{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this blog post, I'm going to write a short tutorial on cepstrum processing for pitch extraction. For context, I'm currently working on a [side-project that involves spectrograms](https://github.com/flothesof/pyqtgraph-spectrographer), so I'm naturally wanting to try pitch extraction (to tune my guitar, for example). In that context, I've encountered the cepstrum representation. Since I'm always willing to learn something new, the goal of this blog post is to figure things out while I go along, with the goal of extracting a pitch from a musical (voice, instrument) sound." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# What is a cepstrum?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the name suggests, a cepstrum is related to a spectrum. But how exactly? To find out, we're going to tackle this hands-on. Let's start by generating a sinusoidal signal." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'time signal')" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('bmh')\n", "\n", "import numpy as np\n", "\n", "def make_sine_wave(f0, sampling_frequency, frame_size, phase=0):\n", " \"\"\"Generates a sine wave of frequency f0.\n", " \n", " :param f0: float, fundamental frequency\n", " :param sampling_frequency: int, number of samples per second\n", " :param frame_size: int, number of samples in frame\n", " :return:\n", " - waveform - ndarray of waveform\n", " \"\"\"\n", " t = np.arange(frame_size) / sampling_frequency\n", " return np.sin(2 * np.pi * f0 * t + phase)\n", "\n", "\n", "def make_harmonic_wave(f0, sampling_frequency, frame_size, n_harmonics=10):\n", " \"\"\"Generates a 1/f weighted harmonic (multiples of f0) wave of frequency f0.\n", " \n", " :param f0: float, fundamental frequency\n", " :param sampling_frequency: int, number of samples per second\n", " :param frame_size: int, number of samples in frame\n", " :param n_harmonics: int, number of harmonics to add\n", " :return:\n", " - waveform - ndarray of waveform\n", " \"\"\"\n", " waveform = np.zeros((frame_size,), dtype=float)\n", " for f in [f0 * i for i in range(1, n_harmonics + 1)]:\n", " waveform += f0 / f * make_sine_wave(f, sampling_frequency, frame_size, phase=f)\n", " return waveform\n", "\n", "sample_freq = 22050 # Hz\n", "frame_size = 2048\n", "time_vector = np.arange(frame_size) / sample_freq\n", "signal = make_harmonic_wave(440, sample_freq, frame_size, n_harmonics=20)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(time_vector, signal)\n", "ax.set_xlabel('time (s)')\n", "ax.set_title('time signal')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we go to Fourier space, we expect that same signal to be full of peaks." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Fourier spectrum')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "windowed_signal = np.hamming(frame_size) * signal\n", "dt = 1/sample_freq\n", "freq_vector = np.fft.rfftfreq(frame_size, d=dt)\n", "X = np.fft.rfft(windowed_signal)\n", "log_X = np.log(np.abs(X))\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(freq_vector, log_X)\n", "ax.set_xlabel('frequency (Hz)')\n", "ax.set_title('Fourier spectrum')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, we find 20 harmonics in the spectrum. Now the idea of the [cepstrum](https://en.wikipedia.org/wiki/Cepstrum) is that the above spectrum, in log scale, can be treated as a periodic signal itself. And in fact its periodicity, in this case, is linked to the spacing between the different peaks. \n", "\n", "Let's then compute and visualize the cepstrum of this spectrum." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'cepstrum')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cepstrum = np.fft.rfft(log_X)\n", "df = freq_vector[1] - freq_vector[0]\n", "quefrency_vector = np.fft.rfftfreq(log_X.size, df)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(quefrency_vector, np.abs(cepstrum))\n", "ax.set_xlabel('quefrency (s)')\n", "ax.set_title('cepstrum')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the interesting point is that we expect a peak at a frequency of 440 Hz, hence a quefrency of 1/440 s which is approximately 0.0022 seconds." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.vlines(1/440, 0, np.max(np.abs(cepstrum)), alpha=.2, lw=3, label='expected peak')\n", "ax.plot(quefrency_vector, np.abs(cepstrum))\n", "ax.set_xlabel('quefrency (s)')\n", "ax.set_title('cepstrum')\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Extracting a pitch " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, one thing that makes a robust identificiation difficult is that there are also several other peaks, as well as a strong component at zero quefrency. This is mentioned in the 1964 paper by Noll, “Short‐Time Spectrum and ‘Cepstrum’ Techniques for Vocal‐Pitch Detection.”, who attenuates the low quefrency components, which are expected to be high since the log magnitude of the spectrum has a nonzero mean.\n", "\n", "Hence, it is important to take into account low and high f0 frequency values to be detected. In the case of a guitar pitch tracker, pitches would be expected to range between 82 Hz and 640 Hz. This translates to quefrencies between 1/640 and 1/82 seconds." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.collections as collections\n", "\n", "fig, ax = plt.subplots()\n", "ax.vlines(1/440, 0, np.max(np.abs(cepstrum)), alpha=.2, lw=3, label='expected peak')\n", "ax.plot(quefrency_vector, np.abs(cepstrum))\n", "valid = (quefrency_vector > 1/640) & (quefrency_vector <= 1/82)\n", "collection = collections.BrokenBarHCollection.span_where(\n", " quefrency_vector, ymin=0, ymax=np.abs(cepstrum).max(), where=valid, facecolor='green', alpha=0.5, label='valid pitches')\n", "ax.add_collection(collection)\n", "ax.set_xlabel('quefrency (s)')\n", "ax.set_title('cepstrum')\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can implement a cepstrum based pitch tracker and see how well it works with our simple harmonic wave generator." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def compute_cepstrum(signal, sample_freq):\n", " \"\"\"Computes cepstrum.\"\"\"\n", " frame_size = signal.size\n", " windowed_signal = np.hamming(frame_size) * signal\n", " dt = 1/sample_freq\n", " freq_vector = np.fft.rfftfreq(frame_size, d=dt)\n", " X = np.fft.rfft(windowed_signal)\n", " log_X = np.log(np.abs(X))\n", " cepstrum = np.fft.rfft(log_X)\n", " df = freq_vector[1] - freq_vector[0]\n", " quefrency_vector = np.fft.rfftfreq(log_X.size, df)\n", " return quefrency_vector, cepstrum\n", "\n", "def cepstrum_f0_detection(signal, sample_freq, fmin=82, fmax=640):\n", " \"\"\"Returns f0 based on cepstral processing.\"\"\"\n", " quefrency_vector, cepstrum = compute_cepstrum(signal, sample_freq)\n", " # extract peak in cepstrum in valid region\n", " valid = (quefrency_vector > 1/fmax) & (quefrency_vector <= 1/fmin)\n", " max_quefrency_index = np.argmax(np.abs(cepstrum)[valid])\n", " f0 = 1/quefrency_vector[valid][max_quefrency_index]\n", " return f0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test this on our input signal." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "441.43066406249994" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cepstrum_f0_detection(signal, sample_freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Evaluating the algorithm's performance " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With our function defined, we can do a little parametric study, for instance varying the number of harmonics, and see how the pitches are estimated." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "harmonics = np.arange(1, 30)\n", "f0s = []\n", "for n_harmonics in harmonics:\n", " signal = make_harmonic_wave(440, sample_freq, frame_size, n_harmonics)\n", " f0s.append(cepstrum_f0_detection(signal, sample_freq))\n", "\n", "fig, ax = plt.subplots()\n", "ax.hlines(440, 0, harmonics.max(), label='expected', alpha=.2)\n", "ax.plot(harmonics, f0s, '.')\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, due to the fact that the periodicity in the spectrum needs to be visible, a certain number of harmonics is needed to make the extraction work (here, at least three). Also, we see that the identified f0 is not super precise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another question we can ask is how well this works if we use a fixed number of harmonics and vary the f0 frequency." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'cepstrum based f0 (Hz)')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f0s = np.linspace(83, 639, num=100)\n", "cepstrum_f0s = []\n", "for f0 in f0s:\n", " signal = make_harmonic_wave(f0, sample_freq, frame_size, n_harmonics=10)\n", " cepstrum_f0s.append(cepstrum_f0_detection(signal, sample_freq))\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(f0s, cepstrum_f0s, '.')\n", "ax.plot(f0s, f0s, label='expected', alpha=.2)\n", "ax.legend()\n", "ax.set_xlabel('true f0 (Hz)')\n", "ax.set_ylabel('cepstrum based f0 (Hz)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the cepstrum based f0 seems to work better on low f0s than on high f0s. This is a consequence of the grid based processing from the Fourier transform. To see why, let's compare the cepstra of a low frequency pitch and of a high frequency one." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_cepstrum(signal, sample_freq, expected_f0, ax=None):\n", " quefrency_vector, cepstrum = compute_cepstrum(signal, sample_freq)\n", " if ax is None:\n", " fig, ax = plt.subplots()\n", " ax.vlines(1/expected_f0, 0, np.max(np.abs(cepstrum)), alpha=1, lw=3, label='expected peak')\n", " ax.plot(quefrency_vector, np.abs(cepstrum))\n", " valid = (quefrency_vector > 1/640) & (quefrency_vector <= 1/82)\n", " collection = collections.BrokenBarHCollection.span_where(\n", " quefrency_vector, ymin=0, ymax=np.abs(cepstrum).max(), where=valid, facecolor='green', \n", " alpha=0.4, label='valid pitches')\n", " ax.add_collection(collection)\n", " ax.set_xlabel('quefrency (s)')\n", " ax.legend()\n", "\n", "low_pitch = make_harmonic_wave(83, sample_freq, frame_size)\n", "high_pitch = make_harmonic_wave(500, sample_freq, frame_size)\n", "\n", "fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(8, 6))\n", "ax1.set_title('low pitch')\n", "ax2.set_title('high pitch')\n", "plot_cepstrum(low_pitch, sample_freq, 83, ax=ax1)\n", "plot_cepstrum(high_pitch, sample_freq, 500, ax=ax2)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An intuitive explanation for the more accurate identifiaction of low-pitches comes from the nonlinear transformation between the index on the quefrency axis to the f0 value: taking the inverse means that a bin is a lot larger for high pitches than for low pitches. To improve resolution, we could:\n", "\n", "- change sample frequency\n", "- collect more samples\n", "- do zero padding in the spectrum computation or the cepstrum computation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try adding more samples to the waveform." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "less_samples = make_harmonic_wave(600, sample_freq, frame_size)\n", "more_samples = make_harmonic_wave(600, sample_freq, 2 * frame_size)\n", "\n", "fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(8, 6))\n", "ax1.set_title(f'less samples, pitch {cepstrum_f0_detection(less_samples, sample_freq):.3f}')\n", "ax2.set_title(f'more samples, pitch {cepstrum_f0_detection(more_samples, sample_freq):.3f}')\n", "plot_cepstrum(less_samples, sample_freq, 600, ax=ax1)\n", "plot_cepstrum(more_samples, sample_freq, 600, ax=ax2)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not really convincing. Actually, it seems that taking less samples shows a larger valid pitch region, so that is the right way to improve detection. \n", "\n", "What about changing the sampling frequency?" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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oqxz//u//XnwtDs7EknPn7DZBKEMwGLTbBKEMoo1zEQfHXqrm03dZjk3eMGy2RChHTa7GbhOEMkSj0T0fJNiCaONc8vm83SZUNVXk4FgvVNV0+a+OpDdptwlCGZqbm+02QSiDaONcPB7nDZJs3bqVX//61+M+b/HixTz66KN7PrBCXnrpJa644ooJbbNq7vZDEZxCoWCzJUI5/IYk4zmV3dWaEOxFtHEuhgNHDCp1cP4aqSIHx3w2CrJ6ulPxFJz3a0cwyWazdpsglEG0cS57moL+0EMPsWDBAubOnctXvvIVDMNg27ZtnHrqqfT29lIoFLjooot45pln2Lp1K6eddhr/9E//xJw5c7jqqqsYHBwEYNWqVVx88cWcffbZXHbZZUQiEQA2btzIxz/+cc4880zmzZvHpk2buPnmm1m2bBlz587ljjvuwDAMvv3tbzN//nzmzJnDkiVLirZff/31nH766Xzyk5+ku7t71D589KMf5cYbb+T8889n9uzZrFixAoBkMsl1113H/PnzOeuss3j88ccB08G66KKLmDdvHvPmzWP58uUfaHPlypWcddZZbN68uZKPvUjV3FGGIjhKkr4cS8wfs9sEoQxSa8W5iDYTw6233jpsEsnecv3113P99deX3b927VoeeeQRnnjiCbxeL1/72tf41a9+xRVXXMEXv/hFvvrVr3LKKacwc+ZMzjnnHLZu3cq6dev48Y9/zOmnn851113H3XffzT/8wz/w9a9/nQceeICWlhYefvhhvv/973P77bfzuc99ji9/+ctcfPHFpNNpCoUC3/nOd7j99ttZunQpAEuWLCEcDvP000+TyWS48MILOfvss3nrrbdYt24dL7/8Ml1dXXzkIx/h7/7u70bty+DgIE8++SSvvPIKX/jCF3jllVe47bbbmDt3LrfffjuxWIwFCxZw1llnFW0MBAJs2LCBa6+9lmeeeabY1vLly7nhhht44IEHmD59+l5pUEUOjvmcN2SIyqnUZ+rpC05aaSRhHEitFeci2jiXXC5Xtg7OCy+8wJtvvsn8+Wa1lXQ6TUtLCwCf+cxnePTRR1myZAnPP/988Zxp06Zx+umnA/A3f/M3/PznP2f+/Pm8++67LFy4EDCHxdra2hgYGKCjo4OLL74YKF9O4Nlnn2XNmjU89thjAMTjcTZs2MArr7zCZZddhtvtZurUqcydO7dsPy+77DIAZs+ezcDAALFYjGeffZYnnniC22+/vdi/7du3M3XqVK6//npWr16N2+1mw4YNxXbef/99vvKVr/Cb3/yGqVOn7uHT3TNV5OCYHo4MUDmXrFtC7U5FpiI7F9HGuexumrjWmiuuuIJvf/vbH9g3ODjIzp07AXOoZ6iw3cgKvkPvZ82axZ/+9Kdh+8ZaQVlrza233lp0tIZ46qmnxlwxeDS7tNbcd999HHHEEcP23XrrrbS2tvLiiy9SKBSGOTJtbW1kMhlWr149IQ5O1YzXDEVwJAXHuRjKeQl5gsm+LogmVI5oMzHccMMN9PX1Tdjjhhtu2K2DMHfuXB577LFibks0GmXbtm0A3HzzzVx++eXceOONfPnLXy6es337dl577TUAfvOb33Daaadx+OGH09vbW9yey+V49913CYfDHHDAAfzhD38AzKrKg4OD1NbWkkgkim2ec8453HvvveRyZh2y9evXk0wmmT17Ng8//DCGYRCJRHjxxRfL9uWRRx4B4NVXXyUcDhMOhznnnHO48847i3lIb731FmA6Xm1tbbhcLn75y18OS8Sur69n6dKlfO973+Oll14ai2y7pYocHGsW1T5cd0TYO4J5+SXqVGIxyY9yKqKNc9ndLKpZs2bxjW98g8suu4w5c+awcOFCIpEIL7/8MitXruRLX/oSl19+OT6fjwceeACAI488kqVLlzJnzhyi0SjXXHMNPp+PJUuWcPPNN3PmmWcyd+7corPz3//93/z85z9nzpw5XHDBBXR1dXHMMcfg8Xg488wzueOOO/jMZz7DzJkzmTdvHrNnz+arX/0qhmFw8cUXc9hhh3HGGWfwta99jTPOOKNsXxoaGjj//PP56le/yk9+8hMAvva1r5HL5ZgzZw6zZ8/mlltuAWDRokUsXbqUc889lw0bNhAKhYa1NWXKFB588EH+5V/+hddff32vPv8xrSY+meyr1cTT+QKXLHkTn1vx+8+eWHE7TU1Nxde3vXDbbo4UxovP8O2TYSpZqmHvSSaTH/hHJDgD0aYy4vE44XB4n17DMAzcbveEtLV161auuOIKXnnllQlpb6L46Ec/yne/+11OOumkSbneaLqVW028iiI45rNME3cuEsFxLhIlcC6ijXNxYh2caqJqkozdkmTseNyFifmlI0w8Q+PzgvMQbZzLRI6QHHTQQY6L3gD87ne/s9uEslRNBEdJkrHjkTo4zkVqrTgX0ca5eL1eu02oaqrGwXGVZLNLorEzqc/U222CUIahyqiC8xBtnItE1+ylahwckKniTifjzthtglAGSWJ1LqKNc9ldHRxh31NVn75bpoo7Gq1EF6cyUTNBhIlHtHEuYy2UJ+wbqibJGCQPx+kE8gEGvYN2myGMQjwep7Gx0W4zhFEQbSaGJW8vmdD2rj72agzDwOOZuNvsgQceyLZt2+jo6OCGG27gvvvu+8Ax4522fe+99xIMBrniiiv4xS9+wdlnn73bKsK/+MUvWLVq1YSu27WvqCoHx8zD0RTEw3EkA74Bu00QytDa2mq3CUIZRBvnMpHOTSlTp04d1bmphM9+9rPF1w8++CBHHXXUhCyT4ASqaohqVw6OODhOJJSTXAKn0tcni6A6FdHGueyuDs5NN93E3XffXXx/6623cvvtt5NIJPjYxz7GvHnzOOOMM3j88cc/cO7WrVuZPXs2AKlUikWLFjFnzhyuueYaUqnUqNc74YQTuOmmm1iwYAELFixg48aNxev+9Kc/5dFHH2XVqlV8/vOfZ+7cuaRSKVauXMn555/PmWeeyYIFCxgYMH+ERiIRPvGJT3Dqqafyne98p3iNZ555hvPOO4958+Zx9dVXF5eEuPnmmzn99NOZM2cO3/rWt8b5KVZOVUVw3K6hHBybDRFGRSHj1U7FaRXPhV2INn+dLFy4kG984xssWrQIgN/+9rf8+te/JhAIcP/99xMOh+nt7eW8887jwgsvLJvPc8899xAMBnnppZd45513mDdvXtlr1tXV8ec//5mlS5fyjW98g6VLlxb3XXrppdx1113F4a1sNsuiRYu4++67Ofnkk4nH48WFXVevXs3zzz+Pz+fjwx/+MNdeey3BYJAf/ehHPPLII4RCIX784x9zxx13cO211/KHP/yB5cuXo5Sa1MKUVeXgyHpUzmbAK0NUTkWGQZyLaONcdjdEdfzxx9Pd3U1HRwe9vb00NDQwffp0crkc3//+93nllVdwuVx0dHTQ1dVFW1vbqO0sW7aMz33ucwAcc8wxHHPMMWWvedlllxWfv/nNb+7W9vXr19PW1sbJJ58MMGx5hLlz5xbfz5w5k+3btxOLxVi7di0XXnghANlslg996EPU1dXh9/v54he/yHnnncf555+/2+tOJFXl4Az5vxLBcSbhbJi+oITbnUhnZyczZsyw2wxhFEQb55LL5fD7/WX3X3LJJTz22GN0dXWxcOFCAH71q1/R09PDs88+i9fr5YQTTiCT2X0JjbHO1io9bk/naK3LHlPaJ7fbTT6fR2vNvHnzuOuuuz5w/J///GdeeOEFHn74Ye666y4effTRMdm7t1RXDo7VW4ngOJO0J223CUIZamtr7TZBKINo41z2NIV/4cKFPPzwwzz22GNccsklgDkrrrW1Fa/Xy4svvsi2bdt228ZHPvIRfvWrXwGwZs0a3nnnnbLHPvLII8XnD33oQx/YX1tbW8ybOeKII4hEIqxcuRKAgYEB8vl82bZPPfVUli9fXsztGRwcZP369SQSCeLxOOeeey633HILq1ev3m1/JpKqiuDsGqKy2RBBEATBUVx97NWTfs2jjjqKRCLB1KlTi0tuXH755Vx55ZWcc845HHvssRxxxBG7beOaa67huuuuY86cORx33HHFIaXRyGQyLFiwAK01d9555wf2X3nllfzzP/8zgUCAJ598krvvvpuvf/3rpNNpAoFA0UEajZaWFn72s59x7bXXFiNO3/zmN6mtreVTn/oU6XQarTU/+MEPxvLRTAjKaQlqy5Yt07NmzdonbX966Tt0JrLc98mjmVpXPmy4O5qamoqvb3vhtokyTQCaUk37ZIjKjn9c+xtbtmyRYRCHItpURjweH5ZXsi/IZDK7HaKaTE444QSeeeYZmpub7TZlrxhNt5UrV66YP3/+qSOPraohqqHhRIf5dIJF3Be32wShDOUSHAX7EW2ciyy2aS97dHCUUvcopbqUUm+XbLtJKbVDKbXKelxUsu9GpdR6pdRapdT5JdsvsLatV0rdMPFd2TMyi8rZ1OXq7DZBKEN3d7fdJghlEG2cy+5yViabN998868+ejNexhLBWQJcMMr2/9Ran2g9HgdQSh0NXAEcY51zh1LKrZRyAz8DLgSOBq60jp1UioX+CpN9ZWEsaMTxdCqypo5zEW0EYXT26OBorV8AxpoYcSmwVGud0VpvAtYDH7Ye67XWG7XWWWCpdeykMrTYpiERHEeS9CbtNkEoQ2numeAsRJvKUEqRzWb36TVkIdSJJZvNjsuh35tZVNcppT4DvA78s9Y6CkwDXi05Zru1DWDbiO2njdZoV1cXixYtwuPxYBgGCxcuZPHixUQiEUKhEG63uziNrq+vD601ra2tdHZ2FqdLJhIJ2tra6O7uRilFU1MT3d3d6IJZNnvnzp0cEJpOJBLB6/VSX19PT08P9fX1ZLNZUqkU7e3tRCIRfD4fdXV19Pb2fmBBu6ZUEzlXjpw7R02uhqQ3id/w4yl4iPlj1GfqybqzGMogmA+S8CUI5oO4C+7i/ow7g1aaQD7AgG+AUC6EQjHgHSCcDRenTgfyAeK+OHW5OjSapDdJXbaOtCeN0gq/4S+2abgMUp4UtdlaUp4Ubu3GZ/iK+/OuPBl3hlAuxKB3EK/hxVvwFvfb1SeP4aHgKkx4n7Zs2UIgECAYDBKNRmlubmZgYIBsNlvUORgM4vP5iMVitLS0EIvFyOVyxf17+90Lh8MYhkEymSy2Od7vXiqVIp1OF/dPZp/y+Tw+n2+/6tP+olMqlaK1tXW/6tNk6DQ4OEh/fz+1tbWk02ncbjdut5tsNovP5yOXy6G1JhAIFPe7XK5ibZtsNvuB/Uop8vl8cX8mkyEcDpNOp4tF//L5fPEcpRQ+n49MJoPH40FrjWEYo+73er0UCoUP7Pd6vUWbDcMYtn9f9Kl0/2T3KZFI4PV60VoP++6VY0yzqJRSBwO/11ofa71vA3oADXwPmKq1vkYp9TNgmdb6f63j7gYex4wUna+1/ntr+6eBD2utvzDyWvtyFtU/PPweG/tS3PGxmRzeUlNRGzKLat9Rk6vZJ6uJyyyqvScajcqK1Q5FtHEuos3kUG4WVUURHK1159BrpdSdwO+tt9uBA0sOnQ7stF6X2z5p7Fpsc7KvLIwFpSWXwKnsbtFAwV5EG+ci2thLRdPElVKla6l/HBiaYfUYcIVSyq+UOgQ4AngN+AtwhFLqEKWUDzMR+bHKza6MocU2JQfHmfgNZ9SLED5IMin5UU5FtHEuoo297DGCo5R6EJgHtCiltgPfAeYppU7EHKLaDHweQGv9jlLqIWANkAcWa60Nq53rgCcBN3CP1rp8Pel9xK4Ijjg4TiTmn7xVZoXxMVRlVXAeoo1zEW3sZY8Ojtb6ylE2372b438AfKAWszWV/PFxWTfBKGu5TfFvnEl9pl4W23QokUhEquU6FNHGuYg29lJVlYxlsU1nY7hkvNqpSEVW5yLaOBfRxl6qysHZVQfHZkOEUUl5UnabIJShvr7ebhOEMog2zkW0sZeqcnB2VTIWD8eJ1GZr7TZBKENPT4/dJghlEG2ci2hjL1Xm4Fg5ODbbIYyORHCci/wSdS6ijXMRbeylqhwcJbOoHI1bS1lzp7KvS9oLlSPaOBfRxl6qysEp5uDIYpuOxGf47DZBKEMqJdE1pyLaOKQhs6MAACAASURBVBfRxl6qysEZGqKSCI4zkTo4zkXqeTgX0ca5iDb2UmUOjvksOcbOpD4j49VOJRKJ2G2CUAbRxrmINvZSVQ7O0DLrY1lgVJh88q683SYIZfD5ZPjQqYg2zkW0sZeqcnDcVgRH6uA4k4w7Y7cJQhnq6ursNkEog2jjXEQbe6kqB8flkhwcJxPKhew2QShDb2+v3SYIZRBtnItoYy/V5eDINHFHM+gdtNsEoQyNjY12myCUQbRxLqKNvVSZgyOLbToZryHrtjgVme7qXEQb5yLa2EuVOTjms+TgOBNvQRwcp5JOp+02QSiDaONcRBt7qTIHR3JwnIzUwXEuUs/DuYg2zkW0sZcqc3DMZ1ls05lIHRznIvU8nIto41xEG3upMgdnKIJjsyHCqORcObtNEMoQCATsNkEog2jjXEQbe6kyB8d8liEqZ5Jzi4PjVILBoN0mCGUQbZyLaGMvVebgSATHydTkauw2QShDNBq12wShDKKNcxFt7KXKHBzzWSI4ziTpTdptglCG5uZmu00QyiDaOBfRxl6qzMGRCI6T8Rt+u00QyjAwMGC3CUIZRBvnItrYS3U5OLJUg6PxFDx2myCUIZvN2m2CUAbRxrmINvZSXQ6O9SwRHGcidXCci9TzcC6ijXMRbeyluhwcieA4GqmD41yknodzEW2ci2hjL9Xl4BSTjO21QxidrFvCuU5Fprs6F9HGuYg29lJlDo4VwREPx5EYyrDbBKEMPp/PbhOEMog2zkW0sZcqc3DM54K9ZghlCObl145TicUkP8qpiDbORbSxlz06OEqpe5RSXUqpt0u2NSmlnlJKrbOeG63tSin1E6XUeqXUW0qpk0vOuco6fp1S6qp9053dIxEcZ5PwJew2QShDS0uL3SYIZRBtnItoYy9jieAsAS4Yse0G4Gmt9RHA09Z7gAuBI6zH54D/AtMhAr4DnAZ8GPjOkFM0mUihP2cjERznIr9EnYto41xEG3vZo4OjtX4B6Bux+VLgPuv1fcDHSrbfr01eBRqUUlOB84GntNZ9Wuso8BQfdJr2OVLoz9m4C267TRDKkMvJOmFORbRxLqKNvVRaWa1Na90BoLXuUEpNsbZPA7aVHLfd2lZu+wfo6upi0aJFeDweDMNg4cKFLF68mEgkQigUwu12E4/HaW1tpa+vD601ra2tdHZ2UltbC0AikaCtrY3u7m6UUjQ1NdHd3U0mbV6jPx4nk8kQiUTwer3U19fT09NDfX092WyWVCpFe3s7kUgEn89HXV0dvb29NDYODzo1pZrIuXLk3DlqcjUkvUn8hh9PwUPMH6M+U0/WncVQBsF8kIQvQTAfxF1wF/dn3Bm00gTyAQZ8A4RyIRSKAe8A4WyYtMc0OpAPEPfFqcvVodEkvUnqsnWkPWmUVvgNf7FNw2WQ8qSozdaS8qRwazc+w1fcn3flybgzhHIhBr2DeA0v3oK3uN+uPg16BmlKNU14n7Zs2UIgECAYDBKNRmlubmZgYIBsNlvUORgM4vP5iMVitLS0EIvFyOVyxf17+90Lh8MYhkEymSy2Od7vXiqVIp1OF/dPZp8aGxvZtm3bftWn/UWnQCBAb2/vftWn/UWnQqFAOp3er/rkRJ3KofQYhmuUUgcDv9daH2u979daN5Tsj2qtG5VSfwB+qLV+ydr+NHA9cA7g11p/39r+LWBQa/2jkddatmyZnjVr1h5tqoRH3+nmZ8u289GjWvjCGQdW1EZTU1Px9W0v3DZRpgmYDmNfcGSwcO+5+tirJ7zNamPLli3MmDHDbjOEURBtnItoMzmsXLlyxfz5808dub3SWVSd1tAT1nOXtX07UOo5TAd27mb7pCI5OM4m487YbYJQhlAoZLcJQhlEG+ci2thLpQ7OY8DQTKirgEdLtn/Gmk11OhCzhrKeBM5TSjVaycXnWdsmlV2VjCf7ysJY0EqEcSput+RHORXRxrmINvYylmniDwLLgJlKqe1KqUXArcC5Sql1wLnWe4DHgY3AeuBO4J8AtNZ9wPeAv1iP71rbJpVdScZyI3UigXzAbhOEMsTjcbtNEMog2jgX0cZe9phkrLW+ssyu+aMcq4HFZdq5B7hnXNZNMG5ZqsHRDPjKJ4sJ9tLa2mq3CUIZRBvnItrYS1VVMlaSg+NoQjkZr3YqfX2THnAVxoho41xEG3upKgdH6uA4G4Wy2wShDGOZbSnYg2jjXEQbe6lOB0c8HEcy4JUhKqcioXbnIto4F9HGXqrKwRnKwTHEv3Ek4WzYbhOEMnR2dtptglAG0ca5iDb2UlUOjrIiOBI2dCZDFY4F5zFUsVRwHqKNcxFt7KWqHByXzKISBEEQhKqgyhwcqYPjZKQOjnNJJBJ2myCUQbRxLqKNvVSVg+O2emuIg+NI4j4piuVU2tra7DZBKINo41xEG3upKgfHVczBsdkQYVTqcnV2myCUobu7224ThDKINs5FtLGXqnJwhqqsyBCVM9GILk5lKEFfcB6ijXMRbeylqhwcWWzT2SS9SbtNEMrQ1NRktwlCGUQb5yLa2EtVOTi76uCIh+NE6rIyROVUJNTuXEQb5yLa2EtVOTi7KhnbbIgwKlIHx7mEw1KE0amINs5FtLGXqnJw3NYQlURwnInSMl7tVAzDsNsEoQyijXMRbeylqhwcnzVGlZO1GhyJ3/DbbYJQhmRS8qOcimjjXEQbe6kqB8drFcLJGjJG5URi/pjdJghlaG9vt9sEoQyijXMRbeylqhwcvzg4jqY+U2+3CUIZIpGI3SYIZRBtnItoYy9V5eAMDVFl8jJE5UQMl4xXOxWv12u3CUIZRBvnItrYS3U5OB6zuzmJ4DiSlCdltwlCGerrJbrmVEQb5yLa2Et1OThWBCcrScaOpDZba7cJQhl6enrsNkEog2jjXEQbe6kqB8fjUiggX9AYUs7YcUgEx7nIL1HnIto4F9HGXqrKwVFK4S1GcWSYymm4tdtuE4QyZLNZu00QyiDaOBfRxl6qysEB8Fo9llo4zsNn+Ow2QShDKiXRNaci2jgX0cZeqs7B8XvMKEFGIjiOQ+rgOBep5+FcRBvnItrYS9U5OG5MxyYrU8Udh9TBcS5Sz8O5iDbORbSxl6pzcHxS7M+x5F15u00QyuDzyfChUxFtnItoYy9V5+AEvOYQlTg4ziPjzthtglCGuro6u00QyiDaOBfRxl72ysFRSm1WSq1WSq1SSr1ubWtSSj2llFpnPTda25VS6idKqfVKqbeUUidPRAfGbbM2q+VKLRznEcqF7DZBKENvb6/dJghlEG2ci2hjLxMRwTlba32i1vpU6/0NwNNa6yOAp633ABcCR1iPzwH/NQHXHjc1frN0diYvERynMegdtNsEoQyNjY12myCUQbRxLqKNveyLIapLgfus1/cBHyvZfr82eRVoUEpN3QfX3y0uK8lYpok7D68h67Y4FZnu6lxEG+ci2tiLZy/P18CflFIa+B+t9c+BNq11B4DWukMpNcU6dhqwreTc7da2jtIGu7q6WLRoER6PB8MwWLhwIYsXLyYSiRAKhXC73cTjcVpbW+nr60NrTWtrK52dndTWmqX+E4kEbW1tdHd3o5SiqamJ7u5uwuEw5HMAJNMZtmzZgtfrpb6+np6eHurr68lms6RSKdrb24lEIvh8Purq6ujt7f2AN96UaiLnypFz56jJ1ZD0JvEbfjwFDzF/jPpMPVl3FkMZBPNBEr4EwXwQd8Fd3J9xZ9BKE8gHGPANEMqFUCgGvAOEs2HSnjQAgXyAuC9OXa4OjSbpTVKXrSPtSaO0wm/4i20aLoOUJ0VttpaUJ4Vbu/EZvuL+vCtPxp0hlAsx6B3Ea3jxFrzF/Xb1yWN48Ba8E96nLVu2EAgECAaDRKNRmpubGRgYIJvNFnUOBoP4fD5isRgtLS3EYjFyuVxx/0R89wzDIJlMFtsc73cvlUqRTqeL+yezT/l8nmw2u1/1aX/RKZVK4fF49qs+7S86RaNR6uvr96s+OVGnciitK49kKKUO0FrvtJyYp4AvAI9prRtKjolqrRuVUn8Afqi1fsna/jRwvdZ6RWmby5Yt07NmzarYpj3xw2c28uzGGF+bexDnHdk87vObmpqKr2974baJNK3qcRfc+2RF8auPvXrC26w2MpkMfr/fbjOEURBtnItoMzmsXLlyxfz5808duX2vhqi01jut5y7gEeDDQOfQ0JP13GUdvh04sOT06cDOvbl+JeQzZvRAkoydh9TBcS5Sz8O5iDbORbSxl4odHKVUSClVN/QaOA94G3gMuMo67CrgUev1Y8BnrNlUpwOxoaGsySToM0flcjJN3HHkXDm7TRDKEAgE7DZBKINo41xEG3vZmxycNuARpdRQO7/QWv9RKfUX4CGl1CJgK3C5dfzjwEXAemAQ+OxeXLtigj5rFpU4OI4j5xYHx6kEg0G7TRDKINo4F9HGXip2cLTWG4ETRtneC8wfZbsGFld6vYmikLOGqGSpBsdRk6spJiALziIajZpJ+oLjEG2ci2hjL1VXybi+1iwmJ0NUziPpTdptglCG5ubxJ+QLk4No41xEG3upOgenkM8CkJEkY8fhN2S2gVPZ3VRMwV5EG+ci2thL1Tk4ruJSDRLBcRqewt6WZRL2Fdls1m4ThDKINs5FtLGXqnNwWhrNEj1ZWarBccT8MbtNEMrQ3t5utwlCGUQb5yLa2EvVOTiDA+ZNVOrgOA+pg+NcpJ6HcxFtnItoYy9V5+CEgmaehyy26TyybgnnOhWZ7upcRBvnItrYS9U5OK21ZuGlyECW17bFSOUmfmkAoTIMJVo4FZ/PZ7cJQhlEG+ci2thL1Tk4YczVXbf0p/nXJzdyx7LtNlskDBHMy68dpxKLSX6UUxFtnItoYy9V5+BMa2ulvW6XV/3k+302WiOUkvAl7DZBKENLS4vdJghlEG2ci2hjL1Xn4MRiMWY0DF8fpDCeFdXNpSmEfYBEcJyL/BJ1LqKNcxFt7KXqHJxcLvcBHyUyMLbk1k19KU78ziMcdOkXQFXdR7fPcRfcdpsglCGXk3XCnIpo41xEG3upurt0e3s78w5tHLZtQ29qTOe+05nEU1PHlDM+xpTZl+4L86oaqYPjXKSeh3MRbZyLaGMvVefgRCIRzj6skVsvPIyLjzLHRzdHx+bgxNP54uuaAw7fJ/ZVM1IHx7lIPQ/nIto4F9HGXqrOwQmFQiilOHlamOn1Zk2ceHps05PjmV0OjjtYt0/sq2Yy7ozdJghlCIVCdpsglEG0cS6ijb1UnYPjdu/K86j1ma+T2Xy5w4cRz+xyhDw14uBMNFpJdWmnUvp3IzgL0ca5iDb2UnUOTjweL76u9ZtfvoHM2CI4A+nSCE7txBomEMgH9nyQYAulfzeCsxBtnItoYy9V5+C0trYWX9f6zNWrk9mxOTixEgfHsxdDVDuidTy5+nCSGW/FbeyPDPgG7DZBKEPp343gLEQb5yLa2EvVOTh9fbsK+w0NUQ2M0cEpHaJy11QewXl+7aH0JkOs2jq14jb2R0I5Ga92KqV/N4KzEG2ci2hjL1Xn4OiSon5DQ1TJEsfFKGjSZRbiHChNMvYFMQrjL/pXWlMwZ+zdxz+e+oR/DSikiKJT0fvbl20/QrRxLqKNvVSdgzN8iMp0cBJWBKegNd/443queGD1sCnhYDo+CcsRyifNcdVsfvwJZAPpXctE5I3KE9Be3XAgv115NKmsp+I2AHZG6+hLVl5B2CgoXt98AF3xvY++DHj3bojKKCjSOUnq2xdIqN25iDbORbSxl6pzcDo7O4uvg14XLgXpfIF8QfP0+j7e2JlgMFdgU9/w2jiJrIEG8oNx8oNmQbpsBQ5KX7Km+Dqe9lfUB61hY3cTqZyXNTunVNQGwLpIM8+tPZQX1h5ccRvvdbTyfqSVP6+pvC5QbyLIk28fTk935X0BeGX9Qfx25dHDnMjxcv+KDn72yjb55TWC0r8bwVmINs5FtLGXqnNwamt35c4opXZFcTJ5fv9uT3Ff7+DwEttDER3TwTEjDZVEcEqjJemcl1x+/BIMZnclJ2/rq6dQwb3YKChWbjnAas9HtgI7AKKDu2Y+5SscctvQ1URvIsTjm1vpGajZ8wmjEE/52NbXQEG76OivLAE8mTX43zciPLqmhzWdyYraANgRy3D/ig7e7aq8jVTOtKUnObZlRPY1pX83grMQbZyLaGMvVefgjKR0qvimvnRx+wccHCv/Jp+MY6RMB6fU0RgriRFRm0qiOP0lTsVg1veBNsfCQNqPoV3D3ldCf4nD1pOozDkpvfaO/nBFbWzoah61vfHwfs9g8fVT6ytLDowO5vjsr9bwv29E+OnL2ypqA+COZdu5f0UH3396c8Vt5AuaHbH0ng8UBEHYD6k6ByeRSAx7PzRVfENvalhycY/l4BgFzc9e2caS1zsAyCWi5C0H5+V1B7MzOr5oQSJjDp+E/GbV3lhq/LVfYoPDzxlqczzEU8OdgEqcgnTOTTy9y5bugcrycEo/g0qHl7pKrt0/WFk9nXXduxycFzb2j2+VeYu1JU7Sht4URgXhNa01T75vOlhrupIVtQGw5PWdfPZX7/Lfr27fqyG3nfEMq3f0V3y+sG8Z+T9NcA6ijb1UnYPT1tY27H3IGqJ6p3P4F7EvaTo4K3bEeXRND292mPsTG9+EknvFe5GxJ5FpDUnLGTmwyczjiVaQ4NufGn5OsgIHZ6RDU4mD0zsiYlPJ8FIm7yad2xUJqyQapfVwh61/MFjRDLNS5ySRNehJjn8l4NJ1zTSmczBetvQPj7qURpbGwzProwA8/HY3K3dUlsC9I5bh8w+/x7+/HqcrUflw2aa+FJ0Dzhhu298Y+T9NcA6ijb1UnYPT3d097P3QENWja8z8m8OaTefh+U393L+igxXbh98Y+t9bTiG36wYUTQbY1lc/phtqJu8mZ7jxuAzaw6bDVMkMpiFHYlqj6SRV4uAMOQTNtWaeSCUOTv+gafv0RvPXfW+yZtyOxVA0qsaXLdox3jbSOQ85w4PXbeB1G2TyHlLjHD7UWhdzZsLWd2Jr//iHd0qHOQE2R8ffxsjv3Gvbxl8NNZ7OF6OQAG9XmFP0f1/aSiZfIF+AV7dWttp7ZCDDdb9dy+LfvkdvBU6jsHtG/k8TnINoYy9V5+AoNbzWis89/P0p03YNOf3vGxEeeWf4FzTTvZ2OZ35B7xtPm+/zXl58/2AeXH4Cf3r7cHZE69jQ1cTmnoZh523paeDhFccCUBvI0hgyf+lHrWhDQcOz7x7CC2tn7PYGn0j7SGT8eN35YhRozc4pvLmtfVyOwVDuz7QG8+a5uaeRneNMzh0aCprWOEDAmyOb94x7uGzIWWsLJ/C6CuQMNyu3HDCuGkNDzlk4mGaK5Tiu72oalx2bo2l6kjkagx7mHGJq915Xkpwxek2kcmyxIjjHt5vJha9vH79z8p7laM052Fxd/bVt43cs3hnh0KztHr+Dk8warI7simwu31pZ2fnfrekhV9DEMwY/qTAvKZ7O860nN3DVL9/hqXW9FbUxRKVDfk5l5P80OyhoPeaK8OXoSmRZV2G0coh8QbOpL7XXtuyMZ8hPwPfECdpUM3tXRKUClFIXAD8G3MBdWutbJ/P6TU3Db3zHt9fy9PooXrdiZmsNF81q4aG3uoYdE/S6+NgxrZx0QB3nXA/ZaCebHryF5pPmDzuuJxHi+bWHFt+/sn4Gh0/pYVpjnJfXzyhu93vyBH15gt4cqZyXh147bljC77rOBAe3RMnkPazaOpWd0TAnHNTBwS1RXt1wIADt9Qlq/btC/u/saENrhdtVoNafpcafpT6Ypitei89jsLmngda6QdrCCTZ2NxaHxma09LOxu4lExs9z7x3Kke3dTK0foKM/zPSmGJm8m+mNcVxKEx0MotCEgxlWbZ3Klt5GABpqUjSFUuzs9/K7VUdxzLROptQliA4GmdYYxzBcNNWaN/4d0Tp8HoPWukG6B2p4e4cZwj2ouZ/OWB25gou1kVZiqQBT6hIcOqUPo+DC4yrg8xi4XZq84UIDXneB7dEwL6w9BIBwIMNhU/rYEa3nvUgrGsXU+gFWRxK0hrxsj2U4vDlIQ9CM7uQLGo9LsTma4tt/2gjAhw8MM6PBdNzuXxnhL9vjfHnOQTTVeAn73QzmCtR4XcV/XFprlFIYBc2S13ey0YrgzD20gbciCZ5Y24vXrTj9oHqOn1pLQZtOdSZfIOgdPgsvX9A88V4Pz28yI2KfPKGN17bFWdeT4n/fiHDJUS2EA7v/k9Vak8oV+M1q8zt8zmGNPLMhyuvbB7j39Z186qR2vO7yv2u01sTSebxuFw+91UlBQ3udj86BLKt2DvBeV5JZU/aca1XQGpdS9A3meGLtLodk+bYYfYM5mmrGF2F75J1ulluRrDuX72TuIY34PeP7fWYUNP+zfAdPvNfDVadM5RPH//UPH/Qmc9TWN+z5wDLsiGV44I0OmkM+Fh7bSmNw/BMn3u1K8h/Pb6EjnuFfzprBOYeP78cFQMdAhi/8di3xjMHcQxq48eyDcbv27BzE0nkSGYNp9X7i6Txf/t37bI9lOLDez08vnUmNb88zXbdaUdaDGgMUtObny3fw8NvdHN4c5KZzD2VK7Z5/tKVy5pD2AWE/bpfitW0x7l8RoSXo4h/rs7TV7bmNgtZ0xLNMDftwKUUqZ/Dipn7S+QILDm8aU19GI2sUyOYLhHzuqnO41GTW+1BKuYH3gXOB7cBfgCu11muGjlm2bJmeNWvWPrNhy5YtzJgxY9i2wawx7Mtz3l1vDNv/yeOnsOjD04DhDtJnf/EAb29vo8afpaAVzaEUO6Jh9B4q8h7QEGferE0s3zCdDd3Nuz22HB86ZBvTGuP8duUxFZ0PcERbDx86ZAeFAjy/9hA6YqPPYKoPpknnPGTyHkAT8OaH5c38zYff4t2dU1i9vb3stVyqQKHEiavxZRnMmn/0zbVJzjtmPc+/PZOdyfIJwj53nqbaFJ3xWrRWNNYMEh3clfdzwoEdHDOtixffn8G2vvL/9E+YWks6X2BdzyCnTAvzdmeCVM6M1Hx7/iEEvS5u/OOGYecozHytRNagNeTl2PZadsYzdMQztNb62NyXwrD+lGa21vCD8w/jpqc2lh0a8roVlx7dSn8qRzJXoHMgy8YRtZf+uOhEvv2njcUhqpDPTZ3fTSpXoKA1Yb+H0w4Kk8kXGMwV6IhnWN+bKv7ybAp6+PElM/n0L98Z1u6hTUEagx68bkWN101LyEtryMe2WJr3ugY/kPNzxQltbO/u56WdGVwKDmkKckDYTyZfoLnGS43XRWONF7dSxNJ5VkcSvN89SGutl8Fsgf50npOn1eFzK161okAnHlDLIU1BuhNZZjQGaQh48LgVg1kDQ2s29aVZuWMAo6AJeFzDhtsA6gMeFhzeSEHDYM6gNeSjrc5XzJvye1zEUjlW7hygKejl4KYg73cneWPnrojU+Uc20VTjpds65+CGALV+N1uiaetmAD63iy39aQJuF4c2BxnMGazvGWR1JElzjZfzj2zC41K83ZkknS9weHOQGq+btzsTtIZ8hANuXErhUgqvSxXbjabyoDUNQS/pvKnnup5B+lN5jmuvxetWrOpIUON1cXiz+R1vqvGgNQzmCvQN5nh5cz+bomlCXsX8I5rxuhT5AuyIpznxgDoCHhdvdSTIFTTHtYXweVzkDE1XMkvI6yaZNXh+Y5S+lDlD1K1gziEN1Pk9xNN5ZjQGaA35WLVzgEy+wHFTa6n1uekYyPKXbXHq/G4Gcwbvdu36vrgUnDytzvxe+NzU+T1MD/tZ05Ukls5zcGOA+oCHd7uSPL+xn3DAzWHNNbwTSQxbCqeoT9BLq+VgpHMGO+NZanwuGgIeIoksf1zbS9Ywf6iMjLgc1BDgqCk1HFgfoLHGQzxtUON10Z/Oky9oGoNeOuIZHn67C0PDkS01eN3qA9HPsw5t4MiWGur8HlI5A5dSBLwu+lN5PC6FS8F9KzoYzBXwuhQHNgSG/S031XiYd2gjPreLxqCHdL6Ax6WoD3iIDGQJ+dyk8wVe2xbj3a5BZjQEaK318saOgeL/lPqAh48cVE/Q68LnVrhd5ncq6HURzxiEfC60hu2xDO92JWkNeTmuvZbewRzPbogymCtwcGOAeYc2ksgaxR93Qw/3iNeRgQwamBb241KKjX0pBjJ5XEpxcGOAdL5Q/D8U9LjIFnTRiQr7PWQN83XI56bG62ZKrY8jWyubZTsWVq5cuWL+/Pmnjtw+2Q7OR4CbtNbnW+9vBNBa/3DomH3t4ESjURobG3d7zJLXd/JOZ5I1nUk08ODfHku99cu51MH50fO3kcm7CXgNtAaloH/QT0G7yOTcbOtrYH1XMx63wfHTI7TWJVm1dSonz9hJYyhNQUNXvJbBrJc1O6aQNdy4lCabd2MUTGdgRksUBWzqMa/r9+SY1jjAKQfvwOMq8ODyEwAzD8bjLhD05omlAvQmaiyHxMSlCnjdBTJ5Dwc0xJk1tZv2+l3/7AezHl7dcBCRWPlhqqAva+W27HLgGkODXHjcOgazZrQp5M/RGaslmgwOi0qNhkJzSGuU46dHqPHnSPQ38lZPLVt7G4Y5Qy5VQGu1W8fR4zZYcPQGmkIptIZNPY1s6W2gYxzTzmfPqOfGsw8mkTW48hdvl1zf7LGxhz8Vv8fFF2ZPZ+6hjQSs6MIv3+zk7r/sHLMNQ5w6vY5bLjic1ZEEdy7fQV8qR1di7Pkrs1pr+JezZnBgQ4B/f34Lf15X+Zo4/3bR4Uz357j37QGeWd837rpLDQEPd3x8Jm91JLj1uS0V2zGrtYZPndzOt/+0saLaT2DeKC45uoUHV3VOyBDE/sABYR/ZvP6AEzkejmuv5fiptfzijQiVfqrHt9dy0azmvfqOeFyKf51/MD95aVvRcRsvNV4XX517EPf8ZSc745Unxh89JUQyk2VLgGt3PgAAIABJREFUrPLPtaXGS8DrYnts/JMVSnEpKv6bmQiG/p/tK5zi4HwCuEBr/ffW+08Dp2mtrxs65tFHH9U33ngjHo8HwzBYuHAhixcvJhKJEAqFcLvdxONxWltb6evrQ2tNa2srnZ2dxaJKiUSCtrY2uru7UUrR1NREd3c34XCYaDSK2+2mvb2dSCSC1+ulvr6enp4e6uvryWazpFIp2tvbWbl+BwGflyOmNtLb20tjYyP/8R//QT6fp7a2lk996lMEAgGCwSDRaJTm5mYGBgbIZrPF9ntyHlrrAuh0gpaWFmKxGLlcrrh/qE/R/hitra3E+qMUCgXqGlvo7emiMVyH1po3tvfjCoaZ4U8T8LiKfdqQ9JDMGhzfqIf1yR+q4+l3O5g1tYF3OpOc1KxobG7lrc0dHDOlhnA4XOxTKpUinU7T3t7O9p0dbB10cXR7mPd29DJ9ShOvb+3j4FrFCYcewCtrd7A9pThxai3d/XEObW/BbwyO2qfeaAx3bQPbu6N0JQ3q68PoVJz2hlr+snOQGaECZ8ycXtRJKUU+n6evEOC97kGOrofaxmY8qSgej4fOvJ+1O/s4floD2sjz/OY4Mw9o4jD/ID6fj/pR+hTRtQz0R3knqjmspYaNXXFmtIZxG1l8GGzP+QkVUpx1SD0Bv59YLEZLSwvPvt9J0FXgqIPaSUR7CNeGSOZBZZKkfGGeX9dNJGlwykGNxONxDm+toznoxl9If+C7t2pTB55AiGc2xTm2QVETbqCnL8rmgQKHtdahM0ka62qJpbI0ew0G3CHaXYNMawhSV1dHb28vDQ0NbOpJ0DOQIu+vY1tXlKaQn2TBhc6maa6vI0iWqUFNc8sUUv3d1NTU4PP5iPb3Eww3sWJLL9tiGY6e3kJ/fxSP109WK7b1JYkXvDR589R6FYe2N7FiUzcnTQvTPZjn5CaNz+fDMAySOU3CVcOyjd24vX5i6TwBZeAJ1JBMJgl63fj8fk5tKhCqrSObyxLQOQ6ZPpXtOzt4YkuW1nAN8UQCnz9I0FVgRyyN8gUZSA5S6/eg3B5UPsPZR7byx/d68aoCpx06hbARZ0p9iBxuVm3rY0fWZ+qoCsQJsLMvQVudOUSQTGdoDtdS78qSMTSGN8jAQIL5hzXSGvLwxrYob8c9uI00zQE3wVCItR39FFxeGgMuoskM4doQXbEEB4Z9+Px+3u6I01oboFAw+PAUN/0qxKptfbhdLg5srCGoM+xIu0lnc0wJgDcYoi+WwOV243J7SKbSGG4f2VyOWo8mVBOiI5og6POgXC6avQYHNId5bWs/RkHzkUOaifT205lWeNymTQG/HyOfI+RVzGyv58Rwlk39Od6Mgo88wZoQOptiZ9LA6/VzQCBP3uWjO5nDyOepq63Bb6RJFRTNtTU0udKcfmgLvYk0z2+KUR8Os6M3xtQ6H9Gcm0gsybSGEGFPgfd7U3j9QTxGmvY6P3nlIZdJkXf7OWealxqXQdxTz/9j797j46zqxI9/vplLMs2tuTVtoZZbpVxcheUmlFopUmFVtIjCTwWkoq5FV9FVYFdBBWVdZXVF110pNxUrV6mCIhQQkHKtIJRaKLe2tEnTJE0mySRz+/7+eJ4M05DJrUme08z3/XrNa2ae63nm2858c855znnqlWbC4QhpStjS3kOCMDNKlboyoTkVoau7h0g4wuL9KkkmeugsmUal9rJPVYgZM2Zw21830Z0Nk84q3b1JdqbDhDVFLCzMra+kvbOLXsKgytEzSoiXVLJ+ayszyiPs31jNzJIeysoreWxzJ+3dfXRoKds7uqksDZMtCRHVFGWlZbT39FEeUo7ar4HabJztyRA7UyXsFU0yf84M1m9t47cb4uw3o4rm9jgZCTEtGiLRm0QiUcokQzKdIUGU/cozHL/PdP7wchd1kQz7zaxlVjjBzs4utofreKmpDQ1F6EpmCWXTRMum0bSzm8rSEghHKUn3sV99OQfWRlm3rZPe8DRe2d7B6QdVMbuuhmse30xPNsxeFSUkkinKyyvoiMdJZkuorSijLd5DKFJKZyLJ4Q0hQtOqWP96GzXTorxjr0qqtYe/d0dZ3xwnVqLUT69iZ2cnJaEIKiX09PYSLY3R3dtHKp2hYXoFnV3dJDVEFqE6lOGAmdPZsTPOxp0p9q6tQJIJyspKvRrIdJK66dVsaumgL6PUVk5jR2c3GQnTncyy1zQ477h9h/3NbWpqIhqN5r73Bv4+NTU1Dfqbu23bNicSnNOBJQMSnKNU9fP92wTRRGXcYLFxl8XGXRYbd1lsJkehGpzJvotqCzAn7/3ewOjr73fDzJmF+4mYYFls3GWxcZfFxl0Wm2BNdoLzBDBPRPYVkShwBrBqMgvQ1NQ0maczo2CxcZfFxl0WG3dZbII1qQmOqqaB84G7gfXATaq6bui9xtdvf/vbyTydGQWLjbssNu6y2LjLYhOsSR/oT1XvUtW3qur+qnr5ZJ//tttum+xTmhGy2LjLYuMui427LDbBKrqRjNPpsd06aCaexcZdFht3WWzcZbEJ1qTeRTUSq1evbgHGPhDCMNra2upra2t3TNTxzdhZbNxlsXGXxcZdFptJM3fx4sVvmvnauQTHGGOMMWZ3FV0TlTHGGGOmPktwjDHGGDPlTJkER0TeKyIbRGSjiFw4yPpSEfmNv/4xEdknb91F/vINIrJkMstdDMYaGxGpE5H7RaRLRK6a7HIXg92IzXtE5CkRedZ/PmGyyz7V7UZsjhKRp/3HMyLyocku+1S3O783/vq3+N9rX5msMhclVd3jH0AIeAnYD4gCzwAHD9jmc8DP/NdnAL/xXx/sb18K7OsfJxT0NU2Vx27GphxYAHwWuCroa5lqj92MzWHAbP/1ocDrQV/PVHrsZmymAWH/9Sxge/97ewQbm7z1twI3A18J+nqm8mOq1OAcBWxU1ZdVNQmsBE4dsM2pwPX+61uAxSIi/vKVqtqnqq8AG/3jmfEx5tioareqPgz0Tl5xi8ruxOavqto/zco6oExESiel1MVhd2LTo96gqgBlMOYJvs3gduf3BhH5IPAy3v8bM4GmSoKzF7A57/0Wf9mg2/j/+TuAuhHua8Zud2JjJtZ4xeY04K+q2jdB5SxGuxUbETlaRNYBzwKfzUt4zO4bc2xEpBz4GvDNSShn0ZsqCY4MsmzgXy2FthnJvmbsdic2ZmLtdmxE5BDgP4DPjGO5zG7GRlUfU9VDgCOBi0SkbJzLV8x2JzbfBP5LVbvGvVTmTaZKgjOSWcpz24hIGKgG2ka4rxm73YmNmVi7FRsR2Ru4HThLVV+a8NIWl3H5f6Oq64FuvH5SZnzsTmyOBr4nIq8CXwQuFpHzJ7rAxWqqJDgjmaV8FXC2//rDwH3q9fZaBZzh93rfF5gHPD5J5S4GuxMbM7HGHBsRmQ7cCVykqn+ZtBIXj92Jzb7+jyoiMhc4EHh1copdFMYcG1U9XlX3UdV9gB8C31FVu0N0goSDLsB4UNW0nwXfjdfD/RpVXSci3wKeVNVVwArgFyKyES+TPsPfd52I3AQ8D6SB5aqaCeRCpqDdiQ2A/5dOFRD1O+edpKrPT/Z1TEW7GZvzgQOAr4vI1/1lJ6nq9sm9iqlpN2OzALhQRFJAFvicqtp0AeNkd7/TzOSxqRqMMcYYM+VMlSYqY4wxxpgcS3CMMcYYM+VYgmOMMcaYKccSHGOMMcZMOZbgGGOMMWbKsQTHGDMpROSfRaTZn0XZ2ak4RORgEXlyBNt9QUSumIwyGWNGz24TN8ZMOBGJAJ3AMar6TNDlGYqI3ArcrKorh9muDG9y3sNt/B9j3GM1OMaYydCIN7P1oDMo94+8GzQRmQW8G/jtcNuqai/wB+CsiS6XMWb0LMExxuSIyGEislZE4iLyGxFZKSKX+evOEZGHB2yvInKA/7pURL4vIpv8pqifiUhMRN4KbPB32Ski9+Xtu1xEXgRe9JfNF5F7RKRNRDaIyEfyznWdiPxERO70y/eYiOyft/6QvH2bReRiEZkpIj35TWIi8o8i0uLXKg30HmCtn7z0b/81EXndP+cGEVmct/0DwD+N5bM2xkwsS3CMMQD48+r8FvgFUAvcDJw2ikP8B/BW4B140zjsBXxDVV8ADvG3ma6qJ+Tt80G8CQgPFpFy4B7gRmAGcCbwU3/G8n5n4s3IXIPXPHS5X/ZK4F7gj8Bs//yrVbUJLwn5SN4xPg6sVNXUINfwNt5IxhCRA/GmpThSVSuBJew6r9N64O3DfC7GmABYgmOM6XcMEAF+qKopVb0Fb2LBYYmIAOcBX1LVNlWNA99h+Dl4vutvnwDeB7yqqteqalpV1wK34k1W2O82VX1cVdPAr/CSKfx9m1T1B6raq6pxVX3MX3c9XlKDiITwkqRfFCjPdCCe9z4DlOIlYBFVfXXAzOlxvJmijTGOcaLd2xjjhNnA6wNmcn9thPs2ANOAp7xcBwDBm4xwKJvzXs8FjhaRnXnLwuyajDTlve4BKvzXc4D8xCPfHcDPRGQ/vBqmDlV9vMC27UBl/xtV3SgiXwQuBQ4RkbuBC1R1q79JJdBR4FjGmABZDY4xpt82YC/Jy1CAt+S97sZLYgAQkZl563YACeAQVZ3uP6pVtYKh5SdTm4E/5+0/XVUrVPWfR1D2zcD+g63w+9PcBHwM+ASFa28A/oaXBOXvf6OqLsBLwBSvKa7fQYDTd4UZU6wswTHG9FsDpIEviEhYRJYCR+WtfwavFuMd/i3Sl/avUNUs8HPgv0RkBoCI7CUiS0Zx/t8DbxWRT4hIxH8cKSIHjXDfmSLyRb+zc6WIHJ23/gbgHOADwC+HOM49wOH+9SEiB4rICSJSCvTiJXGZvO3fhXcnlTHGMZbgGGMAUNUksBQvEWgHPgrclrf+BeBbeJ15XwQeHnCIr+F1/H1URDr97Q4cxfnjwEl4/Xa24jVH/QdeH5iR7Pse4P3+fi/i3e7dv/4vQBbvDqlXhzhOM3AfcKq/qBS4Aq+Gqgmv8/PFkBsH5xS8Pj7GGMfYQH/GmIJE5Dpgi6r+e9Bl2V3+7ek3qurVw2x3MF7ScpQO8QUpIp8H5qjqV8e3pMaY8WCdjI0xU56IHAkczhs1MwWp6vPAkSPY7sfjUDRjzASxJipjzJQmItfjNZd90W/KMsYUAWuiMsYYY8yUYzU4xhhjjJlyLMExxhhjzJRjCY4xxhhjphxLcIwxxhgz5ViCY4wxxpgpxxIcY4wxxkw5luAYY4wxZsqxBMcYY4wxU44lOMYYY4yZcizBMcYYY8yUYwmOMWZciMg5IpIOuhyDEZHrROTe3TzGPiKiIrJgvMpljJk4luAYY4rBvwCn978RkatF5IHJOHFeYjTwcdmA7Y4XkQdEZKeItInIDSJSN8jxForIfSLS5T+eEJH9hzj/ogLn/9SAc98qIltEJCEiL4rIpSJSOuBYh4nI3X75OkXkLyLynvH4nIwZb+GgC2BMsRGRqKomgy5HMVHVjqDLAJwKPJ73vqv/hYgcCtwD/DfwaaAG+CHwWxFZqP6syCLyXuBW4D+ALwI9wEH+83AOB7blvc//TI4DXgJ+BGz2t/0Z0Aj8s3/uacCfgPuB44EUXuL4OxGZr6qvjqAMxkweVbWHPYr+ATwArAAuA7YDO4HL8Wo5vwE0Ay3A5QP2qwT+11/XCzwJnJS3fh9AgY8BdwHdwPf9dQfg/VjtBNrxfjzeNkw5FwB/AeL+4xlgSd76y4H1eD94m/F+pKrz1p8DpIF3A88CCeDPwGxgIfBXv4z3Anvl7XcpsBH4f8DL/rXeC+w78NgDyvuP/nV1+Z/RbcDcvPV7+5/BDr8sLwP/OobYXQNc4R+nE7gaiOVtcx1wb9616IDHOf66CrzEYjPQB7wKXDwglh8Bfud/xi8DnximfP37LRhim8uAvw9Ydpi/37v99yX++b47ys9nkX+cvUe535eB1rz37/CP87a8ZZX+slOD/j9sD3sMfFgTlTFv+DAQwUsiLgAuBn6P96N3PPAV4GIROTlvn2uAJcDH8X6Q/gL8XkTmDzj2fwA3Am8DfiIijcDDeMnU8cAxwAbgARFpGKxwIhICVgGP4f2FfTjej3X+X+8JvBqAg/ESjkV4tQL5SoBLgE/h/eU+G/gN8C28v9YX4CUeVw7YbxbwOeCjfpkr8WoYpEB5D8ZLntYARwAnABngHhEp8zf7KVANnIhXE7EM2DLY8YbxYaDOL9fHgA/gfeaD+T5eLNb41zQL+I1/Hb/39/28X56z8BKzfFcAvwD+AbgJuFZE5o2gjDeKyA4ReVJELhCRSN66MrykMV/Cf17oPx8O7AtsEZEHRWS7iDwqIh8awbkBHvb3eUREzi4UtzzVeAljvxfxEv1PikjML/9ngTa8z9IYtwSdYdnDHi488GoBnh6wbB3w7IBlz7BrDYwCpwzYZi1wjf96H3+brw/Y5lLg0QHLBK+Z4IsFyljjH2vRKK7rQ3g1ESX++3P8Y7wjb5t/9Zf9Y96yLwE7BpRXgQPylr3VX3Zi3rHTeeuvA1YOKE8pXkL2wbzP89JxiN2rQChv2af96y7PK8u9eeuvBh4YcJzF/vUcUeA8/bG8IG9ZGK926jNDlK8erzbkaLxakH/Bq2X6xSDn/gxekl0H3O4v+19/m4/679vwktN3AP8OZIH3DHH+A/ESkSP8xyVAEvj2EPsc5Jfx/AHL3wo8558zDWwt9HnZwx5BP6wPjjFveGbA+yb/MXDZDP/1wf7zgwO2eRB454Bljw94fyTwjyLSNWB5DBi0NkBV20XkauBuEbkPr3bkdlXd0L+NiCzF65txAFCFV1sTBWbi/RiB9yP57IBrAvjbgGV1IhJS1Yy/rEVVN+aV5wUR2YH3OQx2h9KRwAGDXGNZ3jX+EPhfv1bsAeBOVR34eY7E43nlBK8mLQrsP+C6hvKPQLuqPjnMdk/3v1DVtIg04/VVGZSq7gB+kL+/iMSBFSJyoaq+rqqrReTzwHeBn+AlDz/EqzHpv66Q/3y1ql6dd6xj8Gqc7ilw/g14tYP9nvRrAy8QkW+paip/e7826k94yelVectjwLXA83gJVgovkfydiBytqpsKfQbGBMGaqIx5Q2rAey2wbLj/N+Jvl697wPsSYDXeX+H5jwPxaksGparn4f0Q3wO8C3hORD4DICJHAzfjJVgfwmvS+Ky/azTvMNkByYD6x04NXOZfy1CGWl+C15Qz8BrfileDgqpeC8zF6ys0C/iDiPxymHOOxHDlLmRg3AYzsIP4SP5NDPSI/zw3dxAvmagD5vjPlwENeLV68EaC+vyAY63LP84ozl/uHz/H7+z8IHAnXm1SvjPxmlg/pqqPqupTeP++uvESHWOcYgmOMWO3zn9eOGD58XnrCnkSOAR4XVU3DngM7POxC1V9TlWvVNWT8TpG9/+4LMBrVvp3VX1MVV/A60szXhryb0cWkbfi/RCvL7D9k3j9VF4a5Brb865nm6peq6pn4fXB+ZiIVI2ybEf6tRL93omXiLxUYPskb9SI9HsKqBWRI0Z57rE4zH/epb+Rerapajdwhr/4Dv/5Sbx+OQcOONaBeE10oz1/grw+NiJyJF6t4E3AP6vqwGSvHC+Zy+aXF6+GaawJpTETxpqojBkjVX1JRG4GfurXoryG10n3ULy7jYZyFd6P+W/98VA24yUjJ+M10zwycAcROQA4D+8Ons14nYOPx+vzA14zRIOILMO7lXcBXqfg8dKD16H2S3g/aD/Ga+oqNIDed/Ca5n4pIj/C66y7D/BB4Eeq+rKIXIV3d9kGvKarpf61xUdZtjq8zts/AvYDvg383E8UBvMKcLqIHILXDBQH7gMewutwfAFe09Zs4KC8JqFRE5Fz8JKAtXgdiY8H/hO4Jb9ZR0T+Fa9pqA+v4/oVwHf6mwVVtUtEfgwsF5FngCeA9/uP9+Qd5wZ/+7P8918CNuEl3eof++vAT9QfrkBEFuJ1sL4Fr5mssb8Psqr2N2HeDXwPr2ntP/Ga0T6D1wy4aqyfjzETxRIcY3bPp/B+rH6J1+flWeB9qvr3oXZS1WYReSdeEnCbv28T3g/stgK7deP1XVmJ17TQiteU8BX/mL8Xkcv9Y1bg/TX+r3h3DI2HbcD/4d3WPQuvn8vHB/lLH78860XkWLymlrvxEpjX8RKJnf5mgtfXZA5eAvUocHL/MUXkUuASVR2uhuAWvCTlYbzmuJuBrw6x/Qq8W+UfwfvsP6mq14nIP+F9fj/DS5pexxsGYHdk/bLsi3e9r+D9m/nRgO3eg3fn3jS8hO8LqvrzAdtcjJcAfR+oxas9W6qq9+Vt85YB+4TxrmkOXpPrRryOzivytjkX7664T/qPfAK5Plcn4zWhPozXAtB//seG+gCMCYIU+G4yxpgcP9H4uKoeMMnnvQGYqaonDbHNA8BGVf1UoW2MMcXHanCMMU4SkRK826ffHXRZjDF7HktwjDFOUtUssFfQ5TDG7JmsicoYY4wxU47dJm6MMcaYKce5JqoHHnhAS0tLJ+z46XSacNi5yzZYbFxmsXGXxcZdFpvJ0dPTs2Px4sVvmsPPuU++tLSU+fMHzlM4fjo7O6mqGu0YYmYyWGzcZbFxl8XGXRabybF27drXBltedE1UiURi+I1MICw27rLYuMti4y6LTbCKLsHp7e0NugimAIuNuyw27rLYuMtiE6yiS3BmzpwZdBFMARYbd1ls3GWxcZfFJljO9cGZKJms0p3MsGXLVg4+YN+gi2MG0dTUxNy5o50U2UwGi427LDZjo6p0dXUxkUOldHd3U15ePmHHLzYiQkVFBf3zpA2naBKcLR29nHfr35ldEea6SR1s3oxUWVlZ0EUwBVhs3GWxGZuuri5KS0uJRqMTdo5YLEYkEpmw4xebZDJJV1cXlZWVI9q+aBKcXMY3wsxvIp1xwRm51+89970BlsQtZekyeluszdpFe2Jszjn0nKCLMClisVjQRdgjqeqEJjcAJSVF1wtkQkWj0VH1ayqaBCfk5zXpdCbYggB/uu5PudeW4LxhWmoaveE960e0WFhs3NXe3m63IjsqnU4TCoWCLkbRKpr0sr8GRyyjdlZ3pDvoIpgCLDbuqqurC7oIpgAb5C9YRfNrX9Jfg5PNBlsQU1BpZuJGsDa7x2Ljrng8HnQRTAGZTPAtBgNt2rSJW265ZdT7LV++nDvuuGMCSuR5+OGHOeOMM4bfcBSKKMHxMhzLb9wVztpfO66y2LgrmUwGXQRTgIuTWY81wdkTFVGC4z1bE5W7Oko7gi6CKcBi4y4ba8Vdw91BddNNN3HiiSeycOFCvvSlL5HJZNi8eTNHHHEEra2tZLNZTjnlFO677z42bdrE0Ucfzec+9zkWLFjA2WefTU9PDwBPP/0073vf+3j3u9/NaaedRlNTEwAvv/wyH/rQhzj++ONZtGgRr7zyCt/85jdZs2YNCxcu5Kc//SmZTIZvfOMbLF68mAULFnDdddcBXnL21a9+lWOOOYaPfvSjtLS0DHoN73//+7noootYsmQJxx57LE899RTg3SJ//vnns3jxYt71rndx1113AV6Cdcopp7Bo0SIWLVrEY4899qZjrl27lne96128+uqrY/nYc4rm176/BiftYJWh8VT3VQddBFOAxcZd/T9mZvdcccUV1NbWjtvjiiuuIJVKFTzfhg0buP322/nDH/7Agw8+SCgU4uabb2bOnDl84Qtf4IILLuCqq67iwAMP5IQTTgDgxRdf5KyzzuLhhx+msrKSFStWkEql+NrXvsZ1113H/fffz8c+9jEuu+wyAD796U+zbNkyHnroIf74xz/S2NjIJZdcwjvf+U4efPBBPve5z/GLX/yCqqoqVq9ezerVq7nhhht47bXX+P3vf8+LL77IX/7yF374wx/y+OOPF7yWnp4e7r77br7//e/z+c9/HoArr7yShQsXsnr1alatWsUll1xCd3c39fX13HbbbTzwwAOsWLGCiy66aJdjPfbYY3z5y1/mV7/6Ffvss89uxbRo6p377w5Xgr9N3AwuGbKqdldZbNxlt4m7a6jbxB988EGeeeYZFi9eDHjTOtTX1wNw1llncccdd3Ddddfx5z//ObfPXnvtxTHHHAPARz7yEf7v//6PxYsXs379epYuXQp4/X4aGxuJx+Ns27aN973vfUDh8ZLuv/9+nn/+eVatWgV4E4S+9NJLPPLII5x22mmEQiFmzZrFwoULC17LaaedBsCxxx5LPB6no6OD+++/nz/84Q9cddVVuevbsmULs2bN4qtf/SrPPvssoVCIl156KXecF154gS996UvceuutzJo1a4hPdmSKJsEJ+RmOey2ipl9GrHbNVRYbd030WC5m7IYacVdVOeOMM/jGN77xpnU9PT1s3boV8Jp6+ge2G3i8/vfz58/nT3/60y7rOjs7R1RGVeWKK67IJVr97rnnnhGPGDxYuVSV66+/nnnz5u2y7oorrqChoYGHHnqIbDa7SyLT2NhIX18fzz777LgkOMM2UYnIHBG5X0TWi8g6EfkXf/mlIvK6iDztP07J2+ciEdkoIhtEZEne8vf6yzaKyIW7XfpR6P/8M1lLcVwVS9tfoq6y2Liro8P6R42HCy+8kLa2tnF7XHjhhUPeRbVw4UJWrVqV69vS3t7O5s2bAfjmN7/J6aefzkUXXcQXv/jF3D5btmzJNRXdeuutHH300RxwwAG0trbmlqdSKdavX09VVRWzZ8/mzjvvBKCvr4+enh4qKiro6urKHfOEE07g2muvzTWnbdy4ke7ubo499lhuu+02MpkMTU1NPPTQQwWv5fbbbwfg0UcfpaqqiqqqKk444QR+/vOf5zpa/+1vfwO8xKuxsZGSkhJ+85vf7PIZVVdXs3LlSr797W/z8MMPjyRsQxpJDU4a+LKqrhWRSuApEbnHX/dfqvr9/I1F5GDgDOAQYDZwr4i81V/9E+A9wBbgCRFZparP7/Y8QEYcAAAgAElEQVRVjECJ1eA4ryvaNfxGJhAWG3f1N2sY9ww1Ds78+fO5+OKLOe2008hms0QiEb73ve+xadMm1q5dyx//+EdCoRC/+93v+NWvfsXxxx/PW9/6VlauXMkFF1zAfvvtx7nnnks0GuW6667jwgsvpLOzk3Q6zWc/+1kOOuggfvazn3HBBRfw3e9+l0gkwrXXXsshhxxCOBzm+OOP58wzz+Szn/0smzdvZtGiRagq9fX1/PKXv+R973sfDz30EMcddxwHHHAAxx13XMFrmT59OkuWLCEej/PjH/8YgK985StcfPHFLFiwAFXlLW95CytXrmTZsmWcffbZ3HHHHRx//PFvmqtrxowZ/PrXv+b000/nxz/+MUccccSYP38Z7W1sInIHcBVwHNA1SIJzEYCqftd/fzdwqb/6UlVdMth2/dasWaPz588f9YUMJ5HKcOr1fyMagt9/8rBxP/5o1NbW5l5f+eCVAZbELdV91Xa3jqP2xNgUy1QNW7duZfbs2UEXY4/T2dk54SNAJ5PJcWtC3LRpE2eccQaPPPLIuBxvvLz//e/nW9/6FocdNjm/q4PFbe3atU8tXrz4TZnQqPrgiMg+wGHAY3gJzvkichbwJF4tTzuwF/Bo3m5b/GUAmwcsP3rgObZv386yZcsIh8NkMhmWLl3K8uXLaWpqory8nFAoRGdnJw0NDbS1taGqNDQ00NzcTEVFBeBNotbY2EhLSwsiQm1tLa83bQe8cXBee+01Zs6cSVNTE5FIhOrqanbs2EF1dTXJZJJEIpFbH41GqayspLW1lZqaGhKJBL29vbn1ZWVlxGIx2tvbqaurIx6Pk0wmc+tjsRjRaJSOjg7q6+vfVJ1cnixHRSlLlxGPxilPlSMI8UicqmRVbnj8snQZndFOKlOVKEp3pJvKZCW94V5EhdJMKR2lHVT3VZMpyZAIJ6hIVpAIJwhpiGgmmlufLknTF+qjPFVOT6SHSCZCJBvJrU+VpEiFUkxLTaM70k1pppRwNpxbnwwlyUiGWDpGV7SLWDpGKBvKre8L9Y3pmsKZMLXZ2il1TVMlTiVaQk1vzR51TT09PaP6jmhpaaGqqopMJkN3d3eg3xGpVCq3frjvvUQiQWlp6ZS6psmIU29vL6WlpUQiEVKpFCUlJZSUlJBOp3O/P6q6y3oRIZPJjHh9/7FSqVRuyoZMJkMkEiGdTgMQCoVyUzqoaq42J5VKISK59el0GlWlr69v0PXhcJhsNrvL/hNxTcAu16SqJJNJstnsqK9puPWDXVP/XFT5//YK5iwjrcERkQrgz8DlqnqbiDQCO/Bafb4NzFLVc0XkJ8AaVf2lv98K4C68/j5LVPVT/vJPAEep6ufzzzNRNTipTJZ/uvYZwiVw17lWg+OiUDZEpsQ6s7poT4xNsdTg9PX1UVpqI02P1mTU4GSzWZtwc5yNpgZnRJ+8iESAW4FfqeptAKrarKoZVc0CPweO8jffAszJ231vYOsQyydFfx+cjI1k7Cwba8VdFht32Tg47hpqHBwz8UZyF5UAK4D1qnpl3vL8e7g+BDznv14FnCEipSKyLzAPeBx4ApgnIvuKSBSvI/Kq8bmM4ZXkxsExruoL9QVdBFOAxcZdAztpGndY7U2wRtIH5zjgE8CzIvK0v+xi4EwReQdezvAq8BkAVV0nIjcBz+PdgbVcVTMAInI+cDcQAq5R1XXjeC1Dyr9PP6uaq9Ex7lCx9NNVFht39fftMO4Z6TgyZmIMm+Co6sMw6PC/dw2xz+XA5YMsv2uo/SZaiUBWvUeJ/btzTlm6jJ5IT9DFMIOw2Lirs7OTmpqaoIthBtHfOdcEo6g++ZAIWVWyqgyes5kgxaOFe8ObYFls3NXQ0BB0EaaE6567blyPd86h54x7cjNnzhw2b97Mtm3buPDCC7n++uvftM1ob9u+9tpricVinHHGGdx44428+93vHnIU4RtvvJGnn36a733ve2O+jslSVAlOf22hDWbspvJUOTtDO4MuhhmExcZdbW1tTJs2LehimEFkMpkJaUKcNWvWoMnNWHzyk5/Mvf71r3/NQQcdNC7TJLigqHpA5UYzHuXghmZyiNWqOcti4y77PtszXXrppaxYsSL3/oorruCqq66iq6uLD37wgyxatIjjjjuOu+56c6+OTZs2ceyxxwKQSCRYtmwZCxYs4NxzzyWRSAx6vre//e1ceumlnHjiiZx44om8/PLLufP++Mc/5o477uDpp5/mM5/5DAsXLiSRSLB27VqWLFnC8ccfz4knnpgbc6apqYkPf/jDHHHEEVxyySW5c9x3332cdNJJLFq0iHPOOSc3JcQ3v/lNjjnmGBYsWMDXv/718fkAR6CoanBKrAbHafGINYO4ymLjLmuictdQTVRLly7l4osvZtmyZQD89re/5ZZbbqGsrIwbbriBqqoqWltbOemkkzj55JMLdli+5ppriMViPPzww6xbt45FixYVPGdlZSX33nsvK1eu5OKLL2blypW5daeeeipXX311rnkrmUyybNkyVqxYweGHH05nZ2du5vpnn32WP//5z0SjUY466ijOO+88YrEYP/jBD7j99tspLy/nRz/6ET/96U8577zzuPPOO3nssccQkUmdO63IEhzvH0jW/uJxUlWyirZYW9DFMIOw2LirubmZuXPnBl0MM4hUKlVwEMZ/+Id/oKWlhW3bttHa2sr06dPZe++9SaVSXHbZZTzyyCOUlJSwbds2tm/fTmNj46DHWbNmDZ/+9KcBOOSQQzjkkEMKlue0007LPf/bv/3bkGXfuHEjjY2NHH744QC7DK63cOHC3PsDDzyQLVu20NHRwYYNGzj55JMBb5qKI488ksrKSkpLS/nCF77ASSedxJIlS958sglSVAmO9cFxW//UAMY9Fht39U9rYNwzXP+bD3zgA6xatYrt27ezdOlSAG6++WZ27NjB/fffTyQS4e1vfzt9fUOPQzXS29HztxtuH1UtuE1+0tY/rYKqsmjRIq6++uo3bX/vvffy4IMPctttt3H11Vdzxx13jKi8u6so++BkLcMxxhgTsKVLl3LbbbexatUqPvCBDwDk5ueKRCI89NBDbN68echjvPOd7+Tmm28G4Pnnn2fdusLDy91+++255yOPPPJN6ysqKnL9ZubNm0dTUxNr164FIB6P5+aaGswRRxzBY489luvb09PTw8aNG+nq6qKzs5P3vOc9fOc73+HZZ58d8nrGU1HV4IT6a3CCLYYpwMZacZfFxl1dXV3U1dUFXYw93kTMXTbcODgHHXQQXV1dzJo1i5kzZwJw+umnc+aZZ3LCCSdw6KGHMm/evCHPce6553L++eezYMEC3va2t+WalAbT19fHiSeeiKry85///E3rzzzzTL785S9TVlbG3XffzYoVK/ja175Gb28vZWVluQRpMPX19fzkJz/hvPPOy9U4/du//RsVFRV8/OMfp7e3F1Xl8svfNETehBnxZJuTZaIm2wQ488bnaO1J8aszD6GhfHymsB8Lm2xzcOFMmHSo8F8IJjh7YmyKZbLN/h8fMzrFNtnm29/+du677749Phke98k2p4rcfFRu5XTGV5mqDLoIpgCLjbtaWlqCLoIpYKgmHTPxiqqJKjejuGU4TlKbCtVZFht32XxHZiSeeeaZoIsw6awGxzijO9IddBFMARYbd+U3eRu32ESowSqqBEdsHBynVSatGcRVFht3WRPV2IgIyWRyQs9hTVTjK5lMjqrGssiaqLznrN1G5SQba8VdFht3TXRH2amq/5bo3t6J+7fd19dXcKA/M3oiMqpxn4oqwQn11+BYfwIniVpfAldZbNyVyWSCLsIeSUSorJzYmskdO3ZYAhqgImui8p6tBsdNpRn7S8dVFht3dXdb/yhXWWyCNWyCIyJzROR+EVkvIutE5F/85bUico+IvOg/1/jLRUT+W0Q2isjfROTwvGOd7W//ooicPXGXNbjcbOJWg+OkjtLJm4TNjI7Fxl39A8QZ91hsgjWSGpw08GVVPQg4BlguIgcDFwKrVXUesNp/D3AyMM9/fBr4H/ASIuAS4GjgKOCS/qRosvT3wclYfuOk6r7qoItgCrDYuKupqSnoIpgCLDbBGjbBUdVtqrrWfx0H1gN7AacC1/ubXQ980H99KnCDeh4FpovILGAJcI+qtqlqO3AP8N5xvZph5Gpw7C4qJ2VKrC+Bqyw27opEIkEXwRRgsQnWqDoZi8g+wGHAY0Cjqm4DLwkSkRn+ZnsB+bODbfGXFVq+i+3bt7Ns2TLC4TCZTIalS5eyfPlympqaKC8vJxQK5SYja2trQ1VpaGigubk517u6q6uLxsZGWlpaEBFqa2tpaWkhm/Fu2Xt9axP7VO1NU1MTkUiE6upqduzYQXV1NclkkkQiwcyZM2lqaiIajVJZWUlrays1NTUkEgl6e3tz68vKyojFYrS3t1NXV0c8HieZTObWx2IxotEoHR0d1NfX09Gxa1V/ebIcFaUsXUY8Gqc8VY4gxCNxqpJVubtXytJldEY7qUxVoijdkW4qk5X0hnsRFUozpXSUdlDdV02mJEMinKAiWUEinCCkIaKZaG59uiRNX6iP8lQ5PZEeIpkIkWwktz5VkiIVSjEtNY3uSDelmVLC2XBufTKUJCMZYukYXdEuYukYoWwot74v1Dema0qGktQmaqfUNU2VOCXCCWp6a/aoa+rp6Rn1d0RVVRWZTIbu7u7c/+EgviNSqVRu/XDfe5FIhNbW1il1TVMlTn19ffT29k6pa3IxTgVzlpHWZohIBfBn4HJVvU1Edqrq9Lz17apaIyJ3At9V1Yf95auBrwInAKWqepm//OtAj6r+IP88EzkX1RdXvcDz27v5r/fN45CZI7/VbLzZXFSDq03U0hZrC7oYZhB7YmyKZS6q1157jblz5wZdDDMIi83k2K25qEQkAtwK/EpVb/MXN/tNT/jP2/3lW4A5ebvvDWwdYvmkKbHZxJ2WCCeCLoIpwGLjrupq6x/lKotNsEZyF5UAK4D1qppf3bAK6L8T6mzgjrzlZ/l3Ux0DdPhNWXcDJ4lIjd+5+CR/2aTJjWSctT44LgqpDWvuKouNuyZ6NF4zdhabYI2kD85xwCeAZ0XkaX/ZxcAVwE0isgzYBJzur7sLOAXYCPQAnwRQ1TYR+TbwhL/dt1R1Uuu8rQbHbdFMNOgimAIsNu5KJKx2zVUWm2ANm+D4fWkKDWO6eJDtFVhe4FjXANeMpoDj6Y2pGqwGx0U21oq7LDbusrFW3GWxCVZRjWT8xkB/xkU21oq7LDbusrFW3GWxCVZRJTi5qRpsHBwnpUts5l1XWWzcFY1a86GrLDbBKqoEp3+yzYx1wnFSX6gv6CKYAiw27proCSPN2FlsglVUCY7NReW28lR50EUwBVhs3NXa2hp0EUwBFptgFVWCY7OJu60n0hN0EUwBFht31dRM6pR+ZhQsNsEqqgSnvwYnazU4TopkbN4WV1ls3GW3IrvLYhOsIktwvGerwXFTJGs/oq6y2Lirt7c36CKYAiw2wSrKBMf64LjJxlpxl8XGXTbWirssNsEqqgRH7C4qp9lYK+6y2LjLxlpxl8UmWEWV4IRsHBynpUpSQRfBFGCxcVdZWVnQRTAFWGyCVVQJjo1k7LZUyH5EXWWxcVcsFgu6CKYAi02wiirBEZuLymnTUtOCLoIpwGLjrvb29qCLYAqw2ASrqBKcN24TNy7qjnQHXQRTgMXGXXV1dUEXwRRgsQlWkSU43rPV4LipNFMadBFMARYbd8Xj8aCLYAqw2ASryBIcvwbH8hsnhbPhoItgCrDYuCuZTAZdBFOAxSZYRZbgeM92F5WbbKwVd1ls3GVjrbjLYhOsYRMcEblGRLaLyHN5yy4VkddF5Gn/cUreuotEZKOIbBCRJXnL3+sv2ygiF47/pQzPanDcZmOtuMti4y4ba8VdFptgjaQG5zrgvYMs/y9VfYf/uAtARA4GzgAO8ff5qYiERCQE/AQ4GTgYONPfdlLlRjK2GhwnJUNWnesqi4277FZkd1lsgjVsw7qqPigi+4zweKcCK1W1D3hFRDYCR/nrNqrqywAistLf9vlRl3g3iNXgOC0jmaCLYAqw2LgrGo0GXQRTgMUmWLvTc/B8ETkLeBL4sqq2A3sBj+Zts8VfBrB5wPKjBzvo9u3bWbZsGeFwmEwmw9KlS1m+fDlNTU2Ul5cTCoXo7OykoaGBtrY2VJWGhgaam5upqKgAoKuri8bGRlpaWhARamtraWlpIdWXBqCtvZ2+vuk0NTURiUSorq5mx44dVFdXk0wmSSQSzJw5k6amJqLRKJWVlbS2tlJTU0MikaC3tze3vqysjFgsRnt7O3V1dcTjcZLJZG59LBYjGo3S0dFBfX09HR279mUoT5ajopSly4hH45SnyhGEeCROVbKK3rA3WVtZuozOaCeVqUoUpTvSTWWykt5wL6JCaaaUjtIOqvuqyZRkSIQTVCQrSIQThDRENBPNrU+XpOkL9VGeKqcn0kMkEyGSjeTWp0pSpEIppqWm0R3ppjRTSjgbzq1PhpJkJEMsHaMr2kUsHSOUDeXW94X6xnRN4UyYWDo2pa5pqsSpREsoy5TtUdfU09Mz6u+IqqoqMpkM3d3duf/DQXxHpFKp3PrhvvcSiQSZTGZKXdNUiVN7eztlZWVT6ppcjFMhMpLmGr8G5/eqeqj/vhHYgTco8LeBWap6roj8BFijqr/0t1sB3IXXFLZEVT/lL/8EcJSqfn7gudasWaPz588ftkxjcc0TW1n5TDPn/OMs/t9hwXX+qq2tzb2+8sErAyuHa6KZqDWFOGpPjM05h54TdBEmRXd3N+Xl5UEXwwzCYjM51q5d+9TixYuPGLh8THdRqWqzqmZUNQv8nDeaobYAc/I23RvYOsTySWV3Ubktlrb2aldZbNw1sFbYuMNiE6wxJTgiMivv7YeA/jusVgFniEipiOwLzAMeB54A5onIviISxeuIvGrsxR4bu4vKbaFsKOgimAIsNu5KpWyeMFdZbII1bB8cEfk1sAioF5EtwCXAIhF5B14T1avAZwBUdZ2I3ITXeTgNLFfVjH+c84G7gRBwjaquG/erGYbV4LjNxlpxl8XGXTbWirssNsEayV1UZw6yeMUQ218OXD7I8rvw+uMEJjebuOU3Tqruq6Yt1hZ0McwgLDbuampqYu7cuUEXwwzCYhOsohrJWKwGx2l9ob6gi2AKsNi4yzqxustiE6yiSnBC1gfHaSoWGFdZbNwVCln/KFdZbIJVVAmO1eC4rSxdFnQRTAEWG3d1dnYGXQRTgMUmWEWV4NhdVG6LRwsP2GSCZbFxV0NDQ9BFMAVYbIJVZAmO92wJjpvKU9Ze7SqLjbva2qzzt6ssNsEqsgSnvwbHMhwXCRJ0EUwBFht32eTB7rLYBKvIEhzv2f7NuSkesWYQV1ls3GXNIO6y2ASrqBKc/tnEM5bhOKkqWRV0EUwBFht3NTc3B10EU4DFJlhFleCErAbHaf2zVxv3WGzc1T+js3GPxSZYRZXgiPXBMcYYY4pCUSU4NheV22ysFXdZbNzV1dUVdBFMARabYBVZgmPj4LisM2qDYrnKYuOuxsbGoItgCrDYBKvIEhzv2Wpw3FSZqgy6CKYAi427Wlpagi6CKcBiE6wiS3BsNnGXKRYYV1ls3NXft9C4x2ITrCJLcLznjH1XO6k70h10EUwBFht31dbWBl0EU4DFJlhFluD01+BYhuOiyqQ1g7jKYuMuawZxl8UmWEWV4IjNReU0G2vFXRYbd1VV2SCMrrLYBGvYBEdErhGR7SLyXN6yWhG5R0Re9J9r/OUiIv8tIhtF5G8icnjePmf7278oImdPzOUMzeaicpuotVe7ymLjrkwmE3QRTAEWm2CNpAbnOuC9A5ZdCKxW1XnAav89wMnAPP/xaeB/wEuIgEuAo4GjgEv6k6LJZLOJu600Uxp0EUwBFht3dXdb/yhXWWyCNWyCo6oPAgPnfD8VuN5/fT3wwbzlN6jnUWC6iMwClgD3qGqbqrYD9/DmpGnCWQ2O2zpKO4IuginAYuOumTNnBl0EU4DFJljhMe7XqKrbAFR1m4jM8JfvBWzO226Lv6zQ8jfZvn07y5YtIxwOk8lkWLp0KcuXL6epqYny8nJCoRCdnZ00NDTQ1taGqtLQ0EBzc3Nu3o+uri4aGxtpaWlBRKitraWlpYWeRASAnkSCvr4+mpqaiEQiVFdXs2PHDqqrq0kmkyQSCWbOnElTUxPRaJTKykpaW1upqakhkUjQ29ubW19WVkYsFqO9vZ26ujri8TjJZDK3PhaLEY1G6ejooL6+no6OXX8oypPlqChl6TLi0TjlqXIEIR6JU5WsyvV9KEuX0RntpDJViaJ0R7qpTFbSG+5FVCjNlNJR2kF1XzWZkgyJcIKKZAWJcIKQhohmorn16ZI0faE+ylPl9ER6iGQiRLKR3PpUSYpUKMW01DS6I92UZkoJZ8O59clQkoxkiKVjdEW7iKVjhLKh3Pq+UN+YrimcCZMtyU6pa5oqcSrREjIlmT3qmnp6ekb9HVFVVUUmk6G7uzv3fziI74hUKpVbP9z3XiKRoKGhYUpd01SJU3t7O/PmzZtS1+RinAqRkdxRJCL7AL9X1UP99ztVdXre+nZVrRGRO4HvqurD/vLVwFeBE4BSVb3MX/51oEdVfzDwXGvWrNH58+cPW6ax+Ovrcb72h428fVYF//lP8ybkHCORf+vglQ9eGVg5XFPdV201BY7aE2NzzqHnBF2ESbF161Zmz54ddDHMICw2k2Pt2rVPLV68+IiBy8d6F1Wz3/SE/7zdX74FmJO33d7A1iGWT6oSm03caYlwIugimAIsNu6qrq4OugimAItNsMaa4KwC+u+EOhu4I2/5Wf7dVMcAHX5T1t3ASSJS43cuPslfNqlsNnG3VSQrgi6CKcBi464dO3YEXQRTgMUmWMP2wRGRXwOLgHoR2YJ3N9QVwE0isgzYBJzub34XcAqwEegBPgmgqm0i8m3gCX+7b6nqwI7LEy5kd1E5zWoJ3GWxcZfVErjLYhOsYRMcVT2zwKrFg2yrwPICx7kGuGZUpRtnkZBXYZXMZIMshikgpKGgi2AKsNi4K5lMBl0EU4DFJlhFNZJxWcS73N60JTguimaiQRfBFGCxcVciYbVrrrLYBKuoEpxYf4KTsgTHRXvaXTrFxGLjLhtrxV0Wm2AVVYJTFvYuN2E1OE6q7rP2aldZbNzV1NQUdBFMARabYBVngpPK2IziDkqXpIMuginAYuOuaNSaD11lsQlWUSU4kVAJ4RIhq5DKWILjmr5QX9BFMAVYbNxVWVkZdBFMARabYBVVggNQ6t8MYs1U7ilPlQddBFOAxcZdra2tQRfBFGCxCVbRJTixiJfhWEdj9/REeoIuginAYuOumpqaoItgCrDYBKvoEpxS/4oT6UywBTFvEslEgi6CKcBi4y67FdldFptgFV2CEynx+t4krAbHOZGs/Yi6ymLjrt7e3qCLYAqw2ASr6BKcqlgpYE1ULrKxVtxlsXGXjbXiLotNsIouwZFMCrAmKhfZWCvusti4y8ZacZfFJlhFl+BMK/Wm37ImKvekSlJBF8EUYLFxV1lZWdBFMAVYbIJVdAlOuZ/g2HxU7kmF7EfUVRYbd8VisaCLYAqw2ASr6BIc0t7srlaD455pqWlBF8EUYLFxV3t7e9BFMAVYbIJVdAnO9ApvwLLelPXBcU13pDvoIpgCLDbuqqurC7oIpgCLTbCKLsEpyVoNjqtKM6VBF8EUYLFxVzweD7oIpgCLTbB2K8ERkVdF5FkReVpEnvSX1YrIPSLyov9c4y8XEflvEdkoIn8TkcPH4wJGK4yX2NhUDe4JZ8NBF8EUYLFxVzKZDLoIpgCLTbDGowbn3ar6DlU9wn9/IbBaVecBq/33ACcD8/zHp4H/GYdzj9qM2umANVG5yMZacZfFxl021oq7LDbBmogmqlOB6/3X1wMfzFt+g3oeBaaLyKwJOP+Qers6vWerwXGOjbXiLouNu2ysFXdZbIK1u/XOCvxJRBT4X1X9P6BRVbcBqOo2EZnhb7sXsDlv3y3+sm35B9y+fTvLli0jHA6TyWRYunQpy5cvp6mpifLyckKhEJ2dnTQ0NNDW1oaq0tDQQHNzMxUVFQB0dXXR2NhIS0sLIkJtbS0tLS1UVVURFS+xifemee2114hEIlRXV7Njxw6qq6tJJpMkEglmzpxJU1MT0WiUyspKWltbqampIZFI0Nvbm1tfVlZGLBajvb2duro64vE4yWQytz4WixGNRuno6KC+vp6Ojl3/Ei5PlqOilKXLiEfjlKfKEYR4JE5VsoresDfUd1m6jM5oJ5WpShSlO9JNZbKS3nAvokJpppSO0g6q+6rJlGRIhBNUJCtIhBOENEQ0E82tT5ek6Qv1UZ4qpyfSQyQTIZKN5NanSlKkQimmpabRHemmNFNKOBvOrU+GkmQkQywdoyvaRSwdI5QN5db3hfrGdE0ZyVCbqJ1S1zRV4pSRDDW9NXvUNfX09IzpOyKTydDd3Z37PxzEd0QqlcqtH+57L5PJ0NraOqWuaarEqaenh97e3il1TS7GqRBR1eHTmEI7i8xW1a1+EnMP8HlglapOz9umXVVrRORO4Luq+rC/fDXwVVV9Kv+Ya9as0fnz54+5TMNZ+0ozF67eyv51Mf7nQxN3nqHU1tbmXl/54JWBlMFFsVSMRMQmp3PRnhibcw49J+giTIqdO3cyffr04Tc0k85iMznWrl371OLFi48YuHy3mqhUdav/vB24HTgKaO5vevKft/ubbwHm5O2+N7B1d84/Ftk+73bXeF96sk9thhFL26BYrrLYuGtgrbBxh8UmWGNOcESkXEQq+18DJwHPAauAs/3Nzgbu8F+vAs7y76Y6Bujob8qaTHNn1gPQ2WudjF3TFe0KugimAIuNu+rr62PuezsAAB2dSURBVIMuginAYhOs3emD0wjcLiL9x7lRVf8oIk8AN4nIMmATcLq//V3AKcBGoAf45G6ce8yS3XFC4nUyTmayRENFNxSQs2LpGMmQ3VbpIouNuzo6OigvLw+6GGYQFptgjTnBUdWXgbcPsrwVWDzIcgWWj/V84yWdTlNZGmZnb5p4X4a6aZbguCKUDQVdBFOAxcZdqZTNE+Yqi02wiu7XfebMmVSWel/W1g/HLTbWirssNu6ysVbcZbEJVtElOE1NTVSVeRVX1g/HLTbWirssNu6ysVbcZbEJVtElOOXl5bkanE6rwXFKX6gv6CKYAiw27rI+Hu6y2ASr6BKcUChEValXgxPvsxocl6iMfUwmM7EsNu4Khax/lKssNsEqugSns7Mz10QV77UaHJeUpcuCLoIpwGLjrs7OzqCLYAqw2ASr6BKchoaGXBPV1ngfuzOSsxlf8WjhIbdNsCw27mpoaAi6CKYAi02wii7BaWtro9Jvorrr7618+ta/83LrnjUE/VRVnrL2aldZbNzV1tYWdBFMARabYBVdgqOqvG1mObGId+mv7ezljy+0BlwqAyBI0EUwBVhs3GW10O6y2ASr6BKchoYG5tbEuP2sf+AbJ+4LwGvtvQGXygDEI9YM4iqLjbusGcRdFptgFV2C09zcDECJCPvXehMIbto5uQlOSWmMygMOAym6j39IVcmqoItgCrDYuKv/O824x2ITrN2Zi2qPVFFRkXs9oyJKaUho7UnR1ZdmWjREXzpLLDJxt/bF+9LM/+cfMW32/mx/5I7hdygivWGrSXOVxcZd+d9pxi0Wm2AVdRVCqESYM927/fUvr3Vw3i3rOfPG53i9Y+K+zH+xtolps/cHYMaxp9LUEdx/gM5EKX99bRYvt9QEVgYAVWiJTyPeV3T5tjHGmAlSdAlOV1fXLu/f4ic4P3hwE5s7+uhJZbn/5Z0Tcu5MVnngpXYAdq5/FIBXdwSTXCSSYe5+bh7rt83g0Zfm0NwR3F0yT2+axT3r5nHTc/vwyo7pgZUjkxUee3lv/rxhH9q6Y4GVw0U2Do67Bn6nGXdYbIJVdAlOY2PjLu/3r3vzD9mjr03MxILPbIuzszdNb8sWttz5fwBsaasim52Q0w1p3dYZpDL9TXHCE6/uTRAd/lu7Yvx9m9cRTxHWvjqbZDqYf5aPv7w3L22v4/X2au59fn96U8HUKKnCKy013LNufzY21wYSl4E6ozZgmasGfqcZd1hsglV0CU5LS8su7w+a8UbNRWm4hNKQ8MKOHja19/KHDa08uWX8vtjv92tv2p6+j97tr5FoepVkJsz2+OQ2U/WlQ2xsrgOU977tBcoiKToTZYHUWqzfOgNFmD9rOzPL++hLR3hpe92kl2NnTymv7KgFIBLKkM6EWPf6jEkvB8BL22tZ89JbaIlX8Pgrc/h7U30g5QCvVqu5o5zejtrAymCGNvA7zbjDYhOsoktwRHYdz2Ne/bTc6/1rYxy+t3e3yKduXc9/PbSJf7/7JdZv795ln55khnXNXWSyI//TOpnJ8pdXvZqhtmfuB2Dn+jUAbN1ZOfoL2Q2vtNSQ1RJmVcepLU8wt85rkntlkpvLEskwm9urEZT5s1o4bIb3+bzcMvm1Fv21SPMad3DiwRsB2NhcRzI9uXPJ9KbC/HXTLACmT/MGoHx2y0wSycmvTepLh/jTc/NYvf4AbnphFk++spcTtUlmVwO/04w7LDbBmvQER0TeKyIbRGSjiFw42eevrd31L9HS8BsfQahEeOdbqndZn1W4+I8v8bW7NvLHDa2sfb2Tj974HF/63Ytcft+rQyY5Ld1Jvnv/q3zpdy9w/m830JXMsF9tjN7tmwDo3PAEANt2VvJiUx3PvT6DdEZQZZcfkuyA92PRlw6xpa2K7Z3lvNDs1Qgc0OiNsrlvg1ez9NqO6STTJWxpr5rQZqJs1rumF5rrURX2qulgWjRNfe0OyiIpOhJltHZNozMRnZRmokQy7PeF8hKtmvJeGqviZLSEV3ZMH5fPf6Se39pAKhNmVnUnJ7/tBWZP7ySdCfH81smtTcoqPLRhH9p7YoQkCygvNNezMYDaNYDORJRHNs7hgb/vywtNdWSy9sPRb+B3WjFLZbJ09KZH9cfnRLLYBGtS/ywUkRDwE+A9wBbgCRFZparPT1YZWlpamDt37i7LPnXUbK55YiufOmo2MyuiueWfPWYvntjcyVOvx/nrVu+R7+FXd/Lvd79ETSxMTyrLnOpSmuJJKkpDHDSjnKsf38rOARN6fuDgem7yX3e9to5wSYaORIwnXt0b8P5aL5Es2WwJs6Z3Uh3r44WmeqREOWhWCwfMaCWdLaGiNMmOrmns7I5RGeujvrKbpp2VpDIlzKjqZlo0RVdflBJR2rtjPP7K3vSmIrlyVJX1std0r8akZlqCqlgvnYkybnnybQBMiyY5ZK9mSkQpL02RypSwsbmOdLaEfevbmVu/kx3xaUTDGWrLE6QyIbIKZZEMvakQnYkyykuTxKIptndW0JOMUFGaZEt7FS821yMoqt6P1EGzvWrc6nQl+9a3s37bDP70/9s78yC7rrPA/767vLXf611qrZZlSbZlJ3ZC4mVIFUOMYxMCoUwIoUKAP8jUMAmZzKRqwMBMZahhyQBFSAKVAqogBFIOJMZOEYJjHMJMgpMwcuw4SqxYttXauqVeXne//W7f/HHuaz21W+qWelX7/KpOvfvuWe/9zrn3O98595yjBwFwJOE1151lpFyjHXlk/YjxmRL1wGe4VGdbuc7ZSpkwdtjZV6WYDYgTB9cxE5sagY8jSs6POD9XZKpWoJRv05tv89zYELV2llorQ6IOewZmKOUCAA5sn+LcXIkjJ3bz9MmdoHDjjklu2nGemUaeYjbAdRLmmjkKmYBCNmRspkQr8OkrNhnqaZCo4IgiYhSGIHLJejFh7DBZLaLAtlKdyVqByVqRrBfxfKp83rZ3HBG4bc8YZ2fKHBsfohl6hLHL9nKNG0cmqbd9HIFi1pS501mstTLMtbIUMgG9+TYLO5GJgqThVc0wlOsoYewyUS3guwnn5no4X+0h54fc/6rv0ZzazmOjQxw5sZNCJiCMXXJ+xLZyDQESNWl0owph7OA6+jK/pego2J6bcGxsmG+dGiFWc+7sTJmXJvt5w8FRfDcmThxyfvSy61wLVJXxasBEPaAn43Fdfw7XMRm3I1PnMq6sSs89USVKlIz78s6GqjJRD2mFCeNj49x2aN9FnbVOmNUoR5woQZyQ8xxEhDBOqAcxWc/hxakmTxyv8PRYlTBWDg0X+OEbB3ntrhKOCIlqWtdWXzhT9ZBTsy2aYUIzjHny5CxfG52lHSulrMsP7O/n7a/exkgpu+p5dxPGCSdnWsQKngjPTdT55tkqL0w18TTi7v1DfP++Pg4O5letXrSjhIzrzNe9xagHMS9MNZlrmbZRyrqMlLIMFvzLxrtSVJVEWdU0VwtZz6WkReRu4IOqel/6/0EAVf3tTpgnn3xSb7rppjUrQ6VSob//4qEYVSWIdf4B8ZGvnuJEpclv3X+ArCscOVPl8een5+fQ3DCY59137ORXvvDCkvm9eqSHu67r5bFjU9x7aIC3v3r7RVr9Lzz0SZ45uQMRpScbMNda3tcqgqKXXD5f8d2YML5Yfy3lWrRDjzhx+KFbjjPYc2EPrqNntvHMqR3Lynth/q4k8y+frBfRjlxI/S5fTthWrvFDh819LIQFxsKYz3/r6uXvOglx4uC7Ea6j80rdUuUQlHtvfZ6h9J7EifDYtw8y07i6eUm+GxHFrpFrLphXonw3JkqceeVusXLtHZjhDYdG5///y7F9nKlcbFnsjue7EUni4LkJvhdTa114oPtuhKqQqFDKBUSJUG9ncSShmA1oBj5R4uI5plwsKMu/v+lFdvZVKYQFnhgdnJ+n1MF1YlAhVodCJrhIwZxr5mhHHqAUswGeY+pJ1jPlbYUe7cgoSvlMiO8mNAOPepAhSifAu05MnJjjfUMVtpVqfPvMdhpB5qJy+G5MIROgCJ6T4LsxI8UdxKqompdCkv6a/+mDGfMCb0UJQZQQdyl/wEUvZwHacUIzvPBVQNYVBosZ5loRtSAGwBEo+C5536Hgu+TSbWE6eSsXlI+s65DxhCjR9EVtXtaNMJlXmEpZl+FihlLWnQ83XjVffHZwxKzrpQqNMKYZJiSqDBZ8+vM+GU/IuA4ZV/Bdh0ozZHwuIEHxHQffFXxH8FzBcwTPcfAcqLZjRmdahLFSzLj05z3G5trES7w2BvLm2TPdjPAcoZxzKWe99KUMrgiuI4SxMl5tM9OK8NPyZV3HXHNPhnoQUw9ienMecaJU2zGtKCFWZbIeLpp3wXfm740rsG8gz0zTdDT78x7lnEcYK6pKKevhCNSCmKlGyEQ9BDXvgqznkPddBgs+iZo60ooSfEcYKPjUg5haEHN2tk24DItROeuS910SNUprb87DdQRVJZfWlSBOaAQJM62IRhCT8RxyqStmXObaESemm7Rj0/p7si69OY9ixiWMTRnb0YU6tBiumJELEcERs+htT8allHUpZT1yvkOcqHGa/iYQp+XOeQ6NMGa2FTHXiphrx0SJ4rtCPr1nBd9BBIJYqQcxt+8s8eAP7lvyHl0tTz311JF77rnndQvPr7eC8zbgflX9hfT/u4A7VfW9nTCPPvqoPvjgg3ieRxzHPPDAA7znPe9hfHycYrGI67rMzc0xPDzM9PQ0qsrw8DDnzp2bX1SpVquxfft2JiYmEBEGBgaYmJigXC5TqVRwXZeRkRHGx8fxfZ/e3l4mJyfp7e0lCAKazea8fyaToVQqMTU1xZTmeXasyqv6hVuu38XH/u+LfPFEi/sP9NLnhrSdLL1ezMmZNkcrCdvz8J/vGKYnn2V2dpahoSFmZ2f56Ec/Sk9PD7VajQ984ANUQ6UyW+XA7u08+q2zFH3h5t1DfPgrJ+nN+bzlYJlao8k/nox4sdLEd4R6qPT4wm0jBY6ebzLbTrh+IEfRiTk6FZIo9PjmYZao8qa9WX7mzn2cOjuOOh67hvqYmpqiv7+fZrPJVLXBZ15K2JENefPBPv7hpRZPvDjLgcE8p2dbVIOEt906TNSs8dnjTZqhsrfs0oiEiUaElz602rHiObC7nGGsGtCOYXvBZXfJ5UxdKXnKz90+SH/O5Ttjc9x1cAdBtYKI6fVGUcTvf7POc5Nt3v2qIv19ffzhv55BFfb2ZTlfC9jfn2NP2eXrpxucbybsK7sMFzyenQxoRYorzD+ASxmXOEloRMpA3uWWAY+TdWV0JuC2YZ+bd/Ty4vk57j9Q5taR0kVyOjXT4k+OtrihBHfvLfPJZ2c4XQ3Z22teaPUwYf9AnpemmwQJ3NCfYVsOnqvEVFoxgnmZdci65v4AHOjzUISXZkMyDtw+UuDIWIMdRZffffMB5qYn5uveyfEJvnhGeXG6yY19Ll87F3GuFtKfc0hUmG3HF7WzvO+wp8fhfCNhpv3yh9zCcnkCkZqX5P5ej0oAU42Id97aZ+perYbv+9TaIR95qspUSxnKQaUN5xvmxeGkVqqFZF0hTHRRv8uRcQARgljpywrv+3e72ePVyefztNXlw0+O8exkSMY1veZGtH7Psd6sw3DeoRYJ47ULL1lXjGIUreJXkd11+eXlcMm7SpTAdDu54nt8JWQcIUgzEKDoC+0Y+nPC3XvLvGbQxUkijrey/P13J5lurf2noXlP2NXj0lfMQRSws+TzlsPbkOYss+T5u+9O86+nm6xHzdhecMj5LkGs7CgIr9vbz85MyLnZOqNhka+emGE2WL2SZFyjHF4uRc+BPSWf4Z4M7SCglbiM1wJmF3kmrJSFz5SF3Dzg8b9/5NAVv3M776dWqzXvn8vlyOfzVCoVBgcHqVarjI2NbQoF5yeB+xYoOHeo6i91wqy1BWd0dPRlQ1QroRnGa7ry8WJo2pvomIxV1ZhHUxNhI4iphzGDBR9nDUzDYWx6CT1Zb95U3pszPaHRSotdvVnyvks9iJlpRuwsZ5Zlmu3IptIMGZsLOLzdfOE20wxxRCjnLrZIJarMNiP68h4iQitKmG1GbOvxOVFpESbKgcE8Asw0I0o5Dy/tMU03IgYK3hWbjONE502xnV54PTC9ysGCP39+qhFSynq0o4TnJurcMFhgIO8xlyojvem1NIIYzzW9647Z31vC1Juo6RWVuu5/znNoxwnnqgHXD+QpZkxPcbIeUsy4CHB6ro0A+wfytKOEs3Nt+vM+AwWP2VZEMePiuw5hnDDVCC8y7S/WbqJE+c65OjvLGfrzPmPVNudrAXnfpRUl7Chl2N6TIVYYr7YJY9PLqzQjsq5Df8GjJ+My24qYrIfUg5ihoj9vrSCVWznt6S6k0gwpZ41fpRlSaUS4DjTChFaYIMJ8D1XSX6frVzDnXUfIecZ6YHrUJv2OpUXTPwqpNeJCPez0YktZl3LOw0mHcDrWmEZo6kbHKtTJs6MQBqlVwHOEfMb0fDs94I5FebYZMVEPqQXGypH1HIYLPv1pfRsdHWXH7j2cqwYmndQagJhhnJlWRBAlhOlQUxAp5ZzLznIW3zH1JoqVMEmIEjMsFsXmN+c77Os39Wm6ETLXjhguZihmLv3MS1QZm2sDsKOcJYyVuba5T2HcsQoYi4ADjJSyDBQ8osRY0ttRMl8n8r6x5lSaEZnUspPzHKJE2VnOLjksMteKGJ1pMVT0cUXmryGbDvtV2zEJSinj0Zf32NaTwREz3NiOTDubbAT47gVLSiOImWvHFDMuxYzDSCl7yfvRaTeJKpVGRBAnOCK044S5dK6QeXbF1IOEjCsUMi59qVUmiE1dbkUJ1XZMwXfYP5inlO1YtCLmWsaS5LumHud8Z96Sstj9CeJk3oKVqGnHtSCm2o6opRYy1xFcMda8jsXNcYR2Wl+Lvks5Z6xH5ayH75rOSMd62AzNc853HYq+S0/WfdkQ6mqyWSw4Gz5E1W63yWbXdkzWcnVY2WxerGw2L1Y2mxcrm/XhUgrOen9F9W/AQRG5XkQywDuAz61nAcbHx9czO8sVYGWzebGy2bxY2WxerGw2lnVVcFQ1At4LPAZ8F/gbVT26nmV45JFH1jM7yxVgZbN5sbLZvFjZbF6sbDaWdV8HR1X/QVUPqeoNqvqb653/ww8/vN5ZWpaJlc3mxcpm82Jls3mxstlYXnErGUdRtHQgy4ZgZbN5sbLZvFjZbF6sbDaWdZ1kvByeeOKJCWB0yYBXyfT09NDAwMDkWqVvuXqsbDYvVjabFyubzYuVzbpx3T333DO88OSmU3AsFovFYrFYVsorbojKYrFYLBbL1scqOBaLxWKxWLYcVsGxWCwWi8Wy5bimFRwRuV9EjonIcRH5lUX8syLy6dT/6yKyr8vvwfT8MRG5b7lpWpbHGsnmhIg8KyJPi8j/W58r2XpcrWxEZFBE/llEaiLysQVxvi+VzXER+YisxfbRrwDWSDZfTtN8OnXb1udqthYrkM29InIkbR9HROSNXXFsu1lLVPWadIALvADsBzLAM8DhBWH+E/Dx9PgdwKfT48Np+CxwfZqOu5w0rdsY2aR+J4Chjb6+a9mtUDZF4A3AfwQ+tiDON4C7MfvufQH44Y2+1mvNraFsvgy8bqOv71p2K5TNa4Cd6fGtwJmuOLbdrKG7li04dwDHVfVFVQ2Ah4C3LgjzVuAT6fFngHtSDfmtwEOq2lbVl4DjaXrLSdOyNGshG8vqcNWyUdW6qn4FaHUHFpEdQFlVn1Tz1P5L4MfX9Cq2JqsuG8uqsRLZfFNVz6bnjwK51Npj280acy0rOLuAU13/T6fnFg2jZpuIWWDwMnGXk6ZladZCNmA2dP5iaub9D2tQ7lcCK5HN5dI8vUSalqVZC9l0+PN0eOq/22GQq2K1ZPMTwDdVtY1tN2uOt9EFWAGLNdKFi/pcKsylzi+m8NmFgq6ctZANwPer6tl0DsHjIvKcqv6fFZTzlchKZLOSNC1LsxayAXinqp4RkRLwWeBdGGuBZfmsWDYicgvwIeBNV5CmZQVcyxac08Cerv+7gbOXCiMiHtALTF8m7nLStCzNWsiGjplXVc8Df4cduroaViKby6W5e4k0LUuzFrJBVc+kv1XgU9h2czWsSDYishvzzPpZVX2hK7xtN2vItazg/BtwUESuF5EMZlLX5xaE+Rzwc+nx24AvpWOdnwPekY6DXg8cxEz2Wk6alqVZddmISDHtgSIiRUwv6NvrcC1bjZXIZlFUdQyoishd6fDHzwKPrn7RtzyrLhsR8URkKD32gbdg283VcNWyEZE+4PPAg6r61U5g227WgY2e5bwSB7wZ+B5mdvuvped+A/ix9DgH/C1mouo3gP1dcX8tjXeMrpnri6Vp3cbLBvP1wjOpO2pls2GyOYHpldYwPdDD6fnXYV6cLwAfI90GxrqNlQ3m66ojwLfSdvOHpF8lWrc+sgF+HagDT3e5bamfbTdr6OxeVBaLxWKxWLYc1/IQlcVisVgsFsuiWAXHYrFYLBbLlsMqOBaLxWKxWLYcVsGxWCwWi8Wy5bAKjsVisVgsli2HVXAsFsu6ICK/KCLn0h2vl7O9wIYgIoeXs1u9iLxPRH5nPcpksViuHPuZuMViWXPSRebmgLtU9ZmNLs/lEJHPAn+rqg8tES6HWfPktWpW17ZYLJsIa8GxWCzrwXbMQmhHF/NMl7bfcNIdnn8QeGSpsKraAr6AWYHWYrFsMqyCY7FY5hGR14jIUyJSFZFPi8hDIvK/Ur+fF5GvLAivInIgPc6KyO+JyMl0KOrjIpIXkUOYVakBZkTkS11x3yMizwPPp+duEpHHRWRaRI6JyNu78voLEfkjEfl8Wr6vi8gNXf63dMU9JyK/KiIjItLoHhITke8TkYnUqrSQe4GnUuWlE/6XReRMmucxEbmnK/yXgR+5mnttsVjWFqvgWCwWANI9dh4BPgkMYJad/4krSOJDwCHgduAAsAv4H6r6PeCWNEyfqr6xK86PA3cCh9M9xh7HbAi5Dfhp4I/TXZg7/DTwP4F+zPDQb6ZlLwH/BPwjsDPN/wlVHccoIW/vSuNngIdUNVzkGl7FBWUMEbkReC/welUtAfdhtkTo8F3gtiXui8Vi2QCsgmOxWDrcBfjAh1U1VNXPYDYZXJJ0s8B3A/9FVafV7Fz9W5hNCS/Hb6fhm5iNIE+o6p+raqSqTwGfxWxc2OFhVf2GqkbAX2OUKdK446r6+6raUtWqqn499fsERqlBRFyMkvTJS5SnD6h2/Y+BLEYB81X1hF7YDZo0bO8S12ixWDaATTHubbFYNgU7gTN68ZcHo8uMOwwUgCNG1wFAAHeJeKe6jq8D7hSRma5zHhcrI+Ndxw2gJz3eg9mwcDEeBT4uIvsxFqZZVf3GJcJWgFLnj6oeF5H3Ax8EbhGRx4D/qqpn0yAlYPYSaVkslg3EWnAsFkuHMWCXdGkowN6u4zpGiQFAREa6/CaBJnCLqvalrldVe7g83crUKeBfuuL3qWqPqv7iMsp+CrhhMY90Ps3fAO8E3sWlrTdgdt0+tCD+p1T1DRgFTDFDcR1uxuxwb7FYNhlWwbFYLB2eBCLgfSLiicgDwB1d/s9grBi3p59If7DjoaoJ8KfAH4jINgAR2SUi911B/n8PHBKRd4mIn7rXi8jNy4w7IiLvTyc7l0Tkzi7/vwR+Hvgx4K8uk87jwGvT60NEbhSRN4pIFmhhlLi4K/wPYL6kslgsmwyr4FgsFgBUNQAewCgCFeCngIe7/L8H/AZmMu/zwFcWJPHLmIm/XxORuTTcjVeQfxV4E2bezlnMcNSHMHNglhP3XuBH03jPYz737vh/FUgwX0iduEw654AvAW9NT2WB38FYqMYxk59/FebXwXkzZo6PxWLZZNiF/iwWyyURkb8ATqvqr290WVZK+nn6p1T1z5YIdxijtNyhl3lAisgvAXtU9b+tbkktFstqYCcZWyyWLY+IvB54LRcsM5dEVb8DvH4Z4T66CkWzWCxrhB2islgsWxoR+QRmuOz96VCWxWJ5BWCHqCwWi8VisWw5rAXHYrFYLBbLlsMqOBaLxWKxWLYcVsGxWCwWi8Wy5bAKjsVisVgsli2HVXAsFovFYrFsOf4//+ZMj/K2sBMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "low_sample_freq = make_harmonic_wave(600, sample_freq, frame_size)\n", "high_sample_freq = make_harmonic_wave(600, 2 * sample_freq, frame_size)\n", "\n", "fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(8, 6))\n", "ax1.set_title(f'less samples, pitch {cepstrum_f0_detection(low_sample_freq, sample_freq):.3f}')\n", "ax2.set_title(f'more samples, pitch {cepstrum_f0_detection(high_sample_freq, 2*sample_freq):.3f}')\n", "plot_cepstrum(less_samples, sample_freq, 600, ax=ax1)\n", "plot_cepstrum(high_sample_freq, 2 * sample_freq, 600, ax=ax2)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, sampling at a higher frequency allows a larger valid pitch region and gives better results. We can do the simple study we did before again with this in mind." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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77rtXqzWHnp4eW/dXKXTw1MER9PFcy+hQBsbRPnTw1MER3ONpKmNAJpNxWqEsFvJcaWWsErhlzpal0MFTB0dYnWcmsrzBNobS6HCtGEf70MFTB0dYnWcumSKXSNniYSpjsKJRg4vx7W9/m9///d/nyiuv5H3vex8DAwNceumljI+Pk8/nueaaa/jFL35Bf38/L3zhC/nLv/xLdu3axdve9jbi8TgATz75JNdeey0veclLuP766wmFQogIx48f5zWveQ0vfvGLueqqqzhx4gS33norjzzyCFdeeSVf+MIXyOVyfOxjH2P37t3s2rWLO+64A7D6nH3oQx/isssu4/Wvfz2jo6O2njew7P56TqGDpw6OsHLP9ESY+IlB4icGTYVslehwrRhH+9DBUwdHWLlnPp0hfmKQ2PF+Wypk7h9CuArCew+VlS6fz5PwlF8vbd658BImhw8f5vvf/z4//vGP8fv9fOADH+Chhx7i3e9+N+9///u55JJL2LZtG1dffTX9/f0cPXqU22+/ncsuu4x3vetdfPnLX+ad73wnN998M3feeScdHR1873vf4xOf+AS3334773jHO3jve9/LtddeSzKZJJ/P87d/+7f88z//M3fddRcAd9xxB01NTdx///2kUile+cpX8pKXvIR9+/Zx9OhRHnroIUZGRnjRi17Em9/85rLPuxxWMgLTCXTw1MERVuaZCU+TGLTuSH2NQdtviJ5t6HCtGEf70MFTB0dYmWc+myV2fIB8OoM3WIenZvVdndZ0ZaxccrksHo89tfhf/epX7N27l927dwOQTCbp6Ojgwx/+MHfffTd33HEHv/zlL2fTn3322Vx22WUAvO51r+NLX/oSu3fv5uDBg1x33XUFvxzd3d1MTU0xNDTEtddeC0BtbW1Jh//+7/+mt7eXe+65B4BIJMLTTz/Nww8/zPXXX4/X62XdunVceeWVtpxzMePj4zQ0NNi+X7vRwVMHR1i+ZzYaI953GpSiprudms62Cto9O9DhWjGO9qGDpw6OsHxPlcsRPz5IPpXGW1tDcPN6ZBmNOQuxpitji7VgFZPL5fB6vbYcUynFG97wBj72sY/N2R6Pxzl9+jRgTd46Uxuf3yIw83r79u389Kc/nfPe1NRU2Q6f+tSnZiuEM/zsZz+reAtEa2trRfdvFzp46uAIy/PMxhLETwyCUgTaW6jt6ayg2dqgdzjG3qFpdq6zYsbeoWmaanxEUll2rmtkR3dQi2vFONqHDp46OEL5nr3DMfaeCrMjE0HFExwOp2k4bxORp0Znv4erwfQZw94pI6688kruueee2f5Yk5OTDAwMcOutt/La176Wj3zkI7z3ve+dTT84OMijjz4KwHe/+11e+MIXsmXLFsbHx2e3ZzIZDh48SDAY5KyzzuJHP/oRYK02H4/HaWhoIBqNzu7z6quv5itf+cpsh/9jx44Ri8W4/PLL+d73vkculyMUCvHggw/adt4zuGWY8FLo4KmDI5TvmUumiJ8cROUV/pYm6ta7YxSTm+kdjnHzvUf56hNDfPBHR/jgj45yx+ND3P7QAHc8PsTN9x6ldzimxbViHO1DB08dHKE8z97hGDf/6Ag/+PlTfPanh/nMw6e4I+Th9t8OzfkergZTGcPeytj27dv56Ec/yvXXX8+uXbu47rrr6O/vZ8+ePbznPe/hta99LYFAgDvvvBOArVu3ctddd7Fr1y4mJyf50z/9UwKBAHfccQe33norL37xi7nyyit59NFHyefzfPGLX+RLX/oSu3bt4hWveAUjIyNceOGF+Hw+XvziF/OFL3yBt771rWzbto2rrrqKyy+/nPe///3kcjmuvfZazjvvPK644go+8IEPcMUVV9h23jMkk0nb91kJdPDUwRHK88yn0sSPD6CyOXxNDdRtXFcFM/3ZOzRNJq/IK8jmIZtXzAx1UEAmr9g7NK3FtWIc7UMHTx0coTzPvacj1I2P4U8kyeBhrK2LXGE1nOLv4WoQnUcxPfLII2r79rmPIiORCE1NTcvaTz6fx2PDM9/l0t/fzxve8AYefvjhstJX03Ml+QhWa11NTU0FjOxFB08dHGFpz3wmS+xYH/l0Bl9DPfWr6GOxZ8+eJ3bv3n3pSl3dRKn4NZ+ZlrFMXuEVAJmtkHkAv1e47ZrzOa/F5/prRYfrWQdH0MNTB0coz3Pfkyf43P99ioyCSGc32UBNye9hOY8qF4pha7rPWLlkMhktLhodPEOhEJs2bXJaY0l08NTBERb3zGezxGdGHdXVUn/O2bZ0dn22sKM7yG3XnL9kn7G+vj7XXys6XM86OIIenjo4wtKeyaFRNkmKd+/ayMFAMzvP6wJKfw9Xg6mMgSOtYgAbN24su1UMnPNcDguN8HQbOnjq4AgLe6p8nviJQXLJFJ6aAPXnrkdsGijzbGJHd3BOoC8V9HW4VoyjfejgqYMjLO6ZGhknNTIOIlz4/C1c3PTMqMvVVr7m4/7/7lVAh0oO6OFZV1fntEJZ6OCpgyOU9lRKET95ilw8iSfgJ3juBjw+c+9XKXS4VoyjfejgqYMjLOyZHp8iOWQNxKvbsA5/U2Wn6TDREchms7ZNbVFJdPCcnJxcUV+zaqODpw6OYHkOJrzPNNsnMzSNjxGbjLC1pwn/Od3s6x2fbdIvbtoHZh/B2X2n+WxCh2vFONqHDp46OMJcz5lpZC4KQnZwiCNjcYLre4j0xdmZ9lY0Rq25ypiIkE6nl7XEgU+TO/ZqeabT6RXPR9be3m6zTWXQwVMHR4AxVc8t9x4lnbM6tDZNjlMbj4FHiEz4yB3tmzMKEEAAn2cIEHJK4feEyu4AazgTHa4V42gfOnjq4AjPeM4MlpF4nJ9MjAJCpKGJaDiCECHgrWyM0qMWsgxm5txazrDaeDxOfX19Ba3soVqeIrLimZOnp6e1mHVZB08dHAGeGJgiU6hsNUxNUhuPoUSYausk6w3AvIoYWMPBs3nrr+Kh4aYytjJ0uFaMo33o4KmDIzzjuXdoGhIJGsfHyCmINzQQbWwGqEqMWnOVMRFZ9lpTk5OT9PS4fwJKHTzT6bTTCmWhg6cOjgBbmgS/R/BPTVEfm0YEpto6yNXU4vNA8XQMArPDwb2F96yWMZl9bGlYPjpcK8bRPnTw1MERnvG8qMVPx+QYORTphiDJ1jakePqKCseoNVcZWwlur+DMoIOnDo6gh6cOjgBXbN9Ap3+UgwdiBP3dTLd30NjRcka/MNNnrHLocK0YR/vQwVMHR7A8c8kUG2MTvOfy9RxOCs953hZExPbpKxajapUxEWkB/h14DtbN8Z8Ch4FvAecAJ4HXKaUmxeqwdDtwDRAHblBK7amU21qZD8UN6OAIenjq4AgwePgoG5WPjVvbqVvfQ6C95Yw0iwUxHSphbo5foMe1YhztQwdPHRwBhgYGac+AyuY4f1MHOzevn+0zXc3YVM25Em4H7lNKbQd2AgeBDwP3K6XOB+4vvAZ4JXB+4ecdwL9WUkz3IbhuQgdH0MNTB8dMeBrvhLUMSO1ZXSUrYmsE18Yv0ONaMY72oYOnDo75bBYZmbQmpa4vTEq9wsFrq6UqlTERaQKuBL4MoJRKK6WmgD8EvlpI9lXgjwp//yHwn8riN0CLiFRsMbvljLx0Eh08dXAEPTzd7piNxoj3ncbn81HT3U5NZ5vTShXB7fEL3H+tgHG0Ex083e6ocjnixwfx5hXe2hqC525wdHWQaj2mPBcYBb4iIjuBJ4D3AN1KqSEApdSQiHQV0p8NDBR9frCwbah4pyMjI9x44434fD5yuRzXXXcdN910E6FQiGAwiNfrJRKJ0NnZycTEBEopOjs7GR4enh3lEY1GyWazTE9PIyK0tbUxOjpKU1MTuVyOWCxGT08PoVAIv99Pc3MzY2NjNDc3k06nSSQSs+8HAgEaGxsZHx+ntbWVRCJBMpmcfb+2tpa6ujomJydpb29nenqadDo9+35dXR2BQIBwOExHRwfhcJhMJjP7fjweRylV1jl1d3czOjpa9XM6deoU4XC47HNaTjnZeU7RaJRwOFyRcrLrnE6fPk1dXZ0rrr355zR26jTJvtO0NrcwkoxR5/cQGx+v+LXnEK6OX93d3QwMDBCNRk38MvHLxK8lzmmcBh47PsqWxBhNvgCP9Y/R4Wtl+rd9bA7muXzb+opeewtRlYXCReRS4DfAFUqp34rI7UAE+CulVEtRukmlVKuI/Aj4B6XUrwvb7wc+pJR6oni/5Sy0Ww6xWIxg0P39VnTw1MER9PB0q2MukSJ2vB+VzeFvaUJ1NFfN04mFwt0ev8C910oxxtE+dPB0o2PvcIybf3SE+rER6lJJ8h4vo+3d5Hw+BAgsY8HvlbJQDKtWm9wgMKiU+m3h9XeA5wPDM833hd8jRek3FH1+PXC6UnLhcLhSu7YVHTx1cAQ9PN3omE+liZ8YQGVz+JoaqNu4zpWeNuPq+AXuvFbmYxztQwdPNzruPR2hbnwMfyJJBg9jbV3kCpOpF88l5gRVqYwppULAgIhsK2zaDfQC9wBvK2x7G3B34e97gLeKxWVAeOZxQCXIZDKV2rWt6OCpgyPo4ek2x3wmS+z4APlMFl9DPfWbzkJEXOdpN26PX+C+a6UUxtE+dPB0o+OFkqQhlUA8QrSzC6kJMNNdvxpziS1GNecZ+yvgThEJAMeBt2Od/7dF5EagH3htIe29WMPCj2ENDX97JcV0mg/F7ejgCHp4uskxn80SPz5gjTqqK4w6KnR2dZNnBXFt/AI9ysA42ocOnm5zTA6NsklSvHvXRg4Gmtl5ntXFc8/AFK3BmqrMJbYYVauMKaWeBEr19dhdIq0Cbqq4VAFd5kPRwVMHR9DD0y2OKp8nfmKQXDKFpyZA/bnrkaIF693iWUncHL9AjzIwjvahg6ebHFMj46RGxkGEC5+/hYubnlmmKZgcY9Omsx20s3BuHKeLcFsnw4XQwVMHR9DD0w2OSimrIhZP4gn4CZ67Ac+8Bevd4PlsR4cyMI72oYOnWxzT41Mkh0YBqNuwDn/T3PUy3eJplkMCvEV3+W5GB08dHEEPTycce4djzywBkszQND5GbDLC1p4m/Od0s693/Ixljc5tUHR0VF3VUIS5nu1BB0fQw9MNjpmpCL37TnBkLE5wfQ+Rvjg70945jyLd4AmmMgZAJBKhtbXVaY0l0cFTB0fQw7Pajr3DMW6+9yjpnLU4btPkOLXxGHiEyISP3NG+2QW/ZxDA54H/1dikxbJGaxVzPduDDo6gh6fTjtnpGAeePM7nHxpgKthENBxBiBDwhuZMX+G05wzmMSXQ2dnptEJZ6OCpgyPo4Vltx71D02QKla2G8CS18RhKhMm2TlLewBkVMbCGg+cUjg0HN1iY69kedHAEPTyddMzG4sRPDnJkNEakvoFoYzNQevoKt+SlqYwBExMTTiuUhQ6eOjiCHp7Vdty5rhG/R2iYDlMfnUYEwm0d5Gpq8XnA55HZYeDFw8G9gmPDwQ0W5nq2Bx0cQQ9Ppxxz8STxE4OovGL7lnWkWtsWnb7CLXlpHlNidVLWAR08dXAEPTyr7bijO8jfX9bJwf0xgv5upts7aOxomR3yDTzTn6yoz1iPN24eUTqMuZ7tQQdH0MPTCcdcMkXsxAAql8ff0shFG8/itrPic+LW/Okr3JKXpjKGe5opl0IHTx0cQQ/PajumJyNsTE+zcWs7det7CLS3nJGmVKVrsfXWDNXBXM/2oIMj6OFZbcd8OmO1iGVz+BqD1G20JqXe0R1c9GbRLXlpHlMCw8PDTiuUhQ6eOjiCHp7VdMyEp0kMWJPE157VVbIithA65OVaR4cyMI72oYNnNR0PnIrwX/f+jl8dHuW+/igPJGq4a+8wvcOxJT/rlrw0LWMwuwq929HBUwdH0MOzWo7ZaIx432lQipqudmo625b1eR3ycq2jQxkYR/vQwbNajgdOR7jt6w+hkmkyfj+THd2o4VOFhb9DSy787Za8NC1jBsOzmGwsQfzEIChFoL2F2nXuaLI3GAyGpVD5PPufOAqpNFmfj6n2LlRhmTanF/5eLqYyBkSjUacVykIHTx0cQQ/PSjvmkiniJ61RR/6WJurWr2wtOR3ycq2jQxkYR/vQwbPSjkop4n2n2dbgwZ56T9kAACAASURBVOPzMtXeRd7rXfbC327JS/OYEuju7nZaoSx08NTBEfTwrKRjPpUmfnzA6uza1EDdxnUr3pcOebnW0aEMjKN96OBZSUelFIn+IbKRKOd2NfDBt1zBvonUGSO9y1n42y15aVrGgNHRUacVykIHTx0cQQ/PSjnmM1lixwfIZ7L4Guqp32SNOlopOuTlWkeHMjCO9qGDZyUdk6eGyUxFEI9Qf856LtzYyhsv7uFVF3TM+V3OlDtuyUtTGYNV/SOqJjp46uAIenhWwlHlcsSPD5BPZ/DW1VJ/ztmIZ3VhQIe8XOvoUAbG0T508KyUY3JolPT4FIhQv3k9vmDdqvbnlrw0jymBtrbljR5zCh08dXAEPTztcJyz8HcizY50GJVIcjicoWFLK5GnRpfVpF8pT8Pq0KEMjKN96OBZCcfU6ASHDg1aC3+fs57IsWl2ris9/2G5uCUvTWUMq5ly06ZNTmssiQ6eOjiCHp6rdZyz8LdStI6P8pNMkrzXx2hbF7mx07Npyx0GXglPw+rRoQyMo33o4Gm3Y3p8ioP7+/j8QwOMNbWRDE+sKm5VynOlmMeUQFNTk9MKZaGDpw6OoIfnah1nF/5WiubJcfypJBnxMtbWSc439z5sNcPAdcjLtY4OZWAc7UMHTzsdM1MREoMhjozFmWxqIVlvVbzsmL7CLXlpKmNALpdzWqEsdPDUwRH08Fyt48zC381TE9Qk4ohHmO7sRAKBkgt+lzMMvBKehtWjQxkYR/vQwdMux+x0jHi/tTrIBRdsINvYZEvcmsEteWkeUwKxWIyOjg6nNZZEB08dHEEPz9U67ugO8slLWjh0OEawppFIZxc7z+0CSi/4vdI+Yzrk5VpHhzIwjvahg6cdjtlYnPhJa1Lqms42Ljqri9s62xdd+NsJTzswlTGgp2dlk11WGx08dXAEPTxX65gcHmOTSrJpWwfBzevxNT4TsFYTvOajQ16udXQoA+NoHzp4rtYxF09aC3/nFYG2ZmrPsm4kl1r4e7m4JS/NY0ogFAo5rVAWOnjq4Ah6eK7GMTU6QSo0BkD9xnVzKmJ2o0NernV0KAPjaB86eK7G8UD/JN+973c8eGyC+04lOe5vpHc4xjefDJW1+PdycEtempYxwO/3O61QFjp46uAIeniu1DE9GSF5egSAuvU9+Fsq20FVh7xc6+hQBsbRPnTwXKnjgcEpPn3nw+TTWVI1tYTbA/hCRwEhpxR+z+pGT9rlaTemZQxobm52WqEsdPDUwRH08FyJYyY8TWLA6uxae1YXgfYWu7XOQIe8XOvoUAbG0T508FyJYz6bZf/jR1CZLOlAgKm2DpQI2Txk84q8sn/xb7fkpamMAWNjY04rlIUOnjo4gh6ey3XMRmPE+05bnV272qnprM5khjrk5VpHhzIwjvahg+dyHa3VQQbZ1uyHQIBwexd4PHgAnwd8HsEjqx89uVrPSmEeU+KemvFS6OCpgyPo4bkcx2wsQfyENeoo0N5C7brOCprNRYe8XOvoUAbG0T508FyOo8rniZ0YJJdIcl5PEze/5Vz2jSXmjJgEaxT4akdPrsazkpjKGJBOp51WKAsdPHVwBD08SznOLG9UHJyaJE/s6T6CHiFaW8dFPY1QlM7OwFWup6G66FAGxtE+dPBcyLF3Xmw6EIqyf89RttUBPh8Ha4PsbPPxxovPHOVYiVjmlrw0lTEgkUg4rVAWOnjq4Ah6eM53nFneKJNXeGUIEFQ6TcvYCJ5cjnRtLeG2AL7TR6hUZ9dyPA3VR4cyMI72oYNnKcfiGOb3hHjnZeu5894n8cVi3Ov1MNnRQ9o3hn//eMXj1mKeTmD6jOGeeUaWQgdPHRxBD8/5jjPLG+UVZPOQz2RpHh/Fk8uRCdQw1Vr5zq7leBqqjw5lYBztQwfPUo7FMSyTVzz2xDF8sRg5hLHWTlJeX9Xi1mKeTmAqY7hnnpGl0MFTB0fQw3O+48zyRh4Bv8rRPjGKL5sl6w8Qbu+sSmfXcjwN1UeHMjCO9qGDZynH4hjWHA3zggbweoRIRyfU1lQ1bi3m6QTmMSUQCAScVigLHTx1cAQ9POc77ugOcts157P3VJgd6TAq4eVwOEPDlk1EsqoqnV3L8TRUHx3KwDjahw6epRxnYti+3gG2A5vb69l04Waeiqmqx63FPJ3AVMaAxsbq1MBXiw6eOjiCHp6lHC/oqmdTbILstOBpbuK5V2zEEyg9aWG1gpkOebnW0aEMjKN96OC5kOMWX4az2wDqqNuwjue0NvGcoverFbdmcEtemseUwPj4uNMKZaGDpw6OoIfnfEelFIm+U2SnY4jPS/3m9QtWxKqJDnm51tGhDIyjfejgWcoxMxUhMWg9Fuz3N/DdvrjtyxstF7fkZVktYyKyAdgJtABTwF6l1EAlxapJa2ur0wploYOnDo6gh+d8x8RAiEw4ing9BDdvwFtb45DZXHTISxPDnMc42ocOnvMds9Mx4v3W6iD93no++tux2VGV1Ro5WQq35OWCLWMi4heRd4nIU8Ah4JPAOwu/D4nI/sL77njgugrcMrR1KXTw1MER9PAsdkyeHiEzGUY8Qv3m9Xjrax00m4tb89LEMHdhHO1DB89ix2wsTvykNSl1TWcb+7OBOaMqqzVycilPJ1msZWwv8AvgL4DfKqVyM2+IiBf4PeDNwO+ACyspWWmSyaTTCmWhg6cOjqCH54xjcniM1OgEiFB/znp8wXqHzebi4rw0McxFGEf70MFzxjGXSBE/MYjKK/ytzdSe1cVObwy/J1RoGaveyMnFPJ1mscrYVUqpkVJvFILaI8AjIlLWuisichKYBnJAVil1qYi0Ad8CzgFOAq9TSk2KiAC3A9cAceAGpdSess5oBbhlnpGl0MFTB0fQw7Onp4fU6ASpkLV2Wv3GdfganWnKXwwX56VtMczN8QtcXQazGEf70MGzp6eHfCpN7Hg/KpfH39xA3QbLe3ZkeJVHTi7k6QYWfExZHMRE5EoRaZifRkSuUEqNLuN4L1FKXayUurTw+sPA/Uqp84H7C68BXgmcX/h5B/CvyzjGsnHLPCNLoYOnDo7gTs/e4RjffDLEjw6O8c0nQ/z60YMc3N/HT46M8+tEgO+cdL6zayncmJdQkRjmyvgF7i2DYoyjfbjds3c4xn88eJQf/3wf9/WO8OuRNHdPejk4Ep9Ns6M7yBsv7nG0Igbuyctyp7Z4AKuPxR8opZ4u2v5joGkVx/9D4KrC318tHOfmwvb/VEop4Dci0iIi65RSQ6s41oLU1rqn/81i6OCpgyO4z3NmmZB0TqGA2kSc1skxRIRwYzOxcBghTMDrbGfXUrgtLxfgAeyPYa6IX6BHGRhH+3CzZ+9wjA//8BANwyE82SyZQIDJ9lqkL0TgyWETvxag3KktYsBngYdE5GVF22UZx1LAT0XkCRF5R2Fb90yAKvzuKmw/Gyge6TRY2FYR6urqKrVrW9HBUwdHcJ/nzDIhCvCnkjRNjpFXEAk2Emuw6goK5zu7lsJtebkAq41hro1foEcZGEf7cLPn3sEpgqMjeLJZsn4/U+1d4PGY+LUE5baMKaXUv4nIQeBbIvIZpdQ/LfNYVyilTotIF/AzETm0SNpSAVLN3zAyMsKNN96Iz+cjl8tx3XXXcdNNNxEKhQgGg3i9XiKRCJ2dnUxMTKCUorOzk+HhYRoarCcW0WiUbDZLOBxGRGhra2N0dJSmpiZyuRyxWIyenh5CoRB+v5/m5mbGxsZobm4mnU6TSCRm3w8EAjQ2NjI+Pk5rayuJRIJkMjn7fm1tLXV1dUxOTtLe3s709DTpdHr2/bq6OgKBAOFwmI6ODsLhMJlMZvb9eDxOLpcr65y6u7sZHR2t+jkNDAzQ0NBQ9jktp5zsPKdoNMrk5GRFymkl57TOm8XnEVQiScv4KKIg1dBAqqUVKVTSBPAKnNdoXfvVvPYWO6eTJ09y9tlnV+XaWwWrjWGujV/d3d309fXR2tpq4peJX47Er5lzGhkeZlN4gtpshqTPx1R7F8rjmf1SPNvj12KDBcRqSV8cEYkopZoKf28Avg8cBF6jlDqjH0YZ+7sFiAJ/jtXJdkhE1gEPKKW2icj/Kfz9zUL6wzPpivfzyCOPqO3bty/38GcQjUZnLzA3o4OnDo7gTs8D/ZMcePwQQY8Qra1jy/azqKurZ+/Q9JyljtzUxA/Vzcs9e/Y8sXv37kuXTjkXO2OY2+IXuPN6no9xtA83eiqliJ88RTYS5UQkw15PPR1tzURSWRO/ilgohpXbMnZ85g+l1ICI7AK+ApQ1xl5EgoBHKTVd+PtlwMeBe4C3AZ8q/L678JF7gHeJyF3AC4FwJftbTE9Pu+7CLoUOnjo4gvs88+kMG6PjrD+vFV9TA/XnnE0oFGJdd9B1wWs+bsvLBVhxDHN7/AI9ysA42ocbPZ/a8zSHjg+ztbuRi16wje6pCdat63Baa0nckpdlVcaUUhfPe50E3lj4KYdu4PvWiG98wDeUUveJyGPAt0XkRqAfeG0h/b1Yw8KPYQ0Nf3uZx1kR6XS6kru3DR08dXAEd3nmM1liT/eTz2TxBuuo33QWIuIqx8XQwXOVMczV8Qv0KAPjaB9u89z35Ak+9+NeMgqiEz4+uS1L0GWOC+GWvFy0MiYiVy+1A6XUL8pIcxxrKZL528eB3SW2K+CmpfZrF26ZZ2QpdPDUwRHc46lyOeLHB8inM3jragluXo8U+li4xXEp3OxpRwxze/wCd5fBDMbRPtzkmQyNcujoaTJ5xUR7FzlfgL1D01x3gXscF8MteblUy9iX573ewNxRQgo411YjBwiFQmzatMlpjSXRwVMHR3CHp8rniR0fIJdM4akJUH/uesTrnX3fDY7l4HJPE8NcgnG0D7d4pkYnSA2Ps7UzSHxUyNXUzs6o7xbHpXCL56KVMaXU5uLXIjI5f9tawC1DW5dCB08dHMF5z5nOrrl4Ek/AT/DcDXh8c7+OTjuWi5s9TQxzD8bRPtzgmR6fInnamld5x85z+bsLvHNm1B8Zcd8E1aVwQ15C+R34Z1h66KWGBAJ6rBOsg6cOjuCcZ+9wjL2nIzRNjBObCLO1uxH/5m729Y6fMdLI5GVFMDHMIYyjfTjtmZmK0LvvBEfG4gTP7ibSF2fnukbeePEzj/ycdiwXt3gutzK2JgmHw7S0tDitsSQ6eOrgCM54zsyyXzM2Rm08Bh5hetxH9lgfOaXwe+bOrm/y0lAuOpSBcbQPJz2z0zEOPHmczz80wFSwiWh4GmH6jNVBTF4uj3Jn4F/TdHS4f/gt6OGpgyM447l3aJqayQlq4zGUCJNtnSR9AbJ5RV6dOTu1yUtDuehQBsbRPpzyzMbixE8OcmQ0RqS+gWhjM1B6dRCTl8tjqdGUDzK3Wb9RRH5VnEYpdWUlxKpJOBwmGHT3XE6gh6cOjuCM53N8aX4Wj5IRmGrrIFdTi88DIIWWMavjq5OOK8HNniaGuQfjaB9OeOYSKeInBlF5xfbzekhFp5HCWroeMPFrlSz1mPLf572ePzJpTZDJZJxWKAsdPHVwhOp7pscm2ZiL8+4rNnDI10hjR8vsjNTAnI6vTjmuFJd7mhjmEoyjfVTb88DAJAceO8zW1hqksYFebz3vvGzx2fVNXi6PpUZTfrVaIk7ilnlGlkIHTx0cobqe6ckIiVPDAOx47mYubj+zf0KpWfZNXq4eE8Pcg3G0j2p6Hhic4tNffxiVyZKtrSXcDjmi+D0yp4+Yk46rwS2eC/YZE5FXl7ODctO5mVAo5LRCWejgqYMjVM8zE4mSGLBWwqk9q4tAiYrYQpi8XB0mhrkL42gf1fLMZ7Psf/wIKpMl5Q8w3tJBVlGyj6tTjqvFLZ6LdeB/g4jsF5GPiMjlItIuIoHC7xeJyIdFZD/wumrJVgo3PC8uBx08dXCE6nhmozHiJ0+BUtR0tVPT2basz5u8XDUmhrkI42gf1fC0VgcZZFuzHwIBIu2d+HwefB7BI2f2EXPC0Q7c4rngY0ql1JtE5CLgL4CvAZt5piPs01jrr71eKXWg4pYVxls067mb0cFTB0eorGfvcIy9J8ZoGgkRS2XZfv5Z+Dz17H0ydEa/Cqcc7cStniaGuQvjaB+V9lT5PPGTpzh2apLD4TSvf9XziORYtI9rtR3twi2eS/UZewp4F4CI1AMtwJRSKl4Ft6oRiURobW11WmNJdPDUwREq59k7HOOjd/cSHA4h+Typunri01NAuORcYk442o2bPU0Mcw/G0T4q6amUIt53mqP943zukVOMtnfhmZwbt0z8sp+y5xlTSsWVUqfXWhAD6OzsdFqhLHTw1MERKue5t3+ChtFhJJ8nXVtLuLWdbJ4F5xJzwtFudPE0McxZjKN9VNIz0T9ENhLlyGSS0bZOMl7/suLWDCYvl4eZ9BWYmJhwWqEsdPDUwREq45nPZLkgFSag8mQDNUy1duARweeh7H4WlXasBLp4rmV0KAPjaB+V8kwMhshMRRCPsON55+OpqVl23Kq0o924xdMsh4TVLKsDOnjq4Aj2e1qdXQfY3OjjPbu30Btopqm+Zsm5xKrpWCl08VzL6FAGxtE+KuGZDI2SHp8CEeo3r+c5DUFuq69bdtyqpGMlcIunqYzhnmbKpdDBUwdHsNdT5fPEjg+QS6bw1AS46MKN7PSd+dVabjB7NualYWXoUAbG0T7s9kyNTnDo4CBHxuLsuHgLnhjsPRY6Y/FvJx0rhVs8y3pMKSJBEXmeiFxZ+O2OsaA2MTw87LRCWejgqYMj2OeplCJ+8hS5eBJPwE/w3A14SlTEVsKzLS8riYlhzmMc7cNOz/T4FAf39/H5hwb4RijPzQ+e5oM/OspXnxji5nuP0jscc9yxkrjFc9HKmIi0iMg3gQngV8A3gF8C4yJyp4g4v9S5DTQ0NDitUBY6eOrgCPZ4KqVI9J8mOx1DfF7qN6/HE/DbYGfxbMrLSmFimHswjvZhl2dmKkJiMMSRsTiTjS3E6xpWPOCoUo6Vxi2eS7WM/QeQBy5QSjUqpdYrpZqAHYXt/1FpQYPBrSQHQ2SmphGvh+DmDXhra5xWMpyJiWEGQwmy0zHi/dbqIBdcsIFsUxMeYcUDjgyrY6nnKS8FuucPBVdKHReRdwLuWEdglUSjUdrb253WWBIdPHVwhNV77tt3kkOHTxGs8RHp7GLndA6mYyvu7FoJx2rhck8Tw1yCcbSP1XpmY3H2P3GMI6NRgl1tRJoDvPOy9asacGS3Y7Vwi+dSlbFx4HnAQyXeuxir6V97uru7nVYoCx08dXCE1Xk+tb+fz92zj0xeMdnWSWZkCt/BKUCWPbFrpRyrics9TQxzCcbRPlbjmUuk2P/4UT7/6z6ma+oJh5MIQwS8suyJXSvlWE3c4rnUY8qPAj8Wka+LyAdF5B0i8gER+RrwI+DmyitWntHRUacVykIHTx0cYeWe6bFJDh4cIJtXTLV2kK6tQ4Ft/SzscKw2Lvc0McwlGEf7WKlnPpUmfmKAIyNRYoFawi3WerkK++LWah2rjVs8l1oO6Rsishd4E3AF0ABEgQPA5Uqp3sorVh4RcVqhLHTw1MERVuaZnoyQODXM1o56Em3tpGvrAeuOxuuBZ1rG7OlnsZbzslqYGOYejKN9rMQzn84QOz5APpNl26YO4tP1SN6qiHmwv3/YWs7LSrBgZUxEvqWUer1S6oCIHFNK/c9qilWTtrY2pxXKQgdPHRxh+Z6ZSJTEQKGz63M2ceuOGvYOTdNU47O1n8VqHJ3CrZ4mhrkL42gfy/U8cCrC/scO0UCeqNfHcy7dxm2bPGfEMDvi1kodncItnou1jL1cRERZ09PeDnylSk5VZ3R0lE2bNjmtsSQ6eOrgCMvzzEZjJPpOgVLUdLVT09nGDkr3qbAzmK3FvKwyJoa5CONoH8vxPHA6wm1ffwiVTJPx+5lq78J/39Pcds35K57Q1W5HJ3GL52KVsQeBR0TkCFArIv9ZKpFS6q0VMasiTU1NTiuUhQ6eOjhC+Z65eJL4yVOovCLQ3kLtuurN1rzW8tIBTAxzEcbRPsr1VPk8+/ccg1SarM/HVHsXea93tn+YnTePK3V0Grd4LlYZey3wx8AmrMfKT1fFyAFyuZzTCmWhg6cOjrC4Z++wNUVFk+SJPd3H1tZaPE2NHBhVNE2PVaRJf7mObsLFniaGuQjjaB/leCql2PfEMSbHI+D1Em7vJO/1VqR/2Eod3YBbPBesjCmlksDXAUTEr5S6tWpWVSYWi9HR0eG0xpLo4KmDIyzs2Tsc4+Z7j5JNZWgdG8aby5GrryXcBlk1jQIECHjtmb5iJY5uw62eJoa5C+NoH+V4PrXnaW7/ySHSCJHOLl5+4Tq2tNdV7WZyLeVlNShrET2l1C0V9nCUnp7KPTe3Ex08dXCEhT33Dk2Ty2RpGR/Bk8uRDtQw1dwBympagbnDwCsZ0HTPSzdhYpjzGEf7WMozMRji0PFhMgom2jvJ+wJ0Nfh51QXVq3SslbysFmUtFL7WCYX0mIRbB08dHGFhz+d21dMxMYovmyXrDxBp78Tn8+DzCDMDoKvVzK97Xhqqhw5lYBztYzHPZGiU9PgUWzuDxDq7yNfUOLKs0VrIy2pSVsvYWsfvt29x50qig6cOjlDaU+XzbIpN8P4X9nA4nKFhyyYiWTVn2opKDQMv19GN6OK5ltGhDIyjfSzkmRqd4NDBQY6Mxdlx8RY+cUGDrdPt2OHoNtziaSpjQHNzs9MKZaGDpw6OcKanUor4yVPk4knO62niuVdsxBOY+yWtdjDTNS8N1UeHMjCO9lHKMz0+xcH9fXz+oQEmmlvJ/Xqo4tNXLIbOeekEi036enU5O1BK/cI+HWcYGxsjGKzuP9qVoIOnDo4w11MpRaL/NNnpGOLzUr95/RkVMSfQMS/dhIlh7sI42sd8z8xUhMRgiCNjcSYbW4jXNeCpQr/W5Ti6Fbd4LtYy9uV5r8/G6rs8DrRjDSobBM6tjFr1cEvNeCl08NTBEWA4W8PDT4ZoqvER7T/NtkAOPB4O1rSwM5xlR22N04ra5KWLPU0McxHG0T6KPfc/PULvnqME/V5GahtINyo8Ni7LZoejm3GL52JTW2ye+VtEPooVvP5GKRUXkXrg41hBTXvS6bTTCmWhg6cOjr3DMT7+yxCZvCIYniQYneZerxBu7yIZyOM/OFnxaSvKQYe8BPd6mhjmLoyjfcx47j8xxj/d9Vuy2TyxYCOxlhp8Hnjltg5een6bozFMt7x0mnL7jL0POEsplQEoBLOPAKeBf6iUXLVIJBJOK5SFDp46OO4dmiaTV9RNh6mPTqMEJlo6SPtrUKo601aUgw55Cdp4mhjmMMbRPhKJBLlEit49R8nl8iTqg0RbWgHIKehq8Jv4VSZu8Sx3aosY8Hvztr0AiC/nYCLiFZHficj/LbzeLCK/FZGjIvItEQkUttcUXh8rvH/Oco6zXNwyz8hS6OCpg+POdY00JqI0RsIATLd2kK+vw+cRPFKdaSvKQYe8BG08Vx3D3Bq/QI8yMI72MZmr47s//h1Br5Crr2e6xVrsulrT7pSDLnnpFs9yW8b+BrhPRH4IDAAbgGuBm5Z5vPcAB4GZxaBuAz6rlLpLRL4I3Aj8a+H3pFJqi4i8oZDu9cs8VtmEQiFXLBS6FDp46uC4JZDjneuSTPR0ENywjkht/ZzpK5wYBl4KHfIStPG0I4a5Mn6BHmVgHO3hwGCYz9z1KGRz5GtredOrnkckk6/qtDvloENegns8y52B/2si8gRwPXAWcAj4hFKqt9wDich64FXAJ4H3i4gAVwNvKiT5KnALVjD7w8LfAN8B/llERCmlqACBQKASu7UdHTzd7piJREkMDLG5tY4XX7Sdmq72Oe+7IYjN4Pa8nEEHz9XGMDfHL9CjDIzj6slns+x//DBkcqQCAcKtHUQyecemr1gMt+flDG7xLHueMaVUr4gcArqVUkMrONbngA8BM+2n7cCUUipbeD2INdqJwu+BwnGzIhIupB8r3uHIyAg33ngjPp+PXC7Hddddx0033UQoFCIYDOL1eolEInR2djIxMYFSis7OToaHh2loaAAgGo3S0NDAwMAAIkJbWxujo6M0NTWRy+WIxWL09PQQCoXw+/00NzczNjZGc3Mz6XSaRCIx+34gEKCxsZHx8XFaW1tJJBIkk8nZ92tra6mrq2NycpL29namp6dJp9Oz79fV1REIBAiHw3R0dBAOh8lkMrPve71eJicnyzqn7u5uRkdHq35OqVSKvr6+ss9pOeW02nPqaGhi4PG9+H0+arraCSWitEb8tpeTXecUjUZJpVKuuPYWO6doNMr4+HhVrr3VsMoY5tr41d3dTTweZ3Bw0MSvNRy/ujs76X/0SbpJoQIBIm2d+HxeNtRk5jib+OXe+JVMJhcMMFLOzZqItABfAP4YyCilgiLyauD3lFJ/XcbnrwWuUUr9pYhcBXwAeDvwiFJqSyHNBuBepdRFInIAeLlSarDw3tOFY80Z+fTII4+o7du3L+m/FH19fa5oplwKHTzd6Ng7HGPviTEuSE1BPs+hjI+u7jqu3rnFabVFcWNelqKannv27Hli9+7dly73c6uJYW6PX6DHtWIcV47K54mfGORo/ziHw2nSrQ34mttd80iyFG7Ny/lU23OhGFZuy9gXgUlgEzDTrP8I8E/AkpUx4Arg1SJyDVCL1efic0CLiPgKd5frsUY2gXWXuQEYFBEf0AxMlOm6bFpbWyu1a1vRwdNtjr3DMT56dy8NIyF+ovKk6oJMtrThO5Wjpyfm2kAG7svLhdDEczUxzNXxC/QoA+O4MpRSxPtOc7R/nM89corR9i5kMsOnr3FvRQzcmZelcItnuaMpdwPvLjTtKwCl1CjQVc6HlVIfUUqtV0qdA7wB+IVS6s3Af2PdqQK8Dbi78Pc9hdcU3v9FJftbuGVo61Lo4Ok2x739EzSM6ZPtJwAAIABJREFUDkMuTzxQy0RzG3mEbM6avsLNuC0vF0ITzxXHMLfHL9CjDIzjykj0D5GNRDkymWS0rZOM12/il424xbPcylgY6CjeICIbgZX0HSvmZqzOsMew+lTMzJj9ZaC9sP39wIdXeZxFWew5rpvQwdNNjvlMlgtSYQIqT66mhlh7Bz6vB4+A14Mrhn8vhpvycjE08axEDHNF/AI9ysA4Lo/e4Rh3/Ww/R44Pc2IyRaipHQI1Jn7ZjFs8y31M+e/Ad0XkfwIeEXkR8PdYTf/LQin1APBA4e/jnDn3D0qpJPDa5e57pbhlnpGl0MHTLY4qlyN+fIDNjT7es3sLvYFmdq5vAazpK3Z01Li6iR/ck5dLoYmnLTHMjfEL9CgD41g+vcMxbr3rMWrCYe4TmOroJhnI4xVrdv2rzmkw8csm3OJZbsvYbcC3gX8B/MB/YDXJ314hr6oSCoWcVigLHTzd4KjyeWLHB8glU3hqAlz0gq288ZKz2dEdZEd3kDde3ENLLuK05pK4IS/LQRNPE8McxjiWz77eAWrCYfJYq4Mk/DXk1TOz65v4ZR9u8Sx3njGF1WH1c5XVcYba2lqnFcpCB0+nHZVS7Hv8KIf7xgjW1xDp6mbneIod3XMvdac9y0EHR9DD08Qw5zGO5fHUodNM9YfwiBBpaSUXrMeHkCta/LsWcVpzSdyQl+XgFs+yKmMi8hLgpFLqhIj0YN1l5oCPKqXcUa1cBXV1dU4rlIUOnk46KqV4as/T3P7Tw6SUMNHRTX5ojMD+8TMW/jZ5aR86eJoY5jzGcWn2Hw3x2e88TjaviLe08pLnncNLz7eWOipeHSQSyTnqWQ5O52W5uMWz3MeUX8AKXACfwWrmV8CXKiFVbSYnJ51WKAsdPJ10TA6GOHR8mIyCyfYucn4/imcW/i7G5KV9aOJpYpjDGMfFyU7H6H3yabJ5xXRDE9Fg4+yC3zPdK2ZuKE1e2odbPMvtwH+2Uqq/MGfOy7Hm6knzzLw6WtPe3r50Ihegg6dTjsnTI6QnwmztbCA27iXns5a4WGjhXJOX9qGJp4lhDmMcFyYbS7D/iWNMxDOkGhpJNLcsuuC3yUv7cItnuZWxiIh0A88BepVSUREJYN1das/09PTsEg9uRgdPJxxTI+OkRidAhOdcsoVPXGA16S+2cK7JS/vQxNPEMIcxjqXJJVLsf/wIn/91H9HaemJt7bxyawcvPb9twRGTJi/twy2e5VbG/jfwGBAA3lvYdgXWYrvak06nnVYoCx08q+341MFTHNx/kqDfy3R7B8+NM9usvxgmL+1DE08TwxzGOJ7JgYFJDjx2mInpFLFALVPNbXgKIyYXi2EmL+3DLZ7ljqa8TUS+D+SUUk8XNp8C/qxiZlXELfOMLIUOntV0fOrIEJ/97hNkcopwSxupsWkCx6JndNYvhclL+9DB08Qw5zGOczkwGObTX38YlcmSq60h2taFR2TRx5MzmLy0D7d4ltuBH6XUkaIgNvP6qcpoVRe3zDOyFDp4VssxE4lycO9xq7NrUzPJYMOCnfVLYfLSPnTxNDHMWYzjM+SzWfY/fhiVyZLyB5ho7eRl2zt42yXryrqZNHlpH27xLHdqiybgFuB/YC0pMjvJiVJqY0XMqohbhrYuhQ6e1XDMxuIk+k6xtaOedFMziYZmYOHO+qUweWkfOniaGOY8xtFC5XI89dgRJsNx8v4AkfZOfD4vLz2/vexZ9U1e2odbPMvtM/YFYD3wceDrwFuADwLfrZBXVQkEAk4rlIUOnpV2zMWTxE8MovKKbeev42M7ti7ZWd8JTzvQwRG08TQxzGGMo7U6yL7Hj3H7/cdIebxEOrt5xQXdi3bWL4XJS/twi2e5jylfBlyvlLobq8/F3cDrgT+pmFkVCYfDTiuUhQ6elXTMJVPETgygcnn8LU3Unt09O//Oqy7omDMPj5OedqGDI2jjaWKYwzzbHZVSJPpPc7h/jLR4mGjrJOPxLtlZvxTP9ry0E7d4llsZ8wAzxlERaQGGgC0VsaoyHR0dTiuUhQ6elXLMpzM89dgR7usd4WTaw4maJu7aO0zvcGxF+3s256XdaOJpYpjDPNsdE/1DHDkxykQyR6SjC+X3l92tYj7P9ry0E7d4lvuYci9WX4v7gQexFtuNAkcq5FVVwuEwweDy7kycQAfPSjjmM1n2PXqYz//yBAlfgEi4Fp46VlirLVRWh9dqeNqNDo6gjaeJYQ7zbHZMnBrmyPFhbn94kNG2TlSNf8m5xJzwtBMdHME9nuW2jP05cLLw97uBJNACvLUCTlUnk8k4rVAWOnja7ahyOeLHBzgyFCbh9TPR1kkWD9m8Iq/KHz1Zac9KoIMjaONpYpjDPFsd9z3Vxw8fPsZvBiKMtXb8v/bePEqu6jz0/X019TxPEmIyASHMjRlMDHjABhlsMIkT7MTGfglJtJYfz/g6DvGzse+NbXKda+A+G8TzTZy8OCG5cMED2MgQY2NwbIwERgipJw2tgVa3pJ7U3VXd1UNVV+33R1W3W00P1d116uyvtX9r1eqqfU6d+p29S5927fOdvUmEi0jlMJfYYpyudekFtnjmOs/Y4VnP+4Etnhn5gC3zjCyFBs98Opp0mviRblITk2w8o5p4tBiRAEEBkOzI2MqG+U+3uvQSDZ4uhvnP6ejY0t7NA0/uyUzBU1dPuqSEwCri1jSnY116hS2eOc8zJiJ/LiLPikhb9u8WEZGl32k/tswzshQaPPPlaIxh7PVjpOLjBCJh3vI7G7nndzdx21vX8z8+sJH/8YELcp6Tx0tPL9HgCHo8XQzzl9PNMTEYZW9bJ1Npw3B1LePFpdywsXZVccsLT6/Q4Aj2eOY6z9h9wAeBB4BOMovsfha4EPicZ3YFwobrxbmgwTMfjtN3HXV0DnBgaIKy3zqHWPtJLllfwa2X/uZXzGqC2elSl4VAg6eLYf5zOjkmh2O07znM4FiSsepaEmXlhAOyrLnEFuN0qkuvscUz1wT+PwUuN8Z0TxeIyFPALtZAIAsGg34r5IQGz3w4TnT3cOBwH1u3d9NX00hysBcBIsGVJet75ek1GhxBjeef4mKYr5wujlMjcdp2H+bBF7sYLqtksqp8Vcn683G61GUhsMUz18uUI9nH3LJYfnX8IRbTcRoaPFfrOHG8j8RglAMnxxmoqSeZnZBvOUsd5cLpUJeFQomni2E+czo4TsXHaX31IE/v7SdaXM5oRdWqk/Xn43Soy0Jhi+eCI2Mict6slw8AT4jIPUA3cBaZ2avv91avMDQ0NPitkBMaPFfjONl3ksn+QRDhzZeeDy8cR1IGw/KWOvLas1BocAR7PV0Ms4u17pgan6R15wEe/FUnI0WljNTU5D1uTbPW67KQ2OK52GXKg2QGJGYnuF47Z5/rgG/mW6rQDA4OUlpa6rfGkmjwXKljy95j7G19nbJwkJG6et7SVMa9N12woqWOvPQsJBocwWpPF8MsYi07tnUN0fbKfgZHJolHiolW1yLAZRsq+OPL1+d1VGw1noVEgyPY47lgZ8wYk/OdltoxxvitkBMaPFfi2HLgBPc//irJlCFaXcvkwAiRg6Pce9MFpyTs55O1Wpd+YKuni2F2sVYd27qj3PfwdkxyilRxEaO1jQRECAfEk47YSj0LjQZHsMcz1wT+NY0tw5RLocFzuY7J2Ch79xzOzMNTWcVEWXmmPJsf5kUgg7VZl36hxXMto6EN1qJj27EYTzzzGunEFIlIhFhNA+/fVE9jeSSvI/mr9fQDDY5gj+dp88txMXp7e/1WyAkNnstxnBqNM955jI31pSQqqxivqALynx82H2utLv1Ei+daRkMbrDXHtuMx7nl4OweORUmGw8RqGwiFglx/QR23XrrOs47Ycj39QoMj2OPpRsaA8vJyvxVyQoNnro6psQnGXj+GSRsuPH8dX3rzRs/yw1bj6ScaHEGP51pGQxusJUeTTtO66yAyOUkyFCJa18ilZ1d7dllyLmupLv3GFk/XGXMUnLajQ7Tt3MfGmmIClRW0DcAlZ+BZfpjD4XDkC2MMzbsOMXQyBsEgsfoGQpFQwTpijrWJ64wBo6Oj1NXV+a2xJBo8l3Js6x7mvkcyya5TJcVEayHFCOHdvXmb0DUfnjagwRH0eK5lNLTBWnFsee0wW5/ZS9JAtLGJGy5en9cJXXNhrdSlDdjimVPOmIhcIiLPi8igiCSyj6SIJLwWLARNTU1+K+SEBs/FHNPJKVp37sckp5gMF3Gyqp4pA2mT3wldV+tpCxocQYeni2H+sxYcx4/1su9QD0kDJ+saSYQieZ/QNRfWQl3agi2euSbwPwq8CFwDXJR9bMr+VU9/f7/fCjmhwXMhR5NKMXa4iwurIlAUyQzthwKEAkJAvE/Yz9XTJjQ4ghpPF8N8RrvjRE8/iYEhNjaUEW9oJF1UVPC4NY32urQJWzxzvUy5DviSsWVCjjwjIkvvZAEaPOdzbDsxQuvOA5SnkowS4CMfuJzYlJkJYntOjHiesJ+Lp21ocAQ1ni6G+Yxmx8n+Qfbt7ebAwBhvvvR8vnpRuS9xaxrNdWkbtnjm2hn7V+BjwCMeuvhGbW2t3wo5ocFzrmNbzyhfe3gHMjZOKhhkqL6J0NCJU/LD/AhmGuvSVpR4uhjmM1odE4NR9rZ28uCLXQxW1ZD61QlPJ6TOBa11aSO2eOZ6mfIe4L+JSFs272Lm4aVcobBlmHIpNHjOdjTG0PraQQLj46QCAYbqGkmFQgXPD5sPbXVpM0o8XQzzGY2OyegI7XsO8/S+AQbLqxkrKXfxK0c0OII9nrmOjH0fOAL8ABj3TscfKisr/VbICQ2esx0nunu4sNjwTDDAyZpGUuFwQSZ0zQVtdWkzSjxdDPMZbY5TI3HaXjvEgy92MVxawVhlhYtfy0CDI9jjmWtn7FKgzhizJu48mksqlfJbISc0eE47Nje/zr79x9jYUM5ffexqWqJTBZvQdTmeNqPBEdR4uhjmM5ocp+LjtL56kKf39hMtLme0strThb9X6mkzGhzBHs9cL1O+ALx5pR8iIsUi8msR2ZO9THB3tvxNIvKyiHSIyHdEJJItL8q+Ppjdfu5KPzsX4vG4l4fPGxo84/E4LW1dPLCtmR/tHeC/7R0jUFrCrZeu4wMX1Xu+TMhyPG1HgyOo8VxxDLM9foGONtDg2HxsmEdf7uQnz7fw4K862T0qjFTXEAAiQe8W/l4uGupSgyPY45nryNgR4Kci8gPglIWcjDFfyuH9k8B1xphREQkDvxKRHwN3AvcbYx4TkW8BW4C/z/4dMsacLyIfBe4FPpKj67JZt07HzO8aPGvDxbzcfpCptGG4pp5kpNjTBb9Xioa61OAIajxXE8Osjl+gow1sd2zvjfPAr4eo7OslmEoxXlRCtLrWqhGxaWyvS9DhCPZ45joyVgo8DUSAs+Y8lsRkGM2+DGcfBriOTC4HZO52+v3s8w9mX5Pdvlk8vP+0p6fHq0PnFZs923vjPPZCB0/9bDeDY0niNXUkS0utyK+YD5vrchoNjqDGc8UxzPb4BTrawHbHPV1DlPf2wlSKiUgRI7V1BAJi1YjYNLbXJehwBHs8cxoZM8b82Wo/SESCwKvA+cD/BA4Bw8aYqewu3cCG7PMNQFf2s6dEJArUAQOr9ZiPcDjsxWHzjq2e7b1x/vqJZkr7+zAG4pVFJKrKuHFjfcGXCckVW+tyNhocQYfnamOYzfELdLSBzY7pqSkumozyU5NioijCeEMjn3r72dbkuM7F5rqcRoMj2OOZU2dMRM5baJsx5nAuxzDGpIBLRaSazB1N8818PT0h43y/It8wWWNfXx9btmwhFAqRSqW45ZZbuOOOO+jp6aGsrIxgMEgsFqOhoYHBwUGMMTQ0NNDb2zuzUvvo6CgVFRV0dXUhItTW1tLf309lZSWpVIp4PM66devo6ekhHA5TVVXFwMAAVVVVJBIJxsfHZ7ZHIhEqKio4efIkNTU1jI+PMzExMbO9uLiYkpIShoaGqKurY2RkhEQiMbO9pKSESCRCNBqlvr6eaDRKMpmc2R4KhRgaGsrpnJqamujv7y/IOb2yd5iS/n6MgbGKSuIVVQQMRKbi1EsRw8PJBc9pOe2Uz3MKh8N0dnZ60k75OqexsTEmJyet+O4tdk5jY2OcPHmyIN+9lbLaGGZz/GpqamJ8fJzu7m4Xv1ZwTsWRCDt/1ULPSJrrz68g2tjE2y88g+pUjJK6EiKRJJ2dnS5+ufiVl+/eQkguE1KLSDobTGYHGQNgjAkueYA3Hu/LwBjweWBd9tfj1cBXjDHvE5GfZJ/vEJEQ0AM0zJ09e8eOHWbTpk3L/fg30NnZyTnnnLPq43iNjZ6psQlaXtnPgy90EisqJVZTl7n9OygFXfh7udhYl3PR4AiF9dy1a9ermzdvvmK578tnDLMtfoGO74qNjiadpvmVDrY+u5/JQJBYQxP3/t5F1sataWysy7locITCey4Uw3K9THlKbpmIrAO+TOYOpSURkQYgaYwZFpES4L1kklp/DnwYeAy4DXgy+5Zt2dc7stuf93IZk6qqKq8OnVds82w7OkTbzn1srCnmMze+mbZAGWGTJBmIWDm0Pxvb6nI+NDiCDs/VxDDb4xfoaAPbHI0xNO86xFO7jjJJgMHaBowErbzhaC621eV8aHAEezxzvZvyFIwxPSLyGeAA8L9zeMt64F+zeRcB4LvGmKdEpB14TES+CrwGfDu7/7eB/yUiB4FB4KMr8cyVRELH1EM2ebZ1D3PfI9sxySnSJSV84Y8v4NZ15fT19dHY2Oi33pLYVJcLocER9HjOZpkxzOr4BTrawDbHltcOs/WZvSQMDNU3YUJhQpbecDQX2+pyPjQ4gj2eK+qMZbmQzB1KS2KMaQYum6f8MPC2econgD9chduyWE0uSiGxxTOdnKJ1535McorJcBHR6jqae0a5eF25NY5LocFTgyPo8ZyHnGKY7fELdLSBTY7jx3rZd6iHpIHBukZS4QiXb6jg+jP8WSt3udhUlwuhwRHs8cw1gf8FTk1ALQUuBv7GC6lCY8s8I0thg6dJpWh55QBD0XHSkQixugbCoeDMr0kbHHNBg6cGR9Dh6WKY/9ji2NzSyb593ZRFQsTrG0hHiogEMtNX/Fb1asYnCoctdbkYGhzBHs9cv3n/NOd1HNhjjOnIs48v9PT0qEg09NvTpNM07+xg6/MHmcgmu77/osZTpq/w2zFXNHhqcAQ1ni6G+YwNji3t3Tzw5B6m0oZ4fQNbrt14yvQVWpLObajLpdDgCPZ4LtkZy+ZJXAd8whgz6b1S4YlEIn4r5ISfnsYYxl4/xv6jJ5mUAIO1jRAI0lgePmVY39Vl/tDgCPZ7uhhmB347tuw/wbZf7CWZMkRrakkUlRCbnOLWS38zMuK3Y65o8NTgCPZ4LtkZM8akROQGIF0AH1+oqLA/YRP88zTGMH70OB2dAwxOphmpb4JQaN7Z9V1d5g8NjmC/p4thduCnY2tHL/d/7xWSKUOsqoZEabmLXx6jwRHs8cx1OaT7gbuz67KtOaYnfLMdvzwnuns4cLiPrdu7eWokQioc4sYL6+edR8zVZf7Q4AhqPF0M8xm/HKdG4rTvzqyXO1pRyUR5BZdtqHDxy2M0OII9nrnmjP1nYB1wp4j0MysR1hhzthdihaSmpsZvhZzww3PiRD+JwSgHTo4zUFNPIhwhYHjD5Uk/HVeCBk8NjqDG08Uwn/HDcSo+TuurBxkcSzJZXsF4VfVMsr6LX96iwRHs8cy1M/Z/eGrhM+Pj41RWVvqtsSSF9GzvjdPcdpSKWJR4MkXZuWfCyBCBtFl08W9Xl/lDgyOo8XQxzGcKHb/2vD5AZV8vj+/pYbS4lHht3ZLr5WqoR9DhqcER7PHMtTPWaIz53txCEflwnn18YbH1omyiUJ7tvXG+/N1dFA8OYoBYTR1mdIjbrzpzyYVzXV3mDw2OoMbTxTCfKWT8+sK2dir6egmmUowXlTBcVbvoiH6hHVeLBk8NjmCPZ645Y99eoPwf8yXiJ7bMM7IUhfJsPnCckqFMR2ykuoaJ0jKSaTNz59FiwczVZf7Q4AhqPF0M85lCOe7pGqK8vw+mUkxEihiprSMQkEVH9AvtuFo0eGpwBHs8F+2Mich5InIeEBCRN02/zj7eC9jRpVwlPT09fivkRCE8Ww/2MXzkOAER4pVVjJdVZBb+znGZEFeX+UODI9jt6WKYPRTCse1YjOGOTsKpFKmiCOMNjXzqnedw21vXz5uw74djPtDgqcER7PFc6jLlQTKJrgIcmrOtB/iKB04Fp7i42G+FnPDas/XIAF//zsukUmkmKip5z+/8FufXlSx5abKQjvlCg6cGR7De08UwS/Dase14jHse3o5MTmLCIa66+iKu39SwrOWNNNQj6PDU4Aj2eC7aGTPGBABE5BfGmHcXRqnwlJSU+K2QE156psYmaN/VQSqVJl5SRryymsbyMB+4qH5Zx3F1mT80OILdni6G2YOXjiadpnXXQWRykqlAkOG6Jhqripe9zqSGegQdnhocwR7PnHLG5gax7BC//+sH5ImhoSG/FXLCK8+2o0M8/sxrlAWFVFkZ8ZranC9LzuV0r8t8osERdHi6GOY/XjkaY2jedYihkzEIBok2NBIMh1z88hkNjmCPZ64LhT8K/L/GmO0i8mfA3wFpEfm0MWahxFg11NXV+a2QE154tnUPc98j2zHJKdIlJXzsA5cRS6RyvixZCEcv0OCpwRF0eLoY5j9eOba8dpitz+wlaSDa2MQNF69fdPqKxdBQj6DDU4Mj2OOZ692Um4Gd2ed3Au8F3gbc5YVUoRkZGfFbISfy7dnWHeWJH+8mnZhiMlzEQHUdsURqyTsmC+noFRo8NTiCGk8Xw3wm347tvXEee7aV7S3dJA2crGskEYosOX1FIR29QoOnBkewxzPXecYixpiEiGwAao0xLwKISJN3aoUjkUj4rZAT+fRsOx7j3ke2YyYSJMMRYnUNhEPBFQ3tz+Z0rEuv0OAIajxdDPOZfDq298a5+7FXKIpGCQiM1DWSLipacXqFF45eosFTgyPY45lrZ2y3iHwBOAd4GiAb1GJeiRUSW+YZWYp8eZp0mtZXO2AywVQoRLSugUvPqlpwiRA/HL1Gg6cGR1Dj6WKYz+TTsXlvF0XRKGkD0dp6rnvLBhrLIytOr/DC0Us0eGpwBHs8c71MuQX4baAE+Ots2dXAI15IFRpb5hlZinx4GmNo3tnB0OAIhEJE6xsJRUJ56Yjly7EQaPDU4AhqPF0M85l8ObbsP8FwZw8BEUZra0mXlXH9BXWrSq/It6PXaPDU4Aj2eOY0MmaMOQR8bE7Z94HveyFVaGy5tXUpVutpjKFl1yG2/nQ/CYRYQxPvu3jdipNdvXAsFBo8NTiCDk8Xw/wnH46tHb3c/71XmEobxqpruPayc138shQNjmCPZ66XKRGRPwduBc4AjgOPAf9sjDEeuRWMSCTit0JOrMazvTdOy+5DDPUMkTQwWNdIOhReVbJrvh0LiQZPDY6gx9PFMH9ZrWProT6e/FkLyZRhtKKS8bIKF78sRoMj2OOZ02VKEbkP+DzwBPB/A48DnwXu9U6tcESjUb8VcmKlnu29cf7m0Vd4+uUj7OiKMlLfSLoosupk13w6FhoNnhocQYeni2H+sxrH1iMDfP2xl9nXFydeVsF4ZbWLX5ajwRHs8cx1ZOxPgcuNMd3TBSLyNLAL+JwHXgWlvn55s8z7xUo823vjPPbzvYSjUdICsZp6Nv/2GXlJds2Xox9o8NTgCGo8/xQXw3xlpY6p8cmZ1UHGS8uIV9dw+YaKvOW55sOx0Gjw1OAI9njmmsA/kn3MLVsTdyLZ0jNeiuV6tvfG+fJ3d3Fk/zEMMFJdhyktzVuyaz4c/UKDpwZHUOPpYpjPrMQxPZlg7EgXG2uLSZWWMlpTSyQonnTEVuroBxo8NTiCPZ65jow9ADwhIvcA3cBZZIb67xeR86Z3MsYczr+i9ySTSb8VcmK5ns0HjlMyNEgaGKmu5c0XrPMsiE2zVuvSDzQ4ghpPF8N8ZrmO6eQUza8c4MCJKBeeXc8XP34Vzb1xT0b0V+roFxo8NTiCPZ65dsa2Zv9eO6d8M/Bg9rkBgvmQKjS2zDOyFMvxbD3Yx/CR45nbvysrSVd6M6w/l7VYl36hwRHUeLoY5jPLcUxPTdHyygEe/I/DjIfCxGMl3HNugFsv9fY8NdQj6PDU4Aj2eOa6UHggh4fKIAb2zDOyFLl6th4Z4OvfeZntrw8zVl7Bu6/4Le696QLPO2Kw9urSTzQ4gg5PF8P8J1dHk0rRsrODp/YcY0KCDNY0kEDYc8L7ZWs01CPo8NTgCPZ45jy1BYCInAVsMMa85JGPL5SVed9JyQe5eKbGJmaSXeMlZcQrq/N++/dirKW69BsNjqDHE1wM85NcHE06TfPOg2z9WQcTBBhsWIcEg57cOblSRxvQ4KnBEezxzHVqi7NF5EVgH/CzbNmHReSfvJQrFMGgjh/ES3mmJiaJTye7lpURr6ktWBCbZq3UpQ1ocAQdni6G+c9SjsYYmncd4qldR5kkwFB9IyYY5LINFQUb2ddQj6DDU4Mj2OOZ692U/0BmPbcKYDrb7Vngei+kCk0spuOGqsU804kkLTs7eKa9Dykr5Ysfv4rbrjijYEEsF0eb0OCpwRHUeLoY5jNLOba8dpitz+xl78A4Q3UNmFDY0zsnV+JoCxo8NTiCPZ65XqZ8G/ABY0xaRAyAMSYqIlXeqRWOhoYGvxVyYiHP6buOMsmuEUZjJdx7jnie7Dof2uvSJjQ4ghpPF8N8ZjHH8WO97DvUM7M6SCoc8WwusZU62oQGTw2OYI9nriNjvcD5swtE5M3A0bwb+cDg4KDfCjkxn6dJpWh55QBPNx9nPBBisLaBZIGSXedDc13ahgZHUOPpYpjPLOR70emAAAAgAElEQVTY3NLJj7YfpCwSIl7fQLqoqOAjYks52oYGTw2OYI9nriNj/w/wlIh8DQiJyK3AF4F7PDMrIFqWppvrmUl27WDr8weZkCBD9U1IIFDwPLHFHG1Fg6cGR1Dj6WKYz8zn2NLezQNP7sks/F3fwJZrNxKbnPJ0LrHlOtqIBk8NjmCPZ06dMWPMP4vIIPAJoAv4E+CvjTE/9FKuUNgyTLkUsz2NMTTv7OCpXV2Zu47qMsmufgztL+RoMxo8NTiCDk8Xw/xnrmPL/hNs+8VekilDtKaWRFEJsckpX9IrptFQj6DDU4Mj2OOZ62VKjDE/NMbcZIy52Bhz41oJYgC9vb1+K+TEtKcxhpZdh9j60/20D0wwVNcIoZBvQ/vzOdqOBk8NjqDH08Uwf5nt2NrRy/3fe4V9fWOMVFWTKC33dUR/Gg31CDo8NTiCPZ65Tm3xoIi8fU7Z20XkAW+0Ckt5ebnfCjkx7TnR3cO+w70kDQzVNZIOhwt6+3cujrajwVODI+jwdDHMf6YdWw/38+TPWkimDKMVlYyXV7r4tUw0eGpwBHs8cx0ZuxXYOafsVeBj+dVxLEVzcyc/eukwZUUh4g2NpIsiVoyIORyW42KYBbQeGeDrj77Evr448bIKxiurXfxyOMi9M2bm2TeY6/tF5CwR+bmI7BWRNhH5i2x5rYg8KyId2b812XLJ/pI9KCLNInJ5rie0EkZHR708fN7Y3XyEB7bt4Ud7B/jnY2m2vPt8bnvreit+UU6jpS41eGpwBDWeK45htscv0NEGsYHBmdVBxkvLiFfXWDMiNo2GegQdnhocwR7PXDtjLwBfFZEAQPbvV7LluTAF/JUx5iLgKuCO7G3ldwHPGWMuAJ7Lvga4Ebgg+/gE8Pc5fs6KaGpq8vLweaFl7zG2tw9mkl2r64hHimeSXW0JZKCjLkGHpwZHUOO5mhhmdfwC+9ugrWuIHc19lAWFVGkpozW1Vo6I2V6P02jw1OAI9njm2hn7C+C9wAkR+TVwnMzM1f85lzcbY04YY3Zln48Ae4ENwAeBf83u9q/A72effxD4N5PhJaBaRNbn6Lps+vv7vTp0Xmg5cIL7H3+V/QPjxKprSJSWWZHsOh+21+U0Gjw1OIIazxXHMNvjF9jdBm3dUe57eAc/bh/g0QNRPnbjJb6sDpILNtfjbDR4anAEezxzndqiOzvU/jbgLDK3hv/aGJNe7geKyLnAZcDLQJMx5kT2M06ISGN2tw3Zz5imO1t2Yvax+vr62LJlC6FQiFQqxS233MIdd9xBT08PZWVlBINBYrEYDQ0NDA4OYoyhoaGB3t7emaS90dFR0uk0XV1diAi1tbX09/dTWVlJKpUiHo+zbt06enp6CIfDVFVVMTAwQFVVFYlEgvHx8ZntkUiEiooKTp48SU1NDePj40xMTMxsLy4upqSkhKGhIerq6hgZGSGRSMxsLykpIRKJEI1Gqa+vJxqNMjEUpbVlIJPsWlnFRFkFF9WG+JO3nkFlcoiursF5z6mpqYn+/v6Cn9Po6CidnZ2LnlMymZzZvpx2yuc5JRIJOjs789ZOXpzT8PAwjY2Nvn33cj2n4eFhSktLC/LdWyn5imE2xq+mpiai0aiV8SsxPkHznj7SiSTJcIRodT1H+we57W1nMzg46OKXi1+nVfyamJhYOLYUcsIzESkHfgH8rTHmCREZNsZUz9o+ZIypEZGnga8ZY36VLX8O+Jwx5tXZx9uxY4fZtGnTqr3GxsZmGsMmpuJjtL7SwUudQzw/aIhVVhMOiJW/KKextS7nosFTgyMU1nPXrl2vbt68+YqCfNgcbI1fYOd3xaRSNL9ygB37e3nx+BgDdY2EwiEXv/KABk8NjlB4z4ViWM7zjK0WEQkDjwOPGGOeyBb3Tg/fZ//2Zcu7yfx6neZMMpcVPMGWYcrZpMYmaN3ZwYO/6uS5/iniVdW864yI1YEM7KzL+dDgqcER9HiuBpvjF9jXBpnVQQ6y9WcdvNA9ynB9I+88q8TFrzyhwVODI9jjWZDOmIgI8G1grzHmG7M2bQNuyz6/DXhyVvmfZO9KugqITl8O8ILKykqvDr0iUhOTxI90caBvlNGiEqJVtaQMrK8utTqQgX11uRAaPDU4gh7PlWJ7/AK72sAYQ/OuQzy16yiT2dVBkoGgi195RIOnBkewxzPXtSlXyzuAPwZaRGR3tmx6XbjvisgWMgv2/mF2278DNwEHgTHgz7yUS6VSXh5+WaQTSVp2dnDgRJSy6grG60oJGAgHhE11Eb/1lsSmulwMDZ4aHEGP5yqwOn6BXW3Q8tphtj6zl4SBofomTCjs4lee0eCpwRHs8SxIZyybOyELbN48z/4GuMNTqVnE43Hq6+sL9XEL0nYsxi9/2cLLB08yGY4w2lDC7W8/e2bh3LKJAb8Vl8SWulwKDZ4aHEGP50qxPX6BHW3Q3hunufkIw8dPkjQwWNdIKhyZWS/Xxa/8ocFTgyPY41mokTGrWbfOv4Vpp2k7HuPeh1/ETCRIhsMM1TYgyCkL505O2t9cNtRlLmjw1OAIejzXMn63QXtvnLsf20lRdJiAwEhdI+miIiKB38wl5uJX/tDgqcER7PEsWAK/zfT09Pj6+SadpvXVDphMMBUKMVzXCIHAG+YS89szFzQ4gg5PDY6gx3Mt43cbNO/toig6TNrAUE09175lwxtWB/HbMRc0OIIOTw2OYI+n/T9VCkA4HPbts40xNL96kKHBEQiFiNY1EgwHuWFjPddfUHtKwqufnrmiwRF0eGpwBD2eaxk/26Bl/wmGO3sIiBCrriFdVsb1F9S9IVlfw/dEgyPo8NTgCPZ4us4YUFVV5cvnGmNo2XWIrT/ZRwIh1tDE+y5e94ZO2DR+eS4HDY6gw1ODI+jxXMv41QatHb1843uvkEobxqqqufbyc138KgAaPDU4gj2e7jIlMDBQ+MTS9t443/1pC9tbj2WSXWsbSYTCNJaHF7z92w/P5aLBEXR4anAEPZ5rGT/aoPVwP0/+rIWplGGkvJLR8koXvwqEBk8NjmCPpxsZo/A94/beOH/z6CtEYlEkIIzUN5KORJZcb9KWHvxiaHAEHZ4aHEGP51qm0G3QemSArz/6ElNTacbKyhnPrg7i4ldh0OCpwRHs8XSdMSCRSBT085rbjhKJRUkDsZp6Nv/2GTSWR7hkfcWikyIW2nMlaHAEHZ4aHEGP51qmkG2QGp+k/bUOUqk04yWljFbXzkxf4eJXYdDgqcER7PF0nTFY1QLEy6Vl7zGGu3oJiBCtrsWUls6b7DofhfRcKRocQYenBkfQ47mWKVQbtHUN0fbKfsoCQrqkhNGaOiJBWbIjVkjH1aDBEXR4anAEezxdZ4zCzTPScuAE9z/+KlNpQ7y6husuO2fBZNf5sGU+lMXQ4Ag6PDU4gh7PtUwh2qCtO8p9D+/AJJOki4u59QOXEUumlxzRL6TjatHgCDo8NTiCPZ4ugZ/CzDOSjI2yd89hptKGWEUV8bKKRZNd58OW+VAWQ4Mj6PDU4Ah6PNcyXrdB27EYTzyzm3QiSSIU4WRNPbFkmlsvXZdzDNPwPdHgCDo8NTiCPZ5uZAyIRLxdM20qPkbbrkMMjiWZqKhkorJqyWTX+fDaMx9ocAQdnhocQY/nWsbLNmg7McI9D2+HiUmmQiGidQ2EQkEXv3xEg6cGR7DH03XGgIqK5QWV5ZAam6B1ZwcP/qqTkeJSxmrruHGeCV1zwUvPfKHBEXR4anAEPZ5rGa/aoO3ECI8/sxsmJkkFgwzXNXLp2dU55YgVyjGfaHAEHZ4aHMEeT3eZEjh58qQnx207OsTjz7zGS68PM1pUQrSqlpRh2Zcnp/HKM59ocAQdnhocQY/nWsaLNmjrGeW/P/ISHUcHSQWDROsbCRWFV9QR88ox32hwBB2eGhzBHk83MgbU1NTk/Zht3cPc98h2THKKqeJi4nWNBGBFlyen8cIz32hwBB2eGhxBj+daxos2aN19mODYGKmAMFzXwCXn1K64IwY6vicaHEGHpwZHsMfTjYyR/1tb01NTtO48gElOMRkuYrCmnhsurHvDwrl+e3qBBkfQ4anBEfR4rmXy2QbtvXEee7aV8okxgsEA0fpGgsVFq+qI5dvRKzQ4gg5PDY5gj6cbGQMmJibydiyTStHyygGGomOkwxFi9Q2EQ8Gc5xJbjHx6eoUGR9DhqcER9HiuZfLVBu29ce5+bCdF0WGCAeHD77+UWGjpCakL6eglGhxBh6cGR7DH03XGyN88IyadpnlnB1ufO8hkIEisoYn3X9S4omT9+bBlPpTF0OAIOjw1OIIez7VMvtqgeW8XRdFh0gai1XXEQhFuvTQ/x9bwPdHgCDo8NTiCPZ7uMiX5mWfEGEPzzg6e2tXFBAFO1jaSDARXnKw/H7bMh7IYGhxBh6cGR9DjuZbJRxu07D/BcGcPARFGa2pJl5WtOL91PjR8TzQ4gg5PDY5gj6cbGQOKi4tX9X5jDC27DrH1p/uZNMJQfROEQqtK1p+P1XoWAg2OoMNTgyPo8VzLrLYNWjt6+cb3XiGVNoxVVXPt5efmbUR/Gg3fEw2OoMNTgyPY4+k6Y0BJScmq3j/R3cO+w70kDQzVNZIOh3NaOHe5rNazEGhwBB2eGhxBj+daZjVt0Hq4nyd/1sJUyjBaUcl4eWVeR/Sn0fA90eAIOjw1OII9nu4yJTA0NLTi9zY3d/Kjlw5TVhQi3tBIuiiS88K5y2U1noVCgyPo8NTgCHo81zIrbYPWIwN8/dGX2NcXJ15WwXhldd5H9KfR8D3R4Ag6PDU4gj2ebmQMqKurW9H7Wtq6eGDbHpJpw1hDI1vecwGxyam83Hk0Hyv1LCQaHEGHpwZH0OO5llluG7T3xtnz+gDRjqOkUmnGS0qJV9d4MqK/Ukc/0OAIOjw1OII9nm5kDBgZGVn2e1r2HWfbL/eRTBmi1XXEI8XEJqeWtXDuclmJZ6HR4Ag6PDU4gh7Ptcxy2qC9N84XtrXz9M9aeOnIIFMlJYzW1nk2or8SR7/Q4Ag6PDU4gj2ebmQMSCQSy9q/5cAJ7v/+TpIpQ6y6hkRpmWdD+7NZrqcfaHAEHZ4aHEGP51pmOW2wp2uI8v4+mEoxUVzE1VdupLGy2LMR/ZU4+oUGR9DhqcER7PF0nTGWN89I68E+tj3XRjJlGKmsYqKswtOh/dnYMh/KYmhwBB2eGhxBj+daJtc2aDsWY7jjKOFUislIhLH6Rq6/sMHz2AU6vicaHEGHpwZHsMfTXaYk93lGWo8M8PXvvJxJdi2vYKKiyvOh/dnYMh/KYmhwBB2eGhxBj+daJpc2aDsxwj0Pb2dHRz+pUJCr3n4R99x8YUFiF+j4nmhwBB2eGhzBHk83MsbSt7a298bZc+Q3ya5jpWXEq7xNdl2Jpw1ocAQdnhocQY/nWmapNjDG0PpqBzI5yVQgyHBtI41VxQWLXaDje6LBEXR4anAEezxdZwyIRCILbmvvjfPFJ9sp7+shZNIkS8uIV9cWdEQsF09b0OAIOjw1OIIez7XMYm1gjKH51YMMnYxBMJhZ+DsS9jzHdS4avicaHEGHpwZHsMfTXaYEotHogtv2HB2krL8XUmkmIsVcdeUF3HbFGdx70wUF7YjB4p62oMERdHhqcAQ9nmuZxdqg5bXDbH1mLy8ejTFc38ANF6938WsBNDiCDk8NjmCPpxsZA+rr6+ctbzsWY/jgUcLpNJNFRcTrG7h+Y33Bg9g0C3nahAZH0OGpwRH0eK5l5muD9t44zc1HGD5+kqSBwdoGUqGIJ7Prr9TRNjQ4gg5PDY5gj6frjJHpGZeVnRqc2o7HuPfhF2EyQToc5qqrL+L6Tf51xGB+T9vQ4Ag6PDU4gh7PtczcNmjvjXP3Yzspig4TEBipayRVVFyQKXhydbQRDY6gw1ODI9jj6TpjQDKZPOW1SadpfbUDJhMkgyGidY00VhX52hGDN3raiAZH0OGpwRH0eK5l5rZB894uiqLDpA1Ea+u57i0baCyPeD6X2HIcbUSDI+jw1OAI9ni6zhinzjMyk+w6OAKhTEcsGA759mtyNrbMh7IYGhxBh6cGR9DjuZaZ3QYtB04w3NlDQIRYdQ3psjKuv6DO9x+TGr4nGhxBh6cGR7DH0yXw85t5RowxtOw6xNaf7ONXXSMM1zXwvovX+ZLsOh+2zIeyGBocQYenBkfQ47mWmW6D1o5evvHdV9jeGWW0soprLz/Xxa9loMERdHhqcAR7PN3IGFBWVkZ7b5yW3YcY6hnKJLvWNZIOhX1Ldp0PG65rL4UGR9DhqcER9HiuZcrKymg93M+TP2thKmUYrahkvLzSxa9losERdHhqcAR7PAvSGRORfwZuBvqMMf8pW1YLfAc4F3gd+CNjzJCICLAVuAkYA/7UGLPLS79Dw0nuf6qVSCyKBISR+kbSkYivya7zEQwG/VZYEg2OoMNTgyPo8VwNtsewgydG+IdtrUxNpRkrK2e8strFrxWgwRG89TTGMDo6ijFm1ceJxWJ5svIOrzxFhPLycjLhYGkKNTL2EPBN4N9mld0FPGeMuUdE7sq+/jxwI3BB9nEl8PfZv56xp/UokViUNBCrqWfzb5/he7LrfMRiMWpqavzWWBQNjqDDU4Mj6PFcJQ9hYQxr742z5/UBTuzeTyqVZryklNHq2oKvDpILGr4nGhzBW8/R0VGKiopWPRnq5OQkRUVFebLyDq88E4kEo6OjVFTk9oOoIJ0xY8wvReTcOcUfBN6Tff6vwH+QCWQfBP7NZLrlL4lItYisN8ac8MKtZd9xkoOjBESIVtdiSkutSHadj4aGBr8VlkSDI+jw1OAIejxXg40xrL03zhe2tVPR10swnWKqpITRmjpfVgfJBQ3fEw2O4K2nMSYvs9KHQjqyoLzyjEQiTExM5O7hiUVuNE0HJ2PMCRFpzJZvALpm7dedLXtDIOvr62PLli2EQiFSqRS33HILd9xxBz09PZSVlREMBonFYjQ0NDA4OIgxhoaGBnp7eykvL2f/6yf5x3/fSyoN8Zoarrygjvdf1EjZxABDQwlSqRTxeJx169bR09NDOBymqqqKgYEBqqqqSCQSjI+Pz2yPRCJUVFRw8uRJampqGB8fZ2JiYmZ7cXExJSUlDA0NUVdXx8jICIlEYmZ7SUkJkUiEaDRKfX090WiUZDI5s31iYoLGxsZFzwkyv2yampro7+9HRKitraW/v5/KykrPz6mrq4vS0tKczymXdvLinMbGxgiFQp60U77O6cSJE2zcuNGK795i53To0CHOOOOMgnz3LGNVMWy18WvH/pOU9fXBVIqJoiIuuXgDZzZUcmZkkvWRBAMD4y5+ufi17HYqKSmhtLSUVCo1892ETKclmUzOXCJNpVKEw2GmpqaAzKXTqakpgsEgxhiSySTFxcUkk0lE5A3b0+k04XD4DdtDoRDpdPqU7YFAgEAgMLM9lUphjDllu4ic4rzU9ulzmpycnOl8LnVOCzkvtD2ZTNLZ2XlKOy2ErPa6cK5kf1U+NSvfYtgYUz1r+5AxpkZEnga+Zoz5Vbb8OeBzxphX5x5zx44dZtOmTSvyaT3Yx5PPNrOvL85IZRUTlVXc9tb13HqpHbe5zkdXVxdnnXWW3xqLosERdHhqcITCeu7atevVzZs3X1GQD5tDvmPYauJXemqKll8fYOvzBxkPhhlpaOS+391k3WjYbDR8nzU4greesViMysrKVR8nkUhYs+7jYnjpOV9dLhTD/JzaoldE1gNk//Zly7uB2d+yM4Hj+fzg1iMDfP07L7OvL068vILxiirrkl3nQ8MQugZH0OGpwRH0eHqALzHMpNOMHenm3LIAn772t/i9G97CV9/3Jqs7YqDje6LBEXR4artMefToUb7//e8v+/133HEHTz755Ko9/OyMbQNuyz6/DXhyVvmfSIargGg+cy1SYxO07+oglUozVlpGvKqGi2pD1szFsxi9vb1+KyyJBkfQ4anBEfR4ekDBY5gxhrEj3aTGJghEwrzldzZy61s3UJMeycfhPUXD90SDI+jwtGVm+6WY9lxpZyxfFKQzJiKPAjuAC0WkW0S2APcA14tIB3B99jXAvwOHgYPA/wd8Ml8ebUeHePyZ1ygLCqmyMuI1tUSCwkf+k50J+3OZzj+wGQ2OoMNTgyPo8VwNNsQwYwzjnceYGh0jEA5Rdt5ZBCJhQEcbOMf8ocFztdNvfPe73+W9730v11xzDX/5l39JV1cXV1xxBSdPniSdTnPTTTfx/PPPc/ToUa688ko++clP8s53vpPbbruNsbExAHbv3s3NN9/Mtddey4c+9KGZCV4PHz7MH/zBH/Cud72LG264gSNHjnD33XezY8cOrrnmGv7u7/6OVCrFl770JTZv3sw73/lOHnroISDz7/Bzn/scV111FR/5yEfo7+9f1XlOU6i7KW9dYNPmefY1wB35dmjrHua+R7ZjklOkS0r42AcuI5ZIccn6CppCud/x4HA4Tj9siGHjXT0ko6NIMEDpm84iUGR/Po5DN9E9+1b83lQqtWCHrOqSxXMl9+/fzw9+8AN+/OMfEw6H+exnP8uLL77Ipz/9ae68807e+ta3cuGFF3Lddddx9OhROjo62Lp1K1dddRWf+tSn+Pa3v83tt9/O5z//eR555BHq6+t54okn+OpXv8o3v/lNPvGJT/CZz3yGm2++mdHRUQKBAF/+8pf55je/yWOPPQbAQw89RGVlJc899xyTk5PceOONXHvttTQ3N9PR0cGLL75IX18fV199NR//+MdXXE/T6Liou0rajsV44pndpBNTJCJFRKvriCVSM8n6nZ0D1NXV+Wy5NKOjo9Z7anAEHZ4aHEGPp2YmjveRHMpMSl36pjMJlpw6L5KGNnCO+UODZzq9cGdsKX75y1+yZ88eNm/O/NaZmJigvr6eu+66iyeffJKHHnqIX/ziFzP7b9iwgauuugqAP/qjP+If//Ef2bx5M3v37uWWW24BMp3DpqYmRkZGOHHiBDfffDMA4XB43nnGfv7zn9Pe3s62bduATDL+oUOH2L59Ox/60IcIBoOsX7+ea665ZkXnOJc13xlrOx7j3odfxEwkSIbDxOoaCIeCpyTrNzU1+WiYOxo8NTiCDk8NjqDHUysTvQNM9g+CCKXnnkmorPQN+2hoA+eYPwrludQI1mKk02kCgZVlQhlj+OhHP8qXvvSlU8rHxsY4fjxzL0w8Hp+ZUHXuLPfTrzdt2sRPf/rTU7bNnW0/HA4v6HDPPffMdAinefbZZ3OeVX85rPmFwpt7RkkQYCoUIlrXyKVnVb0hWT9f13y9RoOnBkfQ4anBEfR4aiUQDGY6YmevJ1Qxf26rhjZwjvlDg+f0XF0r4ZprrmHbtm0z5zk0NERXVxd33303f/iHf8gXvvAFPvOZz8zs393dza9//WsAHn/8ca688krOP/98Tp48OVOeTCbZu3cvlZWVnHHGGTz99NNAplM3NjZGeXk5o6OjM8e87rrr+Jd/+ZeZBP+DBw8Sj8d5+9vfzhNPPEEqlaKnp4cXXnhhxec5mzU/MnbJhir+d0MjqakUoXBo3pmpvejleoEGTw2OoMNTgyPo8dRKpL6GUEXZojliGtrAOeYPLZ4rZdOmTXzxi1/kQx/60MxEql/96lfZtWsXzzzzDMFgkB/96Ec88sgjvOtd72Ljxo089thj3HnnnZx33nn8+Z//OZFIhIceeoi77rqLWCzG1NQUt99+OxdddBHf+ta3uPPOO/na175GKBTioYce4uKLLyYUCvGud72LW2+9ldtvv52uri7e8573YIyhvr6ehx9+mJtvvpkXXniBd7zjHZx//vm84x3vyMs5F2zSVy/IddLE9t44e06MLLjW5NjYGKWlbxz6tw0NnhocQYenBkcorKefk77mm9VM+joXDd8V55g/vPTM16SviyXw55OjR4/y0Y9+lO3bt6/o/V56apn0tWC8uamMWy9dt+D0FRqGfEGHpwZH0OGpwRH0eK5lNLSBc8wfGjxXc5mykNjieVp0xpYiH78CCoEGTw2OoMNTgyPo8VzLaGgD55g/NHgWYlQM4Oyzz17xqBgUznMpXGcMZhYNtR0NnhocQYenBkfQ47mW0dAGzjF/aPDUkgJli6frjJG5m0IDGjw1OIIOTw2OoMdzLaOhDZxj/vDSU0RIJBKrPk46nc6Djfd45ZlIJJZ1o8Wav5syF9atW+e3Qk5o8NTgCDo8NTiCHs+1jIY2cI75w0vP6SkeJiZWtzJNKpVicnIyT1be4ZWniCxr2SrXGQN6eno455xz/NZYEg2eGhxBh6cGR9DjuZbR0AbOMX946SkiM5OprobOzk4VdWmLp7tMCfzwhz/0WyEnNHhqcAQdnhocQY/nWkZDGzjH/KHBU4Mj2OPpOmPAE0884bdCTmjw1OAIOjw1OIIez7WMhjZwjvlDg6cGR7DH03XGsGeekaXQ4KnBEXR4anAEPZ5rGQ1t4BzzhwZPDY5gj6fqGfife+65fqBztccZHBysr62tHciDkqdo8NTgCDo8NThCwT3P2bx5c0OBPstT8hW/QMd3xTnmDw2eGhzBF895Y5jqzpjD4XA4HA6HdtxlSofD4XA4HA4fcZ0xh8PhcDgcDh9xnTGHw+FwOBwOHzktOmMi8s8i0icirbPKakXkWRHpyP6tyZaLiDwoIgdFpFlELi+Q41ki8nMR2SsibSLyF7Z5ikixiPxaRPZkHe/Olr9JRF7OOn5HRCLZ8qLs64PZ7ed67TjHNygir4nIUzZ6isjrItIiIrtFZGe2zJr2nuVZLSLfF5F92e/n1TZ6rlVc/Mqrp5oYZnv8yn629TFMS/w6LTpjwEPA++eU3QU8Z4y5AHgu+xrgRuCC7OMTwN8XyHEK+CtjzEXAVcAdIvJmyzwngeuMMZcAlwLvF5GrgHuB+7OOQ8CW7P5bgCFjzPnA/dn9CslfACKRK3QAAAcZSURBVHtnvbbR81pjzKXGmCuyr21q72m2As8YYzYBl5CpUxs91yoP4eJXvtAUwzTEL7A/humIX8aY0+IBnAu0znq9H1iffb4e2J99/g/ArfPtV2DfJ4HrbfUESoFdwJXAABDKll8N/CT7/CfA1dnnoex+UiC/M8n8I7sOeAoQ2zyB14H6OWVWtTdQCRyZWx+2ea71h4tfnjhaG8M0xK/s51kdwzTFr9NlZGw+mowxJwCyfxuz5RuArln7dWfLCkZ2mPky4GUs88wOne8G+oBngUPAsDFmeua82R4zjtntUaDOa8csDwCfA9LZ13UWehrgpyLyqoh8IltmVXsD5wH9wL9kL5n8k4iUWeh5umFt/dscv7J+GmKYhvgF9scwNfHrdO6MLYTMU1awydhEpBx4HPiMMSa22K7zlHnuaYxJGWMuJfPL7W3ARYt4+OIoIjcDfcaYV2cXL+LiV5u/wxhzOZmh8TtE5JpF9vXLMQRcDvy9MeYyIM5vhvTnw9d/Pw4Xv5bC9himKH6B/TFMTfw6nTtjvSKyHiD7ty9b3g2cNWu/M4HjhRASkTCZQPaIMWZ6wSzrPAGMMcPAf5DJD6kWkdA8HjOO2e1VwGAB9N4B/J6IvA48Rmao/wHbPI0xx7N/+4AfkPmPwbb27ga6jTEvZ19/n0xws83zdMO6+tcUv8DqGKYifoGKGKYmfp3OnbFtwG3Z57eRyXGYLv+T7F0VVwHR6eFMLxERAb4N7DXGfMNGTxFpEJHq7PMS4L1kkiF/Dnx4Acdp9w8Dz5vshXgvMcZ8wRhzpjHmXOCj2c/9uE2eIlImIhXTz4EbgFYsam8AY0wP0CUiF2aLNgPttnmehlhV/xriV9bT+himIX6BjhimKn4VIjHN7wfwKHACSJLp+W4hc039OaAj+7c2u68A/5NMHkELcEWBHN9JZji0GdidfdxkkyfwFuC1rGMr8KVs+XnAr4GDwPeAomx5cfb1wez283xo+/cAT9nmmXXZk320Af8lW25Ne89yvRTYmW33HwI1Nnqu1YeLX3n1VBXDbI1fs3ysj2Fa4pdbm9LhcDgcDofDR07ny5QOh8PhcDgcvuM6Yw6Hw+FwOBw+4jpjDofD4XA4HD7iOmMOh8PhcDgcPuI6Yw7rEZH/S0R6RWRURJY9s7SI3CAiP8yTyxMiMnedQIfD4ZgXF78cueA6Y45lISKvi8h7C/h5YeAbwA3GmHJjzEkROVdEfi4iYyKyLwef/w7cM+uYRkTOn/M5XxGRh3NQugf42+Weh8Ph8B8Xv1z8shXXGXPklVkzROeLJjLz6LTNKnuUzFxBdcB/Ab4vIg0L+PwOUGWMeSkfMsaYXwOVInJFPo7ncDjswcUvh1+4zpgjZ0TkfwFnAz/KDrl/Lvsrz4jIFhE5CjwvIu8Rke457535RSoiARG5S0QOichJEfmuiNTO83kbgf3Zl8Mi8ny27HLgy8aYcWPM42Qm5/vQAto3Ar9Y5nl+Lnt+04+kiDw0a5f/AD6wnGM6HA5/cfFrhv/AxS/rcJ0xR84YY/4YOAr8bnbI/b5Zm99NZsHd9+VwqE8Dv599zxnAEJlZj+d+3gHg4uzLamPMddnXh40xI7N23TNrv7n8Nr8JiDlhjLkve37lZM6pH/jurF32Apcs55gOh8NfXPyawcUvC8n3kKzj9OUrxpg4QGaZukX5P4FPGWO6s/t/BTgqIn9sjJla4r3lQHROWRTYsMD+1cDIPOW7RCQ963UxmUVkZ8iuXfdDYKsx5t9nbRrJHtfhcKwNXPxy+IrrjDnyRdcy9j0H+MGcYJIik19xbIn3jgKVc8oqmT9gQeZXa8U85ZcbYw5Ov8gG1PPn7PNtYL8x5t455RXA8BKeDodDDy5+OXzFXaZ0LJeFFjOdXR4HSqdfiEgQmJ2g2gXcaIypnvUoNsYsFcggkwh7nojMDlCXcGqC7GyagY05HPcUROQu4EIyizLP5SIylxYcDocuXPxy8ctKXGfMsVx6gfOW2OcAUCwiH8je2v1fgaJZ278F/K2InAMgIg0i8sFcPjybh7Eb+LKIFIvIHwBvAR5f4C3/Tia3I2dE5EayeSHGmPF5dnk38OPlHNPhcFiBi18uflmJ64w5lsvXgP8qIsMi8tn5djDGRIFPAv9EZtg+Dsy+O2krsA34qYiMAC8BVy7D4aPAFWSG8O8BPmyM6V/AZRcQFZHlHP8jZH4J7511R9K3YOZW83j2FnGHw6ELF79c/LISMWahUVuHY20gIjcAnzTG/H4ejvU48O05CbEOh8PhCS5+nR64zpjD4XA4HA6Hj7jLlA6Hw+FwOBw+4jpjDofD4XA4HD7iOmMOh8PhcDgcPuI6Yw6Hw+FwOBw+4jpjDofD4XA4HD7iOmMOh8PhcDgcPuI6Yw6Hw+FwOBw+4jpjDofD4XA4HD7y/wN8vZfy6N1SFwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10, 5))\n", "for ax, sample_freq_var in zip([ax1, ax2], \n", " [sample_freq, 2 * sample_freq]):\n", " f0s = np.linspace(83, 639, num=100)\n", " cepstrum_f0s = []\n", " for f0 in f0s:\n", " signal = make_harmonic_wave(f0, sample_freq_var, frame_size, n_harmonics=10)\n", " cepstrum_f0s.append(cepstrum_f0_detection(signal, sample_freq_var))\n", " ax.plot(f0s, cepstrum_f0s, '.')\n", " ax.plot(f0s, f0s, label='expected', alpha=.2)\n", " ax.legend()\n", " ax.set_xlabel('true f0 (Hz)')\n", " ax.set_ylabel('cepstrum based f0 (Hz)')\n", " ax.set_title(f'sampling frequency {sample_freq_var} Hz')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be seen above, the \"staircase\" effect is still there for higher frequencies, but later, and some low frequencies are now failing the detection. It seems that (as often in DSP) everything is about tradeoffs. This sort of benchmark also highlights the fact that maybe a better way of using the algorithm would be to use it as an initial estimate for a more precise f0 estimator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's it! I hope you've had fun following along while I tried to find my way round cepstral analysis for pitch tracking. I'm now going back to my project and will try to integrate this algorithm into my pitch tracker." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This post was entirely written using the Jupyter Notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20191025_CepstrumTutorial.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20191025_CepstrumTutorial.ipynb).*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }