{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.006002, "end_time": "2026-06-30T01:11:43.626548+00:00", "exception": false, "start_time": "2026-06-30T01:11:43.620546+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Spherical Distribution Functions\n", "\n", "galpy includes several distribution functions for spherical systems, both\n", "isotropic and anisotropic. These DFs are tied to a specific spherical potential\n", "and can be used to compute properties of the system or to generate samples. \n", "galpy contains a number of specific isotropic and anisotropic DFs, \n", "but it also includes a general classes for computing the DF of any spherical system \n", "using Eddington's formula for isotropic systems and similar formulas for anisotropic systems\n", "with constant anisotropy or anisotropy of the Osipkov-Merritt type. See [galaxiesbook.org](https://galaxiesbook.org/chapters/I-04.-Equilibria-of-Collisionless-Stellar-Systems_6-Spherical-distribution-functions.html) for more details on these DFs and the underlying theory." ] }, { "cell_type": "code", "execution_count": 1, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:43.636767Z", "iopub.status.busy": "2026-06-30T01:11:43.636566Z", "iopub.status.idle": "2026-06-30T01:11:44.710408Z", "shell.execute_reply": "2026-06-30T01:11:44.709464Z" }, "papermill": { "duration": 1.080067, "end_time": "2026-06-30T01:11:44.711121+00:00", "exception": false, "start_time": "2026-06-30T01:11:43.631054+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from galpy.util.quadpack import AccuracyWarning\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)\n", "warnings.filterwarnings(\"ignore\", category=AccuracyWarning)" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.004218, "end_time": "2026-06-30T01:11:44.719761+00:00", "exception": false, "start_time": "2026-06-30T01:11:44.715543+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Isotropic Hernquist DF\n", "\n", "The `isotropicHernquistdf` is initialized from a `HernquistPotential` instance.\n", "The DF is a function of energy only, $f(E)$, corresponding to an isotropic\n", "velocity distribution." ] }, { "cell_type": "code", "execution_count": 2, "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:44.732690Z", "iopub.status.busy": "2026-06-30T01:11:44.732326Z", "iopub.status.idle": "2026-06-30T01:11:46.337137Z", "shell.execute_reply": "2026-06-30T01:11:46.336324Z" }, "papermill": { "duration": 1.614156, "end_time": "2026-06-30T01:11:46.338274+00:00", "exception": false, "start_time": "2026-06-30T01:11:44.724118+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import HernquistPotential\n", "from galpy.df import isotropicHernquistdf\n", "\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)" ] }, { "cell_type": "markdown", "id": "72eea5119410473aa328ad9291626812", "metadata": { "papermill": { "duration": 0.004466, "end_time": "2026-06-30T01:11:46.348311+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.343845+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Evaluating the DF as a function of energy\n", "\n", "The DF can be evaluated at a given (relative) energy $E$. The relative energy\n", "is defined as $E = \\Psi(r) - \\frac{1}{2}v^2$ where $\\Psi = -\\Phi$ is the\n", "relative potential:" ] }, { "cell_type": "code", "execution_count": 3, "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:46.358019Z", "iopub.status.busy": "2026-06-30T01:11:46.357656Z", "iopub.status.idle": "2026-06-30T01:11:46.565762Z", "shell.execute_reply": "2026-06-30T01:11:46.564893Z" }, "papermill": { "duration": 0.214408, "end_time": "2026-06-30T01:11:46.566859+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.352451+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0 = hp(0.0, 0.0, use_physical=False)\n", "fE = numpy.array([dfh.fE(E * phi0) for E in Es])\n", "plt.semilogy(Es, fE)\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$f(E)$\")\n", "plt.title(\"Isotropic Hernquist DF\");" ] }, { "cell_type": "markdown", "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "papermill": { "duration": 0.004454, "end_time": "2026-06-30T01:11:46.576042+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.571588+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Sampling positions and velocities\n", "\n", "The `sample` method draws random phase-space points from the DF.\n", "By default it returns an `Orbit` object:" ] }, { "cell_type": "code", "execution_count": 4, "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:46.586195Z", "iopub.status.busy": "2026-06-30T01:11:46.585978Z", "iopub.status.idle": "2026-06-30T01:11:46.606347Z", "shell.execute_reply": "2026-06-30T01:11:46.605303Z" }, "papermill": { "duration": 0.02636, "end_time": "2026-06-30T01:11:46.606942+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.580582+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Type: \n", "Number of orbits: 5000\n" ] } ], "source": [ "numpy.random.seed(1)\n", "samples = dfh.sample(n=5000)\n", "print(\"Type:\", type(samples))\n", "print(\"Number of orbits:\", len(samples))" ] }, { "cell_type": "markdown", "id": "664873cf", "metadata": { "papermill": { "duration": 0.004538, "end_time": "2026-06-30T01:11:46.616279+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.611741+00:00", "status": "completed" }, "tags": [] }, "source": [ "Let's plot the spatial distribution of the sampled orbits:" ] }, { "cell_type": "code", "execution_count": 5, "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:46.626479Z", "iopub.status.busy": "2026-06-30T01:11:46.626265Z", "iopub.status.idle": "2026-06-30T01:11:46.759725Z", "shell.execute_reply": "2026-06-30T01:11:46.758724Z" }, "papermill": { "duration": 0.139582, "end_time": "2026-06-30T01:11:46.760484+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.620902+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the spatial distribution\n", "Rs = samples.R()\n", "zs = samples.z()\n", "plt.scatter(Rs, zs, s=1, alpha=0.3)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Sampled positions from isotropic Hernquist DF\")\n", "plt.xlim(0, 15)\n", "plt.ylim(-15, 15);" ] }, { "cell_type": "markdown", "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "papermill": { "duration": 0.004749, "end_time": "2026-06-30T01:11:46.770949+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.766200+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Velocity dispersion profile\n", "\n", "We can compare the velocity dispersion profile of the samples to the\n", "analytical prediction. The `sigmar` method computes $\\sigma_r(r)$:" ] }, { "cell_type": "code", "execution_count": 6, "id": "b118ea5561624da68c537baed56e602f", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:46.781667Z", "iopub.status.busy": "2026-06-30T01:11:46.781454Z", "iopub.status.idle": "2026-06-30T01:11:46.990297Z", "shell.execute_reply": "2026-06-30T01:11:46.989379Z" }, "papermill": { "duration": 0.215324, "end_time": "2026-06-30T01:11:46.991116+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.775792+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Analytical velocity dispersion\n", "rs = numpy.linspace(0.1, 10.0, 50)\n", "sigmar = numpy.array([dfh.sigmar(r) for r in rs])\n", "\n", "# Velocity dispersion from samples\n", "r_samples = samples.r()\n", "vr_samples = (\n", " samples.x() * samples.vx() + samples.y() * samples.vy() + samples.z() * samples.vz()\n", ") / r_samples\n", "\n", "# Bin the samples\n", "rbins = numpy.linspace(0.1, 10.0, 11)\n", "rmid = 0.5 * (rbins[:-1] + rbins[1:])\n", "sig_binned = numpy.zeros(len(rmid))\n", "for i in range(len(rmid)):\n", " mask = (r_samples >= rbins[i]) & (r_samples < rbins[i + 1])\n", " if numpy.sum(mask) > 2:\n", " sig_binned[i] = numpy.std(vr_samples[mask])\n", "\n", "plt.plot(rs, sigmar, label=\"Analytical\")\n", "plt.plot(rmid, sig_binned, \"o\", label=\"Samples\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(r\"$\\sigma_r(r)$\")\n", "plt.legend()\n", "plt.title(\"Velocity dispersion profile\");" ] }, { "cell_type": "markdown", "id": "72511469", "metadata": { "papermill": { "duration": 0.004882, "end_time": "2026-06-30T01:11:47.002476+00:00", "exception": false, "start_time": "2026-06-30T01:11:46.997594+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Jeans equation tools\n", "\n", "galpy also provides tools for computing velocity moments from the Jeans equation\n", "in `galpy.df.jeans`. These are useful for comparing with DF-based calculations\n", "and for quick estimates when a full DF is not needed.\n", "\n", "The main functions are:\n", "- `jeans.sigmar(pot, r)`: radial velocity dispersion $\\sigma_r(r)$\n", "- `jeans.sigmalos(pot, R)`: line-of-sight velocity dispersion $\\sigma_\\mathrm{los}(R)$\n", "\n", "Both of these functions allow the user to specify the anisotropy profile $\\beta(r)$, which is defined as\n", "$\\beta(r) = 1 - \\frac{\\sigma_\\theta^2 + \\sigma_\\phi^2}{2\\sigma_r^2}$ as well as the tracer density profile $\\nu(r)$, which is needed to solve the Jeans equation. By default, `beta` is set to 0 (isotropic) and `nu` is set to the density profile of the potential." ] }, { "cell_type": "code", "execution_count": 7, "id": "ad85600f", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:11:47.013506Z", "iopub.status.busy": "2026-06-30T01:11:47.013293Z", "iopub.status.idle": "2026-06-30T01:12:51.275062Z", "shell.execute_reply": "2026-06-30T01:12:51.274255Z" }, "papermill": { "duration": 64.275078, "end_time": "2026-06-30T01:12:51.282485+00:00", "exception": false, "start_time": "2026-06-30T01:11:47.007407+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import jeans\n", "\n", "# Compute radial velocity dispersion from the Jeans equation\n", "rs_jeans = numpy.linspace(0.1, 10.0, 50)\n", "sigmar_jeans = numpy.array([jeans.sigmar(hp, r, use_physical=False) for r in rs_jeans])\n", "\n", "# Compute for constant beta=0.3\n", "sigmar_jeans_b03 = numpy.array(\n", " [jeans.sigmar(hp, r, beta=0.3, use_physical=False) for r in rs_jeans]\n", ")\n", "\n", "# Compute for Osipkov-Merritt-style beta(r) = r^2/(r^2 + ra^2)\n", "beta_om = lambda r: r**2 / (r**2 + 1.4**2)\n", "sigmar_jeans_om = numpy.array(\n", " [jeans.sigmar(hp, r, beta=beta_om, use_physical=False) for r in rs_jeans]\n", ")\n", "\n", "# Compute line-of-sight velocity dispersion\n", "sigmalos_jeans = numpy.array(\n", " [jeans.sigmalos(hp, R, use_physical=False) for R in rs_jeans]\n", ")\n", "sigmalos_jeans_b03 = numpy.array(\n", " [jeans.sigmalos(hp, R, beta=0.3, use_physical=False) for R in rs_jeans]\n", ")\n", "sigmalos_jeans_om = numpy.array(\n", " [jeans.sigmalos(hp, R, beta=beta_om, use_physical=False) for R in rs_jeans]\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "axes[0].plot(rs_jeans, sigmar_jeans, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[0].plot(rs_jeans, sigmar_jeans_b03, label=r\"Constant $\\beta=0.3$\")\n", "axes[0].plot(rs_jeans, sigmar_jeans_om, \"--\", label=r\"OM ($r_a=1.4$)\")\n", "axes[0].set_xlabel(r\"$r$\")\n", "axes[0].set_ylabel(r\"$\\sigma_r(r)$\")\n", "axes[0].set_title(\"Jeans equation: radial velocity dispersion\")\n", "axes[0].legend()\n", "\n", "axes[1].plot(rs_jeans, sigmalos_jeans, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[1].plot(rs_jeans, sigmalos_jeans_b03, label=r\"Constant $\\beta=0.3$\")\n", "axes[1].plot(rs_jeans, sigmalos_jeans_om, \"--\", label=r\"OM ($r_a=1.4$)\")\n", "axes[1].set_xlabel(r\"$R$\")\n", "axes[1].set_ylabel(r\"$\\sigma_\\mathrm{los}(R)$\")\n", "axes[1].set_title(\"Jeans equation: line-of-sight velocity dispersion\")\n", "axes[1].legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "938c804e27f84196a10c8828c723f798", "metadata": { "papermill": { "duration": 0.005255, "end_time": "2026-06-30T01:12:51.293427+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.288172+00:00", "status": "completed" }, "tags": [] }, "source": [ "## King DF\n", "\n", "The King DF models a tidally-truncated, lowered-isothermal distribution.\n", "It is initialized with the dimensionless central potential $W_0$, total mass, and\n", "tidal radius:" ] }, { "cell_type": "code", "execution_count": 8, "id": "504fb2a444614c0babb325280ed9130a", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:12:51.305436Z", "iopub.status.busy": "2026-06-30T01:12:51.305214Z", "iopub.status.idle": "2026-06-30T01:12:51.548060Z", "shell.execute_reply": "2026-06-30T01:12:51.546889Z" }, "papermill": { "duration": 0.249968, "end_time": "2026-06-30T01:12:51.548774+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.298806+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "from galpy.df import kingdf\n", "\n", "kdf = kingdf(W0=3.0, M=1.0, rt=1.5)\n", "\n", "# Sample from the King model\n", "king_samples = kdf.sample(n=5000)\n", "r_king = king_samples.r()\n", "plt.hist(r_king, bins=30, density=True, label=\"Samples\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(\"Density\")\n", "plt.title(\"King model radial distribution (W0=3)\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "74bb50cf", "metadata": { "papermill": { "duration": 0.005616, "end_time": "2026-06-30T01:12:51.561598+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.555982+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can compare the sampled radial distribution with the theoretical King density\n", "profile. The King DF provides a `dens(r)` method that returns the density at a\n", "given radius. To compare with the histogram of radii, we need to weight by the\n", "volume element $4\\pi r^2$:" ] }, { "cell_type": "code", "execution_count": 9, "id": "ed1c1963", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:12:51.574041Z", "iopub.status.busy": "2026-06-30T01:12:51.573835Z", "iopub.status.idle": "2026-06-30T01:12:51.769244Z", "shell.execute_reply": "2026-06-30T01:12:51.768144Z" }, "papermill": { "duration": 0.202419, "end_time": "2026-06-30T01:12:51.769857+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.567438+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Theoretical King density profile weighted by volume element\n", "r_theory = numpy.linspace(0.01, 1.49, 200)\n", "rho_theory = numpy.array([kdf.dens(r) for r in r_theory])\n", "# The histogram shows the PDF of radii, which is proportional to rho(r) * 4*pi*r^2\n", "radial_pdf = rho_theory * 4.0 * numpy.pi * r_theory**2\n", "# Normalize to integrate to 1 (since histogram is density=True)\n", "from scipy import integrate\n", "\n", "radial_pdf /= integrate.trapezoid(radial_pdf, r_theory)\n", "\n", "plt.hist(r_king, bins=30, density=True, alpha=0.5, label=\"Samples\")\n", "plt.plot(r_theory, radial_pdf, \"r-\", lw=2, label=\"Theoretical King profile\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(\"PDF\")\n", "plt.title(\"King model: samples vs. theoretical radial distribution\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "0654d7d6", "metadata": { "papermill": { "duration": 0.005807, "end_time": "2026-06-30T01:12:51.781794+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.775987+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Differential energy distribution\n", "\n", "galpy can also compute the differential energy distribution $N(E)$, which is the number of stars per unit energy. This is related to the DF by integrating over phase space at fixed energy:" ] }, { "cell_type": "code", "execution_count": 10, "id": "da7366cc", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:12:51.794809Z", "iopub.status.busy": "2026-06-30T01:12:51.794574Z", "iopub.status.idle": "2026-06-30T01:12:52.156534Z", "shell.execute_reply": "2026-06-30T01:12:52.155364Z" }, "papermill": { "duration": 0.369555, "end_time": "2026-06-30T01:12:52.157257+00:00", "exception": false, "start_time": "2026-06-30T01:12:51.787702+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)\n", "\n", "from galpy.potential import NFWPotential, PlummerPotential\n", "from galpy.df import isotropicNFWdf, isotropicPlummerdf\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "dfnfw = isotropicNFWdf(pot=nfp)\n", "pp = PlummerPotential(amp=1.0, b=1.0)\n", "dfplummer = isotropicPlummerdf(pot=pp)\n", "\n", "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0_hp = hp(0.0, 0.0, use_physical=False)\n", "dMdE_hp = numpy.array([dfh.dMdE(E * phi0_hp) for E in Es])\n", "phi0_nfw = nfp(0.0, 0.0, use_physical=False)\n", "dMdE_nfw = numpy.array([dfnfw.dMdE(E * phi0_nfw) for E in Es])\n", "phi0_plummer = pp(0.0, 0.0, use_physical=False)\n", "dMdE_plummer = numpy.array([dfplummer.dMdE(E * phi0_plummer) for E in Es])\n", "plt.semilogy(Es, dMdE_hp, label=\"Hernquist\")\n", "plt.semilogy(Es, dMdE_nfw, label=\"NFW\")\n", "plt.semilogy(Es, dMdE_plummer, label=\"Plummer\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Isotropic DFs\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "c98e8906", "metadata": { "papermill": { "duration": 0.005937, "end_time": "2026-06-30T01:12:52.170282+00:00", "exception": false, "start_time": "2026-06-30T01:12:52.164345+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Using the Eddington inversion\n", "\n", "The ``eddingtondf`` class can be used to compute the isotropic DF for any spherical potential using Eddington's formula. This is useful for potentials that do not have an analytical DF, for comparing with the analytical DFs of specific potentials, or for computing the DFs of tracers in a given potential, e.g., a Hernquist population in an NFW potential. We give an example of the latter here:" ] }, { "cell_type": "code", "execution_count": 11, "id": "15c62173", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:12:52.183677Z", "iopub.status.busy": "2026-06-30T01:12:52.183469Z", "iopub.status.idle": "2026-06-30T01:12:52.523681Z", "shell.execute_reply": "2026-06-30T01:12:52.522766Z" }, "papermill": { "duration": 0.348143, "end_time": "2026-06-30T01:12:52.524519+00:00", "exception": false, "start_time": "2026-06-30T01:12:52.176376+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import eddingtondf\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "df_edd = eddingtondf(pot=nfp, denspot=hp)\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "phi0_nfw = nfp(0.0, 0.0, use_physical=False)\n", "dMdE_edd = numpy.array([df_edd.dMdE(E * phi0_nfw) for E in Es])\n", "plt.semilogy(Es, dMdE_edd, label=\"Eddington inversion\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Isotropic DF from Eddington inversion\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "new-trunc-md-1", "metadata": { "papermill": { "duration": 0.006243, "end_time": "2026-06-30T01:12:52.537374+00:00", "exception": false, "start_time": "2026-06-30T01:12:52.531131+00:00", "status": "completed" }, "tags": [] }, "source": [ "## N-body initial conditions for a truncated NFW halo\n", "\n", "A common application of these sampling tools is setting up N-body initial\n", "conditions for a dark-matter halo in equilibrium. The\n", "[NFW profile](../../reference/potentialnfw.rst) is the standard choice, but it\n", "has a well-known problem for this purpose: its enclosed mass grows like\n", "$M( finite total mass.\n", "# (The total is a bit below M_vir because the cutoff also suppresses the\n", "# density just inside r_vir.)\n", "tnfw = ExpTruncNFWPotential.from_nfw(nfw, rc=rvir)\n", "tnfw.turn_physical_on()\n", "print(f\"\\nTruncated NFW M(" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.potential import evaluateDensities\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(11, 4.2))\n", "\n", "# Cumulative mass profiles\n", "rr = numpy.geomspace(1.0, 3000.0, 100) * u.kpc\n", "M_nfw = numpy.array([nfw.mass(r) for r in rr])\n", "M_tnfw = numpy.array([tnfw.mass(r) for r in rr])\n", "ax[0].loglog(rr.value, M_nfw, label=\"NFW (diverges)\")\n", "ax[0].loglog(rr.value, M_tnfw, label=\"Truncated NFW (finite)\")\n", "ax[0].axvline(rvir.value, color=\"k\", ls=\":\", lw=1, label=r\"$r_\\mathrm{vir}$\")\n", "ax[0].set_xlabel(\"r [kpc]\")\n", "ax[0].set_ylabel(r\"$M(" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(11, 4.2))\n", "\n", "# Density profiles of the two components\n", "rr = numpy.geomspace(0.05, 3.0 * rvir_dw.value, 120)\n", "rho_dm = numpy.array([evaluateDensities(dm, r * u.kpc, 0) for r in rr])\n", "rho_st = numpy.array([evaluateDensities(stars, r * u.kpc, 0) for r in rr])\n", "ax[0].loglog(rr, rho_dm, label=\"Dark matter (truncated NFW)\")\n", "ax[0].loglog(rr, rho_st, label=\"Stars (Plummer)\")\n", "ax[0].axvline(b_star.value, color=\"k\", ls=\":\", lw=1, label=r\"$b_\\star$\")\n", "ax[0].set_xlabel(\"r [kpc]\")\n", "ax[0].set_ylabel(r\"$\\rho\\ [M_\\odot\\,\\mathrm{kpc}^{-3}]$\")\n", "ax[0].set_title(\"Density profiles\")\n", "ax[0].legend()\n", "\n", "# Sampled radial distributions\n", "bins = numpy.geomspace(0.05, 3.0 * rvir_dw.value, 40)\n", "ax[1].hist(\n", " dm_samples.r(),\n", " bins=bins,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=\"Dark-matter samples\",\n", ")\n", "ax[1].hist(\n", " star_samples.r(),\n", " bins=bins,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=\"Stellar samples\",\n", ")\n", "ax[1].set_xscale(\"log\")\n", "ax[1].set_xlabel(\"r [kpc]\")\n", "ax[1].set_ylabel(\"PDF\")\n", "ax[1].set_title(\"Sampled radii\")\n", "ax[1].legend()\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "new-trunc-md-8", "metadata": { "papermill": { "duration": 0.00711, "end_time": "2026-06-30T01:13:05.424259+00:00", "exception": false, "start_time": "2026-06-30T01:13:05.417149+00:00", "status": "completed" }, "tags": [] }, "source": [ "Because the stellar DF is computed in the *combined* potential, the stellar\n", "kinematics reflect the dark matter that dominates the mass budget. The dark\n", "matter inflates the stellar velocity dispersion well above what the stars'\n", "self-gravity alone would produce — this is exactly the dynamical signature used\n", "to infer that dwarf spheroidals are dark-matter dominated.\n", "\n", "Both examples above used *isotropic* DFs (`eddingtondf`), but the same recipe —\n", "build a DF in the (combined) potential and call `sample` — applies to the\n", "*anisotropic* DFs described below (e.g. the constant-$\\beta$ and Osipkov–Merritt\n", "models): just swap `eddingtondf` for the desired anisotropic DF class to give\n", "the sampled populations radially or tangentially biased velocity distributions.\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "new-trunc-code-8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:13:05.439924Z", "iopub.status.busy": "2026-06-30T01:13:05.439722Z", "iopub.status.idle": "2026-06-30T01:13:05.749427Z", "shell.execute_reply": "2026-06-30T01:13:05.748563Z" }, "papermill": { "duration": 0.318762, "end_time": "2026-06-30T01:13:05.750252+00:00", "exception": false, "start_time": "2026-06-30T01:13:05.431490+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Stellar sigma_r with dark matter: 8.8 km/s\n", "Stellar sigma_r from stars alone: 3.5 km/s\n" ] } ], "source": [ "# Stellar radial velocity dispersion in the combined potential\n", "sigma_with_dm = numpy.std(star_samples.vr())\n", "\n", "# For comparison: the same stars in equilibrium with only their own gravity\n", "df_st_nodm = eddingtondf(pot=stars, denspot=stars, rmax=3.0 * rvir_dw)\n", "star_nodm = df_st_nodm.sample(n=n_star)\n", "sigma_no_dm = numpy.std(star_nodm.vr())\n", "\n", "print(f\"Stellar sigma_r with dark matter: {sigma_with_dm:.1f} km/s\")\n", "print(f\"Stellar sigma_r from stars alone: {sigma_no_dm:.1f} km/s\")" ] }, { "cell_type": "markdown", "id": "59bbdb311c014d738909a11f9e486628", "metadata": { "papermill": { "duration": 0.007577, "end_time": "2026-06-30T01:13:05.765365+00:00", "exception": false, "start_time": "2026-06-30T01:13:05.757788+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Anisotropic DFs\n", "\n", "galpy includes anisotropic DFs for spherical systems.\n", "\n", "### Constant-beta Hernquist DF\n", "\n", "The `constantbetaHernquistdf` implements a Hernquist DF with constant velocity\n", "anisotropy parameter $\\beta$. Unlike the isotropic case ($\\beta=0$), this DF\n", "has different radial and tangential velocity dispersions. The anisotropy\n", "parameter is defined as $\\beta = 1 - \\sigma_t^2 / (2\\sigma_r^2)$, so\n", "$\\beta > 0$ corresponds to radially-biased orbits and $\\beta < 0$ to\n", "tangentially-biased orbits." ] }, { "cell_type": "code", "execution_count": 20, "id": "b43b363d81ae4b689946ece5c682cd59", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:13:05.781301Z", "iopub.status.busy": "2026-06-30T01:13:05.781075Z", "iopub.status.idle": "2026-06-30T01:13:06.269638Z", "shell.execute_reply": "2026-06-30T01:13:06.268721Z" }, "papermill": { "duration": 0.497725, "end_time": "2026-06-30T01:13:06.270584+00:00", "exception": false, "start_time": "2026-06-30T01:13:05.772859+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "from galpy.df import constantbetaHernquistdf\n", "\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfb = constantbetaHernquistdf(pot=hp, beta=0.3)\n", "\n", "# Sample and compute the velocity anisotropy from samples\n", "samples_b = dfb.sample(n=10000)\n", "r_b = samples_b.r()\n", "vr_b = samples_b.vr()\n", "vt2_b = samples_b.vx() ** 2 + samples_b.vy() ** 2 + samples_b.vz() ** 2 - vr_b**2\n", "\n", "# Compare analytical sigma_r with isotropic and Jeans equation\n", "rs = numpy.linspace(0.3, 8.0, 30)\n", "sigmar_beta = numpy.array([dfb.sigmar(r) for r in rs])\n", "sigmar_iso = numpy.array([dfh.sigmar(r) for r in rs])\n", "sigmar_jeans_beta = numpy.array(\n", " [jeans.sigmar(hp, r, beta=0.3, use_physical=False) for r in rs]\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "# Left panel: velocity dispersion comparison\n", "axes[0].plot(rs, sigmar_iso, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[0].plot(rs, sigmar_beta, label=r\"Constant $\\beta=0.3$ (DF)\")\n", "axes[0].plot(rs, sigmar_jeans_beta, \"--\", label=r\"Jeans ($\\beta=0.3$)\")\n", "axes[0].set_xlabel(r\"$r$\")\n", "axes[0].set_ylabel(r\"$\\sigma_r(r)$\")\n", "axes[0].legend()\n", "axes[0].set_title(\"Radial velocity dispersion\")\n", "\n", "# Right panel: measured anisotropy from samples\n", "rbins = numpy.linspace(0.3, 8.0, 12)\n", "rmid = 0.5 * (rbins[:-1] + rbins[1:])\n", "beta_measured = numpy.zeros(len(rmid))\n", "for i in range(len(rmid)):\n", " mask = (r_b >= rbins[i]) & (r_b < rbins[i + 1])\n", " if numpy.sum(mask) > 10:\n", " sig_r2 = numpy.var(vr_b[mask])\n", " sig_t2 = numpy.mean(vt2_b[mask])\n", " beta_measured[i] = 1.0 - sig_t2 / (2.0 * sig_r2)\n", "\n", "axes[1].axhline(0.3, color=\"r\", ls=\"--\", label=r\"Input $\\beta=0.3$\")\n", "axes[1].plot(rmid, beta_measured, \"o\", label=\"Measured from samples\")\n", "axes[1].set_xlabel(r\"$r$\")\n", "axes[1].set_ylabel(r\"$\\beta(r)$\")\n", "axes[1].legend()\n", "axes[1].set_title(\"Velocity anisotropy profile\")\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "8a65eabff63a45729fe45fb5ade58bdc", "metadata": { "papermill": { "duration": 0.007542, "end_time": "2026-06-30T01:13:06.287155+00:00", "exception": false, "start_time": "2026-06-30T01:13:06.279613+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Osipkov-Merritt Hernquist DF\n", "\n", "The Osipkov-Merritt DF is a widely used model for radially-anisotropic\n", "spherical systems. The velocity anisotropy varies with radius as\n", "$\\beta(r) = r^2/(r^2 + r_a^2)$, where $r_a$ is the anisotropy radius.\n", "This means the system is nearly isotropic at the center ($r \\ll r_a$)\n", "and becomes increasingly radially anisotropic at large radii ($r \\gg r_a$,\n", "$\\beta \\to 1$). Smaller values of $r_a$ lead to stronger overall anisotropy." ] }, { "cell_type": "code", "execution_count": 21, "id": "c3933fab20d04ec698c2621248eb3be0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:13:06.303603Z", "iopub.status.busy": "2026-06-30T01:13:06.303405Z", "iopub.status.idle": "2026-06-30T01:13:07.151720Z", "shell.execute_reply": "2026-06-30T01:13:07.150708Z" }, "papermill": { "duration": 0.8576, "end_time": "2026-06-30T01:13:07.152420+00:00", "exception": false, "start_time": "2026-06-30T01:13:06.294820+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import osipkovmerrittHernquistdf\n", "\n", "dfom = osipkovmerrittHernquistdf(pot=hp, ra=1.4)\n", "\n", "# Compare velocity dispersion profiles: DF vs. Jeans equation\n", "rs = numpy.linspace(0.3, 8.0, 30)\n", "sig_iso = numpy.array([dfh.sigmar(r) for r in rs])\n", "sig_om = numpy.array([dfom.sigmar(r) for r in rs])\n", "\n", "# Jeans equation prediction with the OM beta profile\n", "beta_om = lambda r: r**2 / (r**2 + 1.4**2)\n", "sigmar_jeans_om = numpy.array(\n", " [jeans.sigmar(hp, r, beta=beta_om, use_physical=False) for r in rs]\n", ")\n", "\n", "plt.plot(rs, sig_iso, label=\"Isotropic (DF)\")\n", "plt.plot(rs, sig_om, label=\"Osipkov-Merritt (DF, $r_a=1.4$)\")\n", "plt.plot(rs, sigmar_jeans_om, \"k--\", label=\"Jeans equation (OM $\\\\beta$)\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(r\"$\\sigma_r(r)$\")\n", "plt.legend()\n", "plt.title(\"Comparing isotropic, Osipkov-Merritt, and Jeans predictions\");" ] }, { "cell_type": "markdown", "id": "1908e31c", "metadata": { "papermill": { "duration": 0.00792, "end_time": "2026-06-30T01:13:07.168661+00:00", "exception": false, "start_time": "2026-06-30T01:13:07.160741+00:00", "status": "completed" }, "tags": [] }, "source": [ "For all anisotropic DFs, the sampling and evaluation methods work similarly to the isotropic case, but the velocity distribution will reflect the specified anisotropy.\n", "\n", "We can also compute the differential energy distribution for anisotropic DFs, which will differ from the isotropic case due to the different velocity structure." ] }, { "cell_type": "code", "execution_count": 22, "id": "296e26da", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:13:07.185751Z", "iopub.status.busy": "2026-06-30T01:13:07.185553Z", "iopub.status.idle": "2026-06-30T01:14:25.814777Z", "shell.execute_reply": "2026-06-30T01:14:25.813814Z" }, "papermill": { "duration": 78.648291, "end_time": "2026-06-30T01:14:25.824913+00:00", "exception": false, "start_time": "2026-06-30T01:13:07.176622+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)\n", "dfh_constantbeta = constantbetaHernquistdf(pot=hp, beta=0.5)\n", "dfh_ombeta = osipkovmerrittHernquistdf(pot=hp, ra=1.4)\n", "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0_hp = hp(0.0, 0.0, use_physical=False)\n", "dMdE_hp = numpy.array([dfh.dMdE(E * phi0_hp) for E in Es])\n", "dMdE_constantbeta = numpy.array([dfh_constantbeta.dMdE(E * phi0_hp) for E in Es])\n", "dMdE_ombeta = numpy.array([dfh_ombeta.dMdE(E * phi0_hp) for E in Es])\n", "plt.semilogy(Es, dMdE_hp, label=\"Isotropic\")\n", "plt.semilogy(Es, dMdE_constantbeta, label=\"Constant beta\")\n", "plt.semilogy(Es, dMdE_ombeta, label=\"Osipkov-Merritt\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Anisotropic DFs\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "0a5f7b62", "metadata": { "papermill": { "duration": 0.00839, "end_time": "2026-06-30T01:14:25.841865+00:00", "exception": false, "start_time": "2026-06-30T01:14:25.833475+00:00", "status": "completed" }, "tags": [] }, "source": [ "General formulas for computing constant-ansisotropy and Osipkov-Merritt DFs for any spherical potential are also implemented in the `constantbetadf` and `osipkovmerrittdf` classes, which can be used to compute the DF for any spherical potential with the specified anisotropy profile. For example, again embedding a Hernquist population in an NFW potential, we can compute the constant-beta and Osipkov-Merritt DFs for this system as follows and sample the different DFs to compare their velocity distributions:" ] }, { "cell_type": "code", "execution_count": 23, "id": "42a09c9e", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:14:25.859503Z", "iopub.status.busy": "2026-06-30T01:14:25.859309Z", "iopub.status.idle": "2026-06-30T01:14:34.746295Z", "shell.execute_reply": "2026-06-30T01:14:34.745255Z" }, "papermill": { "duration": 8.896748, "end_time": "2026-06-30T01:14:34.746956+00:00", "exception": false, "start_time": "2026-06-30T01:14:25.850208+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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gCMmxo4eHh1CvXj3h3bt3Yv/Zs2cLZmZmwqVLlwRBEASlUilUqlRJKF26tPDq1Svx2JAhQ4RixYoJVapUEfs2a9ZMqFq1qpCYmCgei4iIELZv357mZ6DrcylRooTQs2dPtXMB0Pis0lKrVi2hQIECwvDhw4X4+HhBEJI/t08VLFhQr1iqSZMmBt1Hly5dBADCiRMn0my3bNkyAYBw5MgRjfd69OghABASEhIMujZRRnGmFJGJXb9+Hdu3b4dCocCdO3ewYMEC1KhRA6NGjdJoq1AocO3aNbx+/RqJiYlwcnKCUqlEYGAgfH19oVKpsHjxYrRq1QpNmzYV+zVt2hTly5fHgwcP9BrT8+fPce/ePcTGxkIQBJQuXTpDBbP79euHOXPmYMOGDRg/fjyA5Ked69evR7NmzcSnPAEBAbC2tsaiRYvEZW5mZmb49ddf8ccff2DTpk0YMWKE1mv8+uuvKFu2rNpSrtKlS2PcuHEYM2YMzp8/Dz8/P/z666+Qy+X4/fff1WZ8FStWzODdbXSZM2cOkpKSsHLlSnFWlUQiwc8//4xVq1ZhzZo1mDZtGl6+fAkLCws4OTmJfWUyGfr166fXdaKjo3H9+nW8ffsWSqUSxYsXx5YtWxAcHKxzWn16Ll++DCB5GV3K51GiRAmNdjVr1jT6rj4PHz7EyJEjUahQoXQLicbGxgKAuKQhtZRZhjExMUYdHxER5QwRERG4efMmoqKioFKpUKZMGaxbtw5xcXFq3wsWFhZq9QWbNGkCHx8fHDx4UFwivnjxYpQrVw5DhgwR21WoUAGNGzfGxYsXxWMps5mmT5+OGjVqiMcrVaqEAQMGYPHixZg+fbo4ezcpKQmDBg2Cg4MDgOTvpl69emHcuHF4+/atXkv1tUlMTMS1a9cQFhaGpKQkuLi4ICkpCadOnVJbdpae169fQxAEuLm5qR1PmW2dmp2dHQYOHCi+rlatGvr3749FixZh7ty5cHFxwYwZM+Du7o7Zs2eLn4GFhQXmzp0LHx8fbN++Hb169cKKFSsQFhaGY8eOqe0yPWbMGCxZsgRLlizB2rVrceLECdy6dQt//PGHuGRPKpVi5syZWLdunVoM9/LlS7i4uKiVMHBxcdGYlaRLaGgo7t69i5iYGAiCgDJlymRqgxiFQoEbN26gYMGC+Omnn8RlhNqWjrZu3RrR0dHpnjOlxIY+Nm7ciC1btqB169ZaZ6Wnpm88lVL7kygrMSlFZGJXrlzBhw8fIJfLcfnyZchkMixYsEAtYQEkL8kaPHgwzMzMUKlSJdjZ2UEikUAikeDVq1cAkpNJb9++VVsbnqJmzZrYvXt3mmOJjIxE165dcerUKVSrVg3u7u6QyWR4+vSpeA1DlClTBnXr1sWaNWvEpNThw4cRGhqqViT83LlzKFy4sDhVWBAE8cfBwQE3b97Uen6FQoHbt2+jR48eGuv0/fz8AABXr16Fn58fLly4AB8fH6PXR0rt3LlzKFSoEE6cOKFxH87OzuJ9dOzYEQsWLECFChXQuXNnNGjQAA0aNBAD2LRMmTIF8+bNQ4kSJVCiRAlYWVkhIiICAPDq1atMJaV8fX3VanxpM3z4cLXlopn1+vVrNG3aFAqFAjt37kw3WE9JWioUCo33kpKSACDdWhJERJS7JCYmYtCgQdi4cSMqVqwILy8vWFhY4OnTpxAEAa9fv1Yr6qxteVXRokXx4sUL8fX169e1LjP/tG/KsjmVSoXdu3eL3+tA8rK+qKgoPH/+HMWLFweQ/DDq0yRE0aJFASQXp85IUmrz5s0YNmwYrK2txV1nU8ZgaHxWsWJF+Pr6on///ti/fz8aN26Mhg0ban0QpSueVCqVuHnzJho1aoRz586hfPny2L9/vzimlM/I3NxcjH3OnTsHa2trPHjwAA8ePFCLkZycnMR2V69e1XptR0dHlClTBkqlUjzWo0cPjBs3DtWrV0e7du1Qv359+Pn5qS3R1Ob9+/f45ptvcPToUbFelUwmw+PHjzMU76a4ffs2EhIS0KdPn3TrfRl7s6EjR46gf//+qFSpEtatW5due8ZTlJMwKUVkYql335PL5WjZsiWaNm2KK1euiEUnIyIi8M0336B9+/ZYv349pFIpgOQnGDt27BCDgJQtlbU99dB27FNjx47FlStXcPfuXbXgrlevXti6dWuG769Pnz44c+YM6tSpgzVr1sDd3V2s0wD8Vz9r48aNGv2//PLLNItqCoKgtUBmyrGU9foJCQlZvr1yfHw84uLitN5H7dq1xaddn332Ge7cuYO1a9ciMDAQS5YsgSAIGDJkCH799VedhTB3796NWbNmYfXq1WrFwHft2oVTp06J/z8w1Js3b/Dy5Uv06NEj3bbGqCmVIiIiAl9++SVev36NgwcPionEtHh6ekIikeDNmzca76UcK1y4sF7jIyKi3GHhwoVYv349jh8/rlYDZ86cObhy5YrG95+2GpgWFhZ49+4dgOSkSWJiojirObVP46WUGCUoKAi3b9/WaN++fXu1JIiFhYXGP+ZTEgAZmWn84sUL9O7dG3369MHy5cvFGOH169fYtWuXwd/95ubmOHv2LNavX4+DBw9i4sSJiIyMxOeff47NmzeLNaWAtOPJ1PFVRESE1tindevW4iyu+Ph4SKVSre1KliwpfnenF8umng09duxYVK9eHVu3bsXmzZvx/fffw8XFBQsXLkTXrl11fgaTJk1CUFAQbt68qbbD3KBBgxAcHKyzX3pSZp2nXq2gS2ZrSqV26tQptG3bFj4+Pjh69KjaTDRdUj5vXfGUg4MD7Ozs0j0PkTEwKUWUg1haWmLNmjUoU6YMhgwZgsOHDwNInk0VHx+Pnj17igkpABrBUZEiRSCTyfDo0SONcz98+DDd6wcFBeGLL77Q2EJWWxCmr06dOmHEiBFYvXo1ypQpg71792LkyJFqAZyPjw8SEhLEnU30ZW1tDTc3N4SEhGi8l3Is5cllqVKlcOLECSQlJem9ox8Ag3ZK8fHxwf379/W6Dx8fH/z0008AkguW/+9//8PcuXPRoEEDtGnTRmufoKAgmJmZaSSPtP3+GDLuS5cuAdA+df9TCxYswKZNm/Q6b1qB8rt37/Dll1/i6dOn2L9/P+rVq6fXOe3s7FChQgWxAH1qly9fhrW1NSpXrqzXuYiIKHcICgpC8eLFNYoyZzQ+kUgk8Pb2xuPHjzXe+/RYSkw0cOBAdOrUKUPX0zUGfVy4cAFJSUno3bu3Wp/MxGbW1tYYPHgwBg8eDEEQcOTIEbRt2xYTJ07En3/+KbZLK55Mia9KlCgBDw+PdGMfHx8fBAUFYePGjWnOwEk576NHj8QZZkByTPH48WO4urqqtW/YsCEaNmwIIDmB980336BXr15o2bKlztlKQUFBqF27tlpCCtD8TA3dLe/y5cuwsLDQOsPsU3369BE3rklLkyZNcOjQIZ3vnz9/Hi1btoS3tzeOHz+usSxTl1q1akEikeDKlSvo2LGjeFwQBFy5ckVjZ2mirCRNvwkRZScvLy8MHToU//zzD44fPw4A4pr6p0+fiu1UKhV+++03tS9MGxsbtGjRAn/++Sfev38vHn///r3aVsq6FCpUSGMWzKFDh3Dv3r0M34+NjQ26dOmCbdu2YenSpUhMTFSb5QMAAwYMwK1bt8Std1OLj49HZGSkzvN36tQJx48fVwsklEolFi1ahIIFC+LLL78EAPTt2xdRUVFYuHChxjm0PSVKkTLNPioqKu0b/fc+Xrx4ofUpYGJionid1MsHgORZXSlP9MLDw3Wev1ChQlAqleK20EDy7622adoFCxbUa8zAf0/29JmpVLNmTbRv316vH12io6PRpEkTPHz4EPv27dP4R0Zqx48f11h22rdvX9y4cQMXLlwQj0VERGDnzp3o0qVLls+IIyKi7FWoUCFERkaKO6ABycmRv//+O8Pn7NixI06cOIH79++LxxQKhcZ3eMOGDeHj44O5c+eKy5pSe/78eYaur+/3tLYYUKlUao1n9BEZGam2w7NEIkHjxo1RpEgRjRjk9OnTag81U2pzVq5cWUzoDBgwAGfOnMHJkyc1rhUbGyvGo/369UNSUhLmzp2r0U6lUuHly5cAkmcZ2dnZYenSpWptdu7cKc50S/HpZ+/l5YWmTZsiKSkJHz580PkZFCpUCM+fPxd3qgOAEydO4Nq1a2rtnJycIJPJDIqnqlWrplcdptatW+sVS6VVVuHq1ato2rQpChcujOPHj6vtOJ1aYmIitm/fjvPnz4vHihQpgq+++gqbNm1S+3P1999/4/Xr1xna1ZEoozhTiigHmjhxIlasWIHJkyfj/PnzqFy5Mho3bozx48fj7du3cHZ2xvbt29GyZUuNZNP8+fNRp04d1K5dG9999x0EQcC2bdvQu3dvzJo1K83rjhkzBu3atUPnzp3RvHlz3Lt3DydPnkSPHj2wfv36DN9P//79sXLlSsyYMQN169bVKMg5YMAA3Lx5E+3atUOvXr3g5+cHpVKJu3fvYs+ePdi0aRNcXFy0nvunn37CmTNn0KBBA4wePRouLi7YsmULLl26hO3bt4tTj1u3bo1JkyZh3LhxuHr1Kho0aICYmBjs2bNH3D5am7p168La2hpTpkxBp06dYGFhgXr16ml9EtWxY0dMnjwZvXv3xj///IM6depAKpXi/v372LlzJ5YtW4amTZti8eLFOHbsGFq2bAkfHx98+PABy5cvR8mSJdNM5vTo0QNz5sxBq1atMHz4cMTExGDTpk0YNGgQJkyYoNY25f8vP//8M3x8fGBra4vmzZtrPe/ly5dRqlQpnZ9xasaoKdWqVStcvnwZ3333Hd6+fav2dNXGxkZtnOPHj8f9+/fFgpwAMGTIEBw8eBBt2rTBxIkTYWdnh/nz58PT0xOzZ8/O1NiIiCjnGTJkCNatW4dmzZqhT58+ePXqFf766y8MGzYMM2bMyNA5v//+exw6dAgNGjTAqFGj4OTkhB07dqBFixY4c+aM+NDP3Nwcu3btQosWLVCpUiX06dMHnp6eCA0NxYkTJ2Bubo59+/YZfP3GjRtjz549WLJkCdzd3XUu06pduzbq1KmD4cOH4+XLl7C3t8eWLVvQoUOHDF03ODgY3bp1Q5s2bVCxYkVYWlri4MGDePr0KX777Te1tt27d0ffvn3RsmVLODg4YO3atXj16pX40BQARo8ejdu3b6NJkybo27cvPvvsMyQkJODOnTvYt28f9u7diwIFCqBWrVpYsmQJRowYgcuXL+Orr76CjY0NQkJCsHPnTowdOxb9+/dHgQIFsGzZMvTq1Qtff/01WrVqhUePHuHOnTuoV6+e2oPEtm3bomjRoqhTpw48PT3x6NEj/Prrr+jWrRu8vLx0fgajR49Gy5Yt0aFDB7Rp0wYPHjzAkSNH0LdvXyxZskRsZ2ZmhoYNG+KPP/6At7c3nJycULx4ca01yxITE3Hr1i21wvlpyWxNqRcvXqBJkyZISEjAkCFDEBQUpPZ+6nFGR0ejY8eOaN++vVrMtWzZMnzxxRdo1KgRBg8ejPDwcAQEBKB79+5GnRVIlB4mpYhMxNXVFe3btxfrRqXm7OyMefPm4dChQwgODhaXva1atQqXLl2CtbU1JkyYAH9/f5w5c0ZtuVKxYsVw48YNLFu2DBcuXICXlxc2btyIR48eITg4WG19eOvWrdWKcbZt2xZnz57Fli1bcOzYMVStWhX//PMPduzYobaG39LSEu3bt0epUqX0utcaNWpg8ODBiIiIQJ8+fbS2WbRoEXr16oVdu3YhMDAQTk5OKF++PK5evQpnZ2cAybuvtG/fHuXLlxf7OTo64vz589i8eTOCgoLEoGX16tXiFPAUs2bNQrt27bB9+3acOHEChQsXxqxZs8Rla9rOX6RIEQQGBmLz5s3Ys2cPlEolypQpAzc3NzRr1kxjqePMmTPRuXNn7NixA6dPn4adnR3KlSuH8+fPi0+wfvnlF9y4cQN79uzBkSNH4ODggHHjxqFz585a61ukcHNzE39vT58+DU9PT2zZsgVJSUm4ePEiPDw8xLYjRoyAg4MDzpw5gytXrsDZ2VlnUsrb2xuNGjXSeV1jK1y4MNq3b483b95gy5Ytau8VLFhQbZz+/v4oV66cWhsLCwscPHgQf/75JwIDA6FQKDBw4ED069ePs6SIiHK5qlWron379mo1hSpWrIhbt25h1apVOH78OEqWLIlDhw7h7t27uHv3rlps065dO/j6+mqc94svvlCbPWNvb49z585h5cqVuHz5MgoWLIh58+aJM8ZTf59UqlQJ9+7dw9atW3HhwgXcvn0b3t7emDBhgtr3p6+vL9q1a6dx7ZTvvdRFzhcuXIjy5cvj/PnzSEhIgK+vL+rWrYvixYujffv24vWlUimOHj2KlStX4urVq7Czs8OPP/4IPz8/BAYGqsUslStX1nr91OrUqYNr167hzz//xJUrV6BQKFC5cmX88ssvavWkAMDBwQE7d+7E0qVLcePGDfj7+2Pr1q1quxabmZlh/fr1GDhwIPbu3Ytjx47B2dkZlStXRkBAgNomLt9++y2aNGmCLVu24OLFizA3N0fp0qVx6NAhtXN2794dZcuWxYYNGxAYGIgaNWpg6tSpmDdvntrv4eXLl3HgwAGcOnUKN2/ehLu7O7Zv3w5/f/80P4NmzZrhwoUL2LRpE44dO4bKlSvjyJEj2LdvH8LCwtTabt68GcuWLUNgYCDkcjm+/PJLrUmp8PBwtGrVSmcJBmOLjo4Wd9hL2WAntdTjTInba9eurdamRIkSan+ubGxssHbtWnz99ddZPn6i1CRCRivjEhERERER5SHz58/HqFGj8Pz58zRn2+R1EokEEyZMwM8//2zqoRBRHseaUkRERERElO98WrMyISEBy5cvR7Vq1fJ1QoqIKDtx+R4REREREeU77dq1Q+XKlVGtWjW8e/cO69evx+vXr3H06FFTD42IKN/gTCkiIiIiIsp3Dhw4gEqVKuHixYu4ceMGunXrhnv37qFGjRqmHprJtW/fHpUqVTL1MIgoH2BNKSIiIiIiIiIiynacKUVERERERERERNmOSSkiIiIiIiIiIsp2LHSuhUqlwqtXr2Bvbw+JRGLq4RAREVEOIggCYmJi4OnpCak0/z7fY7xEREREuugbLzEppcWrV6+4DSwRERGl6cWLFyhSpIiph2EyjJeIiIgoPenFS0xKaWFvbw8g+cNzcHAw8WiIiIgoJ4mOjoaXl5cYL+RXjJeIiIhIF33jJSaltEiZgu7g4MAgi4iIiLTKSUvW5HI5du/ejVu3bsHJyQnNmzdH+fLl0+13/PhxHDt2DFZWVmjXrh0qVKig9zUZLxEREVF60ouX8m8hBCIiIqI84MWLF6hatSr27dsHW1tb3Lt3D1WrVsXixYvT7Pf999/j66+/hlwux9OnT1G1alXs3r07ewZNREREBM6UIiIiIsrVbG1tceLECbi5uYnHPDw8EBAQgKFDh2rt8/DhQwQEBGDHjh1o27YtAKBAgQIYMmQIWrVqBTMzs+wYOhEREeVznClFRERElIs5OzurJaQA4OPHjyhQoIDOPnv37oW9vT1atmwpHuvZsydevXqFixcvZtlYiYiIiFLjTCkiolxAqVQiKSnJ1MMgyhfMzc1z5UyhZcuW4d69e3jw4AGio6OxefNmnW0fPHgAb29vyGT/hYI+Pj4AgJCQENSuXVujj1wuh1wuF19HR0cbcfRERJnHeIko+xgrXmJSiogoBxMEAWFhYfjw4YOph0KUrzg5OcHDwyNHFTNPj7u7O2JjYxEVFYUrV67g5s2bqFy5sta2cXFxGrvh2NrawszMDHFxcVr7BAQEYPr06UYfNxFRZjFeIjINY8RLTEoREeVgKQGWm5sbbGxsctU/kIlyI0EQEBcXh/DwcABAoUKFTDwi/bVr10789eLFizFw4EC0aNFC6zI+e3t7jX+8RUdHQ6lU6ty6edKkSRg9erRaey8vL+MMnogoExgvEWUvY8ZLTEoREeVQSqVSDLAKFixo6uEQ5RvW1tYAgPDwcLi5ueXKpXy1atVCfHw8nj17pjUpVb58eaxbtw5yuRyWlpYAgPv374vvaWNpaSm2JSLKKRgvEZmGseIlFjonIsqhUmoi2NjYmHgkRPlPyp+73FCb5PLlyxr1nXbs2AF7e3uUKlUKABAfH4+RI0eKRczbtGkDhUKBP/74Q+yzbNkylCpVCr6+vtk2diKizGK8RGQ6xoiXOFOKiCiH4xR0ouyXm/7cRUREoGfPnihbtixcXFxw/fp1PHnyBOvXr4etrS2A5CLlCxYsgK+vL2rWrInChQvjt99+w/Dhw3H48GG8e/cOly9fxv79+3PVvRMRpeDfXUTZzxh/7jhTioiIcoTExETcvn0bCoVC7zYJCQm4ffs2lEpldg0zy8TExODRo0cA8sZ9hYeH48mTJ3q3Dw0NRWRkZBaOKO9q1qwZzp8/jz59+qBGjRqYPn06nj17hq+//lpsY21tjd9++w01a9YUj3377be4fv06GjdujF69eiEkJAR169Y1xS0QEZGeGC8xXspr8RJnShER5TKtFgUhIkaefkMjcrW3xN5h+v1jNSkpCcHBwVrfK1q0KBwcHLS+9/z5c1SqVAkvXrxAkSJF9Gpz//59VK1aFREREXBxcdHvZvSQkJCAhw8fonz58pBKs+f5zeDBg1G+fHlMmTLF6PdlivtZunQpjh49iqCgIL3anz17FnPnzsWFCxf4tDsDHBwc0KpVK53vW1paYuTIkRrHS5cujdKlS2fhyIiITIPxEuMlQzFeMg0mpYiI/tV5X2dExhv+5MHF2gVbW27NghFpFxEjR1h0QrZdz1AvX75EpUqVUKxYMXHpUIrffvsNX331ldGuZW1tjQoVKkAmM+7X2e3bt1GjRg28f/8eTk5ORj23NpcvX8aBAwewcuVKAMa/r+y+HwBwc3NDiRIl9G7fsWNHTJs2DVu2bEHXrl2zcGREZCxP2neAQs8n9jIXFxTfsT2LR0T0H8ZL/2G8pB/GS6bBpBQR0b8i4yMRHhdu6mHoTSoB3OytsvQa4TEJUAkZ67t27Vo0aNAgzTYfP35EeHg4ihYtmqE23t7e2LJli7iFfVxcHB4/fowKFSpAqVQiNDQUnp6esLCwSPO8SqUSDx48QNmyZSEIgjgt/N69e7C3t4eTk5P4NFKhUODp06ewt7eHu7u72jkNuX5qCxYsQOfOncWg9NP7ShEZGYn4+Hh4eXlpnEPXuJKSkrTej7OzszjWjx8/IjQ0FF5eXuIYoqOjERYWBk9PT9jZ2aldKywsDHK5HN7e3oiOjsbbt29RvHhxtTYdOnRAs2bNNMaZmJiIFy9ewNPTU9y1BUiuSdC7d28sXLgwzwRZRHmdIjISijdvTD0MojQxXmK8lBrjpRxIIA1RUVECACEqKsrUQyGibNTor0ZCxXUVhcrrKwuN/mqU7k/l9ZWFiusqCo3+apQl44mPjxfu3r0rxMfHqx2vNfOo4D1hn1Br5tEsuW5mr/XkyRMBgBAYGJhmu2XLlgnW1taCp6en4OjoKIwYMUIAILx48ULvNteuXRMACBEREYIgCMLp06cFAMLEiRMFFxcXwcvLS7C1tRX++usvtWsvWLBAsLKyEgoXLiw4OTmpnffly5eCj4+PAEAoV66cUKFCBWHs2LGCIAjChg0bBGdnZ6FQoUKClZWVUL9+feHVq1fiefW9fmoKhUJwcHAQdu7cKR779L5ev34t+Pn5CQ4ODkKxYsWEokWLCgcPHhTbpzUuXfeTMtbx48cLTk5OQvny5YWLFy8KiYmJwsCBAwULCwvBy8tLsLS0FEaPHi0olUrxemPGjBE+++wz4csvvxTc3d0FGxsboXLlysKTJ0/ENtOmTRPq1KkjvlapVMKPP/4o2NnZCYUKFRIcHR2FiRMnqn0WV69eFQAIL1++1Pl5ZRddf/4EgXFCCn4O9KBefeFumbLC3XLlhQf16mv9uVuuvHC3TFnhQb36ph4u5VGMlxgvMV4yHWPESyx0TkT0CRdrFxzreCzdHxdr463Jz4uePHmC27dvq/2kFNy8d+8ehg4divXr1+Ply5d4+PAhjh07ptZfnza6PH/+HC9fvsTz588xZcoUDBo0SNyq9vbt2xg1ahQ2bNiA0NBQPHz4EIGBgWJfT09PbNmyBUDyuv3bt29jzpw5CA4ORt++fTFv3jy8evUKb968QWJiIgYNGmTQ9T917949REdHo0qVKjrvJyAgANbW1oiIiMCTJ09w7tw5PH78GADSHZeu+0kREhKC169f486dO6hRowYWLlyI3bt34+bNm3j+/DnOnTuH33//HevWrVMb0+XLl9GoUSOEhYUhMjISbm5uGDhwoM57WLBgAebOnYv9+/fj1atXiIiIgIODg1px0sqVK8PMzAznzp3TeR4iynlkrq4odfKE1h+Zq6uph0eUozFeYryUWn6Ml0yalHr//j3mz5+P2rVr45tvvkm3/fbt2+Hr66v158WLFwCA+Ph4re///fffWX07RESUyo8//oguXbqo/bx9+xYAsHr1atSoUQMdO3YEALi4uGDy5Mlq/fVpo8uMGTPEKeDdunXD+/fv8fz5cwDJ0+Rr1qwpnrdgwYJ6nXfVqlWoVKkSevfuDSC5sPSsWbOwd+9evHz5Uu/rfyosLEy8P11iY2Ph4OAg1kzw9PTEd999Z/C4tPnxxx9hZfXfsobly5djyJAhKFOmDACgatWq6Nu3L5YvX67Wz93dHePHjweQXNNh1qxZOHLkCJ49e6b1OgsXLsTQoUNRr149AIC5uTkmTZoEMzMzsY2ZmRmcnZ3Fz4SIiCivY7zEeCm1/BgvmaymVGJiIipWrIj27dvDw8ND584DqTVs2BAlS5ZUOzZ27Fg8ffpUXLuqVCpx48YNbNiwAZUqVRLbpbX+loiIjC+tGgmPHj1C+fLl1Y5VqFDB4Da6eHp6ir9OWfMfExOj87zlypVL95wPHz5ExYoV1Y6lfM88evQIhQsX1uv6n0oJxhITE3Vee8yYMWjZsiVKlCiBJk2aoGnTpmjTpg2kUqlB49ImdW0DpVKJp0+faj3fhg0b1I6VKVNGLUBK+b15+PAhvL291domJSXhyZMnqFq1appjAQC5XA5LS8t02xFR5rBIOVHOwHhJ+/U/xXhJXV6Kl0yWlDI3N8fDhw9hbW2NkSNHijOd0lKwYEEULFhQfB0VFYWzZ8/ihx9+0NgOsVSpUvD19TX2sImIyAhsbGwQHx+vdiwuLs7gNsa69qevtbG1tdU5nk93zTFESpATGhqq8+lf+fLl8fDhQ1y8eBGBgYEYPXo0li9fjsOHD2d6XJ8+ebOystJ6vk/PZcg1zczMIJPJ0v39i4mJQXR0tEYRUCIyPhYpJ8r5GC/9h/HSf/JavGSy5XsSiUStinxGbN68GUlJSeIUvNRGjRqF2rVro3v37jh9+nSmrkNERMZVtWpVnD59WqyZAADHjx83uE1G+Pr6IigoSO28J0+eVGuTMj07dV2DatWqISgoSO0J3dGjR2FjY4PSpUtneDxeXl4oXrw4zp8/r7NNYmIipFIp/Pz8MGnSJKxZswb//PMPoqOj9RqXtvvRpWrVqhq1KI4eParx1O7WrVuITDXL4vjx47CyskLZsmU1zimVSlG7dm3s27dP7Xjq3wMAuHDhAiwtLVG7du10x0lERiKVQuburvUHUpafJTIlxkv/Ybz0n7wWL+Xqb5rVq1ejVatW8PDwUDv++eefY8SIEfj5559RpEgRNGrUCBs3btR5HrlcjujoaLUfIiLKHG2FO1NqJAwcOBBJSUno3r07goKC8Pvvv6sVk9S3TUYMGjQICQkJ6NmzJ4KCgrB69Wr88ssvACDOuvX29oa1tTXWr1+PW7duITQ0FIMGDYK5uTk6d+6MU6dOYePGjRg7diwmTpyosRWxoXr16oUdO3bofL9nz56YMmUKjh8/jrNnz2Lx4sWoWLEiHBwc9BqXtvvR5ccff8TGjRsxc+ZMnDt3DpMnT8ahQ4fwv//9T62dQqFAhw4dEBgYiG3btmH48OEYNmwYnJyctJ43ICAAe/fuxbBhw3D69Gns3LkT9erVUyvcuWPHDnTo0AE2Njb6f3hElCksUk5kWoyX9Md4KVlei5dMtnwvs27cuIErV65gxowZasdtbGxw6tQpcXpd/fr1ER8fj3HjxqF79+5azxUQEIDp06dn+ZiJiIwpPCYBfrP0210lM9cwlIWFBSpUqIB58+ZpvDd27Fj07t0bDg4OOHnyJKZOnYrRo0ejbNmy2LZtG0aOHAlzc3MA0KuNtbU1KlSoIBa0tLW1RYUKFSBN9XRfJpOhQoUK4uxcR0dHnDhxAj/88IN43qVLl6JLly5iG3t7e2zatAnLli3Dhg0b0KRJE8yZMwdBQUH46aefMHr0aNjb22PmzJlqu8noc31tvvvuO8yfPx/BwcEoU6aMxn2tWrUKixYtwsyZMyGXy/HZZ59h0aJF4jXTG5e2++nWrZvGWAGgQYMGOHDgABYuXIgdO3agWLFiOH78OKpVq6bWzt/fHx06dMDs2bPx7t07DB06FBMnThTfd3NzQ4kSJcTXderUwdmzZzF37lyMHDkSPj4+WLRokfh9HRUVhb/++kvvHYOIiIj0wXiJ8VLKNRkv5UwSQRAEUw9i5MiRCAoKwuXLl/XuM2zYMPz999948uSJxv9BPrV79258/fXXiIiI0Lr+VC6XQy6Xi6+jo6Ph5eWFqKgoODg46H8jRJSr+W/zR3hcONxs3HCsY/p/0Rva3lAJCQl48uQJihcvrrbbh9+sYwiLNjz4yQwPByucn+yfrdfMSgqFQgxgAGDJkiWYMWOGSXcxWb58OUJDQ/HTTz+ZbAz6Gjt2LG7fvo1Dhw4Z7ZyrV6/GgwcPxKewpqbrzx+QHCc4Ojrm+ziBn0PuFlK/ARRv3kDm7o5SJ09kqI0xzkGUWYyXsg7jpcxhvKRfnJArZ0rJ5XJs2rQJI0aMSDchBQAvX76EmZmZzqyrpaVlnqlcT0R5n6t99v99ZYprZqXevXvjq6++QtmyZXHlyhVMmTIFEyZMMOmYBg8ebNLrm1q/fv1MPQQiIspDGC9lHuOlnCcvxks5OikVExODL774Aj/++CNat24tHt+5cyeioqLQt29fjT47d+6Em5sb6tatCwC4e/cufv75Z3z99deZqvZPRJRT7B1W19RDyPVmzJiBWbNmYdmyZXB3d8fSpUvRrVs3Uw8r1yhUqBBiY2NNPQwiIiKdGC9lHuOlzGG8pB+TJqU6dOiAhw8f4uXLl/j48SN8fX0BAOfOnYO1tTWUSiVu3LiBd+/eqfVbvXo1mjVrBi8vL41zVqhQAcOHD8eVK1fg4OCAly9folevXkYp9kZERHlD8eLF8fvvv5t6GLnWmDFjTD0EIiIiymKMlzKH8ZJ+TJqUmjlzJuLj4zWOpyyls7e3x7Vr11C0aFG193/99VeNHfdSlClTBocPH0ZUVBQiIyNRtGhRscAbERERERERERHlDCZNSpUpUybN983MzMTZU6lVrlw53XM7OjrC0dExo0MjIiIiIiIiIqIslH6VcCIiIiIiIiIiIiPL0YXOiYgyqvO+zoiMjzSoj6HtiYiI8gNFRARC6jfQepyIiCgzmJQiojwpMj4S4XHhph4GERFR7qdSQfHmjalHQUREeRCTUkSUp0klUrhYuxjUx9D2REREeZHMRb/vQ33bERERfYpJKSLK01ysXXCs4zFTD8O4VtQHYrN5FpidGzDopMHd5HI57t+/j6SkJPj4+KBAgQJZMDjdTp06hQoVKqBgwYJGPW9MTAyuXLmCunXrQiZL/6s0JCQE48ePx/nz5yGTydC8eXMsXrzY6LvDxsTE4O7du3B2dkapUqXSbX/69GkolUq1YyVKlNDY9ZaI8qfiO7Zny3WetO8ARaR+S+hlLi7ZNi7K5Rgv6Y3xUtoYL2UtJqWIiHKb2HAg5pWpR5EmuVyOyZMnY8WKFShSpAgcHR3x+PFjVKpUCfPmzUPVqlWzZRyNGzfG9u3b0bJlS6OeNzg4GA0bNsT79+/h5OSUZtuoqCh8+eWXaN26NS5fvozw8HA0aNAAjRs3Rvv27Y02pnXr1mHo0KHw9vZGaGgoqlWrht27d6e5E22zZs1QrFgxuKSa5TBw4EB069bNaOMiIgJ016UCYLSlgfomt5jYyicYL+mN8RLjJVNiUoqIKLeSSAE7j6y9RmwYIKgM7ta+fXvcvXsXZ86cQZUqVcTjp0+fxtOnT9WCrBcvXuDFixfw9vZG4cKFxeMqlQqnTp1C1apVYW5ujvv378PV1RVeXl5q11KpVHjw4AHi4+NRvnx5WFpaAgDOnTsHlUqFW7duwc7ODpaWlqhduzZevXqFBw8eAADs7e1RunRp2Nvb633dhIQEXLlyBQAQFBQEOzs7uLm5oXz58lo/iy1btsDc3BwLFiyAVCpF4cKF4ezsjMTERIM/V13u37+P/v37Y+3atejRowc+fPiAWrVqYcyYMVi1alWafX/66Se0bdvWaGMhItJKz7pUMnd3rccVERGAKu3vI0VkJGtfkSbGS2I7xkuMl3IiJqWIiHIrOw9gzL2svca8cgY/ZTxw4AD279+Pw4cPqwVYAPDFF1+Iv05ISEDPnj2xf/9+lClTBvfv30e7du2wdu1amJubIzExEQ0bNkTPnj1x9OhReHp64vbt2+jfvz8WLVoEAHj69CmaNm2KuLg4uLu74+XLl5g/fz46deqEX3/9FQqFAps3b8bhw4fh6uqKbdu24fLly/j1118BANHR0QgODsaMGTMwevRoAEj3uh8+fMDKlSsBAD///DNkMhkaNWqEH374Qevn8c8//6BJkyaQSqUAkqfIv3jxAnXq1NFoGxISgpcvX6b5+X722Wews7NTO7ZhwwZ4enqiR48eAAAnJycMHToUEydOxJIlS8TAU5tXr17h/PnzKFasGDw8sjhoJ6J8x5B6U2nNYAqp30D/hJNUCpmrq8ZhfRJblAcxXmK89C/GSzkTk1JERGRU+/btg6urKxo3bpxmu19//RVnz57FvXv3ULRoUTx69Ah+fn5YvHgxRo0aJbZ7+vQpHjx4AFtbW1y4cAF+fn4YMGAAKleujNmzZ8PHxwf79u2DRCJBdHQ0/v77bwDAtm3bYGVlhYCAALXp6K1bt0br1q3F15cuXUL9+vXRpEkTVKhQQa/rrlixAjVq1MC+ffvSnY5+5coVTJ06FUFBQTh9+jTmzp2LCRMmaK1DcODAAezatSvN861atQolS5ZUO3bt2jVUr15d7Vj16tURFxeH4OBgVK5cWef5fvjhB3h7e+P+/fv4/PPPsW7dOrUnsEREmWGKZXIyV1eUOnlC47hBiS2iLMZ4SR3jpfyLSSkiIjKq0NBQFCtWLN12a9euxeDBg8Vgw8fHBwMGDMDatWvVgqwRI0bA1tYWAFCrVi24ubnh9u3bqFy5MpRKJRQKBRITE2FpaQkHBwd079493WurVCo8fvwYYWFhUCgUKFKkCM6cOaMWZKV1XX29e/cOz549Q7Vq1dC3b1/cvXsXVlZW8PPz09p+xIgRGDFihN7nT/H+/Xu1sQMQ6x68f/9eZ7/FixejZ8+ekEqlePPmDZo3b47u3bsjMDDQ4DEQERGR/hgv/YfxUv7GpBQRERmVtbU1oqKi0mwjCAKePn2KMmXKqB0vW7YsFi5cqHbMzc1N4/xxcXEAgIkTJ6Jjx44oVKgQGjZsiKZNm6JHjx6wsrLSee1Lly6ha9euiI2NRbFixWBlZYU3b97g9evXel9XX1evXoW5uTkqVKiAa9euISEhAT/++CPat2+PsLAwODs7q7XP6HR0CwsLxMfHqx1LGauFhYXOc/Xu3Vv8tbu7O6ZNm4Y2bdogPDxc4/6JiIjIeBgv/YfxUv7GpBQRERlV1apVsXv3brx//17nlsYSiQT29vaIiYlROx4TE5Pm7iefKl68OC5fvoyHDx8iMDAQCxcuxOrVq3H+/Hmdfb777ju0aNEC8+fPh0QiAQBUrFgRgiDofV19Xb16FRUqVBADHSsrK3Tu3BkBAQH4+PGjRpCV0eno3t7eeP78udqxlGDN29tb7/G6/luD5dWrVwyyiIiIshDjpf8wXsrfmJQiIiKj6tWrF3766SdMmzZN4ykekLzlr6OjI2rVqoWDBw+ib9++4nv79+9HzZo19b5WdHQ0HBwcULJkSZQsWRJlypRB/fr1xWvY2Nho7Nry9OlTjBs3TgywHj58iODgYIPu0cbGBgDS3RHm2rVrGgHRkSNHULZsWY1dcYCMT0f/6quv0L9/f0RERIiB0u7du1G+fHl4enoCAF6/fo3g4GB88cUXMDMzQ0xMjNouOgBw+PBhWFlZaYyZiIiIjIvx0n8YL+VvTEoREZFRFSpUCFu2bEGXLl3w8uVLdOrUCY6Ojnj06BF27dqFZs2aYcyYMfjpp59Qp04djBgxAv7+/jh48CBOnDiBixcv6n2tQYMGwcHBAf7+/rCyssKiRYtQq1Yt8elhpUqVsGHDBjg4OMDW1ha1a9fGl19+iR9//BEymQwfP34Uf22IYsWKwd7eHvPnz8dXX30Fd3d3rVscX716Fc+ePcPixYvx2Wef4eLFi/jf//6HjRs3GnS99HTt2hXz589Hq1atMHbsWNy6dQtr165Ve4q4f/9+DBgwADExMbCzs8OhQ4ewatUqdOrUCe7u7jhx4gQWLlyIgIAAjenuREREZFyMl/7DeCl/Y1KKiCi3ig1L3oI4q6+RAS1btkRwcDDWrFmDP//8E0lJSfDx8cH333+PBg0aAEje7eTs2bNYsmQJFi9eDG9vb1y4cAEVK1YEAEilUtSvX19jerqfnx8KFSoEIHlr33Xr1mHHjh2Qy+WoX78+hgwZIrZdvXo1Zs+ejV9++QVOTk7Ytm0bVq5ciV9++QW///47HBwcMGfOHBw7dkwsNqrPdW1sbLBnzx78/vvvmDFjBho0aKCxxXFsbCxCQkIwaNAgrF27FosWLULp0qWxZ88e+Pv7Z+hz1cXc3ByBgYGYM2cOVq1aBWdnZ/zzzz9o1KiR2KZQoUKoX78+zMzMAECsLfHHH3+IxVZPnz6NWrVqGXVsREREJsV4ifHSvxgv5UwSISsWheZy0dHRcHR0RFRUFBwcHEw9HCLKAP9t/giPC4ebjRuOdTyWK6+RkJCAJ0+eoHjx4uqFKOeVA2JeGf16abL3BMbcy95r5nKnT59Gw4YNER0dLU5fp9xD558/ME5Iwc8hdwup3wCKN28gc3dHqZMnTD2cdOkz3vTa5LZ7Jv0wXsrdGC/lbsaIlzhTiogot7EzQUFFU1wzl7t69SrKlCnDAIuIiMgUGC/lCoyXiEkpIqJMioyPhP82/acXu1i7YGvLrRm/4KCTGe9L2cbOzg4DBgww9TCIiIjyJ8ZLuQLjJWJSiogok1SCCuFx4aYeBuUw/fr1M/UQiCifetK+AxSRkWm2UUREZNNoiIh0Y7xETEoREWWQi7WLQe0j4yOhElRZNBoiIqJkishIKN68MfUwiIiI0sWkFBFRBhm6BC+lMDoREVG2kEohc3VNs4nMxbAHLERERMbEpBQRERERUR4kc3XlLnNERJSjMSlFRERElMsFBQVh06ZNePz4Mby8vNC/f3/4+fnpbB8fH4+vvvpK4/iUKVPQrFmzrBwqERERkYhJKSIiIqJcbNmyZfjzzz/RrVs3tG3bFqdPn0adOnWwbds2tGvXTmsfpVKJM2fOYMWKFShfvrx4vHTp0tk1bCKTeZfwzqBdc7XJ9E66REQEgEkpIiIiolztm2++wbfffiu+btKkCZ4+fYp58+bpTEqlqFy5cpozqojyIqWgZI1HIqIcgkkpIiKiLJaUlIQ1a9bg/PnzkMlkaN68Ob7++mtTD4vyCAcHB41jjo6OSEhISLfv5MmTYWZmBh8fHwwYMADVq1fPiiES5UhSiZQ76RLlIIyX8icmpYiIcpnO+zojMj4yW6+ZkWUK//zzDxYuXIgrV64gKSkJPj4+aNeuHYYMGQI7O7ssGqk6Jycn/Pnnn0avkXP16lV8/vnnePPmDRwdHdNsq1Kp0LJlS7x9+xbffvstwsPD0bFjRwQGBuKLL74w6rgMsWrVKsybNw+vX79G+fLlMXfuXHz++ec62+/duxcdO3bUOP7o0SMULlw4K4dKBnrx4gU2bdqE0aNHp9muatWq6NatGwoVKoSDBw/Cz88Pf/75Jzp06KC1vVwuh1wuF19HR0cbddxGtaI+EJvJmTB2bsCgk8YZD+VILtYuONbxmEF9uJNu7sF4SX+Ml3RjvJT1mJQiIsplIuMjc3xAPHv2bPzwww/48ccfsXjxYjg6OuLRo0fYtWsXli5divHjx2fLOBISEqBUKo1+XpVKBblcDkEQ0m27b98+XLp0CY8ePUKBAgUAABs2bMCTJ09MFmT99ddfGDJkCNatW4f69etj/vz5aNy4MW7duoXixYtr7aNUKiGTyRAZqR7gW1lZZceQSU9RUVFo3bo1ypcvj4kTJ+psZ2Njg/Pnz8PCwgIA0KJFCyiVSowaNUpnUiogIADTp0/PknFrlZnEUswr446FiHIdxkv6Y7ykHeOl7GHypFRUVBT27dsHOzs7tGnTJs22CoUC69at0zhev359lCpVSu1YaGgoTp8+DSsrKzRq1CjdzCwRUW6TkWUHhsrIMoU7d+5g4sSJmD9/PoYPHy4e/+yzz/DZZ5+ptV2zZg3mzZuHFy9ewNvbGxMmTED37t0BJM/KcHR0xG+//YZdu3bh+vXrcHV1xY8//oj27dsDSA6ixo0bh7179yI+Ph6ff/455s6dCx8fH5QsWRJyuRzt2rWDVCpFkSJF8PDhQ6xatQpDhw4FANjb26NSpUoICAhArVq19Lrus2fPUKdOHQCAh4cHAKBTp07YsGGD1s9jz549aNasmRhgvXr1CiEhIahQoYJBn6sx/fLLL+jevTu6du0KIDko/uuvv7B48WLMmzcvzb4MqnKumJgYNG3aFDKZDAcOHBATTtpIpVKN9xs3bozly5fj7du3KFiwoEafSZMmqc2+io6OhpeXl/Fu4FOx4cZJLtl7GnjdMIDLsygdkfGRGS6WziLp2YvxEuOljGK8lD1MlpRSKpUYPHgw9u/fDysrKzg7O6eblEpISMCAAQPQunVruLq6isfLly+vlpTasGEDvv32W3zxxRd4//49Bg4ciIMHD2r84Sai3MPQKdjZPV3bFDKy7MBQGVmmsHHjRtjY2KgVXtZm165dGDJkCFatWoWvvvoK+/btQ9++feHi4oKmTZtCEATI5XLMmjULGzZsQOXKlbFmzRp0794dfn5+KFy4MH755RcEBgZi//798PDwwNmzZ7FkyRL8+uuvuHPnDhwdHcXp6BKJBADQp08fMZCLjo7GqlWr0KRJE4SEhMDV1TXd6xYtWhSBgYGoU6cOnj17BkdHR5iZmem8z0uXLqFv375QKBS4desWvvvuOzRo0EBr7Z5Ro0Zh2bJlaX5uFy9eROXKldP7bdApLi4O165dw6hRo9SO+/v748yZM2n2jY+PR+HChaFQKFCpUiX873//Q926dTM8FjKelIRUUlISjh49CicnJ4PP8ebNG0ilUlhaWmp939LSUud7WUoiBew8MtY3I0vw5pUz2UyrJ+07QBGp3/eXzMUFxXdsz+IRkS4qQZXhWTjhceFMaGUjxkuMlzKC8VL2MVlSShAE1KxZE/Pnz8eUKVMQFBSkd99Jkybp3CkmLCwMgwcPxuzZs8XMbteuXdG7d2/cvn3bKGMnouyXG6ZgU7Lg4GCUKFEC5ubmabYLCAhAv3798M033wAA+vbti9OnTyMgIABNmzYV202bNg0NGzYEAIwdOxY//fQTLl68iK+//hoPHz6En5+f+BStVatWaNWqFQCI/3g2NzdXe1plZmYmBkVWVlaYPHkyNm3ahMOHD4vBV3rXTZlhYmlpmeaTsISEBNy7dw9Vq1ZFpUqVcP/+fTg4OODcuXNa28+ZMwcBAQFpfm6ZTQqEhYVBEAS4ubmpHXdzc8OxY7qDdisrK8yaNQudO3cGACxevBgNGjRAUFAQd28zsdjYWDRr1gxyuRxHjhzRmpCKjY1F06ZNMWXKFDRr1gx79+5FkSJFULVqVQDA48ePMXv2bLRo0SLbapjozc4DGHPP1KPIForISCjevDH1MCgNmZlxkzqOYUxDjJf+w3gpfzNZUkomk2HAgAEZ6nvmzBk8evQIPj4+qFGjhlrGdc+ePQCAfv36iceGDRuGOnXq4ObNm5nKlhKR6Rk6BTurp2uTJkEQIJVK02139+5djBgxQu1YnTp1sHfvXrVjpUuXFn8tkUhQoEABvHv3DgDQo0cPfP3113j37h2aNWuGxo0bw9vbO83rvn37Ft9//z2OHDmCsLAwKBQKJCYm4tmzZ3pfV183b96EQqGAr68vtmzZgpcvX2LOnDlo3LgxHj16pBEwyWQyyGSGfzWfPXsWjRo1SrPNuHHjMGPGDPH1p79HUqk0zZoPTZs2VQt+586diwsXLmDOnDnYsWOHwWMm45kzZw7OnDmDSpUqif/IAJKXWxw8eBBAcgmEM2fO4M2/CY9ixYrh22+/xfPnz+Hk5IQHDx6gXbt2WLRokUnugT4hlUKWalVAaoqICEDF5YWmkplZSpkpvM1d//Iexkv/YbyUv5m8ppShpFIpdu3ahUKFCiEoKAienp7YuXOn+Ifq9u3bKF68OKytrcU+KRnh27dva01K5ardZIjyuayagt1qURAiYuTpN9TB1d4Se4dxWi4AlCxZEseOHYNSqdQ5TVsQBKhUKq1f9J8W2tQWsKUEA40bN0ZwcDB2796NQ4cOYfjw4Rg+fDh++eUXneMbMGAA3r9/j7/++gslSpSAlZUVPv/8cyQlJel9XX1dvXoVJUqUgKOjI6pUqYIqVaqgSJEiqFKlCp4/f65RDzGj09Fr166NDx8+pNkvJXhzc3ODRCJBRESE2vvh4eFwd3fX886SVa1aFYGBgQb1IePr27cvvvrqK43jqQN2e3t7nD59WvzHQ6VKlRAUFIRXr14hIiICxYsXh4ODQ7aNmdImc3VFqZMntL4XUr8BZ1PlUplJaHHXv7yH8dJ/GC/lb+mnZnMQc3NznD17FkFBQdi2bRsePHgAiUSC/v37i22io6PF4mgpUtav6ko2BQQEwNHRUfzJ0qKdRJQjRcTIERadkOGfzCS08pouXbogJiYGa9as0dlGIpGgbNmyuHz5strxixcvoly5cgZdr0iRIhg6dCh27NiBrVu3Yvbs2YiNjQWQHFioPplRcPr0aQwZMgTVqlWDk5MTkpKS8PDhQ4OumRKwfHruT127dg2+vr5qx4KDg+Hi4qJ115Y5c+bgw4cPaf5UqlRJo59EIoGVlVWaPyljtrOzQ8WKFXHypHqdnRMnTqB27dqGfAy4c+eOWLyUTMfb2xt169bV+Em9TMDMzAx169bVWIbg6emJKlWqMCFFRJTNGC/9h/FS/parklKWlpZitX8g+anf8OHDERgYiISEBACAtbU1YmJi1PrFx8dDqVSqzZ5KbdKkSYiKihJ/Xrx4kXU3QUQ5mlQCeDhY6f0jlZh6xDlP9erVMWHCBIwePRq///47oqKioFQq8ejRI8ydOxcLFy4EkFx3YOXKlTh48CDkcjn27NmD9evXY+zYsXpfa+TIkdi1axeioqKQkJCA8+fPw9XVFTY2NgCS/7F+5coVtSd2JUuWxPbt2xEbG4vw8HD069dP43sjPV5eXpBIJBpB4qeuXr2KCxcu4MGDBwCABw8eYPLkyfjuu++0TjuXyWTpBkspBUgzY9SoUdiwYQMOHTqEjx8/YtasWXjx4gW+++47sU3jxo3RqVMntT7//PMPYmNj8eHDB/z00084fvy4WL+RiLKXIiICIfUbaP1RfPJkn4hyHsZL/2G8lL/luuV7n7K2toZSqUR0dDSsrKxQsmRJ/PXXX2rTHB8/fgwg+Q+WNibbTYaIchw3eyucn6z/jjh+s44hLDrBoGvou420q7krBhcZDLNoM5S2Kq3xfma2o9ZXRmtf/Pzzz/D19cWiRYswbNgwAEDRokXRrl07MYjq1q0bwsLC0L9/f7x+/RqFCxfGnDlz0K5dO72vM2DAAPzwww/o27cv5HI5qlWrhr1794p//8+cORPDhw9HQEAAihYtiocPH2LlypXo06cPChQoAFtbW3Tp0kXrzi5pKViwIKZPn44uXbrg48eP6Ny5s8YWxym7x5QsWRJly5aFg4MDEhMTMXToUEybNs2g6xlbnz598PbtW/Tu3RsREREoU6YM9uzZgzJlyohtEhMTkZiYKL7u27cvpk6dik6dOkGpVKJChQrYv38/mjdvbopbICKVKl8v49NWn2lGfAQKAIiIj8BgLd+PKe8n12bKVc/mKRMYLzFeyijGS9kjRyelEhMTsWHDBtSvXx+lSpXC8+fPUaRIEbV1q1u3bkWJEiXE6egtWrTA+PHjcejQIfE3fvPmzXBzc0PNmjVNch9ElD0yUxcqPMawxFJm6LuNtJmFGZSCEkqVUuv7mdmOOjt06dIFXbp0AQCt9RAAYPTo0Rg9erTW962srBAfH6/x0CA4OFh8alahQgXs2LEDgiBofSLWtm1btG3bFgqFQqy9UKlSJVy+fFntmomJieKv9bkuAEydOhVTp05FYmKi1mvfuXMHcrlcrCEQGxsLLy+vDBXmzApjx47F2LFjdf7e/PPPP2r3ValSJezevVvnZ01E2UPmov8GHoa0zW207cqbUghc1/cjC4XnT4yXGC9lBuOlrGfS3+mdO3fi3bt3uHPnDiIjI7Fq1SoAQO/evSGTyRAXF4cBAwZg7dq1KFWqFE6dOoWFCxeiadOmcHJywoEDB3D58mVs27ZNPGe5cuUwYsQI9OjRA8OHD8e7d++wdOlS/PHHH+lut0lEuVtKXaicytCdACVK7V9kpthRMLPXTG93GV3va9s+WNvM1vS+9LXt0pL6milbFht6XW19U1y9ehVFihSB6787aLnq2EnL1HR99rruiwEWkWkV37Hd1EMwGkN2o/t0FlRKv9S78kolYQBUkEqkcLNx0zjHp+9zh968jfES4yVjYryUdUyalLpx4wZevnwJb29veHt74/z58wCSt6yUyWSwtLREv379xJ1iunfvjs8++ww7d+7Eixcv0KZNG2zZsgUunzwF+u2339CgQQMcP34clpaWOHv2LGrUqJHt90dEpiGVJC/DywhX+6xbymvorjtddncxynnINB48eIC6dbkjIxGRLtpmO+miaxZU6l15QxY3gCL6DVytXbXu1Jve+5S3MF7KHRgvkUmTUtOnT0/zfWtra3H2VIqyZcti8uTJ6Z67TZs2aNOmTabGR0S5k6F1oYiyQkBAgKmHQESUK6Se7aS7jfZZUJztRJS7MV6inLFQk4iIiIiI8qXUs5104SwnIqK8idtOEBERERERERFRtuNMKSIiIiIiY1lRH4jN4E5fsf/+92OE0YZDmhQREQip3yDNNjIXlzxVVJ6IKKdiUoqIiIiIyFhiw4GYVxnrq3IHYAb8W9Q7t2i1KAgRMXKD+8V5yAGz5N1z/WYdg6u9JfYOy4aCxyoVFG/eZP11iIgoXUxKEREREREZm0QK2HkY2EmZJUPJahExcoRFJxjcz9ZNgNQMUKoEhEUnICw6AX6ztNeLmhcjhzOA8Bg5emhp42pviV/TuZ7MJf2i6IqICECVu5KCRES5GZNSRERERETGZucBjLlnWJ/N5bJmLNlEKkneAVdfcVIJhE+O6UpuqVSC+N+MJMAA6LUcL6R+A86iIiLKRkxKERFRjqRUKlGnTh0sXboU1apV06vP33//jbVr12LXrl1ZPLqcJSAgAHFxcZgxY4bRzjl8+HA0btwYLVu2NNo5c4qePXtiwIAB+OKLL0w9FMrJYsOAeRlIEsWGGX8suYSbvRXOT/bXu73/tlkIjwPMzaTwcEg7mSWVSsT/pm4bHpMA1aeZLaJ8hPGS/hgvGSa74iUmpYiIcpkn7TtAERmZrdfMSMHX4OBgLF++HLdu3YIgCKhUqRIGDx6MsmXL6tVfEARcuHAB0dHRel8zPDwc165dM2icxrBq1SqsWrUKn3/+OX79VX0ByYEDB/Djjz+iWLFi2LJlS5Zc/9GjR4iNjRVfDxo0CDVq1ED//v3FY4GBgZg1axaOHDmS7vlOnjyJ3bt3Y86cOVkyXn0JgoCjR49i5cqVePHiBXbt2oVChQrp3f/48eOYPHky6tevj19++UU83rRpUwwbNgzXrl2DRCLJiqFTXiCoMl4bigxS0M4Cx9JJZoUcngFFHOBmb6mW+PKbdSzDM6cob2O8pBvjpWSMl5KZOl5iUoqIKJdRREbm+KUF27ZtQ48ePdCjRw+MGzcOEokEu3fvhq+vL/744w907Ngx3XPIZDKcO3cO5cuXz4YRZ05oaCju3buH69evY/LkyXBJVbdk4cKFCA4OxocPH7Ls+pMnT4YqVQ2UO3fuaAQjb9++xaVLl/Q636xZs9C/f39YWloadZyG6tmzJ16/fo1atWph+/btkMv1L6QcERGBvn37wtLSEsHBwWrvdezYESNGjMChQ4fQrFkzYw+bcjs7t5x1HlLz6c5582LkUKkESKUSKBL0/0c55X2Ml3IexktZI7fHS0xKEVGOomsHn0936NEmPCafPSmVSiFzdc3SS2Sk4OvLly/Rq1cvDB8+HLNnzxaPN27cGC4uLujVqxf8/Pzg5eUFpVKJ5cuX4/Dhw0hKSkL9+vUxatQoWFpaQqlUYuTIkeJ09Pv376N3795YvHgxVq5ciYcPH6Js2bKYNm0a3N3dtY4lKSkJQ4cOhUqlwpIlS2BhYYHHjx9jzpw5uHv3LlxcXNCnTx9xyvWiRYtw8+ZN/P7772rnGTVqFJydnTF16lSd912oUCEULlwYGzduxMiRIwEAz58/x4kTJ9CzZ0+cOnVKrf2NGzewcOFCPHr0CF5eXujXrx8aNGgAAIiKikKTJk0wZ84cbNq0CXfv3sWoUaNgYWGBFStWYPz48ViwYAFevXqF3bt3Y+vWreJ09AkTJuDmzZt4+vQpDh06BCB5uvrkyZMRGxsLPz8/AMkBzHfffaf19+/IkSNYsGCB2vG//voLe/fuxTfffINVq1bh9evXOHLkCGxsbHR+Jpm1ePFiODo6IigoCLNmzdK7nyAI6NmzJ4YMGYIzZ85ovG9ubo42bdpg7dq1TEqRpkEnTT0CQKXM2NJBIDkZlhPuIat8snOeswmHQrkE4yXGS4yXtMop8RKTUkSUo+jawefTHXoIkLm6otTJE1l6jYwUfF2/fj2USiUmT56s8d64ceMwb948rFu3DlOnTsXs2bOxcuVK/Pzzz3B2dsapU6cwbtw4LFy4UGM6emxsLC5cuIAWLVpg+vTpaNOmDWbPng1/f3/cuHEDZmZmatf6+PEj2rdvj+joaOzfvx8WFhaIiIhAzZo10ahRI0yaNAk3b95E+/btsW7dOnTt2hXVqlXDyJEjMX36dHh6egIAPnz4gGXLluGvv/5K99779u2Ln3/+WQyy1qxZg+bNm8PNTX3GxKlTp9C2bVuMGzcO33zzDe7du4e2bdti3bp1aNu2LZKSknDhwgW0a9cOU6ZMQY8ePVCqVCkcOHAAhw4dwtOnTzF16lR4eXnB0dFRbTp6v379cOjQIbXp6KVKlUKfPn0wa9YszJ8/HwBQuHBhrfdw8uRJODo6okyZMmrHjx07hp07d+Lly5cYOXIkChcurFeA9e7dOzRv3jzNNo0aNdIaRDk6OqZ7fm3mzZsHuVyOMWPGaA2yAKB27dqYMGFChs5PlC24dFCNrp3zwlPNlHKzt0yzLeVPjJcYLzFe0i6nxEtMShFRjvTpDj4pO/SYfVLgVBtXe9NOoc3vrl+/juLFi8PJyUnjPXt7e5QsWRLXr18HAJw5cwbdunVD586dAQBfffUV4uPj0zz/9OnTMXjwYABAnTp14OXlha1bt6Jbt25im3fv3qFFixZwdHTE0aNHxWBgzpw5cHV1xdatWyGRSNC0aVNER0djwoQJ6Nq1Kz7//HN4e3vjzz//xJgxYwAA27dvh52dnV5PiNq3b4+hQ4fi0qVLqF69OtauXYulS5fi3Llzau1GjRqFiRMnYvz48QCSg4z4+Hj89NNPaNu2rdhu/PjxYsCWIikpCVu3bkW5ctpnUZQuXRr29vYoUqSI+JQPSA60zMzM1I5p8+jRI3h6emrUDrh+/ToqVKiAf/75BzKZ/uGDvb29GNjpUrBgQb3Pl55Lly5h7ty5uHz5MqRSqc52Xl5eePv2LaKiojIczBEZnUQKQAVIzQB7T8P6xoYl18HKo3TV6enxb00pDwfDiqwTmRrjJcZLqeXneIlJKSIyic77OiMyXrP4ZJyHHLZuAsykEtimSi7Fx8dAEJITTsf6MujMyRISEuDg4KDzfQcHByQkJM92a9SoEWbOnAl7e3s0adIEvr6+sLa2TvP8X375pfhrJycn1KxZE5cvXxaDrNjYWNSrVw8VK1bEH3/8AXNzc7H9pUuX0LhxY7UAonnz5pg5cybCw8Ph5uaGbt26YdOmTWKQtWnTJnTq1EntPLpYWVmhW7duWL16Nd69eweFQoGmTZuqBVnR0dG4evUqEhMT8ffff0MQBAiCgHfv3iE0NFTtfJ9//rnGNZycnHQGWMaQkJAAKyv1xK9KpcLt27exdu1agwIsIHnqd3qBnbFER0eja9euWLRoEYoUKZJm25R7jI+PZ1KKcg5bVyD2DWDnDow5YVjfeeU4u4ooF2G8xHgptfwcLzEpRUQmERkfifC4cM03zJIfEAsAwuOyfVhkBF5eXhpPulJ78uSJWJNg9OjRKF26NLZv345ly5YhKSkJixcvRrt27XT2t7W11Xj96Y4zCoUCSUlJGn1jYmJgZ2endizldUxMDNzc3NC9e3fMnDkT9+7dg729PU6dOoWZM2cCgFinIcXgwYPVXgPJ08EbNmyI0NBQ9O7dW2OafMq08cGDB6N69epq7336tO3Te9V1zJjc3d0R+cluRQ8ePEBcXBwaNmxo8PkyMx3dUKdPn8bz588xb948zJs3D0Dy2AHAz88P27dvF4OvyMhImJmZqRVZJSIiyi6MlxgvpZaf4yUmpYjIpKQSKVys//tLLiJGDqUqeaaUtmV4qdtSztSqVSssXboU+/fvR4sWLdTeO3r0KF6+fInWrVuLx1q2bCkGXTNmzECfPn3w9ddf6zx/cHCw2k4pwcHBak+W7OzsEBgYiIYNG6JLly7YunWr+LTKx8cH9+7dUzvfvXv3IJPJULRoUQBA2bJlUa1aNWzatAmOjo4oVqyY+ATOy8tLbWq1l5eXxviqVauGEiVK4MCBAxrFLwHAzc0N9vb2akU0jU0qlUIQhHSPaVOjRg28ePEC7969g7NzcgnhGzduoFChQnD9pFBsZGQk+vfvD4lEAg8PD4wZMwYlS5ZUa5Od09Hr1KmjUSA1pQ7CL7/8ojb+69evo3r16gY/ySQiIjIGxkuMl1LLz/ESIzEiMikXaxcc6/jfbnp+qWpD5KZleuExCTp3BUyPq70l9g6ra+QRmU7Tpk3RsmVLDB06FN7e3qhYsSKA5Kdm3377LVq0aCHWG/j111/RqVMn8WmMvb19utO+Z8yYgVq1asHa2hpr167F06dP8c0336i1KVSoEAIDA9GgQQN06dIFW7ZsgUwmQ//+/dG8eXMEBQWhbt26eP/+PQICAtCzZ0+1637zzTdYvHgx7O3t1c5ta2urV2C0a9cuvHv3Dj4+PhrvyWQyDB48GHPmzMGXX34pPv0LCQnB8ePHMWjQoHTPnx53d3e8fPlS41hsbCyio6PTXC5Qo0YNeHp64ujRo+jUqROA5ICkSpUqGm3Nzc3Ru3dvCIKA27dvY+DAgTh+/LhGm6ycjt6iRQu0aNEC3333HZycnDSuVaBAAQDQOH706FG1ehRERETZifES46VP2+TXeIlJKSIiI1AJ4K6AqWzbtg3jx49HrVq14O3tDYlEgqdPn6Jv376YM2eOOO3a09MTdevWhbm5OaRSKaKiorB69WqNadmplSxZEkWKFIGzszNevnyJJUuWwNvbW6NdSqDVsGFDdO3aFX/++Se++uorTJ06FY0bN4a3tzdCQ0NRq1YtzJkzR61v165dMX78eCiVSmzbts3g+y9WrBiKFSum8/2ZM2dCLpejbt268PLyQkJCAmxtbdN9Qqav/v37o0OHDrh06RKsra1x4MAB1KpVCzVr1kTp0qVRrFgxnVscy2QyDBkyBGvWrBGDrBs3bqBy5coabV+9eoUzZ87g2bNn+PjxI+LijLvmdtWqVVi1ahViYmIAAF9//TUsLS0xdepU8anylStXUKlSJYPO++DBA1y/fh179uwx6niJyHT4cIhyI8ZLjJeMIbfHSxJBn7lp+Ux0dDQcHR0RFRWVZnaUiDLOf5s/wuPC4WbjpnOmVG7YRafVoiBExMgz1Dc8JgEqATrvtcvuLhhQeAA8vTxRzuO/Qo3itsNSKWSfTA82NkVEBKBSQebunqHtlBMSEsQ16qVKldJalFMQBDx69AgqlQrFixdXewJ3/vx5lC9fHg4ODrh8+TJq1KiB9+/fQyaT4dGjRyhWrJha0cWIiAiEhoaiatWq4rG3b98iJCQEZcuWFXe4iY6OxsOHD+Hq6qp1SjmQ/LRLoVDgs88+S/c+Q0ND8fbtW61Px9J6PzY2Fg8fPoSLi4taoUmFQoHLly+jcuXKatsIa7s/AHj8+DFUKpXaVPCYmBg8fvwY8fHxqF69OszNzSEIAh4/fozIyEh4enrqvPe4uDiUK1cO27ZtQ82aNXHz5k24u7vD3d1dbBMZGQk/Pz+MHDkShQoVwq5du1CgQAEsWrQo3c9LX6GhoRrFTIHkZQUpU8uvXr2a5u9jyv//SpcuLR7r0aMHSpYsiWnTpum8dkJCAp48eYLixYtrFDJlnJAsyz+HlMLd9p7AmHvpt88DUv5+z9DfuSb8vDL63a0rFsjItTMj9bgz9XuQhYzxWeVVuv6+ZrzEeInxUu6IlzhTiogoEzLzZDXTgbRKlRxs5WBWVlZanxilJpFINNbVp9A1jdnOzk5rQOPq6qqxjr9gwYIaa/AdHBxQrVq1NMfl6+ub5vupFSlSJM3dS3S9b2dnp/U6MplM671ruz8AKFGihMYxe3t7jc9IIpHAx8dH6zT51GxsbHDq1Clxi2Btv4dJSUl4//499uzZg/j4eERHR2Pq1KlpntdQ6X2uANL9fUwdXKUYPnx4uv+/JKLcQVv9SX2lPByiPI7xksZxxkv/YbyUzJTxEpNSRES5jMwEu4WZ4ppkWtqm+KdWqFAh3LhxA3fu3EGNGjVw7949g6eFm0qNGjVMPQQiMhKTPhyiHI3xEmUHxkuZx6QUEVEuU3zHdlMPwSTKlSuHc+fOwd7e3tRDoX+lfjJXp04dE4+GiEyh877OiPN4CVs3AXFSCfy36b9deWR8ZPqNskHqelTzYuRwBhAeI0cPPWtUsSZVzsR4ifFSTsF4KW1MShERUa6g704uRESUfSLjIyGYRUFqBggAwo1bvzdbpN6sRPXvej6VSuAsKsqVGC9RbsOkFBERERERZYogSCBVOWSoxpOLtWmWPGkbq1QqEf/r4WCl8X5qrElFRJR5TEoREeVwCkGB4HfBereXSWXwcUq7MCMREVFqGd1NNs5DDpgBgsIeNuHTcaxvzt85N4W2JXchh2dAEQc4J0Tjj8Mz0uwforDAd1+MyKrhERHlC0xKERHlUMK//4MAKFQKUw+HKF8RBE5/oPwlIkaeoeVqtm4CpGZZMCBT02PHNkcbp+wZC+mFf28TZT9j/LljUoqIyMRSF1hNTXBPhMJDBSERgIX2iF/27zIDgIkrImOKi0sujGNubm7ikRBlL6kEcLNPe9laanFSCQQAZlJJhpbu5TT67J6miIgAVKpsGA3pI+Xv6bi4OFhbW5t4NET5izHiJSaliIhMLHWBVTXR/XFEZoGWEgUKJDlBIrMAJP8loWRSKbzd7MTXTz48gUJQQCVRISGBxVmJMkIQBMTFxSE8PBxOTk4wM8uLU0CIdHOzt8L5yfovwfPfNgvhcf/uQNc39+9Ap8+ObSH1G6Q7i4qyj5mZGZycnBAeHg4AsLGxgSRVvERExmfMeIlJKSIiE9HnifLZl0rYW35EbYUK5lIJIJFApRLEp9LSj/89zX7z8Q2UghJmEjPgfRYOnCgfcHJygoeHh6mHQUSkJjI+Ev7bMla3y8XaBVtbbjXyiHKGlL+vUxJTRJQ9jBEvMSlFRGQi2gqs6qJUKpGUlAQA6LziHCJj5XCxs8TWQbXFNtMPTce7+HdwtnbGuqbrjD1conzD3NycM6SIKEdSCSqExzHx8imJRIJChQrBzc1NjJeIKGsZK14yaVLq9u3bWL58ObZu3Ypy5crh1KlTabZPSEjAqlWrsGnTJjx+/BheXl4YMGAABg0aJLb5+PEj3N3dNfquWLEC33zzjdHvgYgoO5iZmYl/6b/5qEJYjBJKiQpWVv/NlIpIikB4YjiUMqXacSIiyhmetO8ARWSkzvcVERGZv0hsGDCvnMHd/k5MQJiFIwZiXubHQEbnYp1+rStdIuMjoRLyRw2s1PESEeUOJktKyeVydOnSBQMHDkTLli1x69atdPusXLkSISEh+O2331C8eHGcPn0avXr1QmxsLMaMGQMgeW3jx48fcfz4cdSoUUPsy3+gEREREZEpKSIjs74WkaACYl4Z3M0NgJJleHKszCy789/mz9lVRJRjmSwpZWlpidu3bwMARo4cqVef4cOHq73u0KEDAgMDsWnTJjEplcLa2hp2dnYgIiIiIspRpFLIXF11vq3PDnAa7NwyPp7YsORkFhERUTbL9TWloqOjYWNjo3G8Q4cOkMvl8PHxwaBBg9C7d2/uwkCUhTrv64zIeN1LEj5lSFsiItItLi4OK1eu1Chv8N1336UZ+7x69QojR47EsWPHYGVlhc6dOyMgIACWlulvwkCZI3N1RamTJ4x70kEnM953XrkMza4iIiLKrFydlLp48SK2bNmCZcuWqR3v1q0bRo0ahUKFCuHgwYMYOnQoIiIiMH78eK3nkcvlkMvl4uvo6OgsHTdRXhQZH8mp4UREJrB69Wo8e/YMy5YtE8sbdO/eHXFxcRg3bpzWPkqlEi1atEDBggVx4cIFvH//Hu3bt8fHjx+xYsWKbL6DvCG9elGAkWpGERER5SG5Nin18OFDtG3bFl27dkX//v3F43Z2dti0aZP4un///njx4gVmzZqlMykVEBCA6dOnZ/mYifIDqURqUDHOzBTuJCIiYNiwYWqv27Zti969e2Pz5s06k1L//PMPrl+/jkePHqFEiRIAgFmzZqF3796YOXMmXDKyfCyfy5Z6UURERHlMrkxKPX78GI0aNUK9evWwdu3adNtXq1YNUVFRCA8Ph5ub5nr7SZMmYfTo0eLr6OhoeHl5GXXMRPmFi7ULjnU8ZuphGG5FfSDWCDO97Nwyt4SCiMgIPnz4kGZtzaCgIHh7e4sJKQDw9/eHUqnE+fPn0bJly+wYZt6UTr0oIIM1o7KBG97j78T+wDwDNggqYAaYSYCYN8nfpfwOJCIiA+S6pNSTJ0/QsGFD1K5dG5s2bdJry8/79+/D0tISjo6OWt+3tLRk/QSi/C42nPU0iChPOH/+PLZu3YqVK1fqbPP69WuNB3Wurq6QSCQICwvT2oflDvSTJfWisomZRIAb3gExBnRy8gQgAwSlcR7u5BH6LOcEkhOUxXdsz4YRERHlTDk6KRUVFYXChQtjxYoV+Oabb/Ds2TM0bNgQfn5+OhNSq1atgkwmQ+vWrWFvb4/Dhw/j559/Rr9+/Zh4IqL0SaSAnYfh/VJ2LooNSy4YmxGcZUVEmfTgwQO0bdsW3bt3R58+fdJsK5VK1V6nFEUXBEFre5Y7yMPs3BAekwClkDzpyc3egJlSkvQfEOdHXM5JRKQfkyalatasibt37yIxMRFKpVKcZv7mzRvY2tpCEAR8/PgRSUlJAIDly5fj2bNniIiIgJOTk3geJycnhIaGAgBat26N6dOnY8KECfjw4QOKFCmCSZMmYdSoUdl+f0SUC9l5AGPuGd4vZeciQcUZV0RkEg8fPkSjRo3w5ZdfYvXq1Wm2dXd3x8mT6knwyMhICIIAd3d3rX1Y7iAPG3QSrWcdQ1h0AjwcrHB+jL/+fbf5A/l0oxOn+Cj8cWgGpFIJQg7PUHtPLGqvYzmnIiICUKmyY5hERDmaSZNSJ0+ehFKp1Dhua2sLIDnZFBMTAyur5Kc106dPx5QpUzTap97u2M3NDUuWLMGSJUugVCr1Wt5HRJRpdpr16vSWMsuKiCiDHj16hIYNG6JevXpYv369xiyoT9WuXRs///wzXrx4ISaWAgMDIZVKUbNmTa19WO4g7+q8rzPiPF7C1k1AnFQC/22z9O4bGZ/+ErW8SioIcEmIAgAo4rS30bWcM6R+A86kIiKCiZNS1tbW6bZJXaTTwsICFhYWep+fCSki02m1KAgRMfL0G34iPCYhC0aTDTKz7C5llhURUQak1NusV68eNmzYoDX+iYqKgru7O37//Xf06NEDzZo1Q9myZTF06FCsXr0a79+/x7Rp09C1a1d4eGRgCTPlapHxkRDMoiA1AwQA4ToSLJQspVB9eIwcKlXyclepVKK1bZTCAj1maW4AMy9GDmcAkbFylMqykRIR5Xw5uqYUEeVeETFyhEXn0gQTEVEusnLlSrx48QLbt2/Hjh07xONOTk5i0XJBECCXy8UZ6ubm5ti/fz8GDRoET09PmJubo1OnTli0aJFJ7oGMI6MPhOI85IAZIAgSSFUOcLU3cEZczBu4KJUA8scD4ZTC5D3+XfKYLi1tUpJZKu0l3IiI8g0mpYgoS0kNLZj6L4MDYiKifGrGjBmYNm2axvHU5Q2cnJwQHx8Pc3Nz8ViJEiVw5MgRqFSqdJf7Ue6Q0QdCtm5C8iwphT1swqfjWF8DakoB/874fQPYexp87dyMsQoRUeYxKUVEWcrN3grnJxsQ3K6on7yldCKAeRm8KHexI6J8RCaTQSZLP6RLqdH5KSak8h5DHwjFSSUQAJhJJUy0GGDvsLoZ7ntm+/dGHAkRUe7FpBQR5Syx4ayvRERElAmGPhDy3zYL4XHJM3/29s14ooWIiMhQTEoRUc4kkQJ2Bhbb5S52REREREREuQaTUkSUM9l5AGPuGdaHu9gRERERERHlGiwiQERERERERERE2Y4zpYgo74kNS541ZWgfIiIiIiIiyjZMShFR3iOo8sUyvvCYBPjNOia+jvOQA2bJW4KnPq6Nq71lpnYNIiIiIiIiyiwmpYgo77BzyxnnyCYqAQiLThBf27oJkJoBSpWgdpyIiIiIiCgnYlKKiPKOQSdNPYJs4WpvqfV4nFQCAYCZVAIPByutbcJjEqASsnBwREREREREemJSiogol9G17M5/2yyExwESWQxsS83S2sYuRg6lSkCcVAL/bcltXKxdsLXl1iwbLxEREZleZHwk/Lf5Z6gvYwUiyipMShER5TEqQYXwuHDtb5oBUjNAABAel63DIiIiIhNKMz4gIjIRJqWIiPIIF2uXdNtE/DtTykwqgUQWA5WgyoaRERFRvpCR3W9T2Lnlm2X42U2f+ECXyPhIxgpElKWYlCIiyikyGcxv1SOY95t1DGHRCfBwsIJtqVl8YkpERMaTT3a/NSaVSkh3x1xd9N1JNzPL7vy3+TNWIKIsxaQUEeVLT9p3gCIyMlPnkLm4oPiO7UYaERjMExERWi0KQkSMPEN9w2NMtPNqZnaujQ1L/v7Lx7hjLhHlZ0xKEVG+pIiMhOLNG1MPIxmDeSIi+ldEjDz3JSkys+xuXrl8+UBGKvn3v2nsmKsLd9IloryESSkiyt+kUshcXQ3qooiIAFRGTAQxmCciok9IJYCbvWHJihSu9pZGHg0Zm4udJRQfATd7S5yfbNiOeClL8YmI8gImpYgoX5O5uqLUyRMG9Qmp3yDnzLIiIqI8yc3eyuBkBRERUW7DpBQREREREZEJKCIiEFK/QZptjF7DkogoB2FSioh0MqTYapyHHDBLroXhN+uY6YqtEhEREeUWKhVnXxNRvsakFBHpZEixVVs3AVIzQKkSWOeAiIiIKA0yF5d02xi9hiURUQ7EpBQRpUufYqtxUgkEAGaf7CKTlcVWn7TvAEVkZIb6KiIijDwaIiIiIv3osxyPNSyJKD9gUoqI0qVPsVX/bbMQHpechDrWN3sKsyoiIxmsERERERER5VJMShGR8a2oD8SGZ6xvbJjhfaRSyFxdM3Q5fabPExERERERkfExKUVExhcbDsS8yrbLyVxdUerkiWy7HhEREREREWUek1JElHUkUsDOI2N97dyMOxYiIiLKuWLDgHnlMtbXzg0YdNK44yE1kfGR8N+WsfIMLtYu2Npyq5FHRER5BZNSRJR17DyAMfdMPQoiIqJM0WdjDW6gkUmCKltnWZNhVIIK4XEZLM1ARJQGkyelQkJC8Ndff8HZ2RnffvutXn0uXLiA48ePw8rKCm3atEGJEiUy1IaIiIiIKD3cWCMLZWZmdGxYcjKLsoyLdcZrb0bGR0LF3x8iSofeSamjR48iKioK7du3BwC8e/cOSqUSrhksLqxQKNCsWTM8e/YMNjY2kMlkeiWlAgICMHPmTHTv3h3v37/H5MmTsWvXLjRt2tSgNkRERESmYOyYirKRHhtrcAMNA2Vm2d28cpxdlcUys+zOf5s/Z1cRUbr0Tkpdv34dYWFhYgC1Zs0ahIWFYe7cuRm6sEQiwfjx4/Hll19i1KhRCAoKSrfPkydP8MMPP2Djxo3o3LkzAGDYsGEYNGgQnjx5AqlUqlcbIiJjUEREIKR+gwz3l7m4oPiO7cYbEBHlCsaOqSj7cGMNIiIi4zLZ8j0zMzN89dVXBvX5+++/YWNjg3bt2onH+vbti8WLF+Py5cuoWbOmXm2IiIxCpcrUcg7FmzcZTmoxoUVERERERLmdyWtKGSI4OBje3t4wNzcXj5UqVUp8r2bNmnq1+ZRcLodcLhdfR0dHZ9UtEFEekNmlGakTWaxRQkRElEn5dOe+8JgE+M06lqG+rvaW2DusrpFHRERkOIOSUrGxsQgNDQUAREVFqb1OYW9vD0dHR+ONMJWPHz/CwcFB7ZidnR3MzMzw8eNHvdt8KiAgANOnT8+SMRNR3pPZGUr67OKkiyIiAlCxaChRbmfqmIooT8mnO/epBCAsOsHUwyAiyhSDklIrVqzAihUrNI6lNmbMmCyriWBnZ4eoqCi1YzExMVAqlbCzs9O7zacmTZqE0aNHi6+jo6Ph5eVl5NETESXLTFIrpH4Dzq4iygNMHVMR5Qn5dOc+V3vLDPcNj0mASjDiYIiIMknvpFSnTp3g6+ubbjtvb+/MjCdNZcuWxR9//IHExERYWFgAAB48eCC+p2+bT1laWsLSMuN/uRNRxmV61hARUS6TE2Iqojwhn+7cl5lld36zjnF2FRHlKHonpYoWLYqiRYtm5Vg0JCQk4KeffkL79u1RtWpVtG7dGmPGjMFff/2F7t27AwB+//13FC9eHNWqVQMAvdoQUc6hiIzkzB9j0LOext+JCVBaAmaJQNcYW8BMAnxkco8oO5kipiIiIiLKiTJU6Dw+Ph7Xr1/H+/fv4ejoiCpVquhcGpeWRYsW4c2bNzh37hxevXqF77//HgDwww8/wMLCAgkJCZg5cyZKliyJqlWrwtvbGwEBARg0aBCOHTuGd+/e4ejRo/j7778hlUoBQK82RJQDSaWQubpmqGtmC4/nCXrW03ADAElKHysAMtaoIjIhY8VURERERLmRQUkplUqFqVOn4rfffkN8fLx43NzcHIMHD8bcuXPFJXP6sLS0hJWVFVq1aqV2XCJJ/heTtbU1ZsyYoTbDacyYMfD390dgYCAsLS2xePFijfpP+rQhorR13tcZcR4vYesmIE4qgf+2WWm2j4zP2BK8FDJXV5Q6eSJT58iXDKynER6TAKWQPEGKiEzH2DEVERERUW5kUFJqypQpWLRoEcaPH4+vvvoKBQsWxIcPH3DixAnMnj0b8fHx+P333/U+38CBA9N839LSUpw9lZqvr2+6tRj0aUNEukXGR0Iwi4LUDBAAhMeZekSklYH1NFr/W0vCw8EKtpIRWTQoIkqPsWMqIiIiotxI76RUdHQ0Fi5ciIMHD6JevXpq7/n5+aF58+aoVasWpk2bhiJFihh9oERkGoIggVTloPdOLy7WLgByZ+FQIqLskJUx1aNHjwAAPj4+abZTqVS4e/euxvEiRYrAycnJoGsSERERZZTeSalz586hSpUqGsFTisqVK6NJkyY4ceKEWGCciHI/QWEPm/DpONbXX/9OwekX3CYiyq+MHVMJgoA1a9Zg2bJluHv3LsqXL4/Lly+n2ScuLg6VKlVCiRIlYG1tLR6fOXMm2rRpY9gNEREREWWQ3kmpp0+fokqVKmm28fX1xePHjzM9KCIysRX1AfO3gJkEbpIP2JrYH5hnpX//2LCsGxsRUS5n7JgqKSkJZ8+exdKlS7F582YEBQXpPZZNmzbBz89P7/ZERERExqR3Uurjx4+wtbVNs42dnR3Cw8MzPSgiMrHYcMAJAGSQQgU3vANidDd/ctgFigSzVEf+3UVPCuDvBmleShERkamhEhHlNsaOqSwsLLB69WoAwObNmw0aS1RUFB49eoSiRYvC3NzcoL5EREREmaV3UkqlUiE2NhahoaE620RFRUHFrcWJ8hQVpAiHM9zsdc+UUiQCingdb358kzUDIyLKpXJSTPX111+jYMGCePPmDfr06YN58+bBzs4uy69LREREBBi4+96KFSuwYsWKNNuMGTMmUwMiopwlXHBCa4uFOD8mjZpSfzdITj5JpZC5umboOjIXl4wNMJ9SREQgpH4Dg/vNi5Ej0sIOAa0nGn9QRKQ3U8dUZmZmWLhwIQYPHgxzc3PcvHkTzZo1g0ql0rnrn1wuh1wuF19HR0dn2fiIiIgof9A7KdWpUyf4+vqm287b2zsz4yGiXEzm6opSJ0+Yehj5g0oFxRvDZ6E5A1CpBOOPh4j0lhNiKmtrawwbNkx8XblyZUyaNAnjxo3D8uXLYWZmptEnICAA06dPz7Ix5RWtFgUhIkaefkMdwmMSjDgaIiKinE3vpFTRokVRtGhRPH78GA8ePECxYsVQtmzZrBwbERF9IjMzyhQREQCXWBOZXE6NqYoUKYKEhARERETAw8ND4/1JkyZh9OjR4uvo6Gh4eXll5xBzhYgYOcKimVgiIiLSh0HL977//nvMmjULgpD8lL1fv35YtWpVlgyMiIg0Fd+xPcN9Q+o3yNDsKiIyvuyOqVQqFe7evYsiRYrAyckJiYmJsLCwUGtz8uRJFChQAK46lmFbWlrC0tIyy8aY10glSLMeY3pc7flZExFR3qd3Uuru3buYM2cOli1bhi+++AJXrlzB4MGD0b17dzRo0CALh0hERESUd2RFTPXw4UMkJCTg7du3SEhIwO3btwEA5cuXh1QqRXR0NCpVqoS1a9eid+/eWLx4MR48eIDWrVvDyckJBw4cwOLFi/Hbb79pXbpHhnOzt8L5yWnUYyQiIiL9k1KXLl1C27ZtMWjQIADJQc7Fixdx8eJFJqWIiIiI9JQVMdW4ceMQEhIivu7SpYt4LWtra5iZmaFChQooUKAAAGDkyJHYtGkTli9fjoiICJQoUQLHjh1DvXr1MndzRLlNbBgwr1zG+9u5AYNOGm88RET5jN5JqcjISI26Ad7e3njDpSBEREREesuKmGrXrl1pvm9vby/OngIAqVSKHj16oEePHhm+JlGeIKiAmFemHkWa9NlxV+bikqkl/kREpqJ3UkoQBMTGxiI0NFQ8FhUVhZiYGLVj9vb2cHR0NO4oiYiIiPIIxlREOYCdW+b6x4YlJ7SyQwZ33CUiyg0MKnS+YsUKrFixQuvxFGPGjMHcuXMzPzIiIsoy4TEJ8HYXAEgQKQUqr6mrd1+pRIIyrp7Y2nJr1g2QKI9jTEXG1HlfZ0TGR2a4f2b65lqZXXI3r1yWz7DSZ8dd7qxLRLmd3kmpTp06wdfXN9123t7emRkPERFlA5WQ6tcSCWAWpXdfJYDIeIt02xGRdoypyNgi4yMRHhdu6mGQkemzHI876xJRbqd3Uqpo0aIoWrRoVo6FiIiygVQqgYeDFZyVAqRQAABUkOrV952ZJDmJFfPmv8KwLPJKZBDGVJRVpBIpXKzTn12jS2b6EhERZYRBy/eIiCj3c7O3TN6mfJ5g8NIDfy9PhMtkgKDM8YVhiYjyGxdrFxzreMzUwyAiItIbk1JERPmVgUVew2MS/ptRJTEDJNLsK/JKRERERER5DpNSRET5lYFL7lrPOoYY4QdIEQ3YuwN2nC1FREREREQZx6QUEVE+o4iIQEj9Bgb3mxcjx3v7GEzqKzH+oIiIiCjD9Plul7m4ANW/zZ4BERHpiUkpIqL8RqXK0E49zgAEqQSAmdGHRERERJmQwe92IiJTY1KKiCifkLlkfFclRUQEoGL9KCIiIjWxYf/tRmsoI+xeq893O7/DiSgnY1KKKI9rtSgIETFyg/r8nZgAOFll0YjIVIrv2J7hviH1G/AJLBER0acElUnrK+rz3c7vcCLKyZiUIsqrVtQHYsOxOiYBSsGwrgXxHkChLBkWERERUa5n4A62amLDuHstEdG/mJQiyqtiw4GYV3ADgEzUpTaTSuBqb2msUREREeUoT9p3gCIyMs02ioiIbBoN5RqZWXY3rxx3ryUi+heTUkR5nBJShAtOMJMAbvYGLMmTJBezdrW3xN6+dbNodERERKaliIzk0ibKd8JjEuA361iG+7vaW2LvMP3iw8j4SPhv88/QdVysXbC15dYM9SWi3IFJKaI87i2cUFu+GB4OVjg/xoCAYJs/EBeedQMjIiLKSaRSyFxd02ySmQ0jiHISlQCERSdk07VUCGdMSUQ6MClFRERERPmezNUVpU6eMPUwiLJUZksyhMckQKVnrVIX64wncSPjI6Fi3S2ifCFHJKXi4+Mhk8lgbm6eZruEhATExsZqfa9AgQIwM0tebhSppS6Avb09LC1ZF4eIiIiIiPInfZfc6eI365jeM6wys+zOf5s/Z1cR5RNSU178/v37+Pzzz+Ho6AhbW1t06tQJUVFROttv3boVZcuWVfspWrQoXF1dERYWBgCIjY2Fq6srSpYsqdZu165d2XVbRERERERERESUDpMlpeRyOVq0aIGiRYvi3bt3ePr0Ke7evYv+/fvr7NOrVy9ERkaq/dSuXRtffPEFChcurNb20KFDau26dOmS1bdERERERERERER6MtnyvQMHDuDJkyc4ffo07OzsYGdnh//973/o1KkTXr16BU9Pz3TP8eTJEwQGBmL9+vUa76lUKnz8+BG2trZZMXyiPOfTLbFnxEdAJagglYQhZHGDNPtyq2wiIiIiIiIylMmSUufPn0eJEiXUkk/169eHIAi4ePEi2rZtm+45Vq9eDUdHR3To0EHjvYYNG0IikcDJyQmDBg3ClClTYGFhYcxbIMpTPt0Su4D4KxUU0dwqm4iIiIiIiIzLZEmpiIgIuH6y7W7BggUhlUoRocesC6VSifXr16N79+6wtrYWj0ulUkyePBmjRo2Cs7Mzjh8/js6dO+Pjx4+YO3eu1nPJ5XLI5XLxdXR0dAbviigP+HdL7AhxppQUrtZpb5GdgltlExEREeVMiogIhNRvkGYbmYsLiu/Ynj0DIiKCCZNSEokESqVS7ZhKpYJKpYJUmn6pq8OHDyM0NBQDBgxQO25jY4OZM2eKr7/88ktMmjQJ//vf/zBnzhxIJBKNcwUEBGD69OkZvBOivCVlS+zB/+564mbjhmMdj5l6WERERESUGSqV2qx4IqKcwGRJKU9PTxw9elTt2Jt//5IsVKhQuv1Xr16NmjVronLlyum2LVWqFD5+/Ig3b97Aw8ND4/1JkyZh9OjR4uvo6Gh4eXmle14iIiIiIqIMiQ0D5pXLWF87N2DQSb2a6jOTXRERAahUGRsLEVEmmCwpVa9ePfz0008ICQlBqVKlAAD//PMPzM3N4efnBwAQBAFv376Fvb09LC0txb4RERHYu3cvli5dqnFeQRA0ZkNdunQJdnZ2KFiwoNaxWFpaqp2fKC+Kd50H/22zdL4/Iz4CBQBExEdg8DZ/RMZH6mxLRERERJkkqICYV1l+GX2W44XUb8BZVERkEiZLSvn7+6NWrVro06cPlixZgnfv3mHKlCkYPHgwnJ2dAQBRUVFwdXXF2rVr0bt3b7Hvhg0bYGlpiS5dumicd8GCBfjw4QNat24NJycnHDhwAPPmzcOkSZNgbm6eXbdHlOMIZtEIj4vS+b5KUIn/DY8Lz65hUS7j9FHAssWK5F0ZlQBU7oAUwN8N0u3LOhVERERInuWUUbFhycksIqI8wmRJKalUir1792L8+PFo3bo1LC0t0a9fP/zwww9qbQoWLAgrKyu1vnv27EGfPn1gZ2encd7Bgwdj0aJFGDx4MCIiIlCiRAmsX78enTp1yvJ7IsoNpBIpXKw1p3FLJWEAkgubu9n8Fyxpa0v5l5kAFIwBABUUyUeS3/jIp6tERER60XPZnVbzymXL7CoiouxisqQUAHEWlC4ODg6IjNRcQnTq1CmdfaysrDBu3DiMGzfOKGMkymtcrF20Fi4PWdwAiug3cLV2ZWFz0iBzcUF4jByCNAqQCMm7MipVgEoJSM0AO3edfVmngoiIKG8Jj0mA36yMxYuu9pbYO6yukUdERLmVSZNSRGRcT9p3gCIlkRsLQOUOFaT4Q5gBydEYQKJKXna1uIFGX0VERLaOlXKX4ju2o+usY4hx+wFS8+jkXRmfvwJi3gD2nsCYEzr7sk4FERFR3qISgLDoBFMPg4jyACaliPIQRWTkJ//4T15a5YLUtaRUUEQzQUBEREREhnG1z/jmUOExCVAJRhwMEeUJTEoR5UVSKWTWyUurVJAiXHCCRJYyU0oKV2tXnV312TaYKCJGjvCYBLghOchsncYU/nkxcjgDiIyVo1S2jZCIiIiMLTPL7vxmHePsKiLSwKQUUR4kc3VFqdZvgJg3CIczmiRMhUPpAAhmUcnLrlgzijJJqRKgFABIAGU6U/hV/z4W5dNRIiIiIiJKjUkpIiLSi6u9JeKkEggAzKQSmEmSj5tJAA8HqzT7EhERERERfYpJKSIi0sveYXXhv80S4XHJCSo3eysgBnCzt8L5Mf46+53Z/n02jpKIiIiIiHILJqWIiChbOMVHIaR+gwz1lbm4oPiO7cYdEBERERERmRSTUkRElDmxYcC8cjrfdhEEqCCBVBA+2R2SiChnarUoCBEx8gz1DY9hIWciIiJ9MSlFRESZI6iAmFc637awcoECZtrflJoBdu46+yoiIgCVKrMjJCIySESMnLuEERERZQMmpYiIKGPs3PRqZtskAUpBBTNJcv0pAMmzqwQVYO8JjDmhs29I/QacXUVEJiNN/feWgVztLY08GiIioryHSSkiIsqYQSf1atZ61jGERSfAwyFVQfR55dKcXUVEhouJicGBAwdga2uLli1b6tXn9evXCAoKgpWVFRo0aAB7e/ssHmXu4mZvhfOTdW/kQESGC49JgN+sY2m2ifOQA2bJsxZTt3W1t8TeYXWzeohElI2YlCLKyVbUB2LD9W8fm/LfN8kzUYiIKM9TKpUYOnQodu/eDUtLS7i4uOiVlNq0aRMGDhyI2rVr4/379wgNDcXBgwdRrVq1bBg1EeVXKgHpLo+1dRMgNQOUKoFLaYnyOCaliHKy2HDDZpOo3AGYASpl8tIoIiLK8wRBQOXKlTF79mxMnToVQUFB6fYJDw/HwIEDMWvWLIwYMQIA0LlzZ/Tq1Qu3bt3K6iETUT5kyJLWOKkEAgAzqQQeDlYIj0mASsi6sRGR6TApRZQbSKSAnUf67aQp/zVLrtUD4G2sddaNi4iITE4mk+Hbb781qM/u3bshCAIGDBggHhs+fDjq1q2LW7duoVKlSsYeJhHlc4Ysu/PfNgvhccmJrGN9/eH3bykAIsp7mJQiyg3sPIAx99Jv93cD4OOb5N3MxpwAAPSZdQyI55c4GVdkfCT8t+lXZyXOQw4bZzvg3bgsHhUR6ev27dsoXrw4bGxsxGMVK1YU39OWlJLL5ZDL5eLr6OjorB8oERER5WlMShERkcFUggrhcXrWOzMDJDLOuSfKSaKiov7f3p2HN1WtawB/s5OSlo6UNJRCQSyDiDggnhZBWyiIE1QELyg4ACIqcGW4DogexQFQD04cHK4ecFZEDhfEEYpVzyNDHY7HoSAqoCJtk7a0adOmTfa6f4RuGpp5Tvv+noendu21dlYTk6z97bXWh7S0NIey1NRUqNVq1NbWOm2zcuVKLF++PAy9IyIios6CQSmiEDg4eQqsRmNA59DodOh3fpA6RBQkugSdT/WNjUbI3N+MKOokJCSgoaHBoayxsRE2mw0JCc6XfS9duhSLFy9Wfq+rq0N2dnZI+0lEREQdG4NSRCFgNRphragI2fmnbpsKY2P7oNeDjQZ0A2BoNODm40urzJkWJOoFhGQKWX+o89hw+Qaf6hduLPR+RhURhU1OTg42btwIWZYhSfYNCQ8ePKgcc0ar1UKr9X6jYiIiIiJPGJQiCiVJgiYjw6cmVoMBkN3PLDE2Gp1e6LfOSHFYWqW273tORESdV3NzM9544w2MGjUK/fv3x2WXXYY777wT27dvx/jx4wEAb775JjIyMpCbmxvh3hIR2bXuYdl6k9UsqVC4cYXX7XUJOp9vqBFReDEoRRRCmowMDPi0xKc2B/ILYK2ogNVgwIE3AMg97Fn1thYodR5sNCgBKEklKeWp9VDK9F31AACDyQKbLKCWVMhI1vq8/IqIiKLfli1bUFNTgx9//BFVVVV46aWXAAAzZsyARqOB2WzGzJkzsX79evTv3x+nn3465s+fjxkzZmDhwoWorq7G008/jZdeeglxcXGR/WOCzNOSeqvBEMbeEJEvlButx2+yCgCV5kj3ioiCiUEpomgly7A2AMDxaU4NJ5YDdnOs2K5pRkIGiq8qBgAlhW5mSjyKZ3mXLY2IiGJLaWkp/vjjD2RlZSErKwslJSUAgKuvvhoajQZdunTB9ddfj/79+yttnn76aeTn52Pnzp3QarX4/PPPkZeXF6G/IHRCvaSeKCLqy4HVg/1vn6QH5n4avP4E2ck3UU++yeoJ97Qkih0MShFFGY2uzZdwfQUg2+y3hpJ6KMWG4zOlJJWEjIT2ywMdzkFERB3eQw895PZ4165dldlTbU2ePBmTJ08OUa+ijIcl9ZH+7nS1X6Q3/G1HMUzIgOnPSPciZE5ecufrTVbuaUkUOxiUIooy/Ta9c+KX1YMBUwWQnAUsKVGKbz7+RavvqldmRBEREZFr/iypDydX+0USOUjSB9a+vtwe0CIiihIMShERUeR4Wn5Q3/qzon29KF96QETkD0kl+b3/I/eN7AQC/d5bPbhDz7AiotjDoBRRjJiw5l8wmCwAAHOmBVDb19fnrXA/U6rS1BSO7hH5x9PyA7kHALV9GauJe8IQUcenS9BxFjQREXUaDEoRxQiDyYLyOnuAKVEvIKkBmyyUMqKY4u3yg9bkkpLavowV4NIDIiIiIqIOgkEpohgjqQC1pIKA/WdmSrxX7bzJVEIUNt4uP9haYM88mdTjxL5qXHpARERERNQhMChFFGrP5wP1fm5cWl/erkifHI/EZC0qzfZAkzcZSIiIiIiIiIiiDYNSRKFWX8lZHUREREREREQniXhQ6u2330ZxcTHi4+Nx1VVXYdSoUS7rWiwWzJ49u1353LlzccEFF/h9XqKwUElAUqZ/bZP0gCW43SEiIiIiastqMOBAfoHL4xqdDv02vRO+DhFRhxfRoNS8efPwzjvvYNGiRaipqcGYMWPw4osv4rrrrnNav6WlBa+//jruv/9+5OTkKOW9evUK6LxEYZGUCSwp87+9hyx7REREREQBkWVYK5jtlojCJ2JBqR9++AHPPPMMPv74Y4wbNw4AEB8fjyVLluDqq69GXFycy7bjx49HXl5e0M9LREShU2lqQp6PwdXVJgvSATRXVp64c1sPQO5hz8y3tcDjOXhXl4iI6CT15fbEIcdpbAASXVe3mgEIAPUV9v1SvU1YQkTkQcSCUu+99x7S09NRWHhik+Zp06bhgQcewO7du9stx2trzZo1+Mc//oGcnBzMmDEDvXv3Dsp5iYgodGQBlNc1+dZGFgAASYiT7tyq7T8aeDeXiIjIZ0J22PO031j31Q9s6QFroxqQbf4n8CEiciJiQalff/0V2dnZkCRJKTvllFOUY66CR7169UK/fv3Qs2dPfPDBB3jooYewbds2FBQU+H1ei8UCi+XEhj11dXUB/nVERNSWWlIhMyXe53Y18ckAAElSQZ+stRfWV9gHxZIaSOrhsq3VYABk2a/+EhERdUhJev/aSZ6rEBH5I2JBqcbGRiQlJTmUJSQkQK1Wo7Gx0Wmb+Ph4fPfdd+jWrRsA+95R06ZNw80334x9+/b5fd6VK1di+fLlgf5JRETkQkayFsWzCj1XPEke7LOrMlPisfvu4+1XDwZMFUByFrCkxGXbA/kF3BeDiIioLX+X3W0t4OxkIgqJiMW8U1NTUVNT41BWW1sLm82G1NRUp200Go0SkGo1ZcoU7N+/H7W1tX6fd+nSpaitrVX+/f777/7+WURERERERERE5IWIBaWGDh2KgwcPwmw2K2XfffedcsxbDQ0NAZ9Xq9UiJSXF4R8REREREREREYVOxJbvFRUVYdGiRXj++eexaNEiAMBTTz2FM888E2eccQYAwGw246abbsLcuXNxwQUX4PPPP0dOTg6ysrIAAMeOHcMTTzyBCy64QJkF5c15iSJlwpp/wWCyeK7oRKXJtw2iiYiIiIiIiKJZxIJSer0eL7zwAm688UZs3boVNTU1qKiowAcffKDUaW5uxuuvv46xY8cqG5SPGzcO3bt3R1paGnbt2oVBgwbhlVde8em8RN44OHkKrEajX22tBoPTcoPJ4nP2MSIiIiIiIqKOKGJBKQC4+uqrMWbMGHzxxRfQarXIz89HYmKicjwxMRGvvvoqzj//fADABRdcgG+++QZffvklDAYDHn74YadL8jydl8gbVqMxZJskSypAn+x7JjLAvmG02XM1IiIiCrOp26bC2OjfDS1/2xF1JpWmJuStKPZYz5xpAdT2G8Jt62cka/HuglGh7CIR+SiiQSkA6NGjByZNmuT0WFxcHGbMmOFQ1qVLFyVI5e95iXwiSdBkZPjVVKPTAWgf2NInt8kk5ofCjX43JSIiohAxNhpRaa6MdDeIOixZwKtVB4l6AUkNyFIdTPq/KuVmSYXCjVqvHkuXoMOGyzf43Vci8k7Eg1JE0U6TkYEBn5b4f4LVg4PWFyIiIop+kkqCLkHnV1t/2xGFg7VJwoE3AGwtcFlHo9Oh36Z3gvq4GcneBZJamSUVBACVSkAVV6eUCwCVXHJAFFUYlCIiog7NajDgQH6BX21DMbAmoo5Pl6BD8VWelxgRxRyhgrUBQENotrhwxdcld1O3/S+MjScCWQaTBTZZQC2pPAa4jI1GyEL2q59E5DsGpYiIKDbVl7ufiVh//Kcsh2x/OCIios5Ao9MB9RWAbAMkNZDUo10dq8EAyNERzDl52V3eimKU1zUhMyUexbPcb6FRuLGQy3CJwohBKSIiik1CBkx/ujys6aIDZLXzgy4G1K2iaWBNREQUaf02vWO/EWSqAJKzgCUl7eocyC/gTSAi8hmDUkREFFuS9F5V6zfFSWF9uT2Y5WJA3YoDayIiIhdczVRunaFcX+F6JnOSHpj7aci6RkSxh0EpIk8aDIFtVl5fHry+EFFgg9nVg93OriIiIiIPXM1UlnsAUNuX+Jl4Y4eIvMOgFJEnHpYIERERERF1eJ5mKkutP9X2Gclttc5UJiI6CYNSRN5SSUBSpv/tk/SAJXjdISIiItcmrPkXDCYLVpssSAdQabLg2hXeZcSrNDWFtnNEscjTTOWtBfasfEk92i+R50xlInKBQSkibyVlAkvKAjuHl4Nhoo7G2GhE4Ub32W7a0iXo2mXOISLyhcFkQXldE2RZAABkWaC8jsEmIiKiaMKgFBERhZwsZKZXJqKIkiQVMlPifWqTkawNUW+IOi6rwYAD+QWOhfWw7zklAdhaAI1OZ8/oR0SdHoNSREQUMroEnU/1jY1GyNxzgoiCSJJUAAB9sha77/Z+xiYR+UmWXWSwVdt/NHATdCI6gUEpIiIKGV+X4BVuLOSMKiIiohik0bm5EVVfAcg2WJvUgAhfn4go+jEoRR3WwclTYDUa/W5vNRiC2BsiIiIioo7L7XK81YMBUwUOvJsFa0P4+kRE0Y9BKeqwrEaji6nDREREREQUdrINgNo+c2r1YN/aJuk9ZwAkopjDoBR1fJIETUaG3801Nga2iIiIiIiCRrYBJo6xiYhBKeoENBkZGPBpif8nWD0YMAWtO0REREREnUuS3v5TOv67pAaSs7xrW18OMAkKUYfFoBRRFJi6bSqMjd7vf+VLXaKOoNLUhLwVxT63y0jW4t0Fo0LQIyIiIvJa67K7rQX27HtJPYAlJd61XT0YMP0Zoo4RUaQxKEUUBYyNRmYcI3JDFkB5XVOku0FEREQxzJubXOZMC6AGDCaLQ13e6CIKDQaliKKIpJKgS3CTTvckvtQlikUZyVq/2lWamiAz5TRRh+cu0+5qkwWyLJBmqQtzr4goWnlzkytRLyCpAVmqg0n/V6XcLKlQuNG7cYkuQYcNl28IqK9EnQWDUkRRRJegQ/FVvi9RIuqo/L0jmbeiOCgzq6wGAw7kF/jVVqPTuU+PTRRkH3/8MYqLixEfH4/JkyfjzDPPdFm3ubkZixcvbld+7bXXIjc3N5TdDCp3mXbTw9wXIopevtzkMksqCAAqlYAq7kRQWwCoNAe/b0SdHYNSRERErsiyywteomiydOlSPPfcc5g7dy7Ky8sxfPhwvPXWW7jyyiud1m9ubsbatWuxZMkSnHLKKUp5ampqmHocZE4y7VYenyklSSrok7XQ6Di7mKiz8uUm19Rt/wtj44kglsFkgU0WUEsqj8EtY6MRMjdlJ/IJg1JEREQnCeTi1WowADIHpBQ+P/30Ex599FFs3rwZEydOBGAPLs2fPx8TJ06ERuN6uDdlyhTk5eWFq6sh4yzT7rXHZ0xmpsRj992FkekYEcWck5fd5bX5LCme5f6zpHBjIfeJJfIRg1JEREQnCWTZ3YH8As6uorDatm0bUlJScNlllyll1157LR577DGUlpZixIgRLtuuX78emzZtQk5ODqZMmQIdZxMRERFRGEmR7gARERER+e/AgQPo06cP1Gq1Unbqqacqx1xJT09HXFwc0tLS8Prrr2PQoEHYu3evy/oWiwV1dXUO/4iIiIgCwZlSRERERDGssbERycnJDmWJiYlQq9Uwm53vyhsfH48ffvgBmZmZAIBly5ahqKgIc+bMwbfffuu0zcqVK7F8+fLgdp6IiIg6NQaliIiIiGJYUlISjh075lBWV1cHm82GlJQUp200Go0SkGo1ffp0TJ06FSaTqV2QC7Bvpt42Y19dXR2ys7MD/wOIiGJApakJeSvcZ8k2Z1oAtX1z9LZ1M5K1fmcUJuroGJQiIiIiimFDhgzBSy+9hKamJsTHxwMAysrKAACnn3661+exWCwAAKvV6vS4VquFVut9WnUioo5EFkB5XZPbOol6AUkN2GThsS4R2TEoReSHCWv+BYPJ4nO7ShO/nIiiQn05sHqw/+2T9MDcT4PXH6IAFBUVYdGiRXj55Zcxd+5cAMDatWsxaNAgnHXWWQDsS/xuv/12XHvttcjNzUVpaSlycnKQnp4OADCbzVi7di3OO+88dOvWLWJ/CxFRtMlI9j4Yb5ZUEADUkgqZKfGoNDVBFqHrG1FHEPGglNVqRVlZGeLj4zFgwACv2phMJhw6dAi9e/duN3CSZdnpJp05OTnIyMgISp8pBj2fD9T7mZ61vrxdkcFkcXv3o+spa6DSmNqVJ+jtP82SCoUbVyjlxkajf30jIv8IGTD9GeleEAVFVlYW1qxZg9tuuw0ffvghqqur8Z///Afvv/8+VCoVAPssqLVr12L48OHIzc1FbW0tRo4ciQEDBiAtLQ0lJSVIS0vDhg0bPDwaEVHn4suyu8KNK1BptgeyimcVIm9FMWdMEXkQ0aDUZ599hmnTpkGtVqO+vh79+vXDli1bXO5PsH//ftx5550oKSlBdnY2fv31V1x66aVYv349kpKSANjv9I0YMQJDhgxRygDg3nvvdUiVTJ1MfWVILkAlFaBPjm9Xbu5SD6F2nZVIAKh0vvcsEYVSkj6w9vXl9oCWF6wGAw7kF/j1MBqdDv02veNXW+qc5syZgzFjxuCzzz6DVqvF+PHj0b17d+V4165dsWbNGuTl5QEAxo4di9LSUnz22WcwGAyYM2cOzj//fIcMfkREREShFrGglMlkwpQpU3Ddddfhb3/7G5qbmzFu3Dhce+21KCkpcdqmrKwMM2fOxObNm6FSqfDnn39i1KhR+J//+R8899xzDnVffPFFZeBFpFBJQFKm53rOOLmY1SfHY/fdhe3KW++SSCoJugSd1w/hS10i8kOgS+5WD/Y+wC3LsFZUBPZ4RD7IyclBTk6O02NdunTB/PnzHcqSkpJw6aWXhqNrRERERE5FLCi1ZcsW1NTUYNmyZQDsg6WlS5fikksuwS+//OJ0UHXFFVc4/J6VlYUrr7wSH3zwQbu6R48exbfffotTTz3VaQYZig0HJ0+B1ejf0jarwdC+MCkTWFIWYK+8p0vQofgq91k6iKg9Y6MRhRvbB3xd0SXosOHy6Fh2pNH5H1y2GgyA7N1MLCIiIiKiWBexoNTXX3+NnJwchz2hcnNzAQDffPONyzt9zs7Tr1+/duWzZ89Gjx498Msvv+Cqq67CM888g9TU1OB0nsLGajRypgFRJyQLGZVmP/eBi7BAlt0dyC/gZx4REZEzTFJC1CFFLChVXV2tZHxplZaWBkmSUFVV5dU5XnjhBXz22Wf49NMTHy5qtRrr1q3DDTfcAJVKhQMHDmDcuHGYP38+Xn31VafnsVgsShpkAKirc70XEEWIJEHj50b19lkLvMgjigW+LmE1Nhohe7nHExEREcWwQJOUmP70P6jFgBZRyEQsKBUXF+cQCAKAlpYWyLKMuLg4j+3/7//+D/PmzcOzzz6LkSNHKuUJCQmYOXOm8vuAAQNw1113YeHChVi/fj00mvZ/8sqVK7F8+fIA/hoKNU1GBgZ8WuL/CQK5q0JEYePrErzCjYUxO6OKiIiIvBBokpK2gSxm3iWKOhELSvXt2xfbtm1zKDty5IhyzJ2tW7di2rRpeOqppzBnzhyPj5WZmQmLxQKj0YjMzPabXC9duhSLFy9Wfq+rq3OZAZCIiIiIOq6p26bC2Ojffpb+tiMiNwKdofR8vj0Ttz98yLpLRP6JWFCqsLAQ9957L7788ksMHz4cgH3z88TERCVrns1mQ2lpKXJycpBxfOnWtm3b8F//9V94/PHHccstt7Q7r9lsRteuXR3KduzYAZ1OB73eeZRdq9VCq9UG888jIiIiohhkbDRyBiZRRxJIUMuXrLtE5JeIBaVGjBiBiRMnYvr06VixYgWqq6tx7733YtmyZUhMTAQAmEwmjBgxAuvXr8cNN9yAnTt3YsqUKbj66qsxbNgw7N692/5HaDRKYOuFF15AaWkpJk6ciLS0NLz//vt4/vnn8dxzz0GSpEj9uURERETkg4ObAWtDD0ACsLXAaR2nmXaDRFJJPu9z18rfdkTUMbRmETZnWpCoFzBLKhRuXOFV22jKKEwUDhELSgHAhg0bsHr1ajzzzDPQarX4+9//juuvv145rtFokJubq8yS2rdvH84++2yUlZVh4cKFSr3k5GRs374dAHDbbbdh8+bN2LhxIwwGA0499VTs3r0b5557blj/NiIiIiLyn7URsDaq7b80hD9hiS5Bh+KrisP+uEQUhbzN/NdNDahVJ7IIqwFJDQgAleaQ95IoJkU0KBUfH49ly5Zh2bJlTo8nJSUps6EA4NZbb8Wtt97q8byTJk3CpEmTgtZPIiKKTZWmJuSt8O+iMiNZi3cXjApyj4jIZypAo+/htoo90y4RUYh4mflPl9wDEGqHMhkSqlTdkJHsfrsYZhSmziqiQSkiIqJQkgVQXtcU6W4QUQA0XRFYBl4iijpWgwEH8gvc1tHodOi36Z3wdMgVHzP/bTC1+eX4JulHRTomaZ9G8axCt22ZUZg6KwaliIiow/F0N9KdSlMTZOGhkrfT+J1J0geeSYioE5BlAUAFWRZ+zXisNDEgTRS1ZBnWivAvy/UZN0knCjkGpYiIqMMJZNld3opiz7OrvJzGT0SBE+CMR6KOwpultlaDAZC5jI2os2BQioiIyFs+TuN3cHwaPxH5LjMl3u+2gcycJKLg8mY53oH8gtiYRUVEQcGgFHVaE9b8CwaTxa+2XBJAFF1aUy97y+90y2Gaxu/NXhvuRMU+HERBogKw+27v399EREQUOxiUok7LYLJwOQBRB6GkXu4oYmWvDSIiInJLjxpsbb4RWO1hxmc3NaBWAaaKE/tWch9K6gQYlKKQOzh5CqxGo19trQZDkHvTnqQC9Mn+LQvgkgCiyNIl+JYGPtrTLQea1p77cBAREUUXtUpAj2rA5KFiWhYADSBsyszqSlMTJvqR6KGtjGRtQHttEoUag1IUclajMarv+OuT47ksgChG+boEL9rTLQe65I77cBAREUWJJD0qTU2wecroe5wMCQBgVKtRmJ2llJnEX71+SGFNhvnQAp+7ShRJDEpR+EgSNBkZfjXV6HTA8/lAvZ8Xk/Xl/rU7buq2qTA2ej/by5e6RERERETUwcz9FLN92MPWrLoPQC1klQqVmhOX6RLqvH5IlaRSEkNUmpogexkQI4okBqUobDQZGRjwaYn/J/Bhk+BgMzYao3p2BRERERERRRdfls1N3fa/MDYe3xrEVGFfxqdSA8k9PLZt3Z4gI1mL4ln2FSB5K4q5fy7FBAalKPaoJCAp07+2gaRzByCpJJ/2sPF1vxsiIiIiIup8HLYkaL0Zn5wFzPK8p1S0b09A5A6DUhR7kjKBJWUReWhdgg7FVwW22SARERGFlq/L7tviEnwiIqLwYVCKiIg6HWOjEYUbnSc4MGdakKgXMAE4c919AACVLQUJhiVen5+Zbogii8vuiYiIYgODUkRE1OnIQnZ9waoGJLX9P1v3B7XJInj7MtSX26fl+yNJD8z9NDj9IOoEfF123xaX4BMREYUeg1JERNRpeHORWVXfDFnYw1FCqgNUAuo22Wzc8SrTjZAjlrSBqLPhsnsi6kzazgRvnfltllQo3LjCY1tdgs5xXyuiMGFQioiIOg1fB1utG4e2zWbjjttMN4EkWqgvtweziIiIiFxwmAl+fOa3AFBp9tzWYLIgb4VjEJ/bEVA4MChFXjk4eQqsRv82/rQaDEHuzQkT1vwLBpPFr7aVJqZIJaIwCmTZXWsWHiIiIqKTOJsJbjBZYPM4fRtQaUxQqURwtyog8gGDUuQVq9EIa0VFpLvRjsFk4YcnERERERF1Ws5mgnt7896ceR+EutZhqwKvtiMgChIGpcg3kgRNRoZfTTW60G0YKqkAfbLn/V6cyUjWBrk3REREREREAQogOcq7ANDdc4KUwo0rUGmGw1YFbrcjIAoyBqXIJ5qMDAz4tMT/EzyfD9T7maK5vtzlIX1yPHbf7Xm/FyKizsBqMOBAfoFfbTU6Hfpteie4HSIiIiLfBZocxfSn56BWNzWgVgGmCqXu1uYmlHdJxU1Y7f9jE3mJQSkKr/pK7otCRDGnbTYbd9pmupm67X+Dn8XG0x3T+uM/ZTkql1wTERGRFwJJjgI4Xm95uvZKywKgAYRNqasHYFMF1gUibzEoRZGhkoCkTP/aBvohTUTkI4dsNu60yXRjbAzB0mAPd0w1XXSArHZ+UFIDST1ctrUaDIDMDH9ERBQdPM367dAzewNJjgL4tjpFpT7xMzlLyfirRw22Nt8IrPZji5Qkz8sGiVoxKNWJRFUGvaRMYElZcM/pg6nbpsLY6P1z4UtdIuo4nGWzccdgskCW6qBSCaeplT1xmXrZy2B8vylOCo8PLpGcBSwpcdn2QH4BrBUVXPpHUaNGrUIqgCq1yquZim3xe5uoA+CsX//5EhDaWAiYK4HkHsCsYiXjr1oloEc1YApdN4kABqU6laBk0Gsw+L3ZHgC3+0KFk7HR6N2sByLq1Hxdfpe3ohgm/V+hiqsLbmrlQO42Hh9ceo0XARQlWuftySrwO5uoE/GUHIkze0MsSY9KUxNswr7VlE/JpFpvhBH5gEGpziiQDHq2iqjcE6oxYzUKN67wun7rHVRJJfk0E8LXWRNE1LlkJGthllQQgENqZU+iIfVyIBlSeYFAoabv6t/SfX5vE8UeTzNuW2f2UojM/RQTj2ffk1SAvov3Qamt4kboUY1KUxNmr/mX89nfRCdhUKoTCiiD3urB9imcgewJBQR9XyihrkOludbndroEHYqv8m15DRGRK+8uGIXCjdp2qZU9iYbUy4Esu+MFAoWSJMDvaiKiEGub1KU1cQvg3eo9YU2G+dAC2LQAVIBN2Lc0IPIGg1LknxDuCeXLfk+tH5hCsn9ccuYTEVHkcD8qIiIKF2++c/jd4j2HpC7HE7d4S3V8dri6OTR9o46NQSmKOj7t93TSByZnPhFRLKs0Nfm8OXorl5ukhxP3oyIionDhd05QBHKT3thohCzkE7PDV8dzY3TyGYNSFLW8mfVkMFlgkwXUkgoZyVrOfCKiqNF2Grwn5kwLuqYnwXxoQcSX8fmD+1EREVG4ePOdw+8W7/ma1KWtwo2Ffiei8DUbujO6BF1A/afoENGgVFNTEx5//HEUFxcjPj4eU6dOxXXXXRdwG3/OGysOTp4Cq9G/N6/VYAhyb4Jnwpp/KeuOzZkWQG1fm9xw4G637eqPbw6cmRLv9d4tRETh4DAN3hM1oOkCrzdGb8vrTdLrywPLnpqkd5kFkPtRRV6oxlRERNHGm+8cfrdEnqfZ3+bMIxBq3/cEpo4nokGpadOmoaysDA8//DBqamowb948/Pnnn7jrrrsCauPPeWOF1WgM/AO2vsL/C5P6cpeH2gaWfNV2ZkCiXkBSI7jp1ImIwsTXGZutU99VGhMSB3ifRbT17qDXm6QLOfzZU5/PB+o9BObqW3+6+G5yEwyjE0I1piIiIvJEmR3eTQ2kZQEA+uIOt20aJRUEVJCEQLrtxN01GyRUiRRlJYyrx5OF7NOs9JNF0yyrQK6jgyHSW0BELCi1a9cubNmyBaWlpRg+fDgAoKGhAffccw8WLFiAxMREv9r4c96I8WawfrLWwbtKQBPv35RUTRcbYApsqqQzBpMlKEEktR/p1F19YBERhZuvA5zWqe8+zazyRaDZTuvL7QEtv9pWeg6EyT0AqAHZBph4V9sfoRpTEREReUMZw6hV8DXEoLPZUPy741jhqEgHcPx0TkzN7gqjRgpo7FRprsTofwxxKJMhoVZKQ/ekLt6fqCHwpaLWriqYElICOoc3WrMkRpuIBaWKi4uRmZmpDIQAoKioCIsWLcLu3btRWNg+4ulNG3/OG27KErz6Svsg3AfWJgmACpp4GQOKjg/ek7Pa1TM2WCC7Wc9RiXSfHvdkVfUJmHnSdMxKkz0gJakAffKJYFJjxmoIdZ1X55VUKgi1CUL4lk6diChW+TuzqvXuYGsWUhOAM9fd175BHIBu3V2eT1KpnA6+lDuIqwfbA0ttlv95+o5p1R3HoMbxu55Ic3xcSQVdohaQ7L9bm9Q48G6b7zPl+9EGvOF+dq8mAeg3ycmBTjLLKlRjKiIiInfajWH8CNDohNp+PdvmJlZPVbXbNnpbHCT4kB6wjUrNiRCIUSM5qXEMlWYfTqiC6+iZDyR4d70cCJ3qGDbEz1d+twnAIFJxE1aH/LHdiVhQ6vDhw8jKcgym9OrVSznmbxt/zmuxWGCxnJguV1trX9taVxea/zGOlZfDWunv3XD7m1yyCfxiSUM10nCL/GC7WpUhnv4X1+0LxCU77vfUJdn+Uy2poE06MXOprtEA+BZ7AwBYYQ3Za0BEFC1euPAFn+pP2DwBhkYDbLDhqPmowzGrn3046uQro9zWgOF/3YoNLWZkQACwAU1HAADe3j9saD2XSMFYy6PtjuutWqywPohutuN7Srj8yHf/JaJpsaHO6GTfxCYbEILvkdbvJiG82cwr9EI1pjpZuMdLDTYb4mxAgy10j0FEHVO91QqrzQaNldcToeTrGMaVOgBYdwnQYEBVQzNkD9+vKw76f627KDMeNScFkSScCKTJcBaoci3YbSWVDwEu4d1FdpVaDVmlgmy1It5S5XDMJGRY0RCS94m346WIBaVaWlqg1TouuYqLi4MkSWhpafG7jT/nXblyJZYvX96uPDs72+u/JyK+A4DfABRFuCOhUYYypN6QGuluEBF1YkXoH5TzmAD8V7vS3wGMD8r5cfw70cnj3hO67xGTyYTU1Mh/T4VqTHWyiI6XouB5JqIY9PMBfn4QHVcGoP27wQSgCKnt57kEjafxUsSCUunp6aiudpyWd+zYMciyjO7dnS8z8KaNP+ddunQpFi9erPwuyzKqq6vRvXt3qHyJVPqgrq4O2dnZ+P3335GSEvr1oxRafD07Fr6eHQdfy44lWl5PIQRMJlO7mUaREqox1cnCPV6Klte7s+DzHV58vsOHz3V48fkOr2h+vr0dL0UsKDVs2DCsWbMGNTU16NatGwBgz549AIBzzjnH7zb+nFer1ba7W5iWlhbAX+e9lJSUqPufh/zH17Nj4evZcfC17Fii4fWMhhlSrUI1pjpZpMZL0fB6dyZ8vsOLz3f48LkOLz7f4RWtz7c34yXfFj0GUVFREdLS0vDwww8DAJqbm7Fq1Srk5+cjJycHAFBfX4+8vDy89957Xrfxpg4RERFRRxGqMRURERFRqEUsKJWcnIxNmzbhjTfeQHZ2NjIzM1FbW4tXXnlFqWO1WrFnzx4YDAav23hTh4iIiKijCNWYioiIiCjUIrZ8DwAuvPBC/PbbbygrK4NWq8XAgQMdjicnJ2PXrl0Od+w8tfG2TqRptVrcd9997abBU2zi69mx8PXsOPhadix8PV0L1Zgqkvh6hxef7/Di8x0+fK7Di893eHWE51sloiWfMRERERERERERdRoRW75HRERERERERESdF4NSREREREREREQUdgxKERERERERERFR2DEoFWa1tbVYs2YN8vPzceutt3rVpqGhAcuXL8eYMWMwYcIEvPXWWyHuJXnrp59+wuzZs5Gfn4/rr78e//nPf9zW37x5M/Ly8tr9s9lsYeoxAcCWLVtwxRVXYPTo0Vi6dClqa2tD0oZCz2KxYNWqVRg7diwuu+wyvPTSS27rNzc3O30Pbt26NTwdJrcOHjyIpUuXYsSIEXjxxRe9anP48GHcfPPNyM/Px/Tp07F3794Q95KC5d1338WkSZMwevRo3HXXXTh27FhI2pDdK6+8gssuuwyFhYVYsWIFmpqa3Nbfv38/Fi9ejHHjxmHq1Kl48803wa1ovWO1WvHUU0/hoosuwvjx47F27VrIsuxVWyEErr/+euTl5WHfvn0h7mnHYDab8cADDyjXSm+88YZX7Xbv3o2ZM2dizJgxuOOOO/h54qXq6mrcfvvtGD16NCZPnowPP/zQY5uvvvoKc+bMwZgxY3DFFVdgzZo1sFgsYeht7Dt8+DCWLVuGESNG4Pnnn/eqzW+//YZbbrkFBQUFuOaaa7B79+4Q9zIwDEqFUW1tLQYPHox9+/YhPj4eP/74o1ftioqKsGnTJixYsACXXHIJZs6cib///e8h7i15cvjwYYwYMQLNzc246667oNVqMXLkSLcDiIqKChw5cgRPPvmkwz+1Wh3Gnndur776Kq666ipceOGFWLRoEXbs2IGLLrrIbWDQnzYUHtdccw3+8Y9/4Oabb8akSZPw3//933jooYdc1pdlGXv27MGsWbMc3oMjRowIY6/JmY8++ghjx45FUlISfv/9d/zxxx8e21RWVmLEiBEwGAy46667oNfrceGFF+LLL78MQ48pEG+++SYmT56MkSNHYtGiRSgpKcHYsWNhtVqD2obsVq5cifnz5+OKK67ALbfcgpdeegnTpk1zWb+0tBRXXnklsrOzceedd2L06NGYN28ebr/99jD2OnbNmzcPjzzyCGbOnIlrr70Wy5cvx+LFi71qu2rVKnz99dfYs2cP6uvrQ9zTjuHKK6/Ehg0bMH/+fFx66aW48cYb8eSTT7pt89prr6GgoAB9+vTBfffdh759++Lmm28OT4djWHNzMwoKCrBnzx4sXrwYw4cPx+WXX47Nmze7bPPNN99g5MiR0Gq1uOeeezBlyhQ88sgjmDNnThh7HpuKi4sxevRoJCQk4MiRI/j99989tjEajRgxYgTKy8txxx13ICsrC/n5+dizZ08YeuwnQWHT0tIi6uvrhRBCzJ49W+Tn53ts8/HHHwsAoqysTCl78MEHRXp6umhubg5VV8kLt956qxg8eLCQZVkpGz58uJgxY4bLNs8++6zIyckJR/fICVmWRe/evcWdd96plP32229CpVKJd955J2htKDxKS0sFALFr1y6lbM2aNSIhIUHU1dU5bdPY2CgAiM8//zxc3SQvmUwmYbPZhBBC5OTkiPvuu89jm7vvvlv07t1btLS0KGWFhYXi8ssvD1U3KUhOOeUUsWTJEuX3I0eOCEmSxFtvvRXUNiREfX296Nq1q1izZo1StmvXLgFA7N6922mbhoYG5f3Yau3atUKr1XL86cEvv/wiVCqVePfdd5WyN998U6jVanHkyBG3bb/44gvRp08fUVJSIgCI0tLSUHc35u3cuVMAEN99951StnLlSpGamiqampqctjEajSIxMVGsWrXKobyxsTGkfe0I1q1bJ7p06SKqqqqUsrlz54rTTjvNZZuHH35YZGZmOpQ98cQTIjk5OWT97Cjajo0GDRokli1b5rHNX//6V5GZmenwWT1+/Hhx8cUXh6yfgeJMqTDSaDRITEz0qU1xcTH69++P0047TSkrKipCdXU1vv7662B3kXxQXFyMyy67DCqVSimbOHEiduzY4bZdZWUlxo8fj0svvRT33HMPqqurQ91VOm7//v34448/MGHCBKUsOzsb55xzjsvXzZ82FB47duyATqdDXl6eUlZUVITGxkZ88cUXbtvefffdGD16NGbPnh31U5o7i6SkJEiSb8OS4uJiXHzxxdBoNEpZUVERiouLvV4qQ+H3888/49ChQw6fq1lZWRg+fLjLz1V/2pDdrl27YDabHZ67vLw89OjRw+Vz17Vr13bvx6SkJNhsNs5M82Dnzp2Ii4vDRRddpJRNmDABsizjk08+cdmutrYW06dPxwsvvIDu3buHo6sdQnFxMfr27YszzjhDKSsqKkJtba3LWbP//Oc/0dTUhLlz5zqUx8fHh7SvHUFxcTHOP/98pKenK2VFRUXYt28fjhw54rTNueeei+rqamU1ic1mw65du/CXv/wlLH2OZYGMjeLi4pSyoqIifPLJJ1G7yoNBqSh3+PBhZGVlOZS1/n748OFIdImOc/XalJeXo7m52WkbSZIwbdo0LFiwALNmzcLOnTtx5plnoqqqKhxd7vRa3zPOXjdX7yd/2lB4OHsP9uzZEyqVyu1rc84552DWrFlYunQpUlNTccEFF3i9/wRFF1efw42NjTAajRHqFXnCz+Lwan1+evbs6VDes2dPr587i8WC1atXY/z48UhISAh6HzuSw4cPQ6fToUuXLkpZYmIiUlNT3T7fN954I4qKihyCWeTZ4cOH0atXL4cyT9dKP/74I3JycvD111+jqKgIF198MZYtW4aampqQ9zfW+XNtOn78eKxfvx7nn38+zjrrLPTu3Rv19fXYtGlTyPvbGbl6jSwWCyoqKiLUK/c0nquQK0ePHsWkSZPc1rn44otx//33+/0YLS0t0Gq1DmWtg4GWlha/z0vtbdiwAU888YTbOitXrsTo0aMBeH5t2g5GWl1//fW46aablN8vueQSDBw4EI899hhWrVoV6J9AHrS+Z5y9bq4GIv60ofBw9h7UaDTQaDQuPx+1Wi12796tvD8vuugiyLKMxYsX45prrgl5nym4+B0Zm9x9rrraaNifNmTX0tICSZIc7poD9ufOm/eJLMu44YYbYDQa8f7774eqmx2Gs88lwP3z/dxzz2H//v147bXXQt29Dsef74GmpiYcPXoUd9xxB+655x5oNBo8/PDD2Lx5M7766isGXt3w5/kuKyvDkiVLcPXVV2PSpEn4888/cc899+CRRx7BihUrQt7nziYWx0YMSgUgPT3d4yZ6GRkZAT/GoUOHHMpaZ9Vwam9w5efno2/fvm7rDBw4UPnv9PT0dkvvqqqqEB8fj65duzptf/IHRGJiIkaMGIFvv/3Wz16TL1qnGldXVzvcQaiqqnL5XvWnDYWHs/egyWRCS0uLy89HlUrVLmA8duxYPPXUU6ioqECPHj1C1l8KPlefwyqVCt26dYtQr8iTtp+rffr0Ucqrqqpcvnf9aUN26enpkGUZtbW1SEtLU8q9ee5kWcbs2bNRUlKCkpKSdjNSqD1nn0uA++f75ZdfhslkQn5+PgCgsbERADBz5kxcccUVePDBB0PX4RiXnp7eLsmQp2ul9PR0mEwmvPzyyxgyZAgA+yzq3r17Y/v27Zg4cWJoOx3DXH3vAq6f7xUrVqBv375Yu3atUpaSkoIrr7wS8+bN4+dKkLl7jdouu4wmDEoFQKvVOuxlEgrDhg3Da6+9BrPZrAQ69uzZA5VKhbPOOiukj93ZZGZmIjMz0+v6w4YNQ2lpqUPZnj17cPbZZzvsM+VJeXm5T49L/jvjjDMQFxeH0tJSZe+BlpYWfPPNN7jzzjuD1obCY9iwYXj88cdhNBqh0+kAQMkscs4553h9nvLycqhUKt4ZjUGuPocHDRrk8uYARd6QIUOg1WpRWlqKs88+G4B9j5Gvv/4aCxcuDFobshs2bBgAe0a9cePGAbBfoPz6669uPyuFEJgzZw4++OADfPLJJxg0aFBY+hvrhg0bhtraWhw4cAADBgwAAPz73/9Gc3Ozy+f7xRdfhMlkUn7/9ddfMX36dCxZsgSjRo0KS79j1bBhw7Bu3TrU19cjKSkJwImxQOtnxcmGDx8OwHE5sF6vh1qt5ix4D4YNG4aXX34ZQgjlemfPnj1ITExU/n8/WXV1tdMllkII1NTUMCgVZK7GRv3790dycnKEeuVBhDda77RcZd+rrKwUubm5YufOnUIIIQwGg0hJSVGyEJnNZvGXv/xFXHbZZWHsLTnz9ttvC61Wq2Su+fbbb0ViYqJ44YUXlDobN24Uubm5wmq1CiGEWL16taiurlaOr1u3TgAQGzduDG/nO7FrrrlGDB06VNTW1gohhPjb3/4m4uPjxW+//abUWbBggUOGJ2/aUPiZTCah1+vFbbfdJoQQorm5WYwZM0aMHDlSqWM2m0Vubq7YsmWLEEKId999V+zZs0c5/vPPP4t+/frxMzXKuMq+9+GHH4rc3Fxx7NgxIYQ9Q60kSWLHjh1CCCEOHDggunXrJh577LFwdpf8cN1114khQ4Yor+WTTz4ptFqtOHTokFJn4cKFYuHChT61IecuvPBCMXr0aGGxWIQQ9udWp9M5ZCqdOnWqeOSRR4QQ9syzN954o8jMzBQ//vhjRPocq1paWkROTo6YMWOGkGVZ2Gw2ceWVV4rBgwc7ZDS88MILxSuvvOL0HN999x2z73mpurpapKWlKVnJGhsbxYgRI8T48eOVOlVVVSI3N1ds375dqZOdnS0eeOABpc7TTz8ttFqt+Pnnn8P7B8SY/fv3C41Go1zvGI1GkZOTI+bOnavU+f7770Vubq74/vvvhRBCrFq1SqSkpIgffvhBCGF/j1x//fVCr9crn0nkmavse9u3bxe5ublKRsSdO3cKSZLERx99JISwZwTt3r27WLlyZVj76wsGpcLsiiuuELm5uSIjI0MkJyeL3NxckZubqxz//fff2wUpPvroI5GRkSH69OkjUlNTRW5urjh69Ggkuk8nufvuu4VWqxUDBw4UXbp0EQsWLBCyLCvH16xZIwAo6crXrVsnevfuLU477TTRq1cv0b17d/Hss89GqvudUnV1tSgoKBBJSUmiX79+Ii0tTfzzn/90qFNYWOgQpPCmDUXG559/LrKyskSvXr1Et27dxJlnnikOHjyoHDeZTAKAMnj68ccfRUFBgejZs6c4/fTTRZcuXcT06dOF0WiM0F9Arf7880/lO1Gr1YpevXqJ3Nxcccsttyh1Xn31VQFAGAwGpWzVqlUiPj5eDBw4UGi1WnHDDTcoNwIoetXU1IgxY8aIxMREceqpp4rU1NR2N2jGjx/vcGHpTRty7vDhw+Lss88W3bp1E7179xY9e/YUn376qUOdQYMGKReW7733ngAg+vTpo7wvW/8xCOjZv//9b3HqqaeKHj16iIyMDDFgwADlgryVVqt1eZHIoJRvtm/fLvR6vXKtdN5554kjR44ox48ePSoAiDfffFMp+/LLL8Wpp54qTjnlFJGTkyMyMjLE22+/HYnux5zXXntNJCcni5ycHNG1a1cxfvx4hwD3rl27BACxa9cuIYT9puENN9wgtFqtOOOMM4Rerxf9+/cXn332WaT+hJjROmElNzdXxMfHK2Ojm266Sanz5ptvCgAO8YHHHnvMYWx03XXXKdej0UglhBARmqTVKX3zzTewWCztyluXATY3N+Prr7/GwIEDHdZ8Njc3Y9++fejatSv69+8ftv6SZ9XV1Th8+DB69+7dbo+hiooKHDx40GGZpyzL+PnnnxEXF4c+ffpArVaHu8sE4ODBg6itrcVpp53WLgVwWVkZJElqt1TBXRuKHKvVirKyMmi1Wod93wD7+23v3r3IyclxeH8aDAZUVFSgX79+SExMDHeXyQmLxYJvvvmmXXlKSgpOP/10AIDRaMTPP/+M4cOHQ6M5sQNBbW0tfv31V2RlZXFfsBhz6NAhHDt2zOnnaus+MaeddprXbci9n376CRaLBYMHD3Z4DwHAt99+i5SUFPTr1w81NTXYv3+/03OcffbZfN69IMsyysrKoFKpMHjw4HZbO+zduxe9e/dulyULsO8p9e2332Lo0KH8jvJSS0sLysrKnF4rtbS04KuvvsKAAQMc9j2SZRn79u2DRqNBv3792iUDINfMZjN++uknpKenO+zzBwD19fX4/vvvccYZZyhLKgGgrq4Ohw4dQmpqKrKzsyFJUri7HXNaYwMnazs2qqqqwoEDB3Duuec6/D/cOjbq2bNn1G8Vw6AUERERERERERGFHcOTREREREREREQUdgxKERERERERERFR2DEoRUREREREREREYcegFBERERERERERhR2DUkREREREREREFHYMShERERERERERUdgxKEVERERERERERGHHoBQREREREREREYUdg1JERERERERERBR2DEoREbWxY8cOjBs3DkIIh/KXXnoJs2bNilCviIiIiKIHx0tEFCwMShERtZGWloYdO3bg8OHDSlldXR3uuOMOjBs3LoI9IyIiIooOHC8RUbAwKEVE1MaQIUMgSRLKysqUskcffRTZ2dmYNm1aBHtGREREFB04XiKiYGFQioiojYSEBOTk5ODHH38EAJSXl+PJJ5/Eo48+CpVKFeHeEREREUWeN+Oljz76CJs3b45kN4koBjAoRUR0kqFDhyqDrPvvvx+jRo1CYWFhhHtFREREFD08jZe2b9+OhoaGSHWPiGIEg1JERCdpHWT99NNPWL9+PVatWuVwfNGiRdi7dy/mzp2Lzz//PEK9JCIiIoocd+OlrVu34p133sG6deswY8aMCPaSiKKdJtIdICKKNkOHDsWTTz6JpUuXYurUqTj77LOVY2azGWvXrkVVVRXGjh2LAQMGRK6jRERERBHibrzUt29fNDY2YtasWUhKSopcJ4ko6jEoRUR0kqFDh6K2thbvvfce9u/f73Dsyy+/xLBhw/Dyyy9zjykiIiLqtNyNl/R6Pfr27ctZUkTkEYNSREQn6d+/Pz755BOkpaWhb9++Dsf27t2LSZMmMSBFREREnZq78VJJSQkKCgoi0zEiiincU4qI6CSSJKGgoMBhGnqrvXv3YuTIkeHvFBEREVEUcTde6tKlCzZs2ICpU6eipqYm/J0jopjBmVJERD6YPXs2zjvvvEh3g4iIiChqTZ48GT169MCRI0eQmpoa6e4QURRTCSFEpDtBRERERERERESdC5fvERERERERERFR2DEoRUREREREREREYcegFBERERERERERhR2DUkREREREREREFHYMShERERERERERUdgxKEVERERERERERGHHoBQREREREREREYUdg1JERERERERERBR2DEoREREREREREVHYMShFRERERERERERh9/9JhS98SYbGPQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import constantbetadf, osipkovmerrittdf\n", "\n", "r0 = 2.0\n", "n_samples = 8000\n", "numpy.random.seed(1)\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "df_edd = eddingtondf(pot=nfp, denspot=hp)\n", "# Use half-integer beta, for which the numerics are much faster\n", "df_constb = constantbetadf(pot=nfp, denspot=hp, twobeta=1)\n", "df_constb_low = constantbetadf(pot=nfp, denspot=hp, twobeta=-1)\n", "df_omb = osipkovmerrittdf(pot=nfp, denspot=hp, ra=1.4)\n", "\n", "samples_edd = df_edd.sample(n=n_samples, R=r0, z=0.0)\n", "samples_constb = df_constb.sample(n=n_samples, R=r0, z=0.0)\n", "samples_constb_low = df_constb_low.sample(n=n_samples, R=r0, z=0.0)\n", "samples_omb = df_omb.sample(n=n_samples, R=r0, z=0.0)\n", "\n", "vr_edd = samples_edd.vr()\n", "vr_constb = samples_constb.vr()\n", "vr_constb_low = samples_constb_low.vr()\n", "vr_omb = samples_omb.vr()\n", "\n", "vt_edd = numpy.sqrt(samples_edd.vT() ** 2 + samples_edd.vtheta() ** 2)\n", "vt_constb = numpy.sqrt(samples_constb.vT() ** 2 + samples_constb.vtheta() ** 2)\n", "vt_constb_low = numpy.sqrt(\n", " samples_constb_low.vT() ** 2 + samples_constb_low.vtheta() ** 2\n", ")\n", "vt_omb = numpy.sqrt(samples_omb.vT() ** 2 + samples_omb.vtheta() ** 2)\n", "\n", "fig_vel, ax_vel = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "ax_vel[0].hist(\n", " vr_edd, bins=31, density=True, histtype=\"step\", lw=2, label=\"Eddington (isotropic)\"\n", ")\n", "ax_vel[0].hist(\n", " vr_constb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=0.5$\",\n", ")\n", "ax_vel[0].hist(\n", " vr_constb_low,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=-0.5$\",\n", ")\n", "ax_vel[0].hist(\n", " vr_omb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Osipkov-Merritt ($r_a=1.4$)\",\n", ")\n", "ax_vel[0].set_xlabel(r\"$v_r$\")\n", "ax_vel[0].set_ylabel(\"PDF\")\n", "ax_vel[0].set_title(rf\"Radial velocities at $r={r0}$\")\n", "ax_vel[0].legend()\n", "\n", "ax_vel[1].hist(\n", " vt_edd, bins=31, density=True, histtype=\"step\", lw=2, label=\"Eddington (isotropic)\"\n", ")\n", "ax_vel[1].hist(\n", " vt_constb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=0.5$\",\n", ")\n", "ax_vel[1].hist(\n", " vt_constb_low,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=-0.5$\",\n", ")\n", "ax_vel[1].hist(\n", " vt_omb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Osipkov-Merritt ($r_a=1.4$)\",\n", ")\n", "ax_vel[1].set_xlabel(r\"$v_t$\")\n", "ax_vel[1].set_ylabel(\"PDF\")\n", "ax_vel[1].set_title(rf\"Tangential speeds at $r={r0}$\")\n", "ax_vel[1].legend()\n", "\n", "fig_vel.tight_layout();" ] }, { "cell_type": "markdown", "id": "073bcf0b", "metadata": { "papermill": { "duration": 0.008616, "end_time": "2026-06-30T01:14:34.764344+00:00", "exception": false, "start_time": "2026-06-30T01:14:34.755728+00:00", "status": "completed" }, "tags": [] }, "source": [ "Note that the calculation of constant-anisotropy DFs in this way requires the [jax](https://github.com/google/jax) library to be installed, as it relies on automatic differentiation to compute the necessary derivatives of the potential and density profiles. The Osipkov-Merritt DFs can be computed without ``jax``. Both can be quite slow." ] } ], "metadata": { "kernelspec": { "display_name": "py313", "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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 172.827038, "end_time": "2026-06-30T01:14:35.590591+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/distribution_functions/spherical_dfs.ipynb", "output_path": "doc/source/tutorials/distribution_functions/spherical_dfs.ipynb", "parameters": {}, "start_time": "2026-06-30T01:11:42.763553+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }