{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Vertical mixing with analytic inputs\n", "\n", "In this example, we look at turbulent mixing in 1D using an analytic diffusivity profile to drive particle movement. In so doing, we examine the ability of different numerical schemes to reproduce the Well Mixed Condition (WMC), which states that if a tracer is initially well-mixed it will remain so over time (Thomson, 1987). The example illustrates a problem that was identified in several models of turbulent mixing back in the late 1990s. As described by Visser (1997), the problem related to the inability of standard (\"naive\") random walk models to reproduce the WMC in spatially inhomogeneous diffusivity fields. Visser (1997) derived a formulation that corrected the problem, which later became widely used in particle tracking models for marine applications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background theory\n", "\n", "In 1D, and without advection, a standard (\"naive\") random walk model computes changes in particle positions using an equation of the form:\n", "\n", "$$\n", "\\begin{equation}\n", " z_{n+1} = z_{n} + \\left(2 K \\left(z, t \\right)\\right)^{1/2} \\Delta W_{n} \\qquad \\text{Naive scheme,}\n", "\\end{equation}\n", "$$\n", "\n", "where $K$ is the vertical eddy diffusivity and $\\Delta W$ is an incremental Wiener process that builds stochasticity into the model. While such a model works fine in spatially homogeneous diffusivity fields, it breaks in spatially inhomogeneous fields, as particles tend to accumulate in regions of low diffusivity. Grawe et al (2010) presented multiple numerical approximations, including that derived by Visser (1997), which correct for the artificial build up of particles in regions of low diffusivity through the inclusion of a deterministic drift term. Three of these have been implemented within PyLag. Without advection, and while taking the form of the diffusivity profile to be invariant with respect time, these are:\n", "\n", "$$\n", "\\begin{equation}\n", " z_{n+1} = z_{n} + \\left(\\dfrac{\\partial K\\left(z\\right)}{\\partial z}\\right)\\Delta t + \\left(2 K\\left(z\\right)\\right)^{1/2} \\Delta W_n \\qquad \\text{Euler Scheme,}\n", "\\end{equation}\n", "$$\n", "\n", "$$\n", "\\begin{equation}\n", " z_{n+1} = z_{n} + \\left(\\dfrac{\\partial K\\left(z\\right)}{\\partial z}\\right)\\Delta t + \\left(2 K\\left(\\widetilde{z}\\right)\\right)^{1/2} \\Delta W_n \\qquad \\text{Visser Scheme,}\n", "\\end{equation}\n", "$$\n", "\n", "$$\n", "\\begin{equation}\n", " z_{n+1} = z_{n} + \\frac{1}{2} \\frac{\\partial K\\left(z\\right)}{\\partial z} \\left(\\Delta W_{n}^{2} + \\Delta t \\right) + \\left(2 K\\left(z\\right)\\right)^{1/2} \\Delta W_{n} \\qquad \\text{Milstein Scheme.}\n", "\\end{equation}\n", "$$\n", "\n", "The Euler and Visser schemes are identical, with the exception that in the Visser scheme, $K$ is evaluated at a position:\n", "\n", "$$\n", "\\begin{equation}\n", " \\widetilde{z} = z_{n} + \\frac{\\Delta t}{2} \\frac{\\partial K\\left(z\\right)}{\\partial z}.\n", "\\end{equation}\n", "$$\n", "\n", "In the language of stochastic differential equations, a given appoximating process is said to converge in either a \"strong\" or a \"weak\" sense: strong convergence relates to how closely the approximating process reproduces sample paths; weak convergence to how closely some function of the value of the process is reproduced, for example, the mean particle position. The Euler and Visser schemes converge with order $\\left(\\Delta t\\right)^{1/2}$ in the strong sense, and with order $\\Delta t$ in the weak sense. In contrast, the Milstein scheme converges with order $\\Delta t$ in both the strong and weak sense. Here we are insterested in the mean position of particles within the water column, meaning we are most interested in each scheme's convergence in the weak sense. Given this, we expect each approximation to perform equally well.\n", "\n", "We will test this expectation below using the same diffusivity profile that Visser (1997) used. The diffusivity profile is given by the analytic experession:\n", "\n", "$$\n", "\\begin{equation}\n", " k(z) = 0.001 + 0.0136245 z - 0.00263245 z^{2} + 2.11875 \\times 10^{-4} z^{3} - \\\\\n", " 8.65898 \\times 10^{-6} z^{4} + 1.7623 \\times 10^{-7} z^{5} - 1.40918 \\times 10^{-9} z^{6}\n", "\\end{equation}\n", "$$\n", "\n", "where $k(z)$ is the vertical diffusivity as a function of depth, $z$. Depth is measured up from the sea floor ($z = 0$m) to the sea surface ($z = 40$m). A plot of the diffusivity profile is shown below. As in previous examples using analytic expressions, we encode the profile within an object of type `DataReader`, which allows it to be used with *Pylag* in the same way as any other `DataReader` object. In the following, we instantiate a new `DataReader` object and plot the analytic profile." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 40.0)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib\n", "from matplotlib import pyplot as plt\n", "\n", "from pylag.particle_cpp_wrapper import ParticleSmartPtr\n", "from pylag.mock import MockVerticalDiffusivityDataReader\n", "import pylag.random as random\n", "\n", "from pylag.processing.plot import create_figure\n", "\n", "# Ensure inline plotting\n", "%matplotlib inline\n", "\n", "# Seed the PRNG\n", "random.seed()\n", "\n", "# Create data reader\n", "data_reader = MockVerticalDiffusivityDataReader()\n", "\n", "# Get z min and max. We give dummy values for the time and\n", "# particle arguments, which in this example, aren't used to\n", "# compute z_min or z_max.\n", "z_min = data_reader.get_zmin_wrapper(0.0, ParticleSmartPtr())\n", "z_max = data_reader.get_zmax_wrapper(0.0, ParticleSmartPtr())\n", "n_z_levels = 41\n", "\n", "# Reference heights above the sea bed\n", "z_levels = np.linspace(z_min, z_max, n_z_levels, dtype=float)\n", "\n", "# Generate the profile for plotting\n", "Kz = np.empty_like(z_levels)\n", "for i, z in enumerate(z_levels):\n", " Kz[i] = data_reader.get_vertical_eddy_diffusivity_analytic(z)\n", "\n", "# Create figure for plotting\n", "font_size = 15\n", "fig, ax = create_figure(figure_size=(10., 10.), font_size=font_size)\n", " \n", "# Plot the diffusivity profile\n", "ax.plot(Kz*100., z_levels, 'b')\n", "ax.set_title('Diffusivity profile', fontsize=font_size)\n", "ax.set_xlabel(r'K x 10$^{2}$ (m$^{2}$ s$^{-1}$)', fontsize=font_size)\n", "ax.set_ylabel('Height above sea bed (m)', fontsize=font_size)\n", "ax.set_ylim(ymin=z_min, ymax=z_max)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The profile is designed to reflect observed diffusivity profiles found in stratified, shallow water environments, where the diffusivity is often high in the surface and bottom layers, and low in the middle of the water column.\n", "\n", "We will evaluate the different schemes using the WMC. Brickman and Smith (2003) outlined an algorithm for demonstrating the WMC, which involves running an ensemble of $M$ model simulations, each involving $N_{p}$ particles, that are initially uniformly distributed in space. The same basic algorithm is followed here. Each simulation uses its own, random particle seed of $1000$ particles with initial $z$ positions uniformly distributed between the sea floor and the sea surface. Each simulation is run for 4 hrs using a time step of 6 s, and 5 simulations are run in total. At each time point, the concentration of particles is computed at $N_{z}$ (=41) equally spaced z-levels using an Epanechnikov Kernel Density Estimator (KDE) to compute particle concentrations. The time mean concentration $\\overline{C(z)}$ at each depth level is then computed for each member of the ensemble. Finally, the ensemble mean concentration $\\left\\langle\\overline{C(z)}\\right\\rangle$ is computed across the full ensemble. The WMC is said to be satisfied if the ensemble mean at each depth level lies within one standard deviation of the initial particle concentration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running the particle tracking model\n", "\n", "The experiment requires us to run an ensemble of simulations. Furthermore, we want to be able to do this using different numerical integration schemes. To make things a little cleaner, we will use a helper function that will run a single simulation and return particle positions over time." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from configparser import ConfigParser\n", "\n", "from pylag.mock import MockOneDNumMethod\n", "\n", "\n", "def run_particle_simulation(model_name):\n", " \"\"\"Run a single simulation\n", "\n", " An initial particle seed is created. Particle starting depths are uniformly\n", " distributed over the vertical grid. Particle trajectories and final positions\n", " are then computed by integrating the model forward in time using the named\n", " iterative method.\n", "\n", " Parameters:\n", " -----------\n", " model_name: str\n", " Name of the iterative method under test\n", "\n", " Returns:\n", " --------\n", " particle_depths: ndarray[# particles, time]\n", " 2D numpy array of particle depths\n", " \"\"\"\n", " # Create a run config\n", " config = ConfigParser()\n", " \n", " # Specify that we are not restoring to a fixed depth\n", " config.add_section(\"SIMULATION\")\n", " config.set(\"SIMULATION\", \"depth_restoring\", \"False\")\n", " config.set(\"SIMULATION\", \"fixed_depth\", \"0.0\")\n", " \n", " # Set the coordinate system, which here is a simple cartesian coordinate system\n", " config.set('SIMULATION', 'coordinate_system', 'cartesian')\n", " \n", " # Specify the numerical scheme we will use\n", " config.add_section(\"NUMERICS\")\n", " config.set(\"NUMERICS\", \"num_method\", \"standard\")\n", " config.set(\"NUMERICS\", \"iterative_method\", model_name)\n", " config.set(\"NUMERICS\", \"time_step_diff\", str(time_step))\n", "\n", " # Use a reflecting vertical boundary condition\n", " config.add_section(\"BOUNDARY_CONDITIONS\")\n", " config.set(\"BOUNDARY_CONDITIONS\", \"vert_bound_cond\", \"reflecting\")\n", "\n", " # Create test object using the run config\n", " num_method = MockOneDNumMethod(config)\n", "\n", " # Initial z positions - uniformly distributed in the first instance\n", " z_positions = []\n", " for i in range(n_particles):\n", " z_positions.append(random.uniform(z_min, z_max))\n", "\n", " # Create array in which to store particle depths\n", " particle_depths = np.empty((n_times, n_particles), dtype=float)\n", "\n", " # Integrate the model forward in time\n", " for t_idx, t in enumerate(time):\n", " # Save z positions for the last time point\n", " particle_depths[t_idx, :] = z_positions[:]\n", "\n", " # Compute new z positions\n", " z_positions[:] = num_method.step(data_reader, t, z_positions)[:]\n", "\n", " return particle_depths" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To speed things up a bit, we use an object of type MockOneDNumMethod to help manage the integration. While not strictly necessary, it cythonizes the particle loop, which yields a speed up over doing the same operation in python. Note the function references a time array, which we are yet to create. We set these below, then run ensemble simulations using different numerical approximation techniques. The data from each method are saved into separate arrays." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Time variables (s)\n", "time_start = 0.0\n", "time_end = 3600.0*4\n", "time_step = 6.0\n", "time = np.arange(time_start, time_end, time_step)\n", "n_times = time.shape[0]\n", "\n", "# No. of particles to use in each simulation\n", "n_particles = 1000\n", "\n", "# No. of trials to use in each ensemble\n", "n_trials = 5\n", "\n", "# Store outputs in a dictionary\n", "particle_data = {'Diff_Naive_1D': np.empty((n_trials, n_times, n_particles), dtype=float),\n", " 'Diff_Euler_1D': np.empty((n_trials, n_times, n_particles), dtype=float),\n", " 'Diff_Visser_1D': np.empty((n_trials, n_times, n_particles), dtype=float),\n", " 'Diff_Milstein_1D': np.empty((n_trials, n_times, n_particles), dtype=float)\n", " }\n", "\n", "# Run the particle ensembles\n", "for method, data in particle_data.items():\n", " for i in range(n_trials):\n", " data[i, :, :] = run_particle_simulation(method)[:,:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualising the result\n", "\n", "We can quickly visualise the output using 2D histograms to highlight the position of particles throughout the water column and how these change with time. We do this for one of the trials for each method under test." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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sCc1bgQR4bNX0R3imI+/Vxj3A755m/oW6wq4X96MutqfiSimH5dy5hyszhv+B08fsE+uVEcu6cQ9XZqyeDhvHVyb3cPXF4vnwk6ji07XAa1E1p+GL0JfVee+6DwxEZBNqjPGDxphoDYmvKaBtjElWTW8ARRHJXQSH1MsOY8wh9LbRFU2mbX3fRufDsv5cqTFsjFkEFjc6H5b140qN1dNh4/jK5GqMxfPhWvEkEpEi+g7Be1c82ndZnfduxB2DdwJfNMb879Mss9ZzkHKqeSLyOuB1AJLL3e1fN0MuF5NzElxJKTgDQuPTS3w8SREMjhgKzoBemsMRQyAR7SRP1evhYOinPjknphXndb4T0U0CBEM3zpGmggECTx97ixIXYwSTCqSCxGB8o79TMML4wS0xeH6CQXCdlEHPR1IgSDFGRqWUSH8P15UIjAtuCEkAYoAUTLYXJQETGIh1mxitteH2xYBxdB1kRU064ISatpNA6ujs1M0Wc7L8GHRMm6WJycqU5cE443SdAaTB+DcOpN54myZncEIZrSPpKLv6I3sLwbhZ2dOsfE5WlgScVPMKYHydNqoPo2lJkqUxrIskq0/JtuGCE2XTxruH7skjJ40xM2vE4UXlGbHr5+7OT23Wejc8Yx+mWT4hqytvHBepC06cLZ+O94MkWi/GWVFGWbGfUl3fiXRa6o9jxetBksvSzfZZmu2H1M/qNtvmcJ+wMrZW1KVxs31jxvWcBuD2s3zG2b70dP3UW5FEmm0/S8c4+j8dxnw8jgPJYtSwIg9ZHJhV8T5K3h+3DWcAaU7bggBuP8U4gnFknKcsL6m3Il8Oz4ijUR6cFcsN49Uf5wvR6bi6D3ENMhCNX0f7jhFG5zvhuH9w4iw90e26A62H/okNiN1c7u5gcrM+4Z7F3bCMxjM4fRnVv5NobLlhVndO1kZX9ktZLHkhYAzGEZJAy2wYx4DxsrjPtilp1k6Mxlya9UteaEj9cX/qxON+zTjj/iP1NA/OQNN2wnHMG9FpbsioPzSi+9Wg81J33O6cSOMzCbQ8kuj/YfszAm6k23SiZ8a9cXTZYd8oJuvrsjbsxLqtUX9I1i6jrGzuuN2Z7MltZ8XDGMN1kXF8Sqrx7w7Gfe2w/kDzSrZ73BhIDZIYjCeknozradi+snwPjw3D8gzbkKRZ3tDp/fmN6XMLE5t13w6blj+OqdEbG8n4+Dg6hg7LuaIsxs32wYpjrhNp/ELWztH+z+tC4o9jUUzWnrN2IMn4GCpJtu0szSTQdJzBuF8c5sWJdP3UG7c1rz9O14iu44VZHGR5GpbLuFn5s/RG+yiL4WGfPdyXw/ga7W8ZH0skeyvAZMe0NAe4RpeNNHAlyvqLFXVqctpnGEf7D7cj47ae5XWYF2cw7gtIx33P8HzHCVeUj3HdDvMv2TFn2I6HeXcH0GmMY/LbX1Eyi/XV5+3K/Q+GX0NlUYe81xjz3jUX1kFBmWc7qJ/Tee+lZF0HBiLyHODHgG/MXANBDUIAJkQkQUdIFRFxV42eJlGDjWc9a5btgPcC5Oe2m61vfz07ZhfZXl5iwu9xe+koB/ubeWR5C5NBj5wTU3Ajbi8d5eHOLEU34ob8CT63dCPfVvsaRSdkf38bc7k6n166hYIbcVPhBPc1d5JzYu6f305/4JPEDjds0VckjjQmSVKHQceHrkew4BJujZHQwWs5pIEhKWZR7Ro2zS0RxS6TxR5PPbIVr+UgN7eJ+rpLTCJ480HWOei6+XmXqGqoHhCau/UkwQ0hnNZ0cw2HwQ19aOTwWo4ePDztgNKcNqCoov9HJ2tAXITqQRhUIN8whFXBSSCc0mXionZezgC8jq7rd3VeEuiBMpzS5VJPly0dhdbO8e8kgP70eJv92ZjSQW+0zso8OfG4MUdVTddvQa6pv5MA/CYETc0rQH9G5zshDLJ8S6LTBlVGdZFrakc5POjHJSgdMyTB+CTMDQ33//F/Xmn0c8l4RuzObjc3vfpNhFNap153nO9wCoqZWrbfMfRrQpKDJA+DKUN+QfC6ul5U1LrMtaA3o3VWnB+Xe1jnwwFmcV6ndWdT3K6D8QybHoTmLqGwoPUBEFYFvwvdrVq3+brmJSoJcaAHseEAc1SXA63/XFPLEmcHtM6ulIl9DqkH+boh107pbXJwQ+jOaPzpvgCvb5AEBlUhKmqa/Wmdn2uM48ALNa+pJ6M8aDzp/h3G3vCgClqWNDBILFQOQ3sOKod1nYnH+yR5l6js0pt2cWKjA6VE8+iF+jsqPjOOhnkYxvyw3QRNQ2ebxtmobXZ03cGUIakk5I96DGopaSHF6Y1HMBILSSWhdNDL/kNxQdNLPW3flcNaDw//9pvWPXaDHdvNja9+E3FJy9Tbqvsu9SDaGlHe64/qv1A3NHcJEwc0dpJAY8TtZyf6sca124epxxOc2DAoOzR3ORQWtG69vqE7I/RntG8YbtNv6X5wYvDbKb1pl6gItcdiOls0KJJAyNfTUUxEJaGX9R/9ac1z+Qj0a1A9ZPB6Kd0tLnGgfcvEATOKq9QTcu2U1IVw0qE/JaN2VzpmCJZSlq93SfKafr6uZTautoXysZR+zaF4PBnFGGie8nWTXQgyeH2tA+Nq/gqLKeGEM2p7TqKxnF/QuBhUZdTuBlVdp3RsfG7RnxLiUnaym8Wn34XOrMaR39FY7s7ocgDlI7p+6gml4wluL8FvRQxqAb1NLm5o6G52iLMjuhPqyWe/psed/MJ4/0qi2xtkD44YD/a+a/3jtrhlu7ntu99IEsiob+rPaN87bJugv6MqBI3seBhmJ+1oefyu1nM4BYV5bevDvqB0PGFQ1rYcTuh38waY+UpKe5tDcUFjwutrex72obnW+BjqN/XYPExzebf2I+Ujut1hnUui/blxNQaDBrR3Gqb2ZgNxF+K8MKho2wonHMIJTWtYrqiq5R2mF1X1dxJoPGmfPT7WD+PL7WvfnOSgt83gdYRcQ9eNqrr9zs4EqUSYrkcw72laC9p2va5uw7iQzPbJP5onqkA8E1H7ok84pcsM8zrMS/motp1wSvPfnxmfr0QVPbcB7adhXLfD8w2/o31J0NT23N2q5a8cSfnCB948ismT9YQvfnRuzZjytx3oG2Oef5Yh+Frg8aFvScY5n/deStb75eObAB81mmhkn9/L5h1BX0h+FB2nr3bpvTWbZ7FYLBaLxWKxXDGIyAT6MvHquwWX1Xnveg8MPou6Ka78/Ho27ztR2dJ/Q50Fv2+40opnsv5pPTNrsVgsFovFYrnWMSQmXfNzDnwvEPDsgcFldd67ro8SGWNOAp9eOW2FFNdnVjgfvwt4q4g00NHSm9BBzHvWK68Wi8VisVgsFou++njBj/q/FviqMeaRZ6RtTP9yOu/dKLnSM/EutELeAmxCVW6+1RhzfENzZbFYLBaLxWK55kg5p7sDz0BEpoFvRt2N1+KyOe/d8IGBMeb9wPtXTTOoetE7NyBLFovFYrFYLBbLRSF7YsY/zfzL5rx3wwcGFovFYrFYLBbL5YrBkJh1VQ3dMK66gYEbQvmhgMVHrqPduA4nNtwXP49wQuUdD5RU+qtQN9yfPI/ujEow/mtfJcP2hbeNJOaKC2akl/4lVKZt8kCIe3PApnpKd7ND/8lZnNhQnXSZ3LtM8+YiTmRI/ZTcl6A/qWK5UUkIloWgEZMUXJx4kjgQCk8IW2+G9jbY/FGX/rRP6UiXJO/R3ZaSeiolNvFYl85ckereOosvnGb3X7WRKCGcKZJ/ukVSydO8ocjk3/aBPv3ryqSeEOd1m34rwumr4pVECRKntG+pkWsMyJ1okxZ80rxP6jvkTrRJqnkkUtUspxeRVPMkeY+44uO1IrxWSHdHBbeX0JvxmX6grct2BxjfpbujwuSBmOBok8HmMsZ38FoD4koOiVJyjzxF+6W7yTUGeK0Q47vElRzB0SbGc5DegHhzFUlSjOvQ35zHb8dIpLfynChlUAsoHYdcPcRt9UkqeQC8E02IIpKtUxjXwW31iWpFvFY4KpPx3WfUg99WwWWvNWAwuULPch1xQ5VZc0OVBmzPCUED/NBQPKExFFaF7lahesgQTqi2c/GIMMik3AaVsbxcWFNJt4kDKm83ccCweJchf9zJZOgMflOIi9DbljJzn9DaDrmmUN+jsnvtOSjOy0gu1biw6eGEpZtclSEsCvlGJhEaq+xc0NDtRsWxRG2SU83soWxd7UGhP6USfABuL6F03NCfdKk9FhMHQrAc07g5GMlJThww+B1o3CIEdZW0NC50tslIKjQqaTsfppsEQnurjCRKhxJ3Q2p7DfU9wtQ+Q6+mkqXGBbcD8y8pjGQeS8cT6re6pJ5KWDqJykh2tgm5pk7rbB1KQKp0rNcdS0EOpqCzy1A5oHVJrBKj7Vv7eE/mkVio3e/RmYXSIYe4pNKUfpNsW+D1XZZ367RcC3o1lTYcytQO62EjcPsq31g9pFKZk/sN/SkhqkLlIX8kgRhVIQ2Ema8mHH2FUDim8ec3x/uz2IDS4wm9TQ7NHWPtW913KvXZnRGmHk8YzDss3Sz0Kpksck6X6c1Af8Yh14At9w44+vIclcNQOp7Qvs6lX3PINTWvuaahcFIlSSuHx3Khw30qieahUDdMPpFSv9Ul14TejGQSwg6DTDZ5GHeTj2fSnr4eX/wu5OspTmTozrgMpiB/ElpzDpUjKqvqZcegfD0lWEqJC2OJSydKKCxEJAWXxo0uqedSORojiUvrDiG/MGwfhqUbnZF081Cy0u+YkbRwa6fgDHRfBcvpaBtxXtj8Za2fofxvrqWfylGVey0spri9hOauHMGysLgnR6Gu8q1LNzqUjmkbjUoykuR1+9qGWjtlFLteX7ddOWrobXIpzq+rGuOIoQcMqAR0VFG54u5WcDKJ5dIxldcd1mNnVijMr9Do97Sep/altENn1CfVHkkIJx0Wb/UwmSS339F2sekhQ7/mEFVhcaum15nVfmPYh9ZfFDF1n15gbs9BWMvmz6aUDmsMNncbyoe1HygfS2nNOSNZTq+j8rMT+7U9DOVrJx9LcGKHE8/TeHezOBlK4Rbnx5LXw2OJcbVekiCTtt6qfVs4o7LTuabG1lB+du5TCZ0t7qhPMq7Q2ZlSe8CldByaO1z609lxoqppD2WxezOCdzTP8l0RlYd84pZP/e4YPMPEAz5JTvNQWNB91kbTKh3VfNX2qsTw8vUu1UO674wLW+6Pac1q59+Zhc1f1j5mKB/cn9Ljqd/U9rpmvKyvncCGcdUNDCwWi8VisVgslouF+gDagYHFYrFYLBaLxXLNc63cMVhvHwOLxWKxWCwWi8VyGWLvGFgsFovFYrFYLKfAgH352GKxWCwWi8VisXABLgZXFnZgYLFYLBaLxWKxnAKDsS8fWywWi8VisVgs1zwGkmtjXHD1DQxSH0rzhvxSMtLxTwKhfDTBbyckBZfUhXDSIWinBE1HNcJ7KcX5hPacT1R2mH5ogJMYOltzOLGheCykvT3Pwh0Bfld1n4sn9MaS20+YeKxH+/oKxWMhccWnV3aII2HisTat60tUD0U4iaE9m6N8dIDXGpCPEuJKQPnJHtX9Ee3rK+RPDghnCrj9hOKxECdKcfoRUa2AFxqae2pUDvUZTAY4iSH/dAsApx8x8Zh6CUQ1XT9oDXCPnIRqGeM59K+rUHhyeeRJUP7KUcKbtpBU8/S2FSl/5SimWoIoRqKEND826XMX2ziFHG4/h0QJUa1A4VgX4zoEC13615XJP91G4pSkkseJDcHRJr0dExSeXMZ4+p67BxjXIb5xltKBJeT4Isn12zSdx45jqiXSYg4HRv4DuRNtSq0+/esq5I93kWaHwa4Z3V6UYHx3VAdxJSDZVCbJe3itEHexTVotkDu6BFGEqZaQ44uYThfZtgVTyFE6sASAxClpwafw6Pw6ReuziYpj3ezSMfUHaO0UivOqRR0XIb8AJ14eU9rvU1gwFBZT6oFL86aU4KSjGvI11YdPPQirqtN/4sUpsx+HxduhsACbHlat9M5WYeZe1fqffDwlKgkzX1FfAOMK7Z0GrzP2Ajj+QpfaXtX9dxJoz+m8uJKy6QGhPyV0t+qyzoCRx8DSbeqVMNSrbu0UQEjysLw7h98EL7p4xz8AACAASURBVIQkcEkC4cTdLrP/MmDh63IU53U7AFu/lNDc4eJ3oV9Tve6wqnkB1cNvzwleR/sCN1Rd9bioWuKg+uW9rbB0s7D9kyELdwSkAThNw8m7EyqPeKQeVJ5Sfe7OFpfSMdVrb+4SKk+pN8TkfkN3RkZa2eUjBidWj4HOrHo4uH39Lj7l0N5pmNivXgalozD9VZ+lm6B6SD1Lcg0hDXT/FE4mpL72X90Zwe+oVn1nm9b30LuCEFx0nWEdrTfGhXAKetsMbkcI6oI7gKkvJ/jtmM7WHO051clv3Kha/DP3GpZ3q26639F4Cpq6v55+mcPUXvUlMJ5qlrsh9GvqUwEw/0KXoK716MTaVpKcapQnARjPkGsKT36nh3FSBhWHzqzLxAFD4xbB6wpuf+gfIsQB+B1tM6mr+znX1PTyC9DaLtT3aF8jse7r1BP6NSF1obhgSAIty5BwwiFfT8m1U47f7Y3qauKAxpUb6nLdrVA+ouu25pyRh05U0rQroaE95+PEsOXeHsdfUGD+hR5eF2Y/E7N4q0dhMeXE81ycgea/fCwlqQuFxYTmDo+TL0qQ0KF8UH1PgMzTQWM0qkI45apefzfTsS9qOr1Nqknf2eaSr7v4HUN9j0P+pOZREo2/MPNzcBLVzXcyL4TONt33g7KDExtybU3Tb6dIAifvyMFH1ydWV+KGul/7W1JyDfUxSb1xO8s14eTzDFs+r74Di3cZqo8J/enMoyHU/qfYgOYuB6+rj5v0ZhPquBhX2/5wH+cXhFxL4zUq6v6vHjIs3gleR/uFNJ8iscPUfT7tOYhmQ/IHA/qzMdW5JaKHppFY08s1tL79LnQ3O5TmtV9yQ20D1YO67bioXgGtnbB4u5vFrnoG9GcMxjNs+Tz0aw7drVqmuMSoz8yfZDS9P2OQWD0Vik+pb0J7TkgD9VRIXTh+t4ff1L5/ebf6fVQf03OAOC/k64Z8XfPWr6l3R+MWB68zbuvFf3ZpzZH5IHhM7Us5/pIUp+9Q22s48fUJwbxHa3fK9o+lnLjLI2iox0kauOrXkIDbd8k3zMhPQmItz9L1egzx+gavr3GcaxoKCxHLu3OceIHAB9Y5IC8TrrqBgcVisVgsFovFcrEw2HcMLBaLxWKxWCwWC0LCxtyRXW/swMBisVgsFovFYjkFBkivkXcMrMGZxWKxWCwWi8VisXcMLBaLxWKxWCyW02EfJbJYLBaLxWKxWK5xDHZgYLFYLBaLxWKxWIDU2IGBxWKxWCwWi8VyTWPvGFzBSKTmIXEgpL7g9Q2FkxG5421aN0/iJFB+ooV3XRmvFVE8ljKoBaSeEE55bPrKMsZ3cZt9wtkqk3uX6e6okORd8ksJXk8oHuvTuK1I4WSE243pb86TuhowSd5FopTy0YSo7KnRVt8QLHQJZ4pMPNZlUAtwu/retxOpMq7xXSr7l5A4Ja5MkTveJqoViSo+TtHDaw3wWpBzHVJfTcXSvD829+pFmINHkW2b8Vou7hPHGNy2HeamMa6Dd6JJ/ukW8ZSm6fYT8H2CQ3Xo9SnPu5hqiaSSh0qe1HdGpmD4PvHmKk4/0m01e3i+i3EdnH6E04soPrpAvLmK8V28wydwW1UACgcWGcxO4rVCnGYPtzfAFHIklTxpMQfXbxuZsAFIb4Cp5GndPEmwHOO1BqQFNVrLP93C+C4SJ+ROtEkLWn5nsQm+T1osj+rTa4U4xxuaX8CcrCPTNaTZIb5xVsvS7On6vQi6vWx/xGrytgEYUaOayqE+xXmXpOASTjhUDqtxkNeBqX0pzV0O2/7Zpb4HkkA4ebuab9UeNTR3qNlM6ZjBidWwBTJTpUdcorLhus+FSJSyfGOe/pTgd2FQFVo7AdS4Ji4Kfmuct8n9hs5WNSPzW7C8Wygd1XSTIDOpOiA09kCuocZm4UyKv+zQnlPDnamHHcIJSF2hUDds/nJC+zo1mXFDQ1hV87OhSVf5CBx5ZY4tX0pYvt4lLqqZ1dMvczBeSu1BNWCLqmrEIwkEmWnOxAE1iVu6Wc2XJg4YzLKaVrmhLl+Y1/pu7szhJOB0tVy1+z2Wb1aznuXdQlwypFtCyvfn8UKIKtC4RSgfydLr6zaHRmvtu/vQyOEMhOrBsdmb8WDTgxCV1DSoMwudWZfSUZ3f2arlDhrah/WmtW37HUOupftVYsg1tb7cUCicTFi6yWV5zuA3Bb95KSP0NIjGSFh1SAMta/FISm+TQ5z3ac8JhQUzMiXrbTMkeaF6SI2W6nuE6kGN58YeQ/GI0M8M05LpAZ3boPBYQG82wZ0KSbo+tS/6DCowqGgGkjw4scZjYR680GFQVROmfMMQlSD01LAqV1fDOyCLTyFoqDFdGmh85BpqFBY01DTP7auJF6hRVHEBOts0HoIGI1PCXDvFa0XUn1NQA76+0JrwKB/RGA+yNplrqjled6szMqcb7r/ujLbL4omU1pzD4q0e+YaawBUWfdwB5A+rmV5ni8vmB0Laszlqe1PCCTURa9ziEDSgtd0jXwf/pBqiGRfmPtFj+cY8EwcGQI7Ug9J+w6CqJlteF/rTagTVr6mJ1eYHYvqTLks3C5P7dZlBFdIcxCVDriEUFqByNGZQdkgCIZzQGE0CV00JOwbjCidu9LJ95TK1L6W4sN4Bq6S+xszUw3o87s1o+4pKw7ZmmLlXRmZ3xaMO4ZSWd/O9hu7m8Xq92YTp+xyWbhZu+P9ijr3YxW+qEaEkapJXXNB+NCo6xCXtM+p7BCfU+vSbkGs5dGbVcC6upLgnc9r3HfQw90/DDdDdrkZfzgCaN6WUDms+cu2UwoL2G/2a5ivNaX+8tCdlcq+mPeyTU09N15xQOPECM8qH8TROanu1fXa26b7tboXCMWHq8YT5F7o4MVQOGyQR4pKaOhpPDdP8pjMyiRtU1SyyVxNaOx3KRzQtSbStdWY1ViXRPkD3g7aBYCnFDTWeJvZpf9rZJgTzHsV5iBsOT347zNxnCCfUvC8JYPl6l6iqfX+anekWFgz9KaF4ImXpRoeoCukdHXJfyM4/EsG4Pvl6ihteG4OAtbjqBgYWi8VisVgsFsvFwiAk14iQpx0YWCwWi8VisVgsp8G+Y2CxWCwWi8VisVzj2HcMLBaLxWKxWCwWCyAk5tp4lOjaKKXFYrFYLBaLxWI5LfaOgcVisVgsFovFcgoMkF4j19LtwMBisVgsFovFYjkN9h2DK5ThbguWY1JXcPsJTpTS2zmBFxrcfkLz5iqpJxSiFCdKydVDJEmJKzn615Vx+wmDyYCk4JLky5T3qTh6OFtlUPaJKj61h9vElRxRxSfXGGB8h+KxPu0dBXLtFH+hjV+HcKZIeV+d3o4JnMSoP0A9JKqoNr/fiuhvzuO3Y4LMO0GilKhWxO3Ho3KFMwW8VsRgKoffjglnihjfoTVbonAyoXisT7r5BnIn2rjNPsn12/DrXdJijqTo0b99M/kTfaKKT+HAIvT6mFoViVO6t24nWOjhNvtIkmJcR30CqgXCmU0kBRe/HeM1upgooX37ZkoH1HOBKMYUcqTVss73HJK5adz5BhQLJJvKY8+BQg4Ac/Ap3Bu2A9C/rkJhMQ+LDdK5zcSVAL/eJe/ryNxdbIOfhWkUAzm6X7edwuFl0ryP2+rT/rpZik+q6L53+ATplimcXkR423VIlJI70YbtWzEAhdwon2m1MPI6wFMfB2l2EH9jmoWTQPF4QuPWAuEUOKFqSbsD8EKIA2jNOeSa0LjFoXLYkASqne6G0NzhEiwbgmXw2yl+m5EWflSE8jHVOF+4I8ALVaO7ciQdaXFXDuv2l6/XdcKZlFzdYWqv6vsPdd+Dhmp9d2YhnEkIFlzCKXBDYWqvoX6n+hdMf1lIPdVsb+0UkkDXBQgnhO6MS+VISnubQ+OuhMKTHt051fJOAtXhlgTasy7uAJJMi7twzEFiYfGulPzxsY9AEkBYU93q5d2CcVW/O1+Hfk3wO1pPg6rqc+faqrMflYTU1frPL4DXN+QXVJPbDVW3O7c/T28G+jOw5UsJzR0uqaca3JOPq7eEJNCdM0x9Js+goprlfjshKqqethNCnBcGVc2D12WkDV6/yyBxSv64gz9vtCyZnvygIkw/NKAR5AiWVau7tVMozEN4k0vQgNQTejdEeHv99QvYVfRm1Atg4Op+a805ut8CoXzE0K8JU/sMre1CfkH9MoZ6/ZseMtT3CMV5kFjUL6IIE/sF9gc0bk/pb0nxmi6bPlegXxM2vfZJDn55O35TGNRSik/pPggaqh3vzatu+cnnp0QLLtGExqWz7OA3IZozxKiee2FB49RJBKcL1UPaVpo3aEzgqa58VFXPjql9hhMvj/EWfOJqgtfV/eCGMP9Cj+K8RxzA9MMJnS0uTqweBv0ZKNQ1DoLlFL87PtFwQ23nbmjobBOMB+059TFp7YSwpprwrVn1AFjeLQR1revFPQFJDiaeSPE7w7pOST0hyamXx/SD6vGSejLqY5ZuzlE6qnG8NK1ttHoQGren5BoOSU7j0G9C/SaPNNA2deJFhuCkEFUNEguFY+ojERXh+N0eXkfzVagbTj7XZeuXYo7frX4Ky7vVk8V4WubmLu3TNoK0YLI2xsgHI1hWvf3SvBl5i3hd1fwfxonfMbS3ja8eu32o7Hdpz6nXysIdAXFR+x5vXpdf3i0MpoT8SS23ydqJ39L+NC5CXNJpuQbqd3FYt9/Zpv3boKJtZXm3el8MqpA/7lCaVw+KE89zyZ/UPiW/oNvwOpAGMHOvcPwbY/AMhYM+bl/7s9JRSHIw/RXobIVc5l8jsbbPsJZ5OxQzr4UuHH2F4C9rX3vixSn5efVsiCqaTnfGoTunfiRpoB4GUUnb9cQB/V06CsFySlQS+lNCrpX5QWxVT5TWTtE+NnCJS9DfkuJ2hdpeM/LRCae0DiYfcajvybxUpoTZz8ScuMvDGWgZjKf7T/1U1KdieNzwP1lWP4e6et94HSGqaptZiTH2HQOLxWKxWCwWi8VyDbGuAwMRebWI/JuILIpIX0T2icgvi0huxTKHRMSs+syvZz4tFovFYrFYLJYhKbLm52pjvZ+Z2AR8CvhNYAl4IXAPsBX4mRXL/TnwnhX/B+uUP4vFYrFYLBaLZYT6GFwbD9ms68DAGPOHqyZ9SkSqwOtF5GeNMSabfswY84X1zJvFYrFYLBaLxfJsrp13DC6Hl48XgdwZl7JYLBaLxWKxWNaZa0mudENKKSKuiBRF5BuANwC/v+JuAcCPichARJZF5K9FZOdG5NNisVgsFovFYrlW2Kg7Bh0gyH7/KfBfVsz7O+ALwBHgNuBXgM+IyB3GmOW1EhOR1wGvA8iVpi5Vni2Wi84zYrdoY9dy5bAydr2qjV3LlcHKuHU3TW5wbixXEom5+l40Xgt55oX6ddqoyPOAIvry8duAPzfG/PQplr0deAB4szHmd86Udrm23bzozp8irvi4/YTetE/xWEhc8YkDoXSkSzhTQKKUpKB67YVjXQaTAU5iCB55mnTLFEt7Jqge7DKoBXitiLjiU/zKUyRz0wAkeQ/jO+SOt0mLOYzrEFV8nMTgdmMGtQC3n5DkXdx+gttVT4KhT4Db6hPVivSnc1T31kmqefVFKHuUDiyx/JwpJr+6yGBzOdue5tX4DhKlGN8hWOgBEFdy9KZ9nMhQPNbHa3SJp4q4LRXqjWpFvFaI8V3cxTbx5ioA/c15ik+2ML5Lb1uROC9MfnURgMHmMn69C0BazCFRQpr3kUS1sIdlSCp5nH6ERAkSp8RTRZKip/4BR5cgiujdupX80yqOLHFKWvCRg0eRUpFkbhrjOjj9CKcX0d09hdeKML6D241x+lFWbpdwpqD+BcUc7mKbZFMZ4zp4jS5JNY/b7GM8B+kNSDaVcRfbdG+dUY+GbPkkr2Nhv95VH4Zuj3RTlahWwK/3RmX82Bd/5X5jzPPPHM0Xj+Lm7eb273wjqad62s1dqqWcr6uHQaGu+s+5pn4nAfSnVVd86GXQnsumz8aUDno4oWpV55pQPmI48SLD1MMOg0qmod1Vret8PcWJDOGkQ+l4wuKtWT11VVt66Ang9iHfUE12UF33oTeBG6p+9pb7Y5o7PKKiLtvZJlSeMsR5YWmPeiMEDUhd1f0vH1aPhLioWt2getmg+umtu0IKjwUjrW8nVM+BuKjlas+pNrYbql9BOAVR1ZBraLpeFwZTBq8jVA5r3Q3za1zV5watp8n9ht6M6sX3ZnT7fle9DdLsMkprp2poe331FOhuVV+EqCQjXe4k0OlDH4V8PaVfc4iH5QvHXgb5uvoW9GaEwoJh6WYZpdfaqcsEDdUaL81rf21c6NVkVA9eV+e390Qc/rFfWPfYLU9tN9f/6JuIqurNkHpQPJGydKPelPY6mmdQ/frR/u0Y+lNCXNL1mrsNU3tVZ3wYE6C67mmg/1MP0kDjprtV0/I6qgEfVXS/JoHuk8YtQn5B4zQJICmpl8FgKiU4qX4GnV0pxgGmBhQfzmtdB6pnn3rqw+B3VNu+UNfv/oy20eK8xk+S1/IN/7dvSJl8xKE9p3k1nqF0SOvCSTT2oypUDxn8dkrqC05k6G5xkUTTau1UjXvjMvLfMC7EUzFTD3jk6+oBUnssprfJxW+nRGWHYFk9GEA13HMtjdXifERzVw6/ozHUrz2z/oKm+qI07kjY/AUHNzQ0blG9/DjQ/Lqhtrl+bdwXDPuc/IKWzYnH88Oalt8JhYkDGtulo9pvDabUK8HPPAy+9u43rXvcFq7bbra882fJH/YpLKi3S32Ptn+JtU8ozDOK6zhgVN/NXeqBIbGWM7+gMVg6pn3esL8a9hteZxyHTqzTJw5onVefjFm6wcPvGFJPGFQ0zeK89g9eT4+7vWn1xAiWUrpb3NGxorsV4pJ6SoD2F4UF9QLwupqn1nbV8O/NaH+Ya8jIS6F6aOwjMuw/i0d0/tDXoHmD7n9noHG46eGE+m0ucVH/Bw09xizv1nSSQGO28pRu2+toX7q0J2XmXk17uGyuqbEB2tYHU1A5rH3xIIs7v6neMFFJRv2xk3ktxCVG3hjTD8eZd4jWcW9G6yAuap2od4aM/B1yTd2vadY3Bw316IkmUp74T28exeTuO0rmXX9765px9Jobv3zG2BURD3gz8OPADmAB+KAx5o0rlhHgLcBPAdPAvcAbjDEPnFtkXxgbcsfAGPPl7OdnReQk8Cci8lvGmANrLPuwiOwDnreumbRYLBaLxWKxWID0wl4+/p/ANwNvBx4FtgN7Vi3zi8Bb0adoHgXeBHxcRG43xqybbP/l8PLxcJBwPfCsgcEK1v/WhsVisVgsFovlmuZC5EpF5FXAa4HnGmP2nmKZPDow+G/GmN/Npn0eOITK+f/yeW38PLgcXrH++uz7ibVmZo8S3QLcv245slgsFovFYrFYLpwfAz55qkFBxkuBKvBXwwnGmA7wD8B3XNrsPZN1vWMgIh8BPg58DUjQQcF/Bv7SGHNARP4d8IPAh4GngVvRUdKTwPvXM68Wi8VisVgsFotBLuTl4xcBfy8ivwv8EHru/RHgZ4wxT2fL3IqeFz+2at1HgO8/3w2fD+v9KNG9wI8Au4AYOIi+aPEH2fyngM3A7wCTqMfBR4BfMsY01zmvFovFYrFYLBbL6XwMpkXkvhX/32uMee+K/1vRc9+voo8UVYDfAD4kIi/O5PqngLYxJlmVdgMoikjOGDO4CMU4I+vtfPxW9MWKU81/EH05w2KxWCwWi8Vi2XCM4XTOxyfPoEok2ed7jDGLACJyDPgX4JXAJ4abOcW6p5p3Sbgc3jGwWCwWi8VisViuRhrAQ8NBQcZngQFjZaIGUBERd9W6k0DXGBNd+mwql4Mq0UXFuFB/TiHTpfWoPZrQ3p7H66U4CSzfpL4Ak3vbRLUCqSu0ri9R3d8kqhVovngHfjuherBLf3MeJzb0p3MUj/VpvngHpSNd4koOgN60z4m7NuF3VY9bEig/pd4BqSeQd+ltcinOpySZH4KX6fIPtpRxuzFeaFh84TSSgNdLyZ8csPycKby+oX73NBOPtTGuQ5J3cRJD7ullkkqeQS0YeQ94fYMTGfx2wonnl6g+madwTIXCV3oYAOB7DGoB/UmX/FKC8V0kSigc65LkPXo7JgAoPLlM+5YahWNa3tzxNoPryuSfbuM0ewxmJ0lrRZwoRSJNZ7CljEQpbjdWv4ZCDvE9CgcWSTaVR/sonCmQy+9CkhT3yEninZuJKwF+lFA80CCp5pH7DuCUioR37iR1hdxSSPFAg8HmMk6U0nzuZkpHuiPPBgCabQa3Xaf17wo5IFcPkSgZ+Rk4UYp3oslgdhK3HxPPVgkO1XHzPsZ3SYoeuePtSxmip8Q4jPSevVA1rAcV1WJ2krH2cntOKB9RDefaXtUsb+1ULXGvq7rU0190ae2EXAjlI6or3p4TZu4DN0xx4rHWfvmIobvZIV83ODEcv9tjap/q8bfnhKCh8T3Uf+7NqFdA6ajmO1/PtMxzqm3d26T62hNPJLRnVU+6s01wQpi5V3WpezO63cKDsHinIb8g+E3wPEb61HFRyz31xYDWTm3bflM1rqe/muAkMCg7bP1SysJzNb6H+vXLu9U7IZwQ+tOQa+hFl96MjHwXlm9WbwOvq9us7dU27ISqaz3U9O6VINfUfDuxeh1EJaFxi+6H2l7DIPN16G52KB9NiMoOk/tVYxsgnHDozWT6+HWtz4kDEcu7c3S2CsZTje1h/pq7VOe7dFQ17wdVmHw85djLDYWjLl4Heluz+l9Qzf3ujDB1n8/h9QvZEakP5WMpzcAZ7b9jr0zxGg5+SzXy/Y4Z6es78TP1xAsLmk71gIx035MA8iezMta1fJNHDJ2tQnEBwFB9MqW3ydEYC1Qj34m1DTR36b51Epjapz4d7VmXcAqqjzn4HUP9TkOu7uh+OZynfXNM2PDwWzCojttiOCGUj6mWfNAEvyuUjiecvF33BWh8Nm5P8VoOpcNaD/kFXTYqqvfBULd+6D8SlYTONldj0B2nU1wweF3Vwk9yqqdvPG0nhXn1COnXHErHDM0dHs3dBid0yTUhKrkaq6H6XjR36cXKOJ+jdDwhnHCI85L1H9p2/a76Nbihxtfybv1fmNe+Iy6qlvzQM8OJM03+vFA+ohcyo5LQvCnFGQjFI0KU+S7kFwSJ4eTXx5T3+izfllA67OJ1HcIpCPdEOK3V50LrgxNCab9PEqj/hCRaL8MyVr6S0ppzcEP1lZjcbzj6Mk/9HBrqW4CX9dVV9QvoTwn5uvYppWNj3wvjwqCWUjng0N5pKBwTUk+IA6jf5NGdM2x6EKKS+mJMP5iSBEJnq+B3tX6m9ockeZc4yDxumtr3SKL13J8x+E3ta4fHh37NGfkqJIG2tXxd+7M4p/2w7iftR8pHU5o7XPyu9n/G1f5qy5dSetMuSQDtnWbkYVA5rO05rOrxojg/9iwpLMDinVpXxQVtw7OfMhx7iXrZDOutPad+I0FT6y/19Jgx+bjmf+iL0ppzMB70PO3fo5L6dBgP3AFMPhoTB5oPv6neP9VDeowc+kH0pl2qhwwLLzAUjjkjv5k0p/lp3J5SPuhQ27taEUdIOe93DB5hbOr7zEQhzX4/CrjAjcC+Fcvcms1bN+wdA4vFYrFYLBaL5RQY9FGitT5nwYeBO0VkesW0bwR89L0DgH8DmsD3DRcQkSLw3cA/XYwynC1X3R0Di8VisVgsFovlYnK+PgbAe4E3AP8gIv8Vffn414GPG2M+C2CM6YvIu4C3ikiDscGZA7znQvN+LtiBgcVisVgsFovFcgoMQnqecqXGmKaIvBL4f4EPoO8W/B3wxlWLvgsdCLwF2ATcB3yrMeb4+eb7fLADA4vFYrFYLBaL5RJhjHkc+M4zLGOAd2afDcMODCwWi8VisVgsltNwAY8SXVHYgYHFYrFYLBaLxXIKDJCe3YvGVzx2YGCxWCwWi8VisZwSITl/udIriqtyYCCJaubm2imdLS7GVW3nqUd7gHoQDD0MnMQw+dVF6neritTUV+v0r6vQ35zHb8cEh+rEm6vqaZCA0x3QuLuCG6ou98QTCX47ISq76pNwYx6/o/q65SMRk4/26MwVcRLobguIbsyTBEL1yZhwwsNvJ5SPJvSmfZzMCDvXTokDoV8TnOtLFE6q94FEKb2dE3S2uLih6mxPHBjQ3epTWExICi6b9oYs7Q5w4gKDcomgEZPki7TnfIKllO6WCvl6SvWg+hws3VomWE4ZlB1K85qW304JCj5+O6Yzpx4BSX5iVG/Rjgp+O8ZrDWhdXyLXVo8GtxuTFD2kH9PbVqSzpYLfMRQWIozvkKuHJEWPwuFl+tdVAPDdzUQVn+5Wn+g5BaYfUFHwzqvuIH9ygF/v0b+uzGAyILy+BIDXNwTLMeFMAWYKBAs94kqOk99zPRMHBvRmfAoLEb1tRUoHlujtnCBY6BHOFPBaEeGuGlHZY1DOU7v/JM3nbqa6t87SczfptrfW4KFLG6NrYTzVUh7kwDQ1jieeSGjucOnO/f/svXmYJFd5p/t+EZEZuVRmVWZVdlepV3W3ViTc7Ju5gNlsMB57zOIN29cLxoNtjAAvLPZ4bAPesGfM2AaPrxe8AONtMHc8tjEwDAKMEAihXepWb6Wu6qzOrMrKLSIj4swfX0Rmdau7VZJarZZ03ufJJzNjOXGW75zIkxHx+xnybaG8ZHBD1Xn21wyd3foPRmlp4g3QWxDWdwn5NuT6qs9tXMi3YFAXorIQlVRPv9hU/XEngpWnQK6j2u2tqx3Ki1A9pLG8erlqmm+9QWMk3xHa18Zs+yT0t7pUD6V60zlhVBYKLcNoSvNWbKp2u8Sqo514WX61HPm2LjclLXOuA4mv2tJBTfM4+3VDnKpA+x1YvUw1293AsNpwmb1F66nUh7W9QvWQScuqWvj+mtZLsal626C632FV89dbENb2D/lxRgAAIABJREFUqg5+qTk5VuIJSR7686ptHlbhxLMMhWXV6y60EvpbHPw11XKPCsLapS75ddX2BvVEyPXTui6p3nZnt7C+I48TqZa6xHosv6166ZmWelgFd6j68SeeIdS+7qiGfUM11XsLQm//kMGyT+22SdkuNEkOmk9xmLkr9bTwoXzQ03ic17otLWmc5XqGXDfhxNO0DRMfpK+eHaDa8MbVdsv8MyDVOK9rH5g6OiQuuKztzeMGZqwZLzEM64KbjqVJPvXZWHBIfPDbGtNRQeO0cQMY19C+QmOlcrvHsDHRNI980vSF7oLDYF713gFGJRdXbWtwIn3Ptx2C7SPisgq5+01HfW76MPOlmOY3uBSbadvNC8O67hvnUT12V2OtXZexP4YTQbwOTqTx6unQTaGlXgPDusZy4um6fMeQ76g2fL+hWvCjsvqWdC9xkVjHCuNqXVWOal/J9SGoCvXbY9Yudam0NX4TX/NQWoLeNu2TXg8qh9UHIsk7lJa0rap3qzdBf7vBCVSbvryk7bbj4w6dnbDliw5re7V9JQKaOcpL5jTN+AtD4sHM3RosoymHfkOYPqB6+8M59YrI9PKjko4tuXVts8TXNpBY++zczQmr+xzcoXo/JHlY2x9R+3KOQlPjunhcPTdmb4aokI4rPejujdnyRYfW1UJSSJi+0+H4Cwx+0xl7EeR6hs6uPIOGehLkN3gYjMf/wxojGcG0Q1jVek5cbfM4rz4JM/eovv+wpmnM3hbS3Z6jv1U9DMrLMeVl9YppXS04kUtpCYZzsOUGQ+tqYcuN6lWTmfN66fnGiXXMCmow91WIfZOmAc2qS3FJ668/r14tQU39aUapd8j0AcPq5ULrageJYf6LIcvPyOP1GHvNZJ4/UVnH1uJKzJGXO5QW1SMhrMIAwbhCIY3l1lUuQSPBzIbMfton9tMYTMnqLvH1HLiRJ9IVgydGKS0Wi8VisVgsFss5eVxeMbBYLBaLxWKxWM4X9lYii8VisVgsFovlCY4x8oS5lchODCwWi8VisVgslnMQP0EmBk+MUlosFovFYrFYLJZzYq8YWCwWi8VisVgsZ8EAiX3GwGKxWCwWi8VieaIjT5hbicQY82jn4bxSntthdv/odUQl1UM3nmpXh5VUI70PlcWIzk5vrAMcViHfYewJAFBaGuHEhsFcjsQTjAvFkzGDWZdcN8ELDO4wJnGFzu48xlXNay+Azl5D7TbVmAbVF5ZYNYQlhspR1dH21xK8oeHEU12mDxhm7uiy+KIKxaZqd5eXQjq78gRVofH1gGDaYzCnvgzTB0JGUy5rl7rM3hERTjl4QzPWTu9tdYl9odBKcEa6rLvNpXRCj6nrYeZgxGDWxV9TTWOAfkPo7o3Zer3DqCxUD2m9lJZG9OdzuIHqguf6qh2cpZt4QmE1RkYJfrNP+9pp3MDQ3+JQOpGM9fLdQD0m3KFua3IOoymPfDuku6OAE6nu/agsRD7M/1uPsO7jDmNW96rAfOxD9UhMVBCGddV2rxxTvefqkQhvfcRwLk8wo7rRiac621nZK4sRiScMZh3cgLFu/dSxEXHR5XN///YbjTFPv5CxW9q6w1z9qrfQerK2l990CGvqX7D1hpCg5tFdcHBi1Mci1X3Pr6t29Oxt2k7+WkL3EpfI15jLpdrma3tV99mkfwfkO/qeeKojPXuL6pcX2hp/WbyOyjJu5/W9CaWjDrV7YtxBzPIz8uQ7k7bIdLwLbdXYz3dUP9uJVfu7u139EzLt6UFD85Adq3pINenVc0O14AcNLW+S5rvQ0ndJteqDmmpR59dVFxtU1zusqCdBptGe66nG/tQx1SU3rtbL8v8TU1j0VN99W0xhSbXew5qheFwYLBgkUv1y42pevL7qgRsPepePKBzOpf1S89/dLuPytK4Wpo7psYyrWuiFFd1/VFU998RVnf7YF/VmuFwwniHZGuDfXcC4qhvf3T7R7g7rCcXjzinjm3Hh1t+87oLHbnHrDrP3+68jLqQx19E8Zj4NURlGFdUsB20nv6V+DJku/+wt2qDdbe44ZnI99WYwrvo/uIGOOf2t7ri8pWX9rp4HZjzOJJ56Q4xKWs+Z1n7s63viqc5/VE69IsqavhPoseO85q/QnPSZYtOMdeRhcuxCS8fP9V26PIuToBHjN92xJ0WmZ5/vTPTk3aEex2/DYCGhcYPQm1ft9azsWfyOykJ/Xts6KkHUGOEfy1FY0eOtXp0gW4eU/q009uNIPPWVSFw9P41Kml5G5Ktu+9QxHXe0/sz4vAe6T3dvTP0ml0FDtffDmrZz1u/cQL0keguCRNpeSbq/F0z6cdZXe9tSr5YDhhPPMhz6ybc9KmPupT90HXHqcZERVtWHIPEYx1LtTj1v53rqQZGdbzI6e9W7Id9J9/cNSd6QW+jjfH1qHK/GhbCW4K+o/0PWHrmeobNbKB/XdnYDHdv81OclrOqYlI1FSV49YLxAx9V8R/PpDiGo6/eoNIkV0L5WbKZ9I42r8nLMyjX6u8LrTTwOsv6RxR/ofrO3BYymtEN0droUWprvylEz3mZY0zFXYsb9L9dJfRQKk7xldV1o6rpsO9BzyPouYe5r6lHjdyYxme+kvgRXC5d8Xs/lrStd6nfE9NKxIPY1H26oseb1Ne2sLN5w8jusu+BgXK236QMGJ9K8f+nP3zqOyYUn1cwP/dWLzhhH7/mGv7vgsftIYq8YWCwWi8VisVgs5yB+gjyW+4ATAxFxgJcDLwGeCcwDBaAF3AVcD/ytMebII5hPi8VisVgsFovF8ghy1umPiFRE5BeAY8DfAy8C7kk//ynwf4Ai8HPAQRH5ZxF5/iOfZYvFYrFYLBaL5cJgEBJz5tfjjXNdMbgX+CrwduDjxpj1s20oIk8BXgv8rYj8kjHmA+c3mxaLxWKxWCwWy6NDYm8l4uXGmBs3k4gx5qvAV0Xkl4Gd5yVnFovFYrFYLBbLo4wxED8Orw6cibNODDY7KThtnz5wx8PKkcVisVgsFovFchHxeLxt6Ew8aFUiEfGA/OnL00mBxWKxWCwWi8VieQyyqYmBiEwD7wW+A2jAGe3f3POYL4vFYrFYLBaL5VFHHz62zxhs5E+AFwB/iCoThY9Uhh4uSV7NMzJTEL9pCKaF8pKamZWXY1qXeVSPqDHN1H0xg0Abe+nZeSRWk49+I0/lWDI2lHIiCKY9wiqUjzv0faGz1yXfnpg4JT7kWmputrZX505xOcHtqclW7KvJRme3mnSs71JzrfIirO8QTrygwNz1anLUW4Dudp9i05Drw5GX+nh9zVvlWEJnd57iSsz0vVqeXB/6W0jzpyYzxSY0n6Jl89tqPBJWnbFBkjuExed7auoTuoQ1g/EMEkHlLpfObqjfHrO2N093O3R259MyqMnSoAFhxSW/DitPdvBb0JvXkMqv51NTHTU6CaYdOnu0rL1tQnHJwQs8OnsNXk+YPmA4/pwixSXwAq27YV3NrI6+tEyxCZHv4XfUYMgJoHWlOzbSyfWhfYWWrbPTY9BQw6okr8ZQvQXBidTox+vBif0elaNqJNNb0NiZuyWmsztP+5pEtbcuMEkO2lfD9J3aZhKDOxRm74jobs8xKmu9FFpq7uINdRsnMjiRjM3Ggmk1nZGyEFbUOKffkLGBT+RNzHCS1HBn9paY1ctcysfV9GVUnphJFVbVFM4NYO4rgsSG1UtdorJuv3q5sLY/oXxXDq+nJjXtBYhLMUlejagyEzkngsGCodAUhnXNf7GpJju9rS69BSHxYFTW/xnC1PBm2FBDrMzMLUn7Um8bbP2SGuDE/sQkq3WVi9eDYFqYOp6k9WVwApfObiHJayx2dgtbrneRWMcHd+gSlWG4NUES6O8wVA44JC4M5lFjIY+x0duwYah9Ocf6Lu1jJ14Q4R/LkW9rva48BWq3afyt79L2qxyexHapmRrP9dWMR022JB2/hOrNPie+KQDAXD0iWiwRzIG37uA3HQYLCV5f4yWsgfMojcxi1JBo0BC8DvhrhiAW4ry2VZLXtg5q2v9KS2rwtfCFiSHRYM5NY1nTjEoQVrWtMnOyzIhxo3lfZ6e2GQjrO4S5W2LCKYfRtJpReYFQTc37wooah3UXtM6KLUPU1/F47uvheIwLqzDYGTF9i4757jA17PKEYlPHjdKJhNZVLtVDZmyy6Le0HkZlobcNCksuYT0h9p2xwVVYM8T7e/jXT40NnyqHNa7rNwthVcfMbAyvLEZp/9NzWWbsV1wC73CO7nbtx3FFTRHdoyWiMvTSsTefGuclPgyqEMypuZbf1jp2UmOy1ct1HM711ICys1ONK4Nph8qxhOl74eQ1E2OqfFtN+VYvVzMugPYVQuWwfh6VdH3xZEJvq0sjNapKXDXky3W0Tk88S887jxYSgSlB5zIdJ0qLDpWjapYX+6nJl6djRbHJ2HxudZ9DsanmblPHDNUDaqYHatgFgt+B0d1ThFUd53rbINgV4C35p5hUOlFqmnbUpKaSOvZWFg0r1+g5tdACJ5KxAV9Y1fdhHaaOaTqjkpp0OZEaL/rHchSbGgP9hozPn4mn6RkXlp7pMnVMjUcHDaF6SPtHZgoIOnZm55/25f6knG3Nd/m4ScdtIXGhvKTtGaYGfcWmmrBlZoaJq/VeaOu46wXav91jZmwMC2o2tvRchySfMOhrH/JbWrdrVyRM3ymcvNIjKkPtzmQcX0Ftcr7rbdO+MmyA60Po6nH7DTWvzHX0d4MbankzQ8DIv3+sxGf8T/zxx2YnBi8GfswY81ePZGYsFovFYrFYLJaLCcMT5xmDzV4XOQI87GcIROTVIvJ5ETkpIkMRuVNE3iUi+Q3biIi8Q0SOishARD4rIvsf7rEtFovFYrFYLBbL2dnsxOBngHeJyMOVIp0FPg38CPAtwP8HvBN4/4Ztfg54N/BrwKuALvBJEZl/mMe2WCwWi8VisVgeJPqMwZlejzc2dSuRMeZ/ishLgHtE5BCweoZtnrmJdD542qJPi0gVeJOI/CTgoxOD92YmaSLyBeAQ8BPAuzaTX4vFYrFYLBaL5XyR2GcMJojIbwI/DdzA+X/4+CQT+dPnAlXgY9lKY0xPRP4BvcJgJwYWi8VisVgslguGNTi7Pz8CvNMY897zcVARcdGrA08Ffgr4fWOMEZErgRi4+7Rdbgdedz6ObbFYLBaLxWKxPBgej7cNnYnNTgz6wIN2Qj4HPXRiAPBnwNvTzzWga4yJT9u+DZREJG+Mud/VChF5A/AGAK9aO4/ZtFgeWU6J3Rkbu5bHDhtjNzdlY9fy2OCUuK3YuLVYTkeMeWD9YBH5WeAZwGvMZnZ44PSeCpSAZwK/APylMeY/iMg7gbcZY2qnbf+jwIeAvDFmdK60S1t2mCtecx2FVkJ/S6rvXVXt7Ez7vHQiYXWfo5rvNcbeBU4M3V1avEJT6F8zRE7mcXsOia9ay8aBfNshrKkWdFhX7WPZOoTFIsnWYLyPcSGqxngdl6gW4S95BI2YfGOA6yQM+3lM6FI8mCNoJOTWHMI9Qwp3FADVUjd+Ap6hcDg31oFP0ulcdf8KrQN1vPX7H6uw6DGqGnIdYbgtQkoRzrIP2wYkkYOJBW/JJ96mZZy6dI1R5BLeW6HQFNVH39anUhqy2ikRt32kMsKs58BPyC3l2P2cI9yzuAXHS3R9JBjP4NYCts2tcvxLlxBVErx1B7m8y+h4CeMZnFCoXdYi5ySs9QsM+3onmYkFcQ1mPYfbd5BItYgHCwmydYjrJYyGHmY9hxMKEgnurh6V0pD+ME94r4pCx3Mh7koeJxBGcxHV+XW6904DkFRiqnNdOu0Sl+1cZj3Qum51S7zk0jv5t+VdnGxWOPwDP3+jMebpDyPMHzTFrTvMnh+6jthXzf98R1+rV2ms5TrqP1FsqoeEOwTjaTwUm6qF3d2uutG5jmo1d7cLwz0BhYM+Emt6wzlNPy5p24zmIiRw8FdSbfemajhHZY23sKr7SaQ+Av157S9xQd+rR2JGUw4nXhBRvisHaD/L9QzDmoz1291Ql8W+alCXjjrk+pm/Bszco33WiVSPO9ODD2qMy55pYo9KqktdaEJ/R0L5kPYB46nOemlJ8ymxvgbb9L8Gv+kyfcDQuloophrdia865N4gISo6jMpahxKnZagL63sTKgcc4vzEhyGsav3kOloXg50RuRWPuJzgN52xv0mW79JSqmNf1fqJSoy1tr2hoX2F+hkUWlonud5ELz/TU48LmkZUUm3uLV8ZMJzLp14rhsQTPvf3b39UYvfKV1+HG+j4GfvqIdBbkLFeuRvAyWtTL45m6gvgqpdD7KsGur+mXgWJC1HRYVgXphZjoqKjngap94YTT+ovqKkO/6CuaYe1iUZ+Nl5mPhqF1uRYbqB1CRPN8lLT4ERmvN6JDOvbHUpN9fcYNGBUUd+B9V3aBrlUr8+J1APAb0cENU813T2thyyewqoQ+dpnTl6j3iBZPBSb4K/pual83BBUJ+XROk29C1LPgMSblK+3DaLGCLft6bgYqKfFcKuOHVmfGVXVvyOsaP1Uj6jnQ5gea1Ri3CdnDkZEvhDM6LiQ+So4kbarm/qo+B2Nu0FDY3dUmrRtFvt+W30rcv3J+qxNQH0vbvjTt17wuC03dph933MdpRMJiaf9fm2vEJXVX6e0pPr+uZ5q+/d2J+RbzrjfOtHESybxBG+oXhOgsRZWhUJLfyNk8eCvaX/u7BaiknqjZONa9Ug09vXItjeu+hAM0/jOxmSJtD2dUPefOqZ5KC/HJGlcj6accdwBlJZjct2YuOjS3ueO26dyWMdq0PEt82TI0s/ONaC+F6B9MKhpvmESx3F6Y3hUTj1LmoZcN9Htpx3cQPtU7Z6Ywawz9rnwhurhkPktOBEM6vo581AAPWbsq59BFk9mw1/csT8ZVzMvnqio54cg9TZZ36Vjbfm4pp3raf82rsb+cE7f73nHdeOYnL2qYV7xJ//ujHH058/+owseu48km71iMAc8C7hTRD7D/R8+NsaYn93sQY0xX0k/fk5EVoA/FZHfQq8MVETEPe2qwQzQf6BJgcVisVgsFovFcr6xDx+fyquBCMgBLz3DegNsemJwGtkk4VLgDsAF9gF3btjmynSdxWKxWCwWi8VywXgiGZxtVq700kcwD89L3+8FFoEO8BrgVwBEpIT6GXzoEcyDxWKxWCwWi8XyhGazVwzOCyLyv4BPArei6kPPA94KfNQYcyDd5n3Au0WkjV4luA41YvvdC5lXi8VisVgsFosFnjiqRGctpYi8PpUV3TQisk9Enn+OTW4AfhD476hXwauAnwdev2Gb9wG/mi7/BOpr8FJjzPKDyYvFYrFYLBaLxfKwMUJyltcDISI/KCLmDK83bthGROQdInJURAYi8lkR2f9Qs/tgf79v5FxXDN4K/LKIfBj4a2PM185y8Fngm4HvAl4I/PDZEjTGvBt497kylKoe/Wr6slgsFovFYrFYHjUM5+Xh428CBhu+H9zw+efQ38dvZ3K3zCdF5BpjzNK5EhWRGvob/CWo2ucWwBORLnAXcD36O/5zm8nkWScGxpj9IvI64CeBd6YHuB1YAQJUKehSYCeqJvTnwBuNMYubObDFYrFYLBaLxfJY4Dw8fHyDMaZ7+kIRKaATg/caYz6QLvsCcAj4CeBdZ0pMRHYDv4hOCtrAF4H/xqm/03cDzwbeJCIH0ed3//xc1gPnfMbAGPNR4KMishediTwVmAfKwDLwWXQm8pmLRUpUVDJ4rKPtBqqt3G8I+Y5qm3cug3xbPQu8nmo+D+ZV+zbXEUZVQ39bQv5ggcSDqJKQW+gTtgrkVjyC7SMKh3PkOhDWIckbpFnA2TbABC5mZkRSdHGrIfRzGM/R/RoxTijEh8uM8mmbVEc0XngfRw5uYeeTj3FweY54fxfXSTDLZfL1IWGrwJbn30cYebS6JQSoT/U5ceccztYhUc1hx3yLXpgn5yS0uiW+9Zm3cG9vlk7oc3B5jiRyKF+2SmepgpQiipWAq/cdoeCO2H3tSf7X4lWMIpcrn36IghfRCX22l1NV2jk4MaiwPvJhHsLI43XPvpEP3PwC6vUuT567jxuXdvCynXfyiumb+NpgF4thDV5xhGdN3cNOr8Wfnnwed882+Kmd/8rR0SztqEw/zvOl1i62XNLlZfVb+czqFbxxy2c4EVdoxVP8/sEX8LqdN7IymuK+YJrrj+zhqZce5bblrTz1kmN8+9xXuGu4QDsq87X2JbzhyR+nGVU5ONzC62uf51O9q1gMa3ytfQkf/vY/Zmg8ChLxO8svIdzi8bL6rbx26jjvbz2Jn5+9i/eevJz/eMXNcAV826MRvO5E377QVJ3+qASlRYcg1TKXWPXT3WCiEx1VoX2NehIkfupd0YBhQyg0Yeu/5Ok3VP+8P6+61Pk2JL6DROC3PIL6JBudvYZ8W5i5J6G74DB1TDWq4wL0qpqHuKD61bEPiy+B4qKw9VMeJ6/VfuREjLWnM53z2IfE02ULnzWcvObU4i89D0qLqpMdF6C7XQjr6gmQeSrIUD0cqocMbqh9N3enQ2evllti9QsY1vUd9PPUAZdc6q3QWxDKi6kfQ189Gtb2CrHvEpcT3FS/vLBBP3vrF6C/RfXXa7epxrVEmr5J9eTrN3qpLrveoZlpfGda22ElbcNUh7zY1Dy4AfRKOj45geqmF1oGZ2RIPJdg2lEN/rbBX03wAsNwxiWsCsdeXMTrazn8NdUBfzTwUtvJQUPrK2vrfEfrf5COv7l13a63K2HqoNZTvyFjP4HObqHYdJFUI90JVC8903JfvVzIdSAB6neoBn/sC25gKLY0NqeOG4Jp5xRd9Lii63rzMvYCyfpUvqN6/v2tLt5A6zeY9lK/GBl7GPTTc0T5uOaj0FQPjNZV6l/ht4RBQ4ivyOMG2s65PrrtirYPwNTxhGDGoXan9q9CU/vy6tUJxgFJEkYVh6gag5/gtj0KTSHf1r6UkXjq65CNF/mDOcKKxuPo6V1igOMlgrmE4bxBImHqoDP2KgC47/naBrkOY039zJ/k2Itc4lpE8aB7ig+H24PKUa2TzFsn9rVeAErLyTiPwYxDb0FwIt1uWNf6BtX+H5Umbf+oYBj3tcx/YstXEqKC+gwMGmBcId8Wpo4nVI8YnDimvc+l0Fat/QwnMhRPxoDGb6aPn419sS9M3acxC1qfsa9jEmh7dnZ6jEo6HpWW1Asi19fvXm/i7ZJ5g5SaEBW0z63v0n06O10KLd3OiQyD1EukvGRYu9QlKrtEJR0zMu+D7nb93TN1WCgeF9Z3pZ5P6Ria+ZPkeob+FofSiYRh3aHxNfUiyPUMEmts5dM+XmjrWKu+Dg65bkLxZEzkC24Ig1mth8GsQ3lZ62VYF4ot9SRxYpi5V5f7q+pFAFA6oV44iafeGl5Px+XhnB4334b1veptE1cgrLgEdS2PcSHOa38EHRsK7UksuwHgqdfHBea56G3zH8sWGGN6IvIPwLdwlokB8HXgI8BLjDHXn+sA6d09r0YnINuB955t282qEh0ADmxmW4vFYrFYLBaL5fHCeZIrPZD+QD8AvN8Y88F0+ZWoIM/dp21/O/C6c6R3hTHmvs0c2BhzEvgg8EERmT/XthdUlchisVgsFovFYnms8TAmBsfR5we+hHp1fTfwByJSMsb8NlADuqcZ+4LeHlQSkbwxJjw90c1OCs6w3zmfWbATA4vFYrFYLBaL5SwYzqlANCciX97w/UPGmLH3ljHmn4B/2rD+H0XEB94lIv95fIj7I+dYd0bS5xUuAQqnrzPG3LaZNOzEwGKxWCwWi8ViOQfnUCVaMcY8/UEm99fAa9GHg9tARUTc064azAD9zTzDKyLbUSPgl59pNTq52NQTPXZiYLFYLBaLxWKxXHgMKk/qAvuAOzesuzJdtxk+DOxBVYzuAe5369FmsRMDi8VisVgsFovlbJjz8vDxRr4TlRU9jD6D0AFeg8qJIiIl1AT4Q2dL4DSeDnyvMebjDzdjdmJgsVgsFovFYrGchYejSiQif4M+eHwzemXgdenrp4wxCTAUkfcB7xaRNhODMwf43U0e5jag9JAyeHp+z+ZxICL38iAeeDDG7DkfGXq4FLbtMLt/9Lrxd9UVn+jDw0R3OVueaTEHjRi/6VJaUp3xqKTL3L6DEwijuQh/SfWtq/tXyDkJy3fPUVh2VN850H1G0wnJzAjp5Mi3HcKa6jrn2w7R5X3ifg637ZHkDcYz4CfMzq+x2inhegnXLhzntuWtNKpdji7VcTzd/+WX3c7hbp0w0dvELqs2Kbkjal6Pjx58Kq/adYv6AhS7XP/VK7jsykXyTsxSr0I5r1eVVvtFrt1ynKPdGRrFHgBPnT5CyTn1qtP2/Ek+svwsvrF2DyujKV5cvZVZp89doy3s9FrU3YCywL/0d3MsrPPzs3fx4fU5/rn1JJ5ePcz2/Elm3S5/3XoGL5q+nWZU5WmFQ9wRLtBLfA4Ot7At3+a5pbt5hp/jhmBEQSKGxuNEXOHmwU7eWLuJT/R2Une7tOIpvrV8hE/0dvL6yso4nzcEI/blRtScEn+wto0duZO8sjQ8a3wEZoQvuVOW/czyUwD49a1fHS9zF+6+8SHcM/iwKGzfYXb/yHXqq7GgbZ5bc8ba9G6gcekGjHXSMy+DuABBI6FyQD0PPG1ajKdplY6qBnR+faKdPSrLWM86qKnOe5JXTfO4AGFN/QycSLXHR2n/idNHmryeei1MHdN1EkOxZSgtjYiLLrluhLcesn5pWf0Qjqv2db5j6G4X/LZ6ErhD1bwOquq/AOC3Jrr9SU4HY29oVNe7G9PdnsOJ1E/ADaDYHDFo5DCu6npnuvf9huphO5H6P/jtNO+pjnumrW5cLbcTp/VcgaCepQ2Rr5r1U8cMxmWsj19sGYJpwV8zuIFhfbvWsxuqBnlY02MVm6q9DZO6H9a17JnPgRugU4DNAAAgAElEQVRq+yb5SUxMH5h4KUTpmGVcqBxLSDwZa6X3G6rPP6rAgZ+97sLH7iU7zO43XEexyVhbPyqpZwZoPfd2xdS+7o61ztd3aTuD1ueomvof+IYkb/BXHIK5hMK2LsPFKdy+Q/02Lasbavqxr54Wg7q2uRuqLj2ojnwWs0lad1Eap5kuP0xiCNJ+EGn+vKEh8SaeHPmOtv3UYkhccOns9Ih89UBYu9TFDSexk+tPfDKmjhl685pnJzq1HbM48QKNgVEVCiuaj+oh1VcflbSfZ/uUliYeDImn/XCj9rsTwfSBkEEjR29eCOoQl3UM6O9ItG6bLlHZMH2X4K8l49js7Jbx2JH1v2BGYzr2Zdynsj6QlSErt8RQahqGdaF0IsEZGYIZh+529RhxIu2DWd2Wl3VwC6ccvviRt13wuC1t2WGe9rw3E0w79BtCeckQ++CvJjixtk2SE/UY2C3jMad8XMcr0LZ2IjOuI0jHwpWJ9n6+q94Iw7pDoaX1nevq2NbZ7eD1te87kaYtMQzrerywqsuS9G/cxBPKy+of0FsQCi0otBKKKyOCaY/BnPaxYSOLBR2jhnOq8Z+Ncf5aMh6vQMd1d6h5d+LJWFRaYnzsjd4vU4sa9xJPzgMS6zZZHdRvj1m9bOKbkPU/r8f4vGbciXcGaCwnnpazuBLjBYbIF/y1iM6uvP5WmxYKLYM3SFi71MV4jPtqWNVxpbs3prjoMkrjcuNYPnNvTG+rizc81cPAuNoP44KW8eb/MhlLq1dsNc/4g+89Yxx96pt++5yxKyLvQa8Q7EDv978N+B1jzIc3bCPAO4AfB2aBL6MTh6/eP8UzHuOZqBzpTzyQp8EDca4rBn/DqROD70JnI/8CnEAtl18K9FCDBYvFYrFYLBaLxZJijHkH+qP/XNsY4FfT10PhJvSqxGdFJATWz3CMLZtJ6KwTA2PM27LPIvIO1JDhlcaY3oblU8An0HujLBaLxWKxWCyWxxUPIFd6MfDf0GcU/poL9PDxm4A3bJwUABhjuiLym8Afkj4wYbFYLBaLxWKxPJ4wF/fE4DuAtxhj/uDhJrTZicE0sPUs6+aBqYebEYvFYrFYLBaL5WLkHD4GFwNN4Mj5SMh54E0A+DjwGyLy6tStDRHxReQ1wK8B/3A+MmOxWCwWi8VisVxMmFSu9Eyvi4T/BLwtvcX/YbHZKwY/DvwJ8DHAiMg6UEGfrv54ut5isVgsFovFYrFcWF4JXAYcEZEvA6unrTfGmNdtJqFNTQyMMWvAd4jIk4BnoLcVLQE3GGNu23S2LRaLxWKxWCyWxxgX+TMGc+hDxwA5oPFQEzqrj8Fjlan6DnP1t72FqHBqA2a6y4OGatnG/kRrO/Yht646ulEZhlcOMes5JBKcUJBIqB5UreKT+7W+SouO+hzMR+TrQ8JeDgIXd90lyRvybYfRdIK3rT/Ow/xMhyN3p49qlCIIXPAMuAnOao6kEuM1c0S1CAkcTDmmODMY+xm4iwVyl3W4eusyd5+cI+fFnDw2Q3V+nZftvJPPLe0h70UA/Ma+v+ZHb349r9p1Cy+u3spvHXk5+2eO8dqZGyg5MXeEcwxNjpt6u7gvmKbojhjEOS7x19jmt2lHZe7pN7jEX2Mu1+V/Lj+JLcUueSfi38/eyNHRLG+cXqSd9LlnlONEXOGVpSHtpM8nejv5en8Hn1vaw1X1JcLE49vnvsKs2wXgOf7kYfm7RhE3BTt4aekQRyOfO8IF9vtHuTZfpJ30aSUJdceh5pRoJ31qTonAjPhEv05BRuf0LMi4IRhxJKoz63Z5YWFz8f5o+BiU5yYeHPmO6jL3toHxDHEtwll3ybdU2934Ce66i9eTsUZz5jWw0ROg0AS/M9HCV08C1VUHKC/puvJyTPcSl1xvopc9rMlY0zrDiVSHP9dNGE05FE/GJJ7gDmIGDfWHGNZVMzvTsM93YDin5Sk0obsnwV9xiH2oHNYyxj6UF6F0QjW+R2Vh0NA+OapO9Lcz/fZMA3tUUV30sJrqbbu6fWkp1cR3tU9nXgxhdaJ37QSqH5/vqHZ5pkEe+Yz14GGic+9E6kUQVlOd+XRMcCLGOvqlptZnWJ14Hgzq6jFQbKZ5Lul2YVXrN6hN/BWKKzHBjIMTQWlJvRmy7bzhRMMfdOzKypTls9CCm37vwvsYlBo7zJ4fvE7zGYAbGIY1Gevyh1XVSB82tJ2HcxMPmdhXnf3cmuq5Z74bEmvsJp4Q1CbxXWoaOru1vgsrmlauM4mJ9f0Brh+TRA75gwW8/qTN852J/v6gwVhbP6u7zPfAeBPfm6hsyHWE6QPaZpmufOZfERUmXgD9hlA5ljAqC24A3iChv9Wl0EpoXe1QXtSYKZ5MWL3UZVTVto9KGi8AvXkhl+rae33tE6OyjONzfZf2m0JLvU5GZRnHKmhZcj2DM9L0ghmH8nLM6h6PQkvLMKxreUHjfeq4+mJkevtZmoO64HfM2Msh8ytJ/EldDhpaH6B9qLtd+0swl+D2HYpLqvWf6xmcyNC+wiHX0TYwG/6avO19Fz5ui1t3mPl3/zT5tjOO00xPP9dXb4b8umrzF5uMx0c30Proz8Ooaig0BYkYx/+goXGd7+h7MJdQWHYoNrX9SksQ53WsKi9OPCCMO/GmydYVV2I6O11y/dRvpaexp3nRmAhqE28miXVcLDQ1jcTTOPJ6Oq6N47qk/Scj11N/mVznVM+W3oLgBNoXs2N2dst4/Ek8rZtBQ710pu90GNahctTQW1CPAONO8pdbn3i1lJYmdTpoCPnOZPxNXBjMazmymPPbWleFtqYNE++FzKsk68sw6c+ZT0rWDqOK5gMmHjZhTc9ZxaYeww1P9TGYunzBXPuBHzhjHH3x5b92wWP3kWSzzxggIltE5NdE5F9F5M706gEi8mYRec4jl0WLxWKxWCwWi+XRwxg54+vRQkS+ICLvEpGnnM90NzUxSB3V7kad2w4B+4B0fsYC8NbzmSmLxWKxWCwWi+ViwHBRPnz8d8BLgH8TkUUR+UMR+XYRKT+cRDd7xeC3gU8DlwM/BqdoNn0JeObDyYTFYrFYLBaLxWLZHMaYXzfGvBB9nuA6IA98EDgpIv+c3tGz78Gmu9mJwVOB3zPGJOjEaSMngU3ZLFssFovFYrFYLI8pjEqWnun1aGOMWTPGfNQY8wOot9gLgS8C3w/cld7+/34R+abNpLdZudI1zv6E8x5geZPpWCwWi8VisVgsjykucoMzQDVJ0UnBF4FfEJEF4BWonOnfoYbF52SzVwz+B/BLIrJn4/FFZA54G/C3DybjFovFYrFYLBbLYwHDxffw8WYwxhw3xvyRMebfo5KmD8hmJwY/B3SA24DPpsv+ALgTGAC/8CDzarFYLBaLxWKxWM4DIvKp0/7APwVjzGhT6WzWx0BE8sDrgRejs44W8K/Anxljgk0lcgEoz+0w+1/4ZgAKKyFr+wq4AYRV1f11AzPWhC60krG+e+IJ67tUn7jYVD3jsT64b3AC1XXOt1NN3oLqX/tt1TjONK4Tb6K/G1VjyoddJNLtkzwE20c46y4SCXEpAT/BWXcxDmPvg9JRh+7VI3AT8uURu2ZbBLFHJRdwdG2GYZhj12yLY+0ZttdWWV6vMAxVQ/4ll97JBy75EgeiLkejCv/aeRKHBrN8eNf/5r0nL6cdlfm7O55MPq/C14N1H/oeUtF4qVQHAMyUBvzHvR/na4NdLIY19hRO8LziPQyNx39ZegkAn79nDz+y/3qeU76bXuJzdDTL0wqHeHIe/rizmzdOL3JDMKLuBrRin4JEHIlq3DzYyWIwwyDOcWJQ4bULX+bPF5/FK7beSj/JU3JCVkZTlNyQN9Zu4t1LL2R5WOXbGjfRS3x25E7yytKQ/79f4OholrIT8NziIfZ6U2NfhSOR+hzs9NqUNgjx7/WmuCEY8R9u+x6+edvtvHbmBgCuzRcBxvs/e/ehC65L7O/cYXb8xHX4bdWlTgoJ+ZbqubtD1WF2QhjsSft24CCR4K2r7r3EqlVtPNVyrh4yDOuqpz5oaPxlGty5DhRbp2qxe0P1JxjMuWP9ZyeGqcWYqOhQXgpJXGE05RIVHUZl1ZJ3A/VNmLk3ZjCr/zWUl2OGM+5Yk720HNPf6o510DOt7mFD+44bqM51d7uMy+ClFiD+mhn7GmQa215f+5nfMQwaMu6Hflvzm5XBuOrVYFzIdVX33QvM2HuhP6/9ZmoxpLstT66ruvPDumqz+6sJ3W0upROq895vCLO3hQQ1j+6Co+UPoXpEtcbH7TBUbe5RWcba8VnZQes+8SCoqk48TLTRiysxoymH9R1aF8WWtksw41A8mTCYdQiqMtbtzvTTs/bcqL19oSjO7zBP/cY3q9fEtMZG9UiEjBIGjZx6Sng6BvfmhbmvhwwaOfoN9XhwhzpGGhdqdyb0tzjEedWQ99cShnVn3Cbd7UKxqe0NWvbYn8RLpjdfbI7oz+e0bpojRlNu6k9hCKc0j/6qxjtoGqUTemx/Teu8u80d+xz05yfa8Jom4/hPPBnrq6/v0vPA9AGNzYysX2d67m6QejnkVTM/O49kHjxOlPoaLAiVo2Ycv1HRGceTG07054tNzQtoXGX+HcWm9s/qkRgnhnw7JC64BDWPzm71EwnrOtZkngpRGqt67tRyVg5DdztMHYOp+2LCKYdic4Q7jFnbVwDU+wS0HvzVBH8tYjTlMZh16C0ISV778LChZXcDjV+AW3/zwsdtYfsOs++7ryOoa178trYH6BjkBHourx6c1LPf1vHUibQMTnSqJ0ZY1Tjp7U5IignOwKFyIPU9quk6N9TjZL4nmc/GsD7xJim0GHtCeD3dJ/NlcYcaMxKrVr8TT+Jz6rjGcOKqp0JYnfgNDOfUGyHLf1TSc0rmBVBsGSSGfDehdaVLsTmJp8x3IvHUoyAqqL9INhaPqnrOaV8h+C3NZ3ZO8gL9XFmM6Oz0yPXM2PsFJv4PmXdHnNfyugF09qRjY/rbaKOPixOo/0BWf3HqdZB4GrNZXOvvOu2nvW1a5qxfu0MI6hrfmZ+E31HPmo2eMKXLLjGX/84PnzGOvvatv/Ko+BiISMMY09zwPQH2G2NuFhEHNTx7lTHm1geT7mafMcAYEwJ/lL4sFovFYrFYLJYnBBfDg8ansSwiy8BNwM3oHU8z6ToBdjOxFtg0m54YAIjIFcAzUO+C+4AbjTF3PNiDWiwWi8VisVgsjxUuwucJZoGnAPvTdwE+LSJHUSsBgwoEfeXBJLpZg7OqiHwUuBX4M+DdwIeBW0TkYyJS3WQ6rxGRj6dGDF0RuVFEvvu0bT4jIuYMr8KDKZjFYrFYLBaLxfJwUWnSi+vhY2NM2xjzKWPM+40xr08XvwT1G7sVnSj8mYicEJGPbDbdzV4x+D3gZagm6t8aY4bpD/XvBD6Qrv++TaRzHXAv8BZgBZVQ+ksRmTPG/O6G7T4NvOO0fS+a5xgsFovFYrFYLJZHCxH5CvBV9Faim9ArBCvGmK+LyCeBX0Q9DVx0wrApNjsx+HfAW4wxf5ktMMYMgb8QkRLw/k2m8ypjzMqG758SkUvQCcPGiUHLGPPFTaZpsVgsFovFYrE8YiQX361EvwV8A/CtwDvTZX8lIp8DbkAnCiNjzJeAL2w20c1ODLrA8bOsuw/obSaR0yYFGV9FJx4Wi8VisVgsFstFx8X28LEx5i+Av8i+p6pEH0ENiX8UvZXoH9OrB/9ijPnTzaS7WR+D/wq8TUSKGxemVwveht5K9FB5LuqPsJGXiUg/ff2TiDz5YaRvsVgsFovFYrE8ZC62ZwzOwseNMW8GvjH9/svAIeDHN5vAWX0MROTXT1v0PUAB+BfgBLAFeClqcPYRY8zbH0zO02O8OE3vh4wxf5Iu+yW0EPcAu9DLI5cA32CMOXSWdN4AvAHAq9aetu+n3k2xqfq+9bsjVvd4JK7q/q7vUp1cr6d66E6gy4OafvbSJxkkZqyxW2gltK/QOZTfZqz7Piox1ooeNgzxXIi4hvzBArmOahR3dguxr/rCpVQTuLtdCKswqsXk2noQrw+jCsTbhuzbdoJ7FrfgeAlJ5EA7z46rljh6+zymOiJfHuE6CWHosWfrCnknZn3k0+xM0ah2OXL3VpxQuGr/Ye5uNnTbeyvENRWM3rmzSRh5tLolnrH9CEe7MyyuzNCY6bK8UmXrXIe9Mytcf+deXD/G9ZJJGnMhz7viAKtBkZODMmt9fSa8VAhZ7xdwnYRSIeT7dt/AYljjWVP3ANBP/Qe+0LuMfpxnm98mSFRD/vdvez7XLugFqUvLJ9mWb/PJ5pVcNb3MybDEk6cW2ecv8SdLGueL69OMEocXXXIPewonODjcwqfv20e92KeaD6jmBhTdEcvDKovr02yrrHHl1BJ3dOe5bXkr06Uhr9r+9bGnw/4di9rO7oirp47Tjsr81v6PXRBd4o2xm6vUnnbZm9491lYutCc65sWmak8HjYT6zUJ5OWblGr3g5wSM9fR721K96MOqa53rqL50rqPbZNrXG7XUg5p+jn3Vhi409diJp7Hbn9f4DGuGqcNyyj5BTdMoLanmthPpsQYLhuoBwQ1UDzryJ54D+Y7qoA9mnbGOfOzrvm5gcFJd86iguvfeQDX8s/xEJdWzH5W1H2WfS8vqtzCsC6UTCc5I6y8qqt76oJHDGySMphwSD2Jfxr4Ca5cbch0Z6+Fn40Ps6+dRVT1MnFg1u7P6zujuMng9IddRPX53qFrtfls1xN1Ay+71Vas7aCQUjzsUm6qNXlpirIM/KguJq5rimdb3qAqFFa2jUUnbMdOxz/TQo4LgRIYb/+itFzx2/cLM0572ynfS3+pSaCV4Q8PKNS7FVGG7vKzt7QZQWNXYnTpmiH2YOqZ+A1n+R+XUMyb1d8i8ZjId+cy3oXpE27uwGtPb6o7jJpjWGHUi9cfI0sj8IYon1WOj2BzR2Z0fLwdY3yEUWhM9dX9NvW/6WzTv/XnGbVVeUn+KsKrtDOpfEUzLWG/euIy9AWbuVi+PfEfPCzP3JPjtiLjojr0futu172b+CMC4/4S1if46qP6/8dI+u6LvXl/f8x3dJt9RD49MKz/zTMg07UF17UcljffEm+yfeIzPo37H0FsQ6rdPPEK8QLcBKLT0ONl5M2vLYU3o70jIrTnk24w9O2Dia5G171c/eGF8DDbGbb6U/V4wrO3V/lls6rhWbOrYlflUDBqq399vCJVj6muycTwBxp4q2ba5bkKSEzq71SOiekg9UEZloXgyob3PJdfXdupuF8rHtZ79to492e+WsKJa+8bV9orz2vYS6frudvBbE3+l8nHN5+wdEcMZF+My9lUJajB7Szz26Ih8bfusPyae0J9XT4J+Q8bnjOKKtn3mRZLrw/SBkO723NiPxYnULybz2hg0tF6KTcYxXF7Uvhz7em4rtHSdcdW3JPstNqpOxt7MNyT7/Taq6nhbWGHs0+MO0/aNYf3ymMKSOz5XSQyj+REEDl7HHXsdRCWIywkSCYWmjM8lw7rW423vm8RkYd82s/vXf+yMMXXnd/7io+JjcDoi8sfAu40xx0TEBUbA040xD0qV6Fy3Er3mtO+j9PXsDcvW0/fvBB7UxEBEdgN/CfyPbFIAYIz5xQ2b/Z/0EsgdwE+nr/thjPkQ8CGA4iU7LrKLPRbL2dkYu6WtNnYtjx02xm61ut3GruUxwca4narbMdfy+MEY8/9u+JoAv4Te7v+gOOvEwBhz6UPI16YQkTrwj8ARHkDNyBizJCLXA099pPJjsVgsFovFYrGcjcfSLNLo7UC/9FD23ewzBueN9LmETwB54JXGmE09uMxjq00sFovFYrFYLI8HLkIfAxGZeoj7Vc61/oJODETEA/47cBnwLcaYE5vYZyvwPODGRzh7FovFYrFYLBbL/TFneT16HBGRXxGRvQ+0oYj4IvKdIvJZznJbfsZm5UrPF7+Hmpq9GaiLyMbnFb4KXAG8F508HAZ2Aj+P3iv1Oxc2qxaLxWKxWCwWy0XJS1HVoXeIyNeAzwO3oAbCATADXAo8DXgBKhb0m6gx8Vm50BODl6Xv//kM6y4FTqK6q+8FZtGHmz8DfLsx5siFyKDFYrFYLBaLxbKRi02a1BhzI/AKEbkM+H7gxcAPAf6GzY4A16fLP26MGT1Quhd0YmCM2b2JzV7xSOfDYrFYLBaLxWLZLBebwVmGMeZu4N3pCxGpofYCJ40x4bn2PRMX+oqBxWKxWCwWi8XymMFw8V0xOBvGmPbD2f+sBmf321B9B74PuBydiZyekdc+nIycL4qX7DD7vus61i+PkUgbsXzYwQ3V0MUJ1agp35ZTTJIyc4ygruYuXl8NdMIpZ2y+BGrI0bt8RPmunJpjpBdsomqM33TJt6G3OwFAImH6LjVNyoygvD6s71VDjVxHGFUNhabQ2xVDKcJb8jGemqUROzjrLt62PmGzyOyuNiebFYgdiITiXJ/BapHizICcF9Pr+5jlAkkxwRk4FI87DBYSkpkR9HUO6HVcolrEzj0n6IV51vsFrl04TnNQ5uhSnUIppFHtqplaOYbAobqtQyk/oh/mGIY5wlYBPIP0XN0GkJ4atRW2dcd52jN7EoCDJ2cpFUJWO6VxOyWRQ73e5af2fZpjYZ2SE/KhO55HGGo+n737ENO5AYe7da6aXube3ixbCx1uaS+wtFplNPTIFSLCjk++GjAaesjJPM7QIS4lmHKM5GPq9S7rqQnbtQvHWVyfpuIPCWKPI0caVOe6dBarSCTsuGqJ1X6RV+26hfd8w99dcMOS0pYdZtePXceooiZjoCZZlcMTw6VCS02VEk8/F1ZjBrPu2HDP76ipU+yrMRKomVhmoCSxmssA9BuCkxlFFYTKvT1620sM5lLTvaGaZoWpfoHEato0qmgsbzQsal8NXk+oHFajoNqd+l5Y0Xj3mw5JXvcBNbMJ6hMzscwsKXE1zaAq42VxXo2/nNTYCtQk0AnUcCyoqRnP+g5hVNFtnEiPNXU8YX27Q1xgbFyVeHr8YlM/9+ehdufEIAygeDIhmHboLajpUeKqCVBm/OREUFqOCWZO1W/IzLk0D2qMlBn25Pq6TezD1KKaagXTwtzXBqzvLozbxA3VWCszfsoMlmI/jYMeDOZh5i41RfJ6Gie5dS3jTb93YYyiNlK4ZIe57LuuG5uyOXFmYiTkO6nZ0m0hJufQ2al9PKxC/Y6Y1Utd/I4Zm11lplLDmlBoaxr1W7WOMvOkrG4BhnWh0NJjJL6m6USGk1fqcfLrE7PKyNe68/pqxOcFmo8slvw1MzZIy8btqKR16/UmxnKjKmMzPHeoZlOxD8FcwtRBZxy7WZlyPcPK0xO8jqvGaanpGUwM8HI9o/00Xe7EaliYW9djZOZhEmsfyWKr2NS6ytbn1zUvpRMaw/5aMo7LzDSwNy/k18Ff022y+sziPzOG6zeEYkuNugorIWv7CvirCbmudsTRlMvqZe7YCLDUnBi85fqajywtfy1hWHfoboepY1rmzLyxuBLz+b95+6MSt/u+9zpthzROEo9x++d6huLJhN5WNfYKq0KhldDZ7YwN4HI9Q76r22Tl9YYGfy0hyUxSV0LCWp7VS92xceLYrCw1Mpu5V00AYWJq6USG9V1qgDisa8y4gcZuVJ6YkPkdg7+qfQN0HJo5EHBiv09+fTLmh1Vt/35DMB7jsa3Y0vHaSf9bLh/X42aGeRJPTMaytLJzTGZ+lplQhpVJf/DbOlZmRmcSa7w7kZYn61MwMT0b1jRvmWlgcUXN2OK8fjfp39lOAP1n9cndXhrHXr+RnuP6p5p4hhVt34xBQ8fKzGgz60thVfM2fUD77cax1N+zzWx/z5vOGEcHv/udF4XB2fliU1cMRORpwP8GjqITg5uBaWA3cAx1KbZYLBaLxWKxWCyPUTYrV/obwN8A16APB/+wMWYP8I3oFZZff2SyZ7FYLBaLxWKxPLoYc+bX443NTgz2A3+JyoZCeiuRMebzqLPa+85/1iwWi8VisVgslouA8+RjICLbRKQrImajSZko7xCRoyIyEJHPisj+85T7TbPZiYEBwtRi+QSwa8O6o6hhmcVisVgsFovF8jjjzK7HD/GB5N8AumdY/nOostCvAa9Kt/mkiMw/5Gw/BDarSnQbsBf4NPAF4C0i8mUgBH4GOPDIZM9isVgsFovFYnmUOQ+3DYnI84FvBt6DThCy5QV0YvBeY8wH0mVfAA4BPwG8axNpXwJ8K7Cd+4sEGWPMz24mj5udGHyIyVWCdwD/DNyRfu8Br95kOhaLxWKxWCwWyxMKEXGB3wX+E7B62urnAlXgY9kCY0xPRP4B+BYeYGIgIt8B/BXgonf2nO5fYIDzNzEwxnx4w+fbReQq4DlAEfiiMebEZtKxWCwWi8VisVgeU5jz4mPwRvSf/P8KfO9p664EYuDu05bfDrxuE2m/B/3T/geNMa2Hk8lN+xg8Vig3dpgdb7oOr6e6tf151fzN8ALVsh5VIawnuD1nrHk+qqrmbeKpdq9xJxrSbqia0qAa84MF9R/w+hPN8cRTzfbcmkNUNhjPkOQNUhnhLPskeYPTGOLdVRproSceJHv6JJGDWf+/7L17lBznXef9+VVVd/V9plvT0ow00uhi2bIiOw52nJCQXZyQPZAlsO/uwnIO4Q55390ACw6EawhhuYRNIBB4w5JslsuyQICz5+WyARIIuZDESWzHsRXZki1Zl5loRj3qnul7dVfV8/7xq+4ZCclu2Yo8Ds/nnDl9qeqnnnqe3/Oreqaqvt8U2R0dUl5Eq5nFDFy2za7Tvn+Gwf4+/uMZgpkYidUjIVNT7d2R1vDMC3V+duH4DGbbgMO7z/OF47txWy5ROQQ3Zs+ui5xbrkAjjfEMXtMd6+QPSjCcHUIo7Nl/gUHoMYwd6vUClUqbYejSXC6qf8Kqim17DY/crQ1SXkQl22WxMUrYgdIAACAASURBVE0uM6DVzTBo+qSWU3iHmvRW8uDHEDiQS0whAhen52C2DXCXMhjPsP8rzlHv5bi4PAVAdro39kWoltp0BmkOVS7wieMHcFfTRDMD3NU0EgphKSLVcEk3oV81SKiaxsNdAaVyd6PuLR8Cl9Jsi4PbVgGo9fJjfwTvbIYnfvLGa8Fn53abm7/53rFnxjC3oVkO4K/FxClNTM7QEEw7RL4QJprYmYaul+oYutudsT9B/bBDblnjPsxrPId52HY0orvDpTurus0jHfQwk2wjNGOd6pEOPKh+f5wSGrc4eB31I8jUVOcfNKaHRR07g7Jh28Oqh55pqD/BSLc6vxLR3OPiBrB+s3qLVB6NqN/qUjxn1MPAV5+RyIfCour2hzmN+WxN22eY0/1RPXjGviOjcZ5bhub+DQ3tzkJEdsnFuBs62s0DhtJJ1c8f1dEJzbgvAFLtmN6MO9Z6D0oy3ueZoyGxJ+qFMDT0ZlTTPMzpuMota7905oTpJ2K6252xfviozUbeCc29MvZiiJN/3WRrqqmfbup+5WobWuIjj4ORLv6xt9342M1Xd5v936Z68NNPqm/GyHMg3VY9996My6AI+WWDcRl7yIz6NiipZn7s6TJ/XXXJi4vqRTHyNBhpj/trMd0dLqGveb10NqS1SxtMvSliIl8IpmTcNk6g3hb9ijNu21RH+7lbFaIMl/jbpJsbfiH1g954/IAeAySUscdBrqY67MO8jL01Rt4Y6wdUi36kqT4aU6nuhufFyGvADbRvWwvC9gcj2jtdhjldd+Tv4A4Yj4NBCbY/FNLb5o49BMI8l+jgT59QrX1gPOamTwbEbjLWI0PsCusH0pf4JQxz6nMyiufchRivb1g9ogkhTuvxVaKN42e2ppr66/tcwrzGPmyUmV2NCLMO/Yr6RYy8Ik78zI2P20Jlt7n7zjfQ3pUmezEi9oTmHpdtxwKaC2myF2MGBfV5cIaG7g73Es8JUM+CYV7G33e3O0yfClnb7+EGG5r57Xlti9H5ghuo54wTGvoVZ+xXkl+JSLVDgimP3oz2vXE1vnLLQ5p70wxzG94D6YYu68xqX0q04d8ika438rDx13VM9Coy7g8vgPVbYvKnHWJfx0g/8R1Q7xzN+aOx1ptN/AkCzfl+Q+Nk27EBq7elxz4ao1ge5Sdg7P1kXI2boLKxndEY9etar0FZz8tGxwvjau4b5VwJYdtjIfWD3jhGs6v6OvLgGeXw0ZiKPSGzFtGfdulXdIxXHo1wIh0Xsbux78OZkDOvf9OGj8G+eTP31u+/Yhyd+Y6fOAOsbvrqPcaY92xeR0S2oSf9rzPGfEBEvhP4HaBojGmLyE8BP2qMmb7sd98LvBfwn8rFWETawL8xxvzd1daZlEkfPkZEbheR94vISREJROQrku9/QUS+7tlWxGKxWCwWi8Vi2ZrIVf5YNcbctenvPVf48S8AnzbGfOApNnCl/9TLUyzbzCeBW55mnYmYaGKQnPg/AMwCvw+kNi0OgB+4HpWxWCwWi8VisVi+XBCRFwDfDbxVRKZFZBpIrpEwJSJZoAEUk+cQNjMNdI0xw6fZzL3A60XkO0Rkp4jkLv+btL6TPnz8S8DvGmO+T0Q84C2blj2E3jdlsVgsFovFYrF8+fHM77w/iP5D/VNXWLYIvA/1CnOBm4Djm5YfYkPs56l4OHn9naeo6eWTjisy6cTgEPAjyfvLN9gEKhOWY7FYLBaLxWKxPL945hODfwTuuey7r0VVgl4DnALOoOfT3wT8PEDyX/7XosqgT8d3P6sabmLSicEFYP9Vlr0AOHs9KmOxWCwWi8VisWwpDPAMVYmMMavARzZ/JyJ7k7cfN8a0k+/eBrxZRBroVYJ70Vv+f2OCbfzuM6rcFZh0YvDHwM+JyDE2LoUYEbkZnfG873pVyGKxWCwWi8Vi2UrcABHPt6ETgZ8AtgH3A682xqxMWkBicvaV6J08deBTxpgvXkslJp0YvBk4DHwUSMTH+HP0YeQPovqpFovFYrFYLBaL5SlI/sP/u5d9Z1D1ol+41vI2mad9H5c+SxCJyHuAHzDGxBOVdS0+BiLyKuBVwAw6E/l7Y8yHJi7gBpDbsdsc+NZ78Zuq3RulIUqMoQdHuqSP5nD7qvt74aUxEgpu1xlr4LuB+huk1jd0rmPfEJVDpKNtLTH4NYc4DUE1AiB/xkUSzfPOQky6odrxw5xq9ca+Id4RYFopcA1OzyEu6m8lHVEs9Wg1s3hnMzghOIlOdeyrF8K2h4TVu7RPUw2X4ewQNzckrmXwWg5RPsbpO2SXVe+3N2eYOiE0jsT4qw7BTIzXUhGq4ewQAgdnIEgoRMWI0myLXHrI8tkKREJ2ySXMqQfAyG8AwN/dVg+DSHAGgrerS3yyQFiK1DcghjgbI7kQx4uZLnVZe3Qb0cxg7B0wDF363TSpTEi4lCNOG9yuQ3pfi/CxElE+1rYJBQkcvJaDG6hWeKahWvC9gwEAxYd8hiXoLwzHHgl33nSWh87tIq6pN4LbdXT7AF2P7JJL/1AfM3ApHEvRPqzeDUQaCwCn3vjGG68Fv223ecFrf5jsxYhBwWGYF7IXY9o7XXIrEV5gGBS0fq15h6knI4Jp9eFItWOCaf1NmIPS6ZhhXuiXhXRLtcPjlGrsrx108RvqHZBqCtkatBYgzsQUTzrkLqjOfphTrWjRMCXVVc1xJ9jQ1e5VBCdS/XJ/PaZxi6Ma16Hqw4cZ1csunVW9aScpa1DSMgqLmn9c7U7Vt27H1G91cfs6dtNNVAd/FvJLqgMO0KsIflM10y8eccktb2j9j7wNhiX1E8mdc8jVDK3dwvaHQjo7XDpzgtsH4+lvWgsQlkN2fMxlmNd6x57W1euAE+m2W7uF4rlRvQ1e31A/5JKtbeiY++tmvAygt037LfYEr6/6/CON8Yu3Q5zWejoDofKwsH5A8Osb+9+dhcIipBNPi87shub+qP/bu1yCMhx/643Xg89Vd5t933sv2Zrqlm/Wqh+UtJ7+WowXGNb2e2TqZty+Iz+Ckea5E+q6Iz3yYV69Okb+A6GvsTjS2M8vdmntyxNMOeRXVPd/pMU/8gJxIvUj8HoaK6XTiedHMm5G/ZK9GNHZ4aq3wdDgRNp3TjIOBiWhX1Evg5FvSGFxyPqBNLGnOv8A6XbM2n5v7KdROqtjNdUxFM72iHIendk03aremjAoa87P1jb8crY/qD4fmbqhuVfwOqo57wbaJqmOxpvXN6ztc8nVNrwKnNCMt5+pay4ISjJuh35Fj42jdswvqw6+O4DCUsSw4NC4RcjUVNd9OBPi9BxS6w6DckxuSY+Pbn9DZz6X+JIAtPfHuF09Hg1Lul+jPow9oT2v2vbbjmqcRD488L4bn3OLU/Pm9lf/0DgvjcZxv7zhu+JEmlfcYMNLBTb0/r2ujtFBSfOe39A+zC/pqzOA3p6Q/CmPyNdyph+PWN/nkl/WXJCtG+qHheyy5tVR+4xy6Wjcj/p95DEzzGtdYk9z08iDplfVNh/lGuNt+Km4gebmYV7Gnhrbjg3oVVNEvvpnOAPGfisj7wH1G4GpkwPa8ylaC+rjBLpsUNHjxyg/d6tCmN/Yh9jTba8djsfnTyOPqX4VopzGVeRrvg3zyXE9FLJnvfF528gDwl9Tn5RsTcV6RmNw5BMxinsnZJyzc8sbY3U0foIpZ9weoGOnPS9MnTR85g82YtLfO29m3/yDV4yjs9/7Yzc8di9HRH4efRb4zcD7gRVgB2qO9nPA240xPzNJWZNeMQDAGPP3wN9fU20tFovFYrFYLJbnM8/e+fhLybcDP22Mecem784CbxcRA/wgMNHEYFIfg1tF5KWbPmdF5BdF5P8TEethYLFYLBaLxWL5skXMlf+2CNvZkCy9nIeT5RMxqfPxu1HJpBHvAP4zkAF+WUR+dNINWiwWi8VisVgszxvMU/xtDU4A33KVZd/Cpd4IT8mktxIdAX4FQERSwOuAHzLGvFdEfgj4v4G3T7pRi8VisVgsFovFcl34eeCPRWQP8GfoMwbbUV+Ee7j6pOGfMOnEII8aLwC8NPn8v5PPDwILk27QYrFYLBaLxWJ5/iBb+hkDY8yfiMga8Fbg11Gn5SHwAPC11yIUNOnE4BQ6IfgY8H8BnzPGXEyWzQCtSTdosVgsFovFYrE8r9g6tw1dEWPMB4EPioiDnpuvTipRuplJJwbvBH5LRL4JeBHwXZuWfTVXf+DBYrFYLBaLxWJ5frPFJwYjksnAhWf6+4kmBsaY94nI48CLgR9PZEtH1IFfe6YVuN7ErmpWr90suAFkVvX7oAKlj+VoHjCkG0L9sLD9PocwIwxzwLLLMNEr9xuq3duvqs67EwpRzsF4hlTDxQkhqMbE00MIXPxlj86tAaWyivo6j08T+dC4LWLbQoN2rcidN53l2MoOBis+UTkc/9ZreBjPI34oQyaj3gUjbeDcMjih0J0VLt7TJ/N4hmFJdcv9xRSDsmpGh8UY48ek6w7DEgQzMfkzDr0q+KuO6ngPZKwlnD2V0vpnYyRwkMChuVSi6RpSq57qph/pk8qEpE4UCPf0yZ7KEJRhMPDAjyBwiYsx4VIOB/Vx6FfVc8Ff9gjzLsYzNFYymB0BAmRmurSaWVKZkGKpR3O5CNNDvGWfcDYgfKxEugk0HQqfFVZfBKmm6jmPtPTrtxtS60LhER+JoDuv28yfSGk/l10ee/QgTgniPX0E2HWwztmzVfVFCIXe/uG4LXt3dfHO5DCeIcrFRLlrnlxfP0T7J/RlrMkeTDlk6qq13k50ljN1Q/mJiLV9Lk6U+AVk1cOgsBTR3uXSuMVh6qQhv6za7d0dqu3endUYHxQht6g+AL2qqNZ0oHFfe5FDqqXa8/2yrtNaEOJEyxpUw7tXEbxANbYjH9pzDqXTqt8P6rXgDiBKw+I9LuVjBjcYlSFjv4TYVR3toOzRmnWQio6xTEN17VMd1XHPLyXNFEG/IuRqhkFJqN/qUlhUHeqR70Kqm7w2Bb+p22zuFXLLcPGQR6oLmTr0K7qfsSeUTkGq4zIoCa0FHYfGVR3yYUk1uMOc+kRcvB2mTgi9ivodOIF6FDRu0T4KykK2pl4F/npM5AvdWZj7xID1A2mKizHBlEPtLoO/6pBqavv6DejMgV9XHe9sDZoH1JNkUITmASicEbY9pl4MkS+AIZhW/fDS2XjyJ8yuIyal7dWZ0/YIyi5OAH7TEKWFXlXozGm+Kp1Wvf3YhWHBIcxueDyMPAyGBY3/3jbVGM/UtY9iT/s28lXTPNWOWHlJcazNHkypvn5hRX07MnWIfNU97253aC84TJ1QPXiJQCInaUP1NGjt8nBCk3iIqF586cyA3kwKr28onBtgUg4yjIkyLibl0LglTapjAB23/nqMDGN2fLpFZz5HnBJS7YjCky36Owt88V/kSTdV93/6SejsUA+CblXoVWH6hI7Zzg6XKK0xOP1EjDM0XLjTpbCo3hCDkgCa1wuLOgZrB9yx38tI175xi0OqqeUM8tA6YMifFvLLhtUXQfkYrPyLiOKj6i9x8Yj6+biBHkudELZ/IvHwiQz1ww5BWWM11dV278wJ/Yqu44TgtRwytUu9SkJfWL3doXzcUDqtfgbr+/Q37uAGBusmorTQm3GT/oMd9wdEGZdUx2HtJodMXXNmbll9GLpVGXsRpLqQPW5o3KIxn61tlJtb1hybbiTeE32PdEt9BXoV3W+JoPZig18T1stC5Zj218Xb9D1AMCXj/No4DKWTGrteX48V6abGKOj32VX1R8jU1Z8i8tWPoXFY88bIYyDytd/8dZPkrTT9Gc110ydG62juDXNCYVHPO9YPCINSmn7VUDqpbTM6Jrgdh+ZB9a8Iq0Oyp1KUj8es3eRgXI2X5n7In3YI8xseBsaD4hnIrRjqt2o7DnMaN9laitDX/Gs89SMondbxEWYdBiWhW03jBZrv/cQ7Z+rkgIuH04C2/8zRiNUjLq3dadw+FBe1XsOienV0Zzf20Q0MOx6I6E9v9gjbmojIfwXeZYxZTN4/FcYY82OTlDuxj4Ex5mPorUSXf/+zk5ZhsVgsFovFYrE879h6Vwy+CfhfwCLwzTx1DQ1wfScG14PkVqRvA+4EplD5pHcYY/7osvW+D3gTsBv4AvCmy65SWCwWi8VisVgsX3oMW+7hY2PMvk3v916vcif1Mbhe3Au0gR8GvgH4B+APN5ukici3AP8N+H3g69CJwV+JyJEbXFeLxWKxWCwWi2VLG5yJyLeLyLarLKuIyLdPWtYNvWIAvNYYs7rp84dFZCc6YfiN5Lu3Ar9njPkvACLyUfSB5x9H/RMsFovFYrFYLJYbxxaZBFyF3wG+Erh4hWX7kuW/P0lBN/SKwWWTghGfI7FqFpH9wM3An2z6TQz8KXr1wGKxWCwWi8VisWzwVPc5bWPDi+xpueYrBiIiwBxwwRgTXuvvr8DLgGPJ+0PJ62OXrfMoUBGRqjGmhsVisVgsFovF8s8UEflG4Bs3ffVmEbn8HDkDvAL47KTlTjwxEJHXAG8B7gBc4G7gQRF5D/AxY8wfTFrWpjJfhe7UdydflZPXtctWbWxabicGFovFYrFYLJYbxlZ5nmAT24HbNn0+AMxets4A+CDw85MWOtHEIHlo4X+gskjvRu9VGvE48D3ANU0MRGQv8IfAnxtjfveyxZc3v1zl+1FZrwdeD5DOl2kejCmcUk3/QSnRIg9Vs7x0UjWg40xM4xZHNZe7qgkM6neQSaYemZputjcX4wyE6WMOg6JqLgcLQ9zVNBIKwfyQ7OM+cd8nzEM0G4Efky4FdPtp3NU0D7q7SZ/KYKZi3IaHhEJ2WXX4y8egX1ZddUk0fAdl9VFINxLt+scy9A4GOGspynfXqLdzuCcLZGrQuaNP4aGM7m85xniG7u6Y+Rcsc/bUdrbNrzF8ZAbnSJNw4NFr+OTPuES+Q382wi0HRIFL8SGtv/uyBma1wKCVgnJE9rEMnZuHABTuzxFUYLgrgMClsG+dTtenU04jgYPXcggWAvwzSVkLHQa1LFIckvIizOMZbWcXqEaklnyMC9JMEe7pE11Mkz3vsPLqAdnHfZxQdZK9DvRmwa+p1n5vTv0L3K5D/rzQr0JYisgsu3R3xfirDvGKj4RC65M7KeRUF14icPsOvTmDhIJ7IkeqCZ0F9agYzoS4rRunX7w5dlOlMvmViJU7PbwODHMusQ9eV+jPaJxmE+3+btUd67kP84n++7ph7aBL/rxqqtdebBLNaJd0E8ISVD8fUT/kqp9FTXXnR5rX3XlDVA5xGx7DorC6P6T4SIrWgox1vNNNaC3oGEm3wAkN/YrqXftNQ255yLDgMiw45GoGibSOU0/GNPe4Y93zytEWa4cKY13txi1p3EDbxIkge96MPQJ6VWHmaESYEfoVh25Vx8T6AfUUAOiFQm8uxq85dPOqgd1a0DE2zAtRWusx8ifI1QyxB8Vz6seQrWtdh3n1MMgvae4oLJqxxvnq7Q7D2SE7PuzRmRXar26Tvq9Av6p1GCa+B6mmapx3Z7Wc9pzmouIZQ+OWdJKLHNzAsO0hGevmx0lblU4bjAvDrmrtl06qB0KqqTlpUILVIx758+oZsXazkGrCzCMDurOp5yZ2i2UyddU8z55XXXtJridPPaneGiOvgWxtSFD21KOiHeNEEPkj3wKX5h4Xv6ltnr0Y09vmEGbUl2X6CfWEmD45YO2AT3NvmsqjEal2RHs+Reypf82w4IxzeuQL6weEqZMG94T61oy8OYLZiPwpj9Jp9U6I/ET7vW5o7lE/je6sx/QJQ3OPg7Mzm+i/x6TaIcOsjOMDdDw09zrMtB1WXlJk+lRIZ9oh8lN0Z6eQaOSbAe1dLrkLMdnViGHBwW8app9U/wJQ7XeJVLs9fx6CknoABFMa/9kaNI5orlt5uerHF86QxLrQmdPxmluGoKweORJB5WFhmIeVV4b4iyku3hFTfNRjWIJ6VcYeGtuORqwddCme0Tgb5oXhlLZjvyyqK78A2WXt62Auxu04hMWY6Ucdhsn2Il/9GSRSf47GLUJuWTX1Mw0dX+25G3dX8yXnC9lpSqcHDAsuwbRDMOXRm3EZFPV4PChteBgMyroPuWUdp91ZyNaE8nFDa7fo+cXpjXwYexpH7XkhW9MY6cypZ0yvCm5fNf0BnKb6nQRTLsUzqqUf+ULp7Ebe2/lx9bUZ5oVgSojdUZ7RPDH9REz9VvUwiL3EPyEwBCXhwJ9ovg2m1PdCIo3VdtXBidT/KbOqMTLyOFjb65Buag5sz2vMTZ00XLwdnEDzkNfVHDfMad5OndT8Wbw/RbqpYyFT13YPfZj7lO7PyO9jRDDlcPGIeju059XXYJiXsc+C39C+mH4ipl9xGOZdhjnN47nEpyfVSfw/5lxq5TSFRc2jAL1tui8ApbPqjzL9RJzke/WmWD+gx7koLaRbztif4RK2nirRe4H3AojIPwD/0Rhz+R0318yko/GngLcbY76DfzoB+AJw+Fo2KiIV4K+Bs1z6QPHoysD0ZT8Zfb78SgIAxpj3GGPuMsbc5WXz11IVi+U5ZXPsujkbu5bnD5fErs27lucJm+M25Ree6+pYni+Yp/jbAhhj7rkekwKY/FaiBeBDV1nWB0qTblBEcsBfAWngXxtjOpsWj3bqEHBm0/eHgLp9vsBisVgsFovFYrkUESmit+ffjD5bcAnGmDdNUs6kE4NzqGToh6+w7C7giUkKEREPVRg6CLzcGHNh83JjzCkROYG6uf1t8hsn+fzXE9bVYrFYLBaLxWK5fmyRqwNXQkQOAJ8AckAefR63gp7nN4B11Dj4aZn0VqL3AW8RkdcB2Y16yKuSDb13wnLeDbwG+C+oytBLN/2N7uj6WeC7ROSnReQe9NmGg8DbJtyGxWKxWCwWi8Vy3djKBmfAO4H7gR3oc7mvQc/XX4caC/+HSQua9IrBLwO7gd8DouS7T6LqRL9tjHnXhOX8q+T116+wbB9w2hjzRyJSAH4MeDP6DMPXG2OOTrgNi8VisVgsFovl+rF1JgFX4m7ge4FExoO0MSYC/lBEZtDz7pdNUtBEEwNjjAHeICLvBF4JzAB14MPGmBOT1toYs3fC9cZPWlssFovFYrFYLJarkgGaxphYROrAzk3LjgIvnLSgSeVKc8aYrjHmCSZ8nsBisVgsFovFYvmyYGtfMTiBCgUBfA74f0TkA+hdPt8DfHHSgkQvBjzNSiJd4C+BPwY+YIwJnuYnzxnZnbvNHf/yh1i7yWFYVL31YUl1fUc66WFONe9TDRevC8MihNUh+RMpurtiTD6CwEFCQWLVzs/WoLlffydh4i2wsuGD0DwYIzGk1h0kgv6ukMyS6tEHFSgswtqtqtvrtVSjOpwNSC35RPmY3Dl93KO7W7XYM3XVOg5mYryWgxuo9jAkfgcRrN+sfVc+BkFJSHW1jtllaN02xG14RDMDssWAfjcNgFxME2djJBdiIoHAJbPkIRGk7m7w2oWj/OnjL0KOFYh8MAtd5EwOr6vtFmdi0nUHr6Na16P2NJ56LvR3xGRWNh5dyZ9XnXU3gJnPRyx9Dfg1l6Ca7Iyr+yCBg/H0vVsOiGsZ/FWHYckwdUIIylpWc68QzMTklhzy502ieyz0q4ZtD0O3KuSXDd2q4DdVw9lvqgb3oKR+COErmoSPlYh9Q6am+vf50w6DMjgDiNNw4mfufcAYc9eXJkqvTHbnbjP/A/dSTPS4Ih8KSxHNPSrGHPuqKe2EBmdoCLMOXqLhDKpZPfVEn0E5TSfRdR6UhHTT0JkVpp6MuHjEHetwD0qqhe6EZjw2QNsw9qHymG471TE4iSb9SHe+vdMd67f76zGDgvZ5Z1bjMN00l+hAD/Oq7T3Mayw4of429rRv081Ep/rx6JL9iXwZ66H3q6ohDonO9s1CpgaZxsb7VFc1tds3h0wd9QhzjDXEC4vDsc5/Z06IPdUdz6xFxJ4QZjY0qp2hYVhwxnrhw0R3LVtT7XY3UE3vzpzgBBu+BYVF1d3uVTXWhiWte7qp+vLDksaYl2ix+U0z1uof0atqmSMN7tE+ZRrafkFZt3PxDkP1fsFf19/3qqqX/sD73njDYzdf3W1u/uZ7ya1ozDgR5C6o5jhoGwTlRF+9o/s28sFwQph+rM36wQLDvPaB1zeEGWFQ1DbLrOpYANX/j9LaLiMt9ZGfxfTjEb0ZdxxrxoVMPcbrGzo7XPWZ6KhHBuiYij0YlA3GM+Pcnm4IXke16zOrsH4kpPyQN9aFdyL1xnEDja2R5nprtzD9REztRQ7bHjGsH1AN9igNUUZ/k25qe2RXI+q3ugzKBq8jFM+Ycb07c0JQ1bw0ii03YOwNkW5B/Y6IwkkXd7CRJ5xI37d3uYQ5bR9g7E3gBozHZaoJ2bqhfljHZJjXejgDbc90E/V3yAu9quZJCYXCGRmXk7sQ093uELuqY++va/0LX4xY27fhtTJaf9Rv/Yrm815VyJ9Xb4aH33Xjc26hstvsfsO9435p3BYx9ajG1+g4EuY38mRrQT0D/IbuU3dW34O2RXOvg99gnNMk0vw4iutUR7X9Y4+xfwxA+YmIL77CoXwsKbcqY3+BkccKbLRluq3nEu2dLqWzIRcPeYT5jfwDWgfQ8QEaF2HWYVAS3MCM47d+2FGPlIbmovZOFzfQWByNw837FSXHoV5Vxl4ho3yW6kJ+JUq8ODZibXTsTXW1HUc5b3RcBvV1MJ7Wd1DS9pk6qR4T3R0u5RMBK3f5SOLDUDiv+SXVUZ+N1ryOldF4b+906VcYH7sAnED9HQbJOWG6qf0GmnMWXyVkVjY8DzbHZGZ+t5n/zz98xTg6+aYbn3MvR0TuBXYZY94oIi9FBXyyQIxeBPjOSY2IJ33G4E2oMtCfAW0R+Qt0kvC3xpjwKX9psVgsFovFYrE8n9liBmebMcb86qb394nIEeBr0cnBh6/l/UBS0wAAIABJREFUOd2JVImMMb9pjPmX6APIb0Ftl/8CuCAi7xORV1/LDlgsFovFYrFYLM8btqjBmYhkROS9yZUCAIwx54wx7zXGvOtaxXuuyYfcGPNFY8yvGWNehqoI/SI6I7EeAxaLxWKxWCwWyw3EGNMHvoUrmJo9E65pYjBCRG4Cvg34dmAOWLoelbFYLBaLxWKxWLYaW9zH4MPAPdejoEmfMUBE9gLfjJok3AGsoM8c/EdjzCeuR2UsFovFYrFYLJYtx9aZBFyJ/xf47yKSBz6AnqNfUmNjzLFJCppUrvTTwF2od8H/Bn4E+IiZRNLIYrFYLBaLxWJ5vrK1rg5cib9JXu9N/jbXVpLP7iQFTXrF4FH0oeMPJU5qFovFYrFYLBaL5bnnlVynaxqTOh9/5/XYmMVisVgsFovF8rxjC18xMMZ85HqVNfHDxyKyX0R+S0QeEZGl5PXdIrL/elXmemAEWvNqwFX9nBpXBNWI8nHDsKS96nWh/IhL7BvCxDypfH+KftUw/ahD9lQKciH+qoNx1IxnmIPUwSZe06VyoE71fiHMqYFHdxacgeD0HZwB9BeG5E95DEuGdAuKZ3QbuSWHdMOhsAjTJwz+GR+vC+m6gztQI5/cOYcwB+15NTdzBsKwHNFfGBKn1YyttaBGI04geB2hX1YzlMaRmHA2YM+/eRK34eF1hMwpH+/j6iDinc0gO/raTq3U2Nysvz+gtytiR7HFH33k5eM2kwjSR3PEmZjIh3zyiPmgEqth0Uw8NmHyOkKchsIpNZZL3d2gt39IZ07IL6lJUG/GJX9Gzc28pktm2cVreKRWPcpHHaYe1cK8EzlyS2oUt/2zhkFRzUg6c8KgEjP/9wYngF5FaM8LEkLppIxNiy7epsZGQSkxeimpIc/0EzHZuiF8rIRxIbeofTh13CHMbxhRFc88N6PfGSaGfDnGpmK9GZfpJyNSXTU3Wj+gZjPDgpqbxSkZmyy5AazflMEJDaXTAyJfy+rMajt0d7hMnVTTmkEJiufM2ARnZETjhIbS2YjKYxHBlEPuQowTqoFTtyqsHXSpH3LJ1GPCjJBqx6wecROjGjU3iz0YlITYS4yakvZvzwuZuhq01W/fMKCqfm5A7Klpzvo+l3TTkFuJCBJztuJizKCs48hfN8RJ3+74TER+2eCvxWSXtf9iT42cKg94Y1Ol9rwwzAurt6XJLQ/Hxjbppi5bvMdl6R6hu93BGWpbhlmH6cfalM5GxL6aQeWSbXhdqByLCabUWK87b2ju13V6VaE7q+Y8TgTl4zGZOpTO6ngK89qvJjFNc0KoH3KJPSHytc1GJlYSqSlWqqN5pFdVM6Dcso6F6UcdmnuF2gtdWgsy3tfnhFjz4Po+Fy/QOrfnHMJNJnf582ZsjFhcjMmuqrFcqh1Tu7OIcTX+Uh01lupV1chr+4MRsavGZu1dLpm6wXgbJlmgfZI/b2jvcikuhRhXDYtyKxFe3xBMObQWoHlAzc38psFvGryuGi/lFoXUukPppLDz4/HYnC7VhEzdMHVUzc36ZaF0NiJTNzQPqAFfUNI+b+4VMnVo7nXwurDySq2HG+h+hLkN86ZeFdYOujghFM4IlWMx/lrMhRdreZVHI6qf1fHRWtA6dndp3m0fiOhVYeZ+Z1zuyATRCbXc1oEYCdWEb+bhmFR3wyDNb+h+Dcpw8XYdV6mmtsH2ByOCaszUSYOEsHaTMzYyzJ/W9gGtf+xC/bBD60CM3zQUlqJkbBkaN7lqMFnWY1VrQWMi01CzrpmjOr4Li2oSODKvu9EMi/rqBNC4IySzrO1oPM2b2bph+omYoKw5cPqEobBo8Nf1uGTcxLwurW3lNzTnVB6LxqZkw7yMTeKcoRmPg35FTdTCPJz7hphtD+sYX3m5mkiCGoIFU5pbx7HUjoldWD2iBl6L97ikWxoj7Xk1QEx1tJ7Vzw0So0sdmyODv86csH5A67Xwf1psfyggezGms8NlUEry/XaHxk0uF16sxolOqHXP1jT/lk7HVB6N1CSsZqg8rolrbZ9LfiUanxs4oRrEpbrQ2aWmlrUXunTmhCituTJT1zbPnzeXmAAuvjJNmHXIrURcPOwzczQct2sw5TAoQWu3sHq7Q65mxnUfmZtpfTWWS6f1+N+e3zDwcwMtp7vdoX7IJX/GGddhZJp4CVtUrhRARCIRufsqy+4UkYkH2UQTAxG5E3gI+HfAZ4HfT17/HfA5EfmKSTdosVgsFovFYrE8n3imqkQi8u9F5JMiclFE+iJyXER+WkTSm9YREflJETknIj0R+ZiI3HEt1XuKZSlgYjPiSZ8xeAfwOeDrjDHdcS1EcujTz+9A72+yWCwWi8VisVgsyjbgH4C3A2vA3cDPArPA9yfr/DjwZuBHgcfQB4j/TkSOGGOWr1SoiOwB9m766kUicrmXQQb4DuDJSSs76cTgbuCbN08KAIwxXRF5B/D+STdosVgsFovFYrH8c8AY89uXffUPIlIC3iAiPwD46MTgl4wxvwkgIp8CTqMTh5++StHfhQoDjW5q+q2rrNcDvnfS+k46MeihM54rUQH6k27QYrFYLBaLxWJ5XnF9nye4CIxuJXoZUAL+ZLwpYzoi8pfA13H1icG7UT8xAR4GvjV53cwAOGuMCSat2KQTg/8DvE1EThlj/nH0pYh8FfBLwF9OukGLxWKxWCwWi+V5w3XwMRARF7068BXADwK/ZYwxInIIiIDHL/vJo6ip8JWrZEwNqCVl7wPOG2MGz66Wk08M7gX+HPioiNRQR7Xtyd8ngTc+24pYLBaLxWKxWCxbkqtPDGZE5P5Nn99jjHnPFdbroBMDUBGfH03el4H2FXzCGkBORNJPd8JvjDkDICI+sAt9tuDyda6f87Ex5iLwVSLytcCLgTngPPBpY8wHJynDYrFYLBaLxWJ5XnL1icGqMeauCUp4GZBDn9v9GeA3gf/0FKXLUyy7dEWRncB70FuPrlTOdXc+1poZ8zds2C5vSSRUPVx3oHrSnZuH+Isp1l7bJnN/gc7+kOxZj9hTjfzV20W1n2+N8VoOzQPa/lMP+DQPxrhdh+GtXfqBS/bBEqZsiP9qhvpdMW5X+ywsxmRWHAZlQ29XTPGRFMaFqROqKdybi6k8LOo7AIQ+NF4yoPiQP9b2HXx1k2AlT5h3iMohuDHuapp0Q/AWXZxI+zN2wW8a1g8IuWXIXYhp7nVYPxDhdh3Sj/t8IZqHXExUNBAJ/YWY1NkM6SZEj+bIJRrWsadavZlTPmEOlv9iDzkX5t4vLL/EpXA+prvdwe07421XHhYah6E7b8gtOUQ+zH0qYvWIaiQ7kfodZB6ZJko8BtxA9fTbNxvKx8Bv6L4MiqqfHeZVAz3MQf6MS28uJvZ0m6u3q++DO4DmwZjq/cKFr3CoHIupH1bfiGxDdbVH2sSpFmOt49LZiPYurdvaTeoRsf2BiGHBYZgX4q7+NpVoMTuhoTU/sb3H9SWG6iMBzYU0xoXCFyPCjDAoOHh9g9eHYVe1/fsVoVtV/WpItKlnhWEJelVP230AmYZqr0ukutnDnJCrGdURn3LI1nS5akAL6abqQKc6htiDXsUhWzdk6jESOWNt6vacQ6qr2thOCPWXBWQf9/E6qu3dn1G9/ZmjEY2b9Ee5ZVi7WciswtRx3UaYEbqzKdwAVl4eI6FgPIfIdyksqp59tg6znwnpbXPpVVRbfJhX747MWsTKnR7Vz6vWfTDt4K+r9neUhp2fCOjM6m2cg5Kw/NK0ao0nd3bmzxvSTfVXaNwCnV0u0ye0/OEdRYpLIaXTceIzoDrhpdMGZ2hwA8ieF6aejOgm+t/pJmTqMf2KQ5TW+M0tq+Z4uqk5Z+0mIUz8CBq3qMdDUFYfh0FJSLcYt7Pf1DbKrkZ4fYfC0oC1Az6ZusZH7LmUzkY4oWFtvzfWnL/RGAfSDa1vryr4DcELdBz2qqpj3quoFnvptLZv7DlkV6OxN8EwL5ROD1g/kCZX08/+eqx+GjWNb+PBIBRiT3Xb1w9obEsEQVlINeHCHR5eB7J1Q3OPS28WssvqEZKtQ7eqevFeVzXWR+2//cGI+iGXNT/Rsnd1DK0f0HIbhyG3qD4BAIUzum9eB8rHtd07czqGUh1D5KeYPmFo7hWGRc2L63cM2fFhj/a8xtOgElM86Yx9FnKL0JuF1m0xxUdcUl3Nj1EGtj0ktOfVv6C1AP2yxl6v6hLmNJ5iTzX5Kw8Lw7zqzQ/zOha8rtZL+0f3L7+k9XAH2gbnXmMoPurSmdPlo7yZqWs/j+LLX9dtFc6rXwUYwqxDe16YOqk+E24A2ZquP/JCGSba8L2qS7YG3aQu3R0Tna9cd5zkruvWrSHbP+EyzOu5gDPQ4zUI+WUSHX9tj86cMCgbyscMuRqEGd2vbE09DKI0NG5yKS7GtOccBmWheMaQ6sDFIy5eB4KKtk9zr+aT8nGXxi2S5EzDyp2aD4Z5SWJU27F+WIh9BycQ/ET7v3RS88Mw51L9vB74Vo9oe3armui8DsS+jsEwr3nZ7UV0Z1Os3qFmDpGvx8tB0aWzC0qn9Pxi6knt22FeYyW3EhGnhPacQ+yTjCPDxUNecgyFQcEh9vScIXbBC3SspBt6rB9hPB27nV3qHzTyGMnUDel2THZVvXMKiw7+uqGzKU4GRT3fcxOfhNZu9RGJPfV78TqMj23pFvQr6nugHkYbbeqvqd9Ve5fL9vs7rN6RJ/Zg9lM9Jvr3+jVgjHkwefuPIrIK/J6I/Ap6ZaAoIu5lVw2mga4xZjhB8f8dvUXpXuAY+mzBM+KaJgYi8q/Qmc7mKwYfeqYbt1gsFovFYrFYtjLCs3/G4DJGk4R9qDypC9wEHN+0zqFk2SS8HPg+Y8yfPO2aT8OkBmc7ReTT6NWC7wdekbz+rYh8RkR2PduKWCwWi8VisVgsW5Lr63z88uT1SfRZ3SbwTaOFiU/Ya4G/nrC8C6iC6LNm0isG70GvEnyVMeaToy9F5OXAHwG/DXz99aiQxWKxWCwWi8WyZXgWqkQi8jfA3wFfQNWHXo6K9rzfGHMyWedtwJtFpMGGwZkD/MaEm/kZ4MdE5KPGmOYzq6ky6cTglcB3b54UABhjPiEiPw6899lUwmKxWCwWi8Vi+TLks8B3oi7FIXAK+Angv21a523oROAnUN+w+4FXG2NWJtzGvwX2AGdE5LOow/JmjDHmqtKnm5l0YrDC1S9R9IDVCcuxWCwWi8VisVieXzzDKwbGmDcDb36adQzwC8nfM2EGOJm8TwHVZ1jOxBODXwR+TkQeMMYsjr4UkXnUjvmZ7ojFYrFYLBaLxbK1eW5E3ybCGHPP9SrrqhMDEbn8yeZtwEkReRB9yGE7Ko10Afga9DkEi8VisVgsFovly4rrrEr0JUNEBH0u+IIxJrzW3z/VFYPLL0M8zoZdcwnoo09Sg17C2BKIUW3bMJdo9J9JqYb7+RymBIUTHlFGtXTX74jwF1ULP93Q1xBhuCugTZrckkNQhriWQcoDjAtRMaJf8ZAYwlJEWDYUH/UI81A4IzihS+lsyOoRj2EOOgvqL7D6kgh/2cPrQvvOPoWH1JSutaAaz/2lAu5AfRG8WoqwHBLlYpyaavCHvvohTB136FWFTE11kFdvdxjODiEUMjUhf96QraXG+tpeALGnOuErL4/Z8QmHfkXIL6m3wLCk5Yx0/Id5ob0nS65maO512HF/QDDlceFOlygf45x02P3BARcPq9a+eHD+K11Kp2D9ZkNueUN7vLBoqB9Wre3p9ZDgrEd3h0vhixGDgjPWEHfOq3dAYdEQ+YLf0HavPKbrdauqbVw+6hBMQeVYTGveoXjG0JlTDel0E3Z8dkBQ9siuDmkupHFC1SZ2Qt1XrwNuf0MzWyKNFS8k2V8hWxPKT1xuPnjjWDvg4/UNrd1CmNF69qq6fyNt5u7Nqnfdn1F989Jp9TVwB5Ba1vWMx1jFuLio/TH9pHoXSKTa0iO/glRX18vUY5yhYerxLq19eYZ51YDuVoXCeUNxKUz0qYWwqrFqPNUzn3rAp5Nok+XPG1JdoV+B5gGH3KKOtx0PhES+R1BWLelB2VA+KmOd+O33OQRTQmcXTJ/QvgW4cGtE9qzH9BMxsa+67G5gGBQcBiVh21H1e4h8/Ss/2qE7p+MrmPIwrup3D0sa526gWuOprrYBqFZ7blnHY3tetdWHOVh6hY5Z0DpPn1APkTDn4jdUa3ztoDtep1+BVEdoLUDxjPpIjPajfHxAc2+a4rmRjj/q0REYgpLQr6hmuRMaYoTiUkjsCcGUisdJBBcP+zih6sk397iqhb5nQ9t7/YDwXGA8bZ9eVXX8R/kHND4HJfWfkAgu3iZEuZjcktCrumTqWm+/ASsvTjP9RJxo46tfxsi3wng6XruzkFlV3X2vy9izozsLpgzOADp7Y9r7wV8VUi31V8ldiMmuDgmmfCJ0/BTPaH/6dejsUO+Mzqy2YWZ1w+fAbxoGHdWAd/s67sIkp0QZEj8OmDqpv+/OCoVFjSWvo+M3zMHUQylWXh1Q+aRPrwq5c87GuFlSr5bckkOmpl44g5K2X5jROmVrWqfiGfUjWN+nfgBe35BqxwTTDvkV9fZINXW/neS0IHchpnGLQ/XzOl78dWjc4uAGWj+/ARJ5eIEeN0Z5uj0vhL76QnSrQqrL2LPDX4vZdmxAez5Fe17HYnuXtuPazXqc6c5qbMSJt4H6J6gOvTtQDXt57lIuYQ4qD3jEniHdNGRWHPLn1dOmuVdYu1l9CEa5YvoJ9Q7qVbXNOru034MpjQG/TuIb4+AFkDuhbRHmDammxsvMwzGRrx4ckQ8SaU73+upHMvL6GJQgU4f67XpGOn1MMK7QuC0CXMrHDf56TP2Qy477A2q3+eM+z5/X4++Oz0T46yHNhTT9suaY1SMupdMOxdN9wmKK3jaXyBdqL3SZvU/70wl1/BXOq85/5Gv/tXdteLb4iW/B2k0OxXN63PI66pM08jWJPfVZyNSF2BOoaQzUDwvFM9p+s58J6exw8QLIXoxp73RpzeuxqnRa26p+WL1HRl4NzT3q4TIoOFy8TWOtX9F997rqydDb5tCZ0/OiXkWoPLbhd9Orqs9Se94dj4HTX59n6qTmqy++IgsfvSxYtvjEQEReg97Fcwd6fv9i4EEReS/wUWPMH0xSzlUnBtfzsoTFYrFYLBaLxWK5/ojItwP/A/hfwLuB39m0+ATwPcBEE4MbbvEqIjeJyG+LyOdFJBKRj1xhndMiYi77W77RdbVYLBaLxWKx/DPnah4GW+cqwk8BbzfGfAf/dALwBeDwpAVN7HwsIkXgG4Gbgczly40xb5qwqBcArwHuA9JPsd4fcql+6zO2d7ZYLBaLxWKxWJ4pW/wZgwXgQ1dZ1kcfAZiIiSYGInIA+ASQA/JADagkv28A68CkE4O/NMb8eVLun3H15xPOG2Pum7BMi8VisVgsFovlS8PWnhicA14EfPgKy+4Cnpi0oElvJXonarawAxD0P/5Z4HVAG5jINAHAGBNPuq7FYrFYLBaLxfJcI+bKf1uE9wFvEZHXoefnoAJFr0L/cT+xEfGkE4O7UYe2IPmcNsZExpg/BH4F+PVJN3gNfLeIDERkXUT+TEQWvgTbsFgsFovFYrFYns/8MvA/gd8D6sl3nwT+Fni/MeZdkxY06TMGGaBpjIlFpA7s3LTsKPDCSTc4IX+OPoOwCNyKyi99XERuM8asX76yiLweeD1AqlC+zlWxWL50bI7ddN7GruX5wyV5t2Rj1/L84JK4Ldq4tVwDW+fqwD8hcU5+g4j8KvAq9Db9OvBhY8yJaylLtKynWUnkM8BvGGP+p4h8CG2ebwAi4HeBu40xB69pL9h4xsAY89VPs94R4CHgR4wxv/ZU62Z27TYH/8O99KuqlZtqqe50cVE1nLM11SrP1FRruDtviNMGt+sQZ2JS685Yq7y/PyC15DOcCcHTdvIXU2M933RDtwHqB+B1VTs4zKgG+Zl/ayg+ksJJdOONq7rmI/1ciVRLfVCE/LJq5460kZ1keWsBwmKMv6o66yPNZ6+zoQGdaqm2cuQLrd2Jl0GiBRz6Iy8D1VE3KYf6QW+sLzwoJm0cQeXxkNAXejMuxSUVvz7zr4XiCXe8vnFV37q5R/0Bdnz8IusvKNOvOJTOhizf7RHmDXv/ok93zh9rsAPkV1R/uLNDy+9Pa+M54UjXXcivRHR2uJQf69Gd8+lXHIY51X7e/aEWnfkcYdahMysUF2OGeaFXlbH+eKahmvCprurQp7qqv+yvG2IPYm/DZ2GYU/8CgG5V2HZsQOOWNLkLMff98Y88YIy561ri+dmS37bb3Pwt95Kp6912wZTDoKh1lAhKp7o0bs0RlITeLGx7RNvNCXUfSmcG9GZS1A87ZFZ1n1u7hdJpQ355wMpd/jg+/XXVdG/vSuMGBmdocCJo71SN6tjTWAYoLA6Jsi7BlPoMlI8PGBbcsUdEph4n3gLQmRXaN4d4DQ+/AdmaGetIt+eFbE21puO06s0PixrvsKFHn+oY+mUhymgdgpLQ2Rvjdhy87oanQ5zWvp0+of4XbqD1DUqi+uErERePaIwFMzHbP62eCaMxWzxjaC3IWAs/qKgGeVDRMUd5gLuUUc310oYW/ahdYEN/PVsbEpQ92nMOYR52frzH6gv1aq4T6u87CxGphksu0VdLdXRMjeJwNP4v159vHjAYz5A7p7rehfMx3e3OuO1B/RiCkuBE8PC77r3hsZud3W0OfNu9hHkoH1ed98jXZSON8O6s6tdnVyO6O9yxj8pwKiZOG/JnNPaKZzQnSqS5K0zKMa6uH3vaT6mu9vGwoFrl2dpGTuvujnH6Gi/l4zFrNznqQ+ND+bhqmvcTf5D8ec0N/bKQbmnecCLtszAHuWX1TCgfV/+UKKOxl25A7Cf6/H3GfiAjvX4nNDQOQ/kYdOZUP76waMisRSze45JqyrjsyIdBJSZ/eiNfOpF6LUikYyRKQ7ql7ecFZuxxIREMSkJ7Xn83LEcUT7jjtnMiyCQeBKM83tyvx43S6ZFev4Pf2PCfcCLdh+xqxPo+l/ITEWv7XGJf43j7fc44n46PgTkdvyOfknQD+lWN43RD+xIg3TTjcTh9QuN+mIMvvOPGx21mfre5/Wt+mPUDwnAqJnfOGe8DwOx96tkzihUAJ9C+7iXnGIVFzXGZuuY2r6PnFVExIrOkfhKjdq/fGVJ+yCP09bsg8ffoVtXTwLh6LtCZ1c8jf510U9uxtQDGM6QbiedRR2Ow8lhEe6dLbiUizOrYUw8OQ3vOwW8a3EDzxCh+etvcsSdMqmNItzWX+LUexnVYP5gjtzxkWHDHuv9eV/0wIl/oVjfGi3GhsxAz/ahziZdApm6IfIh8jc/iGY310tkItxfRq+r51MjvI9PQ40T18xv705txCcqMvQhSXY3LYcFR36V52PnJkOYej9yKnpt4AeP9Gh1HU90ND5RR27gBiX8R+Ot6HPPXYvKLXdYOFfjs771xHJPZHbvNTd967xXj6Og7b3zsfimZ9FaiP0YNEwDeDLwEaAIt9PmCt17/qm1gjDkKHEedli0Wi8VisVgslhuCPMXfVkBEflBE3naVZb8kIt8/aVkT3UpkjPnVTe/vS/6D/7XoAw4fTk7cbwRb+EKOxWKxWCwWi8Vyw/lPwDuusuwE8KPAb05S0MQ+BpsxxpzjGp5wfrYkE5FbgN++Udu0WCwWi8VisViArf6v6QWuLkn6JLB30oKe0cTg2SAiOVTuFGAXUBKRf598/gBwDyqD+lfAF4FDwE8DZ9HnGSwWi8VisVgslhvGFpImvRIN9B/oH7nCslvQ2/8n4oZPDIDtwJ9e9t3o8z7UpGE78GvANHAR+BvgJ40xE++YxWKxWCwWi8VyXdjaE4O/BH5WRD5pjHlk9GVyx81bULXPibjhEwNjzGme/nmNV92AqlgsFovFYrFYLE/P1p4Y/ATwMuBzIvI54Dwwh7ohHwV+fNKCJlUlslgsFovFYrFYLFsMY0wdeDHwBuAkKg70/7P37lGSXPd93+fWreqqfk/3vHcG+8DuAuBq8QYfIkXTkixRUqTonESS4zws+w/7RDlyFMuWLTuRLNvJkXKiKMe2JFuyHMWOj6RIjh0dUqIjiqQkhyBFgAAILHeBXSywj5mdR890z/Sjuut588evp2e53F0OgQWwxN7POX12uqu76tate2/13er6fi4CPwK83xjTOei6DnTFQCn108CvGWOu3WTZIvBXjDH/4KAbfStRKQwXJINZRRC0JY+6t+zgdSVzt3lW8t+7xw1BS+FEe1nMDlETdo8r/A7UPl2g9VRO8YpLoSu544PF/VxpJ5VM/80nNDNfkvzc3n2KvAC9Iy7BZcn31SHEs1BswdZTOc0XJJd38NgI0/MorkoQ9F4GMuznpldWIPX352/BluRZBx3JTq5elvL0Fx2SmpSrdjkmqrs0zkd0HvDxBgYdGXaPF+g8nOG3wAtln+uvSx5wGigG8xp/J8cdGQbzmqimWPrDjKRi8MYZx+G8pv2QZuZMSu4qhkfquCNDaSNDJTlzz2XkGtrfVKR+MaZ2PiQ8LLKEuCL5ytXVlOG0pvHSLuHhKv1DmtyVbONcw8wLPXrHyjiJoXIto9CJyQLNxvurTL2W4mQ5xZcyrn6nR2lFTXLwQY5JsW2orMYADGc8ilsJScWV/P6O5M17A4M7gkI/ZzjtMPV6hpMZps9GZIF+y9vp7egt72dpl9YhDRTewBAuBngDg5NCUlMkZTV2csixjGoS+F5elazowaJi7oWU9kmXzC8wdWEcuo9D5is2H/MJOpLlnBadsUtCctiLLcl1DzqGtQ8VKHQkU9vfNWyfKgCSw52U1Tj/2iGccyi1DKWWZrAoed8AM2fETeEOoL8s7brYGufFp9JnjSsZ7dXVlMG8Rsfy3EllO/6L+76GwaJkXjOQY900MdHdAAAgAElEQVQ9qpg+k7FzUk/WlWhpq7VLhqiuKK07hGNHSPdkTuOMI64EX/K2vXDfK1LogdEO4UJAoSM+iKihSEvyXpUxcWbkgdR9f7mAP/aa6JG0/9Km+AYKXYM3gNyVdhUuyHHdfsxg/IziFZe+LxdRG69IRrjXzxnOaOIqTL8IoBg2ZX/7iw7FtrgtessyZqkH+pQ/XSF/J34cCmBkTKIDOyecST5+VHfYfcAwXDSULzk4qWH7tKayYth90KAHDsU1h/KaoXtUjvdwVsbtvVx3J9v3kGSBwhv/oLS0kbH1qJYx5bL4K/yuwQsVM88pdCTegbXvzCifd3DH/ovNj6RUznocejqlt+TKcY/EnbHXvwCcVKFa0g8rK5L1X+hK++gdkfz4Qlf6izfYd8eECzJuRyVFcU3a/PSZjGhKxvGr3+FQurqfAV9sidumdNXBCyVPfeeEgzuAueek70h5ZNmeZ6Z/SNM4HxHVXZKynvg9nFiR1CCsGSqXFVEDRjOSQT9YVMQNQ+2i5L/3lxWZrybnndolgzvM2T6tx94HTdAx7BwTlw3A7PMZw1ln0va9wXgc6Il/ojh2BCUlyMo5pYsOoxlwx/6OcFaOoRdKhnxegLT8zv1XbPeootCB8qqDO5J+FbSlj1/+XpfZZw1upAgX5P2FiY9B2saooSZjW2ldjsHC0znhvHTG3IXhrPTv5hddjBZn0GB+zw8EaZlJnWw9DsU1cXaEyLprV8QjEbSg0BNPUuor+ksav2VYf59GRzBqiltm6oLk/4ezMk55AzNxnziZ+Cd0dJ3bp5MAkBU1w8USweaI4nZG58ECOhq7ltbEt7A3PhXG50knk7F++VOG/iFonpNt+7s5W4+If8kbGA49nbF1Wr5LDeY1/q6cwwBmv5QxnJbzUmXF0Dmhqb+esfmknngyVKrGYzNsPqnxx2NE/aI4GVQG7ffoyfmmd0ThxNJGS+vgjgxuqAja4hJRSU73aIHqVXH79Jal//WXNE5WIg1u+GGLuevvMcAYM0JCet5UUM9Brxj8PWD5FssOjZdbLBaLxWKxWCzvPswtHncZSilXKVW68XHQzx90YqC49e4vI3dDWywWi8VisVgs7zqUufnjbkApVVNK/aJS6howQgTENz4OxC0vPCulfhj44fFTA/xTpdSNqUAB8DDwBwcvvsVisVgsFovF8g3EXTIJuAW/Anwv8GvAWSB+oyu63S9SQyQqFOSKwS7QvuE9MfAJ4JffaAEsFovFYrFYLBbLG+ajwF83xvzam13RLScGxpjfYewXUEr9OvAPjTGvvdkNWiwWi8VisVgs30jcLT8bugUDYOVOrOhA9xgYY/6ynRRYLBaLxWKxWO45bnXj8d0zWfhfgf9GKfWmNQQHDrdTSj0F/CfIzcbBjcuNMT/0ZgtjsVgsFovFYrHcddw9k4CbsQQ8CryilPoMsHPDcmOM+dsHWdFBPQY/AvwSsAVc4E3c1PCWoyFogY4haBs232+ovOYQN6DQgdGsZPjvPphTvuRgtGQIO6nk9KpMUWpJLnPnQUVpVbLdnVTyfqdelYzpXMv6d45pps4boinJwu8fkjzdzIep11LiikNveX8CN/d5h2FTMpBrHy/QX3SorOUkZcX8MzHdowXckUFHkqEbV6HxaoaTGnpLLpXVDK+fMZz1CNqgI0Ptckx/qUDtSo6/m5JUXNzIMFgoULsiZUjKitqVlNoVAMlQbrwUkpVcwKWymjKc8caZ4ZLtP/fckLhRoHpphPEcVJIDBSrXIPUV/m7KznGfqYsRSUWa0mBeU7sUUyg6ZEVN/1iVtOjgDnMqV0foUUpaLVDchp1TdYKdjJkXBmQld7x+yZAvbiUMFgq4w5ws0BR2IhqvQNRwx3n7mvv+IMbJDP5ql7RRItjxyV1FsDmarM/vpPSXCvi7+eQYVK4MSaoeAMG1HsGmzHPjpk+hLbng7wR5AVJRERDXJDs98yVvvHpZ0T2qqV6VXP7aJcPmt8WUz/kktbF3YNyuMl9yo0Gx8aRLaV0y3ntH9CQbvjTOFC9vZMQVh/6yIq6J/8PrynuCjmS7Vy+LM2OnoQi25HPFtmQ/165k5K7kUXsDw+5xyQTfy/TPfEVUF3/FJHN6VuGODMWtHCeDzgmN35F8/8wXx0Q83qfBoqLYMvg7+ST/3onGud4nNbvHpXw7JyXPvtSBwRKT7Gx/N6d7VE+y7+MaTL+g8HcyvIFD49WcwbymuJXRX9Ik40A3J4OFL0g/6R5V1C9K9nX7pEs4q6i/nk22Of/FlM3HXHYfMBz5RMz2KTmIUV3Gid3jks1dbEmWdlSXvl1adXBDec/eNjsPOhRbkAay7kJP+nhv2aHQY+L76B7WONm+f6F0tsz2w3yF0+PtxMn3/RKSp6/oHpc89vp5RVJSuJHUBUDviKL5ojgLRrOG3JW88WALRjNy7Hr3yXv1CKK6on/EMPdMTlSXcXv3mPhPVCZtR2UQLkPtIuKpOSqfL77mETUgXBJ/RfWqS+8+2HzMFZ9GWWG05L1n4/43nFXULkkOe/WyjP2FsQcnC+QcA7LdYEvW0V8WV8fMi+KvcMd598aF7dPi1OgvK8qXpFx77XTUkHNMuSX10F90aJ7LSIsO/UMaHck4UNqQ415qGXbud8dOEZ9cM8l6z31Dcc1huJjj7TpEDWkTgyU5/01dyNg+Le3cDSEtSRlKGxm5p+gedXAiPcmV337MMPenCi+UOgDoL3uMGoq0DKOFjPJlTVqCmS9lxFU5Jv7A0L1fUb4k7dsb+x7SkoxP7kDObXlBvCtx9YbM+LcJlUnZ0rI87x1RBC0m3wvcnkPrqZzyZfFA1C7ljJoOSUn8KjNfGhE3Cuwc09QvynhpNAxnNN7A0HlQ1udE0L8/p7w29s8suWT+vq/IH/tSevcp6ucVuw8YGmelzuMq4vrxYeaMOIC6h2WczLW01erlsUujleBkhs3HfKZflnN/f9GZ+AK8gWE47UzG6+J2jh5mRI0954K4XfqHyuNziByv8rph1FQ0XpU2mLvifMhdGeO9gThL5Bwky7YeEe+HjuT8M1h09502I8Oo6Yy3Cd3DeuJbimqKqAmrx8HrgHENxjWozCFckDZUXIfeAxnV85rcVXiDfOKz6ZzQZOP/uk6q4jgpb4gHorxmMBq6h13CBWl7pfWEcMEjXJBxPfcU6+/Tk3PkNxA/AOTI9/rvuMlyA9y5iQHwN4H/HfivjTHpAT9jsVgsFovFYrF8Q6O4u+8xMMYcu1PrOujEYA74TTspsFgsFovFYrHcc9zFE4M7yUFvUvgE8P63siAWi8VisVgsFsvdiDLmpo+7BaXU/Uqpf6qUekkptTr+95eVUvd/Peu5neDs1HVPfwn4VaWUB3ySr76pAWPM2a9nwxaLxWKxWCwWy13P3ZVA9FUopZ4EPoNYjz8ObADzwH8K/BdKqW81xjx3kHXd7qdEZ/jKalDA3wN++sbyjN+nD1R6i8VisVgsFovFcqf4eeB54LuNMeHei0qpEvD74+XfdpAV3W5i8K1vpoQWi8VisVgsFsu7gbv55mPgfcAPXT8pADDGhEqpnwf+r4Ou6Hbm4z9+4+WzWCwWi8VisVjeJbzBiYFS6geB/wp4EqgDrwA/b4z5zRve91eAvwXcB3wZ+FvGmE8dcDNDYPoWy5rIT4wOxJs2pN1tODFETcmX3nlAMXVOMq+bZ3OMhtpr0Hk4o3xp7Dbo7ecI9+5TNC+kDBYky7e0LrnFcy+kkqt9RDJ7lz89oHkhZdRU+F1pKaOGYueYZE47qaGyKvnwuStehOa5TPLl+znTZ2MKXTPJ4+4vOowaio33FihvZABMXYwwWhwGuYbhtMZJDf5uih5lxDXJtfZ3clSSU78Q4kYGlUgucepLnnJccfA7Kf6O5LUX2hFxxaG4ndM/XATA303JAk3lypC44pAGCn8np3c0IKo77J4IyALN7omA2tk2xTXZVq4V5Y1ssk3jOcx/ao3ixW3K66K6KK+EVK6OqJ7fQY9SjHZwezFuL6F+oY/bS8g9eW00U8BJcrKSiw5Tiq0Er5/h9RIGyyWMJ/nIlZVEXAk7EV57SLRUQ2W51EvFwRklJBWX/n0BWVFTvTRCDzOqrw/Iipqs5OK3QvxWiEpzdG+E7o3wW0NUllN5vffONF4FzQsppZZh8fMR/WXFqAkLX8gwWvLcvX5O0JY2N/MnBYaLOSqD/jIMlzJGM+LXyHxF1BAXgjsyOBksfjamftFQWpf+UV43tE+6bD3ioFJp741XcmpXMkobGUlZUV3JyXxFsSV531lBsvMHi7L+zgnN5hMaJ5W86syHpCY54CqD3hHoPCiOBKOhvyz58MXtjOGMpnNC3AoAtUuSyy3uAnBSgxrnoLmRYfrM2JlQkwz7uCZZ7Jmv8DswfSbDHRnqFw31izGtpwzdw5IvHjdguABBW7K606LDzgOSV200rP45yRTfcwPENVj9sEvuioMgrilyV1FsG8Jlw/oHHYotcRP0llyqVw0zz0N/qYCTws57csIF8aboSPbbSQ3DpqKymhG0Dc2XM3QEpZZhuDB2LJzJyF2pKycV70H7lIOOpW6Hs4rNJzV+15AVoNDdP1PVXnvnPAZpiUlGeFoaOyvOS/690eK90JEh96X9OTF0TkHUkM/v5fCXNsU3sntc2sDw/oTRLPQ/GFLoKHZOSDZ/6osfoH5R9n8vk7+4psQt0M5xB9KmgzbMPp8zdU58GuGseEDMOP+/vJGhI8l0j8bHGaB9ShwGTmqIGpK3rmPph2lZjpvXlTIPlmSfdQxbjzgEbYM3kIcz9hl0j0o79buGYls+Gy6IF6F5LpvkxhsNW49qNt9vSH1p34WuIak4pGXYelz2NaorRjPj+i9LHcw8L+WcOutQvSzrCxdg6rzsbzgvroW0DDNnMtxQ+uj6ByXvvrJiyH1oPapJyorGGYdRU9E5nYsLYkHOdeLXYJwjLy6HjfdpvFDes/0INM8aKms5Xih1lZakfSY1Q6En/SwtG8KFt6GB3gI9AjeStpv7UodJTcZGHUkG/tQ5h1LLMPt8TPuUw3BWPjNqKDafKLJ1WvY7KYsLo7Iidd16yhC0JG/fjcRbsntckfrQvZ/JfocL4jDYPa4mbbJ+XtFfVhM/B8hYvnO/i46kLw2b8t1i/tmI8ni8bj1e4NqHfKorOd3DLk4iZdFj98uwqdDR3voStk5r1j5UYOObIZwb+0HGrpGJv0mLl8RJ5ftEVhiPoYH0lcpqxmBR4e/mNM9lbD+sGDYVjVcMbrjft5c/PSAN5LtV+5S4DyrX9tt9eUP+LrUMlRVwYnFAlFYU9VfEC+IOIA9yBkdz6uc0wwWpv/UPyfmjvyQOg/KanAeO/e6AoJ2LJyGUfUrK0p/qF+W72upHCvK97Iy4Q9qn9v0LN6LMzR8H4MeBPvDXgf8YuRfgN5RSf22ybqX+M+CfAf8K+G5kYvBxpdTpAzbn3wN+Tin1LV9RZnn+s8DHDrieAwvOcm49VzJAF/gS8I+NMf/uoBu3WCwWi8VisVjuet74T4m+zxizdd3zTyulDiEThn8yfu3vA//SGPMPAZRSfww8Dvwk8F8eYBs/Dvwu8MdKqRZy8/Hc+PE08DcOWtiDegx+fPzoIrOO1nhj3wdUgX8BfBj4N0qpHzbG/OuDFsBisVgsFovFYnk3csOkYI/nge8HiRkFHgB+7LrP5Eqp37n+ta+xjW3gW5RS3wW8F1gE1oA/Ncb8wddT3oNODA4BnzXG/IUbXv9JpdRvAQ1jzJ9TSv0r5PdRdmJgsVgsFovFYvnG5+A/GzooHwT2Yv4fGv/78g3vOQc0lVKzxpjWQVZqjPn3wL9/MwU76D0Gfxn49Vss+3XkpgqQu55PvpkCWSwWi8VisVgsdxXmFo+vE6XUtyNXC35p/NL4bquvcoR1blh+43qmlVL/t1Lqo7fZ1kfH75k7aPkOOjFw2Z/R3Mh7rltPzNdx57PFYrFYLBaLxXI3o7jtzcczSqlnr3v81VuuR6mjwG8Av2uM+T9uWHzjNEPd4vU9/jvgfuB2PxX6A+AYb8E9Br8F/KxSymX/HoNZZMbzD9i/mvAEX30pxGKxWCwWi8VieTeyZYx56mu9SSnVBD4BXOErbyjeuzIwBexe9/rU+N8bryTs8UPALxhjbnndwhhjlFK/giQi/e2vVUY4+MTgx5CrAf8j8L9c93oE/HPgJ8bP/xQ4aOaqxWKxWCwWi8Vy93Pr799fk7GB+ONAAfiPjDGD6xbv/Yf6Q8Dl615/CGjf5v6CI+zfp3A7zgFHD1rWA00MjDEx8GNKqb8PPAwsAOvAS8aY9nXv+6ODbthisVgsFovFYvlG4I3efDz+tc3vIPfgfsgYs3n9cmPMa0qp88APAv/v+DPO+PknbrPqIVA7QBEq4/ceiINeMQBgPAm4q43IuSdSkqQkEpfKtYzWo5reskOhJxIN9/MO3aMiv0lK8rmp1RR3pGmfdEXIspHhRkaEX76ishrj9V383ZStx8pUromkKNjJ6B52Ka8bKlfl9or+fYHIaAKRQM2cESmZk0Hl+VX6jy9R6OeU11NUkjOaKZB7arIPOjL0lwo0vzxkNFPA6++XJam4tB/SFFuG0tqIuOkzmikAIoFykpy06pFUHJFhbcXEjQKltRHllZzBconiVkKuFcFmwmguoNCJySsuziihvB6Ta4XxHEBkX0mzSBZoZv94neHx6bEcbEgWSPPRoxTjOeheBMMR0XsO4bWH+KsJaaOEk+TkpQJGi3zMeBq3F5E0ixQ2+sTzFRhB7dlVhg8toEfZRDqm0pzt981QvxCKmKwXE0/5IjMb/6vDFJVkFDb66DAgrfoUOjHBZk7uye0vWVGjL/apdEekDTnoTndINl1BJRlOd4juDjC1MqND1bensd6ASmHjSZfSOmyf8pn/YkpvSY43iLTl2p9VzP0pDJsi25p5TrH9iKHQUVRW5H3do9KWvC5ENZFMAQxnPYyGUVOERP1lhROJ4A9EZNNfdBguQHFdREydBx1UJu8ptQxRfV9+A1DsjEVFgch4mmcNpfWEqOGSlBW110TslZQVaQkOfTYiCzSjKT0R30y9LmK6PTlaaV2kUjqCmZdiwgWP3pKLk8qoXFqH3QcMc88YRk0p33AW4qpGxyIL2j5VYPlTGa1HISsokbPNyvb83Zz1D8Hss1LuuArNFzTljYxCJ6b9TUWKLZh6NWfUdHBGsr+r36ooX1LMPG/YeUCRuzK+XP0oNF6SnUl9kXlNv6DGgiCDk4qMykllWfs9mkIXMl/aZn9ZMXXeENUUu8c0QUf23WiRwzXPGvrLimLLACKIC+cckUnNqrGQTVG5ljGY129V87wtbl9EXCqD4aKUs7wm7SUrSPniGtTPi9TMHUCxJUKnQlcEfZUVQ/eoQ3lVpEWDJSif90hL0Px/AnLXMGqqiWQvrMk2Z17MaZ9yKK6PZVXrsp5CV+qfFHZOOCTjbj3/hYxoyqHYEkHcyrcrCh3FYFGTliANIS9IO/MGhsyHYkuO4+5x2cfaJWkD1cuGzfcqahflXBK0DVOvZVz7oEv1MhNh00ArskAkdcWtnGhKjl9Sk369+aRm5sWcmRd6XPtwldI6NM/CzgmYPhuz8d4CeUHEcMY15K4i10zqSmUiHzRa6nY4C0lV+mrQ2pdvRTVF/fWM/pKmf0gzdSHD300ZLBToL8v7nEjae64hGBiGs4rS6liC2JHtBR1D8+WcnWNSZ3okErXhrBq3bUVSlnafa+mToBjOioQtnBXhYOWyuqlI6u3CuOPxsC11lZbAb4tErn5ejqkXSv1uPVygvCptyt/J8fqZnFeGGUlFE4773qih6D+Q4nZceo9FVF7yCReg0IFqy7D1VE5xVRO0RcTXX3QmY3ZlReqwsmLwuiJQLW7nbJ3WVK7lgDP5LuN3pW22HvZFcDcAJxKJXPeogxtCNOXQeDVj55hm55im2BbhWWU1o/OgyBiLLYi7jsjrZhR+W47/Xv+R/ill2nlAUehIvdSuyHea7mFNec2wdVqjRyJazHwZW4O2wR3mOBlsPlXGG5ixoFPGx+G0SGC9gcg2YV+GeOzfRmy8t4iOpZ/u1VH9FUdkia60udxVZL5D7hrimsgC06KDO8xZ+bYyzXMZzliUmbtqIozz+jnDGRFg7n1fMlokd24ocsmvbCy8GY/BLwPfg/z6pqmU+sB1y543xkTAzwD/Wil1Cfgs8MPIROI/v816n0OEab/3Nbb//eP3HohbTgyUUt8D/H/GmO7479tijPn9g27UYrFYLBaLxWL5RkHlb/ij3zn+9x/dZNkx4JIx5jeVUhXkPoCfQszH32uMOXOb9f4S8NtKqaeNMf/ypmVW6i8iyaJ//qCFvd0Vg48DHwC+MP5bpnk3xwAH+q8qpdQJ5J6EDwCngf9gjPmzN7xHAX8H+BFgBngG+G+NMS8cZBsWi8VisVgsFss7jTHm6AHf98+R+3YPut5/q5T6R8CvK6V+FPEXXEG+kx8GPgo8Bfxvxph/d9D13m5icAyxpu39faf4JuSSyueRmzBuxk8iM6afQG7K+HHgD5VSp40x63ewLBaLxWKxWCwWy+25s4KzO4Ix5m8opf4IiS79m4A/XhQhP0n6fmPMx7+edd5yYmCMuXyzv+8AHzPG/C6AUurfIFcEJiilAmRi8LPGmF8cv/Y54BLwo8D/cAfLYrFYLBaLxWKx3JY7bD6+YxhjPgZ8bHyT8/T45W1jTPpG1ndQwRlKKV8p9SNKqX+hlPoDpdTJ8et/Xin1noOuxxjztX6l9UHkLuvfvu4zA8Sf8N0H3Y7FYrFYLBaLxfKmMUhc6c0edwnGmNQYszF+vKFJARxwYqCUegA4D/wskoX67cBedMuHkfsB7hQPARlw4YbXz3Fr+7LFYrFYLBaLxfKWcBvz8buKg14x+MfIDQ1HkZsZrr8J+Y+Bb7mDZWoAfWNMdsPrHaCklPqq+xKUUn91T0WdhYMbF1ssdy3Xt910aNuu5RuHr2i7kW27lm8M7Jhrsdyeg04MPoz85n+Hr779YgNYvKOluvktHupWy4wxv2qMecoY85QblOneL3nW7kCyx5f+aIiOYepiRP+QRmVQv2ioXUmpXcmYPhszmNf4uzm1KxlBOyctOgynNX4nJdiKUUlOeSVkOOPR/PKQNFDUXgsZTWlqV1IqV0fEjQJbjxYJdjK8fs7UxYj5ZyPcnngDcg0b33WYqO5MMtmN5xBsxbgjg99JyTUU+jnF7QzjOfi7KUlFS457YojqDlMXMppn+iRVDz3KSCoOTgYqySXrvzWk8dIuwVZMuOijhxm555BWC5RXQvxLbfyWeAFKV3pkgabySpukWUQluZTpWp9gK8YZJqgkp3SxQ7w0RfHiNkmzCIDbiyi+vE7vWBn/wga6NyI9MofXHuJ0hxhXmpfKcpwwxu2EGE+TBS554OH2Yoyn0WGKXtkin64RXOvhtUOyaoBKc7JaQPO5NnHTx1/tEk/5OJmRbV/cxklynFFCWvXFj9AJcZIctxfhbnbRoxSvHVJ5flUaS5KieyOc7e5XOAzwXNKlaeL5Cn4rvMPN+dZc33Z1pUz9oiFcgLgG2w+5eANDZUWypJOyonbBkdz71zNyV/K1SyuKoC0Z+qkPQVuyqadez3Aj6B0Zb0tLrnjzXEZck5zqpAa1SzleKLnYbiQeEJDt+Z19z0E4K1n87fcnzL2QUmyN86p9WXdpHAuw8m0Festy7ItbGToCJ5Vs6OGMx/r7XOKa5FiXWobhtDgMnBQar+REDclBHzUV4YJHGiiqqymZr8h8iKsQtBSjpkP9Yow3MEy9mlNqGbyB5FsnNca+D8kqVxnocV10jzrULji0Tyna708wY99AGijCRR9vYKhdiuktOyQlya43GpY+Y/C7Bic1LP1JRFyFzSc0jZc09YsxpY2MYlu2n/mK3hH57O5xcTgMm4rBohyrrCDZ4EZL9nhSFi9FWpbP7jyg6DyoqF4WB0ChK+vKCkzqVkeGpCaZ4pVrGd3DmsHS29Z0v3LcLZbJXWkHC0/nzJxJScpS3vK6meSiJyVpb0lNjoWOJIt96kJGf1kxeiyk/WSKO4BoNiNqSHb/1iMOcU3h7xp0LFn6mT/O6y8rFr6Q4ncNuw/mdI9KO/HGGfwgOfteT3L/d05qBouKxvmIuKaYOueQ1HPSEmTlnOFSRmld2nVSVgxnFZmvCGfFN1FZMahMXCCjhqJ+fryNGAYLiu5hl8qKbH/UlGNcfz2jvCZjfjTl0DuiSH3Jtu+ckj639YhD68kq9XHfzl1F9aph9SMFapcM9YuG6lVDoe0QN6StRA1xKoDUs8qkTwVt2dfyqrxeWc2Iago3gqTiUFnNGI69Hmsf8EnKCjeUvgUyhjiZ5PnvuSaiJnQ+PKKyYugdUWyd1uN2KH1sz4vid2D6TEZSEn+B3xXfSHnNULskOfqDoznVy+J9yPx9n9Db3W5VrUz1qiH1mThd0jIU12TMKbUMcVWOK4gDxUlh95hm+1SBtW/WbLy3QFp0yF3xxhgX3I5L7TWof9HHuPvel60/E1M/J+6HuCbeGKPH4/V5Q+bLuNhfVlTWcvydnDRQzJwRF0HmQ6Enxx2kjbmRuDDcaPy9Z2Rwx6ewUUO+dziZ+AGiuiKqK8J5ze6TEbkL3fvFPeK3pU+pTNbbPiVj0Nbjex4PQ/OsjLNGi79g8wmNNxBPTXnNUF3J8QZm8ij0c8J5eV/jlZjeEekPpc2c/rIiKUu9Zr7CGbfdpKzwd3LCRZ/qSj5pI3uOjkJ3vL2NjNxV+LvSlqKa9Jf+kmawoBjOaBY/H7FzUr7zFbcy3JGUy0kNw5n99gtSRyB1WVm98f+l9xrPLR7vMg4qOBsBxVssWwJ27kxxALkyUFVK6RuuGkwBoTEmuYPbslgsFovFYrFYboni3fmzoZtx0CsGnwT+rqGzlksAACAASURBVFKqft1rRinlA38NuJNys5cRJ8KJG15/aLzMYrFYLBaLxWJ5e7jVjcd30c3Hd4qDTgx+ApgFXgX+T+TiyU8DLwGHgP/+DpbpaaAL/ODeC0qpEvB9wCfu4HYsFovFYrFYLBbLmAP9lMgYc1Up9SgiGvt24CJyX8HvAL9gjNk+6AbHX/K/Z/x0CagppX5g/Pz3jTGhUurngJ9SSnXYF5w5wD856HYsFovFYrFYLJY7wb3yU6KD3mOAMaaD2Ih/6k1ucw6ZUFzP3vNjiMjs55CJwN9BZA3PAt9hjNl4k9u2WCwWi8VisVi+PuzE4K3BGHOJr4w7vdl7DPA/jR8Wi8VisVgsFss7xj1/xUAp9Qxfx/zIGPO+O1Iii8VisVgsFovlbsEA+b0xM7jdzcdfvuFxFngKWL/Jsi+/tcU8OEbB4ucydCT5yfd9Mqd3NGDu2QGDhQIqk6ze2mshccWh8noPJzM0zoXkGnJPUbkyJNjJaLy0i5MZskATNwoMF0skZYUepRS3EpKqR6Gf0z4p86u44rD4mW30KMONDLlW6DAlrXoE13r4uynuyFC9NKJ0sQNAYaM/KXtW1Pi7KXqUUWhHeO0huVZUXu8x/6k1ySLezvB3U8nfzwxee8j0Jy6gh+I96C8VSKsF0qqP1w4p9HO8XoIepfgXNsgCl+HxaVSSkWtFNFsiuNYjL4pXoLDZp/T8VfLAw2uHGNehsLoD3T5uL8IUC7i9GN0VF8DwoQWcxJAuTaOGsTgLhgl4LqotAfh6vYPqDsiLHirJ8Noh7mYXnnsZlWS4nRCKAWnVF3dBNSD3HIzrkAUuKs0JrvUZHq5TvLKLv9oV9wCgeyOi2RJOkqOSbN+dkGSYYgGjHdQwlvqdroi7IM3JFhrobal7UyyQNkq4HXE87K377caJJbO+2JJc6+pKzmBB8tNTX/Kb05JkbUv2v8Id5hTbks08mpUMbpAc6qjuUOiaiV8gdyU7G2D+mZjchYXPx4RzDjqSAW/UlEz8UsuQa8nLnvnSECeVfOukBJWzHtsPuRgNaUmys1N/vN1+zvKnY4KOIXcV7fdIprSODHPPDiR/enU/t3zYlJz/UUPRPSq51jNnUgpdQ1aQ7P7yRkZvyd3fRihOhMq1jHDBo3tULkAWt8WZoMcOE5DtFMe52/WLhtnncyorhrgm+3P/b+TMPytB1uGcQ2/ZIQ0UUcOluiKZ3ZP60+JaKPRzOg/4BB3D8qeGFLqG1uPiXRwsyr6oTLLpG68YknrO7PMxbgSzz8foyBA1ZZ0qk/oD6N2nmP1SRve45NG7IZOs+dqVlOZZI66GUOo9qincAcw9N6T1qCYrwNxzt8jffotRqdRNeV3ywa990EVHUtZsfNymLmR4IbRPOfgdSA+PGM4qekcUOyc1bgjBCyX8dZcsgPo5zfRL4qhwQzmWe21YR1BZEXdGUlZsPOmSlBWFtkP1quHIx3bE2fFyxu5xhY4ln3zPcwGwfcpn1BSXwtRZGTeaLyqCdS3tpm1ISvvZ7qWWIa4potrYWxBJf4urcpyCtiELxvWRSV8O2obuUUV/STNqiM+iv6wItiQ33e8aZp6H2qWY3DeMmhDOayqrGa33GsJZRfOsob8sDozBohIHz0Xxkey5TKpX5T1OahgsSBa+NzBEDfGPDGc0zrj/poGS89yKYeN9mvKa7KeTiovBjaROwgWYflH2c689ls4EbL0/ww1lm07G5JzqdyD3xQkSzmsar2ZEdXGfxDXp66OmlG3+c3Isd48rosZ+H3i7URlsPWGYel36TXlN+nupZegtuZOcfeNC0DGTz6RliBuyz0Fb6tgbGHJf1lFelfr3dw1+R8aBUsvQfNpHRzDzYk7uynrK64bhLBP3RvNcht+Rdr19WrP2EUP/kJ7k7DupuDR0BE4i7XnU2P8RxvYjMj6kJSn3zkk9Kbe/K+eQURNm/qRAoQtBCyqXx2PouvgC2o+IO6d+0TD3jIzlvWWH1uMOSVlNvDeldTmGlWsZ248ZwjmHcOwOCWcVhU4szpwOrH2oQHlVxrmdEw7uAHrHxVuz55lJynKua79Hj50O0qa9gWH+i+mkD5Y284nXIZxzKG/IOcvfFY9CoSd10XnAnzgYoinp44MFRfuUI/6FEnSPyjkoqouLQkfSL3r33faHLe9qbnnFwBjzl65/rpRygb8I/Iwx5rm3uFwWi8VisVgsFsvdwb1xweDrusfgHqkSi8VisVgsFotln3v+HgOLxWKxWCwWi8XCu1JmdjPsxMBisVgsFovFYrkN98oVg4Oaj6/nHqkai8VisVgsFovl3uF2caUtbj4J+JRSKr3xRWPM3J0smMVisVgsFovF8o5juGf+W/x2PyX6Je6ZarBYLBaLxWKxWL4aBah7/R4DY8zPvI3luGM4qeQ07+Wuj6Y0pfWErCS567VLMcZzyEoulStD+seqpEWHYEcTbMW4vYidU3Vqr4WEh6sABJsjild2SRslgk3YeH+Vyqq4CoprIaUrGduP1ylu54wOVTGeg9tLcJKcfPz38Eid4uVdmhughjF5rYjbizGexmuHeO2QvCQOAgBnlDA6VCF31bg8HpXnV4mPzqJH4jHwV7vEcxWyx4/it0KclU0KJ5bo3l/CHeaMZgrUzrbJagFOGEOpKG6D7gBTK1O8uE10tEleKpAFLsZzSKsFdENC5lWaixfAc0nn5sg9ByfJcV9dJV+eI2+IA6E4jCFJMLUyThiTFz3ywMMperivrsJ0g7zoYTyNXtkies8hCht9sg+eRq/uAOISKKzuQJLghkOyhQZ5qUDhUot8uoaz0cEHjDv2EnR75MtzONtdCqXCpLxpo4S7ug2eJ86Fy5tkyzM4YYzzyhVUuYRp1qQ+PBdnowOuxvG0fHaz+/Y32j0cCBcki37zCU3nNFRek7zs0vo4F7ormeC5K3+nRYfSesJw1mPuixm5J3nMgwUlLoFgP0e8d9ww8xwMZzT9Jcm2Xv1IgeZZyYYOF2Q7/UOa4az87XcN4aLPcBamz2SkRYe4tp/v7HckV7u/rMi74KQOaVFypdsnXcprhsyXMmw9VqZ73DD3TA44+Ls5vWWH5lnD7nFF7ZJh2FQMZ2VYql3K2TnhsPmEptCB2hXpcwBuL6F3NCCclXX3Fx1KLfE65J4CpH5GY19A0DF4/ZxwXk9cDoeeTtl4ykeN8/eL2xmdExp/N6e/6FBsi08gaOdEdYfuYamzYdPFC+UY7J4I6C9L2XePaYot2V+QeqleGpG7AbvHC+jIsP6BAsUWNM8ayQMfyL+4kofeP6RxB+B1JUff383pHtbEFQcjm2c4K56L4azkjG+8t8jC52N2jxcYzOu3to3eBm9gJmUMWpKtXl3J2fhmmP+cYfu0ZnQkoXzeI65B7QsB4YLk48c1cCJxdDiRtPmoIXWyc0LcBNuPgHEVQVu8GSqT95TXDEFbtltZzUkqDtc+MoUbSX3WLxp2HlA0z0pGeXlNMtPjmqJ61dC7T03y3HNXjmVlNab1sAgYKiuGUUPamY4MtSsZqx+WNup3JPu//no2aXepL66NuAZJSXHfJwfsniwxbEqf7C8rKqsZ/SVN7iqiGuw8UKC4hvgt2tJHZ58xOKm0xT33gtHiQXAi2D2mMVpy2IO2uCS6Rx1ql3KKWwlR3aV2OWWwUKB9SlG9zMRNMlhypI2tg7+TE9U0o6bUpY5krAlakjlfu2QYNcWZUWoZoobL4P6U0WMx6nKJ6uXrHCcrBneYkxadSf58aT0hdz16R8TBAEzGhLiZU734Rn7RfGfQiTgV2g9pnEjcCpkvef9RXdE/Ijn+e2XOfEVUVyx8Pmb7VAE3kjFbZRA3FIWOuEzKazKmVVakT0R1hb+7tx5p03v12j0qdZy7Ut9Ga4otcEZIW1xx2HlAxoyoriYuG4D+ssbvwNyzA9Y+KBKboCX+jvZD4qjYekI8HbvHpf5VCsaXdlRaH7tZulKWaOxmcEYOUQMKXfF2OJm06cJr0gZHTXAHMs6V1pFxcwu6J3MWPgvuyODvwJWPFglach7xQkU29jzsfT/LAnGaRA0YLubMfw78XfEz7JzUqBS8UDw47kjRX1bMPh+z9XCBpCbjX+6K12c4q6isyL97Y787AJUpjJb2qcb7UX89I5pyxt4N0COpe3cgY0P1shzXryJ/y5vkXcE71yMtFovFYrFYLBbLXYNNJbJYLBaLxWKxWG7DPf9TIovFYrFYLBaL5Z7H3nxssVgsFovFYrFYwFjBmcVisVgsFovFYrGCM4vFYrFYLBaLxXIPYa8YWCwWi8VisVgst+Me+SnRu+6KgcqguJXg9XPcYU6wk2E8h8FCgcpqTNRwSX1FFmicUQJA5eoIvzXEeA7h4Sr1C312T5YoroVUnr6IynL6DzbJSi6551C7kgHjHPOTFZzukPqrI4prIYWdCD3KcHsRAFmgyQKN20smZcym5TN6u08eeGTVYLLMv9TG7cWkVR+/NaR8cYfGl9qM5gKyhYbsY5IRz1fIagF6lIrDoDuEYoC72aXxpTbV8zvUzkq4t+6OyKoB4XFxA2QLDeL5CiQJ/moXox28dojbi/EvbJCVXNxOiFnbRG1sk9UCcs+hsLpDUvXEH7DRwRklqO4Auj3io7OoYSyPJMO9vInxNEw3oNsHwGiHfL6Bf+7axN9AkoDnTuogXZoGz5u83+z2cLa75POy78bT4LlQDHCGCfl0Db3ewQlj4rkK7uo2piZ5zvF8hXy+gV7ZQnUH5A8exjRrqHaXvFTArG2SzzeIj87ibHcn7SGvFe98wzwAKoUjv9dj55hm7rmM6RcUw7FbIFyApCb57eIOkKxtd5hjPIf+spLs8MTgjgzTL6cMFiU3unYlpXYpp3TVIZyV7Gl/VzLGZ17M2T2uSEpQ6Mj6h7OSn+2kksm/8c3jzPgpB3eYU78Y01+W9w1nJd+78Yph9vkYb2DYflix/ZBLUpNseyXdhbgGc88YukcdwgXJXC+1JOfbaMkQL7YNTgRTFzI236uYejUn2IJw2ZBUHLYfchlNacJFH6+fU16XXO5i25D54nXoLTs0Xs1IxxnVlZVEfAEVh1FTylG9ati538WJJNcaJAtbx5Kh7Ur3xUkNhX6OkxpyH9KyZHJnvuzbYFHhj7PLAaKaYvaLPbLxtq98tEjtckxcY/JelcFgQVHeyIhrUve1KxlxDbrHJZc7bkiudq4haI9dB0gdTZ+RCtWRrCepwe7xArUrKe7onTlxZUXJ+O8eFTeD3zWUWoZR02H2GUVv2cEdQONZ6dvD+xNGM5CVc5xU2njuyzqaF1KcWDLx26cko799SlG7qBjcn1LoGoptQ1yVvrB7XE1cGl4/I5xVhO8P0WPnhY5g+iVxQgAMZxXBTkZpIyOqK/RI3gOSMZ8Gis3HxGHQvJDipDBclGOQu4qNJ12mXzJMv2SorEgm+/ZpTTjnUF4zVNZyvIEhrsmxfvUvFAlnFV4obcAdwNajGieVbHU3gubZnMarclxHTenvTip9xWjJY3dS8Vf4HXAyGQ/2+lZpIyPomImjYzjjTbwb3aOK5lkZF9KytCGvC4WeeAl2TmqKbUPtkvT3UVPaWtzY22ZC0JbjGc4qyYLfcgleKDH9kkFHhupqihdKP46mpMyDeU1/WbH1cIHMV1QvS/sYNhW9+xSjJsw+Iz6D3QffmYD43IVR05l4AbyBjIu9ZcnxL66JF2bnhLgk9rwpUcPFyaT+S+vjYxLvrzecVeMxVDwoTirHobiVoce+jv6yIq5Jrj9I25h6NccdiFdg+xFZz3BWTVwROpI2qiNDKk0Ufzfn6nfIOU/H4n9pPyR+g6iuWPqMrH9v3Ok/HE3W5Q3MuHwGf9dQv2hIS+JMWPxcRuVaRrFtJv3DHRkKXUP1qhm7CaCymlFdyaldMix8Vpwy/UOa7dOaoCWf2z0u56LKasZgUY19DTBzJmOwBM2XM078xoCtRxw6D8rX0kIXZl6KxUfVkLGw2DJsvLdA0DETJ4aTyjaaL2dsPS4eFG9gKK/JuWVvTDSu9BtvYAjHbVOl+/XvpHvjsHgTgq0bGosBld/88W7DXjGwWCwWi8VisVhuh71iYLFYLBaLxWKxWO4V7BUDi8VisVgsFovldtwbFwzsxMBisVgsFovFYrkd94r52P6UyGKxWCwWi8ViuR3G3PxxAJRSJ5RSv6KU+pJSKlNK/dFN3qOUUn9XKXVVKTVUSv2JUuqxO70bXws7MbBYLBaLxWKxWG6FAfJbPA7GNwHfA5wfP27GTwI/BfzPwPcBfeAPlVILb7TYbwQ7MbBYLBaLxWKxWN46PmaMuc8Y84PAl29cqJQKkInBzxpjftEY84fADyJTkh99Owv6rpwYdB7wCbZiKq/3ABhNaUZNRVR38TspwVZM6ivCw1VKayPcXsTuyQo6TCldkc9Mf2ELox2iR44wXBSnQWGjj/EcimshtWdXCTZHTJ3dJZ2roUcpWeCSBS46lGBdZ5SgRxl+KyRc9InnK8TzFYyWat/Ly0+q4jLQ2336p+fQ3RGFV9fJApfRoSp5qUBxLUR3R6RVj/BwFRCfAUAeSDZ4dHKedK5G0iyNPQUpbHcgSVFZTuliB90dYbRDYaM/8SK4m12yaiD7e3Ief7Ur7oH7FjDz0+jtPoXNPnguwbUextPk8w1UkmFqZbJji7L8un3C1ejuCLp9hqeXSJpF3M44ML4YYDyN6g5Il6bJi95kmbu6TTpXQyUZzighefT+yb46w0TcBUWP4UMLGNcRrwFMvAj5dG3iRPBfvCxlbNbIFhoY7aDSXBwIr1xBzTRxhgmFc1ehVMTZ6JDO1XCG+86Jt5O0CFe/o4rRkqUe1RTTL8llSndcdWlZMs79jrxn95hm8zGXhc8Nqb0WsnNSk5QVw2nJSZ96LSWuSDa0Gudu75zKGTYlHzucc6isGLJAMshjaRJsPwJJWZH6MPOcorxm6B1RRFMOUcMlGOepl9eMOBbKiqjh0nnQobgubgB3AOGcw3BW8sJVCr1lyXr3O7KdwaIiDRTlVeicgq0nxBewc1JTP69wR5LNHrQUuQvldUNck5z1/pLGSQ3VlZyoLq91jyrSMnROaCpr8l856x+QHHWVQfNcRmkditsZi5/ZpnZFfAe7xxX9Zcko33pUM/PCAB0ZorqDHmWUNzLKa4b7PtnDGxgqq5J3XehKLrYbStncCLYeq4o3oazw29BfKlBZkZz4vRzy8rqsu3Itw40ks775ckaho5j7YsbUecnhTouSCQ9yvDNfsX1aXmi+nFFeNyx/aoiODCrJaby0+za01JuQS375nmMh85Vk9w/GPoxA2oSODKNZw9LvOZTWofmiuB2CtuyvjmD9fS61S5Inv/CFjNyFpf+QMpyFmT/VFPo5xW3JTo+rksnfPuXgd6D1eAHjwqHf8vF3crrHJXt/1FS0HtXsnJD2t3O/S/ewJtdI+2lAZS0n13I8p19OcSPYud8lDRTTL8JgSR7eOPM+rqlJH/E70D9i8HdyessO3aPi9hjNQuOMQ1Jj4iOovy51tOcwKG1kJGVF+yFN4xXJiG+8kpOUFZUVWYcz9hWoTD63lzlfvWqkn81Lf2+8Yia57V4Iq3/Gp3rVMGoqth+RMjjpXt59TObL2KIy6QPewMg+hlBeFZfE1sMFukcV3aMKv2tovGLw2+ID2XlA2uTGk3K7Yhooycfv5wwWFQufj0nL4jvZ83gYDXokdTFYUFSuZdz3yXcmDF5l0Dgvuf7iQpH9CTqSgT/zUkzviJR197iMMakPa9+dkBUgrsrzqAFBW7wQha707zRQ+Lv52JNgmP9iyu4xPfYQSL0XW1Ivw6ai2JLxcc8X4XXFfbHnWBgsiPNkL7/fC2UdUd1h4fMxpZahdiXDSQzFlng+nBQ2n9DiZGjJ/s78SYG0tO8JCeccukcdkrL4QIotQ+8+xdo3azonNPULIcNZ2c/c3XfOZL5iOCvjZVSX80s45+CF0jYar+Q4mfSrhS9k9I7nbJ/WzJzJcFJZR/ewZuZLGd3DmivfVaXxirT9nZNa2npFS3uJZbz3d3KCthyL3eOKqK4YLMq4nWuoXFZU1uR8kLuK6kpO7z45bpUVOZcMm+KPqF0Sx05UV0RNGU+HM5rUF/fN1GvpV7YVDMrc/HEQjDFfq5F/EKgBv33dZwbAx4DvPtBG7hDvyomBxWKxWCwWi8Vyx3gT9xgcgIeADLhww+vnxsveNmwqkcVisVgsFovFcjtuPQmYUUo9e93zXzXG/OrXufYG0DfGZDe83gFKSqmCMSa+yefuOHflxEAp9ZeAX7/Joh8xxvyzt7k4FovFYrFYLJZ7lb2bj2/OljHmqTu0lRtRt1n2lnBXTgyu49uA4XXPX3unCmKxWCwWi8VisbwFdICqUkrfcNVgCgiNMW/bzY93+8TgGWNM/50uhMVisVgsFovl3uUtFpy9DGjgBPDKda8/NF72tmFvPrZYLBaLxWKxWG7HW3vz8dNAF4koBUApVUJ8Bp+4Uxs5CHf7FYOLSqlp4CLwC8aYX3mnC2SxWCwWi8ViuZd4c5OA8Zf87xk/XQJqSqkfGD//ffP/t3f3QXLkd33H37/unu55np3ZndVKWq1WD3cnDvnOZ84PZ4pAFSbEuCokQAIkJHE54OSPFARDnEBIcaGSFKSKp8AflIsUpKgQp3hICDjGgF12Liac7Tv7zirdo04raXXa1czO7M5zz3T3L398Zx9O1vP5tLPa76tqS9p56PlN97e7p7d7vh9re8aYnwf+jTGmiZwl+AjyB/xfu/tx37lJPTC4gqS/fQE5tfKDwG8YY7LW2l++9sHGmA8DHwbwM1P3cpxKvSk7a9crlXd5NErdvp21mypo7aq94Q2fF3Jat+qemQV+75rbNn8/BiwBP48cCPwUMA18CfgOa+3qPRojAMa+tddMfd0YY/478D6gerOgiMzcEfsNf+sjZOox+fNtknSKOOuRavS3w7A2A8ZSDl47pPm2EtmVEUGth7N8FabLDGfz+K+u0HvsCNlzTfoLJTIXN4iLaZzekI1vlA2K30kwowQntlvBZpvTtimHVKNP55gEqcVZD689xOkNqb+rwvSXN3DWWpDNEB4u4vYi3PaAUSW7NR1nlNBZyFB8uYUZxSRZH7c1IC6miQo+iWskdO3CBsMDefzVjoR49fqQzZBkUphRjGl1SaaLMs3xawJYz8E0WhI6lvEx/SGkPKJyFhMnxGkPrx3Ke0qnSFIO/tUOSSaF0+rDaARRDMX89mvtnF6UkGRSb3huXEzjrjShP4DpMqw1CR85itce4q40SaaLMu3xOOKsR/DKKqRSMBoRz5WJ03JM67VDRpWM3B/F4LmQzWA9R+bVcl3GmEljizmppSiBVgdbKWJTLs5ai3iuLIFsvT5EMX96+dee+Tp1Gbht2eoR++j7/jmJJ+EtxSVL4kG/asjULM2HJcDFHQdideYlACnVtRIs05WAniiAoGW3AmgOPBOReIZhfvvKQa+f0Dks60PsQ1iBqJAw/RXD2tstflMCa/LL8rrTz8vzugcNg6qlfBaC9UQCz4oG68o0SucsiSevm25IGNvMc7GE02xYUp2EjWMuuRUJAPMGEqYzcyamc8jFDeX53kACgkZZKF6M2TjmYj0JxZn9SsRgSoJvTAz5SwN6BwM6Bx2SQILUNpVfjamfdpn9isyDxIXslQGD2TS1R11K52QcmXpM/VGXwgVLv2rwepC/HJOkpCGE30loH/aIA8heTfA7CWunvHG4mkNYhkHVkq4Z4kDmmxvCoCLhO6OshB/1K4ZszZJejxnmHQYVh9K5Ia1FX5bLwJJZi1l5l0e6Du0TCUHNIcpKmFHiS/DUsCAhSun1mPppDyeU8Du/Bc//p4/c89rNHDhiH3/vjxGWHKK0oXt4+750XeZla8HdCuoKy3Do8yGjvMfKuyScyxlC4ZKVELSKQxTIeyouSa0DW4Fy/YoEGXkDS/eAyygLlVci2oc9wvFnPfe9TTrnS2SuOGRqsp9rHzX4TZmuO2ArjGlzuu0jhsoLUm9RTsLo0jUJv2ofkaC/UU7qqHgxJpxycCIJTQpact9gRt7LzmVl4vFrFaB3JKH6RYPfSVg/JnU8qEL1ywmJJ2FsgxmonE2oP+KQrkEyDpdKfFmf1k67uCFMvRJLGFQkr1G8KDXbfEiCC8OiIdOw1N9hKb3kMKjI+3aHEgjlxDCYgcKF7flTuCDroBNJDXfnDH5bgq1GWQn96synJChtvKxA/u+GEvxmYln3MzVoH5X5kG7Ia3TmDcUlWW9yqzFX3+Fy8PNDPvepf3XP6zZfPmIXf/gjhBUoXJD3mOrKtidTj+kdcMmuyjytP+JQOifz1AvlcWHJ0DlqyS4bql8NWT8RyPa4KvWaBJCpybbYb0nYnzOy9A64lF+Wx/fmJPAMpBa9ngRHprqW1Sdg6qwjIYGBYeOhhAP/D1qLDokn64uJ4eq7LfOfttRPu4wKMr3cZWgdl3/DsqxHa4/AoacSmiddsrXt/YsTShDZ+kmpZ78F+ddl2+l1Zdu1GWzWmTeUzlm6cxIg1jkoAX7V52L60w6DsgSzjbKQbsq4BxV5/cbDsv/aDFtzou3tvRvKfswNJUhw5rkYL7QMpiTIcnP7nqlZcqsxjQc8vPF888frXus4FF+T6W5KPNmPRDnZJ7WPyjzeXH+ijEOvaujPQWZF9p2ZNfmI+X//57/YqslS5qB94uSHrltHnzrzH+557b6V9tJ3DH4fqACLuzwOpZRSSim1nyQ3+LnPTOqlRDezN05xKKWUUkqp+8Jb3JVoYuylA4PvBerAhd0eiFJKKaWU2kf0wGD3GGP+APni8fPIl4+/f/zzozf7foFSSimllFLq7kzkgQES7vAh4AgSB30W+IfW2t/Z1VEppZRSSqn9xQKJnjHYNdbanwZ+erfHoZRSSiml9ruva5jZcHArxQAAH7NJREFURJvIAwOllFJKKaUmxj45MNhL7Upvi4khU5e+w72FAr2DaeK0y+BQnqjg4/SG9A6mGVYCbMph/eESpVd6AITVLL13HYdRJPd9y1HcQSwZA4N4q08/QOF8l6nn1jCjhFR7hNceSt//rEeScogKqa0x5c+3t/4fpz1MlFB+oYdNuQwXq4SHiwRLDUaFFEnWx7+8jh1Pw2v2mHpujVElQ1xIA9BfKBEVpO95UOsR1PryvNWOPKbXl8yCkTR0N40WyXSRwaE8Tn8kA1lrYq9cxayuMTw5R1LMMDhUIJ7OS7ZBnOD0hvivruCsSYaC2x7gX+1gPWc7wyA1fp+9Pk5LsiI2p2dW1yT3oT/Cu9rCX6oxnM3L47MZ+o8tyjw5dpBUo4/bGhAdnt6ax7I8E7z2kM5jh7eeB+AOIvylGk6rT/DKqmQU7MgqsCkXd60juQfHDmKLOUyrKxkLmy6twEtL0B+M8w4ieT/F/N0X4JtgLKyflJ7KpXPS1znVtRSX5Gs1h55KcCLphR4WDeWXEvpVQ2/WIfalH3XiSU/0Uc6QbiQETbj8LZ70es8ZRjnDsGgIpxwSFzpHLXEasitw6LOW+uMJ+dccZp+NCZrQeMRSell6cvcr4/7+F2Q64ZRD4hk6xxNGRekLvf6g9D9PNyDdSJh62VJ/1CXKypg2jkn/7GFRHterGvwW0n87y9b7az4keQCd45K3EOW28wkaD3iMcob2EUOvahiWfdrzDlEOnFD6++dWLNMvRvSnHSovxPSnXa484bL+gEv97TkSF4KmZCA4kSWccqicTcisyTw78HSb3gGX9rxDe95h/bgnPcgjaDzs0HjAY+arQ1qLDqOs9B8/9FSC35JtUL8q86h4MaZ4MSJbs1u/O5GlfdijtehQvBhRe8ynX4VgIyHYkHyE2WdjEld6mPstyYcoXLKUzsmOaWcP8NwVua1wyZK4975uQfrh1x516VcMjfeGTL1s8XqQakmffJAsACeCKAvllxLitEtYclj8ky65y9LbvPmQISw59KvSA94dSN2YCIpLyVbWgBdCe96hteASbCQ4MQzzkuWxKfk/ZekBH0pdhUVDug5T52OsK738R1npiz7KSh/+ygvS17x/0DJ9JsaJpK95v2LwurI+JC705i1rp13iQJYzyDg3+9GnG/LeR1lZVsOy9PVPNy3H/jBkUDH0px2mzsdka5bMyriuHjakurKc2/MO2RWYPjtk5kzEoaf6VM7K+mBdGXd/xiW/bPHbMn83jrn0Zh2KS9KL3QsleyR7yZH18dVEMhxCGBVlvpTOSU5EHJit/u7eYDtzIMpBvyp9+60H9bf5BOsJhaUBcSDbHBMz7lcvOSqt47JN6c1B5aws9ziQnIDcFelJH2wkXH2HS+4ybJzw72m9btWID4XlhNlnYlJdy7AoyzHVtbQWXOnbf1jm6aG/jAjWZVvcr0JrUTIMMlcMTgxX3x6Qqcd05yRjI39FHhsHhvzrMZnaiOyVkHDKwW9ZOod9vIGl+lyM35L5EjRkPQYISw5TZ2X70pk3NB8fUXrJkfyHKxa/BVHaUHunJXvZYZiX2+c/M6RyNpEcgZos4/JLCY2HDX7TUHvUJd2UTINU12IiWS4r3yz5BUFznFdwSPJFevNWlmvajPdHsv1ON2WbNn12SHHJUntUHp9uyr6rdD5m44RkGKQbkp2TXZH5Xjo3JCzL2AB6VUPiyfqTW42pnJW8m/XjHn5H5mPQshz4UkhYNKwf9whadpydYdk4IVk6858ZYl2ZX2HR0HxY6i5/JaG4JPO1+Jqsm5vbzc3MicyKvNf88ojGKdk2fQ1rr/9zn7nvDgyUUkoppZRSd04vJVJKKaWUUupG9MvHSimllFJKKfny8f7olq8HBkoppZRSSt3Mffh9guvR7xgopZRSSiml9IyBUkoppZRSN6TfMVBKKaWUUkoBeinRXuXE8hMHhtaCNPVOPOmRK3kGBYKNiO4Bl7WHA/xOQut4FoCw7MnjpvN47SHFl1t47SFhSY6fRpUMZhSTZCUPIS6miTOu5CJMBfQPZnF7Ee4gIqj1cXsRa4+V6C0Utvrx25RDeLgIQHc+i9cOCS636J+YJix7NE7naT06i9ceEtT6DGfz9BdKeO0hg9k01nVIv96mc9inc9jHWWsRpz2681naD04xKqSI58o4/RFJMYPT6hMdncWmXNKvd6DVkV7902Xa334KpsukGj2ctRZBrYfTG8p87A3pHy3ReecCrcclQ8D0hzCKMFFCPJ2HVAqb8SEj+QrxdB5n+Sr+C5dw1lqQShGnPaznEC5WoD8gTm/mC0SkX28TF9NEBR8zkrwIEyfbWQOjCLc1ACB9dUBSzBAeLuL0hkQFn2S6SDydp39qjlFFlmGS9cc5FC7RbBGKBZzeUKaZShEdnYVRRDw/Q/fbTuFMlbAHpgm/4ZC8l9GIuJi+B5X6tawBrwteKD2yBxUHb2C36nezT3thOSFoWcKSQ+JJr3CAQdUSZaUv+bAIzsgSluW+sCw91a0rPcfDoiHVg5kvS694N4TWgkv5qy7TZ4esH5PsgZlnDZl6TJQ2jKRsSXUt+csxwXrCsAALn5L+1Jma9IIOi9LLPCxtZzKYCPyWJdXbzlgY5Yz0P/dh6tWEwnKCiaF0Pia/LD2uZ5+WHtPV52IGVXn9/hx0x7EW1oXGKZdBVR7vxDL9OIDVb/IYlA2jvEOUNtJPPZR+9a0Fl6nXIjpH0rihjDkODPXTLk5kefmDWem/3ZQe8cGGLIdhEXKXIdWTfu6VF2PyVxJK5yz107K9ydQgv2wZFmSMrQWPVEd68AcbEYln8AaST7F+3CNTs3hduPpOQ+eQy/SLEVHaMHU+Jg7kvToRpDoJbmjJ1GOClqU361A/Lb3Wk0ByJpLgXlTq10p8GBUtSQCVvwzozpmt/A1nCP0Zl7Aky73yYkziGfrTLoWlAfW358itSr7D7DOSYVI6Z8ldkTyKjQctZhxt0qtKv/JhEawny0V64ltqjzlbmQeZmjx3s4d54sl6lW5Yugek9/+wCNmalT7/Ncv6SYdwyuHquy3Fc7L/SNdh44Tcn7+ScOTPEwZVmP2iJVOTfu9+y5Ktybq38aAd5wJITkLQsgQtKzXTkjq7+o4M02fD8TKN6Fdk+oULlvwytI8awpKhezRh6rWI+tt8hnmHlScyDCqSWTL3hYhBWeocZJ3sVwx+W2qlVzWsH3NlXS/LOtWed+jNSjZCHMg83sx9yC9LP/igCen1mH5F8hlmzkSYWHq+u6Esk9mvhAQbEe3F9HZWx9KQKGArR2P6qxYnsqR2xMZsjtHEbNVv7vL2fbvBGtledA679KqG/LIluypZBJVXIoINS/ZqslU3a6ddgpYluyLbpNkvyvbYDcEfxxXlVra32Zu98psnXVqLPsOyT355ROmVDiD1s7ldH+UMpfMxqU7CoCyZAdaVbVqmBoWvbmcjbWZnOJElt+RQXEroVaV3/8p7fFqLDkkg2ym/JZkYhQuSkbCZJVA8Z6g95lBYTsjWLNUvGcLNvI2GpTcnuQbZZUO6IWMZVBw2Tkh2xWZmR2vRJ/Fkfpjx9rdfNfQOuJTOSaZNqisZG24IxSVL/W0+fout/dfmfsEbWNaPSeZOnJbXqD3qMqg4OBGsPh5QvBgT+zLN9QcNmbWEVEumc+mvyzzKrsi+Yfp5xhkahvylAdlV2ZBYF9pHJFcHoPJKxKAq73XlPT79gwm17wivUzD7I8dAzxgopZRSSil1Q/fnQcD13HdnDJRSSimllFJ3Ts8YKKWUUkopdSMWSDTHQCmllFJKKbVPLiXSAwOllFJKKaVuRg8MlFJKKaWU2u/svskx0C8fK6WUUkoppe6/MwZRGqK0IdVJyKxZokB6g2dXY1oL8nbzl2PcEHKrkmcwyhlGOZ/casww73D1AwWcofQOdiJLsC5fOOkc9kmOVgjWE0b5PKmO3J7qxNiUQ3/aobWQI92wpNdj2oc9MnXpm9s+liMODG4o/YpT3RRxYFh7rIQbSg/f4tKQ7JWY5qkMkCXYiAgut7CeQ1yQ3vqD2TROJaD81Q2ctRaNbzlCej0mXR/ijBLc9oDuiSkyQP9glihdJH+xT1jN4LVHDI4tkFvuMZwKKH7pMp3HDpO92Gb4wAFSjT7NRyuk16XPOEiP5fylAcMDeeK0ZCGE1SxxxiU6lsMZWbzQEtT6bDyQx556gPzlIW4vYjCbJn11wOBQAX89pPeu40SBYfToLF5o8Rshw0pA4hnMSHIIooJP+NgRAPrTLpk1GUuqE8m8bvRpPzhFbrlH68EimfqIVHtEnPVYf/wA2Ssh0WKFsOSRpAzxA1myKyMyUSI5CaOE/olpqYMzV7GVIv2jJbIv1iRr4UCeVKP/1hfqddjxYfqgAumG9J9eP+ZiXcb9yS1O3xJlpO91WDK4A+kxPigbymdhlJOezV5XesdnV2BYkJ7qAOvfkBDU5YWClqXxsCFdk175Uy9L7/HmQz5ODKmmZB60Flw6xxOylx0GM+BEhnDKoTNvSLVgMOVSvBhx9e0exSWL30noHnDxBhYnkn7RfgsGFcNgBipnE3qz0pc6Gb+3OJB1trXo4PVcBjOM+8EbnFDW6cyK9LtON6T/dfZqQnveoXs0Jn/OJbdi6c5J1kDiG5whFJblMdaDYMmSach7inJSX+0jMq+SQKaZbkC/aiBISDdcwqKsB63jhtxl6ffeq27nBVx5wqVwAcovhziRT3ZlxMp7fExsKC5JXoIbQv3RcU/5UiDv24MoawiakFlLAIfpPxuxccJnMCVZClHaEPtw7I+6XH08R5R2GWVl7MUlO56G5LRMvRLTO+AS3duS3Wbh0FMJrQUZu/UMjYcdKmcT4kB64gcbVmpzIH91i9KG5qmM9I0/4JKpxzix9Bh3IkuCoTtnKJ+1BOsxo7xDumkZIJka2RWpLXcg08pdlqyOdFOm73cSMrWY1Xf6ZGpQOjektegTlmX+5a5I9kPhkmyT3cE4o+M1Wb9MLDkBQUNyRbyuYVh2mHk+ISw5mFjqJg4kn6C4lJBfNnTmpd5TXbtVP6keZBoyrl7VcOH9Pn7T0D0YkHgw6hmcSO7PXZZ5MPu0ofGAh/Wg8bDD7LMyn3IrlsYDHummZDBEWVlHihdj1h9wGRZh8U+kZgAOPxUxzDtka5bsygh3IPuYzb7xo5xhlJX1MLcay3a3YQk2JGdD+s0berPSz74/k8IZSX1uqj3mU1ySZZ140J0b56R8dUhvLsXMV7qsvS2HF273qw82LPnLQ/ozKZoP7c7fKE0Cg7Ih3bRb+7z+jIs7lO1DqpMQTkk+RuxvZ1FMnY+3tnGJJ/Nt/ZhL+IBL9cuSV7QpSsuyigNDWHKg5DDKu1t5LtkrIVEhRb/ika4PaS+mKb8q0091JT9ic53pTzuERclYqJ/2GBYl16NedfB6klOQBJKfMMoZ/JZsQxNP9gGjnGTMZMefbdxQsgxSbam5TA3SDdk+p+vQr0q2TnfOEFZkXaiclW1qryrzIUobmg85JJ7LsCB1NBxn3rihvI6JoXs0ofRZ2X+lm7JvANmmdg8a0g35fTOL5tBTfc5/T8DMs4YobWgtGjI16B2Q5ZN4ss43Tm3mVbG1D9z5yXZYhGHR0D2YIQ7kfabrMj8SV/aD68c98suyz21UpQ6yZ67JM7JgrX75WCmllFJKKbVPLiXSAwOllFJKKaVuZp98+Vi/Y6CUUkoppZTSMwZKKaWUUkrdkLUacKaUUkoppZRi31xKpAcGSimllFJK3YTVMwZKKaWUUkrtd1bPGOxZDqR+eIUTxTrfVXmeXhLQiPI8mrlAzgx5xIdmEvLnvUVO+VfoWp//vfF2vrXwAu/LtAlMCoBP9NJ8U1DnUhRwNS7wgeyAL4YjnhksciS1xvP9Beb9Bn/W+EYeL15g3l/j6c5Jjqev8s2ZV6m6Mb+1/g6e3VigmOoz7fcIzIisO+SJ3Ct0k4C/6pzk7bkL1KIiH19+nEHk0Rum6PYsBw+u8kqtSiVv2eilgJjhMCRu+RDEmFaR1EEP12mz2g5YONyk1spTysbU1kOmiiHrLenvm5rZYGW9yGjgUSi2mCqtMxgFZDMh3f4qfWC9Z2m3Mth2Atl4e372PK4WDIVij8EwRSEbkfPr1Ft55svrtMM0U5kuR/MNnq0dodVLUyqv82j5dV7YOMCljSkGQ8tokCKd7ZGcKTIqJSRTEX7OMuzGeCsBSTrAOmCLI4wbYYcuEOEXQwBGA4+Th9fYCNNcfckAOXl8zgF8cBOIY8ADN8G0DEHdIZxJsJ7L3DHLynkPZ2hIfIuJDDY3Q2aqz/C8i/Peg3g9GJatTO/Ze1eym6wLo6L07x9UDOsPSv/pwgUINrZ7/w8q0qc/XZc+/YOKg9+Wvs7phsW60ou/c1wyC6wLoQdxLmHqBYdhEfoHEzo4FC5IH/bZZ2P60w7p9QRvYOlPOySeYVg0DKpQ/ZJhlAMz7j3dmTfSozqWvuyDisfMGckBkV720D0o/dWnXpUxRoH0wK4/4uCG0od+6nxMa8ElLBuc0CVoynw4+Pkh9bf5ZGrSC74975BbkYyE/rRDFEjvbBND4WWXVA/WHzRkV6SPdrAh7yMsSf/2YCORLIQ1yTMpXNrunZ3qSs/vftVgIvBbEDydojcnOQFROaJ0RjaVcbC9vJxQsh/cEFpHfZxI+rlXn4tx+zGd+RTBhvQ5n31W/tLUWnCJAulrP/WaZD9YV3IgRnmX0jnp++51LMO8w+xXQlrHs7ghhGUImpCtbY5X+opvPGjpV2Vd97r3tGS358VI3luwIf3tMzXJf2ktuDLeLIAhuyrzJtOP8fqu1MqU1OjGMcl6yF9JSDzpz55bsQyLht4Bd+u10k1L6bz0l/dbhlRXcjxSPZlH2Zr0LV8/5pLquRSXZH41H/JJdS1+S2rHDcd5Ej1D/nXpG79+0qFwydKvyPTyl+OtPvZOBFPPSo3HAQQb0ou/Pe9QWE7oHHRIAskVCTbGWR4hRAFk6jFRRnq/+23IrUh/9SiA6pel1tNNyK7G0kc/lPfthZC9KBkOnUMu5ZdDRnmP4msDOgsZZs5IXQ8qDp3DrvSEnzO89r1ZymelNtuHPeJAespvnPABxjkNMp/cUDIbnEjWl/YRyXYY5h0SV9bR/rSDN4BMTbI23NCS6kruSeOUi4mgtSi9TJxQ1kFvYAnLHsFGIhkGO/IrNnv4hyWPUc5Qfml3/hJrHbAeOBG4oWXjhGSzeKFs1+Ijsi2LA8m+6B6U7JHEleyCVCfCjBJ6BwOmzw7pV1PEGXcr4yCzFjPzlTZx2qO9mKZfMeNpuxSWpc6vviNDpmGZe7rL638tR6Ym89QJIdVla9sZtGT+jYpw5YMDip/M0ZnfHk9/DtYegeyyjD1bk8wVR3ah48wT+f9G0WBi6eefuJLHYQaS8bJ+UpajO5DtTViGUdGSuSL7grDikF2BwQy8Pu+QuWK28nLSTVnXZs7E1E9Lhosbyjb95H/r01nIyLRDybWJfcm6yKy5NE+6DIuyz/NbsPztGXJLEJZkzPllu7Wtzr8uWSLFizFXnnDJrMh+0okkkyfVlkyG5kOGoCEZCjZIKLzgkWlYWouGYSXB7TqMirIv81uw+s0Jbs+h8rzs7/ar++/AQCmllFJKqa8Xy77JMZjYdqXGmIeNMZ82xvSMMa8bY37OGOPe+plKKaWUUkp9Hdnk+j+3YS99pp3IMwbGmDLwF8BZ4LuBE8AvIgcyP7OLQ1NKKaWUUvuIBexdnjHYa59pJ/LAAPinQAb4HmttC/hzY0wReNIY8x/HtymllFJKKfXWsva2zw5cx576TDuplxK9H/jUNTPr48iM/dbdGZJSSimllFJ3ZE99pp3UA4NTwIs7b7DWXgR64/uUUkoppZS6J2xir/tzG/bUZ9pJvZSoDKxf5/bm+D6llFJKKaXujbu/lGhPfaY1dgIDG4wxI+AnrbW/es3tl4Hfttb+62tu/zDw4fGvp4Ez92Sge9cMUN/tQUy4o9ba6lv9Ilq7d0xr99a0dieP1u2tad3uPq3TN9qqSWPMnyLz53rSwGDH7x+z1n5s85c7/Uy72yb1jEETmLrO7SWuc9Q1XgAfAzDGfMla+/hbO7y9TefR5NDavTM6jyaH1u7t0/kzObRub0znx41Za//Gm3j6HX2m3W2T+h2DF7nmuitjzBEgxzXXaSmllFJKKTWh9tRn2kk9MPgk8J3GmMKO274f6AOf250hKaWUUkopdUf21GfaST0w+A0gBP7QGPO+8TWBTwK/dBv9Xj92i/uVzqNJpcvl1nQeTSZdLjen82cy6XJ5I50fb40385n2npvILx+DxEcDvw48gVyD9ZvAk9baeFcHppRSSiml1G3aS59pJ/bAQCmllFJKKXXvTOqlRHfMGPOwMebTxpieMeZ1Y8zPGWPc3R7XJDDG/B1jzP8yxlw2xnSMMc8YY35wt8eltG5vRWt3cmnt3pzW7uTS2hVao+p6JrVd6R0xxpSBvwDOAt8NnAB+ETnw+ZldHNqk+AhwHvhxpEfxdwG/a4yZsdb+2q6ObB/Tur0tWrsTSGv3tmjtTiCt3TfQGlVf4764lMgY81PAR5Ewitb4to8iX+6Ym8Qvd9xL45W8fs1tvws8Ya09tkvD2ve0bm9Na3cyae3emtbuZNLa3aY1qq7nfrmU6P3Ap65ZoT8OZIBv3Z0hTY5rV/yxLwOz93os6g20bm9Ba3diae3egtbuxNLaHdMaVddzvxwYnOKakAhr7UWgxzWhEmrLe5FTqWr3aN3eHa3d3ae1e3e0dnef1u7NaY3uc/fFdwyAMtePlW6O71M7GGO+Hbm28kO7PZZ9Tuv2DmntTgyt3TuktTsxtHZvQGtUwf1zxgDgel+WMDe4fd8yxiwCvwv8kbX2t3d1MAq0bm+b1u7E0dq9TVq7E0dr9xpao2rT/XJg0ASmrnN7iev/ZWBfMsZUkGjui8AP7fJwlNbtbdPanThau7dJa3fiaO1eQ2tU7XS/HBi8yDXXBhpjjgA5rrmWcL8yxmSBPwF84APW2u4uD0lp3d4Wrd2JpLV7G7R2J5LW7g5ao+pa98uBwSeB7zTGFHbc9v1AH/jc7gxpchhjPOD3gAeA91trr+7ykJTQur0Frd2JpbV7C1q7E0trd0xrVF3P/ZJjUEa+RX8G+AXgOPBLwK9Ya/dbYMnXMMZ8DPgR4MeAL1xz95etteG9H5XSur01rd3JpLV7a1q7k0lrd5vWqLqe++LAACTiHPh14AnkOsHfBJ601sa7OrAJYIxZAo7e4O5j1tqlezcatZPW7c1p7U4urd2b09qdXFq7QmtUXc99c2CglFJKKaWUunv3y3cMlFJKKaWUUm+CHhgopZRSSiml9MBAKaWUUkoppQcGSimllFJKKfTAQCmllFJKKYUeGCillFJKKaXQAwOllFJKKaUUemCwK4wx9jZ+vs0Y88Hx//MTMOY/Nsb87I7fP2uM+f1bPOewMaZjjDn+1o9Q3Qtau2qv0tpVk05rVE0CDTjbBcaY9+z4NQN8Bvh3wCd23H4WCIATwBestcm9G+EbGWPeDXwaWLDWNsa3fRaoW2u/7xbP/c+Aa6394Fs9TvXW09pVe5XWrpp0WqNqEni7PYD9yFr7V5v/33HEf27n7TvU7s2obupHgT/aXPHv0G8BnzbG/IS1du3rPC51j2ntqr1Ka1dNOq1RNQn0UqIJdu3pQmPM4vj3HzDG/JYxpmWMWTbG/ND4/o8aY143xtSMMb9gjHGumd5pY8wnjDHt8c/vGWPmbjGGAvC3geueGjTG/D1jzKvjsXzSGDN/zUM+DzSAH7jL2aD2IK1dtVdp7apJpzWq3kp6YLA3/QJwBfhe4CngvxhjfhF4F/Ah4FeAjwJ/d/MJxpiTyIqYBv4B8EHgG4E/NsaYm7zWe5FTmn95nfveDfwz4CeADwPvAD628wFWrlX7K+B9d/ge1f1Ja1ftVVq7atJpjao3TS8l2ps+Y639aQBjzNPA9wF/EzhlrY2BPzXGfDdyNP/x8XN+FlgB3m+tHY6f+zzwIvBdvPEaxp2+CblecPU69xWBD1hrm+PpzQG/bIzJWGv7Ox73HPAjd/1u1f1Ea1ftVVq7atJpjao3Tc8Y7E2f3vyPtbaFXGv4ufGKv+lV4PCO398H/A8gMcZ4xhgPOA8sAY/f5LXmgPoN7vvi5oo/dnb87+FrHlcHZm/x1we1P2jtqr1Ka1dNOq1R9abpgcHetH7N78Mb3Jbe8fsM8C+B0TU/x4EjN3mtNBDewTg2n7NTiJyd0jNUSmtX7VVau2rSaY2qN00Xxv7RQP4q8JvXue9GR/2bz5t6k689BXSstaM3OR21P2ntqr1Ka1dNOq1R9QZ6YLB/fBo4DTxj7yy84iXgkDEmsNbe6K8Dt7IIvHyXz1VKa1ftVVq7atJpjao30EuJ9o8nkZX/E8aY7zOSnvj3jTG/bYz5tps87/NACnjbm3jtx8fTUepuPInWrtqbnkRrV022J9EaVTvogcE+Ya19GXgP0EPahn0S+LfINX6v3uJ5Z4D3383rGmNmkO4Ff3A3z1dKa1ftVVq7atJpjaprmTs7c6T2I2PMjwP/2Fp7+i6e+0+AnwQevMPTlEq9aVq7aq/S2lWTTmv0/qRnDNTt+BhQNcbcURDJuAXZjwH/Xld8tUu0dtVepbWrJp3W6H1IDwzULVlru8A/AnJ3+NQ54L8Cv/N1H5RSt0FrV+1VWrtq0mmN3p/0UiKllFJKKaWUnjFQSimllFJK6YGBUkoppZRSCj0wUEoppZRSSqEHBkoppZRSSin0wEAppZRSSikF/H9EYtLMpPVl0AAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pylag.processing.plot import create_cbar_ax\n", "\n", "# Grids for plotting using pcolormesh\n", "bin_edges = range(int(z_max-z_min) + 1)\n", "time_out = np.arange(time_start-time_step/2., time_end + time_step/2., time_step)/3600.0\n", "depth_out = np.array(bin_edges)\n", "time_grid, depth_grid = np.meshgrid(time_out, depth_out)\n", "\n", "# Create figure\n", "fig, axarr = plt.subplots(nrows=1,ncols=4, figsize=(12, 6), sharey=True)\n", "\n", "# Store plots and calculated concentrations in lists\n", "concentrations = []\n", "plots = []\n", "\n", "# Loop over each method and plot the concentration of particles\n", "for i, (name, data) in enumerate(particle_data.items()):\n", " concentration = np.empty((len(bin_edges)-1, n_times))\n", " for j in range(n_times):\n", " hist, bins = np.histogram(data[0,j,:], bins=bin_edges)\n", " concentration[:,j] = hist\n", " concentrations.append(concentration)\n", "\n", " plot = axarr[i].pcolormesh(time_grid, depth_grid, concentration, vmin=0, vmax=70)\n", " plots.append(plot)\n", " \n", " axarr[i].set_title('{}'.format(name), fontsize=font_size)\n", " axarr[i].set_xlabel('Time (h)', fontsize=font_size)\n", " axarr[i].tick_params(axis='both', which='major', labelsize=font_size)\n", " axarr[i].tick_params(axis='both', which='minor', labelsize=font_size)\n", " \n", "axarr[0].set_ylabel('Height above sea bed (m)', fontsize=font_size)\n", "\n", "# Add colour bar to the last plot\n", "cax = create_cbar_ax(axarr[3])\n", "cbar = fig.colorbar(plots[3], cax=cax)\n", "cbar.ax.tick_params(labelsize=font_size)\n", "cbar.set_label('Concentration (#/m)', fontsize=font_size)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure, the problems with the \"naive\" scheme become immediately apparent, with uneven particle concentrations throughout the water column. Comparing with the diffusivity profile above, it is clear particles have accumulated in regiond os low diffusivity, as explained by Visser (1997). In qualitative terms, the other three schemes exhibit a more even particle distribution.\n", "\n", "We can quantitatively test whether each scheme satisfies the WMC in the following way." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pyqt_fit import kde, kde_methods, kernels\n", "\n", "# Dictionary in which to store mean concentrations as a function of depth\n", "means = {}\n", "\n", "# Dictionary in which to store std's as a function of depth\n", "stds = {}\n", "\n", "# Compute KDE, means and std's for ...\n", "# - All methods\n", "# - All trials\n", "# - All time points\n", "for i, (name, data) in enumerate(particle_data.items()):\n", " particle_kde = np.empty((n_trials, n_times, n_z_levels), dtype=float)\n", " for i in range(n_trials):\n", " for j in range(n_times):\n", " est = kde.KDE1D(data[i, j, :], lower=z_min, upper=z_max,\n", " method=kde_methods.reflection, kernel=kernels.Epanechnikov())\n", " particle_kde[i, j, :] = n_particles * est(z_levels)\n", "\n", " means[name] = np.mean(particle_kde, axis=(0,1))\n", " stds[name] = np.std(particle_kde, axis=(0,1))\n", "\n", "# Compute reference particle concentration (#/m)\n", "ref_conc = n_particles/float(n_z_levels - 1)\n", "\n", "# Create figure\n", "fig, axarr = plt.subplots(nrows=1,ncols=4, figsize=(12, 6), sharey=True)\n", "\n", "# Plot means and stds\n", "for idx, name in enumerate(particle_data.keys()):\n", " axarr[idx].errorbar(means[name], z_levels, xerr=stds[name], fmt='-o', c='r')\n", " axarr[idx].axvline(ref_conc, ymin=0, ymax=1, c='k', linestyle='--')\n", " axarr[idx].set_title(name, fontsize=font_size)\n", " axarr[idx].set_xlabel('Particle conc (#/m)', fontsize=font_size)\n", " if name == 'Diff_Naive_1D':\n", " # Naive is known to fail so we set broarder xlims\n", " axarr[idx].set_xlim(xmin=0., xmax=2.*ref_conc)\n", " else:\n", " axarr[idx].set_xlim(xmin=ref_conc - ref_conc/4., xmax=ref_conc + ref_conc/4.)\n", " axarr[idx].set_ylim(ymin=z_min, ymax=z_max)\n", "\n", "# Tidy up x and y tick labels\n", "for ax in axarr:\n", " plt.setp(ax.get_xticklabels(), fontsize=font_size)\n", " plt.setp(ax.get_yticklabels(), fontsize=font_size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure, the vertical black dashed line marks the initial particle concentration, while in red is shown the mean particle concentration $\\pm$ one standard deviation. The failure of the Naive scheme to satisfy the WMC can be clearly seen (note the different x-axis scale for the Naive scheme). Meanwhile, all the other schemes successfully pass the test for this particular analytic profile. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\n", "Brickman, D. and Smith, P. C., 2001. Lagrangian stochastic modeling in coastal oceanography. Journal of Atmospheric and Oceanic Technology, 19 (1), pp. 83-99\n", "\n", "Grawe, U., 2010. Implementation of high-order particle-tracking schemes in a water column model. Ocean Modelling. 36(1-2) pp. 80-89\n", "\n", "Thomson, D. J., 1987. Criteria for the selection of stochastic mod-els of particle trajectories in turbulent flows.J. Fluid Mech.,180, pp. 529–556\n", "\n", "Visser, A. W., 1997. Using random walk models to simulate the vertical distribution of particles in a turbulent water column. Marine Ecology Progress Series, 158, pp. 275-281" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }