{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Transformations of random variables (3.1.4)" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Often, our observables (e.g. flux, angular size, etc.) must be translated into physical properties (e.g. luminosities, sizes, etc.) before we can interpret them. Occasionally, we also translate observables (flux) into arcane measurements of the same thing (magnitudes) because otherwise, anyone could do astronomy!\n" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "However, nonlinear transformations often do strange things to statistical descriptors of the data. Below, we make a distribution of measured fluxes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# import stuff\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from scipy.stats import norm\n", "%matplotlib inline\n", "\n", "# fonts\n", "from astroML.plotting import setup_text_plots\n", "setup_text_plots(fontsize=8, usetex=True)\n", "\n", "#------------------------------------------------------------\n", "# Create our data\n", "\n", "# generate 10000 normally distributed points\n", "np.random.seed(1)\n", "dist = norm(1, 0.25) # THIS IS WHERE WE SET THE ERROR!\n", "flux = dist.rvs(10000)\n", "flux_fit = np.linspace(0.001, 2, 1000)\n", "pdf_flux_fit = dist.pdf(flux_fit)\n", "\n", "# transform this distribution into magnitude space\n", "mag = -2.5 * np.log10(flux)\n", "mag_fit = -2.5 * np.log10(flux_fit)\n", "pdf_mag_fit = pdf_flux_fit.copy()\n", "pdf_mag_fit[1:] /= abs(mag_fit[1:] - mag_fit[:-1])\n", "pdf_mag_fit /= np.dot(pdf_mag_fit[1:], abs(mag_fit[1:] - mag_fit[:-1]))\n", "\n", "#------------------------------------------------------------\n", "# Plot the result\n", "fig, ax = plt.subplots(figsize=(10, 7.5))\n", "\n", "# first plot the flux distribution\n", "ax.hist(flux, bins=np.linspace(0, 2, 50),\n", " histtype='stepfilled', fc='gray', alpha=0.5, normed=True)\n", "ax.plot(flux_fit, pdf_flux_fit, '-k')\n", "ax.plot([1, 1], [0, 2], ':k', lw=1)\n", "ax.set_xlim(-0.1, 2.1)\n", "ax.set_ylim(0, 1.8)\n", "plt.xticks(fontsize=20)\n", "plt.yticks(fontsize=20)\n", "\n", "ax.set_xlabel(r'${\\rm flux}$',fontsize=20)\n", "ax.set_ylabel(r'$p({\\rm flux})$',fontsize=20)\n", "ax.yaxis.set_major_locator(plt.MultipleLocator(0.4))\n", "ax.text(0.04, 0.98, r'${\\rm 20\\%\\ flux\\ error}$',\n", " ha='left', va='top', transform=ax.transAxes,\n", " bbox=dict(ec='none', fc='w'),fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAHfCAYAAADQseUFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", "text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Now, let's look at the distribution in magnitude space." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# next plot the magnitude distribution\n", "fig, ax = plt.subplots(figsize=(10, 7.5))\n", "ax.hist(mag, bins=np.linspace(-1, 2, 50),\n", " histtype='stepfilled', fc='gray', alpha=0.5, normed=True)\n", "ax.plot(mag_fit, pdf_mag_fit, '-k')\n", "ax.plot([0, 0], [0, 2], ':k', lw=1)\n", "ax.set_xlim(-1.1, 1.1)\n", "ax.set_ylim(0, 1.8)\n", "ax.yaxis.set_major_locator(plt.MultipleLocator(0.4))\n", "ax.text(0.04, 0.98, r'${\\rm mag} = -2.5\\log_{10}({\\rm flux})$',\n", " ha='left', va='top', transform=ax.transAxes,\n", " bbox=dict(ec='none', fc='w'), fontsize=20)\n", "\n", "ax.set_xlabel(r'${\\rm mag}$',fontsize=20)\n", "ax.set_ylabel(r'$p({\\rm mag})$',fontsize=20)\n", "plt.xticks(fontsize=20)\n", "plt.yticks(fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 29, "text": [ "(array([-0.4, 0. , 0.4, 0.8, 1.2, 1.6, 2. ]),\n", " )" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAHfCAYAAADQseUFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDwDEZuckjLuBAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The resulting magnitude distribution is nongaussian and further, the mean magnitude is not coincident with the mean flux. Toy with the error parameter above and see how this nongaussianity depends on the error. Open question: If you heard the phrase \"average magnitude\" in a talk, would you take that to mean the magnitude of the average flux, or the average of the distribution of magnitudes?" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Note that for most transformations, rank-order statistics like the median and the quartiles are robust to transformations. Open question: is this true for all distributions?" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Skewness and Kurtosis (3.2.1)" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The book discusses many different descriptors for the shape of a distribution: mean, variance, standard deviation, absolute deviation, mode, quantiles, skewness and kurtosis." ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Skewness is, colloquially, the tendency of a distribution to have long \"tails\" away from the central values. Below, we plot Gaussians with different skewness." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# importing\n", "import numpy as np\n", "from scipy import stats\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "\n", "# fonts\n", "from astroML.plotting import setup_text_plots\n", "setup_text_plots(fontsize=8, usetex=True)\n", "\n", "# begin the plotting\n", "fig, ax = plt.subplots(figsize=(10, 7.5))\n", "\n", "# First show distributions with different skewness\n", "x = np.linspace(-8, 8, 1000)\n", "N = stats.norm(0, 1)\n", "\n", "# The modified Gaussian is a normal distribution multiplied by a Gram\u2013Charlier series (see eq. 4.70),\n", "# with a0 = 2, a1 = 1, and a2 = 0.5. The log-normal has \u03c3 = 1.2.\n", "# If anyone knows how to play with the skewness using these parameters, please let me know!\n", "\n", "l1, = ax.plot(x, N.pdf(x), '-k',\n", " label=r'${\\rm Gaussian,}\\ \\Sigma=0$')\n", "\n", "l2, = ax.plot(x, 0.5 * N.pdf(x) * (2 + x + 0.5 * (x * x - 1)),\n", " '--k', label=r'${\\rm mod.\\ Gauss,}\\ \\Sigma=-0.36$')\n", "l3, = ax.plot(x[499:], stats.lognorm(1.2).pdf(x[499:]), '-.k',\n", " label=r'$\\rm log\\ normal,\\ \\Sigma=11.2$')\n", "\n", "ax.set_xlim(-5, 5)\n", "ax.set_ylim(0, 0.7001)\n", "ax.set_ylabel('$p(x)$',fontsize=20)\n", "ax.set_ylabel('x',fontsize=20)\n", "\n", "# trick to show multiple legends\n", "leg1 = ax.legend([l1], [l1.get_label()], loc=1,fontsize=16)\n", "leg2 = ax.legend([l2, l3], (l2.get_label(), l3.get_label()), loc=2,fontsize=16)\n", "ax.add_artist(leg1)\n", "ax.set_title('Skew $\\Sigma$',fontsize=20)\n", "plt.xticks(fontsize=20)\n", "plt.yticks(fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 42, "text": [ "(array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]),\n", " )" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAm8AAAHbCAYAAACdhX12AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XtcVGX+B/DPjKaZF4YxLdNSZuiqJjBgVq6pMNi9VQTX\nym1fKQ5WW9aqTGWr7ZYKbLW1tspgVltbqwymaRdlSE39dUGG0tZclQOp3XU4mHeF8/vDnVlHZmCA\nM/PMDJ/368VLOZfn+cIwhy/PVaMoigIiIiIiigha0QEQERERUeCYvBERERFFECZvRERERBGEyRsR\nERFRBGHyRkRERBRBmLwRERERRRAmb0QU0Ww2G0wmE7RaLeLj45GVlYXq6mpIkoTY2FjPdWazGVqt\n1vNBRBSpOooOgIiotTIzM1FZWQmbzYbRo0ejuroadrsdJpMJsbGxOHTokOfa0tJS1NXVITY2FhqN\nRmDUzdNqtTAYDBg/fnyjc5IkQZIkOJ1O6HQ6uFwuARESkUgaLtJLRJHI4XAgPT0dkiRhwIABXucq\nKythMpmg0WhQX1/vdc6d1J17PJwUFBQgNzfX59fmVllZieTk5LD+OogoONh3QEQRqbS0FAB8JjeJ\niYmYNWsWIvVv05kzZyIpKclny5tbYmIiZs6cibq6uhBGRkThgMkbEUUkWZYBACUlJT7PW61WAPDq\nOo0kRUVFcDqdKCoq8nuN2WyGJEkhjIqIwgGTNyKKSMnJyQDOjHvLyclBZWWl13mdTge73Y4ePXr4\nLcNutyM5OdlrIsOYMWO8rpFlGRaLBfHx8dDr9UhPT0d1dbXnfG5urtf9jz/+OCorK2E0Gj3HUlJS\nUF1djfz8fOj1emi1WvTs2RM1NTV+Y3O3Hubm5vptXUtNTYVOp2vuW0VE0UYhIopQRqNR0Wg0Xh9m\ns1mx2WyKLMs+79HpdIpWq/V8Xltbq2g0GiU9PV2prq72ura2tlYxGAxKcnKyUldXpyiKolgsFkWj\n0SiSJHmuy8/PVzQajZKTk9OoLr1e73XMbrcrWq3WU15zYmNjlczMzICuJaL2gRMWiCii5eTkoLi4\nGLIsNxrjVlhYiOzsbK9j505YMJlMGDp0KBYtWtSobIvF4um+TEhI8BzXarVIS0vDunXrAMAzi/Xc\n2Z/uurZu3YrExEQA/2upmz9/fkBfX1lZGcxmMxwOB0aPHh3QPUQU3Zi8EVFUKCsrQ2lpKex2O6qr\nqz2JXFVVFeLi4jzXnZ28mc1myLKM8vJyn2VqtVrExsbi4MGDjY6fO5M1PT0dDocDpaWlSE1NhcPh\nQFZWFmRZxtSpU7F48WIAQHx8PBwOh99ZpL6kp6cjPz/fK4EkovaLY96IKCKdvQAvcGb814IFC7Bn\nzx7s2bMHaWlpAM60vp1LURSkp6ejrKwMFRUVXmPY3NwTAWpra6HX670+3M4es2axWAAAxcXFnn+X\nLFkCg8EAm80GAJ612VqSuEmShKysLCZuROTB5I2IIlJdXR3Kysp8nouLi/N0aZ47kcHNaDR6ErvM\nzMxG592zWY1GI1wul9dHQ0MD6uvrvZKwjIwMAGdmicqyjOLiYowbN86T1JWUlKCwsBA5OTkt+jpL\nSkowZcoUn+fq6ur8fn1EFL2YvBFRxMrLy2vyvMFggMFgaHRco9Fg0aJFyM7ORlJSEpxOp2dpETej\n0QgAfpfi8HV86tSpUBQFWVlZMJvNAP6X1BUWFqK4uBhZWVnNf2H/VVBQ4En+fNm6dWvAZRFR9AiL\n5M29llFJSQkKCgr8/jV9ttzcXJSVlXn+Oiai9sfhcPhdB829jZQ7ifLH3c2Zn5/v1YoVExODpKQk\nKIrSqA5ZlpGent5oDTl3ouVwODz/NxgMSEpKgsPhQEpKSpNLl5ytpKQEZrO5yeuLi4s9SSYRtSPC\n5rn+V1VVlWI2m72OZWZmek3D9yUtLa3REgHuj/j4+GCGTERhQKfTKfHx8UpsbKySm5vrtTRIVVWV\nkpSUpGRlZTW6T6PRKFqt1uv6WbNmKRqNRomNjfV69jidTs9zJT8/X6mqqlJKS0sVo9GolJSU+IzL\nYDA0Wh7EZrMpGo3G7z3nqqqqUmw2W5PXLF68WNFoNAGVR0TRRfhsU4vFgjFjxmDcuHGeY2VlZSgs\nLMTy5cv93peTk4OcnJxGC1SWlpYiJSWFg3uJopxer8dHH32EuLg4zJ8/Hw6Hw9MSr9Pp8MQTT3g9\nV2w2G6xWq2fB25iYGE+369kL4SqKAovF4lk6pLq6Grm5uZ7yTSYT8vLy/C7bYbVaodFoGi0F0rNn\nz0azVv1JTk72mhhxNpfLBUmSIMuyz5mwRBT9hCdver0eTqfTa+CvLMvQ6/VoaGjwe19RUVGj9Zua\nOk5EREQUDYQmb+4kTZblRuM6tFotJElq0ZR6Jm5EREQU7YROWHCvRO5vQG5LNlwuKyvz7HVIRERE\nFK2EJm9qzhR1Op2e7WeIiIiIolVYLBXSVna7ndPliYiIqF3oKDoANSxYsAAfffRRk9ckJCTgyy+/\nDFFERERERK03ZMgQfPHFFz7PCW15c698fu5Cl+eeb4osy3A6nc0ufPnll19CUZSo/ZgzZ47wGPjB\n1689fvC1i+wPvn6R/RHNr19TDU5CkzedTgeDwdBoYoIkSQFv3uxwOBqt9UZEREQUrYSPeUtLS0N5\nebnXMafT2eyWNm7l5eUc70ZERETthvDkLS8vz7O3oJvNZvPacFqWZRiNRp97GEqS5Hcl8vZk5MiR\nokOgNuDrF7n42kU2vn6Rrb2+fsJ3WACAyspKLFu2DCkpKZAkCSaTyWvrGVmWYTAYkJ+fjylTpnjd\nm5OTA41G49nKxh+NRoMw+FKJiIiImtVU3hIWyVsoMHkjIiKiSNFU3iK825SIiIiIAhcV67ypQa/X\no7a2VnQYRNSM2NhYz9Z6FN34XKZo1pZnGbtNAzxPROEh0t+rx48fx7FjxxAbGys6lLAX6a81UVPa\nkpew5Y2IKIQefvhhdOnSBS+++KLoUIgoQrHlLcDzRBQeIvm9unfvXiQmJqKmpgbdu3cXHU7Yi+TX\nmqg5bclLOGGBiChEDhw4gBkzZjBxI6I2YctbgOeJKDxE03u1oaEB+/fvx2WXXSY6lLAUTa810bnY\n8kYRTZZl0SEQCbF582Y88cQTosMgogjDlrcAz5P66urqMGXKFJSUlKChoaFVZUiShPz8fK/9bdPS\n0qAoCqqrq5GRkaFWuKrTarUwGAywWCxexw8ePAi73Q5Jklr9fQmmgoICGAwGzxT37Oxsv9fKsoyi\noiLodDpUVVUBABYsWNDomgULFiAlJQUulwvJyclITEz0Wybfq+0HX2vfwvm5Z7FYoNFosHjx4pDW\nGw7P05Y8G4E25iVKO9Hcl9qOvhVhR6PRtOq+4uJixWw2K3V1dV7HHQ6HYjQalaKiIjXCCxqbzaZo\nNBqlsrLS5/msrCxFkqQQR9W0WbNmKWVlZZ7Pc3NzFbvd3uT1ZzOZTIrNZvN8Xltbq5hMJs/n+fn5\nSmZmZpMx8L3afvC1bizcn3sOh8PvMy2YRD9PW/psVJS25SXt5p3B5C18tSZ5q6qqUmJjYxs9wNwy\nMzO9koRwZTabFaPR6POc0+lUHA5HiCNqWmxsrNfnDodDMZvNfq8/95dJZmamV3I2derURr9sZFlu\nMoZIfa+uWrVKKS8vFx1GRInU1zpYouW5Fywin6ctfTYqStvyEo55o4hksVhgNpvRo0cPv+db6tyx\nd6EYi1dcXAxJkmC1WhudS0xMhF6vD3oMgXI6nY2OxcbGwuFw+L3H4XBgypQpns+rqqowdOhQz+dF\nRUVIS0vzuicmJkaFaMOTRqMRHQJFsHB/7tXV1cHhcKCysrLVZbSFqOdpa56NbcVFesknh8MBq9Xq\nNYbA6XRCp9MhLS0NTqcTLpcLpaWlWL58uec+9xgng8EA4MzYjJkzZ3qVbbVakZKSAqD1v6jLyspg\ns9n8nk9NTfXE4I69uroaAFBaWgqLxeIZV1VWVoZZs2ZBo9Fg69atXmPxZFn2PCgLCgqQlJQEWZa9\nyvB3PBAxMTEoLCyExWLBhAkTGt0XaDmh4HK5Gj38dDodAODQoUM+f6EMGDDA83+n0wmtVosZM2YA\nOPOzAZxJ6CoqKuByuSDLcqOfl2hx5513+j23ceNGXH311ejdu3cII6JIE+7PPZ1OB5vNBlmWsW7d\numZj8PV7prS0FEajsdnxYr6Iep625tnYZoE3Cka25r7Uln4r5syZowBo9DFnzhyh1/s73xp2u10x\nGo1KdXW1oihnurM0Go1Xv77ZbPbq1zeZTF5N+g6HQ7FYLJ7P09LSvMYkVFVVtbjbtLa2VtFoNEpJ\nSUnA95hMJs/1kiQ1auK22+1eY68U5Ux3rvtrsdlsXl9nSUmJ4nQ6Gx232+2K0+ls0dejKGe+j1lZ\nWS26x2KxBPTRXDdkoIqLixt939yvhftnxBdZlhWbzaaYzWav701paWmjn6f8/HwlNze3yTii8bE1\nYcIE5bXXXhMdRthpyWvt63kZTh9tFSnPvXO7CwOJwdfvmbZo6fO0rc/S1j4b25KXRN9T0A+1k7f2\noLS0tNH4gXN/GC0Wi2eMRWlpaaMHgfueuro6paKiotEPuPt8S2k0Gp8Dc202m5Kbm6ukpaUpmZmZ\nngfKuWNEYmNjvb4OX7Gf/RBzDwa22WxKVVWVoihnHjL+jrdUfn5+k2/yYKqtrVVkWfb74VZaWtro\n9XMn3/7G4JwrKSnJ8/NSUVHR6F73saZE43v1+eefVx544AHRYYSdaHyt2yISnnulpaVeyVsgMfj6\nPRPoM8WXUD9PW/tsbEtewm5TapK76fds5zYPu8fxOJ1On2MKdDodysvLUVVV5dWk3xZpaWlYt26d\n13gq4H9Ts7VaLWw2m6eZvEePHnA4HKiurm7VuIfU1FQUFhZ6muSTkpJQVlbm93hLlJSUIC0tzauL\n0c1dR7CUlJSgtLS0yWt0Oh0WLFgAvV7vd3yMv24BWZa9foZycnJgsViQnZ3tOX72vUHvaghTo0eP\n5pIY1KxIfO4FEoOv3zOtJeJ52ppnY1sxeSPVGI1Gr/FvbrIsw2g0QlEUzzintiosLITJZEJdXV1A\n4+bMZjOmTZvmeci1dDxFSUkJMjIyPG98q9UKm80Gg8Hg83ig47acTic0Go3PsRi+BsGeLScnJ6A6\n8vLy/H6PMjIyAl4TKikpqdFD1uVywWw2+7ze4XAgPT3da/yMO0E5dOgQDAYDdDodqqurERcXByD4\nDzxRysvLsWfPHkycONHn+SFDhmDIkCEhjooiTSQ+99oaQ0u09nna1mdpS5+NqmhBy2BEa+5LbUff\nioD5a1I/uytt6tSpXlPTjUaj11o6xcXFXmMPTCaT17gnX91kVVVVza6Poyj/G69x7to97iZsd/eC\nr+5ajUajSJLkqaeqqsqr6d4dl/trzc/P95pm7nQ6lfz8fJ/HCwoKPGUWFxf7jb+qqkrJz8/3ez4p\nKUlYV6o/565dlJub6zUG5+zXTpZlJScnx+v+8ePHe/085Ofne/38zJo1y/P98ycS36vPPfec8vDD\nD4sOI+JE4msdbOH+3Du72zSQGAL5PdPcs9R9jcjnaXPPRl/akpdwh4UAz7c3lZWVyM3NRVlZGfLy\n8pCdnY158+bhL3/5C6ZOnYpZs2ahtLQUVqsVRqMRCxYsQGpqKurq6jB//nzPavl1dXWe2YUAvM7r\ndDrIsozMzExkZmbCZrMhJiYGRUVFsNvtWLt2bbNxVldXIy8vz/NXT8+ePWEwGGAymVBVVeX5yzAn\nJwdGo9HT2iNJEioqKpCVlYXRo0cDgOdr0ev10Ol0yMzMxIQJE7BgwQJPi6K72d89i7aoqMjncQDI\nz8+H1Wr1u6p3cnIyUlJSvH7u3DMuHQ4HNBoN6uvrA3/RQsS9irgkSYiNjfXqwjn3tausrPRMlz94\n8CA0Gg3mz5/fqDw3jUbj9fPiSyS+Vx955BH0798fjz32mOhQIkokvtahEK7PPffvjYqKCuTl5WHK\nlClNxhAbG9vs75m4uLhmn6VAeDxPm3o2+tKWvITJW4DniVoj2GPW2qNIfK+uW7cOffv2xcCBA0WH\nElEi8bWm4IjGZyk3picKU6FY6JfCX3p6erOJW11dHZ5//vkQRUQUWfgs9cbkjShIqqurVZtdS9Hv\n/PPPx/Hjx9nSRHQOPksbY7dpgOeJKDzwvdp+8LWmaMZuUyIiIqJ2gskbEVEQuVwuPPHEE6LDIKIo\nwuSNiCiIOnTowFmmRKQqJm9EREEUExODe+65J6BrT58+jWnTpnGcFxE1ickbEVGY6NixI1avXo1v\nvvlGdChEFMa4tykRURi59tprsW3bNp8ba7c3sbGx0Gg0osMgCorY2NhW38ulQgI8T0ThIdrfq5s3\nb8Yll1zCda2I2jlujwUmb0TRItLeq6+99hqMRiN+9atfiQ6FiCJIU886dpuST5WVlVi2bBl69uzp\n2Wi9vWvr90Sr1cJgMMBisXgdP3jwIOx2OyRJanLjZbXY7XZs3boVCxYsaNX5s7k3lS8vL0dKSgp/\nVnxYu3Yt7rjjDtFhEFEUYfJGPiUmJmLr1q0oLi7mL+T/auv3pLCwEBaLBWazGQkJCV7nFixYgAkT\nJqC6uhpxcXFqheylrKwMTqcTpaWlMBqNLT5/LqvV6pXgJScnAwB/Xs4hyzJ0Op3oMIgoinC2KfkV\nrCQikrXle5KdnY20tDSMHz/e53mr1QpJklpdfnNSU1Mxc+ZMJCUl+WyKb+782erq6tCzZ0+vYxaL\nBfPnz1c15mjw+9//vlGyTkTUFkzeiEKouLgYkiTBarU2OpeYmAi9Xi8gqpY7ePAgcnNzUVNT4zkW\nGxsLWZbFBRWmbr31VlxyySUtuueFF17A+++/H6SIiCjSsduUAibLMoqKijyz4CRJ8uoikyQJNpsN\nKSkpKC8v9+p6y87OblSew+GA1Wr1Ggfm7rI7+/qm6nWXkZycDLPZjGXLlsFsNsNgMGDWrFkwGo2e\nsp1OJ3Q6HdLS0uB0OuFyuVBaWorly5d76nI6naiurvbEYrFYkJiYqMr3DzizYKu7+3TChAmNylaz\nrmAyGAxwOp1ey1mUlpbCbDaLCyqKmM3miEnkiUgApZ1o7ktt6bdizpw5CgAFgDJnzhyf5/0dD+V9\nbVFaWqqYzWbP5yaTSamrq/N87nA4FIvF4vk8KSlJqays9Jw7+15/7Ha7YjQalerqakVRFEWWZUWj\n0Xhd01y9NptNMRqNSl1dneJ0OhWn09lk2WVlZZ57zWazYrfbveoqKSlRFEVRJElSYmNjm/yetJbZ\nbFaysrICvt5isQT0Ictys2Xl5uZ6ff9aet6X2tpaJTY21vO9DqZ29NgionasqWddu3kKqp28tQdn\nJyqlpaWKyWRqdI1Go/EkVmf/v6qqqlHi468Oo9Hot8xA6i0uLvaZUPkr++wEw2KxKDabzfP52Umi\noiiNEhK1krf8/PyQJDq+BCN5M5vNnsQ92PheJaL2oKlnHce8UUCcTqfPbhydToetW7cCAMaPH4/S\n0lIAZ7ozJ0yYEFDZTc3EC6Tepsrwdbyp7qgePXrA4XCgqKgIJSUlTYXdaiUlJUhLS/O5gn5ZWVlQ\n6gwmq9UKq9XKQfk+yLKM6dOniw6DiKIMx7yRX2dvS2M0Gr3GhrnJsuwZizZhwgS4XC6UlJTgwgsv\nxKJFi9ocQyD1tnX7nLPvN5vNmDZtmmfM3blj9dpal9PphEaj8Tm2zel0+r0vJycnoPLz8vIQExPT\n6vhaqqSkBOnp6Rg9ejSAM2vhRcq4vVDo2LEjbrjhBtFhEFGUYfJGfilnLReRkZGB3Nxcr3XI7HY7\nMjMzPS1I5eXlAS3s2pK6A6lXaeFq+2dfr5wZOgDgTPJUUVGBcePGec7LsgxFUVBSUoKMjIxGdUmS\nBKfT6Xf5j3OvLSsr87sOWnZ2tt/WvsWLFzdbfqCa+375Oy9JEiorK5GRkQHgTOuqy+VCWloaZFmG\ny+XCsmXLmLydpVu3bsjKymrVvXPmzEFSUhLuuusulaMioogX9E7bMNHcl9qOvhUBcTqditlsVrRa\nrVJQUKAoypkB/7m5uYrdbldsNpvnuFthYaESGxurGI1GxWg0NpoM0Fwdsiwrs2bNUrRarZKTk6NI\nktRsve4y9Hq9p4xAy3bHm5yc7JnEYLFYlPz8fMVutysOh0Ox2WyKxWJRysrKfH5P8vLyGk2w8Mdk\nMik5OTleEwwyMzMVs9msaDQaRavVBvjqtI7T6VTy8/MVo9Go6PV6JT8/3zO5I5DzNptNSU9PVxTl\nzAQFjUbT6KMlkzBaq728V//4xz8qs2fPFh0GEQnS1LOOe5sGeJ6a5nQ6sXz5cjzxxBPo0aMHDh06\nhKqqKmRnZ6OoqCiqW2PKysqQmpoqOox2o728V5ctW4bly5cHbewlEYU37m1KQVdWVoaUlBT06NED\nwJmB/4mJiUhOTm7zOLFwx4VpKRhuueUWjpcjIp/CouXNPdZIr9dDkiQkJSUF3JLhbvHp2bMnDh48\nCIvF4nMLI7a8BV9RURGAM7M5XS4XZFmG0Wj0GkMWbaqrqyHLclS3LIabSHqvrl69GkePHg145jUR\nkVtYt7y5twpat26d51hWVhYMBkOz+0ja7XY4HA6vwdwWiwWFhYVBi5f887WLQrTj/q/UlIqKCtEh\nEFEUEr7OW15eXqNlECwWC3Jzc5u8T5ZlTJ061Stxs9ls+Oijj4ISJxFRSx0+fBjdunUTHQYRRRnh\n3aZ6vb7RHomyLEOv16OhocHvfbm5udBqtZg/f77X8ZqaGp+Ln7LblCg6RNJ7tby8HN26dcPVV18t\nOhQiijBNPeuEtrzJsuxJ1M7mXhW/pqbG771FRUVISUlpdNxX4kZEJEJKSkqbErcPPvgAkyZNUjEi\nIooGQlveJElCfHy8zxY2rVYLh8PhWbnd1/nS0lJIkuQZIK/X6z0LiJ6LLW9E0aE9vVePHj2K+vp6\ndO/eXXQoRBRiYTthobVLLEiSBODMVjwzZszwHLdarXC5XO1y4DwRRZ8LLrhAdAhEFIaEzzZtDXfS\n597b0m3ChAlITU1tVfIWGxsb9euREUWD2NhY0SEQEQkVkcmbO2k7N3lLTEyELMt+Jy00xeVyqRUe\nEREAYNasWXjkkUfQt29f0aEQURQRmry5k69Dhw55Vub3df5c7gkN7n/PJUmSz+Rt7ty5nv+PHDkS\nI0eObFnAREQtMHz4cFWWCjl9+jQ6dozIv7WJKEAbNmzAhg0bArpW+FIh8fHxsNvtSEhI8ByTJAnJ\nyclNtobFx8fDZrM1mtCg1Wp9Jm/taZAzEUWPt99+G++99x7efPNN0aEQUQiF7VIhAJCWloby8nKv\nY06nE2azucn7LBZLo9XLnU4nYmNjuVwIEUUNo9GIHTt2iA6DiMKI8OQtLy8PxcXFXsdsNhvy8vI8\nn7v3yHTvnQkAU6dObbQNltVq9bqGiCjSXXXVVaipqWHPARF5CB9EERMTg7y8PFitVqSkpHj2Oj23\n9ay2ttZrNmhMTAxKS0uRk5MDo9GIqqoqWK1Wv+vCERFFoh49euDnn3/mbHgi8hA+5i1UOOaNiELp\nwIEDePrpp/G3v/1NdChEFIHCeswbEVE0OnjwINatWyc6DCKKQkzeiIiC4PDhw6osE0JEdC4mb0RE\nQdC/f3/Mnz9flbIURcFPP/2kSllEFPk45o2IKMz9/PPPGDFiBL7++mvRoRBRiDSVtzB5IyIiIgoz\nnLBAREREFCWYvBERERFFECZvRERBsHr1au5HSkRBIXyHBSKiaBQfH4/jx4+rVt6pU6dQXV2NK664\nQrUyiSgyccICEVEE2L9/P5KTk/HDDz+IDoWIQoATFoiIIlzfvn1x9OhRuFwu0aEQkWBM3oiIIoBG\no8Ett9zCxXqJiN2mREREROGG3aZERCH2/PPP49NPPxUdBhFFISZvRERBsH79evz444+iwyCiKMTk\njYgoCI4dO4YuXbqIDoOIohCTNyKiIHjyyScxZMgQ1cvdtGmTquvHEVHkYfJGRBQEo0aNwkUXXaR6\nuUuXLuWMU6J2jrNNiYiIiMIMZ5sSERERRQkmb0REREQRhMkbEVEQTJo0CceOHRMdBhFFISZvRERB\n8Otf/xqdOnUKStl2ux0nTpwIStlEFP44YYGIKMJcddVVsNvtGDRokOhQiChIOGGBiCiKXH311fj6\n669Fh0FEgjB5IyKKMOPGjYNOpxMdBhEJwm5TIiIiojDDblMiohDat28fHn30UdFhEFGUYvJGRKSy\nn376CRs3bhQdBhFFKSZvREQqO378OM4//3zRYRBRlGLyRkSksiuuuALPPvtsUOv48MMP8dVXXwW1\nDiIKT0zeiIhU1qtXL4waNSqoddTV1eHIkSNBrYOIwhNnmxIRERGFGc42JSIiIooSTN6IiIiIIgiT\nNyIila1btw6FhYWiwyCiKMXkjYhIZfHx8UhOTg56PW+99Ra2bdsW9HqIKLx0FB0AEVG0MRgMIaln\ny5Yt+Pnnn3HttdeGpD4iCg9seSMiilDXXHMNduzYIToMIgoxtrwREUUos9mMyy67THQYRBRiXOeN\niIiIKMxwnTciohB65ZVX8N5774kOg4iiFJM3IiKVlZeXY+/evaLDIKIoxeSNiEhlJ06cQOfOnUWH\nQURRimPeiIhUVl5ejl69emHAgAFBr2vTpk3YuXMnsrOzg14XEYVOU3lLWMw2dTqdqKiogF6vhyRJ\nSEpKQmpqapP3SJIEi8UCq9UKk8kEl8sFm80Gs9nc7L1ERMGUkpISsrr69OkDjUYTsvqISDzhLW+S\nJCEnJwfr1q3zHMvKykJeXh7i4uKavC8+Pt7zuU6nw5IlSzBu3Dif17PljYiIiCJFWM82zcvLQ05O\njtcxi8WC3NzcJu/TaDRwOByQZRmSJMHlcvlN3IiIiIiihfCWN71eD6fT6TU2RJZl6PV6NDQ0+L2v\nuroakiQF3EXKljciIiKKFGHb8ibLsidRO5tOpwMA1NTUCIiKiKhtZs2ahd27d4sOg4iilNAJCy6X\nCwDQo0cvJmR+AAAgAElEQVQPn+clSWpytpYkSZBl2VOWXq9HRkaG6nESEbXEzTffjAsvvDBk9W3Y\nsAH/93//hyeeeCJkdRKROEKTN3fi1Rru1rqzk7WsrKxGx4iIQm306NEhra9jx45YuXIlkzeidkL4\nhIXWiomJabSuUSATHYiIos2gQYOwY8eOJscJE1H0CIt13tQSFxcHSZJw6NAhn12xc+fO9fx/5MiR\nGDlyZOiCIyIKEp1Ohw8++ICTsogi2IYNG7Bhw4aArhU629Q9WUGW5UbJllarbXLMW35+PmbNmuWz\nPKfTiYSEBK9znG1KREREkSJsZ5vqdDoYDAZIkuR1XJIk6HQ6v4mbJEmwWq2NZqO6J0AYDIZghEtE\nFJCJEyfi+PHjosMgoiglfMxbWloaysvLvY45nU6YzWa/9xgMBhQWFjZK7hwOB0wmk9/Zq0REoWC3\n26HVCn+8ElGUEv50ycvLQ3Fxsdcxm82GvLw8z+eyLMNoNKKoqMhzTK/Xo7q62usam83mdQ0RUag1\nNDSgvr4e5513nuhQiChKCZ+wEBMTg7y8PFitVqSkpHi6RM9tVautrfXafDkjIwMlJSWw2+04ePAg\nZFmG3W5vcl04IqJQWLFiRcg3i29oaEBiYiI+//xzdO7cOaR1E1FoCd8eK1Q4YYGIot1//vMfXH75\n5eyyJYoCTeUtTN6IiIiIwkzYzjYlIiIiopZh8kZEREQUQZi8ERGpaO/evXj44YeF1c/hIUTRj8kb\nEZGKYmJicOeddwqpW1EUxMXFoa6uTkj9RBQaTN6IiFQUExODtLQ0IXVrNBpcdNFF2L59u5D6iSg0\nmLwREUWRhIQEJm9EUY5LhRARRZGjR4+iS5cuIV8kmIjUxXXewOSNiIiIIgfXeSMiCpHy8nI8++yz\nosMgoijG5I2ISEX79+9HeXm56DCIKIoxeSMiUtHJkyfRqVMnoTGcPn0ahw8fFhoDEQVPR9EBEBFF\nkxtvvBFxcXFCY3juuefQ0NCAxx9/XGgcRBQcnLBARBRlFEXhbFOiCMcJC0RE7QgTN6LoxuSNiIiI\nKIIweSMiIiKKIEzeiIhUZLfb8cYbb4gOA7/88gv27dsnOgwiCgImb0REKho8eDCSkpJEh4F3330X\nM2bMEB0GEQUBZ5sSEUWhf//73xg3bhz+85//iA6FiFqBs02JiNqZK6+8Enq9HqdPnxYdChGpjC1v\nRERERGGGLW9EREREUYLJGxGRil5++WWsW7dOdBhEFMW4tykRkYq2bt2KCy64QHQYRBTF2PJGRKSi\nkydPolOnTqLD8Pjggw9w8uRJ0WEQkYqYvBERqejRRx/FTTfdJDoMjxUrVsDlcokOg4hUxNmmRERE\nRGGGs02JiIiIogSTNyIiIqIIwuSNiIiIKIIweSMiUtGsWbOwc+dO0WF4Wb16NWpqakSHQUQqYfJG\nRKSi22+/Hb179xYdhpd33nkHa9euFR0GEamEyRsRkYpGjBgBvV4vOgwvJpMJW7duFR0GEamEOywQ\nEUW51NRUdOnSRXQYRKQSrvNGREREFGa4zhsRERFRlGDyRkSkovvuuw+1tbWiwyCiKMbkjYhIRWvW\nrEFDQ4PoMIgoijF5IyJS0cmTJ9GpUyfRYTRy4MABPPXUU6LDICIVMHkjIlLR22+/HZYzO7t3747+\n/fuLDoOIVMDZpkRERERhhrNNiYiIiKIEkzciIiKiCMLkjYiIiCiChEXy5nQ6UVRUhJKSEhQUFKCs\nrKzFZciyjJycnCBER0QUmF9++QX33HOP6DCa9Nvf/hY//vij6DCIqA2E720qSRKsVivWrVvnOZaV\nlQWDwYC4uLiAy8nNzeXCmEQkVOfOnXHvvfeKDqNJP/30Ez777DPceeedokMholYS3vKWl5fXqMXM\nYrEgNzc34DIkSUJtbS00Go3a4RERBaxTp0645ZZbRIfRpGHDhuHTTz8VHQYRtYHwpUL0ej2cTicG\nDBjgOSbLMvR6fcCrlBcVFQEASktLsXz5cp/XcKkQIiJg//79OHXqVIt6Nogo9MJ2qRBZlj2J2tl0\nOh0AoKamptkyysrKkJaWFozwiIiiTr9+/Zi4EUU4ocmby+UCAPTo0cPneUmSmi1DkiTExcWxVY2I\niIjaBeEtb21RUlKC7OxslaIhImqbb775Br///e9Fh0FEUU74hIXWamviR0SkttraWmzatEl0GEQU\n5YQvFdJaxcXFXq1ugcw0nTt3ruf/I0eOxMiRI4MQGRFFsz179sDhcGD79u3Yv38/jh07hq5du6Jv\n376IjY1FfX296BCbJUkS7rnnHnzyySeiQyGi/9qwYQM2bNgQ0LVCZ5u6JyvIstxo3JtWq4UkSV6z\nUN0qKysBAImJiZ5jNpsNDoeDs02JSHVHjx7F66+/jr///e84cOAAbr75ZiQkJKB///7o0qULjhw5\ngr1792Lz5s346KOPcPnllyM7Oxu//e1v0alTJ9HhN1JfXw+Xy4VevXqJDoWI/GgqbxG+VEh8fDzs\ndjsSEhI8xyRJQnJysmdCw7mKiopQVVXldczpdEKSJIwfPx4pKSnIyMjwOs/kjYhaqqGhAa+99hpm\nz56NoUOHYvr06RgxYgS0Wv8jTk6fPo3S0lK8+OKL2LlzJ5599lncfffdXIeSiFokrJO3nJwcmEwm\nry5Qu92O4uJiLFu2LOByCgoKsHXrVr/3MHkjopaorq7GpEmToCgKXnzxRSQnJ7e4jM2bN+Ohhx7C\nxRdfjCVLlqBfv35BiJSIolHYrvMGnNlhobi42OuYzWZDXl6e53NZlmE0Gj2L8fpy4MABJmdEpIoV\nK1Zg6NChGDduHDZt2tSqxA0Ahg8fjvLycgwfPhwpKSlwOBwqR0pE7ZHwljfgzBi2ZcuWISUlBZIk\nwWQyYfTo0Z7zsizDYDAgPz8fU6ZM8bq3uroaeXl5WL58Oerq6pCdnQ2LxeI1Hg5gyxsRNU9RFMyf\nPx+LFi3CypUrYTKZVCt7/fr1uOeee/DUU09h2rRpqpXbFkeOHEGXLl2a7AYmIjHCuts0VJi8EVFT\nFEXB9OnTsWnTJqxZswaXXHJJi8v45JNPsH79ejzxxBM+z0uShDFjxuDuu+/G3LlzhY+Du+aaa7Bs\n2TIMHjxYaBxE1FhYd5sSEYmmKAoeeOABfP755/joo49albgBwIABA5rcrs9gMGDLli1YuXIl/vjH\nP7Y2XNUMGzaM69IRRaCIXeeNiEgtf/zjH+F0OuFwONC9e/dWl9OnTx/06dOnyWt69+4Nh8OBkSNH\nokuXLn5b6UJhxIgR+Oqrr4TVT0Stw25TImrXFi9ejOeffx5btmwJ6bpn33//Pa6//nrMnz8fEydO\nDFm9Z1MURXjXLRH5xjFvYPJGRI29++67yMnJwebNm2EwGEJe/7Zt25CamopVq1bhhhtuUL18SZKw\nfv16GI1GJCQkQKfTqV4HEQUHx7wREZ1j165dmDJlClatWiUkcQOAa6+9Fq+//joyMjJQU1PT6nJ+\n+uknn8cPHz6MzZs3Y/bs2bjsssswfPhwFBYW4siRI62ui4jEY8sbEbU7R48exbBhw/Dggw/CYrGo\nVu6aNWuwf/9+5OTktOi+5557DsuXL8emTZtatJ3Wtm3bkJubi/3792Pbtm1NdoEeO3YM69evh81m\nw4033oiZM2e2KEYiCi22vBER/ZeiKJg2bRoSEhIwdepUVcuuqqrCjh07WnzfY489ht69e2P27NkB\nXX/s2DE89thjSE9Px2233YaKiopmx6516dIFt956K1auXIkZM2Z4jp8+fRoff/xxi2MmInE425SI\n2pU33ngDFRUV+Oyzz1QfrH/69Gmcd955Lb5Po9Hg1VdfRWJiIkaNGoVbbrnF77U7d+7E2LFjkZCQ\ngH//+9/o2bNnq+o7+//z5s3Dddddh86dO7e4LCIKPXabElG7sW/fPphMJpSWlmLIkCGql79nzx6c\nOHECAwcObNX9H3/8MSZMmIAvvvgCF110kc9rduzYgc8//xy/+93v2hBpY1988QWuuuoqnH/++aqW\nS0Stw9mmYPJG1N4pioIxY8bgpptuwpNPPik6HL+sViskScLy5ctDWm92djaqqqqwevVqdO3aNaR1\nE1FjHPNGRO3e4sWLIcsycnNzRYfSpDlz5mDbtm0oKSkJab2LFy9G//79ccstt+Dw4cMhrZuIWoYt\nb0QU9fbu3YukpCRs2rQJV199tehwmrVlyxZkZmZi+/btrRrT1loNDQ2YMmUKvv32W6xevbpFM1+J\nSF1seSOidm369Ol46KGHIiJxA4Abb7wRmZmZyMzMxMKFC0NSZ1lZGXbu3AmbzYbzzz8fU6ZMCUm9\nRNRyTN6IKKq999572L59O6xWa9DrWrJkCVatWqVKWXfccQc2btwYshmgDocDb7/9Njp27Ii3334b\nkydPDkm9RNRy7DYloqh19OhRDBw4EIWFhUhPTw96fV999RW6dOkCo9HYpnK+++47pKSkYNKkSfjg\ngw9QUVGBjh2Du7JTaWkpnn76aWzevDmo9RBRYNhtSkTtknv9slAkbgAwaNCgNiduJ06cwPjx4/HA\nAw9g/vz50Ov1KCwsVClC/2688cYm15cjovDBljciikrffPMNkpKS8OWXX6Jfv36iwwnYrFmzsGfP\nHtjtdmi1Wnz11VcYNWoUduzYgV69eokOj4hChOu8gckbUXtzzz33wGg04k9/+pPoUFrk22+/Rffu\n3dGjRw/PsenTp+P48eNYvHixsLi+//579OnTR1j9RO2NqsnboUOHvB4qvixZsiTsZioxeSNqPz7/\n/HOMHTsW//nPf9CtWzfR4bTZwYMHceWVV2LLli248sorQ17/kSNHEB8fj9WrVyM5OTnk9RO1R6qO\neYuLi2vyfF1dneqbPRMRBUpRFDz22GP485//HPLELS8vD5s2bVK93J49e2LWrFl4/PHHVS87EF27\ndsXzzz+PSZMm4dixY0JiIKL/aXHyVltbi2nTpvk8V1lZCZPJpPpmz0REgVq5ciV++eUX3HfffSGv\n+/PPP8dPP/0UlLIffvhhVFRUYMuWLUEp3+3ll1+Gw+FodHzixIm49tprMXfu3KDWT0TNa9Vs02XL\nlmHMmDE4dOiQ51hBQQFMJhMkSVItOCKilqivr8dTTz2FefPmoUOHDiGv/9SpUy1e0sPlcqG+vr7Z\n684//3w888wzmDlzZlCHgFx33XW4/PLLfZ578cUXsXTpUnz11VdBq5+Imtfi5C0xMREulwupqakw\nmUxYsWIFkpOTkZubC51OhwULFiAmJiYYsRIRNWn58uXo3r07br31ViH1z549G9ddd13A1yuKgszM\nTLz11lsBXX/PPffgyJEjWLNmTWtDbFZycjL69+/v89zFF1+Mp59+Gk8++WTQ6iei5rVptqnFYkFR\nUREAIC0tDcXFxYiJiUFJSQkyMjJUC1INnLBAFN1Onz6Na665BosWLUJqaqrocAKydOlSLFq0CJ98\n8knALXbvvPMOnnnmGWzdulXIEJX6+nrIshzSPVeJ2iNVJyykpKTg0KFDSE9P9yRuBoMBRqPR0+Km\n0+naEC4RUcu98cYb6Nu3L0aPHi06lID88MMPsFqtWLJkSYu6Wn/961+joaEB7777bhCj869Dhw5M\n3IgEa3HLm1ar9WSDBoMBxcXFSExMRGZmJmpqamCz2ZCVlYXdu3cHK+ZWYcsbUfQ6efIkrrjiCrz5\n5psYPny46HAC8rvf/Q4XXXQR8vLyWnzvqlWrMHfuXDidTk4QI4pSqm+PpSgKxo8fjz179iAxMREA\nUFxcjOzsbE5aIKKQe+WVV3DVVVdFTOLmdDpRWlqK2bNnt+r+O++8E1qtFitXrlQ5sjO+++47XH/9\n9UEpm4jarlXJW2FhIZYvX97o+NSpU7Fs2TK2cBFRyJw4cQLPPvtsWOykMH36dOzZs6fZ64YMGYIN\nGzage/furapHo9Fg7ty5mDt3LhoaGlpVRlP69OmDmpoaVFVVNXstn/dEodfi5C07OxvZ2dl+z2dm\nZkbMYGEiinxvvPEGBg0ahKFDh4oOBWPHjsWFF17Y7HUdOnTwuxxHoG6//XZ06tQJ77zzTpvK8UWj\n0WDMmDE+13s7V0ZGRlAWJiYi/7i3KRFFrPr6elx11VV45ZVXMGLECNHhhNyaNWswe/ZsVFZWqj72\nra6uDt27d4dW2/Tf+P/85z/x0ksv4dNPP+X4OyIVqT7mjYgoHNjtdvTu3Ru/+tWvRIcixG233YaG\nhgasXbtW9bJjYmKaTdyAMzsvHDt2LKhrzxGRNyZvRBSRFEXB/Pnz8cQTT7TbFh+NRoPc3NxWzVhV\ni1arxZ///Gc89dRTQRl/R0SNMXkjooj0wQcfQFEUYbsptNT06dPx6aefql7uhAkTUF1djc8++0z1\nsgN155134rzzzoPdbhcWA1F7wuSNiCLSvHnz8Pjjj4dVq9ukSZPgcrkaHf/iiy/wr3/9CwMHDlS9\nzo4dO2LGjBlBaX1TFAW7du1q9jqNRoOCgoKAulmJqO04YYGIIs6mTZtw//33Y+fOnUI2oPenV69e\n2LFjB3r16uV1/JZbbsFtt92Ghx56KCj1Hj16FHFxcdiwYQOuvvpq1cqtr6/H0KFDsXHjRnTr1k21\ncomoeZywQERRpaCgADNmzAirxA04s7/quTGtX78eu3btwtSpU4NW7wUXXICHHnoIBQUFqpbboUMH\nVFRUMHEjCjNseSOiiLJr1y4MHz4c33zzDbp06SI6HC8ffvghUlNTcd555wE40+04bNgwPPLII7j7\n7ruDWrfL5UJ8fDy2bduGfv36BbUuIgo+trwRUdT461//ipycnLBL3ADg5ptv9iRuwJmEavDgwfjN\nb34T9Lr1ej0mTZqEhQsXBr0uIhKLLW9EFDEOHjyI+Ph4fP3117j44otFhxN2qqqqMGzYMNTU1KBr\n167C4jh16hR+/PFHtgAStQFb3ogoKhQWFmLs2LFM3PwwGo0YPnw4/vGPf6habnV1NT766KOAr3/n\nnXeC3k1M1J4xeSOiiHDixAksXLgQjz76qOhQwtr06dPx4osvqrpg7r59+zBjxoyArx83bhy+/fZb\n7nlKFCRM3ogoIvzrX//CoEGDMHjwYNGh+FRfX4+77rpLdBgYMWIELrjgAlW3zLrhhhuwd+9e7Nu3\nL6DrO3bsiNzcXMybN0+1GIjof5i8EVHYUxQFzz//PB577DHRofil0WiQnZ2NhoYGHDhwQGgc06dP\nxwsvvKBamR07dsT8+fNx8uTJgO+577778OWXX2Lbtm2qxUFEZ3DCAhGFvY0bNyInJwc7duwIqx0V\nfFmxYgVefPFFbNy4UVgMJ06cwIABA+BwOIKyq0Og5s2bh927d+PVV18VFgNRpOKEBSKKaAsXLsSD\nDz4Y9olbQ0MDnn76acycOVNoHJ07d8YDDzyAv/71r0LjsFgsGDt2rNAYiKJRWLS8OZ1OVFRUQK/X\nQ5IkJCUlITU1tdn7HA4HHA4HevbsiaqqKphMJmRnZ/u8li1vRJHp22+/xeDBg1FTU4MePXqIDqdJ\nK1aswLx581BeXi480fzpp59w5ZVXoqqqCnq9XmgsRNRyTeUtHUMcSyOSJMFqtWLdunWeY1lZWTAY\nDIiLi/N7n8PhgEajwYIFCzzHkpOTIcuy8L96iUg9hYWFuPvuu8M+cVMUBU8//TSeffZZ4YkbAPTu\n3Ru33347Xn31VfzhD38QHQ4RqUh4t2leXh5ycnK8jlksFuTm5jZ5X2FhYaNjaWlpPo8TUWQ6ceIE\nbDYbHnzwQdGhNKu4uBh79+7FbbfdJjoUjwcffBCLFi1SbdmQEydO4LbbbsOpU6dUKY+IWkd48lZc\nXIykpCSvYyaTCXa7vcn7NBoNHA6H1zFFURAbG6t6jEQkRklJCQYOHIirr75adCjN6tWrFzp27BgW\nrW5u1113HXr06OHVs9EWnTt3Rm5ublh9jUTtkdDkTZZlyLLcaDyGTqcDANTU1Pi9d/ny5Zg/f77X\nMbvdjgkTJqgeJxGJsXDhQjz00EOiwwiIwWAIu/1WNRoNHnzwQbz88suqlTlixAh07NjyETeyLKOq\nqkq1OIjaM6HJm8vlAgC/Y1kkSQq4LJvNhuTk5BatAk5E4cvpdGL//v244447RIcSkF69eoXlkhgT\nJ07EJ598gurqaqFxvPvuuxHR/U0UCYS3vLVVSUkJcnJyUFlZiWXLlqkQFRGFg5dffhnTpk1rVSuP\nCBdccEFAs+RD7YILLsB9992HxYsXC40jKysLTqcTu3fvFhoHUTQQulSI0+lEcnKyz8G0Wq0WDocD\no0ePDqisuro6pKamoqioCImJiY3Oc6kQoshx8OBBGI1G7N69G7169RIdTsTbvXs3brzxRuzduxfn\nn3++KmUeO3asxd3Ejz/+OI4fP67q7g9E0SqslwpRS0xMDCwWC1JTUz3dseeaO3eu5/8jR47EyJEj\nQxMcEbXIq6++ijvuuCPsEzdZlnHgwAHEx8eLDqVJl19+OZKSkrB8+XL89re/bXN5X375Je69915s\n3769Rffl5OQgKSkJzzzzDLp27drmOIiiyYYNG7Bhw4aArhXa8uaerCDLcqNxb1qtFpIkYcCAAQGX\nJ0kS4uPjUVpa2qj7gi1vRJFBURRcddVVWLp0KW688UbR4TTp2Wefxe7du/Haa6+JDqVZq1evxjPP\nPIPPPvuszWU1NDTgsssuw7p163DNNde06N677roLt99+u98F1YnojLDdHkun08FgMDSamCBJEnQ6\nnd/ETZIkxMbG4osvvvB5vq6uTu1QiShENm/ejA4dOuCGG24QHUqTjh8/joULF3omSe3evRuPPvqo\n4Kj8u/XWW/Hjjz9i69atbS5Lq9Vi4sSJrSrr6aefbrQ8FBG1jPBu07S0NJSXlyMhIcFzzOl0wmw2\n+71HlmUYjUYYDAav4+4kkA8GoshVVFSEKVOmhP1aYm+88QYSExMxaNAgAGdmm44bN05wVP516NAB\nU6dO9czMb6v8/PxWvUZnP+uJqHWE721aV1eHzMxMr0Uk09PTYbPZPC1vsizDZDLBarV6mtoLCgow\ndepUxMTEeO4zm81ITk5utP4bwG5TokggyzIGDBgQ9hMVGhoacM0112DRokUYNWqU6HAC9v333+Oa\na67B3r170b17d9HhEFETwnrCQkxMDPLy8mC1WpGSkuLZ6/TcLtPa2lqvv/JmzpyJoqIiVFVVeTam\nnzBhAqZMmRLir4CI1PLWW28hPT09rBM3AFizZg26desWcZOe+vTpg9GjR+Ptt9/G1KlTRYdDRK0k\nvOUtVNjyRhT+kpKSkJeX1+SwiXCwb98+/PzzzxE5RGPt2rV48sknVRn7RkTBE7YTFoiI3CoqKuBy\nucJyodtzXXrppRGZuAFnhpccOHAAFRUVqpT33nvvNbmVYVP27duH06dPqxIHUXvC5I2IwsKSJUsw\nefJkaLWR+VjaunUr5syZIzqMZmm1WmRnZ8Nms6lS3rfffova2tpW3Ttx4kS8//77qsRB1J6w25SI\nhDty5AguvfRSbNu2Df369RMdTqusWbMGixcvxpo1a0SH0qzvvvsOAwcOFD5x4dVXX8WKFSuwevVq\nYTEQhSt2mxJRWLPb7bjhhhsiNnEDgNOnT6NDhw6iwwjIJZdcgpEjR+Jf//qX0DiysrKwZcsW7Nu3\nT2gcRJGGyRsRCbdkyZKwnyl+4MABfPrpp37PDxs2DLNnzw5hRG3jXvNNpK5du2LixIlYunSp0DiI\nIg27TYlIqK+//hqjR4/G3r17cd5554kOx6+5c+fiu+++E57wqKW+vh5GoxErVqwQOvniiy++wJ13\n3onq6uqIabkkCgV2mxJR2HrllVdw3333hXXidvToUSxatAh/+MMfRIeimg4dOmDKlCkoKipSpbzH\nH38c69evb/F9CQkJePjhh3H06FFV4iBqD9jyRkTCnDx5Ev369cOWLVtw+eWXiw7Hr0WLFmHt2rVY\nuXKl6FBU9e2332Lw4MHYu3cvunXr1qayXnjhBXz55Zd47bXX1AmOqJ1jyxsRhaV3330XAwcODOvE\nrb6+Hs899xxmzpwpOhTV9e3bFyNGjFBl4sJvfvMbrFq1CsePH1chMiJqCpM3IhLGvQl9OFu5ciV6\n9eqFG264ocnr1q5di7/97W8hiko9U6dOVaXrtE+fPti+fTvOP/98FaIioqaw25SIhKipqUFycjL2\n7duHLl26iA7HL1mW8eOPP+LKK69s8rpvvvkGsixjyJAhIYpMHfX19ejfvz8+/PBDDBo0SHQ4RPRf\nTeUtTN6ISIg5c+agtrYWL730kuhQ2r3Zs2fjyJEjeOGFF0SHguPHj7P1jghM3gAweSMKJ/X19Rgw\nYADee+89XHvttaLDafckScJ1112H/fv3o3PnzsLiKC4uxrJly2C324XFQBQuOGGBiMLK2rVr0adP\nHyZuYcJgMGDw4MFYtWpVm8tSFAWbN29u1R/LY8aMQVlZGX788cc2x0EUzZi8EVHIRcKOCu3N5MmT\n8corr7S5HEVR8Je//AUul6vF9/bo0QNjx47lciNEzWC3KRGF1A8//ICrr75a+KboTfnhhx+wdetW\n3H777QHfs2zZMhw/fhz33XdfECMLnmPHjqFfv35wOp3o37+/sDi2bNmCyZMn4+uvv4ZGoxEWB5Fo\n7DYlorDxj3/8A+PGjQvbxA0AXnrpJXzwwQctumfXrl3YvXt3kCIKvi5dumDixInCW71uuOEGKIqC\nTz75RGgcROGMyRsRhYyiKGHfZXr48GHYbDY89thjLbqvvr4+4vfmnDx5Ml599VU0NDQIi0Gj0WDW\nrFk4ePCgsBiIwl1H0QEQUfvx8ccf47zzzsOwYcNEh+LXK6+8glGjRsFoNLbovokTJwYpotBJTEyE\nXq9HWVkZzGazsDgmT54srG6iSMCWNyIKmSVLliA7OztsxzKdPn0aL7zwQqu2wrryyiubXcg3Ekye\nPDuweEoAACAASURBVBlLlixRpazZs2djx44dqpRFRP/D5I2IQqK2tharV6/GvffeKzoUv9555x30\n798fQ4cOFR2KMHfffTfWrl2rSrdlQ0ODKjNYicgbZ5sSUUgsXLgQmzdvVmUT9GA5efIkfvzxR1x6\n6aWiQxHq3nvvRUpKCh555JE2lVNVVYXrr78ee/fu5a4JRC3E2aZEJJSiKCgqKkJ2drboUJrUqVOn\ndp+4Af9b862tf/AajUaUlZUJ3bWBKBoxeSOioKuoqMAvv/yCUaNGiQ4laBYtWoQ1a9aIDkMVN910\nE44cOYKtW7e2uazBgwe3eoxjXV0dRo4cidOnT7c5DqJowuSNiIJuyZIlmDx5MrTa6H3kDB8+HIMG\nDRIdhiq0Wi3uv/9+1SYutFZMTAxOnDiBtWvXCo2DKNxwzBsRBdXhw4dx2WWXYfv27ejbt6/ocChA\n3377LQYPHox9+/aha9euwuIoKirChx9+iJKSEmExEInAMW9EJExxcTGGDx8etonb/v378frrr4sO\nI+z07dsX119/Pex2uyrlbdu2rVUzWCdMmICysjL8/PPPqsRBFA2YvBFRUIX7jgovvvgivvjiC9Fh\nhCW1NqsHgOXLl+Prr79u8X09evTAXXfdhTfffFOVOIiiAbtNiShoduzYgbS0NOzduxcdO4bfhi51\ndXWIi4tDZWWl0M3Yw9XJkydx2WWX4eOPP8YVV1whLI6NGzdi0aJFYb3MDJHa2G1KREIsWbIEv/vd\n78IycQOAwsJC3HLLLaokbgsWLMCmTZtUiCp8dOrUCZMmTcLSpUuFxjFixAgmbkRnYcsbEQXFiRMn\n0K9fP3z66act3ic0FE6cOAGDwYD33nsPCQkJbS4vIyMDd999NzIyMlSILnzs3LkTo0aNwt69e3He\neeeJDoeo3WDLGxGF3KpVq3DttdeGZeIGnIlv0KBBqiRuwJl9UTt06KBKWeHkqquugsFgwPvvvy86\nFCL6LyZvRBQU4T5RITMzU9WuuNmzZ2PYsGGqlRdO1Jy4UF5ejqlTp6pSFlF7xW5TIlJddXU1hg4d\nin379nFPyyhw+PBhXHrppdixYwf69OnTprKOHDmCAQMGYMuWLUInQRCFO3abElFILV26FPfccw8T\ntyjRrVs3jB8/XpX18Lp27YqcnJxWt+QtWLAA1dXVbY6DKJKx5Y2IVHX69GkMGDAAH3zwAQYPHiw6\nHFLJp59+ikmTJmHXrl2t3qvU7ciRI+jcuXOrZiE/8sgjiImJwZ/+9Kc2xUAU7tjyRkQhs3btWvTr\n14+JW5S57rrr0KlTJ3z88cdtLqtr166tXj7m/vvvx2uvvYb6+vo2x0EUqZi8EZGqioqKwnaiwldf\nfYWXXnopKGXPmDEDO3bsCErZ4UCj0WDKlCnCN6sfMmQIevfuDYfDITQOIpGYvBGRar7//nts3LgR\nv/nNb0SH4lN+fj6OHDkSlLLHjh2Liy++OChlh4tJkyZh9erVqK2tFRrH/fffL3zhYCKRmLwRkWpe\nf/11jB8/Ht26dRMdSiN79+7Fe++9h2nTpgWl/BtvvBF6vT4oZYeLCy+8EDfffDP++c9/qlKeoih4\n+umncezYsRbdN3HiRKxbtw6HDh1SJQ6iSMPkjYhUoShKWK/t9vzzz+P++++HTqcTHUpEy87ORlFR\nkSoTwDQaDS6++GIcP368RffFxsZi9+7d6NGjR5tjIIpEnG1KRKpYv349Hn74YWzbtq3NsxHVdvDg\nQVx++eXYvn07+vbtKzqciNbQ0IDLL78cb7/9NoYOHSo6HKKoxdmmRBR0S5YsQXZ2dtglbgDw/vvv\n49e//jUTNxVotVpMnjxZ+MQFovaMLW9E1GYulwsGgwGSJIXtuK9Tp04FdWP17OxszJ07t10kiN9/\n/z2uueYa7Nu3LyzHNxJFg7BveXM6nSgqKkJJSQkKCgpQVlYW0H3u63NycpCeno6SkpIgR0pEvrz5\n5pu49dZbwzZxAxDUxA0AysrKWjx2K1L16dMHN910k6p7wzY0NOCbb75RrTyiaNa6VRJVJEkSrFYr\n1q1b5zmWlZUFg8GAuLg4v/eVlJTAYDAgIyMDAFBXVweTyQSXy4Xs7Oygx01EZyiKApvNhoULF4oO\nRaj6+np06NBBdBghM2XKFDzzzDOqTVCprKzE2LFjsWvXrhZtq/bvf/8bhw4dwvXXX69KHESRQHjL\nW15eHnJycryOWSwW5ObmNnmfJElITEz0fB4TE4Pc3FxYLJagxElEvn3yySc4efIkbrrpJtGhCLV0\n6VJcdNFFosMImZtvvhn79+/H9u3bVSnPZDIhKSkJf//731t0386dO/H444+rEgNRpBCevBUXFyMp\nKcnrmMlkgt1u93uPLMtYtmwZ6urqvI6npqYCAGpqalSPk4h8KyoqCtuJCqGUmpqKLl26iA4jZDp2\n7Ij7778fRUVFqpX57LPP4tSpUy2654477sDXX3+NPXv2qBYHUbgTOmFBlmXo9XrIstxovR6tVgtJ\nkjBgwACf9+r1enz00UdISEjwHJMkCfHx8T7v44QFIvXJsowBAwZg165d6N27t+hwvLz22ms4duxY\n0BblpTN/KCcnJ2Pfvn1CE9c//OEP6Ny5M+bNmycsBiK1he2EBZfLBQB+F1qUJKnJe89O3ADA4XAg\nNjbWb8JHROp66623MGbMmLBL3E6dOoU//elPGDx4sOhQotqAAQNgMpmwYsUKoXHcf//9eP3113H6\n9GmhcRCFitDkTZZlVcsrLCzk2AeiEHFPVAjHCUJvvfUW+vfvj+HDh4sOJeq5d1wQaeDAgbj00kvx\n4YcfCo2DKFSEj3lTi81mw4UXXogZM2aIDoWoXdi6dSt++eUXjB49WnQoXurr/7+9+45q6vz/AP4O\noCiOQBxYN8OB4mApKiqiKJ6j4sQtrYrgHl8HrlptHRG/tWpdQaudikDd1soQbF0FgqKIilwEXCBC\niIPN/f3hjxz5ghYxyZPxeZ2To9zk3s+7jcAnz733eUqxadMmrF27Vq11R48erTdThbxrxIgRSEpK\nwv3795V63KKiIsXZmeqQSCTo2bOnUjMQoql0onnjOA4SiQR//vkn6yiE6A2JRIKZM2fCwECzfowE\nBwejcePGGDBggFrr+vj4qHwuOU1Uu3ZteHt74+DBg0o97p49e7B///5qv75r165o0qSJUjMQoqm0\n9oaFd3l5eeHAgQMfXKRYIBBg3bp1iq9dXV3h6upa0+iE6LWXL1+idevWSEpKQrNmzVjHqWD9+vVw\ndnbGkCFDWEfRG/fu3UP//v2Rnp6O2rVrK+WYpaWlMDAw0Pu7mIn+iIqKQlRUlOLr9evXv/eGBebL\nY1lbWyMkJKTSXaOOjo7VGjL38/ODv7//vzZ5dLcpIcojkUhw/vx55heqE83Rv39/LFy4EKNHj2Yd\nhRCdoLF3mwLAoEGDEBMTU2GbVCqFu7v7v+4bGBhYqXGLiIhAamqqsmMSQt4RGBiIWbNmsY5BNIgm\n3LhAiL5g3ryJxWIEBwdX2CaRSCAWixVfy2QyWFlZVfjBUD6Jb05ODqRSKaRSKcLDwxEcHPzBZbUI\nIZ9GKpUiKyurWh+wiP4YM2YMYmJiVLY+aVlZWbVeV1paisTERJVkIERTMF/bVCgUQiwWw9/fH05O\nToq1Tv/3NGhubq7i2geZTAYvL68qj2dlZaXqyITotcDAQMycOVOv1vH8NwUFBZg0aZJen0auW7cu\nJk2ahIMHD2LDhg1KPfauXbvw/Pnzah03OzsbLi4uSE9PR4MGDZSagxBNwfyaN3Wha94I+XSvX79G\nq1atcOvWLbRo0YJ1HIVXr16hfv36zOrL5XK0aNECL1++ZJZBEyQmJsLd3R1paWlKvfP20aNH6N69\nO65duwZra+t/ff3IkSMxfPhwzJgxQ2kZCFE3jb7mjRCiPY4ePQoXFxeNatyKiorQtWtX3Lt3j1mG\n0tJSGonE28ly27Vrh5MnTyr1uC1btsTKlStx6tSpar1+xowZSp+6hBBNQiNvhJBqc3R0xNdff42h\nQ4eyjqKwd+9enDx5kuns+kVFRYiKisLgwYOZZdAUR48eRWBgICIiIpR6XJ7nqz1tSElJCVq3bo3w\n8HB06tRJqTkIUZcP9S3UvBFCqiUmJgbjx4/HgwcPNGZi3vz8fLRr1w7Hjx+Hk5MT6zgEbxvZ1q1b\nIzo6Gh06dGCWY9WqVcjPz8f27duZZSDkU9BpU0LIJ9uzZw9mz56tMY0bAOzbtw8ODg7UuGmQ2rVr\nY/r06di3bx/THL6+vnB2dmaagRBVoZE3Qsi/evHiBaytrZGcnIzGjRuzjgMAyMvLQ/v27REWFoau\nXbuyjkPe8fDhQzg6OiI9PR0mJiZKPz7P88jNzYVIJFL6sQnRFDTyRgj5JIcPH8bw4cM1pnED3v4C\n3759OzVuGqht27ZwdnZGUFCQSo5/4cIFLFy4UCXHJkQb0MgbIeSDysrK0L59e/zyyy90Guo9Hj16\nhA0bNkAikbCOojHOnj2L9evX459//lH6sXmeR0lJiVKnIyFE09DIGyGkxsLCwtCwYUP07NmTdRSN\nZWpqikmTJrGOoVE8PDyQlZWF2NhYpR9bIBBQ40b0GjVvhJAP2rNnD+bMmVPtaRr0Uf369eHq6so6\nhkYxNDSEr68v9u7dyzoK8vPzUVhYyDoGIUpDp00JIe+VlpYGe3t7pKeno169eqzjEC2TlZWFDh06\ngOM4mJmZqayOTCaDqanpe5+fOHEi3N3dMX36dJVlIETZ6LQpIaRGJBIJpk6dqjGNW2xsLK5evco6\nBqmmpk2bwsPDAz/99JPKarx69QqdO3f+4GL0U6ZMwf79+1WWgRB1o+aNEFKloqIiHDx4ELNnz2Yd\nBcDbi9Tnzp2L1NRU1lHIR5g9ezb27t2LsrIylRy/fv362LBhAyZPnvzeU6MeHh549uwZ4uPjVZKB\nEHWj5o0QUqXff/8dtra2TGfJf9eRI0dQWlqKCRMmsI5SyZ07d7B06VLWMTRS3759YWxsjLCwMJXV\nmD59OoYPH47c3Nwqnzc0NISPjw+NvhGdQde8EUKq1LdvXyxatAhjxoxhHQWvX79Gx44dcfToUfTp\n04d1nEouXbqENWvW4NKlS6yjaKQffvgBoaGhOHv2LLMMT548QefOnZGeno4GDRowy0FIddE1b4SQ\njyKVSpGeng5PT0/WUQAAmzdvRr9+/TSycQPeLoRuaGjIOobGmjhxImJiYpCcnMwsQ/PmzbF8+XK8\nePGCWQZClIVG3gghlXh7e6Nz585Yvnw56ygoLCyEvb09/vzzT7Rs2ZJ1nCplZ2cjJSWF5sL7gFWr\nVuH169fYsWMH6yiEaIUP9S3UvBFCKnj27BlsbGyQkpKiMWtHlpaW0siWlsvIyEC3bt3w8OFDNGzY\nUKW14uPjkZCQAG9vb5XWIUSV6LQpIaTa9u3bhwkTJmhM4waAGjcd0KpVKwwaNAg//vijymsJhUII\nhUKV1yGEFRp5I4QoFBYWom3btoiMjISNjQ3rOETH/P3335g+fTru3r0LAwMaOyDkQ2jkjRBSLUFB\nQejatSs1bkQl+vTpg/r16+PPP/9kHQXFxcWsIxBSY9S8EUIAvJ0Ed8eOHVi4cCHrKMjLy9OqX66X\nLl3C5s2bWcfQeAKBAAsWLMDOnTuZ5sjKykK7du1ovVOitah5I4QAAC5fvoxXr17Bw8ODdRTMmjUL\n33//PesY1WZtbY0hQ4awjqEVJkyYAKlUirt376qt5pw5c3D69GnF102bNkW7du0QHBystgyEKBM1\nb4QQAMB3332HBQsWML8W6fz584iNjYWfnx/THB+jefPmsLe3Zx1DK9SpUwd+fn747rvv1FZz2rRp\nmDFjRoWGcf78+Vr1AYGQd9ENC4QQpKWlwcHBAQ8fPkT9+vWZ5Xjz5g1sbW2xd+9eGsnSYVlZWejQ\noQPu3buHpk2bqqXmwYMHkZubq1jGrLS0FNbW1jh27BicnJzUkoGQj0HzvIGaN0I+ZPHixTAyMkJA\nQADTHKtWrQLHcTh69CjTHET1fH190axZM6xfv55ZhoCAANy+fVst05cQ8rGoeQM1b4S8T25uLqyt\nrZGQkIAWLVowy5GSkgJnZ2ckJCTgs88+Y5aDqMe9e/fQt29fPHz4ECYmJkwy5OTkYM2aNdi9ezcE\nAgGTDIS8DzVvoOaNkPfZtGkT7t+/j8OHDzPNwfM8kpOT0b59e6Y5auL06dN49OgRZs+ezTqKVvH0\n9ISHhwf9fyOkCjTPGyGkSgUFBdi1a5fiOiCWBAKBVjZuAMBxHJKSkljH0DrLli3Dt99+i9LSUrXX\nPnDgAEJDQ9VelxBloOaNED32888/w97eHra2tqyjaLXS0lIYGRmxjqF1+vTpg0aNGuHUqVNqr+3s\n7AxHR0e11yVEGei0KSF6qqysDDY2NpBIJOjfvz/rOFqN4zgUFBSgU6dOrKNonZCQEGzfvh2XL19m\nHYUQjUKnTQkhlZw6dQpCoRD9+vVjliE/P59ZbWWytLSkxq2GRo0ahadPn+LKlSuso6CoqIh1BEKq\nhZo3QvRUQEAAli9fzuwuu8TERNja2upMA0dqxtDQEEuWLGE+TU1wcDDc3NyYZiCkuqh5I0QPXb58\nGZmZmRg1ahST+oWFhZgyZQpWrlyJunXrMslANMcXX3yBK1euIDExkVmGp0+f4vr167h48SKzDIRU\nF13zRogeGjFiBDw8PDBnzhwm9VesWIF79+7h+PHjNL8WAQBs3rwZt2/fxq+//sqkPs/zGDBgABIT\nE5GZmcl8mThCaJ43UPNGSLmbN29i6NChSElJYTLqFR0djYkTJ+LmzZto0qSJ2uurwqFDh1CvXj14\neXmxjqK15HI5LC0tce3aNVhbWzPJkJubizZt2uDOnTto2bIlkwyElKMbFgghChs3bsR//vMfJo1b\naWkpZs2ahQMHDuhM4wYAvXr1goODA+sYWq1hw4aYO3cutmzZwiyDmZkZZsyYgR07djDLQEh10Mgb\nIXokKSkJrq6uSElJYbYA/ZMnT9C8eXMmtYlme/HiBdq1a4cbN26gdevWTDKkp6fj8OHD+PLLL5nU\nJ6QcnTYFNW+EAMDUqVNhY2ODVatWsY5CSJWWL1+O/Px87Nq1i3UUlJWVYePGjZg3bx7MzMxYxyF6\nhk6bEkKQkpKCP/74A3PnzmUdhZD3WrJkCX755Rc8e/aMdRQIBAI0bdoUxsbGrKMQUgGNvBGiJ3x8\nfPDZZ59hw4YNrKMQ8kHz589H3bp1sXXrVtZRCGGGTpuCmjei39LT02FnZ4f79++jUaNGaqvL8zwu\nX74MFxcXtdVk4bvvvkPHjh3h4eHBOopOSE9PR/fu3ZGcnKzWf6+EaBI6bUqIntu4cSNmzZql9l+E\n27dvx8KFC1FcXKzWuup28+ZNPH36lHUMndG6dWuMHTsW27ZtY5qD53k8f/68wrarV6/i0qVLjBIR\n8hY1b4TouJSUFISGhmLZsmVqrRsZGYmAgAD8/vvvqFWrllprq1tJSQkMDQ1Zx9Apa9aswf79+5GZ\nmcksg1QqRa9evVBSUqLYlp+fj7FjxyI0NJRZLkLotCkhOs7b2xuWlpZYt26d2mo+fPgQzs7OOHLk\nCAYMGKC2uqzcvHkTjRs3RosWLVhH0SkLFiyAoaEhtm/fzixDv3794OPjg6lTpyq2SaVSzJw5E9HR\n0WjQoAGzbES30TVvoOaN6KekpCT0798fycnJEAqFaqn55s0b9OnTB9OmTcPixYvVUpPopqdPn6Jz\n585ISEhgtuJBZGQkfH19kZSUBCMjI8V2nudpaTeiUhrfvEmlUsTFxUEkEoHjONjb22PgwIHV3j8k\nJARmZmYf3IeaN6KPxo8fD3t7e6xYsUJtNVNTU7F3716IxWL65UY+2fLly/Hq1Svs2bOHSf3yNU+/\n+OILeHt7M8lA9JNGN28cx8HPzw8XLlxQbPPy8oJYLIaFhcW/7h8eHg4vLy+EhITAzc3tva+j5o3o\nm5s3b8LDwwMPHjxAvXr1WMchpEays7PRoUMHxMbGVut3gipER0dj+vTpuHv37nuv38zKykJmZia6\ndOmi5nREV2n03aZisRh+fn4Vtvn6+v7rSEFqair8/PyQmpoKkUikyoiEaKUvv/wSK1asoMaNaLXG\njRtjzpw5TOcn7N+/P7755huUlZW99zU3b97E6dOn1ZiK6DPmI28ikQhSqRRt27ZVbJPJZBCJRB/8\nRnmXtbU1JBIJjbwR8v/+/vtvTJ48Gffu3UOdOnVYx9F5a9aswahRo2hxehWRyWRo3749IiMjYWtr\nyzoOIWqhsSNvMplM0ai9y9TUFMDbO9YIIR+H53ksW7YM33zzjVoaN5lMpvIamm7EiBHMFlLXB6am\npli1apVar90kRJMxbd5ycnIAAA0bNqzyeY7j1BmHEJ0QGhqKgoICTJ48WeW1nj17BkdHR1y7dk3l\ntTRZjx490KRJE9YxdNqcOXNw9+5dREZGso5SbTt37sTZs2dZxyA6iPnIGyFEeYqKirBy5UoEBATA\nwEC1394ymQweHh6YNm0anJ2dVVqLkNq1a2PTpk1YtmxZtS+pYc3Ozg5z5szBokWLUFRUxDoO0SHM\nb1gghCjP/v37YW1tjUGDBqm0zps3bzBs2DD0798fa9euVWktQsp5eXnB0NAQR48eZZojODhYcebo\nQ/r27Yv4+HgIhUKVf5gi+sXo31+iO7766ivF311dXeHq6sosCyHKlpeXh2+++QZhYWEqrVNUVISx\nY8fCwsIC27dvp7nciNoIBAJs27YN06ZNw+jRo5ndjBMWFoaYmBhs3br1X18rEomwfv16NaQi2i4q\nKgpRUVHVei3Tu03Lb1aQyWSVrnszMDAAx3EV7kJ9H7rblBDA398fWVlZ+OGHH1Ra5+nTp9i8eTP+\n+9//6vyapdU1b948LF68GFZWVqyj6AVPT0/07t2b2Q0MT548QZcuXXDjxg20atWqRseQy+Xvvd6b\nEECD7zY1NTWFpaVlpRsTOI6DqalptRo3Qghw//59HDx4EJs2bVJ5rc8++ww7d+6kxu0d0dHRePPm\nDesYeuO///0vAgIC8OTJEyb1mzdvDj8/P3z55Zc12j8zMxMuLi4VFrwn5GMwPwk/aNAgxMTEVNgm\nlUrh7u7OKBEh2mfx4sXw9/dHs2bNWEfRSyUlJRXWvSSqZW1tjVmzZjGdOmT58uU4d+4cbt269dH7\nmpub459//qF/M6TGmDdvYrEYwcHBFbZJJBKIxWLF1zKZDFZWVggMDHzvceiUKNFXZ8+eRUpKCubP\nn886it7at29fjU+fkZpZtWoVLl68iMuXLzOpLxQKsXbtWuzatatG+9Pk2eRTMF9hAQDi4+MRFBQE\nJycncBwHBweHCtevyWQyWFpaYuvWrZg5cyaAtxdnb968GRzHISQkBJaWlhg0aBDc3d0xZsyYSjXo\nmjeiiwoLC2Fra4vvv/8eQ4YMUfrxeZ7HiRMnMHLkSLoxgWic3377Ddu2bUNMTAwMDQ3VXr+kpAQ8\nzyvlEoLc3FyMGTMGGzduRK9evZSQjmg7jV6YXl2oeSO6aMuWLbh27RpOnDih9GOXlZVh3rx5iI+P\nR2RkJOrWrav0GoR8Cp7n0a9fP0ydOhWzZs1iHeeT8DyPoKAgLFmyBL6+vli3bh3rSIQxat5AzRvR\nPenp6bC3t8c///wDS0tLpR67uLgY06dPx8OHD3H27Fm6K45orBs3bmDIkCFITExE48aNWcf5ZDKZ\nDGlpaejWrRvrKIQxat5AzRvRLTzPY/jw4ejVqxdWr16t1GMXFBRg/PjxKC4uRkhICExMTJR6fEKU\nbcmSJXjx4gV+/PFH1lEIURqNnSqEEFIzISEhePjwIZYtW6b0Yy9cuBB169bFiRMnqHGrpnHjxuHl\ny5esY+itDRs2IDo6GuHh4Uxz5Ofnq+S4GRkZ8Pb2pgEIokAjb4RomdzcXHTu3BkhISHo3bu30o+f\nnZ0NMzMzJheAa6uwsDC4urrS3HcMnTt3DgsWLEBCQgKTDx08z6N37974+uuvlb48XWFhIWJiYuDi\n4qLU4xLNRqdNQc0b0R2+vr4wNDTEnj17WEchRKNMmDABFhYW2Lx5M5P6Z86cwaJFi3Dr1i213ODD\n8zzdBa7DqHkDNW9EN/z111+YOHEiEhMTIRQKWcchRKM8e/YMXbt2RVhYGLML/seNG4f27dtj48aN\nKq3D8zz69OmD4cOHY8GCBahXr55K6xH1o2veCNEBr1+/xvTp07Fr1y6lNW7//PMPysrKlHIsQlhr\n1qwZtmzZgs8//xxFRUVMMuzYsQMSiQS3b99WaR2BQIDDhw/jxo0bcHR0pO9jPUMjb4Roiblz5+Ll\ny5f46aefPvlYPM9j586d2Lp1K65du0arAxCdUX4ntp2dHb7++msmGfbu3YtffvkFf//9t1pOa8pk\nMpiamqq8DlEvOm0Kat6Idrtw4QJmzpyJhISET/4hXVRUhLlz5+Lq1as4c+YM2rZtq5yQeqq4uBij\nR4/G6dOnWUch/+/p06fo3r07Tp06hZ49e6q9fllZGWJjY9GjRw+11y73119/oUOHDmjatCmzDOTT\n0GlTQrRYbm4uZsyYgYMHD35y45aZmQk3NzdkZ2fj6tWr1LgpQXFxMSIiIljHIO/47LPP8P3332Pa\ntGl48+aN2usbGBgwbdwA4OLFi3j06BHTDER1aOSNEA03depUCIVCfP/99598rHHjxqFTp05Yt24d\nDAzos5syyOVytGjRguZ500CTJk1CkyZNsGPHDtZRNAbdoao96LQpqHkj2unIkSNYt24d4uPjlXI3\nWVFREWrXrq2EZKRccXExoqKi4O7uzjoK+R85OTno1q0bJBIJhg4dyjoOc3FxcZg6dSoWLVqEyZMn\n0x2qGo6aN1DzRrTP/fv30adPH4SFhaF79+6s4xCilS5dugQvLy/ExcWhRYsWzHJowgcnnucRROwH\nDQAAFwhJREFUFRWFHTt2oGXLlkoZzSeqQ80bqHkj2qWgoADOzs7w9fXF7NmzWcchRKtt3LgRf/75\nJyIjI2FkZKT2+nFxcfDx8cGVK1dQp04dtdevCp0+1Xx0wwIhWmbJkiXo0KED/Pz8arT/+fPnMX36\ndCWnIkQ7rVy5EnXq1MFXX33FpL69vT0sLS2xdOlSJvWrUlXj5uHhgfv37zNIQz4WjbwRomGOHTuG\nVatWQSqVomHDhh+1b2lpKb766iscOnQIv/32G/r166eilIRol8zMTNjb2+PQoUMYPHiw2uvn5eXB\n3t4eW7Zswbhx49Revzo4jkObNm1oXWMNQSNvhGiJW7duYe7cuTh27NhHN27p6ekYOHAgrly5gri4\nOGrc1OTRo0eYMWMG6xjkX5ibm+PXX3/FtGnTwHGc2usLhUIcO3YMc+bMwYMHD9RevzosLS0rNW73\n79/H0KFDcfToUeTn5zNKRv4XNW+EaIjs7Gx4enpix44dsLe3/6h9b968CUdHR3h4eODChQswNzdX\nUUryv8zMzODt7c06BqkGV1dXrF69Gp6enkymdnFwcMC6deswf/58tdeuqZYtW2LKlCn44YcfMHPm\nTNZxyP+j06aEaIDi4mIMGTIETk5OEIvFNdo/KSkJXbt2VUE6QnQHz/OYNWsWsrOzERoaqvb5Dnme\nR25uLkQikVrrKkNpaWmlkbnHjx+jSZMmzO+k1UV0tymoeSOabd68eUhNTcWpU6foehNCVKyoqAhu\nbm4YOHAg1q9fzzqOVlu6dCl69uypsdfxaTNq3kDNG9Fcu3fvxq5du3D9+nUIhULWcQjRC5mZmejR\nowc2b96MSZMmsY6jc06ePAknJyc0b96cdRStRTcsEKKhQkJCsGnTJvzxxx/VatyuX7+OgQMH4tWr\nV2pIR4juMjc3x7lz57B48WKEh4ezjqNTeJ7H77//DltbW/To0QMFBQWsI+kcat4IYSQ6Ohpz5szB\nmTNnYGFh8cHXFhQUYMWKFfD09ISvry/q16+vppTk39y+fVuj5u8i1de5c2eEhIRg0qRJiI+PZ5KB\n53l8++23kMlkTOqrgkAgwI8//ojMzEzs2rWr0sTEhYWFyMrKYpRON1DzRggDt27dwrhx43DkyBHY\n2dl98LWXL1+GnZ0dOI5DQkICvLy81JSSVEd2djZiY2NZxyA11LdvX+zfvx/Dhg1jMoWIQCDAo0eP\nMHz4cLx580bt9VWpVq1a6NmzZ6Xtt2/fpjtXPxE1b4SoWXJyMoYOHYqdO3di4MCBH3ztgwcPMH78\neGzYsAHBwcFo2rSpmlKS6iopKWGy5BJRnlGjRmHNmjVwd3fHo0eP1F5/27ZtaNu2LcaPH4/i4mK1\n11c3BwcHnDp1qtL2ixcvYtOmTbhy5QqKiooYJNMedMMCIWqUnJwMNzc3rF+/vtrLVxUUFGjMeoik\nsuzsbHAchx49erCOQj7Rtm3bsH//fkRFRal9Efvi4mKMHDkSjRo1wuHDh9U+hYkmuHHjBn7++WdE\nRUVh9OjRWL16NetITNHdpqDmjbD34MEDuLm54csvv6RTBoRoqICAAEgkEiYN3Js3b+Du7o4RI0Zg\nxYoVaq2taXier7T+6vbt29G7d+8qT8Xqog/1LTTWT4gapKSkwM3NDWvWrKmycXv58iUiIiIwcuRI\nBukIIeWWLVsGnucxYMAAXLx4Ua0NnImJCc6cOYPCwkK11dRU/9u4AYCTk1OV70dYWBiaN28OGxsb\nvRmx1I//SkIYio+PR9++fbF27VrMmjWrwnNlZWU4fPgwOnTogDNnztDoMCEaYPny5fDx8YGLiwvu\n3bun1tpmZmZo1qyZWmtqCxcXF7Rs2bLS9nPnzsHT0xONGjVCeno6g2TqR6dNCVGhyMhITJgwAfv2\n7cPo0aMrPHf9+nUsWLAAAoEAO3fupGumCNEwhw4dwsqVK3Hy5Em9OVWnzTIzM9G4ceMKq9TwPI8x\nY8bgt99+07prh2mSXkIYOHbsGCZMmIDg4OBKjZtEIsHo0aMxd+5cXLlyhRo3LRYZGYmtW7eyjkFU\n4IsvvsCBAwcwbNgw/PHHH8xylJaW0kS31WBubl5pecGysjLMmjWrUuP25s0bLFu2DD///DMSEhLU\nGVMpaOSNECXjeR4bN27E/v37cfbs2SoXi8/NzYWxsTFMTEwYJCTK9PjxY2RnZ6Nbt26soxAVuXr1\nKkaNGoXVq1dj3rx5VV6PpUo///wzJBIJTpw4gUaNGqm1tq6Sy+XYvXs3EhIS8PLlS5w5c6bC8wUF\nBcjJyWG6vBfdbQpq3oh6vHr1Cp9//jkeP36M0NBQWtePEB2RmpqKkSNHwtHREXv27IGxsbHaapeV\nlWHlypU4ceIEzp07BysrK7XV1lfx8fHYsGEDjh8/XmG7XC7Hixcv0KZNG5XfHEGnTQlRA47j0Lt3\nbwiFQkRFRaFevXr4+uuvafZ9QnSAhYUFLl++DLlcDldXVzx58kRttQ0MDCAWi7Fo0SK4uLggIiJC\nbbX1lZ2dXaXGDQCkUin69u2LBg0aYMGCBQySvUXNGyFKEBQUBGdnZ/j4+GDbtm0Qi8WwtrZGcnIy\nneYgREfUr18fx44dw/Dhw+Hg4ICzZ8+qtf7s2bPx66+/YsqUKQgKClJrbfKWq6srHj16hGfPnmH5\n8uWVnj948CD+85//VNoul8uVuvwZnTYl5BO8evUK8+fPx+XLlxEYGIjIyEjs3r0bw4YNw+rVq9Gu\nXTvWEQkhKvDXX39hypQpGDlyJMRisVrvZHz8+DGMjY3RuHFjtdUk1VNSUoLXr19DKBRW2L5v3z4s\nXrwYIpEI/v7+mD9/foXni4uLYWRkVOF6SjptSogKXLlyBfb29hAIBJBKpejWrRuys7Nx7do1HD58\nmBo3PRESEoLAwEDWMYia9e3bFzdu3MCTJ0/Qo0cPxMfHq612ixYtqHHTUEZGRpUaNwDw8/PD69ev\nce3atUqzDwDA+vXrERAQUO06NPJGyEeSy+VYuXIljh8/jp07d2Ls2LGsIxGGxGIxcnJyIBaLWUch\nDPA8j59++gnLly/H559/jnXr1tFd5KRGSktLK0x1QiNvhCgBz/M4evQo2rRpg9TUVCQmJlLjRlBS\nUgIjI1ppUF8JBAJ4e3sjISEB6enp6NKlC8LCwtSeo6ysDFOnTkV4eLjaaxPl+N856j6ERt4IqYbQ\n0FAsWrQIT58+hbOzM7799luaWJcAeLtubVlZGZ0mJwCAM2fOYOHChejUqRMCAgLQsWNHtdU+ffo0\nFixYACcnJ3z77bdVLiVFtAeNvBFSQ9evX0ezZs3g5eUFW1tb3L9/H3///Tc1bkTBysqKGjeiMGzY\nMNy5cwf9+/eHi4sLFixYgKysLLXUHj58OO7cuQMbGxt0794dmzZtwuvXr9VSm6gXNW+EVCEjIwNz\n586Fh4cHevfujWfPnuGPP/6ApaUl62iEEA1nbGyMpUuXIikpCTzPo2PHjli6dCkyMzNVXrtu3bpY\nv349rl27hps3b+Lo0aMqr0nUj5o3ovdKSkoQEREBmUyGu3fvws/PD926dUO9evVw7949/P7772jS\npAnrmIQQLdOkSRPs2rULCQkJKCwshI2NDRYvXozU1FSV17a2tkZQUBBmzJih8lpE/eiaN6KXCgsL\ncfHiRYSEhODkyZMQiURo3LgxHjx4AF9fX8yfP58aNkKIUj158gTfffcdfvjhB7i4uGDhwoVwdXVV\n+1qphYWFkMvl9DNOw9E1b4S8Y/fu3WjSpAnWrFmDjIwM1KlTByYmJvDx8UFaWho2bNhAP9RIte3Z\nswcnT55kHYNogebNm2Pr1q1IS0uDh4cH5s6dCxsbG2zatAkZGRlqyxEXF4d27dphwoQJiIiIQFlZ\nmdpqE+XQiJE3qVSKuLg4iEQicBwHe3t7DBw4UKn70cib/qlqCoesrCwcOnQIx48fB8dxmDhxIry9\nvWFnZ6f2T79EN9y5cwf16tVDmzZtWEchWobneVy7dg0//vgjgoODYWdnh6lTp2L48OEQiUQqrZ2b\nm4tffvkFgYGBePPmDaZMmQJvb29YWFiotC6pvg/1LcybN47j4OfnhwsXLii2eXl5QSwWf/Af0cfu\nR82b7nv8+DGuX7+O6OhoREdHo1WrVjh9+jTu3buHkydP4uTJk0hMTMSQIUMwefJkDB06FLVq1WId\nmxBCUFBQgNOnT+O3335DZGQk7O3t4enpCU9PT5U2VDzPIyYmBkePHsXQoUPh7u6uslrk42h08+br\n64shQ4ZUWC4iIiIC+/fvx7Fjx5S2HzVvuis1NRUuLi4oKiqCk5MTunXrBmNjY6SlpSE6OhpFRUUY\nMWIEPD094erqCmNjY9aRCSHkvfLz8xEeHo6TJ0/i9OnTEAqFcHNzw4ABA+Dq6gpzc3O15gkPD0fX\nrl3RtGlTtdbVdxrdvIlEIkilUrRt21axTSaTQSQSffA8/MfuR82bdioqKsLdu3dx+/ZtpKSkYO3a\ntRWef/36NWJjYxEeHo6UlBTExMQgNzcX/fv3V/yws7GxoVOihBCtVFZWhlu3buHixYu4ePEiLl26\nhGbNmqFHjx5wcnKCo6Mjunfvjjp16qikPs/zmDhxIs6fP4/mzZujV69eikenTp3oZ6sKaWzzVt5s\nyWQyNGzYsMJzBgYG4DiuQnP2KfvpevMWFRUFV1dX1jGUgud5eHp64u7du8jIyICFhQU6deqEZs2a\noV+/frh//z6SkpJw69YtPHjwAJ07d4aTk5Pi0alTJxgYaNe9OLr0/ukbeu+0m7a9f6Wlpbh16xZi\nYmIQGxuLmJgY3L17Fx06dECXLl1gY2OjeFhZWSlt6baSkhLcunULV69exdWrV3Hnzh3ExMQw/1mr\nbe/fx/hQ38J0Qb6cnBwAqNSAlXtf81bT/XSZpv8Djo6ORmpqKh4/flzhce7cOTRt2hT5+fnIzMxE\neno6Hj58CJFIhK5du6Jly5bIyMjAmTNn0Lp1a2RkZMDGxgaDBw/G4sWL0aVLF504Darp7x+pWnJy\nMhYvXoz4+HjWUUgNadv3nqGhIbp3747u3bvDx8cHwNvTrAkJCUhMTERSUhIOHDiApKQkPHnyBG3a\ntKnwaNu2Ldq0aYNWrVrB3Ny82iN2RkZGsLOzg52dHebMmfPe1yUnJ8PZ2RlWVlawtLRU/NmxY0f0\n6dNHKf8P3qVt75+yMG3eZDKZWvcj1cfzPAoLC1GrVq0qF8s9duwYHj16BLlcDrlcjpycHDx//hwB\nAQFo0KAB5HI58vLykJeXB7lcjh07dqCwsBDGxsYQCAQoLi5GYWEhnJ2d8fz5cxQXF8Pc3BytWrVS\n/HB592FhYaETTRrRLQ8ePIBcLmcdg+i5unXromfPnujZs2eF7fn5+UhNTUVaWpricebMGaSlpSEj\nIwNZWVmoU6cOmjZtqniYm5ujSZMmEAqF7300bNgQJiYmVY66WVtbIykpCSkpKUhJSQHHcbh06RKk\nUmmVzVtKSgq2bt0KkUgEMzMziEQiiEQitG7dGo6Ojir7f6btmDZv6rZx40YAbxuT8uviOnfuDBMT\nE8XQZPmfCQkJePXqlWJb+XZbW1vUr1+/wmt5nkd8fHyl1/M8Dzs7O9SrV6/S6+Pi4vDy5UsAqHCN\nnr29PRo0aFApz9WrVyGXy1FaWoqysjLFn/369YNQKER8fDwOHTqkeP3p06fx4sULlJaWoqSkRPHn\nkCFDIBQKK2wrKSlBUFAQnj9/rtheWloKAwMDDB06FMbGxigoKFA88vPzkZGRgaKiIsVry48THR0N\nU1NTxTd4+Td7586dFX9/94dE+d8bNGhA104QrZOeng6hUMg6BiFVqlu3Ljp16oROnTpV+TzP85DL\n5cjMzERWVhaysrKQmZmJ58+f4+nTp0hKSlJ8CH/3IZfLUVBQgFq1asHExAR169at9DAxMUGdOnVQ\nq1YtGBkZ4eXLl5gxYwaMjIxQq1YtxaOwsBCPHz8Gx3EoLCxEYWEh8vPzYWZmhrFjx0IgEMDAwEDx\nJ8dx2Lt3L4yNjWFsbIzXr1/jyJEjsLCwwLRp0yq9/tmzZzh//ryirqGhIQQCAczNzTFgwIBKv3de\nvHiB69evVziGoaEhRCIR7O3tK7xWIBBAJpPh9u3bim3lDa1QKIStra3ideXy8vKQlJSk2Fb+Z8OG\nDd/7Pr3vzWMmLi6OFwgEVT4nEAj4iIgIpe3XrVs3HgA96EEPetCDHvSgh8Y/unXr9t7+ienIW/ki\n33K5vMrr1963CHhN9rtx48anRCWEEEII0QhMbxMxNTWFpaUlOI6rsJ3jOJiamr73poOa7kcIIYQQ\nou2Yz6cwaNAgxMTEVNgmlUr/dZbnmu5HCCGEEKLNmDdvYrEYwcHBFbZJJBKIxWLF1zKZDFZWVggM\nDPyo/QghhBBCdA3zFRYAID4+HkFBQXBycgLHcXBwcICbm5vieZlMBktLS2zduhUzZ86s9n6EEKIq\nUqkUcXFxEIlE4DgO9vb2GDhwIOtYpBpCQ0PBcZxiKgtfX1+MGTOGdSxSAzKZDP7+/ti3bx/rKGql\nEc0bIYRoE47j4OfnhwsXLii2eXl5QSwWq3QRcfLpQkNDYWlpCTs7OwBvp25wcHDAihUrFJPeEu3h\n6+uL3NzcD66FrouYnzYlqieTyeDn58c6BvkIoaGhCAgIgJ+fHwYPHozQ0FDWkcg7xGJxpe8pX19f\nrFixglEiUl0cxykaN+DtfFwrVqyAr68vw1SkJjiOQ25url7OEUojb3pAXz+ZaCsaGdB8IpEIUqm0\nwp3t5WsuvzvpNtEsMpkMgwYNQkRERIXJlTmOg7W1tV4urajNyq+DDwsL07vfbzTypuP0+ZOJtqKR\nAc0mk8kUjdq7TE1NAQAPHz5kkIpUh6mpKTiOQ2pqKuso5BNFRERg0KBBrGMwQ82bjouIiIC7uzto\ngFU7yGQyBAUFIS8vr8L28gvhqTFgLycnBwCqnCAcQKX5J4lmycnJQffu3StsCw8Ph5mZGY26aRGO\n42BhYaG3v9uoedNh+v7JRBvRyIDmk8lkrCMQJdu/fz9WrlzJOgapptDQUL2/hESvFqbXNxzHYeDA\ngXr7yURblY/svItGBghRDYlEgsaNG2Pp0qWso5BqoA9Pb1HzpqPok4luoZEBQpSP4zhIJBLExsay\njkKqKTg4uMLvNn29nptOm+og+mSiW2hkQLNYWloCAORy+QefJ5rP398fkZGRrGOQaoqPj4ejo2OF\nbfp6ZolG3jTYx1z43KhRI8Wt7/TJRDPU9P3732PQyIBmMTU1haWlJTiOq3DhO8dxMDU1pVPbWsLP\nzw9bt259740nRPPExsYiJSUFQUFBim1SqRQcx8Hf3x9OTk56s1IGNW8aKjU1Ff7+/tV+fY8ePbB0\n6VJIpVL6ZKIBPvb9c3JywrJlyyptp5EBzTRo0CDExMRUaN6kUinc3d0ZpiLVFRgYCH9//wqNdkRE\nBCwtLWmFDA1W1aVAAQEBiI2NxZYtWxgkYocm6dUxgYGBSElJqbCt/JPJ2LFj9eqTibbz8/Or9AuG\naIa8vDyMGzeuwvJYgwcPhkQiofdLw4WEhCA3NxcODg6KbTk5OQgJCdG79TF1wYoVK5Camqp3k/RS\n86YHyj+ZvDvUTDRbYGAg3N3daWRAg8XHxyMoKAhOTk7gOA4ODg5wc3NjHYt8QFWTK5ezsrJCcnKy\nmhORmkpNTYVYLMaxY8eQl5cHHx8f+Pr6VpjgXJdR86YH9PWTibaikQFCCCEfQs2bDtP3TybaiEYG\nCCGE/Btq3gghhBBCtAjN80YIIYQQokWoeSOEEEII0SLUvBFCCCGEaBFq3gghhBBCtAg1b4QQQggh\nWoSaN0IIIYQQLULNGyGEEEKIFqHmjRBCCCFEi/wfOXX0K7o9DncAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Contrary to what it sounds like, kurtosis is not a disease. Rather, it's a measure of the \"peakedness\" of a distribution. This is demonstrated with several different distributions below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# next show distributions with different kurtosis\n", "fig, ax = plt.subplots(figsize=(10, 7.5))\n", "x = np.linspace(-5, 5, 1000)\n", "l1, = ax.plot(x, stats.laplace(0, 1).pdf(x), '--k',\n", " label=r'${\\rm Laplace,}\\ K=+3$')\n", "l2, = ax.plot(x, stats.norm(0, 1).pdf(x), '-k',\n", " label=r'${\\rm Gaussian,}\\ K=0$')\n", "l3, = ax.plot(x, stats.cosine(0, 1).pdf(x), '-.k',\n", " label=r'${\\rm Cosine,}\\ K=-0.59$')\n", "l4, = ax.plot(x, stats.uniform(-2, 4).pdf(x), ':k',\n", " label=r'${\\rm Uniform,}\\ K=-1.2$')\n", "\n", "ax.set_xlim(-5, 5)\n", "ax.set_ylim(0, 0.55)\n", "ax.set_xlabel('$x$',fontsize=20)\n", "ax.set_ylabel('$p(x)$',fontsize=20)\n", "plt.xticks(fontsize=20)\n", "plt.yticks(fontsize=20)\n", "\n", "# trick to show multiple legends\n", "leg1 = ax.legend((l1, l2), (l1.get_label(), l2.get_label()), loc=2,fontsize=16)\n", "leg2 = ax.legend((l3, l4), (l3.get_label(), l4.get_label()), loc=1,fontsize=16)\n", "ax.add_artist(leg1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 44, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAHfCAYAAADQseUFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8U2W+P/BPCsii0CRsKjjSpMoiAt0ExQXpgjIKQmm9\n6sy4IE3Rueq9Slv4zQiiI00rrqg0wcHxutGmyKIsbQKIMjpCE1B27QmbKFt7UpCdnt8fTDINadok\nTXKS9vN+vXhpzjnPOd806dPvOc+mkCRJAhERERFFjRi5AyAiIiIi/zCBIyIiIooyTOCIiIiIogwT\nOCIiIqIowwSOiIiIKMowgSMiIiKKMu3lDiDcRo0ahS+//FLuMIiIiIiadccdd2DdunUe2xVtbR44\nhUKB1vyWZ82ahVmzZskdBgWAn1104+cXvfjZRbfW/vl5y1vYhEpEREQUZZjAEREREUUZJnCtzKhR\no+QOgQLEzy668fOLXvzsoltb/fzYB46IiIgoQrEPHBEREVErwQSOiIiIKMq0uXngmqNWq1FbWyt3\nGERhpVKpUFNTI3cYFMVYdxIFJtD6l33g/NxP1Brxe08txe8QUWACzUvYhEpEREQUZZjAEREREUUZ\nJnBEREREUYYJHBEREVGUYQJHREREFGWYwJFXdrsd+fn5iImJQXx8PIqLi2G320NyLZvNhoKCAhQX\nF4fk/IGwWCzIyspCTEwMpk6dCpvN5rZfq9VCrVbjlVdekSlCT6Ioori4GEajEQUFBSgoKJA7JCIi\nCgFOI+Ln/rYoPj4eubm5eO6550J6HaPRiLKyMlRUVIT0Ov4oKipCWVkZNm7c6LbdZrOhqqoKjz/+\nuEyRNS4/Px96vd71Ojk5GTqdDlOmTGmyHL/31FL8DnknCAKKioqg1WqhVCoBXPzdlCQJdrsdmZmZ\nAZ9bp9NBoVBg/vz5wQrXZxaLBfPnz0d5eTl0Oh1ycnKQkJDg2q/ValFbW4sZM2aE/O+HP4qLi6HR\naFxzrzVVP5pMJgiCgKysLKhUKhiNRkyaNAlxcXFu51MqlRBFEUqlstn69lKB5iWcyJciRsNfiEhR\nWVmJtLQ0t20WiwVqtVqW5M1ms0EQBK8Vfnl5Oa677jpXbBqNBpWVlX5XKEQUHCaTCQaDASaTCd26\ndXNtt1gs0Ol0LX5Knp2dje7du7c0zICkpqaiqqoKe/bswbvvvuu2z2azYfr06RF5kztmzBiMHj0a\nAFBQUIDy8nKvdWpNTY2rNUOpVGLBggVuf6t0Oh3GjBmDiRMnArj4eWg0GqSmpob8vbAJlagJFosF\n6enprtdGoxHJyclud5mRxGw2u1WY1dXVuOmmm2SMiKjtEgQBOTk5HskbcDH5SUtLa/FTy9TUVAwb\nNqxF52gJbze5ACIueQMu1uHO5A0A0tPTUVJS4vV4hUIBURQhCAJqampciRpwscuK0Wh023b//fe7\ntYKEEp/AUVBYrVZX/7jKykrodDpXkmM2m1FQUACNRoP09HSo1Wps3LgRWq22ySdDTZ3TqaCgACkp\nKQAASZIwadIkABd/sQoLC5GSkoKNGzciPT3d7zsiq9UKABg9erTrEXpVVZVf5wi3fv36uf7farUi\nJiYmopouiNoSnU6H9PR0j+TNKSsrC4IgBHx+h8OBjRs3onv37rLdVFosFkyfPt312mg0Ijs7G7Gx\nsbLE0xRnnd6QSqWC2Wxusly3bt0a/Qw3bdrksS0uLq7R7aHABI6CIicnBzNmzMDEiRORmJiIpKQk\nV/+CtLQ0TJ8+Hfn5+SgtLQUAZGZmIjs7G6IoYtq0aX6fEwCSkpLw3nvvue4+1Wo14uPjMWzYMCQl\nJcFisaBfv37IzMxEfHw8qqqq/KpUzGYzEhMTYbPZcOzYMdjtdhiNRr+aI3Nzc306Tq/X+xSbL3fr\nDocDpaWlKCsrg8Fg8On6RBR8Foulyd/B1NRUaDQaAP95muN8LQiCW91YXFyMxMREiKLouqFVKpUw\nGAwQRREVFRVuN8s6nQ7AxZvfS2+Wg3GDC0TfTW5NTQ3UarXbNmefxLq6Oq+JttFodJVr+Llcei4n\nURSDFXLTpDamubfsz49k5syZEgCPfzNnzpT1eG/7A6XVaqXi4uImj3E4HG6vVSqVZLfbXa/Lysqk\n9PR0t2PMZrOkUqlcrysrK92OaeqcVVVVbmUlSXLtKysrk7Rardu+rKwsyWAwNPkeLpWWliYlJye7\nzpufny8lJSX5dY6Wys/Pl3Q6netfVlaWlJ6e7rYtPz9fEkWx0fJJSUk+ve82WBVQkPn7HWpYvzVW\nZ82cOdPr9nCWC1Rtba2kUCik8vJyn45PSkpyq/PMZrOk0+kkSZKkkpISyWQyufaZTCbJarW6jmtY\nb5pMJkmr1brqLVEUJYVC4XYtjUbjVj9rtVqvdUhT9Hq9lJSUJFmtVqmyslJSqVR+17MN67Km/gUS\n36XKyso8/m44P6eGP4+GBEHwiLfhe1QoFG6xlZSUSAqFwuPvV1MCzUvaXK0dzASurfCWwDWsUCTp\nYgJmMBgkk8nkUwJXXV3tVrFcmsA1dc6SkhKvyZSzUjGbza5/RUVFksVi8edtSyqVyq2MIAiSQqFw\nVZxysFqtHj/3hmpra91eGwwGj8q7MfzeU0vxO+RJoVBIRqOx2eMqKysbrc+cyYHZbJa0Wq1kMBik\n6upqSZIkV9Jwab1ZWVnpcQPbMKEI1g2uJEXGTa4kXaz3RFH0+s/JmWQ25Pw75GvC5UyQnQwGg1RU\nVOR6rdfrfapzGwo0L2ETKgWsYd+N9PR0TJ061fWY3pdmRkEQoFKpXK8VCoXb/qbOqdVqvfYd0Wq1\nAODWJBBI/zdRFJGcnOzaFhcXh7S0NMyZM8fVFNycYDehNsVsNiMjIwOiKLqaAqR/N7k21TxARKGR\nlpaGiooKr535HQ4HNm3aBJvN1mhznFKpRFVVFVJTU1FSUoKSkhLodDokJia6Bgo0xtks2BhBEKBU\nKt3Kp6SkuOpNf1RVVcFkMrn63up0OhQVFcFms4WtT155eTkqKyubPEapVKKwsBBqtdqjedP5urH6\nURRFVxnn/tjYWLe/PVOmTIHFYkF5eTmAi39/AvlZBoIJHDVLuvik1m2bIAiorKzEtGnTYLVaUVVV\n5TE6R5Ikt+HZlyZcBoPBbbROw2v4ck6NRgOLxeJKzux2O0RRRGZmJubMmQO73e4a7u1wOCAIAhIS\nEiAIAqxWq2vAQ2PMZjM0Go3HL3VeXh4yMjLgcDh8SrjCOTdTSkoKdDqdW8yVlZXIyspi8kYkg5KS\nEiQlJXmtLzZt2oTk5GSIoujWv9dJFEVoNBpXnees6woKCmAwGLz2H25KMG5wgci5yc3MzPR5Hr3E\nxESP5LampsZtpoGGFAoF8vLy3OpPQRA8ErSGP7/8/Hzk5+f7FE9LMYEjr+x2O+bPnw+73e72y7hx\n40aYzWbX6M/ExERkZ2e7JkdUKpUoKSmBXq9Hdna2q5yzIlIqlbBarcjIyHDdmdpsNhQVFcFiseCV\nV17Bc8891+w5LRYL8vPzIQgC1Go1lEql6xfJYrFgzpw5rhgBuH7JTSYTCgoKUF9f7/GeHQ4HXn75\nZRiNRnTv3h0LFixwu3suKyuDQqFAWloaDAZDRE0nEhsbi5ycHNdqFseOHUN8fDzmzJkjc2REbVNc\nXByMRiOysrJQVlbmloA4bzhjY2ORmZmJ/Px8t5tOk8mErKws9OvXD2VlZW43q/fff3+TT+Aa47xB\nDsYNLhCdN7nAxcFxDR8smM1m14AP4GKCZrPZkJmZidjYWI859kwmk9uDh/j4eJSVlSEhIQGiKMJi\nsYRtGhGuxODnfgpMeXk5SkpKImaVhYaVYTRpbiLfQPF7Ty3F75B3drsder3ebSWGSyd7dTgcrpvO\nmpoaOBwO1xRARqMRADxGQtpsNuTn56Oqqgp6vR5JSUnIz893JRFTpkzByy+/jFdeeQU5OTnIy8tD\nXFyc27WcnHVKUVGR1xtcZ5wNb3Lz8/PdbnJ1Oh0WLFiAxMTEiLvJdXI+GHB242kYv9FohMlkwurV\nqwFcfL8GgwFKpdI1r2bDliGj0ehagaG6uhozZszwu8Uj0LyECZyf+ykwztnIIyWBa2rm7baI33tq\nKX6HWo9ovcGNVoHmJVyJgULOZrPBYDCgqqoKCxYskDsc2O1211xLRETkLmzzmFGL8Amcn/uJWiN+\n76ml+B1qHZx98yKx6bO1ivomVOeoQ7VaDUEQkJiY2OwjXEEQXIsBO2fpNxgMTc4qzQSOyBO/99RS\n/A4RBSbQvCQiRqEKgoCCggK3/lHZ2dnQaDSuUTLeWCwW12gcpVKJBQsWsO2eiIiIWrWI6AOn1+s9\n5oLR6XTNzqWiUChgNpshiiIEQUBNTY3b6BAiIiKi1igimlDVajWsVqtrNmfgPzMgexvKDFxsqxcE\nwa8nbmxCJfLE7z21FL9DRIGJ2lGooii6krWGnHPl7NmzR4aoiIiIiCKX7H3gnMuHeJv4ThAEtydz\nje13DnmuqamBWq3m/F5ERETUqsmewLVkvhnnU7uGCZtzmSUmcURERNRayd6E2hKxsbGYMmWK2zZf\nBj8QERERRbOoTuAaExcXB0EQUFdX5/WYWbNmuf6tW7cufMFFMUEQkJubi+LiYtc/m80Gq9WK8vJy\nWWPT6XQeo5jDyWKxICsrCzExMZg6dSpsNpvbfq1WC7VajVdeeSWkcRQXF6O8vBxGo9G1diIRycNu\ntyM/Px8xMTFITk5GcXGxa5/NZkN2djbUajWmT5/u13kbq+9MJhOKi4uRnZ3tUf9EikipJwNhMplQ\nUFDg07HOv4/Z2dlun7k/1q1b55aneCXJrLa2VlIoFJLD4fDYp1AoJLvd7rWsXq/3ej6bzdZomebe\ncgT8SCJOWVmZlJ6e7vEZmc1mSavVSkajUabI/hOHt887XPR6vZScnOyx3Wq1huXnk5eXJ1ksFtfr\n/Px8yWQy+Vye3/uWKSsrk3bs2CF3GLLid6hxWq1WKi4ubnRfUVGR3+e7tL6rra2VtFqtJEmSZDKZ\nJEEQAgs0DOSuJ/1lNpuloqIiKT09XcrNzW32+Pz8fLfXSUlJPn3GgeYlsj+BUyqV0Gg0EATBbbsg\nCFAqlV4HMDgn/710lKpzUATXugwOQRCQk5MDk8nkMdAkNTUViYmJsk8dkJqaimHDhskaQ2VlJdLS\n0ty2OSeYfvzxx0N+faPRiNGjR7tep6eno6SkJOTXpYv9eLOysvDyyy/LHQq1AZfWd5s2bXL9vcvM\nzGx28ns5yV1P+is1NRXTpk3z6e+cw+FA9+7d3bbpdDrMmTMnZPHJnsABQFpaGjZu3Oi2zWq1Ij09\n3WsZjUaDkpISjwTPbDYjKSnJ66hW8o9Op0N6errXn6dOp/P7nJcOXGnJQBaHwwGz2Sx7s4HFYnH7\nvhqNRiQnJ4dlPUGr1eqxTaVSwWw2h/zaBHTq1Alz5szB7t275Q6FWrlIqe8CJWc9GWrHjh1Dfn6+\n20MllUrVor9vzZF9FCpwcSWGrKwstwEJBoMBBoPB9VoURSQlJaGgoMB1nFqtht1ud91xiKIIg8GA\nBQsWhPcNtGIWi8Xtc7hUamqq29NOq9UKu90O4OLdlk6nc/1yWiwW5OXlQaFQYNOmTXA4HHj88cdR\nXl4OURRdSWJxcTESExMhiqLbORrbrlQqYTAYIIqiaym2pmIwm80oKCiARqNxJZ+VlZXQarUeA2J8\n5UygRo8eDUEQkJWVhaqqqoDOFQjn9DkNOedRrKur481MiHXq1AmTJ0+GXq+HJElQKBRyh0RRyJe6\nybnet7O+s9lsMJlMEATBVT+mpqZCFEUYjUZX3SwIAqZNm+Z2neTkZKSnp2PRokVIT0+HRqNBXl4e\ntFqt6/pWqxVKpRJpaWmwWq2oqalBZWUlSktL/X5/cteToabRaDwWJKisrGzyQVRLRUQCFxsbC71e\nj4KCAqSkpLiaRy99ulZbW+tWOWZmZqK8vBwmkwnHjh2DKIowmUxNzhtHvnPeOVyaHFyq4SP7nJwc\nzJgxAxMnTkRiYiKSkpJczdqpqamYMWOG65FybGwsysrKEBPznwfBzkrHubqG8/O+dHvDa+t0Ouj1\nep9iSEtLw/Tp05Gfnw+tVot+/fohOTkZKpUq4ATObDYjMTERNpsNx44dg91uh9Fo9Pl8vg7A0Ov1\niI2N9dguiqLr/Tk5P7OamhomcGHQo0cPKBQKHDlyBL169ZI7HIpCvtRNl9Z3CQkJyMrKckvQnOda\ns2aN63ffYrEgNzcX8+fPR1pamuscRUVFriQvISEBM2bMaPT6ZrPZNTVXWVkZysvL/Z6qq6X1JNDy\nujLUGjZti6KIsrKyRltIgiUiEjjg4penqceoSqXS448UIO98b5F8px2MfmnOpziN/dyNRiOqq6tR\nVVUFlUqF6dOnIyEhwa3ScCZ2e/bscSXVzf1SOe8+a2pqkJqaiokTJ8LhcKCmpsZte2ZmJhwOR6Pv\n1dcYLn0d6NOqyspKKBQKqFQqJCQkICcnByUlJT5XTPPnz/f7mg05P6eGnJ9Zc8k3BYdCocDHH3+M\nzp07yx1K1HCOrovU/8rBl7rp0vru0tfOrhMN67LU1FSkp6ejqKgI3bp1g0qlgkajQbdu3dz+7nq7\nfsNWFo1G0+jfhOa0tJ4EWl5XAhcTq6b+dgcr8cvOzsaaNWtC+kApYhK4aCR35/1wSEtLQ0VFhUcH\nU+cvXUxMDAwGg6sS6NatG8xmM+x2e0DJQ2pqKkpKSlBSUgKdTofExERYLBav2xvjSwyNJT2Bqqqq\ncnvyq9PpUFRUBJvNFpa+HWq12mu/Qj59C5+77rpL7hCiyqWJUqS9DhaNRoOjR4/6fHxL6yar1dpo\nvadUKrFp0ybXYCdv12lsezBuBOWuJwGgvLwclZWVTR6jVCpRWFjYousUFBSgoKAg5IPrmMBRk0pK\nSpCUlASHw+HTnUl6ejqmTp3qSvD8bZZ0Ppp3NpUWFBTAYDBAo9E0ur1hs0GwYvCH1WqFKIpITk52\nbYuLi0NaWhrmzJnjU1+RljYLJCYmelS6NTU1Ie17QUS+SUxM9JhlAbhYdyQmJvp9vkufHl36WqvV\nNlrviKLoepLW0tYjf8sHo54EWl5XZmZmhrzVrry8HBkZGa5EOZQJKhM4alJcXByMRiNSU1NRVlbm\n1t/NbDa7JQ5WqxVVVVWYOHGia5soipAkyZWYaTQat6dFzv4BzqeZgiC4nrgBwP333w+z2dzo9sae\nwPkSgzcNn6gKggCr1YpJkyY1+fMxm82upoiG8vLykJGR4VPiG4xmgZycHLf3ZzabAxohTP45cOAA\ndDodvvjiC7lDoQhVWFiI+Ph4twF3AFBaWurzk56GdVNzTaiZmZnIz893u57JZEJWVpbr6Ze/rUeX\nXt/fujIY9SQQnLoyEN5+XoIgwGazudW7NTU1SEtLc/VNXrRoUeieMDY7w1wr09xbboM/Ep8IgiDp\ndDopPz9fys/Pl4qKiiSTySTZ7XbJbDa7jtPpdK59ZrNZMhgMkk6n85hk1mAwuI5RqVRSbm6uJIqi\nZDAYXPtMJpNrEkRv261Wq5Seni6p1WrXRJBNxeA8PiYmRiouLpZEUZTy8vKkmJgYKTc31zUJpl6v\nlxQKhdefh7OcSqWS4uPjPSahzMnJkWJiYqTk5GTJarUG50NohvM9FxUV+T0pJr/3gamoqJBGjRol\ndxgRgd8h70RRdNVLBoOh0cldfambLq3vGr52lnFezzmZt8FgcJtI2FsZX65fUlIiqVQqKTk52VWn\nN1VXRmI96Q+r1SoVFRVJWq1WUqvVUlFRkVucBoNBysjIkCTpP4sIXPovOzu72esEmpco/r2zzVAo\nFE3efTS3n9qOhk/8Wjt+7wMzb948bNu2De+++67cociO36G2qy3VlaEQaF4SERP5EkWiUE7ASK3D\nzp070b9/f9frRx99tNH+TkStGetKeTCBI2qE3W7ncmzUrF27drklcIcOHcK2bdtkjIgovFhXyoeD\nGIgaEcnrCVLk2LVrFwYMGOB6ff3112PXrl249957ZYyKKHxYV8qHT+CIiAL01Vdf4dprr3W97t+/\nP3bt2iVjRETUVjCBIyIK0LXXXuu2FBwTOCIKFyZwRERBwgSOiMKFCRwRUZBcffXVWLVqFafTIKKQ\n4zxwfu4nao34vaeW4neIKDCcB46IKIyYrBCRnDiNyCVUKlWLF/olijYqlUruEKJKfX09rrrqKgiC\ngMsvv1zucCIC606iwARa/zKBu0RNTY3cIRBRhPv5558RExPD5K0B1p1E4cUmVCIiP126AgMRUbgx\ngSMi8lNTCdyZM2cQHx+PCxcuhDkqImpLmMAREfnp0iW0GurYsSPOnTuHPXv2hDcoImpTmMAREfnJ\nbrc32YQ6cOBA7NixI4wREVFbwwSOiMhPS5cuxZgxY7zuHzRoELZv3x7GiIiorWECR0Tkp5iYGLRr\n187rfj6BI6JQYwJHRBRkTOCIKNS4lBYRUZCdO3cO58+fR+fOneUOhYiinLe8hQkcERERUYTiWqhE\nREFw+PBh1NfXyx0GEbVxTOCIiPwwcuRI7Nq1S+4wiKiNYxMqEZGPTp8+DaVSiePHj6NDhw5yh0NE\nbQCbUImIWmj37t3QaDQ+J28nT54McURE1FYxgSMi8tH27dsxaNAgn449ePAg4uLiQhwREbVVTOCI\niHy0Y8cODBw40Kdjr7rqKpw+fRrHjh0LcVRE1BYxgSMi8tGZM2eQkJDg07EKhYIT+hJRyHAQAxFR\niDz66KO45ZZbMGXKFLlDIaIoxUEMRERhNnDgQC5qT0QhwQSOiChEBg8eDFEU5Q6DiFohNqESERER\nRSg2oRIRERG1EkzgiIh8YLPZ4HA45A6DiAgAEzgiIp889thj2L17t9xhEBEBYB84IqJmXbhwAV27\ndsWhQ4fQtWtXucMhojaEfeCIiAK0d+9e9OzZM6Dk7fTp09i2bVsIoiKitowJHBFRM7Zt2+bzElqX\nOnjwIMaOHRvkiIiorWMCR0TUjK1bt+LGG28MqGy/fv1w7Ngx1NXVBTkqImrLmMARETWje/fuuPPO\nOwMqGxMTg0GDBrEZlYiCqr3cARARRbqcnJwWlb/hhhuwdetW3HzzzUGKiIjaOj6BIyIKscGDB2Pr\n1q1yh0FErQifwBERhdjw4cPZB46IgorzwBERERFFKM4DR0RERNRKMIEjImpCeXk5Dh48KHcYRERu\nmMARETWhoKCAi9gTUcRhHzgiIi9OnjyJHj16wOFwoEOHDnKHQ0RtEPvAERH5afv27bj++uuDkrw5\nHA589tlnQYiKiIgJHBGRV1u3bsXgwYODcq6zZ8/i0UcfZQsAEQUFEzgiIi+CmcD17NkTnTp1ws8/\n/xyU8xFR28aJfImIvLjlllug0WiCdj7nigx9+/YN2jmJqG3iEzgiIi8mTpyIYcOGBe18XFKLiIKF\nCRwRUZgwgSOiYGETKhFRmNx22204f/683GEQUSvAeeCIiIiIIhTngSMiIiJqJSImgbNarTAajSgv\nL0dxcTEsFovf5xBFEbm5uSGIjojamhdeeAEHDhyQOwwiokZFRBOqIAjIzc1FRUWFa1t2djb0ej3i\n4uJ8Po9Op0NtbS1KS0u9HsMmVCJqTn19PZRKJfbu3QuVSiV3OETUhkV0E6per/d4cqbT6ZCfn+/z\nOQRBQG1tLRQKRbDDI6I2xm63Q6lUMnkjoogVEQlcWVkZEhMT3bYlJSXBZDL5fA6LxYL09HQ+XSOi\nFtuyZQuGDh0aknOfOnUKM2bMCMm5iajtkD2BE0URoihCrVa7bVcqlQCAPXv2NHsOi8WCtLS0UIRH\nRG1QKBO4Tp064e2338bRo0dDcn4iahtkT+BqamoAAN26dWt0vyAIzZ5DEATExcXx6RsRBUUoEziF\nQoEhQ4bg+++/D8n5iahtkD2BE0WxReXLy8sxZcqUIEVDRAQ8++yzGDVqVMjOP3ToUGzZsiVk5yei\n1i+qV2JoafJHRNSY2267LaTnHzp0KDZs2BDSaxBR6xbVCVxZWZnb0zdfR6DOmjXL9f+jRo0K6Z02\nEbVOkiShuroau3btwuHDh9G5c2dcddVVSEpKwhVXXNFk2SFDhuDdd98NU6REFE3WrVuHdevWNXuc\n7PPAOQcwiKLo0Q8uJiYGgiCgX79+HuVsNhsAICEhwbXNYDDAbDZzHjgiCpkDBw7g3Xffxccff4yz\nZ89iyJAh6NWrF86cOYO9e/fi+++/x80334zJkycjKysL7dt73iefPHkSK1aswKRJk2R4B0QUTbzl\nLbIncAAQHx8Pk8mEYcOGubYJgoDk5GTXIIdLGY1GVFdXu22zWq0QBAGTJk1CSkoKMjMzPcoxgSOi\nQJw4cQIvvvgijEYj/vCHP2DKlCkYPHiwx5P/U6dOYdmyZXj77bdx5MgRzJ07F2PHjpUpaiKKdhGd\nwOXm5iIpKcmtOdRkMqGsrAyLFi3y+TzFxcXYtGlTk2WYwBGRvzZu3Ij7778fI0eORFFREa666qpm\ny0iShJUrV+LPf/4z0tLS8Nprr+Hyyy8PQ7RE1JpE/EoMZWVlbtsMBgP0er3rtSiK0Gq1MBqNXs9z\n9OhRJmdEFLDz58/j5ptvxrlz51zb3n//ffz+979HcXEx/u///s+n5A24WOmOHTsWmzdvxqlTp3Db\nbbfh559/DlXoRNTGRMQghtjYWOj1ehQUFCAlJQWCIKCgoMCj75u3pbLsdjv0ej1KS0vhcDiQm5sL\nnU7n1j+OiKg5P/74Iw4fPowOHToAAIqKivDOO+9g/fr1GDBgQEDn7NatGz744AMUFhbi5ptvhtls\nxvXXXx/MsImoDYqIJtRwYhMqEXnz6aeforS0FIsXL0ZRUREWLlwIs9mMPn36BOX87733HmbNmoW1\na9ciPj4+KOckotYtoptQiYgigXMFBqPRiHfffTeoyRsATJ48GX/961+Rnp6OQ4cOYdKkSTh06FDQ\nzk9EbQcTOCKif9uyZQvatWuHv/zlL6ioqAhq8uaUk5ODP/3pTxg/fjyOHDnimhKJiMgfTOCIiP6t\nqqoKb75Q0pG5AAAgAElEQVT5Jj788ENcd911IbvOrFmzEBcXh2PHjjGBI6KAsA8cERGAM2fOIDk5\nGQ8//DCee+65kF/vxIkT6N+/P/r06YPvvvsu5NcjoujEPnBERE14/vnnodVq8eyzz4bleldccQXe\nfvttVFVVYefOnWG5JhG1HnwCR0Rt3ldffYXs7Gxs2bIFvXr1Ctt1L1y4gM6dO2PgwIGoqqpqdNkt\nImrb+ASOiKgRx48fx8MPPwyDwRDW5A0A2rVrh61bt6Jnz5545ZVXwnptIopufAJHRG3a//7v/6Km\npgbvv/++bDHY7XakpKRgw4YN6N+/v2xxEFHkiei1UMOJCRwROW3evBljxozB5s2b0bNnT1mbMN98\n802UlZVh/fr1ja44Q0RtE5tQiYgaqK+vx9SpU/HSSy9h586dyMjIkDWeJ598EidPnsQnn3wiaxxE\nFB2YwBFRm7Rw4UIAF1dHsFqtGDx4sKzxtGvXDm+88Qby8/Px22+/yRoLEUU+JnBE1OacOHECf/3r\nX/Hmm28iJiYGVqsVCQkJssZ04cIF3HrrrbjttttQWFgoayxEFPmYwBFRm/Pqq6/ijjvuQEpKCgDA\narUiMTFRtniefvppLFiwAACg1+vxzjvvYO/evbLFQ0SRjwkcEbUpv/76K9544w28/PLLAC4+jdu7\ndy8GDRokW0zXXXcdrFYrAOCaa65Bbm4uZs+eLVs8RBT5mMARUZsye/ZsPPLII4iLiwNwcQqPm2++\nGR06dJAtpoSEBLc1UZ977jksW7aMKzQQkVecRoSI2ox9+/Zh2LBh2L17N3r06CF3OC4nTpxA7969\nIYqiK5EsLCyE1WpFaWmpzNERkZw4jQgRtXlz5sxBTk5ORCVvwMV1Ua+55hq3J25PPfUUvv76a1fT\nKhFRQ0zgiKhN2L9/P0pLS8O2WL2/brrpJvz000+u1126dEF+fj7+9re/yRgVEUUqNqESUZvwxBNP\noGvXrtDr9XKH0ihJkjxWYDh58iTi4uKwdu1aWQdZEJF8uJTWvzGBI2p79u/fj2HDhmHnzp3o2bOn\n3OH45eWXX8bOnTvxwQcfyB0KEcmACdy/MYEjanueeeYZdOjQAcXFxW7bq6ur0aVLF1x11VUyRdY8\nURSh1WqxadMm18hZImo7mMD9GxM4oraltrYWWq0WP/zwA/r06eO2b/LkyUhOTsbUqVNlis43M2bM\nQG1tLd599125QyGiMOMoVCJqk0pKSnDPPfd4JG8AsHHjRtdqDJHsmWeewaJFi/DLL7/IHQoRRQg+\ngSOiVuvs2bOIi4vDihUrMHToULd9v/32G3r16oXa2lpcdtllMkXo7rfffsP+/fsxYMAAj31Tp05F\nr1698MILL8gQGRHJhU/giKjN+eSTT3DDDTd4JG8AYLPZcMMNN0RM8gYAW7duxYMPPtjovqeeegrz\n58/H6dOnwxwVEUUiJnBE1CpJkoS5c+d6nfctEptPhw4dip07dzaapA0cOBCJiYn45JNPZIiMiCIN\nEzgiapUsFgskSUJGRkaj+1UqFcaOHRvmqJrWqVMnDBgwAJs3b250/zPPPIM33niD3UCIiAkcEbVO\n8+bNw3//9397TI7r9Mgjj+D3v/99mKNqXnJyMjZt2tTovoyMDJw5cwZffvllmKMiokjDBI6IWp19\n+/bhq6++8tqfLJKlpKRg48aNje5TKBR4+umn8frrr4c5KiKKNEzgiKjVKSkpwR/+8AdcccUVcofi\nt1tuuQW9e/f2uv+Pf/wjvvrqK+zduzeMURFRpOE0IkTUqpw5cwa/+93vsH79evTv31/ucELiqaee\nQmxsLF588UW5QyGiEOM0IkTUJphMJtx4442tNnkDAJ1Oh/feew/nzp2TOxQikgkTOCJqVd555x08\n+eSTTR5TVFSEM2fOhCmi4Lvhhhug1WqxfPlyuUMhIpmwCZWIWo0ffvgBd999N/bs2YP27ds3eszB\ngwcxZMgQHDlyxOsI1Wjw0Ucf4R//+AcqKirkDoWIQohNqETU6r333nt45JFHvCZvwMUJfJOTk6M6\neQOAzMxMbN68GdXV1XKHQkQyYAJHRK3CmTNn8NFHH+Gxxx5r8rhNmzZF3AoMjVm4cCGOHTvmdX+n\nTp3wpz/9CSUlJWGMiogiBRM4ImoVli1bhhtvvBEajabJ47777jvcdNNNYYoqcIsWLcKGDRuaPGbK\nlCn44IMPOJiBqA1iAkdErcJ7773X7NO3+vp6/Otf/8Lw4cPDFFXgRowYgW+//bbJY/r37w+tVotV\nq1aFKSoiihRM4Igo6u3btw8bN25EZmZmk8edO3cOr776Knr16hWmyALnSwIHXFwSbOHChWGIiIgi\nCUehElHUmz17Nn799Ve88847cocSNDU1NejXrx9qa2vRrl07r8c5HA5ce+21+PHHH9GzZ88wRkhE\n4cBRqETUKtXX12PhwoWYPHmy3KEElVqtxlVXXYXt27c3eVxsbCzuuecefPzxx2GKjIgiARM4Iopq\na9euRWxsLBITE+UOJegKCwsRGxvb7HGPPvoo3n///dAHREQRg02oRBTVHn74YSQkJOCZZ56ROxTZ\n1NfXIy4uDkuXLsWwYcPkDoeIgshb3sIEjoii1m+//Ya+ffti586d6N27t9zhyOr5559HXV0dXn/9\ndblDIaIgYh84Imp1li1bhhEjRviUvM2fPx8ffvhhGKKSx8MPP4yPP/4YZ8+elTsUIgoDJnBEFLU+\n/PBD/OEPf/Dp2M8//xydO3cOcUTy0Wq1uP7667F69Wq5QyGiMGACR0RR6fDhw9iwYQPuu+++Zo+V\nJAnffvstRowYEYbI5PPQQw9xNCpRG8EEjoii0qJFi3Dvvffi8ssvb/bY6upqdOnSBX369AlDZMG1\nZcsWPPvssz4dm5WVhRUrVuDEiRMhjoqI5MYEjoiikj/Np998803UPn3r0aMHPvjgA58GX/Xo0QO3\n3norli5dGobIiEhOTOCIKOrs3r0be/fuRWpqqk/HR3PzaZ8+fdC5c2f89NNPPh3/4IMPshmVqA3g\nNCJEFHVmzpyJuro6vPbaaz4dL4oiAECpVIYyrJB54IEHMGbMGDzyyCPNHnvixAn07duXS2sRtRKc\nRoSIWgVJkvxqPgUuJm7RmrwBwMiRI/H111/7dOwVV1yBsWPHoqysLMRREZGcmMARUVT59ttv0aFD\nh1a5dJY3I0eOxIYNG3w+ns2oRK0fEzgiiiqLFi3Cgw8+CIVCIXcoYTNkyBB88cUXPh+fkZGBXbt2\nYc+ePaELiohkxQSOiKJGfX09ysrKkJWVJXcoHi5cuBCy/rXt2rWDRqPx+fjLLrsMkyZNwqeffhqS\neIhIfkzgiChq/POf/0T37t0xcOBAn46/cOECfvvtt6Bc+7fffkNlZSVmzpyJ9evXe+zPzc3F3//+\nd4/ttbW1sgycevDBB/HRRx+F/bpEFB5M4IgoapSWliI7O9vn47///vugTR8yd+5czJ49G+fOnWt0\nQITRaMRjjz3msf3JJ59E37598cQTT+Dnn38OSiy+GDlyJERRxPbt28N2TSIKH04jQkRR4cKFC+jb\nty/WrVuH/v37+1Tmrbfewg8//ACDweDXtRwOB2JjYwMJ04MkSfjxxx9hMpnw+OOPo1evXkE5ry+e\neeYZqFQqzJw5M2zXJKLg4jQiRBTVvv76a/Tu3dvn5M1ZZuTIkX5dRxAEpKamBu1GT6FQ4Prrr8eM\nGTM8krfz58/j9OnTPp/rwoULOHXqlM/HZ2VlcToRolaKCRwRRYXS0lLcf//9Ph8vSRK+/vpr3Hrr\nrX5dR6PR4JtvvgnLKNdVq1ZBp9P5fPy0adMwb948n4+/+eabIYoiduzYEUh4RBTBmMARUcS7cOEC\nysvL/Rp9unfvXtTX1zc5elOSJDgcDo/tHTp0CChOf91zzz2YP3++z8cPHz7c5wl9ASAmJgaZmZl8\nCkfUCrWXOwAnq9WKqqoqqNVqCIKAxMREn9Y5NJvNMJvN6N69O6qrq5GUlIQpU6aEIWIiCpf169ej\nT58+iI+P97nMvn37MGHCBK9P0o4cOYLHHnsMPXr0wMKFC4MVqt86d+7s87EjR47En//8Z0iS5PMT\nwqysLEydOhXPP/98oCESUQSKiAROEAQUFBSgoqLCtS07OxsajQZxcXFey5nNZigUChQWFrq2JScn\nQxRFTJs2LaQxE1H4+Dv6FABuv/123H777Y3uO3PmDEaMGIGsrCzMnj07GCEGzYYNGzBv3jyUlJSg\nW7dubvv69u2LLl26YPfu3T73BbzllltQU1ODnTt3YsCAAaEImYhkEBFNqHq9Hrm5uW7bdDod8vPz\nmyxXUlLisS0tLa3R7UQUnc6fP+9382lzOnbsiC+//BKFhYW47LLLgnbeYEhKSkK3bt2QkpKCnTt3\neuy/9dZb2YxKRJGRwJWVlXmsa5iUlASTydRkOYVCAbPZ7LZNkiSoVKqgx0hE8li3bh369evn10oE\nvujbt29QzxcsnTp1QklJCWbOnNnoVCbp6ek4fPiwX+fkaFSi1kf2eeBEUYRarYYoih7NBTExMRAE\nAf369fP5fFqtFlOnTsVzzz3X6H7OA0cUXXJycnD99dd7/Z32xbFjx9C1a9eIe9oWLvX19ejbty/W\nrl3r1zQsRCS/iJ0HrqamBgA8kjcnQRB8PpfBYEBycnKLKnoiihznz5/HkiVLMGnSpBad54UXXsCy\nZcuCFFX0YTMqUesjewInimKLz1FeXo7c3FzYbDYsWrQoCFERUSTYsGEDrrnmGr+ewgOAyWRyWwP1\n1VdfbXESKLd9+/a1aMAFm1GJWhfZE7hgyMzMxPz581FYWIjk5GTYbDa5QyKiIFi8eDEmTJjgV5nj\nx4/jkUceQbt27Vzb2rePiAH3LRIbG9uiUaQjR47E4cOHsXv37iBGRURyif5arYHY2FjodDqkpqa6\nmmYbM2vWLNf/jxo1CqNGjQp9cETkF0mSsHjxYqxevdqvchs2bEBSUhI6deoUosjkERsb6/dUKg21\na9cOmZmZMJlMmDFjRhAjI6JgWrduHdatW9fsca1uEIMgCIiPj0dlZWWjEwFzEANRdNi4cSP++Mc/\nYseOHX4ta/XEE0+gvLwcVqsVffr0CWGE8lq5ciVSUlLQo0cPn8usWbMG+fn52LhxYwgjI6JgCskg\nBofDAZvNhj179qCuri6gcyiVSmg0Go/BCoIgQKlUek3eBEGASqXC5s2bvcZGRNFr8eLFmDhxol/J\n2+HDh7Fw4UJMmDChVSdvwMV5MN944w2/ytx+++2w2+3Yv39/iKIionDxK4ErLy9HdnY24uPjoVar\nkZqaivz8fOTk5CAxMRFqtRrJycl45ZVXsGfPHp/Pm5aW5nFHaLVakZ6e7rWMKIrQarUec0M5E8FL\n55UjoughSRLKy8sxceJEv8r9/PPPqK+vx2uvvRaiyCLHiBEj8NZbb/m1lmr79u1xzz33YMmSJSGM\njIjCQvJBUVGRlJ6eLhUVFUmCIDR7fFVVlaTT6aT09HTJYrE0e7woilJ6errbtvT0dMlut7te19bW\nShqNRjIYDG5xiaLoVi4tLU0qKCjwei0f3zIRyWjr1q3SNddcI9XX1/tV7ujRo9I777wToqgii9Vq\nlTQajXTllVdKX3/9tc/llixZIo0aNSqEkRFRMHnLW5rsA2e326HX66HT6ZCQkBBQgmgwGOBwOJpd\nm9Q5BUhKSgoEQUBSUhJGjx7t2i+KIjQaDYqKivD444+7thuNRlRXV7sWs09OTnbbfyn2gSOKfC+9\n9BKOHDnidxNhW3LhwgV0794dy5cvx/Dhw32epPjUqVO48sorUV1d7Vf/OSKSh7e8xWsC53A4UFpa\niilTprT44qIooqysLCjnaikmcESRLzExEa+99hruuOOOZo89f/58q5gmJBD33HMPHn74Yb/Xic3M\nzMQ999yDRx99NESREVGw+J3AtVZM4Igim91ux/Dhw/HLL7+4zeXWmJ07d+LJJ5+E2Wz2a7BDa7Fq\n1SqoVCoMHz7cr3IffvghSktL2/TqFETRIugJXF1dndflryIZEziiyPbqq69ix44dMBqNPh1/8OBB\nXH311SGOKnpUV1dDq9U2eUxtbS2uvfZaHDx4EFdccUWYIiOiQAR1GpGsrCyoVCqPkabl5eUBBUdE\n5OTv6gtM3v6jvr4ekydPxoEDB5o8TqVSYcSIEVi1alWYIiOiYAsogcvIyMCiRYs85mhLTU1FcXFx\nwHPCEVHb9ssvv2Dr1q2NTsLdHJ1Oh59++ikEUUWPmJgYrF27Fn379m322AkTJuCzzz4LQ1REFAoB\nJXCiKCIjI8Nju1KpxLRp07igPBEFZOnSpRg7diw6duzo9Zjq6mqP5oTjx4/j448/bvWT9/rC176A\n48ePx4oVK3D27NkQR0REoRBQAjdt2jRMmjQJ06dPx5o1a4IdExG1UZ999lmTzae7du3CiBEjPFYS\nWL9+PVJSUtC5c+dQh9hqXH311Rg4cCDWrl0rdyhEFICAErjc3FxIkoSKigqkpaUhJiYGKSkpmDp1\nKgoKClBVVRXsOImolXM4HPjnP/+Ju+++u9H9Z86cwQMPPIDZs2fjd7/7nds+s9mMtLS0cIQZkSZP\nngy73e6x/dixY6ioqPBajs2oRNEroAROq9WisrISVVVVqK+vR0VFBUaPHo3vvvsOZrMZer0+2HES\nUSu3atUq3HbbbV5HRV64cAGPP/44cnNzPfZZLJaA+s21FqdPn4bFYvHYfuTIETz00EPYvn17o+Um\nTJiApUuXor6+PtQhElGQBZTAKZVKt9dpaWnQ6/WoqqqCwWBAaWlpUIIjorZj2bJlGDdunNf9Xbp0\nwRNPPOHRx+vw4cPYv38/kpKSQh1ixEpNTW00gRswYAAKCwvxwAMP4Pz58x774+Pj0aNHD3z77bfh\nCJOIgiigBC41NdXrHE0qlapFARFR23Pu3DmsXLkS9957r99le/bsiW3btrXZ1RgAYPTo0VizZk2j\nc0U99thjWLBggdefz4QJE7i4PVEUCiiB02g0yMrKQnFxMRwOh2u7IAjQarWwWq1BC5CIWr+vvvoK\nWq02oFGkCoWizc8F169fP1xxxRXYunWrxz6FQoGUlBSvZcePH88VGYiiUMC3rM4pQxrSaDSoqKho\ndhZwIqKGli1bhvHjx3ts/+yzz3Du3DlkZ2fLEFV0cTaj3njjjX6VS0xMxPHjx7Fr1y70798/RNER\nUbBxLVQikpUkSdBoNFi6dCmGDBnitm/Hjh04ffo0EhISZIouehw7dgxdu3bFZZdd5nfZqVOnQqPR\neNyUE5H8/F5Ky+FwBG1pLIfD4fO6hkTUtmzduhWSJDX65GjgwIFM3nzUvXt3n5K3nJwcbNiwwW3b\nuHHj2IxKFGW8JnCxsbFISEhAbm4uNm/eHPAFjEYj5syZgylTpgR8DiJqvZYuXYrx48f7vIJAQwcO\nHOATdT89++yzuOmmm9y2jR49Gj/88AOOHDkiU1RE5K8mBzFoNBrMnz8fFRUVyMjIwCuvvOKxgH1j\nbDYbCgoKkJGRAY1Gg8LCwmDFS0StTHPTh3hTX1+PhIQE/PzzzyGIqvXq378/OnTo4LatY8eOSEtL\nwxdffCFTVETkL7/6wJnNZphMJpjNZtTU1ECj0UCtVgO4OAK1pqYGarUaaWlp0Ol0Edn0wT5wRJHj\n4MGDGDx4MA4dOuRKKmbPno0HHngA1113XZNlq6qq8NBDD2Hnzp3hCLXV++CDD7BkyRIsXrxY7lCI\nqAFveUuLBjGIoghBEKBUKqFWqz0m+I1ETOCIIkdJSQm+/PJLfPzxxwCANWvW4NFHH8XWrVvRtWvX\nJsv+7W9/w5EjR/D666+HI9SocfjwYVx++eW4/PLL/Sp37NgxaDQaHDp0CJ06dQpRdETkL78HMfhC\nqVQiMTERGo0mKpI3IoosDZtPJUnCs88+i3nz5jWbvAHA6tWrcdddd4U6xKgzefJkLF++3KdjP/zw\nQ7zxxhsALg6CGDZsGNasWRPK8IgoSAJ+Ame322E2m+FwOJCYmIjRo0cHO7aQ4BM4oshw4sQJXH31\n1di/fz9iY2MBXFy7s2fPns2WdTgc6Nu3Lw4dOoQuXbqEOtSoMm/ePFRVVWHhwoXNHltdXY3hw4dj\n48aNiIuLw9y5c7F7926UlJSEIVIi8kVQn8CVl5cjKSkJer0eeXl5SEtLQ/fu3bFgwYIWB0pEbUNF\nRQWGDx/uSt4A+JS8AcAvv/yCKVOmMHlrxJgxY1BRUeHTjapWq8Wzzz6Ld955B8DF6USWL1/Oxe2J\nokBAKzFs3LgRNTU1rteCIMBkMqGwsBCVlZVYtGhR0AIkotbJ2+oLvhgwYABeffXVIEfUOsTHx6NT\np07YunWrT6syTJs2DTExF+/lr7vuOiiVSlRVVTW5/BYRyS+gJ3CXLpWl0WiQl5eHn376CUlJSXwS\nR0RNOn/+PL744ouAFq+npikUCowZMwarVq3y6fj27du7EjiAk/oSRYuAEji1Wu11Pri8vDz2MSOi\nJn3zzTfo06cPrrzySowaNQp1dXVyh9SqZGZmomPHjgGVHTduHJYuXRrkiIgo2AJK4DIzM5GTk4PF\nixc3WvGKotjiwIio9XI2n3bs2BHz5s1Dt27d5A6pVUlNTcVTTz0VUNnk5GQcOnQIdrs9yFERUTAF\nNAo1Ozsb1dXVsNvtEEURWq0WaWlpSE9PhyAIHqNSbTZbxEzqy1GoRPKSJAn9+/fHJ598gqSkJLnD\noQZWrVqFTz/9FO3atcPQoUMDTgKJKHiCOpGv0Wh0rW0qCALMZjMqKythsVggiiI0Gg3S09ORlJSE\n1NRUFBQURMzABiZwRPLauXMn0tLSsH//fr/XPz116hReeOEFzJkzJ6C1U6lpZ86cwcmTJ7F+/Xq8\n+eabsFgscodE1OYFNYEzm82w2WxIT0/HsGHD3PY1TOhsNhsEQYBCocCFCxcCjz6ImMARyUuv12Pv\n3r2uqSv8sXr1arz00kv46quvQhAZOZ08eRJXXnkl9u7dC5VKJXc4RG1aSJbSstvtiIuLa/IYQRCQ\nnZ2NTZs2BXqZoGICRySvm2++GSqVCuXl5ejcubNfZZ9++mn06tUL/+///b8QRUdO48aNwwMPPIAH\nHnhA7lCI2rSQLKXVXPIGXJxiZPr06S25DBG1EocPH8bmzZshSZLfyZskSVi+fDmnHvHD6tWrA16c\nntOJEEW2FiVwvsrMzAzHZYhaDVEU3WbDby2vFy9eDEmS8Pzzz/tdfvv27Th37hxuvPHGiHk/kf76\n1KlTePfddwMqr1KpsGTJEpw9ezZi3k+oXp8/fx5EUUdqY9rgW6YoUFdXJ61cudL1evDgwdK+ffta\n3evx48dLb7zxRkDlZ8yYIeXm5kbU+4n018ePH5e6du0qDRo0yO/yVqtVat++vbRw4cKIeT+heL1n\nzx7X94ooEnnLW1rUBy4asQ8cRaKDBw9izpw5eOutt+QOJWROnTqF3r17Y8+ePVCr1X6X//nnn3Hu\n3Dn069cv+MG1YnfffTcmT56MSZMm+V32rrvuwoEDB7B169YQRBYZfv31V/z444+47bbb5A6FqFEh\nGcQQjZjAEclj+fLlmDt3LtatWyd3KG3K22+/je+++w7/+Mc//C5rs9kwbtw47Nu3j9O2EMkkJIMY\niIh81ZLF6ylw99xzD1asWBHQVE7Dhg1Dx44dsWXLlhBERkQtwQSOKALU1dVh9erVcocREpIk4ckn\nn8TSpUsxbtw4ucNpc6699lpUVlYG9ARNoVBg3LhxWL58eQgiiwxbtmzB7Nmz5Q6DyG9M4IgiQF1d\nHVasWCF3GCEhSRKuvvpq9OzZE1qtVu5w2qRhw4YhJiaw6r61L25/5ZVXYtSoUXKHQeQ39oEjopCb\nMWMGAODll1/2u+zx48fRpUsXtGvXLthhkQ/Onz+P3r1748UXX0THjh0xefJkuUMialPYB46IZNOS\n5tOXXnopoMSPgqN9+/YYO3Ysjh49yidVRBGECRxRBHA4HKioqJA7jJD46aefcOzYMdx0000BlV+2\nbBnGjBkT5KjIH+PGjcM333zTKpvAf/jhB8yaNUvuMIj8xgSOKAI4HA6sXLlS7jCCat26dTh69Khr\n+atA+mDt3LkTdXV1SE5ODkGEbc+RI0cCKnfXXXdhw4YNOH78eJAjkl/v3r1x5513yh0Gkd+YwBFF\ngN/97nd47bXX5A4jaOrq6nD//ffj0KFDWLZsWcDNp0uWLMF9990XcAd8+o/ffvsN8fHxqKur87ts\n165dccstt7TKkdK9evXCHXfcIXcYRH5jrUhEQTd37lzcdddduOqqq1BVVYXU1NSAzvPZZ5/hvvvu\nC3J0bdPll1+OW2+9NeDRzuPHj3ctbl9RUYEDBw4EMzwi8hMTOKIIIIoiKisr5Q4jaG666Sa88MIL\nWLFiBUaPHo0uXbr4fY6zZ89yiocgmzhxIhYvXhxQ2XvvvRcrVqzA+fPnsXbtWrzwwgtBjk4e27Zt\nw/PPPy93GER+YwJHFAFEUcSqVavkDiNofv/736Nfv34taj697LLLsHTpUnTo0CHI0bVd48aNw+rV\nq3Hq1Cm/y/bt2xfXXnstNmzYgLy8PCxZsgQ7d+4MQZTh1atXL4wePVruMIj8xnngiCgkzpw5g969\ne2PXrl3o3bu33OHQv9155534n//5n4AS69mzZ8PhcGDu3LmorKzEkCFD+NkShRjngSOisPryyy8x\naNAg/oGPMFOmTMHp06cDKutclUGSJKSnp/OzJZIREziiCFBbWwuz2Sx3GC1y8OBB7Nmzx/W6Jc2n\nFDoPPvggsrOzAyo7dOhQnDt3Djt27AhyVPLZsWMH/vKXv8gdBpHfmMARRYDa2tqon6LhX//6FxYt\nWgTg4vqny5Ytw/jx42WOioLJubi9czRqa9CzZ8+AR0kTyYl94Igo6Gw2G7Kzs7F7924oFAq/yp46\ndQdjbfMAACAASURBVAp5eXl48803/S5LoVdZWYnnn38e33zzDQDgwoUL+PrrrzmXGlGIsA8cEYWN\ns/k0kARs5cqV2L59O5O3CHXHHXdg586d+PXXXwFcnO7l9ddfD2hkKxEFjgkcUQSoqamJ+j5wDbWk\n/1tZWVnAfbQo9C677DKMGTMGn3/+OQCgc+fO+Oyzz9C5c2eZIwvMrl27MGPGDLnDIPIbEziiCBDN\nCVx9fb3b6wMHDmDv3r0YOXKk3+c6efIkVq5ciYkTJwYrPPLiyy+/xFtvvRVQ2YarMkS7Hj16IC0t\nTe4wiPzGBI4oAsTHx6OwsFDuMPy2e/dujBgxwq1/xvLlyzF27Fi0b9/e7/OtXLkSKSkp6NmzZzDD\npEaoVCrMnTs3oD7Bd911F9atW4eTJ0+GILLw6t69OyfypajEBI6IAvbiiy/i3nvvdeuvtnTp0hY1\nn2ZlZQUrPGrCjTfeiM6dO+Nf//qX32VVKhVSUlIaXf7t/PnzwQiPiJrBBI4oAhw7dgwWi0XuMPxy\n/PhxVFVV4emnn3Ztq6urw4YNGzBmzJiAzjlv3jw8+OCDwQqRmqBQKPBf//Vfrqlf/NVYM6rFYsF9\n990XjPDC5scff0RBQYHcYRD5jQkcUQSIxgSua9eu2Lp1K7p16+baVlFRgZEjR6Jr164BnbNHjx64\n4oorghUiNeP+++9HaWkpLly44HfZcePG4fPPP3cre9ttt+GHH34I6KmeXLp374709HS5wyDyGxM4\noghw/fXX4+WXX5Y7DL/FxLhXIVx9IboMGDAAPXv2DCjh6tevH6688kq3spdddhny8vKwatWqYIYZ\nUmq1mhP5UlTiRL5EFBTnz5/HlVdeic2bN6Nv375yh0M+qqmpgUqlCmjevb/+9a84d+6c2wAcSZI4\nhx9REHEiX6IIdvToUaxZs0buMFrkn//8J6699lomb1FGrVYHnHA5F7dvKNqSt+rqauTl5ckdBpHf\nmMARRYBoSuCef/55fPXVVx7bWzL6dNOmTTh37lxLQ6MwS0pKQl1dHXbv3i13KAFTq9XIyMiQOwwi\nv0VME6rVakVVVRXUajUEQUBiYqJP/RLKy8shCAKqq6shCAJ0Oh0yMzO9Hs8mVKKW+f7773H11Vej\nR48erm2SJOG6665DWVkZEhIS/DpfbW0t+vXrh3379iE2NjbY4VKI5ebmIj4+Hs8995zcoRC1St7y\nFv9n2gwBQRBQUFCAiooK17bs7GxoNBrExcV5LVdeXg6NRuNK2BwOB5KSklBTU4MpU6aEPG6itmjI\nkCEe23bu3ImzZ89i2LBhfp/PZDIhIyODyVuUGjduHAoLCxtN4B599FHMmDED1113nQyREbVuEdGE\nqtfrkZub67ZNp9MhPz+/yXKCILjd7cfGxiI/Px86nS4kcRKFypEjR7B27Vq5wwhYSxav/+ijj/DQ\nQw+FICryR3V1NbZv3+53udGjR2PLli04evSox76pU6fimmuuCUZ4IWO32/n0kKJSRCRwZWVlSExM\ndNuWlJQEk8nktYwoili0aBEcDofbdmez6549e4IeJ1GotJYEzl/79+/HDz/8gLvvvjsEUZE/Kioq\nMHv2bL/LderUCWlpafjiiy889t10003o1KlTMMILGZVKFfDE00Rykj2BE0URoihCrVa7bVcqlQC8\nJ2JKpRKCIMBut4c6RKKQGzRoUEB/PMNFFMVGBy4AwOHDh7Ft2zbccccdfp/3k08+wcSJE9GxY8eW\nhkgtlJWVhZUrV6Kurs7vstG8uL1SqeREvhSVZE/gampqAMBtNveGBEFosuylfW7MZjNUKhX69esX\ntBiJ2rq33noL7733XqP7li1bhjFjxgSUhA0ePBhPPPFES8OjIOjRowdGjx6NsrIyv8uOHTsWZrMZ\np0+fDkFkRNQY2RM4URSDer6SkhJMnz49qOckCrXDhw9j3bp1cofRqBMnTuCtt97y+nu1ZMkSTJgw\nIaBzjx071u9RqxQ6f/rTn/DBBx/4Xa5Hjx4YOnSo16lw6urqYDabWxpeSOzduxf/+7//K3cYRH6T\nPYELJoPBgB49erBDKkWdSE7gTp06hRdffBH9+/f32Hf8+HGsX7+efdhaibFjx2Lbtm0BdU1pqhn1\n+PHjyM7OxpEjR1oaYtAplUrcddddcodB5DfZ54GzWq1ITk5GfX29x76YmBiYzWaMHj262fMIgoDs\n7Gxs2rSpyeMUCgVmzpzpej1q1CiMGjXK77iJCCgtLcXChQuxcuVKuUOhIPn888+RkpKC3r17+1Xu\nxx9/xB133IEDBw54rJELXJwvrmfPnnjxxReDFSpRq7Ru3Tq3G/oXXnih0XngZE/gnAMYRFH06AcX\nExMDQRB86s+WnZ2NBQsWeO1L58SJfImC54EHHsCdd96JnJwcuUOhCDBo0CD84x//QEpKisc+QRCw\nadMmZGdnyxAZUfSK2LVQlUolNBqNx2AFQRCgVCp9St5yc3NRVFTUbPJGFKkOHTqEL7/8Uu4w/HLm\nzBmsWrUK48eP97vs+fPnQxARyW3cuHFYsmRJo/s0Gk1EJm/79+/HM888I3cYRH6TPYEDgLS0NGzc\nuNFtm9Vq9Wlot9FoREFBgVuiZ7FYOL0IRZVITOAOHTrU5NPqNWvW4IYbbvC7qU0URWg0Go5YbIUm\nTJiAzz77TO4w/BIbG8s+nBSVIiKB0+v1HkPXDQYD9Hq967UoitBqtTAaja5tzol+a2pqYLVaYbVa\nYTabUVZW1uQSXESRZsiQIXj++eflDsPNU089hfXr13vdv2TJEtx3331+n3fRokVRMcEr+S8lJQV1\ndXXYsWOH3KH4rFu3bpzIl6JSRKyFGhsbC71ej4KCAqSkpLjWRr20+bS2tta1VI8oil4fx2u12lCH\nTNTqffrpp173XbhwAUuXLsWGDRv8Pu/777+Pv/zlLy0JjcJAkiQcP37cr64pMTExrqdwAwcO9Hrc\nkSNHoFar0a5du2CEStQmyT6IIdw4iIEi0a+//ordu3fj9ttvlzsUn2zYsAFTp07F999/71e5HTt2\nYPTo0di/fz/at4+I+0fywmQy4e9//ztWrFjhV7m1a9ciLy/Po1tMQ2PHjsVLL73ksYSiHH7+/+3d\nd1iTZ/s38G/YoIAyXagMF2gdgKO1VhG0rbOCo67HWgWqVDscSLV1K47+Oqy1WvXRx4WgVsU6AMXW\nLcOBA6xhqTgxgAMFcr9/WPOWspKQkIR8P8fBoblzXdd9Wgo572vevo3w8HD88MMPmg6FqFxau4iB\niF4lcJUNV2qbPXv2KLV576ZNmzBmzBgmbzrg/fffx9mzZ5Gdna1QvbfffhsZGRnIysqqsEx0dLRW\nJG/AqyHU999/X9NhECmMCRyRFujQoYPODCsKgqB0Apefn49x48apPihSOQsLC4wYMQIbNmxQqJ6R\nkREGDBhQ6WKG8vaJ0xRLS0tu5Es6SXt+iohI465fv46vvvqq0jKXL19GSUkJ2rdvr3D7q1evhru7\nu7LhUQ2bOHEi1q9fj5KSEoXqDRkyBLt371ZTVEQEMIEj0go5OTn4888/NR0GVqxYUeWh9K/PPn29\noIhqrw4dOsDR0RFHjhxRqJ6vry8uXryI+/fvqyky1cnJyUFISIimwyBSGBM4Ii2gDQncvXv3sHv3\nbkyePLnScsoOn5JumjVrlsI9cGZmZujbt2+FZ6O+lpqaihkzZlQnvGqztLREv379NBoDkTK4CpWI\nALya2yYWiyvdhic9PR1dunRBTk4Ot4CgSkVERGDTpk2VrmJ99uwZnJ2dER8fX+m2I0T6jKtQiahS\nIpGoyj0Uf/vtNwwcOJDJG1Xp/fffx4kTJ5CXl1dhGQsLC3z66af49ttvazAyotqBCRyRFrhz5w5O\nnDih6TCqtGfPHoVPX4iOjsa8efPUFBFpK0tLS7zzzjtV7iM3ZcqUUqfu1LR79+5h0qRJGrs/kbKY\nwBFpAV1I4O7evYvLly/D19dXoXo//fQTXFxc1BQVabMPPvigytWoVlZWsLGxqaGIyqpbty769++v\nsfsTKYtz4Ij0XHx8PBo3bowWLVpUWm716tU4deoUtmzZInfbGRkZ8Pb2RlZWFszNzasbKmmYIAgK\nrT5++PAhXF1dcffuXX7/iZTEOXBEVK6bN2/iwYMHVZaLiopCQECAQm2vW7cOo0eP5od3LSCVStGx\nY0fcunVL7jp2dnbw9PRUeBsSIqoaEzgiLXD79m2lDoZXhY8//hhvvvlmpWXu37+PpKQk9O3bV+52\ni4qKsGHDBgQGBlY3RNICBgYGePvtt7FmzRqF6g0ZMqTSUxn+aePGjXj69Kky4SntwYMHCA4OrtF7\nEqkCEzgiLaDJBE4ee/bswXvvvadQT9qlS5fg5eXF7SFqkcmTJ2PdunV48eKF3HUGDx6M/fv3o6io\nqMqy9+7dQ25ubnVCVFidOnUwYMCAGr0nkSpwDhwRVcnPzw/BwcHw9/dXqJ6ic6ZI+/Xp0wdjxozB\nmDFj5K7TrVs3zJ07V6EeXCJ6hXPgiKgUeXpEgFcT0c+dO4f33ntP4Xsweat9QkJCsGrVKoXqDBs2\nDDt37lRTRET6iQkckRa4desWTp06VWP3u3DhArp06SJXb/Rvv/2Gvn37wsLCogYiI23Xr18/NGvW\nDPn5+XLXCQgIwG+//Sb3Q0NNevToEedpkk5iAkekBWo6gVu2bBk+/PBDuXrIoqKiMHTo0BqIinSB\noaEhdu7cCSsrK7nrODk5oVWrVoiLi5O7TmFhoTLhKczCwgIDBw6skXsRqRLnwBHpmefPn+Ott95C\nfHx8lR/Cubm5cHZ2xu3bt1G3bt0aipBqo++++w6XLl3Chg0bqix77NgxfPPNN/jjjz9qIDIi7cY5\ncEQEADA3N0diYqJcPSh79+6Fr6+v3MlbYWEh/P39FVqlSPohICAAe/fuxcuXL6ss+/bbb+PWrVta\nvTKbSNOYwBFpgezsbJw+fbrG7ifv4gJFh0937NiBp0+fwtTUVNnQqJZq0qQJ2rRpg9jY2CrLGhkZ\nYebMmTWSwD1+/BgTJkxQ+32IVI0JHJEWqOkETh4SiQQnTpxAv3795CovCAJ++OEHTJ06Vc2RkTZR\nZEqKIqtRg4KCMGPGDGXDkpu5uTkGDRqk9vsQqRrnwBFRuTZv3ow9e/bIvYv+0aNHMXnyZFy5cgUG\nBnw21Afp6ekYMWIETp8+Ldf3/Pbt22jXrh1ycnLYS0skJ86BI9Jzv/76KyIiIuQur+jZp+Hh4Zg+\nfTqTNz3SvHlzlJSUIDo6Wq7yjRs3hoeHh1zDqERUOf6mJdICWVlZOHPmjFrv0atXL3h6espV9vHj\nxzh+/LjcRwzl5uYiNzcXo0aNqk6IpGNEIhGmTZuGFStWyF1H2zb1zcvLw/jx4zUdBpHCmMARaYGa\nSOBcXV3h5uYmV9ndu3fD19dX7r2+bGxscO7cOQ6L6aGAgABkZWXh7NmzcpX39/fHvn375F6pLJVK\nMXjwYDx69Kg6YVbIzMwMgwcPVkvbROrEOXBEVIafnx+CgoIUGkIl/fX999/jxIkTiIyMlKv8O++8\ng2nTpsndw3v69Gl4eXnB2Ni4OmES6STOgSMiudy9excJCQlyrz4l+vjjj2Fubo6SkhK5yis6jNqt\nWzcmb0T/wgSOSAtkZmbKPQSlqBMnTijU6xwZGYn+/fvD3NxcLfFQ7VO3bl1s3rwZhoaGcpX39/dH\ndHR0jR2XVZmCggKMGzdO02EQKYwJHJEWUFcCd/r0aYwdO1bunhEA2L59Oz788EOVx0L0WoMGDdCx\nY0f8/vvvmg4Fpqam+OCDDzQdBpHCOAeOqBYbPHgw/Pz8MHnyZLnKZ2RkwNvbG3fu3KlyyCo/Px/9\n+/fH4cOH2VtHClu/fj1+//137Nq1S+469+7dw+3bt9GpUyc1RkakXTgHjkjPSKVSeHh44KOPPpK7\nzo4dO+Dv7y/XfKNVq1bBycmJyRspxd/fH7GxsZBIJHLXSU5Oxrhx4/gQTgQmcERaISMjA+fOnVNp\nmwYGBli0aBEsLCzkrrNjxw6MGDGiynIFBQX47rvvMHv27OqESLVUQUFBlWXq1auH3r17Y/fu3XK3\n27dvXxgYGODgwYPVCa+Up0+fYuzYsSprj6imMIEj0gLqSOAUde3aNTx48ABvv/12lWV/+ukn9O7d\nG23atKmByEiX5Ofno0WLFnjw4EGVZUeOHIlt27bJ3bZIJMKyZctQp06d6oRYiomJCYYMGaKy9ohq\nCufAEREA4Ouvv8aTJ0/w7bffVlruyZMncHV1xbFjx+Du7l5D0ZEuCQ4Ohq2tLRYtWlRpuefPn6NR\no0a4cuUKGjVqVEPREekWzoEj0hOFhYUKrToFAEEQsH37drmGTzMzM/HRRx8xeaMKhYaGYs2aNXj8\n+HGl5czNzTF48GDs2LGjhiIjqj2YwBFpgfT0dJw/f14lbW3duhWhoaEK1UlMTIQgCPD29q6yrIeH\nB5YuXapseKQHmjdvjsGDB2PlypVVlh01apRCw6iq9vz5c4wePVpj9ydSFodQibTA0aNHcf36dUya\nNKnabQmCgBcvXsDMzEzuOp999hmsrKwwf/78at+fCHjVU9upUydcvXoVjo6OFZYrKSlBkyZNEB8f\nj1atWil0D4lEgnr16lUrzuLiYuzfv597wZHWqihvYQJHpOeKiorQpEkTnDhxAi1atNB0OFSLbN++\nHb169UKDBg0qLff555/DysoK8+bNk7vtwsJCvPHGG0hOTlbpogYibcME7m9M4IhKO3DgABYtWoRT\np05pOhTSUwkJCRgxYgRu3LgBkUgkd72ioiKekUq1HhcxEGkxsViMhIQEjdx78+bNGDNmTKVl8vLy\n8OzZsxqKiPSNp6cnDAwMFJ4Hqork7cWLFxg5cmS12yGqaUzgiLRAdRM4QRAwa9Ys5OfnK1RPIpHg\n0KFDGD58eKXl5syZg4ULFyodH1FlRCIRRo0ahS1bttT4vY2MjBAQEFDj9yWqLg6hEtUChw8fxrRp\n03Dp0iWFhqB+/fVXHDx4sNLzKNPT0+Hl5YVr167BwcFBFeESlSEWi9G1a1fcunULJiYmmg6HSGtw\nCJWoFgsPD8eMGTMUSt6AV8OnVR0j9PXXX+PTTz9l8kbVcvHiRVy7dq3C911cXODu7o4DBw4o3Pah\nQ4ewffv26oRHpHOYwBFpgZs3byIxMVHp+suXL5drE95/Sk9Px7Vr1/Dee+9VWObSpUuIiYnBl19+\nqXRsRABw+vRphISEVDoCMm7cOPz3v/9VuG1ra2uEhYWhuLhY4bpFRUUK/+wQaQMmcERaoLoJnKen\np8ITurds2YLhw4dXOlw1a9YszJo1C5aWlkrHRgQAEyZMwN27dxEdHV1hmYCAABw/fhz37t1TqO1u\n3bqhadOmiIyMVDguQ0NDDB06VOF6RJrGOXBEekgQBLRs2RJbt25F586dKyx39OhRdO/enXOSSCUO\nHjyIzz//HJcvX67wgWPcuHFo3749Pv/8c4XaFovFcHBwQN26dVURKpHW4Bw4IpI5ffo0DAwMqjw6\ny8fHh8kbqcy7776Lpk2b4pdffqmwzLhx47Bx40aFH7RdXFyYvJFeYQJHpAX++usvJCUlKVTn7t27\nOHfunFL3W79+PcaPH6/wogei6hCJRFi5ciV+/PFHlJSUlFumR48eyM/Px4ULF2okppKSEgwbNqxG\n7kWkSkzgiLSAMgnczZs3cfToUYXvVVBQgN27d+M///mPwnWJqqtdu3ZITk6GoaFhue8bGBjgP//5\nj1KLGZRhYGDABI50EufAEemZ9evXY//+/fjtt980HQpRuW7evImuXbvi9u3bCg/hP3/+HIcOHeLh\n9FRrcA4cEQF4tXnvxx9/XO57169fx+LFi2s4IqLSXF1d4e7uXumK1YoIgoDff/+9wiFaotqCCRyR\nFrhx4waSk5PVfp+rV68iMzOz3L3fBEHA1KlTYW5urvY4iKoyfvx4rF+/XuF6FhYWWLduXYVDtOXh\nUVqki5jAEWmBtLQ0uRM4qVSq9H3Wr1+PcePGwcjIqMx7kZGRuHPnDkJCQpRun0hRUqkUL1++LHN9\n6NChOHPmDLKystQew/Dhwzm1hnQO58AR6ZCXL1/Cy8sLhw8fRsOGDRWu26RJE5w6dQpubm6l3svP\nz4e7uzsiIiLw1ltvqTJkokrNnTsXxcXFWLhwYZn3Pv30U9jY2GDevHkaiIxIO3AOHFEtsGXLFjg6\nOiqcvAHAvn374O7uXiZ5A16dd9q3b18mb1TjAgMDsWbNGqSlpZX73vr165U6Ius1zoWj2ooJHJEW\nSEtLk2vfqz179uCrr75S6h7r16/HhAkTylyXSqV49uwZwsPDlWqXqDoaNWqEsLAwfPrpp2V6Gdq1\nawcnJyccPHhQqbYXLVqEpUuXVllu2LBhTPRI53AIlUgL7N+/H48ePcK4ceMqLSeVSiESiRTegDcr\nKwsdO3bErVu3uEiBtE5RURE8PT0RGhqKkSNHlnrvv//9L3bt2oX9+/cr3O7Vq1fh4+OD9PT0Sv+/\nj4qKwpAhQ2BgwD4N0j4V5S1M4Ij0wOzZs1FQUIDvv/9e06EQlev8+fMYMGAAUlJSYGdnJ7v+7Nkz\nODk54cKFC3ByclK43YCAAEyaNAk+Pj6qDJeoxjCB+xsTONI3L1++RNOmTREfH4/WrVtrOhyiCv3x\nxx946623ymwBEhISAnt7e3zzzTcKtymVStmzRjqNixiItFhqaiouXryolrZ3794NDw8PJm+k9Xr0\n6FHu/m0TJ07Er7/+qtQ8NXmStxEjRqCoqEjhtok0iQkckRa4fv16hQncsWPHsGLFCqXbXr16NSZN\nmlTq2sGDB8td9Uekjdq3b4/GjRvj999/V0v7Q4cOZS8d6RytGUJNSkpCYmIibGxsIBaL0alTJ/Tu\n3Vvu+lFRUahfv36VdTiESromJycHt27dgre3t8J1U1JS0LdvX2RkZMDY2BgAcOfOHXTo0AGHDx9G\nx44dVR0ukVps2rQJ27dvx6FDhzQdClGN0uohVLFYjNDQUEycOBH+/v6YPn06fvnlF6Snp8tVPzY2\nFoGBgQqvzCPSBQ0bNlQqeQOAn3/+GYGBgbLkTRAEfPLJJwgKCmLyRlrvnx9aw4cPR3JyMlJTU5Vq\nKycnB+PHj+cDPNUaWpHAhYeHIzg4uNS1oKAgzJw5s9J66enpCA4ORnp6OmxsbNQZIpFaXb9+HZcu\nXVJpmwUFBdi+fXupvd+2bduGmzdvYvbs2Sq9F5GqPXz4EJ6enpBIJAAAMzMzTJgwAT/99JNS7Tk6\nOmLYsGHlvjdy5Ei8ePFC6ViJNEErhlBtbGyQlJSE5s2by65JJBLY2NjIfe6jm5sb1q5dW+VScQ6h\nkjbas2cPnj59itGjR6uszZ9//hlxcXGIiooC8GovOC8vLxw8eBCenp4quw+RukyePBkFBQXYvHkz\nAODWrVt44403kJGRASsrK5XdZ/fu3Rg4cGC5ZwQTaZrWDqFKJBJZsvZP9erVAwBkZGRoICqimvXB\nBx+USd6OHz+u9O7wgiCUWbyQnJyM0NBQJm+kM5YtW4YzZ85g165dAIAmTZrA19cXmzZtUul9hgwZ\nwuSNdI7GE7jc3FwAqPBpSiwW12Q4RFrh8uXLGD58OAoLC5WqHx8fj5KSEvTq1Ut2bdCgQfjiiy9U\nFSKR2tWpUwf/+9//MHnyZOTk5AB4dcD9qlWr5B6dIaqtNJ7AvZ7fQKTPrl27hsuXL8tez58/H9Om\nTUOdOnWUau/bb7/FZ599xoU9pPO6dOmCwMBABAUFAQC6d+8Oc3NzxMTEKN1mZmYmrl69Kns9evRo\nPH/+vNqxEtUkjSdwRPTqzMbXCZwgCOjUqRM++eQTpdpKS0vD2bNnMWbMGFWGSKQxc+bMwdy5cwG8\nmg/06aef4scff1S6vfj4eISEhMhe+/v7cwiVdA4TOCIt4O/vLzvEWyQSYdasWUr3vn3//fcICgri\nofVUaxgbG6NTp06y1yNHjsTZs2fx119/KdXeyJEjkZmZiT///BPAqzmor7faIdIVGn/kcHFxAQDk\n5+eXOw/u9fuq9PpJDgB69uyJnj17qvweRJqQm5uLbdu24erVq9i+fTvq1KmDgQMHajosIpUyNzfH\nxIkT8d1332HVqlUK1zc2NsaqVatgYWGhhuiIqic+Ph7x8fFVltOKbUTc3NwQFRWFDh06yK6JxWJ4\neXnJFjnI0wa3ESFddfXqVUilUrRt27Za7SxduhTXrl3DzJkz8c477yAuLg5vvPGGiqIk0h45OTnw\n8PBAWloa7OzsqtXW2LFj8fPPPyvd602kTlq7jQgA+Pr64vz586WuJSUlwc/PT0MREdWsK1eu4NSp\nU9XaTPTly5dYtWoVgoODMXToUISHhzN5o1qrqKgIQ4YMwerVq6vd1pAhQziESjpHKxK48PBwREZG\nlrq2du1ahIeHy15LJBK4urpi3bp1FbbDnjXSVUOHDkVubi7Wrl2rdBs7d+5EixYt8PPPP6Nz584Y\nP368CiMk0h65ubnw9vaGj48Pfvrpp2qvIB08eDBMTExUFB1RzdCKIVTg1SajERER8Pb2hlgshqen\nZ6nhUIlEAhcXFyxbtkx2NFBeXh6WLFkCsViMqKgouLi4wNfXF35+fvD39y/3PhxCJW0mCIJSW39I\npVK0b98ePXv2xLFjx3Du3DnO76Fa7cCBAwgKCoK7uzuGDBlS5jhGRaSnp8PZ2VmF0RGpTkV5i9Yk\ncDWFCRxpoytXrgAAPDw8lKq/f/9+fP3119iwYQMsLS3h5uamyvCItNLChQsRERGB58+fIzU1FYaG\nhgq3IZVK0aBBA5w8eRItWrRQQ5RE1aPVc+CI9F1KSoosiVOUIAhYsmQJZs2ahY4dOzJ5I70RFhYG\nV1dXFBQUYO/evUq1YWBggLVr16Jp06Yqjo5IvdgDR6Tjjh8/jokTJ+LatWtK9UAQ6bL8/Hz035iy\nhgAAIABJREFU6NEDIpEISUlJPH2Eah32wBFpoXPnzsmOCFLWkiVLMGPGDCZvpJesrKyQlJSEoqIi\nHD58WNPhENUYJnBEGvTVV1/B09MTKSkppc5mlNfWrVuRkpLCY7NIrxkYGGD27NmYP3++UiMs48eP\nR15enhoiI1IfJnBEGnL16lVkZWXho48+wuXLlxVO4DZt2oTAwECEhITA1NRUTVES6YbXW/EcPXpU\n4bqDBw+GqakpMjIy4OvrC6lUqoYIiVSLc+CINOjZs2dKbfcRFxeHYcOGQSQSITMzkzvIEwHYvHkz\nNmzYgPj4eEilUhgYKNZHIQgCunbtii+++ALDhw9XU5REiuE2In9jAke6LiUlBT4+PmjTpg0GDRqE\nL774QtMhEWmF4uJitG7dGiNHjkRaWhq2bdumcBIXExODZcuWISYmRk1REimGixiItNjly5dx7dq1\nKsvdunUL/fr1w2effYYbN25Ua/NSotrGyMgIs2bNwsmTJ5GTk4MpU6bI9cA+YcIEPH78GMCrox0P\nHDig7lCJqo0JHJEWuHTpklwJXGFhIcLCwnD27FmEhobytAWifxkzZgzEYjFmzpyJkydPYsGCBVXW\nGTRoEMzMzAC86u3gsVqkCziESlSDiouLMW7cOKxevRpWVlZKtZGQkIDBgwfjr7/+kn3oENH/t3nz\nZqxduxZRUVHo3r07vvzyS3zyySeaDotIKRxCJdICIpEIo0aNUjp5A4BvvvkGs2bNYvJGVIFRo0ZB\nIpEgMTERR44cwY4dO1BYWKjpsIhUij1wRFrg0qVLMDExQevWrSstd/LkSXz44Ye4ceMGtw4hqsRv\nv/2GuXPnyk5nqOyEhsDAQCxZsgS2tralrkdHRyM5ORlz5sxRd7hEFWIPHJEWu3jxIq5fv17q2osX\nL7Bjxw7Za0EQMH36dCxcuJDJG1EVXs9ri4iIqPJ4rYEDB8Lc3LzMdW9vb4wePVpdIRJVC3vgiLTQ\nixcvEBAQACMjI0RFRcHQ0BC7du3CggULkJiYyGOziORw9OhRBAYG4tq1azA2NtZ0OERKYQ8ckQbt\n2LFDtk1BVV68eAF/f3+YmJhg586dMDQ0RFFREUJDQ7F8+XImb0Ry8vHxgYuLC9atW1fquiAISh1d\nR6RNmMARqdnVq1fx6aefVtrze/HiRaSmpqKwsBBDhgyBmZkZduzYIes1+OWXX+Di4gI/P7+aCpuo\nVli+fDnmzZsHiUQiu5adnY1evXohKioKABAcHIwHDx5oKkQipXAIlUjNBgwYgJ49e+LLL7+ssMym\nTZtQv3597Nu3D/n5+di6dassecvPz0eLFi1w+PBhdOjQoabCJqo1AgMDYWlpiZUrV8quXbhwAe+/\n/z4WLlwIR0dH9OzZs9Ij6Y4ePQpzc3N069atJkImkuFRWn9jAkc17ffff0fv3r3lWniQk5MDBweH\nUsOkoaGhyMnJwaZNm9QZJlGtde/ePXh4eODUqVNo2bKl7HpaWhr69OmDKVOmVHkkXUREBJYtW4bz\n588rfDwXUXUwgfsbEzjSJWlpaXjzzTdx+fJlNGzYUNPhEOmsZcuW4eTJk9i7d2+p69nZ2fDz80NI\nSAhCQkIqrC8IArp3746PP/4Y48ePV3e4RDJcxECkxS5cuIC0tLRS1wRBwJQpUzBr1iwmb0TVNHXq\nVKSkpCA2NrbUdScnJ3Tr1g3du3evtL5IJMJ///tf9O/fX51hEsmNCRyRhly/fl32VJWcnFwmgdu3\nbx+ysrIwZcoUTYRHVKuYmppixYoVmDp1Kl6+fFnqvaFDh6JFixZVttGiRQs4ODioK0QihXAIlUgN\ntm7dCh8fnwp7zjZs2IDQ0FCcP38ezZo1K/P+8+fP4eHhgbVr18LX11fd4RLpBUEQ0L9/f7z99tsI\nDQ3VdDhEcuEQKlENunXrVrkTnaVSKWbOnInFixfjjz/+KDd5A17N1/H09GTyRqRCIpEIq1atwooV\nK5Cenl5pWalUir/++quGIiNSHBM4IjWYOXMmHB0dS117+vQpAgICcPr0aZw5c6bUuafJycm4ceMG\nACA1NRU//vhjqS0PiEg1nJ2dMW3aNEyePFnWqxESEoKcnJxS5a5cuYJu3bohIiKi3Hb27duH+Ph4\ndYdLVCEmcEQ1JCgoCNbW1oiJiYGdnV2p95KSknDjxg1IpVJMmDAB33zzDZo2baqhSIlqty+//BJZ\nWVnYtWsXAKBfv36wtLQsVaZdu3Y4cuQIQkNDMWPGDBQXF5d638rKCnXr1q2xmIn+jXPgiGpIXl4e\nrKysKj1Ye/Xq1di6dSv++OMPHplFpEYnTpzAiBEjkJKSgnr16lVY7uHDhxgxYgREIhF27NgBW1vb\nGoySiPvAyTCBI3U5efIkvL29YWJiolT9rKwseHp64o8//kCbNm1UHB0R/dukSZPw/PlzbNy4sdJy\nxcXFCAsLw61bt7Bt27Yaio7oFSZwf2MCR+ogFovRuXNnJCYmVrgwoTKJiYn48ssv4evri9mzZ6sh\nQiL6tydPnqB9+/Zwd3fHmjVr0Lhx40rLv3jxQq4TVYhUiatQidREEARMnjwZ06dPR7NmzXDw4MFK\nd3Qvz48//oisrCzMmDFDTVES0b/VrVsXGzduxKlTp1BUVFRl+YqStytXruDkyZOqDo+oUkzgiKpJ\nEAQMGzYMkydPxmeffYagoCAMGzZM7vp//fUXDhw4gH379ik9/EpEyunRowfGjBmDsLAwpeqXlJQg\nOzsbY8eOxfPnz1UcHVHFmMARVZOBgQE6d+6M7t27Izs7GxcuXECPHj3kqltUVITRo0djzpw5aNu2\nrZojJaLyLF68GImJidi5c6fCdcePH4/Y2Fi0b98eixcvVkN0ROVjAkdUTUePHkXPnj0REhKCqKgo\n2NjYyF134cKFqFevHt58803cvHlTjVESUUXCwsKwcuVKhISEQCwWK1R35cqVyMzMxOXLl/kQRjWK\nixiIqun58+d48OCBwvu2nTp1CkOGDEFycjL27dsHZ2dn9OnTR01RElFFDh8+jG7dumHDhg3Ytm0b\nTpw4odB0BkEQEBERgalTpyIwMBBz5szhdAhSGa5C/RsTOFKFwsJCfPvtt5gxYwaMjIwUrv/gwQN4\nenrip59+woABA9QQIREpShAEDB48GG5ubkqdhJKTk4OgoCD4+vpiypQpaoiQ9FFFeYvinzxEeiwv\nLw/W1tZ48eIF6tatq9RmuyUlJfjwww8xevRoJm9EWkQkEmHjxo3o2LEjevbsqfDPZ8OGDbF3715I\npVI1RUj0/3EOHJEc7t69i9GjR2Pw4MEAAGtra0yZMqXSUxUqMmfOHADAggULZNcSEhIUnntDRKrx\nxRdfIDMzEwBgY2OD7du3Y8KECbLziRUhEolw9+5dBAYGMpEjtWICR1SJoqIi/Pjjj2jXrh2aNGmC\n6OjoarW3d+9ebNmyBdu3by/Ve3f+/Hmkp6dXN1wiUsK7775b6jitN998E/Pnz8egQYOQn5+vcHsN\nGjTA4MGDSz3gxcfHIzExUSXxEgGcA0dUoWPHjmHSpElo3Lgxvv/+e3h4eFSrvZSUFPj4+GDfvn3o\n2rWriqIkInWZNGkSsrOz8dtvv1X7bOLIyEhMmTIF7777LhYtWoRGjRqpKEqq7XgSA5GCpFIpVqxY\ngZiYGHh4eODcuXPYtWuXUm3dvXsX/fv3x3fffcfkjUhHfP/99ygoKJBNe6iOoUOHIjU1FY6OjmjX\nrh0WLlyIZ8+eqSBK0ldM4Igq0Lt3b/Tr1w8ikQhPnjzBqFGjlGrn2bNnGDBgAD7++GOMHDmy3DIc\nQiXSnGnTppX782dsbIzIyEjs2LEDGzZsqPZ9rKyssHTpUpw/fx4XL15E//79q90m6S8mcKT3srOz\n8eTJk0rLLFiwAD169IC/v79CbZeUlGD06NFwd3ev9JD6c+fOISMjQ6G2iUg1+vbti/r165f7nr29\nPQ4ePIiwsDDs379fqfanTJmCs2fPyl67uLggMjIS+/btU6o9IoBz4EiP3blzB0uWLMG2bdsQFRWF\nXr16VVg2Pz8fBgYGqFu3rtztC4KA4OBgpKWl4dChQxUehE1E2u/s2bPo378/9u7dizfffFOhulFR\nUZg1axaSk5MV+h1CBHAOHJHMX3/9haCgILRt2xYmJia4du1apckb8GroQ9Hkbdq0abh48SL27dvH\n5I1Ix3Xp0gWbN2/GBx98gCtXrihUNyAgAN27d8fu3burLPvixQu8+eabWLNmDQoLC5UNl/QAEzjS\nK6mpqejWrRscHR2RmpqKlStXwsHBQeX3mTdvHuLi4nDw4EFYWlpWWZ5DqESaM2PGDLnOIn7vvffw\n7bffws/PD1evXlXoHr/++ivGjh1bZTlTU1MsX74c0dHRcHFxwfLly1FQUKDQvUg/MIEjvdKqVStk\nZmZi/vz5sLe3r7Tso0ePlLrH0qVLsWPHDhw5cqTCeTX/dvbsWdlGokRUs/r06QMbGxu5yo4aNQrh\n4eHw9fVVKIlTZBuSt956C9HR0Th06BCSk5Ph7OyMX3/9Ve76pB84B45qpdzcXEilUtjZ2SlVPzMz\nE8OGDcPp06dhYCDfc44gCJg9ezb27NmDmJgYNG7cWKl7E5H227JlC2bMmIHY2Fi4u7ur9V4ZGRl4\n8uQJ2rZtq9b7kHbiHDjSC8nJyZgwYQJcXV0RExOjdDvNmjXDiRMn5E7epFIppkyZgoMHD+L48eNM\n3ohqudGjR2P58uXo3bs3zp07p1BdQRBw+PBhuTsTmjdvXmHyxnly+osJHOm8vLw8rFq1Cp6enhg0\naBBcXFyQmpqKDz/8sFrtGhsby1Xu5cuXGD9+PJKTk3Hs2LEqh2bLwyFUIs0JDQ1V6tzTUaNGYe3a\ntejXrx8OHDggd72ioiL873//Q15ensL3/KfCwkI4Oztj1KhROHr0KM9e1TNM4EjnPXjwAKdOncLS\npUuRnp6OsLAwtSxMKE9ubi7effddPHr0CIcPH4a1tbVS7Zw5cwZZWVkqjo6I5OHn5wdbW1ul6g4Y\nMAD79+/Hxx9/LPdmvyYmJtiyZUup81eVYWZmhpSUFHTp0gWfffYZWrRogYULF3JBlJ7gHDjSGa+/\nb/88IFqVdu7ciUGDBsm95ceNGzfQv39/9O/fH8uWLav2WYlEpLtSU1Px3nvvISAgAIsXL4aRkVGN\n3l8QBCQkJGDjxo0wNjbG999/X6P3J/WpKG9hAkdaTRAEJCYmIiIiAjt37sTevXvRoUMHld9n/fr1\nWLp0Kc6ePSvXarTDhw9j7NixWLBgAQIDA1UeDxHpnocPH8qmbuzYsUPpXj11kUqlcs/rJe3BRQyk\nUy5cuIDp06fDzc0NH374IUxNTREdHY327dur/F7Xr19HWFgYoqOjq0zeiouL8dVXX2H8+PHYuXOn\nypI3DqESaU5YWBhSU1Or3Y6dnR0OHjyIjh07wsvLC0lJSXLVy8nJwYgRI/D06dNqx1CZ4cOHw8fH\nBz/88APn3NYCTOBIK6WkpMDCwgKRkZFIS0vDwoUL0a5dO7UMn7Zq1Qrnzp1Dq1atKi13584d+Pr6\n4ty5c0hKSsI777yjshhOnz6N7OxslbVHRPLz9fVVesuhfzMyMsKyZcsQHh6Od999F8uXL69ycYGj\noyPMzMwQEBCAly9fqiSO8mzatAlTp05FcnIyvLy80LFjR8ydO5cbBesoDqGSRkilUly8eBEPHjxA\nnz59NB1OpQRBwLZt2/DFF18gJCQEYWFhnO9GRFXKyMjAmDFjYGxsjE2bNsHJyanCssXFxRg7diym\nTZuGTp06qT224uJinDp1CtHR0Vi4cCFMTEzUfk9SDufA/Y0JnOZkZWUhJiYGMTExiIuLg42NDcaM\nGYPZs2drOrQK5eTkIDg4GGKxGBs3boSXl5emQyIiHVJSUoLw8HD83//9HxYuXIiJEyfqxDy0+/fv\n4//+7//g5+eHrl27wsLCQtMh6S3OgSONevjwITp37oy4uDj06dMHiYmJSE1N1UjylpGRgc2bN1da\npri4GD/99BPat2+Pdu3aISEhQa3JG4dQiTRn9uzZuHbtmlraNjQ0RFhYGI4dO4bNmzfj7bffRkpK\nilrupUqCIMDIyAhfffUVHBwc8NZbb2HWrFk4ceKEpkOjvzGBI5V4+fIlEhIS8N133+HFixdl3rez\ns0NOTg62bduG8ePHo2nTphqI8hVBEFBUVFTh+8ePH4enpyeioqIQFxeHhQsXyr21iLJOnTqFW7du\nqfUeRFS+3r17K7UBtyLatm2LP//8E2PHjoWPjw8+++yzKs9bLioq0tiIkaOjIxYsWIDTp0/j/v37\nWLBgAUxNTZGQkKCReKgsDqGS0qKiohAfH4/z588jJSUFLi4u6N69OxYuXKh1y+flcfnyZXz99ddI\nTEzEihUrMHToULXtOUdE+uv+/fuYP38+IiIiMH36dEyZMgVmZmZlys2ePRvNmjXDxIkTNRClYlat\nWoVDhw6hc+fO6NKlC7y9veXakomqxjlwf2MCp5jCwkIIggBzc/My74WHh8PY2Bje3t7o2LEj6tat\nq4EIqy81NRXz5s1DXFwcZs6ciU8++aTcfy8RkSqlpqYiNDQU58+fx7Rp0xAYGFhqrllBQQFMTU11\nYoHBvXv3cPLkSZw9exbnzp1DQkICHB0d8d1336F///6aDk+nMYH7GxO4iuXk5CAxMRGXLl2SfaWn\np2Pbtm344IMPNB2e0vbv34/OnTvD0dFRdk0QBPz5559YuXIlTp8+jSlTpmDq1KmwtLTUSIynTp1C\n06ZN0aRJE43cn0ifff311xg+fDg8PDw0cv/k5GQsWrQIJ06cwNSpUxEYGKiToxj/VFJSgtTUVNja\n2pb63fvapk2bUFxcDHd3d7Ru3Rr169fXQJS6gYsYCADw5MkT5Obmlvvehg0bsGrVKkgkEvTr1w/b\nt2+HRCLR2eRNKpVi3rx5+OSTT3D//n0AwLNnz/C///0PnTt3xsSJE/Hee+8hIyMDs2fP1ljyBgAn\nT57E7du3NXZ/In3m4+NTY+cnl6djx46yObepqalwc3PDuHHjcP78+TJl8/LyNBCh4gwNDeHu7l5u\n8ga8SkqOHz+OKVOmoGnTpmjQoAF69uyJtLS0Go5Ud2lND1xSUhISExNhY2MDsViMTp06oXfv3iqv\np089cBcvXsSBAweQnp4OsViM1NRU5ObmYtGiRfj88881HZ7anT9/HjNmzMC2bduQmZmJjRs3IjIy\nEt26dUNQUBD69++vE8v5iUi/PHz4EBs2bMDq1athZ2eHMWPGYMSIEbCwsIC7uzvmz5+Pjz76SNNh\nqowgCLhz5w6uXbuGzp07w8rKqkyZyZMnw8TEBC4uLrKv5s2b68V0F60eQhWLxQgODsaRI0dk14YN\nG4bw8HA4OzurtJ6uJ3BFRUXIycnB7du3cevWLWRnZ6N58+YYMmRImbJxcXE4cuQInJ2d4eLiglat\nWsHJyUkvkhZBEHD+/HlERUVhz549AIDx48dj7NixaNy4sYajIyKqWklJCWJjY7F161bs378fXbp0\nQY8ePbBx40Z89NFHCAsL03SINSY6OhrXr1+HWCyWfWVlZSE7O7vcFcRXrlxBgwYNYGNjo/OL0bQ6\ngQsKCkLfvn1LJSFxcXH45ZdfsHPnTpXW09YErqSkBLm5ubh//z4MDQ3RunXrMmV27tyJ0aNHw8HB\nAU2aNEHjxo3RpEkT+Pr6YsCAARqIWrtIJBIcPXoUMTExOHDgACwsLODv748hQ4agU6dOWv1DfPLk\nSTRv3pzJJZEGzJ07F/7+/mjXrp2mQ6nQs2fPsG/fPkRGRiI2Nhaurq7w9/dHv3798MYbb+jFg/m/\nlZSUwMDAoMzvdkEQ4OnpifT0dLx48QJNmjSBk5MTmjRpgvXr18PIyKhMW4IgaO1nhFYncDY2NkhK\nSkLz5s1l1yQSCWxsbCo9Q06ZejWVwEmlUuTl5SE3NxeCIMDNza1MmRMnTmDSpEm4f/8+Hj16BGtr\nazg4OGDgwIFYunRpmfIvX76EoaEhj3H624MHD3D27FmcPn0aBw4cwJUrV9C7d2/4+fnh3Xffhbu7\nu9b+QP5beHg4fHx84O3trelQiPTO8ePH0aZNG43Og1PEixcv8OeffyI6OhrR0dGQSCTo0aOH7Kt9\n+/b8nPjbkydPZKNVOTk5GDt2bJkyhYWFsLGxgaOjY6mvxo0b45tvvilT/nUOUVOfL1qbwL1OuCQS\nSZlxbwMDA4jF4lIJWnXrKZLAFRcX4/HjxygoKEB+fj7y8/Px+PFjmJubl3t+55kzZzBq1Cg8fvwY\neXl5sLS0RP369dG3b1+sWbOm3H9DZmYmHBwcYGdnB2NjY7ni0jeCIODu3bu4cuUKUlJScO7cOZw5\ncwa5ubno3Lkzunbtih49egB4dSg1EZE+yc7OxoYNGxAbG4tHjx4hOzsb7du3R6dOnWRfbdq04WdM\nJZ4+fYp79+7h7t27uHfvHu7du4f8/HzMmDGjTNnc3Fw0bNgQNjY2sLW1lf3p5OSEH374oUz54uJi\nXLlyBdbW1rC2toaVlZVCCbbWJnBisRhubm7l9pgZGBggNjYWPj4+KqsnEokwd+5cWUJWUFAAJycn\nLF++vEzZ06dPY8CAAbCysoKlpSWsrKxgY2MDLy8vzJkzp0z5J0+eICcnBzY2NrC2ti63m1bd4uPj\n0bNnzxq/rypIJBJkZGQgPT0dGRkZSEtLQ0pKCq5cuQIDAwN4eHjAw8MDXl5e8PT0RLt27WrVsIEu\nf++I3z9dVhu+d5mZmbh58yZ8fHzw+PFjXLhwAUlJSUhOTkZSUhLEYjGaNWuGVq1aoVWrVmjZsiVa\ntWqF5s2bo1GjRhr5vFIVTXz/CgsLkZubi0ePHsn+LCwsxMiRI8uUffDgAXx8fJCXlyfLO8zNzdGy\nZUskJSWVKZ+Xl4fly5ejbt26cHZ2xogRI8pN4DT+HZNIJDVaD3g1vNmwYUO0atUKVlZWFc476tat\nGx4+fCh3u3Xr1kWLFi2UjksVtO0XUXFxMfLy8nD//n3ZU83rr9fXsrOzkZ6ejuLiYjg7O8PZ2RnN\nmzdHmzZtEBAQgLZt28LBwQF3797Fpk2bsGzZMvznP/9B+/btNf3PU5kTJ05g//79WvW9I8Vo288e\nyW/evHmoX7++Tv9OadasGZo1awYAqF+/Pnr16oVevXohISEBbdu2BQDcvHkTqampSEtLw6lTp7Bx\n40ZkZmbiwYMHcHBwgJOTk+yrQYMGsLe3h52dHezs7GR/t7Ky0rqpKZr42TMzM0OjRo3QqFGjKsva\n29vj8uXLstdSqRRPnjzBs2fPKm1fIpFUesSixhM4TZg3b56mQ6gxUqkUJSUlKC4uln1V9bq4uBgv\nX75EYWEhnj9/jufPn1f49+fPn+PZs2fIy8sr8yWRSFBYWAgrKyvY29uXmV/g5eUFR0dHODk5oXnz\n5qVWC718+bLM7uOXL19Geno6Nm7ciK5du2riP6fa/PnnnygoKNB0GER6qXnz5mjQoIGmw1CLxYsX\nIyYmBt26dcPOnTvL3az49e4G2dnZsq979+4hJSUFDx8+xMOHD/HgwQM8fPhQNl/M0tJSNjJV3t/N\nzMxKfZmampb72sTEBEZGRjA0NKz0z9d/L2/Rgq4xMDCAlZVVudulAIC1tTVmz54tez1t2rTyGxI0\nLDExURCJROW+JxKJhLi4OJXWAyAYGxsLdevWFZycnIS6desKrq6ugqurq+Dg4CAYGhoKzs7OgrOz\ns9CoUSPBwsJCaNiwoWBkZCQYGhoKhoaGgpOTk+Dk5CQ4ODgI5ubmgr29vWBmZib7s2HDhkLDhg0F\na2trQSQSCYaGhoKpqalQv359wdTUVLC3txfs7e0FS0tLwcDAQLC1tRVsbW0FKysrwcTERHZdJBIJ\nIpFIsLa2FqytrYU6deoIRkZGgoWFhWBkZCSYm5sLRkZGQp06dYQ6deoIJiYmAgABgCASiWR/NzIy\nEszMzAQTExNBJBIJtra2gqOjo2Bvby9YWFgIjRs3lv37jIyMhI4dOwqdO3cWPD09hQYNGgi9evUS\nGjVqJAwaNEhwc3MTvvzyS2H27NnCsGHDBCMjI8Ha2lro2LGjsGrVKsHHx0dISUkRsrOzhQ0bNggN\nGzaU/be/cOGCMGzYMCExMVFwdHQUbGxshAYNGpR5/8yZM0L37t1lr//9fm19/c033wiku/j9012v\nv3dLliwRNm7cKLteW14/fvxY2Ldvn7B48eJS7y9evFiwt7cvU76kpERo3bq1YG9vX+p3+JIlS4S1\na9cKt27dElxdXYWQkBBhxowZwt69e4UtW7YIAwcOFCwtLQVbW1vBxsZG6Natm/DOO+8IY8aMEYYO\nHSq0bt1aMDExEXr06CF07txZaNCggdCgQQPBzc1NMDY2FgwMDAQDAwPBwcFBsLW1FUxNTWVfrz/P\nAMg+U42MjEp95pmYmAhmZmaCtbW1UK9ePcHMzEz2mWdnZyfUqVNHsLS0lH3Wi0QiwcDAQGjcuLHQ\npEkTwdraWrC1tRWaNWsmGBsbCzY2NoK9vb3g5uYmuLm5CTY2NoKhoaFgbGwsGBsbC7a2toKDg4PQ\nokULoUWLFoKtra1gaGhY6rWjo6PQokULwcTERJZDtGzZUmjZsqVgZ2cnODo6Ci1bthRMTEwEOzs7\noUGDBkKrVq2EVq1aCXZ2doKZmZlQUaqm8TlwNb2IoUOHDrh48aIq/wlEREREatG+fXtcuHChzHWN\nD6HWq1cPLi4uEIvF6NChg+y6WCxGvXr1yk3CqlOvvP8IRERERLpEK5bw+fr6ljnzLSkpCX5+fmqp\nR0RERKTLtCKBCw8PR2RkZKlra9euRXh4uOy1RCKBq6sr1q1bp1A9IiIiotpG43PgXktOTkZERAS8\nvb0hFovh6elZah83iUQCFxcXLFu2DBMmTJC7HhGRuiQlJSExMRE2NjYQi8Xo1KkTevf8/66RAAAF\nwElEQVTuremwSE67du2CWCzGzZs3IRaLERQUBH9/f02HRQqSSCQIDQ0td8P82kxrEjgiIl0iFosR\nHByMI0eOyK4NGzYM4eHhcHZ21mBkJI9du3bBxcUFHTt2BPBq81RPT0/MnDkTEydO1HB0pIigoCA8\nfvy40rPTayOtGEIl9ZNIJAgODtZ0GKSAXbt2Yfny5QgODkafPn2wa9cuTYdE/xAeHl7mZyooKAgz\nZ87UUESkCLFYLEvegFd7b82cORNBQUEajIoUJRaL8fjxY53fG04Z7IHTE/r6hKKr2Dug/WxsbJCU\nlFRqxfvr7Y3KO+KPtIdEIoGvry/i4uJgbW0tu/76iMaKtqEi7fN6XnxMTIzefb6xB04P6PMTiq5i\n74B2k0gksmTtn+rVqwcAyMjI0EBUJK969epBLBYjPT1d06FQNcTFxcHX11fTYWgMEzg9EBcXBz8/\nv3IPwyXtI5FIEBERgby8vFLXX0+OZ3Kgebm5uQBQ4VE4YrG4JsMhJeTm5pbaQxQAYmNjUb9+ffa+\n6QixWAxnZ2e9/WxjAlfL6fsTii5i74D2k0gkmg6B1OCXX37BrFmzNB0GyWHXrl16P51E4ycxkHqJ\nxWL07t1bb59QdNXrHp5/Yu8AkfqsXbsWdnZ2FR8cTlqDD1CvMIGrxfiEUruwd4BIPcRiMdauXYuE\nhARNh0JyiIyMLPXZpq/zuzmEWkvxCaV2Ye+AdnFxcQEA5OfnV/o+6YbQ0FAcPXpU02GQHJKTk+Hl\n5VXqmr6OMLEHTsspMhna1tZWtiSeTyjaQdnv37/bYO+AdqlXrx5cXFwgFotLTYQXi8WoV68eh7l1\nSHBwMJYtW1bhghTSLgkJCbh58yYiIiJk15KSkiAWixEaGgpvb2+9OU2DCZwWS09PR2hoqNzlO3fu\njGnTpiEpKYlPKFpA0e+ft7c3pk+fXuY6ewe0k6+vL86fP18qgUtKSoKfn58GoyJFrFu3DqGhoaUS\n7ri4OLi4uPA0DS1V3rSg5cuXIyEhAUuXLtVARJrDjXxroXXr1uHmzZulrr1+QgkICNCrJxRdFxwc\nXOYDhrRDXl4ehg4dWuoorT59+mDt2rX8fumAqKgoPH78GJ6enrJrubm5iIqK0rszNXXdzJkzkZ6e\nrncb+TKB0xOvn1D+2e1M2m3dunXw8/Nj74AWS05ORkREBLy9vSEWi+Hp6QkfHx9Nh0VVKG8T5tdc\nXV1x48aNGo6IlJGeno7w8HDs3LkTeXl5mDhxIoKCgkptgl6bMYHTE/r6hKKr2DtARESVYQJXy+n7\nE4ouYu8AERFVhQkcERERkY7hPnBEREREOoYJHBEREZGOYQJHREREpGOYwBERERHpGCZwRERERDqG\nCRwRERGRjmECR0RERKRjmMARERER6RgmcEREREQ6hgkcERERkY5hAkdERESkY5jAEREREekYI00H\nQESki8RiMeLi4iCRSHDz5k2sWbMGy5cvR7169XDkyBFERkZqOkQiqsVEgiAImg6CiEiXSCQSREZG\nYuLEiQAAPz8/iEQiREVF4ciRIxg+fDgeP34MKysrDUdKRLUVh1CJiBS0bt06WfIGALm5ufD09ISV\nlRUCAgJw8+ZNJm9EpFbsgSMiUlBeXh6sra1lrw0MDBAbGwsfHx8NRkVE+oQJHBFRNcTGxqJPnz6Q\nSqWaDoWI9AiHUImIqiEmJgaenp6aDoOI9AwTOCIiBYnFYtnfY2Nj4eXlJXstkUiwa9cuTYRFRHqE\nCRwRkQJiY2Ph5uaG9PR0JCUlQSQSlZoPt27dOvj7+2swQiLSB5wDR0SkgPT0dCxbtgydOnUCAAwb\nNgwzZ86UDaMOHz6cK1CJSO2YwBERERHpGA6hEhEREekYJnBEREREOoYJHBEREZGOYQJHREREpGOY\nwBERERHpGCZwRERERDqGCRwRERGRjmECR0RERKRjmMARERER6RgmcEREREQ65v8BUqAygMNsNeMA\nAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Distributions with positive kurtosis (\"leptokurtic\") are highly peaked. Distributions with negative kurtosis(\"platykurtic\") are flat-topped. The book notes that skewness and kurtosis are higher-order descriptors, and thus are poorly defined for data sets with small N. Open question: what are common uses for skewness and kurtosis in astronomy?" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Errors in Data-Based Estimates of Descriptive Statistics" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "In practice, we measure things and then use those measurements to estimate descriptors of intrinsic probability distribution function of the population. This section describes how we assign errors to those descriptors. Below, I've included equations for standard errors in the mean, standard deviation, and the median in terms of \"s\". \"s\" is the sample standard deviation, i.e. the standard deviation in the measured population." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "import matplotlib.image as mpimg\n", "import numpy as np\n", "%matplotlib inline\n", "\n", "fig,ax = plt.subplots(figsize=(10, 7.5))\n", "plt.axis('off')\n", "ax.text(0.35, 0.98, 'Error in Mean',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=30)\n", "ax.text(0.4, 0.9, r'$\\sigma_{\\bar{x}} = \\frac{s}{\\sqrt{N}}$',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=40)\n", "ax.text(0.15, 0.68, 'Error in Standard Deviation',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=30)\n", "ax.text(0.15, 0.6, r'$\\sigma_{s} = \\frac{s}{\\sqrt{2(N-1)}} = \\frac{1}{\\sqrt{2}}\\sqrt{\\frac{N}{N-1}}$',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=40)\n", "ax.text(0.35, 0.28, 'Error in Median',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=30)\n", "ax.text(0.35, 0.2, r'$\\sigma_{q50} = s \\sqrt{\\frac{\\pi}{2N}}$',\n", " ha='left', va='top',\n", " bbox=dict(ec='none', fc='w'), fontsize=40)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAAHDCAYAAADm5lRyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkkYsknRMggAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The median is more robust to outliers than the mean. In return, however, it takes ~25% more data to achieve the same accuracy in the median as in the mean. Open question: do people commonly use other descriptors for probability distributions? what are the advantages of those?" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "The Central Limit Theorem (3.4)" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The Central Limit Theorem, from the book: Given an arbitrary distribution h(x), characterized by its mean \u03bc and standard deviation \u03c3,the central limit theorem says that the mean of N values drawn from that distribution will approximately follow a Gaussian distribution, with the approximation accuracy improving with N" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "This is demonstrated below with a uniform distribution between 0 and 1, calculating the mean with N=2, N=3, and N=10 a million times each." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# import\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from scipy.stats import norm\n", "%matplotlib inline\n", "\n", "# fonts\n", "from astroML.plotting import setup_text_plots\n", "setup_text_plots(fontsize=8, usetex=True)\n", "\n", "#------------------------------------------------------------\n", "# Generate the uniform samples\n", "N = [2, 3, 10]\n", "\n", "np.random.seed(42)\n", "x = np.random.random((max(N), 1E6))\n", "\n", "#------------------------------------------------------------\n", "# Plot the results\n", "fig = plt.figure(figsize=(10, 10))\n", "fig.subplots_adjust(hspace=0.05)\n", "\n", "for i in range(len(N)):\n", " ax = fig.add_subplot(3, 1, i + 1)\n", "\n", " # take the mean of the first N[i] samples\n", " x_i = x[:N[i], :].mean(0)\n", "\n", " # histogram the data\n", " ax.hist(x_i, bins=np.linspace(0, 1, 101),\n", " histtype='stepfilled', alpha=0.5, normed=True)\n", "\n", " # plot the expected gaussian pdf\n", " mu = 0.5\n", " sigma = 1. / np.sqrt(12 * N[i])\n", " dist = norm(mu, sigma)\n", " x_pdf = np.linspace(-0.5, 1.5, 1000)\n", " ax.plot(x_pdf, dist.pdf(x_pdf), '-k')\n", "\n", " ax.set_xlim(0.0, 1.0)\n", " ax.set_ylim(0.001, None)\n", "\n", " ax.xaxis.set_major_locator(plt.MultipleLocator(0.2))\n", " ax.yaxis.set_major_locator(plt.MaxNLocator(5))\n", "\n", " ax.text(0.99, 0.95, r\"$N = %i$\" % N[i],\n", " ha='right', va='top', transform=ax.transAxes,fontsize=20)\n", "\n", " if i == len(N) - 1:\n", " ax.xaxis.set_major_formatter(plt.FormatStrFormatter('%.4f'))\n", " ax.set_xlabel(r'$x$',fontsize=20)\n", " else:\n", " ax.xaxis.set_major_formatter(plt.NullFormatter())\n", " \n", " plt.xticks(fontsize=20)\n", " plt.yticks(fontsize=20)\n", " ax.set_ylabel('$p(x)$',fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAo8AAAJzCAYAAABuwPkZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiIuowFo9ERERE1GH/P46iLhbyLKi3AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "This ONLY applies to distributions with a well-defined mean and variance. This means that the tails of the distribution fall off faster than 1/x^2 for large x. One distribution of astronomical significance where this is NOT true is the Cauchy (Lorentzian) distribution, shown below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#input\n", "import numpy as np\n", "from scipy.stats import cauchy\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "\n", "# fonts\n", "from astroML.plotting import setup_text_plots\n", "setup_text_plots(fontsize=8, usetex=True)\n", "\n", "#------------------------------------------------------------\n", "# Define the distribution parameters to be plotted\n", "gamma_values = [0.5, 1.0, 2.0]\n", "linestyles = ['-', '--', ':']\n", "mu = 0\n", "x = np.linspace(-10, 10, 1000)\n", "\n", "#------------------------------------------------------------\n", "# plot the distributions\n", "fig, ax = plt.subplots(figsize=(10, 7.5))\n", "\n", "for gamma, ls in zip(gamma_values, linestyles):\n", " dist = cauchy(mu, gamma)\n", "\n", " plt.plot(x, dist.pdf(x), ls=ls, color='black',\n", " label=r'$\\mu=%i,\\ \\gamma=%.1f$' % (mu, gamma))\n", "\n", "plt.xlim(-4.5, 4.5)\n", "plt.ylim(0, 0.65)\n", "\n", "plt.xlabel('$x$',fontsize=20)\n", "plt.ylabel(r'$p(x|\\mu,\\gamma)$',fontsize=20)\n", "plt.title('Cauchy Distribution',fontsize=20)\n", "\n", "plt.legend(fontsize=20)\n", "plt.xticks(fontsize=20)\n", "plt.yticks(fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 35, "text": [ "(array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7]),\n", " )" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnEAAAHyCAYAAACEQZjTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgghRAFRiCOEEEIIUUD/D7TfNZuNUC4bAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "So what happens if we draw randomly from a Lorentzian and try to compute a mean?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# import\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from scipy.stats import norm\n", "from scipy import stats\n", "%matplotlib inline\n", "\n", "# fonts\n", "from astroML.plotting import setup_text_plots\n", "setup_text_plots(fontsize=8, usetex=True)\n", "\n", "#------------------------------------------------------------\n", "# Generate the uniform samples\n", "N = [2, 3, 10]\n", "\n", "dist = stats.cauchy(0, 2.0) # mu = 0, gamma = 2\n", "x = []\n", "for i in range(max(N)):\n", " x.append(dist.rvs(1e6))\n", "x = np.array(x)\n", "#x = dist.rvs(1e6) # ten random draws\n", "\n", "#------------------------------------------------------------\n", "# Plot the results\n", "fig = plt.figure(figsize=(10, 10))\n", "fig.subplots_adjust(hspace=0.05)\n", "\n", "for i in range(len(N)):\n", " ax = fig.add_subplot(3, 1, i + 1)\n", "\n", " # take the mean of the first N[i] samples\n", " x_i = x[:N[i], :].mean(0)\n", "\n", " # histogram the data\n", " ax.hist(x_i, bins=np.linspace(-10, 10, 251),\n", " histtype='stepfilled', alpha=0.5, normed=True)\n", "\n", " # plot the expected gaussian pdf\n", " mu = 0.0\n", " sigma = 1. / np.sqrt(12 * N[i])\n", " dist = norm(mu, sigma)\n", " x_pdf = np.linspace(-1.5, 1.5, 1000)\n", " ax.plot(x_pdf, dist.pdf(x_pdf), '-k')\n", "\n", " ax.set_xlim(-5.0, 5.0)\n", " ax.set_ylim(0.001, None)\n", "\n", " #ax.xaxis.set_major_locator(plt.MultipleLocator(0.2))\n", " ax.yaxis.set_major_locator(plt.MaxNLocator(5))\n", "\n", " ax.text(0.99, 0.95, r\"$N = %i$\" % N[i],\n", " ha='right', va='top', transform=ax.transAxes,fontsize=20)\n", "\n", " if i == len(N) - 1:\n", " print 'hi'\n", " else:\n", " ax.xaxis.set_major_formatter(plt.NullFormatter())\n", " \n", " plt.xticks(fontsize=20)\n", " plt.yticks(fontsize=20)\n", " ax.set_ylabel('$p(x)$',fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "hi\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAJcCAYAAAB5fZnuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiKDAMcERERUZH5/wFpU0n5UxEnpgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Nonsense! This distribution of \"mean\" values actually follows a Cauchy distribution, with an infinite variance." ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "So for some distributions the Central Limit Theorem works, for others it doesn't. But what do we do when we don't know the distribution a priori? The book will tell us a maximum likelihood / Bayesian approach in 5.6.4." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }