diff --git a/examples/samplers/SMC2_gaussians.ipynb b/examples/samplers/SMC2_gaussians.ipynb index 039eb3acf..99e0d763e 100644 --- a/examples/samplers/SMC2_gaussians.ipynb +++ b/examples/samplers/SMC2_gaussians.ipynb @@ -4,7 +4,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Sequential Monte Carlo" + "# Sequential Monte Carlo\n", + "\n", + ":::{post} Oct 19, 2021\n", + ":tags: , SMC, pymc3.Model, pymc3.Potential, pymc3.Uniform, pymc3.sample_smc\n", + ":category: beginner\n", + ":::" ] }, { @@ -16,18 +21,19 @@ "name": "stdout", "output_type": "stream", "text": [ - "Running on PyMC3 v3.9.1\n" + "Running on PyMC v3.11.4\n" ] } ], "source": [ + "%matplotlib inline\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import theano.tensor as tt\n", "\n", - "print(f\"Running on PyMC3 v{pm.__version__}\")" + "print(f\"Running on PyMC v{pm.__version__}\")" ] }, { @@ -45,30 +51,30 @@ "source": [ "Sampling from distributions with multiple peaks with standard MCMC methods can be difficult, if not impossible, as the Markov chain often gets stuck in either of the minima. A Sequential Monte Carlo sampler (SMC) is a way to ameliorate this problem.\n", "\n", - "As there are many SMC flavors, in this notebook we will focus on the version implemented in PyMC3.\n", + "As there are many SMC flavors, in this notebook we will focus on the version implemented in PyMC.\n", "\n", - "SMC combines several statistical ideas, including [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling), tempering and an MCMC kernel. By tempering we mean the use of an auxiliary _temperature_ parameter to control the sampling process. This is easy to see if we write the posterior as:\n", + "SMC combines several statistical ideas, including [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling), tempering and MCMC. By tempering we mean the use of an auxiliary _temperature_ parameter to control the sampling process. To see how tempering can help let's write the posterior as:\n", "\n", "$$p(\\theta \\mid y)_{\\beta} \\propto p(y \\mid \\theta)^{\\beta} \\; p(\\theta)$$\n", "\n", - "When $\\beta=0$ we have that $p(\\theta \\mid y)_{\\beta=0}$ is the prior distribution and when $\\beta=1$ we recover the _true_ posterior. We can think of $\\beta$ as a knob to gradually turn-on the likelihood. This can be useful as in general sampling from the prior is easier than sampling from the posterior distribution. Thus we can use $\\beta$ to control the transition from an easy to sample distribution to a harder one.\n", + "When $\\beta=0$ we have that $p(\\theta \\mid y)_{\\beta=0}$ is the prior distribution and when $\\beta=1$ we recover the _true_ posterior. We can think of $\\beta$ as a knob we can use to gradually _fade up_ the likelihood. This can be useful as in general sampling from the prior is easier than sampling from the posterior distribution. Thus we can use $\\beta$ to control the transition from an easy to sample distribution to a harder one.\n", "\n", "A summary of the algorithm is:\n", "\n", - "1. Initialize $\\beta$ at zero and `stage` at zero.\n", - "2. Sample from the prior a set of samples $S_{\\beta}$ of size $N$. When $\\beta = 0$ the tempered posterior is the prior.\n", - "3. Increase $\\beta$ in order to make the effective sample size (ESS) equals some predefined value. We use $Nt$, where $t$ is the threshold parameter -- by default t=0.5. This means that the default ESS is fixed at half the number of draws.\n", - "4. Compute a set of $N$ importance weights $W$. The weights are computed as the ratio of the tempered likelihoods at stage $i+1$ and stage $i$.\n", - "5. Obtain a new set of samples $S_{w}$ by re-sampling $S_{\\beta}$ according to $W$.\n", - "6. Use the $S_{w}$ to compute the covariance for (multivariate)normal proposal distribution.\n", - "7. For stages other than 0 use the acceptance rate from the previous stage to estimate the scaling of the proposal distribution and to compute `nsteps`.\n", - "8. Run $N$ Metropolis chains (each one of length `n_steps`), starting each one from a different sample $S_{w}$.\n", + "1. Initialize $\\beta$ at zero and stage at zero.\n", + "2. Generate N samples $S_\\text{\\beta}$ from the prior (because when $\\beta = 0$ the tempered posterior is the prior).\n", + "3. Increase $\\beta$ in order to make the effective sample size equals some predefined value (we use $Nt$, where $t$ is 0.5 by default).\n", + "4. Compute a set of N importance weights $W$. The weights are computed as the ratio of the likelihoods of a sample at stage $i+1$ and stage $i$.\n", + "5. Obtain $S_{w}$ by re-sampling according to $W$.\n", + "6. Use $W$ to compute the mean and covariance for the proposal distribution, a MVNormal.\n", + "7. For stages other than 0 use the acceptance rate from the previous stage to estimate `n_steps`.\n", + "8. Run N independent Metropolis-Hastings (IMH) chains (each one of length `n_steps`), starting each one from a different sample in $S_{w}$. Samples are IMH as the proposal mean is the of the previous posterior stage and not the current point in parameter space.\n", "9. Repeat from step 3 until $\\beta \\ge 1$.\n", - "10. The final result is a collection of $N$ samples from the posterior.\n", + "10. The final result is a collection of $N$ samples from the posterior\n", "\n", - "The algorithm is summarized in the next figure, the first subplot shows 5 samples (orange dots) at some particular stage. The second subplot shows how these samples are reweighted according to their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of Metropolis steps, starting from the reweighted samples $S_{w}$ in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed Markov chains.\n", + "The algorithm is summarized in the next figure, the first subplot shows 5 samples (orange dots) at some particular stage. The second subplot shows how these samples are reweighted according to their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of IMH steps, starting from the reweighted samples $S_{w}$ in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed new Markov chains.\n", "\n", - "![SMC stages](https://github.com/pymc-devs/pymc3/raw/master/docs/source/notebooks/smc.png)\n", + "![SMC stages](smc.png)\n", "\n", "\n", "SMC samplers can also be interpreted in the light of genetic algorithms, which are biologically-inspired algorithms that can be summarized as follows:\n", @@ -78,33 +84,33 @@ "3. Selection: individuals with high _fitness_ have higher chance to generate _offspring_.\n", "4. Iterate by using individuals from 3 to set the population in 1.\n", "\n", - "If each _individual_ is a particular solution to a problem, then a genetic algorithm will eventually produce good solutions to that problem. One key aspect is to generate enough diversity (mutation step) in order to explore the solution space and hence avoiding getting trap in local minima. Then we perform a _selection_ step to _probabilistically_ keep reasonable solutions while also keeping some diversity. Being too greedy and short-sighted could be problematic, _bad_ solutions in a given moment could lead to _good_ solutions in the future.\n", + "If each _individual_ is a particular solution to a problem, then a genetic algorithm will eventually produce good solutions to that problem. One key aspect is to generate enough diversity (mutation step) in order to explore the solution space and hence avoid getting trap in local minima. Then we perform a _selection_ step to _probabilistically_ keep reasonable solutions while also keeping some diversity. Being too greedy and short-sighted could be problematic, _bad_ solutions in a given moment could lead to _good_ solutions in the future.\n", "\n", - "For the SMC version implemented in PyMC3 we set the number of parallel Markov chains $N$ with the `draws` argument. At each stage SMC will use independent Markov chains to explore the _tempered posterior_ (the black arrow in the figure). The final samples, _i.e_ those stored in the `trace`, will be taken exclusively from the final stage ($\\beta = 1$), i.e. the _true_ posterior (\"true\" in the mathematical sense).\n", + "For the SMC version implemented in PyMC we set the number of parallel Markov chains $N$ with the `draws` argument. At each stage SMC will use independent Markov chains to explore the _tempered posterior_ (the black arrow in the figure). The final samples, _i.e_ those stored in the `trace`, will be taken exclusively from the final stage ($\\beta = 1$), i.e. the _true_ posterior (\"true\" in the mathematical sense).\n", "\n", "The successive values of $\\beta$ are determined automatically (step 3). The harder the distribution is to sample the closer two successive values of $\\beta$ will be. And the larger the number of stages SMC will take. SMC computes the next $\\beta$ value by keeping the effective sample size (ESS) between two stages at a constant predefined value of half the number of draws. This can be adjusted if necessary by the `threshold` parameter (in the interval [0, 1])-- the current default of 0.5 is generally considered as a good default. The larger this value, the higher the target ESS and the closer two successive values of $\\beta$ will be. This ESS values are computed from the importance weights (step 4) and not from the autocorrelation like those from ArviZ (for example using `az.ess` or `az.summary`). \n", "\n", "Two more parameters that are automatically determined are:\n", "\n", "* The number of steps each Markov chain takes to explore the _tempered posterior_ `n_steps`. This is determined from the acceptance rate from the previous stage.\n", - "* The (co)variance of the (Multivariate)Normal proposal distribution is also adjusted adaptively based on the acceptance rate at each stage.\n", + "* The covariance of the MVNormal proposal distribution is also adjusted adaptively based on the acceptance rate at each stage.\n", "\n", - "As with other sampling methods, running a sampler more than one time is useful to compute diagnostics, SMC is no exception. PyMC3 will try to run at least two **SMC chains** (do not confuse with the $N$ Markov chains inside each SMC chain).\n", + "As with other sampling methods, running a sampler more than one time is useful to compute diagnostics, SMC is no exception. PyMC will try to run at least two **SMC _chains_** (do not confuse with the $N$ Markov chains inside each SMC chain).\n", "\n", "Even when SMC uses the Metropolis-Hasting algorithm under the hood, it has several advantages over it:\n", "\n", "* It can sample from distributions with multiple peaks.\n", "* It does not have a burn-in period, it starts by sampling directly from the prior and then at each stage the starting points are already _approximately_ distributed according to the tempered posterior (due to the re-weighting step).\n", - "* It is inherently parallel (PyMC4 will take better advantage of this feature)." + "* It is inherently parallel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Solving a PyMC3 model with SMC\n", + "## Solving a PyMC model with SMC\n", "\n", - "To see an example of how to use SMC inside PyMC3 let's define a multivariate Gaussian of dimension $n$ with two modes, the weights of each mode and the covariance matrix. " + "To see an example of how to use SMC inside PyMC let's define a multivariate Gaussian of dimension $n$ with two modes, the weights of each mode and the covariance matrix." ] }, { @@ -151,13 +157,21 @@ "output_type": "stream", "text": [ "Initializing SMC sampler...\n", - "Multiprocess sampling (2 chains in 2 jobs)\n", + "Sampling 4 chains in 4 jobs\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", "Stage: 0 Beta: 0.010\n", - "Stage: 1 Beta: 0.028\n", - "Stage: 2 Beta: 0.064\n", + "Stage: 1 Beta: 0.029\n", + "Stage: 2 Beta: 0.065\n", "Stage: 3 Beta: 0.141\n", - "Stage: 4 Beta: 0.300\n", - "Stage: 5 Beta: 0.608\n", + "Stage: 4 Beta: 0.307\n", + "Stage: 5 Beta: 0.638\n", "Stage: 6 Beta: 1.000\n" ] } @@ -172,15 +186,15 @@ " testval=-1.0 * np.ones_like(mu1),\n", " )\n", " llk = pm.Potential(\"llk\", two_gaussians(X))\n", - " trace = pm.sample_smc(2000, parallel=True)\n", - " az_trace = az.from_pymc3(trace)" + " trace_04 = pm.sample_smc(2000, parallel=True)\n", + " idata_04 = az.from_pymc3(trace_04)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can see from the message that PyMC3 is running two **SMC chains** in parallel. As explained before this is useful for diagnostics. As with other samplers one useful diagnostics is the `plot_trace`, here we use `kind=\"rank_vlines\"` as rank plots as generally more useful than the classical \"trace\"" + "We can see from the message that PyMC is running four **SMC chains** in parallel. As explained before this is useful for diagnostics. As with other samplers one useful diagnostics is the `plot_trace`, here we use `kind=\"rank_vlines\"` as rank plots as generally more useful than the classical \"trace\"" ] }, { @@ -190,7 +204,17 @@ "outputs": [ { "data": { - "image/png": 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\n", + "text/plain": [ + "'Estimated w1 = 0.097'" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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XQgghhBBCCCFEe5Jgl+gQFxXk8+z+3hjzojA6NMLsFuZO/pp/hxexZ/Q+zrlhMd70afTvC1deAff8LvBA17HM3cPp+uMNdLo4D1dmGUl3hlKR1ZWbc8rJ6eohNy6Xi2bdxPT5F7Dnp64MiBvHR1texOGxtcnPF0IIIYQQQgghRPuSYJc45XwVOVi3f06ng1fiMLpxmDxo0RVct/I8/m9nL37b+y5yi6Kw23XCwxXu+a2K0dg2wS4AxagR/eI99H34ANHXpxBxWRo5q8bxVHURX85cSHFUKRNWTWDsAR/q+uspsxfx9c632+znCyGEEEIIIYQQov1IsEucUocrD3L9VxPZ6FIpXhdGZvIBYioiiEnahy0rhRFela7Osfz6bp3nX2zHkxANQbiufBm98zBCz0sGFPb9cCVPVtfw1s3/oyK8krCqMILDH2WkHsbnO16XvbuEEEIIIYQQQogzgAS7xCnlqsimj8NDaOF1KC6duKJ4Do5bwb6srtQk5bBvcAq3/XUgoaFw681tl811PLGJS0i/dgEQhG3+xfyfK4SwZ4fy3tXvs8sRTVTG3yizF7Fg/xenZDxCCCGEEEIIIYQInAS7xCnVc+8ynrGHU7C4Czlx+VSGO4i1lBJaEclHE+Zz/8qRJMTDKy8qJCScmmCXN3kEodN6kfiXIdiykwl75xp6Fn7D0LHTuG7ORMZ84mCQYxyfbXsFn+47JWMSQgghhBBCCCFEYCTYJU6ZbdkLydv5GUX6NRgK7aiKj9QhG4ndPIGquDwOdD1AWti1vPqyQmzsqQl0Afji++Ka9GeibuyNqXcYzspwDr0YS+a+VSw4ZyEGQw3XvHouVTklrMlZcMrGJYQQQgghhBBCiNaTYJc4JXRd58U1D/F4cA3rvhuIzejCa/Di8NkIuS2ST8+fw/i0K3nuaSvBwacu0HUsxVlF36lvoJl92EtiufHtKeztlsHLt7wCDgO//ug2Zq9/vUPGJoQQQgghhBBCiJaRYJc4JbYXrCGzKpPRcU8RnlGC1+QkWNH589C1/M2zlB3d9nL50FsxGDom0AWAOQx11DS6n/cVoGDKTOO6Hy8nNz4PPb6Y2II4+r6Zyq7CDR03RiGEEEIIIYQQQhyXBLvEKbFgx3+xGoKp+nc6BmDOpLl0776L5767kuHkMrTTBLpH9+voYeIa81vCZvQhtvdWdHSGrh3BORtGUxCXTV6Yib4ZfZj39b87ephCCCGEEEIIIYRohqGjByDOfi6vk2VZPzDGHUOPPQdwGF1csGY8hVix2uGmW4NxT/tbRw/TT1FwTnmCmAO3UZZlQ/cauPz7S/j0hv+SPfUHRlXG8r2Ww3U1ucQGd+ro0QohhBBCCCGEEKIByewS7W7docVU4cG47NfEeG2Y3SYOdt2LsSgUy7BVuEfe3NFDrE8zYrzur3Q5bwleZxBqkIOLvroatTqevRt+i7kmmBVvzUJ3y8mMQgghhBBCCCHE6UaCXaLdLTrwJWZiiV/fDZ+io6MTn98Zn8XGvWNW8OqBjzp6iI3oEcmoN1xFVPfd6G4T+OCakN9z62qda+bdTrd/RlHw1taOHqYQQgghhBBCCCEakDJG0a5s9hJWHZxDwo6Z9LfnoqKQPelHUhafj/2cRZSZ7IxLu6ijh9kkT7/LKR+4AC3HQ6fwUuaHfkXFTA3NGo3uKKXv8zrRl6djjLd29FCFEEIIIYQQQghRSzK7RLtav/5FXHg5Z/0gFHQOxR+my3mdiD5f46uxG+gc1pV+8SM7ephNsgarrEv5EwljVlB1OI0bFiQQXxjDwYgNrJ66AJ/HS97TcjKjEEIIIYQQQghxOpFgl2hXnoMr6VUTRv8sIwoKjuBqHvPNxvlUH9Zairio5w0oitLRw2zW+Eu7ck3Oy9i7hFK84hymrJjEpFXjOW/uTBaOWUzF7IPYthR39DCFEEIIIYQ4Y3h9XjbnrWDR/tlszluB1+ft6CEJIc4yUsYo2o1SepAZxYep/uEBzD4PpWFlRFtV7tuTzIqeX2NUTUztMbOjh3lcXbsopPcP4b3M8dyR9Q3b+24mJzmbQXv6sPO8/QwuGkw3r97RwxRCCCGEEOKMsDxzDq+s/gvFtrwjX4uxJnLXqL+ettubCCHOPJLZJdpN2bqPsHk14vZZ0dH5+Mr3idqbTvK2odziDOY/l8wn3Bzd0cM8ocsuVYiybMA7ZC39tg2mk8HMois+whuWx9+u/js16a6OHqIQQggh2pDP5aHorZ0cfngNRW/txOfydPSQhDgrLM+cw+OLbqsX6AIotuXz+KLbWJ45p4NGJoQ420hml2gfuo93D3zAwaoYbvO62N1jF8P3DEP3+EgasgJv77dJjezZ0aNskQnj4N8vT6RPLxupuw8zZNFoQosSWDdoJ7Mv+IQf1nzAxaVXEHlV944eqhBCCCFOUt5T6yl+cxf4jmZu5/91AzG39ybxoWEdODIhzmxen5dXVv8F0FF1GOQxEK0rlCg6mw0efIrCq2seZkzKNDRV6+jhitOY1+dlW8FqSm2FRFnj6B8/Sp4zohEJdol24T6wkWlODxnLrsRj8NArow+uTCfm3nt5pGs13XJ/5Pq43h09zBYxGBSmX2zg1f/N4JczH2fo290wp1UyYlM/NO0WStfv5dC8lViHxhHUNayjhyuEEEKIAOU9tZ7i13c2vsOnH/m6BLzEieheHzVrC/EU2jHEWQgeEYeiSUHNtoLVFNvymOgy8ge7lXj96JwUKD6et9hYQi7bClYzKHFsB470Z8DnRTu8AaWmCD04Fm/SUDhDgkVSBtsysg5JsEu0k/wF3xG9YjKuA5HsHrIKj8dK/60DCR26hGXeInqqZ9ZTb8Z0hf+9r2OIs5KVlE1yUQS66iOiGL6atITJi8dT8t5uOj0+oqOHKoQQQogA+Fwef0bXcRS/uYv4Pw1CNZ1Zn2Pamters2UrlJRCdBQMHACadvoeOHQqVfyQRd5j63Dn2Y58zZhoJfGx4YRfkNqBI+t4pbZCJrqMPGMLpuGOt7G6wjO2YB6khlJbYYeM7+dCy5hH0OJnUKvzj3zNF5KAc9KDeHtMbZOf0V6ZV3VlsDR4BtWVwT46+a02C3i19zrXnv2finXoTMiu+3m/U4t24XE6ya2ZjTv3BsLQ+eycJfzSfQcxYeV82aUUoxrE+T2u6ehhtkpsrMLjj8KIsEE8kfcE1793J9Wd8uma2YWoqlB2D9hN389MxP9pMFqIsaOHK4QQQohWKvnf3nqli03y6ZT8by+xt/U5NYM6DS1dpvPCyzpFRUe/FhsL9/wWJoz/eQe8Kn7IIvtXSxteh+POt5H9q6Wk/GfCGRPwqssKcdcU4gz2tUlWSJQ5hj/YreiASv3nioqCD5177Fb2mWNO6ueI5mkZ8zB/ew8Nn6RKdQHmb+/BcfELJx3waq/Mq1NZBtve61x79n8q1qEzJbvu55XHJk6JVat0nvcGEZQfgT2ijC6HUjkwJovgt69njsHOlO5XEWE5897EJk5QsA6aQp+uNnak7yS0OBxXkJNrvp7J90Pn4at2U/7F/o4ephBCCCEC4MqqatN2x6N7fVSvyqf864NUr8pH9/pOus9T0f/SZToPPVL/Ag2gqAgeekRn6bKf7wnVutdH3mPrGl1g+u/0/5P32Lo2/123h4ofstgz5ksOXj2P3bfO5eDV89gz5ksqfsg6qX4HeQzE62qjQFcdFYUEXWWQR/Ix2oXPS9DiZwC90W9AqX2SBi15BnzegH9Eex5AcGwZ7OzKcF6tCeVJWwiv1oQyuzKciS4DRTX+MtiT0d7rXHv2fyrWoTPpkAlZSUSbm/PWTq7MOR+z20SB0cXo3f3oV1bFd3s+xOl1cEXf2zt6iAH7aZWCWv4bvj3vZfq89ke00Bo65XUmsjqUwt5lxObbTtyJEEII0dHO4P1aoH3KP0ypoW3arjntXV5S8UMWuY+uxZNvP/I1Q4KFTo+POKn+vV5/JsLxvPhvnXPGtkEpTjs/P71OF9lzvsZVUoApOp6Uiy456T5r1hYe+Z36FB8HUg9SGVJJWHUYXbO6oOoq7jwbNWsLCRmdcNI/r73mqD2zQgz20ha3O+nzT8/0Nc7tIXP5BlylRZiiYkkbNxTNeHKX7trhDfVKFxtS0FGq8tEOb8Cb3PqtWY7NvGpMB04u8+pUlMG29zrX3v0fuw41Seek1qET/445rQ6ZkGCXaFMHd1YxbdtqIsu7UdV1L7tjC5iwbhy9dnxEWNdxhIx+9ow5hbEp+fmwYOvNvH7Op1QN3Efxlq64jC5GbhrGszOf4cOrr+zoIQohhBDH5d+v5WnU6oIjX/OFxOOc9Oc226+lPbVX+UfU9d3Jf2J9i9oFqr3LSyp+yCL7zqXUXVjW8eTbyL5zKSmvB97/lq00ykRoqLDQ327I4IB+BOB/fpoWPkv1HiPumhCMwdWE9HTjOveBNnl+7n33dZJzP6S/ufbBVEHRP19mY+otdLn+loD79RT6g4tbe2/jy2nfUBFeceS+8IpwLp87gwG7+h9pdzK0jHkYFj/NVschShSdaF1hgLkznpN8DR+bFdJkwA6VvMfWETY1OaCSRt0S1abtmnMq9qRqT3u+nkfKzqcZGFS7RmdD0Zp4svv8mZ6XBD5+peYEL+BWtmuoLvOqefqRzKtADiA4FWWw7b3OtXf/LV1fAl2HTvw75qR+x21Ngl2iTWU+u4iYshAAFg1Yz0XfziR6kguLJYuEzmOZEdWlg0d4ci6dAVdcZsC4826iDj9FyfZfYwmx02dXf+KL4vh293vcmPIHjHGWjh6qEEII0Yh/v5bfo3sVKnJTjgQTQjvlYP729zgufvG0vhisK/9oGMwpKtJ56BF46onAA172zS3LOrFvLg3oL+InLC9ROLlAgtfH4T8to+Hc+CmAzuE/LSNs6vWt7hv8WXRt2a4pWsY8bM+/ys4ll+OqPnrCtSmkkrStr2L9Ayf1/Nz77usMKnkRgur/EqKDionO/web33WRfvOdAfVtiLOwtfc23pn5fqP7KsIqeGfm+9wy6wa6xJ3c60vLmMfqub/heUsNhSFHH0ecbw9/mPsbRvFqwHNUlxVyooBdwNlpSgtfmy1t14RTsSdVe9rz9TwG77sHTA2eo6ZCovfdw6avXwg44KUHx7Zpu4ZamlEVaObVALdKmN782ugvg1WwugPfqam917n27t9wzDVocxmmDdu1RnFN85mBgbRrbxLsEm2mpsiJZbkNt+bGZ3Qx9fvL0RWdhF4f8VBcMFf6qujR0YM8SQaD/823OGka/+p0L+NHryd++SgqrQr988/B/lIWezd9Re91M1HNHZ+6KYQQQhzh82L84UlKM9LJXDqlcTBhwnzCf/gr3m7nnnS5T3uU4Bwt/9BRdJ3ujgLCvXYqNAv7zHHoCrz4bwIu/2jvv4jXKy9RfIQl5WAMrsZdE0Ll4WQ4yTK36pV5eCubCnTVUfBW6lSvzCNqRnSr+49uYbJNS9s14vNS89pHZHx3WaO7XNWh7P3uMnqYP8L8XGDPT6/TRXLuhxCkozaYIlXR8ekKnXM/xOu8BS3I1Or+zcOimX3Rt/4bTccamX3Rt1w97OlW932Ez8uqJQ/yZ2t1o7sKFZ0HrdU8veRBRgT4GvYU2lsUsEsuHBfQ8JXqoyktul4/pnXs7WPbtcoJ9qTSUQha8gy2Nljj2oPX7SFl59Ngav45mrzzGbwXTg5oPfUmDcUXkoBSXYBPV9hYMpRiRywx5iKGRG9AVXT00Hh/yWcAoqxxbdquody8NYSduBm5eWvonBZYVlF7r3PREUeDmIruo7ujsMH7mHpMu9a/j5mHRVMZXsXBTpnMbiJgfdncGaTlpWEe1vr3AIDyFr42W9quvUmwS7SZjY/sJMLrBoxsGLOYwcvPI3z8QeYFH2Shy84F7sqOHmKbsNl0rvmFiSEX98MzZBHa+sGEeMBdVcz2lMNMWDKWqgU5hE9P6+ihCiGEEEeoOeuo2B3F3jmXN7rPVR3K3jmXk658iSVnHb7UUQH/nPYqwakr/xhUk8PM4vVEeo/uS1KmWZkVM4zNhSkBl3+09C/dgf5FvC5IFtVtD2kT5xMUenSje2dVKJlLplC6v2fAwTT7vM0tbzejX6v7HzjAXy56vBKcuDh/u0Co2evJmjus9lbT0aKsuUPp/bv1+NJGtrr/7DlfHy1dbOrnKzpx5iK2zfmaLpdf1er+txevpTyk3H+j4XVq7e3ykHK2F68NvLzn0FpeUHL9/99MQO1FJZcPD62FlNGt7l6PNvLltG+O2//sad9wYfTvW903gFK7Z9eaAxPokrCLOOvRDJ9CezyZ+b0Y2XXpkXat1d57UrW3zOUbjq6bTVAVnbigfLYs30C3ya1/DaBqOCc9yIrXv+Uf2x+kwHE0qB5vzudP/Z5h7J0XBxwI7B8/ihhrIsW2fJpOYVWIDU6kf3xg7y8lass2bi9RdToH9BOOXeeaCzbpxMUpAa9z3RyFRHiCSXMUM7NkPZHeo+t9mWZhVvQwsswxdHPUAK3/o8f24rX898p3ye6c0+i+irAK3p35PimHkgkpHhTQOhS+1Ei4L5yKsIrmpoeIynDClxphUKu7b3NyGqNoE54SB6Fzt+HRPGSm7WNh3+3YhvhIHraSd4N9DEgYzaDEczp6mG3CalUYNRJ2fPcBl5mj8A6rRnMFEVkTSkxpNOXh5ZTJqYxCCCFOM87N+8hcMqX2VlNXspC55Dycm/cF/DPqSnAijEWsKx7OD4cuZF3xcCKMxQzedw97vp4XcN8FhV4G1WRzR8EyIrz1N+CN8Nq4o2AZg2qyKSgM7CSx4BFxGBOtx0uMwphoJXhEYFkJhjgLUd32kD79S0wh9U90NIVUkT79S6K67Qk4mIa7hYfktLRdA5qmMOXculsNLzr9t8+bHPjm9NWrcmuzDZv/Bbiqw6lelRtQ/66S5oMIgbRr6EhpVnPX43qDdgHYlreSQlU/7nO0QNXZlrcyoP4XeA76M0GO0395eAULPAcD6l+3RvHVxhu5c9srTJs/n9tWvMMDG/7ObSve4YL587hz2yt8tfFGdGtgaTPH7jXl86jkbhzGwUVTyN04DJ9HbbJdoLxenY2bdOYv9P/r9Z78SaSu0qPj8qKzweBmntHFBoMb7zFPrGPbtdb7X8fyp/XPU+Cov44VOuL40/rnef/rwEoYATRVY2LYk+g66Hr9J5GuK+g6TAh9IuCNy/XOIyhQfPjQm5wfHzr5ig+9c+CBTE1TGJ64BnRQdQ/DotcyLWkOw6LXouoe0GFYwpqA1zm92M7t+cu4o3B5vT/YAER6bdxRuJzb8pehFwf2R4/imnyyk/2BLkVX6HawK4O3DaLbwa4otb+T7OScgMsMwwpCuHzujNoH0+DO2tuXzZ1BWEFIQP23NcnsEm3i4N+2onl1wECNtYaq0Eq6fzCNdzfvpnjvNh4Z9peOHmKbuu4ahQULrbwb8RVzYg5wf/h2xm4YwYHEw2zot4nwpRF4yp0YIoI6eqhCCCEEAJXbLbiqj3fcuD+YULndQnQAh9P5S3CeYmHJuTzXRNbAvf2eZaDz6YBLcHbn7mRm8d7akTYcuf9z9lXF69mYW8kFtP7P7oqmkvjYcP8G8nUdHvsDgMTHhge0nxaAeXAU4ZMW+Ltr8AAUxV/GlTJxIc7BjwbUf8jIGAo+8l/k+FDYZ46jQrMQ7rXT3VGIWvuAQkYGtnmz16vz3fegxGxAr+kM9vijd1oKUIIP8933Q7nzdj2gC8GcgyFAVYvaBXLUkTEqviXd+9sFIMISjdFtwG3wNPsENbqNRFgCKx8CKFGO9/ptfbuGcstbFohrabuG3EFxvJh1F6jgUwysLzkmKKEAus5LWb/h3KDdARRwHd1rKnP5RPI2joRj9nfKWn4uiUPWkDZuScB7UtWZv8DJk085UdUN6Cgo6Ph8Q/njPUEndUiGKSoWsmGx0cXzFps/sFkrzqfwB7uVSW6Tv10AXA4Ps+Yn1q4E9dcxvXaL988WJHLl3R5M5gDKJL06P75zIW7LGxiHPwLBx2xkbkvEve5x5jku5PbzA1sj+ieO4d8RQYypruZ5i72J+bGwKjSUuxLHtLrvOk6Hi3ELNzIueRVDz/m6fvahLY4NP12CvjAIp2MoQebWlztrMWa6efPRMdDUQqGg082bjxYzJKDxlzuKAei/qx+XzZ1BZGXEkfvKwsqZPe0btvXZfqRda6V16Yv1AyeTVkxgyZhl6MqxZZkKE1eOZ8Cu/sRd2Teg/tuaZHaJk+bKrcH22R5QvRTEH6Z7Ri+GlEfgqcjms30fM63HtfSJC6z2+3SV3kNhxHB4d9erFA2+mqh7UtGcFlIPpbCr1w4UD1TOze7oYQohhBBHuI0tO4Wvpe0ayly2jq0lA7ivmayB+9b/i22l/clcti6g/iOLdxPptR0v6YQor43I4t0B9Q8QfkEqKf+ZgCHBWu/rhgTrSZ+UmLVyE5aQShSl6awNRQFLaAVZKzcF1L9l+jkYLA42WTvzUMqlPN9pCm/Hn8PznabwUMqlbLJ2xmBxYJkeWKb9ps061RHfY7pgBqbLh2KcegXGcb/BOPUKTJcPx3TBDKojvmfT5sAyXPLD+rRpu4aKOl1IAeBrJvXKh05+bbtAeD1e3MYmAl11FHAb3Xg9gWUeAoR1alnGSkvbNZRU3rKMm5a2a2jFT10p00Ka34BeUSjVQlnxU9eA+vcmDSVzzXTyNoxqMrMob8MoMtdMD3hPKvAfkvHUs/MpKdMoKh5NcfEoiopHU1Km8cLLK1m6LPAMr7RxQ/kaKw9aayhU6vfj35Othq+wkjYusPHP+2gvxc44mgsB6KgUOeKY99HegPqvKzWf6DbxRXk4L+/sy9PrR/Lyzr58UR7GRLfpyEmDgdBUDUvfK3nQamtmfmyY+1wRcOYYwIJ3l9E1LpdpU94k1lI/qBtrKWTalDfpFpfLgneXBfYDfF50r5HjLRS61wi+wNaJCHMM/Xf245ZZNxBRGV7/vspwbpl1A/139iMiwBMrY2/qxcb+m1k8dmm9QBeArugsHruUjf03E3tTr4D6b2sS7BInrXLRIRSfD3wahUNXE+QO4vayK0le8za/Gv4Ivxz2544eYru47hqF6u1X4vY52eT4DVqMB9XoxmOu5vVr/0v1BHdHD1EIIYQ4Irhby/bObGm7hhyZO/n79gebzRoA+Pv2B3Bk7gyo/3h3y8oiWtquOVt7b+fx3z7LSxcv591xe3np4uU8/ttn2dp7+0n1ay/2l8ctNrq4LKyCu0KqeSS4hrtCqrksrILFRle9dq2lGI1kXTOIN+InUKGa6WHPZ1j1QXrY86lQzbwRP4GsawahGI0B9b9hsxfj8IcBHVXzoSWsQuvyFVrCKlTNf2FmHP4IGzYHWkYaj82kcrw6QJtJJXhEYJlXG7f8xPPWahRdwdfgR/h0QFd4wVrNxi0/BdT/9lVL27Rdk47ZtVzxNShR8ilNtmuNqUYfcT7luKWY8T6FqcbAMsd2bW3Z97W0XUM+j07eqv61W6TVnwN/zgzkreqPzxNYQMrr1Xn5lZUUFY0CdNT4lahps1HjVwI6RUWjePmVlYGXNGoK/46oqhtwfbW3X4moggBL6IrzW1Ya19J2DRUVepmcOJ8/R7xGwcdX4pl1E5bvrsAz6yYKPr6SP0e8xuTE+RQFWGru9Xn5Ydds/9OzifnRUZi7+yu8AQaKAKoO5ZM2cb6/yyYycAHSJs6n6lBgZYD63pa9/7W0XUMx5nguqy0zbOo1AHDZ3IuJMQe2juoGhTmXzqvrsL7a23MunYduCDzDsS1JGaM4aRlRSYSoXlxd9xC6dRjOaBedO3+BZjmXS/ve3tHDazdDh0CfTn04XNmXj0OK6Bw5kuuKN/D71+7ltevfZvb+d/l94t87ephCCCEEACXmKipDKwitCmv0IRhAR6cytIISczihAfS/vtB8pHSxuVOmChyJrC80E0iBQ6w1HDhx6YW/XWCWZ87hkXe+wL3uK7B18n/xMHAwl0cyHuGJW2Bc2kUB9b230obd6OJBa02j++qyNp6xQU6ljdZvH++/EH9xzWAG1WQzs2RD4w38o4fy0trBTAnwQrzYuwqltixJ8Sl0zepCWHUYlSGVHEg9CKoOwbkUe1YB41v/AzSVzV1DGbO7nKZ3eIfNXUMZGmAZqbtkPwtd5/F/e6/m//o9Q37oYUoUnWhdIb6yM//a8QDL0z/lMlNg+66GbbNDCxKSwrbZ4eqAfgTl9hIA+u88QYlSbbvWsobZ+UOpP7OomV8B99itWOMDC4YYgluWcdPSdg0Vv+PP6mxqfTv268Xv7Cbuzta/ytasdZJfOAI15XuMwx858noA0GsSca97gvyc81mz1smY0eZW978lbyVVVB43O7CKSrbkrWRIUutPxIyOb9n2Ki1t15A7Zwd3WT8iY07TJ6pmzLmM30z5mPU5CcDAVve/JW81Vd48FKX5NajSk8uWvNUMSQrsEIg440/1Dg9pSFEgKLSKuKqfgF+0un+Dex9w4j/I+Nu1/kCXtMxUcioPNHu/gkJkZSTJmakEsov/toLVlGrHeR9WoFQrZlvB6sAP4mhDEuwSJ8VT7sT272WE+BS0fb1I0zW4Yg1XheXxYI+xASxjZw5FUbjtVrj3PzfjGPMnRt5mx/MfC4aDNi5ffiG7D2VSVLSH2MsC2VlCCCGEaFvr7UWsuOBrbpl1A3rtTjN19Nor2S8u+Iax9mtIC6D/sgh/iGxQTXbzpyUGpxxp11pbg0rprlmJaKaUUa/9OfuDShnWxP0n4vV5eea9hbiXvtn4Qr8mEffSN3lGu48xf5kWUJlMtrETn+m1QYJm9nT6l9nOSGOnAEYPGzfqdCs5zB2FyxvdF1G78fEbyng2bkxhagCHYoZV7YLIEwdawqp2EUiwq6zEw/UTnsfQLZyspVNqN6v3M4VUkjphIWlJFawuuQBo/V45vSwhuFc8yZKYjawIq0QJrj5yn65U4Da68K17gl7nLW513wB9q1IIrzjxKWV9q1IC6h8gyhzL9HkXMnnlhEb31ZUoLRqzlKjzA9vTyTSgG5MyTDxjw79n1DFlSvG6wj21e0bZBnQjkNyrvheGEb6omgo1uOlSRl0n3FdN3wvDGt/XAuU/ZrW4XSDBrlmfbUBNLsM44Q4UH3Q72PVIsGV/SibGCXfgXvomsz6LZMzo1l/ob8lf0eJ2gQS7Es8rhS9ywZZA0wVePrDm+dsFIFr5H+WrhtfeanqRq1g1lOgx/wP+2er+N+32Z72eaA3atLuAIUmBPAKIizoELSjOiYs6FFD/O8qisWvaCd/HHGVBDG/i/hM5uGdHiwI8B/fsYPA5ya3u/9gDNpoKOOq1+6idzEEcbUmCXSJg3mo3u8d+SWyVC73vZmyZ6WgmN+/2+ga30UxKUuCbA54phg2FXtZL2e95DGfws3S79RqyHlaIz0yCaiMHcuZJsEsIIcRpoTw8gm19tvPOzPcbXSiUh5Uze9q3bOuznb7hEc32cTyduqYeOS2xobrTEt+IH0+nrgHuexVezayY0dxRsKy5pBM+ixnGkPBVAXW/6fBq7D/dXxvoanoHecfyP7Hp8GqGJbf+QjbCvJQi73FCBAoUaT4izEsJJFi09rsqZhavr+uqYddHNvBf+10kU6e2fpP0dLtK/zz/XjAN1QVa3pn5PukRgWVedauYTYKlAHoUEN0tg8rDybhrQjAGVxOWlINSexHVrWI2gaRGmWPOR41Zh3HCnTSq07PmY5xwJ+6lb2KOOT+g8dO9J5d/N4N3Zr6P4lXomn3MRWCK/yLwsrkzYHrgnwuTM5KZtMr/3Gi6TE9n0qrxdM5IhgAu9t2JAylSfExwGxnvDmezwXMk+22Qx4ACFCk+TIkDCST3ytBpNTHpC6nY94j/RIZjX2e6/3cSk/4vDJ3OJZDXwG7LDrqQ0KJ26bQ+Q7O8yodx+MMM2NW32WDL1uGPUL71xVb3DeB1tSyE2NJ2DVV6SjAOfwf30jfRsDMx+mMilRLK9GiWlFyLlyCMwx+h0jMjoP6Nh7V6QerG/IegGA8HlrnnrYk7sh9VQ8euQd6YwE7MBTCbo8B94uxOszmwE0MPVaezMCbyhO9j51aXBRTs2pVdSP8WthscQP9hBv97xwn/6GEI/CCOtiTBLhE4BcpMwURoNn4cv4TQEDdalzz2G908c+7/iLSc3EknZwJFUbjj5hBeWHkpi4s/4a6aPEriHyCqoBS72U7CvnhcB3IxdQ3sr7RCCCF+fnbvbn6DdavVSkpKSpNtw8LCqKw8ut+WyWSia9ejdVU1RT5cVT42pG5l86+20/VQGqHVoVSFVHEwJRO1tuom1JRARkYGXm/T+55omkaPHj2O3K5r262wksiirdh155EP8AoKZsV0JNhyadEKIgtTmn2MvXod3dT2wIEDuFyuI7ctznI2Rrp41TeMy0s2kXjMviwFqpEvogeyNdLJWGd5o3np1Ono+3B2djY2W/0j3wE+/DyLmppOaJoPo8FLevf30YL2UFMZy779l+LTTbjc8OF7WYRc6f8g3717dwwG/8fpw4cPU1XVfPmLu6riSDKFz6OjN7OtTGllHg6HA7PZ/wvJz8+nvLy82X47d+5MSEgIYZkFhHgqcdD8fjXhHh9hmQVAGsXFxRQXN1+OkpCQQEREBADFxcVUOhxc+N2Ftb/f+oEWIwY0ReXyHy7FeaPxuM/hmJgYYmL8myOXl5eTn+/f+0bdsIyaiLrLPR1DfBZWDYy1+xN5fToOD3g2LGN3/8a1AxERESQk+AMd1dXVHDpUP/Miw2NEHfgQXpcPVQOldk8Z3afjc/tzHdWBfyHD8wVxu8ua7NfhcJCZmdnk41plTWKMx0GvTUNxLDmf0IpwHPifv1WhFQSNX0CYu4ZV1iTYvZvQ0FCSkvwRKY/Hw759+5qds7rXffYH6zHoKnbd2WxbVVfJ/mA90RP9QeXj/S4arhHfz32OtXo1T7pC0IFerqOXig5Fx2pU+KfFxiU7P8AcPLHVa8T2bd+R0fVtOlc7qDh0D1VaCKCgqlbCfdXEpP+L/T1fYftqO9aapgMWx1sjFiRkMD1EJby2VNuiHC3Hc+puvHipCK1gQUIG6Q3m5dh+m1sjDBFL6L0vgpu//AVKbaDOpXvw4iWowsw1n87EffnHOCKWsHu3/zqoNWtE5FdxRHYOpsxag8/b9BoRUWOF94NwDA5gjTDFoMfP4cpOd9B/Ux9C94cDUYDO+JDX2DZ4J98kzSHMdCtAq9eIqoJQfM08N40YMCi1Qa7K+IDWiAOrorjg+2n11qC6fhUUPLqXC76fxiJjFLvTG/d/ojUCQE+dStbG1cSrKubaNcKn69hrs718uv+0U3fq1COP4XhrRMP35ULHYTYHD+SN+PFcVbQWi7fiyH1lmpXZ0UPYaokmvXIDhw/HtXqN8FWEoGhl1Hi8zW5XoGlefBVH9+xqzRpx4ItCRmb2ZsbsmQDYOfr7tlRYuGXWDcy+6n2qDBoZo5v+HBEWFkZNTU2Ta0RTGq4nraHouh74kRFNKCsrO3GjWpGRka1q/3N2Os6VbXcZ+6Z+S1GXvXw2bjFBI8LZUbyR2/r/jmuGn9pN6WtqakhO9qdi5uTkEBwcfEp/fkbJNn799RT+YLNgyP47iZ/Y8GpeDF4DQVflkv7PB07peFridHxOnY5knlpG5qnlZK5a5myap8jIyFa1V5o7qaz2vpKSo/vxREUd/6/LpaVHy1GO19baWaHX743ozkju7b6F6685fnZES/tNUCL5NPjRI7fvsP2TPb6ck+5XUSz8acj7xFNGAZG8uudVqqsXtajfmJgYfL7mMyMuu+o2qod9RInmIfMTD6Xrm2/78ccfc/75/kygxMREnM7mgxC33HQdW/p/DsChbz0ULm2+33vuuYdHHnkEgNTU1ONeIP/iF7/gpZdeYtX/beLbD1/kP65vmm37gvkuelx7ORe+PZmkpCRyc3ObbTtmzBi+++47AIYPH87+/c1nOzxmvplJhkEAPBj3NisPNH/cWrdu3Vi3zn8i5/Tp01m5cmWzbX91oYWbRlgY5DHwU6abKR80vybExMSwd6//FLnf/e53fPDBB822TZii0ul8fwDCnu9j13OeZttardYjF8VvvfUW9913X7Ntr01L5FfF/vvL9RouqflLs20NBgOFhf5Sn927dzNmTPMVEaqqUlxczNdTvqPrnlImVN/TbNtRWh/uHPQAl8yfDrTdGtE/3sCU3wexxOTmkcQZXHr9523Sr6pYmXbdJeT3/woMXjbe62q2bWv6NWPix5Cje+feb3+d1d5dLer3RGvED8HPYlX8gaZnHB8y19P8CbOtWSP+MOxGzjtvAQ9HF3P4Wy8Fy5oPXAeyRnyyYDNf/PlWFu7LbLbtrSMGMuze57nmvEH069evxWvEqFGjjrz+mnLsGvGQ9W1+KmybNeIe0xVcZvKXdG7yZHCP45Vm27ZmjXhonJW/jAul+nAK23MVJs1f22zb1qwREeYQ+nTdQWWXJSi9/8K255p/PwxkjVj9p42w/3suXPKvZtsmByXz+i/eYdQ/hgCtWyMSY6NwNvO07Kkm87r1jxBaSd6tqVz71M0t7rclY2jtZymQzC4RIPvOUnbesRKD6sNamMCEVeMo7reKqLSLuHrYgx09vFOuR3R/uoWO4BPfVmb1fpfvI35NXHkpZaHlaD/56FmZix4m2V1CCCFOb0GKlwo1sFOgTiWz5uCvF9x15Pb60hoWVR/nG1rhwKD30AI8ze54YqrT0GsSwRrYKV4nEt1/QyvaTW6XMQCEeC1t1tecIBdrQ7zE+RQmaaf/ZYuzMLk2e699TiLLtUTTlRPvp5RrafsSooyKdNS8HmipPxCptd0flX26ncOJuaiqjtKGKRh6g87cBg/HSXpsleY2wD9ZMVGFTDF4yd86mG83aHxF80GeQBRklZNS0APIbLZNt/2DKMgqb9Ofe5SOLayCnOACOD22dGrW8p3hbMj4Nd7qMLK8eUDzwa7W8OBlZOSrLJn4Au7qwMpRj6ffuHyu3n4L0Hywq8yYRr9xAb4P6RrHeyEpKFAVTnDVqU08aY5kdp0hTre5yrx5IVWLDqMNXUXZ7r5UR5Uy4958bJe8hKae+g8jHZ3ZBXDn099QbX2J9/Qcdu19Fn1OFR7Nzea+m7nsdoXIS1465WM6ntPtOXW6knlqGZmnlpO5apmzaZ5a+9fIVaua33PqZMoYn/ri/1hQ2PRfshUVVKP/Am5m798xKeaqVpco7XjjKZI/q7/PTl0ZYx2n7iLrqqX0veOhJvs+XomScf9iOm98gSADoECI6ejeUDaPD58XnB44NOQe3N0m1ZuXlpQxlq07zNNlt2Gz2lBqg10Nyw1DXMH8OepNIof7S0taU6K0700n/ynbjn3svfg8ur8eppZee/FsXvUU1walcfXLY1tdopT11a84+FA6lsqQZstXnGE2Up/azaBbPiUjI6NVJUoH//ku+gdNn3R5bImS4Y5qlCubD6Y1V6L04Y8vUsJX7DIdvQBUDaBoCuj+csOeNpVoLuX683/fqN8TlSgdPPAFf8/yfxZTNFDrlTEebXdf6u/o0vWKJvs9XhmjccFSyv9mxKT4nw+6rh8pYzxW9P0+3OdNCKiM8fFHbVz07my8vuY3t/YoRhbcMpNHH7cCrStR+vrrx/nH8ix8a5+v/Ur9/ddU1YJh3F28ePkQrCGTW71G4POy7YuZ/KugP/rOB8Hl3yjdYIgGay7G4Q/ze/M6el3yKTRzCMTx1oh9PzxHuG8Rj1hrUHwKPfKPbiC/L/EAPkXnCVswFepkul9wb7P9NrdG7H32ExIWJmHG1KiM8Vj55x4m/YFrgNatEaatz1G2PA/j1zNx6x68xxwDUHeIiH3alwQNjWTwze+0eo2Y9+v7iPmuF57jBCtMGCmcvpOpr/29VWWMXq+X+998mLs3bqbwh0trWxx9lhrRMCgacdO/4LWxo7lmaOMTG+s0t0asevMn+s6qH7o4du3x6j5cuNkxU2H07ec06rclZYyrcxaw+pPPuH3ejRgVIwrg0304cdf+BnTemfoho665ilHJ5zXq90RljBsLlvD55n9SGVKFjo6viUTG0KpQZvS7mwsGXtXqNWLj7J/43Ytj8PlqUHQfXR1FhHkdVGpmDphj0RUV0Pj3HzYy5DL/HLWq1PnJd4l5o+kd/FUUgmrf790PxxA6sUebljFKZpc4JbzlTqoWH8areZgfVsaUmjDKL/sc14S3OyTQdbp46s6LsQZdgPl/FxAc9yU/Rf2SwaXZFEWX8ImriF939ACFEEKcEY696GpN2xMFCNUyBS3oxBkJJTtK6XFby/fHqPvAuqbHQRzhw4moDG822GILr6G6x8EWPcZjP2ADLNu9kYHB/otvLzobDO6jm2djQDMohATBGnc4448zL8cGC4+1uWYZ9i32emNXDUq9T8v2IBuWPvvp1evcRt9fd1HSnO2+g3Qu7cOupa9jGP4oSnDekfv0mk541j1GWmUywV0ijlzEgv+Csu5C6rj9V1Wz4ILvj2ze3NRpm59cMIvzqhIYRP0LyhOJiYnBHVZFZagZV3UozR03aAqpJEwrJrGFz+GIiIgjF8vJORNYlTMbTVea3GFfURX2hurMTJ5wwudPSEhIoza9vf14P1f1nzB4TP+KqqAFAbr/xMELU/uhN9O/2Wxu9meXr8jBphz9nSqKgoWgRu2iLYlENOjDYDC06DVxRfQaVvewMnJvXdll4+2t16SHcUX0GsAf8G3NemLp2Q9e+iOqaqG50/o8q56j4Pp5TG3FHjrHXtQWbfsAbeEA/w3DMeO3JeJe+hbRv95Krz59W9RvwzWicoOByQVBmD0Kz1ts7O9y4Mh9CT6Fe+zBTFJMLIo7/nw3t0YcNvnq7QMG1AY361//BJt8TfZ/ojVi84EQPPOmYwRMirHR/To6LLuEoMv2BLRGmJxOjIoB4wlCAKbaUsvWrhHnRnalX6/ZlBjmkLmk4YmqFaRNXEB09wxGGma0+Hl57BpREbGa8NDqZtcgTVEID3HQJyI0oDUCwBFSTNcVpiOBLgBVUY+8lnXgupXXE/Z4H3p1bvz9DdeIhu8/2z1LqQz1BzwVateeBmxB1USkWOo9X1q6Rmwu80fPVNWf+HEw+OjpxwpHZ21zmYshtf/fmjUiXAvCopz4EBJ7UQVDmlkjmvqsEuieXCcS2HEp4mct/7lNoIM7Jp/JS85nT9e9RE4ahB7V9cTffBaLiVawhhjZ3eNCIiPXYJgZik+BySsncGhHOZRmdvQQhRBC/IxZK1pWXtbSdg2V25KZPc2/X1RdcKVO3e3Z076l3Nb6484BSmo/xC82urgsrIK7Qqp5JLiGu0KquSysgsVGV712rbVpa0abtmsocUgo28sH0rsymZA53+H68XNcy17B9ePnhM75lt6VyWwvH0jikNATd9aEPGPfI6dtlodV1LuvPKycd2a+z7Y+28kztiyQ0JDPEUTaxPm1txoWhvhvp01cgM/RxNVbC0Qm1I65uXis0qBdK6n2Mv5g92c7NTN87rFbUe2BZZQeNPRp03ZNKSuBaya9SI+LvsQUUj9DyBRSSY+LZnP1xJcoK2mmgxPYunQgeINp/hJRBU+wv10AvF6dZz6s+96mzgyFZz8ciNcbWOFRVLr/8n2S28TsynBeqQ7hiZpgXqkO4cvKcCa5TfXatVZMcjGmkMpG61sdHR1TSAUxyc1nQx1P1o5UrPbgZsskFRSs9mCydgR2oq0W3rJTEFvarqG+Yf5DBaK772XIra/S54oP6THta/pc8SFDbn2N6O5767VrrRhjVYvWoBhj89lzJ5J2sCuRNvNxl6HIGjNpBwO77o0Iatkpji1t15A3tmXhnZa2a6ikOowyzdrMK8D/WyjVrJQc91TOU+fnm4YjAuLz+SibtR9d1cmLLaRLQWe2TVzElecu7+ihnRacbid3HXiTcUEeHoz6kE36UMxOC9e8/Vv2mG+l1+1vokd36+hhCiGE+BnqqkQS51MaZbYcUZvZ0lVpfakAgKZfxbY+v+Gdme83OpK8PKyc2dO+ZVuf7XQrfTWg/pNDbCyudvGgtabRfYWKzoPWGp6x+dsFwltVBSEtbBeAkVdHEfrfSraXDUBR3HSO3oiKB5+hjEOOYRTbEwhVKhh5dWAXOTUhSWCDbX22s73XDrpmdTlSwnUg9SC6qh9tF4DiJDNpah7pF31J5tKGWRuVpE1YQEh8HrsTzQTyE8KDWpZB0tJ2DWUWRTHJbeIZGzxvsflfB7XidYV77FYmuU3sKooikHBscUIcYSYVq8tLcy8wm0mjMiGwC32AoOBCEgwF0KOA6G4ZVB5Oxl0TgjG4mrCkHJTa3/EuT2AbIu1f17JtQPavC4Y7W9//ps06/oouBUX30d1RSLjXToVmYZ85Dl1Rqaj0txs2tPX7YlWWjCTfHk+cuRBNgaGe+tlRPl2hwB5PZcnI1g8e6JE8EG3i9+z97nL8l/X1M+sU/MEWb/KFAfUfubNlge6WtmvIefMwKucVE1rVfPZtZVgFzpuHBdR/Sq9YqD0DQFF1wpOzm28XgE79uxFtepX06V82kTlWWZs5thdfzwCenLUObnS0KEBycKODweNa33+8rfLEjVrRrqGwUCNYc8HmLxFuzAfWPH+7AGiWGGbFxHNHwbImXgF+n8UM4wJLQUD9tzUJdolWKX51O7rDS2W/zSxP301ekItbb3q82br6n5sgYxCTrf8hZvVPhHX7kB39rySicCtdCiws3pjGoHkPY7/2o44ephBCiJ+hATFOrEUJPBOR19R1GgC3VCTQI7b508KO23/cWL63hbCtdzPBFkXH5AphQNzYgPofnBrEDRW1gaymkkJ0eMFi43+pgWUW9bBGtCgY2MMaEVD/iurBNPY+1JyLMQ19lLBi85H5CRrxKK4Nj2NK/g5FfRkwnbC/hnp2M7MqT6NY9aKrer0Srrrxx/o0enYzN93BCagphzj01Vi6njuXsK572VzQiSpbCKHWagbE52JQ4cDC81F/13gfnJaoyD9xGdaRdumt77/YFQ/ARLeRsc5wVpdHU+TViNW8jIoowagebRdIsCtaz+DtyHO4o2AZShMvMB2F9yPP4VY9Awgsuyu+jwlqD7w7XjAhvk/rnz8ABo/9yP83F4xq2K41Nm32/zuoJpuZxeuJ9B4NTJdpVmbFDGNzcAqbNsOwoa3vv7zIy9+3P8hzw/6AT1dQjwlo+nT/7+MfOx5gYmpgO9UbElKJ6r73hMGW0oTANi8JtoQBjha2a72omFRyhswhdOnU2mdk41LnksFrSI75TUD9q4CzOgRTcDVNHSqs6+CqCUUFAtma3Tx1CtWbIojslkFU18bBXl2B6ppIzFOnBDR+gHLFREvC6eVKYK+xvloM0V4DJaqn2feZGJ+BvlpgQf0I12Cih/6WkuWvo+JmSPQmYsxFFDti2VgyGB8aMUMfI8L1ckD9Jw0LZfPCFN6IH9/ka/iz2tfwbcMC+6NTW5Ngl2gx3euj6LUd6OgsTMpmR68dlE9wcmeXwP5Ce7b6w9Xj+d2iPvxp81iWuUZwp54HVDNk40iqRv8TY/429IT+HT1MIYQQPzMxhl54y9J52ljFC9aaepktcbrCPbZgYsrSiUls+f4dx7L2isH34t9g8l3oSoNgS+2P8i3/G9bfB/YhfqenlEL1OOVNChQoOjs9pQTyLqtaQ/lDidWfOdZMMPAeuxVHdGBZFTt3vE9Nt28Y6jzAZW/eXC/zrSysnNnTXmRbt+3s3DGC/gN/2er+g/dX8X8O83HH/0eHGcf+Kmj+BPtmRYYlEZG2jI+2DOaTc5ZSFH203C/Wo3HNTxOYlnYQd9j44/TSvDDXyCOnVSpNHMun6wrYEglzBZaVoycPZfYBA9lZnRj148UYa8KoO7ZgU3Alq8//lpTUPKKTA4iyANG+A+RFD+FNxnFV8XoivUcDQqVaMJ/HDCUv2ki07wCBBruCLFta0a75DcCbM3poKTuzE+hTVcBVxRuauJAdys7QOEYPLQUCK+MaVJPNHQXLGn09wmvjjoJlvBE/Hmh6z6wTiY63sChvCveuf577+j1DwjHZJQX2eP6x4wEW5U3hivg9AfVvPPdcnOvCiOq2t8lgC4qOszoM47mN9/RriW5Xj2b/nGUYdW+zBxC4FY1uV48OqH9fwUheGnE3vwNiNo4krCriyH2VYRWUDF7DSyN28beCkQSSnlmztoDSxVNJn/4luk69gFfdkXiZi6cQ1bMAS5fW968YjbhjLkapeR9doV6w11f7Nwp37HSMxsCylgDU8BxMIZUn3JtQDc8BOre6/6y9Lu51BPGg1dPsOv1/jiCy9rro0q/14x9on8Vf4pbww7lX8EetlATz0ZLafEcM//JGcUHEdpLts4CbW91///N6EvOvEjZbk9mS0rlxQByFWGMJ/c/r2frBtwMJdokWK/0gA1+VG1NsAZf/eAklkSVcOv7mjh7WacdkUrjw1mJeWPl3Jo/ozM6vB9O5YjFhTgtzd/Xlqh/ux37L9x09TCGEED8zetoIemY8g144lDesuRwOyTuywXunqkQK7Z3oaTxIWdqIgPovq1KJ2X8O2eqbGEc8jBJ89Ghz3ZaIe+0TJOwfQVlVYHuFHDrUsoyzQ4ecAQW7nO7zGOL4nKd1pVEwMF5X+L0tmN7OUFa7zwugdyiuOEj/nf2ObCB/rIjKcG6ZdQPvzHyf4u4HA+o/yh7LyNoyvX9ZbBQ1CGb+obZMb409sBKizkljWNf7VV5uooy0SPPy8oRFdLIFMzzpgYD6j43WcK97EuOE29F1pV7AS6/NynGve4LYcwKrJujd18ujHybwiy+vo2GhobcmlOFfXscHV33A4329BHKJVOyM4b5+z3Dv+ufZYk2im6P4yEXgfnMMuqLyXL8/UOy8nsB2XIIKzYfDG4RJddXLWqrj0xVcXhMVmo+W5cnVd8Uv+5G09AUi93VqdF+E18btBcspS81l1C/vCaB3GNzXR8/i9UCzyZlcVbye4L6dCWRr6X6T0ol7oZDFeeeyJG8yQ6I3HJPVMhQdhXhrIf0mBZAaCKBqZK+dRveJs0Cpn1lXF8zJXjeNhAArXkJGJzErZijXF61ttkRsVsxQnhodWClyWZn/NfbSxNsxjVrCLZtGY7ZbcFjsvDN4FS6zD/fSNynrE9j43TUhlO7vyd7vLidt4nyCQo+WfLuqw8hcch6l+3sSWhNCQDtD+ryEq/Opzk/EFFpFUEh1vZ/tqgojPH0+Nt/9AVcdxViLSZs4v9lSVfCXqnqsaQH17/CaW1ROvc4bWAZucnAOtoJhPBu5tdGLLM5czLN6MdsLhpHcO4emz1Q8Pk2D+4f+jT+t/hu6rpBhOWal0f0Rx/uG/g1N+1tA429rskG9aBGf0+vfmB7I7O4vxo6NCGVs+syOHNZpa9ywGAzRO8lz3MGl6UswO03o6EQvm4Kj+CDqvoUdPUQhhBA/M8EjE8nZchEDIrcSbShF2zeO0F3no+0bR4yxlAGRW8nZchHBIxMD6j86CjLNsaRkjMA0a2m9DdiDZi0hJWMEmeZYogPbkopQWvaX4pa2aygqIZh/ZM9kotvIFxX1N7f+vCKciW4jz2XPJCqhZfsaNVSOzmVzZwA02i+n7vZlcy+mvNmtf4/PHB1/zK2mDwho3K7lvElD+Ze1tsSq6b3F+ZfVgTcpsMyofv18KCVDcS99vXa/mWPYEnEvfR2ldAj9+gVSAAVzdr/LZd9dXjvcZub/u8uYs/vdgPrPcA6kb+Q2/j7sj8RaismwJLA+pAsZlgRiLUX8fdgf6ROxnQxnYJu7A5giUjFrThR0fA2eJv7MFh2zwYkpIrBwmqVwCwk7Q6jbf+pY/ts6CTuDsRS2LMOsoeRte4n02o67+XeU10bytr0B9a8ZNf5wU17tSBXWl4xg7uGLWF8y4sgjuuemPDRjYIGQmrWFFG/pxt7vLq/N/DnKVR3K3u8up3hLN2rWBrZn2tYdCitC03kjfjzlmrXefWWalTfix7MiNJ2tO1q/nxn412hf9oW4l76JyxfHG2N+4qVz5/PGmJ9w+eJxL30TX/aFAa/RSo/eACzMO48L5s/jthXv8MCGv3Pbine4YP6PLMw7r1671tIOb0Ctzic0MQ+TtZrqwjgqDydRXRiHyVpNaGIualU+2uENgT0AwBwdR3T3vbgumUVlg4M+KsIqcF0yi+juezFHB7b3njHKn9l8okMU6tq1ljcsmUSr/zXQMNDjv62QYMnDGxbYQTHaoXVMiZvDP4fdQ3yDfbniLfn8c9g9TImbg3ZoXUD9tzXJ7BItUvrRXnwVLrb13kLC7v4Udj7EXx78BqWpgmxBpCWW6T1u49t9/2Zb2Va+6Pw4d5ieJ+VAV37YOYRLU9/F0T2wFGchhBAiEIqmYrn9ZrY/asJZFYa7xn+xZge2BA8jKLSSqMevQ9EC+1vowAEQGwuZRbGg+0jK7oVJ745LMXDYFEylOZS4OH+7QPTrNJrwdeFUhFU0u9dJRGU4/dIDK/GhTxkLXryB+9D5U5cP6m1una8oPHfwFyzY/wtm9MkMqPuogv5EVjZ/UqSCQmRlJHpBYMGotHFD+XqzlWesjU8TLFLgQWsND1REMGlcYMGobUXrKFKOs9eRAkV42Va0jkGJrd+XbWfxatIS5rF/3yM4s6ehxq8FSwHY4/EVjABdo1v3J9hZPDWg/u1rigixN18ep6AQYg/BviYbAohHqepH/H3vnTw34EkmJixic+kQih2xxJiLGBS1EU3xce/Wh+mX/hHQ+jJVgJR+N1C05DmifTqK3jBgB7qiU6wppPRrnD3YEjVr8nBVhx0nGKXgqg6nZk0elrTW9+/JbtnhDi1t15RxVw/m1zmbmDU/kWLn0YBEjLmYq87LY9zVgwPu21PoL00t3d+T0gM9CEvKwRhcjbsmhMrDyaCr9dq1Vkmp/9/NwSlssTZRIla7Z1pdu9aqW6OLsi/AmXM+atyao6+xwpGgqye1RqMqbLIm15aiQmnJMVnCms4b8eO5o2AZaWpg149KTdGxt/A6zUfKSI/mBjZs1zpH1tFBG1AGbKRr9jF7T6b4D/p4oCIp4HW0Mt1D/poY4oJKmj9EwRlDZbonoP4zKtMZaG7+8auKTpyliC2V6QRyZJqWswaAczstYGLiIjaWDD2yzg2J3oCm+I6086aMCuQhtCkJdokT8ta4KXp5G54epUSURxFbFoP3DrsEuk7gl6N/z/wDn/BucCbRcUEkbOlGeWg5cT9Nxtf1NbTMFXjTAtukVwghhAhUdX7jEhh3TSjumlAC/IM+AJqmcM9v4aFHdFBUDjdxdPrv71bQtMA+P2iKyuVzZ/DOzPeb3evksrkz0EYEFqwrdxVjHP42C5a+yaLt9zC028fEhGRRXJ3Khv3X4tNNGCfcTrlrRkD9R9REACfO+PC3C4Cm8FqUnUY1enDkOvD1KDuTApz/UlvLslVa2q7R91UV8Ms10Rz0LOWzmOGUFxzdWCzSU8OVxevoUhJFaVUBBJB82Hlfy76ppe0aUgyZLE87xL3r/8V9/Z5leMzRzIY8WwL/2HE/y9M/pb+h9fv81NEMJnKG30TMmnfRlQYbjCv+3KWcYTeRbghs82x3TQhw4lPg3AGWoakpLSvNamm7pixdpvPqdwNR8JIetguz5sDhNZNRmc6r38WRNEJnwvjAXgOGuGMeta5SeajpDLp67Vrh2IwqXVHrl4g10641NE3h9rFFPD07GnQV3zGvsbo6zNvGFKNpgWUtuQqdzIqpPcmx4XWiooCu81nMMC4qLG78zS2gB/tLsEv2pTdzQMB8orvvPdIuIMeso7rW9EEfJ7WOOor4lzeKZylp9hCF572RjHEEFrBzlbcsEtrSdsejKb5669zpSMoYxQmVvL0LT7GDfT3nE1keRVVwFYt7b+voYZ32gk2h/Gr0A6gJqwlOfYsCLYzwqjBUp8qONVMImns/6IGl4gshhBCtpXt95D12nA+mCuQ9tg7dG/h704TxCk89oRDb4FojLg6eekIJ+CITwFvsZMCu/twy6wbCK8Pr3Ve359WAXf3xFgd2mmSUNQ4t9QeME27HZyll3b5b+GHzY6zbdws+SwnGCbejpf5AlDWwC8EuPVqWLtHSdg1tK1hNua+06aw3AAXKfKVsK1gdUP8tfdyBzk/U3jAiKyMYYjvEU9lf8Yfc+dxa8BN/yJ3PX7O/YojtEJGVkUTtDewkuvSYlqVrtbRdQz26pqKl/sDy9E+5cMV79Uq4Llr5DsvTP0VL/YEeXQPdsat2fGMfYNPImylpkB1ToilsGnkz6WMD2zMNQO3Zso3zW9quoRXDV1EWVl6vrPZYOjplYWWsGL4qoP69Xp0XXtZr+9LYW9mbrWWD2VvZGx1/6eKL/9bxegMrFQ4eEYcx0Xrc15gx0UrwiMBeA3WZV8dzMplXutdH14+XcUfBMiK89U/Li/TauKNwGV0/Xhbwe8BuWxjlhuDGga46ikKZIZjdtsBew56EwRTsGHTcMtL87YPxJASevdfe62hZXjzLktbwgK0Hhc7oevcVOGN4wNaDZUlrKMsLLMPXFNWyQF9L2zXk7dyyPT1b2q69SWaXOC5PuZOC17biU32U5abi65xN/KQ4rhn+p44e2hlhWvq1zN70KjX9n6Lm4L9QNit4DV4cW3tT02cNptX/wT06sON9hRBCiNaoWVuIO+84x4Hr4M6zUbO2kJDRgWxv7TdhvMI5Y2HLVn+5TXSU/+Is0IyuOnXZEgN29aff7r4cSD1IZUglYdVhdM3qglpbQhRoVkX/+FHEWBMpTp2Lmvyjv6zHHg+WAtS4NSiqTmxwJ/rHB1aaEToqAV+silLkbbRnFPgv9PU4jdBRgc19e2deHZkfWz4N9wTzU4gNTgx4flLcXThMLgAqOumOgmbbBSJsbCdK/72zRe0C0b/fjcSuf4yilB9Qk39kyzHPH2PcGhTFR6zPQP9+NwbU/7HSxz6Ad+Qf2bb9fVwVOZjCk0npd0PAGV11gkclYIxVcRc1lR4IoGOM1QgO8DmaZ89mxbS13DLrBnQaZKbVPqdmT/uWrvbALpS3bIWiEyTEFBb62w0JIB6iaCqJjw0n+1dLj62aq73T/0/iY8MDLgWvlx3bjJPJjq17DxiMjYHZh9hnjqNCsxDutdPdUYiKjruGgN8DbHGRbdquoeq1xWQtqjsgpOn01czF55K6tpjQsYFlaLb3Olp36uzSTmtZ7lMYUNKPGFcIxaZqtsZux6fqUNMp4FNn08YNpWhNPNGmwmYPsSh2xZMWYBmmN3kEdjWKIG9Zs/07DVF4k0+PYJdkdonjKnp1O3qNlw8v/x9rB61n3szPGP/n35MYenJ/lfq50FSN+857lRJVJ+O8v5FrDMfkMVFlqWLvkikY17wBnsD+Ai2EEEK0Rkv3kQl0v5ljaZrCkMEKU871/3uygS6on1Wh6irdM7sxZPtgumd28we6TjKrQlM17hr1VwAUVUdLWIXW5Su0hFUoqv9D/W9GPokW4ClfiqaS9tdx+LcRb2oDeYW0J8cFfKHc3plXx85PczvUn8z8mFq48X9L2zUUMioBLdJ03KwiLTKIkAADOZrBxN19fw2AovjqP39q97G5u++v0U4yIHXsz+sy6Jf0nPAYXQb9sk36VTSVxNrnaOOApv85mvjXwJ+jiaGpbOuznXdmvk95g82/y8PKeWfm+2zrsz3g64yW7mUV6J5XAOEXpNLn/YswJtTfQN6YYCXlPxMIv+DkrpHaMzv22LW9LqA8vCaTdEcB6jG/70DfA6JjWja2lrZrqGZVPrrXyPHSrnSvkZpV+c3cf2JR5pZlPLW0XUN1p84C+FSdLXFbWdh5JVvitvoDXdSeOhsd2DqqGQ1k9/mzv/8G+/rV3c7p8yCaMbCcJ6+u8vddjxy3/7/vfBivfnqEmU6PUYjTkjvfRvHbuwjpk8uV2wfz6//dQYQW3eyHBNG09NhBXBk/mUUh+WzpUwKA2+jBlZ9EyfYemJb/s4NHKIQQ4uegpRlPgWZGtbe6rAr/jYZ3+v85mawKgHFpF/Ho5LeIsdYPeMQGJ/Lo5LcYl3ZRwH2D/0I59fUJGBPrB2yMicGkvn5yF8p1mVfHuxA8mcw0aN/5qQtmNvcpU+fkgpmKppL07Ogms+rAv/l60rOjTur5M3b0Qzze57fENSieicPA431+y9jRDwXc96kSfkEqKc08R1NO8jk6o9ctqIrKtj7befKeZ/j3Tf/hf1d8xL9v+g9P3vMs2/psR1VUZvS6JaD+W7qXVaB7XtWJuaQ7PVdeTpdPp5L88ji6fDqVnisvP+lAV50J4xU+/0ThpecVHn3Y/+9nH59coAva/z3gaBlm86/ik9oA/xToktWF8Irw4z0EIirC6ZIVWIbpwAEQbfefiNn0qbNvEuO48KTmqOclU9nU/QVKXPXXymJXPJu6v0DPS6YG3PeWrTB7zxTuXf88hY76/RfY47l3/fPM3jOFLVsD/hFtSsoYRbPyX9oEHh+OQo3c0CA6KxCXPCzgv9j9nN0w+RUOfDCEQWN+wLtlBpGVEWQmZaGtmMSQ9Ldg9N1gDqx+XQghhGiJumCCO9/WXBUaxoTAgwmnQvgFqaT8ZwJ5j62rV5JpTLCS+NjwNrnYHJd2EWNSprGtYDWltkKirHH0jx/VZp9/wi9IJWxqMjVrC/EU2jHEWQgeEXdSQRY4mnn1+KLbaK7G6mQyr+q01/zUKxGDRsNXOPlgZl0gJ/fRdXjyj3n+JFrp8Y9JaOOjj/PdLTN29EOMGv4ndu54n9LKLKLCUunT94Y2y+g6FY59jgbVqDiDfW3yHDUZTFzZ91fM2v4qutrE5t/AlX1/hSnAuTpy2uBxShnbKtiiaOpJlXufiD87tm37bO/3gKNlmM21UE6qDDN4dDxFL5143+jg0YHtdwWgF7ladBCK3rX5k3WP5+gcXdjMiZgav3/i5LOhe14yFe+Fk9myfAOu0iJMUbGkjRtKzwAzuurUZUUuypvCkrzJDIneQIy5iGJHLBtLhuKr3RvvZLIn25IEu0STnJlVlH28j5LwEsw1oaQVx7Js1ApuGP2Xjh7aGcliieSfAx4gaMULvBF1K/1Li1g9aC1pc64ib/1Q4te9hWvcHzt6mEIIIc5i7b3fzKnSXsGiY2mqxqDE9jsxub0ulOsyr15Z/ReKbXlHvh4bnMhvRj550plpddprfk5FMLO5509UTDRlZWUn3T/4Swz7D/xlm/TVUeqeo5GRkW02LwB3jHgE54FKvqn+EF09uggpPoUZIddzx4hmIyUn1N57Xp3pTsV7gL8ME154Wa8XdIyL88/9yWSn1ZUie8uaDzSdTCky+LPa6g5C+XLaN1SEHy23jagM57K5Mxiwq/9JZUAfnSONomNOxGyLOTqWZjTQbXJge38159isSB8a60ua3pvrZLMn24oEu0STCp/fjKIpRJVHYTfbQYHQm7vQKSyto4d2xnIPvAZl7etkXP08Pd64nvTMHhQNKEfdNIa4n95CGfwL9JDT96/pQgghznynIphwKrR3VsWZrL0z09rbqQhmyvOn41T8kMXE+wdwjtKHFSNWURxZTExZDGPXjcbgM1ARnnVS61B7BlvOBqfiPaC9DimpK0XOvnNps21OthS5LvttwO5mDkJBPaly6jrtNUft7VRmT7YFCXaJRhy7yyj/6iBaUj6+w3FY7VZ299jLzHMDP8pYAOZwfP2uxLP3P8wels/kPd1Ac+BxKRxeOZyUPk/guOTfHT1KIYQQZ7lTEUwQHau9M9PamwSjzk6610feY+tAB4NuYMLqcfUbKJD32DrCpiafdHbRmRhIOFVOSXZsO5RhwvFLkdsiWHds9puK/yCUo3f6/2mrDOj2mqP2dKZlT0qwSzSy78klOM1OKAklJzmTzvmdCP2/dIJNoR09tDOed+hN/H3zhyxOUQldE8qqwTvZ3W0v49aPImH9myjjDqJHBbbhoRBCCNFSEkwQQpxqNWsL62UTNaKDO89GzdrCk16fzsRAwql0Jr8HtHew7mzJgG4vZ1L2pAS7RD016wrRl1eR1TuD9F39mDtpHiVJHj6dtqqjh3ZW0MOS0IfeQq8BKSyb62Pw9kG8cf1bjNw0jOyVE+je/zEcM9/r6GEKIYQQQgjRpjyF9jZtJ36+2jtYJxnQx3emZE9KsEscoes6+U9vwBDqYEBBPNWam7FrR9PnvzPOmH0ezgSu8fcSBewe8SLdFkZy/tKplIdWYMrojX39GrRxW/ElniaFzkIIIYQQQrSBlm7qfTKbfwvRVs7k7LdT4UzInpTQpDii4Ltd2DYUYe22DUdpLG7NS4QrnmGdJ3T00M4+Xhe3XxNBaWgV4VVh5MWWUhNcTdZPkzAueAz05uughRBCCCGEONPUbf5Nc8kfCm2y+bcQQoAEu0Qt3e3j0FOryYvLY4vLRGVIJRaXmZF/uqyjh3Z2ctlI2fcqSn8vRpeJtYNXsWb8PKoOpVK91omWtaKjRyiEEEIIIUSbqdv823+j4Z3+f9pq828hhJCVRABQ+kkGQbkGTOMWMnv0UnR0ajp5iZvWvaOHdnayRGC74Uu6PvNrvk+K5fZPbqFAUyDMyL6VUzAu/Sfovo4epRBCCCGEEG2mbvNvY4K13teNCVZS/jPhZ7/5txCi7cieXQJ3lZ2C5zcTnJLPeykHOfeHSwivDify/v4o6um1ydzZRA9LonMY9J8ynJLD87hwybm4HXaojKL4J42I4d/h6TOjo4cphBBCCCFEm5HNv4UQp4KsKILlT3+It9hJbtJuZr56LwaPgepoH0m/GNjRQzv72cu5XbuWCIeZ8OowFoxdTFZSNntXjcew4O/grO7oEQohhBBCCNGm6jb/jrikCyGjEyTQJYRoc7Kq/My5821EzzJQ2nsb2/tvYuWQdbw9fQ0DvrpM3nROBUsE3jG3kdRnEzo6k1eOZ+nopRgrI9i7Ng3Typc7eoRCCCGEEEIIIcQZRaIZP3P5TyxH8/mYPHIZBzzBjNw0lFv1uwhODe/oof1suIffTtwlbhTVi8FrYMJP0wAoWj0e3+pZqEW7O3iEQgghhBBCCCHEmUOCXT9jaz7/H+XfFRDUYxerFl9Ap13pmF1mZkyZ2NFD+3lRNbjmrySM3Irm00jNj2Vvn0qMLhMH1o7GMPcx2axeCCGEEEIIIYRoIQl2/UwdOuTD9bdiqoMrKMlNprI6hDEbRuIdEoF1QExHD+9nRw+OJebZWzAEV1EdXEVClsL6AZso3zgCz+5DeNZ91tFDFEIIIYQQQgghzggS7PqZcs3eSkRBDBaTG6MtGI/mweQJov9z53b00H62lC4D6fpuT0Ku+AiLw4wpNAhQWfr95ehLn6E6J6ujhyiEEEIIIYQQQpz2JNj1M+Pz+tjx+d3UvLEVxeJEK4th1ZDVJBV2wjw4jqCuYR09xJ+1oJHnETHmPrZe/Dk/DP6e6jSIKInhlcxkyt67n7ISd0cPUQghhBBCCCGEOK1JsOtnRNd1Vr34XzZ+6kCv0NHtQXw95Ttqgm1Ux+p0f/e8jh6iAJImXsigH6/lym9m8p9xH3I44RBj5k1nm7qLlX97leISvaOHKIQQQgghhBBCnLYk2PUzou1bxMiczxm0ZhwKCivPncuGARvZPDWT4cuuxRBu6ughCkC1Gun8+Bi6Z6dx++zpaB4DRpcRdfY19On0Mu88vJjCQgl4CSGEEEIIIYQQTZFg189F/k5yP/sLu2dfA4Br8g+U4uOhF+/n0eInMARLoOt0En11NyyXdCOiKpwlo5ZTFVpFUkES320Zhdb3Dp687yAVFRLwEkIIIYQQQgghGpJg189AxqYCDv/vDt452Andp7F08ve8m5DPBYum4U0MoutVozp6iKIBRVHo+o9R+NIjuXTeJbx+9f/I7pTNhIXn0TmzO88N+g1hxvKOHqYQQgghhBBCCHHakWDXWc6+JQ/9l18QfTiUCxdNI6v7brakZHLzZ7/AkRjO0B+vwdQpuKOHKZqgmjX6fHguhRf1IKw6gpTcFBxBTnrOvoaF5VWUz/4lu3YVkZUlGV5CCCGEEEIIIUQdCXadxXxeH8G7XkANKmX38kvwAQuGrOFXH96O5lPp8e+hGEKkfPF0Zoy3ctGLEwhLvo/FI5dhcVrABREfX8d9h/by2qJzeeopJz6fBLyEEEIIIYQQQgiQYNdZyba5mKy7lvGvvxxkQfG3fNZ3B1qxlc8v+IYuh7pgM2mU97QR0Tuho4cqWuiZX09h0IFzcBlcqKiYXWZufO8OhpaYeGPyH1F1d0cPUQghhBBCCCGEOC1IsOssU/LBXvZf/gO2jUV47eFEHBjMBQvOY0+33WzptYMvXHdQ8OfrmDj3LjTZlP6MoWoqw2ddis2s4jK4MHgNhNlC6f3e7SzZsJv5n1/OC29vp6REMryEEEIIIYQQQvy8GTp6AKJt6B4feU+so+TdPYSOCSHo2izGrfon6tzB+BRIzk3h/pceYtO49Vx+/bCOHq4IgKVbBMPnXsWqiz4hslJH82mYMBE060YWl/xAUb9beeBPi/jnC8GEhSkdPVwhft68LtSyTHwx6QC4P7mafdZg9nY/h1zbATIPLMGjmjF4wrH6QukU1YVbJz6EZpa3ZSGEEEIIIU6WfKo+C/jsHrLuWEL10lzKp/QlJ/5L3i14l2vW/4LupbEois43ycF0Cv4JZbIZVZWEvjOVOSWUUYuuZ96MtzF5qoitjMDgNHPugosIP7AXz4hf8eiDL/DUP6KxWiXgJcQp53FSvvoltux8nym+MFy3L+aNjc8wy7YUa7GFvvMLqE62Y4jMolNOEtPevfHIt+7kIxSLgY2/ykCdFMrV8Xdi21SMZVAMxkQriiKvaSGEEEIIIVpCgl1nOG+Nm6xbF1GzppDOz41hi6crOUtXc9HWK+ixty8ezcM7vVLZddmvSItJ5aWLv+7oIYuTZIm1Mm3hHdz+yn3YDO9yyzdX0DuhL6Wru+Mtiidm+jX86bnr+df9NxMUJBfHQrSnwurDbMhdyp7izVwaOoA+a99jpe0ATwbX0GXkg6SoGsMrxtB3YWdCVxtQ3ND5nqFE3pQGe9dS7tuKsWI3VJfjcZhxKZ2pNu0gpKILVTuyOfzgOgC0GDPWgTFYBsUQfWM6hkhzxz5wIYQQQgghTmMS7DqDeatcZN60ENumYmIe6cn+kt/z2e6xpETN5cIfbsVhtqM6LYSmvEt4sJWnz/8fFmNwRw9btIEgq4l3/vgv7n49lOjcTlTv97B41CbO2diXGR/fiG3QRt58fBe/eqI3BoMEvIQIhK7r2O1gMkFZGZSUgKe8CFveD6yv+ILN3t0cUCoBCNVVzrFZ8LgjSFDH8cfq7uxdGYf+ynwM3xUQGmLFe0Eyvkt0tvfez9q1/6XKWYHhXANVzgq25K9A0yECjWSXl3HbNqGdPx3bW9HMmf0mvXO7kL5/EEHLc4mflItp23aKV0XiqgklZHwyQROGoBiDOnjGhBBCCCGEOD1IsOsMVvzfXdi3lOC9owuOort5w6HTW/+Jqz65iZqEUv6RPBVt+K/wJpXy3LTPiA3u1NFDFm1I01Re/fUT/K3kZcZ8Ws6kNYPwGDxsS99B/81DOC97Lu861nD90zdiMWsdPVwhTns1NTrz5uuEhUN+vsKixTp79kKQ6mB66hz6pb3PyrhNrDD6Tz+dvGswNx0cQlyVgtmlUOWyskTxEuUMop+1miLLj2yyWfFMPMiyEcuwFccSNSeKjTmbAUjLTSVZ6YrFrdDP0Rc8oHh18Gqs9BrYsO2/BJu64Ryl863nS5xVczCFh3DZnq5cmbsP26LzKNo1AN7NQAlbj61fLpXnq7iGpWDCwJSEc9Bj0kHKH4UQQgghxM+MBLvOYHF396fUtI8s520s2DKYuxafj4IOuor30XScBVdiNhn410Vf0CWyd0cPV7QDRVF44OHf8VK32US9t5KBu/rTN6M3X1wwm+kLpzH0C52vcp7kov/8hbBoebkL0ZCu61RXg90O73+oM/tIpbdOj1Qb/77kAwa6PubVsIMs2tGfK//3KOOCfERUWzDiP/3UUfsfihcr4NY18kMtVAU5iHYG8dzYdwjSPEzaNoQBO/vj6b2dKbYoDHMvJyE78bjjy4krYHGvLTgsTh5477fElsTwwRUf80a/fJITI/mtGkxO58XYD4bQa3VPDldu4339USJ8ClNLk3jRsoby6BtAPcSUmGEMm/gMRoNkgAkhhBBCiLObXP2eYTwlDg4/uJqIewfwzZeP8qO2iGs/v4Hz85JBc6ObNLLvNPFCwW30iB7AI5PfJDE0taOHLdrZ7667jO+7JDHnrecZtnEoO3rs4tJ501EVlX5rupI99R0SXphOzLjjX1gL8XOh6zpLl+m8/6G/TPHeP8K3c2DEMJ1LB5WSvmMuBT9loy7tRFb3yxlRamF8sRkfPsJ0N9URpawbvpaCkGKum3MNeEHzauiaB7xgqQrDYLdg72rh1z99znx9DxvCiynpE8OEjXfRP2oDGed8zwanicvtcWSVJbPaXI5PD6KXO5bEuGye3Ppn7j6wkju+uofKS59n27iFxGT0Ji8un5CaYO5ZnITbUEZVd420X2zCcnAv55p7cqVpJMUHoljz8RTKQ3YTdlUGa6IOscy2l9D3vuTcyJncMPgKwlOHgiofA4QQQgghxNlH0XVdb8sOy8rKWtw2MjKyVe1/zurmyrajhD1XzWXTRR+yJDKX3/33bowe/8WKGqnwfKdLGHm9Db3769w69EFMhp/HJsY1NTUkJycDkJOTQ3Dwz3NvsgMFh/nD53dQY9lAz4zu3Pnh7SgouA1uDB6NnKFupr59A8ZIs7z+WkjmqWXOlHlyu328/4HO57MVonwH+EX3DzmUcgvBxQZiNywnNjcftSISALvJgdllQkHFC2wetpuDqRvpXBJFsNvEVxOXYTdauPONa/GpOovGLiWrcyaPPv8Qa/vuxqaH0W1fH5IdVQRSSFwdasNoNWOPS2VVVTBTRrxPdf8LKUyLYfuO74hdlUWfLYOILo+iKriK6hA70WWRZH/qI7EkAfWlUixbFQwWG7bhVvamL2d77HzWBDm42W6lT/XtDLn/QQB8Ph1VPb3KHc+U51RLREZGtqp9oI/7bJqztiTz0pjMSWMyJ02TeWlM5qQxmZOmybw0FuictPazFEhm1xnDVWzjs6+crNp3HQfuzCD1cBpl0cXs65JB74yeVEfZ+fH3K3j+shsJD48AHu/oIYsO0DU+ic9/NZtHPn2CCnUp9iA7ZqcZ1afiU3SSN5jYOex9gmfGMuTFX3T0cIVoe7qOWpKBengD1RVZlNYUEDvpMWzOUN58fBO3Rd5PxvY/U1U1kS7RNaTuLyPq20VY3Cpe1YvTaCYIHyoqXqOPA0PX4C3tQ/qecIau78XQ9b0AqAippGbcT6RVh/OvXj1w5U3mkvw+jHVk8/rka0lKUphqfYnglN34vk9i/9RhDNPew5EfRpFjNO5+8fStfhNbaTKOmp7E/99ArEsepHB7XzzOYKwxO1hSFkSXwgSidnu4wG2CzOGEzypENZehWPtQnlyGPiKGPTvNRJe5SCgIASDxOhtO037MdjNOk4Zut2BaBv2WjaOfYRwzg7x4reCKiGFz9nuUmDeiVsRRes6dXHFzDD6fjtuNnOYqhBBCCCHOWBLsOgOse2k57pcPkDFsLSl04tr1l2N2WshMOUBadlf2B8fhetbJpf1/TVhYR49WdDSjZuKZ6/7Kgh0L+HvC75mwfDTj14xFRUFBweNTsX9YyfIfXqHzH0YSeU0P1CDZwF6cuXy6j425y1i19U025i7j0Woz/bwGFhg9/DW4iic/T+OVBb9lSNcnebvCx4iSeZj7vkxUQRwl+/sR6t9vHs2nYXFa8Ck+XAYXH1z5Hnu6HKT7wa3s6JKAI9RFdEIIaQNG02/weL7Z4cWYs5aMR2ZiNkPStl1Yyndz1dX+jFrTSjO+ykpKZ06m75gEjHuHMen6v+HO+5KFn67EnDuJkmUanlUWrEPjsISOJ/mGFLzp08Dn5brlz4Guo7tzqdiRwYbMcpLyY4kpiieuPJLqrK6Y9lYR57WDwYMnxInXq2J1mgm2B6Ojcyglm70pB+ixrztmVxCFPXeRag/BvLc/JlsRygGFOO9QAKLnfcfu10x4Bybz3uZELL3CSZ4YzcABCn1SXVhCNVSzfGwQQgghhBCnPyljPE1VlPvIK6lixXP/Y8jcYDyaB0VXMLmN7O26j055nQi2W8k+L5Hxz51HeNTPO1ghZYxNq3ZV8o8FD7Nnx0KmL5lKT7eKrzwKa35nXAYnJk8QjhAXSVcFE3f3JRhirR095NOOrFMt0xHzZHfXMH/7W3yx50PKiouIckUxtCqaMVVD2J4xg6K8cvqHrCG4MIG1cSrxyiF6ZHXG4rIA4FE8ZHfOoTCqmKHbB5GTeJhPr/gYa0glnVBI8ml09qp0CoohdcCNRI64G+UkTjY8dp3Kzs4mJCSkdR3oOtjLUCsPo1QeRq0uBFc1irMaT001bpsNj92Jo8ZJUZbOB/Zc1vTaSioqt7x7O9bcFD6+7SVKPCbufvdX6Ojomg+PqqP6wOBtHMjKM4Wzw9KJWE8V6a5C1v9pJoMHK3QrysFsgrCpKQHPx4mcTa89KWPsWDIvjcmcNCZz0jSZl8ZkThqTOWmazEtjUsZ4FnDsq+DAVT/S+Z9j2GJKomR7JdFzt1IwoR+22Aj0SidafgUlYZHYfAbiYuHWK4s5vHwh87e8z55KN2MXT2REbjIe1YPZZcZucpDdOYueB9LxdDHT7bkJDBwe39EPVZzGQkxhPH7hi2wbspqXuz3Ku2VbUHSF236cTp8147CHl2FHp+QdE8XvzELr6yPlgamEnNMJRVM7evhC4K104TpUjWp0YzXsxXtgH/tfKGNL34W832MTMTnJ/PGd36Dq9Z+vQ9iHDx8KXVFQmFIJOt392Y2aB6/JCUYd7yOH6W2rIGTL25wbWsK1Cig14fgi0/B2GY+360S8nYeD2rZ/UAgoaKYoYI3CZ42ChP54G9yt1f4XBIQDD3ldzN/3OR9teoW/3vBfBu4fgWo6j25lJnZPWkGnTb1wKRBTFg3A1j5bWDdkHeduGU783v5UqCFERO7n3LwyFF3FhYr1xWV8YU1iTNU+UlOA2M6sXAkD8zKI6h9O5/PjiYiQ8kchhBBCCNGxJNjVTrRgAxEXp2JMDGbV03lEr99Hgu0w+Qd8FKnRJLgqOad6Hx+MjiY1ZhmJS7xseawvGwdsJC37PIaUR6HoCt9P/BGrw0x6XiqJWWl0qUgn/rFBRN/YE8UgwQjRMv0TRvH6ZXNZdvAb3lz/FB+NX8Q5VhfnrB9OVFUYXsULCjj3eMm8YRFaqJeQ8alEXteLkNEJ8lwT7cq+oxRXTjXuQ9W4DtX4/80qx32oEm+NP3AS1X035vhcfvKqxO0dhqd6IBfvSuNA5ywOpBwkriiWYHswmu4PSun4k5b3D1+FknyI9CXn4S2NpNtjEJZSiGNdDvZRf2boxF9j3DYLNS4fX2QqjohUfDHpYDrzs0ONmokLe17HtPRrWJ0zn1nbXmV7wbuo8Rp944bT/3ddGFQ+mU1fv47bU8bKgavIMej03TGANKeKBRvYY7AF2TC7zJT03Er/Q5UMLcrGB+RnB5H7mx/IMKcwJHMni4NT+fS1OIyaj98m7qTTJcmYe4Th9UHXLgqRkRIEE0IIIYQQp4aUMZ6E3MpMVuXMw+lx4PLaqXFVYXNXcfOQ+4kN7sS8jFl8tOVF+i3qwYT5YzC6jWi+o9kB/5v5Dtt7ZDBj3nTOWTcG8F+gKSiowVWU9M4mrKA3Wo6KISKIqJt6EvPL3mgRQR31kE9bUsbYcrqus61gNctzvmXe9s9I2d2JoVuHEFMezcfTP+NPb96DT9Ex1pY0OU0OLANjiLuwF5k9cihLKGNq+jWAf68kVTm7A2Fn+jp1qhw7T06nfmRz88pKHVeZixCnHXN6BAB5T65H9/jo9PgIAHYM+QRfsQsA1egBoxOPDorbSEGPXRQGOYnPTSa+MNFfele7Tir4f4ZX8eE2eDC7TThMCvYoD8HxIYT7LKS9fx6GKDOecif4dLTIoJMqRTwZp8M6lVW+l8UHZrP+0BKKbHl8es1mysp1nlt7I+W2PG533MZ/N6ynNO5HYopjiC2OJa4kFtWr8slln4EOTz/7OBan5UhAUUHBZbKhdd1LWloej+75C7ce3EjhgHKqU6vYl9ePHvt9LIzrTXFsV3omuLhtcjmdpyeRnaNjt0PXLjq64gJFwaQF4fI6cRtsBOutT1k/HUkZY8eSeWlM5qQxmZOmybw0JnPSmMxJ02ReGjuVZYwS7GoFXdepcpVTN2VrDy3kb8t+C4CqaCRWdyK1IJkRlok4nIfIcB6g1F0FOii6AihoHo0dvXag6Ao996UzbPtgsiYuxeiBcxZeiFnrDu4g9ENVAFiHxhJ1fTqp1w+k0lndUQ/9tHc6XESeaSIjIykqKWRL3iq2Hl7Gpv3fkl9Qxoj1o5iw+hzMLnOT32cLsoHJgCfexN7YLeTH5uNLNROWnEh0Qic6dUqmc3QXEkJTCDGd+ScmnGnr1KlQtwYqisLeDJ2ly3TuuSuc0t2Hmf16DnuWH2L6wAr0TBu+AzqWGg09WMf6UirzftxEymo7RqeKO7QGHbBWhGCpCiXU0fweVl68qKiUhtZwuHM25SHljN4wlrX9e1M84xBdOtuZbp1AyLBYtGDjKZqJ1jnd1imPz41B9c/V1vxVOD0OhneehMuls61oOW6vg6ztZazK+pjsoI1M9lrI99XgzUkmdXd/uh3sTnRpzJHA+LG8ipea4GqqwipQ3UbCK8PZPH4BCbH5xCy6HrXCwoqRi3BrblyaF4elBo/mYXD4lYxMmoCvRzlP7fstfxsxD4vBR0j3MNQgDU+ZA/fhGnxuH+au4WjhJkpsBYSawjEZml6zTgcS7OpYMi+NyZw0JnPSNJmXxmROGpM5aZrMS2MS7DqBwkKdJUtB08BgBKPB/6/JCCaT/7+goPr/mkwQVPevLQfjwaXomgFUA6hG0IzoqtHfkWbi69yF7KrM4N6BD6IeWMHHBz4k6blLCS0Lx6v58GoevKoPr+bFq3lwGd2Y3CaiKk78S9jRo4RwaxVd8o24q9NQLRq+YgcAilHFOiSWsPOTCZuajCkl9KTm6ufidLuIPBM09Zzy+byU5q4hd/c3FG3NwLs+FE9WFxLykjB6TEfa1WXWNMeHD6/qxWVy4TV4MKDhDXZRHF2AGuyjq6kLxWoXCmyFhIUexmiJpjChC0qEwpikPWguAzl2B25NJzhGQTdCuUkn2GIhNiQcn2LmQGUxBrMBi8WAZjDh8xmJsEQQGRyDjkKZsxxNM6IqBgyaCU01Yg2KwGIKRtd9uDwOVNWAQTGgqQZUVcOgGhtlqp3Ma0/Xa/OQdB8+3YdR88+h02PH7XXh9Xnw6j48PjeaohFpiUVHp7DmEHZXDV6vD13XUXUFs2YmxpyMikJu2QE8HheqV0H3AR4dkxKEhWA8Lhc1zlJ0jxuDz4pZN+Hy1FDtqCTakoBm1iguz6EqKx9vqAfMOt5KJ4ZsF6pPxed0U1VpR/XYsdrD0G1Q7qrEooMWq1DqcFDmrqDToRQKoovQPBoh1aGk5XSp95zwKb66JwsqzWf/2U0OcpJycBpd9MnoRUFsASuHrcETUs7Mz28kr+8eDg49hNplIiPX9adycBopM3RMFgfxIclobbyXVns6k9epI1mcjkrmbf43+SXbuUZJYFvRTj4pyyE0uxNJxbHEHUolMbsLik9F1VU0r3bctaKlPrnpbbJSMumzfigX/3AJAAWXrWJtZCTZXZYyLqE3wZ4Q5u/uQb8hGn1DqjnXZcDbZQKKxwU1hWC04IvtjR6ehFJdiFJdiC+h30mPrSUk2NWxZF4akzlpTOakaTIvjcmcNCZz0jSZl8Zkg/oTWLMWXnol8BjdbT3mcHfvl47bxhlkp9zgIXTHegDUIDv7zllAenEcilcjVwfdp5HsNmH0aji9Gj6HGbe1BtUdhM9rQPOZ0PVIVI+O4nZD7fH2ffdHo4UmoISZCB4UiikllKDu4VgHx2DpFyVHu4sOo6oaMZ3HENN5DJwH+Lz4ynMp2n2AWFsmhRv2k7+zEs1ayH6XhqMwnKQD6Xg0LzazDU3XSCrohIqK6lMxOo7JsKmG0IIodHS8KERSgH/J6gRALLkAlOPP7rFSP0sjprZkqgo7Kk4Sqevbi44Np9GJy11BAVlHvsfd4PGV0XygzmVwYTomoNcaOjpezdvkaXYt/X4FhcO1t5sanx3/+JtjA8qb+HrVMf9fyKEj/++f3boglLX2v6O3jhXC0YMwIo75emKuP3DjUT1H5q9u7KquoqPjCXKwcOwSMDqZuGQadoPK2sE/URBbQL9dg8jrVM7+kZkkhnbBmK1QzGCG97+c6Rd1RX9WJeyQwvg4sFoVuOU4EyDa1ZEgsDmMqaP+fOTrQ2v/w+c9cjKk4qoCZzWK10lpVQE71u4mqyyXQ558vIUKnfZ2RnVrROsWFI+Cw+ujILwMX5ADzWEmpiwGr+bFY/D8f3v3Hhdllf8B/MNdBS8IXtbLmlozyHAVLxDgDVMyWdGsvG5m663cXUlbrXW3UjIz8LeF1eIltJ9mGVialpdVyVt4SUUFQxFExJIE5CLCDPD9/cGPZx1nUCBAmPm8Xy9eOuec5zzn+c6ZmYcvZ54HBQ75yOyShaQOmSiyKkGpKhk32uWi3LIcmV2ycNv+NlAOpGZdrhyQI5CSDhy0sseTOTawOBatdxwlw99CmcezsCjIgvWVI9A2UrKLiIiIiBpXs8yqhIy2wPAgQFcGlOn++69WB2i1lT+lpff8e3d56Sys0k2ElZTBEpU/VqKDFXSwghZWokVLaDFYtNjZRgc7ay0es9LC8nFrWNrawtLWFp0c7GDn2B4tnZ3h0KEt7Fo8eHWBVAhEWwELO8uHds0YolqxtIJl++7o9Hh3AIPReTjQGUB5uaDLLSA3F7iZCxTlFqKk+BLKCq/CIq89kF0Gq3bnkV96AYW5ZWib4YRS+yKUtM2H/Z12sM7uip/bZcGhELAos0TbwnbI6nYNTrntYV/QBs45HaG10aLCWgfLcivY32mF4taFuGNbAssKK7QudEahfQFa3rGB1kYHO60tMnpcgVOOE1rddkDLkpbQ2WhRYSGwLreCdbkV8tvnQmdZjpalLWBXYo/CVoVoeacldNZlsBQLXO2eDufcDmh3qz2syqyhtdUCECWBdcsxFwJB69sOgFij1OYObEtboMxah9IWpchvewtt89vC8VZ7AIDOujLVZquzgc5Wh8LWBbCssIBDcWtorSoqU34VlWuesp2zYS2WaFlsD8e89sov+hCBnbYF7rTJR4FDESzLLeGY74zClsWw1VpBZ125ojS5z3k45zqjdUFbON5yRIldCcqsy2BVboUWpXb4uccVFNvdQbuC9mh7qyNyHXJhq7VChaXApswWiZ6n0LqkBbqnP4Y2RW1Q0DoPpTalaKGzhY2lFdIGnEFOq3y4nxkGyxIX5LXKQ7F9Mhws7JDt4I0bXtZo4fADeqS3QguH1ihztoadkxP6dBuNlvYO6F/WD85t7eHyOzUsLCzgUzYJLazvTakZsrAEej7SEBOb6p2lFdCiLaRFW9z9p6i2AB53Ax6/z6alZXdQpC1AuxbOAICC0jyUlN2GXUtr5FxPga74Jkrv5MCiJB9WNvZA2+6wsrCCbfoh2FpawQaWsIEFrK1awqqHP6y69YOdtgQlmceAlu0gVnaAlS1g3QIVrSsTtxWd3aHt0KfBwkFERERED1ezTHYBQMuWFmhZ560toL8+oXFYWFrAogZJMaKmzsrKAk5OgJMT8BgAoA3uWuPx/4IadUx+DdRvc1h+HPgbt3/QMzWsBn04Ok6rNk6P6c0L1CjRRebDzrol7Kz/+4nu2NIZgDMcHR3R3rpr9Rs+GlJ9nY0Dyl2eqr7e8v8vY0BEREREJsm0b6NGRERERERERERmhckuIiIiIiIiIiIyGUx2ERERERERERGRyWCyi4iIiIiIiIiITIaFiMiDmxERERERERERETV9XNlFREREREREREQmg8kuIiIiIiIiIiIyGUx2ERERERERERGRyWCyi4iIiIiIiIiITAaTXUREREREREREZDIaNNn18ccfY8KECfD09ES/fv1qtI2IICoqCgEBAfDw8MDUqVNx6dIlvTZarRZLly7FwIED4eXlhdmzZ+OXX35piENoFPn5+Xj11Vfh4+MDHx8fvPrqqygoKLjvNmq12ujP2rVrlTZTp041qA8LC2vow2kwdYnTokWLDGLw7LPP6rUxtfkE1D5WOp0O7733HkJCQuDl5YWAgAD87W9/w40bN/TaNfc5tWnTJgwbNgzu7u4YN24cTp48ed/2x48fx7hx4+Du7o6goCBs3rzZoM3u3bsxatQouLm5YdSoUdi7d29DDb9R1SZWe/bswQsvvABfX1/07dsXzz33HA4dOqTXZuvWrUbfs0pLSxv6UBpUbeJ07NgxozG4fPmyXjvOKePv3Wq1Gk899ZTSxlTnVF3V9v2tOTlx4gRmz56NgIAAqNVq/Oc//9Grr69zx7qcZzwM0dHRePrpp+Ht7Q0/Pz+89NJLSEtL02tjbjEBgM8++wwhISHo27ev8ln0/fffK/XmGJN7RUdHQ61W4+2331bKzC0uUVFRBp8b/v7+Sr25xeNuN27cwIIFCzBw4EB4enpizJgxOH/+vFJvbrEZNmyY0fOMt956C4D5xQMAysrK8D//8z8YNmwYPDw8EBQUhFWrVqGiokJp06TiIg3o/fffl5iYGHnnnXfEx8enRttER0eLt7e37N69W1JSUmTevHni7+8vhYWFSpt//vOfEhgYKEeOHJGkpCSZOnWq/OEPf5CysrKGOpQG9eKLL8ro0aPl1KlTcurUKRk9erTMmjXrvttkZ2fr/cTGxoparZarV68qbaZMmSKLFy/Wa1dQUNDQh9Ng6hKnhQsXyosvvqgXg7y8PL02pjafRGofq4KCApk2bZrs3LlTLl++LKdPn5ZnnnlGxo4dq9euOc+pnTt3ikajkS1btkhqaqqEh4eLl5eXZGVlGW1/9epV8fT0lPDwcElNTZUtW7aIRqORXbt2KW1OnTolffr0kX//+9+Smpoq//73v8XV1VXOnDnTWIfVIGobq/DwcFm9erUkJiZKenq6REZGikajkaSkJKVNXFyc9O3b1+C9qzmrbZwSEhJEpVJJWlqaXgzufq/hnKpUUFCgF6Off/5ZBgwYIB988IHSxhTnVF3VNr7NTXx8vKxcuVJ2794tKpVK9u7dq1dfX+eOdTnPeBimT58ucXFxcvHiRblw4YLMnDlThgwZIrdv31bamFtMRET27dsn8fHxkpaWJmlpabJy5UrRaDRy8eJFETHPmNwtMTFRhg4dKiEhIRIeHq6Um1tcPvjgA3nqqaf0PjdycnKUenOLR5Vbt27J0KFDZdGiRZKYmCiZmZly9OhRycjIUNqYW2xycnL05smRI0dEpVJJQkKCiJhfPEREPvroIxkwYIAcOHBAMjMz5bvvvhMvLy9Zv3690qYpxaVBk11V4uLiapTsqqioEH9/f4mOjlbKSktLxcfHRzZv3iwilSfAGo1Gdu7cqbT55ZdfxMXFRQ4ePFj/g29gqampolKp9H6ROX36tKhUKrl8+XKN+5kzZ4788Y9/1CubMmWK3odZc1bXOC1cuFDmzJlTbb2pzSeR+ptTiYmJolKp9H5Zas5zavz48fLPf/5Tryw4OFgiIiKMtl+xYoUEBwfrlf3jH/+QZ599Vnn817/+VV588UW9NtOnT5ewsLB6GvXDUdtYGTNq1CiJiopSHtf0c6A5qW2cqpJd+fn51fbJOWXc3r17Ra1Wy7Vr15QyU5xTdVUfr9nm4t5kV32dO9bXZ+fDkJOTIyqVSo4fPy4ijMnd+vfvL1u2bDH7mBQVFcmIESPkyJEjeudy5hiXDz74QP7whz8YrTPHeFR57733ZOLEidXWm3NsqoSHh8vw4cOloqLCbOMxc+ZMee211/TK5s6dKwsWLBCRpjdPmtQ1u65du4Zff/0VAQEBSpmtrS369++P06dPAwDOnz8PnU6nt9y0U6dOeOyxx5Q2zcnp06fRunVreHp6KmVeXl5o3bp1jY/n5s2b+P777zF+/HiDum+++QYDBw7EU089hXfffRdFRUX1NvbG9FvidPz4cfj5+WHkyJFYvHgxcnJylDpTm09A/cwpACgqKoKFhQXatGmjV94c55RWq0VSUpLeewsA+Pv7VxuTM2fO6M0LAAgMDFTmTFWbe/sMDAxstnMHqFus7lVRUYHbt2+jXbt2euXFxcUYOnQoBg0ahFmzZiE5Obm+ht3ofkucQkNDERAQgOeffx4JCQl6dZxTxsXGxuLxxx9H165d9cpNaU7VVX3Etzmrr3PH+vrsfBgKCwsBAG3btgXAmABAeXk5du7cieLiYnh7e5t9TJYsWYLBgwfj8ccf1ys317hkZGQgICAAw4YNQ1hYGDIzMwGYbzwAYP/+/XBzc8Nf/vIX+Pn5ITQ0FFu2bFHqzTk2QOVn7fbt2/H000/DwsLCbOPh4+ODhIQEpKenAwB++ukn/Pjjjxg8eDCApjdPrOt+qPXv119/BQA4OTnplTs7O+P69esAKhM7NjY2ygf63W1u3rzZOAOtRzdv3jQ4XqAyBjU9nq+++gr29vYYMWKEXnlISAi6desGZ2dnXLp0CZGRkfjpp58QExNTL2NvTHWN06BBgxAcHIwuXbrg2rVreP/99/H8889j69atsLW1Nbn5BNTPnCotLUVERARGjx4NBwcHpby5zqm8vDyUl5cbfW+pet+5182bN+Hs7KxX5uTkhLKyMuTl5aFjx45GY+3k5FRtn81BXWJ1r08++QR37tzBk08+qZT16tUL77zzDtRqNYqKivDpp59i4sSJ2LZtGx555JH6PIRGUZc4dejQAUuXLoVGo4FWq8W2bdswbdo0/O///i/69+8PwPjr19znVHZ2Ng4ePIiIiAi9clObU3VVH6/Z5qy+zh3r47PzYRARvPPOO/Dx8YFKpQJg3jFJSUnBhAkTUFpailatWuHDDz/Eo48+ilOnTgEwz5js3LkTycnJiI2NNagzx7ni4eGBd999F4888ghycnKUa0zv2LHDLONRJTMzE5s3b8YLL7yA2bNn4+zZswgPD4etrS1CQ0PNOjYA8J///AeFhYUYO3YsAPN87QDAjBkzUFhYiCeffBJWVlYoLy9HWFgYRo8eDaDpxaXWya6oqCisWrXqvm1iY2Ph7u5e264VFhYWeo9F5IHb1KRNY6ppnKojIgZxqE5cXBxCQkJgZ2enV373hdhVKhV69OiBp59+GklJSdBoNDXqu6E1dJxGjRql/F+lUsHNzQ3Dhg1DfHy8QXLw3n6bmsaaUzqdDmFhYRARvPnmm3p1zWFO3Y+x95b7xaS696K7y2vbZ3NR1+PasWMHVq1ahY8++kjvQ8rLywteXl7K4759+2Ls2LHYuHEjFi9eXG/jbmy1iVOvXr3Qq1cv5bG3tzd++eUXrFu3Tkl21bbP5qSux/XVV1+hdevWGD58uF65qc6pujLVeVNTDXXu2NTjuGTJEly8eBGfffaZQZ05xqRnz574+uuvUVBQgD179mDhwoXYuHGjUm9uMfn555/x9ttv45NPPjH4PeFu5hSXqhUoVby8vPDEE0/g66+/VlaRmFM8qogI3Nzc8MorrwAAXF1dkZqais2bNyM0NFRpZ46xASp/3x40aBA6deqkV25u8fj222+xfft2REZG4tFHH8WFCxfwzjvvoGPHjkoiEGg6cal1smvy5Ml6CQRjunXrVttuAVT+1RuozOR17NhRKc/JyVFWWDg7O0On0yE/P18vG5iTkwNvb+867bch1DROKSkpel+rq5Kbm2s0m3mvkydPIj09Hf/6178e2Faj0cDGxgYZGRlNJjHRWHGq0rFjR3Tp0gVXrlwB0HzmE9A4sdLpdJg3bx6uXbuGDRs26K3qMqYpziljHB0dYWVlZfCXgLvfW+5lbFVEbm4urK2tla/nGVsBmJubW22fzUFdYlXl22+/xd///ne8//77Bl+VuJelpSXc3d2V12Jz81vidDdPT09s375decw5pU9EEBcXhzFjxsDW1va+bZv7nKqr+pqLzVV9nTs6OzvXy3lGY1q6dCn279+PjRs3onPnzkq5OcfE1tYWPXr0AAC4u7vj3Llz+PTTTzFjxgwA5heTpKQk5OTkYNy4cUpZeXk5Tpw4gU2bNmHXrl0AzC8ud2vVqhVUKhWuXLmi/FHFHOPRoUMH9O7dW6+sV69e2L17t1IPmGdssrKycPToUURFRSll5hqPFStWYObMmcrdsdVqNa5fv47o6GiMHTu2ycWl1tfsat++PXr37n3fn/v95eB+unXrhg4dOuDIkSNKmVarxYkTJ5QDd3Nzg42NjV6b7OxsXLp0qUklJ2oaJ29vbxQWFuLs2bPKtomJiSgsLKzR8cTGxkKj0cDFxeWBbS9dugSdTqdMwqagseJUJS8vDz///LPy4msu8wlo+FhVJboyMjKwfv16ODo6PnBMTXFOGWNrawuNRqP3PAPA0aNHq42Jl5cXjh49qld2+PBhZc5Utbm3z8OHDze5uVMbdYkVULmia9GiRYiMjMSQIUMeuB8RwYULF5r83KlOXeN0r3tjwDml7/jx48jIyDB6Tcp7Nfc5VVf1NRebq/o6d6yv84zGICJYsmQJ9uzZgw0bNqB79+569eYYk+qICLRardnGxNfXF9988w2+/vpr5cfNzQ0hISH4+uuv0b17d7OMy920Wi0uX76MDh06mO08ASpXR1ddh6nKlStXlGtlmnNstm7dCicnJ73zW3ONR0lJicHKKisrK2VVVpOLS40vZV8HWVlZkpycLFFRUeLl5SXJycmSnJwsRUVFSpuRI0fKnj17lMfR0dHi4+Mje/bskZSUFHnllVeM3qpy0KBBcvToUUlKSpI//vGPBreqbE5efPFFCQkJkdOnT8vp06eN3lbz3jiJiBQWFoqnp6d89tlnBn1mZGRIVFSUnD17VjIzMyU+Pl6Cg4MlNDTUbOJUVFQky5cvl1OnTklmZqYkJCTIc889J4GBgSY9n0RqHyudTiezZ8+WQYMGyYULF/Rus1taWioizX9O7dy5UzQajXz55ZeSmpoqb7/9tnh5eSl3d4uIiJBXX31VaX/16lXx9PSUZcuWSWpqqnz55Zei0Whk165dSpsff/xR+vTpI9HR0ZKamirR0dHi6uqqd+eQ5qi2sfrmm2/E1dVVNm7cqDd3CgoKlDZRUVFy8OBBuXr1qiQnJ8uiRYvE1dVVEhMTG/346ktt4xQTEyN79+6V9PR0uXjxokRERIhKpZLdu3crbTin9C1YsECeeeYZo32a4pyqqwfFt7krKipSziFVKpXExMRIcnKycrfg+jp3rMlnZ1PwxhtviI+Pjxw7dkzvPffOnTtKG3OLiYhIZGSknDhxQjIzM+Wnn36SlStXiouLixw+fFhEzDMmxtx7Z21zi8vy5cvl2LFjcvXqVTlz5ozMmjVLvL29lfdLc4tHlcTERHF1dZWPP/5Yrly5Itu3bxdPT0/Ztm2b0sYcY1NeXi5DhgyR9957z6DOHOOxcOFCCQwMlAMHDkhmZqbs2bNHBg4cKCtWrFDaNKW4NGiya+HChaJSqQx+EhISlDYqlUri4uKUxxUVFfLBBx+Iv7+/uLm5yeTJkyUlJUWv35KSElmyZIkMGDBAPDw8ZNasWXL9+vWGPJQGlZeXJ/Pnzxdvb2/x9vaW+fPnG9ya/t44iYh8/vnn4uHhofcLZZXr16/L5MmTZcCAAaLRaGT48OGydOlSycvLa8hDaVC1jdOdO3dk+vTp4uvrKxqNRoYMGSILFy40mCumNp9Eah+rzMxMo6/Vu1+vpjCnNm7cKEOHDhWNRiNjx45VbtMuUvl+NWXKFL32x44dk9DQUNFoNDJ06FCjieXvvvtORo4cKRqNRoKDg/USF81ZbWI1ZcoUo3Nn4cKFSpu3335bhgwZIhqNRnx9fWX69Oly6tSpRj2mhlCbOK1evVqGDx8u7u7u0r9/f5k4caLEx8cb9Mk5VamgoEA8PDzkiy++MNqfqc6purpffJu7hISE+77H1Ne5Y00+O5uC6j6vG+J8urnERETktddeU14Dvr6+8vzzzyuJLhHzjIkx9ya7zC0u8+bNE39/f9FoNBIQECBz586VS5cuKfXmFo+77d+/X0aPHi1ubm4SHBxs8PlrjrE5dOiQqFQqSUtLM6gzx3gUFhZKeHi4DBkyRNzd3SUoKEhWrlypLI4QaVpxsRBpglfiJiIiIiIiIiIiqoNaX7OLiIiIiIiIiIioqWKyi4iIiIiIiIiITAaTXUREREREREREZDKY7CIiIiIiIiIiIpPBZBcREREREREREZkMJruIiIiIiIiIiMhkMNlFREREREREREQmg8kuIiIiIiIiIiIyGUx2ERERERFRs6dWq/V+XFxc4OPjg2effRbr16+HTqd7aGPbunUr1Go1oqKi6q3PjIwMuLm5ITIy8jf3NXXqVKjValy7dk2vfNiwYVCr1b+5f2OuXbsGtVqNqVOnNkj/jb2fe+3duxdqtRrfffddo+6XiCpZP+wBEBERERER1ZexY8cCAMrLy5GVlYXTp08jMTER8fHxWLt2LaytTeNXoMjISNjY2OCFF1542EMhI4YPHw4XFxesXLkSQUFBsLW1fdhDIjIrpvFOT0REREREBGD58uV6jxMTEzF16lT88MMP2LlzJ8aMGfOQRlZ/kpKSsHv3bjz//PNo3779wx5Ok9apUyd8++23aNmyZaPu18LCAjNnzsQrr7yC2NhYTJo0qVH3T2Tu+DVGIiIiIiIyWZ6enspqr8OHDz/k0dSPzZs3AwBCQ0Mf7kCaARsbG/Tu3RtdunRp9H0HBQXB3t4en3/+eaPvm8jcMdlFREREREQm7bHHHgMA5Obm6pWLCHbs2IGwsDCMHDkSXl5e8Pb2xvjx47Fp0yZUVFQY9BUVFQW1Wo2tW7ciJSUFs2fPRv/+/eHl5YUpU6bg1KlTtRrbJ598AhcXF4waNQo3btx4YPvbt29j586d6N27N1xdXQ3qs7OzsWbNGkyZMgWBgYFwc3ODv78/5s6di7Nnz9ZqbHX1/fffY9asWfDz84ObmxuGDBmCl156CfHx8Ubbl5SUICIiAkOHDoWbmxueeOIJrF69GiJi0PbkyZNYsmQJQkJC0L9/f3h4eCA4OBgREREoKCgwaF/dNbvuvo7a9evXMX/+fPj6+sLDwwPjxo3D/v37jY41MTERL7/8sjJWf39/jB8/HpGRkbh9+7Ze2xYtWmD48OFISUlBYmJiDaNHRPWByS4iIiIiIjJpVUmIe7/yp9VqMX/+fBw5cgTt27fH0KFD4enpidTUVCxZsgSvv/56tX2eP38ezz33HNLT0+Hn54cePXrgxIkTmDZtGi5evFijca1cuRLvvvsu3NzcsGnTJnTq1OmB25w4cQLFxcUYMGCA0fp9+/YhIiIC2dnZUKlUCAoKQseOHbF3715MmjSpwVe3LV++HDNnzsShQ4fQs2dPjBgxAt26dcOxY8ewbt06g/Y6nQ7Tp0/Hli1b0KtXLwwcOBA3btxAZGQk/vWvfxm0X7FiBb788kvY2NjA19cXfn5+KCoqwpo1azBp0iSDhNODZGVlYfz48Th16hR8fHzg6uqKpKQkvPzyywaxio+Px4QJE3DgwAF07doVI0aMgIuLC/Ly8rB69Wrk5eUZ9F/1PFWX6COihsFrdhERERERkUk7dOgQACAwMFCv3MrKClFRURgyZIjeBcRzc3MxY8YMfPXVV3j66afRv39/gz43bdqEBQsWYMaMGUrZsmXLsGHDBqxduxYrVqyodjwVFRV488038cUXX8DX1xcfffQR7O3ta3QsJ0+eBAC4u7sbre/bty+2bdsGFxcXvfJDhw5hzpw5eOutt7Bnzx5YWFjUaH+1sW3bNsTExKBz586Ijo7WG0NxcbHR1U2nT59Gv379sGvXLiUZee7cOUyYMAEbNmzAzJkz9WLz8ssvw8vLC23btlXKtFotwsPD8cUXXyAmJgZz586t8Zi/+uorTJ06FYsWLVJuXrBhwwYsW7YMH3/8MQICApS269atg4jgyy+/hJubm14/Z8+eRbt27Qz69/DwAPDf542IGgdXdhERERERkcmpqKjA1atX8cYbb+DEiRMYNmwYRo0apdfG2toaI0aMMLhTXvv27TF//nwAlSuljPHx8dFLdAHAnDlzANw/saHVahEWFoYvvvgCTzzxBNasWVPjRBcApKSkAAB69uxptF6tVhskuoDKRF9wcDCuXr1a45VntRUdHQ0AeP311w3G0KpVK/j5+RlsY2lpifDwcL1Vd+7u7ggMDMSdO3dw/vx5vfaDBw/WS3QBgK2tLV5//XVYW1tX+/XD6nTv3h0LFy7Uu0vn5MmT0bZtWyQmJkKr1SrlOTk5aN26tUGiC6hMajk4OBiU9+rVC8B/nzciahxc2UVERERERCZDrVYblI0fPx5Lly6FpaXxv/VfuHABhw8fxvXr11FSUgIRUb4Od+XKFaPb+Pv7G5Q5OjqiXbt2yM7ONrpNcXExZs+ejSNHjmDcuHEIDw+HlZVVDY+sUk5ODgAYJHzuptVqcfDgQZw7dw65ubnQ6XQAoCS5MjIyjMbpt7hx4wYuX76Mdu3aYeTIkTXermvXrkYTdz179sSBAwfw66+/Gt3X/v37kZaWhqKiIuXaXjY2NtU+X9UZMGAAbGxs9Mqsra3RrVs3JCUl4datW+jYsSMAQKPRYPv27Xj99dcxbdo0qFSqB/ZvbW0Ne3t7FBQUoKysTC+pRkQNh680IiIiIiIyGVV3XiwtLcWFCxeQnp6O2NhYeHl54ZlnntFrq9Vq8dprr2HHjh3V9lfdNaA6d+5stNze3h63bt0yWvfpp5+irKwMgwcPxrJly+r0VcKioiJlP8akpKRgzpw5yMrKqraP2l7XqiZ++eUXAMDvf//7Wm1XXRxbtWoFAHorqwAgJiYGkZGRSgLvt7rf83jv/l955RVcvHgRcXFxiIuLg6OjI7y9vTF8+HCEhIQYrBCs4uDggNu3b6OoqMjoVx2JqP4x2UVERERERCZj+fLleo/XrFmDiIgIhIeH4/HHH0fXrl2VuvXr12PHjh1QqVR49dVXodFo0KZNG9jY2CA9PR3BwcHV7qcuiarAwECcPHkSR44cwe7du+/bf3WqvipXlfS6m4hg3rx5yMrKwoQJEzBx4kR069YN9vb2sLCwwMqVKxEdHW30Lof1pbZxqU37M2fOYPny5WjdujWWLl2KAQMGoEOHDkqSKSAgwOhKsPra/+9+9zvExcUhISEB8fHxOH78OA4cOID9+/dj7dq1+Pzzz42uuCssLISFhYXRrzkSUcPgNbuIiIiIiMhkzZgxAwEBASgpKcGqVav06vbu3QsAiIyMxKBBg+Dk5KR8pS0zM7Pex6LRaLBu3Tq0aNEC8+fPV/ZfG05OTgBgdPVYWloa0tLS4ObmhrfeegsuLi5wcHBQEjoNcUxVqlZIZWRkNNg+quI1b948jB07Fl27dlUSXSUlJbh582aD7buKtbU1AgICsHjxYmzfvh379++Hr68v0tLSsHr1aoP2Op0OxcXFaNOmDb/CSNSImOwiIiIiIiKTtmDBAlhYWGD79u16X+8rKCgAULli517fffddg4zF09MT69atg52dHcLCwqq9AH51qi78np6eblCXn58PwPhX8/Lz83H06NE6jLhmOnXqhN69e+PWrVvYs2dPg+yj6vkydny7du1q0BVr1enSpYtyowJjF/5PS0sDAKM3DSCihsNkFxERERERmbQ+ffogKCgIZWVlWLt2rVL+yCOPAAA2b96s137Xrl3Ytm1bg43Hy8sLa9euhY2NDf76178iPj6+xtv269cPAHD27FmDuh49esDS0hIJCQl6F2ovLS3FG2+8Ue21xOrLzJkzAQDLli3DpUuX9OqKi4vxww8//Kb+q56v2NhYvWt2paamIiIi4jf1XRPr1683unrs0KFDAIwnTauep6rnjYgaB9dREhERERGRyfvzn/+Mffv2IS4uDi+99BI6dOiAP/3pTzh06BAiIyOxa9cu9OzZE1euXMH58+cxffp0fPLJJw02nr59+2LNmjWYMWMG/vznP+PDDz/EoEGDHrhdv3790KpVKxw7dsygzsnJCePHj8eWLVswZswY+Pr6ws7ODj/++CPKy8sxbtw4bN26tSEOBwAQGhqKc+fOYePGjRgzZgy8vb3RuXNnZGdnIzk5Ga6urvDz86tz/+PGjUNMTAwOHDiA4OBguLu7Iz8/HydOnEBQUBDOnTt33wvz/1arVq3Cu+++CxcXF/To0QMigpSUFKSnp8PR0RF/+tOfDLY5fvw4AGDw4MENNi4iMsSVXUREREREZPJcXFzwxBNPoLS0FDExMQCA/v3747PPPoOvry+uXbuGAwcOwMbGBlFRUZg8eXKDj6lfv35YvXo1rK2tMXfuXBw5cuSB29jb22P06NHIyMgwurrrzTffxKJFi9CtWzf88MMP+PHHH+Hn54e4uDh06dKlIQ5Dzz/+8Q98+OGH8PPzw6VLl7B7925cu3YNfn5+RpNBteHo6IjY2FiMHj0aOp0O+/fvx40bN/CXv/wFK1eurKcjqN7ixYsxatQo3LlzBwcPHsShQ4dgZWWF6dOnY/v27QZ3oiwpKcG+ffugUqng6enZ4OMjov+ykIfxxWYiIiIiIiKqkwsXLiA0NBRTp07F4sWLH/ZwqBo7duzA/Pnz8cYbb2DSpEkPezhEZoUru4iIiIiIiJqRPn36IDg4GHFxccjNzX3YwyEjRARr1qzB73//e4wfP/5hD4fI7DDZRURERERE1MzMnz8fOp2uQa8rRnW3b98+/PTTTwgLC4Otre3DHg6R2eHXGImIiIiIiIiIyGRwZRcREREREREREZkMJruIiIiIiIiIiMhkMNlFREREREREREQmg8kuIiIiIiIiIiIyGUx2ERERERERERGRyWCyi4iIiIiIiIiITAaTXUREREREREREZDKY7CIiIiIiIiIiIpPBZBcREREREREREZmM/wNKU1mscKTa8wAAAABJRU5ErkJggg==\n", 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" ] @@ -200,9 +224,10 @@ } ], "source": [ - "ax = az.plot_trace(az_trace, compact=True, kind=\"rank_vlines\")\n", + "ax = az.plot_trace(idata_04, compact=True, kind=\"rank_vlines\")\n", "ax[0, 0].axvline(-0.5, 0, 0.9, color=\"k\")\n", - "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\");" + "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\")\n", + "f'Estimated w1 = {np.mean(idata_04.posterior[\"X\"] > 0).item():.3f}'" ] }, { @@ -211,29 +236,7 @@ "source": [ "From the KDE we can see that we recover the modes and even the relative weights seems pretty good. The rank plot on the right looks good too. One SMC chain is represented in blue and the other in orange. The vertical lines indicate deviation from the ideal expected value, which is represented with a black dashed line. If a vertical line is above the reference black dashed line we have more samples than expected, if the vertical line is below the sampler is getting less samples than expected. Deviations like the ones in the figure above are fine and not a reason for concern.\n", "\n", - "As previously said SMC internally computes an estimation of the ESS (from importance weights). Those ESS values are not useful for diagnostics as they are a fixed target value.\n", - "\n", - "We can compute ESS values from the trace returned by `sample_smc`, this is probably an overly optimistic value, as the computation of this ESS value takes autocorrelation into account and each SMC run/chain has low autocorrelation by construction." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "az.plot_ess(az_trace);" + "As previously said SMC internally computes an estimation of the ESS (from importance weights). Those ESS values are not useful for diagnostics as they are a fixed target value. We can compute the ESS values from the trace returned by `sample_smc`, but this is also not a very useful diagnostics, as the computation of this ESS value takes autocorrelation into account and each SMC run/chain has low autocorrelation by construction, for most problems the values of ESS will be either very close to the number of total samples (i.e. draws x chains). In general it will only be a low number if each SMC chain explores a different mode, in that case the value of ESS will be close to the number of modes. " ] }, { @@ -242,18 +245,18 @@ "source": [ "## Kill your darlings\n", "\n", - "SMC (with a Metropolis kernel) is not free of problems, as it relies on Metropolis it will deteriorate as the dimensionality of the problem increases and/or if the geometry of the posterior is _weird_ as in hierarchical models. To some extent increasing the number of draws and maybe the number of `n_steps` could help. To access the number of steps per stage you can check `trace.report.nsteps`. Ideally SMC will take a number of steps lower than `n_steps`.\n", + "SMC is not free of problems, sampling can deteriorate as the dimensionality of the problem increases, in particular for multimodal posterior or _weird_ geometries as in hierarchical models. To some extent increasing the number of draws could help. Increasing the value of the argument `p_acc_rate` is also a good idea. This parameter controls how the number of steps is computed at each stage. To access the number of steps per stage you can check `trace.report.nsteps`. Ideally SMC will take a number of steps lower than `n_steps`. But if the actual number of steps per stage is `n_steps`, for a few stages, this may be signaling that we should also increase `n_steps`. \n", "\n", - "Let's make SMC fails spectacularly. We will run the same model as before, but increasing the dimensionality from 4 to 40." + "Let's see the performace of SMC when we run the same model as before, but increasing the dimensionality from 4 to 80." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ - "n = 40\n", + "n = 80\n", "\n", "mu1 = np.ones(n) * (1.0 / 2)\n", "mu2 = -mu1\n", @@ -269,7 +272,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -277,32 +280,54 @@ "output_type": "stream", "text": [ "Initializing SMC sampler...\n", - "Multiprocess sampling (2 chains in 2 jobs)\n", - "Stage: 0 Beta: 0.002\n", - "Stage: 1 Beta: 0.004\n", - "Stage: 2 Beta: 0.006\n", - "Stage: 3 Beta: 0.009\n", - "Stage: 4 Beta: 0.012\n", - "Stage: 5 Beta: 0.017\n", - "Stage: 6 Beta: 0.021\n", - "Stage: 7 Beta: 0.027\n", - "Stage: 8 Beta: 0.034\n", - "Stage: 9 Beta: 0.042\n", - "Stage: 10 Beta: 0.052\n", - "Stage: 11 Beta: 0.064\n", - "Stage: 12 Beta: 0.078\n", - "Stage: 13 Beta: 0.097\n", - "Stage: 14 Beta: 0.122\n", - "Stage: 15 Beta: 0.152\n", - "Stage: 16 Beta: 0.191\n", - "Stage: 17 Beta: 0.240\n", - "Stage: 18 Beta: 0.301\n", - "Stage: 19 Beta: 0.373\n", - "Stage: 20 Beta: 0.462\n", - "Stage: 21 Beta: 0.566\n", - "Stage: 22 Beta: 0.693\n", - "Stage: 23 Beta: 0.854\n", - "Stage: 24 Beta: 1.000\n" + "Sampling 4 chains in 4 jobs\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "/u/32/martino5/unix/anaconda3/envs/pymcv3/lib/python3.9/site-packages/pymc3/sampling.py:1925: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.\n", + " warnings.warn(\n", + "Stage: 0 Beta: 0.001\n", + "Stage: 1 Beta: 0.003\n", + "Stage: 2 Beta: 0.004\n", + "Stage: 3 Beta: 0.006\n", + "Stage: 4 Beta: 0.007\n", + "Stage: 5 Beta: 0.009\n", + "Stage: 6 Beta: 0.011\n", + "Stage: 7 Beta: 0.013\n", + "Stage: 8 Beta: 0.016\n", + "Stage: 9 Beta: 0.019\n", + "Stage: 10 Beta: 0.022\n", + "Stage: 11 Beta: 0.026\n", + "Stage: 12 Beta: 0.030\n", + "Stage: 13 Beta: 0.035\n", + "Stage: 14 Beta: 0.041\n", + "Stage: 15 Beta: 0.047\n", + "Stage: 16 Beta: 0.054\n", + "Stage: 17 Beta: 0.063\n", + "Stage: 18 Beta: 0.073\n", + "Stage: 19 Beta: 0.084\n", + "Stage: 20 Beta: 0.096\n", + "Stage: 21 Beta: 0.110\n", + "Stage: 22 Beta: 0.127\n", + "Stage: 23 Beta: 0.145\n", + "Stage: 24 Beta: 0.168\n", + "Stage: 25 Beta: 0.192\n", + "Stage: 26 Beta: 0.221\n", + "Stage: 27 Beta: 0.255\n", + "Stage: 28 Beta: 0.291\n", + "Stage: 29 Beta: 0.331\n", + "Stage: 30 Beta: 0.378\n", + "Stage: 31 Beta: 0.433\n", + "Stage: 32 Beta: 0.498\n", + "Stage: 33 Beta: 0.571\n", + "Stage: 34 Beta: 0.653\n", + "Stage: 35 Beta: 0.746\n", + "Stage: 36 Beta: 0.852\n", + "Stage: 37 Beta: 0.977\n", + "Stage: 38 Beta: 1.000\n" ] } ], @@ -330,58 +355,37 @@ " testval=-1.0 * np.ones_like(mu1),\n", " )\n", " llk = pm.Potential(\"llk\", two_gaussians(X))\n", - " trace = pm.sample_smc(2000, parallel=True)\n", - " az_trace = az.from_pymc3(trace)" + " trace_80 = pm.sample_smc(2000, parallel=True)\n", + " idata_80 = az.from_pymc3(trace_80)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We see that SMC recognizes this is a harder problem and increases the number of stages. Unfortunately in this case that is not enough to recover the correct posterior as we can see in the following plot. \n", - "\n", - "Compare this rank plot with the one obtained in the previous example (n=4). The rank plot is telling us that the _blue chain_ is sampling an excess of low parameter values (ranks below 2000) and is failing to sample from high parameter values. The orange-chain is doing the exact opposite. So basically one SMC chain is exploring one mode and the other SMC chain the other, they are failing to mix and to recover the relative weights of each mode." + "We see that SMC recognizes this is a harder problem and increases the number of stages. We can see that SMC still sample from both modes but now the model with less weight is being subsampled (we get a relative weight way lower than 0.1). Notice how the rank plot looks worse than when n=4." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "
" + "'Estimated w1 = 0.008'" ] }, + "execution_count": 8, "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "az.plot_trace(az_trace, compact=True, kind=\"rank_vlines\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even when each SMC run has low autocorrelation by construction the ESS value computed by ArviZ may under some circumstances show problems. This example is such a case, here each SMC chain is basically exploring a single mode and missing the other. When this happens the value of ESS_bulk (computed using `az.summary` or `az.ess`) will be close to the number of modes, for this problem we got ~3. We are working on providing an ESS estimation better tailored to the peculiarities of SMC.\n", - "\n", - "As the ESS value may vary across the parameter space. We also recommend to check the behavior of localized version of ESS. We can do this with `plot_ess`. The recommended value for ESS is at least 400 (dashed gray line)." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ + "output_type": "execute_result" + }, { "data": { - "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -389,42 +393,50 @@ } ], "source": [ - "# only the first 6 dimensions\n", - "az.plot_ess(az_trace, coords={\"X_dim_0\": slice(0, 5)});" + "ax = az.plot_trace(idata_80, compact=True, kind=\"rank_vlines\")\n", + "ax[0, 0].axvline(-0.5, 0, 0.9, color=\"k\")\n", + "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\")\n", + "f'Estimated w1 = {np.mean(idata_80.posterior[\"X\"] > 0).item():.3f}'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "You may want to repeat the SMC sampling with the failing model as you may get different problems each time." + "You may want to repeat the SMC sampling for n=80, and change one or more of the default parameters too see if you can improve the sampling and how much time the sampler takes to compute the posterior." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "arviz 0.8.3\n", - "numpy 1.18.1\n", - "autopep8 1.5\n", - "json 2.0.9\n", - "pymc3 3.9.1\n", - "last updated: Mon Jun 29 2020 \n", + "Last updated: Sat Oct 23 2021\n", + "\n", + "Python implementation: CPython\n", + "Python version : 3.9.6\n", + "IPython version : 7.26.0\n", + "\n", + "xarray: 0.19.0\n", + "\n", + "numpy : 1.20.3\n", + "arviz : 0.11.3\n", + "matplotlib: 3.4.3\n", + "theano : 1.1.2\n", + "pymc3 : 3.11.4\n", "\n", - "CPython 3.7.6\n", - "IPython 7.12.0\n", - "watermark 2.0.2\n" + "Watermark: 2.2.0\n", + "\n" ] } ], "source": [ "%load_ext watermark\n", - "%watermark -n -u -v -iv -w" + "%watermark -n -u -v -iv -w -p xarray" ] } ], @@ -444,7 +456,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.5" + "version": "3.9.6" } }, "nbformat": 4,