{ "cells": [ { "cell_type": "markdown", "id": "3e048b8e", "metadata": {}, "source": [ "# Timing methods\n", "\n", "This notebook demonstrates some of the \"quick-look\" timing analyses available in `opticam`.\n", "\n", "## Preface\n", "\n", "`stingray` is designed primarily for analysing X-ray data, and so is perhaps not ideal for OPTICAM data products. That said, `stingray` provides a number of useful routines that can (mostly) be applied to arbitrary time series, provided some care is taken.\n", "\n", "## Generating and Reducing Data\n", "\n", "Before we can explore the different timing analyses provided in `opticam`, we need some light curves to analyse. For this example, I'll quickly generate and reduce some gappy observations (see the [Reduction Tutorial](reduction.ipynb) for more details on data reduction):" ] }, { "cell_type": "code", "execution_count": 1, "id": "e1dfb3b9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] variable source is at (65, 57)\n", "[OPTICAM] variability RMS: 0.02 %\n", "[OPTICAM] variability frequency: 0.135 Hz\n", "[OPTICAM] variability phase lags:\n", " [OPTICAM] g-band: 0.000 radians\n", " [OPTICAM] r-band: 1.571 radians\n", " [OPTICAM] i-band: 3.142 radians\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Generating observations: 100%|██████████|[00:20<00:00]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] timing_analysis_tutorial/reduced not found, attempting to create ...\n", "[OPTICAM] timing_analysis_tutorial/reduced created.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n", "[OPTICAM] Scanning data directory: 100%|██████████|[00:00<00:00]\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101g200000343o.fits.gz and 240101g200000002o.fits.gz (48.995 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101g200000182o.fits.gz and 240101g200000481o.fits.gz (19.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101g200000191o.fits.gz and 240101g200000043o.fits.gz (58.994 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101g200000013o.fits.gz and 240101g200000414o.fits.gz (10.999 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101g200000338o.fits.gz and 240101g200000018o.fits.gz (24.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101i200000166o.fits.gz and 240101i200000418o.fits.gz (48.995 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101i200000099o.fits.gz and 240101i200000370o.fits.gz (19.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101i200000186o.fits.gz and 240101i200000476o.fits.gz (58.994 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101i200000345o.fits.gz and 240101i200000382o.fits.gz (10.999 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101i200000107o.fits.gz and 240101i200000124o.fits.gz (24.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101r200000124o.fits.gz and 240101r200000200o.fits.gz (48.995 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101r200000136o.fits.gz and 240101r200000321o.fits.gz (19.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101r200000386o.fits.gz and 240101r200000314o.fits.gz (58.994 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101r200000312o.fits.gz and 240101r200000382o.fits.gz (10.999 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/opticam/utils/data_checks.py:205: UserWarning: [OPTICAM] Large time gap detected between 240101r200000472o.fits.gz and 240101r200000358o.fits.gz (24.998 s compared to the median time difference of 1.000 s). This may cause alignment issues. If so, consider moving all files after this gap to a separate directory.\n", " warnings.warn(string)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Binning: 8x8\n", "[OPTICAM] Filters: g-band, r-band, i-band\n", "[OPTICAM] 341 g-band images.\n", "[OPTICAM] 341 r-band images.\n", "[OPTICAM] 341 i-band images.\n", "[OPTICAM] Creating source catalogs\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[OPTICAM] Aligning g-band images: 100%|██████████|[00:00<00:00]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Done.\n", "[OPTICAM] 341 image(s) aligned.\n", "[OPTICAM] 0 image(s) could not be aligned.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n", "[OPTICAM] Aligning r-band images: 100%|██████████|[00:00<00:00]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Done.\n", "[OPTICAM] 341 image(s) aligned.\n", "[OPTICAM] 0 image(s) could not be aligned.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n", "[OPTICAM] Aligning i-band images: 100%|██████████|[00:00<00:00]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Done.\n", "[OPTICAM] 341 image(s) aligned.\n", "[OPTICAM] 0 image(s) could not be aligned.\n", "[OPTICAM] Photometry results will be saved to lcs/optimal in timing_analysis_tutorial/reduced.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[OPTICAM] Performing photometry on g-band images: 100%|██████████|[00:00<00:00]\n", "[OPTICAM] Performing photometry on r-band images: 100%|██████████|[00:00<00:00]\n", "[OPTICAM] Performing photometry on i-band images: 100%|██████████|[00:00<00:00]\n" ] } ], "source": [ "import opticam\n", "\n", "opticam.generate_gappy_observations(\n", " out_dir='timing_analysis_tutorial/data',\n", " n_images=500, # generate lots of observations to create long light curves\n", " binning_scale=8, # use large binning scale to reduce disk space\n", " circular_aperture=False, # disable circular aperture shadow for simplicity\n", ")\n", "\n", "reducer = opticam.Reducer(\n", " data_directory='timing_analysis_tutorial/data',\n", " out_directory='timing_analysis_tutorial/reduced',\n", " verbose=True,\n", " remove_cosmic_rays=False,\n", " show_plots=False,\n", " )\n", "reducer.create_catalogs()\n", "\n", "phot = opticam.OptimalPhotometer()\n", "reducer.photometry(phot)" ] }, { "cell_type": "code", "execution_count": 2, "id": "ce4f2654", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Filters: g-band, r-band, i-band\n", "[OPTICAM] g-band target ID 2 was matched to r-band target ID 2\n", "[OPTICAM] g-band comparison ID 1 was matched to r-band comparison ID 1\n", "[OPTICAM] g-band target ID 2 was matched to i-band target ID 2\n", "[OPTICAM] g-band comparison ID 1 was matched to i-band comparison ID 1\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] } ], "source": [ "dphot = opticam.DifferentialPhotometer(\n", " out_directory='timing_analysis_tutorial/reduced',\n", " show_plots=False,\n", ")\n", "\n", "analyser = dphot.get_relative_light_curve(\n", " fltr='g-band',\n", " target=2,\n", " comparisons=1,\n", " phot_label='optimal',\n", " match_other_cameras=True,\n", " show_diagnostics=False,\n", ")" ] }, { "cell_type": "markdown", "id": "79137bea", "metadata": {}, "source": [ "We now have an `Analyzer` instance that provides a number of quick-look timing analyses routines. Under-the-hood, these routines use the `stingray` Python package, so if a particular `stingray` routine is not implemented in `opticam`, a light curve from the `Analyzer` instance can be passed directly to `stingray` instead (more on this later). By using `stingray`, the results returned by `opticam.Analyzer` methods are intended to be compatible with existing analysis pipelines, or provide a feature-rich framework in which to develop analysis pipelines.\n", "\n", "Let's first take a look at our `Analyzer` light curves. Since these observations contain gaps, we can also visualise the Good Time Intervals by passing `show_gtis=True` to `plot_light_curves()`:" ] }, { "cell_type": "code", "execution_count": 3, "id": "dbd3c0c6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = analyser.plot_light_curves(\n", " show_gtis=True,\n", ")" ] }, { "cell_type": "markdown", "id": "6a0641e5", "metadata": {}, "source": [ "As we can see, we have three clearly variable, gappy light curves. Let's now perform a few quick-look timing analyses on these light curves.\n", "\n", "## Periodograms\n", "\n", "Often times, users might want to compute the periodograms of their light curves. `stingray` implements both the Lomb-Scargle periodogram (LSP) and the classical periodogram (FFT). Both of these are also implemented in `opticam` for convenience.\n", "\n", "Since `opticam` computes *relative light curves*, while `stingray` assumes that light curves are in units of counts, any `Analyzer` methods that use `stingray` routines will default to `norm=\"frac\"`. The fractional RMS normalization is valid for relative light curves, while the absolute RMS normalization (`norm=\"abs\"`), will give the same results as the fractional RMS normalisation *provided the light curve is normalised to a mean flux of 1*. In general, try to stick with `norm=\"frac\"` since it's scale-invariant (more on this later).\n", "\n", "Let's first take a look at the Lomb-Scargle periodogram:" ] }, { "cell_type": "code", "execution_count": 4, "id": "347b8a5c", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lsps = analyser.compute_lomb_scargle_periodograms()" ] }, { "cell_type": "markdown", "id": "ee343dce", "metadata": {}, "source": [ "We have three Lomb-Scarlge periodograms, all of which show a strong peak at a frequency of about 0.14 Hz.\n", "\n", "Like many of the timing analysis methods of `Analyzer`, `compute_lomb_scargle_periodograms()` returns a dictionary of results. In this case, the keys list the filters and the values list the corresponding `stingray.lombscargle.LombScarglePowerspectrum` instances: " ] }, { "cell_type": "code", "execution_count": 5, "id": "2983f95f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'g-band': ,\n", " 'r-band': ,\n", " 'i-band': }" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lsps" ] }, { "cell_type": "markdown", "id": "88c7f75b", "metadata": {}, "source": [ "Let's find the peak frequency for each periodogram:" ] }, { "cell_type": "code", "execution_count": 6, "id": "0a9caa29", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Peak frequency: 0.13528395820116063 Hz\n", "Peak frequency: 0.13528395820116063 Hz\n", "Peak frequency: 0.13528395820116063 Hz\n" ] } ], "source": [ "import numpy as np\n", "\n", "for fltr, lsp in lsps.items():\n", " print('Peak frequency:', lsp.freq[np.argmax(lsp.power)], 'Hz')" ] }, { "cell_type": "markdown", "id": "9f8aeed0", "metadata": {}, "source": [ "As we can see, all three bands show a periodicity at $\\sim$ 0.135 Hz (which is the true frequency of variability for our source of interest). We also see a bit of aliasing due to the gaps in our observations.\n", "\n", "Let's compare the LSP to the classical periodogram:" ] }, { "cell_type": "code", "execution_count": 7, "id": "afb32a02", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] Unable to compute periodogram for g-band light curve due to gaps. Consider using either the compute_lomb_scargle_periodograms() or compute_averaged_power_spectra() methods instead.\n", "[OPTICAM] Unable to compute periodogram for r-band light curve due to gaps. Consider using either the compute_lomb_scargle_periodograms() or compute_averaged_power_spectra() methods instead.\n", "[OPTICAM] Unable to compute periodogram for i-band light curve due to gaps. Consider using either the compute_lomb_scargle_periodograms() or compute_averaged_power_spectra() methods instead.\n" ] } ], "source": [ "periodograms = analyser.compute_power_spectra()" ] }, { "cell_type": "markdown", "id": "7148e1ed", "metadata": {}, "source": [ "As we can see, computing the classical periodogram fails because the data contain gaps. Let's try computing the averaged periodogram instead. When computing an averaged periodogram, a segment size must be specified; to avoid issues with units, `opticam` requires this segment size by an `astropy.units.quantity.Quantity` instance:" ] }, { "cell_type": "code", "execution_count": 8, "id": "39531468", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[OPTICAM] 8 g-band segments averaged.\n", "[OPTICAM] 8 r-band segments averaged.\n", "[OPTICAM] 8 i-band segments averaged.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import astropy.units as u\n", "\n", "segment_size = 30 * u.s\n", "\n", "averaged_periodograms = analyser.compute_averaged_power_spectra(\n", " segment_size=segment_size,\n", ")" ] }, { "cell_type": "markdown", "id": "a19103e0", "metadata": {}, "source": [ "Computing averaged periodograms works, since the gaps can be filtered out, but we don't really have enough data in this case to get meaningful results (note each averaged periodogram is comprised of just eight segments). When averaging Fourier products, the general consensus is to average at least 30 segments to get trustworthy results. However, generating enough data to get 30 complete segments would take up a lot of disk space, so I'll leave this as an exercise for the user.\n", "\n", "## Phase Folding\n", "\n", "It is common to phase fold light curves on candidate frequencies or periods to visualise the pulse profile. This is implemented in `opticam` for convenience via the `phase_fold_light_curves()` method of `Analyzer`. First, however, we must define our candidate period. To avoid issues with units, candidate periods must be an `astropy.units.quantity.Quantity` instance:" ] }, { "cell_type": "code", "execution_count": 9, "id": "961e7042", "metadata": {}, "outputs": [ { "data": { "image/png": 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GXQjxNykjy7MT6w8rEb2E0kiZkTsDL+S8gKlZU72mMRBLIDNnpHkiVolVzUcCZNiFEDaqkJqawVeeHYBeBERsYLVaUVtbC4fDgb59+6Jbt25ITU2FVqsN2jkDeUEFW/M0o0d0ddw1n5CQAL1eD5VKFbRzRvtsORl2IYSNKsSkZpCaHkHMi4Agoh2bzYba2looFAr07dsXSUlJshl2vjLQ+0OwNR/NLx+CEIO75pOTk6HX66FWB17qPhiajwTIsLtMpFWeYJ220Wjskg8eQUQa4R4ckeYJIrSEW/Ni8KfyROAmbxehrKwMycnJYTm32WxGfX09srKyPL5zfvCCOfVMELGOxWKBwWCARqMJutZI8wQRfkKpeX8pLS1FaWkpDAYDUlJSRO1DM3YRgFxLKnIWRiaIQAk0t1SosVgsaGlpgd1uD8m55FpGXV+7PqruM9F1Ic1HBmTYRRj+pEdgfgLfGb+TrTAyEbmEOmLL3/P5m1vKZrPBYDBwRo/FYkFzczM6OjokHSdaCETzVqsVK0+tDFkOLyI8xJrmgc6gibq6uoheJo1UyLCLMPxJj8CWbsbFjZO1MDIRmbjP9gS70xeaXfJ1XvfcUswY4dvebrfj/PnzyMzMBAC0tLT4NOzY8Uwmk+Bx5ZzFZjpzjzxnUXv+3v9ANG+z2TC732ykqUj3XZmuqHmGTqeD3W530TzQaey5G3bOFSmam5t5Z7yjQfPBhgy7CMPf9AgAMCpulKyFkYnoIFzRkb7O655binWSfNvb7XacO3cOvXr1Eu3rwo7X0dEheFy+ckViUKlU0Ov10Gq1nGHZ1tbG62jNovYCTa7qj+YBoERfghdyXiDdxxBdQfMMKcYRO397e7ugYSeH5oFO4626uhrV1dWyaz7YhNWw2759O2699VZkZ2dDoVBg7dq1PvfZtm0bCgoKEBcXh9zcXLzxxhsu3y9fvhwKhcLjz2QyBekq5EVKegSCiCU6OjrQ0tIiaWmmOLHYr1ls1snrdDqvS8HM+TqQ5SLSPEHwY7PZ0NraGnLNs3PzLQXLoflgE1bDrq2tDUOHDsXrr78uavtTp07h5z//OcaMGYOKigo88cQT+O1vf4vVq1e7bJecnIz6+nqXv7i4uGBcQtQR7Rm1Cfkwm804ceIEjh8/Lvg8RFLi646ODskdalF8Ef7Q4w8YqRkpyzPvvszDjL6mpqaIHb2T5glGtGnebrdLNuzk1vxu0+6o03xY051MnToVU6dOFb39G2+8gd69e2PJkiUAgIEDB2Lv3r14+eWXMXPmTG47hULB+eqIxWAwuPxbp9NxlnukwKZ/+/fv73fb2FR2jx49Iu76iNBisVhQVVUFAMjKyuJ9HthSSjD5uv5rLNcsx02WmzASIwM+nvsMG9ON82hciAPKA9hn3IcJigkoQpHH987LPPOGzgPQ+fIxGo1B6eRJ84ScRJLmlymX4dLZS8hFbsDHC6bmt5m2odneHDLNM8xms4th6m6jeCOqfOx27dqFSZMmuXw2efJk7N2712WZxGg0ok+fPsjJyUFJSQkqKip8Hluv1yMlJYX7W7RokeztD5RIX9fng2YLYg8xpa5YJOh/TvwHK46tQAtasLV9qyznDySKdq9yL1ocLdhi3ML7vb/LPP4SjZoHSPexhl+ad7Tg09pPZTl/MDUfrqDERYsWudgker1e9L5RZdg1NDQgIyPD5bOMjAxYrVacP38eAHDttddi+fLlWLduHT7++GPExcXhxhtvxIkTJ7weu7a2Fi0tLdzfwoULZW17JE1vh5JYLXsUay825+sV85uzSNAPT3yIsXFjkapMRXFiseTzqlQqZGdny5ZcdKR9JFIUKShOLOa9jqL4ItEBSrGqeYB0H2u6NxqNkjWfpvQ/YEij0chWStCX5sMVlLhw4UIXm0TKLGpUGXZA5zKrMw6Hw+XzG264AXPmzMHQoUMxZswYfPLJJxgwYAD+8Y9/eD1ucnKyy5/cSxbO6QnEJhSlPD7RS6y92KRer3MkaFF8ERakLkBRvOcyiDObGzdjmXoZdpt2c5+p1WpkZ2fLUjcSAIbYh2B+4nwUxRdx1+SvYUaajz1I98K4a/7JXk/6DBgqs5ThPd17LpoH5DXs+DQfCb+fTqfzsEvEElWGXWZmJhoaGlw+O3fuHNRqNXr06MG7j1KpRGFhoc8Zu1AiNqGoUFQOQciN1AL0gSIlEnR97Xq8iTex8vRKtCpasc20TdK5bDabR44sbyiVSpe0B77a9p7uPRxUHfS6HWmeiERCOcMoRfNrqtbgT+f+hM3mzVGr+XASVYbd6NGjsWnTJpfPNm7ciJEjR0Kj0fDu43A4UFlZyVuTMVz4k1B0t2k3Fjcvxs72nUFsGRGrRNJI1Rmz2YwPT36IVkUr7A47khxJGBc3TtIx7Ha7R1Z7b7jns/LGylOdxma5utzrdqR5IhKJRN2bzWa8e/hdNNub4XA4kGhPjErNh5OwGnZGoxGVlZWorKwE0JnOpLKyEjU1NQA615jnzZvHbf/www/jp59+wvz583HkyBEsW7YM77zzDh5//HFum+effx7ffPMNqqqqUFlZifvvvx+VlZV4+OGHQ3pt3vAnoSiLzBFy8PSHWPMHIcLHzvadoowUrVaLo3FHsUy9DOtr18NiseBnmp8hyZGEYnUx7jHfg1Fxo0LU6ivY7XY0NDR4zKTN7jcbSY4kFFgLvO5PmidiDbGaV6lUOBZ3zEXzY+PGIkWRglGWUZhnmhcWzbMceu51ZMVqPpyE1bDbu3cvhg8fjuHDhwMA5s+fj+HDh+OZZ54BANTX13NGHgD069cPX331FbZu3Yphw4bhj3/8I/7+97+7pDppbm7GQw89hIEDB2LSpEk4c+YMtm/fjuuvvz60Fycju027YXaY0U3RDePjx8tWyiQSR2uBEusvrki6/o6ODi5SbYtxC5rtzfjW8K3X502r1WLDxQ1oVbRyJbZGxY3CPeZ7UKAW7kidS/xotVqkpqZi07lNePHciyizlHHb+XN/NtRvwNvKt7G+dr2HYVeiL8E95nsw2DZY9PHEQJoXTyQ98+EiUu6BP5pXq9XYZNjkovmi+CLMT5yPQdZBgvsFU/Pra9dj0YVF2NW+K2Sal5OwGnbjx4+Hw+Hw+Fu+fDmAzioSW7duddln3Lhx2LdvH8xmM06dOuUxE/fqq6/ip59+gtlsxrlz5/DNN99g9OjRIbqi4LDNtA2XHJegU+hQqC2MyvQHoaIrvrikEEnX79zJFycWI0WRghG2ET7bNrvfbCQ7knkj5g6qDmJx82L858R/XCJOndOCsE7+PzX/QZO9CTssO7j9/bk/q0+vRqui1eU4wYY0L55IeubDRaTcA381PzNnprDm1aHX/MpTK9Fsb47o5VZvRJWPXbTjax1fqODwuLhxSFWmevUzEDvtTRBywkbNvjpNNgIfYh/i85gl+hI8iAd5nazL1eVotjfjwxMfetRtdc/59ovev0CKIgU3qm/0OA5fsMj62vUeUbdA50snyZGEMdoxPtsOuOb0CrbmXzz3ItbXrhfVLoKQA+eZMm9I0fyUrCmCmt+n3hdyzc/uNxupylTRy62RMmPKIMMuhKjValGdPEuP8OK5F7GydSW2mbZhXNw4r34GbNpbrD+O0AuFIKQgJYGuzWaD2Wz2K4koo8BagFRlKu/I3r0tN/e6Gb+y/AojVCM8tuUbxTOnaPcIvClZU3Cf9T4UagsF2+VwOFBTU4Pjx4+75PQKtuab7E3c8pUvSPOEHEhNmu1wOFBXV+f3bOII64iQa75EX4IFqQu8LrcKaT4SIMPuMoWFhcjPz8fSpUtDcj7nUQ/LyO088l55aiWa7E34oeMHNNubfYZ7FycWS0ry6vxCIQhngjX6tNvtARt2g22DsSB1gaiUCVIZlDoICocCeqVe8tKn3W7HmTNncOrUKcH9gqF5KUleSfOEEMFMd2S32wMy7AZbo1fzcrB06VLk5+ejsFB4YOkOGXaXKSsrw+HDh1FaWhqU47OSJ+wBcB5psIzcziPv2f1mI02Zhus01/lckgEgOskrQfjCYrHg5MmT+PHHHyNmBBoKDjUfgkPhQI2txmsnb7PZUFVVhePHj3u9P6HQvJgkrwThC9K8b83X1tbCYDCgrq7OI1I2mJSWluLw4cMoKyvzvfFlyLALEe6dvDPOGbkZJfoSPNnrScxOmo0FqQu8LsmsqVqDF8+96OEnQHRN2GyPryoGgcC33OI8qmflsvyZ/eno6PC6JLi+dj3ewlvcbNZu0268p3sP5VZxjszODtxSYGkMfPnS2Ww21NTU4NSpU16XNa1Wa9A1Tz61sUG4NA9cmcE3GAx+a54l3hbSy4b6DS6aBzqrTqzotgIH1b4TAYdC87W1tWhra0NdXR1X8SpSkacODyEa9lKz2WxcfcsZuTPQu6k38vR5ONB0QNRx2Es2Kyurc/Rvb8I20zaMSb7ygJrNZtTX1yMrK0v2EmlE+GCzPSuOrcC8ofOwpmoN3j79Nh5IeyAo9Qx3tu/EFuMWzP1xLq5pv4ar8rLq2Cp8Z/wONyXehCHwdJBWq9VITU3FxrMb8fG5j5GNbFSnVkNRp0B+R77LtrtNu7G9eTseqHoAK0+thEFhwMqqlbgx8UZsvbQVrYpW7LTuRH/092jXkMohqGysxFjdWIzTjvO7ky/Rl0BxQIHu2u6835dZyvB92/c+fd/4sFgsMBgMSEhIACCf5rcYt+BhXMkMQJrvmnjT/Lyh83wfQCJMWw9UdfYp1dXV0Ol0LpovgufqkLvmc5Q5qNZVY5xpHFR1Kg9f0/W167Hi9Ap0KDpgVBg5zdtsNuyw7IBRacQ+9T5MwRSXdoVK8wdVB1FhrMD4buNFB09FAjRjF2KcDbtAcHYEnZs3F2nKNBTHF7s4aguFeXurR+nNvyrSIn9iFTbbw6oYOHf6wUDISd9XwA5LQfBp7adosjfhsP0w2lRtWHd2nce220zb0GTvvAaW7uT2nNtRW1uLMdoxSHIkoUjt+iJh7dpxbgdaHC3Ybt4u30U7saF+A5apl+Fb87e8vm8HVQexotsKlFnKBGcmLBYLWlpaAtI9r+YTi6HVatG3b19otVrSfBclXJp3P75UzR+0HvSaKoiV2gPgonmbzYYx2jFItCdihPVKIESoNA90Dja3qbehxdHioflD6kM+NR9OyLCLMKSUNmHMyJ2BJ3s9iRsTb4Rer/c5UvdWj9Jbzp9IyZUU67Cai2x2zr3Tlxt3J33mhD8+fryogB3mO5avzEeCLQHTMqZ5bDMubhzSlJ3XwNKdTOg5AQaDASNUI3CP+R4AcCkIztp1Y88bBZdTlEol0tPToVT639WxPHYOODx83zbUb8A29TYYlUbssOzwq9ZrIJovii/iDDtvuifNRzfh0jw7PhsYSNX8YPVgr0udrNTenD5zXDRvs9lQqC3EiI4R2KfeF3LNA52DTYfCAQUULprfbdqNHdodAWk+2NBSbARhsVhgNBqRkZEhupO3WCw4e/asy9KuN9ZUrcHb597G2LixopeT2PJOUlKSqO2J0MKW9Qpy5S9xs752PbYYt6A4sRgl+hIcO3aMM+wKtYUo1Bb6fFZL9CXo3dQbzc3NONN4BhPTJ6Kurs5lm1FxozAmeQyKcotgNBoBdM5ut7S0cM/dTutOLjVBKUoxSjcKg62DMTh3MP6v/v94l1OUSiX2Yz8+VX4KW60NsweKiyB1ZmbOTHx48kOMixuHogTXWcPVp1fDoXAADqC3urfkY/sDaZ4IleaZIcmMF6mab2trQ6OxEenJ6YLbXdN+DfRZeuw4uYPTfPfunVrep9kHo9IYcs0DnYPN79q+83C9YAZfKDUvFZqxiyC8OVsD/EXBpaYwcPbHE0uwRu20zCMdFrQgNO3vLUjHnTVVa/DM2Wfw9NmnBZPcshQcUuqV8qXykIMidRGSHEnc6Nlms6GlpcXjXjBH7M2NmwEA686u6/TZc1tKFpto1Vseu5k5M6FwKAAFUGOr4dnbN97ygpHmCV+aB8Tr3lnzQoEY/mh+fe36oGh+RMcIJNoTQ6554EopQ3fdj4sbF7Dmgw0ZdmGCPaBSOk45ioIz3xxnochVh5IPb9FctMwjHV8vdSmG3YpjK9DuaMclxyXBJLdsSUVsfkR2XPdUHgyHw4HGxkau/Swpr5iI7gJ1Ae4x3+Nz1mn16dUwKAycL9+0jGm85YpsNhuqq6vx448/+v38T8magnHWcUi0J+JG9Y1obW0V/G3sdjtaW1u7vOYBYd2T5qUjxpAXq3tnzQv55/mjeeYrJ6T51tZWLkUI07yYiO5B1kGYZ5onq+Zra2sDSig8Km4UxljGiNJ8uCDDLkRwKRxOr0dLSws6OjpgMBgkPViszJAYwRkMBpSXl8NkMrl8znxzmFCkZhGXSrCdfINNNM8wOLed7zrm5s1FvCIe3RTdBJPcshQcvvIjshH7mqo1vKk8GO6GHZsd+L7je1HLimJgdSeZL9/E9ImC5Yrcn3+lUomMjAyoVCrumjbUb+C2V6lU6NWrF9ra2rhrGGwbjLmX5mKEaoTLC4zNInxe/TnngyPVsItGzQOk+3DR0dEhWvNC/nliNQ9cMeAHpQ7yqnlnvTDNbzdtl+RX6g0pmgeuDDCsViuv5p1nHpVKJXr16gWj0chpZpB1EK/mIwUy7C4T7MoTLIXD2rq1MBgMoh4EVv+VzWaMihvFm4TYZrNxDqeMtrY2nDx5MqAs/3IQbCffYOPvDEMo8k75wrntfNcxI3cGXsh4AX/M+KOkJLdsUOL8vLER+4pjKzhHb2/HZAEDd19zN9JUabj76ruhVsvj8svqTk5Mnyh5X6VSiczMTKjVau6aVp9e7dLunj17wmg0+hyls1mET376RHTuq66geYB0Hy7dM8NOjOalpEZigxL3Z54Z8IeaD/nUvFKpdNH8vfn3ymbYya1555lHpvnW1tawRL5S5YkACHblCZbCgS8iUAgutLx9i9eXiM1mE/WikYJcJWbco7lihWiZsWAuAVKMAebg7Dw4YdFtYl/kzLD7xTW/8PlCADpTivzD9A8cVPlOVurO5sbNHslPxcCuaWbOTMnnBK7MIkjZvytoHiDdR7Lu/XEDYoad+4SEt9l5d9w17+vZkJKg2J1ANS+2TF8ooMoTEQxL4SBlRFGcWIwURQpGdIwI+VQv+cIERrTMWLCZny9qvuBmGlgyXSlGQ4m+JCgv8gPKA/iH6R/Ypd6FFrRgn2af5CVbIUdqoVkIBrumKVlT/Go7m0WQsj9pPrqJBt0zzVssFm6G8fPqzyVrHoCo2XmpHFAewCvGV/Ct+VsYlUZUaitl1bw3o5ZpPtrL9JFhFwbE5tkpii/C/MT5GGwbLOn4ZrOZW/rx5ijNF3FHyEO0zVisPr2am2lgyXQtFkvY8zPtVe5FC1qgUCiQokhBcXyx5E7e3ZGa5eSyWCyiHZ/Zy0aMVtiL03kWVKVSISEhgTTfxYk23bMZxk9++iSyNO9ogUKpQJIjCWN1Y2XVvMFgELWkykoZignscjaWIwEy7MJAIAkUd5t248VzL3qdYmbitNvtsNvtgo7S3iLupERXRhtCjtHun/tKMxAtDtYsqk7oOhwOB25OvtljpsFutwfUybs7Ipdby/Fp909F13wFgJH2kUhRpGBy/GT8v7T/Jxgd583wcnakXlO1Bi/Uv4A1VWskzYixl427VjQaDZKSkqBQKLjP7Ha7x/K2SqXy2E4spPnAkaJ5X7OW0aB7MZqvq6vDXVff5eJuILfmyyxleD/ufRxSHxJ9jJH2kUhVpmJev3mCaYaA4Gt+m2kblzfTGZVKhcTERF7NR4p2yLCLEpRKJbKzs7nSS0LpKaTgLeKuvb0dDQ0NaGtrC/g8gSC1ExXjvCy05OT+uZjUInIvXYm9XqFZGS762skIYNfB/uu+j91uR54pD0+mPynrTIO7I/JO6060qdqw0+p9toiVJdJoNBhiH4L5ifM9DLr1teuxuHkxDig766wyw2uNYY1LFKs7LKfbxksb8YrxFdE+e8zAdNcKM+wCzXLPB2k+PJr3pelw6d7bTCzTPXv2xWi+rq4OU7OmBuRu4I675rl6r5p9XvdjNWaZ5hekLvBok1yaZ/v7YlzcOJe8mQxm2AVD83IRuS2LIdhIef1pz5cyQ6VSITs7Gzcl3uRS3ikQhCLugM6pa5PJxM06sKnsUEcFSe1Eo8F52Rtir9c9ZQVLvLmyaiWvbwnfPr7w5YMGeJ9NcnZEVqlU6B/fHwqHAjnKHK/ndTbshFh5aiWa7c3Yq9wLoNPwUkABBxxcFOt3F7/D28q38d3F77j9WE43AGhxtKBc7Xv2UKPR4GeJP8PjyY+LSgFRbi3HMvUyLlkqH0zza0+tFczpFW7NA+CKq4dyJiLWNA+Iu2YhzZvNZi7rgnMEN98+vpCieT5D2l3zt/S8BTqHDh3o8LqkGUrNs/29odVqMSN3Bu7tuFdUtRamebkTNPsLGXYRANfJ163lfSmzkbtWq0VRfBGe7PVkwM6dzNdGjP8A4L3WJBA5yxPMefmuq++KiPaECtaB355zu0diTn8L0LOEumz5gr3knV/87rNJzktAzo7IarUaNdYaOBQOnLaf9vs6ndOkpCpTMdI+EgAwxD4Et+huQZryyrLS5/Wfo8XRgs/rP+f2ZzndJnWbhBRFCgqsvksyaTQapKSkePXzOag6iJdNL+Mt3VvYYt2CVkUrlyyVD6b5/9T8hzfLfyRoHvBu2JHmw4uz0cayLrBnXy7Ns2O1trZy6XqY5pkh7Tzod9f8nXl3QgstzEqzpMonzjinSZFD82x/b2i1WmRnZ3t1neDTvByz6nJAhl2Y4AvHFsqWrVAouE5eCOcXgRiYr42/YnMnUiLqmPPy1KypXHsi5QUUKMznz1tnzSIxmRFgtVpx+vRpj/Qk7jg7/66vXY9l6mUevnB8ht24uHEus0nelq+nZUxDgi0BRWrfs15COKdMWJC6AEPsQ7jvCrWFeLLXk9wSzsycmYLpSkZqRuJBx4MYZB3k8d2G+g0+yyMdUB7A4ubFV/wH1eUwwQSzovMZS3IkeaQ2KrOUeYzqZ+bM5M3yT5oXT6xrHriSdWFK1hRJmmcG2Yb6DbyaB64YduxYTPPMH9fXoL/AWuBSFkwqcmv+Ott1Ht+J0Tzb7sVzL6LMUsar+UhJk0KG3WWCnaCY+UAI1bKz2+0YiqG4334/SvQl0Gq10Ov1otfx2YtAp9OJ2p752vgrtmgiHC+gYDiiS60RCnR2umfPnvXpNOzs/Lvy1Eq0KlqxwbrBpw/aqLhRvLNJzi8NxsT0ibiz+U4UqOUvXM7HlKwpgv5DdrsdbW1tLkmD2XLQZ6c/EyyPBHR27luVW9Fsb+a2KbAWIA5x0Dl0KFYX4z7rfQDg4ve0w7LDZVRvt9sxTDEMf+jxBxTFF5HmZSQcmhdT01UqwdY8M8hWn14tWfPu/rh8mgeuVGYRs6QZKGI073xfNBqNaM2/hbfwwU8foMnehB2WHbyaD0aaFEpQHADBTlDMfCD4atlptVokJSXh4sWL3EOn0+mg1+uh1WqRkpIiW4ZuBvO1CYXYYpFojjCc3W82FI5O3xVnHzTnQtssIk1oWc/bKL7cWi7ooyMHrJ3eHKr5SExMxLBhw3D3gLu9JildfXo1HAoHFFBw2wy2DcbjcY/jQfODnOHKBm/M/2eMdgw3qmeaP3/+PHePmGFHmo9O/DHCIoWZOTN5NQ90Tkq8p3sPm7Sb/Nb8IfUhLG5eHHGaT0hIEK15g8IAAEhTpmGMdgyv5oMBJSiOYJgPxICEAXgLbwEAt2Sm1WqRnJzMO1JXqVRITk726OT5atq5c1B1UHTuLWesVisaGxs9SiB5c5plyJm9vqtgMBjw3//+FwaDIdxNEUWJvgTj7eORAlcfNOdC2ywizZ9lvZ3WnS4+OkKw5aEyi/cObXPjZpftWDvdHcl9odPp0LdvX5/VMGbmzOxcao2f5nWEzgZvM3NmYmf7Tuyw7MBI+8io0jx7YfpKtUKad8VoNEaV5qdkTeHVPABuBv9H9Y9+a36fZh+a7c2iNe/LD1QuzWu1WtGaT3YkY06fOXiy15OCKVgiBTLsQgTzgTjedtxl5s5f+GrauVOuLufNveVej9IZlvNnQ/0Gj07e3WmWj0jxu4kk2tracPToUdnSSLBoSalJO6UwxD4E/xv3vy6Jcp0LbY+0jUQykjFGO0bysUerRiNFkYK7rr6L93vW2X52+jO0Klqxw7LD6/WuO7uO2865nXx+NixBaSBVHaZkTcF91vt4Z75Y6bMDygNcLq0pWVOwxbhFdESeEOHQPHthejsnad6T9vb2LqF5oHNSIsmRhP7W/n5rfrhlOJKRLFrz20zbvAYthUPzQlVknDUfKZBhF2LYKF5KzVjAc5rfPaycb+mmwFrAm3uL1aPkG3mxnD98ucbcnWYjjWD4uASDQB27WSevVqtlbhk/LCrt1t634kE8CADYq9qLYeZhGKkRF2HWt29fdOvWDTqdDiNUI/Ary68wNWuqxzZarZabORuUNggKhwJ91H14X2rsub9DfwdSkIKxurEAvHfC/kYLiqVcXY4WeBpwrFSYmIg8RiRonr0wI8Up3J1o0TwQmO7DpXmtVosSfQkKrAVoUDX4pfmkpCQMsg7CPNM8F807b5eYmOii+d6q3tBoNEhOTnbRfTRpPpyQYRciOjo6YDKZMD5tvGDNWL6oOYZ7J8/CygHgLxf+goPqgx6d/GDbYMxPnO+Rs6o4sVjQiZrl/HGOXFxTtQYvnnsRAHidZv1FTGJRKUjxcXHOARVqAp3hcHdSZr5ZgYzmbTYbzGazS8SrO2w2h42WKzQVyMjI8Divey4s1nknJCRAp9PxLj+ybZwDAQ41H4JD4UCNrYa3PbvNu/EP0z+g1WrxdObTGB0/WvJ1i4HdX41Gg8zMTJw/f95lZotVlVAqlZ2GFToNOKb5jo4OrlSYc0Qfdx0CLg7h1vwzp58BAJco60CJVc0Dgek+WJoXWx+2XF0Oo9IoWfNJSUleK66wQRzTfaRonl1DWloasrKycP78eZcZP6VSyav5SIEMuxDh3MkD/OlO3KPmxLDy1ErePFjOuGcsL4ov4nWiNpvNGKkZiT/0+APnDGqxWPDu4XfRZG+SLU0Cw1tiUTGlfQJBauLOUOEt6MJiseC7C9/hz+f/jDVVa7hOlAXaqNVqF58oKSNVh8MhaNixElXspTItYxqSHEkosBUgMzPTYxaBdfKBFrFnS0BCUZxbjFsCqshwSH0I78e979Ofh71E4+Li0KtXL5w7d467NvYCS01NxT7bPpSry1GkLsIQ+xCPhL9CAzcxLg7OhEzztibJPku+IM174m3WUYzmAaeKM6fXi9a83W6H0Wjk3da9LB1LWSKkeb78d/4QCs2/p3tPVJCFVqtFjx49cNVVV7lonqVf4dN8pECGXZhwT3cCuEbNiWV2v9m8ebCc8dahOc8W8I1+rVYrxsaNFZ0mQUqmepZYdG7eXI9lilj12/Fl2O2w7PDqwOzsEyWHb4lSqfQYoU9Mn4h7zPdILlQPdOZ/E+uPUqIvcfFlYx0qm6UqTiwWVZGBpTRwn93ap9kHo9KIde3r/J5Bcp45YQMzoZJpQgM3qS4OodK8c+JXb5DmA8PbrKMYzQNXsi6srVsbFM0Ptg3G3W13+6X53abdWNFthajyfaHQfKuiFR/89IHfM8dqtZpzDfGl+XBBhl2I2dq0FW/hLQxIGODhu1KoLfSaC4fPgbZEX4Inez3psfSysnUlluqW4tNLn7p87j6FL2a2QGi0z4eUepMsseiM3BkR26nvbN8Z1NQcUmE1S4WMbGefKOdEw3zRklqtFn369EFKSorgUolCofAYoW9u3Iz3dO8JdtTOS5Pu7FXu9dsfRa1WQ6/Xc8s2QhUZWKfOyhMJdfIjOkZwKR6klKPabdqN93TvcTN9TFNjdWOR5EjySMC8uXEzXjz3InqrevMO3ITyggHh1bxz4ldvdDXNA1cikCNB9740D7hmXRCreaF8iXyaP6g6iA8TPhTUvPPSpDvbTNtgVBpFle9zJxiaT3IkAYCkMnS7TbuxTL2Mm+nzpflwQ4ZdiPnq/FcwKAw43nZcsu8KGym4T4PzGR8/dPwAh8KBg9ZOIbIRPACXTl7ugAj3JWdnp/hohE39y1mHMpAcd0PsQzA/cb6gke1ceYKlKdhp3SkYLbnl4hYs7ViKSkel6DYwHzuhjpoZdnz+PyPtI138UYLxfLh38kIMsg7CmI4xSFWm8j7/QjNR20zbuMg94Mqy2Oj40bjHfI9HTqt1Z9ehyd6EGluN5CSm0ah5IPp1zyKQ5dJ9IEEevjQPuGZdEKv5fbZ9otvAfOz80fy4uHGdy7iX06iEW/P3mO/BnD5zuJljZ3xpnrkmMMNOSPPhhgy7ywS78oRGo0FcXBxKepVIioplHbi3PFJ8xsd1muugcCgwWN05dS60NCM0W1BuLccnqZ94LWQuBnfnWCECTegrtvSOVNjUv5yRwOxa29raXJaizGYz6urqAvZTYTB/lSJ1ERctOT5+POd7ZbFYsLp2NZrtzZKWEjgfO6d8V2I7a5ZSgfmjiH0+gsEh9SHsU+/DuLhxvLNl7qk/GOPixnn1A2Iwzc/InsElNRVDtGseEPe7RqrmgSsRyHLpni23sv86a17Oa2DaFKN5lipEDJyPnVuOOzFBHKPiRmHupbncMm64Nf+e7j0A4GaOnfGleTGuCXLjT+WJ0MRORwFlZWVITk4O2vFZJ39j5o3oeaYnCtILUF7jfWpaq9Viu2k75yz6dMbTvNsVJxZji3GLSyc0O2k2xtaNRXpyul/t3WndiTZVG9adXYf87vl+HUMKfJ28c3FpMfuzDlLOXE9F8UWdf7nSptpZeSqtViv44uro6MCpU6fQ3t6O/v37w2KxyGrYlehLoDigQFK3JDTbmlGcWAyNRoPa2lro9XoAnc/Od8bvMFp5Jbpsfe16vKt+Fz+z/gwDMMDjuBPTJyL+RLzH9fbt2xetra2ytD0UMB+7baZt+J3ld6iurkZWVhb3vfNv6MyouFHQX9Qju0e21+Or1WrExcXh5pybkWfKQ1tbGy7iotd9SPPh1zzQqZ1r2q9BQa60mRi2dC40c2Sz2VBdXQ0AnOblvIaJ6RORVJUkSvM/0/wMuNS534b6DfhQ/aGg5gfbBiPPlOdxXWy2OloqbuzT7INRYcTq06uR1zMPtbW16N+/P/e9N833bemL4qxibhY8VJSWlqK0tBQGgwEpKSmi9iHDLoLR6XS4N/9evP3D251+Oe3827kbH2uq1uCt5rcwTDUM8aZ4fN/6PcbFjcM4rfgakUXqImw3b++cWRTOgBFUWIh/NC7niDHsgCuzKqzTDTVF8UUYqR6J9vZ2nMEZAFcyzW+xbsH36u9hrjdjEAaFpX2MQJZv3Pc9oDyAfaZ9yLRlogENGBc/jvP36tGjR8BtLbeW43v192htbEUa0iTtS5qPXs0DV3zCjEaj4DaRovmOjg40ohEAuFqxsaD5s4qzmJkzE7Y2+X4HpnlHrQMPZj0Y8PEChZZiIxzmbCzFL2fFsRVotjejXF2O/+v4PxhgwHbz9iC2UhyBJub1dkwpyzksL5972SX3HFtC2wltH0rElHdjlFvL8Z7uPXx66VMsbl7scT27TbvxD/M/cDLhJNRqNbeEC8DFryQcKJVKZGdncwlM/Vm+cc+RxwI4GlQNmGeaJ3vt1J3WnWhVtPpdXYY0L+6YwdK8r7Jt4dK93Jp/xfgKDqoOIjs7G7/o/YuY0fw95ntEBQVJgWne3zQsckOGXYRgs9lgNBoF1/j5YMsW7lPgc/PmIlWZigJrAYrURUhyJEkuA7PFugVtqjasqlvl8Z2Y2pB821gsFpw8eRI//vgj5+/hy8fGV2fmT2Qdy7Tv7lTsnmNLaDuh7eWARV95e7EA0nKfsU7noPUgmu3NHtezzbQNLY4WVOoquUzz91nvQ7G62Ktfid1uR0NDg+CymXuqAn9gnbzUzt3bkh4L4BjRMcLvdnmDac6XH617UlcxkOZDoHkfZduCpXtfRlswNF+uLkd2djam95tOmg8AprlIqdBChl0EsKZqDRZdWITd5t0+/aucp5jZsoV7Jz8jdwYWpC7AYNtgFKgLcI/5Ht6ixVLqD+427eZGfu4dK1/El9Vq5e18nR26xXTyUpO3ioFl2nfPA+acY8vbdu7bl/QqkW1GgkVf+Rr5uUc2slkEvsSbrNMZrB6MVGWqx/WMixsnudwV0OlofPbsWZfnj82M7Dbt5jp51kF7K3wfKO7PspA2tFotxiSNwaPxj2KQVfxSk5RloQJ1Ae6z3sdbXYbBNL+rfVfEah6AS8LrmNG8ynuetLuuvstrrWN/EHPNQprnMwYjSfPZ2dmC6ZQCIRI1L1eFlkAJq2G3fft23HrrrdwPv3btWp/7bNu2DQUFBYiLi0Nubi7eeOMNj21Wr16N/Px86HQ65OfnY82a8Oci8gZbRtmn9h1+LmeouLf6g8XqYiTYEjArexaAzo6Hb+QHdI6gVx1bhRfqX5Alos4ZqakZWMfydf3XXKfn3gHOyJ3BmwfMOceWt+2ct38y/Ulca75WtlxcLPrK18jPPbKRzSJ8dvozF+ffA8oD2GLdAgss6KPqgwWpCzyuZ1TcKIzRjsFe5V6XmUI26mfLMuwlL/Qbm81mr1VKtFqtYFFvqbhH46nVavTt2xdXX301d+18swfMuKx0VOLDhA9xSH1I1PlYJJ9cvl/OS6e+CJfmgSsJr92X5rqy5n0tg0/NmooH7A941D0NBDHXLKT5FcdWcD69Go1GVs0DncFU7+new2HNYY82+dK8TqdDdna2LIO5aNd8KAmrYdfW1oahQ4fi9ddfF7X9qVOn8POf/xxjxoxBRUUFnnjiCfz2t7/F6tVXHsJdu3Zh1qxZmDt3Lvbv34+5c+fizjvvxO7d3ssGhZO5eXPRTdENHYoOnIg/EZQHidUFFGuAFKgLcGfzndysw7i4cbwjPwZLv+DsV2S1WlFVVYUTJ074PaPlLXkrH0zYH5/8mOv0grF0EixGxY3Cfdb7MDlzsseyFks4XGYp89iPm2nIne1i2O1V7oUJJpgVZq/pDfiqIrBRP1uWYS9559/YuSO1WCxclZLeqt4eS0usY5ajk3cvqcSO79wRu88eOLPdvB0GGLBPIz6Xl1iUSiWSk5O95tRimrfAgmNxx2SP6gQC1zxwJeE139IcaV4+2DXfknOLi+7FaH5u3lwXw05OzQNXgqkqtBUApGke6NSlUPJiKcil+b0q6cnRfcE0HylGYFgNu6lTp+JPf/oTbr/9dlHbv/HGG+jduzeWLFmCgQMH4oEHHsB9992Hl19+mdtmyZIluPnmm7Fw4UJce+21WLhwISZMmIAlS5Z4PbbBYHD5C2Wh6Bm5M6BT6GBWmLEbuwN+OCwWi0fdPrvdjpaWFr9nlkbFjeId+TFYvjdnvyKbzYaamhpUVVWFPLu8c6fnvtwiF95qsYp1sLbZbGhpaYHRaHRJGdDR0eGxrMU6WL7OWmimYaR9JOIQB51dhxvVNwq2g6+cHVteYI7G7CXv/BsrlUquI7VYLBhsHYzfJ/0eNbYaj6Ul1jEHw4iRCluKcs/L5S9arRa9e/dGSkoKNBoN918hnDW/ybCJdwZNCsHQPHAl4TWfs3ksat5brslANQ94+g+K0by7ASyn5oEr+TCHW4YDkKZ54IphF4zlWCn4u/wsBJ/m5TTszGazh10ilqhKd7Jr1y5MmjTJ5bPJkyfjnXfeQUdHBzQaDXbt2oXf/e53Htv4MuzcQ56fffZZPPfcc3I0mxf3kifj4sbhu7bvRNVj9QXr5L0FYrAlGbkeRJZ+ITs9G9/iW1mOGQgzcmegd1NvLg+V8//7i9lsRn19PbKysrhOzWAwoFu3bh7bOs8YmM1mLMdydNR2eITCs1mV9vZ21NbWevW3mt1vNt49/C7G6MQ7xQ+xD8Eo3SjU19d7Desv1Baiv7E/btHfIrjNlKwpSDiZgIL0Auw8sZNrP8sFxQzd7t27Y1zcOGw3bZf9xSoXo+JGYYRqBBobGz2+87X0qVKpkJKSgt69e3Pb6HQ65ObmoqGhQdCgUSqVLp0/0/zMnJmA9IIELpDmg6N5Zmg5a17IsBOrebvd7qJ5b8Ez4dY80JnTz15h76wsoox+zV+86JlLUqzmu3Xrxm0nRvOBsGjRIjz//PN+7RtVwRMNDQ3IyMhw+SwjIwNWqxXnz5/3uk1DQ4PXY9fW1qKlpYX7W7hwoaxtd54qBzwNu1Fxo3CP+R7ZUy/wYbFYYDQakZGRwfsg7zbtxj9M/8BR3VHJx97cuBmrkldJ8rvxJzGvPykPAkVKNJ7zjMG7J96FQWHAuyfeDej8LFqVzykekJbc1RtarRZpaWnIzMx0WT5xLttzUHUQK7qtwG7TbknVDQDxkb/BwNnRWwhfvjUqlQppaWnIzc31GrmnVquRmprKzcapVCqX5Rq27C536gU+Ik3zAH8pMm+Q5j2xWq28+pOKkObZd0lJSTisORzTmk9OTkZSUlLIqmYsXLjQxSaRkhg5qgw7AB7TuWyE6vw53za+poGTk5Nd/uT+4ZhhFx8fL6qmnTtyFqX2Fplms9mwpX0LWtCCA90OuHxuMBh8pmZYd3YdjCqjpBxezCCRYtjJWUA8GC8MoWUSsUgtt2SxWHDx4kXRGeCdM967o9Vq0aNHD+Tk5Agadqx25PeW78Vf1GVY5O+qas+0Gv7gPtr2VuaIpb3gc/SWG+ck1VKjUYHwa57t58v48kfzgHTDrqtrnkV1ih2YMc2LvQ5/NM++S0pKQqW2kjQfQnQ6nYddIpaoMuwyMzM9Zt7OnTsHtVrNZYwX2sZ9Fi9ciC1W7I57UWoxNfqUSiXS09MlOa3abDaM6BiBZCRjyKUh3Od2ux3t7e2CI37GtIxpSLQleuTw8tapyAVfYXR2bm9GkpwvDD7uveZeJDuSce819wLofGG/hbd4U5MwrFarZMPOYDCINo7df48yS5mkEfVI+0ikKFIwrpun60CZpYw3KSrjpsSbkKZMw7y8eV7PIVTeh28751E0n5M1g+V7G4VRfj2LvpJWC6FWqwWjUYUIt+YBz0EyH6R5T9w1z9q6uHkxbyAEIJyuQwimeSnbB6L5AlsBaT5KiCrDbvTo0di0aZPLZxs3bsTIkSM5Q0lom6IiabU+5UZMRnNvuBeldndEZ34PzkEfCoUC6enpkpxWVSoVRsePRqmmFNear3X5TqFQ+PTRmZg+EbMMszxyeMnRyfvKYs9XGJ2d272TF3ohBIMSfQkexINcpOvKqpW8KSTE4qsTZbCIugp7hc9j8kXIMTbUb3B5dtVqNX6W+DM8nvw4r+vADssOwdQ4QKdvlpioR7GdvBRYvrdr2q/xqyavr6TVzjNzbMYtmjXPalx7G4iS5j1x17zFYsEW4xY025u9RqoKIVbzG+o3yKp5dq/YM0Ka98Sf2fhgE1bDzmg0orKyEpWVlQA605lUVlaipqYGQOca87x5Vyz8hx9+GD/99BPmz5+PI0eOYNmyZXjnnXfw+OOPc9s8+uij2LhxI1566SUcPXoUL730EjZv3ozHHnsslJfmgZiM5t4o0Zd4neZ3TgLqzgHlAfzD9A8cUHYuswiJZ03VGvzlwl9wWHOYe0g3N27Gi+deFBxluuOvv407fH4RvkbZLEpPjPOu0AvBX8Rk5meRrrfn3C6YQoKNovnuHzPUNps3e+1EGSyibpd9l8/280XIMVafXu3y7PrKRzdGO8ZrahyxyJm/TS58Ja12npljM27RqnmxMxSxqnmmZzGat1gsKE4sRqoy1aMiCEv+zucDJlXzrOarXJpn90qlUiEpKYk0z4M/s/HBJqyG3d69ezF8+HAMH94ZRj1//nwMHz4czzzzDACgvr6eM/IAoF+/fvjqq6+wdetWDBs2DH/84x/x97//HTNnXnlBFhUVYeXKlXj33XcxZMgQLF++HKtWrcKoUcEPSvCGmIzmrJSKlIdazGiB1cnbq+zM3yPUyfP5Iqw7uw5N9ibstO0Utbzj7G/jyy/POaDE3bnWH78IsaNCQNoLQQxSlnaEUkjYbDZsN2/n6oza7XbU1dVxL46VVZ2GmlKpdOlEhVIwsDQFo5WjfbapUFsomDl9Zs5Mn8+u+7G8pcYRC3NoFvJ3DfQloFQqvb6s+PCVtNoZNuPm675pNBpJ1xEqzW83bRf1svJH81qtFhvqN2BV8irOJSHaNM+XksgbRfFFWJC6wCUQgvk3Ntubsc20jUuFwqU7kaj5mTkzZdW82HsVTZr3lYrIHSmajxTCamKOHz/ea3j+8uXLPT4bN24c9u3znlT0jjvuwB133BFo82SFheLn6fNw7NgxlweUiZgtdUoJ3GCjBRYVzMdI+0jsU+3DCLtrnTyLxYKzZ89yzrpz8+bi7QNvY2zcWOByfzEtYxrW1K3BnX3uhPLkFcOORWP179/f5ZgDEgbggvkCBiQM4OrfCjl9Oht2zqW05g2dh5JeJfi09lMu/Yt7WwOFpWooypUuVmbE+ZuXaUP9BnyEj9BW34be6M19brPZMMwyDBWaCkzLmAZ7VadhN2DAAOh0Otyeczs+OP4B7tTfifyOfJf21NXVweFwcDmmWM1XxQEFumm6oR71Hu3Y2b4T3xk7U+yMUAnXUJySNQWDrIO4ZzcYuKeSEQN7CfiLSqVCXFycoIG0pmoN3j79Nh5IewDzhnr3DQI8Xzol+hJc036NV80DnYZdVlaW6HaHSvP35t/r8gKVU/NarRarT6+GUWXE6tOr8YD5gYjWPHCljJo/S8vra9djxbkVGBs31kVrzL+xQluBcXHjuFQo7PkQo3ngyrOXq8yF7qhONs0Hmi7GG+HSfEJCgqBhF6jmI4Wo8rHrSrg7fwaTIfYhKFIXeZSPYZ0DmyVkIxNnH4qJ6RPxQs4LvLNLfMtAx9uOw6Fw4Hjbcd62uI9IGb1VvaFwKDAodRAsFguuNV+LBakLuLYI+etIjR6VA2bY+fvCESrTtNu0G/vU+1BgLeCtMzolawqvL5Mz3jKvs3O8eO5FrK9dz/n8hDJaTCgAINjO7EJ4K1ouVL1AaB9fKROiTfPus2Bya/7apGuhcChwbdK1Ea955/b446e18tRK3tnI3abdKFeXY4x2DK/vmhjNA1eeLT6DhTQvvk1yaz5ckGEXYkJl4atUKvTt2xfx8fEArtQAdPf3UavVXg0BqQhFyDHcR6SMGlsNHAoHDjWLq+PHYNGj62vXByVyyduL319YBYdrk67FH5v+iDfUb2BD/QZsM22DUWkUVT9UDMwXTqlUck71rNj4ylMrOZ8f56TYHR0dHsXd+Y7rbwUJb9Fr4cDb7ytUvUCqZkjz/Jo/2noUDoUDR1ul5c4LtuYB+X+z2f1mI02Zht6q3ljUushF80KVJfzBH80Dvo3lQAIEIk3zwJU+zL1Ncmk+3JBhd5nCwkLk5+dj6dKlQT2PnKN2JkYAHi9atVqNIUOGcJ08qwEo1k/KX4Qi5HwxLm6cR/uYU7GYjnv16dVeI5cA6T4xQOd9zMjIQH19vWwjS+Zjd7T1KC45LsGsMGP16dUYFzcOifZEWctcJScnu3TyLO3A7H6zURRfhIU9FmJG7gzOf5IZdt6WmwIx7CIJ52VrvnJQgeYlY5Dm+ZmZMxOJtkSXIKJI0HwwKNGX4MleT6LGVsPVcWWaT3IkeQRU+Is/mgeuPFdCAzq2/E+aDz1Lly5Ffn4+Cgv5k1TzQYbdZcrKynD48GGUlpaGuykueBs5unfyfCMiFlUFQNBRlg+lUgmdTic5356/sCz8zu3bZtomKhIMuOzs6yVyCXDt5IWWh/iQe8mAJWadnjUd3RTdoHPoMDNnJkbFjcI80zwMtg2W5Tx8MGdzdp/5RuJsFitUv324cF62jqSi8bGiebbM6Ozm0ZU1bzAYMEY7prOOq5Pm7zHfI1hZQg7EaN69MlJXJVI1743S0lIcPnwYZWXiMlMAZNhFPN7W8FmiW295sljKi51WacsVKpUqoE5+c+NmLG5ejIOqg9xnO9t34hXjK1wKBuBK1Qm+GaJxceN8htBvqN+At/AWAEiKXGLRe2I67o6ODjQ3N4vOkC/meCaTCcXdi/F02tN42PqwbGWl+HKbSYUtOyQkJHjt7FnC1UhM3Cm2IDtDzqLxgS7jxYLmhdK0dGXNt7S0YKRmJBYmLYw4zTPDrlu3bqR5P4i0IAoy7CIEf2rprTzVmejW3YfGOfLs7mvuRooiBTdqbpTUHqVSieTkZN4ZAfdM3HyZudedXYdme7OLv9gW4xa0OFqwVbkV62vXY03VGrxQ/wLWVK3hdUgeFTfKZwi9UCCCVJiBaTKZPDpJb538AeUBLG5eHNQaiGz2QMxLxm63e7w02UwMAEmZ6n2N4pkjtpjZlVDjbTTOl5NLziUYsQ7V0aT5DfUbZNX8qmOreJf9okHzLNekt8oxgcJmGknz4okEzUeKDx4ZdhGCc7oPsczuNxvJjmQPHxrnTv4X1/wCT2c8zRtx5Y7FYkFLSwtsNhtUKhVSUlKEowWdfFv4MnNPy5iGVGWqi79YcWIxFFDAoXBg5amVovJWsVG2cwfHotOsVisXiMCX7FcIrVaL7OxsFx8Tm82Gs2fPIj09HXV1dbBYLNwozPlFx14GVqsVGo0G+9T70Gxv9jsJrRj4DDspQR3OMzF86YX47ocYmCM2m11hS4Bik1kHE2+jcV/JVkNFNGne3Z8tUM37Mgzcy2uFW/POhhOr2PDZ6c9En18qfIYdad470aD5UEGGXYTAnGh/0fsXPrOZM1jZGjE+NGLqAjrXG/UZLejk28KXmXti+kQsSF0AANyMVlF8EW7R3cJdZ0mvEt4ILXfcOybnNAhCyX69IdSpqVQqpKenw2g0wmKxuMy82O12NDQ0cOkibDYbNBoNJiRN4ByT+WDbi02RoFAokJiYiC0Xt2CZehlvNnrAM0qLdVzeOmqNRsNbMcLfTp4lXGWzK2wJUK4Iv0AIhxO0r/JX7kST5t392QLVvLelVpVKhYyMDJw9e9bDsAuX5p0Nu/HdxndqPlcezQNXktPv7dgrOBtImvdONGg+VERO/HEMw/JJ5e7Pxbhe41BdXY0ePXrIOq3rXBdw9kDfUXKsk2doNBpuRmBG7gxkNGRw37n/m7HbtBvb1NvgsHeO1lnW9f7G/ijuVYyTJ09yLwL3JQc2U5eQkCA5U3ggsCUYdz8cu92Os2fPurSD5YUaHz8eI1Qj0GRt8jier05+t2k3vlN/h31H9+GH5h8wTD0Mk5In4Z36d9CqaMU20zaUwndAD+vk+fC2xOYNqX4jg1IHobG+EQMSB8TMyNgZNrMqRrvRoHnWztTUVNzU+yZc3XY193mgmud7ppjm09LSuATMgdSZFYsYzbPneWf7TmwzbUNxfLHfmi+zlGGbetsVzauGIVuVjezsbOw43PmbrT69GoMyB3ltN2k+/EjRfCihGbsIQKfT+TV6EoLPidRbXUAxMMMOAG86DPZScO5Itpm2waFwQAGF5POyDPb+JAO1WCyor6/HVVddBa1Wy72cAs2jxApxs1k0lnR0S/sWwQAQX7DluP87/38u/kmsNJCv2UxfqFQqnEg4gdctr2Pj2Y2C2/H51rj7ivF1+iz56ZqqNTjUfAgOhQPVHdUR38kHIz+hFKJB80Dnb56YmIjGxsaQad4fHQVb88yXkPMxC0DzzOB21zxwZRZXyjKzO1I176wBPo27f0aaj3zIsIsQ5OqIAH4nUue6gOwl4I/Dv1A2eLZM4Cwa1klNi5/mdelot2m3R+ScL3a278SL517kXbJgI+bMzEzodDrBOplS2WHZ4ZK1nSUd5TO+xI582T26seeNLv5JU7Km4D7rfS5+UhqNBnFxcYKzl3w5wNRqNTZc3OCzGL2YdAd8+dhY8tMVx1Zw/l8zc2ZGfCfqq0JHKIgWzbv7uzEC0TzQGUXrXCvWF+HUPPMJFErwC4jXPDO43TUPXEn7xJaZQ6F5X+11H+CR5iMfMuwiBLk6IsB3GDd7CQTT4R8Al6PJlxP3NtM2tDiuFCx3Rij31BbjFjTZmzwi49hLiC/SLVDGaMe4dOos6Sjf9YmNjBypGYm72+7Gb/v/FgtSF3A57DbUb+B87NhSEQDBTn5n+06sa1/HG7HGV4xerqz94+LGcYXVmf/XlKwpUZepPRzEsuaBzihaVivWHeegDoYvzVutVtnzzzHNM59A5mMWiOZHqEbwan597Xosbl6MA8oDLvkKSfOEVMiwu0yoKk+EAl9OpOwlwLdUckB5AK8YX/EQ//ra9X6P+Nn+L557kTd6aqxuLJKRjJG2kR7fsXJE7qkRihOLkaZM81iyYJ08q6AgpoPnS93AR6G2ULBT94ZGo8HVV1/NVQRwxm63w2w2e/gYrj69mvOxE5NTa4txCxzoXAJzd0wv0ZfghZwXXGZQuGXkANMWjIobhSd7PRlRmdq9odVqcVR3FC82vig631U0EAzNA1e0IRTE4w1vmrfZbChOKEaCLYF32dFqtXJBHQxfmrfZbKINO6maF5srj+GP5leeWolmezP2KvdyZdNI84ET7ZqnyhMBEKmVJ8QiJTkjewmU6Eu4UH42s7VXuRctjhZsN213GXmuPLVS1IhfrVbzjjBXVnV2KnzRUwXqAtzddjcGWb07CzvDsqmLiYxj92btqbW8TtJiUzD4S1xcHAoKCrDp3CY8c/oZbG7cDIfDweu3BHS+qG5OvlnQx47P2ZstEU2LnybqJcSWkb1FJ3ojkLJi4UzmqdPpsP7c+qjIOO+LYGsegKiURIKav2xIbDdv94hst9lsyLuUhzub7xQd3SpF82wgGima31C/AQ6HQ9CH0GazYUr3KUhRpGCk3XOAC8DjdyPNiyPaNU+VJ7owvoThb3kUlrWcdXwj7SORqkzFvfn3ukyp803tC7WTr5O/Ped2JDmSUKSSNvJ1hvnYCM0aChWqZvfmk58+QUNDA9ra2ly+n5s3F6nKVIxWjfY707yzQ7EQrB3rzq7jDDu+4BC73Y48U57gkhafYedtiYgPtowsdSaCwQp7+1sUPJzJPOXMOB9Mwq154EpaE29BPEKan91vNlKVqRhmHuZXEBTQGbzgj+bZQDRSNL/69GrY7XYYjUbevHJ2ux3Xmq7F/MT5GGIfwnss99+NNC+eaNG8XJBhFyLkKjMkJAy5Htwh9iFYkLrAY5qdb2rfF7tNu/Ge7j3sNu3mggEK1P4XuGc+NkKzhkKFqtm9mZYxDSaTCW1tbTh37hySkpK4tBMLUhfgmvZr/O7knR2KhWDtmJE9AzqdzmdE5EHVQSxuXsw5i29u3Iy38Ba2XNzi4psltFwm5Znztq3UZ1ej0URUeR13Asl3Jdc9FUO4NQ903ishP1I+nDVfoi/BgtQFkmbi3dlh2eGX5tlANFI0PzNnJpRKJRITE6FQKAS3Z7kHNzduBnBF85vObXIxqkjz0giV5iMFMuxChFwjFqGEiN4eXJbw05chodVqeZNZ+gtL5eFtGYePNVVrsLh5MU7En+DavKF+A0wOE+IV8fhF719IKpPD7s3E9IkAOpc0GhoakJiYKEmsNpsNra2t2NW+y2MWwdmh2NdvdEvOLdDpdB73mb0Uj8Udg1KpRLm6HM32Zs5ZfN3ZdTAoDFhbv9bFsBNaLhPrzO1rW6nPLuvkpTzrUus8hgsp94I0Lx5nzbO2HFAegMVh8UvzbCAql+ZtNhvnM8iMKSman5I1hUs+7nyvnTWvUqm4VCjrzq4DcEXz/6n5j0tqGTk1z/d8kuavEO7ZRn8gwy7K8CfqS61WIzMz06OTd4+S0mq1SE5Odul4hEYrzssQLIKLleRhaTNY6gPnZZxya7nPOosrjq1As70Zu7Gba8vq06txyXEJOoUON/e6mYuU/eTYJ3gTbwa1biPDbrejtbUV283bPWYRnB2K/Y3MYy/FTYZNUKlUKLAWIFWZyjmLT8+ejhRFCu7sc6fLfmKWyyIdf5cVY4FI1DxwxecLgFfNH1Ifwnu69yRrfq9yLy4hMjRvs9k4n0FmTAVD8ywVyrSMaQCuaP7ua+522Y80T3iDDLsYRkyUlNAI0HkZghl2bW1tOHv2LBITE6HRaHhTH+y07uQyqzujVCq5ZRK+Tsu9pBHQ2el+ef5L3uMFkzHaMV7LiPmLe3LSwbbBWJC6gHMWL8kpwZ96/wm39b3NZT+py2WRSCT6wETjEowvpGjefYbCfenRZrOhuroadXV1XjW/T7NPUPOsnimf5kfaRyJFkRIRmge85630F3fNs9yDbKaRaf4X1/zCZT/SfHDoKpqnkmIxglqt9siZNbvfbKw4tsKvKKlxceOw3bTdRZQdHR2oq6tDdna2oDCK1EX4vuP7zo7MyZ9ZoVC4+L9kNGTAYrFw/i9Tsqa4lDRijNGOwTbTts7jWT2+dmFz42Z8kvwJHI0O5CNf9LWur12Pd9Xv4mfWn6E/+qNQW4jxaeMxRD8EB5rEJVW2WCw4e/YsrFYrNBoNkpOTPWZTRsWNQt+WvijOKsbhpsOi2+cvzPHc+bdaU7UGb59+Gw+kPYB5Q+cFvQ2MGbkz0LupNwpy/ffBlBtm4EQrodC8zWbD2bNnvb4MR3SMQIW2wkPzzoXqnTXPGGIfgvGJ45EQn+ByvHBoHuhc3u3d1Fv0rJxUzZ88eVJ0+/yFT/NAeHRPmg8eZNhFMetr12M5lqOjtsNnLUi+ZKiso/KHUXGjMCZ5DIpyi2A0GrnPWZJKIQrUBRhwaYBHR6ZQKLgOR8pyBqtDOan3JNjtdq8jLZYQdd3ZdWiO60zq+UDVAz4dalmh653WnVwnLxVWsQMAvmn4BivMKzBWMRbX4TpuG5VKFfS6uM4dO19CUeflkVAadoQ4IkXzzvDVmHVmkHUQhjiGYGLWRBfNs3qmUmdHSPPS8KV5gHTf1aCl2MtEY4LiladWwqAwBD2bvDvODsVyoVQqkZ2d7dLh+HIAZ+1wOByiorKmZUxDoi0R0zKmcRG2Yvw7BqUOgsKhQI4yR3AboQoZfDj76mRmZiIuLg5qtRoqlQrJyckBdfK+UjDwlYFyJhKXR0JBtCzBdCXNM6PG+Z4zI9GbBmw2GxekQJoPXPNAbOo+WjRPCYoDIBoTFLM6fd58vYLx8MrVydtsNmxr3iZYJ1alUvE6gDPsdjva2tpE58iamD4RswyzMDF9IpfFnnVku027XdIMOMMKXZ+2nxY8NquQIaaTZ746NyXehJycHMTHx3v9fTbUb8BbeEuUs7i3FAwsaau3KLRA0gJEM9ES+RYuzTsHEQQC0/xLTS/xVrMQY9gJVW7gI1o1z9KchELzQGzqPlo0TwmKYwxWp89bbjkp4e9iy+yIQavVIjs72yVnk1KpRHp6Omeo2Ww27LTtFKwTC/AbNayOarm1XHK7WGLgUTrXsjgsOm1V3Sq8hbdcUpnM7je7M7myuggHVQcFyy+JRWqi0NWnV8OgMIhyFndOweAOS9oqVxRaIJnog020jMalEm2aV6lUSEhI4NW8t5Qo62vXY5l6GVeOjGmerzyZL+TQ/OLmxX6XUwSka56lOSHNi6erat4fyLCLENhD+XX916Jz+8hZRBwQX2ZHpVK55GNyTnHC0Ol0yM7OdpltczbsNtRvwOLmxdAr9V7L6PAZNayO6k7rTpdoWjEIlfJi0WlWuxUGhQHvnniX+65EX4KR9pHYad2JXepdaHG0cPdIpVLhaNxRwVlHlqspkJfCzJyZSHYk89bUdMdbHUeWtFWu5RaWiZ7l1ookwjEal5qXK5o0z5LrOmve/QXPp3mVSoWkpCQoFAoPzXuLLmU+bqwEIdP8DssOl2haMcih+WZ7M7f8HQrNT8uYRpqXSDRoPlSQYRchsIfy45Mfix5hyd3Js5QDviLmmF+IN8NOCI1Gg9TUVHx2+jM025tRp6jjLaPDyoddm3StRwc3M2cmN5p2jqYNhFFxo3Cf9T6olfwd1l7lXrSgBQBcUjCo1WpsuLhBcNaROSUH4hM1JWsKHsSDomtqCsGStsbScksokZqXK5o1L6W8lFKpREpKiovm/1/a//NI1cE0v6ZqDTdjNkY7BsAVzY/RjnGJpg0EKZpPVaZyy98qlSromp+YPpE0HwVEai4+MuwijGA5sbLZAYfDgdraWlitnnkCWG4kb8sF7tnXpcIMu9m53nNCMUfno61HPTo4X+XJdrbvxOLmxX4tL83KnoVkRzLuveZel89H2kciBSkYbR2N+YnzXe4Rq4nJN+vIfk+pOe/YTEckLnkIIbfREW34q91ga55Fmjc3N3v4pYnRPNOTv5pnRqFYza84tgIl+hLcZ70PhdpOh3GmefZvvjZ6qynrDTGaX5C6wGX5OxiaB64YwcGMkpUT0nxkBp1E3nxqjBOs3D5sdqC1tZULwfcH5+iuMcljfG7Pol3dOyrnnFB8TtDFicXYYtzSOVMnMb3TFuMWNNs7Uxs8jscl7TsxfSLSatIwWT/Z5fMh9iG4MeFGNJuaPfYp0Zcg82wmzp496/Ed+z3z9Hlec95pNBro9XrU1dUBcDXsNtRvwEf4CG31bRgE/+tuBpvExEQMGzYMiYmJ4W5KWPBXu8HWPABcvHiR17ATA9OTVM27v+x95YFjmvfnJelcR/rpjKcl7Rspmgc6dd+tWzd8e/5b0nwUEIm5+ACaseuSBNOJlEV3jdGO8Rnqr9Vq0b17d/Tt21fyCLQovghP9noSAERHhwGdPg8mhwkaaGBymILq+yDHfd54diPeVr6Nzec3C/quSAmeCFY7xRw7WqLMuiLB/I2LE4uRqkyVrHmpbWGan5E7wyN4whtM8/GKeAxKHRSwf5s3WNQuaZ40H8mQYdcFCabYWHTXSM1In6H+bJoeAOrq6gTTkpRZyrBMvYy3M5bawa04tgKXHJdghRWXHJdk9X1ggRrMOdxX58kSlPItezM+rf0ULY4WfHzyY8FtpARP8CElStLfY1PHHl6C+TsUxRdhQeoCyZqvra0VTI+y27Tbq7uEe/CEN5jmdQodDjUfCti/zRmmeeYS4SsnHGmeiATIsItBnEedzg7LwcJisXSWrFG+zTvztsOyozPtQPUqj++EOjj31CkM5gx+neY6jxQAmxs345PUT/xKkwJI93tjnTzfy43d90Gpgzx8NNbXrseLjS/iaNxRqFQqj+AJodxULMO8mPZRaoDYwjnAKVSar62txc42fn/XbaZtaLY3Y7tpO+8z6B48AXRqni9huXMACIsCZf5tXUXzAH8EJmme4IMMu8tEY+UJf3EedbpnY5djqYEPljPqs9OfeXw3vtt4pCnTMC+vs5SNxWKBwWCAzWYTjAhlhp1zzizgijP4L+J/gf+N+1/cknML992qulVoU7Vhi9U1tYPD4cBe614sUy/DNw3fwGQySSpr5g/svh9qPuQRtcZyT224uIF3mYYvN5VKpULfvn3Rt29fUakIYnnUHYsvOGfDLlSaV6lU+L7je87f1RmWe+3e/Huh0+lcNA/AI3gC6NR8ZmamhxHDND9KNwojVCPwTOYzXKBDV9E84BmBSZoXTzRrnipPBEC0VJ4Qypvj74Prno1dqJZgoMK4KfEmpCnTMDvXM1LMPQ+TxWJBS0tLQFnu7Xa7oD+QFVaXWQSFQoHvjN+hVdGK9efWw2QywWq1wmw2o7q6mnM4L7OUBRwdyF6g7L7zRc65zzoIfe884hdTNojoJNpecOHSPDuHvwlp1Wo17r76bt50KsHQvM1mQ11dHe8xAtW8vwmc5dI84BmBSZoXT7Rp3hmqPBEDCOXN8ffBdXZY9oY3nw0xCTnZebxlzPcF6yQ3nt2It/AWbykgPtgL8Jf6XyLBlgA11B6zCCxZ6c97/pz7zGKxuHTyOyw7uOhAbwjdD+eO2Nv9YLmnhO4V5aaKLcKleXYOIcNOTNUKqRUX3FEqlS6aFxtEJbfmfSVwDrbmgdgs+0X4Bxl2UUYk5s2RIyGnGFgn+WntpzAoDFhVtwrL1Mt8zqCxF+AtObfgzuY7UazujPJznkVgyUrHp40XPM4Y7RikKlN583A5FzQP1v3QaDS8xnU0LzMQvolEzQPiq1YEAhvMMc1/8NMHWNy8mLfigzNME3Jpni+BM2meiFTIsIsyInHUxl48LNUAWzLyt/PRarUuWe4B1w6OFUIHgFZFq88ZNHcK1AVYkLpA8ixCobawc7+EIo8lEJaEVavV+p2g1P1+sX8z/xmhTj6alxkI30Si5oFO3XdTdIPZYQ6K5p3z4TlrvtneLFhbWoiANR9f5HFtodS8u7ZJ84Q3yLCLYQLxn2EZ0rVaLffiYakG2JIR3/KtmI5fq9UiJSWF17DT6XRcIfRZ2bOQ5EjCtMxpIR25slkE507VZrNxqSDY/XBeVhGKZHXG/X7F0qg8lq41nMileaDT4IxTxKHd0e5V82KCM/g0zww7Z83P6TOHy6kX6meFPaNM96T5wIilaw01YTfs/vnPf6Jfv36Ii4tDQUEBduzwnrdo6dKlGDhwILp164a8vDy8//77Lt8vX74cCoXC489kMgXzMqKSQAo6s9EqAC5vk5iC03KKeWL6RDyEhzBn8By/R64sPYFQjj2x2Gw2r8lb+SJZiSvQDERoYIZdoJqvrq6GxWLxCMTgQ04n/ylZU/BUr6dwU4+b/D4eaT4yIM0Hj7AadqtWrcJjjz2GJ598EhUVFRgzZgymTp2Kmpoa3u3/9a9/YeHChXjuuedw6NAhPP/88ygtLcUXX3zhsl1ycjLq6+td/uLi4kJxSTGBcy1W57xNoXbq39y4GW/hLdFZ5jUaDXQ6ncusgLe8Uwy1Wo3k5GSP/FnO7DbtFkyyDPBHskYiNIom+HDXPDPspARiyNkWsXn4SPPiIN13LcJq2L3yyiu4//778cADD2DgwIFYsmQJ9Ho9/vWvf/Fuv2LFCvz617/GrFmzkJubi9mzZ+P+++/HSy+95LKdQqFAZmamy58vDAaDy5/ZbJblGoNJuMToXIs1EAItLr7u7DoYFAbRDsusk1cqlZJyd/EtE7nD8vQJtcXZ6A1kOSzY0Cg6sol1zbO2OOfh8wZpXhyk+8jDbDZ72CViCZthZ7FYUF5ejkmTJrl8PmnSJOzcyR8+bzabPWbeunXrhj179rgUtzYajejTpw9ycnJQUlKCiooKn+3R6/VISUnh/hYtWuTHVYWWcImR1Y7kixSTgnNxcX+YljENyY5kSQ7LB5QH8IrxFew275bUyfvqlFnqBDFtCWQJ3Bc08u7axLrmWVt8Lf86Q5onopFFixa52CR6vV70vvI/ZSI5f/48bDYbMjIyXD7PyMhAQ0MD7z6TJ0/G22+/jenTp2PEiBEoLy/HsmXL0NHRgfPnzyMrKwvXXnstli9fjuuuuw4GgwGvvfYabrzxRuzfvx/XXHONYHtqa2s5/xEANHLxQlF8EUaqRwbckRQnFuM743eYljkNKoX0kezE9IlIq0nDZP1k0fvsVe5Fq6MVW4xb8DgeF7UP6+S9Ld+MihuFvi19cYv+Ft7vA4FVDRBzv9mLX+g49AIg/CFSNM/aUhRfhKJccRGupHnSfDSycOFCzJ8/n/u3wWAQbdyFzbBjuJeEcjgcHp8xnn76aTQ0NOCGG26Aw+FARkYGfvWrX2Hx4sXcyOqGG27ADTfcwO1z4403YsSIEfjHP/6Bv//974LtSE5OdjHsYpFQdwKsgx4yeAiOHTvGu41GoxHdwfHR0dGB6upqZGVlAQBG2kdin3qfx8wDy0nVrVs3xMXFQaPR8B4vWOWXvCGlk/eGtxcAEZtEouZZu/x95m02G2pra9G/f38ApHnSfHSi0+n8nmAK21Jsz549oVKpPGbnzp075zGLx+jWrRuWLVuG9vZ2VFdXo6amBn379kVSUhJ69uzJu49SqURhYSFOnDgh+zUEg2B3tELliYDQLvOI9TnhM+xYpyfUETvDDDsWuTbEPgTzE+d75LNSKpVITk5GSkoKMjMzkZCQwNte9l+dTseVH3I4HMjOzvbqaE10fQLJ4RZs40pI95Goebats+7Zv8UsZTLDjjRPBJtInREN21Op1WpRUFCATZs2uXy+adMmFBV5n2LXaDTIycmBSqXCypUrUVJSIigwh8OByspKbsYm0gl2RytUnijU+PI58TZKlmLYSUVohpCvvSw6UKFQCHby4RjtE+HBX+2GwriKBN3Loflg6Ig0T/hLpAadhHW4MX/+fLz99ttYtmwZjhw5gt/97neoqanBww8/DKBzjXnevHnc9sePH8cHH3yAEydOYM+ePZg9ezYOHjyIP//5z9w2zz//PL755htUVVWhsrIS999/PyorK7ljxjpylSfabdqNF8+9KCrViJiaku50lQLXXeU6iOhGDt1L1byv+tHuMK1E2ktSKqR5ItyE1bCbNWsWlixZghdeeAHDhg3D9u3b8dVXX6FPnz4AgPr6epecdjabDX/7298wdOhQ3HzzzTCZTNi5c6eLD0FzczMeeughDBw4EJMmTcKZM2ewfft2XH/99aG+vIgk0PJEbFlim2kbmuziaiOGoqakMyqVChkZGWFfJhGTeV4MkTrdT0QPgejeb82HoH40Q6VSITs7O+zpREjzRCQQdgeB3/zmN6iurobZbEZ5eTnGjh3Lfbd8+XJs3bqV+/fAgQNRUVGB9vZ2tLS0YO3atcjLy3M53quvvoqffvoJZrMZ586dwzfffIPRo0eH6nK6PGx54qbEm5CmFFcbcW7eXKQp0wJOlSAGrVaLq6++Grm5uejevbsonxzn5KtyIibzvJgOPFKn+4nYwG/N+1E71R+Y5pmOxBh4pHmiKxN2w46ITljGeefaiELMyJ2BJ3s9KViA272jc3b0ljpyZR3ipnOb8IrxFWw8u9HnPs7JV+UacQPiMs+7158kiEhFqubda6c6403zfN97g2n+y9Nf4oWGF7DPts/ngI40T3RlyLCLcUI15e/LMdq5o3N29PZ35Mq3FKTVannLBDknX3UecXuLIBaDtxJr3u67r9+ElmmIQAjl8yN0Lm+aB/ybserKmhe7DUEAZNhxFBYWIj8/H0uXLg13U0JKqKb8pThG+3L0tlgsaG5udqk2InQM56WgxMREDB482KNjLIovwsIeCzErbxbuvuZu7tzBjCT0dt99/Sa0TEMEQqhTnIg5F2ne929Cuo9Nli5divz8fBQWForeJ+wJiiOFsrKyqEhQHAujthm5M9C7qTcKcgt4vxfTybNj5OnzuESozFeotrbWY3s2o6iHHrmGXO7cb//wNveyiYV7T0QesfDckeYJgp/S0lKUlpbCYDAgJSVF1D5k2EUZkZhJnEWkharzk5KslA/n9rIkpny4v2y83fv1teuxHMvRUduBeUPn0cuAkI1I1DxwJVq2rq4uJOcizROEOGgplgiI9bXr8ULDC9jbsTfkhl1CQoJfSUudl4X9ybHHx8pTK2FQGLDy1EruZUCdPNEVYcEGX57+MmiF7d1hmk9MTBRdvcIZ0jwRS5BhRwSEs+NxqJctAq0jC8iXY292v9lIdiSHJL0DQYSTcGqezRIGYkyS5omuDhl2REA4h/dHo3OvXDn2SvQleBAPYnLmZC4vozPkq0N0FUjznZDmiUiFfOyIgCjRl+Ca9msEnZ4jnRm5M5DRkCHb8To6OlBbW4sePXq4fB6pflIEIRXSvCukeSLSoBk7QjJsOSTc5XsiaUQcqHM3QUQykaJ51pZI0D1pnohUyLAjJMNSCATaoQXaQUdSBnfWyYf7ZUMQwSBSNM/aEgm6J80TkQoZdkTYCEUH7V4uKFJG+wQRi5DmCSL4kGF3mVitPNHVcS/KLeeLJdDyQwRByA9pnuhK+FN5ggy7y5SVleHw4cMoLS0Nd1OCSqyNXsUU5faXYJYfIgg5iSXdk+aJrkRpaSkOHz6MsrIy0fuQ12eMEWuRWsGM4JubN9el/BBBRCqxpHvSPBHrkGFH+EUszQAI4au+JUF0JUjzpHkiOqClWMIvpJTQoRcCQUQ/pHmCiA5oxo4IOrG0DOQMvdyIWIU0T5onwgfN2BFRh5jINCkdrEqlgl6vl70zjpR8WwQR7ZDmCUI8ZNgREYevDlpMZJqUZSO1Wg29Xg+dTudybhp9E0RoIM0ThHyQYUdEHL5GvXPz5gYtnYHzuWn0TRChgTRPEPJBPnaXKSwshEqlQmlpaZfPZRftUGQaQcQWpHkiVlm6dCmWLl0Km80meh8y7C5TVlaG5OTkcDeDiFJoCYcgYgvSPBEK2GSTwWBASkqKqH1oKZYgZECKfw9BENEPaZ6IVMiwIwIi2ketcrefakkSXR3SvCukeSLSIMOOCIhodzaWu/1US5Lo6pDmXSHNE5EGGXYEISPBjN4jCCLyIM0TkQYFTxCEjFD0HkHEFqR5ItKgGTuCIAiCIIguAhl2RJcm2h29CYKQBmmeiHVoKZbo0gSzGDm9QAgi8iDNE7EOzdhdprCwEPn5+Vi6dGm4m0JECdEeHUgQhDRI80SoWbp0KfLz81FYWCh6H5qxuwxVniAIgiAIIpKgyhMEQRAEQRAxDBl2BEEQBEEQXQQy7AiCIAiCILoIZNgRBEEQBEF0EcJu2P3zn/9Ev379EBcXh4KCAuzYscPr9kuXLsXAgQPRrVs35OXl4f333/fYZvXq1cjPz4dOp0N+fj7WrKHizF0JSjlAELEFaZ4gxBNWw27VqlV47LHH8OSTT6KiogJjxozB1KlTUVNTw7v9v/71LyxcuBDPPfccDh06hOeffx6lpaX44osvuG127dqFWbNmYe7cudi/fz/mzp2LO++8E7t37w7VZRFBhlIOEERsQZonCPEoHA6HI1wnHzVqFEaMGIF//etf3GcDBw7E9OnTsWjRIo/ti4qKcOONN+Kvf/0r99ljjz2GvXv34vvvvwcAzJo1CwaDAV9//TW3zZQpU5CWloaPP/7Y45gshLilpYXSnRAB09raivLychQUFCApKSnczSEIIsiQ5olQIMVWCduMncViQXl5OSZNmuTy+aRJk7Bz507efcxmM+Li4lw+69atG/bs2YOOjg4AnTN27secPHmy4DEZBoPB5c9sNku9JIIgCIIgiIAxm80edolYwmbYnT9/HjabDRkZGS6fZ2RkoKGhgXefyZMn4+2330Z5eTkcDgf27t2LZcuWoaOjA+fPnwcANDQ0SDomQ6/XIyUlhfvjmzEkCIIgCIIINosWLXKxSfR6veh9w155QqFQuPzb4XB4fMZ4+umn0dDQgBtuuAEOhwMZGRn41a9+hcWLF0OlUvl1TEZtba3L9Cb5chD+QE7eBBFbkOaJYLBw4ULMnz+f+7fBYBBt3IVtxq5nz55QqVQeM2nnzp3zmHFjdOvWDcuWLUN7ezuqq6tRU1ODvn37IikpCT179gQAZGZmSjomIzk52eWPDDvCH8jJmyBiC9I8EQx0Op2HXSKWsBl2Wq0WBQUF2LRpk8vnmzZtQlFRkdd9NRoNcnJyoFKpsHLlSpSUlECp7LyU0aNHexxz48aNPo9JEARBEAQR7YR1KXb+/PmYO3cuRo4cidGjR+PNN99ETU0NHn74YQCdU5FnzpzhctUdP34ce/bswahRo9DU1IRXXnkFBw8exHvvvccd89FHH8XYsWPx0ksv4bbbbsPnn3+OzZs3c1GzBEEQBEEQXZWwGnazZs3ChQsX8MILL6C+vh6DBw/GV199hT59+gAA6uvrXXLa2Ww2/O1vf8OxY8eg0WhQXFyMnTt3om/fvtw2RUVFWLlyJZ566ik8/fTT6N+/P1atWoVRo0aF+vIIgiAIgiBCiyPGaWlpcQBwtLS0BO0cJpPJ8eyzzzpMJlPQzhGp0LXTtccisXz9dO2xee0OR2xff7CvXYqtEtYExZFAKBIUx3ISZLp2uvZYu3Ygtq+frj02rx2I7esP9rVHRYLiaGbp0qUReY5Q7BOKa/fnPJF6v/whUn9HuvbgEqnPMGm+a/z2sXzt/uwTqc+9KIIyZxhFsOnNAQMGOAYOHOh4/fXXfe4zcOBAv84hZblX6jlCtU8ort2f80Ti/QrVtfuzD117cM9BmifNB+sc/u5Dz310Pvevv/66Y+DAgY4BAwaIPn5Ygye2b9+Ov/71rygvL0d9fT3WrFmD6dOnC25fX1+P3//+9ygvL8eJEyfw29/+FkuWLPHYbvXq1Xj66afx448/on///njxxRcxY8YM3mPabDYAwJo1a7jpzdOnT3ttt8Vi8bmNM62trQCAM2fOiC4LIvUcodonFNceinaFYp9QXbs/+9C1B/ccpHnSPD339NzLcZ7bbrsNt912GwwGAwYNGsTZLF6RZFrKzFdffeV48sknHatXr3YAcKxZs8br9qdOnXL89re/dbz33nuOYcOGOR599FGPbXbu3OlQqVSOP//5z44jR444/vznPzvUarXjv//9L+8x9+zZ4wBAf/RHf/RHf/RHf/QX0X979uzxaVtFTPCEQqHwOWPnzPjx4zFs2DCPGbtZs2bBYDDg66+/5j6bMmUK0tLS8PHHH3scp6mpCd27d/coKeaNwsJClJWVidoWuFIKJJjnCNU+obj2ULQrFPuE6tr92YeuPbjnIM2T5um5p+dezvOw41+8eBFpaWletw17rVi52bVrF373u9+5fDZ58mTeJVsALjVmndHpdIIlYlQqlV9RL1LKgvhzjlDsE4prD1W7QrVPsK/dn33o2oN/7QBpnjQfOe2i5z66nnuz2Qyz2cy7vS+6XFRsQ0ODR13YjIwMj/qx7uj1eqSkpHB/ixYtEty2tLRUlrZ6w59zhGKfUFy7P+eJ1PvlD5H6O9K1B5dIfYZJ813jt4/la/dnn3A/94sWLXKxSfR6vehjdrmlWK1Wi/feew933XUX99mHH36I+++/HyaTyeM4LDeM+/Sptxk7qVBuH7p2uvbYIpavn649Nq8diO3rl/va3Wfs2FKsmON3uaXYzMxMj9m5c+fOecziuSN1+lQKOp0Ozz77rGyGYjRB107XHovE8vXTtcfmtQOxff1yX3sgk0tdbsZu1qxZaG1txVdffcV9NnXqVKSmpvIGT8TyCIMgCIIgiMhHiq0S1hk7o9GIkydPcv8+deoUKisr0b17d/Tu3RsLFy7EmTNn8P7773PbVFZWcvs2NjaisrISWq0W+fn5AIBHH30UY8eOxUsvvYTbbrsNn3/+OTZv3ozvv/8+pNdGEARBEAQRasI6Y7d161YUFxd7fH7PPfdg+fLl+NWvfoXq6mps3bqV+06hUHhs36dPH1RXV3P//vTTT/HUU0+hqqqKS1B8++2387aBZuwIgiAIgohkpNgqEbMUGy7IsCMIgiAIIpKRYqt0uXQnBNHVMZvNqK6u5s1xRBBE14M0T0iBDDuCiDIsFguqq6thsVjC3RSCIEIAaZ6QAhl2BBEEaIRNELEH6Z6IBMiwu0xhYSHy8/OxdOnScDeF6AKEcoRNLxOCiAxCpXvSfOywdOlS5Ofno7CwUPQ+XS5Bsb+UlZVR8AQRlbCXSY8ePWIyMShBxBqk+dihtLQUpaWlXPCEGGjGjiAIgiAIootAhh1BEARBEEQXgQw7giAIgiCILgIZdgRBRATkEE4QsQVpPjiQYUcQRERAuboIIrYgzQcHMuwIgiAIgiC6CGTYEQQRVthyjJRROy3hEET0QpoPLmTYEQQRVvxZjqElHIKIXkjzwYUMO4IgCIIgIopf/epXSExMDHczXNi6dSsUCgW2bt0a7qZ4hQy7y1BJMYKIPtgonpZnCCI2iDXNU0mxAKCSYgQRfVBpJYKIbkwmk6TtY03zVFKMIIiIgZydCSK28KX55557DgqFApWVlXj22WcxcOBA3H333V6PeejQIUyYMAGZmZmYPn06nnjiCQ9jcOnSpRg7dix69eqFhIQEXHfddVi8eDE6Ojpcths/fjwGDx6MsrIyjBkzBvHx8cjNzcVf/vIX2O12l22PHj2KKVOmID4+Hj179sTDDz+M1tZWP+5K6CHDjiBilGAbXuTsTBCRRaRofs6cObjqqqvw73//G7/73e8Et+vo6MDPf/5zTJgwAR999BFmzJiBDz74AC+88ILLdj/++CN++ctfYsWKFVi/fj3uv/9+/PWvf8Wvf/1rj2M2NDTg7rvvxpw5c7Bu3TpMnToVCxcuxAcffMBtc/bsWYwbNw4HDx7EP//5T6xYsQJGoxGPPPKIxDsSHmgpliC6EGazGfX19cjKyvK5TGGxWHDy5Em0t7ejf//+MbGsQRBdEbG6jxTN33XXXZgyZQry8vKQkZEhuJ3FYsHvf/97/Pa3v0VraytSUlKQmZmJv/zlL/jvf/+Lm2++GQDwyiuvcPvY7XaMGTMGPXr0wL333ou//e1vSEtL476/cOECvvrqK1x//fUAgIkTJ2Lr1q346KOPMG/ePADAq6++isbGRlRUVGDo0KEAgKlTp2LSpEmoqamR/X7IDc3YEUQXQuosmc1mQ21tLc2qEUQUI0X3kaD52267DQDgcDhgs9lgtVq5P3fcl2pnzJgBANi+fTv3WUVFBaZNm4YePXpApVJBo9Fg3rx5sNlsOH78uMv+mZmZnFHHGDJkCH766Sfu31u2bMGgQYM4o47xy1/+0o+rDT1k2BFElKHZvwI37HoAmv0rwt0U2bFaraitrSW/PIJwoqtpPjMzEwDwySefYOLEiejevTs0Gg00Go3Ldmq1Gj169HD5LD09HQBw8eJFAEBNTQ3GjBmDM2fO4LXXXsOOHTtQVlbGZbi4dOmSy/7uxwMAnU7nst2FCxe4NvK1O9KhpViCiDK0e16H0twI+57XgZ/9JtzNkRU2m6DX62lpmCAu09U0r1AoAAA333wz/v73vwPonDVLSEhw2c5qteLChQsuxlhjYyMAoHv37gCAtWvXoq2tDZ999hn69OnDbVdZWel3+3r06IGGhgaPz/k+i0Roxo4gogzL9Y/ApEuH5frQOPJSdCtBhJeuqvnu3btjwIABGDBgAEaMGIGRI0d6bPPhhx+6/HvNmjUAgDFjxgC4YiQ6DwQdDgfeeustv9tVXFyMQ4cOYf/+/S6ff/TRR34fM5SQYUcQQSCYSycdQ+fiv6PfRsfQuUE/F0DRrQQhlmBpMVY1r9Vq8be//Q1//vOf8d133+G9997Dyy+/jFGjRmH06NEAOmf9tFot7rrrLnz99ddYs2YNJk+ejKamJr/P+9hjj6Fnz5645ZZbsHz5cnz99deYM2cOjh49KtelBRUy7C5DlSe6BpEyu6Td8zrizI3Q7nm9S52LICKNSNE8EDotxormNRoN1q9fj02bNuGuu+7CZ599hrvvvhvPPvsst821116L1atXo6mpCbfffjv+93//F8OGDeOWeP0hMzMT27ZtQ35+Pv7nf/4Hc+bMQVxcHF5/PfT3mypPBABVnugayJ2VXEr6EJd2XP8IsOMV4PpHEBdwK1zbU1tb6xI95nwugog1glGJIJJ070vzcvYvwea5557Dc889h9bWVlRXV3vddvny5Vi+fDmAzijV1tZWlJeXIy8vD8eOHXPZtqSkBCUlJR7HcDgcLv8WqvHKzuPMwIEDsXHjRp/HDDb+VJ4gw44gvODvS6Nj6FyUW/NRMLRA1o7XYrGgtrZW8Fxyw/dSIYiuTiTp3pfm5TbsSPPRDy3FEoSfRNISULBgLxWbzRbuphBERNDVdU+aj37IsCMIP4kUB2M5YNcSzpdV/OGVGFv+G+Q0eC5/CGGxWNDc3NwlfgMiOuhKug+3keqP5gHKd+kLMuwIogvhr6ETCS+rhIo30c1yHrln1orex2q1kmFHxDzRqnt/NA9ERvWMSIYMO4KIIAIdQYdyBkvu0X7b8IdwSdsTVVdNl+V4BBEtRIvuSfPRAQVPEIQA4XAiDkaEX7CQu63t+bPxX2s+AKB3wEcjCOmwaNikpKSQnjdadE+ajw5oxo4gBCAn4uDhPPJnyVbjD68UvT/bJ/n4p0FsJRFrhHtpsisjl+al7BOrkGFHEJeRc5mBnPpdcb+3zi9Qze7OZKsJ+/4t+ngsQWvqwXeD1WQiBpBT85QmxJVgaT6h4s1gNbnLQIYdQVxGztG6s2EXrsizcEe8OePt3hqHPQijKg1Ng+8Vf7zLtTNN6UNxR+1zNIon/EJuzbMZ/nBFmXd0dHR5zXdkDvcrkjaWIMPuMlRSjAgWRqMRlZWVMBqNsh2TRYV568CjZVmpPX82PtU/B8OAO0Tvw2pnxjXuR6KtiUbxREQRLs0zw64ra17TUOFXJG204k9JMTLsLlNWVobDhw+jtLQ03E0huhhyLcuypR6bzUbh/pdpHnwvjKo0tA1/KNxNIQgOudLwkOY9ibVI2tLSUhw+fBhlZWWi9yHDjog5ImmJUgqBBHPwXbNm/wreJQ257g9zdtbsXxHQcbxhGHAHPtU/h/b82dxncrQ/Wp8Rgp9o/T1DpXm5lo5Dofn2/NnYXvBPnM6cxH1GmneFDDsi5gj3EmUwOhCWib2jo4P3e75r1u55nXdJw2Kx4OTJk/jxxx8DukfM2Vm753W/j+EPcvy+4X5GCHmJhN9Tbt37qr5Amg/9MSIFMuwIIsQEowNhyzTdDn0sOpjAcv0jsKgSoLKZPLaXY9mHOTtbrn/E72MQRFdBbt07azT+8ErcUfucz/Q/zpp3n1UjzXcdyLAjiC5E6sF3RQcTdAydC5uqG7Q2Y8DBB3yzEczZuW3gLNFpIHIaNmJs+W+CupRDEF2NhIo3kWhr8pn+x1nzcsyqueueNB8ZhNWw2759O2699VZkZ2dDoVBg7dq1PvfZtm0bCgoKEBcXh9zcXLzxxhsu3y9fvhwKhcLjz2QyBekqCCJy4AsmYH46fJ1s1VXTcUnbM+DgA+fZCNbZs5G/FD+h3DNr0c1yPuRLOQQRzbQNfwhGVRqaL6cPEaN5OWbVmO6NRiNpPoIIq2HX1taGoUOH4vXXxf2gp06dws9//nOMGTMGFRUVeOKJJ/Db3/4Wq1evdtkuOTkZ9fX1Ln9xcXHBuAQiCogmp9hAI2j5ggm8dbKnMydhe8E/XbYPFKElJzHpGuR86RCxSzRpXo7Exu7pQ8RovmPoXL/P5w5pPrIIa63YqVOnYurUqaK3f+ONN9C7d28sWbIEADBw4EDs3bsXL7/8MmbOnMltp1AokJmZKXdziSgl0uowejPexBh2KpUKGRkZaGpqCmYzOXIaNiL3zFooEn4P/Ow3fh+HdfJ6vV5wm9OZk3A6cxKKhhaBhmKEv0Sa5r0Zb8wI8wZpnpBCVPnY7dq1C5MmTXL5bPLkydi7d69LNKDRaESfPn2Qk5ODkpISVFRU+Dy2wWBw+YuGkV40EOqRcyjC7QMllOXGrFYrampq0NTUxL1AnH8Lm82GlpYWwWhaIPRLJWJG+cGESkMFTih1Hy2aD1XdabGa99b/kObDj9ls9rBLxCLZsNu8ebPgd//+t/i6b/7Q0NCAjIwMl88yMjJgtVpx/vx5AMC1116L5cuXY926dfj4448RFxeHG2+8ESdOnPB6bL1ej5SUFO5v0aJFQbuOWCLUIeQs3F6z+3VZXiz+OvZqtVqkpqZCq9UKbtPR0YETJ07g+PHjMJvNMJvNqKurg91u593eYrGgZ/U6jK94BJr9K0S9JGw2G86cOcMZb+5RbzabDQaDwathx5ZK2kc87HFPWcqFYET4hivtQChfwl2VUOpebs0DQPzhlX4ZiyqVCnq9HhqNhvd7m82GqqoqF817e9aCqXlvv43z8qi7ke4rzYo/kOY9WbRokYtN4m3W0x3Jht0tt9yC3//+9y4/QGNjI2699VYsXLhQ6uEko1AoXP7tcDhcPr/hhhswZ84cDB06FGPGjMEnn3yCAQMG4B//+IfX49bW1qKlpYX7C8W1EPLDwu2Nwx6U5cXi78hVrGFXVVWFU6dOwWKxwGKx+DTsBpz7EvEdF3B1wxcu59Lr9VCpVJLaKIb4wyuRe2Ytqq6ajta8X3jc01B0yOzFYjAYosZviggdcmse6Iwy9Scfm1qt9mnY1dTUuGjel2EXTs13DJ3rYaST5kPDwoULXWwSX8v1zkg27LZv344vvvgChYWFOHToEL788ksMHjwYRqMR+/fvl3o4SWRmZqKhocHls3PnzkGtVqNHjx68+yiVShQWFvqcsUtOTnb5iwS/DEI6LNzeVzCA2FFnpDn27k+6CW2aHjiZeSv3mU6ng16vh1rtv8ts8vFPeWcoEireDHtdRvZiaWtr6zIJRAn5kFvzQGeUaaTkYwuW5oEry9jOeSxJ85GBTqfzsEvEItmwGzVqFCoqKjBkyBAUFBRgxowZ+P3vf4/vvvtO0lShP4wePRqbNm1y+Wzjxo0YOXKk4AjJ4XCgsrISWVlZQW0bEV2IHXV6iyALh2/P0cQifDPwZfyUPkG2YzocDiTtf5t3hkKoLqOvJaRQkXz8U9EJmYnYRspMU3v+bPx39NsRoftgab6urg6a3Z3L2M55LIU0H0nLlZT7zjt+BU8cO3YMZWVlyMnJgVqtxtGjR9He3i75OEajEZWVlaisrATQmc6ksrISNTU1ADqnIufNm8dt//DDD+Onn37C/PnzceTIESxbtgzvvPMOHn/8cW6b559/Ht988w2qqqpQWVmJ+++/H5WVlXj44Yf9uVSCECRc5XPkxm6340iPKdzMpMVigcFggM1m463LCIjr5Ds6OtDc3OzVfy9QpCRkJgg56Aq6t9vtqKurg3HYgzDp0mEYcn/UaB6g3He+kGzY/eUvf8Ho0aNx88034+DBgygrK+Nm8Hbt2iXpWHv37sXw4cMxfPhwAMD8+fMxfPhwPPPMMwCA+vp6zsgDgH79+uGrr77C1q1bMWzYMPzxj3/E3//+d5dUJ83NzXjooYcwcOBATJo0CWfOnMH27dtx/fXXS71UgvCK5fpHcEmXjrNX/1I2H5A+jd9iVv2f/J6B8ncG61SPYm5m0mKxoKWlxavfT21tLa6q34AJPzzmUVCcIaWTt9vtOH/+PDIzMyX5DfElZHYmmvKZEdFB+4iH0a7pgfYR8k0W9Gn8NqAZKLElxdxhM5NN/Wd41bzVakVdXZ2smmfodDrOV14s3lxkSPN+5LF77bXXsHbtWi7/3KBBg7Bnzx488cQTGD9+vKSbOX78eK8/6PLlyz0+GzduHPbt2ye4z6uvvopXX31VdBu6EmazGfX19cjKyiIfQRnQ7F+BseV/u7wkUeTxfcfQudjZ1h8AUGSxyHLPr274AvG2Jlgr3gQm/E7y/qkH34Xm8v4tw+ahpaXFI+AoUJhhN6ZuHeIv++I043HfO3rBbrfj3LlzGDlyJM6cOeMzao9hGHAHvjybgcn5k5Ei0NZIymcWDEj38tG5zPoKzLZSQDWcd5vWvF/gm+pkTM6bjESZznt1wxfoZjkP+57X/cobl1DxJtS2Jmh/WIaWvn+UXfM2mw11dXWY4KR5K56T5dhmsxl2u1205gHvue9iQfO+kDxj98MPP3gkFdZoNPjrX/+KjRv5rXgiNIQ6tUhXR7vndb+diP31wzmZeStavcxA+cJ5BostqQpF2QbKycxb0c7jiyMG5/sTf3glZtX/CX0avwUgLs8WcQXSvXywZVZ/lvYD8b07mXlrQEFarKRYY96cqNG88wyj3W4nzcuIZMOuZ8+egt+NGzcuoMYQRDhx75gt1z/C60TM8LZkKdYPx92I+Sl9AlZlPeV3iS++kmJi4MttxUbpQsszP6VPwLfXLfHwxeEjp2GjyxKO8/1JqHgTSbYml3QOBBEK+DRv0qV7XdoXSknkr+aBTi0FUuaLlRS7mDtd9D5M385JeUOp+URbE1IPviu6vYR4JBt2xcXFuOmmmwT/CGFo7T+yce+YO4bO5XUiZjgHGXh8d/kFYbn+EW50yuf3JpQstKOjI+Bnhc2E9W/a5nNbvhEzc7B2v76Ojg7B6xYi98xabgkHuHJ/2kc8jIar70Kbujuqsqf5PA5LWeFwONC3b1/BaPhIgTQf2fBp3lvqFG+5JsVq3tuyI5t99fd56V61VpLm3fUtpHmbzYbW1lZ5Na/pAcOQ+30ex13z3nKDEp1INuyGDRuGoUOHcn/5+fmwWCzYt28frrvuumC0MSQUFhYiPz8fS5cuDdo5aMkkuARaFsa5Yw4U9oLoGDoXiXteRaKtCYl7hH0/WYZ41nEyw07oWRHjbM1mwgae/zqwi+Fpa0tLi6TlnqqrpqNd0wOHu0+GxWLh7k9r3i9wqNsofDf07ziTNcXncVjKCoVCERWGHWk+uHQlzQPenxcxmk8/tiIommeGnZya/37kv2AZMkfUuZ01H2uG3dKlS5Gfn4/CwkLR+0gOnhAKTHjuuedgNBqlHi5iKCsrk5QAkAgNUhzDxRTT9kbH0Lkot+ajYGgBbzFqf53UFW7/5T335U7eW8fZOQP3Gk46bsXVjV/5dLZuG/4QlDtfw7GeU3m/94XNZoPJZEJ8fLxf+ztzOnMSjiXdiIsXLyLbYpHUObPaunyRdmIqfBDRRSRpnhlawdS8t1kwqZpvzJuL5APvRL3mgSuRuDabzSVSnlXdqKurC7iN0UBpaSlKS0thMBiQksIXIuaJX3ns+JgzZw6WLVsm1+GIGEDMMlUwZjw6o11/IxiyL3dbWq//HYyqNLReLz3K1Rk2Azfg3JeinK3b82djVdZT+DFtHAa27cLkI4+Luma2hNvvwhbJo/RgINWwkyOBLCVADQ6keWlI1fzF3Ol+aT75+KcRpXlA2N+Pr+oGad4V2Qy7Xbt2IS6Ob8xDEPyEa5kqkGhXf2COzcxvx9+cU23DH0KrKg3He93i4WzNOjahYw43bkFCxwVR18xeJiMaPsbANmm5Kb1hs9lgNpuDnrxUjgSylAA1OMSq5oErwQT9LmwRfRwxmhcyRKRoPvXgu0HRPHClykUwf3PSvCuSDbvbb7/d5W/GjBm44YYbcO+99+LXv/51MNoYU5CzdfDxFe0aLJjfXMK+f/uMCGOzVM6dIZuBO9Wj2GN71rEJHbMisRhtmh6irrlt+EOwQwEl7BhuFP8ScketViM1NZUbWdvt9pAYdnL4TYWyRjBpPviEW/MWi4ULJhhw7kvebfmiVMVoXsgQkaL55sH3BkXzwJWAjGAadtGm+WAj2bBLSUlx+evevTvGjx+Pr776Cs8++2ww2hhTkLN18PEV7eoPYqLZWCffdDnXXPPgewW3tVqtHoad1/Nf7tiEjnkkYTS+GfiyyzVrtVpkZ2dDqVS6zKa158/GztTb0abujopEzxcKH/GHV3rMHrBl0tSTn2Fs+W9ERerJgbMTu794qxEsN6T54BMMzYuJXHc27Kqumo52bU8c73UL77a+Uo2448uYEaN5Ft1uGHCHZM0DV2YNWfSvu+alzE4GQrRpPthIDp54913KO0MQ7kjJds6qJYwZMAY4fNjlu34XtuDmhi9gqLofgF70+ZkTeL9+/ZBqroBWq+UMhf5N25B37kucVE5DfdxU1NbWon///tDpdOjbty+qqqrQ0dHBGXYajQZHE4twJmsympubkc7OcblcUGZmpsf5EyrehNrc2OnYDbhk70+oeBNqy3lcd24trnGoYTneAfSSnl3fHV8RkRaLBWfPnpUUMcmO6e6wTRDusOAHsRUOTmdOQlX38Z0z1hcvcp/3afwWVzd8gZOZt+Kn9Aniz+8U+KG1WJCamspFiYvRPNBZr50FDfJpHujUUWtrK2+VKO2e16E0N0Kz51XcAK2H5vMbVuNqxzqc0swAMFL0tQnBAmuSkpJ4vyfNdyKbjx1BhBNncbojh2NtqBhw7ksk2ZqQfsy/tvIFEww8/zWS7M0YcO5LLnWAxWKB2WzG2bNnkZCQIKpD81YHsm34Q9zsgXv2/rbhD+GSticAB1IcLX4nJWVpVthv7KsouZii5XLsQ4SHrqL5qxu+QLzlfEAJupnumWEnl+aBK4adt9x9CoBf8w4gyd7s97W558/zNbtNmu9ElGGXlpaG7t27i/ojiHDgTZxyONa6nyuQpbPk45/yBk/YbDb8kDIRrapUNObJtxxwpOdUtCpTPZaALBYLHGXvYHzl/wa8TMqKiXcMneuRvb89fza2F/wTP/SagRZFitclaOelInf8SYxMdF1CqXnAuyHpi/jDKzG2/Ddc2TyGzWbDwdSb0a7pgZOZt8rVVFGal2OZlMtNd/3veDV/OGsmWpWpXq9NpVIhIyODV/N2u11yYmRC5FLskiVLgtwMoqvCimpDPd+v4tZyYLn+EWDHK8D1j3jNTyc0ve9xvMuGnV4vfqnUmdSD70Jja4Lu4LvAtX/lPrfZbKhQDcf+XgUoyi0Cystd9mM5rZqMA9Cz/Uecumo6gCKv57rWuBPXGb6Gw+FAj7ZjyPvhK5f9WCTYwPNfY3v8//p1Pe6wJaK8vDzg2DHu8x/TxmF7+9X4eb+fwy6whKrVanF183bknXkNtsMtQFZg6SL8IadhI/qdWct7f/3NZRhrhFv3cmseuGJI+pMKhC1NXt3wBU6mjuU+Z5o/PXASb7LtYGp+wLkvsafnYMnXwkd7/mxUqIZ7aP5Uj2LssQ9GRvcMdLgFhjDUajUGGL7H0DP/Is3LhCjD7p577gl2O4guCvPB8JZUMxjEH16JG/YsBdTzRSchzcvLC0nbmgffi257/wVH+lBMrvw17HYHWo8/hj6N9RjfuOay83IRF03WvXt36HQ6JOz7N9S2JiQ0l0EJO3LPrIUVz3HXcOHCBdTU1Lh0nkNbv4PO3g4AyOHZr+qq6eh3Zi2OdJ8MtPO3V6lUQq/XI+3HNbij9nW0pN0PIAtAp3/QNQ1fwKJ+BFANF3X9HR0dXpOLJlS8CbWtCdaKN4EJvjt5ttTEfIgChb34nO8TQ4ovZSwTDt1Hsubbhj8E7e7XcTHhGtxy8BE4HE6aP7sGJ5XTcDpzkkcdWTGar6qqQk5ODncusZo/nv5zQMBGZZrXarWIP7wSvzy7BPsSxuMCbuM0r0j4vehAA9aXCSUpZoNdsZrnyxoQCF1N86J97J555hm0t1/p+ZuamoLSoHARipJisYicJXukkFDxpuxLMXJxod9t+CD9D4g7VwmtrQ1xjnakHnwXVzd8gSR7M5duwD1NQNPge9GiSEFtcgHa3VI3WCwWNDU14cyZMy7LFvuTboJZGQ+Tohtqk0d67Hc6cxK+vW4JfkwbJ9helUoFvV6P5APvINHN/+/qhi/QzXKe862Rg7bhD8GoSkPb8IdgNpth2fkGZtY+h5w9z2FW/Z94l7OYD5EcsOjFUKfG6EqEQ/eRrPmWa2Zi/TV/QXfjcejsnppnKVDc68iK0XxNTY3Lsy9W83wpVBhM8zqdrjOvpb0Zw9u2AriieTnvc/PlTAFM88Ytr2FM+W8wsuYN/PLsnz00LzVrgC8iWfNBLSn24osv4pFHHuFKjfTp0weVlZXIzc2V3tIIhEqKBQdfI+dAcV9SYR2SSfc/UO/6OyDwYslp2IjcM2sljTrloqOjAyaTCefy5iD9wL86Z+wG34v6+nr0O905Y5fGs59hwB1Yd1SLoUOH4pDJBJVKhd4+znU0sQg/pU9AfX099FfpER8fD61W67Jfn8Zv0b/uc+xSjwZwm8cxmOGUcd190O1Zipa8uUBj53cnM2/tnLG77FsjB+35s/FNbRom50+G0mJB+rEPEG9rgr32Oyhhx9UNX8CGP8p2PndY9KL7fSLEE0zdR6vmW1pacKzXLcivX905Y+ek+ZMCKVCCqvn6dSjvNhYtmOlxDOdZcNPwh6D8vyWoSBgP4IrmFTIa7SxTANN86sF30c1yHjmWC1DCEdOaD2pJMfdQZ77QZyJ8BFoMO1pxD2Rgnbyj4F6veY3EZhlXqVTIyspCfX297HnGLuZOxzfD/o0PrvojDAPuwE/pE/BB+h9wJGG04D4KhQLp6emyhuVf3fAFEqwXUWj+HsCVkmL9m7ZBqVQiPT0ddXV1aL76dnyqfw4Xc6fjWuP/YdLh+bDb7dhe8E+XDPtyczLzVrQqU1GbXODTETuWYImNYy3/XbA1D3S+3+Li4mR/z53qUYwvB7/uovmPMp7wOnsWNM13XOBWB1hJMXfNWywWtOfPxkcZT8DhcLhoPpjGcdVV09Gm6YGTuiGkeT+gdCdRgq/s9F0tZDvYLy2xWcbVarVLJ+fOtcadmPDDY1yCzmjkZOataNP0QEXCeKjVaq6k2MDzX0OhUCAzM9MlkzwADDV8h0RrE645u97lc/YcWq1WLmmx871xOBxobGyU9Jyyl99/r3oQH2U8ISnXVzQjRvNdybCLFM0DncaUyWSCQqHw+K7fhS2YVf8nySUBIwmm+cqkm5CdnY20yyXFvGl+RPs2Xs1brVauYoaQ5qXWnz2dOQnfDHwZm1Nm44P0P8SM5uVCtGGnUCjQ2toKg8GAlpYWKBQKGI1GGAwGlz/CN2KqFAjt01U6cV/Ieb18jrZSsowL5W/TaDQY3rYV8TL7mEnFbDajrq7Oo+NkM2/XNG/3uv9P6RPwzcCXcTJ1LLRaLVef8kjPqbzbd69aC43DjEuKbrzpFNgAg/k8Od8bIcOuT+O3XAFuVktXjLGsUqmQnZ0tOJsRKYW9SfO+iQbNA0De5VyTaX7mY5QDIc2zmTexmj+WdCOys7PRNuLXXjU/sG0XtAKad66YIaT5trY23sEcMwR77XhCtOaBzr7XPV8nI1I0H04kLcUOGDCAy2lnNBoxfPhwpKWlIS0tDampqUhL4/MMItwJVoct5oGOxbqUgUZQOXfyzqNTjUaD6pwZuKTtyeVv4js3XwcsJ+wc7stGbOYtv2mjpOOx+pRCARXpx1YgznEJHQqd1yUklrRY6N444+yQnVDxJhJtTaKMZbVajezsbJfZBfZ7d3R0SFp+8ydPmVg9BdNI4yvn5k8buxJya945OOdk1rROzY/gr40eTs2nXp55k1vzw41bZNc8cCXgJfGnjaI1D3gadpGo+XAiOnhiy5bQ1HwjPBHrP8ceaG8pBqIxdDuSYKNT1qGczpyE05mTMCR/iEv+JoYcnTz7zfhmD9xxTlPQNvwhKHe+hiNpk4BL3vdjpczsh1s5f7n+TduQ1/gVTMcvAN1Gcds25s1F8v63UZlYjIyMDFy6xH9wl9xWBw54Pb+zQ7bZbIZq52uwDX/IL18R506+6qrpnQ7zAvnM3Pfj6+Sd81jx7RMMPUnxmXUp58aje9J8YLBAAjZx8VP6BNRfNTWommc1ZsVoHujM/9i3b1+0Wh6AZvfrsmu+IrEYw4xbZNU80GkI6vYsRUdWARS1u2Na83Ii2rAbN044HQIRXNjD5wspDzThG9ZZKhQK2O12NDQ0uHQAndnkX8eP2dNQ17OnX4ErfRq/xfj6tZ0dKfKhUCiQmJiI9J++wKz6N3FKOR0Wy0iuI/GFc5qCi/mz8eWpJHTr1g24VO91vwHnvkTC5TxSrJMfeP5rJNiaEHfwXaBwFO9+mZmZop5NIdg9PJF5K7YX/BNFQ4vQbjRyUbGJfh+5k9OZk/BT+gT07d4X/c1mrx2xxWKBwWCARqNxWdp17shDhVjNA1dejkLJeAnxCGmePQ8skW1VAJpnBhXTPNA5IMvOzoaq4j3cXL8OpkMXcKjbKNHPHGt3ve5ufFaTGhWar7pqOtonPY4K1XDo9Xrs2LEjpjUvJxQ8EUJY/cJgOdpL8SHxh2BOQfMd23nZM9iwc5lMJtTW1sJ8uUPo27cvtFot7HY7zp4962LYJVS82ZnUsm4d52PCYB2tUEJOxtUNXyDJ1oTuFa9jwg+PIb/9v0hOTkaPI+8jydYUUP1Ib7iPVI/3ugWtl/NIMY70nIpWVZpHCbD0Yytc8u3xwWY2nX+7/k3b8GDb39G/aRtngCZWvoVulvPIa/zKw0+OFVl3vq8D23Zhwg+PSfKfEZvnzmKxoKWlRdYltGBrHnAt5yY3pHlXzeeeWYv4ADXP6kEzzQ9s28X5irLv/K2n7I1AND/cuAXJfmi+34UtmNP4Fwy6tJtbTWCav+bseo97xaf5/Pb/RpXmIwEy7EKIe3F0b7ARg8Fg8OkDEEgNQykE00+I79g2mw2a/Stw455fe4iaL4LOl48hW96wWCweGd5Zp2QymXDo0CEYjUafbWaFrvlC8Z1fEN443usWGJSpgAOIt5znOs7mwfeiVZUWtDB/907+VI9irMp6yiVtyY9p47Aq6ykYBtzhsm9j3ly0KlMvV8jgx9mhGuicSRzUtBEpjhYMPP81Z9h1jOpMZGsa+T8eUXisk3fudIcbtyDech6a3a9HRXqfYGs+2NdPmneFJbINRPNHe07l1TxwObUPj2ElB4FoviKxGAY/ND/wwgYuubG75u1Fj4oy7EZcDlCLFs1HAmTYXSYUlSfci6N73fZyp9fW1uazk/c31Um4nUDZbIZm/wpBZ2ehLOd8LwVfTrPunbxzhnegsyNKT09Ha2sr74us34UtmPDDY1wWdFbo2lcovkqlQkpKCm8tyKru4/F24qNoGPwQ2rU9uY7TMOAOrMp6KqAwf61Wi5SUFN7i2mLo37SNN63Dxdzp+CjjCa/59txRq9W4mH8PWhQpLpF3rIi4tzx4/S5swS/P/hn9m7ahIrEY7dqeMA57MCrS+5DmXYlWzec0dAYjsKoNgWj+ZOpYXs0Dnf57fIaVWIKl+SMJo/F+9/9PsuZbhz7QOQi8nNwYuKJ5XzPM/S5swZzzL6Fe0yeqNC83/lSeIMPuMmVlZTh8+DBKS0uDdg4xL7FQInY0Hqz8Umw2Q7vndcFO/mTmraJzT0nJU8WHSqVCZmamYKc44NyXiL9cyFsKWq0WgwYNQkJCguA2F3On49vrlojuONno19vsgFarRXJyst+d/MDzXwdtWUgMHR0dMBgMnctT9mYMPP81jiSMxrfXLfHQEItcjLRINdK8K9Gq+dwzayUdlzTfiWHAHahILMbwtq0eZcH4YJq32WwYcO5LJNubkdXxU1RpXm5KS0tx+PBhlJWVid6HDLsIINyjaF8EazlGTD3Jn9IniPYbDLaP4fFetwguw3hDrVZDr9cj4cgq3LDrAXSvWutzH5aPyrkz1Gg0iIuLg0aj4Y7p7hjMfEvkeJaE/G18YbPZ0Nra6jGyTj+2gluKFQMrw3SkxxS0KlMFc2yxc8pZLzbYkOajS/NSa4i6a15MMuP4wysx4YfHcK1xJ/dZtGseuOKfJ2ZAzDRvt9s5N5V9TrN97ueMJs2HElFRsbfffrvoA3722Wd+NyZWcY7A6VyqeAVmWymgGh7upgUV53qSEOHfIhdarRbZ2dlobGyUtN+pHsU4nTmp8xj+nHfP61CaG9Hr2AfQJj6KixcvCi4rpB58F5rLwRPnO+ajubkZmZmZXCfvjkql4mpn1tbWQq/Xu3zPyhKZTCbe8zmnPrAOm4e0tDS09ZyF/2hHYtyAcYCEKDjWycfFucZoNubNRWLlWzjhxUDj48e0cShXDEVqairQ3Oz1vCwtRWpqKnef3H2rxOA8OxJM/zLSfGgIVPNarRbd/TnvZc2rDr4LpD0OjUYj+DwlVLwJteU8htq+w2nL/xdVmrfb7byaB66kSqnOvBX9RB+x897v6hgIhUKBHIFtoknzoUTUjF1KSgr3l5ycjG+//RZ79+7lvi8vL8e3334rukAtIYwUZ+tIIlwzEP4kImWdvL/LFXw4V04Qgs1WNF93H7RaLS5cuMAbjWWz2VCjv50LnvCWBZ/BOnmhCgysk2ftdI/SZNF4CRVvQqvVokePHsjJyXG5R8nHP8Udtc+JmnHk42LudLyT9JhgEtRAYZ08AKSmpiLlxGqMLf8N+jR+6+FbJcS1xp2YfORx9Gn8lpsdYc+Y0WgMivM2aV4aUan5yzNgHR0dvGXKbDYbzvS7E+2aHtifdBOsVmtEaB7onEn85dk/Y9Cl3YJt8caRhNH4oOf/C0pZsGBpHuhc6q2qqkJVVVXUBWyIesrfffdd7i8jIwN33nknTp06hc8++wyfffYZqqqqMHv2bPTs2TPY7e3ySHG2Dug8TjU9nfG3sw5X+SPWAXbmRvoN5+QcapwdvoXuIfO38uUYbbfbsV87Eh/1Wih7Z8iczRMq3kROw0YuGIQv9YE7qQffRaKtCenHwlOqp3/TNvzy7J+55WkWESmUSoSloxlw7kvR5xja+h0SOi64+FQxQ6K9vZ3XeTtQXx/SvDS6quYPaEdiw8CXcTSxSNZ2BqJ54HIFG3szCi55L1MWDAZd2o05jX8JueaBywPsmhrU1NTIrvlgI3n4smzZMjz++OMuowSVSoX58+dj2bJlsjYuFvHmbC2nL4VQVF2gnbU/NTHF4u0FlHrw3c6cchKdnP2BbwTs7PDt7z3s0/gtfnn2z+h3Qd4qL0qlEjqdDhqNhnM2bxv+EJeT6+qGL3hTH7jTPPheGFVpaMzz9GdyzuHFZhLYyJ99x7ecJIWB579GkpOvjvMLiw/DkPvRpumBoxKWfvcn3YQ2TQ9JPlWB+vqQ5oWJFM0D4AxJZmTEguaBzrROrcpUlHcb6/GdVquFXq+HRqMJiuaHt23tkpoPNpINO6vViiNHjnh8fuTIkS6X5C/SiPSHCQh93itG8+B7cckPJ2egMwWDmJE/8x27un6dR+cixeFbiKsbvuiM/rywQdYlI5VKxS0vHI6/AVuG/QPt+bO95uTiwzDgDnyqfw4Xc6cDAJeZ32q18hp2bPDHvouPj4dOp/P72o70nIpWZSrXXvbCMgy5n4ukc6ap/wx8nPEETqZ6vpCEOJpYhG8Gvsz5UvqCZa4PVgoG0nxkaJ4VuO/mFBUvt+aFllT9QS7NA51pnT7KeAKHuo1y0TzQmbuP+aXxaT4hIcHF4JNKRcL4mNO8HIguKca49957cd999+HkyZO44YYbAAD//e9/8Ze//AX33it/UkWi6xJooW5nDAPuwD7lMABAb7fvtFotUlNTPRLgct/veR1Ky3n0Pf0ZajseFDwHcxA+1usWXNv4FSzDHwL8cL3QaDS8KQlOZt6KfmfWwjT0AaisKgxs24WRP+xAm/ohABnoXrUWd9S+A+ORh9BszfdI1HpNzccAgBO97wLguZzDIs6Yg/PpzEmo6j6efSn5OhwOB86ePes1pYP7det0OuRe3Iprj38Nh+4xOArE9xksiCI7PRvpuFKnd4StElOO/n84mXkrzvUu8XoM5xqQ/tR5zGnY2Fm2L+H3wM9+w2Wu53MaJzyJVs0nJSWhbfhD0O5+3a+k4aI0r1RxAQ2GqvsB6DnNXzr+P7BqClBbW4v+/fsDiA7NM4Mvp2EjRuzfBiT9TpLmD3UbhcPxNyAnPSdsmu/T+G1nHeso0rxkM/rll1/GH/7wB7z66qsYO3Ysxo4di1dffRULFizAX//612C0keiiyNnJe4N18kL5nyzXP9KZKDShWFTR7VM9irG94J+ScpM5+zelnFiNW08uRO7FrS7buCcnZVUWWE6p9GMrkGhrQvfDyz3uW+6ZtdDa2qC1tXksTfW7sAWz6v+E9J++QHJysocbhdxO5b64tvErJHRcQNzef/ne1rgTJSf+gIFtuwS3ST34LpJsTaL8aqTMLolNiOtwOEQ7asc60ap5QHxCcu4cfmieBTQwP1am+dSD73rM3kaT5ocZtyDRelG05icfedzr8nQoNc+XMDvSNS/5l1UqlViwYAHOnDmD5uZmNDc348yZM1iwYIGsU8lE10Bs/UR/YZGaYvJECdExdC6+vW6J7E7Lzjj7N7kv6TDcs9WzKgssou7CwHvQrumBluvu93hpVV01HRZVAiyqBJelKZVKhfwLG5Bka0LPI+8jJSWFt5P3pt3k45/ihl0PIO3HNS4pBdj+vpKmusNyZQk5bbOXskaj6XRstl7E9a0bPAw8Vkng/LVz0apKw/FetwCAqChib35hrKYlAFRXV7sEG/AlxLXb7TAajRHbyYeDYOq+K2ueBTQwP1am+fYRv4Zer3fRaSg0r9m/gpt1Y9G8/mieLakKaV6tVrtqvuMC8utXY875l5Df/l9uu1Bp3lnLfAmzI13zfpnsVqsVmzdvxscff8z92HV1daJq7UUqoSgpJhVWpFrutXwxx5XLIZrVT9TpdAGlRxCK6GORmu6Z0oNtULojJW8SqzFblT2Ny1OlVquhUqmQnJzMdfKsygIbzbfnz8aeG5fBOmyeh2F3OnMSvhn2b3wz7N8uviJqtRqmwt90Rl2O+LVf15Z68F3EmRuRfOAdrvMd2LYLc86/hH4XtvAmTfUGq0cpNOPpbNgxx2aFQoEE60WXuprsnp/vOw2rsp7CqR6dpZmkdPJ8v5e3F1ewE+J2Bc0DV3QPgDQP8ZpnAQ3Mj5VpXnn9A9Dr9S5Ly6HQvHbP65xhN9i0x2/NH+o2Ch9lPCFa8+2aHlAqlUi2N2NE21Zuu3BoXg5fykAISUmxn376Cddddx1uu+02lJaWcgkfFy9ejMcff1zq4SKGYJcU86dot3tRZW+wMHYxof/OxxWKujMajaisrOSMdfZi8NV+JjA+8QgJy2KxoK6uziX4hjk3swg0oYg+FqnpnCndYrGgpqaG9zz+LAPFH16JWfV/Qv+mbYLb2O120VPzbEnnTNYU5OTkID4+Pqgvo/b82aLLWrEi3M6/c/Pgez3ScUjJJu8MW1p1zq7vDebYfCxnFto1PXCk59SoWRkIhea9pX4QOq5YzQPe9SxmG28v046ODphMJu5lHKjm6+vr0b17d9TX13PnI82Lcxdxv09M886zVCPatvql+T6N32LO+Ze8ulM4czSxCN8OeQ3NBf+LVlUaDnWfHDWaDwYhKSn26KOPYuTIkWhqakK3bt24z2fMmIFvv/VdCy5Wce6k4g+v5Ka5xdKn8VtM+OExXFW/gbdTZmHsUkP/haLuWK4o9rnYF46vFwFf/h9mNDobdto9r/MuXbjDIjWd80RZLBZUVVXh1KlTsFgsXOFx3Q8foqGhAc3NzTh37hySkpJEda4JFW8iydYkuhRWqHF/IUrFOXkrM+ycf2fDgDs8XhL7k2+CUZWGquxp3GdmsxnGLa9hjJe2sKXVoa3fSWrjT+kT8O2Q13BWf0vUdPKh0Ly31A9CiNU8ELhhx47L1353wy5QzVdXV6OtrQ3V1dVQV75PmveCe8JmZtixQQjTvPMsVUVisV+av7rhCyTbm11m28VgGHAHVmU9hbrsKVGj+UhBsmH3/fff46mnnvIQR58+fXDmzBnZGtaVSah4k5vmFsvVDV90Gm5163g7ZRbG7iv0P9AOwRfunbU7YtI3mM1mnL36l37VZeWDZfbvfng5TCYT2tvb0dDQgMTERFGdfEfmcNihwPn4/hjYtguTjzwuOikqMyrFzKr4i9gXouD+bp08W5bwloPqaOKN2DjoFdT0upl7aRuNRiT/sIzLk8W3vLE/6Sa0qbtjf9JNfrU10mBZ+X3NRgRL8yw/mTdiUfPsfsul+Qk/PCZaw9GoeeelUCGOJIz2S/MnM2+FQZmKisRiv9oaaYjVfDiRbNjZ7XbeWZvTp09zdesI77QNf8hnIWx3Tmbe6rXTO505Cd9et8TF14LPp01sh2CxWLx21kL46uTFYLFYcEBXiG+vW8IbgSbkewPwzyyyzP58iXXFoGmogBIO9Gz/EcONW1yylKtUKgyx7MWUI4/zLi/KUS7Kl7O45fpHcEmmFyL+f/bOPEyK8mr7d++z9uwLA8OuwLjggOwBFxTESCRxgSRijBoljlFf4+UX1ERJfEP0dSFG1JCEoBgFDYprFDfACGFzICqbCgMDM8Ps07P2Wt8fzVNT1V1VXdVdvc75XVdfSk9VdVV33U+d5zxnQX8Dc7lB3mw286UbhA9tl8uF6swL0W0pwDel8/lBXhiLczBrOt4+4w9BQet6xkeF2/qMLb8FGkD2w//EVbUPAbv+FjT2sar8obwR0dJ8YHb2QNa88G/s+9ZL8xkCz2gsNO8vcxI7zYcy7IRFx7Vq/ljRbLxY+P9wIHOa5OfqoXu9NZ+xfx1m7rkNJbXvBNXnVav5eKLZsLv00kuxYsUK/t8GgwFdXV148MEHcfnll+t5bikLi39QG4w5rOkjjG54C9+UztfUYkoqvkXtgODxeCIerKOFXOwNIG3Yscr+LCBZK92Vt6DPkAGzz4kG63BRlXKz2YzBR19BhrtFcnlRj3ZRcsHiDPf4xZJlGKIVTG61WoMy7RgsJk5rKzR2rjabLeKq9cLWZ0ajEePde7Cw/uGQHpTsnU8i29uGsSdfCTpetrcNpd+uC7rnWFX+UN4I0nxkaNU8+7710nyPwDNqMpmirnlhmRMpYq15pb604Woe6E+yycrKSijNZ1avQoarGeOa/xW25uOJZsPuySefxJYtW1BRUYG+vj786Ec/wvDhw3Hy5Ek88sgj0TjHAQ9bkgk141aThi43IKhBTdNrPWExRtHoBckCzwOvhc2UhQNCT8UiuI022HzdKHXVBFUp7668BT3WQsnlRaV2UWqRChZXAxs0pe6HaPfZjOReYeed8/UGLKx/WHO7JWHrM6PRiJF1G/lm50pwCscTllYQwqryS3kjIkGt5oHQD/NINM88IdFcVhSSqJr/6JwVIg1HW/NNYxYPaM1rDRvQW/Ps95Uy3qKleT3RbNiVlZVh7969uOeee3DrrbeisrISf/jDH1BdXY3i4mJNx9q6dSvmz5+PsrIyGAwGbNy4MeQ+W7ZswcSJE5GWloaRI0fiueeeC9pmw4YNqKiogM1mQ0VFBV5//XVN55UIMBFWHlkJs7cXLlOm7IxbGEOjNQ1dC1KFGuXQWjphWNNHQTMsPsZIp16Q+Uc24saOJ5B/ZGNQoVn2+SVfrkKWxIDAYsPkhB5uTSw1NbmkgsUjhdXVYt+t1FKM3PIM6w+pFNCs5V5ROke5IqQZ+9dh9hd3SS6FBbY+Yw/JUB6Ursn/g05THvYPuloUE8aCuFlphWgRjuaHNGwSeTv1hnlC1CwratW8/fA/cWPHE6J7nzTvp3XkgphpXmgECuvJCVFT+05PzUtNaGKpefb7JrLxpkRYdezS09Nx44034umnn8YzzzyDm2++WZQhq5bu7m6MHz8eTz+t7kY4evQoLr/8csycORPV1dW47777cMcdd2DDhg38Ntu3b8fChQuxePFi7Nu3D4sXL8a1116LHTt2aD4/vQnlURPGkTARlrXtgNXbDY8pXXbGzWJoot0MW6pQoxwejwc1NTXo6upSNdiPPfkKsr1tyNr5pOjz5BJC2OxbS5HSokNrYec6UHRobVCh2dENbyHb2waD1wUfDHCXVor2ZbFhQqGH8pQoxQUx8k4/OPO+WiMylpSWPvSAr6t1+rvV27BTe68ofYfdlbcEecqYhrL2/gUZrmZV2bXsIRnKg9JTsQjrBz2AI/kXRtSflcW5uVyupNc884SoWVbUqvn86qdh5zqQX90//ie65rX8nnLIaR7wF8oVFizWEznNC69FTvNmszmkYaen5oUTGlY8OBk0r0cNSD3QbNiZTCZcdNFFaG1tFb1/6tQpzQ+hefPm4eGHH8YPfvADVds/99xzGDp0KFasWIFx48bh5ptvxo033ojHHnuM32bFihW49NJLsXTpUowdOxZLly7F7NmzRXGBUjgcDtErGj8QC0oPNSh4vV5ehHV5UyQDqIWzYxZDo7UZttZlj3AKNWptEG4I+LxNFY9jf8bUoLgfNvsWxqCEmlU2jVkMhyEHTWMWBxWa/aZ0PjpNeeBMFhjBwdJQHfJc1Rp2SiViuifcij5bETxTfyEqQBptw47V1VLb+ForUveK1WoN6pcpLGCtBvZgdU+5XbQUxtoQRWuZSYhUHTiO41BXV+fXo+CeT3bNM0+I1vZ5WjQv5FjRbD6BIjBuLhE0r+X3lENO8+x6hAWL9SRemmcrcoxU17xeOJ3OILtELZoNO47j4HQ6cf755+PLL78M+ls02b59O+bMEd+Uc+fOxe7du/kHv9w227YpF0QtLy9HTk4O/1q+fLm+J6+AVHo8E2H1yCrJTDHhjcRiaAIzYkPNHNUue4RbLkFtUWMAODj4WnSa8tA5+X+C/iZ1X7HZtzAGJdSssnXkAqzOuVsyoJr1bDx19q2yHgqj0chnhumF1qD6UOgZB6l3ILZS0oUUbFlmTOM7Qb9rYEso1oZIiwdLrr5aKLxeL2pqavDtt9/yA7nP50Ntba3oPSWSQfNTt9+suW2XFs23Vt4OhyEHrZViD4/JZEJJSQlOnTolMpDiqXk9J1gDSfM2m01TX1rhUqzFYhGNF/HWfG1tLbq6uviaq1o1r5Xly5eLbBLW8kwNmp9QBoMBGzZswPz58zF9+nS88cYbor9Fk4aGBpSUlIjeKykpgcfjQXNzs+I2DQ0Niseura1FR0cH/1q6dKm+Jx+A8AaLJD1ebobY1dWFr776SvGGU1r2EBJuzSRhtprUeQrd/myQDfQMBPZSZLDZt9YYFI7j0NTUJDujVnLh6+lF09I1QEtvTD3iXBhKgdhKjGj5RNIrxJZw1Q7y/LLMoO+FXAbal30xnMZMmLx9qo0RNfXVQu0rNGDYQK+mUG8yaD7N2SSblSmHWs1brVY4zrwaq3PuDtKwnBeONC+NnpoP17CT0zw7ptoJsXAp1mKxwG63y373sdY80N8liTkbQmk+EpYuXSqySWpra1XvG5bHzmQy4Y9//CMee+wxLFy4EA8//HDUvXWMQOORfa7wfaltQhmddrtd9NI7EDmwZYuoFlAE6fFyg7zL5UJHR4fikgBb9gh0zXs8HjQ1NYHjOLhcLl0Kh4Yy7GJFqEE+Vih1DcjYvw6zPq/Cua7dMJlMIcudCNESBxktzmx8R9IrZLPZQsbmCWHxL2qyOQ9mTYfHlAartyvoe5LKetSC/fA/sbD+YZx//DnM/uIu1Z7rZNd8r61Ic1ZmqPOUiuuKNqT56COneaDfsFPj+EkUzQN+T+hPGh7Ed7+6PWrFvZWw2WxBdolaIlpTuuWWW/Dee+9hxYoVWLw4+g1yS0tLgzxvjY2NMJvNKCgoUNwm0IsXa9gg393dHTTY6ZEeL4dcX0gWayN1w3q9Xn6Q93g8ioVDGWzpRmuBSKXzZn0YlRpta5nZxgq5yvPCwGulrgGZ1auQ7mzC4KOvwGw2ayp3Eu+G1QBwuPi7qrxC0fjcwKU6oL8mmNQDVU4fQlgduyHtu1SXIAHELbpcLhccDgev+2TQ/NYJKxW9Y9HSPPP2yRmppHkxpHltmgfUxYGObngLaVwvbN7usDt8xAvNht2wYcNEM+4LL7wQ//nPf3DixAldT0yKadOm4YMPPhC9t2nTJpx//vm810dum+nTtaelRwOpXpxClLKuwqnxJOcqlquTxeLplJpfB+J0OmHc9kekOZtQdEg5zsPr9SoaasLturq64PF44HA44PF4JJcytMxsowlbMrZarbLLbMLAa6muAQxWNZ89APQsdyJ3f+kZW3O04CJJr1C0OVpwkWipjs3auwvOkY2hUrM0w+rYncidJOm5Hte9Hdc1P4IRLZ9IdkEAlL1ppPn+7bq6uuD1ennds/gx0nxk50maF8MMO6VY0G9K56PPkA6nRNmhs3p3hNR8PNFs2B09epT3jjFGjx6N6upqHDlyRNOxurq6sHfvXuzdu5c/9t69e3H8+HEA/jXm66+/nt9+yZIlOHbsGO6++24cOHAAq1evxt/+9jfcc889/DZ33nknNm3ahEceeQQHDx7EI488gg8//BB33XWX1kuNOS6XC11dXSgpKZEUm1zgs3Cmqxa5dkUsnk5L82uXy4WvS67wz0YLzuHrRknh8/l4TxzQH2yt5tz5pYzP/8wf43j5D9AZRiFPOVh7JKmHEIsjkfJ4sGw2q9UaceV5FlyttzcnY/86fGfXEoxs3Rx0f6mJpwt8EAxp2BS1YrJqYA/WomNvSRYyLjr0on/W3vKl6sxOo9GIkpIS0eSV1bHbPXRJkOfafvif+I5jI+y+dpzZ+I5kF4RISFXNq41LOrPxnYTQvNQ9niqaDxV2JNT9QNE84PeEPl+6DO+c9bRI88OaPsLMzjeipnk90C29Ly0tDcOGDdO0z+7du1FZWYnKSn/9oLvvvhuVlZX4zW9+AwCor6/njTwAGDFiBN59911s3rwZ5513Hn73u9/hqaeewlVXXcVvM336dKxbtw5///vfce6552LNmjVYv349pkyZosNVRhfh0o0UcoHPwpku4J9NCwM8pRCWFRDCyigcKJwnu69UIVI2G81s+YKvG6UGJorAfnxSsKWMtrN/io6ODrjdbuyzno/1gx5A71k/1GX2ydoqeTwevjYRy7hmcSSh3PLRXGYD/IP11O03a86CC2xEr6ZTiZDAQrgjT24Mq5isVDFqNQSeL3uwFhx4QbKQccc5N6LPVoSOc27k37PsW4sp22+Ga9tzcLlc6OzsFA3IRqMRpaWlohIUSuR++XcYwcEHg2RnCjUoeQ1TVfOhsncZbKkt3poPdY9HW/NA/3KvFt1HqnlAPOlLBc0Heo+1an50w1sRaz7aqDLs8vPz+azTvLw85Ofny760cOGFF4LjuKDXmjVrAABr1qzB5s2bRftccMEF+Pzzz+F0OnH06FEsWbIk6LhXX301Dh48CJfLhQMHDqiukxdL1C5PCJELfA6EZe6oMZYCYWUUvs27QPH4cvEJwrpRobwKWsuoKGXFWSyWsAd5l8uFktp3sLD+dyg69pbofeEgz8eRlH0vaHAUxgRKocYYU7s0EjhYqyWwET1bJgo3UejI4AVhxdWwwrBaM0IDz5ctzfcVjZds+eU482r8Z9pfRfeLdefTSHc2oejQi3C73UGGnRD2mynFcrWf/VP0GdLhMqSFPH+fz4fOzs6k1DwrPqyX5tV6fAKX2kTHiqXmBy8I0mcsNQ/0Zypr0T1pPljzLLRHCvabKRmg35TOR69KzccLVSbqk08+iezsbAAIWeiXUIdweSKWGWJKsDpYkbiUW0cuwKtHszF75Gx4T1ehl8vmse58GsbTHrBvcmcpHtd++J+YVb3KP6CMHg3AP7D29PTokpFd0fo+srztsH67DkirktzmaMFFOFE6B1arFdMDBkehoS71e2ZWr4LZ2QTfzqdlg5zZzLizsxNA/6DPssnYg6wPP4d5+1PA5NshHFpY/a+2tjbJ4/dULEK1qRITx09U85WE5ETpHBzJvxBWqxVDNex3pOx7GHFyI7jzf46sCD6fLc17mvbhtTGPwmq1Ih0suP5Z9B7+OZAu9tS7Jt8ObuvjaM08A3MP3IM96bPQgaskj89+M9OXfwfy/OEewhprgP9BkrbrGWSfXpY5kDkNGRkZksfjOI437Aa65kee3IhvJtygeNyxXdtQeWozaoZ8n9c84Nea0+kMKlquFa2aH3paj4DfAIyl5tlyLz59AhBkv5LmtWu+OvNCANLtAdlvZq5eBYx5FIDfo1dWVsZ/x8eKZmP4idf5pVglzccLVR67n/zkJ/xD7Cc/+Ynii9APFs8Qq1RrYXmCUW1bcFPnCt0y3gD/9cw9cA/f648tAakpo5L75d+DWij5fD50d3eH5aUQYrVacaTsSnSa8lA3KryllFBLDYEzZ7XnJZzNs0Gem/jToAKnJpMJw4cPx/Dhw1UvKcSLk4Muw7/Pfw7cxMhipPgswwm3igqZKgXXM+9UfvfXyHS3oLLrk6BtGOw3E8ZymUwmFBYWipZBq7MugsOYiwMFl6GzszOi+3GgaF6Nx0euAK3P54vYsEs2zdtsNn65l+meNB+e5pVakgUmsQBizTPvbHXmhbppPhqoMuwC21oovZKVSZMmoaKiAitXrozK8TP2r+Pr6oSqNcXg4xnq3tA1MFP48JCrWn5O4+vI4TpQ8uWfNR1b2HQ7kJEnN4qExQQHQDT4S9F+9k9VPxCGNGzC3L234qKdN4quK//IRtzUuUIy+48VSG4aFl6tvlBLDcJq82p6rWpFqdWRluUeqTgevavRa4HNljMzM4POQS7LUE2piG9K56PbUiDZ4J3BfrPAZUCWsck0eSBzGl4s/H9BS5msLIfti3+oXiYdKJo/UTqH309uqXtf9sXothSo1vysPbch96NfipbSSPPqNBuo+1TWPGtJJoVcEguLf2dLuF+lT5HUfDRYuXIlKioqMGnSJNX7qDLscnNzkZeXp/hi2yQru3btwv79+1FVJe2Sj5TM6lXI8rah4MDzcDgcqpMFui0F+DzjAn57qfR/rbCHx+iGtxSqlhtE/1VbdkHYdFvqepymTFh8Tti++AfvKRjd8FbImZTjzKsl+xyylj9C8Y88uRFWbzes3i7RdZV8uQo5XAfOO/Wq7pldrO+kmqw4Vqg3VrNsLR0kpOJ41GbPZexfJ5mpFglskLfb7ar7S6opFXGsaDbeH/eYqMG73jAvQva+v4ZMbGAkkuYBdTXjwtG8cD+5siUHs6bj/XGPSWreZrOJCpuzJbq0b98TlR0hzatMjArQfSprnrUkSxaqqqqwf/9+7Nq1S/U+qgy7Tz75BB9//LHii21DSNNdeQu6THloGqO+iOSJ0jlBDx82KIfTiojBAmC/KZ0vW7X8i+IF6DDk4NTZt/CfqyYbqrvgHPhgQHfBOZLX4zGmIY3rQfa+v/KDfOBMyrJvLWZ/cRfGdW8PeS0GgyHIsDsyeAFcpky4TFkB1+V/sBo5t6bMLrPZHNS8PhC5lmixQM/ZNSvbEGr5iHkgRrR8zHt/snc+iWxvGyoaNkR8HtHG6/Wis7Mzqh1ztBSZZSSS5gF1NePC0TzQn3TRfvZPNWneZDIFGXZsia5v1GUBS2mkeTWo0T1pPnlQNX244ILouxtTnZ6KRXi/Ng8TR04EmnZo3p/NYo60fA+j6t6EK2CWyP5utVr5OIBx3dsxsXmrP/gY/bMUFgDLqB88D9PHK89ivimdj9ENb+Ho4AVQyn3ObPkCRnDIbPkCKA7+++Hi72J0w1voEzzsjhXNxje5s9Da2opR6A+wnuDbgn8Zg9PJ/S2ensUhz+XYYxgv+ptl31qMPLkRBwdfG3Rdp86+FVl7/4L27DNR1HcURwcvUBUAzJrXR6MfoB6w2TWAiM/RPX4x9ngqMHH8RCjlfPEeiI1vIt3VDN/Op8GGS6PBKLvkxB4OdXV1EZ1nuLAOEAaDAd3d3ar7W8sF8kvBsiVbzrkS/zlVgplnzgT279d8rvHWPOA3TtN3P4teBeM0HM0D/UkX88+cj4I35vOa32q6NugYTPPfcPNxtEC8fM40f2TwAuTPvgeHDh3CmDFjgEOHSPMqUaP7VNG82uXwYU0f4cJTr+Oo5fsAKhS3DZUhHWvCrmPX09ODgwcP4r///a/oRYTGaDSiqKhIdTN0oL8x9slBl0nGGBgMBpSVlYnc1pVdn0gGH6thXPO/kCNYXlFbdkFY+kCKowUXYf2gB0Quc5/Ph66uLn4mxQdYl10pKULW4kmqoCortjq6/k1R1vHw4cPROeYa/C37Lvxn8M/4a2HB40pL48L4GK11oMKpG5VMME+Ja/Lt6Jr8P34P1cRfyA6esV6SCkRNP1Up5AL5pfD5fHzNNYbJZEJmZmZSaR5Qt8QVjuaFLcwA9ZoPrFsG9Gt+xMmNfAcA0nz0GCiaH93wFrJ97araiTHNJ61h19TUhCuuuALZ2dk466yz+ALDwkLDhDLhGHbhUJ11UVDwsdog3gOF89ChMFjL0TpyAVbn3A0AqpdWWLFVNtCyAGu53rSsxZNUQVX2gDhU/F1eaGx2K1y64beXaaguRGqQt9lsfDFTjuNQVlYm+XsqBTirJR6N09XCgpnd4xejp2KRbm2QIsFisSA3N1fy91aCfc+537wmCsC3WCw4XHQ5eiQC+S0Wi6oG5yaTSXUj9EhIJs0LDTu1mpcqCCvMrmcdAJhhR5rXn1TSPNsvUPNWqxVNY65DpykvqGqDyWRCVlZW1LUcCZoti7vuugttbW34z3/+g/T0dLz33nt4/vnnccYZZ+DNN9+MxjkOeIRLLlo4kDkN7497DMeKZvNNwdnsKdQg/23eBfhb9l1oHbkAgPYWRkWH1iLD1axYTiJcWIsnqYwk9oAIXK6JFKmHIytmyjwn0TLUE3mQT0QCB3n271DfH/uec75YLQrAt1gsaB5xJT46949BHmtm2On92yeC5gH/Pd7X16eqtEgsNC+l61BGYbiQ5pOHcDXPtgvUvNVqhXX6Eqwf9EDQfcUMu2g7ZiJB85l9/PHHePLJJzFp0iQYjUYMGzYM1113HR599FEsX748GueY8rhcLrS3t4tKoghhg0i4Ivd6vaipqcG3334ragmkBZ/Ph56eHtk+toE0jVmMHmshGqzDMfuLu8LK6GPFN6MhIK3LJeEsJ4Tb+isWxLOcgRTMEyK8P/V6uGkx7IYPH46+838eUd/PUW1bsLD+YcV6cEzz1v++KNmJIRE0z85DLXppvry8XLPnRcuxSfOkeeHn6an5SDLX9UTzE7O7uxvFxf4I2fz8fDQ1NQEAzjnnHHz++ef6nt0AgQ3yBQee9zcwrl7FzxYtFgtycnKCblBh6xPWGFnpJlbqR6kWLQ+b1pEL8NE5K1DqqkGGiow+qbIlJpMJZzr+jWtP/lax3IJaLBYLbDabZNwM+w7T09ORlpamy4NFTeuveA22assZhIvWh6hUmzqlQT4adcHYd8IKQMtlO/oD+R8WFREe170dCw7dhZ80PIhzGjci29um2DuVad7+37/xhbcTUfMWi0W1HsLRfGB2K7tvcr7eoEsZDdJ8P6T5YNhvoUbzgWV/pDQfSea6nmg27MaMGYNDhw4BAM477zz8+c9/xsmTJ/Hcc89h0KBBup9gqpJ/ZKPIO+fz+XCkbAFfF4nNFq1WK+x2e9CNzgaQzOpVfGNk4TbDmj7Cj079Xtf6QkI8Hg+/1CPHsKaPYOGccJkyQ86EjEYjxowZg6wsccMZNeUW1MIGeSkPoNFohN1uR05ODkpLS5GZmRnx56mpPM8GlmgNtvEi0p6UodAjIPus3h24rukPmrs8sED+s48/z+u3susT2Hw9SON6AXDolChtNKLlE9Gs3ufz4Xj5D0S9SAeS5i0WC4qKiiS1llm9SjZZQguk+diRLJr/0anfa3YUsOdQfvXTmLXnNoxo+URS8+F6/PQmrBi7+vp6AMCDDz6I9957D0OHDsVTTz2F3//+97qfYKpSdGgt750D/IP8PstE1XWR2ADiLq2UXMphGT1KAyPLugtnBqTGGzC64S2kcb3wmNLh9Xrxnd0/l32IspiiwEFBrhZYuAkoY7u2Ye6Be2QLlap14atBWHme0I4Wz0Y493Jl92bVWW9C2s/+KXwwwAgfr9/qrIvgNGagz5COL4q/j/WDHhDFqgHAmY3viGb1Pp8P+6znq8o2B5JP8wAwc89tKKt7T7J2mJLXsbvylqBkCaPRGFZoBmk+eYiV5rU6CthzCADSXc04s/EdSc3Ho6ahFJoNux//+Me44YYbAACVlZWoqanBrl27UFtbi4ULF+p9fjEjVi3FWNxN05jF6Dpt4bOaSUo3aGAmFxtALA3VQT1UAaA18wz4YEBLpnzNLSaMwBnQsKaPcMXXv8K5rt3hXexpvimdj05jLr4pnY/sfX9FprsFY5veVbUvaxEEQDLrihl2WjOTtJStSEYSLY4mErQsHZnNZtG97PF4+NIXclRnXsjfn1pwnHk1tuX6PW1shn4gcxo2jlmB50uX8Uk9zCvPvAOHi7/Lz+oHguYzq1chw9WMitb3VXXaYZq37FuLnopFQckSRqMRpaWlmo1S0nzyECvNaykaDvSX/Wmt9GdgHy7+rqTmo0HUWoopkZGRgQkTJqCwsDDSQ8WVWLUUK/lyFa6ufQiA32DpqVjEL70ozUTlUvS7K2+R7KGa3/01jOBQ4vgSF+27A+WnPlB1nl6vFyPr3kCmpxWTnP9G/pGNmPV5Fca7dmueKR8rmo2XSu7DsaLZfLmC5oxRWFj/cEhXOGsRlF/9dMiWRlrQ0n8ymmgZjLVsG+04GjWwxuWxftAIvyev18uXvpDjq/Qp+DzzQoxueEtzsPvBrOn46JwVijN05pXP/fLvGNKwCWc2voN92RcnjebPde7SvOwl1Hx35S3+ZArLMFXLX0zz1p1P69qqijQffZJJ8y+V3AcAYSW5sNaWelddUCJqLcWEcByHV199Fbfddhuuvvpq/OAHPxC9CGlYSzGAQ1aIwGot9FQskuyhymbOAJDlacUZp95WdTyv14vPMy5Alzkfu2zfQdGhtUh3NmFo7WuyDyHLvrWSS0NCWLmCwp5vka0iZo4VwQSgW4wdIN9/MtYoDcaBg3oiDNxaYIN8rM9X7mGo9JCc0L0ZGZJ9U8X7qw3aHte9HVd8/SuM7drGe+Xbz/4pRp7cGLIfslpipfmSb16SfVCr0XxPxSJ/MoX7mKrlL2HhW71i7ADSfCxIJs0D/pg5NUkuobzqgFjziYLmKMQ777wTq1atwkUXXYSSkpKELtKXSLCWYpfm1SLnv39Dx5jFQJt4mxEtn+DShrfg298JDPof1cce0rAJI09uhCHzl8B3/MuXx4pmY7t7HCZy+zCm8R18I1HYU44DmdNQW3IpTp06hXGjxqFg//PoPPunwCnp7VkLsDNOvY1vzTcrH7twHsY0vcu3FxrW9BFG1b+J6swLAfSf44nSOThROgcTfHuDWhr5M5Sehds7EcPr96A17yewWvUZtDP2r8PUnSsBs7/g6tTtT/j///T3qoZIl0aE7YKIyGG/RyBn9e7gA/19k2+XbaXEDLu6ujoUFRWhublZtt9kZdcnyPS1Y3znx6gZ+RY+aCvHzDNnorGxEcNPvI59mRdiVMA+w5o+whkNb8GQ+UvVsVmx0DyUEgA0aL4680JM6N4s0vzohrfwTel81A/uLzLOND99/HQ4nU4Yt/2Rvwamee7TKRhUtxsH8ufCav2+6utTgjSfeihpfkL3ZvQNnQqvxwOE0H1eXh6veblwAqHmu/S7hIjQbNi9+OKLeO2113D55ZdH43xSFrfbjb6+PjQOvQIftJX7e8bu2SPa5szGd5DpbYOnehUwO9iwY/ExbW1ii5AtYfh2Pg1857bTDbUfx+60mfh28DzsMYxHUUERMiWOFWogah25AF/nzER5eTlw6lMAbLb++Omljen+DLBPnwCm3xnyeN/mXYC95gm46MyLgG++weiGt5Bx2pMhJQrHmVfjndP9Nk1Hj6KsrAx579wJs7cN3ImPYeB8SD/6Csy2ZZKf53a7UVNTo5ixPaRhE0ac3Iijgxcgs+ldmJ1N/u8SgJH9f4hB3h9D+Ud497fBNvt//O2MOjsV9yGii1z5hbFd21DZ8AlM3l6kcb3oMRXCO36xYm9cwB/TU1xcjN27d4sGedZVwmg0ojrrIkzs2YJ9WRch47Tm3W43TpTOwaHsGXw/ZCGjG97i9Rto2MVT8xPHTwS6/Kq0H/4nZlWvCkvzX6VPwcGs6bjkzEv6Ne9qxuiGt0SGnZCeikV452g2CgsLcWZ5eb/mj22CgfOhovV9eKyPSO7LkjxGjQr8pvshzacmajXvbtqHz6b9NWRPbDnNs/JcgZqXv+Nii+al2JycHIwcOTIa55LSuAWDPBBc7gQQB1dLERgsyhAuYQD+2XRgBfjAJsVybW/UtD5ivRlZMLJ7/GI+E8xsNvM1oVj5BblMWK/Xiy9zL0W3pQD7si+W/Tzh9ZeXl6N7wq3+Ja4hF/MJKHIww04pk2/kyY3IOH09wnIFrsm3i0oXKM3KWQxlotQxkkLvIOto1JUK9zykrkvYCkrI+M6PkelpBQcoJk+43W60t7cr3jvss3Nzc2EymXAgcxrePuMPOJg1HR6PR6T5wHInjG9K54v0KyRRNJ/75d911XyPpUBV0gr7DZnmu4bNkYwvDPyMUNm7pPnwj5cKmpdLnlCjefYZUppPFDQbdg899BCWLVuG3t7eaJzPgCGw3AnQ3yxba8q0sHcf4O+d2GMtRHVWf4CnsEkxK44aePNa9q3FRXt/gbP7dipn67GG3RKDq9Vq5Qf5UE2UvV4vqk2VeHv0ck2iYP0JewrPU72PEkcGL+BriQnLFQgfXoBy3AuLoYxFHaNwB2u943bCrSsVjYeNluval30xus352Jk1Fy8W/QrHimbzxVKFNdrUGnbsQTei5RP86NTvMapti+S2geVOGMeKZov0q4ZYa7797J/qqvn3Trc9UwvTfOPM3+PI4AUYeXJjRN0dkk3zQHi6Ic37EWr+pZL74Djzasm6jGo0zyZbajQfLzQvxV5zzTV4+eWXUVxcjOESTZap+4Q6msYsRs5//wZv5S2RpyYH4B6/GJvb/DFBuRJ/Fw7yQqGxuJnRDW/hwKhpisff1u13Og9VOI9vSudjxInXcbR0PqRKfzJPQbizv6JDa2FVWLpWy4nSOThWNDuigYfFUF58xsVok1j61XNgS/Z4HL3OP5zv1Gq1on7wPNRjHpqamsB8VMywKygo4Lc1m82S9c2GNX2EC0+9jqOW7wO4kDfuhu9+Bxm+doxr/hf2lk4I+uzDxd/F6Ia34EtCzTvOvBqfG88DoF7zRRJ/Fy5bh0vgMnQ4JJvmgeTWfSJpnj1tmGe3vLyc31ZR8/Ub0Xe4BUifolrz8UKzum644Qbs2bMH1113Ha666ipceeWVohehTNGxt4LKnSjBajvFogcd88Rpreslh7D0QSD2w//kPQVqBnmpdHphLcBI0doOJxDWCofjOMml32TLcksG5L5TpeUiYVeHrKws5ZADmfZGgV4p5sX4ZtD30GnMxYFCcdxY/pGNfE1GNR75gaB5NZM5VrQ88PsPXIYOF9J88qGH5pWeN4qaF1RnYJ8np/l4o9lj98477+D999/Hd77znWicT8pT9u062LxtsB5aCxTfp7it1WrFGafehtXVDEv1KuD8Z0V/ZwUZvV6vLjEPzBPncrlg7OsL6uOoJ7lf/h2W056Cb3Jnif7mcrngcDhELX4sFkvQjLh15AJ80FaOuRVzkRNwfNYuKJL2M1qQGxCI2MMMrcbGRtltRrR8glH1b2JP+ix04CpNxxd6pUYI3mdZqbm5uYAgiL7o0FpYT1er31MyXvHYA0XzgYaflOblutEIs2cDA99NJhNKSkqCkk2iAWk+cdCieX8FhtAx3UK+KZ2PESc38pndDDnNxxvNHrvy8nLY7fZonEtciXbnCUbdqEXokugjKYXNZoNv+p3osxVJeqXkCjK6XC50dnbKpmerGZBMJpPkIO92uyWLpqpB2AaMxex8UzofRqNR1FrI5XKho6MjrM9g515eXo78/HzxspOKorADnVSqYq/E6Ia3kOluESUbqEXJKyVF05jFfLX6UCSi5n0+HxoaGsLSo8lkQmZmZpDm2d+Yx0wPzTPvnjDZhDSvjoGge6b5cGpJHiuajfWDHgjqgBQLwuk8odmd8fjjj+Pee+/Fc889l7Tr/VLs2rUrqgarxWJBWloa2kZ9H1u6R0mWO5HCPX4x9ngqMGbMGODQIVUCZIO8XK0tNsgDQENDAz8gCpcSAj1erJ8iAN6wk3N75+bmSs762Qzc4XCg96xL8LnxPLhcLoxkdbwG/TLsmBkhLLg1sPRAVlYWzj77bD6uwmq1gtv1N1HploFOJLEwmZmZGDt2rC7N1KMFK9XTknkGOI5Ddfqs0DtpZFTbFoxpehdt+TcgLa0UnWMuw5dpk9Hd3Q20tobcP1E0z/bLzs72xyaZTJo1z/rBut1u9J41l9c8X7vP/kvYKipCfiehIM1HRri6T0bN78u8EPLFr8KDaV5rDVo1VFVVoaqqCg6HAzk5gWtT0miexlx33XX45JNPMGrUKGRnZyM/P1/0IqRhhl2kyxx6zqxcLhdOnjyJQYMGBS13BDboZoZdqPPPysrCeeedJyt0qeOwOl6sCjibZYez1MS+n+xDr2Lq9ptFcUrMXS/8b2DpFkIbwvvRbrdj6tSpCe3RZ793fvfXeH/cYziQKZ8wEC7jmv+FbG8bSr95Kak1zz47lBZDad5kMsFut5PmU4Rk13w0ypIwzSdK6RvNHrsVK1ZE4TSIaMCWPgfXv4fKps2nSyGoq0avJbCYZdx1dXXB6XRi0KBBiunigXxTOt8/ez9dBdxqtSrOTJQ8BGzm6XvtORidTTBLxCmJzn3y7eC2+mfvStl+Ulj2reWr1GspVZFKJFumnmvy7fBtfRxf5l6qadlPi3HFuqs4JLrLRJtYaR7wx/sdOXIEGRkZGDp0aEw0LxUzS5qPLaT5YJjmfZW3BMV7xwNNhp3b7cbmzZvx61//mooU64zX60VXV5fsUko4GAwGFBUVYXjnJ8j0toVsecLiXKxWK5/1w2Btd5zeKgAVQfu1t7ejp6cHtbW1opIRajhWNBv1g+dJBkNLoWTY8ed0ujK+M0TGrNrSLZLnsfNpvkr9QB3kkw1RWRCZeDQp2MNMTWcB1l1lysgpiuEWXq8XnZ2dyMjIUH0eodBT80D/MtbXpfODYgq9Xi+OHz8Oq9WK0tJSTecZruYVl6NJ84QEsdT8dyu+mxCGnaalWIvFgtdffz1a5zJgsexbiwv3/gLDmj6SDX6OhH3ZF8NpzIDF51QsocAy06TOIbN6FdKcTapdzSyIOV69hFmhUa3FnrUQWKWeCB+/J+TmiIrO6kUsAsmZ5oc0bEpYzQP9y1hyBYdF25LmCQ0MNM3HEs0xdt///vexcePGKJzKwIW1A5rQvTnsY7Bii8Iq2oyDWdPhMaYhjesJOwaAtd1RWzPOZrOhrKwspbPRAqvUE+Fj3fk00pxNfMxVPGEz9WgO8lItwLQSbc0D2urckeYJLQw0zccSzTF2o0ePxu9+9zts27YNEydODAqYveOOO3Q7uYGCa/LtMH7yMCw+Jyq91bBatadUS1XRFiKMAQhn2O2pWIRqU6U/U++//+3Pasv8JTDq+7L7sUzYcAPIWbJFMgou1WaB0YRvKn865iqZYdmloUIFmObHu3bjqF1bXS0g+poHxHXuhJpXMmzkCgtrIVlrxJHm1ZOKmk+U312zYffXv/4Vubm52LNnD/YExI8YDAYy7MLAPX4xTFsfR4a3GWe3fwCv9f9C7sPiYWpqalQFhApjALJ0OGeW1ebb+XRIw66oqAjcrr/hqtrn0Xf450D6FNWfk8yGXbIFGccTVuJj4viJMRvkjUZjWC3tWPbo0KFD+fvSarVi6NCh6O7uhsViQXp6uqJhJ9T80NrXUFs6J+TnJpLmQxl2RUVFOHXqFAbXv4eRdW/i6OAFwLnnqv6sZDXsSPPqiZfmc3JyNDsamObT09NFhnug5hPlftU8kTt69Kjs68iRI9E4x5Qk0GD5pnQ+Oo25skseGfvXieIRWPq+3EPJaDQiKysralXkvymdH7Ktj7B2VtGhF5HtbUPe6ZYsBBFN1MTvhNur2GQyIS8vDyNHjuRLhthsNowcORJ5eXmKmhSWE/mmdD46TXloD6hmz0h2zdfV1eGMU+8gg0qLEDFAreZDedOV9svOzuZbmqnRfLyIKBiC4zhdszhTmcBMzkDDLlQ1e5a8EBiPwCquB95YBoMBdrsdBUffwML6hzGqbYuq8xzbtQ1zD9yDIQ2bFLc7VjQbWyc+ozhzF17z0dP9Hbsn3KrqPKIFLZUMDBIhfoc1FGclOtjDQah5pWr2ya55s9mMvvN/jl5r4eliwPGBND8wSATNJwphGXYvvPACzjnnHKSnpyM9PR3nnnsu1q6Nf2ZLJES7pZiaEh1KsOSFwNkyq7geOMizOJe8L/+ObG8bxjX/S9XnjO/8GJnuFn+/Sh0HwhOlc7B14jOqM9YibdAtBzXmHhgkQvZipMuJya55wB+bu3XiMzihYqmZNE9EQiJoPhqE01JMs2H3xBNP4Oc//zkuv/xyvPLKK1i/fj0uu+wyLFmyBE8++aTWwyUMu3btwv79+1FVVRXVz1HbwSGQnopFmrKx2CDfN+k2dFsKcLDoclX77cu+GD3WQvim3+mv0i4x22X1t1icjxajVe3s2Ww2o7y8HFlZWUHbs7p5brc75OcFLmcRAwO12YtajQl/XbfbQnq3pD5HyhhTItE1r7QsLETtd8w0L3UOpHkiFFoylrXcv+FqXi+qqqqwf/9+7Nq1S/U+mg27P/3pT3j22WfxyCOP4Hvf+x6uvPJKPProo3jmmWfw1FNPaT3cgIGt/+d8vSEiz51WuIk/xb/Pf1Z1w/KDWdPx0TkreHFIpYHrZdgNadiE2V/chWFNH8luLzXb1jLIyy1nEQSgbHRIxeyEakclNOCYgZGxfx3vZZPqnKA3emleqDmfzyfSfKh4PyHMYFOrealzIM0TesIMu0A9Rqr5REGzYVdfX4/p04N7rU2fPh319fW6nFQqwtb/lWpKhVsmQM3sY0TLJ1hY/zAy9q/jb16lwqWxYOTJjchwNWNM07uaRMEMyYyMjJBLXXLLWUrHZoanltgciuNJPoxGI29wyA3ogQYCq+smFzMmNODUFvW2WCya752BrPlQ102aJ+SItuYTBc2G3ejRo/HKK68Evb9+/XqcccYZupxUKsLW/1mBX6lBwWAwoKysTHMsSODsQyq258zGd/gmxWqMTCVMJhOysrIinqEcOZ1Q0Xf+zzWJQothp2Y5S+i1EXoKtMTmsG0zD6ynZaAEh2XDMt2wxvBSA3qggeAev1h1zFhgUW85Q4AZdlp0H2vNs4zbeGs+KytL0tMihDRPBBIrzScKmk3MZcuWYeHChdi6dStmzJgBg8GAf//73/joo48kDT7CD6vZM2bMGODQIX6QB6CpebYQtjzhcrlEA7rUIH+4+LsY3fAWfJW3+Aet0z0VPR4PamtrMWrUKNWfy7L7Qg3yoWa0J0rn4ETpHJxbcS5w6JDqz9cbYWxPpAh7SeI7t+lwdoTeSJU5kSqWqrXOVuD9LirqTZoHQJon4kOsNJ8oaPbYXXXVVdixYwcKCwuxceNGvPbaaygsLMTOnTvx/e/LF6ol9Me89wVc8sVdMO99IeS2RwsuwvpBD6CnYpGopyKrXs8eFDk5ObrFCkS7TUsiiipVM7NSHS2B13JxebFoSzTQNQ8knu5J88lJsmg+HMIqdzJx4kS8+OKL2LNnDz7//HO8+OKLqKysDOsEnnnmGYwYMQJpaWmYOHEiPv30U8XtV65ciXHjxiE9PR1jxozBCy+IB7g1a9bAYDAEvfr6+sI6v0Qms3oVsk4vtQgJt7my1WoNOSvP2L8Os/bchvJTH6CjoyNsz4MSas+fDfCJVMaAekmmPnp6e7QSD82zhIdE0DyQeOVLSPOpTzw1Hw5x7da8fv163HXXXbj//vtRXV2NmTNnYt68eTh+/Ljk9s8++yyWLl2Khx56CF999RWWLVuGqqoqvPXWW6Lt7HY76uvrRa+0tMToRqd1tqm0fXflLegy5fExPPw+Kgs1MiNNSxp3ZvUqpLuaccapt+FwOMIe5JWCv6nQJJFKJLvmWcIDaZ4gkgPVhp3RaITJZFJ8ac0KeeKJJ3DTTTfh5ptvxrhx47BixQqUl5fj2Wefldx+7dq1uPXWW7Fw4UKMHDkSixYtwk033YRHHnlEtJ3BYEBpaanoFQqHwyF6OZ1OTdeiFq1eJiVXb0/FIvyz/KGgor9qlwaYkaal3U935S3otRbicPF3Ve8jBSuXIHXP0NIGEW2iVQxXimTX/JHBC9BDmieSnFhqXg+cTmeQXaIW1ZbY66+/Lvu3bdu24U9/+pOm9mIulwt79uzBr371K9H7c+bMwbZt2yT3cTqdQZ639PR07Ny5E263m6+j1tXVhWHDhsHr9eK8887D7373u5BLxeXl5aJ/P/jgg3jooYdUX08iIQwAVaK78hZYdzyNI4MXYKjKY/dULMJ/PBXo7u4GWlsBsGWUJ+D0VgEm7UvygR6KeDSHJgYGzGtUV1eXVEsroYim5k+UzsGR/Av9NeROax5ghVsfP10GIrgElhKkeSJWJKvmly9fjmXLloW1r2rD7sorrwx67+DBg1i6dCneeust/PjHP8bvfvc71R/c3NwMr9eLkpIS0fslJSVoaGiQ3Gfu3Ln461//igULFmDChAnYs2cPVq9eDbfbjebmZgwaNAhjx47FmjVrcM4558DhcOCPf/wjZsyYgX379imWY6mtrYXdbuf/nSw/fiQwIw2A6kFeCpYVZt35JKbCCpjv1pQdJswW1Au1y1+JFohNRBebzYaRrZsxctcTQJq2+1QtiXxP6aV54LTuXc0Yd3Q1XPtGkeaJhCRZNb906VLcfffd/L8dDkeQA0qOsGLs6urq8LOf/QznnnsuPB4P9u7di+effx5Dh2ofKgwGg+jfHMcFvcf49a9/jXnz5mHq1KmwWCy48sorccMNNwAAH7cxdepUXHfddRg/fjxmzpyJV155BWeeeSb+9Kc/KZ6H3W4XvWJt2A1r+ogvJhovwm2dwpZROCBh4mTUZislWiA2EX2iHc+l9t5LZs0Dft37YIQRPtI8kdDESvN63lM2my3ILlGLJsOuo6MD/+///T+MHj0aX331FT766CO89dZbOPvsszWfdGFhIUwmU5B3rrGxMciLx0hPT8fq1avR09ODmpoaHD9+HMOHD0d2djYKCwsl9zEajZg0aRK+/vprzecYS0Y3vOUvJvr5n1FTU6M5xk8pq8xkMqGkpARGo/LPHap1ihwsK6xr8v8MqDgZmvknJ4kSz5XMmgf8uj8w4kb0Wgvj/l3GCtJ8cpIomo8Vqg27Rx99FCNHjsTbb7+Nl19+Gdu2bcPMmTPD/mCr1YqJEyfigw8+EL3/wQcfSLYsE2KxWDBkyBCYTCasW7cOV1xxhewAxnEc9u7di0GDBoV9rrHgm9L56DTloe3sn6KmpkZz5pnSjMRsNqO0tDTkIK/UOkXNgKa1aXmyQzP/5CRa5SmcTqcmAy3RNQ+Ebl12onQOtk58hjRPJDSJovlYoTrG7le/+hXS09MxevRoPP/883j++eclt3vttddUf/jdd9+NxYsX4/zzz8e0adOwatUqHD9+HEuWLAHgX2M+efIkX6vu8OHD2LlzJ6ZMmYK2tjY88cQT+PLLL0XnsmzZMkydOhVnnHEGHA4HnnrqKezduxcrV65UfV6xxmq1wj1+MV7FubjgzAuA2lrNxxBW0ZbCbDaHbL/lHr8Y27r91egDF9XZgNbZ2Snex+1GbW0tPB6P7HEjCbImBgap4AlxuVyoqalBQUFByAd/Mmge6M9krRWcn9vtRk1NDbKzs2WPG2lCFZH6DDTNxxLVht31118vG/sWLgsXLkRLSwt++9vfor6+HmeffTbeffddDBs2DABQX18vqmnn9Xrx+OOP49ChQ7BYLLjooouwbds2URBue3s7brnlFjQ0NCAnJweVlZXYunUrJk+erOu564nNZkNZWRm++OKLsI8RKitOquWQHjDDTgkWZD3y5EZ48JCun0+kBmziMFBIBc2PGTNGdhuWUGWuXgWcL12+ihjYDDTNxxLVht2aNWuicgK33XYbbrtNOksl8DPHjRuH6upqxeM9+eSTePLJJ/U6vZjBBmGttQDjhdFoRE5ODl9iRgnX5NvBbX1cU4kFgkh1Ul3zrDctQRCxJTlGlAFAqNl1ormtTSYT0tPTVQ3y7vGLsaPvTJSVlSXM+RNEvEl1ze/xVOCcc87B8M7OhLkGghgIkGGXJMTKbW0ymaJigCVbrz0iuUk0oygckl3zQHTq1RGEFKmgeb2Ia69YQjtas3C03uxqDDDWFDyc2ld6EG7Dc2LgkErZi6R50jwRmlTSfKSQYXeaSZMmoaKiIqGzZ4H+LBy1pRECi3a6XK6QWayhYE3Bw6l9pQdaik3SLI7Qk3jcT5Fqnh2jvb3d3xYsDEjzxEAl3vfTypUrUVFRgUmTJqnehwy70+zatQv79+9HVVVVVI4f75uDwQw7r9cb9jFYU3C52ldqCfc70VJskmZxRLhI3Z9a7qdE0TwQuWFHmicGApFqPhpUVVVh//792LVrl+p9KMYuRkQjXiZj/zpcXftHePe3AZNvVtxWbkAd0rAJI09uhCHzl6qLN7Km4FarFflhn3343wk1DCdiQaSaJc0HQ5onEplUKcFCHrskJrN6FbK8bcisXhVyW+HyjMlkQnl5OaxWK0ae3Ih0V3NC9HokiHiRSN41JcLRvM1m4zNwLRYLaZ4gkDyaDwcy7JKY7spb0GXKQ7fGWlEsWNpqteLI4AVh9Xoc1vQRZu25La4NzBORVB4sUpl4L7eoJVzNCw070ry+kOaTk2TRfDjQUmwS4znvenzSOQIzz5uJcIeUE6VzcKJ0DqaP19bqa3TDW0h3NcNSvQo4Z0WYn556pIorn0hMEkbz1E2ChzRPJBrksUtiotUySA3flM5Hr7VQs+dADTQDJghpSPMEQYSCDLsURO0gabVaUV5eDpPJpOnY5eXlOFE6B1snPoOeikWRnm4QqewiJ4hoQJonCIJBhl0KonaQtNlsKC8v19Srku2j5cFAEER0Uat5ZqSR5gkidSHDjogYYZYtQRADg3C8fwRBRB8y7E6TKJ0nMvavS7rWOSzLNisri+JkiIQn0eK5klHzgP97HDVqFEaPHp0w3yVBSJFomtcCdZ6IgGh3nggFu/Gy9v5FdeucaJ1DuDc/xckQyUC07lOt/UxJ8wQRGxJF8+EQTucJMuwSBHbjuaeob50TrXPQcvMnq7eBIPRGSz9TgDRPEMmOVs3HCjLsEgz3+MX4z7S/qm71w4iXqzmzelVC3tgEEWu09DMVQponiOQkXM1HGzLsUoR4LYl0V96SkDc2QcSacA20cCHNE0R8ibXm1UKdJ4iI6KlYhGpTpWJz7mQOXCUIQgxpniASG/LYJRmxCNbUGwqwJojwIc0TBKEFMuySjEQN1iQIIjqQ5gmC0AIZdklGpMGayTj7J4iBjB4B2qR7ghg4kGGXZEQarKnH7D/eFecpfocYSOgRoB2p7knzBJE8kGF3mkTpPBFt9Jj9h9NjVk8ofocgtBGp7knzBBEfwuk8QVmxp9m1axfsdnu8TyPquMcvxh5PhWJGG0EQqYVQ9wRBJA9VVVWoqqqCw+FATk6Oqn3IYzfAoSUOghhYkOYJIrUhj10So8cAzZY4CIJIfEjzBEGEggy7JCaeAzTN+gki9pDmCYIIBS3FEmHBHjA0yBPEwIA0TxDJARl2BEEQBEEQKQIZdgRBEARBECkCGXYEQRAEQRApAhl2BEEQBEEQKQIZdgkGZZ4RRHISrnZJ8wSRnCSqdsmwO02itBSj1jkEkZyEq13SPEEkJ7HQLrUUi4CB0lJMbxJ1xkIQRHQgzRNE7AinpRgZdkREUBV7ghhYkOYJIrGhpViCIAiCIIgUgQw7giAIgiCIFIEMuySD4lsIYmBBmicIQgsUY5dkUHwLQQwsSPMEQWgh7h67Z555BiNGjEBaWhomTpyITz/9VHH7lStXYty4cUhPT8eYMWPwwgsvBG2zYcMGVFRUwGazoaKiAq+//nq0Tj/poNk/QQw8SPcEMXCIq2G3fv163HXXXbj//vtRXV2NmTNnYt68eTh+/Ljk9s8++yyWLl2Khx56CF999RWWLVuGqqoqvPXWW/w227dvx8KFC7F48WLs27cPixcvxrXXXosdO3bE6rISGqqZRRADD9I9QQwcDBzHcfH68ClTpmDChAl49tln+ffGjRuHBQsWYPny5UHbT58+HTNmzMD//d//8e/ddddd2L17N/79738DABYuXAiHw4F//etf/DaXXXYZ8vLy8PLLLwcdk9WGqa2tFdWxs9lsNAgSBEEQBBFznE4nnE4n/2+Hw4Hy8nJ0dHSErLkbN4+dy+XCnj17MGfOHNH7c+bMwbZt2yT3cTqdSEtLE72Xnp6OnTt3wu12A/B77AKPOXfuXNljMsrLy5GTk8O/pAxLgiAIgiCIaLN8+XKRTVJeXq5637gZds3NzfB6vSgpKRG9X1JSgoaGBsl95s6di7/+9a/Ys2cPOI7D7t27sXr1arjdbjQ3NwMAGhoaNB2TUVtbi46ODv61dOnSCK5OjNPpxEMPPSSyvgcKdO107QORgXz9dO0D89qBgX39el/70qVLRTZJbW2t6n3jnjxhMBhE/+Y4Lug9xq9//WvMmzcPU6dOhcViwZVXXokbbrgBAGAymcI6JsNut4teei7DOp1OLFu2bMDe7HTtdO0DjYF8/XTtA/PagYF9/Xpfu81mC7JL1BI3w66wsBAmkynIk9bY2BjkcWOkp6dj9erV6OnpQU1NDY4fP47hw4cjOzsbhYWFAIDS0lJNxwyHlStX6nYsPT8jFvvE4trD+ZxE/b7CIVF/R7r26JKo9zBpPjV++4F87eHsk6j3vSq4ODJ58mTu5z//uei9cePGcb/61a9UH2PWrFncD3/4Q/7f1157LTdv3jzRNpdddhm3aNEiyf07Ojo4AFxHR4fqzxw3bpzqbWP1GbHaJxbXHs7nJOL3FatrD2cfuvbofgZpnjQfrc8Idx+675P7vtdy/LgWKL777ruxePFinH/++Zg2bRpWrVqF48ePY8mSJQD8a8wnT57ka9UdPnwYO3fuxJQpU9DW1oYnnngCX375JZ5//nn+mHfeeSdmzZqFRx55BFdeeSXeeOMNfPjhh3zWbCBerxcAcOLECdWuTpfLhRMnTqi+zs7OTgDAyZMn4XA4ovIZsdonFtcei/OKxT6xuvZw9qFrj+5nkOZJ83Tf032v5+ewYzKbRRFNpmUUWLlyJTds2DDOarVyEyZM4LZs2cL/7Sc/+Ql3wQUX8P/ev38/d95553Hp6emc3W7nrrzySu7gwYNBx3z11Ve5MWPGcBaLhRs7diy3YcMG2c/fuXMnB4Be9KIXvehFL3rRK6FfO3fuDGlXxbWOXSLQ1taG/Pz8oDp2SkyaNAm7du1S/Rms/kw0PyNW+8Ti2mNxXrHYJ1bXHs4+dO3R/QzSPGme7nu67/X8HHb81tZW5OXlKW474HvFsmxaLVknJpNJ0w/HiPZnxGKfWFx7rM4rVvtE+9rD2YeuPfrXDpDmSfOJc15036fOfR+KuJc7SUaqqqoS8jNisU8srj2cz0nU7yscEvV3pGuPLol6D5PmU+O3H8jXHs4+iXrfq2HAL8WylmJnnnkmTCYTqqqqdP+i2WeoaQWSatC107UPtGsHBvb107UPzGsHBvb1R+vaV65ciZUrV8Lr9eLw4cOqjj/gl2IZu3btitqNaLPZ8OCDDw7I3rN07XTtA5GBfP107QPz2oGBff3RunbmbGKGoxrIYzeAZxgEQRAEQSQ+WmwVirEjCIIgCIJIEciwIwiCIAiCSBHIsCMIgiAIgkgR4mrYbd26FfPnz0dZWRkMBgM2btyouH19fT1+9KMfYcyYMTAajbjrrrskt9uwYQMqKipgs9lQUVGB119/Xf+TJxISp9OJmpoaOJ3OeJ8KQRAxgDRPEGLiath1d3dj/PjxePrpp1Vt73Q6UVRUhPvvvx/jx4+X3Gb79u1YuHAhFi9ejH379mHx4sW49tprsWPHDj1PnUhQXC4Xampq4HK54n0qBEHEANI8QYiJa7mTefPmYd68eaq3Hz58OP74xz8CAFavXi25zYoVK3DppZdi6dKlAIClS5diy5YtWLFiBV5++eXIT5ogCIIgCCJBSbkYu+3bt2POnDmi9+bOnYtt27Yp7udwOEQvcusTBEEQBBEPnE5nkF2ilpQz7BoaGlBSUiJ6r6SkBA0NDYr7lZeXIycnh38tX748mqdJEARBEAQhyfLly0U2SXl5uep9U7LzhMFgEP2b47ig9wKpra0VFf0biJWzCYIgCIKIP0uXLsXdd9/N/9vhcKg27lLOsCstLQ3yzjU2NgZ58QKx2+3UeYIgCIIgiLhjs9nCdjCl3FLstGnT8MEHH4je27RpE6ZPnx6nMyIIgiAIgogNcfXYdXV14ZtvvuH/ffToUezduxf5+fkYOnQoli5dipMnT+KFF17gt9m7dy+/b1NTE/bu3Qur1YqKigoAwJ133olZs2bhkUcewZVXXok33ngDH374If7973/H9NoIgiAIgiBiTVwNu927d+Oiiy7i/83Wk3/yk59gzZo1qK+vx/Hjx0X7VFZW8v+/Z88evPTSSxg2bBhqamoAANOnT8e6devwwAMP4Ne//jVGjRqF9evXY8qUKdG/IIIgCIIgiDgSV8PuwgsvBMdxsn9fs2ZN0HtK2zOuvvpqXH311ZGcGkEQBEEQRNKRcjF2RGJB7X4IYuBBuieI+EGGHRFVBmq7H3qwEQMZ0j3pnogfZNgRRBQYqA82ghjIkO5Ds2bNGhgMBj4uXo4bbrgBWVlZsTkplWzevBkGgwGbN2+O96koQobdaSZNmoSKigqsXLky3qdCEARBECnJd7/7XWzfvh2DBg2K96kkBStXrkRFRQUmTZqkep+UK1AcLrt27aICxQRBEAQRRYqKilBUVBTv00gaqqqqUFVVBYfDgZycHFX7kMeOIAiCIIiYoHYplvHVV19h9uzZyMzMRFFREW6//Xb09PSItlm5ciVmzZqF4uJiZGZm4pxzzsGjjz4Kt9st2u7CCy/E2WefjV27dmHmzJnIyMjAyJEj8Yc//AE+n0+07cGDB3HZZZchIyMDhYWFWLJkCTo7OyO69lhBhh1BEARBEAmH2+3G5ZdfjtmzZ2Pjxo24/fbb8ec//xkLFy4Ubfftt9/iRz/6EdauXYu3334bN910E/7v//4Pt956a9AxGxoa8OMf/xjXXXcd3nzzTcybNw9Lly7Fiy++yG9z6tQpXHDBBfjyyy/xzDPPYO3atejq6sLtt98e9WvWA1qKJQiCIAgi4XC5XPjlL3+JO+64AwBw6aWXwmKx4P7778dnn32GGTNmAACeeOIJfh+fz4eZM2eioKAAP/3pT/H4448jLy+P/3tLSwveffddTJ48GQBwySWXYPPmzXjppZdw/fXXAwCefPJJNDU1obq6GuPHjwcAzJs3D3PmzAlqmpCIkMeOIBSg8gUEMfAg3ccGjuPg8XhEr0B+/OMfi/79ox/9CADwySef8O9VV1fje9/7HgoKCmAymWCxWHD99dfD6/Xi8OHDov1LS0t5o45x7rnn4tixY/y/P/nkE5x11lm8URf42YkOGXZEStHY+Cq8vnvR2Piq7DZaBm0qX0AQiY3emgdI97Hi+eefh8ViEb2EmM1mFBQUiN4rLS0F4Pe8AcDx48cxc+ZMnDx5En/84x/x6aefYteuXXyFi97eXtH+gccDAJvNJtqupaWF/xypz050aCmWSCnq6lcDaEFd/WqMGnWj5DZs0C4oKIDNZovtCRIEoSuk+eRl/vz52LVrl+zfPR4PWlpaRMZYQ0MDgH4DbePGjeju7sZrr72GYcOG8dvt3bs37PMqKCjgP0eI1HuJCHnsiJSibNCNAApO/1cbtPxCEMkHaT55KSgowPnnny96BfKPf/xD9O+XXnoJgD/DFQAMBgMAiAx2juPwl7/8Jezzuuiii/DVV19h3759kp+d6JDHjkgpiouvQW3tSOTmnoOamhq+CGZ9fT0GDRqkOFunWT1BJB+k+dTFarXi8ccfR1dXFyZNmoRt27bh4Ycfxrx58/Cd73wHgD+hwmq14oc//CHuvfde9PX14dlnn0VbW1vYn3vXXXdh9erV+O53v4uHH34YJSUl+Mc//oGDBw/qdWlRhTx2p6HOE7EnmrNlYYxMuPEyTqcTtbW1kgG9BEFoJxk0T7F1iYPFYsHbb7+NDz74AFdeeSWeeuop/OxnP8Orr/bHU44dOxYbNmxAW1sbfvCDH+AXv/gFzjvvPDz11FNhf25paSm2bNmCiooK/PznP8d1112HtLQ0PP3003pcliao80QEUOeJ2JPos2WXy4Xa2tp4nwZBpAzJoPmamhqMGTMm3qeSstxwww244YYbQm63Zs0arFmzBoA4A1aKK664AldccUXQ+xzHif4t1+OVfY6QcePGYdOmTSGPGW2o8wRBEARBEMQAhgw7IqGh4GaCGFiQ5gkiMsiwIxKaRK4nRQ8ggtCfRNY8QLonEh8y7AgiTBL9AUQQhP6Q7olEhww7giAIgiCIFIEMOyKqqGn3oxdaypN4PB7U1tZGbTklltdNEIlGrO7/RNI8QLonEgMy7IioImz3E21YeRKv1xtyW6/Xi9ra2qgtp0TzuinGh0h0YqX7RNI8EL3rJs0TWiDDjogqkbT7SWaied0U40MkOqR7fa+bNE9ogQy706RC54lEnNUVF18Dk/FRFBdfE+9TiSkD9bqJ2EO6TxwG6nUT0YM6T0RAKnSeSPSq7gRB6A/pniBSF+o8QRAEQRAEMYAhw45ICVh2nJog6lQjEZfiCCLakOZJ84Q0ZNgRCQkbuNQGC2vJjtOCwbgVJvMDCV2+gAKriVQgUTQPAK1tGxO6bAlpnlCCDDsiIYnmwNXY+CpM5gdgMG4Nua3RuAkGQ2tMyrUQxEAmUTQPAC3NaxGrMk0EoTdk2BFJjdZZPuCvNWUwtMJo3BRyW59vDjguX3P5ApfLhfb2dppRE4TORFvzAFBQuBhay5ZoKZZMENGEDDsiqQlnll826EZwXD58vjmi96WqxnO+WfB6HtZcvoAMO4KIDtHWPADk5y3QXLYkmkvDBKEFMuwI1UQzYFevY5tMJpSXl8NqtfLvBQ7excXXwOt5GJxvlmjfWHbJIIhkgDRPEMkHGXaEavSOgREOvlLH9ng8qKur07S0wQb59vY3+GOrHbwDq8ZrjcshiFRjIGre67sXrW0bw7g6gkgMyLA7TSp0nkg2hIOv1NKl1+tFXV1dWEsbwmOrbfMTWDVea1yOHFSagCD8JIPmgZbTyRPhw4xW0jwRKeF0niDD7jS7du3C/v37UVVVFe9TGTAIB1+9Y9KExw63zY9cXI5WqDQBQfhJBs0DBaeTJ8KHNE/oRVVVFfbv349du3ap3odaihFxo7j4GtTWjkRx8UR0dXVJbmM2fwaT+SM0Nv4c2dnqM9SEx47k/L75ZnDY+zMokYIg/CSD5mtrRyI/bwyaGg+FfRzSPBFPyGNHhERNeYFoLTeaLR9K1pELp+RBvKBBnkg2SPOR4fF4SPNE3CDDboARzmCsZlkhWksPHvclknXkEmGpQ65UAkEkEqR5fSHdE4kOGXYDjGgPjnoHDXs8M8KqIxd4Tkqz53A9AVQqgUgGSPPBROL9I90TiQ4ZdoSuxHNWLdfXNdQgH+45q828I4hUZiBpHiDdE4lPXA27rVu3Yv78+SgrK4PBYMDGjRtD7rNlyxZMnDgRaWlpGDlyJJ577jnR39esWQODwRD06uvri9JVJC/xLsOhd+yZlr6ucg8ELRQXXwPO93s4nVNj+h3SUhARLqT5yDQPALm5V6LTcR9yc6+M6DhaIM0TWoirYdfd3Y3x48fj6aefVrX90aNHcfnll2PmzJmorq7GfffdhzvuuAMbNmwQbWe321FfXy96paWlReMSkppYzLStViuGDx8uqgov/Hw9B3ktfV21PBAYUg9Fr9eL2tpaTdcQ6cOVloKIcImVd01O98mmeall5nCvIRLdk+YJLcS13Mm8efMwb9481ds/99xzGDp0KFasWAEAGDduHHbv3o3HHnsMV111Fb+dwWBAaWmppnNxOByif9tsNthsNk3HiCd6NaB2Op2or6/HoEGDdLl+m82G4cOHR3wcNXC+WfD6ZqG4eHrIbX2+OTAaN2laTmGDfEFBAWw2G1wuFzo6OpCVlRW0rdVqRW5uLqxWa9ADIPA4QtR8/2WDbkTNsedoKWiAw+6V7OxsXY6jl+aB2Ok+1pp3Op2oq6uDz+eT3N5kMqGsrAwWiyXksYSE+g1I8wMPp9MpmgQE2ihKJFWM3fbt2zFnjrhY7Ny5c7F792643W7+va6uLgwbNgxDhgzBFVdcgerq6pDHLi8vR05ODv9avny57ucfTVwuF06c/AdgWBqRuz6aM/pIPVVS+4c7e+Z8s3QJ0HY4HJJV8oWGndZjhvr+wy2+SqQW7F5pOPVKRMt0pHn1uFwuRcPObDajvLxc0rALdVyl34A0P/BYvny5yCYpLy9XvW9SGXYNDQ0oKSkRvVdSUgKPx4Pm5mYAwNixY7FmzRq8+eabePnll5GWloYZM2bg66+/Vjx2bW0tOjo6+NfSpUujdh3RIpylBr1xu92yg67L5cI333yDb7/9NmigVhoshdtJ9ZZsb2+P2FOZLOjlmSVSB3/7q/gt04WjebZfX1+faFIutT9pnjQ/EFm6dKnIJqmtrVW9b1IZdoB/mVUIx3Gi96dOnYrrrrsO48ePx8yZM/HKK6/gzDPPxJ/+9CfF49rtdtErXsuwkcxwtcSbuFyuqAwWPT09aGhoQHd3t+TfpWLSWOPvUIadEo7Ot2EyPwCDcWvYx0gG2O8m10sz3sHxhHYi/c387a9CZ2kmkuYBdYadEqT5fkj3qYfNZguyS9SSVIZdaWkpGhoaRO81NjbCbDajoKBAch+j0YhJkyaF9NglCpEsi2hZagg1WAQGDTPjK9RDIdLBmtHY+CpM5gdgNn+mavuOjnUwGFphNG5SPLdEKHCqdwC5MGMuUYq4EuqJ9DfLz1ugaplOq+YBZW+ccBvSvDJ6e90Cs2RJ94SQpDLspk2bhg8++ED03qZNm3D++efLxjRwHIe9e/di0KBBsTjFlCFwoPB6vairq1OcNepJXf1qvh/mFgAAY+tJREFUGAytMFs+5M9HaWDMyVkEjsuHzzdH8u9A4gzyeht2qZIxp8XrQB4K/ZEyDtQYdnqR6poP5XXTAmmeUCKuhl1XVxf27t2LvXv3AvCXM9m7dy+OHz8OwL/GfP311/PbL1myBMeOHcPdd9+NAwcOYPXq1fjb3/6Ge+65h99m2bJleP/993HkyBHs3bsXN910E/bu3YslS5bE9NqSnXj2N3U6nUhL+z44Lg8e9yX8+UgNjI7OtzGo7CkAgNfzMDjfLFWf4fV60dHREbXri2XdqVQpmKrF68C27erqosFeJ0jzkUGa1w5pPjrE1bDbvXs3KisrUVlZCQC4++67UVlZid/85jcAgPr6et7IA4ARI0bg3XffxebNm3Heeefhd7/7HZ566ilRqZP29nbccsstGDduHObMmYOTJ09i69atmDx5cmwvTmeUZivMza+nNy2eTaxdLhdaW85Gb8+D8HhmKG7b0bEOZnMHOjrWqT6+1WpFSUkJurq6Ql6fyWRCeXm55uxWNTNq5k2IdIAayBlzqbwEpUbzesbLkebF28vV35RDjeZZvCFpPnxSWfN6EVfD7sILLwTHcUGvNWvWAPB3kdi8ebNonwsuuACff/45nE4njh49GuSJe/LJJ3Hs2DE4nU40Njbi/fffx7Rp02J0RdFD6WaOxM0vN9C4XK6guBmz+TPVldvZ+TocDlXGi9n8GYaUr0Rr20ZN55+TswgeTw5ychap3sdqtaKsrAxGY//tLxdDyMoXCJNp1AwsambU8V4moqWNxCYRNM+8Y2p0qVXzjs63MWbsGjg639Z0/tHWPNs+0LALNYFWo/lwCprrCWl+YJBUMXbJTiKKSm6g8Xg8wYad5UPV5VQ8Hg9qamrQ3d2tyngxWz6ExeI4Xbrh9Hvmz5CWviwo600Ye2PPvgL1dXfAnn2FmsuVhcUQsmMHlmMRXgP7t/CBEBh4rnZG7fF4RJ8Xy+WwRJn5RtKQPdFJds0z75hQl3Jo1XxHxzpYrZ0iz1uial54Dix7P9DjrlbzgYZ1LMuZkOYHBmTYxZBEERWbqWqd7Xvcl6gup6IVn3cEOM6A9Ixz+PfMlg9hNLYFZb3pHYjMMJlMKCkp4Qd74eeF+t2Utmlt2yjr9Qh8yMY6zinQsIwHiaILIXoZZIlybeFqnnnH/CVV9MVmOwscZ4DNdhb/XjJpXsnjrlXz0bg2OUjz0iTiJCxcyLA7zaRJk1BRUYGVK1fG+1SiTrgZrh7PDE2V20OVSGHdGSwWC4ymozAYOPT2fNG/v/sS+Hx5illvcgiXUtjnmM3KHfRMJhOKior4OBx2DMAfuxluOYeW5rWqvB6h2hVFI5Yy3ktDiUoiPngiIVzNM+9Yft4CVdur1bzVaoXT+RUMBg5O51f9+w9AzYeqS0majw2JqvmVK1eioqICkyZNUr1PXHvFJhK7du3SVAAwliRr5XH2MGH9Uk+dOgWv1wuTyQRAbNh53JfAYHwfpaX9ngGPZwY8nhlhteVqaWnh+y66XC7V7b2E5R1Yv8v6+vqIBvn0jHPg6mgUeSPlzlvJsBPO7Nl3SKQmqa55q9WKnJxFaGj4O0pL+2PlBqLmlTRNmieqqqpQVVUFh8OBnJwcVfuQxy4JiLWrPhA1hUNZqn9v73uSfw91DR7PDJyorQryDHi9XjgcDk0DrMsl38YoHvT2fBHkjYwUpQD4eGU2EvqRCJr3+u5VTGyIVPP27Ctw6OANkrFyWj2MgaUw4n3/x1LzAOmeEEOGXYKjtytea3V3ILhwqNw2QAu6ezbocJZiWNs4IQbjVpjMDwQ9eAIDohNhoCsoXKx7nJLccgoN8MlPomgeaFEsKRItzbO4N+btY4TSvMfjSZjltFhqHiDdE2LIsEtwolGxPJSRFkjZoBvBcfl84VC5bYACWCxjMWbsGtlZvNoiocxTBwA5OTlBnUWMxk0wGFqDHjxSM33mWWhq+qfk4McefEo9J30+HxoaGvg4OC1LZPl5CzTFKaUKqRSMHEsSRfNAgWJJkWhqvqysLGjpUYvmW9s26qp5rZNE0jxpPp6QYTfAUGOkCXG5XHA6p8LlXCZbONTpdMLpnArO93u43QdhtXbKzuJ9Ph8cDgc/SMpl63m9XnR1dcnGm/l8c8Bx+apqWTHPQmvbS5LNytmDT6nnpM/nw6lTp/g4OK/XC4vFguLiA0jPWKa5/t5AIFG8JwOdcDXP+X4vW1IkUs1LGUpM83IGrRbN+5MW9NO88Hxttv9g6LBn0d3zr5DnMdAgzScGZNglKNESSHHxNfB6Hlas7u7xeNDU1ASO4/hBWMl7IPQwZGZcBZcrG5kZV/EzcLl9GxtfBQxL0dj4qqwBJzfb53yz4PU8rKqWFfMsZKT/QLJZOXvwac3Es1gsyMjcCoOhTVWdLyI0iVCKIV4MJM2fOPkPRa+3y+VCR0eH6DhaNO9fAtVf8wBgtX0Mk6kd7W0vad6XCGYgaz5akGGXoOgxyIdyi8sVA/V6vfwgr3RuUsdNT78Mhw7egPT0y0LOwNUsEbHZvpqlT5PJJLmEwwqHpqdfJrkfe/CF6jlptW5HWvoyUawS8yKoiaVhda+amv6JQWVPwdH5tm79K9ngKHyA6bUsEsvllUQoxRCvjNSBpHklTxngv58dDofshI8hp/n8vAW6al74fbF6nlo073K5YDBuRVr6MhiNn+qqeeFvolebQtJ8ckOGXRKhlBXFBg3hABTqQSFXDDQUenkWtC4RseBpuWVPs9ksOcgH4nK50NjYiOzsbL4cAjOwlLJvbWkfw2hs4w3R1raNMBo3weeboyqWhg26rW0v8b0umYeDfZdKrdVcLpesN4TdG8Lz1+t3SuTllWgEjcc7I1VIKM0H6iFammddJfTSvFpPmdW6PSE0z74vg3ErzJYPNWve5XLBaNwEo7ENVttHIs37r0O6XaMazQuPo1ebwkTWPKC/ly+RNK8HZNglEUozGzZoaBmwpYqBsqDitLQdupyzEINxK7Lt/4vs7M8BqFsiEsKCp5ub1/KDHetlqaXfpMfjQUNDA7KyskSDfKiyKs6+i+Hz5fGGaEvz2tPeh/c1JVQo9bqUaq3GEC5PWa1WWe9KOCh5ZBKZeDaujwWhNG8wtGoKA0gUzYfylDFsaR8nhObZ99U/zmrTPOD37vt8eXD2XRz0N7l2jdHUPJC8yQ6J4OVLZMiwO00sO09E4yHKBg0tMSMezwz09T4oGmTZUkl6xpawzqO39z3ZDDn/oNiOgsJNohm42fyZaPCXgy172u0L+aWM1tZ/8N6vaONyTUNf74O8IVpQuBgclw+36xJNNbekel263W7/QOW8GG63XXaZJzv7c9hzfg+f7xMYDIbIL+o0iT5DT3aipXm1S4KMRNG8cD8lA83Zd3FCaJ59X2yc1ap5wB8j2Nf7IFyuaQD6Ne/1ehXbNUZL8wDpPhkIp/MEGXan2bVrF/bv34+qqqqof5aSmFhpDq1ZlpxvFtyu32LI4B+rqrbOYm0Ca1uxpZLengs0fT6jq/tFWK2d6Op+Mehv/geRAQYDh+bmtfyg5l8eakdO7nbFYwcGT/t8PvT2XAC3264qU07pARQO+XkLNHkclWCDvNM5VbJQMyMndzuMxnbZuETmzdArSzfVYk/iRbQ07/U8jNKSa/lWWkokkuYBoLtnA6zWTkUDzeWallCaZ8aZnpr3er2K7RpDaR7o702rxYspB2k+saiqqsL+/fuxa9cu1fuQYZdgsNIc4WRZmkwmlJeXw2azhRQni7UJHCzYUgkAjKt4gR8Q5YKuteAfFL8Pt9sOu32haLbq8+Wio32a7L6Ozrcl6065XNNworZKVaYce5BEo4iyFtQsJckFQXe0T4PPlysbl9jRsU5Vj0q1pFrsSSISieYBiPqb6ql5QN29qoSc5gHw2bRyBlp29ufItv9vSmi+tW2jqiLRUp7dUJoH+nvT6uHFJM0nP2TYJRisNIfc8opSMLWQkC28TsfayA0W6RlbRAOi2qDrrMzr4HJlIyvzOpnzCh6UPZ4Z6HTcj87OCbLH7ehYp5hNZ7FYQnothGUZWOB5YLCyEl6vF52dnREPeMz4UhqE5YKgOzsnoNNxv6zHgMXvBd4/yRBLwx5+aiYPSi2vkuFahSSq5gF192o4mgf6s2nlDDTmqUoFzbN43FBFoqU8u6E0D/R3uhAaycmgg3A0L+XZToZrjSVk2CUYrDSH3FKcXkGjLNZGOFgIWxm53UPBcQZYLGP920sEXUshLH2gFp/Ph66uLj4wuLHxVaRnLENx8QEYjf5bNCdnkWI2nZpBXnhuLPA8MFg51Hl2dnaGLMEQiuysa+B225GdFbzsEg5WqxXl5eUwmUx8/F7g/ZMMsTT9ySihE4CYl6ut7e9BS8/JcK1CElXzgHKiDyMczQeWVxFqnmW4Mk9VImg+UsMuN+9H8Hpz4XIGJ06Eg1DzQH+nC6GRnAw6CEfzjY1/DjIGk+FaYwkZdglApLMNqfY4LE2ezeLVHFs447dYjsNg4OB2HwQgHXStRG/ve0hLXwZ7TnXIbQO7TPiDuduQlf1vfuCyZ18RlE3HZtPhZIqxwHOpYGU9YZ0qhMag1XopDh74CbxeL9LSl4VMGgmFzWZDeXk5zGZzpKerCb1nySwZRU0CEPNyGQzQdek5ViSD5gHpRB85tGpeaNhJaZ55qgLHHK/XC6fTqZjNKkU8NZ+ZMQ/Hj/0cHMepShQLxUDWPGBQbQwOVMiwSwDkZhvCdltygc+AdNFPlibPZ1vK1bWSqZ8kNXvXQnfPBhiNbSgo+BRp6dpabqmtb+fz+dDd3a3Jg8ZxHJqamuBxi4OVWf04NUHWoWpr+bfpj3sKHOQZ7DsKlTQSKezhHRh7paZfZqjj6jlLZskoaiYPzMuVm/tT3ZutxwLSvBgtNS19Pp8mw04PzQOh4+TUaN5fFy90olikpLLmi4tvCbtryECBDLsYojX7TdjcWi7wGYisPY5c/aTA2XuoVkGBZGZcBZ8vDwBgNGpruRWqvp2j820MKV+JtLQdMBqNoqKjoWCDfOB1sPpxXd0vBi3ttbZt5D8P6K+tJbymwIelzWZTFf/j82XAaHTxsWJW63YMKV+JtraNutVnk4u9UtsFINqEmxUKQHbpOVFIZs0D/ntHqiWXFLHQvNW6HUajETabDRaLRdWx9dA8EBwnF47m/XXx0kWaZwY8hy2aa+PJkcqa12IMDlTIsIshkWS/KQU+ay36ybpUmM2fydZP6u25gA86Bvyz5J6eHpSUlKgyotLTL0Nf74NoaZkJny9PV49KR8c6WCwOpGdsgcFg0GTYyeFxXwK32w6Oc8Ns7kBj4yr+b42Nq2CxOJCR6R8MWW0t4TXJPSyV8Mck2WAy9fHB6ba0j2GxONDZ9aouhp3QAxSI3zjIANCnW3mUcIg0KzQahBNoL0Uyax6AprppsdC8Le1jmEwmTYadHFo0D/QvG7LfIxzN+2vYiTXPDHiTaZPm2niS16VS85He25GQyppPBMiwiyGhst+UCAx8Zi5xh8OhOTWdVU83Wz6UrZ/U1zcFB/ZfLwqINhgMKCsrg9VqVdXSxWz+DHl5O+BxXwKv1wuD8T7ZZQwpz5vJZEJJSQmfQMHIyVkEt9suW3dLqr1aKDyeGThRWwWDgT0shHF74hg+VltL6CVSKjCq+LmnHy45OYvAYQs4rg9eb5ro4cpgXgSrVf0yDgu8b29vD7pH/L95GgyGnqgPsIGxOcJ/FxddD58vD7l5P4rqOWhBLtBea4xRsmveYrEgLS0NFotFs+YBwGS+Hz5us2QcrJTnjZVsCjTamOalujYAodsNSqFF80Bw3cpwNe/su1ikeaAXnC9D0oCPpua1GKThMFA1nwiQYXeaWHSeCJX9JodUrA0b5Lu7uzUP8qx6utoerVKoydRjSx1my4dobf0HTKZ2pKVvltzWaDRizJgxyMrK4t8zmUzIyNyNwUOeFpW1sGdfgRO1VejrmyJzLO3t1RhZmdfB48lBcfGt/HvFxbfC7bajp1t+2UupwKjJZEJOTo6kh4E9XOzZV8Bk2gSTqQ8+n1Uyw7CleS3vtdCCUmafVPcCp9OJw4cP4+uvv9YtliYwNkf4b7t9Pk6euB2ZGfN0+Sw9kAu01xpjNJA171+6bENW1qeS8WYWiwVFRUXIzMzk32OGXWfXOyKDhmmedW0IJJz2aoxYa15Y/sVk2gSjsQ8crJLL0NHUvPDedrlcpHmdNK831HkiAmLZeUIrSrE2QHD8m9PpRF1dnWy2qJ7V05Vg3iiP+5KQXjaj0YiysjLYbDbR+2rqaAnxu9H74PNZEM5yQ3r6ZUExW/l5CxQNyUACZ3gmkwl2uz3k0hH7vtrapD+noHAx77WQC4BX6jwhVQ+NdS8QXq/L5cLRo0dx5MiRAVs+gH0vUg9tIdGazaeC5gsKF8Pny0NLy2TJbZnxIxVGocWgYZrnuAykZ5yjOXYrETQv54lUo3lAvvOEkuaF9zZpPv6al4M6T6QgZvNnMBic8Mm46oH+ciFskJdKt48HHs8MHKtZAo9nBj/jBoAh5StVV7JXU0dLiD84uAcGg0fX5Ybs7M+Rl/8oikvelKyGLyRwhse8EKHiAD2eGTh65BY4Oiol/84eNi7XNNn4HqXOEz6fjxpn60w0ZvOpovn8vAXo630QADBs+HOaulcIDZpQMM0Daejt+QJ6xW4JNR8qyzcSzR+rWSLriVSjeUC+8wRpXn/i7cFTAxl2CY5fzD0AbFGfbcshF+vG0JJCn56xBRaLI6QHjsXMAFBdRwvozxb0eiqD3Oodjsdx7vhnkJWtve1OTu52mEztyM4+pFgNXwqz2axqkNeCXHyPXOcJObxeL18iQ29Y5ls8g5GTMT4mUTSvVCdNi+YLCnZq0nxj46sigyYUwgxh/33fH9Oon+a1ZfnGUvOAdOcJOZjmo2GYkOYTAzLsEpxQbYC0ElixPBS9ve/BYLwPGZm7ZQ07lkJvsXwUsmBmYANvs/kzyYKdLGZG7mFgNBpRVFQUdE4sW7C398doa70XublX8n9zOj+DwcDBZvsi5HUH0tE+DV5vLjo7xyhWw9cTn8+Huro6yQFKLr5HWP6D1TVTisViS3rRMOxY5lu0g7SV0Dq7FnZiiBeJonmb7T+yhokWzbe0TA7SvFR9vlCdIYxGo+QEky+V4p6Bvt7J4Hy/55dV9dO8vlm+cigZXUoxfazzRJptjmrNR8OwI80nBmTYJSisGCaAsGNj7DnVQcuGrGK50iBvNn+GvPxHUVDw5em+kS0iAytwts4y/4aW34KMjAw+i85s/gzDhj8nGsD7+qaI+kb6Y4mCC3ayQFab7SzJ2BFm2MmVY/D5fPwAyQqHpqfNBMcZ4HSeI9qW47iQM+vOzgloa70Xjae+J1sNX+9ZMDPswj0m60QQ6fJcuGUA2H2hJWsw3iUH4tkAPdE0L3w4OzrfDlvzHe3jcaxmSYDmg+MHhcHrUtmgRqMRpaWlstchrAGot+b7eh8MSoCJluYjMbo8Hg9pXiPx1Hy0IMMuQZFqGs1mumrLeOTl7Ti9bPi+6hZDXq8XJvMmmEztKC75/HTZjQKRiz+wyGV/RfBrYLVa+wd5QYac3Gd1dX4HXm8uOtrFSy4skNXp/EpT8oQUrHBoScn9+O++29DVKV6uMBgM8Pk+0VSFnmEymVBWVgYAIQdktkwh/Ayj8VMMGfI02tvfCPlZbrcbTqdTctBmxxYawFJFVsNBTY9NqeUP4X2h52dFm3DK5ehBomleFMbQsU5XzUt5JIXB6+FmgzKYYZcomhfq0mz+TFfNCw2i3t73YqZ5IFj3pPnEgAy7BCWwGCbQP9NVG9/V1jYFPl8u3K5LUFNTg2+//TbkQO/1etHSMhleTw4aT01AevplMBkfFcW4qa16L8yQk6O3dzIcHUvR2TlB8u9akyfUkJa2I0jE/VXo/4m+vj7VM2az2Yy09J3IzHo4ZP9Htkzh94j4sdo+gsXaCUfnKyE/q6X1dYwc9RekZ/wj6PzZsYUGMHs4pmdsUTwux3FoaGiQrXivpsemcPmDDfbCMgdS7Y3C/SwhSlnA4RJJuZxISDTNCx/OOTmLdNV8d9cDih5JLckTatBT8yaTSbPmhbpMS9+sq+aFBlF3zwbVmldaDVCrQ6b7rq6umGke0N/LFy/NRwsy7BKUwGKYQH/sjdr4LkdHJTod9/tjMyRqULGZZ+DShqOjEk1Nv0RLy9mSx1Vb9V6YISeFyWRCdna2bOweIN2EnD3Mtc60GekZW4JEzB5IVuv30NfXJzkgsSLKgefb0rxWVc9Xtkxhz74WVqsVra2t6O25EC5XNiyWsUhLX4acnL2y+3d0rIPV2gmb7Yug82fHFhrA7OEoV2KG4fP50Na2ETAslRwo1ZYBYEjVr2L3XigvEuebBZdzGZzOqUHbSXkFlbKAw4XVfIt1L8pE1rw9+wpdNR8q3i8weYJpXktmrZBINR94vlo1z3RpsVjQ0z1LpHl7TrXs/mo0LzSIMjOuUq35uro6NJx6RbI8TCJrHtDfyxcvzUcLMuziQGvbRsnMoVCzHFaJXq8eeWyQDxX8HA1YzI5cJwopWKaew7EeZnMHurpfxJDylZqOAfgTOAJFzAoFWy2X8u+xQYUlFgQ+lPqXe26Az5cXtJwcSH/j+ithtVrR0tKC3t7JOLD/erjdB2E0tiG/YCeysrIk61/l5CyCy5UNp/OcoPNnxxYawFpqcbH+t4EDJYv7Mhi38oN3uNlmagrcSm3HfodArwCgPQtYDazmm569KEnz4WneaDSKNN/e/nekpS8L6SkLRC/NszFIq+aZLv1Lq1NFmvcvn/vreEp12QmleaHxlZ5+mab6e/4Jkbg8jFDzwu8kHN1HQ/NAeF4+JaKh+XhCht1pYtF5gsHEFPgQjSSIkw0MkabXs4FMS49ItQgzWVnMjlwsjhSshEDh6dR+AKfjcD7RdN19fVNUiZgZMnIZo8ywKyv7Ifp6H5RdTlYDa6De1jZFtrCpPfsKHDzwE6Sn/QJu1291HYRY/9uyQTfySRder5eP+zIaN0lmm7E2U9Gs6aSU5SbMAo4WepRPGKiaN5lMyMzMDFvzzJBimuc4+I2h/B1x0Twbg/TWvJwnNZqaB8CXh8nN+5Gk5oFg/alpLRcpoTJbtXoUtZJIJVOo80QExLLzBBOTXrMNoL+PK+vcwLLTtPQYBNQvlchhtVqRm5sraZiwB1F+fj7y83/MxxMZjUZRBXqhYSEFS+1nrYBKSm4I6lgRDazW7ZJlGtQQyjPDGqiz4sSOzrclvZEGgwFFRUVh/z7y5zeNHyiFZVJY3JfcEoXaGXkyE+oho+ZBN1A1z7pL5ObmijTP/sZqvanVfF7eT8Fx+QAu07VGnBxM8+EE1WvVPHA6saJ8pWhpNFqaB/zfq8n4KDIz5pHmBeiheb2gzhMJDKuV4/F4eDGFM9tgbWVCBYuzwGC5rDKpyuisjImS4eJ2uxU9DEqDPOCPMcnNzUVR4VV8PJHN9h/k5T/KZ4mpqb8GSLcCUsJiscBms4kGSDb4qikPYEv7WLHNkxJaPTMdHev47MJQXgQ1SJXBECJX24rFfSXTEkWsi6TKPehSRfM+nw8NDQ1ha5611xJq3mz+DFbbg7DZ/gObzaZa82pj/Rh6aT6coPpwvLHsN2xuXhsTzdfV1QUZnqT50CS6cUuGXYxQK/JQrWhYW5lQweKhehBKVUZnZUz8mXhG2Gw2frBmBhmAkIbd8OHDNc2mlVrlMCwWS9Bxe3vf05QRyQZ5YRyLlsHX2Xex5sKxbMARnmN3z78wdNizsNn+I7sf663rcV+iybAzm83Izc0N+v77y2BIP6CEdf/UkMhFPcMtkhruNckZxcmuecCv5+zsbDQ1NcVc83JLzVoyIvXSvJag+nA1D/T/hnb7Qk2GnZRxrUbzrO6fGhK53luiaD5RIMMuARAOBKFa0bC2MmqDxY3Gb2FLexBG46cht2VlTDzuS2CxWFBUVIT09HQA/Yad1Kzc5XKhvb0dXV1dqK+vx6BBgzQN8kqtchjMsBMuuXb3bNCcEZmd/Tmy7f8Li3W75pY/Ltc0zYVj2YAjPMf2tpdgMrXDapOv0cV666r9LJfLhZaWFjQ0NCArKyvoulgZDD2yvlwuF7799lscr30RFutvdKn95PP50NzcjNLSUgDy9cHYEgjHcRg+fLjk/ciyBYuLrlddcgEI/8EVTqHaZNA84DcY7Ha75DKgx+PBkSNHcPz48ahonhl2gWEWWjMi9dC8Fu9VuJoH+hM61LRQZJo/cuQIAASNz3pq3uPxoKamRlfNM2w2m6KhFKh5qd8vGTQfS8iwSwDYQNDcvBbt7e38zcKKJgqXSVhbmVDLj8ylb7X9FyZTB6y2j/i/MUMs8KbkW/N4ZvCxMWoGQXa8np6esJojB7bKUXqYCMnMuEpzRmRO7nYYje0wmz/QvZejFGzAEZ6jVL2yQORi7ORwuVxoa2vDyZMngwaptLQdyMvb4U+Q0PCAElbyD/ys2tpamEzKtZ/cbjfa29tVeR18Ph8aGxtRXFwMALKDJlsCMRgMGD58ODIzM4M8lHwmon2+rh4GqZgpl8uFzs5OcByn6VjCh78wASVZNA/4f4vjx4/jyJEjMdM8oD0jMlk039q2UVPGL9P88ePHg75/vTXP3tdT8wxWgFmt5rOysoI6qSSD5mMJGXYJAF/fzL5QNPiyookm8ybFG1VqQOaXZZznBC3PyA3ySrByDWqXPa1WK8rKysLKtLNarcjJyQk5yKuJsXO73aLspo72aTHr9Qr0DzjCc+RjWLhZkm3RvF4vWlv/oVjBXwvpGVvCquIfaqkmVI21cAZ5rbAlqFgE0kvN7tkgr7WFk/DhL4zXSSTNA+pi8Bix0DwQOiOSfZ/JpvlTp9aoqo2nhlTWPGuRF4uSPXpqPpbE1bDbunUr5s+fzw8GGzduDLnPli1bMHHiRKSlpWHkyJF47rnngrbZsGEDKioqYLPZUFFRgddffz0KZ68dYSyNMKtGqgYZwIom5qKlZTIASKbDs+Pa7XbxIH+6UGhX5yIcq1ni7/Ag4eqWi48JjPuRqnekhM1m4+tllZWVyQZWRxtm2LHr7uycINnrlT0opc7TbDbDbrfzcTqhYqIYobLiTCaTaJAX9tns7bkgZAV/htPpRF1dneRAk539OQwGJ7zeNDj7LhY99NiDWKlAtBRutxsOhwNO51Rdaj+x1mfhZBvrSajMTEB7xftQmg+clCSS5gFxDF4oAjUfC2NbisDAdj00D6iLJYxE886+i+DzBbdXlCLWmvd6vejs7NRV85EUnNaLaGg+EYirYdfd3Y3x48fj6aefVrX90aNHcfnll2PmzJmorq7GfffdhzvuuAMbNvS3aNq+fTsWLlyIxYsXY9++fVi8eDGuvfZa7NgRWe88PRDG0qjJquF8s9DpuB+OjsqgOkfMg3bi5EOiYpJyyLm6WR/VwDiWwEGelWtgywssUy/Uzc7iZDq73tFNyKGy8MLBaDTCbrcjPT2d73sp/DyhN4F9N8LvTMqDoiZ+w2KxIC0tDWazmV9KS8/YErKCvxCXy4W6ujrJpQH/MlQvjEa/90J437EHcaD3QGhodXZ2Bp2/2+1GR0eHphlrYC9GFmNWV/cyTp1ao+idZN6maHoB2OdIXZfw87XGdyWz5gFxDJ5WzVutVt16cDLN6+ml0aJ59p7we9Nb8xzn/+3V1MbTW/PC0A8pzTPDTk/Nh+oB7vF4NCV3hIOc5oWfbzS+H/detlqJq2E3b948PPzww/jBD36gavvnnnsOQ4cOxYoVKzBu3DjcfPPNuPHGG/HYY4/x26xYsQKXXnopli5dirFjx2Lp0qWYPXs2VqxYoXhsh8MheiVCYUIlmAfN4fhYVEwS8AtIqVUNGyQBqC7CyMo1MA+Dmqw2htvtViVktUTDsGNkZGSgtLQUmZmZos8LjOkIROhBkcqKk4MN8larlV9Ky8//sW41qzrap4HjDDAYONjS/hX0kGUPMMDvBXC73XyP2YzMN2AwbtVlySGwFyOLMTt1ag1crtnwenLg9Uov78TKsBMSWGONfb6a+K7AXrl6EWvNA+IYPK2ar62thdH4vi49OKO55D6QNc+8Vay8Ukw1781Fft6PZPeXi/eLFoETG/b5blfoRJ9oFDR2Op1BdolakirGbvv27ZgzRzz4z507F7t37+YHfblttm3bpnjs8vJy5OTk8K/ly5fre/IRIJX2zzxodvvF4LgMAH38TLqufjXfqkaKwEFe2N9PTS0pQF1Wm/BzeCHn/zj0BUeIyWRCSUmJ5uUGoD/7V/hdqxnkhVldUllxavDP2O9DQf73Re+zuBUAQZ6FUHR2ToDDcQWcziwAEA20TqcTp06d4h9ozLDzB3r7Hwxy95BWWC/G7u5ZcLlcohgzAy6A07kMBij3t4wlUl5ZIDi+q7VtI4YNf05kUIUqbqqGVNB8XV0dMtKvAsdFvwenXOcGNSSi5tlkAoiu5ru6uuD1epGTsyjmmud8v0dR0dW6fJYeyGk+MNEnWpoPZPny5SKbpLy8XPW+SWXYNTQ0oKSkRPReSUkJPB4PmpubFbdpaGhQPHZtbS06Ojr419KlS3U9d2FJEK1ZO6zCvHDgYR60IYMfApAGg6GHn0mXDbqRb1Wj9RwdDoeq2VrgzS6F0LPGC7nwKk3nJDXohsJsNmPIkCHIz8+PWU9MYfq7VFacGpgHIHAQ12LYsd6aonp/PZOw/6vF6OkWN7p2uVw4cfIfsFh/g7S0/sE8P28BWprnwOvN1XwPyeFfYrwPTY3j4HK5ZGPMtMBqUPX19cWsCnwgzLsp9TAUJiyoieURkgqaN5vNGDHiBng9/6s5Jkurh04Y1xeugaeVaGre4/FoMuzYMjHbTo3mhR1K7NlXJI3mWQ/ZcJKB9EBJ83qydOlSkU1SW1uret+kMuwABMUGsBgD4ftS24TK1LLb7aKX3i2qhCVBWLyDXnVwApeHiouvCWpVk6xoNezYANfX9z6y7b9HV/e7UT7DYPQYwAB/5fi09GWScYlyCRzCWSeLlUvP8LeikeqXyZZL0jO2iI7T2TkBba33JtQ9xGL7mHHE4pnYsp+UlrQGPrOaZ2pjwgoKF8Pttks+DNnDmRl2bW1tuj2MUlnzgDbDjmne4XgLBuN9SEvfGbMJHUMvzVut2zGkfCV6e98L+ptS0hb7Djq73lGt+cCM2UTUPIvtE2q+pqYGPT09slqKp+b1xGazBdklakkqw660tDTI89bY2Aiz2YyCggLFbQK9ePHG5/Opqlwd2EdVimg3RA6Flpg3tVXq1WaeBsICwxubXkA4SyNysKUZi8UieV5SPR4jxV85vk0yLpEF5StNQNjMMitTfsBiyyW9PdFfBvV6vfxybziwbFwt3m6tyQ6s5pnRuEnV8kp+3gIcq1mi6mHIcRw6OztTRvOhlioZarVMmve3MLNYHOju2RD0N701L9ehRG84jkNdXV1YExqfzyeZzKFEImk+XiSVYTdt2jR88MEHovc2bdqE888/nzcq5LaZPn16zM5TT6TKGoQikjo7amYvgbOocA07qWKsjFDV+EMhtTSSmZmJ0aNHB52nmsw9VjspLS1NcnBl2W16PVQAVjk+Dzk5iwD0t1BTm1nMZpZd3fLLYJxvFvp6H0RfX+jZp9YaVay9GfOe+Hy+iAy7cNBazFZY84wN8mqq2HMch+PHj+Pw4cMRe+SSQfNMD2oMO6GW1Wg+3NWSVNC8s+9iuN12ZGb4Q1aiqXmXK3RZFUBbQd5AzQP9tfFitWyqh+bVnKuemtebuBp2XV1d2Lt3L/bu3QvAX85k7969OH78OAD/GvP111/Pb79kyRIcO3YMd999Nw4cOIDVq1fjb3/7G+655x5+mzvvvBObNm3CI488goMHD+KRRx7Bhx9+iLvuuiuWlxYxgTNiLa1PAoVoz6lGXv6jqiqaC2cv7DwCPWyBg3y49C8JfKJ7TIzU0ojdbsfEiRODHpjC7C1WUkKNG1+Y/ciy27TG2Dg635YduB0dlejrfZCvb8haqKnNLM7PW4ATtVXo7ZmkuJ3Z/Bny8h9FQcGXitspGXbC741lCHZ1v4vc3Fx0db8Lk/kBURxfrOB8s+ByLoPTOVVVDJ5czbNQ+Hw+nDx5EkePHg17kE9kzYfjOZGCNK+seZdrGk7UViE9/TIA0dV8tv1/ZbOoxeckP2lgWj9x8iFJzQvj+GJFMmk+WsTVsNu9ezcqKytRWel3ad59992orKzEb37zGwBAfX09b+QBwIgRI/Duu+9i8+bNOO+88/C73/0OTz31FK66qj8gf/r06Vi3bh3+/ve/49xzz8WaNWuwfv16TJkS3fVwvQmcEYfT085oNKKoqAh5eTtgMrWjoHBTyGUD/+zF7yWyWq38ModwYDSZTMjKygo5MIdadmUzq5KSG2RjYtQu3UYCW5rw+ebwJSXUuPGFszvW41EpxkZqqcnhWA+zuQMOx/qQn8daqDEPnl6YLR/CZGpHcYm0EcASMpQ8ssLvLTBDsKV5LQyGVmRkbsK4ihcUvQ/hFlAVElgeRU39uEQgEsOOoafmhR4qo9EYM82rOU6kkOY/hNHYLpsAIJWEJQXTusPxMaQ0b0v7F1+AWY5IqhgwklXz0SKuht2FF14IjuOCXmvWrAEArFmzBps3bxbtc8EFF+Dzzz+H0+nE0aNHsWTJkqDjXn311Th48CBcLhcOHDiguk5eLNBSXiAQrSn9BoMBRUVForpGoZYNOjsnoK/3QYwdc4vskghbKgp1HlJGoRAWJ6Q0MEo9ZCKtaxY42HK+WXC7foshg3+MkpIbABSgbNCN/Gw01ExerTESuCRlMj+AjIxzABSgUMWsn7VQk2oQbjKZkJ2dDY7jRFXmc3JyQp6Xx30JvN5cNJ6SLozKvi9WZFoqsJuV4igbdGPQkhjrkwkAVmunovfBarUiLX0nBg95mjdI/FXq/4jGpv9V1aEi0vtD6qHm8/nQ0NAQFMQd+OBgta+Ey7dut1u2S0AoBqLmhcdh50Oa11/zPp98BmxgEtaw4c8hJ3df0Hb97TAvhpzmQ7VGNJvNyMjcLdK8v5Xd/TBb1oQ0DIHoaF6qKLNUxw8pzcebpIqxSwU8Ho9seQHmopebYbOUfq0ZX52dE9Dd9b2wlg0SkUhFLBXLwwaysrIfwmR8FMXF1/Cz0VAz+XC8TCzAt7fnC5iMj6K05NqQMUvC+JW0tDRRzAsb5A0GAz9TtVqtQW2RpPB4ZqCt9V60tJwNoL/zRODSaUvzWpjNHZKB3awUR3HxNUFLYqxPZk/3HLhc2SG9D+xzWprXnq67tQZmswMctzvoIRFJ/TI5Ao0AR+fbKBv8J7S1bQwy7AIHc6miqsywk4pRam3bqNhFgjTvZ6BrPiMjA4MHD0Z9fT2/vBip5lmHE6C/84RUuARLyCgo2Bn0N6b1IYMfktS8s2+eqtaIHR3rRJo/XrsKBkMbMjL2SxqG4ZTBUiJQ861tG2Gx/gYG49agPrGBWo51IWU1kGGXALBBq6O9/+ZWg5aWK319U0IuG2hBWMMpHJSy6kLNmlmyRkZGRlQbwLPZqNogXCUC43jYkhR76LLvI9TyFLvevr6+sJqty2E0GmGz2WA2m/mBnJVAYcsaubk/hMeTwwd2A/2t5dRkBvb1TcGB/dcjPW2uYj/NgsLF8HhyUFC4GC6XC86+i0TN7YUPiXANHy2wqvysPIQeM3Sm+ebTS1ZqOzOQ5jNUJ22EQ6JqPisrC6WlpbonIbB6iQ7HeknNO51OPiGD9S9W21oO8McMHqtZAqdzqqJmcnIWiTTvds+Gz5cLh2OMpGGot2EXSEvzWlHB72Rb2iXD7jSTJk1CRUUFVq5cGZXjs6bHvb3v8XEwbFblcrnQ2toKr+9SeDzqZ9jxmCkwD4PZ/Jmqci1ysBhCqUEt1KxZT8PO7/KX9piw2ageJSUC43jULkkBysHW4RIYv2UymWCz2WC1WvmBvLfnAv5eraurQ2bm5aivu4MP7Ab6W8tpyQxkdefk7tv8vAWor7uD/24Cm9ur6Z8rJFKDJCdnkd+wPF0eIlB39pxqjBz1l6BAceHvZjKZkJmZGaR5YJ6mzgzx0LwwkzXems/KygppDIUiGTSvNRtWDVIxm6zDSaGM5l0uF1/eo6N9PABt7SQZLDNW7r61Z18h0jzrmdxQ/10cPXJLzDVfULhYVPA70LDLyd0nqflosHLlSlRUVGDSJOWEGCFk2J1m165d2L9/P6qqqqJyfOEyVqBhB/hv/Oams1B7XL8ZdjToD4r9OPTGYaLnrDkUdfWrNXlMwkUYg6YGtsxiMpn4ZQo9+uwyAgd5Vhi1tW0jn1nX1zcFBoMBpaWlQQ/SrOzPkZn1MLye4SIvRCKitmakHPbsK3Citkq2PERe3g6RR48h/N2Ey2bC82ppPgu9PQ9qzsiLJXIFbfWENO+H1TDs6X0t4TSfk7NXpPlY/FbhEqnm8/MWKBb8LijYKan5aFBVVYX9+/dj165dqvchwy5GsOUl4TJWOMhliwld50B/FpvL9YFs7EQ4sKBYYXHLwJR3tRW/GYHXpOesORRlg24Ex+Wr8phEkqknjEFTg9CwY8sUSrFpBuNWpGfch7T0+1RXUBfCCqOq8bz19r6HwsJNMJs7YDIfVe2FUEK4vMO823oWfmUoNetmsYWhArUD6e0tA8cZ4HYNE5UEUfO7qSHempcraOv3fN0Dk/ke0rwEWjUP9CepJJrm7TnVKCn9WKR5PX4rfrm6aXlSab6nR1rziQIZdjGCLS8Jl7HCIdQgz2YoBoMBdrsdnV2vimIngH5DrLVtIzweT1BGlVL8CguKFXovAlPetbjohdektTCpHiURiouvgdfzsCqPiVSGbjhoqdoP9C9TSGXGMfyB2T0wGnskPREsW1LuM1lhVKHnLS1tB4aUrwxaDuru2QCDgQPHGYIe9swr4PF4+EFbOFhzHIempqaggVC4vCNMngj6Lk63Waure1kUpxd4H+fm5qK7519BtbSUCpCy2EKlDL5AHJ1vIzv7EAwGDmbLMVEWnZrfTQ3x1rxcQVu/56tH1LNW6zWFo6VIdU+a96NF83l5O2Q1z+I+lTQvVwePLVf39GyR1XxOzt6E0rzZ/BnsdmnNJwpk2CUAbHBNz9gV1KKGpciHO5PJz/8xvN5c9PVeyL8nrDMmfDiwjCqtgcmBKe+xctGreThoKT4aDaTqWCnFGgHiOEa1+AOzM+DzZUh6IkIN8qwwqtDzlp6xBRaLI2g5KDPjKrjddpw6NTvoYS9c7mGDtnCwljPsPO5L+OUdYfJEIKzN2qlTa0TLSl6vFzU1Nfj2228BALm5uWhve0k2bIAN9sJZPIstdDkvlgyUtlq3B3VN6OhYxz/wtLRlExpUgcHoyaB5gHm+MsBxGTFdlgtlbJHm/eip+ba2KXC5siU1L4z7lNN8d3e3pFeLLVdnZFwgq/n8gp1x07w9pxrZ9v8V/S7+Sah2zccSMuziBAuObW3byA+u6emfiFzjVqsVFstHmoPTgf6g2MFlPwTn+z2MRiNvNEq13omEwJT3ePWvlCIwgDkWBY8ZrW0bYTDeB5vtP5o+j8Uxqp1FNja+CqNxE9yu76Kv9/dBngiW8WqxWDQZDb09F8DttssuBxkNBpSUlMg+ONigreY+83hm8Ms7gckTQlibNaljBnqwcvN+BK83F709FwZtqzSLZ3XBAv9mS/sYRmOb6HdhiRWnTs0O2ZZNGNMkLEsh9FYmi+YB5vl6DF7PY6T505Dm1WseECxXFy2V1Xxry+S4ad4/kWwX/S6s44gazccLMuziBGsVIxy8A13jNpsNQ8tvQTgDMhvk2eAijKdghhgAxRpaamAZjolUnFFIYACzXksratBS0V4Ii2PMzLhKlSeFBYPLPRRYxquf98IyGoR092yAxeJAXv4OySBrBhu0leLvlDwV7N4yGj/FsOHPIS1tB99mTU1MX2bGPBw/9nP09k5WdV1sWSZwts9qfHk8w+Hz5YlKL9izrxBlDAL+h43D4QiquSYX0yT0ViaL5tX204wHpHn9NZ+XtwNWa6eumpe6B4UZ81brdowc9RcAiLnmAf+Sq9Hogs+XLtK8xzMDR779maTmE0UTZNjFCdYqRjh4S7nGpfofhoNUPAWbJarJDpOb9YYqXQEolxeINuEEMOtFOFlxgP+czab/w4gRym2XGCwYXKoIqMlkQkHhVygfuhIOx1toa5X2eAm9SYxQS7FyVeu10J9lHdw7lN1bVttHQTFj0YAtywTGELE6dmZzDfp6HwxZesHn86GjoyPIsJPSICD2VgKJo3lAOjZMjWEnjOmLNaR5/TXPlmL11LzF8pHi84RNTPIlCiPrhZzmAdZqsQ+ATbXmybAb4LBWMZEO3mor70sZjWyWyOIzlAywUK2ClIhVeYF4IpXJqfUBI2c8h6pjx4LBpQYf/0PiXzCbHejpeY1vH5Wft0BUn0zKmyS3LJOefhmO1SyRLQUAhC7iy+KQWDsnqd6hbrcbDocDvT0X8jW2ogkr+RAYQySsY2cymVBcXCwbMwT0B6AHtl6T0mA4xErzQHDParUE9gtORQaS5h0dlfj2m5sj0jxr28U0P7T8FknDzuFwwOv18hOT1hZ13rdwkNM80L/k6nLORnFxMbq6umQNN6b5eExkpCDDLkawQaDD8bhsv00tsJk0a20TTvAzy3Bl8RlaDDBWb0mpMTyDzS5Zk/FURCmTUy1yxnOkdewKT3sR8vN/JAqUZ/XJzJYPRd4dq9WKvLw85OZeibqTvwgrqzOwkK7JZEJh0Vc466y1SEvbEdTOScrYcbvd6OjoQG/vZByrWRIUz8Jih47X/gYG430wGj/l94uk/VQgwjp2JpMJhYWF6OrqkjXsmNejq/tF/uFsMG5Ftv1/kZ39edjnkWyaZwZ7rOLbYg1pXoyU5gsKv8KIkauQk7tPsoVbIEzzPp8PLtc0/5Jnx3n832OleaC/MLrPNxOFhYXo7OyUNVqZ5hNlIkOG3Wmi3XmCDQJO52cwmzv4QT9cC18py0rYekoLWuo7sXpLagb54uJrYDb9n2KT8WRHmMmpd7B2pPXQmBehqOhqUWkLVp/M475E5N2xWq0oKCjAkCFDNPXCVMJsNsNo3ASrrSvsJdW0tB2ihuCs92ZX12aYTO2w2j4CEJ1BXgvM6wGAfzj7H6jtKCjcNGA0bzI+irKyH8Ysvi3WkOaVMZvN4Lh3ZfvMqiEndx9GjFyVNJqPRqF26jwRAdHuPMEGAZttBjyeHACIeLbHCIyDCXeQ11LfiRAjzOSMZNlaCr3qoQXC+WbB7fotiouv0W0wV8JiGesv6ukeGtb+bFbMAsZZ782MjAtk42QigZXNUGrrZLFYgjpKsB6tWZnX8Q9n/7kaYDBwpPkUgTQfmpycRfB602A0ujQXAQb6OzzEWvNKky+TyYSsrCxJzUejaxR1nkhg2CCQY/8l6uvu4Ad9PSz8wGbSoRpqRwqL04hHMoRaYlniIFqwawi3L6aa70BtvBbQH/cTKozA6/VKVmN3uw/CYOBgsRxXdwEBsFkxCxj3uGegrfVe5Ob8UjZORqp9n1pYhqPSchgz7HLz9iG/4HcYMfIpvuMDi6O1Z19xusjv93Wb1ZPmgyHN6695wG/sDBv+HHLz9sluI6d5e/YV8PmsMJn6NBUBZrS0TI6L5pUmX8ywk9J8okCGXZzQmjyhpehmqIbakcLiNBI5GULvGbQUUg9TljEo1b5GK5E+qPT+DljcT3fPBsXt2CAfWI09M+MquFzZYSdB9PVNwbGaJXzAOGv0rVRqx99maw8GD3k6aBbu8Xhw5MgRHD58WNSWi9XpYhmOapbD/PWuemEy9ckuNWtNniDNa4M0H53vgJUEKSiQ9xj5fD7ZDgxtbVNExpkWOtrH4+iRW3TVfG1tLRwOB5/ZLaV5NZMvNZqPF2TYJQla6iNFu6E2i9NQE5ejRKLMsKUqxatB+DBlS2EcxyV0ja9IYHE/4fY7Tk+/DAf2Xx/1op6BnkWpmpGA/yFx/PhxHD16lP+9jEYjX6eLxSmpWQ7zF05Oh9ebplv2Lmk+epDm1cNKgrS0qI/xEuLoqMSRb38WsmRIJGjRfG1tLbq7u1FTUwOPxyOpeTWTr2hoXi/IsIsRbrcbfX196Op+J6ysWC31kQIbaptMJpSUlKhyTasZ8FjvyEjjcsItHKr3spPZbEZ5ebnm8xA+TMONcdLyoLNYLCG3DWxPpScs7of1O/b5fGhoaIDH4xFdh8lkQnZ2Nn+/sb+pCbqX/eycauTlPwp7TnXIbQM9i1I1I7WSnf05su3/yy9FZmd/jrT0ZbxHwNFRidaWX6OlZSbSM7YgO/tzXvPt7W8E9a9UA2m+H9J8fDQP+MOIjtUsQXvbeJHmgf6QABaSoKfmWYHinJy9IbeNhubN5s9EyVqA34BkWpbSfKJAhl2MYIN8b+/rkstZXq8XXV1d4DhOcn+p+kh1dS/D7bkHdXUvK3622WzGkCFDkJ+fH3IwCXfAiyXRXHbSMugGPkwj+Tw13zcb5Nvb35B9yAnbU2k5h7KyMhiNRk2dRDiOw6lTp05XiQ827ISB/cOHD0dGRgZsNpum2Jfs7M+Rl/8oCgo+hcnUjry80LEsgZ5FPWpG5uRuh9HYzi9F+v/dFuQRyMvbAZOpHTm52+HxeNDX1wdH5yuS/Svl4pIYpPl+BrrmbTabrHEbqeYBf7ut9vb2kF5HoeaB/kxtq9UqqfnMzEyRwacGNomypf1LdYHiaGjebPlQlLgBsN7QYi0LNZ8okGEXY6zW7wUtZzU2vgqL9Tcwmz+TjFGQ49SpNXxz5NCfG97sUg42S4xHQcZoLjsJPQrRXDaK5NhKDzlheyot5xJo2AmNDUfn2yGzQ9VgsVhgs9lgs/0HBuN9IY0TwG9AmUztMBgAny8XvT0XhAz6DvQsyhHKsBLS0T4NPl8uvxTp/3dwNf+2tinwenPR0d4f1J2ZcRU4Ll+Uwcc0bzBuJc2rYKBrHpDXfaSaB/oNOzahY5qP1AvIDL6cnL2wpT2oWvP+SZQRbrcdXV0zddW82g4RrECxMDYwJ2dRkJalNB9vyLCLMVbLpUE3YF39ahiNbSgu+QjFxQdUC19YRynWsFliPAoy6jFrVkM0e0xGcmylh1xgeyo5lPo1BuLPCm2Bw7Eeubm5ES2vAEBaur8GlZxxwgwSi8XCG1Qe93z09T4Es3m25sK8vb3vSdaMVGvYWSwWGAwXorvr1+B8s+DofNvvkXNfEuQRcHRUoq31XnR2TuDfS0+/DF7Pw6IMPqb5oqIPUVD4leprIs0PTM0D8rqPpuZZLGFgSR+t5OXvgMnUIat5s9kcoPk85OffhBO1VTAaLtRV8w6HI+SKhNVqRXHxNag9fhs8nhl8DB+AIC1LaT7ekGGXAPiLhPprXGVl/1u1YSesoxRr2CwxGg+YWAZYx+qz9PwcPR5ySj1DWcwVM+D8WaEFKCxczA++9pxqjBz1F9jSdmgOQg9VzFNo2HV2TkCn4/6IAq/lAqnVYrFYREVe+d6xYZRvYAg1z3Hvqi5vQZpPns/S+3Mi1b2S5oWaA/o1z2IJs7OzkZf337A1z8qWqNV8X++DEdXwi1TzzKPJjNlIO4HEGjLsThPtzhMWiwVpaWmSA3hx8TVwu64OOyUciH4dKwYLluW4WfB6Ho7KAyaas+Z4fVYkn6P3khoQ3DNUCIu5YoO8PfuKoEyxvLwdsFgcsFo/0hyfFc1inlIEBlJ7PB5R6yOtsN6xTKsspjA9fSeGDX+Or2nFNC/l4RRqPtzuAqT5xP6sZNJ8oGHHNC80IvNPFwsOR/Md7eNxrGZJUmte2AnEaDRKaj4aUOeJCIh25wmlQR7o70sXrmci3OBi1ntP7cMh3KbgRPhEY5AP7BkaOLCHor19GjyeHHi94ocEayovV2WeJUNEmkHW2rYRaenL+OMEZq0KEQZSNza+ChiWorn5D8jM+p2qLNtAWO9YplXesMvYDIvFwde0MpvNITV/orYqbM8EaT51iaXm1X5GW+uUsDRvNn+GkaP+EpbWhOil+XDGnsBOIHKajwbUeWIAoza42OVyibIeWe+9SLLN2NJdZmZmQtSoGqhorSgvRIthZzabYTRciN6e38CA/vpNDocDNceeg8HQKrtMyZIhIs0ga2leC6OxjT9Of8D1K3ySB4uzEZYWYk3vTeZqGI3iLFv2HXR3vxuyrZAQ9r27nLPhdttjVtNKS0IBC453u926aB7wf18jRozAyJEjSfNxQg/Nq/ntTCYTOG5WWJpn2aVqMtqV0EvzwrHHYrEklebVQoZdiiAXfxEY58EMO+aSZr33ws02a23bCIPxPths/4Hdbk/Zht+JjslkwvDhwyNqRxSInLFntVr5mDNW8NPpdKK7uxvNTeefTna4RLI+Wkf7NMkMMuF9yv6/u+dfGFK+UlT/jR2zpOQG+Hx5/HE62qedjlnz8XEwPT2vwWzuQE/Pa/z+rOm911MJny8XbW1TROeQm5uL9vaXEaqtkHCf0aNHY/jw4fD5ZuJYzZKoF2BmqNU8IDbs9NC813cv2tvfwJlnnokzzjiDNB8HoqF5YRJD4GexciZaNc+yS4VaYwjLogg1L/T+GY1GXTUvHHuYYadF88LvPdaaV4s+dwOhC0ajEWVlZbrOflmcR2dnJ/8em21YrVZwvlnw+mahuHh6WMcXVscfNSo6Ve8jIVEq3WshnHNmcXFK+LPiVp+OsTlX1XmE8uKxQZ59dmfnBFgsl8BiscBqNQXF4vgzxy4Q3Y/ss4YPH87/e/jw4di69SVYLA6YTB+jr9e/fMQeHMAPcfjwIHR2nuKPm5mZibT0zXwcTE7uIrS2/gM5uf0xbMXF1+Cbbwajt7cXHR0d6O3tRVam+JoKChejoeHvKChcjKbG/vcDk0qE5y28nrS0HcjJ/QS9vW0AimS/O4aaIrRakNK88LckzSceqax5j2cGamuHSnoV2b0KAHa7nde8z/chgJ8B0F/zUqVO5DTPnsnC70Pqe2eab21zY9Cgn8t+d7GCPHZxgs0UhEI2GAwoKysTiUKvQUp4HHZj6jHwaamOHw9iGZQdSLi/ndZzVvs5LCvOYvkoot+eBdNHO+aKtTIS1oxSwuWaBq/nYT4OhgWAS8Ww+Xw+dHd3SxYEl2srxLo5NDU1yRYSB4D0jC2wWBxBRciNRiNycnKCvnthEVogOprXGkOpBGlenlTVfCRLvlpgmlebRBiO5qXqRspp3mg0oqioCE1NTYr1Jpnm41EKSAoy7OKElGEnhV5NnaWOo8cDWqo6PuEn0bLv2AN5aPktqu4nuYeHmvtGbZsjNQ8oNuGJ9kNFzfW6XC40Nr6K8qHPyAaLs3IugT11TSYT7HZ7zDUfOFEkzUePVNW82WwOqUE9NQ8ElxmKBkrnwiZDgD9BpGzwn2SLtIcq4RRryLAbwLBsN73iM+RIxqWRVIJ9/6Ul18o+kKV+o0gMDLVtjpQeUC3Na/3lFWwfKz5UenvfE8XisWKiWjtlyF0vM4aYTqRaDQlh5VxCVcGPB4HXEs3PIc3Hj3A1H8nvpqfm/RqzwG63S+peL82rMewsFguvebk6drEu4RQKMuwInmgNxvFcGokV0XyQRXpsOYNFGOisl5eIEU6bo0DULst092yAxeLg+zcqFRN1uVxwOBya2ngFItVqSIjRaITdbtdl2TPakObDJ1U0r9dvNBA0L1dzkmk+USYyZNjFCGb9Z2Rk6BbrojcDYTCOFnobRlLH1vt3iWbzd6k2R1arFXa7XXVD8Py8BaJ6cYGYTCbk5OTAnn2tKBYvsJioEJfLhY6OjrALlQKha06y80pPT0dubi7MZnPMYpS0QpoPH9K8GDnNCzs4hCKRNa9Uc5KdFxl2CUa0O08EGnZU841IVazW7UhLXxZUODQrKwtnn3122JOawFIKZstnyMt/FBaLBY6OpfzDILCYqBw5ufswYuQq2Vg5t9uN9vZ2VQ3DpRDWCTObzRg+fDhGjx5NmidSDjnNMwM1JydH9YROSDQ0P2z4c7JLtpFqPhpQ54kIiHbniUCYq51myqlFrNo8JTK2tI9hNLYF9aSMtINBoLeBFdptb385rCDrgtMtkizWf0r+XkqZr+FAmk9NSPPymgf89312drZqr52QaGm+re3vkr+Z3prXA+o8kcAw8autbJ3IxKrcRTISbpunZEBt3I+z72L4fHmSPSn1hBXaDTcTraVl8ukCp5zk7yX0uKmBFXFlnglWyJc0n9qksuYBdbpPJs273Xb4bczg3yxSzScKiXU2KQwTf6g6N263GzU1NXA6naL3mbg4jpP8u9S20VryiVU2baIj9T1rafOUbAR6nAzGrZLLLy7XNPT1Psj3pIwWnE9dU3q50kId7ePReGo2fL68iH8v9t3k5ubyxg8r5EuaTx0GmuYBcSxhKmj+WM0S5Ob+FJH+ZlKaTxTIsIsRTPxyMw2z+TMMKV+JltbXUVNTE7TGz8RlMBj4v7e2bcSgsqeCPAIUEB0bpL5nuTZPyYKWZSWjcZPs8ksiITfI5+TuQ37BTnjcl0T8e0ktM7MaYqT51CEVNQ+o130qaH7Y8OcAIOLfLNLQkmhChl2MYOKXm2mEqpMjRUvzWpjNHQlT7TpWUI0seSL9brQsK/l8c8JafmEGjZYlSi3XxQb1UEkaLN7GbPkQLpdL0SsW+Ply7f+E2a9y1ewZpHn1kObl0eO7Uav7VNF8R8c6eDwevuet2s+Xav+XiBnvZNjFGLmbNVSdHClYU+SSkht0PsvQxHOgHejeCaXvPtLvRsuyEuebFdbyi8XqN2haWl4MuS0zoLKyslRfl9pBnsXbeNyX8IadXDZcYGkLqfZ/QH+FfuGSJWk+cga65gH571+P70at7lNF8zk5i/iet2o1zz4n8JykNB9v4m7YPfPMMxgxYgTS0tIwceJEfPrpp4rbr1y5EuPGjUN6ejrGjBmDF154QfT3NWvWwGAwBL36+vqieRmqkcuMC1UnR4qysh/CYn4MZWU/1Ps0QxLNGk6EMtF8yEktK+n9QPf55oLj8jG47KaQ27JBXs9rzc7+HHn5jwIAjh65RbZmll6Q5gk9iKXuU1nzx2qWaNJcMhJXE3P9+vW466678Mwzz2DGjBn485//jHnz5mH//v0YOnRo0PbPPvssli5dir/85S+YNGkSdu7ciZ/97GfIy8vD/Pnz+e3sdjsOHTok2jctLS3q1xMuVqsVQ4cOhcvlSiirn0hdtAzc7IGiF5xvFry+WSgunq7bMZUIvNac3O0wmRwoKNgJR8d5mo+nRzFS0jwRa0jzfs13dU7QfLxEK0Acirh67J544gncdNNNuPnmmzFu3DisWLEC5eXlePbZZyW3X7t2LW699VYsXLgQI0eOxKJFi3DTTTfhkUceEW1nMBhQWloqeoXC4XCIXkoZaHpjs9kwcuRIFBQURP3GoZpLBBD57D/Ry194PB7U1dXB4/EEecw62qfB681FS8vksI5tMpkk2wdpfXDGSvMA6Z4gzcdb81pxOp1Bdola4mbYuVwu7NmzB3PmiIMw58yZg23btknu43Q6gzxv6enp2LlzJ9xuN/9eV1cXhg0bhiFDhuCKK65AdXV1yPMpLy9HTk4O/1q+fHkYVxU/1N5gqV5ziYgNfPkLy2cwmR9AY+OrOHHyIQwf8QekZ/wj3qcHr9eLuro6yTZCnZ0T0NZ6Lzrax+v6mbFeqtTyUCHdE5FCmg8mmppfvny5yCYpLy9XvW/cDLvm5mZ4vV6UlJSI3i8pKUFDQ4PkPnPnzsVf//pX7NmzBxzHYffu3Vi9ejXcbjeam5sBAGPHjsWaNWvw5ptv4uWXX0ZaWhpmzJiBr7/+WvF8amtr0dHRwb+WLl2qz4XGCLWzscAgWco2IyKBVYKvq18Nh+NjGAwcrNb/Rn1WH+g9UJuZZrVakZOTA4vFgqysrLCq4ScKWjwwQt2T5olISHbNJ1oxYTmWLl0qsklqa2tV7xv34I7AgZXjONnB9te//jUaGhowdepUcByHkpIS3HDDDXj00Uf5H3fq1KmYOnUqv8+MGTMwYcIE/OlPf8JTTz0lex52ux12u12HK0psiouvQW3tSBQXTwSgfywFMbDw+ebAaNyEskE3orVtBzo6PkJm5gXwuKUHWzY419XVRfS5zHvQ2NgIAHwvVuHSZmCfSfb5drsdPt8nyLZ/gObmSQAGB52jnOHT2PgqTOZnT5d7iE28kB4IdU+aJyIh2TXf2jIFwMVB55homrfZbGEvm8fNdC0sLITJZAryzjU2NgZ58Rjp6elYvXo1enp6UFNTg+PHj2P48OHIzs5GYWGh5D5GoxGTJk0K6bEjwoNm/wMbVgm+uPgaDBn8EE7UPoDiInlvt5YOBlrb+wTei2yQlxoczZYPYTS2Iy9vh+Q5yt3TdfWrYTC0JnyB1mhCmh/YJLvmc3K3S55jKmk+boad1WrFxIkT8cEHH4je/+CDDzB9urJVbLFYMGTIEJhMJqxbtw5XXHGFrHuV4zjs3bsXgwYN0u3ciX6ovlTykMgPZKfTGVQgWOsgrwWP+xL4fLloa5uiab+yQTeC4/IVC7Qm8vesB6T55CGR78V4ab6jfZqm/ZJR83Fdir377ruxePFinH/++Zg2bRpWrVqF48ePY8mSJQD8a8wnT57ka9UdPnwYO3fuxJQpU9DW1oYnnngCX375JZ5//nn+mMuWLcPUqVNxxhlnwOFw4KmnnsLevXuxcuXKuFwjQSQKibwExwoEFxQU8AZDNAdLj2cGensnw9HRhKxM9fsVF1+Do0eHYsjg4K4TDPY9d3Z26nS2BBEepPl+mOY7O1s17adF84lCXA27hQsXoqWlBb/97W9RX1+Ps88+G++++y6GDRsGAKivr8fx48f57b1eLx5//HEcOnQIFosFF110EbZt2yb6Qtvb23HLLbegoaEBOTk5qKysxNatWzF5cnhpzgRBaIcFNkcyQEdjsGTxMmbfbLjd4Y0JZrNZcrnH6XSivr4egwYNIm8WMeAgzSeO5uOePHHbbbfhtttuk/zbmjVrRP8eN25cyNIlTz75JJ588km9To8giDCQGwijQeAsXylYm8XLmMyb4PVO1PU8pDwQBDFQIM0njuaTI++XIAhChsBipErB2mWDboTPl4eWlsnw+XyKx6WivgSRmJDmlSHDjiCIpCSceJzi4mvQ1/sgHB2VIbelor4EkViQ5tVBht1pJk2ahIqKioRPskiVGQWRulgslphkiEWanWk0GpGdnS1b4DSwmHe8IM0TiU4yaZ4VK5YiUTQvZOXKlaioqMCkSZNU70OG3Wl27dqF/fv3o6qqKq7n0dq2UXEQT5UZRaqSaGnv8YAN8okUcyKFyWRCbm6u7O9VXHwNTMZHUVx8TVTPgzSf3JDmk0vzdrsdmZmZkn1vY6V5LVRVVWH//v3YtWuX6n3IsIsRasXf0rwWSoN4Is4oiH6oxldyIVWpXi9I8wMD0nzywZIt1BRNTkbIsIsRasVfULgYSoN4Is4oiIFJYO/GZCYay52keSLVIM0nB2TYJQhsdl9acq3qQZyWAAi90XJPaWkVFO5nRBOj0ch76+Kx3EmaJxIFtfcVaT45IMMuQVDqVRdqH1oCIPQiFvdUoty3wr6S8VjuJM0TiUK076tEuW/jrflYkZoLzARBEBooLr4GtbUjUVysbwFTgiASk1TWPHnsCIJIOZTiZ0wmk2KZE4Igkg/SfD9k2A0wEiXWgSCiiVL8zEAb5AHSPZH6kOb7IcNugJEosQ5EaiA0GDIzMzF27FhkZmbG+7RSOn4mHEj3hF6Q5hMfirE7zaRJk2AymVBVVRX3IsUEkSwwg4H9/9SpU+N7QqdJ5fgZgognpPnYsnLlSqxcuRJer1f1PmTYnWbXrl2w2+3xPg2CIGJANAsTEwSReCSr5pmzyeFwICcnR9U+tBRLEETciXWxUGHZAy1QrBpB6ANpPnqQYUcQRNxJlmKhSrFqqVzJniD0hjQfPciwIwgi7sQy8Nlg3AqT+QHdB+NkeVARRCJAmo8eZNgRBBF3YtUP1Wq1wmL5CAZDq+6DMWXlEYR6SPPRgww7giAGDDabDUPLb0E0BuNYPagIglDPQNQ8ZcUSBDGgUFsWIRmDpgmCCGagaZ4MO4IgCAmE9boIgkh9UkXztBSbZKTKjIIgCHWQ5gmC0AIZdqeZNGkSKioqsHLlyrieR6hBnFoDEURqQZonCEKOlStXoqKiApMmTVK9Dy3FniZROk+kiiuYIAh1kOYJgpCDOk8QBEGEAS13EsTAIpU1Tx47giAGPOQ1I4iBRSprnjx2BEEQBEEQKQIZdgRBEARBECkCGXYEQaQcqRw/QxBEMKT5fijGjiCIlCOV42cIggiGNN8PeewIgiAIgiBSBDLsCIIgCIIgUgQy7E6TKJ0nCIIgCIIgAOo8ERGJ0nmCIAYiFPhMEAML0rw6wuk8QYYdQRBxJxUCn+lBRRDqIc1HDzLsCIIgdCAVHlQEQagnUTVPMXYEQQwoEnWWTRBEdBhomiePHUEQA4pEnWUTBBEdBprmyWNHEARBEASRIsTdsHvmmWcwYsQIpKWlYeLEifj0008Vt1+5ciXGjRuH9PR0jBkzBi+88ELQNhs2bEBFRQVsNhsqKirw+uuvR+v0CYIgCIIgEoa4Gnbr16/HXXfdhfvvvx/V1dWYOXMm5s2bh+PHj0tu/+yzz2Lp0qV46KGH8NVXX2HZsmWoqqrCW2+9xW+zfft2LFy4EIsXL8a+ffuwePFiXHvttdixY0esLosgCIIgCCI+cHFk8uTJ3JIlS0TvjR07lvvVr34luf20adO4e+65R/TenXfeyc2YMYP/97XXXstddtllom3mzp3LLVq0SPKYHR0dHACutraW6+jo4F99fX3hXJIkfX193IMPPqjrMZMFuna69oHIQL5+uvaBee0cN7CvX+9r7+vrE9kktbW1HACuo6Mj5L5xM+ycTidnMpm41157TfT+HXfcwc2aNUtynwkTJnAPPPCA6L1f/epXnMVi4VwuF8dxHFdeXs498cQTom2eeOIJbujQoZLHZIZd4OvBBx8M88rkP0PND5Jq0LXTtQ9EBvL107UPzGvnuIF9/Xpf+4MPPihpm6g5ftyWYpubm+H1elFSUiJ6v6SkBA0NDZL7zJ07F3/961+xZ88ecByH3bt3Y/Xq1XC73WhubgYANDQ0aDomo7a2Fh0dHfxr6dKlstvGou1YOJ8Ri31i1XItFucVq31i8RmJ+n3F4jPo2qO7D2k+NX77gXzt4ewT7/t+6dKlIpuktrZW/UF1MS3D4OTJkxwAbtu2baL3H374YW7MmDGS+/T09HA//elPObPZzJlMJq6srIy79957OQDcqVOnOI7jOIvFwr300kui/V588UXOZrNJHjMcK3vcuHGqt43VZ8Rqn1hcezifk4jfV6yuPZx96Nqj+xmkedJ8tD4j3H3ovk/u+17L8eNWx66wsBAmkynIk9bY2BjkcWOkp6dj9erV+POf/4xTp05h0KBBWLVqFbKzs1FYWAgAKC0t1XRMjuMAAA6HQ/W5e71eTduzbaP5GbHaJxbXHovzisU+sbr2cPaha4/uZ5DmSfOJdF6x+gy676P327NtmM2ihIFTs1WUmDJlCiZOnIhnnnmGf6+iogJXXnklli9fruoYF1xwAQYPHoyXXnoJALBw4UJ0dnbi3Xff5beZN28ecnNz8fLLLwftf+LECZSXl0d4JQRBEARBENGltrYWQ4YMUdwmrp0n7r77bixevBjnn38+pk2bhlWrVuH48eNYsmQJAP8a88mTJ/ladYcPH8bOnTsxZcoUtLW14YknnsCXX36J559/nj/mnXfeiVmzZuGRRx7BlVdeiTfeeAMffvgh/v3vf0ueQ1lZGWpra5GdnQ2DwRD9iyYIgiAIgtAAx3Ho7OxEWVlZyG3jatgtXLgQLS0t+O1vf4v6+nqcffbZePfddzFs2DAAQH19vaimndfrxeOPP45Dhw7BYrHgoosuwrZt20StQqZPn45169bhgQcewK9//WuMGjUK69evx5QpUyTPwWg0hrR+CYIgCIIg4klOTo6q7eK6FEsQBEEQBEHoR9xbihEEQRAEQRD6QIYdQRAEQRBEikCGXRg888wzGDFiBNLS0jBx4kR8+umnittv2bIFEydORFpaGkaOHInnnnsuaJsNGzagoqICNpsNFRUVeP3116N1+hGh5dpfe+01XHrppSgqKoLdbse0adPw/vvvi7ZZs2YNDAZD0Kuvry/alxIWWq5/8+bNktd28OBB0Xap+NvfcMMNktd+1lln8dsky2+/detWzJ8/H2VlZTAYDNi4cWPIfVJF81qvPZU0r/XaU03vWq8/VTS/fPlyTJo0CdnZ2SguLsaCBQtw6NChkPslkubJsNPI+vXrcdddd+H+++9HdXU1Zs6ciXnz5omSPIQcPXoUl19+OWbOnInq6mrcd999uOOOO7BhwwZ+m+3bt2PhwoVYvHgx9u3bh8WLF+Paa6/Fjh07YnVZqtB67Vu3bsWll16Kd999F3v27MFFF12E+fPno7q6WrSd3W5HfX296JWWlhaLS9KE1utnHDp0SHRtZ5xxBv+3VP3t//jHP4quuba2Fvn5+bjmmmtE2yXDb9/d3Y3x48fj6aefVrV9Kmle67Wnkua1XjsjFfQOaL/+VNH8li1bUFVVhf/85z/44IMP4PF4MGfOHHR3d8vuk3Ca11QimeAmT57MLVmyRPTe2LFjuV/96leS2997773c2LFjRe/deuut3NSpU/l/X3vttdxll10m2mbu3LncokWLdDprfdB67VJUVFRwy5Yt4//997//ncvJydHrFKOK1uv/5JNPOABcW1ub7DEHym//+uuvcwaDgaupqeHfS6bfngGAe/311xW3SSXNC1Fz7VIks+YZaq49lfQeSDi/fapovrGxkQPAbdmyRXabRNM8eew04HK5sGfPHsyZM0f0/pw5c7Bt2zbJfbZv3x60/dy5c7F792643W7FbeSOGQ/CufZAfD4fOjs7kZ+fL3q/q6sLw4YNw5AhQ3DFFVcEze4TgUiuv7KyEoMGDcLs2bPxySefiP42UH77v/3tb7jkkkv4UkaMZPjttZIqmteDZNZ8uCS73vUiVTTf0dEBAEH3sJBE0zwZdhpobm6G1+sNak9WUlIS1MaM0dDQILm9x+NBc3Oz4jZyx4wH4Vx7II8//ji6u7tx7bXX8u+NHTsWa9aswZtvvomXX34ZaWlpmDFjBr7++mtdzz9Swrl+1vJuw4YNeO211zBmzBjMnj0bW7du5bcZCL99fX09/vWvf+Hmm28WvZ8sv71WUkXzepDMmtdKquhdD1JF8xzH4e6778Z3vvMdnH322bLbJZrm41qgOFkJ7FDBcZxi1wqp7QPf13rMeBHueb788st46KGH8MYbb6C4uJh/f+rUqZg6dSr/7xkzZmDChAn405/+hKeeekq/E9cJLdc/ZswYjBkzhv/3tGnTUFtbi8ceewyzZs0K65jxJNzzXLNmDXJzc7FgwQLR+8n222shlTQfLqmiebWkmt4jIVU0f/vtt+O///2vbOcqIYmkefLYaaCwsBAmkynIwm5sbAyyxBmlpaWS25vNZhQUFChuI3fMeBDOtTPWr1+Pm266Ca+88gouueQSxW2NRiMmTZqUcDO4SK5fyNSpU0XXluq/PcdxWL16NRYvXgyr1aq4baL+9lpJFc1HQipoXg+SUe+Rkiqa/8UvfoE333wTn3zyScjuVImmeTLsNGC1WjFx4kR88MEHovc/+OADTJ8+XXKfadOmBW2/adMmnH/++bBYLIrbyB0zHoRz7YB/1n7DDTfgpZdewne/+92Qn8NxHPbu3YtBgwZFfM56Eu71B1JdXf3/27m7kCbbMA7g/9HmPlRSsOyDtGxiIBRKEYk4RFfDEBGEoAyneTKQcGAkfa46yKLyIEwIxDMLstWBisWQhSR9WDuphZFSEgUdDWsqTna9B9kDo963d72l7n7/P9jBfO7d3hf3c8mfx+dZTG0q7z3w9QmzN2/e4NChQz/9Pct17+OlSs//KlV6/ndIxH7/rxK950UETU1N8Hq9GBoawqZNm376mWXX87/9cQzF3bx5UwwGg3R1dUkwGJTm5mZJTk7WnvxpbW2VgwcPauMnJibEYrGI2+2WYDAoXV1dYjAYpLe3Vxvz8OFDWbFihbS1tcmrV6+kra1N9Hq9PHr0aNHr+yfx1t7T0yN6vV46Ojrk48eP2isUCmljPB6PDA4Oyvj4uAQCAamvrxe9Xi+PHz9e9Pp+Jt7629vb5c6dO/L69Wt58eKFtLa2CgC5ffu2NkbVvf+mtrZWdu7c+cM5E2XvP3/+LIFAQAKBgACQK1euSCAQkHfv3omI2j0fb+0q9Xy8tavU7yLx1/9Nove8y+WSlStXit/vjzmHp6entTHLvecZ7H5BR0eHZGdnS1JSkhQWFsY8Bl1XVyc2my1mvN/vl4KCAklKSpKNGzdKZ2fnd3PeunVL8vLyxGAwyJYtW2L+GCwn8dRus9kEwHevuro6bUxzc7NkZWVJUlKSrFq1Snbv3i0jIyOLWFF84qn/woULsnnzZjGZTJKeni7FxcXS39//3Zwq7r2ISCgUErPZLNevX//hfImy99++xuLvzmOVez7e2lXq+XhrV63ff+W8V6Hnf1QzAOnu7tbGLPee1y0UQkREREQJjvfYERERESmCwY6IiIhIEQx2RERERIpgsCMiIiJSBIMdERERkSIY7IiIiIgUwWBHREREpAgGOyIiIiJFMNgREf2E3++HTqdDKBRa6qUQEf0jBjsiIgBOpxM6nQ46nQ4GgwE5OTloaWlBOBxe6qUREf1r+qVeABHRcuFwONDd3Y1IJILh4WE0NjYiHA5j3759S700IqJ/hVfsiIgWGI1GrFmzBhs2bMD+/ftx4MAB3L17Vzv+7NkzbN++HRaLBUVFRRgbG9OOjY+Po6qqCpmZmUhJScGOHTvg8/li5r927Rpyc3NhMpmQmZmJmpoa7ZiI4OLFi8jJyYHZbMa2bdvQ29v7x2smIrUw2BER/Q2z2YxIJKK9P378OC5fvozR0VHo9Xo0NDRox758+YKKigr4fD4EAgHs2bMHlZWVmJycBACMjo7i8OHDOHv2LMbGxjA4OIiSkhLt8ydOnEB3dzc6Ozvx8uVLuN1u1NbW4sGDB4tXMBElPJ2IyFIvgohoqTmdToRCIe0K3ZMnT1BRUYGysjK4XC6UlpbC5/OhrKwMADAwMIC9e/diZmYGJpPph3Pm5+fD5XKhqakJXq8X9fX1eP/+PVJTU2PGhcNhZGRkYGhoCLt27dJ+3tjYiOnpafT09PyZoolIObzHjohoQV9fH1JSUjA/P49IJIKqqipcvXoVwWAQALB161Zt7Nq1awEAnz59QlZWFsLhMM6cOYO+vj58+PAB8/PzmJmZ0a7Y2e12ZGdnIycnBw6HAw6HA9XV1bBYLAgGg5idnYXdbo9Zz9zcHAoKChapeiJSAYMdEdGC0tJSdHZ2wmAwYN26dTAYDACgBbtv7wFAp9MBAKLRKADgyJEjuHfvHi5dugSr1Qqz2YyamhrMzc0BAFJTU/H8+XP4/X7cv38fp06dgsfjwdOnT7U5+vv7sX79+pg1GY3GP1s0ESmFwY6IaEFycjKsVusvfXZ4eBhOpxPV1dUAvt5z9/bt25gxer0e5eXlKC8vx+nTp5GWloahoSHY7XYYjUZMTk7CZrP91zKI6H+MwY6I6DewWq3wer2orKyETqfDyZMntStxwNd/805MTKCkpATp6ekYGBhANBpFXl4eUlNT0dLSArfbjWg0iuLiYkxNTWFkZAQpKSmoq6tbwsqIKJEw2BER/Qbt7e1oaGhAUVERMjIycPToUUxNTWnH09LS4PV64fF4MDs7i9zcXNy4cQP5+fkAgHPnzmH16tU4f/48JiYmkJaWhsLCQhw7dmypSiKiBMSnYomIiIgUwe+xIyIiIlIEgx0RERGRIhjsiIiIiBTBYEdERESkCAY7IiIiIkUw2BEREREpgsGOiIiISBEMdkRERESKYLAjIiIiUgSDHREREZEiGOyIiIiIFPEXieJHDEuh38AAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f_signal = 0.135 * u.Hz # periodogram peak frequency\n", "p_signal = 1 / f_signal\n", "\n", "phase_folds = analyser.phase_fold_light_curves(\n", " period=p_signal,\n", ")" ] }, { "cell_type": "markdown", "id": "3c0f513d", "metadata": {}, "source": [ "We can also phase bin to make the pulse profile clearer:" ] }, { "cell_type": "code", "execution_count": 10, "id": "56d34cf5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phase_bins = analyser.phase_bin_light_curves(\n", " period=p_signal,\n", " n_bins=20,\n", ")" ] }, { "cell_type": "markdown", "id": "46629648", "metadata": {}, "source": [ "Now we can see the pulse profiles more clearly. Let's compute the RMS and see how it compares to the expected value of 2%:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d46dfa2a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "g-band RMS: 2.4%\n", "r-band RMS: 1.9%\n", "i-band RMS: 1.9%\n" ] } ], "source": [ "for fltr, phase_bin_results in phase_bins.items():\n", " print(f'{fltr} RMS: {100 * np.std(phase_bin_results['flux']):.1f}%')" ] }, { "cell_type": "markdown", "id": "6426c335", "metadata": {}, "source": [ "As we can see, the fractional RMS of all three bands is about 2%.\n", "\n", "It is also clear from the above plots that there is a lag in the pulsations between the different bands. Let's quantify this.\n", "\n", "## Lags\n", "\n", "One of the great things about OPTICAM is that it provides simultaneous three-colour observations. As such, it is possible to search for wavelength-dependent lags; `opticam`'s `Analyzer` class makes this easy via the `compute_cross_correlations()` method:" ] }, { "cell_type": "code", "execution_count": 12, "id": "2024f430", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Stingray only uses poisson err_dist at the moment. All analysis in the light curve will assume Poisson errors. Sorry for the inconvenience.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corrs = analyser.compute_cross_correlations()" ] }, { "cell_type": "markdown", "id": "cc4e239c", "metadata": {}, "source": [ "The `compute_cross_correlations()` method computes the cross-correlations between each pair of light curves in the `Analyzer` instance. As we can see from the above plot, the $r$-band lags the $g$-band by 2 s (since the time shift is negative, the second filter lags the first filter), and the $i$-band lags the $r$-band by 2 s as well. The true lag between these bands is a quarter period; since the period is $1 / 0.135 = 7.4$ s, this is 1.85 s. Within the time resolution of our light curves (1 s), we can therefore correctly recover the lag.\n", "\n", "## Using `stingray` Directly\n", "\n", "### A Cautionary Tale\n", "\n", "Since `Analyzer` stores light curves as `stingray.Lightcurve` instances, we can pass them directly to a number of `stingray` timing analysis routines. However, `stingray` assumes light curves are in units of counts with Poisson errors, while our light curves are relative (unitless) with Gaussian errors. As such, care must be taken in regards to units (e.g., in normalisations), and some routines either won't work as expected or won't work at all. As an instructive example, let's say we want to compute the cross spectrum between our $g$- and $r$-band light curves:" ] }, { "cell_type": "code", "execution_count": 13, "id": "dc7360e5", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "8it [00:00, 17716.17it/s]\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/fourier.py:1134: UserWarning: n_ave is below 30. Please note that the error bars on the quantities derived from the cross spectrum are only reliable for a large number of averaged powers.\n", " warnings.warn(\n", "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/fourier.py:1161: RuntimeWarning: invalid value encountered in sqrt\n", " dphi = np.sqrt((1 - gsq) / (2 * gsq * n_ave))\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from stingray import AveragedCrossspectrum\n", "from matplotlib import pyplot as plt\n", "\n", "avg_cs = AveragedCrossspectrum.from_lightcurve(\n", " lc1=analyser.light_curves['g-band'],\n", " lc2=analyser.light_curves['r-band'],\n", " norm='frac',\n", " segment_size=(segment_size).to_value(u.d), # stingray assumes all time values are in seconds but OPTICAM uses Barycentric MJD\n", ")\n", "\n", "avg_cs_amplitude = np.abs(avg_cs.power)\n", "\n", "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "ax.step(\n", " avg_cs.freq / 86400, # convert freq from cyc/d to Hz\n", " avg_cs_amplitude,\n", " where='mid',\n", " c='k',\n", ")\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Power [(frac. rms)$^2$ / Hz]')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5f1fc122", "metadata": {}, "source": [ "That looks how we'd expect. So far so good. Let's try to compute the coherence between these two light curves and check it's in the expected range ($0 \\leq \\text{coherence} \\leq 1$):" ] }, { "cell_type": "code", "execution_count": 14, "id": "6fcabe0b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/zac/miniforge3/envs/opticam/lib/python3.13/site-packages/stingray/utils.py:486: UserWarning: SIMON says: Number of segments used in averaging is significantly low. The result might not follow the expected statistical distributions.\n", " warnings.warn(\"SIMON says: {0}\".format(message), **kwargs)\n" ] } ], "source": [ "coh, coh_err = avg_cs.coherence()\n", "\n", "print(np.logical_and(coh >= 0, coh <= 1).all())" ] }, { "cell_type": "markdown", "id": "7d985924", "metadata": {}, "source": [ "Uh oh, we have unphysical coherence values! Let's take a look at some of them:" ] }, { "cell_type": "code", "execution_count": 15, "id": "22f3456c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coherence: 145786.42979469124, error: -27831888.517072193\n", "Coherence: 149251.12158688065, error: -28829924.14132792\n", "Coherence: 51569.663803655276, error: -5855352.333431175\n", "Coherence: 673.2232166696651, error: -8720.935095251942\n", "Coherence: 88721.1153985241, error: -13213126.6842703\n" ] } ], "source": [ "for i in range(5):\n", " print(f'Coherence: {coh[i]}, error: {coh_err[i]}')" ] }, { "cell_type": "markdown", "id": "0f9d4bb2", "metadata": {}, "source": [ "Our coherence estimates are in the thousands, and our error estimates are negative. Something is very wrong...\n", "\n", "The issue is due to `stingray` assuming Poisson statistics. Since we know the phase lag between these two light curves, let's see what happens if we try to compute it from the averaged cross spectrum:" ] }, { "cell_type": "code", "execution_count": 16, "id": "22bc3840", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plags, plags_err = avg_cs.phase_lag()\n", "\n", "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "ax.errorbar(\n", " avg_cs.freq / 86400,\n", " plags,\n", " plags_err,\n", " fmt='kx',\n", ")\n", "\n", "ax.axvline(\n", " 0.135,\n", " c='red',\n", " label='Lag frequency'\n", " )\n", "ax.axhline(\n", " np.pi / 2,\n", " c='blue',\n", " label='Expected lag'\n", " )\n", "ax.legend()\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Phase lag [$\\\\pi$]')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "367c021e", "metadata": {}, "source": [ "We get the correct phase lag at the correct frequency. However, we don't seem to have any error bars, and so it's impossible to quantify the significance of this lag. Let's see what our error bars are:" ] }, { "cell_type": "code", "execution_count": 17, "id": "53c5cb83", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[nan nan nan nan nan nan nan nan nan nan nan nan nan nan]\n" ] } ], "source": [ "print(plags_err)" ] }, { "cell_type": "markdown", "id": "4256290a", "metadata": {}, "source": [ "Our errors are all `NaN`s! This is another consequence of our light curves not having Poisson errors.\n", "\n", "### A Hacky Fix\n", "\n", "To work around `stingray`'s requirement for Poisson errors, we can trick it into thinking our relative light curves are actually in units of counts by scaling them by a suitably large value (e.g., 10,000). We'll also want to convert the time values from Barycentric MJD to seconds:" ] }, { "cell_type": "code", "execution_count": 18, "id": "04c49788", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "8it [00:00, 20687.07it/s]\n" ] } ], "source": [ "from stingray import Lightcurve\n", "\n", "scale_factor = 1e4\n", "\n", "lc = analyser.light_curves['g-band']\n", "t_ref = np.min(lc.time)\n", "t = 86400 * (lc.time - t_ref) # convert time from MJD to s\n", "gti = 86400 * (lc.gti - t_ref) # convert GTIs from MJD to s\n", "f = lc.counts * scale_factor # scale fluxes so stingray thinks they're counts\n", "g_lc = Lightcurve(t, f, gti=gti) # do not pass errors or define err_dist\n", "\n", "lc = analyser.light_curves['r-band']\n", "t = 86400 * (lc.time - t_ref) # convert time from MJD to s\n", "gti = 86400 * (lc.gti - t_ref) # convert GTIs from MJD to s\n", "f = lc.counts * scale_factor # scale fluxes so stingray thinks they're counts\n", "r_lc = Lightcurve(t, f, gti=gti) # do not pass errors or define err_dist\n", "\n", "avg_cs = AveragedCrossspectrum.from_lightcurve(\n", " g_lc,\n", " r_lc,\n", " segment_size=segment_size.value, # segment size in seconds\n", " norm='frac',\n", " )" ] }, { "cell_type": "markdown", "id": "c850f28f", "metadata": {}, "source": [ "The fractional RMS normalisation (`norm='frac'`) is scale-invariant, so it should give us the same averaged periodogram as before (provided we use the same segment length). Let's verify this:" ] }, { "cell_type": "code", "execution_count": 19, "id": "58254a51", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "8it [00:00, 41272.36it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "from stingray import AveragedPowerspectrum\n", "\n", "avg_ps = AveragedPowerspectrum.from_lightcurve(\n", " g_lc,\n", " segment_size=segment_size.value,\n", " norm='frac',\n", " )\n", "\n", "print(np.allclose(avg_ps.power, averaged_periodograms['g-band'].power))" ] }, { "cell_type": "markdown", "id": "4c3449d2", "metadata": {}, "source": [ "As we can see, our scaled $g$-band light curve gives the same averaged power spectrum as our initial relative light curve. Let's now try to compute the averaged cross spectrum, coherence, and phase lags using our scaled light curves:" ] }, { "cell_type": "code", "execution_count": 20, "id": "fb3cb353", "metadata": {}, "outputs": [ { "data": { "image/png": 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bL7rNtm3bFB8fr+DgYHXv3l0vvfSS28cHAABoiTyaY2ez2ZSUlKRnn31W//rXv/TRRx9p4MCBeuWVV9S5c2cNGTJEzz33nA4dOuTSfquqqtS3b18tXbrUqf4HDx7U6NGjlZSUpIKCAv3iF7/QnDlz9M4777jztQAAAFokm2EYRlPs+Ntvv9V7772n9957T0lJSXrooYfc2o/NZtO7776rcePGnbfP/Pnz9d5772nPnj32tpkzZ+qTTz7Rhx9+6NRxKioqFBkZqfLyckVERLhVK8ytqqpK4eHhkqTKysoGr7/zJTPXBgDwLVcyittvnriYqKgoTZ8+XdOnT2+qQ9h9+OGHSk5Odmi76aabtHLlSp0+fVqtWrVq8hoAAAB8rcmCXXMqLS1VdHS0Q1t0dLTOnDmjsrIyxcTENNimpqbG4WaPioqKJq8TAACgKVnmOXY2m81h/dwV5h+2n5ORkaHIyEj7Ehsb2+Q1AgAANCVLBLuOHTuqtLTUoe3o0aMKCAhQu3btGt0mPT1d5eXl9qW4uLg5SgUAAGgylrgUm5iYqD/96U8ObVu2bFFCQsJ559cFBQUpKCioOcoDAABoFi6P2J08ebLRx5d8/vnnXilIOntXYGFhoQoLCyWdfZxJYWGhioqKJJ0dbUtNTbX3nzlzpr7++mulpaVpz549WrVqlVauXOn2nbgAAAAtkUvB7u2331avXr00evRoXXvttfrHP/5h/2zy5MleKyovL09xcXGKi4uTJKWlpSkuLk6PPfaYpLNvvTgX8iSpW7du2rRpk7Kzs9WvXz/96le/0osvvqjbb7/dazUBAACYnUvPsevXr5+ysrIUFRWlvLw8TZkyRQsWLNCkSZMUFxengoKCpqy1SfEcO+sz87PizFwbAMC3muw5dqdPn1ZUVJQkKSEhQTk5ORo/frz27dt33rtPAQAA0DxcuhTboUMHffrpp/b1du3aKSsrS3v27HFoBwAAQPNzKdi99tpr6tChg0NbYGCg1q9fr23btnm1MAAAALjGpUuxl1566Xk/Gzx4sMfFAAAAwH1eeY7d6dOnVVpaqurqakVFRalt27be2C0AAABc4PabJyorK/Xyyy9r2LBhioyMVNeuXXXVVVcpKipKXbp00f33369//vOf3qwVAAAAF+BWsHv++efVtWtXvfLKKxoxYoQ2bNigwsJCffHFF/rwww/1+OOP68yZMxo5cqRGjRqlvXv3ertuAAAA/IBbl2J37typrVu36pprrmn08+uuu07Tpk3TSy+9pJUrV2rbtm26/PLLPSoUAAAAF+ZWsHvrrbec6hcUFKQHH3zQnUMAAADARW7PsTvn5MmTqq6utq9//fXXWrJkiTZv3uzprgEAAOACj4PdrbfeqrVr10qSvvvuOw0YMECLFi3SuHHjtHz5co8LBAAAgHM8DnYff/yxkpKSJElvv/22oqOj9fXXX2vt2rV68cUXPS4QAAAAzvE42FVXV6t169aSpC1btmj8+PHy8/PTwIED9fXXX3tcIAAAAJzjcbDr2bOnNm7cqOLiYm3evFnJycmSpKNHjyoiIsLjAgEAAOAcj4PdY489poceekhdu3bVddddp8TERElnR+/i4uI8LhAAAADO8fiVYnfccYeuv/56lZSUqG/fvvb2G264QbfddpunuwcAAICTvPKu2DZt2qioqEibNm1SfX29vb20tFRXXnmlNw4BAACAi/A42H3wwQeaPHmyjh071uAzm82muro6Tw8BAAAAJ3g8x2727NmaMGGCSkpKVF9f77AQ6gAAAJqPx8Hu6NGjSktLU3R0tDfqAQAAgJs8DnZ33HGHsrOzvVAKAAAAPOHxHLulS5fqzjvvVG5urq655hq1atXK4fM5c+Z4eggAAAA4weNg9/rrr2vz5s0KCQlRdna2bDab/TObzUawAwAAaCYeB7uFCxfqqaee0qOPPio/P4+v7AIAAMBNHiex2tpaTZw4kVAHAADgYx6nsSlTpigzM9MbtQAAAMADHl+Kraur07PPPqvNmzfr2muvbXDzxOLFiz09BAAAAJzgcbD77LPPFBcXJ0natWuXw2ffv5ECAAAATcvjYLd161Zv1AEAAAAPeTTH7vTp0xo+fLi+/PJLb9UDAAAAN3kU7Fq1aqVdu3ZxyRUAAMAEPL4rNjU1VStXrvRGLQAAAPCAx3Psamtr9eqrryorK0sJCQkKCwtz+Jy7YgEAAJqHx8Fu165d6t+/vyQ1mGvHJVoAAIDmw12xAAAAFsF7wAAAACyCYAcAAGARpg12y5YtU7du3RQcHKz4+Hjl5uZesP+6devUt29fhYaGKiYmRvfdd5+OHTvWTNUCAAD4nimDXWZmpubNm6cFCxaooKBASUlJSklJUVFRUaP9t2/frtTUVE2fPl2ff/653nrrLf3zn//UjBkzmrlyAAAA3zFlsFu8eLGmT5+uGTNmqHfv3lqyZIliY2O1fPnyRvv//e9/V9euXTVnzhx169ZN119/vR544AHl5eU1c+UAAAC+Y7pgV1tbq/z8fCUnJzu0Jycna+fOnY1uM2jQIH3zzTfatGmTDMPQkSNH9Pbbb2vMmDHNUTIAAIApNFmwu/HGG9W9e3eXtysrK1NdXZ2io6Md2qOjo1VaWtroNoMGDdK6des0ceJEBQYGqmPHjmrTpo3+53/+57zHqampUUVFhcMCAADQkjVZsLvttts0ZcoUt7f/4cONDcM47wOPd+/erTlz5uixxx5Tfn6+PvjgAx08eFAzZ8487/4zMjIUGRlpX2JjY92uFQAAwAxshmEYvi7i+2praxUaGqq33npLt912m7197ty5Kiws1LZt2xpsM3nyZJ06dUpvvfWWvW379u1KSkrS4cOHFRMT02Cbmpoa1dTU2NcrKioUGxur8vJyRUREePlbwQyqqqoUHh4uSaqsrGzw+jtfMnNtAADfqqioUGRkpFMZxXRz7AIDAxUfH6+srCyH9qysLA0aNKjRbaqrq+Xn5/hV/P39JZ0d6WtMUFCQIiIiHBYAAICWzONgl5GRoVWrVjVoX7VqlX7zm9+4tc+0tDS9+uqrWrVqlfbs2aOf/exnKioqsl9aTU9PV2pqqr3/2LFjtWHDBi1fvlwHDhzQjh07NGfOHF133XXq1KmTe18MAACghfH4XbEvv/yyXn/99QbtV199te666y7Nnz/f5X1OnDhRx44d01NPPaWSkhL16dNHmzZtUpcuXSRJJSUlDs+0mzp1qk6cOKGlS5fq5z//udq0aaMRI0a4HSwBAABaIo/n2AUHB2vPnj3q1q2bQ/uBAwd01VVX6dSpUx4V2FxcuX6NlsnM89jMXBsAwLeadY5dbGysduzY0aB9x44dXAYFAABoRh5fip0xY4bmzZun06dPa8SIEZKkv/71r3rkkUf085//3OMCAQAA4ByPg90jjzyi48eP68EHH1Rtba0Mw1BISIjmz5+vRx991Bs1AgAAwAlee45dZWWl9uzZo5CQEF1++eUKCgryxm6bDXPsrM/M89jMXBsAwLdcySgej9idU1RUpGPHjqm2tlYHDhywt99yyy3eOgQAAAAuwONgd+DAAd1222367LPPZLPZ7A8EPvf6r7q6Ok8PAQAAACd4fFfs3Llz1a1bNx05ckShoaHatWuXcnJylJCQoOzsbC+UCAAAAGd4PGL34Ycf6m9/+5uioqLk5+cnf39/XX/99crIyNCcOXNUUFDgjToBAABwER6P2NXV1dknfbdv316HDx+WJHXp0kVffPGFp7sHAACAkzwesevTp48+/fRTde/eXQMGDNCzzz6rwMBArVixQt27d/dGjQAAAHCCx8Fu4cKFqqqqkiQ9/fTTuvnmm5WUlKR27dopMzPT4wIBAADgHI+D3U033WT/d/fu3bV7924dP35cl1xyif3OWAAAADQ9j+bYnT59WsOHD9eXX37p0N62bVtCHQAAQDPzKNi1atVKu3btIsQBAACYgMd3xaampmrlypXeqAUAAAAe8HiOXW1trV599VVlZWUpISGhwTsuFy9e7OkhAAAA4ASPg92uXbvUv39/SWow145LtAAAAM3HrWD36aefqk+fPvLz89PWrVu9XRMAAADc4NYcu7i4OJWVlUk6+4iTY8eOebUoAAAAuM6tYNemTRsdPHhQkvTVV1+pvr7eq0UBAADAdW5dir399ts1dOhQxcTEyGazKSEhQf7+/o32PXDggEcFAgAAwDluBbsVK1Zo/Pjx2rdvn+bMmaP7779frVu39nZtAAAAcIHbd8WOGjVKkpSfn6+5c+cS7AAAAHzMrTl2RUVF9n+vXr36oqHu0KFD7hwGAAAALnAr2P3kJz/R/fffr48++ui8fcrLy/XKK6+oT58+2rBhg9sFAgAAwDluXYrds2ePnnnmGY0aNUqtWrVSQkKCOnXqpODgYP373//W7t279fnnnyshIUG//e1vlZKS4u26AQAA8AM2wzAMdzc+deqUNm3apNzcXH311Vc6efKk2rdvr7i4ON10003q06ePN2ttUhUVFYqMjFR5ebkiIiJ8XQ6aQFVVlcLDwyVJlZWVDV5/50tmrg0A4FuuZBSPXikWHBys8ePHa/z48Z7sBgAAAF7g1hw7AAAAmI9bwe7TTz916W0Tn3/+uc6cOePOoQAAAOAkt98V68r7YRMTEx0ekQIAAADvc2uOnWEY+uUvf6nQ0FCn+tfW1rpzGAAAALjArWA3ZMgQffHFF073T0xMVEhIiDuHAgAAgJPcCnbZ2dleLgMAAACe4q5YAAAAiyDYAQAAWATBDgAAwCJMG+yWLVumbt26KTg4WPHx8crNzb1g/5qaGi1YsEBdunRRUFCQevTooVWrVjVTtQAAAL7nUbA7ffq0hg8fri+//NJb9UiSMjMzNW/ePC1YsEAFBQVKSkpSSkrKBZ+FN2HCBP31r3/VypUr9cUXX2j9+vW68sorvVoXAACAmdkMwzA82UFUVJR27typyy+/3Fs1acCAAerfv7+WL19ub+vdu7fGjRunjIyMBv0/+OAD3XXXXTpw4IDatm3r1jFdecEuWqaqqiqFh4dLkiorKxUWFubjiv7DzLUBAHzLlYzi8aXY1NRUrVy50tPd2NXW1io/P1/JyckO7cnJydq5c2ej27z33ntKSEjQs88+q86dO6tXr1566KGHdPLkSa/VBQAAYHZuPcfu+2pra/Xqq68qKytLCQkJDUYaFi9e7NL+ysrKVFdXp+joaIf26OholZaWNrrNgQMHtH37dgUHB+vdd99VWVmZHnzwQR0/fvy88+xqampUU1NjX6+oqHCpTgAAALPxONjt2rVL/fv3l6QGc+1sNpvb+/3htoZhnHd/9fX1stlsWrdunSIjIyWdDZR33HGHfve73zX61ouMjAw9+eSTbtcHAABgNh4Hu61bt3qjDrv27dvL39+/wejc0aNHG4zinRMTE6POnTvbQ510dk6eYRj65ptvGp3/l56errS0NPt6RUWFYmNjvfQtAAAAmp9XHneSm5ure++9V4MGDdKhQ4ckSa+99pq2b9/u8r4CAwMVHx+vrKwsh/asrCwNGjSo0W0GDx6sw4cPq7Ky0t725Zdfys/PT5deemmj2wQFBSkiIsJhAQAAaMk8DnbvvPOObrrpJoWEhOjjjz+2z1s7ceKEnnnmGbf2mZaWpldffVWrVq3Snj179LOf/UxFRUWaOXOmpLOjbampqfb+kyZNUrt27XTfffdp9+7dysnJ0cMPP6xp06Y1ehkWAADAijwOdk8//bReeuklvfLKK2rVqpW9fdCgQfr444/d2ufEiRO1ZMkSPfXUU+rXr59ycnK0adMmdenSRZJUUlLi8Ey78PBwZWVl6bvvvlNCQoLuuecejR07Vi+++KJnXw4AAKAF8fg5dqGhodq9e7e6du2q1q1b65NPPlH37t114MABXXXVVTp16pS3am1SPMfO+sz8rDgz1wYA8K1mfY5dTEyM9u3b16B9+/bt6t69u6e7BwAAgJM8DnYPPPCA5s6dq3/84x+y2Ww6fPiw1q1bp4ceekgPPvigN2oEAACAEzx+3Mkjjzyi8vJyDR8+XKdOndKQIUMUFBSkhx56SLNnz/ZGjQAAAHCCx3Pszqmurtbu3btVX1+vq666yj5fqKVgjp31mXkem5lrAwD4lisZxeMRu3NCQ0OVkJDgrd0BAADARR7Psbvnnnu0YsWKBq8TAwAAQPPyONiFh4dr8eLFuvLKK9WpUyfdfffdeumll/Svf/3LG/UBAADASR4Hu5dffln/+te/dPjwYS1evFiRkZF64YUXdPXVVysmJsYbNQIAAMAJXnlXrCS1bt1al1xyiS655BK1adNGAQEB6tixo7d2DwAAgIvwONjNnz9fAwcOVPv27bVw4ULV1tYqPT1dR44cUUFBgTdqBAAAgBM8viv2t7/9raKiovT444/r1ltvVe/evb1RFwAAAFzkcbArKCjQtm3blJ2drUWLFsnf319Dhw7VsGHDNGzYMIIeAABAM/HaA4rP+eSTT7RkyRL94Q9/UH19verq6ry5+ybDA4qtz8wPATZzbQAA32r2BxQXFBQoOztb2dnZys3NVUVFhfr166fhw4d7Y/cAAABwgsfB7pJLLlFlZaX69u2rYcOG6f7779eQIUMY9QIAAGhmHge71157jSAHAABgAh4Hu5tvvlnfffedFi1apD179shms6l3796aPn26IiMjvVEjAAAAnODxc+zy8vLUo0cPPf/88zp+/LjKysr0/PPPq0ePHvr444+9USMAAACc4PGI3c9+9jPdcssteuWVVxQQcHZ3Z86c0YwZMzRv3jzl5OR4XCQAAAAuzuNgl5eX5xDqJCkgIECPPPKIEhISPN09AAAAnOTxpdiIiAgVFRU1aC8uLlbr1q093T0AAACc5HGwmzhxoqZPn67MzEwVFxfrm2++0RtvvKEZM2bo7rvv9kaNAAAAcILHl2Kfe+452Ww2paam6syZM5KkVq1a6ac//al+/etfe1wgAAAAnOO1V4pVV1dr//79MgxDPXv2VGhoqDd222x4pZj1mfm1XWauDQDgW65kFLcvxVZXV2vWrFnq3LmzOnTooBkzZigmJkbXXnttiwt1AAAAVuB2sHv88ce1Zs0ajRkzRnfddZeysrL005/+1Ju1AQAAwAVuz7HbsGGDVq5cqbvuukuSdO+992rw4MGqq6uTv7+/1woEAACAc9wesSsuLlZSUpJ9/brrrlNAQIAOHz7slcIAAADgGreDXV1dnQIDAx3aAgIC7HfGAgAAoHm5fSnWMAxNnTpVQUFB9rZTp05p5syZDnf0bdiwwbMKAQAA4BS3g92UKVMatN17770eFQMAAAD3uR3sVq9e7c06AAAA4CGPXykGAAAAcyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AAIBFmDbYLVu2TN26dVNwcLDi4+OVm5vr1HY7duxQQECA+vXr17QFAgAAmIwpg11mZqbmzZunBQsWqKCgQElJSUpJSVFRUdEFtysvL1dqaqpuuOGGZqoUAADAPEwZ7BYvXqzp06drxowZ6t27t5YsWaLY2FgtX778gts98MADmjRpkhITE5upUgAAAPMwXbCrra1Vfn6+kpOTHdqTk5O1c+fO8263evVq7d+/X48//rhTx6mpqVFFRYXDAgAA0JKZLtiVlZWprq5O0dHRDu3R0dEqLS1tdJu9e/fq0Ucf1bp16xQQ4Nxb0jIyMhQZGWlfYmNjPa4dAADAl0wX7M6x2WwO64ZhNGiTpLq6Ok2aNElPPvmkevXq5fT+09PTVV5ebl+Ki4s9rhkAAMCXnBveakbt27eXv79/g9G5o0ePNhjFk6QTJ04oLy9PBQUFmj17tiSpvr5ehmEoICBAW7Zs0YgRIxpsFxQUpKCgoKb5EgAAAD5guhG7wMBAxcfHKysry6E9KytLgwYNatA/IiJCn332mQoLC+3LzJkzdcUVV6iwsFADBgxortIBAAB8ynQjdpKUlpamyZMnKyEhQYmJiVqxYoWKioo0c+ZMSWcvox46dEhr166Vn5+f+vTp47B9hw4dFBwc3KAdAADAykwZ7CZOnKhjx47pqaeeUklJifr06aNNmzapS5cukqSSkpKLPtMOAADgx8ZmGIbh6yLMoKKiQpGRkSovL1dERISvy0ETqKqqUnh4uCSpsrJSYWFhPq7oP8xcGwDAt1zJKKabYwcAAAD3EOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AAIBFEOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AAIBFEOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AAIBFEOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AAIBFEOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWIRpg92yZcvUrVs3BQcHKz4+Xrm5ueftu2HDBo0cOVJRUVGKiIhQYmKiNm/e3IzVAgAA+J4pg11mZqbmzZunBQsWqKCgQElJSUpJSVFRUVGj/XNycjRy5Eht2rRJ+fn5Gj58uMaOHauCgoJmrhwAAMB3bIZhGL4u4ocGDBig/v37a/ny5fa23r17a9y4ccrIyHBqH1dffbUmTpyoxx57zKn+FRUVioyMVHl5uSIiItyqG+ZWVVWl8PBwSVJlZaXCwsJ8XNF/mLk2AIBvuZJRTDdiV1tbq/z8fCUnJzu0Jycna+fOnU7to76+XidOnFDbtm3P26empkYVFRUOCwAAQEtmumBXVlamuro6RUdHO7RHR0ertLTUqX0sWrRIVVVVmjBhwnn7ZGRkKDIy0r7ExsZ6VDcAAICvmS7YnWOz2RzWDcNo0NaY9evX64knnlBmZqY6dOhw3n7p6ekqLy+3L8XFxR7XDAAA4EsBvi7gh9q3by9/f/8Go3NHjx5tMIr3Q5mZmZo+fbreeust3XjjjRfsGxQUpKCgII/rRUOGYai6utrXZTRQVVXl6xIAAGhSpgt2gYGBio+PV1ZWlm677TZ7e1ZWlm699dbzbrd+/XpNmzZN69ev15gxY5qjVDTCMAxdf/31Ts+HBAAA3mO6YCdJaWlpmjx5shISEpSYmKgVK1aoqKhIM2fOlHT2MuqhQ4e0du1aSWdDXWpqql544QUNHDjQPtoXEhKiyMhIn32PH6Pq6mrTh7rBgwcrNDTU12UAAOB1pgx2EydO1LFjx/TUU0+ppKREffr00aZNm9SlSxdJUklJicMz7V5++WWdOXNGs2bN0qxZs+ztU6ZM0Zo1a5q7fPy/I0eOmPKxHaGhoU7N1wQAoKUx5XPsfIHn2HkHz2NzDz8395h1Puc5/BEBmFNT/O5oyv/vrmQUU47YAcDFtIT5nIMHD1Zubi7hDjCRpvrdYZY/yk37uBMAuJCWMJ9zx44dph5RBH6MWsLvDk8wYgegxTPbfM6qqqqLPp4JgO9583eHWW7KI9gBaPHCwsJMFewAtAxW/N3BpVgAAACLINgBAABYBJdiAZMx46vPeGwHALQMBDvAZMw46Z7HdgBAy8ClWMAEQkNDNXjwYF+XcV48tgMAWgZG7AATsNlsys3NNV144rEdANCyEOwAk7DZbJa77R7MmQTQvAh2ANCEzDjiyZxJ15n5vcQEdXwfwQ4AvOzcnMkdO3b4upRGnZszyQixc8z+XmKCOr6PYNdMzPzXnjeZ8bIT0NyYM2ktZn+3KEEd30ewaybV1dUKDw/3dRkAmonZ50ya9Y8ws19WNNN7iQnqaAzBDk1i8ODBpnkhMoCGzBoIzH5Z0YrvFoW1EOyaSWhoqCorK31dRrMx+1/dwI+R2ef+SWcvK3777bemCk9mHd0EGkOwayZmvywDwPrMOvdPcrysaNbRRKAlINgBwI+IWf/IbAmjiUwxQUtAsAMA+JyZRxPPYYoJWgKCHQDAFMw6mgj3mPUxX1afM0mwAwCghTNbWDEMQ0lJSSosLPR1KT86BDsAAFo4bjhxnVXnTBLsAABogVrCDSf9+vUz7XMJrTpnkmAHAEALxA0naAzBDgCAFoobTvBDBDsATjHb5Gyz1QMAZkCwA+AUJmcDgPn5+boAAOZ1bnK2mVn1zjYAcAcjdgDOi8nZANCyEOwAXBCTswGg5eBSLAAAgEUQ7AAAACyCYAcAAGARBDsAAACLINgBAABYBMEOAADAIkwb7JYtW6Zu3bopODhY8fHxys3NvWD/bdu2KT4+XsHBwerevbteeumlZqoUAADAHEwZ7DIzMzVv3jwtWLBABQUFSkpKUkpKioqKihrtf/DgQY0ePVpJSUkqKCjQL37xC82ZM0fvvPNOM1cOAADgOzbDMAxfF/FDAwYMUP/+/bV8+XJ7W+/evTVu3DhlZGQ06D9//ny999572rNnj71t5syZ+uSTT/Thhx86dcyKigpFRkaqvLxcERERnn8JAAAAL3Alo5huxK62tlb5+flKTk52aE9OTtbOnTsb3ebDDz9s0P+mm25SXl6eTp8+3eg2NTU1qqiocFgAAABaMtMFu7KyMtXV1Sk6OtqhPTo6WqWlpY1uU1pa2mj/M2fOqKysrNFtMjIyFBkZaV9iY2O98wUAAAB8xHTB7pwfvtTbMIwLvui7sf6NtZ+Tnp6u8vJy+1JcXOxhxQAAAL4V4OsCfqh9+/by9/dvMDp39OjRBqNy53Ts2LHR/gEBAWrXrl2j2wQFBSkoKMg7RQMAAJiA6UbsAgMDFR8fr6ysLIf2rKwsDRo0qNFtEhMTG/TfsmWLEhIS1KpVqyarFQAAwExMN2InSWlpaZo8ebISEhKUmJioFStWqKioSDNnzpR09jLqoUOHtHbtWkln74BdunSp0tLSdP/99+vDDz/UypUrtX79eqePee7SLTdRAAAAMzmXTZx6kIlhUr/73e+MLl26GIGBgUb//v2Nbdu22T+bMmWKMXToUIf+2dnZRlxcnBEYGGh07drVWL58uUvHKy4uNiSxsLCwsLCwsJhyKS4uvmieMeVz7Hyhvr5ehw8fVuvWrS94kwaaX0VFhWJjY1VcXMwzBi2A82ktnE9r4Xyak2EYOnHihDp16iQ/vwvPojPlpVhf8PPz06WXXurrMnABERER/KKxEM6ntXA+rYXzaT6RkZFO9TPdzRMAAABwD8EOAADAIgh2ML2goCA9/vjjPHfQIjif1sL5tBbOZ8vHzRMAAAAWwYgdAACARRDsAAAALIJgBwAAYBEEO5jCsmXL1K1bNwUHBys+Pl65ubnn7VtSUqJJkybpiiuukJ+fn+bNm9d8heKiXDmXGzZs0MiRIxUVFaWIiAglJiZq8+bNzVgtLsaV87l9+3YNHjxY7dq1U0hIiK688ko9//zzzVgtLsaV8/l9O3bsUEBAgPr169e0BcJjBDv4XGZmpubNm6cFCxaooKBASUlJSklJUVFRUaP9a2pqFBUVpQULFqhv377NXC0uxNVzmZOTo5EjR2rTpk3Kz8/X8OHDNXbsWBUUFDRz5WiMq+czLCxMs2fPVk5Ojvbs2aOFCxdq4cKFWrFiRTNXjsa4ej7PKS8vV2pqqm644YZmqhSe4K5Y+NyAAQPUv39/LV++3N7Wu3dvjRs3ThkZGRfcdtiwYerXr5+WLFnSxFXCGZ6cy3OuvvpqTZw4UY899lhTlQkneeN8jh8/XmFhYXrttdeaqkw4yd3zedddd+nyyy+Xv7+/Nm7cqMLCwmaoFu5ixA4+VVtbq/z8fCUnJzu0Jycna+fOnT6qCu7wxrmsr6/XiRMn1LZt26YoES7wxvksKCjQzp07NXTo0KYoES5w93yuXr1a+/fv1+OPP97UJcJLeFcsfKqsrEx1dXWKjo52aI+OjlZpaamPqoI7vHEuFy1apKqqKk2YMKEpSoQLPDmfl156qb799ludOXNGTzzxhGbMmNGUpcIJ7pzPvXv36tFHH1Vubq4CAogLLQVnCqZgs9kc1g3DaNCGlsHdc7l+/Xo98cQT+uMf/6gOHTo0VXlwkTvnMzc3V5WVlfr73/+uRx99VD179tTdd9/dlGXCSc6ez7q6Ok2aNElPPvmkevXq1VzlwQsIdvCp9u3by9/fv8FfjEePHm3wlyXMzZNzmZmZqenTp+utt97SjTfe2JRlwkmenM9u3bpJkq655hodOXJETzzxBMHOx1w9nydOnFBeXp4KCgo0e/ZsSWenShiGoYCAAG3ZskUjRoxoltrhGubYwacCAwMVHx+vrKwsh/asrCwNGjTIR1XBHe6ey/Xr12vq1Kl6/fXXNWbMmKYuE07y1v9NwzBUU1Pj7fLgIlfPZ0REhD777DMVFhbal5kzZ+qKK65QYWGhBgwY0Fylw0WM2MHn0tLSNHnyZCUkJCgxMVErVqxQUVGRZs6cKUlKT0/XoUOHtHbtWvs25+7Kqqys1LfffqvCwkIFBgbqqquu8sVXwP9z9VyuX79eqampeuGFFzRw4ED7aEJISIgiIyN99j1wlqvn83e/+50uu+wyXXnllZLOPtfuueee03//93/77DvgP1w5n35+furTp4/D9h06dFBwcHCDdpgLwQ4+N3HiRB07dkxPPfWUSkpK1KdPH23atEldunSRdPaBxD98zlJcXJz93/n5+Xr99dfVpUsXffXVV81ZOn7A1XP58ssv68yZM5o1a5ZmzZplb58yZYrWrFnT3OXjB1w9n/X19UpPT9fBgwcVEBCgHj166Ne//rUeeOABX30FfI87v2vR8vAcOwAAAItgjh0AAIBFEOwAAAAsgmAHAABgEQQ7AAAAiyDYAQAAWATBDgAAwCIIdgAAABZBsAMAALAIgh0AtFBTp06VzWaTzWbTxo0bvbrv7Oxs+77HjRvn1X0DaDoEOwCm8f2g8v1l3759vi7NtEaNGqWSkhKlpKTY284X9KZOnep0SBs0aJBKSko0YcIEL1UKoDnwrlgApjJq1CitXr3aoS0qKqpBv9raWgUGBjZXWaYVFBSkjh07en2/gYGB6tixo0JCQlRTU+P1/QNoGozYATCVc0Hl+4u/v7+GDRum2bNnKy0tTe3bt9fIkSMlSbt379bo0aMVHh6u6OhoTZ48WWVlZfb9VVVVKTU1VeHh4YqJidGiRYs0bNgwzZs3z96nsRGuNm3aaM2aNfb1Q4cOaeLEibrkkkvUrl073Xrrrfrqq6/sn58bDXvuuecUExOjdu3aadasWTp9+rS9T01NjR555BHFxsYqKChIl19+uVauXCnDMNSzZ08999xzDjXs2rVLfn5+2r9/v+c/2B/46quvGh0dHTZsmNePBaD5EOwAtBi///3vFRAQoB07dujll19WSUmJhg4dqn79+ikvL08ffPCBjhw54nD58OGHH9bWrVv17rvvasuWLcrOzlZ+fr5Lx62urtbw4cMVHh6unJwcbd++XeHh4Ro1apRqa2vt/bZu3ar9+/dr69at+v3vf681a9Y4hMPU1FS98cYbevHFF7Vnzx699NJLCg8Pl81m07Rp0xqMVK5atUpJSUnq0aOHez+wC4iNjVVJSYl9KSgoULt27TRkyBCvHwtAMzIAwCSmTJli+Pv7G2FhYfbljjvuMAzDMIYOHWr069fPof8vf/lLIzk52aGtuLjYkGR88cUXxokTJ4zAwEDjjTfesH9+7NgxIyQkxJg7d669TZLx7rvvOuwnMjLSWL16tWEYhrFy5UrjiiuuMOrr6+2f19TUGCEhIcbmzZvttXfp0sU4c+aMvc+dd95pTJw40TAMw/jiiy8MSUZWVlaj3/3w4cOGv7+/8Y9//MMwDMOora01oqKijDVr1lzw53Xrrbc2aJdkBAcHO/wcw8LCjICAgEb7nzx50hgwYIBx8803G3V1dU4dA4A5MccOgKkMHz5cy5cvt6+HhYXZ/52QkODQNz8/X1u3blV4eHiD/ezfv18nT55UbW2tEhMT7e1t27bVFVdc4VJN+fn52rdvn1q3bu3QfurUKYfLpFdffbX8/f3t6zExMfrss88kSYWFhfL399fQoUMbPUZMTIzGjBmjVatW6brrrtP777+vU6dO6c4773Sp1nOef/553XjjjQ5t8+fPV11dXYO+06dP14kTJ5SVlSU/Py7kAC0ZwQ6AqYSFhalnz57n/ez76uvrNXbsWP3mN79p0DcmJkZ79+516pg2m02GYTi0fX9uXH19veLj47Vu3boG237/xo5WrVo12G99fb0kKSQk5KJ1zJgxQ5MnT9bzzz+v1atXa+LEiQoNDXXqO/xQx44dG/wcW7dure+++86h7emnn9YHH3ygjz76qEFwBdDyEOwAtFj9+/fXO++8o65duyogoOGvs549e6pVq1b6+9//rssuu0yS9O9//1tffvmlw8hZVFSUSkpK7Ot79+5VdXW1w3EyMzPVoUMHRUREuFXrNddco/r6em3btq3BSNo5o0ePVlhYmJYvX64///nPysnJcetYznrnnXf01FNP6c9//nOTzOMD0PwYcwfQYs2aNUvHjx/X3XffrY8++kgHDhzQli1bNG3aNNXV1Sk8PFzTp0/Xww8/rL/+9a/atWuXpk6d2uBy44gRI7R06VJ9/PHHysvL08yZMx1G3+655x61b99et956q3Jzc3Xw4EFt27ZNc+fO1TfffONUrV27dtWUKVM0bdo0bdy4UQcPHlR2drbefPNNex9/f39NnTpV6enp6tmzp8MlZG/btWuXUlNTNX/+fF199dUqLS1VaWmpjh8/3mTHBND0CHYAWqxOnTppx44dqqur00033aQ+ffpo7ty5ioyMtIe33/72txoyZIhuueUW3Xjjjbr++usVHx/vsJ9FixYpNjZWQ4YM0aRJk/TQQw85XAINDQ1VTk6OLrvsMo0fP169e/fWtGnTdPLkSZdG8JYvX6477rhDDz74oK688krdf//9qqqqcugzffp01dbWatq0aR78ZC4uLy9P1dXVevrppxUTE2Nfxo8f36THBdC0bMYPJ5YAgMUNGzZM/fr105IlS3xdSgM7duzQsGHD9M033yg6OvqCfadOnarvvvvO668Ta+5jAPAeRuwAwARqamq0b98+/fKXv9SECRMuGurOef/99xUeHq7333/fq/Xk5uYqPDy80RtGAJgXN08AgAmsX79e06dPV79+/fTaa685tc2zzz6rhQsXSjp7F7A3JSQkqLCwUJIafZwMAHPiUiwAAIBFcCkWAADAIgh2AAAAFkGwAwAAsAiCHQAAgEUQ7AAAACyCYAcAAGARBDsAAACLINgBAABYBMEOAADAIv4PuuxmufNq3pMAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "ax.step(\n", " avg_cs.freq,\n", " avg_cs_amplitude,\n", " where='mid',\n", " c='k',\n", ")\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Power [(frac. rms)$^2$ / Hz]')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1c2c56b8", "metadata": {}, "source": [ "As with the averaged power spectrum, the averaged cross spectrum looks the same as before (since we're using `norm=\"frac\"`). Again, so far so good. Let's see if we can compute the coherence this time:" ] }, { "cell_type": "code", "execution_count": 21, "id": "841fd70c", "metadata": {}, "outputs": [ { "data": { "image/png": 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W1tbCX3/9VWn/jRs3Cra2tkJISIhw7do1Yffu3YKNjY1w4MABTZ+dO3cKFhYWwq5du4Tr168LR44cERwdHYUZM2ZUua6cnBwBgJCTk1Prc6xMfn6+AEAAIOTn59fJZ9SUIddGpEtvvfWWAECYOnWqps1Qf/8bal2CYLi1GWpdgqD/2jIzM4V///vfgr29veZzW7RoIXz22WdCXl5endRVVlYm3Lx5U4iMjBS2b98ufPjhh8KECROEvn37Cs2bNxdkMpnms570UiqVQq9evYRx48YJc+fONdjrqQ/VySWi7mPn6emJbt26ITg4WNPm5uaGUaNGYcWKFRX6e3l5oU+fPlizZo2mbcaMGYiLi0N0dDQA4L333sOVK1e0nvk4e/ZsxMbGPnM0UK0+72NnyLUR6UpRURGUSiXy8vIQHR2NPn36ADDc3/+GWhdguLUZal2AeLXl5ubi66+/xrp16zRPGGnUqBHef/99vPfee1AoFNWqKycnR2u69PEfb9y48cTn66pZW1vD1dUVrVq1qvCji4uL1ucb8vXUB6PYx664uBjx8fGYP3++VruPjw9iYmIqfY9Kpaqwy7ZCoUBsbCxKSkpgZmaGvn37YufOnYiNjUXPnj2RkpKCsLAwvPXWW3V2LkRkXA4ePIi8vDw4OztrPWbI2tpaUjeZEz3Ozs4Oc+fOxfvvv4/vvvsOq1evRnJyMj766COsWbMGEydO1OpfXFyMv/76q0JoU399//79p36eXC5Hy5YtnxjeHBwc6vW2JHVFtGCXlZWFsrIyKJVKrXalUvnEZxX6+vpi8+bNGDVqFLp164b4+Hhs2bIFJSUlyMrKgqOjI8aOHYu7d++ib9++EAQBpaWlmDp1aoUA+Tj1ppZqubm5ujlJIjJI6tWwb7zxhlHcSE6kS5aWlnjnnXfw9ttvY+/evZqVpRs3btT0ad++PdLT05/5H50mTZpUCG3qr52cnGBqyjWa+ib6r/jf07ogCE9M8IsWLUJmZiZ69eoFQRCgVCoxceJErF69WrMB5fHjx7Fs2TJs3LgRnp6eSE5ORmBgIBwdHbFo0aJKj7tixQp89NFHuj0x0qn6PgxPunPv3j2EhYUB4KbEJA5DGRmWy+V47bXXMGbMGPz+++9YtmwZjh8/DgC4efMmgEePY3s8rP09wHGbIMMjWrBzcHCAXC6vMDp3586dCqN4agqFAlu2bMHXX3+N27dvw9HREZs2bdLsNg48Cn/jx4/H5MmTAQAdO3ZEQUEB/vWvf2HBggWV/u88KCgIs2bN0nyfm5sLJycnXZ0qERmQPXv2oKSkBJ06ddI8coqoPpPJZBg0aBB69+6tCWp//PEH3N3d0bRpU06XGhnR5iDMzc3h4eGB8PBwrfbw8PBnbjRoZmaGFi1aQC6XIyQkBMOGDdMEtsLCwgrhTS6XQxCEJ/4PycLCAnZ2dlovIpKmx6dhiahyPXv2hFKpZKgzQqJOxc6aNQvjx49H9+7d0bt3b2zatAmpqakICAgA8GgkLT09XbNXXVJSEmJjY+Hp6Yn79+9j3bp1uHjxIrZv36455vDhw7Fu3Tp07dpVMxW7aNEijBgxQlLPCySi6ktLS0NkZCQAYNy4cSJXQ0Ske6IGO39/f2RnZ2Pp0qXIyMhAhw4dEBYWBmdnZwBARkYGUlNTNf3Lysqwdu1aJCYmwszMDAMGDEBMTIzWw54XLlwImUyGhQsXIj09HU2aNMHw4cOxbNkyfZ8eERmYkJAQCIIAb29vtGzZUuxyqsxQ7skiIsMn6j52hor72BlebYZaFxmXrl274ty5c/jqq68wZcoUscuRBEP9s2modRkyQ/41M+Ta9KE6uYTr/ImoXrh8+TLOnTsHMzMzjBkzRuxyiIjqBIMdEdUL33//PQBgyJAhaNy4scjVEBHVDQY7ka1cuVL0hzETSZ0gCJpg9+abb4pcjbSo7/8TBKHeTY8RGSIGOxEUFRVpvv7kk0/QrVs3nDx5UsSKiKTt5MmTuH79OmxsbDB8+HCxyyEiqjMMdiJQKBSarx0cHHDp0iX06dMH77//PvLy8kSsjEia1KN1o0ePhpWVlcjVkD5wJJHqKwY7kcXHx2PixIkQBAFffvkl3N3d8csvv4hdFpFklJSUIDQ0FAA3JSYi6WOwE1njxo2xdetW/Pbbb2jdujVu3ryJESNG4PXXX6/wuDUiqr7ffvsNWVlZaNKkCQYNGiR2OUREdYrBzkC89NJLuHDhAubNmwe5XI4ff/wRbm5u2Lx5MzcmJaoF9SPE/P39YWoq6p7sRER1jsHOgCgUCqxcuRJxcXHo3r07Hjx4gHfeeQcDBgxAUlKS2OURGZ2CggLs378fAFfDElH9wGBngLp06YKTJ09i3bp1sLKyQkREBDp16oRly5ZxaxSiajhw4AAKCgrQqlUreHp6il0OEVGdY7AzUKamppg5cyYuXboEX19fqFQqLFy4EB4eHjh9+rTY5REZBfVq2DfeeAMymUzkaoiI6h6DnYFzcXHBoUOHsHPnTjg4OODixYvo3bs3AgMDuTUK0VNkZWXh8OHDALgalojqDwY7IyCTyfDmm2/iypUrmDBhAgRBwBdffIEXXngBv/76q9jlERmkH3/8EaWlpejatSvc3NzELoeISC8Y7IyIg4MDtm/fjiNHjsDV1RVpaWkYNmwYxo4di9u3b4tdHpFB4SPEiKSDG05XHYOdEfLx8cGFCxcwZ84cmJiYIDQ0FG5ubti6dSu3RiGNgoICyGQyyGQyFBQUiF2OXv3111+Ijo6GTCbD2LFjxS6HiEhvGOyMlLW1NdasWYMzZ86ga9euuH//Pt5++20MGjQIycnJYpdH9ET6CJy7d+8GALz44oto3rx5nXwGEZEhYrAzct26dUNsbCxWr14NhUKBP/74Ax07dsTKlStRUlIidnlEolBvSsxFE0RU3zDYSYCpqSnmzp2LixcvYtCgQXj48CGCgoLQo0cPnDlzRuzyiPTqwoULuHjxIszNzTFmzBixyyEi0isGOwlp1aoVjh49iu3bt6NRo0Y4f/48evXqhZkzZyI/P1/s8oj0Qj1aN3ToUDRo0EDcYoiI9IzBTmJkMhkmTJiAP//8E2+++SbKy8uxfv16dOjQQbOnF5FUlZeXa21KTERU3zDYSVSTJk2wc+dOHDp0CM7Ozvjrr7/g5+eHN998E3fu3BG7PKI6ceLECaSlpcHOzg5Dhw4Vuxwio8ItRaSBwU7ihgwZgosXL2LmzJkwMTHB999/Dzc3N2zfvp1bo5DkqKdhX3nlFSgUCpGrISLSPwa7esDGxgbr1q3DqVOn0LlzZ9y7dw8TJ06Ej48Prl27JnZ5RDpRXFyMH3/8EQA3JSai+ovBrh5Rr5JduXIlLC0t8dtvv6Fjx45YvXo1SktLxS6PqFaOHDmCe/fuoVmzZhgwYIDY5RARiYLBrp4xMzPDvHnzcOHCBQwcOBBFRUWYN28eevbsifj4eLHLI6ox9aKJsWPHQi6Xi1wNEZE4GOzqqTZt2uC3337Dli1b0LBhQyQkJKBnz57497//LXZpRNWWl5eHn3/+GQBXwxJR/cZgV4/JZDL885//xJUrVzB27FiUl5fjiy++0Pw8n1xBxuLnn39GUVER2rZti+7du4tdDhGRaBjsCEqlErt378bBgwfRokULTbu7uzs+/vhj3L59W8TqiJ5NvRr2zTffhEwmE7kaIiLxMNiRxtChQxEXF6f5PiMjA4sXL0bLli0xfvx4xMbGilgdUeXu3LmD8PBwAJyGJSJisCMtNjY2mq+//fZbeHp6ori4GDt37oSnpyc8PT2xc+dOqFQqEask+p8ffvgBZWVl6NGjB9q2bSt2OUREomKwoyfy9/fHqVOnEBsbi/Hjx8Pc3FzzdcuWLbF48WLcunVL7DKpnlNPw3K0joiIwY6qoEePHtixYwfS0tLwySefoHnz5rhz5w4+/vhjODs7Y+zYsThx4gSfZEF6l5KSglOnTsHExAT+/v5il0NEJDoGO6qypk2bYsGCBbh+/Tp++OEHeHt7o7S0FKGhoejbty88PDywdetWFBUViV0q1RPqvesGDhwIR0dHkashIhIfg50IjP1By2ZmZnjttdcQGRmJhIQETJo0CZaWlkhISMDbb78NJycnzJ8/H6mpqWKXShImCILWalgiImKwo1rq0qULNm/ejJs3b2LVqlVwdnZGdnY2Vq1aBVdXV7zyyis4duwYp2lJ586dO4c///wTFhYWGD16tNjlEBEZBAY70onGjRvjgw8+wLVr17Bv3z4MHDgQ5eXlmq87deqEr7/+GgUFBWKXShKhHq0bPnw47O3tRa6GiMgwMNiRTsnlcowaNQq///47Ll68iKlTp8La2hoXL15EQEAAWrRogdmzZyMlJUXsUsmIlZWVYffu3QA4DUtE9DgGO6ozL7zwAjZu3IibN2/is88+Q+vWrfHgwQOsW7cObdq0wfDhw3H06FGUl5eLXSoZmcjISNy6dQsNGjSAn5+f2OUQERkMBjuqcw0aNMCMGTOQlJSEX3/9FUOGDIEgCDh48CB8fX3h7u6O//znP8jNzRW7VDIS6tWwY8aMgYWFhcjVEBEZDgY70hsTExO8/PLLOHToEBITEzF9+nTY2tpqvm7RogXef/99JCYmil0qGTCVSoWffvoJADclJiL6OwY7EsXzzz+Pzz//HOnp6fjyyy/Rvn175OXlab729fXFwYMHOU1LFRw6dAgPHjxA8+bN0a9fP7HLISIyKKIHu40bN8LV1RWWlpbw8PBAVFTUU/tv2LABbm5uUCgUaNeuHXbs2FGhz4MHDzBt2jQ4OjrC0tISbm5uCAsLq6tToFqwtbXFtGnTcPnyZRw9ehTDhw+HTCbTfN22bVusW7cODx48ELtUMhDq1bBjx46FXC4XuRoiIsMiarALDQ3FjBkzsGDBAiQkJMDb2xt+fn5P3Ng2ODgYQUFBWLJkCS5duoSPPvoI06ZNwy+//KLpU1xcjMGDB+PGjRv46aefkJiYiG+++QbNmzfX12lRDchkMgwePBgHDhxAcnIy5syZgwYNGiAlJQWzZ8/G888/L3aJZAByc3M1f965GpaIqCKZIOLOsZ6enujWrRuCg4M1bW5ubhg1ahRWrFhRob+Xlxf69OmDNWvWaNpmzJiBuLg4REdHAwC++uorrFmzBn/++SfMzMxqVFdubi7s7e2Rk5MDOzu7Gh3DWBUUFMDGxgYAkJ+fL+qTMQoLC7Fr1y785z//wYULFzTtiYmJDHpVYEjX8nG1qWvbtm345z//ifbt2+Py5cuQyWR1VSYRkcGoTi4RbcSuuLgY8fHx8PHx0Wr38fFBTExMpe9RqVSwtLTUalMoFIiNjUVJSQkA4MCBA+jduzemTZsGpVKJDh06YPny5SgrK6ubE6E6Y2VlhXfeeQfnz5/HoUOHNO2//fabiFWRmB5/hBhDHRFRRaIFu6ysLJSVlUGpVGq1K5VKZGZmVvoeX19fbN68GfHx8RAEAXFxcdiyZQtKSkqQlZUFAEhJScFPP/2EsrIyhIWFYeHChVi7di2WLVv2xFpUKhVyc3O1XmQ4ZDIZvL29Nd+rR2epfsnIyMAff/wBgKthiYieRPTFE3//X7cgCE/8n/iiRYvg5+eHXr16wczMDCNHjsTEiRMBQHMTdXl5OZo2bYpNmzbBw8MDY8eOxYIFC7Sme/9uxYoVsLe317ycnJx0c3JUJxjs6qfQ0FCUl5ejV69eaNWqldjlEBEZJNGCnYODA+RyeYXRuTt37lQYxVNTKBTYsmULCgsLcePGDaSmpsLFxQW2trZwcHAAADg6OuL555/XWi3n5uaGzMxMFBcXV3rcoKAg5OTkaF5paWk6OkuqC2lpabhx44bYZZCeqTcl5qIJIqInEy3YmZubw8PDA+Hh4Vrt4eHh8PLyeup7zczM0KJFC8jlcoSEhGDYsGEwMXl0Kn369EFycrLW/mdJSUlwdHSEubl5pcezsLCAnZ2d1osMW0REhNglkB5dvXoVZ86cgVwux+uvvy52OUREBkvUqdhZs2Zh8+bN2LJlC65cuYKZM2ciNTUVAQEBAB6NpE2YMEHTPykpCTt37sTVq1cRGxuLsWPH4uLFi1i+fLmmz9SpU5GdnY3AwEDNI6yWL1+OadOm6f38qO4w2NUv6tG6wYMHo2nTpiJXQ0RkuEzF/HB/f39kZ2dj6dKlyMjIQIcOHRAWFgZnZ2cAj26WfnxPu7KyMqxduxaJiYkwMzPDgAEDEBMTAxcXF00fJycnHD16FDNnzkSnTp3QvHlzBAYGYt68efo+PapDkZGRYpdAeiIIgmY1LBdNEBE9naj72Bkq7mNn2HufmZiYoLy8HDdv3uTG009hDNeyKnXFxcWhR48eUCgUuH37NmxtbfVRJhGRwTCKfeyIaqpz584AOB1bX6hH60aOHMlQR0T0DAx2ZHT69u0LgMGuPigrK0NISAgATsMSEVUFgx0ZHQa7+uPYsWPIzMxEo0aN4OvrK3Y5REQGj8GOjI6XlxdkMhkSExOf+JQSkgb1NOxrr732xO2KiIjofxjsyOg0bNgQnTp1AgBERUWJXA3VlaKiIuzZswcANyUmIqoqBjsySv379wfA6Vgp+/XXX5GXlwcnJyf06dNH7HKIiIwCgx0ZpX79+gFgsJMy9abEb7zxhubJMkRE9HT825KMkjrYXbx4EVlZWSJXQ7p2//59/PrrrwC4GpaIqDoY7MgoNWnSBO7u7gB4n50U7dmzB8XFxejQoYPmfkoiIno2BjsyWrzPTrrU07BcNEFEVD0MdmS0GOykKT09HcePHwcAjBs3TtxiiIiMDIMdGS31fXbnz5/HgwcPxC2GdCYkJASCIKBv375wdnYWuxwiIqPCYEdGy9HREW3btoUgCIiOjha7HNIR9abEXDRBRFR9DHZk1DgdKy1XrlxBQkICTE1N8dprr4ldDhGR0WGwI6PGYCct6kUTvr6+cHBwELkaIiLjw2BHRk0d7M6ePYu8vDyRq6HaEASBq2GJiGqJwY6MmpOTE1xdXVFWVoYTJ06IXQ7VwunTp5GSkgJra2uMGDFC7HKIiIwSgx0ZPfWoXWRkpMiVUG2oF02MGjUK1tbWIldDRGScGOxIi7W1NQRBgCAIRvOPK58ba/xKS0sRGhoKgNOwRES1wWBHRk89YnfmzBkUFhaKXA3VxG+//Ya7d+/CwcEBgwYNErscIiKjxWBHRs/V1RUtWrRASUkJTp48KXY5VAPqRRP+/v4wMzMTuRoiIuPFYEdGTyaTcdsTI1ZYWIh9+/YB4KbERES1xWBHksBgZ7x++eUX5Ofnw8XFBb179xa7HCIio8ZgR5KgDnanT5/Gw4cPRa6GquPxR4jJZDKRqyEiMm4MdiQJbdu2hVKphEqlQmxsrNjlUBVlZ2fj0KFDALgalohIFxjsSBJ4n51x2r9/P0pLS9G5c2e4u7uLXQ4RkdFjsCPJECvYFRQUQCaTQSaToaCgQK+fbey4dx0RkW4x2JFkqINdTEwMiouLRa6GqiImJgYymQzjxo0TuxQiIklgsCPJcHd3h4ODA4qKihAXFyd2OVRF/fr1Q4sWLcQug4hIEkzFLoBIV2QyGfr164e9e/ciIiICXl5eYpdkMHbv3g07OztYWlpqvSwsLCpts7Cw0NsKVU7DEhHpDoMdSYo62EVGRiIoKEjsckSVm5ur+fqdd96p9vsfD31PCoA1aXucmZkZXn311VqfKxERPcJgR5Kivs8uOjoapaWlMDWtv7/FDx8+rPl60KBBKCkpwcOHD/Hw4UOoVCrN14+/HqdSqaBSqZCTk1NnNfr6+qJRo0Z1dnwiovqm/v6rR5LUsWNHNGjQAA8ePEBCQgJ69Oghdkmi2b9/v9bX1tbWT+0vCIJW+HtaAKysvaptj98DOWfOnLr8JSAiqncY7EhS5HI5vL298csvvyAiIqLeBruCggKEh4dX6z0ymQzm5uYwNzeHnZ1dHVX2qDYbGxsAQPfu3evsc4iI6iOuiiXJ4UbFwKFDh1BUVCR2GUREpGcMdiQ56mAXFRWFsrIykasRx549e8QugYiIRMBgR5LTpUsX2NraIicnBxcuXBC7HL0rKirCwYMHxS6DiIhEwGBHkmNqaoo+ffoAqJ/TsUePHkV+fj43/SUiqocY7EiS6vN9dupp2BEjRohcCRER6RuDHUmSOthFRkaivLxc5Gr0p7i4GAcOHAAAjBo1StxiiIhI7xjsSJK6d+8OKysrZGdn4/Lly2KXoze///47cnJy4OjoiF69eoldDhER6ZnowW7jxo1wdXWFpaUlPDw8EBUV9dT+GzZsgJubGxQKBdq1a4cdO3Y8sW9ISAhkMhlHLuohMzMzzbNi69N07E8//QQAGD16NExMRP/jTUREeibq3/yhoaGYMWMGFixYgISEBHh7e8PPzw+pqamV9g8ODkZQUBCWLFmCS5cu4aOPPsK0adPwyy+/VOj7119/Yc6cOfD29q7r0yA9sLa2hiAIEAThmU9QUKtv99mVlJRonjYxZswYcYshIiJRiBrs1q1bh0mTJmHy5Mlwc3PD+vXr4eTkhODg4Er7f/fdd5gyZQr8/f3RqlUrjB07FpMmTcKqVau0+pWVleHNN9/ERx99hFatWunjVMgA9evXD8Cj++wEQRC5mroXERGBe/fuwcHBgf+hISKqp0QLdsXFxYiPj4ePj49Wu4+PD2JiYip9j0qlgqWlpVabQqFAbGwsSkpKNG1Lly5FkyZNMGnSJN0XTkajZ8+esLCwwO3bt5GUlCR2OXVOvRp29OjRMDXl0wKJiOoj0YJdVlYWysrKoFQqtdqVSiUyMzMrfY+vry82b96M+Ph4CIKAuLg4bNmyBSUlJcjKygIAnDhxAt9++y2++eabKteiUqmQm5ur9SLjZ2lpqVlAIPXp2LKyMuzduxcA8Oqrr4pcDRERiUX0u6tlMpnW94IgVGhTW7RoEfz8/NCrVy+YmZlh5MiRmDhxIoBHD3/Py8vDP/7xD3zzzTdwcHCocg0rVqyAvb295uXk5FTj8yHDUl/usztx4gTu3LmDhg0bYuDAgWKXQ0REIhEt2Dk4OEAul1cYnbtz506FUTw1hUKBLVu2oLCwEDdu3EBqaipcXFxga2sLBwcHXLt2DTdu3MDw4cNhamoKU1NT7NixAwcOHICpqSmuXbtW6XGDgoKQk5OjeaWlpen8fEkcjwc7Kd9np14NO2LECJiZmYlcDRERiUW0G3HMzc3h4eGB8PBwjB49WtMeHh6OkSNHPvW9ZmZmmsclhYSEYNiwYTAxMUH79u0rPBt04cKFyMvLw+eff/7EkTgLCwtYWFjU8ozIEKlHd9PT05GSkoLWrVuLXZLOlZeXa6ZhuRqWiKh+E/UO61mzZmH8+PHo3r07evfujU2bNiE1NRUBAQEAHo2kpaena/aqS0pKQmxsLDw9PXH//n2sW7cOFy9exPbt2wE8uqeqQ4cOWp/RoEEDAKjQTvWDlZUVevTogZiYGERGRkoy2J0+fRrp6emwtbXF4MGDxS6HiIhEJOo9dv7+/li/fj2WLl2KLl26IDIyEmFhYXB2dgYAZGRkaO1pV1ZWhrVr16Jz584YPHgwHj58iJiYGLi4uIh0BmQMpH6fnXoadvjw4Rx5JiKq52SClG88qqHc3FzY29sjJycHdnZ2YpdDtXTkyBEMGTIELi4uuH79us6PX1BQABsbGwBAfn5+lTdQ1gVBEODq6oq//voLe/fu1bqtQcy6nsZQ6yIiMlTVySU1HrG7du0aFi5ciHHjxuHOnTsAgMOHD+PSpUs1PSRRnfDy8oJcLtcsuJGS+Ph4/PXXX7CysoKvr6/Y5RARkchqFOwiIiLQsWNHnD59Gnv37kV+fj4A4L///S8+/PBDnRZIVFu2trbw8PAAIL3pWPWmxEOHDoWVlZXI1RARkdhqFOzmz5+PTz75BOHh4TA3N9e0DxgwACdPntRZcUS6IsX77ARB0Nxfx02JiYgIqGGwu3Dhgta9PGpNmjRBdnZ2rYsi0rXHnxsrFRcuXEBycjIsLS3x8ssvi10OEREZgBoFuwYNGiAjI6NCe0JCApo3b17rooh0rW/fvpDJZLh69Wqlv3eNkXq0ztfXF7a2tiJXQ0REhqBGwe6NN97AvHnzkJmZCZlMhvLycpw4cQJz5szBhAkTdF0jUa01aNAAXbp0ASCd6Vj1/XXclJiIiNRqFOyWLVuGli1bonnz5sjPz4e7uzv69esHLy8vLFy4UNc1EumElO6zu3LlCi5fvgwzMzMMGzZM7HKIiMhA1CjYmZmZYdeuXbh69Sp++OEH7Ny5E3/++Se+++47yOVyXddIpBNSCnbq0brBgwdrnq5CRERUq0eKtWrVCq1atdJVLUR1ytvbG8Cj0a47d+6gadOmIldUc+r76zgNS0REj6vRiN2YMWOwcuXKCu1r1qzBa6+9VuuiiOpC48aNNc8MNubVscnJyTh//jzkcjlGjBghdjlERGRAarxB8dChQyu0DxkyxKj/wSTpU0/HGvPvU/U07MCBA9G4cWORqyEiIkNSo2CXn5+vtTGxmpmZGXJzc2tdFFFdkcJ9dtyUmIiInqRGwa5Dhw4IDQ2t0B4SEgJ3d/daF0VUV9QbFV+4cAH37t0TuZrq++uvvxAXFwcTExOMGjVK7HKIiMjA1GjxxKJFi/Dqq6/i2rVrGDhwIADg999/x+7du/Hjjz/qtEAiXVIqlWjfvj3+/PNPREVFYeTIkWKXVC3qaVhvb28olUqRqyEiIkNToxG7ESNGYP/+/UhOTsa7776L2bNn4+bNm/jtt984ikAGz5inY7kpMRERPU2NtzsZOnRopQsoiAxdv3798PXXXxtdsEtPT0dMTAwAVPqsZiIiolrtY1dcXIw7d+6gvLxcq71ly5a1KoqoLqlH7M6dO4ecnBzY29uLXFHV7Nu3DwDg5eXFZzITEVGlajQVe/XqVXh7e0OhUMDZ2Rmurq5wdXWFi4sLXF1ddV0jkU41b94crVu31jzj2FhwNSwRET1LjUbsJk6cCFNTUxw8eBCOjo6QyWS6rouoTvXv3x/Xrl1DREQEXn75ZbHLeabbt28jKioKAIMdERE9WY2C3blz5xAfH4/27dvruh4ivejfvz+2bNliNPfZ7d+/H+Xl5ejRowecnZ3FLoeIiAxUjaZi3d3dkZWVpetaiPRGfZ9dXFwc8vPzRa7m2TgNS0REVVGjYLdq1Sp88MEHOH78OLKzs5Gbm6v1IjJ0zs7OaNmyJcrKyjQrTQ1VdnY2jh07BoDBjoiInq5GwW7QoEE4deoUXnrpJTRt2hQNGzZEw4YN0aBBAzRs2FDXNRLVCWPZz+7nn39GWVkZOnfujDZt2ohdDhERGbAa3WOnHj0gMmb9+/fHd999h8jISLFLeSpuSkxERFVVo2CnHukgMmbq38exsbEoKiqCQqEQuaKKHjx4gPDwcACchiUiomer0VQsAERFReEf//gHvLy8kJ6eDgD47rvvEB0drbPiiOpS69at8dxzz6G4uBinTp0Su5xKHTx4ECUlJXB3d4ebm5vY5RARkYGrUbDbs2cPfH19oVAocPbsWahUKgBAXl4eli9frtMCieqKTCYz+PvsuBqWiIiqo0bB7pNPPsFXX32Fb775BmZmZpp2Ly8vnD17VmfFEdU1Qw52eXl5OHz4MADeX0dERFVTo2CXmJiIfv36VWi3s7PDgwcPalsTkd6ofx+fOnVKM/JsKMLCwqBSqdCmTRt07NhR7HKIiMgI1CjYOTo6Ijk5uUJ7dHQ0WrVqVeuiiPSlffv2aNq0KR4+fIgzZ86IXY6Wx1fD8rF9RERUFTUKdlOmTEFgYCBOnz4NmUyGW7duYdeuXZgzZw7effddXddIVGdkMplm1M6QpmMLCwvx66+/AuA0LBERVV2Ngt0HH3yAUaNGYcCAAcjPz0e/fv0wefJkTJkyBe+9956uaySqU4Z4n93hw4dRWFgIFxcXdOvWTexyiIjISFR7H7uysjJER0dj9uzZWLBgAS5fvozy8nK4u7vDxsamLmokqlPqYBcTE4OSkhKtBUFiUU/Dvvrqq5yGJSKiKqv2iJ1cLoevry9ycnJgZWWF7t27o2fPngx1ZLReeOEFNGrUCAUFBYiPjxe7HKhUKvzyyy8AuM0JERFVT42mYjt27IiUlBRd10IkChMTE3h7ewMwjOnY8PBw5OXloXnz5vD09BS7HCIiMiI1CnbLli3DnDlzcPDgQWRkZCA3N1frRWRs1NOxhvDcWPWmxK+88gpMTGr8cBgiIqqHavSs2CFDhgAARowYoXX/jyAIkMlkKCsr0011RHqiDnbR0dEoKyuDXC4XpY7i4mL8/PPPALgaloiIqq9Gwe7YsWO6roNIVJ07d4a9vT1ycnJw7tw5eHh4iFLHsWPH8ODBAzRt2hR9+vQRpQYiIjJeNQp26tENIqmQy+Xo27cvfv31V0RERIgW7NSrYV955RXRRg2JiMh41fgGnqioKPzjH/+Al5cX0tPTAQDfffcdoqOjdVYckT6JvZ9daWkp9u3bB4CrYYmIqGZqFOz27NkDX19fKBQKnD17VvOMzby8PCxfvlynBRLpi/oJFFFRUSgvL9f750dFRSErKwuNGzfmqDgREdVIjYLdJ598gq+++grffPON1mauXl5eOHv2bLWOtXHjRri6usLS0hIeHh6Iiop6av8NGzbAzc0NCoUC7dq1w44dO7R+/ptvvoG3tzcaNmyIhg0bYtCgQYiNja1WTVQ/devWDdbW1rh//z4uXLig989Xr4YdNWqUQWySTERExqdGwS4xMVEzuvE4Ozs7PHjwoMrHCQ0NxYwZM7BgwQIkJCTA29sbfn5+SE1NrbR/cHAwgoKCsGTJEly6dAkfffQRpk2bptnMFQCOHz+OcePG4dixYzh58iRatmwJHx8fzXQx0ZOYmZlpFizoe9uT8vJy7N27FwCnYYmIqOZqFOwcHR2RnJxcoT06OhqtWrWq8nHWrVuHSZMmYfLkyXBzc8P69evh5OSE4ODgSvt/9913mDJlCvz9/dGqVSuMHTsWkyZNwqpVqzR9du3ahXfffRddunRB+/bt8c0336C8vBy///579U+U6h2x7rOLiYlBZmYm7O3t8dJLL+n1s4mISDpqFOymTJmCwMBAnD59GjKZDLdu3cKuXbswZ84cvPvuu1U6RnFxMeLj4+Hj46PV7uPjg5iYmErfo1KpYGlpqdWmUCgQGxuLkpKSSt9TWFiIkpISNGrUqEp1Uf32+EbFgiDo7XPV07AjRoyAubm53j6XiIikpUbbnXzwwQfIycnBgAED8PDhQ/Tr1w8WFhaYM2cO3nvvvSodIysrC2VlZVAqlVrtSqUSmZmZlb7H19cXmzdvxqhRo9CtWzfEx8djy5YtKCkpQVZWFhwdHSu8Z/78+WjevDkGDRr0xFpUKpVmAQgAPj2jHuvRowcsLS1x9+5dXLlyBe7u7nX+meXl5ZptTrgpMRER1UaNtztZtmwZsrKyEBsbi1OnTuHu3bv4+OOPq32cx59cAfzv6RWVWbRoEfz8/NCrVy+YmZlh5MiRmDhxIgBUuufX6tWrsXv3buzdu7fCSN/jVqxYAXt7e83Lycmp2udB0mBubo7evXsD0N907JkzZ3Dz5k3Y2NhUGMEmIiKqjlo9iNLKygrdu3dHz549YWNjU633Ojg4QC6XVxidu3PnToVRPDWFQoEtW7agsLAQN27cQGpqKlxcXGBrawsHBwetvp9++imWL1+Oo0ePolOnTk+tJSgoCDk5OZpXWlpatc6FpEXf99mpR+uGDRv21P+AVJe1tTUEQYAgCLC2ttbZcYmIyHDVaCq2oKAAK1euxO+//447d+5U2PMrJSXlmccwNzeHh4cHwsPDMXr0aE17eHg4Ro4c+dT3mpmZoUWLFgCAkJAQDBs2TOth6WvWrMEnn3yCI0eOoHv37s+sxcLCAhYWFs/sR/XD3++ze9IIsi4IgqC5v46rYYmIqLZqFOwmT56MiIgIjB8/Ho6OjjX+h2/WrFkYP348unfvjt69e2PTpk1ITU1FQEAAgEcjaenp6Zq96pKSkhAbGwtPT0/cv38f69atw8WLF7F9+3bNMVevXo1Fixbh+++/h4uLi2ZE0MbGptqjilQ/eXp6wtzcHBkZGUhOTkbbtm3r7LPOnTuH69evQ6FQwM/Pr84+x5CoRxKJiEj3ahTsDh06hF9//bXWDyn39/dHdnY2li5dioyMDHTo0AFhYWFwdnYGAGRkZGjtaVdWVoa1a9ciMTERZmZmGDBgAGJiYuDi4qLps3HjRhQXF1e4Cf3DDz/EkiVLalUv1Q8KhQKenp6IiopCREREnQY79Wjdyy+/zOlSIiKqtRoFu4YNG+ps+5B33333iVukbNu2Tet7Nzc3JCQkPPV4N27c0EldVL/1799fE+wmT55cJ5/BaVgiItK1Gi2e+Pjjj7F48WIUFhbquh4ig6B+skpERESdTRteunQJSUlJsLCwwNChQ+vkM4iIqH6p8ohd165dte6lS05OhlKphIuLS4XnWlb3ebFEhsbLywumpqZIS0vDjRs34OrqqvPPUK+G9fHxgZ2dnc6PT0RE9U+Vg92oUaPqsAwiw2JtbY3u3bvj1KlTiIiIqJNgp56G5abERESkK1UOdh9++GFd1kFkcPr3749Tp04hMjJSsxG2riQmJuLixYswNTXF8OHDdXpsIiKqv2q1QXF8fDx27tyJXbt2PXNRA5GxqcuNitXTsIMGDULDhg11fnwiIqqfarQq9s6dOxg7diyOHz+OBg0aQBAEzbNjQ0JC0KRJE13XSaR3ffr0gYmJCVJSUnDz5k3Npti6wNWwRERUF2o0Yvf+++8jNzcXly5dwr1793D//n1cvHgRubm5mD59uq5rJBKFnZ0dunbtCkC3o3YpKSlISEiAXC7nvatERKRTNQp2hw8fRnBwMNzc3DRt7u7u2LBhAw4dOqSz4ojEVhfTsepp2P79+1d4xjEREVFt1CjYlZeXV9jiBHj0DNe/PzeWyJjVZbDjalgiItK1GgW7gQMHIjAwELdu3dK0paenY+bMmXjppZd0VhyR2Ly9vSGTyZCUlKR57nBtpKWl4fTp05DJZBg9erQOKiQiIvqfGgW7L7/8Enl5eXBxcUHr1q3Rpk0buLq6Ii8vD//5z390XSORaBo2bIhOnToBACIjI2t9vL179wIA+vbti2bNmtX6eERERI+r0apYJycnnD17FuHh4fjzzz8hCALc3d0xaNAgXddHJLr+/fvj/PnziIiIwOuvv16rY3FTYiIiqkvVGrH7448/4O7ujtzcXADA4MGD8f7772P69Ono0aMHXnjhBURFRdVJoURiefy5sbWRkZGBEydOAABeeeWVWtdFRET0d9UKduvXr8c777xT6XMt7e3tMWXKFKxbt05nxREZAnWwu3TpErKysmp8nH379kEQBPTq1Uune+IRERGpVSvYnT9/HkOGDHniz/v4+CA+Pr7WRREZkiZNmsDd3R1A7e6z46bERERU16oV7G7fvl3pNidqpqamuHv3bq2LIjI06m1Pahrs7t69q5nKZbAjIqK6Uq1g17x5c1y4cOGJP//f//4Xjo6OtS6KyNDUdj+7/fv3o7y8HN26dYOrq6suSyMiItKoVrB7+eWXsXjxYjx8+LDCzxUVFeHDDz/EsGHDdFYckaFQB7vz58/j/v371X4/NyUmIiJ9kAmCIFS18+3bt9GtWzfI5XK89957aNeuHWQyGa5cuYINGzagrKwMZ8+ehVKprMua61xubi7s7e2Rk5NT6UIRqp/atWuHpKQkHDhwAMOHD9e0FxQUwMbGBgCQn58Pa2trrffdv38fTZs2RWlpKRITE/H888/rtW4iIjJu1ckl1drHTqlUIiYmBlOnTkVQUBDUmVAmk8HX1xcbN240+lBH9CT9+vVDUlISIiIitILdsxw4cAClpaXo2LEjQx0REdWpam9Q7OzsjLCwMNy/fx/JyckQBAFt27ZFw4YN66I+IoPRv39/bN68udr32XFTYiIi0pcaPXkCePSopR49euiyFiKDpr7P7uzZs8jNza3SNH1ubi6OHj0KgKthiYio7tXoWbFE9ZGTkxNcXV1RXl6OmJiYKr3n4MGDKC4uRvv27TV74REREdUVBjuiaqjutifq1bCvvvoqZDJZndVFREQEMNgRVUt1gl1BQQEOHToEgPfXERGRfjDYEVWD+rmxZ86cQUFBwVP7Hjp0CEVFRWjVqhU6d+6sj/KIiKieY7AjqgZXV1e0aNECpaWlOHny5FP7Pr4altOwRESkDwx2RNUgk8mqNB1bVFSEgwcPAuBqWCIi0h8GO6JqUge7yMjIJ/Y5evQoCgoK4OTkxG2BiIhIbxjsiKpJHexOnz5d6XOTgf9Nw3I1LBER6RODHVE1tW3bFs2aNYNKpcLp06cr/LxKpcIvv/wCgKthiYhIvxjsiKpJJpNpVsdWdp/d77//jpycHDg6OqJ37976Lo+IiOoxBjuiGnjaAgr1psSvvPIKTEz4R4yIiPSH/+oQ1YA62J08eRLFxcWa9pKSEuzfvx8Ap2GJiEj/GOyIasDd3R0ODg4oKipCfHy8pj06Ohr37t1DkyZN4O3tLWKFRERUHzHYEdXA4/fZnThxQtO+b98+AMDo0aMhl8tFqY2IiOovBjuiGlJPx0ZHR2va1KthuSkxERGJgcGOqIbUI3anTp3StN29excNGzbEgAEDxCqLiIjqMQY7ohrq2LEjGjRogPz8fK32kSNHwszMTKSqiIioPmOwI6ohuVxe6QIJroYlIiKxMNgR1YL6Pjs1Ozs7DBo0SKRqiIiovhM92G3cuBGurq6wtLSEh4cHoqKintp/w4YNcHNzg0KhQLt27bBjx44Kffbs2QN3d3dYWFjA3d1ds1KRSNf+Huz8/PxgYWEhUjVERFTfiRrsQkNDMWPGDCxYsAAJCQnw9vaGn58fUlNTK+0fHByMoKAgLFmyBJcuXcJHH32EadOmaVYiAo82jPX398f48eNx/vx5jB8/Hq+//nqlz/Qkqq0uXbrA1tZW8/2oUaPEK4aIiOo9mSAIglgf7unpiW7duiE4OFjT5ubmhlGjRmHFihUV+nt5eaFPnz5Ys2aNpm3GjBmIi4vTbDnh7++P3NxcHDp0SNNnyJAhaNiwIXbv3l2lunJzc2Fvb4+cnBzY2dnV9PSonvDx8UF4eDiAR6tiHRwcRK6IiIikpDq5RLQRu+LiYsTHx8PHx0er3cfHBzExMZW+R6VSwdLSUqtNoVAgNjYWJSUlAB6N2P39mL6+vk88JlFtPX5PnUKhELESIiKq70QLdllZWSgrK4NSqdRqVyqVyMzMrPQ9vr6+2Lx5M+Lj4yEIAuLi4rBlyxaUlJQgKysLAJCZmVmtYwKPAmNubq7Wi6iq/vWvf4ldAhEREQADWDwhk8m0vhcEoUKb2qJFi+Dn54devXrBzMwMI0eOxMSJEwFA6/FN1TkmAKxYsQL29vaal5OTUw3Phuoj7llHRESGQrRg5+DgALlcXmEk7c6dOxVG3NQUCgW2bNmCwsJC3LhxA6mpqXBxcYGtra3mvqZmzZpV65gAEBQUhJycHM0rLS2tlmdHREREpH+iBTtzc3N4eHhobjpXCw8Ph5eX11Pfa2ZmhhYtWkAulyMkJATDhg2DicmjU+ndu3eFYx49evSpx7SwsICdnZ3Wi4iIiMjYmIr54bNmzcL48ePRvXt39O7dG5s2bUJqaioCAgIAPBpJS09P1+xVl5SUhNjYWHh6euL+/ftYt24dLl68iO3bt2uOGRgYiH79+mHVqlUYOXIkfv75Z/z2229aD2onIiIikiJRg52/vz+ys7OxdOlSZGRkoEOHDggLC4OzszMAICMjQ2tPu7KyMqxduxaJiYkwMzPDgAEDEBMTAxcXF00fLy8vhISEYOHChVi0aBFat26N0NBQeHp66vv0iIiIiPRK1H3sDBX3saPqKCgogI2NDQAgPz8f1tbWIldERERSYhT72BERERGRbjHYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRIge7DZu3AhXV1dYWlrCw8MDUVFRT+2/a9cudO7cGVZWVnB0dMQ///lPZGdna/VZv3492rVrB4VCAScnJ8ycORMPHz6sy9MgIiIiEp2owS40NBQzZszAggULkJCQAG9vb/j5+SE1NbXS/tHR0ZgwYQImTZqES5cu4ccff8SZM2cwefJkTZ9du3Zh/vz5+PDDD3HlyhV8++23CA0NRVBQkL5Oi4iIiEgUoga7devWYdKkSZg8eTLc3Nywfv16ODk5ITg4uNL+p06dgouLC6ZPnw5XV1f07dsXU6ZMQVxcnKbPyZMn0adPH7zxxhtwcXGBj48Pxo0bp9WHiIiISIpEC3bFxcWIj4+Hj4+PVruPjw9iYmIqfY+Xlxdu3ryJsLAwCIKA27dv46effsLQoUM1ffr27Yv4+HjExsYCAFJSUhAWFqbVh4iIiEiKTMX64KysLJSVlUGpVGq1K5VKZGZmVvoeLy8v7Nq1C/7+/nj48CFKS0sxYsQI/Oc//9H0GTt2LO7evYu+fftCEASUlpZi6tSpmD9//hNrUalUUKlUmu9zc3NreXZERERE+if64gmZTKb1vSAIFdrULl++jOnTp2Px4sWIj4/H4cOHcf36dQQEBGj6HD9+HMuWLcPGjRtx9uxZ7N27FwcPHsTHH3/8xBpWrFgBe3t7zcvJyUk3J0dERESkRzJBEAQxPri4uBhWVlb48ccfMXr0aE17YGAgzp07h4iIiArvGT9+PB4+fIgff/xR0xYdHQ1vb2/cunULjo6O8Pb2Rq9evbBmzRpNn507d+Jf//oX8vPzYWJSMctWNmLn5OSEnJwc2NnZ6eqUSaIKCgpgY2MDAMjPz4e1tbXIFRERkZTk5ubC3t6+SrlEtBE7c3NzeHh4IDw8XKs9PDwcXl5elb6nsLCwQjCTy+UAHo30Pa2PIAh4Uoa1sLCAnZ2d1ouIiIjI2Ih2jx0AzJo1C+PHj0f37t3Ru3dvbNq0CampqZqp1aCgIKSnp2PHjh0AgOHDh+Odd95BcHAwfH19kZGRgRkzZqBnz5547rnnNH3WrVuHrl27wtPTE8nJyVi0aBFGjBihCYFEREREUiRqsPP390d2djaWLl2KjIwMdOjQAWFhYXB2dgYAZGRkaO1pN3HiROTl5eHLL7/E7Nmz0aBBAwwcOBCrVq3S9Fm4cCFkMhkWLlyI9PR0NGnSBMOHD8eyZcv0fn5ERERE+iTaPXaGrDpz2US8x46IiOqSUdxjR0RERES6xWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSwWBHREREJBEMdkREREQSIXqw27hxI1xdXWFpaQkPDw9ERUU9tf+uXbvQuXNnWFlZwdHREf/85z+RnZ2t1efBgweYNm0aHB0dYWlpCTc3N4SFhdXlaRARERGJTtRgFxoaihkzZmDBggVISEiAt7c3/Pz8kJqaWmn/6OhoTJgwAZMmTcKlS5fw448/4syZM5g8ebKmT3FxMQYPHowbN27gp59+QmJiIr755hs0b95cX6dFREREJApTMT983bp1mDRpkiaYrV+/HkeOHEFwcDBWrFhRof+pU6fg4uKC6dOnAwBcXV0xZcoUrF69WtNny5YtuHfvHmJiYmBmZgYAcHZ21sPZEBEREYlLtBG74uJixMfHw8fHR6vdx8cHMTExlb7Hy8sLN2/eRFhYGARBwO3bt/HTTz9h6NChmj4HDhxA7969MW3aNCiVSnTo0AHLly9HWVlZnZ4PERERkdhEG7HLyspCWVkZlEqlVrtSqURmZmal7/Hy8sKuXbvg7++Phw8forS0FCNGjMB//vMfTZ+UlBT88ccfePPNNxEWFoarV69i2rRpKC0txeLFiys9rkqlgkql0nyfm5urgzMkIiIi0i/RF0/IZDKt7wVBqNCmdvnyZUyfPh2LFy9GfHw8Dh8+jOvXryMgIEDTp7y8HE2bNsWmTZvg4eGBsWPHYsGCBQgODn5iDStWrIC9vb3m5eTkpJuTIyIiItIj0UbsHBwcIJfLK4zO3blzp8IontqKFSvQp08fzJ07FwDQqVMnWFtbw9vbG5988gkcHR3h6OgIMzMzyOVyzfvc3NyQmZmJ4uJimJubVzhuUFAQZs2apfk+NzeX4Y6IiIiMjmgjdubm5vDw8EB4eLhWe3h4OLy8vCp9T2FhIUxMtEtWBzhBEAAAffr0QXJyMsrLyzV9kpKS4OjoWGmoAwALCwvY2dlpvYiIiIiMjahTsbNmzcLmzZuxZcsWXLlyBTNnzkRqaqpmajUoKAgTJkzQ9B8+fDj27t2L4OBgpKSk4MSJE5g+fTp69uyJ5557DgAwdepUZGdnIzAwEElJSfj111+xfPlyTJs2TZRzJCIiItIXUbc78ff3R3Z2NpYuXYqMjAx06NABYWFhmu1JMjIytPa0mzhxIvLy8vDll19i9uzZaNCgAQYOHIhVq1Zp+jg5OeHo0aOYOXMmOnXqhObNmyMwMBDz5s3T+/kRERER6ZNMUM9hkkZubi7s7e2Rk5PDaVl6poKCAtjY2AAA8vPzYW1tLXJFREQkJdXJJaKviiUiIiIi3WCwIyIiIpIIBjsiIiIiiWCwIyIiIpIIBjsiIiIiiWCwIyIiIpIIBjsiIiIiiWCwIyIiIpIIBjsiIiIiiWCwIyIiIpIIBjsiIiIiiTAVuwAiY2dtbQ0+cpmIiAwBR+yIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJILBjoiIiEgiGOyIiIiIJMJU7AIMkSAIAIDc3FyRKyEiIqL6Tp1H1PnkaRjsKpGXlwcAcHJyErkSIiIiokfy8vJgb2//1D4yoSrxr54pLy/HrVu3YGtrC5lMJnY59P9yc3Ph5OSEtLQ02NnZiV0O1QKvpbTwekoHr6VhEgQBeXl5eO6552Bi8vS76DhiVwkTExO0aNFC7DLoCezs7PgXjkTwWkoLr6d08FoanmeN1Klx8QQRERGRRDDYEREREUkEgx0ZDQsLC3z44YewsLAQuxSqJV5LaeH1lA5eS+PHxRNEREREEsEROyIiIiKJYLAjIiIikggGOyIiIiKJYLAjg7Jx40a4urrC0tISHh4eiIqKemLfjIwMvPHGG2jXrh1MTEwwY8YM/RVKz1Sda7l3714MHjwYTZo0gZ2dHXr37o0jR47osVp6lupcz+joaPTp0weNGzeGQqFA+/bt8dlnn+mxWnqa6lzLx504cQKmpqbo0qVL3RZItcJgRwYjNDQUM2bMwIIFC5CQkABvb2/4+fkhNTW10v4qlQpNmjTBggUL0LlzZz1XS09T3WsZGRmJwYMHIywsDPHx8RgwYACGDx+OhIQEPVdOlanu9bS2tsZ7772HyMhIXLlyBQsXLsTChQuxadMmPVdOf1fda6mWk5ODCRMm4KWXXtJTpVRTXBVLBsPT0xPdunVDcHCwps3NzQ2jRo3CihUrnvreF198EV26dMH69evruEqqitpcS7UXXngB/v7+WLx4cV2VSVWki+v5yiuvwNraGt99911dlUlVUNNrOXbsWLRt2xZyuRz79+/HuXPn9FAt1QRH7MggFBcXIz4+Hj4+PlrtPj4+iImJEakqqgldXMvy8nLk5eWhUaNGdVEiVYMurmdCQgJiYmLQv3//uiiRqqim13Lr1q24du0aPvzww7oukXSAz4olg5CVlYWysjIolUqtdqVSiczMTJGqoprQxbVcu3YtCgoK8Prrr9dFiVQNtbmeLVq0wN27d1FaWoolS5Zg8uTJdVkqPUNNruXVq1cxf/58REVFwdSUkcEY8CqRQZHJZFrfC4JQoY2MQ02v5e7du7FkyRL8/PPPaNq0aV2VR9VUk+sZFRWF/Px8nDp1CvPnz0ebNm0wbty4uiyTqqCq17KsrAxvvPEGPvroIzz//PP6Ko9qicGODIKDgwPkcnmF/zXeuXOnwv8uybDV5lqGhoZi0qRJ+PHHHzFo0KC6LJOqqDbX09XVFQDQsWNH3L59G0uWLGGwE1F1r2VeXh7i4uKQkJCA9957D8Cj2yQEQYCpqSmOHj2KgQMH6qV2qjreY0cGwdzcHB4eHggPD9dqDw8Ph5eXl0hVUU3U9Fru3r0bEydOxPfff4+hQ4fWdZlURbr6sykIAlQqla7Lo2qo7rW0s7PDhQsXcO7cOc0rICAA7dq1w7lz5+Dp6amv0qkaOGJHBmPWrFkYP348unfvjt69e2PTpk1ITU1FQEAAACAoKAjp6enYsWOH5j3qlVn5+fm4e/cuzp07B3Nzc7i7u4txCvT/qnstd+/ejQkTJuDzzz9Hr169NCMKCoUC9vb2op0HPVLd67lhwwa0bNkS7du3B/BoX7tPP/0U77//vmjnQI9U51qamJigQ4cOWu9v2rQpLC0tK7ST4WCwI4Ph7++P7OxsLF26FBkZGejQoQPCwsLg7OwM4NGGxH/fa6lr166ar+Pj4/H999/D2dkZN27c0Gfp9DfVvZZff/01SktLMW3aNEybNk3T/tZbb2Hbtm36Lp/+prrXs7y8HEFBQbh+/TpMTU3RunVrrFy5ElOmTBHrFOj/1eTvWTIu3MeOiIiISCJ4jx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RERGRRDDYEREREUkEgx0RkZGbOHEiZDIZZDIZ9u/fr9NjHz9+XHPsUaNG6fTYRKR7DHZEZHAeDyqPv5KTk8UuzWANGTIEGRkZ8PPz07Q9KehNnDixyiHNy8sLGRkZeP3113VUKRHVJT4rlogM0pAhQ7B161attiZNmlToV1xcDHNzc32VZbAsLCzQrFkznR/X3NwczZo1g0KhgEql0vnxiUi3OGJHRAZJHVQef8nlcrz44ot47733MGvWLDg4OGDw4MEAgMuXL+Pll1+GjY0NlEolxo8fj6ysLM3xCgoKMGHCBNjY2MDR0RFr167Fiy++iBkzZmj6VDbC1aBBA2zbtk3zfXp6Ovz9/dGwYUM0btwYI0eOxI0bNzQ/rx4N+/TTT+Ho6IjGjRtj2rRpKCkp0fRRqVT44IMP4OTkBAsLC7Rt2xbffvstBEFAmzZt8Omnn2rVcPHiRZiYmODatWu1/4X9mxs3blQ6Ovriiy/q/LOIqO4x2BGR0dm+fTtMTU1x4sQJfP3118jIyED//v3RpUsXxMXF4fDhw7h9+7bW9OHcuXNx7Ngx7Nu3D0ePHsXx48cRHx9frc8tLCzEgAEDYGNjg8jISERHR8PGxgZDhgxBcXGxpt+xY8dw7do1HDt2DNu3b8e2bdu0wuGECRMQEhKCL774AleuXMFXX30FGxsbyGQyvP322xVGKrds2QJvb2+0bt26Zr9gT+Hk5ISMjAzNKyEhAY0bN0a/fv10/llEpAcCEZGBeeuttwS5XC5YW1trXmPGjBEEQRD69+8vdOnSRav/okWLBB8fH622tLQ0AYCQmJgo5OXlCebm5kJISIjm57OzswWFQiEEBgZq2gAI+/bt0zqOvb29sHXrVkEQBOHbb78V2rVrJ5SXl2t+XqVSCQqFQjhy5IimdmdnZ6G0tFTT57XXXhP8/f0FQRCExMREAYAQHh5e6bnfunVLkMvlwunTpwVBEITi4mKhSZMmwrZt25766zVy5MgK7QAES0tLrV9Ha2trwdTUtNL+RUVFgqenpzBs2DChrKysSp9BRIaF99gRkUEaMGAAgoODNd9bW1trvu7evbtW3/j4eBw7dgw2NjYVjnPt2jUUFRWhuLgYvXv31rQ3atQI7dq1q1ZN8fHxSE5Ohq2trVb7w4cPtaZJX3jhBcjlcs33jo6OuHDhAgDg3LlzkMvl6N+/f6Wf4ejoiKFDh2LLli3o2bMnDh48iIcPH+K1116rVq1qn332GQYNGqTVNm/ePJSVlVXoO2nSJOTl5SE8PBwmJpzQITJGDHZEZJCsra3Rpk2bJ/7c48rLyzF8+HCsWrWqQl9HR0dcvXq1Sp8pk8kgCIJW2+P3xpWXl8PDwwO7du2q8N7HF3aYmZlVOG55eTkAQKFQPLOOyZMnY/z48fjss8+wdetW+Pv7w8rKqkrn8HfNmjWr8Otoa2uLBw8eaLV98sknOHz4MGJjYysEVyIyHgx2RGT0unXrhj179sDFxQWmphX/WmvTpg3MzMxw6tQptGzZEgBw//59JCUlaY2cNWnSBBkZGZrvr169isLCQq3PCQ0NRdOmTWFnZ1ejWjt27Ijy8nJERERUGElTe/nll2FtbY3g4GAcOnQIkZGRNfqsqtqzZw+WLl2KQ4cO1cl9fESkPxxrJyKjN23aNNy7dw/jxo1DbGwsUlJScPToUbz99tsoKyuDjY0NJk2ahLlz5+L333/HxYsXMXHixArTjQMHDsSXX36Js2fPIi4uDgEBAVqjb2+++SYcHBwwcuRIREVF4fr164iIiEBgYCBu3rxZpVpdXFzw1ltv4e2338b+/ftx/fp1HD9+HD/88IOmj1wux8SJExEUFIQ2bdpoTSHr2sWLFzFhwgTMmzcPL7zwAjIzM5GZmYl79+7V2WcSUd1hsCMio/fcc8/hxIkTKCsrg6+vLzp06IDAwEDY29trwtuaNWvQr18/jBgxAoMGDULfvn3h4eGhdZy1a9fCyckJ/fr1wxtvvIE5c+ZoTYFaWVkhMjISLVu2xCuvvAI3Nze8/fbbKCoqqtYIXnBwMMaMGYN3330X7du3xzvvvIOCggKtPpMmTUJxcTHefvvtWvzKPFtcXBwKCwvxySefwNHRUfN65ZVX6vRziahuyIS/31BCRFRPvPjii+jSpQvWr18vdikVnDhxAi+++CJu3rwJpVL51L4TJ07EgwcPdP44MX1/BhHVHkfsiIgMiEqlQnJyMhYtWoTXX3/9maFO7eDBg7CxscHBgwd1Wk9UVBRsbGwqXTBCRIaHiyeIiAzI7t27MWnSJHTp0gXfffddld6zevVqLFy4EMCjVcC61L17d5w7dw4AKt1OhogMC6diiYiIiCSCU7FEREREEsFgR0RERCQRDHZEREREEsFgR0RERCQRDHZEREREEsFgR0RERCQRDHZEREREEsFgR0RERCQRDHZEREREEvF/1JWCwB1IyoEAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "coh, coh_err = avg_cs.coherence()\n", "\n", "ax.errorbar(\n", " avg_cs.freq,\n", " coh,\n", " coh_err,\n", " c='black',\n", ")\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Coherence')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7e976dba", "metadata": {}, "source": [ "We have a coherence plot!\n", "\n", "Let's see how the phase lags look now:" ] }, { "cell_type": "code", "execution_count": 22, "id": "30d928ab", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plags, plags_err = avg_cs.phase_lag()\n", "\n", "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "ax.errorbar(\n", " avg_cs.freq,\n", " plags,\n", " plags_err,\n", " fmt='kx',\n", ")\n", "\n", "ax.axvline(\n", " 0.135,\n", " c='red',\n", " label='Lag frequency'\n", " )\n", "ax.axhline(\n", " np.pi / 2,\n", " c='blue',\n", " label='Expected lag'\n", " )\n", "ax.axhline(\n", " 0,\n", " c='black',\n", " ls='--'\n", " )\n", "ax.legend()\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Phase lag')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "939fbfce", "metadata": {}, "source": [ "We have errors on our phase lags, and now we can tell that the lag not only reproduces the correct value, but is also highly significant! Let's quantify its significance:" ] }, { "cell_type": "code", "execution_count": 23, "id": "110d0b7e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(tight_layout=True)\n", "\n", "ax.step(\n", " avg_cs.freq,\n", " plags / plags_err,\n", " where='mid',\n", " c='black',\n", ")\n", "\n", "ax.fill_between(\n", " ax.set_xlim(),\n", " -5, 5,\n", " color='grey',\n", " alpha=.5,\n", " edgecolor='none',\n", ")\n", "\n", "ax.axvline(\n", " 0.135,\n", " c='red',\n", " label='Lag frequency'\n", " )\n", "\n", "ax.legend()\n", "\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('Phase lag significance')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e2943f80", "metadata": {}, "source": [ "Now we can see that the phase lag is significant to $\\gg 5 \\sigma$, as we would hope!\n", "\n", "That concludes the timing methods tutorial for `opticam`! The timing methods of `Analyzer` demonstrated here are intended as \"quick-look\" analyses, while more complete analyses are made easy thanks to `stingray`. Note that special care (and hacky workarounds) may be needed to get the most out of `stingray`." ] } ], "metadata": { "kernelspec": { "display_name": "opticam", "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": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 5 }