{ "cells": [ { "cell_type": "markdown", "id": "a1b2c3d4e5f6", "metadata": { "papermill": { "duration": 0.005812, "end_time": "2026-06-30T01:14:53.046210+00:00", "exception": false, "start_time": "2026-06-30T01:14:53.040398+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Orbit Examples\n", "\n", "This notebook gives some detailed orbit examples,\n", "including the eccentricity distribution of thick-disk stars, integrating the LMC orbit with dynamical friction, and taking the barycentric acceleration\n", "due to the LMC into account for Milky-Way orbits." ] }, { "cell_type": "code", "execution_count": 1, "id": "b2c3d4e5f6a7", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:14:53.056352Z", "iopub.status.busy": "2026-06-30T01:14:53.056036Z", "iopub.status.idle": "2026-06-30T01:14:55.343170Z", "shell.execute_reply": "2026-06-30T01:14:55.342205Z" }, "papermill": { "duration": 2.29295, "end_time": "2026-06-30T01:14:55.343898+00:00", "exception": false, "start_time": "2026-06-30T01:14:53.050948+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)\n", "\n", "import numpy\n", "import copy\n", "from astropy import units\n", "from matplotlib import pyplot as plt\n", "from galpy.orbit import Orbit\n", "from galpy.potential import MWPotential2014, ChandrasekharDynamicalFrictionForce\n", "from galpy.util import conversion" ] }, { "cell_type": "markdown", "id": "e2dad8a4", "metadata": { "papermill": { "duration": 0.003916, "end_time": "2026-06-30T01:14:55.352118+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.348202+00:00", "status": "completed" }, "tags": [] }, "source": [ "## The eccentricity distribution of the Milky Way's thick disk\n", "\n", "A straightforward application of galpy's orbit-integration capabilities is to\n", "derive the eccentricity distribution for a set of thick-disk stars. We use the\n", "SDSS/SEGUE thick-disk sample compiled by\n", "[Dierickx et al. (2010)](https://ui.adsabs.harvard.edu/abs/2010ApJ...725L.186D/abstract),\n", "which we download from Vizier:" ] }, { "cell_type": "code", "execution_count": 2, "id": "652d9dad", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:14:55.364692Z", "iopub.status.busy": "2026-06-30T01:14:55.364320Z", "iopub.status.idle": "2026-06-30T01:14:55.428874Z", "shell.execute_reply": "2026-06-30T01:14:55.427979Z" }, "papermill": { "duration": 0.073626, "end_time": "2026-06-30T01:14:55.429835+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.356209+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loaded 31535 thick-disk stars from local cache: dierickx_2010_thick_disk.fits\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "WARNING: UnitsWarning: 'log(cm.s**-2)' did not parse as fits unit: 'log' is not a recognized function If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html [astropy.units.core]\n", "WARNING: UnitsWarning: 'log(Sun)' did not parse as fits unit: 'log' is not a recognized function If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html [astropy.units.core]\n" ] } ], "source": [ "import os\n", "\n", "from astropy.table import Table\n", "\n", "from galpy.potential import LogarithmicHaloPotential\n", "\n", "# Cache the Vizier query result locally so re-runs of this notebook don't\n", "# repeat the catalog download, which is occasionally slow or unavailable.\n", "_dierickx_cache = \"dierickx_2010_thick_disk.fits\"\n", "\n", "if os.path.exists(_dierickx_cache):\n", " dierickx = Table.read(_dierickx_cache)\n", " print(\n", " f\"Loaded {len(dierickx)} thick-disk stars from local cache: {_dierickx_cache}\"\n", " )\n", "else:\n", " from astroquery.vizier import Vizier\n", "\n", " v = Vizier(columns=[\"*\"], row_limit=-1)\n", " result = v.get_catalogs(\"J/ApJ/725/L186\")\n", " dierickx = result[\"J/ApJ/725/L186/table2\"]\n", " print(f\"Downloaded {len(dierickx)} thick-disk stars\")\n", " dierickx.write(_dierickx_cache, format=\"fits\", overwrite=True)" ] }, { "cell_type": "markdown", "id": "d32a6ef7", "metadata": { "papermill": { "duration": 0.003966, "end_time": "2026-06-30T01:14:55.438161+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.434195+00:00", "status": "completed" }, "tags": [] }, "source": [ "Set up the phase-space coordinates as `(RA, Dec, distance, pmRA, pmDec, vlos)`\n", "and initialize orbits in a `LogarithmicHaloPotential` (a spherical potential with\n", "a flat rotation curve). All stars are formally bound in this potential\n", "(which has an infinite escape velocity), but a handful have such extreme\n", "kinematics that their orbits cause numerical issues, so we filter those out:" ] }, { "cell_type": "code", "execution_count": 3, "id": "a6b7c6db", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:14:55.447540Z", "iopub.status.busy": "2026-06-30T01:14:55.447335Z", "iopub.status.idle": "2026-06-30T01:14:55.480605Z", "shell.execute_reply": "2026-06-30T01:14:55.479753Z" }, "papermill": { "duration": 0.039017, "end_time": "2026-06-30T01:14:55.481255+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.442238+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Keeping 31491 of 31535 orbits (removed 44 extreme outliers)\n" ] } ], "source": [ "vxvv = numpy.column_stack(\n", " [\n", " numpy.array(dierickx[\"RAJ2000\"], dtype=float),\n", " numpy.array(dierickx[\"DEJ2000\"], dtype=float),\n", " numpy.array(dierickx[\"Dist\"], dtype=float) / 1e3, # pc -> kpc\n", " numpy.array(dierickx[\"pmRA\"], dtype=float),\n", " numpy.array(dierickx[\"pmDE\"], dtype=float),\n", " numpy.array(dierickx[\"HRV\"], dtype=float),\n", " ]\n", ")\n", "\n", "lp = LogarithmicHaloPotential(normalize=1.0)\n", "all_orbits = Orbit(vxvv, radec=True, ro=8.0, vo=220.0, solarmotion=\"hogg\")\n", "\n", "# Filter out stars with extreme energies that cause numerical issues\n", "E = all_orbits.E(pot=lp, use_physical=False)\n", "keep = E < 3.0\n", "orbits = all_orbits[keep]\n", "e_dierickx = numpy.array(dierickx[\"e\"], dtype=float)[keep]\n", "print(\n", " f\"Keeping {keep.sum()} of {len(keep)} orbits (removed {(~keep).sum()} extreme outliers)\"\n", ")" ] }, { "cell_type": "markdown", "id": "397d03da", "metadata": { "papermill": { "duration": 0.004339, "end_time": "2026-06-30T01:14:55.490079+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.485740+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now we compute eccentricities in two ways: (a) by integrating each orbit for\n", "many dynamical times and finding the actual peri- and apocenter, and (b)\n", "analytically using the [Staeckel approximation](./fast_characterization.ipynb),\n", "which avoids orbit integration entirely:" ] }, { "cell_type": "code", "execution_count": 4, "id": "f238e272", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:14:55.499497Z", "iopub.status.busy": "2026-06-30T01:14:55.499288Z", "iopub.status.idle": "2026-06-30T01:15:05.401827Z", "shell.execute_reply": "2026-06-30T01:15:05.401086Z" }, "papermill": { "duration": 9.908754, "end_time": "2026-06-30T01:15:05.403060+00:00", "exception": false, "start_time": "2026-06-30T01:14:55.494306+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Analytic eccentricities (Staeckel approximation, very fast)\n", "e_ana = orbits.e(analytic=True, pot=lp, delta=0.01)\n", "\n", "# Numerical eccentricities (orbit integration)\n", "ts = numpy.linspace(0.0, 20.0, 1001)\n", "orbits.integrate(ts, lp)\n", "e_int = orbits.e()" ] }, { "cell_type": "markdown", "id": "8733a01e", "metadata": { "papermill": { "duration": 0.004189, "end_time": "2026-06-30T01:15:05.412667+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.408478+00:00", "status": "completed" }, "tags": [] }, "source": [ "The eccentricity distribution of the thick disk peaks around $e \\approx 0.25$:" ] }, { "cell_type": "code", "execution_count": 5, "id": "d614613d", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:05.422904Z", "iopub.status.busy": "2026-06-30T01:15:05.422691Z", "iopub.status.idle": "2026-06-30T01:15:05.726265Z", "shell.execute_reply": "2026-06-30T01:15:05.725363Z" }, "papermill": { "duration": 0.310012, "end_time": "2026-06-30T01:15:05.727029+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.417017+00:00", "status": "completed" }, "tags": [] }, "outputs": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(e_int, bins=50, range=(0, 1), density=True)\n", "plt.xlabel(r\"$\\mathrm{Eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{Density}$\");" ] }, { "cell_type": "markdown", "id": "c299c1d3", "metadata": { "papermill": { "duration": 0.004103, "end_time": "2026-06-30T01:15:05.736387+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.732284+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can compare galpy's integrated eccentricities with those published by\n", "Dierickx et al. (2010). The agreement is excellent for most stars:" ] }, { "cell_type": "code", "execution_count": 6, "id": "30e227f2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:05.746044Z", "iopub.status.busy": "2026-06-30T01:15:05.745819Z", "iopub.status.idle": "2026-06-30T01:15:05.876615Z", "shell.execute_reply": "2026-06-30T01:15:05.875774Z" }, "papermill": { "duration": 0.137024, "end_time": "2026-06-30T01:15:05.877671+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.740647+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_dierickx, e_int, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Dierickx\\ et\\ al.\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{galpy\\ integrated\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "a0ba9ff9", "metadata": { "papermill": { "duration": 0.004348, "end_time": "2026-06-30T01:15:05.886941+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.882593+00:00", "status": "completed" }, "tags": [] }, "source": [ "The analytic Staeckel estimates are equally good:" ] }, { "cell_type": "code", "execution_count": 7, "id": "ac71a49f", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:05.897079Z", "iopub.status.busy": "2026-06-30T01:15:05.896850Z", "iopub.status.idle": "2026-06-30T01:15:06.027412Z", "shell.execute_reply": "2026-06-30T01:15:06.026507Z" }, "papermill": { "duration": 0.136756, "end_time": "2026-06-30T01:15:06.028167+00:00", "exception": false, "start_time": "2026-06-30T01:15:05.891411+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_dierickx, e_ana, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Dierickx\\ et\\ al.\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{galpy\\ analytic\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "2bbc9de0", "metadata": { "papermill": { "duration": 0.004621, "end_time": "2026-06-30T01:15:06.038563+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.033942+00:00", "status": "completed" }, "tags": [] }, "source": [ "Because the `LogarithmicHaloPotential` is spherical, the Staeckel\n", "approximation is essentially exact. Comparing the integrated and analytic\n", "eccentricities directly confirms this:" ] }, { "cell_type": "code", "execution_count": 8, "id": "3378e9a9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:06.048954Z", "iopub.status.busy": "2026-06-30T01:15:06.048734Z", "iopub.status.idle": "2026-06-30T01:15:06.175506Z", "shell.execute_reply": "2026-06-30T01:15:06.174640Z" }, "papermill": { "duration": 0.133728, "end_time": "2026-06-30T01:15:06.176914+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.043186+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_int, e_ana, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Integrated\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{Analytic\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "c3d4e5f6a7b8", "metadata": { "papermill": { "duration": 0.004641, "end_time": "2026-06-30T01:15:06.186523+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.181882+00:00", "status": "completed" }, "tags": [] }, "source": [ "## LMC orbit with dynamical friction\n", "\n", "The Large Magellanic Cloud (LMC) is a massive satellite of the Milky Way, so its\n", "orbit is significantly affected by dynamical friction -- a frictional force of\n", "gravitational origin that occurs when a massive object travels through a sea of\n", "low-mass objects (halo stars and dark matter; see Section 19.4.1 in [galaxiesbook.org](https://galaxiesbook.org/chapters/IV-03.-Hierarchical-Galaxy-Formation_4-Dynamical-processes.html#Dynamical-friction)). We investigate the LMC's past and\n", "future orbit using `ChandrasekharDynamicalFrictionForce`.\n", "\n", "First, we load the current phase-space coordinates for the LMC using `Orbit.from_name`.\n", "Because the LMC is unbound in the default ``MWPotential2014``, we increase the\n", "halo mass by 50% (corresponding to a Milky Way halo mass of approximately\n", "1.2 x 10^12 Msun). We use `copy.deepcopy` to avoid modifying the global potential." ] }, { "cell_type": "code", "execution_count": 9, "id": "f6a7b8c9d0e1", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:06.197639Z", "iopub.status.busy": "2026-06-30T01:15:06.197387Z", "iopub.status.idle": "2026-06-30T01:15:06.205433Z", "shell.execute_reply": "2026-06-30T01:15:06.204554Z" }, "papermill": { "duration": 0.014736, "end_time": "2026-06-30T01:15:06.206086+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.191350+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "o = Orbit.from_name(\"LMC\")\n", "\n", "# Make a deep copy to avoid modifying the global MWPotential2014\n", "mwp = copy.deepcopy(MWPotential2014)\n", "mwp[2] *= 1.5 # increase halo mass by 50%" ] }, { "cell_type": "markdown", "id": "a7b8c9d0e1f2", "metadata": { "papermill": { "duration": 0.005815, "end_time": "2026-06-30T01:15:06.216728+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.210913+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Orbit without dynamical friction\n", "\n", "First, integrate the LMC orbit backward for 10 Gyr without dynamical friction:" ] }, { "cell_type": "code", "execution_count": 10, "id": "b8c9d0e1f2a3", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:06.227604Z", "iopub.status.busy": "2026-06-30T01:15:06.227397Z", "iopub.status.idle": "2026-06-30T01:15:06.421674Z", "shell.execute_reply": "2026-06-30T01:15:06.420676Z" }, "papermill": { "duration": 0.200806, "end_time": "2026-06-30T01:15:06.422384+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.221578+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts = numpy.linspace(0.0, -10.0, 1001) * units.Gyr\n", "o.integrate(ts, mwp)\n", "o.plot(d1=\"t\", d2=\"r\");" ] }, { "cell_type": "markdown", "id": "c9d0e1f2a3b4", "metadata": { "papermill": { "duration": 0.004812, "end_time": "2026-06-30T01:15:06.433315+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.428503+00:00", "status": "completed" }, "tags": [] }, "source": [ "The LMC is bound with an apocenter just over 200 kpc.\n", "\n", "### Adding dynamical friction (M = 5 x 10^10 Msun)\n", "\n", "Now add dynamical friction assuming an LMC mass of 5 x 10^10 Msun:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d0e1f2a3b4c5", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:06.444524Z", "iopub.status.busy": "2026-06-30T01:15:06.444306Z", "iopub.status.idle": "2026-06-30T01:15:13.085264Z", "shell.execute_reply": "2026-06-30T01:15:13.084323Z" }, "papermill": { "duration": 6.647769, "end_time": "2026-06-30T01:15:13.086057+00:00", "exception": false, "start_time": "2026-06-30T01:15:06.438288+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator dopr54_c instead)\n" ] } ], "source": [ "cdf = ChandrasekharDynamicalFrictionForce(\n", " GMs=5e10 * units.Msun, rhm=5.0 * units.kpc, dens=mwp\n", ")\n", "\n", "# Make a copy of the orbit for the dynamical friction integration\n", "odf = o()\n", "odf.integrate(ts, mwp + cdf)" ] }, { "cell_type": "code", "execution_count": 12, "id": "e1f2a3b4c5d6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:13.097213Z", "iopub.status.busy": "2026-06-30T01:15:13.097007Z", "iopub.status.idle": "2026-06-30T01:15:13.442177Z", "shell.execute_reply": "2026-06-30T01:15:13.441176Z" }, "papermill": { "duration": 0.351803, "end_time": "2026-06-30T01:15:13.442884+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.091081+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "o.plot(d1=\"t\", d2=\"r\", label=r\"$\\mathrm{No\\ DF}$\")\n", "odf.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=5\\times10^{10}\\,M_\\odot$\"\n", ")\n", "plt.ylim(0.0, 660.0)\n", "plt.legend(fontsize=17.0);" ] }, { "cell_type": "markdown", "id": "f2a3b4c5d6e7", "metadata": { "papermill": { "duration": 0.005047, "end_time": "2026-06-30T01:15:13.453458+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.448411+00:00", "status": "completed" }, "tags": [] }, "source": [ "Dynamical friction removes energy from the LMC's orbit, so the past apocenter\n", "is now around 500 kpc rather than 200 kpc, and the orbital period is much longer.\n", "\n", "### A more massive LMC (M = 10^11 Msun)\n", "\n", "Recent observations suggest the LMC may be even more massive (> 10^11 Msun).\n", "We can change the mass in the existing `ChandrasekharDynamicalFrictionForce`\n", "object without re-solving the Jeans equation (necessary to initialize the dynamical-friction object):" ] }, { "cell_type": "code", "execution_count": 13, "id": "a3b4c5d6e7f8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:13.464767Z", "iopub.status.busy": "2026-06-30T01:15:13.464510Z", "iopub.status.idle": "2026-06-30T01:15:13.474572Z", "shell.execute_reply": "2026-06-30T01:15:13.473748Z" }, "papermill": { "duration": 0.016835, "end_time": "2026-06-30T01:15:13.475365+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.458530+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "cdf.GMs = 1e11 * units.Msun\n", "\n", "odf2 = o()\n", "odf2.integrate(ts, mwp + cdf)" ] }, { "cell_type": "code", "execution_count": 14, "id": "b4c5d6e7f8a9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:13.488194Z", "iopub.status.busy": "2026-06-30T01:15:13.487991Z", "iopub.status.idle": "2026-06-30T01:15:13.724674Z", "shell.execute_reply": "2026-06-30T01:15:13.723633Z" }, "papermill": { "duration": 0.243688, "end_time": "2026-06-30T01:15:13.725343+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.481655+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "o.plot(d1=\"t\", d2=\"r\", label=r\"$\\mathrm{No\\ DF}$\", yrange=[0.0, 660.0])\n", "odf.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=5\\times10^{10}\\,M_\\odot$\"\n", ")\n", "odf2.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=1\\times10^{11}\\,M_\\odot$\"\n", ")\n", "plt.legend(fontsize=17.0);" ] }, { "cell_type": "markdown", "id": "c5d6e7f8a9b0", "metadata": { "papermill": { "duration": 0.005295, "end_time": "2026-06-30T01:15:13.736246+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.730951+00:00", "status": "completed" }, "tags": [] }, "source": [ "With a mass of 10^11 Msun, the LMC barely completes a full orbit over 10 Gyr!\n", "\n", "### Future orbit: merging timescale\n", "\n", "Let's see what happens in the future with the massive LMC. We flip the sign of\n", "the integration times (limiting to 9 Gyr to avoid numerical issues at very\n", "small radii):" ] }, { "cell_type": "code", "execution_count": 15, "id": "d6e7f8a9b0c1", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:13.748305Z", "iopub.status.busy": "2026-06-30T01:15:13.747989Z", "iopub.status.idle": "2026-06-30T01:15:14.545178Z", "shell.execute_reply": "2026-06-30T01:15:14.544171Z" }, "papermill": { "duration": 0.804244, "end_time": "2026-06-30T01:15:14.545894+00:00", "exception": false, "start_time": "2026-06-30T01:15:13.741650+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "odf2.integrate(numpy.linspace(0.0, 9.0, 1001) * units.Gyr, mwp + cdf)\n", "odf2.plot(d1=\"t\", d2=\"r\");" ] }, { "cell_type": "markdown", "id": "e7f8a9b0c1d2", "metadata": { "papermill": { "duration": 0.005603, "end_time": "2026-06-30T01:15:14.557110+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.551507+00:00", "status": "completed" }, "tags": [] }, "source": [ "The LMC merges with the Milky Way in about 4 Gyr after a few more pericenter\n", "passages. Mass loss (not included here) would somewhat increase the merging\n", "timescale, but the merger is inevitable. \n", "\n", "This example also illustrates thhe continuation of an existing orbit integration when \n", "integrating starting from one of the previous integrations edges. The `integrate` method continues the integration from the last point of the previous integration, so we can seamlessly continue the integration into the future. See [Continuing integrations](./integration_and_plotting.ipynb#Continuing-integrations) for more details.\n", "\n", "
\n", "\n", "**Warning**\n", "\n", "When using dynamical friction, if the radius gets very small the\n", "integration can become erroneous, leading to unphysical kicks. Always inspect\n", "the full orbit to check whether a merger has happened.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "f8a9b0c1d2e3", "metadata": { "papermill": { "duration": 0.005427, "end_time": "2026-06-30T01:15:14.568098+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.562671+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Barycentric acceleration due to the LMC\n", "\n", "The LMC is so massive that it pulls the center of the Milky Way towards it,\n", "meaning the Galactocentric reference frame is not truly inertial. We can\n", "account for this using `NonInertialFrameForce`.\n", "\n", "Our approach: (1) compute the LMC orbit assuming the MW is at rest, (2) compute\n", "the acceleration at the origin due to the LMC along that orbit, (3) use\n", "`NonInertialFrameForce` with that acceleration." ] }, { "cell_type": "code", "execution_count": 16, "id": "a9b0c1d2e3f4", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.580462Z", "iopub.status.busy": "2026-06-30T01:15:14.580253Z", "iopub.status.idle": "2026-06-30T01:15:14.583466Z", "shell.execute_reply": "2026-06-30T01:15:14.582548Z" }, "papermill": { "duration": 0.010302, "end_time": "2026-06-30T01:15:14.584134+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.573832+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import (\n", " HernquistPotential,\n", " MovingObjectPotential,\n", " NonInertialFrameForce,\n", " evaluateRforces,\n", " evaluatephitorques,\n", " evaluatezforces,\n", ")" ] }, { "cell_type": "markdown", "id": "b0c1d2e3f4a5", "metadata": { "papermill": { "duration": 0.005504, "end_time": "2026-06-30T01:15:14.596580+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.591076+00:00", "status": "completed" }, "tags": [] }, "source": [ "We already computed the LMC orbit with dynamical friction above. Now we\n", "re-compute it over 10 Gyr backward using the massive LMC setup:" ] }, { "cell_type": "code", "execution_count": 17, "id": "c1d2e3f4a5b6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.608824Z", "iopub.status.busy": "2026-06-30T01:15:14.608620Z", "iopub.status.idle": "2026-06-30T01:15:14.620641Z", "shell.execute_reply": "2026-06-30T01:15:14.619802Z" }, "papermill": { "duration": 0.019167, "end_time": "2026-06-30T01:15:14.621290+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.602123+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Re-integrate LMC orbit backward with the heavy LMC\n", "o_lmc = Orbit.from_name(\"LMC\")\n", "ts_back = numpy.linspace(0.0, -10.0, 1001) * units.Gyr\n", "o_lmc.integrate(ts_back, mwp + cdf)" ] }, { "cell_type": "markdown", "id": "d2e3f4a5b6c7", "metadata": { "papermill": { "duration": 0.005713, "end_time": "2026-06-30T01:15:14.632838+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.627125+00:00", "status": "completed" }, "tags": [] }, "source": [ "Define the LMC as a `HernquistPotential` and create a `MovingObjectPotential`\n", "that follows its orbit:" ] }, { "cell_type": "code", "execution_count": 18, "id": "e3f4a5b6c7d8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.647106Z", "iopub.status.busy": "2026-06-30T01:15:14.646898Z", "iopub.status.idle": "2026-06-30T01:15:14.651637Z", "shell.execute_reply": "2026-06-30T01:15:14.650760Z" }, "papermill": { "duration": 0.013384, "end_time": "2026-06-30T01:15:14.652267+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.638883+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Hernquist potential for LMC: rhm = (1+sqrt(2)) * a, amp = 2 x mass\n", "lmcpot = HernquistPotential(\n", " amp=2e11 * units.Msun, a=5.0 * units.kpc / (1.0 + numpy.sqrt(2.0))\n", ")\n", "moving_lmcpot = MovingObjectPotential(o_lmc, pot=lmcpot)" ] }, { "cell_type": "markdown", "id": "f4a5b6c7d8e9", "metadata": { "papermill": { "duration": 0.005364, "end_time": "2026-06-30T01:15:14.663325+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.657961+00:00", "status": "completed" }, "tags": [] }, "source": [ "Compute the acceleration of the Galactic center due to the LMC by evaluating\n", "the force from `moving_lmcpot` at a small offset from the origin (to avoid\n", "numerical issues in cylindrical coordinates):" ] }, { "cell_type": "code", "execution_count": 19, "id": "a5b6c7d8e9f0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.675761Z", "iopub.status.busy": "2026-06-30T01:15:14.675504Z", "iopub.status.idle": "2026-06-30T01:15:14.679296Z", "shell.execute_reply": "2026-06-30T01:15:14.678503Z" }, "papermill": { "duration": 0.011173, "end_time": "2026-06-30T01:15:14.679991+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.668818+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "loc_origin = 1e-4 # small offset in R\n", "ax = lambda t: evaluateRforces(\n", " moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False\n", ")\n", "ay = lambda t: (\n", " evaluatephitorques(moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False)\n", " / loc_origin\n", ")\n", "az = lambda t: evaluatezforces(\n", " moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False\n", ")" ] }, { "cell_type": "markdown", "id": "b6c7d8e9f0a1", "metadata": { "papermill": { "duration": 0.005357, "end_time": "2026-06-30T01:15:14.691043+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.685686+00:00", "status": "completed" }, "tags": [] }, "source": [ "Set up the `NonInertialFrameForce` with the origin's acceleration. We can pass\n", "the acceleration functions directly: by default (`cinterp=True`),\n", "`NonInertialFrameForce` builds a fast cubic-spline interpolation of them in C\n", "over each orbit integration's time range, so these (relatively expensive)\n", "functions are evaluated only when setting up an integration rather than being\n", "called from C at every integration step. This makes the C orbit integration\n", "much faster and removes the need to manually pre-interpolate the acceleration." ] }, { "cell_type": "code", "execution_count": 20, "id": "c7d8e9f0a1b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.703115Z", "iopub.status.busy": "2026-06-30T01:15:14.702869Z", "iopub.status.idle": "2026-06-30T01:15:14.706252Z", "shell.execute_reply": "2026-06-30T01:15:14.705330Z" }, "papermill": { "duration": 0.010287, "end_time": "2026-06-30T01:15:14.706847+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.696560+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "nip = NonInertialFrameForce(a0=[ax, ay, az])" ] }, { "cell_type": "markdown", "id": "d8e9f0a1b2c3", "metadata": { "papermill": { "duration": 0.005573, "end_time": "2026-06-30T01:15:14.718273+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.712700+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Effect on the Sun's orbit\n", "\n", "Compare the Sun's past orbit with and without the barycentric correction.\n", "When including the non-inertial correction, we must also include the LMC's\n", "gravitational potential (`moving_lmcpot`) to keep the model self-consistent:" ] }, { "cell_type": "code", "execution_count": 21, "id": "e9f0a1b2c3d4", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:14.730303Z", "iopub.status.busy": "2026-06-30T01:15:14.730067Z", "iopub.status.idle": "2026-06-30T01:15:15.094850Z", "shell.execute_reply": "2026-06-30T01:15:15.093894Z" }, "papermill": { "duration": 0.371827, "end_time": "2026-06-30T01:15:15.095553+00:00", "exception": false, "start_time": "2026-06-30T01:15:14.723726+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: You specified integration times as a Quantity, but are evaluating at times not specified as a Quantity; assuming that time given is in natural (internal) units (multiply time by unit to get output at physical time)\n" ] }, { "data": { "image/png": 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qwnGcLAGhBQ9JJSZ9p512GmZnZ/Ha174WRx99NHY8dC/+99rrseHW23HlV7+CpxxzNN7+9rfP+7nzzz8f//Vf/wUAeMYznoHnPve5WLFiBf7yl7/g0ksvxW9/+1uceOKJuPXWW7FiRWe69HWvex127NiBM579LJx2wlOQju2DpUvGcNwR++Jz//peXHzp1bjzjttw2mmnzRMPP/axj5U6v1//+tcYGhrCC17wAhxwwAHYZ599sGPHDvzud7/Dd77zHfzghl/g+a99C2745pcQuACSEHGawqva8Ko11fY/nTREGCfVjpGgFARFKQpOdj85SNHqB7CJm2C6qTRqwOkHsMlFlg/QvbFyr1UAAIdQTO3YAmC/Spf2JzNg0xw7ANPToxil05ja8QiAgytdFwDon76T4dY/fQfXf+mf8VevfX/la9abWwEAzthjgNoYmqSOOm1i5yMbgUPknlft+NXnEIRFSXnn5vuwdx+ATS3cCQCYXnEk8PDvsCrZnAH4ioHkWJqNKxpeunel68jEANgspoiLMlRIMt0HKwdVGknRIeQ6DuBkt41Hso4s2+G6Ln73u98V+pSHb8G73vAKnP2af8T3f/wLfPrTn54HbL7xjW9wUPOxj30Mb33rW9v+/W1vexue8Yxn4L777sO73vUufPazn+249o4dO/ClL30Jr37u00DiJv6SPgYH7LMKZPPvcd7+++GKH/wKd95xGw4//PB5pSjZ+NSnPoUnP/nJ8DsIgn//+9/jWSc8E7/8ze/xrR/djJec/nR4SNAIE4zVKwY2eSdYSD0EJEaAGFOtGCuqBDZpwkgaEMflwCYrRfVBOxYVLElrdhpDY6sqXzJt7ISDjHU9YNkYGs4ohtJpzE5ULGqlFCONTExLl+6PmS3LMBpNo7HjkWrXzWMGwxhFlvwOe+ByAO+vfM2RKAM2wbJ9AUIw6e+FergR4Y7qWYzt/3crRBnt5KP3ox8pvx5nzEltzTFIH7oUQ6SFya0PYcle1YHmNEmwhE4DBBhbtvDAZiAethCUUsyGcfV/Gg3MRil2RC4aMTAbpWhFMaaaIWZakdW12hx2c9+cBE420TsHNi4SJBWIh//lX/6lXXRLXLiui3e84dUAgAceeACbNrV7UXz0ox8FAJx55pnzQA0ArFq1Ch//+McBAJdddllXQe6ZZ56J17zmNVw8nBAPjgDmQM2T7THHHNMR1ADAkUccgVe9KPNluuaGGwEAAWLMhn3QhuUAtpGT5wEiNKteN9fXJNTJrjPJQJSLFElSPWOTCsCGxI1KgPrcaExlOqZpDGPVkjpaQVYaDycrbkNu7kQ9ycwQ6yv3RxgsBQC0JvvQJRQ1MZoWA4hX0p0IqxbwUoqlSXath/OOqOkgK5O4M5urXRvAzi3ZOyqi2T3d2tYfrctYXhIa33s/PEIyZnrLxmq9bKYmtsEj2btxyfLqNwdlMWBsLEQjSnDY+67r86r/J/y3/Yf0jg+cgeEgvz3SAth4ArDxkCCsIBE897nPLf5HmnBgdfCB+/O/3rJlC1avXg0A2LZtG37zm8zg7JWvfGXX33v66afDcRw0Gg3ccssteMYznjHvM89//vNz1+FsTcoAjeMDaQwi2e5dFpRS3Hjjjbj55pvx0EMPYWZmBmmaAjTF72/5IwDgvvuzXaXXpw4h5ifTQA3jmIWPuPp5YOlc0JzttRxCkfSBsaFhAWxqiLB9pokVY0OVrjk7uQMjACJ/DL7rIK4tA5oPIZraVvqzRrHjfgDAFjqOFcuWIR5aDswAyfTWatcFMoG2EDUSYdP2bVi9qsLdfXMCNWSasSW5cLhZWwlMA95s9WCuFmag6nZ6AI4i9yKdeKjkJ+zEGJ0CCDCydBW2+vtgdbQV05vuAXBqZWtObHsE48gkEiP1ap8fmRgAm0GUxzzGRthVV5D42mZ/CYMoR0eG+X+LAynvuusuzjB985vfxE9+8pPssPO/E/9/rVZDo9GYN3OMxWMf+1jBdbgAcXB9IG7AsQBsNmzYgFe/+tWlrsTTM9nu2kfSV2DTRNZy7RLKy1OVBTdCzO8t4oIi0xD3Y6wCiQXGhgCtxgxQMbBpTWcJj9QzpoYOLQMmANqoeK5PDi4epiuw95IaMJTrzKpeF0A6uQkOgP9LV2EvshMjpIUdWx+uFNhEk5vhA5ikw1ixNNNO0SDvLgynu/+gpRiJdwIAHqgdhKOie+FNVz/KoTE7gxGSaSLHVuyN+4f3Ayb+gGjLvZWuO7szYxsnnTFU32tWHgNgYyGGfBd3fKAPQ78mNwEzj2IbXYKZ2io8NrkfSELcm67GyuXLMD5kz9xrSOx0ynfVKRx4bjtjU4WPTVtLdi6WblIf3XL75GRBcX/961/v/KE5MZODhrkRBMF8FgF5xw540452PPjggzjttNMwOTmJsbExPO95z8Ohhx6KFStWZGtHTVzz3avxze//GDRfzSdJX9gLBjKIGyClHhwagyQVd2TlayZw4RACEAJKXBCagFYNqpIYTl4Km6E1jJAWvD6McqDN/H6tZcmW+X44jR3dfsRO5OtO0mHsu6QOdyzbQHjNipkiALPbNmIUwCNYhpoLjKSPYGrrwwCOqmzNyZ3bsQLAJIaxz3Dem1TLgI1TNbBJU4ylWUlodsWTgM3XYrhZvZZpYvsjGAKQUILRJcuRjj4mA83T1ZY5G7k+bNrdNTqO9xhgU6WPDSGkKNtUGR4A38EU9UDqHoYjH4hjjKYENc+t7hh6aWyqZhLyxBrBQ0I6i1jFie0XX3yx1AT3448/vvs/5joaEdiAOzubne/69esxOTmJNWvW4Ne//jUe85jHtH+gsRP33/l7fBM/BgEBZf83rdhEjVJefnM9DzQNspZ+WvG6Aoj02bUmDkAT0LRiDUbO1rSoh5YzjBHagp9Wb4botLKEl+TAxh/NgI0f7qzUbbk1swM1ZMNGVy2pY3os05vU8y6aKmN224MYBbDdWYGVPgFaj6Cxs9pEPz2xAysANMkwd1YmedebG1cMbJo74SJ7j9T2OwrYDIxH1Y9ymN6RrTFBxrDccTkr6IRTvX7MOKK8nNn0BsCmr7Fb+NjwJODmWhdWEkqqFT3OTT6csemD14gw2oAIwEZkig499FC4roskSXDUUUfhlFNOMVuTMoaKFMCGMO2H2a++5ZZbAAAve9nL5oMaAEgj3Hp7LvQjAHV8kDQESaoHGOzUXM8HkgCIZ+FWDKjEOVHsWlPiAoj4fVdZ5F2GLQSAVwMiwKsayAFwozzJ5EmnPp6VY5akk5huxRiraKzCzMR21AA0nRGM1DwkSzOR53AygThJ4bnV9ZLE+WiDqWAvtGoEaAHRZLXAJmpkDFXTKUqLbj1jbPy4M2NrK5LpLXCRsWP7Pf4w4DfAUjqZGaxWaNLX2JkzJ84SLAdAhrJ7zI+rBTbJdMb6tYI++CFJxKArajEFZ07IvLbrKrqTeLBSFHUyL5WKu6LaggMbr82tNBJMCZcuXcrBDOt8Mgqh9FYAmwxU1WuZ/qSbuV7pr85LSlNTnV80d915J679yU3ZkgBoPs6BlUwqi7S9O4l4GXXvIa50bAblpSgHLmkv+1UObPLfH8PlA1kdpJWPCfFzYMN204yxWUamsXW6utJfYzordSW5zmQkb8tdhilsn6m25JhOZvqeZn0vJLm2h05XK+BlwKblFNo8bzhnySoGNtPbs4aObXQMTzxgDWZp9t6Y2VptZ1RrKrums27OTOXAJqgY2NDZTKeV1JZWuo5sDIDNYgoOMNz+loS6iYcJBa1a+8FnNnnZKIc8ojnePR/4wAfgeR6++93v4rWvfS127OisV/j973+PSy65pPeaeSmqDdjk3Tpr9s1Ylg0bNrS3xEvGEUdkU3avuOIK/OEPf2j7tz//+c84+2WvQRznWheCrBsLgEsjrfWkg7Ikn50z4fdWxaxcUmhseAUmv7+cfjKRPvOFqp6FrOVJxsmTDvKhgcvIFLZOV6fxSRpZCSwN8qQ3mpWiVpBJPFrxnCovb6+ORx4DMpoBKme22m6spJFd59At5Kz+UHbu9bTaOWiz2zMgt9NZivHhgLdd79h0X6Xrxqwk5GfMSTCyFAB4m39V4TYzYEOHFn4AJjAANosrBIDhzelO6lcC8HjnSr67TpNqE25u8R9Rt+hQAua1IT/96U/HZz/7WXiehy996UvYZ599cPLJJ+Occ87BS17yEjzrWc/Cvvvui6OOOgof+1jJQLq5QA7gjM0Zp5wIICspHXbYYXjFK16Bc889F+eeey42btxYejpr167FyMgIJicnccwxx+DUU0/FOeecg5NPPhlPfvKTcefd9+LJhz6Bf564hRFjpflWEPG6hGRmeag+0TMdTUpcri0R166y3ZyKz5NXAJuqW9xrSabvcIeXZn+RJ4OlmMZUs8JSWC4eZowNB1SYwpYKARUA1Bp52WlsH/hjGbAJWtV2Y6X5+UZeAWxqo3n5L6020TcmMq3LjLsUALDTy0Dk1KP3V7puOpNd0yhnTmqjGcAZqvh82RgHMrLwc6KAPUhjU3U8vLOBOKF4zHgdgVcRXpzn+VF0J1VZEqI001/wdUkOqtKYJ1y3KrduoRTFkjyAjkDuta99LQ455BC8613vwk9/+tO2eU8sjjnmGLziFa/ovWbKGBsyD9icesLT8Po3vQWf/89P4c9//jP+/Oc/8x8TZ0V1i8c97nH4/ve/j3POOQf3338/fvzjH/N/e8xjHoN/fd9b8NDGjbjoT/8BAgLCfF1Aq2UShJKQ4xCAsnUrTvT5ulTQTxHO2FRbFqJJXNzXbsFQtZIUsDD/rGNETfi5jidgwIYzNtO4s1Vd+c1pZYk+5cAmYxFGSAszM9NAVb64lGI0zEok3tJ9MTSSfecjUbXdWDQfEZL4BbCp54l+mDaQpLR4vi1HnJeEmrnmZKb+GGD69wi3V+t4zIbYpvVs3fpYdm8N02qBTY0PwNw1GJsBsLEUE40IUZJi5ViAoCoirAdjU23S66A5cTwB2FC4Eo3Qf/VXf4XPfz6bdDvXeffggw/m/8YHXNKUJ74ILoZHRvD5f3svGjTAPl3mMh1//PH4yU9+gkceeQS//e1vsW3bNgwPD2P16tU48MADsWrVfFdM13X52gcffHBbV5RP2ktRDlJc+E8fxD+/50Js2LABW7ZsQRRliUqcFfWhD30IO3fuxAknnDBvvRNPPBH33HMPbrrpJtx3332o1+s44IAD8NSnPhVky5/xxz/+Eemy/XHYQU9oZ04oxSte8QocddRR8wZ5Ggf3k3HhE/Cyn4sUYYXlRpLOMUIE2pnISvU9OYggLpz8nqvcGJCBC0o4e1AwNlOYqZCxYaJlmndjobYEMTx4iBFPbQXw+GoWbuyATzPmdWj5PhgbzX1Wkp2VgguSt3SnfjExfWg0O/dR0sB0K7ZqkSFGmuuHWrXsu6VDS4FpIJqptqXfbea/Pwetw2MZwBlDIwPyFU1VH2FjHJYs/DgFYABsrIXrEERJZybBStB0fhuyqIOoKgHQlLvtUpJ7jQDzNBgyG9zDDz8chx9+eMd/W7169fzZS4JRXgIXfm0I5778BZihNewY7jzEksWqVavaHYx7BCGkfe18AnIn8bCTn+9ee+3V8/e/6EUv6rmm53l41rOehWc961ltf0/TGEcc9kTUDz0FB+2zEpjd1rbuM57xjI6OycYhMDb1PjI2hImixVZ+0p8SKxMuZ1PFC2PAJImB3KTQejSzBDCNIYzWc2+VnLEJSIJwdqKadQF4c0TLIAQz3jjG422gMxXqXXJjwO10FMvHl2BsPHMMX0EmsW2mhb3HqukSImHGUnBTPhQs2Qia2NKMKgM2TD+UMhPEIAdXFfvnBHnrvpsL0kfGCwalMTOB4SW935u6wcZlDI0v/GRvYA/S2Kxfvx6HHXYYjj322Ep+P0v4lY23EXaRPOHyBFChyJLtqGlRIgAgtD9XyBYJLIIjCFq9qsXSHbuisvN1qywJiaMciJdpTkgBMPpxzuxa94UNpJSD5rZ7q42xqWZpoGCLiOsChCDNX4eVOh4zkzwMY7SW7yv9YUQkAznJTHXlmSD3bnGGC7uLWW9p9h8Vrou8Y2Y7XYKVozV4SzIB/jJM49Gd1ZVIeFt9TfDCzQ36aiTGzGx1a3u5fohpTki+Lj+mimIodzv2c/PFkeERtGgG3mYmq9E0UUoxTrPzGlk2ADZ9jbVr1+KOO+7Ahg0bKvn9LP9Vx9jkZSiatXoTMoexqYo975TkASHh0urYoq6aoooFrZwZI/MM+jKAUdHFFkAkNwTkSb5ajQ1N5rRdiwxVVWhdGCjaDpqL+7rKUhTJ12eAmel8aAUmnjyaOwEAU3QYo/Uc2BCCBjM2m61OUMtEy95QAWxCP2czWtUxRUzrMo06Vo7VgOHlSEHgEIqd26rzsnHzlm4GKgAUzAmAxtTOytau58DGzTvACmBTrdZlJMmAc31JBjAIIZgmWbv7bEXAJgybCEj2/mClr4WOPQbYVB0sAfYtyQM86XkkRUrTarqTBF2P0wXYVA3m0rmlN5JyP5hKQvDtmcvYEILq1m4DkU7butUzNjk7RtsZG4cAaVV+MrQAco4jvIpEEFlZiZWCIGlbjwObKkc55KWoSQxjRHAKD/18llGjIoCRJqinmfeSz0TLAFIvS3pJq7qEywDENB3CipEAcFxMOxm4mtm+qcdPmoUfZy3dTl1wIndcNJCVvhoz1YG54Zw5CfLSjDPUH/+csTRnTpYWWpfZHNg0p6rR9zSmipE2wyPlru/9iAGwsRTMXKxvSR5oa392aIJKcoAIqESrd6ddc1JJiMxJ3onFVmIlm0qW5eUgh5cYQZzq1xbOl2NI0oeSEIpknjIdlXC+1QGbDn5BwBwbg2qWzrRjWZA57FiVxoBxDlwm6TDG6sXzm+QAI21VpMFoFcknGFvK/5vmHUNMj1JFTOfApuUOo56L8abzEliVJn1BkgEbb2i07e+ZE3E4XRWILOZEDS3Nym7MP4cdUxXRClsYJ9n3OLa8ADYNJzv/sCLhcmM2N0KkPlw/qGQN1RgAG0vhLARjkw8MBCoUEAuAqq15gWtOKtxVzy2DEcLLFKTKXTXLpm2C1qI8Q2hFJRLhWntzjAGrbvcmgp9M9hcENP+OK5vZJLTVOyJoFsXDld1bOZCjpGCL2LlXCJqj3P13EsMYqRXAhgEMVAUwcm1Pk/oYGSqcePm6FZZIWrkgOhb8ZGb9TNRKZqsDNsyrRiy9AUArN+yrTKgtzIkaW551YTLRcq1CP5nZqeJ8RpYUouGmmwGbqCKGqjWbsUSzpLpREaoxADaWwuGMTUULCMCmvSJU8Y6+bd35pShSsZiWrc3nCLEp2zSuzhgwX5cldh5CWagaYFMwGE7HbqyKbi5KAdadJLZd89JM1QxVZ8bGqdLZms6/r9mzRCpkbMLZnQCAWTICX5jNRIOKgU3O2EyhnSkiQQZynKg6JoE5AEeCA3CUa3toszoxLSu91YbbgQ1zIo4bk/N+xkbQvNw4Q2tYtiQDFcHwWNsxVRHNHLiE1IUXFCAj9LJjSCoqc7ZmcsZmAGx2v2DvqMp2mB1exACqb40t0dhU2pLbQbjMfBjcqkpvEEpNc4GNIOSlVeRbfr7zh28SggqTfFGW6dR2XVlphhaMzVxhOv9qq2LmOjCg3OOjQsYmyYFNy20vj5Bc1OpUpcFg3Vi0nSkitWxdN64O2NC8vCYyNtTPWaOq2p8pxRAyEBGMtAMbdhxpRcCmkSf6WdSxYiSzDajn5b8RVFiKms2uZXMOwEgYiGzsrGTdKAeuA2CzGwZv9+5Dkm8DNoJxXCUlobTYVXcqRWUlEvvLAuic+PicqqpKb4Jvj9ipA4CQiq91J81JH7UuWUv/fBEvoRWNzRB1Y233FgHNX020EgSJjkxkm+NxRc8xEwczxoKFk7ckO3FFO3rO2AwVbeYA3HzdaoENcwAWSmA5kCNVAZuowctBzJSPRZwb9qWtatiimbwkNIs6hoJ8eG5uxjiEFmhSjQljq5EDG8wBNvlsMFFnZTM4sBGmqC90DICNpWCJqC+MjfitcT+ZikpCtAugqjrJC2u37ap5aaai8xVYETKvFFWwY9UkeqE0w0XLhbanMiaBdmCK0IfRBgJwbWMDIZQBKy5FtbGBgp1AXNG6rEwRenOATT1Ltl5FjE2cM0VTdBhjtcKUzq1nx+En1ZVISMiAzfy2a1KRtocKDs/Dc4ANB1UVAZswLwk1SJHoR0aX8v9mmhTbwaaZN512YEPzrrCqzjduZoAqcodLPtm/2GOATd8M+ipmbBK4/QUYaZdSlFMxwBDWTtsSfcXtzyzhUTIf2DB2jFRkHNcFYFQu4hWZog5lTqeq7qRu6wL8e14YxqY6A0jSYoMo25OtlwObqgBGOL0TQKaxGakVTKQ/lIGNoMJp1w53AC7Kb04OqLyKgE2Yd+rMoI7h2pxOndyJuCq2qNWBwciM8jLgPFtR23WUMzbhnJIQyYFNVeaASYtpqAbApu9RtUFfwdhU8ut7iHgLgFEJfV4iHq50UCFLfKKfjFPxulQsvc1NtsK1rrDsN98MsZidVQlTlHZmTkjFM5tol3XzxfMPVdWRJbKB+d/1wfHYDbOEy+c15cEAhp82KnmOC9HyMDxBtBzkrdBB2qxMjO/mjseiOZ7DtD0VtT8zIe0M6hgJ5sx7yUGVE1UDbOIc2IQCsHEcghlk/7tZUZt5nHsRRW57ScjJu8L8sCKxdCv7Dpllwa4QewywqTqKkQoV+9jQblqXityHS9etKMkLaycdpmxXV4oqWJN5s/l44qtohEWH0htQ6F4cmlYjmO7qJ1MtiKTdypwQSlEVMTaUz8YSGNCqrRNQOM+y0hOLIPc5GUELM6F9wXSctzbPFS2zbp1hNNGKq7nWHjfKK0pRHmOKKtL2tKaZzmWoDcgBgJO7AFdV9kvyTq9wDoPBjPIaOXtmO1iH2VzmxGWt5kk1QI6JwwfAxiAajQb+/d//Hc973vPwkpe8BNdff/1CHxIAngMq7xCaxyRULR4WwIXTgUWorEwBdGYwRP+cSsBFh5ZrFm1jJOwv3SaW7qevi6h16bJuJefb5mPT/k+8DFgRwKCdSqwCY0Mreo6dpJmtIc4vQmEiN4wmZlr2Wao0Fy2Hc0TLteElfN3ZsBp2jLntisCm6hJYi+tc5idb5mvDZmfZjjTXnMRu+3fcdLJjYWUy25HkzEk8h7EJRpYCAGpJNUCO6aSov+sAm0U13Xt6ehonnngiXNfFO97xDgwPD+MTn/gExsfHcdxxxy3osXHnYUpBKc1mOdmMUoBRUSmqq/6iesaG0iSbttxRY0MR9tOQEKgcYNA0O9+5oIq0aXv61I0FzCnNVHO+AEDhzH9eWJt7xRqbNrZInL1W0T3t5cDGr89t986S4AhpYrpln7FhouXIa1/XzUtCw6SFmVaM5SP2nWMZePEEYBPk3jJV+boUQtr5nTr+cLUuwDRk7e3tib7lDANpdUZ5NNcyzWVOaiPZ/KbhiswBC2AzUvLJ/sWiAjYf+MAHsGnTJtx5551YsiS7Oc8880w0GtUp+mVDTEQJpfCsA5u8Bblr23VVDEb2O+ftqoVuLJpWBOZ6MDaVteTy9nYyX2MjsGNRlVoX2lljk4FI+8u2iZbbvuOKx2Z0M0IEBI1NtaUo2sG3pzLPIErhpxmwCebY/CMHNhljYx/YFKLldsZGXPfRCkpgAFBnow0Eo7zaSG5YRxuVvDuYzqXlzk+2BaiqSDCdl2bSOYk+9EaAGEia1TA2zBNoLnNSzwdTjqAaYMPMHUlt1wE2i6oUddlll+FVr3oVBzUshoYWvn/e2Xo3DiEbUUNUcQfJ3HIBK81UNGW7xD8HyBKf9ZUpBcl9KOAIO/qqu7EExmY+iyC2P1ewNFubzL3W/SpFde58cysCVKzjiXZ4DbFSFKmotZ6ZMNI5YzMosyqswhgwCeHk93QwNCcJ5MLakaqATd5yTed0YyF3Hh5Bq5J1EYfwEeVLFWvX82GJI6SaEhgDD3GHTh0/X3s4B1XWgzEYQft3HHnVOh6THGDQOYwNG68wjBbSKLS+bjFFfbTkk/2LRcPYbNu2DZs3b8Zhhx2GCy+8EL/97W+xzz774NWvfjVOOeWUrj/XarXQarX4/56crAgtpxECEsOtbI5Qb2BTFYNBafaqp/NKYA4oCDIrtawM5rgWd11CNwxpSz5Vi6W7GBICQimKVqPBYOxEj1EOmzZtxkjNw/LlyxEElsoGXR2AK/axYaWoDozN9olJxBNb0Rj2kVLA1q01MzODqakpeNu3Y+XSkXnAJoUDF0k1rfXCuIT6cGfGZoi0KilFOVGX5JMDqhqJMNNozf0x8xBaqkUH4HrOmgwjK72Jbsg2ImVCWm8+i+DnGpsR0kCUUASeXbaItbdjDmOT5MdCK/KTYczJXEA1KsyNmpneibFle8NmMIsCZxcCNouGsWHlpre97W0IggBvf/vb8YQnPAGnn346vvKVr3T9uXXr1mF8fJz/WbNmTTUH2ObEazkJ0BQAKwn16k6yu6zImvQSeDqQ69aZnZ3F5s2bsXnzZmzZUjL8Lk2x+dGtePiRbQhDYZdRufuvwFDNPeHKW827JHoBYDzhgDVYvXo1fvnLX9pbN+2io3KEsRmWzndychKbN2/Gzp07C/1MB2DzonNeh9VHn47PXPI5q9f64x//OFavXo3nv+Yfsr9w2teu1Bgwyt5hIXUxOpdlZhqbirqi3NzR2K3NYTCEJFiJcVyexJvUx0i9xv+aAawRNDHdrMCJl7sdz0+2Qc7YjGEWjcg+gGUMBmrtZb+U+edUBWzy75jMATb1eg0Rzd4hzJ3YZng5sHHrYyWf7F8sGmCzfPlyEEJw2mmn4QMf+ABOP/10vPe978UrX/lKfPzjH+/6cxdddBEmJib4n40bN1ZzgFX6ugg6g3meH1W6w7at28nXRe2cP/e5z2H16tVYvXo19t57b/z617/u+tlmYwarjz4d+x7zV/jB974trNkf5+F5zFjb2tWUokg3zYkAMKoI2s0BuG0OmZ213vGOd2D16tU499xzuzNUc6IyOwHMYQMhmCFWoe3JgU0TtfkMRb67HyYtzDQrKBfkomVvbvJxAyR5Gqgi6THGZhpD7eecM0UuoZidtb8uM9+bq3MBAL+e/V0dEZoVABve3j5Xc1LxGIli3XbwSghBAxmorAK8BrkAfK4gfiFj0QCb4eFhHHzwwdh3333b/n7ffffF9u3bu/5crVbDkiVL2v5UElVOu2bCYZqXhLowNtbrxeLLnZCunSu6nVEXXnih1Nptq1YtHm4bNjrn3wQ9k30QSYVEP8dQTABze++9CqtWrbJXhkLRnTR/bEYxZTutItH3EA8vX7YMq/ZagdGRoersBDBnNhYA/kqswhgwLxU0ELS5/wKYw5xUsatmouU5yZYQ7pAbVdGGnLMT03QII4EAbASBaxWGdYS5HXcoj5Ac7NRIhGbLPoj0crH0XAaD1qo1BmTrdioJtUgGbMKmfQFxjQGb4QFjoxXnn38+vvnNb+LRRx8FkOluvv71r+PUU09d4COD0CVUHXPCZjB3dwC2uyzXm1ACp9Ou2tFbmwGkG264Adddd13nD6XJvM+3rUlQbbLtxFA5haC1inJjMWG7s8bGRYo77r0fmzdvxvHHH291baBDuVEcAlqB5oSVOeeNrgDwza98GZtvvR4X/P1rq2Vs5gKbKruxcsamQWuo+3OAjT/En282VNBmsF11bW43FoAw91eJmvbXZVqXbLSBcM6Ow2cpNWfsAypWlnGCDp06flEGbFaS6PMusDnX2uVjJKoBNqzjzuvAnLCJ32EFoHmIsnurItJAIxYVsLngggtw+umn46CDDsIxxxyDxz3ucTjkkEPwr//6rwt9aHM0NpZ/t9i1Mpc5mcOaWGVteJInc6UI+dp6IwaGh4dx1llnAchYm47HLIqHO6w59zNxHGP79u1IkvIEPDExgc2bN2Nion2nODs7y/8upZ1KUQWoqoodo7RDohfKjZs2b8LmzZvbdUcAkiTh+iXxGqRpiu3btyOKeugYBDAn3ltxkmDbjkkkSVLa/vzoo49i8+bNaDabbX8/NTXFj3fz5s1cK9dqtfDII49i86Nb8eiWrdi8eXObyH/7jglsfnQrZmemS++tRqOBiYkJ5e8kpYDTV2CTJdEGgvnAhhBuhR/aLgklEVxk98S8NnMUhm5smKHNaOUs0DTmMDYAWjmwiRoVMDbdNEUA4BWzlMJZ+8CGgUhvTqJ38plNfkX+OXzdDsCGzY+KKwByQzRnAweMjV44joPPfvazuOuuu/C5z30O99xzD77zne9gfHy8/IerjioN60SA0aVTxyFZ95JVImEOoJoXAkulesrr1q2D4zi49dZbO4u/xVJUW+mtaMmNmg18/OMfx5FHHokgCLBixQoEQYDjjjsOn//857uCnAsuuACrV6/G2rVrMTk5iXe84x3Yb7/9MDIygqWPPwarjjwNH/rQh9BqzvFHEgCHdQ1GL9GywMo9+aDHdRQP33fffVy/tHHjRvzgBz/As5/9bNRqNaxYsQJDQ0M46aST8Itf/GL+2kJ30szMDD7ykY/wa7rySScjOOBpOOs5p+KKK67oeviHHXYYVq9ejW9961u45ZZb8MIXvhBjY2NYsmQJVq9ejeuuuw6rV6/Gf//3fwMAvvvd72Kfo/8Kq48+HUcffjBWr17d5iL+wpe/GquPPh3/cckX5z1P//d//4ePfexjeNaznoUVK1ZgeHgYS5cuxdjYGJ7znOd0ZwHnXvIewzcrZWxQw9BcYIOiNTmxzZz06sYCEHsZwEgrSHpRPsphltZR99vTTasqIAfAzdkLN+gAbBwHLWSl3CpKM3XuVdSe6LnbckUOwLUcYMxligAgcrJSlG3wmiQJhpBtSOojuw6wWTTt3mKsWpXpDHapqFL70a3VW1iXr00pXHQAIbbXFdbWAXOHH344zjnnHFx66aV473vfixe/+MXwfb/4QLdSFAAQFzt2bMc5rzoPt/7ut9kxOA6WLl2KnTt3YsOGDdiwYQOuvvpqfOMb3+jqc7R582Yce+yxuOuuu+C6Lv/5R7dux+c++1ncc/c9uP76Hwi7egKKnEGyLfyQEC27km5B//qv/4rPfOYzAIDR0VFEUYRWq4Wf/exnOOWUU3D99dfjpJNOKn4g/57vf2AjTnv1s3HXXXdl67kuxpeMYmJyGrf89rd4xStegR/96Ef4r//6r66Gat/73vfwqle9CnEco1ar8eeU/ffk5CQajQZqtRqWLslewCnJ5jXV6+JU4nziNui8S33hhRfiyiuv5P97yZIlaDQamJmZwXXXXYfrrrsO69at663hQpfhm+y7rqD8lYazcNClFIXcqTYEaMty4ssBVUwdDHd4FtLc94TN/LG7dN4V5QzPu2cidxiIgKSC0pufa4qcTsAGmeakRkNEtlmqNMUwsuvNvHr4MY1UawxYz4FNrQNzwgZyxqHdtRuz0xgl2bMyPLoLEAx5LCrGZpcOUTxcmcamU2eSYL1vW0Dctm6Hfxe0Hzos1T//8z+jVqvhL3/5Cz772c92XBtAh2GUDs57+wdx6+9+C8dxsG7dOuzYsQPbt2/H1q1beUK75ppr8Pa3v73r+j/60Y/w8MMP43Of+xwmJiawY8cObLvzJqx9zUsAAD/+8Y9w9dVXC+dLUIhLbTM2PfxzhFKUTHzmM5/BmWeeidtuuw1TU1OYmZnBj370I+y7776IoghvfvOb5609M9vA/zvnHNx1111YvXo1vvrVr2JqagqP3nEjdv7pp3j3+/4Jnufhi1/8Iv7zP/+z69qXX3459t9/f1x33XWYmZnh5bHTTz8dmzdvxjnnnAMAeN6Zz8XmW6/Hpluuxx/u+j9s3rwZp5122rzfl7GQ7ffWgQceiPe973249dZbMT09jYmJCTSbTdxxxx34f//v/wEA3v3ud+PWW2/teZ3mzeQCKh3lEDWLUlQnxoYBjNQ2wOCi5RqGgvl7Wd45FNlPuHFeimp1MMqLc1+XtAJtj5dmLILXqRQFIMrFtFHT8jkL17A+0p7oa7l3z1DFwCbo0HaduNmmwTZobgj6qNpcYfoCxh4DbNavX4/DDjsMxx57rP1fTikQN4GoASeazca4hzP2/rSmgaiBNGrCTeb87mgWiFtA1IAXTSNtWVpT6NLpytjkCZdoeug89rGPxdq1awEAH/zgBzE9LbzQaXfG5pbb/oxvfP9HAIAPffhfcOGFF/Jut+XLl2PdunV4y1veAgC45JJL8MADD3Q9hq9+9as477zzMDKSPZTLxsfwHx96Jw49/EkAgO985zvtP1BVqUIYa9CtFCXrOv/MZz4T3/72t3H44YcDyJiXU045BZ/4xCcAALfeemu77QFNsf7SK3HP3XchCAJcc801eOlLX5oxXcTB6Mgw/v71r8e73/1uAMCHP/zhrpqdkZER/PCHP8Tpp58O152fvIs1RV+mTmxgwdjM3Sh8+MMfxj//8z/jyCOP5N+b4zg49NBD8cUvfhEvetGLkKYpvvCFL/S8Tp3KfkQQiNsOBmyaqKHmzX/18lk7ttuBBWDTiSmqbF0UDsBhh9EGbKZRWoG2J6AlwIaVZlqWQUZe9kspwdCcsl99dCkAYJjaBzZJkmCEZOc8NDpfxMt0VKllYNOcyUDpLK2BOD2e9z7HoixF6cTatWu5psK6JieaBf7jGADASru/uS1G8z/d4ok2F3vXw90daVkYMjYA8K53vQtf+MIX8Oijj+Liiy/GP/3TP2X/INQf5q78je9mWoylS5fijW96U8ff+573vAfr169Hq9XC1VdfjQsuuGDeZw499FCceeaZ7X9JUxBC8MxnnYQ/3X4b7r777vZ/J07mlUjTthk309PT7cBMMfYa9eCi2ygHtdLiW97ylo6g4owzzuD/fffddxdmlTTFl7/+XQDAa1/7Whx55JHC2gWQe+c734l/+Zd/waZNm7Bhw4aOnVkveclLcMABB0gfa4IONgJCdCpFzY3Z2VlMT08jzT/4jGc8A1dddRU2bNjQ8+fmzcYCKmVskjyBt0h9PnhF4RjLOnqsRV5+aNAAQ8H8+4Lk5RqnAsaGuezGHRyA09w8j1YAqHwGbOrdgE3GYCSWSzNhYxIBsi6wkZrf9m8McNRJBJrEIK699Ds7MwXG0wx10LqkuY6KWv6OWUdbgwxh15ntvQcBm0FoRFvrc4d/FzQ2sWYFbMWKFXjHO96Bd7/73bj44ovxhje8AXvttVd38TCAW2/7MwDguOOOg+d39nNZtmwZjjnmGNx000245ZZbOn6GMRptkQO0x+yzD4Csq6ctBCYh62DK/vojH/kIPvzhD/c8115x3+2/xQFLSZep4sX4CpnoeF4AxsbGMDY2hqmpqeK8KMXk5ATuuOsvAIBjjjkGW7duzf+JItm2E040ja1w4DsO9t9/f9xzzz247bbbOgIbeUZUYGw68saE/99OoPkHP/gBPvOZz+AXv/gFP965UeZuPW+aOcB3naysa3M4Y5Lv5hlbMC9y5sSz3TWTJ7NZ1DDegbFhLsAkrgLYZKAl6QBsOJCroP25lgMbv8tgxjgvzaSWGZvWTAFsls8BkaJwu9WcmVeqMonmbAFsOrX0szInLAM5rqEi9ZJP9jcGwMZG+MPABX8EJh/EJB3GFn8fHLiXxXrj9KPA1CbsoKOYrq/GmuVzsPGWu4C4gf9LV2H58hVYMuR3/j0q4Q9zarpjeQRoE0ybaHve/OY349Of/jQ2bdqED37wg/jUpz7VJh6eW6rYun0nAGD16sf0FGrvt99+2ee7JL5arUOCyQGVkye4eec1RzDt5Al4bGzMSNDOEmy3sp8KsOl4XnkwITQ/L0rx6JbC4PL888/H+eefX7pGN1PMpUuXSh1j+9T4HowNofM60C666CJ85CMfET5DMD4+zs+72WxiYmKirX28U6Qg8OesLY4JSSmdr8ExiLSVi3idLkN78yTsWQYYSTgLF1kJ7DGdgE1ulhdU0IbMhm+mHfxkCHPitc0UUYo6MjsE5jI8N5jmJLWc6FuzkxgDMIs6HjOn3FgXNCithl1g0xJKQsMdSkI09+6xDV7DfKBnq9s9vUAxADY2ghCgNgr4Q3BoDYk31OYkahx+PTPwosPZHJC5Sv/aCEAAktaR+sNABcMRS7uiDDrBhoeH8b73vQ+vf/3r8dnPfhb/+I//iNV+91IUK7OkSdwTULF2755aDzEoLcBDl4RGusyLeuc734l3vvOdcut0iqnNwNSmXDzc5VpXaEjIYuXKle3XiyYApTmzUryo2zuYhMOUBgJyGpvsEItjvPnmmzmoOeecc3DBBRfgyU9+cltH3Ze//GW85jWvKT2CjvPPHBG4AjZVAyyJxm5n4MnM5GwDjKgxDRdZKaqTxoYxNqyTyGaQkA1m7OAAnK/r2mZs4uI8gqHOBZKUiWkju2W/MG9v78Rg+J6HJvVRJxFaDctaF86c1DqWhGgOXonl803yVv1wAGx20xDM6qoyb+vocQLMYREsrpuKXVG9GRvTdc8991z8+7//O+6++268973vxX+tK0DCXL+6VXvvBQDYuHFjz3Xvu+++7POyTEpbku+iq6/sWhc+Nn7Hsh+BJGGjFjTBY/ZeAUIIKKW46qqr2lrB6Y4HQBrbsJkuw8rVj4XXuW6kHZ3AxbxDFL4X1qV27LHH4stf/nLHz2/atEly7fn3NRFNJy0jG5qXopiQc24wK3xmtGYrotYM6shKUZ1Ey8wRN6CWtT0ACGu79uefM3fitV0CE5J30KUUxTUntjU2ubNvk3RpM0eAOiLr/jkRX7fzvcVYOdv6rTjXUEUdut4WMvaYrqjKg3dTVDFlu/uE7WzRisY5lK3rCEnAcF3P87hG5YorrsDvb7ujWGYOZ/O0px4NAPj1r3+DHTt3dvx9GzduxO9///vs8097mtxBtM3G6vYh1qFk2YhRkh2zHjTFkrFRHHn4wQAy47z2ZUVWzny5gm3rMp+qyzGyYKDl0EMP7frx73//+1LHknYSLlc4zJYJNxOvc/Jxc8dYP21Y3RzFbFdNah03Rm6e/GuWARVQJNJORnkeN6yzCy4YMxZRF0NDnZlFmjM2xHaiz5mTsAt4bbI2c8uMDRuH0eqidSF5d5ib2D1fZuoYd7mnFyoGwMZWVDndu5Q5qYgtkmaK1J2HO8WLXvQiPPWpTwWlFBd+6OJimTlL/+2LXwjXdTHbaOCf3/ee+YdNKf7xH/8RaZpiZGQEL3zhC+UOgJ1vp3EK/GDsJvp5a5dca+uRr/u6c14KAPj0pz+Nm2++ed66RLivZcZWdAumwXnk0UzYK8PYiMBmxYoVAIBf/epXHVvOL7vsMvz85z+XOpaOonhS3QaFlQFoV2CTJfphtBAl9hZP8hbfbuUC5lRbp03rbHMxVXw+sHFzYFOzzBSFuTdNs9Poijy45sRyaSZu9mYwQjaM0rJomTkKR25nYMOMCj3LwIaxkMmAsdlNI0+E1ksUwJyRCtWWhDqtW8YiEEtjJAgh+OhHPwoA+Mkvi1ZdMoc+2X///fHmc18OAPjSf30OL3/5y/HLX/4SDzzwAH7605/irLPOwje+8Q0AwPvf/34sW7ZM7gAEQWtXEqGLxsY4JFk565Gv+6qXvgDPPvWv0Gw2cdJJJ+GCCy7ADTfcgPs3PoR7/28jfv3rDbjiiv/Bq171qqJNXCOOPjpn2357C77wlW/hnvsewKOPPDJvVpQYYuv12WefDQC48847cfbZZ+OnP/0pHnjgAWzYsAFvfvOb8ZrXvEZa59OZsWHPcWrdaLMM2DDL/WE00YjsDR1lwCZ2Oic9T1jXJqACiqniXoeSkJcDubplpoiNaGgiQL1D6Q0AH4RJbCd63t7eG9jYntnEgA0baDo3vLzM6dnWUTHfng6lxoWMPUZjs379eqxfv95ot9kzhJ08pZZbRcWk1+k5FcoFcT+TLeyDuVNOOQWnn346fvCDHxSrdNhVf+Rd/4BNO6Zxxdeuxle+8pWO86be9ra34a1vfav84sL5zgVT4tqAPTA3d+0y8Go98nWJ6+OLl38F73rLP+ArX/kKPvWpT2XdaR2CmeLpxPOe9zwceOCBuPfee3Hu2z7Q9m//+7//i+c973ldjxEAnv3sZ+O8887D5z//eVx77bW49tpr2z66zz774LWvfS0+9KEPlR9Mp2s6V2NjMXgS7ZIEWEloBE20ogSw0d0IoTTTDVDlnUNDaKEZJwi6gQGNYA7AfgfGhgG5Idqw+r5kbEgTATy387kUmhO7iZ4Z4MUdDAmBvNU/te+fU6zbjQ3MzpdNALcW+fXrBtYXKvYYYFOpQR/QxpoA2TDKeeZfulFWIuEv47SS8gilHUzjAOUkPzIyglWrVpUmxo985CP4w62/y3xU4GB4eM5DQxx4nofP/vuH8YJXno/vfP0K/O53v8Pk5CSWLVuG4447Dueddx6OO+64jr9/fHwcq1atmt+aLICL4ZFhrFq1CitXzrFcrIqZ499xZ88gdv332msvOI6DYE7nm+d5XCTdqwts1apVqNfrRVdTWjgej46O4oorrsAFF1yAyy+/HDfffDO2PPoIap6DlXvthf2fcAie99y/xnOf+9yOv9fzvK5zuVjU63XceOON+NcPvQ8//8WNePjR7YiTlP8bi+XLl2PVXisxOjI8b27T5z73OZx88sm49NJL+ZyvNWvW4IwzzsDatWtx/fXXY9WqVdh7773nrT86OopVe63EimXjoJ0I66rE4QDcXM/BnX7nLp2XC4ZIaJWxYcAm6VKm8HP9RQ0RmmGCJXU7gAoAfNq97drPp1+P5ExR4FkCNjlj00IP24Mgu09d6wxGbpHhd2ZO4tzDKLFciir8grqUG5kwnfa2QFANMgA2u3kItveEMq2LLcamrDV2YcsjsuLh8847D+edd17p544+6ihsuiVjbO5IH4tD9l0+Z91iV/3MZ52EF531nNLfKcYnP/lJfPKTn5z/D4LO5W9f+Wq89Y1/P/8zFV1rStPMjK4rY5Od8623/AZ7P2a/eTvRAw44AJs3by5d584775yz8Hz91tOe9rRCcD27Hdh5P6boEJJlj8fS4c5WArfffnvp2ixWrVqFf/vAu+A0tmMzXYa999l/3jl/85vfRLLlLrjRDB7q0Ob+8pe/HC9/+cs7/v6/+Zu/wd/8zd90/Lc3v/nNeOPLnwsvnsHDHRkbJsSnSC2317t5EiBBlyTgZcCjDrvAhpmypV128yRnkOokRDOyeM6U8onTnRgbNluoTlpoRPaYojj3C2Jln07BNCe2gQ1vb+8KbHLH45ZtrUv+HXcpgfm5jqpmmbFh4nDi71oGfQONja1om7Jd0W7eEsDQW7e714hDKKjNExYSSmGBJ0RlOhearykpHq5g7W7XmjiF9mPhwKu9ZUV2rCv8F4TLNoNrdnoAG6DdP8dGuClLAl0Yyxxg1GAZYEQs6ZUDqmZsEVDFBTvQibFhc5zqiNC0CORiLpbuAWzysp/90kz+HXeZKp7kHka2RxuQiGldOq8bMGADu4yNk+S/bxdjbAbAxlYQB+2ak2qST6+SUHXiYaezmFZMAhUkebZG95Zc28lWHETZ5TNC+c2qtlRM9B0zfUXdOr0mxwPVMVRpMa6jq7aisoGjvYBN4e9sG9gwAzy31iUJCMxJI7SX6JmzL+0m8MyBTc0ywBAnXQcdhlGy5F+H3fNlZZ64B2Pj5d+Bn9ouzWTAppNvDwAkbBhlaLm1vqQkxNixIWoXyDHGi+xi4uEBsLEZlkYMzAuFmU22yyOApLcKtXjOgqaIlLSZ222tl7H5r5Yd6wjk8r+vct2unWCijsoqK9fb4Tn7p/a5TRYXz/5vV2CTj52wCWwo5UJat5sreZ6UbDMnXAdRwhQNkRBNiwCDJduIughqHUoVOaDySYJmy17CZcLcqEsXGFB0adkGNg4zJOzC2DD/HFhmbLgIugvAqA3nnkEkRhrPt0nQDTdl5zsoRe2+UTFtX87YVOdj0znpEVA+rJDaM8Zt6xDqtG617EVXAAm0tQNXwdh07X6q+JxLy40VArmuIZQcbZ4yK0WRLmtTdh2oxSSfhHCRj/gY6gYwWEkosgow3NzZt+uu2iuYjZZN7Ufe3p75yXS41kLZxOaIAcaGJF1GVwBFaSywzmBkQMnpoqNKPQZsLGtdGHPidQYY9eFi4jcbv2AjvISB9YGPze4bwuTnhdBBWE16lJYnPUA4Z4vsSZ9mVPVat3t5xJ7bcqe1uwMbQWNTwTmXs4HVlDk7siZs6YoBe3dQxQaF2te5AEVb97zIGZth0kIjjK0tzcsFJUwRAEQ2/VXagE2HTj2vhjTfGDFTPRvBJnbHXbrAAMDPwWWNtqzeWz5nMDoDm2IYpd1SFNe6dAGvQ/VhpDS71s1Ze7O5vLzLyu1QalzI2GOAzfr163HYYYfh2GOPrW4Roe3a2rNCKYoSSbcyhbCrtpV9KOWiThmBp2NTcyLJIhBiOfmI63b7TBt4tbWuOHyzfEZVFXomKRBZQTmoVymqElBFaSFG7srY5H9vsxSVJ/mIuqh3KssAnLEBgNBiaYbZ6HcTtML1keZ3fGRT+5GXR5pdhm+CEEQI8o9aBFQ5aEh7AJsg79KqkQhhYu975uXGLuCVaWBsAxs3X9fxuwxYdR008vb35ow9YOOnA2CzoLF27Vrccccd2LBhQ/mHdaMK2r6tQ6isc8VmAhDnJnUXeJIqNBhtgtZOizrzPmtnXdF5uKwryqamqF0s3XtdCqvmsLJlzoo633pAyLY5VTavNTtL0k0hXoVoOQc2jW5lGaCdObHoc+Jz3UcXxoYQhIQBDHvrMsfjXg7ALTY7yaavS36tu3m6AECQz+UaQgvN0N73zBK91yXRs3KgY7nNvCiBdQcYfE5V014pivkUdTvfhYo9Btj0JarQ2HCTvPLkY7UEJgp4e7reVmFYV9Z2LXSuVMDYdAWQQKXfcfbryzU2NhkbKqlnEj9rZ+H8d/WcFl5FibUdsHcM/vcWzze3nm+ghqEu84tE5iS2mOi9tPu8JhZxDmxsOuIysNLoMbMpcrJ1qyiBQUJjM2TZM4gZ4JUCG8uOx7wk1M0jCUAzH5AZWtQz1fJ1/QGw2Y2jiinbbTb/6FwSmlMusJL4yrpluqxtJaRKUWxXXZVYunykgv0uMEj451Tj3dPd1boadqy09AZUyoCmlMDpCiLzcmMVjA2tdU3yICSz3IdFgJGm3CSv07wmfnjcEddeiYSBlV7DKFnnkk1ARbjDc49kK3Sg2dQzBTzRd77WTHvjWfbP8dOMOekFbPgAzoa9UtQA2OwJUYUOYk6y7aWxIcSiv4qMcFhcu5Jz7sWckLbP9m/dClm5bl4yVa0LgbEh3dq9i863Kq51TzawCs8gCcBOc62c3VJUOXsBAIlty32BGXDz8kvHj3FAZS/hMtaphRrcLg9UXAGgYu3t6NIhBICLbB1C0WxYutaUogY2QqJzondqzPHYbpu5DGMTctdji4xNfr5BDzZwIWIAbCRDKmlXqHWRccPN1ra0uxWSrTxjY77s3LWdbghD0EHYBlRURmNDFgbIVdVxhx4sFbWtOaEUjgJjY7fEKpgwSujG+I+Zrs87hGrdNTYoOnnSyFKiF03yhronn4Sva485YYJgVm7quG6ebFOLjA3Xr/RqQRa6h1q2ymBJBDcvXwZdWvpZW7Rtx+OAa126AxvGjtkSaidJijrJPHFq3SwMFigGwKYkGF0tNRXcqVDr0rMkRIT/sgQwpBkbNiOrqnbv3uva7cYSZ3J1W1f4B2s7eqEzqQTIWT1fQMooz7qYVjgBGcam/99xfk8L58ue/67lq7JgjA0NumtsIAAMWwxGvm6T+hgKugOM1GFW/zaN8tjMpu7MSZKzKtQWkIPohtuDsXF9RPmoxMhWaUbodKp1GCEBFN1SnmVjQAZsepWEYoe5HtsBkU1BqzMANossfN+H7/uYnpa4+Sttfe5VpiD2tS4y4IKtjaqSj0x3kj0QycsytHzd7IO2En1JF5iwblWMTS8/GftdQsLv6XVzVSiK78mA8g1KcZxTU1P8XaAVrPW5pBSVsllCttqBQ1YC6yFaFta1xhSh0M3EPWY2pbYZKgAeBza9yyOsE8yWhw4fREkJavXOoIpPUrc8ZbsANt0ZmwI02wFyoqliNyC3ULHHABtdHxtCCMbGxjAxMYFGo+Thq0LgKSvitT2nSqYsA1TbkdWzXFBFmULiWlehOVEpgVXkeNyLOaGcwbAMLmgJY8PvaZulXVaKkrAwyI+z0WhgcnISY2NjvZ+FHsHYixb8ngCDW+7b8pPJGZtZ1FAPegCbChxxUw5sujMnxYgBi4wNH11RBmwywBVb0pwwgNRAgHrgdfwM60zzLQObeom2Byja322xY01WaqQuHL87G7gQ0fnq74axdu1arF27FpOTkxgfH1f62ZUrV6LRaOCBBx7AkiVLMDY2Btd157/kwgSIKWIaI2y10GxawI3NJhBTtCgFRYhms8uLJwZAKdK0hUazCSc1/GpbLSCmaFKK1Gmh2ezyUoxSIKZI2Dl7FjJQKwRiipCmcMIWms0OvzOmQEyRphEajSbSHslCNmgYgyQUUZqdS9xNcxITEKRIaKv796ES+XfcoBRJFKLjr0wiIM50PWGraefeApBGKRxQxE7U9VzSmMKJKeJe959KxGF+zxAkUavz+QJAGPH7oNVsoulaAJL5tW5SCoRNNMn8EnMSJXAiijCNsGnTJkxOTqJWq2HlypXay8ZhEy4yYNOLsaEMYNhibJi2p6QEVqxrD9jQXIic9DDKS5kTr0Vgw/QrbomgNXLqQGoX2NSQsXJLulzrIC9F1S1O2Y7jGAHJOrt6MSdsujsN7ZxvlAO5FgmgyWNWFnsMsDEJ13WxZs0abN26FVNTU9i5c2fnD7amgMYONFDDrNdEa0d3ClY6WtNAYzsaqGHaDZFOdvmdk1uBNMIWGqExubPny1Nu3eJcGn6EcGcXRN7YAbSmMIkZkPoMdtYt3OKz24FwGpOYhTfcxM5Ou5+ZLUDUwA40MTU1jaCLAZhK0MnNIGmMLTRC3MPrgU5uBUljPIoYdHbCeF2EM8DsNjQRIB5KMVHrcL40BSa2AAC2eQ7CnRbuLQB05yMgoNjmUoRTOzt/ZvpRkLiJHWiiOWPhpZhEwNQWJHDQGPI6n6/wuRQOZuoOdtYtvK6E+9qZpKh1uG9oawqksQOzqY/RvTwsXboUK1euhOvqP1NxmPm+NmnQcU2+NrfctwQwoqIUNdrrnZCXohyLjrg0Xzvt4SfDOpdsOvFyN9weHUJAUSKzZUoYNrMSTwsBfLfzdxzwUQ6hlTUBoNWc5Yk8qHc/59TLgB6xJBBnfjgtBOjeb7cwsWiBzebNm/GLX/wCBx10EI488sjK13NdF6tWrcLee++NKIqQdrJbv+N/gRv/Gb9ODsE393sHPvI3h5gvfOtXgRs/hhuSo3Dtfm/CR7v9zq+8C9h2Nz4TnYezn/dCnPC4vczWveVy4MZP4PrkGPzx0LfhLac/rvPnbvxf4Jb/xtfik9B62j/gVc84wGxdAPjBF4G7rsF/Rmfh8DNfj5Met/f8z3z/M8BffozvRC/AyS96Aw5es8x42fgLb4DX2IKLk7fg0xe8vOvnkv9+K9zJB/CJcC0+dsGru77EpOOPXwdu/Ch+ljwZM6f+C/76kNUdDi4ELnkpAOBLe/8HPvCSZ5itCWS1oPUvBgBcttfH8b6XHt7xY+H/rkdw/0/w7eiFuODNF2mXY3g8cjtw7VvxCF2Ku07+bzz3kH06f27ng8C1b8UsDXD1cV/BKw7d32xdoO2+3v9lF+Nxq8bmfSS9/dtwfvEB3BQ+HgdccBVWjJqDSNbOHDtBd4E4wIcY2gI2NJoFQVYe2atHKYp3CcUWSyQSDsBsEKY1IAfRJK+37oOVyKi1RJ8LtdH9fgnY8E0SgyYxiGuegsNmA+xMa0PdIQbhoNnOdxznzA/TKu1KsSiBTZIkePGLX4xf/epXeMMb3oBPfOITfVubEIKgW3eBT4DpjfCSMTw8naDeRUCmFPFOYHojZpLHoZE43X9nPAlMb0Qj3InZ1DVfO9qRrRsfiIj0+H1ODExvBIk3YyIkds65sQmY3ojtUQN+UOvyO1vA9EYk0RY75wsgmfwL3NZObEHv80iTSTjTG9EIdwCuj7opSxXtzL/jx8Lxgs5r0xro9EMgSLFjaMbOdY6awPRGAMD0yi7rAnDRhD+9EXG0FcTrLX6Vi+y7i9MYrt/t+wUwMgpMb4RPCSaa1NI5F/f1yPBQ598ZuMDMgwiScbRiOzoqJqRNeghpgSL5uJYs95OwCQ9Ai/YugbE5VVat/nNgQ3uUoooRA/YAVZlJHovYsr4nzkW5UY9EXx8pgEerOYP6iJosolOwdvWYOvC8Hu+ifIo7sXSt42Y+/4zYYY9txqIUD7///e/Hfvvth8MOO2yhD6U98t1WjURo2bLpztF1k/qo9XwxFU6aVtZm65Z0cbBzriNEK7Z0zqJLq9dlbZ+tG6EZ2lmX0eFpL2MvFC/j7JwtJL5csNnoNiwQAAjhrbHW9BfC7+nlf+HkCWIYLTRt3FsRE9L2LsuwF7FLKMIoMl8XaLuvu2pO8nVrJLJzvgDS/DtOy4BNYDfRM0Frz/NFNQCDsTBpl4nTQOHEywZ1GgelhZC2h28PUAWwye/rHu3tdUH307I02kAsCfUMj4FXO98xA+sDYGMhbrjhBlx++eX4zGc+s9CHMj8YsEFkb/5IXCSBboPkABTAhthKtkUXR1dwIaxbI5G13W1hZhagVjIwsE5CzNoANmlaPPA9XsRAO7Cxk+iZQ2tZK3BeprDVuZIn+YQSBF2mAgOAmw9PHCItNCML3zFvfS4B6wLAjC15b6RhcW91BzbsOQ7tnC+AhAEbr3cSYEMMbTEnzP03JAF8t3sJzLHMFAEAYb+rx0aBna9nC1AJJa2gpAU5tQ5s8kTfw5DQ8zw0acaqtCz558Ss466kJER8u8CmON9dD9gsqlLU1q1bcc455+Cyyy7D0qVLpX6m1Wqh1Sq+yMnJyYqODnynFyCy9kJkyacFv3uSB9pAlRWA0cbYlK9bR4jQMrBpIECtlLGxNMROZEFKGBumCxgilhJf/jJuoNYTvFKvDrQsCi0FANmtPRUAB3pDlhmbMiGt+D0kltqfk3AWDkq6kxhjgwjTllhIyhmb3snH5bOEbCWfXNtDaj21UZw5Se2JWrkQucdGwbU9O0kAKbLAxlZHlmy5sYUAdUTW/HNYd1JYwthw8Grp3mLjN+IepcaFikXD2FBK8epXvxqvfOUrcfLJJ0v/3Lp16zA+Ps7/rFmzprqDrISxyW6eFpVjTqyxCIwp6lUeAeaUomwDmx7288IQOyuASmBBnBLGxn6iL1xpe19ry5OB2b1V0oLMQGSACE0biV7SrA6EIM6BQGpphhF7Gbd6gSpxk2Bpg8KADS0BzW6NWe63rIzsKEzyZAGVPcamcADuAWzy87XmxJu/OyLqYqhEk0UZe2ZpbebbEzm93x9NPozSTimKMTa9tD0A4ATZ9bAFbKgkkFuIWDTA5mtf+xpuvPFGHHHEEbjqqqtw1VVXYWJiAvfccw+uuuqqri+Biy66CBMTE/zPxo0bqztIsTZvSfchMjZ9BRjCur1q8yzpZaUoy+U36pczNrZKb3xNr9xdtk1jYwPYyCV6ynUQtjQ2xboyzEmdWGIixVJjSZt+yocz2tpV5wyGW+venSQ+x9bu6ex56iWkzZbOEr2t+zrhXjK9kw8DNr5FxoYBG6eHAzA7X1uGdVFLnChekt7ya2KrS4gBm7JrzYwBI0uDTmVKYADg5O9Mz9J3zNyie/kULVQsmlLU+Pg4TjvtNHzjG9/gf7djxw7ceeed+OpXv4oXvvCFHanWWq2GWq1PiFKgsO29EItd9YiExmaItDBpJdlK6FwAziLULJaiaNTIW1Rr3RN9/rK0By4ELVNZ1w8vOcZ2dvSC10ivRM8FnrZachmgomXfcaE5adgA7G2Aqve1TtwaEE9ZM45jrb1UwlslY2zsCtNRorHxggI0N8LEuAONaYrKkg8Tj9t0xGUsjNtjfpFfZ74udtZtNWfhI9NvjZU+x3kpypLmRMaQEMiBDbU4jJKB9RIRb8HKWQKvrLxaAuQWIhYNsHnOc56D5zznOW1/d9RRR+Hkk0/ua7t3zxCATZRQxEkKz9TjRLk7KcIWi7oP2TJF3Za2BxASfS/xcMFQ2RW0lrMIbKdXI6HV0kzZtWbAxksboJSa+8lwYXoPZgywD9g5oPJLd9UMgNgazsi7k3olH/F8LZWiWPKkJcCGjQFg2jFTd6Y0v7doSbmAMScBjey8t1A4ADs9jPIYsAloiCSlcHsOpisPpltpIcDKsueYtz9bSvSSXZWxUwPSokxoGoyVKxPxuoyxsWUOyDYJZZrEBYhFU4paFCHsbAGKps3uJFoiHrbdgszbzBdCY1MwCd3bvS2Xg+LsYQ/h9b7OgPXExyjsBu2hKUIBbAJEiG0MT+LlRrlSlC0Gg7a1e/feVXNgY5ml6pl8xK6oMLayLGcFSoXptjvu8mRbwiIwz5c6Ce28tyAyNt1FvLV6AeRsnC8TS0fwS4E/yTsBbXUJUQnfHiAf5QB7jseUsXJlwIbPqbIF5HLQvAuWohY1sPmrv/orHHXUUQt9GEUIvhseEku0fZF8eoqHuQ7Cko+N2DEjpb+wBGySCCTNPEuapNa9RdX2urIibWHtDNhYSPRh4TXSC0Syna/17iRZYGNJY5O0nW8JY+Mxt1S73j2kJ7ApnuNWaCfpOYwVKAM2wn1tp9tPrs2cTYW2Bqgo5ROnvV6lqBrrMLRzT0et7Hxl3HCJZ7cTjNkw0JLmAzbKIbWkG6Nc61LyHefvj8BS2Y/5FJWd70LEoilFdYp/+7d/W+hDaA/hpWUr6YllChnGplaBeLh3KYqta0mPILZeekPdd11iCcxGuSAR2Is+Mza0rb29+9pOTdQVpZg/DEAxBDAn4ydjK+klYSNzwy0rgQFFucBaJ5gEc9Lmn2NnXcYKkB5+QQAExiZCw2KJtaemCAVoDmy9t5IQDrLj93oMo3T4UMgQUzYYG643KXcDd/LvwlaXEBf1l4BXpsFJbXkzSWpdGHgNYMfskj+Tg1LUbh7CjWUP2Ag+NjKMjbXSTOE1IluKChN7L2IAIL12mbzdu2XpfLPrHMKTSLYig2GxXODUe9LnbIc5ZJmlKmdsRCBnfr5sp5oNCyzRVHC3ZTu7atYqT3oNSBSe49jSrponT0krgZolEMl31QpMkc3ONwDwgx4OwJZBcwFsyhkb1v7sWNLYcBuGku+YARtqyT9HvtzIGBtL58va+Xt9vwsUA2BjMxwHcLMHypqXjVgiWQCNTWm7d/5iGiIhWjZKb7kgbZbWUPPLTeOsl6LKmDGgLdHbXDvtNSwQ4OdsbVcdyQIb0Z/JHkMVlwA5oHBLdS35q8i44cJx+I4/btlZl+lNHAWAYaPLcKG1PQklqNV6rJ13N9ZIjEbTnElgfkdSwMaymJYn+h7t7YAAMi0N32TvalnGpk4i0E5DnBXD5SzkrleK2mOAzfr163HYYYfh2GOPrXah/KYNSGSn/VnoiurJJPjFTWujNENFjU1PQFW8tKwIPHmylQdydpix7OXW0zuHBfuOLQEMkr/gkrLkI4BmK+U3Gb8gwPrspKIFubxN1LYNvJvvzonf+1onuSeILf8cpuNgLEHXsHxfu5IsAvuObTO+DdRQ7zlVvLgeoQVfl4SNCXHKS1Eu7zK0A2y4IWEvNhCC2NaWID6WK4EFQ4WIO7KgHfN419ugFLVgsXbtWtxxxx3YsGFDtQtVtJtvlSV6wYnXdgtyb/1F8RATG3NmokJYKld66/N1Bqy3PxcsQlnyEbqTLJbfSr2KxPKIxaSXOuUvRLardiw58br8ZVwyIDE/ttRSuYAlz1JXa8aAWmJenXzdnmJpQPCjsm/CKOOmDQChhdlJnLGRcMN184Rsq0uIs3Il9xYXclsC6+z9UVZurIkDOC10ZDHGppcB40LFHgNs+hauCGwsA4yejI2gsbHp60JLGBvXByXZv1sReLK5SSWtz1VNM5cTtBYaG+NrnSZFjV9yV22rO0m+K4rt5m2xgXKdOkAhaq1RCxouSoWXce8kkObsmBX/nCSGi+we9RQYm1Zk3mrOh1qWrpuXZUiKlo3yW5ubdo97y3EQImNXbDA23A1XAtgwM0QfloBNfq3dEsbGtuMxkRHEA6gFNaQ0K/2GLXNzQJ/m59uj622hYgBsbAffzdsFGK0ygCFMuzYGVEkMkmYv1RYJEPQy6yJEcPBsmu+q8/MNJSc/O4TyrgCjSJh4WIWxsVAuEMXSZS9EoQTWV9Bs2deFtW6nbnltniUJK2AujXmnThlzwvQKqUWwDhQsQdcQ7usoMk98TLRczhQV/x41LbBUYsddyUYhyh1zbfi6UK43KdfYFG7LdrqEmGtzr/Z2oGiKsOV47EhqXYjjoJWDSBvfsc98isreWwsQA2BjO8TdvCmVnKZAvpuXdQC20u7d1plULvCkQlkoSkyBjciclDM2gF2mSE5jY7FLSCh1OKWlKEFjY7MrqnTKduHrEkbmu9uiU0eCseH3tQU7AfFa1+SADbUALkQthVfWQSLc14mF5CNfAiu+iyQ0381T2UGnAMKcXYktsAhcSFsyNwko2LOARlbKnCzRlwEbDl6t6cZYx115aTfMRfFRywKwyUt4/oCx2QPCs1iKEm780kRvU3Mi23LNPyOCKjsMRimQcwPLJTARQJYxNqLWxfBaC87SQVBiK2XbGFAQasvMAwPstD8X/hflOz3SJqa1d197JUmA+77YYAOFAatBr04/AHADpMg2EjYs97n7bxlTRAg3tbPh3cMSpwwDGlk0rGOASmZ+EesSqpHIilVFYUjY3WkZqEAQz3RjEt1JIbLvOLQAmpnRn9/Dp2ihYgBsbIfNpCe8iEt3PmwIpg1XWs5eeKgF5d0FVlvNGWNDS4AcIUV3gQ2Bp1gCk2VsbHQJKWl72PBNO4yN9GgDAdzaSD6sLVZmhyluFMLEzn3dpH5vKwGAP8fUCmiWZCEBgBBuuW8sXKaU76pdCa8RVhKy8R2zydWlGxSITrwW2p/5FPVyYBPU7Zqa1iCX6G0bAxai5fLnKeLg1fxa1xhjUx81/l22YwBsbIf4IraU5GPqIIErxdh4JEViamYWMdYk6O1hkwcRWs3Nz7lYu+yFSAVtj3GoJJ825sTW+UowRW4BqGy8iFMObErWJoS3P9vQM/Gdqoz/hc1xDrK+PYBdgafwHQdl66IQvhoDjCTimiK3pPQGADH7jq0Am2Kj4JcM1GQdaDYM6wohrQRjw92WY3M9ZBLDR6Y/C0oSPWdsUjvaHmYlIKN1YaxcYoGVq+WiawYQd6XYY4BNv31srCQfIfF4Duk9cVdIEn7aQmxCrQpTn2VexO0eGJYYGxmAkZ+zYwPYMPEw9UoBldV2b9nRFYD1YZSsNbZJSwTiEDUn5tfa1QE2NpytxWnmZSDSZ6DZJrApH/oJFAwGNTVwE9gmGR0EZ04sAAw+jFLCKM+mEy+foi7jkSQ8T6Hxc1wce1DK2OSbUEuMjYqINyJ2/JmSJEUtH80QDDQ2Cxf997Gx0IaswSIAFnQ2spO9+dqFB0bfNDYAP2c/aSExnXatca0Dm4xNmbM0YN8jSRieVyoQZ4nCtDSTpnDzLhRXAdhYaTUX7+sSgEFsCjzF8mrZdwzBuNA00YvARqJMUQAqc4CR8LbrcmCT2jpfAER22CjAnyeHUPMWdwHw14d7J3rXsuMx78aSKDfaMp4MW004JHvnisZ/u0rsMcCmb8GTXmxNYyNTlgEhRXcSMWxDlvU3YZF36wQWy29SiV4Yq9DPEhh7IXokRWTaJSR2jyg4HttgbFSEluzeMmZsBKAg5VhqU5gu3tcl9xbTQdhmbMqYMaCY+ZOadmSx8y0bcppH4lj6jlGUOmJSfm+x87WhZ+Ktz145oBLBj2mXEOvoyt5bvXWJjFmx5Xjsc9GyRLkx/z5MS1Et4XoFEuv2OwbAxnbYbMltS/ISWpe2JGDO2JS6DrOwWX6T9VZBYd5mxQY+1yVlQzDl2THjrhklhiq/t0iEps0ZVSXD8wDB1dQ0+YidSTL+F35xb9kDrxL3Vg6aXRvAJhLWlWBsUlvsmOw4Fr5uDgasMDY5sJHwk2Ft/8RCa70jOxsLaNPhmAIbluibEs9x4Z9jB9gwrUtpmzmAxGVaOVPGpiiTlppOLkAMgI3t4EneXuuzNHNiqzspVmRs3AoYmzLHUhSi5ZrFVmApECkwHMa7W8GAUUW0bIOxIZG8nww3FTMV07JZPpTAL9nZApgztd7OdyxzXzM2ybWRfETxsARjU5T9TK+1gqYIgo7KwiR17i4t4QDMuxstaOX4CAmZjjtCuOuxaYt72GRdYOX3FgMCniVjwCD/PTIi3kJHZXa+zOCvSf3MpHUXiwGwsR02dRCqzIlvicGQbblmYXOGkcKumml7hiyAyFQAVKXn7Dig+ZA9Y/pcSTxst92bz5iRYGwKd2nTZCuW/EpargG7zxPripIAkeIcISMhPjBHY1P+HPNuP1uMjQxoBkDZGAkLJSEObCTKnPzestCBJj1sNI8Idgzr2M+34MNxeid6l3djmQMbSilnbPwS/xxAAJqmwIb5FEmIwxciBsDGdlj1sRF2XFIAQxirYMJgtGlsZEpRjLGx0DapIqb1Bc2J4bVmL/MQntTullpjMDTavW1NFecOwDJGeYWY1silVTBClLnOojDdnA0UGYySckFQrGta9qNtYF2GAWX6HlNBq9pzXDAn5gCD67ckxMOwaFjHPV1kSlEQfF0sARuZRM+MAQMLbGAcR/BJ9i6oSTA27L1lCl5FA8ZdMQbAxnaIO0xLXRzyzImlxNc22VuBsSE2WnJ1258Nk0+kwBQJa7s0NOvIUmHl2kTL5ru9YsZMeRJw/CLRm5U5FZM8sxKwUtqVZ+VcEdgYgkjWgSJtn8CFy6bCdPFZkm8CIFZKUWxmk3yZ0wqw4YaEksDGsePrEueakwgKwMYCYyNO6S5rMwfEDjTD880N/mTa+Rci9hhgszA+Nn1sfRbXtpR81DU2FhkbqbZre+Mr2PC8xAngllDJc9c2YhLapqjLATnAglFeEsOh+UBLKWBjqeMuVvALAioZXyFzXxMBrJsCGzaGQrYkZGuWEPPBUWVsbHSCcTZQwU/GseDr4qbMSkAO2MR5Yk5jM8aGgddIgqFiXUQ+SZDGZuAmbBTApiYBbPj3YcgGJnl7/ADYLHD0z8fGUmcS0LbjUjHKM04CXIugxl7Y0dioMBiiUNvOtZZ5EQMW52MJTFFdEsgBFpxDheRFJGj7tmGUVhgbWUF8sa61rigZrUsb+2m2LvuuZMXDtjx0GKCS9c9hLdJWWtyZUZ6MMJ0JtS0AG976LMnYJPlQSHPGhrW3SwAbAYCEhiUw9vMRdeF48mJ80xI6u7dkznchYo8BNn0Lq+JhRebEFlukmnwqOGe5LiGLmhOFHSZQJJ+AxFYYGylWznGRkkxwa0u0DBSgpWfYKvuplBqFdYdIiFYU668LcehnIAEii/M1vbdSYTdfZoQIFN+HaaLnTJHkc1zoqGxMcJdvu3b9LNG7FtYtZmPJeavY6hJi7dOxBGMjamFCQ2PAKAdkESSE+BDH0JjdW7ydX0ZDtQAxADa2QzToszaMUpY5EV2PLe2qpWrzFmcY6WpsDNflegZJYGMNzKk4HkNsybXTZh5RF0EgY2bGvmPTjjs9jQ0AxKHhyzhkpRl5xsZGmzlLmomEWR0gtJobGrjFTUHbI8UU5VoXC8ZxhZ9M+Tk7vP3ZAmOT61akPJIAazPQikRffr6e5yOi2f0n+sHoBBM9tySZkwK82gJyku/LPscA2NgOtzBRMxbSCsMo5UpRwi7TWvKRAFSuxTZkkcGQnbJtoQRGFKjzbG1L5TeBoZJhMCif2WSvG0vNI8lSKUrSdLJNV2QI5riIV8UzyIIxYMpHV8glH1uzhNhYg4iUj8wAiqRnoyREUuYALMHYMGBjCqgo5YJcvyZXikotPU+MDUwkEj0hBGHOsIRNQ8djxgZKdicVZU6za83mzMmMzFiIGAAb2yFqL/oppAXsdWQp+H3MXdeeQZ+ELkAsvRlea/agy7yIs7WZw7ShOaBiaYZ5jRibmSkyRW1soAmQS4R2b0lhOkWWlFNDPQLblbdINlS2Z1jUjbGkKZP0gKKMYsrYpAqCVgBw8+/YdF1AeJ4kypzsfI2deJMIDrIORZnxAkDRjm7KgLL5WjKGhEDRFm48yoGVoiQZG17mNBamK7TzL0AMgI3tqMygT1VjY2e6t0rSy+Zj2Su/yZaijMsFSQxC8+NWZWxMmTlxVpSCfw6MGRsR2CgKxC2UOUNZjQ0hHBCYDmekTPDo1MsZDIvPMUuassCGCV8DREbmgAzYyK7rWJxh5CowNp41YFM8E7Lzi1JLLs+piiEhIDgem5WieDcWkWRsLLFy/J6WLd33OQbAxnZU4cJLfdQkauTWSjPCjBm5coHNJKDgAGztfIvdGvE1NDZW9Exq88DMHYBZ27UsaC50VGZlTkWmCAXdTY13mfmuWsEN10p3o2LSc/MpzTWYgWZeApMFNvm971qw+ucOwBLPk5/POApoaGj+KAAbCbM6QNwo2GFAZZsPGMOSGIqHE8XuJNeSfouxkHTA2OwhUYmQNlAbRmn6MhanAis4pQYWBxXKDJMTz9eoHCTUm0mfNTa8PEIlNEUAv7/sjTZQc7W2BuRkNTYohjOaTrtWYk7E59hSE4AssGGMjWk5mzM20uvmjI0FR1zuACxRivLrxcw3EyDHknxIXdRk5pBB9HWx8zylku8P7nhsKlrOBfWyIl7X1neseE/3O/YYYNN3g75cb2K2A9HX2NgwUVMHVJbLb7KMjaX29oi6CCRfiLZ0RWxXLVtuLFxa7exu5UtRosbGjqZIShAPe26pBXOi2N5uCazL7uZtewbJa3uyz/mmzAmKcpYrURJiTrymm8GopdhsAVjbKKi0twNAbMk/J+Xfsdx7i+uZTAXijKGS1ST2OfYYYNM/g74i4QGwor+QN+izpbFRBVTFdG+j3S2lfO2YBPDLym+WdR8qyZa39Rtea0bpyl5rIhrWWbq35Oz2LTFUfLxAIMdQQaC7jUcMZGtLAQyLgnjtjjtDwK40iBKAl5fAAkSITcaEQBhtIMPYBHbYQNY6rVLmLOZymQIbNfAa81EOhoJ41p0kXYqyo2fic8xk7+k+xx4DbPoWQnkEgKXWWA2jPAudOsrGgKbJNo1BaPbzUiUha14y2XcVwpNjLyyuTQVKV6Ul19htmXUnqXokGQK5JFJnbDggMOxcYbtqqmxIaMdKQHY3b280CtN9yK3rc9FybMxSFQ7A8gNWTUFzzAczeuVdbywszanic9ckv2PmaWTK2PA2c8Vyozmwya/XoBRlHvfeey/+4R/+AU95ylPwtKc9DW9961uxdevWhT6s9uA7+QQEqTWX1r6ONmCdK1Qy0bNZUcRwVpSYuGReEKLuw5LTsipjY2ttqfIIAEfoQLPheBxKs3J2dB+JoCmSvtZcB2FnlymV6FnCIxSRobZHxaxO/JzpBoXkDFUqmWxZ0gtMWaokhovs56XartueY4NSFNPYQM7hGWifWm8SPNHLzqiyZAyYxvLDRgFhTpXhAE7V0lu/Y9EAmyRJcOaZZ+KQQw7B5z//eVx88cW46aabcOqpp6LVsjDbxFZ4BSVo3P6sXBKyJKbVbTM3FP+12fyrMDampbc29kIt2dYQGiUBEqlR2MTabl64t2S+Y0u76sKx1JcbNoqCsTHeVefnLOOtIr6wTcsFjjZjY+YZRBQBFetgMgbrwvckB2xybQ9J0DR4lxeeLpI6OQjAJjVL9K6CWBoo/G6oYZs53xhJdid5tREAQM2QseEMleT59jvkBkzsAuG6Lm6//Xa4bsEgXHrppTj44INx880346STTlrAoxNCeHn1XWjJdvPEFqCSLUUJ072tuPB68H2JW7MNyFlgqOApiw5rJMKkEajSdzw2Y2yKe2tEgQ009Qzi1LnC8DxiqXOFu6368skWMC8XuApmdeLapoCd2earrmvOvBbfky8zjFJ4Z5oY1ukMZmQbKFNflyLRS45y4I7HZqAZqoyN0IEGSgFJZmtusHbxXRXYLBrGBkAbqAEyFqfT3y9oOB5AsstqszVWvRRlrvvov3mb6oBEWxobdd2HrXNW11+wUpS9UQ5K+i3DZJsqagIAAL4lxoabxkmsTQhPkKlh8mGzl6RYSMBambNgiuSSrb3Ot6LLsBbITJwurktkMGIg0WBs+FwuwzJn4dsj9xwzB3FzxkbNP4cBG5dQxJH+OasyVP2ORcPYdIr3vOc9ePzjH4/jjjuu62darVZbqWpycrLagyIkezFFsxbakMW26z5O2RZLMzLrugWVHMcGlK526c0OoAplgRzQ3jWT2Eg+Grt5o3NWHG1gS0yruMMELA1npJR7q8juMhMngJeExnOEVJOeLY2N8pgQXl61N7Fe6nlyXETw4CM2cuJNFMcLAIDjM18Xs++YtU87MgwVCm8mUwsD1XJjkJshAkCrOQsv0BP/Kt/TfY5FxdiI8Z73vAfXXXcdrrzyyp7TidetW4fx8XH+Z82aNdUfnK1WUQ5sPKnpvO0CT83kQylvXdSZwJwa7ALaS2DyjI1HUkQ21lXR2NgAVWnCa/s6jsc22r1DeJJeRba6wNSBDUs+Rrtq4Wdd5XKBQfKhVKn1GYA1EOmolgssO5ertF2z2UmxQdkvVRhEycK1NEai+I4lHY8tlVdVu5NqgiNzaFD28xSBXL9jUQKbD33oQ/jEJz6B73//+3jqU5/a87MXXXQRJiYm+J+NGzdWf4Bcj2CvRKJqe6+9rpAAQviSgKp4qIyGybHzlbb5Lx4qK+uq+F/YuNYCDU2kywV2upPUh2Da6VxRNasDClGrkxoYxwn3h/Sumgs8De6tNAbJBzM6srtjJmg17MhSTj623JZVGRsUupioqc/YFLOx5EtRDGx6hmMkGLCRHb7JjO2IoYWBKuPruC5CmhVqWgbXmp2vIwnk+h2LrhT14Q9/GOvWrcP3vvc9nHjiiaWfr9VqqNX63Gtvq1adCPN8lLUumi8m4UGjnpy3ChwPlDggNDUzulJuQRYAlUm5gF1nXY2N7u5WTLayu2q3EGqblMB0NTY+SYzYMd4mqgRsmHdPxlJJlwvFUBW0omCVzEBz8bOyu3lbYlpWLpBfV9C6mAimhQ3KsMwGBcLsJAM9E2t9Zh4xMsHGV/gwY2wK3x61sp+5hQETxMufcxMBAsRG9xZjuGR8ihYiFhVj85GPfATr1q3D97//fZx88skLfTjdw4ZzaJoAaQxAvSvKaFfd1nItWasmpHhQY5OSkKKI13GR5rszGhsIPE0YG5NyoyCy9KVHOQj3lrWWfnnQDBh2Cal2gUFsQzYwjmMzyKjk+cLSJHXheXClk17x3MUGreYs+UgzNq4dYJMI7tKyzxP3dTEqReXARgE0M4YlMGRsAgZs6sMln8yC2BLEc2NA+XPmZb+WPmPj59fLqw1KUUaxfft2XHTRRQCAV7/61TjggAP4nyuvvHKBj25O2BD/CQBD3UTNBNiICUCe0GNJwKMtJLp27BoUNi9pmHQXCBob5ZEKFq61NLgArGls2KRsVfEwYNYl5GgwNoxxMPIMUhVLo7i3uH281ro5C0ld+eeJEPPpz2kCD9nGyJfdVQvJ0QRQMVCk8hwzXYwJsCnMLuXFw2xOVQCz+VhBzvhIX+vcJNIU2Oh0J0XINlEmjA0z+GNjOHa1WDSlqKVLl+K+++7r+G8rV67s89GUhEWAAaiLeH2S6LfyaSQAAMWE77yjYijQLxeoiXhrQDRtVqvmIxUkPV0A7t1jQ2OjxhQVgGrSaPJzEy4Uym+Og9Tx4aSRkZjWUXRoBYrdqJHVv6owHeDPk1F5VafMiWxas5+E+iBSAPrSTBEhiODDR2Qk4mWjDVTsEziwMbi3uDBd0qwOEBgbxPplziSGlzstB3U5YMME3ab+OS5vPlAANk4ApEBiAGwCGgIE8HdRxmbRABvHcXDAAQcs9GHIBddBRAh1S1F57TShBAlcpSGYQFZ7TVIq7e7KQ9Wcj603x7VUD9ior8131TYYG1mxNNDutmyBsZEaRAm0s4EGjE0aZcCmRX3pYZSpW8u6uAxAJPOSURqeZ0PUqipMR8FCmt1bGuAVWas5EoNEL3xHKskndgL4aWRUbmRsTwR5d+miA02/PKIjTA9qghg/1tVvFddKbKfuFcUoB9NurOz+ku64Q6FnMmHlgpyx8SXF0v2ORVOKWlRhY8q2kOQBKHcnaYtauaeLwkBIFO6wZqUZRd0HihcESVr6VHIisFTSAMOGeDg73yZVZxFMO1dEE0bflUs+vEXbCNgwbxWFF6JgSqhdflO1MEDh/+KY7Kp1PJKQAxuYAJts3Zg6CBS8SuLc3M4KsFHwk2Esi4lhHR9yqjC/yMZkcVFcHkhqbBzO2BgCG1UdFYoONN3vOElSPuTZlwRy/Y49BtisX78ehx12GI499tjqF7Mi4hUnTjuS3UkuaC6m1X5QRU8X2SQPtIE5GwyGsp8MMU960u3tgJ3vOCooe3X/HLO5XKycJDtVHLDDjjEvGkehi8OOZk1d98GutZEOQqe8CgseOjrPEuwMZ2QJU2W0gQ3QXHi6KIzryPVbdaLPrjMg16IeapJNAKw86BrObHJzEa8KYxPnZT/dDrQwDOGSbBMpC+T6HXsMsFm7di3uuOMObNiwofrFLLYCK9n8QxiSqMsWaZaiinlR5gyGShLgLyaTwZ8G4uEaiRGGsea6YplCMtkK7d42uqIShSTAS526wCaJ4SC7N5QcS22zgZLfsZVddSIyoPLPk7GHjs69hWKGV2rQCcYEwLGC1oV3oJkwNqysozJxWmC5W5pC7bApbFAkN4MMiPiGjE3RZi7PgMZcqK0HbET/m5qkpqjfsccAm76GDVfa/CGV9rDhaxu6h4plGaV17QmmVcDcXG2P3rrsnBXKb6KHju6OXgSRWiUwc2BDXZUkwMp+5roPR8X/wmJrfYvKX2sObCwwNqriYWrKYOjcWyg6iowYm4gZ5SkAGze/H2wwNir6LbHFXVNMGzZnAKiB5sIY0AzYBKr+ORDKfprfcSi0iQ98bPak4DoIA4M+TSq5feK1CWOj2hUlTvg23VXLa06IDRApJAFVxgYwMAfU7QKDYckPABg40WBstBO9sBtXmlFjY2q9OGBV8t7iwMYk+WgyJ8Y2BsK9JXu+gB2tC9UYbcAM5ky6G9l9qVPmBPSBDfu5EIF0WZd1Y/mGwMbXEPGysp8ueGWDSlvU154OXnUMgE0VISRb/R2mKDpUATaGDAZbl0rOEOLrCiUwKzoIdY1NX9uuc7fl7Odt6CDUdB+m07250FJlGCXr5NAV0wqeLr4nb3vfNkbCimeQJGOT74IDGiLW1TOJ7uEKzElRmrFwbymsa2M+VjHBXQU0m7fWk1SjFEUIQubrojligLW3hwpTxW0Bm4Ab5akDG13wGuWMjcr59jsGwKaKsDFMTtWFl6+98Bob484VlSRg4VrTRABzsudMiGDgZrirVrnWzD/HcMAq0XAAJoIuQCvRJ8L5qgjTxTESVsCrHIh0c/MxG07eSlYCQFH2M2VsFDdGlDE2BgCj8JNRuLcsCLV1zOqAwok30QRzRXu7gn9OXsJhjItu8LZrhZKQqVCbGTCGCufb7xgAmyrChg5CFB0qMSeGHSSaL0Q7c6o0aHsLu3m2O1UybwN4fV4/+aiLDm1pbJh/BlHY3Yozm/RAs15ZxqoYX6Hs54qtwMbMq6fYZcgs93WNNjXYQNh18laZ4E4s6Jl467NKKQoFIIk0xcPMzDBSmFHF2qRNRjnEUQSfZM9DoMDYmA7gZKMYogFjs4eFTVda6qOmsdOrIUJTB2BovhBFU8K+6ooEIKd1vih2mOrsWJ580hZSnTESbRobNSCXDaPUfClSqjwVGCgm+Wonet5W7yle5/zeslZuVNPYmMx8S6PinlZhbBjgJKmm10hY6CCUGBsbpoSRepmT3VuOQZcQc+FVZWxix8y7hyd6BbG0aAwITf+tUOhq8hW6k0yF6QWQGzA2Cx799bGxoINoM6vT0dhoMhisQ2hBfGw0AIYFjQ0T/yonXL8AkVrlNwMgBxh0rqQxSG4B7yiIeNmuuo7QSL+lmmztaNZ0OtDMu7FYeSNUmQcGkcHQS/RxpHG+QMFCGo2RyNamSn4yeZeQgRkid+FV7NSJDSeLpxq+PUzs6xKqPf4mbBTHW1NxAObdjXrXmoFmlfPtd+wxwKa/Pjb2hmBql4R0d5na3Vj2JjC3dJx4LXRFxSRQGkFh7hmkobERdsHUQts1UWr3FtmxPuq3LHTcicyJjhmi7rqMBWhRRcbGsDQTtzSZVxt+MhoOwNywzgDYsInTysCGTxbXAzY67e3iTKlQc8p2lB9vQgk8XwFEMqZZ8zseAJs9NaxqbPTKI6blAt0XojWWSjn5GKyr4ViarW3agSZ2rsga9HlISfZZGpq3XbtKbdemoNlUvxVq67faSzP9A80iYyM7ugIQzQE1k0/ExhrIz2sCIJRX9UtChQOw+gR3z2BdT8PTBRBMCTUTvU57u6iJYQZ/qhE2i42CUtu1YXcj2ySoGDD2O5SHYP75z3/Gtddei1tvvRU7duzA+Pg4nvSkJ+E5z3kOjjjiiCqOcfGFFUMxsVNHU2ippbEpks+YxnTvGiJM97El1874iryLQ+FFDIgeOqHR+IpsVpSKiVoNTjxbADLldVlJyIPvKbwCjIXphqCZJGjFei7PRoyNgcYmEVx4ZT1OgEJzomvgVow1UL2nC92YbjD9lsrEaRvtz7z1WZGxMZ3LxUpRicL7w/M8hNRDQGKEmqLlKCzarlUGG3A9k+b7g5/vLgxspN+mN954I5797Gfj0EMPxac//Wls3boVo6Oj2LlzJ770pS/hqKOOwtOf/nRce+21VR7v4gj+QtTUIgAGu1uhXGDC2ChrbGyIhw26ogzMELlQUsX/AhBYqlhPY6OTbCG05GobA+oCjGJ8hbF+S+OeBoBEk6USd5mOLINhATQzYXriqHWQsNKMLoPByiqqu2obU6cLYKPA2OSt9SbAxof6eAFA8HXRBDZUowsMQOGfo1mKYv45EdTuLWLIBhY+RWrn28+Q2q5ddtllePe73403vvGNuPzyy7HvvvvO+8yjjz6Kr371q3jTm96E888/H29729usH+yiCRssgnYpSkj0xu3emgZ9fWzJFa/1Vs0yBUnVuziytUV2zJDBUBCWUq8GhIC+eZtg/qgjTLeg31qqwQYC+l4j7GWcqiR6C2XOVMeFFwWwCZB5BnkqnZEorpPqrpq1SpvMx9KZ4M4Ym4CGoJQqsVsAgCSGlwvi/braBsV4AKcusCE+gAYHKMrLakxRBwQ2UPM75kBO8Z7uZ0gBm+OPPx533XUX6j1umL333htvetOb8IY3vAH33nuvtQNclGFlbpI5YzOhNStKQ9AKWDFRo3ELRHVt02tNabE7VZkxI3xeN9EX56vI2LjM48ScsdExjTMtvYXKVgI+KAgIKFLNzhVxmrl0iJPUDRkbJUAFwJtjDqgKbKgOkIOdwZ8O95ORBxjMYC5AhDilSnokAG1lWRWzOsDciZfd16obI2ZwF2mKlnXbrgs20KyUrQrk+hlST8uBBx7YE9SI4XkeDj74YKODWvRh0axOfQimYaIXDcV0BZ6GGpumTru37rUWKXdF/wvT1nqu+9BsfzbX2OhaCVgw6FNZlxBBB6Ep8NTZVbcBVzMrAZXW52xps+c41QFysDOckRvlKYh4mQ9LXbekLICSQHHiNBv8CcOZb6qlbAZIYk1gU7SZ97fMqbVJ6HNodUV98pOfxG9+85u2v7v77rvxwQ9+0MpBLfpwLRr0GXVFGZQLqFp5RNSb2GlxV9XYmHWBAYVwUjoM/VVom8ZG5Vpn95cNV9rAVVi3zaDP7N5SYoogTiQ2Sz5Ku2obA1YTvSTA2I66rk5Ps1zg+GZJL/vZfLSBwvPEuoQCTaNNmjN5MXVQCxRFrey70dwoEE3Ghjn3JpriYVZuVG27NhZqa55vP0MZ2PzhD3/ApZdeiqc85Sltf3/QQQfhZz/7GW644QZrB2czFsqgL04pEh1X2sSQOSG6XiOapShx6rSOkJbStlKFNBVtyhSJrc+eSbu3BrARfF1UqHfjuTo5INI1fzTdVSuvC2FXrVkuICaMjckcslwwravfCjRBFdUsF7BWac/A6p+xPSp+MsTQ1ToUfHuUNoIA/5513ZZ5e7uq43HesaarG0s02649Q6E2P1/VjWAfQxnY3HjjjTjuuOM6iruOP/54/OxnP7NyYLZjoQz6AOjV500Bhnai1+vUYbsebR+bNAah+fF6NXnxoKVp5i3qI/AV3Q9MBdP5LjN1Fc5XWNdJM6GlcrRpXfo3D4y23dMKTBFEHYSmwFNjhISNkrLubt4UNPN1FZMPAyM+DfU2ZCjYHlfFT8bwWoctYe6aIrChrtlGQWc8CVB0yiWapSgd/xxAEGrDFNgolu77GMrAZunSpbjjjjs6/tttt92GsbEx44Na9CE8pAA1SriZzX8/fWyE3byG14i2d4+YsJTccIvzNWOo1F+I5ues7tAKFJ0rxloX2l/zR2Yap7OrZi3uuowNd1lVSfTM04VQRJq294QL01XZQMOOLF56U7u3GGMTEM0mAEr5xGnGDMgtzDYJMVqhOlsUc2ATKJc5WVs60RTTMndo9RlVhv45HNioaWy4UFuTldN6lvocysDmjDPOwB/+8AdceOGFmJiYAADMzMzgIx/5CL773e/i+c9/vu1jXHwhvBB9JGbMicFcHeN1NcoU2j42QsJS0rq0lUfMWpDVKWzTMlj+QlM1BhSGM5rPqFIHzbrfMTONy0wnFYGNoWCaaJjGiTtS3V21jguvuLY+Y8PKI3qlKO1OMOE59pTmFxXHGWoMo2SdRRE85VZxbkqoy9ikGvcWCqZFF9joiniZUFuXsdE9336GsvPw8uXL8fWvfx1/+7d/i49+9KMYHx/H5OQkRkZG8N///d94/OMfX8VxLq4QXojarbH5Tq//XiOCx4mmxsbI04V6CAIVN1xDgWdiztgEiDGrwY6xpKfO2Mxpu1Z9v2gL081Kb+wFHhIfnorNP1CMu4gNX8Yq11roZNIdkEhsWAlo3Ne6OgiX31tx/h2rsQEi8+rX9EBk2FQ3rItyxibUmF9kakrIjO5UGRvTTj/edq1YiqrVMiYtIAmSOIar4j6O4p5Wepb6HMrABgBOP/103H///fjRj36EzZs3Y+XKlTjllFOwbNky28e3OEN4mdiYI6TnNaJXmqFxU/BWUfEaEbqitFgEIdkqna+9sow6sCkS/Q6NtR3N5EM4c6LpeCxoXUY0gE1dE6yLmgDVXTUDf7q7ajYlW2mXSQgiUoNPW7y1VjV0xgsAmMMGqr8/CiCn1vrMjlObec2vc0oJAhWNjeshgQMXqZZhHWMDI6gDG+7dQ/XuraK9Xdc/R5Ox4eVGtXMOhooSYas1i2FvidLPM4+j3YqxYTE6OoqzzjoLW7ZswcqVK+GqtI3u7kFIluiTlkHCFTtX9LQuxuJhXY8TLW2PWXkkW1djjlAbQ6V4D5tobCgtkrTqC4LZCRhe65B6WK49rkOfsVEVOwIAyTUqRAfYUKq/q3YD+HFLu1zAzep0GRvN59jhQE5xXbdgioxGsqi+twCEpIYhqufEm2h6ugDiJHU9zYmf31uqoxyosX+OXimqbQBno4HhEVVgkz9LisNG+xlaPjZ33nknnv/852NoaAiPecxjMDQ0hNNPPx233nqr5cNbxGHJX0V3ro7uTk+bwRA0Nibi4RYCLUDlEIpEp0zB2QtPXWPjitda8ZwF2luZ0jWdj2VaijJ0Hk5Vp6hDaHHXEXgmEQiyDh/VlzEDYVSzFMXn8WgyNnWiB9h1gZy1LkONln4Tw7pYczYWIEwW12VsqEYXGMxHObCSkGrnm+cHiGgGOkONOVW8620XZmyUgc3WrVtxwgknoNFo4IorrsDNN9+Mq666CkuWLMGznvUs3HfffVUcp3H01ccG4F0Q2i8IrrFRTLgmtfk0BUmzXYt2CYzECA2YE2VA5Re7D61dtQCoVLspjJKAkCjVyxRF2c8YROqIh0mCMFLf3ep6qwCiwFMHvBb3hWqiL4wB9ZKPmz9PriZjAwBRSz3hunysgRqLYGuDEqq+P1AAGx2hNnv2VccLAOZOvD7V6AKDYAFgKIjXabs2GcDJgZzqvdXHUC5Ffec738GBBx6Ia665Bo5T3Lhnn302zjrrLHz1q1/FRRddZPUgbcTatWuxdu1aTE5OYnx8vPoFLXXMqPvYGLSJig+YV1fTQQi78FSLORG9VVS0PcW6WrVqBiA1OnVEVk45CbAkTwm8PhsDare4C6BAy1RMx/03D2Iyw0js1FF8GRe7ak1tDwcYqsCmOE4dBkPLSwawq1lTLEXFTgAkmsAmL0WpzsYCik4wX7P9mRndeSpiaRS6MaLL2OQ/RzSep5AEGEETYVP9WrPzdVW63vocyoyN53l48pOf3AZqWBx55JEDrQ0L0xEDccHY6PrJKK/bNl5Az3cDALeRV1tbM9kSwpMPMWJsTNq9NZJAmxZB1RjQ0D8n0WTHhBeoDoNBDIANAwY+jRCrCqZ1x4RAOFad5JMmcJFtLlRceLMf8JEi21jodGSxsor6ugIbaDDaQKfLMGGMjca9leb3luo0c0AwJdRsf2Zt00FNjbFh15podmMx/ZZqSz9QMDY6oNnP1/V2J43N8ccfj+uvvx4PPfRQ29/v2LED3/jGN3DSSSdZO7hO0Wg0cPXVV+OSSy7BjTfeWOlaRmHqSrsQPjbs5UCJ+ngBVxDt6exuDUSH3IRMJ/lYMujTvdY6WoR2jY2Z+aMaO+YhJRkI0wI2OeDVAzYG3j3Cta6r3lueAWMjjutQLTcSwmcAxaqzhCjl7IMuY+MQijBUP+fIwAHYRM/EfkZHmF7MTtJgbNIUAeL896gBG8ZCagniIQjEdUpR+TgHHaE2A4Cq59vPUC5Fbdq0CWNjYzj44INx5plnYp999sGWLVvwve99D8uWLcPVV1+Nq6++GgBw4okn4rnPfa61g928eTNOOukkBEGAo446Cu95z3vwvOc9D5deeqm1NayFyWiDNAXy2ryu7b1PEiRJhDSlcGQ9Q9oEvIrMGyGgXh0kboLELVBK1UpZohuujtYl1HxBCF1RSg7PgFlLLp9krlhqBKxqbFRZqtQN4MSxJrDR1wS4YhtylGJYBXfrjgmBKWgufkYZYCBnH5KWOmMjlt5UGRtR26NplBdAo7sRQJID3lQDUBX6LXXGxmduywg13lvFNVJlbEyNAV3e0q8O5mISAFQP2AQ0AkjhYLwrhjKw2bx5M1atWoVVq1Zh27Zt2LZtGwDwoZji1G/bZn0XXnghhoaGcPPNN6Ner+MPf/gDjj76aLzgBS/A//f//X9W1zIOk8nPwo2uO9oAyAWASYq6I/nzbeMUNBrm3ACIm5kde5KqHbduVxTAz1mL0tVlxoR1tezn28TSioDKLZiiKc2p4oVXkSqwqQPxrFai1/Z0gWhK2G92zEC0nP9MQgmCQCP5ODUgmVL30BG+G1Xdh1hu1NG6iKMNVAa7Ama+LibCdL9WDODUfW8BQDCk5xmkpRuDqN9Sf54iJwBSvTInK7359V23FKUMbF784hfjxS9+cRXH0jPSNMU3vvENfPCDH0Q9v6BHHHEEnvnMZ+JrX/vaLghszMsUAGMS9HQQmUlfIk+/63rJsPDqQGuSgzm1F4RJSShnqdIQUZLCV2F8hEnXSmZ1wrp637E+ZS8yRds0gE0aNeFCY1YUijIS0dBRObouvMLPaHXrtIFXPVZO53xNmDGg0Isos2OCMD1Q1V84DmJ48BAj1mBsEt6d5CubMHJQotNarztsFO3ApqX43orDBjwAMXVQC9TYIsdjwMZQmK7BBrK2eFXwmqSUD3f2d+FSlPLTdv3112NycrLjvz344IO45JJLjA+qUzzwwAOYnp7GIYcc0vb3hxxySNehnADQarUwOTnZ9qcvYaKxEV5MEVxFYOMBToZXlRMuK8tQT31nC/AWdy3XUgNQRfJOFy1fF91J10B7S7+yUNucRdDVb1EDEMnHP+gwNiaOpSat9bodhhB31TplTrEBQP150mYwhGeprjKeJI/IYDhjzI3y1EtC1KADzUSY7vNp1+rPMesq0tFvkcCMsWFt1zqMDRNqq7KBYRjCI9k1Cnanrqg///nPOPvss9Fstl+QBx98ECeffDJ27Nhh7eDEmJqaApBNFxdj2bJl/N86xbp16zA+Ps7/rFmzppLjmxcm3UlJIe70XQeu6lwdEVSprG2QAIBCxGZULtAoCRGxTKHayaFrVgdY0dgoe8kA7R13mowNkLm0eprePUQ1+VAKj5vGaTA2blH2MypFqd5bFvxztO4tCMBGk7HRLSknuXtvosHYsESp4ydj1IHGh43qmz/qmCGyuVZNDR8s17AUVRjlqQMMrmdSvNat5gz/71p9NwI2559/PggheOlLX4okyV7mGzduxMknn4xjjz0W73jHO6wfJAAMD2e011wQMzk5yf+tU1x00UWYmJjgfzZu3FjJ8c0LE1da3blJLHR3t20vRI1SFE8+BuUCDQaDWCj7hVplimxdl1DEkeLLyWhGlR2vEZ0OEgbmlBO98HmdHaZZaVe/486IseEeSXoAQ9tDx0AsDeTaHugxNqy0odN2XZT9NBgbPlBWv8wJqE8WZwZ3IXz5Jo08WJs5Y15Uw2PGgKo6KggdaKqMjSA2Vham9zGU7/parYZvf/vbePDBB/F3f/d3uP/++3HyySfjuOOOw+WXX16Zj81jH/tY1Go13HvvvW1/f++99+Kggw7qebxLlixp+9OXMKLOhflFqt1JgL45oOEL0cY56zkAsx2XIYjUZGyy36NXLtDritL8fuesrZMEiknI+oJWLcdSQWOjfW9pAAzHyBjQTLNWMBh6XVFamiIUjI3O1OliHpgOsGFsoIl+Swc0Fz8TKRrWRTmQCzWGb7rcGFDX8VifsUk17y12fSLqArJNKQsQWrOilixZgmuvvRY33XQTDj/8cDz96U/HZZddVqk5n+/7eO5zn4srrrgCaZq9zB944AH85Cc/wfOf//zK1tUOk1lRhlRy27BCldKMaNymBagM2pANdtV29Bca11qs55vsqjXPV6sbCyg0XFrDKAsGg1KqvCYAeDqlKAtdhjrfMd9Vp6Ha+QJzrAT0n2Plsp9JhyGKpKdapgDaJ7grBwPNGiCSd9zpMDZC+SpSFNOyLjCd0ptnCGx4d1JN/ZwpL3Oq3VtxmDFULY3z7WdIKctuvvlm/PCHP5z39yeeeCKuuuoqPPGJT8S6desAAM94xjNw6qmn2j3KPD760Y/i+OOPx1//9V/jaU97Gq644gqceOKJePnLX17JekZhkuQFgKH3QtQEVdYAlb6IV680UyS9prKeiQk8NdZ1HKROkL2IVZNPZA6odOeQcapfA2AQwU9GqTWWMVTUR6ADmvPkE5AI0wYbBVWBJ+s4qSHUaAUWjRDVnyfmoaNcmhHOd6lRN5Y+Y6M1D4yzgerrFtPMNRgbQjIQiFCZsTEDNpmEItAc5cD8ZHSM8grjScVSVLNottiVQwrY/OUvf8F3v/vdjv928MEH45prruH/e3x8vDJgc9BBB+G2227D//zP/+CRRx7B+9//frzsZS/bNcc4mJQLTDp1AAONjeG6osDTpEvIpO1aWTxcACrtXXUYgionn2LdMU1tj+5IBZ4odRyAA+Faq7TGmnokWRlfoV72YzoCLQsDgSlSthIAQHzWWq92b9G4IfgUqb8bmcmd1uw1NsFdoxTF2UCN1vrCrE7PWyUiPmo0VB7nwEYSRBrny3xg9Ec5sLZr9VIUN55UvLf4+e4OjM3LX/7yXYYVWbVqFd7ylrcs9GGUR1tXlGqyZUlA0fKery0mel3GRr8UlRldmZSENBO9ocZGSwfh1YBwSqNcUKy7ss8amwLYqCeBwigvzO4t2V9h0gUGCFYChmaIioyNK4xyaMUpxpTWDYt1DZ5jVQYjDpvw2boapSjKGBuDMRKpxr3Fyn46eiYnd2rX8XQBgAgBgBllJ96Ut7drjHLIz1eHsUmTBAHJOri0gI2mP9NiATZaGptBSISRxsbM2EssCTU1GBvdF6LZAE4DXxe/2FWrXmsqlAu0rrVbJB81zUnxHauWRwqNTYJIsT0VlMJliVLDDZd44rVW77jTvs4GrfXUoOxHjByP9Tv9xLVdDWDD1q0biJaVwTrAv2cdYbpj0IHGh37qlKIARA4bCqmW6NPcTDDWYWxqRZs5TRX9cwQApuMnw5gtR/E7TnYnYHPllVfi8ssv56LdbkEpxdVXX43Pf/7zVg5uUYeJoJW3ierV5vV9bOyJlvU1Nvqzk3SudZH09Lx7CpO+UG04Y36tmwYGfYDGJGSxTVtjV63dgWaioQIEjY16mTMxmDhtUuZk300IT8u2gTnTOoqJ3mSsAVCAEi3GxqDt2qT92TNw4QUKQ0HV54l5/eh0gQX1Ef7fkeJ8rJYwGLVW13AA9vXmVCUtxlDt2sBGqhR1xBFH4O/+7u/wrne9C694xStw4okn4olPfCLGx8cxNTWFu+++Gz/72c9wxRVXYHR0FF/4wheqPm7lWL9+PdavX8+9dyoPK5qAPgMMoeW6/z425hqbOiuPKIQpY0PmlCpUxbR6QK54eeuatwGaSUCXlTPs1GnrilKc7p2ETXgwLHNqPMcJG12hec7s+/EUSzOsXBBrjDUAwJ9jolES4iyPQSnK11jXpPUZKIBJqtgVRbmmSB3I1QSmpdWcRaBgeMf8c1JK4PvqIMPRFGonfIr6bgBsDj30UNx444347ne/i//8z//EJz7xiTbnYd/3ccIJJ2DdunV40YtetEuKedeuXYu1a9dicnIS4+Pj1S8olIN0k7x+m6gIqvTKBeYCz4XQ2ERqpTdh3RA+PFWHZ8xxW9bSnGicr+OBwgFBilRT2wMArpaZmdm9lZlOmlgJqJc508iAweDsp7qeie3mQ6rH2LAkrao5YevGOi3XQDH4U4Ox4YnS66+vCzer02RsEs0xEry9XUOIXxOM9TKgskL6Z6MW88/xUHcMypyKbCB3Lde9t/oU0oNECCE466yzcNZZZ6HVauGuu+7Cjh07sGTJEjzxiU/s6f67R0bbPJ/+ClrNd9U+lhjNiuqv7b2YbCc0GZvUrWntbokuk2DCyhGC1A2y7hFdjxPdtmtdzYmBlwwAo3KjaBqn/B0L687oAhsSqI+uQJHoPZp56Mgeu4nuI1uQMTb6DsA63UlsqGKgAWw4Y6MNbPS8eyhvb1dflzgOmtRHnUSIWmrrcmBDAum9lBi6xpP8fHcHxmZu1Go1PPnJT7Z9LLtXmLAXbFaUrh5B2GWqiYdZ94hu50oh8Jzo6wRm/XKBSevzvLVVNBgmYmlkQCwDNnqlKNO2a3WNjdiZpG8lUCMxQkWtC/Nj0SkXiM/xdlVAxUZXED3PD5e3moeIUyrNNqWGyYcLSzXmY/G2aw0RrziMMk5SJTBo0voMCN49qvOx+FRxvWsdIkAdUZsYWCYYENL1k3FzDx3VMqcJQ9XPGHRFVRWWOoTMuqL0GRsjgacRY6OhRzDomCEGXRxtaysyc1y0rNkKTC1MfjZmTpSAXPEiNpl/BqgLPItdtf78Ip3nODWZm4SirKIK2FMDQStQDCnVcgA28JPxagWQU3p/pCl85K3PmvOLiknqegwo1ThfAAgJ68ZSAzasOynUFPGy7jGfqnoksWdpAGz2zMhv9MBkMKMNH5u+lgvEJK+4q+azkwxKURplP5LvSnVfTKL2Q0VLVZyvXjcW2yGSWHUYpWmZU/PeamOo9MurgPoMo+JlbCCW1ri3Ul7m1Ew+gjmgCohk56u7qzYZ/Okl+t1JjG1RvtaCANbXnDjN53Ipimk546u5MYpyxiVSZGxY51tsyAYqd6CxjeAA2Oyh0fZC1B0IacFPRne6t1byYYyNaVeUailKc1edxCA02+kRDbHjvLVVdtUmIxVgwW5fu8yp23Fnhw0Eis4M+bUNXsYW/HO05iZBMEPUHI2im3wcNrU+UTeOcw26k1h5RNcxHTBhbPL7S5ENLICNpn8OazNXBDaMtYw0hm8CBTumLNTeXYFNFOnNtdjjYk7CUzJvEzQ2erS97guRdXH02faeUrPRBrqGhAIooDq7+ba1FV/GTOCpKSzlnSuaoxz0O+7Yrlox0QuASmtdQoTOFcVdtcE0cxP9Fhema4t49Z4nBqh0k08hWtZgbEz8ZDRL6Ow6J5SgVtO81pobBcdALA0IwEbTP0dXIM71TLrARrd036dQfsN85jOfwRVXXFHFsVQa69evx2GHHYZjjz22PwsKDymlQJyqT0LWZ2yKXabSdG9TYalblGWUmJM0BqHZ5xMngKvadm04QgIodsfKIY5z0HgZa9eq2YtUVeBpyYSx3m/9FgTmQ1UHYbKr5mLpSF20nJcJdYWl7R1o6gyGNrDhpSj1Taxn0p2UX+shEqKp4KgtCmlrvlY/jDAUUu154hsLzfcHAyaJsuOxmY6qADZq37HJOJZ+hvIb5uijj8b555+Piy++eN6/XXPNNfjSl75k5cBsx9q1a3HHHXdgw4YN/VlQSLYAtKjk0Ea7t3a5wGBdotf6nP0OUx2EOpCLqQPf05xW2zYfS/2cdZMPK52p2u2L37HpaAMVdoyK4nCdewtFuUDVu4f7sRj49gBApGyGaCi0FMtgCiCSJR9dFpL7yWgMZ2SlDU8n0QvfT6jQ/szM6kxAM9FkQNnzp7sx0nY85n4yusAmb61X/I4dNlvK380Ym2c961n48Y9/jI9+9KN461vfCkopbrzxRpx44ok466yz2oz79ujIX0o+SeAi0eogMU8+BiMVDLQ9AWKt1megeMGorasraBWAnM75zltb/pyLbiy9F6Io8EyV2EA7gxlVx3WImiKtexoCCIzV9AhGAk/h+0kUvUaYMB26jI2mcJm7/2omHwZsApq1XUtHEsNF9nlPp+1aBJEKmpPCrE6zdA8I3j1q37FJezsAJAysK+rGqCXGpk4ipArfMbMA0C299Su07oLjjjsOv/zlL3HVVVfh4IMPxoknnoj99tsPt99+O17/+tfbPsbFGcLLTLkzis2K0nYANmMwbAhLtczqqIdAh0rWZaj4dTZ/IaqCSL6rNgQ2uuyY/mwsvWvN2lNbuvPPUEydVi0X8OTjaSRb1wdFVhpNFFtyTVuBdUGzY9ipw6ZOmzCvWsBGeGeqAZsCNDsa7uEA+LVW9e5hmiJ9Y0A2ykHRwoDdW5rAJhgqDHVDhfuaa4p0S/d9Cq2C5D333IMPfOADeOihhzA6OopnP/vZ+NKXvoRabdemp/oawstMm0nQmSMkrK0sOoxbILAwK8qEKdI5Xz7dO9RmxowZGxJhWmnnw5KtWccM8wySnhDOr7XmlO22Sery19q0CwwodBCqU6fZtXZ1GAxCEDsB/LSl3I3FGRtTjyTF58kxAXIo/HMy5jXFsGzuFL4XXyfRE5K9exAqARvmAaPbIQSIs5N0gY1mN5aj50fFBdOaZc66MDiz1WigPjTS49NFsE2CtiaxT6H8hrnyyitx6KGH4r777sNPfvIT3HXXXZiYmMAZZ5yBnTt3VnCIizRcDyBZslEX/+XlAlPGBpGieJglH8+szVyZKTLV9uQvYpIgVOnaEzt1tBkbDR1EEoHQpO3nVYOZqCnPIrOlo1I0URNbn7UGMwKFO7RK8qGU28brvoyZaFl14Kgpc6LLjrHk7OiWonTHZvCuShe1QA9ksC4hFcO6mJvVaerkUFwrV7ETjHWOsVZ11eD6K8VOP3B3aU1Wzq8hpdlzGOYaJZkwfZb6Fcpv86GhIXzrW9/Cz3/+c5xwwgnYe++9ccMNN6Ber+OEE07Axo0bqzjOxRk84Sr6ulhK9MoOnpY6ZgLtuUmBkdMyoDjEznQml7B2xpxIgjlhd6b7giCaZQrjtmvOUMUIQ/nOFTbWwGQqMNUReKYxnFz3odWCDMFuXzH5MOdeXVauXc8kf61Z8iGak651TSeNy5wAItYlpJBseeuzpgsvUJRWPEXGhrVLe8aOx4raVF7K1ry3CEEzZ7jCpjyIdE3a+fsYynff2WefjTPPPLPt70ZHR/Hd734XT33qU/GpT33K2sEt+rCg/TDX2OiVwIz8c3RLUbraHoGOJSovCNMp6oBe2a+tzdws6QVEcXyFJY0NoNbJYdzeDgEgqAAb4X7o94BEY6GlcK0jBQ0GKxe42hYGmqA5YUyzj7pmaTcmtfxXyZ8vL0UZgGZmKKjqxMu7wGp615pbAWgabWpbCaBguCIFEMlGMOgYMPYz9Jr+O/0iz8Oll16K2267zdavtBrr16/H+vXrkSSKLsAmoZ3oGcCw0RUleb5JLJRHNMsF+UNWU50VJZjG6Q1I9ECJB0JjtVkvFrxV2lrcpYGNKJbWpM/5tVbcVVsamwGosmNm1DkgDGdUsfoX7gfdl3FRLlDtmGEuvIZeRVBjMIxM8oBi5huJ1IbZmjLNKNqXVbqE+GwsA8aGmxIqzsfiwzc1S1FFp5/qKAfWcafPnIQ5YxOr3Fu5743uJqFfYX2kwpOe9CTbv9JK9N3HBjAYbSAyNmY+Nk3ZF5O4Y7BAnSuZmeUPddPA46Qw2FJIPolhWQYopk6rlP3aPF0saHu0PJI0xcOujzTXjikxGCZeMnkQNpxRpVwggMh6oGneplkuMBZaOh7S/BWt0pFVmOTplqJ0NTaGzCuKsp8KY8NAkK6nCwC4NcbYKGj0KEUt94HRnVHFrrUS0wyAMD8Zg+cp0hjAyRmqPQ3YDEIIw9EG5s7D2W5eapyDqZcMwGdFAYomahaYE5Z8lDpmTI0QAT3wapMp0tVBUAOjPMa6qLQ/GxoSAgWw8dJQfkSJBR1VqrmrdvMkqQ1s8o4sQKHsR6mZ+y+AYuabgm4MwsRpg9JuotElZOrCCxSGgkqmhALA9ut6jI3uaBRmOkkMjPKYJilW6EArSm+a59unGACbKqOtg0S9Vh3CM9K6cHNAmcSXv0gi6sLXLY8I1DlV0kGY7/RYG7ISY2NqhAjo7W6F1mfpNu156+YCT6KWfMREr3vOzAFYpexHTMWOAFymK0IsL0630tKvAZopLWh7C8lHmrFJIjjIQJ+vqfsQ2UAV0MxatG2ASJUOtJQL0/Wvs9ZQSOFdE2gmelZeJYqiZSZMNylF6XSgMbG07rDRfsUA2FQZNnbVBm3XgII5oA0WQRCyqTEn5rV5ds5uGiKRdeK1kOS1hNqChspGKUq/487UAVg++Ri5/+bBNCPZAE5VYKNf9uP+OYkKaBa0PQZJgAuXZRO9aJKnqftgz7FLKMJQPuGKwEYfNDNgo74x0h42iiJRB4ik2UCmTUkpQV3Tw411YzmK2h7ecWdQEorZvaVQ9uOaIt3SW59iAGyqDJ2uKErnOA/rG+UVa0vs6G20PhPCVfpuqmDHbgFgsJ1PnSgk+rZSlAXGRlYgLiZbQ8ZGx4QxW1ufwaC58ZtKondMBlGy39E2skPx3tIdIQEIrrQKyTYRgY3+OReW+7LAplg3MGRsAD0/mQi++iDbPHTGZrCylUnHHRsxoPI8sTbplsHwTVb2V535xmdUGTxPHNhICrXTlPLZh/6gFLUHh85cHeHFpJ3oXQ9wsgdNOuFaSHgABAYj1CgX6O+qic4kZFNPF0BTY2PYmQQU7d6IlRgbBmxC6qPmmgm1icKumu9IDV7E4nesem+FBi3IvBtLSbQsuPAalKJSVXNAkQ3UTLYiqxaH8t8xK5dFBt1JfPyEBuNrot8SgY3svRVaYKjEmW8q4VIzE0ZAGOcgeW+FUQifZO+4QGdkRh9jAGyqDJ2kJyB3K0yCrAuwDZ0LIIxVUEi44tqGyUfNT8aGiJcBDPV276buyAygaPdWdHmm4mgDU82JBmNj8iJuH9mhAyL1gFzRjaVeimpRH7VAkymCRmnGBmh2XCTIjlmlG8uGUR5vAlC41jTvIjVjbNSZV3GquC5Dxdg8V7EUVbT06wMMdr1kS1GtRnEv1AalqF0j1q9fj8MOOwzHHnts/xY1NG+LiQdPe6ibOFZBXmNj1CEEGwDDQmlGerRBYShmDiBjhLLusFYcj/U0NiKw0R0jQVRLM2kCl2bXxjHQ2GiV3yyAVzZzSUkHIZZXNZkxQOzIUmRsDJ/jmLcCq4t4YwMRr45Qm3/W0wdU7DtWcXmO+VRxA90YczxWNAbknW8Gow1U51SJoxd0nZb7FXsMsFl4Hxt19iLwXP25Oqo+JzZ2eoDQKqrCYNgrzdRIhKZi27WNdm9AocU9FmvzNkpgKqWoojVWdxIyUR0YKFoJmMyY4Z1gGveWARvIk48KsOFGiPrTzAGhvCLLYFgqKceqomWADwk18ZMB12+pdNzlx2jQISQ+x6Fk+zNjbExmVDFhuZcq+OcA8A2nigNFd6Os8SQTh0fUzeQOu3DsMcBmQaJNY9M/6jxbW3GGUVtbrMm6iiWwuWtrt3sLQE5VxGtBYyP+vvJ17WpsdEzUUoMkwGYQubSFVKYDrW2sgcFOz4ix0fftKcoFOp1+mvPPWKgyGDY67lAwNirARhx0qhsFaFbQb1mwEhC1X1FL7pwZY2OiKWJGd8qMTS7iNTHKS9n0d8l7K7QA5PoVA2BTZYhGebJiR0s7PQhdQkriYWONTcHYSJXAgLb29sC4NKMCqCyUohwPlOQ/q1ouMOrUETU26sDGZMYMSz51SArE8zVj6sD3DXbzriJYF9Y2mV/EGBufhnJADijcw6md51gZ2BgAOUBdWCp+NnVNpmyrg0jCh40aMDbCMUeSuiIbmiI25kPJPwdAQBmw0e9O4kAwkWSomqz0ZvAM9ykWFbD5xS9+gRe84AVYtWoV9t13X7z0pS/FX/7yl4U+rO4hGvRptALb2OlJJ3oOqAwErYAemLPCYJjpL7SvNSHq815slt5UzR/ZMRoILV2hO6kpw0QK86nM7mkNXZEFzYmr0TFjjwHNhcuSiT4RxeEG1zrlwEYeYDDGxmgeGAM2CoyNm5h3CIEQtPKEHUlOu2alN5Phm16dMa+KwzdhNnwTAH8HyIJmpreKBoyNvUiSBBdddBFe85rX4I9//CNuvPFGzM7O4tRTT8X09PRCH17ncHWSrd2dXl1aY8P0Jp6+Gy6gJ+K14g4rMFRabdf656xsWMe6oqBpwAgISV6t3ZvR9qnRzCZFgbi18iobzihffuNiaQMmkgklpdlPQPCi0hdpA+pCbZZ8TDU2ic58LAsT3HXEtAz0Gem3UJRYZL17OGNjAOTY8MxAZUaV8HnfZGYTdz2WvbeyUpRJ6a1fsWsrgIRwXRc///nP2/7u05/+NA444AD86le/wqmnnrpAR9Yj2lxpdfQmFrQuOj42NnbVSudso0vIAFCZaGyA7JxbKuUCC+crTPdWKUWxl5j2PDAInW+y/kym09tZzJmBJhNp1IQLs2vtzPNIktixCsNGRw3OWVVzErcaqMGwzAmA5iyEymgDG34ynsaUbfZZU2ATkQCgM9IDOJmxnYmmiPnnMEdfmaBpijoxdwBm7wDZeyvhjM2uD2wWDWPTKbZt2wYAGBsbW+Aj6RI6rc/iTs+WxkZFPGwwHDFbV2OMhNURAwpdUdaudfGCkLJjz1+ILRMfG51J6pQKRnkGIl5f8VqLnX4G7IWo35IFzUVpRp8d07MwsKNZKwzc5BI9YxtCEmh7qwAC66JhSmg0D4x3CSmUoliHkG9wT0O9xZ2G5sCGGd0FJAZN5e7pSDBNDGoj2muT/FqrAhsTTVG/YtEwNnMjSRK89a1vxZFHHomnPOUpXT/XarXQahVf3OTkZD8OLwvTsoxJsm3TQfTTedggCdjS2Eheaxo3QUzXBfi1Dkg2nLEUGFpkqACFyc9tE9xNWnKFMqcCY7MQ9xYzmLNybykItdm9ZQqamQGbrJiWdeqYJh8OTjTmgVGDjjs3L814CqUZjwMbA40NimuWyI4Y4KU3/WsdCIxLq9lAfXi09GfCVoPLd2t1g+5GTw00s/eMUTt/n2JBGZu/+7u/g+d5Pf/ce++9836OUorXve51uP322/G1r30Nbg8DrHXr1mF8fJz/WbNmTZWn1B6iwFNadChobCy0XddlxaXWSlGGLbnas5MYgyE/ILHNrM5kV62acC1qigC9AYk2/GSUGRuLGhuVUhSQJS1zTyhJsTTminj1z9lV9NCxlXyoorAUsDPolIlhAyq/LtPjOCZ6E0B9KGRkXnoTp4K3JP1zwmZhlBcY2Cdw0CzpkZRaaOfvVywosPn85z+PZrPZ88+BBx7Y9jOUUrzhDW/At7/9bfz4xz/GE5/4xJ5rXHTRRZiYmOB/Nm7cWOUptQc3FIsVfGyErigT2l452dpKPkKJRIOx0T5njXZvarlcUEMol/hsgEihPZUqantSSuBaYGxqRPZ8bXX6iZ1gksAmT1KJwa5aB6wnIdPYmN1bLPl4NJQqczLdhy3GRsUoz+H6LX2A4eWJPkCERLK1nrVKm7rhqra4Wxm+6ftIaAa4IwGw9Ao+RZ36cAxyhKpQuwA2uz5js6ClKMdx4DhqX8wb3/hGXHXVVfjRj36EJz3pSaWfr9VqqGmOlDcODbEja40N4dmh7UmICZWuKFMfG62hkILGxrhLSH3gqHHniijkVSjNNE30TIQgcWpZiUJ1QKItE0ZVYbqlOWQ1yG8UGOgz2mUKgGqn5D0dh4WI1+TeYsm6hghRQhF4vVmnwkvGLPkoj80QPksMvIoC3lqftfQPSczZ8rmnixmw4S3uikabJqU34jhoIcAwWnxaeFlEwvBNk8zmKgq1uQGjAZDrVywq8fCb3vQmfO1rX8OPf/xjHHHEEQt9OOVhMlLBku6jLkufW9fYyO+qbWpspNvbAZ7oU7emX6YA5nSCla9NLemo+BA7WcambTaWnTKnSikqNDadFJ4nydIutdCpo/r9AmIJzNceXQEUXUKyGwUaWgBygHIrMFDM0iIGwnSPARsiX/Zjni4m4wWAgomgkqUoNhSVGjBUQNFmHkmuG1nyk/EENlAmbPgU9SsWDbDZtm0b/uM//gPbtm3D0Ucf3abD+eIXv7jQh9c5dEzUWBIwZk6EtVUFnpbazGVZKmpjbXFWlOQLkeSJ3ijpAcosFSsXmIJIvitX9M+x1QWmOmDVWimKRGiFks9TVIBX/XVFYbqkxoZ7nJgxJ57AYMiB5uzeSg3XZRPN1Yzyss86BvotkaGSApFpigDZ0ErWOq0bfJK65EahGL5p9v5gTr6xpMaGdb5FMrYDPYIZT0q7HnOGatcHNoumK2rFihWIos5K+V7i4QUNsZtCsTxibVct6ydjWzys5WNjw7BOY5K6IW3fLi6VSD5Rcb4mZQplgaetkpCqV5Fl8TAAxLKOuImFl7HGvcU7ZkwBhjIbaG7AKK6rMtqAddcYiXiFaz2t4JgOtHcY6YTqJHU2fNNolAPyNnNaGOCVRSK09JtEYQ4oCWw4QzUANlbD8xbV4eqVorjGxiJjI7N2YivpKbZdU2rJx0ZR25OmBXVuaOylLFyOi04dz0ggzrxGVOcI2RptoMjYWAJUgIJxHEtSRgMSRYZKUttjqzW2Tc8kf2+Z7qpJnvRkW4EBoTvJxE9G2TFd9HTRn5sEQHk0Cptub24MmAEbWWPA2JKfjMfNAeW+YxItHsZm0ZSiFmXMmZskZd5WgcZGrSvKoOUaaDfok9FBpDEITfO1bXRFqQE5AICh/0UxSV2t3duUwmaiRWkdhK1y4zwn3rJ1Ld3TArMm691TlAsssAhEvhRli7FR3hzx5GOWbB1PTViafTZb20jrkp+vR1K0WhJrC51+QWB4rRkDKvk8uZZGOUQkW1d9lIMhY8OAjaRnUNHOb7gR7EPsMcBm/fr1OOyww3Dsscf2b1HhpQRACWCE8Ky1xqq05JoLPPW0PUBGn2uLeH0x+ajt9BzTB1U18VlwaM3WzV5sjqw7rI1p5kC7eFjmWicisDEAVIQUraaS5QLe1WPBtwcoOlJKw4a2B9AA7HbKBbxjRslPJu9OMhnMKDyLYau8NBOLBowmGzKIpoSqwMbU8Tg3BlQc5WDK2AT1jOGqIQRNy+8tVnoz3ZD1I/YYYLN27Vrccccd2LBhQ/8WFRIeQNWYE+PRBopiWktTgUWNjRRj0+aGa0sHIQ8ujD1dAOVdNeEiPLMXonJLrjA2w4p4WBHIGZfAoD512sZsLDHZStvt8+/Y0r0lea0dS4LWohVY0gGYUj7vyAsMSkIiiJRof2bgxxg0A/x7diQN66wwVCiYF1n/HFt+MkyT5BKKVli+OXJsPEt9ij0G2CxICDeAdMK17WOjON27SU1LUXp6k0x/YaChEtq91Tp1zHd6BbCRY6m46NCwBMYocPlSlK22a7V7i+0wQ+qjbnJPA0jyEovs1Gm2qzZi5VwfFBmTmEiWC6yIlgFl4TJJ7ZQL2MwmH3LGgOIGxTNJ9I6LKJd+ypRm4pYl3RiKhE0ky2+2ZlSlqsCGt/SbAZtavZgz1WqUs2PWNIl9iAGwqTKEl0uAWLnt2sh5WNHHhrWJNmEwmBFQFw9bnipeJxFaUVz+edHTxRqwkRgxkCZw8l2wSVssULyIPRohlXFptTWHTFFMyyj2FnzUTcsFvBNMEtiw3bfJtSaE76plywX2yo1qbCDbVTuG6/K2a5oZA5aG8H0YARsU06NlgA0rDYbwjYZ+AuDXWra066eW/XNkgU1sB9j4wnGHrZnSz9to5+9XDIBNlSHQ0PKjDcSEa0tjIyM6zBkbY2CTrRvIioetDUgUhkLGMqLDwtOlbrjTa9fYlJxzW+nNENgIoxxUyn7mbddZ0qtLlkfSyBJYh2LnCqXwebnArGOGGd7JDkhkHkmw1hUl54XFfWcMWYTCKE/t3spEvJaAjYSeKQoLYGMaLGHLevewLjDXRFOEwslXloVEfg+a6reI46BJs+sWSjA2vJ3f8N7qRwyATZVBSNuLScqwrq00008fG3EKsoWuKGkRr7Cbt3C+4u/sva7Q3m6RsSm91sKxOYYW8G7bBHf5MqeRXxDQBiJlNCfchdepGbnwAoXLq5QOQth5m76MC1daWWBjqYOEbRRIglZYrndhug/Te6vNKE9pHpj581SIacuvdZKDn8hQSAsIwEbSu4f5v/i1kZJP9g7m5EsldWM0Zsai5ufcyq+bjFCbCckHjM0givk2sgAjfxmbzi9SZmyEdm/ftTBeQHWquKn+wg24DkJq52OrLAOo6SDy842pY9yeyl4wAWJFYbqdewsAUglTsZS3IJu/iFlpx5FhbAR2xTF0pU1UXWkZqLJUigLkQKQtYOMIoFmZDTTUUbEp2zLAJs5Bsx1gk4tpJTU2zP/FqAsMxT0tP8zWUscdgDCfNhU1y0tRnqXSWz9iAGyqDlUfClulGRWNTRKDpJkuhXp1O3OTlM/XsAuMEF6mkKpVCwMwzYGNguaEibQRGAtpC3ZMo6XfCET6WiAyNfRWAcDvLynBdL5uQgl8Q6E2O3YqWYoqOkjslKIAOc0JBza+WelNfdCpuFEwY2xUpmwz8BMbzk0CCsdkT8bXRegC8w3LnFTR8diaMB2Fe7FM2Y+X3gxBcz9ijwE2C+JjA2g4aTLGxrM0sylEnKaIe+26YuGmNk0+ykCu2OmZJno+jE5m52NLbwII5QIZxsZS6Q0wuNYBApMxJIQU3UkSiZ6DHwuMDeHlAokkwGdyGXb6QQBlit1YxDQJuB4SZMcuI1wudtWG67aNRunjBHcAiSsvprVlVgcAbg5+pUwJ0xgususSGLKBVNEYkAvnrQCb3BxQohTFZkqZTlHvR+wxwGZBfGyAOcZxCrtqasf23iUUPpLeLycRCBhT5+x8Y4QSmoC2RG9J6+JIMTbiuvYYm3LxsM02c0WNjS02EEDqMWAjz47ZmDHDZxjJdK5wdsxCNxYDzZKdKxzYWHBpLTqySkBkmsDPWQTXMNmqagNpG/NqCGycbG0pxoZPUTe/t5SGQgoA1x+yAyJlZ77x4b0Wnid2b8kAm8CGAWOfYo8BNgsWgr+Kys7HVncSIOE+zHa21EcQGM7jEh42qZpxm8bGErBJW0jK2p9Zu7epSBtoBxil4mFLmiKA79jkRznY21XzcQ5xOWPDd5g2gE2+W3RkBJ6RJQsDQN28LbHE2ABI8nJBWgZsxJZrw7lJqrPXWNu1DcCeKnQJMf2WaeszUDARMsBGZM/qhuLhos1cdkaVTdAs3+3HGRvTe6sPMQA2VYcndBdIJR+7fjJArrPpydgUO1tbSR7ov4i3fRKynNYltMBecIG4jEGfsLO1BeSk3aUtOgDT/L6W2WVyit2CxoaLWmnYu7wKzDGdtMPKSfvnMD2ChQ4SVpopdVuObAKboqsylLi3InG0gam7NCuxyJQ5WeuzBWDj58DGQznTHOZi2xb1UQssOR5LdmMxozwbM5sYsJFpAmCjgXxTNrAPMQA2VYfoNSI1xE7w/DB5QcxpNZdibGzsbB0PlOS/Q1HrYproSVv7s1x3kp2uKIXON6vrLpzAk93XMome7zAtJHlHKO2WduvYEqYD3BdGyuMkTeDRTIxvhbFhyaeMHWOWDdRDzbfHvEYS2p5YMMrzTFv6FbyKWIt0YkFvwodCIiplfMNmAeRMvZkKB3G5bqzieTI/Z1b2K7MxSFPKu8BMNUX9iAGwqTq4mZlc+zMVd5mW2JN6WdcMK39ZKFGIgMqlkfSu2thbBQJjIzP4swLxsBygEruibImHFdu9LTA27L72EolSVP7CtkGdM6M9KXYsEq+1afLJS2Aypag2F15z2p77nJQBjKh4lszvreK7khn8yVrRI+KbdVUCSpoT9r5MLQjT2ewkGauKSJhR5RkCG1X/nMIozxzYpJKdpGEUISDZNfHrg1LUIFQ6V5IIhGY3T9NGiUQ24baVvwxfiED77CRJX5cWtdAlpGJYx9f1rImH6zLePSz5UBuOx8V1lhubUaxtXPbz5TUnfIdpwf9CyV+F3dcWNgmFx4mMtqe4JjY8PxJZnxPBZHPIFNi4PtK8pT+WKFMUbdfmAIODKikQyczqzK9zkJfv6hIblGKUgw3/nOz7lfXPsekAXDQB9AavLWEgaa0+YGwGkd98dQX9BcBacg2/Hu5lE/buyBIne5smeUCtW8dqV1RRppBlTmyWKaRGDFTQBSbbkkttlTlRlFg8Gvam7SkthgVaYGzaDCClGRt7QM6TATa8s9FF4Jv7q0j7nLDzpRYYG0KEmU0ybdf2HICVxLT5NbFh/shAqMxGIeKOxzZGOeTPkjKwscHYsG6/3sAmbBbgdtDuPYg5PjZyu3nAsgaDlHTr2BIs50FUWKoKtC51hBLdSfZEy0qCaYuaItV271Rc2xKDUXpfpzGc3O/DseFYysC6lJ5J1I6ZnS/zhVEBNraeJ85GSDI2VswfUbAvqcLYDKYHMgpe9pMXptswq2PlVZnxFcwsMbTRZq4CmmHXKK/w/iopReVALqYOiGsO5qqOPQbYLLhBH5EpyxSlgsBzLdSqxR1IuY+NFV2PuK5Mt04VjI2U27JghGiaBARKuNSwzqZ/Tr5LlR6pwDw/4JuNzUBh2V/KRAovTCuOpW0jOxQYG8NrzbQ9gUI3lhXQjMKvhJSUZihvb7dQioIws0miO8lm2zX3KpJI9NZmcgFtE+BbJSMGkrw8Z4OhclUcj1G0XdsoczJgU6Zn4sNGLTBU/Yg9BtgsuEEfovKuKLHt2rQMBcgnept+H4CaroiDOYsjBlSM8myAOdcHJdnvKO0Ssjp8U0EsjUKjkbo1Y9DsBEyPUMKOCS9MzwZjozSXq9DYmCZ6cdq1LKCyUubMFgdQnnxYZ1LTgtMyUJi3lYqWUZQ5bTA2jNmTMWHk18R0dAXAGRsAiBolwKaVbxJs+OfUirKuTPgWGRtZUXzUtKcp6kfsMcBmwcKTpOyBORbwFr4aQWPTm7GpSmOj1p1kV2Ojsq6NXbVk+7PoY2OrG0va9j4/NgtGeWK3nwwbaKUFGVAq7VKhK8qcsRGfYxXm1UZpV3JX3cqScdPGJgFCm7mEAzAvRVnQuqh0CXHvF88CG+g4CJHdo2XTrhmLZUMszQB/IAlsGLPjWyztlgIbztgMgM0ggDmaADm9SdOGGy4gn+htCmkBPcbGsq+LrMbGeCZXHjrAxpZpXIBYirGpgravlznT2iw1Am2C6TIGlAlabbTWF6U3GdBslwFlib7MwC1uFRsj48YDCMMoFYw2qY2ZTQHrQCtP9NxuwIJHEiA/O4npjmwwVMwY0JcwBgSEqeIWGBs2LLXMn4lpiiIMSlGDANS6OASxo42dnri77ZnohW4KO6UoXebElq9LCYsAtHmc2DlnZuDWBKU9uoQqGYIpN66D+8nYSAICEynD2ISWmLG2LkNJYNOCeSmqcBBXsDCwBOaYUFu2FBU55qVGQDC9k2BsijKn+b1VaE7KGRuWkG20PgOFZqZs2jUDe7EF0TJzia5JMjZsZpNvYbQBL/uVDJW1OWy0HzEANlWHV+xsZecI2WhPFdcu1ZwI/hd9Z2yEOVXmGptifIX0rtqG3T4ACDv6nucs+tjY1BRJmD8SPmPGRucKYyJbvVvcbbodA0r3FrOJbyGAb8s6QQasR8W9ZQPMOQHzOemd6Lmg1UZnEtRmNjGm0sZgRpawfRnGhl0Ta8Amn51U4t1TjHKw63hcGpTyz9koRTGtnFfC2CS8vd3OvVV1DIBN1eELO71SFsGyiNdXZGxsaXtUupPaztmWr0s5Y0MtCzx5+zMp6xLKzrdh0R22TiK0wpLrnCZw0uyFaJ2xkZgcbwXIAW33lmwpKrXYCiynsbHoag15c0CWfGxMugbURhvYnODuczFt1Jv9RAFsrHTcoQCFSUkpir0/rDges/MlKeKoN5iLoxAuya5JYMEoj9sYlLBjRTv/gLEZBNA+qFBh8rPNUlSNlDE2tktR6hqbBmoWGAx5QEUFQGW/RNJ9bZrvBLPztQPkACCR7MYC7Iw2EDU2cvotu7oxmRElfFdtBdgIHkkK95aNjQLvmknDnomeMVQ25iYBBbCRmQdmc9CpXys67qKkN7Dxc2Bja+I0n3ZdOkmd+eeYn29tqJgO3izpxhJFzTaBjV8GmqNBKWqXjIXzsSkSXqNsV219tIHYFVWefKxM9waKadekxPEYAKLsQbUimBYAVRmIpEK5wIbQkkj6q7Dk07DS3l682EpN1Kz7yUgyGJa7z1QGf7LvOLGQfCAyciVgPRYmXdvQ2DCRaFn3W8pZBMvARsIoj5vpWWBsGINRQ4hGyfvDp3aBDRMDl81OsslQ1YTZS60SYCPO7bIxjJJdN79E32Oznb8fsccAm4X2sVGnsPvvY2NluvecdcvOmT0wdhgM+aTHym+RExgPsQPAE99QCZOQikyRDf+c/BEuNQbMhcMxdRAEFjob/II56XlvJeyetlB6A9rAa+msqIjpPuz655QxNqwk1KQWvmMU7cC1ks2RVYYKUBpGyduFLWhdCs+g8hElrEXahpAWKEBwWvI8cU2RhWvtuA6aNHsmwxJjwDD3zwmpC88zt09g1y0oKUVRi11v/Yg9BtgsWLR1j8jrTayUoqR9bJho2ZbGRmBOFFpjrYlppbqxWBKw0ybazo51v9aUDQt06nAcw84VQpBIDrEr2ttttV2LzsPlBn02Bm8CaAeQpQwo21XbY2xkuqJiwaXV1OEZKBi2UiYysnxP5+8PGcbGy4ENsQBsiC/J2FDKW59tTZxmZTxaUoriLtCW2sybuS4qbPTW9tg2ymPXrQY5xsaGpqgfsWiBzW9+8xu87W1vw3e+852FPpTeoZRsi44Z623XMrOiqG+lLKPkDtvWQdI/J96ii8NWEpA0YoyYDsLOuqzG78RymgArbeaAfNu14Bdkk7EBynVFhF0TK4xNobEpYxFYR03s1K20XYvPU89yNr+n7QhpWUlZxiiPtQvbADYcvJYBmySCm88hswVsOCgsubfY82brWjOgwkwWuwWbtG5rtEFQl2s1Z4yNNdBccViwAu1/7Ny5Ey972cuwbds2xHGMs88+e6EPqXsICaCsXmzfKE9SYyN0RQ0Fdk3Ueq6bphxghCSAZ8pgCOMryrqirAMb0RG3x9qE6T4svRCpVwdaKPcasTmjCiiudan5o+3yanHdkhKvEWKRRWgbkBj1bsu13kHCQFVJtx8X+Vq6pwl3pZUxysutBGzot3LTuCG00OwJ5Irvv1Yf6f45hSiGQva+tzzO2NgBVCGpARSIm70ZG1aKsmWUF+TXbYiESJIUbpeNLWHvFxtWEX2IRcnYnHfeeXjlK1+J/ffff6EPpTzmlCh6ti8KAMNqV1RZohd8bGwMz5MeVCjsiqg/ZHHoZwlDlUQgNP93S/4Xori099p2kw93PE4kGRtaQSlK4ju2prFxfVBk90mZ1b/DtCFWWITi+yo1b8vLGNaElr7cXC7GUFFL5REi2WYOFF01JLCQ6Nm6hKLZ7HGtWXmEEtQsdAgB4Pc1Kbm33Pw5dmycLwp/mDLH4zhvErAxfBMogA0AtHqtzcqcloBc1bHogM0ll1yCBx98EO9973sX+lDkgie8CACVTAK29AiSAk++q7Yv8JTpxgIAYoPBaNvZlmsRsp/pL2PjRCz52AVUTpkOwjZz0qbf6iVoZWJHC1PUAYCQYjijbPKxyNgAEuZttml7oTTTi8Fg94AVhgqFK23ZKAeg6E5yrYDIInlGPcS0rMOwiQD1wE7xodgo9L63GGPj1uwwRaEjB2xYG7otYFMfFoBND30PL3XbKnNWHIuqFHXbbbfhfe97H2666Sa4rlwCbrVaaLWKB3NycrKqw+scAnXHunW6ggfRT8aKiFdyVy3oXOyUoiQ1NrneJKQufN8CtSq21kv49gCWPF0AOXEppXD5bBu7O0xH0scmhIWp4sK6ZeWCNGzARdb1ZqW8CiBx6vDTVmnnCmMaHBsMhuMgJj48GpWWwLjQ0rZ+q4QNtA1sGEjxyhyAKeVdNa6N7iTXRwwXHpKewCZszqKOzKbCCtOMovzmlgGblAEb2/45ZcM37TI2rhcgoQQuoWj1KIPxsq4lI8SqY0GBzZVXXlnafn3RRRdhxYoVmJ2dxUv///bePMyOqk4ff0/dpe7Se2fpLJ2FJEKCgRATAiQsRsEgIvKIIOAYHVmGyWAQg+BXFPE3iIP4ICCiIBBHRlBwhkVhgMgMJCqLGBzCHggkJCEkvdzuvvtyfn/UOVWn+lbde5Occ2+6+7zPk+dJ36VPVXXVOe/5fN7P+znrLFx33XWYNWtWzWNce+21uPrqq/f3UPcdAsPlKv9Wv/yoELFpq5G4VYSg76nVRE1OKsrR2FQsu7ZTb6acxVbY2VYUeNpELgRT0k5PjMz5iodlR6gAELvXSxaUUv90nuxmlHwBIBS5nP+OvpBLIgCJRohg5cyFKhEbSh1XWmmLTxjBYt5ONfmCl5nLqiARNCfpnP/z5KRH5NxbvOy6aipK9EiSFcEgJoI0VSOxCaNVErGpNQIaZsQmKOl8azUGLNrNNyU1oyQEWYQRQxa5Ch46ARaxkZJqrAMaSmxaW1vR1dVV8TM8MnP33Xdj+/bt2LRpE9asWQMA2LFjB9avX481a9bguuuug2GUT5zf/OY3cemll9o/DwwMoLu7W+JZVEEgBBADoKUa/GQcjY2UiI0owquULihkQNi4cjU2NVZjSWshwc6X5JDNVRB4FoTrLGNcwJWKGvQjc0KEQVZuntjkNYtcseQfFREq7uQY5TmLZ6HCLrOUdZyWpVTcwfFpKVYiNq7FVqJ5WzFpp0CqjS2tOklMRVV4jp0IlVxiEyxV6WEk3NempOqkvBEBiqmKrQ1yrIIoizAC+1t4wGDUGLHhEaqQJNEyr5KsZtvAyXxBUsQGALLERAxZ5CtEbHiESta8pRoNJTYrVqzAihUravrskUceiSuvvNL1WigUQjweR1dXl+9O1TRNmGYDldyEWItePlVdWMpFvLLKvcN8oc/W1JhRXipKaKlQMWLjRE7kRBEEJ958hR2XzP5Uw8auGB1j4+ZoAKGwnInJCDvjZguViI3kcu+gCQoCAloxNVOyS5/ldJwGHB1ExUVAIDZBSZNxMRAB8tVFy7Y+Q1YFCSPsMZJFOlfw/VhQcnuBELu3wsihVKL+vkvCfR2RNNdaxKYyaeYLcQ7y5ne7KWSVKJVDbGSVmbNzqEKaSwocgHMkDFAgX2FsW1OkiY1cLFiwAAsWLHC9dvfdd2PhwoV2BOeABSc2VauTHKM8OQZ97p2eZ6qiVLINuKRFMEQ/mRoMxaT0iQJcxIYUKkwQsrVMQG0GfTahkqc34RMxJ1QtEZ8QtWwHYEJQDJgIFjMVUzO8N1YhIC83X1MPI76zpQbCphwSaS8mVXbVtt5JcsQGAPIVIhghyQ0hQ3ZrAyvyGvNL28ruuwYnNVOq4OvC01Q5idELuylkFWITASM20SYp4xbZ81FNN2a3zZDoAMxLzStFbEKSNUWqMeKqokYkRC+bSr4MsiMJQiqqRKl3QzlR9xGSZChWa6dr14Qo4XyNgLDoVSoT5YRKYipKcMT19SsSU2+SFgBiC6arNTrl4uGgRK2LReYqTcY8qlKQ2WPG9hqplIpyrrUsYSnfVVerxiLM90WKaBmouSLLrkySRmxE0lzdLiIjoy0Kg52aqXC+/FrkJd5bRi3EpphHENYzLt8/p/K9xSvuZDU6BYACM/urlPaTnXpTjRETsfHCpZdeWl+9zL6i1giG9JJcxw8ijAIyhWJ5JEh4kGTl5l3annpqbMD8cIpZGIW0v5hWtrcK4IrY+KYLOKGS4bLM4WrOWINAnIbQISlaRIMRIFclJcQq30oyy0RDNSwCecliaQiLTxXPoIBku30Egk5Flt+uWnDhDUfl7KqdVg41GnzSkJxUNoACJ82ViE1WPml2mkJWSmU7x2TG5ERsuB6raid1tkbIbG2QN0ygWFm4HLbTnJrYKMcXv/jFRh9CbeCLXrWmbnZrA1mpKGeC4wLislQFe5DyNICwJN2HuzqptjJzqQt9pt/WnHj+3rx8QiWWe/tGbPKOkFaKzgWw7y3r71vHLtsQxLEViQ0zq5OYiiK210iFxUdmDzIGm9hU0m/BEfFK8XRhyBsRBIt5FHM+qRnhbxAKS1p8hChkqiKxcfxkmmRFx9i9VYk0FwX9liwE7aaQ/iXu+WwKIQBFShCTpLGx+3JVi9iwe09G802OgmGNXSkaaIJVgUXkEDnV0KmoemAvm1FKi9gEQgArC4wi600y7M7e8hY8V6PCvL/Y0aWxkbTQEyFa5EuqRI2NZIIRIRU8dBRoEWpuzqgwSlWpnQOR3FMHcLw0ApW6TouCeMnRsWp2+5zYEFNSxAZC12m/dIGwIIalLba12UXwnX4aprRrbUcwKhCbUk5+xIaLgSt1u86khwCwecuUXGZe5d7iZF6alQAc7VglrRzvJWVGR0bEZswQm1tuuQXz5s3D4sWL6z940BHhVewXJbu7N+AqgfacnITSZ1lhZJf5XKXFxx5bDanyTYMpjNhU1FHJ1hQBexENlB+xIbbnh/+EyJ2WpZnVAQjU0nXabhMSluORBEfPVG1XzQ3tZEZsqpYDixWGkp/janYRXMQr876uJTVTsqOB8u4trisyWSWYF3Ipi9hkEJZmYcBlANXKzB0rAXnnXLC1Y973VrFEbbG0KUksrRpjhtisWrUKr7zySlVDQCUQOgPX1SgPGDY5eezoRWIjbbGtsTqJh7CpxMWnFu8egVDJr4rKI+0XpRI0NrL/vtXdpa1rnaLyKrKcJokZ3x5ohuRmgYAjyg3RHPJFv6gcr/ST70prVFp8SkUEqeX7IqvMHBBSeX7pAuE5lpfWZeJhkkemQpk570htRUDlbhQqFQHYDs8SiQ3vnVTpeeJGdlnIszBwNgmV05wqWhuUbNLsfV9nslmYxPr7a2Kj4UC0RPdLU1DqSpFIi56Eqwh5uchSlpcMAASCdqg0WMyi6LPz4WNbqSj5kZOqZdc0LE/rIkZssn7ExtHYyI6OVe/ZxMeWt/BxF9IwtcwBveAQG3kTccAUn6cq0TGJ+i1eMVNx8REilNzgTgbsiJffRkFFNFD4m+UqOADbfjKG6e91s9djW/dWxdSMgmggT+NFKpip8ghVlqioxqocsVGxUShViQZmBEdinYrScODqsu0zERfzALUWB7kRm2qpKCdkL21MwKU58a3WyctPF1Q9X8DtPCw5BWYQikLeR3golJnHZBEbsflmhYgN12ZY7SvknLNTNZNHxsfqP6iC2ISEcavpqCTqmQI1ERtnYQpJJDZOasZnoecRKipRvyVEBSq1NuBlwnmJC72to6pUgcYbykoU0gaFEne/1K7jnyOT2FiEoZp/Dm9tYEi9tzhp9iE2LPUGyGvXoRqa2NQDtXRCFiZEqSRDSEV5aj+ExVZaFAFwlXz7i3jVlT9XTEUJu1t5BEN0Pa6cLshSieOKmqIKERteNpuWGKUyhGhRyiv9VszDoNbrhqxKHYhtJKpHbGRuEmzztmLWN/UmVhmakowBAYCy58lPTMuFn1JTyoZhm98VKpi3FRWIeLnxZCXNia2/kUia+UbBIBQZH0ftAku95aRWY1nnEKpGbOxmlPIiNpzY+DXSzQliaUhKvamGJjb1AI/Y1BBFAJjAU9rCxwlGDikvYpNztBcyIzauxcc3YiNETmSlosLO+Wb8IhhChZC0cw6EQIl1Dr7VBUIqytfFdW9RY8SGG51liYlQQFa6QPTu8SLNzmIodacntOzwE+PzsHpKomlcwHbizfmm3lwpIVlpTkComvFefPJ2RE5iShlOFKaS43GRLfQyRbzcuj9UITXjtK6QN24t6bcCe52XSctATf45ELqKS90oVCbNOVsc3sDWRHsJTWzqgVrs9m19TQgAUZCKynoTm7x106YlLgDDx/WN2CjQfTiCx0oRG1HLJIlgEALKJ3a/iI2KVJRQ7l2LxqYYiEoTPDrX2se7h1etUAJTYumzW7Pmfc58sU1Tefe17cRLcr6pN3f1mcyNAo9geC8++cwgACBNI3KJTQ2tDXh1ksyF3mDXOlghYmOoiNgEwijBej5yPlEqxz9HPrEJl/z9cwA1rQ149MdPz5RnERuZqTfV0MSmHhA1ATVEL4IGQUhSGaGYmkl5VTbwiI1MQatr3AoRGxUVWbV0QrbN2yRqmQBQXobsZ+DGiRxVIB4m1aqiGMmQubsN1haxScNE1PTpYbUvqJZeBVDMWJNxChGJGhteCpz3Tr0BStpmAKLmxCdiw843Q0xpna4B1owSlR2AeTRQpoiXO9xWimBwrRORSWwIQRZW+s2vd5Ld2FViZZLtn4PKERueqpJplEdM63f5kuasfE2RamhiUw8I5d6+HicF+ZoAANVTUXYZcETyuEIZcpWITUaq5qQGbY9AIqWNC8fnJFDKoOCVqrDHDUlMRdVWFcXDzCWJDsDivVUpYiM1QgUAoTgbN+ubiipmudeIKc1rxCFy/oTKjtjIrDJE9dRMke2qsxKjCIDQnNHP8Riw72uZbTOCrOy6klFegF0LQ3LHab6AF/zSbzke/ZRZjWWRi0iVVFSYMgdgia0NApxEFn0iVHbVm9x7SyXGDLE5EAz6IqSS7kOoapC5CISd1Iy3xsaasFISXUMBCKLWGlJCCswBa2pGKVO0LIwd8Vnoad6pTJJH5HhLhQrnCzUOwLaeiVQWpmeoxPMVxo0R/zYSJVvgKamxK1CdyAGuSj+ZGhuDLT5+qRlO5LJEbtVKwW5GWaE6id9bEquTQux8TZr1NcoLsoiN7EqdPBdM+5wzf46pxE2CGXGMAWnJP/JqMuITltiMMsBIVcgnYqMi9aYaY4bYNNSgL1RDubeCKg5rbOvhiyHr3Zwx76SipBKqWozjVFQncd0HfIgcoIZQwTFw89OciJVJ0sYNCkTOzz8HTv5cajNKJmCMI+MTsXE0VEpIc4XKN8oIe0FmhMpFqKpEbGS6acPRVISotxkiJ3J5mecLp6N5pQ7udtm1xJRQOMqjcv7zBy+NltXNnCNfLWLDI1QSzzfEzjdAKPJ+dhFwIjphSc03AYfYhEs+xIZdh4JE4qoaY4bYNBR88angjeA4pcpeBJzUTLJCxCYtPRVViwMwL/eWGcFwrrWnpghOxUwGYcRUVYJ5iEs5sZE6rtBBOu+3q6bUJjZUZtiepYRiyFSxEjARNyX227XHrU5sigGZ5+vc076kWVE0kKce/BZ6fr6yiU0tPZvssmuJpJmnZqLEP92oQkgLiIJp73MmPGIj8XwjQkd20RDPBUoRAevZJDFiE2Zuwib1jgZSBak31dDEph4Q0jJV0yOQnIoSUzP1TEUJLQZ802+uyImkhc8llva+1iWB2EgVTAvn7CUupUL1SFCa7sOZXAs+EzEKWRBYu3ypQksWsYn5Vtw5RE7qdbZTYBVSQgoEnvb5+hE5OKX+0hrZMgRtq38f7ZiKCBWcCF+l1gZcdCozJWQIRnm+xIY1ZgxJJja8KWTRh8zZ1UMyI1ThCIqUV2N5E5t8Lg2DWM+xzNYG4WiL9Tt9iI3Tk2tkmPMBmtjUB2FH7Ohv8++0NohKDGG7UzOVU1HRsPxxLf2FX+RERQTDWfT8U1FqFh+7+s2HRHKdgtR0UCCEErGuXbGKfw4gWWgpLvSeqSjWMoOaUiNjYuTEb9Hju2qp11q8p33GLdjVWHLtE8SIjad+ixGbUlDuIl9LzyZu808k2vzzTUKliC8XFstsXQE4KRe/SjDCiJxMkzxiGHY1VjblTWzSggNwJC4vYmPGmwEAUR9ig7z8qjfV0MSmHmAPfKXQuegnoyIlFPNNRTklyKqEtP5he94rSr542JfIAaBC6FyasNQ1tvfiY4ewJZenlqpMxDaRo0GEQ/LccEWNjed9LRJXWRE5QLinM8j43Fu8+WpJ5mIbrv4cc/M2+b5QVcT4OX5vSe7lU0PPpgAvu5apdRGF2j7aMZOlZUIS0zKA0zvJz2gzwOYPQ+a9Baf3VN7HM4h3FZf9HEeiFrGJIYuChzUHT0NKLTxQDE1s6gGhesSX2Kj2k/FLRTFClYSacm/flBCl9kKfk+k8XK28HQDhXWxl70CCzjl7Xmu2OEhNB6F6Ezt3g0SJjzyPRPqmohS16+B2+4Qin/PeZRq2oFW+piiKHFI+i61YZi7TT6aaLxRhzzEkOtKK41ZqbeC44cq81k7vtaxXirVYQBDWdQhLLH0GnBYDfsSGV6YZklNg1fxzsmnn3pK5IYs2WcTGIBSp9FD5BxSIw1VDE5t6wCV2rOzpkpIdOQk7uflKBn1SO04DLuM470Xe8Wsg4ZjEklxBz+RHbIpqCIZYNeMVseFOqVJ3thCa2PkSGyeKYMq0+bcjNj6pGU5sZPoUAa7OxkUfPUKAeXJITY9wh1ZCfXfVRbvMXPK9JaSUve5rg0WoiGRiw1OXRkVioyAlJLY2SHss9EIEyYzKJRj8eaI+DuJBRaJl3nvKr31FTkFXccARagNAemiw7H2Dl4HLTnMqxJghNg31sQk7xCZXLKHo5cvAq5OURU6qGfQp8rGpMi4gmWAIEZukF5ErlWAUc/LHBYCwNUHEvBYfSu3FwZCdLmCRomoRm7TMzs+AQ9hJFplsvuztYs7pMSOV2ARCKBIrtVXKeewwAQTtKjCJ17oGQmX758isxgKq+jM5XZ/VEJtQBWITtt1wJZ5zIIQ8rL8xd1V2Ie8cj2xiw//OxCe1G1LQrwkQysz9xMNpNcSGBIJIU67vGSh7n99bMjVFqjFmiE1DfWzYA2CSPAIoIuvVYkAU8SrS2HgRDKrMoE8UeHoQDFcXZIkPqqCx8Y4UORNiQLLokBMbT81JMQ+DWq/JDmHbu1ufBokQjAFVRAMBx+tCBO8ILT0VBaf6h3otPsUCAtQiWiFTXvUIjIC9+BR9IjZUlZmZ+Dx53NdBFrEJyDxfOMQm6NeMklK77YFMN1xAdAAuv9b8NcvhWWK7DgCUPcek4P03tkXLkrU99r3lkwJT2dogQ6z7NZsqJ5GGgo7iqjFmiE1DIez0fNNRdpftiOSwPU8J+Sz0to+NIoM+v+okseRaQaQoTIrIZD0mY2Hxlx+xYakZki4/ZyF0HpJMqPh5+HV+drc2kCnijYKyhoHUI3LCF/+szLYG/HcHKxCbvLMgBaJyFx/uxFvKekeK+NhSy8wBlzB9yEPfE2LmagGJZcCA2JzR594q5mAwKwHZIl7epyrvEcHIKupmDgi9k3xSUZzYyD5fXo1V9IkU8ecpr8ABmBObXLo8FWVrijSx0XAhaALEutS+Jap5J3Iil2A4qZlcsYS82MOoVARhFQ3yfWyqiIdtYhNSpr/wtIFn4+ZoABFTYoUQAJg8YuPxNxY6XYcka2y4f0iolHH/fYeNnaYm4qbEa02IQzA8dtVF29hLcvUZnLJm4rX48HEpQVRmegROpMi3FJgbA0onNsxynxSQSpf3E+KusSGJzRGBGno2Cdc/rMgoz4vY5NKibkzuMkZYxCbo02LAVEVsjMrtK3gEVAWx4T3G8l7ERpGmSCU0sakHCBH0CD6lsXVICQHUTTKExnY5Iyqvozgg7DDzFVNCWdlRhEAYlJFIT82J0FFcKqECBI2Nh68L2+EnEUFMpgsvHDFyhOQr66hkC8QBFINscs+XLz588ZfaUZz/bk4cvIiNfb4RxGR2FQdQ5AJKv6aQeU7mFKUbAWSHO9OWiggzs7owK92VBaeVQ86zlQPXuhSogUhE7t+ZR8e8NCf5tKUFSSEKQ2b1GcTeSR73FqWIsA7cpsS2BkD19hUlhT2b8kzs7nWtebROdqpRJTSxqReqeWAIfjIqUjMBQmEOJxnceIkSGCFFmgDiV43FysxpRO5iS4jtt0DzqfIGeqr0JoArFVVG5nLWTiiJqHRCZYitHCpUJ2UQRlwmiYTjE0M8FnqeJlLhf0Er+avknN281AgVBELlE7Hh1UlSy8wBIBhBiaX9ssNLcgVyx83WZIE3W4wi692zyeUuLfne4sTGS7+Vsp6nNJG/yAcZOQx7ERsh9WZKTnMW7Yaj3veWyo0Cr+IrZsojNiG76k0TG43hqNY7SUhFyS27dibYyPBKIU4uEEFE8qRU1aAvxx1aJWuK4JT4enp+sHMekq1lAtzlz8PPOTvIxo1Kj5qQatc6L5Bm2efMIpGBgn/kRKr7rz0uJzYVIjbUVEfkvMaF458D2cSGEHunXpaa4ekvShCVnB7hzSh9SbNgsim14g5AiaX9PIXpLGUiu5s5AISi/k0hxWOJSNYzlewy88o9m0oKejbxdgklj5Qyb7UgO/WmEprY1AtCX51ktkLERnYkIRAEApaWpKyiIu+MKTVKBLgM+jw1RUoJRgV9T9YhVNLPmaeiSJVUlHRyITgeVzHKk73Q8/s64LG7tRsnqjD2YsQhUOeIjV0K7CMsDSiqTgKc1EyZh46dxo4gFpH797VbORCfoge7PYncpp+AQ4hLHtFArgXJGvJ1H6GI1Tsp4tFigJdDF6iBqOTUG+VpTo+0rvW6uo1CgY3tda1tTZHkCJVKjBli01AfG2BY2XWFnk2yU1GAywPDrbFRP2bEz6WVRTAsgiFZcyL2ixpOInMOwVBFbJqQLt/dsnGHaER6yN7dw8j/3pJuwgg4xMYjgsG7PkuvPoNTeurpiCtoiqTqtwAhQuXnSqvGTwZwUhWF4c60ApFrkqzfEosPvCI2fIcvPYUOwYPIY7EtsJSJ7G7mgJPOi9F0WSo7m+Ip5Yh00TJ/lgwf0sxJpApiY/cY86j2szuKS45QqcSYITYN9bEBnLYK8IvYOLsu+ekCsV+UsPAJjrRSK7EAl7ankPeoqOARG0TkNt8Uxo4gW95lmxMbFQRDMGIsI3M8FYWY3IaQw8etUlovO4LBF/BQsXwRMBQ0C/QatwyMsCdpBHHZQm2TEyo/V1rreIIKFgE7gjF88cnz85VshAi4mlF6RV7zGWehlz5vmRbBCOTLF1t+DQpB+QQyEm8F4B15zSUTAKznWLZomVdVGj4RGztKKDvNCUETNoxUZfMFRyytIzYaZRBcWj0dcZWmhXzs2IVKrGZFOz3AMgEsq6jgGhsaUbCrFtyHyyI2AoGUrAngE1OIFJEfTuayzgKgTNvjJVoG3OXekq+1YTqVYMPFpdxXR2oPIXtcRmxK6fJ7K68uFcVbFoS8IjaFHALMhFG2eRvgpCqGpwuKzJk3jYj8VCOfO0gemVy5u3SOpWaSNIKIzHYdAIhNbDwq7hihKipY5M2YNW4cmbK5OjPUDwBIE/nj2mXmPsaAdmsDBRFQ6hMtGkwmESTWcx1vapE+riqMWGKTTqeRy+UafRi1w47YZMoX21LRFuFJ7xUFOBGb4c0KhVRUs+TcPAIhUMP6nSbNlVdU2MLlqFp9T1l1kpMSUpWmAACSHVZd4EpFqUmB+fVsonaqQr4DMC+NjXsQdu5/oSItY2s/vKp1hIayshf6gECoyiAswOGI3OokAKCmtbAEcu57K2OnR0zpESpXmblHc0Yu4k0T+WXXBruGoYKHGSJ7nkoh+ZExTqgiJI90xr1B4UQuo0Dbw5+loJ8w3U7tKvCT8RHjpwb6AFiVs4GIJjbK8Nxzz+GYY45Be3s7Jk+ejH/6p39CMukjtjqQUEljI7BkFV4jPJLQhLR7bGFnK53YALZJn2cjTB7BUBE+dxG54SkhRzwsPf0WCNpeFGXhZDbuEKLyCZVNbDwcj+FUcqQVLPSGnQbLYCgjXGtKbcfSoIKITcAmNuXaj5Lgpi17oeeiYM9IESNUeRpAJCq/coWnZoLDUjNcSJtBBGHZug+B2Hh5nPDy4Izspp8AAlFrIfUqu+b2AlJ7gXEIvzOddJPIXKofAJANyB83wImcjzFgQGFql7stD7dPSA9axCZFooAxcujCyDlSAJs2bcJHP/pRnHDCCejv78euXbuwePFivPrqq40+tOoICzvbsvSI4ycjvcUAALCdXjNJeUZskoigSbKRGeCIRj0bUooRG+lEzjrfJq+FXtT2yL7OEHaQwwWANpGT72NjOx6TjGcqivtfZBSU5IqNPwdFYpNLwoAVSTGi8nd6nGB46SB408SU7OabcLQzUdbQ1j2wQyCli3gBELZjDhWGLbZ2hZCC6jMjgBysuSHnQWx4SiinIIIRZPeNWSof1944hBUIWgNhFGDdN9mkuylkkRkD5hV0ug4x/xyz5KPfKnIHYAUk0tasucfOJDmxGTmuwwCgYJuuDldeeSXmz5+P73//+/ZrX/nKVxp4RHsBVypqeMTGSRUARP6CyybEZgwjNoK/iZKITQ0pIUtzInlstrNt8urZ5NL2yCc2NBwHMj3lefIcFw+rSEU54mHvVBT3v4hJb21gG0+SDAYzggYj65TFyrb5F8f1urcKmSGYsPrfyK5c4ecSQxaZXAmmqCsRNGvS72kIEYxhqZkCI3J5FcQGQM6IIFzKIzfcGBBAiRH2rILqpDAT8UZLKVBKXfcuT5kYCsrqQQjSJIJmmkR2WIuBUobd10H544ZjjMhR74iN3VVcQWqXX8fhbSTyQ5ZYOmOMHOEwMIIiNoVCAY8//jjOOOMMAEAikWjwEe0l/CqTAJcmAID8MkIWwWghaXe1jigeVkJsuPDQwzhOcB6WH8FgxGZ46g1wESrpWiZAKNl0C6Yp97FREbHhZeY+4mGq0ijPNiXMYECM2LAFYBAxxBXeW14C8SKLLBQU9KjikaKoV8WdyxhQ/r0VjLUBACKlFApCtKhgn6+C9BeAAusmnU2XRxK4cFlFdZIZY9VJSJfpqEJs42CY8rVMgGP8V0i7Izb8OS6G5I9rMmITrUZsFKSigj6mhPmUtc6qSL2pREMjNolEAum09x+RY/z48QgEAti9ezfS6TQGBgYwZ84c7Nq1C6VSCV/84hfxox/9CNGo96SdzWaRzToCsIGBAc/PKUfYMboqW+SFyEkkZMgvIxQiNrvy5RGbFExMVLL4OKWi5UZ56stEm0ka2+tJqODsfKI0g1SuaGs8aHYABExjI9m3R+xRVancm0huvimOHUUW77siNoLTsgoCKeioXJEiON4q0htRAkKEyisK6aSiZPcDA4AQi2A0kzSSuSJao9YGSGXpM8AIU9FJ8bnAxi6pIDbsfJuQxlC24NqI8JRJUHJvLI6cEQVKQD7lPmdeFEAVpMDMuDVPxzyMAQGhtYGCCCiPRJrDurgX0xaxySmIUKlEQ4nNd77zHfzmN7+p+JlnnnkGM2bMsHdet956K5588knMnz8fr7zyCpYvX45oNIof/ehHnt+/9tprcfXVV0s/9r2GELEZGp6KcpUgK1gETIfYpD00NmmqRmMj7qrLjOPqFrHxdwBWca15JUccaQxk8g6xyXDxsLpUlFUVVW4lQAqKbP6F3xknGbfGJmtNiIOIKUnLiKmoD4Y9T7wKrKRAB+EuAhi+QXEioG0qIjZRRmyQRjJbQGvUemad81WTiipU6NkEW8Qrf+Hjz1ITsdL345pM+z0uKA6pIjaBGFAAihn3RtjgFWkKIkXRpjbrV5M88rksQmHT9b5KB+AwK3E3h5Eqlak3lWhoKurGG2/E+++/X/HfjBkzAADjxo2DaZo455xzMH/+fADAvHnzsHLlSvzhD3/wHeOb3/wmEomE/W/btm31OLVyhCtU6qj0sAGciA1Ju/U9OUdkqSQVZQum/bUuSUTkRzAqpKKo0KNKOsGA43NiRRKcsSnXIhgx+ZUrbEyT5F3RSQ5e6WAoCGGL+p5Bz1SUgtQbIBCMYdVYgCPcVkHkwk6Zefk97UReVURsxCIA13PMIlSlkJqIDe9NVPIQDxP2PEFFg0ThOR6+GbT7F8XUEJs8685eHNa+wmAVaURBOX9UaGCaGipvRmkyo7ywgogN7wpflgZjWrliWM11VoURIx4OBoNYtmxZWWn30NAQYjH/Ccw0TZim6ft+3RASJkQ/0ziqwAEYAEy+00u5xaVCKkoJsbFTYOXEhuaSIFCbivIUD9taFzXExim9zmAg7aRIiMKdnlgZUvJIFwSUEhsnDTbokYoapFE0KSQ2UZIrj4DmFXXYFsb1SoEVskMIwiLNTSqiVEK1n+uceYWQivOFQ5i8+ggFmNaFqLiv2fnGSBbJtJuwR6n1N47E1HirFFm0jw5zeebanoCCSr+wGUGOBhEmBaST/WjtGOd6P0KzAHE6rstEhBHECLIolagjh+CpNxUibYUYMeJhAPj2t7+Ne++9F7/61a/w9ttv45577sHatWtx/vnnN/rQqiNcSypKdcRm2E7PNuiLqCE2ttZlWAqMUldrA5WpqOE6CGqXmStK+wmNMAf4wkep7bthKNjpIRhG0WCpxNwwYlPMw6DW3zxgqiA24kIvRhEc8bCSiI2Qihr+PHH3VKLQ48Rr3HzaiYAqIc2CVk4UTNtW+yqIK4ASu6dJrjyKwIlNQDFhd5VdF3IIw7r2ZlOr/HEBFHn0a9jzFC6qIzYAkGSi5cywMnNazCNM2DnH5JOMCNP3mKSATNZJR9lmkKaa66wKI4rYHH/88bj//vvxi1/8AsuXL8ett96KW2+9FRdddFGjD606QtXFw/XQ2IiVK9SVilKgsfHTuuTTINSqclDiPCyIh4dXoPHQedaIIRRQcPuzha8JGQyk2diFrE0uQoomxGLQeyIWGwiqEB2KVVGDWSGCwVNRVBGxCQkpsLQ7cuKUAisgNkIKbGDYuFxcm1VhlAe4NgoiqQqoLH0WxjU8iE2ooFDEGwzbHjrZZL/zunCPx+JqFlxqExt3lMpk2p6wokhRBlbajzscc2TTznFEFGhsokJKLznoVBxzM0hjBLkOAyMoFcWxYsUKrFixotGHsfcIOxNiMldw+zKIXbZV7vRIGv0ppw0FTfeDAEjQuBJDMTF0vkMkGMLEREMRBc3kfAhVqWgLaVX0mAHgnZoR2iuEFWkCSqE4kOsv74TMIicZGkLYVFAOzKuiSA5DYrrAbvoZld9sFLA9kgxCkU67zzlYUNdhmz/HAUKRTrnFtLafjKKya/F5SgppsKDi0mc+7nDHYwAIl9RWJ2WNGMKlhGuhL2QGEQSQpSHEY2oE0zyNOdxBPEKtn8Os9F42sqwaazixSQ32IwLuaq3AxyYcQQYhRJDHYKIH4yd0AXA8k1RFqFRhREVsRjSEagpKgUxe8GUQWhu0KImcOBGb/lTe8VdJW66SCdKkZlft63gs9k0KKxs3RrLIiGJaYdEnCnrMABAaUgq+LjmnfURLTM2ix3UQZQ0DudYFUfl9hACXriMnEIxCut8al8bQokSY7kzuOVFXRCnCReucjYiC3bwg0OU9mji40LSowKwOgL1BCZMiMoKQN1KwFkGiaLHl17GsZxOlMJnvSTimJnLC/VMKaSeKwNscJBU0ObUR5i0G3OQ1xsS1EVbBJBtZ5uCcH2YMmGKtDYYQQ0BFpBnAILHur2T/bvs1nnoLxtuUjKkKmtjUC2wijpA8DJTc+flcfUS8JikgUGLagFIRBivJLYTb5DvSAk7oHGmkRNGy0K9Jpc4FgDs1w/6fpwFEo4oiNry9gZiqsEvMo3aJrnT4TMRiSkiNn0wUlFi/tySUxhaYsVeSxNREA40AioZFiguiI24uaXfYNmLt8scNBFEg1t8wn3EvPtT2z1F0b4XiKMF6TnMpZ6GPFTmx6VQyrNOzaRhpzqdgwNokmXE1EZscr04SFvoMc8NNIup2fpYIw6shZTGPCKyId6y5Tcm4OUaKi8OITXZQfWuDpGH9DTOJPfZr0ZL1bIUVpfxUYcwQm1tuuQXz5s3D4sWLG3MAws7WMlIrr2pQ0mUbAMLNAJsQm5FGfyoPZJyJkZpt8scEbEJV5ojL+zWpEi0Hw04zSrHLtiDSbompIhheERtrchikKokNi9gMb+UgiHiV7G4JQZHdP4Fsn/0yd2wthZvUkGY4BKIoEoxMPwAgRwMwFYTsAcvRGEBZiwG7dYWqNKdhIMciGEVObPJp298k2KSG2AS5I+5wYsPN+ShBVJHmhPunUOE5zvIO20RRyg9OWk8kNnnBhTiuiNgU+D09rBqLa4zSCnpycaSDFnkpDDnEJsaqz8y4gk2CQowZYrNq1Sq88soreP755xtzAKEoOLmIYlgjTMGxVImI1zBcwsP+VB5I9QIABmgUsaiicng/PxnBS0ZJ6g0A5b4LIrERdB+qIycxCFVRgsuyqnF5uW1ZJ2TBAViJUR4AGrUmvXC233mREWdqqsvNF8PWRMwjj+K4CcQRU2E6CcfRuDgsYsM3KDSkKBUF2MSmxBdZlk7O04DdgkA2eJopQlPujuaCF1WTovuaVydRIRrIo1W87YEKcKF9WGhIyTtdZxRqe7h7dGkYsckxYpMJqCu7zrPnqZC01gZKKeKM2KiKUKnCmCE2DQchjpkZGdYvSqiKUhK2B9w6m3TO0dfQJjVRE8BVneSlsUkighZVBIONHcgPIc/76th+QeoIlaePjdDZW9X5BmxL9LRzvoC90CsruwZAWMonVhywxyYsUqRE58JQirQBAIIisWHangFVgngAxTAja8NcafkGBYqM8gAgz7RhdtqPbVD6EUdLTIFeDYDZbP19m4b7YAlVlaqutVNq7iz0vKw+G1AXvQjYxMYxrEsN9gOwdC5KKiohuGUPIzY8tZtX1DYDAPImi8qweyqVzSMOq/Q72qwjNhp+EBthejSjVNZlG3B52fSl8jax6UdcTZQIcFVxuFJRgkleS1TN+RpRpxIswQmG7WFjqiNUFVJRQ4iiTdG4fIfZRIY58TKCMQR1ERuDaTvayZDtZWPk6lBNEW0DAITzYsSmHwAwgLgyIlcyeaRomN1+gfvnqFtwefNFwslcmhEb2oxxTYqITUzo2eS6t3gRQFQZseGRV0MgNjzNmVdIbHg5d0QgNpmkdc1TCiNFlM0fZJhtQynDiY06B2AascgLYc9QcjABg1gROk1sNPxhe34M93URxcNqSUYz0kiknIhNH21WHyUiaaRFjxPBJE9dasYhVf0pTmycDtvqiI0TsRle7j2k8Hy58Z8rBSaMPaiiqzgfO24RmzYM2ufMK2hCCqspuDjYLAwIlX79ACwLAyVVYADAq4REQgXH4ZmoKDNnKLGFni98uUFLD9GHJoxrVpNSJoJdhFj0wMXTSUTUXWs78uroe0p2Wb06YsM7bUdo2r63cozYZAx1f19O5GzTRf56Rn1rAx55DTKtXGrAIs15BECC6vRMKqCJTT3BJsQWPwdgmGpKYwHfiE0CceWpKAAouUS8PDWjMCUktFVIpJl3j0vbo+icWRShmaSRTDEHTyFC1apMtOwQqoRoHMcmxAFV4mEAYBqbNpK0IjaFHIKsE7GpkNgE2ETcRJPIFlj6TdDYqFpsCdcU5d0RG+V+MgAoN8tj0aIkq2AZQBOaFZMLq/mmsyHj1UkqU+icsAeLTgSDzyWqemMBQEtrGwAgigwG2VydS/UDcEqyVYD4FAHwruIlhcQmwDYoPAKaHuoHAAwhbkkpRhA0sakn2KLXiuSwJnbOQq86YtPCvGycEHaTujFDEVBWklsUKgqciI1CEa8gXE4MK7seUqntiXaAEuuxCmd7ADgVHUOIKa+KihPB8RhwUlE0iqjsZqMcsQ4AQDsGrWiRQGJjLW1qxgQQYhNxC5JOJIGnomgMcUURqoAdKRp0iWkdPxl1YfsgSwvxeyqTsDxHMsFWZdVnfO4wSR7JlLPg5piPT5pEEZBtsskQYMQmLCz0vC1KUSGxMVl5cwvS6B20SHqBVWPlFOpcuHv0cGITyLF7S0VLFoZws/U8Rdl9nGXERmUllipoYlNPsJ1eK0kiKaai2GTcD4VCXiFi0y+kopSOCWeHidwgiiW2CNi+Lgq1LoJw2UlFOeJhZQTDMEBjVvO6lmI/MvmibS42pHJcr2osQDDoUxmxsYhNG9fYMP2HZUioTo/ADenayJCt/SgJkcg2RWLaUJP1HDeLkaJ8GmFWdm0woqcCETY2yVrptzxLRWXDbcrGFCOv2SEn/ZZj97XKCAYncqKHjq0/UUhswHRjJsmjr9/aBPIqOJUCXiPKiZw7FRXgXcUV9myKtFjzVrxo/V159ZnK1JsqjBli03AfGwBgVRytSDrlz4WcnSLpV1qh5Ghs+tOCeJgqTEXBKUNuoilHc8IjNip9XYSIjUNsHE2AshQYANI0HgAwjiQwmCmgMLALANBHWtWY5AGunk1iDyPKq6JoTJl42I7Y2MTGIVPtisgFANfzxCM2uSFrEUrQONoVpf1Ccet8W0nSIZFM21OgBkKKyq4BIMqITZxaKeUiK80tRRSKO42A7RmTY+cJOCZyBYValzhz+A0XkyixjRFvc6C043Q4jjTr2zTUu9Maj+tcVLmWAwiyiExIEC0DQLjA3LQV3luxNmveaqZDoJSiwFJv3GJgJGHMEJuG+9gAdiqqjQw5uWoWrQGshUBZWkjoDNwnRmxUiofhFh56Ewy1uoAmTuQAgVCpq8YCABKfAAAYh4S18A2+b40bHqcwXWCdb5y4NTZ8MraqotRGbNq5eDjjpL/aVGmKACe1KxCMAvP7yIdbEFRUkmuwcVuQdKqE2PNkaZnUnTOPYDSTND4YzNjj8miwKvBdOxfQAkCRi3gVRjCaWhmRQ8aatwCEuLZJoUcSAAwGrbEz/dbGhBN2GlZHbMIsYmOW3BEbk0WsQoraZgBAc7s1b7UiiXQ2Z8sH8iF16S9VGDPE5oAA22G2EEFjY1dxxBAKBtV0BQZcfZsSgkGf0nJvYVwXwaiLmJaLh1NOBKMO1VjWoIzYkAQG0nkEktbEmI5MUDemGLERUlHc7yRF1PnY8IiNk4py3I7VEhuW2hUIRillLfRUYcheJFSDw4hNP1XUd43DFvKmsGsga7s9B+Lq0l+A07OpKDRn5CLeokJiE4w688eeIdbOIMcM5OIKnycAqZB1TfMD1sbELjlXSGxCHmXmgENsVLY2iLVaqSiDUPT396DEUo0qI1SqoIlNPSGIh+1yb2FCVEowWEVWecSmCZNaFZbyCdVJfMdFmXC5D03Kq6KsFhLWuMUUbySnsNwbAOJWSLeTDGAwlUEobekg8tE6EJvh4mFu5BZRKC7lGhsMYTCdtaNEgzSqTOcCwElFkSE7FUVY6o1HVVSO6yVaTqBJXemzMHYbGcIHAxmYOWvcUPM4dWMCyAW5MaBQ4s42KDSsMFXBzreDDGLPkKVhai5YonyzbZK6cQHkTOu+pkOWQNvMWs9xMTZe2ZhmzJq3oswYjyPGuoqbTeoicyRoIsnSb8m+D1AYsq6zoTBKpAqa2NQTgnh4MOve6SktuwbsxaeTDCCRzoMK4uFpnQpV70IKLMFSUXyi6KUt6jU2xIkUlQY/AAD0oBVNqvQmgCtik03sAkEJRUqAuMLFh0WoXOXelMJgab+gSqM8FrEJEIrUQJ9t/z6AmDKdCwDXRmGIRakCOUZsFFYmuSM2XGPjaNaUEpu2bgDAVLIbHwxmES1Y5xttVbfYAkLPJrGNBIuAqkzNoLkLgGWR0dffD5SKaC5Z59wybrK6cQEUo9bzSpIWoYlnrPkj3D5F2ZhRFpGJ0gxoyXEQb2KtDaKKWxvwDt+pxB5EktsAAIGOGUrHVAFNbOoJQezIowh2RZRK4TAAtM8AAEwnHwC05PTyibQpFdK6q5NyAKUgKWsn0Eda1YXtvcq9k9bElAp1wlBUngoAEDQ2hYQlPNyNNrTEFEbGeLsOZDDAfXsKGRjUItAqc/MImraAdKB3FzJMwJsmijqKc7DnKUyKSKdYF2Kmvwg3K0zN2BGbFAbZvUXt1G4TOuMKo1Rt0wEAnWQQ/X09iJcsohFvU5uWKfGojFDKb/BKHaURm1bkiGU8mOzZDprqQRAllChBx3i1xIayyGsoY81XrQWL4DSNm6ZszDjTFIVIEcmkdS8XsimEifUcx1vUNDrlSAWseTM7sAdt2R3WmBNnKR1TBTSxqSeEnV4PyxfXLWLTNg0gBmIki1lkBwisCoO2DrUTYpmINzsIUrRCysVIp3IxbTNJW5EiShFIsdLYiNrJgaeixpMESozY7KLtanU9vBsxKdn+IjwNVaIEkbhaoSWvykn2f4Bi71YAQH9wvLq/LwCE4ygS65kpJnuBfMY2BowqJTbWrjpISrbNPq/G6qdN6FTU2sAauwWZEPPR2fMyArB29S3taiM2vD8WyTvExsxZc1cpqvB5IgRDYStykkvswMAea7HtQxMmtKvVfgRbrLkxkusBzWfQDutv3TFpurIxY/FWZKg1TyR2s6ID5gAMAE3NCrVjADIh6/enEnswuWSN39F9sNIxVUATm3qC58eRRG/STWz6aROaFVZTIBgGWq0w9gJjMwBLAzG5U+2CJ4odra7iFrlIUhNmTOHExNI+HRhAIpUFMgkYJeuaF6JqFwEI5d7JnvcAAB/QNrXEJhxHMWBFhAy2wxT7RLXHFXVwZzCYeLWU6gX63gEA9JnqQvYAAEKQCVr3bzHVa0chS5Qg3qKQ2ISiKBDrb5kfsp7f7KB1zVOBZnVl9QyZJus57ki8bI1JTXS2qV3wbOKcE8wX82zBbVL7PGWY6J4m3kdit/U89ZI2mEGF0UAA4ZaJAIB4vg/9H1hpmSwNYdwEhdoeQtBP2gAAQ33WpshuvkmjCIUUziEAcswPKb1rM9qJFZFr7tIRmwMWB4SPDYvYmCSPUp41hqxXxAYAOmYCAA4nb9ljTleprwGcqijejJLlq3tpi7pSbwBo6gIFgUkKCGR6QYesNNQAjSIaVezLwFJRHRhAsX87AOAD2o6p7QqvNSEosp1zMO0mNgOIoS2udkIMNLFGmBhCMPGONW6sW+mYAJAPWfcXTfULDTBj6GxSmPYjBBnWjLDInl8utMyHFRMMAKU2KxUycegVAFb0okNl+guAwZ7jIEs/oVRCvNBv/T+mVrhciFsEI5DchSTzlBkMKo66Aoi1M31PqR99778DANhN2mGqcvBmGAxY91CalZmnBi0COUTUOwCXzDYAQGvfSwCAPtJme5GNJIwZYnNA+NiEm227/VYk0ZPM2uXeyquiAKDjIADAR4w37DGnddSJ2PDqpKQlHO5Bi9rKpGDYSQnRXqTZ7mcPbVUbOQHsaFGAUHSmLBK5i7bjw1MUL3psgYmwclgI1UlKjfIAECZOn0D60ZS1JmQeWVCJEouCZgZ7XA0wVS/0uaBAqOCUmfOorEqExlnP8Xz6JgBgkDSrs4lgMJj4nDc3RbrPToMFW9RGbEizFSExM7uQ67ee40xYPbFp6rQ0PJ1IoGfnuwCARFBxtBdAmqUacwPWZsxpbaDeKC/SZpG5uYXXAAB9YbU6JlUYM8TmgIBhgNglqiwdVdeIjTUhzjWssOqm0gxM61D8sN6OqVYAACJISURBVAhal76UE7HpoYqJDQDSYk2IE0kvUn1WvngPWpWa8wEAAiFQttDPxTsAgF6jHXMmqtUEkGbmHFpKIJMvulNRKquTALsyar6xBQYoktREsHmi2jHh9G3KDTmpqAHElBObAtOc8CiRkbGeY5V9ojiiE6zUwDTD2iS8F1QnZuUwmQMwb/TJNyj9NI7WuNo5JNhqPcfx3B4UmYt3Pqo2SgQA0Tbr/m0nQxjc9TYAIKnSi4ohy8rMi4PWNc6zKkOVrSs4phy+HADsNFSqDpsTFdDEpt6wS1SH0CMSG8WtDQAA7TNdPz5dOkxtqTdgCy1bMcRSUSxio7LUm6PF0nhMIr3IJRixoa1qq8AYCCv57maLT6RjCkKKnHA5grzMHAPu1gY0ptZPBrCjRYsNa6e3lU7EwhlqTeMAwGQiYZLpRyHptFNQTWx4yJ4TG96kMBhXH0kIdrqf43fHHa98zGamWTKLQygUS/ZzvIe2okulDxasZwcA2gp7QFLWuNxSQSVIrANFtkSaeyw9UyHWpXzcYoTd0+waF1jPpmxAvVFe68HHI0Wc/m6lthnKx1QBTWzqDTFiM5RzlXsrX3BZxAYAipTgOXIYulrUTkpgUZNJpBf9ySzASr170aL+fJudiE1BIDbKCRVgp8E4OrrUVVJw8B5VnSRhkUieilLdswkAplratYmkH4BFbD52iPrFx2yyFoEWJPHBB1aaIgH1xCbAyueLSWtjYuatxcdsVk9suHUDAOQRxGc+t1L5kE0trPEnUuhJ5lActCInPWjBhBa1wvSmcVbUYAL6YDDLhmCLeoIBI4AB5usyKW2l/XgUWCV4mXkgw5tv1rG1QTCMnZ1H2z+Gxx9U4cMHLjSxqTd4vyhbY+MY5TUpj9jMsP/7dzoLLe3jEVDp5wIALVNBQRAlOQQzPbY53566RGysSagLfa4dpuoUGIAyYjO1e6bPB+WP2UkGrLYKPBVF65CKmrEMxYCz08s2T0Nnk9oFD7B21QAz6dtuiWl3GJMQUemfAyDCCAzN9IMW84gUrdB9tFV9igQtU0CJdX7GzGXo7FSv+zCarPMaRxLYNZBBkqV2e9CKTsUVd6E2S+cxnvQjkrU2RpF29QQDcPpFHQSrCCDUPlX5mAGWUg5nWesI1tqgUKfWBtFDT7b/3zppTl3GlA1NbOoNIWLTMzRcPKyY2IRjdhRjS+tR+MqxdVhsg2HbPXQydqNguw43q9e6sFRUF+kFWFXUbrRi5rg6dKs99DP2f3M0gA8dNEP9mJzYYAAD6bxVeg1WFaU6YhOKIDvtOPvHunlfMC3TRNKH4J7XAQA7TfX3dbTVGjdeGkJfz2779ea2OhCbQBCEORAH5n5K/XiAbRUxkfRjd98g0ozYJIMd6jdHtvtwGt2wIkXNnfURtWbD7nQqjx6pRJj558TyTLeVZTYG4fpUJ036yKn2/yfMmFuXMWVDE5t6Q2irkBzoB6jVM6oe4XMAwOyPA6EYPvvF1Th3ifr0CAAQVp46heyxIzb12OlxEtdFelEasibEPbQVcycp9u4BgHmnYc9Xnse/F1fgBmMlZk9UXwbMdS7jWNuMQq8lEt9BO9U2o2QIz1th/3/2wfOVjwcA6LLGOdx4C+PTVgVaT3y28mGDPFJEkviAGakN0Cg6mutAmgHg2K8DB58CHHZmfcaLj0OWOQAP7X4XeVaxk4+o11HBbEaa6T5ixDJgbJ+g2COJYdwwM762OqSUo60WsWkuWoQmnLLur1JTHdJvYOm2T/8E+OT1CLSOzKooxVtmjTKwVFQLktjOTL0yNIQswuhWXXoNAKfeBJz8b7YFf13QNg3Y9iymkt0gKV4V1YzZExQfQ4v1UHaRPgykswCxqinGN6tPkQDAuO4PYd5XbsWicBBBxcJhAHaZeSdJ4IVMAbTfcgDuCXYpFy4DQPBDnwD+YP2/a+Y85eMBACYvQAkBdJE+gAIFaiDVXIdIJCM2nRhA3x6LNCdUuw6LWPhF61+9QAgGwhMxPrsVuZ53bV+oksKGkCLS5nhEM9b9XKxDOwWO9uVfBTb/p/3zcKKjAk0d1rm10gRoqYSmFEuDdc5QPraNhf9Qv7EUYMxEbA4Igz7AlYriVRz9aEJbLFSXah0YRn1JDWCHsaeSPTCYeVyCtGF6Z32ITQtJYSqxCFVHnXZ6HItmdGDe5DpEiAA7FdWBQQyksggMWBGbwUh9dnponQKc+P8Bx13m0nMpRTiOwdYP2T9uoZMws6sOAt5OKyo0x9iORI+1yCcQrx+xaQBSUaZrSWxDgHWsJ4pdhznaJzopoD1GJwLBOu3JJx+BzD/+L/YEu/BW69EIhhUXWwBoG289r1GSQyo5gM6CRZxbJqmPRI4WjJmIzapVq7Bq1SoMDAygtbUOaQE/sIhNOwbtDtsJGke3SlfaRoOlouYa7yLAmjI2ddYhimA2W12vBRv4rsn1Sb81BCxiEyJF5Hq2Isg6XWfjdSRzS79av7EYcpM+AiReBQC8TqfirMV18N4YfwgAKxqYed/S9vTTOA5RrWVqIPLNU4H+ZxEa2m4LW3nbAdUgcz8NumMjejsWIL/4X+oyJkdk2hGI/L9XMU5l3zMBsXgLMjSECMmj5703MQ1WEcD47g9V+aYGx5iJ2BwwYF4ys8kO29Qrgbh6B+BGggkdDyOWydUgjWLGxDrk5gFbeAgAQzSC2VPqs8NsCIImcszqP/D+RgBAH22CGW8gka8DzBlL7P8nWz+EWePrUD0SacFQxIpgzN9j5d/eDUyvT8qxQTBarYqgeHoH4qxPVKyjTtHAo/4J5P/tQOdFj2LqolPqM6YIwwDqRGyIYaCfWM9sz+t/AWCR5s7OOgjTRwlGXMRm3bp1eOSRR9DX14dp06Zh5cqVOOigEVRr3/VhAJZx2/zCK0DQ8vyoi76mUWizoiQmsaI1e2gL5kyoT+kiYp1Aj+VBcX/xOCyph3C4gSjFOoGBQXT0bwIAvEfHqfewaTCaZzu+G1MO/kjdxk23H4ymnTsxq/QOAOCt6IfrNnYjEO60nuOJuW2I0jSA+lUnAagbsTgQMBhoQ1dxD4rv/RUAsDvQhbYxdP77ixG1vbj22mtx2mmnobm5Gccddxxef/11fPjDH8bf/va3Rh9a7Yi2g7Kdz+mBDQCAF0uz0N0RrfStkY1Wt/fDY6UjMatexOawM5GLdOI7+ZW4hn6pPrv5BiLYbFVUzMpZ/cC20/HqPWwaDNI5G8nIJBRJEEctXV6/gSe4S2F3NB9ev7EbgPhEK9p8SGkzANbpukNHEVSA94vq6LeaUSYiI7M6qVEYURGbO++8E//yL/+Cq6++GgDw5S9/GQcffDDuueceLFy4sMFHVztI12FA4j20khQAYGNpNj4xmiM2ITdpu6OwAr+cUKeOsYu/gtKCL2Hb3S/g/EktypsFNhqc2BxmWKXP79Fx6kXajQYhiJ/3e8vssqN+GqrYlPnA363/byuNx/y5h9Rt7EaghRGbMLEsKvagBRMVt1MYq8iaHUAGOKhgpe9zTeqNAUcTRhSxOeigg/Duu+/aPycSCfT29mL27BGmFp/4YeD1RwBYpd6v0+7RLR4WsLE0G3tIOw4aX7/FNhIK4K4vH1m38RoKJiCOM7+P7XQcPj97DOyqx9V/Doh1O6mnjTgY5x87glLi+4BA21SUQGCAAgA20Vk4cZSnORuFfOsMIOH8TNtGcdGDAoyo7esvf/lLZDIZHHHEEfjMZz6Dww8/HF/72tdw/vnn+34nm81iYGDA9a/h6HLMy16iM1FAEJPbRnEqCgDO/BV6p34cF+S+hjkTmpRb3o9ZdB/l+nHAnIwPKe4qPlZBxh1sN0n8yLKTR300EIGQTWoA4C7zH2Codh0eo5j58QuQp84cGZkwukmzbDQ0YnPrrbfiqaeeqviZG2+8ERMnWiWF69atw5/+9CdccMEFmDVrFiKRCO68806ceeaZvlGba6+91k5dHTDocnZ6L5as4x71k+K8T6Nj3qfx7b/vqJ9weCxi/ufQ/8R1aEtaIewJ0+aAaNGhGoQiIDOWgb73PKY0olKnAehrmoP2oTfxR3IUjlt6TKMPZ9Ri0rTZeKb5ozhqaB0AoFV72OwVCKWUVv+YGjz77LPYsmVLxc986lOfQlNTE9LpNMaPH49//dd/xSWXXGK/f8IJJ2D8+PG47777PL+fzWaRzWbtnwcGBtDd3Y1EIoGWlgZVyJRKwA+mAblBrMp9Ff/X9lGs/0YdRY8aoxqv/s+vMfepiwAA//WJP+P0ow9t8BGNYmQGgOygZU44FrD9b8DmdcDR/2L1ntNQhr8/9z84/JHPAAAGv74Vzc2j27ahFnAfumrrd0MjNkuWLMGSJUuqfxBAb28vkskk5s51VyIccsgheOGFF3y/Z5omTLM+Fvo1wzCApatRfPt/MX/yZ7Fqvg4zashD58LT8aN1f0QaJr48V99bShFpsf6NFUxZaP3TUI7DFp+Ax7Zci2A4io9pUrNXaGjEZm9AKcXkyZNxyimn4Be/+AUASzx8xBFH4KSTTsLPfvazmn5PrYxPQ2Mk47an34JBCM4b5YJWDQ2NsYNa1+8RQ2wA4IknnsC5556LiRMnYubMmXj22Wcxffp0PPLIIxg3rrbKD01sNDQ0NDQ0Rh5GJbEBgGQyiY0bN6KnpwfTp0/HggUL9ur7mthoaGhoaGiMPIwIjc2+IB6PY9myZY0+DA0NDQ0NDY0DEKO8xlhDQ0NDQ0NjLGHMEJtbbrkF8+bNw+LFixt9KBoaGhoaGhqKMOI0NvsLrbHR0NDQ0NAYeah1/R4zERsNDQ0NDQ2N0Q9NbDQ0NDQ0NDRGDTSx0dDQ0NDQ0Bg10MRGQ0NDQ0NDY9RAExsNDQ0NDQ2NUQNNbDQ0NDQ0NDRGDTSx0dDQ0NDQ0Bg1GDPERhv0aWhoaGhojH6MOYO+RCKBtrY2bNu2TRv0aWhoaGhojBAMDAygu7sb/f39aG1t9f3ciGuCub8YHBwEAHR3dzf4SDQ0NDQ0NDT2FoODgxWJzZiL2JRKJezYsQPNzc0ghJS9v3jxYjz//PN7/Xs5k9zXSNC+jjsSv6uvVe1o5LXa3++Ptes10r6rr1Xt0Neqdqi8VpRSDA4OYvLkyTAMfyXNmIvYGIaBqVOn+r4fCAT2K0XV0tKyT9/fn3FH4ncBfa32Bo24Vvv7/bF2vUbidwF9rfYG+lrVDlXXqlKkhmPMiIdrxapVq0bcuCPxu/uDkXi+I/Fa7e/3x9r1Gonf3R+MxPPV16o+390fyBh3zKWiVEF3Da8d+lrVDn2t9g76etUOfa1qh75WteNAuFY6YiMJpmniqquugmmajT6UAx76WtUOfa32Dvp61Q59rWqHvla140C4Vjpio6GhoaGhoTFqoCM2GhoaGhoaGqMGmthoaGhoaGhojBpoYqOhoaGhoaExajDmfGxUYM+ePdi6dSu6u7sxfvz4mr7T19eHt956C5MmTcKUKVMUH+GBg927d2P79u2YMWMG2traKn42lUrhb3/7W9nr8+fPr8nLYKQjkUjg7bffxpQpUzBhwoSavlMoFLBp0yaEw2HMnTvX04RytOKVV15Bf38/jjnmmKqf/etf/4pMJuN6berUqZgxY4aiozuwsGXLFmzfvh2LFy+uWeS5efNmJBIJzJs3D9FoVPERHjh477338P7772P27NlV5yx+XUVEo1F85CMfUXiE9cfu3bvxzjvvYPr06TXPTfvynX0G1dhnvPzyy/TEE0+kXV1d9IgjjqCxWIyedtppdGBgoOL3fvCDH9BIJELnzp1LI5EIPeecc2gul6vTUTcGf/7zn+myZcvohAkT6IIFC2g0GqXnnXcezefzvt956aWXKAB65JFH0qVLl9r//va3v9XxyOuP119/nZ522mm0vb2dLliwgDY1NdFPfepTtLe3t+L3NmzYQCdNmkSnTZtGx48fT+fNm0c3b95cp6NuHP7jP/6DLl68mLa3t1PTNGv6zvTp0+ns2bNd99VPfvITxUfaeKxbt46edNJJtKOjgwKgW7Zsqfqdnp4eumzZMtrS0kLnzJlDW1tb6X333af+YBuMbDZLzzrrLBqNRu25+oc//GHF76xevZq2t7e77quzzjqrTkdcH6xZs4aapknnzZtHTdOkF198MS2VStK/sz/QxGY/8Pvf/57++c9/tn/euXMnnTx5Mr388st9v7Nu3TpqGAZdt24dpZTSLVu20HHjxtFrrrlG+fE2Er/85S/phg0b7J9ff/112t7eXvG8ObHZuXNnPQ7xgMEjjzxCH3jgAfvB3717Nz344IPpP/zDP/h+Z2hoiHZ1ddGvfvWrlFJKC4UC/cQnPkEXL15cl2NuJL797W/TZ555ht5+++17RWxuv/12xUd24OGGG26gjz76KH366adrJjaf//zn6eGHH04HBwft32GaJn333XcVH21j8d3vfpd2dXXRrVu3Ukqt55IQQp966inf76xevZqecsop9TrEuuPuu++m0WiUvvDCC5RSSv/+97/TWCxG77jjDqnf2V9oYiMZy5cvp1/4whd83z/nnHPosmXLXK9dcskldNasWaoP7YDDGWecQU8++WTf9zmx+dOf/kQ3btxoT6xjEVdeeSWdOXOm7/u//e1vqWEYdNeuXfZr//u//0sB0Jdeeqkeh9hw7C2x+cEPfkCff/55+v777ys+sgMP69evr4nYJBIJGgqF6Nq1a+3X8vk87ejooNdee63io2wspk2bRq+44grXa4sWLaIrV670/c7q1avpiSeeSF944QX65ptv0kKhoPgo64vly5fTM844w/Xa5z//ebp06VKp39lfaPGwBGzYsAF//OMfcdVVV+Hll1/GpZde6vvZjRs3luVbjzzySLz11lt25/GxgEKhgBdffBGzZ8+u+tkzzzwT55xzDjo6OrBq1Srkcrk6HOGBheeff77itdq4cSO6u7tduesjjzzSfk+jHNdccw3OO+88zJo1C8cddxzefvvtRh/SAYdNmzYhn8+75qxgMIgFCxaM6vuqt7cXW7du9Zyrq533k08+iZUrV2LZsmXo7u7Ggw8+qPJQ6wq/9avSNdmX7+wvtHhYwO7du/H6669X/Mzs2bPR1dVl/1wsFnHFFVcgmUzijTfewAUXXIC5c+f6fr+3txednZ2u1/jPvb29aG5u3o8zqB+Ghobw4osvVvzMlClTMHPmTM/3rrzySuzatQuXXHKJ7/dbWlrw6KOPYsWKFQCsB2T58uVoa2vDNddcs6+HXneUSiX8+c9/rviZ9vZ2HHrooZ7vrV27Fk888QSefPJJ3+973VfRaBTRaBS9vb17f9ANxHPPPVeRvMoQY1511VX4whe+gFAohJ6eHpx++un43Oc+h+eeew6BQGC/fnc98dJLLyGRSFT8zLJly/b59/N7x2vOGmn31VtvvYWdO3dW/MzChQsRi8X2+byXL1+OK664Al1dXSiVSrjqqqtw1llnYePGjRXXhZEASin6+/s9r0kqlUI2my0Tou/Ld2RAExsBGzduxPe+972Kn7nssstw2mmn2T8HAgFs2LABALBjxw6ccMIJGBoawu233+75/VAoVFaNkU6nAQDhcHh/Dr+u2L59O6644oqKnznzzDPx1a9+tez1G2+8ET/+8Y/xwAMP4KCDDvL9/rRp0zBt2jT75yOOOAIXXngh7r333hFFbLLZbNVrddRRR+H6668ve/3hhx/GhRdeiJ/85Cc4/vjjfb/vdV9RSpHL5UbUfQVYkZSenh7f96dOnYp77713v8b48pe/bP+/s7MT3//+93HsscfijTfeGFEL0G233VZ15/vUU0/tM1kLhUIA4DlnjbT76r/+67/wwAMPVPzMr371K8ycOXOfz/vTn/60/X/DMHD11Vfj5z//OR544IERdV95gRCCYDDou37xa7a/35EBTWwEnHTSSTjppJP2+fuTJ0/Gueee60tqAGD69Oll5YDbt2+HaZrqS+Ak4uCDD7YJ3d7gJz/5CS6//HL87ne/syMxe4OJEyeWXb8DHdFodJ+u1R/+8Ad87nOfw/XXX4+LLrqo4menT5+OnTt3glJql3jv3LkTxWLRRQ5HAhoRup84cSIA61kcSQvQzTffrPT3T58+HYB1XcTo6/bt27FkyRKlY8vGmjVrsGbNmpo+O3nyZIRCIc+5em+eJ8MwMH78+BE3Z/lh2rRpntdk6tSpMAxvZcu+fGd/oTU2+4FkMln22ubNm11htz179mDDhg3I5/MAgBNPPBGPPfaYK9T+4IMPYvny5SMqBL4vuOWWW7BmzRrcf//9OOWUU8reTyaT2LBhgx1a97q+TzzxBD784Q8rP9ZG49FHH8VnP/tZXHfddbj44ovL3qeUYsOGDXj//fcBWPdVX18f1q9fb3/mwQcfRCQSwbHHHlu34z5Q8fzzz+Odd94B4H1fPf744zAMY0SRGlXYtGkTXnnlFQDWBqa7uxsPPfSQ/f67776LF198ESeeeGKjDlE5QqEQjj/+eNd5ZzIZPPbYY67zfvvtt/HCCy/YPw+/t9555x28+eabo2bOOvHEE/H73/8elLWYpJTioYcecl2THTt2uDZytXxHOpTJkscATj/9dPrNb36TPvjgg/Thhx+mq1atooFAgN5///32Z+655x5XyXJPTw+dOnUqPfXUU+lDDz1EV69eTU3TpM8991yjTqMuWLt2LSWE0CuuuIKuX7/e/rdx40b7Mxs3bqQA6P/8z/9QSi3vgwsuuID+9re/pQ8++CA9++yzaTgcpo8//nhjTqJOeOqpp6hpmvTss892Xas//elP9mfS6TQFQG+99Vb7tbPPPpvOmDGD/vrXv6a33XYbbW5upt/73vcacQp1xWuvvUbXr19PL7/8choOh+3rJfpJTZkyhX7961+nlFL6xBNP0BNOOIHecccd9L//+7/pd7/7XRqNRulll13WqFOoG9599126fv16+tOf/pQCoPfddx9dv369q5ruYx/7mKtk+e6776bBYJBed9119He/+x1duHAhPeqoo2ixWGzEKdQNf/nLX2g4HKZf//rX6YMPPkhPPvlkOm3aNNrX12d/ZtWqVa6K1kMOOYT+8Ic/pI8++ii944476OzZs+mCBQtoMplswBnIx5YtW2h7ezs999xz6UMPPURXrlxJW1pa6Jtvvml/5oYbbqAitajlO7KhU1H7gV//+te47bbbsHbtWuRyOcyZMwf/93//h3nz5tmfGT9+PJYuXWrnZTs6OvCXv/wFP/jBD/DjH/8YkydPxvr167F48eJGnUZdsGXLFhxzzDFYv369K6owZ84c3HXXXQCApqYmLF261HYV/rd/+zf8+te/xu9+9zsMDg7i4IMPxquvvlpRlzMasHnzZixatAhbt251aXNM08Qf//hHAFaIe+nSpZg0aZL9/tq1a3HzzTdj7dq1CIfDuOmmm/ClL32p3odfd9xzzz1Yt24dAGDx4sX2NbvtttvsZ/HII4+0Uykf//jH0dLSgjvuuAPvvPOOXbkymiMQHOvWrcOdd94JAFi6dCl+/OMfAwC+9a1v4eSTTwZgOXuLOpJzzz0Xra2tuOuuu/DYY4/hk5/8JC677DJlaYQDBUcddRSefvpp3Hzzzbjxxhtx6KGH4vbbb3e5D8+aNQuLFi2yf37qqadw880346abbkJraytWr16NCy64YMTpkfwwY8YMPPPMM/jhD3+IG264ATNnzsQzzzzjqticMmUKli5dulffkQ1CKYsPaWhoaGhoaGiMcIxuyq2hoaGhoaExpqCJjYaGhoaGhsaogSY2GhoaGhoaGqMGmthoaGhoaGhojBpoYqOhoaGhoaExaqCJjYaGhoaGhsaogSY2GhoaGhoaGqMGmthoaGgc8PjP//zPip3gZSOTyeBjH/sYtm7dWrcxNTQ05EATGw0NjYbhpJNOwmOPPVbxM+l0GqtXr8YZZ5zher1YLOLee+/Fueeei2XLluGTn/wkVq9ejeeff36/jysSieDoo4/GN77xjf3+XRoaGvWFdh7W0NBoCHbs2IEpU6bglVdeqdh88rbbbsNPf/pTvPjii/ZryWQSp5xyCrZs2YJLL70UCxcuRDqdxptvvom7774bF1544X63k9i2bRsOOuggvPHGG67O1hoaGgc2NLHR0NCoOx5++GF84xvfwGuvvYaFCxeCEIJLLrkEX/jCF8o+e/TRR+NTn/oUvvWtb9mvXXTRRbj33nvx2muvYeLEiWXfSSaTiMfjuPzyyxEMBnHNNde43j/ttNNw+umn40tf+hLOO+88LFy4EAMDA3jssccwf/583HTTTfbYK1aswFVXXSX5CmhoaKiCTkVpaGjUHYsXL8Zxxx2HhQsX4uc//zl+9rOf4ZOf/GTZ55LJJP76179iyZIl9muZTAZr167FxRdf7ElqACAejwMAlixZgptuugnJZNJ+79lnn8XDDz+M448/HgDw2muv4dJLL8XWrVvx3e9+FxdffLH92aOPPhpPPvmklHPW0NCoD3R3bw0Njbqjq6sL/f39WLJkias78nBs3boVhUIBU6dOtV974403kMlkcNhhh1Ud59RTT0U8Hsd9991np6buvPNOnHDCCa700qJFi/DTn/607PtTp07Fb3/72704Mw0NjUZDR2w0NDQagr///e84/PDDK34mm80CAMLhsP1aJpMBADQ3N7s++9GPfhSLFi3CokWLsGbNGgBAKBTCypUrceeddwKwhMj33nsv/vEf/9H13WOOOcZz/EgkYo+noaExMqCJjYaGRt3Bhb7Voi481bRnzx77te7ubgDAli1bXJ+94YYb8LOf/QxNTU3YvHmz/fp5552HDRs24M0338T9998PQgg++9nPur4bi8U8x9+zZw+6urpqPzENDY2GQxMbDQ2NumPTpk2glGL+/PkVPzdp0iRMnTrVVRE1adIkLFq0CP/+7//u+uyCBQuwaNEitLW1uV6fM2cOjj32WNx111248847cfbZZyMajdZ0nBs3bsRRRx1V02c1NDQODGhio6GhUXd88MEHCIfDCIVCVT/7mc98Bo8//rjrtRtvvBEvvPACLrzwQiQSCfv1dDqNvr6+st9x/vnn4+c//zmeeuqpsjSUH3K5HJ5++mmcfvrpNX1eQ0PjwIAmNhoaGnXHMcccg+7ubsyaNQuLFi3CSy+95PvZiy++GI888ogrHXXMMcdg/fr1ePXVVzFu3DgcdNBBmDdvHrq6utDc3IzLLrvM9TvOOOMMlEolHHrooVi8eHFNx/jQQw+ho6MDJ5988r6dpIaGRkOgfWw0NDQagkKhgM2bN2NoaAiHH354xejNP//zPyMWi+H6668ve6+/vx/btm1Dc3Mzpk6dimCwvNizWCxixowZuPTSS/G1r33N9d7rr7+O5uZmTJ482X6NUoqFCxfiO9/5jo7YaGiMMGhio6GhccBjaGgIW7ZsqarJ8cNvfvMbnHfeedi2bVuZBscL2WwWL7/8MhYuXLhP42loaDQOmthoaGiMWrz33ns49dRT8dprr+H666/HqlWrGn1IGhoaiqGJjYaGxqhFNpvFpk2bMHnyZEyaNKnRh6OhoVEHaGKjoaGhoaGhMWqgq6I0NDQ0NDQ0Rg00sdHQ0NDQ0NAYNdDERkNDQ0NDQ2PUQBMbDQ0NDQ0NjVEDTWw0NDQ0NDQ0Rg00sdHQ0NDQ0NAYNdDERkNDQ0NDQ2PUQBMbDQ0NDQ0NjVEDTWw0NDQ0NDQ0Rg3+f6P7vSUEK7AoAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sunts = numpy.linspace(0.0, -3.0, 301) * units.Gyr\n", "\n", "osun_inertial = Orbit()\n", "osun_inertial.integrate(sunts, mwp)\n", "osun_inertial.plotx(label=r\"$\\mathrm{Inertial}$\")\n", "\n", "osun_noninertial = Orbit()\n", "osun_noninertial.integrate(sunts, mwp + nip + moving_lmcpot)\n", "osun_noninertial.plotx(overplot=True, label=r\"$\\mathrm{Non-inertial}$\")\n", "plt.legend(fontsize=18.0, loc=\"upper left\", framealpha=0.8);" ] }, { "cell_type": "markdown", "id": "f0a1b2c3d4e5", "metadata": { "papermill": { "duration": 0.005823, "end_time": "2026-06-30T01:15:15.107678+00:00", "exception": false, "start_time": "2026-06-30T01:15:15.101855+00:00", "status": "completed" }, "tags": [] }, "source": [ "There is essentially no difference for the Sun, because its orbit is close to\n", "the Galactic center where the LMC's pull on the origin is largely cancelled\n", "by the direct attraction to the LMC.\n", "\n", "### Effect on a distant dwarf galaxy (Fornax)\n", "\n", "For objects orbiting far in the halo, the effect is more significant:" ] }, { "cell_type": "code", "execution_count": 22, "id": "a1b2c3d4e5f0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:15.121043Z", "iopub.status.busy": "2026-06-30T01:15:15.120828Z", "iopub.status.idle": "2026-06-30T01:15:15.453551Z", "shell.execute_reply": "2026-06-30T01:15:15.452384Z" }, "papermill": { "duration": 0.340479, "end_time": "2026-06-30T01:15:15.454265+00:00", "exception": false, "start_time": "2026-06-30T01:15:15.113786+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fornaxts = numpy.linspace(0.0, -10.0, 101) * units.Gyr\n", "\n", "ofornax_inertial = Orbit.from_name(\"Fornax\")\n", "ofornax_inertial.integrate(fornaxts, mwp)\n", "ofornax_inertial.plotr(label=r\"$\\mathrm{Inertial}$\")\n", "\n", "ofornax_noninertial = Orbit.from_name(\"Fornax\")\n", "ofornax_noninertial.integrate(fornaxts, mwp + nip + moving_lmcpot)\n", "ofornax_noninertial.plotr(overplot=True, label=r\"$\\mathrm{Non-inertial}$\")\n", "plt.autoscale()\n", "plt.legend(fontsize=18.0, loc=\"lower right\", framealpha=0.8);" ] }, { "cell_type": "markdown", "id": "b2c3d4e5f0a1", "metadata": { "papermill": { "duration": 0.00596, "end_time": "2026-06-30T01:15:15.466563+00:00", "exception": false, "start_time": "2026-06-30T01:15:15.460603+00:00", "status": "completed" }, "tags": [] }, "source": [ "For Fornax, the past orbit differs significantly when the barycentric\n", "acceleration is taken into account. The abrupt change around -8 Gyr is caused\n", "by the LMC's previous pericenter passage in our model.\n", "\n", "### Checking the acceleration: displacement, velocity, and force\n", "\n", "We can verify the acceleration is realistic by integrating it to get the\n", "displacement and velocity of the MW center, and comparing to the results of\n", "[Vasiliev et al. (2021)](https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.2279V/abstract):" ] }, { "cell_type": "code", "execution_count": 23, "id": "c3d4e5f0a1b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:15:15.480724Z", "iopub.status.busy": "2026-06-30T01:15:15.480483Z", "iopub.status.idle": "2026-06-30T01:15:15.819737Z", "shell.execute_reply": "2026-06-30T01:15:15.818764Z" }, "papermill": { "duration": 0.347853, "end_time": "2026-06-30T01:15:15.820542+00:00", "exception": false, "start_time": "2026-06-30T01:15:15.472689+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import integrate\n", "\n", "vo, ro = 220.0, 8.0\n", "int_ts_phys = numpy.linspace(-3.0, 0.0, 101)\n", "int_ts = int_ts_phys / conversion.time_in_Gyr(vo, ro)\n", "\n", "ax4plot = ax(int_ts)\n", "ay4plot = ay(int_ts)\n", "az4plot = az(int_ts)\n", "\n", "vx4plot = integrate.cumulative_trapezoid(ax4plot, x=int_ts, initial=0.0)\n", "vy4plot = integrate.cumulative_trapezoid(ay4plot, x=int_ts, initial=0.0)\n", "vz4plot = integrate.cumulative_trapezoid(az4plot, x=int_ts, initial=0.0)\n", "\n", "xx4plot = integrate.cumulative_trapezoid(vx4plot, x=int_ts, initial=0.0)\n", "xy4plot = integrate.cumulative_trapezoid(vy4plot, x=int_ts, initial=0.0)\n", "xz4plot = integrate.cumulative_trapezoid(vz4plot, x=int_ts, initial=0.0)\n", "\n", "plt.figure(figsize=(11, 3.5))\n", "\n", "plt.subplot(1, 3, 1)\n", "plt.plot(\n", " int_ts_phys, xx4plot * ro, color=(0.5, 0.5, 247.0 / 256.0), lw=2.0, label=r\"$x$\"\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " xy4plot * ro,\n", " color=(111.0 / 256, 180.0 / 256, 109.0 / 256),\n", " lw=2.0,\n", " label=r\"$y$\",\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " xz4plot * ro,\n", " color=(239.0 / 256, 135.0 / 256, 132.0 / 256),\n", " lw=2.0,\n", " label=r\"$z$\",\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{displacement}\\,(\\mathrm{kpc})$\")\n", "plt.legend(frameon=False, fontsize=18.0)\n", "\n", "plt.subplot(1, 3, 2)\n", "plt.plot(int_ts_phys, vx4plot * vo, color=(0.5, 0.5, 247.0 / 256.0), lw=2.0)\n", "plt.plot(\n", " int_ts_phys, vy4plot * vo, color=(111.0 / 256, 180.0 / 256, 109.0 / 256), lw=2.0\n", ")\n", "plt.plot(\n", " int_ts_phys, vz4plot * vo, color=(239.0 / 256, 135.0 / 256, 132.0 / 256), lw=2.0\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{velocity}\\,(\\mathrm{km\\,s}^{-1})$\")\n", "\n", "plt.subplot(1, 3, 3)\n", "plt.plot(\n", " int_ts_phys,\n", " -ax4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(0.5, 0.5, 247.0 / 256.0),\n", " lw=2.0,\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " -ay4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(111.0 / 256, 180.0 / 256, 109.0 / 256),\n", " lw=2.0,\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " -az4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(239.0 / 256, 135.0 / 256, 132.0 / 256),\n", " lw=2.0,\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{acceleration}\\,(\\mathrm{km\\,s}^{-1}\\,\\mathrm{Gyr}^{-1})$\")\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "d4e5f0a1b2c3", "metadata": { "papermill": { "duration": 0.006142, "end_time": "2026-06-30T01:15:15.835015+00:00", "exception": false, "start_time": "2026-06-30T01:15:15.828873+00:00", "status": "completed" }, "tags": [] }, "source": [ "The main trends and magnitudes are consistent with Figure 10 of Vasiliev et al.\n", "(2021), confirming that our simple approximation gives a reasonable estimate of\n", "the Galactocentric reference frame's acceleration." ] } ], "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": 24.477505, "end_time": "2026-06-30T01:15:16.659163+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/orbits/examples.ipynb", "output_path": "doc/source/tutorials/orbits/examples.ipynb", "parameters": {}, "start_time": "2026-06-30T01:14:52.181658+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }