvhwtpyZFmgciMIsi7gUhSHZJXbNx4ZbdwurTogf/2A8oKKO0lxljluicklbTLuGPDu3ZtfsCUhms/jLqZNGEQSsGdcZOjBoqKwuKISw8kGY47ZLfb62oyvAj7P7XGi50aWByo3giDrAp/nJmmHhxtQx4B4Z8saYgUDPMLfKnuJwHHsHn6bOb2X2ZeUsjMnI0XA4y6pLTeId2J02MGigrD4vXW2B5rNO/RO+QoHSQ0AntsDnhuVG1kWqNwIgqwLuDRF+j33tK/lhHh9w5kty+XCQVwM3WdNqLUciYzP27srQyzkL/x4OygQT0SFKk4dLIxNKqq1naozFRrdkpWLNy/wnBtry5FlgcqNIMi6gKbAc3NXOHL4NB4vOeEIOzv+cGR87u6dGSq5hE1YOgRByMSiRw8XZGcVtjiPX5o44as29y4roHgbPmljPNhCDVkmqNwIgqwLuDRJ+Dw3d4WiCIBsjzvCL2geC4/J3u/vus0mLBfw6jRFgnE/tHu3UbjvldEnxxwRK+ktxifsXsZld+AU3chyQOVGEGRdAJ6bJOmVe24Q/nF7RIXhaIhk+6HC3FCVHESXTVsBHA5HLORnpCQc3L2XDt1zSfNorzXR5hGwyUsElDuEcdkcTvY1giwFVG4EQdYFXH8LNTsjWGH77SmXssFcoOfm7s3LSYwJ53NXcxwViUiQlhBzqKiQCD1Qbn6o07LV7BazaUuBIlyE12FH5UaWBSo3giDrAnDcFEXbfS52mcoNkg8muFpfNOwt3JmVu2Nr0vTI56sIn8dNiYt6+FAhoSgo1R9vM6Uvo8Gab0R0rwM9N7I8ULkRBFkXkCTB4/LtDH/ZU3y4GapWn9tuz9+WUVCQnQoHZBNWm8AI5/t2bfMIkhuMuywe4VLrCfzKbbc7ltPbDUFQuREEWRf4lJvHt3lAuZfjucFtt5nTK42Htmfn52Vu4dKr77anYRivVm8sqWsROpsPqS8uYzR1inBzfJ4bW6ghywGVG0GQdQFJkKDcDkawjClF7B7+oC2uVH8sNXVXbuY2qViwjK7bi8TDMCar9VJ5o2OqcZf4RhR/hOAwbNqiCXhurC1HlgcqN4Ig6wLK57l5y/PcVo+wybB9whmTlZYiEwsochUakweF8XpNFltlY1tfV3Um/0qyqGt6+s7F4/VCXMFwvC67w+ld9rMB5D4GlRtBkHXB9HNu9vVSANcbxhsTksaO3n6jxbZ2o4ra7I723v6KmsqtvOKt4mYxZYI4g/ESHv8sZy7G1x/dwfDsHr7NI7B6RBa32OSWGN1Sg0umd8l1LsWUUzXpDJ2wh1tcAqfLzXiX7NcRhOPFkA9BkHWAw+mqa+t5/eyZLyZ/V0RZ2a2LJvCc+8LEqS1bdhzM3x4XGbrqFeYMw1Q3d18tvRHhKTkZfibgtj0MZfdLtYPxhR0Oj++vb/GtCG576WFfurw0lL0kSSbHRX78Hcd4XHrt6vaRTQkqN4Ig6wK3x9PcNfDCa69/LvH7MlpPcJZWNIHxBbM7YIsrNjzMV2UfyM9NS4gmiFVTRCgqb3X2n7lRbdCNh9EDXMLhZHgQLvhlmOBwCJKiKYqm/X+nF4DH5fH5PPgPFgGPB//CXwGfy6VpPpeWioUo28hSQeVGEGRdwHi9nf0jv3nxbx+P/2kob4LkLLnG2xvCcTLcAWt8veWQXZSbt31XVmr8qjhaKCeNZtvVysZRjY4ivBI+h+tTXp5/4cIpuCDTvv7opO8vScxYJwmSQxI+4C9JcAIrEFLAGio2sjxQuREEWS90D479319ffk/kr6L5gzRx5x5TgWfMviXE99fjJQPOe9AWV2M8YONtO1SQtS05TiISgFiy71kWUE5a7U6j2epyu0GMaVBlvzCDLvvl2SfF7K4IsvagciMIsl7oG5743cuvn1D8PkHQDcoNwuz1cnx/fcIcWHl7i+8vSDXBPk5mhHav769v8QpsjFjnUo054yUi/pHCHTvSEvg8LnsOBNn4oHIjCLJeGBid/ONrZ1PJc3H83hCOr5e2r9nX2428/M27BP6mXv6XDN83sViIry6ax6VBm2ER+JfACp9H87hchVScHBuxklk+EWS9gcqNIMh6YXhC+6czVy3GCR7l5dK+Ycx9jbx8fwHa17rL384L/hf4VnxroNAg2yDenLchOL55vQJrRAiHIAnaX63NngNBNj6o3AiCrBesNkfv8LjT5Z5+fuz763ue7FvxNfbyPVCe2c7Lt+6T6E3X1kurndJotB7PEprpQUZIJBK1WgVBDbtpBgzDTE5qb9wocblcW7em7tq1nU2Ygd1u1+sNOp3earXC8SQSsVwuk8mkEDOxe9yO2Wypqanv7OyKi4spKMiDPdkEZI1B5UYQBFl3XLp07W9/ew2klH29CCiKys7OfO97nwTxZje9DZTzFov11VffeOmlVyMiwj/72Y/v2JHNpvlTHQ5nX19/c3PrrVstAwNDJpMJ1EGhkCckxG3btjU9PS0+PpbL5UJwwL7HDyj39evFP/nJr0Czv/jFz8DZhcJlTliOLAlUbgRBkHXH88+/+MMf/txsNrOvFwEo64EDe/7xH58GB8xuehuIANraOr7ylf8HB3z3u9/5kY+8XyplH/wHRB1Sf/GL3zQ1NZtMZpIk4VCQ5HI5PR4G9ty+Peszn/lYcnISCPMs8e7t7fvmN79XWVl76NC+z3/+U8nJibN2QNYCfPaDIAiyyZmc1P7xjy9OTmpSUpL27i2alm3A4/G0tLT++79/o7y80mg0gXGPjo7at2/3/v27Y2Nj4KVebyguLvu3f/sGOHL3nGFlw8PD3ve+p/h8XklJ+bVrN91uN5uArCXouREEQdYd056bpumvfvUfU1NT2IT5IQiOTCaNjIyc9ZzbarWVllb8+7//l91ug0OdPHlMKv37A+nW1o4f/OCnZWUVILpbtqS8613v2LeviM/3jR7vcDjgjX/5y8vt7Z0g4Xv3Fj799GfS0rYE3hiAYRiQ9q997ZtVVTXp6Wlf/vLns7Mz2DRkzSC//vWvs6sIgiDI+qCxsbmiotrlcpEk+cEPvmf79szw8NCFl7CwULlcTtPUrPrq7u7e3//+Tz09faCsTz31jsjICOLtcWOcTufFi5fPnr1os9kVCsWnP/3RI0cOgo0W+RBKJJKoqAiQ+draervdbjZb4uNj4SAzjw/r8AkhvKiraxwbG4cteXm7YAvWma8pWFuOIAiyfgEFpCifNC6GuZJptVohAmhqagHTfPDgXlB32IdNCwnR6fTNze3wF06xY0dmTs4OlUo5fQRYUSqV27dngRcnSWJqStfb22+z2QKp08CRc3N3xsZGQ1JlZXXQSnVkdUHlRhAE2bSMjo6XlVWC6AqFgsOHD4CNZhP8gI222awg52FhYYcOHQDLzibMAMx3YmI86L3H49Fqp+AtbMLbgINXq1WFhbkSiXhsbPKNN846HHZ8DrumoHIjCIJsWsAEd3V183i89PS0yMgILpdmE/zEx8f+y798+X//9+uf//wni4ryQKTZhBmABDMM66EXqAPftWtHZGSkyWS6fr0YTDzD4LzjawgqN4IgyCYEXK/NZrtxoxSMslgsKirKpyiKTXsbcNJguLdvzz5y5OCsivRpQIw7Orrdbg9FkRER4XK5jE24nbi42OTkRBBss9kKJzWZltCfDVkqqNwIshmAEtNisY6Oji11gXJ5gZ48k5MaMG03b5YODQ0vZjwv2MdstgSOHHQUEUitrW24ePFqd3fv3CemyCoC16Krq2dsbNzpdEkk4m3btoL0smlvAx4a5JzP54HbhpVZlhpuqoGBobNnL/b09MLRYmJitm1LC3T1notMJgUHLxAIXC4X3DNGo4lNQNYA7BWGIJsBh8PR1NR85sx59vWiyc/P2bu3cGY3oQBQMsAxz5w598YbZyH1C1/wDbIR1JPNZHR0/MaN4tbWDlj/wAfenZSUMEsM9HrD66+/efr0W6mpyR/4wHu3bt0y3c4ZmUmgV5jFYqZp7g9+8J07drWiaUokEs3Mbbvd8dprZ375y9+Oj09kZWXAQUJDVXfMbQjjIAQ0GIxwariaJSXl16+XgPyHhqqfeOKRJ554NDIygt11Dm++ef7ZZ388MTEB+zzzzLcyM9MXqF1HVgIqN4JsBkwm85tvnvvGN77Nvl4073vfuz760Q/MLY6hBG9ubvuv//o2lNrHjx/+l3/58tzBL2dhs9nPnr3wi1/8ZnBwGF7+8pc/LCrKnyX2Doezt7fv6ae/AvLwznc+9uEPv0+hCNIqCpnuzw1G+amnnoiJiWYT5iEsLBQu08zchhz+7nefO3/+stVq27u36Ec/+u5igiTQ7GvXbhYXl4EADwwMT03pwG2DIwfNfu973xUdHbnAPVBTU/ftb3//1q1WONFPfvLs7t0FEE+waciqgtEugmxCoHhdPOx7bgdk+De/+UN//2BKStJjjz3E4/Hm23Oa7u6et966EJDt+eDxuPHxsQ89dBIK96tXb5SXV7IJyDy43Z4//emvoIgLL7AP7DnTiQXquiFUEgoFMTFRi6zb0OsN4LPBPVdV1YFZd7lccOm3bdt66NB+pVKx8D0gl8sCQ6bDqYeGhvFpyNqBI7EgyGbA6XR2dnZdv14C61B6njp1/NFHH9q3b/cdl/z8nNjYGJq+rcmx2WyprKx+4YWXoKB+5JEHDx7cP2uHWUBJbTAYfvSjX1RV1cAnCWx8+OGTsbHRcwUDtkREhFdUVA8MDBqNpj17ChcTFtxvBEZimc7MOxIZGfHoo6fAcwdyEiQcrDbEXnBdJBJxYWFeTs6OwJ4LA8rd0HALTHZCQrxUKvV4fJXnGo2mpKRMpzOEh4eCfrO7zsFqtba2tre0tMN6YmJCRsZWsVgcSEJWF1RuBNkMzFTu0FD1O97xyJEjB1JTU+64REVFgQ+eqa9Q6I+MjP7617/v7u5NS9vyznc+BgK8sLLa7fZXXz1z7twlnU4/bfvmU244lFgsmpiY7OrqMRqNarU6JSVxbrPn+5xp5SZJ4vDh/QUFeZmZ2xZYduzIgmW6ttzj8YyNjb344is2mx20dv/+3enpaYGkhYEjJCcn7t5dAFEd/M3OzoS4anBwCGQb/jocDlD0+WbzBH/f09NbXV0H6yqVMjd3Fz4KWSOwthxBNhtQ+AqFQvniEAj4Mx+OAiaTqaGhqba2AUT2yJGDCQmxC8s2eLvm5raXXnoV7BrYO1jYhHmAo4GDP3hwX0JC3NSU/vXX35yc1OJMFfMBV+fRRx/6xCc+tPASMNzse/zKDZfD4/F1qobclskWq6Bw+SCe27ZtK/zdvj3z2LFDH/vYB48ePQgH0Wi0EBqWllbM1zgK9pnuM2Y0mux2R2AdWXVQuREEuY3BweHTp98ymy1qtTInZweoO5sQDL+3G//Tn16Ed4GTzs/PBcfPpi0IWLesrAwQ7NbWtuLiMovFyiYgM4AoB1Aq5ZGREQsvsx5CM4zX6XSFhPg0FhR9vq5cdwQMd2Ji/Mc+9iHw0HCc8fGJa9duOp3OoE2b/SdiJzuBG8PjwWhsrUDlRhDk70CJ3NBwq6WljaKo7OwspVK5cMsmsFbXrxdfunTN5XKdOHEUnHRgmqk7At4uLW0L6AEIzIULl7XaKTYBWR28zIxRzFbSigCcdHh4WFFRvkgkBM2emJgcHh6ZefCZTJ/I62WCqjuyKqByIwjyd6BcBtkGB0zTVEFB7syJnOcCjrmszDcLJKj7jh1ZjzzyYHh4KJu2CJKTE+PiYvzdz1pHR8dA+9kEZMVwOMS0zwb/vcKHEXB9ExMTwH/DusvlhnAtqCrDxukTgf8GAuvIqoPKjSDI3xkYGOro6AJHBeX+rl3bhUIBmxCM9vauN944p9Fo5XLZBz7w7rlt1BdGrVZt354Fxb3ZbKmurtPpDGwCsmJANWUyaaD+3O12zfcworW1/aWXXn3uuZ8+88yPYJ8FXPJ0VTz8SxDBLTzEXtMnEolEAaVH1gJUbgTZbED56/F4oBhdmKA+rK6uAWw3CHB0dGRoqHq+Jt8g7Vrt1Msvv97U1CwQ8E+ePFZUVCAWi9jkxQGGPj09DTQGPjCcd3Jykk1AVgxJEqDccB1Bce12x/j4BJtwO52d3S+99Nqf//y3119/s6enb75OaHA79fX1Oxy+FmcQ0ikUcvD0gaSZwInGxtgTqVRKVO61A5UbQTYbdru9t7e/vr5pgeXWrZa+vgEokdn3+AE9bm5uMxiMfD5vy5YUmp49kHUAEFooo0tKym/eLLVarSkpSe9+9xMg2ws/EZ8LlOwREWGg33CWsbHx4eFRNgFZMXAt+Hy+Wq2C2Mtms42MBM/b8PAwuAdMJpPFYrl06WrQwcYhyIMorby8ymq1gWyDJIeFhQa13XCi4eGRwHpUVKRAsFCFDbISULkRZLMxOjr+7LM//tCHPrXA8slPPv2jH/3cZvv7pCCgx1A0azQasFY8HjcxMZ4ggj+ndLs9oAS/+MVvwMnFx8e9+93vTEjwzd/MJi8aEGyhUBgVFQHv1esNWq2WTUBWA8hVCKogPILLCoIatCY8ISFuy5ZkuBD+doJXYLdZwRy8S6fz9dyDG8PtdoeGqg4e3AvHDBrSQcyn1+sD60lJCRLJ0upgkMWDyo0giA8w3KDEgT64FEWDtZrvcebo6NhPf/priA/AZx87dmj37gI2Yen4ewD7ujNZLFYwditsSIXMBJQ7PT1NKOSDGOv1RpBVhpkt3nCVi4oKYmKiGQaisZEf/OBnJSUV0xN0QgzX1tbxxz/+5c9//pvD4YSLVViYd/DgvkDqXKampuAsYPfVamVkZPiyu6IhdwSVG0E2GyKRCIxUQUHuAktu7s4tW1JmTvsIyj02Bsrtc+Fcrm9IjaC+yj8cx82KiiqXywWaffTooTsOvbIAcCKFQgYhAqjL1JTOYrGwCciKgYubmZkuFovBN5tMpu7unll+GqAoqqAg553vfFShUHg8THNz6/e//+NvfON/f/KTX/785//3zW9+DxYw3EajEeKAoqL8xx57GMSeffPtuFzuwcFhCL9gz9TULdPt45C1AJUbQTYbUqn4Xe96xz//85cWWL785c8/9tipmU3BwZAZDAbQY1iHAt3/+Hl2+QAmrKGh6ZVX3gAlSEpKePLJx2NjY1ZSQM88EVg9qzXIlN7I8gAFTU5OCg1Vw1WGvG1qagk6NArs8OCDx+GGgWgPXnZ2dl+4cPn5518Eq3369Ft1dY1mszkqKvL48cOf/vRHt25NnXnPzESv1/f09FmtNrimu3ZtnztvLLKKoHIjyGZDIBBER0emp6ctsKSmpsTEREPhzr7Hh29C7sB4mbDd/ywzsP3vjI6OnzlzDtwbpJ48eSwqKgJsnNlsmV5sNvu0sbPbHeChYaPVOm93I4Ig4NMGTuRv7Y615SzgWePiYhIS4mFZXlMvyFulUuEXUQlciKqqWqfTNfdCwLUGYf7Yxz7whS98avfuwri4WJVKxeVywbLL5fLo6Kjs7MyPfOT9//zPX8zM3CYSCdm3zWF0dKy3tw/CONhn796ipXY0QJYEKjeCID6gSGd8A2OxJXvQhuIvv/x6ZWUN7CkDYZFKa2sbrly5PnOpqakDixbYua4OUm9cvXqjrKxyfknmTJ8Izu7/AIiPU6ce+POff/Paay/89a+/B6fLbl0ioKP79u1OSIgDK9zU1Ox/1B0kh/1yKzp8+MAzz/zPL37xg29849++/OXPfelLn/va1/71Jz955uc/f+69730yNDQUzDT7hmDA8cfGJvh8fnZ2RlISO2wLskagciMI4gOML9ivQNU3ODO3e/YzUWBoaMRms0HpPzEx8eMf/+K73/3Bd77z3MzlL3/528SEJrDzSy+99r3v/RCWX/7yd4GGb8HwjboV8IEkScDi34j4IidQygAreR6RnJwIppmmfX3Dbt4smW59FhQ4aWRkeG7uzmPHDh8/fqSgIC8+PvaOGgx3C3j60tKKqakppVJ+8uRxmsa2aWsL/k4QBPERqOckSZ+vAm12OOxza1YZxgNJAV3X6w1TU7pZCwhD4Ek5AOY7sHE+qwd4PIy/Z5rvRAIBH1sjzwSuSAD29bIAM11YmJeYmBDo96XRaOde1mngXBAogG+GOwEWuCK0fywXNnkeXC53TU1DX98gvDclJTkvLwcCBTYNWRtQuREE8QEFtFQqDZS5UMqDMM8t4nNzd506deLhhx+cbykqyp+eW6ygIPehh04+9NCJw4f3c7nBmzWBzOv1+kBvJdAYHLtj1QEbvXVr6smTx+DKtra2t7d3zjcS6vKAm8RutwfmjImMjHj44ZOhoaqgj1qQVYT8+te/zq4iCLJhcTqdnZ1d16+XwLpCId+9uyAhIT6QtHjgIFev3gBbxufz0tK2pKengYti0/ykp6fu27f74MF98y3h4WFNTc1wBNj5q1/9h/e+912HDu0vLMwFGxfUuk1Oat588/z4+ARBcPbsKQThx0J/1REKBRKJqLHx1ujouNvtyszcplQq2LQVA0Fef//AT3/6a4fDcezYoUceeXCBVmzIaoE/EgRBfPifcUZCKQ8KC1Y46EyOXC5XIOAvsPB4vGnpnd55PtkGoLifmNDAicRi8R3bQCHLAzIfruxTTz0BAVlDw636+sb5Hl4sA71ef+bMObPZHBsbvX//HrVaxSYgawkqN4IgPqB8B5WNi4sVCn3TMA8NDa9i+R4Ur2+8VTsYdIbxQokfERHGJiCrjUgkAlk9eHAfXNMbN0p6enrZhJUB90lvb//585domvve9z6ZlZXBJiBrDCo3giAsIN47dmyXy+UOh7Orq8dqta6peJtMZpAQsN0g4fHxcTEx0WwCstoEpg774Aff+/DDJyGr9Xojm7Ay3G6PTqffvbvwwx9+7549RWLx8kfTQ5YEKjeCIH9n27atUVERbrd7akrX3t41f2+uVUCn09XW1oNskySZk7NDpVq1h6/IXCiK2ro19SMfef+73/1EcnIiu3VlwIUrKMj55Cc/8tRTT4SGqrFT310DMxpBNgMEQYhEoujoKFigDBUKl9lIG2Q7Lc03wiWId0VFzVIHEufzeWq1KvAx/IOjLdShaGhopL29Ez65UqnIzs6USCRsArI2UBQZFhYKl0ahYNv/rxAej6tUKmNjo+GA2BPsbsKZ2/EDQZANh8fjMRiMIyNjsM7nc8PDw5YthG+8cfb73/+JVju1Y0fWf/zHvy7Jn4HSj41NBCYPjY+PFYtF84k3lDzPP//ij370c5fLdfTowS9+8bNYW44giwQ9N4JsBsC5yuWy1NQUWOLj48F/swlLJyMjPTs7Azx3W1snyPD0yCqLAXw2CHbgY4hEwgU89+SkpqOjy2q1cbncEyeOKRRYVY4giwWVG0E2A6CRIN5cLg0LTVPTXbOWAfj1kyePQxxgtVovX742MTHJJiwCOC9FUYGPsfBnaG5ubWpqFgj44OyzsjL5fBzmGkEWCyo3giC3IRQK0tPTioryKYqsrKxua+tY3RbmXv8w1xcuXBkbG1erVY8//ohcLiVvm7UMWUfA9Vrr/oHIUkHlRhDkNsC+g6C+613vkMlko6PjNTX1C09TsVQ8Hk9HRxd4bo+H2bZt6969hfNN+Yzcc1xuj9FsHdXoHMFmCEXuFajcCILMBmx3Rkb6oUP7uFy6rq6hvb2DTVgNHA7HW29d1GqnkpMTnnjiUbFYvHATdOReAUKt0Rneuln9u1cvdQ+OOlw4e/p6AZUbQZAg8Pm897znXUlJCf39g6++esZqta2K5bLb7Z2d3ZcuXSUI4tCh/dnZOOrW+kVnMJfWt3Z2NokcjS9fuF7f2mO02Ng05J6CM44gCBIE8MFSqVihUBiNRoIgk5MTlUrFShq+BbBYrNevF09N6fbuLXr44ZNhYaFouNchEKVZ7Y7rVbeGuiu2C87nyMo9LkvraIjdTSmkYiE2J7zXYH9uBEHmRa83aDRal8ulVqtVqlVQbpvNNjo6bjKZw8NDISzg8XBC7nUHiILd4axq7qqpvZlCXNwlqxCTZr1LXq3PH+HsiU/OzcvaFqaSkSu+GZBlg8qNIAiCsIAg2B2OroGR05euptJX82TFKq5vzlbA7BY3GHY02o9GxWUd3Z2rlEpomsIKk3sCKjeCIAjC4vZ4eofGXj53Ve0uO6J+S81jZTuAg+F1mlMvaR5WRWx78EBhTISawrHK7wWo3AiCIIgPkIOugdGLN0vcupqHw/8qp3UUx8Om+fGGcBwe3pgj8pL2UY4k/WBhYUZyLI5YfvfBcAlBEATxMTyuLa9r8BiaDyrPyWn9LNkGOCFeHumI5g8dU70qsVeWVBZXNHVY7b55Wtk9kLsCem4EQZD7HYbxThlMl8qqpwbLdgjObpM0k3NkeyaMlzNqj6o17dGQBZmZBbvSkyQiIc7yedfAjEYQBLmvYRjGYrNVNLYO9Tdu5V5NFbcvLNsAwfFGC4aLZFeimatllTfK6lt0RrPLfYd3IasFKjeCIMh9jdXurG/rKa2p2847lyG9xSMcbMKdUPM0uxXXcoVvFleUXqmo0+gMWIl7d8DacgRBkPsXm93R0jP41tXr2dxzOfJyCWUiOEuYX4TxEg6G32VJKTU8qIzaeSB/Z1JMOI6us9agciMIEgQoF9xuT0NbL0FytsRFSUQCNgHZRDhd7uaugeKKYoX96n7lVSltuGM9+Vy8IRy7h99vTaizHmWkubtzdm5NjMGu3msKjn6KIEgQXC53W+/QjYqK/uFRbwghk4h4NI1eajPhYZieobGK2krSWLFHcVXF1ZJLcdvTwD1BE24JbRJxNBMmomuc4XIFUpHQJ954w6wNqNwIgswGrNi4ZurM1Zu0tYnn7Owdt7sYnkoho2ly5QOgIusBj4eZmDKcu1HimaraI78QIxjicFZU/0pxPDLaoKaHh/Tc1mGnUCiWisRcmkTxXgtQuREEuQ2v1zuhNZy5VuqYanxA/UqmtIHjNhR380w2JiJUKeDxsCze6DBer8Vqf/VymXmyoVB6IVnUtSqXlOAwYsqSKOyaNHNr+1xuLx0VpqYpFO/VB5UbQZDbGNXorlXUjg3WPxj2cgR/VEDa1VyNijveMCIemrTJZVK5RIRl8YZGZzRfLK0d7Gs4JD+dJOqiiFXrzQW3BcVxxwn7PR5P22jIsI6JClPyuVy8YVYXVG4EQf6OVm8qr28e6q3eLT2TIOrlEi6C4/VXhOqV1Gi/XjiocfL5IoVMQhAEFsYbEZDtmub2Wy11hZIzyaIOiMxW9zpyOF6acKnoSV6IsW+K6pnwhCpkfD6XIkl2D2TFoHIjCOLD6/WabfaKxraejvIt1JVsaQOPdHJ8bcx9ZTFFuBW0TkJMjhuJngkXxRWB84ayGL3UxsJstTe19zQ2VSQRV3bJqoSkDSIzNm31gHuCRzqklF4Yoh3QcoamvGKRWAjqjSOcrxKo3AiC+KdkdrqaOvur68oSOVdz5FUiyjpTk2Gd4DAg3nJqYsTAvTVoEwolUomIpkgCxXsj4PWGuNzuzv7h8ppyqb3soPqKiLSuhWxPwyWcclqnpkZujfGHJh1i3/0iRPFeFVC5EQTxNSbvHRp77XLJFvJyrrxCThvYhNsB8y2ljdG8foONU9LppWheqELG42JvsQ2Ah/EMjmnOXCuT224cUl+CS3wXLhrF8cANEy/s69by20e9JMWLClNCqIc3zApB5UaQ+x2X2zMwMnH6ys1ob2mR4oaCq1vYinEJV4xgiAqxNAySOitHrZCJhXw2DVmXuD2eySnDSxdKwG3vVlwN5U2uqdueCUR7fNIeJ+w32bxNwxyTPSQ6TLXIBufwEd1uDyr9XFC5EeS+hmGYvuGJq2VlhLH6gOq8iqulCDebNg/+NmsuJVcrCNH1aqkBDSOXiiUiITZZW58Eum6fv1nhmarcI78QyR+hCRebdleAG4ZLOFX0OMGYWkfpSZNbrZDzefTCYwP4BhXQ6jr6hpVSCU4BPgtUbgS5f/F6vaOTurLaWuN4TZHsQgx/iL6TbAcAC8QjHDJKTzP6YT0xOMURCYUigQC8FLsHsj7w9c6fMlTUNw71VsEljhP0gwNm0+4iIN5wXgWtCXFbuiYIvTVEIpIIBfz5JgZ1uT3jWv2lsgabwxkXFSrgcdkExA8qN4LcpzBer8lsvVhaPTlUmys6t1XSRhJLG/ySS7gU9JSCHGmdEPRNOJRyOZTFOPLGusJksVU2tLS3Ve4UXsqQNvHJxc4DNgu31+d6VzLOGryXRzoi+KOU19QyRk8Y3GqlSsDnkoSvOpzdyQ/DMFMG8/XKxqb2LplUmhofLeTz2DTEDyo3gtyPeL0hDqfrckVDd1fjDsH5bGnDUmU7AEX4miDFCXo6NcLmQQePJwxXKUiSROleD3g8zM3a5lst1Snk9d2qYnq5I654vOSkI4wJISnCvaSZxGYBdwXJ8UTwRiXEVOcE1TzkDlMpZBIhwbmtg4LF5rhRfavuVpOI1AvEoVsTY0QCbEhxG6jcCHI/YrHZqm91ltfU5InfypLUgxlattaClxKQ9kRhr9bKbR1xW5xkdJiKQud9r3G5PdUt3ZV11Umca4XK4pW4ba1D/droE03G7ULSqqSnljcxyTRwX8hoQxhvTGvhVHR5xEKhXCoK9BYLdF27VtXU0Va+hVcexps0kylpSQliIU5Vdxuo3Ahy32Gx2Tv6hm9UVKRzL22XVEso80paGoM+w9t5hDOUN+px2zvHiXGDN0KtgLIYpydZdRgGrtSdgyK7w9k1MHK5tDLWez1HWuLvA7acSwxuG2T76tRJrzyfFkWOWNUul0vF1VCEZyVxGWi/gLSF0qPwOZuGCTiLXCLm87hOl7uyqbPxVmUyeSNTUmtlJBPMtm0pyTjJ7CxQuRHk/sLhdHX2j5RWl8ltN/cor8to4wotVAC/87bJKW2Ix9wz4Z00E3KpBMpiHPNyFQHZ1uqNerOVJIgFhjSBSzw8rr1aXiUwlxTJr6h5mmXMug14vRytU11r2jdO7TtYWJCenGR1C3umxCC3clpP+0fGZXddOvCR4IYJ446abY6eSY7NRdI0d3hcc6OyPNpbslNSJqWNeqdq0JWZkZoiEwvZtyF+ULkR5D7C42FGJqduVFa4tdVH1OdV3JXWfM4ETJh/epJJfoiufog7aXAq5QqBgI/ivVp4GGZoXFNS20pRJNjQoOLt9jDjWv3V8sqp4eoTYadDuZOL7C8wF7NbUmcs7A05WJhTsDM9KVQpC1MprR5B46jU5XIr6CkuB8R7+fcPvJdP2qMFQ1abs32c6hkxdPcPiGw1+xQXIdpgvByjW95py8remiaXiNj3IH5QuRHkfgEcm85kfv1ymVtbul9xIUa40imZgwJWLJQ3qaZHb40K+jWMTCJRySU4Quqq4PWGmKy2kvrWrv4RLkXOHY8MLqfRbLlSUT/cW/lA6Bu+AXOWK9seL1mhK+pwHdi2Lf9AXmagy4BIwI8KU9E8cUmvyOoklPSkkLSu5C6Cjw43TJRgiPAYOzWCEPvoIxGvqHhaCCiZENLiETcbd+zYtlUhFbNvQPygciPIfYGvD5jV9vrlcutkdb70cpKoZyVuaWGgKJdRxmjB4KiBbBhkKIobrpLP13MXWQpem9PV0tlrMoyMT06Y7d6Z45F5vV6bw3muuHasryxfejFN3E4u92m0i6EbjDvqLYe3phfuz80S8P/enZoiqTCVPFylvDVCDxtFElIvp3UrDMwIjlfF1W4RdWwRd0DYR/nr9r0hHJtHUKvbuTMjXSmTBPZEAqByI8jmB8p0vdF8taJ+qLemSHI2SdTFI5bZ0ngxQDEeqAhV0WN2p/vWMGlzhijlEj6OcL4yfE2vXe6Gtp44TnESv6lljDtpdKuVcj6PC/lqc7huVDf3dFZm8K5uEzdC/i8vr+0Mv9+adFN3Ijm1oGhnlkIqmXnVYJ0ifQ3K1ErViJ7snpJQIVYQb7jiy7608EaScAtJm5C0UIR7+jgQQFTp87PSUlXy2z4DgsqNIJsfvcnS0NbZdKtqu+BymrhZTFnYhLWE5DBCyqakxq12Z+cE4fSQErFYwOPhIKkrgWG8ta09Yd7andJKgjF3+8cjEwvF3hBvc3d/ZW35Fvp6lqRGShvZNywRJ8MdtUeV6B+QRRUeKMgJU8rmVpaAiILRl4qFEqlCY6G7tGIqxCamTDTHtWx5hfdxOF64Z2YewOMlKnVFaSkpYYogH+N+BpUbQTY5VrvjVkdvdV1FPOdGkbJYePv0nWsK+DABaYsSDNrtzpZRwmznqFXKOw5YDfhmHXW4bA4Hj0uzmxAfoIyc6uZusatlq6Q1ij9EeY2tY/S4wcV4idLq6gimolB+Q8HVL+8S+0ZccYaVGY6bBIWPHN4TrpIvMGC4z3lLReHqsCE90aFV8DlGMWnkEiDeq9N4Ar6qx0tV6/MT45PD1UocWHcmqNwIspkBi9bcNVBeUy2zlx4LPS+g7BxfM6a7B5S/UJrHCftD3LbmUWpA444JDxXw7+C8XW73rc6B/pGJhOhwdhPiz0zIt6rmLp6jLVHYzScdgfHIOiaImg6NKqT9wfDTMtqwvM5avtZtbmnJ1KEJev9Dh3bHR4XS1LyyHQAiMLGQnxIXrTFz6kZVcNXCeaM0iDebvlLcXqrBuDM6KikqLBQn9p4JKjeCbFo8HqZnePx8cYXcdvOg6ryUNq1FY/LFAFqi5k7KKO2Ajq7rc4SrFFDiz9dbDAx39a2ua9W3KIrKTIljtyJ+OBxOY0cvZeuIF3TxCCdoOUh1BH9MQhkLlaUKWr+8bn7eEI7dI7g6eUzLO7AvPz8jJc43Ch6buBD+mnMqMTqcCaHbJ8XDRmEEf4RPOFblTvN46WZjliosOToynI+1LzPAJwcIsjkBAzSm1Z2/WS2xV+fKbsq5yxxFC97DeInAhBMrgUc6EoTd++Vn5Lbrb1690dzVb7LY2LQZuD2e5q6B0tpGnUFvta9hM7qNC5/HYzh8N8MqGXjccN5YvqJczV3uiCs+2eaVTe2ZIAu2Z+5IT4r1tVdnE+8MQXBEQn7B9vQ9+bstor1nxx8ZsUc7mVWZ3cvLJ20Opx1iUHYD4geVG0E2IaB/Gp3xWkWtW1eVJ7nkm6CJs8x+vUaXrMmYfcuYbfUIQcLZrctCQNqi+YN75Bdk1islFTfrWrt0RjOb5sfpcg2NTt6oquPb6hWcfofzrk4jvVEQ8GiGw/PMiKW4hFNIWpd9ia1uYYspu815YOvWXVmpyxxqVCYWZqQk7C3Y61UeuKE72WdNghuGTVsuEGvyCbvDYfcwy5wrZbOCyo0gmw3G6zWYLJWNzb1ddUWyS9H8oWX3AbN5BB2WbcX6EzcNj7aYssxusce7ooZCoDFR/JHD6vNS282a2pLKhhYQbw/jc1Rutz/aqKyzaeoKpecjeYOg3Iw/CZkJn8cF5XatuBYkgN3DH7bHVZqPx8Zn5WVtU8qWP+YJSH56ctyJA3vs0v0lxod7rFtWLt4+zw3KjZ77dlC5EWRj4PWGgIwtpgizO5yVTe0tLVUFsitbRO1Q9rEJSwQcdrdlS6Nln1CdHZe448rU47WGfBBvr3dFLZAIDqPkTj0QfjaJc6Gqvup8cY3ZYoPvNWU0l9bd6u2pP6I6HS0Y5BNWUHSHy+2Fb47MQMD315avhnLDJR60xZcYHhCrs07uL1DKVtptmselE6LC331ivyi8sFh/qsGw08XQXl+fr+XACQHPbXO6HG5U7tvBFmoIsjEA2R7X6lt7BsMWHI8MyriSutZbTeVb6OICRSlNLrOhL3jrAWv8takHw+KLHj5UlLklnscT1g+LdFZKydWKVtwjnOJ4wnljIkLbNCrqHbcKBfy6tp7u9vKDijeTRD08wjFgTZgiMrenJYIY4CgcMxnT6MbHuqPIWwqunt20XIbtMeWGw155weNH96hkklXpMw0XS8DnJsaEm53cplGhwUFH8kfpGeOrLB64CccdkQZia0JcEg6AOhNUbgTZGIB4aXTG169WWm2OUKU06HhkTpe7trW7pq4yNuRGnqxUTJuXp3jgkzTO0IuTp2SRefvzciNDFTweV62QiSWyHi3drxfJKL14hXODcrwg3jJKp6RGe6aE7UMmw2RnJu9qhrSJTzrgyEO2OC0nIyMlUcjno3LPBG6DkeHuME6zmqdlNy0dcNtap+qa9oEQRdHhPbtjI9SrODEMweFwaTpUpeTyJC2j3EmrUElr+KR9qTcMfEiNM0wTsi0+Lkkll7JbEawtR5CNAqgXFHs6o7nmVnNZXTP471k1574pmQdHSmtq1J6KbEmlnF6mIXN7ySmnskR3mFDk7s3LiwpTURQJZbHU3wSpIHePV7G3WH+827LF5hGspCKb8A2yZk0RdeyRvim1laSQ1zKkDb4ZLPw9zn3dgr1Oh9Pl9b9EpuHz6BCCdjDLn7IavKzRLS3X7bGLcnZm58RHhq76fG5g38HE78xIy8vZPUbuK9MfGbFFL7WRBNzyXMLBME6nG1uo3QYqN4JsGEiCEHAJibuloamypKZ+Umd0e9gSDdz2uFZ3vaKaNtflS6+E8SaW1wfMN7WiS1Zv2j0csnt/QV5cZJhPJ95GLORnbok/sne/U7q32HBqwJZodYuW/RQTAJHmEs40ceuJsDfzFBUzow2acBKg3C43CvcswM5yCK6d4bOvlwgYWYtb1GDM6fbsz99VmJ4Uw+etSg+u2RAERyYW5mWmJSSk9dgz281b4e5i0xYN3B6Mx+WC2wCZASo3gmwYfB1neSG75LVZ/Evd7WVvXCvT+MSbYbzeiSn9jap67UjjUZVvSubl9esFHAyvzpDb5TmwL3/XtuTYmZNEBeBz6cTo8CdPHOSpCy7rnmg2ZTs93JWIN8DhhCi4OjF1Ww8xmuMivC703HOhSIKkeHbPMpXbyXA7LVurjMcKduakJ8eJhcv37ncE7kyb3TEyPqmgxpJE3UvttwaBHQ88t8fldKNy3wYqN4JsGAiC4HJpl5ebLa0/oHjTPl72pzPX+4bHxyZ1JXXN4wPVD4a/EcabJIllyrbHS9bo83uYA1npmfmZW+arQSVIIlQhe9eJPQkpuTW2Uze1B/zV5qv8KNo3fUWIv7Ychft2aIoiQLmX5bndXrLVtK3KcipzW1bh9nSxYA1l2+v1avXGM9fKHFO39svPxgoGltFcAT13UFC5EWTDQBIEj+baGQFNuBKFXfsVZ6S2629cvv7i2RtjfZX5kktxwgH/JInL0TrflMyGHa2O/SkpO6BM908cGbygha0kScgl4sOFOTuyC/s5Ry5MnNA5FavST2ka+I6+2nLfYCwo3bdBQUi1XM89ZIutNeRRopi9uzKEgrWdt02jN5bUNo4Nt+yTn43kD8MFZRMWjf9hisPjcTpRuW8HlRtBNgxQzoLndjBgcAkBaYvhDwTGI3NO1Wyhb6SIO3iEY3myDTLQa02uNh2Ojt+Zk7mo4Tjgw6jlktysbTt37NHyDt+YOjZmj3QwPDZ5xfiUO8RlR889BxBukvQFcOzrpUByPCLS4naaRyamfAPdrFnmGkyWupbOvu76HYJLyaIOPmlnE27H6+W4vaST4do8AotbbHRJdS6F1qmecISN2KIGbXEjtmiri3a53XgXzAR7hSHIhsHucPYMDnstXXH8HigKoRSWUOZI/kgYbzxZ1CVb7pTM4LYnnJE39Sd5qtxjewoiQhV3nIUzQKDnbqhSJhLJGob5k1aRnNLwSduyh+GcidUtGnCkC+VJSbERODfzTNweT/fgqFHbvV1Wz25aNGLKIqf1E1ZRy5BNLJZKRcJAxwE2eTXwzdDqdNW391XX16o9lbnyatjoZPg2RmDzCK0ekcUtsngkJrfU6JbpXfJJZ/i4I2rUETvsSBp0pPQ7tvbYM7vtO3oc2/uc24c8WU5SHR8dnRAdjp0Dp+Hg+EQIslGYMpgv3CxzDL1+SHlGwZ1it64Mbwhn1B5Vojs6Th94/0MHI9UKKMrZtEXj8TDdg2NvXq8kjFVF8sup4vZlN5GbZtweccP4TlniQw8dyMNZumdiczghqwdaTn88/hfL6EEAb5hyqm5qD3U5C/cX5OVmpErFwlUURfDHLd2Db1yrJK1tqeI2muNyMAIHwwPxdnjhL88BKwwfVpxentsLV5ZDkSSfS/P5XAEPFh6Eg74V/18elwtJUWHKyFAFKvc0qNwIsmHQmyxXy6o1XaePqV9VcTXs1pUx5VTe1B4e5x45dehAcmwERVHLKB6hEPG4PWMa3ZXy6pH+2jzp1R2yOi7hZJOXhcahLjE+EhL52DuP78EZHmficnveulHd2fD6h+N+yfWNkbfkMtzjJcH+VukLm+0H0tJy9+VkhCplbNrKcLnco5O6v10q1RstPMor4hN8mqS5XC4Ff2gQYj6fB9rMh4Xv+xvQaS7cdf5H7qDNcPu9/cf/2v+HJAlycfVA9wmo3AiyYTCarSU1DT233jih/msYb4Lduly8Xo7FI7qmOaLhHSzI3Zedmsjjgmwv39Y4Xe6JKUNVQ1NnR9VWfvlOWZWMWubUooDOqSg3PWCQvfMDDx9cow7HGxQotM8W196qfu39Mb8RU+bldtwnTG5Jiymr2XlUHrH9SEF2dJhq5U8lGMZrsdknpwyM1wta61Ncv+gG1n1wQKN9/7y9zoHNK7nr7k/wOTeCbBjAbE1odcPD3VuEt2b1fl4qUHDbGUGNPm8g5GBWZkH21kSRYKWDjELRLBTwQlUqByPs1PBtTo6YNApI2/IGSXUxvHFnzFRI+q5tyfTSK/A3MXCZ+kcmxkY6t4qa+KQ9oNwQhzEhpNtLOxlYeHBxrf6Hyma3xOiW6ZxKjVM96Qgfd0SO2GOGbLEDtvgRe7QWNlrFY0bCZLGp5BIhn7dC8YbPxuPSCplYKZMopGKZRCQVCcVCAdxdAp/J5kIql6ZoytdAPqDlKNvLAD03gmwYrHZHQ1vXjRtvPBb2+yj+MLt16XhDODaPoMuy9Zr+iZ3b8wt3bINylk1bMYHBN0pq25paaiO9Zfmyayqudhlt1sxucZ2p6Bbzvs+/7xQoCrsV8XO9+lZ52dkDslchb+ElxGFuL+nwtwJzwuIVOrwih1cAIRSsu708D4f2hHAZ30LDX3jpW+fQYH1BPUFFQVmztsRnpyZA7BU4BbKeQeVGkA2D3eFs6xk4c+GNJ8J+HSMYZLcuHRdD91qTzmnelZiS88DePDBbbMLq4fEwFU0dZbW1Amv1MfUZNU9DcpY2WxTEFo3GnBLbB77ykXegnMyivLH93I0Kr1NDc9wuLxc029fUy1f3zAFfK+BxfX/ZBl+wAmaX9rf2omHh+9t88Xiw4nsJDhiML3tcZIOAyo0gGwany90zOPrC62eeCv9pnLCf3bpEvF5Op2XLTf0jgtCcdz6wTy4Rr7CCdD4cTldn//DNqhrDWP3J8DdiBENLarPmZLjNxqyz+o/82yefXNMROjciQ+Oa9t4hDidEyAqzv7UXn8vzy7C/+pnjJyTQ1Mv3/9ubYO3v/7B/kA0GhloIsmGAQha8FHgsj5dcdsQ9ZI+pNR3kKbad2Jcnk4jWSLYB8HNqhSwiLNzkljoY3lKbQJMcD5+0MYyvczD8ZbcifsKU8oLsrflZW7O3JqclxibGRESHK9VyKVxQiUgAgY5YyBcJeEK+T84DT5cD9pqmSP8TZt8DZt8TZpTtjQkqN4JsGKCsBYPFhJBOL+31LvnHy3iJCUdYhf6gV5qzLz8vZlWnZJ6L1eboGx4fHGjPltWB4V5qD2+Cw3B9Q8IxdruT8d42nykCGgzaDAtoMwgzvIRLCbcHm4xsdlC5EWTDEHiKyeEQDo9gqVMd++Z29IiqdIVacuf2rJzUhGgo6dm01QYMssvt6R+dqG2oEdqqdyuLRaQFlJhNXhzg0SmOh+Q4bQ4Hem4EmQkqN4JsGDgcDk2SNEU6vHzPEj23i6F7LMl1hpyU5IyUuMg17WfFeJgxje58cRXXXH5AdVlO6+8o294QDiyMFxYCFohLAqEJ16fc4LlRuRHk76ByI8iGghMi4HGdXiGzRM9NE84kUXeauLW5rbGurcdic7AJq43Hw0wZzK9dLueZq/LkxaG8STZhfty+Ib34BpdM4wgdsUf1WRM6zanNxswu8xY3Q9rsTi+DteUI8newbTmCbCRAxn7+17PJ7r/kSm9KqKVNMQI2XedU1hkLB0P2xibuPJiXKZeIV/fhKMN4J3WGc8VVw32Nu2VnI3lDFOF2M7TbS8Fi9/Ad/mGr7Qzf4fH/9b90MTQEIl4ORZBcDkkThP8vSTMcoZdS7M3J2pYcy8MBUBHkbVC5EWQjYXM4f//aFbX5pQLpJTmtY7cuhSmn8pZpZ5d7X3RiftGO9FCFjEuvzrzaUJRopgyl9W2l9S0871SccIhHMZ4QPsPheTh8L4fn5dAcggvyTFA8318S/vIIiktRNE1SvpbPtO/vzIXPpVVy6crH9kKQzQQqN4JsJOwO54vniunJV3ZL3wyMn7UMTG5JpzmtzHAsJiFnf96OMJWCz1sFR8t4vY3tfRWN7UaLDSyykJ3xiTc9HoivhxKoMQi1v28STf79LywEJ9ARGUGQO4DKjSAbCYfT9fqVCuvg6X3SV4JOOuIN8amf/2ftX5nx1/979/0DLx0Mr8+acG784YiYjIP5O1ITolbeQ4xhGIfLDefmcum1a7iOIAgqN4JsJEC5L5TWjXW8eUD6l0j+KLvVD+ixhyGcDNfp5fomP4YVhuvyPUiGv1w7w7d7BDb/X1i3eQQWt1jvUnhJQVSo6lB+1s705JU/8w6UJzi+B4KsKajcCLKRcLrcN6qbG+qvJZE3RZQ50M4r0OALbLTL62vqFcKhAu28CJLmkFyCoP0PlX3V0jSXx/WNqcXncnn+v3z4RyoWquVStUKKiosgGwJUbgTZSLjdnvr23sr6BsZp5NNef1MvtrUXSXFBmmnK37bL//e2Bl++ZmC+p8mByRWnV+B//+hbPthzIAiyvkHlRpCNBMN4tQbTlMEEMutr6xW0qRcOg4kgmxpUbgRBEATZSGD7TwRBEATZSKByIwiCIMhGApUbQRAEQTYSqNwIgiAIspHAFmoIgiDIPQDUZxkC5O/AOG/nCYZhPB4PrPg6PC5irHv4APAWOCAxz6h/sIPb7Ya//k6Uvu6TbMI9BZUbQRAEuduAXtpsNpPJxL5eNCKRSCgUgo6yr29nZGS0paXN6XRu27Y1NjZmvt2mmZrSwcLlcqOjI4PurNcb6uoatNqpjIz0xMR4Pp/PJtxTULkRBEGQu43FYrl+veSPf/wL+3rRPPTQAw8++IBCIWdfvw1omdVq+/nP/+/mzdKYmKh///d/DgsLnc9JBxgfn3jppVdLSyuSkhL/v//vHyEgYBNmYDQa33jj3Asv/DUqKvIzn/n4zp3Z68F2k1//+tfZVQRBEAS5K4Dhrq1tePnl10E+l7Rs2ZKcmZkuFovYA72Ny+W6fr34xRdfgSMfPnxg9+4C8NDzqWxA5t9668Irr5zu7R0Az/3gg8d5PB6bfBscMPlXr94YHBwGnwtnl0jEbMq9A1uoIQiCIPcSEE6VShkdHbWYRSqVUNTsGeXdbrdWq/vzn1/SaLQZGVuPHDlI0/R8ss0wjNlsqaysfvHFl0GP2a3zwONxY2NjHnroBBytuLisqqom8Bz93oK15QiCIKsPlO/AUgtYgiBAloJKDhwKJMdud8A6lwvCFGRKddjHf1rGf15YOAQBi69x1XzHdDpdbrcLzsvn8+eTurXAYDC89tqb3/7292E9IiL8scdOpaZuCSQtTFJSQlxczKznzXC0s2cvPvPMj8A3f+ELn37yycfmqyeHPDSZzDU1dd/97g+Gh0dB8uEtGRnpP/vZsxKJhN3pduAt4PX/6Z/+raWlbefO7d/+9jcgzli4Hn6tQeVGEARZfZqbW9vaOsDbsa8XAWh2WJj6wIG94EHZTTNwOp39/QPf/Ob3oMx+6qknTpw4OktoQWD0ekNHR9fg4NDkpMbhcAoE/PDwMJC6pKTEoHW8NpvtT3/668WLV1NSkr7yladlMtldE++Zyg1n/4d/+HxRUX4gaWFIkpoViICKtbV1/r//91/w3ffv3/30059JTU1h0+YwNDRy6dKV3//+z1rtVCC0uqNyAxAM/frXv//LX/4G5/3IR94PkcG9baqGyo0gCLL6vPzy63/5y8ugoOzrRcDn8zIzM/7zP/8/kWh2UykoqAcGhn74w5/duFG6e3fBF77wKVA7Ns3v7ycmJq9cuX7p0jWNRmu1Wl0uNwg5+EJw52KxOCYm+uGHT+7ZUyAUCmeaRXjjzZulP/7xL8FTfuhD73388YfBTbJpa8xM5Qah/cpXvrhnT2EgaalAJr/66plf/OL/IJf+8z//7dCh/XOfgjOM12w219U1vvLK642NzZBLgdoIyAGSJO+o3EBra8czz/wQzDqEQc89978RERE0PbvS/q6Bz7kRBEFWH4vFCq4OBHXxy+SkFvQMFJc9xAz0en1paUVFRZVYLDx16oGIiHA2wW+1u7p6fve7F2Cprq7r7e23WGwQBEilEpqmdTpDZ2d3WVnFz37265deeg0Ua6ZbA9FKT0/bv3+P1Wo7ffotOE6gNn5j0d3de/HiFZfLlZAQDwFN0LjHZDL99rfP/+AHPy0rq4TrIpNJjx8/snNnNo8XpHojKDExUSDwHA4BIRRESBAHsAn3AlRuBFkCUMAZjSbwNOzreYCSAsrTmUVkUCDet9vtcECbzebxBCmv7ysgN2y2QG7Yg6rXNIvMXtgB5BMOCJl8x53XDoqiUlOTd+zI3rVrx8LLjh1ZIDwUNbtXMXxZEKfXX38Tvk5u7q5t29JmesqpKd2ZM+dOn35zZGQURCstLeXUqeOf+9wnvvjFz3ziEx8CVY6Li4Xd/Or+p6qqWpPpNslRq1WHD++PjY3u6+s/e/aCRrOESoL1AFzchoZbfX0DkM+QyQqFYm6FP2SgXm948cWXOzq6QHqTkhIef/yhp5/+TGJi/OJ9s0QiTk1NUSjkTqfz2rWbIP/38KbC2nJkcwIBuNPpYpgltQL1jaMEZiXogAzwS4FjBgL2sLDQPXsKZxUQgR3cbo/b7XY4HFBY8Hg8KBcCBD0mCHZLS3tvb194eBiU2mKx+K49ZVwJ8E0hzrDbbUstPSiK5nLpoFkBQNna1NQ8Pj4JBSuI06zniJCfkLGQvXBN4coCJElADsPRAjk8t8UQXA0wqeBlY2NjMjPTBQIBm3BX+MMf/gxKOTY2DiX+T3/6bGbmNvi0bNoSMZstv/717+GAcHM+++y3tm/PnPld3nzz/M9//n89PX1w/EOH9n/ykx9OTk6EDAmkOhzOmzdLf/GL37S0tMH12rVr+5e+9Lnc3J2B1ABgxP/611d+85vnwYl+4Qufevjhk/Ndo1VktWrLwQE/88yPwHPDz+d//uc/du/OF4lmV5VDUDg0NPLBD34SbiA4y2OPPVRQkAvf8Tvf+f5rr52x2RyLqS0HWlvb4VxQCEBWP/fc/xYV5QdtJ3gXQOVGNieB0mpkZJx9vQhACRIS4r761X8E5WA3zQAC7eLi8h/96BegrR/4wLsff/xhNsEP/I5MJlNJScWNGyXNza2BeByKErBQ+fk5+/fvjo+Pm1saggJBKfCf//ktOPV//Me/wp7LLtzvJhCXNDe3fe1r3wQLyG5aHIWFuZ/+9Mfi4mLY1zOAIhUU6Gc/+zWsQPm7fXs2qBSb5gcksK6usbi4tLW1A5QGdoP8BAO0ZUvyvn27wYnGxESxu74NiBaYyP/7vz+CQwU9A1VjE+4Kq6jcpaXlP/jBz3p7+0Fv/vu//0MqlQQiPLjHIB/+6Z/+7caNUliH+/YHP/h2RET4TDmB7eBK4Tb713/9usViEQoFn/3sJz70offODHTgIIODw5/4xBcgY48dO/T005+GWIdNWzNWS7kvX77+3HM/gcxRq1V/+ctvg46+AoHm1NTU73//wu7dBenpqSKRGCJI2L5U5Z6c1LzwwktQsED+f/SjH3j/+5+CmJtNu7tgbTmyOYHSyv+UcUlMwlvAzLGHmAFsHB+f+O1vnx8dHU1LSwGJZRP82Gz29vbOr3/9Wz/84c+uXr3R1zeg0+nBQY6OjlVW1kDx/e///l+vv/7m1JSOfcPbgDFKTIzLydkB+4PjaWvrZBPWNwzjBfGGUozNtkUDeeJ2B8leoKWl/Y03zkIokJOzMyUlOVCwBgBdKS2t+Na3noUCGorp7u5euExwKMhPyOqbN8t+/ONffutb37t2rRguEwgV+7aQEJqmCgvzwsNDBweHoMDt7x8E78WmbRDg60CegMLBNwVDfPToIQhopitmGIYBKzkyMgZhJUQnBw7sVSqVs1wg7Mzn8yEkzc7OgPsN7tXh4ZFZFeYQA4Hs7d+/RyDgQ3gEObmBDF1VVa1GM8XjcSFKntX+bhqC4Mjlsg9+8D07dmTLZLKZd9eSAGnfujUVTgHXpaGhaWLinj1ZwDHUkM0JlO9Q3ENcD78xlUqpUqnk8NtdEIVCBr5t//69sCN7lLcBZX311TOXLl1Vq5VPPvk4FILTBtrfV6cfzGJJSfnUlF4kEoILBMHIysoAzYBUEJixsQmQDTCIEKHPrOeEUhXKWdgOZn1ychIKXzAfUHqyyesVkFKwkufOXQT9BjEACwjfi83EBfHXQOTC/uyB/ATECeKbyspqhULxiU98KDExfrqyF8S4urrul7/8LSgKqDXY1uTkxNzcndu3Z4LF5HK5JpMJrg7EVf39A2Fh6qiov48+DdkbKMqbm1shigK7CdbqrlVvNjTcqq9vMpstICqnTj0AXnD6Sy0et9tz61bzK6+8ASIRFxf7wQ++F27OaXHyK/dwTU290+mASwBngaybW7UD+WC3OyG47OzshmsXHx+fn79r5pNy2AGCAQjIamvr4URw04I3hfvQt3XNgJsHQlX41cA6nAg+WE9PX21tw3zLrVstcKGjo6OmvyDcOS6X+/nn/wKGGy40fOaioryg1xeOD+8SiUSQOvNLwdnb2jogk+HqPPTQA3esFIGDQNAD0bnD4SRJCsoBuBvZtLsLKjeyOQHlLiurNBqNsP744w8HusQUFuYusBQU5IEkQPk4q57W6XR1dfX8+te/1+l0Dzxw5MSJoxAEsGn+CrS//e3106ffgh8z/P4feODoRz7yvuPHD+/ZU7hz5/a4uBgQFY0P7ejoOIg6FD0zyw6K8il3X18/fGCj0ZSWtgW0Z01LzJXztnJfgiIeXMixY4effPLRWZkZdMnL2xURETarfISjNTY2/fnPfzOZLFD4PvXUO6aLV7DIUFg/99xPGxtvQfaCOD344PH3v/8pOGOghjw7OxN0cXx8ErIO9gT3WVSUD7HRtLbBcaRS6fDwcGtrO4jc3r1FoFhztW0tWBXlBnmDkLGmpg7yIydn12OPnZr54UG6AKVSERsbm5qavGvXDriXgppOiG/KyyvhNoYshXusqKhgpnIDkFGQbzdvlsKVhXW4USGKXdOMmqncgVorCN0qKuZdGhub4VaBn9V0Z3f47hAWv/baGfjMMpn00KH927ZtXVImL1W5IWegSCkvr4KiAMImUO7MzG1s2t0Fa8uRzQ/Y36NHD4KmLryA3IJyQBHAvu1t4Fd6+fL1np5eKOxAM2Y+2YKyo6mp+cqV62ANocR817se//jHP7h9e1ZoqBq8ERigkyePf+lLn4uMjIDUjo4uKIBAgdg3+4ESGQIFKNnValVvb9/LL79utzvgsGzyukckEm7dumVWTs637NiRDTrKvtMPfFOr1fbSS69NTEzGxUWfPHkMSs+AbANQoIOhBN0C/QNNevLJx7785c/l5OyMjo4EuYqKivC3t/osbIdUOA546+Li8llP3yMjw/PyciDCgPIdAiww7mzCugcyx263X79eDD4Pvm9+fs4sKYWXEOedOnXiM5/52Cc+8eGkpISgWgvHgQwEYwqyDXkLeTW33xTcn5BRcAQej6/XGyEbwc6yaXcF+GDwGRYEdoEb4+9BLWgnhMWQRbAO0R5kERwjkLR2wIkgA+FEkKVare5ePX9B5UaQOwDO6eLFKzRNga6DZswM6kGGW1rah4dHoMSEUm/v3t0gwGyaH4oiY2OjwSDCDx4cA5SeExMTbNrbwAHBLYHM+6tGW8AbBX3Wvimx2WwNDU1lZZWgu9nZWeCZ2AQ/4G/8T699EgL2+vjxI7NqO2EdtjzwwJHt2zPhJeRwRUUV+MtA6jRgjHbu3A4X68yZcwMDQ5DPbML6BmK4zs4uCDjge4WGhqakLLNiFo4DQWFrawfIjEQijo6OEgqDNLOHzMzI2AYRp8VigWwERbxrESTEVRDvHj68f4Fl//49GRlgqf8emoByQ+ZMDwfrf47w93tjjZg+EWQmOH7Qbzbh7oLKjSALAV4QpBT+gkIcOrQPfrRsgh+n0wk/YLDUKpUyN3enWj17NGMoDfl8flJSYmC7Xq83m2e3x/bvwztwYB+8fXJS89prZ/y2m03d3Gi1U6+++ga45NBQdWZm+qwROqFY7OnphRzm8bhpaVsiIsJmynYA2BIeHpacnAjBk8fDjIyMgVNn094mPDwUin7YQaPRXrhweW7wtKbA5x8cHOrs7G5v71xgARGaVR8DYU19/a1AszswxCrVbUHhIoH3trd3/OlPL8G9CuspKUkQA826S6eBVLjD4QODm4Qoc9bnWTsCFSr/8A+fX2D5/Oc/eeLEMfgZsu9h6xLMENbAOoS/cPPMvT1WnZknslqtDse9GbgGlRtBFqK7u/fWrVYoy8BMQ5HH599mViAAf/jhk//wD1/43Oc+eerUiVlVwQGgfIFCE/6FdV+dX7BCEwoC0K3Y2BiwnmDxodB0OjfeUFZLxel0DQ+P1tbWQ+EbFxcLsjGrslckEu3atf3AgT2FhflpaSnzjRTN5XIhKVBoQ1aDFfNv/jsCgSAhIS42NhquRWVlTU9PH5twV4Cv+cILf3v22R9/97s/WGB5/fW3wOyy7/EDrrevrz8wRE/g+Utg++KB+K+vbwBiwY6OTrjxVCrFY489HB/vG5glKKCgcCLIJbfbBW+8azchRGYQ+8bERC+wREVFzprnA74d5G3gcsP2WfUxawScyP+g3XciuG8DccPdB5UbQeYFBLukpBxsnEDAB9mGonPW+FYgGFu2JB8/fhgcA2jM3EpIKFbAOLa2tkP5C7/50NBQmSx4n1EwVWAcoeiB/YuLy+5VLdzdxGQygWxPTmohl3Jyts9sQBAgNFT10Y9+AAKjf/zHL+zcuZ3dOgewPnq9b9BQKLdFIuHcNkqQq3DtMjLS4fKNjIzC5bibVgkKd/9DkKrS0ooFls7OrsAj22nsdsf4+Dh8L/hGMplsqZ0O3G7P8PDICy/89dq1YridIGf27YMYKG9uS45pJBJJID6Akw4MDN41z71cvAzz97qpuyDbAaZPBLkUWLn7oHIjSHDAeZhMZnDAer0+YP5IcgnNVv3GxW02m1taWktLy10uV6AxF3gado/bgaIZfCHsA++qrq7dQA2plk2gvzusgKBu3541s8V+ADA3YWGhiYm+wagXmAljcHCkvb0TCnGC8LUqmNnvbhqxWLRjRxZcQdCwjo4urXZ23/q1Awp6+EjwAcQLAlHgTEMJgJCPjU2APMDbl1oVDLI9NaX75S9/+9ZbFyYnNaD6kMOf/ezHgz5xmAZCz0CbczgphDjrXrk5NM3OiOr/uXnuwjMmOJG/4YXvTBBRzbpkdw1UbgQJDihoa2sbyDb8VkFQA09S2bQ7AW+xWKxNTc2//vUfvv3t5wI6ceDAXljmOsJpoqIi1WoVnLelpV2n09/DiP7u0NvbD8YOcjUy0lcRukDOLIDHw1y9eqOzsxvW4QhFRQWzHpYH4PMF27ZtDVzBwHkD2+8CoJpf/OJnnnnmmz/60XcXWD784fcpFLfFLiCcgQqJaUFdJPCWwcGhZ5/90blzFw0GI4/Hg7jzq1/9h4iI8IUzGT4qxBCwAmGQRqO9Vw9xFwloNoTUgW/k8XgcDntAUNcUuN8gWwIhAkRUd+xItkagciObn/PnL/34x7987rmfLLD86U9/1WimZool/ET7+gYDXYyEQmFsbAxJ3vn3Yrc7ysoqP/vZL3/mM1/62te++corp0H75XLZU0898fGPfygm5rbO3LMIDw8D5farvmV4eCTQaHadYzQar1y5MSszZy0//OHP/vznl0AJ2Pf4gaweHR2HAAVcCxhlEKelWEoWp9N582bJxYtXQJ/gCJmZ6bm5O+c+swDAnEFgJJNJQLz1egOIN5uw9hAE6W8XlrF9e+YCS3x8LE3fNm8Vw4Aa+boIwofnLXpKK8iT2tqG7373B9evF1utNgg6Dx3a9/TTn4mJib5j6Ak7wIngPoeTwu23zmNHguDIZFLIHFiHbz3r97tGwIm0Wq3X6zsR5G3QCp67ACo3svmprKx57bU3/va31xdYoPQ3mUxQYLHv8ZebgUd9UJxBaB/oxMmmzY/dbm9r6ygpKYfSs6urZ2pK53S6aF9nUzkcZ+EKTzgLqAus+D3T8B1nJFsP2Gx2+KazMnPW8vLLpy9dumY03tZZC0QFSkDIXlDusLDQZXgXiG/q65t+//sXhoaG4cJB1r33ve9SKBRB9QnOAqcImE5449303HDNQQ75dwJuklmdmuBLgZWEFfjwQGDjAsD+ZrPlxo2SX/7ytzU1dSaTGW7aBx88/pGPvD8lJXkxDbhgBzhRYDc49cyfwzoEPmp4eChkHazDjTQx4XuyEEhaOyCWmpjQwIkEAr5SqVj2QKorBJUb2fy4fZN3OeEntwDTjVSngZdQvkOI7dddhb/gY5MWIHCQtLTU7OxMsIBgpMRiMdhNELDnn/9LR0fX3D5L0/D5vOmn4IODQ7NGFFmf+NXFNzfawrhcs7MX4iQIa2AFlEKtVkH2BrYvErPZ3Nra/qtf/a6urgGyNDw87OTJ43v3Fi5QkkJBDyECnAj2HxoaCbTZXt+AhvruORDQO2ooCK3BYLx5s/QnP/lVVVUtOGb4spAnH/nIB9LT0xZv2eGCBs41K4xYh/gvaBgYX1iB3+nw8OjMBmtrAWQNhOaTk6DcXrD7YWFqODWbdndB5UY2P8nJvgm7CgvzFliyszMEAsFMUwJKA8YXSgQo9dTqeZtHzUIoFD7wwJHnnvvfn//8ueee+/ZXvvLFY8cOCoWCiYnJv/711Z/97P9Aktld5wCmcPpEo6PjG6J5OShlYmL8rMyctRQU5GZlbZtViQ0WPKDcYPNAuZf0kBtCAXDbIFElJb6hvqRSySOPPPjUU++YdQVnAVIEgRFNU/4Kzymr1cpq1HqFJH1zzsI3AlWG8IjdGgy4VyE/r127+Z3vfD8wxCmEMu9+9zu/8IVPxcbeuZJ8GsgQt28eVV8rfbgbF//GewLkjFgsio2NAfsL1xR+rfDF2bS1AY5vMpkDbVBUKlVERASbcNdB5UY2P+961zv+8z//7Vvf+voCyxe/+JmIiLCZETSE1SAt8FvlcrkKhYLdeidA5iMiwiMjI0BOYGXv3qLPfe6Tn/70x/y65a2pqXvhhb/Ocp/TzDyRzQbKsgGUWy6XP/roQ7Myc9byP//ztc9//lOzOn3ZbLZApQKUvwqFfPHKDVfk2rXin/3s17W1DfBeUOv3ve+pJ598/I7dnSFEmK5Ld7vdsx6OrEMoig5M6Ak+b+EKGL3ecOHClWee+VHgWW9a2pbPf/6TH/jAUyBs8HZ2p0UATj0Q0EBeSSSSJYVT9wT4djk5O5RKBXzytrYOu902349rVYDwqLm5LXCKrVtTIyPDA9vvPqjcyOYHjMsd++SAAMyUbSi8QCHgJworsJ3LXWwRBkUJ7A8EVkCMwVA+8MDR7duz4BRQ/ra1dQ4NBTcHsP90pTGcfEMM0gmfGYIVNhPnRQTffZaBgy8Y8JGgLJBLixEYuBwGg/HPf37p5z//dXt7J1yasLBQiAkef/zhWWN0zAdcx8CJ4FCBsckC29cnPB6tVPq+l9ls8fu84J/WYrFcvnztd797PuAFd+3a/rnPfeLAgT0L10AExWz2GUpYgftXpVLAdQlsX8+kp6dFR0fBFzcajbdutS7wNGrlaDRaCL5hBWKa3Nydiw/oVx1UbgQJDhTrMwr2pZWAM4EfOXhK/yxV4oD29PrmfgjuDKZLWv/Z17WurJi/f7/F6AsI7dDQyPPP/+UPf/hLb+8AyFhycuKnPvXRRx456X96vcjQ6u9nWv+5y+fzwdWBcsN3B0GdNU5LAMjEhoZbr7/+ZmDw/J07sz/xiQ/v2rVDJlvygGtAYMo1WIGTxsfHLv7p+DKAIDU6OnLfvt2wwMcG38wmLJGoqAiwvxBkOJ2uqqraWePQLUxSUmJhYf6ePYXbt2dS1J1bWvT1DfT3+/oxBsYYENy7CXlRuREkCAHHTJI+6+z1gv0N/pQRbLHNZtPrDVNTOthnPq0N/NTBA8F64CFroFfJLGDj9ARN8Jb1X1e5Eny5+7YL92fvQkIK0jU4OPziiy8///yLIyOjoNNbt2755Cc//Nhjp/w17Yt9HDt9jeCyQvYu1ZLeZeCGSUiIC/TRghts7kwqEAjCvffSS692dHRBLAjqdezYYbVaZTAYBgeH5lvg9gORYw9xOxBWBhofwN2XkpIcaLa9RsCnzc3d9ZWvfBGWj33sQ7GxMWzCEpFKpdnZGaGhari4jY234CvM9zOcy8GDe7/whU9/+cufe897nrxjK3G73dHd3aPRaCDmKCzMg3xeTDXPGoHKjSDBAV2RSCTw4/TLc/AqOKPRWFfX+NZbF0BUJiYmg9aBBwChelsnoGAJXrLA26d9FdidexjR3wV4PF4glIHcsFoXejwJSZC3f/jDCy+++AqYQpDtrKyMz3/+U8ePHwFpWbz6zjwRyLZYLFznyi0UCrKywAv6ArjJSU3ADc8EtApcZktLu9lsge8CGl9eXvWLX/zme9/74QLLq6++Afcte4jbAeMOqg/3vFgsSkvbwr99ovrVBb6XXC4D5wpLTEwUnJFNWCLwxcFz79q1Ha5sW1snBHYQ57Fpd0KtVkNInZycuJjJyCcnJ9vbOx0OB1yXkyeP3bFdxZqCyo0gwQk86oPyBdR0bGyc3Xo7PT29P/nJL5999scvvPBSdXUt+G824XagTBkdHfWP8QRWg6dSqcDSB5JmAvHB9InE/kfvgfVNiX+4Lt8s0QzjHR0dn88FQtZptbof/OBnZ89eguwFYwSC/a//+o9g1+5Y1M7C6/VNCulyuaGsDzybX+fKDTcAuEmRSARSOjw8GhgnbibwXW7cKAGthXXIKJPJXFpacf16ycILKH3QGxUim5qaOvDcoEzT52XT1jeRkZEgpRBnw0/14sWrcDuxCatKRUV1S0sb3Db79hUlJSXe20YAqNwIEhwotmJjo0EqIMoOlPhzrbJKpZTJZFarFQpNKDLmuiIACkQ4wrVrxQaDCaRCIhFBmA/2iE2eAZSnUEAH1mNifMOKBdY3JTKZNPBo0x/WjAVVbsg6i8Xym9/8AawkrIDLefTRU5/+9Efj4mLuWLc5FwgRhoZGXC4nBA2RkRFLFf6lAseHwp3ng7s8CQx43/z8HBDRqakpCA0hr9g0P/Cyv38AVvxn4cHp4C1wj90JeMfskAUOBba+q6sHwkeQwD17ipaRw/cK+KgpKcnHjh2kabqysgb0Fe4cNm01gMyBn/aFC1cgiIyICH/yycchqArk470ClRu5j4Dfs8li6xoY1Zssd/xtEwQJkTUUiB4PY7FY/QOYz67RVavVW7emQsHqdrvr65saG5tnzRQCZ4Hf/KVLV5uamsEQgMxnZWXM6n42DZxl2nMnJSVAdB9Y35RApkHu0TQFxeLExCQEN2zCDMxmS1lZ1blzlyBXJRJxQUHu+973VGxszDJqceFCQHAAIQJEYCCHkL1rXfLu2JH10Y9+4OmnP/2pT30sKioyUOm9VECMDx3aDyELCCrIqn8MkL/fhJD6xBOPfuYzH4ezLH45derE3OnCPB5PR0fX1JQv9AwNVefk7FjeB74nwKWEKPDxxx+GXxb8Tmtq6rXaKTZtNYBfd3V13cDAkEgk3Lu3MD09bfFNK9YI8utf/zq7iiCbiO7u3rKyysDzvKNHD/nmC6Eou8PZ0N5bVnfL6XLJpWJwKQsU36DT4POqqmoMBiOUdHl5u+a2SYEjgCR0dHROTGjAeY+PTyoUcrB0ULyCtwMjDkpcWVn9298+Pz4+QZJUZmb6Bz7wHvDTQc8LReelS9f81ZXC9773yYSEuOV5tbUGCjL4XiCoTqcT/NmuXdshHGHTFg2UfVAU1tU1QkADInHo0D7I3pnZAhk7PDz6q1/9rqurG+QWMvbAgX1wIUB9h4dHgi4jI6NQZEPxOrcmEz4z7PDiiy/D6UBHH3roBGQvm7Y2hIWFZmSk79yZnZ2dAbHC8i4lZAjIdnl5FdxakGOpqSkzn8jCFggcIUSAsyx+SUyMh3g0cIRpIHI6c+Z8XV0D+NeDB/edPHlsreskVhcIAaVSKUR4nZ3dJpMpJSUpLi5mgV/34oHA3WAw/Pa3f+zp6du2bSv8fuH+WZUjrwT03Mh9ARhssFw9g6OXSyu0ow0VNZVXK+rBf3vmbxgFcgIFJRQH8CsFCYdQIGgDtMzMbR/84HuVSl8LZzDWzzzzo2ef/fEbb5y9ePHaSy+9+s1vfu/b3/4+vBcOAobg8ccfAfFm33k7fqEaAeGBEhPKVpCxDWR6lgd8zcjICIhy4IuD25uVvS6Xq6+vH+IekG14CbHCD37w04985DMLLB/72Of+9V+/BgFB4AgzAc/a3NwaOEVsbHRcXGxg+zoH9B4c8MGDe8FTgixduXLT4XDCrcImrxIgTkaj+cqV62azBQKaw4cPbCzZDsDn8975zke3bEmemJg8ffotuOKrklEQ0zQ3t1VX1/L5/OPHj8Dx2YR7Cio3cl/g9ngGRifPXCuJI8rfGflCjuB0V0fV3y6UThlM83WthkIzIiIcCjLw0FCiVVfXgW9j02YADm/37oJ/+qcvgpMGrYVS4+rVmz/4wc++9a1nfvWr38O7wHnD9oyMbV/96j8eObJ/vm6jFosVBF6n00MEABZWKpWwCZuXyMhwiGOgeAXv3tDQNOtBA7ysq2uCeGtVyl+z2QyFr9vtAU1KSkqEK8smbASOHDkIXhm+ws2bxSMjI4FQZhUxm03XrxePjo7Dvbd7d2FGRvDgcp0DVzYqKupTn/rooUP74VfZ29sXNNReKlartb29Y/v2rI997AMQQi2m2/ddAGvLkc0JSODo6KhcLouKiti7b7crhLpeXk6baw+r31JxtWrupJwc69HyO0ccoUqFkM+jgpkMEG9wfuDVtFod/IAfeugEqPisijJ46R9TIionZ6dEImYYsPFe0HjQGzABYJ23bk1997vf+f73P5WWlioUCol5JnLo7x98883zAwODsM8nPvHhxMSE6fHU1hteLwOhDBjisDB1XFxMbu5O+LRs2lLwf0HOtWs3QVAJwjeKCGQXm+bvPtvZ2QU5CVdw0UskRFr79u2Z+xx3aGjkhRdemprSwT4PP3wyLW3LPa/wXDw8Hh/uw7a2Dr3eN9n21q1bQJnYtNVgeHj0N7/549DQcFbWNrhX4WbeQJkzE/hxwU9++/bMXbt2QnC28OOwRQJhd0JCQmDsfYing7YtvftwVr3iBUHWAwaDQaOZstvtcH97SW5da6txtHKv9Ey8qJfieGCjzSPssybVGPdxVXm5O3K2xEeJBEHaPQ0MDD333E8vXLgsEom+851v5OXtAmVl024HAnyNRjsyMjoyMmY0GkGNQLmVSgVIBRQioCULP+kE2f7xj385MTEBjueZZ765yOE87wkMw1itNv90W24QEigrZyru4oHCp7u75xvf+DYY7rCwsH/4h8+dOHFsuqiFawfhV2BgkEUC7+VyuSDhs64RHKq4uOxf/uU/IBp48MHjn/3sJxIT49m0DcLg4NDvfvfCK6+cjo+P/cY3/m3btq2r9TAFrDwY7v/+7+9yOMQ//dPTR44cmBv3IOsN9NzI5oTP982eq1arKT6/tP6WbqQ2V3Q+VdJOcnx14yAONOFS0Fo5Ndk3RQ9q3AKhVCIS0HPG1QKTDXp861aLw+EQCASZmdvma/INQisWiyIjI1JTU7KyMiDwBw1OSkoIDVXPdeozAQEDaQFH2NzcAgd/8snHwX2uW8MNBAQS1DosLBQyeb5Q5o7AcUAtIGPr6posFguEOGBrphtPgTJJJGI4xeIXyGr4PHOzbnx84o03ztbXN0H49bGPfRBkbwN1eQoA955CIa+raxwYGISvCffVqthuuPd6e/uff/4v/f0Du3cXvOMdj0A2LnCvIusEfM6NbFqgVLI5HMU1zYMDrRn8q2mSVoJzWw0TRXgSRb1H1WdE5msXbt6sbem22h2z5nUAicrJ2ZGRsRU8NPg20IBVeXg2Ezhgd3cvBAc2my06OvLgwX00vQFmelgVpFLJsWOHoqLCIRPq6xtBRdiE1YPxDa3VUVFRDaEAhFNpaatc1Xx3gFAjKSn+Qx96Dxji4uLS9vZONmFleDxMVXVtR0d3TEz0Jz/54YiIMJTtDQF6bmTTYrHZa5o7S2uq80VnMqUNPNIRtEwSktYI/ojLaS/roe2ukHCVXMC/TTglEgl4tRs3SvR6PVhqsDvLdplBsdsdf/7z32pq6lUq5bve9XhRUf46eZZ2FyB806Nx4fuCuE5Oavh8XmFh/uqKh9lsOX36LYi6hELBl7/8hbS0lPVcn7EAXC4vMTF+2zZfT7PY2Bi5XLbyjHK53A6XOy4p6d3vegxiGohTUbk3BOi5kc0JyHZ73xDI9k7R5XTJLQFpn69AIjiMjDbkysv2Sl5vbak8e7NiaFzDzGj/wePx0tPT/M1KycuXr/f09LEJq4HL5ZqcnITD2u32Xbt2HDiwd90+3l4jeDzu4cMHIR6CrKiqqoPsXd1ajY6OztraeoFAcODAvuzsjDWdRWNNIQgOfPhdu7bn5eWsViMyu9Oltbn7pmy9kya7c94pc5D1BnpuZBPicLra+obLqsrUzhtFimIpbQw83p4PguPlEk4lV8P16vp03AkjIxKKpWJhQEShiKRpSqlUVFbW6HR6hUKxipMx6PWG06fP3rxZAm7+qaeeyMxM34hdaVcCZC+4YcjhtrZOjUYrkUi2bdu6KrbY97jEZnv++Rfr65vCwkI//vEPJSTErVbDrntC4FbkcumV3ySQOeC2a1u729uqxa7mCb3ZaCMVMgmPyyXvs9hxI4LKjWw2PB5mYExTWlXh1VUeVF1WcrULy3YADsdLE+4w3hjXq+/V0P0TDrlMIRLwCf9En1Dcg3KbTOaurh6r1ZqWlroqHYLdbndvb/8f//gXMNzveMcjBw/uvz+b9UIOy+Vyo9HU3d07MjK6Z0+hSCRcuTiBd29paX/ppddg5eTJY6dOPQABAZyLTb6PAdl2ut0dfcOllWWh7pu50mLaq2sZ8ZpsHLlUKuDz7p/nNRsUVG5kU+FhGK3e+Oa1Us9U2V7FpRjBEEgym3YnoEQHjQ/lTkqIyb4pftOAQ6WQS0RCivRN0AninZKSBKYQbBx48R07sleuARAE1NbWd3R0wdHe8553RkdHsgn3HyDVEBuZzWYIYhQKeWxs9NwROpeK0+m8ePGKTqeDUOCJJx6Dw6JsB3C7PaOTU69dvKlylRXIb8QKB6P4w7wQU+MwPW5kQpVKMcSs6LzXMdifG9k8MF6vyWz964USy1j5bulbqeJ2krOcJ6YeL6lxqG/qjg54Co7uKchOS5D4p+1iGAbEAP6SJMXjrULzb/j1ge2GY0IpyeVy77d68lmAM3a5XB4Pw+XSECetXGV9ztIJB3RDxoLbRikKwDDe4QntqxdvcAyVx9WvhfPGIGAFGfB4qV5LUqn+qEOcd2JvXlpidNDhiZD1AHpuZJMAxbTOaL5UWjM6UL9XdiZR2MMlnGza7VjcIrNbzHhJLhF8TmiC4+URzkj+EKhq81CI1UUpZRIhnxdw3qAB1CrNFAQHBFEBzUZdASAHIHsDD3FXxRz7r5dPs1clDtg0jExMXS6rNI43HlO9FsYbpwnfWKqQOwSHEVNmNT02ZSEb+j0UxVNIRXBrBt6FrCtQuZFNgt5kqW1ub2mt3SU8v0XUJqSsc4tqbwjHyXAbjTsrdUVmj1hO60Hdg1angwvhE3YVrXG5LH0azpSVlEnEIN7zjV2KIBuCySlDWV3j2GBtoeRsogiiW9fMG5rieISkVU2Nmm3u9nESXLhELBKsxhiiyOqCyo1sBiw2e2N7T11jRQJxLV9RLiRtc4sakG0XQ/dYUqotD5q5GXomxuF0yWgdFF7gNtidZgCKLiBtau6k22XumqA0phClXMrncrEKEdmIeL1es9VeWt/c2121jb68XVYHbnuuIJMg3pQ1kj+kNTNd416nh5JJpSje6w1UbmTD4/Z4WrsGK+qq5I6Sw6GXhKQ9qI12M/SkI+Ls5DvCY3cdLMhRKCPLe4UWJ6nmTvBIR1DxBniEM5Q7KeJM1A2LhrXOMJWSbXDOpiPIBgBkG+LU2pbumobqLcSlXEUlj3TOdw/7nhaRjnhBn9Xhah6lNEZPTGQYj6Y5BKr3egGVG9nYeDxM39DE2ZvlCvuNQ+qLUtrEAXc9B6+XM+4IPzf5mEC948T+wsTo8HCVQq1UVvXToxaJnJqSUfr5iiWS8MhpfQy/r2VC0j5sFQnFoYo7TB+CIOsKu9PV3jv01vXybdwLOfIKMWVZWIMhFW77KP4I12tsn+S1jzhiIlRCHg9v+3UCKjeygXG53RNThlcvl4lt5UXyy2revF23xxyRJYYHLLxdDx/ZHxmq9DVeJkmFVBwZFtozwfQb5XyOScHVzRrYPACUYuDIRaQlmj8wbhZ0jToZDi9MKSP9Xb3ZnRBkvQJuu3908tz1kriQG/nyEjltmK+GaSY+8eYwckqnpkYHdbyWIYdSIRcJ+PQqNc9EVgIqN7JRcXs8k1PGS6VVjsny3fLzkfzR+dqKa52qGuNeLV14oHD3lvhorm84Dn/DY5KUSYQKuUprIbumpF6PXU7roLSaW9keKMXAqaioMbOD6RpnLE5arZBCAIBt1pD1DPxMeofHb1aUU8ayfcrLSu4U5W9MvhjgzqYJl4g0y8nJSZO3Z9xD0kKpWMjbaDOtbT5QuZENCeP1avWmivrGns7KfYpz8YJ+Pmln02bgDeFY3OJaQ+EwsX97dmFuxhbQ2mmfDCvgmxUysVyunDCRHVol5TVJKCNNuIObb45XTJuU1ITF7m4Z9jg8XLlUwuNSOFoksj6Bn8mYRldSXWMcrdqruBAtGJkr2/AbcXj4epcCRBpu+7lxKLxFRutV9MSgnuyfBPEWScUiLhc72t1LULmRDYnF5iira25pKc8VX8qUNvFIB5swA1+RxPBuGbMbbEcyMnfv3pnO9zWRZVOnITgcmVgYHR5msJHVIyqO16GkNfP1FoN3CylrOG+E47GU91AWJ0etkAt8vcVQvJH1hW9gIovt7I3KqaGqAunFVHF70HjUyfAGbAnXtYfltF5A2kjCM1eQ4Y1S2hjJH54yuxsGOW4vFaFWUhCyonjfI1C5kY2Hx8PcrGlubq7YQt8sVJaCJwhafoCT6LEkX9A8vGN7UdGObRKRYD6XANv5fG5iTEQIwasdEuttRChvUkha2eQ5gDsJ548r6InGYd6wzquQSZUyMZu2Snj9gxuirUGWB9w9dofz3M3a4b66XaKL2yRNJBHk2bbXy+mwpF7SnJpktnQYE6WUAfQ7MDbLXPiEI5I/EuIxV/TxdWZXpFoZGJ6ITUbuIqjcyAbD6XLXNHfVNFQmEjfy5KVBR1wBnAx3yB5zZerRlLS8fTlZCql44TptKIAokgxTyqVSWdck3aOTKWiNmLLM12aN5DAyyhBKjwzque0jboFAqIRTrNI8DSDbHX0jWoNJLb+PJiDRGc2tPUMOp1MiEmLrgRViMltL61putdQWiN7cKvbNcssmzACCw35bQqXpOF+18/HjB90hgtZJGfy+FLQuaCUWh+OFKFnF1cjIieZx8ZDGqpDKpHix7gWo3MhGwuZwdvUPX6uoimRu7pKUKrlTQSN+t5ccsMVXmk4IwgqO7M5Ry2X0IuZ2BPHmcWkZ6IZIPmag+nQCPmERkZagFgROC6WYiLJIOBM6a0jHWAiH5EklIi690ud/bg/TMzh2obSez6Xjo0LvE09jttrqW7tLapqGxsYFfIFYJFjMJUOCYrLYWrv7K+uqt9KXMyV1Eso09ybyeMlxR2SJ7hilKjhQVJQUExGuUjgZIdz2BluIjNLzg42LAIEszXEp6CkhRzOk54/o3HyBCH4yBKj3fXGfrhdQuZENg8PpGpnQXimr4poq9sovhvImg3Zu8YZwJh1h1aYjNlHRkd15sZGhS9IALk2DQVcp1T0a7oBBJCZ0AtJK3z5I5DQUxyOljCp6dNRIdo25uTyhWCjiraDxjsvt0eqNF0ure4fG1Qppcmzkph+yzev1gs9r6xmqqS/nGOsY61C/xi0WS0QCwcrDoPsQu8PZ0TdcVl0mt5fuV18B2Z5bbwSybXTLSnUHTIKiwpzCtMRo+I2IhYJQldzpFXVqQLw5cnqKRzjmdrMEOYdYFn59ohDNgI7qGXeKJaDdApJYndHmkcWAyo1sDBiGGZvUXa+omRyqPhX+GhQcoJps2gy8Xo7ZI76qPWnk796bn5+REreMht805estFhcZ0T1JdGgVdIhFSWuoYC13AH9Xb2ucsFdjJpoG3S4vHa5S+jueLbkUg++oN5qvVdUP9NR63DaVIjQpNmpz98ABSXF7mP7RiQs3SxX2G0fU51PFzb1aftuwk6YFoQo5Rd2/euD1Qv54l/T1PQwzMDZ5s6IqRFfxQPhbEFbOjW7hN2JyS2r0BW2uQ0f27k9Pjp2+xwQ8boRKIRApqvp5k1ZhKD3GJ21zxRuAaEDJnZJTEyMGuq7XKZFI5BIRRWKkdZdA5UY2BlMG89WqhpHe8hNhr0cJRihO8EY0DoZ/RXNsjCgozC3cmZ607HkzCYIQCnip8VGTZqJ5Qmp1hETxh+cTb3AhXI4zQdjncDHNwyGjBm9cRCiPt2Tx1psslU3ttfVVx9Svu8HYiOITYuNEAj6bvBnx+DrlG/56vhgMYqH8egR/TEjaEkXdGgvVPOy1OIi4yFB/E+b7UQ8gcwwmC5emFtlzASK/Sa3h9SvlpL74sPpsmK9SKkgrDatHdMuUXW46eXTv7swt8bNamUHYqpJLo8NDGwY5PQaVmNT5n0kFa+3BCQFDH8UfNDuYkg4vRfNVMgl/NWa/Re4IKjey3vF6vRab43xJ7Xh/RaHkXLKoe77G5Ga3pNpQ2ObYv79wb9aWRAEUSWzKcgC5AOscFa4KIQTtk/xRkyiSPxro88ruMQMoxUjCo+ZOCDn6Hi23fdgZGaqAUmzxbdbMVnvVrY5bTWV54rPpkmatU20lU+JjE2ViIbvHpgMM4sSU4cy10hBD9X7F+XDeqO/K+p6kuiN4IyGMvX2cHJpyR4erFq9emwm709XcNVDf3gtS6u/QuNDt7PEwBrP1tSsV7qmqQtmlaIEv0GTTZuDw8JpM2Y2OkzuyC/Kz0oQC/qyMhbPATSsRCWMjwwe1nl6DgsNYVVwt3PZzT++LWQmn78J5zbeGCb2No5RLxcLNHGuuE1C5kXUN4/Xa7I6Sutbersp0+upWSbOAtAUtwCxuUaclvd5yJDOrcNe2VKlEtPI2M1CKCXhcpUzK5Ul6pwSjRp6M0vFJOxmsoh5OxiOcEsog5mhGDJzeSa9YJIKSEVSH3WMe/A96PXWt3c3NFdHM9V2yKiFpmXKqtSGpsTEpSrmE3W9zAd96XKsvrakbH6jZIzsXwx+Ybs8MesAnHHJaS3kNvZPEqN4r909Xdb/N0uZ0uYcmtKX1bUaLTSoRgiLOF76A29YZzdcr6yG6LZCcjxf2Bh2YyO0l203pzY5jEXF5e3Oz5BJR0GdJcNtDVktFQrVKZbDTXVMSh9Oj4GopTpARiggOA7e9kqvluI0DU+SYMUQiEotF835UZFVA5UbWL1C4W22Olu7+0sqSVOp6lqRGRhvZtNtxMLwea0qN5YHQuPxju3dB2L9a45r5xJvPU8llAoG0bUIwaRGIiSmIHsAdsnvcDlgQGa1XkONdk9SAxi0UQikm4NHzPquG7+hyezoHRkoqS1XO4nx5sYKrg5DD6JaOutNDI5Ii1Qp2182F3mSpaGzu6azaKbyULmnmkU42wQ/kAGiPktLyQgxtY8S43iOVyIT8+2vQbLDRoMeNbZ1G3YjZapNL5UKBb8yfWREp3ELgthta2+ubKnaJr6SJW0RUkKEI3F5q0BpXajwli8w7kL8rQq1Y2MTDeWQSkUqhAPFu0yjcboeUMgSdEtcXaZEOJU9DeAw9GnpE51HI5Xx/pLXi4BkJDio3sn4Bz9E3NHruRnE0p6JQfkPJ1bEJt8N4iRF7TLnxOKUqeORQvkJyh67bywB8c7haDqVYyyg1ZBRJyKlA25+g5RLF8choQzR/sHeK1zXOECQ/TCWf72Gt2+MZ1+peu3hTaq8q8D/oDWy3esRDrq0SZVJCVFhgy6bBX8fgLqltbmut2UJdLVCWzTf0B024QnkTSmqidYw3oAHxlsilYp9y3R+CAE7aZLG2dbZt4xePT1m6x11hKhXEgXB7z8wB//SdndW1Zb6BiRSlAsrGJswA3LbeqTw3+RhXufNAQV5C9KJuKjiLRCSICg91eXmVA1Kn26ukJ0Gkgz4wAlFXczUyYrR5XNwzalMrFRKhAGflWSNQuZF1itcb0tE/cqm4lG+rPRF2Gtx20GYyINtap+rcxEO8sD0n9uVHhiqhWGPTVhXwOgqZOC4ibMjArRuRczm2MN5E0Ga3AHxUIWmLF/bpLEzdIGV1hMRGqOc2kwYNG9PqX79c4jXWH1GdieCPTJeJdo9g0LGFkiSlJUQHtmwa3B6murmroq42mbhUpCzhEbe57VlAhshpfbRgaFjPqe0PoWkemMXVGvFmnROoc6pu7jmgOJco7BjRk+VdLrVcBlZ4uu4B9qlp6a6qqw7zlB0OvTDfrNtTTtUlzYMWfs6pQ3sTY8KXVJXN49Jw94rFkroh/oSZq6Q1UtrEpt0OwfFIaWOCoKd7StzUb+Pxhf6Y9f56xnF3QOVG1ikDoxM3Kqs8+rpj6tPgtoNqpMdLmt2Sc+OnvLL8/QX58VFha1pMgH0Q8LiRoWqHh9swIrK7CSWtna+sBPH2WUbuONdrbBrhj+scYSqFgM+Fg7B7hISMTuqulFVpR5seUL8Szh+baT2dDHfAnuTiJWenJrCbNgW+sXQGRs7frEjiXMuTl/oHCQkSkM3EVxlL2MN5I3anu36QsDkZtULG5y6n390Gwwt+2l3W2JkhqowRDEXwhi12prafoWm+VCzi87huj6etZ+hGRVWou3iv8vJ8k9NDaFtp2D/kLTx1eH9CdPhS+xlCPkOopJJJQ1WqXg3ZMSWXkPqg/c3gekCkxSftMfx+nY3uHHVZnFSkWgFxBjrv1QWVG1l3+Lpua/VXymqcGl9zm1jBYNAWYeC2DS55uf6ghrtvf2FhSlyUgMdj09YMKMJAvKEIYwhh+wTX6iLFhB7sdVD5gVKMRzjklJb26rs1XI3JIxaKxUJ+wDJq9Mby+qaRvtoC8VtJom7u7YO9wLfrsySYyC25GSmbptRzOF2DY5rLpZUKx81C+TUldyrolZ0LxG180qGixz0ua8cEbXaESMUS30PfTa0H8OU8DFNS25oiaAjjTwhJKwSCdru9YzzE7qb4fL7OaLpYUiW2leVIroXzJuZKKWBwSRtM+QMhBwpy92SlJtyxjXpQ4C00TYlFAplUqbFQXVohGWKHqAtizVnHgpfwMeCjqrjjcLm7J0OmbKRaLr0/ewesHajcyPrC42GMFuuN6lvjA1Xb+Re3iDuCPgQFnTS5pa2Wna3OY/k7czK3JIqFAjZtjYECSMDnRYarnF5hl0ZgdFBSUisg7UHLTVB0MOVhvHGSMfZMUhNGRir1zS1mdzgrm9q6O6pSqas75LX+Mdpu034oAfut8TpO+q5tyf7RqdjtGxcwiCOTUzcqK83jlUdUZ9W8yfkebwcFshecdwRvxOm0d04QRhtHLpUJN/UsbaCXjIcpqWuL590K5U1yCaeAtEXwRo02d+9kyJjO1Tc0ahmv3K94K4offPpOu4ffbMrudB9J3JK/N2cbBJ0riQJpipJLRKGq0CE93aOT8DkmEWGmfbPqsTtMA1tElEVBTXpcttaREKODUPjmwwXvjTXnqwMqN7KO8Hq9Jqu9qqm9ur6iSHImTdIKTotNux0nw7tl2tFgeyA9PedAXtZdHq4Eij8eTcdHhnFoUesYb8goCecO8wlfy5255SJsoTieSN6YkDPVrSE7R10yqbRveLKqriqZczlPUQ6qP/ddRAgzZIvVcjIyUhL4/BUVuOsBuLI6o/laRe1YP8j2WzHCwfka5y8AhEFcwhUjGCTc5tYxelDrigxVgxpt4jZrEO5UNXdFkq1hPN9YAv5A0BHFH2ZclqYhSq8bOxF2OlowDKLOvuFtQLZdDN1jTSk3nkzYUnQwL3uBufIWD+nr6i1IiIkY0ZMtk3LG41RzJygOfDB2h5nAjR3KGxeGTPnnFvOoFDKRkL/qrUfvT1C5kXWEze5s6uy7XFJWJD2bIWkSUsG7bnu9IU3G7XXWI9EJOQ/uy11eBeDKAbcXoVaA8+vVUPVj6nDemJiyzFf9Cx9QwdWFcsfGDJzLTba2noEswbU8ebmENgf96LD/mCNKE5KekpAAZeWGrhYG2bY7nG/dqBnvLyuUXtoqaZ2vZd9igPAojDchITV9U3RNrzNSrYD82axmzu321LX1KrztEbyh6aZ8FOGBHEgU9SQI++Cvv8JmNm6GHrVHvTH2eHJq4b7cbJVcslq/EbgV4ReXEhdpclDN45IpKx0jGAr6GQCIz9RcTQRvpHlM0DvJSETiUIV0s4ZZdxNUbmS94HC6Gzv6yqpKtpBX8xQVQtIatP7Z7aV6LCllxgeiEvKPFOXIJKJ7WBCAgZCKhVHhoVoz0TCmEhIGEWUGX8gm3w5Ijq+2kz/C8TpCuSP5ijI517CAhmkcoRPM1pjoRCh2N26dsF+2XZcrGvu7q7P5V9Ilt+YaxKUCN4aYNodzh7UWoq7fJRb5H3pvxgHe3R7mVme/0NURxeufHlwFbne4bUSUVUYb5j5nAeA3Mu6IuKR9TBWTe6gwJ0wpX93W+PCLoykyUq3k8USdGm6PThbJH4XLOvdmho8Kt72EMkXyB8ZMdMuwhyC5oQoZSZJL+tFabQ6j1Sbkr3lDlo0CKjeyLvAwTFvPYFVdhcReXqS4IaeDS5qT4UKRdH3qAVlU/u6cnIhQxT2vfKMoElQjVKUyOfldWrHb7ZZShqAjWAHgyCEpgjcKNkVO6xd+0GtwyUfcW8Miknz9oDascput9pqWzrrGym3cy9vE9ZJ5OhQtFYrjhjBITY+bbK7OMcbt5frmq9p0JbvH42nrHeJYu2J43fB92a2sIjIUJ8hA+oyXGLVHVhiPusSFR/fkR4X5xo5l01YPEG9w3nKpRCSSDep5A3qhhNQHHaHIH2d4hKRNTk6Y7Z62UV9gIZdIeIuelcdotjZ29g+PaxNjwtlN9z2o3Mi9x+3xDPmaHJdxTZVFssuR/LGgTbXhB691qkr1h+3iPUf3FMVGqtfJFM5gIEA1IkKVWiuvTyeyuzwySs8jHPM0OPc1kxaS1jvWGJs9kiFnmkSZFBcZurqe6a4BVql7cLi4ojw6pCRXVgoB2SrWj4AeiClzGG9Ma/b2TjJ2N9fXDIpHb6YG5xDRdg2Muozdsbz2oCOjzWXKpawx7dfSe/YVFKQmRHPnH79v5fC5tFImkcnkHRP8EZNYwNGLKAsdrM4J7na4WCp6VGcJaR/xhJA8qVjM5/raKLB7BMPrH7SnuWvgRk0zZMWOrYlswn0PKjdyj/HNlGC0nL5a5pxqKJReiBf2BS14vV4OeNAqw94e5uDDh/fGR4etq9pRcA/g+GIj1HZG1DjM09u5EfwRKMKIO3VWXgD/YCyppCQxJW5DztLtdnu6BkZulJdzLZXHQ9+S0saV5EZQIDYCMxfNH7I77JDtOosnOky9mTogwa+jb2TSNNUbx2sB5WO3zoM3hOPw8G9qDw0Te/J2FuZlbrkLtw1Ezyq5FJx95wTZpxdzQ8z+zn5BhheEqy+kbHGCPrOdaRz0WpwEBLvwK54v0vJ6fTF979DExeKKce2UVCLJzUhh0+57ULmRe8yUwXS+uGpsoPGI8tUEYS9JBHeiNkZQrtvdzRw7uqcwIyWOy6XXobECzYgKU0rE8pp+YtCkDOONiklLUOe9GOwMf8wZb6OSM1LiqQ04Xnf/6OT1ilqntuJUxOvgtoO2WlgVIEIK542JOJq6YXH/uDUiVOWbnGNTOG+G8Q6Damm6Y7mtEPqwW+fBzdDV+oI6Y0FGRt7+nEx6DSrJgwJZLRUJE6PDJy3cumGJ28NE8kaCzlQGl4Qi3HGCfo7X1jpK9E4y0eEq0e3TjE7jYTzjWt8MsGJ7NZ9j5PBj8rO2LLKCfdODyo3cS7R6U3lDc1t7/SHFa/HCHh4ZpIUqOAkokip0RX3eo9uzcnMzUyFOX58/YPhUJEkqpOLo8LCOUU+PMUxM6KSU8Y4V40FxMfSkM3KCSd21LXljzbTB+KfvfOt6pWeq/KDyTPj8w8SuCnArwPFltD6SN9CplXYNmyViqW8irI0/SKrHPyrRxGh3NNWimGfc/hlwGC+n35ZgYyRqpVIhE9+1nwmcCH6VkWEqDiloGObrHAI1dzLoA6PAxVJytVJSO6DjNg04wpRyoYA/q3oAvvi4Vn/magllqtorv2D1iEzU1pyMFIJcm8GNNxqo3Mg9w2i21jZ3trVWZPLOZ0gb+YR9bm0qvHYx3CbjjhbnseTU3Pzt22Ri4XqOu+GzgcpKxSKVUjVh5AwaxV6PTU7rwIIs9UMzIaTWqeq1pRdlp901/7Ry/BNFWy6V1ZtGq3aKLsYL+4M++FxdQCHAzEkok5wcmzDTA1q3lxQoZWLQg/V8t9wRxuud1BmGh7qjqFYVV8NunQf4okLKKqP0U1a6Z8JN0QKF1Be+3J0cIAiCz+WqlXKKK+mcpPV2nog0wOcJWtcCt4TYd7HGJ03ezvEQHk8gntE7wOv1jmp0xdW12qGaffJzUfzBUUeUjsjckZ7EpagNfUFXC1Ru5B4Av0yH032rq7++sTzcfbNIWSqkbEEfgjo8vEFbwk3Dw1HxO3fvyobwnE1Yx0DJAoKhlktFQnHXmLtPS8UL+sTUcqrNDS5Zsyl7946t67aaYRYM4zVarBUNrW0t5fmScymizpktotcUyB2S41HSOjk1MWYkusfdJC3xTc4B2nUnn+b2eMw2OxzCt+t6ymcv450ymAcGe8KJljDeBLt1HuBzUxwPhIliQjNspP//9t4CPpLjTv/WMLOYmbXilbTM4AXTmpLYiRMHnAvD3T/0npNc7nK5+JJcwE7ixAHHTMtMWjFrV9KKmVnDPO8z072KVhpphauVt76f9rrVNdPdU11dz++prq5q6jWJhFIo4l0bNhyZx3cO7K9ksMUtI7xRA0/CHHG93ulmhCKINyItL05vxwirfcjK5opww/B4XHxybEJbXF3T0VyaLr4QI74J795lDBlhJCZFh/FnaVq/3yDKTbjbOBweFquttXvgYn6Bl+XqJmWulKN2ey9a7ewBs9+l0UNCr5S9m7J8USOsnZsWbklnMLZ1dXnoW+MkdbONbT4HDA+Hziqq0WamxIaLhPx7v9cVrqzeaLrR0JJXUog6N15yA/EKnXa3QAGRsdWe3AG13lrS6mCzeUq5FEZtDvFGtDGh1ZfeaILI3WvDqaIUqbX65vZWb0adH7+P3jonrgcHEz7c7n4Nt6rdxBeIlDLpXRNvHIXDZgf5qvgCSeMgt21cpuL0iVxjM8w8vOvtAF2woKNXzWnsc5jtbB9Phc1mv1Ze09RYHsu9lKkocQ6NzvDoNQQOe8THRIRLhHyi3IAoN+FuA3/TPzL+9plr3pa8bEWuJ29othux1xiQP7ZHJ8x4bO9WH5V8Db3TDDGAVTp6sdg+mr9DdcZP0L+IbtWooLRWSYMuOSosTC51NvzSCfcqNrut4mZrXnFeJDt/o+qaYJYh8FYchgd8ni+/l2XXXmvimmxMTwWs56zj42r1xoq6lksl12PCAvHBe+rpOIIhxH/1rW2eHnUBgm56651AjIhIMVTYojExyttsRivH10sBN0wnrzwQVy+FzFOh6JngFHd7qjgjUrba7Xi3OFU+ywTx1pvM1d3cvlHz4Mh4dd31aNbFLEXB5KA9/Sa/IUd8RFiETCy6YwvK/QBRbsJdBQE1ZPvE5XyetmSz4rxzKo5ZhgsdNnsWT2yd4Occ2L450MeTzWKvlVDbZrdrdYZjl0v0w2VZkvPBwk72/GbEmonOKm42JPj5h3ur5PfIy+uz4XA4aps7C0sLFdbybZ7nqTZSOm2B2B0MqO9SrjaKCpth9eQOydlDN/t5feM2hUwqk4jo5CkYTGbI9uWSGyazJTYsEBp/j3Xjd+AMaxrbVI46FCR62zxwPvhn2Hz5fRwPXeMAq2vYBjs7bZLZFQX6KhLy/X08dRZORa+c42GQsNU8d9MQ4IRwsby4g2LmcN2AsL1vLI53LUNWMPUB06DJZ8CREBIcrlzL4wkuI0S5CXcPVO69Q2N5peVjveWb5af93c2UAFBxa6zSwrHNY7zN69Nz4iKC1lC3FLvDMa7W5ZZVd7eVrBefDRM1C2YZT20+6O2iNkOMTBUa4OM12X/nHsRqs7V09l0tKhYbinJkFzx5w4uTbZuDpbFKSseyuQwrl2VedMQDcAIcpkXOGed7jPaOszuGbTyeEOKNep8qSjg/q9V2o6mjqrqYbahzMNghgaGQt3sqQsJJWqzWqvp2hb02VNhGb50Bbhmbg22xc8wOntHON9hEOpsYi8nOd95NRnbrqGBwXC+XCGf24l45cCDECj6eKpND2DQk1JsdUvYEQjo6eQpQaFQFUva4hDkk8BhJlxXJb5+Sf8Ts2WeLDwiI9FbKiHIDotyEu8eos+PJjc7WsgzxuWhxwyyyzTTYhVUTaW2OHUmJ2alxEcK10ycF9axaq7/R0FxRXbROeCVevNQHvah5u4wRTFFYaKD/3WztXBCQlqEx9fn8Utt4eabkQpCga3GyjUuPiK1iIqtKv2vI7EmNprmgmUCngUID8VZwxyAGnWPclgGzVCIVQbpcD30h223dA1cK8xFtJIrLRqz+Xj4R/t5eKzFW6FJAvFte18ozt3pyh/Q2kdYqRi5NWOTjFsWoWTVq8Rw2eQ2YfPuMAd3G4G5TWKcxstMU22GKbzcntZmS++1xOmaggyXUGWzYlb+3is+7e70dWUwmYgU/L6XWzG8fFYwbWDL2CN85Je70EoIzQoXgzRsM5HdLOJppQduYWdlrjfPxj8Su1u5IwMsIUW7C3cDVmdySW3ajubE8jnsxQ1Hm9qGXcxAoO79RG5s3fjA9NSc9IUomFtJpawH8xqr6lpLyolBW3kZlroCtX2IFabZze4whZl5kREjgXZ5uwdWR0Nk5aO5a3ma3j05oLhdX9nZU7FAeDRZ0uh2C446gIjfYBPW6pCL1/pioxAG9sk8nFTNHZa4hXJaSjdAAiLcnp6d9TFDbaZBKJDKJGNtx2kcv5LG1ldnyC0ruaJshVqyKCPLzubfaNpy5z6isbxvRWEesfq3G+BZ9YpMhudGQ0mBIqzdk3NSvrzNkNxjXt5rTu60pI8xUHS/ZKlzHkiUKlQkKn3ifgPjQkOjosNDo0IAA5zBBQoQmdzMUxrEQdAb6etpZ4poedr9e4stzNrZBvGeeBMw3gq2Zuq62yrot8UrvyEAf1UfgNf2lw0CVSq8SCCuGxWItqG4oLCuKY53aoLw224QcFjunRRd5ZvixuPj127NSlXdxKIlloby25VpJodyQu9/7mKt/1lJvLo1VUjy+dUB05KHdO3w97+obcbCk1Q3tIf5euApztE9C/woqa0vKCw56vxMubHb7IHM+2Oysyom0Yt3hqOiMfZvTx9Xai4UVXW0V2fJLqbJy1Ob05xaLzWXoLw7t7bZnrE9bHxnsd7mocrin/AGvd4IEnfCv50ceVkUc2pGTKXf3OHwVQRX9/sWi4dExPpfF53J5PC7+FeBfLHyea4X6l0tJsvOGcf13awX//PN/zg+sxj0FnTFbLE0dPaeuFrB1tbs8TwQtpP9Htz4oV/tkWMLBbeuT7rVGkVWBeG7CimMwmurbui/kF8dwLqXJisRsrduqA3Vrqy4yT33YMyB536ZMuVS0hprFrDZbU2ffpcJipSl/s/KcjKOe7FyzFGwONkSlyxwXHxUhvbvND1abvaq+tai6QSwUzDYemUZnKK5uqKstzJGcjBbXc51jZtFJCwLVeoM2rsKwzztw3Z5NmRKhQCjg+Xt7muzcqh6R3sJWcod5LPNSBMf12NscIOjGlbrZY69s7NdPtO9WfRDI7+IyLSab86kEQxQVHhxwr004BqGF0YwNC4oND44MCQwP9AsJ8Anw8fT1VHkqZQrnAwAhsosHQWOzcJmcC9O5TIHhXCjRXg3ZBjgsTkkqFoX4+7QP2RrHvPkeGhlnfJ4tNHqbqNMUy5VFrNEx/JcdotyElcVoMnf0DUHSvK25mbJrits7nkwCles2BJdpd7KV6bs2rvdVydfQ/Wm2WPuHxs7ll/J1RemSSz78Abe/cRHYHUytVVKvS1wXG32XvaDV7nznvrmzu3dwhMNxTgnFnjIal/Pxh8VaVtN082ZRKONKiqxi0Z3JbQ5Wuz68ULNP4Z+5NSvDRyWHzKCWh4n0Vio9WOKGAY7GzJGwJgRL6K8O8F0+y6hgDzNtGkSTKZKiGHE9j2XCTzLbed2mUDM/OiokGCpIf+GeAaospO01F+tcDhY2h81yKjUl0asnyfMHZ4jYAoGgt0o1ZmC1j4vgwhWcMQ7DcsdzN9iE3eZIhygyLjyIKDcgDwwIK4jFausZHM0vLXWMl26QX1JyRt22j0Gfhk1eRRPbLZL0TZkZof7eqJDotHseeLiRcXVuWZV+sDxTfD6A38NmLL5T1TSYDJuErTYajcjJu/xgi+HBgJHjOLSGkRsFJXnV9W1w2Da7MyLBmSBYqW/trrxR5mUtSJWVidmaxbUxWOycYbNX4fh2tnxdZkpKgI9qUoFQQavk0k3pScnJm3qYO0o12waMflYHe4m5gNgxWVa5x/t0krTaJdvO/TEZdh7DYDabqR9IWCFwaTlsdniQ7/bsTLl/VoV2e506weq4883OYti4DL3BaCaPdymIchNWCtxj42ptYUX1WF/VDs9zXrwht08rIdt6m7BgbOsYKzkjOTM61P/edw+T4DdOaPTF1XVNjZWbFaf9+e7fc3MLaiCHs6OJc5YIZAK1wIBSCyTKpVJMPlNvtVl1BuNdFhVcBD6PI+eqUySF3pYr53KvltU2qrV6m82OMKJ3aPRsXpHMVJYqLVZyR+jvLBD83gmrvHBs6zgnfXvOxvBAHxhIOs0FvKRYyN+WmZSduXGAvfXS6MFBo7fVzkG+0Z9YFGK21o/fJ2D9syMCw8POZxpMZovdToThbuCllEWFBDrYqnZ9OEo7vXV2EMIitMIVIpeHgig3YUWApOkNpjP5FcPdJRsVF4IFHbONuKKziUrHs5tMWZuzNyVEBa+tpjBUJcXXG27eLNmiPBcuauHN79Vt2AabnWmxs002rsEm0FlFGqtk3CIbNSuHTZ6DJp8+o1+vIaDLENSlDx40+ULdIZkWy3y78ywTztmfHAyOgjO6RXkpTXDqUn7e1dKaoTH1wMj4sYv5AsN1XFkf3ryG5HTLhFVaOZHRZN74wNYNIf5es71IzWazMhIi9mze5JBveK/3iU5DMJw6nbZMOD03lNtCPPddoqt/qKKuXmy9udP7HHce3Q9Re3BcnvtWrHW/Q/qWE5YfFCrcY2cLKtsaC1MFpxMk1bNNO6G1iuu1CXnqwxvWb8pIjJGIBHdtjKclgvsGVji3rDavosbD0BErquFAi2GaPVym2c6iV5wL+9YKvdgdLKfbdnX1de7K9S/D2YXI9bzS+dSSenLp7FmEWktjk23NTM5aFy0SzDqE57Lj7MnV2n3l6qk0zusJ0hq9TdiojS3X7+fLopCoG7l50OtNH17//NsYpoF4BRFbg21vTuaW1PgIPu8Ow3sZTZaBkbHLRWX9XVWb5WfCRc2wznTakjHa+PXaxDzDMx9/8ECwnxe9lbACUDPAfngh32OsYIvsqL+gd7aYfiooflXq9aXmT3zjkw/e5dcj702IchOWHxjE8trGkvKCFMGZBHGljDNBJ9wOqss6TUKVcX9w5ObtWesg29MaS+9l7HZH98DwldKa0XE1m2kRsU1MJssluM5/nT158adzzfkv1l29iKgk179OnP2wXCrt/B8l1c6/nf9z/unaiWs7k+GjlHsqJHdzeC+bzd7S3X/6wqlk1uvp8jKEFwaboEETe12bZXHws2UXosX1CFYWEWdhV2Y7p2I8o9G2Nyx64+b0RFx6/Eo6eXbMFivEu7Cqrr+9NIqbi4hQwbnjlNXzwmTntekiT409+8lHHwoN8Ka3EpYbhIMTGv2ZvPKx7rwM4alIcROPOa/XCHGBbqiTL6o/9Z3PHrmb8es9C1FuwjKjMxgbWjsv5l8LdlzZoLwq44zPrJJR5uBEW3XhJdqDQt+ND2xZr5JLIVd08loAyj2u0Wn1BijcpNy6RJbGJb3039RG6gPOFerfKUmA3u89g81u7+4f+eDM6QSP17OVBdRGVKBdhiCdVRwvqWUzrYt4YR2ybbFzmrTRhdoHgyNztmQmeylkdNo8gGMbmdBeLb3R01EZyshNlpZCvN3OAL0gcErdhqC3+j/76ccfjQjypbcSlhVcu3GNvrCy5sb1vE3y41GiBrcjobrFamff1MYfHfnsdz5zRCa5p2fovzuQ59yE5cRitTV39uaVlsjNZZtUl6TsCbd3mN3BGjR5543t5Xut356V4uUci3iN3Yo4YaVMHOznFRboE+LvjZVAH88Ab5Wfl9LXU+GjkuNHqRRSpUyikIplEpFULBQLBbALQj6PercHBprteqfn3qyGGK7n3HYG1+L450NlOKRIUXOyrMrlthcT9DtnbjX5Xhl9QOWfnJWcsCDZBsguL4V0z4a0+IRNNy27ro3uGrfIrY6lNkVA+/ksg8VqhSkkZmYlQKbqjKaaptay6rJU8eUIYdMcso3wjuqt6eynaXeOx251sFgMKxIMJrOdXCCi3ITlpaN3sKDiOlPjfOtGzNK5ffsW96TGKj0zcJCjTM1JWxfo60knEO4pGB48LtvhwUG9uVxVpcPBGDJ5nR16UOyVsCM7w99LSScsEImIvyktbtfmbR2OTScGHhkw+qBQ0WmLgunhVG6coNFkIZ3UVgKb3Xa9ob2gtCCOX5AmKxXNPp4/LqXJxlNbpcMmz16Df5s+vF4TW6Ne16qLdDhnTjOR/v+AtJYTlgfUdwMj4x9eyGeNF2yRH/Xj97nteIJoetSsvDyyb5Sz4cCObaEBPjCgdBrhXsLZzdBkfvmt08GmN3Z5nZtPN6I70mf0uza2f5Sz/sj+nZBteHo6YeHAeBmN5q7+wdNXrjF09Rtlp8NFrUsZJFVnE/2q+VsP7T+YEhu+lBMjzARlqbK+7WJ+MUd/Y4PiEp9phDwb7XzXtGYCo02Ifw34Eyt2AWTb7sFkODuBsFlsDotF/ctxviDJVRzalhngoyKDsRDlJiwDVpttXKM7fa1sojs/U+TseDJbl2PIdoV6Q5N1x7YNmxIiQ0VC0tnk3sVms//69RO+und2eZ+ZZ0+iORgxq4rHt/Vztm7O3pwYGcLhsJf4kAB1l8Vqbe0eKCgvN41UxvOuxknq+Czj4prxDTbh71q/vGP7wYzEWNJ7eRlB5dDa1X8it2xkbEzCmlDy1B5MnoPJ9WBwGUwOi81lc3hsNo/F5rlW+BwOl8sBzkHiOGzXUHHOFeeC7V4KKZIh7PTe71eIchOWit1uH1PrCipr6mqubZYdjxDN+gRLaxVXqdfXW3cnJG7YnJZwN2cbJCyO3715Wjr+7i7PU3M0b94RhwdDZxUVj23qYu5cl7wxJzkWNfJyXXmY786+ofyyqqHe6+t4Z2IlN1H8FtFCANv3547PpWcdyk5JkogE9FbCkoFyF1U39A2N2ex2sZDP53Jck6Zw+K5/nb092DDXzpFcodCuFSZE+p7t/3GPQJT7PgX1HcD9Qf+9WLATrd5YXttwteDaBtmpJEmV2yoedbfVzq5Wp1Yb9gZHbtq/JR03Lbkz731e/eAia/C9Hcrjs73ad0dw6U02XrU6pVx/ICVly+a0+JUYGBzCUFhVd6OuMlN8PklaKWFrFireRhv/H93PRCYd3piRrpCu+BDxrs5wdmf2zBvcL9AzCB399+3gTsQ+9XoDi8Xk8XgwrXTCLODzFovVbrexnJLpft5P7NBkMttsNthc7HPRNyyORW725YUo933KhFZnNFl8VEudONJiRUBdn1eUG82+ssXz8uRA0NOwOljN2qgLIw9GxG7auzFDdo9NpEiYjTdPXzN1fbBV/oFqsUOcQrZbdJHHBx/Lzti4MS1BLhWvRBWOekytM5TeaLxSVJokvJIpL/LiDdFp88No57/f87hn1OFt2dkquZTeumI0NjaPjIzaF9IbDvLp4+MdEODvdlR/k8nU1NTy3nvHpFLJvn274uJi6IRZgCrfvNnY19fn5+cbExPF5brpbtLX13/69Pn+/sGsrPTNmze4/QxhVSDKfZ/S2N5TUN2wLjokMTJk0fPdwrhX1bddK8pVmAp3qk6K2Rq3ncnNdu6gyfto/+P+oet3bszyVSlgC+g0wr3N0UvFoy0fbpa+68MboDctBFz6LkPQ2eEjIZE5O7LToIgrd+kRRI6Mq18/eZWlLt6qPBshaqYT5ofJzjvRf5gb8ODOTVuWHtHekZ/85H8KCorN5gWMQCeTyQ4f3v/444/yZzyGRwTQ2trxs5/9orb25oMPHvzUpz7m7T3XSHBmswWq/P3v/6ivb+DAgT3PPfdJiURCp03BYDD+4x9vvf32+yKR6Kc/fSE0NATOm04jrCqkAr1PQTU3NDpxvqCqqLphQqNfRABntdrqW7sLy0qUltIc+RUJR+1Wtq0O9pDJK3d0n8IvdXNmmpdiBetuwrLD53HtDJ7VvpjYzupgdRqCizX7Vf6pmzPWKWTilbv0KMA6g7GyrsmiaU+SVHgvPM5geDj4TKPZZLo7b4WNjY1DO3t6+ua/DAwMqtUah8PN6Q0NDZ89e+H69Vq5XLZlywapdK42A5vN1tvb98orf7l5swHnoFZrXe32bkCIkJaW7Ovr09HR+Ze/vIGjEKd3j0Dq0PsUZ/8Pu8E00VBUXlR1s2FkXLOgCstssfYNj14tqWBpq1LEeago3TaB2p3Td3qWa7ZoBFlbs9L9vFTcOz1+I9xT0Mq98KFOHA7GoMmnSrPJIkrduj7Fx1O5okO3avTG+pb267UVMfyCGFGtmK2hExaCwDkYixkhKf33ysNgMHg8bmJifErKujsuCQlxfn6+zBl9U6xWa01NHZTbYrFs3745PDx0pimfxGKxdnX1HD9++ty5S7DUcysxTi88POzQof0cDjc3N6+m5qZON99RzwgrCmktv09paO+5ePVsgPm4xirpsWfGx6VtzEiWiYXz6bOGCH1obOJ8fmlve/F+z/eCBJ1sppsZqR0eDOy8YGx7h8furTk5KbHhHPb9/hbmmqOkpqmy9EQW9+8LbXy2OVgn+g932bNyMjdvTItz9oGiU5Yfs8VSXd+aV1KgMuXu8T4tZP9z+s65QRFFhOH81zmUOrd8LLOTe2TXtj2RwX70J1aMb33re5cuXTWbLZ6eyl/+8r/F4jv3/GCx2FKpRKGQTxPv4eGR3/zmD0ePnlCplL///a+Cg4Pcdk9DVY/DDQ4O/f3vb544cXp8nO5y+MQTj371q8/DrFN/zqS5ufWHP/zp9es3cnKy8MnY2GjS3WzVIZ77PgWWG4uQZdjtfS6Jf66uNv/YpeKxCe18xicaU2sLq+qamqp3qY76C7rdyjaw2VlFoxs6HJtTk5LT4iOIbK9FBFwug8Ex2hf82j2LYYsSNfJsPZX1LV19w/ZZ2mOXhaaOvuKq6yJDxS7vcyjS85FtfMLqYBlsgnGLfNDk3a0PbNeFjZhVRquHxeq+PK8QUNnQ0GBY2zsu+JhSqZjpuQsLS0pLy4VC4c6d23x9fWfrVW612qqrb/zkJ//z/vvHJibU9NZ54OXlefDgPi6XW1FRhWPB4tMJhNWD9cILL9CrhPuJcY2uraNFaqsLEnT58AYkrLG2EV5tl8nfS8nncecYokit1RdU3WysL9wsOxEpauaxzG7Db7OdUzqW1WDdnpSQmZUSLyADpa1NcLnbO5pl9gZ/fi+9ad5I2Bpv7sCAllfRZpZIxFKxcNkbzG02e2f/0NncIp62eIPiAp9pMNoEWqt4wiobNytGzZ5DZu8eQ2C7PqxFF1Wvia/RrKucSC8byyoc21Q0urFsPOu6JrNen9liTu+ypWqYUWKpZ2RIgFLmprvW8nLu3KW2tg6cP3IGrlcg4MPIzgf6+y7sdjsM9+9+90pjY7OPj/ezz37Cbc9zg8HY3t7xj3+89corf4WBNpmMPB4P3t1odLaWJybGZ2dn8vmzBmdsNsvTU3n5cu74uNpiscTERM3d/Y1wFyDKfZ8yodG1drRKrDeDBN18llHMUstYg/1qRvOAXSQUiQT8mR3OcZMbzZbi6w2NDUWRrMvrpFUCtvvxqmBlGrVxpdo9MXFZmUnxCql4Wo1zb4J6cHR0bGhoCLUhVua5jI9PoDoTidy3dmKfg4ND589frqurl8mkqKbnzgrsamxsvKOjCyssFnumf3I48Bnz1av5MEB6vQH19UwTtoyodfqOzjaRpSFI2ElvmjdsplXI1qvYfWqDraGP4cHkSMUixIXLVRQsVtvwuPpkblln35DNqodOtxhimw1JbabkdnNKpzUVYtzrSBtipI5z1hn46+ziJLY8UahKkPvE+/jHBQbHhYXGR4THR4bHRYbHRkXExEZExEUEe6vkd6E3xlTlfvzxR+Z4Mj0HZrPl2rWCs2cv6nT6uLiYp556jIoA6ORb1NTUvvLK3yC9/f2DLBYzKipy//49EO/u7m6cwB2VGwWMyWT19PS1tbWjtOMQmZnpa+KO/ghDnnPfp3T0Dp67cs5X9+4GVR41UqnJzus3+uWO7HDIMjJTM2PDgmCSqA8DlBOTxVrb3HGt8GqA/XKW7JqC635qZOyn2xBydeygPDBn76b1XkrZ0sd7uTuYzeYLFy7n5hbodAsYL4zN5qxblwC7Q/99O8PDw2fPXnrttTeDg4P+9V+/GhYWOofQ2u0OxA3vvvthSUk56tNnnnkKwkyn3QIXwmq1/vrXv8/PL0LqN77xpdDQELgiOnm56e4fPn/1nFL97g6vC/SmBWJ1sMfN8msjW8e42Qnx6Slx0Sq5ZFnqfaPJfL2xvay2GfkGQWKzWBwOi8/h8nkc3q0huqgV/OscQRNu1PWxybG6sOKaAJ3e4d1k8jm3n5/Pu+++hqiOTpg3KAkajfaHP/yva9cKoaYf+9hjn//8p+m02zlx4swvf/lbxKPwyhD4Bx884O/v99Zb7x09etJoNN3xOTfArZGbm//zn/8f9Ds5OfHFF//Ty8tzRUNGwtwQz32fotHpW9pbBeaGEGEHNdoUm2GTstUB/K6uMU7TgMPB4MJ8oGqjKlmzxdrdN3T88jVfW2GmPM+TN+zazXRsDlavMaBwYo9FmvXwro2eCukcDe/3GqieLl68cubMhdraeviheS49Pb2wTXv27KD3MgWLxQp9/ctfXkOlefjwA6mpyULhP4OhmWi1uuLispdffrW1tU2hkGdkpCgUCjrtFrgc0B8ul1NWVtnY2GwymVNT1+HPFfJAeqOprbPLQ9cUJW6kN7nD1dWLaffAwkIZsDnYrvkZOVYHB+soWj78viEtp7aXA/8d4K2Cki59Xle7wyHgcRMiQ9LiwtMTIjMSItPiIhKjQmLDA6NC/MMCfIJ8Pf28lIgdlTKxXCKSiARioWuWVS7HJeWQ7RXKtjuzdM9ts9n6+vpfeulParU6LCzkyJGHAgLcd6xrb++orb3p6en5iU88gSUhIc5ut6P8NDQ0Wa22O3pugGxC0b16NW9gYJDNZkdEhAUHB7odEIZwdyBB032Ky2o4Z8Cl/3bBZNghyQ/4HA+yn88rLTmbX2kwmhDaw9P0DY8du5QvNVflyC97cwfpL8xg1KwsHtukFWQ+tDPbU76WZHslGBgYOH/+cnd3Dwz3oUP757Y1qExdsv2nkZERrNNbZyEhIX7Tpg0Gg/HEidM3btTCOdEJyw3HaU55c/dQszmYRht/wiIbMnn16APbdOH1mrjrE8ll45l5I5svDu06PfDA+cH9/UY/tU5fVtP09tm8UbV26a9NQ30RGnrKJVKxCBK+ci+L35vodLqSknK9Xo/SEhQUCBtNJ8wgIiL8K195/uWXf/nII4cX93gFX8EX/fx8uVyuRqPBcUk/tdWFtJbfp/QOjp69fEE0/sFOr/PT5vWCnGut4nrdujLdXv+ghN05aUaY0YLi8b7KQ95venEH3c6laHcwtFbJ2cEDevGmbRu2xIQFsFnLNqvE3cFgMLzyyl/ffvuDkZFRVFJPP/0kTMwdjQUqNS8vT/gY+u9b4M7629/e+OtfX0cmfOELzx08uE8gcK9/+KTFYsnNzf/jH//S2NhiMjlleMeOrd/4xr+Eh4dRn5kGvgLB/p//+RX+3bAh+9/+7WshIcF02rIyodGdvFrY13R+m9dFk41vsAuMNoFzZka781/Xn3yz3Tkto/OtJecA2BwWNb2Ta2ZG5zqbzeXwYOl4PAGPJ8QK7G+gr6dcLLyfm1snW8uhiH/96++lUjGdMAs8F/QfLnp6ev/v/16Gd0fhefbZj3/xi58VCNxPlIKjwKDzeNzJDId1Row4/9Zyipdf/vMbb7w9Pu60+DjnRbTwE5YLotz3KX1DY+euXuQOf7jH+yx3xgSOdgdTaxM3aWMrdTul3glmq908XpcjOhYpbppFtpmox/NGtvawd2ambUyODRfNolL3MlOVOzIy/IUXvhMdHQk1opNnAcLMZDqbr+m/XaCibGvr+OEPf9rQ0BgfH/uTn/x/vr6+bk2h2WweHh6BNUc12tnZpdcbqO1zKzcYH584dercz3/+fwgIoNzbtm2RSpe/R7TeaLpYWFXTUKvkaRnMKdMyumZmZLP5bA6X43yaDHmGRlMzMzqfIrvUm1p3NkuzkEfQDeeKa+Jl5zZnWzV9mPsPSrlNJjMu33yGBEd52L17+9RYp6mp5d///Sc1NTcRFH35y5//+MefmH8ktDjlvnDh8i9+8dv29k58+B//eCUwMABXnE4j3F3Ic+77FJ3B2N7Z6dA2QozZM2ZVYjAcMOKe3CGex3jLoIdJ25cizkuQ1rCZ1pl1rcODobeJazXJNea9acnr18VGSEVzPc29Z7FarRUV1bW19ZBwT0/Vnj07fH194FScUwXPvoBpvhzRsMFg/PDD43l5hVD0Bx7Yu23b5pm1Kg43OjqGw7377ofvvXest7cPnxEKBajNkRoWFpqTs37mc+5JUNfj0OXl1f39/VqtHvEBrP8KaCEDv9FL6R0SEhsWFhsVERsZHh0ZFhEZGhYZEhIZEhQZ4h8R5Bce6BPi7x3k6+nvrfT1VHgrZSq5VCEVy8TOp8sI45xPl109xVwC7xTx+1m2AfWcG2XAYrG2tLQ1NjbPvYSGBq9fnz61FKHAvPvuUa1Wh0KyffuW2NhoOmEe6HS6BT3nplCrNaWlFVB9FAkUTh8f7zvOSEZYIeYboxE+YqDehAOy3/6ceyoMD6d4J0mrd3md2eF1LlF63a1sA5ON16EPL9bsjY5alxofJb/v5wGD4YaN/vDDk7DFISEhOTlZblUK9eCxY6d+9rNfvfnme3D58F5QX9ShdPKdQCWO8GLjxiwY3ZqauqKiUrPZTXPIEoFpjgz225AamxYfkRAZHBHsF+LvFeCt8lHJVXKJTCKEKkOPEbvc50q8aHAdJRKxTCade3F1YftnDtvtdp1OT3WJQLSHPdAJK4lQKKQO5HyNvrObCjEJqwJR7vsUWB4Yn2k91GaC2jhU1B4lbhKwjPSm27E7GM26yDz1AecT8Y1pRLYBbFBubj5qVZvNGh0dHhISRCfcTnt755kzFxoanH22pVLJE0888vWvfyk5OZFKnQ/41qZNOTBAGo32+vWa/v7FTOdFWEUQ7kgkok9+8uOf/eyzcy8ZGWlTQyOj0YTLDb+O9UlBXWkmD4Rwoaure0ETnRGWF6Lc9yvw3CyW9U7KDWC+5xhOskMfWqndLvWMe2BLppC/+Ln3P0qMj4/n5RXCASuVisjICNEszw6oDuQqlXLv3p2/+MVPn3nmY4GB/rgsVOp84HK5UVHh/v5+EO+mppa6upt0AmGNgPsFcnjo0P5HHz0095KQEDu1qdxqtSJApNa5XM582rqXDsrbrV6WDqpPu2udsAoQ5b5PYTI8oNx2B8sxpQluQThf3TYEFE3s5Hum7diQ6Zy+c94dZD7CoEodHh6pq6u32Wze3l6hoSGz9U6HZu/bt+ub3/zyv/zL51JSkvDnHbspTQNVOZ8vWLcuAf8OD4/m5xfj6HQaYY2AiyiVSmR3Ypo2QzWtVvrhCBN38l15/dLZq5DpPJBrID/rfOY4IKwQpKq9T0Gwz2I6B82Y3U7PhXNgLIu8eHyTRZSWnpwW4reyY3DefaC7er1Bo9HOvZhM5mnOA16kvr5xdHQM24OCguYY4dnLy/Pxxx954IE9ERFhPN4imytQZcfFxQqFAhy3paVtZGSUOKH7hn8WmLvzipDrKMtzINxcvb39zc2tC1ra2jpwx832Y81mc3X1jatX83ADWixu+nzgi1qtrq+vv7GxGbE1PtbV1eMavXjWeLe3t6+goDg3t2BsbBx1Ar31HoD0Lb9PMZotXb19Y4NNidIbs032NQd6m7BifP113aadmzfHhgfyPxITisCwTvYth5TK5bKRkbGOjs729o7ZFsikTCaZ2sN2cHDo9OnzqBSwvm/f7rS0WcdNg8MGU92S0WjCF/Pzi7B+x77lFK5+7PrCwhLECiKRMDk5ydfX++44MMJSWOIYahCbtrb2q1fzse7j471xY/aCZgFZXN9yyB5KGoooh8OOj4/LzEwTixf5fL2/f/D1198+ceJ0QUHR/Jfy8ircUCjnM30CpLqnp/ff//2/Tp48g0AWP2pqCxZuE+j60NBIRUXl8eOnT548e/lybn5+cU3NTY1GI5VKuFzcxG4GIqysvPGLX/z2+PFTyOTAQP9FR9jLDvHc9ym05/ZY5OuYBpuw0xDG5Qmdr0x9FHViYGDwpZf+9O///h/f//6P51imznNMASOOOJ1aDw4OnG0mkuUCVZifnx9V7UL4+/oGiOe+H4DSTL6BDU3CpafWVxTXgZw9VVF74OhLeZlbrdbA9UI7F7S4xowzuPXcQ0PDr776j6amlsDAwKyszGnznSN/amrqvvWt733nOz986633i4pKq6pulJdXnj597mc/++XXvvaviLapEZCmkZAQu3v3Dtzjf/zjX5qaWhFp0QmrDVHu+xSGh7OHms2BArCYEFLOGdvvc9SfUXY+93LJjUad3n3P87ULagebzQZHAiM+BzNlcnR0nNJyaOoiHl0vFBxFoZBT48Cg6oHt+KgqN3K1tbUNhm/+CzxlZ2cXJTYzodpOP/jg+Kuvvnb1ah69dQYGgxGhWHV1TWVl9c2bDf39A26reAroSlFRye9//+djx06NjrqfkmdZgEGUy+WUdiJYRJmjtq8oONDYmPNADIbzjcSlKDey327H4sTpIlzD792R2YZF0un0tbU3L168zGQyHn74YFRUBJ3ggpLtH/3ov3H5DAYDHHZMTFRWVkZSUgLiD5xAZ2cPLtk773w485LJZNLNm3Og34gM3n//aHd3D52w2pAx1O5T1Fp9YeX16rJjnwr+k4BFj9u1IGwO1qDJp0KdPczeEBmVnpUcIxOLlj6NxCoydQw1qVSalBSPm3zu5/cbNmTt2LFFJvvn+FPHj5/+xS9+C8suFotffvmXqanr6IR5AHH68MMTMAFYv+MYapMgvPj8579SXFwmEgm3b9/ygx/860ob/VWhoKD4rbfem9bCMTfQg4iIsGeffdrf35feNAUo+vHjZ9544x2lUvHcc5+c9iY9KnQcq6ysEoLd0dHpesxpR4SkUCiCgwM3bsxOSUni8wXTCjxcaWXl9Z///P8sFssXv/hZ7BNFiE67naXPFXbjRu1Xv/pvg4ND+O5Xv/rFxx9/mE6YB4sbQ62wsASFE/GQRCL+3//9z7S0lNnGW70jENr//u9flpVVIASBiCI/59PwjvzfsmUjjj7troQk/9//vYTTy8hI+3//7xvh4bfNyIcY7qWXXrl8+RquaWJi/MGD++LjY7ETFICWlvZTp87iEiMfQkODv/e9b7su620PDnDpEYf95jfO0V6ff/65Q4f2r3Q4Ph/Ic+77FLPF2jsw1N3dlCYv5yz8OTdgMhwStkbJGdIZTM2DHjoLVy4V87jO8bHoT6w14KEnn3P7+np/7nPP7tmzE5Xv+vUZsy2xsdHQy6nPlSsqqvLzi1Ajq1SKAwf2LujpI6oP1DILes4NUElduXKts7Mb66h/cc68j0S3g2lAEaE0jY3NcMDzXKBPcGmbNmVDm+m93AK+ubW1/de/fgmfgXLs3LltarhjsVhHRkZOnDjz2mtvwkOjfkf1rVZr+vr64fubmloaG1ugNF5eKv7tb0KiJOCvlpY2SP7Q0FBUVKSPj7fbJ6NLnytMq9VVVV2HcuNsIUiIEeeOMqeyuOfcpaXlUEccF+HIs89+AqZ//kecBiwsyjmuEcoqws0jRx7KyEiNj4+Ze4FXnpbhAL/l7NmLyE8Y0U9+8ik46akTBMCOQ5tPnz6Pmysw0P9f/uVzCLXDwkJUKiUuDVb8/Hw7O7twJrjEiAzi4mIQtdNfdsHhsHGhr10rRFbj0PDf+OF02uqxVitZwhKhWqjmGENtnnhyh7MU+YmckxWV+ZeLK4bH1JaPxItJPB4P4g13FRISNMcCpZzaPQ1QrejIXgTmi67XFgrOFlfT4bC7hrX66LeiQTk8PVVeXp5zL0Aul7JnNOo6HI7R0bH33jsK7cR+YOOmBlhIVavVx4+f/v3v/9zc3Ip7xdfXJz09ZfPmHARqSqUSSllTU/fLX/62pKQcwkB/7RYqlerJJx/FcWtqbsJVazRaOmG5QcgYHh7GYjFh9IeHR/S3RrxfIZAtUDj8XsgbSr5MJpsasK4iXV09eXmFExNqaDDlyOkEF/39A+XlVbjcOG0EtcnJiVObN3DjwGR/8pMfQ2biz9LSyvr6pmnt0Cg/KCS7dm0XCoXXr9deupSLG5xOWz2Ict+nIGyFrsxnJJY7ImWrU2SVe1XvNNwsPn65qKNn6H5+BGO349c7f77LGbgxWysBLiWOhsPeUy+urByf+cwz//M///Hii/859/Kzn/34S1/6/MxmD+RSe3vHmTMXoHkHDuyNj4+lE1zAhsLZv/baWzCX8Fs7d2791a/+++WXf4UjvvrqS9/73rep+a37+wf/8pd/1NZOH/0GpjAiImzHjq2QCvh12GI6YbkRi0WZmWlUXAJNXdER9FCkERTW1NQjphGJnMdFztBpqwpODDHWzZsNCOa2b98sFrtpSMe1xgouB9R35kMBPp8fEhKMa4qc7O7uvnmzfqYwIzrfunWTUqlAJp8/f2lgYHDVu6oR5b5Pcc7OzWK7PPcyqAuXaQoXtTzk+5ZpqOjstbyaps57pxPmXQZGxOVFnB3c7loEg7oGEYPL6HPuWriwisDzoapNTIy/0xIXFhY689lBd3fPhx+ehH1E6sxH0V1d3W+//T71Zjzq60996hORkeGuaWVYAgF/48bsr3zlCzg6/oQjLyoq1Wqnu2oul/fAA3th1Nrbuz744Dhs90qUBIFA4HKQMpwbztnVPLBSoDA3NbUMDw8jT5BdGRmpM1sy7j44K1zKiopq5LBUKl2/Pn1mPFFVdYNqBvf39w8M9J/WQkaBGCguLgYXFLVWZ2f30NAwnXALJKEM+Pp6Y/+Dg8OFhSWTw+CsFkS571OcreVMps2DtSw1CpPh4LFMQYKuLfJjYn3e1cJrRdcb9AbTfTjKEupTLpeLitpgMNrtd8MBQxX0eoPNZkX9gvrL5fWn4+qY3d7Q0DT/BTV1d3fvbB2zUYPDfp08efaddz4oLa2gt87J8PAItVu9Xu9WyXCsioqq115789y5i3P3REP9y+Px4G7nXgCq7GkmDN6xrKwS54ztGzZk+fh4TxUhnFh9fWNNzU2Hww5/dvjwA4gSsB8qFXmLWh6VuKubEsdgMFy/XtPVNb2/MaQ0JiYKCw6Bn5yfXzRzYBDEBE8//dSnPvXxxx57eHH9EnC5IdubNmXDBI+OjuEX4aLQaXdCJBLm5GThBJ599hMbNqxHXtEJs2C12mpq6tRqDcp2YGBAbGw0jk6nrR4IWCsrqxFP4Lp4eiqR4dPOChnS09ODy4TTDg0Nwb9u7w5cX1xlFouJqw9XDaWnE26BbyFoS09PRYaj2F++nDvHgDB3B6Lc9ykoi0xqDLVlguHh4DAtIcKO9ZILUkN+Yem1strGcY3ufjPfqNmFQiHualgxl3iv7M/HgXCUiQk16lYIhkqlcFs33bzZ8Lvf/fHFF38z/+UXv/jtW2+9NzGhoXcxBRzUbDZfu1b46quvnThx5o5PWF0nabhy5drPfvbL3//+VXgatyEdakL8kHfe+fBPf/obdEKno8flXl6GhoZglFHdQ662b58+qTmiB8QWOENoQEREeHBwkFA4vfu0RCLZsmUDgiR8BhZtZns4LgGKwZYtG3E5EK8cO+b099N+8o4dWyHbn/nM00888SgUhd66QPBF/ASlUoH9I+AYGnJOHUanzQniy02bclwn8MzGjdlzn4DrcptKSspRpHEsfFGhUEyLh1YFxEP5+cWIJ3CNoqMjFYrbeszhtFEykWqxWPEDYbhnO2cEYQEBdCo+j0JIbZ8KrmlycqKnpwq3GwK7gYHB1X3aTZT7PgXVO+od57jlyxo4shi2AH73VuXpQEdebsHVkura+028YdRQa1OCilp7JWbenAr0YHR0FHqDI6J6Cgjwc1s9wUnAk+XlFcx/gVOcTT5RZ/X29kNfu7q6IW/x8TF0gjtc9b65rq7+jTfeRe3f0tKq1zvPlk6eAmxNeHhYUFBgQ0Pz66+/DVF0+7ElcuNG3c2bjcglf3+/2NioaX2q4fWpWbBYLHZcXPS07k4UHA5bpVKFhQXD+uPz16/Xuj3PuLiYkJBgiEdV1Y329k6L5baZteB6oTSQQJlMOpui3BGcSWpqMsILrKCwwYBCpei0OcG9D7XDCUCJEWjOfQIQyL6+fuwcRhMCmZ2dQScsB8g55DZyCcHHHAtK+DSlRIyC7RUVVfgu8jA+PnZazIpbA+6ZugHxe1267v5BEq6jr68P9XX82Nnae3x8fPz9fXFcvV5fWXn9jgHrikKU+z4FxdT1+hbD7mAub/XIYDgU3NFdnqdThedKyvPPFVSOuPNtH1VUKuVkl6ienj54TWp9hUA9Mjg4RI0NAhFCJc5irfhNPTIy9tZb73d0dKK+g7OEEaET3GGz2SDzP//5r1tb27FOb50FHx+vp59+EqJSXFx26dLVOcY8WRzIritX8hDHiETinJz1XO70V4zgt6jGUmQjwojZ3pWC1AUGBvJ4XFTiXV09VOREp90CNi4yMhwr+BWXL+fCzFHblxGcPGKLBx98ACczOjp2/PgpqCCdtnwgT06dOq/ROK3thg1ZYWF3HmNg/qBItLV1IH/OnLkwx3LtWuHw8Cj9HRf4pYiHkKvYg1wuD5kxl67DYZ+YmKCeU0C5Xe+Lu1duXE0EUlRJwG5nU27Xi2Q+WMER6+purvStPTdEue9TGB4M53MdlEIHe7YCPX9sDqbRxh+3yAdMPh36kEZtzA31Oo1VYreZqutb3j6b1967+r0x7w4I/+FLqPXu7p4VavKdBFLU3z8I5cA6ap85piab5Gtf++Lvf/+rP/7x13MvL730i29+8yu+vt70126Bqq2zs/P8+YtwM3v27EhImO51pmIwGOFxX3jhvxobm+cjKlwuNyYmCtEAVmD6Z/bcXgqocOGn29vbIaVisSgpKYHNnp5XsHGUxDIYMOW+bjs0AdT1AQF+VCp+F7RtpnJD14ODA2H14IPLy6vctsEuC+vXp2dnZ+IE4P7r6pyjEdAJywGc68DAEDVozPr1GVDu5Q0N4aQrKqpfeeWvv/rV7+ZY/v73N6eNX2YyoRx2ofxjXaVSTB0NaRLkPPUBnDMux2zl1Gljbt01qKZmixcRuEC82Ww29tnXN0DddKsFUe4Fg8s2NDQ82ZFnnktTU8vIyOjMjioUqFNaWtree+/oiRNnULnQW28HleDAwCD2g/uzuvpGvWuimzkCeZzkuXOX/vGPt65fr5nZsOMsrK4mMts8Jvp0CTwL2gwxHjGr+o2+nfqQek18xXjGtZEtZwf3H+97+Fj/o6eHjlwcfyJf/7Fyy9NNrCf18gfCItalxIbHhAQgUJi9ev9IIZFIXNNuOs1cc3MrLjqdsDKg5KAk6HTOPjg+Pt7+/u5by6cSFRWRnp6akXGHJT09JSYmcuYgWaizjh07DYcHf5+TkzXzNZtJYG3PnDmPavfGjVq3rnQmOHmhULh//x6FQgErdvToSa1WN/OLRqNJp9PODQSMqrUnQV7hToSjwnZEOeHhoTOjHPwu6mZhMqmhud2HQbi4KpWKUm5oD27DmSeJ34LLgbredXejJIys0JNRiNbWrRvCwoKRVydPnh0bW8Awc3dkbGystLS8t7fPy8vzoYcO+PnRrcrLBfJNr9cj24eHR+ZYcNWmKSUCpo4OWrlx0+GCUtsnwQWZUgAYrvti1jN3lQQq1Tkmq2tlOviMVCoWCPhQd5RtFEI6YTUgY6gtGNx+Z85ceO21twoLS+a/lJVVcjjsoCBnCxu9o1vgxka5fP31t48dO4VAEhH01EF8kAof0NjYVFxcDiU+e/bixYtX8vIKSkoq6usbBgfht0yoXlGJTIuFcT9cvpz7zjsf9Pb2x8ZGS2cM5Dmq1lTV3UyTlwpYBtyMdgfL4uCY7TyDTaC3iSDS4xYFdHrI7NNv9O8xBnUYItqNse2mxDZzarslvdeeMsxMneCk6vkpNnEyS54k9kr09Ev0D0oIC42PjoyLiYyOCQuJCQsMDfCWS8Uo9/e4dlPhPzWGGircnTu3enqq7iiE00BIjpi9tLQC1xTXLiYmOjo6ap6V3ULHUEOtB0//5z//ra+vD2Vm9+7t+IrbY2G3RUWlKBJYf/DBA2FhISgwONW5cV6y2/eG8pmbm//hhydQje7evWPbtk1Tx7WgsFptGo0GGnn8+Ol33/0QRRf5gNPDv6gTkaU7d25D9s6WsTC7SqW8oqKyo6MbUoQ4w8/PF2eCHeInUG0YcD8o1fCXMOWzLf39g0FBAfiZkz8Bdf3Fi1crK6/jAoWEBD/xxKMuH3bbD6yoqMK1gxLzePynnnoM4u32PPFTYPiKi8vwS/GZja6pumZ+EtF2VdUNxOLIN0RCyHYEWHTa8oHjujpFOsdDHRoaSk5OhMri8tLJSwDXCzn5j3+8PTo6vmfPzr17d84cjW5xwFegnCMgwJUNDPSPi4uJiAgNmTHS0eQSFRWZmZmG30V/3zUo6YULl1tb21CuEIlu3pwz+QoABU5+cHDoypVrCAtQ+2VlZeAQKNV08u3gln/99XdcjTHi5OSk1NRkOuF2EE2iJkchRCHft2+Xr6+z8XxVIMq9YOCbz527CJXt7Oye/4J6BDF+fHwM7jF6R7eAMBcUFP3xj3+xWKwHD+7NzExHaaaSUCgnJtQo4r/97R/gPyorq7u7e3AXjY6O9vT03LzZgFoGJQmfDAx0Thg1+UWAWglF+dKlq3V1DXK5PCIibNqhx9Ta8pr6aHEDk+FhsApHYaZN/t3GsHZjTLMhqdmY3GxIaTKmNxrXN5myWi0ZAx7JJmEKW75O5pPkH5QYFp4QFRkXHx2zLjY6LT4qPSFyXXRodGgAdNrfW+mpkMokIrFQIHC+mOMcEnVe2rWqoDpubna+CoXqFW5py5aNqKcWqtwAVw3GtKmpGXc4FAK1wDyrURQA1PINDc3wEJGR4evXZ8zUxamgKHZ0dP7tb2+gCKFqe/zxhyFydNrtTFXuQ4f2I4JcxO8CEIa33/4A4icUip5//rnQ0CDKd04Ffvfy5WsvvfSnq1fzUGmiWAYE+G3cmNXT43zHbB7KzeDzeRqNFsUbhg8OmOr83NjYPKnc1M+ZFhxPWwYGBnfs2Dr5/BJAuXHbtrS0YT0+PvbQoX3TZBtAaCHe+Ak4h0984gmJRDzzMwCXGIYP5wCNh3Jv2pRNhRd08i2gBM3NrRA/rEdGRrjGyl2RIeURu+Meb2/vQFWDwhYX5xyXm05bAgglz5w5jxomIMD/G9/4EoRq5m9cHJPKjWoKAcEXvvCZAwf24XrNtmzYkIXYaGoTyMjICJxMT08fFDo7O9PVjH/buTkc9pGRURRFFELkBoTf9V6+mzsRQQ9ixDfffBfXC646LS0F4k2n3Q7KcGlpOYJylKWDB/ehYLstHneBxdy9hOUFxfcvf/mHRqND+UNgOLUqRHk6f/7Sj3700xs36lDtouD6+PigCGZlZUISIMwoQKjrf/Ob36P67r99ECWU0ZCQwIMH96Nsffjh8fLyqqkNetiIqtNs537Y9+gf2p//devX/9D55fcGP1NofLqd+4TJ82FZ2OHIdYezNxw+vO/Qp48c+uYzD3/nuSNf/tjBZx7c8dCOrO3rE9PjI2LDAoP9vL2VMrGQD3Gmd71mQSXy+OOP/OlPv3n77b+++OJ/um1NnQ+oyhGP4zoiMG9ra4eE0Al3QiwWoTrA0bH82799w+08GVOBYCN0o3rPJiXFQxuo7SvH9es1EFRki5+fT1xcNJ/vZsKJ4eHRY8dONzQ0QnThdXbt2vbf//0jRCELEi0YRzhmlH9oMAr2srQzu4yy0/7ixoF7c1vnulpK6dsEtwi1MhN8lcViTu5hZlM5hetAdPc9HBrXi1pfdnAmcK7f/OaXP/GJJwMDA6j4ZukgfvLy8nrqqSP/+q9fw+VADE4nLB84c4QdCoUcId0cC+6paa2VdrvD1ZHemfNU+xG1fRLsGXEbtR0XCMEWtd0djskCxmKxZza8T+I8zK0dIm52lZbVgSj34sGti9L8wgvfmda1x+3y29+++OCDB+Cl6C/fAlFhQUExfABiPZghPz8/OsFViRQXl/31r6/jhkdBSUlZ98IL3/3DH/7vhz/87r//+//7zW9efPHFn2zbtgnVKArlyZNnz5+/PK1qkMlk2Ke3tyeizry8QhhBOsEF9DY7JT47a8cDux549tFD33jmkW89e+QLTx54+vDOR3dv2LsxfWNafEpceGSwv6+XQiwSsPGDmQxndXUb9N4+AuDHwCBKpVJUEwjSF20vYBCjoiJwvYRCYXNzG6SOTrgTOAHU9Tg6FrFYyGTe4QQmJiZQeFCDoBxSh6MTVgYUs6tX8xGIIMJwdczmzH71HTgZOFEU1K997V9CQoJme2A8G3AzcEjYP2zQzI7ZcOFHjjz0xBOPzLHs2LEN5zBZQHEHIcxFlGy1Wvh8rqenkto+DVfbEP2VuQfSmY/G42qqVLRyDw4OrtwY5gCKEhAQ8NRTjz788KHg4EB669KAoMIQP/bYQwkJsZRirQSLrURwSWnhdLsHbMS9TJ027pGxsfFpr9RPAtlGPYzdYZ3Pd0Z11HZ3/PNACATptdWAKPdSYAiFgri42Glde9wuqanJ/v50Z9RJUFZgTU6dOotCAFMSHByEckOnucacguHo6+uHOU5IiPvc5z61ffsWVIK+vjDe3kFBgZmZ6c899ynUYgg5US5RiU/r3YbDoRTi3kMNUl5eWVxcSpVOCplEtGdD6oa0dSlxUdFhgYG+KrhnT7kUFhpJEpFAJOBTbd2UZtNf+0iDux25TbHYCoV+7nj48AOugTiGz5+/pNG46cHklskTwMrcx4ejbWlpr611jvaVk5OVmBiPq0SnrQCQ7e7uHoSYBoNRLBavW5c4W1WO8HTr1k3f/vZXv/nNr0DgUQJdD3cXlpkw6CjqYrEEvsr14Pm2jtn79u1+7rlPfvazn5pjOXLkwalN5RBa5BjEG9U3m82Z7TEETnUyYsNPnu2qYTPuWSoVF8uVFW5+IG7AyQMZjaYVfY8IvxT1AIJ1qVTiyvBlADtElAb9Q0R7h+J418GNgutIZfvktZgKThhFEVUfLhCUm2pXp9Nux2y2IKSjUlHw5nhEhc9Q8k/l9irmCVHuxYOrhtIDZUPhmAfOGmHalYbc5ucXtbd3CgR8VEbTen+gqMGumUxm3P+7dm2n5oFHKaRSsSfcVNHREQixcV+h4HZ2dt+4UUulToLjQu9Rew4MDMGX9/cPTIaKkGSVXALnLYI+c9iTeyYsHdzV2dmZiOpwxRsbm2tqbi5Le+9UhoaGL168AjOKiHD//t3e3nMYhduAgEEIJybmWnQzxvyCjN3eMTtstjYJVHyIWg4d2h8dHYmqc3G1G3YeEOCPOwLHRQbiTplqcZRKuZ+fL374HItKpZx6hrhBUH1T1TtCnNm0DSqFa4cVfB5aS9Xm7nDOwEGdEo4yNUSYCg402caLH7LsZeB+xpXtAirbEZDh4lLbJ0ESMt/f3xd2COmIO2e7mtQzRyrV1d7mfkp1QB2I2jPq9FWsM0llvZrU1zcWF5ejMKAaSk9PmfZ8pbW1DV4N4TxK3tatG92WJ0SI+KJreCCmVqttbW2nE26B8g39CA8PRV3T1taRl1c4s4gTlh1cDigHgqrAwIDR0bGzZy/M87WoeQIZgNsuL69C2di9e0doqLPTA512J8rLK8+du3Tu3MU5lqKiErPZNPWEXcrdrNfrUW2h1M02WBtALIsCiXLrVszmj7e3l6enEvXp8PBIb28/Kk06YbG4qubJX+T+3BQK+nkqfvvIyKjV6r7BHGHN+Pg4pcQIAlw34B1+LHY4NT8JSwR+BmEWVcZQT7rtQ4BUar5tFJ6Ojq6ZLwpSGAzGlpY2xGEo0r6+PhBvOmEGCJSpW8DVsLH8T/3nD1HuVQO38fnzlxHruZ4aZsF2z6zpoOiBgf4IG7HitqDgKyjBroeyTIvFOrNnCj6AL8L/KZVKGJfTp88vvQYkzJOMjJRNm3JQX1y+fA3as4yWCzVIaWlFf/8A5O2xxx5GlEAnzIPXX3/7xz/+2Q9/+NM5llde+Zv29hepUa91dna5unc5XxwXCmm7s3IgVEXhp9Y7O7upjvGLhroRqHOG7s52LYRCoWuwLafM9/T0zhbmOhz/TKUiFbe5gQycPBBiaECtE5YOsh0qS4WPqNkg3tT2acTFRePuQNyJz9y4UQuRphOmMDExcf16Da6UQCAICwvB1aQTbgdXkzoQDurp6TnZmrIqEOVeHVCSoNk3bzZQ/W8zM93Mmgcv9R//8YPf//7/fvWrn83W3RH7gVpT5gBFGdElnXA7CQlxqASh2Y2NzYgujas6hsD9AyqC3bu3p6enajTav//9zaEZswcuDtQg+flFRUWl3t6en/nMJ728PGezv26BbkGW5sbV9+c2g4iNUG4UIZj7yf7SKwoONNm9CzfLEjtmI4sgySyWsyUAdfRscQBqecQlWMHv7e7umS3MRRzT3d2LVD6f5+npHJLFrXK7gmn6QPjkSnchvK9AfkZGhlF9O0ZHx6f1YZwkMjI8MTEOHzOZTG+//T6CXVxZOs0Ftly5co16Ch4RETZz/PNJEIK7GlpsKEsBAf64u+mE1YAo9+qAy19Tc3N01DkHMOQ2OjpqpnJD0RFUBgUF+Pv7zRato14oKSnXaHTYD5w3NU7yTLCfkJAgVMcIOYuKSpbrpRHC3OAORwj/3HOf3LFjC+Iq1B1TXeziwA7MZsvAwOC6dQmPPPLgli0bEPvPVte4JSdn/YMPHnj44YNzLFu2bOTx/tkIhNKFaG9gYAiaB0GdrWP28uLqAU4rd19f/xILLX4LbjHYKdxKRqMR9TWdcDtyuczf3xefREyMMNdtuIAk6ERbW7vJZMbNGx8fN1v+Tz0Q4gaRaDXr+o8YKIdRUZFc18SdMM3DwyN0wu3gAmVkpAUEBKDoVlfX/O1vb9TW1iNuo5pDOjq6jh49iQXruD6HDu13PVh0Dy461QUdRSgqKmJ14zCi3IsHdShleaf17pm24HrPbKKx2azl5ZVarQ4VOmJ8mKcF2SYKyD9q8LNnL5jNJhTfoKDAuDj3szYhCID8o6zjuFVVN1b07RTCVFxDMiV+6Uuf+9jHHvf0nG8nsrmBgdi3b9cXvvCZxx57CNq20JJz+PADzz//meef/+wcy+OPPzK1PRwmXKvVUj22UGLlcvfNicsLh+N8fkyt611zSVHriwb5FhTkj7oegjrZl3gafD4/NDREqVTg5mpoaOrv74c802m3wJmUlVWMjo7h9sfNm5q6jk6YAU4bZo5aDwz0J557GUF0hWqTmnUbdezNm41uw2J8LCUlac+e7TKZFPXthQuXf/e7P37wwYlz5y6dOHHmj3/8yzvvfIhrJBDwc3KyNm6cazTfwcGh3t5+3BS4BXDRcYPQCasBUe7Fg4Ki0Wjy84um9e6Ztly8eIUaRGkqqBeoUTZFItEcY/LNAY4+NjZ+9WpeYWGpxWKF4c7ISIVBp5NvB/uH7Ub4ieO2trajBNMJhJVHIBCgfomMDMc1ms2czR/sAFczIMAfbn7Ski4IyBK+DiGZY8GepzbzOBx2V7uxs2ZkMlkIAantKwqEdrIHODQSrohaXzQ4c1wFvrOnsRnmyW2fQVyg+PjYmJgoJPX1DZw5cxGmeeqhTSZTV1f38eOnzWYLj8dNSIgNDQ2m02YAb4e6HivYbXh4GFwdtZ2ALEHEiTIGXDfFgu8Ll4Jy169PR67Cc1dVXUdk6Va8YVoeffTBbds2q1QKXJHc3Pz/+q8Xv/OdF37wg//44IPjQ0PDEPXExLjPf/5ZX1/fOeLgurqGvr5+nLBKpZo5P+xdhij34kHM3t8/+PLLf57Wu2fa8tOf/gLBHf0dFyheqDsQ9ePmF4mEQUHT56ebD9jDhQuX/v73N6k22OzsTBTNOYJ6lUqJcBLnjMiRaiyiEwiEO4HCMulQUc0uPf6YH6jcJ02/mxd2FwpCgago5xwq2BNqedwIbm03wt8DB/ZyOBx87MSJ06+//vbkKHj4PIz4q6++VlhYYrFYgoOD5p7kFLH1xMQ4sgt7Cw8PRZhOJ9z3IPqEXqJSAqgDFzdcBHaSlZUhk8lgXSDAs00ji/zHlfrud7/9hS98JjY2BvEWriPiNnwYx8XlPnLkof/8zxeioyMR1dHfmQG+UlpaMTo6ivh706YclKK7dRe4hyj3UkGFgos6B0ifVulAsF2ybcb2RTw1xLf0esPbb3/w17++gaoBxTchIe7pp58KmTFD7VRQ4KjmHRgI2Ai3fSwJBLeggoP2UOsofku3v/MBN87kgVyznyy1YzbuFPhpqdT5dqXGOSdKs9uKHl4qLS3loYcO8vlc3CbHjp368pe//R//8T8vvfSn73//R9/73o9g2vAx3FBPPPHobANcA2RUp2vCApx5VFQEVGoRT8Q+qoSEBH7/+9/+29/+8Morv37yySNzDH4yB1TVFxwcCMVVqzU1NbXWWd7ig8oKhfwDB/a9+OJPXn315Z/97Mc4+g9/+L1XXvnN7373v5/61Me9vb3mKGAoJ93dPd3d3ai0lUrFzp1bJ2+H1YKUpMWD0gAXu337locfPjTHcvDgvmlPwiwWc1cXPSwAXDJVlcwTlKHx8Yk333znjTfegQCj7EZFhT///GdQNczdeuM6kPP2QIXS3d27osM5ET5iQHIkEnquuan9pVcUyDYiVGqdy+UKBEttnMT5+/v7wWPBMGk0usrKarchCD7m5aX6xCeegBXz9fXGObS0tJ48eRY33YULVzo6upADQUGBn/7009u2bZ7j5kVw0NbWrtFoEXYkJyfCGq6uS7unQGXl5eUJ0Q0MDIBsox6jExYC8hN+fffu7dBd5Pa1awVun4BQ4LJS3X3i42O2b9/8wAN79+7dmZqajBNQuIYfoD/nDpST8vLqkZExlJzIyPCYGDcdiu8yRLkXD4oC4q+nnjry/PPPzbE899yntm3bRH/HBQLD0dExuHGswwfP/6kh1cb+/vvH/v73N3t6el2yHfHss0/n5GTBAdAfmgUEiZOdL3B07IpaJxDuCIo6bA3KGHyJyeRsZ6YTVhKqNzu1jjo3LCxk/fr0LVs2YlGpVItoX0VFD/nfuDEb9lev11dUVMNSUwH0NHBL4nDPPPOxT37y41u3boyJiVYoZHy+AGKTmBi3a9e2L3zh048//oiPz1xGDSdPtd+iut+0acMd71DCIsA1TU9PWbcu0WazV1fXNDW1oNjQabOAmlAkEqEyRKFCRIiyTSfMAkqIq2vbpYmJCQj/vn278MVVD8KIci8eXDtceNzM03r3TFv8/X2n9cVFUXAJp1O5UYzmGb6hxoRa/+Mfb//hD68ODg7ji7GxUZ/73Kf279/tdhSXaaCKmQwRYPqpgRsJhHmC8oNqC6XOYDAgfJzN2Swjro7ZvdS6n59fVlbmv/7r1370o+9hiYmJvGOFOxtpaSmId+GiOju7Ojo6za6Z1maC34ub9+Mff/wHP/i37373m9/85pe/9rUvfutbX/3+9//1e9/79oMPHqBeMKM/7Y7GxubOzm5UEQgC4LlXtyvyRxiY5s2bN8BE6XS6U6fOjo+P0wnLBCrehoYmxHkIwrKyMjIyUumEVYUo9+ow+YANgjvP8K25ufXXv375jTfe0Wi0qDfhP7761X/Zvn3r3NXHJFMPBNm+CzUv4aMElDIiIgzO22WFBy0W60qXIJ1O39fn7JgNcGiEyPDK3t5eWBCDLtr0hIQEpaQkQVAtFsuVK3maWcbeosCvxnGTk5N27NgKs7Vt26a4uBjYtTseHTd4Xl7h0NAQPowvzie2JiwOXCOo6a5d2xCEXb58rb9/cHkrt9HRsePHT6PYh4QEI0SYHB1odSHKvQrgHkbFgf9jHSLqtr1uKqhiiopK/uu/Xrx2rchqdTa+PfLIITiAxMS4+bcZ2qeM+Aifz1r702kT7iYIEGNioqBAqBZhu6FJjltzLK4QME/j4xO4WXDQ8PCQ5fKs+CFwTklJ8a6KPndwED/kDhU9zmEq9NbZwY12/XptfX0j9DsoKACq77rfCSuFp6dq796doaHBExMTV69em3wXYOmgkHR39xQWFnt4OA4ffiAhIY5OWG1I9b0KoO6Qyeix8k0m89yPnOGw8/OLfve7VxoamoxGo6+vz8c//sSzzz4dHByMGo3+0DxAbaK/NeKjTCbjrHbfSMLags1mwW5S095otbrm5rbZ+vEuCwhnu7p6hoaGcbOEh4cqlcrl6hOE+w7m6eGHD4nFop6e3tLS8rGxZW5fxR194cLlwcFhHx9vVPf4d9Ft+4T5gNoM1/Txxx+Bq7l0KRdh06RLWSIoIR9+eBKV8MaN2Zs25VCdfO8FSHlaBVAHqVRKSrk1KBSzj4uCpJqauj/96W/V1TXQ+ODgoEcfPfyxjz0WGhoyx6uHboFPmhwgUKlUEBNAWBBQUHgaX19vHo+LMnv9+g2bbQXfDdPpdG1t7Wq1GhFDUlLi4t4amg2pVJKSsi4jI81ud7i6i3cuY/sqXFpfn3MobKvVkpGRmp29HllHpxFWDJSQBx7Yc+DAXsp537Ehc56Mjo6hBG7YkPXMMx/z9/fDOp2w2hDlXgU4HLafnw8KAcQbPnjyYd40bDZba2vbq6++Vl5ehVrS29vryScf/djHHkftuYi2bhgLtWtQfoT/fn7OOWup7YT7AfhLX1+fwMAALMJFTfOFr4jF4qysTLlcrtPpS0srEErOU/DwXZFIgHKLo6MYc51zdtFJs3GrY7adz+dv2pQ9x5TJiwDn4+Xl+cQTj8jlsra2jrKyymUc3gCxOAz3wMAgovOtWzcHBPjRCYSVBOGRUqn80pc+/53vfHPHjq301iUTFRX++c9/5nvf+zaCsNmmfVoViHKvAhwOx8vLC0EiRHTqyMbTgOE+efJsUVEJKhqBQPC5zz374IMHJt/sWihQbtQp2BUqQS8v1fxfRSN8BNi+fcurr/7ugw9ex5KcvG7RjbfZ2Znh4aFGo7GpqWVw0DkBCZ0wJyjwOTlZL7/8Kxz9l7/8KVzRHW1oU1NzV1c3vhgUFJiWlrLsHbNRC6elJe/fvxt3RF5eYUNDE52wNGDiu7p63n//uNVqe+yxh1DdY/90GmGFYTIZqFRhSxAzLVebolQqDQz0R9R7rz3vIMq9OrDZ7Li4WIGAD8/d3d3j1rsUFBTn5xfBdqDQhIWFwoKXlJRdupQ725Kbm3/zZgP95dvB/kdHx+C5UWOGhYWQURjvN3DdEfxRLKVzYnCws2M2yq2rY/Y1qhVnPrhOgI+jw0PPLdsoq9g5Sv7Q0DDi1AMH9i6lJ/kc8Hj8p59+8qGHDiIWmXz9bIlQL7unpyd/+tOf2LNnp3QhgywRCPOH9cILL9CrhPkBnwEFraq6AUFVKpW7dm1bxMQPdrsdJrim5ibqPviJLVs2ok6brJ5QeRmNpj/84dW6unrUYthiMBixjuNCzmdbSksr4OA3bsymdjIVHOXixSs4Z5gYHCsnZz2Z/OC+AkVrKvTWhcPhsLGzhobmgYFBrVablZWhVCrms0PquBT0pllAhIoA9J13PsQNEhkZ8eyzn1Aq5SvheGDRhEJRdHQkYhGIN6IKOmEJ4Md5e3utW5cIQ4+cwe1GJxAIywrx3KsDPHdSUoJMJoVIo4ZqampBhUWnuXQdNWNXVw81+iM+o9FoYAva2zvnWDo6umabpBZ7a2vrwG65XA41uw6dQCAsBOhuZGT4wYN7YZ1RaGtq6uboX7k4TCbzpUtX4Vw9PZX79u0MDg68Y9P6omGxmN7engEB/lBZetPSwH2NmzooKADRPOkESlg5iHIvGFReMpkMN2dgYICPjxePt5j7E5VRdHREQIAfbm8YYrjhqY8MIdWoEOVy51HmvwQG+isU7iugxsbm7u4eVCswBHAYZDgnwqKByOXkZMXFxVitttOnzyOgRHGl05YM7oLR0dGzZy8ajca0tJQtWzbda88XCYR7AcYy3nX3Ccgxi8VqsVhcLX8MKPeiK5f33jv6hz+8OjQ0nJSU+Jvf/HzqyMaw4GazZUHvNjAYzoBgZtcznPALL/wnKllECUeOPPS5zz1LlJuwFHQ6XX5+8fe//yOUty996XNPPnlkuWzx6OjY0aMnfvvbPyoU8q9//UtUDzI6jUAg3ILEswsGVQmHw4b4uXrb8JbiCTIz02Jjo81mc0tLK5apY+WjKsTOcZT5L2BmAx0igK6unoaGJoPB4Omp2rlzK5dLnr0RlgRKGoru/v172Gx2bm5BQ0MznbA0UFa7u3s++OAE1h955DAOQWSbQHALUe7F4PTat6A3LQpvb6+srExPT0+93nDq1LmJiQk6wQV9gAVCf/kWFoslNzd/YGBIKpWiKoyICFsue0S4b0G0KpGIn3rqsX37dgcGBgwNLc/UYa6m8rH4+NjHH38Ebhu2m04gEAi3Q/qWryawLLAv8BktLW2Q7YyMNKj4Mo4oDhMzOjr+8suv9PT0xcZGPfPMx4KCAmeqO4GwUCDeSqUiJiYyMTEuIMBfKFyGQSrsdjvUOikpYf36DC8vT9Ixm0CYDeK5V5mgoIBHHjksk0k7O7tKSsrUajWdsBwYDIbKyqr6+iYOh71580bUs3QCgbBkIN6+vj4hIcGLeCvSLVwuV6lUhoaGQLZJx2wCYQ6Icq8yPB4vIiJ89+4dcBgXL15tamqhE5aD4eHRY8dOm83m1NTkjRuz4O/pBAKBQCCsWYhyrz4qleKppx4LC3MO5JSbmz86OkYnLA21WlNdfb2iogoO5qmnjoSGBtMJBAKBQFjLkOfcqw+TyRSJhNBXFosll8siI8OWZS45KPf167VCoWD//j05OZkSiYQ84SYQCISPAOR97nsCXAWDwTjmmidYIhEvy3DHer1+YkJjNpuVSgX0m3QpJxAIhI8GRLkJBAKBQFhLkOfcBAKBQCCsJYhyEwgEAoGwliDKTSAQCATCWoIoN4FAIBAIawnSQ20VsNpsRpOZzWJxOeylTFhCIBAIhPsQIhurwLhadyq3vLK+VW8005sIBAKBQJgfxHPfbYbGJvLLa8praphMzvrkxPVJMV5KGZ1GIBAIBMKdIMp9V5nQ6Aqr6upqC2LZ5+0erGbbNv/glA2pSQE+KjLAGYFAIBDmA1HuuwTy2Wgyl9Y2V1ddC7BdzFHmQahr1OsaLFskPqkb09OCfT3ZbBbRbwKBQCDMDXnOfTeAbJst1qbOvtLKUm9rfqaiWMzWidi6VHl5muDUcFf56St5Xf1DRrOFBFIEAoFAmBui3HcDq83WOzT64cUiL0tBhrxIznGOTw64THOcpHav6i3LaNkbJy81tvdA4KkkAoFAIBDcQlrLVxybzd49MHz04jWuunCH6qQXb4DN+Kc8I/etds64RXFlZO8wKy0rLSs9IVIs5NPJBAKBQCDcDlHulQXZ29U/fKWoZKS7ZJfqqB+/h8c00WlTsDlYw2bPSnV2H3NjWETaxtQ4uUTMZJJn3gQCgUCYDmktX1mGRidKr9eM9lVnSS8G8LvcyjZgMWw+vIFMWV6I40JLQ35u2Y2BkTHSck4gEAiEmRDPvVIgY/VG07n8svbm0nW8U+nyMsgznTY7aqukURNXMLEnNCJ12/pUL6WMy+HQaQQCgUAgEM+9clistqLqhpuNN6PYV1JklfORbSBla5Jk1XtV7zY3FJ+4XNjeM2gnoRWBQCAQpkA894oAt13X0nnycl4K/0y6rEDKUTOcfdHmhcODYbZz+42+V8YOOSTJmzIz10WHslgkxiIQCASCE6Lcy4/BZG7t6jubm+9jubhBfkXBHZ2n4Z4E4m21s3uN/pXarWPc9SmJ6ekJkQI+l0nGaSEQCIT7HtYLL7xArxKWA4vV2t4zkFdSzJoo3Kq6ANlmL1C2AfSZxbBL2FoZa2hC72jos9o8+DKJmMwtRiAQCAQiA8uJ3e4YHlMXVVZph6q2qC6quMNTX91eKHDq/vzeTYrzQR7XCktyi6pujKm1VtuC4wACgUAgfJQgreXLBnJSqze+ezZP3Zu3QXYmVnKTTlgyZjunZCy7RL0tMipzV06Kt1JOWs0JBALhvoUo9/KAbNQZTCdzS3taizNEp+Il13nMZZt72+HBMNl4TbrYUs0ujjJt3+aMED9v0meNQCAQ7k+Ici8P1PSd1deLM8UnYkU3JGwNnbB86G3CTn1ohW67Rbx+c2ZKVLC/UMCj0wgEAoFw30B82zKg0RlutnTcqKuK5l2LFtaK2Vo6YVkRsvShwtYN0lO8iSvXiotqm9sQLpDAi0AgEO43iOdeKiazpba5/VpRgdyYu8f7NPSVybDTaSuA1cEeN8svDO3V8DPSk9NT46IlIgGZ1ZtAIBDuH4jnXhKIetp7BgsqrnO05bu8zopYuhWVbcBmWFW8kcN+H/har+SXFF4qrjaYzCT8IhAIhPsH4rkXj81u7xsc++BCHl+Tu1Vxwoc3sNKyPYndwdTZRNXqjFrjNu/AlAc2pyukIhaLRScTCAQC4aML8dyLxGqzjY5rzuaXszQVaZJcFXfkrsk2wLHEbG2SpHy96MRod8HxywVd/cMms4VOnh2bzd7S1afVG+i/CQQCgbDWIMq9GOC2x9Taa2XVY71l6eLzQYJO7vK9AzZPGB4OGUcdI67NFJ/V9F67VFDQ3NmrN7ifRZTCYrH2D49dKr4xMq6x20lbC4FAIKxJiHIvGIfDodEZqm821tSVp0suhwrbBKxFWtili6eQpU+Q3NiqOKnpK7pSWNDS1as3mtw+AYHbRrRxpfTGzdau0Qktgg86gUAgEAhrCqLcC8ZitVXWtZRWFK8T5a2TVgpZOjphgVBzgtkcS304zWLYwkWtB7w/EKivHL2YV1HXgjOk06aAaKOsprGyts5qtRpNZhsZRZVAIBDWJkS5F4bd7oA0VteUhnDKsxX5HOadHy27BYLdZ/R7t+fJ4tFsnVVEb10CKt7wdq/zsexzlwsLzhdUwF5Pdd56g6mkprGmtmiL6ryMPWYyGYnnJhAIhDUKUe4FAC9b09xRUlXubSvOlucK2fr5z7o9FauDPWaRXx7aPc5OumHcdW1k65hZYXcs6VqwGVY5ZzxTdi2df6KuruRiQVnv4KgdgYbDw2yxltc1N9SXRnLyEyU3xGytyWy02YhyEwgEwpqEzPLpZHhc7bA7OGzWHEOamMyW7oHhC/klQn1xhuSKL3+AyViMbNsczAmLvHh86whvy4aMLLHMt3NCOK5nSNnjPKaJtYQO6kyGHXvw4g44rNq2EfaoziEWSXhcTn1bT3F5obc1P0NWIGFr6rVxEmVEkL+fgMelv0kgEAiEtQNRbidlNU0j4xqpCFrGcSveVqtteGwCRlY7WL5Ncdxf0Mta+KzbwOHB0FqlN7QZtabdW7PXp8SGB/t584SKym7emJGr4gy5xHvxT6AZDAeHafHn97IdE40D3PYBA58vvJBfLDFXZMsv+/AHbB7sZl0UVxoZEhBIhj0nEAiEtQhRbic3mjoKqxvUOn1ogA+bNd15w1lD16+VXW9oKDvk826AoJfDXOSs21Y7p2Iio8q0P31d2sbUeEQKiBW8FDJvT8/iNnavViJljfxpdQMAAB5qSURBVMo5Y0sZzBRfhfn25g1IWMMtw9xrNSMSe/NurxP+/D4k2Rysdn24XRAZFhwiFvLp7xAIBAJh7UCU20lX/3Bbd2/fwMDAqDbQRwU1ZTL/KZ5qjS6vora5oWiH6nioqB2mdnHCancwqibSaky7wyKSd2Wn8nm0v2cxmTKxKCzQp3XIo2VMxvHQe/KGF9cUPwl2LGGrAwVdbIZ1i+cVL94Q22Xl7Q5WlyFYz4kKDwmTioTUhwkEAoGwhiDK7aRvaGy0vyGMXTA8oW8fsqnkUgGfB/PtcDiMJnNuRV1bU3E870K8pJbPMi2yV5qd3aCNK9PtDgxbvyUzVSETTzp7rLBYLDhgH0/PcSOncURisthV3GEWw8ZYgn6zGHY+0+TH71Nwx9hMK3UwZ592k7+GFRMaEi6XLEOfdgKBQCDcZUjfcicCHlfAsQTw2jLFZ7V99HhkOgNU21JZ39bYUB7EyE+Q3BCyFtmZ3Gzn9hgDiye2K/xSMtcleilkdMItIKscNjvI12tjRnpQeHaNeV/5ePa4Rb7Et705TIuMMwHbPXnaWOEzjTab1WJZZIM/gUAgEFYXotxOBHwug8GBSXWNR3aKGo+soa27pavvSmGRt604RVIq54zTn14gVgd71KwqHN9hl6ZuzVof6OM5tSl+KiwWM9BHtT07PSo6s8p0oFy9ccyiwNfp5GWB4cFlmuw2CDdRbgKBQFiTEOV2wuVwGCye0S5wjUfW8oD3B3z1lbdOXXzn9CW5tSpbfsWTN0R/dIE4PBjjZkXpxMYej/UHt23y91ax2XPZaAaDoZRJ9m3O2JCZXWvee2V415hZgZ3QyUsGnpvHNNlsZrOFjKFGIBAIaxKi3E7YLBaLzTXa6L7WnrzhHV7ns2UXPB21e71PKjhj1PZFoLFIysbX9zA3H96eHeTnyZlTtifhsNnZ62IObd+oE+84PvBIhz5k6YOkUkC5Kc9tJq3lBAKBsDYhyu2Ew2Yy2fDctHJT45FlKQr2eJ9QckfYi3oHDEYZoUDpeFY/a3NmSnpMaACXw572vtls4GN8Hjc6NHD7hhyxb87F4UM3tfF6m4BOXho8ppm0lhMIBMLahSi3EzYbrvufnhtAvCVsjR+/Fyv0poUA2TbZuDfU69psmyKi0pNjwkUC3jxlexKhgBcR5Lc9Z4M8aHOpZl+9NmnCIltiy/ktz20mPdQIBAJhjUKU24mrtdz5nJv+e8mYbLwuQ2iRel9gaEpGYoxCKqYTFgicd7Cf14FtObKAjeX6A7XaVI1V4nAsSby58Nx2i5l4bgKBQFibEOV2wna1lpumeO6lYHOwBky+50cOewfEb8lM9VbJ6YRFwWazPOXSI3s2hEZlV+j3XhvZZrALFi3eDIaDxzQ67FazxWa3L2mwFwKBQCCsCkS5nXBY0Eeuyc5bop2l6DYE5o49wFfEH9iarZRJ6K1LgMFgCPi83TkpORkbuhnbjvc9NGpRLq7Pmqu13Mxk2C1Wq5VM0U0gEAhrEKLcTqDbHA4HWmhxcJb4IHnA6FOh3mwTr9u3OctTIZ1nZ/I7wmQwxEJ+anz0tg2bDZLNZ4ce7DEEItSgkxcCm2FjMyDcZqLcBAKBsBYhyu2EzWJyOGwHg704LaSwO5hjFkXpxCatYH12emZEkB+bvZyDqMB5yySiuIjQzVk5NsXWfPWBVl2E3rbgsccZDNcwalazxUqUm0AgENYeRLmdQBSd5pjBNtu5i2swh2wbbILqibQeR1ZiQmZiVAh8/DK0vM9AJOBh5zs3rB9mphSMbh4yedEJC8Gl3CYrUW4CgUBYgxDlpuFCulmcRXtuo51fr40vmtiZlpqTGhcu4HHphBWA6RpnTcDjsxY7HwmP5fLcpLWcQCAQ1iBEuWm4bDaTxTHbeYt4zm2y8dp04dfGH8hKS0+JDRcJVnDea7vdodYZjl0qZuquZyny/Pm9dMJCgOe2E89NIBAIaxOi3DQcDpTb1b18gcptdbBb9RHFmn0BQYnZyfFSsXC2CUWWjsPhGFNrLxaWj/ZVrZecDxE6Jwun0xYCn2Ww2YhyEwgEwpqEKDcNh/LctgW3cjM8HGNmpd4m5HJ5bBZEe6VkG4xrdFU3G5ubqpKFV0IFLUKWnk6YHYfrGbzF7ux8h5PUWsUTFpndwTJZnC+G0R8iEAgEwtqBKDcNl8OiW8sX2EONxbBFiRsi+NUdHbWlNxrGNNoV8rJ6o6mmqa3yenkouzBRWsllmiHGRhsfeqyzirRWidoinbDIxyyKUbNyxOw5ZPIaNPkMGP26DEGtusgGTUKNJq1Ss6FUvb3JmG7z4NvsdnrXBAKBQFg7MBwOMpCWk5bOvgtXz4aa385UFC+iCRpetnIiLX9sd+q6tE1pid4qOXOBo5TPjd3hqKhruVpcKtAWbvO86MFgOGXbLjDZ+BBvrJixbueZ7HzXdue/Zue/fMQidkQXDAaPw+bzOHweV8DjCfhcb6UsNS482G8xXdMJBAKBsIoQ5abp7Bs6e/mct/a9TZ65sLP01nljdzChl43amCL1fs/A1G3rU8ICfOi0JWO12Zo7+45dLukfGvWwm/gsI4fN5nA4XPznhMth0+tcLpcPYeYBvoDPo9b5zhXnY3yGK5qAigMWi8lhOYeOo49BIBAIhDUCUW6a3sHRc1cu8kc/3O19jss00VsXgsODYbDxO/ThlfpdHrL0jempMWEBkFg6eQlAuetbu0cmNAwPBjSY53qDDdLLYjKd/2cx2c4V18J0wXD+x3L9z4VTsgG9OwKBQCCsZYhy0wyMjF/MyzV3Hzvod5TnTrmRTQ4H0+Zg2j1YcNg2BwuL3YNpd61YHWyLnW11cHRWcYsuosG4Xqny25aZGB0SIBbyl6iadofDYDRBtiflmcgwgUAg3LcQ5aYZGVdfKSzubzpxwPcYh2FxQJKdmcNwrtD/Ms12jsEmMDmEJrvQ+a9DaLQLzQ4sAquDa/fg2Dy4WCwOPrY4mHxPhXTPhpQQf29oLX0YAoFAIBCWBlFumnG1LresqrziWrS4wfnSlMPZvWuyn5erqxe02dn0zXV29eIK6K5eHNezZKw7O385F65rhcvhOf/kCPk8Ppe7cm94EwgEAuF+gyg3jc5gut7QWlrTKOI5oM1cDt3Viw/wr1OkscIV8LlslrOrNsP54rbr/9T/nP/Qf09Pwv8IBAKBQFgmiHLT2Gx2ncGo1hnYdM8vqmsX1cmL4fqLQfX8IkpMIBAIhFWEKDeBQCAQCGsJ0nOKQCAQCIS1BFFuAoFAIBDWEkS5CQQCgUBYSxDlJhAIBAJhLUGUm0AgEAiEtcRHqm+51WqzWi12u4PH41Lvb9EJiwIZY7fbTSYT9sPhsAGdsHpQ56PT3Xla7mkIhc5ZSFgs9/OLTEyoNRoNCoNSKRcIBDPzzWazm80mg8FotVpRYJAVXC5XIOCzWGy3eYyTHBkZMxqNCoVcLBYj9+gEAoFAICyZ1VFuHNTmYqEHZ7NZsyko9jk0NNzS0maxWOPjY6AZswkVBVSQOgd8DPucKVf4gFarq66uQVJERKivr88SQ4GlYzAYcD5Xr16j/543WVmZGRlpYrGI/nsK+JlHj556990PuVzOV77yhaSkhGk5DLWGtNfXN5WVVQwPj+DzCoUsMjIiNXUd8oTDcTNCXGdn969//TJO9ZFHDj3yyGFvbzKXKIFAICwbq6Pco6Nj779/LDc332xe2Hyajz764JEjD7lV0PHxib///Q2IUGCg/4sv/qdSqZhbaLu7e996670LF65s3Jj13HOfhAjRCbdAxsCJfu97P6yvb9y5c9unP/30qisQfiN+4G9+8zL997x55pmnnnzyiJeXJ/33LaDK+HU//vHP+vr6t23b/L3vfQtmejLfUDZMJvPZsxfeeeeDtrYOi8UC2Ua2MJlM2GiJRHz48AFo88yYRqfT5ecXv/DCf/L5/Oef/8yDDx7Abuk0AoFAICwN1gsvvECv3kXUai1ku6CguL9/EDZu/kt8fCy840xJhqKcPXsRAgPD/fjjD8M4cjgcOs0darXGJUgfwqb7+/uuX58hlUrotFtQB4EjLykph24JBILExDiIlitxdTAYjLW1N69ezYeILojk5KR16xJFots8N4QZEvvSS3+qrr4RFhb67LOfCAoKmCrbsPhvvPHuG2+809rajkPzeDwfHx8Its1mQwZqNFpky9jYOL6FOIn6FgUyTS6XtbW1d3Z2wa9HR0cS200gEAjLxeooNwSjtLSirq4enhtuDGIgkUiE8yA9PTUlJWmackNIoBC///2fYaPj4mKeeeZjMpl0NomFIOn1hry8wrfeer+9vYPFYoaFheTkZEqlUvoTU8BOVCpVfX0TRGhwcCghIQ4StYribTQab95sKCwswTrOZMOGrA0bsiHJd1wyM9NCQoJ5vNuMr16vLy+v/utfX8f6gQN74LmhzVQSQC5B0V966RXkKqxzcnLio48efuCBPZs25UCJ8UkEUpDt/v4BoVAQERGGyIb+pivfYMpFImFFRRXcPJPJSEtLdvtIgkAgEAgLZXVaywcGBl9++c9Hj54wGk2hocF79+709FTRaXMCMw0dov9wQSkxfOHf//6mQMB//vnnHnzwAJ02A2g8nGJl5fVf//pl+EjEDRCzHTu2fv3r/xIYGEB/aAbwuP/7v78eGRl96KGDn//8s2KxeLUUCEr5/vvHXnzx11iPiYn61re+kpWVSSXNDTXc+tTTttvtnZ3dv/jFb69ezYMS/9u/fT09PYVOc+UqgqEXX/xNbm4+/szKyvjiFz+blBRPRS1Wq7Wrq/uVV/567twlZH58fOy3v/3V9evTXV+lwR50Ov13v/vDwsLigAD/F174TmJi/Gx9FAgEAoEwf1b/rTB/f7/9+/d8/ONPzGeZJtsAYjw0NPzee0fHxyeSk5Om6cdU8Eko37lzF3/0o582NbXM/xE7FCs9PVmt1pw4cQZqZ7FY6IRVBTIMHXV12bvzgk9OlW1gMplh369dK4AMI3IKDw+lE1zgNzY3t+Xm5lksZi8vT4QsyPnJxgYIMBz8l7/8BVhtLpcDjT99+hxCASqVAocTi0X79+/28fHu7x/EBTIYjKsSJhIIBMJHjNVX7iVCdXYbGhqRyaSpqckzO2FRmEymsrLK//qvF//3f38zPDyCLZM6dEew5/T0VF9fb4j3m2++Nzw8SiesZdra2pFvUGj8LrjtaY/5kUUFBcUWixVSm5ycGBcXPa2VAbknlUoh+cgceOu6unrENIiN6ORb4LuxsTFarfbKlbz6+kaj0UQnEAgEAmGxrG3ltlptvb39585dgjCHhoYkJMTNbI+FF+zr63/ppVd+9rNf5ucXaTRaHo+3ffvm7Ox5tTMDFosVExMNBYJNh0ltb++AYaXT1iaQ2OvXayGl+GlJSQkqlRIrdJqLwcEhOHLKIq9fn65SuXmWweGwk5ISJRIJcnh8XN3Y2DxTufHF2NgooVCg0+nOnLkwMaGmEwgEAoGwWNa2cqvV6rKyip6eXohHVlaGn9/0N7uAzWbv6emD54O0QOljYqKeeurIZz/7qZCQYPoT8wBWHkrPYDCGhoYh/2NjY3TC2mRkZLS29ub4+ATUNyvLTe88/MzR0TH8XoGAHxISBOmlE6YAsQ8M9Kc6phkM+ubmlpnKzeNxIyPDvb29YN9LS8th5ac1qhMIBAJhoaxt5YaZhgmGGEBa0tKSZTI3/cM9PBxw5BwOx8fHOyMj9ctf/vznP/9pyAk0iU6fBxKJOC7OOboLxKykpKyrq5tOWJvg/BsaGpFvPB4PeTJTmGGOtVotfqxCoRCJxNMcOQVSlUoFlJvJZJrNlu5uZ/xEp00hKCgwLCwUot7W1tHW1m40GukEAoFAICyKNazcDoejsbGlvb0TugJtUKmUs7zDzeDzeXDM3/jGl3760x9u375FLBbN/yE3BT4vl8uioyNxrM5OyF7TqntH/HycAxRxbtyeZ3l51eDgELIrIMDP29tzZr6p1Rq9Xk/96tnejIdyc7lc+Gn8a7Va4dHddkDDHhIS4rCCk4Htxseo7QQCgUBYHGtYuQ0GQ0tLK5QAahoREeZ2aE/AZjsf5cJn79ixZeZwK/NHJBLiKDiWTqdvaWkfH5+gE1YJKGtra3tV1Y05lpqaus7OLkgm/R0X0Nfr12vGxiYQ0MTERM3005BhjUZrMpmhzfjVyEA6wR0SiXNYcqvVNj4+bre7UW6JRBIVFY5dYR2R1tCQs3sggUAgEBbN6it3b2//yZPnXnvtrTmWN998r6rqul5voL/jAtrZ19cPWWKxmNBUPt996zdlDaHr+MBCrfZU8HWXzjHhYnHcVX/UPTw8+ve/v/GTn/xsjuV//udXx46dMpv/+RobxHViYmJ0dBzyzOPxQkNDmMzpwowstVgslIHGZ/CTqe1ucY2v4swT19Vxo9zQdaVSCeeNC4FLRnXsJxAIBMKiWX3l7u8feO+9o3/+89/nWP72t9dLSytMptveKRobG598vys4OGilR8bG/kNCgijtx3EhftT21cJgMHR399bXN82xNDW1IDCy2//puR0O++DgsNHofLWay+V4eXnOnC8E6k61scMnw5FTdnk24MjxAewNoYDbt7WRCnOvUMiRdWq1enT0o/BOHYFAIKwiq6/cZrNZo9HAws7JOIRqWqsvtR0r8Hw+Pl6zPY5dLuAdvby8qLZlrVYH201tXy34fL63txdM8xwLAhqXNv/zKkOSBwYGqW5iyDGZDFZ4ZhmAELsT4Vm4peyzCjwOBM+NEAH5NjIyNu06EggEAmFBrL5yC4XC0NDgmJioOZaoqEgo0LR3tbu6eqn2c0iCSqVa6ZE1odlSqYTH4+Fwer2+u7uHTlglfHy8n3/+Mz//+X/Msfz4xz948slHcc70d1zKPTw8Sr2PPimoVNIkrsHZnAUD8o3Pz63iVqsNH4GxdplveuM0qANht/DlExNqMh4LgUAgLIXVV+64uOgf/ODffve7X8yx/OpX//3QQ4em9S8bGRkxm02uxli+WCyc+3HssgA9UygULBbbZDKt+vNaPp8XEOCPmGaOJTIyzNfXZ6rnhgqbzWaHw9kYjhzj8f45p+ckXC4HWUpthz+eW7ltNiv2hkPgK7PZbteBeNRxrFYL9Nu1mUAgEAiLYfWVG4YMkqxUKuZYFAq5QDC9f5nZbLHZnJrBdU4pfZd+CJ/PhUnFcad2+1oVoKwsFovDYc+xgBldxx0uMabWneaaWpsK9iwSCZGr0GytVgdXTSe4Q63WICtwIC8v1Uz7ToEdTh4IWbegpngCgUAgTGP1lXvRTDbkznSNKwSO4woRnIej+nCtQZx6T6+6OqPRa1NAforFIqFQgN84MjIyrWPgJMh8qu3BYrEiSvD29p4tfsInJ7MLEn7XrheBQCB8JFnDyg0FggxAFe5ajyfECa4e1A6oz9xvOd+zQDQFAj4l3na7zWw2UdHPNBQKuUQiRtLIyJjBYHAbpiB1bGxcp9NjPxwOx8/vtmb5qeDrriZ65zqPx8WHXZsJBAKBsBjWsHJLpRJYPegHnB/Ew60CLS84hNGIY9nZbLZE4nak1Xsd2GIq37AOr6xWa9zmm6+vr5eXp+v3Gvv7B93abuRDX18/1U2dz+cFBgbMpty3DmR3tcOL8GE6gUAgEAgLZw0rt1KpoJ7FWiyWu/Cukd2OEME8OjqKA+G4SqWcTlhTMJ398JU4f6wjChkcHHLrp/GZmJgoar2kxDlTCLU+FavVWl1dA0nGulQqjY+Pna0dAsLvOpBDKBTKZNLZBJ5AIBAI82EN16F+fj5QAqy4ZgPrXekuY1arZWBggBpcDMf19/ejE9YUUE0/P19qgi+z2ewap8WNcisU8pycLLFYDJdcWlpRW1s/rUM4bPTw8Oi5c5fUarVEIo6KipittZwy7tB+HEgul3l5uZkwlEAgEAjzZ017bqWnp1MGIAnd3VDulZ0zG5EBNZ0o1uVyqb+/L7V9bQFxhXx6e3vxeDzkWFdXt1vl5vN5YWEhKSlJbDZ7YGDw2LFTlZXVer2ealo3GAzt7R2vvfZWU1MLsiU0NOSBB/a43vty0/UMR4HG6/UGfBfXy8fHm04gEAgEwqJY263lrpeVGdCezs6ulVduU2dnN/w95AnHpYKGtQjEOCkpXiaTmEzm1tZ2/Evp8VSgwTDHDz98yMvLE9kL2/2LX/w2Nze/oaEJS1lZ5Suv/PW9945CyxEHbN++JTk5kf7mDDQabXNzK3WI6OhILy8vajuBQCAQFsfaVu7Q0GAul2ez2VpbO3Q6PZ2wMsA1NjY22+02FouF43p6etIJaxAILRQUsQ4int7ePovFzYMGiUSydeumRx45hBjFZDJWV9d861vff/75r2P52tf+3/Hjp+G8uVzO7t3bsUils/bXGx4egV/HCux+enoKrhq1nUAgEAiLYw0rN5QgPDzUz88Hyl1f3zA+Pj7TOy4jExPq2tqbVqsNmhceHgbRohPuLnD8+OEAttht6/R8CAsLjYqKwIrVai0uLtNqddT2aQgE/Gee+dhXvvKFtLQUPp8P8z00NDw4OGQ0GvHzg4ICP//5Tz/33KdCQoLoL7ijo6Ozo6ML4Q4+hnzDPukEAoFAICwK1gsvvECv3kVg8trbOyEYcGCQkKysjDlM2xxAv6AKDQ1NsI/x8XHQhqljdM8BNL6trX1kZMzb2zs2NhpeUCRydnabDfjL69drjh49CeVOTU0+eHDfqrSWs9ksPz/fzZs3HDq0f8+eHYsWQujuyMhIXV29weDU4IyMNLlcRqdNAZEBl8vFEVNT1+Ez0dGRwcFB8fEx2dmZjzxy+LHHHsKKSqWY4/1sk8l08WJuXl4hi8WENd+8OUciEdNpBAKBQFgUq6PcUFxfX5/k5IScnKzMzDRvb0/qPaWF4novmVFQUAzlFotFSUnxcvm8XtaCJiFoWLcuccOGLMgSZJh6xXk2hoZGTp06V1V1A+f59NNPpqQkrcpLyXCuUqkkODgQi4+P96L9K/aDHEDE09XVA/FGJrimQXPfAINfqlIpccSoqEjkGKIcWPC4uGh4bqFQSA3qMhu9vX0nT55tbm6RyaQw6CEhwWQYFgKBQFgiq9NaDmccGhqcmZkO0xYTEyUWL9KHiUQiGEHsAWb05s3GtrYOtz2lZ8J0TemNo69fnx4ZGT63BMKgd3f3VFZeh7bhtNetS5g298laJDDQHyYYqjwwMFhaWjExMUEnuIMy34h1AgL8AgL8vbw8qffx5gb5dv16bX19E58vSE5Oio+PJU3lBAKBsHTW8HNuCtjl/fv38Hj87u5uiCscJJ2wfJjNlsrK6vb2DgQcu3fvgG4t+gHzvYNcLkfkBDVFOHL5cu5k9+/lAnszGAynT5/r7x/w8fF67LGHBQLBRyDfCAQCYdVZ88otkUjgHWG7WSw29LWxsYlOWD7a29srKqpsNntgYMCDDz4wzwb5ex9fX5+Pf/xxGOLW1jb8QLdDnC4ai8VaUlLe3t6JcCc1NXn9+vS5n0cQCAQCYZ6seeWGZZRKJU89dUSlUra2tl+4cGXuWSkXCrxjbm5BQ0OzUil/8slHlUrlGp1rZCYCAT89PXXDhiw2m11eXoXcoxOWDDLNaDSePn1+eHgkKir80UcPT074TSAQCIQlsuaVG3A4nKysDGowkNLSiubmlmlDdS4am83W2dl97Vqh2WyOiYnevHnD4nrS3ZuwWCyZTHrkyIP+/n4wx2fOXDQYnCOd0clLQK83VFVdh+eWSCQ7d24NDw+jEwgEAoGwZD4Kys1kMmG4jxx5KDQ0ZGRk9Pz5yzB8S1cg7MFkMl+9mtff3+/n50sp3GwdsNcocNuZmWmHDu1HBra1tQ8Pjy6TcusRQkmlzrFctm3b8hHo0EcgEAj3DoxlqanvBcxmy4kTp19//R0+n/eTn/x/gYEBc7+wdEfsdvvw8Mh3v/vD0dGxRx45/OijD35Uu0ar1Zqurm6EKQhNvL09EQnRCYtFq9U2NTWbTJaoqAiFQr70HRIIBAJhko+OcrssssloNDEYDLFYtETZpoB4Q4TsdgePx0NA8FF9UoufCZCBTCaybRlUFruyWq0oWWw2i8g2gUAgLC8fHeUmEAgEAuF+gPghAoFAIBDWEkS5CQQCgUBYSxDlJhAIBAJhLUGUm0AgEAiEtQRRbgKBQCAQ1hJEuQkEAoFAWEsQ5SYQCAQCYS1BlJtAIBAIhLUEUW4CgUAgENYSRLkJBAKBQFhLEOUmEAgEAmEtQZSbQCAQCIS1BFFuAoFAIBDWEkS5CQQCgUBYSxDlJhAIBAJhLUGUm0AgEAiEtQRRbgKBQCAQ1hJEuQkEAoFAWEsQ5SYQCAQCYS1BlJtAIBAIhLUEUW4CgUAgENYSRLkJBAKBQFg7eHj8/1FYvyE/iYp2AAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![fib.png](attachment:fib.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do you notice anything inefficient in our recursive algorithm based| on the drawing? Take some time to decide for yourself, and then move on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorithm 2\n",
    "Hopefully you noticed that we are repeating unneccessary calls in our recursive tree.  For example, $f_1$ was recursively called 5 times!\n",
    "\n",
    "Now, if we had a way to store this information each time, then we wouldn't need to continually recalculate, which would in turn produce a much faster algorithm here.  This concept will be talked about much more in class with dynamic programming!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import array\n",
    "\n",
    "def nth_fibonacci_2(n):\n",
    "    if (n == 0 or n == 1):\n",
    "        return n;\n",
    "    fib = [0] * (n+1)\n",
    "    fib[0] = 0\n",
    "    fib[1] = 1\n",
    "    for i in range(2,n+1):\n",
    "        fib[i] = float(fib[i-1]) + float(fib[i-2])\n",
    "    return fib[n];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Play around with the plotting!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_values_2 = []\n",
    "y_values_2 = []  #this initializes two arrays that we will use to store the points that we want to plot.\n",
    "for i in range(30,41): #this loops through all inputs between 30 and 40 inclusive.  \n",
    "    t0 = time.process_time()\n",
    "    nth_fibonacci_2(i)\n",
    "    t1 = time.process_time() - t0\n",
    "    x_values_2 = x_values_2 + [i] # this appends i to the end of the x_values array\n",
    "    y_values_2 = y_values_2 + [t1] #this appends the amount of time to the end of the y_values array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x_values_2,y_values_2)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"time taken\")\n",
    "plt.title(\"Fibonacci 2 algorithm time analysis\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If your computer is fast enough, then you may have a horizontal line at 0. This means that your algorithm is too fast and the amount of time it took for the process to complete was not detectable. What we are going to do is run the algorithm for much bigger inputs so that it will take longer. (it may take a few minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_values_2 = []\n",
    "y_values_2 = []  #this initializes two arrays that we will use to store the points that we want to plot.\n",
    "for i in range(1,11): #this loops through all inputs between 1 and 10 inclusive. Then we will multiply i by 10000 to iterate through the inputs 10000, 20000, ...  \n",
    "    t0 = time.process_time()\n",
    "    for m in range(20):        #run the same process 20 times then divide by 20 to get the average time.\n",
    "        x =nth_fibonacci_2(i*10000)\n",
    "    t1 = (time.process_time() - t0)/20\n",
    "    \n",
    "    x_values_2 = x_values_2 + [i*10000] # this appends i to the end of the x_values array\n",
    "    y_values_2 = y_values_2 + [t1] #this appends the amount of time to the end of the y_values array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x_values_2,y_values_2)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"time taken\")\n",
    "plt.title(\"Fibonacci 2 algorithm time analysis\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your graph should look almost straight here. That is because the algorithm is a linear time algorithm! (See if you can analyze the runtime of nth_fibonacci_2 yourself.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorithm 3\n",
    "This next algorithm is a bit more subtle, but ends up using less memory than Algorithm 2.  See if you notice anything we don't use in Algorithm 2. (Hint: Do we *really* need to store every previous fibonacci number, or can we get away with less?)\n",
    "\n",
    "When you have your answer, read through the algorithm and see if your idea was used!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nth_fibonacci_3(n):\n",
    "    if n == 1 or n == 2:\n",
    "        return n-1;\n",
    "    prev2=0\n",
    "    prev1=1\n",
    "    for i in range(n-2):\n",
    "        tmp = float(prev1) + float(prev2)\n",
    "        prev2 = prev1\n",
    "        prev1 = tmp\n",
    "    return prev1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a constant space complexity rather than a linear one by recognizing that we only need to store the previous 2 fibonacci numbers at each step!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenge\n",
    "\n",
    "Design an algorithm for the following problem: \n",
    "\n",
    "You are climbing a ladder.  At each rung i, you can either climb to the (i+1)th rung, stretch up to the (i+2)nd rung, or stretch further up to the (i+3)rd rung.  How many unique ways can you climb to the nth rung of the ladder?\n",
    "\n",
    "Notes: To test your code against our test cases, fill in the designated spots, and then run sequentially through the tests.  If you made a mistake, please rerun your function before you do the test cases again.\n",
    "\n",
    "*Hint: Try to modify Algorithm 3 to the needs of this question.  In order to pass the test cases, you should not use floats!*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ladder_climb(n):\n",
    "\n",
    "    # Type Solution here!\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if ladder_climb(0)==1:\n",
    "    print(0, True)\n",
    "else:\n",
    "    print(0, False)\n",
    "if ladder_climb(1)==1:\n",
    "    print(1, True)\n",
    "else:\n",
    "    print(1, False)   \n",
    "if ladder_climb(2)==2:\n",
    "    print(2, True)\n",
    "else:\n",
    "    print(2, False) \n",
    "if ladder_climb(3)==4:\n",
    "    print(3, True)\n",
    "else:\n",
    "    print(3, False)\n",
    "if ladder_climb(4)==7:\n",
    "    print(4, True)\n",
    "else:\n",
    "    print(4, False) \n",
    "if ladder_climb(10)==274:\n",
    "    print(10, True)\n",
    "else:\n",
    "    print(10, False) \n",
    "if ladder_climb(33)==334745777:\n",
    "    print(33, True)\n",
    "else:\n",
    "    print(33, False)\n",
    "if ladder_climb(100)==180396380815100901214157639:\n",
    "    print(100, True)\n",
    "else:\n",
    "    print(100, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3:\n",
    "enter the result of ladder_climb(200)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_values = []\n",
    "y_values = []  #this initializes two arrays that we will use to store the points that we want to plot.\n",
    "for i in range(30,41): \n",
    "    x_values = x_values + [i] # this appends i to the end of the x_values array\n",
    "    y = ladder_climb(i)\n",
    "    y_values = y_values + [y] #this appends the amount of time to the end of the y_values array\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x_values,y_values)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"value of output\")\n",
    "plt.title(\"Ladder Climb output analysis\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_y_values = [np.log(y) for y in y_values]  #this takes the natural log of each value in y_values\n",
    "plt.plot(x_values,log_y_values)\n",
    "plt.xlabel('size of input')\n",
    "plt.ylabel(\"value of output (log)\")\n",
    "plt.title(\"Ladderclimb output analysis (linear-log)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can you use this linear-log plot to estimate the rate at which the outputs of ladderclimb grow? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4:\n",
    "Estimate the rate that the *o ladder_climb(n) grows as a function of n."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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