{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Two-level molasses in 1D\n", "\n", "This example covers a two level, 1D optical molasses and compares results to\n", "P. D. Lett, et. al., _J. Opt. Soc. Am. B_ __6__, 2084 (1989), https://dx.doi.org/10.1364/JOSAB.6.002084. This example is an excellent oppportunity to review the subtlties of extracting accurate temperatures, like integration time and binning, even under the most basic approximations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp\n", "import lmfit\n", "import pathos # used for parallelization\n", "from scipy.stats import iqr\n", "from pylcp.common import progressBar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the problem\n", "\n", "As with every example in `pylcp`, we must first define the Hamiltonian, lasers, and magnetic field. We will make a two-state system that is addressed only by $\\pi$ polarized light. Note that because we are also using the heuristic equation, we want to make sure that the detuning is not on the Hamiltonian, but on the lasers." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "mass = 200\n", "\n", "# Make a method to return the lasers:\n", "def return_lasers(delta, s):\n", " return pylcp.laserBeams([\n", " {'kvec':np.array([1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':delta, 's':s},\n", " {'kvec':np.array([-1., 0., 0.]), 'pol':np.array([0., 1., 0.]),\n", " 'pol_coord':'spherical', 'delta':delta, 's':s},\n", " ], beam_type=pylcp.infinitePlaneWaveBeam)\n", "\n", "# Now define a two level Hamiltonian, connected using pi-light.\n", "def return_hamiltonian(delta):\n", " Hg = np.array([[0.]])\n", " He = np.array([[-delta]])\n", " mu_q = np.zeros((3, 1, 1))\n", " d_q = np.zeros((3, 1, 1))\n", " d_q[1, 0, 0] = 1.\n", "\n", " return pylcp.hamiltonian(Hg, He, mu_q, mu_q, d_q, mass=mass)\n", "\n", "hamiltonian = return_hamiltonian(0.)\n", "\n", "magField = lambda R: np.zeros(R.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate equilibrium forces\n", "### Generate the equilibrium force profile\n", "\n", "Do it for all three governing equations at the same step." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 23.30 s. \n" ] } ], "source": [ "delta = -2.\n", "s = 1.5\n", "\n", "laserBeams = return_lasers(delta, s)\n", "hamiltonian = return_hamiltonian(0.)\n", "eqns = {}\n", "eqns['obe'] = pylcp.obe(laserBeams, magField, hamiltonian)\n", "eqns['rateeq'] = pylcp.rateeq(laserBeams, magField, hamiltonian)\n", "eqns['heuristiceq'] = pylcp.heuristiceq(laserBeams, magField)\n", "\n", "extra_args = {}\n", "extra_args['obe'] = {'progress_bar':True, 'deltat_tmax':2*np.pi*100, 'deltat_v':4,\n", " 'itermax':1000, 'rel':1e-4, 'abs':1e-6}\n", "extra_args['rateeq'] = {}\n", "extra_args['heuristiceq'] = {}\n", "\n", "v = np.arange(-10., 10.1, 0.1)\n", "\n", "for key in eqns:\n", " eqns[key].generate_force_profile(np.zeros((3,) + v.shape),\n", " [v, np.zeros(v.shape), np.zeros(v.shape)],\n", " name='molasses', **extra_args[key])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up the equilibrium force profile, solid for the OBEs, dashed for the rate equations, and dashed-dot for the heuristic equation." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(3.25, 2.))\n", "lbls = {'obe':'OBE', 'rateeq':'Rate Eq.', 'heuristiceq':'Heuristic Eq.'}\n", "styles = ['-','--','-.']\n", "for ii, key in enumerate(eqns):\n", " ax.plot(v, eqns[key].profile['molasses'].F[0], styles[ii],\n", " label=lbls[key], linewidth=1.25-0.25*ii)\n", " #ax[1].plot(v, eqn.profile['molasses'].Neq)\n", "#ax.legend(fontsize=7)\n", "ax.set_xlabel('$v/(\\Gamma/k)$')\n", "ax.set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "fig.subplots_adjust(bottom=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the rate equations and the OBEs, also plot up the equilibrium populations of the two states:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "for key in ['rateeq', 'obe']:\n", " #ax[0].plot(v, eqn[key].profile['molasses'].F[0])\n", " ax.plot(v, eqns[key].profile['molasses'].Neq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate the damping parameter\n", "We calculate the damping coefficient $\\beta$ as a function of $s_0$ and $\\delta$, and compare to the Lett expression for the damping." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 0.42 s. \n", "Completed in 0.94 s. \n", "Completed in 9:26. \n" ] } ], "source": [ "deltas = np.linspace(-3, 0., 101)\n", "intensities = np.array([0.01, 0.1, 1, 10])\n", "\n", "betas = {}\n", "Deltas, Intensities = np.meshgrid(deltas, intensities)\n", "\n", "eqns = {'heuristiceq':pylcp.heuristiceq, 'rateeq':pylcp.rateeq, 'obe':pylcp.obe}\n", "\n", "extra_args['obe'] = {'deltat':2*np.pi*100, 'itermax':1000, 'rel':1e-4, 'abs':1e-6}\n", "extra_args['rateeq'] = {}\n", "extra_args['heuristiceq'] = {}\n", "\n", "for key in eqns:\n", " it = np.nditer([Deltas, Intensities, None])\n", " progress = progressBar()\n", " for (delta, intensity, beta) in it:\n", " laserBeams = return_lasers(delta, intensity)\n", " hamiltonian = return_hamiltonian(0.)\n", "\n", " # Next, generate the OBE or rate equations:\n", " if key is 'heuristiceq':\n", " eqn = eqns[key](laserBeams, magField)\n", " else:\n", " eqn = eqns[key](laserBeams, magField, hamiltonian)\n", "\n", " # Use built in damping_coefficient() method:\n", " beta[...] = eqn.damping_coeff(axes=[0], **extra_args[key])\n", "\n", " progress.update((it.iterindex+1)/it.itersize)\n", "\n", " # Just update it to be sure.\n", " progress.update(1.)\n", "\n", " betas[key] = it.operands[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot it up:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "for ii, key in enumerate(eqns):\n", " for jj, betas_i in enumerate(betas[key]):\n", " if ii==0:\n", " kwargs = {'label':'$s=%.2f$'%intensities[jj]}\n", " else:\n", " kwargs = {}\n", " ax.plot(deltas, betas_i, styles[ii], color='C%d'%jj, linewidth=1., **kwargs)\n", "\n", "for ii, intensity in enumerate(intensities):\n", " ax.plot(deltas, -4*intensity*2*deltas/(1+2*intensity+4*deltas**2)**2, 'k--',\n", " linewidth=0.5)\n", " \n", "ax.legend(loc='upper left')\n", "ax.set_xlabel('$\\Delta/\\Gamma$')\n", "ax.set_ylabel('$\\\\beta/\\hbar k^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate many atoms to extract temperature\n", "\n", "We'll run about $N_A\\approx 250$ for a time $\\tau$ to generate some histograms and understand what velocities we obtain, etc.\n", "\n", "Because we start at $v=0$, the amount of time that we will need to integrate for will depend both on the mass and the scattering rate. We must integrate for sufficiently long to allow the atoms's velocity to randomly walk to a standard deviation that corresponds to a temperature $T$. Using the basic Doppler limit $T_D=\\hbar \\Gamma/(2 k_B)$, the expected standard deviation in the velocity at $T$ is given by\n", "\n", "$$\n", " \\sigma_v^2 = \\frac{k_B T}{m} = \\frac{k_B}{m}\\left(\\frac{\\hbar \\Gamma}{2 k_B}\\right)\\frac{T}{T_D} = \\frac{1}{2} \\frac{\\hbar k}{m}\\frac{\\Gamma}{k}\\frac{T}{T_D} = \\frac{v_R v_D}{2}\\frac{T}{T_D},\n", "$$\n", "\n", "where the \"Doppler velocity\" is $v_D = \\Gamma/k$ and the recoil velocity is $v_R = \\hbar k/M$. In our default unit system, $t_0 = 1/\\Gamma$, $x_0=1/k$, and the dimensionless mass, defined above simply as the variable `mass`, is $\\bar{M} = x_0^2 M/ \\hbar t_0 = \\Gamma M/ \\hbar k^2$. In these units, velocity is measured in $v_D$, so the corresponding dimensionless standard deviation $\\bar{\\sigma}_v$ is given by,\n", "\n", "$$\n", " \\bar{\\sigma}_v^2 = \\frac{\\sigma_v^2}{v_D^2} = \\frac{1}{2\\bar{M}}\\frac{T}{T_D}\n", "$$\n", "\n", "where we have used the fact that the dimensionless mass can be written as $\\bar{M} = v_D/v_R$.\n", "\n", "Now, assuming that the atoms' velocity engages in a random walk, after $N_{\\rm sc}$ scattering events, the atoms' velocity will have a variance of $\\sigma_v^2/v_R^2 = N_{\\rm sc}$ (assuming 2 recoils per scattering event and equal probability scattering left or right). Thus, we need at least $N_{\\rm sc} = \\sigma_v^2/v_R^2 = \\bar{\\sigma_v}^2 (v_D/v_R)^2 = \\bar{M}/2 (T/T_D)$ scattering events.\n", "\n", "To turn this into an integration time, we need a rough estimate of the scattering rate $R_{\\rm sc}$. From the heuritistic equation,\n", "\n", "$$\n", " R_{\\rm sc}=\\frac{\\Gamma}{2}\\frac{s}{1+2s+4\\delta^2}\n", "$$\n", "\n", "for a given detuning $\\delta = \\Delta/\\Gamma$ and saturation parameter $s$. Thus, the dimensionless total evolution time $\\bar{\\tau}$ should be *at least*\n", "\n", "$$\n", " \\bar{\\tau} \\geq \\bar{M}\\frac{T}{T_D} \\frac{1+2s+4\\delta^2}{s}\n", "$$\n", "\n", "In practice, we might expect the maximum $T/T_D\\approx 10$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Non parallel version:\n", "\n", "Plots up the first ten runs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "s = 3\n", "delta = -1\n", "\n", "laserBeams = return_lasers(delta, s)\n", "hamiltonian = return_hamiltonian(0.)\n", "\n", "eqn = pylcp.heuristiceq(laserBeams, magField, mass=mass)\n", "#eqn = pylcp.rateeq(laserBeams, magField, hamiltonian, include_mag_forces=False)\n", "#eqn = pylcp.obe(laserBeams, magField, hamiltonian)\n", "\n", "N_atom = 256\n", "v_final = np.zeros((N_atom,))\n", "#num_of_scatters = np.zeros((N_atom,), dtype='int')\n", "#num_of_steps = np.zeros((N_atom,), dtype='int')\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "sols = []\n", "progress = progressBar()\n", "for ii in range(N_atom):\n", " eqn.set_initial_position_and_velocity(np.array([0., 0., 0.]), np.array([0., 0., 0.]))\n", " if isinstance(eqn, pylcp.rateeq):\n", " eqn.set_initial_pop_from_equilibrium()\n", " elif isinstance(eqn, pylcp.obe):\n", " eqn.set_initial_rho_from_rateeq()\n", "\n", " eqn.evolve_motion([0., 10*mass*(1+2*s+4*np.abs(delta)**2)/s],\n", " random_recoil=True,\n", " max_scatter_probability=0.25,\n", " freeze_axis=[False, True, True])\n", " progress.update((ii+1.)/N_atom)\n", "\n", " if ii<10:\n", " ax.plot(eqn.sol.t, eqn.sol.v[0])\n", "\n", " v_final[ii] = eqn.sol.v[0, -1]\n", "\n", " sols.append(eqn.sol)\n", " #num_of_scatters[ii] = sum(eqn.sol.n_random)\n", " #num_of_steps[ii] = len(eqn.sol.t)\n", "\n", "ax.set_xlabel('$\\Gamma t$')\n", "ax.set_ylabel('$v/(\\Gamma/k)$');\n", "\n", "eqn.generate_force_profile(np.zeros((3,) + x_fit.shape),\n", " [x_fit, np.zeros(x_fit.shape), np.zeros(x_fit.shape)],\n", " name='molasses')\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Parallel version:\n", "\n", "Adjust chunksize to equal the number of cores." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 4:47. \n" ] } ], "source": [ "s = 3\n", "delta = -3\n", "\n", "laserBeams = return_lasers(delta, s)\n", "hamiltonian = return_hamiltonian(0.)\n", "\n", "eqn = pylcp.heuristiceq(laserBeams, magField, mass=mass)\n", "#eqn = pylcp.rateeq(laserBeams, magField, hamiltonian, include_mag_forces=False)\n", "#eqn = pylcp.obe(laserBeams, magField, hamiltonian)\n", "\n", "eqn.set_initial_position_and_velocity(np.array([0., 0., 0.]), np.array([0., 0., 0.]))\n", "if isinstance(eqn, pylcp.rateeq):\n", " eqn.set_initial_pop_from_equilibrium()\n", "elif isinstance(eqn, pylcp.obe):\n", " eqn.set_initial_rho_from_rateeq()\n", "\n", "N_atom = 96 # Needs to be divisible by chunksize\n", "\n", "if hasattr(eqn, 'sol'):\n", " del eqn.sol\n", "\n", "def generate_random_solution(eqn, tmax, rng_seed):\n", " # We need to generate random numbers to prevent solutions from being seeded\n", " # with the same random number.\n", " eqn.evolve_motion(\n", " [0., tmax],\n", " random_recoil=True,\n", " max_scatter_probability=0.25,\n", " freeze_axis=[False, True, True],\n", " rng=np.random.default_rng(rng_seed)\n", " )\n", " \n", " return eqn.sol.v[0, -1]\n", "\n", "chunksize = 4\n", "v_final = []\n", "ss = np.random.SeedSequence(12345) # \"It's the same combination as my luggage!\"\n", "child_seeds = ss.spawn(N_atom)\n", "progress = progressBar()\n", "for jj in range(int(N_atom/chunksize)):\n", " with pathos.pools.ProcessPool(nodes=4) as pool:\n", " v_final += pool.map(\n", " generate_random_solution,\n", " chunksize*[eqn],\n", " chunksize*[10*mass*(1+2*s+4*np.abs(delta)**2)/s],\n", " child_seeds[jj*chunksize:(jj+1)*chunksize]\n", " )\n", " progress.update((jj+1)/int(N_atom/chunksize))\n", " \n", "x_fit = np.linspace(-1.1*np.amax(np.abs(v_final)), 1.1*np.amax(np.abs(v_final)), 101)\n", " \n", "eqn.generate_force_profile(np.zeros((3,) + x_fit.shape),\n", " [x_fit, np.zeros(x_fit.shape), np.zeros(x_fit.shape)],\n", " name='molasses');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should be zero, but it might not be because of bad seeding of random number generators during parallel execution:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(np.diff(np.sort(v_final))==0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bin the final data and extract temperature\n", "\n", "To extract the final temperature with uncertainity, we must calculate $\\sigma_v$ and its uncertainty. The standard error in $\\sigma$ for a Gaussian distribution is $\\sigma/\\sqrt{2 N-2}$ for $N$ points. However, we will obtain more accurate estimates of the uncertainty by restricting the Gaussian distribution such that the mean is zero. To do this systematically, we will bin the data and fit the resulting histogram.\n", "\n", "We use the Freedman–Diaconis rule to determine the bin size, and use bins that are symmetric about zero and span the whole range of $v_{\\rm final}$. We normalize the counts in each bin to $N_A$, which gives us the \"experimental\" (i.e., through the numerics) probability of landing in the bin between $x-dx/2$ and $x+dx/2$. We then fit the numerics to the associated expectation from a normal distribution given by $p(x)dx$, where $p(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-(x-\\mu)^2/2\\sigma^2}$, $\\sigma$ is the standard deviation, and $\\mu$ is the mean. Because the bin size here is fixed and known, we eliminate one additional variable compared to `lmfit`'s built in Gaussian model, namely the amplitude.\n", "\n", "We also plot the distribution expected from Lett, *et. al.*, eq. (18):\n", "\n", "$$\n", " \\frac{T}{T_D} = \\frac{1+2s+4\\delta^2}{4\\delta^2}\n", "$$\n", "\n", "When simulating with the heuristic equation, this should basically be exact (as it is derived using the heuristic equation). The only exception is when the mass is low, $\\bar{M}\\lesssim 100$. In this case, the force vs. velocity curve across the distribution shows curvature, usually with increased damping out near the wings. This increased damping causes lower temperatures that that predicted by Lett, *et. al.*, eq. (26). We can easily see if this non-linearity exists by plotting the force vs. velocity curve across the distribution, shown here in black." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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bYxaVxWeJdoMGDTpoOv+jjz7K5ZdfTl5ehRtmVaHkeHN44ZcX7HLXBl05teGpEYyoZC497lJ7ILbP+Hj2l2c1IVdKlZroD5DwEpGc2NjY2JycnEiHUibWrl1Lv379WL16tV3Xq1cvJkyYQEpKSgQjq7hSU1OpVi04EXPv3r1UrVq12OePWjGKl397GQCXuJhw9gSapzQPcZThNXPDTG6eGZwn8UavN6IquVOVS1xcHLm5ubnGmLhIx6IOFtU9Rqr8adasGfPnz+fUU4O/lH788Ue6devGxo0bIxiZKsy+vH188McHdnlYq2FRlxQBnNboNDrX62yXX1/6On7jj2BESqlopYmRCrnq1avz/fffM2zYMLvujz/+oFOnTvz++++RC0wdZMxfY0jPsxbnTHAlcFXbq8Jyn5ycHEaOHGm/Qt2DKiLccuItdnnlnpX8uEE3O1ZKlZw+SguzyvYoLT+/38+DDz7I008/bdclJiby5Zdf0rdv3whGVrGU9lFaak4q/b7qR4bH2g7wmnbXcGOHG8tVjCV168xb7YToqJSjmHDWBJwOZ8jvo9SR0Edp5Zv2GKmwcTgcPPXUU7zzzjs4ndYvp4yMDAYOHMh7770X4ejUR39+ZCdFSTFJXNr60ghHdORuaH8DgrUg5X9p/zF17dQIR6SUijaaGKmwu/rqq5k0aRJVqlQBwOfzcfXVV/PAAw/o7KEI2ZW9i89WfWaXr2hzBckxBy4iH31aVmtJv2b97PJby97C49dNjpVSxaeJkSoT/fr14+eff6ZeveBKyk899RQXX3wxubm5EYyschq1YhTZ3mwAqsdV56JjL4pwRKFzffvrcYrVQ7lx30a+/ffbCEeklIommhipMnPCCSewcOFCWrdubdd99tln9OnTh71790YwssplV/auAlt/XNnmShLcCRGMKLSaJDfh7Bb2gvi8u/xd7TVSShWbJkaqTDVu3Jh58+bRq1cvu2727Nl06dKFtWvXRjCyyuPTlZ+S57cW3awZX5Ohxww9zBnR55p21+ASFwBbMrcwfd30CEeklIoWmhipMpeSksLUqVMZMWKEXbdq1So6derE4sWLizhTHamMvAzGrRpnly857hLiXBVvYkz9xPr0b97fLn/wxwc6nk0pVSyaGKmIiImJ4cMPP2TkyJF23Y4dOzjttNOYOHFi5AKr4L78+0v2efYBkOROYujRFa+3aL/LW19uv/9n7z/M2TwngtEopaKFJkYqYkSERx55hI8++giXy3rskZ2dzeDBg3n11VcjHF3Fk+vL5ZO/PrHLFxx7AYkxiRGMKLxaVGvBaQ1Ps8ujVoyKXDBKqaihiZGKuBEjRvDdd9+RnGxNFzfGcMstt3Dbbbfh8/kiHF3FMem/SezK3gVAjCOG4a2GRzii8Luy7ZX2+992/MbvO36PXDBKqaigiZEqF3r16sW8efNo1KiRXffyyy9z/vnnk5WVFcHIKgaf38eHf3xol89pcQ4142tGMKKy0b52e06ofYJdHvWH9hoppYqmiZEqN9q0acPChQvp0KGDXff111/Ts2dPduzYEcHIot+MDTPYsG8DAA5xcFnryyIbUBnK32s0a+Ms/t37b+SCUUqVe5oYqXKlfv36/Pzzz/TvH5xRtGjRIjp16sSqVasiGFl0G/PXGPv9mU3OpFFyoyJaVyzdG3SnZbWWdvnTVZ9GMBqlVHmniZEqdxITE5k4cSLXXnutXbd27Vq6dOnCnDk6s6ik/tz1J7/v/N0uj2g94tCNKyAR4dLjgvvATf5vMmm5aQe1y8nJYeTIkfarMm78rJTSxEiVUy6XizfffJPnnnvOrtu7dy+9e/dm7NixEYws+ny6MthDcnyt42lTs00Eo4mMfs36US22GgA5vhwm/DPhoDY5OTk8+uij9ksTI6UqJ02MVLklItx111188cUXxMbGApCXl8dFF13E008/rQv2FcOu7F1MWzfNLleGmWiFiXXGct7R59nlz1d9jtfvjWBESqnyyhXpAJQ6nPPPP5/69etz9tlns3v3bgDuv/9+1q5dyxtvvIHb7Y5whEeu6b1TSn2uPyejQLndyOk44qz1iWJqziC2lpUA+D3JXPeOByj8XuueGVDqGKLBBcdcwId/fIjXeNmauZVZG2fRu0nvSIellCpntMdIRYWuXbuyYMECWrRoYde99957DBo0iPT09AhGVp55cVdbZJc8ezsBzsiFE2F1qtThjCZn2OUxK8cU0VopVVlpYqSiRsuWLVmwYAFdunSx66ZPn0737t3ZtGlTBCMrn1zJK3C4rO0/jN+FJ/WUsg0gaw+s/RlWjCdm6Yc8fnosI0+L5bqT3Lj/mQLrF0BeZpmGNPy44KPEX7f/yqo9OtNRKVWQPkpTUaVmzZrMmDGDESNG8OWXXwKwfPlyOnbsyJQpU2jfvn1kAyxHYqrPt99704/H+MK8/YffB2tnw38/WQnR1uWANQ4sAXjw1Nhg2ynXW18dbmh4MjTvAS16Q4MTQSRsIbar2Y42Ndrwx+4/AGtg+uNdHw/b/ZRS0Ud7jFTUiY+P5/PPP+euu+6y67Zs2UL37t357rvvIhhZ+eGI24QzfqNdztvTpYjWRyg7Fea/Bq+2h9GDrfdbl7E/KSqS3wMb5sOsp+H9XvBOd1j6KXjCMyNMRAr0Gk1bO63QqftKqcpLEyMVlRwOB8899xxvvvkmDof1zzgjI4OBAwfy7rvvRji6yHNXDY4t8mU1wZ/bIPQ3yU6F6Q/AS8fB9w9C6oaD2yTUgPod8DQ9nY9+z2P0sjym/+vFW+s4iE0+uP22FTDxevhfa5j7MnjzQh52nyZ9qB5XHbA21p3036SQ30MpFb30UZqKatdddx1NmjRh6NChZGZm4vP5uOaaa1i7di1PPvmknTRVKo4c3CnL7GLe3o6hvb4xsOxz+OEhyNxZ8Jg4rUdiR/W0Ho/VOhZEyExN5fLLq9nN9r4+japJiVbP0tpZ8M8Mq+dov6xdMOMRWDoG+j8PR50esvDdTjfntDiHD/74AIAv//6y0i5joJQ6WCX8raEqmv79+zNnzhzq1atn1z3zzDNcdNFFlXKRvpjqfyAOq6fF+OLx7msbuovv/Bs+7AffXFswKYqvBt1ug1uXw/AvoNO1ULtV0eOFnC5oeCJ0vwOumAbXLYATRoArLthm9z8w+hz4YgRk7DzkpUrqvJbBNY3WpK3h1+2/huzaSqnopomRqhA6dOjAokWLaNs2mASMGzeO3r17s2vXrghGVvZiav5mv/ekngAmROs8rRgP754GGxYE61zx0PNBuO0v6D0SUhqW/vp1joOzXrWudfJVIPl+PP31DbxzKmxYWPrr59MouRGd63W2y1/+/WVIrquUin6aGKkKo1GjRsydO5czzgiuVTNv3jw6d+7Mv/9Wjh3V44+Kxxm/wy57UkPwGM2bC1PvgglXgiff9PpWg+DGxXDqXRCTcOT32a9KDRjwAlw9CxrmW2Jg3xb4aADMf916nHeEzj/mfPv9D+t/IDU39YivqZSKfpoYqQolOTmZKVOmcOWVV9p1//77L506dWL+/PlFnFkxVD+tuv3em9kMf17tI7tgxk74sD8szjegPTYFLvgULhgDVRsf2fWLUu94uGI69H3GmtYP4PfC9w/AlyOOeObaaY1Oo2Z8TQA8fg/fbdQZjUopTYxUBeR2u3nvvfd44okn7Lrdu3fTs2dPvvjiiwhGFl6OBAcpp6TY5SPuLUrdAB/0gc1LgnX1jodrZkOrgUd27eJyOKDTdXD5NEjO95jur4nw6XmQU/pVz90ON4NbDLbL36779kgiVUpVEJoYqQpJRHjggQf47LPPiImJASA3N5cLLriA5557rkJuQFu1S1Ucsda3tN9bBe++NqW/2I5VMKoP7PkvWHfCCLjie6je7AgjLYVGJ8M1P1uz3fZbNwc+HgSZpR9Ddu7R5yJYA8Q3Zm6kyrFVjjRSpVSU08RIVWjDhg1jxowZVK8efMR0zz33cN111+H1Vqzd1audGpwO7007EUwpV+PY/Ct82Nca07Nfr4dh0Cvgjjv0eeFWpQZc9CUcPyxYt/V3q1crrXRbwjRIbECXBsHFL/P/N1RKVU6aGKkKr3v37ixYsIDmzZvbde+88w6DBg1i3759EYwsdOKaxBHfON4u56WeXLoLbfvDWr06e2+gQmDg/6wp9WHcqqPYnC44+03odH2wbve/8PFZpZ7Of27Lc+33yScl40jQH4tKVWb6E0BVCkcffTQLFy6kU6dOdt13331Ht27dKsQGtNW65+stymiIyatV8ovsWQNjhkBOYIsMhxvO+wBOuiJEUYaIwwF9nrKWCdhvz38wZnAw9hI4reFpVIu1/vs5YhykdEw5zBlKqYpMEyNVadSqVYuffvqJ884LLu63fwPa33//PXKBHSnxktIp+Ms8b/fxJb5EbfbCJ+dAxvbANR1WUtRmSIiCDDERa5mAXg8H67atgM8uBE92iS7ldroZ0HyAXa7WTR+nKVWZaWKkKpX4+HjGjRvHnXfeadft34B22rRpEYys9Nwpq3ElWuOJ/Ll+PKnHlej8ZDL5JOYZSF0frBz0Khx3VijDDI9ut0PnG4PlDfOtVbJ9JRs/NrhlcHZawlEJxDaIDVWESqkoo4mRqnQcDgfPP//8QRvQDho0KCo3oHXXCO6LlvZLGviL/0vdgZ/X3K9xrGNjsPLMJ+GES0IZYviIwJlPQIeLg3X/TLf2cSuBo6sdzTEpx9jl/I8mlSqvRGSQiCwUkb0iMkNEDjkV9XBtRSRRREaJyBYR+UdEHhUJDiwUEYeI5ImIOeDVJ5yfMRI0MVKV1nXXXcekSZOoUsWaor1/A9p77rkHv98f4eiKR1ypuJLW2OW9P+8tovXB7nWNpYdzebCi2+3Q5cZDn1AeicDAV+DYfGsrLXwTln5aossMaBJ8nFa1S1W8/oo1a1FVLCIyAPgKGA10AnYAs0WkfknbBhKgH4A2QB/g9sDr6XyXaQi4geZA1XyvH0P92SJNEyNVqfXv35+5c+dSv37wZ8lzzz3HhRdeSHZ2ycaqRII75Vd7slju9lyy/s4q9rlDHD9ztWtKsKLVWdCzZD0t5YbTBUPehbrtgnWTb4WNi4t9id4NeuP3WAmxK9nF/O0Vf6V0FdVGAhOMMW8YY1YDV2D9Tr+6FG0HYCVMI4wxK4wxk4AngRtEJCnQpjmQZoxZa4xJy/eqcH9BaGKkKr327duzaNEi2rUL/lL98ssv6dWrFzt3hm5H99Dz464a3BU+dW5qsc9sL//ytHuUXf7L3wQGv23N+IpWMVXgws+gSmBGni8PPh8OaZuLdXpSTBLpS4IraU/dMDUcUSp1xESkGXAS8PX+OmNMDjALK8kpadvzgVXGmFX5Tp0GJAKnBsrNgEqx6WQU/xRUKnQaNmzInDlz6NMn+Lh8wYIFdOrUidWrV0cwskNzxq/DEbMHAOM3pM5LLdZ51UjnrZiXiRUPALtNElfl3W4lFtGuaiMYOjq4t1rmDvjiUvB5inX63rnBR5ELty9kV3bpV9VWKoyaBL6uOaB+A9Yjr5K2bXKI4+Rr0xxoIyI7RWSliLyQrzepQtHESKmA5ORkJk2axNVXB3ui16xZQ+fOnfn5558jGFnhXClL7feZf2Xi2VOcX/6G593vUE+shMpjnFyXdyubKcW6R+VVk84w4MVgefMS+OmJQ7fPJ/OvTPJ25wHgMz6+W6sby6qwiRGRPwt7FePcuoGvqQfUZwAHzhwoTtu6hzhOvjajgOOBfsDbwGXADBGpcFM4NTFSKh+3283bb7/Ns88+a9ft3buXM844g88++yyCkR1APLiTV9jFvfOKN+j6cud39HYGE6pnvBey2LQKeXgRd+II6JBvZt28l+HfYowRNZC2ILhI5KQ1k0Ifm1JHbn9XZvIB9SnAtlK03XWI4+xvY4xZZ4xZbYxZYox5BbgUOAXoWvLwyzdNjJQ6gIhw9913M27cOGJjrT+G8vLyGD58OE888US52IDWlbgSceYAYHxu0n89/C7zbWQN97mCyd2Pvg6M8vUPW4wR1+9ZqBmcgs/X18C+7Yc9LXV+qv3+r91/8V/qf4durFTp5RljWhf2Ksa5+5frb3pAfZN8x0rSdtMhjuc//0D7u9HbHeJ41NLESKlDGDp0KD/99BM1atSw6x566CGuvPJKPJ7ijVkJF3fKb/Z7T+qxmLyik7UqZPOa+zVixAfANlONuzzXAOVg/7NwiakC538IzkBPf+ZO+PpqOMxSDLlbcsleG5yROOk/7TVS5c7qwOvs/RUiUgU4DZhQirYTscYPNc933kBgJzDnEDGcFPi67BDHo5YmRkoVoUuXLixcuJCWLVvadR9++CH9+vUjNTU1IjGJMwNn4t92OW9v28Oe85BrNM0cVm+Jzwi3em5gz0E95xVQndbQN99SLGtmwaK3Dnta/l6jyWsm4zfRsa6VqhyM1W39FDBcRK4WkWOAj4A04EMRuVxEdolIu8O1DVxyPFby9ImItBGRs4G7geeNMbki4hKRB0XkRBGpHzj+MfCtMWZmGX70MhH1iVFxV/4Ukb4i8p2IbA2Mqv9aRJoc0KbIlT9V5dSiRQsWLFhAt27d7Loff/yRrl27sn79+iLODA9X8jJErF/Ufk8yvn1Ni2x/muN3LnTNssuv+waz0F+ybUOi2klXWGs07ffjY7Cr6FnHqQtTcYoTgO1Z2/ll2y/hjFCpEjPGfIK1DtFNwDwgFuhijEkF/EAO4C1GW4wxHqAHgYUfgceB+40xzwduVw04Aatn6V/gCawB2OeH+WNGRFQnRiVZ+RMYgfU/tRvW2g1NgB9ExB24VnFW/lSVVI0aNZgxYwYXXXSRXffXX3/RsWNHfvmlbH9pFniMltaBor6Nk8ngGfd7dnm5vxmvec8JY3TlkAgMfDm4vpE3B765Dvy+Q57i2+fjlNqn2OVv//s2zEEqVXLGmFHGmLbGmJrGmLOMMRsC9R8bYxoaY/46XNt8x7cbY4YYY2oYY9oFBljvP7YzcKyhMSYhcJ2njTF5Zfdpy05UJ0aUYOVPY8wwY8xbxpj/jDGLgTuBlkD3QJPirPypKrHY2FjGjBnDgw8+aNdt376dHj168M0335RJDI6YHTjjgwsWetM7FNn+YfcY6oo1Yy3XuLjTcy1eXGGNsVyqUgMG/i9Y3rQYFrxR5Cl9GgXXtJqxfgbZ3vK/ErpS6shFbWJUkpU/D2H/FMb9SU9xVv5UlZyI8PjjjzNq1ChcLivByM7OZsiQIbzyyiuHOfvIufL1Fvly6uPPrXvItr0cv3KeM7j+0sve8/jbNAprfOVaq0HQdmiw/NMTsPPQi3d2q9uNRHciAFneLH7cUOG2hFJKFSJqEyNKtvJnYboCBvg93/UOt/LnIRWxUFdMMWJRUeaKK65g2rRpJCdbA5iNMdx6663cfPPN+HyHfkRzZPy4U363S9ZjtMIlk8lT+bb8+N1/FO/6ivP3QgXX71lIrGO99+XCN9cf8pFarDOWM5ueaZenrJlSaDulVMUSzYlRSVb+LEBEEoEHgPHGmP2jZ4uz8qdStt69ezN//nwaN25s17322msMHjyYjIyMIs4sHWf8BhzuVACMEbxp7Q/Z9i7XOOqI1TbXuLnDcy0+nCGPKeokVIdB+Xr2Ni+BJR8csvmAZsFkcsGWBezJ2RPO6JRS5UA0J0YlWfnTFhhkPRpwYQ2uzn+9Ilf+LEoRC3VVyMFpytK6dWsWLVrESSedZNdNmjSJHj16sGXLlpDey5Wvt8iX2QLjK3zoW3vnGoY7g499XvEO5j/TIKSxRLVj+kGb84LlHx+DfYV/i59Y50RqJ9QGrC1Cvl/3fVlEqJSKoGhOjEqy8md+LwNnAoONMfnblWblT6WoW7cus2bN4uyz7fXT+O233+jUqRMrVqwo4syS8OFKWm6XPOnHF9rKKfB0whgcYi34+Le/Ae/5BoYohgqkz1MQG/i7Jzcdvruv0GZOh5N+TfvZ5alrp5ZFdEqpCIrm6Sn5V/OcAAVW83y4sBNE5DngKmCgMWbBAYcnAheISHNjzP6xRodb+VMpAKpUqcKECRO46667+N//rNlPGzdupGvXrowfP54zzzzzMFcomjPxHxyuLACM34V3X6HLdXFLpxhaO4N5/AOeK/GE6Nu86b2lH2Pjzyn4aLHdyOk44hJLfJ11z4RonFRSHThjJEy+zSr/+RWulmcX2rR/8/58/NfHACzdsZTNGZtpkKg9cEpVVFHbY1SSlT8BRORp4BbgEuBXEUkJvOIDlyxy5c+y/XQqGjmdTl566SVee+01HA7rW2vfvn3079+f99577zBnF82d/Lv93ptxLPjjDmrTOEV47LTgRtefe0/jF3PsEd23QjvhMmgYXKso/qcHiS8kh2xVvRXNUprZ5Wlrp5VBcEqpSInaxAiKv/KniHQG7sWaITYea5D1/tebgWsdbuVPpYrlxhtv5JtvviEhIQEAn8/H1Vdfzb333ov/MPt0FUrycCX9aRe96e0Lbfa/PnFUibEWat9tknjGO6zk96pMHA5rbaPACtfO9I3c2y32oGYiQv9mwc12dXaaUhVbVCdGULyVP40xC4wxcojX5fmudciVP5UqiUGDBjFnzhzq1atn1z377LMMGzaM7OySLRToSvoLcVib1hpfHN6MYw5q07OZkyGt3Hb5Kc9wUtF1SQ+rbhvofINdvKtLDE1SDt4FKH9i9G/qv/y99++D2iilKoaoT4yUKq9OOOEEFi5cSNu2wU1ev/jiC3r16sXOnTuLfZ38j9E8+9qAcRc47sLLK32Dj9aWeJszwd8dVUw97oZEa/WPeLfwwpmFPKZMbky7mu3ssvYaKVVxaWKkVBg1btyYuXPnFhh8vWDBAjp16sTq1YdedXk/cWbiTAz2ThS2dtElMbNpU9t6HOQ3hkeyhwG693GxxSbBGY/axfOOc3N604PXfOrfPNhrNG3tNPymFI9FlVLlniZGSoVZcnIykydP5qqrrrLr1qxZQ+fOnZk9e3aR57qS/kDE+gXs9ybhy2pe4Hh10rk9bpJd/mCphxW+JqgSajsUb93gSuKv9I0Dv7dAkz5N++AQ60fm1sytLNu5rExDVEqVDU2MlCoDbrebd955h2effdau27t3L2eccQajR48+5Hmu5OAvX296Ow78lr3D9SUpDmsaf1qO4f4fdQJlqTgcZJ8W7DVqW8dJzPIxBZrUjK/JKXWDs9h0dppSFZMmRkqVERHh7rvv5ssvvyQuzhrH4vF4uPTSS0md+xnWChT52rvScSastcuetIKLOh4rGxjm/Mkuj5ydy86sgtdQxeerezyjlgYXqo9b8BJkFdwCpF+z4GKP09dNx3tAr5JSKvppYqRUGTvvvPOYOXMmtWrVsuvS5n3G7ikvYbweu86VtBwJrGDtz6uKP6dRgevc7/rUXuF61S4fry/W3WeO1P0/5pKea/03deSmwZwXCxzv1bgXLoe12NGenD0s2b6kzGNUSoWXJkZKRUCnTp1YuHAhxxwTnHqf+edMtn/5ML7AKtHu5AO3AAkOqO7uWM6pzuB2I3f9kItXxwIfsR2Zhqfn5nscufhd2LvOLqbEptC1fle7/N3a78owOqVUWdDESKkIad68OfPnz6dHjx52Xe6GFWwbfSfejFU4EzbY9d58e6M58HO/6zO7PN9zNJP/1kc6ofLywjw2pgWyTF+etclsPn2b9bXf/7D+Bzw+D0qpiiOa90pTKupVr16d6dOnU+PEfmT+ORMA755NbPvoIWKr1SOhRQK+3Fr4c4MLRZ7r/JlWjmDS9GTO+YA+0tmvtHu67d/PLccLD/yUyyeDA7sF/TGBs389nmWmhVV25JHY0oU4vKTnpXPs06/iyyi49UrI9nRTSpU57TFSKsJiY2OpMeB2UrpeZNf5MrNZ++xa0hanBWajWY/R4sjlDteXdruvfV11en4YjFnu4Q9vcEzX/e7PgMDAdn8s3oxW9jF3sk7bV6oi0cRIqXJARKja7SJqDLwDHNbigsZj2PjmRnZN22zPWLvSOY26sheAXOPmBc/QiMVckRngyZzz7HJHxyrOdAR75axk1eJK/BNEH6cpVVHoozSlipCTk8Mzzzxjl++99157qn04JLY+nbiG69k2+mt8mT4A9v40Hs/ufTQ/42KuiQ0u5vihrw+bqQVkhC2eymyetxUzfcdzutPqEbrT9QUz8k7EjwNvxrEYXwzizEOcebgSV+Hd1/YwV1RKRQNNjJQqQk5ODo8+Glz479Zbbw1rYgSG5A67SWjSnHUvrcOz0+qJyFg2HU/6MszQLIgT0kwCb3rPCmMcCuAZ7zB6OJbjEMPRjs0Mdsxlgv9UMG68Ga1xpywFwJW8XBMjpSoIfZSmVDniiN2OM3YnsfViOeqho4ht2MI+tnLtNrp9mMmGND9ve88incQIRlo5rDaNmejvYpdvc48nBitZ9RR4nLYKRFcdV6oi0MRIqXIk/xYg4m5KnQueI+HY7nbdHzv8nPx+Fm9tblHY6SoM/uc9D4+xxn01lF1cGFht3JfREuOzeg/F4cGVtCpiMSqlQkcTI6XKDYM7Kbhooye9HeKK4cSzL+HursHHdzsy/Gz47CGy/lkYiSArnQ2mDp/7TrfLN7m+IZ4cwIV3X2u73pW0vJCzlVLRRhMjpcoJR+xWHLG77LI33Rqzcof7K57tHcP7g+JwBb5jjSeXnV89SfqSieB0k9J1mP0SV0wkwq/QXvUOJttY/11rSRqXO60Vrws+TlsNDn2cplS0C3liJCLXh/qaSlUGrnxbgPiyGmO81ThWNnC2cz4AV54Qw6ChFyIxCYFWhr0/vkfqrA9J6XIhVbsNp2q34ZoYhcFOqvGRr49dvtY1mWQy8GW2wHit/x/i8OJK/CtSISqlQiQcPUavi8izYbiuUhWYOWBvNKsn4lbXBLtutb8hvze5iLoXP48zObgB7b7fJrPzqyfw52WXXbiV0NveQaQbKwlKliyudE0DnHjyP05L1sdpSkW7cCRGzwN3icg4ETnoT1cR6S8is8NwX6WiliNuM46YPXbZu68trWUtfZ2/2HUvec/Dj4OYWk2od8lLxNRtaR/L/u8Xtn16D959u1DhkUYi73v72+UrnN9RlX149+V7nFblb3BogqpUNAt5YmSMuQe4BBgE/Cgi1UXEISLDRWQZMBnoHOr7KhXN8vcWebOaYrwpBXqL/vQ34Xv/SXbZmViNOsOeJr5lJ7vOs2MN2z65g7wda8om6EroQ19fUk0VAJIkm6tcU/BlNsfvterE4cOVpI/TlIpmYRl8bYz5FOgC1AYWA/8Bo4EmwP+Aloc+W6nKxRhTYEaTN70t7eQ/znD+Ztf9z3se5oBvV0dMHLXOuY+kk8+x63wZu9n26T1k//cLKvT2kcC73uAGsZc5p1OdTLz72th1bn2cplRUC+estIbAdqA50Bi4F2hgjLnDGLM+jPdVKqqs2LUCR0wqAMYI3n1tuc013j6+3N+MGf4TCj1XHE6q9/w/qp9xHYj17Wzystkx4XH2/Va6XeZV0T729WGPsRbXrCK5XO2aXGDvNGeVf0jLTYtUeEqpIxSOWWlXi8gqYCJwPPACsBq4ATipqHOVqoymr5tuv/dlNaW9b7u9PxdYY4tAirxG0gkDqH3uQ0hMvFVh/Oz54S32/PQ+xu8LR9iVVibxvOMdZJcvdf5A1azq+L1WsiTi56cNP0UqPKXUEQpHj9HbQA3gEaCJMeZurDFF/wE/iMgtYbinUlHJGMP367+3y9597Qr0Fi31t2CWv32xrhV/1MnUvehZnIk17Lp9v3zDzm+exp+XE7KYFXziO4NdJhmABMnlWtcUvOnBx2n5/58qpaJLOBKjO7ESoieMMakAxpg04EzgU+B/IvJRGO6rVNRZvms52zK3AdZjtGP2VeFUZ3D16/95z+VwvUX5xdRpTt1LX8Rdu7ldl/3PQraPvQ9fxt6QxV3ZZRPH2/l6jS52ziBhX/C/+cItC/VxmlJR6ogTIxE5XkSc+8vGmJeMMVkHtjPGeI0xlwMPARcf6X2VqggKPkZrxm0SLP/mb8HP/naFnVYkV1JN6g5/lvijTrbr8rb9w9bRt5O3c90RxauCxvh6szPQaxQveVyV94f9OM1rvPo4TakoFYoeo6XAPhFZICKvichlItJGRAq9tjHmSeCiENxXqajmN35+WP+DXa69rz69nEvt8qveIZSktyg/R0w8tYY8SNIJwRlUvvSdbBtzN9lrlxZxpiquHGJ5L98MtRHOH3CmH22Xp6+fXthpSqlyLhSJ0TPAHOBorAHWo4BlQLqIzBWRl0XkEhE5bn+yZIz5IgT3VSqqLd9Z8DHazdkr7WPL/M2Z5T/+iK4vDifVel9LtV5XsT/BMnlZ7PjyEfYt01/aoTDGd0aBGWoDs9LtY4u2LNLHaUpFoSNOjIwx9xtj+hhjamCtT/QrsCHwtS1wM/ARsALIEZF/RUR/KqtKL/8A3bisepxL/t6iwZS2tyg/ESH5pLOpNeQBxB1rVRo/e757jb2zP8IY/xHfozLLIo738/Ua3Z23AAKLPerjNKWiU0gHXxtj/sNa1PF/xpgexpgU4Fis5Oj3wP3WA01DeV+loo3f+Pl+XTAx6p+ZYb//09+EHw+xblFpJbTsRJ1hz+CsUs2uS184nl0Tn8Pv0R3hj8QnvjPs1bCrSjatMhLsY/nHkCmlokM4ZqXVAOzNgowxfxtj3sBaw+gZYBdWsqRUpbV853K2Z20HwIFwS3ZwG4lQ9RYdKLZeS2vGWq2mdl3W6rls//x+fJmpIb9fZZFBAh94+9nlG7L+sd8v2rqI1JzUCESllCqtcCRGq4HuB1Yay4NAAtYaR0pVWvl7Ek52JlHDbz3SWuVvVGBPtFBzJdem7vDniGsW7JHK27KabaPvYOXKlUWcqYryka8P6cbqKeqWm05Np7XQptd4+WmjPk5TKpqEIzEaC5wvIofaKPYb4LIw3FepqHDgbLQzdwR3yHnDe/ZBe6KFmiM2gdrnPkxi+752nTdtO126dGHmzJlhvXdFlU4VPvadCYAT6L0vOAhbH6cpVXwiUk1EXJGMIRw/gV8GfgO+EZHBhRzvAFQNw32VigoFH6NBr4xMANb46zLF36lMYhCni+pn3kDV066w61JTUznzzDP56KOPyiSGiuYDb1+yjDXAvU/aHrteH6cpVSK7gMJyhzIT8sTIGOMDLgT2AuNFZKmIvCkij4nIDOA6YG6o76tUtCjwGC07136M9pbvLPxh7i3KT0RI6TiEmufch7hiAPB6vVx++eU89NBDGGPKLJaKYC/JfObrCUCHnFxq+q3/fj7j08dpShVf6AdYllBYfgobYzYC7YDHgSbAtcCDQE+sNY6uC8d9lSrvDnqMlmn1Fm02NfjG1y0iMVU5pit1hj1N7dq17bonnniC4cOHk5Oje6yVxLvegeQaF07gjH3BmYb6OE2p6BG2P0+NMXnGmJHGmOrAUUB/oIMx5oRA4qRUpVPgMZox9Mq0ds95xzsQD5F7rB5b/xgWLlxIq1at7LqxY8fSu3dvdu3aFbG4os0OqjHe1wOAM7OCOyPp4zSlokeZ9NsbY9YaY74zxiwri/spVV4VeIyWE3iMVqUW43ynRzAqS7NmzZg/fz69evWy6+bNm0fnzp35559/ijhT5fe2byCI03qc5vUB+jhNqWgS8j9RA6PJTwYaYS32mADsBHYAvxtjNof6nkpFg4MfowV6FDrfQO7kmAhFVVDVqlWZOnUq1113HR988AEA//77L506dcLd927iGrWJcITl30ZTB9qeh3P5OM7IzGJsShJgJcVDWg6JcHRKRYUeIhJXkhOMMaNDdfOQJUYi0hu4EWscURUKH0BlRGQlMA54wxizp5A2SlVIhT5Gi0uBk66EyXMiHF1QTEwM77//Pi1atOD+++8HYM+ePTDuQWr0u4XE1pHv3Sr3ut0Oy8dxZlYwMdr/OK1qXNXIxqZU+XcdxR+LLIAByk9iJCLHAe8DnYBFwEvAbKytP3ZhrYJdA6v36ATgdOA24G4ReQJ43uiGTaoSyL832kn7H6OdfBXEJUcwqsKJCPfddx/NmzdnxIgR5Obmgs/L7skv4k3dRkqXCxGJ+OSR8qv2sXDMADqsnkJNr49dLqf9OE17jZQq0shIBxCKHqPfgMnAScaY3w7RZlvgtRz4SEQSgMuxZqoBPBuCOJQqtw7cG61PZha44qFT+Z6gecEFF9CoUSPOPvtsexB22txP8e7dQo2+NyMud4QjLMe63YZz9RR9nKZUCRhjHot0DKEYfH2uMea8IpKigxhjsgL7p7XC6l1SqkIr9DHaCZdAlZoRjuzwunTpwsKFC3FVb2jXZf45k+1fPIQve18EIyvnGp0MTbvr7DSljoCI3FfW9zzixMgYM+UIzk01xiw80hiUKu8OeoxmBLrcFMGISuaoo46i7iUvENu4rV2Xu/EPto25C8/erRGMrJzrdhsdcnKp5fUCOjtNqVJ4UkSuPdRBsVwcyhuGdbq+iNxUnFc4Y1Aq0gp9jNb2fKjaOIJRlZwzLpE6Qx+jSpuedp13zya2jb6DnE26AW2hjuqJs97x9M7Mtqt0sUelSuQj4HURGXbgARG5APgT+DiUNwz3Oka3FeN165HcQEQGichCEdkrIjNE5JDziUWktYhMFBEjIiMKOf5Q4Fj+14IjiU+pQh+jdbs1skGVkjjd1Oh/Gyndhtt1/ux0tn9+P5krf45gZOWUCHS77YDHaQv1cZpSxXcl8CnW+OQBACIyRESWA58B9YEnQ3nDsCZGxpjmxXgdVdrrB/4jfYU1Ta8T1lpJs0WkfiFt2wO/Ap4iLtkMeBdrk9v9rzNKG59SUMiiji37Qu1WRZxRvokIVbsOo8bAO8AZmL/h87Dr2+dIW/CF7rF2oFZn0SGhQb7HaX5+3PBjhINSqnwSkdj8ZWP9QLkMa5mfL0VkGTAeaAg8BjQxxjwcyhjKbsfKABFxi0hS4FVVRI7kecJIYIIx5g1jzGrgCqzPdHUhbVdj7d92RxHXaw6sNMak5XtlFNFeqSL5jZ/v1wSH4Z2ZmQVdb41cQCGU2Pp06lzwBI64JLsu9edP2D3tFYyv4N8f4oohpesw+7V/09pKweHE2fUWzsj3OO37/yZHMCClyrV0EflVRN4Rkf8TkeOxfq+PACYAbYHngabGmEeNMWmhDqDMEiMRaSUiS7DWNUoNvHYDa0t5vWbAScDX++uMMTnALGDAge2NMdnGmL8Pc9lmwL+liUepwizfuZwduXuBwGO0aq2hcccIRxU6cY3aUPeSF3BVq2fXZa6YwY4vH8GfE/ybQlwxVO023H5VqsQI4PhhnGmCC/ku2vEre3P2RjAgpcqtH4EGwFVYT3B+A9KBOcBeYAPWmoiZ4QqgLHuM3gKmYn2YvsAgYAFwfimv1yTwdc0B9RuwuthKRERiAud9IiKbReR7ETmzBOf/WdgLqGS/AVR+0/8aa78/OSeXGt2K6rCMTu7qDah78QvENjzOrstZv9yasZa6LYKRlSOuWDqccE3wcRqGn/4r9YRepSosY0x/Y0xdrG3FBmONH5oNtMTaXaMx0AvYIyI/i8grInJZKGMoy8SoDfAIsAnYYoyZCgwH7i7l9eoGvqYeUJ8BVCvF9QxwItAZ65FcDjBVRM4rZXyqkvMbP99vmGGXz3SkQMti59pRxZmQQp0LniThuB52nWf3RraNvoPczasiGFn54Tj5Cs7I8dnl6X+OiWA0qiIo4eSjItuKSKKIjBKRLSLyj4g8Kgcsb1+S+x0pY8xmY8xEY8zDgWSpDlaHyBCsZGk+cCxwEzAqlPcuy8QoA2sPtXnA/ml3VYCjS3m9XYGvB+6nkIK1ynaJGGM8xpjfjTGrjTHTgXOAJcDNxTy/dWEvIK+ksaiKYdnaGeww1v9+hzH0PvE6a5ZSBSUuNzUH3klKl+CsWn9WmjVjbdXcCEZWTsSl0KdJcC7H4qxN7M3YHsGAVDQr4eSjItsGEqAfsDow+gC3B15Pl+Z+4WKM2WiM+cYY85Axpp8xpjbQFAhpB0ZZJkZfYk2rexG4RkQ2A78Dk0p5vU2Br00PqG+S71ipBfZvm4s1YFupEpv+6+v2+5O9UL39pRGMpmyICFW7D6dG/9vAYc1YM948dk18hrRF4yv9jLX2pz5Aba/Va+QT4ceFz0c4IhXFRlL8yUeHazsAK9kZYYxZYYyZhNUrc4OIJBXzGhFhjNlgjPn68C2Lr8wSI2PMXcaYvwP/QU8EnsDaL+3KUl5ydeB19v4KEakCnIY1cj0UTgKWhehaqhLxZ+3mh33/2eU+DU8DZ+XZVyyxbS/qDH0MR2wVuy511kfsmf46xueNYGSR5UiuzxlVmtjl6et/AL/uoa1KpiSTj4rZ9nxglTEm/3PvaUAicGpJJzuFkogcLSKzRSRLRHYGZqy9JyLXisgpIhJ3+KuUTCSm6zuwRpaPAb4F4ktzncDaBk8Bw0XkahE5BmuFzDTgQxG5XER2iUixenxEZGBg0aimInKsiLwNdKX0Y6BUJbZ07jPscFrfXk5j6NXl3ghHVPbimrSzZqyl1LHrMpZNZ8f4R/Hnhm1CSbnX54Tr7feLnT72/PllBKNRERRTxKSdwynJ5KPitG1yiOME2oR0slNxiMgtYm04/wHQHdgJrMcalH0l8CbWBK70wNpGIeMK5cWKIiItsKbedQJiDzjsLM01jTGfiIgba/Xsp7AGY3UxxqSKiB9rAHVx/zytFbhOMyAL+AU42Rjze2liU+VH03tLP/sn/5RzgHYjp+OISyzynFjyGFp/IqRY/8zrZqVQPTksPzvKPXeNRtS99CV2Tnic3C3WH6M565aybcxd1D5vJK6U2hGOsOwd33IAtRc8wg48+EWY8curDG17QaTDUtGlJJOPitO2LtYCyAceJ9Am1JOdiuNhrDFNHYBxxhh78KKINMSasn9i4NUhlDcus8QIqzcnC7iOUq5dVBhjzCgKGZFujPmYQvZPMcasBw4aAWuM+RD4MFRxqcprsPNn5lYJfmttS+8WwWgiz5mQQu0Ln2T31JfJWjUHAM+uDWwdfTu1z32Y2HqlnX8RnRzi4MxGpzNmo7V/3vS8HQzdsBAad4pwZKqM5QUm6JRGSSYfFaftrkMcJ9AmpJOdSmgj1iM7mzFmE9ZY4m/DccOyfJTWCjjLGPOxMebn/K8yjEGpsHLgp3OVaexyWZ2gDgOp+06McFSR53DHUvOsu0juFFy2zJ+ZyvbP7iPr7/kRjCwy+rYNDsRfEhfLrrkvRDAaFYVKMvmoOG03HeL4/mNhneyU34FbggDvE+JZZ4dTlonREqxng0pVWGc4lrAiKccuOzKbgq/KoU+oREQcVOsxghr9bgaHlTgaby47v36a9MVfR3zGWlluW9KuZjvqxVhPIPwizNi6AHauDtv9VIVTkslHxWk7EWgjIs3znTcQa1zPnBLe70ili8hvWAO/hwHfA9tF5H8iUqphNyVVlonRa8DXInJpYJEo+1WGMSgVRoarXd/yQ5UEu2Zf+kkRjKd8Smx3JrXPfxSxZ6wZ9s4cxZ4f3sL4fUWeG05luW2JiHBmi+CPvu+qJMD8V8N2P1WxlGTy0eHaBi45Hivx+URE2ojI2VgTj543xuQW8xqh8gPWmF838AywFGsF7JuB30Tk5sAEqbAtCleWidG3wHFY/zEn5nt9U4YxKBU2p8gqPAmb2eMM/FFjHHj3HVf0SZVUfNP21L34eZz5Z6wtncqO8Y/hz82KYGRlp2+zfvb73+Ji2fHHl5C+JYIRqWhijPkEaw2hm7AWTo4lMPkIKDD56DBtMcZ4gB4EFm0EHgfuN8Y8X8z7hfJzDTTGNMIa6H0F1iDs74EtWBvIvgz8CewTkfki8qaI/F8oYyjLxCgBcBpjHAe8yqRrTKlwu8Y1men5eou8GUeDP6GIMyq3mJqNqXfJC8TkG3yds/ZXtn16N970nRGMrGy0rtGaBokNADAi/BDvhkVvRzgqFU2MMaOMMW2NMTWNMWcZYzYE6j82xjQ0xvx1uLb5jm83xgwxxtQwxrQzxrxS3PuFyXbgR2PMk8aYwYFkqR7WPquPYw3Ibg5cC7wTyhuX5QKPOSbSgwiUCpOjZSOnOpcyI19i5EnXRdMPx1mlGnWGPUXC0V3sOs/OddYea9v+jWBk4Sci9Gnaxy5Pr5IASz6EnPQIRqVUZAXWLsIY08oYszH/sUDyNsUYMzLQs1QXa1PZc0MZQ1gTIxHpne/9oEO9whmDUmXhatcUfomPIzXwGM34nXgz9DFacTjccdQ8516SOwZ/tvky9rD9s3vJ+ndRBCMLv/yJ0dK4OLZ5M+HXjyIXkFKRty3weOz44jQ2xmwyxnwTygDC3WP0ZL73Ew/x+ibMMSgVVnXZzdmOedYA2gBv5tHgD/lK9RWWiINqp11O9T43glg/lownh51fPUn6krAsVVIutKreikZJwcm606skwMI3wat7T6tK6yHgVKyB1osCA8lLtUNGaYU7MdqXb02C0woZX6RjjFTUu9z1HYiPGQn5EqP0Yv2xow6Q1L4vtc8ficQEfg4aP3t/fJc9M96J6Iy1cBER+jbta5enV0mAfVthReHbhOTk5DBy5Ej7lZOTU2g7paKVMeYVY0wbrORoFfA6sFVEXhORtmURQ7gTozZYaxFAvs3nlKooksnkIudPzI+PY19gbzTjd+Pd1yrCkUWv+GYnWDPWkmrZdft+ncTOr54gIyOjiDOjU99mwcRoRVwsm1xOa+p+IZvL5uTk8Oijj9ovTYxURWWMmWeMGQHUx+pF6gH8HpiJdmk4No/dL9yJ0VRgsYi8BySIyIuFvcIcg1Jhc5HzR5Ikm2mJwUUcvRnHgjlw8VZVEjG1mlL30heJqdvCrsv+7xdOPfVUNm/eHMHIQq9l1ZYclXKUXf6uShXYuQr+/SGCUSlVPhhj0owxrxlj2gHdsNZbehPYIiKviEjIB3OGPDE6YNGla7EWf6qHtVFsh0Je7UMdg1JlIQYPl7u+I1uEmQnBR+D6GC00XInVqTPsGeJbBvcQW7p0KR07dmTZspBuph1RIkKfZsFB2PZYtbkvRyYgpSJIRM4RkUJ36jbGLDDGXE7BXqQVIjJXRLoUdk5phKPHaNn+2WjGmDxjzBPGmIHARGNMz0JevcIQg1Jhd45zLnUklTnxcWQ5Ao/RfDF4M46JcGQVhyMmjlrn3EfSyefYdZs3b6Zbt25MnTo1coGFWP5xRqtjY1jjdsGG+bDxlwhGpVRETADOKKqBMSbdGPOGMaY90AVrLFLnUAUQjsSoKTBdRKaKiD3Qwhhz/qFPUSq6CH6ucU4G4LsCj9Fag3FHKqwKSRxOqvf8P6qfcR2OQAKakZHBoEGDeOuttyIcXWg0S2lGq+rBcWn2QqHzD1pjT6mKrtCtPkSkioiMF5Gm+euNMYuMMf9njAnZsJxwJEbNgFewNpdbJiJviEitok9RKrr0dvzGUY6tZIrwc3xwDKBHH6OFTdIJA5g0aRKJiVYvu9/v5/rrr+eOO+7A54v+GWv51zSaVqUKBmDlZNhVsRe6VKqYnMAQymAz+pAnRsaY3caY24GWwMfAVcA/InK3iIRvV0alytA1Lqu3aGZCPLn2Y7R4fBktijpNHaH+/fszd+5cGjRoYNe99NJLnHfeeWRmZkYwsiOXf3ba2hg3f8e4AaObyypVxsI2K80Ys9kYcxXQGpgGPA38LSIXhOueSpWFE2U1Jzn+Bgo+RvOktwFcEYqq8jj++ONZtGgRHTp0sOu++eYbTjvtNLZt2xbByI5Mg8QGtKsV3EZm2v7HacvGwr7tEYpKqYiI6PZhYd8rzRjzjzFmGNauuLOBT0RkQbjvq1S4XBvoLUpzCHPj889G073RykqDBg34+eefGThwoF23ZMkSOnbsSN7OdZEL7AjlH4T9XVKy9dvBl6eby6rK5kEReVlErhGRU0WkJocYexQOYUmMRCRRRE4UkYtE5DERGQeMAc4G3MAp4bivUuHWwrGVM5y/AjAjIQFf4FvV703El9U8gpFVPomJiXzzzTfcdNNNdt2GDRvYNuYustf+FsHISq9P0z5I4Of/ZqewPDYw+uCXUZC7L4KRKVVmFgOtgJuBt4CZwHZgLVZP0iUiMkBEaocrgHCsY7QJSMP6cGOAB4H+QB7wJXAr0PtQ5ytVnl0TO91+/2Vidfu91Vuku9uUNafTyauvvsorr7zC/iXUTF42O74cyb7fv4twdCVXO6E2J9c92S5PTa5mvclN081lVaVgjOkEJGENw7kYeAkrOfJj9Rr9H/At1jYh6wMz1e4OZQzhGBCRDswFVux/GWPWhuE+SpWpBknC4Bhrt/cdTid/xgV7dnU2WmTdfPPNNG3alGHDhpGVlQXGz57pr+NN3UbVHpciEvZRAyHTr1k/Fm9bDMD05GTu2rnd+kG94E04RodoqorPGOMHVgZen+2vF5FGHLxI9BBgMPBcqO4fjllpxxljLjTGPGmM+VaTIlVR3NIphhixpoWPq1LTfuLtz6uGP7txBCNTAGeddRY///wzznw9eemLxrNr4rP4PbkRjKxkzmhyBi6H9Tfrbn8ui6sEFgHet4WYVRMjGJlSkWWM2RjIKx41xpxjjGkC1OQwC0KW1BEnRiLS5gjOdYqILhOsyr2UWLjmxOBqE19WqWm/t3qLymxcoCrCiSeeSN1LXsRdq6ldl7V6HtvH3o8vMzVicZVESmwK3Rp0s8tTGwYXfoz99W39l6ZUPsaYPcaYn0J5zVD0GP0qIk+ISI2SnCQi/YClwNAQxKBUWF13cgzJsdavpBXOJPbGBQfCetPbRygqVRhXci3qDn+OuGYn2nV5W1ezbfQdeHZtjGBkxde/WX/7/Y/+feQGxk859/zLwKN1SQilwikUidFArAFSG0TkYxEZLiJNDthMdv9y3t1E5GER+QuYBCwCXg5BDEqFTawTbukY7C16sUpwM2dfTh38uXUjEZYqgiM2gdrnPUxi++D0d2/adraOuZPs9eV/A9oeDXsQ77KWgsjwZjGnRbAH6Z6uuk6uUuF0xImRMeYH4GjgNqA9MBpYA3hEZJeIbBSRLKxB2bOBO4ElQHtjzFXGGJ2Dqsq1Ee3d1E20vlWyjZtfE/PsY9pbVH6Jw0n1M2+g2ulXsP9Rp8nNZMcXD5OxYkZkgzuMBHcCPRv3tMtTqwV3Vera2EXXRjoDUqlwCcnga2NMnjHmXWPM8UBD4FKsafqfAFOAF7Gm6Z8OVDfGXGqM+SMU91YqnBz4ubNz8C/01+UkiN1tl3U2WvkmIiSfMoRa59yHuGKtSr+P3VNfJvXn0RgT0QV2i5T/cdrs3cvJaBLcPFx7jZQKn5A/rDbGbAE+DfV1lYqEfu7faFnV+uvc5zd8nlQT2GyVsxpjPNWLOFuVFwnHdKFOUg12THgcf1YqAGkLxuFJ3UbN/rcgrvKXaHSu35mqsVVJzU0lz5/HjJbdOGe9tWnAoGPctK4VPTPtlIomYVvcQ0TaiUgfEWkarnsoFV6G62ODiwR+/qeXnKpr7LL2FkWX2PrHUO/SF3HXCC6tkLVyNts/fxBfVloEIyuc2+HmzCZn2uWpWRvw1TzWLt+tvUZKhUU4Vr6uLyK/Ys04mwr8JyKpga1B4g9zulLlRjfHH7R1bbDLz25z4oixhsQZ48CriVHUcaXUoe7FzxHXpL1dl7v5L7aNuRPPns2RC+wQBh4V3Atu0bZFbGx/iV2+qK0bSd8UibCUqtDC0WP0FtZqlLOBJ4GPgW1YY45WikiLMNxTqZC7zvmt/X7qPx72HJtil30ZR2N8iZEISx0hR1witc8fSWK7YG+Md+9Wto2+k5yN5WvoY/ta7WmQ2AAAv/HzXayDtXv9ALgcQtxv70UyPKUqpHAkRt2Bd4wxPY0xDxtjrsDaEG4EkAh8LSIJYbivUiFzvPxLV+efdvnphR6ST062y570DpEIS4WIOF1U73sTVXuMsOv8OfvYPu5BMv6cGcHIChIRBjQfYJe/3zyD5+cHxxbF/PE5ZO6KRGhKVVjhSIwygV/yVxjLaKw1j5oBD4XhvkqFzHWuSfb7+Ru9LK+RgDPeGoRtfDF497U61KkqSogIKZ3Op+ZZ94DTbVX6vOye/CKp88aWmxlr+ROjf9L+4dMdDnZkWr1G4s2BRW9HKjSlKqRwJEbjgUGFHTDGLATGAueG4b5KhcRRspm+zmBu/8zcPKp2qWqXvfvagNGBrxVFlVbdqXPhUzjigz2CaXM/ZffU/2F8nghGZmme0pzWNVrb5fiTq/LywuBaWix+F3J1OTilQiUcidG9QE0ReeAQx2cDjcJwX6VC4lpnsLfob189pm0xJLVNsus8afoYraKJa9iKupe8iKt6Q7su84+f2P7Fw/hyMiIYmWVg8+Ag7JTOKby5JI/03ECPVk4aLPkwQpEpVfGEIzGaibXK9WMiMiewRUhKvuO1gT1huK9SR6w+uzjHOc8uv5XTl+RTUhCXtXKy35OIL+uoSIWnwshdrR51L36e2EbBfbFzN6xg2+g78aRui2Bk0LdZX5xiPcqNqRmDp3ECby3J12u04A3w5EQoOqUqlnAkRnFAN6w1+LtirX69W0T+EpFPgOuxZqclFXENpSLiKtcU3OIDYJOpyUTPyVTtXNU+7tnThjAu/6UizBmfRJ2hj1Ol9el2nXfPJrZ9cju5m1dGLK6a8TXpVL+TXa7axXqcZpyB1bwztsGyzyIUnVIVS8h/whtjTjDGpACNgQFYA62/BmKxNpttDvQEUkVkjYh8LSKPhDoOpUqqBmkMc/5kl9/2DsIfk05Cy+Akyry9bQo7VVUg4nJTY8DtpHS9yK7zZ6ezbez9ZK6aG7G4CjxOOyWF7bmQ1/r8YIO5L4PPW/aBKVXBhO1PX2PMJmPMNGPMU8aY840xRwHVsPZLuwNr25BMrJlqD4crDqWK6wrXNOLEGmy706Twpa8H7urL7eM5m3PwZ9eJVHiqDIkIVbtdRI0Bt4MjsHOSz8Ouic+QtnB8RGas9WzUk3intUauM8FJUvskck+8BgKP2EhdD39+VeZxKVXRlOkzAWNMmjFmtjHmf4GNZNsCSUDnw52rVDglk8klzh/s8vve/uTiIqb6CrsudW4q+3dpV5VDYpue1LngcRxxwcU8U2d/xJ7pr2PKuHcmwZ1Aj/o97HK1btXwpzSGtvl6jea8BH5/mcalVEUT8cESxpgcY8ziSMehKreLnT+QLNkApJkEPvX1wpmwFkestYeW8RtSF6RGMEIVKXGN21L34hdwVa1r12Usm86O8Y/iz80s01j6Nuprv09sk8junN3Q7bZgg50r4e/vCjlTKVVcEU+MlIq0OHK50jXNLn/k60MGCbhTfrPrMv7MwJuq4zcqK3eNhtS95EViGwQX9sxZt5RtY+7Gm76jzOLoULMDebus2WjiFH7Y9APUPhaODY4/Ys4LUE4Wp1QqGmlipCq9i5w/UUOsBfKyTCwfefuA5OFKOvAxmqrMnAkp1LnwSRKO7W7XeXatZ9snd5C77d8yicEhDlLnp9rlaRunWeOdut8ebLT5V1gzq0ziUaoi0sRIVWqx5HG1a7Jd/szXk70k40r6A3Faf5n78xxIbF9Sug5DXLridWUmrhhqnnUXyZ2C43p8mXvZ/tk9ZP2zqExiSJ2Xar9fk76GVXtWQYMT4aiewUY/v1AmsShVEWlipCq1852zqSt7Acg1bt71Wo8k3FWDj9G8mSeS0vkSqnYbromRQsRBtR4jqN73ZnAE9s/z5LLzqydIXzIx7PfP255H1j9Zdvnb/7613px6V7DR+rmwfn7YY1GqItLESFVaLrxcm2+z2HG+09hBNcSVijPhP7vem3ZiJMJT5VzS8WdS+7yRSMz+da4Me398jz0/vI3P5wvrvffO22u/n7p2Kh6/B5p0gSZdg41+fj6sMShVUbkiHcCREpFBwAPAMcCvwK3GmD8O0bY18BRwFnCZMebjA44nAq8A/bDWWPoMGGnKyzbbKqQGO+fSUHYB4DFO3vZaex+7U5YiYv0v9+fVwJfdJGIxqvItvlkH6l78PDvGj8SXvhOAfb9N5pxzzmHs2LEkJiYWel7Te6eU6n7+wL5taYvTqDe8Hg63gz05ezj2qZfxZRxHV8epfBoT2NLmv584+75XWGZaFHqtdc8MKFUMSlV0Ud1jJCIDgK+A0UAnYAcwW0TqF9K2PVbiVOh22SIiwA9AG6APcHvg9XQ4YleR5cTH9c7gY48Jvu5soSZgcKf8atdbG8bq2kXq0GJqNaHeJS8RU7elXTd58mROPfVUtmzZEpZ7+rP87Pttn13e/292nr8NS/3BROhG1zdhub9SFVlUJ0bASGCCMeYNY8xq4Aqsz3R1IW1XA+2wVt0uzACs5GqEMWaFMWYS8CRwg+7rVvEMcCykmWM7AD4jvOU7CwBn/DocsVYvkjGCJ+2EiMWoooczsRp1hj1NfMvgfmZLly6lY8eOLFu2LCz33Ds3+DjNlbQSce4DhNe859j1Zzh/4zhZF5b7K1VRRW1iJCLNgJOw9mEDrMUigVlYSU4BxphsY8zfRVzyfGCVMWZVvrppQCJwaihiVuWDAz835ftLeqK/K+uNtXifu+ovdr0v8yiMp3pZh6eilCMmjlrn3EfSSWfbdZs2baJbt258913oF13M+CMDf571N5uIH1fKUgB+8nfgT3/w8a/2GilVMlGbGAH7v/PXHFC/AWhYyusVdi2Kcz0R+bOwF6DTmMqZ/o5FtHRsBsBvhDe9Vm8RjhxcycG1izxpJ0ciPBXFxOGkeq+reP3113E4rB+vGRkZDBw4kHfeeSe0NzOQt6edXXRXXWJVIrzmHWzX93cu5hjZcPD5SqlCRXNitH99/tQD6jOwNqstzfUKuxalvJ4qhwQ/N7nsTkam+Dvyr7HyXnfycsRhDUEzvni8+46LSIwq+t1www18++23VKlSBQCfz8e1117L3XffjT+Ee5l5dh9vv3fG7sARbyVA0/0nscrfyD6W/9+8Uqpo0ZwY7Qp8TT6gPgXYVsrrFXYtinM9Y0zrwl5AXiliUWHSz7GYYxybAKu36FXvEPuYO2WJ/d6T1h6Mu6zDUxXIgAEDmDNnDvXrB+eCPP/881xwwQX4PbkhuYc/rzrezOZ2ef+/YYODV/P3GjkWc7RsDMk9laroojkx2hT42vSA+ib5jpX0eoVdK/+9VBQT/Nzi+souT/Wfwj+B3iJHzHacCcHHDZ7Uk8o8PlXxdOjQgUWLFtGuXfCR1/jx49n++f34MlNDcg9PavCRrzt5GYiVdE3zn8Jqf+Dftxhu1l4jpYolmhOj1YGXPdJRRKoApwETSnG9iUAbEWmer24gsBOYU/owVXnR1/GL3VsEFBiHYY3PsPhy6uPPbVCmsamKq2HDhsyZM4e+ffvadXlbVrNt9B14dh95L453X2uMLxYAcebZ4+SsXqNgj2h/xyJaiP6Np9ThRG1iFFh08SlguIhcLSLHAB8BacCHInK5iOwSkXZFXSef8ViJ1ici0kZEzgbuBp43xoSm31tFjODn5vy9Rb5TWG0aB0peXCnBLUDy/wWuVCgkJyczadIkrrnmGrvOm7adbaPvJGfD8iO7uInBk97eLuZP8qf6T+Fvv5Xka6+RUsUTtYkRgDHmE6w1i24C5gGxQBdjTCrgB3IAbzGv5QF6EFgkEngcuN8Yo+vqVwB9HEto5Qj+dZ7/L2lX0kocrkwAjN+FJ+34g85X6ki5XC7eeustnnvuObvOn5vJ9nEPk/HHj0d07fyPfl0J63DE7ACsXqP8PaMDHQu110ipw4jqxAjAGDPKGNPWGFPTGHOWMWZDoP5jY0xDY8xfB7Rfb4yRA7cDCRzbbowZYoypYYxpZ4x5paw+hwofB35uc423y9N8J7PK7i0Cd9XF9nvvvtbgT0CpcBAR7rrrLmqefW9wQ2K/l91T/kfq3E8p7e5D/pyG+HLq2uX8/6an+DvxT75eo1tdpRlpoFTlEfWJkVKHM8CxsMBMtJe959rHxL0bV+I/dtmT2rHM41OVT5Vju1HnwqdwJKTYdWnzxrJ7yksYb6G7Fh2GFPi36075DcS6jh9HgX/zA52LaCXrSx27UhWdJkaqYvN5C/yFPMXfMd/YogNWus6thS+rWZmGpyqv2AbHUveSF3FVD64fm/nnTLZ/8RC+nIwiziycJ60Dxm8tMSGuLFxJwb20p/pPYWW+dY2010ipQ9PESFVsK77kKMdWwNoTLf9fzuAtMFDVk3oKumGsKkvuqnWpe8kLxDZua9flbvyDbaPvxJNawuXY/HF40oPj49zVFtnvDQ5e9p5nl/s4l8CWpaUPXKkKTBMjVXH5PDD7Wbs40d+V/0xwGr4r6S8cLusvc2vQtW4Yq8qeMy6ROkMfo0rr0+06755NbBt9B7mbVxVx5sE8e4OP06xB2Nvt8nT/SfzhbxpsPPOpUsesVEWmiZGquJaNhb1rAfAaB6/km4kGBw66bgO+KmUanlL7idNNjQG3k9L1IrvOn5XG9s/vJ3P1vGJfxxqEXc8u5/83DsJL+XqN+Od72Jj/uFIKNDFSFZU3F2YHV1qY4DuV9SY4a0fcu3Al/muX8/+lrVQkiAhVu11EjQG3g8MFgPHmseubZ0hb9FUxZ6xJgX/L7qrBQdgAP/k7sNTfItj8pydCFb5SFYYmRqpiWvIhpFlbfOQZJ6/5Bhc4XHDQdW182U3LMjqlDimxTU/qXPAYjtj9PZiG1FkfsOf7NzF+32HP96S3x/itpQDEmY0raUW+owf0Gq2dDWtmhSx2pSoCTYxUROTk5DBy5Ej7lZOTE7qL52bAnBfs4lhfTzaZWsHj4ik46HqvDrpW5Utc43bUvfgFXCl17LqM36ex69tirDfrjyuwSGlMtYUFDs/xt2Whv1Ww4sfHoJTrJ6nyT0SuFJGlIrJbRL4VkYZH0l5E6ojIeBHZKSIrROSGA443EhFTyOuYcHy+cNDESEVETk4Ojz76qP0KaWK06C3I3Gm9d8Xzurdgb5EreXm+la7dOuhalUvumo2oe8mLxNQL/j7JWf97sc7Nv6aRM2EDjrjN+Y4Kz3kuCBY3/wqrphxhtKo8EpFrgTeAp7F2dkgA5ohIfGnai0gCMB9rl4nuwAvAK4Hz9msGZADVgKr5Xv8QJTQxUhVL1h6Y91qw3OladlK1QJP8f0F70trrSteq3HJWqUqdYU+ScHSXEp3nz2mILyvfel3VFhQ4/ps5Go7uF6z46XEoxmM6FT1EJAZ4CHjZGPOFMeYP4FKgCXBBKdtfATQALjHGrArsIPE+cLeI7M8nmgP/GWNSjTFp+V7+MH7ckNLESFUs816G3DTrfVwKdL2lwGFH3Eac8cE90zx7O5dhcEqVnMMdR81z7iX5lCEHHcted+i1iPLy/dt2J/8OzsyCDXo9hP0IeecqWP5FCKJV5UhXoD5g7xxsjNkCLAMGlLL9+cDMwH6k+03D6iXa/3y2GfAvUUwTI1VxpG+FRe8Gy11vgfhqBZrE5PvL2ZvVBH9u/bKKTqlSE3FQ7fQrqHb6FQXqd337PPuWTi30HO++tvi91gBucXhxp/xasEGd1tD2/GB51lPgzQtp3KpIMSLyZ2GvEF2/SeDrmgPqNwCFjTMqTvsmhzhOvjbNgX4iskNElonIgyLiLlHkEaaJkao4Zj8D3mzrfZXa0PHaAofFmYErebld9uwt2eMJpSItsd2ZBSuMnz3fv8nemR9w0JMK4wqs5m6xHiEf0Ob0++ylAUjdAEs+CH3QKlL2r0+SekD9/vE/pWlf9xDHydfmcaADcBYwHrgP+LJ4IZcPmhipimHnavhtdLDc426IKbhgo7vqEsThBcDvTcSb3rosI1QqbNIXf8Wuic/i9+QWqPfs7Ygx1o95R8wenImrC55YvTmcMCJY/vk5yEkLd7jKkmeMaV3Y63AnisgFh5j5Zb+wBkgDJB9wegpQ2H4zu4rRftchjrO/jTHm78BroTHmceAu4GwRaX64z1VeaGKkKoYZj4IJDB6tfhSceNkBDfy48w+63tsRcJVVdEqFhbtmcIB11up57Pj8AXxZwcTGeKvi3Recmh9zwCBsAE67F9yBPyKydsO8V8IWrwoNY8w4Y4wU9QL2b5bX9IDTmwCbCrns/rqi2m86xPH85x/o58DXdoc4Xu5oYqSi3/oFsDrfdONeD4Oz4CNtV+JKHO5UAIxxFHjEoFS0qn3eSOKaBZebyN2yim2j78CzO/g7Kv8jY1fi30jMzoIXSawNXW8Olhe8CelbwhazKjM/Yz32Ont/hYg0AdoAE0rZfiLQU0QS8503EFhujDnUgOuTAl+XlfgTRIgmRiq6GQM/PBQsNzgJjjv7oGbu6nPt9959rTHelIPaKBVtHLEJ1D73YRKP72vXeVO3sW3MneRs/AMAX1ZzfDnBhSJjqhWy91rnG61xeWCN05v1dFjjVuFnjMkCXgLuFJHBItIG+ARYDnwLICIPi8hWEalVnPbAe1hjij4RkWNE5ErgEuCpwPVqishdItJORBqIyCWBa75mjFlbZh/+CGlipKLbykmwKbi9B2c+DlJwFWtH3CZcVYLfk3l7upVVdEqFnThdVO9zA1V7XGbX+XMy2D7uQTL/moW1f1pX+5i76q/gyCp4kdhE65HafkvHwI5VYY1bhV9gjM8TwHPADGAzcJox+8cd4ANyCIzKP1x7Y8wurIUdk7Ae1V2LtabRuMD1qgO9gOnA38CtwL2Br1FDEyMVvbx5MGNksHxMf2hy8EyzmHy9Rb7sRvizGx/URqloJiKkdDqPmmfdE3yM7POya9ILpM0fR15q+3xT9z3EVFt88EVOuBRqBDaYNX6Y8UgZRa/CyRjzlDGmpTGmrjHmImPM3nzHnjTGNDPG7C5O+8Dxv40xZxhjqhpjTjbGjD3gWF9jTD1jTBVjzInGmHejaXFH0MRIRbMlo2DPf9Z7cUCvg3+Qb8/cXmCKft7ubui+aKqiqtKqO3UufApHfHDiUOqc0eye+hZ5u06y69zV5uPxeQqe7HQX/B76+zv4b2a4Q1aq3NHESEWnrD0w65lg+cTLoPaxBzX7fPXniFh/rPg9KXj3tSmjAJWKjLiGrah7yQu4qgUXL81c8QOb3p6NN7DijMOdzvT10w8+udUgaJyv13X6A7pViKp0NDFS0Wn2s5CTar2PTYbTHzioSZYniy//Dq4rlrenK+Asm/iUiiB3tfrUveQFYhseZ9flrPuDNU9uIm+3tbr1J39+gjGm4Iki0OfJYHnHn/DbJ2URslLlhiZGKvrs+gd+eT9YPvVOqFLzoGaT/ptEWmDfNOOPwZN6cllFqFTEOeOTqXPBEyS0OtWuy9uayprH15C9LpuVe1by6/ZfDz6xwQlw/LBgeeaTkJNeBhErVT5oYqSiz/cPgt9awZqqTQ7a+gPA5/cxZuUYu+xJPQn88WUVoVLlgrhiqDnoTpI7BfdE86Z6Wfv0WtJ/T+fjvz4u/MSeD4Er8P2SuRPmvlQG0SpVPmhipKLLfzOtQaH7nfEYuGIPavbTxp9Yl74OAGMk8BhNqcpHxEG1HiOo3vcma5IC4M/1s+GVDUz4aAJrUg/cExRIaWBtwrzfgjdh77qyCVipCNPESEUPnwem3RMsN+5S6GKOxhg+WBHcDNO7ry3GU6MsIlSq3Eo6vg+1z3sEiQn0BBnYOnorF113EX5/IbOpu94MSfWs975cayC2UpWAJkYqeix+D3bt3wRToO9TBy3mCLB422L+2P2HXc7b3aOMAlSqfItvfiJ1hz+HMzk4nX/R54s4a8hZZGdnF2wcUwV6Pxosr5oM//5YRpEqFTmaGKnokLGj4DYFJ46A+h0KbTpqxSj7fZf6XfDnNAh3dEqVCXHFkNJ1mP0SV0yJrxFTuxl1L36ZpKZJdt2UiVM4/fTT2bFjR8HG7YZCo47B8nf3WgurKlWBaWKkosOMRyE3MDMmLsUaHFqIP3f/yYKtwR3Er2xzZVlEp1SZEFcMVbsNt1+lSYwAXEm1eenLl0hsF9wLdNGiRXTu3JnVq1cHG4pAv+ewF0Xd9TcsfucIPoFS5Z8mRqr827QEfg/OMOP0Bwudng/w4R8f2u/b1mzLyXV1ir5ShRnefjjt725PtdOq2XVr1qyhc+fOzJkzJ9iwfntrAdX9Zj0L+7aVWZxKlTVNjFT55vfB1LuC5dqt4aQrCm26Pn09P6z/wS5f2eZKpJAxSEopiHfFM7zNcOqPqE+doXXs+r1799K7d2/Gjh0bbNzrYYirar3P2wc/6D5qquLSxEiVb79+CFt+C5b7PwdOV6FN31/xPv7AXoVNk5tyeuPTyyJCpaLWsGOHkeBOoFb/WjS6vhGuGOt7Ky8vj4suuoinn37aWh07oTr0fDB44vLPYd3cQ1xVqeimiZEqv/ZthxmPBcttz4em3QptunHfRib9N8kuX9n2Shyi/7yVKkpKbApDjx5qvT8lhTYPtKFGjeDSFvfffz9XX301Ho/H6qmt2y548uTbdSC2qpD0N4cqv75/AAJbehCbAmc+ecim7694H5+xNrtsmNiQgc0HlkWESkW9y9pcRpwzDgBvEy/3jL6HFi1a2Mfff/99Bg4cSHpGJgx8meBA7NWw4LWyD1ipMNPESJVPa2bBiuAGsPR6CJLqFNp0075NfPvvt3b56nZX43IU/rhNKVVQzfianH9McMuQqfumMnPOTLp2Da4W//3339O9e3c2UafgGL/Zz8GetWUZrlJhp4mRKn88OVY3/X71TzjkgGuweou8xto7rUFiAwYepb1FSpXEFW2uINZpba2zK3sXs/bMYsaMGQwdOtRus3z5cjp27MjvNQdDlVpWpTcHpt0NxkQibKXCQhMjVf7M/R/s+c96Lw4Y+D9wOAttujljMxP/nWiXr253NW6HuyyiVKrCqBlfk/OPDvYajfpjFLhg7Nix3H333Xb9li1b6H5Gf6YnXhA8+Z/v4a+JKFVR6PMGdUSa3julVOf5czIKlNuNnI4jLpGWsokpMc8TExjG8IHnTB57dTOwudDrxNb9iphqwd6iQUcNKlU8SlV2V7S5gi///pJcXy67sncx4Z8JDG81nGeffZZmzZpxww034Pf7ycjIYMBNz/LWJa25qsk66+Spd0GzUyGhOjk5OTzzzDP2de+9917i4uIi86GUKgXtMVLlhgM/z7nfJUasQdSbTQ1e8p53yPbi3o276hK7/H9t/097i5QqpVoJtTjv6OD323vL3yPLkwXAtddey6RJk6hSpQoAPp+Pqz9azv0zvfiNgcwd8L01nT8nJ4dHH33UfuXk5JT9h1HqCGhipMqNy5zT6eD41y4/4LmCDBIO2T621g+IWOsWNUhswNlHnR32GJWqyK5oc4U9Q213zm4+W/WZfax///7MnTuX+vXr23VP/5zFxV9lk+s18Pun8N9PZR6zUqGmiZEqFxo5dnGn6wu7/LWvK7P8hW8SC+CI3YIreZldvqH9Dbid2luk1JGonVCbYa2G2eUPVnxA2v4lM4D27duzcOFC2rRpY9eN/cPLGaOz2JNtYNItkJdZpjErFWqaGKly4en40SRILgC7TRKPeS4psn1sre8RsWbCtKjagv7N+oc9RqUqgyvbXEmSOwmAfZ591kDsfBo1asTcuXPp3bu3XTdng48uozJZs3Yd8fNfKNN4lQo1TYxUxF11gptT3Svt8kjPCPaSfMj2zvi1uJJW2eVbTrgF5yFmrSmlSiYlNoUr2gaXx/hs5Wdsz9xesE1KClOnTuXyyy+361bv9tPp/UyWTn6P7o31+1FFL02MVEQ1qyq81Cc4Y+UH3wlM8ncu4gxDTO3v7JIvqzE9GvYIY4RKVT4XHXsRNeNrApDry+Wd5e8c1MbtdjNq1Cgeeyy4bc/OLEPPjzMZ1tZNFX2yraKUJkYqYgT48Ox4EgNz8/eaRO73XIm95UAhnIkrcSWst8u5O/oicuj2SqmSS3AncG27a+3yV/98xbq0dQe1ExEeeughRo8ejdttrf6S7YUbpuTQr6WuBqOikyZGKmJu7hhDj6bBH54PeS5nJ9WKOMNHbO1pdsmbcTS+7OZhjFCpymtIyyE0TGwIgM/4ePHXFw/Z9uKLL2b69O9JqWL1/hpg/F9eGqcIPp+vLMJVKmSiPjESkUEislBE9orIDBFpU9q2IvKQiJgDXgvC/ykqn6McW3m6V6xdnpR3EpOLfIQG7moLccbuBMAYIXdH37DGqFRl5na6ueXEW+zyrI2zWLh14SHbn3766cyfv5Am1WPsug1phhEXX0RWVlY4Q1UqpKI6MRKRAcBXwGigE7ADmC0i9UvZthnwLlA13+uMsH2ASsqNl1cSPiDebT0C25bh54Hsi4o+yZFFbK0ZdtGTejL+3IP+NyulQqhPkz50qB1cNuP5X57H5z90D9Bx7Y7nh8lfcUK94K+WKd99z+mnn86OHTvCGqtSoRLViREwEphgjHnDGLMauALrM11dyrbNgZXGmLR8r4xCrqWOwB2uL2nnCo4TumpSDqkmschzYmvNQJzZABhfLHk7NV9VKtxEhLtPDu6V9vfev/n636+LPKdWq670aOJk4NHBx+SLFy+mc+fOrF69OmyxKhUqUZsYiUgz4CTA/i41xuQAs4ABpWzbDPgXFTZdHSu41jXJLr+1JI/Jf3uLPMcRswN3tWAXft7u0zG+pLDFqJQKalOzDYOaB/cgfG3pa2TkFf334iuLPNza0c11JwWnpq1Zs4YuXbowd+7csMWqVChEbWIENAl8XXNA/QagYUnbikhM4P0nIrJZRL4XkTOLG4yI/FnYC4g57MmVRHXSecn9ll3+a6ePO6Yffh+l2NpT7a0//HnVydvTNWwxKqUOdvMJN9tbhezJ2cO7K94tsr3fwGUTc3ji9Fie6x0cS7hnzx569+7NuHHjwhqvUkcimhOjuoGvqQfUZ8BBU5uK09YAJwKdsR6z5QBTReTQu5iqEjA8636XOpIKQK5xMWxCNtlFdxbhTPyrwGKOuTv6gdEFUpQqS3Wr1OXyNsHFHEf/NZo1aQf+nVnQpnTD1ZNzuKtrLF+cF09sYM3H3NxcLrzwQp577jmMMeEMW6lSiebEaFfg64FLJKcA20ra1hjjMcb8boxZbYyZDpwDLAFuLk4wxpjWhb2AvOJ9nIrtSuc0znD+Zpefzj6X5dv9RZ8kecTV+dYuejOb4d13yEmHSqkwuqz1ZdStYv2N6fV7eXLhk4dNbCas9JLb5kLOb+3mx0sTqBEfXHPsnnvu4frrr8frPcxfR0qVsWhOjDYFvjY9oL5JvmOlaQuAMcYPzAXalTpCBcAJ8jf3usba5Zm+4/kgr+dhz4up+ROOmFQAjHGQu+0cilr8USkVPgnuBO49+V67vHjbYqaunXrY87J7PAI1WtK1sYv5VybQvHpwUPbbb7/NOeecQ0aGznFR5Uc0J0arA6+z91eISBXgNGDCEbTN7yRgWRHH1WFUI53XY17FLdYU362mOnd4ruNwCY4jZgcxNebY5bzd3fHn1QlnqEqpw+jZuCenNjzVLj//y/Ok56UXfZI7Ac7/CFxxHF3DycIr4ujUPMU+PGXKFHr06MHWrVvDFLVSJRO1iZGx+nCfAoaLyNUicgzwEZAGfCgil4vILhFpd7i2ACIyUESGiEhTETlWRN4GugJ3H3x3VRyCn5fdb1Jf9gDgMU5uyLuZPUVsEGsxxNb9BgkkU35PVfJ29QpztEqpwxER7jvlPmKd1oDq3Tm7eX3p64c/sW4bGGCtnF2rioOfLvQzuMvR9uHffvuNTp068ddff4UlbqVKImoTIwBjzCdY6xDdBMwDYoEuxphUwI81gNpbjLYAtYBHgOVY0/gbACcbYxaVzaepeG50fkMP53K7/Iz3Qn4zRxdxhsWVvBRXleDAztxtg8Do5D6lyoOGSQ25ul1w+bdxq8fx564/D39ih4uh/cUAxLuFL3tt5dZLgssAbNiwgS5dujBr1qxQh6xUiUR1YgRgjBlljGlrjKlpjDnLGLMhUP+xMaahMeavw7UNHPvQGHO8MSbZGFPXGDPIGPN7BD5ShdDL8St3uMfb5em+kxjl63/Y88S5j7g6k+2yd18rvBmtwxKjUqp0Lmt9GU2TmwLgN34emv8QHp/n8Cf2fx5qW9/PTofwv2OW8MoT99kbQaelpXHmmWfy6aefhit0pQ4r6hMjVf4cJZt52f2mXV7nr8Ndnms4/MDpwCM0l7WvkvHFkLPtrPAFqpQqlRhnDA93ftgu/7P3n8OubWSdmABDP4HYwON0TyY3J05hwmcfERdnrZPk8Xi4+OKLeeqpp3Q6v4oITYxUSCWTyXvuF0kSa/uODBPHVZ47SKfKYc91Ja3AnRzsks/d0R/jPXBJKqVUeXBy3ZO54JgL7PL7y99n1Z5VRZwRULMFnPs+9h9Ke9cxOO8rZs74gZo1a9rNHnjgAa655hqdzq/KnCZGKmQc+HnF/TrNHcFlpG73XMc/5sCFyA8mrkxi6060y97M5nhSTwlLnEqp0Lj9xNupX8XazNlrvDw07yG8/mIkMkf3gZ4PBstrZtIpYxoLFiygZcuWdvV7773HoEGD2LdvX6hDV+qQXIdvolTxPOD6lNOdwdUNXvYO4Xv/ycU6N67hdByuTACM303O1nPRvF2pyGl675RitXMm9COhySgAVu1ZRed3HylwvN3I6TjiCtsk+lhed3dkoDMwv2XB67z3cy7ZfUcSm/UEuZtXAvDdd99x6qmnMmXKFOrXr1/qz6NUcelvHhUSlzqnc6Vrml2e7juJV7xDinVuSucUYqoFp+nm7uiL8dQIeYxKqdDzZbUkb2+wdze27lzim8UX40zhLs81rPQ3tmuedI2iR+IGal/wBAnHBPdE/P333+nUqRN//lmM2W9KHSFNjNQR6+n4jUdcn9jlP/xNuc1zPaYY/7zctdzUvzT4V6A3qymevZ3DEqdSKjxyd/TH77EWbRTx0/CahjhiD//9n00cV+bdyQ5TFQCX+HnT/TLHxuyg5tn3cMcdd9htN27cSNeuXZk5c2ZYPoNS+2lipI5Ia1nHa+7XcIo1e2SLqc4VeXeRRdzhT3ZAo6sb4Yy3dpc0vlhytgxF/1kqFWX8ceRsvgBjrAHVsXVjqTe8XrFO3UJNrsi7kyxjLRqZLNl8EPM8tSWNF154gVdffbXAdP4+ffrodH4VVvobSJXenjV8GPMcVSQXgH0mnivy7mYHxZtJVvus2iS0TLDLOduGYDzVwxKqUiq8fNnNydt9ul2udmo1kk8+3Cr3lj9Mc2723Ig/kFg1lF18FPMc5KRx00038dVXX+l0flVmNDFSpbNvG4weTG1JBcBrHNzguZlVpnHR5wW4krdQ66zadjlvb3u86ceHI1KlVBnJ29kLb2YDu9zg8gaIO7VY587wn8hj3kvscmvHehg7DDzZnHPOOcycOVOn86syoYmRKrnsvTB6COxdZ1fd5/0/fvYXL7ER5z7iG3+JBP71+fNqkLtjcBgCVUqVLSdZ687Bl23tc+hMcJLQ7CuQYqyKDXzk68vb3oHBivXz4MvLweehU6dOLFy48KDp/GeddZZO51chpYmRKpm8LPjsQtgRnB3ypOcivvSdVswL+Ihr8BkOt/WDzBgH2ZsvAH9s6GNVSpU5k1eNLZ9sscuuKluIrTOp2Oc/4x3GF94ewYq/p8HEG8Hv56ijjmL+/Pl06dLFPjxt2jR69OjB1q1bQxK/UpoYqeLLy4KxF8DGhXbVW95BvOcbWMRJBcXWnoarylq7nLt9EP6c4j1+U0pFh7QFaez+cbddjqm2GFfKL8U8W7jP+3987zsxWLX8c5h8K/j91KxZkxkzZnDeeefZh5cuXUqnTp3466+/Dr6cUiWkiZEqHk82fD4M1v4crOtwCc96Lyz2JVxJy4mpMTd4ybQOePZ2CmWUSqlyYtvYbWT9l2WX4+pOxBG3uVjn+nByk+cmaNo9WPnbxzD1TjCG+Ph4xo0bx+23324f3rBhA126dGHWrFmh+giqktLESB2eJwc+Hw5rZgXr2g6FQa9w+I1hLY7YLcTVH2+XfTl1ydk6uNjnK6Wii/EaNry+Ab/HmnkqDi/xDUYjzuKNB8olBoaNhUYdg5VLRsHUu8AYHA4HL774Iq+88kqB6fxnnnkmn332Wcg/j6o8NDFSRcvLgnHD4b8fg3VtzoVz3gKHs1iXEFc68Y0+Rhx5ABhfHNmbLgETE46IlVLlhHevl6x1g+31jRwxqcQ3+qTYg7GJTYLh46Fhvq2FfnnPSo78fgBuvvlmxo8fX2A6//Dhw3nmmWd0Or8qFU2M1KHlpMOYc+HfGcG61oNh8LvgLOY2e5JHfMOPcbjTADBGyN48TLf8UKqS8GU0I3dHf7vsjN9IXP0vAH/xLhCXDBdPgPonBOt+eQ8m3gA+a6r+kCFD+Omnn6hRI/hz5b777uP666/X6fyqxDQxUoXL3A0fD4IN84N1x50DQ94rflKEn7gGY3HGB8cV5G4/C1/mMSENVSlVvnn2dCNvb/CRmDt5BTG1vi/+BeJS4JKvCyZHyz6D8ZeB11pgtnPnzixYsICjjjrKbvL2228zePBgMjMzj/QjqEpEEyN1sLTN8FF/2Pp7sK79xXDeB+B0F/Mihtg6k3EnrbRr8vZ01X3QlKqUhNxtZ+HNONquia05C3fVRcW/RHxVGPEtNOkWrFs5CcZeCLkZALRs2ZIFCxbQsWMwCZs8eTKnnXYa27dvP9IPoSoJTYxUQdtWwPu9YeeqYF3H6+Cs14o9pgggpuYMYqoHe5u8+1qRu31AKCNVSkUVJ9mbL8KXU8euia37Da7kZcW/RGwSXDweWvYJ1v33E3zYD9KtdYxq1arFTz/9xDnnnGM3WbJkCZ07d2b16tVH+iFUJaCJkQr690f4oB/sCy7Oxql3Q9+nwVH8fyru6nOIrRUcrO3Lbkj25gvRf25KVXL+OLI3Xo7fY+2hJmKIqz8OZ+Kqw5yYjzseLvzUmgSy37bl1h90O6we6oSEBMaPH8+NN95oN1m7di1dunRh3rx5IfkoquLS31TK8tsn8On5kBeYSisOGPAi9HwApPhT6t0pvxBXZ4pd9uXWJmvj5WB0ZWulFBhvVbI3/B9+bxUARPzENxiDM+G/4l/E6bbGO3a6IViXvglG9bGXFXE6nbz66qu88MILdpM9e/bQq1cvxo8fj1KHoolRZefzwNS74dubwFj7G+FOgAvHwsn/V6JLuVKWEFvvK7vsz6tO9ob/A1+VUEaslIpy/rzaZG+8AuOz/mASh5f4Rh/jTFhT/Is4nND3Kej7LPZ6aLlp1j6OC98CYxAR7rjjDsaNG0dMjLU8SG5uLkOHDuV///tfiD9V+SQiV4rIUhHZLSLfikjDI2kvIlVE5CERSReRmaG4Z3mjiVFllrkLRg+Gxe8E66rUhsumwDF9S3Qpd9WFxNcfj4i1bojfk0zWhisx3uRQRqyUqiD8OQ3I3ngZxm9N6BBHHvGNPsRZ5e+SXajTtXDBGHDFW2Xjg+/uhW+utxanBYYOHcqMGTOoVq2a1cQYbr/9dm677Tb8/mIuGxCFRORa4A3gaaAHkADMEZH4I2j/MzAI2BmKe5ZHmhhVVpt/g3dPh3VzgnX1joerfoIGJxz6vEK4q88hrt43dtnvTSJ7w5W6VpFSqki+7GZkb7oE47eWABGHh/iGH+NMXHmYMw/QaiBcMQ2S83VMLPvMGpSdugGA7t27M2/ePJo0aWI3efnllxk6dCjZ2dlH/FnKGxGJAR4CXjbGfGGM+QO4FGgCXHAE7a8AOgIbjvSe5ZUmRpWNMVY386gzIS3fv+u2Q+GK6VC1UQkuZYipOaPAmCK/J4Wsddfgz6tTxJlKKWXxZR5N9sbLMX7rUZc4fMQ3HF2y2WoA9TvA1bOgcZdg3Zbf4O1usHIyAK1atWLhwoWccELwj78JEybQu3dvdu/eTQXTFagPfL2/whizBVgGFDZFuFjtjTHLzKGXFC/pPcslTYwqk6w91p5n390L/sCS/OKAM5+AIe9asz2KyeP3MHLBSGJrBVfF9udVJ2v9NRhPzVBHrpSqwHxZR1mP3vePORI/8Q3GMmrFqJJt65FYCy6dWHB8ZE6ata3RtHvBm0vdunWZPXs2/fr1s5vMnz+fLl26sGZNCcY4HbkYEfmzsFeIrr+/a+zAD7UBKGzMT0nbh+Ke5ZImRpXFmlnwdndYHezdIakejJgEXW4q0cyzjLwMbvzxRr76J99A69yagaSoegiDVkpVFv7sJmRtuArjTbDrXv7tZZ5Y+ARefwm29XDFWDNqh7wH7nwTPxa9Be/3gu1/kZiYyLfffsv//V8wgfr777/p3LkzS5YsCcXHKQ/qBr6mHlCfAVQLQftQ3LNc0sSoosvLhCl3widnW9NZ92vRG66dC027HfrcQmzO2Mxl313G/C35Fm/MakLm+usw3pRQRa2UilLiiiGl6zD7Ja7ibxbtz2lI5vrr8OcF/8D64u8vuPmnm0nPSy9ZIO2GwjWzoU6bYN22FfBuD5j7Mi6H8O677/L444/bh3fs2EGPHj2YMmVKIRcMuTxjTOvCXoc7UUQuEBFT1AvYv0bKgTNgUoBthVx2VwnbFyYU14g4TYwqsnXzrOfrv7wXrHO4ofejcNGXUKVkj7zmbZ7HBZMvYPXe4OqxnvR2OiVfKWUTVwxVuw23XyVJjABMXi2y1l2PL6uxXTdn8xyGTR7G33tLOGOtZkv4vxkFH6358mDGI/Bhf2TX3zz44IN89NFHuFzWAPCsrCzOOuss3n333ZLdqwwZY8YZY6SoF7B/v5WmB5zeBNjEwfbXFbd9YUJxjYjTxKgiytoDE2+09jvbk+9Rb+3WcPVM6HZriVay9hs/7yx7h+tmXEdabppdf3mby8nZfCGY4u6fppRSh2d8iWRtuIrejXvbdRv2beDiqRczdc3Ukl3MHW89Whs+wRo+sN/GhfBWV5j5FCMuuoCpU6eSlJQEgN/v55prruGhhx4q2Rin8uVnrEdaZ++vEJEmQBtgQgjah+Ke5ZImRhWJ3w/LPofXT4alo4P14oBut1lJUd22Jbrkruxd3Pjjjbz+++sYrB8Qcc44nur2FLefeDv6T0gpFRbGzYunvcj17a9HAgs4ZnuzuWfOPTy+4HGyvSWcYt+yN1y/ANqeH6zze2D2s/B2V844ys2cOXOoX7++ffiJJ57gsssuIy8vLxSfqEwZY7KAl4A7RWSwiLQBPgGWA98CiMjDIrJVRGoVp30o7hkN9LdaRbFpCYw6A76+BrJ2BevrtIErf4DeI8FVsm05Zm6YybnfnsuczcG1jhomNmRM/zEMOmpQiAJXSqnCOcTBdcdfxxu93iA5Jjhs5Yu/v2DopKH8uauEE7jiq8G578OFn0Fyg2D97n/hk7M5fuVzLJj6Oa1bB4f5fPLJJwwYMID09BKOcSoHjDGPA08AzwEzgM3Aacbs3+YAH5AD+IvZPhT3LPc0MYp2qRvhq6ut2Rab882mcCfAGY9b63o0PKlEl8zIy+DRBY9y88yb2ZOzx67v0bAHnw/8nGOqHxOi4JVS6vC6N+zO5wM/p1X1VnbduvR1XDz1Yt5Z9g6e/cuPFNexA+CGRdDxOqtHfb9Vk2k8cTBzH+vLaacGJ6bMmDGD7t27s3nz5iP9KGXOGPOUMaalMaauMeYiY8zefMeeNMY0M8bsLk77A657ujHm9JLeMxpoYhStMnbAtHvgtRNg+biCx1oNgusXQtebrc0WS+DH9T9y9sSzGf93cJPFOGccD3Z8kNd6vkZKrM48U0qVvUZJjfi0/6dc0eYK+9Ga13h5/ffXuWDyBSzbWcIFIWOToN8z1mr/jToG6/0eqi5/j+96r2NYr/Z29fLly+ncuTN//hmqZYZUeaWJUbTJ2AkzRsIrx8Oit60ZFvvVaQsjJlv7BlVrcshLFGZrxlZu/ulmbp11Kzuydtj1x9U4ji8GfcEFx16AlGCtI6WUCjW3081tJ97GB30+oF6V4EDqf/b+wyVTL+GJhU+UfFp//Q7Wqv/njiqwpUisL50xXf/j7tOq2nUbN26ka9euzJo16wg/iSrPNDGKFqkbYOpd8HIbmPs/8GQFjyU3gLNes9bsaNa9RJfN9GTy6m+vMuibQczcGNwo2e1wc0P7GxjTbwzNUpqF6lMopdQRO6nuSUw4awLnHX2eXWcwjFs9jgFfDeDTlZ+W7PGaCLQ9D278BXo+CIGecYcIz/bw81q/OHsN3LS0NPr06cPKlSXcz01FDVekA1CHkboRZj4FK76AA1d/TagJ3e+Ak64Ad1yJLuvxe/j6n6954/c3CowjAjil7ik81OkhmqY0PcLglVIqPJJiknik8yMMaj6IxxY8xn9p/wGQmpvKM4uf4fNVn3PribfSs1HP4vd2xyTAqXfBSVfC/NesXnlPFjeeEkODJOGir7LJ8cLVfdtxbNN6h7+eikqaGJV3fg8s/xyMP1hXpTZ0vh5OvgpiE0t0OY/Pw8T/JvL+ivfZnFFwIGHN+JrccsItnH3U2frYTCkVFU6ocwJfDvqSj/78iPdWvGdP41+Xvo5bZ95Kq+qtuOb4a0qWICVUh96PQMdrYcFrsORDBrfK4KdLhfd/8/By592Is2QLV6rooYlReVe9ObQ5F1Z8CVUbQ9dboP3wEm34CpDlyeKbf7/hoz8/Ymvm1gLH4pxxjGg9givaXEGCO+EQV1BKqfLJ7XRzVburGNxyMK8vfZ2v//0af+CPyZV7VnLrzFs5ptoxXNn2Sno36Y3bUcxJKUl1rE22u90Oi9+j86K36NxoL3S9wepdUhWSJkbR4NS7oMUZ0GZIiWeZbc7YzNiVY/nqn6/Y9//t3X2wVdV5x/HvTxAur0pEirx4UST4go4WxdcqEUVTpJTRRC2xoLVMG9NqktbYOFGsQSeapGLiOFYbFZN0tEYbTUXFMuAbVVRQ1ErHCCIgAlEERC4IT//Y6+jlcF/OuZxzLufc32fmzIa11177WesA92HvtdfetnGnfZ3VmfFDx/PNo79J/x79m2nBzKw69O3Wl2knTWPSYZO49ZVbmbti7uf7lny0hCufvpJ+3ftx4aEXct6w89i3bt/CGu7+JRj9PTjxMnhlJhwzqSzx257BiVE12H949inQ1u1bmfveXB56+yHmr5r/+f+ccjqrMxMOmcClR17KoF6Dmm7EzKxKDeszjJ+N+Rlv/uFN7nj1Dua8N+fzfWs2r2HGKzO4fdHtjKkfw8RDJnL8Acezlwp4Fqlrz2wag9U0J0Y1YvuO7Sxcs5Anlj3B48seZ33D+l3q9Ni7BxMPmchFh1/EgJ4Ddm3EzKyGHL7f4cw4fQZLPlzCzDdn8tjSx/gsPcSydcdWZi2dxaylsxjQYwDjDh7HWUPO4st9vuw5lh2cE6MqtnX7Vl764CXmvTeP2e/OZu2na5usN7jXYCYdNokJQyfQs0txk7XNzKrd8C8NZ/op0/n2yG9z/5L7eWDJAzs9jbvqk1XcufhO7lx8J0N6D+HM+jM5bfBpjNhvBJ326tSOkVt7cGJURSKC5RuX8+LqF3lu5XPMXzWfzZ9tbrJuXac6zqw/k4nDJjLyj0YWdpnYzKyG9e3Wl8uOvoypR07l6RVP8/DbD/PMymd2mm6wbMOyz5OkPl37cMrAUzhp4EmM6j+Kft37tWP0VilOjPZwm7ZuYva7s1mwegEvrH5hp1Wp83VSJ44/4HjG1o9l7JCx9OrSq4KRmplVh7077c2Y+jGMqR/Dms1rmLV0Fk8ue5LX1r22U72PGj7i0Xce5dF3HgVgSO8hjOo/iuMOOI4zDjyDznv5R2gt8re6h9uyfQvXPH9Ns/vrOtUx6oBRjB48mjMOPIM+dX0qGJ2ZWXXr170fk4+YzOQjJrNy00pmL5vNvBXzWLhmIdvzXgi/bMMylm1YxlPLn+Ks+rPaKWIrt6pPjCSNB64GhgMvA1dExOttqSupJzAD+CrwCfBrYFpERFk70YK+3foydJ+hn6/qCjB0n6GMOmAUpww8hVH9R1HXubhVr83MbFcDew5kyogpTBkxhQ1bN/D8qud5dsWzLFi9gFWfrPq83nH9j/ME7RpW1YmRpHHAQ8AVwFPAtcA8SUdGxKpi6ir7Uz6b7P1xZwFDyBKjrsBVlehPc84Zeg6rNq1iVP9RHNv/WPp269ue4ZiZ1bzeXXpz9pCzOXvI2QCs2LiCBasX8OLqF/mTgcW9k9KqS1UnRsA04DcRcRuApEuA94GpaV8xdccBJwCHRcRbwGJJ04GrJU2PiI20k0uPvLS9Tm1mZsCgXoMY1GsQE4dNbO9QrMyq9lElSQcBxwIP58oiYgswlyzJKbbu14C3UlKUMwvoCZxa8g6YmZnZHqearxjVp+07eeXLya78FFu3vpn9AK0uDy3pjWZ2dW1oaKCurjbnATV8tqP1SmVWd0vL+b1jLEwtxAjVEadjLEwh33c1amhogGyahu2Bqjkxyr3ca31e+SYg/9GsQur2J5uQnb+fJtorWkP6m9AB5V5BvbVcJ2jY3nqddtYlxVi2MSiFCozjbv9ZqILvGmgxzrL/fShUO49lQeNQLd93G3QF2j/ztCZVc2K0Lm1755XvA6xuQ911zeynifZ2ERFHtFanI8pdSevI4+MxyHgcPAY5Hgfbk1XzdcoVaTskr7y+0b5i6q5oZn/j483MzKyGVXNitCR9JuQKJPUARgO/aUPd3wIjJB3c6LhzgLXAM6UN3czMzPZEVZsYpUUXbwAmSZoqaThwD/AxcLekiyWtk3RUa3VTkw+SJU8zJY2QNAG4Erg5Ijrq/CAzM7MOpWoTI4CImEm2DtHfAc+RTWg7KSLWk01s2wJ8VkBdImIbcBqwBpgHXA98PyJurlyPzMzMrD2pHd92YR2AJ1l6DHI8Dh6DHI+D7cmcGJmZmZklVX0rzczMzKyUnBiZmZmZJU6MzMzMzBInRmZmZmaJEyMzMzOzxImRmZmZWeLEyMzMzCxxYmQlJ+mvJC2U9AdJj0ga1Ew9SbpA0tz0+paVku6VtF+lYy6HQsehUf0TJT0jKSSdVqk4S0nSeEn/I+kjSU9JGlGKutWmyHE4QtJv0/c+uZJxllOhYyDpbEmPS3pf0lpJD0uqb6quWSU4MbKSkvQ3wG3AjWSvWOkOPCOpWzOHXALcBYwEvgGcyq4vAa46xY6DpPHAU8CHFQuyxCSNAx4C7gNOIL1eR9KA3albbYoch6OBl4FtlYyx3Ir8fieTvcT7FGAcUA/MlrR3hcI124lXvraSkdQFWArcFxFXpbIBwArgkoi4p4A2LgH+DRgaEe+UMdyyacs4SOpL9v6+Q4C5wOiImFepmEtB0gLg9xFxQfp9HfA+MCMiprW1brUpchy6AYOBBmAZMCUi7q1owGWwO9+vpNOB/wbGRMSccsdqls9XjKyUTgYGAA/nCiJiFfAq2f8EC7EubXuVNrSKKnocImJdRKysTHilJ+kg4Fh27vMWsiRvXFvrVpti+xYRn0bE/1UswAoowfdbC/8GWBVzYmSllJsXkH+lZznQ4vyaRk4GPgXeKlVQ7aAU41BtiulzLY9PLfetULs7BicDASwqYUxmBXNiZKXUP23X55VvAvq0drCkgcBlwM8joqG0oVXUbo1DlSqmz7U8PrXct0K1eQwk9QSuBh6MiHdLH5pZ65wYWUEknZ+emmn2QzZHBqB33uH7AKtbab+ObLLmcuD6knegRMo9DlUsd/ujkD4XU7fa1HLfCtWmMZAkssnanYHvlCc0s9Y5MbKCRMT9EaGWPsALqfqQvMPrySYeN0lSZ+BXwEHAn0XExnL0oRTKOQ5VLtevIXnlTfW5mLrVppb7Vqi2jsEtwFhgYkR0lLGyPZATIyulp8kun0/IFaT1SEbQzCP4kjqR/S/xVLKnUN4uf5hlV/Q41IAl6dO4zz2A0eza52LqVpta7luhih4DSTcBfw2Mj4j5FYjRrFlOjKxkImIz8FPgHyRNTAu6zQReAx4BkHRNWsht/5QU3Qt8FTgXWC5pn/Tp2sxp9njFjkM7hloyka37cQMwSdJUScOBe4CPgbslXaxsEc+jWqvbPj0ojWLGoT3jLKdix0DSjcDlwEXAy43+DWhu7TOzsurc3gFYbYmI6yVtB24ie9x2DvDnEbE9VdkObAF2AF8HJqXy/DV7pgHXlT3gMilyHGpCRMxMi/JdQfaD8XngpIhYL2kHWX8/a61uO4ReUsWMQ60qdAwknQhclQ57MK+Ze4CLKxOx2Re8wKOZmZlZ4ltpZmZmZokTIzMzM7PEiZGZmZlZ4sTIzMzMLHFiZGZmZpY4MTIzMzNLnBiZmZmZJU6MzMzMzBInRmZmZmaJEyMzMzOzxImRmZmZWeLEyMzMzCxxYmRmFSXpckkbJfVsVHampK2Sjkq/v1ZStPDZr8B2H5O0TVK3JuqfI6lB0ohy9dXMqk/n9g7AzDqcqcCvI2ITgKSuwF3ATyLitby6twPzmmhjY2vtJiOBNyLi0/zKEfE7Sb9L5z6h+G6YWS1yYmRmFSPpZOBw4KJGxZOBfsBPmzjkhYi4vy3tShqU2n2khUNvAF6SNDYinmy9B2ZW63wrzcwqaSrwUkS80qjsW8CDEbG2xO0em7YLmjsoIl4GXkgxmJk5MTKrNZLelLSqifK+kjZIel1Sp3aIa1/ga8AdjcoGAkcCbb5a01S7yci0XZDq7SXpF2mO0tWN6j0BnC6pS1tjMLPa4cTIrPYsBg6Q1Duv/PtAL+C7EbG98mFxEfAZ8O+Nyr6Sts+WuF3IrhhtAV6XtBdwNzAF+FZETG9Ubx7QAzhuN2IwsxrhxMis9ixO2+G5gjTf5m+BJyPiiXaJKrvd9cuI+KRR2WAggOUlbheyK0aLgO3APcBfAH8ZEbfl1Xu3USxm1sE5MTKrPbskRsC1wN7AdyF7EizdVvpA0hxJCySNLcXJJS2VdHle2YnACOBf86r3A9a39QpWc+1KOhDYH3gZuBf4OnBuRPyyiWbWNYrFzDo4P5VmVntyidGhAJKGkd1CuisiXk/7/pHsNtaRwMamHmcvsalkT5gtyivvDuzOuZtrNze/aDxwIPA68GgzbeTO33034jCzGuErRma1ZynwCV9cMfpnsh/+1zaqcyIwJyLWlDspkrQP2RWb/MnRAGuBXRZrLEG7ucTo98CPya4qndtMU7nz785TcWZWI5wYmdWYiAjgDWCYpCOA84EbI+IDAEkPAmOBSZI+knRaelJrQtrfLf1+vKQnJX0o6bl05YlU58eS3k37npZ0eAshfQPYBjS1HtEaoKukXm3oakvtHgtsAs4GfgisB6alSdj5crfQ1rQhBjOrMU6MzGrTYuBg4HvACuBfcjsi4jyyp8Buj4g+EZG/snRD2v4I+HtgELAZuLNRnbvIbsP1JXuq674WYslNjt7cxL5X0/aYAvpUTLsjgVcjYmtEfAzMAHJJYr4/TttFbYjBzGqMEyOz2rSY7NH8C4GrImJLoQdGxI70y5sj4q2UePwKOEFS43mJPyGbu3M5cEx6tcdOJB0PHEXTt7sAnie7snN6ofG11q6kerKEbWGj4luADcC1Tazh9BXgfyPivWJiMLPa5MTIrDblJmAvZNf1fQr1YaNfLwW6Aj1S4vEs2dNc5wPnAQLqmmhjKjA/IhY3sY+I2Ab8J3CBJBURW0vt5uYXLWp0nvXArWTzriblyiX1IJug/UAR5zazGuan0sxqUETMIUtWymEcsC0i/glAUkvr/7xFtrBiS24iu6X2p8B/AUTEdcB1bWk3Ih6iib5HxA+AH+QVTwG6AD9vJUYz6yCcGJlZsTYA+6eJ3ZuA3Os1dnnNSETc3FpjEbFY0i+AH0l6Ml1Fau2YVtttjaQ+ZInS9IhY11p9M+sYfCvNzIp1P9ntueeA/+CLid35ryApxndSW4fsXmhFOZRsUvZNFTynme3hlD3Za2ZmZma+YmRmZmaWODEyMzMzS5wYmZmZmSVOjMzMzMwSJ0ZmZmZmiRMjMzMzs8SJkZmZmVnixMjMzMwscWJkZmZmljgxMjMzM0ucGJmZmZklTozMzMzMEidGZmZmZokTIzMzM7PEiZGZmZlZ4sTIzMzMLPl/DmHBns4yqzgAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#print(2*np.std(v_final)**2*mass)\n", "def normaldist(x, mu, sigma, dx):\n", " # Gaussian probability distribution function \n", " # probability of landing in a bin of width dx is p(x)dx\n", " return dx/sigma/np.sqrt(2*np.pi)*np.exp(-(x-mu)**2/2/sigma**2)\n", "\n", "def lett_temperature(s, delta):\n", " \"\"\"\n", " Returns the ratio of the expected temperature relative to the \"bare\" Doppler temperature.\n", " \"\"\"\n", " return 0.5*(1+2*s+4*delta**2)/2/np.abs(delta)\n", "\n", "def fit_vfinal(v_final, N_atom):\n", " dx = 2*iqr(v_final)/N_atom**(1/3)\n", " xb = np.arange(dx/2, 1.1*np.amax(np.abs(v_final)), dx)\n", " xb = np.concatenate((-xb[::-1], xb))\n", " \n", " x = xb[:-1] + np.diff(xb)/2\n", " y = np.histogram(v_final, bins=xb)[0]/N_atom #Probability of an atom landing in this bin.'\n", " \n", " ok = (y>0)\n", " weights = np.zeros(ok.shape)\n", " weights[ok] = 1./np.sqrt(y[ok]/N_atom)\n", " model = lmfit.Model(normaldist)\n", " params = model.make_params()\n", " params['dx'].value = dx # bin width, probability of landing in the bin is p(x) dx\n", " params['dx'].vary = False\n", " params['mu'].value = 0.\n", " params['mu'].vary = False\n", " params['sigma'].value = np.std(v_final)\n", " \n", " result = model.fit(y[ok], params, x=x[ok], weights=weights[ok])\n", "\n", " return result, x, y, dx\n", "\n", "result, x, y, dx = fit_vfinal(v_final, N_atom)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "\n", "ax.bar(x, y, width=0.8*dx, yerr=np.sqrt(y/N_atom)) #Poissonian error\n", "\n", "x_fit = np.linspace(-1.1*np.amax(np.abs(v_final)), 1.1*np.amax(np.abs(v_final)), 101)\n", "\n", "ax.plot(x_fit, result.eval(x=x_fit))\n", "ax.plot(x_fit, normaldist(x_fit, 0, np.sqrt(lett_temperature(s, delta)/2/mass), dx))\n", "\n", "ax_twin = ax.twinx()\n", "ax_twin.plot(x_fit, eqn.profile['molasses'].F[0], 'k-')\n", "\n", "ax.set_ylabel('$p(v_{\\\\rm final}) dx$')\n", "ax.set_xlabel('$v_{\\\\rm final}/(\\Gamma/k)$');\n", "\n", "ax_twin.set_ylabel('$F/\\hbar k \\Gamma$');" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Model

Model(normaldist)

Fit Statistics

fitting methodleastsq
# function evals9
# data points7
# variables1
chi-square 2.07748283
reduced chi-square 0.34624714
Akaike info crit.-6.50327217
Bayesian info crit.-6.55736202

Variables

name value standard error relative error initial value min max vary
mu 0.00000000 0.00000000 0.0 -inf inf False
sigma 0.11124057 0.00727687 (6.54%) 0.10332026124494349 -inf inf True
dx 0.06282566 0.00000000 (0.00%) 0.06282565569345401 -inf inf False
" ], "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Measure the temperature vs. detuning and intensity \n", "\n", "We can compare to the formula in Lett, *et. al.*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Progress: |██████████--------------------| 33.3%; time left: 2:20:08\r" ] } ], "source": [ "deltas = np.array([-3, -2., -1., -0.5, -0.375, -0.25, -0.125])\n", "intensities = np.array([0.3, 1, 3])\n", "\n", "Deltas, Intensities = np.meshgrid(deltas, intensities)\n", "\n", "N_atom = 256\n", "\n", "v_final = {}\n", "result = {}\n", "\n", "# Make a progress bar:\n", "progress = progressBar()\n", " \n", "it = np.nditer([Deltas, Intensities, None, None])\n", "for (delta, s, sigma, delta_sigma) in it:\n", " # First, generate the new laser beams and hamiltonian:\n", " laserBeams = return_lasers(delta, s)\n", " hamiltonian = return_hamiltonian(0.)\n", "\n", " # Next, generate the OBE, rate equations or heuristic eqn:\n", " eqn = pylcp.heuristiceq(laserBeams, magField, mass=mass)\n", " #eqn = pylcp.rateeq(laserBeams, magField, hamiltonian, include_mag_forces=False)\n", "\n", " eqn.set_initial_position_and_velocity(np.array([0., 0., 0.]),\n", " np.array([0., 0., 0.]))\n", " if isinstance(eqn, pylcp.rateeq):\n", " eqn.set_initial_pop_from_equilibrium()\n", " elif isinstance(eqn, pylcp.obe):\n", " eqn.set_initial_rho_from_rateeq()\n", " \n", " key = (float(delta), float(s))\n", " v_final[key] = np.zeros((N_atom,))\n", " \n", " # Now, evolve however many times:\n", " # Non-parallel version\n", "# for ii in range(N_atom):\n", "# eqn.evolve_motion([0., 10*mass*(1+2*s+4*np.abs(delta)**2)/s],\n", "# random_recoil=True,\n", "# max_scatter_probability=0.25,\n", "# freeze_axis=[False, True, True])\n", "\n", "# v_final[key][ii] = eqn.sol.v[0, -1]\n", "\n", " # Parallel version\n", " v_final[key] = []\n", " ss = np.random.SeedSequence()\n", " child_seeds = ss.spawn(N_atom)\n", " for jj in range(int(N_atom/chunksize)):\n", " with pathos.pools.ProcessPool(nodes=4) as pool:\n", " v_final[key] += pool.map(\n", " generate_random_solution,\n", " chunksize*[eqn],\n", " chunksize*[10*mass*(1+2*s+4*np.abs(delta)**2)/s],\n", " child_seeds[jj*chunksize:(jj+1)*chunksize]\n", " )\n", " \n", " # Now bin and fit, just as above:\n", " result[key], x, y, dx = fit_vfinal(v_final[key], N_atom)\n", "\n", " sigma[...] = result[key].best_values['sigma']\n", " delta_sigma[...] = result[key].params['sigma'].stderr\n", " \n", " sigma[...] = result[key].best_values['sigma']\n", " delta_sigma[...] = result[key].params['sigma'].stderr\n", "\n", " progress.update((it.iterindex+1)/it.itersize)\n", "\n", "# Finish updating the progress bar just in case:\n", "progress.update(1.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "deltas_thr = np.linspace(-3, -0.125, 51)\n", "fig, ax = plt.subplots(1, 1)\n", "for ii, (s, sigmas, err) in enumerate(zip(intensities, it.operands[2], it.operands[3])):\n", " plt.errorbar(deltas, 2*sigmas**2*mass, 4*sigmas*err*mass, fmt='.', color='C%d'%ii)\n", " plt.plot(deltas_thr, lett_temperature(s, deltas_thr), linewidth=0.75, color='C%d'%ii)\n", "ax.set_xlabel('$\\Delta/\\Gamma$')\n", "ax.set_ylabel('$T/T_D$')\n", "ax.set_ylim((0.1, 5));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig.savefig('20210610T1200_heuristic_eqn_M_200.pdf')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }