{ "cells": [ { "cell_type": "markdown", "id": "9a42c11d", "metadata": {}, "source": [ "## Hamiltonian Monte Carlo\n", "\n", "
\n", "\n", "The MCMC samplers that we have discussed so far can be thought of as a guided random walk towards regions of high posterior density. This random walk behaviour is inherently **inefficient**. Model reparametrisation and other tricks can help to improve the situation, but the inefficiency remains, **especially in high-dimensional problems**.\n", "\n", "
\n", "\n", "**Hamiltonian Monte Carlo (HMC)** is a dramatically more efficient way to draw samples from the target posterior distribution, thanks to its departure from the random walk approach. Instead, HMC uses concepts from Hamiltonian mechanics to direct the Markov transitions and avoid diffusive behaviour.\n", "\n", "
\n", "\n", "An excellent introduction to HMC that is suitable for researchers in the physical sciences can be found in [this paper](https://arxiv.org/pdf/1701.02434.pdf) by Michael Betancourt. Here, I will try to summarise the main concepts, borrowing notation, figures and explanations from this work.\n" ] }, { "cell_type": "markdown", "id": "7c6bd06e", "metadata": {}, "source": [ "### Computing expectations with MCMC\n", "\n", "
\n", "\n", "The goal in the implementation of any MCMC algorithm is the computation of expectation values. Consider a target sample space $Q$, of which any point $q \\in Q$ can be parametrised by real numbers, in $D$ dimensions. In this parameter space, let our target distribution be a smooth density function, $\\pi(q)$. \n", "\n", "
\n", "\n", "Computing expectation values over this distribution is done by integrating over the parameter space\n", "\n", "
\n", "\n", "$$\n", "\\mathbb{E}_\\pi[f] = \\int_Q \\mathrm{d}q~\\pi(q)f(q).\n", "$$\n", "\n", "
\n", "\n", "In practice, we approximate these integrals through the Markov chains returned by our samplers.\n", "\n", "
\n", "\n", "Given that we want to compute expectations, an obvious way for our sampler to be inefficient is to **waste time evaluating $\\pi(q)$ in regions of parameter space that have negligible contribution to the expectation.**\n", "\n", "
\n", "\n", "So we should just focus on regions with large density, $\\pi(q)$, right? *Not exactly*. The expectation is an *integral* of this density of the *volume*, $\\mathrm{d}q$. While the density will be largest at the mode, there is relatively little volume here, especially in high dimensions. Recall the curse of dimensionality as illustrated in the figure below. The relative weight of a partition containing a point of interest decreases from $1/3$ to $1/9$ and $1/27$ as we scale from 1 to 3 dimensions.\n", "\n", "
\n", "\n", "\"The\n", "\n", "
\n", "\n", "Actually, volume will be largest in the tails of the distribution, away from the mode. If we have $\\pi(q)$ largest at the mode, and $\\mathrm{d}q$ largest in the tails, the region of interest is somewhere between the two. Let's refer to this region as the **typical set**.\n", "\n", "
\n", "\n", "\"The\n", "\n", "
\n", "\n", "So we have understood that we want to focus all our computational resources on exploring this typical set. As we discussed above, standard MCMC algorithms, such as the Metropolis-Hastings algorithm, will eventually explore the typical set, as long as the Markov transition *preserves* the target distribution. \n", "\n", "
\n", "\n", "Given sufficient time, samples from the Markov chain can be used to approximate our desired expectations:\n", "\n", "
\n", "\n", "$$\n", "\\hat{f}_N = \\frac{1}{N} \\sum_{n=0}^N f(q_n),\n", "$$\n", "and\n", "$$\n", "\\lim_{N\\to\\infty} \\hat{f}_N = \\mathbb{E}_\\pi[f].\n", "$$" ] }, { "cell_type": "markdown", "id": "74d00fd6", "metadata": {}, "source": [ "### The basics of HMC\n", "\n", "
\n", "\n", "So how can we explore the typical set more efficiently than with just randomly walking? We can exploit information about the *geometry* of the typical set, and use this to move through it. Imagine that we knew the *vector field* of the typical set, we could just follow it, like a ball rolling along a slope.\n", "\n", "
\n", "\n", "Great! But how can we find this vector field using only information about our target density? The *gradient* of the density will give us a vector field that points towards the mode, but we want to move around the mode in the typical set. We can imagine this as a physical system, like a satellite (our trajectory) in orbit around the Earth (the mode):\n", "\n", "
\n", "\n", "\"Exploring\n", "\n", "
\n", "\n", "We too can avoid \"crashing into the mode\" by giving our \"satellite\" enough momentum. But we don't want to add too much or too little momentum either. Let's start by expanding our parameter space by introducing auxiliary momentum parameters, $p$\n", "\n", "
\n", "\n", "$$\n", "q \\rightarrow (q, p).\n", "$$\n", "\n", "
\n", "\n", "In doing this, our target distribution is now a joint probability distrbution over $p$ and $q$. We can express this as\n", "\n", "
\n", "\n", "$$\n", "\\pi(q, p) = \\pi(p|q)\\pi(q).\n", "$$\n", "\n", "
\n", "\n", "This choice ensure that if we marginalise out the momentum, we immediately recover what we started with. Any trajectory in this new joint space can therefore be projected down into our original parameter space.\n", "\n", "
\n", "\n", "Continuing the analogy with classical mechanics, we can now use Hamiltonian dynamics to construct trajectories in the joint space. The Hamiltonian energy of the system\n", "\n", "
\n", "\n", "$$\n", "H(q, p) \\equiv -\\log\\pi(q, p),\n", "$$\n", "\n", "
\n", "\n", "is composed of two terms\n", "\n", "
\n", "\n", "$$\n", "H(q, p) = - \\log\\pi(p|q) - \\log\\pi(q) \\equiv K(p, q) + V(q),\n", "$$\n", "\n", "
\n", "\n", "with $K(p, q)$ and $V(q)$ the kinetic and potential energies, respectively. The potential energy is set by the target distribution, whereas the kinetic energy is to be determined.\n", "\n", "The Hamiltonian contains the geometry of the typical set, and so we can use it to find a vector field aligned with the typical set via **Hamilton's equations**,\n", "\n", "
\n", "\n", "$$\n", "\\frac{\\mathrm{d}q}{\\mathrm{d}t} = \\frac{\\partial H}{\\partial p} = \\frac{\\partial K}{\\partial p}\n", "$$\n", "\n", "$$\n", "\\frac{\\mathrm{d}p}{\\mathrm{d}t} = - \\frac{\\partial H}{\\partial q} = - \\frac{\\partial K}{\\partial q} - \\frac{\\partial V}{\\partial q}.\n", "$$\n", "\n", "
\n", "\n", "Here we recognise $\\partial V / \\partial q$ as simply the gradient of our target distribution, satisfying our above physical intuition.\n", "\n", "> Evolving Hamilton's equations for some time generates trajectories in the joint space that efficiently move around the typical set. Projecting these trajectories back into our parameter space via marginalisation gives what we set out to find!\n", "\n", "The Hamiltonian Markov transition\n", "* Lift a point into the joint space from the parameter space by sampling from the conditional distribution\n", "$$\n", "p \\sim \\pi(p | q).\n", "$$\n", "* Integrate Hamilton's equations for some time, $t$, to move around the typical set\n", "$$\n", "(q, p) \\rightarrow \\phi_t(q, p).\n", "$$\n", "* Project back down into parameter space via marginalisation\n", "$$\n", "(q, p) \\rightarrow q.\n", "$$" ] }, { "cell_type": "markdown", "id": "cb541cbb", "metadata": {}, "source": [ "### Tuning\n", "\n", "
\n", "\n", "In our above explanation, we left two quantities to be determined:\n", "* The **kinetic energy** $\\sim \\pi(p|q)$.\n", "* The **integration time**, $t$.\n", "\n", "These degrees of freedom need to be tuned to suit our particular problem. \n", "\n", "
\n", "\n", "Optimising the kinetic energy\n", "\n", "Each time we sample a new momentum, we enter a different *energy level* of the system. For efficient exploration, we want to explore different energy levels in a uniform way, and for our momentum sampling to imply energy sampling that is close to that of the marginal energy distribution of the system. I.e.\n", "\n", "
\n", "\n", "$$\n", "\\pi(p|q) \\Rightarrow \\pi(E|q),\n", "$$\n", "and we want \n", "$$\n", "\\pi(E|q) \\sim \\pi(E).\n", "$$\n", "\n", "
\n", "\n", "As there are an infinite number of possible kinietic energies, it makes sense to restrict our search. A standard choice are *Euclidean-Gaussian* kinetic energies, such that\n", "\n", "
\n", "\n", "$$\n", "\\pi(p|q) = \\mathcal{N}(p | 0, M),\n", "$$\n", "\n", "
\n", "\n", "where $M$ is typically referred to as the *mass matrix*. Because of the dual behaviour between the momentum and parameters, it turns out we can define an optimal choice for $M$ by setting its inverse equal to the *target covariances*. In practice, this is estimated during the warmup phase of an HMC algorithm implementation.\n", "\n", "
\n", "\n", "Optimising the integration time\n", "\n", "If we integrate for short times, we won't explore so far away, but if we integrate for too long, we will end up revisiting regions that have already been explored. The optimal choice will depend on the kinetic energy and where in the joint space the transition occurs. \n", "\n", "A practical solution to this is the [*No-U-Turn*](https://jmlr.org/papers/volume15/hoffman14a/hoffman14a.pdf) trajectory termination criterion that allows the intergation time to be chosen dynamically. Samplers implementing this criterion are often reffered to as No-U-Turn samplers, or NUTS. " ] }, { "cell_type": "markdown", "id": "e251b4ca", "metadata": {}, "source": [ "### Implementation\n", "\n", "
\n", "\n", "In practice, we have to solve Hamilton's equations *numerically*. This leads to inaccuracies that add with integration time and scale with the number of dimensions. The geometry of the problem motivates the choice of **Symplectic integrators** for which the errors at least oscillate around the true values. Another aspect of their performance is that in regions of extreme curvature, the numerical trajectories diverge to infinity.\n", "\n", "
\n", "\n", "\"Divergent\n", "\n", "
\n", "\n", "While this may seem like a bad thing, the existence and location of **divergent transitions** is actually a very helpful diagnostic when implementing HMC in practice.\n", "\n", "We can also correct for the error induced by integration by defining a **reversible transition** (positive and negative momentum) and introducing an **accept/reject Metropolis step**, as the acceptance probability can be calculated exactly from the Hamiltonian.\n", "\n", "As we integrate numerically, the integration time becomes defined by a **step size** and **number of steps**. The step size can be optimised during the warmup phase, by defining a target metropolis acceptance rate (typically around 0.8). The number of steps, or trajectory length, is optimised dynamically during sampling via the No-U-Turn criterion mentioned above.\n", "\n", "
\n", "\n", "Stan\n", "\n", "[Stan](https://mc-stan.org) is a software platform with a robust implementation of an adaptive HMC algorithm, including NUTS. Given a model specification and data, Stan will automatically optimise the *mass matrix* and *step size*, letting you focus on your model and inferences.\n", "\n", "We will work more with Stan in the second block of the course as a tool for implementing a Bayesian workflow." ] }, { "cell_type": "markdown", "id": "5635be79", "metadata": {}, "source": [ "### Diagnostics\n", "\n", "
\n", "\n", "Like any MCMC algorithm, the **effective sample size** and **Gelman-Rubin statistic** can be used to judge the within-chain correlation and convergence of chains. The implementation of HMC also permits two new diagnostic tools:\n", "\n", "* **Divergent transitions:** As mentioned above, in regions of high curvature the results of numerical integration will diverge. We can use divergent transitions to notify us of the presence and also location of regions of high curvature.\n", "\n", "* **E-BFMI:** The energy Bayesian fraction of missing information quantifies the mismatch between $\\pi(E|q)$ and $\\pi(E)$, allowing us to diagnose poorly-chosen kinetic energies. If the E-BFMI is below around 0.3, it seems that the warmup is unable to find a decent mass matrix for the presented problem.\n", "\n", "
\n", "\n", "If these kind of divergences are encountered, it is likely that some form of model reparametrisation can help out." ] }, { "cell_type": "markdown", "id": "387c3f69", "metadata": {}, "source": [ "### Visualisation\n", "\n", "
\n", "\n", "A nice visualisation of HMC and other algorithms can be found [here](https://chi-feng.github.io/mcmc-demo/app.html), by Chi Feng. " ] }, { "cell_type": "markdown", "id": "2300118b", "metadata": {}, "source": [ "### Demonstration\n", "\n", "
\n", "\n", "We can demonstrate the power of these diagnostics with using Stan and the classic *Eight schools problem*. See Section 5.5. of [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book/) by Gelman et al. for more information.\n", "\n", "In summary, the goal is to understand the impact of extra coaching programs on student grades, conducted in parallel in $J=8$ different schools. For each school, we have an estimated impact $y_j$, and a standard error of this estimate, $\\sigma_j$. \n", "\n", "Let's say we want to consider the data from all schools in our final conclusion. We think the schools and coaching programs are similar, but admit they are not identical. To capture this, we use a **hierarchical normal model**.\n", "\n", ">We will discuss hierarchical models more in block II of this course.\n", "\n", "We introduce parameters $\\mu$ and $\\tau$ to describe the average impact and variance across all schools. Each school has a true impact $\\theta_j$, and an observed impact $y_j$, as introduced above.\n", "\n", "
\n", "\n", "\"The\n", "\n", "
\n", "\n", "The initial model is given in `stan/schools.stan`, and the data are introduced below." ] }, { "cell_type": "code", "execution_count": 1, "id": "6711dcef", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:52.880203Z", "start_time": "2021-09-02T17:59:52.016556Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import arviz as av\n", "from cmdstanpy import CmdStanModel" ] }, { "cell_type": "code", "execution_count": 2, "id": "aaba1b74", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:53.008162Z", "start_time": "2021-09-02T17:59:52.881660Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data {\r\n", " int J;\r\n", " real y[J];\r\n", " real sigma[J];\r\n", "}\r\n", "\r\n", "parameters {\r\n", " real mu;\r\n", " real tau;\r\n", " real theta[J];\r\n", "}\r\n", "\r\n", "model {\r\n", " mu ~ normal(0, 5);\r\n", " tau ~ cauchy(0, 5);\r\n", "\r\n", " theta ~ normal(mu, tau);\r\n", " y ~ normal(theta, sigma);\r\n", "}\r\n" ] } ], "source": [ "!cat stan/schools.stan" ] }, { "cell_type": "code", "execution_count": 3, "id": "ad608c80", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:53.017382Z", "start_time": "2021-09-02T17:59:53.010604Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:cmdstanpy:found newer exe file, not recompiling\n", "INFO:cmdstanpy:compiled model file: /Users/fran/projects/bayesian_workflow_prep/stan/schools\n" ] } ], "source": [ "model = CmdStanModel(stan_file=\"stan/schools.stan\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "6bd696c9", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:53.044039Z", "start_time": "2021-09-02T17:59:53.040678Z" } }, "outputs": [], "source": [ "data = {}\n", "data[\"J\"]= 8\n", "data[\"y\"] = [28, 8, -3, 7, -1, 1, 18, 12] \n", "data[\"sigma\"] = [15, 10, 16, 11, 9, 11, 10, 18]" ] }, { "cell_type": "code", "execution_count": 5, "id": "961b40b5", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:53.558417Z", "start_time": "2021-09-02T17:59:53.366538Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:cmdstanpy:start chain 1\n", "INFO:cmdstanpy:start chain 2\n", "INFO:cmdstanpy:start chain 3\n", "INFO:cmdstanpy:start chain 4\n", "INFO:cmdstanpy:finish chain 1\n", "INFO:cmdstanpy:finish chain 3\n", "INFO:cmdstanpy:finish chain 2\n", "INFO:cmdstanpy:finish chain 4\n" ] } ], "source": [ "fit = model.sample(data=data, iter_sampling=1000, chains=4, seed=42)" ] }, { "cell_type": "code", "execution_count": 6, "id": "a1789226", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:53.906996Z", "start_time": "2021-09-02T17:59:53.728004Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:cmdstanpy:Processing csv files: /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools-202109021959-1-a16ki1ig.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools-202109021959-2-1s8521o3.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools-202109021959-3-4mkm3lm7.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools-202109021959-4-sm8ngg5r.csv\n", "\n", "Checking sampler transitions treedepth.\n", "Treedepth satisfactory for all transitions.\n", "\n", "Checking sampler transitions for divergences.\n", "84 of 4000 (2.1%) transitions ended with a divergence.\n", "These divergent transitions indicate that HMC is not fully able to explore the posterior distribution.\n", "Try increasing adapt delta closer to 1.\n", "If this doesn't remove all divergences, try to reparameterize the model.\n", "\n", "Checking E-BFMI - sampler transitions HMC potential energy.\n", "The E-BFMI, 0.25, is below the nominal threshold of 0.3 which suggests that HMC may have trouble exploring the target distribution.\n", "If possible, try to reparameterize the model.\n", "\n", "Effective sample size satisfactory.\n", "\n", "Split R-hat values satisfactory all parameters.\n", "\n", "Processing complete.\n" ] }, { "data": { "text/html": [ "
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MeanMCSEStdDev5%50%95%N_EffN_Eff/sR_hat
name
lp__-15.00.456.0-25.00-15.0-5.2180.0820.01.0
mu4.40.113.1-0.734.49.6790.03600.01.0
tau3.80.173.00.843.09.9310.01400.01.0
theta[1]6.10.165.3-1.405.516.01089.04995.01.0
theta[2]4.90.124.6-2.304.813.01475.06764.01.0
theta[3]4.00.134.9-4.004.312.01483.06801.01.0
theta[4]4.80.134.7-2.804.912.01433.06572.01.0
theta[5]3.50.144.5-4.303.910.01036.04753.01.0
theta[6]4.00.124.7-3.504.311.01559.07153.01.0
theta[7]6.40.175.1-0.985.816.0904.04149.01.0
theta[8]4.80.135.2-3.604.813.01577.07232.01.0
\n", "
" ], "text/plain": [ " Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat\n", "name \n", "lp__ -15.0 0.45 6.0 -25.00 -15.0 -5.2 180.0 820.0 1.0\n", "mu 4.4 0.11 3.1 -0.73 4.4 9.6 790.0 3600.0 1.0\n", "tau 3.8 0.17 3.0 0.84 3.0 9.9 310.0 1400.0 1.0\n", "theta[1] 6.1 0.16 5.3 -1.40 5.5 16.0 1089.0 4995.0 1.0\n", "theta[2] 4.9 0.12 4.6 -2.30 4.8 13.0 1475.0 6764.0 1.0\n", "theta[3] 4.0 0.13 4.9 -4.00 4.3 12.0 1483.0 6801.0 1.0\n", "theta[4] 4.8 0.13 4.7 -2.80 4.9 12.0 1433.0 6572.0 1.0\n", "theta[5] 3.5 0.14 4.5 -4.30 3.9 10.0 1036.0 4753.0 1.0\n", "theta[6] 4.0 0.12 4.7 -3.50 4.3 11.0 1559.0 7153.0 1.0\n", "theta[7] 6.4 0.17 5.1 -0.98 5.8 16.0 904.0 4149.0 1.0\n", "theta[8] 4.8 0.13 5.2 -3.60 4.8 13.0 1577.0 7232.0 1.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit.diagnose()\n", "fit.summary()" ] }, { "cell_type": "markdown", "id": "a2b283bc", "metadata": {}, "source": [ "\n", "Note the presence of divergent transitions and low E-BFMI. Let's visualise the location of the divergent transitions." ] }, { "cell_type": "code", "execution_count": 7, "id": "9b21d404", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:54.730884Z", "start_time": "2021-09-02T17:59:54.413691Z" } }, "outputs": [ { "data": { "image/png": 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jSClfM/15SAhRA61k+J9AC5qc7rMBwAZA63M01H1ItUiDq0xYA5SIRPY7UgCR7Ws9sjXIdRJPMJCqz+9w9FeK5XmO1qCXiIgom6WqIMMd0NYKfQhgGYAdAPIBfB1AM7T0t6STUrYIIZoBXJWK7Q+3aIOrbA0KEtnvaAFENq/1iCdIyKSZCPu+xBsMpOLzW9PYhbXb6xBQtfMePn/yg81Yn6f5MzvgV7Gltjnt7xkRERFFlqqZo/UA/hnAfwfgB/ATKWWtEGIWgH8H8HEqHlQIMRHADMRYKjzTxTKjkK1BQbz7na2zZLGINUjIpJkIp31JZAYs1s9BpKDQfN3+hk6ocnBCWFFE0j8rsT7PJeUl8CoCvqDWCPfNmmasXFSald9XIiKi0SJVwdECAD8GoEKrWjcWAKSUjUKIdQB+BvfS3AYhxDgAc0N/KgDKhBDXAjgf+rcOwBZowdBsAP8TQBuAt5L1RNJpJAcE8crWWbJI7AP+aM8plkF5vDNLyawamKrPa6Sg0H7d2rsqkOtV4AuoUITA+nsrk/5ZifV5Lp5VjAerZmLjgSZIAMFgdqdMEhERjQapCo4uA1CklFIIcRbAlQD2hK67AKA0xu1UAdhl+vtnoX//CuA/AVgI4E8BTIAWIO0C8G0pZe9Qn0AmGIkBwVAMdZYsVSlpiWw3kVmgaIPyeLeZ7KqBqfq8RgoK7dd19flS/p2J53muWFSKLbXNPMFBRESUJVIVHH0OYB6AD6CtO/ofQogz0Bq0rgdwKJaNSCk/BiAi3OSPh7abmS9b0+YyjdMMg73iXTK2G2uAYR7U+/wqnt15DE/dfvWQ1ujEm9a2tbYZA34VEvEXgnDbl2R/Xmsau9DS3Q+vIhBUZViA4RakRQsKhxo8xfo8eYKDiIgou6QqOHoWwJzQ//8IwDvQ1hoBWkGG+1P0uESOLMFIQMXa7XVQpRzy2p1EK83pg3qfX4UK4HcnOnDw1PmYihi4XW/ephACxQW5rtupaezCG9WnjU7NHk/8sxqpDtzNgadHEaicUYRV15UNqShJtvYGIyIiouGhpGi7VQit+5FSngGwGNpM0rXQqtf9SYoel8iRHjh4BKAIbRbCHNAkY7vxpE3pg/qvXzURikBS9mXxrGKsvasCiiKgSon179ajprHL8bb7GzqNim4CwAOLU18ooKaxC8/tOuG6T3aWwDMo8YfmHsfntHhWMZ5cPjfhqoepfA5ERESUXVI1c/RTaA1aWwBASikBHAcAIcTi0PXrU/TYRGHMMwzFBblY/259TDMs8Ww33rSpxbOK8dTtV+PgqfNJW5PS1eeDKmVMldTM6WgrF8W6DDAxQ1ljpaf+6el/W2ubE05TG0rRiEyqFkhERESpkargSABGxo5dKQCedqVhZ09v0lPr1r9bj3lTC1O+/sTtvslckxJPJbXhXAuTaJnvVx9dgq21zXij+jSCqoTHo+CN6tMIqImlREZ73pHWI42kZr1ERETkLGnBkRDizwD8WehPCeD/FUJcsN1sDLQKc+8n63GJEhHrDMtwSOaalHiCnuFcC5PojI2+jxXTi7Cj7izG5Hjw4ZHWIb1vbs/baWYIgPFasrQ+ERHRyJfMmaM+AHoCvwDQA60XkZkPwA4Av0zi49IIkYpS2/o2iwtyLdXpYhnoxro/qSoRnqhMLAAwlJmqmsYuLQ0yoMLrUVwr1w2VfWZoS20zttY2WyocrlhUCgGtRHemvcZEREQ0dEkLjqSUbwB4AwCEEP8fgPVSypPJ2j6NbKlYz2Hepiq1iD0vZ3Db0dKrYtmfkbYOJZWBXqJBmzloCQZVPHR9GaZPyE/6PtoDZgG4VjhckeI1WkRERJQeKVlzJKX881Rsd6TLtBmI4ZTIeo5or5d5mwDC+vnYB+vm7cW6P+lYh5LKZraZGOjZg5ZIszZDeW3sATMAo4GrCFU4TKQnFBEREWWPVBVkoDhl6sB0uMS7niOW18vo+xMKXhS4l9t2ahIby/4M9zqUaM873uAgkYBwKPueaFW/WFLykvEdsgfM9gqH6VxvNJpPnhAREQ0XBkcpkMggZrRXwop3TUosr5e9fLd5zVG07XX1+WLan0yq+hZvcJBoQJiIaMUOYqlcl4zPRLzMjztvamHagpPRfvKEiIhouDA4SkCk4CfRQQwrYcW3JmVJeQm8Hu318ngil6xO9PWP9b6JrqVJJIiO9LzjDQ7cAsKttc2udfgTZX+srbXN2GIqdpCMwX6qv0PpLHSRKSdPOHtFREQjHYOjOEULfhIdxAz3DMSIIKX1v0Mw3K//kGYCXJ53pODAaVBbXJALRWgtycy314OWrbXNSZuhMKc4CiHQ1jtgfE8G/FpluGTM8qT7O5Sq4CETTp5w9oqIiEYDBkdxihb8DGUQk4klmDPV/oZOBEIL5IOqTHoKVaolGkRHet5uwYFbStv6d+sRVCUUAdx01aQh7Vc0i2cVY+1dFVi7vQ5BVeKTY+1QBKBKrVDGmzXNWJmE8tjp/A6lMnjIhMAvU2aviIiIUonBUZyiBT+ZMIiJVTanyER7HzLtudn3J9EgOpbPn/35Og1qAa08tQQQlMAHh1ux+3h7TOuOEn1t9ca7ElpJ7soZRfhDc4/xt9tgeyhFJobzvY8neEhkH2MJ/FL53DNh9oqIiCjVGBzFKZbgJxtmgLI9RSbS+5Bpz81tfxIJohO5n9ugNterYMCvBUh6iepohSiG8traU+uWlpfgaGtvxDRAvUpcokUmhvO9j7Wx8JbaZrxZ04xAMLn7mOrnnk0nfoiIiBLF4CgB2RD8mDmdTR5KikymzMq4vQ9uzy2Z+x1tW9FKZOv7mWg/nmSUwn710SXGQD0YjK0QRbTPTbTX5aarJuHDI60IqhIv7zuFtXdVhFURNA/ylTj7C6Uz9Sta8KA/Lz0gBZK7j8Px3LPt2EdERBQvBkcjnNvZ5ERTZGI9O52uAKqmsQtnuvvh9SjGgL+4IBdPv3UIb1SfRkCVQz6rXtPYhdUv7jdeu02PhfcailQiu7ggd9hnN5wGtfplKxeVWhqfPrfrhOv75va5iTYj4hYYdPX58OTyuZbHsDbvlcbaJEArIhHpszVcqV9u+xBLYKk/fwH3vluJYNobERHR0DE4GuHczibbz3IDkQfF0bZnlq7UJvPjehWBh64vQ8X0Iqx/tz6hs/VuA+CtoWpuAIyqbpEqFtpT1TJtYbv+eYjlfXOaHYllRiSWwMCcSqcP8j2KQFACUkoEJbB2+yEoiuKakjYcqV/JKNfvUQQerJqJFUkoQqFj2hsREdHQMTga4SKdTY5nUBzL9nSpHPxHmjUwP25QlZg+IR9dfb6EztZHek3shcPtf8fSMylZZ/iTOUNnfv0G/CrWv1OPtXdXuM442e9nfh2EECguyDX+tgQGHgUPLC61VKdzmm3r6vOhpbsfGw80GdsJqIBQ1YhpdqlO/Urk862/T05phMnEtDciIqKhYXA0wsVyNjmewV60Qgj2M//JTO+JFsRFKjzgNii377v+nMyviS+g4tmdx/DU7VcbaWivH2xCQAW8CrByUWnMr1Es1yfr9Yh1G/p+LCkvsZTX/ry5B6s37MOmx5dGrLp2prsfHkVADQ6GRwFVYv279Zg3tdBxptL+uXl257Gw2bYnl89FTWMX3qgZnKnzKoCiKJY1UsMt3vS1ZM2kZspaPyIiopGMwdEwSPegJtrZ5HgHe07bczvzn8znHC2Ii1R4IFrxBPvg1VxZTZXA3uMdOHjqvNEjSFEUCFWFoigxv0bxXB8L++uxpbY5YtAararf2rsqICFgngvzB917SJnvLwDbPcPfo0ifGz0lTxHWmb3Fs4qx7u4KbD7YhMnjx+D7N19pPPfhatZrf6x4g9tkzKRmWgVGIiKikYrBUYplw6AmGTMZTuts7AvtgaEFirEEceY1Lvrf0QKRLbXNxuBcH7w+uXwuXn10CZ7deQx7j3dYrgOAQFC19OfRH1PfJ6f/T/b7bl/D4lQMwb4Oy7zOxf6e7ag7CymtSYI5HuEaLJvvrwDa7JGUxt+xBNrmlDwFwNfnTjRm6ADt82KU8m7txfdvvnLYUsfcmufq76fT59tJpCIWwxlgERERUXQMjlIsWwY1Qx1wxtrjZSiB4uJZxVh7VwV21J3FnZXTAIQXkYj3MWoau/BmTbMx4+FRhGXW4qnbr8bBU+ddU/Xs1ee8HgWQEgFVwqsIQIik97Mxvx56UNvS3Y9NnzaFfc4s6YFBiY0HmrClthlr76pAS3c/vIpWKjvHq+DOymk4eOq80Yfo1msmG8GIE/t7rs8WFhfkOpbndgoE7NswB0ZAer8/TjNzejGOWN9Pt7VG8X5OI32/0j0zTURENJIwOEqx0VJeN9lrm5yYZxEONHQ6Bh7xPsb+hk4Egtp6FgHglnmTw2adoqXq2R8TCDVVDWrtVe3FA5I5mDUX1dhS2xz2OdM/f+Zmrz6/irXb66BKCa9HwarrZ1rWYenB55obyhzfA/O+xzLjGCkQiLaNoXx/hvo62x9bAHF9tiI973g/p26vUzbMTBMREWWTjA+OhBA3AfivABYDmA7gz6WUL5uuFwB+CuBxAMUADgB4UkpZP/x7Gy5Zi++zQbLXNtlZBpQugUe8j2GsLfKrEIrAR1+04oPDrfAoAuvvrcSaG8ocn5f9MnPRB0iJoCrhCc0cmYsHOK3zqW/pQXvvACYW5hlBSqR1Qm79ddw+ZysXlaKtdwCfHGtHMKjNCunpb8GgihkT8o3H1IPPg6fOG8UUzI/tNBB32z/9PTvT3R91rVisBUAA95Lz9sceatDg9NhOAaibSAFQIt8Fp9cpW2amiYiIskXGB0cAxgGoA/Cb0D+7vwLwlwAeAXAUwFoAHwgh5kkpe4drJyMZrjUSukxNsxlKoGhv7uoUeER6jEhBxdq7KrB2ex0C6uB6m4AqsXZ7XViA4LQtp0G025qj53adsFTB+8n2OgRNj/tm9Wmsu6dycJ2Ny/ohtx4/kYKZdXcPpr2tf7c+bGAebaAd7XrL+iaPAlVKBIMSXo+wpO/FUt3N/vpGe/7261YuKk1K0GB/TeP5/EYro5+MkyajZWaaiIhouGR8cCSlfA/AewAghHjZfF1o1ugpAL+QUm4JXfZnANoArAHwwnDuayYYiWk2Ts1dV4TKZ7sFPLHMeOi6+nxQbYUIAECV0rHYgtvsidNZffvCffNgVghhCcgAbUZsR91Zx4F9rNXp9Of87M5jRjrdgF9FfUsPnrl/IQBg3tTCsPtGG2hHu95e/tz8nL6xYAq+OnNC1ECgprELq1/cbzzGpsdiS0WzXycRey+peE4mRDrRES1ojjb7mIjRNDNNREQ0HDI+OIpiDoCpAN7XL5BS9gshdgP4GkZhcBRrmk06ZpciVU6LxPyc9Oau5jUr0UR7TSwBiyIgJSClRK6t2EKuV8FNV00Kq2znFJjEssamuCAX696ptwQSOR5hFEZwWz/kVJ3OvOAfGAzg9NBLAnij+rTxerulCr766BJsqW2GAHD0XG9cg/3iglyo4TEmAGBiYV5M1d30ggeAFmBtrW2OGLy59dZauUjrZzWU9VDxiJRymOrv13DPTBMREY1k2R4cTQ39t9V2eSuAGU53EEI8Dm19EsrKwhecZ7vhqBrnJlrA5VY5zZw2Zr5/PE1lIz12tNckUlqcfTbkwyOtRsChKAJnuvtR09gVV/qZeTA7b2ohttY2h605cprZMe+nuTqdLzBYYMGeUmbuPRRUnXsW2dfqbDWVNlcEHAf7NY1dYWt/uvp8Yb2OBACPRxiPE+1zZo+tzH87vU/RemvFE3hHm42LZztc+0NERJSdsj04ipuUcgOADQBQVVXlcp47e8WSZpOMgZxTIBMt4HKqnGbuHWQf6JrX3URqKhttLYpTKWWn52Gf2bAHZkIIY32QAKCqEq992oStoQDP6T6xrAOZPiE/bAYt2mxAxfSisP3SX09zSpm5QIRedtwc1Lit1dG/GE6fEbfXe0l5CTzKYKqgAPCV0iIcOXvB8jpFel4rF5XizerT8AclcjwCK0Ppk07sn2O33lqRxNIrKt7tcO0PERFR9sr24Ohc6L9TADSZLp9ium7UiTawtg8IWxxmPyJxqri2o+5s1HQzc9rWmzXNlmIK9oGufd2NfeC78UATNh9swpTxYwAg7LEBGI8TCA6m8UV6HnqAY76fOTAzFzIwV3zTZxzerBmsZKYXP4g0A7HxQBPWhgoymKvjxfO6OxVYsKeUAYNBm73Qg9taHZ9fhQpt5sg+2I8UXC+/ZjI++qINUpXIzVFQOaMIh870RCziYE/dW3dPpVFOPNLasbV3VQw5IHGbjYv3pAHX/hAREY0M2R4cnYQWBN0B4CAACCHGALgRwH9L435lNHuQsulTa3pbNJZUM1PPHAlAQfhg2v7Yi2cVO64HMQ90ndbd6APp3n4/nt/dENpij2X7Hs/gOiE9YAK0NL5XbWl89pS59e/U48jZC/AHpXE/e2Cmp7vZA5KO3gHLWhlz8QMnNY1dlgp55up4+mtsb6YaaabELQ1PfywAqG/pMe5/2a8931XXlbmu1XFq5gq4r/2xrCe7oQwV04tQ39LjWKlO78tkD0LrW3rwRvVpBFQZVk7c6fmb12+Z+1PFw5wqGE+pbrftZKJMrWBJRESUaTI+OBJCjAOgTxkoAMqEENcCOC+lbBJCPAvgR0KILwAcA/BjABcBbEzD7mYNfbAdCMafXmevuKbPoCgC+PrciXjq9qvjrvrldObdPOAHBtPu3AgADywuRVefz5IaZuYLhPdE0gfcnzf3hG3PqQSzeb2Qvn8vfPKl5b76Y2880GTMgphvv7+h01LCG9DS9LbWNmNLqCiBvmYoL0eb5YlWGtqt8IY5aPEoAmpQe9zPm3tw5Fy94yxXpPfP6b0ylyjXU/z0WSp7o1l9xsxcqU8PsvX7Atps4JZQQYaaxi60dPfDG0rbE0KguCDX2M9krKEbqbM/I7GCJRERUapkfHAEoArALtPfPwv9+1dovY3+DkA+gOcw2AT2G5nS4yjTmM8gJ7pOwl5xzTyDEikwinb22ilg0v82D76d6IEMAMuaHwAImu6jCBHWE2n9O/VhgVGux1pNz61YhL6tj4+2Gff1egQqpxfh8d9U4/3DWq2QPcc7kOPRZlAUIfDosjnI8Qj4goPrc3JzFEjA8jzNqYJPLp/rOnh3e23tlf7mTByLE+2XjOujrdWJ1B9K3z4QPpvU0TuAy37t9Q/YGs3aAyMBrbiFPvuo0yvsVU4vMgItjyIgoD2X9e9qfZ7dSp8nIpNnfxLFYhFERESxy/jgSEr5MbTxk9v1EsC60D+KwOkMcqJnyt1mUBIpmew2ADdXq9MbwOozXXaK0PoSvfZpk+N6HJ9fhRJa12Mf5FfOKLIER18tLcLauytcCxCsvasC696uM4oGPFA10zLYn1KYF1aiG9D6/QDafr649ySE0D7Y3lAgphcf2GqaObKnKTpVizt6rteYddFnmfR9t87yAQ0dlyz7FCkojvae2fsRmQPmtW/XGdtRpRawAtpA3dxTyiOAh67XUvDWv1tvSYUEgICt75MMvYZ6EGmebVKEllbpVEEwXiMpDY3FIoiIiGKX8cERJY/TGeQnl89NeKZHF8vZ9v0NncbA1+cfPHvtNgA3X66nl3kUYHJhHs5dGAjbvioBBAcrtkVbj2O2YlEp3qhpNmYmVl1X5jr74g+o2HywyZjx8QUlOnoHQsGZdvsz3ZcdXwN7WW39b1WVxswKAEuQ4VZhT39thBCQqoQehtlfW71SX11LDzYfPG0JTOxBoNN7Zl6TZZ5xcOpH9Mz9C40Uu2DQGsF29fkADA7UfQEVirAWodDLmm8+2AQ9rrSvPzNX3zNX6VMALJwRX2U8N7GmoWVLADVS0wWJiIhSgcFREmXyYKmmscuYfTFXidOvs+93MtYpmLdbXJA7WB4a1pkEp5Qf8+WAFkQEVBiBkZ6KJSAhJeBRBCAEgsHwCnxOsy3m4KG4IBe3XD1J62EktXQtcyEA+5n3vFD6nq67zwcZ1uEnnH6tkQJoKrEdy/ohneW1kdbHVBRtLc6P3jpkqdQ3f9p4qKbZLa8iwmbH7J8Bc1NX8+yP+bk4/b2kvAQ5oQAI0FIUzc9vxaJSCGjlyLv6fGHv04pFpUYj2sI8L3bUncUjS2ejMD/Hsfqe/r5MGT8Gf2juidqgN9p3NJY0tGxbxzMS0wWJiIhSgcFRkmTyYMm+KP+h68uMtTT64ni9gahTJbdE1ik49c/RZ1cUET6TYE/5KS7IhSIEpG0dCmAt/AAMNmwF4FqBzyk1Tl/HYk/Tc3q+KxeVGo1aT7Ral7MNBFRL4AFoMxlVs4vxWXOPUSI72r7bm6raX089YKiYXgQlVAjD7q6vTAtLT/MFpZE2qM3AWdML3T675qauCgbfM/310PsRKQKonF5kXLd4VjE2PbYEW2ubIUO3tb8HXkXgDaEFb/YZJH0gv/FAE3701iEA2pqtn4dmpvTbANbqgeverjOes8cTnj4W63fUUureJU0vke9HJp88ISIiIg2DoyRJ1qLnWAZQsQ6y9Nud6e63LMqf7rI43qmSW6LrFNz659i355TyU9PYhfXv1mvFCxRteB4MpVkpQtuOufCDfdDqVIEvUh8lO/PA2p7eF3bbUBre0VZtXZN5ddwfzvRg3d2D5an1WSL7voeVwa6aacyq6PuxesM+I5Uv16vg0WVzTOXMB3Vecq/UZ68mqH8+WkyfD7/tM5CXozXthQCOt/ZaArh191Qaa37ss21OMxWW9yAooYe9qhwsY26+z466s5b776g7G9YHSn+cH711yFjTpVctjPj4UWaWzGXFndL04u0VlsknT4iIiGgQg6MkScai51gGUPGshzAG3B7FsdeMvZy0EMJyljzaOoVIQZr99Vi5qBSV04scm3va0970YE5fj2PsH4CyKwrwzYqprj1t3N4H++V3Vk7DgZPnjcDNkhQXmpGpaezCszuPhRUJMJOqRH1Lj1EAwt5ItKvPh2fuX4gVDn2ddJa1PaF+TPrzzctRsGJRqREYAVoQu+2zM2H74lFgXZ+jCNwybzI+PtZupFLqgZG5AW2ORzimWy6eVYxHls7G87sbICWw7bMWS2nxrj6fUWHO3Hw3ls+ERxEIhoJ1hN5ne7ByZ+U07DneYfnbSU1jF96saTbeoxyPMIpbuD2+03fU/t1asagUAVU6BlP69yPWXmGsGEdERJQdGBwlSTIWPUcaQEU7yx9pW8GgioeuL8P0CfmWfdNnBnx+FSK0fsd+ljzRM+H21wMY7Htjb+5p357Xo0BRBGRQwuvRSjfrg9RTnX14fneDMYPk9rh6Spf5tXtk6WzUn71g9BzSgyCvoqWq6etVgqrEltpmo+hApJVEKoBXDzRhTChgAODYSDTSa7mkvARez+AaHZ0edHT0hhegcCpK4REC86YWOs7Emd+HH711CJsPnjYCE19QYu6kAtxQXmKkW+rqz15w3Cd9e+ZgQ2++61RswTwjo8+I6VX2VFUiNyc8WNHvqwfU9lkjnT5bCGgB5YNVMx1f62jfUfv3T8B5ttO8vVh7hWVixTim+REREYVjcJREQ1307DaAsqddOZ3lj7Yt+6BX3199sHimux+vhWY8Bvxa9bFYiwK4DQrNr4e5T5EvoOLZnccs6WXm7ekDXa3egMTP7l2IHXVnsfd4x2BRB9vj2gMAvZHqmzXNgJShNC4ttezgqfO46apJxmVSApWhSmf+oDR66UTrq2S+Sk9JNPciKi7IDZvhch2QOqwf0gs3TCzMs1TDcxMMzb7YKxCaZ+Yefmm/0X/I7ET7JTSd78MK24yLffZG3yf9ddaLK+gzY/osmzlVDnBu0rp4VnHUSoJrbihzDYp0Tp91N9GCVPt2Is34Od3H7fuYjJMnycQ0PyIiImcMjjKI2wDK3shz1fUzMcM2CxTrtpxupw+c36wZnCl5o/q0Y0Cli/dMuLmEsyqBvcc7cPDUeWNQZt4eQiWaAa1CXV1LD566/WocPHUePr8KFVqQoz+uU/EHc+AGwBJUDfhVfPhFm3GZhFYVDSIU8giBiulF8CgCajA8IvF6BBbNnIBPT3UZl9mbywLaOiG9F9Kmx5cCcA4S9jd0Wvokmc0pGYv23gFjJk0R1qa2xuMjcs8iYLCcuhtfUJsxM7/n86YW4o4FU9B24TKWlpdYKsaZn9+KRaWWioSANtv3/Cdf4tqZE2JOKbMHubGWkh9KCmi07Qz1sWN9/OHEND8iIiJnDI4yjNOZbaf1O7EMZOKZyVo8qxgPLC7FpgNNRmpZpAFTtEGhfTCo3/7ZnceMGSCf3zqDpG/v89PdeP9wq7EtYXs8vf9PcUEuttQ2o/5Mz2APpYCKujM9xuya3hfHvGbHvpZJlcCLe09CDfXMCQa1tUILpo23NIfVLZ83GZ8cazf+9gjg0WVzLLNEW2qbLb2Q1r9Tj4oZRa6FD5xmhiSAI+d6ceTcYHU8j0fB3ZXamqu2CwOQADwegW+HmshGer+XlJfAowjXQAwAXvu0CR8dacV9187AHRVTrRX+TKW/f/TWIcvz04Mg+4zaB4dbceXEsTHNiOrro/wBFYoAhCK0lLsYZjaGkgIay3YiBTfRvmeZOEuTiWl+REREmYDBURYYrpSclYtKsTW0XiaWClzmQaF58GisJbGVB188qzhsBuh3J6wzSPoslj5I9noEZGj7Oj1Vy1zBDdCCKFUCf2juQY5nsGT50XO9+PG2QxHT0lRVS6eTcrBoRXFBLj5vPmS5ndcj0HbhsjEjpb8OL+87hQG/apTJtq8T+ry5B4fPXoAI7SeEwOenu43nFS1lThcIqHj3D2eN5qeAVhRihqkCYaRB/Pp7ByvMOT2kKrX1TM/vbkBNU5fr7IKw3e+jL9pw5cSxjtusP3sh6oyoLygtAXFQwpgiG+rMhuVx/KoRqMZ6kmGowU0mztJkWpofERFRpmBwlCWGup4p1seIpwKXzj4DYK5C5gs4V/l6ducx/O5EhzFg3FrbbBmo6X1yXjvYhI0HmrD5YBM8ioJA0JQ6ZwuMZpUUoLGzz5j50kuW72/oDFvSYx/E53gVrLu7wpiR0vfl5/cvxOaDTag704OgBAJBaRRuMD9/VeqNaiWe3nYoLHgAYJSaRmj/3j/cio+PtePmqyfFFBwJaE1eVVPvJ30NUHFBLh7/TbXWyBYwejnpxQ/013/NDWWYN7UQL3zyJT443Bqx2MTp832uswsrFpUaVfkALUDbF5o5s9OrE7rNiEaqBmhf42Tm1rzYfpmR0hkKyD9v7sHnzT14s/o0Nj2+NOpM0VCDm0ydpRmOYwoREVG2YXBEFtEqcDkNPsP711gVF+SGPYY+g6Q32nyj+jQCthSqFz750uhvFFSBoKr94Q+oaLPNzHg8Ao/fdKVWEc+vQghhPO6S8hIoirCULdcJAdwxfwqeuPlKS9ECvWreA4tLMXn8GKim9Dr7VsICL2m9jSLCL9P5AipOtl8M3y8AJYW5OH/RBym1GasHq2aicnqRUfVPCIFbr5mM5fMm46dv11mCrwG/ih9vOwQpB5u+mgsb7D7eHrY/UwvzcM70uuqpdXrzWWDw/dea9A7OeHk8AvUt4SmI31gwxbWggj0YDwZVCAFIaDN4+uvvNMPjNJsDuBd+0ANyc3EJf9A5ddQp3c+pFH4snKr0MSAhIiLKXAyOKEwsVfPMg0/z7fXBrdG/RiKsQSjgXinPHIw1OAQNnlAhhsmmCm4CwKqqmZg3tRA3XTUJHx5phSolfvp2HTYfbMKciWMhXaZmhAS+OnOCsW9ba5st65f0NVhuFAF4Q+t4HArOGc/1y/ZLOH/J53h94/k+eBQYgSCgBVIdvT54FGDhjCKsum6waltT5yVs2NMAVZXYc7wdAtZZKf3++v4EVGuTVT2YtRuT68FNV03EH8704JarJ+GvvzUfNY1dRknzN0KV/wKqhCIEzJsozPPifJ9/8HWF1g/piZuvjPDqDc5erDRVhQOcCzFEm80B4DrDowfkB06eN557jkc4Bjr2dL8PDrcix6tg1fXR13WZZeJaIyIiIoqMwdEIMNRKWG7FE+zb3GIKHMyDT/sMgC/UI0YfrruVBrdUyqs+bZTR1ges5ZPG4UT7JeP2s0sKMPOKAqNPkd5PyONR0NY7gNUv7jeaugKAGpRGCpUbryn423igKSwYMv+/AHDlpLH4sv2SVhYcWuACwPUxBIDapi5L4AMAMyaMwZnuywC0FLuFM4owefwYtF24bNlWUNW2Xd9SB0Bbb/XS3pPGjI0voKL1wmXX56czN1l1S2dr7OzDqc4+CAC/rT9nBEbm91x/TaQtEjQHRl6PwKqqmRGrHdrZU7yizRStvavCMYCP1pdIT9eUgGugY3999CId+rquWGXiWiMiIiKKjMFRlhvq2Wm3+9sHq3qpb31IbA5igMF0PHvpbP3/o5UGN5fR1j1x85X48Is2YxbqVGjwfuDkeWx6bInR7PWN6tPYGWX9jONDAsb0Sk1jF36yvQ6q7XrzNr0egdvnT8GpTq2yndcjcORcr6U4g522/in88orpRei85MOAXxs8f97cg1xvL777tdnG+iYzffbn29fNDEsPnDNxrCWgsqfHAQhrsqr3JyrM82LbZ2dwLlT5Tt9nfR3YG9WnjcsVRbtSShhpik6v+berZuKZ+xcaf8cTvLvd1h5odPX5HAN4ewNgu1jW2Til+yWyVihT1xoRERGROwZHWW6oZ6djvb++Dkl3y7zJjgvs3UpFO/XQsW9bP0NvnpG69ZrJ+MBUxQzQZku21jbjmfsXGj2CzAUKhENZbCB87Y9eQEFPybIHHePyPOgdCBp/Ty7Mw8v7TkGVEkpoLcrOI/EHZQDQ3efD2rsq8PRbg9XwfAEVG3Y3QCI8MENoX0+09iIvRzE1WwW2f9ZiuZ09MJo7eRxuv2Yy9jd04ui5XmPNkj4D45Tu51GE8froQku+4FEEHl02By/vOxXWKDfXI7DS1IT1F+8dwYY9DZBSS7OLFLxHCvSdAg23QEdvALw1hmIibpzS/eLdDivCERERZR8GR1luqGenY7l/TWMXznT3W5qifny0LazM9+JZxXh02Ry8EBrg271efdpIZTLPENj3obggF8/tOoEl5SWYXJjnuN/69peUl8DrUYx1JIoArp5SaOkNBABTx+fhvmtn4Ne/P2VZb6NK4LPT3Vg+bzI8pqINXo/AzCsKcPjs4HYuDQRxOdREVUBiUmGesd96oBKr6sYuDATCq7SZJ5k8oSDPfJtPT3Xhvmun47PT3UZlvmgPe6LtIk60XYQALMGrz69iR91ZSwCkB2VBCYzP88KrCKMqoJGuKCUK83MsfafqW3rCUtV+8d4RPL+7wdj2gD9y8G4O1Af8qiWYjjXQsAf7W2xVEOMVb0U3pxRVBkVERETZg8FRlhvq2elo99fP5g/4rblhfoeZoJrGLry875TrYD0Yqg7m1AfJPNBe93YdfEEJRQDzphQ6NkitnF5k7P8Di0ux8UCT9hgSONbaa39otF4YwK9/fwqqGp7j9sHh1rC0vK+Vl+D3ttLU3f2mggNCS40DtKChbyCAbbYZnEj0VLpIJIDVN5Thk6NtxvokQJspSmS2KmwmCFow5BQABVWJl/aexK3XTLb0HwIAIQTOdPcDAJ5cPtfxsWoau7BhT4PlMiEQMXhfUl5i7IsE8GZNsyXYMq9R04Nnt/Lgeq+uN2uajfLvqS6IwAIMRERE2Y/B0QhgPjudSHGGSGe39zd0OvahcRq8ulVBM9+nt9+Pf/rgmDFI14s1TJ+QjyXlJVpKVHCw0p19BkhX39KDmsYubKltxu9PdFiu09frCABTxucZ62n0QhFu+2a2+3iH4+104/NzsXb7IQRVrerZg1UzI94+EaoE/qOxC2d7rAUXYgmMBICyKwrQeL4v4u12H+/A/KnhM20AjHTFXK91Zk5AYtOBJrx+8HRYiXD98/f56e6wgLZqVjGOnuu1VKXTy4Tr69EerJqJjaGiGOYUS/P2IwUg5vVC9Wd6cOhMz7AVRGABBiIiouzH4GgEMPeesa8nibe3ij24irSOKBBQ8ezOY3jq9qstVdC0PkPAbfOnAIDRbFQRQP3ZC5a1PRLA5oNaGe9cr4KbrpoU035uPtiEzdWnEbBXLgg9DqAFCFeMzcW5CwOW6xzuEjfzOh1fUKK2sWvoG3XgFhw68ZiemyKACQU5aDwf/X5fRHiMT461Y93dFUbaHACjop+9RLh5ltFe5U8ILSXw01NdUISW3hcMSiON8I2aZmx6bAlWLCo1qhA6pXnGGoCYq+wpwr2RbDKxAAMREVH2Y3CU5cxn0hUhoEqp9WcJqGGpa7FUCrOXS+7q8+HRZXPw4t6TYQULVAC/O9GBg6fOG9tfe1cFfrK9DkFV4uNj7fju12Zra5VC+3Fn5TTs+7LTEmwF1cEKaRML88J6/jjRJjKco5zCfC96+gIAYFkzJABUzijCH5p7EkpLc6oCp+vqc+5hNFw8isBjoSIJ/oAKoQgcOhM5bc+NuRiEP6CtS7qzchq6+nwoLsi1BMuqHCwRrgcuTrOM5srfqoSxdk2nBzpPLp9rSbHUi2VEKsxgZ94PBcDX5040AngnQy2Fr2MBBiIiouzH4GgYJWsQZmY+k45QFTUBCSEGSy2bz7BH2gdL80tTcKUoAqpLtQH9tvoMUn1LjxFE+QIqXtzToDVqFcAjS2cbKVhrt9dp5bC9CiAlgqpEjlfBykWl6OgdsKxzmTt5HMonjrVc5hGAUITjzJEeGNlJAMfbLmqNahOIjtwCI30tTbQ1R04V6GIVbZ9VVaKh4xJuvGoSPmvqQvvF2IK1qePz0HHRZ3xWFGglu/XsSAlgz/EO7DneAUVos3uPLpsT6rWkBbx6AY3iglxj5jBKbBvGHOjon0tz0K+n78USgNgDqGiBUTLXCbEAAxERUXZjcDRMUrVY2z4Q1Gd79BQ78xl28z54FW2djLn3kHlb5uDKfpYf0IITj0dBIKgFU3uOd2Dfl51YVDbBcjv9rlICG/Y0oKxkLNbcUGY0cdV77dSfvYA7K6dh8axiTLRVqJszcSwmhirDBYLavt12zWSUTxzrWhnPTZ8vGP1GcZJSa5p6/exifHrKPb0u4cAIwJTCPEt6oNO27YUTovEoWnpgUNWa737tyhI0ne/D5MI8HDzVFV5JL5TKVpifg81PLLUU0PAHJXI8AuvuqURXnw+9/X4jgPLqZcGDWm+o5fMm4+OjbQio0ngvn7j5SgAwCi2YA3VVSvx4m1byXA+QIn134pnB4TohIiIiMmNwNExSNQiLNBCcN7XQcvlzu04MzgwFJV490IQtpl4w+ra21jajrXcAnxxrN8pUm3kUgb+5txLzphbi2Z3HsCdUvCCgStQ0dcMbSovzeASkKo0ASZUw1qgcPdeLzZ82WdbIHDx1HvOmFmLlolK8WX0a/qCER9HWvQSCWkB3+/wp+OhoGz443AolNOjOBD6/irlTCvFZc0/EohSJyMtRcPWUwojBUbzmTh6HORPHGlX6gqo0ilCc6uyDR9H6GplfX6e1Ox8fbTMKaPiCEnUtPfh5qAHsHRVTLcUXzJ9F+wxmTWMXVm/YZwmy9DRRwPrZiTYDCsQ+g8N1QkRERGTG4GiYpHIQ5jYQtF9uLpWs8zn0ntGbaHoVgTsWTMHHoeDEfJZfH6CWXVFgKQSgqhJfKS1C5YwirFhUiqPnevHjbYeMymWqKrG1thmvmQIjAJag8cnlc7HpcW1moqW7H5s+1Qo2BFWJ1guXjVS6oCody3yngwqtnLdTqXAnN101EZ+d7saFy84pgGbfrJiKdz6PvUx4NAJAcUEOPjQ1sA2bJbIFRnpFPr3Bqz4Daa/+19E7EFZmWw9izGW/7RUW179THxZk3fWVaZZURXPD3mTNwnKdEBEREZllfXAkhFgH4Ke2i1ullFPTsDuuMmEQppdKfjXUEwgAFEVYAjXzDFdQlfjqzAl44uYrw/bbnKIHaLMKMtSw9A/NPTja2ouK6UXo6vPhnq9Ox9uft0BKIDdHQW1jl3PFOCHw2eluo7ns4lnF2HigCUpowU2OV8Hk8WMADBYayITASBdPn6O9JzpwxdjcmG67+3hHUirs6SSAg7b0P3uQGR4sScyYkB82A2kPjj76ohU7j7QaBT3M1ROdghi3PloCQOcl67opJbS2K9osbLxr+7hOiIiIiHRZHxyFHAVwi+nv5C8sSYJMGITppZLNC93ts0v2GS6n/bYUgoC2kP8rpYOV4Hx+FT/ZdsjSc8ijCFw/+4qwHkJ66e2gKvHB4VZ8eLgVf3v/QsybWoj179ZDlRJCADddNQnlE8diJxJfv5MpVAl0xFg0oetSaivhCVtgNLEwFx291sc0z3a6rU0DrJUHd9SdjZpK6lThzqMIVEwvQsX0IiNlEwAev7HcuL/bLCwbsRIREdFQjJTgKCClPJfuncgkbmfPo81gma93KqWsW1JeYpk1UAFMGT8GeTm92mBXhs9ESCnxB1t5aY/Qtm0uZKACeHrbIdwxf4olAIu34EA8BIAbr5oYtflrOjgFgnpA6TZzNn6MN6aUPSC8Cl5Pn98op+5RgIeuK7MU7jA3Wu3oHcDHx9oRDKrweKyVB++snIaDp84bQYxe1c78ubMGWoCEVhlx/bv1ePXRJfj5/Quxo+4sKqaNR2F+jjGr6PYZZoEFIiIiGoqREhyVCyFaAAwAOADgR1LKBqcbCiEeB/A4AJSVlQ3fHg6jaGfPY6n2BURe16FvwxzUTCrMw9q7KrB2ex0CthG3gDb78JUZRZYAJCjhWOFNSmDn4VYIPV8vxaZPGIN2l1LdmWhcnhdeReB8n9/x+lgDIyeBoLaWSwDwCGEJjMy2mtamPXS9FkAB1sILelGQ4oJcrHtnsHripsesRUDM68vM5eefXD4X86YWOn4WYynjzQILREREFI+REBwdAPAIgC8ATAbwYwC/F0JUSCk77TeWUm4AsAEAqqqqsj07y1Eyzp47bUO/XB9wfna627i9J1Q5rq6lx6gwptMX81dOL8L6d+tj3gcVGLZFRWe6L+MMLg/LYyVDIsGPAsTUf0hPs5PQiiM8/8mX+L5t3Zl9bdr00HokAI5B9NNvHTLWp/kCKrbWNlturxf42FLbHBbYxPN5zoS1fURERJS9sj44klLuMP8thNgPoAHAnwH4x7TsVJotKS+B16OdPfd4Ejt7bj8DX1yQa5Ra9ihAxfQi+E1VAoKqxKYDTcjxKvAqwuidY+6lpC/kB4bWEHWkGY7XQhHamp3C/BwUF+TiJ9sPIegQKXkVEWry2mA0gv3gcCs++qINUkp4PQoeWFyKyulFcc3Q2J+f0/N1C2zinQ3KhLV9RERElJ2yPjiyk1JeFELUA7gq3fuSVvrsTYIpafaB6pbaZqPUckAFPm/uCbuPhDYrMHfSWNxQXhKWjlVckGtMBEkA86cW4si53oT2byRJVWCU4xH4o5kTUN3YBVUCv/79Kay7u0Kb3bMFRnMnj0N5qNnuHRVTsa+h0/IeB0NvnC+gYtOBJuTlaNXo6lt6Ytp/c++qHI8wSoKbJbpOjoiIiChZRlxwJIQYA+AaALvSvS/psr+hE4FQBbFgqDdMIgNKc5+aDof1OIoAxufnoNu27uVE+yU0ne8z1qDouvp8xiyJAuCPZhXjZOclDPjDG81GoheC4MyTOz1ArQ0FRoAW2Jh7Tpl92XYRJ9ouAgDerD6N7359jmMADAxWo6tr6THWHW01NRN2snhWsdG7yinAGeo6OSIiIqJkUNK9A0MlhPh7IcTNQog5QogbALwJYCyAf03zrqWNnobkERjSonR9wPoP7x/Fx8fa4fUM1qdThFZO+Sszihzv6wsONuzUFRfkwqMIKND6Ha1cVIq1d1VAmMreeZTw3jkAcEVBDuZOHof7rp0eqmpGkTR0XMKrB5rCZubclnCZL/YFJb7suITv31QedjutSIP2uRKA47o0N4tnFePJ5XMdgxy3NW5EREREw2kkzByVAtgEYCKAdgD7ASyRUjamda/SKNE0JHtak2XRfVDFQ9eXYfqEfBQX5KKrz4figlys3V7nuC0BGEGZvtD+zZpmLT1LwAiqPj7aZhmwqypwzdRCfHGu1zJg7+rz43yfH1+2XxyO4nVZxd7AFYi9joUi9DLr1ss/+qINy++tNEp66564SVu3pL+3W2qb4Qs1cP3c1MA3XkOtMhdv41ciIiIiJ0KO4pFmVVWVrK6uTvduZASntCZAK+etD1jtqU7P7TqBv//3o46zON+/qRx//a35+MV7R7BhT4PjYN0jgKkT8nGmqz9FzyozXTq8C4F9r6Cnsx1FJZPgXfodjF2wPOHtJVLQQQC4ctJYnGi/5Hqbr5YW4dCZHuO9u352MW6eN9kSgGw80ISfbK8z1iR5FWDzE19LKEBJNMBh49fsIoSokVJWpXs/iIiInIyEmSOKk9Mg1Cmt6cnlcx1noPT7a2lyWoEGAW3GJ9erYNV1ZVhzQxk2HmjC87sd200B0HocjbbA6PwHv0TBsd/i9RVjsKxsHPY2XcSat5/DJSDhAMktMHIKwgpDj+H1CFwciFwO/PDZC5bKg58196C6scsSgHT1+YzACNA+C1tMZbrjkei6IjZ+JSIiomRhcDTKuJ1ld0trsg9Yzff3KMIo9ywB3Hz1JPz1t+Ybt91Rdzbs8UdzCe9Lh3dBObwDm76dj+VztK/e8jlebLwngBXvvQIMYfbI6bG8e57D6/coliCsF8C4BcsRlEDrhchNb1VVGqmUn5/uxgeHWy0NWhfPKkZxQW7Y/ZzWjKUSG78SERFRsmR9QQbS1DR24bldJ1DT2BXxdm4L3/V1Sn/xjXlGwOS0za21zRjwh+4ftIY5G/Y0WG57Z+W0sMcfrYERAAT2vYLeAYllZR7L5cvKPOjpbE/6Y228R8HyOV7keEQoCFMQ2PeKUcUw0nshoBVdWLGoFEvKS/DxsXbj9h5FGAFIV5/Pcj+PIsKqFKaa02eXiIiIKBGcOcoAQ11MHs+ai0hn2c2zRG5rkN6oPu06qJYSlpSmNTeU4R8/OIqOiz6Xe4wuPZ3tWDBRwd6moDFzBAB7m4IoKpmU9MdaVjbOcpkehDnXFxykAJg8Pg/3XTvDaN4bCA42732waqalQeuYHAU+vwpFEVh/b2VaghOW+iYiIqJkYHCUZslYTB7PmotYK9m5zTAFIpRBy8tRLBXqttY2o5OBkaFg3Dh0X76I237Th/JigZ/enIfS8QpWb70M7/L/lNTHKiqZhL1NF12DMI8C3HbNFHz0RauRGqkIYN4UrTHvuQsDeH53A8pKxoY17y3M8+K5XSeMzw8btBIREdFIweAozZKxmDyeNRexzlK5bVO/zKMIbf1JKLXOI4BHls7G/oZOHD3Xi/Xv1rs2d83UdUfJriJn33ahuIxX7svHsjIP9jYFsXpLP3p9Ep6F38IVSVxvBADepd/Bmrefw8Z7AsbjrXlbhffG72g3kMATN1+JJ26+Es9/8iU++qINqirxha0v0uaDTfhGxVTjPRMAXgxVH8zxCGx6fOmwztqwZDcRERGlEoOjNEvGYvJYz97bZ6nW3lWBrj6f433ctmm+bEttMzYdaIKE1lfnxb0noaoSiiIgZeQ1LZnGrYDBUKrImQX2vYLX78uxFGLYtDIf92/3YsIdPxjy9u3GLliOSwBWvGcK9m4cDPaCoRTIJ5fPxaTCPKgua5CmjB+DJeUlyAl9RmXovoDWLHb9O/VYe3cFAKQ8aGHJbiIiIko1BkdpNpxpSeZZKl9AxdrtdVCljGugaZ4leGXfKWNArS/yR+i/SoSSZYrQ1iep0GYiFEXAI7TB9lAlOvsT2PcKXg8VMACSX0XObQ3QhQu9mDDkrTsbu2A5sGC56xqj4oJcbDzQhM0HndeRKUKbXQIAVXWeBfxDcw9Wv7gfkBIBNb7PUrxYspuIiIhSjcFRBhhqWlKsZ9TNs1RCCKNimdNAM9o2f/HeEWz7rMV1nyIsTYIKrQHp7fOnoHcggDeqTyctMEp09mcoBQxiEW0NUDrUtfTg9YOnLX2KdALA7fOnANCCklA9hjASWqCtp92lMmhhyW4iIiJKNZbyHgHsZ9S31DY7lvU2lzxef28l8nIUeAQcB5pOZ+lrGrvw9FuH8NhvqvHCHvfmrtFICZxov4SXfncSQHhJ8ERFKl8djRa8BC2XJTN40dYAqdh1MgB/UGLXyYC2Bmjpd5Ky/bj3xyMgAKjS+bWXAN4/3IrVG/ahuCAXOR5hue/1s63Bj0eB62cpWViym4iIiFKNM0cjgPmMukcReLOmGYGg84yPeZZq3tRC13Q++1n63n4/vv3CPsdZhkQFgtLSP2eohjL7E7WAwRDpa4DufmsDxEAvLvmA8UXjkZOUrcdm0rhcFBXkonziWCNdbkttM3wBFVI6F8nwBSXqWnqw7p5KbD7YhCnjx+CJm6/E/oZOVDd2QZXaLFPF9CJMHj8GkwvzUvocWLKbiIiIUklIlzPHo0FVVZWsrq5O924khV7Fq6W7H5s+bYIqtTP5f/GNeXhy+dwhbbO4IBdrt9dFLOOdCXp+9V1s/ZY1dW3XyQDue30AvQNq1DVIqaxWp2/f+8m/YON9OYMB2DY/Ajf/56Q9TrRKgLmmCnPA4Hvc2+/H87udZwO/sWAKdh9vD+t59fBL+8MqEgpoJd05s0NuhBA1UsqqdO8HERGRE6bVjRCLZxXjyeVzsWJRKXK97ulyiWyzq8/nmn4FaAv3TVlXaeOYura1Hz+8zoOBp8dh67cuwrvnOVw6vMvx/mMXLEfR936Nsr96B0Xf+3XcAculw7vQ86vvounv7kbPr74b9jj+3S9iY6hinZH2d18O/LtfTPg520ULX/1BafSsMge/hfk5+P5N5fhqaRGun12MnFDaXa5XwaTCPMdCCGvvqoCwve/mdUdERERE2YZpdSPMUKvfOfWR0VPs3NKvyieOxZxJ47DraBuCQQmPR2D2FQU40X4pSc8qNvby1YV5Cn54XQ7+9tYxAJJfgc4slmIQF3ouYFlZoeV+y8o8uNBzIWUV65zoVerMs4ECWt+iB6tmomJ6EeZOKYQAsGJRKQAt/c5eCKG+pSes8IaC1K47IiIiIkolptWNkLS6ZDBXqFOEwPp7K7HmhjLjui21zdjsUN1ML9vtVQYH1z/ZdghJqrNgiDftrenv7sbA0+MsxQT8QYm8Zy6i7K/eibi9eB/LLaVvxXvjUPS9XwMAOv/pLrz9UEHYbe55rQ8l/+XdhF+XeOV6BAKqjFhR0J4eZw+aaxq7sHrDPqPKoEcReGzZHBTm57BBK0XEtDoiIspknDkig7lCnSol1m6vw7yphcZ1AOAUTOuDbL3qXFefLyWBkXlm5mefdOP/+eAf0fTuP6CoZLJj8BKpfLbjTM+2f0H7zl+iv78fk8cKvL4yP+aS4LEUg5B5hXhk+0W8fG++seboke39kHmF4RtMgllXFGBsngeHz/ZaLvcHozfotZflthdC2N/QaZl1WnXdTPz1t+Yn9wkQERERDTMGR2RYUl4CRQhjfZGqSmypbcbWUEUzr0eBV9FmHZzS6ySAN6pP47tfn5O0fdJncAIX2oxZl02H/Nh4yI+3vq0HGc7BS6QKdI5NX+8DVrzeByUX2LQy37Uh7PkPfglx+N/RezmIwjEeyAV/HFMfo/xbHseFD/8Fj73Tj5PdEnMmCFzwe5F/2+NJe73MGs/3Wf72KDDeNKfgVZ8BVGX09Dh7NcOVofQ7IiIiomzG4IgMi2cVY/29lVi7vQ6qKpGbo0AAxmxSMKjioevLMH1CPooLcrH+3Xr4AyoQaigLAEFVov7sBSgiciNYXbTUNn125/ZXtJkYAHhmzwB+dY978KIbu2A5zu57HfdtPo3eAaAwD7hcOBPjAfR0tDmu/+m5rP3/D3dcxpEOFfMnKnj6xjw8sMCLns52BD/4JcYe24GN3x6c/VmzdQdaL0qs3qpg04oxxuWrt15Gz8U+4FffNZ7XJQCd+16BRDs6PZPgvS16RbxkVdFbXFaMvBwPKqaNx0t7GxAwNXZVBPD4jeXoHQigrXcAkwvzsGJRqWt63FDXthERERFlIgZHZLHmhjJL/yPAuhjfPGDWb2cOlHK8Cu6snIaDp85rfZc8CiClYypXpCIGA2eOQNTvwOurtCBo/kQFe5uCWD7HiyMdqhEo6bQUtjZLP6O2zU+joPc0SgoELvokJhUInOo4Dd/7/4CxuTC2BwDffOUS9p3RmsBOHivwv+4cDHLWbOnHw1slxuYCgT+8h41rCqyB2Yp8rHy9D0tnCNy3uc8IxG6d7cHrDxaGz2wtWB6171Isr5E9QIpWxvvgqa7Qf8/j1mum4IPDrcbtVQn8+venACkRUCVyQ+91JOw5RERERCMNgyMKYx/0us0QRGooaw+wnt15DHuOd1gexzG17Z4A7n7zlyhULqPNJ40g6Okb8/B/bO3Hv63ItwRKur1NQYzPE7h0eNdg0ND8OcaPFXjxbvMsTz++90c5mFei4JHt/Vg0VcH/PhZEyViBbasKsPL1PiOlbtMhP57ZM4C2PokJY4AfXJeLl2r9aL6gTbno1x/pUJGrALVnVWxbVWA81vfe7sebhwNYvTAn4Sp5bq+R07YkgNIJY9DcfdlxW3og5POrmFiYh7wcxdKnyB+aSrKvNyIiIiIaLdjniKLS+x1FGijbb2P+e/GsYtxZOS3sPloRg/AZIE+wHxtNQRAA/OtnPvT5JR57px+H21Ws2dpv6Wf0vbf78X9el4PAvleMbXkU4OV78619hVbkY9sXAXznq7mYX6Jg/xkV+bnAxhX5eOq3/ei+rO3DpkN+PP3RZfyvO8fg8tOF2PLtAmw85Meji3Lws08Gwq6fMV7g5fusj/Wre/LxzJ4B43n1dLbH/dq7vUY9ne2YOC437PYtPZdx01UTMS7PA0VoX3B9LZFOUQRWLirFq48uweobyix9sXI8Iik9soiIiIiyEWeOaFh09fnC0r7cihj0DmgBwNM35uF7b/fjV/fkY9+ZILatGkxn23TIj8fe6UdDl8SCSQqeuXUMHljgxc/3DlaHu+SDY2BxpEObIfm0JYgt3y7Abb/pw7IyD071SJQXC+xtCjqua/rVPfm457U+KAL4T/+7H2+Z9udkt4z4WPbiDE68CizrgCK9RkUlk9Bx0Re2DSmBG8pL8Jvv3WBp8rr+3XpLiXZzELtyUalllo/riIiIiGi0YnBEw2JJeQnycqyNZJ2qyf3puxKFY7QZo9ULcwBoxRH0gEm3emEOHljgRd7f9qLuB1oJ7V0nA5YAZFxBrmP63fyJ2oSpPktUmDcYlM0aD2PdkFOw0+cHdn6nAGu29uONw35j226pfvMnKth1MmBUyYvEHhjB5TVy25bem0gPciKlPZrZ0ygZFBEREdFoxeCIhoW5ullvvx/P724wqrd99+PX0NTcgvlXlqHqT7+PD3fvwZqtO7BxRT4eWODF1HFaoQOn4KMwT+vb4xQ05N32Q6ze+iw2rUDYmiN/UKJojLaNpTM8WLO1Hx4BtPcD21YV4Ic7LrsGO3p63orX+/DLP8kHoK2JemR7v6WH0eqtl9F2UcWK98bBe2NiFeb012jFe6ZqdbZt5XoVrLu7Al19PtcZHxZPICIiIopOODX1zEZCiB8A+G8ApgGoB/CUlHJPpPtUVVXJ6urq4dg9stl4oAk76s7izsppWHNDmXF5TWMXVr+4H607/h8g1EuoKN+DMRMmA73nsHGFtbhCd7/EQBAYN8aLvDv+r7AAxFwGe8LESbgk8zCmtxm9AxI5CnBFgcDGFfn4n3sGcKBlMHVPX1P0q3vyLQUWnrl1DFYv1IKrvL/txYd/OliA4aE3+1CQI9DYI1E00bkxrdl9107H25+1wGHCCF6PwKKZE3D+kg+N5/ugqhI5XgVr79KCoOKCXNS19EAAEUtuE2UaIUSNlLIq3ftBRETkZEQER0KIVQD+DcAPAOwN/ffPASyQUja53Y/BUWbS18rYZ0G++Y3bsW/3R+gdkCjMg6V3Udlj/y8WTC+CAPBZcw8ALc3smqmF+KPQuprFs4pR09iFLbXNRlDx8t89jVf+vw240K8Vfhj4cSFyPFoFA70a3eF2FeXFAn+zfIyR6rfrZAD3b+6DEMCFARj9kKaOE1i5YxzGf/fXlud001UTsWDaeLxefRr5uR48ufwqrLmhzLI/FdOLHAMet9eDKBsxOCIiokw2UoKjAwD+IKV8zHTZcQBvSin/h9v9GBxlt+v+9gO0X/Rh0rhcHPzxHcbliQYTRWMUbFuVb0ml23UygG/+W58xw2SeteryeVGYK/D6Cq9x+SP/G/jFP29AY/EibPy0CVJKPHzDLPz1t+Yn9bkTZSsGR0RElMmyPjgSQuQC6AOwWkr5huny5wBUSilvdrsvgyMy++Y3bsfn+z4KD4L6JO68yoNPGoPovgxj1kqVEptefRXP/OxpHPmyCfOvLMPTP30Gqx9+ON1PhShjMTgiIqJMNhKCo+kAzgC4WUq523T5WgAPSynn2W7/OIDHAaCsrGxxY2PjcO4uZThr6p7A0ptuxQcffIhxpjS+iwNAMMu/N0TpwuCIiIgy2airViel3ABgA6DNHKV5dyjD/Pb9neneBSIiIiJKEyXdO5AEHQCCAKbYLp8C4Nzw7w4REREREWWjrA+OpJQ+ADUA7rBddQeA3w//HhERERERUTYaKWl1/wjgFSHEpwB+B+D7AKYDeD6te0VERERERFljRARHUsrNQogSAD+G1gS2DsC3pJSstkBERERERDEZEcERAEgpfwngl+neDyIiIiIiyk5Zv+aIiIiIiIgoGbK+z9FQCCHaAWRi6t1EaFX4Rju+DoP4Wmj4OgzK1tdilpRyUrp3goiIyMmoDo4ylRCimk0S+TqY8bXQ8HUYxNeCiIgo+ZhWR0REREREBAZHREREREREABgcZaoN6d6BDMHXYRBfCw1fh0F8LYiIiJKMa46IiIiIiIjAmSMiIiIiIiIADI6IiIiIiIgAMDgiIiIiIiICwOCIiIiIiIgIAIMjIiIiIiIiAAyOiIiIiIiIADA4IiIiIiIiAsDgiIiIiIiICACDIyIiIiIiIgAMjoiIiIiIiAAwOCIiIiIiIgLA4IiIiIiIiAgAgyMiIiIiIiIADI6IiIiIiIgAMDgiIiIiIiICwOCIiIiIiIgIAIMjIiIiIiIiAAyOiIiIiIiIADA4IiIiIiIiAsDgiIiIiIiICACDIyIiIiIiIgAMjoiIiIiIiAAwOCIiIiIiIgLA4IiIiIiIiAgAgyMiIiIiIiIADI6IiIiIiIgAMDgiIiIiIiICwOCIiIiIiIgIAIMjIiIiIiIiAAyOiIiIiIiIADA4IiIiIiIiAsDgiIiIiIiICACDIyIiIiIiIgAMjoiIiIiIiAAwOCIiIiIiIgLA4IiIiIiIiAgAgyMiIiIiIiIADI6IiIiIiIgAMDgiIiIiIiICAHjTvQPpNHHiRDl79ux07wYR0ahRU1PTIaWclO79yDT8PSIiGl5uv0ejOjiaPXs2qqur070bRESjhhCiMd37kIn4e0RENLzcfo+YVkdERERERAQGR0RERERERAAYHBEREREREQFgcERERERERASAwREREREREREABkdEREREREQAGBwREWWFmsYuPLfrBGoau9K9K0SUIvyeE6XfqO5zRESUDWoau/DwS/vhC6jI9Sp49dElWDyrON27RURJxO85UWbgzBERUYbb39AJX0CFKgF/QMX+hs507xIRJRm/50SZgcEREVGGW1JeglyvAo8AcrwKlpSXpHuXiCjJ+D0nygwZnVYnhLgJwH8FsBjAdAB/LqV82XT9ywD+zHa3A1LKJcO1j0REqbZ4VjFefXQJ9jd0Ykl5CVNtiEYgfs+JMkNGB0cAxgGoA/Cb0D8nOwF8x/S3L9U7RTQS1DR28Uc4iyyeVcz3iYaM3/vMxu85UfpldHAkpXwPwHuAMUvkZEBKeW7YdopoBODCX6LRh997IqLoRsKao2VCiDYhxDEhxItCiMnp3iGiTOe28JdlZIlGpprGLjy78xgX/BMRRZHRM0cx+C2ArQBOApgN4G8BfCSEWCylHHC6gxDicQCPA0BZWdkw7SZRZtEX/voDqrHwl2eViYbXcP0e6d/tAb8KCUDhgn8iIldZHRxJKV8z/XlICFEDoBHAn0ALmpzuswHABgCoqqqSKd9JogzktPD3uV0nws4qMzgiSp3h+j3SZ4oltHSRr8+diKduv5rfbyIiB1kdHNlJKVuEEM0Arkr3vhANl0QXWNsX/jrNJhFR9rN/t5MdGLHIAxGNJCMqOBJCTAQwA8DZdO8L0XBIZiocy8gSjUyp/G4zHZeIRpqMDo6EEOMAzA39qQAoE0JcC+B86N86AFugBUOzAfxPAG0A3hrmXSVKC6fCCkMZmLCMLNHIlKrvdrKPQURE6Zbp1eqqAPxH6F8+gJ+F/n89gCCAhQC2AzgG4F8BHAWwVErZm5a9JRpm6eqozqp2RASk7xiU6XiMJMpeGR0cSSk/llIKh3+PSCn7pZR/LKWcLKXMlVLOCl1+Ot37TTRc9HSZv/jGvLB0lk2vvorKq2fD41FQefVsbHr11aQ8pp5G8w/vH8XDL+3njz/RKLZ4VjG+M+k0Aq8+geM//xP82R1/lLRjTbbiMZIou2V0Wh0RReeULrPp1Vfx9H95Ar+6U2LZqnHY29SO7/2XJwAAqx9+eEiPxzQaItJtevVV/Opv/wIv3ymxrCy5x5psxWMkUXbL6JkjIkrMMz97Gr+6U2L5HC9yPALL53jxqzslnvnZ00Pe9nCm0TA1hSizpfJY4yQbjglMNSTKbkLK0dvqp6qqSlZXV6d7N4iSzuNRcPlH45DjEcZl/qDEmJ9fRDCoDnn7w1G6l1WwRiYhRI2Usird+5FpsvX3KNXHGrNsOiawvDlR5nP7PeLMEdEINP/KMuxtClou29sUxPwry5Ky/cWzivHk8rkp/dF3Sk0hosyS6mONWTYdE4bjGElEqcHgiGgEevqnz+B7OwR2nQzAH5TYdTKA7+0QePqnz6R712LG1BSizDecxxoeE4hoOLAgA9EItPrhh9HQeQmP/P16NJ9pwfwry/DMPz2TVQuk2ZSWKPPpx5Qf/uxpHPm3pqQca9xS0nhMIKLhwDVHWZjjTRTNcOXmM6+e4sU1R84y4fcoE77P2bSuiIiym9vvEWeOiNIg1YOQ4Sglu/FAE9Zur4MqJQcxRFkuUlAynEHTUI5dmRDcEVH2Y3BENMziOTOa6I+9npvvD6gpyc2vaezC2u11CKjazLOPvTyIsppbUDKUmZxEjl+JHrs440REycLgiGiYxXpmdCg/9vHk5icygNnf0ImgOpiSqwjBxdFEWcwtKEl0JifR41ei64rcKtlxJomI4sXgiGiYuQ1CzEEKADy78xgG/CokhpZeAgDP7TrhOEBIdBZrSXkJcrwKfAEVHkVg/b2VHHwQZamNB5qwo+4sHlk6G4X5OZbjRnFBruV4VVyQG/F4oh8jhpIet3hWcdzHE/txtbffj1Uv7ENQlcjL4UwSEcWOwRHRMHM6M2oOUrweBZASAVVCQqu3H21QYua2Lad1BLEGYPYgau1dFYCUEAA8Apg3tTAlrxURpdbGA0340VuHAAB7jnfg+zeVY0ttM96saUYgOPh97+rzobggF+vfrXddl2Q/RqQytdfOfFwtLsi1pv36mfZLRLFjcESE4V/Iaz8zaj/LCkALjATw9bkTcWflNNdBiZ3bttzWEZgDMLcBjH2bO+rOGsGbPyjxl69/hsdvuhJrbkh+40ciSp3NB5ssf7+wuwGAdswAtO97V58PTy6fi+d2nXCdDTIfIwb8KupberD2rgrsqDuLOyunDetx9bldJ6CaKvEqSmal/bJwBFFmY3BEo14mLOQ1p4R4QrM9QVUix6vgqduvjitFJdK2nNYR6AHYU7dfHdM2c7wK7qychoOnzhuzTqc6+4yzzwyQiLLHlPFjAPQYf5ubewhYT5pEKpawpLwEXo9inHDZfLAJiqIgEFRx8NR5zJtaOGzHVX0/fQEVisistN9M+L0hosgYHNGoNxxlr6Oxp9rp+2U+sxhrikos27IEUIpA2RUFce3f4lnFmDe1EH/5+mc41dln3G5H3VkGR0RZ5Imbr8RHR9sQCIbSZLXzKfAoAg9WzcSKRaXGcSNSsYTFs4rxwOJSbDrQBAkgqAJBNbE1k0OVyc1iM+H3hogiY3BEo16qy17Hyp5qN5TO8E4LmvXqTfp1rz66xFhbsOnTJmypbY54FtNp/x6/6UpjxggA7qycFvsTTiKmqRA5i/bdWDyrGOvvqTR6limKggcWl2KlKSiy397tO7ZyUSm21jYbJ10gBAIBFUIIFBfkJv25RZJIUYfhkCm/N0TkjsERjXrDcZYxGYP3RH/s3dI4Fs8qxv6GTgSCiZ/F1GeJ9HUF6Zg1YpoKkbNYvxtdfT6oUkKVQDCoYsaE/IQawNqPpUfP9RpB1/p364c1tS5TZfKsFhFpGBwRIbVnGdM9eI+UxlFckAtFCADS9Sym2+DIfHk6U+mYpkLkLNbvRqT2AvYKdF19voiDevOxdH9DpxF0xfLdzLQZ4FTtT6bOahGRhsERUZzi/cFM9+BdD4CklEZ6S01jF7bWNuON6tMIqhIeRWDtXRVGJTvzeiWnwC7dAZ/ZaE9TybQBJWUOe3GWM939qGnssnxOzD2OegcCloIM5mOXL6Aas0Cxfufj+W4OxzElnu9KJh3jRiMe1yidGBwRxSGRH8yhDt71QEYCrusAIt13/bv1CIbKbgdUiXVv1wFCwB+qKgUAUkrUtfTgR28dwps1g2sGll8z2TGwS3fAZzaa01Q4gKNI9O+GfiLktU+bsNW0ttDe48irAKqEcRvzsQtCGH2D4pkFijbbpN/uTHd/2DEFCC8mk6h4vyuZdIwbbXhco3RjcEQUh0R+MIcyeK9p7MLqF7UfCQB4s/o0Nj2+NOZt6PtrPhvsD0pI0yVahSphBEX6NQFV4qMv2uBVRFgp8OGYrYl3rcNo/PHkAI6iMdYWquHpbTvqzlpuGzrMGLd5cvlcI7jaXH3auJ0nSt+gWAe39obV5mNNcUHukAfI5mOI23elprELW2qbIQBLZb7RPiOdTjyuUboxOCKKQ6I/mE6Dd3v6mlMgsL+h02jkCmiBjdMPhVsgYe73oUotEDIHSjkerVyvALDp0ybLdYA2o/TgdWWQ0O5rfj6pnK0xD5r0PiUsER6OAziKpqaxCy3d/Y4nOe6snIY9xzuM2yrQjg/m9Ft9BkcNzRoJAA9WzUzKrIv5dsGgioeuL8P0CfkRg5lYn7M+WxZQpbFeyv5dqWnswuoN++ALas/tjZpmbHpssGCN/RjHVK/hweMapRuDI6I4JBIU2H9Q9TOVb9Y0IxBU4dVL3gbDFz1rjRUF/KEfbwmgt9+P53adMH4w7IMA8xlW8/4WF+RiR91Z/O5EB0LjHNwybzJ+fv9C1DR24bVPmyz7LaD1VqqYXoT179bDF1At5b5TOVtjHhipUmLt9rq0VLrK9MHQaE4ppOjsMzOrrp+JyulFRsCz5oYyNHVewrbPzqD94gBUFaEeRRLr3qkHpIQ/KKEIQFEERCi4WrGo1Ni+U8pvrINb++0qphehvqUHW2qbUTm9KKEBsv6c9QbVgBZc1bX0YOWiUsu+PrfrhHFs1W9nDsLMxzimeg0fHtco3RgcUVwyfbA4HOIJCpyqPa1/t976wx2UQCjRzecPX/T8YNVMbDwwGLi8tPckVCnhDXVr1NLkQtsKBTDm98i8v/OmFuJAQ6dxpnTX0TY8/dYhVEwvgqIIBEOXexVg1XVlWLGoNGI6Sqo+C0vKS6AIAVVq+6OqMuY1CMnar2wZDI3WlEKKzj4z0947YDm+PLJ0Nl7ae9JYk6jTG7fqlwUl4JHAquvLsDIUGP3orUN4o/q0EVyYU35jHdzaT96se6feSCHO9Qisu6cyanU8t+es77s5bVg/AaU/hyXlJcjxCON46PUIx6IV9tcyE1K9Mv23eKj7x+MapRODI4pZtgwWUyme4gg1jV14ducxyw/qjrqzYT/cOR5t5igY1Jol6qVvB/wqttY2Y3ye9WtqXhQNIOIg4JGls7GvoRNTxo/BEzdficWzivFg1Uy8Ggq2AkGJjQea4FEGF1sDWmD0zP0Ljb+d0lGS8Vlw+wFdPKsY6+8NNaZUJXJzYluDkMzPaKYNhojiZZ6ZEYrAziOtCJ1vwIBfxYY9DVCl830lAEXAuF5VJWZMyAeAsJkZAPAFJbbUNjueOImUQqz/e27XibAU4q4+H55cPjfq89Qr7t1ZOc3ynBVFYMG08Zgyfgx2Hmm1HFf1x930+FJsqW1GR+8APj7aFla0wum1jDSTNRxBS6b/Fmf6/hFFw+CIYjYaB4v2H/VYiyPYUzsEtDz+imnjcfDUeaMa3INVM40UFfvZUwlgc/VpSJfRi6IIeIQW4EAA5ZPGoXziWLx/uBUAcNmv4vndDaFb92DX0Tb87J5KHG/ttWxHr2JnVmgKyBbPKsbauyqMwYc+kBnqZ8H8GnmU8HVFa24ow7yphZaUQP31dHvMZH5GmfdO2U6fmXnhky+N44LBFPg4EQCqZhXj01NdALTjRHFBrmORF92bNVo6nJ6Ga54t11P79NlujyLw6LI5KMzPcU0h/vx0N2oatcd3Czh+8d4R4zi353gHfn7/QkuFvkNnenDk7AV4FAE1NMv+RvVpo/iCOTjTAyinY0css2HJCApiCa4SPc4N12zTaBwr0MjC4IhilmmDxVQf6O0/dCsWlcZUHAHQ1gFZAyMtj//lfadcS9vq/1/X0oNNB7TiCIFghNGLlPjusnJs2K2d/T3RdhFftl10vbk/KPGTbYcQaZO6+rMXjNfAvD7q4KnzmDe1MCmfhf0NncZrFFAlfrK9zlgXYM75BwZ7LUloi8bdHjOR/Yo0e5UNee+Znl5D6bfTHhgBgIRRrMWJAHDVlEIcPNVlfO/045bRO0kRKCsZixOh404wODg7rkotTXjD7i8tvZJ0AVXi+d0NUARcU4g/ONyKj4+2GcfCHK9iFEwAtM/+hj0NMNtRdxZrbiizVOgLqBILZxThD809xpoq+7E7lmNHtFSvSEFBLM20Aee+cnaJHueGazYn08YKRPFicEQxy6TB4nAc6O0/dALaoFz/gfcoQEsoP12/vf4j8Eb1aePMqqJoDVj1GY9oqSKV04ugCEQNYlQJbPvsDMxDm0h3MafIRHNn5TTXhc3mEr+JlifXZ4PM6XxBVWLTgfCUlq21zbjs156lAPD1qybiqduvdnzMeD+j0T5HmZ73zvQVcmIecG+pbYZT+CMBXFtahOrGLsfjggRw4OR5eDwC0lTlzv4dO3qu10h/zfEquLNyGg6eOg+fX4UKoLGzL+JxST++6uW0vcpgSXEJWNZU+gIqXvjkS3x15gSjop20bfzOymkAtFkuIyVQAkvLS3C0tdd1wJ7o75v5tXYLCty+p/bLVy4qjWnGxWk2P5rhnM3JpLECUSIyPjgSQtwE4L8CWAxgOoA/l1K+bLpeAPgpgMcBFAM4AOBJKWX98O/tyJcpg8XhONDbf+hWLCrFikWl2FrbjLbeAXxyrB2bPm3CG9WnLdXmViwqNQb8AsCckgI0dfUjGAz/UXbKzV//bn3UwEgvyX3uwkDU5zF30lgj5e7FPQ3GtoVA2MBi6vg8/OfbrsaaG8qM1DnL+ijT/ifyWbBXz/qjsgmobeqGGloQbk+Zq2nswuaDg2eSJRB1MBDPfmV7+ke27z8ln33AfdNVkyLe1n4M0EnAmBG6fnYxJhTkYkttM4DB75h+vFKlhFAEbgw91spFpag702PM1ESiCEAoApsPnjaOA8Z1CM26my788Egrdh5pNVL29BNWQgBP3FhupOZ29fmM46QCoDA/J+qAPd5jmlPQ4/QYbt9T++US4es73R5XT1XUZ/Oj7fdwz+ZkyliBKBEZHxwBGAegDsBvQv/s/grAXwJ4BMBRAGsBfCCEmCel7HW4PQ2TVFczS/WB3u3sl56f/qGen26qNqfPMJl7C33Zfgk5HoGHri+zNBl0qmSnr6uJ5KarJqKn34/Pm3uiPgcB4P5FpVhSXoKHX9oPVQIeAdw2fwpumTcZ696uMyo15XgEnnt4sbF/2hqAUPqMR2BVaH3UUN5L82DAF1BRfaoLOR6B2xZMwcdH28L6sOxv6ETQ9HIIaIOeZFlSXgKvIow1EMn+HKU65Y3pK2RnH3BHokrnkyR2+rojwLrW0vxYkBIfHG7FB4dbtdLfIvJMNqDNvt92zRR8eKQ17ISQIoCvz52IOyunYd3bdUZJcVXCqOy5+WATVDU0q68I3FEx1TIznZdj/W64Ddhj+Z6aiz7oAZhT0PPk8rlh23D7ntovX7moFCtDFUKTveYoWbM5TOOl0SDjgyMp5XsA3gMAIcTL5utCs0ZPAfiFlHJL6LI/A9AGYA2AF4ZzX2lQqtN9kjltH+lg7/Zjas+716vNmWeYnt15DHuPdxipIfr29Md8ducxI2XNXMI72oDidyc6cNv8KQCiB0cSwFv/cQafn+62zAJ9deYEo+CBU3f4wQ1o91Dcro/A6XUtLsiFIgbTDPX8/6/OnIAnbr4y7Pb2Urv2VJWhpMAY9xGh88tCxPzcYn2sVKe8MX2F7PTvGKSEx6Og9cJly/WlE8bgbM9lBENBhpRaIDKzuACN5/uibt+81lI/Dtor16nSGnApQivu0NY7AClhPI6qAg3tF8MCI/0Ek54+ay7Msv7deiNlz3yCKKhKbK1txpbaZssJJ6f1nfpaSgFY+ri5fU83HmjCj946BABG09w1N5TFfHIi0ok2t8sjsT9ucUGu0fsuWbPqTlJdpZQoU2R8cBTFHABTAbyvXyCl7BdC7AbwNTA4SpvhSPeJdKCP9eC78UAT1m6vQ1CVyMuJfrA3b9f8owaEV1N66varceDkeSMoefVAEwrzvCgrGWs8pl6wAaGCDbEsCQpKoPXCZSiAZS2BEhrj288Vn2i7iBNtF+H1DDZxjCU1Tl/Q7LaAORKnH1EAWsqgKrWGkpCQEhHP6i6eNVhq1xzARfqRjrTw2X6f/Q2dCAS19ycYTO7ndLhS3pi+Qjp7mpuqqmEzzC09l8PWGKkSaDrfF9O6xByPdYZ15aJStIfKYAeCEiq0Y5He3Fr/DlSHCjuYNy8BnGi/FPYYioCRDuj0fd6w+0vLWiY95VcClu+c0/rOmsYurN6wzzjh4lGEkc7n9j3dUXc27O81N5TFdHLCvP9Oa00T+f6aH9cIGIdh3WEyjmlcJ0nZINuDo6mh/9pL8bQCmOF0ByHE49DWJ6GsrMzpJpQE6Uz3ifXgW9PYhbXb64z1QT5/5IO903btP3Z6o1J9G2VXFBh5+wDw/O4GIw9ep5+9dXPp8C4E9r2Cns52FJVMgnfpd/A5lltu41EE/ubeStS39Bg9jOymFOahfNK4iGt2YllcbL+dHqyY/3b6EQUwOHslJVZdX4bpE/JjOtsJDL62gLUaoH2Nktt777RPqfycMuWNokn275H5My6kxEWHY8fYBcsd7yuhBTRqhAWPs64owNevmgjAtn5QEbh25gQMBFQsLS8xynO/su8Utn3WAiD8pE0kQalVqvvwCy3VFhhsCmtuoq0IreBNxbTxWHWdNhP+ZqgxrVua7P6GTmMmH9D6N3lCRXPcZqbvrJxmzBgBg0UfgOgn6VJV2lt/3GS0VYhVsqqUcp0kZbpsD47iJqXcAGADAFRVVcVYu4vilc50n1gPvvsbOqGaohLF4cfU/MMUrUyrff3Q+nfrjSprZvF86C4d3gXvnufw+j0KlpWNw96mi1jz9nO4BFgGOaoqUd/Sg4rpRcgx9QoxO9N9GWe6L+PAycEFvGF9nDbsM3L7/+a+hY7vodtzNQ8A3H5E7QUunNJX7Hn9To9nrgbo8Qw2pjWnKtrfI6d9SuXnlClvFE2yf4/0z7gvoKK3PrZjh5nTccOs8XwfGg804fWDp3HrNZMH04KD0liXdOTsBWNN0pOv1sS1/+aZK33GWucLSmw+2GQp6b9wRhGOnOvFoTM9ONpaj7V3VRhpsiq0kyiANU3NKVX3u1+bjfqzF4wTR05Bzc/vXxh2bIrG7SRRsqpp6s9nuE7CJOOYxpNGlA2yPTg6F/rvFADm0+VTTNdRmqQr3SfWg695IKEIrQlppDSstXdVuG7X/CM4EFoo7NY/JB6Bfa/g9XsULJ+jfVWXz/Fi4z0BrHjvFcA0wJHQAou8HAXL503GB4dbXYMwX0A1Bg3mynFlxfnGgCEogR+/dQirbygLC2LsP/jmvibRSn1H+mF1y+t3ejxzNcAHFpdanos+cLK/R5Hy+1P1OWXKGw0n/TP+7M5jePel2I4diQioMrypbIh5TdLMKwpiqqipU+XgbJBTj7cp48dYynFXzijCoTM9RoGXHXVnjTTZQFDi1QNN2HzwNNbfW2msW1pSXmJJ1TWvOdIrv7kVWoglKIo0+15ckBvXTFIsJ/qG+yTMUI9pPGlE2SDbg6OT0IKgOwAcBAAhxBgANwL4b2ncL0qjWA++0W5n/2Hq6vMZndftP9t6ZTd9cF7f0mP8PRQ9ne1YVjbOctmyMo+WJmO7rQSMM7l5OYqxaNmJRHjlOHvuvwotYNli6ztk/8HX+5rYg0a3NURua4Pc8vqjPZ5e3Ul/LnqVK6deSAxWhoYLqTPf4lnFqJg2Hq/GcexIJiG0ohAA8Nd3zseDz//eso7JnlZsp0rg9nmTAcASgHkU4Imbr7QUbjl6rtfSy6hi2nhjnacuoGrNrz0exWi3oM8EAXBMS0t0diNaae94U8riKfiweFYxNh5owrM7j8U1u5UOPA5Tpsv44EgIMQ6AvrBDAVAmhLgWwHkpZZMQ4lkAPxJCfAHgGIAfA7gIYGMadpdSKJ6BWawHX7fb1TR24Ux3P7weJaw/kV4Nyd6stKw43wgwpNRmNOrP9FgWROd5FQzEETAVlUzC3qaLxtlfANjbFERRiXPvEgktV3/+1ELkehXHct8CWqPZeaHb2CtN2bdn/xG3B5WAtihbhv4brTCCfp19EOGW1+8UxJrPAuvbNg8i3JrEUuK4kDo7/OK9I3h+d0Pcx45kUSXwk23aDPCaG8pw2/wp+MAU5Fw5aSxOdV5CpMPgxMI8/Pz+hdh4oAm/3tsACIHvfn2OEQDohQjMvYwAoKHjkuMCzqAE1EDq022jlfY+eq7XqCQYS9AVz364zbwTUfwyPjgCUAVgl+nvn4X+/Su03kZ/ByAfwHMYbAL7DfY4GlmGOjCLJ7AyP5YigMoZRVh1XZmx+NVcflvPIV/1wu8tP/YeRRg9K1a/uN84kxlPYAQA3qXfwZq3n8PGewJYVubB3qYg1rytwnvjdyLe78i5XngUOFafkgDWvl2HVVUzsfauCtS39OCN6tNafr8Qljx/vQqU/UdcDyr1yk/+oESOR3vO9tfQ6f1yG0QAcMzrtwexTn8zVSO1uJA689U0dmHDngYAiR87kiEogR+HAqQeW1+y8knjcPv8KXi9phnnL2nXKUI71qgSluPIvKmFaO7uhy+gYt3bddj2H83G2qY9xztw/exieDyDKXg7D7eGyn9aeRVAUcJPdAHJTbeNVsRGrySoKAJr76oY0gk8O7eZdyKKX8YHR1LKj+F4uDOulwDWhf7RCDWUgVm8gdX+hk4jAFIl8IdmbbHvvKmFKC7INc5SqgA+P92Nz053h50FfbBqpnGWs+yKAjR1XjLW88Rj7ILluARgxXumilM3ulecMguqwNxJY9HQcSksQNLz8XM8ArfMm4xb5k3GpMK8wfx7v9Zx/rb5U/DEzVe6vl5bapuN5+ULSmypbTaq1dmDSPuiaPsgoqaxC119voRnfZiqkVpcSJ359jd0GhMn9mNH8cTJUG78P2I6dpjlmooXxEOVMGYyzLr6fHh+d2vYbb0egdVVMy2zz5bUX1PRB92np7q0Fgb6dqCll5hnkwSAVddpayf1GSd7VdFkHTsinaQxPxdIiR11Z43COMkQqaIeEcUn44MjImBoAzN7sYStoQG8G3MABFhTywDrbMwHh1uhKNbYXe8Mr6e3DNXYBcuBBcsTWifwZfslCOGe5+8PSiPlJTdUQe6RpbOxYU8DVAnsPt6OJ26+0nX79rMW9Wd6UNPYFRZEfna6GzWNXRFT80ZDylY2r9nh7Fzms1diG8qxQ5dIYOTGI+C6DjMYlJgxId/xJErE1F+HmfErJ41F4/k+qKG+buaiMsPRmNkptdgoABRaC/q7Ex04eOp8zPugb0tPJ7R/B/VZongr6hFROAZHlJHsg8ihDMzsxRI2V592LCOtP+6OurNhZx71SkP1LT3wKlqpbAk49hEpXLAcr33aFFfJ7mTT9z9aDyUzf2gd1eaDp43gb8Cv4tmdx/DU7VcDCC9Bu2JRKV4P9RUBtFm2h1/aj5WLSi1B5M7DrfjkaBserJppvPbmQcRw9upIV4AyEtbscHYusy2eVYwHq2Zaep059UmLd/YoFvo5IrcmsgLAYzeWo6xkLD5vDp9RUgTQ2+/Hc7tOWBprr72rAnUtPXjt0ybHbSuKNkuuk1I7KZTjEXjoemu1zeFMDXUrzvDszmP43YmOuPbBvC1Vaq+lU9PyNTeUDTkoyuYTOETJwuCIMo7bIDLRgdniWcW45epJRuWjQFA6zh6ZH1cvB+31KnhgcSkqpxdh3dt1WnNBj8DtC6bg3a2bHfuI9MK9j8hQeT3OJW7NPIrAY8vm4KW9J42S12ZO65AArXxuW++AZc2RBLD3eAcONHQCQliqPemvn3n2SJ9lk4DljK/eC8Wp+h2Q+MygWzNat7Or6QxQuGaHhsOKRaXYXH0agaCMuU9avDwKMDbXiwuXA8ZlVbOK8YczPY693QDtGLBhTwPu+ep0KLA2hRWhY5LeJDvHIyzHm7V3VUBxaVAbdHg4vUfSdJeZKF9AhRDCqKoXr1gCCHs1UP0k01O3X+1Y3TMSS0oenAvlJMNIOIFDlAxKuneAyM6tcV4iahq78NyuE2GzONLhNltDVej0M3NlJQVYd3cFfn7/QtS19MAXmi0KBCUEgMu/+w02hvqI5HhEqI+IgsC+VxLa13G5nsjX53mw+fGluO/a6ZE3JCUK83Ow/t5KeBVhCV70xok6AW1dkkcRUFWJj75og2I7Kkho6Xd+h/dkS21zWONIETqF/MjS2fhKaRG8nsF9sKco6vSZwb/4xry40kwefmk//uH9o3j4pf3YeKAJD7+0H3//70fxo7cOGZfXNA6uU0jmZyte+sDMI5yLXBAlw+JZxfh21UwAWp+0ZB6jdHMmjsMlX8ByWU1TFxbOKIIty9hClcC2z1rCAiPzTL1+vDEHFjvqzkJ1m5JyEKmQzNq7KqCECs+se7sOT791yHKMiMZ+3HG7r/59109G7TnegdUb9gFA3Mc687YA5z5uyZDO4yNRJuHMEWWcZC38Np8F83oUeEPpF25V1QS0WRcEte7qjZ19WLu9DkD42pqGjktx9SCKxUVfMOL1lwaC+KD+HN79w2BVIgHgjgVTMLEwD2/WNBvVmPSZk/X3VuLjo2348EgrZGjR85TxY5DruYBgKB//hvISNHRcCutIb34M/UyuudpTTWMX3qwJ7/kkVYlNB7S0QkUAXkXg1gVT8PGxdsdqUTqnmcFIZ2jdmtEaa50cZmjSWVSAa3ZouPQNaIFLso9RuhNtF8MuC6rAwVOxBxk6RQAeRetBpEpt4K+YZsi1taJBeBUtoBFCOM6I27fpVg2uq88HVUrLbPYbNc14YHGppRiEm1hngPXv+/p36o2WCnrRmp/fv9D1cWoau4xeeitNKcj6scNtVjwZWHSFSMPgiDJOPIPIWAfPwaCKh64vw/QJ+ZYUrGd3HrMs9pVBicnj83DuwoA2S6RK/GR7He7+irXyT0fvQEJ9RIaS/y+BsAIPHkVYCiYIWDu+exUtqJHQZnRUADuPaEUkKmcUYakeGLmMNbzKYKUn/TXVqz21dPcjYMtp0WegLAFKUGJiYR42PRbfe1pckGs8D3OKh/l6p+aw+oJnxWGGJhUBSir6bxElauOBJmz/rAVAbH3ShmtNkiup9YSbMSHfGPif6e43TrAAWlU6jyKw6voyjM/z4oXdDWEnZSyzT1ILgpzYizxIaLNTmw40YWttM9beVWEEH0D4Okt7AFFckGusk7J/txfPKkbljCJLv7kIE2taawRT64fNnzbhb+5biDU3lA3LsYMncIg0DI4oJsO9SDOWH4Jo+dH2H7EVtgalD7+0Pyw/XgVw7sKA5bKgKsPSC7r7/XH3EUlF/v9doaDNmCFTBA6UnDeel5bypgUrQpqClqDE5809jk1iLYQIK15hfiwRamiou+2aydh9vN0IUABt8PFmTTNWLio1ehm5sfaY0s4U21PxzO+5PpDRB1X2v90GLMn6DDNHnzJJTWMX1m6vM77n0Y5RqVqT5MR8qNADGT09zD5jU9PYhTerT1sq5QVViROtvfisucex2I35MhVwXU+kBwBbapvxZk2zsUZSbzuwdnsdVCnh9SiAlAio0nKsWVJeYpnFMZ/AcTr+rFhUijdCj6P/DrnZ39AJv6maX1ACa7fXJbXkdzQ8gUPE4IhikKkDQLf0BnMg53YWbEtts+vCYSdlVxSEBU1OPYgm3vFd+MuXOW4jsO8VvB7K/wcQyv8PYMV7rwAJDkS2fdaCS77gYE+hoLSkvAihFVqQqtZ40L4+yM5e8jsYlJa0EctsnCpx6/wp2PVFG1RVIjdHwRM3X4knbr4S+xs68fnpbnxwuFVL1wvGtnjYuvBYwqMISFM3eft7rg9AWGQhMlagGh32N3RCNZ2siNYnLRXHJCcCwIyiMRiT40HljCJ0XvKhYtp4FObnGDM09tmXspKxYel7R85esJQC92hZ0I6PV9/ifuJHDwAqpxfhJ9vrjHRirTCENL7PwODMkhE0KcKoumn+/l/2q/jJ9jpj5lwRMI5Hsc6aLykvQU6oYIROlTJjjytEIxWDI4oqlgGgefCl3yfVAzG3RqL2gbJ9tkJfK2MmAHyltAiHz15AICgtAYLXI7CorBjVjV1hVd7sfUT8Efa3p7MNy8oKLZclI///9yc6XMuGqxLwCoEHrp+JE629YU0UzRShBYGnOvuMyzweYbyu9lQ2jyIwuTAP6++tDJul0YPU3cfb48pfN7+nHo+CW66ehImFeZYzy/b3PJ0BSjw5+iwhTqlmblugi9TrKJE1SYmk4UkAzd2XAQAn2i8BgNHjB4Bltviur0zD25+3OFbUHJPjQe/A4NpMt3M9EsAbppYNblUtW7r7LYUebps/xThmeUIzR/rstb7OyVx1c+1dFZbX27xm03w8enL53Ji+c4tnFWPTY0vwwidfautEoR3vuPaHaHgxOKKoog0A7YUPzKkI5oFYsgeHenrE8598ibYLl3H0XC+6+nyDsyh+59mk/Q2dYWtl8nIUrLquDOverrMEGgLA8nmT8dLek679O2Jx6fAujM8T2NsUjGuNUkzbjlLIIRhUMWNCPj61pQZOHZ+H/3zb1fj4aBt2Hm6FKmEJjADg1nmTjfQTc1ndupYevFnTjE2fNrkOuPXKUHpTwlgHB68+ugRba5vxRvVp7DzSitxQ2o35evvnKNOLLNgDFHOKTqoDlWyZ3aIkibWxGWJbk5TjGZxxTmYant5DreyKAuPzqUqJbaH1Uk46LvpcG1rb+YMS69+px6rrysJS3/S/9YbduvKJYzGxMA8dvQOYVJiHiulF+Phom9EGQqfPJnX1+fDA4lLL+iidXuAn3uPR4lnF2PCnVRF/L+P5LeWsMVH8GBxRVNEGgPbBFxDehyHZZ6/1A35vvx8fhH64Pm8+hPuunT64rgZa3rnTwNR8ts8jtLLTO+rOhqWdSQBHWnocq7jFI7DvFfyf1+Xge2/341f35Bv5/6u3XoZ3+X8a0rbd6GVf9UXDp85bA5/7rp2BNTeUoavPZ7yGZl6PwMdH2yx5//6AirqWHpw+32dUl4o0m6gPQg6eOh9z3vziWcVaAKtKx+075cSvXFRqqe40nGLJ0bf3PNFTdIZjJocVqEaPrbXNlu9rNLGsmzQfE5OZhicB/O5EBw5Eqv3tcB87t2BJAvi8uQd1Zw5BlYO/SXpVS1Va40gBrQ+TfqjXK21eMdZ57ZIqtd+XJeUl2FrbbMym3zJvMnYdbdOq7YnYn5ud23Elnt/SZPzuMrii0YjBEcUk0gDQngqlpyKYB2LJPHu98UAT1obyxO2/PZ+d7jb6SggAO+rOaj2KbOtUHlhcio2hLvJBCbywpwGQzj+yejpIJNHOZvZ0tuOnN49DxSQPfrjjMo50qJg/UUHbRRVlKaoMpUot8LvpqkmDP9YmL+87hTsqpmJJeQk8Ds1lZ19RYKTAGAQsi5j1s6NOFZuG8p7bP1NnuvtR09jlGICZf/xXRljsnE7m5yMcCk2kctDBClSjQ01jFzYfbIrrPtHWJNkluzS4Xs2yeGwOzl+KlJTsTACYXpyPM139ER/DvHbRXtVSJ2ENllSppdDZ15rqFAB1LT2WQjB6ZsLOI/GttYxHPMfVof7uMiWXRisGRzRk9sEXEL386VB6F63dXmfkf9szSL5ZMRUv7ztl/PD97kRHqMeRNvjXu6LbKxnFkYniKNrd9fQVs8sBiYLCQpd7JEdQIiwlROcPqHjhky/R7w9iRlE+Gm0zS+WTxqGh45IlnXDSuDy09Q5YGjZKAOvergtLpdTXP+gBTrT33H6G0pxe99qnWpld+49zqlPGknXW1N6nZP279cM6k8MKVCOfNtsa//30NUne0Fqiznf/EYF9rziuJUqkfUE0EkCXQ2A0Y8IYtPUORCwi4/EITC8aEzE4yvEIrLun0lKe+8arJuFQczdaLwzElKInABQV5OCWqyfht/XnjFkiPd3Y61HwwGLtxEyqZ2rj2b5+W59fNX774pGs4ytnnyjbMDiipLAPvpzWn7idvY7nwGmvxuRVBB5dNgf1Zy/gzsppWHNDGe6omGo03tN7HC2epRVUCKoS69+tx01XDW2dT7y8S7+DFW/+C8bnBPDyvYNpdWu2Xcalw7uSWjb3q6VFqG/piTpQUhThGjgpAnji5itRPnGspbfSfdfOwMv7Tll6Q+kzTo4zIaH3SlVVbK3VimDEkyrilF4HDAbfqRyIJPusqfk7Mm9qIQcLlFS9/fHPvOhiXUsUb/uCWNkDlByPlp626dPIM2HBoERxQa6RLWA2d/I4zJk4FpML84yU3prGLqzesM+SeqgIwOtRoEqJYFBLObCfLJMAuvv8+G39OWOWqKW7H5s+bTJSZTcdaMLrB09j/b2VKZ2pjWcmWF/3qafxrn+3Pq6y4Mk4vrodRxkwUSZjcERxS/Sg5nT2Ot4BqHEmLFTZaP29lVhzQ5mxred2nUBxQS6OnL1g3EdRBA6e6jJ+gAf8Kj484hwUpMrYBcvRvftFvHxvwJqvfx+SXja34+IASosLwoormCkCmDze/Yzr39630Hi/ykrGYvPBJkwZPwZ3VEzFHRVTjSINwWDkVMqAUekJRoUnp/fY7QylU8NF++clVQORaGdNh/LjzpkcSrZ60zEvXrGuJYolDS/WggmR+IMStY1dYX3U7CSAj462ORbLmTNxLPYcb4cvoBrHnf0NnWEzUV+fOxF3Vk7DurfrEISWiqx4FASDKoQiEDRVLx3wq6hv6cH0CfmomF4U1kw2oEqs3V6HzU8sjdrTLV72440eYDg1oDXftqvPZylPHs/sTzJScp2OowCYrkcZjcERxSXZZ9PjmbbXD/iPLJ1tzBTNm1qIp986hLbeAXxyrB2B4GDzUED7obYHARLhJWCvn12M2tPdYetukunChd6k5uu7OeOyRmriuFx0XAx1jZdAi0tgZF8fPW9qIY629uLQmR58+EUbFpdNwISCXNx89SRMLswzmhrqKWP6j59TJ3q399jtDKX9x9np8xJrmdx4RTpr6vQ90F8DngmldBjKzFE8a4kilQYHtO95lJjGYmJhLjp6fWGXHznXi1jKGbgdswVgOVZsrW3W+g8pgLlY6YA/iI+PtsEfCoKkBB5YXIoZE/Jxprsfmw4Mzl5JAJurT0NVtX5Ht8ybDAD48Eir8Zuiqs59iYbS7sLteGMuga6fKHQqQDSU2Z+hnshxOo6ygiZlOgZHFBd71a1ndx7DU7dfnfCBLdZpe/MBXy+2cKChUxtwh/04WpuHxvIrfb7Pr6VUpFAq8vVjtWBaoaW4gh6sOFHlYFd2AHh257HBNDopLb2SvIr23xWLSrGkvASrX9xvvJebHlvi2IneaRAX6Qyl/cd5uCqvRdon+4/71tpmbKltxoBfW4tgntEkSrWNB5rwWXNPwvdP9rEpnjWcfQMB9+3Y/p6Q78V1c0rw0RdtkFIaxU2cfPRFK7yhGSCPR8Eb1acRUGVYwGXv/eZRhFH1cqNDiW59JskXlPjgcCvychQ8dmO51u4h1AxbPy6Z+8PplTu9igCEMFojOJ1gtM8SmY83A37teDN9Qr6lBLp+zLbftq6lJ60FWTKt/QJRLBgcUVzMaW2qBPYe7zCa+SVy0HU7cEb6cQBgBEX2Hy4BLX/8lqu1H/WJhXk40drrOpuis3did2NvgBgsq4KnqTqmhoipytd3o+fhKwKYUVyAI2d7jeuijV0CqtYj5MjZC46v8+DtgFdD6XI3XTXJKI/uCwUMz9yvpeeNz/Pi+d0NkBJ4fncDykrGhgUPsZyhjCXNI5m57G77ZA/qJWAEkHpqTTy5/URDsaPuLC4d3oX+jzdADPTikg8YXzQeOTc9FtN6xuE+Npn1+WKvInHZr912TkkByieNQ/3ZC66pwQEVmFuSjxvKSyABvBZaH6QIOK5R0l07c4Ix+13XYg04FQBe72AbCH02vDA/B5ufWBrWaNY8s2NUqAxqp6bcZtKdZonMzX0ltAa36+6phCKEsQZXn7FaUl4CryLgCx2336xpxspFpUlP84uH05pkVtCkTMbgiOKiH9Se3XkMe493JKUcsf3A6fbjYA7KFGh9eMwzR14FuPWaKVpT0yOtxgxTjkfAo7ifYYyVvmh52RQ/Prko0d3RhsLe9zD3CoHfPx29IWK8ZXN1eg6/EvpDf16Rns38qYUovaIAH33RBlWV+PhoW9zrAD43nYnWz7a6bcPnV9F6wRqAmm9rXw+xo+6sZa1YtGaHxQW5lqapsfT18CoCD1bNxIoU9D5yqtD4+sHTRhVFVTqn1jg9Nw4OaKiKzhxA4MN/QUlOAC8/VBAKcAJYs+1fcAnAwJkjEIf/Hb2Xgygc44Fc8Me44o4fGPdP9Ng03C4HVKMnW1ibAQcn2i+hubvf6G3nD2iV5b77tdl4cU9DWHo1oM0kHTzVhbwcJaxwz+0LpuCWeZPxk1ArCUBLIWzp1gI0cwBiPaE3mM3gMc0cmSvI6ceDM939jqnD5mazQVWiq8+H9fdWasUWTDNWi2cV48GqmcasVyrKiScD111SJmNwRHFbPKsYT91+NQ6eOp+SaXG3dSXmUshdfT4UF+SivqUH7b0DmFiYh5WLSo0eE/YZpq+UahnynzuknsS6gDiw7xUsm+LH/jMqtny7YPAM69Z+/MW/X8b/+lZ+1IaI0fL1zfJzFMybUmiky6j6E3LZXxF6Il6PwJftF/HFud6winKxUELrBfR7CAB5OVruel1LD0609uJE+0VLXxJFEVh1XRmOnK2DPyjhUbT76b2JKqaNx57jHcbt76ychprGLrzwyZf4MPR+5XgGgxkAYel4ikDUdW6WtM+gjFgEYqjsP+7GQCXU3DXSd4L9QyiZPv63f0RJXgAv3p0fVvDlztefQ7F3ABu/baqSuXUHzgNhAVKsx6ZUEABKXNYfxbsd89FuwK9i19E2S+XM3oEA/ua+hahr6UFH7wAOt/RY+tmZZ4L1GWKvR2BiYR7qWnogTXmDQelcbMY+u2zuhXT0XK/Rq2/9u/UAMJh2F2o9YS9ws3JRqdbkN6ACQuDz09144uYrw2asAC3NeUuoMW0yfp95IodGGwZHlJBUTotHWpxvTruzL0Y15zKbS01LaEGRIgCPbTGufr2ZPXVOT5Xr6WzHJxcltny7wDoAWZGPla/34WszvXhmzwB6OvqAX33XMcXObdtO+v1qXOsI7v3qdFw1pdBYRGx+XkIAIhTwKIrQFkyrEh6PYhRWqJheZASdeh8eT6h/h56Dr7/uA37ri/josjlYc0MZ5k0tNIKaTZ9qA4a1d1Xg178/ZezHEzeWY97UQqx+cb+RngIMBjNv1DQDUoal88WyeDeeIhDJpj//WL4TXJBMyXTkyyZASiwr81guX1bmgRLow9h8gdtf6cP8iQqevjEPG1fk477X/x2XZsyP+XgUTTzHNicSQJ5HSeixzfSUOfPxX59B19JetVRgvQ3EmzXNluOQeX8+OdaOdXdXoL6lx+i3Zu6bp2JwfZXPb/0eO80u6+l6egU5CS0FecPuL41jVjCo4qHryzB9Qr7lOKKX5f7JtkMIqhLvH27Fx8fasemxJWEpc8n8feaJHBqNGBxRwpI9LW4+OxXtwG4eXKpS4um3DqG+pQcrFpXi1UeXGH2OzNRIVQhCIvX7KCqZhO6ONscBSPdl4OmPLuNX9+hnZ8NT7GLtJRJJpFz5tz9vwcIZRZgzcaw1MMLgfRQAf3NvZdRBvNv1+utu34Xe0KJqozdRcHDgv/lg02COvtRuu7+hE36XAYl+udN6smiNDPVBgbnUeCJnTpNZrt5JqhtF0ugy/8oyXO5owt6moKWows8+GcD4PIEX7x6cNfre2/342S156L0cxJQhHo90yTi2AUBLlLWh0cyYMAZney5rFfMweAzRAyOzgCotPdx0pRPG4Ez3ZeNYVNfSgxkT8o1+a3rwUnemx5p6rAgsKS9xTAUG4FhBTv8Na+zsM1Knc7yKayqwFlQN/u3U+80cTCXj95kncmg0YnBEGcHp7FSkBaT2waSEdjZw88HTeHTZHBw51+t8xygi9fvwLv0OCt//h7AByN6mIArzgF/dkx+xT0isvUQiUQRQNavY0rdJp0pthsweFFpmXwDsOtpm+dF26pMRrRCBeWYOANp6B4z/15oyakOTHK+CyePHABjcJxnaTo5pYbMW+GhXer2DfZM8oXVDhXlerRpUDI0M9X3X0yzjDXCG40wpFyRTMj3902fw1H/6Hh7Z3m80mf7ZJwP4X5/6sG2Vdab7V/fk47F3+lGYJ7BxiMcjXSLHtlhm8eOhCGD6hHycuzAARUp4PaG1PQEVsZd8AM5duGyU+9YLGnz3a7Mtx7SK6UWoO2M9zt56jVbWW59ZN6cCr1hUagkwuvp8YWt3FaH1XIpU/XVJeQlyPMJoYuvW+204MjmSiWl7lGkYHFHKxXLg08sgx5oGtXhWMaZNyA+rVBRQJTbsCT8bGCtzv49Nh/x4Zs8AjnSoKMjpg//jDfAXzsSarc3YuCIfzRdU/OyTATR0aT9UTjNKPZ1tRg5/PL1E3ARUoNohMIrHh0da8eERrcwtpERAlTGXlNUH9Vtrm/Hap03GguZPjrWjplEribv+3XojsFl7VwXmTS3EJ6E+IjmewTK5mx7TtmPpUaUIrLu7Imzm6rldJ+JuZJjomdPhOlPKBcmULKsffhgA8P0nf4B7XrugVavLA3oHgB/uuIynb8zD6oU5ALRjTkOXVtXF+ZgVf9+1eI9t15YW4UT7RVwcCMb5SM4UoZ1gORgqyy0E8N2vz8EdFVPx7M5jlvWO0ajSWorcH1Dx0t6TxjHtkaWzjfVBulyPwPdvvjJsZl0/hgiEl652WrsbrS3G4lnF2PT4UmypbYaAtrYo1cerVJ/IYdoeZSIGR5RSsRz4ahq78GZNs/GD4lG01KnHf1ON1guXseq6MqO5nTl/214dTSeltg39PGQ8Rer0fh/nLkpbmlwQj2y/iAt9l9Hp9+LuTX0YlyuwaaV2/eS/73WZUfKEbXuovUTsZ0E9isCkcbk4d2HA8fZh9w+9Hub0tWglZe2V3/Tb2SsiATAGB1JqFZX0H3S3tI/ndp0wijIIDN7HvC/DmYbm9Fij6czmaHquI8nqhx/GCy3TUfva32Py0R3GsUlPpQOA1QtztOPSuHwoYwqT1tso3mPbUHoyOZlWNMbSrkFK4KW9J3FHxVQ8dfvV+P2XHWGzVE701F3VHB0JGGW4pZSoP3vB0m/vK6VFWHt3BQCtap15PZIiBtPkVjjMZCcSeDidVEn1sTGVJ3IyMW2Px0BicERRDeVA4dS8zr4NfY0KoP3Y3DJvMta+XWdUWPu8+RCaOi/h5X2njCabt14z2bFpq15Z7ZGls/HS3pNGaeVY6f0+xoqBsDS5l+/Nxz2v9SFfAQYCwKaVg9f3XAa+93a/JZj63tv96L0sUWzbdrJ7idz9lWl4+7OWuO4jAKNBrrkqkvm9jlb5za0iUrRiGnaxBD7DmYbmtJB6tJzZ5Fnc7PTDJ3+AV19+Ed19ARTmAZscUul+uOMypo4TWLPNj9zl/xkAknY8SnWfJAHgmqmF8KsSDe0Xw054OfWxC4b6/jy5fC5ef+Jr+PFbh6KmW18ztRDH260977RCPoPV4yqmjcfvT2gzURLAkXO9OHqu11Jt7qEbZqJyepFRTXVLrXuvoaEGHtmeoptp6y95DCSAwRFF4XagiDVgKi7IhRACCFXmeaP6dNhiU/vBcWJhXljp6d/Wn7M02dx5pDUstWzGhDGomF6EJ0LpDYn2NeoN5qC197JjykmfH9j5nQKs2dqPNw77jQHIgkkK7rvGix/uuIwjHSrmT1SwZmEO/vmADz2mynWp6CWyLYbASBEwzmgKAdw2fwqeuPlKAHAMAryKwC3zJsOrCKNqnH2Gye1HOZEzobHcJ9Igwq0fUqLMj/XcrhMZd2YzVTLxLC5FNmvmDPi6z2LLA/lYVpaPMc/0Oh67DreruG9zH/oDHgTe/UcUlUzCQPmtWPFe9ZCPR6nukyQBHGu7iNefWIoP6s9hw56GqBkBEkBvvx8bDzRhR91ZzLyiAEdbe40Znynj8zAuz2vpl3S0NTx4UlXgtgWT8dWZE4xKnuafp2BQxY66s8b3JhjU0ujqQhXu9D58mz9twt/ctzCs+XUyuB0bs2EGJNOCOx4DCWBwlPHSfXBzOlAAsZ1Jr2nsMtaf6PSzefbF/2ENNatPWwKkb1ZMtTTtkw4/jGe6L+NM92WUTxyL3oFAzP2LBkvQtmF8nsBT1+Vg2xeKY5rc/ImKUb57xet9+OWf5AMAnr4xD3/94WVjMbSWhtePX35rDErH2yo3paGXyEPXl2F8ntcYVOw+3o5b5k22BBLmIMAXlPjgcCtyvApuXzAZnxxrd6z8pv8o1zR24bldJyw9qPTPSiKpIvF87s3lxWPthxSPTDuzmUqj6bmOBN/8xu3obm+xFF2YP9H52FU0BsjzAIoIou2/FoYqyn2EwI1PoiwJQUyqj22qKo0qlLGe93phT4Plt8KjAB5oM0G3zZ+CiulFWLu9ztS8WTuJBCmN9GUJ4OOjbbhl3mTsqDtraWOgz8BXTBuPfV92AlJrj6AHRebdDEpg7fa6iMVkgOT95qdqBiQVY5JMWn/JYyABIyA4EkKsA/BT28WtUsqpadidpMqE6V2nA4U9VW6LQ6ocMBhY6fQfEre0KX0bNY1dWFU1E8dbe3H+kg/lk8ahrGQshCKgR0cej4AAjLNyZi/saYDQHzCu0t2F2NsUxMNb+/GVyQoe2daPl++zpsk9c+sYAKHFxpeBXSe1NJKp4wQu+L24f7sXF3ouoLxY4Be3jTEWQSdaBSoZcjwClaFBgD6oGPCrRhNCj6L1iXLqERQMqrh25gRjsbHTD6L5c2oetCQapMT7uXdbBG0Owofyg55pZzZTaTQ915Fg3+6P0DtgLazw9I15YSm+a7b2IxgE/u9vjsGfbbuMHI8YUnW6dPB6BDp6Bxx7Ermxn0QLqsD1s4vxWXMPNn3ahFyvgru+Ms0y+/7osjm4MBDAa582Da7PDEqjwbNectsbalpdMb0I69+thyolFEXg5qsn4UOHzAZAazsRaSYiWb/5NY1deHbnsaTPgGTCmCTVeAwkYAQERyFHAdxi+js5JXDSLNHp3WSe2XE7UHgVrZyoXup0pUNfBnNgZS7J/OzOY7izcpqRXmAvtGCkdoWqqTV0XMKHR1otqQzL503G92++Eltrm/HxsXZL1TopYy8Jay9B+//bO4BLfon3G4IY4wXuea0Pl3xAebHAM7cOBjt7m4IoHKNgxXvjBtNIbtPSSC783d048uQ45HiE8TiJVoEaCgHgutnF+O93zg9LMxQCxtnSgKr98G9+YqnRI+gNfeYu1Fco0pk98+fULNEf5Xg/9/rnzOdXLYug9c9TMn7QM+nMZqqNpuea7XoHJMbnwTJTtHphDurbg7hvcx96B4CxuUC+F3jh7nxMHSdQmDd4/3QclxKln7AZqurGLuM3wh9QcbLjkuX63oEAZkzItwRWwlSUQRHAwhlFqJhRFFYtTkBicmGe5Xfv2pkTUNPUDSm1qqDFBblh7RP038Az3f1DDmjsM+kCgMeTnBmQ0ZJyxmMgjZTgKCClPJfunUi2RKZ3k3lmxxy0mBeSLp5VjAerZoZVKrM/jj2wOnquFz966xAAYM/xDiNVQV/ImutVsNLUD8IXKoHq9IP48dE2LJ83GdMn5OPJW+Zi7fZDCKjaGb14elqYS9B+85VL+LxNxbZVBZYzrgVeiUt+YOo4bf2NfrlccCeK7vhB2MAiWVXpzOyvgwBw77XT8fbnLa4pJhLAVVMGUzjycrQAQlFE2NnSgCrx7M5jeOr2q7FyUSlePxh6b1WJde9E7itkBCemCk76IMKjCLR096OmsSvmz2G8n3vz58xpzdFo+UGn0ccjgEAQWLO1HxtXDM4U/eo//LjsB6aME5bL12zth6kl2ZCPS8MpGJQQ0W8WlV7NVEpt1vySz3ouVUI7BpmPl48um4Nf/+6kkalQ39KDQ2d6sLW22Wjoqh+vnCrTmddE6r93itBm7OdNLbScEPSaij8kEtDYZ9Kl/qSTYLRX8qTRY6QER+VCiBYAAwAOAPiRlNKx2Y0Q4nEAjwNAWVnyF0YmUyLTu8kaCNqDrLV3VVgGnW6VyuzbMO/7szuPWa5//3ArPvqizTgj5w8d0L2eweagbof0gCnNIderYP29C9HV58Pnp7vx/uHWmJ+nOZDZdyYY1jBx44p83Le5D7fOVLDy9T50XwYKQ/1Dyu74geM2U1G5yevRysvq5WglgHf+cBZVs4rxaai3h5Pjrb14+q1DkIDlPdTXA5ntPd6Bg6fOY8WiUkvZW5/L58j8/tqDk+KCXNS19ODNmmZs+tRa5S4SfZv2z1s0Q62GlywcKFA8hvp7VJALbFtVgK1H/MbxqWgM0OcD/CrQelEaM0gTxgA3z/LgtyeCqPzlRRzpUFGYJ6AuuCXJzyo1JIDuPl/Ma0ntBLQZIK9Hwc1XT4IA8PGxdjSYqtPlhlKQ7ccgAPjV/7+9d4+Pqr7z/5+fM5MEAiFE7ghB0YqSaFtAhdYWbbWt1ivWUum3u+7Wqttuf9vd/e72+62tZfm2u9s+drt2u/ZbL+3XrhVEhXpbaSsVL7SAEFblJogIIdzCJYRAIMnMfH5/nEvOOXPO3DKTzEzez8eD2kxmznzOycz7fd6f9/v9ev/hfUvO2zsOwR7oGiTTDV6xmKXrmzlj9SwltOnD5l862SPm8IXL6pk4cmjONiRoUHdQr28uZKvkmW3vqNhOoVgoh+BoHXAH8A4wFvg28EelVIPWOukOUGv9EPAQwKxZs/KznVJAsk3v5utG0CPjHEt4AhHbAKYK3IIyWNc2Tkgaxpewdu+0NnfKbp0xCYAlVlYqDHeZQ1dPgs3727l1xiR+tyW7BGJ0zpe4ffm/sWTekKTafTB/7uiCl3fH6egyA6MLzlLsOBa+ukIoNyUSmsaza3nLNR8kntCs391GRcRUoQta0YY9bU7wFDHgC5eaN2Czp45iSIXXgWp6s3URwxw4a/PW3uOe7E/Q39cvU/vAqp3E4pkH6oWqZ++vGvLBUI8v5Je++iPbZl11bpSfXGeKw/TENVXf66CmCo78XY0nA24KMyh+cu0Q18bNy5zaelHelOUKyfrdbRhWZsXPyOoKjnf2JD2uMDeXrpw21gyItreycushLBFVT6ncuBFDWPjc5qTB2KYt00nHrbDK5Ozgxy9CE9aPaZOwfJg/85QPaW9bvCJISKcvZKrkmY09FNspFBslHxxprVe4f1ZKrQV2AX8K/GhAFjWA5OtG0B1kKaU82R23lHMmfSj2a2ZPHcWnpo9j15FT7D56Cm2VDgRlCZZvbPHcuPtRVn2F7dyeeKOZJ9Y1Z1VSB2Ygc2zfNm5Z+iI1vtp9sAe5klRq19FtkOrK5ku5yd7tVEpRO7QiaddUYzrYBZfXU1MVZc2uo2ze105Cmw7fIzmbgMfXNbN0/V4W3dTI43fOTpoebyjFPCtAfXxds/P4S1sP8dq7hx2nFZahbNrT5kxvb5hY63H6QbX2bgpZ/pZrDXk2u5lSvif0NzVVKtRmnemmV3jByoAr4MnbvPPbSkmUwS71DeLKC8bw7Jv7Pfbx5g9NZFhVlKc27OX328yKAvvldqWZGTwZbDtwgrdb2p3Xu7/Ds6eOoiLaW9FgKHMcwlWusnC7pLiqwgi0k0FEI4pbZ0zi1oABsX3Btnf+4/YlOxP02lSbsdnYQ7GdQrFR8sGRH631SaXUFuADA72WgSIfzYT+Po5FL2zJKhs1e+ooZ0ZOxDCb+t07Q3d+9Fy2HDjhCDPYhtf93t9c9jY7W08GHt8/7TzHkUYAnHXNVzkGnNz4YlLtvl2jb5em1FRBR7dB/d8/l/sbZoG2/iemNa/5sm42cQ2t1qBBu259/sxJNE6s5TuWIp0bW4Bh0U2NDK3wZsruvOJc57OzzBWg+gPjsNrz+Q/+0ck4RQzFV644l5qhFZ5a+7B5WWGONlOH7g7M+rr7ah8vm91MkYAV+ps5H/8EC5a/nGSzTnZB/LsjnOfZGXClgrPjpSLKEEbEUDz/1v6kzbT3j5yi4ezaJFltN0oRqDCnLDEaMH3Swhsa+MUf3nfK8F7dcZjWE2eSs+89Cb759FsMq4oyx9ePGfjmWZBtcONXgc01OxP22lSbsdnYw77aTinJE/JN2QVHSqkhwIXAqoFeS6njNqzTxtdkVTu8bGNLr7QysHR9s+NEumMJHln9PgmtWb/7GEDgjfNl554VGhzlm9ixfdRUwaQabyB0wVmKzh4zczTvxeHUfvkXKTNGhSCTuG/ltkPgUmBSmH+zT1w4lt9vO5TkmOMJnRQ4GUDNUFONz3Z6yy3lOn+DcJBT/NavN3lK8eIJzSOr32fp3XM8gVaqeVn+YzbtaeP2h9c6TnPJV8Jnat3+0Bq6rVTZU00toc/NlGx3M0UCVuhvfvO7lXzmU1dz89KX6ejS1FQpOrs1K/+k2vM8O5tk//98isUUA2HZpLdaTOGEdDbUrTCnDGX1FZliNJv3t9NoyXW7A6HuWMJT5myTAGew7Fst7dzz8anUDK3gzb3HecnXD9sTS/Dgq+/x2ruHUwYttk99uqmFWDy3/p509izV61O9NmwzNht72BfbKSV5QiEo+eBIKfUvwPNAM2bP0XeAYcAvB3Jd5Ua6bJRfjcftRGJx7TgRA7N0y90vtHR9c6DhbZxYm1RGlq0aXSa0Lr2X2iNvUz0UWjqSS+hGD6XPggqFxi1GpDFL4uy+rYgBt19mlt09svp9Egnt9Gy5iUZU4IBXv/KS//c2QXug7sGN9rspQyXNy7L/7nbfkh08LbeyYWDejCxPMVPLPfMqH6UZuSgz5SNrKwjZ8JvfrXT+/5/8fB1L/9dtLFjekpRNOt0Nk2tJnoH0TA/RucVr2/pKuqoCDdRURZ2b8/3HT7PEmnHUHUuweF0zhkp/HAWMG1HFwRNdnse3HDjBY1++nKY9bbz+7uGkTNNKV7lfWNDiluaG3Pp7wrIzi9c1s3R9M1v2m+XYQa/PNbOTjT3M1XZKSZ5QCEo+OAImAUuA0cBhYC0wW2u9Z0BXVUakuyF0G2Z34OPHUPDR80dzbeMEFj632ZmTtHn/CacETwMdp3to2tPGwue3JB3nwgk17Dh00pnRky2tS++l4sDbzi5rz4RLqDjwNovnm3X4H/y/Hd4Sui6oHT2W6Jy+CSoMBHYQGUvA5n3t3HdDA9c0jGftrqPBqn5Ksf1gR1alae7PxrwZk3jSmgwP5s1CZYWBAmKuOkid0Gw/2MG+46eJRgxPw7DfyX/8A94d7cMdXYF9S7OnjqIiopzMUT7K2rJVZhKEgUYDE778f2n5wfUeO3ZOrWLxvGpuXtrJzz47hK+vOMO2IwlGVEFPRQ2jS8y25ROt4Wev7aJ+1DBmTx3Fso0tRAxFwrXZ4nY30YjiE9PG8vI7hzyZcg3UVVcmBUfXNk4Aeu2Jv88zYUmLK60D5xH5pbltIQh/f49TmdGT2WiNmVPqWLyu2RmvYRMUYBRzVlzKmYVCUPLBkdb6CwO9hnImkx0pr3iCdlSAbAzr52jE4BtXX8DMKXW8sr3VuTmPJzTTJtSw9UCH46g2NrcFTkLvjiVCSyjSYWeIFs/v3TW9YfFbdMR66/Df+osaoFfxCaD2y7/I6f3yxVnVFRwLUGGKKEuQwbocqXY3325p54uPrHVU5Zr2tPHK9lYnmAAzgPn2M5ucYzzV1MKff+QcpwQyGjG48oIxjK6pclQF7R3NiDULRGEPHVRcNW0sY2uqaJhYi6FMKXKs9drqh1FD8YXL6p1AzK9+NLqmisqI1bsWUabS1LZDSZ/FmVPqWHLXnLz2HNnHzUSZSRCKgWsbJ/DsTxeRwFSqcw+i7olrOrrMIbG3X1xBT1wz5Psd6K7+KV0udpaub2b7oQ5HsTMMA7h77nmMqanyiNYAvHOww/PzzR+a6Aw7B9Oe+FVbI4Y5PBYInEdUV12JYTnVaMQcpu63b3XVlZ4ydrtXyo8/O7Ni84Gk54QFGIXMivelZ6iYAzehdCn54EjoG/moU35qw17HMNsTwTc2H0cnNNGoQSKRMFXTXIZ/tHtMO3Cw/Yzn57Beo11HTmU14+LU1lXE1piS2jWVmi9fVunU2y/f1kPNEEWkR4cqPqEiIUfuP4ICow9OMmVn3dmfVDFjkNKgHUzYcq8or0RudyzBQ6/vco7bHUs47/f0hr3cNmuyExTHEpqHXt/lvFcirln1Tqsj/37nFec6JX22FK+tPDVx5NBQ9SO3ktO+46d5wip3CdvdzMQx5jp7Q3YohWJnzX/+M8N2rEClUN50/3zuSMXRSGn3G+ULt3CCAc4wVr9ZtWcG+TPlkNwfeqo7npTpbuvsdjayFNA4sdbpi+qJm2XIgKdMPaFNu7nwxkZPsGXjPqahzJ8zwR+oXTN9HPfMPa9fA4x89AxJObOQbyQ4GsT0pU7ZZu2uo54St1hc07SnjaihuO3yekdm274Rtm9ob50xiactx1IRUZw/drhnmGllxAhcczZJo1NbVxF9/QGevNHgivrhrG6O8+XnTtMwJsLtF1fwq009LP98NT9Y3RWoUtfVA5Uf+nTmb9iPbN7fzqaAZmA3l55TxwXjagIFFSBZ7tVfaufPALqxSyAjhnL+/vbkeYVGWZkiO5CpGVrB0rvnpFU/DNsFtMUZlqcZPAypg5++zt6QHUqhmHn80YdZ9rmhoTYtFoev/tdpfvdejF1tZmmxbpiV0bHdG021o8YUTamxgTWryEhWMQ19jTL/eWa5tbQ7AVFF1OCOOWbW3F/CHbF6JmdOqeO2WZNZ7MseuXlp6yFWbj3kkff2+9T5l9az7UBvmfnS9XtZavlMT5m61qFBT64bN3agtWLzAUc5NhWFUIWTniGhGJHgaBCTiVFKl7K2jbJ9HDtBFLMyArOnjvLc0Lpn3Sy5a45z3O0HOzzB0cEOb912LsTWPMaTNxqemR4/v3EoX19hZqnaz1gDFL80jM88dspTo9/VAyhF1dkX9Xkd+cItTpHqJkBhOvBbPjyJBZebJWvLNrZwxJL73n6wwzNXyv7XtKeNV3YcpieWwLBkuB9ds5vuHlPBCbTzvhXWfI7GibWeAcH2zKqgACiopOPaxgmBn7lc1Y/SBT9BqnlhjjhMMEIct1CsHO+McUX90ECbdvnECJdNivDz/+7xBk0ZDIFN3mg6yYLnHuAUDFiAVBU1mDp6GNusUrZ4AsbXVKX0HfZ8ojE1VTzxhjeoiccTfOGyesdvLdvYEljCfeW0sY4NuHXGpLQz+YKy9n47tmV/O4vX9W4i2iRcu1PpyuVy3bhZcHl92qAICqcKJxl5oRiR4GgQk6lRSpWyDmsyNVTv7pp/XpLdo7LopkZHteytvcfTrjeioKoiQmd3HEi/k9l+9DBX1A/3HOOK+gjbjiT4/utd1A7pLT35zZeGAbDq/Ri3PtnJiv9RzVeeP83RNcUzHDFV0kwBV08fx3mjhzk9Qote2MK08WYP1dNNLZ4eLkMlqxLNnFLHkq94Hawt4GAHsEvXNzN2xBCn9GLmlDpH5r2uutITdIXJvy9e1+wEVOt3H2Pa+JqU2Rv3MdKVT6QK+Jv2tHlU8+wd4DByUatLt35BKCQ1QyKhNu13fzKMxp+eZPG87IfABm005Wt4rF+RNFPiiQQ7Wr09Pgc7uvj4B0Z7ZsIp4KYPTeQD42qoq65ky/52Dnd0eUSAACIRw+nlWWwNyw5a18vvHOLeX29ynmv7t47TPZ4yZBuD5D4evx1rmFjrycI7r1W9g87tcrkwm5Kv0rKw4xcqwyM9Q0IxIsHRIMYfuLiHsGaKbUivbZzA+t3H6O4xsw53XnGu53h2s727R+U7z24mosz/n6oB1iau8QRG6XYya0eNYXXzyaS6++GVsPVwgntmVQSWnnzx4gquqI/w/nGNpjDDETO9Iah0KbCl4u6PT+V/XXcRD6za6Slns/8GPT5xC1um1nZwbodoy2lD79+uaU9b7yyqQx3cM/c8z3MgWcktiKY9bdz37GbnJqA7hZPNZKfS78jTTWy3VfMUcNusyWmDMjsTlotanXv90YjB52aa/VPi/IVCUXXJtSxY/l+BNg1g25FETkNgwzaa8jE8Njd5HW9JnJsdh7wB06Xn1DmB0cLntzibRKYQQu/721ka20bZGRwFnDd2OO+1nrR8l7nB89SGvXxo8ki6YgnmTB3Fml1HPYGRwrTLNUMrUt7027Y1obVTlpwwW0C5YFwNO1pPohNmZt4/TD3fipmpbG4hMzzSMyQUGxIcDXLCbmz9N8yZ3Lz6S6r8x5s9dZRndyyR0CSwdsUwd/IzVaLLZCczOudLLHjuARbfGHOVkCTQDddRs/W33Da9goiCW5/s5PgZqB1iruMn1w1l1fuxgjYrZ3pDkIlkuaJ3eKvfgdVVV7J5fztRS/HNTULDm3uPs3hdc+Dfy026XUP377t6Evzs1fd4PWCw4dpdR72DZ1V49iYTMZCgz22mE9vnWYp7fsKOm61anXv93bEES9Y1s3xji0iACwXjb777Q/7xOwluXvqiU073iXMi/OS6oQBcNNrIaQhs2EZTMQ6PrT+r2iOnvWFPG+t3tzlCMDb+0uSYJYaw91inx+5GDMWff/Rcz/w+DXTHtVMKHjQMFky77N5sCsJtJyJo5l9m9uo+uWGvUzIYMZTjXwvZn+O3Wf5hr4XM8OQzyy4Ze6GvZBUcKaXWk+a+Tmt9WZ9WJPQrTXvauH/ljiSDC+l3yf03r22d3XztqvP51q83JfV12M+/84pzedhSLYtGlDUDx1Tiuf6SCbzw9gEnk5Tqg5bJTuaw6VdxCpj3oqv07mNf4qzpV3Hq7IuswKmCH316CKub49zx7Gm+d1UVq96PccezpznREyX6ycIMR3SXS6Qik1jRXR4WVMbYHUsQNRSfmj6OQyfOeBz5yq2HHFW5VA433a7h7KmjiBrKaSp++Z1WElYjsfuYs6eOoqrCcDKMi25qDM0G1VVXphUDCbpRcO9C+p1kmHN3Py/suNnunNrPd99QScOxUEj+13UXcfDE9/j3BSv45c1VfOv3XaxpSbDqfXOD6OYLo8nZ8gwGXIdtNA3EYOygkQXDKiOMrK7ghksmcqIrxn/vPU4sbo6VsJ8bNPQ6EdeeoeJL1zc7IjR27+aimxqZNr6GW2dMorWji1etvsx0prkikrzxE3TTHrRps3bXUeLuOUsJ7WSww2xQPgKCuupK53oldHKPU6EyPPnsZ8pWdMd9zSSoEmyyzRxtIfl+rg74CHAa+H0+FiX0D/7J24bqrY3OpL44rCfD3dehlGlgb39oDT1xjWH0BgVaaz5cX8eGPW3EEprn3z6AtjyTJnXpWaY7mcOmXwXTr0oq/fAHTiNG1NDTPYQ/feY0VRHzOpzs7qF2zWNZNx1XWEFfWDncqa2r4I1fcbS1NWvVJ0PBtHE1zo4iwPWXTEgqYUwqY4xrRtdUMaamim0HTji19hoceW1FsqKdTbpdQ7dyk/23jRgKrb3HTHecsGxkKjGQsGAlzElm8p5Bx81259R+/vKNLaGKgYKQb+7/wod58VuTmDTiKD+8ZgjfevkMn/zPToZVQlwrohdfy7wXN3g2jNLZn7CNpqDXFVrVburoYbx32DvS4VR3nFPdcR5e/T7xhMZQpix1W2c3611CPzaGgjs/am7UEZBNsgeWf+PqCwDvRuHCGxpYtb2VlVsPBfqnMcMruaZhfFIJbSp7FGRXgoZahz03X8FFW2e343cNMpcE7yv57GfK9FhBdj9dBYUweMgqONJa3xH0uFJqOPAc8Mc8rEnoJ9yTtw16nYFtENLtkgcZarv0yEajWOUaNuouZYgl8CjU+Xf2Uu3M5WMnMyhwsnuZFt9oWMfNXpXJX77mxnv87FWftIYTZ7xzj55/az+aZIEF/2DAJzfstTJ2BtdMH8sr21udG/ZUQYhNul3DeTMm8ZQlzx61ZnL4j5lOZvv+lTs8WUc7Gxm2nlTBSqZOMigDGnbcXHZOJ44cGngtBKFQ/Ok3vs2t3/pLaqIxHr3JlSV6pofY2Rcx7JqvZt0rFLbR5KY/VO12Hj4V+jvbhyQ0vLTtUOgoAq1hy4ETJEJS81FDOb7QvcnU3ZNg1fZWXn6n1eOf3Bt5h09288b7x2icWOv5rj/46nuc6TEdoL+iIihDs+SuOfzs1fdoPXGG+ZfWe8rbcrV16bAz+/2tHJfPfqZMj+W/Zis2HxBJccEhLz1HWuuTSql/Bf4DeCQfxxQKj9+IuAOjTHfJ7cdtQ+838omEpvXEmaTX9ZVsdjKzoZCqTOmOP+ayT3P4ZOqdOg3sO+69nnYs1tWTYNnGFudv4h4MCBC3skXxeIIPTh7J3XPPy38JgbJuE5RKUqEL2t3cfrCDFZsP0DBhhCkb7grWM3GSqYKVTJ1k0PPyUT5SKOlbQUjFP7+4jZ8fOJtEdCiP3hTz2pqbyZstC6IQ9jNT8Ro/YYERmLalYcIIj8Kq9017JYI6Tvd4Nplecs2Cs9c3bkSVp89pZ+tJvvXrTYAplb14XbNnhpxhKEdcwV254bcTdt/m9kNbUqp61lVXYliD6foSXGSbHc9XGVo++5kyPZbf7tuiUiIpLkB+BRlGYpbYCSVCJqVSgKdky28M3bLM0YjBRZZ0tI0G5kwdxZYDJ4gFZFQycXwKqBkS5cSZmOfxTHcysynxKKQqU7rjpwqMgurs/WhgyRvNjKiKUjO0grrqSqIRw8nkuUsnO073cP/KHVzbOAEgaYp7GKlqtG01ODsASyXa0BNL8OCr7zk3DK+/e6S3nEMlZzFzIZsAvxCNxn6RCnfgKgiFYPG6Zn722i4ATpzoyMiW5bMMrhD2M1c1Oz8G5rgD+5gr32kNfW4snmDR81sYN2IIv992KPR5YJa/3fyhs53r7mbF5gMsuLyeFZsPeB6fPmEEbZ3dnvlI/oxFNuVhttqdYQk35GJnwhRL/b/LdymfTT77mTI5VpDdDxs/IRQnhewRy1aQ4bqAhyuBi4C/BlblY1FC4UllCN3PSVWTe9/1DUmyzH7VHoWp2DPf1Y/i5sLxNexo7Ug51LQiajC2piopOEpHLiUeuaoyWZt2aclZ9UmbpR62wh8EB5Zaw89e24UCqioM5l4wxqmNt0snGyaMcBz56+8eIWqYjjmT5tV0n4d0og3u3x/yZRSV6s0Y9TUwssnU4Rai0dgvUvF0U4tIeQsFxX0TnomtyXcZXCFU7eyNIQVURhVdsezDJQV875aLmTa+htsfWhPYD+regEpoW4GuPel5bs4fM4wffO6DzJxSx64jpzzZIcDZfLq2cYInSzX/0nqaj55KKs1z281cysMUOqc+oaBAxz52mPpsoeYe5UouN8p+u18owQkh/xS6MiPbzNEL9PbKu+kBngX+Mh+LEgpLph+qdDW5KzYfCJTeVvRWV1VWmHLS+46fpiJqePqRwCz9SvgCo5FDo1x27ihefueQGTRpTePZtSlrzYPIpcQj116mdIHRlLOq2dvWmdXxDWWWX2hfX1DH6R4esRqPQ9cDnOlJ8P6RU1RElKMIeG3jhKRdTPtP0h1LcP/KHaGBSbrPg7tXJ2huln+nbvvBDt5q2eQcf+aUOi4YV+MMV4TSlmT1i1QEZdPyTSlfL6HvuG/CM7E1+S6DK4SqnW3mNKQMjAwFl5xdy5sBstq3X17PgsvreWDVztCe0AynSDhURpQTGAHcPfc8Xnv3MF09CZSCuz42lQWX1wM4/7VLiNs6u1lj2UebKaOq+dfPfyij0vbF65pZsfkA1zZOyEu/jt+2L9/YwrKN5uBwQ6lANdNCzj3KFilhHnwUOjjPNjg6N+CxM0Cr1pnsmwvFQKYfqqCa3HXvmzW5kUhvjW5XTwKsXX8g6UbeHqhXEVFcdk6dR4Th8MkuIoZ3oN/x0zFWWqUMGlP17Zk392d9nrmUeOTSy2TvFKT6Auxt6yShszt+QsOEEUOYe8EYbrVm8qzddZSOrhgJrTMqN9nZepKIYS4yntDc99xmPjx5pOc5duYooWH1u0dYv/tYoHNJVaMdiRjsO37aeV6Yo3LvzNn/Xbq+mS3722na08amfe3O/KFycHjzZkwybzJ6EiilknrysiHbuWOleL2EvrHg8np+tHI7Rzq6M7I1+S6DK1QvaDoMBd+7+WI2729PCo6ihqJxonk2s6eO8qjABRFRlopnyFOiEcXnZ01OygKnK8+1AyTbH7ramgC46+PnBZa22+XLdunz9oMdTj/T6+8e4R9vuThUwS7TjRK/bdfg3COgg9VMC1WOnAvFlsUSCk+hg/Ns1er2ACilpgFnA0Ps3ynrm661fjGP6xt09MfOb9Cg0AdW7aSuutKjqOU3fkBvikRrpo2vcUrr4glNJGrwoUm1dFmRzuypo5j/4Jresru45gPjahhZXdlbfqDhAz5pajAdU8SfnyR9fbz79zVVBhf+RwdHTuMMRLzgLJW2xCOTXiabiojiqmljkyRjLxpfwzsHO3olyV2ONtXx/eV5+9pO83RTC40Ta1n43GZ64pqIYc7fSLgcvAJGD6/k6KnuJKfuUQiMa9bvbiNqQMPEWuZfWs+08TXcv3IHq989knIWT1iNti1V/cQb5pDTeTMmZdxrs+Dyeto6u9m0rz3nmvtiZuaUOuc7ktCaRS+kbqwOI5PApxyul9A3Fq9r5kiHWVZ1ausq2n/z7ww1ekBDoqOVU5tWeuxlujK4XPqRMrWfI6oinOiK53aiLhRmYDRtfA2/WJ3c9xNLaO57dhNb9rfTMLGW22ZNprWjCwVs2d+eJHBjG+GIMr+/G62ZSTbxuDmHL+i7laosq2lPm6cMXeteMYebP3S2EzwFvc793Z82ztvXa/c1pRO/AVL2F7uz/pv3t5tVC3FzHmGY2maxlKH1RxZLsvLFRaGD82x7ji4GlmD2GAXcuqKBSB7WNSjpr51fvyG064ntuu6qCu8MBnsND6zaScwa7BlPaH726ntsajnuGPueWMI1MXwTn5o+joQvofjUhr0svLHRKT9IaJICI5sRQ6O0dfb2GaWrj0/+fZwFy0/z9csq+O7cKufnziFVeRFXMBR89mJzcG08YTrTMTVVzJ46ihc3H3QyO5re3Ug0BLVXRQz4wqX17DjUkTSXoyeWYOn6Zme3M5aA88dUe2Z9aKD9dA9XXzQODaza3uo49CAxB63hUw3jHYf8jasvyEipJ6hGe+2uo8QSvWUXCrLqtUkVrBdL2UZfaOvsTjtkNx25zh1LhTj78mPp+mbAtJUdL/6IUUNh8bzq3hK35W/TuvRexs7/PpC6DK7Qstz5CIwA6qorAEJ7icC0mY+vM6+None465iaKudxG7tcWYG50efzYZre6zwvYJZRqtECQeMqDp3o4tE1u6kfNSwwAPF/98eNGIK7F8rua/K/V1iZXNi9hf2zW0HPvBDJyqPFRqFvlCUrX5wUMjjPtqzuF5j9RdcDO4H+mRA2SOjPnV/7Q2XPJfLUdYfs9rvlQpVKljT1c+jEGSqjhsfQxq1J359pGJ+2VK6tM+bZuYygqa6ET/6nmQWac3aExTdWOfXxgfXz84by9RVn+N4nhjg/37y0JZdLlkRCw7Nv7Xd8Z1zDwRNdPP92ci9WXJtDCVtPnEkSrQD4xIXj+P4tF3PvrzclBUcVUSPJIaIUFRHlDHMFMzP30tZDVFUYLLqxkc3721GYGaKFz29xprq7ZbLdzvzxO2ezbGNL4K5HKoImvAMZ99qEBevphsCWCvnY1czkGNncIIizLz+a9rSxeZ9pI9p/8+8MjWoOnYSbl3Yy5+wIv/nSMMv+veW8JlUZXPvP/7ygYw3yRVtnjycjkw6NnU3azKKbGp3vlV3m5vaFQbYazGBr8bpmlm1scb476b5T9gwhT+BhvU93LOFRff3czEnOhpL/u3/33PO4ctpYp+coKONkv8Yu523t6Mpq5pt7fYXslcznBk0hb5QlKz/4yDY4ugi4VWv920IsZrAzEA2OjhH1BUj+3X6/XOg5o4exs/Wk51h+12SXbNllV/bA0Y7TPTybQQ+Re+fyn1432HQ4weJ5roGGy0/zT6930X70NLWE189vO5Lw/NzRpfOmOR/UaRdP6EAluTM9ceZfWu8RIbAZW1MFWINUm1ocZ331ReO4e+55ALyy47AjaLHr8EmiEYOrp4/l1R2HncDHLotr6+zmH2+5GDD/dp+bOckJlOxgA0hSn1tu7S66nX46wm7Kl21syfizHBSspxsCWwgyddbZOPV87GpmeoxMbxDE2ZcXTXva+Nz//SMaaF16L6OqYr6M0Wk+89gpnl9QTUcXVG5d5WR/wsrgCj3WoC8ooG5YBW2neqz+IDNzn6KVKMkmxxOaFZsPsPAGcwPmrb3Hk9Tm3K+tiChQKsnWZloG7P4Od5zu4eHXdznrVUoRt6oyumMJlqwzS5RtG3zf9Q1OMGR/x8PK8Oz3cpfzvrrjMFFDOT443cy37p4ECXpHPxSqTK1UNmiKSXxC6B+yDY7eAMK/kUKfGIgGR/d7vrX3OC9Zss/+3SK/XOi5AcGRm09NH+cY75lT6pg3Y5LjFB56fVdGYgLuTNDNSzt5Zn51Ulbo5qWd1I4aC4TXz1802vD8XFOVbW4key4cX8P2Qx2ecrZrGycwbXyNk/GxqYgoNKazmDmljiVfCf4MLLyhgYdee489R01xh3g8wYcmj+SeueexbGMLTze1EI97jXfTnjZuf2gNPXFTEGPeXb0Brz8Q6cuE8KByu1w+y5k4oUKVg2XqrHNx6vnY1cznzqg4+/Ji7a6jjk2tOPA2i+cPDbSVpv0zbWu67E8hZLkzoTJqcN7oYaHl1mAGJsc7e6iIGo7Nu2POOTzz5j7PMFYwA5vzxg7n3NHDaO/spmlPGwltHsMtQGMLygShFFw5bSxXThvL5v3tPLVhL7G4JhLJXHrbPxPO/nsp4JMXjvVsftlBkq34aWfT1+8+5pS4pbOD7nLeeDzBFy6rZ+LIoSlFG/xZ/EJm7Utpg6aYxCeE/iHb4OguYIlSqhNzptFx/xO01p15WNegJV83QNnubNvG9rV3Dwcad7/hv2raWF5+pzUwS2JYjsT/HgDzH1yTsWSqe+eyo8vctXRjZoFg1KdMmdjA+vnlp/nyhyvoiWvn554Jl2S2gDQEZYdsdrR2MHXMcCoMRWXU8Agf2CV3hoKLz65l24ETjpiB+0bbP3x30QtbnJIMhbnb2HG6h7W7jnLrDLMMIyh7Y9fhd8c1yza2OMfuON1jlklaKkR+NUL33z8fMyQyfU0qJ1TI3Ua3s+5O4axLyamHIc6+vJg9dZRjjzq6dKitXLD8NJdPjLByd/rsTyFkuTMhFje/2+lIaDhv9DBG11Qxalhl4HgD+5rsbD3JztaTGAqiEYPG8TW83dLuZH+WbWzhSEcXBsE9oQltlpG/9u5h7ru+gafZa/7CVzowb4aZoQ/qRfJn6f2lcqNrqljs6n8ylHICKbfAzXLLhqezg36fbVcN2OuxKzpiCe05Rn+JLJTaBk2xiE8I/UO2wdERYDfwnymeI4IMOZKJVG8h+wlS3TD5f7d8Y4vjiDTJA/T8qlxNe9q4f+WOjOvCj730U2oqzZ3Kq86NUlPV+/9t7F1Qd3mIv36+c8gofvJGC//4ejc1VYqeCZc4zch9ZUR1lPbO4MG08QROZu38McNoPnrKE9wYytwhbTi7NkmpbfvBDkcB0BbHcNeCm4GRJYrhGvj6+J2zk0rQ/DmyIx1dfPGRtZzp6b0FiFpT1aeNr/GoEdr0d/lDkBOyP/v7jp8uWGBSV13p+QyHyW6XmlMPQ5x9+TBzSh3fv+VivvXrTdRUqVBb+cGxBt+8oor1HcNTHM1koGS5ExoOtZ9J/0RMMR9lqYL6iRiKxokjnCDIPrYtalBV0UG3ZQeXrm92VD3DNr3sQGrF5gMeYSJ7E8sWhIgos3w5laiCeyac29cut2T/DUswwn48GjEc+//UBjMwS2cH3eV4DRNGONmnaMQArT39qqlsaV8z9WGvlw0aoZjJNjj6FTAH+BdEkCGvpLsBzeYGNZOd7VQGK1U/g3381g5v6YItS+qIA/T0vu/idc3OzX4mHHvppwzbsYIvX1bBl587zc9vHMrlEyMsWH46qeeoZ8IHPa/118/b/y2E2Q0LjPzsPHyKnYd3OdfHAD56/mi+cfUFgOkQ3Upt7uZi+zq6b8jd9emQXPvuxt3DVBE1GF1TZc6lcpGwRDJs1Tm3009VS99famfuz340YmRUO58LbZ3dnr9R2KT5oB4AQRho7M9rz4RLWLD87SRbefnECN+8oiqr7E82Yw3yyUGff0lFmFeJJzTjRgyhItrhGT6uMfs3//wj5/DI6vdNW+s6iL8KYtq4GnYc6kBrkua72TbInaGPa/jOM5vMzSZwStT8Gyruig17hlFQsDBzSh2fmzmJJbbAjWWjMyk/tgOiNe8d9Shmus9TEd5XFJTxyqbULt19i2zQCMVKtsHRVcBXtNaLC7GYwUy6gCabUp5Map/DDJadbteQJL/sv0l1lyD4HZRS5joWr2vm289symr6uNr6WxZ/3qyZbxgT4esrzrDtSAIDU3nJnFmU3yxQf6BUr1KcHRit3XXU43DW7jrqkT/XmBkMfy34wuc2e2RrI4YKLIOrq650xBhsFbmlbzR7Gpft95g2vibwcxP0eerPbJL7sx+LJZg6ZhjDqqLMv7Q+9D1zCdxsNal0GSH3TYe7B0AQBpLZU0dRGVGMnf999v3wepethEQCfr87zrr9p6n81N8UPPtTLIyuqWLuBWOSlFXj8QRbDpxIGjXhxz1qws6wL7jcLJF22xe71M05voZFz29h24ETxBIaQynuvOJcaoZWUFdd6WSbILk8zp/9b9rT5ghC2JtCYWXUbtx2M6E1EUMRweyTQmtz/IRPGS/VMbp7whX1wiiHEmRhcJJtcLQbkJ6iApAuoMmmlCddujpVJuD2h9c6u2xPb9jLkrvmBIoyxOMJrp4+jt9bfUd+PnnROADLmPY+HjRzx0/HmbhTM3/7xRXcfrHZM1T1vQ7qvvEC+qWfwtbfcmb3W7T9+Cb09E9z1jVfTX3QAqIwBRh2HOpIqZZ04wcn8v6RU4wbMYTtBzs8ktXu4MIuoQAzcFn43GYAz47dlv3tjlS2Am6bNdkT4NoO177WlZbEtr1T94ZLLlxjlkE+fufs0J1L/+N+MYdCOj2/gtLOw6cA2HYweKBqIcpK3YjDF4qRmVPqWHLXHO655y9o1nDk70zxFxvbhtYPksAoapgbfP7Axc6UNEwYwR93HnEeNxTMmlLHm3uPe0rObBJaO9k5f8Zj3oxJPLlhr0doxy0DntCaR1a/z6KbGj12/1bXwOwgW+LfkJx/2WRPQJLK7syeOsqZNwfm5tz8S+udTbJMNo/8FQt29ilIUS/d60u5BFkYfGQbHP0d8A9KqTe11rsLsJ5BS7obs2zrc1Olq8MM1tpdR52UO5jO1G2snTlHVgN/UBMpmE5pTE0Vy1x9SWA6n8l11ew5ljq+rhkSCa6ZHxLh2Es/JfH2i6BgWKUZSA3f/CKtx/YNWBZJKfjeLRez/WAHS9c3mzuS1m7h9ZdM4OipbhomjOCR1bswL287v3+nFe1yNPev3ME3rr7AKaFwX9PuuOY7z2xySikev3M282ZM8khl2w4PvDfvzjFiZiPvzCl1nD+uxhMcQa9j/tpV5wd+bvyfp/50evZn//6VO1j97pG0dfKFDl7E4QvFyqM/vJeW1U8yIqRHc0iFov3nf97bQzQndQ/RpefUsfdoZ1ZlbrkwYkiUE2cyK1POGKVYvrGFhom1zvc1ElHMnzWZmqqoKeDgspEKmDttLN+89iIWPb8lacaRLZAQxMwpdTxx1xyWb2xh8752p4/UTcKSDnfbJo25GeYXwbEz3/tdPZbxeIKzRw7NShDntlmTnU00ndBMdL0+06y7fwad3TebqpzbvQbpKxJKkWyDo3/AlPLeoZTaTbBa3WV9X9bgJF39bb7qc8MM1uypo6iI9mYtKiLKY6wXvbDFTMVb5QUzp9Sx3Se3etk5dbzZ0s6SN5qdoXpgliQsuqmRf//9jrTr09M/zYLlK5Jq5vX0a+l660WqozBiiOLRm3p/f/uytznlmt0RRHVlhM7u9FPZDWVeI/cwVmv2bSAJDQ+++h6vvWtKsUYMBRpiWvPipgMsuWsOyza24Io7iSc0UcMMNBPaKyl764xJPN3U4qmTt524O4gJczr2zXvQsEEwd1OftnY5bXGIbG/y+9vpzZxSxzeuvoB1u446O6Fha841eMk04yQOXyhWHn/0YeZONnjpvXhSj+a8pZ2MGBJlyXUnuaJ+OKubT7LguQc4BYF2M2rALR+exL2/Tp7Llm/yHhgBsbjm8XXNVEYNZ5aRbQvmP7gmSRxIKdhvyXnfd0MD8x9aQ8yyNRGFRyABgmWwnQoMS5zBOTZQWZHcr9Q4sZanN3iV7zzZIkMRjRhJIxoyxb+Jlu71YTbQPu+guYWZzrAThFIi2+Bos/VPKCKC+ivS9Vy4S+XcP39u5iSOdHQxuqbKk753q6VpV3lBW2e3UypnKKiqiBCLW1kLl+/5wNjhbNnfzuypo3gmzQDYs675KseAm5/8LR1nzIyRnn4tZ13zVdq2vMioasXDN3jneCy5dWjKye0RBXXDKunsDp9lYVgBUNRQ3PLhSfx3c5sT0KQpTefQiTPODp92lWTY8tnK93xDwScuHMuhE2c8krLLN7YwceRQFt7QwNL1zZ7dS4Up322rqAU19NqPPX7nbJZvbHFUmCoiilut7JJdftPXWRb97fTsddvX0y+X635eLsFLNhkncfhCMXK8M8are+D5BdUs39bDrU92cvwM1A4xN1iW3FLpnX90YyzUbsYS8MArOzOaSVfMdMcSbNnfzvetodgPrNoZWAquUSx5o5llG1u47/oGPj9rcqAvBByRoYTWgUIF7oyNoXoFeGZOqfP0KwWJ4NhrTmiIJTRfuGwyZ/vmE0FmfZXZ2sJMBtnOnNI7t1A2h4RyJavgSGv9Z4VaiJAbQTs9kH4GQpAKTVgPDITvxvsft3fGzvgU0bYd7GDbwQ4qowbnjKpm99HUpXVnXfNVuOarSSpzHV1wsjt4jkfY5HZbgWxfW3hgBL29UHFLve0TF44LnZjuZ/6l9Ww/tMUsS7TU5Nzvb6vG2dkgpRQrtx0iGjGcRttIxPDMnbjv+gbnmIahSCTMJlq3THqqnb5UTswdWLmbg4udTIOSXIIXKZcTSpnF65qpGRLhuNWzedW5UX5y3VCgt98oG7sJ6W1mMRIx4NxRw5zeRPAKBtnCK+6ZcRHD20/jDnyClGPdiqJdPcnP92ds7MAIkm2T3+ZsP9g7PDyhoXFirTNQ3b2GTPsqs7GFbhsYiRjsO37aGU6e6zEFoRTJNnNUtCilvorZEzUB2AJ8Q2v9+sCuqvAE7fRA+hkI/tf5a6GDdozcO1BAqPzotPE1/OzV95IUgux1nTjdk/P51lQpxlQH19OHTW43s12ZHd9u1q2rruSV7a0Zvcaw0kL2AMCGibUsfH6Lpx9o5pQ6Ft7Q4DhVO3hyTy7fd/w0T7zR7Az727K/3bm29u/8dd5hg0vdu4p+9SObfCvOhe1k5kPyuz9kw9PtsvaXdLkg5MKKzQfQ0z9NzZYXQ+YcBc8/CrObhcDOzqsMhHlyJZGAqWOGe4KjnYc6WLyu2cnuuPto2jq7TQVQy2a7RyXYQ1fd3/e1u456N79Ur7x2JmXPbmyb464uSDVSIKgXKZO+ymxmKNpVB09t2Bs4nHwwILZeKIvgSCk1H/gx8FVgtfXfFUqp6Vrr5pQvLnHCdrvT7YCHZXwy2TV/bM1unntrP1oHDx+dOaWOh/9kFovXNfMvv9vOsVPeeTHHOnMPjnTDtRzd8iJ3PHva23P0626iVwbP7gibeu4nYsAnLxzHmJoqNu9vz3hgbULj2TmcN2MSS76S7BjbOrs90rF2IGYHT0172pxeI4057G/ejEl87arzHYl1/98naHCprTpoP3fJV4Idmz9AXr6xJWeHEBZo5SMA60/Z8LAd0f4ehCsI2XJt4wRev+arHGjexILlLQEz4S5hwXPbWXxjrPfxLGYe5QNtjxTSvX2cFRErK56nYCkSUUmlgG/sbnNEaOz+V9uuOplzyzYrNNGIcnoybTsMvTOLqioMZ1jrnVecy6NrdifZ5myyK8s3mnbfLukLGimQay9SLjMUJ44cSiyhMw6+ygmx9QKUSXAE/A3wqNb6YevnryulPgP8BfC/B25ZhSdstzvdrlXQ6/yzG9z4Zb5tunpMgx70ugWX15vZj3Xh8enpbauIbljMgQMHQ9WTxo+o4uAJUy3J7kc6vGkFNz7RyaluqBk+lMqr/ipUjCGTwAhAJ8zhgLG4d9hoxFCglKMu5MfsufI6kq9ddT7bD3Zw/8odXNs4gQWX1zvSqj1xTcQwS/EaJtZ6+r78w/5spxT2dw7aZbQdLXhV6vz4SyjcJX3ZOgR/BstW38uHclwxSGcXwxoEIRV26dUvxj7GG4//0NWzadBFFd173sYYPpxbnlWcONFh2tuPpVarC+Os6go+fsEY3j9yyumZzARLq8bTkxqPa2adU8f6PW2BGf7zxw5nZ+tJz2MKQt9TJ3RSj6ebWEJz37Nm67RdSm64skVaQ8PEEc55xRNm36htV909RnbmKdvhqG78tsU+nn/ItGeURkIzP6QXKdXxu3u8yqhB7+8fOj7YSozF1gtQBsGRUqoSmAn8i+9XvwM+EvD8u4C7AOrr6/2/LkmCdqhS7VqFlVyleo37htvPkxv2Eo9rKiLKMxcJkntt3Jzauoro6w/wqxuNlOpJl0waSd2xTmcYn92PBJCLyTaFDZLLOhLgrLMnluCa6eP44OSRjmNYvrGFpda5umvV7Z3Dbqsko666ksXrmvmWpfL0+rvmLI1p42vMN0ZjGAYNE2uT+rzsuRxBTino7xM0uHSZb65H2E2EO+Byl/Tl4hBmTx3lSNK61ffuu74hayfrL2koBkc9EGuQ0o7yJ9/+aMHl9bR1drOz1bSRlZaNfcaxsWa2qOL63AfBRg34n5++0LFdfiXPmqoInT0J4gltmzvHBmlgbE3vZheYdtc/WsD9XlNHD+P9I6c8pWypgrG49X7RiHLU5pKek9A89Np7vbLUWjvl0RVRw9NDWhE1UJAUwMyeOiptRibbWUJ2Sbctmb3mPXPjzN5ccz8v3QBW//HtOXF/2NmrjBpmX3MRtSmV8ul0FIO/EQaekg+OgNFABPA3uBwCrvY/WWv9EPAQwKxZs0pdiCdrskkZuw1V2IWa4hJXsJXZ/L1K1zWOD1Soi615jCdvNFKqJylFxqIImRIx4M4rpvLQ67tC6941sGp7K3fPPc/TSGsLHPhV3upHDeO+Zzf3CiaMq/Ecb8XmA7R1dhOLm844Hg/u88q0Vt3GdmLLN7YESnW7VerCXm+Xv4UFZRk7LK09N0H2TUQ25xP2+Rxo6ez+XoOUdgwOCuGPZk8dRYVVFpaJjc2W+ZfWs3l/uxNYGMo73Lujq3dcgj8TlNB4AqMwbFGF3cc6WbntEIYduWSIAkdt7nhnN03Nx0kkvPZpz9FOz8/KUHx+Vu+QVXclBZAkiR3W7wnZCya4bcvaXUeda+vOcuWaobKPf//KHfxh55GkDbAw25ZNWWCplU+nohj8jTDwlENw1O/ke3ejP3dLlm9scQxvqgxBkJpdZUQlzW6oHVrheZ3fhf3zi9tCpbvbjx7mivrhnsfc6kmpZgv1hfmX1nNNw3ieeXNfSkfdE9dJJWl+h2HLaO8/fpqE7m3irYoanmNd2zgBwDNEN6zPKxcloGVWZs9unrWluv3iGZk66GydvC1Ja2P3U7nlxTMhrKShGNSR+nMNUtoh5MrMKaaU9JJ1zWltbLZEDUXDxFq++9xmJ7BIaBheGeFkBjPkUhExTH8yrmYI7x0+yXuHTznvoRKaT00fx0tbD6Ut4auIKF7Z3uopEYbefiF7RIKd/XcCpIT2DFn1f9/9wglB/Z422X5//e8VMZRjT+NWgBSmnmeT6j5i5hRzTlxYX3FfbVu5lE/bFIO/EQaWcgiOjgBxYJzv8XHAwXy/WSEUvvJxvEwCrKY9bTy1Ya/jDNwTuf0E1UEvvLGR7zyzyWmctcsPth3slZtumNjrcpv2tPHQ67uSjm2Xo5199gRWNx8PVE+KGCpwFoWbqIFnsGomRKw1fvGRtUly4/ba3O/a2tEVGlj4G2QjhiJhldy9ufc493x8KlsOnODaxglMG1/DFx9Z6xmiu+DyemeoXl9iwCCn8rWrzs9aEMGdRbLPOVOH5b5RALh6+jjucWXd3Ncs1ee01Esa8rXRUerXQRhY7PLc2lFjWN18Mi8KdRFlzmZ7ZXsrPb5ytb4GRmOGV3L4ZDfHTvVw7FRPYE9RdWUk0E5edk4dc6eNdbL5QSXCbnu47cAJ57XRiEJBRgNNtx/s4Mn1e0los0LiYx/ovYYGsHl/u2M3Pf2chmK/TxI7XSCz6KZGJyBy90OF2WB77lI8oR2RpKDjunuZIP2mWaa4y6pT3VekO4bYPKFYKPngSGvdrZRqAq4BnnL96hpgWb7fL9+7G/k4nn8gXSa7+wpz4GvYewUZu7W7jvbu5Fmvt5uAbYlquwRgweX1rN11NKlsrXZolMvPHcXdc89jR8MP+dO/uotfftarnnTeTXdzJAOluGwDIzBryx9bszswMHJOzPXWr2xv5ffbDmEoU+FoweX1jmPb55JTjcU1Y13CEbGEZsuBE07j6wOrdnqG6NqOtK66MinrA2R1g53KqWT7+QrMGGbgsNzCEABjaqpSBpNhn9NSLmnI58ZJKV8HYeCxPz//ob/JHT/7Do9+tm8KdR+cVMu2gx2s3HYopdiBn4vG1zD5rGpefucQ8YRZfjfG13MEcMSnaOrP6sQ1oRUIb7a0881rL/IEHu4S4brqSicI+Nmr7znVDwq4ctpYxtRUpRwqbR/TPdvoTE+C32/rLfdWCp5uaiEW7/3u33e9Och764ETznDZTOcQ2htndrZr0Qtb6O5JeIaAh62tuyfYzjftaXP6xNbtOgpKedbbZxtjl3nkWO4RVCIuCANFyQdHFj8CHlNKvQH8AbgHmAj8LN9vlO/djb4eL8kwprgBDmroTInP2LkbOw1D0Whlido6u50sjx0gTRtfQ0fAPKP20zF+t/UQV04bC+d/jNrP/DXzXnzYLPMYNYbKj3+Jz33+dn72WnLGKR8kNI6wQyAuq6zA2SFN6N7Az56HEY0ooobZ9JsADlkOX1nvY4sSPH7n7KSdRNuRGqp3+KAtp73MpYrklsROtdMYdiOd7ecrKGOYicOy+xzsG4+nm1qSGobDZnL1pda9mMj3xkmpXgehOJg5pY6//Mqf8bstB5n34i8dG5tKoW7CiCoO+AKXqKFoPLuWTfvaSejk0ulUbDvYwXtHTrHopotZtb2Vl99pdeykhwDjMm5EchAVRDye/F1zz5yzxQ0UXuVSjbn5FU/0jmAIY9nGlqTRDu4fE4CO9373bXU7u4QdsptDCMnff3sD1D0EHLA2IXsXYxgq0M577FNcA6mzUZnStKeN+1fucKTP3SqrueDfLCx1G1gMIhNC9pRFcKS1XqqUGgV8G3MI7GbgOq31nny/V753dPt6PP9AOkMFG8Zs38vOMrmN3deuOp875pzDQ6/v6hUeGF/D7KmjPDXSCW326ixdvzf0+A+sepd9x8/ApDnUfnmOU/9uKNjYHKxclIq+9CdFI8qcv6G1U86ntTUvQ+Nc30RCs3R9c6+iXdysgz/dE3caXQ0F9WdVO82+drDqFlrYf/w0S6yyD7TGMBTK6kOyX+MPIDLJuIQ52Gw+X2HBVDqHZfc5LLZlyANuWIJUmYqhATdfSFmIUAy4b8bW7jpK1YVzqZg2N6MeI39gpIBFNzUCpm/RLtGVTOmOmQOtV73T6vFV548dTvOxTmdWz2caxnvm510yaSQHfWI80yfUsO1gh2PrFXiyKf7srd0DaoYCycTi6QMEe/5cKrQ2g5KIZceVdd7uSots5hD6sWfkBQVUzqZlLOFUOKTbHLXHU2QyJykV7uutMcsL+3K8Yuo7ygfFIjIhZE9ZBEcAWuufAj/tj/fKdkc33c5BX3aIbSlnO5sTZhizfa+gG72mPW08svp9Z8fMTt9/7arzPTXSlVGDHYc6Ug5R3Xf8TODjCQ3rA2Rd0/Ugfez80fxh5xGnH8pQ5mv8tfF+Ljunjps/PIkt+9s53NHFy+8c8uwIfuWKc81zTmgqKwzGjhgCtDu/H11Txa0zJnkaXT/TMN7JfLkbdd09PW7lo/uub2DL/nZaO7o40tHlzFcKUkXKxWFk8/kKCqbsksB07z9vxqQkRadUxw47r1LdaZNSOGGgCSuLdWcwsmHciCrAnAcUt9NGvgNFlGnnwo6vlNm76bffzUdPsfDGRo/62pfmnOMRklnl6m8yFEyqq2bbAVfmX+Fs1AFJCqDKel2QG4gos+82FkskBVju7/DaXUeJxXtzToaygjLDHF5rn5ZSptiPnYGybWHEUE75HqS2E2G2b/ZU94w87wZopnbH/zzIrnw7aI1uG24o+Oj5oz0zlLKl3DaYyi3YG0yUTXBUrBRacKFQN2RhN8lh6Xt3jXTH6R5PWZwB3PXxqazYfJA9xzrTvrffj31wUi1VUSN0FgbAH9876nGACQ0Ta6qIRgxHahxg0sghTB0znNVWpufNvcf5773HicV10uyjeFxTM7SCpXd7ld9etRy2LZPtv1b+OUOb97d7fg5yUguf2+yUpFVEFPMvq/eUpfWnw/AHU5k6rEw+i/5jBwXgpbzTJqVwwkASVhb7nWc2sfVAinLiEA6e6OLbz2zqtYsu+2go8/NeV13Jqu2tjg3VvkBJa3h1x2FP2S2YQU1bZ3fSrD37PGZPHcUTd83hwVffY+VWc9PKr1Znu6PuWMIRJNDW2iqi5iw5w1DErfeNKDh3zHDOHT2Me+aex/aDHZ5yteajp3hk9fseYQM7MLHXHjEUt1mS38s3tjjZcp3QTHSp3dm20OkZssrtbJuWdU+mPTRKJRc2Zmp3/M8Ly5SF2fB0Pal9CYzs9ZTTBlO5BXuDCQmOCkw+dg7SGc0ww9jXHfigm2RbpMHOUkGv4s32gx2s3XWUA8dPe45z8aRa/td1F/HMm/uyXgP0ztUIHxQYnFVqOX6GyqjBzR+ayNpdRzl8spv97WfY337GcfZ2nTQkl+VFIsklijOn1HlksoP6ZJb7gqMt+9o9SkX+5z+waqcnwxWLJ0vKDqTDyOb9+ytLJQhCMmE3Y++k6rNMQ1DCXgFXXzSO19497GSl7CyNttTV3Ekme6j2mJoqntqwN1QdLsjXja6pcnqFgrJT5vv2KroZ9GYw3GXnCvjkRb2Dve2skF2u1h1LeGbfuSsj3CXDCZ/kd1i23LaFbpvW1ZNIGg9hn/f9K3eEjtmws1dhJcv5It29RljwnU/fVE4bTAPtu4XckeCowORj5yCXAKtgO/C6dwcOenthDCN8GvkcKyMQ9Q3yGzO8kg/X1/HKjsNOH08Qr2xv5cppY+ncuoqeNY/1ijd85EvMvuZm5kwdxSOr3w8s4+uJJRhWFWXciCFJzb0G5iZcWOXd/FmTPefonpmRinkzJvFUU4tzTpv2tXP7w2v53MxJgVPN/WIGYSVpA2lYC/X+uWapBEFIJmzDwb3xc2rrKmIuOxqdkyzQ4K+eU8B5Y4ezs/UkWL/bdeSUp1zP7E+12/y9inO2+MGSu+bQMLHWkZP225QgX5ecJ/Gh4PpLJvDi5oOmUI4vg+H02UQMXtneyspthxxb7rY3Snk32dyVEalKhm+dMQlt/TeoRK6uupJoxHD6cp7asNejjJdJ305/2cV09xpB6xho31TsyPUpTSQ4KjD52DnIxTAWotbVL9Lgru9OpOjtWbPrKL/4425P3XbEUPzsS7OcHpMfrNgWmhl6aeshnv/1k0Ref4ClNxpcUT+c1c0nWfDcA6wFtl/ySa6/ZEKg1Gs0oli6vjlJ9lsBH/3AaK5tnMDC5zZ7MkiAo17kv45hanJuZk6pY8lXvBPJu2MJFq9rDhQ0sLNR9oDBVJKy5Y7stAlC3wjacKiqMPuOOretonL1T3nyBuWxo6fAEyD5rXnEUFx27lm813rS+Z0dKNkBkN2L43YF7uPE4ppFz29h24ETxBKa9buPMW18DdBbRhfm655Yvze051RreP7tAyhs4ZyEk71325Ow+UdB5W9+YYMgu+TfgHSrv/p/d+UFY5ySQL+aWyZ9O/1lF9Pda4h9FgYLEhz1A33dOci1gTPMyOVabldXXYlhFZVXRA2ubZzgCBGoFJmjt1p6e26CjP/MKXXU+mY3uNHAmdW/ZPmNhjPM8Kpzoyy+Mca8Fx+jZ/pVHD3VjeHrGbIbYVf6FI/AVEOy1+CeJ7F5f3tSgOK+jkFqcmG9Nd+4+gLW7TrqqbMPm0FRbLtLAymKUGzXQhBKGbf/+PGTf8GDN6hAO2o0XJXUL2Rz5xXnUj9qWK+ap/W4bc+vbZxAW2c3ddWVnv5JNwm8vsAtee3ebArydZ+4cCwvBdhx59iJ3mxVLGHO/nPPFQJonFjrjKJwCzC47Y17KLcduLmvY6oSs7CApyeWYHRNFVUVwf7Y76ttv+S3wf1hFzMJfvzrKFUBHUFIhQRHJUK2DZxhRi7oNZBataZpTxsPvvoev99mNsVGDMV91zd4RBjsnqOl65vZvP9E6C5fpRVU2RLVthN4+Z1Wz/MmjRxCi0vRrv3oYa6oH+55zhX1EdqPHmacK1DzqDJpzdiaqqRGYKXgjjnnAL39Uu6mYP9194snLA8prwhyZrfNmszj65qd54TNoOgvMnFkpS6KIAiCF9se/X97Wrjii8F2dJSh+MS0sbyy4zA9Phnqjq4Yi17YQkJrDGXasURCE4kYTD6r2jN3B/CKOGDKdruzTgo8ktf+bI7/5vvVHYdDz80+Flo7FQB2344/03/HnHMsxdXkeUE2YWML/LbT3YNrD0q38Qc8t84wS6ozFVUaSBucTRAmvkIoVyQ4KmHSlc4FGTn/a4J27vyO6faH13p6ghKWypD/PWZOqWPB5fV869ebWOwKCGzOHzucqaOHsfA5c2it/X5rdx11dv7ADL6+etUHWPj8Fud9a0eNYXXzSWfHE2B1c5zJkyY6a542voZlG1t4uqnFmd/QMLEWZsG6XUfZefgUYJZhPPz6LqfUL51R91/HTIPOmVPqnP4jt4jFQDmPTB2ZyI8KQnngv6G/6Lx6VjcfTrKjtaPGoBOaD04eyd1zz+PBV9/jd1amRmNKcds2QQGfmDaWsTVVLF3fzJJ1zTy9YS9L7prDzCl1tHV2e3qcFHDu6GFOGZ792H3XNzg2O1XJuFtKWwHnjRlGc9tp4nEzKLF7Obcf7OA7z2xyyvoikeRM/5YDJ5LmBdnvkW68QGDvqW9Quk3Y5mSmPqZUbHCprFMQskWCoxIml14k/2uCdu78RrrH17BjGGZJwgOrdlJXXemZUwFmY+qTvj4fQ5lzLdy7h/b7Bc1qsrNSyze28NSGvVTM+RILnnuAxTfGuKI+wurmOF9eofjnf/uBx/HMnFLn7NC5a8ijEYOIS3whoSERC1YGSkcmQafneC4RC3+pRiryXa6QqSMTUQRBKH2Cbujv/e73+dLXv8JjN/Ta0QXPJaj8+Jc8DfYfnDySlValgAJaT5xxypY1pjT33AvGODa+O65ZZqmwzZ46igprKCmYown8ogoanA22MEEDG789+sHnPggkVzus3XXUk5n63MxJNE6sNUvBSS4FDxpE7Zemds8DChrO7R+Unm5zMlNKxQaXyjoFIVskOCphcmmODCoTS7Vz53d0EWXWn9tBh+087ZkQtkOYf2m9U06mgIvPrmXTvvbAieGpdtns7MuyjZP5f4Zi3ov/SfvRw4wcPYa//fb/4fYvfjHwHGdOqePeX29yyuzi8QSfvGgcL7/TSkJrUzkvDxPC3dcpzKmmcqBhFKJcIZ/zigRBKG6Cbui/9sUv8of3jjLvJ9931Oo+/ZX/yceuvcXzXbdthf36t1vaMYxeDbt4PEHrCe8gbzsAmjnFFKSxe3caJ9ay8LnNnudWRFRSYOIWNHCTaRbGb98aJ9Y6w2sNQ/GxD4xh2vialIOow6Spw2xnoQKDUrHBpbJOQcgWCY5KnFx2pzIpE3M/1+3obvUpuAGB2Re/9On8S+vZfmiLU5/tl7VOdR69v/sTllx4JbWYQdrIi6cByRmWpj1tLN/YwtL1zU4wFokY3D33PO6ee54nMMyXUQ8KOu3MWi4OtBDlCtk4sv5o/hUEoXCE3dD/x33/Hx/59M2OnPaCy+uTXmvbivtX7mD1u0ec+T52fGTb9G0HtzjHn2cFN7Y9tkVtHli10xmzoIBLJtVy3w0NWdm4TOyR377Zx7c3plZuPcTr7x7m8Ttne3pMM5GmDrOdhQwM/OsoVuED8RVCOSLBUQmSbyOZzggHGT/3rmLQXIYgZ+IWb8im4dN+jT2R3A6w9h0/zeJ1zY4Ud0VEsfDGRha9sMUjzGCXWATtOPrP2x0E5hp0Bk0R95cepqNQ5QriyARhcJBqM2TB5fUsuLyepj1tfOvXmwJHCMyc0qu46Yw6CBHkqauuZO2uo2w/2OFUFQTNEqqIGtx3Q4PzPtnauHS+z2/fKqOG4wuCNvHSbRgF+cJU71eoAEaEDwShf5HgKI/0x85OmJHM13tnYoTdDiWo58j9vGxqsIMyQP61PH7nbKcP6Yk3mj1zNbrjml+s3uXsFkJvyV9YyYb7vd3CE0+ub2b+pfU5zRwKKtUIU8MLQ8oVBEHoK6lsbtOeNm5/aI2j5PlUUwtLvhJw062UZ7Cr1l5BHjAHZXf1JLAmPXgCEfcsIX9ZXDY2LtsAwT6+7S/iCZ1ywHbTnjZHvXTmlDoWr2vmvmc3E09oqirSb3IVMoAR4YPyp1gzg4MVCY7yRH/t7IQ1huby3kFfxkyNcCYZiLAve9DjQdfPvZaungT3r9zBN66+gIkjhxJLaI9UrM2uI6eIRgzicVPcYfqEEcy/tD7tWv3CE7GAWRmZGq58ZX0ky1OeiBMUioG1VkbIpifWa2Pd/sA9vFuBk7Vv2tPGzCl1rN11tDc7Yx3OUDiCB6nGJYTZuL74Jj8TRw5l4Y2NnsDGXyUAJGX773t2s1MO2NWT4L5nN5PQOtTHFjKAKUfhg77YwXKzoZIZLD4kOMoT/bWzE2Qkc3nvsC9jvoxwqgxX0ONB51BXXenpa1r97hHW7z7Gfdc3EDVU4KBBtFlCp4CnNuxl0752th9KnmcRNLPCLTxhv2cmcud+iiXrU24OpBwQJygUC7OnjvLMgHPb2CB/EIkYXHnBGF7Z3soTbzQ7c4BmTx1FxFCeviJ7MKy/xC7TTTv7OxI1FLfNmsy8GZMCfVMqG5fKB7mrBJ7esJfbZk32+J8Vmw+QcMlzK0WSBLj//QoZwBSLT8kXfbGD5WhDJTNYfEhwlCf6a2cnzEhm+95hX8ZcSh2CyuvCMlz3r9zh7DK63zcs6OvVR+oNVto6u7lt1mQWrzMFFxSm80JDpVVCt3xji1Mn7zc2YcbVFp5o7eji1R2HHSU7RWq587C/00Aat3J0IOWAOEGhGLDt9sIbG9m8v50t+9p5u6XdYy/B/Lzed30DW/a3O7bWztp39ZgbR/94y8UsuqnRk1n5xtUX5PxZd7+uO649GXy/6E0qGxf2/v4qAdtPuP2PLfndHUtgKMWdV5zLo2t2p/SxhQ5gBtqn5JO+2MFytKHlmBksdSQ4yhP9ubMT1MuTrql02cYWT9Ntqi9jpkbYfQPul/T27zi+tfc4P165w5G19os4hJ2DPf8oQW+pRpAEubseHMyskTuoqquudNadKjB0B1CZyp0XI+XoQMoBcYLCQGP3GtkiNkvumsOtMybxxUfWBs7/iUYM0JpYwhyBYG9EaeDpphZunTHJI87Ql0076P2OBAkpfO2q851jP7BqZ0obN3vqKKKGoieuiRjKeX9/lUBFRHHrjEmOEmuYgFD9qGGOwl+YLS1kAFNOlQB9sYPlaEPLLTNYDkhwlEcGcmcn6L3dktb2Rpm76bavX8ZUkt52E67dDPvS1kNOsGIos+zCXdsedA7uNQYJP4St/4FVOz219AkNC5/b7JTWZWJc/WspNcOVz/LIUjrvYkecoDDQLNvY4pTS2cNb//GWi1PO/wHTvsfiGq16jxUL2VyC3D/r9uuWbWzh6aaW0Fl0Gdk4O5JTvYt2Vwn4lUmD/FHTnjbu/fUmntqwl1hCs373MWeYd399j8utEqAvdrBcbWg5ZQbLAQmOyhTbmLolrSE8U5ILtnNyZ46UUk6Wxi5hsLNFYD7HLrvI5L1TrTHsd/4aeDBLJ8JKBwGPSlEm71XsQUMqB5Ju7e5SyVx6BvJNsV/rbBEnKAwkKuRn/+eyMmpm7ZWhUGi0Nu173GVXDVdGJohcP+v26/zZHD+3zpjkEVVw23FbTMIeAu6X8M6mOsLtR3tiCZZvbDGDTF9fVF++16nsXKaVAKVkK/tiB8WGCoVGgqMyxTamfsmCfM/MsW/AO0738Mjq90lozaIXtiRlaWwn+4kLx3LP3PNSGrZ0TbbpjP/MKXUsuqmR71gyrGCWTgSVDuayI1cqu3hBAZ29GxuLB6/dfW6GdSMU1LfVX5TKtRaEUmHejEk81dRbJjwvYMzBzCl13Hd9g2NDKyKKz186mcaJtc6GiaEUi25qBHqDEshvNiXsJthvF9zrCpuvlIvf8/tRhelDNYT2ReVy3rZseJgaXibnIrZSEPKHBEdlhnvX393zM/eCMYytqcpqdyvTQGTmFHMKepCaj+1kbcP/+ruHuWfueSnfM8zAZ2P87Rr4oNIJ93nl0ptTiv08YTug/rV7SyXNWn2tg+eD9AeleK0FoZixy8rS2fYt+9udzaWeuGbLvnZunTEpVBQhaihQKnTjJZ94RBtiCR567b0koZ+w+Uo2mfg3f+/s52ZOcrJUyze2pBwwmylNe9o8suHdAcfJpJRMbKUg5A8JjsoIf/AQNLTOP+gu02Olc3SpdrbaOrvTyqDapDLw2Rr/sD4s/zXKdnexFBtCw3ZA09Xxpxt8WGhK8VoLQrGTSVmSv+rgrZZ2vvjIWu67vsF5zGOT42aY0B+ZZn9J956jnaFCP5lknsL8W6qgJJO+qExYu+uot1RRBZcqpvubia0UhPwhwVEZ4Q8e2jq7PYP3sgl4MglE/DtvYU4kG6Od6rn5LJNwX6NsmztLsSHUswOaoka+2M6t2NYjCIOFW2dM4ukNez3z5Lp6EnznmU2O9LV7cyliZY76Eihkim0X7l+5g9XvHjEDoxChnyCy2WgLC0oy7YtKx+ypoxxVVsMwSxVz7dMSWykI+UGCozIiXfCQjUNIdyx3jXTUVW4QNgU9U6Od6rn5MP5B55VLc2cxNIRm03yb7d9goM/NTbGtRxDKjSBbMnNKHUvumsOyjS08uWGvqVQH2LFS0OYSZNZzlA/hgJlT6vjG1Rewfvcxx55nKvSTzyxLX+1TPoMasZW5U0piFkLhUVr7k+eDh1mzZukNGzYM9DLySiYTw22HkK5ULuxYTXvamP/gGo8anKJ3xlEqFZ0gSe7+phyMoDTfCqWKUqpJaz1roNdRbAyUP8rEltz7603O0G1Ib++zeb9sSneDbHeu9rwc/ICQH8SfDl7C/JFkjsqMVDtH2e5QhR3LXyMNqRtS7SyTHUwZigE1QOWwuybNt4Ig5INUtsQOIBom1lJVkSxMkIvN8Ygp9CRSqrS5CbuBzdWel4MfEPKD+FPBjwRHg4x0DiFTBR+7Rto9AyOoPMGvxAMMKgOUyfXMZQdTmm8FQcgHddWVGNawVLct6UuGJxVu26WUyotYTxD9lRmSDFTpI/5U8CPBkeCQq4IPhNeZr911lISvdNNQ+Z23VKxkcj1zTedL860gCH2laU8bi17YQjxhyvbfd31DqDqoX+AnV9y2yx403VexnqDz6o8yKSnHKg/Enwp+JDgqAKW6k5Stgo/9mtlTR4U6TbfkqqEUd15xLjVDK0ru2uRCJtezL+l8KQsRBKEvuCX+tda0dXY7vyvkbrrbdk0bX9NnsZ6w88q1SiFTH16M5Vilev8x0Ig/FdyUdHCklHoFmOt7eKnW+gsDsBygtHeSCrEzl8uOTLkY90yup6TzBUEYKFLZn6AKgUxm5GVLNjelmT63L3Y1Gx9ebPa7lO8/BKGYKOngyOL/Ad9y/Xx6oBYCxbmTlCmF2pnLxKG51ewWvbAlZ+NeTIFVJtdT0vmCIAwU6eyPbbuzuekuBhtsn9eyjS2oLF+brW8rJvtdyvcfglBMlENw1Km1PjjQi7Aptp2kbOmPnTk/bsdrZNGgm+o4xbJrlsn1lHS+IAgDRSb2J9Ob7mKzwcs3ttAdS7BsY0vGa8nWtxWT/S71+w9BKBbKITj6glLqC8AhYAXwD1rrjrAnK6XuAu4CqK+vz/tiim0nqVDk8zzdjhetMSwFvGyNu+yaCYJQShTaH+WLTG+6i8kG57qWUvbhpbx2QSgmSj04WgzsAfYDDcA/AZcAnwp7gdb6IeAhMIfuFWJRxbSTlCuZlEbk6zz9jjdXyVjZNRMEoZToD3+UDzK96S4mG5xqLen8Wyn78FJeuyAUC0rr4rLHSqnvAfemedpVWutXAl57GbAOmKm13pjuvQZqInmxMxClEfmqUy+GendBEMIJm0g+2CkXf1RMNjhoLcVW+icIwsAR5o+KMXN0P/CrNM9pDnl8AxAHPgCkDY4GI5k4rmzKEfLlCPO129Vfu2bFdAOQD8rtfARBGBjcYx7cPw/UWjIZn2A/nq3960+7KTZ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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit_a = av.from_cmdstanpy(fit, coords={\"J\" : np.arange(data[\"J\"])}, \n", " dims={\"theta\": [\"J\"]})\n", "av.plot_pair(fit_a, var_names=[\"theta\", \"tau\", \"mu\"], \n", " divergences=True, coords={\"J\": np.array([0])});" ] }, { "cell_type": "markdown", "id": "2d33ec20", "metadata": {}, "source": [ "We see that the divergent transitions are clustered around small tau values before an abrupt stop. This indicates a funnel geometry that the sampler is not able to penetrate.\n", "\n", "
\n", "\n", "This is a well-known problem for models of this type. We can try to reparametrise our model using a [non-centred parametrisation](https://mc-stan.org/docs/2_18/stan-users-guide/reparameterization-section.html). We can introduce $\\theta^\\prime$ such that\n", "\n", "
\n", "\n", "$$\n", "\\theta = \\mu + \\tau \\theta^\\prime,\n", "$$\n", "$$\n", "p(\\theta^\\prime | \\mu, \\tau) = \\mathcal{N}(0, 1).\n", "$$\n", "\n", "
\n", "\n", "This is implemented in the `stan/schools_nc.stan` model." ] }, { "cell_type": "code", "execution_count": 8, "id": "1639478b", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:55.340780Z", "start_time": "2021-09-02T17:59:55.212381Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data {\r\n", " int J;\r\n", " real y[J];\r\n", " real sigma[J];\r\n", "}\r\n", "\r\n", "parameters {\r\n", " real mu;\r\n", " real tau;\r\n", " real theta_prime[J];\r\n", "}\r\n", "\r\n", "transformed parameters {\r\n", " real theta[J];\r\n", "\r\n", " for (j in 1:J)\r\n", " theta[j] = mu + tau * theta_prime[j];\r\n", "}\r\n", "\r\n", "model {\r\n", " mu ~ normal(0, 5);\r\n", " tau ~ cauchy(0, 5);\r\n", "\r\n", " theta_prime ~ normal(0, 1);\r\n", " y ~ normal(theta, sigma);\r\n", "}\r\n" ] } ], "source": [ "!cat stan/schools_nc.stan " ] }, { "cell_type": "markdown", "id": "f9a43894", "metadata": {}, "source": [ "We can now try to fit this model instead..." ] }, { "cell_type": "code", "execution_count": 9, "id": "f6020cf9", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:56.381136Z", "start_time": "2021-09-02T17:59:56.225838Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:cmdstanpy:found newer exe file, not recompiling\n", "INFO:cmdstanpy:compiled model file: /Users/fran/projects/bayesian_workflow_prep/stan/schools_nc\n", "INFO:cmdstanpy:start chain 1\n", "INFO:cmdstanpy:start chain 2\n", "INFO:cmdstanpy:start chain 3\n", "INFO:cmdstanpy:start chain 4\n", "INFO:cmdstanpy:finish chain 1\n", "INFO:cmdstanpy:finish chain 2\n", "INFO:cmdstanpy:finish chain 3\n", "INFO:cmdstanpy:finish chain 4\n" ] } ], "source": [ "model_nc = CmdStanModel(stan_file=\"stan/schools_nc.stan\")\n", "fit_nc = model_nc.sample(data=data, iter_sampling=1000, chains=4, seed=42)" ] }, { "cell_type": "code", "execution_count": 10, "id": "8ee9c37e", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:57.101545Z", "start_time": "2021-09-02T17:59:56.865987Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:cmdstanpy:Processing csv files: /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools_nc-202109021959-1-l88z3sq5.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools_nc-202109021959-2-fu__im24.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools_nc-202109021959-3-aban8y1p.csv, /var/folders/8d/cyg0_lx54mggm8v350vlx91r0000gn/T/tmpzj3y24z3/schools_nc-202109021959-4-jbwdsw96.csv\n", "\n", "Checking sampler transitions treedepth.\n", "Treedepth satisfactory for all transitions.\n", "\n", "Checking sampler transitions for divergences.\n", "No divergent transitions found.\n", "\n", "Checking E-BFMI - sampler transitions HMC potential energy.\n", "E-BFMI satisfactory.\n", "\n", "Effective sample size satisfactory.\n", "\n", "Split R-hat values satisfactory all parameters.\n", "\n", "Processing complete, no problems detected.\n" ] }, { "data": { "text/html": [ "
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MeanMCSEStdDev5%50%95%N_EffN_Eff/sR_hat
name
lp__-6.9000.0612.40-11.00-6.500-3.61500.09200.01.0
mu4.4000.0523.30-1.104.4009.64000.024000.01.0
tau3.6000.0593.200.232.90010.03000.018000.01.0
theta_prime[1]0.3100.0150.96-1.200.3101.94289.026151.01.0
theta_prime[2]0.0860.0150.94-1.500.0971.64219.025729.01.0
theta_prime[3]-0.0840.0140.95-1.60-0.0821.54489.027371.01.0
theta_prime[4]0.0450.0150.94-1.500.0371.63772.023001.01.0
theta_prime[5]-0.1600.0130.93-1.70-0.1601.45229.031884.01.0
theta_prime[6]-0.0730.0140.94-1.60-0.0701.54289.026152.01.0
theta_prime[7]0.3700.0150.96-1.300.4101.94290.026156.01.0
theta_prime[8]0.0730.0140.97-1.500.0591.74492.027392.01.0
theta[1]6.1000.0905.60-1.605.50016.03933.023981.01.0
theta[2]4.9000.0674.60-2.504.80012.04796.029245.01.0
theta[3]3.9000.0815.10-4.704.20012.03994.024354.01.0
theta[4]4.7000.0724.70-3.004.60012.04191.025554.01.0
theta[5]3.6000.0704.70-4.603.90011.04505.027471.01.0
theta[6]4.1000.0794.90-3.804.20012.03819.023289.01.0
theta[7]6.3000.0805.00-0.935.80015.04005.024418.01.0
theta[8]4.8000.0895.30-3.504.70013.03543.021606.01.0
\n", "
" ], "text/plain": [ " Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s \\\n", "name \n", "lp__ -6.900 0.061 2.40 -11.00 -6.500 -3.6 1500.0 9200.0 \n", "mu 4.400 0.052 3.30 -1.10 4.400 9.6 4000.0 24000.0 \n", "tau 3.600 0.059 3.20 0.23 2.900 10.0 3000.0 18000.0 \n", "theta_prime[1] 0.310 0.015 0.96 -1.20 0.310 1.9 4289.0 26151.0 \n", "theta_prime[2] 0.086 0.015 0.94 -1.50 0.097 1.6 4219.0 25729.0 \n", "theta_prime[3] -0.084 0.014 0.95 -1.60 -0.082 1.5 4489.0 27371.0 \n", "theta_prime[4] 0.045 0.015 0.94 -1.50 0.037 1.6 3772.0 23001.0 \n", "theta_prime[5] -0.160 0.013 0.93 -1.70 -0.160 1.4 5229.0 31884.0 \n", "theta_prime[6] -0.073 0.014 0.94 -1.60 -0.070 1.5 4289.0 26152.0 \n", "theta_prime[7] 0.370 0.015 0.96 -1.30 0.410 1.9 4290.0 26156.0 \n", "theta_prime[8] 0.073 0.014 0.97 -1.50 0.059 1.7 4492.0 27392.0 \n", "theta[1] 6.100 0.090 5.60 -1.60 5.500 16.0 3933.0 23981.0 \n", "theta[2] 4.900 0.067 4.60 -2.50 4.800 12.0 4796.0 29245.0 \n", "theta[3] 3.900 0.081 5.10 -4.70 4.200 12.0 3994.0 24354.0 \n", "theta[4] 4.700 0.072 4.70 -3.00 4.600 12.0 4191.0 25554.0 \n", "theta[5] 3.600 0.070 4.70 -4.60 3.900 11.0 4505.0 27471.0 \n", "theta[6] 4.100 0.079 4.90 -3.80 4.200 12.0 3819.0 23289.0 \n", "theta[7] 6.300 0.080 5.00 -0.93 5.800 15.0 4005.0 24418.0 \n", "theta[8] 4.800 0.089 5.30 -3.50 4.700 13.0 3543.0 21606.0 \n", "\n", " R_hat \n", "name \n", "lp__ 1.0 \n", "mu 1.0 \n", "tau 1.0 \n", "theta_prime[1] 1.0 \n", "theta_prime[2] 1.0 \n", "theta_prime[3] 1.0 \n", "theta_prime[4] 1.0 \n", "theta_prime[5] 1.0 \n", "theta_prime[6] 1.0 \n", "theta_prime[7] 1.0 \n", "theta_prime[8] 1.0 \n", "theta[1] 1.0 \n", "theta[2] 1.0 \n", "theta[3] 1.0 \n", "theta[4] 1.0 \n", "theta[5] 1.0 \n", "theta[6] 1.0 \n", "theta[7] 1.0 \n", "theta[8] 1.0 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_nc.diagnose()\n", "fit_nc.summary()" ] }, { "cell_type": "code", "execution_count": 11, "id": "20df87b5", "metadata": { "ExecuteTime": { "end_time": "2021-09-02T17:59:57.986280Z", "start_time": "2021-09-02T17:59:57.676526Z" }, "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit_a_nc = av.from_cmdstanpy(fit_nc, coords={\"J\" : np.arange(data[\"J\"])}, \n", " dims={\"theta\": [\"J\"]})\n", "av.plot_pair(fit_a_nc, var_names=[\"theta\", \"tau\", \"mu\"], \n", " divergences=True, coords={\"J\": np.array([0])});" ] }, { "cell_type": "markdown", "id": "f67b8284", "metadata": {}, "source": [ "### Further reading\n", "\n", "* Michael Betancourt's [*A Conceptual Introduction to Hamiltonian Monte Carlo*](https://arxiv.org/pdf/1701.02434.pdf), on which the above is based.\n", "* A more mathematical approach: Betancourt at al. (2017) [The geometric foundations of Hamiltonian Monte Carlo](https://projecteuclid.org/journals/bernoulli/volume-23/issue-4A/The-geometric-foundations-of-Hamiltonian-Monte-Carlo/10.3150/16-BEJ810.full), Bernoulli 23(4A), 2257-2298.\n", "* The No-U-Turn algorithm: Gelman et al. (2014) [The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo](https://jmlr.org/papers/volume15/hoffman14a/hoffman14a.pdf), Journal of Machine Learning Research 15, 1593-1623.\n", "* The [Stan website](https://mc-stan.org).\n", "* The eight schools problem: Section 5.5 of [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book/) by Gelman et al. " ] }, { "cell_type": "code", "execution_count": null, "id": "efe34fd2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "bayesian_workflow", "language": "python", "name": "bayesian_workflow" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }