{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Markov Chain Monte Carlo\n", "\n", "Markov Chain Monte Carlo (MCMC) is a method of sampling from a probability distribution. Their purpose is to approximate a probability distribution and it is supposed that they can approximate any probability distribution. This notebook will use MCMC to to approximate the distribution for the best line of fit with 3 points. For simplicity and visualization, the intercept of the line will remain 0, so perhaps it would be more appropriate to say we are modelling the best *slope* of fit. In any case, the example will work like this." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup\n", "\n", "We have 3 data points defined as `pts` below. We are quite confident after plotting them that the slope of best fit lies somewhere between 0 and 2. Linear models are often evaluated based on the $R^2$ or sum of residual squares (SSR)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "pts = np.array([[-2,-2],\n", " [ 1,-1],\n", " [3, 1]])" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(pts[:,0],pts[:,1])\n", "plt.hlines(0, -2, 3)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of y = mx + b, we just use y = mx, so that we can visualize R2 and SSR as slope changes" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "slope = np.linspace(-2,2,200)\n", "ys = np.concatenate([np.atleast_2d(slope * pts[i,0]).T for i in range(3)], axis=1).T" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "sst = np.square(pts[:,1]).sum()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sst" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below is a line plot charting the reciprocal of SSR ($\\frac{1}{SSR}$) against different slopes and we can see a peak around a slope of 0.5. Where SSR is lowest, $\\frac{1}{SSR}$ is highest. The point of this plot is to demonstrate that MCMC does not have to be used strictly with probability distribution, but also with any kind of scoring function. Essentially, we will be using MCMC to sample a distribution that is proportional to the \"distribution\" that we see in the plot." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "ssr = np.array([np.square(ys[:,i] - pts[:,1]).sum() for i in range(ys.shape[1])])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "r2 = 1 - ssr/sst" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(slope, 1/ssr)\n", "plt.title(\"Our 'Distribution'\")\n", "# plt.vlines([-.5,-.25], ymin=0, ymax=.3)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## MCMC\n", "\n", "MCMC works by chaining together steps. Each step works like this:\n", "\n", "1. The model has some value (or vector) for the parameter(s)\n", "2. The model obtains some score for these parameters\n", "3. The model parameters are then changed by a random amount in a random direction (this is called sampling)\n", "4. Three things can happen:\n", " 1. The model can obtain a higher score based on the new parameters. In this case, the model instantly accepts these new parameters and adds a new \"link\" to the chain with the values of the parameters.\n", " 2. The model can obtain a lower score based on the new parameters. A randomly generated number may ___reject___ the new (worse) parameters.\n", " 3. The model can obtain a lower score based on the new parameters. A randomly generated number may ___accept___ to accept the new (worse) parameters.\n", "5. Steps 4 and 5 are repeated until there are sufficient links in the Markov chain\n", " \n", "At every step where the new score is less then old score, a random number is generated such that the probability of keeping the new parameters is proportional to the ratio of the lower score over the higher score. Otherwise, the new parameters are accepted immediately. This way, the Markov chain tends toward optimal parameter values and the chain \"converges\", not to one value, but to one distribution that can be visualized." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "slope = 0\n", "slope_history = np.zeros(1000)\n", "slope_history[0] = slope\n", "\n", "y = slope * pts[:,0]\n", "sst = 6\n", "ssr = np.square(y - pts[:,1]).sum()\n", "ssr_history = np.zeros(1000)\n", "ssr_history[0] = ssr\n", "\n", "drift = lambda : np.random.normal(scale=.25)\n", "\n", "accept = False" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "for i in range(1,1000):\n", "\n", " # Make slope wander\n", " slope = slope_history[i-1] + drift()\n", " y = slope * pts[:,0]\n", " ssr = np.square(y - pts[:,1]).sum()\n", "\n", " # if current ssr is less then the previous ssr, accept and continue\n", " if ssr > ssr_history[i-1]:\n", " p = ssr_history[i-1]/ssr # The current SSR's \"power\" relative to the previous one\n", " accept = np.random.choice([True, False], p=[p, 1-p])\n", " if not accept: # If we do not accept, we go to the beginning and try again\n", " slope_history[i] = slope_history[i-1]\n", " ssr_history[i] = ssr_history[i-1]\n", " continue\n", "\n", " # If we pass all the tests, record all the results and move on the next step\n", " slope_history[i] = slope\n", " ssr_history[i] = ssr" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7597993976531564, 0.2402006023468436)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p, 1-p" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.878467082737986" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ssr" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(slope_history)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.hist(slope_history[500:], bins=20)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4531158903239566" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.median(slope_history)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PyMC3\n", "\n", "PyMC3 is an API for MCMC that makes defining a model and sampling a posterior easy and straightforward. By defining random variables and their relationships, PyMC3 is able to easily combine and transform distributions by using the log-probabilities as the scoring function. Then after providing observed data, PyMC3 generates a Markov chain which can easily be plotted and analyzed. Below is an example of our best slope-of-fit using PyMC3." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_16225/3189802570.py:15: FutureWarning: In v4.0, pm.sample will return an `arviz.InferenceData` object instead of a `MultiTrace` by default. You can pass return_inferencedata=True or return_inferencedata=False to be safe and silence this warning.\n", " posterior = pm.sample()\n", "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [noise, weight]\n" ] }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pymc3 as pm\n", "\n", "X, y = pts[:,0], pts[:,1]\n", "with pm.Model() as linear_model:\n", " weight = pm.Normal(\"weight\", mu=0, sigma=1)\n", " noise = pm.Gamma(\"noise\", alpha=2, beta=1)\n", " y_observed = pm.Normal(\n", " \"y_observed\",\n", " mu=X @ weight,\n", " sigma=noise,\n", " observed=y,\n", " )\n", "\n", " prior = pm.sample_prior_predictive()\n", " posterior = pm.sample()\n", " posterior_pred = pm.sample_posterior_predictive(posterior)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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3WpxX8tSx2LSeLQpqKqeT1Eeh7nlhmQWVF3PUndGoOyWUdBgLI57N2HAcdQ5kdSArjto2hLzJpZcow6hskaO2DSEXrxDd82RqJV/dikKrgyeiCjoYiV6kMKL2KIyjjrw+xtaYSBp1J1c6KtpqTMxBBDpBnQNZ/Sdt8NGpZGSiifpo1pgY30dcrqdw1DYeByrXHdEFGg58rNFo0ZebbmlVo24FRT65eI66M9QH0WrdoVEX26ZPbh5K5PRg44D6KHfkqS0iS3hqzypRYwk/apPXR5PfRbyPJgHRmBgEe+QrJ+CoNfVqoo5F2InERYjPgVLOMjvrnke5PgrUqBN/tAYK4R5rQR3Ra10gqIuuwjlfvxMAsObLF0bHYj/qfCvcscS41KhN7RktPTXKcSb1YTAmNitDxE5OHiVMOm8noMRJyUSXdGpA8Za1+myqYGik3t4E9m3hqIM/Hl2/A+/66dKm618pdSbgpRuMvCq6JTLRGRNzIJOj1ow+9Rb14zy+cQibdg5r7qOlV74PJPZxynUteppwbt5QV35+/HfD1ydy6lRkojiQmxnUNDemUR9Hf/pmfOTah3OXbV2HtnDUwe/3//xB3LT8OTy1pdn9HAOMda6PWKMe08emoq1JmUIVysoLq0P2lHEqqPOfV4Wi+lGuvONJnPzFW5P35a1cdJ+gUdeTHDVHfm7WFG7djKwpIhGN2M7N1EG3W410Piz0ugfW5S/ctg6FatSyoG4V9P5jrcXR9xjrrH06aKm+ghFx1KY6CA/vVODNuBTUWZqoVpgpv237YCEcdeRHrRgTcxovfMHrw3SNCcO1RuFLaPG5zRgEda6GItpr6ac6xA95cvMQfv2AIamXBeg9ihrMYxHsoUMrEaO1hl+oK128om0/zJRq/Hen5q5xKaizGkt3Our0OdO8NNvpZI6aNGrhvG/n9SFRH5wbaJ3sco79zC044lO/j+8poOvr9m3M0150j2miGQtNUvwE533jTvzzLx5qoaxiNeqs9mkXYhfQfPeN1Bs49OM34Ss324XcW9VFrVQbEBkTDWNCPOo46hwwCQM6qg14SZRh+Sz7akmQOOrIjzo/9SFewTnXap82A4rycsRtlH1PFiRtv5movPBaUzuMjdueONm0WFKkDBSDTnlfRBNEzgYZHA78vX9x/7OF1aXoNtWCpXPUEvXhNGp7ZPYfG47a8lnNLj/F55FGzaTzdgNBLKfh62f9ZrTjIjqcrzEm5hEqWQJhLHhJewrMZlJtF0ddTHm2oG+Z10BMykAlr59mCsZiZ3eq7bPbdmszQsq2GKdRWyN7m6vsMmwFShHZ8+qmgBereop/J+9hrLmBXISWJtct+D/PvnNZ2r1tHVsRC7bNkO9bFcOrRu5+HaI+8q5oSFBX27CFlzoOh2sNfPiXD0mbcTQLGpbXLVuHT13/aOqzHUedA9kctY7H1f+v4uG127X35YUoZEbJj1rZicRKEIkctZ906Ssxlmsgt7qUlDR8xdC5YsNOvPOnS3W3aZEV8GKt7Vo/UfcMu7ttNj9um9eH4dH/8N9LsOCyG6Rju0freNX37saKDTubfm4z9gYgjsCtlooTK6bxev2D6/DLpWvxrzetbPkZogfUn57YbKwD4Lw+cqEZjVptYFMJF39H3my1+aRMwf//fe8a3PPEFgBK9jxul+ZUrHcg3OXzJY815xon3LRt16h1UIakRSvGxJ059z/Mcj8bi4AL2yfYbFKvJmVqlQDI4qhvfnRj4tiGHcN44JnteGx984KaJuC87U8bZFTLxW04wA2rk8j3uYBniONS57bqvD6aRCZFbeFrnFdbyPt9qPxPXv8obl0Z0AGeEkJupVCLGjVPRiaWPNbUZMI58O7/WYYrFq/GCZ/7Az7xv8sT19y+chMWXHYDnto8FB3T5dkGmhOqPEMQ2X6jNIH40LPbtbxj2s7TumN2mQ6b00RNiL0+7O+J+GVNHbbvHrX6TtFKJ+dr0Ka4rVIff/+TJbj+wcB33jhBtilVti5KUaI+OiSprVuUMVZijD3AGPtdOytkgyKy51l7fTRNfSSPyV4fPLfXhy6RUyCo89ePc44bHt6Aby5+HABw/YPrE9fQYHnw2e1SHQii/OO8icksI+BFPHz3E1tyb/216rlBXPLdu/HVFHcxfUh+8rqGhdQqOilTvOy3L5HaSO0nw7UGjv/sH/CZ3yY52ORzm5twhsMIyr4WqY8/rt6Mh9cG+6GaDLR59jnMAjP8TeiUp4eIPC36PgAr2lWRPMjkqHWCWlmW2nJNRWTPI8h+x3a0iuoCpwr3cpPUh9qGtu9pyoOtE7bP7RjGNUvMrlpUlg318Xf/cR+uWLzaqo6EzeEeleomyCJ0j9bVJ0/u8KJcyprxo469b+TjlGP6tw8lJ2TTc/OukoZrxRgTG35MC8ZtKdeFRbuytC5FRS1azQEEmFeRYwmrFmWMzQdwIYD/aG917JDlzqX3o5ZHj7W1v8nYfo7k5q9qgEhAf9ivDoJETvL5gKNugnZQftuOSVOn1bX5W370Z3zk2oexffeooQ4kEAx1VMr8S86cGVR+Wrj8B655KJH2Uiuoc1AGRQ3lZqiPuoH6oN9qel8d6HvkF9TFUB91wWge1cBUlSI0apmkTn1Ep7Rr2xb9FoCPADCKLcbYpYyxJYyxJZs3Jy2nYwmbtrSmPvIUKsDnPOq4BHHwxJNK1vNlYainPuwrFy8l5XvShP3mwRH8fvlzUR0I6ga7ahEbB4fDc/pys4xlOlfEPLBtln+/88nM++x2qG6OMjCXZ/9sAm1SYcptwywaUU0uZYtIULdAffh+0I8aSluqVWnXbo5Z1EfXatSMsYsAbOKcp/pdcc6v4pwv4pwvmjt3bmEV1CGrsWy24rL2o27W68OPl4KEup8cRJlai9hJNNRHiTXLUSv1TSnjSzetxDt/uhSjdV+6TvQU0SfCCv43DarY/cwkqJPC5tYVSU8HE+hunWwStWx11aTrG6Z85Vn3AQHtoMvMmAWVSrEBuRGq/YrqZqFQx9RH5mqP45mtu6PfIxTw0oJGTc/0lXdXx2FWIqVmoZvI5HS+BT/QEjYtehqAixljawD8HMDZjLGftrVWGWiGo05cY/msZr+LVqOOds6Qr7N9vs+TQq1UYk3VMSkEdXSR+lv24xa3L2v4+jwkgFkTpqKMIeTKu97wyAa8/b+W4O7Q3TELVNcsLTLhuqnTqMO6PL5xMOJ7E9cYBOurr7xHm5kxC81w1PRN1DFS16Qx8H2O79/5JHYOy26VWf7thF8uXYuXfvV23PfUVgDFaNQNRZmhGiSMiSleO3khlqGbyORHdKlGzTn/GOd8Pud8AYDXAbiNc/7GttcsBdleHzqNmj48jSa7Z7XSEVRBrVuW5lkdNLhJo85RR8Pr22gKnMvXjQoatW5QZy2hszhY033P79Jz3on7U87JPu36eomgYKPzv3kX3vFfS7Rl+mofM5Rvi5aMicpDdRss3/n4ZnzpppX43G8fk5+rWfnp8MAz2wAAT4TumyMFRCaq4etZnjRFiE2xqbR+1Mq12yz7X5EYn37U9myB8R5rr48WBplKfegEU5bWovJjOj/qVvYrzHMN53J9RWMp50g0PP00+knTeUvqIzfC27NW++pzIu5cqFfdj8P37w01yMTjmqAqlj79PBZcdgMeWZv0TIk5fPvy6oqAi45TGgNhxO8KN81Vt/qypz6C/0n4k2JStuFXDIjrLz8joVHnSPafBbGtdIsv8fz1D67DCZ/7g+SyOhbIJag553dwzi9qV2Vy1CP1vE32vLzhyc3s8EIBAATdIMpBUYepUeXzzUYmNiMEA4OhKKhlbT+BDEGTtcRuNXte5PWRJTcSE1JwQDWWZk+q6SsIHSg3yl2rNaHLSrk2IIGstp1Oo6b38RTBGn+X9GdRH6K7SVC34jJn0qST7nmQzreCTMVPOH/3E8Ek3UrkZzMYlxp1K37U8e+x0KhVjjpZWFakk5piUSyDsWDgjZUlWk0KVZOMiebJ0ZiWNkNzy0pnm4UsYybBqFErRt9IMBkKjN3zivke9P6LV2zCpT/R0y0qYoO1clzDUVNfUjVg21wfUfuGt9MKshWDW4K6GYO+Lb6n1pgopXHgiWNjgQm5C3maH3W0lLJ8VrNCkPPkpqS6VKB5oix9haNmCDpWMwOjmVBYNUhHEtR+8qtk8ovRWDRRH7mrqC0/y5ho4qhFjVoU1OZy8mvUNuUBwC2Pmb1dOOfRO5q8Pui42BQ6LRuI+4atHzXREJFG3UIDqAE7qrweGqlL46oIY6LMUSchj8GWH9cUxqdGnbEks9Oo7Z7V7HfhnGO4rg94kTjqXIJaFrAeY/BYc53V5g71Gq5w5CL1keaeZ+aoSSDon2+d5jRDZdadlnKDG56rbt5LP83uhvrymoVtsJXYTKQ5JwV18LukeH0AOo06+D+tbw7XGniOXA7D24dCb5hmg8SCesrUjTr9n/eNO3HSFxYLkYmtQ3yGp5GIYjO47Hk50Equj6zluKmwvLLQ5xqvD401PdswKi+7xMHjMQbGmtPgmuOo5UEouqk1fP1+jnSf9njGLuS2Gp3puXQ4S5An2oIElSioLThqP0NS551Qbb+R2H6qextBR31EGrWR+jA/810/XYo/rg6zQobHNuygAKfWNWqV76ff9IyoxgXIzWyvD0EhcbuQ2yOPcFNvyrtZZisa9YgiqH2dRp3L66N1jpqubIouUTTqlc8NCvVMUgP0HYwh/4YoybjM/HUUEdcnXVLf8PAG/PBPfxHuC/6XQv792JBqolJM7nkE3fuk1cz2/aVVDtEWCWNikvqg+4wadfjH4sc2YtOgHLBz+6rY+Ent8dyO9EhUG8QcdfDbNPfljVJNQ7bXR/x3h5iPcSqoMzlq3T3K//kU6twINOrsyMR8AS88QX3k5aizogHToHMPJOh8vGNtyFReeG9O9zxTlJoJ2vPKwc/9LvYl1lEfdd/G60P+X0VeL5ZmEmU1GnqDno6PJi1bzf8hvn/D53jHT5bgdVf9n/H5DIG3CQnzIjjqOEIxXbsvhIqQNGrNaWkF3NwKu1WMS0EtdsJv37oah33iJul8Wj5qnUU//VnNfRHOOfYYvD4kLdnSBYr+Ft/dY0HHylNDut8mJFoF5+mudqZ9KbMErtE9r1Xqo+lJNrhR3NXFt+CoY68PPfImObK9XJd/JRHwQtSHl7zPJKh9zqM2eGqzOSEWY8CmwZHcY0sHnTIDJAVy+/yo0zcO6BTGqaCOW+7rf3g8iogi6No1jkjMnhF1HHLeb+Vzc/a8Zr0+OJe1MtaEMZGutN3RRYTqRy2d0/h4I2Pg2mrcWTBfRlpkdhnqNmmAoqmmrCbi+/RChpBXgDXDUWcGvGg46oSgFsqw4WQZAzbs2CPU26raWqiRiaY+EoeQN/8sgsRRZ4SQi/Jg++5RvPvqZdiRc2ejZjAuBXXWrhxpGjWdSfu+0odpon7BfTyhtTZ8jnpDTmyUvRxWNOqcHPW9T25NpFcF7DRqtR19jUZNO043fA31QRy1URDLy9ys55vrmX48Lc0poSKomjqNOsuP+pmtu7EtTOdalEZtTc+JE0ok6ORr6HuLGmPDJKg5nbejaxhYZK+olrxCjImqdq6WWKSWK2nUmvOSQV/4+z/++Bfc8MgG/Nc9a4qrjAHjRlCLOYN1H0kcBOnaMv1vvsjPEPo2eNMP/5zIwzza8LHw4zdJSYXy5KNe+vQ2ScAG7nnmyMQVG3bi9T/4P2lXjyy6QXq28tvX8LTlUMDptO2stqajrW9um16+DuqAFIWVbgnf0Ly7iJd+9faEz6+KvB4DzWjU0Q4vBmNiSXjxSFCrftQC9WHTTxgDHl2/E9MmlbH/rP6WhKi6IogUK6XMLMNtHohl04qDc47BMFmVTqMGj5OQtSvlqohxIahvW7kRZ3z1Dvx++QYA+gEsh/smz8eatLyk0sHXfZgmsGbLbu3xux6PLeZZDIT4+Kvve0Y65zEALOi03739CXzolw9J52mQ/eTep+PywgKb56jl+0jABYNaf5/6qKvvexqrNw5mcppFcdQ631gVoueDLoRcdD/M0tCNGnXOzmR7uTqhqMeA9MjENI7a1uj86PqdOGrf6U3v4al7NpA9yRehWcuRicH/37vjSRxz+S3YPDgiK27SffI97cS4ENSrNwbZuZY+vQ2AfmDLCYKS51XeMW0mNi11CM8+v9u4a4kISnqTLD9Gnux5KijgxefAV29ehWuXrs2sU7Ssb5qjlo9RH234ybrSL/H4k5uH8PFfL8eHr304+ijmHXtsBbVJIyeNJ3sklUtJjbouBfTYaZdhhbSH8xsT7a4X268WpTlVNeo8gjo+b0V9MIbNO4ex38z+llMaRGlao3FKUFdrPHGUc45VgsuoLXSf5cZHAqVw485h7XjlwrNtNmNoFeNCUA9Ug+3nKcuXrh/UU6LkRuoNLFnzfHBveMyGHhH/FoXBS75yO8782h2Z9TblLc6zcUBaPVlEfaQLKvmY+bk2ya7UMvsqQRfaU2skBbWiHQHAb8JNdPeb2R/XxUQVtCYXUwWGOrZKgtqtq3dd4Kiz5L7pqVkCrNbw8a3Fj0ch0vYadfx3Iwohl6+JOWrhWm4Q1ILniK1GvbvWwEC1ZHQXrTd83Pl49s5PiaRM0fiTr9O15U/ufRov+9ZdUX5sFWr/3jQ4jOd2DEvKGAldaqeEclLQajsvxoWg7q8GKUniDqzRqAUCUNWCL//No1gSauM2AS+mpY6I7buzLb1q+khdmc1EWRIYQ2pkol4Yh+c0NyXokMTgSNa3P5xEh4ZriXM6znb1pkDjmTlQyQyIsaUKTFdF72+h8JQkt7Xgf9tcHyZu3lgfAx5ZtwPfWrwa9z61JayH3fvrvD6SkYmx18ftqzZJnLs6acX0g73RefdoA/3VktEL6du3PYG3/OjPuCdj04ek/3QssKUdhZSAGCBoPwB4+nk95ai+yslfuBWnfOlW2esj+j92/+MGeWCdnbEAjIukTKpGrbrTBB9RaEzlgzy2IbkcShsEYvmtLOPMGrX+WdprU6YUL8PrQ8vVR9SHZrJr+Kik7M4RRB/Kx/oroaAeqWPKpIrhvvjvddsCN65aPXb9MtffJBjtrsshpyOjqFieOIGIPuxieX9cvRkjNdU91DDxZHxset5oPanR29wHpOT6CI/f+9RW3PvUVnzs5Ydr/fqD54b1taR76g2O0bqPgUo57I/Ja57YFNCX2zIUHHUXJCqKQ86dk61KJWEz0ZLQFdOo6hQrLpywodZaxbgQ1LQy210jQR03XYkx1DlPFdQisvIxqOW3srzZZdCoRbRCfegiE8VMajrNRud6RqjVOVA1P0+nUZc8D9Wyh8GROuZZCNx120NB3fBjrw9LTZWgtpnusq1DI7hjVZDr2SaIYafgC6tzYWz4+m/1ph/+ObNstVwduCAU65ot29KgC3gx5aMmrNm6C33lYJIVBb0UNZuyihCxO7TF9Fe90GaiVwIA2RaggzrRiNSHmDvHJh+JCtO14nHi8Fl0TqY+pL/D/51GHYJWPLtDDVVsby+0pklRZKkDAokyEteERf3vA+uwZsuuzOtNMAlhafnUAvXhMZaITKz7PPJtTvN+0dWNtta69CdL4DGm9QZQaQrOOab2lbFrpJ7JlQ/XGtgyNBo9K3NzW8userq7T/z84uhvvW+sjEFh9RPRQ5Kg9lP9qKWyDd9M1+a6LcFIqDXDUdcN96rG41qDo+yR5q6vo60BdWgkEKD91bKRo6Z3ytpPUaU8ROOdKKibcZs1ud1qXXuF7HwyFRrXj8poYUMba4wLQU1COKY+4oajRhI1hlQhTP+nCfPwqvf/4sHcdbVBLmNiytsEAS9yeSP1mL5IMybquEe6nnIfX3jMPonz6m0Nn2PKpDKGhuuZ7nnrt8fRa7VGLPhM95k07cR7ZQxafbRZ9mTeUDRq67SjhuNZMo/eq1aXhVUW1HSs6jEg+b3rDR91TT+hyyolhlrDTqMeGglWIwMVM0dN3iiZGnVkTAx+yxp1ctd7WelJr6eJchwSs0DSZCzcY9KoYyqsR70+bnxkQ7ScAuJOt0eTmJwaKWu3EUI8U8fH/unshZgxEPOrPk8JwmjC/xgwb/iZyVFnaNQqRy0tD1M8O3QctQ0NQ/e/5NA5wTM4x5S+MoZG6pkcoDggao14SWlrpCOo1UzYQJX71m7bg7/+3t3YIfCjWfTY0Eg9kebU1t2v2RDySFBH1IddXxOfZwwhV2aZus8F7VvWooHYE6RmcskRsCvUqAeqJaPNhManru0eXrsd1z+4DoB5ouHgikZN/9uPR1PqBtExgMZMPLlzSVkSV+T0d0/6Ua/dthv/ePUy3PJovKMFfTQS3jrNRhI8Kd8ubuj4ovmzBvDWFy+Ifvs8MI7oUGsyIW2fsOQTq5fp9ZFyLvD6YFJ7iHlPdHJX5UF15+Jny79FjfrwvadGz5jcV8bgsFlQx0v6+LyoUecxhtrUU9UeV27YiWXPbMfTz+8y3iNiw45hHP3pm/Hvdz4ZP7Pht7yH43XL1kUCSQd6r1pdz1HbeMfUDUI+qVFzIYoxPk63UUi9mq8GCLyoRNAE3E+CWjc+U/rdxd+5G+/7+YNRvcT6izalEWEP0nhjgRh58o6LHlnbNfYJ4qp9nj6pjxW6jvqgjy59lEhQ0+aZMVhEfVhq1PS/cAlppuL9JkGt00RtUC17wIhSiYy6Zp2PNg4QjukMLiLi7Gr5nhWcj6+hFYIfctQbB4czdxMXB/1oXTAmmgRQRnmEJB8rH6hptLS0V6V0Bff95fm4TF/MRx0ce9MP79PebyqbBP8lx++XOPfw2h248o7gfFrQSlVDiIrfUgwY2b57FMd/9g/41EVHJtqk7vOoXaTIxvBvoih0GvWPldwWkTGxUgLLMCZmrdrS0puSNwwQp3PNI0TFSyk8HIAUvEavGwdycYXuiOs1lru9dJ1GTTyUOJHTxxutm5eEtRSvD7Fr6/LJMsgGAc6BkYbssUHX6zQMG4jUxw1h1BPQasBLUG+xTiO19Akr0to0kjrLZ9bncaQaeQxIHLXh9jgaku71Aq8PTufT70scV25Q71ffjd55pO5HWd7SXlXNIw4AP7//2YTQoh1OVDQzgG95bGPkJURG3aQfe/bEJXp90FZZP7//mUQ/a/i+VnP3I0Ft1qhVDEXUR9mYe4bGbhaVoiZliox3UCcURMdtISavGhyOabg06qPh66kP8e+ejEykoBbd9kJxakONpqiE+4rgmr/FMjxP3o5Ip1HT1TacnQ4mjjpbI0jXqD3GpM0+xZWIrmwTBwhk8++ipTvSqP2Yo87aqYUE6EC1JGmotv7S0TsoxxPUh3IBvesv7n8W533jrkCbT2n44bo8SZ97xDw8sWkocuFjsDNGNgt1+U+wWWGIAS8iH6wK3LrPoQuOIWFW8ZK2HxOGQu20v1qC56Wv5LIUk0RSJhLIXM5G2dAoGlntLtZLFNR7NKtQarsgIlV4hjBxEMYiKVNXUR+fun55LKiFDkIdNy1ZuByZaIZoDCCo1AfnSFIfmuV7HpjckrI67qPrdxrPeWFkoiicRW1QK4zTjIkZlILP42V2X0R9BEvePaPJEHL1maTBDVTLGK3H6V5b3eFF/eCmPCabB0cwNFJPCGIV6l6Xe0+fFJQr1DNtwm51QazjjgGzF4zqRqge4zz5vYPfyRVqmkYt+uiLsDEm0jcZHK4ZywEgha+L78EhC2dTBGYaxHrtNOSQ1q08tPnpeZIKaye6SlBfu3QtZg4EERdiv1L9V3XjWg54kS8Q29HkKK9eM6oM9sitrWCNOo0X3j1ax6euf9R4ngJedhs0av2AMWs2WYEkYgAEvU+Dc5RKLNyqSl9P1SVwoFoKA17SNWpb7lq9qma4jybfkZqf2u4q9VFRhBZjLNE/pPq0qFLXGj4+8IsHEzsEmW0A4r08OiZG1+lyo+vyhasctcgLjzb8iPISQXaltFwfVK/LrnsEO/bU8A9nHKJ9F9U9T/Qpl+hQzTjMNibGfw+O6AW1KmuCZGPJMgKOOnxu+mMLQVdRH5WSh53hMkoKiyXqI/ydNmMDSQEj/ow16vioOrvrNGq6Pm2ApqEZQa2GJuvgMSYN6CyvD9UFTET2LttxmbRC4Jyj4nly0iIFJLho0AWCWgghNzzXTH3IJ9T7awZD8Ej4/JF6I3WZTJMddYtYUAsateEZgJ5ey4Nag+O6B5LeISYbgsTdWrrn1Xw/Cj7SadQ6rw+TgX2nSH1o/Kh37K5FEakA8NuH12vLufw3jybyaUeaM2SNOvL60DTJR659GLev3JQ4Lo554tVVUBPHgtqHjjz1eWxkVHdxbwe6TlDT7KwmxAGCEPK7Ht+sNyb6YmfLfpZ4jdrMOo6a+ojOvcgGZurDfE+WF0YUmShclhW9lcYVZhs2Y2HcV4mNiSWPBUmLMgQuafP9oUYdPVeo51Obh6K/bblr9SrTNyLhKnqc6EATJOWorpRkvpYhY8JuTaE20mvmCE5BqRG8K+IwbC7ZMQBg1XODUf4NnYGsXEpy1CZBPThcx5wpVfSVS9pcH+/+n2XSb1O3/vE9a7CMUhmTO18jfgedTDDhKzevShyjXdIBYKRmENSRUhhz1Lr2ET2gSH5sGhzG2m36hFCtossENRMaIvlROAfe/KM/Y+22eHamRpI0amWkZHl9cKi+zTqNOkCt3twoNCU7ShPGWV4YnpcMX83UqNOMiaqmmvgtuOeVYo6aBJlJeKnueZOrZW1k4k2PbMDZX78Ttzz6nLH+urqrTWjij0cjjTqd+qAVSikS1MG71i2EFgA8tWUXbl+V1OhsYRLURo5aY0wUw785krnRRbpMN9ZokhKpvjReft8Z/QCgzfUhTr5ZUL0+aOXHIX/3WNOOj4mPVZUvzjku/s7d0W91n9Xo+QnqQzUmIqyf8OTw4isWr8Yrvxs/o0h0maCOq6P7KATdZpJp+ahVIaweTe4NyKNlsnpNswEvat4M8VkmmIQBlaUaQYFg2RdpVZqy6ZiOa3/1lffiL1vioBCd4Kb26xP8qCmXs6m+8aCLNepRQVhS264Ik76TAdU2hDyxzDcJakGjFjvF6QvnSNfRqoQy6umoj5uWb0Aa3vaf96eeJ+gi9UwC0Zg7Rjgs+lGLAn+XYakPGKiP8J1HDSsfFftODwS1jqM+er/pxvtUiO6Fkg8z14fKm6qk7uqjtp0qqA/feyouOX7f6DoaV/WGvMVc5CKsaNpAmEGyrz1mvy4T1MndJ4Dkkk9ctkSaruj1kdKhTFtxycsbjXuesnzPi3ITgtqkWZGgZoxpLRlEH6W5MZq09e8L0XjqJT7Xu+fRdzNpKbGnicxRU/VULU5csmvLy1hpmCbTyJioUB+qEWo4oVHTMjj0XBip44s3rkytQ1BuVqY4P7H6E5+vwqQjUHv9z33PYNXGYLITNWrAnHI3CFCJf6dRH2ntLmrU6nebM7XPeJ8K8dvXlFWyjvowCuqw7bcOjaDe8BOTn0p9lEsMlZKXCAsPjK4xaGwFk5bcT4eG65jcG4Ja1qhJu1OFijjLx9SHfgkkXiOekzJiaYS2KqhXbRzEgstukDbZzQNTMhpVFl+xeDU+dt0jAMyaFW1GSvmoCactnA0gbp+0gBedHyqg36WawEXqQ3DPK2X43CaNiUR9hM8Jz1M5dZ/jK79fadzdObFistWoGwJHLdyjrnbUDR90GnUr8H2OrUMjWPjxm/Dju9ckzutWjICZe6cJ9FPXL4+ONUROl5s3sagKwonKAkS6x7yyFbFP6MKoc89rNLiUSycNomuilGjNpFEbDAIMgdfUiZ9fjM/+7rHE5K0qFbStXcPneFbYeMBkJPe5IEvCugz2jkYdV+fn9z+Ls752B+59cmtCqIiNHGnUyuy7ffdoxHWK4Mr/gJ6LNS3j71il307onie24PjP3qI9B9hTH99c/Dh+9udgE1uT4CtL1Ed8/Mh9poX3xctfFRH1YRh0ctpNDfURlkkcdYPzyOc2k/oI60UBL6qrZKxR+/jeHU/iyc36STHh762cN/lRxxp1QxL26i7cxFFT+6vuea2i5vuRF4QuZ/n2Pfr9ONP81EcbvvRNN+0cwQeE7I+m/TurZU+atNTVjUR9pAhq2ulHZ0ys+xyTNG59OogBWep3lOnQ2G0PAH5x/zP41TJhz1DGsHNP8M6/X/5cwkuHVi00fhiCMfrczmG85Cu3R1GnDc61xmFxdUFz2dBwHVMn9YSgjgfMlqEgMcbqTYMJrVMS1ERJKLPvu366DJf+91JsGhyW7tUaEzVLfJNhTPJTFp75tVtWpW7PVTZshS2WIbowASnUR9hOQeh73GZTwx1W4tBgjSagWNNV6HzO49+xkKS9En2fawe1fJ/8TNqxhwSnuslqZii7r9ZL/p3pR12XKQfVvYr4XKpvtUlBbaJuao30PM/bdpmCMfTX+z4SXh3rtu/B+tDLgcNMfVRLnmQrUANeRiXjtLnO5YiOS36fhu9L7qkpxUjGUDUthJp2lt4NAD76q0ekcjwWC/OyxxJ9aqTuw2PxypBp7D1AEHinq67onkffeddo+zTqrgp4KWs8IwI3I8UHtC5rz4CynxoPdrAIjieX78H/QidQnpmWlEmcJGq+jz4vEDpZwsVEfYi3nfbl26Rz2dQHkzRg6iRpiedJ0IqdXteRgaRGLnLU0e4gXBDUmRp1MDgmVRRBTcJB4ahNyE7KZNCoJeojPq4udvaE2ictl+nbNWufSNQjw+vERH0YA4A4N1Ib9DxTX6qWPfg8UIwWfX4x3nLqgQCSvHza8wHZwK1LJqXr/6s3DuJnf35WOhZRH748makcdV2V1Ao8xoQc2F6ib47UG6iWvVCB8hM0olh3LYXIxYCh4P+h4TqmtEmj7ipBrfM11m1Zr9Oo5dlXyB2stD1X7qPrpWtSqA8xCKXe4KAJNGsQq8trQpol3SRwSoL2InLK1ElIIGm9PiJjYlx2teyhrtmPMhlSHnt9iBx1HMWWwVH7PsolL+FRQOdpos6a9NRmUa/O4pLVgBd1gO5SdgEvF8xR1xp+qv/8kEH7TQsoShPUpvI8FvQln8e87DVLAvqg5CXfOU1Q0zf1FOMkEIwNnTH973+yBGu2yn7HI9FqUA1fV+gGQfPWgUHw3iklFZHhWrDBBtWKaXY0oufQIyinDdUntncF/wcctR0XnxddJah1s27DTy4TxUg8XZ7bwOgV/G0yPImHOWSjhC31UbfsxIBZo1YNbSJMdTBx1NMmkUZt7sRqiC5Agyy5KUPSbVGMXGNYdOBM/L/TD4re3Yb6qHgs4VOe9N1NpxiovKe37sLgcDIZVFZQkmpMTFuKA0BVo122gtG6n9lfdDCH1CepDxEm2qPseYlsdzQ5VzSTbysadUlD/em8Ymh8+VzWoDnkCdy0QUJcdiyoK56XGF8j9Qb6wtVEUG+9Rv2Vm1dF7z1joBJ7ffhckDEcI/UGRus+pvTZcfF50WUcdbI6wU4U6myYzFUteX1AcP1SqQ/6X1Kpk5y1ydVMpT50f+tg4qijqEuNn6uR+ggHkefJfriTFepDN650WrbJf10dmKIfNWMM177rxXjFMftEAtbonhcerjd8VMqeZIsInkNlhtdZUh9nfPUOXPTtP2mojyyN2lcm6vTrizYmjjaaE9RpIeS7DcZC8b7JVUWIsGSACo8mYlrd2PlRxxx1LPh/cNdTeGz9TjR8P/HNxXtE0IrV57IxMeCok3UxfWrGWJSzpVxiSUEdatSiq6vO3i9+J8pDRPUTXX3JrtETXh+21IdOexCFWuA6k9S0gXj5lDZQ0zhqcYmZR6M2e30E/w9pBppJs/RYUqOulr3Y6FWXKQXpeZp6Vg3+6+ogENtVfJ0srw8qZrTBUfY8DFTlzqxGKGYml9e4DYrIEqhZkYkq8lAfpu8sotbwMdowa8AmmOp8zZJnsdvgey1Cx5+qXhqRYZf8qIVI3DQ/6lijjn24v3DjCrzye3eHGnWyXXSKGSlhAfUhj1LJj1oILdeBIU5XWy55ST/qcG/RaIJB9rcTPTp8n0cd2/c5hsK0qVMmtYf6yBTUjLH9GWO3M8YeY4w9yhh7X1tqAj09UM+gPghix+fCEl3VQuhXmh91mnveTmFnCHESyNLijAEvYf10y1MTlSDWl5aPk8oeKmWZ+9UNLJ1WJlrkddqV+FuN3AJgYUykVU+gWe07Y5L2fJbrYHy9/FudaNdvlz19VIwoxsQ0mc2YPSUD2O1IXaubFYE0mCawP67eghUbzOlwCYlgDE4BL7KSA+jzUad9Fxq7RH1EOXvC1YOu/+u07Jij5kk6U0N9mNrEYywKail7LPHtyJgoRflmfDxxYhHkNHweZ+NrF/Vho6fXAXyQc76MMTYVwFLG2B84548VXRnTDJsQ1BqNes+o7EZEt5i9PoRjSllqVJQIMeG4HAyQPvBKpoAXshhrBLVJgyPBJHp99FVKghtZ+rJQRVnpgARd28WcniCoM3J9cEEAl0sM82cOSOcj31nKxZGRNTDp/iWf/+bix1PvV5MypTVTSWhjk9ufiKBd0q8bbTSMNFEa0jTaNI6aoKYo5eAhR53MDx2tIoRnpj2fqL1g44B4q6uBajmhUVMpuvEeG5jV2Ag1UZuZ3qN6DAvJtdS+OVzzMbmvHAlwzzMb/AnixCJ6QAUcdVAOJSsrGpkaNed8A+d8Wfj3IIAVAJKbvhUA3YfbPVq30qj31GJBxyEup7nk+RG5rgn36jRqY2IcaVa316grJj/q8OE6jtqkwfFIWMYCc1LFS3Cptmk2JY6ai4MhSQnRABEnnlKmRh38P9oIlptBprWkFk9NqAuhFjUylQIwhVybEHh92LWN57FoAN/wcHp+D1uM1nlTgpq+zdX3PY1NO+VVg015fUqqXc4RbUartmkUQi6U+/jGQdz0iL4NZI6aRwpNf7WEesPX2mh0K2ixGrJ3F9fScqbJg4FFhslyiSXGp1ajzlgNyRo1j7cD47EdzTTOW0WuUhljCwCcACCxqydj7FLG2BLG2JLNm/XRe1nQLYV2jzYSSy6toB4VqY/YmKga+cSw2uh6RQNavWnQio98788exAPPbJPLNcDIUft6jbrhm7X6WFDHnauvXIrab7jWwB2rNmHz4Ij2fhUiRy0KMLXtRN5Q/FaVDI5aoj48D4wxzJ/ZH5+PuOngD933FekZ1WYxaPBqMCEP9VEyuG21gjse39QU9VH3OdZu242P/3o53vnTpdI5cbNWE3Q50Yn6UAUeCRxRE738t4/hXVcv05Ytc9TxyrO/UopS4RIig6UhoyRBbSPdTjbpXh+kUSe9PoZrPqolJk0guagPPx67Po+VKpN3V6uwFtSMsSkAfgXg/ZzzBCHGOb+Kc76Ic75o7ty5TVVG9+H2jDYSnUj3bXaPyhw1FzRqEYFfpOzErpb38V8vt8oru2LDTrz9v5Zon6PCnJQp+F/lqOu+j9GMyUKMpuorxxr1B655CG/9z/vx/bueynwHQBGCwnuondsXKCFRc4g0aqN7XvB/vREHPswVEvXEQTjB76VhTmJTHdX+YCOkRGTloxZR8rK5y7z4/p1PNSWofZ9Hqwc1KIbCpdOQ0KgRGxPVyVGXlCkNSY463EygEqQLECd26iemMUH45uLVUl3lgBfZrqEi8PoI3fNKTGNMbKBS8qJv6zGWSX2IQrghaPg+j3d01ymbRcDKl4QxVkEgpK/mnF/XlprARH3YLWvVDSpNHDUQJgMXfnMkaQIKYc8CfZasDm3kqMmYqHh9vPvqZXh47Q79M8OiPBZXYFKlZNxFJguiVpHOUQdLPI/J2kclI80ptS1RHwBQFfjSOEe2uQ2rBh4dQGRxt8VIYnNbs9j2WDZ3KcLWmaQp6sPn0dZY6ljZaTFZqYIaCLjZxSs2YvGKjdLxvC6JEUfNGHxfpj6Gaw1Jo1ZzqJjw0LPbwzKTIeRqnpjEe2Vo1CN1P4xMjFcCmRq1p1If8WRBGrXOX7wI2Hh9MAA/BLCCc/6NttQihG42Sts0Vb2OIHt9JDuammNW97WzqAyCmA4x7bxJe4hSJCoa9eIVm7BJQ12cedhcLDpwZlS2TqPOi7KJ+kho1HF0oYhMjlrwdadvXPFk7QQw57IAgMP2nipdf/F3/hT91hli02TrqJKUKa17eV4+6sM2KCYvrw7InhDqpLzTYrJS7+Gca4M8gLi/2kZjilwv53F9SKMWlYGaYbIxoVLygo0DhA+V5fUhuuepHiRA8M2TftQZgros2El8cQeduD5Zq4RmYdNSpwF4E4CzGWMPhv9e0Y7KaDXqWt0qx4K6YwXdoRO4NT9Y+s6eHDiw7z9rIHGNKFRsYBLspI2ZZlrqfKboMRUfPO8wrR91nyaQxBZi55Kpj6Qxsd7gCX/3LK+PaHXjx0Yl1dUpeHby/ql9Zaz58oWYNzV26bvh4Q3SamNQI6TSjDqqRp3Wu0SvDxGvO2n/KLWnCNs4FtvvLaLhx5q4KhBs6B/y+qBbOcw5syNPl5TZ860vXhD9HVMfQT8ZUoyJ4mQ3mpPPDVKxcil4LSuE3BOoj4bPtTszqRp11ryhrjyjOviCMbFJZSkLNl4ff+KcM875sZzz48N/N7ajMroPV6unZxojqBpK5BKmoz7CpPV/d8qB+O17TseZh83DUcouFKMN3zI1Y3pnm9YfOMD3G9x26NXSMu+J8Lz4kcGeieT1UWpBoxYNdfFxrUbd8BPfKUuLiLfi4pGvt1hGRH1oBh0tR9NeTadRpwkB4qiP238Gfv/+l2g9QCZVyN1Mr1HPmdKHwwUt3xYnL5gFwJx2NA33PLkFV94RbOyQoD4sOGqaYCcLAUemT0dC3aRRv//cQ3H5xUdFvyOB5zHJPY8Sfol9ZM9oA9ctW2u9UqE+o+OojV4fAvVR97k2criqaNSm6OGoHgpHTf3a50Kmvk5y1GMFXWRi3fdTQ1cJqkadpqVFvpMMOGZ+IKDPOmwevvOGE/Ce/3kAQDCY+yqlTI+CtNVS2WP4xIVHYP32PXjtovn4l18/kriGOtq23focxCpE4RxQH8HxlqgPkT8U6AsdR11r8ESHzurgkQdOw48oD13Yum5VQlXL63mRNnmQ18eJB8zE4XtP017TXylhuOYHXh+aj9ysJ8ikMIw7bWssE66+75nob/Vb5/H6mDWlisGReuSep+K0hbOxaEFAr5k0avU+6gPkRSLmxGj4cva8PbUGPnDNQ1bBQUAgICk/NEEUknrE7nl139fuGl8psaheDPGEYK5HfP7JTUNY+Vy8m06tze55XSWodYKm4XMrvlg0JopeH7p7aeml7le3vxCIsWe0ganT9M1TLcdpEzcPjuDEz/1Be92tHzwD82cOpA5q6nDP77IX1OLf68IovH1m9DctPHTLUvVvgJZ4ybwNWVoEvWMw+XmJZ0aDTiuoY40nD9IMq+RHTUXqeleQirVm9PooeSx3nYAgghRAam4OG6htnsePeuZAFU+HWet0Xeb4/Wdk7tqj9jWVoybFqR6OXx31Z0sTmXIAAWavD5/HHjL1hl6GBH7UsRG0kjF+xJUnCWmAjOw9pFHTS5Y8FmlZtUbSxzMLPpddwlTQ7KeOM1EIjjZ8rZUcCBKvPF+PBetWg5A9cPbkzLrSODAli1dR8mSvj/1nBf7Ibw7zCDcDcdCJ2QFV+FyfWziL+qAvMFL3o1WTLoCl7nNM7StLqxgShqpWO21SOdWAlqblE/WRVm3KmW2KWCt5um1ps0E7oZhSj9oiaxWjA3kezRS2xdJNNpWSF72zcYMJ5TaVoxb5YVMIuS1MOYAAc1DXbSs3Sdfq7Cdirg/P0+fDl65PcbEl97yO+1GPBWjmFDNQ2WrUIkQaQee2VBOoDxFq51NDbglFZsiKNGpL6oMxJuXQfc9ZC7HkE+din+n9qfelQZygdEYXsa6iix0hq4OLGjVpuuLk8PyuGjYPjsD3ecKNsSIIABFZG6aWSwxX/t0LtecoKRMJKd1YJ0FdMngD2AgeraYe9ilbt1MTmhF89G2n98eCWldMpeRFbWMyEKuTl5rmlPjhWsOPjIk/fttJOG7+9ERZWdBr1EH5Nv7ougycQKBRRys2sExjvGmVJmb664rIxHaDBoeYpSpIyuSncsEqrhICPT51/aN44Jnt0nn6uKo2oQ5IMiipGFDTRWrwo7cusqlqlDNgex6OOqwmY4GQnDPFfpdnHcS3Ng1MIHRDCqMLRWRRLiQIgxzAQduJg2/L0AhO+sLiYInMmCSEIk1NecacyenvXCl5ePkx++Alh85JnKMdXqhEPfURGxN1Yy+gPlKrYJgAgsKa8fqQnp8iVK543fG46X0vkY55LE6zMENI16mbhCollpv6qEQcdWBMpJUZKVplj+HMw+bh4uPzZ5/QaalkehrOyAtDddC9R1XMnseyVykDBgVN9ABJ+y6toKsE9blHzMNXXn0sDp03JTrW8IPsW0W6vRgNJMojJimeGqRJZy1vPnHhETj78L2s6kKGF2t/VcGYmOX3aQ2hmDQNhdzz1PfP0kSuW7YWX7pxhVGjFssveUwqn767qsFNz9jVWsw9oSLKR51hCKbn6upaEqONDNB5K1GfysrwlwVqj1e/cH7i3KzJVRyxj2wkLZe8yIApa9Tp1IfOCAck27WkrHz2qBx1eL7ahCBL1ahDjT0NdZ9rx1el5An1ztaoBwyeW3wMjIldJagHqmX8zUn7S4aHergRqI6nIrz86L1zPSfWqOXjKuuoCurTFs4GkB2plsfI1PDt+emgbCUysQCI751mlCIuzhTwYsKTm3fh+3c9hdFGLKh1S/d6IxDUYmen7z6tXxbMaf0BiOkYXdVG6z4geDzoeE7RV133vcsWGvUzzyfTEFCf0uUzkZ8PvOeshXjpC/TpGGgSqJaTldCx5yXGIgPmDImjTpYdUB/B37UG1y75VZkm7joEiMbEUNHyKCJVLmvOlD7877tPS1ZCqk+ykuIkmJWLu+H7eo1a8aPOUgYnG1KY+mNgTOwqQU0QBxfNhibDHhB87H8442Dr8mn2U7UJdVCr1McpBweCOivUNM+n8n0e8dOzJlczrg6eHQvq5jrFVGUJJ77OaKoxMeiQqlZkq0WI39G0P51Jo549RW6b7AQ65lXHSD2Idk0rIeJcjV4fQRbAvFAnfxM8xvChlx0Wba+mgigqnXDR7VgjusyJgjqL+hht+NpJUW0TMSkTEE9EpGjRebW+86b2SRq+DtrdwQVBPZzB99d9rtW61cjELCHbXzVTH5ExsYORiWMOMh4yFvNLaYLaY9kaloha5J4nQ9WExYCX//n7F2F2yAVna9TWVYHPObaFXiMzM5bz6rN1mvt33nBCZhnqTh9iMekcdfAtVC7Ps9AuCWka9e7RICeEuKKigTRbmcSyxoO4c4eIgWoJtUaQpyFyz9OwTiQcSp5eUJQ84BMXHom/PsGOc6XJUay3zcRsQj1NUGvep+FzA/WRvFYUYMHv5EVmP2rSqINJYVSJpFTrW/KykyHpTosOBlmxDk9t3oV7ntyaOC5q1DYctTFoLZwIyk26bNqgKwU1GSKm9pVR833UfR4l5BYFsshD5hHU63fsCe+Tj6udtk/QqF98yBzjh1Jh0nSP2S9p8W5wHvlQW2nUDIAQ8KLiomP3zSwjzWsljSsPIhOTHDVgr1WTMVHnV7t9z2hAfQjl0zeZrRhMs1YTRH2oA4e2ATMFe0Tlixy1VlB7mNxXxhst3SJfoIlinJfiucKV/1XUUkKWdffUfR65Bs4SDLEmjlo8rFsFqPeJXh9ATH2Qmx5xwWp9dcbaw/aK2ypwg0zXqHfuyaYOV28aShyrlmKlwIajNmnctBFvu2gPoEsFNc3CUydVwHkYKEEatdAWYufIkznu479eHhalUh/yb1X4k6DOShJlGv+/fe/p0d99ZQ9zp/aB89idUNw801w2a5mjVrdkEtshLVyfktvohINtsE1VE0JO2L67hhJjOG7+jOgYfROaxMoew/LPvCxTgze59Yk8I53SUQVUPZPXBykJJ+w/Ax+94HCcf2S68fjrrz0On3vl0TgxTKgV1MU8YUa8uVK1c4+YByBeFeqMcybf4m+//gRc/ldHSoIwy48a0Atqk16kGhOHFY1aXRmXNJrsogUz8cVXHRM+R79akzTqnNkTCeqeiWq/PvvwedLvtFTFNY03VJHockEddOQ9tYZ2ixuRF2smxWdawAuQ9A/urwa/dUrn/R8/Vyg3W2jd/4lzMbkaJFXftnsUZY9pNx9V4bFYwDTNUSvPse1fPg9zSms6rG3792kCXgjbdweRgN/42+Nw7hGB4KN3JHe8us8xpa9sXC4fNGeydJ/aRtJqIsWPOqI+Ur0+gm/9rjMPSWj8KmYMVPCmUw6U+lQz/vgfftnhOGa/6bGgztHv95o2CW897SDtikVEtSy/s452NPVxajcSpLRvIWmuOupD7X9lYVVVMQhqMQjOJsWrDuIOL6ptBAD2m9GPG/8pdnNU+8EJB8wI6hLmpm6Xax7QpYKaPA+mhTv6Nny9MVFs5OYENVN+y+eTEXjBM3Qay4yBipEX1aHEWJjAhuP5XTXMGKhaCV5Rw2hWUCfb0q4cTgEvmrZOsyFI12lCyAlEfQxUyzjl4FkA4klkWr9qANXX+TUnBu5q9G3Vy0ThmLYIiBLKe/qAF7X+WZ+CrhcnqLSJmXqYqtVNqgTCRUd9HDI3mKRoZXbVm07EJccnqTCqy6SKp323sudJY6Ov7CXayjRRqodpLEeCVxlTJS+ZDKnkeZIbp4760GnUn3vl0Vjz5Qtx3P4ztHVTUSl5kZvfPtP7tZOIWF+1nj/7+1OwcN6UcH/HZA6cItGVglrVqIFYEIifrFmOmqB+frWTqUsZ6tQ6eqAseAfYyM9SKADImDhrst0280zwo242t0fWBCVC5M3Jj1oXSmvrzaALIScM1/zoeNmT35Exhk9edGTkymUaEyVlslQFkdinqB11GnXJUqMmXHJcIBBVjxqCLr3rFIMXgVinV584H49+5mXR8f5KCWWPaZPvf/aSo/Hfbz85ElTnH7W3NrUAYwyfu+Qo/O69p2vbMWlM9BLva2p/tb1JoNL9qkKlMyaWvPi9VL5crmdwgjhq6pe2KSeqZQ9rtwX2qgVzBhJ90lO+vdoGkyqlKGRelwOnSHSloB7RCmod9RH7yjajUavjL0l9yL9JGyRNn1AtBxoIdTgbTZf8c30/SMhkw09TnYkjNy2ds4yS5EGhulTpsNe0OOeyH0Ym6kLGTVGcKiJNyTCx0hhTjVMA8PbTD8LxoRAyLb3LymSpXibywpHXh4ajJkFEEyrhnFDDVYXLiw6ejTVfvhAHzknmNhffR+xTfZZtJtZ5UrUUatSypgoE3hwvOVT2uzZNoG86dQEWzpuqbcdqWRaelVJS8zb1cbEviZeYvD48lqQ+Sl6cCTJNGSHDMFEf1C9FbVuXM5xQLXl4NvR1P2jOZE3dZC1ap1yQstWTxsQRwZhIEDv1yQcFy2JqV48x66W3iKwQcvXDHTpvCj550ZG44vXHS8erSqeyoj5CCqPBOTYODmOvaZOs7yOLuso1E279wBn47CVHac8B8UYJtDJISy8kdnTaG06nOZjyopiuMyW4oTzNJcXdS4Vp6a1+A/V+cXKjM2JeZULEcXvy7tQ0SZo0StMGL5Gg0rge5kF/pYSysAdgkEeZqIzkN8jyVDJ5fYjvVylrNGqToBapHWHFQN9Tp1En0+YKHLUyBicL6RvoW9ImzlNCQzFp1F977XHRxK6DmNNkgUZQq7y12Aafe+XRAOKQ+R41JiYFUUR9MOCnb38Rln/mZcI+bc1p1Gq4tDpu1BmUMYa3n36QtNsIED+bLrfTqIMP7/scG3cOY69psTGq5DH87aL9DfexKHDBpFHPnFzFQiEMX8V+M+QETmp1Re1Y1KgffGY7Ng+OaL0+rHfrMAS8RIbjUTI+BcdNssx0XA0dV68TJ38SKofvPQ3ffv0J0nXiakMU9qSsmSY3444jGo06T1qEH7x5Ec54wdyQhvCEnOrx8lyXg6Y/Iy+Nrh1VDbpaStI/pklGVJhEDp6+i0pRlrQadUxllkuxb/L5R+4lRTHS+xJ9MSsyOAdtM29qX2qkbbXs4QdvXoQvvuoYTJtUSfThmmI4F8+/6ZSAUvIY8PTWXdgz2mirRt1VaU4JWo1a0Niq5cDYQB844KjtNDoRahivqn1lZYUj0OwfXW/xvWiPth17ahiu+dhr2qRol5cvvupo444djMUJfdKMUWkrjLkZmedmDVSxfkeQi2JvQVDf95fnAegDA2wNmyb3vFmTqxgcrkerBdHrQgdTNFukiRvq9cLQUq9CfUzJ8HwSxKbXzdrjwqShZeG8I/fCeaELYNlj0Q71jAWCdaTuawX1QCV9iBsjExXqw1ajFhUmkbIhOk41RHtajppF14npZKdMKkuTW3+1BMaAZ7cF9AVFr9JkWi17qWl7KyWGg+ZMjjyFVI14w449kgzQfa96g+PxjUN4fOMQjlTyqxSJ7tSoG2ZjogjRBasZjVoV1Op3sDUOxBq1PfUBBJ10QygQ502TtXQSCG8//SAs+UTs+ldiLBbUKe5daRMXdUzRe+Tej50dew0IHPfe05NCXSdfbGVOHEIufy/K6EYatSlrHuEfz1qIj15weESDEbI46tlTqrg4NPzNnxmvLFTBE2nkhuebBFXWbkS6gK28KHks0hppZQbotedJ1fRxoatBQH0ogjpBE+rLExUqUVAThZbYdMLTa+skkMWcKlVF02eMYXp/Bc8+H2jUZHuJ86B4qdn1VJmiKg/rt++R6qZTUIaFiaDnOGrq65KgrpCmFDdGLKjt3cNEqPssJjKCWQ4k6lTT+ylM2O4+jwWzNhAs08TbaMCXS0xKYypSHyaOGjBTQdWyh31n9GPxB87ARy84PDq+z/T+SNMWDZt7TUsaY7ZrIsFsQ2epXipHTRryqLCkD/7XlzOpUsK7zjwkGUAR3UCTplxApeThK685Fvf9yzm4REi5qT6G5KlJozZ946xgqLIkqJsbfmWPRasvxliUm0Pn+ZTlDWUKeAHitlcFN2BJfQjBRXuHgrpPUSCC9AMMa758IV530v7R+8XeP170bVTuHEA0Nsoek9x5geDd03Z7V6kn9ff6HcPSZKp7ZzG7YLvyfABdKqh/9NZFePnRe0udTLfRbKQRegzH7Dcd7zzjkFzPUT9iQqO2HEhUTxJ0tu7NpdAQASR5YxrvSU0v3m9vSp/Zpc8kqGl5vHDelIT2SXURfZbVdJlAkD9aBbWdKYkQwZSUSaUydF4fOiQ3MZDfSf2m1bKHSZVSYgJKUB+KeyCBjIVNUx9Cef0p2m6akiCeY+HvgUpJK3SzJlATRy0+p1pmWtc1IDkRiBp1lBbYYxGNWVGy/YkTodg3SNiKHLXKnT+5aQhzQ0E9c3I1mkxEjVrkqF900Cz845mxjEgK6rjsA2YN4NN/daSkJesEsZgbx5YqbQZdKajPPnwvXPnGE+XoKI0rU7yfXiCsL3v54dL5k8INOk3YM5rFUefTEsnIaLshDXWsA2cPSMtwcc9HtW8wkfpoQqPWeQGQ1klRZFOFCWCvaZOw/DMvkwSpXlAHZXzmkqPwjb85zlgv2gFbbdvpSkCLaaJSoQ6eLD9qGwPeO04/yEh9kCufqVpZGrXkR22YaP/53Bfg+pTUn+I7eyzwmsgyGppg4qjFc1r3vLAO93/iXImaE8cpUR/iilDnWUGgPhvksI5DzyONuiy7SvqcRzv9iEm7aDVaLXl47Ylxvu75MwfwEWEVqY4Rcfzf9ZGzcNGx+0qrHt3kKTokDDUZym6DrhTUBMnnNJypxf5iGoyEX77zxfjCq442lp/FUdvOkKpGvVUjyHSg57300LmJSYImat27DYUubGkBE6YlrzigY2EY/E98nkqpTOkrSzuS7DU1SYfEGlYpdUVB/PchcwOvFBpgqkYdu8Hl06jV0HF1UWSmAoLrzztyL3zioiMFY6J8lZ8xgWQJanGwm6ir9517KI7WJPCKy4jfIdjrj2XuOnTwXP3+naaAF0AR1Mp19BrT+yuSIJapj+D95gkeTSbNPLg3eIfRuo+5U4I+dvqhc6P+1FeSIyRH636UalZ0IxU16ktfejAufenB4Xvkn7Rljjr5zUWf7cc27Mwsr1l0taAWO2S6MdFcho4yIaiGhoT2lVKwqJnSB6dsaJsG7QQ16QozNQEqsXdBsg4kC0yJzIFs6kN+RvCbDCN0r7iNFXXIV52wH76u0ZipjEpJH3INQLKKHzh7Mh65/Hy8/uQDACT9sKluWYsaVTOntomrYDc4D90rmDjOOiwMaCHqRdWoqc0M9SFq5J/OOTS94khfEaVBrBJDQEuYciUDwAOfPA+/ExKCiUjjqMUc0ur8Y/LG0RkTD5gVBwEl7UDivcGPkXoDB8wewF0fPgvvP+fQSPCKfs+ALCSPERJ5iSlgmRBjoX77vHatLI26nehK9zyCKCj1iWGC/9OWx7oggNmTq9i6azRBjajlqJ4YIu657Gx86aYVuGbJ2siVSOyQNqDlnRrVx2GmPoAg/8NtKzelavymTrhwbtK/mjo/UUEnHjgTn7jwCLxW48t9yfH7SnvuEajtyiUGaHLk/PofX4wX7CWn+pw6qRJPFsr1aSsKEapBTqUmdBy1DofMnYKHLz8/CgGn+1UtKp4I0jXqQ1P82AmmcPMsiAKKsaAN0jRqnSJA0HPUMs+vy9Bnen+xfXeHq7AFs/XaPCArY3TvSKhAHTA7GE9RXhNNzpFZYV88RfD+Ed3zgveRjaMEWz/26f0V/MMZB2vfmb7FX5+wHy7IudNUHnS1oJY56pD6EM6TEE4zmKhC8J7LzsaMgQqe3zWKfaebAz/u+NCZWDDH3MFmTq5Ggplue9lRe+PTf3WkVsDpQL6wOq3/bacdhBXPDeItpy5InLvyjS+MDIom6Jb433nDCVKSH3WRTsbVyX1lvOMlB2vLPUQj6IF4EJjyPJ9wgN5eEFEJHsNrTpwvZSQDso1hqiBVA1KSHLW5PDE1AN2nCjkendeXQfW2yX0ydZJdfhcVohGcdiaxzZWuQmyfv1k0H5+5+Oi4zcOX1WrUFl4fz+0MXE8PnG1WYMRuSoJV3byCKErVPQ8ALj3jYJy4YCZefEi8+osMkZogI5t3UPHQp8/PvOZtpx2EY5rYYd0WXS2oZY46KXhIi9C1Ny311CX1vqF3xYBmqUidsa/spQppAs30VKbnMbzttIMy74vur5NGTZNQ/CIzJ1fxgzfrdzLvK5cyQ7Z13K66qYBKE5CFfHLKMnp/w6qBBpDP7b1egFgD9hjD114bUyppKwoRSeojktTa+221KDIMqVGoWROIL/QhE/79jSdi4bwpTRsARU8GjwWrHDX/jC3ou73y+H3xldfIlBYZ5XTZEs1+1PG1rz/5ANz86EacYdj3EVC9PmKOWsSrXzgf0/srOP+ovRKCuq9ckoQ0AHzzb4/Ht29bHU1ezSRsywvbvC3NorsFdQZHHQvqZK8hY4xtsiB6xikHz4qMDwDwy3eeauQjl6/bAUDmcrNw78fOjnZ0Ic0hTx2LREw7BG8YCWoN9/3zS0/R+lQTWCSoeWruEBWqQZNASlWW1mMSvHSXKlBtBy15toih/UCQlOmBZ7Ybk/1Qnok0QU1L5B2CP/odHzoTZ37tDqu6jUqCmuHSl+ZzSxVBzaPbcUfkhlWYjLxi3vgzD5uHNV++MHHNpS89GFfd9VSinJijlgX1G150AN7wosCWYZN7+oKj95ZoCFU+XP2OF+FPT2zJLCcP0mxhRaCrBbWcvDxJc5ABJdWYmGNJ6HkMP7/0VOnYSQtmGa4G3nP2QjQ4T+QMTsM+0/uxT0i51BqyRt0pqPOcbucR2tjXhJj64NL3uO2DZ6QazUgYqIPJ1usji0NW3y2rPAIJalWj/sczF+L1Jx9g3CggD/UhRpYumDMZd3zoTCstWwyLzrF40SL27EiWFAeOJJPqm2wHNga6f3nFEdgyNILrlq2TNGpKz3rOEebx1EwOdvWW0xbOwWkLzcpVln1Bt7dpb2vUQufQaZ0DNBg0QSFp9xWFEw6YiR+/7eSm7x+tyxr1OUfMwy+WPCttRVUUTtZMOCYPhixXLx0+9oojsGu0jpccOhd/XL0ZQCBEDzZw2gRT7gwSYuqmtipUg2pkTAx/N7u5wpahYNWjatSex1J3c7n84qPw6d88arX/pbpasKHbAFnjbHUzVXq/jSGfLCKiPkoe5kzpw9Nbd0fnTF4fttF5FP0qtsHCeVPw+OdfnpoOoo3BfwCAFZ+9IHXHoxv/6SXaXDk9rVGL1Idu+UXax4hgXLnpfS+RBolt+s1OINKowzqef9TemR21Gfzfx87RJjEyBZXo+PssHDRnMq5+xynhr6C8rORPaXW4+Lh9MThSx98smq+5K4aqCaq8e7Pjelp/Beu275He4RCDL7KIS47fD5ccvx82DSYFX1EQqQ/T/oi2OP/IvfHFG1dqfYCp6ErJS2zEaxJmthMHaaWq33lW32924rVF1ormyH31iZd6W6NWEsMA8sAjzU+MMFRDntvdgK2ANCOR1zN11F++81Q8tr45h/q9TXxqwuc4QLM7xxDo9jkZ+wgGddAbDT2PRakk0yBP5rEGvyjcRNaW6lDxo7cuwtKnt0WT1srPXZBLSNjm8fjBmxdh3xlm7l8HUaNWPSTyYsGcyXjv2QsTBjkRlbJGULcoMKeHGnWzG9MCSE3lO9ZoJtdQHnS1oBYFBgnlFwlcKR3bnZJ4pdP8bxpqOYyJJy2YlcqXF4Hj5k/HQ2t3tFwOCV8bjToKbGlSoBI9duZhcyMa6q4Pn4X9ZwV2gGblyT7T+3HRsbH7Zt5+ZDtwz8vYvVwHcQWZlm/ZFh88/7DU89USS8QUtPrcGeEKL+/GtKSwfej8F+BdZy5sqQ5FolUKKgtdLahFumPqpDJu+eeXYv+ZsXsYGRPVnB0iRO5o8QfOaEMtm8dovbPGRNpAlrSpn196apSZrxVsDb1a5lpp1MH/zXZ08uIQ6YADBL/ddi+VTZjcV8Y3/uY4fOCahwove9GCWfjNQ+sBjE1kXNnzErmWd7XYT4iKM+VdN6HkMa0nyURH9/ICUOLsSx5esNdUiUOKNOpR88eulBjOPnwe/vNtJ3XVUgmIhVS7BPV9/3KOlDBHxYsOno1Vn78Apx4SrFL6qyUrLTgLtDXSnKnZBrXYX7o5gUp+3aKhS8TsyVUrCqYd+OsXpvPrzeIrrzkWp4deC0Vo1CZQprn+aglnHT4PP337i3DF644HEOc0bxaU52Qwp0bdq+hqjXrGQAX7zejHSL2BSSl+1LtTNGrGGH701pPaVscioHu3IpDm90xoh7GV7ARpLlCE2D2vuWcdvncQlr5u+x7t+TefugCvOmE/nPj5xc09oEVceOw+CX63VUyqlHDUvtPwpye2tFWj/vDLDsN5R+4VeSGdHsYLiHm8dThw9gAOTAkbBwJjLQDsbGPGuYmErhbUlZKHP330LPhcz2GSNtXq7N5pdDOP3gxedtTe+PPHz0n4IOtAqT6bjdLLyq9SLXuYPaUPyz55XmQTGEt89w0vbEu5Ubh1GwU1Y8wY+p+GOz98VuY1FDD0tyfZpVsoAq35x+jxy3eeivUGJaFIWAlqxtgFAK4AUALwH5zzL7e1VvKzjRnUXnjATFzzD6dG+SHGKyaaoAaSgSImfOhlL8Be0/oS4e228DyG15+8P47N8D238WseTyAtPS2DYjdjoFrGX770irYb4YDA7fVLN62MohuLRLsN/ASW5YfJGCsBeBzAeQDWArgfwOs554+Z7lm0aBFfsmRJkfWckFhw2Q0A0JPGEYfW0PA5rlnyLF574vy27iziMHZgjC3lnGsT/Nh84ZMBPME5f4pzPgrg5wAuKbKCDg4O+VDyGF5/8gFOSPcIbKiP/QA8K/xeC+BF6kWMsUsBXAoABxxQ/BJjIuL6d5+GR9a17rfs4OAwsVGYMZFzfhWAq4CA+iiq3ImM4/afESWicXBwcDDBZt20DoBomp0fHnNwcHBwGAPYCOr7ARzKGDuIMVYF8DoAv2lvtRwcHBwcCJnUB+e8zhh7D4CbEbjn/Yhz/mjba+bg4ODgAMCSo+ac3wjgxjbXxcHBwcFBA+fb4+Dg4NDlcILawcHBocvhBLWDg4NDl8MJagcHB4cuR2auj6YKZWwzgKebvH0OgGL3cu9+uHfuDbh37g00+84Hcs7n6k60RVC3AsbYElNikokK9869AffOvYF2vLOjPhwcHBy6HE5QOzg4OHQ5ulFQX9XpCnQA7p17A+6dewOFv3PXcdQODg4ODjK6UaN2cHBwcBDgBLWDg4NDl6NrBDVj7ALG2CrG2BOMscs6XZ+iwBj7EWNsE2NsuXBsFmPsD4yx1eH/M8PjjDH2b2EbPMwYa88W1m0GY2x/xtjtjLHHGGOPMsbeFx6fsO/NGJvEGPszY+yh8J0/Ex4/iDF2X/huvwhTBYMx1hf+fiI8v6CjL9ACGGMlxtgDjLHfhb8n9DszxtYwxh5hjD3IGFsSHmtr3+4KQR1uoPtdAC8HcCSA1zPGjuxsrQrDjwFcoBy7DMCtnPNDAdwa/gaC9z80/HcpgCvHqI5Fow7gg5zzIwGcAuDd4fecyO89AuBszvlxAI4HcAFj7BQA/wrgm5zzhQC2AXh7eP3bAWwLj38zvG684n0AVgi/e+Gdz+KcHy/4S7e3b3POO/4PwKkAbhZ+fwzAxzpdrwLfbwGA5cLvVQD2Cf/eB8Cq8O/vI9jhPXHdeP4H4HoEu9j3xHsDGACwDMHeolsAlMPjUT9HkN/91PDvcngd63Tdm3jX+aFgOhvA7wCwHnjnNQDmKMfa2re7QqOGfgPd/TpUl7HAXpzzDeHfzwHYK/x7wrVDuLw9AcB9mODvHVIADwLYBOAPAJ4EsJ1zXg8vEd8reufw/A4As8e0wsXgWwA+AsAPf8/GxH9nDuAWxtjScFNvoM19u7DNbR2aA+ecM8YmpI8kY2wKgF8BeD/nfCdjLDo3Ed+bc94AcDxjbAaAXwM4vLM1ai8YYxcB2MQ5X8oYO7PD1RlLnM45X8cYmwfgD4yxleLJdvTtbtGoe20D3Y2MsX0AIPx/U3h8wrQDY6yCQEhfzTm/Ljw84d8bADjn2wHcjmDZP4MxRgqR+F7RO4fnpwPYOrY1bRmnAbiYMbYGwM8R0B9XYGK/Mzjn68L/NyGYkE9Gm/t2twjqXttA9zcA3hL+/RYEHC4df3NoKT4FwA5hOTVuwALV+YcAVnDOvyGcmrDvzRibG2rSYIz1I+DkVyAQ2K8JL1PfmdriNQBu4yGJOV7AOf8Y53w+53wBgjF7G+f87zCB35kxNpkxNpX+BnA+gOVod9/uNDEvkOyvAPA4Al7v452uT4Hv9TMAGwDUEPBTb0fAy90KYDWAxQBmhdcyBN4vTwJ4BMCiTte/yXc+HQGP9zCAB8N/r5jI7w3gWAAPhO+8HMCnwuMHA/gzgCcA/BJAX3h8Uvj7ifD8wZ1+hxbf/0wAv5vo7xy+20Phv0dJVrW7b7sQcgcHB4cuR7dQHw4ODg4OBjhB7eDg4NDlcILawcHBocvhBLWDg4NDl8MJagcHB4cuhxPUDg4ODl0OJ6gdHBwcuhz/HwjK0d0pJ7LkAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(prior['noise'])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(prior['weight'])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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rqmpLVU0x/2/mq1U1liOvUaiqZ4Cnk7y6a9oBPDbCksbNU8DFSc7ofs52MKZfOI/srZB9neJXHGw0lwDvAB5O8o2u7cNV9aXRlaQN5D3Ard2g6XHg3SOuZ2xU1aEkB4EHmb8r7SHG9FUEvn5Akhq0kadlJEnLMNwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg/4PBneLQ/SRc8YAAAAASUVORK5CYII=\n", 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vvNnmSc+G8H56gs+fnC4c5+Jh1CLyQ3gTfQDKFjo/dc+Rk1i4+aDrSaUI+KgnzNuK81/8Ke60kuUWirSoLwZwFWOsAMAXAPozxj7x1CrI5VPzi/D6xJpj1dtCieXHq9PWu2yV+wQhgPYGMP2e8KJng7/p6XHjvxfi5nG/up4fqjvPyvVhFZ1UVlGFAh/nHBw5UY4Za/f5lp4WS6HmnD/KOc/knGcBuAnAz5zz33tumWRYle2VO4swZaX7O3Sorg/RR2XN7qMC14zDIEf4k6DkbkZbqPfbdNaiTqkQi8gQ+1zdY7O8kkfYJIJZGm7dp8cmr0K/12a7OvBsxn2fLcP/fZTr6aQ3I2r4nqIgvje6rAqvxdev+ldovdthXU9zxx4FtUzbGQyzwv8GrXWCJeWVGPzWHNtX1j7zpuJg+8p+ojeYaOTyiT3u9kBYdAUQ/d61VQp1ju0pEt+AWd0e682fNiI1heHJYee4ZJk+6i5NQcxDsDXhhXM+m3M+zCtjgORqFTklcjBReZHknqD8/cew7aB320TZag16ZkX86On3+LlbUFyirtmhz+bCaheB7jNm47kTzZ8xs/KRNWpqTOViFHXCOY9Zm8YM9Sr/WVAQ916kssuOtDMTfcfBnbr/s2XCs6tEKiC9hzDFg6gPGfhyyXZs2me9sI7TaJlEQmv3yp1FAKp/d3T8vF52rN9bjGf+qz8dXV2N0XK1OZN8dtID4+B4ffoGALFx+0bjTxUeFPJTaTAxEGRzfegxZeUe/PFj02AYRybotThERUjkvKAFjQN45JtVGPSmfVdHMqK9HQ9NNF+W1sgloraoo1m9y/5mylbPnmjx8To2WfbYZzeRTqi9XDDdDKsok0Sumc95alrE+8oqjj1HxH2B787ejKxRU3G8tMJt0xxxsqwSB4/HrrCXDDu8bLJo+Rqvjqf8jzpB16etfa032cYoDYcZE/0tP5/xZIkek06oVeLJ4PV7j+IPHyy2tROEV4VnzKx8vPeL+caYZrghGieiJg78Y+Ym9Hr5Z+w4JOYT/uTXbQCAwyfcm8YejZ3G0fXvLrC99G2ixUQbmRtx3IWfJJIvjlwfXP91vNd1iptPdxBFSVqhjodHJ63C7A2Ftrp9XtW8f/9xA0b/IBbbrBYA/a2Z3KNICWfaXywWZmRX5PL3FwtfW8Woopy9IXaW69o91iGIbhD9q79dvsuTdHTjqI0m+tgsp26WarX1XWBz0DcmasTHTnOC1c+GSCvU8WSwOgCXLDfJDp7utSf4hA18Yw56vfxz+H0890FdDzxe3JC3ET7u0O20FRotik7W04hxnyjX1FbYIrHLdmfV2p1M4qbg21rdMgDvrHRx1G5kQnXscfzXcotl24osz9GdwOChj83oAZq5bh+KSypwTY/To84Xt8Vshb7oy2SNmooGtZwVxWQYT3KjcjUUdqu0dX3U1ve5zOWlCpYUHMK9ny5z7Xol5ZWYvaEQvTumC51vpzERRANQOqFWiScv7E67FiFewVy/V7y7rtty9UCQHvlmJW6/KAu39cqKOH7Xh7kAgA37inFP3w6W11m67RA27D2GmjVS8NR3q2M+FxHTYocDldpbbNbil1nP9V0f+ojOKhQ9v6KqCqN/WI/rep5ueI6Tx0i7VZjI9w8LLOO7fPthfL9KLBz22f+tweeLd+DTuy8QOl8Eq3W6vURaoY4nwsDutGvA+1pSpta9yubC43jquzUxQq3y7uzNOFBcHV1hJITXv7sQANCwdo2YgUtADheUTGUhmlk627sZzky0jPsQOVrNj6v34r1fNmPNbuPxHL1rHCutQOO6aUhLDXlPF2w+ELGN1x8/XooaKepzKD7L0oxbxi3S2MRNGwDq9HejsMVoZO+ZSeuj/t34RdYnGRDvtGuRSSw7D9scUPFodD0atwtcWWWV1AFOsj9gIpSUx7oRRFrUIvfFqtypLqpSzbRokXJ46Wuzced/loTf3zJuER74fHnEOeoElujr6U6MtHkj3565CVUC3hc1bS8m0/iJtEIN6Lc0REgJ+z6cpSsyieUym5M17FQaoutXqPR4bjpGfLHc+kRZCOCZMcrHIyfLbfXeOOd4dNJKLN56yCXL7GGcdaFSo85sdDVNJfOiZ0nO3XRA7Psu2aHV8o37jmGXjXVBEh2phXqNJrwua9RU4VWynOi03cKk18U3vX6cpdVswOnwiXJ8m+f+yn0A8F3eblubzYrg5gJTJ+NcXL7bs9Nxt+KTVzGzrooDny/egZvGLqw+32Vfyf7iEpOoD2PXx9YDx/HIN6siji7T2S9S9woRcc/6adzw3kLd41YEGcMumrLsPTPphNps1tSeo2I1qPo1NwUhXmy1qCUtNG6Z9W4cE4CieeZ/1WtcOLVv4Rb7i+Mb3c2dh0/gWJwzOHNenIkKg369WSnS21fTavDNyOXwzH/XCKUpgohXXeTe2bm/1QEFYuc7lYpN+4p92axDOqGOl5LySszPDz14bun07qKTmLQsvskObpgS9Ka0dlOftlpfJNbFMWFl6bbYFqJX6JUfvdhg7ever8zCde/MjzvtikqjATj98zl3t4L/z4ICyzRFifFR25i27laaXrC76CQGvTkHz0/RXxDLTZJOqJ/9n3stAZW/fR3/1ltiC7rrxVGH+C5vFzo89j3mbIx/P0q/yN+vvzqe04dofv4BXP/uAmdf1knTaGdyM/tETN+4z2KlOge8MGUtHvxiuakBejqd0aCW7bRcFzmHk3fcSVoskei6QyScVp3h68d4hdRC7aSFoF13V3U3cM7x/JS12LDXellNPdxwoURfY9O+Yp3lH0MwnYNfKBvq3vb+4rhtcYrd22HUrXaan1aDR3bLi5MQUL19/Pzo54yftxXf5e2OEJ6YdZ51MuDaHsbx0Voirhv7YVy4NWnLTmRIvL2LZw2WjdVLw48KRzqhNrsZ09fswwfzt5p+X7tNjlqQC4tLMWHeVvx+gnHIn9cDHtW/iiN//zEMenMOXp++ASfKKjBzXeTU2WRfvlGWsYPUFPv5rOcH9gJtFo2ds1n3uNh1xL5gdtrIiXnIGjXVXsIC147YIMPx1e2l6SbhpSp8qKqlnfCixxszNgIA7ri4neE52l1C1JslgyxobVAXLHpn9mbsPVqCSct2YdqIPsEYFgBOHyK3H+YUA6GWbWnMl76vXtTrV4OBTy8tnrneWZisikhMuBmqoDu5/8JpRF1dpAxUBy3Ytco+0rWotcS7BoJMMe7VBSbyN6kVy7GSCilm8HlB9M/y6meWGwzAeY0XvTEjofiTyXoYok+Lnrle5lwQ4Xl2Q3Sj8/vXLdZ+5/Bu6j78PrmFOs4mVOxebSbnxpeUJds1az/rVUARoUpMe9yeZV66TVy7tOYnubVR6Hd5u0wHGtV8LNRMibe7Ep2fiDQy5uVHTjhxcn+mrxVbOyMehMLzBGx3shCUl5WEn6t0Wgo1Y6w2Y2wxY2wFY2wNY+xZ780yZ8ehE0IDg4ng642YhShZl9stou+CtgXy+eLtrqTxg+BiPRGDgS5FI3hx10QERru2hvF1zD9XQ1llGTfQI94lIbxC1RdZWtSlAPpzzrsB6A5gCGPsQk+tUjCS2T6vzsLgt8SncEt2fy2Rv3qpxijEDTDufmrf29mFJx70u/vmBSOobeEA++LPOde1d8rKPTHRRVNWejOL1YgfVu1x5TpeNbxW7TwitG5IkFgKNQ+hBoamKX++SJ/b90WWBrbuutMBViaiO6nrMeD1Xww/MxI6p91Rtx9UqwgO0R5OeNDazWV1HVxKT4D3Hi3BN8t2Rhx7Yeo6V9ITZdHWQxj9w/pwhaG7iq/JrfWyZ7xs+2Fc+a95tnYNitmxxm2jdBCK+mCMpQJYCuAMAGM45zFxboyx4QCGA0CbNm3ctNEX4imo2vApgZRs2WDHrtKKSkcTYv748VJsfukKpKawiHWERdDGNos+UNoGnl8VVHlVVUwM9OOTY9fOBpzbJLpIkQhORN9IbA6KuEgi0radtClTVoZa1PVrpaJrZmP99AXS9CLqY6+DdWxW7jyCts3q+TpIKjSYyDmv5Jx3B5AJIIcx1kXnnLGc82zOeXZGRoZjgyJjK+Orq8orq3zJTG34lBW7ikqsf5fDFsTT362xPsmE/UdLcLsPE2q098Svol50ojxiIBEATpq4beygtrDcuh4gV8SSW7w2fWPEhC21HKzZfQRj52wx/F5lFUd5ZVXEUqyiWD1KTp60P0ct5+rHWJitqA/OeRGAWQCGeGJNFPH+/ns/XYbxc7fiJ2VCyb6jpfjDB4sjFlEZN2eLq0tDTl1p7o+LbvFGRnjEhzp70Qk/rN6DnJdmxmlBJEb3b8XO6lUR3ahHx84JxaPbxfWZ0lEX3He0BHuOOFuK080Gxri5xiKoSdC19Owy9O15WGQxDXvY2/McXfvBL/IcfU8EP3PM0vXBGMsAUM45L2KM1QEwCMArXhl04Fip9Uk2mLR8F9qn1wu/n72hELdOWIQvhvcCALz4fchf1611Y1fSe+CL5WjbrC7GzMrHKhu7oAPVz0pkJIg//OOnTZbneDG4ZifSxSh1Oz2ayMT109batDuONY8vUCq+gtFDbX/X9mCiyWd+zaYUZeFm+6sVbtjnbPkHK9xoDG89cNz6pDgR8VG3AvCh4qdOATCRcz7FK4PciqtV4ZzHPOErd8YK6IodRa6lOeyfzmr/IEkRKLHHyyqw9cBxtNNUfGaIPANBDqKKJH3R6J8tz6n+De79mHgqCNlZ73DNHW+QJMLAApGoj5Wc8x6c866c8y6c8+e8NMhJUT9WWoGnv1stvIi83UX/7SDSZdXdzFTzvSe+XY13Zue7aZYlIi2W341bhEtfmy18zc2FoWAhsyyp8skZ62Sg1v66GvbON2PkxBXuXUyAIOrLE2WVqPBhLWcz4mlR+9nIkHpmoihjZuXjw4Xb8Mmv23Q/N7oXdiMcRLB774zcCa9O2xC/MS4T7QeOHpyLZmLuTuw7WoKXvo8NBxPh/z7KtT5JEP2dviPv1pGT5fhg/lbHD2Aij/8F0bN5Y8ZG3P/ZcusTPSQx2tMSLsqkLTCio6lqfGalQWnTu05JeaUnEQ4iBf7IydgtxTiAqVFxsIPfnOOZb84N7vnEem/Jv3690nR5UrPsmrF2n8mn8RM9yeHxyaswZeUePDXsHADyxN2LMHtD4qxTrmVaHDH88cA5x/GyyjgjNmJL75GT5WhUJy2Oa+ojdYtaNAtN1/CIdVEDgC/b5xih53/8ZWMhjpZEro8ss0gDwEGBgV+rrm2Q04KjU1Yr0BJltqTdbZwSbQasFqfLF4gssC8jS7cdRpenf8TP6503BmasjV1V8JZxv8ZjliFyC7XNys7JNOEg0LPz3dnu7SOYSAQ6mKhJXDsV3rnrQ/+LE3N3IGvUVNPp9kGj/c2Tl+80PjGKv3zpry/dLZZvLwIALHAQgQKElpt9ZVpstNGa3d5UXNK5PrSIRCJYkcitnGRAuz64HgUHxUOb4ikOVgPNZz05Lfza7t6UVo2B16eHxhvUrZtkRPucFFjcs8jvJc4DtknTQ41XWopO+BvyKHWLOs/FkDlpSSA/qBUnymK3trLaPuu7PPEFgnYcch6ydv/nses47zikL0iOW9QSL5tKAFePiX/T4aCQWqgnLxfc+dtE7Dj0B6zokXEfrxfun5jrfOalnsgfN2hlq4Lq1qSTRJgO7tTEBGpQexqW6zVSC7Vd9Fel49KtY6vFjx2M3SaRurtOsCuseqvnjddM27YKY5QBvd7QqUCidGil9lGLosYiG20xVKnT0uv6zHSPrUpeOAcOnyiz5ctMJNyoiPSWEpUZp40ZDp6QjY1EI6Fb1F8s3o7l2w+HN4vV40BxKSokWxU80dujHEDP52cEbYZn7LO5wNNlb84RmrEZ5EYEVsTjl7/x3wvdNcYhfm1CAQAv/+BwfRmHJHSLetSkVRHv9UZiK6o42jYTW5uCECPZXR9HT9pzA6gDplYRLjIPJibDbMx7P1mGF67tglaN6ni+9KjVvXYbqYT6WGl8frJxc7fGHDtRVokJ82KPB8kRn0N73Caoh9MqgsQtnM6We2PGRpct8Q+nro/8/cesT/KJmev3Y+bLP+PmnDaWG2is0FmYTWakcn2ILqqU6Lz9s78LLrnNkoJTwyeZCIOAbpFMnSSRDZOXJJhfXSqhXr07sWq5U5VbxsXsxEYkODJHRnmB6hkxWh9INqQS6js+WBK0CQThGXZnPPrJ/lOo96AlnklUfiKVUBNEMtP7lVlBm0Ao7HGwqW2QkFAL4HThFoIgCDcgoSYIgpAcEmqCIAjJsRRqxlhrxtgsxthaxtgaxtiDfhhGEARBhBCZ8FIB4CHO+TLGWAMASxljMzjnaz22jSAIgoDYLuR7OOfLlNfFANYBON1rwwiCIIgQtnzUjLEsAD0A0IwHgiAInxAWasZYfQDfABjBOY/ZGIwxNpwxlssYyy0sTMwdkQnCb7o9S8vtEtYICTVjLA0hkf6Ucz5J7xzO+VjOeTbnPDsjI8NNGwkiaVF3PicIM0SiPhiACQDWcc7f8N4kgiAIQotIi/piALcC6M8Yy1P+rvDYLoIgCELBMjyPcz4PibO1GEEQRNJBMxMJgiAkh4SaIAhCckioCYIgJIeEmiAIQnJIqAmCICSHhJogCEJySKgJgiAkh4SaIAhCckioCYIgJIeEmiAIQnJIqAmCICSHhJogCEJySKgJgiAkh4SaIAhCckioCYIgJIeEmiDioGFtyyXdCSJuSKgJIg44D9oC4lSAhJogAqABtcQJG5BQE0QAUEucsAMJNUHEQdP6NR19r7KKlJoQx1KoGWPvM8b2M8ZW+2EQcery18FnBm2CbS47p0X4dY0U8T2gK3Wa1EPPbeWKTSr9z2ru6vWI4BBpUf8HwBCP7SAIZDSoFbQJtmFMXJy1ZDauE3OsZ9sm8ZoTZvNLV2D8bdmuXS9Z6N66seU5N2ZnGn52dffTXLRGHEuh5pzPAXDIB1sIDe/8rmfQJviOM8mL5dYL22LkoE6Y8ufeLl3RGDutaC2jLj/LZUuqaZdeD6kpDCkObTPjtEa1Xb+mn1zb43TLc/7U7wzDzxrVSXPTHGFc81EzxoYzxnIZY7mFhYVuXfaU5TwXW1dOqVcz1bVrLX5sAKaN6OPa9VTe+/15MccqOccDAzqiy+mNXE8vGq1QX27DdVE7zb28jcbLsrPg0QF49qrOjr57Yfum+PXRAS5bZI9OLRqEX6dq7t1N57cGADw4oCPs1m+pHlSI0bgm1JzzsZzzbM55dkZGhluXPSW5vmcmqnwOC7i3X4eYY4seH+ja9Zs3rI2zWjY0PceJG2FIl5Yxx3gceVcz1d4joW21PjH0bOHvtc+oF36tTpqJx24j3BSROX+9FABwywVtIo7/ZWAn3fOjk+6QUR8t42yRx/tzOraoH36dllp9sTOah46n16+JmjXslYFzfWgQJFTUx32XxopJonFOq0ix0rvJjAFOggK0hXhI55b42xDxwbkROg9b/VrGsb4PDuhoyzYjhnatboXafQbPatlA9/jQc+35EWc+dEn4db8zzRsZTww9G2dqWmU92lS3XlMEK5oljw9EZpO64feqmJpVVEa/1Qo914yZD9aMNs1CNqelpqBdenVFs3zHYd3zRfPDjJ819waAbi/pog7NhK61YFR/pNevHgdJ01TKf7goCy9fdy5uuaAtWjWqg9N1xhAA/bBKP5pUCSXU2m6LXaJ9Uw1MRMgObZrWtT5J4abzW2P87ZEDPNf1jPWZndOqIaocKPXGFy4Pv37v1vMMCxsA1I1ya2ifKZEBk3SHYWnRaFuwdWy6WqKFbfK9F2HVM5ehd8d0w+/0bNMYAFBL02pqrRHNGqnm4nLnxe0wbUQftG4ayttLOoWEXdTdUCOFoXFdfT+nWcppqSk4P6s6DbN7G51eNKkp9h/723q1jXivfZ4qqzia6PwmJzr93NWRbhWOSPfWh3fkIL1+LTTXDDx3bF4fIkSXea37qUZqCm7OaROuNI0iZlo0jB3wrqkpMwM8irQRCc/7HMBCAGcyxnYyxu7yxBIDRgzsiMuV7m0NwQKm15K84+KsiPdGroWHBsW2LN++uQdqpDDcc0lsi/6z/7tAuMvbs20TnBb1gEXr8dQHeuOOi7N0C7lVOtHCZSYe0ZfXvn/zxu7Y9OLlEZ8P7twCdrg5p7XQedru55DOLXFVt9PQrJ5YJRD9G3q0aYIGtc0He169oSua1quJOX+7FNlK/qSlsnCZiRax5zXCkcJCrg7GGP57X2/88GDI5z7r4X54//bzLYVp5TOXIf+lK8ItuZGDOuHKbmKt/5o1UvDxXReE388f1V/oe3qt9Npp9oU6+tmLfnxmjLwknB9GaevlT8HoofidxpVyW6+smHO07q0m9Woi94mBWOzALceiSkx7Ta8gmo9/3aZ7PFoDXv9NN1zbI9RD+ejOnJiGmFuIRH3czDlvxTlP45xncs4neGKJASmMoVWjkLjp1dpA5Ej0l8MvxL39zsDqZwdHnBN9k9Q41v/dHxkZ8GedLv1V3U7D6mcH4xGdCiCzSV3c3ad9xDGjkeEup0V2256/unOMX7LzaY3AGENmk7p4YujZEeIcnY4R9196Rtg2UbQPVUoKi+gWAsC/bumJvKcGhd9btfdbNhRr8WlbLikpDG/f3AO5TwzEb7Nb49+3xg4UaqnlQHDOaN4Ay54chBYNa+Pft56HmQ9dAsYY0uuFWkq1aqRECIo2ZFDbbW5SrybOVtxY7dLroZFB2dTSMKoSeWBAR/zz5h5CvvkL2ze1HIB8+DJ9X3E0daKuc/EZ5q6DpvVqYmjXyLGAlo2q8+KSThlIr18rwiWUmsLw5LBzhOyJZtFj1QOO6n0xY0iX2EFcq98EAIM7t8Rbv+2Op68Ut7NG1HMx8JwWuDmnNaY+0Bt9O2U4Dte0TNeTq7oIA/DI5WciO6sJLjojHb+/sA0++XV75DmM4eeHLkHzhrXDflWtf3X5k4NQXlUV8Z0XrzkXL/+wDs11ujJ62Bmlf/d3PXHL+EXh9306pmPcbdnha3x8Vw4qqjguPbM5/v3LZsPr3N2nPaau3AMA4V7FsK6tMEU5pqVlw9pITWEoGD3U0r4HBnTEhLlbAIS6sG2a1rX0D6elpqBx3Zro0zEdczcdiPgsvX4tvHrDuejYvAEem7wKczcdADeQ8p5tGmPZ9qLwe72HjDGGV27oiq0HjpvadHEHYxeHHtHrazSrXwvNFPHNUlpXOVlN8dpvuiFr1FQAQENNpduioflAWLxjgfVN1v+41yRkDAD+3P8MNG8Qa5/eYGK0C0BbgfRo0xjLNfcHAJY+MTBGgG7Mbo0mdWuiQ/P6yGoWyjvtKZtfugIA8OS3q8Np3nphlulvUNHms0gF2CvKR73++SGonZYavodhorKiV4dm4crWDk3qpuHwifLQJVmovHY+zdsBRel91IwBtWqk4gol9KlfJ30fUPuM+oaDX03q1UTzBrWxRtPKvv68TOQ+MciwuxrP6HLn0xohP8p1oBX6Ph0zcOmZod/RysLX2EPxqd6UE+oevvnb7ljx1GXhzyf+sRcKRg/Fr4+Zhz1pW/kjNe6d56/pgr8M6mSYD90yG4Vb6ADQtll1K/2V688FAJzdqgH6n9UCrZvWjRhc0+ObP12ExY+HbG1q4eJoZ9I1fePGbviLjpvKjFXPDDb8LKddU/zy1374TdRAW6/21SIw4Q/m3VqtO+2PfcV6P0C1fqhlQuXOi9uFX9ezGFOpqOK6Tu6HdFrZpzepLnM3nJcZrmBeuf5cfHb3hbH26RQOxhgu69wSHTLqCw2Grn1uCM50OCAKAFP+3BtPCbTQX72ha0yj6uO7ctCnY3rMuJTZNH6z6J/vNS6e6F6SV0gl1OqDr63xL2wfWVvG07PQK+wZ9WvF+J0m3J6NWQ/3w0vXnmsZBaCijQ9NSYnsImm7zNFcqYl6eOGaLjGfn9a4DgpGDw0PWqWlpkS0MnLaNRWyb8XTl5l+bvSQfXd/bzxsMLW7udLy0X5XtbNvJ/18Y4yFKw01JHDu3y7FTyP7mtoXzXU9M4VCz16+7lzha7ZtVi/8WxY/NgDzHrk04rfptVi1VCgPfqtGtfHoFWdj9sP9woOXZmizXo1surdfB8NeSTS92jeLGYNR0fP59uvUHP+4qTvWPjcYr/2mW3gAtVGdtJgB3ehBRCtysppizC3mk7U+ujMn4n0rgZC9Lqc3wp2921med2N27NhIn44Z+PiuC2ImAB0vrTC8jtr7+uSu2DEo1RXrJ1K5Pn57fhvUrVkDXTMb4dp3FuDQ8bJwl1RFL+THTtzjTyP7YldRSfg9YwyjLj8L72lcEAPODg2ctW1WLyZmVIvWZ96yUW30OzMDszcUxvh3n9cRYG36Kr+/UPyhGN63PTqfZq/b9u19F2PjvmJb34lGbYQwxpCq2K6NUDmvbRNL90utGqkR57Q2iZz5w0VZSEtlGDd3KwDgyWHnoFOL2FF+owGym3PaILNJnZjuvhXNLdwcelRUhtxrqvBlpdez7DUAISGZvHwX6tRMxZDOrTBm1mYM63oaZq7bJ5Tu58NDrWC1B9I107wb3qReTVzdvTpq45mrOiOjQa1wuddidwblxHt6Rbx/67fdY9wX0ZX4PZd0wGvTN+ICwUaHKA9f1gk/rdsfc/zl687Fo5NWIVMgYuusVg3Qu2M6Xpi6zlXb7CKVUAMIj4LfcF4mxs7Zgno1o0xUdK1768Y4r20TTJi31TDcSY8zmjfAGc1ju2Bf39MLRYrfSYQ1zw6OadG987ue2HbwREzXyywe2SmPXSEWafK15sHp3rqx0FoHZqiinMpYuNK0mpzzbhzT4Z9RZsHVr5WGvB2HcZdOq+qzuy+IqdC19OkY3wSskYM64Y0ZGy3PUwesm2kGwB4cEBILs0iW0defixEDO6J+rRo4N7NRuBLr2KI+DhwrRTfNPVvy+MCISBkt52c1xU8j+6JDhn64Wvv0ejhaElvG0+vXwtNXVke3rHtuCCo5x6FjZagb/fzZ5BqBKds1UlOw+tnBEe6GJY8PtDXpa+Gj/VFWETkOdX//jri/f2xwwM05bXBtj9NNx51kW9tQOqFWGTXkLIwY2DGmK6YW+G6ZjfDE0LPRtF5N3HCeswB+LdlZYrX5jyP6Ii2V6bpR6tasETE4MX9Uf9PulRbRcDa7GP2uLqc3wqKth2yvVaH69VJTqv34Vg+UnanVRjw40HiCzUVn2BtUtMsDAzriAYEJPm2a1cXTV54TsQqe2ogwE4VaNVLRtllsRZOWmoJnr47sjVktXKXXCPn4rhwUHDiOW3XcIHqoz5wXDQyVV2/oGrGNWXRadhfosuuOEA0O8H5yuBjSCnVKCtOtzbtmNsaHd+bgwvZNwRjDfZeaj4a7jZ0BEdFJCSKRGm4z7vZsbNpXHFFgB57dHJfrRGFoUcMaUxhDe6XlNqyrfizwh3fm4KvcHS5ZnBjccbG1H9UtupzeEGt2H7U8r0/HjLh7FW6j50uWia6ZjUJuTMWtenNOa2RoxpraNquLbQdP+GaPtEJtxiUGA1WEOA1rp+G8tpGt7fG3n2/5vet6ZGLSsl3IadcULRvVxsYXLjfsil/SKeOUv1fqEIQX63hEzwE41bigXVPk7Sjy5Nr/uqUnNu4rDkd1vHxd14jPZ468xFf3SEIKNREcvTumR/QA7C5gc6qhjmN4sVqeV5MrEoUv/9jL+iSH1K9VAz1NQk2jJ754TVIL9U8jL4nwgxGE37RsWBsPX9YJV3WzHlQjCCOSWsXOEFyshSC8gjGmG3lAEHagfitBEITkkFATBEFIDgk1QRCE5JBQEwRBSA4JNUEQhOSQUBMEQUgOCTVBEITkkFATBEFIDvNiDQLGWCEA/d0hrUkHcMDyLP8hu+xBdtmD7LJHMtrVlnOuuziOJ0IdD4yxXM65N1v5xgHZZQ+yyx5klz1ONbvI9UEQBCE5JNQEQRCSI6NQjw3aAAPILnuQXfYgu+xxStklnY+aIAiCiETGFjVBEAShgYSaIAhCcqQRasbYEMbYBsZYPmNsVADpFzDGVjHG8hhjucqxpoyxGYyxTcr/Jspxxhh7W7F1JWOsp4t2vM8Y288YW605ZtsOxtjtyvmbGGO3e2TXM4yxXUqe5THGrtB89qhi1wbG2GDNcVfvM2OsNWNsFmNsLWNsDWPsQeV4oHlmYlegecYYq80YW8wYW6HY9axyvB1jbJGSxpeMsZrK8VrK+3zl8ywre1226z+Msa2a/OquHPet7CvXTGWMLWeMTVHe+5tfnPPA/wCkAtgMoD2AmgBWADjHZxsKAKRHHXsVwCjl9SgAryivrwDwA0K7yV8IYJGLdvQF0BPAaqd2AGgKYIvyv4nyuokHdj0D4GGdc89R7mEtAO2Ue5vqxX0G0ApAT+V1AwAblfQDzTMTuwLNM+V311depwFYpOTDRAA3KcffA/An5fW9AN5TXt8E4Eszez2w6z8AbtA537eyr1x3JIDPAExR3vuaX7K0qHMA5HPOt3DOywB8AeDqgG0CQjZ8qLz+EMA1muMf8RC/AmjMGGvlRoKc8zkADsVpx2AAMzjnhzjnhwHMADDEA7uMuBrAF5zzUs75VgD5CN1j1+8z53wP53yZ8roYwDoApyPgPDOxywhf8kz53ceUt2nKHwfQH8DXyvHo/FLz8WsAAxhjzMRet+0ywreyzxjLBDAUwHjlPYPP+SWLUJ8OYIfm/U6YF2ov4ACmM8aWMsaGK8dacM73KK/3AmihvPbbXrt2+Gnf/UrX833VvRCUXUo3swdCrTFp8izKLiDgPFO68XkA9iMkZJsBFHHOK3TSCKevfH4EQDM/7OKcq/n1opJfbzLGakXbFZW+F/fxLQB/A1ClvG8Gn/NLFqGWgd6c854ALgdwH2Osr/ZDHuq/BB7LKIsdCu8C6ACgO4A9AF4PyhDGWH0A3wAYwTk/qv0syDzTsSvwPOOcV3LOuwPIRKhVd5bfNugRbRdjrAuARxGy73yE3BmP+GkTY2wYgP2c86V+phuNLEK9C0BrzftM5ZhvcM53Kf/3A5iMUAHep7o0lP/7ldP9tteuHb7YxznfpzxcVQDGobor56tdjLE0hMTwU875JOVw4HmmZ5cseabYUgRgFoBeCLkOauikEU5f+bwRgIM+2TVEcSFxznkpgA/gf35dDOAqxlgBQm6n/gD+Ab/zKx4Hu1t/AGog5PRvh+oBk84+pl8PQAPN6wUI+bX+jsgBqVeV10MROZCx2GV7shA5aGfLDoRaHlsRGkxporxu6oFdrTSv/4KQDw4AOiNy4GQLQoNirt9n5bd/BOCtqOOB5pmJXYHmGYAMAI2V13UAzAUwDMBXiBwcu1d5fR8iB8cmmtnrgV2tNPn5FoDRQZR95dr9UD2Y6Gt+uSYuLmTCFQiNjG8G8LjPabdXMnEFgDVq+gj5lmYC2ATgJ/WGK4VjjGLrKgDZLtryOUJd4nKE/Fh3ObEDwJ0IDVjkA7jDI7s+VtJdCeC/iBShxxW7NgC43Kv7DKA3Qm6NlQDylL8rgs4zE7sCzTMAXQEsV9JfDeApzTOwWPntXwGopRyvrbzPVz5vb2Wvy3b9rOTXagCfoDoyxLeyr7luP1QLta/5RVPICYIgJEcWHzVBEARhAAk1QRCE5JBQEwRBSA4JNUEQhOSQUBMEQUgOCTVBEITkkFATBEFIzv8DdSRyp/rCniIAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(posterior['noise'])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(posterior['weight'])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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