{
"cells": [
{
"cell_type": "markdown",
"id": "ec15d163",
"metadata": {},
"source": [
"# Tutorial: fitting a FSRQ broad-band SED using angpy and Gammapy\n",
"In order to perform a fit of the broad-band SED of a jetted AGN, `agnpy` includes a `gammapy` wrapper.\n",
"The wrapper defines a custom [SpectralModel](https://docs.gammapy.org/0.20/api/gammapy.modeling.models.SpectralModel.html), representing the emission due to a combination of radiative processes. The `SpectralModel` can be used either to fit flux points or to perform a forward-folding likelihood fit (if the instrument response is available in a format compatible with `gammapy`). \n",
"\n",
"Several combination of radiative processes can be considered to model the broad-band emission of jetted AGN. For simplicity, we provide wrappers for the two scenarios most-commonly considered:\n",
"\n",
" * `SycnhrotronSelfComptonModel`, representing the sum of synchrotron and synchrotron self Compton (SSC) radiation. This scenario is commonly considered to model BL Lac sources;\n",
"\n",
" * `ExternalComptonModel`, representing the sum of synchrotron and synchrotron self Compton radiation along with an external Compton (EC) component. EC scattering can be computed considering a list of target photon fields. This scenario is commonly considered to model flat spectrum radio quasars (FSRQs).\n",
"\n",
"In this tutorial we will show how to use `ExternalComptonSpectralModel` to perform the fit of the broad-band SED of PKS1510-089, measured during its gamma-ray flaring activity in 2015 [(Ahnen et al. 2017)](https://ui.adsabs.harvard.edu/abs/2017A%26A...603A..29A/abstract). We select the MWL SED corresponding to the period identified in the paper as \"Period B\" (MJD 57164-57166). \n",
"\n",
"[Gammapy](https://gammapy.org/) is required to run this notebook."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "39abfeed",
"metadata": {},
"outputs": [],
"source": [
"# import numpy, astropy and matplotlib for basic functionalities\n",
"import numpy as np\n",
"import astropy.units as u\n",
"from astropy.constants import c, G, M_sun\n",
"import matplotlib.pyplot as plt\n",
"import pkg_resources\n",
"\n",
"# import agnpy classes\n",
"from agnpy.spectra import LogParabola\n",
"from agnpy.fit import ExternalComptonModel, load_gammapy_flux_points\n",
"from agnpy.utils.plot import load_mpl_rc, sed_y_label\n",
"\n",
"load_mpl_rc()\n",
"\n",
"# import gammapy classes\n",
"from gammapy.modeling.models import SkyModel\n",
"from gammapy.modeling import Fit"
]
},
{
"cell_type": "markdown",
"id": "4e2c0367",
"metadata": {},
"source": [
"The `ExternalComptonModel` wraps the `agnpy` functions to compute synchrotron, SSC, and EC radiation. It returns a `gammapy.modeling.SpectralModel`. To initialise the model, the electron distribution and a list of targets for EC has to be specified, the remaining parameters (the ones of the emission region and of the line / thermal emitters) will be initialised automatically and can be modified at a later stage.\n",
"\n",
"The `ExternalComptonModel` class provides both the `sherpa` and `gammapy` wrappers. You should specify, through the `backend` argument, which package you want to use.\n",
"\n",
"In this case we choose to consider only EC on the DT radiation."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "90b627f3",
"metadata": {},
"outputs": [],
"source": [
"# electron energy distribution\n",
"n_e = LogParabola(\n",
" k=1 * u.Unit(\"cm-3\"), p=2.0, q=0.2, gamma_0=1e2, gamma_min=1, gamma_max=3e4\n",
")\n",
"\n",
"# initialise the sherpa model, consider only EC on the DT radiation\n",
"ec_model = ExternalComptonModel(n_e, [\"dt\"], ssa=True, backend=\"gammapy\")"
]
},
{
"cell_type": "markdown",
"id": "990ffd73",
"metadata": {},
"source": [
"Let us set appropriate parameters for the emission region. The size of the blob, $R_{\\rm b}$, is set by the variability timescale, $t_{\\rm var}$, via\n",
"\n",
"\\begin{equation}\n",
"R_{\\rm b} = \\frac{c \\delta_{\\rm D} t_{\\rm var}}{1 + z},\n",
"\\end{equation}\n",
"\n",
"where $c$ is the speed of light, $\\delta_{\\rm D}$ the Doppler factor, and $z$ the redshift.\n",
"\n",
"The parameters of the accretion disk and the DT are taken from [(Ahnen et al. 2017)](https://ui.adsabs.harvard.edu/abs/2017A%26A...603A..29A/abstract)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6ef9d4a7",
"metadata": {},
"outputs": [],
"source": [
"z = 0.361\n",
"\n",
"# - blob parameters\n",
"Gamma = 20\n",
"delta_D = 25\n",
"Beta = np.sqrt(1 - 1 / np.power(Gamma, 2)) # jet relativistic speed\n",
"mu_s = (1 - 1 / (Gamma * delta_D)) / Beta # viewing angle\n",
"B = 0.35 * u.G\n",
"# size and location of the emission region\n",
"t_var = 0.5 * u.d\n",
"r = 6e17 * u.cm\n",
"\n",
"# - disk parameters\n",
"L_disk = 6.7e45 * u.Unit(\"erg s-1\") # disk luminosity\n",
"M_BH = 5.71 * 1e7 * M_sun\n",
"eta = 1 / 12\n",
"m_dot = (L_disk / (eta * c ** 2)).to(\"g s-1\")\n",
"R_g = ((G * M_BH) / c ** 2).to(\"cm\")\n",
"R_in = 6 * R_g\n",
"R_out = 3e4 * R_g\n",
"\n",
"# - DT parameters\n",
"xi_dt = 0.6\n",
"T_dt = 2e3 * u.K\n",
"# Ghisellini and Tavecchio's Formula\n",
"# relating the DT radius to the disk luminosity (check the reference)\n",
"R_dt = 2.5 * 1e18 * np.sqrt(L_disk.to_value(\"erg s-1\") / 1e45) * u.cm"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "fcdd45fe",
"metadata": {},
"outputs": [],
"source": [
"# emission regions parameters\n",
"ec_model.parameters[\"z\"].value = z\n",
"ec_model.parameters[\"delta_D\"].value = delta_D\n",
"ec_model.parameters[\"log10_B\"].value = np.log10(0.35)\n",
"ec_model.parameters[\"mu_s\"].value = mu_s\n",
"ec_model.parameters[\"t_var\"].value = t_var.to_value(\"s\")\n",
"ec_model.parameters[\"t_var\"].frozen = True\n",
"ec_model.parameters[\"log10_r\"].value = np.log10(r.to_value(\"cm\"))\n",
"\n",
"# we freeze the reference energy of the log parabola\n",
"ec_model.parameters[\"log10_gamma_0\"].frozen = True\n",
"\n",
"# target parameters\n",
"# - disk\n",
"ec_model.parameters[\"log10_L_disk\"].value = np.log10(L_disk.to_value(\"erg s-1\"))\n",
"ec_model.parameters[\"M_BH\"].value = M_BH.to_value(\"g\")\n",
"ec_model.parameters[\"m_dot\"].value = m_dot.to_value(\"g s-1\")\n",
"ec_model.parameters[\"R_in\"].value = R_in.to_value(\"cm\")\n",
"ec_model.parameters[\"R_out\"].value = R_out.to_value(\"cm\")\n",
"# - DT\n",
"ec_model.parameters[\"xi_dt\"].value = xi_dt\n",
"ec_model.parameters[\"T_dt\"].value = T_dt.to_value(\"K\")\n",
"ec_model.parameters[\"R_dt\"].value = R_dt.to_value(\"cm\")"
]
},
{
"cell_type": "markdown",
"id": "3486e440",
"metadata": {},
"source": [
"We can display all the parameters of the model at once"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "188c46f7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
" type name value unit error min max frozen is_norm link\n",
" str8 str7 float64 str1 int64 float64 float64 bool bool str1\n",
"-------- ------- ----------- ---- --------- ---------- --------- ------ ------- ----\n",
"spectral z 3.6100e-01 0.000e+00 1.000e-03 1.000e+01 True False \n",
"spectral delta_D 2.5000e+01 0.000e+00 1.000e+00 1.000e+02 False False \n",
"spectral log10_B -4.5593e-01 0.000e+00 -4.000e+00 2.000e+00 False False \n",
"spectral t_var 4.3200e+04 s 0.000e+00 1.000e+01 3.142e+07 True False \n",
"spectral mu_s 9.9925e-01 0.000e+00 0.000e+00 1.000e+00 True False \n",
"spectral log10_r 1.7778e+01 0.000e+00 1.600e+01 2.200e+01 True False "
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ec_model.emission_region_parameters.to_table()"
]
},
{
"cell_type": "markdown",
"id": "7916d810",
"metadata": {},
"source": [
"in case of the `ExternalComptonSpectralModel`, we can display also the parameters of the targets (i.e. of the line and thermal emitters producing the photon targets for EC scattering. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a0d3c685",
"metadata": {},
"outputs": [
{
"data": {
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"
Table length=8\n",
"
\n",
"
type
name
value
unit
error
min
max
frozen
is_norm
link
\n",
"
str8
str12
float64
str5
int64
float64
float64
bool
bool
str1
\n",
"
spectral
log10_L_disk
4.5826e+01
0.000e+00
4.200e+01
4.800e+01
True
False
\n",
"
spectral
M_BH
1.1354e+41
g
0.000e+00
1.000e+32
1.000e+45
True
False
\n",
"
spectral
m_dot
8.9457e+25
g s-1
0.000e+00
1.000e+24
1.000e+30
True
False
\n",
"
spectral
R_in
5.0589e+13
cm
0.000e+00
1.000e+12
1.000e+16
True
False
\n",
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spectral
R_out
2.5295e+17
cm
0.000e+00
1.000e+12
1.000e+19
True
False
\n",
"
spectral
xi_dt
6.0000e-01
0.000e+00
0.000e+00
1.000e+00
True
False
\n",
"
spectral
T_dt
2.0000e+03
K
0.000e+00
1.000e+02
1.000e+04
True
False
\n",
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spectral
R_dt
6.4711e+18
cm
0.000e+00
1.000e+17
1.000e+20
True
False
\n",
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"
],
"text/plain": [
"
\n",
" type name value unit error min max frozen is_norm link\n",
" str8 str12 float64 str5 int64 float64 float64 bool bool str1\n",
"-------- ------------ ---------- ----- --------- --------- --------- ------ ------- ----\n",
"spectral log10_L_disk 4.5826e+01 0.000e+00 4.200e+01 4.800e+01 True False \n",
"spectral M_BH 1.1354e+41 g 0.000e+00 1.000e+32 1.000e+45 True False \n",
"spectral m_dot 8.9457e+25 g s-1 0.000e+00 1.000e+24 1.000e+30 True False \n",
"spectral R_in 5.0589e+13 cm 0.000e+00 1.000e+12 1.000e+16 True False \n",
"spectral R_out 2.5295e+17 cm 0.000e+00 1.000e+12 1.000e+19 True False \n",
"spectral xi_dt 6.0000e-01 0.000e+00 0.000e+00 1.000e+00 True False \n",
"spectral T_dt 2.0000e+03 K 0.000e+00 1.000e+02 1.000e+04 True False \n",
"spectral R_dt 6.4711e+18 cm 0.000e+00 1.000e+17 1.000e+20 True False "
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ec_model.targets_parameters.to_table()"
]
},
{
"cell_type": "markdown",
"id": "a1e350e0",
"metadata": {},
"source": [
"### Fit with `gammapy`\n",
"Here we start the procedure to fit with Gammapy.\n",
"\n",
"#### 1) load the MWL flux points, add systematics\n",
"A function is provided in `agnpy.fit` to directly load flux points in a `gammapy.estimators.FluxPoints` object. It reads the data from a file, included in the package, containing a MWL SED following [these specifications](https://gamma-astro-data-formats.readthedocs.io/en/v0.2/spectra/flux_points/index.html).\n",
"\n",
"The same function allows to add a systematic error on the flux points, this is done with a dictionary specifying the instrument name and the systematic error, expressed as a relative error on the flux. The systematic error is summed in quadrature to the statistical error.\n",
"\n",
"In this example, we use a very rough and conservative estimate of the systematic errors ($30\\%$ of the flux for VHE instruments, $10\\%$ for HE and X-ray instruments, $5\\%$ for all the other instruments).\n",
"\n",
"Specifying the systematic errors through the dictionary is optional.\n",
"\n",
"We can also set the minimum and maximum energy to be used in the fit. We exclude points below $10^{11}\\,{\\rm Hz}$, as they are measured in the radio band with large integration regions. They hence include the extended emission of the jet, while in our model we are considering the emission from a finite region of the jet, the blob."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "6f7b9bc1",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n",
"No reference model set for FluxMaps. Assuming point source with E^-2 spectrum.\n"
]
}
],
"source": [
"systematics_dict = {\n",
" \"Fermi-LAT\": 0.10,\n",
" \"KVA1\": 0.05,\n",
" \"KVA2\": 0.05,\n",
" \"MAGIC\": 0.30,\n",
" \"Metsahovi\": 0.05,\n",
" \"NICS1\": 0.05,\n",
" \"NICS2\": 0.05,\n",
" \"SMART1\": 0.05,\n",
" \"Swift-XRT\": 0.10,\n",
" \"TCS1\": 0.05,\n",
" \"TCS2\": 0.05,\n",
" \"TCS3\": 0.05,\n",
" \"TCS4\": 0.05,\n",
" \"TCS5\": 0.05,\n",
" \"TCS6\": 0.05,\n",
" \"UVOT\": 0.05,\n",
"}\n",
"\n",
"# min and max energy to be considered in the fit\n",
"E_min = (1e11 * u.Hz).to(\"eV\", equivalencies=u.spectral())\n",
"E_max = 100 * u.TeV\n",
"\n",
"datasets = load_gammapy_flux_points(\n",
" \"../../agnpy/data/mwl_seds/PKS1510-089_2015b.ecsv\", E_min, E_max, systematics_dict\n",
")"
]
},
{
"cell_type": "markdown",
"id": "673ab97e",
"metadata": {},
"source": [
"For the gammapy wrapper, we have to define a spectral model and associate it to the list of datasets we obtained from the flux points."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3159dc0e",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: divide by zero encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: invalid value encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: divide by zero encountered in true_divide\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in expm1\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in multiply\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
]
}
],
"source": [
"sky_model = SkyModel(spectral_model=ec_model, name=\"PKS1510-089\")\n",
"datasets.models = [sky_model]"
]
},
{
"cell_type": "markdown",
"id": "51031e9d",
"metadata": {},
"source": [
"Let us plot all the flux points and the initial model "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "c6f335de",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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SiCnXT9Hs3OXLl2fYsGF88sknnDp1CsjdG2f16tWcPXvWcywsLIzq1avjcrn4+++/mTNnDn379mX79u3cfffdmkw6Vz04PpKcnGx0CLqzbds2Wrf2/83azDjBMTU1VdNJuO4hKjdLlizhrrvu4syZM/Tq1QshBOXKleP//u//fD73hx9+yPDhwwkODqZFixYMHDgQl8vF/Pnz6dGjBx07dvT0XDz33HOMGTOGKVOmkJOTw8CBA/n3v/+tlWapqVIrwq85N0Xx5JNPFrj93HPP8cADDzBlyhSklAwYMIB///vf3Hrrrdx///107tyZhg0bMmvWLIQQ1KlThyuuuIJ77rmHG2+8kebNm5d4zQcffJB77rmH7t27I4RgxozcJKJ27dpUq1aNc+fO0bRpU80cC6Oo12tERAMqVMidY+VPzw3kbpL5r3/9i6CgILKzs7n55pu54oorqFOnDm3atAGgTp06Jbq2bNmS/fv3M2TIECZNmuRZtLBt2zbWr1/PW2+9BcDUqVO5++67PZOa3atwu3fvzpNPPsmePXsC3osDUL9Sfc3m3HiTlpZG06ZNeffdd7nrrrvIyckhOzvbMyx47733epLD9u3b06tXrwKrMqOiopg9e7YmNa2EO6tXFI7XJOPrmjdvXv2ff/4xMiTdyc7Otv2OzVZ2dE+QLAkppa5DCmbAaEf3hGMtE5zCMNozEBTn6J507G+CYzRmakf3hGOtExy9Hb3f/6KiooiJiYmRUkZ5P9aa7/ABREo5F5gLIISIrlSpkn6z7EzCvn37SvWpz8o4wTE9PZ2IiLIvW7YCRjvqndi4MdozEBTnaPXExo2Z2lHrxMaNmRzVHBwfCfSERiMI1F4MRuIERzPtmqoXTnAEZ3gqR3tgJkeV4PiIE2qJJCQkGB2C7jjB0T3ObWec4AjO8FSO9sBMjirB8RG7V4KF3FUBdscJjlrvg2NGnOAIzvBUjvbATI7micQiOGFSthN6qZzg6H6tDpiylgFT1hocjT4Y/fc4e8LjzJ7wuO7XMdozEBTn2HvTbnpv2h3AaPTBTO148NbbOHjrbZqf10yOapJxCXiXajh9+rSR4QQEl8v/HVnNjhMcFQqFwsmoHpwS8C7VEBkZaXRIumNkAcNA4QRHrbuKvSuKv/3225qcd9asWaxcufKi4/feey/r1q0r9DnNmzdn0qRJBAUFcdNNNxEVFUWdOnVo27YtUVFRfPTRR5rEFijc1cQXLVrkOdakSRNmzZrFq6++SlBQEKmpqTz22GNERUXRrVs37rjjDs6cOcM///zjaZNOnTrxzTffALlV3ps1axbQOl3+oPfQhhZVr5OSkrjuuuuoWrVqgcrvpcVMwzda4f177d69u8+/V+/3Fne5EX9RPTg+4oShjbNnz1KtWjWjw9AVJzhmZ2dz7EIme08mk5Ht4sb3Yvh85DU0qFH25K6wcg1FUdpin/fee69PMWzatImOHTuybNkyJk6cyM8//+w5zwMPPEDXrl19Ol9ZOX/yBGeOxJGTlcWsfz/M4KcnUTWy6N1vS6J58+a88cYbDBw48KJ9RLKzsxk/fjxXX321p37Xjh07yMjIYNKkSbzyyit069YNKSXnzp0D4LbbbuPBBx8s1Z5JZqCovakOp2WwOyWdDCnp/vs/zG51OZdF+L6aVYuq1xEREfzwww8Fyi9o4RhoMuPjydi3D5mZyf7+A6g//WPKlaKmXGF4/14/++wzQkJCfK4m7st7S2kx/jdtMZywTPySSy4xOgTdsbOjZ76NhL2ncpMbyP35xvdjaBpZkSXjuvl9nfj4eMaMGUNaWhoRERHMmjWLWrVq0aRJE+644w42bNjAU089xYcffkjVqlXZtm0bb775JnPmzCE2Npann36au+++m5deeokmTZowYsSIUl13zpw5PPTQQ8ybN48tW7bQuXNnv118wT3nxp3c5P4cz6x/P0yNeg0AuPvN//h83ksvvZRmzZqxaNEiBg8eXOC+kJAQVq1axccff+w55t49t2LFiqxatYoWLVpQvXp1T4Vmq/U2519enH++jTu5AdiTmkH332O5okI4K665wu9rzp0716eq1yEhIcWWcCgJo5dQu+fcuJMbgMz9+znQfwBheT19jRZ879c1ypUrx5w5c3yuJr5t2za6detGo0aNeP/996lRo4ZfcYAaovIZLepjmJ2DBw8aHYLuOMHRJaUnuXHjfdtX8lcUv+eee3jhhRdYvXo1Dz30kGd7evcW+GvWrKF8+fKcOXOGuXPnMnPmTMaMGcOXX35JTEwM7733ns/Xz8nJYfPmzXTp0oWRI0cye/Zsv3z8IcerN9f7dll49tlnefPNNy+aqHnkyBFq1qxZ6A6xb7/9NklJSXTp0oWOHTuydetWv+MwgoyMwquEZ3j9Lrxv+4OvVa/9pSjHQONOboq67Q8ZGRk+/17r1q3LgQMHWLt2LV27duXpp5/WJBbVg+MjTpi7YfcdfsHeju7eGSklvd//lb2ncuunBQloXMu/3pv83cjuIpCQm9S453oEBwfTqVMnz3NatWpFUFAQ9erVo1mzZpQvX57y5ct76vK4WbdunacA4ZIlSwq9/sqVKzl58iR9+/YFYM+ePQHv9nf3zsz698OcORIP5BawrH5pvTL13OSnXr16tG/fnoULFxY4Xr9+fRISEgrdBr9GjRq89957vPfee8TExPD4448TExPjVxxGkL/2UP7eme6//8Oe1NzEIAhoUj5Mk94bwOeq1+45I2VFi/pK/uDundnffwCZ+3OriRMURLlGjfzuuXETHh5ept+re3RkxIgRTJ06VZNYVA+Ojzih2KZVPwH6ghMcU1NT+XzkNYTlVbxuXKsin4/UrrRAixYteP/994mOjmbdunV8+umnQO4/+6KqhxdXo6Zr166eqsxF7VP09ddf88MPP7Bs2TKWLVvG7bffzooVKzQy8o3BT08iODQUgOqX1mPw05M0Oe/EiRM9vWFu0tPTueGGGwq88e/cuZNjx46xe/f/hnPq1q1r2RWCqamphR6f3epywvJeN03KhzG71eWaXdPXqtf+UpRjoKk//WNE3nBZuUaNqD/94xKeUXrS0tJ8/r1euHDB8/zVq1d7qtn7i+rBKQHvZeJmeYHqSbt27YwOQXec4FihQgUqVICmkbnJghbzbvLz7rvv8sgjj3iS/lGjRpV6Hk1p+de//kWVKlUAGDduHH/++SdXX3215/6bb76ZadOm0a9fP02vWxqqRtbxa85NUdSrV48OHTqwbNkyz7EKFSrw3nvv8cwzz9CjRw9cLhd169Zl+vTpzJw5k0WLFlG+fHlcLhfvvPMOAN999x2ffPIJx44d44YbbmDy5MkBn6/kCxUqVCj0+GURYVxRIbfnQ6ueGzcNGzb0qeo15L7mdu7cSfny5Vm3bp1PE46Lcgw05erX12zOjTfly5enXr16Pv1eFy1axOTJk6lUqRLh4eGeavb+oqqJ+4AQIrpdu3Y9Nm/ebHQourJ582bat29vdBi6YmXH0lYTT0lJMc0bql44wRGc4akc7YHejr5UE1dDVD5SqVIlo0PQHav+4/cFJzja/Y0UnOEIzvBUjvbATI4qwfERJ8zB2bJli9Eh6I4THFNSUowOQXec4AjO8FSO9sBMjirB8REnFGls06aN0SHojhMcnbDizwmO4AxP5WgPzOSoEhwfccIk49jYWKND0B0nODphzyYnOIIzPJWjPTCTo0pwfMTofQwCQaNGjYwOQXec4OjZdfuT7rlfNsToncVPTvmLk1P+0v06RnsGguIcB0xZ+78dui2Mmdrx29c38e3rmzQ/r5kcVYLjI2bZiVJPjh07ZnQIuuMEx0wNdyeF3IJ4N9xwA5BbdLBHjx5ceeWVBerJ7N27ly5dugCwfv16goKCOHDggOf+H374gSuvvFKzDwpaOxpFScU2MzMzfS62eccdd9C5c2c6duzIrFmzDDIrPXq3pRbFNpcvX06nTp3o0aMH/fr148yZMz7FYJfXa360+L1C7u/2+uuvp2fPnmXa5bxQpJTqq5RfQHSXLl2k3Tl79qzRIeiOlR137dpVqsdlZWVJeeaAlK/UknJSZSk/ujb3dhk5ePCgvP7662VSUpLs0aOH/O9//yuff/55OX36dM9jJk2aJKdOnSqllHLs2LHyiSeekK+88orn/oSEBJmWliYbN25c5jjyk5WVpcl5ynTthFQZ/9xaGf/Mr/L4u3/KrITUMp/r4MGDsnnz5rJjx47S5XJJKaVs3LixnDlzpnzllVdkVlaWHD16tJwyZYrnOdu3b5dHjx6Vt99+u/z111+llFK6XC555swZKaWUe/bskVJKz+87LS2tzPEFgqLa8nBCimz23FJ52TNL5A3vRsvDCSl+X6tHjx4yPj5eHjx4ULZr106ePHnSE8OqVavkzp07Za9evTyPd/9ODx8+LNPT06WUUk6dOlU+//zzPl3XyNdrfs6fSpUfP7JGfjT6F/n1Sxvk+VNlf+3mp0ePHvLgwYM+/15Pnz4t+/fvLzMyMkq8hvf7X48ePSQQLQv5n602+isB743+Tp48aWQ4ASE1NdX2lbZt7Zg3HBUkJSTshuy8XsfTsTCtI9RqDqN/LdOpk5OTGTBgAGPHjuWOO+6gVatWjBkzhtGjRwMwf/58oqOjycrK4q+//mLNmjX06tXLU4JBiwJ6+TFi1173kFTWyRTIzt1HLPtUKife30xoZO4S2chxbX0+b3HFNrOzs30uttm0aVMAQkNDCQoKKnYXaTOQvy3zD0ftPalfwVhfi202aNDA89xy5cr5XCLE6F2m3UNSZ4+lkJP3Oz13PJV5L/9O9UtyX7t3POvfbucul4tvvvnGp9/rTz/9RPXq1Rk4cCCQu4loixYt/IoD1BBViUgp50opB0gpBwA7atWqZXRIuhMUZP+XhRMcgf8lN0Xd9pHY2FguXLjgeSNq3rw5qampxMfH8+eff9KoUSNq1qzJ8uXL6devH2FhYbRp0wZbbo6ZLYu/XQaKKrZ5+vTpMhfbfP311xk6dKip5kb4gtYFY/NT1mKbJ0+eZMqUKTz88MOaxRJIcrx+h963/cXX3+uxY8fYt28fixcv5q233uKhhx7SJA7Vg+MjZv8UpAWhefV17IytHfN6Z3Kysgj6tGtuzw2ACIKazcrcewPQoUMH+vbty5133sn3339PSEgIQ4cOZd68eRw/fpzhw4cDuZ+Mjx49yrp160hMTGTOnDm6bK5oxN+ju3fmxHubyT6Vt6pSQEit8mXquclPUcU2a9euXaZim1999RV///038+bN8yuuQJDfK3/vzI3vxWhaMDY/ZSkKmZiYyJAhQ/j00089PRSlxej/H+7embkvb+Tc8dzXrhBQtU55v3tu3AghfP69Vq9enV69elGuXDlat27N6dOnNYnFIR9jtSMnJ8foEHTHCZsZOsHR5XLB0G8gJO+Te81mubf95Mknn6RFixbcd999SCkZOnQo33zzDUuXLmXQoEEkJydz5MgRYmJiWLZsGevXr+e3337T5W/HyC7/miOvgpDcf1ghtcrn3taAwoptAj4X21y0aBFz585l9uzZluixLKot9SwY62tRyLS0NG655RaeffZZOnbs6PP1jB6ictN/bGuC836nVeuUp//Y1pqd2+Vy+fx7jYqK8my+Gh8fT+XKlTWJRfXg+IitP/nnUbNmTaND0B0nOIaEhED1RrlzbsCvnhtvXn/9dR5++GEee+wxpkyZQs2aNWnZsiURERF89dVXdO9ecFl6q1at+OWXX4iIiODll1/2FIAcO3Yst956a5nj8HUOhJaE1Ijwa85NURRWbDMkJMTnYpvDhw+nefPm9O7dG8itxH7ppZdqFqfWFNWWDWqU161grK/FNt999122bdvGW2+9xVtvvcWNN97Ic889V+rrGfl6zU+VWhGazbnxJiQkhMsuu8yn36sQgqioKLp3705WVhb/+Y82xWtVsU0fEEJEX3PNNT3++OMPo0PRldjYWJo3b250GLpiZcfSFttMS0sjIiLif3vgaJjgmAWPo0G4JxxrmeAUhtGegaA4R/ekY60TnEBjpnZ0TzjWOsHR29GXYpvmSCcthFlenHrSpEkTo0PQHSc4evaasWFi48bojTf1TmzcGO0ZCIpztHpi48ZM7ah1YuPGTI7mH5g1GWYqJKYXO3fuNDoE3XGCY1pamtEh6I4THMEZnsrRHpjJUSU4PuKEYputW2s34cysOMHRTEXv9MIJjuAMT+VoD8zkqBIcH0lKSjI6BN2x5Z4lXjjB0Qm9jU5wBGd4Kkd7YCZHleD4SKVKlYwOQXf02K/EbDjBsUKFvFUSP97BHT/eYXA0+uB2NIpPPvmETz75RPfrGO0ZCIp1tEnBWDO14+wJjzN7wuOan9dMjirB8RHVg2MPnOBopk9SeuEER3CGp3K0B2ZyVAlOCQghhgkhlgghlgAtzTSBSi+c0LvhBEetP0lpUU38iSeeoFOnTnTq1Ik333zT75jM9GnRH1wuF6NHj6ZLly5069aN4cOHM2vWLIKDg4mLi/N4NmnShHvvvdfzvKNHjxIcHMyaNWs8x1566SWuvPJKevbsSdeuXdmxYwf33XcfUVFRNGzYkCuvvJKoqCief/551q9fT8uWLQkPD+fIkSOB1i6A3m2pRdXrPXv20LlzZ89jt23b5lMMdnm95ic6OpoHHnjAc/vcuXMIIRgyZEiBxz377LPMmDGDrKwsnnrqKbp160a3bt146qmnPHvfREVF0aZNG+rWrUtUVBQDBgzwL7jCKnCqr6KriXfo0KGEWqfWZ/v27UaHoDtWdixtNfGUlBQZlxgn233VTl4962o56IdBMi4xrszX1aKauLvCdU5OjuzUqZPct29fmeORMtfRKM6cOSNfeeUVOWnSJPnRRx95KiOXhZ9++kmOGjWqwLlnzpwpO3XqJN98802ZkpIiN2zYIK+77jo5cuRIz+P+7//+Tz7xxBPy/vvv9xybNGmSnD17tpRSypiYGHnHHXcUep+UUp4/f97TnvHx8WWOXwuKbMszB6R8pZaUkypL+dG1ubf9pKzVxLOysjzV3n/55Rc5ZMgQn65r5Os1P+dOHJfvDx8s37mjv5w5fow8d+J4mc+1Zs2aAq+/PXv2yO7du8tmzZrJ8+fPe45fccUV8uzZs3Ly5Mnyqaee8hx/6qmnCrxHeJ/PG1VNXEecsA9Os2bNjA5Bd+zsmH++zf7z+8l0Zeb+fGE/gxcOpnHVxnx787dlOre/1cTdFa6DgoIIDg4mODjYH1VD9txwz7k5ffq0Z0fW06dPM23aNNzFeN2/j9JSsWJF/v77b88mZu4qy3369GHFihU89dRTfP311wwbNow///zT87wff/yR5cuXc+ONN5KRkXFRQc2zZ89eVLgzP1WqVPEpTj0p0Jb559ucjv1fkdjTsTCtY+7u3Brs7+RrNfH8OxEnJibSqlUrn65n9B4x7jk3Z47EkZOVlfdzPLP+/TA16uVWSr/7Tf92EQ4LC0MIwS233MKCBQu47777WL9+PVdeeSXVqlVj7ty5BaYITJo0iQ4dOnjeI7REDVH5SEaGf9WYrUBRRdLshBMcpZSe5MaN921f0aqa+OzZs2ncuDENGzb0K57MTP98/MGd3BR12xe6d+/O6NGjPdvZf/DBB0DuP9QrrriCTZs28ffff9OmTRvPc/7++2+aNWtGREQEgwYNYsmSJZ77XnvtNVq3bs3YsWOZPHlymeMKJEW2ZXZG8bf9oCzVxDdv3sx1113HI4884imDUVqMfL3mx53cFHXbH9yOI0aMYO7cuUBuIjlixAgA0tPTCywlr1ChAunp6ZpdPz+qB8dHypUrZ3QIuhMZGWl0CLpjZ0d370xOTg63/Xgb+y/sByCIIBpVaVTm3hvQppr4qlWr+PLLL/nxxx/9NDWmNpy7d2bq1KmeqsdCCGrWrOlzz01+Ro0axahRo0hMTKR79+489thjAAwdOpRHH32UQYMGFXj8nDlz2LFjB3379iU9PZ2aNWty2223AfDcc88xbNgwJkyYwB9//GGJsiQF2jJ/78zUjrk9NwAiKLdorEa7c5elmnj79u3ZsGEDf/zxB48++ii+lO4xupahu3dm1r8f5syReCD3tVv90npl7rmJiIgokKDk5OQQERHB1VdfzZkzZ4iPj2fFihWeGmlhYWGkpqZ6kpzU1NSLeh61QvXg+Ig/n9Kswvnz540OQXec4Jidnc2U66dQLig3KW9UpRFTrp/i93n9qSb++++/88ILLzB//nxNhnuN/HscOnSoZ8iiZs2aDB06tMznOnbsGImJiUDuVhQVK1b0DC117dqVFi1aeD4BQ27v3KpVq9iwYQPLli0jOjqa8+fPc+7cOc9jgoKCeOGFF3jrrbdM03NQHEW25dBvICTvH2DNZrm3NcLXqtf5/5FXrVrV503tzPL/Y/DTkwjOS7aqX1qPwU9PKvO5rrjiCrZv3+4Z3fjll19o164dkPs38uCDD9K9e3fP8NzQoUN55ZVXPM9/5ZVXGDZsWJmvXxwqwfGRoCD7/8qMHicOBE5wDAoKon6l+jSu2pgrq1/JwsELqV/p4u74svD6669TsWJFHnvsMerUqUPNmjXp1KkTERERLFiwoMhq4vfffz9JSUkMHjyYqKgov5frG/n3WL16dWrVqkXdunV55JFHPPM0ysKRI0e46aab6NatG507d6Zfv36e+UlCCGbMmFFgOG/t2rU0b968gH9UVBTfffddgfNWqlSJvn37Mnv27EKvu2fPHm644Qa2bdvG0KFD+fjjj8vs4C9FtmX1Rrlzbuq2hkd+z72tEfmriffo0YPu3btz/PhxLly4wO23306XLl3o0qULNWvWpFevXvzyyy+eVVWjR4/2DCWWFrP8/6gaWYca9RpQu1Fj7n33Y6pG1in7uapWZeLEifTs2ZOePXuycuVKnnrqKSA3mVm5cqWnZxdg4sSJZGZmelZRZWRkFBgC1BJVTdwHhBDRnTt37vHbb78ZHYqunDp1yjPpzq5Y2bG01cSzsrIM7xLXGyc4gjM8laM90NvRl2ri5kgnLYTL5TI6BN3Ra8KXmXCCoxNeq05wBGd4Kkd7YCZHleD4SP5lgnalatWqRoegO05wdMJr1QmO4AxP5WgPzOSoEhwfscJkPX85efKk0SHojhMcszRc+mlWnOAIzvBUjvbATI4qwfERvZazmYkGDRoYHYLuOMHRCVsaOMERnOGpHO2BmRxVguMjTqhFtWfPHqND0B0nOLrnGR289TYO3nqbwdHogxPmUoEzPJWjPTCTo0pwfMSOxdK8admypdEh6I4THH3do6MkDh06hBCCOXPmeI7df//9NGr0v2W7zZs3Z9KkgntqfPfdd3Tv3p2oqCi6du3Kf/6Tt9nYrFm8+uqrQO5mX4899hhRUVF069aNO+64gzNnzpQYk9aOZsUJnsrRHpjJUSU4PpKUlGR0CLrj794kVsAJjikpKWTGx5Oxbx/pu3axv/8AMuPj/Tpnu3btmD9/PpBbtiQ+Pt6zX8umTZvo2LEjy5Yt8zx+/fr1TJ8+naVLlxIdHc2vv/5aaHI5fvx4mjVrRnR0NGvXruWFF14oVVmUlJQUv3ysghM8laM9MJOjSnB8pFKlSkaHoDvuLfXtjJ0d3UNSp+6+hwP9ByDzJsZn7t/Pgf4D/BquqlatGiEhIZw6dYolS5bQr18/z31z5szhoYce4pprrmHjxo1Abi/NxIkTqVixIpC70VmvXr0KnNPlcrFq1SoeeeQRz7GWLVtyySWXlBiPE3pUwRmeytEemMnRUQmOECJYCPG1EGKNEOILIYTP69lUD449cIJjjsvlSW7ceN8uC7fffjvffvst//3vf7nzzjtzr5WTw+bNm+nSpQsjR47k66+/BgoWM1y5ciVRUVEX1UU6ffo0NWvWRAjhcyxm+rSoJ07wVI72wEyOjkpwgFuAA1LKnkAscKuvJ1A9OPbAzo6NFnxPowXf02ThD5Rr3Ph/dwQFUa5xYxot+N6v8w8cOJB58+aRmppK3bp1gdzk5eTJk/Tt25cXXniBn376iezsbOrXr0983rDYjTfeSHR09EX1eGrVqkVCQgJl2VXdTJ8W9cQJnsrRHpjJ0WkJTmNga97PW4Buvp4gOTlZy3hMybZt24wOQXec4Jiamkr96R8j8pZtlmvUiPrT/a81FBERwS233MLYsWM9x77++mt++OEHli1bxrJlyxg+fDgrVqxg5MiRvPHGG56/GyklOTk5Bc4XFBTEDTfcwNSpUz3Hdu7cybFjx0rl6ASc4Kkc7YGZHM2z5aAXQohHgXuBlsA8KeW9+e6rDnwO9AYSgIlSyrmlOO0uoC/wPXADUM3XuMyUnepFixYtjA5Bd5zgGBERgahfn7AmTQD87rnJz5NPPun52eVy8eeff3L11Vd7jvXp04dp06Yxd+5cxowZw0033URISAjBwcE8+OCDF53vvffe45lnnqFHjx64XC7q1q3L9OnTS4xDi4rkVsAJnsrRHpjJ0bQJDnAMeBXoA3j/xqYCmUAk0Ab4SQixTUq5UwhRB5hfyPmGAEuAKCHEamAn4PN2tk7YB2ffvn0XzZOwG05wTE9P1/TNpmHDhqxateqi4wcOHLjoWNeuXenatSuQO2fn9ttvv+gx9957r+fn8uXLM2XKFJ9j0trRrDjBUznaAzM5mjbBkVIuABBCdADquY8LISoAtwFXSymTgXVCiMXA3cAEKeUJoGsxp/533nleAlYX9gAhRHQRz23jhJ2M69WrV/KDLI4THN07imrZc2M2zLRrqp44wVM52gMzOVpxDk4zIEdKmX8r2m1AiWMOQog6QohoIcQvQKaU8ldfL56amkpCQgLHjx/n6NGjnDt3jv3795OWlsauXbtwuVxs2bIF+N9KnS1btuByudi1axdpaWns37+fc+fOcfToUY4fP05CQgKHDh0iOTmZ2NhYsrOzPXNE3Odwf9+xYwcZGRns3buXxMRE4uLiOHXqFKdOnSIuLo7ExET27t1LRkYGO3bsKPQc27ZtIzs7m9jYWJKTkzl06FABp7i4ONs5ebfT6dOnLeuUk5NDZmYm2dnZpKen43K5SEtLQ0rpWcGQkpJCdnY2KSkpSClJS0vD5XKRnp5OdnY2mZmZZGZmkpWVRUZGBjk5OZ5zuMfQ85/L/dp3nyMnJ4eMjAyysrIKnMMdT3HncMeT/xzueEpycn93nyMrK8t2ToW1U2Zmpu2cvNspKyvLdk7e7eT+m7STk3c87r9JvZxcLleB9/LiEGVZuRBIhBCvAvXcc3CEEN2A76SUdfI95kFguJQySudYojt37tzjt99+0/MyhpOQkEDNmjWNDkNXrOz4zz//0Lx58xKXVWdlZREaGhqgqIzBCY7gDE/laA/0dJRSEhsby5VXXuk5FhUVRUxMTExh//+t2IOTDFT2OlYZCMgGNWZPCLXATNVg9cLKjuHh4Zw5c6bE16ITXqtOcARneCpHe6CXo5SSM2fOEB4eXurnmHYOTjHsAUKEEE2llHvzjrUmd9Kw5gghhgHD8m62PH36tB6XMRUul8voEHTHyo716tXjyJEjlPRazM7OJiTEin/ipccJjuAMT+VoD/R0DA8P92n+pGl/03m7DIcAwUCwECIcyJZSpgghFgCThRAPkLuKahDQWY848pafz82LKToyMrKHHtcxE2YqlqYXVnYMDQ0tUOCyKM6dO0e1aj7vhGApnOAIzvBUjvbATI5mHqJ6HkgDJgAj8n5+Pu++seQuHT8FzAMellLq0oPjjZWHNkrL2bNnjQ5Bd5SjPXCCIzjDUznaAzM5mrYHR0r5EvBSEfedBQYHMBwPTlgmXpoih1ZHOdoDJziCMzyt4DhgyloAlowrfhP8oh5nBUd/MZOjmXtwTIEQYpgQYokQYgnQ8ujRo0aHpDsHDx40OgTdUY72wAmO4AxP5WgPzOSoEpwSkFLOlVIOkFIOAHa4KyPbGbvv8AvK0S44wRGc4akc7YGZHFWC4yNOKLa5detWo0PQHeVoD5zgCM7wNLtj3JlU9p5M5u+jidz4XgxxZ3wvKml2Ry0wk6PpN/ozE0KI6B49evSIjo42OhSFQqFQ6Ix7Lg3A3pPJZGT/b3uJsJAgmkZWBArOtYk7k8qN78eQke2iae2KfD7yGhrUsO6qTbNjt43+Aor3HJzDhw8bHZLuuEsF2BnlaA+c4AjO8DS7Y/7kxvv2gClrPV/u5AZg76lkbnw/xnOf2R21wEyOqgfHB1QPjkKhUDiTG9+LYe+p3CkKQQIa16rIyvG526Ll7+n5+2jiRc+9+tLczfdLWn2l8B3Vg6MhTpiD4y5CaWeUoz1wgiM4w9Psjp+PvIawkNx/mY1r5Q49uVkyrpvnq2ntip7jQQKa1q7ouc/sjlpgJkfVg+MDTunBcblcBAXZO/dVjvbACY7gDE8jHf3d3yY/xc3BKYtjeno6+/fv59SpU5w8ebLAd3d1b/eXy+UiODiYli1b0qVLFzp06BDwXdsD3Y7F9eCYdqM/s+Iu8W5nYmNjueqqq4wOQ1eUoz1wgiM4w9Mujg1qlC908jGUzjEzM5Pff/+d6Oho1qxZw4YNG0hPT7/ocUIIwsPDEUIU+MrKymLevHkAhISE0K5dO7p06UKvXr3o378/QgiNTAvHTO2oEpwS8C62mZh48fiq3ShNnSOroxztgRMcwRmeTnY8c+YM8+fP5/vvv2fdunWkpaUBULt2bQYNGsQ111xD3bp1iYyMpHbt2kRGRlKjRg2Cg4MvOpfL5eKff/7ht99+83y9//77vP/++3Tp0oWPPvqINm3aBNzRCFSCUwLexTarVKli+2Kbx44do3HjxkaHoSvK0R44wRGc4WmUo3t/m4xsFze+F1Pssm5/Jwnnd0xNTWXx4sXMnTuXZcuWkZWVRbVq1ejXrx89e/akZ8+eXHnllT71uOQfQmvRogUPPfQQACdPnuTjjz/mzTffpH379jz88MO88soruhTFNNNrVSU4PhIaGmp0CLpTvXp1o0PQHeVoD5zgCM7wDKRjUfvbuJd1FzXE5C/Vq1dn+/btvP/++8yfP5/k5GQiIiK47bbbGD58OL1796ZcuXKaXhMgMjKSl156iXvuuYcnnniCqVOn8u233/Lmm29y7733ajpnxkyvVZXg+EhOTo7RIehOamqqacrd64VytAdOcARneBrlWNz+NmXFOzGSUrJ27VpefvllVq9eTVBQEL1792b48OEMHjyYihUrFnEmbbn88stZvHgxP/30E48//jj3338/Tz75JNWqVaNSpUqer2rVqjF+/Hjat2/v8zXM9FpVCY6P6D1BywzYfbUGKEe74ARHcIZnIB3zJyCF7W+jVc+Ny+Xixx9/5K233mLDhg2EhYUxevRonnzySZo0aaLJNcpC//79uf766/nPf/7D+vXrSUpKIikpiVOnTrF//35Onz7N6tWr2bZtG7Vr1/bp3GZ6raoEpwS8JxknJCQYGU5AcMIwnHK0B05wBGd4GuX4+chrPMu6vfe3KStSShYuXMiLL77I33//TeXKlZkwYQIjRoygRYsWGkTtP+Hh4TzzzDOF3rd8+XL69u3LPffcw9KlS31KWsz0WjVPqmVSvKuJm2l8US+csJmhcrQHTnAEZ3ga5ehe1n31pZVZOb6HX3WjpJQsW7aMa665hltvvZXjx4/z5ptvEh8fzxtvvEGFChU0jFw/+vTpw4QJE1i+fDlvv/22T88102tVJTg+YqbsVC9q1qxpdAi6oxztgRMcwRmeVneMiYmhe/fu3HTTTezdu5fJkydz8OBBnnnmGSpXzi3VYCXHyZMn07lzZ5577jnWr19f6ueZyVElOD6SkZFhdAi6c+TIEaND0B3laA+c4AjO8LSaY3x8PLNnz+b++++ncePGREVFsWXLFiZOnMjBgwd54YUXqFSpUoHnlNXRXawzkISGhjJv3jwqV67MXXfdxdmzZ0v1PDO1o5qD4yMRERFGh6A7Rk5+CxTK0R44wRGc4WmkY2knFZ8+fZoXX3yRFStWcODAASB3Um2HDh0YOnQo48aNIzIyssjnW60dGzRowMyZMxk8eDCjRo3ihx9+KHGhjZkcVQ+Oj6SkpBgdgu7s3LnT6BB0RznaAyc4gjM8ze64fft2rr32WqZPn06NGjV46qmnWLp0KefOneP333/n1VdfLTa5AfM7FsagQYN4/PHHWbRoEVOmTCnx8WZyVD04PhKo/QqMpHXr1kaHoDvK0R44wRGc4Wlmx4ULFzJixAiEECxcuJBBgwaV6TxmdiyOt956i7Vr1/Lkk0/SoUMHOnfuXORjzeSoenBKQAgxTAixRAixBGh5+PBho0PSnc2bNxsdgu4oR3vgBEdwhqcZHaWUvPrqq9xyyy3UqlWL9evXlzm5AXM6loawsDC+/fZbKleuzKBBg9i/f3+RjzWTo0pwSsB7mfhll11mdEi6U5bdK62GcrQHTnAEZ3iazTE1NZW77rqLF154gR49erBp0yZatmzp1znN5ugLjRs3ZuHChSQmJtKvXz/OnDlT6OPM5KgSHB9JSkoyOgTdMVMGrhfK0R44wRGc4Wkmx23btnHdddfx7bffMmbMGFauXKnJ8mczOZaFrl278uWXX7Jnzx5uueWWQlcVm8lRJTg+4r3sz46YKQPXC+VoD5zgCM7wNINjZmYmL7/8Mh06dGDv3r18/PHHfPzxx5rtf6ano7sq+t9HE7nxvRjizqTqcp277rqL1157jbVr1zJq1CiklAXuN0M7ulEJjo84YRXVjh07jA5Bd5SjPXCCIzjD02jHv/76i2uvvZaXXnqJ6667ju3btzNmzBhNr6G1o3t/nAFT1nrKTcD/qqLrtX/OxIkTuf/++5k7dy6TJk0qcJ/R7ZgfleD4iBP2wWnWrJnRIeiOcrQHTnAEZ3ga5ZiZmcmLL77Itddey969e/nwww+Jjo7WZT8Xb0ctExA9qqIXhRCCjz/+mBtuuIFXXnmFWbNmee4z02tVJTg+4oSdjOPi4owOQXeUoz1wgiM4w9MIx7i4OLp06cIrr7xC165d2bFjB+PGjdOtIrbWjkvGdfN8Na39vy1MggQ0rV3Rc58ehIaGMn/+fFq0aMEjjzziGd0w02tVJTg+Uq5cOaND0J2SNquyA8rRHjjBEZzhGWjHVatW0a5dO7Zu3cr777/PL7/8wuWXX67rNcviWNq5NZ+PvIawkNx/6VpVRS+JKlWqMGHCBFJTU1mxYgVgrteq2ujPR7Kzs40OQXfOnz/vKQ5nV5SjPXCCIzjDM1COUkreeustnnvuOWrXrs2aNWvo2rWr7teF0jvmH7baezL5ork1TSNze2vy9864q6J7H9eb/v37ExwczMKFC7nllltM9VpVCU4JCCGGAcPybrYsau2/nQgPDzc6BN1RjvbACY7gDM9AOCYmJnLvvffyww8/0LVrV7799lvq1q2r+3XdlMUxkHNrykK1atXo0aMHS5YsITs721SvVZXglICUci4wF0AIEV2rVq0eBoekUCgUCh/ZtWsXt9xyC3v27OHxxx/n7bff1mz5t9bk74G58b0Y9p5KBnLn1jSuVTGgPTSlYfDgwaxevZp169Zx1VVXGR2OBzUHx0dcLnNlz3qQnp5udAi6oxztgRMcwRmeejr+97//5dprr+XIkSPMnTuXDz74wJDkpiyORsyt8ZWBAwcCsGjRIlO9VlWC4yMhIfbv9KpatarRIeiOcrQHTnAEZ3jq4ZiVlcX48eO56667qFu3Lhs3bmTo0KGaX6e0lMXRPbfm6ksrs3J8DxrUKK99YH5y2WWX0bZtWxYuXEiVKlWMDseDSnB8JDMz0+gQdOfkyZNGh6A7ytEeOMERnOGpteOJEye44YYbeP/99xk4cKAmtaT8Jb9joHYeDhSDBg3i0KFD/Prrr0aH4sH+3REaExYWZnQIutOgQQOjQ9Ad5WgPnOAIzvDU0vG3337j9ttv58SJE7z22mtMmDBBt71tfOGJpccRQSeA0q+OsgqDBw/mpZdeYtOmTdx8881GhwOoHhyfSUtLMzoE3dmzZ4/RIeiOcrQHTnAEZ3hq4SilZOrUqURFRZGZmcmyZct49tlnTZHcAKRn/G9+itlXR/lKq1atuOyyy5g/f77RoXhQPTg+UqFCBaND0B2ju3EDgXK0B05wBGd4+uuYlpbGmDFj+Oqrr2jXrh0LFizgsssu0yg6bfjl6d6en62wOsoXhBAMHjyY//znP8TFxZmi19Ecaa2FSEpKMjoE3TFTuXu9UI72wAmO4AxPfxwPHTpEly5d+Oqrr7j33ntZt26d6ZIbKOhohdVRvjJo0CAAFi9ebHAkuagEx0cqVapkdAi6Y6Zy93qhHO2BExzBGZ5ldVyxYgXt27fn77//Ztq0aXzxxRemLYqc39EKq6N8pVu3blSrVo2FCxcaHQqgEhyfUT049kA52gMnOIIzPMvi+M4779C3b1/CwsKIjo7m4YcfRgihQ3TaYPd2DAkJoXPnzsTExHDu3Dmjw1EJjq+oHhx7oBztgRMcwRmevjhKKXnmmWd46qmnuO6669iyZQudO3fWMTptcEI7jho1iuzsbJYuXWp0KCrB8ZXk5GSjQ9Cdbdu2GR2C7ihHe+AER3CGZ2kdc3JyGDNmDP/3f/9H//79WbVqFXXq1NE5Om1wQjtecsklhIeHs2jRIqNDUauoSsK72GZKSoqR4QSEFi1aGB2C7ihHe+AER3CGZ2kcs7KyuOeee/jmm2+46667+Oqrr0xbT6ownNCOHTp04IYbbuDnn38mIyPD0L3jVA9OCUgp50opB0gpBwA7nDBEtW/fPqND0B3laA+c4AjO8CzJMTU1lcGDB/PNN98wevRo5syZY6nkBpzTjoMHDyY5OZnVq1cbGotKcHzECTsZ16tXz+gQdEc52gMnOIIzPItzTExM5KabbmLp0qU888wzfPzxxwQHBwcwOm1wSjsOGDAAIYThy8VVguMjWVlZRoegOwkJCUaHoDvK0R44wRGc4VmU4+nTp+nZsye//vorb7zxBm+++aapV0oVh1PaMTIyklq1anH06FFDY1FzcHzEip8afKVixYpGh6A7ytEeOMERnOFZmGN8fDy9e/dm9+7dfPzxx4wZM8aAyLTDSe0YGhpKdna2obH4lOAIISKB3kBroCpwHtgGrJRSntA6ODMipTQ6BN1xQi+VcrQHTnAEZ3h6O+7Zs4cbb7yRY8eO8fXXXzN06FCDItMOJ7VjaGio4b6lGqISQlwphJgP7ALuBkKBE3nf7wZ2CiHmCyGu0i1Sk+CEBMflsnbRt9KgHO2BExzBGZ75Hbdu3Uq3bt04deoUCxcutEVyA85qx5CQEMMTnNL24MwC3gaGSykzvO8UQpQDBgGfA9dpFp0JccIQVfny1t8yvCSUoz1wgiM4w9PtuG7dOgYMGICUkhUrVtCtm3ULUHrjpHY0wxBVqXpwpJQdpZTzC0tu8u7PlFJ+J6W0dXIDzuhiPHv2rNEh6I5ytAdOcARneJ49e5ZVq1bRu3dvypUrx5o1a2yV3IBz2hHMMUSlJhn7iBOWiV9yySVGh6A7ytEeOMERnOH5zz//cPvtt1O9enV++eUXmjdvbnRImlPWdlwyzjqJntvRDENUZVomLoS4R+tArEJ6errRIejOwYMHjQ5Bd5SjPXCCI9jfc8WKFQwZMoQaNWoQHR1ty+QGLm7HJeO6WSp5KQ1uRzMMURXbg1PEpGEBjAa+0iUik+OEMVS7vrnkRznaAyc4gr09ly9fzqBBg6hZsybR0dE0adLE6JB0w87t6MbtaIYhqpJ6cDYCTwJP5ft6ErhM57hMixOKbW7dutXoEHRHOdoDJziCfT2XLVvGoEGDqFWrFlOnTrV1cgP2bcf8uB3NMERV0hycf4CnpJRn8h8UQvykX0jmxgkbNbVr187oEHRHOdoDJziCPT1//vlnBg8eTGRkJGvWrKFx48ZGh6Q7dmxHb9yOZhiiKqkH50ZyN/MrgJSyvy7RWICkpCSjQ9CdzZs3Gx2C7ihHe+AER7Cf5w8//OBJbqKjo2ncuLHtHAvDSY6mH6KSUiZKKXPct4UQtfUPydw4oZp4+/btjQ5Bd5SjPXCCI9jLc/bs2dx+++3Uq1ePmJgYLr/8csBejkXhJEczDFH5uopqvi5R6IAQoooQ4g8hRLIQ4up8x18TQqzN23nZ5xnDTpiDs2XLFqND0B3laA+c4Aj28Zw2bRr33HMPV1xxBWvXrqVRo0ae++ziWBxOcrTCEJU3Virhmgr0J19SlpfoNJZSdgNWAaN8PakT5uC0adPG6BB0RznaAyc4gj0833rrLR555BHat29PTEzMRXvC2MGxJJzkaPohqkKwTCEmKWWWlPK01+FuwM95P/8MdPX1vKmpqf6GZnpiY2ONDkF3lKM9cIIjWNtTSslzzz3HhAkT6Nq1K7/88gs1a9a86HFWdiwtTnK04hCVLgghHhVC/CmEyBBCzPK6r7oQ4gchRIoQ4rAQYpgfl6oGXMj7+QJQ3dcThIeH+3F5a5C/29iuKEd74ARHsK6nlJKnnnqK119/nd69e7N8+XKqVKlS6GOt6ugLTnJUQ1T/4xjwKvBFIfdNBTKBSGA48LEQogWAEKKOEGJdIV91irjOOcD911UF8LkwSEZGoeW4bMWxY8eMDkF3lKM9cIIjWNfztdde49133+Xmm29m8eLFxW6UalVHX3CSY2hoKDk5OUhp3MCPr7WohugRhJRyAYAQogNQz31cCFEBuA24WkqZDKwTQiwG7gYmSClP4Nsw0zpgIvAl0Af4rbAHCSGii3h+m9DQUB8uZ02qV/e5Y8tyKEd74ARHsKbntGnTeOGFF+jZsyfffvttiXX8rOjoK05yDAnJTS+ysrIoV66cIbH41IMjpTwphOgphGgEIISoK4T4UgjxRTG9Jv7QDMiRUu7Jd2wb0KI0TxZCLAV6AzOEEPdKKXcAh4UQa8lNcArrMSqW9PR0EhISOH78OEePHuXcuXPs37+ftLQ0du3ahcvl8swid+8HsGXLFlwuF7t27SItLY39+/dz7tw5jh49yvHjx0lISODQoUMkJycTGxtLdnY227ZtK3AO9/cdO3aQkZHB3r17SUxMJC4ujlOnTnHq1Cni4uJITExk7969ZGRksGPHjkLPsW3bNrKzs4mNjSU5OZlDhw4VcDp16pTtnLzbKSUlxXZO3u2UmppqOyfvdjp//rztnAprp5MnT1rKae7cuTz66KN06NCBt956Cyllie2UlJRkaict3iNSU1N1dfro5vrMGnqlof+fLly4wN69ez09N8eOHdO1nYpD+Np9JIT4B+gjpYwTQszNO5wG1JJSDvTpZBef+1WgnpTy3rzb3YDvpJR18j3mQWC4lDLKn2uVMb7o6667rsf69esDfemAcvz4cerWrWt0GLqiHO2BExzBWp4//fQTgwcPpkmTJqxdu7bQCcWFYSXHsuIkx6eeeop33nmH8+fPFznvSguioqKIiYmJKSwn8HWICuDSvOQmhNxekMvInSOjx+BiMlDZ61hlwLDthIWw0kr5suGEYTjlaA+c4AjW8Vy7di1DhgzhkksuYeXKlaVObsA6jv7gJMf8Q1RGUZZVVIlCiEigB7Arb24MgB4ttwcIEUI0zXesNbBTh2sVihBimBBiiRBiCdDy5MmTgbq0YThhM0PlaA+c4AjW8Pzrr78YMGAAlStXZuXKldSrV6/kJ+XDCo7+4iRHd6Jj5EqqsvTgTAE2AeWAJ/KOdQHKvMA/rzcoBAgGgoUQ4UC2lDJFCLEAmCyEeABoAwwCOpf1Wr4ipZwLzM2LM7pu3bo9AnVto/DlU5dVUY72wAmOYH7PPXv20KdPHyC3QnizZs18PofZHbXASY7uBMdSPThSyreAG4AuUspv8g4fBR7wI47nyZ3HMwEYkffz83n3jQUigFPAPOBhKWXAenC8ccIy8SNHjhgdgu4oR3vgBEcwt2d8fDw33ngjycnJ/PTTT7Rt27ZM5zGzo1Y4ydEMQ1Rl6cHBa1XTRbfLcL6XgJeKuO8sMNif82tJRESE0SHoTpMmTYwOQXeUoz1wgiOY1/P06dP07t2bY8eOsWjRIrp29XlzeA9mddQSJzmaYYjKFDsZmxnvOTjx8fFGh6Q7O3ca1kEWMJSjPXCCI5jTMzExkZtuuondu3fz1Vdf0a9fP7/OZ0ZHrbGz48Fbb+Pgrbd5HC05ROU0pJRzpZQDpJQDgB0NGjQwOiTdad26tdEh6I5ytAdOcATzeaalpTFw4EA2b97M1KlTGTp0qN/nNJujHjjJ0QxDVMUmOEKIYCHErUKIwXkTgd3Hb9c/NHOSlGTYCvWA4d5wyc4oR3vgBEcwl2d2djZ33nknMTExvPbaazz88MOanNdMjnrhJEcrDFF9BbQjd/XSOiGEewBRm1e0BalUqZLRIehO+/btjQ5Bd5SjPXCCI5jHU0rJ2LFj+fHHHxk/fjwTJ07U7NxmcdQTJzlaYYjqEinl83mTgIcCnwkhovQOykx4z8E5fPiw0SHpjpM+ZdgZ5WgfzOL56quvMmPGDIYOHcrbb7+t6canZnHUEyc5mn6ICggTQoQBSCkPAjcDTwJX6x2YWfCeg3PZZZcZHZLuOOlThp1RjvbBDJ6zZs3ixRdfpGfPnsycOZOgIG2ncJrBUW+c5GiFIarxQDX3DSllErkb7Y3XMygzk5KSYnQIuuMugmZnlKM9cIIjGO+5fPlyHnzwQa6++moWLFhQYmXwsmC0YyBwkqMZhqiK3QdHSrkx/20hRG0p5Slgjq5RmRgn7INTll1IrYZytAdOcARjPbds2cKQIUOIjIxk6dKlVK1aVZfrOKEtneRohSEqb+brEoWFcMJOxnFxcUaHoDvK0R44wRGM8zx06BD9+/cnKCiIn3/+mfr16+t2LSe0pZMczTBE5etOxvYvpe2FEGIYMCzvZsvz588bGE1giIyMNDoE3VGO9sAJjmCM59mzZ7nppps4c+YMy5cvp2XLlrpezwlt6SRHMwxR+dqDI3WJwsR4TzKuXr260SHpjhOSOOVoD5zgCIH3TE9PZ9CgQcTGxjJr1ix69uyp+zWd0JZOcrTiEJXj0XrlgBkJDw83OgTdUY72wAmOEFhPl8vFyJEjWbduHW+88QbDhg0r+Uka4IS2tKtjZnw8Gfv2kb5rF2kPjSYzPt4UQ1S+/rd23BCVQqFQOIlnnnmGb7/9locffphnnnnG6HAUJufgrbdxoP8AZGYmAK5Dh4gf87Aphqh8nYMzRJcoLITL5TI6BN1JT083OgTd0drx7NmzTJs2jezsbGrVqsXQoUMxejhTtaN9CJTnRx99xDvvvMOAAQP48MMPNd3IrySc0JZ2dXQnN24yDx0yxRCVTwmOlPKkXoGYFe9JxmfPnjUynICg1zJQM6GV4yeffALA6dOnPV2xp0+fZtq0aTz//POaXKOsqHa0D4HwXLhwIY899hjXXHMN33zzjecfVKBwQlva0bHRgu/Z338Amfv35x4QgnING5JlgiEqn1/BQogqwGNAW6Bi/vuklL01iss0SCnnAnMBhBDRVatW7WFwSLpz8uRJKleubHQYuqK1o/cfsV5/1FJKjhw5wt69ewkJCaFq1apUq1aNatWqUaFChQKfuFU72ge9PX///XeGDh1Kw4YN+fHHH6lQoYJu1yoKJ7SlXR3rT//4f8NU9epRf/rH7E9OBizUg5PHd0Aw8AOQpm045kePHTzNRoMGDYwOQXe0chw9ejQAU6dOJSEhASklQghq1qzp97mllPz222+sW7eOf/75h127dhEbG0ty3huHNyEhIVSrVo3KlStTuXJlKlasSNWqValcuTLVq1enQYMGBb4iIyMJDg72O04jccJrFfT1PHjwIDfffDPly5fn559/NmwpsxPa0q6O5erXJ6xJbi3uS+bNpVxYGCF79wLWS3A6ATWklMZFbSBpafbP6fbs2aP7nhdGo7Xj0KFDmTdvHgkJCdSsWZOhQ4eW+VwJCQl8+eWXzJgxg927dwO5e0o0bdqUPn36cOWVV3LFFVcgpeTcuXOcO3eO8+fPe35OSkoiMTGRw4cPs3v3bhITEwsd+w8JCeG6665j2LBhDBkyRJOkLNA44bUK+nmeO3eOfv36ceHCBVatWsUVV1yh+TVKixPa0kmOZlhFVZYEZx1wJbBd41gsgRFdt4HG7n+AoL1j9erVeeSRR8r8fCkl0dHRfPrppyxYsIDMzEwaNmzIq6++yq233kqTJk08bxhlITk5mfj4eOLi4oiLiyM+Pp4DBw6wbNkyHn74YcaNG0ffvn0ZNmwYAwcOtMzr3AmvVdDHMzMzkyFDhhAbG8ucOXPo1q2b5tfwBSe0pZMcrbiKCuBeYKkQ4negwKRjKeVkLYIyM0lJSUaHoDubN2+2fdVbszimpaUxZ84c3n//ff755x9CQkIYNGgQDz30EDfccINf+y7ld6xYsSJXXnklV155ZYHHZGVlsWLFCubOncvChQtZsmQJFStW5LXXXmPcuHEBXUVTFszSjnqjtaeUkjFjxrB69Wpeeuklhg8frtm5y4oT2tJJjmZYRVWWd8/XgPpAJNA031cTDeMyLZUqVTI6BN2x+x8gGO944sQJXnzxRRo0aMBDDz3EhQsXeO211zhy5Ajz58+nd+/efm8qWRrH0NBQ+vfvz9dff83Jkyf5+uuvadKkCY8//jiDBg0iISHBrxj0xuh2DBRae77xxhvMnDmTESNG8OKLL2p67rLihLZ0kqMZhqjK8g56F9BGSjlESnl3vq97tA7ODAghhgkhlgghlgAtDx8+bHRIurN582ajQ9CdQDumpKTwxx9/MGPGDO6++24uu+wyXnnlFRo0aMCcOXM4ePAgzz77rKYTPH11rFixIsOGDWPjxo3861//4scff6R169ZER0drFpPWOOG1Ctp6/ve//+W5556je/fufPbZZ6bppXNCWzrJ0QxDVEJK38pLCSG2AddLKc390U4HhBDRPXr06GHmN3yF8WRkZPDnn3/y66+/smXLFrZt28a+fftw/60JIRg4cCDjx4+nW7dupvkH483SpUsZOXIkZ86c4bnnnmPSpEkB3xtFoS2bNm2iW7duXHbZZWzYsMHwzSgV9uHgrbcBufviQO7we/ny5Rk3bhwffvihbteNiooiJiYmRkoZ5X1fWd6tZgOLhRBTuHgOzuqyhWgdilqiaye2bdtG69atjQ5DV7R0zMzMZN26dfz666/ExMSwceNGz6qlChUq0LJlS3r27Enr1q1p1aoVLVu2pEqVKppcuzj8dezXrx/btm3j7rvv5tVXXyUmJoZly5ZRvnx5DaP0Dye8VkEbz4SEBIYMGUJ4eDhLliwxXXLjhLZ0kqMZhqjKkuC4l4q87nVcApf7F475scrqEn9o0aKF0SHojlaO27ZtY+jQofzzzz8AREZGcvvAAVyRk0xYcDA1Lq3P9fePZfUX0zi7dhn79u/g6qaTIAAJjhaOl1xyCStWrOCVV17h5Zdf5pFHHmHmzJkaRKcNTnitgv+eOTk5DB8+nLi4OBYtWkTTpk01ikw7nNCWTnJ077FlqUnGUspGRXzZPrkBZ+yDs2/fPqND0B1/HaWUfPTRR3Ts2JHDhw/zzjvvsHv3bo4fP06vejUJDw5GAGePxvPd5ImcORKPdLk4cySehf/3sjYSJaBVOwYHBzNp0iTuueceZs2axRdffKHJebXACa9V8N9z8uTJrFixgokTJzJw4ECNotIWJ7SlkxyFEISEhFgrwRFCfCiE6Ox1rLMQ4gPNojIxTtjJuF69ekaHoDv+OCYkJDBo0CDGjRvHVVddxZYtW/j3v/9Ns2bNEEJw9tjRYp9f0v1aoWU7CiGYNm0aLVq04JFHHmHbtm2andsfnPBaBf88ly5dyuTJk7n++ut55ZVXNIxKW5zQlk5zDA0NtdwqqqHAn17HNvO/gpS2xshsNFCYfWmwFpTVcfXq1bRu3Zoff/yRf/3rX2zYsOGi3V+rX3Kp52chBEH5JuYKIQrcrydat2OFChX47rvvCA4O5vbbbycxMVHT85cFJ7xWoeyeBw8eZMSIEVx66aXMnTvX1KU5nNCWTnMMDQ213EZ/kosTo+BCjtkSM79BaEXFihVLfpDFKYvjBx98wPjx46lZsyY//fQT/fr189yXsP0AS97ZSEpELSpk9aRntXRqVrmMVBIpf0t9Vn/3CWePHaX6JZcy+OlJPl33/MkTLPy/lws8v2pkHV0cS+LKK6/k008/Zfjw4TzwwAP897//NXQVmBNeq1A2z/T0dIYMGUJycjJLly6ldu3aOkSmHU5oS6c5Gj1EVZYEZy3wqhDiaSmlSwgRBLyUd9z2+Lqs3oo4oZfKF0cpJc899xxvvPEGnTp1YsGCBdStW7fAY5b8509SwmuDCCIlpDqb00/yUafHqJcRyZ1/PMakqoOhXDahFUO5IieM60q4Zv6kRrpcnuNnjx5h4f+9zL3vfqypoy8MGzaMtWvXMn36dLp3786jjz6qy3VKgxNeq+C7p5SSRx99lC1btvDRRx/RqVMnnSLTDie0pdMcrThE9ThwA3BcCPEHcAy4ERinZWBmwXujv9OnTxsdku648v1DtSuldczJyWH06NG88cYb9O3bl1WrVl2U3ACkhFQD987DQUFkhtXGJVzEh53grYgPICUbISErKYu7v9hU4nVn/fthz8Tk/EgpSz2HR892fP/992nXrh3jx4/njz/+0O06JeGE1yr47vnuu+/y+eefM3z4cMaOHatTVNrihLZ0mqPRQ1RlWUV1BGgHDALeBgYD7fOO2w4p5Vwp5QAp5QBgh5Y7zZoVM+1zohelcUxPT+eOO+5gxowZDB06lEWLFhW5TUCF9LPg/sN2uQjNyN0iSgpJUOgp3IM4AshKyeKTTz7xPPfs2bNMnTqVl19+malTp3L27FlyinlTkC4X7945gFn/fpjzJ0/45VhWwsPD+e677yhfvjz33XefYW/cTnitgm+e33//PU899RSdO3c21U7FJeGEtnSao9FDVGWaNyOldEkpN0opv8v7bv+0NA8ndDGePXvW6BB0pyTHxMRE+vXrx4IFCxg3bhxz5syhXLlyRT6+Y6UwKmScAZlDWOYJfrrqUwCCpKRelgv3wKYEgsJz/+w++eQTPvnkE6ZNm8bp06chI52UjWv44uF7CkxMBggKCUF41aY6cySezx97oMhER+92vPzyy5kwYQK7du1i+fLlul6rKJzwWoXSe27cuJERI0bQpEkTFi1aRHh4uM6RaYcT2tJpjlYconI0Tlgmfskllxgdgu4U53jixAl69uzJmjVrmDx5Mv/5z39KLHxZ7fL63FD3EgZVC6dP4ycQ1U4SLCWNsrKYfvIEQRFBSAFBEUHcXvMEo0eP9jzX/QYQEb+XoMx0BODKzgYhkIAoX4FbX3yT8fMWF3pt97wcXxy1YvTo0ZQvX553331X92sVhhNeq1A6zwMHDjBw4EDKly/P0qVLqVmzZgAi0w4ntKXTHC03ROV03Fvw25mDBw8aHYLuFOX4999/07FjR7Zu3cq0adN44YUXStXFX3PkVYTULg8C6shL+OHoCbYeimfhsVNcWrkhT9Y8wKjwP3my5gEmDB0E5CYHo0ePpmqNqrhweZIbN1JKkq/sQFLDq1iy6hcAatSrf9G1pZScORJ/US9OINqxWrVqjBo1il9++YWtW7fqfj1vnPBahZI9z549S79+/bhw4YJpdyouCSe0pdMcjR6iKkuxzclF3JUBHAGWSSlPFvEYS+OUYpsul6vEHgurU5jjypUrGTJkCDk5OXzzzTcMGDCgbCc/exDm3QUJe6FmUxj6DVRvVOTD7/jvHdTbV486sXGeJEcCrnLhpDa+GsjdP2fSpEme1VVnjsRfdJ4a9eoXWF0VqHbcv38/TZs2ZcSIEXz11Ve6Xy8/TnitQvGeGRkZ9OnTh5iYGObOncvQoUMDHJ02OKEtnebYoUMHXC4XW7Zs0e16xRXbLMtvuhnwDNATaJL3/RmgLfAwcEAI0bfs4ZobJxTbNOKTeKDxdvzss8+46aabqFixImvXri17cgO5ycwjv8Oks7nfi0luAPZk7GFlvZWcblQHV7lwT3KTVj/3U7gQwjPcUDWyDve++zH3f/jZRefxXl0VqHZs3Lgxt9xyC/PmzePo0cDs0uzGCa9VKNpTSsnDDz9MTEwMr776qmWTG3BGWzrN0YpDVEHAXVLKblLKYVLKbsAdQI6UshMwFnhTyyDNhBM2amrXrp3RIeiO29HlcjFx4kQefPBBWrRowe+//07btm0DGkvDyg0BWNvgT040b0DSle0Jv6Y71erU9SQ33v+4qkbWKTBcVdgOyYFsx3//+99kZ2czZcqUgF0TnPFahaI9P/30U2bOnMmIESN49tlnAxyVtjihLZ3maPQQFVJKn76AC0Cw17FgIDHfz0m+ntcKX0B0u3btpN35888/jQ5Bd/7880+ZlJQkb7vtNgnIm266SSYmJhoSS1xinBz0wyDZ+svWctAPg2RcYlypnnfuxHE5c/wY+e5dN8uZ48fIcyeOF7g/0O3YqVMnWbVqVZmUlBSwazrhtSpl4Z5//PGHLFeunGzVqpVMSUkxICptcUJbOs2xZ8+esnHjxrper0ePHhKIloX9zy7sYHFfwBbgUa9jjwB/5f0cCZzw9bxW+AKie/ToUbZWUJiKPXv2yBYtWkhAPvLIIzIrK8vokCzPd999JwH54YcfGh2K7Tl9+rSsX7++rFKlity3b5/R4SgUhdK7d2/ZoEEDXa9RXIJTliGqB4AnhRDxQoiNQoh44Cng/rz7rwBeKMN5LYET5uDoOSHMDPz000+0a9eOffv28cUXX/DRRx8RElKWqiXmJtDtOHjwYBo2bMgHH3xATk5OQK5p99eqm/yeOTk5DB06lPj4eGbPnk3jxo0NjEw7nNCWTnM0eoiqLAnOVqApudXD3weGA02llFsApJS/SilnaBahyXDCHJw2bdoYHYIuuFwuJk+ezM0330y1atVYu3Yt9913n9Fh6Uag2zEkJIQnnniCAwcOsHDhwoBc066vVW/ye06aNIlVq1bx3HPPcfPNNxsXlMY4oS2d5mipjf6EEMFAChAkpVwrpfxvXkJj/+1980hNTTU6BN2JjY01OgTNuXDhArfccguTJk2iR48efP3111xzzTVGh6UrRrTjqFGjqFKlSsA2/rPja7Uw3J4//vgjr732GjfeeCMvv3zx5o5Wxglt6TRHS62iklLmAHuAGvqEYz68i20mJiYaHZLuNGpU/LJmq/H3339zzTXXsHjxYv71r3+xcuVKOnToYHRYumNEO1aqVInRo0ezYcMGNmzYoPv17PZaLYpGjRqxb98+7r77bho0aMDcuXMJDg42OixNcUJbOs3RikNUXwNLhBAjhRDXCyF6ub+0Ds4MSK9im1WqVDE6JN05duyY0SFoxty5c+nYsSNHjx5l7ty5vPfee4SEhJjL8exBmNoRXq6e+/2sNrudGuU4btw4hBAB2fTPVO2oI/v27ePWW28lLS2N+fPnW64MQ2lwQls6yfHgrbeR8dt6Q4eoyjKz8uG87y95HZfA5X5FYwFCQ0ONDkF3qlevbnQIfpOZmcmTTz7JlClTaNasGQsWLKBFixae+03lOO8uOJ3XrZuwJ/f2I7/7fVqjHOvVq0e7du1Yvnw5Ukpdq1mbqh11QkrJpEmT2LFjB5999plth1ad0JZOcwwJEtbqwZFSNiriy/bJDRCw1SFGYvV5RkePHqVnz55MmTKFW265hU2bNhVIbsBkjgl7//ezdBW87QdGOvbp04eDBw+yb98+Xa9jqnbUiffee48ffviBhx56iPvvv7/kJ1gUJ7Sl0xxDhMDlcuFyuQyJpUxFMYQQNwohPhdC/Jh3u71dh6i80fPTqFmwcq2UtWvX0q5dOzZu3Mj//d//8f3331O5cuWLHmcqx5r5CiOKoIK3/cBIxz59+gCwfPlyXa9jqnbUgdWrV/P000/Tvn17PvzwQ6PD0RW7tyU4zzEk72ejhql8/m0LIcYBHwN7ge55h9OBVzWMy7Q4IcGx4jCclJKpU6fSq1cvXC4XK1eu5KmnniqyvUzlOPQbqNUcRDDUbJZ7WwOMdLzuuuuoVKmS7gmOqdpRY+Li4rjzzjupVasWM2fOJCwszOiQdMXObenGaY4hIjfFMGqYqizp5BPADVLKNwF3v1MsuRv82R4nDFFZbTPD9PR07r//fh599FFatWrF5s2b6dWr+A5FUzn6WJyztBjpGBoaSq9evVizZg2ZmZm6XcdU7agh6enp3HbbbZw/f57vvvuOSpUqGR2S7ti1LfPjNMeQvA+YVkpwKgHxeT/LvO+hgH7vYibCCRm4lVZoHDlyhB49engKDq5bt44GDRqU+DwrOZYVox379OlDSkoKv/32m27XMNpRD6SUjB07lj///JN3332Xbt262dLTG+VoD/I7hgTlJjjZ2dkcvPU2Dt56W0BjKUuC8yswwevYY8Aa/8MxPxkZGUaHoDtHjhwxOoRSsW7dOtq3b8/mzZv54IMP+Oqrr4iIiCjVc63i6A9GOwZiHo7RjnowZ84cT8I+btw4wJ6e3ihHe5Df0T0Hx0o9OOOAW4QQh4BKQojdwO3AeC0DMyul/QdqZZo0aWJ0CCUyc+ZMevXqRU5ODitXruTxxx/3aX6UFRz9xWjHyy+/nCZNmuia4BjtqDX79+9n7NixNGvWjI8//tjzmrabZ2EoR3uQ39FyQ1RSyuPANcAd5NajGgl0lFKe0Dg2U5KSkmJ0CLqzc+dOo0MokpycHJ5++mlGjRrFFVdcwZ9//knPnj19Po+ZHbXCDI59+vRh69atnDx5Upfzm8FRK7Kyshg2bBgZGRnMnTu3QN07O3kWhXK0B/kd3ZOMLbOKCiCvSvkfUsrvpJQbpZTGLHI3ACcU22zdurXRIRRKcnIyt956K2+//Tb9+/fnt99+o2HDhmU6l1kdtcQMju5hqhUrVuhyfjM4asVLL73EH3/8weuvv0779u0L3Gcnz6JQjvYgv2OoFYaohBCPCSGKXaMohAgTQjymTVjmJSkpyegQdGfz5s1Gh3AR8fHxdO3a1VNPatGiRYXub1NazOioNWZw7NmzJ6GhoboNU5nBUQuio6N54403uPHGGxk//uLRfrt4FodytAebN28mMz6ejH37GJaVxeKGjcgyaO6RkFKW/CAhXgfuBpYCMcBuIIncFVXNgCjgJuArKeXzegVrNEKI6B49evSIjo42OhRH8ccffzBo0CASEhKYNm0aDz74oNEhKXygZ8+e7Ny5kxMnTjhiozNfOXv2LK1atSIjI4Pt27dTt25do0NSKPwitlVrZN72EDlSIurXo3zl3DqOjRZ8r+m1oqKiiImJiZFSRnnfV6p3Gynls0Bbcjf3ux/4Gfib3IRnFLn74LS1c3LjRvXgBJYff/yRqKgoMjIyWLFihWbJjZkc9cIsjn369OH06dP89ddfmp/bLI5lRUrJgw8+yNGjR5k5c2aRyY3VPUuDcrQHmzdv9iQ3AMFCII4dNySWUn+cklImSCnfkVJeL6WsLaUsJ6WMlFLeKKV8X0p5Rs9AzYITNtzyHv83ik8++YTBgwcTGRnJ+vXryzSZuCjM4qgnZnHUc7m4WRzLyowZM1iwYAGPPvooAwYMKPJxVvcsDcrRHrRv355yjRt7budIiatOHUNisW1/sRCiihDiDyFEshDi6qKO+YoTVlHt2LHD0OtLKXnuuecYM2YMrVu3ZsOGDTRv3lzTaxjtGAjM4ti6dWtq166tS4JjFsey8NtvvzFu3Diuvvpq/u///q/Yx1rZs7QoR3uwY8cO6k//GFGuHC7gYGYm5x8Za0gstk1wgFSgPzC/hGM+4YR9cJo1a2bYtTMzM7n33nt5/fXX6dOnDzExMdTRIfs30jFQmMUxKCiI3r17s379ehITEzU9t1kcfeXAgQMMHjyYSpUqsWjRohLfV6zq6QvK0R40a9aMcvXrE9akCasrV2bgoYNkZ2eTsW8f6bt2sb//ADLj40s+kQaUOsERQsQLIT4VQgwWQlTQMygtkFJmSSlPl3TMV5ywk3FcXJwh101KSmLAgAF89dVX3Hvvvfz444+6DQka5RhIzOTYp08fsrOzWbNG2w3PzeRYWi5cuMDNN99MYmIiCxcu5PLLLy/xOVb09BXlaA/yOwbnbfRX6eXJnnk5mfv3Ez/m4YDE4ksPzrXA7+SupjokhFgphPiXEMLvlFQI8agQ4k8hRIYQYpbXfdWFED8IIVKEEIeFEMP8vZ4/lCtXzsjLB4TIyMiAXzMhIYFevXqxcuVKXnjhBb744gtd634Z4RhozOTYu3dvQPt5OGZyLA3Z2dnceeed7Nq1ixkzZtC1a9dSPc9qnmVBOdqD/I6hebWoIlwFt8rLPHQoILGElPaBeTsYfw58LoQIAboD/YCFQohy5K6oWgqskVL62s1xDHgV6AN499VOJbeQZyTQBvhJCLFNSrlTCFGHwoebhvizs7IQIrqIu9oYtSNjIDl//rxfe8z4ytGjR+nduze7du3io48+4pFHHtH9moF2NAIzOdauXZu2bdtqnuCYybE0/Otf/2L58uVMnDiRe+65p9TPs5pnWVCO9iC/o3sn48zatQk7dSr3AUFBlCvjBq2+UtadjLOllKullE9KKa8CbiB3b5xxeV++nm+BlHIhUGAlVt5Q2G3AC1LKZCnlOmAxub1ISClPSCm7FvKlW9mI7OxsEhISOH78OEePHuXcuXPs37+ftLQ0du3ahcvlYsuWLcD/lgRu2bIFl8vFrl27SEtLY//+/Zw7d46jR49y/PhxEhISOHToEMnJycTGxpKdnc22bdsKnMP9fceOHWRkZLB3714SExOJi4vj1KlTnDp1iri4OBITE9m7dy8ZGRmeCW3e59i2bRvZ2dnExsaSnJzMoUOHCjhlZWUFzGn//v107NiR3bt38/bbb3P33Xfr4uTdTmFhYZZvp5Jee+Hh4aZy6tOnDwcOHGD37t1ldvJuJyGEZdrpvffe46OPPuKWW27h1ltv9em1l5mZaUonLd8jQkNDbefk3U7h4eG2c/Jup+DgYPbu3UuOKweZkwPA9psHgLtH/tJLifzwP5o5FYuU0jRf5PbizMp3uy2Q5vWYJ4EfS3m+peT2Dm0A7i3qmA/xRXfu3FnanZMnTwbkOjt27JB16tSRYWFhcuHChQG5pptAORqJ2RyXLl0qATl37lzNzmk2x6JYsWKFDAoKku3bt5fJyck+P98qnv6gHO2B2/HALbfKuV27SUB+/fXX8sAtt8oDt9yq+fV69OghgWhZyP/sUg9RGURF4ILXsQvk7qBcIlLKfqU55gsul/3LbqWnp+t+jT/++IO+ffuSmZnJ0qVL6dWrl+7XzE8gHI3GbI5t2rQBYOvWrQwdOlSTc5rNsTBOnDjBiBEjqF27NosWLaJCBd/XaFjB01+Uoz3I7xhicC0qvxMcIUQ3oDmwTkr5j/8hFSAZ8B6wrExumQhDCAkxe07oP1WrVtX1/OvWreOmm26iXLlyrF69mmuvvVbX6xWG3o5mwGyOdevWJTIykq1bt2p2TrM5euNyuRg5ciSnT59m5cqVXHrppWU6j9k9tUA52oP8jiF5q6hMXWyzBLoA54FnhRCTNDhffvYAIUKIpvmOtQYCVnNeCDFMCLFECLEEaHn8uDFbTgeSkydP6nbu3377jZtuuomIiAiio6MNSW5AX0ezYEbHNm3a8Ndff7mHfP3GjI75ee+991ixYgXPPPMM119/fZnPY3ZPLVCO9iC/Y0jeKiqjFuf4neBIKd+UUn4npbwbOCqEeNfXcwghQoQQ4UAwECyECBdChEgpU4AFwGQhRAUhRBdgEDDb37hLi5RyrpRygJRyALDjkksuCdSlDaNBgwa6nPe3336jb9++REREsHr1alq2bKnLdUqDXo5mwoyObdq04fTp05w4oc06ADM6utm0aRMTJ06kY8eOTJ482a9zmdlTK5SjPcjv6F5FZdkeHCHEDCHET0KITcAjwHVlOM3zQBowARiR97O7cOdYcpeOnwLmAQ9LKQPWg+NNWlqaUZcOGHv27NH8nO7kJjw8nNWrV3P11WWqlKEZejiaDTM65p+HowVmdARITExk6NChlC9fnnnz5vm9p5NZPbVEOdqD/I5GD1FpMaHkY3JXJZ2UZex3llK+BLxUxH1ngcFljM1v8jYWdG8u2NIJtai07llZv369qZIb0N7RjJjR0Z3g/PXXX9x0001+n8+MjgCPPPII+/fv55tvvqFRo0Z+n8+snlqiHO1Bfkf3JGPTD1EJIQotHiGl3CJz96PRZlDdZHgPUTmhFpV7PwIt2LBhA3379iUsLIxffvnFNH/gWjqaFTM6Nm3alPLly2vWg2NGx9mzZzNnzhxGjRrFnXfeqck5zeipNcrRHuR3DDV4FZUvQ1RV898QQmzTNhRroFdtJDPRvn17Tc6zc+fOAqulWrVqpcl5tUArRzNjRsfg4GBatWqlWYJjNsc9e/YwduxYrrjiCj788EPNzms2Tz1QjvYgv2OwhVZReffQ2H+2VCEkJRm2Qj1gaPEp4+jRo9x0001kZ2ezbNkyUyU34LxPUmaiTZs27Nu3T5O/JTM5pqWlcfvtt5OVlcU333xTpv1uisJMnnqhHO1Bfkcrr6Ky5ZCUN97LxJ0wydjfTxmJiYn069ePY8eO8e2339KhQweNItMOp32SMhNt2rRBSunZqt0fzOT4xBNPsH37dv7zn/945hpphZk89UI52oP8jqEWWkVVUQhxWggRI4T4GCgnhGibV3jTtnjPwSlfvrzRIemOu85IWcjMzOS2225j+/btTJ8+nX79/No4Wjf8cbQKZnXUciWVWRznzp3Lp59+yl133cVDDz2k+fnN4qknytEe5Hd0D1FZoQenOnA78ANQHtgP/A4kCSE25SU9tkfLbmez0qJFizI9T0rJAw88wKpVq3jxxRd54IEHNI5MO8rqaCXM6tiyZUuCgoI0SXDM4Lh7924eeughmjZtyqefforIe1PXEjN46o1ytAf5HS0zyVhKeV5KGQ18CnwJjAdqkruT8SeAMSlagHHCENW+ffvK9LwXXniB2bNnc9999/HSSy9pG5TGlNXRSpjVsXz58jRr1oy//vrL73MZ7Ziamsrtt99OdnY23333nW6LEIz2DATK0R7kd7RiLarDwC5yN99rBIyVUn6maVQmJiwszOgQdKdevXo+P+err77itddeo0+fPnzyySe6fIrVkrI4Wg0zO7Zt25YFCxaQnZ3tV303ox0ff/xxduzYwSeffELr1q11u47RnoFAOdqD/I7uHhQrDFG5aSKl7CGlvBa4CXhZCDFB47hMgxNrUSUkJPj0+Li4OB599FGaN2/Od9995/eurYHAV0crYmbHNm3akJGRwe7du/06j7+Of2wayB+bBpbpuXPmzOGzzz5j2LBhPPjgg37FURJmbkutUI72wO3YaMH3XP7DAkJDQ63TgyOlvJDv5z+FENcCPwghgqSUr2sanQmQUs4F5gIIIaIjIyN7GByS7lSsWLHUj5VS8uCDD5KSksKXX35pmX2CfHG0KmZ2zD/R2J95CUY57t+/nzFjxtCsWTOmT5+ue4+lmdtSK5SjPfB2dCc4jRZ8H/BYfO7BEUL0EUKMEkK8IISYDnwD1ANe0Tw6E2LTDZsL4Eu2/fnnn7NixQqeeuopwyqDlwWjPlEEEjM7uodz/J1o7KujPz02bnJychg5ciQZGRnMmzcvIEm9mdtSK5SjPfB2DAkJMWyIqiyD3+7aU8eAo0AMuUUwj2oYl2lxQoLjcrlK9bi4uDjGjx9P8+bNTT+p2JvSOloZMztGRkZSt25dvxMcIxzffvttfvvtN1599VXatWsXkGuauS21QjnaA29Hqw1RXa5HIFYhODjY6BB0pzR7/Ugpeeihh0hJSWHWrFmEh4cHIDLtcMJ+RmZ3bNOmDZs2bUJKWeYhnpIc3b01116zuEzn92br1q28+OKLdOrUiWeeeUaTc5YGs7elFihHe+DtaGSC489Oxo7ECV2MZ8+eLfExX3zxBcuXL+fJJ5+kY8eOAYhKW0rjaHXM7ti2bVsSEhI4erTsnb/+OKalxZGSso+kpJ1s3NiHtLS4Yh+fnp7OiBEjCA0NZfbs2X6t/vIVs7elFihHe+DtaLUhKkchhBgGDMu72fLChQvFPdwWXHLJJcXeHx8f7xmaevnllwMUlbaU5GgHzO6Yf6JxWZfP+uLoTmhcrgw2buxDatphpMz9wJKSuo+Nv/elZ9SuIp///PPPs3PnTqZPn06TJk3KFG9ZMXtbaoFytAfejqoHx8R4l2qoXLmy0SHpzsGDB4u8z71qKjk5mZkzZ1puaMpNcY52weyOWpRsKM7Ru4dmw8beuFwZQG5C405u3LjvK4yYmBjee+89+vXrp0sphpIwe1tqgXK0B96OlpqD43ScMIbavHnzIu9btmyZZ2iqU6dOAYxKW4pztAtmd2zcuDEVKlTwK8EpznHbtgcLJDTFE0SF8oVPL0xMTGTkyJFUr16dzz77zJBNLM3ellqgHO2Bt6ORQ1SqB8dHkpOTjQ5Bd4r7hzNr1ixCQ0OZMMHaeztqUQfJ7JjdMSgoiNatW/sVZ3HPTUkt7tNyEBHhlxEUlLszeYXyl9O69YyLHiWlZMyYMRw+fJjp06dTt27dMsfqD2ZvSy1QjvbA21ENUVkIJ2zUVNTS13PnzrFo0SJuvvlmatSoEeCotCVQy3uNxAqObdq0Yf/+/SQmJpbp+cU5VijfKN+tixOatm1nUaFCEypVakGnTsuJiGhw0Tneffdd5s2bxwMPPMCQIUPKFKMWWKEt/UU52gNvR5XgWIikpCSjQ9CdzZs3F3r822+/JSMjg5EjRwY4Iu0pytFOWMGxbdu2AGzfvr3Exxa2SV9xjq1bz/A5ocnP8uXLeeaZZ7juuuv46KOPSoxPT6zQlv6iHO2Bt6MaorIQVilF4A/t27cv9PiXX35JzZo16du3b4Aj0p6iHO2EFRz9nWhcnGNERAOfEpr87Nu3j7vuuos6derw/fffG15k1wpt6S/K0R54O6oeHBPjXWzz8OHDRoekO1u2bLno2J49e9iwYQPDhg2jXLlyBkSlLYU52g0rOLZo0YLg4GD++uuvMj0/v6MWZRggd1LxwIEDSUtL44cffjBs3k1+rNCW/qIc7YG3o1pFZWK8i21edtllti+26f5UnZ+vvvoKwBbDU1C4o92wgmNERATNmzcvsQfHew8bhCAoqBwd2i+86LH+7F7scrm4++67+eeff/jyyy9NU1/NCm3pL8rRHng7qiEqC5Gammp0CLoTGxtb4LbL5WL27NlcffXVnjkTVsfb0Y5YxbFNmzb8/fffnk953j0xf2wayMbf++Zb8n3As+twSY7XXrO4QKLjfdubl19+mcWLF/PEE09wzz33lNlJa6zSlv6gHO2Bt6MaorIQVt3YzhcaNWpU4HZ0dDRxcXGMHDnSkD1A9MDb0Y5YxbFdu3ZkZmaya1fRuwgX3ITPhcuVQVLSTs5feIK0tLgCm/rl9vRklura+ROeJUuWMHnyZK6//nrefvttf5Q0xypt6Q/K0R54O6oEx0JkZBS926ldOHbsWIHbX375JUFBQQwfPtygiLTH29GOWMXR3StY1PyEa69ZTIXyhZdGSEs7wLZtDxbY1M/lyiAlZW+p6ku5OX36NPfffz+XXnop//3vfwNaZ6o0WKUt/UE52gNvRzVEZSFCQ0ONDkF3qlev7vk5OTmZ77//nj59+phisqVW5He0K1ZxdCc4xU00zr/kuyCSlNSDhW7ql5K6j23bHizx+lJKRo8ezalTp5g5c6Yp93iySlv6g3K0B96OqgfHQuTk5Bgdgu7kn2f0/fffk5KSYpvJxW6cMJfKKo5Vq1alUaNGxa4wyb/ku2BvjiAoKISgoMJ7XIrfzTiX2bNn88MPP/DII49w4403+hp+QLBKW/qDcrQH3o4qwbEQdpmDUhxBQf97WXz11VdUqVKFQYMGGRiR9uR3tCtWcmzXrh1bt24t1QeI/L055cpdRkREAyIiGhTSwxPktZvxxcTFxTFu3DiaNm3KW2+9VdbwdcdKbVlWlKM98HZUQ1QWwgkJjnsYLi4ujjVr1nDnnXfabnK1E4YareTYrl07UlJS2LevpKKYBXtzLm/0Xt4E47159zUssb6UG5fLxb333ktycjKzZ8+mQoUK2sjogJXasqwoR3vg7RgaGorL5cLlcgU8FpXglID3Rn8nT540OiTdcRcUnT17NlJK2w1PgTOKplrJ0T0PZ+u2VZ7VUKWZJBy7+84Ck4szMo6XevfiKVOmsGbNGp599lk6duyonYwOWKkty4pytAfeju6Ex4hhKpXglICUcq6UcoCUcgCww04TbYuiZs2aQG6C07RpU6677jqDI9Iet6OdsZKju0BfcPB7+fa72cfG3/9XFqTwPWwKvmm6XKXrCv/nn3+YMGEC7dq144UXXih74AHCSm1ZVpSjPfB2dK9INGKYSiU4PuKEZeJHjhzh9OnT7N69m5tvvtmWw3JHjhwxOgTdsZJjZGQkNWuGUaWKLHC84P43/8Od7ISE5O+hyZ1zU9JmfllZWdx9991IKfnqq68sUXrESm1ZVpSjPfB2VD04FiIiIsLoEHSnSZMm7NixA4DWrVsbHI0+NGlS+L4qdsJqjh073sDRo/nH6YOK3P/GTbu2X5R6zo2bF198kc2bN/P666/TokULf0IOGFZry7KgHO2Bt6NKcCxESkqK0SHozs6dO9m+fTsALVu2NDgafdi5c6fRIeiO1RzbtWvHsxOPkpOT+4ZYmoTlwIFEnyqGr169mrfeeovevXvzxBNPaBW67litLcuCcrQH3o5qiMpCVKxY0egQdKd169Zs376d4OBgrrzySqPD0QW79kzlx2qObdu25fjxbLb+VanUCYsvjgkJCdx9993UrFnTszu3VbBaW5YF5WgPvB1VD46FSEpKMjoE3dm8eTM7duzgiiuusN3ycDebN282OgTdsZqje6Lx7j0XSv2c0jpKKbn//vs5duwYs2bNok6dOmWK0Sis1pZlQTnaA29HIxMccxVcsQCVKlUyOgTdcVd3ttvmfvlp37690SHojtUcGzRoQLVq1dgdW/oEJ9ex6AnFbqZPn87ixYt5/PHH6devnx9RGoPV2rIsKEd74O2ohqgshBN6cBYtWkR6ejqtWrUyOhTdcOInKbMjhKBdu3bs2ZNY6ueUxvHvv/9m/PjxtG7dmjfffNOfEA3Dam1ZFpSjPTBTD45KcHzECT047h0n7ZzgOPGTlBVo27Ytp0+ncyYhvVSPL8kxLS2NoUOHIoRg3rx5lh1ytWJb+opytAfejirBsRBOWEW1atUqwL4rqADPMng7Y0VHX+fhlOT49NNP8/fff/PBBx9YesK8FdvSV5SjPfB2VENUFsIJ++AcP36cypUr06BB8StYrEyzZs2MDkF3rOjoTnD27C7dMFVxjsuWLeOjjz7illtu4cEHH9QkPqOwYlv6inK0B96OqgfHxHjXojp27JjRIenOX3/9RcuWLW25g7GbuLjiaxzZASs6Nm3alIiIYGJ3l64HpyjHM2fOMGrUKCIjI/n0008t/1q2Ylv6inK0B96OKsExMU6rRZWUlER8fLyt599AbmkAu2NFx6CgIJo2q8yeUiY4hTlKKRkzZgzHjx/niy++sEX9Hyu2pa8oR3vg7aiGqCyEEY0USNy7UNo9wTl//rzRIeiOVR27dxvO0aOpnDt3rsTHFub49ddfM3/+fMaMGWPJJeGFYdW29AXlaA+8HVUPjoWw0u6nZcHuJRrcWHU1jS9Y1dE9D2fr1q0lPtbbMS4ujkceeYQmTZrwzjvv6BGeIVi1LX1BOdoDb0eV4ChMgzvBufrqqw2OROFU2rZtC+TOBfMFl8vFyJEjSUlJYc6cOVSoUEGP8BQKhQ+oISoL4d4jxq7s2LGDevXqUaVKFaND0ZX09NLts2JlrOp41VVXUa5cObZs2VLiY/M7fvDBB0RHR/Pcc8/RsWNHPUMMOFZtS19QjvbA21H14FgIdzZqR6SUbN++3fbDUwBVq1Y1OgTdsapjuXLlaNmyZal6cNyOO3bsYOLEiXTo0IHnn39e5wgDj1Xb0heUoz3wdlQJjoXIzMw0OgTdOHLkCOfPn6dhw4ZGh6I7J0+eNDoE3bGyY9u2bYmNjS1xY82TJ0+SmJjI7bffTnBwMLNnz/a8odoJK7dlaVGO9sDbUQ1RWYiwsDCjQ9AN9w6UXbp0MTgS/bHzJoZurOzYrl07XC6XZ05YUdSvX5/77ruP3bt3M2PGDJo3bx6gCAOLlduytChHe+DtqHpwLERaWprRIeiG+59JxYoVDY5Ef/bs2WN0CLpjZcfSTjSeOHEiCxYsYNy4cQwfPjwQoRmClduytChHe+DtqBIcC2HnlRnbt28nLCyM/v37Gx2K7jhhnpGVHVu1akVQUBBffPEFhw8fLvQxv/zyCx9++CGdO3e21ZLwwrByW5YW5WgPvB3VEJWFSEpKMjoE3dixYwdXXXUV27ZtMzoU3dm8ebPRIeiOlR3Lly/P66+/zl9//cXVV1/N9OnTC6xgjIuL46677qJatWp89913lCtXzsBo9cfKbVlalKM98HZUPTgWolKlSkaHoAsZGRnExsbSqlWri8rd2xHlaH6eeeYZNm7cyGWXXcbDDz/MjTfeyMGDB8nIyGDIkCGcO3eOBQsWcMkllxgdqu5YvS1Lg3K0B96OKsGxEHbtwYmNjSU7O5tWrVo58lOGHbGD4zXXXMPmzZt57rnniImJoWXLlvTt25dNmzbxzjvv2HrIOD92aMuSUI72wNtRDVFZCLv24LhXULVs2dKRnzLsiF0cw8LCePXVV/n9999p1KgR0dHR3HXXXTz++OO2cSwJJ3gqR3ugenAsTHJystEh6IJ7BVWrVq0cMQdHOVqP9u3bs3nzZhYvXszMmTMRQtjOsSic4Kkc7YG3o5EJjm235RVCVAFWAlcBnaSUfwshrgPeAzKBY8A9UkqffutGd4lfOJ3GvJd/JyfbRbW65ek/tjVVakX4fd7t27dTu3ZtIiMjqVGjhgaRmpsWLVoYHYLu2NGxXLly3HzzzZ7bdnQsDCd4Kkd74O2ohqj0IRXoD8zPd+ww0EtK2QM4AAzy9aRG74Pz07Rt5GTnriY5fyKVn6Zp84lgx44dnuV9+/bt0+ScZkY52gMnOIIzPJWjPfB2VENUOiClzJJSnvY6dkxK6c5QsgGfK2cavZPx+ZOpnp+lLHi7rCQkJHDs2DFatWoFQL169fw+p9lRjvbACY7gDE/laA+8HR2f4AghHhVC/CmEyBBCzPK6r7oQ4gchRIoQ4rAQYpgG12sE3AQs8fW5RjRSfqpGlvf8LETB22XFPcHYneAkJCT4fU6zoxztgRMcwRmeytEeeDuqIarc+TCvAl8Uct9UcufMRALDgY+FEC0AhBB1hBDrCvmqU9SFhBCVgS+Bu6WUPlfODA4O9vUpmtJ/bGuCQ3KbrWqd3Dk4/pJ/BRU4o1SDcrQHTnAEZ3gqR3vg7RgcHIwQwrmTjKWUCwCEEB0AT/+WEKICcBtwtZQyGVgnhFgM3A1MkFKeALqW9jpCiBBgHvCSlHJ3MY+LLuKuNlLK0l5OF6rUimDMR1GannP79u0EBQVx1VVXAcb3UgUC5WgPnOAIzvBUjvagMMfQ0FDnDlEVQzMgR0qZv3rXNqBUU9GFEEuB3sAMIcS9wFCgI/CiECJaCHGnrwFlZmaSkJDA8ePHOXr0KOfOnWP//v2kpaWxa9cuXC4XW7ZsAf634dGWLVtwuVzs2rWLtLQ09u/fz7lz5zh69CjHjx8nISGBQ4cOkZyc7Nlwz73Uzn0O9/cdO3aQkZHB3r17SUxMJC4ujlOnTnHq1Cni4uJITExk7969ZGRkeHpmvM+xbds2srOziY2NJTk5mR07dlC/fn3Onz/P0aNHSUxMtLzToUOHim2nnJwc2zl5t5P7tp2cvNspPT3ddk6FtdOFCxds5+TdTllZWbZz8m4nl8tlO6fStFNwcDAXLlzQxak4hNE9EvkRQrwK1JNS3pt3uxvwnZSyTr7HPAgMl1JGGRBfdJcuXXqsW7cu0JfWlYYNG3L55ZezevVqAM6dO0e1atUMjkpflKM9cIIjOMNTOdqDwhyrVq1K7969+fbbbzW/XlRUFDExMTGF5QRm78FJBip7HasMGFYvwW5djNnZ2Rw5coSGDRt6jp09e9a4gAKEcrQHTnAEZ3gqR3tQmKNRQ1SmmINTDHuAECFEUynl3rxjrYGdgQogb9WWe+VWywsXLgTq0gHh6NGj5OTkcNlll3mOOaF4oXK0B05wBGd4Kkd7UJhjSEiIc1dRCSFChBDhQDAQLIQIF0KESClTgAXAZCFEBSFEF3I355sdqNiklHOllAOklAOAHZUre3coWZvDhw8DFEhwDh48aFQ4AUM52gMnOIIzPJWjPSjM0emTjJ8H0oAJwIi8n5/Pu28sEAGcIncF1MNSyoD14HhTvrz/+86YiUOHDgEUGKJq3ry5McEEEOVoD5zgCM7wVI72oDBHRyc4UsqXpJTC6+ulvPvOSikHSykrSCkbSCnnGhmr3YptFtaDs3XrVoOiCRzK0R44wRGc4akc7UFhjkYNUZl9Do7heM/BSU31vzSCmTh8+DBBQUEFttdu166dgREFBuVoD5zgCM7wVI72oDBHR/fgmBnvOTgREf5X7jYThw8f5tJLL/XUC4H/7UdgZ5SjPXCCIzjDUznag8IcVYJjESpVqmR0CJpy6NChAsNTAO3btzcomsChHO2BExzBGZ7K0R4U5ujoVVRWwk5zcFwuF3FxcRclOO6dLu2McrQHTnAEZ3gqR3tQmKPaB8ekeM/BSUlJMTIcTTl58iSZmZkFVlABtGnTxpB4AolytAdOcARneCpHe1CYoxqiMinec3DsNETlXiLu3YMTGxtrQDSBRTnaAyc4gjM8laM9KMxRDVFZhPDwcKND0IzClogDNGrUyIhwAopytAdOcARneCpHe1CYo+rBsQgZGRlGh6AZ7gTHe4jq2LFjBkQTWJSjPXCCIzjDUznag8IcVYJjEfIvp7Y67gSnQYMGBY5Xr17diHACinK0B05wBGd4Kkd7UJijGqIyKUKIYUKIJUKIJUDLkydPGh2SZhw6dIjIyMiLht3stplhYShHe+AER3CGp3K0B4U5qh4ck+I9ybhWrVpGh6QZhw8fvmh4CiAoyP4vC+VoD5zgCM7wVI72oDBHleBYBCGE0SFogpSSw4cPXzTBGOw1DFcUytEeOMERnOGpHO1BYY5qiMoi5OTkGB2CJpw5c4aUlJRCExw7bWZYFMrRHjjBEZzhqRztQWGOqgfHItglAy9qBRVAzZo1AxxN4FGO9sAJjuAMT+VoDwpzDA0NRUoZ8A4CleD4iF2WiRe1Bw7AkSNHAh1OwFGO9sAJjuAMT+VoDwpzDAnJLZoQ6GEqVaqhBLxLNSQlJRkZjmYUtYsxQJMmTQIcTeBRjvbACY7gDE/laA8Kc3SPfGRlZREWFhawWFQPTgl4r6KqUKGC0SFpQnE9ODt37gx0OAFHOdoDJziCMzyVoz0ozDF/ghNIVILjIxUrVjQ6BE04fPgw1atXp7DaWq1btzYgosCiHO2BExzBGZ7K0R4U5mjUEJVKcHzELkNURS0RB9i8eXOAowk8ytEeOMERnOGpHO1BYY6qB8ci2KWa+KFDhwpdQQXQvn37wAZjAMrRHjjBEZzhqRztQWGOKsGxCHbowUlMTOT8+fOqB8fmKEf74ARP5WgPCnNUQ1QWwQ49OMVNMAbnfsqwG8rRPjjBUznaA9WDYyG8i23GxcUZHZLfuJeIFzVEtWPHjsAFYxDK0R44wRGc4akc7UFhjirBMSney8Tr1atndEh+U1IPTrNmzQIZjiEoR3vgBEdwhqdytAeFOaohKotgh52MS0pw7NBLVRLK0R44wRGc4akc7UFhjqoHxyKUK1fO6BD85tChQ1SsWJFq1aoVen9kZGSAIwo8ytEeOMERnOGpHO1BYY4qwbEIRpR815rDhw/TsGFDhBCF3n/+/PnABmQAytEeOMERnOGpHO1BYY5qiMoiBAVZ/1dW3CZ/AOHh4QGMxhiUoz1wgiM4w1M52oPCHFUPjiIgpKWlcerUqWITHIVCoVAotEIlOBbB5XIZHYJfuCcYF7VEHCA9PT1A0RiHcrQHTnAEZ3gqR3tQmKNRQ1QhAb2aBRFCDAOG5d1sefbsWSPD8ZuSVlABVK1aNUDRGIdytAdOcARneCpHe1CYo+rBMSne++BY/QVamgTn5MmTgQrHMJSjPXCCIzjDUznag8IcVYJjEcLCwowOwS9K2sUYoEGDBoEJxkCUoz1wgiM4w1M52oPCHNUqKouQlpZmdAh+cfjwYcLDw6ldu3aRj9mzZ08AIzIG5WgPnOAIzvBUjvagMEfVg2MRKlSoYHQIfnH48GEaNGhQ5B44AC1btgxgRMagHO2BExzBGZ7K0R4U5qgSHIuQlJRkdAh+cejQoWKHp6Dwcvd2QznaAyc4gjM8laM9KMxRDVFZhEqVKhkdQpnJzMzk2LFjJe6BU1i5e7uhHO2BExzBGZ7K0R4U5qh6cCyClXtwjhw5gpSyxATHqZ8y7IZytA9O8FSO9qAwR5XgWAQr9+CUZpM/cO6nDLuhHO2DEzyVoz0ozFENUVmE5ORko0MoM+4l4iX14Gzbti0A0RiLcrQHTnAEZ3gqR3tQmKPqwbEIVl5FFR8fD5Sc4LRo0SIQ4RiKcrQHTnAEZ3gqR3tQmKNKcCyClffBiYuLIygoiLp16xb7uH379gUoIuNQjvbACY7gDE/laA8Kc1RDVBbByjsZx8XFcemll3pebEVRr169AEVkHMrRHjjBEZzhqRztQWGOqgfHpAghhgkhlgghlgAtjx8/bnRIZSYuLq5UW4UnJCQEIBpjUY72wAmO4AxP5WgPCnNUCY5J8S62GRkZaXRIZUJKSXx8PPXr1y/xsRUrVgxARMaiHO2BExzBGZ7K0R4U5qiGqCyClNLoEMrE2bNnSU1NLVUPTqCzbCNQjvbACY7gDE/laA8Kc1Q9OBbBqglOXFwcULpqti6XS+9wDEc52gMnOIIzPJWjPSjMMSgoiKCgIJXgmJ3g4GCjQygT7iXipRmiKl++vN7hGI5ytAdOcARneCpHe1CUY0hIiBqiMjtW7WL0pQfn7NmzeodjOMrRHjjBEZzhqRztQVGOoaGhqgfH7Fh1mbgvCc4ll1yidziGoxztgRMcwRmeytEeFOWoEhwLkJ6ebnQIZSIuLo4KFSpQrVq1Eh978ODBAERkLMrRHjjBEZzhqRztQVGOaojKAlh1DNW9RFwIUeJjmzdvHoCIjEU52gMnOIIzPJWjPSjKUfXgWACrFtss7SZ/AFu3btU3GBOgHO2BExzBGZ7K0R4U5agSHAtgxY2asrKyOHbsWKkTnHbt2ukckfEoR3vgBEdwhqdytAdFOaohKguQlJRkdAg+c+zYMVwuV6mWiANs3rxZ54iMRznaAyc4gjM8laM9KMpR9eBYgEqVKhkdgs+498ApbQ9O+/bt9QzHFChHe+AER3CGp3K0B0U5qgTHAlhxDo4vS8QBtmzZomc4pkA52gMnOIIzPJWjPSjKUQ1RWQArzsHxNcFp06aNjtGYA+VoD5zgCM7wVI72oChH1YNjAVJTU40OwWfcQ1T16tUr1eNjY2P1DMcUKEd74ARHcIancrQHRTmqBEdDhBBVhBB/CCGShRBX5x2LFEKsF0LECCFWCyHq+nre8PBw7YPVmbi4OGrXrl3q2Bs1aqRzRMajHO2BExzBGZ7K0R4U5aiGqLQlFegPzM93LAHoKqXsAXwF3O/rSTMyMrSJLoD4sgcO5K66sjvK0R44wRGc4akc7UFRjqoHR0OklFlSytNex3KklO5a7pWAnb6eNzQ0VIvwAkpcXFypl4gDVK9eXcdozIFytAdOcARneCpHe1CUo2MTHCHEo0KIP4UQGUKIWV73VRdC/CCESBFCHBZCDPPzWm2EEL8DjwI+T2nPycnx5/IBJykpifPnz/vUg2PFeUa+ohztgRMcwRmeytEeFOVoxBBVSECvVjTHgFeBPkCE131TgUwgEmgD/CSE2Cal3CmEqEPBISg3Q6SUJwq7kJRyK9BRCHEHMBEY40ugpanlZCZ83QMHICjIFHmvrihHe+AER3CGp3K0B0U5GtGDY4oER0q5AEAI0QHwLPURQlQAbgOullImA+uEEIuBu4EJeUlM19JeRwgRJqV0T6K5QO48ncIeF13EKa7buXMnUVFRpb2k4Zw9exaAzz//nMWLF5fqOVlZWZYcivMF5WgPnOAIzvBUjvagKMddu3Zx/vx5zf9/5tW+alLYfaZIcIqhGZAjpdyT79g2oEdpniyEWEpur88VQohPgN1CiLeAHCAdGOVjPMGJiYmZMTExG3x8nuHs2rWrtA9tk/d9qy6BmIM2ed+3GhiD3rTJ+77VwBj0pk3e960GxhAI2uR932pgDHrTJu/7VgNj0Js2ed+3GhiD3rTJ+761qAfExMRofc0mwOnC7jB7glOR3J6W/Fwgd4JwiUgp+xVyuHspnhdV2HF3z05R99sB5WgPlKN9cIKncrQHZnM0+4BgMlDZ61hlwHoVLxUKhUKhUAQMsyc4e4AQIUTTfMdaU4bl3QqFQqFQKJyDKRIcIUSIECIcCAaChRDhQogQKWUKsACYLISoIIToAgwCZhsZr0KhUCgUCnNjigQHeB5IAyYAI/J+fj7vvrHkLh0/BcwDHpZSqh4chUKhUCgURWKKScZSypeAl4q47ywwOIDhKBQKhUKhsDhCSml0DAqFQqFQKBSaYpYhKoVCoVAoFArNUAmOQqFQKBQK26ESHIVCoVAoFLZDJTgaI4RoKIQ4LYSIzvuqZXRMWiOEiBRCrBdCxAghVgsh6hodkx4IIaoIIf4QQiQLIa42Oh4tsKOTNw56fTrhvaZrPr89Qoj3jY5Ja4QQwUKIr4UQa4QQXwghTLH4x18Ke68J9PuPSnD0IUZKGZX3VWiNDIuTAHSVUvYAvgLuNzgevUgF+lN4xXqrYkcnb5zy+gSbv9dIKde5/YD1wEJjI9KFW4ADUsqeQCxwq8HxaEVh7zUBff9RCY4+dBFCrBVCvC6EEEYHozVSyhwppSvvZiVsurO0lDLLbv807OjkjVNen3nY+r3GjRAiFLgWWGt0LDrQmP8Vp9wCdDMuFO0o7L0m0O8/jk5whBCPCiH+FEJkCCFmed1XXQjxgxAiRQhxWAgxrJSnPU5uddPuQG0MzsZ1ckQI0UYI8TvwKLl/lIail6dZcYKvP45me30Whx+epnqvKQ4NXq83Ar/kS1xNhx+Ou4BeeT/fAFQLUMilwsrvNbYY6/ODY8CrQB9yd0vOz1QgE4gktwT8T0KIbVLKnUKIOhTexTZESnkCyAAQQiwAOgHf6xN+qdDFUUq5FegohLgDmAiM0Sn+0qJXW5qVMvkGNEL/KbOjCV+fxVEmTyllBuZ6rykOf1+vtwMzAxCnP5TVcQkQJYRYTW5v48mARVw6LPte4+gER0q5AEAI0QGo5z4uhKgA3AZcLaVMBtYJIRYDdwMT8v7xdS3snEKIylLKxLyb3YB/dFQoEZ0cw/LeXAEukDuuaih6eJqZsvoaEWtZKaujGV+fxeGHp6nea4rDn9eryB2eugaTz6Xy4z1IAv/Oe+xLwOoAh14sVn6vcfQQVTE0A3KklHvyHdsGtCjFc3sIITYLIdYClwJz9QhQA/xxbCeE+FUIsQZ4Anhbh/i0wh9PhBBLgd7ADCHEvdqHpzkl+lrQyZuSHK30+iyOkjyt8l5THKX5+7wBWG3m4akSKNZRCFFH5K4S+wXIlFL+akSQZaBM7zWBfP9xdA9OMVQk95Nffi6QO2GxWKSUPwI/6hGUxvjjuIHccX8rUGZPACllP80j0pcSfS3o5E2xjhZ7fRZHSZ5Wea8pjtK8Xn8Gfg5kUBpTUjueAKICHJMWlOm9JpDvP6oHp3CSgcpexyoDSQbEohdOcATneLpxgq8THMEZnsrRupjeSyU4hbMHCBFCNM13rDX2Wm7qBEdwjqcbJ/g6wRGc4akcrYvpvRyd4AghQoQQ4UAwECyECBdChEgpU4AFwGQhRAUhRBdgEDDbyHjLghMcwTmebpzg6wRHcIancrSuo6W9pJSO/QJeAqTX10t591Und9fMFCAOGGZ0vMpReTrJ1wmOTvFUjtZ1tLKXyAtSoVAoFAqFwjY4eohKoVAoFAqFPVEJjkKhUCgUCtuhEhyFQqFQKBS2QyU4CoVCoVAobIdKcBQKhUKhUNgOleAoFAqFQqGwHSrBUSgUCoVCYTtUgqNQKBQKhcJ2qARHoVAoFAqF7VAJjkKhUCgUCtuhEhyFQmFZhBDVhBBSCJHs9fW41+MuEUIcKeU5lwshJhdyfJAQ4oQQIkSr+BUKhX6oBEehUFiZNsBZKWVFr6//eD2uH7CslOecBdwthBBex+8GvpZSZvsVsUKhCAgqwVEoFFamDbCrFI/rByzNfyCvV+d7IcRpIcRBIcRjeXctJLdKcrd8j60GDAC+0iJohUKhPyrBUSgUVqYtJSQ4QohQoDuwMt+xIOBHYBtwKXA98IQQoo+UMg34Frgn32nuAGKllNu0DV+hUOiFSnAUCoWVaUPucNL5fF/veT2mO7BNSpmU79g1QC0p5WQpZaaU8gAwA7gr7/4vgduFEBF5t+/JO6ZQKCyCmiynUCgsiRAiDLgSuE5K+WcxD71oeAq4DLhECHE+37FgYC2AlHKdEOI0MEgI8Qe5CdGtWsWuUCj0RyU4CoXCqlwNSGBHCY/rB9zidSweOCilbFrM874it+fmCmCFlPJkWQNVKBSBRw1RKRQKq9IW2CmlzCjqAUKIRkCYlDLW664/gEQhxDNCiAghRLAQ4mohxDX5HvMVcAPwIGp4SqGwHCrBUSgUVqUN0NJr/5skIUSVfI/pz8XDU0gpc4Cb885xEEgAPgOq5HvMIWA9UAFYrJODQqHQCSGlNDoGhUKh0AUhxFLgIynlRUmOQqGwN6oHR6FQ2JloYI3RQSgUisCjenAUCoVCoVDYDtWDo1AoFAqFwnaoBEehUCgUCoXtUAmOQqFQKBQK26ESHIVCoVAoFLZDJTgKhUKhUChsh0pwFAqFQqFQ2I7/B3jI17v3ZLaxAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"for dataset in datasets:\n",
" dataset.data.plot(ax=ax, label=dataset.name)\n",
"\n",
"ec_model.plot(\n",
" ax=ax,\n",
" energy_bounds=[1e-6, 1e14] * u.eV,\n",
" energy_power=2,\n",
" label=\"EC model\",\n",
" color=\"k\",\n",
" lw=1.6,\n",
")\n",
"\n",
"ax.set_ylabel(sed_y_label)\n",
"ax.set_xlabel(r\"$E\\,/\\,{\\rm eV}$\")\n",
"ax.set_xlim([1e-5, 1e12])\n",
"ax.set_ylim([1e-13, 1e-8])\n",
"ax.legend(ncol=4, fontsize=9)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "78cbcbff",
"metadata": {},
"source": [
"#### 3) run the fit"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "ed5204a0",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:67: RuntimeWarning: overflow encountered in true_divide\n",
" return np.where(tau < 1e-3, 1, 3 * u / tau)\n",
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: divide by zero encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: invalid value encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: divide by zero encountered in true_divide\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in expm1\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in multiply\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 4min 48s, sys: 14.9 s, total: 5min 2s\n",
"Wall time: 5min 4s\n"
]
}
],
"source": [
"%%time\n",
"# define the fitter\n",
"fitter = Fit()\n",
"results = fitter.run(datasets)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "4e95d740",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OptimizeResult\n",
"\n",
"\tbackend : minuit\n",
"\tmethod : migrad\n",
"\tsuccess : True\n",
"\tmessage : Optimization terminated successfully.\n",
"\tnfev : 317\n",
"\ttotal stat : 220.71\n",
"\n",
"CovarianceResult\n",
"\n",
"\tbackend : minuit\n",
"\tmethod : hesse\n",
"\tsuccess : True\n",
"\tmessage : Hesse terminated successfully.\n",
"\n",
" type name value unit error min max frozen is_norm link\n",
"-------- --------------- ----------- ----- --------- ---------- --------- ------ ------- ----\n",
"spectral log10_k 2.4521e-01 1.577e-01 -1.000e+01 1.000e+01 False False \n",
"spectral p 2.1681e+00 1.243e-01 1.000e+00 5.000e+00 False False \n",
"spectral q 3.3617e-01 3.368e-02 1.000e-03 1.000e+00 False False \n",
"spectral log10_gamma_0 2.0000e+00 0.000e+00 2.000e+00 6.000e+00 True False \n",
"spectral log10_gamma_min 0.0000e+00 0.000e+00 0.000e+00 4.000e+00 True False \n",
"spectral log10_gamma_max 4.4771e+00 0.000e+00 4.000e+00 8.000e+00 True False \n",
"spectral z 3.6100e-01 0.000e+00 1.000e-03 1.000e+01 True False \n",
"spectral delta_D 2.5823e+01 1.788e+00 1.000e+00 1.000e+02 False False \n",
"spectral log10_B -4.0655e-01 3.696e-02 -4.000e+00 2.000e+00 False False \n",
"spectral t_var 4.3200e+04 s 0.000e+00 1.000e+01 3.142e+07 True False \n",
"spectral mu_s 9.9925e-01 0.000e+00 0.000e+00 1.000e+00 True False \n",
"spectral log10_r 1.7778e+01 0.000e+00 1.600e+01 2.200e+01 True False \n",
"spectral log10_L_disk 4.5826e+01 0.000e+00 4.200e+01 4.800e+01 True False \n",
"spectral M_BH 1.1354e+41 g 0.000e+00 1.000e+32 1.000e+45 True False \n",
"spectral m_dot 8.9457e+25 g s-1 0.000e+00 1.000e+24 1.000e+30 True False \n",
"spectral R_in 5.0589e+13 cm 0.000e+00 1.000e+12 1.000e+16 True False \n",
"spectral R_out 2.5295e+17 cm 0.000e+00 1.000e+12 1.000e+19 True False \n",
"spectral xi_dt 6.0000e-01 0.000e+00 0.000e+00 1.000e+00 True False \n",
"spectral T_dt 2.0000e+03 K 0.000e+00 1.000e+02 1.000e+04 True False \n",
"spectral R_dt 6.4711e+18 cm 0.000e+00 1.000e+17 1.000e+20 True False \n",
"spectral norm 1.0000e+00 0.000e+00 1.000e-01 1.000e+01 True True \n"
]
}
],
"source": [
"print(results)\n",
"print(ec_model.parameters.to_table())"
]
},
{
"cell_type": "markdown",
"id": "3907095b",
"metadata": {},
"source": [
"Now let us plot the final model and the flux points"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "4aaa6815",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: divide by zero encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/work/agnpy/agnpy/synchrotron/synchrotron.py:66: RuntimeWarning: invalid value encountered in true_divide\n",
" u = 1 / 2 + np.exp(-tau) / tau - (1 - np.exp(-tau)) / np.power(tau, 2)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: divide by zero encountered in true_divide\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in expm1\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
"/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: overflow encountered in multiply\n",
" result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"for dataset in datasets:\n",
" dataset.data.plot(ax=ax, label=dataset.name)\n",
"\n",
"ec_model.plot(\n",
" ax=ax,\n",
" energy_bounds=[1e-6, 1e14] * u.eV,\n",
" energy_power=2,\n",
" label=\"model\",\n",
" color=\"k\",\n",
" lw=1.6,\n",
")\n",
"\n",
"ax.set_ylabel(sed_y_label)\n",
"ax.set_xlabel(r\"$E\\,/\\,{\\rm eV}$\")\n",
"ax.set_xlim([1e-5, 1e12])\n",
"ax.set_ylim([1e-13, 1e-8])\n",
"ax.legend(ncol=4, fontsize=9)\n",
"\n",
"plt.show()"
]
}
],
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