{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data Analysis and Machine Learning Applications for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Material for a* [*University of Illinois*](http://illinois.edu) *course offered by the* [*Physics Department*](https://physics.illinois.edu). *This content is maintained on* [*GitHub*](https://github.com/illinois-mla) *and is distributed under a* [*BSD3 license*](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import scipy.stats" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from mls import StochasticProcess" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **stochastic process** is a black-box generator of random sequences\n", "\n", "$$ \\Large\n", "x_0, x_1, x_2, \\ldots\n", "$$\n", "\n", "where, in general, the value $x_n$ depends on the history of all previous samples, so the black box has long-term memory. The values appearing at the $n$-th position of many runs of the black box sample the random variable $X_n$. In general, samples can be multi-dimensional, $\\vec{x}_i$, but this does not present any special challenges or require new concepts so we will stick with the cleaner 1D notation in the following.\n", "\n", "Here is a simple example of a general stochastic process (implemented using `mls.StochasticProcess`):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class StochasticExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return 0.5 * (np.mean(history) + gen.uniform())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two useful visualizations of a stochastic process are:\n", " - Plots of a few long runs output by the black box: how does it evolve in \"time\" $n$?\n", " - A pair plot of the first few random variables (from many short runs) for a more detailed look at short-range correlations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StochasticExample().plot(nsamples_per_run=50, nruns=3)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StochasticExample().pairplot(nsamples_per_run=4, nruns=1000, x0cut=0.5)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** For each panel of the pairplot above:\n", " - What distribution of random variables does each panel show?\n", " - What correlated random variables are marginalized out, if any?\n", " - What conditional probability do the two colors indicate?\n", " - Explain how the pairplot answers the question \"Are $X_3$ and $X_0$ independent?\", i.e. $P(X_3\\mid X_0) = P(X_3)$?\n", " \n", "Hint: the top-left panel shows $P(X_0\\mid X_0 \\le 0.5)$ and $P(X_0\\mid X_0 > 0.5)$, with no marginalization since $X_0$ starts the random sequence." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The histograms show the distributions $P(X_n)$ which are marginalized over $X_{n-1},\\ldots, X_0$. The scatter plots show the joint distributions $P(X_i, X_j)$ which are marginalized over $X_{n-1},\\ldots, X_0$ with $n = \\max(i,j)$ and excluding $X_{\\min(i,j)}$. Note that these are distributions of random variables $X_n$, not random values $x_n$.\n", "\n", "More explicitly:\n", " - $P(X_0)$ has no correlated random variables marginalized out since it starts the sequence.\n", " - $P(X_1)$ is marginalized over $X_0$.\n", " - $P(X_2)$ is marginalized over $X_1, X_0$.\n", " - $P(X_3)$ is marginalized over $X_2, X_1, X_0$.\n", " - $P(X_0, X_1)$ has no correlated random variables marginalized out.\n", " - $P(X_1, X_2)$ is marginalized over $X_0$.\n", " - $P(X_2, X_3)$ is marginalized over $X_0, X_1$.\n", " - $P(X_1, X_3)$ is marginalized over $X_0, X_2$.\n", "\n", "The two colors apply the conditions $X_0 \\le 0.5$ and $X_0 > 0.5$, so, for example:\n", " - The $(x_2, x_3)$ scatter plot shows $P(X_2, X_3\\mid X_0 \\le 0.5)$ and $P(X_2, X_3\\mid X_0 > 0.5)$.\n", " - The $x_3$ histogram shows $P(X_3\\mid X_0 \\le 0.5)$ and $P(X_3\\mid X_0 > 0.5)$.\n", "\n", "The difference between the two $x_3$ histograms demonstrates that $P(X_3\\mid X_0) \\ne P(X_3)$, therefore $X_3$ and $X_0$ are *dependent*. In other words, $X_3$ \"remembers\" $X_0$.\n", "\n", "Note that dependence nearly always implies correlation, but it is possible to construct [artificial counter-examples](https://en.wikipedia.org/wiki/Uncorrelated_random_variables#Example_of_dependence_without_correlation).\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An observer watching many different sequences generated from the same black box would need to measure all these conditional probabilities to fully describe the process:\n", "$$\n", "P(X_0) \\;,\\;\n", "P(X_1\\mid X_0) \\;,\\;\n", "P(X_2\\mid X_1, X_0) \\;,\\; \\ldots \\;,\\;\n", "P(X_n\\mid P_{n-1}, P_{n-2}\\ldots, P_0) \\; .\n", "$$\n", "The equivalent Bayesian network (up to $n=3$) is:\n", "![Stochastic process graphical model](img/Markov/stochastic_graph.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov Chain" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **Markov chain** is a special type of stochastic process where $X_n$ only depends directly on $X_{n-1}$ and not on any earlier samples. In this case, we say that $X_n$ and $X_{n-2}$ are [conditionally independent](https://en.wikipedia.org/wiki/Conditional_independence).\n", "\n", "In other words, a Markov chain is a black box with very short-term memory. The samples $x_0, x_1, \\ldots$ produced by a single run of a Markov chain are referred to as a **Markov-chain Monte Carlo (MCMC)**.\n", "\n", "Our observer now only needs to measure:\n", "\n", "$$ \\Large\n", "P(X_0) \\;,\\; P(X_1\\mid X_0) \\;,\\; P(X_2\\mid X_1) \\;,\\; \\ldots \\;,\\; P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "\n", "The equivalent Bayesian network is:\n", "![Markov chain graphical model](img/Markov/markov_graph.png)\n", "Random variables without a direct connection (arrow) are conditionally independent.\n", "\n", "An important subset of Markov chains are **stationary**, which makes our observer's job even easier since they have the property that\n", "\n", "$$ \\Large\n", "P(X_1\\mid X_0) = P(X_2\\mid X_1) = \\ldots = P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "\n", "In other words, a black box with very short-term memory **and** no sense of time. Our observer now only has two conditional probability distributions to measure, the initial probability,\n", "\n", "$$ \\Large\n", "P(X_0) \\; ,\n", "$$\n", "\n", "and the update rule for $n\\ge 1$,\n", "\n", "$$ \\Large\n", "P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "\n", "Here is a simple example of a stationary Markov process:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "class StationaryMarkovExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return 0.5 * (history[-1] + gen.uniform())" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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FHa4v1SdOVA5tOEshlMSGiVjdRVY0XQSGaS4dBy1eObrF43IegThRuptHBqdI3I+iiSCpKDpzZCAVyrx2jEHmNAkEFksUG7xTJMbPG5e5G84Dh4V/60aj4TSbzWKW7v3Av2o2mzvjPmxxsY7jnO7CdYOYv/Xx/5u7O20eW5vl49/zJ6hVrtYgaClxKi7X1+dP5A0ApOewfxQwv1CnXnXpxm1kPMuHnn4fWy+9wDMbX8H6xsrEx1tdnTvP5RMdd1BRnceuLSOlpOMe4SmX1fnzPc5pEOAT2Tq1G0uoSgWrNYuLddRMjVp6/v/phc28kmPn0Kdar3B9vUcH1WdrHLYCarNV5uqjczLdIOaLX+iysTrL0no5peSbDvGxpL5UP5GEvUicx/dtoojOUR1nbo5q+nl+5PPD//afcK+9zZPOEj/wlr/E/OIMbuF7n41c7HHAQq3KUm2ydfgGvJrHxvX5Ui9ZS0mrE7G4NDNWsC479/CoTRAr1pcWCOIQfdRlvlplpX519yiA1wqIkdSqDl0/Zna+xsLs/dO9Z/3OL3MnPAKKq5QDhgDgm4D/ZpIP29/vnHoBL9055G4qBHdrq8XnXrh3paVcAFu7bcLIsFctN2wdP2L/oAtxzMJshWBznyO/Q9ebZ0Ze42DnGLlwPNGxVlfn2N6e7L2TwFrLvdY+jnTY1cl1PWx1Efh4wdVVRoT3DjC+T2fOR8iQ1dU59g86yE6M58wC4GD78jF1R/Rdmyg27B+06bR9NpaHn4sfxnzs538Le/c215bm+O4PLZZGnNFBF33UoV09RFYuJ79zXt+37nSI9js4eDgy+byXD1/lXjuZdXyvs8OLd2/xhDuPU1Avj3TEfrtD2BLo2mSO29b2MUpJdnbK3390HHDYDvCEHenIFc99u3WU/F8fo41mv9XBdyy2fnlG2fg+wZ3bffIx++m5iLkq+8c+kR8SXqud+nOKmOQ7H2YsLtMY/Afg64FfSnMGny++2Gg0FoBKs9n88kUtIBOF2z7wub509aVckOQM5BCKCJKxfwBBbBI9+SjGZHyqcgjj4Mqoh9BEWGvzKiJIQt4rTyBHIcJ1+q6JkKqPxpBS8Oy7n0EIweNrsyc2cNeR1CsOnSAeqRX16laLnd0Wy8Ddw3BowrknSfHgVRQN0m6QzDperi6x6++xXFthpbZUkkDOKJnJSnRjnc49VqOeh54sxehtswdtNZ70emsSl0sT6U6HVz/2HNHOdp98jEnzhVVPIYUgiEavyfg+r/zwDxFt3sNdv86TH/6hc+0xukxj8MvA1zUajd8gSZ2/r9FofC/wYrPZ/BXgTcCXLnIBVc/hr/2Ft7N1HPBEsYnrCqEHpHoH4TpJ800U6fyh1EqASBKkYdhJBNkuydssIizkCzIoIYmvUCLYao3VBukNXA8l8yQvQBwbqp7DE+vDQ+q5ukcniDlqh6X3irWWiitZm3PRu7C0NDPcwcglKa6eqz4tdLtNcPsWztJS/ruqU+Fb3/Lfs9nZ4W0Lb0Ru7Z4wdFJIhJATN3kV5x4PQyZRMakshTYabE8rCcAR9zd457TofvElop0kisrkY2qvez3aZmXlAs9VSXf1COcwuHObaPMeANHmvfxzzguXths2m00DfGjg1y8UXn+epOLoQlGvujw5U8V5DTRGGZNI9aoRnhCQ3yjaTzju2FE4wkF6NfzjY+IoxLsCY5DpERWF6UReUXQ1A0SG6gNJhU0jGUgqOTx39PpqFQfPUXSCmCg+2Qh12A6xFt77xx/n8IU2T/2RNw91MO43MtCtFsGd21SfePJSO86N73PnEz9BtLN9whtV0uGJ+ZtU3SohnKgmgqTxbFKV0FGVRBlOW16adx8XokQlFUEcXFr1jjMzUyofo9PzlUJQSZ/xINJD6a/KjZu4K6v5d3HeMjRX7xpfMhwliOgv67oqjCorLcJzJH4IQddHYrCOxJEObqWODwRBG2/28pNhgQ5RUvXVa2flpVc1TSozBiemjWUVRVoTI0/o5Q/D/IzHzmGX407I0nxvE/bDmINWgIoi5D//aRZ2djj83K+z/JGPlm7WuVjdGXoNMnrgKlRqgzu3c6+26I0aa7DWoITbN/pyEEpIIhtN5Bz0KomGPw9SJtPPJlUvLTac9dbUqyhyLrjxzPhdEDKRj9nbZe6revIxxiQaSyI1BsBIYyCrVTY+9O0Ed24x+9V/6NzvgQerxu0ckFXs6NdAN2iv4Wz015CVm4WdIAl7HQdXOlQqdQCCoHuxCy1BbGK00X35AiB/4O0V5Q1MQaCuD4VpY6MamwYxU3VQUnLciXKOVxvDTlqJNN/ZxewkxW9ma3O4gqws73WYBP6tL1+ZSq23cQNnOalW6/Nqba92Px/lWWoM0l6DCYxgNEFkAImxyPIL41BmDJz7GLxzWsRHSTJXVqsnkr7a2NwRrHjJOQfhmDVJQfXJp1G1STMmk+ORiwyUFKAtsXmwIgOAsOujZiVCJpFBxa2CgDC8fGOQ9RcMzi6QBZroKjCKJoIkpxClSxtUxSyDEIL5ust+K+C4G7Ew47F76BMbw7XZCnPXnmA3pQDk2vDQXdyHPpG3uprTDO7a+qWq1ErX5fr7P4BuHTPz5rfmm1lR70eIJIdVZgzyjddq3DGNZ/HA3ONhcB1JEGniCeryyxwulXfKX6wxMFGE6XQQnoeQEuP7OTU1qFaspMRRcmQS2WqddNZXL6YK6pEzBo6SEOvXRmSgewmkUXCdZM1RpPHSTU4JhVIOrqoQht1L5+izfEExeQyvDWNQKiNdSODGOrnek9BEALN1l4NWyHE7RACdIKkuWpjxEEKw8ewHufvyHSpvedvw0D2nqc5wXaTMVWrrja+41JyBjWOkV8F9eq3vuGbA405yMicdrEk7frO5x+PyOJAlmCMiPd4YDK6z+PNZ5LVPA32cRAXO/Dy6m5bCGwNK5Y5gMVlcdRUtPyKKdWkSfVxj4/3ikaOJIDEI+gHKGQgh8NDE2iSVRICT8vRepQqxJtSXK3UQ6jBZl+z3UuQVSlJYY7CxLtUHKiZwh+nlD4OSktmay27nkP/9hd+hEyVdy0IkXbfC9XAefwLtDG9OE0IkYnVniAxsGOUqtajRm995oyez0X/coiw0kFBFZTTRhENuYm0mzuOcpqKoj85K4Uy4Jj8OePnwVfw4GPm+sr/phl106xihFHJm5kRkmFGOqpDA9rwsb1B+Xtl3cVFNi49cZAAJ56iNvXItkLxNPwhov/witSefGur1uVbjY/HTf2c3dMWr024f4ofdSxOrM9YQ6oiK8k5cv0yD/io044vTzQZRTOBGsSzVyx8FLUI+9cKnwOvyf23P8rdX/joLtZlcFtv1XII09B/2uWedxZwN6kl+vlyjnxsD1b9VZJ6+zCMDgYlPbq6TRgZRnGyOk+RxTlNR1FvnSZpo1Jr8OODvPf+TbHd3WKut8v3v/K6xz1c38vnRz36C7e4OT4glvu2J/5r68lrqCBQiQ7fgCBZYgSyJ7Icxs7WT93BPOXYaGZwbHJVUk+grzhtoY7FBwJ0f+Si3/8Hf45WPPYfx/dL3OmnjTtdalFT5zV2pJImkIGhfzqIp6BGVPBzZ5mCvoHR3pHJo5g3Geqhe/ij853svgZfkZozX4vN3XkleSPsGVPqAjqIfhTzbLGYThsk5SXH5xiA1doMbUDFnACSRgeXEnIBJk7WnidYcJRLBugkMqzY67XfobbpZ49moNd1tb7LdTZL2W91EDHIcXjx8Of+b1v4WO/4eajbpeB+suCqjiTwnEeIbHhkMHzB0HnhkjQFw5VSR1ha27hFvbwEQjahGcYwGIQis7ec/vQpKKsJLrCjqNZudpEVkKsV7FXNmB9VKi8gexigdWDNO12YQT62sIKKkekuGc7ztxpMA2NQbdtJoZGTJsjz9LOZcjttzka6LjaNLHcwyLjLoo4ngBFWUbcTjkrVReh0noYmEEGhj+OLdo7EDiLQ1pbMUxjWerddXWaouArBUXcx/HoZAh9RUlaXqIl5kWPMWWVt+POf3xcD1yWgip2AMhBB4riSKdf56ETaKQIoLyxk8kjRRFprFxlCZUGf9IqCNxdm4AWkjibO8gre6duJ91hgUGus4RLHO8wWQeAmudAniiEhHuOri9VaOwha3W/dYri2deC0vLb3KyKDMc0q59jiKoDIZHZFBG43jCv7q13wTL27f5Y899TUs1JJOY5tGBo7rQjRaJuEss5hNmBhe6XpYISAIEznpSxK7s7FOpKsH1qutQQiZf99Fz3dQ5lqJ8Y1nbT/i1naLtcUa3phn0g9j/umv/C7bBz7/ZulLfORb3lna7FfshRiEEpJAh0OpYikE733mPRyFx8x7c3TiDvPebOl7jTXsdvfwlMt7n3kP7Xu3eJ13nfpiQUBSjY8MIFFJCCJd2m9gowhxgYOsHklj4L4GIgNrbTLcolZl5QMfIrx3F3d1FRNFJx4FG0WJx11JjEExMhCOwlMuQRwT6PDCjUEn6vKpz/8Ce/4+66+u8X3v+M4+LlUWms4uG6M8pyyBG4fxqY1BJ+6Chdlqja967HXMFfI6tkgTRXr0PZV5qKeJDLK+Cc/N55/YKIJLMwblG5A2uhcVAIjyyAASWiaO46EVb34Y84//9X9m59Dnf/vNV8dOlyvODr631+UPbh3wtqeXT2zUZcnj3poc0OHQxrMgzYk9s/RGfB3QCtschkdcq5zUnToMjohNzJw3i23vMyNmqc7M9QkS9iKD5H4ZNtSqklZTDRoDG8dgLy55DI84TXTa8XnnCWMTKQopBcJRVJ9+HapWR7eOT9AINvUOVdXBYhG2EFoqB1d62FjnXH4Z/DjgC7svn6oyYhDWWl7Y+wJ7/j4Am52tE1yqSDsqL7vpbJjmfhFCqTPRRO2oDQLq2YznIk2TGgOvktFEI3IGhchgUtgwy4N4eTRwWXmDbAMazBckNfL99MuoLmQnT9iWX5tb260T0+VG4ebKDNeXku9iZaFK1VXc2WnT8fspoxN5jQLUGKelqLt1rbKAkoqj8Dj/fYZu7HMctnCkw0JlHvYPiW7fQQzehwNNh71KwpPjboET/QYXnTyGRzQyyLuQrzCBnPcYGJM/cLJeIz44xLTbqLmevETWVSurDnRA66Iap8R1PURH57X/gzhLZUQZDsMj5rzZXK1yvb5WOlhHnkKc7Lxgoyi9jsM9J6EUOo4RiJGSB0WEOiLUETWnltNzCf+dbswDCeSRxuAMkYGJQpAC6boYknumWF009O98n+PmXUx98cx9Cdm5Dc8XFDbZUV3IY0ZNbizVT4x3HYWq5/CRb3knt3faXF+s0Q01rW7E1kGHqudQryj2OhEQnlxniuy71CaGktxXaBKplWztS9VFtjs77Pr7XK+vpXkQkzhGAlZqS9iuT/ipz2D3Drj1f/77Ph2nspyBQJygiRyVVLoNdiJfdPIYHlFjkG0EVxkZ5Jwh6QPnuKjZOeLDQ+Ljoz5jkHuHnkqMwUDOTLourpVEunz4+CtHt/oqI+607vG6a0+ear2dqMNRcMyMW+cH3vndbHa22ZhZLzUqUshLafUvYmS+IINUxLHBEZOXFLejxEudcWu5gStGBlYnnLqUyUM8kiY6ZWRgrU0owtTLFE5CFY2LDM5L6rjXYzBoDAZ6DDi52RUxrpTTcRTPvvsZ2n7MM0+Wz4MYRNVzcqnwmRrM1z32WwGHrYCP/8vfZ+fQZ31V8a1//ql+OmtgTWWNZ5nUSt3tZX9qTpUZd4Z21KOL9vwDtNEsVObxlEf75T/A7h0AJaqiA30Go6TrK56i7Ud94ojjZmyfBx5JmkikLe9XGhmYQmRAwv0Lx0HW69gwSgSuUmT6/MoRSde/7r+JhOMkuQKt85nEGYw1eMrtq4wo3uSTINQRu/4+QghWasvU3RpPLzwxNLqQQmKtudSqF91qEdy+NbJSR5Ns5K6cbF3WWjpxFyEkNadWGOvZO4bVcZ6cVkoQm+HnfVrl0jzayYyBEAjHzSmDYSiTOj4Let7oQMNZGf2SbmylNNGY8lKtk8Hwr9uYP7OsvOcq1hfrBJHJKafNgzbbB9283LmIUc1ww6RWFqsJXbTT2ePz27/Hvn+ApzzmvcRxc5eXEUvJc+a8PeWQAAAgAElEQVRe75cmEVL2SXZobYc2m1ZKqKLLMAaPZGQASXQQDqnnvQzk8rXpxpKF4s7cPGG7Q3x8jFetYeM40eevVjHEeI5LONBsIxwHT7p00rxBzelt9nv+PkpIvuPtz+LOWo4OfEId0grbzHrjh/sYa9jp7mKtZaW2hDdBglrSk6QoC9HPG8b3uf0TP1Yqs1yETjOw7oS9Zr5OhAFnvZnEgci6q9NKKWtMUvaZfXeptkysLa5TcpBTKpdmuaJiAle4LjaK0oik/Nr2SR2vrp1Zyygrmx2MtspoojwyKKEHx2kBZZHWqCFPk+LJ9dmcclpfqrJ6rVYaGTgjopUsL5ANxMkghWTGqfNPPvfz7AcHLFau8f3v/K5elCkEC+/9S7S1z8YbTkqTZAOWsnzhWGMQ6rz5zMZxuczKOeKRNQZKirTxzIwVxroI5DSRzR645KuQ1SrC8zCdDjaO89JCHAdjQ6quh7GWWJs8CSocN4kM4qgvidwK23SiLhXlsVZfYW1lnjt6n832FnvBPo5UVJ3h9IG1lp3uHrGJma/MUXfrE51bLkmBvZTC3WEyy4OITfLwKSaLDNpRoicz4yZGUxSMHBQaslLPuViYUFatJAaSiOOQ900UOqqLSeRhxkBUKlx/9oNUOofEa4+dPWcwlCYa6DGAvJqoXMZ6XGQwmXrvJKhX3WSCnaOo1bsYEZUnkEc0ngU6BEGp47PZ3mM/SKig/eCAO8fbNJaTxjIbhsj6LGplHVspK2+WoHs9BMOMn+dKwkjz4t4BM7UVKq7CRjGyerEKA48kTQTFB/dqqKLcGJh+YwDgzM2Bhfj4OE8W6nTDqaebQVgIIYWjkEgcKwjT2ulQR+wHB0ghWa4t5d6LKx1WassAbHf3iEZoGm11dnjp4EsIIVnw5ic+N1lCp1wkKjdulsosDyKLDJwJaCJjDd24m6jDpnSBGhThyxOsmTHIGu6GfL68/8hATlBRZKMI4bjMPPnEfVWfWB0npbqDPQZZWeRpEsgjRk2WSTOcFUomU8Oe3FjAcRJqbZiAoxLqxJqMNYQmxJNe6d+Z7iymO5P+PIPppoYgjeCdtJy0rIBCSInVZqwmWRBpfvbf/D7/9Fd+j+d+7rfY2j4iiGKMSgbgvHTncGyz3Vnw6EYGxbkGY5QPLwLZDSGMPvHAyZkZxME+pnWMqKSDMJSAGKquRzdKxKzqqcOXhfGelXStJdABe/4B1lqWa0t9TWqQjCxcqi6y193nVusuxhpuzm7gKRc/DujGPkfhET/3u/8je/7+qSuQZE4LXI4xkNUqGx/8ENHONrNv/+qhnnDGrpUxOIPoRF2stcx4vWhoUJE1o1FQJyODMgghEEpOHBnYKEyogUIEkEUGZf0oGUzQkzSxJXpBk8LGcWnPRh4ZlJaWlhvCUR2/kwo2ToJk80/mHegxNKUjFIHpbzyLTFJOW9ZdD/D02iLzt/4kO+EOK5VVnv66JEeQRfBOtQrE5R34We4kyq5f+fkW+yi2D3xefHWHDeETxx6f/p9+i53DZIb7sGa7s+LRNQYy60K+oshAJ9rtaH3igRNSImfn0IeH2E4HpEA7iTGoVTy6HZ237wPJZiTAtZIusOvvo41mzpsdmiyedWdohx0++blPs+fvs1xd4r3PvCcPjbc6O3k/QabN8vTCExOd22VHBpBskuNGQkY2WZucILHdjjOK6KQx0DlNVB4ZjKxSk2qiyCBTYJW1Ad55ksjA75UYn6anoe8zMu18dXKLMFaf9LhHRAYwuuP3PI1B9jlaG7TVVOTwvhMlFej+3FbZKNciqp7Dd/z5r+aVzWPecGMh34zzXqBKFUyrND8i0vMzmfrokPO9uTLDxnKdu7sdri/VeNP6DPZY80rQS47f2+tye6edV1SdBx5ZY5CH9FdIE0nB0AfOmUuMgQkD4sMDooUKCKg6HkoGfcnvpMrEwUlzBjutPW7Mrpd2SxbRibv5hr/r73EQHvHGa09Tdaqs1lZYr6+x2dka2k8wDCfolAtGlshlBOdsrSW2IvHex8kpm5ggDqg4lX7pj4GGusE6fDUB9SiUxETRWMXcMooIEkdBKJVX+pTBBH4iIeE4MKT3ZBzyfEEJzVTmcfckuocYgxEdv7ow/vE8IKUgijU2FXUchtwAtI5ga4fqY48T2vJKoiIcJXlsdRZZaFzMIwOvCn6rvM+mIJYIw3MkVc/hw9/8Dm7vtLm5MoM6PkBrj7c+uc7G8/e4u9uZqB/jtLgUY9BoNCTwU8DbgQB4ttlsvlh4/c8Az6X//E/AtzebzQvdpbMv4iqG3JhsyhFZWWmJfILjIJTi3s/+TDJFa30N93v+Cs6cwnMl3SDuS34Lx8H4HX7x9/5n9oLJqJ2NmXXWaqtsdbdZq63y1uWv6L1fwfe94zu5294c2k8wDOKyB9xkG9AIYxBri5USpcRYmmave8Dt1j3etHgyCd3XUDcQGcgCRTEUxcazEbMJ8kbDko5q4brJ1CxjTvD5No6TiKJeRzjOmVRSoZAcH3BUrLWl404h/d6HfOfFjt/Bu11rc25RASRGWdskUTuSJpIONgi4++M/gd7ZxV1bx/3r34b0vNLmuHy92fjTwvdswwChFMr1wC+vnMq+qziOATXynIt9FGEaBVbr1T4jcZ4UEVxeAvkbgWqz2fxa4AeAH89eaDQac8A/AN7dbDbfBXwJWCn7kPNET6zu8iODvJqg0GNQhrjdymffms0t2NxBComXvr8vOnAcdrp7HLb3gMlkd6tOhe9/53fxN/7Qd5QajqpTGdlPMAyXPe0s89RHld1FcbJxOmo0TePHAZ/83Kf5Zy/8Ep/8nU+fkO+QQualkDkFU9jUXWd041kuSTFmk+41GpYbA+h570WYIFmvrFQSI2XPRhX1ykr7N5zsOy31uIcMuIGBjt/icVLHSJ1SRXYUVNodbAylPQa990nsvS30zi6QqAZHL3/pxPS+QWTfbxYBWq0TQT/PS1Vah3Tgp+eYzX2YtJQ2EahzEELkRuK8DQFcnjH4o8CvATSbzd8E3lF47Y8Anwd+vNFo/Dqw2Ww2ty96QZkXdxWRQXYzSVPufWWoPfU07vr15D1rq3g3bgC90rM/uHWQVxUIx2GltsRGNbGjk1I7Z93wR+HSR19mBn3E2M/MW3c9Z2TT1xf2X2LXH25Qiw11VscJHVPUyk9nZQyNDopDTkbARkl5Y+nUthF5gyx5LCsVpNOb+3xa9BrOJpCiyNY1iiYaogU0TL3zfqBUIpltrC3tMcjfJx1YW0WmjWJqeQkcB6cznFrLegSStSf3QUYRZYZbCVl674tBmmiC6ilrDFabC5WhyHBZOYN54LDwb91oNJxmsxmTRAF/EvgqoAX8eqPR+H+bzeYfjPrAxcU6zhCPehKsrs7hm6REc3V1bvwfnCNa3QjfwLyGegy1jUVUaeJzjpWf/DGOv/QldhYU8/NLrM7OUWkH/PAvfJat/S6Prc3y8e/5E7g1gU/IR9/wndwTHR6f36DqnvzMyzhXbTS+e0Tdq7M6e/HHizsK36/jLc/jLZYfb26hhlWK5ZkIF8NsyXU4Clps2CXW6stsdXa5OXedr3zy9X3XUbd8OqFi+doM3VYF6XrUC58lXIeD44DFxRmqlZOPV+hqQhlRXazjzA7nfFvHO8iFKvW1kyW98YzCtz7efAVvqf88Ov4hxplh5rEVov0DFhfrVBdrOPXJekQydOM2WmlmNhb7qpk6YZfAq7NUm+darf/Y3WgO3ekyszxzIkrzYw995LNQrbJc7/2dH8a0I8vCbIXVxdN1xg+DV/P44maXufka6ysL1L3yz42NJpCHqG//VuYiSfzUBgdbd1gWhlkRUllZPvE3Uaw5Dnob/eJSktwNwzrV60s4s7NElTZ+HLA68N3EMwo/bqO1h56ZYb3kux2E9n26i3XchQUqEz67Z33GL8sYHAHFFcrUEADsAs83m817AI1G4/8hMQwjjcH+fufMi1ldnWN7+5jDww7dIGbWlRAG+Le+TPWxx+974LgfxiN5vaNOyP6Rj41aBDqkM9NFOMMTgv61FQ47O1jjI7rHvHTnkK39RK7i1laLz71wj6eXq4T7HZRWXFta4fgg4pj+z8zO+6JhrWX/uENHxaju8Gvpx8GZchKD0O020X4HR1Zx4pPXe3V1js2tY/wwpkIIfkBn5rBvw+rGPtvdHSSS7/2ab2enu8fGzPqJ63jQ7dKOOlT8fcxuG1kztKu9a3rUDtk/9nEwzFRPenO61SXa7+DKQ1R3+KzbYLeFmpmhXfJ92Tgm2O+gQoGrCzLHxhDc20dWK3R3WlyrKPb3O7jqEDV7uugg2DrExhHdvf7nrBW22fc7CL9C1Orf8MODLqbdobN5eDKiMJr9VofAtZha77VuELN/0IE4Tv47B7T9CG01x/tt9mWHtir/XGst+3st3G6Et/oke0GMX52l1rF0Xr6DeHUTHQZUb/Ya9/wwXW8KT1jU0R6m3cGrh8juMQcdn27c5V500EenmSAg3O+wGwXI2GG7Mt6Z1a1W795m/LM7yTM+zFhcljH4D8DXA7/UaDTeRUILZfiPwFsbjcYKcAC8C/iZy1iUk24GYbvD3R/5KNH21n0Je0Fys3z0M8+zuddlY7leqs3eo4l0QgWMmVyUiWllVRg3V2ZYvVZl+yCpN765MoNIQ877qSs/LyRVNzJX2SyDHwf86POfyJPXZ1VShR7/LkbRRLHBkRIlHDRBwm1n378O2ekmvPFKbZmqU2HOmy39nLxsdqD7OENeXjpsPq8cnzPo0Q7l1IBwHJDihEZRli/IelMyj94OKhtOAh2X0pejaaL03KxhkADJy3IHzvtCaCKZ5Az0mASyEAJlBbE1IAWhifAqNarXVgm+/GVuf/IniXd3+vaEbL2uo4hinVRChVGuLJscv0eJqWI3iOzlDNwJG+wuQ600w2UZg18Gvq7RaPwGiVzT+xqNxvcCLzabzV9pNBp/E/i36Xt/qdls/ufLWFT24HZv3ybKRk+OkDOYBLd32mzuJV57ps0+WAucJZCV1RN1iMZpbiET/Kp6Dt/7F9/OF24f8uYnl3rGRoqRJYeXiWG8aYa77U22uklq6LR9DCcwpprIGEtsTHqdCtPGHIfYxGwXtJfGGaQsIanjEAUnJCHGdbb3Nujh12ZYWWnf5zjuie/aFpLHyXucsccqPX7KU5dVMo0yBr0BNyfPPRGHVCdUQs9TiiKDkiKvJhrWfZy/1wpiq4lI+P+K8hBSYuIoL94o7gmZMaik4ymjKMaJoj7nsZcz60mdQ/LdG2uxxkxs/EaNcj1vXIoxaDabBvjQwK9fKLz+L4B/cRlrKSKrYBDLyzjLK4kXsLZ+ZmEvgLVrtVwoK/PaB5ElnoQ1Q5PHRWT6KcWa9/mZCo+t9o/hE45TWmFyFZBCEI3wfjdm1lmpLrPj77JSXT5VH8Mgsq7XYdVE2eB0V0mE7SmHdqIuv7v7AtcqC1yfWZtIeymPDOI48fmGGYNhSeoJJClGlZXmH+O66DDs6xIuJo+hcD1OmUAepkkERSmKMu2l4fpEyd+oE6q6591wlnyWRBuNYHzvggKw4JsQVK+/oHrzMdy1daKtTdzV1XxPyKJ6z1XQjYi7yTUvVn2pIcN8hJSJI2gMasKeChvFFzr3uIhHtukMejegjgzX3/8Bou1tam98033lDJQUPPvuZ9g66NJ4/FppzkAbi9A6KUObIAkemxhEvzdWJnMrHBcbjla0HMS4/MZZkVTd2KHNVVWnwrNv+8vcOr7D43M376+aKdt8hpQnRuk1ch0JJnlPN+jw93/7Z9j191ipLvM3//D3THSovComjnA5GRlImfUa3E9kMH7weZ8sheMkVS1BgHDd/Bi9yOAcjYFNqM2hpaUworxUEWr6Zm6cpy5RbxkiUZa146MNlb6na0LAyTuWZbXKEx/+IVqf+228lTVEpjmUnlv2/EXBScM9qunSiKTiatJSWhtHl2II4BEWqoMCv9vpIL0KlZuP3bdeeBQbPFfx2Oosw1QPtLaorDZ+gi86NjGOcPo2VSkFrqMIQp3r52eGZdLowA9jPvaZ5/k7v/gf+dhnnj9X8atJykuVkNycvZ7nbs6MrF9jCCWQSX47SublfV8+/HJeQrrj747tyciQn1fG5ZZEdkrJoTmDnq59+QY9yfhOOFleasMQjO1TtuxpIZ3SGAxpOIPEGAzj4UcNuIHyITcXERkYaxDCYicwBtk7YjRCyL4Z4qpWo/6mRtrQmUQAGcXrKpkY/fT3olIQExwhj20RYCejiWwcJwoFlzTv+pE2BkpJrDHoTjdvBjoxRuyUyDYeKQR+YaMuQhuLyqSrx9BExhqMNXm+oIiKm9S0R3FmWIY3I5Xh9k6be2l+I9M6OS8Myj2XIbbJOkfRSZPAjskZZNfHdWT+PS958/nAn9PIbfSMQbZhloxUVD159DJkuval5xKG6fjO0xmDXrPZQFSr1KkTyMMazmC0MRg14AZ60URRNvq8pSiSNaaetxn/mSqbJy4llRLJalVPFUrbrXy92bhKR0m0H6RRXMGI5Mny8sgAM1nH9WUmj+ERp4mkEMgoJDYGOTODPjo+s7BXhjA2CAQzVZfjbkgQ6T76xRibDrXPJDTHVBKV5AsyVFxFqxsRRBrPVT1aYMIkcrEqaWWheq5aJ8WKirJbOU7VISGpPikb1zkxsqqsIcYgjHQ+99ia5Bgukvc+8x60NTw1//gpFFmLkYEqlZRwVSIYGGtbzlwpOdRg5xOthlQSZci/6ywyyCuJ+s9DKJVQhyXSFcMwtOHMaLBDkscUrv9QSQpFoENePnyV1197iqpTOXcpimydSgiESJrE5AhDI/uMQckI12oV4Sh0p4Njbd+EMiWTa2XUTH/joRweGWgEWIucYKbGZSaP4RE3BgAyChJPvT6DbrVOXXlRhLWWOJ1bWqsojrvQDfqNQeYt9MpKR2+AvUqicmMASd5gjsIGMWFkUPUcPvQNb+H2Tpu1a7VzrejIIgNL+fUcHCqire4vwzsFrLFjpSgclXqfWXmfjqmoKtdn1kaKkg1CFnIGojJT6tGOk0dPIoNysbqsrFSOiwxkkm/qRQaJON3gxiGKWkiTfr9xkqMaNHT57ONhnzNmrGdsYn7x9/8le/4+6/U1vu8PfUei0TVhfmtSGKuRKlFVNcYiR+QjpLWEJmK3s8VC7Vr5e+oz6KMjTLeDNhbPTc7f0TFYi1UnJ6IhyqNimz4XkxgDG2VigVOa6FKgQj9J6rheEvLfR2QQa4PF4jmSqucgECd4+DjvMegfdzn0M1MqxSnxxlxHIhAEYS+sN2FA9+Uv5hznOEiRKDB6rqLjTxZRGN+n+8WXRh5jmPxAhvy8UiMXm/ug50ZsdNoYjLG9yWPpxqNT6mRc6eEgsge9OPt4ED0p6yEPfD7+smSziPqlDUZBuC5Wa0wYJto4gxQR5Gs8TcRr46Ts9oTU9KiyUsbnDLY6u7lK7mZni1utZE7zefYYJOtMqnWUGK0TBRBHEb/6pX/HP2v+K37ytz91QosKQM0kEXPcamPpDbJX6T2rSxy6ssE5kNJETGoMyiO0i8IjbQxMGCKNRlRqGGuTkFqX8/yTIOemXYWUAs9NZuKaQt11cdylUHJs6K5H0ERCCCqeItLJhmfDkHs/+zPc++mf4tW//dGxBiEzXpnh6gTjN2Tj+7zy0Q/z5R/54ZHHyELzYdcyO6+MnhmsPz8NrDVDdYmiQvIYelLLuab8KY0BgDDJ+odVbGUJ8aFDbnIPuoRGaLUI7t3Jew1GriP1GHUr6TiVlZM0x2kbz5IeA33qhrNkAaMH3Nycvd6Xp1mrrQHgnLsx0GlVlxo+dS7FTmeHgyi5fsPEHWWlgnAdolYrqQRK1yvTKYGmLNcwpM9G22z06ngGIpl7LCeuDLxfPNI0kel2kpC+Uk34XVUIqc/wBWTJYzfdeGoVhyDS+GFMPZUm0IWGM8aoI0I6eYlyYwAJVeSHcVJieud23igT3rs7tnku2ygrrkIA3TDum61cBv/Wl4m2t8ceozcIpnyTzyKBqqrQon3myMBam86EKF9zqxtxZ7/LjYLujVAOxk+okLMYA2ks2tqhFJ8aM+SmV6xgwE2VO9ttop1t7n7qp4l3d9i/vsETP/jcyDLnvLy0nST+y94rThEZ+HHAnYNbrGhNzSnvj4ERNFEWSQyJDOpujW9+83/LgX/IW1eewWoFxOcfGRiNVBJJT2F2GFYqiyxWF9nleGQhgazPoDs+BD5qLrmXpI5BCHTJsymFwtoIY03fPWZEUoU0tNQwxaRVZeeJR9wYdJPmj0rSZu7I3oNzFmucGYOMU6x5DgcEdAOdGwNjLFZrpCgfHDKI2MRIIYduWsW8wfyNm7ira4msxgTNc7mSpyNxlKAbxrT9mIWZ4Tegt36916C3fn3oMbL1DosMskggS9qdmSYaUUnkhzE/9s9/m60Dn/WlGs+lYwKFkhg9oipmDKSxRJjhkYFK6LuhNJFUmDCg8+IX8NbWsWGAjTXB7dMZ83wesk7kFErlrjODNcQYWGuJTMRhcMw/+p1Pc3y8zeuiBd73rg+eSPybcTTRmAE3ADWnSm22StWp0EppkHNPIFuNkilVM6qfw1o84fDs27+ZnVlGamSpmRnM9i50Oyi5hLUWGSezpstk8Is0afHZ1Talxcap1sZxWlV2OfkCeISNgTUGEwQ4tSpCKWJtqJ6SXx0UWoviZJRl5ll7buIFdAv0i9YGdLLBT9R9bGM8OfyGqHjJsYJII2frPPbXv49O8wXqb2qMbZ7LNitHJT0Le0eCjh+NNAbSdfMGvZm3vnXoMcb1GcQmRkmFkgop5ImE8qTINp4yuu32TputdJbsZnFMoFSJx3bGYgFhSOYEjNjEHDV8yI2NonxokbO8wsazH8RZXmZ2+e3sX98gvHcX7/rGWGNeLDmUnldenllyTx+HLV45usW1ygIWi7WG26177Pq7VDXs+XtshfvM0u8lj6WJSL+HEd+lEjKPdi9CigKSDbiikpzHSJooayDzqjy9sDbyM6XnYaSD9dtIYbFRlJTEupVSo99rqtN9g3KMELhCjJ9nkeULXuvGoNFofAXwNPDbmdrogwbT7YIFZ7YOcdIIlnt6A8bAjwPutO6xWl9GCUVkYtpRh5/+/36eXX8vr4yIY5NHBUA6jELRCWKitMpIGws6qXYYlxjSRhPEIbvRPtcq10q9FiUljpJ5ElnNzVG5+Vhe8z0K2RxlR0mUlFS8hHIaRRVZrfMGPU7IkfVQnBfshzG3tls8tjpL1XPyaVlebOm89CJqsULknrGKK/NCSyKnjaV6Lg3SNyZQJqMr1RnnGsl0gzEjNjFHSSIdl5Y2hjvbeQQQ7+5ghcBdSuSSn/jB5wju3KZy4+ZYY57Ij0SEm5vUXl8eQWQOR1Yldxy2+Puf/Ufs+fssVRf51rd8E/PeHG9afD3L1SX8zjaLlUWuz2+c+CxtRnQfZ5DDy2ahnz65iIazbJ2eU01/Hv4l5wKHk5bcVmtw2EIEXaxJrqtT9UqjjzJnSJsktyWlGJpXyd/bahHcvoWavzx5/bNGBn8f+F+BP9doNG40m81vOMc1XQpMN5Gh9WZm4DDpNcjKAAe9qH/w2U+y6++xVF3kvc+8h4ryUk8q6WDd7Gzx5aO7uCz3qlZSVCsOnSCmG8a4jkdsLNJkxmA0TdGK2v2leO/4zlKDUHEVbT9KSig9L6l2mSABGWmb1t8na65XnURffgRVVPRoRh0jq7rxw4iP/w/Ps7Xf5fpSjY98yztRTlIX3/r4P+FoewexvIT7be8jrq3jnLLBZlRkAPDsu5/Bq3pcX6j0hpdnFR32bJtQZgxGRQYqn7Ft8iEzGWpPPoW7fp1o8x7e9Q2qjz3e++xqdWKRROP73Pv0p4h2tnHX1nnyIx89YUDyjuc0gfzl4zt5RU/2/+VaktT9rq/+IC998Xd4Qi1RrZzUaSqbfTwIIeXIAowifXIRUhTJ5DSDqxygv3jjBLJNfML+FltNcgWi28XY5Plw6lV8a5MS1sL9UNZtbdI53UqI0dpUvs/tn/ixc1FRPg3Oagx+tdlsXorM9EXBdLsIpRKa6DAi1rbgRfW+qC8evpJv+nv+PoEOuDm7wWL1GsvVpTwyWK6uchQZ3MEHP92A/CBmvp54EdIYUOPLSm+17vaV4g1T9syMQRBpXMdNZuROMHQ964nIMFN12DtiNFVU8IJMOHrYukRye7+dz17IupxvrlUwd+5hthPv2O7uYV58mY6tUZtfRM3OgrWTecgjcgbdIGnGe+vrV2gddfPf23TzEWcMRkR6TDsi0V5ULx1MDclqlSc//EMTRwDDENy5TbSTJPOjrc2hOYasSg5gubrIUnUxdzCKCdPFygLrlUVsbEuj1nGUZXIwmVBoQ5rcsqjioiKDzBN3lUIKMyYyyByJCRVElZPQNoGfaB8BjleBIImmvYJRKYsM4iRhMHIiHKTf6zmpKJ8GZzUG395oNJ4G/g/gs81m8+Ac13Th0L6P1QY1l2jWOyoZfzlIE1lrmXNn+h6eN1x7Xe6df+grv4VXjm7x1uWvIA5dIMAbiAyS5KzED5MxfMZa3EyKYgxNNOrBLSJPIoea2ZqL9Dx0GCUiV0Oal7KyUqewXiWT/ohRVFEeWiuJjeKRna1SSFavVXKqZn0xUXGNTYCYqaOWl9C7e6i1NeTTT6CFQR8fE+3usPlzP0O0s4M3rqpmRGTghzEypepaxT/JI4OzWYOcJhqxh2TXLtKGsjlbp4kAhqFy4ybeBDkGoVTezKZk0nktEDw2d6Mv0lRS4VhBJHTSJV+gAY01YHu6O8PQ12tQ8p0U5xpcjBSFJtAhrx7ewdhrCDOiGie/dyaLDLS2iNosUkTYMEJ4Lq6rUmNgKTaNl0YGNo0MxiSQKzdu5kUak+SOzgsTG4NGo/FVzaCXFeAAACAASURBVGbzd9J/vgv4apJZxt8EvO8C1nZhiNsJRSRryWOa87tZnXRqDHwd4EiHv/qV34qvgxPVBnPeLDdnryOEyPn3QZoIkujguBvmiWRpDUg1tmJJiuTBlUJyc3ZjaKWD56bNZ6k6Z2IA2on65RBjEA2UwWbIqKKOHzNfFh2kN7Gs1dCtNiYIULXysYJSSBxH8IGvfzOb+x3eeDMZ5L3fPoQwYuX9z+IqD7u+wq5pIbw5XOPS/r3fJdqZrKpmmC5RrE2yEVdONk9l+mViAu2aUuik9HgU6+vkNNEZExMTQFark+UYlAM2xGpNZGKqToXH505uMNZaPKvoKEugQ2pOYdynGZ88ThbVk7Euu7rZ3xtrLkSKoh11c2p1ubLCX376/UD5oKL83plQQVQbi5qtY463iLa3qT71VN5tPihZXqZcqk0SqUtHjowMRKXC9Wc/SLy/z+xXvv1SKCI4XdPZv2w0Gl8L0Gw2u81m8zeAzzWbzQfKEADoTiepMU85wOyGNIa0NC658TtRQi0sVq+VDo3PyiIDHZyoJCqilo63a3XTUjoz6RyDmJpTzXVchkGIpMEtik2SsEwVFM0ITj8qlJUWUU/n9raHdCNnhlLWEk7ZjqCKpBAYa3GU4LHV2fzBCff2wFqqGzeov/4NePXkYdVWo+p1Zp55M87yCsB4z8iWRwZ+mlCvlUmIp/uPOmNzoTQWlBzaXQ1Fmujs8iYTrSWNMEb2I2QVRUYTm7ivuqUPWlNVHiiFH/c3E+aVROOSrWO6kLPIIDZpcv2cjcGd1r2cWt0Ndtj2t4bnDU6ZQDYmURve/LmfYfPnP82dT34CGSX3/6DRL5vslk84lGpkzgCtka5H7enXXZohgNPRRO8G/pdGo/HdwC2SJPIbgDdfxMIuCjaOMUGArFTzm0AVHlypHEi7kDtxFyXV0I3YlQ5CSHwdEGu3r5KoiFyaItDJlCPM2OSxtZbYxFQm1M2puIog0oSRppJGA6MSvHHemdv/MDpqNFVkjQYp8m5XE4xKIiuMtliS8X+xthjfJ24fQ8XDm00mwGVSG1mvgazXuf7+DxAfHjD7ttGeUa4lNfBAZ1FYrWzObPpecQZjkHi8AqQaqrsEiYOR9BpcrDGYBFmTWxyFWGuHNjDaOMJVHlJpurHPYuG1XJdoLE00RrlUZPSZBpyJdf0nxXKtR62uVFdYqa6ijUk24AH0osoJZhGbhFZl+14etUbbW5ituzC7njtXGYRItJGKDkM+4dAZrloLBaHACfqQzhMTH63ZbH6h0Wh8E/DrQAt4DvjZi1rYRSE+OKB951W43kvE5pUfJulCNlFEJ+piraHuloeYkMpBKJdjv4uwGm9IJUxRmgKtkVKOzRf0Oo8nq66peAo6EESGquclImajjMGQyADGUEVpbkU4TqqIOToy0MZCWoUSa0O0d5AomS6u5fTN4EhEIQSqVkPNzI73jIbkDLpBjJLyREIfQIt0/sOY8r4yWB0jSeYEDJOohuycxFCaaLBH5UKRRgZRFIAY3s1u40Td1avMEJo4maORvneSHgNgbGSQ/X0iW+6cuxSFIxXvfeY9LC3OEB3U8P3kuS59ivToSrS+t2YTzjb68zS1m48hDuOh5aV6sLQUUK6CQA8t8MgF6i5JujrDaXIGHyEZXfmPgT8LbDebzaufvn4KGN/n1o/9aFKKVyjZyrRktDY5f9gJkxb/caMQPeUR6TbChLjO8Pdm0hRJw9kEAnUm8Q7cCegkODn5TLgeptsd2k2d0VplYX+94rBHQhUNGgNrNNJJfie89BiF0YtFSJH0VWSiXPFxCy26mKpHZSDP4EiHIA56D4hSE6mvluUMwihJ1s9Whmx6AhACcRaWSOukb0CNjgwgcTKC6ORD3418fvSzn2C7uzOyZPi8IIrGwAN3iIORXe9apU5IgB8HzKY0W54zGONFi7zzfAxNlNGN52wMYhNTcTy+YvUNvNTexff9oRVFeZn0JMYg8+prtRN5GnXcGtp4Fsdx/v33SmlTZSKtSyXs81kZE0xBPE+cJkZ7EnhHs9n8AeBPAX+r0Wh8y4Ws6oLQV4qXlmxBv8qkUAqDoRu0cKQzlqapqAqxNoQmLPWyM9Q8hzDS3Nk8RBszcWQwlN8dQNY4FqZc+bi8Qazt0MYyR0kqruK4E/IHtw5y5VVrkoqSLKzOqaIhx0iMQTKcR1iLOdonsgaxMI8j+s8rp4qy6EAqMHa8aGBJzqCbXoPqEGOQVXXIMyR3bZxMxEKpkTkDSDzBW9utPFeU4aXDL7HdTaiGrGT4IpE5HnGqiDo0Mkh7EarVJBruFvIGPZro/nIGQgiEkClNdP4NZ7HR+b2VGZqh5aXGjJyDUUSxJ2IwT+M4Mp9rXkQxWZ4cLq2eynI4w+6f+DUeGTSbzfcXft5qNBp/iqTx7DOT/H2j0ZDATwFvBwLg2Waz+WLh9U8A/wVwnP7qG5rN5uGk65sEw0rxejRRQoGEcYiNHeqz5VUyfZ+pPGJtMCYamjOA5Ib49K/+Pv7uHk/OGL7t/TcYFXOcliaCZPJZJ615FsW8wYAXnpWVjjJejhJ8+ld/P+/e/fA3vwMvo1cyBVAvO0YA9ZNnI1MJYWkNlaBNR2ui2hzC4cTktqKUtSudXoXHEO8pgzXmhEhdZryqXrlnZawGJXsDhk4Bq9NB644z/GFO1/DJf/15tvaTktrn3pfoIhlrqDvViUqGzwt5ZBAHgDPUwcjoCc+t4EQOvg4KXm3y2iRNZzBcuTT5DEmkfRTnK0WRTQX0UhXRXmHIsMjATF5Wmn5GGa2V/S7pKSk2nvXEGhUqpaFlL0eRChWeWFcclc6TuGicOUPRbDYPGo3Gnz7Fn3wjUG02m1/baDTeBfw4UOxc/hrgv2o2mztnXdM4ZKV49c4+nfpibtmV7AmLCddJPCJdoz6C9sk/U0gwCm2jkROV7ux22Dn0WbCancOQOwcBb5gfno+ITXJDlM0xGIaKm0hfBJGm5g1PIg/KOpdh9yhg5zDxDO/udri90+bppZTKSD3NcUlkSUITqU4Lbt+CmUWiWh3onPBOeyMR+8dJDitRzKH769mttfiBxlVy6PkZm+Y9rDjVBDAoVFM5zsjI4PZOm639VBdpv6eL1IraOP8/e28abdt6l3X+5jvbtdbuz25Od5vkkixuCEQgcYCF1sAxKEsLxFJEVAwCQSKg9F1JyA3DDsEmkBEVCGIkKhlqBpoIVg20UEDKqNEEcrMuN6S593S7b1Yzm7epD7NZczVzNfvsvc85Ofv5cu/Zq5nvms37759HOLzx2T/FcXzC51z57POvGeRpUJkUXFDjoLod4nt38a5eTYnk4g6RilNFsoxwbepMwJTIAHJjoPExZxoZDKsC5t9d2d6r9czTx0Xxd9wgXakBpexg9bWQdTYZbfCEVTKYFdxVWdr1LOcvZsF9meVWq9Wb/q4CXwL8cva53ySdUQCKqOFVwE81m81fbzab33A/65oEEQQsNl89Upi07TSnpy2IdIRj2YWHMQnaGCxj4ziCRFeLw9xYb3DtSh3baNZXAm5sLU383kRLXOHOdUN4rk2cKF546ZDYZLz9yRhjMKF4nOOJjQbry+k5ynl9hrlc0kJydRFZWKlGrPPT7+T4PT+H/Jc/T9RLazHDHmYe2qtymojppIHDWgZRkg5M1SpSROkxsq4xmLhpjT1elkqxHXeivvON9QZX19KILJcU1UZzHJ1gWYKak6qsnbshIKeksJBJXOlcqF6PO//w73PvXT/Np//q2/Czck2oUoOWMoFO3zinCdxAavi1SeVfz5KKQpk8esmMQR7xV6QajRqNKiu/O5+vGRcZ2OPTUeXIoNAxKRmDseJGWqfruiBBmzIu8ohLQDnto5rNptNqtSTQAH4S+DuADfyHZrP5X1ut1oervmx1tY5zHwWWjY1BAqjjWPHJ20dc3wxYWgxYXV0Zec84hLFks71CbLdZXPFYCqo/8/bv/lJ+979/lGvrC6zdXKt8n9SKE7tGw6uzsTA7UVWnl/C2n0t5gG5uLvDXv/pVuFrSuNIobsCNjUWswx5G2FzbXKjMq28A3/O1r2f/uMfrn71KzXdIjo+Jkjr+5jJuRqAVqjVku0N9JRiRXIylzyc+vI91kNJ5sLeDd7TH4s0nubayOpAqkrpOctih4flsLCySeJrIivFXa7iL48+BMYbOUQ27VqOWXau9ox6r2uLqeoOFWn895WvZcQ7BLLGqfWprdewxojBV6EbHaA/ERoNIRqyvLlQa7J/4nj/Ih1rbLC/4bGwsEuouy07ASm2ZMAkJZTzx82eB/Hcftet0j45Z21hhozF6Po9+69MD9NmrcQ+90cBzbK4sNjixa9TcGhsV1yKHUYpOp47d6F+TYVidhKMkZMkO2NpcOrMi8lFokH6dzaxleWtziXZsCHx75Fk2StE5qmM3GpXrLCPBwg0lV7dG19sIE7SwWV4OWFvqO5mN2MG0I1brdQJRp5MYlhd8Vl1NqHt4q3W8lcFjqyiid1LHXV7Cn2Fd4zDLvjUOcxmDZrP5Z4DPAf4a8FWtVuvdc3z8GCivUmSGAKALvL3VanWz4/x70tpCpTE4OOjOs/QBbGwssrNzUvw7jCV/7Wf/CzuHIZsbCd/whiUCL2EnOJnwLSnavYTOiSRxIm5Z+0QTygzGGJZci14oB44/jFCGHHS7KN9G9KavIcfHbx8VPEAvb7f52KcPuVm36Pj7CN8vfve9gy69SLLgje8myhH1YhY8m/ZxjzYgj46QB11ct4udBQOynSAPurSdvUIeMEciJcfGZWVlBevwEDa22PPrqMMei2r0+h2cdOmIBNELUN0eyUEXhyOcCsE2oxTRQRcRgeel5+nOXoc40Sx6gl47/WD5ehtj2Dtp43ZirJMu5vbuXMM90e4xaMOJZ9NNetSTo4ke8/XVgJ3DHp98SdGzDjBAPVnmKIroJl1qyWFlQfd+Uf7dR4cdjo+62AchdEfvqcSuD1AghPU1uicnHMgOpuNy0O0Su+CE0+/H8KCL6Ck8Z3wa9DDqcnDYRTs+e3tnN1R1EB5xEnfx4pCFqw12d9scHXVpCwt/yN7oJCE+6GInFm1n+m/a3u2glGYvGNeZpzg47JCEMSrqZwciFXPQ6SI7gsBSHBx20zknRxMfdHHMEU4y+Pypbie7730cZn/2cwzvbVXvGYd5Wkv/JnAT+ELgR4Gvbzabr2u1Wt8941f8OvAVwHuzmsFHSq+9GvjnzWbzC0hTV18C/ONZ13a/uLXbYecwBDQ77Q4n7QbOZHrzAnGicISDcBxiNYUpVKlUsGJKu2i/k2i+boIb6w02V4OiaHnt6gocH6V1g5L3Kye0lZbh2BZx0g9l8wGvcqtquaNo2BhIpREygT/5Vdy8ssWuv8aJPqgsQjqWU+R9+9KQE4ZzhojGtDbESUojXuVt5qkdoVShKTCV/6h8TKWwHBeLPt2ATbUxqGUDh3udY4KGZslfTDmASjWS8zIGZeSzFU4lBYfh6jd+E8YYak89jQgCgighkhGdJDXcs6SJgKkCN7Zlo7XBOlVvbzWKmkHp/rJtMV7gZo6Bs/Tt1dPSfUqK8WkibXSRqhLCKo5pxqyrP2Nw8WmieWoGfwj4c0DYarWOgS8D/vAcn38fEDabzd8A/i7wnc1m87uazeYfbbVazwPvAX4T+FXg3a1W67fn+O77wo31BlurNXAka8sB16+sjL1Q45Dn3+uej9RyYPx8GEXf/JQLLedsK80ReA4/+LVfyDf8H5/Nt/3xz6XWSAvg5bqBMSbreph+6W1hYTD94SqVk9T1HyDLS42BiUbrBrrbw1IKa22F+me9CrvmIXU1DbKTic5o05/3mDi2P/RAh7EqNJ0rP5K3+e0ejKiKTYPROpPYtAtDOq29VAgL37U4jI7RBhazIca8RnI/2s/zQObGoIK2W0cxIggGRJFybqKuTKPNWZXhUoGb6vMiSGlKTjfoUQ1lZDHAmMMW6bGG2z6nUZ8PvNekz0BVsVtYFsIanTYXY2oGzrSagXpwxmCeI+Yrz8+qX/rbVLRaLU06tFbGx0qv/y1SiosLR7qJfgG/9sLvsHnFY0XUZhYQTxKNLQQ1t0YcxUQqpi7G54rMjMMkeSH6NB7jcsPnyc1FdEkyr9xRJFVauJvUSZSj2PCUwRbjh3QsIVLK7DFF5PjoGMsSWIuN7L0mY8OsMgYOECG1KobtjJywWQ7NGExrKYX+5u09+eTczJD9B9UuIoNpg2cAyo7RRuPooNionKHuqfOGskwqTDPGGBitU+WuIBioX3i2iy3sEkndjL7jFIGb3Ae1xNkag0SPSpmWZw0GqFfyxoQZnoP+jEH1e11HDETRQNF9pYwuupHSyCDvJhq9t4vI4AIVznLMs9u8F/gFYK3ZbH4HaZTwT89lVQ8AwknQwSG2dRXbddG9cGrbodYGqTU1z8HPbpRIRdTdCmOQbyYzpIkmtQBOQ913aIcJsTTZRl02BtM7iXLYQ10Shdbu0DkRnofqJOgkRrj9Ybek28PyA0TuqecCAhWpivKsgee6aa/1pEhriJeoF0ksrInGoOC7X1jg2pu/hfjuHRZ+zxfMVjMoRUZlkZZJ0EYjrV7qseoyXfTgZO9pEcYy1YhYb0yMiKRlsC270GIYWGMW1YlgtJAe2D4dnbH8zhEZTJozMCanITk7Y6CNxhiNMzQk6pRnDUrLN4UjMf03FW2lEwr9ti0wiRrh87ItO9NuyIb28ufHYnxkIOXYZ+wiMM/Q2Y82m80/BHwKeBJ4a6vVev+5rewCEcqIH/vv72S3t8uKu8qrXvXG9MRUcLLnKGigHYFnpwpjk+oGqtMluvUyzlp1J1F646j7ajmsBakx6EaShWKjTgbWPFtkMNQyp9XYm9Tyfeh0MFFcUGark2O01tBYLB56S+Q3f1XNIJ9CzoymmEzoVeYlKiirvcn92bkoiUDgLC6mkcuMwz1FlGLbxUzJtAnpTtLFsgzL/iJx0s89D5PznQZhLHnbP/7PbIc7bNU2+eE3ftFYg6C0QgtwLWdsq66J0kJ7nvIro+YE7IeH7PZSpb80ITAFOSVFlTOVGQNzhsagP2NQHRkMoILgcBxmUWRzSjMN5cBfWIJYxyUhnzwqGn9vT9IgOW/MlYdotVr/Dvh357SWB4Y7nXvsZvQAh8kBd3q7PGEtZ8XC6lMUlzQMhCXwhEuk47EEVDoMuf0Tf3eEF2kY8pTF4zLyomUvkix6LnTAZHWDuSKDMmcT2cM9ZkReeHk0EGGzgFEK1emghYMV2AjbSj3yGSODwlu27YLBcRz6vEQWh+2Il3favPrmysTfVBSQLYHwg0yTISx+wySYUmRQzgdXoZv0eH7vBdZqq2wsrHHSkamBrrkj5HynwSe2Dzi8/isEtS4HvTqf2G7y7M2NkfdJoyArWo8zBkVkMKbF1kChD7BZ2+D73/CXpzoq0wRuMCIdJDyt1Bzp8xS+/BLBzScQQVA8N6PDjOONwTw1g1kU2QrKcq3xS86ObdlgUi4mC6tfhLbFiNa6kTJtMLlgttIc83QTvXHc3+dsL30oca2xxZXgCnvhHqvuGldqmxBGWVqn+sbPvWwvcwU82yNWCbFORjiNxvEijRNsSSpu6nkghFWI2+tgsG5QDJzNEhmU0kT94umYyGBId1m126ANOqjjCJUVDHVRMDRTjEFSTCELTGwmeJjpb4mk4cf+2YfYOQwLneWqlEnZGFhZWsSE0WDTcwX6xsApjEFVZBDKiL/1X3+Snd4u68EVvucL/hKQprLy+QfHsonUeOdhFohaG1HLhZq6iFqbdEJkEIlOwBYTjYHlOmMjpO3ubqEPsN3bqZReHVxYKTIY87JSOo3IJsoDVUOHIZ962w8PaAQrMdpJBNXGgNOQ1E14b5nfrIz8PkmUKlKDkBohHQ86OuYBcRLlmGfH+dLS/7vA7wf+I/DIG4PA8fmm134tv3v4MlftV2JlhcxJ0nQwmCaClLSuTYdIRSPGYFYpu7x4PG8n0TDqfkpDHRoLD4obL2crnWXQJ3+QpDYDXvEw+kXkdGNTJ8cgLKTXwKUDpB1CxlJYloUx4x+qtOAm+pQUechf4WHm3t2t/W7WGtzXWX7m+vLYY+TGwLYEwnGxbIGOKgYZho9X1Hxs8tNXVTO407lXkNHthnvsRru4Yo1e1GexdIRDpGKkUbjW/Nf7qeXrLLnLHCdHrPqrPLV8fez7pJap3rdwYKgxQicxaIOoj3d6rjW22KxtsN3bmZ1HacoUstJp/eK03UTjNILl9SvAqBMlyjWDEsa1SVchj4wnRQZ5cXm4jTU3IJ0oot0O2VgJUkel1Dpd0FNkxkA8gE4imK9mMKBo1mw210gLyp8RcG2HJ5euY4V+sRlNo0I46cWZN1on8PoMp+PqBpbnpYItx8csvPZzKwuWZ5EmgpQymxMIJfi2wMQp6ZhSZiKhXhmOnXI2KaWn9mUL30fFCeroKGX2bDRAWVkOV2e91gpPuIWwzji4wi4ig5yoqzJdl63pynK90FnOqTOqUI4MIM2TT6LhHvhsN635uFtbRbG1ipIijTbX2Av32axtcK2xRdcyHHdjwlhR850BPqbTGH9XuHz5jf+T/WiPp1erZVGLFIrjjeSpTZimiKyKKezA8fn+N/zlubQXTBIT3XoZe3l57H2e0poLLGHQGefRPPC2rhaOlbuxiX/9Bm09nuakSHUOGyZzOsbSKuSRwbDIjW3ZtMOYn/ulF9k70AXpY25YjFIlY5BFCg+7MRiDNvD0Ga3jgUMbg2vbKCwS+heqCt0w4af+9UcHWD0DL33AozHGwEiJ8Pyp066JlliWmH3ApwKuI3BtQS9SLLsuJoxIYpmylc6hLpULtPQjg/GfzRlM5dEhAKa+ACcJrrCBhESnHrHnOGnaqSI1YlsOsUlQWhXHqroOuXenjMWbvvxZlDa84trSxK4aNWQMRJAaAx1F2BMeQh2G3H7nO5B7uxz80gd48ofeCla1MfBtjzc++6c4jI547fqzBI6P8SXH3VQLu+Y7ozWSOZEk6czGRrAJWhCrZCyfVnpPWdiON1KDyVuCxZjicY7A8aenhvLvC0Nu/b2/Q7J9D3d9gyff8tzIMGKuBWwJ61TGAJMOyCU7OwSvTJ8n2TkamTGACTUDNTtB4Sw1gzLZZRlSwsdvHbN30gP8gvTxyaAU9eZrkg9uxgDmqxn8B/ozBgJ4BfBvz2NRDwL5TWk5gjiabgw+efdkhNXzmevLeMKjJ3sjk6WzzBgYY0h0gifOppug5jscd2NibFwg7KTDQ84MxeMcdj6FXBTcKiIDz0fHEcnODv7NJ9C2CyR4tk0CxCrdhHzHxWgz2vedoei/N6rfGVLVUWRSKu5eoqn7Ljc3q1lgc2iT5aszQyT81DDrKBzZtMoIX/r0yJCavVmvNAZSSzzbHdDODry0C6kbStaWRrun5kWU31NYSKPpyXCsMcgjD8tO6zrl1ISOorSVcYYC+kxrun2LZDvVZ0h2d2h/+H+w8Lmvw17oXxulU+lNgZlI9lcFHfYQno9/42Zfq0GrsXU2kcmPjtBYz8FYqnIdgil1HccZnHaOE8XuYcjKgsfGis/Obp/00eq2gcEJ+0fGGADPlf7fALutVuujZ7ucBwdtNK5wEI4gkQIZGbwJHtvakj82NeE7qTGIVDxoDGaYMZAmpau433pBjtwYRCY1BnE3NV6zdBLlyKeQZT5EVBEZGK0Legd3c4vV7/0rADiOQ2Ig0Wm05DsuKk5rF+PaW8uzBk4pTVR1zEim1MBlUrpJSI1+/6HOi986rJbvBHBWVkZqPpY8rNzMitpPaXO2LIua79AJE6JE4ZQ2stMgzNqFU4GlmFD2WPYHK+Eyi8gc4WI5WVeYklgiTRmZeHTYbOQ4M84ywKBmiLuxibe+QbK7i2q3ca6sIVwPpXQWMcqJ3VhV0L0wbS4wBiPTqX9jNLY13qCNkx9NFftmNAaqevq4DMe2SKRB63Ri+e5+FwvBxkqdb//qz6XX9opzKKOSXke+pkSmA40XTF1drH/aG4YiguHXaLVaf/DMV3XByB9oyxLFRikNuBNrBmlqwrIsnthcKB4ST3hEKubFw0/QXP2swivMe9QnWX1ZTB6fTTdB7on2tGABiLo9wJlpxiBHkXONJYJqYxbfuV14zsn2PeJbt2H9epqqkhDrPDJw6MbV6lPlyVzLzs5d1XXQmjCb+mwEsxsDd6irQ3heWvyeNGSoFFe/8ZvAsgieeDKVO+yISq8+LhoBBtdVD1Jj0A0lKwupITrtrEGcORhetrFHKkbpQarpfneajZVHYkqBS0E9XlUvgGyW4R99kHsHvamdWtDXDMllIS3HIdnbQ/d6xLdvY/kByafvYV9NC77ThvaGoeMYoxT2QiPV0VB9g1LlRAlhFc0ewIhi3yQUOgQzFJpz+dxeLNk/jtDGsL5c41h1cR3B9VJTQ8G9Zfpt20apmQkTzwOzuKDPnfciHjTKRUXPyfvHrWqP1BiiWNGoeSPFSm100Zc9oG87Qwg4r9TlNFiWReA7dHqauNdDbt/DbL0S156d4rZoL5UqJRGo2CyHVeSsjS0w4DkOSAp3InA8uiQDD2cZBWePVpBHMBWes1aaXmJwhUBZMS8e3uXmwvXKIqfOREaGc9SWH0AUY+IIKxidHjdSosMIZ2kZ7+rV/ucsAYaxee+k2KgHjUF5BmR10cexnFN5xwCxTCeua56Ljg3aKEIV0RB9UaaBhgQ7b4zI+JnCfL6gOkX00nabexkT7t39Hv/z43t8ztNr1AOnUswpl4XM4W1toTod4rt3uP3OH0ft7WJtbGK+65tR/pzGoJe10gY1jFLoXoLM6iBVdTbbtoizCFJY1sCw4jSUdQimISV2VHzod3bZXAm4utZgqeFxfDJmHiU/tupHa/DgZgxgBmPQarV+FaDZbPrAHwEWi0nN5wAAIABJREFUyETZSOsGv3qeC7wI6JxR0LJws9AxSauDY73FWKa56sAdvfnudXeKvuxc3/YVy0/OJGWXbyBnZQwgbTHtHLXZ/rl3ofd2YX0TnvsRmNEDKQpwUuFS3Yo37BFudzXEcsSj8t20ljCWSZKS4pmRfbWzceyOxhBFCQgLx9P8zQ++g71wf6LAvCmu8xCdRuCjjtPNUYwxBqqTdaoM1RTKrJQjxkAniDGNAEKkdBlHnYgXXoqpLYGx1KkKqWGSYNtp6k1KC6U69GSPhjvOGDgFF1Du5BTDZhOKx0t1t0iHbqwErC547B71EMcWriM47sY8tbU4NX1kNxopSWIWPZqdbczdbfTilbl+s+6lqU5RqxUtwVKmv2NYV7s4ttWfDhZOycmbg5donNzlMKTShVTs5mqN577+Ddnx7ZF04rDa2YNkK80xz5H/GbAKfBbwn0jnDn7tPBZ10ShHBo6dFpyktgAz0PqVI8oE1/0xHDjXGlts1NbTYaPaetGXbaRKlcEm5AMLqcszNAY138Zs30kNAcDuduXA2zgUaaJEgjPZmyp7hPKkjS0GN8M08sqMbYUxyDdQlVNfiIoIzRi6sQTL5VjtsRemAjplAzyM4U6i4pheLt85vm6gOh2wQAzpPIuSMShDG43UEr8iQhGCYtPY2oJv+MpnUFoh5kjfKZ0ew7bTcxoLC2UEPRkNdGoNkB7auReank8TZ8NmFRuQNoZYGr7pK14DwBObCzi24KSbsHfc4x3/6iPsHk0f9MsR3HwC+8oV1N4eYnML6+rmXGkiozU6CrE8L32W8ppLHIM9SkWRY2TWwMwRGajpnUQ5do/DoqlkuyR1alui3y7dX1T63yzqLYrHU3jLzhPzHPnzSKUp3w78LPBDfIbMGQxMpVqpxxOTFk7T/OpgqB8mmTEYExkEjs/3vv7b+PDOR7m+kGrJGmOyfODkHu1ESxzrbLVPbSEIbtygvb4Ju9tYq1fwrl6b/fNFmkjO1XGiMppsK+vCSIuYdjZsJap1ackmc3NaDyHGpom0lESRwl6ssbm4UQjMb5QM8MhnslB9JE3kOFiuM3b4TCcxJo4RtdpIVNSnpBjc0PIHfzhFlGP/pK8vfW8/ZOewx80lhTtOHb0CUho0GkcIPMcFIlzhYUxMpCKCjH66THqo8/UriU4SjNLYYyKhHJ1egtKaK0uDCl6riz57x73iN0wb9MshgoDVv/BtHLReZPX1n0/bD4trMgt0GIJJowLoe9FJEkE+VDcGxUBYmXARZqoZ5FmDSYylOZ7aWuTalTp39roDTSXCElntoR/99TW+szXlxuABsJXmmMcYbLdaLdNsNj8GfF6r1Xp3s9l8MIxKZ4wyeRmA5wiibMMa55VGscIWorIrp+HWeeXKU0QySj2+7IJPsvpKp6kCzz77U1pfWiD6i99LY+clcL20cDjk5VahGLOXaqawGlKvNaXJzto3LYEy/dY/27ZSreKqWQPhQDaZixjPT9QNYwyGeuBhC8Ebn/1T7Pb2efXqMxNqBuPTRJANzbU76Dge4CnSnUzYZUzbaZ+SYsgYqPHF4xxPbS0WqZetlQU2VmpzF5ETlQ7yuU4/2nLxSYjpyZDACQrSwzxCsUrdWbn+xKTi8XEnxsJiqTF6T97cWODqWo27+71C43km1Bewtq7hOR6WFc3VWqp7ma5CYQwywXkZY1mNyjRbf9Yg58aaJzLIHcXpDlrgObzl614/0nmVD8KpsjGoigwekTTRbzWbzZ8E/j7wnmazeR3GUo88cjClmgFkrZe2jUz0COd4IlM62vqU7pW6UyOSEV3Zo6Gz03yBxeMyar7DtnC4e+VJrkYHyONj7IXFmW48W4iUZyhLc82CfPAm71oSlkDR55p3bEGUqExkp3rWQGmJsO2R3niAbidtVa3XXBIt8W2PGwtXJ/LHDE8fl1FFWleVIip/z2hkMNpWWkbgOXzbH/9cPr19wmteuURbHc5dRJYqm+i2vf55Jo0qezJkFZBZDSrPpZfTbpPI6QC6oSRRmkbgju0+CzyHH/7zb+C3P7nP4oxtvQA6c4gsGWN79lxpIh320pmIfM1FmijEE0uVn7OH0kTjdDmqMMv0cRmB54xESFXpRMsWRZRiZFr/mvUZOw9MPRsZ7QTAXwTem80WvBW4BvyZc1zbhWF4k3AdG4RI89pDkUGUpYjGFY/LqDup99KVvZkGzs6KhmIcjDH8zPuf5+/9wof5+7/yEnGcII+OZv68Tdo7PQv3O5S4XErGAPq1kILhsaJukHP2fPzoU8RmlBpEa0MvTHBsged7xeYLk6d5841nnEhLvsGUFdt0HKeiL7X6WC8ydx7yiCNHPAO/1GLd4+bGAq6VXu+5I4MkiyQdt7TZQWCnDJ6Jlv11lCJSy7YhNwYThs2Ou6mxHRcV5Ag8h9c8tYbn2rR71eyyZejMQAqVFBHjTJ9LEkwiEUGtiCYtx0EbhZGysngMozTW8/ASyRmmj6fBLpybMR1FeQF5BjqU88YsR3+h2Wz+CvAu4P8BaLVa/xr41+e5sIvEsDHwXAHCRio9kibK1bTGFY/LsIWNZ3tEMkKq9L2T0kT3o242Dbd2O0V+91PHhu225KZ7gr20WIjRTIJtGSJtZk4TDT9AiZLcat9lyUtbWp0h0ZyRzytVtOc+bVb55qf/BF5pUrMbSYzR1HwHSwgS1c/1T9pUc1WycSItwvNAWANF5KououIz2fcM570TlUwVJ0o7ikAqslmD+SKDSKVtpb4zWIdZdAJ6skcoQ+oqc27EoDHQiQQdI3x/bJouShRhLFO+rSlOT+ClEqDdUKKXzNR0irHSqBuZpENiFa25w9BhmiIStX7twrIslLAgUpXFYxhDSZF76DNs8PoMjEFlZCAEWqZzE2jzwNhKc8zydD8J/Bvgu4HfbTabP9JsNl9xvsu6WJSHziAjaLMdEmlGZBejOOUl92aY4s0Vz3pRuqlc5IxBGTfWG1y7kqY5rq03uP70tZRj/fBwps/bpDWA8YTEo1BFmsgilBE//ZF38/Mfey9v/9BPEcqoiAyqZg32wv0+bXK4x25vf0CGtBsmoDU1zwZhEWfUH9P0AfKcsaj4HcIPMIksIjnd7YCwioLlyPuLh7xv1PLaz7QILycLjBOFYzlzRwZRIhE2A3UYpQ1BNqjXkz3iYuCstJbcGzbjxWwgrRUALNWnOwqWZdEIHLQx9KLpv0Fqg/B8LKWxso12Fm6moqV0qOCtRTo3MEmfeSRNlEcGM0S6SumZqCgmoV8zGI4MUq2DXGvkoY8MWq1WF/h54OebzeY14M8C72s2m3vAu1qt1iMvfVkUFkubhO87hHqwgKz0bGpaOWpOjUOO6EVtAmpTpo/l2L70s0Be2OpKQ92xCDyHuNdBd7ropagyb5wjN3t6Jt+hn/5xbMFL7dvshntAnw//ZuMmMEr3m+PGwjXWgjX2w32uNNZZr60VwzlaG3qRwhFpbUFjMEbj2j4aTSSjSk9zUs0ABknrLKUwicRuNCoLjfn9Uvb48ghvHEdQGbZIiQSjRBEENqGUM88apHKrEkeIIjrJ6zAg8GyXUEXEMk5blUsbZTk1Mu66S6XphhLXFtSD2TanhZrLcTem3UumToIrpbE9D5AIpcBK03eTPmWMQYc9LNdFDHXbKAEYk3fNjoWVC9YXin3zqZzN0kk0CbYliFTMJ49fGmAlGOCH4hEwBmW0Wq07wI83m81/DvwV4B8xgw5ys9kUwDuB1wER8KZWq/XimPd8APjFVqv1D+ZZ1/2i6CYqPYiuLegJgUySQt4mijMxmymhc/EdwkkfzLiH8WqVm0rRl34OnUQ5As/hiRuL7OycAOCsrhLfvYc8OBiYqh0HOzs/esahqNwY2MLiWmOLrfom97rbBR9+Fd1vsVbH55s/9+t46eQWr228AvfgpCj67Z+EvLRzwjON9MGOycV6HJRWRFDZs1/VWpoj3xx1FEFeYJ1AXldEBpSNwey1H9+1aYdJIfYjtcKbYeNJlEaZlNspL5iX6zCBExBHCbGKR1qVpxmD407apbXUmF121XNtPMcmjBRK68oivjGGMJYcnSQsLypEosAbTbONfC4KU82FhTF02NnPmWQMIK0bDBSQxXRvX+dUFPeRIoI0TZqnPa8Ea/zFz/sGFrw6mIRE9jjYPWCDBu6jYgyazeYK8CdJI4MtUlGbWdNFfwwIWq3WFzebzS8C/jbwlUPv+atAtTjwOWKYyRLAdW0s2yaOE/LtoCgeT6kXlFFzaoSJJPQlVR3dff3Wi8sZiqCWTnH2eqhuF3tCq6nIPF81Y6istEkpfS2LwPH5vtf/pRE+/GmzBotegxsLV4s6i1FpHjtXNPushuTb/vAroeClcbEyT12a8T37GjNyncuwPD8jrQvTxoEJKSIgm6EQA5FBPKWttAzPsyFM0EpkHrKEGWYNpNJoo3Bsq0hB2CWlrZpX4zjKjP5Q2tGynZRddn8P7+rVAW9Ua0O7l2ALMTPxX45GzeXgJKTTk5VF526Y8DPvf56Dww6fXQt54x9/LXju1I4iVZEiAlC5iuQULWpbZOy7AFrPVDw+i3oBwHavrxa3F+7zyeNPc2PhKmF3jw989F9xIE/Y8FZ50/XvrNwjLgKzENV9NfC1wO8DfhF4S6vV+k9zHudLgF8GaLVav9lsNl8/dIyvAjTwS7N+4epqHWdG1sFx2Njo8/P03OP0byv9vzUWE+R+g4ZQrK/VsWybyIDwHG5cX575BlmKPdS2T23JGzhmGXudfU56h9xcXWdjcXbeoNOgvAa15NF+8ePEn3qB1dd/IU6FQXB6J8h2jZXVBa6sT1/fUaTwXbt0rEWeYH3gPZGBMFKsry+M3ZwbiYM4kSy5Ab6s4yzW+GRPF4pmu4c9QgkbV2pYieH60iqxShAdyUo9YCkYXOfGxiJd9wgLa+A6D6ObrGacPQ7O0iLBZnXLIkDPTamZ8++Mjzt4Eq6vrk71PBdjiRE2ti8xDizXA5aD6efXOQ5ZjAJqDZerG8t4jke9l2CEzcpywOpSQHfnkE8f3ebVa69gY7n/nZGI+chf/xmi7R2Ob97gdT/+o0Xf/p3dDoe9hGefvsLmxnQ68DJW1zTcPsbz7Mr7/BO/fSdtZLBsdo9CokiyurrMaq3Oam3CNQmP0HaDxhMbI9F1VzbwkwbrK3W81dFrnkNagk4vYW2tQe8kQLge9Yp15ggjSScxrCz6rK+cfpteXHmGGy9c5dbJXa4vbPG/vvoLsIXDx5JDjuNjbGA/3CesdXlyY/aB0CpUnf9pmCUy+EukE8d/utVqdU51FFgCyr2MqtlsOq1WSzabzdeStqh+FfDDs37hwUH3lEtJT1aeLgHYPWnjCJta0v+bVJrjdkykQpx7h+C43L3XxnUE+3uzGyEdx3TaCSfmGG/7aCRF0UtC/sYH385euMdGbZ0feMO3z6QmdRoM/24dhnzq7/wEye4O7uYWT/3w28ayJnYO2hyf9GCvizaTNzipNAcHHeqBy86EjMfJUY92mHDHscYO7ymtOGh36QrJ8kEXEWrchdX+sNayT+DAvd0jYpOwIENinXDQ6SI7gqj0M/LfvXtygic8dkrXeRhJR5HsHpDs7NB4zefgWNXvBTjq9Ei0LO6deyeHOMJhV7Unfg7StMnhYRctJHaQrjsOZqA9OOqxf3TCshbsiy62iIgTxcFhBxkltDtt/t5/+Ufsjrmnui9+img71eLuvXyLWx9uUXvlM3SjhOd+9oNz0UsMI+xFHBxKbK0Kjq8c7V5CEiXF9VtZXaRuNPt7bZLAQgYVqSUpie4eIIKA3t7o9rN71MVuR+zeO8KV/fUO3+tHRyEnvZia0Oi9DqKm6ASTr203lBwcdiGrH90Pvuvzv7WIjuO2ADTr9jVW/BUOo0OWa6vU5PLAmk+D4d9d9Z5xmKWA/PtPt6wBHDMoOS5arVZ+dt8I3AD+PalyWtxsNj/ZarV++QyOOxXGpAVIMXQqHFsgHAcZpbMGsREpOd0cKSJIb+bACegKO233K5GIGWP42MGL7GUF1p3e7myC42eE6PYtkt10Y0i271VyFgk0WBZ6hjRR0Uk0JXKySznuccbAFja2sEmMLAalbFvwpi9/ljBWvMLp4lqGI6OKvHghFjOOvsKktMXTJ0lNX5chE1ufRCucUw0YY5AmnaqedVbEsiw8V9CNwcLM3F6ayHT62LH70plFzUBr7nR2i6L98D0V3HxigF021+J+4aWjueklhtEIXHqRpN2TrC72n5NeJNk7CotGhu3DHlsiRPTanGSF8yrIw0OiWy9Te9WrR15TWmFsgW3ZRQdYFfJZAzmFfXfw+6drH8+KcWpxgVfjzz371bx4+Amurt48NydwVlxUxeLXga8A3pvVDD6Sv9Bqtb4v//9ms/kccPeiDAGQ8g8xvvfc8RziY5Py4GSdNNPmC0a+X0kCO6Bra7qyVxgDYwx74QELbr3Qyp1ZcPyM4F+/gbt1leTeXdz1jWJjGIYwaa69ai6gjOIBmlIILXQjKorIkEpHdpMe2gJbaeJE47k2T2wuInZ6mXymxsseIjvjPlJjNAb6nUSTr1+yv9/XZcjE1ieR+pV7yKfRUIz9ja5NlNjIxKDs2bxPqQyWZQZJAEXWMaMM1xZHi/bF+4bYZUUQkEhN3bdn1pGuQj1wEMcWnV7C6mJ6TRKp2TlMZwQ2VmrUfIfFuoc6EcRhF+IYVaugKA9DXv7xH00j1zGGWZqUzNC2nanGoGgvzYzBTG2lZ1QzqIJl29SdGtcam2jHrqRnuShclDF4H/BlzWbzN0gpLL6+2Wx+F/BiNsD2wNBnshy9CK7nEGFIIkmY3TzThnCGYaTCFQ6Ol9IEaKOxsNgL9+kmPZa8BX7gDd/Ove7OzILjZwURBDz1luc4+R//HW9js9IDNkphO87Egm8OWZoxmIT8ARvWjC3DFR7QI0EjtCHJZj5cRyC1RqKAQYIy27JJqiIDxk8flxHcfKIwkGXPuQoDxqBoK539sfI9G7opRc24dQ9Dm1RFSwgzKv5up7KLedE+9E4I4sWRe2pYb2D/OMRzbX7gz34+B+14JkWzcRCWRd13aIcJvUjiuYJ7B120MVxZCqj5peE3z8PCwpKqsoAc3nq5H7mOMcz5bIbt+gNzKOPQL7CrdNObITLohgkv77RZW/QH1n5myJ4B3/bo2Wn76YOMDi7EGLRaLQ28eejPHxvzvucuYj1lmAm9514m+hHHCZFIFcLmUQkDClGberDAiUonQztJj57s4Ts+G7UrCEtcWGpoGCIIqL3iGXSvN3Yk3hgD2mC7dr9PewKKGYMpD9s0Sgro9+onlsY3NlGUZDTjAqkNyk7XU2YHdYSDzIxu+ZpOmzHIkRvIsuc88f0lfqKkQt1sEnLnQmsLY/TUWQOZpYhsIUaMQVl2MXB8nriyPjV/3AkTerGk5jmsLdVYW7q/fpZGzaUdJrR7CapjkEqz3PBZHBpgs1wXLLCz3zMO7urqiNRoGXlazfV8iFK2gEq9DSsVnvnk7gmvDCT1KfdnGEve/i8+zM7h6Wso05BHJ7kxCFX4mW8MHmb0p49HPVnPSx/qbjdCNwJqp1AhMkqCBTV/gd2TIz68+zxXglWW/UXWM0PwoCF8Lx22imPs4V7nbOhOOA4GM7GPHEpUFFMig4INdZIxyDZViUIjkIkkqAeFIEhicsPT33xd4RCSC9KX2EdnNAYw6jlPfG/OXIomVgmWJeaiFMlnBWQsIKsbTJo1yAnqbMcauQ65AZZK481Cz6wN+8cRFtYARfX9oOanEWTrpQM2V2qsLPhFyqgMSwgs18UKJSpToBt+Bo1MpUaNMdSeenrEMBeRgeNDlDkzFcYgF55p7x/yTEPx5jeuT9z8Xrx1VHSunbaGMhXZ9XJtD1xDKEPwz/gY8yzngR35IUHBVz4ml+z66SYT9jIx9znrBcDADfru59/LP3n+F/gnz7+XBXfhoTAE0KclMHE88lq+8eZGYlqqSKk0DTYtzzqLroEt0hRQbBRSatA6pWvO1iRJJ1jLFB6FUtoQvUOVsM39Iqc9l1ohjcQ7BZ2I7wosrEKwZhISlcpbOsLCtoabHqan3so4bEcorVle8Crp2OdFGEt++t/8Nj/7gY/xM+9/noV6dZQkXA9BJis6FB0YrdG9LvbCAo3mZ4+N0PLakJOR7U1KFd076LJ7FCKMYfcw5E4m5TkOUmkCL62hAKeuoUyDZVkYmZDcuo2HQ6ySmag5zguXkcGEyMB1HYQQxfTrNKbSYRiTchuJwOd25x77mRrXXrjPve7OA0sNDSOnbNZjjEHOt267OfPiNGNgsGeY7oTpugaQpooSYRHJBGyF64p+ZIDGHZqwLTSUh6ZaJ2kZ3A/y74tVDKaatnoSfNfGtmxiGU9l8UyyHLsvxEhkYJc6iqYhShTH3RjHFhOZSefFrd0O2/ksyFHInb1upUdteV5a0I8TlNHY9J8v3emAqSYJhNQAC0tg2x4aRnjEyri5scDWWo3OdpeVBY+t9eo5iv2TlD/re//07+G4m5y6hjINOgy589P/ELm3i721hfMdf4GwNqhhfZG4NAZDwjbDcDyXOJHYljUzDUWBLMVi2Q7XGmuVHR4PGpbjYNn2AH1zjvwBsx0HzGRjYIxBaVOQsE2D1oaXd9pcWQpGcso5XOGBEIRJBK7CtQXoJPUKrVEOoDxFM+xhT6OiOC3yxoNQRdl65zcGnmtjWw5hMj0ykFlkYDvW2JoBTI/eIC0aA1xZCmYSbpkVOSnisNrXOAjfS48dJ5kR7J+7nDFW1CcYAyPxhFfUuSZ1FAWew1v//BtofeQT1GSPTqQY123fCRO6YZIOTa7U2ViZ/HvvB9HtW0Xnmrp3D/vuNuHC6oCG9UXi0hhM6CaCtG7Q7fTYO+iyuVqby0Mobk7HqaRleFhged7YInLuhbueA9HkHL/SJlM4m77hhrHkJ//Vh9k+CNlaq/HWigKdb7tgC3pJhKs1niswoU6Lh2I0P+9UpInmqRnMg7xVNQ/vT2MMfC+NDBKpps4aSKmxrJQkb9QYTC/KQzq09vHbRzy9tXjmXTJVal/jYLlpZGCSeCBNZKREhyEi8EeI6XIorcCk17uv4DbZkAaew7NPLrN7V9FLDIftiJWF/nOotGbvKMTCKlJE5wn/+o2BmQ/72tXCqXgQeOyNQV/lbLzXry2L9/3HT/BCss3V9QXe8nWvn9kgDIvajBs8eVhQWUTO00SODZGe6HXOIx5+a7fD9kGuA1xdoPNsD4RNlCT4JuU8UtogjQTLGdEZFpZAWGJkU50kbHM/GP6+aWyl4yAsC991kREDQj3D0MYgtcay8zrXUJpIWFhYE41BJ0z4W//0Q/c1aTwN49S+xsGybWzHhbAzkB5T3ZRdYBJJYFLQczup82JRdO5NhNasLHjs2TaH7QjftQuDuH8coY1hdTEYmaA+DwzPfOybLt2kS6ySU91H972eCz/iQ4ZJcwYAx6HmsB1jG82dvS63dmdn5Mg9lUmiNg8LqorIOfe7nXVSqQn56DxXPUtkcGO9wdW1tI1xY6VaQ1dYAuG4RDrGzS6R0RqpUk3mcZ64I5zUWJR/xzlFBuV6xTRBm0kI3PSzYVJtDFTBw6/TtsyhjiHLSgv3kwz2794+Hpk0fpAQng9KoUo617rTTn/fhBRRN+lyq303vQ9IU53TBs8gvZ+FbbO51sDCYuewV9B2d7L00NKEovdZI+9cE0FAzUmjkZ4Mp3zqfPDw71LnjGnpgxtbi1xddPCPtjHXn5qrqyDPtz9onvJZUFVEzovnjuNgkUysGcw6cAZ9Dd0P/c4uGyvBRO9UWF5aZCbbMLRON/sxaSJIUwexIuP8z4zYjFoB80JYKeMo5v4kS/NUUZRIlFZjdS0SmUexowNnOcpF+XFYWfDue9L4LOFkTKQyDKGeylvqKEbUgso20VBGvP1DPzXAvSRsB52EI1rZIzDp675ns7ros38Scmunza29DutLAdevNB7YFHAuTBSqkOWxFY3zxcO/S50zpnmMngVffu/XUPt7OOoqnn4Ds562fpro4T/NRRE5HspZ5uI+tj3V6xzWPp6GwHP4rBvLdMKERI6Sm+UQuCAExqTGwOi0ZuA63tgHt19EVsX/zyoccxrYlp2J09+HMXBFVjdIO4rKnTU5Cv2HMdPHOXKRm3FG2xiD1vDmr/wcDJxbl8w8cPzUG1Zx6g3rQmq0utvndvvuCPfSzUxz3CiJJaq7o4xSxfO41PA47kT8xL/8CLtHIZurNZ77+jfc/486JVKpXJdIVQs0nSce+zRRznFfhXhnG7Wf3ngyG4mfFUalJGsTPZWHCJbnYaQaUHczSmPZqQZALq1YhXx8X05o8RtGPrvRiyd8RotMPDw1BlLGmbrZ+Ie+317aTxtozu/hyjWe9QwtnVVwHRtXuMRSVXYU5dPHzpjp4xyTishhrDAYVhZ8nrm+/MANAYCda0hkEanqZFKjE/Q1lv0l1oJVgKIzL9cPntRemk/Tl3mJerEq0mbbBw8+bRY4ARiIHkAh+cHfDQ8Y2uiJRcXgqacnjsRPwjh6h4cZRRE5ivpiN1qlWq2kBcqqKeQwloWHde1KfeZCey0zBlGsoOr51zYmiwyMMcicEM4ZbwyGB8+0zhlLz94YhDLiZ3/7PeyF+2zWNvj+N/zlU3eK1V2X3SjmxcNP8urVZ0a+J58+dsdMH+ewJwye5RrF58Kzc0oI10UIBxWF6CjCJAmiUZ/oQEUq4uue/RoAbi5eJ3B8lJOlECfVDcbIXT6xuTBzK+xFILB9jjkhlBE152Klbh6eu+IBIRUvrz4Ndr3OtTd/C/Gd2yx+weunctXkMFqnXsgjUDzOYeWTnHEM9Xo6NKd00d6Xb0DpYNngZz9176TwsPJC+ywdJa5jIywrNQYVkAo8108HybQmkXH22YrIIK8TZPWOvFPybsyhAAAZ4klEQVTlrDuJAO507rGXDRPmGs+n7RgTDnzg5V/kRB6NNSyJqm4rzeEU12g0MuhGEgtrbhr284bt+ciwi2qnGhCTBs26SQ+pJavBMldqfWHEvGNvUntpXv+ySjfvPK2wFwHf9rGslNRydczroYzOrT390chfnBNyHvpJaSIAZ3ER//pNRnbASd/9CNULcoiso6goIhee1KC04rhU0XLDO/X4fuDZKQvpmA1M6zQSCbwAYzRxEqXGwLIGuIfK6OsaZJHBOU0fA4XGM3Dfw4R74S4nMtWA2u7t8Kmj28VraUSk004ixtOnQDUlRSIVUmlqvv1AaZLHwfYDjDEkJ8eZ1Gh1iug4TlUJl7yhAmsujzoxMsjOyVBxPm+FfdCGANKOsMAOkFqOpAt7Scjf/ODb+fH/9g5+9IM/QSjPNpX04H/9A0TRSTTFJqZtlx1MFIM72+j+8IzBo4DhIvKwJ1WVjzbGIKXhm77iNVhWOvo/z4MVeA7dSBLGioXa4LWIsxxwLQgw3TZJEiJlAnY1IVzaYmkXlBTqnKaPgTMdJnTlKjqsIYIeuldH9/pF1HxzFyKf5aiYmK+gpOhG6TmoBxffvz4Ntp85IUbhNhYrjVVPhsQqoe7WRmg/+lPIE2oGeRvqOekTnBUCx6cne/RkyKK3gDGGTtLlo/svsNNLJ5bvNwodh8c6MtDM5jGK/GYd7rSZgEdpxqCMgSJyQafRrxnAaGTQixRSa9YWAz7rxsrcHlZeRA7jUa8ulummVs+8xSgJkSrGqegkyuEIB6UV2uiisHteBeR8mPB+w/Znrq6xePd/Ifr4a2m8/Ae4UkqXJDKfMUj/XRUZlEVuysjrBQ9bigjSjiKTJES3Xp74vBzHKR33SFRA6gBYtj15Clnn5/DhOwdlBE5ApGJ+5+B32e3uc7tzl/3wgDV/hfXgCnD/Ueg4PFo71RljGhVFjpx7fRx3TxUepRmDMsqTyCNpIjGe+6adsbpOYqicBM8RCMsiHFM3kLkx8Gt0gF7UxSiFO8XDdSyHiCgzCOkOeh41g7NE4Dn84Nd8MR95+SWW/CW6kWT3qMeVpaCIxkQxfVy9odm2KM4bpKm2KFb4rj2/HsdFQEPynn/B3sEhxxVSo6GMiGRE4PiV6UHLsdFxXDljYcYUkB9GKK34J8+/l71wn7Vgla97zddwJVhlyVvkB3/vd5xbzeDR2qnOGLPy1aTc615xo82Uc30EawZQKiJHUVEjyTs7+jWD/kajtKYXpTMC86rAFce0LHzPphdJpNIDG1YeGfiBhy3soh/dqdgQchQcRUaijJ0d5+HeBACWgjpPX13CsTyIbNq9BJkxwQJgjZ8+LiMXuckjuF4sMZiHqouoDHPvHhwcAtVSo/2oYKn6ixwHorg/GzOMMQXkhxHlpoT98ACA1SBlzLOFfW6UNg/3WTlnzENRIHwPzHjO/7HfnYnaUDFF+bBioIic1waKNFHOu9/3vNq9dKNZrN1fLjqnB4+SwQc5ThSOLRCOgyvcIuKq6iTKUR48O89uorNGruGgSNhaq1H3HcJYcnAS8vJOm0TKiVEBDIrcAPTCh6+ltAz/+k2szQ2Ase3bsUoIZYhvexO94TzFZCqMQREZPOT3wXBTws2F6xdy3Ifz7rggzNNlIjwfRTs1Bv708CwXtXnYOjemIS0iC0wcYbLid7nne3gKud2NsbBo1O7vVvJL8waNLAWktEYbg+/YWNl0ZihTURLXmZImKlFZa52+92ERE5qGwPFpxx2kkWyu1rm71+Gd7/stdo9CNq5FfMtXvm7i54uOIpkqiHUjiS3EqSO384Zbq+N955up7Z2w/vSokE0RFfiTKRqKInIVv1PO7fSQO2gPiuH4QoxBs9kUwDuB1wER8KZWq/Vi6fVvBf48YIAfabVa77+IdU0jqSvDKhWR7Sm8IWVRm0cRluendNZx+lCVHx7btoiT9LyFsSRRmkbgTpTCnAW+a2NhDUwi58fxnJSm2LEc4jjkKDpinacmfl+/vVSdG331eSGwfdp0CGWEb3t0IpnNcGh2j0J2D2OemsCzb5e6vuIkNagLwcPr99mWTexY7K85LDkWZVPQjjv8zsHvcq2xNXUIqzAGFUXkR6VmAA+G4fii7pA/BgStVuuLm83mFwF/G/hKgGazuQ58C/B7gAD4aLPZ/ECr1ZpNu+8+YDJhG2uGbJnluiAs9CxF5JKozaOI/iRyxp5YNgalKeR2NzUWC/eZIoJ+3SCMJVobhLCKDppcklELiw984v/mOD7m3x9/mG//A99Z6TXZIo3KlEk1drEeHWPgZ4RlKSXBYl8wZv+E9eWA62vVvD0wqC/dzbqI6g9pigjSNNC7n/8F9sMDrgRrfONrvxbfdgllxLt++z3shwcFId3ENNG09lKdyqQ+KvQwF42LOitfAvwyQKvV+k3g9fkLrVZrF3hdq9VKgKvA4UUYAphP8MSyLITnYZKk72FUoCxq8ygiLyJjSLmVBmia03OVSE0nlDi2OLNcdJ7GyLuKho3BfnxUDB1thylB2STYlk2iVcoCOiXP/jAhrxtEKm1YyKdkv+fPvI43fcVrqPtT6iV2/xr18qnjh9gY3O1uF4XSvXCfO527JFpyr7tb/D0npJuEaYpnZoiX6BKDuKg7ZAk4Kv1bNZtNp9VqSYBWqyWbzea3AW8DfmKWL1xdrePcx0DXxsYiph3hxoatleWi+2QSIiKSoyNqSx52rTpkTU4giur4G8u4yxdPRTsJGxvT16OTgG6SEnZZrkuj9BnHd3GOQhzfZWXF4spywOrS2ahCNRYDxE6HxqLP+kqNyKTHu351GSEs3O7TbHz8CjvdPa4ubfJ5Tz1D4FYfWwW9jL5AcWVtgY2H7FpMRD3mJGqzvBTgZ8XylXWXnc4e641llvzq6MAYQ0cawljRWAioBw5bG5OjiQeJxZVnuPHCVW6d3OX6whZf9uwXE7gBr0me5lde/n+5dXKXG4tXp15vgHZnAZEZheF7vdMOsGxBfYZn4FHGLM/4OFyUMTiGgUS7yA1Bjlar9Y5ms/lTwC81m80vbbVa/2HSFx4cdE+9mI2NRXZ2TtjpHhPKiIZszxQdqHZCctDlxNrHWapucZNHh8iDLq4bYscPT0ia/+5ZEB2HKS+R79EtfabdSzg46uWdgDRci52oWpBlHmhjODzs0u2EmERyb/sEW1js7aWGOukYvrb51ez29rn61GdzcphwQvWxj8OIk7jL6mqdo4MeQTzbb38Y0EkkB70uprdbDFkdRSccRV2cqEbkTA6eT456LC7VODjsYC0G7HAhwfap8V2f/61FwbR8Xav+XoXoJMLIDvUnnxi517u3d5FHhyxYtZk5xh41zPKMVxmLizIGvw58BfDerGbwkfyFZrPZBP4G8CeAhLTAfHou4DmgjZkrl2z5pR78CXhUB87KsDwP0wtHeFzKkpY13znTISZhWXiuIE40iUwLn0E5+rMFnu1xfeEqnjed0bFMV1Ela/qwws/mKEIZFcZAFy2y03+LbQ9ep4cdVQXTeQuplu1g4mSkvVQeH3P3XT9dsA8/+UNv/Yw1CKfFRbmt7wPCZrP5G8DfBb6z2Wx+V7PZ/KOtVqsF/E/gPwO/Afxmq9X61YtYlDZ6Ki9RGcL10iLylFmDR5GkbhjC99FxRHT7ZXTYl+GzhUWcKF7eaeOew/BO4DkYDO1eTlPd3/gG8r0zFAHLm+ajUjzO4QhnoG4AZfbV6cZAac2n7h6htSlqLo8D8mdOS4lRCnl8THT7Np2PfBi5l/L6xHfvzKVL8rjgQnarVqulgTcP/fljpdffRlovuFAYzNybhPB8dDhZXk93O0R37+BdvYr1iHofRpuxnlSiND/z/ufPTVA9LyKfdFOD67n9c1xucZ2lI2QwMni05j0gjQ46SZdEJ3i2V1ByT7tnw1jyjn/5EbYPQzZXAp77ht/7UDByXgRSSoqI/f/vg/ScWurAWeA/+STu5hbJ9r25dUkeFzwed0gFlFF4EyTyxsHyfQhDTBxhBaOpCtXpcPsfvBO5t8vB1fc/suFocrA/4knVXvkMd/e7I4Lqs+gWzIqcSC0fCPTKXm05EpnJGJQjg0crTQTgOz6dpEuk4tQYGF20zE7Crd0O24eZetdheObX6GGGUbpwYtz1dW589/fhrq5hOQ5P/fDbiG7fwr9+45F8Js8bj0/8OARtcvWr+TzGQji+om7QfeFjnxHhaHDjJt7Va8AgRUDe8w7z6xbMAiGsIjVkYQ3UJIo00VC7a+V3WaLwoh8FKoph5PMGOW+9Mmqm33He1+hhRtmJSXZ3UScnRepIBAG1Vz5zaQgq8NhGBuaUgid9OuvRuoFOYuyFxVPLZD5MEEHAkz/01hFP6iKUoWqeTacXs38SsbVW6x/DTlMAyf4e3ubWTA+1MppPH93mmn3zzNd53nCFgy3sQiDdGDNThJNfo6401B3rsUkRQd+Jie/eeaSfvweBx+cuGcJpKQoK7p4xkYE8OES4Hk98//+FPDx45MPR3JMaRq4MdX4wRV2irKdskqRIARzM0BESyoh3/dZ72Av3ZppgfRjh2z7dpEso07TPrMNzgefwxI3ZW4k/U5A7MfXuAd366iP9/F00Hr3Y+Ywwq7DNOFie3xeAyb8vDNHdLiLwcdfWLsPR+8DecTSipwxp2m2eFFxKBbwHzDbB+jAiyFJF3Yyg7345oB4HiCBgsfnqy+dvTjy2d1besz0LL9EwhD9aN5CH6di8szJOxvoS8+CJzYWxOW//+g3cravAeKrjYZylPvGDQj5v0JszMrjEJebFY5wmyiOD+VsOrYzz38Qx1OuobgcdRoh6/dIbOQNU1SVEEPDUW56buSMkpwIOvROCePGRSxEBuLabivro2WcMLnGJ0+AxjgxOT2tc7igyxiAPDsECZ3UCr/Al5kJelxgufs7bERI4Pq+68opH0hDk8EuqbrNwaF3iEqfBY2wM7qNm4DhYjo2JY3S7jUkS7IWFdMDlEpc4Y+QtpnAZGVzi/PAYG4PZpjmrYHk+RimSg30QFs7yZVRwifNBYPtEKuZW+y6xOhtSwEtcYhiPsTHIIgNOR1MgfC/l7nnpJYTnP9I8RJd4uKGM5t3Pv5ef/9h7+bH/9o5iCO0SlzhLPLY7WK5ydmoCsxJ3j7t1lafe8txl8fgS54I7nXvsh/sA3Otuc6dz78IlES/xmY/HODK4P2MQ7+/1x97v3X1kaScu8fDjM6FF9hIPPx7byEAbjWXNxnEzDpdj75e4KOQtsrnIy6PcGXWJhxePsTGYn766jCrunktc4jwwr8jLJS4xLx5jY6DvW/CkirvnEpe4xCUeNTy+NQP0I0lrfIlLXOIS54HHcjfMtQysS2NwiUtc4hLA42oM9H22lV7iEpe4xGcYHsvdsN9W+ujp4l7iEpe4xHngQgrIzWZTAO8EXgdEwJtardaLpde/E/ia7J//ttVqve0813O/MwaXuMQlLvGZhovaDf8YELRarS8GfgD42/kLzWbzlcCfBX4f8MXA/9ZsNj/vPBdzPyR1l7jEJS7xmYiL2g2/BPhlgFar9ZvA60uvvQT8761WS7VaLQ24QHiei1E5Sd3jmSW7xCUucYkRXNScwRJwVPq3ajabTqvVkq1WKwF2m82mBfwY8KFWq/XCtC9cXa3jOKej8z0Kj1ldrbOxsMiC1zjVdzyq2NhYfNBLeCC4/N2PHx7X337a331RxuAYKK9QtFotmf+j2WwGwM8CJ8C3zPKFBwfdUy/GWTAcHHRxoy49R5/6ex41bGw8fgLpcPm7H0c8rr99lt9dZSwuKk/y68AfAWg2m18EfCR/IYsIfhH4n61W65tbrZYa/xVnh8sC8iUucYlLDOKiIoP3AV/WbDZ/A/7/9u49Rs6qjOP4d2/suqViod0VG7AVwxM12FYWKwJto1ysF7yhEhBx6yU12mgwKVTBQCRR1BKrxljRdqli4qWC9QItClgUQaFV2QpPLV4qgmVpEbbdbtvtrn+cM+3rdmY7u+nOTN/z+yQN874zc+Y8w+Z93nPeeZ9DHdBpZlcAW4AGYC7QbGbz4+uXuPvvxqsz+2My0E1nIiJBRZJBvDC8cNjuRzOPK1rl7cDIYIwL24iI5E2Sp8aaJhIR+X9JHg3DWgb1Y17LQEQkb9JMBoODKkUhIpKRZjI4AmsZiIjkSZJHxMGhQV08FhHJSC4ZHLx4PLa7l0VE8ijhZKCRgYhIQcLJILnQRURKSu6IOHjg7mONDEREChJMBmEtgwZdMxAROSC9ZIBGBiIiw6WXDA7UJUoudBGRkpI7IurXRCIih0ouGQwdWP9Y1wxERAqSSwYaGYiIHCq5ZLB7oJ+tzz7B3v37qt0VEZGaUamVzmpC/8AevvnwKrb376C9tY3FHYtoaWyudrdERKouqZHBk7u2sb1/BwDb+p7iyV3bqtwjEZHakFQyOHFCO+2tbQC0t7Zx4oT2KvdIRKQ2JDVN1NLYzOKORfQf00vL3omaIhIRiSqSDMysHvg6MAPYA3zQ3bcMe80U4D7gNHfvH6++tDQ2c9IJk+np6R2vjxAROepUaprobUCLu58JXAUszT5pZhcA6wDN24iIVEGlksHZwB0A7n4/0DHs+UHgXGBHhfojIiIZlbpm8Hzg2cz2fjNrdPcBAHe/E8DMym5w0qRWGhvHfhfxlCkTx/zeo5niTkuqcUO6sY817kolg+eAbA/rC4lgrJ55pm/M750yZWKS1wwUd1pSjRvSjb2cuEsli0pNE/0WeCOAmb0GeLhCnysiImWo1MjgVuA8M7sPqAM6zewKYIu7r6lQH0REpIS6QhVPERFJV1J3IIuISHFKBiIiomQgIiJKBiIigpKBiIigZCAiIigZiIgIia1nUE4p7bwxs9nADe4+z8xeCnQBQ0A38FF3H6xm/440M2sCVgDTgGbgeuAv5D/uBuAmwID9QCfhBs8uchx3gZm1AQ8B5wEDpBP3Rg7Wffs7sBxYRvgO1rn7deW2ldrIYMRS2nljZouBbwEtcdeNwNXufg7hQPHWavVtHL0X2B5jnA98jTTifguAu58FfIYQcwpxF04AlgO7465U4m4BcPd58V8n8A3gEkKl6Nlm9qpy20stGRyulHbePAa8I7N9OvDr+Ph2QtnwvPkhcE1me4AE4nb324APx80XA9tIIO7oS4SD4BNxO5W4ZwCtZrbOzO4yszlAs7s/5u5DwFrg9eU2lloyKFpKu1qdGW/uvhrYl9lVF/9IAHqB4yrfq/Hl7jvdvdfMJgI/Aq4mgbgB3H3AzG4GvkqIPfdxm9n7gR53X5vZnfu4oz5CIrwAWAisjPsKRhV7asngiJfSPspk500nAv+tVkfGk5mdBNwNfMfdv0cicQO4++XAqYTrB8/LPJXXuBcQimDeA8wEVgFtmefzGjfAZuC77j7k7psJJ7rHZ54fVeypJYPUS2lvNLN58fF84N4q9mVcmFk7YQnVK919RdydQtyXmdmSuNlHSIAP5j1ud5/j7nPdfR7wR+B9wO15jztaQLzuaWYvAlqBXWZ2ipnVEUYMZcee2ymSEg4ppV3l/lTaJ4GbzOwY4BHCVELefAqYBFxjZoVrBx8HvpLzuH8MrDSz9UAT8AlCrHn//11MCn/nAN8GuszsN4RfTi0gnATcAjQQfk30QLmNqYS1iIgkN00kIiJFKBmIiIiSgYiIKBmIiAhKBiIigpKBiIigZCAiIqR305kcBczsImAJ4e+zHljl7l+sbq9qR7y79tp4163IEaGRgdQUM5tKuMX+fHefAZwJXGxmF1a3ZyL5ppGB1JrJhHIKrYR1CXaa2eVAP4CZXQW8m3C7/Vrgyvi+pcCbCWWMnwJ+AfyDzBm0mXUB97h7V4l25hLKWfQBLyPUrrqEUPn188DbCSWxl7v7slL9yVTMLJzFF2vztcX6Fvv8aWAvMB1YA+wkrMVRR6ytBUw2szuAqcADhAVc9ozwHc0FvhD3dceCdoU+Lo3f91RCsbdu4MLEijgmTyMDqSnu/ifgJ8DfzOz3ZnYD0ODuW8zsDYRa9WcAswgHr0uBd8X9rwDeA8wZ6TNGaAfCQfpjhAP3yYRiXxcBZwGnAa8GOs3shYdpJ6tYmyOZTShJ3BHf1+PuHcCfgYvja6YDi4BXEqpTLiwjtlOB12UTQTQLOIHwPU4DTgFefpg+Ss5oZCA1x90/YmbXA+cTDpz3m9mlhIPqbMLyhhBKNG8lrFOx2t33AdvMbM1hPuLcEu08TjhrfhzAzB4hlAQ+A/hBPPPeQzh7xsxKtTNcsTZ7R+hft7v/K77+aeBXcf8/CUX4ANa7+1/ja24hFF1cdpjY3N2z63kUzARmZkYWTcCOEfonOaRkIDXFzN4EHOvu3ycs1rHSzD4EfIBQv/3L7n5jfO0LCNM21w5rprCgzxBhaqWgKf63oUQ7HcTpqGHv3xcfF/o4DegZoZ3hirVZqm8QpoiyirWZ3VfPwZhHim03w5jZdOA5d9+aef2EQvKSdGiaSGpNH/C5eMAl1mWfCWwE7gIuM7Nj4wp1txGmcNYSLjI3m9lxHJxXfxp4iZm1mNnxwDlxf6l2SlkPvNPMmsyslbB06tQxtJNVqm/lOtvMTjazekIN/1+OMbZZwIOZ7dOBDaPsi+SAkoHUFHe/G7gO+JmZOfAosB/4rLv/FFhNuGDaTVjM5GZ3v5NwoXUD8HPgP7GtTXF7E2Ft5Hvj/qLtjNCnWwkLI20A/gAsc/fNo21nWJtF+zYKm4AVhAvS/ybUth91bIRk8FBmW8kgUVrPQHIn+6uhKndF5KihkYGIiGhkICIiGhmIiAhKBiIigpKBiIigZCAiIigZiIgISgYiIoKSgYiIAP8DaQbEOP7Mgv8AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().plot(nsamples_per_run=50, nruns=3)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().pairplot(nsamples_per_run=4, nruns=1000, x0cut=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pairplot above demonstrates that $X_n$ and $X_0$ are still dependent, \n", "\n", "$$ \\Large\n", "P(X_n\\mid X_0) \\ne P(X_n)\n", "$$\n", "\n", "even for a Markov process! Some probability calculus shows how this happens. Take $n=2$ for simplicity:\n", "\n", "$$ \\Large\n", "\\begin{aligned}\n", "P(X_2\\mid X_0) &= \\int dX_1\\, P(X_2, X_1\\mid X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1, X_0)\\, P(X_1\\mid X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, P(X_1\\mid X_0) \\; ,\n", "\\end{aligned}\n", "$$\n", "\n", "where the first two lines are completely general, but the last assumes a Markov process, $P(X_2\\mid X_1, X_0) = P(X_2\\mid X_1)$. Compare with:\n", "\n", "$$ \\Large\n", "\\begin{aligned}\n", "P(X_2) &= \\int dX_1 dX_0\\, P(X_2, X_1, X_0) \\\\\n", "&= \\int dX_1 dX_0\\, P(X_2\\mid X_1, X_0)\\, P(X_1, X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, \\int dX_0\\, P(X_1, X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, P(X_1) \\; .\n", "\\end{aligned}\n", "$$\n", "\n", "The comparison shows that $P(X_2\\mid X_0) = P(X_2)$ would require that $P(X_1\\mid X_0) = P(X_1)$. In other words, the direct dependence of each $X_n$ on $X_{n-1}$ is sufficient to generate long-range dependencies all the way back to $X_0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another important property that some Markov chains have is **reversibility**,\n", "\n", "$$ \\Large\n", "P(X_n\\mid X_{n-1}) = P(X_{n-1}\\mid X_n)\n", "$$\n", "\n", "which can also be defined in terms of forward conditional probabilities as\n", "\n", "$$ \\Large\n", "P(X_n=x\\mid X_{n-1}=y) = P(X_{n+1}=y\\mid X_n=x) \\; ,\n", "$$\n", "\n", "and roughly corresponds to time-reversal invariance.\n", "\n", "*A reversible chain is always stationary, but not vice versa.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update rule for a stationary Markov chain,\n", "\n", "$$ \\Large\n", "P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "\n", "can be conveniently visualized with a 2D plot. For example, taking $n=1$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().plot_conditionals(which=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The blue line shows the mean $X_1$ at each $X_0$,\n", "\n", "$$ \\Large\n", "\\langle X_1\\rangle = \\int dX_1\\, X_1\\, P(X_1\\mid X_0) \\; .\n", "$$\n", "\n", "Note that this is essentially the $(x_1, x_0)$ scatter plot from above, but with samples now histogrammed to yield conditional probabilities." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**DISCUSS:**\n", " - The speckling is due to using finite statistics to estimate the probability. How would this plot look different with infinite statistics?\n", " - This plot shows $P(X_1\\mid X_0)$. Would $P(X_2\\mid X_1)$ look any different? How about $P(X_2\\mid X_0)$?\n", " - Are these conditional probabilities normalized along $X_0$? along $X_1$?\n", " - How would this plot change if we changed the definition of `initial()` in `StationaryMarkovExample`?\n", " - What condition on this plot does a reversible Markov chain satisfy? Is this example reversible?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "With infinite statistics, the diagonal band would be a uniform color, since $P(X_1\\mid X_0)$ is uniform (within the diagonal limits shown) for each $X_0$.\n", "\n", "A plot of $P(X_2\\mid X_1)$, or any $P(X_{n+1}\\mid X_n)$ would look identical since this is the definition of a stationary Markov chain. However, $P(X_2\\mid X_0)$ involves two updates, so its plot might look different.\n", "\n", "A conditional probability $P(\\alpha\\mid \\beta)$ is normalized along $\\alpha$, with the value of $\\beta$ considered fixed. In other words, a numpy array of values `T[n,m]` tabulating $P(X_m\\mid X_n)$ on a grid satisfies:\n", "```\n", "np.sum(T, axis=1) = 1\n", "```\n", "\n", "This plot only shows the update rule and does not depend on how we chose an initial value for the Markov chain.\n", "\n", "A reversible Markov chain has $P(X_1\\mid X_0) = P(X_0\\mid X_1)$, which makes this plot symmetric under the interchange of its axes. In other words, mirroring the plot along the diagonal should not change its appearance. Since this is not true in this example, `StationaryMarkovExample` is not reversible.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Equilibrium Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Repeated use of the (same) update rule associated with a stationary Markov chain reveals a useful feature. These plots show 1, 2, 4, and 8 iterations of the same rule:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().plot_conditionals(which=(1, 2, 4, 8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**A stationary Markov chain eventually reaches an equilibrium $P(X_n\\mid X_0) \\rightarrow \\tilde{P}(X_n)$ that does not depend on $X_0$.**\n", "\n", "We saw earlier how, in general, $X_n$ and $X_0$ are dependent, but we now learn that stationarity tames this behavior and guarantees that $X_n$ and $X_0$ are independent for sufficiently large $n$.\n", "\n", "We will not prove this result, but here is a less trivial example to help build the case:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "class StationaryMarkovExample2(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return np.abs(np.fmod(np.cos(2 * np.pi * history[-1]) + 0.1 * gen.normal(), 1))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample2().plot_conditionals(which=(1, 2, 3, 8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For practical applications, there are two issues to deal with:\n", " - There is no way to know in advance how big $n$ needs to be to achieve equilibrium.\n", " - Given some stationary Markov chain, we can generate samples from *some* equilibrium distribution $\\tilde{P}(X_n)$, but how do we build a chain to sample a specific distribution?\n", "\n", "The second issue requires solving an [inverse problem](https://en.wikipedia.org/wiki/Inverse_problem), which is generally challenging. However, there is a general class of solutions that we will look at below." ] }, { "cell_type": "markdown", "metadata": { "solution2": "shown", "solution2_first": true }, "source": [ "**EXERCISE:** Define your own Markov chain, following the `StationaryMarkovExample` above, and make similar plots. Is your chain stationary? For a challenge, try to build a reversible chain." ] }, { "cell_type": "markdown", "metadata": { "solution2": "shown" }, "source": [ "The test for a stationary chain is whether it only uses `history[-1]` in its `update()` method. The test for a reversible chain is whether its plot of $P(X_1\\mid X_0)$ is symmetric about the diagonal.\n", "\n", "Here is an example of a reversible (and therefore stationary) Markov chain:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "solution2": "shown" }, "outputs": [], "source": [ "class ReversibleMarkovExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return np.fmod(history[-1] + 0.2 * gen.normal() + 1, 1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "solution2": "shown" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ReversibleMarkovExample().plot_conditionals(which=(1, 2, 4, 8))" ] }, { "cell_type": "markdown", "metadata": { "solution2": "shown" }, "source": [ "Note that we can use the diagonal symmetry of the first plot to confirm that this is a reversible chain.\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# Your solution here..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Custom Markov Chains" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Metropolis-Hastings-Green (MHG) algorithm is a general approach to designing a custom Markov chain that has a specified target probability density, $\\tilde{P}(X_n)$. All practical algorithms are special cases of MHG:\n", " - Metropolis-Hastings-Green\n", " - Metropolis-Hastings\n", " - Metropolis\n", " - Gibbs\n", " - Hamiltonian\n", " \n", "The simpler Metropolis-Hastings (MH) algorithm contains the essential ideas so we will focus on that.\n", "\n", "The history of using Markov chains for practical inference is intimately connected with physics: many of the pioneers were physicists motivated by physics problems, including [Metropolis](https://en.wikipedia.org/wiki/Nicholas_Metropolis) and [Gibbs](https://en.wikipedia.org/wiki/Josiah_Willard_Gibbs), and the Hamiltonian method derives from classical mechanics.\n", "\n", "See this [blog post](http://twiecki.github.io/blog/2014/01/02/visualizing-mcmc/) for helpful animations comparing some of these methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metropolis-Hastings Updates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MH algorithm relies on a **proposal distribution** $Q(X_{n+1}\\mid X_n)$ that is easier to sample from than the target distribution $\\tilde{P}(X_{n+1}\\mid X_n)$. (If you knew how to sample $P$ directly, you would not need MCMC!)\n", "\n", "We often use a multivariate Gaussian for $Q$ since it is easy to sample from. Any proposal distribution is valid, but choosing a $Q$ \"closer\" to $P$ generally reaches the desired equilibrium faster.\n", "\n", "The proposal distribution can either be used to update to the current state (\"random walk\") or to generate a new state:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def sample_proposal(x0, gen, mu, C, mode):\n", " sample = gen.multivariate_normal(mu, C)\n", " return x0 + sample if mode == 'random_walk' else sample" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_proposals(n=50, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " mu = np.zeros(2)\n", " C = np.diag((.3, .1))\n", " for xy0 in np.array([-3, -1]), np.array([3, 1]):\n", " xy = np.array([sample_proposal(xy0, gen, mu, C, 'random_walk') for i in range(n)])\n", " plt.scatter(*xy.T, label='random_walk')\n", " xy = np.array([sample_proposal(xy0, gen, mu, C, 'independent') for i in range(n)])\n", " plt.scatter(*xy.T, label='independent')\n", " plt.scatter(*xy0, marker='+', s=300, c='k')\n", " \n", "plot_proposals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During each update we evaluate a proposed move to $x_{n+1}$ by calculating the **Hastings ratio**,\n", "\n", "$$ \\Large\n", "r(x_{n+1}, x_n) = \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)}\\, \\frac{Q(x_n\\mid x_{n+1})}{Q(x_{n+1}\\mid x_n)} \\; ,\n", "$$\n", "\n", "where $\\tilde{P}$ is the desired equilibrium distribution. Since $\\tilde{P}$ only appears in a ratio, it does not need to be normalized: we saw earlier how this freedom is very useful for performing Bayesian inference, where the normalization is generally not calculable.\n", "\n", "In general, the Hastings ratio is $\\ge 0$ but it can otherwise be arbitrarily large. We always accept a proposed move when $r(x_{n+1}, x_n) \\ge 1$. Otherwise, we accept it with a probability of $0\\le r(x_{n+1}, x_n) < 1$. When a proposed move is rejected, the update returns the original value (so repetitions are possible and quite normal).\n", "\n", "In practice, we work with\n", "\n", "$$ \\Large\n", "\\log r(x_{n+1}, x_n) = \\log \\tilde{P}(x_{n+1}) - \\log \\tilde{P}(x_n)\n", "+ \\log Q(x_n\\mid x_{n+1}) - \\log Q(x_{n+1}\\mid x_n)\n", "$$\n", "\n", "rather than $r(x_{n+1}, x_n)$ in order to minimize the effects of round-off errors.\n", "\n", "We can now build a simple custom Markov chain for an arbitrary target equilibrium distribution:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "class MetropolisHastings(StochasticProcess):\n", "\n", " def __init__(self, x0, Qrms, logP, mode, seed=123):\n", " super().__init__(seed)\n", " self.x0 = np.asarray(x0)\n", " self.Q = scipy.stats.multivariate_normal(\n", " mean=np.zeros_like(x0), cov=np.diag(Qrms ** 2 * np.ones_like(x0)))\n", " self.logP = logP\n", " self.mode = mode\n", " \n", " def initial(self, gen):\n", " # Start from the origin.\n", " return self.x0\n", " \n", " def update(self, history, gen):\n", " x0 = history[-1]\n", " # Sample the proposal distribution Q to generate x1 and calculate\n", " # the log of the proposal ratio.\n", " sample = self.Q.rvs(random_state=gen)\n", " if self.mode == 'random_walk':\n", " x1 = x0 + sample\n", " log_Q_ratio = 0. # self.Q.logpdf(x0-x1) - self.Q.logpdf(x1-x0)\n", " else:\n", " x1 = sample\n", " log_Q_ratio = self.Q.logpdf(x0) - self.Q.logpdf(x1)\n", " # Calculate log of the Hastings ratio.\n", " log_ratio = self.logP(x1) - self.logP(x0) + log_Q_ratio\n", " # Accept x1 or keep x0?\n", " if log_ratio >= 0:\n", " return x1\n", " else:\n", " accept_prob = np.exp(log_ratio)\n", " return x1 if gen.uniform() < accept_prob else x0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**EXERCISE:** Define the un-normalized PDF for samples that are uniformly distributed within a (hyper)cube spanning $[-1,+1]$ along each axis:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def logP(x):\n", " return 1. if np.max(np.abs(x)) < 1 else -np.inf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate samples in 2D using a 2D Gaussian with zero mean and unit variance for the proposal distribution $Q$. Use the following utiliity function to make a scatter plot of the results using:\n", " - color to indicate the last position $n$ in the chain,\n", " - a superimposed plus ($+$) to indicate samples repeated twice,\n", " - a superimposed asterisk ($\\ast$) to indicate samples repeated three or more times,\n", " - a larger circle to indicate the initial position, and\n", " - a dashed box showing the boundary of the target (square) distribution." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def plot_square(xy):\n", " _, ax = plt.subplots(figsize=(8, 8))\n", " xy_unique, xy_counts = np.unique(xy, axis=0, return_counts=True)\n", " repeated = xy_counts > np.arange(3).reshape(-1, 1)\n", " ax.scatter(*xy.T, s=100, c=np.arange(len(xy)), cmap='gist_rainbow', lw=0)\n", " ax.scatter(*xy[0], s=400, marker='o', edgecolors='k', facecolors='none', lw=2)\n", " ax.scatter(*xy_unique[repeated[1]].T, marker='+', s=30, c='w', lw=1, zorder=10)\n", " ax.scatter(*xy_unique[repeated[2]].T, marker='x', s=30, c='w', lw=1, zorder=10)\n", " ax.set_title('Chain has {} / {} unique samples with {} repeated'\n", " .format(len(xy_unique), len(xy), np.count_nonzero(repeated[1])), fontsize='x-large')\n", " ax.set_xlim(-1.1, 1.1); ax.set_ylim(-1.1, 1.1)\n", " ax.add_artist(plt.Rectangle([-1,-1], 2, 2, fc='none', ec='k', ls='--', lw=1))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([0,0], 1., logP, 'random_walk').run(500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the unique points in the sample do cover the square uniformly and there is no obvious imprint of the Gaussian proposal distribution. However, there are also many repetitions and, more generally, successive points are highly correlated with each other.\n", "\n", "The example above worked out reasonably well, but there are many pitfalls with the MH algorithm, some obvious and others more subtle:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([0,0], 0.3, logP, 'independent').run(500))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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+jXk85jat9X1h26dgAsEczIXESzhBPYYLMEFlKea9MCVO2ri01tMwPZXvw9TEPiDyC/JWJ2/zMc3Cj2Oa9EPudPa/CfPePBk4yekUFs0JmKb/94APMTWw0P/mDFL/Ht2AuYf5HqaMN2MuPCI4rVpjMe+JtzD/8w3AMVrrgNb6I0zAvQxzcTMDuFVrHXV0PW1Gs3sTWKu1DtViF2Iuyl6Jsc8GTHkfwFzYtYZkPhsxObeJjsQ8lfAZpiXwGSJ77IPpiDkf8+jo85jXDa11JeZCphDzf5lDw8UeJPiucNLcggnUDyY6ntMadBimxeZTzAXu7cmWd1th2XZrt+IIIdqL03rxN631I+2dl5ZQHWCY0nSj2nFIYxGb1LSFEEKITkKCthBCCNFJSPO4EEII0UlITVsIIYToJCRoCyGEEJ1Eh35Oe9268pS33RcW5rBpU0tGlOwYtpVygJSlo9pWyrKtlAOkLB1VqstSVJQfcxCitKtpezzxhufuPLaVcoCUpaPaVsqyrZQDpCwdVVuWJe2CthBCCNFZSdAWQgghOgkJ2kIIIUQnIUFbCCGE6CQkaAshhBCdhARtIYQQopPo0M9pCyGEEB3R2rVr+eabr6isrGT77bvRs+eO9O7dB8uK+Yh1SkjQFkIIIZKwatVKHnvsYWbOfJpffvm5yfaePbfj+ONP4swzz2bXXXdvlTxI0BZCCCHiCAQC3HffVP7v/26gtrYWgNzcPPr334uuXbtSW1vNZ599xtq1a5g27R5mzLiP88+/iCuv/AdZWVkpzYsEbSGEECKGiooKTj/9NN55ZwEAxx47lnPOmcSwYcNxuUy3sKKifNauLeOzzz7loYdm8OyzTzF16h0sWPAmTz89i549e6YsP9IRTQghhIjC5/Px17+eyjvvLKCoqCdPPfUcDz/8OMOHH1QfsEMsy2LgwEHcddd9zJ37GjvvvAtffvk548aNpaxsS8ryJEFbCCGEiOKOO25h0aK32W677ZkzZz6HHnpEUvsNGbI/L7/8Onvs0Y+vv/6Kf/7zHynLkwRtIYQQopHvvvuWO+64BYBp0x5i1113a5Ima+qj5E+6Gq69AwKBiG1FRUU8/PATZGZm8uST/2XRordTki8J2kIIIUQjDzxwP36/n9NO+wsHHjgiYlveJdfRY7vB5F93B1kvvAI3TKVHr/3ocupFEen69VNceOGlAEybdk9K8tWioK2UOkAptSDK+jFKqY+VUu8rpSY467KVUs8rpd5RSr2ilCpqybmFEEKI1uDz+Zg58xkAJk48P2Jb/qSryXryBSw7GLHewibzzXfoevQZEevPPHMCXq+X1157lTVr1rQ4b80O2kqpK4EHgKxG673A7cARwEhgolJqe+A84Aut9UHAY8A1zT23EEII0Vq0/pqKinJ23XU39tyzf8MGn4/MF+ZhAezYC0YMMeuLnRr2iCF41q6Fn36t36WoqIihQ4dj2zaffrqkxXlrSU37B+CEKOt/D3yvtd6ktfYBi4CDgBHAq06aecBhLTi3EEIIEV9lNVTXbPVuy5Z9CcA++wyIWJ93+Y1Y2Gahbx+YdS+MPABKLjK/Z92L1bcPXSdfG7HfgAEDAfjyy8+bUYhIzQ7aWuvngboom7oA4f3by4GCRutD64QQQojUCQbJevQ5CkeeTNEuB1LUdxhdjz2DzBfnJ32I0CNaPXpE3sX1LPu2YWHRYhh3Icy82yzPvNssL1qM65dVEft1797DOW5ZMwrUiG3bzf7p16/fzv369fug0bp9+vXr90rY8u39+vU7qV+/frP69eu3v7OuoF+/fl8mOn5dnd9OtdmzZ9tA/c+0adNs27Yj1o0ePdq2bdsePXp0xHrbtu1p06ZFrJs9e7a9cuXKiHUTJkywbdu2Bw0aVL+uV69etm3bdnFxcUTaxYsX24sXL45YV1xcbNu2bffq1at+3aBBg2zbtu0JEyZEpF25cqWUScokZZIySZmmTbPtQCCyTOTYNrvZo8lpVpmUUk3LhNu22c1+q/g/dlTFd9r2rodErLr++uttwL7qqqui79NUzLhomf9b8yildgae1loPDVvnBb4CDgAqgPeBscCpQL7WukQpdSowUmt9Xrzjr1tX3vzMxVBXV47Xm5/qw7a5oqJ81q0rb+9spISUpWPaVsqyrZQDpCyJZP13FvmXXx83zeZn76Nu1NC4aRYufItx445j8OD9mDfvjfr17qVfUXjEeOqnBBl5gKlhF3WDdRth3IXYCz+k/PYSascfV7/fhAln8NJLs7jjjns47bS/JCxHUVF+zFlHUvbIl1LqNKXURK11HXAZMB8TsB/SWq8E7gP6K6UWAROB0lSde2v06dOnPU4rhBCilWU/9EwSaZ5OmCZ0L/vLLz9ny5bN9esDA/ck2L27WRgxpKFJHBqayg85MCJg+/1+PvjgPQAGDNg32aLE1KKxx7XWy4Ghzt9Phq2fA8xplLYKGNeS8wkhhBBRVddE3nOOwbvky4RpCgu7cdBBI3nnnYU888yTEY99bfz4RbrvfTSuFSvhhPNh0WJKSkooWfgh9skXs/HO4ohjzZ8/jzVrfmO33Xbn97/fc+vL1YgMriKEEKLzc7uTSma7kwt7Z501ETBDmW7YsKFhQ14eG356h/IJ4wl8/RN2VhalpaVUXnAW65+9l2Cv7eqTVldX869/lQBwxhlnNxmvvDnSLmhPmDChvbMghBAi1TK8+IYNSpis7g8HJHW4o48+luHDD2L9+vVceulkAo2GKa05dzwbv36d9T+/D0DVPy+M2G7bNv/85z/4/vvv6NdPcfrpZydZkPjSLmhPnz69vbMghBCiFVRPOC3udtvlovqcU5M6lsvl4vbbp9KlSwGvvvoK5557NhUVFVHTFhdHNon7fD6uueYqHn30QTIyMrjrrvtSNq922gXtwYMHt3cWhBBCtALf6EOpuvisqNtsl4uKf1+Ff2D/qNsJBMiY9yY5t00j+95HcP+4gp133oUnn3yOvLx8XnppFqNGHcj8+fOa1LpLSkrMOWyb995bxJFHHsyMGffj9XqZPv0RBg0akrIytuiRr9bWGo989ezZhbVrU/CAezuTRz86JilLx7OtlAOkLMnyvruY7IeewbP4c3C5qDtof6rPPgX/nnuQ+cobeD79EjxufAcPp274/njfXET+pcW4VzeMDW5bFr6jDqb87n+x7NefmTx5IsuWfQHATjvtzKGHHsbeew+goKArl19+IaecchoLF77FN998XZ9m6tT7GTr0wK3Of7xHviRod1Ly4e2YpCwdz7ZSDpCytIT33Y/IP/cq3GvWRaz377IT7l9XYdX5o+7nGzqYLS8+jM/v58EHp/Pgg9P4+ecVMc9TVNSTv/71TC644BJyc3Obldd4QbtFj3x1Rr169WrvLAghhGhD7mWagvGTsaqqm2zz/PRz3H0zPlhCxutvwxGjOO+8C5g48Tw++OA9PvlkCV9/vYyqqipeeWUOU6Zcw8CBgxgx4g9kZGS0VlHSL2ivWrVqm7lSFUIIkVjOXQ9EDdjJynr6JXxHjALA++tKRuYWMPzsiZCTA8BRR43issuuTEVWE0q7jmihDgNCCCHSQE0tmS+/3qJDuNZtIOfm2+m++5503+9ACo84hh67KLoeOQbXip9ZsqTlU24mnZc2O1MHUVraLqOnCiGEaAdWeQWWL9qElMlz/fwduTffiitsli7LtvF++indhh/MxFOSe4wsFdIuaAshhEgfdkEXgrk5LTiCH9fqXyJXFU+p/9Py1TLj2cRjnqeKBG0hhBDbrgwvtSce2+zdg3kemnTlLvl7k3SulSubfY6tkXZBe/Hixe2dBSGEEG2o6uIJBHt0i7ndv1tfAjtEPllku1zUjD0y6e7a3rfebkkWk5Z2QVsIIUR6Ce7Ym80vPULd4AER6223m9oxR7D51afYuHg+W564h4prLqHihqvY+OErlD9wK9Q5o58VTwF7i/mBhr+Lp7CSPMhOzTClicjgKp2UDLLQMUlZOp5tpRwgZUkFzxdf41n8GZ6vl+H+/jusLZuxi3pQM+5EasccC42ese7ebwCuzRsiD2JvAaugfnEOdQz9eQWkaHxxGVxFCCGEAAJ9+5B31RS8iyMf08p4cwF1901nyzNPYFVUknfFtWS8+z7U1SY85liqWduKA6qEk6AthBAibeRffHmTgB3i/fwLCsafjufzb7D8oWFNLcANhE0SUvLvsL2cu8wpmCs7GWl3T7vxFGpCCCHSg2v5CjJeeTVuGu8nn2L5Gz3XXTwFU8d1QmbpfzDBPAPITH1G40i7oC0jogkhRHrKeONNrKT6cQUjF0uupKHG7QWygRzAi+3NZNo/rk1xTmNLu6Ddu3fv9s6CEEKIdmDV+lJ0JBP47axMyu6/hYn/ui5Fx00s7YL26tWr2zsLQggh2oG//55JprSg+Eqw15sfaPi7+EoChQVUXH0ZGz5ZgG/MUVhWzM7eKZd2QVsIIUR6qvvDCPy77pJESgtKbwKrh/mBhr9Lb6L64vOovngSdpwBW1pL2gXtQYMGtXcWhBBCtAfLovzO27Bzoo9FbmdlEszIhaYDlzakycik+vxzWimDiaVd0G7LKdSEEEJ0LP4D9mPT3BepPeYobLcbMEOW1h5xGJtfep6yR6djN358q+Qmk85yUXb/HU2OOXr06FbPd0jaBe2JEye2dxaEEEK0o8Bee1L2yANs+GopG99dwIZlSyl7/BH8+w6k7tCRbHrtJer2HYjt3Ku2r7uZur33YvPcmfhGH9XkeHPmzGmzvKdd0J4xY0Z7Z0EIIUQHYBcWEthjd+zukfemA/vsxeb5L7B+zY+s+/lr1q/5kc1vzMG/X/Tbq2PGjGmL7AJpGLSFEEKIpCUxnvjcuXPbICOGBG0hhBCik0i7scdXttFE5UIIITo31/LlZD/xBO5vv8POzaV29LH4jjwSnA5s7SHtgvaSJUsYOnRUe2dDCCFEB5Zz083k3HYbVrBhSNOs557D/zvFliefJLjDDvXrbdtus2lG0655fOzYse2dBSGEEB1Y1mOPkXvLLREBO8TzjabgT6dB/SxgMH369DbLW9oFbSGEECKmYJCcu6fGTeLRmox5DbOFTZo0qbVzVU+CthBCCOHwfP457hUrEqbLnNt2z2aHS7ugPW3atPbOghBCiA7KqqhIabpUS7ugLSOiCSGEiCWwyy5NhzGNlm7X3er/nj17dmtmKULaBe22nEJNCCFE5xLs0wffIYckTFfz17/U/z148ODWzFKEtAvaQgghRDyVJcUEu3aNub3q/PMJ7LFH/XKfPn3aIltAGj6nLYQQQsTj/uEHgr164dq8OWJ9oGdPqi+6kOp2vM2adkG7LadQE0II0blkPfQw+VOmRN/oclF7VNNZvtpS2jWPt+UUakIIIToP15o15F17bczt7t9+I++aptsnTJjQmtmKkHZBuy2nUBNCCNF5ZD3+BFZdnVlw25ATMD8uuz5Nxv/+h6vRHBYyIlorassp1IQQQnQenmXLTIDu6YOdamB7n/nZqQaKfGDZWIEAbv1txH5t2Xu82fe0lVIu4F5gAFALnKO1/t7ZNhC4Iyz5UOCPwEfAt8CXzvoXtNZ3NjcPQgghRKrYHgt610KGHbnBBeQHwBuE1ZmQmRGx+ZNPPmmzPLakI9ofgSyt9TCl1FDgVuA4AK31UmAUgFJqHLBKa/2qUuow4Cmt9YUty7YQQgiRYgX+pgE7XJZNcPss6oYMabs8NdKS5vERwKsAWusPgCalUErlAqXARc6qwcAgpdRCpdRMpVSvFpy/WWw7zj9ECCFE2vJ++1HCNHavbMjMjFjXq1fbhbKW1LS7AFvClgNKKY/W2h+27mxgptZ6vbP8DbBEa/26Umo8cDdwUqwTFBbm4PGkdrLx6dOnbzNDmRYV5bd3FlJGytIxbStl2VbKAVKWVlNXB2t+TZjM7a9sku9Vq1a1Vq6aaEnQLgPCc+5qFLABxhMZlN8Eqpy/XwCui3eCTZuq4m1ulkmTJnH88X9K+XHbWlFRfptNut7apCwd07ZSlm2lHCBlaW09snKwauLHnUBeARsb5fuee25l8uTLU5aPeBczLWkefxc4BsC5p/1F+EalVAGQqbX+JWz1A8CJzt8I583mAAAgAElEQVSHAktacH4hhBAiZWoPPT6JNCc0WVdaWtoa2YmqJTXtF4DDlVLvARZwplLqMuB7rfVsoB+wvNE+U4CHlFLnA5XAOS04vxBCCJEyVaddSObrs7Bqq6NuD+Z3pfrY8bi//wbPN5/i2rgWOyMzatrW0uygrbUOAuc2Wv1N2PaPMT3Mw/f5CTi4uedMhbacQk0IIUTnEdhtT7bc9CRdrj0TV1nkuOPBrj3w/W4YhSeNxGVXN2mnzr/qdCquvRs7r0ur5jHtxh5vy4fghRBCdC51BxzKhpe+Jmv+s3g//wAsF3X9BpIzYypZr82BLJoE7MXbQdbrL+DasIYt014Gd2o7UIdLuxHR2nIKNSGEEJ1Qdi41fzyT8n9Oo/za+/B++inuX1eAF3MzOIaMT98jY9H8Vs1a2gVtIYQQIlnW5o1kzptlFmJUoIesafg7a84TrZofCdpCCCFEDO7l32PV1kA2pqadgGvd6lbNT9rd027LKdSEEEJ0YoEA+TeeA0U0NItnADYQvYM5we7btWqW0q6m3ZZTqAkhhOi8uh/bF89vyyPvY1uYyJnTsKo4rMN4zejWHbwr7YK29B4XQgiRSN7NF+OqKoNeO8LgEWbl5GLze/AI6L2j6UkOlBSY33V7DcH3h2NaNV9pF7Tbcgo1IYQQnVPm/KfNH737wl2zYL+RcEGJ+X3XLLPeiaC9V0LtiCPZcvfz4Gndu85pF7SFEEKIRCxfjfljySK4ZBzcMdMs3zHTLC9ZBBbUHHEcq4NQdudM7C6FrZ6vtAvabTmFmhBCiA5o4zoKzjySHkMK6TGoCz0GF1A4eh/cn37QkMZybmRPLobHFkC3IrPcrcgsO03lVac0Hhi0daVd0G7LKdSEEEJ0LK7l39HjiD3I+Px9LDuAZYGFjWf1cgrPPoKsJ+8HILB9X7PDPaXw11GwcZ1Z3rjOLN9Tim25CAwczqBBg9ou/212pg6ipKSkvbMghBCinRSOH4llB01Hsv2dDmaXmlqzdcAI8p68G6qrKfv7vdhgOp2FmsShoal88Ahqh5tOZ0uWtN2ElWkXtNtyCjUhhBAdh3vJu1jVFWZhh74wbRYMHQmXlpjf02Zh7diX/GsnEhg4nKo/XYK9agVcdAJ8vBCmlsDHC7EvOwF74woyP5lLj6O6MLGnm7zbL2qTMqTd4CpCCCG2Pa5fVpA5fy5WVRX+PX6H7/Cjm/Tkznnkjvpb1Xy0CM4bB/c5Hczum2mWP1pERp7pUFZ13nXUHnkqXf75Z9yZLniwFHLA+nKR2cc51ox1Qaa/9gjeZe+z6YGPW7ecrXp0IYQQojVVVZI/+Uy6jRhAXunfyb35egomjqfb0P5k/G9eRFLLX9ewcGkxPLsAujsdzLoXmeVLi6G6iuypd+H66Scy35+NZ8P3WJ4gltvpn7bdjjDQaVqf6Dy7PXAEHn8V2Y/+q1WLm3ZBe/Hixe2dBSGEEClScM5pZM1+HisYjFjvXrOaLhPH433v7fp1NaNPxbadhdtL4eRRsMHpYLZhnVm+vRRXeS151xXT7Zh9yX38xqYn7dUXbp4Fg0fCxBJGjhxplnv1JeeFqa1SzpC0C9pCCCG2Dd5FC8h4562Y2y2/n9xbbjALdXVYdR7q27T3H9HQJA4NTeX7jYCNzv49g02OCcDSRTBlHPzHNK2/MWumWV66CKumMgUliy3tgvaQIUPaOwtCCCFSIOu5JxOm8X78Ad63XqfbgYPocu5ZWOttM+HHrytg0gnwwUK4vcT8nngCfLsCbDdk2BHji0eYWAzTFkChaVp3dysyy6Gm8lYkHdGEEEJ0Sq61axInAvIvmoh73Xqz4APWAv5fYOUvpuJ9WykEgPmLoNKZNDtelXZ6KSxZYGrahUWsW7eOomvGwZKF2Nn5zS5PMtKupi2EEGLbEOyZ3DSY9QE7xI8J3KuA34CVwGp3Q8AGE9wDMQ44cIQJ2FNM0/q4caap3B4wgqqTLt6qMmyttAvaxcWt33whhBCi9dWcdFrCNMG8LvETBHBuc9thP0DQgo1W9H1Wr4ArToAlC2F6CQsXLsT+2wn4PdlUj78y+QI0Q9oFbRkRTQghtg11w0fiO+jgmNttj4dgaMzweDKBgiB0C0JhEPIC4LFhlQU1UdKv+QWWLsK2wZ5WyrRdvFTtsi+bb3i+2WVJVtoF7d69e7d3FoQQQqSCZVF7yDHYlqe+ghxiezMov+U+/HsPjH+MXCAbCLWMW0AGkB8Etw3aRSB7J+zM7PpdAtvvTPn5t7D+1TLWv1rGxB99VE1q3eezQ9KuI9rq1avbOwtCCCFSIGPObPL/McVZcpkgC2BbWLV+sqdPp/Kaa8l6MUYNOAvwxji4BXaOTe2o4ym/axpWXTXuVT9iZ2QR6Pv7hlnAAMuyWLu2LFXFiivtatpCCCE6icoKrC2baBgRJVLuLf8XtmRBwGV+ghZg4f30E6zqGnxDh0c/fkb801sWBHfqCZmZ2Hld8fcbRGDnPSMCdltLu5p2W06hJoQQYutlzHuRnIfvxbvEzG8d6FqIZbmwaqoJdutBzXEn4xt2MJ6vv0p4rKz/PoL30ygjYbpIqtrqXfrRVua+daVd0F6yZAnr1pW3dzaEEEJEkXPb9eTec3PEOvfmTQ1/r/yZ3HtvIfuJB8FlO7Xq2DzffIVVW9v8DLkSR/bRo0c3//hbKe2axydOnNjeWRBCCBGFZ8mHTQJ2LK4tm7CzgzTpgdaIVRHjXnOQ2M9hh/ENHZUwzZw5cxIfKEXSLmjPmDGjvbMghBAiiuwntu772XLR0Os7BrugIPZGX4J9MzKpOeXMhPkYM2ZMwjSpknbN40IIITomz9Ktn4XRzvJgVUavMtecdDJ2hpvs5T9F37kW0xmtCMjHVGN9wBawa72U3fwAwd47JszD3LlztzrfzZV2NW0hhBAdlGfr65E1J55E3d77RKwL5uZRNflCyu+6h5ozzom9cw6wO9ADM8CKF/Pcdm+oO3oIvkOO2ur8tLa0C9orV65s7ywIIYSIwjfikK3fZ/QJbH5jIZvmv0HZ3fex5cFH2fjFV1QWXwceD/6Bg6i84h9Nd7SAfsR8Tjvjm/fJfax0q/PT2tIuaC9ZsqS9syCEECKKmr9MwPbGGu2kKdvlxt9vTwD8+w6i9pRT8Y0Zi50XOdNW1eVT2PLg49TtP7R+XXD3bgmf087632OQxPzYdoznyFtD2gXtsWPHtncWhBBCRBHYZQ/Kb56WXOC2waoNkD3trqSO7Tt2LJtnv8b6735l/bKf8B13aMJ9XFVleL9J/Jz29OnTk8pDKqRd0BZCCNFx1Y45iU1z36P6LxOxvZlNJt/CxjyqVWf+znruKQgk8exWaPf8Ltjdu0MwyX0C/oRJJk2alPT5W0qCthBCiA4lsLuiouQWgrmFJjiHfnzO77B46yrbglW+9eN++/cYnDCN7fHi33WfmNtdG1bjWvfLVp+7JdIuaE+bNq29syCEECIJdrfuidNkZmLn5m31sWsOG4+dkR03Te2wMdiF2zVZn3f/JXT/0/Z0n6jofm5/APJvOwv8iWvlLZV2QVtGRBNCiM6h5viTE6apHXMCbEXntRA7vxvlF92D7Y7+mJm/165UnPN/TdYXXjKU7P89hMtXVb9u9p6Q9e5zdDtv71YP3GkXtK12nJ1FCCFE8mr+dDqB3jvE3G7n5FJ17iXNPn7tH05i879eoXb/Y7CdMcaD+d2oOuESNt/8RpNads5TN+L5pdEkJWcWM9ip6Ls3riT/3guanZ9kyIhoQgghOiS7sBtbnp5Nlwl/xqMjg2Vgu16UT32IgPp9i87h33MoZXs+DbVVWDVV2HldIUbtO2t+lGFWzyyhz1ml2AeZxcz3XqD8ovtblKd4JGgLIYTosAK77M6m1z/Au2gBGW+/CYEAdfsOwXfUmGaNoBZTZg52Zk7cJK7yjQkPY9VVQ00VZMU/VnM1u8RKKRdwLzAAM4LrOVrr78O23wUMB0LzYB6HGXvmSSAbWAWcqbWuog215RRqQgghUqNuxCjqRoxK6TGtzWvIWvQMrg2/Yud3p2b4OILb7Zp4xzOL4cyS+sX6wVUeLsF+qBQ8CUZtaYGWXKb8EcjSWg9TSg0FbsUE5pBBwJFa6/WhFU4gf1Jr/YhSagowCbi9BXnYanPmzJH5tIUQIs3lPHMdOXPuxArUNax77kZq/3Aa5efcGTXwBnvsiHv9z/BwqfkBeNtmYi+L6XuYRTuvMLUtAI20pCPaCOBVAK31B8CQ0AanFr4HMF0p9a5S6qzG+wDzgMNacP5macsp1IQQQnQ82S/eSu6Lt0QEbADLtsla+AR5D0Tv3FZ58lVEG7E0FLABqo+ekMqsNtGSoN0F2BK2HFBKhS4vcoG7gT8DRwHnK6X2abRPORBnotPW0ZZTqAkhhOhgaqvImXtn3CRZbz+Ja+3yprse+hdqh58YGbgfLmHwp+ZPX/+DqPrTNanLaxQtqcOXYWYgDXFprUMPqFUBd4buVyul3sTc+w7tU+383hzvBIWFOXg8CWY4b4aiovzEiTqBbaUcIGXpqLaVsmwr5QApS4stmAeVcUMPlh2k+2dz4LQos4P95zn431PwUDGs/gkevYFPKoBL7yXj+PMoap1c12tJ0H4XGAM869zT/iJsWz/gaaXUIExtfgTwqLPPMcAjwNHAO/FOsGlT6/RR2xbuaRcV5W8T5QApS0e1rZRlWykHSFlSIWvVSpK5VKj6bRWVsfI3cDTcFdapuWcX1o34M6SoPPEuZlrSPP4CUKOUeg/TmexSpdRlSqmxWuuvgSeAD4CFwGNa62XADcCpSql3gWHA1Bacv1nacgo1IYQQHUuwe+zBWpqTDqBXr17Nzc5Wa3ZNW2sdBM5ttPqbsO03ATc12mcN5h53u5k+fTrHH/+n9syCEEKIduIbcBiBbr1xb1wVM43tzaRmxKlJH3PVqlVt1mqQdsOYtuUUakIIIToYt4fK067HjjOkddVxl2N3STxZSUhJSUkKMpactAvaQggh0lvt8HGUT36AQKMm8GBeNyrG/4uqE6ds1fFKS0tTmb24ZBhTIYQQaad2+Dhqh52Ad8nLZH77JvjKCPRW+HcZAAF/zPHH21vHzFUrmj17dntnQQghRHsLBsiZ/y9y3r4Xq855UmkZEIRAVjeqD74Af78DsT2Z+HsNBFfqHz9ujrQL2oMHD27vLAghhGhnec9fQvaHjzbd4AY3G8l75zpYZFYFCnakethkqoedH/VYixcvbsWcRkq7e9p9+vRp7ywIIYRoR+7Vy6IHbAvIwkxtFdZPzb3lF/JenULuK1e0UQ5jS7ugLYQQIj1Z1ZvJWvwIeS9eGL2dOYO4UTHnw2l4Vi1tsn7IkCFRUreOtGseF0II0YkFq7GC5diuruCKMwWmbZP59QtkLX4Az29LsYJ+8Ndh+QNgA5mYIF3n/AAkcds6a/HDVIyNP3Z5a0q7oD1hQuvOwCKEECIJNb+SUf4+tuWlLmcouHLjJnfXfEnOulvJLJ+DZfuwXbnUFJxMVY/LCGb0jUxs2+S/NJGsL5+JciAggAncFiZw46yL/eh2w+7rdeJErSjtgvb06dO3mbF7hRCis3H5fiHvtyuh/FUKCAAQdBVQU3gGldv9Eyxvk328le9QsGIclt0wH4UVrCR708Nkls1h8y7zCGSq+m1ZSx6IHrDBBGY34A9b5220HI83p8mq4uLiJHduubS7py29x4UQon246lbTdfmRZJa/DE7ABnAFt5Cz4U66/HI6TSastuvI//XsiIAdcczAevJXnhexLvvjafEzYhEZ/UKBPJi4DLV7HtdknYyI1oo++eST9s6CEEKkpZx1N+Gu+zXm9szyuWRUvBaxLqNsLm7/b3GP661ejKfaTGptVazBs+HbxJlpHP0sEta2AwU7ULP3uCbre/funfh8KZJ2QVsIIUQ7CFaTuSVGk3WYrE0PRyx7q5OraHmcdFYzZ3K0Q9HQj7nf3Uig606UH30H2W89QM7cm8hY+goETWvB6tWrm3XO5ki7e9ptOYWaEEIIw+VfiytYkTCd2/ejSe/7iewtD5FZOcs0XdvEb762TDgL5m2Hv3BXPJt+jH+isMBs22CFjh0ERhfDy6VgmWSVf7gC71ef0fXWkyIOEei2I+Vn3pOwTKmUdjXtVatiT8cmhBCiddiuvCTT5ZO16X66Ld+XnE134g78YiKVG1PNjNLD28aFL/dgs2BZ1AxJ8JSQjbml7gJyweoO9Aa2A/KAsSVmux8sP+QsuI/ML15rchj3xl8ouOtkBvVXTba1lrQL2m3ZYUAIIYRhe7rjyx2VMJ0/e0/y112JFa1aHeow1oivyxiCGTvVL1fvdy6+HYfHyAimNu0BCoEc55iWs67ASRcWHV2B2C0EVl0NS07eLXaBUiztgnZbTqEmhBCiQVWPy7DjhJ2ApxfuugSdyBr1/K7L2pfy3ndFpnG58e10FFTRcI/axgyiUuP85Eceh1HFUGqbH4DpNjxgw9jEj3NNfOgVrLJ1CdOlQtoFbSGEEO2jLm8U5X3uwbaymmwLeHeibMfHyah5P/GBbGA1BD7Znpo1f8Z2FzZN4/aAD6gAtjg/lUAt5rnsxj26FpRCsWV+AP5pwSQLZieu6M1YAa7ytgnaadcRTQghRPup7ToeX95R9KibSc36D8HKwJd/JLVdxmAFNiZ3kApgNrj5jfyPL8e9+nsqT/y/iCT+Ln2j7wtmCNNEQqOlVWOCfwLB/KIkDtpyaRe023IKNSGEEE3Znu7Q6wrKsyNHp7Td3Qm6e+IKrI1/gEaxPWfhfdTuezz+XYfi2vwb+fdPIOOrheb+dDIBurG3SsxvC2zLhVWReNQVu0vbBG1pHhdCCNExWB6qC/6aON2XTVdlL3oAaioo+M8YE7AByog+YEptguMvKAUb7GrYNGE+dbscEDOpnZHNyndeSZznFEm7oN2WU6gJIYTYOtWFF+PP2Ct2gm+An52/c4F9gZGQ0fV/5H5QimdV2IQeNqZWXobphBaAYHYPAlbfxE3eW6By2PUEdjmALRc/R+2+Y7CtyOfNAj12ZstFz7FkU7IDl7dc2jWPCyGE6LhsdwGbd3yF3PXXkVn+DK6g04ReDnwOfOokHATsQ33V08UmcpgGpwAvYXqIh4R6jHvAqt6IXZiB/asLa6dg1ChoV0P1budRPeZis5xTQNnkJ3Ct+YHML+ZDXS2BHfrj638YuFyM7dmFtWvLUv5aRCNBWwghRIdiu7tSsd1tVBRdh8f3HXmPTcS7TDeMYrYnMDDGzn2A44DwEVMtIAtwgUUQ92ZnkK0fwe4GVgHgAdvvxp+9D+V/nUFgu364N31L1rJHcZf9hJ3RhZo9TqT60PPASmIOz1aSdkG7LadQE0II0QKuPPxZ+1I9+Cq8X55l1lmYGnY8fYAdgNDcJJlEvxlcB9Ya8OUPp/wvDxHs6gxzbdvkvn0lOZ/fH5E865snqdtuMFtGz8TO7tHcUrVI2t3TlhHRhBCi47ICG3D7vo14/Kt28ElUHnWVWdgOM4pZIqGRRUNDoMbh/eE9rNqGUc+yl9zWJGDXp12zhO4P9iP7/Zvq102blmAq0BRKu6DdllOoCSGESI6nejFdVp5E9x92o9vyIXT/YXe6rBqPu9Z0Fa865mo2XrmI2n0OSe6AGc7vBAEbzMxg3q/eMAuBWnKWTjXt0D2AnkCXUEJzPMvtJ2/JDRQ+OACCQSZOnJh0OVsq7YJ2W06hJoQQIjFv5Zt0/fVoMitfqx9z3MJPZsUcCn8+HE/1hwAEdtiHykNvTO6gW7YuD1bQ9AD3/vIGrp4bYC9gR0xT+25Af8xY5aOKzYVABnj8P9H18SFYbXiPO+2CthBCiA7E9pP/23lYdvSHpy27kvzfzq9fDmTvSV1Ogkd3g1DrPoiKcSXUDDslqWz4dxoEQO76m6A7TWcTywV+B/yhBAYDOwPZ4K35Pqnjp0raBe1Bgwa1dxaEEEI4MipewR2I3wLqqfsOb9Xb9csVff6DHYzT7r0UMj95B3+/IZSfNY1A9zhDmgL+3ntSt8eBeMo+wFv7SeRGC8jGNLeHIqYb02zeHzPxCOZRsraQdkF7yZIl7Z0FIYQQDk/tF0mm+7z+b7+nP8zzwm+NElUC7wIfm8WsRQ+Dy0XZmTMIZkafzzuY05WyM6ab9GufbJogA9i9GA63zQ80/L1HMewOoxVkf3hHUuVoqbQL2m3ZYUAIIUQCVnKDg9th6dybVmH9WmMGUZkJzAfmAE8QMcSpe41puvbvNpTNV75Bzf4nY3vMcWxvNtXD/szmq94ksKN5hszla1TjD83f/WMp/M8yP9Dw94+l4IU5l4D31/e2tuTNknZBe8aMGe2dBSGEEI7avCMTprFx4cs9omE5K6zWvBFYDqyiYfCVULrM3Pq/A71/T/mZD7D+1p/Z8J9vWX/rCir+ei+BnrvXpwl6e0YewEXTe9tRjJlG0hcfLZV2QVsIIUTHEcjcG1/OwXHT+PLGEvQ23JcOdu1F3S77JTy2b9/jmq7MyCZYsD14m87pXdvz1MQZ/qGkyaq5S6Fup5GJ900BCdpCCCG2mrv2K3I3Xkv+unPI3Xg1bt+yZh+rbPsHqcvYx9RqXUREprqsoZRvN7XJPlVHXh73mIGC7akZdtpW5aOu4CB8XcOeAw/SpPbOj6VR981ZdQP584/eqvM1R9oF7ZUrV7Z3FoQQolPy1H1Aly3j6bGuK922DCWn7k6y7GfJ8d9Nt43DKFh3GASrt/q4Xt8SXJ5y8GIGNfGAneGmpmAMm3eYi+3u0mQf34BjKD/lFmxX09G4A4U7sOXCF7GzC7Y6L1t+9wQ1PU7AtjEBO5Bghzrzy7Igc/O7dJ3TujNJpl3Qlt7jQgix9bKqH6Xr5qPI9M0xA6CEasUW9R22MviIbhsGg51o3ssG3uo36LL2T7j9P0WstwiQVT2HvE1Xxdy3ZtRENv7rSyqPnULtgNHUDD6BsjOms7H0UwJ99mxWOXHnUq4ewf4iH37C3C9vfB2StSN0HWEC+vbF2FOBXiOw8nfEU/Ut1CaasLv50i5ojx07tr2zIIQQnYIr8BPZNXeRW3UFeZUX1Y9WFnsHcLt+JbfiyqTPkbfxn1jEno86q/wh3HXfxdwe7NqbqtH/oOzcJyk/5xFqDzgVvC3sFOavwUU5dAN6YZrJawG/87enL+w9C3wjYVAJczaMhKNnQX5fLAsKX44zH3gLpd0sX0IIIRKwK8ivuoDMuhewQjd1PZjm4iANNexQE7IH82iU09M6234Ial1UZvwLrOyYp/HUfoqnLv5z2hY2WeWPU9kt+r3k1pBR9hb2XmCFV2v9zo8N/LwIfhsHR80EYOh5M+HVcbB6EQAu37pWy1va1bSFEELEV1A5nqy6WQ0BOyT03LIVtpyBCdphj0ZZFuQEHqCg9sS4TeUuf3J9jFyBX5LPfEsFfeR/f2FkwA5nAcOL4fgFkF0EQFFRkVnerzgsUetIu5p2W06hJoQQnY237m0y/G8ll7hRT+/GMoKLyAo8Q43nL1G32+5uSZ0m6OqeXH6awVX7Kxmb52EFa/Bn/x6XbxOuurXxd/q2FH5aAIfMhOwi1q1bR9GicbBqIQC12yd+9ry50i5oT5w4kXXryts7G0II0SFl1T2VfOIkpr3M8j8UM2jXZQ4l4OmL278i7jFq805OPk/JClSSv/xiMjc8jxXWRTzoLmho+o+l+wjYbybMGwfHL+C7/46j6LyZMO8E7FWLqBj1dOrz62hW0FZKuYB7gQGY2/PnaK2/D9t+KRB6Sv0VrXWpUsoCfgVCPQre11r/vdk5bybLsli7tqytTyuEEJ2CK7gm+cRJtAK7gz/E2d9FZcEUumw4zyxnAjmYi4EgUA21HIY/M/FAKlvFtin47jQyypq2KLgCW8z5AzQE7lBP+ZDqFfDmCbBqEXxUws7VC03ALltB+T7/l9q8NtLcmvYfgSyt9TCl1FDgVuA4AKXUrsB44ABMkd9RSr0AVAGfaK3HtDzbQgghWkPA1Sv5xDbxA7cFePwUBP9IkG5UWRcRsAZGJKnNH0+5vYk8rsXKbvRQdDa4WY1lr8W2Gg0x2gLesjejBuyIfLswgbvR/XoA6n7Brnbux39USp9rIDD1EzYcvgAKf5eyfEbT3I5oI4BXAbTWHwDhT5P/AhyltQ5orYOYx+VrMDOQ9lFKvaWUekUppVqQbyGEEK2gNmN88onjPQGWAWSDy1tBhutNslzPUcgfKAzsB3Zka6cn98emATu0jWUUBP6cfJ6SkLXu8cSJGne6a7w5Owi9LLYMMTXrDSf/1uoBG5pf0+4CbAlbDiilPFprv9a6DljvNIffDHyqtf5WKbU98G+t9Uyl1AjgcSBum0dhYQ4eTxI3TbbC6NGjKSrKT+kx28u2Ug6QsnRU20pZtpVyQFuU5UhYNRoq5yZOGv74V7hQj/JGLAs8bk1RcH+wfzRlCW6E3+IHUa/9AUUFX0LGsCTLkMD3STySFRo0Jl6SDJuuP5jBX9rqPdbcoF1G/dTfALi01vVPxyulsoCHgHLgfGf1YsxTbmitFyml+iilLK11zNv9mzZVNTN7sc2ZM2eb6IhWVJS/TZQDpCwd1bZSlm2lHNCGZfE8SL73UjLrnonopNWkOdwG/GB7TEAGGmqo8ViroPwe1tVOIDP4Il2oSZilqo3PUulOzaAl+XSn6XQhScjaEbL7wqZFZi7t70qh9wiuOnkF61ZtBK83JfmLdwHQ3Obxd4FjAJx72vVPxzs17JeAz7TWk7TWof94MXCJk2YA8HO8gN1axoyRW+pCCBGXlU157v1s7LKM8uxbqci6jir32dhVLnOzM4CpZQfB9mVT5ppBhfdGat1/xO9ViTuoWUDVnc6fiQO2sfVjmsdS2z2J2byiNf1n94XBs6DbSOhXYn4fOIv/nN2Xru8NT1n+4mluTfsF4HCl1Pu1Dh4AACAASURBVHuYl/9MpdRlwPeYa6yRQKZSKjTlyd+B/wCPK6WOxdS4z2hJxptr7twkmnyEEEIQdPWmJnOCWciC6py/kVX5CB7fUiADX9YR1GSPA1cOYMJqYXBgzONFHnwNuMFPcmOEB6z+W1+AGHxdj6QubxjeivejbrcBy49p5g+3aRF8Mg4GmZHQGDQT3h3H4EmLWHxd24xV1qyg7XQwO7fR6m/C/o7V8nBsc84nhBCi/QXdfajqcnXM7S77J9zBH5NswzWB3u8aTF1gIF6Wxj4vXaixxm1lbuOwXGzp9wz5P04ic/O8yHN5e1Ln3YfMytdNN+rwVoM9ik0NOySzCA5ZwJjTS4DrU5e/ONJucBUhhBCtw2N/gRUajzxeE7kNZJ5W3wRd4b6DgsAYM0lHk6QuKty3g5Wb0rzanq6U9XsGd/W3ZGx6GStYhT9nT3xdR+Ou+paMdW9g1drm2fFQWb4rhQ0LTA07swhq1sE74ygtXcjVT/dNaf5iSbuxx227zW+jCyFEmnA6YsWbg9oG2++CLpfUr/K7BrHZ8xq11rHYYb3Y6qyhbHE/T60rhbXsRgLZ/ajufSlVO1yNr9vx4PISyOtP5e43mnKE7uHbQOEIE7A/dvLzzjg4aCbHHT2CzQctarU8hku7oD19+vT2zoIQQmyT6qwDscmt71XeZChQGwhAlfV38O4esSlg9afM8xQbPJpNnrfZ4PmSzZ7XqHMd2ka5j1S942Q2D3iR2q6HY9dgbthvXAGLToAVC+HzEli7EHvhCbx41U7gLWiTfKVd0J40aVJ7Z0EIIbZJtlVAtcsZCCUUuBv9+O1dqHL/Lc4xeuK3BhK0dmr9DCdQ1+0QygY8z/pRm9iyYyn25pXYzvSb9uel2EGLysyBlLy1R5vlSe5pCyGESJlK1/V47O/JsN8wK8Jq2wF6U+Z5FqzUDprV6iw3vt0uZf1ul5rlqp8hp+GiovTgLkyefHmbZEWCthBCiNSxstjifo4M+xWygo/gtpdjW12otU6kxvVnbKtre+ew5XLarxUg7YL27Nmz2zsLQgixbbPc+Kwx+FwymFWqpd097cGDB7d3FoQQQmxDFi9e3GbnSrug3adPn/bOghBCCNEsaRe0hRBCiFQaMmRI4kQpknb3tIUQQrQdDx/iZgU2BfgYhRliTDRX2gXtCRMmtHcWhBBim+flLfKYgoev69cF6UEVl1DNRe2Ys84t7ZrHZUQ0IYRoXV7eooCTIgI2gIv15HENOVzXTjlrHcXFxW12rrQL2tJ7XAghWlcef8eiLub2HG6HwK9tmKPWVVJS0mbn+n/2zjtMqur8459z25TtLB1ERGVE7Nh/GhFFxSB2iRpFMGpsicYkGqNGowaN0dhioqjYxYYFFewVQaQJogxNelvYwu5Ovfee3x+zszuzO23bUGY+z7PP7t577jnnztx7v/e85z3vm3OiPXfu3O3dhTx58uTZZdH4Do0fU5YRWBCYmKUedT69e/fOWls5J9p58uTJk6fzUFmVWUH7587tSBbZsGFD1trKOdHu1avX9u5Cnjx58uyy2GQYplSUdW5HdlFyTrTXr1+/vbuQJ0+ePLssYX6BTff0BR0XdH5nssQhhxyStbZyTrSz6TCQJ0+ePLmHgY/rU5YIMhz0XccpeM6cOVlrK+dE+4477tjeXciTJ0+eXRo/V1PPjcgEoUCCnEQtz2S/U53I5ZdfnrW2ck608+TJkydP5+Pjr1SyiHpuw8/F+PgdVXzBNl5HUrS9u9ehTJgwIWtt5VxEtDx58uTJNgF1IbZShWb1xbAHbO/uZA2bXvj44/buxi5Fzol2NlOo5cmTJ7epNd5kS8E9hLSmyGCu0DF0q78D1e7FFudzBNVlqLKY0uDpFIWHIhDbscd5dnRyTrTz5MmTJxtUO59mU9F1Lbb7ja9Zrp9MCBuE3bh9i+tp3OEh7FnzKrrsls2udgAmmpiDwIclB2KTWymQ161bl7W2cm5OO5sp1PLkyZObWKKazYU3J9wXBkLCjBPsKD59DstLzkEiO7mHHYXEpTxMF30wZfpwSvXT6aLvR7H2KxRWbO/OZY2893iePHny7MRsc7yCFL7G/yURsfY3/KSSZJ8+j236x53bwQ7BolgdTaF2C6poiggmhIVDeZ8y/SQUdp2oZ6kYNWpU1trKi3aePHnydDAhzdv4dxjYBtQBAcBq2BYmuXhXOSd3cg/bh0N5g3J9IA51WtIyithMgZpfYtvR5NycdjZTqOXJkyc3UWQhACYRsU6EbNivQQvXM1vUdlhfNGU+Tu1pNOVHJG6C5i8JmucjKW5TfQ5lMkXqOIRIb8J3KFOos7YiKW9TW3laknMj7XxEtDx58nQ2hcGIudSfppwk8WjbsPbokH4UGDdT5voFLv0ZdHUWhvo5RY4/0cV1CKqyoA012hSot2Uk2ABChFHFyja0s3Px+OOPZ62tnBPtbKZQy5MnT+4gsQmLrVjU4TIPxRE6CjOD46wE28JiEwCm2ExIXYoltrW6P05tAm790YT7FGUzJY6zSW4HSIwuPkMVq1t1jGywOuzKZDMiWs6Zx7OZQi1Pnjy7PqbYxgbXw2x2PkdY3QhSUBIeSmlwJBgz2lRnlfNVUFcQMmYBIKSTouAZFHE3kMlyMJlUsKOoyiac2isEzEsz7pcqWre0ybQHYeFp1TE7I0IINm9u/YtVW8g50c6TJ0+ejsIUNfxY8kt8eoypWUhqjM+o0T8HKSBDU3IcwqbOmIXR8K8UAbY5J/E9n9BHnYrDGpjycFX8hKqk99x2qO+1SrRt2bq5aZ+dIHGIugyhzyCIE9SDwdqrVXXmOjkn2tlMoZYnT55dmzUFd8YLdixCRkQ7DWqS7YmkPkwFmwqvp1/NeynrFCLdbHq0YDCzcg2E5InYshxFbE1ZTkpBvXUbQftXTRuVDShFVyP0TxBC4gPUMoEMn4Bd+xjYPVvVl1wl5+a0s7kIPk+ePLsuFnVscbycupCQIJPJcsRrPJmsJ9vuN74iqC5J3Td7T6R0pu4bYNr7pi0TjwOfdUPKEmF7XyrDC/DbMeVEFWrJCBTj4zgnNiEkivExasmpIKpb2Zcdh5EjR2atrZwT7Ww6DOTJk2fXxa8twVLSL81yWXthWLvFb5QRUU603CtKKjNoUFuYsk1JKUHz7OZNslUFrwPmu+B7F6x1rCOkts6L3G9fQ715C1I64uuXCgHrAqrNL7HZPW6fcE1AaMkjpAltGcL5VKv6sSMxZcqUrLWVc6KdzRRqefLk2XURMrPZRVtUcXDlAjw1r7Bb/a30q7ubfvU3o5NasFM9nEUzwUxEffhvWHZ/ICLYKwxY5YB6FWwBloA657tsKhuKz/F6wjoUsQpDnYKhTkXQNBL22X9ma3gxdeY9+KyrqTdvpTI8j1rrfw3L2ELx9TifT9tfxfVc2jI7KqeddlrW2sq5Oe08efLk6Qjc1r4o0oktAinLSWUL1Y5XqHK+jE+fhZAaheGhdPNdwVbny9hKjNex1NCE2eiAlggh3bjDx6btny17UhX4iAL9TqpdL1OjhZNUaLK16LcY4cPR7H4AKGINhcYNGOqHiIYY6VK6CZgXUhe6C3AhKcdvXxXZh8R2vIzlGofUI1OQInw4qv+3qMFzQFmbtr8ZldlBeffdd7PWVl608+RpYP7PClu2CXqWSfbr1zKZQ548sQg0nHYZPjV+GamMKwOasFlb/Num/QK2OSLm1F51t6DZvQmpa1DtMkqDZ7KudFRcKs/mKJhUu++hrP5WFNwp+yhlD2pDD7G58CMgxXJXEaLONZHS+r+hiI2UOk9GbSaiQvhw6RNQlWXUBN4gVj7MwmuwXfGjaanPwtRnYftnosouICpS9hU7HzUtE3JOtLOZQi1P61i/VfDp9xpBEwb3szlyn0RhJzqeKd9p3DvZYMn6Joeh/Xe3+Ou5QYbtn50+5Nk5KbQ8BNUNWETE2m74iaIQiTGebOS8ufAuBlR9RHnw143b+tS8wtrSUYTVlS3KC0CIEDXu/xDU5tGr5m0EqU3lproCS00fnyKofwWAS7+/hWDHYqifYahTCFlnAmA5Xmsh2LHYricwg6eiO95P2b4Mnpe2j3lycE477z2+41HnhysfdXLo7wv4wwQnf5noZNQdbo77s5v5yzv3En3la43f/McZJ9gAC1epXPiAi6lzc+69Nk8rKAuMxkFElC3iBZuG/31EEoUkY6vribj/Dbs//StnUBw4p3HOWxBZGqbSNA8eML6hNoO54tQ5xZqXC+HUJqUt6dKfafzbcqX3EwqLaqRdlrxluwu2/7dJ9+/oSJm9VKo5J9rZTKGWJz2WDSP/Cm9M1zGteLecn9aonHW3m8VrOucy9QXhlhedyCRraS1bcPPzDqy8pTxPEkqCZ+M0B2KSWhoDkDSkab0+vcU2hQJM7Uc0QKfJMa35lbrNNTFtHzVrAIqVfg20I3wUiqhEETVpy6oiErhFIpHarLTlpbYQq+ZtpNW/5T6rP1bN22D3TVvPjsoTTzyRvlAH0eZhhMfjUYDHgAOBIPAbr9e7LGb/ZcAVRK7Vu7xe77sej6cr8BLgAtYDY71er69F5XlyhmlzNL5IseKkzi/41xsGT16X2tmnLUz5TqPGlzr4xbpKhU8WqJx0UN5MnqclCk52r3mNii5DQKSONB4i2QM3sdyH06zFBgip3rRlBBqFgbFsKxifvJBUKfSPw5aFSKk0Op8lw5alDXULIq8T6d5sFTAPwqqcjzCmIfTpuNwOfDWHIUMns7OPH6+44grOPPP8rLTVnk/qDMDp9XqPAm4C7o/u8Hg8PYHfAf8HnAyM93g8DuA24CWv13ssMI+IqOfJYSZ9rqctM3W2RnXr8hpkxIqNmV3+mZbLk5vY2NhpBBsSJwYBKAgfnXC7IgvS1qnI1I5oUYp9N+AMnZB4p1Qoq3sYzR4AFBKyTk5bX9BqWgMuwr9I38/wcdG/kKFTsevvxs19yNAIdnbBzjbt+bSOAaYBeL3emcChMfsOB6Z7vd6g1+utAZYBB8QeA0wFTmxH+20imynU8qRnfWX6MI9hS1BR0/E3dqErw3LpA0vlyWEE6V88U1HuTzx2cQfTr/0tCJ6eURsCg641r1JW+290c/+IC7t04AqcSffqDygMXNRY1hf+AzLFGnTL7kkg3OQ4p/qvTNu+uhPPV+9otMfLphiInfywPB6P5vV6zQT7aoGSZtuj25JSVuZG05KHAGwLu1JEtG7dirZ3F9pNr3JYuDJ1GSFg7/4FdCvt2LbHnAx3vQapfEgMDX59kpNuJZkr967wvUTZVc6lc89jMIsZRC3Jl2lB4oftAO6mf9nwhOUL+DM/8BqSxPHBBQ76u/6I29Wac7sOuA6JjJi2nYATfMylkhcwqcSgH27zIRyhG4E6JJG5dAkI0R/VPYWuhf1j6jyHGm6jlr8nbLGEeykqHZFw365yfb3zzjtZO5f2iPY2ILaXSoNgJ9pXBFTHbPfHbEtKVVXHT3d3716ctRRqnUm3bkVUVKQPobi9kBI++17lhY91lq9XKHDCaUeFOf/4MKUx6XWHH6zx4ZzUQ15VkQTq66hIEhuirRRrcMbhTt78NvlI6cLjQhAKUpFmiWmU9nwvloQvpMomBN2QHCcs9PSGiE5jR7/GMiUb59HDeSW1Rb9Lul+RDkrD+xPU5yNQKQwdT7n/txSEh1FBsr71p7vxLJuLxyFF/LNQyAK6b3ua+tDu1Cc9Pj029WwtHkfAMTVu+0YVnE4HqmjIUiZBRaCZJRh136AF+2FqMwk5X0OKKhS7H7r5BDjew9a/AQRK6FhU/28JmEcQSNDH2O9FYhOZId+OF3w7GDJkSIdeY6leANoj2tOB04BXPR7PkUBsMNxZwN0ej8cJOIBBwA8Nx5wKPAOMAL5qR/t5dlAsC658yMlb38SL4ewlKv952+DVW/3su3tDlCU7/U1qWoKpszXOPDr9vGFr+felAeqDgg/nt7wVzjoyzF0XtC4LUlt51db4h+1gfcyMVQ9s/qyEuEjp4LeVPB1Or8Al+NRFrHe3nH5TpJt9a16gLNz62cCC0Kn027qIWufzBPTpGA4dpe4IigK/Rm1lmsxEVBZf3kKwARAQEEF0GtaYC7CQWPr3WPoV2Nat2OrmuEMCUuAIXIZ767KMxFdiIZ3PIZ1PgvY9oCJDJyD8VyHCx7f73LJJnz59dop82m8Cwz0eT+S1CsZ6PJ4/AMu8Xu87Ho/nYSKirAB/9Xq9AY/HcxfwbINn+Rbggnb2P88OyH2vGS0EO8rmaoULx7uY+Ug9Dh02VWf2Zr12S+c4q7gd8ML1fr5bpvDadL0xItr5x4bZf/fOW+v1BSqvCA0/AocFk+2Wn9cmFG6wnYSAS/PCvcOzZ/19lIdOZ4PzSeq1hSg46BI8hZ6BsTjt3dJXkARVllPqvw7810VGp/6OGdGF1B/xO1InughDixjpJkAzwQZASIKuJ1Dscly+v6SsV2JRw3nIosnxNTs+QDo+gLq7Ef5rMzuRHKPNou31em2guXfB4pj9E4AJzY7ZBJzS1jY7gmymUMtFAiF45oPUjjnrtii8M0Pj3F+YlBdlFpSgvKhzF0sftpfNYXt1/qh6BYIzhJuNouElJBpGKwX/sB2MFmEKd07LYU5RGj6G0vAx27sbGeF3vJFROYvWCUXA9V+cvt8jUoVYdT1OkMlJd8uCWyB8LMI8qBUt5wY552ufzRRqucjcpSqVtekvq4/nRB4Do4400dM8EdwOyS8P73jTeLapBoaLgnjBNomIdop3l1oEU6TGciF4UDW4UzV4SdGo7/wu59kJkNiYynpMkWD0mwRVWYRqvJlh/a3sj1JN2PgkRX0S6UwTRU1kUGYH4rLLLstaWzkn2tlMoZaLhDLU1mi57qWSq9IEqbt8RIiS9EtWd3gexaBWiGi0yIg7ZojIUMZs+J3kCfkfYXC0XsA/NAePaA6u010cYBTykpIPs5qrSIJUue5nTZf9WV2+D6u77sXasqPZlia0qa59QVnxCbiVZSnLRWmLSEiRYn5XVIC2PH0l+sw2tLx9yGZEtJwT7WymUMtFBvWz0dT07+b779FkE77/Chh3UghViT9OUyVXjQzxl/NCzQ/fKXlJ6BFRDhKZLGz+MdmQLB7mElVFinj7eK0QXKe7eCcv3DmHJMTGkvOoKrwDU13TuD2k/cCWoqvZUvjHJEcGKS4YhxA+ymXEMTwV0XhnrUWx9kxTaybsPPNBQ4YMyVpb+bs9T4fSo0wy4jCTKTOTz2vrmuTCE5ocq1QV7hkb5NpRId6YrlNRLehRZnPuMSY9yrIXiL+zqYu44CYPjRXFJpIZIpYU4QruVQ1G2Tv/9EGezKlxPY7f+Czp/m2uJ3AHT8UdHha33WG8haJE1i9qQFcbKlJcWwatl07VHIRuHpl0v5DdkOYgSJF+FIAMcobvKMydOzdrbeVFO0+Hc9fYIPOXq6ypaPmOLoTknkuDCcW4T7nkd6O2z6i6LgCmBSXuSDCXzkCxJIQyqNwmPjtENFtEEpYqKvOEwsEyn9kkF5BItrmeTFtum+upFqKtq5HkHiawWgWfiLwPNn+PFEQEu7lAiIafpFeaNHDX3Zu2b8J/BbLouuQFpIrw7zqBsDqSnDOPZzOFWq7Sq1zy/j98XHJyiEJX0+d91L4mL/3Fz0XDd5zlS+/O1hh5l4sBVxQx8KoijvhzAf95X894bj5TxlsGPltplVePgqSfaidPxhzD1s5608izw2GLGkz157Tlgtq8FtskGhJY2SDYEBHtaCYxFdAkFNLyslMbymgxZeP2hw+mqOZN9PDQ9CcRGIuTSxLvkwqi7kGENSh9PTsIvXr1ylpbOSfa2XQYyFUCIfhsvsqazQqevjanHhHmuZt8vP13Pycc0rHZsuqDsGyjYGOG671j+eebBuMecTFradN4YuVmhTtecXLBA64OE+4NUvCwzEB5G5H8XgkyU63nZM3MyD7ZK/8ymjMImVms80Qx0cPh46kREBDNy0bEQAUUEXG50IgId/QnNpe3ApQDvYDy8IEUV06npPoL9AxN2gJBCRMRNc9DaCjYJWB3gcBoRPUniMCYjOrZUVi/fn3W2so583g2U6jlIqs2Cc67083PcZmxVN7/VuecX4R55OoAageEk99YLbjvHYM3vtXxBSOPkkP3tPj9iCAnZ5BGc85yhX+95Ui6/8tFGv+bZvC7ke0310+SOlb0cZdBFsNjFYu/qpF2z7fDTEgz1D7QthicN43nDAoFOENHEzC+SVnOHWoZ0zxknkQdbiB1iGibplmaZEgi4S6d+vfUCjttcs5EiNDpiFBmSU92ZG6//XauvvqGrLSVc6Kdp/OwbbhwvKuZYDfx+pc6/brb3PSr9gnhukrByHvcrKuMb2f2cpWLHnVzz4UBxh3fZIKvD8ILX+q8+JXO6q0KJW5JsZF+ZPrMpzo9T7RZi0KJkIzUTXooiY+zJayXgqAJhoyfF18tY/5JI9oCydVa0+ezn7Q5xwrzupp4dKVJyV/N7IRazdNx+JWfqXC+gSmqcVr96BY8F12WZXx8if+a1KItDYoTzgkrhOwBoP6Qto10d4jaUEYAumMyQfPAtHXuqtxxxx150c6z8/HhHJUla1MPoydOM/j9mSFcyQe5abntFUcLwY7llkkOTj3YpGeppKoOzr7fzQ9rmvrlCwo2ZDCtvnarwjWbXY256G4LSC40wtztDDYm8ghL+K9p8Kyls0YqsB72FAVcqoW4VA0jRLNUdoLEnj9E5rD/oQcZpsbvfNgMUCYlz6s6gZi3gX7SZrwZYKjs2CmHPJ2HTZClRb9js2NS3HqrnwtvZff6v9LXnzzpSCwFoZGU1d9MVcE/Wu6UBt1rn8CwBrZsX1Rji0BGbaQaZUfN5VFEqnXZeTqUnBPtd955Z3t3YZflg9npL6eqOsHMn1SOz8CEnYhN1YKpCZJ7xGJaghe+0vnjaSFufNEZJ9jtIYzgmZBBQAoedgcwJYwJufjYju/Pcqlwc9jJPFvlUT3AWUqYx6wYE3fUMzwmEppLSD7T6xmQYCSvAXdbQW6wgnyoaNQhGCBthkor95xSdnKWFF1FhfO1Fttt4efnwltQpJvegd9kVFeZ7yZcoeFscz1JUJsNqLhDwyj2X4put1wnbYtqqkpHYGnpg6poJHelEEQc1YgpY6dcl52nI8k50c7mIvhcwx/MzBkskMmypyT8tE7BtNIf/8NqhY3VgnfnJrnEM5hbpjfgpsXk3qSwzrVWiK+l2kKwY3nN0hmhmoxUTYYLk49kTNnoiLuBm5RgQsGOpQvwq110PXaVspZvXE+x0JhCWPjpYXk4yj+OwaFTUXaRVxOf6m0h2JKmpfsSWFJwG2XBU3DJvhnV6TSH4KzN7JlW7x6PqS3KqKyLyCWaaClYMQ0Oaw3/S+kgHMhtP6HZs2dnra1d425oBX369NneXdhl2TeDrFhCSPbp13ZzriMzx1kcOny7VE0u8Jlc+VFH2ATdfTWs8YyZvjMTG8o8rvgZLloKrobkDyLIlTmcxWuZ/jX/LDuCT9z3s1lbQpW6hsXGx0wsuYDniy/BThuNZudgs+OVuP9tIpFsgzRFsQ0odXxZfgCrnB27ykXix+98KW050bDcKyrKcUvBGn6i30b0nTNQfwuyA9KE5smMnBtp5+k8zh8W5p+vGITM5CPhX+xvsUfP1i1PqgvAm/N1llUoODVJaYGkuj71aHv4ASYpV0GlmFsG4Bjg8Jj/m422N9oKP4n0ZveFdqRMoYAXVT8LpMJkW6cG6CckvxJheqWLJbkL4xfVPF18PkElcbrJ7x1v0cs9mJN8N2a5Zx1PWNna+LcEAiR29pLC5KeiP+K0e9Mj1DFZCS11FVKpSVtOEckDqkQJA0UA0o0tFRzuB9H0bwj5L8NsQ87wXYFDDz10p8innSdPHN1KJHeODXLjBGfC/eXFNuMvzcwJJsqL3+rc+o6DuljTe5qBV3GZZJlHYS+/japILDvFaFsAexLJ7m4DfYGjgeY+PM2erj2FjYpsWsqVBL3ZgQcImwPUvLd3lFnOFwmkEZPpzic5wfcH1ATrjncmHHbvxr+ThJiPY4X7Xx0m2mS4tjsj7CKEqEUIX8MqiToUx1R0x1SCvmsJ1N/dcW3laUHOiXY2U6jlAlLC5kqBENC9i2TsyWF6lEkefMNg/vLIKFPXJCOPMLnxV0EG9Er+qFpQoTBxoc53G1UUAX0Um0++S/CwcRAR7kQW5SLYdqHgAX/EPb1gH0n9j8n77y6W+MYlGF40R8T+KfmVEeZHU+WjFHPaAMPVXXMOuqPwpkjhGKVW3cR6bSG7mYdkoUedR/fABaxyjweRmcG/Rp+LT1mF29693W1r9p6o5kAsbUnKco7oGq4U6KI2aahfh/sRLHMI4eBZbetonrTknGg/8cQTVFQkNsXlyRzThMdf0XnmTYNV6yJ240F7Wlx2Xphfjwpz6uEmKzcJan2CPl1tuhSlru/huQZ3zYhfB7Y42fIxARQAYTimn8nWOsEKVSG4r4CDgJiBfv1IgbJZYm9p+ZQpcEjuujzA9Zor/QnHHH6OFmZPVXIFIT4OqcgkTzkNyaVa7s5VZ0Km89W7wry2096NPv6rWOd+NONotpbouGeV238VtSnifSsSymyoTzPr404j6obr8ZwT7b/97W9ZayvnHNHy3uPtxzRhzI0u7njU2SjYAD8tV/nDeCc33BMR3/49JPvvkV6wpy6Fu6Y7oBJYAXiBZUSCNqV6uunQv5/NWX8wCY4TcCRxgg1AIdiXCQ4+xaRvl4ijXJFLcvFxIT6+tZ4LB5kcp6cZDccm7wBuckaCn/xCtbhTDyISdFJD8pAeYH8lH6ksFf3C6e9Hh11ID2ufLPSm89mj/m761d+IKhOPlyQRA5If8EmYUXwJXtcDhERlu9t2B8bh8v024T5Fwu4WlEpwpLhkmNL3BAAAIABJREFU3XZh2kkKTZ9BxL0ud7j99tuz1pbYkRNoVFTUdnjnuncvzprDQGfSrVtRViwG3y1UePI1g4++1gj4wamD0yHZUqO0ELNYXrjPx0nHZDY6OvetIr74nMT3uSAixEleL08ZHGbFLxWWmKmHB4VCsrxnHVKC0qyuKhsu3OZmdqI6og5rDedZiOSn4jocMef9o60w0dT5zlbRNZUj7RBjtVDaJVw7Otm4xqqUtdzd5QDsBJ71UY72X8o5df9ucxvZuldaQ4X+MXNK40ejkohYJ7pq3NZuHFs9hT3KD2z3uYS0b/G7nsTUfkQVaymhii6yyewqgToB9QpEfUpF6P9Q/VdTWng9iropbRs1FZtp+QYdz474vbSVAw/08P333g6rr1u3oqT2jJwzj+fJnGcm69x0vwM7LBqdv+pCUBf13LZImjZy4mSDk47xp23DtOGL6SR/MZcN+5JYsPuUSmb6FFgI/AjUEnlWDAQOILKoFKiTggDgStDXMgXeLfFxt8/gkUCMiV5p+Klu+DHgrH7hOMEG2Fexuc+InEDkQZRbo4z2UGb35ey6B3i98PfIBF70vc39+WV99kyP2aJb+ER6B0az3tm0DCxIcsOST13DzOKL2YPv2922YR6BUXsEAIpYT2nRcFR1TeN+ARRJKLKg1ncr/uDVCNwAWOYkFDV1gCrL9JBOsHc1NmzYkLW2cs48ns0UajszPy5TIoJtitTe2kncYL9fnNml9eM6BerSFLJJ2ocR+5n4XgdmADUNZX3AfOAVoGFQUCIkrhRzcYqAv7hDHOMwmxakVgJvAS8A7wKTYdpTGo/P2rm9mHc0jgpcwhU1b7NP6EREQ5x2l11CqdWTLeqP3FXu4Zmi8/lRf58N6gI2qj9gsfM7+O1f+z/2rL8J3S5LdYk3UqMvYD1fdmgfbNmb6tqP8QfHIKW7cXvYPJiauucIBP/UKNgAQX96R15N2YToAHN+nsTk3Eh7/fr1u4xJpjN5/BUd204j2FGiI+4Y9AyvrG+WZBhi1KJFAt+zDwnz5EydUGUSNQ4C04CL4FdF6R3CNAEvFPi5xe/glQ064ckCmuU22VyrcOtHTjbVCW4b1v4MYABLhMLTqs6XQsUUgkNti3FWiENzKHPXwPBQBtYMxc82XiwewxLHJ4SpwQZC+FngfI8FzvcQROJel1m9OCJwGcf6rkeJuTDWqz/yletJVmpzUFHZJzSMUVxLswjwOwQClb19N1MWPoRvS8/L6Jg1fEB/9kdp5aM7KCpZ5nyelY7XCSk1FFr92StwMbsHzwDZizrfI9T7/oGirEPKAmy5W8J6rPBx2KYHRUtsChaAqlTjdD6H35/c6W1X45BDsreyIedG2tl0GNhZqaqFNz7WIyPoTKZlE5QZdmRmI6FwBiFJm7fh0iVXHBvizycH+XBxmodXLRSvtLmyML3Ahi348CeN9W8r6G/QQrBj+c8MgxXJXhZawauKxlDdzdOqwTJFZaVQeF3VOdUo4D61NTm4dw1mup5kqSOyDMyiZaTZ6GzJVnUDHxf8nVeLxxJNCvmx6yHGlx3FV64nWaPPY6U+m2kF/+Q6BrLQmJrN02gVm51vZpIyHYB5/IM3u5bzZclprM/wnKrVxUwpO4q5hbdSqX9PnbqSjcbnfF08jk9KzsRsSNMpKcKy90kq2BGCGOrPcbm1o6g0uX84nK9meEa7BnPmzMlaWzkn2nfcccf27kKbCIbg1Skav77GxeljXfzmBpizoHO+vpufcBIKt0KQmom2pkouPTezpU6GnqGzlgm9DZtLjwjy/a11/H1UkBk/q9gyfT9P3mrRW03dTk0ARj3n5vI3XXy6QsOX5vwlgufntU9UFwmF6zQnZpJFr/dpDqYquWMMs7GY6Xqq4e/U74thIqK+yPEWPxrvsNCYyluFtyacFw/h5+niMVQoKzqj2+0mLLa0btwsJBXGF8woGc2P7vEpi9pYfFZyHn418ZzrRuMLZhfenHnTog4hQig0zSJpRMKdxvql5pp5/PLLE6VB7Rxy54mwE7N6neC837pZsapJpGfMgadeKuCCM0M88LdgC4/otrK5SjBluha5CzOdNoxpW1MlD/41wH57pzft1gbg/g8zz9G5vkrhqU8dzFmlsXiLQiDq2hqbvSABJYokJOGjgMZGW1CuSE5ymLhj+v27KU7mrG9dNrD2jrSfVvWkgh3lCVVnxC6aJKQ5VcpqqtU1SNLncoGIcKvAd66n2ZZmHicsAnzpmsDZ9alFrrOx8LPO+TobjLcwRT2F1kCkdDTG927tavSfCsbTPTSUruZRCfevNd6nTl2Zso4Vzpc5uP5vODLI5y1lCbZdgtIQxS7Z1WvbqUbrux4TJkzg7rvvz0pbedHewbFtuPAaV5xgx/LSmwa79ZbccEXm86vTZ6u8+p7O5q2Cnl1tRp9mcuTBkcfF3CVKJHa4k0hw5AyyYfXtbVFQAMceajH2rDB7989sLvbVWTrVvoZoZK3QpfnL1Yg3efQjiaZJ0kn4FAn3goM2FbDFbvoMS4Tk2sIQvysK8XOVYNqS1t8Khe3ICQ7waQaj6OmKRoDc8MUVGRuJI0Svso3aItYpFWnLL3C8lzXR3qas4Qfn81Spy3HIYgYGz6CL3ZuZJWfiV1c3lqvkGyByC7iJ+GS2dqHgCtcEutYmFu0FBXclPS6aYSws/EwrOZNBgUsZEDgHLclSDUVZj9M5ESmLiHh9JicQuDjD3udpLTkn2tlModYRfPiFind56hHgky/pXDM2hCONtbbeD+P+5OKzGfFf+4tvG5x0rMmEe/xN4Ql1IlHHok+RJE+SS0eHGP/nti1x+iLqhBZNJ5RoEjMZJhGPpFgSOMSVFkme7Wm0qLdGCu6qdRAGipfJxFHNov1ptlY7yumD2hftLNP3lJ0/FlhmlNr9KLP6UdkgahlE1ARAlZm9PVUpK3m96DJOq/03jsaM0B3PN+7xzHT/Eymavrn5rqdwSYPuIpTwBcwkchsUE3lXDpG5eG/VZyXcvln/hmrtp4T7TOJviS36XL7S5zLXPZ5hNc/hlOU4ZBkOWQqAw/EyhUXXIET6az4cHkIwcG6Gvc/TWnJuTntnY+pn6ZcXba1S+HZuetPuH+50thDsKB9+pfHn8U6GeGwMreFx4QZKG343u1K6d7O57+ZAmwUbwIp1QhM05QDMhETi3mwitMQpkSNkyqv8oVqD6ubPIYtIlIvo0zNIZBlZzELawd0tTtyrfXJ6sJ3++IG2RUG7Wtl5UFAY4v81YSIfe/R3suQa0UtlcPA0ulj90tavCvje+QovlJzXaUvG5jufZEbB+EbBjo5mTaBWhFhOJOhfovBOtnSjSgM3EV/3zP3dBRYhlhpvMdv1AAucT1IvNrHM+WTCl55k78YSqFHXMrlsGC+VH8gz5XswrfgCKh3PU1h0VVrBllIjGDibbTVvkRu2oSbWrVuXtbZybqSdzRRqHYE/w6RY6cqtWid4+6PUX/frUzWuHhPE5YBQ9JlmNPyU0rheuqzYZvbz9Tjb6dw8pL/FRz8261OmFtIk5YSUdCmQnH2QyZ6H2NyY5uERQFBZFqPqFhGxTkSDeuy3u8VLo/0o7XQev8QKM01N/VI21sqd2OXbxCZmOF9tkQfGbvhpHsdHB3Tp4kj/5Wh2d6YUpnYyjY7HVxpfs9h4n8GhUR3V9YZ+WsxyP9D4vySxNcUPrAF6AF1jtpvCx+Dq17GUCixRj9sayLyCv1Gtz0vZrrB2Z2L5vviUzY3bviy8kSJZ0CLkaPQlomXfY7Y3XNdSWKx0vMta431+JWz6p+hDKDiMurrHsGMymeUSc+bM4cgjh2alrfxIewdnn73S24uFkHjSlHv/My2y7joFliW49l4XNclyVSuALnni5kC7BRvgwqPCGM29ujMVwiQj8ucv9vPTLfXcNTKIWZxZVa7ekgENcckTZg6LxYK/DwvSs6j9IUqHSYtLreS+CMMtkzF27oj2pKLr2KwtS7o/dsTtAJyygPNrXqDc3pPj/VcxIHxk0mMNiBOwuc7nO6DH8azXZlGrrm38P92duwmoIpIVdisRq4KCg17BC+kbuJwu4aHs7b8yZR1+CUv0r+IEG8AWYWqUamqJv1WSXbUp4ycJm7dJfT6qtjRnBRtg1KiOfQFMRV60d3AuPDOMpqUWiOOOsujfN3WZel9marhwWbpLQrC+ov3rkwF6FEv+fX4ANbbJ6Pxx6i4kLiMkN013cs83BpvqBV0yjP3dVZU8fJoflyozmkB+eU7HRUQbbwZ5JOzngBhT+R62zR1mgGdNf86YwiqVNSww3m8c8VkkicFtlzIwdBin1P2NP2xdyN7h4QAYuLim+m1+4ftN3HufQsRn0d2snpoYce0oQjF5wTP1gF9PRLw3AkslfOn6L6GYEIH9gr9iD/+lSY/fJoAEy9yiBBv6kWhddZRM+lkLpErqKYQvg1rydAS58kxoJJsp1DqCHt0kt/8hyC3/TGzm7VJqc/eN6eeVM/XotpPZfGPsal/O1zj/xNbPCa7aIHj+PZ1Fy1UMXTL8CIuzTgiz/y3wp5dNvl3acDkqJH/qRROIJOqmS7C2TvDAtw6eX6jz3Jl+ioSkNsVabg3JmS6TXoWSB0YEuPKV9Gk611Z1zEtLlNG2yWjbpAqwEJQnTfa56/J2wZ2Em4mPTVP49+jnsV/wLM6vezBhHQYuRvr+ykLXU1gNdSVbCei2yzuo502UWAMa/26THUbAEsf7vF5yHscFLmK9cxJBZSM2Eo34FxmFiFEok7vQDxTR9Fk2PybTvm4EkuVas8xBGdaSp73knGjffvvtO10Y08t/HaZHN8mDTxos8kaGmLoOI44Pc/O1QQbsnv62G3G8SdcuNlsqk4+ky0olVc5mj7hoCKoYJ6y339NYs9LFbn0lpg21fli6WsWy4RCPxbjTwhxzYPyQ9bFXdf4+wRFnop86XefeZw2m/RcuPzbcJNpRp7ToZGbskypJghIM4jx3KnwKV7/n4pqzQ4yvS+5dfLE7TK8GE/2Q3TJzLCtzd072rsgq2Z07M1hb+Nw5gZnOSQn3Rd/booYVk9RJaNyynIGh4SxxfJiy3IHB0a3sZXrKrYH0CR/FOn1Gu166VhtfM934OprrptGzvPlln6kLqJQaNGRRU2jbenBIbQDzB8a2ocZdh8cffzxrbeWcebx3751z3uX0k00+e83HjHfq+PDletbNhSf/FchIsAEMHe69MYiaJDKYpkr+fkMgPkKZJOI1HSBOS0xLMGuBxhvTdN7+UufT2TprNius36Lw7nSds25yc/uTTUI55UuN2x93JpxT37RV4ZQrwQ4l6FdUpPWGH5XIKNtNJAFwVNyLgHJaXM0rqhX232pxQ2EQRzMxVJGMc4e4u6Tp0de/i8xIuM8+qHM8j2uB/+g6/+d207+gkIPcBdxpGKxPE4BlZ8YkxLsF96QsE/vetkFL7ZQFcJzvT6gyudNFN9PDAYFzWtHLzBla9w802dwY33o2AxuIOKxtInFq+UwXWmjSxb51N9ItdDTl4UMZGBiNy+7WuD9TEdg7yfZgcASh4FlJ9uYG2YyIlnOinc0Uap3Bnv0lBw226dY1fdnmnHaiyYsP+jlo33hhGrKfxaRH/Yw+1eT0Y2MEySS1Y5adfP9jbxi8+Xlk5PzopNRea5u2wuoVCoWODF5AXEAh0FVAN6BLw7Yk61i+WqNxY3GI+T3qubs4wNUFIW4rDjC3Rz33lAZRm+nhH4cFUVLMEe7Xy2LEoI4X7QohONXl5g6Hk6WKik8I1isKjxgOTnC7+aGjQt7tYCwyPqY2g8Ao0eXyW/TFrNPmpyzbzzyCC7a9mNAE3jd8KJfUvI2eLNdrO+lpDuG86nfpHT68XQ9XH5GXOD9QT0S4NxB/iTughXd4IoRSi4KLE2qmMbz6U46uncCoqs8ZEDgHRRoI0vt/9g4dRYnvt9h2k3enbXfDV38jtdteIPNXiF0TkcUX65wzj++oVIQEr6zX+NmnUKTBGT3CHFTS8Vmehh1tMexoH94VChVbBT26Svbeo6mdf1wWYPEqhYUr1Mzsb2GSRiJ74m2DIwZbzPOmv6E/mqHx6+PC/O/zFAIfHWknw2roR0xfZIP+lquSywrTe2Kf4LF45JwAN77jpC4Yf1KH727y9AUBtE54Pt3gcOBVE1e8VSiMdbr41le/y71lZyLYURxEvtqfjA/oYx6UsuzA0Mn8aetiFjneorp4MSEfeIKn0M88on0dzoBe5qFcUP0xFeoiPi68kVVG69NpJpKAIFBBZKlYtEwZkVF5MqIGqoWuR9ikz0eRKn3CwxgQOIfja58mULeVGnUZNhYzCm9hs94y+FQXczAnbnueetmd+vq/oWmLkShY5mBaRjjK09nknGhnM4Vapjyy0uDeZQahGIepx1YZHNfF5KkD/BR3QvpmzwAbz4CW20sK4Z17fLzwgc7fH3EQbsfs3JzFKhUZxuf2BQS3nBZk5RbBtB8SnLBKxASerrpmYbQO69362btzDzYZsW8db8zXWbxJwWVIRuxrcli/zkmVuUoIPlRT34qrFIW/uKq4zV9EQTtu20oR4iXnGj4zKrCQHGSWMsbfjz3s7RPCpcTumVG5qPgAWKnSr8Wg4eDA4Gi6UURFffb9WLpZgzm/5l1W6p8xzzWRCnURtlKFX2wlmMKaA8nHrT6a3pOhyTPeT0vzuUHkRScMhNWtrFTfAmCF8w2+K7id4TWT6G4ehtOMWCROr/6Anx1vs9j5AvXKBlx2NwYGzmev4NlojW/LBZjmkFZ9Dnk6lpwT7Tlz5uxQjmjPr9W5c2liR6kvKjUu+d7F5EOTO98EgvDDYgVbwr572xR2wLO3wAlXnB7mpck6P/3cvmFl93KbApek3p9abffuZ2NocO1FIT78SMP+WjR54ESfTJkMM2OeXL0LbUbs2TZTdqEDxhyRnTXSM1QVOwPz2kTDx2T3LB6uPZARoczELpav9S2MKZ5DrdL0mXxjVPI/1wrurN+Xy/x7tLrO9rJv6ARKrV5UJ8lCFSX2Dkk3ym4rtcoGluufYIogPcz92K2do/JaZR3fO59iueN9TOGnhzmYA+rGIoBXS87DFolfKKPOYsnw0eRzKaUbh/Bh0JT5LJpzHJJ7lweUCj4oOZuzqmZS0LC+WkVnr+A57BXsnPn+XZmRI0dmra1dzdqWlmw6DKTDlvDvn1Obl76u0phZ1fIWDgbhrocMDjyxkFMvKmDkxQXsf0IhN97toK6+Y/o34tgMBC9Fdq29+lr06gpnn5Be/MaMjJR5rNbAPkDAyUBPIvPWhbT6Si0yJBN+6UdLclzYgkUbFX7YqBDcaZJoCWoUk98Uz+U7rapVR65T/FzcTLCj2AL+WvgjjzmX4c9ypHMVjTPqb0tZxkHT119s9Wbf0Kkd2ocQ9bxVdDkPdRnMO8VX8X7R9UwsG84TpcewPgPHt0Ss1r/kmbLD+bbgX2zRfqRa/ZlljneZXHo2i51vcNa2SRRaveIPkhGxjk4DJKM0dCQDfFdz4LbHsKTeeAsaRN5vnUQ+r3TfZEipZrHzqTadX554pkyZkrW2ck60J0yYsL270MisapW1gfRfweSN8QYR04QzxsLDTzmoqmm6vet9gomvGJx9mZv6Doh1MOb0MEUFaZzDona62CDLDdkIxpwaEeI/jQnRr1dy0/KlZ8KRB1gEJXzgazjXPYHhwB5ERtkZhjJ2GZIxB4T46IJ6Duvdss2wBfd9ZnDwAwUc/98Chv23gIPuL+Cujwz82yn42OGWhZAZOOGpkfnfsJA87E4eOSwRzzpXUZdAsGO5vegnDiyfyh0FPxDsAPHeImp51DWNa4qe4o+Fz/OJsRCZYEnbUcELubj2PxTZLb0rHTR99bp0Mbr2cZQOdHqysZhUMpoFzknYIv7z2agv4MnSodxb3peJpSexwPEydgYro/1iK28XX0BISWzRW+R8iWp1KVdVLuLMmhc4pv5mjq+7k1PrHkwr2ACD/NcyuH48qiwnrNQkfIinyPETx8+OtzIolScdp512Wtbayjnz+I5Ei0QVScvF38ZvvK8x7bPk5ef9oPLUJIPfjcs8XWcienWTvDDez8U3u6ipS/AoMWhaT938WWbDE68ZHHOAxeA9bd57yMftjzuY8qVGqOF8enW1+c2ZYe64xsGWLeC3wURE6qtqqHcgkaf2Oprsf0k4sq/JOxckn0qwbBg7ycWHzdJwbvUpPPy1gzlrVSZd5MeR5btigJQcb1l8qqVoWNSD0pSU4CNjM7UiTJHMzOFhqmNTBqUUqpUQ/3EvZZFWw4ecxGx1GXcWvsQSbQOqVDgutD/X+09nr+ajxGY84/ycWwsnEYwRwudcX7Cv2ZcXa35HH7tLXPn/C1zE4YHzWGBMZZU+h5X6dDZr3yNFGEWqDAqdygm+P3W4aXyJMZWVqRzFhCQotrFGmckafSYLQ68xuuZlNJKv/V/ofJ6Qkjq/wTzX/xjivwpPaBSehhjoEps57geojUnd2Zxi+rBHaAQApoiY1KIrH9tiMAqLuvSF8qTl3XffzVpbQmbyhr+dqKio7fDOde9evMMkDFlUq3D8zPST0Nf2D3Lr3k0CPHKMi1nzUitLvz42s6d2jJ28phYmTdX5dJbGtnrBxirBuiqlKde2mTyJYtdSm88n+OjeJfJVbq0RLF2tYOiSA/a20VTo1q2IiopaLBv2/LQA31IlPmlH9KkEke0JBu2Dulm8dp6f7iksA6/M17j2zdRLff4xIsBvjmz7kDt6Lq1lgxCc7nKzMuHSrhA4PgelMm7rvK3D6GPHn89X+la+NCoxkRwaLuGUUHdUBId2+ZTVaurAJI1tNXA4lcySX0Cz+XYh4Z+1YxgTHJawhveMuYwteSxpC3ubPfms6naMNGOGBdpCHne9zKfGXAKE2ccawBj/GZwTPBmtFeONVN/JpOLRLHFMzbgugKN913NiffLkJK+VnMZq44u09Yyp/JauVnwksdX6p7xTch62aPnCrUidC8VblFUcC0CVuoAPuhzTuF82+8lk8UfP0DH8sub9DEp2PG29V3ZEOlpXunUrSmpwadOYwuPxuIAXgO5ElhOO8Xq9Fc3K3Acc09DGE16vd4LH4+lCJITtDw3F3vR6vQ+1pQ9tJZsp1NIxuMjmoGKL+duSm/sEkgt7x4vIkjT5tQFWr1MIhkibYzsTSorgivPCXHFeUz+WrFZYvEph4ls60+cnv4y2VCs8+67Ony6OPITKSyTl+yceLt/4qQPfwgSiJWlymXXSZIaXksN6WQzb02J1QDDqXTdSwlG9TMYNDnNA13h1f252+g/j2dl6u0S7rfSSkmm+ep7SDR52SII4gSCoq0BbAkr8iMgtVcrtpvNZodYztvh7ftLiy/WxnPxv2/4MMosyEO34F55ZyBaCDSAF/LnoWQ6y9uBAs6Xz2r/dqUcdS7WNTHHM4exgckev940vuKL4NoIx4jVH+YE5+g+8HfyEZ7fdi5HRKuXUbFPWt/qYec5nGFr/lxiP6nistFlnIiQytfcLD+Ps6veYWXA3a/QvGuOK9wkdy5G+mxlYegoVRISuzDqALuFDqNTnAi1WO6YKo9DIPoFLMuprnh2Hts5pXwks9Hq9xwLPAbfE7vR4PMcDe3m93qOICPeNHo+nDDgEeNnr9Q5t+MmqYEPEe3xH4o6BQZQUs09j+oYZ0Gz0WJBBGE1dk+idaOYd2M/ml0ebzF6U/gXizU/Td2TOBoXnFqYR1ahrrEZEvF2CwmK4b6HBy0sMVtQo/LxN4SWvwfDJbv63IP6h/tPm9Jf7ki0KVues7EpLF+BP4RCPhleBcxK43gRjbgvBBjg70Adnw9xupQhxdsmcFoINsE4NcH7JXE4M9WixryXNT7woaUkp4F736y22r1A3sUBPbt6N8pZjVtJ9m8RWfttMsGP5xDGDB9wT07aRCW7ZJX2hZviVKjZo3yfd39M8OG0dDruEMmvPhPt6mUdwZs07jK1cxOiqzxi7dRFn17xHn/D/tSg7pO5faDKxtU6HuMhnzekdOp49cjySWUeRTYt1W0X7GGBaw99TgROb7Z8BjGv4WxJxigwDQ4BDPB7PFx6P5zWPx5N6YqwTyGYKtUyYXaNip3A9WeNv+RWdOiz97NWIYSadGURrgVfhLw85CPpF8pRMDVTXpl/O9PzCDEZNsfEsG/hsjYqdICGIRHDbTCdfr296qXCmyZYGYKjEZx3bDvwy2JNjwskTWnS3HFzv26vx/xec61inJk+oXqdYzNW2cU6gT4pW4zIqN5DaGe1rY3GLbdtEJiZ4qEmRFepF1zsEkgh2lOdcbxHKcESbiv0DbYtBnsihLsqBgUsjbzUp2DdwPnqL3GPxFNl96WEOocjeLWmZcvNQhlW/T4/Q0Lg2i8y9OWrbE5xZ+S17Bs5DiQnrqtvFDPZdzfCaV1Dybk0dwhNPPJG1ttLOaXs8nkuB65tt3gRc4/V6f/J4PAqw2uv19k1wrE5kJL7A6/WO93g8pwP1Xq/3Y4/HcyFwptfrTboo0DQtqXVw+CkhRFbfilIRtKDvW7AlzeTTnFPgkJgBwbKf4cATwJfk+ahp8PXbcEQnxJEJBOHCP8HkjxLsjKbMbPa8Onw/+Pal1PX+3//gm/QDtJYJQ2LnuxNw+kB469zI35e/CBOmp67+vEPgld9k0I9OxofJdczlOVYSjBkBD6M7j3MYe8WMgvfjIxaRej7NhUoNo3gQL4+wlDVERTOaTi2RQC8HFiatU0chRPxoezM19OFKzDSCfzxd+CODOZzT6Uq8KJ3ApXzKtymPB5jH6xyUNO9UZoQJch+HsqFxxi49Dgq5k3W4SJ6w/Wse5N0Wj80IvTmYy/kcZ4rj20INP7ONn3FSRjfiR/s+KtjEPAQqvTkSg+0TTGdXpRN0pe1z2l6v9ykgbjGfx+OZTJPtrAiobn5cgznYo4N4AAAgAElEQVT8deBzr9c7vmHzp9D4tHgT+HuqtquqOidH647i/PBRhcqWYPrkAk/9FGK3gU3KXlIIb00s4qxLJXX18d+tw5A8fGeAAbuZVGQeITJjrrrLyeSPkoyKo8//Zu9ZvzopQEVF8lFRt25FGMIkIxeL5pdymlHxtOWSioqI2fiigxSenekmZCW+H1RFcskhPioq2m4f70jnmrsZxB/EnkzXtxISNgeaJextFQI0zmsCbC4PpP0c/Fis2VLDJbIvF9GHt411XF08uzGFZUtMYEXKOrtZhVRUxp+rQOHk4gN5zzE35bEWr/Ek/+NpeR2HB8/lwtoHMRpGnnUl/oyiY1ZW1VFhpv+s030n54s3ea3kItboM9M3CuznH01dnaCO5HV6uBTd6MNs1yOsMb4CoMDqwf6BiznU/3tqpaA2xfHJSH0uXXESWTZX0aJuJ4UcBUANNrSh7Y5mV3JEg47VlW7dkk9NtdU2Mh04FZgFjAC+it3Z4Kj2CXC/1+t9MWbXk8AbwKvACUDWJ5izmUItHTVmZiE+axNYw4cfB3M/qOOVt3W+/FZDSjjsQIsLzw7TvbxzLAmr1gsmf5zmkokmQW44tSGDLM4Znt6MedreJp+vSlN3M08bgUSmiSQWOz+9T3ebx88NcOXrTgLNPntNkTx4RoBDd8vehPZ3isIE3eBTTcMEDrYsxobDnGaZjadZLg1GhVLPIvW2nFQoqc3JTgmPu96jn9WVkcFDOSvUF7UWrimaQ1BEzRWRVh22jUt+S7WaevXBb32nJNx+c/2ZTNcXU60kfunejVWUs5V6DFaKcj53zuYx4zRG+y+iVlQzW/+edKuVu9gl7G32T1kmUwplD8ZWf8ha7TuWGtPYqC1kmfERMkHEsl7hg1J6jscyIHQKA0KnEBQ1mARwya4dusY8T27SpiVfHo/HDTwL9CKyRuQCr9e70ePx/JPI6Pr/gL8Bsel4oglXnyZyR9YDv/F6vUnjF3bGkq8d6e3uu2qFX36X3kw1sMjijYP99IjJghU9jxmVKj9sUzAUOLGbSR9X55n+H31Z5+//zSDKiQqGQ3L6UJN7rg1QlOYUu3UrYuX6Wo55toB1tSmGjCqNo/jubptexTbfb00t9EO6W0w9I148NtUKnp+jM/1nFQkcvpvFxYeG6Vva/s8u0+troqZzk8OR8KVjdDjMw8FAxlHfn3au5qailvPL8fwEREa/Jbabv9afy+jAcZxfMpdvjJbR1XpZChvUl0g2r727WcKsqocQSXq5WF3HXwpfYrrhbdymE2IAyxjEIlZTxjx2Q7Y4XhJ5pKTOPXWN79fcVn918tONoS33/FrtO2a6HmWxYwq2MCmx+jHEP47D/ZdjUNiqujqSHen51V52pXOZOfNzjjxyaIfVl2rJV36d9nbmF9+4WVwf8/ZtEZlAiEb7B9Cgv8tm6iE+yo3IR/IzRYz50mJxXdOxqpCc1tPkgf0DFHaCf8n4CQb/fj55UIko540IcdsVoca12emI3rxLKxXOf9PF6m3xwq0Iyb7dbVQN3Lpk5ACT0fuE+WytxmWfpF53/ehQP+cNzF6c0kweRD8oCie63Cnjjf8rEOBiMzNHKx8WvyybxSItWbs+In6j8U4QR4UuZoaRfO55ACpb7YnUKJJGo5w0GWQeTn/7eDYqIcqkztmBHowKdseRwEa/VN3ALH0urxZdT1cq0LDYQgFfsRfJRTm6yjhxjNyjQwfzcs0DuDIMk9cecZDYWISSLu/KNruS0O1K5xIO16LryU3araXD12nn6Tju9AS5YJ6LcK2Aj4GZRGwQAtgXOAnwwMqAwv/W6vx1QIifahVGzoTacLypzZKCtzbobAwIJh+RPO52W9mjb2am49N+YWYs2LHs3cXmm0vqeWeJxrTlGgFTMKirxUX7h+lX0rK+UQNMPlod5tWliefYz9wzzLl773iBxSfqetoEIX92OrhXMzgpZPKbYJjBKdahuVF5vXoI1xct4kOjAjuu6s1EFnM091p0MEMPkSo1xQosXt/2b4JiBQvU5RjSzWeO3fja2MZPbG0s96lRyaPmal6tOZAedvxL3d5WL6RSypdsbNy2jG6kNn9HPRqjGWOayg4NHsbz2+7HkaWUkAJlhxHsPDsuffr0ydpgMC/a25njyi3+u7ufy8a5kBWxiaCBRUSsmmOBw+DFDTo37xHiX0sNalMMwmZWaUzbrDGyZ8cI1vKgYL5PRT0EigoktfXJH7i9utmceGTL0VtQwjt1Gu/VadTbgoGGzUXFYfZxxIuRocI5g0zOGZS+70LAI0MDHN7T4qkfdH5qSKwysNRi3OAwl+wbThQbZLszPU0aTgAbQYUQvOg0eNWh82h9gDNDyT+Tcmnw3LaDWaX4+MqoZKoxj48cH5PAR7SBniDSz69+bFTy9/ojGM4RXF+4mK+NxLNZP2n1jCv+gfeqW6ZtLLG7N/4tgY2NOar+n73zjpOqOv//+9wybfuy9C7iWImCvcUSu5DYexfUaL6JJSYxMWKMiTGJP2MsEexRYzeCCRasqFEDGLCOiApI3QW2T7v3nt8fd2ZnZncasIwLc96v17x2995z77l3ZvZ+zvOc5zxPPpJz7BbpLvoRzuCSCbZC0RcpO9EuZQm1YvnXXWamYKfj4C6a2wGaKjVWRGDW6sIf22PfmJss2l9HBVd+42NOe6o/4/sSci3fEpJ9J9msjwsa9JRl/FVccMqKAF/HU6b/G2GY3uLh0toYt+fO/1AQIeDsHeKcvUOcdRF3fXY/X9+d8oHiCjmkExeCyyp8TLA6GOHkP3qkE2BkJMD/jHyCDfmLP6b37RAhzgfGGp7wrcrb9r9mK7PN5cwzX+Ux38us0JroJ2s4MXIIvvjufGCupokaJH7S0trlOFsyOM4gUREagOEFcp4rFFs7ZSfaM2fO7FPzKKsbBc+/XOBjiAPvgOcISWtcwyqQuAFgRWTTTMwVMcGkLwKssjJ97NY+AjzgmyWJrE7roxbYXfC0NHnpaYMHDwmz/2CbmKSHYKdzR7OHHVbByb0QVFvvgw2XxNKzj23xlVaEtZj29saF4EGvybXh4orADHQKWbPpecwFdCX6yIwY/0L7mu/0e4r1Wi2wc8F+z695jIiY3fV3k2jmb4FnQHqBEWktddycXVEKF5E0AQnS4ojYgQWvQaEoNZMnTy5ZX2VXmrOUJdSK4ePPNOLxIgT2azi2v0V/r8yb9jRJg6dnmy+jggfXmtzXZLKwM/9H/5c1nh6C3cUEiPxQwDG4C/cmAsfT9UxuiwvOftXPqk7B8+1GTsFO8qcVbm3xcuH8eLxwKc4sg5g5G5CX9uTI/mh5B3fNmLIZt4zaEbjBE8nX2MQl2LzhfZv1WphiHxWRLMukgBxT2ILC1aOTmCAMflg1lSUbkS9codiclDIjWtmJdilLqBVDvmqM6Wi65MRBce5vMhlYqMY1cNLQ1KR3kyU46ys/+3xWwU+/8fHz5T6+t6iCoxYF+CKLRR5z4Mn13YK7YrhGUXIKuhEYCIwEsri32+OCB0Mm/2ovfINfR2FhNPVVnL9G4+JXfGz7QCWj7qtk4gw/T3/hrkXfGhjnOEyN5UmDp5H1P7PQ7X+pr+QB38vc53uJFq2dsyIH5WmtMdw+BtgJSI/ArwB2BrknNp+S+sCL9U414iaGbwAG4dYUypdASEBRhT/cJWAfmV9waN3ZvG8sLPJ6FIrNz4QJPWM5Nhdl5x7va0z4jk11laS1QH5uMRbO+J8fGRAFn3E7VtlMSsxnf9YmOGFhgMao5n7alXRZcfM6db6/OMBLYzsZmmaZr7cF7ckQ5Bbc2tZJr6zAfa4XkazupWUGAwYWp7SdCavwkc9Mrpzjzcgn/t4qg/dWGby0JM5dh0TQ+mBwWZJlRLklsJIXvS1EcNjB9nNuuIGD4pnLQS6Jx9nZcZhumryqG8QE7gR9UrCz3OMeVnYrtlG08OOqv/GKZwEyLcPZ+Pi2nBrZn2e97xEVqUFcvVPJIbEreco3INvpXMRQ3BFZU2JDa+KVL/VmGFiLK9bpBHC/QE24rvDu92GQXhK0EK1aB+fV/IJ5a5/Bl6eutUJRKubPz58BsDdRov0tUxGAM0+Kc+d9eeY4q8HeVbi1pKNATeLVRo/CTPvVW9y9WwQh4P/m+3h8qZGZwGI97vxzrftno6VxZ6OHG4emLL8KTaIjsRuF2z4dCQXSXHcRtWE7j8MrBQReB8aYDouaNa7qJtjpPLvYZPeBNpN3Ln3pzGKYY7ZxDl/TXpESpa+MGP/2tnBGuJ5b2odnJCM5wLY5wHbb/snn4eZAbgHSpOTcSM/7bifCsbVT+croGSQ23/yCb7QmXlh/LXPNL2kW7Qx3Gjg6OoGj6orJe70fmUkLP8Gt+ZNt1GjjJkrMdQ8eoB+uqCeXc7lfXpG3/EaSzBaN2jqe877CKdGjCx6pUGxNlJ17vC8mk/nFT6IcemCOSO8K4AJSw6ukaJq4tRyrgQCcNTLG7P06eHbvMAO8kss/8PHYUrNnximJK8QtqU2PrzOx096WSh32Mqyegp2kSEt3xzqHs6tjiAKP5En1MNCQ3P+xiV0gyO6+jz190k3eJCzOqf6K9hxBVY/413GPvynrPoD/i8Q4KJ79OyCk5MbOKNs5Pddq/6HiiayCnWSN3sxjvjc4J3IwPw5P5PjoPnjx8ElRpcy6VwXL99l8Dmlrt7PjJSX4qbSpRlFWds8P/R2zdNaNQpGPwYNLt6qh7ES7lAEDxeL1wMN3hbn31jB77mVBvXQTxB4JXA10r8znkMr06AUqoKIKxtW4D/XF7YKnlhmu8RPFdWV34FrqSV1opus52OoIOrrpQU3P0swpipyGPCcYZ4xHcnld7odyg+7wx5Hu72+vLBxCvrhFY1Vn3/OPP+pbS7uWP/nMNH9jTpvSAzzSFub3HRGCCTe4LiVHxCyebgtzQbSnle3gcJ8/W7m1TB7zvdnV74d6Ow/5VqEXFWWfPojQgd3I/cHvAGSvD51JeqIS9/OOE6Zn8pd0JNkizItYRKFQlIQVK0oXHFl27vGLLrqI44477du+jB7oOkw80qJjZ3h/YREfS5wMT2Rr4pkWdeBPX3iRcdFzmtBOe3lxn5MB8AtJoNvwbU17gfGcmThPDp06Nxhjv8HuRf28X4yhhuT2Zg9fJSLJDSRHVlhc2xBljK+SxjaKXq3VFy3tVz2F5wyW6DG+0KOMtbNn2DKBC6JxLojGieNKWr5P4VXPAuIiXVgN3KJ7FumBYy1aBx8azVxa9RkhI/mBVeJGEubj47Tfh1C49NZ2FKoMlmmta6RGleB+mXykQueTZeOyf8n2io8r0JdCURqmTp3KpZdeWZK+yk60t1ZGeCS3rfTwt1UmTau0/HE9yeyQCaE/ri6O0c1q8ekFlFEAPjh1aIxZS0xaYu4Jtql2uGjHGOdtn2kZnlUT58zqOB/FNDodwWjTYYCR2cfeg+2urGa5GFnlMLiI6PlSU8yqPQCryJFJMfHUC4yv3F+kHzgZ5C6ABmItiC+AD4DPMWQNx9QuICrSz7oEN7I7+4UbUvJDIfirFIngtmG4ghol9+iqGnfQkC/SvLvHoLnbvjgg0GVFnrKhUOdUc3zk8Dz9KBSl4/rrr1eiXa7sW2+jIXEKTRwbdD07DU2yLCZ4pClhCUWK6ChRvtovJBf06+l6PWKIxduN+b8ewRqb2/aLEt4rytJ2DVOTjK6SOVOHCgG7eHO7kM/bMc6Dn5o5A9EAztsp1idTk+4a9/NfM38pyxpHZ5Tde9HOptRB7gzOL0mVtyfxvdgetOEg3sAj6+jUug8DmnEDy3aku3CbUvKXtiiXVO/NoPYR/CWgs1pPruuLAkuBxWS6z5PkG3Q5ZLrBk1nRuiOxRTvD7W1ZpvdMmxqQfu5pvbHogiEKxdZE2c1pz5gx49u+hLyMCEgOH1Ag/WjyGWu5r+1Mh0ca01yXxQRXO4ABYU1wwtIAN63xZASjnTYqTr0n/xztJdu55rzfgIEBh1Zb8Hajzh8+9nD8635OeMPPnz/xsLpAdrZPmuCKt70cOyuA1CGXJXf0qDgX9dHI8XMjDeQxDAE4NVKPvxf/5cZae4IzlQzB7qIOnD1A7kunGJVlfwVuNHec5DyHTzocEY3zzrowJ0Zt/ojkmqpBaYIN7rzKWGAfuo/5vVLgl7lcPJKeaVXzr/2+pv1Cftl+MSPsIQBUORWcFf4+L6+/jwPiu+c9VqHYWim70py9XUJtc9AYFZzwnj+j7GYGPlJredMnPpMBuV9RnHDvRMY05ck1cW4fmjLT56/TOGOOn7WxnkLzo2CUa8fFWBEW/PZjLzNXGEQtkTUjpU+T3LV3hGOG9hyMvLZc59zXAoTTdzmA7UZNawJ2aXA4b8cYJ4+1KCro+VviDv8arq/MHpAyLu7n2ZZtqZK9kK81wQ8rPDzlLWC5i09BW9JtYyWwK7kcbb9vszkwLtm/PlDAmf8lrrXuclZ4MOdGKrgpMINXPB/jdI1iorgCnS7oMWAlOYMigNfWPcVO9naAG3SnbeSAZ2sqAanupW+ydOnnjBixXa+dT9XTTqOv1dPORbsFf19q8sg3Jl90aK67XMd9znZ/dgmgPfFKimahd85DNs8o/x7Vwe6B1IO0JQaPfW3y4gqDiCPYscbmnDFxdql1WBEWHPNmgOVhrUtoc3anSV7+Xic71KTO3R6HXZ+opDXPhPDpY2Pcul+e7GF9jP/0j/H72BLe9biu8gG2wZmRflwWHkBlLwr2Qn0JR1QHsUWh2e9W0N8m84PeDfJU2jKkw9HRGDN8hdZyx4GXAYfRlp/nm8fTX7qjwNVaC6u0Zl423+cJ/2y+1t1laVVOgKOje/CE7+/IXClPgd3iO/Nic67KNBvG1iQO6l76JqUUbTWn3UepNOCSbeKMqXY486M8aSAtUommNoQGssYgPdxssnsgJZI1HrhouzgXbZdpuq+2BGfM97uCDfkMJgBijmD6IpNbdk+d+4nFZl7BBnj2S5Prdo9St4UkvppEP/Zp8dAsLKJC0uAY6MUubC+SFz1zuaDqb9jy8SJae0DaIJL/6hXkE2wAS2jM8BWzdtrE71RzcjTA1R2juwQb3IIlA50avmON5ACrgad9T9EpOtnJ2o4TI6fRIOGOwANZz+qVHq7vKE1Qj0LRG+y+++4lMwb7sLNRAfDoqgKW1Ho2XLCrcQOHs/B1Fld4d/7RbDD+swo+bkqzHIvwicxanjlGfG91YcszbAs+aOo9C7VU1EqDgY7Z64K9TrRxUfWtxEQrReWSJQoiQmpUVVFkT8WN559r/g5/bA9mCHaStWIN59UezI9qv8/rvr/zvvdp7q/4PZPqd8IrljCl80T6OXUZx+wS354nWv7G3vHS5XJWKLYkys7SLmUJtd5gRTSPiMbYkJTNqToOOaxsgOoCS73ebNe5fIUPJypSQl3kJEbY3jgB64PB4t8aj/heoVMk4g7EayCPyX+A+AY3YjuOO1ordoTXRFeu2xyMsB3G2dm/nw4Ol9ecwGfmgh77bGHxjP9+dGAbpz+TIkezV+wotrFHsqu1U5HXp1CUJ2VnaffFjGj5qDfzKGKRgn3ASIulp7ax8262W5Erjwr+oDp/5Ppf13rc+fX0b06Rqrp9TaYPfZ+BhQUkYEjGN2yoK6FvYSN53tPKmdVLOLR2MafULOEpbzOxQnMK3WgTNk9624BJ7ksk6kznQKMd+CjRJo6bZnQJxUUpvkL+LGVwamRF1gdIjAi/qzo/q2CnYwPNWiNv+x7kA8/jfMfasYjrUij6Htddd13J+io70S5lCbXe4IQBm77Eae9qG58OlzfkV/ntPDbH5hHtVhve7Ei4qj1kZgAp4pt07pjM/k8cE6c2S93vdE7YJk7NFjKfnY12YXNczdecX7OMl7ztfGhGeM3Tzg+rl3NE3Vc0igLL+xK84mlm1/r/8ZkZBLYH9gZxIGgxsgcU2JwQXQxad+HtBBYV6G0JblT4PeRa9D+ce/kisCMh8y0s4qzWlrFeNBInyg01J/Cy75mi7iv56b/me5b/eF4s6hiFoq8xderUkvVVdu7xUpZQ6w0mDbC4fZnNpx1Z5nULZZVMsPcA11KdWG3x+0ERrlvtJdYtgcmOXptHRoTx5LGaOx2RKkAigDpgTWKnhvsEzqHBhwyyOHFEpkBVmnDvwWHOfjVAR5axyYQGm+v32HIix9NZrEf4h28dz3jb+EZPv+9kbVMPHxuS02pWMbt5WNZzWEgWGjaf6xF+WrWYaEa0daKYh5Cgx9xE3DIxchIOCMknnmpcQe8+ovoIt4b26Cy9LgceTPz+BfA7BHtRxVBs/FTxESO5m/68QkTAtTUnEJMBWjS3WMhgezgt+rJiZ0wyeM53P/vGjsy6b51opkN0MsBpwFvsF1+hKBFDhgxhwYJQSfoqO9He0vBq8MS4MBd87OP91m4flwc310UeXQvW2BwwKPWwv6A+zverLf7RbPJZVMOvSY6usji4wi6YaayfIanTJeuTc9O1uJ7W9aTWjHdLFW2Ykv/bNsYVO8YwsljjBwy2+eAcuOmtGDO+NmiPC0ZXO5y9XZzTx8bxb2HfUAfJTyuX8ZBvbaKgRaqaVSqhSeqNWGjCobUdPN4SoCExkHKQ3O6Pco8/yqquGIPRuGv6GnHf4G4R4EJCtyVUy7V6Uvm7u7/5/8UV5dGJ62sD/odrYSf7FEArQ7iN3ZidcbQNrAJiIgwiZc2v1JflfX+6k/6VW6L3fOi9ar7N7YH7eMvzXwCqnSpOjkzkJ52TGSD7bVBfCsXmYuXKnpn7Nhdb2CNx0yllCbXeYqBX8vz4MHNbNF5aaxB1BBUVHv70Je4c9UqyxhfVeCTT9+/p3mwwJD8q4CrPhinglJo4f1uXZun0x41vaiZVeayargQw1wyLcll9fhf/2Dq4ae8oN+29ZVrV6fyKJTzoT5aoTGbAAdeyzR4B+KEJp9ZEeLHZh47g8sow//B3/3w03De2Arc2a+FAAo80MaTAEjauEKdfj8Sd416GWxgkXdS1jLYr2AkbHzvxGn7c9efJjzsXxYQ5iG7tfN0i2x/2Pc2Vlb9J5D53adXauCfwKC953+BfzQ8x0OmPQlFOlJ1or1ixYotd0L97jcPuNe6jsn9/D4YV5aZlXtdT2kIquYoOew22uHuPCEMCvZuf5scNMV5qN/gyfWmYl1TBKEGXcTnUcDirpm+mHd0ctAmb21ieY28t+aRsoenwgsemVsosgp2OjpvRLE6hsiLjLAja23FHIETKBZIu2uDmEG9LnFMnW20xicYqxtLKAPbjH5iESVZu7aQ/LWyLjQ+TNuoI4aENjYJOoB5Zyg+KTur6fbVo4meVN2YIdjpL9eVcW/FHprXdnPc9UChKwfjx40vWV9kFopUyYGBzc8XwGM/t1MmkAXEaBjr0H+Mwafc4zx3VyczvhntdsMF1kc8Y1ckJNXE83R+oGl2Cva1p89SQTmq2vCXWG81LnlY6MoLCku+PQUYd1Rw85bN4qKikJgaQvzgJwLkRh193jOOqjh2pcJLjczfwoNYxcF3hq3HFvBVXYnM/EjqpYTG7YwFxDJZwJF9xHOvYhRbG0sR4FnEqK9kHiTukqM5yxuS4Ln17lVPLxPC5XX8/4n+mW9nRnvzLO5s1Ym3eNgpFKZg3b17J+io7S7uUJdRKwT41NvvUlHZJ1ABDctfQCDcMFHwa1bAkfG1pfBzTMAQcGrA4NGCjldkC69YeaTmTkXnFjY2bhaRZL+azFLii7SfXYGC09QmHx8YCgqs7d+aH4SCzPCto1qIMtSs4LDaYs2qW86pnddpRhQO8lrET2/AW33Ao7YzIem3r2AWdCAP4gApcGz6aeEUkPb4XtU4Df2h5nH4yVd97ofFpwWuJC4tPjUUMiKu5bcW3y5QpU7jxxj+XpK+yE21F79FgSA4wkiKzZa+l7g1G2dlEL1l+UlJopneooxHfoLqjTbgVvipIOZsjaPIR7mk9MKNlpTQ5KToyY9uZ4dF8qL9Pox7AHVgUdovE8dPCINoZmbfdWsbRwEJi2PhwQxx8UnBy+AJM2UDI+AAdg71ih3FE5BT83eazTVnco8mjHmGKPsD06dOVaCsUWxrfjVcxGh9fZaxtlrg2ZhjIk0MeOCNi8IEhed8sNABKd8G3JV7JAus2P+ncmV3sUXnPcIf/Nq6v/FXiLz+wLXAQqao0Ou4gQ0LCIQ4SIR2+YUzBSDMHL+0Mx+Br/Ikz6ULyuv9eLmm7kws6r8l7/KGx/XnOl3/ddr1Ty/j4uPwXolBsZZTdnPbcuXO/7UvIimXBBx9qvDtPZ936b/tqFBuDhuA2tiF7Jtgm8lVVOSaqo8ko/y+wjEyvRdICTv9XzSbqVtf2/5gjObGmidOrm7jP1067yOw3pH/GbyquTfwlgIOBI0m529OXqQnc2Wk/oHFIbAyRIlPg2Xi65raTZ5RC8kDlz4kUmJP/QfRIBtk5EuQnODd8slqzrSg7lKX9LSMl3H6vh+kPmaxa4z6YvR7JpKMsfn1VlIH9+27pVEVPjqUfD7duw28qVvCpkbK4R9iSEyMWL3l8fGSmRNQv4YywwWkRh6PrlhAVOu5SgH6krN0kGq4w5/9O/MeTypI22xvl5oo2Tg37MAT0dzQ+0R9NRGUL4DhgDBlh/1kRIL0cHqtiobe5qPfCQ2tWq6BTa+E/vmc4OHJWzmN9eHmk5XZOqb2YJm1dj/0To4dxVefFRV2HQrG5Wb4816qR3qfsRLuUJdSK4fJfeXn06UxrIRoTPPmcyfvzdf71j04GNCjh3pI4NFbNobFqPjA6Wa7FaJAGe8Yr0BD8vBPmGzafGQ5+KTg4plMrBRdXfUO0az47QPZ/zaSwSvKvks60rNdpDndWdOBa4yDk2bgDgn8BI0itmC7geBMaUaFRxSKa2AOZ5/HhYT1+VtGKYBUaEqhBMur5v9gAACAASURBVAgHE1iuf57RfpExn1d8j7JeW0O9PYjvRc9gF+s7vLXunzzqe5bnvS/TLjoZY4/i7MgJHBLbH6FKySj6CPPmzWPvvQ8qSV9lJ9p9iXfe13sIdjpLlmnccqeHm3695ScdKUd2swLslmUee7ylM95KBX114DDT20pqIVRlgTMbJOeYXdKDyJLbuq+PT4qygxQGcA7uPPZXafsL06RVU+UY9NPm0cReOVo51PIfPsfATjtvI/AVGjtg45Nu4FmMCH+qvpB3vDMyzjAz8DcOiBzPFW3TuCx8HpeFzyvq+hSKb4NJkyapetrlwEOPF6iVDTzxnEln/mJLii2cZs0m3rXm3UdhAU3mjIXMGeOkMHugK/yr+3Hp7EUx68fT8Ugvx0TOoJ4FDOBNjK40Ky5emhjELBpZlSHYSWwEH6NTbQUBuLPq8h6CnWSO7xnurvzpBl2fQrG1U3aWdilLqBUitLjwmKm9Q7BqtWCbUcpFvrVS5+iYUiSEu9hxdKE56GROsvRI9u5tDVz3+CKKLYp+QHwk4+O/4UvjU+Z73qSGEGEGEaEfOlECfMMaYsg89yER/LbyeurbqnjV+1je/mb7Hub0zl9Q7wwq6voUiq2dshPtqVOn9pk0phVFZiwL+DfzhSi+VQJoHB6t5F++CD0jw5M5wJOFP5IUI/DJqPPkcdm+b+mZ0rIVFkmxc3wA+8SHA3BLy7O87H2S31fexxptJDHqEq0cYAXuMrSqtL8Xkz4PH9KXcm3NyQhh570LS8R51/M8R0cuzHunCsW3yd13312yvsrOPT5kyJBv+xK6OPp7hWspT/iOzaCBysre2rm6c4C7lIAwrnBrpFzfybXTZuL37gKej/SEKdmOWU8yQC2VBKYnQ+wq7mlL5QY3MFmkDeIzbdc0wSZx3cNwa34PBAYDE4Dv41aXcZEILGEVEQsPnaJvDLIVilxMmTKlZH2VnWiXsoRaIU4/IU5Dv/wP38su3PBqXIotjx1sH8dFqxJ/xcnu+k7OZdu4Fbo2BIee8hgGHsYV7nBifxxXvJPtHQIO3Nx2KNvY9V1HfqOt5/cVL+TpL33eHVxX/cG4c+1gpjnQCw0/BtvbFGihUHy7iA3KZLhplJ1o9yVqa+Dx6WEG9O/52NI0yW9+HuGYwwpb44qtg9+2D2CkbVIoc5q7f02RZ7XTXt2ZDswHngE+xHVfW4mfYaATCNOpdXBx9VN8pa2jRbRwh/8uDq+7FFsUktvuDzIPMBaAhjSplome1uOW/EyPe6+zB7JH7Ej+63mRByqu44GK6/iv50Wcoj0NCsXWRdnNaZeyhFox7LKjw/svdfDM8yYvva4Tiwl23t7m7FPijBim3OLlRH9p8Iv2YVxcU0zrWtzKXNV52rQDH2PIMVgi9a9e42hcGNa4JXAvUoCbzCU5/539O9euRbk1MJt3PLewRF8CfDdLKw+uRS1wxT85R59+zmEIFnSJdhRolBDvpu+VwGAp+EH4Ui6p24NVxteQOPNT/D+GWGP4eetDbGPvkuf+FYqtj7IT7Xnz5vWZQLQkAT+ceVKcM08qn9rTiuy87YngLvsqhBdYCOyeo32EneKf8+PwWA6NjuR1T4SVuk1/R+OIaIAAGh+Yh/KqZ3ai/XYFe3zS9z8ssQS6Ffdwxb6GnvW9K3AHFunLwnQqsWjHtec7IGsAfDsQs4fzQMVviYnUFFFyUdsKYzG/qp3EX9bPob8zrOC1KxSbk2OPPbZkfW2UaAeDQT/uZNgA3DDRc0KhUGO3NjNwczHGgXAoFDoqGAxuCzyAO/T+CLg0FAqV1M9VyhJqCkWxtCOZXG3zircYwQbXim0F3sJNQzoc9985BnwFMoSHKv7h+4wWEeHEyFgquonq1R3X8I75FhERwbWSddzBQLKdnTifK5qWEIl2Jm4d7qRY1pI7g1tN4jzhxJZmdFKlOvOxxFjKADKHCJKUo79VW8tM/92c33FDgTMpFJuXmTNnlswY3Ng57UuAD0Oh0AHAQ8CvsrTZFtg/FAodFAqFjkpsuwX4VeI4gRtSWlKmT59e6i4VioJcWm3zirfY6RCJu5xqGLALsBPQgOsqjwGrQET4wGzkNc83/LTqLfatf4KQnlmJZry1O4+1PMMoezRuOFglrignE7UYuPPnSdlsJVVzexWuPZwsMJKPqq7fBJ/RgWthF1PMNddjMOl0f937eBFnUSg2LxMnTixZXxsr2vsDydDRWcD30ncGg8GBuMPvmcFg8K1gMJj0HUwA3sh1nEJRbnyhw2VVklneZCrSYqJQO3CFcl8gSEpIk8utjgVGZRyxUu/g1Jp/EyEzsHHf+P481PIKQjbk6dvEFefPyIwIf59ianAnl64JFqGzAnADz4qZDMon7A7QojUVcRaFYvPy/PPPl6yvgu7xYDB4AXB5t82rcaNXwB0Mdw+d8QB/Bv4C1ANvB4PB9wERCoVknuMyqKsLYBjFPBQ2jP79qwo32gLYWu4DyvNerifK9cSQXZYtpILBsq0akLjWbSvuzFSuf18dtzb2I6RL43K9g1f7r+AcdgLAweHfhLia2UXkQ9NxRTuQdq1h3MdAoVzpIAih81bGtlwL29LJZ1VIYKAYXtT7XY7fry0BdS8bTkHRDoVC9wL3pm8LBoPPkPJ5VeGu1EhnFfC3UChkAWuCweAHuCZB+vx1tuMyWL++s9DlbTDLly/vc4FoG0P//lVbxX1Aed7LY16YmjPwO+ma7i7czbg2qkFyvXNuPLgzVJ9mbH08+hlHt45gudbC6TWP8anRiBvIVmhw7Em0i5OZr7wVGFrgWAd3SVkys5tLcn4630Oo0GPwkI4zaOzM/36X4/drS2BruhegV+8l3wBgY93jbwNHJ34/CpjTbf/3gCcAgsFgJbAz7tPjg2AweFCe4zY78+bNK3WXCkUP7ii0FDvD+k6SFHFPln3Z6N9jS0RYxLE5peYfCcEuHi9R3AC4dLv88xyt0/kaSQyLSiyqsAkgE4OEfBa+h55x6un0swdwTFilN1V8+0hZuuW5GyvadwE7BYPBt4ApwPUAwWDw5mAwuGcoFJoFLAoGg+8CLwHXhEKhJuBK4PpgMPgf3P/Jpzb5DjaQSZMmFW6kUGxGFukQKmrdRvq/ZzLpCRRb3CNbu+2tOp7yfsznRvpccOEFHIK16DTjpwON1rRzrwNCeY6MAu/g2szVSKpxqMNiIBZ1GDkGHwPs/gwi99DEK33c0vwqVbI+RwuFonRMmzatZH2JUo4QNpTGxrZev7gBA6pLVvd0c7I1uZbK7V4WGHBYXd4mCRxScdJrSS2SSgacFRpzvwgsSf0pwS8lYS1ZizuWOKckeynPFB5mYfJu198WGlHqSbnVd8V1qKW77ZfjOtM6c57bIEotTV13KwCPNHll7SfcUXU573h7BvjU2QO5ueVfjLALry2H8vt+bSlsTffS27rSv39Vzn/Gskuu8m0jJTSuFRi6pL6oB7dia2OkDV4piRbMVywRMowUHWSuanZwA9LyZUNrAZZmbhIW4a7Uo4LUmuxkqpPsbnedjzB4r8dW1/pPuuznAQtwC4QYuPPvLbgDi9zz5RZeYvjwEekaghwdPYEGOZBftz7CXM/LzPI9yAr9SwKyigOjx3FY5HQqZFFp4xSKrY6yE+1SllBLJx6Hu+83eeBRD0uXuY+n7+xsM/ncGCcfp/KLlxO1EiZFBU8WzKPyDj+IagxwduAhf4ywSDmetrFaqZQVLDR7CqJfRrF5mViivUdqiaxi2dzgGu7McVtif6KSmIQ9xFDOax3HHM/HzPDlc3qllwBdnuX8+YlQgS9R99uQBqPtMUgkAsEescPZI3Z4wXMoFOVC2Yn2lClTSu6SicfhzMl+XpuT+XYv+Ejnsqv8fPhxjBt+VSg/lGJr4pcd8JInTovWPfVnkk+BpVwYPpw9rHqu7KxhtidMh5BsaxvsF/djAf/2wMN+WKJBtYQfROH0iBeNiSzV2/hUb+Ky6tk5+kiSLP1pkbToj4xtxyzvBTRG29jBupJF+hoWGp9giTg6MSokxBBIUaiud+GAOTthiWsAwuKuihtZrS3n2vbbCh6rUPQFZsyYUbK+yq7KVylLqCW55yGzh2Cnc/f9Ht58u/fXoyv6LkMceHW9wTB7DZkpRNqB/wLzuabjO+xhuRHgtVLnxGgl50Sq2C/uzhsbwKQYPNEC762Hl5vh0jDUSaiRXnaxGliptVMcqe9frePjVx2HAPBX/zQOrp/IXPMTYgIcTOJUEKGefeP7kj3KPZ1iVoDbXVXDk2d6xv8Ac82SLy5RKDaKCRMmlKyvshPtUiMlPPCIp2C7+x/JZXEptlaGO4K56/pzY9tSxlr/AflvNDmDQ2JtPNZ8MD/p3HmT+9A24F9cSDgwNpoZzeewnd3ATF7khsqbs7aNiChzzYWMiReqdV1YtAOEs8r+k757s2xVKPoeQ4cWylXQe5Sde7zUtLbBV0sKPzgXfKgs7XJEQzA5MprJkdHYOGgIRFFrsIvjoPhwiimncWPbIRwaG802TmoJ1Z/5W95joiLKSmMpQopEic9sJGPCc0WPxwmQPYnSF8YnhS9coSgzys7SLmUJNQC9SC3W1fCp7NETkt2b7GL1Z+/YkLxtGhwfF0bGZwh2Ox28wTsFz98pbITI54KXGFLQ4PTrscdDlAaa8qzFLpT1TaEoP8pOKjZ3CTXR6OCZbSM6Jfb2GpX7Gew5weL9efnf6kMOVBHkis3DyZHteNeznOzWrqRJa+Mp72ecFN2ha2t6Dev8CDQ6kZjIjPSmLl7pYVrrXzgsdjCzPK/wofEpJiZveR5jqbkg75kPjh1T5DUoFN8ukydPLllfZSfaEydO5L77Hu39E0cllddE8T0eJ/15Z43V+PXJkmPn5V5Ta5qS888spuaRQrHh/NMXwo0M18h0rjkkl4Hd51+QIdp1spaRDGcJy/KeW2AhAJ0WJF4c/HhkJbVOLUfGvseF4bMI2mMBmBg7gomxIwCYYI3gypozcp63yqnl+PC5G3yvCsW3wbRp0/p8Pe0tls1VQq16cgT/3zMFG8BY5HD0n9u59bjsLkTTlPz15gjBsYVTSSoUG8M8Y2XiN4dUQhSL9HXbHxirkGlBYwLBRZxV8Nwa4UR70Ihi0MwuVn8+XPcOf2z/TZdgd+eQ2ER+0n4DIstkeLVTy20tT9BPDijuBhWKb5lSRo+XnaW9OTBfj+N9Ibd7W0Tgkq87GPuk4P5HPMz/n46uSw4+wObcM2Jsu03fTSWr2PIxihib61kC4H7CFP4Zf5H3zexFdgRhNHq60Z0ic6OfE/4x340dzVO+e/nUWICJh/1jh/H9yJlUydqizqFQ9AXmz59fsr6UaG8CxnybwO0xPP8qPB9tzrHZa4DFHn9WFrWitHw3NoIZvkUF2ozssc2PnyebH+TWwJ383f84TdraxB4LjXCXld2d8dbuRV/bKHssV3XcVHR7haLcKTv3eG8VSPE8H6d2Yife5y1EEacUErSVyqJWlJ4Lw7sV/I5ODu+WdbsfH7/ovIIFa9/i3bWzuaTzFAzWoedYWy2k4Jxw6YJyFIq+wODBg0vWV9mJdm+UUBMtkurLIogNjB1z+pU+G5tCsbc1lBs6vptTuK/p2I+D4z0t7XRMTLZxRnFNx685IHZQznbXdfyOoL1Dzv0KxdbIihUrStZX2Yn2RRddtMnn8D0WR2TPB5GT+AQNZ5uye7sVfYQp4fG80HwaJ0d2YJhdxVC7iuMjQZ5ffwo/6dyz6PN48fL3lqe4rv13bGNtC7jW9UGxQ3m0+Vkmhy/dXLegUPRZpk6dWrK+VD3tjaBqShjfP4tfVy01aHnUT/yQ3gsh2Jpq0ap76ZsUcy9hOjEwMem7aXjL7TPZUtia7qWU9bSV6bcxbEDGUacW2u7y9apgKxR9BT+BPi3YCsXWRtkpSW+UUIt918D3dH5LW5rQ/jsvkZNN8PfeXPbKlYIHHzZ57U3o7Ayw0w4O554VZ++97MIHKxQKhWKLpuxEuzcWwUd/YODcINAac3vvw+eYRM4pXN1rQ3hjjs65k/10dCQHATqhz3Weec5k8vkxbrxe1eRWKBSKUjN37tyS9VV27vFeKaHmE7T83Y+TI//Dp0NNHtipgkhk07tKsnqN6CbYmUy/z8PfH1VuSoVCodiaKTvR7i2s8Trr36yg4woP4ZEaawyNN4WHM41axjU2cOnPA+y6ZwWzX+2dkpsPP2pmCrbEzUKZZuxPu1eJtkKhUJSa3XcvPqHQpqJEexNwBmmsuczL9p4BDNQH8V1PA4/oASzhiuu69RrnTvYz/4NNf5tnv5aYyXCAOG7qaJtUGmkJoc91li5Ta8EVCoVia6XsRLu3S6g9/pTJ0qW538ZYTPCXOzZ9btuK44p0tngzSZdwx1WxMIVCodhqKTvR7o2MaOk89Wxhl/RLsw3aNnE54tht7fSiTFkxhGTY0L677l6hUCi2Rq677rqS9VV2ot3bJdSamwu7o21b0Nq2aW7rmsrCbay44JtvlHtcoVAoSkkpM6KV3ZKv3i6hNmyow+Iv8499An5JfV2mBdzUKHjjVZ1IRDBwiIPuhXff0ulsF1RUSo4+xmLcd1KmdXNLcWIc+lxnzJjis7UpFAqFYtMYMmQICxaEStJX2Yl2b3P6KXHemJP/bTz+B3H8fvf3SBiu+6WXZ54wicVSQuyQGQx+261e9j/A4m/Tw9TXu8JfDP4i220qzpcCa5aBjAi07R2MIyyE+jYpFIoyZOXKlSXrq+zc471WQi0qISo59miLvffMbdk29HP4yY9iAEgJF53v57GHPRmCDe4H0X1x2FtzDM4+I4DjwFFHFrae6+sd9tl782ZGk20QPsdHxz4VRK/3EfuDl8h5fjrGV2C90jvL2xQKhUKRnbIT7U0toeZ9wqb2iBj9hydek2I8d0I7J50QxzQzrdw997B47qkwI4a72+e8rvP6K7nNUUFP4Z4/T+eV2TqHHGKz4475BfmC8+P4fJnb7HXQfIfJ6ot9rL7MR/s/DeRGRphLB8Jn+LFmmSAzBx1ylUb4bD/Wu0q4FQpFeTF+/PiS9VV2Ds2pU6dy6aVXbtSxlVfE8T+cGcJtzpMMmGfx4HltLH7Xw5y3deIxGDfOYacdMts+8Y/CkeauFEpOoZOLaWM8MeS5oB9j8uxVFhN/X83ni3oK4+mnxbjyiljGtrYnDBqv8iEjKYFtf8LEGOEw+OEwnu0LhKN3w56tY7+b5ysTF8T+6MF4OrxB51UoFIotmXnz5pWsYpkqzVkk3n/aVE/J76JuecAgdrSOtlLi+7vE+AikB2KHCWLfk9x3lBf9a0krgqcx+TJLuTCB5B6aOI2eBbulBi2/C/BEfSWzZvlparIYPdrhzDPi7LZbpgB3vqmz8mQ/ONkD2PRBDsPndKDX5L9vp0lgzXcdMtZDHuyXCo/zKj5oR9uApWdbU4k+dS99j63lPkDdS1/ll7+8khtv/HOvnS9faU4l2kVSMymG5938lxM7QBA92qTyWonopu9SgEg73AGewuRi/ERIfT4X08otrM/Zh9Rg/WvV1B9Yl/cLv+IEP+ECAXL9fhOh9uKEr9wGfb4G7QJnjINdI+n8pY/ocwZE3eszhESThaPYAy91oO9avBW/Nf3zqnvpe2wt9wHqXvoqpaynXXbu8Y3FnFt4/GC+L/HMyd5OdNusAScTx4/kXAJ4gWbgIvJ/iYUD/vujcGDuNvY6CL9VeG65/TmT2ovjmPeaeO/woH3jWtRSSCIV0N7ebd66CMFGSMSAvjsQVCgUii2ZshPtjS6hVkzI3kYEeE3EYi2dgMYyHIZTOErc/E/+Nk676BEolr0deG/04P2LN2O7kAJ/OwwGVpK6LYeegXLd0Q+w0YYo0VYoFIrNQdlFj28ssQMKv1Uix/xxYVxX8nCKFLsCUxp6f4moKHyuwAAHz22586LrQH16txTIpOqVeK9WNb0VCkV5sXz58pL1VXaivVEl1GyJLBCw5bKpb2e21do9ie+dPwpd80PViYXN/gE1rlWdDz+Z7phkcTHZbYAhhjv4Hw6j77lhEekKhUKxpTNv3ryS9VV2or0xVF1m4Xsmvxi1/0xHBjb17RS4MpkbB7jDLpyIvO7KGMbQ3NccODKOt4hsp4Kecyg2YNVIvDdG8Pwqiv+RTir+24Hx3c2b2EWhUCj6IpMmTSpZX0q0C2C+4+B7Or9gRw8WhK80iJywsb2kW9d+wJu1lQNcTh2/eKSSF1/If0ZjkGTIzE4CR8ZBT1nFWrWk9tIYg+6NIIsoQgJkddp7jrfwTI7j/b8YxmE2Qn2TFAqFYrNTdoFoxZZQkzbYHVD1UGHr0fOORLRIOq8WeF6T6N9syBVpQLqLWgDVQIQFRNmRGBaCF/BxG9W8hZvy7M7b4Z7785/ZHCYZ/FAEa7kg+rGGMMG3p41W4e5vr3VoSFxBUnOT89bJu44DPWapAxL/lBixuRqRf5rIVoE+ysF/Whx9sApCUygUis1F2Yn21KlT864NjC4TLL/dQ9OTJna74ADRjK9AIWsRBW2FxN5Bo/l5qLhO4v03iMS0ctxIuJl7uKNzzWELFhNgd+oA0SXr6XL45hsFbjQNY6jEGJo5+Gh/1MB3j7fHFyCZSlXgzl+3dD+ZT1I5LUzLz3zE3sw8uv1PHip+HKPqZ7HuRykUCsVWy913312yvspOtPOVUOv8TOPj4/1YTSlfr1XM2mRAJtbCO0MEbdMFS+7UabnBxLEFLZaOBBqwqPA4NJwap+EJgYjk9in/G4MRSOI4rEPDSVjjOolqYJtg0MoYxKZ6GZWnjQbEgPWkrHAHkBFB62+92J9lGWxYgo4/e9HqJRWTNzLBuUKhUGxhTJkypWSJYjZKtIPBoB94GBgAtAHnhEKhxrT9RwI/T/wpgP2BnXEnbGcCixL77gqFQo9v3KVvHPlKqC36oS9DsAGW46V/gQXY8QkCZ1hCtGPw5YU+Wl4wyHR7QxMmTTFY+oSH3a7vpP9UiQj3HBSsJ85ZtPCjhGN6JTr3UcmtVNOBhgb0qy1wozaItQJ8ElmduSv8okF9c+FJ6GTtke4TBFkFO42O2zwEzourUp0KhaIsEEL0aka0fGxs+NAlwIehUOgA4CHgV+k7Q6HQC6FQ6KBQKHQQ8Dzwh1Ao9CkwHrglua/Ugp2Ptv9qdH7UU4yW46WjwNvU+X+p45b+1EfLCybdBTsdGREs/chk3es2nRc7WKMkURPWorGSKHWspzZtJnkwNr+khbdYTXVCQlevhKVf9+xDtEHg9x7qx1XQb+dK+m1bRfVxfszZqWu0lwsCee/IxQAKlzjpibNaI/aOqvalUCgUvc3Givb+QDJ+eRbwvWyNgsHgMOAs4PrEpgnAMcFg8M1gMHhvMBis2sj+N5pcJdTa5mYXGRvBu9TQnuWtsoElB3mJHeUeG10qWPt4cebl+pkmzmjo+I3D4vM13o/7+QqNQT1nkbsIEmMRzUzBwXFg5nOZkipaoeb7AQL/z4vWmLpez9sGNacH8E1322t1ssAsfYqN9cLLlo1NNKNQKBSKXBRUmGAweAFwebfNq0nFKLUBuVKPXAH8v1AolDQb3wfuCYVC84LB4C+B64CrNviqN4FcJdTyuXI70HmVOgYRYxAxNCStGCzDR8P4OCNwA6/W/9PMWVWrO05H6vfmh10xHUxbHvvcpYoObqWaBmBtc2brwE1ejCzegiQV13qJHWrhP9qi9QpJZTx/bxE2KjMrAPpIlWRFoVCUB8cee2zJ+ioo2qFQ6F7g3vRtwWDwGSBpJVfh1rqgWxsNOBb4ZdrmZ0OhULLts8Bf8/VdVxfAMHrXzTplyhSmTZvWY7vvB/D1L7Mc0IVgFV5WdVtDPep4L/36u9vWbUAGz8B2gsWfVxH+Aowv3G2VFBN1LQGLnyN4baFO21UVGIMEAwdIPA+4+1zXfPorcQeOoP6pSsQfYdWPwLol/xegKc8V5JN7/wQYcmhFEfeSon//kjtdNhvqXvoeW8t9gLqXvsjMmTNL1tfGhgq9DRyNazkfBczJ0mZn4LNQKBRO2/ZiMBj8USgUeh84FMib+239+p41pTeV6dOnZ6972h9qDvTT8mbxb0nFbjbOdp00JkLwrHqTVPhWfu5f4vD1/hpXAZXkF8GedGDQwWFzYjAHbDzoVKedSZJKNJpcwOUSf8eipTGM9jNY9ZWXwc+a6Fl6byTLSIxEBDl5kq16JP5rwzQ2Fp8dbWsq0afupe+xtdwHqHvpq5x//uncd9+jvXa+fIOZjZ3TvgvYKRgMvgVMITFnHQwGbw4Gg3sm2gSBL7sddwlwazAYfB3YD/jtRva/Wdj2jgj+YHFi49vGIXhfOGNb/QlxhL/wLHAIeKNd40rc3GdJR/L6AilMXWzchVgpq1wnhmsXN5E+Cy262qeQCbUVAnx3R1n7eifrDrYID3CIDnTonBRn2akxlpM5ny0TZ7JJS77SrSiJsbNN3eNhPPuqdKYKhaJ8eP7550vW10ZZ2qFQqBM4Kcv2q9N+fxJ4stv++cC+G9NnKfAMlOwyq5M1j5s0/sMktkpg9pP4t3eIrRTE12gY9ZL+J8Xpf1IcvVsaUKMWhlwVY/kN2dOQSiQLEfwZmETmkioNWEUlw2jBSFjKqfxk6Q7pfHPF7bir6lIXJkja3O7x8UMyM7xoOzo4j4dJm2LHecxAPkbeIqEOUHdnGN0LTqvAGOVg7qrmsRUKhWJzUnYraQuVUNMrYfAFcQZfsHEhWIN+FEMLSFb+2ZOx5tvo7zBnpMOtc923fFy341yB1PmU/uzIGnQsetq6xdBKumi7uJWwnSpJ5PRu9xUD0SiQAQl17ib/JAtxrcwbAa4Pc/AfbiPUyi6FQqEoGWUn2vPmzWPvvQ/q9fN2rIeFD5nE3jTwOtBvkkXVNg5GlcQzWFJ1oM31R6VWR3fXOokbqd2EnxYc6mlJbDVxT9BUvgAAHpJJREFUrediZ72zR8M5lZK2B8PIhDCLtQLPrR48j5uIRBS6tZ9F9EcxOMSm7oYI637sg24Z4TTAIyQV9Q72uT70YyzEqUWUC1MoFIqtFCll386ItiUzadKkHplrFr2q896DJqs/0TF8ku2PsNjr3Di1wwpbt44NM6d6ab3HZKQtELizzSvfhpVAwzFxgndGEBpUVKbO9yWwfbdzmcQYx8fU9lir3QLUUqhsZ9pVkR6uED3SpuOmMM4Qt3/RKAhMCqAvzgxpMN420N/RidwcpeKcOKIiQstNHqxF7hAjkHhVSoG50EAsBF40sX4hsW+K4JyixFuhUJQf06ZN47jjTitJX2VdUFFKeOYnXh44NcCns0zWLdFYE9J58zYvf9m/gi/e0LFi8L9nDWb91sNLN3v4ZkHmW/bEVV4a7/Yw0s5uCTf9y2TRFe7s9RHHWFQAB+LKavoMsMBhVxZmEWwSLdfR04qWiW3NuPHeTbjz2q0k3elOvaRterRLsAG813t7CHbXdUiB7xdexEpBYKLF4Lc7GfBiB3VHxgngetA9ZNr9RofA+yM/+r0bkz9NoVAotmwuuuiikvVVdpZ2Ov+ZbjLvUU/WfbFOwd/P8qMFJB3rUgI3+09e6sc4XPhoJ1ZcMO8RD0cV6GfNswYjfyY45ACL/2kSryPoAObjpogTQH+aqKa9wJnaSNXalom/04VcAmHgc2AE0hxI219i4AXZCRigtYP5XP6PXVgCz99Nole7EeqeUQ6xNwyqyO+kN6/xYlVJxMnK4lYoFIrNQdmJdrKEmuPAf6ZnF+wkVkRgR3rK1LrFGr/fp4Khu1kMoeebWEGYKjqx0FlLNdLRaJphMn+ZwJuWMW0xruwGgXGsKuLqo7ix5jrQSa75awDJUtr+6KNzWSX2/j7k5zoIiWcXGxEtPD+uLUjNulsvGRhhUTAPuZAC/TI/1icxtKkbkGlGoVAoFEVRdqKdLKG2drHGuiWFZwdyyZvuCFbNMxmdtq2adr7DFwxIS0sSxsMihtGxbiAfPNlT9tYkXvsTp39RdxDDjTWPFLxu88ZGrMaG1EYpcBYW+ZGbKXe6bBe5k6l0QwO404Pcz0IcptZrKxSKrZ8ZM2aUrK+ym9MWIlFCs5c8uMn1zVV08F3+lyHYAH5ijONLRs37inhnbgt3PdnXdndHEiH/CuoUvsb1aN2yh1vkX+nd1e7QlOBqo50NLhwi783vxVAoFIqthQkTJpSsr7IT7ST1oxz8tYWlqFCLNbizyONYjCePmA5+bxUDM1KYZPI2g4q4Fh2xAQlPBVDB6h7bCyWHdRoc4iekxF4/yCY+zClO7JO/vKcWcCsUivJg6NChJeurbEXb9MP4U/MnUEnmIyvEN0QYyLqC7fZlZc59H1NPrIC1nZpVLl64A6ztsa2T3M51p96h85Ew6QW3hQa+myOERf4hTDJ32wZeokKhUCiKpOxEO72E2qFXRxm6a+5512KTcgrCRWnUIDpzWu4DiOOhGrIKt46b5Szdei3uoxNkv79WoGWYTfzIOPa2NvY4m8g1UTrmdOLs1vPO9f1snCkxYkb2O3BwreyuK9xPzWcrFApFb1N2gWgzZ87sylzjrYQLnulkzh0e5j5s0rbaFcLR+1rseKzFv27w4oQLy3G4yLcxjEEUV5Z7njWZH7wGN0I8RqqelombLy3d/V6cKWvlqTpmHW0T/m3hKG+5SEOe4kf7Rusq/KmRqieWbmGLxBU7FxZTZlShUCi2fCZPnlyyvspOtCdOnJhRQs1bCd/7WYxDrorRuU5geCW+anffsPE2d58UIN6WXyCXUMlqfAwsENH9Hv2xcd3TBilb2QK+wEMrOtVdS7p8pIQ621y5RjeHdFY6GJh9hynRzyssrDIC8hQ/fONebVKo89nRAonYVhUPUSgU5cG0adNKlsa07NzjuUqoaTpU9k8JNsCI8Q7Xf9rOmGPjdBqSVnLFbQv+zYi8/S6jgnmkll9ZwHA6OJ+l/JFPuZnPaUIjVd0riiva+UQ5f7CXY3oIU99zhyEx/xJBG1NETPg/jS7BhuLse4HAmOrFc5of80If+j8NMoLY/6fBi7r7U6FQKLZwShk9XnaW9oZieOCi+yK0r4eFsw1aVgo+eNBD87JMwZnPEHYjxji+7jESWk8F09gFmSZ5x7GKE7NEdqeKaBYzJyxwP0KbnuLuJTapHvP4MPYDHpz/aeAB/RAL/YI42o7ZLWEZAfufBs6TJrJJoK8RGzSy0xMvnktbkz7DxNnGIXZpFDHdg/gsNdiQ29vEbqIPF2xVKBSK/MyfP79kfSnRzoOdMKt1AyrrYN+T3A2H/zDO2w8YvHWPh/UrNDoisCeCxYxiJYMYxcqujGjL6c8q6hmL4MvEeSfQklWwIel+jhe0aB0EWtfscrIKWFLoDUAQPr8KfQ8b/bBwUfcr1whiJ/mRn+a24DNLkWSikdv2177U8Fzpw+p2Z+IznfbjQNxlII9X6U8VCoUiH2Un2sWUUHvvaYPX7vXw5VxXgsbsaXHo5Di7f98VlfmzDB76tQ8sd9V0PTAgcWwnPj7JyJPmUgEMAlYBR9KYt39RRCoTDYk1qhLjaydja5LOCyux9iguYUuS+MW+HoLd/UqSzvtsg4pCK7M1RNdMfPeTil95kcdabjUShUKh2IIYPHhwyfoqu0nFadOm5d3/8FVe7r3E3yXYAIvfN5g22c9j13hZ+YVg2mQfmiW6IqiLXVZfD5g47JgnyUrRCGh+egDhsyqQgZSEWqMN2m6qpeN3dRt0OudDDeetnmO4bE76bFnVBMXOd+fY3qQh/l12Y0iFQrEVsGLFipL1VXaina+E2twZBm8+lNvUe/UeD7ef4Uckin6YuFOxOxXZt8S1kAtT+GPp3KeaOx6o4OrIEG48bTQLpg1m3ZxBrH93EJHzq4q8ohTO7NyCmU24bVzxtgMS57g48vzilnjlFfavyu7rqFAotgKmTp1asr7UUzKN1+8rXA+6MSEsGnAQMDyxvRgpbgdMdFYUzDOuI/N8Mg5w6TuDePivXl540uTBe32cOKWOa/5URSy2canIZB7NTQp0xj16JPL4OHJOB/LuCPaPY0htE9PCVm1ohnOFQqH49rn++utL1pcS7TQW/7eYfNmuKI6EjMVUheSmlaRow9v0K9iHU5vb4v+YSt6iusf2V54z+ePVuZOp5EPbJf+6aofEArRbw4hZHYgFHWh/iyCGJ+58sMQ5PH8gWb713dKQyGNUIJpCoVDko+xEO18JNbEBRuo23f7OtugqSRj4OO3vOTTwEbld2PGdPejrwJV4ndSMsQaY7EKM/ckeTPfCEwarvtlwa1s7woIh+YVbbGejn24hJjiIfj3vNj41iuyX+xz5zi5PjsNgZWkrFApFPspOtPMtgg/uX8zaaFdYAln2WLjincxTJoHFwH/JLNDhIJjGaJ5hMJHBqbnkhfj5McPo/CR5HcmkoGbiZZC09E/LUaDEtgWvztjwgC6hg/nXCPhyCGelxLwtf8Y3uY0k+nwn9pFxpJ46jzPCIfa7CPFJ2Qu0mCeC/EPhdKoKhULRF5k7d27J+iq7cN2hQ4eyZk1r1n2HTI7x8av535Jt97L54j03h3g24Xa6/b6M7Ba4g+BVBvCA3Y9FONgI1mMwhBg1zjcF72NMnpSpHa0bN6+tH2AjZnZi3eLBeckAW4Ap0Y6xMK6IoW1fODWpHCOJPRSBVQLtSw1ZIZG7OO7w8MI49sIY4nETVgsYIJGnxqk/tIJI/lVwCoVCoaAMRTsfuxxqc+xVUZ7/U/ZAsR9cE2WfU+LcPDHAkqUahRZVNVF4rrtpjU5T2grncJHOj3zthoz6/+3de3RU1b3A8e/JOyYxqERJeNjlY35aEWvEBxKEWxFBU6qot7XKtYJQq71a+7q+akhrS22tLV5rjQj10eutYKGN2tLqVVQQpQFra5duilarKWrwgZB3Zvb9Y59hZpJ5hJBMMuT3WWtW5uxzTs7ec+bMb/Y+e/bu+7jfWceFyLuvDbsD7Ace3kiLt+ed0WGUJTQqTsvFhBB2gtaqlVL7jokTJyasDPY3DdrdzP5WB4FJQZ5alsvfX8jG8+DISUE+fVkngUkuCF37WAtrfpRHywO57Gfj12q9fMvb7alrvDu6LX9IDuspYnKK33L/kdK46UUlltNn732HLq8UvFK9x6yUUkPJsAvavZlC7agpQY6akvj+dukhls/d2s7OhR38dV4hrVtie53njwpx9M/a+MvVBTGTbXTXDpThAnd03fMODmYS/0hYl/6QbB6K6rueTWSqTK8D7qrN53NXdlA+ToOuUkrtS4ZdR7RkI6J17IJNdbncO3U/bj+smLtPKOLZ7+Wxc5urMe94zeO9P2XR3OiWSwKWU9e1cPyqFg79z3bGXdHB+HtaOXVzMwdNCXLunW3k7hc/cAZxQ5rmQY9BT59kfxYxOu6MYq1F2bzwzQpGSC4esf3LATraPX7zizwuP3M/Xn9l2J1epZRKu5qamrQdy7N26NbGmpp29nvmZs6cxpo1a3ukt7zvsWJOIdvjTJZRvH+IUeWWHcaty8Zy0OEhRk/vYuycLg44vuc95OYmj3+szeatl7JYe3cehbhxykPATuADYmer3OqnFwP744LwKDo4j/c5mla68FhHCY9xAMWjPeoez2L+jBDvJanJH35MkGVPtfT2pRk0ZWUlaZuLdqBpWYaefaUcoGUZqvq7LGVlJQnvrQ675vFEU6g9/vX8uAE7Hyj4OIsdH7tAWgTk4tH5WjZvvJbNG3X5jKgMUnmn6xr21rI83nwkh53venxgPd4HSoEW4F3cb7bjfRMpwdW+o+9Uv0MeP6PnQPStjbDwdHhvW/Ka9Gt/y+Yvz2eztSGLJx7Mpa3FY2RFiItvaGfC5L53VlNKKRVRUVHBSy+ZtBxr2AXteHa85bF1TfyXopjI0CYlxJ/J6qPN2WyYvh9ZzR5Yj2xghP8YA4RP5SdwtetmXE27+4+29qST9vZt4Wk8E/OA2vMLCUYNbfrBv7L49rnZHFkZ5NY1vZuyUymlVGLbtm1L27GG3U3PeFOovb0hGxvq2RpRQOQFyifx1JPZQNauLIjTkzwPOJrIsCh5wAG4EdWih0GV47v2+BtU95OXjfvteLH/KIGYgD3Pv+3i4bF1cw7fvbhvQ54qpZQaHMMuaHefQm3LihzeWJUTdwqP6CCdbJrnVNOM5ADHEhuk3T1rKAQOrAgx//rezZKVSCEuSOf5x8uh58mdvyh2efPjObQN/VveSik1pFVWVqbtWMMuaIenUHvpjlx+Ma6YZ75SyLYncynE3U+ON8oZJH6hwgONppIDjIOYaT48oCzH8pW6NsYcHsLz9qzfXUGxuy+dBynnDYvHWo/f9WJmM6WUUolt2rQpbccadkG7traWP9+ey5++k0+wLbY5O9x8XeQvR/92uj+6bYVr19EOKgQ5OcjBYyyVU3sz9rljgX/tyiKvwJKskXteDay37gGR5+Gm8o8/6NuQp0oppZyFCxem7VjDLmgDbL4ln8gvm52qqJ/ZhZuWu4Bwo3WixuvwxCCphLcpoltTe9TOsy7u6PG/svzts7vtshP3ReLDNi/pSVxeC5M994DI8+X+9K9HVvb+i4JSSqmeli5dmrZjDcugHersWbucsijy3MPdI84rsYz9XAdFY4K7Z++KpzeDhkbvGx2AK6KC5iHjLF3+tnm4e+AH4Xqhh58X4FoAks+31Tv5RZbJ1Rq0lVIqUwy7oP3Tc3pOoeZ1+5sDHORZKlqg7eFcct/Oohj3YsWrVbdgSTZUfPRc25bYQVVOmBdZ+uebHiHc/elSoifijNw7LyH2vngXQC/vhS9bFL1kmX9zf4R+pZRS6TLsgnbBiMjzKTVwnYVr/Zh3rXXL02ogy3rkBD2ygp4/lpkTfhbENVE3Ae/i8SSwhdigbonMsR22g0jN/Pj/6EDOitTTf/3LPDpwAdsDysbC+Cq3bq7ffH9sFRwxNlJbDwE5B6YK2m59uEm8oNhyxU/amHHR3k8sopRSw11jY2PajjXsgvbl904ELB6woRZu9dwD4A4Pfu7Bq8uhosq9OMf7wfKQKigaG/k/4aAZvtedC/wdN/JZZ9Qjulk8CGwDRh0XpPr2VmbdGjtF5YsvZFNE5KQccijctAomTIW5i9zfm1bBqEOhImq/mZd1UHFY4q5yE6Z1cfG32zj/mnauu7+FX72+SwO2Ukr1E+09PsDKJwdjJtkIC78YJYfCjFUwaipULnJ/T18FxYfGbh/987CjgDNwwTte57QCCXLKI81c+fpO5j3ewoTPxw+axVHPX14HN18AN650yzeudMsvr2N3j/GDy0P8+2WdLH60hbPmdZBXGDlyCFerb1iby4M/zicwMcjJM/UetlJK9afZs2en7VjDMmgfM7+zR8B+YVEkiG9bB09eAJ/2g+WnV7rld9fF7hMO/PnAWJIrPTbIyJND5Bcn3uaEScGYmvncGrh1LYwoc8sjytzy3Br3paBiXIi7VrSyfymUjrScMbeTti5X+++A3Z3aANpaPL4/v5A3Xx2Wp1wppfYJe/UJLiLnisiDCdYtEJEGEXleRKr9tJEi8kcReVZEHhKRRGOZDJiamhqa3+7Ze3xjbeT5xBo4ey0U+sGysMwtH18T20werlH3ZnCVpsdy6UwxCcyFl3XQRKSW/kAtfGMafNTklj9qcssP1MKkc+CR55s5XCJhfnVdHl1xesaHdbR5/HapDqailFKZqs9BW0SWAIvj/Q8RGQVcBUwGzgQWi0g+cBPwoDFmCvAi8KW+Hr+vFi1aRF5pz45b0TXchlp4ZBq0f+SWw3+3rY1tJm8FRp/WRV5R6t7boVaPtsbkL/dpZwS58Kr23R3VxldFmsQh0lQ+/jTLLashp9tg5c89lnr08vWPatBWSqn+VFdXl7Zj7U1N+zngywnWnQSsN8a0G2N24KaLngBUAWv8bX4PTN+L4/dJRUUF42Z1kV0YG2g7idRwy6tg+kp44pzYfaf/JtJMbrGcuKSV2Q+38okJvbtPnL1f6uB+9Y0dXLKkhZBnefdN+M4c+MvT8MAi97f2PMu534j/U63ejCOuY40rpVT/SueIaFhrkz4CgcD8QCDwcrfHif66aYFA4Fdx9rk4EAjcErV8fyAQmB4IBLYGAoFCP+2wQCCwLtmxOzu7bH8j0qptAXs1DfZqGmLSLhl7m11dZe3imlvj/o+amprd2zY2Nto7L6+P2f+L1Nn7iD3WiaXV1lprq6urY9Kttbauri4mrb6+3m7d2hiTNtpbYL96mrUTjq3cnVZeXt4jP4A9mgZ7dLcylVNjJ2JtYU757rTKykprrbULFiyI2baxsdHW18eWqa6ursfrV129Z2VqbIwt04IFC6y11lZWpi5TQ0ODbWiILVNNTY211tryci2TlknLpGUa/DL1o4Rx0XP56RsRmQZcboz5fLf02cBMY8wV/vJq4HvA3X76eyJyHPA9Y0x1ov/f1LSz75lLoKyshKamndgQvHB9PlvuzY2ZljMP6w9q4tIqpsKMle6+dmsT1F8AW56GkqOCXPSMq7Z27YJnJhfRvi1xw8WnlrVS/pn++5lVuBzR6u/J5a7rk0+3eeUP2zj7i51Jt0m3eGXJVFqWoWdfKQdoWYaq/i5LWVlJws5JA9WVeCMwRUQKRKQUN6X0y8B64Cx/m1nAswN0/JS8LDjlB+3M2djMcd9s58i5HRx7TTtnPdfM+0XQDIysgjNWwgr/nvKKC6B6JYypsnx2RaSdOacYTnyolYIxPX8r7WVbjqpt69eAncjMizv55EmJjzN+UhczLhxaAVsppVTvpe65tAdE5GvAVmNMvYjcjgvKWcANxpg2EbkZuE9EFgDbgS/05/H7onic5VPfjJ0OZO6fdnHf+GIa3/RYMQf+uQ6eXgRvPg0r5lhGTWunuNt0XSVHhThtQzPv1Ofw3h9yCLV7lHwyyNi5nRSO6fcGg7jyCuDmh1q59/v5PPGrXFp2ui9rRftbzriwk0uubye3L3N4KqWUGhL2qnl8oA1k83gqXV3w2/MLeGdDjrtjARSUWc5c2syYU/s7V3suVTlad8Hrf8vG8yyHHROioCjhpoNOm8mGpn2lLPtKOUDLMlSls3m8X2va+5KcHDjvN5k7oUZhMRxzso5+ppRS+xIdHksppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQyhQVsppZTKEBq0lVJKqQwxpOfTVkoppVSE1rSVUkqpDKFBWymllMoQGrSVUkqpDKFBWymllMoQGrSVUkqpDKFBWymllMoQOYOdgYEkIucCFxhjvhBn3QLgS0AXcLMx5lERGQk8CBQC/wIuNca0pDPP3fJYCPwSOBjYCVxijGmKWj8TuNZf9IAqYDwu/48Af/fX/dwY81C68h1PqrL429QDBwGdQKsxZpaIHAHcC1jgZeBKY0wonXnvrpdl+RHufOQAdxtjlorIgcAWXDkAVhtjlqQv57vzlgXcCRwHtAOXGWO2Rq0f8tdGWC/Kcg3weX/xd8aYWhHxgLeJXB8bjDHXpTHbcfWiLLcDk3HvOYDPArlk2HkRkU8BP43a/BTgHGAjQ+D6iEdETgZuMcZM65b+GeAm3LWy3L/OU34+7I19tqYtIkuAxcQpo4iMAq7CXQBnAotFJB/34j9ojJkCvIj74BpMXwb+6ufnfuDG6JXGmDXGmGn+G+lR3JvqFaASuC28brADti9pWXxHAFV+nmf5abcBN/r7ebgPqsGWtCwi8m/AEcaYSbjA/V8icgDuvPxv1HkZrA+kc4ACP3/XAj8Or8igayMsWVkOAy4CTgUmATNEZAJwOLA56jwMesD2JSyLrxI4MyrfO8jA82KM+XPU59bPgFXGmDUMnesjhoh8C7gHKOiWngv8BJgBTAUW+tdPbz7r+myfDdrAc7gXL56TgPXGmHb/jb8VmID7gF3jb/N7YPqA5zK5XuVHRMYAc4FaP+kE4GwReUZElolIyYDnNLWkZRGRQ4ARwCMisk5Eqv1VJwBPJ9pvkKQ6LxuAef5zC2TjWg9OACpF5GkRWSki5enIbBy782+MeR6YGLUuU66NsGRleQuYaYwJ+q0zuUAb7jyMFpGnROR3IiLpznQCCcvi11yPBO4WkfUiMq/7PmTOeQFARIpwn1lX+UlD5fro7jVgTpz0o4GtxpgPjTEdwDpgCgN8TjK+eVxE5gPXdEu+1BjzkIhMS7Db/sCOqOWdQGm39HBaWiQox7u9zM/XgJ8YY9r95Y3APcaYTSJyA1ADfKOfs5xQH8uSh/s2vgQ4EFgvIhsBzxhjk+w3oPpSFmNMG9DmfxO/D9c8vktEXgU2GWOeEJGLgP8Gzh/QAsTX/f0fFJEcY0xXnHWDfm2kkLAsxphOYLvfHP4j4EVjzBa/NrTYGLNSRKpwTZknpj/rPSQ7L0W498ttuC+BT4lIAxl4XqLS5gMrjTHb/eWhcn3EMMb8WkQ+EWfVoFwrGR+0jTHLgGV7uNvHQHTtswT4KCq9NSotLeKVQ0RWEcln3Pz438CrgRuiklcbY8Lbrsa9+dOmj2V5B7jLv6jfE5EXAQGi71+n9ZzAXp2XA4CHgbXGmMV+8pNA+H7jauA7A5HnXuj+/s+K+jAdctdGCsnKgogUAMtxH55X+MkNuHuQGGPWichoEYn+cjhYkpWlBVgSvl8tIk/i7hdn5HnxXURsUB4q10dvpbpWotP6zb7cPJ7MRmCKiBSISCmumeNlYD1wlr/NLODZQcpfWG/yMx541RjTGpX2BxE5yX9+OrBp4LLYa6nKMh1YASAixbhyvQK8GNViMhTOCaQoi98R5f9wHVO+G7XqHuA8//lgnpfd+ReRU4C/Rq3LlGsjLGFZ/Br2b4GXjDFfMsYE/VU1wFf9bY4D/jkEAjYkPy8BYJ2IZPstOFXAZjLwvPhppUC+MeatqOShcn301ivAkSJyoIjkAafhbo0N6DnJ+Jr2nhCRr+HuQdT7PTGfxX1xucEY0yYiNwP3+b1ntwM9ep2n2c/9/KwDOsL5EZEfAg8bYzbiaqOvd9vvy8AdItKBq8EuTF+WE0pVlt+LyJki8jyudn29MWa7iHwdWOpfFK/gaq+DLWlZcJ24DgMW+O8lgEtxHXKWi8gVQDNwWboz7lsNnCEiz+E6912agddGWMKy4JqRpwL5IhLu2Hgd8APglyJyNq7G/cW05zq+VOflf4Dncf0j7jfG/C0Tz4sxph73JeSNbvsMlesjKRH5AlBsjLnbL9MfcNfKcmNMo4jE/XzoLzrLl1JKKZUhhmvzuFJKKZVxNGgrpZRSGUKDtlJKKZUhNGgrpZRSGUKDtlJKKZUhNGgrpZRSGUKDtlJKKZUhNGgrpZRSGeL/AROEErhuKgmXAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([1, 1], 0.05, logP, 'random_walk').run(500))" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Study the two examples above and describe how and why they are failing to sample the desired target distribution. Do the locations of repeated samples make sense?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The first example uses independent updates with a proposal distribution that is too narrow ($\\sigma = 0.3$) to sample the edges of the box efficiently. As a result, points far from the initial point (the origin) are repeated often and the chain would need to be much longer to populate the corners. Note that, although the density of samples is higher close to the origin, when weighted by the number of repetitions, the generated chain correctly samples the target (flat) distribution.\n", "\n", "The second example use random-walk updates with a proposal distribution that is much narrower than the target ($\\sigma = 0.05$) so tends to explore the target space slowly with long range correlations between samples. We have effectively simulated the [Brownian motion](https://en.wikipedia.org/wiki/Brownian_motion) of a particle in a 2D fluid. With a long enough chain, our particle will explore the full square, spending about the same amount of time in each part of it, but this is not true of shorter sections of the chain. Note how repeated samples occur only at the edges of square, where there is a high probability of a proposed sample falling outside the square and therefore being rejected.\n", "\n", "Both of these examples are \"correct\" implementations of MH updates, but also have peculiar features that you might care about when using MCMC for pratical work. The lesson is that you should generally not assume that an MCMC chain has any desirable properties beyond its minimum guarantee of asymptotically sampling $\\tilde{P}(X_n)$.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the proposal distribution $Q$ is reversible, it cancels in the Hastings ratio,\n", "\n", "$$ \\Large\n", "r(x_{n+1}, x_n) = \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)}\\, \\frac{Q(x_n\\mid x_{n+1})}{Q(x_{n+1}\\mid x_n)} \\;\\rightarrow\\; \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)} \\; .\n", "$$\n", "\n", "The resulting **Metropolis updates** are a special case of MH updates and eliminate the need to evaluate $Q$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gibbs Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When sampling a multidimensional target distribution $\\tilde{P}$, some additional constraints on $\\tilde{P}$, allow us to exploit a different special case of MH updates and are the basis of **Gibbs sampling**.\n", "\n", "For example, suppose we want to sample in 3D from $\\tilde{P}(x, y, z)$, then Gibbs updates require that we can sample from each of the 1D conditional distributions:\n", "\n", "$$ \\Large\n", "\\tilde{P}(x\\mid y, z) \\quad ,\\quad\n", "\\tilde{P}(y\\mid x, z) \\quad ,\\quad\n", "\\tilde{P}(z\\mid x, y) \\; .\n", "$$\n", "\n", "This condition is trivially satisfied when the random variables are mutually independent,\n", "\n", "$$ \\Large\n", "\\tilde{P}(x,y,z) = P_X(x) P_Y(y) P_Z(z) \\; ,\n", "$$\n", "\n", "but is more useful in cases where this is not true and simpler alternative methods are not available.\n", "\n", "The rules for a single Gibbs update starting from sample $(x_{n-1}, y_{n-1}, z_{n-1})$ are:\n", " - Sample $x_n$ from $\\tilde{P}(x\\mid y_{n-1}, z_{n-1})$\n", " - Sample $y_n$ from $\\tilde{P}(y\\mid x_n, z_{n-1})$\n", " - Sample $z_n$ from $\\tilde{P}(z\\mid x_n, y_n)$\n", " - Accept the new sample $(x_n, y_n, z_n)$ with probability one (!)\n", " \n", "We will not prove the correctness of this approach, but the key insight is that each sub-step samples from a conditional PDF that is proportional to the full joint PDF, for example:\n", "\n", "$$ \\Large\n", "\\tilde{P}(y\\mid x, z) = \\frac{\\tilde{P}(x, y, z)}{\\tilde{P}(x, z)} \\propto \\tilde{P}(x, y, z) \\; .\n", "$$\n", "\n", "The 3D example above generalizes in the obvious way to higher dimensions.\n", "\n", "[Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) places extra conditions on $\\tilde{P}$, so is not a general-purpose algorithm, but is efficient and eliminates repeated samples when its conditions are met. Gibbs sampling is often a good fit to target distributions that can be expressed using a graphical model with few dependencies." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hamiltonian Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another special case of MH sampling requires that we can calculate all partial derivatives of our target $\\log\\tilde{P}$,\n", "\n", "$$ \\Large\n", "\\frac{\\partial}{\\partial z_i}\\, \\log\\tilde{P}(\\vec{x}) \\; .\n", "$$\n", "\n", "The resulting **Hamiltonian sampling** method relies on a nifty physics analogy.\n", "\n", "[Recall](https://en.wikipedia.org/wiki/Hamiltonian_mechanics) that the equations of motion for a classical system of particles with Hamiltonian $H$ are:\n", "\n", "$$ \\Large\n", "\\frac{dq_i}{dt} = + \\frac{\\partial H}{\\partial p_i} \\quad , \\quad\n", "\\frac{dp_i}{dt} = - \\frac{\\partial H}{\\partial q_i} \\; ,\n", "$$\n", "\n", "where $q_i$ and $p_i$ are (generalized) position and momentum coordinates for particle $i$.\n", "\n", "We identify $H$ with the total energy of the system and can often split it into separate kinetic and potential terms,\n", "\n", "$$ \\Large\n", "H(q,p) = K(p) + U(q) \\; ,\n", "$$\n", "\n", "where, generically,\n", "\n", "$$ \\Large\n", "K(p) = \\sum_i\\, \\frac{p_i^2}{2 m_i} \\; ,\n", "$$\n", "\n", "with particle \"masses\" $m_i$, and $U(q)$ encapsulates all the specifics of a particular system. Using this split, we can simplify the equations of motion to:\n", "\n", "$$ \\Large\n", "\\frac{dq_i}{dt} = +\\frac{p_i}{m_i} \\quad ,\\quad \\frac{dp_i}{dt} = -\\frac{\\partial U}{\\partial q_i} \\; .\n", "$$\n", "\n", "We turn Hamiltonian dynamics into a stationary Markov chain with the following recipe:\n", " - Identify positions $q_i$ with the random variables we wish to sample.\n", " - Create new random variables $p_i$ for the corresponding momenta. We will treat these as nuisance parameters, but this does not look promising since we just doubled the dimension of our sampling space!\n", " - Assign fixed (arbitrary) masses $m_i$ to each \"particle\".\n", " - Use $U(q) = -\\log\\tilde{P}(q)$ for our \"potential energy\".\n", " \n", "Plugging $U(q) = -\\log\\tilde{P}(q)$ into the $dp_i/dt$ equation of motion above reveals why we need to be able to calculate partial derivatives of $\\log\\tilde{P}$.\n", "\n", "A single Hamiltonian Monte Carlo (HMC) update then consists of:\n", " - Pick a random starting point in $(q, p)$ space, to specify the initial conditions for our \"particles\".\n", " - Follow the evolution of our \"particles\" for some fixed time interval using Hamiltonian dynamics.\n", " - Use the final positions of our \"particles\" as a new sample added to the chain.\n", "\n", "How does this sample the target $\\tilde{P}(q)$? The answer comes from statistical mechanics, which tells us that the probability that our system of particles is in a state with positions $q$ is given by the [canonical distribution](https://en.wikipedia.org/wiki/Canonical_ensemble):\n", "\n", "$$ \\Large\n", "P(q) \\propto \\exp\\left( -\\frac{U(q)}{k_B T} \\right) \\; ,\n", "$$\n", "\n", "where $k_B$ is Boltzmann's constant and $T$ is the system's absolute temperature.\n", "\n", "In practice, you can usually set $k_B T = 1$ and all masses $m_i = 1$ and this works surprisingly well! The disadvantages of this approach are that:\n", " - It is relatively complex to implement, compared with the much simpler (and general purpose) MH sampling, so let someone else do this work for you.\n", " - It requires that you can evaluate all the necessary partial derivatives of your target $\\tilde{P}$.\n", "\n", "However, the main advantage is that HMC can often explore the target space much more efficiently than other methods, since it uses the additional information provided by the derivatives. We will soon discuss computational graphs, which are a general-purpose framework for automating the necessary derivate calculations.\n", "\n", "See this [blog post](http://arogozhnikov.github.io/2016/12/19/markov_chain_monte_carlo.html) for a more detailed explanation of HMC with some helpful interactive visualizations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Practical Advice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is tempting to assume that MCMC samples have desirable properties beyond their minimum guarantees, since this is often true, but avoid this temptation.\n", "\n", "In particular, MCMC samples are only guaranteed to sample your target $\\tilde{P}(X_n)$ for $n$ sufficiently large. Therefore:\n", " - There is no way to know how big $n$ needs to be for a particular $\\tilde{P}$.\n", " - **Burn-in?** Should I throw away the first $B$ samples to ensure that my chain is independent of its initial starting point?\n", " - **No:** There is no practical way to know how big $B$ should be. Instead, ensure that your starting point is reasonably probable (according to $\\tilde{P}$) and use all samples. If you do not know how to chose a reasonably probable starting point, you need to solve a separate optimization problem before you are ready to use MCMC (which is notoriously inefficient at discovering new regions of high probability).\n", " - There are no useful guarantees about $\\tilde{P}(X_n, X_m)$ and, in general, you should assume that the consecutive samples in any stretch of the chain are highly correlated.\n", " - **Thinning?** Should I just keep every $T$-th sample so that my chain is uncorrelated?\n", " - **No:** There is no practical way to know in advance how big $T$ should be, and you can never get a better answer (for a fixed amount of computation) by throwing away valid information. Just accept that samples are correlated.\n", "\n", "How long should your chain be? You should ideally use empirical measurements to determine $k$ such that the [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation)\n", "\n", "$$ \\Large\n", "\\frac{\\langle (X_{n+k} - \\mu) (X_n - \\mu)\\rangle}{\\sigma^2} \\simeq 0 \\; ,\n", "$$\n", "\n", "where $\\mu$ and $\\sigma$ are the long-term mean and standard deviation of $\\tilde{P}(X_n)$, then generate a chain whose length is at least 10-100 times this [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation) length $k$.\n", "\n", "Which update rule should you use?\n", " - Determine which special cases apply to your target $\\tilde{P}$, so you know which algorithms are possible.\n", " - Can you sample from a complete set of conditional distributions? If so, add Gibbs sampling to your list.\n", " - Can you compute all partial derivatives? If so, add HMC to your list.\n", " - There is no \"best\" algorithm, so you will need to benchmark your problem against the available methods. \n", "\n", "Although it is instructive (and fun!) to implement simple update rules yourself, for serious work you should generally let someone else do the hard work for you by using an existing package.\n", "\n", "Which package should you use?\n", " - For initial exploratory work, start with [emcee](http://dfm.io/emcee/), which implements [ensemble sampling](http://dx.doi.org/10.2140/camcos.2010.5.65) where many independent \"walkers\" simultaneously crawl around your target space, and has a nice [affine invariance](https://en.wikipedia.org/wiki/Affine_geometry) property, where the efficiency is not affected by any linear (aka \"affine\") transformation of your target space.\n", " - Look into [PyMC3](http://docs.pymc.io/notebooks/getting_started.html) or [Edward](http://edwardlib.org/) to explore HMC and other more advanced updating rules. These are generally more complex to use and have rigid rules for specifying your target $\\tilde{P}$.\n", " - Consider an alternative approximate method for Bayesian inference, such as [variational inference](https://en.wikipedia.org/wiki/Variational_Bayesian_methods), with different tradeoffs.\n", " \n", "This [blog post](http://twiecki.github.io/blog/2013/09/23/emcee-pymc/) compares emcee and PyMC3.\n", "\n", "You will see examples of performing MCMC and variational inference with [Edward](http://edwardlib.org/) soon." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }