{ "metadata": { "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5-final" }, "orig_nbformat": 2, "kernelspec": { "name": "python3", "display_name": "Python 3.8.5 64-bit (conda)", "metadata": { "interpreter": { "hash": "97ae724bfa85b9b34df7982b8bb8c7216f435b92902d749e4263f71162bea840" } } } }, "nbformat": 4, "nbformat_minor": 2, "cells": [ { "source": [ "# Sequency Basics" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#standard set of imports that save us time in the future\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "\n", "from hotstepper import Steps,Step\n", "import hotstepper as hs\n", "from hotstepper import Sequency" ] }, { "source": [ "If you are familar with Fourier analysis, the concept of Sequency analysis will be easy. If you are not familiar with Fourier analysis, I recommend a very friendly and accessible introduction at [Medium](https://medium.com/sho-jp/fourier-transform-101-part-1-b69ea3cb4837).\n", "\n", "With a [Fourier transform](https://en.wikipedia.org/wiki/Fourier_transform), we start by assuming we can decompose the dataset into simplier pieces, which in the case of Fourier Analysis, are Sine and Cosine functions that are at different frequencies and different amplitudes. As a simple example, we will generate a test signal and investigate how a decomposition would work and ultimately, what do we get for our trouble.\n", "\n", "We will specifically be using the Discete Fast Fourier transform as implemented within [Numpy](https://numpy.org/doc/stable/reference/routines.fft.html#module-numpy.fft).\n", "\n", "\n", "Why would we want to perform a Fourier transform? what we get is the ability to understand if there is recurring patterns in the data, how often they occur and how strong they are. As a bonus, we can also remove noise and possibility unwanted parts of the data using the same techniques. This may seem obvious is our data is fairly simple, sometimes however, the data is very noisy and there may be many overlapping repeating patterns that may be difficult to spot by eye.\n", "\n", "We'll jump into a brief example and then cover the details before we move on. For this example, we will only need the power of HotStepper.\n", "\n", "We will use a test function with three differente frequencies and also a linear term so we can see what happens when there is a component that isn't recurring at some regular interval.\n", "\n", "Our test function;\n", "$f(t) = t+sin(20t)+3sin(5t)-\\frac{sin(15t)}{2}$\n", "$\\; t \\in \\mathbb{R}$." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Test function\n", "two_pi = 2*np.pi\n", "test_function = lambda t: np.sin(20*t) + 3*np.sin(5*t) - 0.5*np.cos(15*t) + t\n" ] }, { "source": [ "We also need to create a range over which we will investigate this function, we will use the proper terminology to ensure we are clear as to why things are the way they are." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# How many time points are needed i,e., Sampling Frequency\n", "samplingFrequency=50\n", "\n", "# At what intervals time points are sampled\n", "samplingInterval=1/samplingFrequency\n", "\n", "# Begin time period of the signals\n", "beginTime=0\n", "\n", "# End time period of the signals\n", "endTime=5\n", "\n", "# Time points\n", "time=np.arange(beginTime, endTime, samplingInterval)" ] }, { "source": [ "Let's have a look at the seperate components of this test function, believe me we will need to understand this simple function better in order to appreciate what is about to be shown." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "fig, ax = plt.subplots(nrows = 3, figsize=(12,6))\n", "plt.subplots_adjust(hspace=0.8)\n", "\n", "# 3*np.sin(5*t) component\n", "ax[0].plot(time,3*np.sin(5*time))\n", "ax[0].set_title(r'$3sin(5t) \\; component. \\; f = \\frac{5}{2\\pi}$');\n", "ax[0].axhline(0,color='grey',alpha=0.5)\n", "\n", "# -0.5*np.cos(15*t) component\n", "ax[1].plot(time,-0.5*np.cos(15*time))\n", "ax[1].set_title(r'$-0.5cos(15t) \\; component. \\; f = \\frac{15}{2\\pi}$');\n", "ax[1].axhline(0,color='grey',alpha=0.5);\n", "\n", "# np.sin(20*t) component\n", "ax[2].plot(time,np.sin(20*time))\n", "ax[2].set_title(r'$sin(20t) \\; component. \\; f = \\frac{20}{2\\pi}$');\n", "ax[2].axhline(0,color='grey',alpha=0.5);\n", "\n" ] }, { "source": [ "To better future proof this discussion, we will also calculate something that may seem odd at first, but it will make complete sense in a moment when we unleash the Walsh transform on the test function.\n", "\n", "So firstly, we will calculate the actual frquencies of these components. Whilst correct and all nice, the formula representation doesn't help when we are looking at a chart and looking for the value of $\\frac{5}{2\\pi}$, therefore $\\frac{5}{2\\pi} = 0.796 Hz$. Now for the rest and in a nicer layout for quick reference later.\n", "\n", "We will also calculate the number of zero crossings of each component, this specifically means, how many times does the function **cross** over zero, not the same as how many times is it zero, as they all start at zero.\n", "\n", "We can use alittle math to figure this out, as we know that the Sine function is zero whenever the argument is a multiple of $\\pi$, Cosine is the same, with an offset of $\\frac{\\pi}{2}$ from the start.\n", "\n", "Using these details, we have calculated the decimal frquencies and sequency numbers for each component." ], "cell_type": "markdown", "metadata": {} }, { "source": [ "Test function component frequency values." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Component Frequency (Hz) \n3sin(5t) 0.8 \n-0.5cos(15t) 2.39 \nsin(20t) 3.18 \n" ] } ], "source": [ "test_function_comp_freqs = {}\n", "test_function_comp_freqs['3sin(5t)'] = round(5/(2*np.pi),2)\n", "test_function_comp_freqs['-0.5cos(15t)'] = round(15/(2*np.pi),2)\n", "test_function_comp_freqs['sin(20t)']= round(20/(2*np.pi),2)\n", "\n", "print (\"{:<15} {:<15}\".format('Component','Frequency (Hz)'))\n", "for k, v in test_function_comp_freqs.items():\n", " print (\"{:<15} {:<15}\".format(k, v))\n" ] }, { "source": [ "Test function component sequency values." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Component Sequency \n3sin(5t) 7 \n-0.5cos(15t) 23 \nsin(20t) 31 \n" ] } ], "source": [ "test_function_comp_seqs = {}\n", "test_function_comp_seqs['3sin(5t)'] = np.ceil(5*two_pi*test_function_comp_freqs['3sin(5t)']/np.pi)-1\n", "test_function_comp_seqs['-0.5cos(15t)']= np.ceil(5*two_pi*test_function_comp_freqs['-0.5cos(15t)']/np.pi)-1\n", "test_function_comp_seqs['sin(20t)']= np.ceil(5*two_pi*test_function_comp_freqs['sin(20t)']/np.pi)-1\n", "\n", "print (\"{:<15} {:<15}\".format('Component','Sequency'))\n", "for k, v in test_function_comp_seqs.items():\n", " print (\"{:<15} {:<15}\".format(k, int(v)))\n" ] }, { "source": [ "## Fourier Transform" ], "cell_type": "markdown", "metadata": {} }, { "source": [ "Now we have setup everything we need to generate some data and let HotStepper to do the heavy lift, let's rip the bandaid off and get some plots, let the understanding, begin!" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# Generate test function data\n", "data = test_function(time)\n", "\n", "# Create subplot\n", "figure, ax = plt.subplots(nrows=2,figsize=(16,12))\n", "\n", "# Time domain representation of test function\n", "ax[0].set_title('Periodic Signal')\n", "ax[0].plot(time, data)\n", "ax[0].set_xlabel('Time')\n", "ax[0].set_ylabel('Amplitude')\n", "\n", "# Our Sequency object we will use for all our analysis\n", "sequency = Sequency()\n", "\n", "# Perform FFT on the test function data\n", "frequencies, spectrum = sequency.frequency_spectrum(data,two_pi*samplingFrequency)\n", "\n", "# Frequency domain representation of test function\n", "ax[1].set_title('Fourier transform showing the frequency components')\n", "ax[1].stem(frequencies[:30], spectrum[:30] )\n", "ax[1].set_xlabel('Frequency (multiples of $\\\\frac{1}{2 \\pi}$)')\n", "ax[1].set_ylabel('Amplitude');\n" ] }, { "source": [ "In the stem plot we can clearly see the spikes at 5, 15 and 20, just as we would expect, since those are the frequencies we constructed the test function with. We can also note that the relative size of the spikes are 5, 20 and 15, which also makes sense, since we assigned amplitudes of 3, 1 and 0.5 respectively to each of those components, this relative \"strength\" within the test function was also extracted by the Fourier transform. What is getting interesting is the strong spike at 0, where did this come from? the simple answer is it comes from the straight line we added at the start of the test function (the t out on it's own at the end of the equation). This linear term doesn't cycle through the same values as the value of t increases, as it grows linearly or in a straight line, therefore it has a frequency of 0, since it doesn't repeat at all, nice!" ], "cell_type": "markdown", "metadata": {} }, { "source": [ "## Walsh Transform" ], "cell_type": "markdown", "metadata": {} }, { "source": [ "Wait, I thought we were talking about Sequency Analysis, what is the Walsh transform? In the realm of Sequency Analysis, the Walsh transform plays the role of the Fourier transform, with a few differences. It is those delicious differences that make this investigation worth the effort, as the Fourier transform is awesome, no doubt, but it does have some hang ups if we give it data that doesn't play nicely in terms of smoothness and jumpiness? is that a word, it is now. We will have a look at the younger but less well known brother of the Fourier transform, the Welsh transform and will show how whilst Fourier is all that and a bag of potato chips, there are some cases (actually quite a few) where we should use a different method and will be rewarded with more insight and a clearer picture of the nature of the data. Anyways, enough woffling.\n", "\n", "The Walsh transform is defined as the sequency ordered Hadamand transform, which is nothing more than a matrix full of -1 and 1's arranged in order of increasing sequency number. Ok ok, sequency number, wtf is that? If we start with the definition of [frequency](https://en.wikipedia.org/wiki/Frequency#:~:text=Frequency%20is%20the%20number%20of,a%20repeating%20event%20per%20second.), in simple terms, the number of times a pattern repeats within an interval T, usually a unit interval of time, such as a second and is defined as;\n", "\n", "$f = \\frac{1}{T}$\n", "\n", "Fair enough, so the definition of [sequency](https://mathworld.wolfram.com/Sequency.html) is similar, except we just use the idea of crossing **through** zero, the number of zero crossings within a given interval.\n", "\n", "So we can define sequency as;\n", "\n", "S = # of crossing through 0\n", "\n", "We can also define the Walsh transform in a manner similar to the Fourier transform, with the bonus that it is a much simplier evaluation. Ok, enough talk, that all sounds good, but get to the Sequency analysis and why I've bothered to read this far, so without further delay, let's have a look at a Walsh transform of our test function." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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}, "metadata": { "needs_background": "light" } } ], "source": [ "# Generate test function data\n", "data = test_function(time)\n", "\n", "# Create subplot\n", "figure, ax = plt.subplots(nrows=2,figsize=(16,12))\n", "\n", "# Time domain representation of test function\n", "ax[0].set_title('Periodic Signal')\n", "ax[0].plot(time, data)\n", "ax[0].set_xlabel('Time')\n", "ax[0].set_ylabel('Amplitude')\n", "\n", "# Perform FWT on the test function data\n", "sequencies, spectrum, sc = sequency.sequency_spectrum(data)\n", "\n", "# Sequency domain representation of test function\n", "ax[1].set_title('Walsh transform showing the Sequency components')\n", "ax[1].stem(sequencies[:35], spectrum[:35] )\n", "ax[1].set_xlabel('Sequency')\n", "ax[1].set_ylabel('Amplitude');\n" ] }, { "source": [ "Now we know why we calculated the number of zero crossings for the components of the test function, remember what they are?, 7, 23 and 31. From the sequency spectrum above, we can see strong sequency components at 7, 23, 31. These represent the same components, but they are now represented via Walsh functions and instead of frequency, we have their sequency numbers.\n", "\n", "It can also be seen, just as with the Fourier transform, the linear term appears as a strong sequency 0 component and as before, there are a few other terms with some strength at sequency 1 and 3. These represent the same components detected by the Fourier transform, while these components weren't explicitly included, they are present due to the presence of the linear term. The easiest way to see this is to simply remove the linear term and look at the Fourier and Walsh transforms to see the difference.\n" ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# Remove the linear term from the test function\n", "data = test_function(time)-time\n", "\n", "# Create subplot\n", "figure, ax = plt.subplots(nrows=3,figsize=(16,12))\n", "plt.subplots_adjust(hspace=0.4)\n", "\n", "# Time domain representation of test function\n", "ax[0].set_title('Periodic Signal')\n", "ax[0].plot(time, data)\n", "ax[0].set_xlabel('Time')\n", "ax[0].set_ylabel('Amplitude')\n", "\n", "# Our Sequency object we will use for all our analysis\n", "sequency = Sequency()\n", "\n", "# Perform FFT on the test function data\n", "frequencies, spectrum = sequency.frequency_spectrum(data,two_pi*samplingFrequency)\n", "\n", "# Frequency domain representation of test function\n", "ax[1].set_title('Fourier transform showing the frequency components')\n", "ax[1].stem(frequencies[:30], spectrum[:30] )\n", "ax[1].set_xlabel('Frequency (multiples of $\\\\frac{1}{2 \\pi}$)')\n", "ax[1].set_ylabel('Amplitude');\n", "\n", "# Perform FWT on the test function data\n", "sequencies, spectrum, sc = sequency.sequency_spectrum(data)\n", "\n", "# Sequency domain representation of test function\n", "ax[2].set_title('Walsh transform showing the Sequency components')\n", "ax[2].stem(sequencies[:35], spectrum[:35] )\n", "ax[2].set_xlabel('Sequency')\n", "ax[2].set_ylabel('Amplitude');" ] }, { "source": [ "See, all gone! So now we know all about the Walsh transform and how it is related to the Fourier transform, we can see that it can handle non-step data pretty well, but what it really does well is performs this type of component analysis with proper step data. Let's generate some and take a look.\n", "\n", "So that all seems reasonable and all that, it also doesn't seem overly impressive on our test function, as our Fourier transform provided clearer insight as to the frequency components present and to be frank, the spectrum stem plot was prettier! That's fair enough, we also mentioned that Walsh transforms are not always the best, in this case, the data is actually made of Sine and Cosine functions and is therefore better decomposed with a Fourier transform. Now for the rub, what if we have step data, you know, like the kind HotStepper deals with for breakfast? Well, in that case, Walsh transform is more suited, we can see this with a simple example." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Test step function\n", "steps1 = [Step(start=n,end=n+1.5, weight=(-1)**n) for n in range(1,10)]\n", "steps2 = [Step(start=n,end=n+2.5, weight=(-1)**(n+1)) for n in range(1,20)]\n", "steps3 = [Step(start=n,end=n+3.5, weight=(-1)**n) for n in range(1,18)]\n", "\n", "test_steps = Steps().add(steps1);\n", "#test_steps.add(steps2)\n", "#test_steps.add(steps3);" ] }, { "source": [ "So if we have a look at our test step function and count the number of zero crossings, we count 16 (don't count the first and last zero, as they are not crossing). Now we have an interesting observation, if we use the step values directly in the sequency spectrum analysis, we get a symmetric spectrum. This seems reasonable as the steps data is completely repeating and symmetric around the center of the peaks or troughs. If we use the step change values instead, which represent the delta values between step keys, we see the sequency spectrum is exactly half that of the step values, nice!\n", "\n", "Now if we look at the sequency spectrum for the step change, as it is usally of more interest to look at how the step values change instead of their direct values, most of the power is at the 16. There is some at the 17, this comes about due to the way this step function holds the zero value for a moment before the next step change, the creates the need for a small offset, which appears for this step funciton, to be at a sequency number of 17." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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}, "metadata": { "needs_background": "light" } } ], "source": [ "# # Create subplot\n", "figure, (ax,ax2, ax3) = plt.subplots(nrows=3, figsize=(16,12))\n", "plt.subplots_adjust(hspace=0.4)\n", "\n", "# Our test steps data\n", "test_steps.plot(ax=ax)\n", "ax.set_title('Periodic Step Signal')\n", "ax.set_xlabel('Time')\n", "ax.set_ylabel('Amplitude')\n", "\n", "# Perform FWT on the test function data\n", "sequencies, spectrum, sc = sequency.sequency_spectrum(test_steps.step_values())\n", "\n", "# Sequency domain representation of test function\n", "ax2.set_title('Walsh transform of Step Data (values)')\n", "ax2.stem(sequencies, spectrum )\n", "ax2.set_xlabel('Sequency')\n", "ax2.set_ylabel('Amplitude');\n", "\n", "# Perform FWT on the test function data\n", "sequencies, spectrum, sc = sequency.sequency_spectrum(test_steps.step_changes())\n", "\n", "# Sequency domain representation of test function\n", "ax3.set_title('Walsh transform of Step Data (changes/deltas)')\n", "ax3.stem(sequencies, spectrum )\n", "ax3.set_xlabel('Sequency')\n", "ax3.set_ylabel('Amplitude');\n" ] }, { "source": [ "## Denoising (Fourier and Walsh)" ], "cell_type": "markdown", "metadata": {} }, { "source": [ "Let's do some denoising with both Fourier and Walsh transforms. We will see that they are both pretty good on our test function, however the nature of the data comes into play, as you will see in a moment. Fourier for smooth data, Walsh for step data, this will be clear in a moment, as the denoising will show the preference each transform method has when processing the data." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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isCOJlr2ug6xWMPHKsCMR8ZS4ioiISEIsfR4mnO1LeQ99GLKyE3esvX/nk48pv03cMST9OAez/wWd9oTOe4cdTbS06Q67/dSffPrig7CjEVHiKiIiIgmw4g147VQo2sN3EG7VNrHH67ArDDwf5twOm1Ym9liSPlZ9BGunwpDv+LJz+ardfub3Tf7opz7JFwmTElcREZEMVV0J62bAZ6/D/AdhyTOwZX384y54BF4eB+37w1EvQm5h/GM2xR6/gNot8OlNyTmepL45t0NOWxhwdtiRRFOrdjDyOlj5Lix+MuxoJNPlhB2AiIiIJFddLcy6BSb9yievDVkWFO3lO/8OPLd529bUbPZ7qs6+FbrsC4c/Dvmdg419RwpLoN94/9x2/znkdUjesSX1VJXBgodgwDmQWxB2NNFV8k2Y8Tf/3u4xNnknokS2pRlXEZEEq62CJc/62awVb8Dqyf42kTCsngzP7AsfXAZdD4BDH4JjJ8CpM+HYN2DPX/v9Uaf9AR4bCk/vB7N3Un5bVwPLXoRn9vNJ624/hXFv+TVyybbHL6G6wievIjsy736o2ejLhKVxWTlw4B2wYSm88x2VDEt4zKXQq2/UqFFu4sSJYYchItIkdTX+g9Env4HKRV/9Xodd4ZD/QOe9QglNMtSyF30Jb35n2Pdv0O/0xtf1bVrpX7+ld8P6mf62opHQ62hfAmxZYNmwZgos+K+/f34XOOhu6DMuaU9pu14e55vJnLE48WtrJXU9va8vLT/5k7AjSQ1TbvBVGgfeCYMvin+8qjJY9DgseBhqKqFNL2jbC7ruB8WnaM1xJjOzSc65UV+7XYmriEjwvvgA3roAyub45HTPq6FND6gu92etJ/7Kf9AfcRXscaXfckAkkSoWwZMjoV1vP7Oa17Fpj3PON69Z+rxPfL94D1zt1u9ntYLe43xZce/j/Gxt2Fa+B88eAPv8FYZfHnY0EkUVi+CRfjDq97DHz8OOJjW4OnjxKL/e9cSJ0HFoy8ZZPwcmXwNLnvQnDtr3h3Z9YMMyf6nd7NccH/Avv8ZWMo8SVxGRJPnsNXjlRGjdFUb/Cfqe/PUzx1vWwfs/8PsHdh8LR7+o5FUSp2YzPHcglM+DEydBwYCWj1VVAVXrffLq6iC/KJpr3p4b45/v6fOjkUxLtEz7I3x8BZy+ANr3Czua1LHxc3hiD19dcezr/u9cU21ZB59cBzP/ATltYND5PkHtss/Wv5GuDqb+DiZfDQWDYOz/oNNuiXkuEl2NJa5a4yoiEqAlz8DLx/kPQuPea7zcKa8jjLnfrxta8Tp8/IvkxyqZ4/0fwOpJvjw9nqQVILe9n7VtXwwF/aOZtIJf67pxOcz7T9iRSBQtfNjv26qktXna7AJjHoCK+fDUKP97ZWdqt8Cnf4NHS3yTp5Jvwvi5sN/N0HXfr/6NtCzY81dwzGu+lPjpfWDN1MQ9H0ktSlxFRAKy8FF49RTouDsc96b/A78zg78FQ38An/7FP14kaPMfhNI7YY9fQZ/jw44meXoeAZ1HwdTf+/XmIvXK5/uEq/8ZYUeSmnoeDuPeBcyX5M+9b/v3q6uB0nvgfyXw4eX+b+NJk+HAf+18prb7GH/f3AJ463w1NBRPiauISABWvgtvnANd94FjXoW8Tk1/7Og/+a1D3r7Qr/0RCUpdtW+mUjQSRv4m7GiSy8zPulbM10kh+aqFj/jrfuPDjSOVdR7p17l23d8nlg/18X8DZ/4TplwPLx4N93eCt78JrbvB0a/Asa9B0Z5NP0ab7n6d69qpMPX6hD0VSSFa4yoiEqeKhfD0aMjtCCd80Lyktd6GZfDkCMjv6tcg5uQHH6dknjl3wjvfhiOfg97Hhh1N8rk6eHw4WA6cPMWXIYo8MQJyWsPx74UdSeqrq4HSu+Cz12Hl27Bxhb+9wzDY5SD/e6f3uPg6BL/5DZj/XzjhI58wS/rTGlcRkQSoKvNbb9TVwpHPtixpBb8FwMH3+W1HZt4cbIySmWq3wCf/5xuf9Dom7GjCYVmw+5WwbjosfS7saCQKykph7RS/FZTELyvH74M79mE4czmcvgjOWQ2nfgoH3OqXJ8S7rc2+f/Oztm9+w/9ek8ylxFVEpIXqamDCmf6D0GGPQmFJfOP1PsafmZ5yPWz6IpgYJXOV3g0blsDI6zJ7P8QBZ0K7Yv++SqEiM0mQBSoTThgzaN/XdxoPUl5Hv3fs+hkwQyd2M5oSVxGRFvrwJ35fy/3/CT3GBjPm6D9CzQaYfG0w40lmqtnsE7VuB/gmRZksqxXsfgWs+hCWvxJ2NBK2hY9AtwOhbc+wI5Hm6H0M9DgcZtykRk2ZTImriEgLzLrVl/QO+xEM+XZw43YYArt+D+b8C9bNCG5cySxz7vBbwWT6bGu9km9Cu74w8Uq/7lUyU/k8XzZefFrYkUhL7PYz2PiZX+8qmUmJq4hIMy1/xe+L2fs4P0MatBHXQKv28NHPgh9b0p+r87MS3Q6E7oeGHU00ZOf5JH7NZHUYzmSLnvDXfU8KNQxpoZ5HQKfdYfqfVPafqUJPXM0s28w+MbNnw45FRGRn1kyF18dDh6Ew5kHIyg7+GPmdYc+rYNkLsPzV4MeX9LbiTahY4GfuNdu61YBzoONwvz1QXXXY0UgYFj8BRSP8OkxJPWYw/Kd+reuyF8OORsIQeuIKXAbMCjsIEZGdWTsdXjjMz4Ye8Qzktk/csYZeCm16wpTfJu4Ykp5K74TcDtD35LAjiZasbBh1gy8XnXNX2NFIsm1cAV98oPdFqhtwpv/bOD0B1U4SfaEmrmbWCzgOuDPMOEREdmbdDJ+0ZufBsRMSf8Y+Ow92+yl8/iasfDexx5L0sWUdLHrMzy7mtA47mujpPc43rPrkN1CzMexoJJmWPA04Ja6pLqsVDL8cVkyA1ZPCjkaSLewZ15uAK4BGWyWY2cVmNtHMJq5atSppgYlI6nEONiyDZS/BjL/Doie3boYejzVT4fmxfr+6YydAwcD4x2yKwd/2ZcNTbkjO8ST1zf+v3+ew5KKwI4kmMxj1e9j0OUz9XdjRSDItesL/7u44LOxIJF6DL4ZWBfDpX8KORJItJ6wDm9k44Avn3CQzG9PY/ZxztwO3A4waNUpLsUXka5yD2bfBpF/DlrVf/37b3r6pw6ALfMOapq77q6v1TSAmX+33pTvm9fj3am2OVm1h2OX+ea2ZAkV7Ju/YkppK7/Jr+DqPCDuS6NrlQBj4DZ+49jkeuowOOyJJtKoyWPE6DLtM677TQW6BryqZew9UlfuvJTOEOeN6AHCCmS0CHgLGmtn9IcYjTVSzya8TWfay78648DF/hl8kDFvWwmunwnvf9x/Y97vFz4qeuRzGvQv7/BW67uf37nvuYPjfIL9H6tppjXcldM5///lDYOIv/Ifbk6f5rWqSbddL/JnlqZp1lZ1YPRnWfKLZ1qbY72Zo0wPePE8lw5lg6fO+IZfKhNPHwPOgdjMsejzsSCSZzEWgn3RsxvWnzrlxO7rfqFGj3MSJE5MSk2zf4qfhgx9C5eKv3t5+AOzzZ+hzgs5mSvKsngSvnuzL/kb93q97sUZOx1Vv8H/g5t4DK94AHLTv57e0adsbcjtCq3b+pMzS56BiPuQW+kR4wNnhvq4n/hKm/h5OnQUdBocXh0Tbe5dA6d1w1meQ1zHsaKLvs9f9uvWhl8J+f49/vJpN/gTZwv9BbZVfi5fVym+9Muh8/W0M0+unw+dv+fdGY38jJLU4B4+WQNs+cOxrYUcjQTOzSc65UdveHlqpsKSWikV+38qlz0KHYTD2EX+2ulV7qFwKH/8MXj0JehwBB90J7fqEHbGkuy3r/GuOLBj3HnT52q+3r2rVFgad5y+bVsKSZ2DxkzDnTn/Wtl52PvQ43DdGKj4ZWndL4JNoomGXw6c3wbQ/wMF3hx2NRFHtFr++tfhUJa1N1WOsf2/NuAl6Hw+9jmzZOBuWwfS/wNx/Q9U6aN8f8ruCq/EVIUuegnn3wQH/gsJBAT4BaZKazX5rsf5nK2lNJ2Yw4FzfaG3DMmjbK+yIJBl2OuNqZm2AnwB9nHPfNrNBwGDnXNL3XdWMazjWTvONaeq2wIhrYdgP/VnkhuqqYdatfi1e215w/Pt+tkokEZyDCWf4ZhvHvwdd9o5vrJoNPhGuKoOC/pDTJrhYg/L+ZTDrnzB+nvYglK9b+gK8fCwc+Rz0PjbsaFJHzSZ4ahRsWAqHP+mT2SY/djN8+mdfxl9bBcWn+L1zdzlk6+yqq/Mnxz6+wp8gG/0XGPr9hDwVacSS5+CVcXDUC9Dr6LCjkSCVz4f/DfQVV3v8POxomq9iEayeCJWL/L/zu/jP2Dr52PiMa1POPd0DbAH2i329HNDOghmiPmnNaQ0nfQK7/eTrSSv424b9EA5/CsrmwoQzoa4m+fFKZpj7b1+Ot9f/xZe0gv+A2aodtOsNnYZHM2kFPwNsBp/+KexIJIoWPebXQvc4LOxIUktOazj6ZWjXF146GhY8vPPHuDrf3+Hxof5kba+jYXwpjH0Yuo/5akmwZcGQi32Zf/ex8P6lsPzVhD0d2Y7FT/j3RvdmnJSQ1FAwALruD/P+03jPiqha+Cg8NgReHw8f/Qzm3+9njx8ZANP+6E+qydc1JXEd4Jy7EagGcM5tBLRSIwOsne7X/+S0hmPfaNoWID0Ohf3/Ccte9G9EkaCVzfVl693HwG4Z9Bpr19t3Qp1zpy91FqlXV+PLUfuM8/v/SvO07QnHve2buE0403cbrir7+v3qamHBI/DEHv7DZnYbOOZVOOwxv15+R9p0h8Me9Q3e3jxP7+Fkqav1+7f2Pg6yc8OORhJh4HmwfobvvJ8KnPNLC14/HYr2ghMnw3nr/eWkT6Drvr5C49EhsH5W2NFGT1MS1yozaw04ADMbgJ+BlTRWPt8nrVl5sX0rBzT9sUO+7VvOz7gJ5tyVsBAlAzkHb38TsnLhkP9AVnbYESXX7j+Huir49K9hRyJRsvId2Lwa+p4SdiSpK68DHPWSL/ed+Et4oAu8dJzfD3rir30TuEf6+yUKdTUw5gE4eWrzZrhz2sChD0PVenjzG37mVhJr5buweZVvkCXpqf/p/jPBvP+EHcnOuTr48Efw0U98P4JjXvVbl9UvrSvaA4563m+9V7cFnj8U1s8ON+aoaUrieg3wItDbzB4AXgOuSGhUEqot6+GV48HVwrGvN22mdVuj/+T/oH94OWxcEXSEkqlWvO4/pI+6PjMbMRQOgn6n+7WuW9aFHY1ExaLHfVMxrd+LT04+jH3UN3sb+kM/i/PBD2Ha7/2Hxy57w6EPwSmf+k7jLTlx1mk32PcmWP6y3yNaEmvxk74KodcxYUciiZLXyc+oL3jQz7BH2Zy7YMbffFO4sQ/7isbt6XGonzQCeH6MkteGmrQdjpkVAfviS4Q/cM6tTnRg26PmTIlXVwMvHQufvwFHvwLdD2n5WOXz4LFhMOAsOPjfQUUomez5sVA2G8Yv8B8yM9Haab5UceR1MOKqsKORsLk6eKiPT6oOfyLsaNKLc1C5BNrsEmwJtnO+THDxk3DaHN8QToLnnJ8l7zgMjkx6O1FJpgUP+zL/496CXQ4KO5rt27TSl/8W7elnVJuyPdb6WX7WFfxyhkzqSt7s5kxmNrL+AvQFVgCfAX1it0ka+uAy+OwV37Y/nqQV/Ezt8B/D3Hv93pgi8Vj5PqyYAMN/mrlJK0Cn3aHP8b5ceHvr8CSzrPoYNi5XmXAimPkO3kGvGzaDff/mGzdN+0OwY8tWa6f6bq0qE05/vY7179NFj4UdSeM++BHUbIT9b2v6ns4ddvUzr67Wd8besjb+OOpqU3uZwo5Khf8cu9wCfAjcDtwR+/ctiQ9Nkm3mP3wJ4m5XQMmFwYy556/8fq/v/yC13ygSvqnXQ14RDPlO2JGEb8S1fr9IrXWVRY+D5fiTGZI62vaAkm/6DukblocdTXpa/KQ/OdDnhLAjkUTLbQ89j/K/D6PYXXjZS76UeY9fQofBzXtsh13hsCf8djmvjffbT8bj07/Ac4dAdWV844Sl0cTVOXeoc+5Q/EzrSOfcKOfcXsAI/JY4kkaWvehnW/ucCHv/LrhxW7WDvW/0+1TN/Xdw40pmWTMFlj7n14W0aht2NOHrPNI3dvj0L7B5TdjRSFicg8WP+34CeR3Cjkaaa/ef+5kUrXVNjMVPQNcDoHXXsCORZCg+1e/HvPrjsCP5qpqN8N73oHAw7PGLlo2xy4Fw4B2+z8d7l7Y8Oa9YBJOv8ZMArdq1bIywNaU502Dn3PT6L5xznwK7Ji4kSbZ1M+D1M6Dj7jDmfn+GMkgDzvb7bH18JVRvCHZsyQxTb/D78A29NOxIomPkdf6MqUoNM9e66b6XQLHKhFNS+2IYeC7M/hds+iLsaNJL+QLfD6D45LAjkWTpc7yvPln0eNiRfNWnN0HFQr8EL55lB4O+Abv/Aubc7k9aN5dz8N4l/jP+fn9veRxha0qKMs3M7jSzMbHLHcC0RAcmybFple8gnNMGjnwmMWdgzHyX4c1fwOzbgh9f0lvFIr9R967f16xSQx2H+g+9M/+hzt2ZatHjgEHfE8OORFpq9yuhdrPfPk6CU7/WUetbM0deR+gx1v/fR6VcuGaTf2/3Oib+vjHgd1ToNx4++imU3tO8xy56FJY9D3v91u8Ln6qakrheCMwALotdZsZukxS3aRW8eKT/0HvE04ndXqTbftDjcJj+R182IdJU8+7z17t+L9w4omjEtX69y5Trw45EwrDocd9Bs3W3sCORluowGPqdBjNv8VvRSTDmPwBdRkP7fmFHIslUfKqvQlk3fef3TYa59/p9hHf/eTDjWZbfw77HEfDOt2BREzvJV5X55YBFI1O/cm2niatzbrNz7q/OuZNjl7865zYnIzhJnI2f+72hymb7LRS67J34Y4642rcDn31H4o8l6cHV+bXRPcZCuz5hRxM9Bf1h8EW+dGj9nLCjkWQqm+s/nKmbcOrb/UqoLlcfiKCsm+E7Cg84N+xIJNn6nuSTuyh0F66LrV/vMhp2OTi4cbPz4PDHofNovwXQ8ld3fH9X5zsab1oJB94OWTnBxRKGnSauZrbQzBZse0lGcOJbXy96Eqbd6M+ur5/t91qNR+VSeO5gqFwMRz6fvE3rdzkIuo+B6X+AGp36kCb4/B2/NmTg+WFHEl0jroWcdvDORercnUkWx860aw1f6us8AjqP8rMzEr/5D4BlQ/8zwo5Ekq11V+h2ECyMQOK6+HGomO9nW5u6/U1TtWoHRz3vGz69dAxMuhpqq75+vy1r4eVxMPceH0fnvYKNIwxNybsbbv6aD4wHOiUmHKk3+w6YdYtvLsA2tfrZedDzSOh/tl+M3tQuq87Bwv/5coGaDXD0S9DtgMBD36E9r4YXxkLpXTD0kuQeW1LP3H/7X9BqPtO4NrvAvn+Fty7w5YbDfhB2RJIMix7zyY4qEdLDoAvg/UthzVQo2iPsaFKXq4P5/4WeR6ibcKYqPhU++KGvQmru1jNBcc43TiwY5HfrSIS8jnDcG/DB5TDl//zJzP1vhYIBfta5fAG8cbbf53v/W9NnK8GmlAqvaXBZ7py7CTgu8aFlprpq3/Xr3Yt9gjryOjjubTh3LZw4EQ6+F4Z8F1ZPhjfOgv92gzfOhSXP7Xhvp4qF8PKxMOEMaNPdj5nspBX8jGu3A2Ha76F2S/KPL6mjuhIWPgL9TtcWODsz8Bu+cmLilf69Lumtcims+sh/QJP00P9MyGqlWdd4rXzPV5MNOCfsSCQs9VUoi0PsLrxiAqyeBLv9FLKyE3ecvE5wyH1wxLN+dvW5g+DBHvDfXeDZ/cHV+M/7u343+FnfsOx0xtXMRjb4Mgs/A5viFdLRtGUdvH46fPYq7HYFjLrhqy/4vL38NP+gb8A+f4HP3/ZnFhc96ktj8or8TGz7fv4sfE5b/+Fm5bt+vUdOa9jnr35hdlg17mZ+reuLR8Lc+2DIt8OJQ6Jv0eO+MmDQBWFHEn1mvtX+48PgnYvh6Jfj/yNVW+U3TF/+qv+DuGWt/yM4+GIoucB/yJZwLH7SX6sSIX3kF0GfE2D+/TD6D3p/tdT8B/wuCeomnLna9oIu+/iqlD2uDCeG6X/2TfMGfiM5x+tzHHSbAUue8l3K62r9rGvxqdC6S3JiSBZzO+kZbWYTGnxZAywE/uycS3orkFGjRrmJEycm+7BJUbMJnt7HN0s64Hb/wbCpaqtg+cs+if3iPdiw3H/ABP8LvMs+fpZz8Lej0QLbOXh6NFSth1NnJ/ZslKSu58f6M+fj56XPmcJEm3Wb3+h85HUw4qqWjVFV5veVnPE32PgZtOnhL3mdYPNqWDMZCgb6Y/Q/I/h9n2Xnnj/Ud4U/9dOwI5EgLXnWb093+FPQ94Swo0k9tVXwYHfoeRQc+t+wo5EwTfsjfHwFnL7Q75ecTBWL4JH+/m/wyN8k99jpxMwmOedGbXt7U+bdLnLOfaUZk5mpwXjAJl/rO0Qe+Rz0PrZ5j83OhT7j/AX8mZZNK/wH0MKS6J25NfObKL9+mj8j1v/0sCOSqKlY7EttRl6npLU5hlzsT15NvhowGPHrpj+2rhbm3AGTfuVnV3scBgfd7as46v8PnIOlz/n7vHE2rHwH9r8lIU9FGrFpFXz+Fuzxq7AjkaD1Ogryu8K8e1Mzca2tgtUfw4o34IsPoPNIGPI9vw4/GZa/7H93qUxYik/1ieuix2G3Hyf32HPu8H8zS76V3ONmiqacK3+0ibdJC636CD79k58RbW7Suj1Z2b5UouOw6CWt9fqe5JPqab+PzkbREh0LHvTXA88LN45UY1lw0D3+5zb5Kvjk/5r2uM/fgaf39rO1HYfDCR/DMa/6D9INTxyY+RNkJ30Cw38Ms/6p7a2SbclTvgGNyoTTT1YrGHguLHnGVzekksVPwQOd4dkDYdKvffXYJ/8HD/eBN78B62clPoa59/olU72OTPyxJNoK+kOnPZO/LU5dtW8+2vu4aFQ4pqNGE1czG2JmpwKFZnZKg8sF+O7CcTGz3mY2wcxmmtkMM7ss3jFTUe0WeOtCX4o3+o9hR5M8Wdl+He+aT/xZUpGGFj0GnfdOfolPOsjKjiWv3/Azr29dAGu3sxm7q/NN3Z4b4xs6bF4Fhz4Ex74BXb5WnPNVlgV73+hL8t6/xK+jl+RY9Di07w+d1Hk2LQ0633/4nf9g2JE03eKn4LXToHAIHPYEnLMaxs+F0+b4ZpKLHvfLg1a8kbgYKhb6ZjwlF0X3hL0kV/GpseVznyXvmIuf8vulDk6TDr5RtKMZ18HAOKADcHyDy0ggiJY6NcBPnHNDgX2BS8xsaADjppQpv4X1M/261tzCsKNJroHnQpueftZVpF7FYlg9UR1T45GV7ct8h/8EFjwMT+wOzx0CU38HH/7UdyJ/bCi8Mg4qFsDoP/n15v3PaHppdlY2HPogtOsLr50KG5Yl9jmJX/7x2at+tlUl9Omp0+7+pMSCFElcFz8Nr4/3jSOPeQWKT/KNpgAKB8F+N/sEtm1vv9/kkucSE8eMvwFZ2g5MtqqvSqlvZpcMs2+Dtn18l39JjEYTV+fcU865C4FxzrkLG1x+6Jx7L94DO+dWOOcmx/5dAcwCesY7bipZP8d/kBx0PvQ+Juxoki87z5cb1q+HEYGtpT39lLjGJSsb9vkTnLXcV3NsWAoTf+nLe79431d5HHI/nD4fdvtJy7YcyusIhz/puz+/dWHgT0G2seRZPxvXV2XCaa3feP8erVwadiQ7tvwV36uiaITfF76xk+9te8Jxb/nlS6+e5E+mBWnLel+e2f9Mv0xKBKDjUF8FkKxy4bK58Nlrftmfmo4mzo5Kha+I/fNsM7t520uQQZhZMTAC+DDIcaNu+p98ScveN4YdSXiGXOy7lTZ1LZ6kv0WP+RmHgoFhR5Ie8jr5veTGz4PzyuH8DT5ZPfZ1GHhO/GV1HYfByP/zM4GJLAUUXwrZpgd03SfsSCSR+o3318len9ccNZvgnW9DwSA4agdJa738znDMa9B1P9/YbdmLwcUy53a/7/duPwluTEkPxafC528mZ834nNvBsmHwRYk/VibbUalw/VL6icCk7VwCYWbtgMeAy51z5dv5/sVmNtHMJq5atSqow4Zu4+cw7z6/R2XrrmFHE55W7fyH6mXPa9ZV/FZOX7wHxaeFHUn6sSzIbZ+YEtMh3/EJ1aSr1WwtUWo2wtIXoO/J2oIo3RWW+JLhhf8LO5LGTf+j365s/1sgr0PTHpNbCEc9Dx1383vWrw1gO6faKphxM3QfC0V7xj+epJfiU8HVJr5cuHYLlN7jG4+26Z7YY2W6HZUKPxO7vnd7lyAObmat8EnrA865xxuJ43bn3Cjn3KguXdJnF92Zf/clX8OT3KY7ina91J+NnXxt2JFI2BY/4a9VJpxaclrDHr+ElW/7UikJ3rKXoHaTuglniuLxscYyEVw7XrHYL3Pqdzp0H9O8x7ZqB0c8469fGecb2cRj4SOwcblmW2X7ivb0VQGJbna26DHYssafxJXE2lGp8DNm9nRjl3gPbGYG3AXMcs79Jd7xUkl1Jcy6FYpP9s0LMl1ue9jtZ7D8JXUnzXSLHoMOQ6HDrmFHIs01+Ft+fdlkzbomxKLHfNn3LgeHHYkkQ3258MIIlgt//DPAWr4TQrvePnnd9AW8cpIvO26Juho/89thVzXDke0z8/v6rpiQ2JNAs/8F7Qf4/c8lsXZUcPQn4M87uMTrAOA8YKyZTYldAtjFNPrm3AVV63yyJt6ul0B+F5h8TdiRSFg2fQGfv6VuwqkqOw/2/LVvKrP8pbCjSS+1VX5vzz4nQlZO2NFIMnQY7EtqF0WsXPizCb6EeY8roV2flo/TeS8Ycz+s+hDeOAfqaps/xvQ/wtppMOJalc9L4waeA7jEzbqum+k/uwy5WK/DZNhRqfCb9RfgfWAdsBZ4P3ZbXJxz7zjnzDm3u3Nuz9jl+XjHjbq6GpjxV+h2IHTdN+xooqNVW9j9F77McMVbYUcjYVj8pN9bVIlr6hp0od8eR2tdg7Xidagu13sj0/Qb76uQNiwPOxLPOfjop9Cu2PemiFfxKbDvTX6JyPuXNu93xtpp/kR3v/FbZ6dFtqdgIHTZF+Y/kJjx59zumxwOUmf9pNjpuQEzOw6YD9wM/AOYZ2YZuHlLMBY97hsaaLb163b9LrTeBSZe6RMYySyLn/ClNp12DzsSaansXNjtClj9sd+LV4Kx6HFo1V5laJkmat2FV0yANZN9ZUVO62DGHPZD2P3nfv/LKdc37TG1VfDmNyC3I+z/T+1pLDs38BxYOxXWTg923JqNMPde31Cydfq04Ym0pkxq/xk41Dk3xjl3CHAo8NfEhpW+Su/2MxJ9xoUdSfTktIG9fusbUpTeE3Y0kkxV5X62vfhkfQhJdQPPgezWfl9FiV/tFp+49B4HOflhRyPJ1GEIdBwene7C0/8M+V39msEgjfodDDwPJl8FU/+w85nXT67zSciBd/jGjiI70+8Mv1VN0LOuCx6BqvVqypRMTUlcK5xz8xp8vQCoSFA8aW3jCvjsFRhwrurgG1NyoS+j/vgK2JQ+ux/JTix7wXfZ7nNi2JFIvHILod9pfj1Rzcawo0l9S5+HLWth0DfCjkTC8GW58GfhxrF+lt+2buglwZ9AMYOD7vLPdeIv4JUTYPOar9+vtgo++S1M+53fSrDvCcHGIemrdRffwGv+f4Ot6Jv9LygcoqZ5ydSU9GmimT1vZheY2fnAM8DHZnaKmakxfzPMf9C/YQaeG3Yk0WVZcMC/oLrCr6WRzLD4Kd+cq+t+YUciQSi5yK/JXPho2JGkvnn3+SUUPQ4POxIJQ7/xgAu/XPjTv0J2Pgz5XmLGz2oFhz4M+97sm7s9OQLmP+RLO6sr4YsP4am9/Kxs8Wn+fiLNMeAc2LAUPn87mPFWT4ZVH/jZVlWKJU9TEtd8YCVwCDAGWAW0Bo4HVPDaDPP+A51H+fIfaVzHoX4N8Lz7fAdDSW+1VbD0OehzPGRlhx2NBGGXg31DDJULx2fzGv/eGHC2uglnqg67Qodh4ZYLb/rC/z0e+I3EruMzg2E/gHHv+df7G2fBE7vDfe3hmX19SeYRT8PYh/02eiLN0fdEv3/wvPuCGW/ajdCqwM/+S/Ls9E+hc059sgKw9lNYOwX2/VvYkaSGPX8NCx6Cd78DJ37syw/jUVfjZ39WfQBlc/wlpy2UfAsGnQ95HQIJW1pgxRt+dq7vSWFHIkExg5JvwsRfQtlc7VfdUgse9iX0A1UmnNH6jYdPfuOXG7Xpnvzjz7rVr7Ue/qPkHK/LKDhlJqz7FCoWQMV8f/uul0BuQXJikPST0wb6n+UnkUb9Dlp3bflY5fP8VlW7/UyfH5OtKV2F+5nZX8zscTN7uv6SjODSybz/+IXh/c8MO5LUkNPar3mpWOjXu7R4g/Jq3+jp0SH+7O2cO2HTSuiyj09cP7wcHuwB734XajYH+hSkiZY85f+gqBQyvQw835f+l94ddiSpa959vst20R5hRyJhCrNcuGYzzLoFeh+X3GqxnHyfwPY/3e8Zu8eVSlolfsN/DLWx13Q8pv/Jl7cPuyyYuKTpmlJ89CRwF35tqzYpaYG6Wt/JrNfR8Z3hyTTdx8Ah9/nNySecBYc92vRyOef89iofXeHP1haNhMOf8t2cGzbGWv0JzPqnX2C/eRUc+ojKVZPJOb++tedRwW2vINHQtgf0Ohbm3Qt7/V9qlrqum+G3Olj1od+Kpvg0v5QhGdbP8ccd/afkHE+iq+PQreXCQy9N7rEXPeb/Ng79YXKPK5IIHYb4JpAz/+G3bmvVtvljbFzhJ0RKLgynAiLTNWWN62bn3M3OuQnOuTfrLwmPLI18/gZsXO7bvUvzDDgL9rvZz8q9c3HTusGt/RReOBxeO9UnQ0c8AydO9B0It+3m3HkEHHQH7HOT3yvxgx82bxN0ic/qSf69oTLh9FRykf8jv/yVsCNpnuWvwFN7w+PDfVOaqvUw+Vp4fBg8Nhw+ez3xMcz7j/99NeDsxB9Loq/feN9UZuOK5B539r/8/to9VREjaWL3n/lO7XNbuO3ijL+Bq4Hd1EA0FE1JXP9mZteY2X5mNrL+kvDI0si8+/0C7j5q3d4iQy+FEVf7XzJPjoDFT389uXQOVrwJr58JT+4Jaz6B/f4BJ30Sm2XdSce34Zf5s2+z/glTb0jYU5FtLH7Sl9D3Pi7sSCQReh/jf/dFZR/Kplj5nl+eULUe9vkrnLUcTp4KZy6D/f7uP7C8eBTMDajBx/bU1cL8+6HHETqjL96X5cKPJ++Y62bAyrdjXVO1hZ+kiW4HQNf94dO/+P4nzVFV5td8F4/3DQgl+ZpSvLUbcB4wlq2lwi72texEXbUvhex7okoh4zHiWr9X1uSr4dUTofPefr9XV+N/xp+/6feZy+3g1xzs8UvIL2reMfb+HWxaAZN+7Td976s9RRNu8ZP+/7G5/1eSGrLz/Pto8ZNQextk54Yd0Y6tnwOvHA9te/nOpg07qLbt4U+iDTzPV3O8dT5ULoI9rwp+K4TFT0DlYhj9x2DHldTVcSh0GBorF74kOcec/S/IylXXVEk/u/0MXjvZl8L3P6Ppj5t2o28mufvPExeb7FhTzqGNB/o75w5xzh0auyhpbaLP34KqddD35LAjSW1mvmz41Flw0N3+Z1p6h5/NXvQYtCr0t5+1HPb5c8sSIcvyDaE6DIWPr/AJsSTO+tmwfgYUnxp2JJJI/cb79+tnr4UdyY5t/BxeOhosB456sfFtP3IL4cjnfTfyydcEv7zAOZj6OygYBH21U7o00G+8/0yx8fPEH6tmo28OVnxqYrfAEQlD3xOgsASm/cFXuDTF6kn+/gO/4ZeZSTiakrh+CnRIcBxpa9ETkN0aeh0VdiTpISvHL4gfPxe+UQHnrYVzvoAT3ve357SJc/xWvk16WSnM0R6UCVXfIbNYH87TWs8jo18u7Org1ZNh8xdw5LNQMGDH98/OhYPugeE/8U0+pgfYQGn5y7Bmsj+jr0Zx0lAyy4UXPOzLIod8N/HHEkk2y4IR1/hlZU1ZHla7Bd66AFp3g31vSnR0siNNSVw7ALPN7KUG2+E8leC40oKr8yVyvY6KP6GS5OlzvC9f/eRaqK4MO5r0tegx6LoftO0ZdiSSSA3LhaNaxTDvfr/H8/63Qpe9m/YYMxh9I/Q73VdoBJWYT/2dL1VWMz/ZVsdh0GFXv39kos2+zR9rl4MSfyyRMPQ/y/+e/eRa+GzCju/7yXV+X+ED74C8jkkJTxrRlMT1GuBk4AbgL8DHgJYkN8HqibGOqSoTTilmsPeNfr/XT/8adjTpqXyBP9OpMuHMEOVy4ZpNfl17571g4LnNe6xlwcH3+kYfb57nGzvFY+V7fr3+8J9Efz2whKO+XHjTysQdY/VkWPWRn20Nev22SFSYwf7/hIISeOPsxt9Tqz6Gab+HQRdC72OTG6N83U4T19jWN+XAOODf+KZMtyU2rPSw6AnfMbXPuLAjkebqtp8/4TD9Rti0Kuxo0s+XZcJKXDNClMuFZ/wNNiz1+6W2pHNqTj4c8RS07e27EZfPa3ksU38HeUUw+NstH0PSW/F4X82VyHLh2f/yS5w06y/prlU7GPuI7yL/xjlQVb71e64OZt8BLx4JrbvDPn8JLUxpoNE/02ZWEtsGZzbwd2AJYLHmTH9PWoQpbPET0H0M5HUKOxJpiVG/87MxU38XdiTpZ9Gj0HkUtC8OOxJJhuw8vx3YoieiVS68aZVf39TnBP+7uqXyO/uGTQAvHQObVzd/jFUfwdJnYdjl0Kpty2OR9NZxmO+wn6iTQFUVsOC/0P9MlURKZui0G+x/i68I+m83eP0Mv3zkuUPg3Yuh0+5w7OuQ1yHsSAV2POM6Gz+7Os45d2AsWW1i7y1ZPwvK5qhMOJV1GOzLsube4zssSjAql/gP6ZptzSz9T49eufCU6/x7e+8/xD9W4SA/87phKbx6EtRsbvpjq8pgwll+bevQS+OPRdKXWaxc+E3Y9EXw489/wPd2GPKd4McWiaqSb8LxH0DJRbDidb/0Y/1Mv1vFsW/4DsQSDTtKXE8BVgATzOwOMzsM0GqHJlr0hL/ue1KoYUichnzHl5BEscQxVdWXuClxzSw9j4RW7WHho2FH4lUsglm3weCLocOQYMbsdgAcfB+sfNd3oGzKNgvOwdsX+RM6hz6ss/qyc/0SVC7snG/K1GlP6DI62LFFoq7rPrD/P+Csz+C4t+G0OX63Cq3zjpZGE1fn3JPOuTOBIcAE4HKgq5ndamZHJim+lLX4Cf+LXx1TU9suh/gzbbNvDzuS9LHoUV96Uzgo7EgkmbLzoPc4WPJU0/fNS6SZsQUve/4y2HH7n+5ncBc+DK+e+NU1U9sz6xa/5nvv30G3/YONRdJTx+FQOBgWPhLsuKs+hLVTYVc1ZZIMltUKdjnQLwGR6GlKc6YNzrn/OueOB3oBnwA/D+LgZna0mc0xs3lm9osgxoyCyqW+o7DKhFOfmZ+R+eI9WPtp2NGkvg3LfedUzbZmpuJT/PrPle+EG0dVBZTeBf1O8+W5Qdv9CtjvFlj2Ijyzn++ivT3LXoYPf+IT+uE/Dj4OSU+JKhee/S/frKb/2cGNKSISpGb1UHTOrXPO3e6cOyzeA5tZNnALcAwwFDjLzIbGO24ULH7SXytxTQ+DzoesXJijWde4zfsP4GCAPhhlpF5HQ3Z+YjuiNsW8e/260mGXJe4YQ78PR78MG1fA06Nh8rWw4k2/kf3n78ALh8NLR/luxIfc27KOxpK5+p3uy4XnPxjMeFvWwYKHYMC5kNs+mDFFRIIW5p/K0cA859wC51wV8BBwYojxBGbxE37j7g6Dw45EgpDf2c8QzrtPTZri4ZxvdNXtICjQTtAZqVU7v9Z18RP+9RAGVwczboYu+0DXfRN7rB5j4YQP/RraT66D58fAfQXw3EF+M/t9/gKnTFfneWm+TrtBl31h1j/8azpec++F2s1qyiQi0RZm4toTWNrg62Wx277CzC42s4lmNnHVquhvqLl5jd8cXLOt6WXId/wMjZo0tdwX70NZqW92IJmr+BTfeXf1pHCOv/QFKJ+b2NnWhgoHwbh34Ny1cPhTMPQHsM9f4fQFMPxHkNM6OXFI+hl+ud83eOnz8Y1TuwU+/TN0OxCK9gwiMhGRxIh8cVKsNHmUc25Uly5dwg5np5Y8A65WiWu62eVg3wxDTZparvQeyGnr12ZJ5upzPFg2LA6pXHjG36BND7++NZnyOkDfE2CfP/mEI6dNco8v6af4FGjT07+m4zH3XtiwDPa8Kpi4REQSJczEdTnQu8HXvWK3pbTFT/g1S533CjsSCZIZDLrQN2mqWBR2NC1TNtdvu/Hi0TD5Gt84Zsv65By7eoPvstpvvC8XlcyV1wm6H+o76Sa7XHjdTPjsFdj1Et85UiSVZbWCoZfAZ6+2vHlgXTVM/Z3fBaHnEcHGJyIStDAT14+BQWbWz8xygTOBp0OMJ27VG2D5y37vVrWSTz/9T/fXQW9BkGjl8+DN8+GxIb6Rx8blMOW38NIx8FAvWJCE57Pocaiu8Mm/SPEpvmx8/azkHnf2rb7R2pCLk3tckUQZfLFveDbz5pY9ft4DULkI9rxan1tEJPpCS1ydczXApcBLwCzgEefcjLDiCcKyF31zA5UJp6f2/fxZ6QUPhx1J062dDk/s6dfmDvsRnLHQN4M5dz0c8xp02gMmnAEf/Tyxe2vOvQfaD4BdDkrcMSR19Im14Utmd+Gajb6rdb/TtD+fpI/8Ihh4nn9tb17TvMfW1cDU66FoJPQ+NjHxiYgEKdQ1rs65551zJc65Ac6568OMJQiLn4C8In04T2f9Toc1k/0sZtRtWQuvngS5BXDabL+2rnU3/73c9r7j6bETYMh3YfqNfga2qiz4OCoWwooJMOgCndEXr20P6LofLHo0ecdc+D//+h6s2VZJM0N/6E+az7q1eY9b8LD/W7bnr/W7WURSQ+SbM6WK2ipY+qxvPJKVE3Y0kij9YuXCySivjUddLUw423dvHfsYtOuz/ftl58IBt8KBd/rk8rVT/Ws5SDNu9s14Bn0j2HEltfU7HdZOhfVzknO82bf7Bmu7HJyc44kkS6fh0OcEmHqD72XQFFUVMPlq6Dgc+qbFRoQikgmUuAbk87f82XyVCae3dr2h6/6+0VCUTb4Klr8E+90C3fbb+f0HXwQH3gGfvQbvfie4pjkbV8Ds23wpW2PJs2SmfuMBS857ae2nvrHa4Is1syTpaf9/+hORb1+482UfzsF73/NrW/f/J5g+CYpIitCvq4B0PxSOe1td+TJB/zNg7TRYPzvsSLZvxRu+S+Tgi2HIt5v+uJILYMTVMPffvnlTEKb+3net3PPXwYwn6aNtT7+sYsFDie8uPOcO35RJs/6Srtr2hH1vhpXv7nx7nLn3wvwHYMRvtLRJRFKLEteAZGXDLgdqM/lMUHwaYNFs0uQcfHwltO0F+7Zgb78R1/rZ0clXw7z744tlw3KY8y8YdD4UDIhvLElP/c7wnYXXtXArj6ao2QTz7oPiU9WUSdLbwPN8yfCkXzVegr9+Nrx/iT/ZvseVyY1PRCReSlxFmqltD3+WOorb4ix5BlZ9ACOugZz85j/ezK937X4ovP1N+GxCy2OZ9ntfsqbZVmlMv1N9mWIiTwIt/B9UrdcWOJL+zOCAf0FOG3jt5K///l71Ebx2mv/+Iff7E+4iIqlEiatIC/Q7A9bPhHUR2sDJ1fkz7QWD/CxnS2XnwmGP+3FeOxnWzWz+GBuW+WY4gy7w2wiJbE/rbtB9rF/nmqhy4dm3+dfyLockZnyRKGmzC4x50O+b/cJYeOFImHsfPH8oPL2P38d7zH/9CVgRkVSjxFWkBYpPBiy5+1DuzIKHfMnlyOsgq1V8Y+V1gCOf8xvbv3wsbPy86Y91Dj7+uU+k9/xVfHFI+ut/ht+SY83k4Mde/Ql88T7s+j01ZZLM0etIOG0ujP6zf1+9db7vNjz6z3DGEvXiEJHUpcRVpAXadPf7UC5+IuxIvLpqmHQ1dNoD+p8ezJjti+GIZ2HzKnjp6KYnr9P/BPP/60uE2xcHE4ukr+JTwHISUy486xbIbu1n/kUySU4+7PZjOH0BHPO6v97tx34PbxGRVKXEVaSFik+GNZ9AxcKwI/FdIivmw17XB7u1QZdRcNgTUD4Xnj3Az4ztyOKn/Wxrv9NhxFXBxSHpK68T9DzSJ66uLrhxt6zzJ1AGnAN5HYMbVySV5BZAj0P9EhARkVSnxFWkher37F0U8qyrc/DpTVA0AnofG/z4vY70Z+yryuCZ/WH1pO3fb80UeONs6DwKDv639gaUpht4LmxYAstfDW7M0nugdhMMvSS4MUVERCQ8+mgp0kIFA3xp7uKQ17mueAPWz4ChP0zcOr6u+8C4d303ymf2h9fG+9nV2i2w4k1465vw3EF+ZuuIp7QtlDRP8SmQ3wVm/TOY8VydH6vr/lC0ZzBjioiISLhywg5AJJUVnwKTr/XrP9vsEk4MM/8OeUW+yU0idRgMx78PU38HCx6ERY/6JlB11dCqHRSPhz1+4df/ijRHdh4M/hZM+wNULoF2feIbb/nLsdL564KJT0RERMKnGVeROPQ9GXCw5Klwjl+x2B978LeTM8vZpjvsdzOc9Rkc8QwM+Y7fD/DslXDw3VBYkvgYJD0N/o4ve599e/xjzbwF8rtC8anxjyUiIiLRoMRVJA4dh0PBwPC2xZl9q7/e9XvJPW5WK+gzDvb7Oww8x5cQi8SjfV//miq9E2qrWj7Omqmw9FnY9bt+JldERETSgxJXkTiYQd9T4LPXYcv65B67ZhPMuRP6nhR/aaVIFOz6fdi0Mr5tpiZfA7mFMOzywMISERGRCFDiKhKn4pPB1cCSZ5J73AUPwZY1sOulyT2uSKL0PBLa9295k6ZVH/vS+eE/0RY4IiIi6UaJq0icuoyGtr1g0f+Se9xZt0CHYdB9THKPK5IolgVDvgufvwWrP2n+4ydf7RuVDbss+NhEREQkXEpcReJkWb6j7rKX/F6nybB6kr/s+r3EbYEjEobB3/LJ5wc/8NvaNNXKd2HZi7D7FZBbkLj4REREJBxKXEUC0P90qKvye5smw5w7ILs1DDgnOccTSZa8jjD6Rp+Izr2v6Y+bdJXvJLzrJYmLTURERMKjxFUkAF32gba9YeEjiT9WdSXM/69PlvM6JP54Isk26ALouj98/DPYsnbn9597H6yYAHtcCa3aJjw8ERERCUEoiauZ/dHMZpvZNDN7wsw6hBGHSFDMoN94WP5S4rsLL3gYqitg8MWJPY5IWCwLDrgVtqyDib/c8X2/+ADe+TZ0PxSGarZVREQkbYU14/oKMNw5tztQClwZUhwigel3OtRVw5IElwvPud03Zeq6X2KPIxKmTrv7Jkuzb4cVb27/PhuWw6snQ9ueMPZ/fn9hERERSU+hJK7OuZedczWxLz8AeoURh0iQuoyGtn0SWy68Zgqs+giGXKymTJL+RlwL7YvhxSNg6u+grnbr96oqfNJaUwmHPw35RWFFKSIiIsmQE3YAwDeBhxv7ppldDFwM0KdPn2TFJNJs9eXCM2/25cKJWH865w7IzoeB5wY/tkjU5LaHEz6G977nS4aXPAv9z4RlL8CK16G2Cg5/EjoNDztSERERSbSEzbia2atm9ul2Lic2uM+vgBrggcbGcc7d7pwb5Zwb1aVLl0SFKxKI/vXlwk8FP3Z1Jcy7H4pPg7xOwY8vEkX5RXDow3DI/bB+BnzwQygrhSHfh+Pfg74nhB2hiIiIJEPCZlydc4fv6PtmdgEwDjjMOecSFYdIMnXeG9oVw7wHYND5wY49736oLvd7t4pkEjMYeA70Osp3GS4YpFJ5ERGRTBNWV+GjgSuAE5xzG8OIQSQRzPxWHp+9AhULgxvXOZj5d+i8l5oySebK7wyFJUpaRUREMlFYXYX/AbQHXjGzKWZ2W0hxiASu5Jt+O485dwU35orXYf1MGPoDfWgXERERkcwTSnMm59zAMI4rkgztekOvY2Du3TDyWsgK4F0242Y/29TvjPjHEhERERFJNWHNuIqktcHfho0rYOlz8Y9VsRCWPAODvwM5+fGPJyIiIiKSapS4iiRA7+OgTXeYfXv8Y828xZce7/rd+McSEREREUlFSlxFEiArBwZ9E5a/CJVLWj5O9QYovQuKT4G2vYKLT0REREQklShxFUmQwRf5bsCld7d8jNm3QtV6GHZZYGGJiIiIiKQcJa4iCdK+H/Q8AubcATWbmv/4Letgyg3Q62jodkDw8YmIiIiIpAolriIJtMeVsPEzmHFT8x879Xd+tnXvPwQdlYiIiIhIalHiKpJA3cdAnxN8Errpi6Y/rnIJzLwZBp4HnXZPWHgiIiIiIilBiatIgu19oy8VnnxN0x8z+Wp/vdf/JSYmEREREZFUosRVJME6DIZdvwdzbod1M3Z+/7XTYe59MPQH0K5P4uMTEREREYk6Ja4iSTDiamjVHj762Y7vt2kVvD4e8jr69bEiIiIiIqLEVSQp8jvDnlfBshfgo5+Dq/v6farK4aWj/frWw5+CvE7Jj1NEREREJIpywg5AJFMMuwzK58H0G6FiARxyH+S09t+r2QSvnABrp8ERT8EuB4Ybq4iIiIhIlChxFUmSrBzY/59QMAg++ilsWALdD4Xy+bB2qk9qxzwAvY8NO1IRERERkWhR4iqSRGaw24+hfX946zxY8wm07wcFA2HkdTDgzLAjFBERERGJHiWuIiEoPgl6rwbLgazssKMREREREYk2Ja4iIcnOCzsCEREREZHUoK7CIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERERERkUhT4ioiIiIiIiKRZs65sGNoMjNbBSwOO46d6AysDjsIEfRalGjQ61CiQq9FiQq9FiUqovpa7Ouc67LtjSmVuKYCM5vonBsVdhwiei1KFOh1KFGh16JEhV6LEhWp9lpUqbCIiIiIiIhEmhJXERERERERiTQlrsG7PewARGL0WpQo0OtQokKvRYkKvRYlKlLqtag1riIiIiIiIhJpmnEVERERERGRSFPiKiIiIiIiIpGmxDUgZna0mc0xs3lm9ouw45HMZGZ3m9kXZvZp2LFIZjOz3mY2wcxmmtkMM7ss7JgkM5lZvpl9ZGZTY6/F34Qdk2Q2M8s2s0/M7NmwY5HMZWaLzGy6mU0xs4lhx9MUWuMaADPLBkqBI4BlwMfAWc65maEGJhnHzA4GKoH7nHPDw45HMpeZdQe6O+cmm1l7YBJwkn4vSrKZmQFtnXOVZtYKeAe4zDn3QcihSYYysx8Do4AC59y4sOORzGRmi4BRzrnVYcfSVJpxDcZoYJ5zboFzrgp4CDgx5JgkAznn3gLWhh2HiHNuhXNucuzfFcAsoGe4UUkmcl5l7MtWsYvO2ksozKwXcBxwZ9ixiKQaJa7B6AksbfD1MvQBTUQEADMrBkYAH4YcimSoWGnmFOAL4BXnnF6LEpabgCuAupDjEHHAy2Y2ycwuDjuYplDiKiIiCWNm7YDHgMudc+VhxyOZyTlX65zbE+gFjDYzLaWQpDOzccAXzrlJYcciAhzonBsJHANcEltuFmlKXIOxHOjd4OtesdtERDJWbD3hY8ADzrnHw45HxDm3HpgAHB1yKJKZDgBOiK0tfAgYa2b3hxuSZCrn3PLY9RfAE/ilj5GmxDUYHwODzKyfmeUCZwJPhxyTiEhoYg1x7gJmOef+EnY8krnMrIuZdYj9uzW+keLsUIOSjOScu9I518s5V4z/rPi6c+7ckMOSDGRmbWONEzGztsCRQOR3pFDiGgDnXA1wKfASvgHJI865GeFGJZnIzB4E3gcGm9kyM7so7JgkYx0AnIefUZgSuxwbdlCSkboDE8xsGv5E8yvOOW1DIiKZrBvwjplNBT4CnnPOvRhyTDul7XBEREREREQk0jTjKiIiIiIiIpGmxFVEREREREQiTYmriIiIiIiIRJoSVxEREREREYk0Ja4iIiIiIiISaUpcRUREksTMihpsD/S5mS2P/bvSzP4ZdnwiIiJRpe1wREREQmBm1wKVzrk/hR2LiIhI1GnGVUREJGRmNsbMno39+1ozu9fM3jazxWZ2ipndaGbTzexFM2sVu99eZvammU0ys5fMrHu4z0JERCRxlLiKiIhEzwBgLHACcD8wwTm3G7AJOC6WvP4dOM05txdwN3B9WMGKiIgkWk7YAYiIiMjXvOCcqzaz6UA28GLs9ulAMTAYGA68YmbE7rMihDhFRESSQomriIhI9GwBcM7VmVm129qQog7/t9uAGc65/cIKUEREJJlUKiwiIpJ65gBdzGw/ADNrZWbDQo5JREQkYZS4ioiIpBjnXBVwGvAHM5sKTAH2DzUoERGRBNJ2OCIiIiIiIhJpmnEVERERERGRSFPiKiIiIiIiIpGmxFVEREREREQiTYmriIiIiIiIRJoSVxEREREREYk0Ja4iIiIiIiISaUpcRUREREREJNKUuIqIiIiIiEikKXEVERERERGRSFPiKiIiIiIiIpGmxFVEREREREQiTYmriIiIiIiIRJoSVxEREREREYk0Ja4iIiIiIiISaUpcRUREREREJNKUuIqIiIiIiEikKXEVERERERGRSFPiKiIiIiIiIpGmxFVEREREREQiTYmriIiIiIiIRJoSVxEREREREYk0Ja4iIiIiIiISaUpcRUREREREJNKUuIqIpAAze8HMzm/hYxeZ2eGxf//SzO4MOLaDzGxOkGM2cpxiM3NmlpPoYzWXmZ1jZi834X63mdlVyYipqcysj5lVmll22LHsSOz/fuBO7jPGzJYlK6Z4mVlrM3vGzMrM7H9hxyMiEmVKXEVEEiSWMG6KJQUrzezfZtauJWM5545xzt0bb0zOuRucc99q7uPMbJiZvWxma81svZlNMrNjY2O+7ZwbHG9s8Wrw866IxfiemX3XzBL+t84594Bz7sgm3O+7zrn/C/r4jSVsZvaGme3w/9s5t8Q51845VxtwTPvF/i+yG9x2RyO33RbksZsY34zYe7PSzGrNbHODr3+ZpDBOA7oBRc658Uk6pohISlLiKiKSWMc759oBI4FRwK+b82DzovC7+hngFWAXoCvwQ6A81Ii273jnXHugL/B74OfAXeGGlLEm4j9njGxw20HAsm1uOxh4K4lxAeCcGxZL2NsBbwOX1n/tnLuh/n4JnuHvC5Q652qa+8AoVh6IiCRSFD4MiYikPefccuAFYDiAme0bmxFcb2ZTzWxM/X1js2TXm9m7wEagf8OZMzPLMrNfm9liM/vCzO4zs8IGjz8v9r01ZvarhnGY2bVmdn+Drw9sEMdSM7tg29jNrDPQD7jDOVcVu7zrnHsn9v2vzPaZ2Ugz+yQ2s/Y/M3vYzH7b8L5m9pNY7CvM7MIGjz0u9tjyWDzXtvDnXeacexo4AzjfzOp/7nlm9iczWxKbBb/NzFo3MbbC2M96Vezn++v6kwpmdoGZ1f88zMz+Ghuj3MymNzj+v5vxsygyX0ZabmYfm9lv64/REmY22swmxsZbaWZ/id3+lRLs2Gvt/8zs3dj/4cux10D9ON9o8Pq6yhqUom/zf1ANfIBPTDGzrkAu8Mg2t5UAb8Xiez/2WlxhZv8ws9xGnsuxZjYzFt9yM/vpNt/f7s+0iT+n+p/HRWa2BHg9dvv/zOxz82W9b5nZsAaP+beZ3WJmz8Vi+tDMBsS+t93Xg5n9BrgaOMP8LO9FtoP39vbiir3u3o2Nv97MFpjZ/rHbl8bGaNESAxGRqFHiKiKSBGbWGzgW+MTMegLPAb8FOgE/BR4zsy4NHnIecDHQHli8zXAXxC6HAv2BdsA/YscZCtwae3wPoAjo1UhMffHJ9N+BLsCewJTt3HUNMA+438xOMrNuO3ieucATwL9jz+1B4ORt7rYLUAj0BC4CbjGzjrHvbQC+AXQAjgO+Z2YnNXa8nXHOfYSf4TsodtPv8YnSnsDAWAxXNzG2v8e+1x84JBbn9pKiI/GJWUns/qfjf4bbs6Pj3YL/eewCnB+7xONvwN+ccwXAAHwC2Ziz8c+tPtn8KXz5+voncA7QvUHsjXmLWJIau34ndml420Ln3DKgFvgR0BnYDzgM+H4j494FfCc2uz6cWHIZs6OfaXMcAuwKHBX7+gVgEP5nMhl4YJv7nwn8BuiIf79cH7t9u68H59w1wA3Aw7FZ3rvYwXt7B3HtA0zDv9f/CzwE7I1/fZ8L/MNauERBRCRKlLiKiCTWk2a2Hv9h/U38B9Vzgeedc8875+qcc6/gyyqPbfC4fzvnZjjnamIzVw2dA/zFObfAOVcJXAmcGZsxOw141jn3lnNuC3AVUNdIbGcDrzrnHnTOVTvn1jjnpmx7J+ecw3+QXgT8GVgRm3EatJ0x9wVygJtjYz4OfLTNfaqB62Lffx6oBAbHjvWGc2567OcyDZ/4HtJI/E31GdDJzAx/MuBHzrm1zrkK/P/HmTuLzfyazDOBK51zFc65+p/Feds5XjX+hMMQwJxzs5xzKxqJbUfHOxW4xjm30Tk3E4h3jXM1MNDMOjvnKp1zH+zgvvc450qdc5vwCe6esdtPA55xzr3jnKvCJ/1uB+O8CRwY+9kfhC/JfR/Yt8FtbwI45yY55z6IveYXAf+i8f/7amComRU459Y55yZv873tvr6a6Vrn3IbYzwDn3N2x//stwLXAHtag0gF4wjn3Uazs9wG2/sya83rY0Xt7u3HhE/97YmuUHwZ6x57/Fufcy0AVPokVEUlpSlxFRBLrJOdcB+dcX+fc92MfNvsC42Olfetjie2B+Bmsekt3MGYPvjoLuxifLHaLfe/LxzrnNtD4bF9vYH5TnoRzbplz7lLn3IBY/BuA+xqJbXks2a237XNZs82avo34mSXMbB8zm2C+HLcM+C5+Bi4ePYG1+FnlNsCkBj/3F2O37yy2zkArvv5z/9pso3Pudfws2S3AF2Z2u5kVNBJbY8frgv8/bfiz29FroiYW37Za4RMn8LOPJcBs86XH43Yw3ufbiQm+/vraSOOvL/Clwu3ws6IHA2/HErKlDW57C8DMSszs2Vg5bjn+pEJj//en4k/0LDazN81svwbfa/T11UxfPk8zyzaz35vZ/Fhsi2Lfahjfdn9mzXw97Oi9/bW4YlY2+Hd9kr3tbZpxFZGUp8RVRCT5lgL/iSW09Ze2zrnfN7jPjmaxPsMnj/X64BOXlcAKfEIKgJm1wZcQNhbHgOYG75xbiv8QPnw7314B9IzNptXrvZ37Nea/wNNAb+dcIXAbYDt+SOPMbG98cvkOsBr/IX5Yg597Yaw5z86sxieA2/7cl2/vzs65m51zewFD8cniz5oZ+ir8/2nDMu8d/RyXAJ0bloTG/g/6EkuEnHNznXNn4Utd/wA8amZtmxnXioYxmV8f3NjrC+fcZuBj4Higu3Nuduxbb8du252tjZluBWYDg2LlzL+kkf9759zHzrkTY8/lSXZc9txSDd+DZwMnAofjy32LY7c36bXZjNfDjt7b24tLRCRjKHEVEUm++4Hjzeyo2ExOvvlGPdtdi7odDwI/MrN+sUSlfp1cDfAoMM5806Vc4Doa/13/AHC4mZ1uZjnmmwHtue2dzKyjmf3GzAbGmsd0Br6Jn03b1vv4tYqXxsY8ERjdxOcFvqRyrXNus5mNxicMzWZmBbEZxYeA++vLj4E7gL+abwqEmfU0s6N2NBZArAzzEeB6M2sfWx/8Y/z/5bbH3js2c9wKPzO9mcbLtXd0vMeBa82sjZkNwa+pbez+S4APgT+YWTszy8MnR/UNkjCzc82sS+znsD720GbFhX99HR9rAJSLL5ndWfL2FnAZ8F6D296J3bbCOVc/698e36m6MvZ8v7e9wcws1/y+uYWxMvryFjyP5moPbMHPLrfBv+eapJmvhx29t0VEMpoSVxGRJIvNWJ6In1FahZ/5/BlN/518N/AffEKwEP9B+AexsWcAl+BnLlcA6/DNibYXxxJ8ueVP8KW0U4A9tnPXKvwM06v4JOFT/If4C7YzZhVwCr4sdT1+Pe+zsfs3xfeB68ysAr9+srkzac/EHrsU+BXwF77aQOnn+MY5H8RKPl+l6esff4BPPBbgE6//4v8vtlWAT5DX4Wc71wB/bObzALgUP7v3Of7/+0F2/HM8Az8DOQ8/E3wYcFxs1hPgaGCGmVXiGzWd2WCdZJPEXl8/wJ8QWIFfP/rFTuJ6MxZXw47I78Rue7vBbT/Fn6iowP/8Ht7BmOcBi2L/h9/Frw1NpPvw/5fLgZls/6RNY5rzemj0vS0ikunsq8uQREREgmVmHwK3OefuCTuWVGZmfwB2cc5FZnuT2Kzgenx578KQwxERkTSmGVcREQmUmR1iZrvESoXPx69jfDHsuFKNmQ0xs93NG42fxX4iAnEdHytfbgv8CZjO1mZFIiIiCZGz87uIiIg0y2B8iW9bfFntaTvY/kMa1x5fHtwD35znz8BToUbknYgvZzX8Nk5nOpVviYhIgqlUWERERERERCJNpcIiIiIiIiISaSlVKty5c2dXXFwcdhgiIiIiIiKSAJMmTVrtnOuy7e0plbgWFxczceLEsMMQERERERGRBDCzxdu7XaXCIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERERERkUhLqeZMIiIiIiKpbMNyqN0UdhTxye0A+Z3DjkIyjRJXEREREZEkWPEmPD8m7Cjil50HZ30GeZ3CjkQyiRJXEREREZEkWDPZXx9wO+S0DjeWllo3A6b9HtbPgm4HhB2NZBIlriIiIiIiSVBW6mcph3w77Eharny+T1zLSpW4SnKpOZOIiIiISBKUlUJBSdhRxKddX7Ac/1xEkkmJq4iIiIhIEpSXQuGgsKOIT1YOFAzwz0UkmUJNXM2sg5k9amazzWyWme0XZjwiIiIiIolQvQE2LEv9GVeAwhLNuEryhT3j+jfgRefcEGAPYFbI8YiIiIiIBK58nr8uTIPEtaDEPx9XF3YkkklCS1zNrBA4GLgLwDlX5ZxbH1Y8IiIiIiKJUj7XX6dD4lpYArWb/QyySLKEOePaD1gF3GNmn5jZnWbWdts7mdnFZjbRzCauWrUq+VGKiIiIiMSpvrS2YGC4cQShPvlWubAkU5iJaw4wErjVOTcC2AD8Yts7Oedud86Ncs6N6tKlS7JjFBERERGJW3kptOkJrdqFHUn8CmINppS4SjKFmbguA5Y55z6Mff0oPpEVEREREUkrZaXpUSYM0KYH5LRRZ2FJrtASV+fc58BSMxscu+kwYGZY8YiIiIiIJEo6Ja5mvkGTZlwlmXJCPv4PgAfMLBdYAFwYcjwiIiIiIoHasha2rEmPrXDqFZbA6klhRyGZJNTE1Tk3BRgVZgwiIiIiIolUVt9ReFC4cQSpsAQWPQa1VZCdG3Y0kgnC3sdVRERERCStfdlROI1mXAtKwNVCxcKwI5FMocRVRERERCSBykvBsqF9v7AjCU797LEaNEmyKHEVEREREUmgslKftKZTSa32cpVkU+IqIiIiIpJAZaXpVSYMkNcJ8oqUuEryKHEVEREREUkQ53w5bbpshdNQYYlKhSV5lLiKiIiIiCTIxs+gZmP6Jq6acZVkCXsfVxEREUkhn78N62aEHUV8LBuKT4H8orAjkUxQXr8VThomrgUlMPdeqK6EVu3CjkbSnRJXERERaRLn4JXjoaos7Ejit3E5jLw27CgkSras9XuSBm31JH9dkEZ7uNarT8ZXfQgdhgU/fk5byG0f/LiSmpS4ioiISJNsWumT1lE3wKALw46m5Z7dH9bPDjsKiZKlL8DLxyZu/Jy20LZX4sYPS+EQf/3C4YkZPysXTl8AbXsmZnxJLUpcRUREpEnq17IV7QVtdgk3lngUDlFDGfmq8nn+evSffJIZtA67gqVhZ5mOw2DsI7B5TfBjl82BGTdBxUIlruIpcRUREZEmqU/2Un2tXsEg+PwtX/psFnY0EgXVFf5610sgJz/cWFKJGfQbn5ixV0/yieuWtYkZX1JPGp77ERERkUQoK/Wle217hx1JfApLoGYDbFwRdiQSFdUVYDmQnRd2JFIvr5O/3pKA2VxJTUpcRUREpEnKSqFgIGRlhx1JfOpnjFUuLPVqKqFVe83AR0lerOu3ZlylnhJXERERaZLy0tQvEwa/hQdo/0nZqrpC27lETav2fhZcM65ST4mriIiI7FRdLZTP35r0pbJ2vX1JqBJXqVdd4RMliQ4zXy6ciMZPkpqUuIqIiMhObVgCdVXpMeNqWb5BU/ncsCORqKiuVOIaRflFKhWWrZS4ioiIyE6VpUlH4XqFJZpxla1UKhxNeZ1UKixbKXEVERGRnUq3xLVgEFTMh7qasCORKFCpcDTlFSlxla2UuIqIiMhOlZdCqwLI7xp2JMEoLIG6aqhcHHYkEgVKXKMpT6XC0oASVxEREdmpslhH4XTZLkSdhaUhrXGNJjVnkoaUuIqIiMhOlZX68tp0UajEVRqoroAcrXGNnPwiqN0ENZvCjkSiQImriIiI7FDtFl9Smy7rWwHyu0BuoToLC9RW+Y7ZmnGNnrxO/lrlwgJKXEVERGQnyucDLr0SVzNfLqwZV6mu8NdKXKMnr8hfq0GTgBJXERER2Yn65K4gjRJXgMJBvumUZLbqSn+dq8Q1cr5MXDXjKihxFRERkZ2oT+4K02iNK/hEvHKJ1s9luvoZV61xjZ76UmE1aBJQ4ioiIiI7UVYKrbv5NaHppLAEcLFSaMlYKhWOrnyVCksDSlxFRERkh8pK069MGLau2VW5cGZT4hpdKhWWhpS4ioiIyA6Vz02vxkz16rf3KVNn4YxWE1vjqsQ1enJaQ3a+ZlzFywk7ABEREYnfyvegYkHw49ZVw6bP0zNxzS2A1rvA8pehbc8EHMCg11GQ3zkBY0tgvpxx1RrXSMor0oyreEpcRUREUpyrgxfG+v1WE6VoZOLGDlPnvWDpc7Di9cSMv9tPYfQfEzO2BEOlwtGW10nNmcQLPXE1s2xgIrDcOTcu7HhERERSTc1Gn7TudgUM+Xbw42fnQ9tewY8bBWMfhY3LEjP282Nh4+eJGVuCU61S4UjLL1KpsHihJ67AZcAsoCDsQERERFJR/Qfv9sVQMDDUUFJOTn7ifmatu+kDdyqorgDL8idoJHryimD9rLCjkCgINXE1s17AccD1wI/DjEVEMsMXH8D0P/rSylS2y8Ew/EdhRyFRUd9cJqdtuHHIV+V1UuKaCqor/GyrWdiRyPbofST1wp5xvQm4AlBxhogkRendsOQZ6LBr2JG03MYVsGICDLtcH7TE+7LUUc1lIiWvKDENsyRY9YmrRFNekV/j6pz+5mW60BJXMxsHfOGcm2RmY3Zwv4uBiwH69OmTnOBEJG2VlUKX0TDunbAjablP/wYfXg6bV0HrrmFHI1FQs8Ff5yhxjRQ1lUkN1ZVKXKMsvwhcjf9/ytX/U0YLcx/XA4ATzGwR8BAw1szu3/ZOzrnbnXOjnHOjunTpkuwYRSTNlJdCQYpv61G/LUlZabhxSHRoxjWa8ougaj3U1YYdiexIdYVO+kRZXid/rXJhCS1xdc5d6Zzr5ZwrBs4EXnfOnRtWPCKS/qoqfJltqu9HWR9/uRJXiVHiGk15RYDzyatEl0qFoy2vyF9rL1cJc8ZVRCSpyuf561RPXNv1haxWUDY37EgkKr5szqTENVI0U5QalLhGm95HUi8Siatz7g3t4SoiiVY/Q5nqpcJZOdB+gGZcZasvZ1zVVThS6meKtM412mq0xjXS9D6SepFIXEVEkqF+TWjBgHDjCELhIK1xla2qNeMaSfkqcUwJ1RUqs48yvY+knhJXEckYZaXQtg/ktA47kvgVlED53NTfj1aCUbMBsPR4bacTlTimBpUKR1tuR3+t95EocRWRjFFemvrrW+sVlkDtFqhcGnYkEgXVlb5M2PRXPVLUVCb66qr971IlrtGVnev/f5S4SiB/4sysjZldZWZ3xL4eFNunVUQkEpzzM67plLiC1rmKV1OpMuEoyi30JxP0gTu61JE7NeQV6QSQBDfjeg+wBdgv9vVy4LcBjS0iErfNq/2WFKnemKlegfZylQaqK/XBO4osy5c5qqlMdFVX+GvNuEZbXie9jyS4xHWAc+5GoBrAObcRsIDGFhGJW3ls65h0mXFt0x1y2m59XpLZair960GiJ18zRZGmxDU1aMZVILjEtcrMWgMOwMwG4GdgRUQioX5mMl0SVzP/XDTjKqAZ1yjL7aRS4Sj7slRYiWuk5el9JASXuF4DvAj0NrMHgNeAKwIaW0QkbuWlYDnQrm/YkQSnQFviSEy11rhGVn6RPnBHWf2Mq94/0ab3kUBAiatz7hXgFOAC4EFglHPujSDGFhEJQlmp3781KyfsSIJTWAKVC6G2KuxIJGw1GzTjGlUqcYw2lQqnhrwi2LJOW8Blurg+wpnZyG1uWhG77mNmfZxzk+MZX0QkKOnUUbheQYn/I16xADoMCTsaCZNKhaNLJY7RVp+45ipxjbS8ToDzTRbr90eWzBPv3MOfY9f5wChgKr4p0+7ARLZ2GRYRCY2r802Meh4ZdiTBKmzQWViJa2bTdjjRlVfkTyzUVvn9KCVatMY1NdTvibx5jRLXTBZXqbBz7lDn3KH4mdaRzrlRzrm9gBH4LXFEREK3YTnUbk6/GdfCQf5anYWlWl2FI6v+Q7bKhaNJa1xTQ34scdX7KLMF1ZxpsHNuev0XzrlPgV0DGltEJC7ladZRuF5eJ8jvrAZNma62CuqqVCocVV9+4Fa5cCRVV/j9dnPahB2J7MiXJ4D0PspoQbUpmWZmdwL3x74+B5gW0NgiInGpT+wKBoUbRyIUDNqamEtmqtngr5W4RlOeZooirbrCz7aahR2J7Ej9+2j5K1CbgA03W7WDHoen5+ugbC6s+3Tr11m50Oe48OKJR1CJ64XA94DLYl+/Bdwa0NjSwJZ18OSI1D/jlNMWxr0DBQPDjkQyQVmpP5vepkfYkQSvsMT/IZfMVZ+4qtQxmupnijan+N/tdFVTqfWtqaD1LpCdBzNu8pdEOPZN6H5wYsYO0ysnQNnsrV/nd4ZzVoUXTzwCSVydc5uBv8YukkBrpkDlYuh/Zup+CK8qh9I7YeX7Slxlq8/fgTm3g3MJGPst34E3Hc+kFpTA3HvhjXPxrfEC1nkkDP9R8ONKcL5sLqPENZLyVCocadUVeu+kgtz2MH4+bF4d/NhbVsMLh8P6GemXuNZW+aqsId/1FwDLDjemeASSuJrZQuBrHzedc/2DGF+2qi8J3PtGaNc73FhaqrYK5t6t8kb5qjl3wPwHoV2f4MfOyvEne9JRr6Ng3n/gi/eDH3vLWlj4CAy7PD2T/nShxDXa1FQm2qorNOOaKtr29JeguTpflZWO/SIqFvjn1+0AKNoj7GjiF1Sp8KgG/84HxgNqVp0AZaWQ3Toxb9xkyc6Fdv3S8xeEtFx1BRQOhlM/3fl9ZavOe8FpsxIz9rQb4eOf+1JUJUXRVRNLXNVVOJpy2kJWK824RpUSV7Es3y8iHT+XlqVZc8pAugo759Y0uCx3zt0EpOiy32grK/VbYFhQ/aBDUliSnr8gpOX04SF61FQmNWjGNdrM/HtJ76Noqq7Ue0f859J0rAQsT7PmlEGVCo9s8GUWfgY2qNlcaaC8FDruHnYU8Sss8esOnVMJonjVapAROQ2byiSihFuCUZ+4qjlTdOV10oxrVOmkqYDvF7Hocair9hUS6aKsFPK7QF7HsCMJRlDJ5Z8b/LsGWAicHtDYElNXA+ULoPi0sCOJX0GJLz/cuALapmiTKQlWdQW06R52FNKQmsqkBm2HE315ReoqHFVKXAX8hIqrhYqF6VNWC7FKzTR6PkElrhc55xY0vMHM+gU0tsRULgJXkx4vwPrnUF6qxFU8fXiIHjWVSQ0qFY6+/CIonx92FLI9qvYR2FpKm26JXvlc6Hlk2FEEJ6iVko828TaJQ1ka1ak3/AUhAkpco6i+VFgzrtFWo1LhyFOpcDTV1UDtJr13ZGuymk6fS6srYeNn6ZWIxzXjamZDgGFAoZmd0uBbBfjuwhKgdOoM1q6330g6nX5BSHy0CXz0fJm4asY10qorwXJ8x3aJprwin7iqr0O0fFmtoL89GS+/yP/NS6cGTWVz/XVBGuQN9eItFR4MjAM6AMc3uL0C+HacY8s2ykoht+PWdWeprL71eDr9gpCWq93iGyKo1DFasvP8Vh5amxdtNeqKGnl5Rf73XO0mv1+kREN1hb9W4irgE7x0mlApT6MJr3pxJa7OuaeAp8xsP+fc+wHFJI0oj9Xdp8vZ2sISWDcj7CgkCvThIbrqZ4okurSdR/R9pUO3EtfIqNGMqzRQWAIrXg87iuB8ucRwYLhxBCmuNa5mdkXsn2eb2c3bXgKITxoom5teZ00KSqBigV9jIplNiWt05Wv/ycir2aA1elGnRmfR9OXfHr1/BP8Ze8MyqN4QdiTBKCuFtn0gp3XYkQQn3lLhWbHrifEGIjtWswk2LEmvOvXCEl8eWrkYCgaEHY2ESeuMoktNZaJPM67Rp0Zn0aSTptJQfePQ8nlQtEe4sQShvBQK06Cha0Pxlgo/E7u+N5hwpDHl8/x1Or0AG3YWVuKa2XTWO7ryimDD0rCjkB1R4hp92hM5mqqUuEoDDbdqTPXE1Tn/+br/WWFHEqx4uwo/A7jGvu+cOyGe8WWrL+vU02zGFfxz631MuLFIuHTWO7ryVCoceTWV0Eb7YUdankqFI0lrXKWh+rWg6dCgafNqqFqfXksMIf5S4T8FEoXs1JedwdJoxjW/C+QWqrOwqFQ4yvI6+Q/brs53A5foqa7UGteoa9icSaJD1T7SUKt20KZneiSu5bGtcJS4NuCce7P+32aWCwzBz8DOcc5V7eixZtYbuA/oFnvM7c65v8UTTzorK/Vn1NPpl6tZ+rUel5bRjGt05Rf5pLWqHPI6hB2NbI+2w4m+nHy/DY5KhaNFf3tkW4Vp8rm0LA23woE4uwrXM7PjgPnAzcA/gHlmtrPizxrgJ865ocC+wCVmNjSIeNJReZp1FK5XWLL1rJBkrvoPD5o1ih41lYm+6g1KXFOByu6jp7oSMO2tK1uly+fS8lKwHGhXHHYkwQqq8OvPwKHOuTHOuUOAQ4G/7ugBzrkVzrnJsX9X4DsU9wwonrRTVppe61vrFZZA5RLfNVkyl856R5eaykSbc37GVSd9ok8duqOnugJatdUyCNmqoMS/T1O9rL++8WlWvItCIyaop1PhnJvX4OsFQEVTH2xmxcAI4MPtfO9i4GKAPn36xBdlitqyDjavSq/1rfUKBgEOyudDp+FhRyNhqan0Zwaz88KORLalpjLRVrvZl3JrxjX68opg9UR49/uJGX/gedBtv8SMHabyBTDjpsTs+f75mzphKl9V/1m7fO7W/ZdTUVnp1t070klQietEM3seeAS/XnU88LGZnQLgnHu8sQeaWTvgMeBy51z5tt93zt0O3A4watSoRjsYp7P6koV0nXEFX9KgxDVzVVf4Dw9mYUci21JTmWirb2yW0zbcOGTneh4O66bDokeDH3vLOti4HI54Kvixwzb3Hpj5d9/QMRF6HZ2YcSU11X/WXvzU1mqwVFQ+F3oeEXYUwQsqcc0HVgKHxL5eBbQGjscnsttNXM2sFT5pfWBHyW0qWD0JXh6XmLFrN/vrtJ1xBd66AN67JPjxs/PhiKeh027Bjy3Bqa7QjFFU5atUONK+3M5D75/I2+NKf0mEV0+BstmJGTts9TNH49OgYY5EX/t+/vfptN/7SyrrtHvYEQQvkMTVOXdhcx9jZgbcBcxyzv0liDjClNsR+iRw19o23aFwSOLGD0tuAezzV1g/K/ixazbA/Ad8aZYS12irn3GV6Mnt6K9VKhxN1UpcBZ/YLX0W6mohKzvsaIKVriWPEk3ZuXDyNNj4WdiRxCerFRTtFXYUwQskcTWzfsAPgOKGYzrndpTKHQCcB0w3symx237pnHs+iJiSraA/HPivsKNITcMvT8y4VeU+cdVMUfRVVypxjaqsbMjtoPdRVNVs8NdqzpTZCkugrhoqF/vPI+nCOb+UqPuYsCORTNK+n79I9ARVKvwkfvb0GaCuKQ9wzr0DaEWbJEyr9r7hj2aKok8zrtGmbTyiSzOuAl/tF5FOievGz6BmY3puBygizRdU4rrZOXdzQGOJBMLMN5ZRU5noq66A1t3CjkIao/dRdH3ZnEmJa0arT+zKStOr2VBZbF2rElcRgeAS17+Z2TXAy8CW+hvr92kVCUu+ZopSgmZcoy2/CDavDjsK2Z4vmzOpq3BGy+8KrQq27kKQLspjiWs67qogIs0XVOK6G3696li2lgq72NciodGG76lBa1yjLa9o68yHRItmXAV8hVFhSfq9T8tKIbs1tO0ZdiQiEgVBJa7jgf7OuaqAxhMJRF4RVC4KOwrZGc24RptOAEWXtsORegWD4Iv3w44iWGWlUDAQLCvsSEQkCoL6VfAp0CGgsUQCo6Yy0VdbBXVVmjGKsrwiqCqDupqwI5FtVdd3FVapcMYrLPFdhWs2hx1JcMrnan2riGwV1IxrB2C2mX3M1jWuzjl3YkDji7SImspE35czRppxjaz8In+9ZR207hJuLPJVNZW+lDLd9u6U5issARxUzIeOw8KOJn51NVA+H4pPCTsSEYmKoBLXaxr824CDgDMDGlukxfKLoHYT1GyCnNZhRyPbU1Xhr3OVuEZWXid/vWWNEteoqa5UmbB4BQ06C6dD4lq5CFyNGjOJyFaBlAo7594EyoFxwL/xTZluC2JskXjk1c8UqVw4sqpjiatmXKNL76PoUuIq9QoH+et0adCkrXBEZFtxzbiaWQlwVuyyGngYMOfcoQHEJhK3hjNF6koYTfWJq9a4RlfD95FES02l1reKl1vo98NOly1xlLiKyLbiLRWeDbwNjHPOzQMwsx/FHZVIQDRTFH1a4xp99e8jrRePnupKnfSRrQrSaEucslLI7bj194+ISLylwqcAK4AJZnaHmR2GX+MqEgn5+sAdeSoVjr58nQCKrJoNKhWWrQoHQXmaJK7lpf75mD5VikhMXImrc+5J59yZwBBgAnA50NXMbjWzIwOITyQuKnGMPiWu0deqACxb76Mo0hpXaaigBDat9NtXpbqyUjVmEpGvCqo50wbn3H+dc8cDvYBPgJ8HMbZIPFQqHH1fJq768B1ZZv4kkBLX6KlRqbA0UL8etCzF17nWbIINS7W+VUS+KpDEtSHn3Drn3O3OucOCHlukuXJaQ3a+PnBHWbXWuKaEvCKdAIoizbhKQ/WJXqqXC5fP89dKXEWkocATV5GoySvSGtcoq67wZajZ+WFHIjuS10nvoyiqVldhaaD9AMBSf8a1vsGUSoVFpCElrpL28jVTFGnVFX62VQ04ok3vo+ipq4XaTZpxla1y8qFd3zSYca3fCmdQuHGISLTEux2OSORpbV60VVfog3cqyOsEa6aEHYU0VLPRX+v9Iw0VDILP34KPrgg7kpZb/gq06a7Xtoh8lRJXSXt5RbB+ZthRSGOqK7W+NRXkFekEUNTU74Gs5kzSUO9jYOU7MPMfYUcSnwFnhx2BiESNEldJe2oqE231pcISbXlFfoavZrMvR5TwfdnYTImrNDD8R/4iIpJutMZV0l59Uxnnwo5EtkeJa2r4ck9knQSKjGrNuIqISAbRjKukvfwicDX+Q16uEqTIqamE/C5hRyE7kx/bE/mZfSErN/jxCwbAUS+Apdnp1NoqePFI2LAsAWNv9tet1FVYREQygBJXSXtfzhStUeIaRZpxTQ3dx8Lgb29tCBSkioWw/GWf3LXrE/z4YSqfC5+/CbscAm17BT9+q/bQZd/gxxUREYkaJa6S9vJiM0Vb1kD74lBDke1Q4poa8ovgwNsTM/ZnE+CFsX7vxnRLXOv3o9znz9B5r3BjERERSWVpVpQl8nVfJq5amxdJSlylsMRfl88NN45EqE9cC7QfpYiISFyUuEraqy8V3qytPCKnrhpqt6graqZr0wNy2mxN8tJJ+VxovQvkFoQdiYiISGpT4ippL79BqbBEy5fbeWjGNaOZ+RnJdExcy0o12yoiIhIEJa6S9rSNR3RVV/hrJa5SWALlaZi4lpduLYUWERGRllPiKmkvq5VPjDTjGj1KXKVeQYnvLlxbFXYkwakqg00rlbiKiIgEQYmrZIS8Is24RtGXpcJa45rxCkvA1frkNV2UxZpNFShxFRERiZsSV8kIeZ3UnCmKNOMq9dKxs3B96bNmXEVEROKnxFUyQl6RSoWjSImr1KtP7tKpQVNZKWBQMCDsSERERFJfqImrmR1tZnPMbJ6Z/SLMWCS95atUOJKUuEq9vE7+kk4NmspKoV1fyM4LOxIREZHUF1riambZwC3AMcBQ4CwzGxpWPJLe8jppxjWKtMZVGiooSa8ZV3UUFhERCU6YM66jgXnOuQXOuSrgIeDEEOORNJZXBFvWQV1t2JFIQ5pxlYYK0yhxdc43Z1LiKiIiEowwE9eewNIGXy+L3fYVZnaxmU00s4mrVq1KWnCSXvKKAAfVZWFHIg1VV4BlQXbrsCORKCgsgY3Lt87Ep7LNX0B1uToKi4iIBCXyzZmcc7c750Y550Z16dIl7HAkReV18tfqLBwtNZV+ttUs7EgkCr7sLDwv3DiCUKaOwiIiIoEKM3FdDvRu8HWv2G0igcsv8tdq0BQt1RWQo/WtElOQRlviKHEVEREJVpiJ68fAIDPrZ2a5wJnA0yHGI2msfsZVDZqipbpC61tlq4KB/jod1rmWlUJWLrTtE3YkIiIi6SEnrAM752rM7FLgJSAbuNs5NyOseCS95cVmXFUqHC1KXKWhVm2hTc/0SFzLS/3+rVnZYUciIiKSHkJLXAGcc88Dz4cZg2QGlQpHU3WlElf5qnTpLFxWqsZMIiIiQQo1cRVJllaFgEHFAqhYGPz4Wa2gba/gx42CuhrYsHTn92uJLWu3loeKgE9cF/4v7CjiU1frG0z1Pi7sSERERNKHElfJCFnZ0LorzLzZXxLh0Ieg/xmJGTtM71wMc+9J3Phd9knc2JJ6Ckr8CY3Na7ZWSqSaDUugrkqNmURERIKkxFUyxhHPwPqZiRn73e/A6onpmbiungidR8HQSxMzfo/DEzOupKb6ZO/ZAyA7P9xYWqpmg79WqbCIiEhwlLhKxuiyt78kwrQ/pse6vG25Or81ya6XwKDzw45GMsEuB8OAc33jrlTW7cDE/b4RERHJREpcRQJQWALrZ4UdRfA2LIPazSp5lOTJLYAx/wk7ChEREYmaMPdxFUkbhSVQMd83ZUkn9bPISlxFREREJExKXEUCUFgCddVQuTjsSIJVn7hqrZ6IiIiIhEmJq0gACgb56/I0W+daPhdy2kKb7mFHIiIiIiKZTImrSADqS2nTrUFTWalPys3CjkREREREMpkSV5EA5HeFVgXpl7iWl2p9q4iIiIiET4mrSADMfIKXTolrbRVULFTiKiIiIiLhU+IqEpDCkvRa41qxEFytGjOJiIiISPiUuIoEpKAEKpdAzeawIwlGubbCEREREZGIUOIqEpDCEsD5/VzTwZd7uA4KNw4RERERESWuIgGp3xInXda5lpVCXhHkdQo7EhERERHJdEpcRQJSmGaJqzoKi4iIiEhUKHEVCUhuIbTulj4NmsrmKnEVERERkWhQ4ioSoII02RKnuhI2LldHYRERERGJBiWuIgEqLIHyuWFHEb/yef5aM64iIiIiEgVKXEUCVFgCm1ZCVVnYkcSnTFvhiIiIiEiEKHEVCdCXnYVTfNa1PnEtGBhuHCIiIiIioMRVJFD1M5Sp3qCpvBTa9oKcNmFHIiIiIiICOWEHIJJO2g8ADNZMgR5HhB1Ny62fpcZMIiIiIhIdSlxFApSTD+37wfQ/+ksq2/X7YUcgIiIiIuIpcRUJ2Jj/wuqJYUcRJ4O+J4YdhIiIiIiIp8RVJGBd9/EXEREREREJhpoziYiIiIiISKQpcRUREREREZFIU+IqIiIiIiIikabEVURERERERCJNiauIiIiIiIhEmjnnwo6hycxsFbA47Dh2ojOwOuwgRNBrUaJBr0OJCr0WJSr0WpSoiOprsa9zrsu2N6ZU4poKzGyic25U2HGI6LUoUaDXoUSFXosSFXotSlSk2mtRpcIiIiIiIiISaUpcRUREREREJNKUuAbv9rADEInRa1GiQK9DiQq9FiUq9FqUqEip16LWuIqIiIiIiEikacZVREREREREIk2Jq4iIiIiIiESaEteAmNnRZjbHzOaZ2S/Cjkcyk5ndbWZfmNmnYccimc3MepvZBDObaWYzzOyysGOSzGRm+Wb2kZlNjb0WfxN2TJLZzCzbzD4xs2fDjkUyl5ktMrPpZjbFzCaGHU9TaI1rAMwsGygFjgCWAR8DZznnZoYamGQcMzsYqATuc84NDzseyVxm1h3o7pybbGbtgUnASfq9KMlmZga0dc5Vmlkr4B3gMufcByGHJhnKzH4MjAIKnHPjwo5HMpOZLQJGOedWhx1LU2nGNRijgXnOuQXOuSrgIeDEkGOSDOScewtYG3YcIs65Fc65ybF/VwCzgJ7hRiWZyHmVsS9bxS46ay+hMLNewHHAnWHHIpJqlLgGoyewtMHXy9AHNBERAMysGBgBfBhyKJKhYqWZU4AvgFecc3otSlhuAq4A6kKOQ8QBL5vZJDO7OOxgmkKJq4iIJIyZtQMeAy53zpWHHY9kJudcrXNuT6AXMNrMtJRCks7MxgFfOOcmhR2LCHCgc24kcAxwSWy5WaQpcQ3GcqB3g697xW4TEclYsfWEjwEPOOceDzseEefcemACcHTIoUhmOgA4Iba28CFgrJndH25Ikqmcc8tj118AT+CXPkaaEtdgfAwMMrN+ZpYLnAk8HXJMIiKhiTXEuQuY5Zz7S9jxSOYysy5m1iH279b4RoqzQw1KMpJz7krnXC/nXDH+s+LrzrlzQw5LMpCZtY01TsTM2gJHApHfkUKJawCcczXApcBL+AYkjzjnZoQblWQiM3sQeB8YbGbLzOyisGOSjHUAcB5+RmFK7HJs2EFJRuoOTDCzafgTza8457QNiYhksm7AO2Y2FfgIeM4592LIMe2UtsMRERERERGRSNOMq4iIiIiIiESaElcRERERERGJNCWuIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERSRIzK2qwPdDnZrY89u9KM/tn2PGJiIhElbbDERERCYGZXQtUOuf+FHYsIiIiUacZVxERkZCZ2Rgzezb272vN7F4ze9vMFpvZKWZ2o5lNN7MXzaxV7H57mdmbZjbJzF4ys+7hPgsREZHEUeIqIiISPQOAscAJwP3ABOfcbsAm4LhY8vp34DTn3F7A3cD1YQUrIiKSaDlhByAiIiJf84JzrtrMpgPZwIux26cDxcBgYDjwipkRu8+KEOIUERFJCiWuIiIi0bMFwDlXZ2bVbmtDijr8324DZjjn9gsrQBERkWRSqbCIiEjqmQN0MbP9AMyslZkNCzkmERGRhFHiKiIikmKcc1XAacAfzGwqMAXYP9SgREREEkjb4YiIiIiIiEikacZVREREREREIk2Jq4iIiIiIiESaElcRERERERGJNCWuIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERERERkUhT4ioiIiIiIiKRpsRVREREREREIk2Jq4iIiIiIiESaElcRERERERGJNCWuIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERERERkUhT4ioiIiIiIiKRpsRVREREREREIk2Jq4iIiIiIiESaElcRERERERGJNCWuIiIiIiIiEmlKXEVERERERCTSlLiKiIiIiIhIpClxFRERERERkUhT4ioiElFm9oKZnd/Cxy4ys8Nj//6lmd0ZcGwHmdmcIMds5DjFZubMLCfRx2ouMzvHzF5uwv1uM7OrkhFTU5lZHzOrNLPssGNpqab+/FOFmbU2s2fMrMzM/hd2PCIiUWPOubBjEBFJG2a2COgG1AIbgBeAS51zlSHE8S3n3KtxjDEM+CswCn+icz5wlXPu+UCCbFoMxcBCoJVzrmY731+E/3nX4H/mM4H7gNudc3XJijMMZjYGuN8512ub29+I3R7oyYqmMrN/A2cDVQ1uvsg593AY8TSFmc0A+sa+bA1U419TADc4525IQgznAT8A9t/ea11EJNNpxlVEJHjHO+faASPxSd+vm/Ng86Lw+/kZ4BVgF6Ar8EOgPNSItu9451x7fOLxe+DnwF3hhpTxbnTOtWtwCTRpjXcGftuZZufcsPpYgbfxJ5vqY7+hweMSOfPfFyhtSdIaxYoEEZGgReGDkYhIWnLOLcfPuA4HMLN9zew9M1tvZlNjM2bEvveGmV1vZu8CG4H+sdu+Fft+lpn92swWm9kXZnafmRU2ePx5se+tMbNfNYzDzK41s/sbfH1ggziWmtkF28ZuZp2BfsAdzrmq2OVd59w7se+P+f/27js8yip94/j3gdB7E+lIEaSX0Js0FVDsXdfu6lrXtqu7a1nX3tuua9e1N1QUadKRFnpVQZDee6hJzu+PM/xEhJBAJmfK/bmuuYDJZN47wyR5n/ec8xwzW77f41uZ2XQz22Zmn5jZR2b2r/0fa2a3R7KvMrMr9vvcfpHP3RrJc/8Rvt5bnHNfAecDl5nZvte9iJk9aWZLzWxNZOpusRxmKxN5rddFXt+/77uoYGaXm9m+18PM7JnIc2w1s9n7Hf+tXLwWFSLTRbea2RQz+9e+YxwJM2trZmmR51tjZk9H7v/NFOzIe+1BMxsf+T8cGnkP7HueP+z3/vqH7TcVPZd5rjGzhWa20cy+MrOqB8uzX6Z97//LI9meMbMNwP37v/6RxzQ0s2GR5/7BzM7b72Nvmdl/zGyQmaUD3XOYd1+uq8xsKTAicv8nZrba/LTeMeZnJ+x/rJfM7JvIaznJzOpGPnbQ94mZPQDcC5xvfgr3VZbN9/zBch3wGm02s5/NrGPk/mWR5ziipQciIrFAhauISJSYWQ2gLzDdzKoB3wD/AsoDdwCfmVml/T7lUuBaoBTwywFPd3nk1h2oA5QEXowcpxHwn8jnVwUqANU5CDOrhS+mXwAqAS2AGQd56AZgIfCumZ1hZpWz+ToLAwOAtyJf2wfAmQc87FigDFANuAp4yczKRT6WDvwBKAv0A643szMOdbzDcc5NBpYDXSJ3PQocj/9a60Uy3JvDbC9EPlYH6BbJeQW/dxLQNXKcMsB5+NfwYLI73kv41+NY4LLI7Wg8BzznnCsN1AU+zuaxF+G/tmOAwvj36L7317+Bi4Eq+2XPFTPrATyCf22q4N/jH+biKdoBP+Onhj90wHOXwM8OeD+S/wLg35Hs+1wU+bxSQG4vBnQDTgBOjvz7W6B+5FjTgPcOePwFwANAOfz30b68B32fOOfuAx4GPoqM8r5ONt/z2eRqB8zC/wx4H//6tsG/7y8BXjSzkrn82kVEYoIKVxGRvPeFmW3GnxyPxp+QXgIMcs4Ncs5lOeeGAWn4wnaft5xzc51zGc65vQc858XA0865nyPrZe8GLoiMUJ0DfO2cG+Oc2w38AzjU+s6LgOHOuQ+cc3udcxucczMOfJDzDRC6A0uAp4BVkZGl+gd5zvZACvB85Dk/ByYf8Ji9wD8jHx8EbAcaRI41yjk3O/K6zMIXvt0OkT+nVgLlzczwFwP+7Jzb6Jzbhv//uOBw2cxPJ70AuNs5t805t++1uPQgx9uLL4ga4vtHzHfOrTpEtuyOdzZwn3Nuh3NuHvD2Ub0K/lj1zKyic267c25iNo990zn3o3NuJ77AbRG5/xxgoHNunHNuD77oP1yDjDsio36bzWx95L6LgTecc9Mi79O7gQ7m1zHnxErn3AuR74+dB3zsVGCJc+7NyMenA58B5+73mC8jswaynHO7cnjMfe53zqXvO65z7o3Ie2I3cD/Q3PabAQEMcM5Njkz7fY9fX8vcvE+y+54/aC5gceQ1yAQ+Amrg32u7nXND8euO6+XyaxcRiQkqXEVE8t4Zzrmyzrlazrk/RU4qawHn7ncyvxnojB952mdZNs9Zld+Owv6CLxYrRz72/5/rnEvn0KN9NfBNlg7LObfcOXejc65uJH86vvHRwbKtcL/t9nfg17LhgLV7O/AjSJhZOzMbaX467hbgOqAiR6casBE/qlwcmLrf6z44cv/hslUECvH71/13o43OuRH40bCXgLVm9oqZlT5EtkMdrxL+/3T/1y6790RGJN+BCuELJPAjuscDC8xPPT41m+dbfZBM8Pv31w4O/f7a58nI90BZ59y+/8vfvIcjxdgGcj56m91rUQtod8D318X4keucfH6Oj21mBc3sUTNbZGZb8Rd34Lfv2YO+lrl8n2T3Pf+7XBFr9vv7viL7wPs04ioicUmFq4hI/lgG/G+/k/myzrkSzrlH93tMdqNYK/m16ylATXzhsgZYhS9IATCz4vipgofKUTe34Z1zy/An200O8uFVQLXI6OY+NQ7yuEN5H/gKqOGcKwO8DFj2n3JoZtYGXwyNA9bjT9Yb7/e6l4k04Tmc9fgC8MDXfcXBHuyce9451xpohC8W78xl9HX4/9P9p3ln9zouBSruP/Uz8n9Qi0jB45z7yTl3IX5K62PAp5Fptbmxav9M5tcHH+r9lZ3fvIcjOSrgX8/0yN3F93v8/kUnZP/9sQwYfcD3V0nn3PU5/PzD2f9zLwJOB3rhp/vWjtyfo/dsLt4n2X3PHyyXiEhCU+EqIpI/3gVOM7OTIyM2Rc036jnoWtSD+AD4s5kdFylU9q2HywA+BU4133SpMPBPDv3z/T2gl5mdZ2Yp5psBtTjwQWZWzsweMLN6kSYxFYErgYNNNZ2A34rmxshzng60zeHXBX7q5Ebn3C4za4svDHLNzEpHRhQ/xG8HM9v5LXFeBZ4xs2Mij6tmZidn91wAkemWHwMPmVmpyPrg2/D/lwceu01k5LgQvgjbxaGna2d3vM/xjYeKm1lD/JraQz1+KTAJeMzMSppZEXwRtJfI/5OZXWJmlSKvw+bIp+Z2m6BP8e/djpH31/0c2YWFD4ArzKxFJOvDwCTn3BLn3Dp8AXtJ5PvjSnJ3geVr4HjzTcoKRW5tzOyEI8h5OKWA3fjR4uL4ryNHcvk+ye57XkQk6ahwFRHJB5ERy9OBe/Aja8vwRUZOfw6/AfwPGIPf13QXfs9HnHNzgRvwI5ergE345kQHy7EUv672dvxU2hlA84M8dA9+JGk4fgucOfiT9csP8px7gLPw01I349fzfh15fE78CfinmW3Dr5/MroHQwQyMfO4y4G/A0/y2gdJf8A1yJkamdg4nsr42B27CFxg/40dw38f/XxyoNL5A3oQf7dwAPJHLrwPgRvwo3mr8//cHZP86no8fTV2IL/x6Av32W8N5CjDXzLbjGzVdcJD1odmKvL9uwl8QWIVfk7v2MLkO9jzD8euvP4s8T11+u9b4Gvz3xAagMfB9Lp57G77x0QX4kcrV+BHmIrnJmEPv4P+PV+D3Dc5u3fCBcvM+OeT3vIhIMrLfLkkSERE5emY2CXjZOfdm6CzxzMweA451zsXMNiaR0b/NQH3n3OLAcUREJEloxFVERI6amXUzs2MjU4UvA5rhmyBJLpjfi7SZeW3xo9gDYiDXaZHpyyWAJ4HZ/NqUSEREJOpSDv8QERGRw2qAn+JbAj+t9pxstvmQQyuFnx5cFd+E5yngy6CJvNPx01YNv43TBU5TtkREJB9pqrCIiIiIiIjENE0VFhERERERkZgWV1OFK1as6GrXrh06hoiIiIiIiETB1KlT1zvnKh14f1wVrrVr1yYtLS10DBEREREREYkCM/vlYPdrqrCIiIiIiIjENBWuIiIiIiIiEtNUuIqIiIiIiEhMU+EqIiIiIiIiMU2Fq4iIiIiIiMS0uOoqLCIiIiKSaDJ2wKrRsHEmbFvsb7s3QIHCkFIUUkpA2UZQoQVUaAllGoBp+EmSjApXEREREZF8tmcrLHwXlg2EVaMgc5e/v2hFKHkcFK8CmXv8/enLYMUwyNrjH1OiJtS5AOpeCOWbg1mwL0Mk36hwFRERERHJJ9sWw9zn4cfXYe82KHM8NPwjVO8Lx3SAwqUO/nmZe2DLAlg3BZZ8DnOehtmPQ4VW0PI+qHmaClhJbCpcRURERESibNcGmPoP+OG/QAGocx40vgUqtc3Z5xcsDOWb+VuDq2DXelj8Ccx+CoafDhVbQ6sHoUafqH4ZIsFodryIiIiISJRkZcK8f8Mn9eGHV+CEG+D8JXDiezkvWg+maEU44Xo4ZwF0eQN2b4ShfWHE+bBzbZ7FF4kZKlxFRERERKJg2xL4pgtMuME3VjpjBnR4HkpUy7tjFEiB46+Ac36A1g/BL1/AZ41g0fvgXN4dRyQ0Fa4iIiIiInls8SfwRQvYNBe6vQt9voPyTaJ3vAKFoMU9cMZ0KF0PRl0MY6+EjF3RO6ZIflLhKiIiIiKSR7L2wvjrYcR5UKahLyTrXZx/jZPKNYJTx0PLe+Gnt+CbrpC+PH+OLRJNKlxFRERERPLAni0wpB8seBma3gmnjoXSdfI/R4GC0OoB6DkAtsyHL1rDmgn5n0MkLwUtXM2srJl9amYLzGy+mXUImUdERERE5EhsXwpfd4ZVI32zpLaP++m7IdU+A06bBIVLw+Befi9YkXgVesT1OWCwc64h0ByYHziPiIiIiEiubJoHX7WD9GVwymDfLClWlGsEp47z616HngpLvgidSOTIBCtczawM0BV4HcA5t8c5tzlUHhERERGR3No4Bwad6P9+6nio2jNonIMqVhn6joIKLWHEObDw3dCJRHIv5IjrccA64E0zm25mr5lZiQMfZGbXmlmamaWtW7cu/1OKiIiIiBzEhpnwbXc/JbjfaCjXOHSiQytSDk4ZBsd2hTGXwZLPQycSyZ2QhWsK0Ar4j3OuJZAO/PXABznnXnHOpTrnUitVqpTfGUVEREREfmfjbPi2BxQs6ovWMseHTnR4hUtB74FQqR2MvBBWDA+dSCTnQhauy4HlzrlJkX9/ii9kRURERERi1rbFMORkX7T2HeXXj8aLQiXgpG+gbEMYfgasnRg6kUjOpIQ6sHNutZktM7MGzrkfgJ7AvFB5REREJH84B9uXwPqpsHke7NkKGdshYycUqQAlqvtb+WZQpkH+7X8pkhM718Hgk/37td9YKF03dKLcK1IOTh4C33SBIX2h/8T4GDGW5BascI24CXjPzAoDPwMx1INNRERE8krmHlgxBBa+ByuHwe6Nv34spTiklPCjV7vWQ+bOXz9WvKpvdlO9D9Q6E1KK5n92kX32bIOhfX334D7DoXyT0ImOXPFj4ZShvhvy0FOh/yRf0IrEqqCFq3NuBpAaMoOIiIhEz45VMOtxWPg/2L3Bj6jWPB2OaQcVWkP5plCwyK+Pdw72bPZ7Yq6bDCu/g+WD/ecXqeC3GWn4x/iamimJISsTRl4AG6ZDry+gcqfQiY5eqeOg5+fwbU8YcS6c/G34vWdFDsWcc6Ez5FhqaqpLS0sLHUNEREQOY+c6mPUYzH8JsvZC7bOh3qVQ/eTcnxi7LFg1Eub/B375wv+7/mXQ+kE/pVgkP0y6HeY8DZ1e9hdPEslPb8OYy6HhddDx35qeL2GZ2VTn3O8GN0NPFRYREZEE4rJgwX9hyl2QsQPqXgIt7z26dYBWwE8XrtoT0lf64mHeC/Dzh9Dkz9Dsbt8tVSRafnjdv+8a3Zx4RSv4C0Gb5/uLTRVaJObXKPFPI64iIiKSJ7YthrFX+dHRqr2hw/O+c2lUjrUEpv4dFr3npzt2eQuqdI3OsSS5rRoDg3tBle6+G2+BBB32cVkwtB+sHAGnfQ8VW4dOJMnqUCOuIbfDERERkQSx8D34vCmsT4POr8IpQ6JXtAKUqg0nvgunjgMKwKATYeJtvtOrSF5JXw4jzoZSdaD7R4lbtIKf2dDtf1CsMnx3zm8bqInEAhWuIiIicsSyMmDSHTD6Ej9Cc9YcaHB1/q2Rq9wJzpwBJ1wPc5+Bge39yK/I0crcA9+dC5m7fDOmImVDJ4q+ohWhx8ewYwWMvsyPworEChWuIiIickR2b/JTC+c8BY1u9NuDlKyZ/zkKlYSOL/lpnNuXwpdt/HRHkaMx+Q5YNxG6vBnd2QOx5pj20PYpWPY1zHoidBqRX6lwFRERkVxLXwlfd/brWTu/Ch1eCL+NRo2+0H+yn+o4+CSY+0LYPBK/Fn3gG4A1uQ2OOyd0mvzX6EaofY5fR75O7WUkRqhwFRERkVzZ9gt80xXSl8LJQ/zU4FhRpj6cNhFqnAoTb4Ypf/V7w4rk1OYFMO4aqNwZ2jwaOk0YZtD5v1D8WBh1EexND51IRIWriIiI5MKWH+GbLrB7A5wyDKp2D53o9wqXgp6f+T0pZz0G466FrMzQqSQeZOyCkedDSrFIM6bAswhCKlLeN2vauhAm/Tl0GhEVriIiIpJDW3/23Xszd0HfkX4tXKwqUBA6/hta/B1+fA1GngeZu0Onklg35U7YOAu6vg0lqoZOE16VE6HZX+CHV2HJgNBpJNmpcBUREZHD2rHarxvN3O2L1gotQic6PDNo/SC0ewaWfA4jzoesvaFTSaz65UuY9yI0/rNfLy1eqwd8x/Bx18DONaHTSDJT4SoiIiLZ2r0ZhpwCO1fDSYOgXOPQiXKnya2+edTSL2HkRX4LH5H9pS+HsVdChVbQ5pHQaWJLwcLQ9R3I2A7jr9eacQlHhauIiIgcUsYuGNYfNs+Dnp/DMe1CJzoyjW70W3ws+RRG/0FrXuVXLsu/JzJ3Q/cPoWCR0IliT7lG0OpB+GUA/PxB6DSSrFS4ioiIyEE5B+OuhjVjfZOW6ieFTnR0mt4GqY/4E+/vNXIkEXOe9ds6tX/Od6WWg2tyG1RqD9/fCDtWhU4jyUiFq4iIiBzUrMdh0XvQ+l9Q5/zQafJG879C87t9s5np/wydRkLbOBvS7oaa/eH4K0OniW0FCkLXtyBzJ4z/oy78SP5T4SoiIiK/s3SgP6GvcwE0vyd0mrzV+iGofxlMvx9+eC10GgklczeMuhgKl4XOr/pmXpK9sg3898/SgbD449BpJNmocBUREZHf2DQXRl0EFVtBl9cT74TezBcq1U/xI0dLvw6dSEKYei9smg1d3oBix4ROEz8a3wIVU2HiLbB7U+g0kkxUuIqIiMj/27sdvjsHUkpAry8hpXjoRNFRoBD0+MR3kR15AWyYGTqR5Ke1k2DOk3D81VCzX+g08aVAQej0CuxaD1P+GjqNJBMVriIiIgL4NWvjr4OtP8KJH0CJaqETRVehktD7Kz9VdNhpfq9aSXwZu2DsFVC8KrR7MnSa+FSxJTS+FX54BVaPC51GkoUKVxEREQH8es9F70HL+6Fq99Bp8kfxKtB7IOzeAMPP8EWNJLYZ/4TN8/108cJlQqeJX60egBI1/XT7zD2h00gyUOEqIiIibJgBE2+Cqr0TrxnT4VRs6bf7WTcJxl2lbqmJbF2a75Zd/wq/xlmOXKES0PHffo/n2U+ETiPJQIWriIhIksvY4dd5FikPJ77r17Alm9pn+W1/Fr0Pc58LnUaiIXO3nyJcrDK0ezp0msRQsx8cdy7MeBC2/BQ6jSS6lNABJP85B1t/grUTYe0E2LIAdm3w06T2bvdrfYpWhKKVoHwzqNwJjukIxSqFTi4iItEw+S7Y8gP0GZ7c3VWb3wPrpsDkO33X1GM7h04keWnGv2DTHOj9NRQpGzpN4mj/HKwY6tfH9xmeeF3IJXaYi6P5MKmpqS4tLS10jLi1cQ4s/B/8/D6kL/f3FSoN5ZtCkYpQtAKklIQ9m32nuF1r/MbcWZF1CxVawfFXQN2L/FV5ERGJf8u+haF9ofGfob1GodizBb5MhYx0OH0aFD82dCLJC+unw1dt/DlMt3dCp0k881+G76+Hrm9D/T+ETiPxzsymOudSf3e/CtfE5rJgyQCY9QisnwpWEKr3gZr9oXJHKHsCWDYTxjN2wYapvmPc4o9gw3QoUBiOOwda3Os3ohYRkfi0az183tTPsuk/BVKKhk4UGzbOhq/aQaU2fgSpQKHQieRoZO6Br9rCzjVw9lxdfI8GlwVfd/EzN85Z4H+miBypQxWuWuOaoJyDxZ/BgBYw4hzYu81P5bhwJZw0EBpeA+UaZ1+0gj+JqdwJmv8FzpgGZ0yHhtfBL1/C541h7DW/jt6KiEj8cM53A929Ebq9q6J1f+Wb+o6zq8fAlLtDp5GjNfMR2DgTOr2sojVarAB0+q+fsTD5rtBpJFGpcE1Am3+AQd19wZq125+QnDUPGt989GuXKrSADs/BeT/DCTfAwrfhk/ow+ynIysyT+CIikg9+/giWfA6tH4QKzUOniT31Lva/5+Y8BYs/DZ1GjtSGmX5ta92LoNbpodMktvJNoMlt8NObvo+KSF7TVOEEkrkbZj0GMx6ClOLQ5jE4/qrodofctgQm3gJLv/Ijs13fgtL1onc8ERE5ejvXwmeNoHRdOPX75OwinBOZe+CbbrB5jp9KXbZh6ESSG1l7/ZTv9BVw9jzfy0Oia+92+LQBFDsW+k/WzxY5MpoqnOC2LoSBHWDafVDrTDh7PjS8Nvo/MErVhl5fQNd3fKe+Ac3hx7eie0wRETk6E27yS0i6vKkTy+wULAw9P4GCxeC7s/xJucSPWY/73hyd/qOiNb8UKgltn4IN0+CHV0OnkUQTvHA1s4JmNt3Mvg6dJV4t/gS+aOVHP3t9AT0+zN8uiGZQ/1I4ay5Uau/3SJv4Z8jKyL8MIiKSM0s+h8UfQ8v7oFyj0GliX4nq0P1D33Rm/B/92mCJfRvnwPQH4Ljz/B69kn/qnA9VToSpf/PbLYrkleCFK3ALMD90iHiUlQETboER50HZRr5xUsj1GyWqwSlDoNHNMPdZGNLXN/0QEZHYsHsjfP8nqNASmt0ZOk38qNoDWt4Pi96Hn94OnUYOJyvDX0QvXAY6vBg6TfIxg/Yv+EZNafeETiOJJGjhambVgX7AayFzxKM922DY6TDveWh8C/QbA6VqhU4FBVJ886Yur8PqUTCwk19bIiIi4U3+i98Cp8sb2uIlt5rf40eRJtwAmxeETiPZmf0UrE+DDi9BsUqh0ySn8k38QMYPr8I6taeRPBJ6xPVZ4C4g61APMLNrzSzNzNLWrVuXb8FiWfoK+KYrrBjiW7u3f9avw4klx18JpwyHHSvgmy6wbXHoRCIiyW31WPjxNWhyu+8QL7lToCB0e883Pxx5vt/nXGLP5vkw7V4/Pfi4c0OnSW6t7ve7WUy4we/zKnK0ghWuZnYqsNY5NzW7xznnXnHOpTrnUitV0mWzzQtgYHvYthB6D4SGfwyd6NCqdIU+38HuzX5Tal2hFhEJI3M3jLsWStaGlveGThO/SlSFLm/Bxlkw+Y7QaeRAWZkw5krfIKjjv/2UVQmncGlo8wSsmww/vhk6jSSCkCOunYD+ZrYE+BDoYWbvBswT8zbO9m35M/dAv7FQo0/oRIdXqQ30G+Vb0n/TDbb8GDqRiEjymfUEbFngT+YLlQidJr7V7Of3qpz/EiwZEDqN7G/us7BuInR4AYpVDp1GAOpdApU7Q9pf1fdEjl6wwtU5d7dzrrpzrjZwATDCOXdJqDyxbv00GHSiX0Pab3R8TfMq38xnJgsGnwTpy0MnEhFJHlt+gpn/8t1V4+GCZzxIfQQqtoaxV8K2X0KnEfAXxqf+HWqeDnUuDJ1G9jHzDbJ2b4Spmu0hRyn0GlfJgXVT4NsekFLSN2GKxw3QyzaEkwf7H1yDT/LNQUREJLqc83u2Fiji+yFI3ihY2G+R4zJh1EXa/i20rEx/EaFgMb9nq6YIx5YKzeGEP8GC/8CGGaHTSDyLicLVOTfKOXdq6ByxaONsGHwyFCnvi9bSdUMnOnIVW0Pvr2Dbz36rHG3kLiISXUu/8o38Wv0TilcJnSaxlK4Hnf4La7+HafeHTpPc5r0Aa8b7izN6n8emVv/057ITbtJeyHLkUg73ADMrDtwO1HTOXWNm9YEGzrmvo54uyW35CQb3hpRivslRLGx3c7SqnAjdP4bvzoTRl0LPz8Bi4vKJSO7t3gwrhsLGmX794Ob5kc3Ws3wHxQKFoFQdf4Jbur5//x/TwU/5F4m2jJ0w8VYo2xga/Sl0msRU90JYORxmPgxVu0PVnqETJZ+tC/1eoTX6Qb1LQ6eRQylSDlo/DOOv9fsh17s4dCKJR+YOc9nDzD4CpgJ/cM41iRSy3zvnWuRDvt9ITU11aWnJsRnU9qW+E2/mjsj04BNCJ8pbc56DSbdC87sh9eHQaURybvcmWPg/+OVLWD0GXAZYii9OyzSA4seCFfQXZDJ2+hkGWxdC+jL/+YXLQNXe/oS3Zn8VsRI90x6A6fdDnxG+qJLo2JsOX6bCns1w5ky//YfkD5cFg7r7i4dnzYUS1UInkuxkZcLAdrBjJZz9AxQuFTqRxCozm+qcSz3w/pycMtV1zp1vZhcCOOd2mGn1QDTt3uinB+/dAn1GJl7RCtD4Ztg8D2Y+AmVOgPq6SioxbttimPMs/Pg6ZKRD2UbQ9A6oeZrvnl2gUPafv2cLrBgOy7+F5YNgyadQooZf99PgGihaIV++DEkS25bArEfhuPNVtEZboRLQ4yP4qi2MuQxO+kYzifLL/H/7C4hd3lDRGg8KFPSNmgZ2gJkPQZtHQyeSeJOTH617zKwY4ADMrC6wO6qpkljGLhjW34/S9PoKKrYMnSg6zKDji37q5LirYc2E0IlEDm7nOhh7DXxSzzeWqH02nDEDzp4LbR6Byh0PX7SCH2k97mzo8hqcvwx6DvDTh9Puho/rwKzH/fe/SF6YdJsvnto9GTpJcijfDNo9A8sHw5ynQ6dJDlsXwpS/QLWTof7lodNITh3THupf5r9PtEWi5FZOCtf7gMFADTN7D/gOuCuqqZKUy4LRl/gGA93+B1W6hk4UXQUKQY9PoUR1GHEu7FwbOpHIr7IyYO4L8Onx8NNb0OgWOG8JdHvbd0g8GgUKQu0zoO93cOZsqNLNn4B9dgIs/kSNK+ToLB8CvwyAFn/3P18lfzS8DmqfBVPuhrWTQqdJbFmZMOZyfx7R5TV1EY43qY9CwaJ+Db5+30luHLZwdc4NA84CLgc+AFKdc6OiGys5TbodlnwGbZ+COueFTpM/ilbwDZp2r4dRF/tfRiKhbfnJT2WaeDNUTIWzZkP7p6FE1bw/Vvkmvtt2n+FQuDSMOA9GnKMto+TIZO7x79vS9aDJbaHTJBcz6Pyan7I68gLfvE2iY85TkS7CL+jiTDwqfiy0vN8vnVmmVq+SC4csXM2s1b4bUAtYBawEakbukzy04BWY+yw0uhmaJtnJRoUW0OEl35lxxj9Dp5Fk99P/4MtWsHURdP8IThmaP3snV+0Jp0+DNo/B0q/h8yaw9JvoH1cSy9xn/fS79s9DwSKh0ySfIuX8/q7py/0yGI0m5b2Ns2HqP6DWmVDvktBp5Eg1vsn3cJl4q5bJSM5lN+L6VOT2EjAJeAV4NfL3l6IfLXmsGgPf3wDVT4F2Sbo25vgr/RqV6Q/6NUIi+S1jJ4y+DMb8Acq39N1B65yXv1PQChSEZnfB6VOg6DEw7FSYfKdmIkjOpK+AGQ/6btU1+oROk7yOae+75S/5DBa8HDpNYsnc4xtgFS7j99DVFOH4VaCQv8C27Wc/gi6SE4csXJ1z3Z1z3fEjra2cc6nOudZAS2BFfgVMdNt+gRFnQ+k6cOIH/sQ1GZlBx5egXBO/v+uO1aETSTLZuQ6+7QkL34GW90HfkVCyRrg85Zv54vWEP8HsJ2FoP78Nj0h2ptwFWXt9kyAJq+ntUL0PTPozbJgROk3imPEv2DAdOr0CxSqFTiNHq1ovvy585sOwfVnoNBIPctKcqYFzbva+fzjn5gAJuEFL/tu7HYb39ycavb6CImVDJworpbjfUmDvdt90wWWFTiTJYPMCGNjenwz1+BRa3R8bF5AKFvEXczq9AqtGwFftfFaRg1nzPSx6H5re6S+ESlhWALq+DUUqwMjzYc+20Ini37opvsCp9wff3E4SQ9un/Pne5DtCJ5F4kJPCdZaZvWZmJ0ZurwKzoh0s0bksX5xtmuPX0ZVtEDpRbCh7gp8uvWKI7+gqEk1rJvgmTHu3Q99RfruaWNPwGugzwu8D+3VnWDc5dCKJNS7LrxMrXhWa/TV0GtmnWCU48X2/bcv312u969HI2Amj/wDFq0D750KnkbxUqrb/ubX4Y1g5MnQaiXU5KVyvAOYCt0Ru8yL3yVGY/qBf/9LmCah+cug0saXhdVDzND/tbaMukUiUrB4HQ06CohWh/0Q4pl3oRId2bGc47XvfdXhQD1j5XehEEksWvgfrp/gtJgqVCJ1G9lelm++euug9v62WHJm0e2DLAujypmanJaJmd0HJ2r4jelZG6DQSy3KyHc4u59wzzrkzI7dnnHPq/3UUFn8G0+/3GzA3+XPoNLHHDDq/7rszjrxI3eYk760aDUNOgeLVoO9oKHVc6ESHV7ou9Bvnsw7pC0s+D51IYsHedEj7K1RsA/UuDp1GDqb5PVClh2/CuGle6DTxZ+VI3y37hBv8mkhJPCnF/Gy7TXNg/r9Dp5FYdtjC1cwWm9nPB97yI1wi2jDTdy2t1B46vqyOeIdSrBJ0fQs2z4Vp94VOI4lk1SgY0gdK1vTTg6OxN2u0lKgK/cZAxdZ+v9clA0InktBmPw47VkL7Z/26Sok9BQrCie9CoVIw4ly/NEFyZtcG37CxzPF+qzBJXLXOgKq9Ydq9sHNt6DQSq3Lyay4VaBO5dQGeB96NZqhEtXszfHcWFC4LvT6HlKKhE8W26qdAg2tgzpN+LaLI0Vo/FYad5kct+47ym6DHmyLl4OQhUKmtb/qyVJu3J63tS2HW41DnAqjcMXQayU7xKtD9fT/ddeyVWu+aE87B2Ktg11q/64KmwSc2M+jwfGQWyT2h00isyslU4Q373VY4554F+kU/WmJxWX6kdftS6PGJ/yUmh9f2SSheHcZe7psziBypLT/5kdYiFeCUoVDsmNCJjlzhUnDyt1C+OXx3NiwfEjqRhJB2t/8z9dGwOSRnqvb0/1eLP9G+lTmx4GVY+qV/zSq2Cp1G8kPZhtD4FvjxdQ1YyMHlZKpwq/1uqWZ2HZCSD9kSyqzHYOlAaPeUroznRuHS0OV12PIjTP176DQSr9JXwuCTAOeL1hLVQic6eoXL+K+lbCMYfgasGR86keSntRP99jdNbodStUKnkZxqegfUPgem/AVWjgidJnZtnAOTbvMzr5rcGjqN5KeW90GJ6vD9dWrUJL+Xk6nCT+13ewRoBZwXzVCJZuV3vuiqcyE0uil0mvhTrRc0vB7mPOP3KhTJjb3bYWhf2L0eTvrWr5VKFEXKQZ9hfr3u0NPU+CVZOOe3vyl2LDTX9jdxxQy6vAFlGvqp/tuXhk4Ue/am+9emUGnf60Jrt5NL4VLQ/nm/q8Tc50OnkViTkx8HVznnukduvZ1z1wJ7oh0sUaQvh5EX+F9SnV9RM6Yj1fZxKFEDxl0LmXr3SQ65LBh1MWyaDT0+hUqpoRPlvaIV/ZrXgkV8p+T05aETSbT9/AGsmwSpj0ChkqHTSG4VLgU9P/e/y747W53z9+ccjL8ONs/3a4KLVQ6dSEKodQbU6OcbNW1fFjqNxJKcFK6f5vA+OUDmHvjuXMjcBT0/0wnG0ShUEjr+23cZnv1E6DQSL6bcDUu/8hvWJ/J+yaVq+zWvezb7dby7NwcOJFGTscNPM63QCur/IXQaOVJlG0C3d2B9Gky4Qc2a9vnhVVj0LrR6wK8JluRkBh1e8BefJ90aOo3EkkMWrmbW0MzOBsqY2Vn73S4H1A83BybfDusm+g2zyzYMnSb+1ewHx50LMx70jXZEsvPjW36rkIbX+/3/El2FFtBrAGz5wW+5kbU3dCKJhtlP+lF1bX8T/2qdDi3+Dj++4Qu2ZLd+Gky4CaqdDC3+FjqNhFbqOGj5D79n+dJvQqeRWJHdr70GwKlAWeC0/W6tgGuinizOLXof5r0ITW6D484JnSZxtH8OChaF8X/UFWo5tLWTYPy1ULUXdHgueaboV+0Jnf4LK4f7NZCSWNKX+0Z/tc+BY7uETiN5oeX9vgHRhBuTu4fDrg0w4hzf7f3Ed3VRRrwmt0PZE/z3R8aO0GkkFhzyR4Nz7kvn3BXAqc65K/a73eycS+Ifr4e3cQ6MuwYqd4E22qYgTxWv4jchXzUSFr4TOo3Eop3r/AlQ8WrQ4yMoUCh0ovx1/BXQ9E6Y/29/8UwSR9o94DL9mn9JDAUKwonvQclaMPx02Ppz6ET5LyvDN2NKX+F7ERStGDqRxIqChaHjy7B9Ccz4V+g0Eguymyp8V+SvF5nZ8wfe8ilf3NmzFUac7bvhJeNJc35ocA1U7uRb5e9cFzqNxJKsTBh1Eexa59eVFykfOlEYqY9Azf4w8Rbt8Zoo1k6Chf/zs3hKHRc6jeSlIuXhpG/8z6+h/ZJvjfqk2/3uC51fgWPahU4jsaZKV6h/Gcx6Qp3zJfupwvMjf6YBUw9ykwM4B2OvgK2LoPtHfnRQ8p4V8NMh927z64hF9pl2n58m2+Gl5N6wft8oTrkmMPJC2LY4dCI5Gv+//U1laHZ36DQSDWWO92vUty3yM0aSZY36j2/AvOeh8Z99cSJyMG2egEKl4PvrtUws2WU3VXhg5M+3D3bLv4jxY87TfhF5m8f8FSKJnnKNodlf/AjEimGh00gsWDYIZj4Ex18FDa4KnSa8QiX9lhu4yJYbO0MnkiP184e+0V/qw34rFUlMVbpB51f96OO4axL/BH3VGL/1TdXemv4u2StWyZ9brx4DP70VOo2EZO4QPxnNbCBwyB+bzrn+0Qp1KKmpqS4tLS2/D5sja8bDN92g1pnQ4+PkaQYTUsYuGNDMr/k6azakFA+dSEJJXwlfNIfiVeG0iZBSLHSi2LH0axh2GtS/Arq8rp9N8SZjB3za0K/76z/Fj6ZLYpv2AEy/H5reAW0TdPu3TXPh685+Ztqp46FIudCJJNa5LH+evWkOnD1PsxoTnZlNdc6lHnh/Sjaf82QU8yScck2h0U1+7zGdGOaPlKJ+yvC3PWD6g9DmkdCJJISsTBh9iT/B7/6RitYD1TwVWvzDbyN1TAdoqJ7wcWX2U5C+DLr9T0Vrsmh5r1+nP/tJKFoJmt11+M+JJ+kr/H7TKcXgpG9VtErOWAHo/Jq/SP39Db6Phc63k092U4VH77sBE4BNwEZgQuQ+2U/h0tD+Gf+n5J+q3aH+5f4X/OYFodNICDMf8V2mO7yo/ZIPpeV9fm/ECTfCuimh00hOpa+AWY9C7bP9NFJJDmbQ4XmocwFM+Qv88HroRHlnzxYY2hf2bIaTBkGpWqETSTwp2wBaPgC/DIAln4ZOIyEcdqcsM+sHLAKeB14EFppZn6M9sJnVMLORZjbPzOaa2S1H+5ySnNo85tfzTbgp8dcEyW+tHgfT74O6F/kLGHJw+5o1Fa/i17vuWh86keRE2t1+q5A2Wv+XdKwAdH3bX3Aadw38lACdRfZu912TN83zo2UVWoROJPGo6e1QsTV8f6Pf/1dyxzn/eyVe5WSL56eA7s65E51z3YDuwDN5cOwM4HbnXCOgPXCDmTXKg+eVJFPsGGj9oO8mqytwyWPPNhh9KZSsDR3/oylDh1O0gj9Z3LXWdxrOygydSLKzbvKv29+UrhM6jYRQsLDvNFy1J4y5An58M3SiI7c33RetaydC9/ehWu/QiSReFUiBzq/D7o1+yzfJnTlPw+CT/IWkeJSTwnWbc27hfv/+Gdh2tAd2zq1yzk2L/H0bfvudakf7vJKcGl4H5Zv7vV3j9ZtRcmfSbbD9F+j2jqbo51TF1tDx3/4iz7R7Q6eRQ9l/+5vm2v4mqaUUg95fQdVeMPaq+Jw2nLEDhvWHNeOg27tw3LmhE0m8q9AcWvwNFr0Hiz8LnSZ+LB8KU+7y68rjtaFpTgrXNDMbZGaXm9llwEBgipmdZWZn5UUIM6sNtAQmHeRj15pZmpmlrVu3Li8OJwmoQAp0fAnSl8OMh0KnkWhb+jX8+JpvWlK5U+g08eX4K+H4q2Hmw7D0m9Bp5GB+/gjWToDWD+mijESK1y+h2kkw7mrfsCte7NkKQ0/zfQi6vg11LwidSBJFi7/5i7Hj/wg714ROE/u2LoKRF0DZRv570XJSAcagQ26H8/8PMMtucopzzl15VAHMSgKjgYecc59n99hY3g5HYsOYy2HR+3DmbL+IXxLPrvXweRM/GtV/MhQsEjpR/MnYBQM7QPpSOGMGlKwROpHsk7ETPm0ARSrA6WnqJCy/ytjll0cs+RQa3wrtnortk8+da3z34I2zoMubUP/S0Ikk0WyaB1+28mvBe32hJUOHsnd75Hf+Cjh9CpSuGzrR4R3JdjgAOOeuiE4kMLNCwGfAe4crWkVyos1j8MsXMPFmOHmwfoglGuf8hvW7N8IpQ1W0HqmUon6/6S9b+Suw/UZBgUKhUwnst/3NOypa5bdSikKPj/wyibnPwo4V0PUdf3+s2boQBp8MO1dD74FQ46hbeor8XrlG0PphmHy7b2B2/OWhE8UelwVjLoPN8+DkIfFRtGYnJ12FjzOzp83sczP7at/taA9sZga8Dsx3zj19tM8nAn4UrtU/YcVQ3y5dEsui92HJZ9DqQSjfLHSa+FamPnR6FdZ+D1P/ETqNQGT7m0eg9llQ5cTQaSQWWQFo9wy0fRIWfwLfdIZtS0Kn+q2VI2BgR7/1TZ8RKloluprcCsd28wMWWxeFThN7ZjwESz6HNk9AtV6h0xy9nEwy+QJYAryA7zC873a0OgGXAj3MbEbk1jcPnleS3Al/8kXNxFt9J0NJDOnLYcINcExHaHpH6DSJoe4F0OBamPUYLPs2dBpJu0fb38jhmfktQXp96Uc2v2gFywaFTuVHdmY+CoN7Q9GKcNr3cEy70Kkk0e3bOsoK+o75mXtCJ4odv3zlGzHWvQSa/Dl0mryRk8J1l3PueefcSOfc6H23oz2wc26cc86cc82ccy0itxj40SvxrkAKdHjRT7eb+XDoNJIXXJbfDiIrQ1Mo81r7Z/2FntGX+osDEsa6ybDwHb92Md6nckn+qNUfTp8KJWv6rWYm3+XXSIewaz0MP8vvPVz7XN9/oMzxYbJI8ilVCzq/BuunwNS/h04TGzbPh9GX+AZWnV9JnKVzOSlcnzOz+8ysg5m12neLejKRo3BsF3+FafaTsOWn0GnkaM3/j9/Cpd1TOqnPaynFoPvHkLkrsr9rHG9MHq+yMuH7P0GxY32nTJGcKl0XTpvgZ07MfgIGNIdVY/Lv+M7BwvfgsxNg2TfQ/jno/gEUKpl/GUQAjjsbGv7Rfx8sHxI6TVi7N8Kw06FgMeg5wP+eTxQ5KVybAtcAj/LrNOEnoxlKJC+0fcI375l4i//lKvFp60KYfCdUP8WfnEneK9sAOv3X77M47b7QaZLPD6/C+qn+woy2v5HcSikGnf8LfYaDy4BB3WDsNX7NdDRtXQhD+/pRnVJ14Yxp0PjmxBnZkfjT7hko2xhG/wF2rAqdJozM3TD8TL/Pfc/PEm/XgJwUrucCdZxz3Zxz3SO3HtEOJnK0ih8LLe+H5d/Csq9Dp5Ej4bJg7NVQsLCfBqQTouipd/Gv+7sm+9Xq/LRznV/bWuVEqHNh6DQSz6r29FvBNbkNfnoLPqkLE2+DnWvz9jhbF/qlG582hNVj/SjrqeOhfNO8PY5IbqUU8523M7bDiHOTb72rc/6cafUY6PomHNs5dKK8l5PCdQ5QNso5RKKi8U1Q9gQ/6pqxK3Qaya0Fr8Dq0dD2KShRLXSaxNfhOSjXxI+gRHu0Rry0v8LebdDhJV2YkaNXqIQfuT/3R6hzEcx7Dj6q7UegVo70FwOPRNZe3wBq5IW+YP35Q2h0E5z7kx9lVd8BiRXlGkPn12HNeJicZI0cpz8Ai971Oy/UvSh0mugwd5g5lGY2CmgGTAF2R+52zrnToxvt91JTU11aWlp+H1bi3Mrv4Ntefpucltr2I25sXwqfN4ZK7f2erTqpzx+bF8CXqb6hQ5/vfLMziY4138PXnaDpndBWnYQlCjb/AHOf8YXmni1QsjZU7wOVO0Hlzr6x08F+tros3x9i3WRYO95vp7FrHRQuB/Uvg2Z3QfEq+f7liOTYpNthztN+r+P6l4ZOE30/vgFjr4L6l0OXN+L/nMnMpjrnUn93fw4K1277/xPoAlzgnGuctxEPT4WrHKkR58HSgXD2At99TmKbc37t1OqxcNZsKHVc6ETJ5af/wZg/QIu/Q+sHQ6dJTFkZ8GUbXwycs0DNbCS6MnbCL1/AwndhzVg/yg+QUgKKHQNFK0NKcdi7BXZvhl1rf/uY6n2g3iW+10DBIqG+CpGcy8rwWzOtneinsldM4LayS76AEWdD1V7Qe6BfXhXvDlW4HvZaunNutJm1BC7Cr3ddDLyc9xFFoqftk7D0a5h8O/T8NHQaOZyF78DywdD+eRWtIdS/FFaN9BuXH9sVqvUOnSjxLHgZNs6AHh+raJXoSykGdS/0t6xM2DTbN2Pbthh2rvHrYDN3+AK2TAMoUgEqtISKbfxyG00FlnhTIAW6f+RnEA07DfpPghLVQ6fKe6tGwagL/Pdqz88To2jNziFHXM3seODCyG098BFwh3Mu2HiVRlzlaMx4yO/vdcpQnYjHsh2r4bNGUK4R9BvjNxeX/JexA75s60dezpypaYF5aeca+LQBVGwLpwyJ/yldIiKxauNsvySj1HHQb2xidW5fP913ES9R3X9tRSuETpR3DjXimt0p4QKgB3Cqc66zc+4FIDNaAUWircntvmX/hJuTr9NcvHDO72eZucM3V1DRGk5KcT8amJEOoy7yozSSNybf5S8MdHhBRauISDSVb+q3hdk0zy8by9obOlHe2DATBvfy685PGZpYRWt2sjstPAtYBYw0s1fNrCd+jatIXEopCu2fhS0LYN7zodPIwSz5FH4ZAC0f8HuLSljlGvlut6tGwYx/hk6TGFaP9VPhm96p97iISH6o1hs6vQwrhsC4Px55d+1YsWEmfNvTX2DuOyIxp0AfyiELV+fcF865C4CGwEjgVuAYM/uPmZ2UT/lE8lTNU6FGP98yPFk3p45VuzbA9zf6brZNbw+dRvY5/nLfRXT6g75Dtxy5zD0w/nooUROa3xM6jYhI8mhwFbS8F35608+8O0xv2pi1cVakaC0GfUdB6bqhE+Wvw07Ec86lO+fed86dBlQHpgN/iXoykShp/6w/gZx8V+gksr+Jt8Lujb6Nu7ZgiS0dXoKyDWHUxX4NshyZWY/B5rnQ8SW/36aIiOSflvdD0ztg/kt+j9d4K17XToJB3ZO3aIUcFK77c85tcs694pzrGa1AItFWup6fprfoXVg9LnQaAVj6jf//aHEPlG8WOo0cqFAJ6P4x7Nnqi1etd829zfNhxr+gzgV+5oeIiOQvM2jzODS60e/xOvVv8VO8LvsWvu3h17T2HZ2cRSvksnAVSRTN74YSNWDCjToJD23PFhj/RyjbGJr/LXQaOZTyTaDji7BqBMx8KHSa+OKyYOzVftub9s+FTiMikrzM/M/hBtfCzEfg+xti/zxw4bswrL/fquq08VC6TuhE4ahwlaRUqAS0ewo2zoQF/w2dJrlNvgt2roKubyT+/mPxrv4VUPcSmHY/rBwZOk38mP8fWPs9tHsGih0TOo2ISHKzAtDpP3723YL/wMjzIWNX6FS/l5UJaX+H0Zf6PdX7joJilUOnCkuFqySt2udAlR5+qsjOdaHTJKeVI+CHV6DJbVCpbeg0cjhm/pd9meP9Fjk714ROFPu2/QJpf4WqvaHepaHTiIgI+OK17ePQ7mlY8hkMOdk3iYwVuzf7UdaZD8HxV8PJgxJrD9ojpcJVkpYZdHge9m7zxavkr73pMO5qv+a41QOh00hOFSoJPT6BPZth1CWxP8UqJJcFY6/wf+/8ivZsFRGJNU3+DCe+D2snwhetfAOk0DbMgK/awMph0PE//vdHwSKhU8UGFa6S1Mo1hkY3ww+vxcYPq2SSdg9sWwydX/d7kUn8KN8U2j8PK4f7NUJycPNeglUj/RThUrVDpxERkYOpeyGcOt6Pwn7TBea+EKZpU1YGTP8XfNkGMtKh70g44Tpd9NyfCldJeq3uh+JVYPx1/oeGRN/qcTDvBd/Zr0rX0GnkSDS4GupeBNPvg1WjQ6eJPVt+hCl/gep94PirQqcREZHsVEqFM6ZB9VNg4s0wtB9s/Tn/jr9pHnzdCab9A2qfDWfOhsqd8u/48UKFqyS9wqV9h7mNM3wxJdGVsRPGXgkla0GqRuvilhl0fNlP9R51IexcGzpR7MjKhNGXQcGi0Pk1XS0XEYkHRcpBry/8OeGasfB5Yz+rKHNP9I65cy2Mvx4GNIOtC6H7h9DjQyhaIXrHjGcqXEXwV7eq94Wp/4Dty0KnSWzT7oWtP0GX1/x6SYlfhUv5/V13b/TNmjRjwZv5CKyb6LcPKlE1dBoREckpKwCNb4az50ONvn5Z02cn+B0o8rLz8M61MO0B+KSeX652wvVw9gKoc37eHSMRqXAVITJ69KJvpjLxltBpEtfaSX7T7wbXQtWeodNIXqjQ3DePWPmd39oo2a0ZD9Pv99Oo61wYOo2IiByJEtWh52dw0iAoUsEvJ/v4OJjx8JFPIXZZsOZ7GHUpfFjD/66o2hPOmgMdXoBilfL0S0hI5kKsPj5CqampLi0tLXQMSWAzH4W0u6H3V1DztNBpEkvmbviiJezd7n9Iq617YplwC8x7Hrq+BfUvC50mjN2bYEALKFAQzpih97iISCJwDlaN8LNpVn7n7yvfHGqdARXb+EafJWv60dr97U33TSg3zoDlQ2DFUNi1FgqVgvqXwwl/grIN8/mLiRNmNtU5l3rg/SkhwojEqqa3w8J34fsb/R6vhUqETpQ4pv8TNs+Hk7/VCX0iavckbJoD466FMg3hmHahE+Uv52DcNbBjJZw2Xu9xEZFEYeZHRqv29IXokgHwy+f+vIbI+F9KCShSHgqkgKXA3q2/3eu8SAWodpJv/lTrTL/URnJPI64iB1gzHr7uDE3v9JtTy9FbPxW+agf1LoWub4ZOI9Gya4Pfey5jJ/Sf5K9AJ4sF//VTydo8Bs00ZVpEJOHt3gSb5sLmub4r8N6tvteDy/CFbKk6/lamAZRv5mfjSM4casRVhavIQYy9Bn56E86Y7veslCOXuccXM7vWwVlzfdc+SVyb5sLAjr5r9KnjkmPkce0k+KYrVDnRzyg4cLqYiIiI5NyhClf9ehU5iDaP+gJr/B/9Yno5cjMehI2z/NYpKloTX7nGvqHF5vkw4lzI2hs6UXTtXAPfnQ3Fq8KJ76toFRERiRb9ihU5iKIVoO1TsHaCb1MuR2bNBJj5sG9CUKt/6DSSX6r1gs7/9Y0ovr/Br/9MRFl7YcT5fjugXgO0756IiEg0qXAVOYR6l/oGTZPvhPQVodPEn73bYfSlUKKG38xbksvxV0Lzv8EPr8L0B0KniY7Jd8Lq0dD5VajQInQaERGRxBa0cDWzU8zsBzNbaGZ/DZlF5EBm0PkVv8h+/HWJO2oULZNug20/Q7f/Jcc6R/m91g/6Anb6AzAnwS5ezHsR5j4HjW+FeheHTiMiIpL4ghWuZlYQeAnoAzQCLjSzRqHyiBxM6brQ+mFY9jUsej90mvixdKAfaWt2FxzbJXQaCcUMOv0Xap8Fk26Fn94JnShv/PIlTLgZap4ObZ8MnUZERCQ5hBxxbQssdM797JzbA3wInB4wj8hBNboRjukAE2/+7Z5ccnA718LYq/3m3K0SdIqo5FyBFN+0qGovGHslLPk8dKKjs3YSjLwQKrWB7u9rewMREZH8ErJwrQYs2+/fyyP3/YaZXWtmaWaWtm7dunwLJ7JPgYLQ5Q3ISIfv/6Qpw9lxDsZdA3u3QLd3oWCR0IkkFhQs4psXVWoHI86Dnz8KnejIbJ4Pw06D4lWg90BIKR46kYiISPKI+eZMzrlXnHOpzrnUSpUqhY4jSapsQ2j5gB8tWvRe6DSx68fXYelXkPoIlG8SOo3EkkIl4eTBcExHGHURLHw3dKLc2fwDDOrht7s5+VsodkzoRCIiIsklZOG6Aqix37+rR+4TiUlN74DKnWDCjbB92eEfn2y2LoKJt0KV7tD4ltBpJBYVLuWLvmO7weg/wA+vh06UM1t+gm+7+z2d+46EMseHTiQiIpJ8QhauU4D6ZnacmRUGLgC+CphHJFsFCkLXtyErA8Zc7k9ixcva67e+KZDiXyOL+bkcEkqhEnDS11CtN4y7GqbdH9vT77f8CIO6++/7viOg7AmhE4mIiCSnYKeXzrkM4EZgCDAf+Ng5NzdUHpGcKF0X2j0Dq0bA3BdCp4kdU/8BaydAx5ehZI3DP16SW0pxv0a0/uV+q5wxl0PmntCpfm/NeBjYAbL2QJ/voFzj0IlERESSV0rIgzvnBgGDQmYQya0GV/t1nGl/hao9tZZz2SCY9Rg0uBbqXhA6jcSLgoV907NSdWDavZC+FLp/FDtrRxd/CqMvgRI1/fTm0nVDJxIREUlumtAnkktm0OU1KFwGRp4PGTtCJwonfblfq1i+GbR/NnQaiTdm0PIf0PUdP2L/RQtYNSpsJpcFMx723Y8rtIbTJqhoFRERiQUqXEWOQLHKfruXzfNhws2h04SRleH3s8zaDd0/hpRioRNJvKp/KZw2CQqVgm97wvQHISsz/3PsWAWDT4apf4M650Of4VC0Qv7nEBERkd9T4SpyhKr1guZ3+y1gFn0QOk3+m3wXrBkHnf4LZRuETiPxrkJz6J8Gx53vpw4PbAfrp+bf8Zd+AwOa+3WtnV+FE9/XxRgREZFYosJV5Ci0esBvkTP+Wr9lRrJY+C7MfcZve1P3otBpJFEULgUnvgcnfuCnoX/VFibcAnu2RO+YWxfBsDNg2Kl+JsXpaX4du1n0jikiIiK5p8JV5CgUSPEn2QUKw/AzYe/20Imib/00GHeN34uz7ROh00iiMfNNvs5eAA3+CPNegI9qw7T7YPfGvDvOzjUw5a/wWSNYORxSH/FFa7lGeXcMERERyTvmYnkDvQOkpqa6tLS00DFEfmfFcBhyMtQ6C3p8nLijNbvWwxetgSw4fWrsdICVxLV+Gsz4F/wyAAqVhPpX+lH+Sm1z/33mnJ9+PO8F+PlDv81NvUsh9VEoUTU6+UVERCR3zGyqcy71wPuDbocjkiiq9YI2j8PkO2DWo37ta6LJ2AXDz4Bda6DfWBWtkj8qtoJen8PGOTDzYVjwMsx7HkrWhtpnQcU2UKEllKkPdsAcoqy9kL4SNkyFFUP9bdtiXwA3vBZOuFHrs0VEROKFCleRPNLkNj+ak/Y3KN8CavQJnSjvuCwYc7lvXNP9I6jUJnQiSTblm0D392H3Zlj6Jfz8Ecx70Y+aAhQsBkXKQUpx//fdG2HnKv/eBd+xuEoPaHqXH7EtXDrYlyIiIiJHQIWrSB7Zt7/r5vkw8jw/KlmhRehUeWPq32HxR35KZZ3zQqeRZFakLNS/zN8y98DmebBhOmyaA3u2QuYOv7dy4dZQsiaUqAFlT/BTiwsUCp1eREREjpQKV5E8lFIcTvoaBraHoX3htIn+5DmeLXgFZj4CDa6BZneFTiPyq4KF/cWhRLlAJCIiIoemrsIieaxENTjpWz/qM6QP7N4UOtGRW/QBjL8Oqp8CHV9K3KZTIiIiIhLbVLiKREH5JtBzAGz9CYad7ovYePPLlzD6Uji2C/T8TNMsRURERCQcFa4iUVK1O3R9B9aOh6GnxVfxunwojDgPKraG3l/7KdAiIiIiIqGocBWJoroXQNe3YdVIGNYfMnaGTnR4SwfC8NN9Q5uTB0PhUqETiYiIiEiyU+EqEmX1LoGub8HKEX7a8N700IkObeG7MPxMKNcE+gz324uIiIiIiISmwlUkH9T/A3R9E1Z9B4O6w841oRP93twXImtau0KfEVC0YuhEIiIiIiKeCleRfFL/Mt+wadMcGNgBNv8QOpGXtRcm3AwTb4aap8NJgzQ9WERERERiiwpXkXxUqz/0G+2nCw/sACuGh82zcw182wvmvQCN/ww9P4WUomEziYiIiIgcSIWrSD6r1Ab6T4TiVWDwSTDlbj/qmd9Wj4MvU2HdFOj2LrR/Ggqk5H8OEREREZHDUeEqEkCp4+D0KdDgapj1KHzdFbb+nD/H3psOE26Bb7r6vVlPHQ/1Ls6fY4uIiIiIHAkVriKBpBSHzq9A949gy3z4vDFMuy96+706B8uHwIBmMO95aHQDnDkLKraMzvFERERERPKKCleRwOqcB2fNgVpnwPR/wqcNYeF7eTt9eNUYGHQiDDkFrAD0HQ0dXoBCJfPuGCIiIiIi0aLCVSQGlKgO3T+AfmOgSAUYfQl8XAdmPAw71x3Zc+5N9/uyDuoBg7rB1p+gw4u+SK7SNW/zi4iIiIhEkznnQmfIsdTUVJeWlhY6hkhUZWXC8m9h7vOwcphfh1q5E1TtDdV6Q7nGfprx7z5vL2ya65strR4Nv3wBGelQshY0uglO+BOkFMv3L0dEREREJMfMbKpzLvV396twFYldm+fDj2/CiqGwceav9xcpDyVqQMGisHc77N0Gu9ZC5q5fP177bKh3qS96TXMrRERERCQOHKpw1eYXIjGs7AnQ9nHgcb/n6qpRsHURpC+H9GWQtcdPMy5UEopWggqt/HY7peqCWej0IiIiIiJ5Q4WrSJwoVhnqnB86hYiIiIhI/tMEQhEREREREYlpKlxFREREREQkpgUpXM3sCTNbYGazzGyAmZUNkUNERERERERiX6gR12FAE+dcM+BH4O5AOURERERERCTGBSlcnXN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}, "metadata": { "needs_background": "light" } } ], "source": [ "# Generate test function data\n", "data = test_function(time)\n", "\n", "# Create subplot\n", "figure, ax = plt.subplots(nrows=3,figsize=(16,12))\n", "plt.subplots_adjust(hspace=0.4)\n", "\n", "# Time domain representation of test function\n", "ax[0].set_title('Periodic Signal')\n", "ax[0].plot(time, data)\n", "ax[0].set_xlabel('Time')\n", "ax[0].set_ylabel('Amplitude')\n", "\n", "# Perform Walsh transform denoising using value threshold method\n", "dnw = sequency.denoise(data,method='walsh',denoise_strength=0.2)\n", "\n", "# Perform Fourier transform denoising using value threshold method\n", "dnf = sequency.denoise(data,method='fourier',denoise_strength=0.2)\n", "\n", "# Time domain representation of test function\n", "ax[1].set_title('Periodic Signal Denoising Using Walsh Transform')\n", "ax[1].plot(time, dnw)\n", "ax[1].set_xlabel('Time')\n", "ax[1].set_ylabel('Amplitude');\n", "\n", "# Time domain representation of test function\n", "ax[2].set_title('Periodic Signal Denoising Using Fourier Transform')\n", "ax[2].plot(time, dnf)\n", "ax[2].set_xlabel('Time')\n", "ax[2].set_ylabel('Amplitude');\n" ] }, { "source": [ "Lastly, we can see that as we would hopefully expect at this point, the Walsh denoising of the smooth data turned it into step data. The Fourier method simply took more of the wiggles out and hence we have an even more Sine wave looking smooth test function.\n", "\n", "As a last example, we will apply smoothing to step data using both methods and see what we get, atleast we can compare the results against step data, since we already saw the results against smooth data." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# We'll add some more steps to our previous test_steps\n", "test_steps.add(steps2)\n", "test_steps.add(steps3);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# Generate test function data\n", "data = test_steps.step_values()\n", "\n", "# Create subplot\n", "figure, ax = plt.subplots(nrows=3,figsize=(16,12))\n", "plt.subplots_adjust(hspace=0.4)\n", "\n", "# Time domain representation of test function\n", "ax[0].set_title('Periodic Signal')\n", "ax[0].step(test_steps.step_keys(), data)\n", "ax[0].set_xlabel('Time')\n", "ax[0].set_ylabel('Amplitude')\n", "\n", "# Perform Walsh transform denoising using value threshold method\n", "dnw = sequency.denoise(data,method='walsh',denoise_strength=0.5)\n", "\n", "# Perform Fourier transform denoising using value threshold method\n", "dnf = sequency.denoise(data,method='fourier',denoise_strength=0.5)\n", "\n", "# Walsh denoising\n", "ax[1].set_title('Periodic Step Denoising Using Walsh Transform')\n", "ax[1].step(test_steps.step_keys(), dnw)\n", "ax[1].set_xlabel('Time')\n", "ax[1].set_ylabel('Amplitude');\n", "\n", "# Fourier denoising\n", "ax[2].set_title('Periodic Step Denoising Using Fourier Transform')\n", "ax[2].step(test_steps.step_keys(), dnf)\n", "ax[2].set_xlabel('Time')\n", "ax[2].set_ylabel('Amplitude');\n", "\n" ] }, { "source": [ "From the last denoising of step data using both Walsh and Fourier methods, we can see that whilst the Walsh method 'Stepifies' smooth data during the denoising process and the Fourier method works very well, they both yield good results. We can seee though when we have step data, a comparison of the denoising methods yields a different picture. The Walsh method does exactl what we would expect, it basically makes the original step data more blocky by removing higher sequency steps, the Fourier method starts to look more like step data encapsulated in a Sine function. This isn't unexpected, it does reveal though that whilst both methods are very useful, the Walsh method slightly edges the Fourier method in terms of range of applicability, atleast based on these scenarios. At the end of the day, both methods have been included in the HotStepper library, since HotStepper is able to process smooth and step data with ease.\n", "\n", "I do recommend the use of the Walsh method with the data is step like, as the results will be neater and somewhat more inline with expectations of what denoising and decomposition would produce when dealing with step data." ], "cell_type": "markdown", "metadata": {} }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ] }